LMFDB - Embedded newform 38.8.e.a.17.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,8,Mod(5,38)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	38.e (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.8706309684$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			17.5
Character	$\chi$	$=$	38.17
Dual form			38.8.e.a.9.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38919 - 7.87846i) q^{2} +(45.5653 + 38.2339i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(-199.214 + 72.5079i) q^{5} +(364.523 - 305.871i) q^{6} +(458.368 + 793.917i) q^{7} +(-256.000 + 443.405i) q^{8} +(234.604 + 1330.50i) q^{9} +O(q^{10})$	\(q+(1.38919 - 7.87846i) q^{2} +(45.5653 + 38.2339i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(-199.214 + 72.5079i) q^{5} +(364.523 - 305.871i) q^{6} +(458.368 + 793.917i) q^{7} +(-256.000 + 443.405i) q^{8} +(234.604 + 1330.50i) q^{9} +(294.506 + 1670.23i) q^{10} +(-2158.51 + 3738.65i) q^{11} +(-1903.40 - 3296.79i) q^{12} +(-5425.94 + 4552.90i) q^{13} +(6891.61 - 2508.34i) q^{14} +(-11849.5 - 4312.87i) q^{15} +(3137.72 + 2632.86i) q^{16} +(-918.718 + 5210.31i) q^{17} +10808.2 q^{18} +(21382.5 + 20896.4i) q^{19} +13567.9 q^{20} +(-9468.81 + 53700.3i) q^{21} +(26456.3 + 22199.4i) q^{22} +(86073.0 + 31328.0i) q^{23} +(-28617.8 + 10416.0i) q^{24} +(-25418.4 + 21328.6i) q^{25} +(28332.2 + 49072.8i) q^{26} +(24862.4 - 43062.9i) q^{27} +(-10188.1 - 57779.8i) q^{28} +(-26260.3 - 148929. i) q^{29} +(-50439.9 + 87364.5i) q^{30} +(6804.21 + 11785.2i) q^{31} +(25101.7 - 21062.9i) q^{32} +(-241296. + 87824.7i) q^{33} +(39772.9 + 14476.2i) q^{34} +(-148879. - 124924. i) q^{35} +(15014.6 - 85152.2i) q^{36} -363856. q^{37} +(194336. - 139432. i) q^{38} -421309. q^{39} +(18848.4 - 106894. i) q^{40} +(-65801.2 - 55213.7i) q^{41} +(409922. + 149199. i) q^{42} +(701708. - 255401. i) q^{43} +(211650. - 177595. i) q^{44} +(-143208. - 248044. i) q^{45} +(366388. - 634602. i) q^{46} +(22378.2 + 126913. i) q^{47} +(42306.9 + 239934. i) q^{48} +(-8431.63 + 14604.0i) q^{49} +(132726. + 229888. i) q^{50} +(-241072. + 202283. i) q^{51} +(425977. - 155043. i) q^{52} +(-912120. - 331985. i) q^{53} +(-304731. - 255700. i) q^{54} +(158924. - 901301. i) q^{55} -469369. q^{56} +(175348. + 1.76969e6i) q^{57} -1.20981e6 q^{58} +(188740. - 1.07040e6i) q^{59} +(618228. + 518754. i) q^{60} +(-205271. - 74712.5i) q^{61} +(102302. - 37234.8i) q^{62} +(-948774. + 796116. i) q^{63} +(-131072. - 227023. i) q^{64} +(750800. - 1.30042e6i) q^{65} +(356718. + 2.02305e6i) q^{66} +(265343. + 1.50483e6i) q^{67} +(169302. - 293240. i) q^{68} +(2.72415e6 + 4.71837e6i) q^{69} +(-1.19103e6 + 999392. i) q^{70} +(1.84451e6 - 671348. i) q^{71} +(-650010. - 236584. i) q^{72} +(733553. + 615524. i) q^{73} +(-505464. + 2.86663e6i) q^{74} -1.97368e6 q^{75} +(-828541. - 1.72477e6i) q^{76} -3.95757e6 q^{77} +(-585277. + 3.31927e6i) q^{78} +(5.86836e6 + 4.92414e6i) q^{79} +(-815980. - 296992. i) q^{80} +(5.55583e6 - 2.02216e6i) q^{81} +(-526409. + 441710. i) q^{82} +(-1.58047e6 - 2.73745e6i) q^{83} +(1.74492e6 - 3.02229e6i) q^{84} +(-194767. - 1.10458e6i) q^{85} +(-1.03736e6 - 5.88318e6i) q^{86} +(4.49759e6 - 7.79005e6i) q^{87} +(-1.10516e6 - 1.91419e6i) q^{88} +(1.33247e6 - 1.11807e6i) q^{89} +(-2.15315e6 + 783682. i) q^{90} +(-6.10170e6 - 2.22084e6i) q^{91} +(-4.49071e6 - 3.76815e6i) q^{92} +(-140559. + 797150. i) q^{93} +1.03097e6 q^{94} +(-5.77484e6 - 2.61246e6i) q^{95} +1.94908e6 q^{96} +(-2.21886e6 + 1.25838e7i) q^{97} +(103344. + 86716.0i) q^{98} +(-5.48068e6 - 1.99480e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 45 q^{3} + 360 q^{6} + 1806 q^{7} - 7680 q^{8} - 3105 q^{9}+O(q^{10}) $ 30 * q + 45 * q^3 + 360 * q^6 + 1806 * q^7 - 7680 * q^8 - 3105 * q^9	\( 30 q + 45 q^{3} + 360 q^{6} + 1806 q^{7} - 7680 q^{8} - 3105 q^{9} + 9786 q^{11} - 11130 q^{13} + 6144 q^{14} - 1818 q^{15} - 65250 q^{17} + 29040 q^{18} + 105906 q^{19} - 47616 q^{20} + 172854 q^{21} + 102336 q^{22} + 101004 q^{23} + 23040 q^{24} - 132756 q^{25} - 92112 q^{26} + 43659 q^{27} + 96384 q^{28} - 273912 q^{29} + 58710 q^{31} - 406965 q^{33} + 84960 q^{34} + 356100 q^{35} - 198720 q^{36} - 2598852 q^{37} - 219336 q^{38} + 1769844 q^{39} + 43377 q^{41} - 79056 q^{42} + 1126698 q^{43} + 818688 q^{44} - 912546 q^{45} - 530880 q^{46} + 588306 q^{47} - 368640 q^{48} - 2778285 q^{49} + 1665288 q^{50} + 3972045 q^{51} - 430080 q^{52} + 6520866 q^{53} - 486648 q^{54} - 1666818 q^{55} - 1849344 q^{56} - 6947844 q^{57} - 4573152 q^{58} - 970467 q^{59} + 4634496 q^{60} - 4037670 q^{61} + 755952 q^{62} + 7946472 q^{63} - 3932160 q^{64} + 1497690 q^{65} + 6499272 q^{66} - 4817025 q^{67} + 1472064 q^{68} + 10299876 q^{69} + 2848800 q^{70} - 25171290 q^{71} + 3179520 q^{72} + 1347750 q^{73} - 3123936 q^{74} + 8817984 q^{75} + 1583232 q^{76} - 11476764 q^{77} - 930960 q^{78} + 10777986 q^{79} - 5365035 q^{81} + 347016 q^{82} + 9745314 q^{83} + 877056 q^{84} + 29258556 q^{85} - 9338208 q^{86} + 25598802 q^{87} + 5010432 q^{88} - 20353740 q^{89} - 30112128 q^{90} + 19748724 q^{91} - 14097792 q^{92} - 18738174 q^{93} + 12376608 q^{94} - 20427204 q^{95} - 23005029 q^{97} + 14869008 q^{98} - 45819771 q^{99}+O(q^{100}) \) 30 * q + 45 * q^3 + 360 * q^6 + 1806 * q^7 - 7680 * q^8 - 3105 * q^9 + 9786 * q^11 - 11130 * q^13 + 6144 * q^14 - 1818 * q^15 - 65250 * q^17 + 29040 * q^18 + 105906 * q^19 - 47616 * q^20 + 172854 * q^21 + 102336 * q^22 + 101004 * q^23 + 23040 * q^24 - 132756 * q^25 - 92112 * q^26 + 43659 * q^27 + 96384 * q^28 - 273912 * q^29 + 58710 * q^31 - 406965 * q^33 + 84960 * q^34 + 356100 * q^35 - 198720 * q^36 - 2598852 * q^37 - 219336 * q^38 + 1769844 * q^39 + 43377 * q^41 - 79056 * q^42 + 1126698 * q^43 + 818688 * q^44 - 912546 * q^45 - 530880 * q^46 + 588306 * q^47 - 368640 * q^48 - 2778285 * q^49 + 1665288 * q^50 + 3972045 * q^51 - 430080 * q^52 + 6520866 * q^53 - 486648 * q^54 - 1666818 * q^55 - 1849344 * q^56 - 6947844 * q^57 - 4573152 * q^58 - 970467 * q^59 + 4634496 * q^60 - 4037670 * q^61 + 755952 * q^62 + 7946472 * q^63 - 3932160 * q^64 + 1497690 * q^65 + 6499272 * q^66 - 4817025 * q^67 + 1472064 * q^68 + 10299876 * q^69 + 2848800 * q^70 - 25171290 * q^71 + 3179520 * q^72 + 1347750 * q^73 - 3123936 * q^74 + 8817984 * q^75 + 1583232 * q^76 - 11476764 * q^77 - 930960 * q^78 + 10777986 * q^79 - 5365035 * q^81 + 347016 * q^82 + 9745314 * q^83 + 877056 * q^84 + 29258556 * q^85 - 9338208 * q^86 + 25598802 * q^87 + 5010432 * q^88 - 20353740 * q^89 - 30112128 * q^90 + 19748724 * q^91 - 14097792 * q^92 - 18738174 * q^93 + 12376608 * q^94 - 20427204 * q^95 - 23005029 * q^97 + 14869008 * q^98 - 45819771 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.38919	−	7.87846i	0.122788	−	0.696364i
$2$	1.38919	−	7.87846i	0.122788	−	0.696364i
$3$	45.5653	+	38.2339i	0.974339	+	0.817568i	0.983226	−	0.182393i	$-0.0583843\pi$
$3$	45.5653	+	38.2339i	0.974339	+	0.817568i	−0.00888651	+	0.999961i	$0.502829\pi$
$4$	−60.1403	−	21.8893i	−0.469846	−	0.171010i
$5$	−199.214	+	72.5079i	−0.712729	+	0.259412i	−0.672836	−	0.739792i	$-0.734924\pi$
$5$	−199.214	+	72.5079i	−0.712729	+	0.259412i	−0.0398933	+	0.999204i	$0.512702\pi$
$6$	364.523	−	305.871i	0.688962	−	0.578108i
$7$	458.368	+	793.917i	0.505093	+	0.874847i	0.999983	+	0.00589112i	$0.00187521\pi$
$7$	458.368	+	793.917i	0.505093	+	0.874847i	−0.494889	+	0.868956i	$0.664791\pi$
$8$	−256.000	+	443.405i	−0.176777	+	0.306186i
$9$	234.604	+	1330.50i	0.107272	+	0.608369i
$10$	294.506	+	1670.23i	0.0931309	+	0.528172i
$11$	−2158.51	+	3738.65i	−0.488967	+	0.846917i	−0.999919	−	0.0126927i	$-0.995960\pi$
$11$	−2158.51	+	3738.65i	−0.488967	+	0.846917i	0.510952	+	0.859609i	$0.329293\pi$
$12$	−1903.40	−	3296.79i	−0.317977	−	0.550753i
$13$	−5425.94	+	4552.90i	−0.684972	+	0.574760i	−0.917454	−	0.397841i	$-0.869760\pi$
$13$	−5425.94	+	4552.90i	−0.684972	+	0.574760i	0.232482	+	0.972601i	$0.425315\pi$
$14$	6891.61	−	2508.34i	0.671231	−	0.244308i
$15$	−11849.5	−	4312.87i	−0.906527	−	0.329949i
$16$	3137.72	+	2632.86i	0.191511	+	0.160697i
$17$	−918.718	+	5210.31i	−0.0453535	+	0.257213i	−0.999051	−	0.0435548i	$-0.986132\pi$
$17$	−918.718	+	5210.31i	−0.0453535	+	0.257213i	0.953698	+	0.300767i	$0.0972428\pi$
$18$	10808.2			0.436818
$19$	21382.5	+	20896.4i	0.715188	+	0.698932i
$19$	21382.5	+	20896.4i	0.715188	+	0.698932i
$20$	13567.9			0.379235
$21$	−9468.81	+	53700.3i	−0.223115	+	1.26535i
$22$	26456.3	+	22199.4i	0.529723	+	0.444491i
$23$	86073.0	+	31328.0i	1.47509	+	0.536890i	0.949478	−	0.313833i	$-0.101613\pi$
$23$	86073.0	+	31328.0i	1.47509	+	0.536890i	0.525615	+	0.850723i	$0.323835\pi$
$24$	−28617.8	+	10416.0i	−0.422568	+	0.153802i
$25$	−25418.4	+	21328.6i	−0.325356	+	0.273006i
$26$	28332.2	+	49072.8i	0.316136	+	0.547564i
$27$	24862.4	−	43062.9i	0.243091	−	0.421046i
$28$	−10188.1	−	57779.8i	−0.0877085	−	0.497420i
$29$	−26260.3	−	148929.i	−0.199943	−	1.13393i	−0.905201	−	0.424983i	$-0.860280\pi$
$29$	−26260.3	−	148929.i	−0.199943	−	1.13393i	0.705259	−	0.708950i	$-0.250831\pi$
$30$	−50439.9	+	87364.5i	−0.341075	+	0.590759i
$31$	6804.21	+	11785.2i	0.0410215	+	0.0710514i	0.885807	−	0.464053i	$-0.153605\pi$
$31$	6804.21	+	11785.2i	0.0410215	+	0.0710514i	−0.844786	+	0.535105i	$0.820272\pi$
$32$	25101.7	−	21062.9i	0.135419	−	0.113630i
$33$	−241296.	+	87824.7i	−1.16883	+	0.425420i
$34$	39772.9	+	14476.2i	0.173545	+	0.0631651i
$35$	−148879.	−	124924.i	−0.586941	−	0.492502i
$36$	15014.6	−	85152.2i	0.0536359	−	0.304184i
$37$	−363856.			−1.18093			−0.590464	−	0.807064i	$-0.701055\pi$
$37$	−363856.			−1.18093			−0.590464	+	0.807064i	$0.701055\pi$
$38$	194336.	−	139432.i	0.574528	−	0.412211i
$39$	−421309.			−1.13730
$40$	18848.4	−	106894.i	0.0465655	−	0.264086i
$41$	−65801.2	−	55213.7i	−0.149104	−	0.125113i	0.565184	−	0.824965i	$-0.308805\pi$
$41$	−65801.2	−	55213.7i	−0.149104	−	0.125113i	−0.714288	+	0.699851i	$0.753250\pi$
$42$	409922.	+	149199.i	0.853746	+	0.310738i
$43$	701708.	−	255401.i	1.34591	−	0.489872i	0.434243	−	0.900796i	$-0.357016\pi$
$43$	701708.	−	255401.i	1.34591	−	0.489872i	0.911670	+	0.410924i	$0.134794\pi$
$44$	211650.	−	177595.i	0.374571	−	0.314302i
$45$	−143208.	−	248044.i	−0.234274	−	0.405775i
$46$	366388.	−	634602.i	0.554994	−	0.961278i
$47$	22378.2	+	126913.i	0.0314401	+	0.178306i	0.996484	−	0.0837824i	$-0.0267001\pi$
$47$	22378.2	+	126913.i	0.0314401	+	0.178306i	−0.965044	+	0.262088i	$0.915589\pi$
