LMFDB - Embedded newform 72.7.p.b.43.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,7,Mod(43,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("72.43");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	72.p (of order $6$, degree $2$, 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:	$16.5638940206$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.19
Character	$\chi$	$=$	72.43
Dual form			72.7.p.b.67.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.16108 - 6.11255i) q^{2} +(23.0486 + 14.0627i) q^{3} +(-10.7264 + 63.0947i) q^{4} +(-44.3287 + 25.5932i) q^{5} +(-32.9969 - 213.465i) q^{6} +(23.6171 + 13.6353i) q^{7} +(441.029 - 260.072i) q^{8} +(333.480 + 648.253i) q^{9} +O(q^{10})$	\(q+(-5.16108 - 6.11255i) q^{2} +(23.0486 + 14.0627i) q^{3} +(-10.7264 + 63.0947i) q^{4} +(-44.3287 + 25.5932i) q^{5} +(-32.9969 - 213.465i) q^{6} +(23.6171 + 13.6353i) q^{7} +(441.029 - 260.072i) q^{8} +(333.480 + 648.253i) q^{9} +(385.224 + 138.873i) q^{10} +(53.8075 - 93.1973i) q^{11} +(-1134.51 + 1303.40i) q^{12} +(-1326.14 + 765.646i) q^{13} +(-38.5431 - 214.733i) q^{14} +(-1381.63 - 33.4942i) q^{15} +(-3865.89 - 1353.56i) q^{16} -2175.58 q^{17} +(2241.36 - 5384.10i) q^{18} -6048.23 q^{19} +(-1139.31 - 3071.43i) q^{20} +(352.591 + 646.395i) q^{21} +(-847.378 + 152.099i) q^{22} +(-5659.12 + 3267.29i) q^{23} +(13822.4 + 207.779i) q^{24} +(-6502.48 + 11262.6i) q^{25} +(11524.3 + 4154.51i) q^{26} +(-1429.96 + 19631.0i) q^{27} +(-1113.64 + 1343.85i) q^{28} +(22871.4 + 13204.8i) q^{29} +(6925.96 + 8618.13i) q^{30} +(-31456.6 + 18161.5i) q^{31} +(11678.5 + 30616.3i) q^{32} +(2550.80 - 1391.39i) q^{33} +(11228.3 + 13298.3i) q^{34} -1395.89 q^{35} +(-44478.4 + 14087.4i) q^{36} +29560.9i q^{37} +(31215.4 + 36970.1i) q^{38} +(-41332.7 - 1002.01i) q^{39} +(-12894.2 + 22816.0i) q^{40} +(7645.99 + 13243.2i) q^{41} +(2131.37 - 5491.33i) q^{42} +(-5647.17 + 9781.18i) q^{43} +(5303.10 + 4394.64i) q^{44} +(-31373.6 - 20201.4i) q^{45} +(49178.7 + 17728.8i) q^{46} +(49746.5 + 28721.1i) q^{47} +(-70068.7 - 85562.6i) q^{48} +(-58452.7 - 101243. i) q^{49} +(102403. - 18380.6i) q^{50} +(-50144.1 - 30594.6i) q^{51} +(-34083.5 - 91884.9i) q^{52} +20567.2i q^{53} +(127375. - 92576.5i) q^{54} +5508.43i q^{55} +(13962.0 - 128.551i) q^{56} +(-139403. - 85054.6i) q^{57} +(-37326.2 - 207954. i) q^{58} +(-29782.4 - 51584.7i) q^{59} +(16933.2 - 86814.1i) q^{60} +(-52425.6 - 30267.9i) q^{61} +(273363. + 98547.0i) q^{62} +(-963.333 + 19856.9i) q^{63} +(126870. - 229398. i) q^{64} +(39190.7 - 67880.2i) q^{65} +(-21669.8 - 8410.78i) q^{66} +(-165375. - 286438. i) q^{67} +(23336.2 - 137268. i) q^{68} +(-176382. - 4275.96i) q^{69} +(7204.28 + 8532.41i) q^{70} +495717. i q^{71} +(315666. + 199170. i) q^{72} -548593. q^{73} +(180692. - 152566. i) q^{74} +(-308256. + 168145. i) q^{75} +(64875.8 - 381611. i) q^{76} +(2541.55 - 1467.36i) q^{77} +(207197. + 257820. i) q^{78} +(742702. + 428799. i) q^{79} +(206012. - 38938.9i) q^{80} +(-309024. + 432358. i) q^{81} +(41488.3 - 115086. i) q^{82} +(305093. - 528437. i) q^{83} +(-44566.2 + 15313.1i) q^{84} +(96440.6 - 55680.0i) q^{85} +(88933.4 - 15962.9i) q^{86} +(341459. + 625987. i) q^{87} +(-507.287 - 55096.6i) q^{88} +529286. q^{89} +(38439.6 + 296034. i) q^{90} -41759.3 q^{91} +(-145447. - 392107. i) q^{92} +(-980432. - 23768.2i) q^{93} +(-81186.5 - 452310. i) q^{94} +(268110. - 154794. i) q^{95} +(-161375. + 869894. i) q^{96} +(-194127. + 336237. i) q^{97} +(-317173. + 879818. i) q^{98} +(78359.2 + 3801.50i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 17 q^{2} + 42 q^{3} + 127 q^{4} - 561 q^{6} + 1774 q^{8} + 654 q^{9}+O(q^{10}) $ 136 * q - 17 * q^2 + 42 * q^3 + 127 * q^4 - 561 * q^6 + 1774 * q^8 + 654 * q^9	\( 136 q - 17 q^{2} + 42 q^{3} + 127 q^{4} - 561 q^{6} + 1774 q^{8} + 654 q^{9} - 132 q^{10} + 2336 q^{11} - 2796 q^{12} + 2346 q^{14} + 8191 q^{16} - 3460 q^{17} + 6306 q^{18} - 4972 q^{19} + 3588 q^{20} - 18577 q^{22} - 50553 q^{24} + 224998 q^{25} + 38352 q^{26} - 27792 q^{27} - 8196 q^{28} - 107130 q^{30} - 191717 q^{32} - 42852 q^{33} + 6125 q^{34} - 62508 q^{35} + 87339 q^{36} + 250223 q^{38} - 27126 q^{40} - 145084 q^{41} - 107478 q^{42} + 74912 q^{43} - 1118662 q^{44} + 22296 q^{46} + 690903 q^{48} + 1210102 q^{49} - 844727 q^{50} + 830778 q^{51} + 62952 q^{52} + 860925 q^{54} - 587718 q^{56} + 748686 q^{57} + 221136 q^{58} + 98960 q^{59} - 960810 q^{60} - 1062312 q^{62} - 784646 q^{64} - 62502 q^{65} + 802866 q^{66} + 596624 q^{67} + 681953 q^{68} + 86334 q^{70} - 2246001 q^{72} - 1186276 q^{73} - 782586 q^{74} + 3451098 q^{75} - 273235 q^{76} - 3340578 q^{78} + 2446320 q^{80} - 621690 q^{81} - 3119398 q^{82} - 179350 q^{83} - 227136 q^{84} + 917117 q^{86} - 1184629 q^{88} + 253712 q^{89} - 4940256 q^{90} - 470604 q^{91} + 1731894 q^{92} + 2055426 q^{94} + 8439666 q^{96} - 1822756 q^{97} + 6531850 q^{98} + 2509818 q^{99}+O(q^{100}) \) 136 * q - 17 * q^2 + 42 * q^3 + 127 * q^4 - 561 * q^6 + 1774 * q^8 + 654 * q^9 - 132 * q^10 + 2336 * q^11 - 2796 * q^12 + 2346 * q^14 + 8191 * q^16 - 3460 * q^17 + 6306 * q^18 - 4972 * q^19 + 3588 * q^20 - 18577 * q^22 - 50553 * q^24 + 224998 * q^25 + 38352 * q^26 - 27792 * q^27 - 8196 * q^28 - 107130 * q^30 - 191717 * q^32 - 42852 * q^33 + 6125 * q^34 - 62508 * q^35 + 87339 * q^36 + 250223 * q^38 - 27126 * q^40 - 145084 * q^41 - 107478 * q^42 + 74912 * q^43 - 1118662 * q^44 + 22296 * q^46 + 690903 * q^48 + 1210102 * q^49 - 844727 * q^50 + 830778 * q^51 + 62952 * q^52 + 860925 * q^54 - 587718 * q^56 + 748686 * q^57 + 221136 * q^58 + 98960 * q^59 - 960810 * q^60 - 1062312 * q^62 - 784646 * q^64 - 62502 * q^65 + 802866 * q^66 + 596624 * q^67 + 681953 * q^68 + 86334 * q^70 - 2246001 * q^72 - 1186276 * q^73 - 782586 * q^74 + 3451098 * q^75 - 273235 * q^76 - 3340578 * q^78 + 2446320 * q^80 - 621690 * q^81 - 3119398 * q^82 - 179350 * q^83 - 227136 * q^84 + 917117 * q^86 - 1184629 * q^88 + 253712 * q^89 - 4940256 * q^90 - 470604 * q^91 + 1731894 * q^92 + 2055426 * q^94 + 8439666 * q^96 - 1822756 * q^97 + 6531850 * q^98 + 2509818 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−5.16108	−	6.11255i	−0.645136	−	0.764068i