$48$	42306.9	+	239934.i	0.0552162	+	0.313147i
$49$	−8431.63	+	14604.0i	−0.0102382	+	0.0177332i
$50$	132726.	+	229888.i	0.150162	+	0.260088i
$51$	−241072.	+	202283.i	−0.254478	+	0.213533i
$52$	425977.	−	155043.i	0.420121	−	0.152912i
$53$	−912120.	−	331985.i	−0.841563	−	0.306304i	−0.114967	−	0.993369i	$-0.536676\pi$
$53$	−912120.	−	331985.i	−0.841563	−	0.306304i	−0.726595	+	0.687066i	$0.758899\pi$
$54$	−304731.	−	255700.i	−0.263353	−	0.220979i
$55$	158924.	−	901301.i	0.128801	−	0.730466i
$56$	−469369.			−0.357155
$57$	175348.	+	1.76969e6i	0.125412	+	1.26571i
$58$	−1.20981e6			−0.814181
$59$	188740.	−	1.07040e6i	0.119642	−	0.678522i	−0.864705	−	0.502280i	$-0.832495\pi$
$59$	188740.	−	1.07040e6i	0.119642	−	0.678522i	0.984347	−	0.176242i	$-0.0563941\pi$
$60$	618228.	+	518754.i	0.369504	+	0.310051i
$61$	−205271.	−	74712.5i	−0.115791	−	0.0421443i	0.283475	−	0.958980i	$-0.408513\pi$
$61$	−205271.	−	74712.5i	−0.115791	−	0.0421443i	−0.399266	+	0.916835i	$0.630735\pi$
$62$	102302.	−	37234.8i	0.0545146	−	0.0198417i
$63$	−948774.	+	796116.i	−0.478047	+	0.401129i
$64$	−131072.	−	227023.i	−0.0625000	−	0.108253i
$65$	750800.	−	1.30042e6i	0.339100	−	0.587338i
$66$	356718.	+	2.02305e6i	0.152729	+	0.866169i
$67$	265343.	+	1.50483e6i	0.107782	+	0.611261i	0.990073	+	0.140556i	$0.0448892\pi$
$67$	265343.	+	1.50483e6i	0.107782	+	0.611261i	−0.882291	+	0.470705i	$0.844000\pi$
$68$	169302.	−	293240.i	0.0652951	−	0.113094i
$69$	2.72415e6	+	4.71837e6i	0.998297	+	1.72910i
$70$	−1.19103e6	+	999392.i	−0.415030	+	0.348251i
$71$	1.84451e6	−	671348.i	0.611614	−	0.222609i	−0.0175950	−	0.999845i	$-0.505601\pi$
$71$	1.84451e6	−	671348.i	0.611614	−	0.222609i	0.629210	+	0.777236i	$0.283379\pi$
$72$	−650010.	−	236584.i	−0.205237	−	0.0747003i
$73$	733553.	+	615524.i	0.220699	+	0.185189i	0.746433	−	0.665460i	$-0.231765\pi$
$73$	733553.	+	615524.i	0.220699	+	0.185189i	−0.525734	+	0.850649i	$0.676209\pi$
$74$	−505464.	+	2.86663e6i	−0.145004	+	0.822356i
$75$	−1.97368e6			−0.540208
$76$	−828541.	−	1.72477e6i	−0.216504	−	0.450695i
$77$	−3.95757e6			−0.987897
$78$	−585277.	+	3.31927e6i	−0.139647	+	0.791975i
$79$	5.86836e6	+	4.92414e6i	1.33913	+	1.12366i	0.981849	+	0.189663i	$0.0607397\pi$
$79$	5.86836e6	+	4.92414e6i	1.33913	+	1.12366i	0.357278	+	0.933998i	$0.383705\pi$
$80$	−815980.	−	296992.i	−0.178182	−	0.0648531i
$81$	5.55583e6	−	2.02216e6i	1.16159	−	0.422783i
$82$	−526409.	+	441710.i	−0.105433	+	0.0884685i
$83$	−1.58047e6	−	2.73745e6i	−0.303397	−	0.525500i	0.673506	−	0.739182i	$-0.264788\pi$
$83$	−1.58047e6	−	2.73745e6i	−0.303397	−	0.525500i	−0.976903	+	0.213682i	$0.931454\pi$
$84$	1.74492e6	−	3.02229e6i	0.321216	−	0.556363i
$85$	−194767.	−	1.10458e6i	−0.0343993	−	0.195088i
$86$	−1.03736e6	−	5.88318e6i	−0.175868	−	0.997396i
$87$	4.49759e6	−	7.79005e6i	0.732255	−	1.26830i
$88$	−1.10516e6	−	1.91419e6i	−0.172876	−	0.299430i
$89$	1.33247e6	−	1.11807e6i	0.200351	−	0.168114i	−0.537092	−	0.843523i	$-0.680477\pi$
$89$	1.33247e6	−	1.11807e6i	0.200351	−	0.168114i	0.737443	+	0.675409i	$0.236033\pi$
$90$	−2.15315e6	+	783682.i	−0.311333	+	0.113316i
$91$	−6.10170e6	−	2.22084e6i	−0.848802	−	0.308939i
$92$	−4.49071e6	−	3.76815e6i	−0.601253	−	0.504511i
$93$	−140559.	+	797150.i	−0.0181204	+	0.102766i
$94$	1.03097e6			0.128026
$95$	−5.77484e6	−	2.61246e6i	−0.691047	−	0.312621i
$96$	1.94908e6			0.224844
$97$	−2.21886e6	+	1.25838e7i	−0.246847	+	1.39994i	0.569316	+	0.822119i	$0.307208\pi$
$97$	−2.21886e6	+	1.25838e7i	−0.246847	+	1.39994i	−0.816163	+	0.577821i	$0.803903\pi$
$98$	103344.	+	86716.0i	0.0110916	+	0.00930696i
$99$	−5.48068e6	−	1.99480e6i	−0.567690	−	0.206622i
$100$	1.99554e6	−	726318.i	0.199554	−	0.0726318i
$101$	1.40517e7	−	1.17908e7i	1.35708	−	1.13873i	0.380208	−	0.924901i	$-0.375852\pi$
$101$	1.40517e7	−	1.17908e7i	1.35708	−	1.13873i	0.976872	−	0.213825i	$-0.0685922\pi$
$102$	1.25879e6	+	2.18028e6i	0.117450	+	0.203429i
$103$	−2.23142e6	+	3.86494e6i	−0.201211	+	0.348507i	−0.948919	−	0.315520i	$-0.897821\pi$
$103$	−2.23142e6	+	3.86494e6i	−0.201211	+	0.348507i	0.747708	+	0.664028i	$0.231154\pi$
$104$	−629739.	−	3.57143e6i	−0.0548964	−	0.311333i
$105$	−2.00738e6	−	1.13844e7i	−0.169226	−	0.959728i
$106$	−3.88263e6	+	6.72492e6i	−0.316633	+	0.548424i
$107$	8.83060e6	+	1.52951e7i	0.696863	+	1.20700i	0.969549	+	0.244898i	$0.0787546\pi$
$107$	8.83060e6	+	1.52951e7i	0.696863	+	1.20700i	−0.272686	+	0.962103i	$0.587912\pi$
$108$	−2.43785e6	+	2.04560e6i	−0.186219	+	0.156256i
$109$	7.70877e6	−	2.80576e6i	0.570154	−	0.207519i	−0.0408243	−	0.999166i	$-0.512998\pi$
$109$	7.70877e6	−	2.80576e6i	0.570154	−	0.207519i	0.610979	+	0.791647i	$0.290776\pi$
$110$	−6.88009e6	−	2.50415e6i	−0.492855	−	0.179385i
$111$	−1.65792e7	−	1.39116e7i	−1.15063	−	0.965489i
$112$	−652041.	+	3.69791e6i	−0.0438543	+	0.248710i
$113$	1.90156e7			1.23975			0.619876	−	0.784700i	$-0.287183\pi$
$113$	1.90156e7			1.23975			0.619876	+	0.784700i	$0.287183\pi$
$114$	1.41860e7	+	1.07695e6i	0.896795	+	0.0680815i
$115$	−1.94185e7			−1.19062
$116$	−1.68066e6	+	9.53148e6i	−0.0999715	+	0.566966i
$117$	−7.33059e6	−	6.15109e6i	−0.423144	−	0.355060i
$118$	−8.17090e6	−	2.97397e6i	−0.457808	−	0.166628i
$119$	−4.55767e6	+	1.65885e6i	−0.247929	+	0.0902389i
$120$	4.94582e6	−	4.15004e6i	0.261279	−	0.219239i
$121$	425241.	+	736538.i	0.0218216	+	0.0377961i
$122$	−873779.	+	1.51343e6i	−0.0435655	+	0.0754576i
$123$	−887218.	−	5.03167e6i	−0.0429895	−	0.243806i
$124$	−151237.	−	857708.i	−0.00712331	−	0.0403983i
$125$	1.17984e7	−	2.04355e7i	0.540305	−	0.935836i
$126$	4.95415e6	+	8.58083e6i	0.220634	+	0.382149i
$127$	−3.07683e7	+	2.58176e7i	−1.33288	+	1.11842i	−0.349481	+	0.936943i	$0.613642\pi$
$127$	−3.07683e7	+	2.58176e7i	−1.33288	+	1.11842i	−0.983396	+	0.181473i	$0.941913\pi$
$128$	−1.97068e6	+	717268.i	−0.0830579	+	0.0302306i
$129$	4.17385e7	+	1.51916e7i	1.71188	+	0.623073i
$130$	−9.20234e6	−	7.72168e6i	−0.367364	−	0.308255i
$131$	−7.49764e6	+	4.25212e7i	−0.291390	+	1.65256i	0.390133	+	0.920759i	$0.372429\pi$
$131$	−7.49764e6	+	4.25212e7i	−0.291390	+	1.65256i	−0.681523	+	0.731797i	$0.738682\pi$
$132$	1.64341e7			0.621922
$133$	−6.78900e6	+	2.65542e7i	−0.250222	+	0.978706i
$134$	1.22244e7			0.438895
$135$	−1.83053e6	+	1.03814e7i	−0.0640337	+	0.363153i
$136$	−2.07509e6	−	1.74120e6i	−0.0707375	−	0.0593558i
$137$	−3.44411e7	−	1.25355e7i	−1.14434	−	0.416505i	−0.300861	−	0.953668i	$-0.597274\pi$
$137$	−3.44411e7	−	1.25355e7i	−1.14434	−	0.416505i	−0.843479	+	0.537163i	$0.819496\pi$
$138$	4.09579e7	−	1.49074e7i	1.32666	−	0.482866i
$139$	3.18347e7	−	2.67125e7i	1.00542	−	0.843651i	0.0176969	−	0.999843i	$-0.494367\pi$
$139$	3.18347e7	−	2.67125e7i	1.00542	−	0.843651i	0.987727	+	0.156193i	$0.0499221\pi$
$140$	6.21911e6	+	1.07718e7i	0.191549	+	0.331773i
$141$	−3.83271e6	+	6.63846e6i	−0.115144	+	0.199434i
$142$	−2.72682e6	−	1.54646e7i	−0.0799185	−	0.453240i
$143$	−5.30976e6	−	3.01132e7i	−0.151845	−	0.861153i
$144$	−2.76690e6	+	4.79242e6i	−0.0772192	+	0.133748i
$145$	1.60300e7	+	2.77647e7i	0.436661	+	0.756320i
$146$	5.86842e6	−	4.92419e6i	0.156058	−	0.130948i
$147$	−942558.	+	343063.i	−0.0244736	+	0.00890765i
$148$	2.18824e7	+	7.96455e6i	0.554855	+	0.201951i
$149$	3.29871e7	+	2.76794e7i	0.816943	+	0.685497i	0.952254	−	0.305306i	$-0.0987589\pi$
$149$	3.29871e7	+	2.76794e7i	0.816943	+	0.685497i	−0.135311	+	0.990803i	$0.543203\pi$
$150$	−2.74180e6	+	1.55495e7i	−0.0663310	+	0.376182i
$151$	−6.99861e7			−1.65422			−0.827109	−	0.562042i	$-0.810016\pi$
$151$	−6.99861e7			−1.65422			−0.827109	+	0.562042i	$0.810016\pi$
$152$	−1.47395e7	+	4.13161e6i	−0.340432	+	0.0954259i
$153$	−7.14786e6			−0.161345
$154$	−5.49780e6	+	3.11796e7i	−0.121302	+	0.687936i
$155$	−2.21002e6	−	1.85442e6i	−0.0476688	−	0.0399989i
$156$	2.53377e7	+	9.22217e6i	0.534356	+	0.194490i
$157$	−5.75637e7	+	2.09515e7i	−1.18713	+	0.432082i	−0.858717	−	0.512451i	$-0.828738\pi$
$157$	−5.75637e7	+	2.09515e7i	−1.18713	+	0.432082i	−0.328418	+	0.944532i	$0.606516\pi$
$158$	4.69469e7	−	3.93931e7i	0.946906	−	0.794549i
$159$	−2.88680e7	−	5.00009e7i	−0.569543	−	0.986478i
$160$	−3.47339e6	+	6.01609e6i	−0.0670400	+	0.116117i
$161$	1.45813e7	+	8.26946e7i	0.275363	+	1.56166i
$162$	−8.21341e6	−	4.65805e7i	−0.151782	−	0.860800i
$163$	3.27527e7	−	5.67293e7i	0.592366	−	1.02601i	−0.401547	−	0.915839i	$-0.631527\pi$
$163$	3.27527e7	−	5.67293e7i	0.592366	−	1.02601i	0.993913	−	0.110170i	$-0.0351395\pi$
$164$	2.74871e6	+	4.76091e6i	0.0486605	+	0.0842824i
$165$	4.17016e7	−	3.49918e7i	0.722701	−	0.606419i
$166$	−2.37624e7	+	8.64882e6i	−0.403193	+	0.146750i
$167$	−5.52878e7	−	2.01231e7i	−0.918590	−	0.334340i	−0.160913	−	0.986969i	$-0.551444\pi$
$167$	−5.52878e7	−	2.01231e7i	−0.918590	−	0.334340i	−0.757678	+	0.652629i	$0.773666\pi$
$168$	−2.13870e7	−	1.79458e7i	−0.347990	−	0.291998i
$169$	−2.18429e6	+	1.23877e7i	−0.0348103	+	0.197419i
$170$	−8.97296e6			−0.140076
$171$	−2.27864e7	+	3.33518e7i	−0.348489	+	0.510074i
$172$	−4.77915e7			−0.716145
$173$	5.18593e6	−	2.94109e7i	0.0761493	−	0.431864i	−0.922769	−	0.385355i	$-0.874079\pi$
$173$	5.18593e6	−	2.94109e7i	0.0761493	−	0.431864i	0.998918	−	0.0465094i	$-0.0148097\pi$
$174$	−5.51256e7	−	4.62559e7i	−0.793288	−	0.665648i
$175$	−2.85842e7	−	1.04038e7i	−0.403174	−	0.146743i
$176$	−1.66161e7	+	6.04778e6i	−0.229740	+	0.0836184i
$177$	4.95255e7	−	4.15568e7i	0.671309	−	0.563295i
$178$	−6.95765e6	−	1.20510e7i	−0.0924683	−	0.160160i
$179$	5.46445e7	−	9.46471e7i	0.712133	−	1.23345i	−0.251922	−	0.967748i	$-0.581063\pi$
$179$	5.46445e7	−	9.46471e7i	0.712133	−	1.23345i	0.964055	−	0.265703i	$-0.0856040\pi$
$180$	3.18309e6	+	1.80522e7i	0.0406813	+	0.230715i
$181$	−1.67763e7	−	9.51430e7i	−0.210291	−	1.19262i	−0.888894	−	0.458114i	$-0.848525\pi$
$181$	−1.67763e7	−	9.51430e7i	−0.210291	−	1.19262i	0.678603	−	0.734506i	$-0.262586\pi$
$182$	−2.59732e7	+	4.49869e7i	−0.319356	+	0.553141i
$183$	−6.49669e6	−	1.12526e7i	−0.0783634	−	0.135729i
$184$	−3.59257e7	+	3.01452e7i	−0.425150	+	0.356743i
$185$	7.24852e7	−	2.63825e7i	0.841682	−	0.306347i
$186$	6.08505e6	+	2.21478e6i	0.0693376	+	0.0252368i
$187$	−1.74965e7	−	1.46813e7i	−0.195661	−	0.164179i
$188$	1.43221e6	−	8.12245e6i	0.0157200	−	0.0891528i
$189$	4.55845e7			0.491135
$190$	−2.86045e7	+	4.18677e7i	−0.302550	+	0.442834i
$191$	7.59866e7			0.789078			0.394539	−	0.918879i	$-0.370904\pi$
$191$	7.59866e7			0.789078			0.394539	+	0.918879i	$0.370904\pi$