$2$	−5.16108	−	6.11255i	−0.645136	−	0.764068i
$3$	23.0486	+	14.0627i	0.853653	+	0.520842i
$3$	23.0486	+	14.0627i	0.853653	+	0.520842i
$4$	−10.7264	+	63.0947i	−0.167600	+	0.985855i
$5$	−44.3287	+	25.5932i	−0.354630	+	0.204746i	−0.666723	−	0.745306i	$-0.732303\pi$
$5$	−44.3287	+	25.5932i	−0.354630	+	0.204746i	0.312093	+	0.950052i	$0.398970\pi$
$6$	−32.9969	−	213.465i	−0.152764	−	0.988263i
$7$	23.6171	+	13.6353i	0.0688544	+	0.0397531i	0.534032	−	0.845464i	$-0.320676\pi$
$7$	23.6171	+	13.6353i	0.0688544	+	0.0397531i	−0.465178	+	0.885217i	$0.654010\pi$
$8$	441.029	−	260.072i	0.861385	−	0.507952i
$9$	333.480	+	648.253i	0.457448	+	0.889236i
$10$	385.224	+	138.873i	0.385224	+	0.138873i
$11$	53.8075	−	93.1973i	0.0404264	−	0.0700205i	−0.845104	−	0.534602i	$-0.820462\pi$
$11$	53.8075	−	93.1973i	0.0404264	−	0.0700205i	0.885531	+	0.464581i	$0.153795\pi$
$12$	−1134.51	+	1303.40i	−0.656547	+	0.754285i
$13$	−1326.14	+	765.646i	−0.603613	+	0.348496i	−0.770462	−	0.637487i	$-0.779974\pi$
$13$	−1326.14	+	765.646i	−0.603613	+	0.348496i	0.166849	+	0.985983i	$0.446641\pi$
$14$	−38.5431	−	214.733i	−0.0140463	−	0.0782556i
$15$	−1381.63	−	33.4942i	−0.409371	−	0.00992422i
$16$	−3865.89	−	1353.56i	−0.943820	−	0.330459i
$17$	−2175.58			−0.442821			−0.221410	−	0.975181i	$-0.571066\pi$
$17$	−2175.58			−0.442821			−0.221410	+	0.975181i	$0.571066\pi$
$18$	2241.36	−	5384.10i	0.384321	−	0.923199i
$19$	−6048.23			−0.881795			−0.440897	−	0.897558i	$-0.645340\pi$
$19$	−6048.23			−0.881795			−0.440897	+	0.897558i	$0.645340\pi$
$20$	−1139.31	−	3071.43i	−0.142413	−	0.383929i
$21$	352.591	+	646.395i	0.0380727	+	0.0697976i
$22$	−847.378	+	152.099i	−0.0795810	+	0.0142842i
$23$	−5659.12	+	3267.29i	−0.465120	+	0.268537i	−0.714195	−	0.699947i	$-0.753207\pi$
$23$	−5659.12	+	3267.29i	−0.465120	+	0.268537i	0.249075	+	0.968484i	$0.419874\pi$
$24$	13822.4	+	207.779i	0.999887	+	0.0150303i
$25$	−6502.48	+	11262.6i	−0.416158	+	0.720808i
$26$	11524.3	+	4154.51i	0.655687	+	0.236374i
$27$	−1429.96	+	19631.0i	−0.0726495	+	0.997358i
$28$	−1113.64	+	1343.85i	−0.0507308	+	0.0612178i
$29$	22871.4	+	13204.8i	0.937775	+	0.541425i	0.889262	−	0.457398i	$-0.151218\pi$
$29$	22871.4	+	13204.8i	0.937775	+	0.541425i	0.0485130	+	0.998823i	$0.484552\pi$
$30$	6925.96	+	8618.13i	0.256517	+	0.319190i
$31$	−31456.6	+	18161.5i	−1.05591	+	0.609630i	−0.924298	−	0.381672i	$-0.875348\pi$
$31$	−31456.6	+	18161.5i	−1.05591	+	0.609630i	−0.131612	+	0.991301i	$0.542015\pi$
$32$	11678.5	+	30616.3i	0.356399	+	0.934334i
$33$	2550.80	−	1391.39i	0.0709797	−	0.0387175i
$34$	11228.3	+	13298.3i	0.285679	+	0.338345i
$35$	−1395.89			−0.0325571
$36$	−44478.4	+	14087.4i	−0.953327	+	0.301941i
$37$			29560.9i			0.583596i	0.956480	+	0.291798i	$0.0942534\pi$
$37$			29560.9i			0.583596i	−0.956480	+	0.291798i	$0.905747\pi$
$38$	31215.4	+	36970.1i	0.568877	+	0.673751i
$39$	−41332.7	−	1002.01i	−0.696787	−	0.0168919i
$40$	−12894.2	+	22816.0i	−0.201472	+	0.356500i
$41$	7645.99	+	13243.2i	0.110938	+	0.192151i	0.916149	−	0.400838i	$-0.131281\pi$
$41$	7645.99	+	13243.2i	0.110938	+	0.192151i	−0.805210	+	0.592989i	$0.797948\pi$
$42$	2131.37	−	5491.33i	0.0287681	−	0.0741190i
$43$	−5647.17	+	9781.18i	−0.0710273	+	0.123023i	−0.899352	−	0.437226i	$-0.855961\pi$
$43$	−5647.17	+	9781.18i	−0.0710273	+	0.123023i	0.828324	+	0.560249i	$0.189294\pi$
$44$	5303.10	+	4394.64i	0.0622546	+	0.0515900i
$45$	−31373.6	−	20201.4i	−0.344292	−	0.221689i
$46$	49178.7	+	17728.8i	0.505246	+	0.182141i
$47$	49746.5	+	28721.1i	0.479147	+	0.276636i	0.720061	−	0.693911i	$-0.244114\pi$
$47$	49746.5	+	28721.1i	0.479147	+	0.276636i	−0.240914	+	0.970546i	$0.577447\pi$
$48$	−70068.7	−	85562.6i	−0.633579	−	0.773678i
$49$	−58452.7	−	101243.i	−0.496839	−	0.860551i
$50$	102403.	−	18380.6i	0.819225	−	0.147045i
$51$	−50144.1	−	30594.6i	−0.378015	−	0.230640i
$52$	−34083.5	−	91884.9i	−0.242401	−	0.653483i
$53$			20567.2i			0.138149i	0.997612	+	0.0690745i	$0.0220046\pi$
$53$			20567.2i			0.138149i	−0.997612	+	0.0690745i	$0.977995\pi$
$54$	127375.	−	92576.5i	0.808918	−	0.587922i
$55$			5508.43i			0.0331085i
$56$	13962.0	−	128.551i	0.0795028	−	0.000732002i
$57$	−139403.	−	85054.6i	−0.752747	−	0.459275i
$58$	−37326.2	−	207954.i	−0.191307	−	1.06582i
$59$	−29782.4	−	51584.7i	−0.145012	−	0.251168i	0.784365	−	0.620299i	$-0.212989\pi$
$59$	−29782.4	−	51584.7i	−0.145012	−	0.251168i	−0.929377	+	0.369131i	$0.879655\pi$
$60$	16933.2	−	86814.1i	0.0783945	−	0.401917i
$61$	−52425.6	−	30267.9i	−0.230969	−	0.133350i	0.380050	−	0.924966i	$-0.375907\pi$
$61$	−52425.6	−	30267.9i	−0.230969	−	0.133350i	−0.611019	+	0.791616i	$0.709240\pi$
$62$	273363.	+	98547.0i	1.14700	+	0.413493i
$63$	−963.333	+	19856.9i	−0.00385261	+	0.0794128i
$64$	126870.	−	229398.i	0.483969	−	0.875085i
$65$	39190.7	−	67880.2i	0.142706	−	0.247174i
$66$	−21669.8	−	8410.78i	−0.0753744	−	0.0292553i
$67$	−165375.	−	286438.i	−0.549852	−	0.952372i	−0.998284	−	0.0585547i	$-0.981351\pi$
$67$	−165375.	−	286438.i	−0.549852	−	0.952372i	0.448432	−	0.893817i	$-0.351983\pi$
$68$	23336.2	−	137268.i	0.0742168	−	0.436557i
$69$	−176382.	−	4275.96i	−0.536917	−	0.0130163i
$70$	7204.28	+	8532.41i	0.0210037	+	0.0248758i
$71$			495717.i			1.38503i	0.721405	+	0.692514i	$0.243497\pi$
$71$			495717.i			1.38503i	−0.721405	+	0.692514i	$0.756503\pi$
$72$	315666.	+	199170.i	0.845728	+	0.533614i
$73$	−548593.			−1.41020			−0.705102	−	0.709106i	$-0.749099\pi$
$73$	−548593.			−1.41020			−0.705102	+	0.709106i	$0.749099\pi$
$74$	180692.	−	152566.i	0.445907	−	0.376498i
$75$	−308256.	+	168145.i	−0.730682	+	0.398567i
$76$	64875.8	−	381611.i	0.147789	−	0.869322i
$77$	2541.55	−	1467.36i	0.00556707	−	0.00321415i
$78$	207197.	+	257820.i	0.436616	+	0.543291i
$79$	742702.	+	428799.i	1.50638	+	0.869707i	0.999973	+	0.00741024i	$0.00235877\pi$
$79$	742702.	+	428799.i	1.50638	+	0.869707i	0.506404	+	0.862297i	$0.330975\pi$
$80$	206012.	−	38938.9i	0.402367	−	0.0760525i
$81$	−309024.	+	432358.i	−0.581483	+	0.813559i
$82$	41488.3	−	115086.i	0.0752461	−	0.208728i
$83$	305093.	−	528437.i	0.533579	−	0.924186i	−0.465652	−	0.884968i	$-0.654180\pi$
$83$	305093.	−	528437.i	0.533579	−	0.924186i	0.999231	−	0.0392177i	$-0.0124866\pi$
$84$	−44566.2	+	15313.1i	−0.0751913	+	0.0258361i
$85$	96440.6	−	55680.0i	0.157037	−	0.0906656i
$86$	88933.4	−	15962.9i	0.139820	−	0.0250968i
$87$	341459.	+	625987.i	0.518538	+	0.950621i
$88$	−507.287	−	55096.6i	−0.000744400	−	0.0808493i
$89$	529286.			0.750794			0.375397	−	0.926864i	$-0.377506\pi$
$89$	529286.			0.750794			0.375397	+	0.926864i	$0.377506\pi$
$90$	38439.6	+	296034.i	0.0527292	+	0.406082i
$91$	−41759.3			−0.0554152
$92$	−145447.	−	392107.i	−0.186785	−	0.503548i
$93$	−980432.	−	23768.2i	−1.21890	−	0.0295493i
$94$	−81186.5	−	452310.i	−0.0977462	−	0.544568i
$95$	268110.	−	154794.i	0.312711	−	0.180544i
$96$	−161375.	+	869894.i	−0.182399	+	0.983225i
$97$	−194127.	+	336237.i	−0.212701	+	0.368409i	−0.952559	−	0.304354i	$-0.901559\pi$
$97$	−194127.	+	336237.i	−0.212701	+	0.368409i	0.739858	+	0.672763i	$0.234893\pi$
$98$	−317173.	+	879818.i	−0.336991	+	0.934791i
$99$	78359.2	+	3801.50i	0.0807578	+	0.00391786i
$100$	−640864.	−	531079.i	−0.640864	−	0.531079i
$101$	−1.59430e6	−	920471.i	−1.54741	−	0.893400i	−0.998338	−	0.0576274i	$-0.981646\pi$
$101$	−1.59430e6	−	920471.i	−1.54741	−	0.893400i	−0.549076	−	0.835773i	$-0.685020\pi$
$102$	71787.4	+	464409.i	0.0676469	+	0.437623i
$103$	1.11680e6	−	644785.i	1.02203	−	0.590069i	0.107339	−	0.994223i	$-0.465767\pi$
$103$	1.11680e6	−	644785.i	1.02203	−	0.590069i	0.914691	+	0.404153i	$0.132434\pi$
$104$	−385743.	+	682563.i	−0.342924	+	0.606796i
$105$	−32173.3	−	19630.0i	−0.0277925	−	0.0169571i
$106$	125718.	−	106149.i	0.105555	−	0.0891248i
$107$	1.92418e6			1.57071			0.785354	−	0.619047i	$-0.212481\pi$
$107$	1.92418e6			1.57071			0.785354	+	0.619047i	$0.212481\pi$
$108$	−1.22327e6	−	300793.i	−0.971074	−	0.238779i
$109$		−	1.87244e6i		−	1.44587i	−0.690918	−	0.722933i	$-0.742794\pi$
$109$		−	1.87244e6i		−	1.44587i	0.690918	−	0.722933i	$-0.257206\pi$
$110$	33670.5	−	28429.5i	0.0252972	−	0.0213595i
$111$	−415706.	+	681338.i	−0.303961	+	0.498188i
$112$	−72844.7	−	84679.7i	−0.0518494	−	0.0602733i
$113$	613903.	+	1.06331e6i	0.425465	+	0.736928i	0.996464	−	0.0840234i	$-0.0267771\pi$
$113$	613903.	+	1.06331e6i	0.425465	+	0.736928i	−0.570998	+	0.820951i	$0.693444\pi$
$114$	199573.	+	1.29108e6i	0.134706	+	0.871445i
$115$	167241.	−	289670.i	0.109964	−	0.190463i
$116$	−1.07848e6	+	1.30142e6i	−0.690938	+	0.833768i
$117$	−938572.	−	604346.i	−0.586017	−	0.377336i
$118$	−161604.	+	448279.i	−0.0983572	+	0.272837i
$119$	−51380.7	−	29664.7i	−0.0304901	−	0.0176035i
$120$	−618049.	+	344550.i	−0.357667	+	0.199392i
$121$	879990.	+	1.52419e6i	0.496731	+	0.860364i
$122$	85558.8	+	476669.i	0.0471178	+	0.262505i
$123$	−10006.4	+	412762.i	−0.00537729	+	0.221812i
$124$	−808477.	−	2.17955e6i	−0.424036	−	1.14315i
$125$		−	1.46546e6i		−	0.750318i
$126$	126348.	−	96594.9i	0.0631622	−	0.0482884i
$127$			900418.i			0.439575i	0.975548	+	0.219788i	$0.0705364\pi$
$127$			900418.i			0.439575i	−0.975548	+	0.219788i	$0.929464\pi$
$128$	−2.05699e6	+	408448.i	−0.980850	+	0.194763i
$129$	−267710.	+	146028.i	−0.124708	+	0.0680249i
$130$	−617187.	+	110781.i	−0.280923	+	0.0504237i
$131$	848172.	+	1.46908e6i	0.377285	+	0.653477i	0.990666	−	0.136310i	$-0.0435243\pi$
$131$	848172.	+	1.46908e6i	0.377285	+	0.653477i	−0.613381	+	0.789787i	$0.710191\pi$
$132$	60428.6	+	175867.i	0.0262737	+	0.0764648i
$133$	−142841.	−	82469.5i	−0.0607154	−	0.0350541i
$134$	−897351.	+	2.48919e6i	−0.372948	+	1.03453i
$135$	−439032.	−	906814.i	−0.178441	−	0.368567i
$136$	−959494.	+	565806.i	−0.381439	+	0.224932i
$137$	1.32744e6	−	2.29919e6i	0.516240	−	0.894154i	−0.483582	−	0.875299i	$-0.660665\pi$
$137$	1.32744e6	−	2.29919e6i	0.516240	−	0.894154i	0.999822	−	0.0188552i	$-0.00600215\pi$
$138$	884185.	+	1.10021e6i	0.336439	+	0.418638i
$139$	1.72768e6	+	2.99242e6i	0.643306	+	1.11424i	0.984690	+	0.174315i	$0.0557711\pi$
$139$	1.72768e6	+	2.99242e6i	0.643306	+	1.11424i	−0.341384	+	0.939924i	$0.610896\pi$
$140$	14972.8	−	88073.0i	0.00545658	−	0.0320966i
$141$	742691.	+	1.36155e6i	0.264942	+	0.485710i
$142$	3.03009e6	−	2.55844e6i	1.05826	−	0.893531i
$143$			164790.i			0.0563537i
$144$	−411745.	−	2.95746e6i	−0.137892	−	0.990447i
$145$	−1.35181e6			−0.443417
$146$	2.83134e6	+	3.35330e6i	0.909773	+	1.07749i
$147$	76497.9	−	3.15552e6i	0.0240823	−	0.993387i
$148$	−1.86514e6	−	317082.i	−0.575341	−	0.0978108i
$149$	4.70904e6	−	2.71877e6i	1.42355	−	0.821889i	0.426954	−	0.904274i	$-0.359587\pi$
$149$	4.70904e6	−	2.71877e6i	1.42355	−	0.821889i	0.996601	+	0.0823842i	$0.0262534\pi$
$150$	2.61873e6	+	1.01642e6i	0.775921	+	0.301161i
$151$	4.40080e6	+	2.54080e6i	1.27820	+	0.737972i	0.976518	−	0.215435i	$-0.0691171\pi$
$151$	4.40080e6	+	2.54080e6i	1.27820	+	0.737972i	0.301687	+	0.953407i	$0.402450\pi$
$152$	−2.66745e6	+	1.57297e6i	−0.759565	+	0.447909i
$153$	−725511.	−	1.41033e6i	−0.202567	−	0.393772i
$154$	−22086.5	−	7962.14i	−0.00604734	−	0.00218006i
$155$	929621.	−	1.61015e6i	0.249638	−	0.432386i
$156$	506574.	−	2.59713e6i	0.133435	−	0.684100i
$157$	−834351.	+	481713.i	−0.215600	+	0.124477i	−0.603911	−	0.797051i	$-0.706392\pi$
$157$	−834351.	+	481713.i	−0.215600	+	0.124477i	0.388311	+	0.921528i	$0.373059\pi$
$158$	−1.21209e6	−	6.75287e6i	−0.307302	−	1.71205i
$159$	−289231.	+	474046.i	−0.0719537	+	0.117931i
$160$	−1.30126e6	−	1.05829e6i	−0.317690	−	0.258372i
$161$	−178202.			−0.0427007