$192$	2.70764e6	−	1.53558e7i	0.0276081	−	0.156573i
$193$	3.09468e7	+	2.59675e7i	0.309860	+	0.260003i	0.784434	−	0.620212i	$-0.212953\pi$
$193$	3.09468e7	+	2.59675e7i	0.309860	+	0.260003i	−0.474574	+	0.880216i	$0.657398\pi$
$194$	9.60583e7	+	3.49624e7i	0.944559	+	0.343791i
$195$	8.39307e7	−	3.05483e7i	0.810587	−	0.295030i
$196$	826753.	−	693728.i	0.00784295	−	0.00658102i
$197$	−234071.	−	405423.i	−0.00218130	−	0.00377813i	0.864933	−	0.501888i	$-0.167361\pi$
$197$	−234071.	−	405423.i	−0.00218130	−	0.00377813i	−0.867114	+	0.498110i	$0.834028\pi$
$198$	−2.33297e7	+	4.04082e7i	−0.213590	+	0.369948i
$199$	3.19899e7	+	1.81423e8i	0.287757	+	1.63195i	0.695266	+	0.718752i	$0.255286\pi$
$199$	3.19899e7	+	1.81423e8i	0.287757	+	1.63195i	−0.407509	+	0.913201i	$0.633602\pi$
$200$	−2.95009e6	−	1.67308e7i	−0.0260754	−	0.147881i
$201$	−4.54452e7	+	7.87133e7i	−0.394731	+	0.683695i
$202$	−7.33730e7	−	1.27086e8i	−0.626335	−	1.08484i
$203$	1.06201e8	−	8.91130e7i	0.891028	−	0.747661i
$204$	1.89260e7	−	6.88849e6i	0.156082	−	0.0568092i
$205$	1.71119e7	+	6.22824e6i	0.138727	+	0.0504925i
$206$	2.73499e7	+	2.29493e7i	0.217982	+	0.182908i
$207$	−2.14890e7	+	1.21870e8i	−0.168391	+	0.954994i
$208$	−2.90122e7			−0.223542
$209$	−1.24279e8	+	3.48364e7i	−0.941641	+	0.263950i
$210$	−9.24803e7			−0.689099
$211$	−6.16063e6	+	3.49387e7i	−0.0451478	+	0.256046i	−0.999025	−	0.0441517i	$-0.985942\pi$
$211$	−6.16063e6	+	3.49387e7i	−0.0451478	+	0.256046i	0.953877	+	0.300198i	$0.0970526\pi$
$212$	4.75883e7	+	3.99313e7i	0.343024	+	0.287831i
$213$	1.09714e8	+	3.99327e7i	0.777918	+	0.283139i
$214$	1.32769e8	−	4.83239e7i	0.926079	−	0.337065i
$215$	−1.21271e8	+	1.01759e8i	−0.832193	+	0.698293i
$216$	1.27295e7	+	2.20482e7i	0.0859457	+	0.148862i
$217$	−6.23767e6	+	1.08040e7i	−0.0414394	+	0.0717751i
$218$	−1.13962e7	−	6.46310e7i	−0.0745009	−	0.422516i
$219$	9.89072e6	+	5.60931e7i	0.0636317	+	0.360873i
$220$	−2.92865e7	+	5.07258e7i	−0.185434	+	0.321181i
$221$	−1.87371e7	−	3.24536e7i	−0.116770	−	0.202251i
$222$	−1.32634e8	+	1.11293e8i	−0.813615	+	0.682704i
$223$	−2.66640e8	+	9.70490e7i	−1.61012	+	0.586035i	−0.981464	−	0.191649i	$-0.938617\pi$
$223$	−2.66640e8	+	9.70490e7i	−1.61012	+	0.586035i	−0.628655	+	0.777684i	$0.716394\pi$
$224$	2.82280e7	+	1.02742e7i	0.167808	+	0.0610771i
$225$	−3.43410e7	−	2.88155e7i	−0.200990	−	0.168651i
$226$	2.64162e7	−	1.49813e8i	0.152226	−	0.863319i
$227$	6.30562e7			0.357798			0.178899	−	0.983867i	$-0.442747\pi$
$227$	6.30562e7			0.357798			0.178899	+	0.983867i	$0.442747\pi$
$228$	2.81917e7	−	1.10268e8i	0.157525	−	0.616137i
$229$	−6.20303e7			−0.341334			−0.170667	−	0.985329i	$-0.554592\pi$
$229$	−6.20303e7			−0.341334			−0.170667	+	0.985329i	$0.554592\pi$
$230$	−2.69758e7	+	1.52988e8i	−0.146193	+	0.829104i
$231$	−1.80328e8	−	1.51313e8i	−0.962546	−	0.807672i
$232$	7.27587e7	+	2.64820e7i	0.382540	+	0.139233i
$233$	2.25446e8	−	8.20558e7i	1.16761	−	0.424975i	0.315799	−	0.948826i	$-0.397727\pi$
$233$	2.25446e8	−	8.20558e7i	1.16761	−	0.424975i	0.851810	+	0.523851i	$0.175505\pi$
$234$	−5.86447e7	+	4.92088e7i	−0.299208	+	0.251065i
$235$	−1.36603e7	−	2.36603e7i	−0.0686629	−	0.118928i
$236$	−3.47812e7	+	6.02428e7i	−0.172247	+	0.298341i
$237$	7.91250e7	+	4.48740e8i	0.386095	+	2.18965i
$238$	6.73778e6	+	3.82118e7i	0.0323965	+	0.183729i
$239$	1.62999e8	−	2.82322e8i	0.772310	−	1.33768i	−0.163984	−	0.986463i	$-0.552434\pi$
$239$	1.62999e8	−	2.82322e8i	0.772310	−	1.33768i	0.936294	−	0.351218i	$-0.114232\pi$
$240$	−2.58252e7	−	4.47306e7i	−0.120588	−	0.208865i
$241$	8.83811e7	−	7.41606e7i	0.406724	−	0.341282i	−0.416362	−	0.909199i	$-0.636695\pi$
$241$	8.83811e7	−	7.41606e7i	0.406724	−	0.341282i	0.823086	+	0.567917i	$0.192251\pi$
$242$	6.39353e6	−	2.32705e6i	0.0289993	−	0.0105549i
$243$	2.28278e8	+	8.30865e7i	1.02057	+	0.371457i
$244$	1.07097e7	+	8.98647e6i	0.0471967	+	0.0396027i
$245$	620791.	−	3.52068e6i	0.00269690	−	0.0152949i
$246$	−4.08743e7			−0.175056
$247$	−2.11159e8	−	1.60305e7i	−0.891602	−	0.0676873i
$248$	−6.96751e6			−0.0290066
$249$	3.26487e7	−	1.85160e8i	0.134020	−	0.760063i
$250$	−1.44610e8	−	1.21342e8i	−0.585340	−	0.491158i
$251$	2.88652e8	+	1.05061e8i	1.15217	+	0.419356i	0.846294	−	0.532716i	$-0.178828\pi$
$251$	2.88652e8	+	1.05061e8i	1.15217	+	0.419356i	0.305876	+	0.952071i	$0.401051\pi$
$252$	7.44860e7	−	2.71107e7i	0.293206	−	0.106718i
$253$	−3.02914e8	+	2.54175e8i	−1.17597	+	0.986759i
$254$	1.60661e8	+	2.78272e8i	0.615164	+	1.06550i
$255$	3.33577e7	−	5.77773e7i	0.125981	−	0.218206i
$256$	2.91333e6	+	1.65223e7i	0.0108530	+	0.0615505i
$257$	−1.04829e7	−	5.94512e7i	−0.0385224	−	0.218472i	0.959470	−	0.281812i	$-0.0909356\pi$
$257$	−1.04829e7	−	5.94512e7i	−0.0385224	−	0.218472i	−0.997992	+	0.0633408i	$0.979824\pi$
$258$	1.77669e8	−	3.07731e8i	0.644084	−	1.11559i
$259$	−1.66780e8	−	2.88872e8i	−0.596479	−	1.03313i
$260$	−7.36187e7	+	6.17735e7i	−0.259766	+	0.217969i
$261$	1.91990e8	−	6.98787e7i	0.668401	−	0.243278i
$262$	3.24586e8	+	1.18140e8i	1.11500	+	0.405827i
$263$	−1.11794e8	−	9.38067e7i	−0.378944	−	0.317972i	0.433344	−	0.901229i	$-0.357334\pi$
$263$	−1.11794e8	−	9.38067e7i	−0.378944	−	0.317972i	−0.812288	+	0.583257i	$0.801778\pi$
$264$	2.28300e7	−	1.29475e8i	0.0763645	−	0.433085i
$265$	2.05779e8			0.679265
$266$	1.99775e8	+	9.03756e7i	0.650812	+	0.294419i
$267$	1.03463e8			0.332655
$268$	1.69819e7	−	9.63094e7i	0.0538909	−	0.305631i
$269$	−3.42573e8	−	2.87453e8i	−1.07305	−	0.900396i	−0.0777243	−	0.996975i	$-0.524765\pi$
$269$	−3.42573e8	−	2.87453e8i	−1.07305	−	0.900396i	−0.995325	+	0.0965794i	$0.969210\pi$
$270$	7.92469e7	+	2.88435e7i	0.245024	+	0.0891815i
$271$	−4.91288e8	+	1.78814e8i	−1.49949	+	0.545770i	−0.955928	−	0.293600i	$-0.905147\pi$
$271$	−4.91288e8	+	1.78814e8i	−1.49949	+	0.545770i	−0.543562	+	0.839369i	$0.682925\pi$
$272$	−1.66007e7	+	1.39296e7i	−0.0500190	+	0.0419709i
$273$	−1.93115e8	−	3.34485e8i	−0.574443	−	0.994964i
$274$	−1.46606e8	+	2.53929e8i	−0.430550	+	0.745735i
$275$	−2.48742e7	−	1.41069e8i	−0.0721249	−	0.409041i
$276$	−6.05497e7	−	3.43394e8i	−0.173352	−	0.983131i
$277$	2.18939e8	−	3.79213e8i	0.618933	−	1.07202i	−0.370747	−	0.928734i	$-0.620898\pi$
$277$	2.18939e8	−	3.79213e8i	0.618933	−	1.07202i	0.989681	−	0.143290i	$-0.0457682\pi$
$278$	−1.66229e8	−	2.87917e8i	−0.464034	−	0.803731i
$279$	−1.40840e7	+	1.18179e7i	−0.0388250	+	0.0325780i
$280$	9.35049e7	−	3.40330e7i	0.254555	−	0.0926503i
$281$	−6.37994e8	−	2.32211e8i	−1.71532	−	0.624324i	−0.717899	−	0.696147i	$-0.754896\pi$
$281$	−6.37994e8	−	2.32211e8i	−1.71532	−	0.624324i	−0.997417	+	0.0718225i	$0.977118\pi$
$282$	4.69765e7	+	3.94179e7i	0.124741	+	0.104670i
$283$	−5.87033e7	+	3.32923e8i	−0.153961	+	0.873154i	0.805769	+	0.592230i	$0.201752\pi$
$283$	−5.87033e7	+	3.32923e8i	−0.153961	+	0.873154i	−0.959730	+	0.280925i	$0.909359\pi$
$284$	−1.25625e8			−0.325433
$285$	−1.63248e8	−	3.39832e8i	−0.417726	−	0.869576i
$286$	−2.44622e8			−0.618321
$287$	1.36740e7	−	7.75489e7i	0.0341435	−	0.193637i
$288$	3.39132e7	+	2.84565e7i	0.0836555	+	0.0701953i
$289$	3.59289e8	+	1.30770e8i	0.875591	+	0.318689i
$290$	2.41012e8	−	8.77212e7i	0.580291	−	0.211208i
$291$	−5.82229e8	+	4.88548e8i	−1.38506	+	1.16220i
$292$	−3.06427e7	−	5.30747e7i	−0.0720257	−	0.124752i
$293$	−1.50733e8	+	2.61077e8i	−0.350083	+	0.606362i	−0.986264	−	0.165178i	$-0.947180\pi$
$293$	−1.50733e8	+	2.61077e8i	−0.350083	+	0.606362i	0.636180	+	0.771540i	$0.280513\pi$
$294$	1.39342e6	+	7.90249e6i	0.00319791	+	0.0181363i
$295$	4.00127e7	+	2.26924e8i	0.0907447	+	0.514639i
$296$	9.31472e7	−	1.61336e8i	0.208761	−	0.361584i
$297$	1.07331e8	+	1.85903e8i	0.237727	+	0.411756i
$298$	2.63897e8	−	2.21436e8i	0.577666	−	0.484719i
$299$	−6.09660e8	+	2.21898e8i	−1.31898	+	0.480070i
$300$	1.18697e8	+	4.32023e7i	0.253815	+	0.0923811i
$301$	5.24408e8	+	4.40031e8i	1.10837	+	0.930037i
$302$	−9.72237e7	+	5.51383e8i	−0.203118	+	1.15194i
$303$	1.09108e9			2.25324
$304$	1.20748e7	+	1.21864e8i	0.0246503	+	0.248782i
$305$	4.63101e7			0.0934600
$306$	−9.92971e6	+	5.63142e7i	−0.0198112	+	0.112355i
$307$	3.47517e8	+	2.91601e8i	0.685474	+	0.575181i	0.917600	−	0.397504i	$-0.130124\pi$
$307$	3.47517e8	+	2.91601e8i	0.685474	+	0.575181i	−0.232126	+	0.972686i	$0.574568\pi$
$308$	2.38010e8	+	8.66285e7i	0.464160	+	0.168940i
$309$	−2.49447e8	+	9.07912e7i	−0.480976	+	0.175061i
$310$	−1.76801e7	+	1.48354e7i	−0.0337070	+	0.0282835i
$311$	−2.87460e8	−	4.97895e8i	−0.541896	−	0.938591i	−0.998795	−	0.0490729i	$-0.984373\pi$
$311$	−2.87460e8	−	4.97895e8i	−0.541896	−	0.938591i	0.456899	−	0.889518i	$-0.348960\pi$
$312$	1.07855e8	−	1.86811e8i	0.201048	−	0.348226i
$313$	1.65144e7	+	9.36576e7i	0.0304408	+	0.172639i	0.996238	−	0.0866605i	$-0.0276195\pi$
$313$	1.65144e7	+	9.36576e7i	0.0304408	+	0.172639i	−0.965797	+	0.259299i	$0.916508\pi$
$314$	8.50988e7	+	4.82619e8i	0.155121	+	0.879733i
$315$	1.31284e8	−	2.27391e8i	0.236660	−	0.409908i
$316$	−2.45139e8	−	4.24594e8i	−0.437027	−	0.756952i
$317$	−1.92908e8	+	1.61869e8i	−0.340128	+	0.285401i	−0.796811	−	0.604228i	$-0.793482\pi$
$317$	−1.92908e8	+	1.61869e8i	−0.340128	+	0.285401i	0.456684	+	0.889629i	$0.349037\pi$
$318$	−4.34033e8	+	1.57975e8i	−0.756881	+	0.275482i
$319$	6.13478e8	+	2.23288e8i	1.05811	+	0.385121i
$320$	4.25724e7	+	3.57224e7i	0.0726278	+	0.0609419i
$321$	−1.82419e8	+	1.03455e9i	−0.307825	+	1.74576i
$322$	6.71762e8			1.12130
$323$	−1.28521e8	+	9.22114e7i	−0.212210	+	0.152256i
$324$	−3.78393e8			−0.618067
$325$	4.08118e7	−	2.31455e8i	0.0659469	−	0.374003i
$326$	−4.01440e8	−	3.36848e8i	−0.641740	−	0.538484i
$327$	4.58528e8	+	1.66890e8i	0.725185	+	0.263946i
$328$	4.13271e7	−	1.50419e7i	0.0646661	−	0.0235366i
$329$	−9.05012e7	+	7.59395e7i	−0.140110	+	0.117566i
$330$	−2.17750e8	−	3.77155e8i	−0.333549	−	0.577724i
$331$	4.61565e8	−	7.99454e8i	0.699576	−	1.21170i	−0.269038	−	0.963130i	$-0.586706\pi$
$331$	4.61565e8	−	7.99454e8i	0.699576	−	1.21170i	0.968614	−	0.248571i	$-0.0799610\pi$
$332$	3.51290e7	+	1.99226e8i	0.0526844	+	0.298788i
$333$	−8.53619e7	−	4.84112e8i	−0.126680	−	0.718440i
$334$	−2.35344e8	+	4.07628e8i	−0.345614	+	0.598621i
$335$	−1.61972e8	−	2.80544e8i	−0.235388	−	0.407704i
$336$	−1.71096e8	+	1.43566e8i	−0.246066	+	0.206474i
$337$	−1.52050e7	+	5.53419e6i	−0.0216413	+	0.00787679i	−0.352818	−	0.935692i	$-0.614777\pi$
$337$	−1.52050e7	+	5.53419e6i	−0.0216413	+	0.00787679i	0.331177	+	0.943569i	$0.392554\pi$
$338$	9.45620e7	+	3.44177e7i	0.133201	+	0.0484813i
$339$	8.66451e8	+	7.27039e8i	1.20794	+	1.01358i
$340$	−1.24651e7	+	7.06931e7i	−0.0171997	+	0.0975441i
$341$	−5.87479e7			−0.0802328
$342$	2.31107e8	+	2.25853e8i	0.312407	+	0.305306i
$343$	7.39513e8			0.989501
$344$	−6.63913e7	+	3.76524e8i	−0.0879339	+	0.498698i
$345$	−8.84809e8	−	7.42443e8i	−1.16007	−	0.973411i
$346$	−2.24508e8	−	8.17144e7i	−0.291384	−	0.106055i
$347$	1.11517e9	−	4.05887e8i	1.43280	−	0.521497i	0.495068	−	0.868854i	$-0.335143\pi$
$347$	1.11517e9	−	4.05887e8i	1.43280	−	0.521497i	0.937733	+	0.347357i	$0.112921\pi$
$348$	−4.41005e8	+	3.70047e8i	−0.560940	+	0.470684i
$349$	−5.07264e8	−	8.78608e8i	−0.638771	−	1.10638i	−0.985703	−	0.168494i	$-0.946110\pi$
$349$	−5.07264e8	−	8.78608e8i	−0.638771	−	1.10638i	0.346932	−	0.937890i	$-0.387224\pi$
$350$	−1.21675e8	+	2.10746e8i	−0.151692	+	0.262738i
$351$	6.11594e7	+	3.46852e8i	0.0754898	+	0.428124i
$352$	2.45643e7	+	1.39311e8i	0.0300196	+	0.170250i
$353$	−1.10195e8	+	1.90863e8i	−0.133337	+	0.230946i	−0.924961	−	0.380062i	$-0.875903\pi$
$353$	−1.10195e8	+	1.90863e8i	−0.133337	+	0.230946i	0.791624	+	0.611008i	$0.209236\pi$
$354$	−2.58604e8	−	4.47915e8i	−0.309830	−	0.536641i
$355$	−3.18775e8	+	2.67484e8i	−0.378168	+	0.317321i
$356$	−1.04609e8	+	3.80745e7i	−0.122883	+	0.0447259i
$357$	−2.71096e8	−	9.86709e7i	−0.315344	−	0.114776i
$358$	−6.69762e8	−	5.61997e8i	−0.771490	−	0.647357i
$359$	−8.22132e7	+	4.66254e8i	−0.0937802	+	0.531854i	0.901334	+	0.433124i	$0.142589\pi$
$359$	−8.22132e7	+	4.66254e8i	−0.0937802	+	0.531854i	−0.995114	+	0.0987294i	$0.968522\pi$
$360$	1.46645e8			0.165657
$361$	2.05489e7	+	8.93636e8i	0.0229887	+	0.999736i
$362$	−7.72886e8			−0.856318
$363$	−8.78447e6	+	4.98192e7i	−0.00963923	+	0.0546668i
$364$	3.18346e8	+	2.67124e8i	0.345975	+	0.290307i
$365$	−1.90764e8	−	6.94325e7i	−0.205339	−	0.0747373i
$366$	−9.76783e7	+	3.55520e7i	−0.104139	+	0.0379036i
$367$	7.77122e8	−	6.52083e8i	0.820650	−	0.688607i	−0.132474	−	0.991186i	$-0.542292\pi$
$367$	7.77122e8	−	6.52083e8i	0.820650	−	0.688607i	0.953124	+	0.302579i	$0.0978476\pi$
$368$	1.87591e8	+	3.24916e8i	0.196220	+	0.339863i
$369$	5.80248e7	−	1.00502e8i	0.0601204	−	0.104132i
$370$	−1.07158e8	−	6.07722e8i	−0.109981	−	0.623733i
$371$	−1.54519e8	−	8.76319e8i	−0.157099	−	0.890951i
$372$	2.59023e7	−	4.48641e7i	0.0260878	−	0.0451855i
$373$	−4.99446e8	−	8.65066e8i	−0.498319	−	0.863115i	0.501679	−	0.865054i	$-0.332716\pi$
$373$	−4.99446e8	−	8.65066e8i	−0.498319	−	0.863115i	−0.999998	+	0.00193951i	$0.999383\pi$
$374$	−1.39972e8	+	1.17450e8i	−0.138353	+	0.116092i
$375$	1.31893e9	−	4.80050e8i	1.29155	−	0.470086i
$376$	−6.20028e7	−	2.25672e7i	−0.0601526	−	0.0218937i
$377$	8.20547e8	+	6.88521e8i	0.788694	+	0.661793i
$378$	6.33253e7	−	3.59136e8i	0.0603054	−	0.342009i
$379$	1.16432e9			1.09859			0.549294	−	0.835629i	$-0.314897\pi$
$379$	1.16432e9			1.09859			0.549294	+	0.835629i	$0.314897\pi$
$380$	2.90116e8	+	2.83522e8i	0.271225	+	0.265060i
$381$	−2.38907e9			−2.21306
$382$	1.05559e8	−	5.98657e8i	0.0968892	−	0.549486i
$383$	1.69900e8	+	1.42563e8i	0.154524	+	0.129661i	0.716772	−	0.697308i	$-0.245619\pi$
$383$	1.69900e8	+	1.42563e8i	0.154524	+	0.129661i	−0.562248	+	0.826969i	$0.690063\pi$
$384$	−1.17219e8	−	4.26641e7i	−0.105642	−	0.0384506i
$385$	7.88404e8	−	2.86955e8i	0.704103	−	0.256272i
$386$	2.47575e8	−	2.07740e8i	0.219104	−	0.183850i
$387$	5.04435e8	+	8.73707e8i	0.442402	+	0.766262i
$388$	4.08892e8	−	7.08223e8i	0.355384	−	0.615543i
$389$	−2.00816e8	−	1.13889e9i	−0.172972	−	0.980972i	−0.940459	−	0.339907i	$-0.889604\pi$
$389$	−2.00816e8	−	1.13889e9i	−0.172972	−	0.980972i	0.767487	−	0.641064i	$-0.221507\pi$
$390$	−1.24078e8	−	7.03682e8i	−0.105918	−	0.600690i
$391$	−2.42305e8	+	4.19685e8i	−0.204995	+	0.355063i
$392$	−4.31700e6	−	7.47726e6i	−0.00361977	−	0.00626962i
$393$	−1.96738e9	+	1.65083e9i	−1.63499	+	1.37192i
$394$	−3.51928e6	+	1.28091e6i	−0.00289879	+	0.00105507i
$395$	−1.52610e9	−	5.55454e8i	−1.24593	−	0.453480i
$396$	2.85945e8	+	2.39936e8i	0.231393	+	0.194161i
$397$	−1.92389e8	+	1.09109e9i	−0.154317	+	0.875175i	0.805091	+	0.593152i	$0.202117\pi$
$397$	−1.92389e8	+	1.09109e9i	−0.154317	+	0.875175i	−0.959408	+	0.282023i	$0.908995\pi$
$398$	1.47378e9			1.17177
$399$	−1.32461e9	+	9.50381e8i	−1.04396	+	0.749019i
$400$	−1.35911e8			−0.106181
$401$	2.35253e8	−	1.33418e9i	0.182192	−	1.03326i	−0.747318	−	0.664466i	$-0.768659\pi$
$401$	2.35253e8	−	1.33418e9i	0.182192	−	1.03326i	0.929510	−	0.368796i	$-0.120230\pi$
$402$	5.57008e8	+	4.67385e8i	0.427632	+	0.358826i
$403$	−9.05762e7	−	3.29671e7i	−0.0689361	−	0.0250907i
$404$	−1.10317e9	+	4.01521e8i	−0.832353	+	0.302952i
$405$	−9.60176e8	+	8.05683e8i	−0.718221	+	0.602659i
$406$	−5.54541e8	−	9.60493e8i	−0.411237	−	0.712284i
$407$	7.85388e8	−	1.36033e9i	0.577436	−	1.00015i
$408$	−2.79790e7	−	1.58677e8i	−0.0203949	−	0.115665i
$409$	−2.89892e8	−	1.64406e9i	−0.209510	−	1.18819i	−0.890183	−	0.455604i	$-0.849423\pi$
$409$	−2.89892e8	−	1.64406e9i	−0.209510	−	1.18819i	0.680672	−	0.732588i	$-0.261688\pi$
$410$	7.28406e7	−	1.26164e8i	0.0521951	−	0.0904046i
$411$	−1.09004e9	−	1.88800e9i	−0.774453	−	1.34139i
$412$	2.18799e8	−	1.83594e8i	0.154136	−	0.129336i
$413$	9.36321e8	−	3.40793e8i	0.654033	−	0.238049i
$414$	9.30296e8	+	3.38600e8i	0.644347	+	0.234523i
$415$	5.13337e8	+	4.30741e8i	0.352561	+	0.295834i
$416$	−4.03033e7	+	2.28571e8i	−0.0274482	+	0.155667i
$417$	2.47188e9			1.66936
$418$	1.01811e8	+	1.02752e9i	0.0681833	+	0.688135i
$419$	−2.26680e9			−1.50544			−0.752720	−	0.658341i	$-0.771258\pi$
$419$	−2.26680e9			−1.50544			−0.752720	+	0.658341i	$0.771258\pi$
$420$	−1.28472e8	+	7.28602e8i	−0.0846129	+	0.479864i
$421$	8.58364e8	+	7.20253e8i	0.560640	+	0.470433i	0.878525	−	0.477697i	$-0.158528\pi$
$421$	8.58364e8	+	7.20253e8i	0.560640	+	0.470433i	−0.317885	+	0.948129i	$0.602973\pi$
$422$	2.66705e8	+	9.70726e7i	0.172758	+	0.0628786i
$423$	−1.63609e8	+	5.95486e7i	−0.105103	+	0.0382543i
$424$	3.80706e8	−	3.19451e8i	0.242555	−	0.203528i
$425$	−8.77763e7	−	1.52033e8i	−0.0554646	−	0.0960675i
$426$	4.67021e8	−	8.08905e8i	0.292687	−	0.506948i
$427$	−3.47742e7	−	1.97214e8i	−0.0216152	−	0.122586i
$428$	−1.96278e8	−	1.11315e9i	−0.121009	−	0.686276i
$429$	9.09401e8	−	1.57513e9i	0.556103	−	0.963198i
$430$	6.33234e8	+	1.09679e9i	0.384083	+	0.665251i
$431$	−5.72062e8	+	4.80017e8i	−0.344170	+	0.288793i	−0.798444	−	0.602069i	$-0.794343\pi$
$431$	−5.72062e8	+	4.80017e8i	−0.344170	+	0.288793i	0.454274	+	0.890862i	$0.349899\pi$
$432$	1.91390e8	−	6.96601e7i	0.114216	−	0.0415711i
$433$	1.17856e9	+	4.28962e8i	0.697663	+	0.253929i	0.666413	−	0.745583i	$-0.267829\pi$
$433$	1.17856e9	+	4.28962e8i	0.697663	+	0.253929i	0.0312503	+	0.999512i	$0.490051\pi$
$434$	7.64533e7	+	6.41520e7i	0.0448934	+	0.0376700i
$435$	−3.31141e8	+	1.87800e9i	−0.192886	+	1.09391i
$436$	−5.25024e8			−0.303373
$437$	1.18581e9	+	2.46849e9i	0.679720	+	1.41497i
$438$	4.55667e8			0.259113
$439$	−3.46635e7	+	1.96586e8i	−0.0195545	+	0.110899i	−0.993023	−	0.117923i	$-0.962376\pi$
$439$	−3.46635e7	+	1.96586e8i	−0.0195545	+	0.110899i	0.973468	+	0.228822i	$0.0734874\pi$
$440$	3.58957e8	+	3.01200e8i	0.200890	+	0.168566i
$441$	−2.14088e7	−	7.79216e6i	−0.0118866	−	0.00432636i
$442$	−2.81714e8	+	1.02536e8i	−0.155178	+	0.0564802i
$443$	−8.57052e8	+	7.19152e8i	−0.468375	+	0.393014i	−0.846202	−	0.532863i	$-0.821116\pi$
$443$	−8.57052e8	+	7.19152e8i	−0.468375	+	0.393014i	0.377826	+	0.925877i	$0.376672\pi$
$444$	6.92565e8	+	1.19956e9i	0.375509	+	0.650400i
$445$	−1.84377e8	+	3.19350e8i	−0.0991851	+	0.171794i
$446$	3.94184e8	+	2.23553e9i	0.210391	+	1.19319i
$447$	4.44775e8	+	2.52245e9i	0.235540	+	1.33581i
$448$	1.20159e8	−	2.08121e8i	0.0631366	−	0.109356i
$449$	1.48757e9	+	2.57655e9i	0.775560	+	1.34331i	0.934479	+	0.356017i	$0.115866\pi$
$449$	1.48757e9	+	2.57655e9i	0.775560	+	1.34331i	−0.158920	+	0.987292i	$0.550801\pi$
$450$	−2.74728e8	+	2.30524e8i	−0.142121	+	0.119254i
$451$	3.48458e8	−	1.26828e8i	0.178868	−	0.0651025i
$452$	−1.14360e9	−	4.16237e8i	−0.582493	−	0.212010i
$453$	−3.18894e9	−	2.67584e9i	−1.61177	−	1.35244i
$454$	8.75968e7	−	4.96786e8i	0.0439332	−	0.249157i
$455$	1.37657e9			0.685108
$456$	−8.29578e8	−	3.75290e8i	−0.409713	−	0.185349i
$457$	2.67975e8			0.131337			0.0656686	−	0.997841i	$-0.479082\pi$
$457$	2.67975e8			0.131337			0.0656686	+	0.997841i	$0.479082\pi$
$458$	−8.61716e7	+	4.88704e8i	−0.0419117	+	0.237693i
$459$	2.01529e8	+	1.69103e8i	0.0972734	+	0.0816221i
$460$	1.16783e9	+	4.25056e8i	0.559407	+	0.203608i
$461$	−2.36361e8	+	8.60284e7i	−0.112363	+	0.0408967i	−0.397590	−	0.917563i	$-0.630153\pi$
$461$	−2.36361e8	+	8.60284e7i	−0.112363	+	0.0408967i	0.285227	+	0.958460i	$0.407931\pi$
$462$	−1.44263e9	+	1.21051e9i	−0.680623	+	0.571111i
$463$	8.09327e7	+	1.40180e8i	0.0378958	+	0.0656374i	0.884351	−	0.466822i	$-0.154601\pi$
$463$	8.09327e7	+	1.40180e8i	0.0378958	+	0.0656374i	−0.846455	+	0.532460i	$0.821268\pi$
$464$	3.09713e8	−	5.36438e8i	0.143928	−	0.249291i
$465$	−2.97984e7	−	1.68995e8i	−0.0137438	−	0.0779450i
$466$	−3.33286e8	−	1.89016e9i	−0.152569	−	0.865263i
$467$	3.18313e8	−	5.51335e8i	0.144626	−	0.250499i	−0.784607	−	0.619993i	$-0.787136\pi$
$467$	3.18313e8	−	5.51335e8i	0.144626	−	0.250499i	0.929233	+	0.369494i	$0.120469\pi$
$468$	3.06221e8	+	5.30390e8i	0.138094	+	0.239186i
$469$	−1.07309e9	+	9.00429e8i	−0.480320	+	0.403036i
$470$	−2.05383e8	+	7.47535e7i	−0.0912479	+	0.0332115i
$471$	−3.42397e9	−	1.24622e9i	−1.50993	−	0.549569i
$472$	4.26303e8	+	3.57711e8i	0.186604	+	0.156579i
$473$	−5.59790e8	+	3.17473e9i	−0.243227	+	1.37941i
$474$	3.64530e9			1.57220
$475$	−9.89202e8	−	7.50967e7i	−0.423504	−	0.0321509i
$476$	3.10411e8			0.131920
$477$	2.27720e8	−	1.29146e9i	0.0960697	−	0.544838i
$478$	−1.99783e9	−	1.67638e9i	−0.836683	−	0.702060i
$479$	7.70350e8	+	2.80384e8i	0.320268	+	0.116568i	0.497152	−	0.867664i	$-0.334379\pi$
$479$	7.70350e8	+	2.80384e8i	0.320268	+	0.116568i	−0.176883	+	0.984232i	$0.556602\pi$
$480$	−3.88285e8	+	1.41324e8i	−0.160253	+	0.0583273i
$481$	1.97426e9	−	1.65660e9i	0.808903	−	0.678750i
$482$	−4.61493e8	−	7.99330e8i	−0.187716	−	0.325133i
$483$	−2.49733e9	+	4.32551e9i	−1.00847	+	1.74671i
$484$	−9.45181e6	−	5.36039e7i	−0.00378928	−	0.0214901i
$485$	−4.70395e8	−	2.66775e9i	−0.187226	−	1.06181i
$486$	9.71715e8	−	1.68306e9i	0.383983	−	0.665078i
$487$	−2.37822e9	−	4.11920e9i	−0.933041	−	1.61608i	−0.778090	−	0.628153i	$-0.783811\pi$