$162$	4.23771e6	−	342516.i	0.996750	−	0.0805631i
$163$	−3.65145e6			−0.843145			−0.421572	−	0.906795i	$-0.638522\pi$
$163$	−3.65145e6			−0.843145			−0.421572	+	0.906795i	$0.638522\pi$
$164$	−917592.	+	340369.i	−0.208026	+	0.0771647i
$165$	−77463.5	+	126962.i	−0.0172443	+	0.0282632i
$166$	−4.80471e6	+	862412.i	−1.05037	+	0.188534i
$167$	1.73636e6	−	1.00249e6i	0.372813	−	0.215244i	−0.301873	−	0.953348i	$-0.597612\pi$
$167$	1.73636e6	−	1.00249e6i	0.372813	−	0.215244i	0.674687	+	0.738104i	$0.264279\pi$
$168$	323612.	+	193380.i	0.0682491	+	0.0407835i
$169$	−1.24098e6	+	2.14944e6i	−0.257101	+	0.445312i
$170$	−838085.	−	302128.i	−0.170585	−	0.0614957i
$171$	−2.01696e6	−	3.92078e6i	−0.403375	−	0.784124i
$172$	−556567.	−	461224.i	−0.109379	−	0.0906413i
$173$	−3.03835e6	−	1.75419e6i	−0.586812	−	0.338796i	0.177024	−	0.984207i	$-0.443353\pi$
$173$	−3.03835e6	−	1.75419e6i	−0.586812	−	0.338796i	−0.763836	+	0.645411i	$0.776686\pi$
$174$	2.06408e6	−	5.31796e6i	0.391812	−	1.00948i
$175$	−307139.	+	177327.i	−0.0573087	+	0.0330872i
$176$	−334162.	+	287459.i	−0.0612942	+	0.0527276i
$177$	38976.7	−	1.60778e6i	0.00702887	−	0.289939i
$178$	−2.73169e6	−	3.23529e6i	−0.484364	−	0.573658i
$179$	2.61325e6			0.455640			0.227820	−	0.973703i	$-0.426840\pi$
$179$	2.61325e6			0.455640			0.227820	+	0.973703i	$0.426840\pi$
$180$	1.61113e6	−	1.76282e6i	0.276257	−	0.302267i
$181$			2.03892e6i			0.343846i	0.985110	+	0.171923i	$0.0549980\pi$
$181$			2.03892e6i			0.343846i	−0.985110	+	0.171923i	$0.945002\pi$
$182$	215523.	+	255255.i	0.0357503	+	0.0423410i
$183$	−782689.	−	1.43488e6i	−0.127713	−	0.234133i
$184$	−1.64611e6	+	2.91275e6i	−0.264244	+	0.467573i
$185$	−756558.	−	1.31040e6i	−0.119489	−	0.206960i
$186$	4.91481e6	+	6.11560e6i	0.763779	+	0.950387i
$187$	−117062.	+	202758.i	−0.0179016	+	0.0310066i
$188$	−2.34575e6	+	2.83066e6i	−0.353028	+	0.426005i
$189$	−301446.	+	444128.i	−0.0446503	+	0.0657844i
$190$	−2.32992e6	−	839934.i	−0.339688	−	0.122457i
$191$	−5.62669e6	−	3.24857e6i	−0.807519	−	0.466221i	0.0385744	−	0.999256i	$-0.487718\pi$
$191$	−5.62669e6	−	3.24857e6i	−0.807519	−	0.466221i	−0.846094	+	0.533034i	$0.821052\pi$
$192$	6.15014e6	−	3.50319e6i	0.868923	−	0.494948i
$193$	4.84131e6	+	8.38539e6i	0.673427	+	1.16641i	0.976926	+	0.213579i	$0.0685119\pi$
$193$	4.84131e6	+	8.38539e6i	0.673427	+	1.16641i	−0.303499	+	0.952832i	$0.598155\pi$
$194$	3.05717e6	−	548741.i	0.418711	−	0.0751557i
$195$	1.85787e6	−	1.01342e6i	0.250560	−	0.136674i
$196$	7.01488e6	−	2.60208e6i	0.931649	−	0.345583i
$197$		−	6.14321e6i		−	0.803520i	−0.915745	−	0.401760i	$-0.868399\pi$
$197$		−	6.14321e6i		−	0.803520i	0.915745	−	0.401760i	$-0.131601\pi$
$198$	−381182.	−	498594.i	−0.0491062	−	0.0642320i
$199$			4.39185e6i			0.557299i	0.960393	+	0.278649i	$0.0898867\pi$
$199$			4.39185e6i			0.557299i	−0.960393	+	0.278649i	$0.910113\pi$
$200$	61304.2	+	6.65825e6i	0.00766302	+	0.832282i
$201$	216429.	−	8.92763e6i	0.0266519	−	1.09938i
$202$	2.60191e6	+	1.44959e7i	0.315673	+	1.75869i
$203$	360103.	+	623717.i	0.0430466	+	0.0745589i
$204$	2.46822e6	−	2.83566e6i	0.290733	−	0.334013i
$205$	−677874.	−	391371.i	−0.0786842	−	0.0454283i
$206$	−9.70517e6	−	3.49870e6i	−1.11020	−	0.400226i
$207$	−4.00523e6	−	2.57897e6i	−0.451561	−	0.290760i
$208$	6.16305e6	−	1.16489e6i	0.684866	−	0.129448i
$209$	−325440.	+	563679.i	−0.0356478	+	0.0617437i
$210$	46059.9	+	297972.i	0.00497354	+	0.0321750i
$211$	4.16299e6	+	7.21051e6i	0.443158	+	0.767571i	0.997922	−	0.0644361i	$-0.0205249\pi$
$211$	4.16299e6	+	7.21051e6i	0.443158	+	0.767571i	−0.554764	+	0.832008i	$0.687192\pi$
$212$	−1.29768e6	−	220612.i	−0.136195	−	0.0231538i
$213$	−6.97113e6	+	1.14256e7i	−0.721380	+	1.18233i
$214$	−9.93088e6	−	1.17617e7i	−1.01332	−	1.20013i
$215$		−	578117.i		−	0.0581701i
$216$	4.47481e6	+	9.02973e6i	0.444031	+	0.896012i
$217$	−990549.			−0.0969387
$218$	−1.14454e7	+	9.66381e6i	−1.10474	+	0.932779i
$219$	−1.26443e7	−	7.71472e6i	−1.20383	−	0.734493i
$220$	−347553.	−	59085.7i	−0.0326402	−	0.00554899i
$221$	2.88512e6	−	1.66572e6i	0.267292	−	0.154321i
$222$	6.31020e6	−	975418.i	0.576746	−	0.0891522i
$223$	1.16147e7	+	6.70575e6i	1.04735	+	0.604690i	0.921907	−	0.387410i	$-0.126630\pi$
$223$	1.16147e7	+	6.70575e6i	1.04735	+	0.604690i	0.125447	+	0.992100i	$0.459964\pi$
$224$	−141651.	+	882305.i	−0.0126030	+	0.0785009i
$225$	−9.46947e6	−	459399.i	−0.831339	−	0.0403313i
$226$	3.33113e6	−	9.24035e6i	0.288580	−	0.800503i
$227$	−3.18020e6	+	5.50828e6i	−0.271880	+	0.470910i	−0.969343	−	0.245710i	$-0.920979\pi$
$227$	−3.18020e6	+	5.50828e6i	−0.271880	+	0.470910i	0.697463	+	0.716621i	$0.254312\pi$
$228$	6.86179e6	−	7.88329e6i	0.578939	−	0.665125i
$229$	−8.75997e6	+	5.05757e6i	−0.729451	+	0.421149i	−0.818221	−	0.574903i	$-0.805040\pi$
$229$	−8.75997e6	+	5.05757e6i	−0.729451	+	0.421149i	0.0887701	+	0.996052i	$0.471706\pi$
$230$	−2.63377e6	+	472743.i	−0.216468	+	0.0388545i
$231$	79214.4	+	1920.36i	0.00642641	+	0.000155793i
$232$	1.35212e7	−	124493.i	1.08280	−	0.00996964i
$233$	−7.82001e6			−0.618215			−0.309107	−	0.951027i	$-0.600030\pi$
$233$	−7.82001e6			−0.618215			−0.309107	+	0.951027i	$0.600030\pi$
$234$	1.14996e6	+	8.85614e6i	0.0897500	+	0.691189i
$235$	−2.94026e6			−0.226560
$236$	3.57418e6	−	1.32580e6i	0.271920	−	0.100865i
$237$	1.10882e7	+	2.03277e7i	0.832944	+	1.52701i
$238$	83853.6	+	467169.i	0.00622001	+	0.0346532i
$239$	−1.65601e7	+	9.56101e6i	−1.21303	+	0.700341i	−0.963417	−	0.268005i	$-0.913636\pi$
$239$	−1.65601e7	+	9.56101e6i	−1.21303	+	0.700341i	−0.249610	+	0.968347i	$0.580302\pi$
$240$	5.29588e6	+	1.99960e6i	0.383093	+	0.144647i
$241$	−6.68974e6	+	1.15870e7i	−0.477923	+	0.827787i	−0.999680	−	0.0253074i	$-0.991944\pi$
$241$	−6.68974e6	+	1.15870e7i	−0.477923	+	0.827787i	0.521757	+	0.853094i	$0.325277\pi$
$242$	4.77496e6	−	1.32454e7i	0.336918	−	0.934588i
$243$	−1.32027e7	+	5.61956e6i	−0.920120	+	0.391637i