$487$	−2.37822e9	−	4.11920e9i	−0.933041	−	1.61608i	−0.154952	−	0.987922i	$-0.549522\pi$
$488$	8.56773e7	−	7.18918e7i	0.0333731	−	0.0280033i
$489$	3.66137e9	−	1.33263e9i	1.41600	−	0.515381i
$490$	−2.68752e7	−	9.78176e6i	−0.0103197	−	0.00375605i
$491$	−3.71633e9	−	3.11837e9i	−1.41687	−	1.18889i	−0.952994	−	0.302990i	$-0.902015\pi$
$491$	−3.71633e9	−	3.11837e9i	−1.41687	−	1.18889i	−0.463873	−	0.885902i	$-0.653541\pi$
$492$	−5.67820e7	+	3.22027e8i	−0.0214948	+	0.121903i
$493$	8.00094e8			0.300730
$494$	−4.19635e8	+	1.64134e9i	−0.156613	+	0.612569i
$495$	1.23647e9			0.458210
$496$	−9.67917e6	+	5.48933e7i	−0.00356166	+	0.0201992i
$497$	1.37846e9	+	1.15667e9i	0.503672	+	0.422631i
$498$	−1.41342e9	−	5.14443e8i	−0.512824	−	0.186653i
$499$	2.82308e9	−	1.02752e9i	1.01712	−	0.370200i	0.220955	−	0.975284i	$-0.429083\pi$
$499$	2.82308e9	−	1.02752e9i	1.01712	−	0.370200i	0.796162	+	0.605084i	$0.206860\pi$
$500$	−1.15688e9	+	9.70737e8i	−0.413898	+	0.347301i
$501$	−1.74982e9	−	3.03078e9i	−0.621673	−	1.07677i
$502$	1.22871e9	−	2.12819e9i	0.433497	−	0.750838i
$503$	3.44346e8	+	1.95288e9i	0.120644	+	0.684208i	0.983800	+	0.179270i	$0.0573736\pi$
$503$	3.44346e8	+	1.95288e9i	0.120644	+	0.684208i	−0.863156	+	0.504938i	$0.831515\pi$
$504$	−1.10116e8	−	6.24497e8i	−0.0383127	−	0.217282i
$505$	−1.94438e9	+	3.36776e9i	−0.671832	+	1.16365i
$506$	1.58170e9	+	2.73959e9i	0.542748	+	0.940068i
$507$	−5.73159e8	+	4.80938e8i	−0.195320	+	0.163893i
$508$	2.41554e9	−	8.79186e8i	0.817508	−	0.297549i
$509$	1.05335e8	+	3.83387e7i	0.0354046	+	0.0128862i	0.359662	−	0.933083i	$-0.382892\pi$
$509$	1.05335e8	+	3.83387e7i	0.0354046	+	0.0128862i	−0.324257	+	0.945969i	$0.605114\pi$
$510$	−4.08856e8	−	3.43071e8i	−0.136482	−	0.114522i
$511$	−1.52438e8	+	8.64517e8i	−0.0505381	+	0.286616i
$512$	1.34218e8			0.0441942
$513$	1.43148e9	−	4.01256e8i	0.468139	−	0.131223i
$514$	−4.82947e8			−0.156866
$515$	1.64292e8	−	9.31745e8i	0.0530018	−	0.300588i
$516$	−2.17764e9	−	1.82725e9i	−0.697768	−	0.585497i
$517$	−5.22788e8	−	1.90279e8i	−0.166383	−	0.0605585i
$518$	−2.50755e9	+	9.12675e8i	−0.792677	+	0.288511i
$519$	1.36079e9	−	1.14184e9i	0.427273	−	0.358525i
$520$	3.84410e8	+	6.65817e8i	0.119890	+	0.207655i
$521$	1.30626e9	−	2.26250e9i	0.404666	−	0.700901i	−0.589617	−	0.807683i	$-0.700721\pi$
$521$	1.30626e9	−	2.26250e9i	0.404666	−	0.700901i	0.994282	+	0.106782i	$0.0340546\pi$
$522$	−2.83827e8	−	1.60966e9i	−0.0873387	−	0.495322i
$523$	3.01484e8	+	1.70980e9i	0.0921528	+	0.522625i	0.995583	+	0.0938887i	$0.0299298\pi$
$523$	3.01484e8	+	1.70980e9i	0.0921528	+	0.522625i	−0.903430	+	0.428736i	$0.858959\pi$
$524$	1.38167e9	−	2.39312e9i	0.419512	−	0.726616i
$525$	−9.04670e8	−	1.56694e9i	−0.272856	−	0.472600i
$526$	−8.94355e8	+	7.50453e8i	−0.267954	+	0.224840i
$527$	−6.76559e7	+	2.46247e7i	−0.0201358	+	0.00732882i
$528$	−9.88350e8	−	3.59730e8i	−0.292208	−	0.106355i
$529$	3.81886e9	+	3.20441e9i	1.12160	+	0.941137i
$530$	2.85864e8	−	1.62122e9i	0.0834055	−	0.473016i
$531$	1.46845e9			0.425626
$532$	9.89545e8	−	1.44837e9i	0.284934	−	0.417051i
$533$	6.08416e8			0.174042
$534$	1.43729e8	−	8.15126e8i	0.0408460	−	0.231649i
$535$	−2.86819e9	−	2.40670e9i	−0.809785	−	0.679491i
$536$	−7.35179e8	−	2.67583e8i	−0.206213	−	0.0750554i
$537$	6.10862e9	−	2.22336e9i	1.70229	−	0.619582i
$538$	−2.74058e9	+	2.29962e9i	−0.758761	+	0.636676i
$539$	−3.63996e7	−	6.30459e7i	−0.0100123	−	0.0173419i
$540$	3.37331e8	−	5.84274e8i	0.0921888	−	0.159676i
$541$	−1.09464e8	−	6.20803e8i	−0.0297223	−	0.168563i	0.966333	−	0.257293i	$-0.0828305\pi$
$541$	−1.09464e8	−	6.20803e8i	−0.0297223	−	0.168563i	−0.996056	+	0.0887294i	$0.971719\pi$
$542$	7.26291e8	+	4.11900e9i	0.195935	+	1.11121i
$543$	2.87327e9	−	4.97664e9i	0.770152	−	1.33394i
$544$	8.66826e7	+	1.50139e8i	0.0230853	+	0.0399849i
$545$	−1.33225e9	+	1.11789e9i	−0.352533	+	0.295810i
$546$	−2.90350e9	+	1.05679e9i	−0.763392	+	0.277852i
$547$	7.34315e7	+	2.67269e7i	0.0191835	+	0.00698221i	0.351594	−	0.936153i	$-0.385640\pi$
$547$	7.34315e7	+	2.67269e7i	0.0191835	+	0.00698221i	−0.332411	+	0.943135i	$0.607862\pi$
$548$	1.79690e9	+	1.50778e9i	0.466437	+	0.391387i
$549$	5.12479e7	−	2.90641e8i	0.0132182	−	0.0749642i
$550$	−1.14596e9			−0.293697
$551$	2.55058e9	−	3.73323e9i	0.649545	−	0.950722i
$552$	−2.78953e9			−0.705903
$553$	−1.21949e9	+	6.91606e9i	−0.306648	+	1.73909i
$554$	−2.68347e9	−	2.25170e9i	−0.670522	−	0.562634i
$555$	4.31152e9	+	1.56926e9i	1.07054	+	0.389646i
$556$	−2.49927e9	+	9.09659e8i	−0.616667	+	0.224449i
$557$	8.63220e8	−	7.24327e8i	0.211655	−	0.177599i	−0.530797	−	0.847499i	$-0.678107\pi$
$557$	8.63220e8	−	7.24327e8i	0.211655	−	0.177599i	0.742452	+	0.669900i	$0.233663\pi$
$558$	7.35414e7	+	1.27377e8i	0.0179189	+	0.0310365i
$559$	−2.64461e9	+	4.58060e9i	−0.640354	+	1.10913i
$560$	−1.38232e8	−	7.83953e8i	−0.0332622	−	0.188639i
$561$	−2.35910e8	−	1.33791e9i	−0.0564127	−	0.319933i
$562$	−2.71576e9	+	4.70383e9i	−0.645377	+	1.11783i
$563$	−3.16199e9	−	5.47673e9i	−0.746760	−	1.29343i	−0.949368	−	0.314167i	$-0.898275\pi$
$563$	−3.16199e9	−	5.47673e9i	−0.746760	−	1.29343i	0.202608	−	0.979260i	$-0.435058\pi$
$564$	3.75812e8	−	3.15344e8i	0.0882051	−	0.0740128i
$565$	−3.78817e9	+	1.37878e9i	−0.883608	+	0.321607i
$566$	2.54137e9	+	9.24983e8i	0.589129	+	0.214425i
$567$	4.15204e9	+	3.48398e9i	0.956579	+	0.802665i
$568$	−1.74516e8	+	9.89732e8i	−0.0399592	+	0.226620i
$569$	−6.19037e9			−1.40872			−0.704358	−	0.709845i	$-0.748765\pi$
$569$	−6.19037e9			−1.40872			−0.704358	+	0.709845i	$0.748765\pi$
$570$	−2.90414e9	+	8.14054e8i	−0.656833	+	0.184116i
$571$	−6.41936e9			−1.44300			−0.721499	−	0.692416i	$-0.756546\pi$
$571$	−6.41936e9			−1.44300			−0.721499	+	0.692416i	$0.756546\pi$
$572$	−3.39825e8	+	1.92724e9i	−0.0759223	+	0.430577i
$573$	3.46235e9	+	2.90526e9i	0.768830	+	0.645125i
$574$	−5.91971e8	−	2.15460e8i	−0.130650	−	0.0475526i
$575$	−2.85602e9	+	1.03951e9i	−0.626505	+	0.228029i
$576$	2.71305e8	−	2.27652e8i	0.0591534	−	0.0496356i
$577$	−2.04724e8	−	3.54592e8i	−0.0443663	−	0.0768447i	0.842990	−	0.537930i	$-0.180794\pi$
$577$	−2.04724e8	−	3.54592e8i	−0.0443663	−	0.0768447i	−0.887356	+	0.461085i	$0.847460\pi$
$578$	1.52939e9	−	2.64898e9i	0.329436	−	0.570599i
$579$	4.17266e8	+	2.36643e9i	0.0893384	+	0.506663i
$580$	−3.56298e8	−	2.02066e9i	−0.0758254	−	0.430027i
$581$	1.44887e9	−	2.50952e9i	0.306488	−	0.530852i
$582$	3.04018e9	+	5.26575e9i	0.639248	+	1.10721i
$583$	3.21000e9	−	2.69351e9i	0.670911	−	0.562961i
$584$	−4.60716e8	+	1.67687e8i	−0.0957168	+	0.0348381i
$585$	1.90636e9	+	6.93858e8i	0.393694	+	0.143293i
$586$	1.84749e9	+	1.55023e9i	0.379263	+	0.318239i
$587$	−1.24703e8	+	7.07224e8i	−0.0254473	+	0.144319i	−0.994884	−	0.101022i	$-0.967789\pi$
$587$	−1.24703e8	+	7.07224e8i	−0.0254473	+	0.144319i	0.969437	+	0.245341i	$0.0788999\pi$
$588$	6.41952e7			0.0130221
$589$	−1.00779e8	+	3.94181e8i	−0.0203219	+	0.0794864i
$590$	1.84339e9			0.369518
$591$	4.83536e6	−	2.74227e7i	0.000963546	−	0.00546454i
$592$	−1.14168e9	−	9.57982e8i	−0.226161	−	0.189772i
$593$	8.58366e9	+	3.12420e9i	1.69037	+	0.615243i	0.994672	−	0.103094i	$-0.0328741\pi$
$593$	8.58366e9	+	3.12420e9i	1.69037	+	0.615243i	0.695695	+	0.718337i	$0.255096\pi$
$594$	1.61374e9	−	5.87352e8i	0.315922	−	0.114986i
$595$	7.87670e8	−	6.60934e8i	0.153297	−	0.128632i
$596$	−1.37797e9	−	2.38671e9i	−0.266611	−	0.461784i
$597$	−5.47889e9	+	9.48972e9i	−1.05386	+	1.82534i
$598$	9.01284e8	+	5.11144e9i	0.172349	+	0.977437i
$599$	8.39632e8	+	4.76179e9i	0.159623	+	0.905266i	0.954437	+	0.298413i	$0.0964573\pi$
$599$	8.39632e8	+	4.76179e9i	0.159623	+	0.905266i	−0.794814	+	0.606853i	$0.792432\pi$
$600$	5.05261e8	−	8.75138e8i	0.0954962	−	0.165404i
$601$	−3.92271e9	−	6.79433e9i	−0.737098	−	1.27669i	−0.953797	−	0.300452i	$-0.902862\pi$
$601$	−3.92271e9	−	6.79433e9i	−0.737098	−	1.27669i	0.216699	−	0.976238i	$-0.430471\pi$
$602$	4.19526e9	−	3.52024e9i	0.783739	−	0.657635i
$603$	−1.93994e9	+	7.06079e8i	−0.360310	+	0.131142i
$604$	4.20899e9	+	1.53195e9i	0.777228	+	0.282888i
$605$	−1.38119e8	−	1.15895e8i	−0.0253576	−	0.0212776i
$606$	1.51571e9	−	8.59604e9i	0.276671	−	1.56908i
$607$	−4.16495e9			−0.755875			−0.377937	−	0.925831i	$-0.623367\pi$
$607$	−4.16495e9			−0.755875			−0.377937	+	0.925831i	$0.623367\pi$
$608$	9.76876e8	+	7.41610e7i	0.176269	+	0.0133818i
$609$	8.24621e9			1.47943
$610$	6.43333e7	−	3.64852e8i	0.0114758	−	0.0650822i
$611$	−6.99247e8	−	5.86738e8i	−0.124018	−	0.104064i
$612$	4.29875e8	+	1.56462e8i	0.0758075	+	0.0275917i
$613$	3.50152e9	−	1.27445e9i	0.613966	−	0.223465i	−0.0162716	−	0.999868i	$-0.505180\pi$
$613$	3.50152e9	−	1.27445e9i	0.613966	−	0.223465i	0.630238	+	0.776402i	$0.282957\pi$
$614$	2.78013e9	−	2.33281e9i	0.484704	−	0.406715i
$615$	5.41582e8	+	9.38047e8i	0.0938861	+	0.162615i
$616$	1.01314e9	−	1.75481e9i	0.174637	−	0.302480i
$617$	7.60499e8	+	4.31300e9i	0.130347	+	0.739234i	0.977988	+	0.208663i	$0.0669112\pi$
$617$	7.60499e8	+	4.31300e9i	0.130347	+	0.739234i	−0.847641	+	0.530571i	$0.821978\pi$
$618$	3.68767e8	+	2.09138e9i	0.0628482	+	0.356430i
$619$	−3.75042e9	+	6.49591e9i	−0.635568	+	1.10084i	0.350826	+	0.936441i	$0.385901\pi$
$619$	−3.75042e9	+	6.49591e9i	−0.635568	+	1.10084i	−0.986394	+	0.164396i	$0.947433\pi$
$620$	9.23191e7	+	1.59901e8i	0.0155568	+	0.0269452i
$621$	3.48905e9	−	2.92766e9i	0.584638	−	0.490569i
$622$	−4.32198e9	+	1.57307e9i	−0.720140	+	0.262109i
$623$	1.49842e9	+	5.45380e8i	0.248270	+	0.0903630i
$624$	−1.32195e9	−	1.10925e9i	−0.217806	−	0.182761i
$625$	−4.18528e8	+	2.37359e9i	−0.0685717	+	0.388889i
$626$	7.60820e8			0.123957
$627$	−6.99474e9	−	3.16433e9i	−1.13327	−	0.512678i
$628$	3.92051e9			0.631661
$629$	3.34281e8	−	1.89580e9i	0.0535593	−	0.303750i
$630$	−1.60911e9	−	1.35021e9i	−0.256386	−	0.215134i
$631$	−2.78091e9	−	1.01217e9i	−0.440640	−	0.160380i	0.112167	−	0.993689i	$-0.464221\pi$
$631$	−2.78091e9	−	1.01217e9i	−0.440640	−	0.160380i	−0.552807	+	0.833310i	$0.686443\pi$
$632$	−3.68569e9	+	1.34148e9i	−0.580776	+	0.211385i
$633$	−1.61655e9	+	1.35645e9i	−0.253324	+	0.212564i
$634$	1.00729e9	+	1.74468e9i	0.156980	+	0.271897i
$635$	4.25748e9	−	7.37418e9i	0.659850	−	1.14289i
$636$	6.41648e8	+	3.63897e9i	0.0989002	+	0.560891i
$637$	−2.07411e7	−	1.17629e8i	−0.00317940	−	0.0180312i
$638$	2.61140e9	−	4.52308e9i	0.398108	−	0.689543i
$639$	1.32596e9	+	2.29663e9i	0.201038	+	0.348207i
$640$	3.40579e8	−	2.85780e8i	0.0513556	−	0.0430925i
$641$	−6.05400e9	+	2.20347e9i	−0.907902	+	0.330449i	−0.753415	−	0.657545i	$-0.771595\pi$
$641$	−6.05400e9	+	2.20347e9i	−0.907902	+	0.330449i	−0.154487	+	0.987995i	$0.549373\pi$
$642$	7.89727e9	+	2.87437e9i	1.17789	+	0.428716i
$643$	−5.18882e8	−	4.35394e8i	−0.0769716	−	0.0645868i	0.603490	−	0.797370i	$-0.293776\pi$
$643$	−5.18882e8	−	4.35394e8i	−0.0769716	−	0.0645868i	−0.680462	+	0.732784i	$0.738221\pi$
$644$	9.33202e8	−	5.29245e9i	0.137681	−	0.780830i
$645$	−9.41640e9			−1.38174
$646$	5.47944e8	+	1.14065e9i	0.0799691	+	0.166471i
$647$	2.56546e9			0.372392			0.186196	−	0.982513i	$-0.440384\pi$
$647$	2.56546e9			0.372392			0.186196	+	0.982513i	$0.440384\pi$
$648$	−5.25658e8	+	2.98115e9i	−0.0758911	+	0.430400i
$649$	3.59445e9	+	3.01610e9i	0.516150	+	0.433102i
$650$	−1.76682e9	−	6.43069e8i	−0.252345	−	0.0918461i
$651$	−6.97299e8	+	2.53796e8i	−0.0990571	+	0.0360538i
$652$	−3.21152e9	+	2.69479e9i	−0.453779	+	0.380766i
$653$	−1.64154e9	−	2.84322e9i	−0.230703	−	0.399590i	0.727312	−	0.686307i	$-0.240769\pi$
$653$	−1.64154e9	−	2.84322e9i	−0.230703	−	0.399590i	−0.958015	+	0.286717i	$0.907436\pi$
$654$	1.95182e9	−	3.38065e9i	0.272846	−	0.472583i
$655$	−1.58949e9	−	9.01445e9i	−0.221011	−	1.25341i
$656$	−6.10956e7	−	3.46490e8i	−0.00844980	−	0.0479212i
$657$	−6.46862e8	+	1.12040e9i	−0.0889883	+	0.154132i
$658$	4.72564e8	+	8.18505e8i	0.0646651	+	0.112003i
$659$	3.35029e9	−	2.81123e9i	0.456020	−	0.382646i	−0.385644	−	0.922648i	$-0.626021\pi$
$659$	3.35029e9	−	2.81123e9i	0.456020	−	0.382646i	0.841664	+	0.540001i	$0.181576\pi$
$660$	−3.27389e9	+	1.19160e9i	−0.443262	+	0.161334i
$661$	−8.31454e9	−	3.02624e9i	−1.11978	−	0.407567i	−0.285208	−	0.958466i	$-0.592063\pi$
$661$	−8.31454e9	−	3.02624e9i	−1.11978	−	0.407567i	−0.834572	+	0.550899i	$0.814285\pi$
$662$	−5.65727e9	−	4.74701e9i	−0.757886	−	0.635942i
$663$	3.87065e8	−	2.19515e9i	0.0515806	−	0.292528i
$664$	1.61840e9			0.214534
$665$	−5.72926e8	−	5.78222e9i	−0.0755480	−	0.762463i
$666$	−3.93264e9			−0.515851
$667$	2.40536e9	−	1.36415e10i	0.313863	−	1.78000i
$668$	2.88455e9	+	2.42042e9i	0.374421	+	0.314176i
$669$	−1.58601e10	−	5.77260e9i	−2.04793	−	0.745384i
$670$	−2.43527e9	+	8.86365e8i	−0.312813	+	0.113855i
$671$	7.22404e8	−	6.06169e8i	0.0923105	−	0.0774577i
$672$	8.93398e8	+	1.54741e9i	0.113567	+	0.196704i
$673$	1.22001e9	−	2.11313e9i	0.154281	−	0.267222i	−0.778516	−	0.627625i	$-0.784027\pi$
$673$	1.22001e9	−	2.11313e9i	0.154281	−	0.267222i	0.932797	+	0.360402i	$0.117361\pi$
$674$	2.24782e7	+	1.27480e8i	0.00282783	+	0.0160374i
$675$	2.86509e8	+	1.62487e9i	0.0358571	+	0.203355i
$676$	4.02523e8	−	6.97190e8i	0.0501161	−	0.0868036i
$677$	1.07867e9	+	1.86832e9i	0.133607	+	0.231414i	0.925064	−	0.379810i	$-0.124011\pi$
$677$	1.07867e9	+	1.86832e9i	0.133607	+	0.231414i	−0.791457	+	0.611224i	$0.790677\pi$
$678$	6.93161e9	−	5.81631e9i	0.854142	−	0.716710i
$679$	−1.10075e10	+	4.00641e9i	−1.34941	+	0.491147i
$680$	5.39637e8	+	1.96412e8i	0.0658143	+	0.0239545i
$681$	2.87318e9	+	2.41088e9i	0.348616	+	0.292524i
$682$	−8.16117e7	+	4.62843e8i	−0.00985161	+	0.0558712i
$683$	−1.29600e10			−1.55644			−0.778222	−	0.627989i	$-0.783878\pi$
$683$	−1.29600e10			−1.55644			−0.778222	+	0.627989i	$0.783878\pi$
$684$	2.10043e9	−	1.50701e9i	0.250964	−	0.180061i
$685$	7.77007e9			0.923651
$686$	1.02732e9	−	5.82622e9i	0.121499	−	0.689053i
$687$	−2.82643e9	−	2.37166e9i	−0.332575	−	0.279064i
$688$	2.87420e9	+	1.04612e9i	0.336478	+	0.122468i
$689$	6.46060e9	−	2.35147e9i	0.752498	−	0.273887i
$690$	−7.07847e9	+	5.93954e9i	−0.820290	+	0.688305i
$691$	6.41714e9	+	1.11148e10i	0.739892	+	1.28153i	0.952544	+	0.304402i	$0.0984566\pi$
$691$	6.41714e9	+	1.11148e10i	0.739892	+	1.28153i	−0.212652	+	0.977128i	$0.568210\pi$
$692$	−9.55667e8	+	1.65526e9i	−0.109632	+	0.189887i
$693$	−9.28461e8	−	5.26556e9i	−0.105973	−	0.601005i
$694$	−1.64859e9	−	9.34964e9i	−0.187221	−	1.06179i
$695$	−4.40505e9	+	7.62977e9i	−0.497741	+	0.862114i
$696$	2.30276e9	+	3.98850e9i	0.258891	+	0.448413i
$697$	3.48133e8	−	2.92119e8i	0.0389431	−	0.0326772i
$698$	−7.62676e9	+	2.77591e9i	−0.848880	+	0.308967i
$699$	1.34098e10	+	4.88078e9i	1.48509	+	0.540530i
$700$	1.49133e9	+	1.25137e9i	0.164335	+	0.137894i
$701$	−7.84713e8	+	4.45033e9i	−0.0860395	+	0.487954i	0.911088	+	0.412212i	$0.135244\pi$
$701$	−7.84713e8	+	4.45033e9i	−0.0860395	+	0.487954i	−0.997127	+	0.0757423i	$0.975867\pi$
$702$	2.81762e9			0.307400
$703$	−7.78015e9	−	7.60330e9i	−0.844586	−	0.825389i
$704$	1.13168e9			0.122242
$705$	2.82189e8	−	1.60037e9i	0.0303304	−	0.172012i
$706$	1.35063e9	+	1.13331e9i	0.144450	+	0.121208i
$707$	1.58018e10	+	5.75139e9i	1.68166	+	0.612075i
$708$	−3.88813e9	+	1.41516e9i	−0.411741	+	0.149862i
$709$	4.86313e9	−	4.08065e9i	0.512453	−	0.429999i	−0.349538	−	0.936922i	$-0.613662\pi$
$709$	4.86313e9	−	4.08065e9i	0.512453	−	0.429999i	0.861991	+	0.506923i	$0.169217\pi$
$710$	1.66452e9	+	2.88304e9i	0.174536	+	0.302306i
$711$	−5.17484e9	+	8.96309e9i	−0.539950	+	0.935221i
$712$	1.54647e8	+	8.77050e8i	0.0160569	+	0.0910635i
$713$	2.16451e8	+	1.22755e9i	0.0223638	+	0.126831i
$714$	−1.15398e9	+	1.99875e9i	−0.118646	+	0.205501i
$715$	3.24122e9	+	5.61396e9i	0.331618	+	0.574379i
$716$	−5.35810e9	+	4.49598e9i	−0.545525	+	0.457750i
$717$	1.82214e10	−	6.63203e9i	1.84614	−	0.671939i
$718$	3.55916e9	+	1.29543e9i	0.358849	+	0.130610i
$719$	−4.15391e8	−	3.48554e8i	−0.0416779	−	0.0349719i	0.621711	−	0.783247i	$-0.286438\pi$
$719$	−4.15391e8	−	3.48554e8i	−0.0416779	−	0.0349719i	−0.663389	+	0.748275i	$0.730882\pi$
$720$	2.03717e8	−	1.15534e9i	0.0203406	−	0.115357i
$721$	−4.09125e9			−0.406521
$722$	7.06902e9	+	1.07953e9i	0.699003	+	0.106747i
$723$	6.86256e9			0.675308
$724$	−1.07368e9	+	6.08915e9i	−0.105145	+	0.596310i
$725$	3.84395e9	+	3.22546e9i	0.374623	+	0.314346i
$726$	3.80296e8	+	1.38416e8i	0.0368844	+	0.0134248i
$727$	7.83402e9	−	2.85135e9i	0.756161	−	0.275220i	0.0649652	−	0.997888i	$-0.479306\pi$
$727$	7.83402e9	−	2.85135e9i	0.756161	−	0.275220i	0.691196	+	0.722667i	$0.257084\pi$
$728$	2.54677e9	−	2.13699e9i	0.244641	−	0.205278i
$729$	7.59664e8	+	1.31578e9i	0.0726232	+	0.125787i
$730$	−8.12028e8	+	1.40647e9i	−0.0772576	+	0.133814i
$731$	6.86045e8	+	3.89076e9i	0.0649594	+	0.368403i
$732$	1.44402e8	+	8.18943e8i	0.0136077	+	0.0771729i
$733$	8.71892e8	−	1.51016e9i	0.0817709	−	0.141631i	−0.822240	−	0.569141i	$-0.807276\pi$
$733$	8.71892e8	−	1.51016e9i	0.0817709	−	0.141631i	0.904011	+	0.427510i	$0.140609\pi$
$734$	−4.05784e9	−	7.02839e9i	−0.378756	−	0.656024i
$735$	1.62896e8	−	1.36686e8i	0.0151323	−	0.0126975i
$736$	2.82044e9	−	1.02656e9i	0.260762	−	0.0949096i
$737$	−6.19880e9	−	2.25618e9i	−0.570389	−	0.207605i
$738$	−7.11194e8	−	5.96762e8i	−0.0651314	−	0.0546518i
$739$	−3.50930e8	+	1.99022e9i	−0.0319864	+	0.181404i	−0.996615	−	0.0822082i	$-0.973803\pi$
$739$	−3.50930e8	+	1.99022e9i	−0.0319864	+	0.181404i	0.964629	+	0.263612i	$0.0849139\pi$
$740$	−4.93678e9			−0.447850
$741$	−9.00864e9	−	8.80387e9i	−0.813384	−	0.794895i
$742$	−7.11870e9			−0.639716
$743$	2.88981e8	−	1.63889e9i	0.0258469	−	0.146585i	−0.969153	−	0.246459i	$-0.920733\pi$
$743$	2.88981e8	−	1.63889e9i	0.0258469	−	0.146585i	0.995000	+	0.0998742i	$0.0318440\pi$
$744$	−3.17477e8	−	2.66395e8i	−0.0282623	−	0.0237149i
$745$	−8.57846e9	−	3.12231e9i	−0.760086	−	0.276649i
$746$	−7.50921e9	+	2.73313e9i	−0.662230	+	0.241032i
$747$	3.27140e9	−	2.74503e9i	0.287152	−	0.240949i
$748$	7.30880e8	+	1.26592e9i	0.0638544	+	0.110599i
$749$	−8.09534e9	+	1.40215e10i	−0.703961	+	1.21930i
$750$	−1.94982e9	−	1.10580e10i	−0.168764	−	0.957110i
$751$	2.45520e9	+	1.39241e10i	0.211518	+	1.19958i	0.886848	+	0.462062i	$0.152890\pi$
$751$	2.45520e9	+	1.39241e10i	0.211518	+	1.19958i	−0.675330	+	0.737516i	$0.735999\pi$
$752$	−2.63928e8	+	4.57137e8i	−0.0226320	+	0.0391998i
$753$	9.13565e9	+	1.58234e10i	0.779753	+	1.35057i
$754$	6.56438e9	−	5.50817e9i	0.557691	−	0.467958i
$755$	1.39422e10	−	5.07455e9i	1.17901	−	0.429124i
$756$	−2.74147e9	−	9.97812e8i	−0.230758	−	0.0839890i
$757$	−1.52794e10	−	1.28210e10i	−1.28018	−	1.07420i	−0.993219	−	0.116258i	$-0.962910\pi$
$757$	−1.52794e10	−	1.28210e10i	−1.28018	−	1.07420i	−0.286962	−	0.957942i	$-0.592645\pi$
$758$	1.61746e9	−	9.17305e9i	0.134893	−	0.765018i
$759$	−2.35205e10			−1.95254
$760$	2.63674e9	−	1.89180e9i	0.217881	−	0.156325i
$761$	1.93560e10			1.59210			0.796049	−	0.605233i	$-0.206920\pi$
$761$	1.93560e10			1.59210			0.796049	+	0.605233i	$0.206920\pi$
$762$	−3.31887e9	+	1.88222e10i	−0.271736	+	1.54109i
$763$	5.76100e9	+	4.83405e9i	0.469529	+	0.393981i
$764$	−4.56986e9	−	1.66329e9i	−0.370745	−	0.134940i
$765$	1.42395e9	−	5.18277e8i	0.114995	−	0.0418549i
$766$	1.35920e9	−	1.14050e9i	0.109265	−	0.0916843i
$767$	3.84933e9	+	6.66723e9i	0.308036	+	0.533534i
$768$	−4.98965e8	+	8.64234e8i	−0.0397472	+	0.0688441i
$769$	3.04584e9	+	1.72738e10i	0.241526	+	1.36976i	0.828423	+	0.560103i	$0.189238\pi$
$769$	3.04584e9	+	1.72738e10i	0.241526	+	1.36976i	−0.586897	+	0.809662i	$0.699651\pi$
$770$	−1.16553e9	−	6.61004e9i	−0.0920037	−	0.521779i
$771$	1.79540e9	−	3.10972e9i	0.141081	−	0.244360i
$772$	−1.29274e9	−	2.23910e9i	−0.101123	−	0.175151i
$773$	−1.68265e10	+	1.41191e10i	−1.31029	+	1.09946i	−0.322019	+	0.946733i	$0.604361\pi$
$773$	−1.68265e10	+	1.41191e10i	−1.31029	+	1.09946i	−0.988268	+	0.152728i	$0.951194\pi$
$774$	7.58422e9	−	2.76043e9i	0.587919	−	0.213985i
$775$	−4.24315e8	−	1.54438e8i	−0.0327441	−	0.0119179i
$776$	−5.01168e9	−	4.20530e9i	−0.385006	−	0.323058i
$777$	3.44529e9	−	1.95392e10i	0.263482	−	1.49428i
$778$	−9.25164e9			−0.704352
$779$	−2.53221e8	−	2.55562e9i	−0.0191919	−	0.193693i
$780$	−5.71630e9			−0.431304
$781$	−1.47147e9	+	8.34511e9i	−0.110528	+	0.626835i
$782$	2.96987e9	+	2.49201e9i	0.222082	+	0.186349i
$783$	−7.06622e9	−	2.57189e9i	−0.526043	−	0.191464i
$784$	−6.49064e7	+	2.36240e7i	−0.00481040	+	0.00175084i
$785$	9.94834e9	−	8.34765e9i	0.734018	−	0.615915i
$786$	1.02729e10	+	1.77933e10i	0.754598	+	1.30700i
$787$	−2.13715e9	+	3.70166e9i	−0.156288	+	0.270698i	−0.933527	−	0.358507i	$-0.883286\pi$
$787$	−2.13715e9	+	3.70166e9i	−0.156288	+	0.270698i	0.777240	+	0.629205i	$0.216619\pi$
$788$	5.20269e6	+	2.95059e7i	0.000378779	+	0.00214816i
$789$	−1.50736e9	−	8.54866e9i	−0.109257	−	0.619625i
$790$	−6.49616e9	+	1.12517e10i	−0.468772	+	0.811937i
$791$	8.71614e9	+	1.50968e10i	0.626190	+	1.08459i
$792$	2.28756e9	−	1.91949e9i	0.163619	−	0.137293i