$244$	2.47209e6	−	2.98311e6i	0.170174	−	0.205353i
$245$	5.18226e6	+	2.99198e6i	0.352388	+	0.203451i
$246$	2.57467e6	−	2.06913e6i	0.172948	−	0.138990i
$247$	8.02078e6	−	4.63080e6i	0.532262	−	0.307302i
$248$	−9.15000e6	+	1.61907e7i	−0.599882	+	1.06148i
$249$	1.44633e7	−	7.88932e6i	0.936846	−	0.511024i
$250$	−8.95772e6	+	7.56339e6i	−0.573294	+	0.484057i
$251$	−2.76521e6			−0.174866			−0.0874332	−	0.996170i	$-0.527866\pi$
$251$	−2.76521e6			−0.174866			−0.0874332	+	0.996170i	$0.527866\pi$
$252$	−1.24253e6	−	273775.i	−0.0776438	−	0.0171077i
$253$			703220.i			0.0434240i
$254$	5.50385e6	−	4.64713e6i	0.335865	−	0.283586i
$255$	3.00584e6	+	72869.3i	0.181278	+	0.00439465i
$256$	1.31130e7	+	1.04654e7i	0.781594	+	0.623788i
$257$	2.51848e6	+	4.36214e6i	0.148368	+	0.256981i	0.930624	−	0.365976i	$-0.119265\pi$
$257$	2.51848e6	+	4.36214e6i	0.148368	+	0.256981i	−0.782257	+	0.622956i	$0.785931\pi$
$258$	2.27428e6	+	882723.i	0.132429	+	0.0514002i
$259$	−403072.	+	698141.i	−0.0231997	+	0.0401831i
$260$	3.86251e6	+	3.20083e6i	0.219760	+	0.182114i
$261$	−932918.	+	1.92300e7i	−0.0524713	+	1.08158i
$262$	4.60231e6	−	1.27665e7i	0.255901	−	0.709853i
$263$	−1.79202e7	−	1.03462e7i	−0.985088	−	0.568741i	−0.0812854	−	0.996691i	$-0.525903\pi$
$263$	−1.79202e7	−	1.03462e7i	−0.985088	−	0.568741i	−0.903802	+	0.427950i	$0.859236\pi$
$264$	763116.	−	1.27703e6i	0.0414742	−	0.0694050i
$265$	−526381.	−	911718.i	−0.0282854	−	0.0489917i
$266$	233118.	+	1.29876e6i	0.0123860	+	0.0690053i
$267$	1.21993e7	+	7.44321e6i	0.640918	+	0.391045i
$268$	1.98466e7	−	7.36184e6i	1.03106	−	0.382457i
$269$		−	5.31299e6i		−	0.272950i	−0.990644	−	0.136475i	$-0.956423\pi$
$269$		−	5.31299e6i		−	0.272950i	0.990644	−	0.136475i	$-0.0435773\pi$
$270$	−3.27706e6	+	7.36375e6i	−0.166492	+	0.374117i
$271$		−	1.79029e7i		−	0.899529i	−0.893147	−	0.449764i	$-0.851508\pi$
$271$		−	1.79029e7i		−	0.899529i	0.893147	−	0.449764i	$-0.148492\pi$
$272$	8.41054e6	+	2.94478e6i	0.417943	+	0.146334i
$273$	−962494.	−	587249.i	−0.0473053	−	0.0288625i
$274$	−2.09049e7	+	3.75228e6i	−1.01624	+	0.182408i
$275$	699764.	+	1.21203e6i	0.0336476	+	0.0582793i
$276$	2.16174e6	−	1.10829e7i	0.102819	−	0.527141i
$277$	3.34053e6	+	1.92865e6i	0.157172	+	0.0907434i	0.576523	−	0.817081i	$-0.304409\pi$
$277$	3.34053e6	+	1.92865e6i	0.157172	+	0.0907434i	−0.419351	+	0.907824i	$0.637742\pi$
$278$	9.37463e6	−	2.60046e7i	0.436335	−	1.21036i
$279$	−2.22634e7	−	1.43354e7i	−1.02513	−	0.660079i
$280$	−615626.	+	363030.i	−0.0280442	+	0.0165374i
$281$	1.86528e7	−	3.23077e7i	0.840671	−	1.45609i	−0.0486571	−	0.998816i	$-0.515494\pi$
$281$	1.86528e7	−	3.23077e7i	0.840671	−	1.45609i	0.889328	−	0.457269i	$-0.151173\pi$
$282$	4.48947e6	−	1.15668e7i	0.200192	−	0.515783i
$283$	−3.74483e6	−	6.48624e6i	−0.165224	−	0.286176i	0.771511	−	0.636216i	$-0.219501\pi$
$283$	−3.74483e6	−	6.48624e6i	−0.165224	−	0.286176i	−0.936735	+	0.350040i	$0.886168\pi$
$284$	−3.12771e7	−	5.31726e6i	−1.36544	−	0.232131i
$285$	8.35640e6	+	202581.i	0.360981	+	0.00875112i
$286$	1.00729e6	−	850495.i	0.0430581	−	0.0363558i
$287$			417022.i			0.0176406i
$288$	−1.59526e7	+	1.77805e7i	−0.667810	+	0.744332i
$289$	−1.94044e7			−0.803910
$290$	6.97682e6	+	8.26302e6i	0.286064	+	0.338801i
$291$	−9.20276e6	+	5.01986e6i	−0.373456	+	0.203710i
$292$	5.88444e6	−	3.46134e7i	0.236351	−	1.39026i
$293$	3.64819e7	−	2.10628e7i	1.45035	−	0.837362i	0.451853	−	0.892092i	$-0.350763\pi$
$293$	3.64819e7	−	2.10628e7i	1.45035	−	0.837362i	0.998501	+	0.0547300i	$0.0174298\pi$
$294$	−1.96830e7	+	1.58183e7i	−0.774552	+	0.622469i
$295$	2.64044e6	+	1.52446e6i	0.102851	+	0.0593812i
$296$	7.68794e6	+	1.30372e7i	0.296439	+	0.502701i
$297$	1.75261e6	+	1.18956e6i	0.0668986	+	0.0454065i
$298$	−4.09224e7	−	1.47525e7i	−1.54636	−	0.557462i
$299$	5.00318e6	−	8.66576e6i	0.187168	−	0.324185i
$300$	−7.30261e6	−	2.12529e7i	−0.270467	−	0.787146i
$301$	−266739.	+	154002.i	−0.00978108	+	0.00564711i
$302$	−7.18212e6	−	4.00134e7i	−0.260755	−	1.45273i
$303$	−2.38022e7	−	4.36358e7i	−0.855635	−	1.56861i
$304$	2.33818e7	+	8.18664e6i	0.832256	+	0.291397i
$305$	3.09861e6			0.109211
$306$	−4.87626e6	+	1.17135e7i	−0.170185	+	0.408812i
$307$	−740303.			−0.0255855			−0.0127928	−	0.999918i	$-0.504072\pi$
$307$	−740303.			−0.0255855			−0.0127928	+	0.999918i	$0.504072\pi$
$308$	65321.2	+	176098.i	0.00223564	+	0.00602701i
$309$	3.48081e7	+	843840.i	1.17979	+	0.0286012i
$310$	−1.46400e7	+	2.62777e6i	−0.491423	+	0.0882070i
$311$	−2.67721e7	+	1.54569e7i	−0.890022	+	0.513855i	−0.873950	−	0.486016i	$-0.838450\pi$
$311$	−2.67721e7	+	1.54569e7i	−0.890022	+	0.513855i	−0.0160725	+	0.999871i	$0.505116\pi$
$312$	−1.84895e7	+	1.03075e7i	−0.608783	+	0.339384i
$313$	2.36689e7	−	4.09958e7i	0.771873	−	1.33692i	−0.164662	−	0.986350i	$-0.552653\pi$
$313$	2.36689e7	−	4.09958e7i	0.771873	−	1.33692i	0.936535	−	0.350574i	$-0.114013\pi$
$314$	7.25064e6	+	2.61385e6i	0.234200	+	0.0844289i
$315$	−465499.	−	904887.i	−0.0148932	−	0.0289510i
$316$	−3.50215e7	+	4.22611e7i	−1.10987	+	1.33931i
$317$	4.34011e7	+	2.50576e7i	1.36246	+	0.786615i	0.989950	−	0.141415i	$-0.0451652\pi$
$317$	4.34011e7	+	2.50576e7i	1.36246	+	0.786615i	0.372506	+	0.928030i	$0.378499\pi$
$318$	4.39037e6	−	678654.i	0.136527	−	0.0211041i
$319$	2.46131e6	−	1.42104e6i	0.0758217	−	0.0437757i
$320$	247069.	+	1.34159e7i	0.00753993	+	0.409422i
$321$	4.43498e7	+	2.70593e7i	1.34084	+	0.818090i
$322$	919717.	+	1.08927e6i	0.0275478	+	0.0326263i
$323$	1.31584e7			0.390477
$324$	−2.39648e7	−	2.41354e7i	−0.704594	−	0.709610i
$325$		−	1.99144e7i		−	0.580118i
$326$	1.88454e7	+	2.23196e7i	0.543943	+	0.644220i
$327$	2.63316e7	−	4.31571e7i	0.753067	−	1.23427i
$328$	6.81629e6	+	3.85215e6i	0.193164	+	0.109165i
$329$	783243.	+	1.35662e6i	0.0219942	+	0.0380951i
$330$	1.17586e6	−	181761.i	0.0327199	−	0.00505777i
$331$	2.86447e7	−	4.96141e7i	0.789879	−	1.36811i	−0.136162	−	0.990687i	$-0.543477\pi$