$793$	1.45395e9	−	5.29193e8i	0.103536	−	0.0376841i
$794$	8.32887e9	+	3.03146e9i	0.590492	+	0.214922i
$795$	9.37637e9	+	7.86771e9i	0.661835	+	0.555345i
$796$	2.04735e9	−	1.16111e10i	0.143879	−	0.815977i
$797$	1.39777e10			0.977986			0.488993	−	0.872288i	$-0.337364\pi$
$797$	1.39777e10			0.977986			0.488993	+	0.872288i	$0.337364\pi$
$798$	5.64741e9	+	1.17562e10i	0.393404	+	0.818946i
$799$	−6.81817e8			−0.0472883
$800$	−1.88806e8	+	1.07077e9i	−0.0130377	+	0.0739404i
$801$	1.80020e9	+	1.51055e9i	0.123768	+	0.103853i
$802$	−1.01845e10	−	3.70686e9i	−0.697156	−	0.253744i
$803$	−3.88461e9	+	1.41388e9i	−0.264754	+	0.0963627i
$804$	4.45607e9	−	3.73908e9i	0.302382	−	0.253728i
$805$	−8.90081e9	−	1.54167e10i	−0.601373	−	1.04161i
$806$	−3.85557e8	+	6.67804e8i	−0.0259368	+	0.0449238i
$807$	−4.61902e9	−	2.61958e10i	−0.309380	−	1.75458i
$808$	1.63086e9	+	9.24907e9i	0.108762	+	0.616819i
$809$	−8.27415e9	+	1.43312e10i	−0.549419	+	0.951621i	0.448896	+	0.893584i	$0.351818\pi$
$809$	−8.27415e9	+	1.43312e10i	−0.549419	+	0.951621i	−0.998314	+	0.0580372i	$0.981516\pi$
$810$	5.01368e9	+	8.68395e9i	0.331482	+	0.574143i
$811$	1.77544e10	−	1.48977e10i	1.16878	−	0.980722i	0.168791	−	0.985652i	$-0.446014\pi$
$811$	1.77544e10	−	1.48977e10i	1.16878	−	0.980722i	0.999988	+	0.00493033i	$0.00156938\pi$
$812$	−8.33757e9	+	3.03463e9i	−0.546504	+	0.198911i
$813$	−2.92225e10	−	1.06361e10i	−1.90722	−	0.694170i
$814$	−9.62627e9	−	8.07740e9i	−0.625565	−	0.524912i
$815$	−2.41146e9	+	1.36761e10i	−0.156038	+	0.884933i
$816$	−1.28900e9			−0.0830495
$817$	2.03412e10	+	9.20210e9i	1.30497	+	0.590350i
$818$	−1.33554e10			−0.853139
$819$	1.52335e9	−	8.63935e9i	0.0968961	−	0.549525i
$820$	−8.92786e8	−	7.49136e8i	−0.0565456	−	0.0474474i
$821$	−2.08767e10	−	7.59850e9i	−1.31662	−	0.479211i	−0.414248	−	0.910164i	$-0.635955\pi$
$821$	−2.08767e10	−	7.59850e9i	−1.31662	−	0.479211i	−0.902374	+	0.430953i	$0.858178\pi$
$822$	−1.63888e10	+	5.96504e9i	−1.02919	+	0.374595i
$823$	1.60799e10	−	1.34926e10i	1.00550	−	0.843717i	0.0177656	−	0.999842i	$-0.494345\pi$
$823$	1.60799e10	−	1.34926e10i	1.00550	−	0.843717i	0.987737	+	0.156125i	$0.0499003\pi$
$824$	−1.14249e9	−	1.97885e9i	−0.0711388	−	0.123216i
$825$	4.26020e9	−	7.37888e9i	0.264144	−	0.457511i
$826$	−1.38420e9	−	7.85019e9i	−0.0854612	−	0.484675i
$827$	2.82600e9	+	1.60270e10i	0.173741	+	0.985335i	0.939587	+	0.342311i	$0.111210\pi$
$827$	2.82600e9	+	1.60270e10i	0.173741	+	0.985335i	−0.765846	+	0.643025i	$0.777679\pi$
$828$	3.96000e9	−	6.85892e9i	0.242431	−	0.419904i
$829$	−2.08436e9	−	3.61021e9i	−0.127066	−	0.220086i	0.795472	−	0.605990i	$-0.207223\pi$
$829$	−2.08436e9	−	3.61021e9i	−0.127066	−	0.220086i	−0.922539	+	0.385904i	$0.873889\pi$
$830$	4.10670e9	−	3.44593e9i	0.249298	−	0.209186i
$831$	2.44748e10	−	8.90810e9i	1.47950	−	0.538495i
$832$	1.74480e9	+	6.35056e8i	0.105030	+	0.0382279i
$833$	−6.83451e7	−	5.73484e7i	−0.00409685	−	0.00343767i
$834$	3.43390e9	−	1.94746e10i	0.204978	−	1.16249i
$835$	1.24732e10			0.741438
$836$	8.23672e9	+	6.25302e8i	0.487565	+	0.0370142i
$837$	6.76675e8			0.0398879
$838$	−3.14900e9	+	1.78589e10i	−0.184850	+	1.04833i
$839$	9.38466e9	+	7.87466e9i	0.548595	+	0.460325i	0.874465	−	0.485089i	$-0.161213\pi$
$839$	9.38466e9	+	7.87466e9i	0.548595	+	0.460325i	−0.325870	+	0.945415i	$0.605657\pi$
$840$	5.56179e9	+	2.02433e9i	0.323771	+	0.117843i
$841$	−5.28077e9	+	1.92204e9i	−0.306134	+	0.111424i
$842$	6.86691e9	−	5.76202e9i	0.396432	−	0.332646i
$843$	−2.01921e10	−	3.49737e10i	−1.16087	−	2.01069i
$844$	1.13529e9	−	1.96637e9i	0.0649990	−	0.112582i
$845$	−4.63068e8	−	2.62619e9i	−0.0264026	−	0.149736i
$846$	2.41869e8	+	1.37171e9i	0.0137336	+	0.0778870i
$847$	−3.89834e8	+	6.75212e8i	−0.0220439	+	0.0381811i
$848$	−1.98791e9	−	3.44316e9i	−0.111947	−	0.193897i
$849$	−1.54038e10	+	1.29253e10i	−0.863873	+	0.724875i
$850$	−1.31972e9	+	4.80340e8i	−0.0737083	+	0.0268276i
$851$	−3.13182e10	−	1.13989e10i	−1.74198	−	0.634029i
$852$	−5.72415e9	−	4.80313e9i	−0.317082	−	0.266064i
$853$	3.81027e9	−	2.16091e10i	0.210200	−	1.19211i	−0.678843	−	0.734283i	$-0.737518\pi$
$853$	3.81027e9	−	2.16091e10i	0.210200	−	1.19211i	0.889044	−	0.457823i	$-0.151371\pi$
$854$	−1.60205e9			−0.0880185
$855$	2.12109e9	−	8.29634e9i	0.116059	−	0.453947i
$856$	−9.04254e9			−0.492756
$857$	1.09996e9	−	6.23817e9i	0.0596957	−	0.338551i	−0.940303	−	0.340339i	$-0.889458\pi$
$857$	1.09996e9	−	6.23817e9i	0.0596957	−	0.338551i	0.999998	+	0.00178819i	$0.000569199\pi$
$858$	−1.11463e10	−	9.35283e9i	−0.602454	−	0.505519i
$859$	−9.54245e9	−	3.47317e9i	−0.513670	−	0.186960i	0.0721625	−	0.997393i	$-0.477010\pi$
$859$	−9.54245e9	−	3.47317e9i	−0.513670	−	0.186960i	−0.585832	+	0.810432i	$0.699232\pi$
$860$	9.52073e9	−	3.46526e9i	0.510418	−	0.185777i
$861$	3.58805e9	−	3.01073e9i	0.191579	−	0.160754i
$862$	2.98710e9	+	5.17381e9i	0.158845	+	0.275128i
$863$	9.80299e9	−	1.69793e10i	0.519183	−	0.899252i	−0.480568	−	0.876957i	$-0.659569\pi$
$863$	9.80299e9	−	1.69793e10i	0.519183	−	0.899252i	0.999751	−	0.0222946i	$-0.00709717\pi$
$864$	−2.82939e8	−	1.60463e9i	−0.0149243	−	0.0846400i
$865$	1.09941e9	+	6.23508e9i	0.0577570	+	0.327556i
$866$	5.01681e9	−	8.68937e9i	0.262491	−	0.454648i
$867$	1.13713e10	+	1.96956e10i	0.592573	+	1.02637i
$868$	6.11627e8	−	5.13216e8i	0.0317444	−	0.0266367i
$869$	−3.10766e10	+	1.13109e10i	−1.60644	+	0.584695i
$870$	1.43357e10	+	5.21777e9i	0.738077	+	0.268638i
$871$	−8.29109e9	−	6.95705e9i	−0.425156	−	0.356748i
$872$	−7.29356e8	+	4.13638e9i	−0.0372505	+	0.211258i
$873$	−1.72633e10			−0.878160
$874$	2.10952e10	−	5.91317e9i	1.06879	−	0.299592i
$875$	2.16321e10			1.09162
$876$	6.33006e8	−	3.58996e9i	0.0318159	−	0.180437i
$877$	1.44457e10	+	1.21214e10i	0.723169	+	0.606811i	0.928260	−	0.371932i	$-0.121305\pi$
$877$	1.44457e10	+	1.21214e10i	0.723169	+	0.606811i	−0.205091	+	0.978743i	$0.565749\pi$
$878$	1.50064e9	+	5.46189e8i	0.0748250	+	0.0272341i
$879$	−1.68502e10	+	6.13296e9i	−0.836842	+	0.304586i
$880$	2.87165e9	−	2.40960e9i	0.142050	−	0.119195i
$881$	1.03182e10	+	1.78716e10i	0.508379	+	0.880538i	0.999953	+	0.00970191i	$0.00308826\pi$
$881$	1.03182e10	+	1.78716e10i	0.508379	+	0.880538i	−0.491574	+	0.870836i	$0.663578\pi$
$882$	−9.11310e7	+	1.57843e8i	−0.00447225	+	0.00774616i
$883$	−1.73659e8	−	9.84869e8i	−0.00848858	−	0.0481411i	0.980269	−	0.197667i	$-0.0633364\pi$
$883$	−1.73659e8	−	9.84869e8i	−0.00848858	−	0.0481411i	−0.988758	+	0.149526i	$0.952225\pi$
$884$	4.16469e8	+	2.36191e9i	0.0202768	+	0.114996i
$885$	−6.85297e9	+	1.18697e10i	−0.332336	+	0.575623i
$886$	4.47521e9	+	7.75129e9i	0.216170	+	0.374417i
$887$	1.31828e10	−	1.10617e10i	0.634272	−	0.532217i	−0.267981	−	0.963424i	$-0.586357\pi$
$887$	1.31828e10	−	1.10617e10i	0.634272	−	0.532217i	0.902253	+	0.431207i	$0.141912\pi$
$888$	1.04128e10	−	3.78994e9i	0.499023	−	0.181630i
$889$	−3.46003e10	−	1.25935e10i	−1.65167	−	0.601159i
$890$	2.25985e9	+	1.89624e9i	0.107452	+	0.0901631i
$891$	−4.43218e9	+	2.51362e10i	−0.209916	+	1.19049i
$892$	1.81601e10			0.856726
$893$	−2.17354e9	+	3.18135e9i	−0.102138	+	0.149496i
$894$	2.04909e10			0.959134
$895$	−4.02328e9	+	2.28172e10i	−0.187586	+	1.06385i
$896$	−1.47275e9	−	1.23578e9i	−0.0683991	−	0.0573937i
$897$	−3.62634e10	−	1.31988e10i	−1.67762	−	0.610605i
$898$	2.23657e10	−	8.14046e9i	1.03066	−	0.375130i
$899$	1.57649e9	−	1.32283e9i	0.0723655	−	0.0607219i
$900$	1.43453e9	+	2.48468e9i	0.0655935	+	0.113611i
$901$	2.56772e9	−	4.44743e9i	0.116953	−	0.202569i
$902$	−5.15139e8	−	2.92150e9i	−0.0233723	−	0.132551i
$903$	7.07076e9	+	4.01003e10i	0.319565	+	1.81234i
$904$	−4.86799e9	+	8.43160e9i	−0.219159	+	0.379595i
$905$	1.02407e10	+	1.77374e10i	0.459260	+	0.795463i
$906$	−2.55115e10	+	2.14067e10i	−1.13969	+	0.956316i
$907$	3.77503e10	−	1.37400e10i	1.67995	−	0.611451i	0.686644	−	0.726994i	$-0.259083\pi$
$907$	3.77503e10	−	1.37400e10i	1.67995	−	0.611451i	0.993302	+	0.115543i	$0.0368609\pi$
$908$	−3.79222e9	−	1.38026e9i	−0.168110	−	0.0611870i
$909$	1.89843e10	+	1.59297e10i	0.838342	+	0.703452i
$910$	1.91231e9	−	1.08453e10i	0.0841229	−	0.477085i
$911$	−2.23856e10			−0.980969			−0.490485	−	0.871450i	$-0.663180\pi$
$911$	−2.23856e10			−0.980969			−0.490485	+	0.871450i	$0.663180\pi$
$912$	−4.10914e9	+	6.01445e9i	−0.179378	+	0.262551i
$913$	1.36458e10			0.593406
$914$	3.72267e8	−	2.11123e9i	0.0161266	−	0.0914585i
$915$	2.11013e9	+	1.77061e9i	0.0910618	+	0.0764099i
$916$	3.73052e9	+	1.35780e9i	0.160375	+	0.0583716i
$917$	−3.71950e10	+	1.35379e10i	−1.59291	+	0.579773i
$918$	1.61224e9	−	1.35283e9i	0.0687827	−	0.0577155i
$919$	6.71298e9	+	1.16272e10i	0.285306	+	0.494165i	0.972683	−	0.232136i	$-0.0745714\pi$
$919$	6.71298e9	+	1.16272e10i	0.285306	+	0.494165i	−0.687377	+	0.726301i	$0.741238\pi$
$920$	4.97113e9	−	8.61024e9i	0.210473	−	0.364551i
$921$	4.68568e9	+	2.65738e10i	0.197635	+	1.12084i
$922$	3.49422e8	+	1.98167e9i	0.0146822	+	0.0832671i
$923$	−6.95163e9	+	1.20406e10i	−0.290992	+	0.504013i
$924$	7.53286e9	+	1.30473e10i	0.314129	+	0.544087i
$925$	9.24866e9	−	7.76055e9i	0.384222	−	0.322401i
$926$	1.21683e9	−	4.42890e8i	0.0503607	−	0.0183298i
$927$	−5.66581e9	−	2.06218e9i	−0.233605	−	0.0850254i
$928$	−3.79606e9	−	3.18527e9i	−0.155925	−	0.130836i
$929$	−2.66424e9	+	1.51096e10i	−0.109023	+	0.618300i	0.880514	+	0.474020i	$0.157198\pi$
$929$	−2.66424e9	+	1.51096e10i	−0.109023	+	0.618300i	−0.989537	+	0.144280i	$0.953913\pi$
$930$	−1.37282e9			−0.0559657
$931$	−4.85461e8	+	1.36079e8i	−0.0197165	+	0.00552671i
$932$	−1.53546e10			−0.621272
$933$	5.93825e9	−	3.36775e10i	0.239371	−	1.35754i
$934$	−3.90147e9	−	3.27373e9i	−0.156680	−	0.131470i
$935$	4.55005e9	+	1.65608e9i	0.182044	+	0.0662584i
$936$	4.60406e9	−	1.67574e9i	0.183517	−	0.0667946i
$937$	1.30059e10	−	1.09133e10i	0.516479	−	0.433378i	−0.346923	−	0.937894i	$-0.612774\pi$
$937$	1.30059e10	−	1.09133e10i	0.516479	−	0.433378i	0.863402	+	0.504516i	$0.168329\pi$
$938$	5.60327e9	+	9.70515e9i	0.221683	+	0.383966i
$939$	−2.82841e9	+	4.89895e9i	−0.111484	+	0.193096i
$940$	3.03627e8	+	1.72195e9i	0.0119232	+	0.0676197i
$941$	−6.43338e9	−	3.64855e10i	−0.251695	−	1.42744i	−0.804415	−	0.594068i	$-0.797521\pi$
$941$	−6.43338e9	−	3.64855e10i	−0.251695	−	1.42744i	0.552719	−	0.833368i	$-0.313590\pi$
$942$	−1.45748e10	+	2.52444e10i	−0.568101	+	0.983980i
$943$	−3.93397e9	−	6.81383e9i	−0.152771	−	0.264606i
$944$	3.41042e9	−	2.86168e9i	0.131949	−	0.110718i