$331$	2.86447e7	−	4.96141e7i	0.789879	−	1.36811i	0.926041	−	0.377423i	$-0.123190\pi$
$332$	3.00691e7	+	2.49180e7i	0.821685	+	0.680925i
$333$	−1.91629e7	+	9.85795e6i	−0.518955	+	0.266965i
$334$	−1.50893e7	−	5.43967e6i	−0.404976	−	0.145993i
$335$	1.46617e7	+	8.46496e6i	0.389988	+	0.225160i
$336$	−488143.	−	2.97615e6i	−0.0128685	−	0.0784578i
$337$	1.28377e7	+	2.22356e7i	0.335427	+	0.580977i	0.983567	−	0.180545i	$-0.0577860\pi$
$337$	1.28377e7	+	2.22356e7i	0.335427	+	0.580977i	−0.648140	+	0.761522i	$0.724453\pi$
$338$	1.95433e7	−	3.50789e6i	0.506114	−	0.0908440i
$339$	−803424.	+	3.31410e7i	−0.0206227	+	0.850681i
$340$	2.47865e6	+	6.68214e6i	0.0630637	+	0.170012i
$341$			3.90890e6i			0.0985805i
$342$	−1.35563e7	+	3.25643e7i	−0.338892	+	0.814072i
$343$		−	6.39644e6i		−	0.158510i
$344$	53240.5	+	5.78246e6i	0.00130788	+	0.142049i
$345$	7.92823e6	−	4.32463e6i	0.193072	−	0.105315i
$346$	4.95860e6	+	2.76255e7i	0.119710	+	0.666934i
$347$	3.39136e7	+	5.87400e7i	0.811680	+	1.40587i	0.911687	+	0.410885i	$0.134780\pi$
$347$	3.39136e7	+	5.87400e7i	0.811680	+	1.40587i	−0.100007	+	0.994987i	$0.531887\pi$
$348$	−4.31591e7	+	1.48297e7i	−1.02408	+	0.351879i
$349$	−6.38737e7	−	3.68775e7i	−1.50261	−	0.867531i	−0.999995	−	0.00301935i	$-0.999039\pi$
$349$	−6.38737e7	−	3.68775e7i	−1.50261	−	0.867531i	−0.502613	−	0.864512i	$-0.667628\pi$
$350$	2.66908e6	+	962201.i	0.0622527	+	0.0224420i
$351$	−1.31341e7	−	2.71282e7i	−0.303723	−	0.627336i
$352$	3.48174e6	+	558981.i	0.0798305	+	0.0128165i
$353$	−1.72181e7	+	2.98227e7i	−0.391437	+	0.677989i	−0.992639	−	0.121108i	$-0.961355\pi$
$353$	−1.72181e7	+	2.98227e7i	−0.391437	+	0.677989i	0.601202	+	0.799097i	$0.294689\pi$
$354$	−1.00288e7	+	8.05964e6i	−0.226068	+	0.181679i
$355$	−1.26870e7	−	2.19745e7i	−0.283578	−	0.491172i
$356$	−5.67734e6	+	3.33952e7i	−0.125833	+	0.740174i
$357$	−767090.	−	1.40628e6i	−0.0168594	−	0.0309078i
$358$	−1.34872e7	−	1.59736e7i	−0.293949	−	0.348140i
$359$			8.17069e7i			1.76594i	0.469431	+	0.882969i	$0.344459\pi$
$359$			8.17069e7i			1.76594i	−0.469431	+	0.882969i	$0.655541\pi$
$360$	−1.90905e7	−	750045.i	−0.409176	−	0.0160761i
$361$	−1.04648e7			−0.222438
$362$	1.24630e7	−	1.05230e7i	0.262722	−	0.221827i
$363$	−1.15166e6	+	4.75055e7i	−0.0240770	+	0.993171i
$364$	447927.	−	2.63479e6i	0.00928759	−	0.0546313i
$365$	2.43185e7	−	1.40403e7i	0.500101	−	0.288733i
$366$	−4.73125e6	+	1.21898e7i	−0.0965012	+	0.248629i
$367$	6.48163e7	+	3.74217e7i	1.31125	+	0.757052i	0.982304	−	0.187296i	$-0.0599724\pi$
$367$	6.48163e7	+	3.74217e7i	1.31125	+	0.757052i	0.328949	+	0.944348i	$0.393306\pi$
$368$	2.63000e7	−	4.97103e6i	0.527730	−	0.0997478i
$369$	−6.03519e6	+	9.37289e6i	−0.120119	+	0.186550i
$370$	−4.10520e6	+	1.13876e7i	−0.0810455	+	0.224815i
$371$	−280440.	+	485737.i	−0.00549185	+	0.00951216i
$372$	1.20162e7	−	6.16051e7i	0.233419	−	1.19671i
$373$	−6.03434e7	+	3.48393e7i	−1.16280	+	0.671340i	−0.951972	−	0.306184i	$-0.900948\pi$
$373$	−6.03434e7	+	3.48393e7i	−1.16280	+	0.671340i	−0.210823	+	0.977524i	$0.567614\pi$
$374$	1.84354e6	−	330902.i	0.0352401	−	0.00632536i
$375$	2.06084e7	−	3.37770e7i	0.390797	−	0.640511i
$376$	2.94092e7	−	270778.i	0.553248	−	0.00509389i
$377$	−4.04408e7			−0.754737
$378$	4.27054e6	−	449580.i	0.0790692	−	0.00832399i
$379$	−1.97780e7			−0.363300			−0.181650	−	0.983363i	$-0.558144\pi$
$379$	−1.97780e7			−0.363300			−0.181650	+	0.983363i	$0.558144\pi$
$380$	6.89080e6	+	1.85767e7i	0.125579	+	0.338547i
$381$	−1.26623e7	+	2.07534e7i	−0.228949	+	0.375245i
$382$	9.18279e6	+	5.11595e7i	0.164734	+	0.917776i
$383$	−2.35922e7	+	1.36209e7i	−0.419925	+	0.242444i	−0.695045	−	0.718966i	$-0.744616\pi$
$383$	−2.35922e7	+	1.36209e7i	−0.419925	+	0.242444i	0.275120	+	0.961410i	$0.411282\pi$
$384$	−5.31548e7	−	1.95128e7i	−0.938747	−	0.344608i
$385$	−75109.1	+	130093.i	−0.00131617	+	0.00227967i
$386$	2.62697e7	−	7.28704e7i	0.456765	−	1.26704i
$387$	−8.22390e6	−	398972.i	−0.141888	−	0.00688350i
$388$	−1.91325e7	−	1.58550e7i	−0.327549	−	0.271438i
$389$	−4.06878e7	−	2.34911e7i	−0.691219	−	0.399076i	0.112849	−	0.993612i	$-0.464002\pi$
$389$	−4.06878e7	−	2.34911e7i	−0.691219	−	0.399076i	−0.804069	+	0.594537i	$0.797336\pi$
$390$	−1.57832e7	−	6.12599e6i	−0.266073	−	0.103272i
$391$	1.23119e7	−	7.10825e6i	0.205965	−	0.118914i
$392$	−5.21097e7	−	2.94492e7i	−0.865089	−	0.488895i
$393$	−1.11002e6	+	4.57878e7i	−0.0182874	+	0.754349i
$394$	−3.75506e7	+	3.17056e7i	−0.613944	+	0.518379i
$395$	−4.38974e7			−0.712275
$396$	−1.08037e6	+	4.90328e6i	−0.0173975	+	0.0789588i
$397$		−	4.66988e7i		−	0.746336i	−0.927764	−	0.373168i	$-0.878272\pi$
$397$		−	4.66988e7i		−	0.746336i	0.927764	−	0.373168i	$-0.121728\pi$
$398$	2.68454e7	−	2.26667e7i	0.425814	−	0.359533i
$399$	−2.13255e6	−	3.90955e6i	−0.0335723	−	0.0615471i
$400$	4.03825e7	−	3.47385e7i	0.630976	−	0.542790i
$401$	−1.66818e7	−	2.88937e7i	−0.258708	−	0.448095i	0.707188	−	0.707025i	$-0.249963\pi$
$401$	−1.66818e7	−	2.88937e7i	−0.258708	−	0.448095i	−0.965896	+	0.258931i	$0.916630\pi$
$402$	−5.56876e7	+	4.47533e7i	−0.857196	+	0.688886i
$403$	2.78105e7	−	4.81692e7i	0.424907	−	0.735960i
$404$	7.51780e7	−	9.07187e7i	1.14011	−	1.37579i
$405$	2.63320e6	−	2.70748e7i	0.0396386	−	0.407568i
$406$	1.95398e6	−	5.42021e6i	0.0291972	−	0.0809912i
$407$	2.75499e6	+	1.59060e6i	0.0408637	+	0.0235927i
$408$	−3.00718e7	−	452039.i	−0.442771	−	0.00665573i
$409$	−1.48558e7	−	2.57311e7i	−0.217134	−	0.376087i	0.736797	−	0.676114i	$-0.236337\pi$
$409$	−1.48558e7	−	2.57311e7i	−0.217134	−	0.376087i	−0.953931	+	0.300028i	$0.903004\pi$
$410$	1.10629e6	+	6.16343e6i	0.0160516	+	0.0894275i
$411$	6.29284e7	−	3.43257e7i	0.906403	−	0.494418i
$412$	2.87033e7	+	7.73804e7i	0.410430	+	1.10647i
$413$		−	1.62437e6i		−	0.0230587i
$414$	4.90730e6	+	3.77924e7i	0.0691578	+	0.532603i
$415$			3.12333e7i			0.436992i
$416$	−3.89285e7	−	3.16598e7i	−0.540739	−	0.439772i
$417$	−2.26104e6	+	9.32671e7i	−0.0311817	+	1.28623i
$418$	5.12514e6	−	919927.i	0.0701741	−	0.0125958i
$419$	−548013.	−	949186.i	−0.00744987	−	0.0129036i	0.862276	−	0.506438i	$-0.169038\pi$
$419$	−548013.	−	949186.i	−0.00744987	−	0.0129036i	−0.869726	+	0.493534i	$0.835705\pi$
$420$	1.58365e6	−	1.81940e6i	0.0213753	−	0.0245573i
$421$	−1.25274e8	−	7.23271e7i	−1.67886	−	0.969292i	−0.962388	−	0.271680i	$-0.912421\pi$
$421$	−1.25274e8	−	7.23271e7i	−1.67886	−	0.969292i	−0.716476	−	0.697612i	$-0.754246\pi$
$422$	2.25890e7	−	6.26605e7i	0.300580	−	0.833790i
$423$	−2.02914e6	+	4.18262e7i	−0.0268097	+	0.552621i
$424$	5.34894e6	+	9.07074e6i	0.0701730	+	0.118999i
$425$	1.41466e7	−	2.45027e7i	0.184284	−	0.319189i
$426$	1.05818e8	−	1.63571e7i	1.36877	−	0.211582i
$427$	−825425.	−	1.42968e6i	−0.0106022	−	0.0183635i
$428$	−2.06396e7	+	1.21406e8i	−0.263251	+	1.54849i
$429$	−2.31740e6	+	3.79818e6i	−0.0293514	+	0.0481065i
$430$	−3.53376e6	+	2.98371e6i	−0.0444460	+	0.0375276i
$431$			1.24377e8i			1.55348i	0.629819	+	0.776742i	$0.283129\pi$
$431$			1.24377e8i			1.55348i	−0.629819	+	0.776742i	$0.716871\pi$
$432$	3.20998e7	−	7.39557e7i	0.398154	−	0.917319i
$433$	1.41972e7			0.174880			0.0874399	−	0.996170i	$-0.472131\pi$
$433$	1.41972e7			0.174880			0.0874399	+	0.996170i	$0.472131\pi$
$434$	5.11231e6	+	6.05478e6i	0.0625386	+	0.0740677i
$435$	−3.11575e7	−	1.90102e7i	−0.378525	−	0.230950i
$436$	1.18141e8	+	2.00845e7i	1.42541	+	0.242327i
$437$	3.42276e7	−	1.97613e7i	0.410140	−	0.236795i
$438$	1.81019e7	+	1.17105e8i	0.215428	+	1.39365i
$439$	7.53641e7	+	4.35115e7i	0.890781	+	0.514293i	0.874198	−	0.485570i	$-0.161388\pi$
$439$	7.53641e7	+	4.35115e7i	0.890781	+	0.514293i	0.0165831	+	0.999862i	$0.494721\pi$
$440$	1.43259e6	+	2.42938e6i	0.0168175	+	0.0285192i
$441$	4.61383e7	−	7.16546e7i	0.537955	−	0.835465i
$442$	−2.50721e7	−	9.03846e6i	−0.290352	−	0.104671i
$443$	2.45515e7	−	4.25245e7i	0.282402	−	0.489134i	−0.689574	−	0.724215i	$-0.742202\pi$
$443$	2.45515e7	−	4.25245e7i	0.282402	−	0.489134i	0.971976	+	0.235081i	$0.0755355\pi$
$444$	−3.85298e7	−	3.35372e7i	−0.440198	−	0.383158i
$445$	−2.34626e7	+	1.35461e7i	−0.266254	+	0.153722i
$446$	−1.89553e7	−	1.05604e8i	−0.213661	−	1.19036i
$447$	1.46770e8	+	3.55809e6i	1.64330	+	0.0398378i
$448$	6.12420e6	−	3.68780e6i	0.0681107	−	0.0410142i
$449$	−1.73856e8			−1.92067			−0.960333	−	0.278857i	$-0.910044\pi$
$449$	−1.73856e8			−1.92067			−0.960333	+	0.278857i	$0.910044\pi$
$450$	4.60646e7	+	6.02536e7i	0.505511	+	0.661219i
$451$	1.64565e6			0.0179394
$452$	−7.36743e7	+	2.73285e7i	−0.797812	+	0.295938i
$453$	6.57018e7	+	1.20449e8i	0.706777	+	1.29571i
$454$	5.00829e7	−	8.98953e6i	0.535207	−	0.0960660i
$455$	1.85114e6	−	1.06875e6i	0.0196519	−	0.0113460i
$456$	−8.36013e7	−	1.25669e6i	−0.881695	−	0.0132536i
$457$	−3.37410e7	+	5.84411e7i	−0.353516	+	0.612307i	−0.986863	−	0.161561i	$-0.948347\pi$
$457$	−3.37410e7	+	5.84411e7i	−0.353516	+	0.612307i	0.633347	+	0.773868i	$0.281681\pi$
$458$	7.61256e7	+	2.74432e7i	0.792381	+	0.285652i
$459$	3.11099e6	−	4.27088e7i	0.0321707	−	0.441651i
$460$	1.64827e7	+	1.36591e7i	0.169339	+	0.140330i
$461$	−6.67712e7	−	3.85503e7i	−0.681532	−	0.393483i	0.118900	−	0.992906i	$-0.462063\pi$
$461$	−6.67712e7	−	3.85503e7i	−0.681532	−	0.393483i	−0.800432	+	0.599424i	$0.795397\pi$
$462$	−397094.	−	494113.i	−0.00402687	−	0.00501072i
$463$	722563.	−	417172.i	0.00728002	−	0.00420312i	−0.496356	−	0.868119i	$-0.665329\pi$
$463$	722563.	−	417172.i	0.00728002	−	0.00420312i	0.503636	+	0.863916i	$0.331995\pi$
$464$	−7.05448e7	−	8.20061e7i	−0.706173	−	0.820904i
$465$	4.40696e7	−	2.40388e7i	0.438309	−	0.239086i
$466$	4.03597e7	+	4.78002e7i	0.398832	+	0.472358i
$467$	−1.46029e8			−1.43380			−0.716900	−	0.697176i	$-0.754439\pi$
$467$	−1.46029e8			−1.43380			−0.716900	+	0.697176i	$0.754439\pi$
$468$	4.81985e7	−	5.27365e7i	0.470215	−	0.514486i
$469$		−	9.01977e6i		−	0.0874333i
$470$	1.51749e7	+	1.79725e7i	0.146162	+	0.173107i
$471$	−2.60048e7	−	630425.i	−0.248881	−	0.00603352i
$472$	−2.65506e7	−	1.50048e7i	−0.252493	−	0.142693i
$473$	607720.	+	1.05260e6i	0.00574276	+	0.00994674i
$474$	6.70267e7	−	1.72690e8i	0.629379	−	1.62156i
$475$	3.93285e7	−	6.81189e7i	0.366966	−	0.635604i
$476$	2.42282e6	−	2.92366e6i	0.0224646	−	0.0271085i
$477$	−1.33328e7	+	6.85874e6i	−0.122847	+	0.0631959i
$478$	1.43910e8	+	5.18795e7i	1.31768	+	0.475020i
$479$	−7.65807e7	−	4.42139e7i	−0.696807	−	0.402302i	0.109350	−	0.994003i	$-0.465123\pi$
$479$	−7.65807e7	−	4.42139e7i	−0.696807	−	0.402302i	−0.806157	+	0.591701i	$0.798456\pi$
$480$	−1.51098e7	−	4.26914e7i	−0.136627	−	0.386026i
$481$	−2.26332e7	−	3.92018e7i	−0.203381	−	0.352266i
$482$	1.05352e8	−	1.89100e7i	0.940811	−	0.168869i
$483$	−4.10732e6	−	2.50601e6i	−0.0364516	−	0.0222403i
$484$	−1.05607e8	+	3.91737e7i	−0.931447	+	0.345508i
$485$		−	1.98733e7i		−	0.174199i
$486$	1.02490e8	+	5.16992e7i	0.892839	+	0.450376i
$487$			4.08614e7i			0.353774i	0.984231	+	0.176887i	$0.0566027\pi$
$487$			4.08614e7i			0.353774i	−0.984231	+	0.176887i	$0.943397\pi$
$488$	−3.09930e7	+	285361.i	−0.266689	+	0.00245547i
$489$	−8.41609e7	−	5.13493e7i	−0.719753	−	0.439145i
$490$	−8.45748e6	−	4.71187e7i	−0.0718874	−	0.400502i
$491$	−3.97287e6	−	6.88121e6i	−0.0335629	−	0.0581327i	0.848756	−	0.528785i	$-0.177352\pi$
$491$	−3.97287e6	−	6.88121e6i	−0.0335629	−	0.0581327i	−0.882319	+	0.470652i	$0.844019\pi$
$492$	−2.59358e7	−	5.05881e6i	−0.217773	−	0.0424769i
$493$	−4.97585e7	−	2.87281e7i	−0.415266	−	0.239754i
$494$	−6.97019e7	−	2.51274e7i	−0.578181	−	0.208433i
$495$	−3.57086e6	+	1.83695e6i	−0.0294413	+	0.0151454i
$496$	1.46190e8	−	2.76318e7i	1.19805	−	0.226446i
$497$	−6.75925e6	+	1.17074e7i	−0.0550591	+	0.0953652i
$498$	−1.22870e8	−	4.76899e7i	−0.994850	−	0.386134i
$499$	−1.20177e7	−	2.08152e7i	−0.0967206	−	0.167525i	0.813605	−	0.581418i	$-0.197502\pi$
$499$	−1.20177e7	−	2.08152e7i	−0.0967206	−	0.167525i	−0.910325	+	0.413893i	$0.864169\pi$