$945$	−9.08106e9	+	3.30524e9i	−0.350046	+	0.127406i
$946$	2.42343e10	+	8.82057e9i	0.930705	+	0.338749i
$947$	−1.31891e10	−	1.10670e10i	−0.504652	−	0.423453i	0.354591	−	0.935022i	$-0.384620\pi$
$947$	−1.31891e10	−	1.10670e10i	−0.504652	−	0.423453i	−0.859242	+	0.511569i	$0.829065\pi$
$948$	5.06400e9	−	2.87194e10i	0.193048	−	1.09483i
$949$	−6.78263e9			−0.257612
$950$	−1.96583e9	+	7.68906e9i	−0.0743898	+	0.290965i
$951$	−1.49788e10			−0.564735
$952$	4.31218e8	−	2.44556e9i	0.0161982	−	0.0918647i
$953$	1.06036e10	+	8.89751e9i	0.396853	+	0.332999i	0.819276	−	0.573400i	$-0.194376\pi$
$953$	1.06036e10	+	8.89751e9i	0.396853	+	0.332999i	−0.422423	+	0.906399i	$0.638820\pi$
$954$	−9.85840e9	−	3.58816e9i	−0.367610	−	0.133799i
$955$	−1.51376e10	+	5.50963e9i	−0.562399	+	0.204696i
$956$	−1.59826e10	+	1.34110e10i	−0.591624	+	0.496432i
$957$	1.94162e10	+	3.36298e10i	0.716097	+	1.24032i
$958$	3.27916e9	−	5.67967e9i	0.120499	−	0.208710i
$959$	−5.83453e9	−	3.30893e10i	−0.213619	−	1.21150i
$960$	5.74017e8	+	3.25541e9i	0.0209399	+	0.118756i
$961$	1.36637e10	−	2.36662e10i	0.496634	−	0.860196i
$962$	−1.03089e10	−	1.78555e10i	−0.373334	−	0.646633i
$963$	−1.82784e10	+	1.53374e10i	−0.659548	+	0.553427i
$964$	−6.93859e9	+	2.52544e9i	−0.249460	+	0.0907962i
$965$	−8.04788e9	−	2.92919e9i	−0.288294	−	0.104931i
$966$	3.06091e10	+	2.56841e10i	1.09252	+	0.916735i
$967$	−1.21227e9	+	6.87514e9i	−0.0431129	+	0.244506i	−0.998747	−	0.0500522i	$-0.984061\pi$
$967$	−1.21227e9	+	6.87514e9i	−0.0431129	+	0.244506i	0.955634	+	0.294558i	$0.0951723\pi$
$968$	−4.35446e8			−0.0154302
$969$	−9.38172e9	−	7.12227e8i	−0.331245	−	0.0251469i
$970$	−2.16712e10			−0.762398
$971$	−1.56441e9	+	8.87222e9i	−0.0548383	+	0.311003i	−0.999873	−	0.0159681i	$-0.994917\pi$
$971$	−1.56441e9	+	8.87222e9i	−0.0548383	+	0.311003i	0.945034	+	0.326971i	$0.106028\pi$
$972$	−1.19100e10	−	9.99370e9i	−0.415988	−	0.349056i
$973$	3.57995e10	+	1.30300e10i	1.24590	+	0.453470i
$974$	−3.57568e10	+	1.30144e10i	−1.23994	+	0.451302i
$975$	1.07090e10	−	8.98595e9i	0.370028	−	0.310490i
$976$	−4.47375e8	−	7.74876e8i	−0.0154027	−	0.0266783i
$977$	3.71800e9	−	6.43976e9i	0.127549	−	0.220922i	−0.795177	−	0.606377i	$-0.792622\pi$
$977$	3.71800e9	−	6.43976e9i	0.127549	−	0.220922i	0.922727	+	0.385455i	$0.125956\pi$
$978$	−5.41275e9	−	3.06972e10i	−0.185026	−	1.04933i
$979$	1.30394e9	+	7.39501e9i	0.0444138	+	0.251883i
$980$	−1.14400e8	+	1.98146e8i	−0.00388270	+	0.00672504i
$981$	5.54158e9	+	9.59830e9i	0.187410	+	0.324603i
$982$	−2.97306e10	+	2.49470e10i	−1.00188	+	0.840674i
$983$	1.87840e10	−	6.83681e9i	0.630739	−	0.229570i	−0.00681364	−	0.999977i	$-0.502169\pi$
$983$	1.87840e10	−	6.83681e9i	0.630739	−	0.229570i	0.637553	+	0.770406i	$0.279947\pi$
$984$	2.45819e9	+	8.94709e8i	0.0822495	+	0.0299364i
$985$	7.60266e7	+	6.37939e7i	0.00253477	+	0.00212693i
$986$	1.11148e9	−	6.30351e9i	0.0369260	−	0.209418i
$987$	−7.02718e9			−0.232633
$988$	1.23483e10	+	5.58621e9i	0.407341	+	0.184276i
$989$	6.83993e10			2.24835
$990$	1.71768e9	−	9.74146e9i	0.0562626	−	0.319081i
$991$	3.98485e10	+	3.34369e10i	1.30063	+	1.09136i	0.990035	+	0.140819i	$0.0449735\pi$
$991$	3.98485e10	+	3.34369e10i	1.30063	+	1.09136i	0.310597	+	0.950542i	$0.399471\pi$
$992$	4.19028e8	+	1.52514e8i	0.0136286	+	0.00496042i
$993$	5.15976e10	−	1.87800e10i	1.67227	−	0.608657i
$994$	1.10277e10	−	9.25334e9i	0.356150	−	0.298845i
$995$	−1.95275e10	−	3.38226e10i	−0.628442	−	1.08849i
$996$	−6.01652e9	+	1.04209e10i	−0.192947	+	0.334194i
$997$	−1.00638e10	−	5.70746e10i	−0.321609	−	1.82394i	−0.532502	−	0.846429i	$-0.678748\pi$
$997$	−1.00638e10	−	5.70746e10i	−0.321609	−	1.82394i	0.210892	−	0.977509i	$-0.432363\pi$
$998$	−4.17347e9	−	2.36689e10i	−0.132905	−	0.753740i
$999$	−9.04633e9	+	1.56687e10i	−0.287073	+	0.497226i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.8.e.a.17.5	yes	30
19.9	even	9	inner	38.8.e.a.9.5	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.8.e.a.9.5	✓	30	19.9	even	9	inner
38.8.e.a.17.5	yes	30	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38919 - 7.87846i) q^{2} +(45.5653 + 38.2339i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(-199.214 + 72.5079i) q^{5} +(364.523 - 305.871i) q^{6} +(458.368 + 793.917i) q^{7} +(-256.000 + 443.405i) q^{8} +(234.604 + 1330.50i) q^{9} +O(q^{10})\)	\(q+(1.38919 - 7.87846i) q^{2} +(45.5653 + 38.2339i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(-199.214 + 72.5079i) q^{5} +(364.523 - 305.871i) q^{6} +(458.368 + 793.917i) q^{7} +(-256.000 + 443.405i) q^{8} +(234.604 + 1330.50i) q^{9} +(294.506 + 1670.23i) q^{10} +(-2158.51 + 3738.65i) q^{11} +(-1903.40 - 3296.79i) q^{12} +(-5425.94 + 4552.90i) q^{13} +(6891.61 - 2508.34i) q^{14} +(-11849.5 - 4312.87i) q^{15} +(3137.72 + 2632.86i) q^{16} +(-918.718 + 5210.31i) q^{17} +10808.2 q^{18} +(21382.5 + 20896.4i) q^{19} +13567.9 q^{20} +(-9468.81 + 53700.3i) q^{21} +(26456.3 + 22199.4i) q^{22} +(86073.0 + 31328.0i) q^{23} +(-28617.8 + 10416.0i) q^{24} +(-25418.4 + 21328.6i) q^{25} +(28332.2 + 49072.8i) q^{26} +(24862.4 - 43062.9i) q^{27} +(-10188.1 - 57779.8i) q^{28} +(-26260.3 - 148929. i) q^{29} +(-50439.9 + 87364.5i) q^{30} +(6804.21 + 11785.2i) q^{31} +(25101.7 - 21062.9i) q^{32} +(-241296. + 87824.7i) q^{33} +(39772.9 + 14476.2i) q^{34} +(-148879. - 124924. i) q^{35} +(15014.6 - 85152.2i) q^{36} -363856. q^{37} +(194336. - 139432. i) q^{38} -421309. q^{39} +(18848.4 - 106894. i) q^{40} +(-65801.2 - 55213.7i) q^{41} +(409922. + 149199. i) q^{42} +(701708. - 255401. i) q^{43} +(211650. - 177595. i) q^{44} +(-143208. - 248044. i) q^{45} +(366388. - 634602. i) q^{46} +(22378.2 + 126913. i) q^{47} +(42306.9 + 239934. i) q^{48} +(-8431.63 + 14604.0i) q^{49} +(132726. + 229888. i) q^{50} +(-241072. + 202283. i) q^{51} +(425977. - 155043. i) q^{52} +(-912120. - 331985. i) q^{53} +(-304731. - 255700. i) q^{54} +(158924. - 901301. i) q^{55} -469369. q^{56} +(175348. + 1.76969e6i) q^{57} -1.20981e6 q^{58} +(188740. - 1.07040e6i) q^{59} +(618228. + 518754. i) q^{60} +(-205271. - 74712.5i) q^{61} +(102302. - 37234.8i) q^{62} +(-948774. + 796116. i) q^{63} +(-131072. - 227023. i) q^{64} +(750800. - 1.30042e6i) q^{65} +(356718. + 2.02305e6i) q^{66} +(265343. + 1.50483e6i) q^{67} +(169302. - 293240. i) q^{68} +(2.72415e6 + 4.71837e6i) q^{69} +(-1.19103e6 + 999392. i) q^{70} +(1.84451e6 - 671348. i) q^{71} +(-650010. - 236584. i) q^{72} +(733553. + 615524. i) q^{73} +(-505464. + 2.86663e6i) q^{74} -1.97368e6 q^{75} +(-828541. - 1.72477e6i) q^{76} -3.95757e6 q^{77} +(-585277. + 3.31927e6i) q^{78} +(5.86836e6 + 4.92414e6i) q^{79} +(-815980. - 296992. i) q^{80} +(5.55583e6 - 2.02216e6i) q^{81} +(-526409. + 441710. i) q^{82} +(-1.58047e6 - 2.73745e6i) q^{83} +(1.74492e6 - 3.02229e6i) q^{84} +(-194767. - 1.10458e6i) q^{85} +(-1.03736e6 - 5.88318e6i) q^{86} +(4.49759e6 - 7.79005e6i) q^{87} +(-1.10516e6 - 1.91419e6i) q^{88} +(1.33247e6 - 1.11807e6i) q^{89} +(-2.15315e6 + 783682. i) q^{90} +(-6.10170e6 - 2.22084e6i) q^{91} +(-4.49071e6 - 3.76815e6i) q^{92} +(-140559. + 797150. i) q^{93} +1.03097e6 q^{94} +(-5.77484e6 - 2.61246e6i) q^{95} +1.94908e6 q^{96} +(-2.21886e6 + 1.25838e7i) q^{97} +(103344. + 86716.0i) q^{98} +(-5.48068e6 - 1.99480e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 45 q^{3} + 360 q^{6} + 1806 q^{7} - 7680 q^{8} - 3105 q^{9}+O(q^{10}) \) 30 * q + 45 * q^3 + 360 * q^6 + 1806 * q^7 - 7680 * q^8 - 3105 * q^9	\( 30 q + 45 q^{3} + 360 q^{6} + 1806 q^{7} - 7680 q^{8} - 3105 q^{9} + 9786 q^{11} - 11130 q^{13} + 6144 q^{14} - 1818 q^{15} - 65250 q^{17} + 29040 q^{18} + 105906 q^{19} - 47616 q^{20} + 172854 q^{21} + 102336 q^{22} + 101004 q^{23} + 23040 q^{24} - 132756 q^{25} - 92112 q^{26} + 43659 q^{27} + 96384 q^{28} - 273912 q^{29} + 58710 q^{31} - 406965 q^{33} + 84960 q^{34} + 356100 q^{35} - 198720 q^{36} - 2598852 q^{37} - 219336 q^{38} + 1769844 q^{39} + 43377 q^{41} - 79056 q^{42} + 1126698 q^{43} + 818688 q^{44} - 912546 q^{45} - 530880 q^{46} + 588306 q^{47} - 368640 q^{48} - 2778285 q^{49} + 1665288 q^{50} + 3972045 q^{51} - 430080 q^{52} + 6520866 q^{53} - 486648 q^{54} - 1666818 q^{55} - 1849344 q^{56} - 6947844 q^{57} - 4573152 q^{58} - 970467 q^{59} + 4634496 q^{60} - 4037670 q^{61} + 755952 q^{62} + 7946472 q^{63} - 3932160 q^{64} + 1497690 q^{65} + 6499272 q^{66} - 4817025 q^{67} + 1472064 q^{68} + 10299876 q^{69} + 2848800 q^{70} - 25171290 q^{71} + 3179520 q^{72} + 1347750 q^{73} - 3123936 q^{74} + 8817984 q^{75} + 1583232 q^{76} - 11476764 q^{77} - 930960 q^{78} + 10777986 q^{79} - 5365035 q^{81} + 347016 q^{82} + 9745314 q^{83} + 877056 q^{84} + 29258556 q^{85} - 9338208 q^{86} + 25598802 q^{87} + 5010432 q^{88} - 20353740 q^{89} - 30112128 q^{90} + 19748724 q^{91} - 14097792 q^{92} - 18738174 q^{93} + 12376608 q^{94} - 20427204 q^{95} - 23005029 q^{97} + 14869008 q^{98} - 45819771 q^{99}+O(q^{100}) \) 30 * q + 45 * q^3 + 360 * q^6 + 1806 * q^7 - 7680 * q^8 - 3105 * q^9 + 9786 * q^11 - 11130 * q^13 + 6144 * q^14 - 1818 * q^15 - 65250 * q^17 + 29040 * q^18 + 105906 * q^19 - 47616 * q^20 + 172854 * q^21 + 102336 * q^22 + 101004 * q^23 + 23040 * q^24 - 132756 * q^25 - 92112 * q^26 + 43659 * q^27 + 96384 * q^28 - 273912 * q^29 + 58710 * q^31 - 406965 * q^33 + 84960 * q^34 + 356100 * q^35 - 198720 * q^36 - 2598852 * q^37 - 219336 * q^38 + 1769844 * q^39 + 43377 * q^41 - 79056 * q^42 + 1126698 * q^43 + 818688 * q^44 - 912546 * q^45 - 530880 * q^46 + 588306 * q^47 - 368640 * q^48 - 2778285 * q^49 + 1665288 * q^50 + 3972045 * q^51 - 430080 * q^52 + 6520866 * q^53 - 486648 * q^54 - 1666818 * q^55 - 1849344 * q^56 - 6947844 * q^57 - 4573152 * q^58 - 970467 * q^59 + 4634496 * q^60 - 4037670 * q^61 + 755952 * q^62 + 7946472 * q^63 - 3932160 * q^64 + 1497690 * q^65 + 6499272 * q^66 - 4817025 * q^67 + 1472064 * q^68 + 10299876 * q^69 + 2848800 * q^70 - 25171290 * q^71 + 3179520 * q^72 + 1347750 * q^73 - 3123936 * q^74 + 8817984 * q^75 + 1583232 * q^76 - 11476764 * q^77 - 930960 * q^78 + 10777986 * q^79 - 5365035 * q^81 + 347016 * q^82 + 9745314 * q^83 + 877056 * q^84 + 29258556 * q^85 - 9338208 * q^86 + 25598802 * q^87 + 5010432 * q^88 - 20353740 * q^89 - 30112128 * q^90 + 19748724 * q^91 - 14097792 * q^92 - 18738174 * q^93 + 12376608 * q^94 - 20427204 * q^95 - 23005029 * q^97 + 14869008 * q^98 - 45819771 * q^99

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