$500$	9.24631e7	+	1.57192e7i	0.739705	+	0.125753i
$501$	5.41186e7	+	1.31198e6i	0.430361	+	0.0104331i
$502$	1.42715e7	+	1.69025e7i	0.112813	+	0.133610i
$503$			1.31836e8i			1.03593i	0.855403	+	0.517963i	$0.173309\pi$
$503$			1.31836e8i			1.03593i	−0.855403	+	0.517963i	$0.826691\pi$
$504$	4.73936e6	+	9.00802e6i	0.0370193	+	0.0703619i
$505$	9.42312e7			0.731679
$506$	4.29846e6	−	3.62938e6i	0.0331789	−	0.0280143i
$507$	−5.88298e7	+	3.20901e7i	−0.451412	+	0.246233i
$508$	−5.68116e7	−	9.65826e6i	−0.433357	−	0.0736729i
$509$	1.51161e8	−	8.72728e7i	1.14627	−	0.661798i	0.198293	−	0.980143i	$-0.436460\pi$
$509$	1.51161e8	−	8.72728e7i	1.14627	−	0.661798i	0.947975	+	0.318345i	$0.103127\pi$
$510$	−1.50680e7	−	1.87494e7i	−0.113591	−	0.141344i
$511$	−1.29562e7	−	7.48024e6i	−0.0970987	−	0.0560600i
$512$	−3.70675e6	−	1.34167e8i	−0.0276174	−	0.999619i
$513$	8.64872e6	−	1.18733e8i	0.0640619	−	0.879464i
$514$	1.36657e7	−	3.79077e7i	0.100633	−	0.279150i
$515$	−3.30042e7	+	5.71650e7i	−0.241628	+	0.418512i
$516$	−6.34206e6	−	1.84574e7i	−0.0461616	−	0.134345i
$517$	5.35347e6	−	3.09083e6i	0.0387403	−	0.0223667i
$518$	6.34770e6	−	1.13937e6i	0.0456696	−	0.00819738i
$519$	−4.53610e7	−	8.31591e7i	−0.324475	−	0.594850i
$520$	−369482.	−	4.01295e7i	−0.00262775	−	0.285400i
$521$	−1.05340e8			−0.744867			−0.372434	−	0.928059i	$-0.621477\pi$
$521$	−1.05340e8			−0.744867			−0.372434	+	0.928059i	$0.621477\pi$
$522$	1.22359e8	−	9.35451e7i	0.860250	−	0.657672i
$523$	1.71767e8			1.20070			0.600349	−	0.799738i	$-0.295028\pi$
$523$	1.71767e8			1.20070			0.600349	+	0.799738i	$0.295028\pi$
$524$	−1.01789e8	+	3.77572e7i	−0.707467	+	0.262426i
$525$	−9.57282e6	−	232070.i	−0.0661549	−	0.00160377i
$526$	2.92458e7	+	1.62936e8i	0.200959	+	1.11959i
$527$	6.84363e7	−	3.95117e7i	0.467579	−	0.269957i
$528$	−1.17444e7	+	1.92631e6i	−0.0797867	+	0.0130865i
$529$	−5.26675e7	+	9.12229e7i	−0.355775	+	0.616221i
$530$	−2.85622e6	+	7.92298e6i	−0.0191851	+	0.0532183i
$531$	2.35081e7	−	3.65090e7i	0.157013	−	0.243846i
$532$	6.73556e6	−	8.12793e6i	0.0447341	−	0.0539815i
$533$	−2.02793e7	−	1.17082e7i	−0.133928	−	0.0773232i
$534$	−1.74648e7	−	1.12984e8i	−0.114694	−	0.741981i
$535$	−8.52967e7	+	4.92461e7i	−0.557020	+	0.321596i
$536$	−1.47430e8	−	8.33182e7i	−0.957394	−	0.541060i
$537$	6.02318e7	+	3.67494e7i	0.388958	+	0.237316i
$538$	−3.24759e7	+	2.74208e7i	−0.208552	+	0.176089i
$539$	−1.25808e7			−0.0803417
$540$	6.19244e7	−	1.79737e7i	0.393261	−	0.114145i
$541$			1.80547e8i			1.14025i	0.821559	+	0.570123i	$0.193105\pi$
$541$			1.80547e8i			1.14025i	−0.821559	+	0.570123i	$0.806895\pi$
$542$	−1.09432e8	+	9.23983e7i	−0.687301	+	0.580318i
$543$	−2.86727e7	+	4.69943e7i	−0.179089	+	0.293525i
$544$	−2.54074e7	−	6.66081e7i	−0.157821	−	0.413742i
$545$	4.79217e7	+	8.30028e7i	0.296035	+	0.512747i
$546$	1.37793e6	+	8.91413e6i	0.00846542	+	0.0547648i
$547$	−1.22454e8	+	2.12097e8i	−0.748189	+	1.29590i	0.200501	+	0.979694i	$0.435743\pi$
$547$	−1.22454e8	+	2.12097e8i	−0.748189	+	1.29590i	−0.948690	+	0.316208i	$0.897590\pi$
$548$	1.30828e8	+	1.08416e8i	0.794985	+	0.658798i
$549$	2.13843e6	−	4.40788e7i	0.0129234	−	0.266387i
$550$	3.79703e6	−	1.05327e7i	0.0228221	−	0.0633071i
$551$	−1.38331e8	−	7.98657e7i	−0.826925	−	0.477425i
$552$	−7.89017e7	+	4.39861e7i	−0.469104	+	0.261516i
$553$	1.16936e7	+	2.02540e7i	0.0691471	+	0.119766i
$554$	−5.45175e6	−	3.03731e7i	−0.0320632	−	0.178632i
$555$	990119.	−	4.08421e7i	0.00579173	−	0.238907i
$556$	−2.07338e8	+	7.69092e7i	−1.20630	+	0.447460i
$557$			1.24690e8i			0.721551i	0.932653	+	0.360775i	$0.117488\pi$
$557$			1.24690e8i			0.721551i	−0.932653	+	0.360775i	$0.882512\pi$
$558$	2.72776e7	+	2.10072e8i	0.157001	+	1.20911i
$559$		−	1.72949e7i		−	0.0990109i
$560$	5.39634e6	+	1.88941e6i	0.0307280	+	0.0107588i
$561$	−5.54946e6	+	3.02708e6i	−0.0314313	+	0.0171449i
$562$	−2.93751e8	+	5.27263e7i	−1.65489	+	0.297042i
$563$	1.43204e8	+	2.48037e8i	0.802472	+	1.38992i	0.917985	+	0.396616i	$0.129816\pi$
$563$	1.43204e8	+	2.48037e8i	0.802472	+	1.38992i	−0.115513	+	0.993306i	$0.536851\pi$
$564$	−9.38733e7	+	3.22553e7i	−0.523244	+	0.179789i
$565$	−5.44271e7	−	3.14235e7i	−0.301766	−	0.174224i
$566$	−2.03200e7	+	5.63665e7i	−0.112066	+	0.310865i
$567$	−1.31936e7	+	5.99740e6i	−0.0723791	+	0.0329013i
$568$	1.28922e8	+	2.18626e8i	0.703528	+	1.19304i
$569$	2.64173e7	−	4.57561e7i	0.143401	−	0.248377i	−0.785374	−	0.619021i	$-0.787530\pi$
$569$	2.64173e7	−	4.57561e7i	0.143401	−	0.248377i	0.928775	+	0.370644i	$0.120863\pi$
$570$	−4.18898e7	−	5.21244e7i	−0.226195	−	0.281460i
$571$	1.46720e7	+	2.54126e7i	0.0788098	+	0.136503i	0.902737	−	0.430194i	$-0.141555\pi$
$571$	1.46720e7	+	2.54126e7i	0.0788098	+	0.136503i	−0.823927	+	0.566696i	$0.808221\pi$
$572$	−1.03974e7	−	1.76761e6i	−0.0555566	−	0.00944490i
$573$	−8.40038e7	−	1.54002e8i	−0.446514	−	0.818581i
$574$	2.54906e6	−	2.15228e6i	0.0134786	−	0.0113806i
$575$		−	8.49820e7i		−	0.447016i
$576$	1.91017e8	+	5.74402e6i	0.999548	+	0.0300572i
$577$	8.80540e7			0.458376			0.229188	−	0.973382i	$-0.426393\pi$
$577$	8.80540e7			0.458376			0.229188	+	0.973382i	$0.426393\pi$
$578$	1.00148e8	+	1.18610e8i	0.518631	+	0.614242i
$579$	−6.33590e6	+	2.61354e8i	−0.0326417	+	1.34646i
$580$	1.45001e7	−	8.52923e7i	0.0743169	−	0.437145i
$581$	1.44108e7	−	8.32009e6i	0.0734785	−	0.0424228i
$582$	7.81804e7	+	3.03444e7i	0.396578	+	0.153925i
$583$	1.91681e6	+	1.10667e6i	0.00967326	+	0.00558486i
$584$	−2.41946e8	+	1.42674e8i	−1.21473	+	0.716316i
$585$	5.70729e7	+	2.76882e6i	0.285077	+	0.0138301i
$586$	−3.17033e8	−	1.14290e8i	−1.57548	−	0.567957i
$587$	1.84530e8	−	3.19615e8i	0.912330	−	1.58020i	0.101565	−	0.994829i	$-0.467615\pi$
$587$	1.84530e8	−	3.19615e8i	0.912330	−	1.58020i	0.810764	−	0.585372i	$-0.199052\pi$
$588$	1.98276e8	+	3.86740e7i	0.975299	+	0.190233i
$589$	1.90257e8	−	1.09845e8i	0.931095	−	0.537568i
$590$	−4.30920e6	−	2.40076e7i	−0.0209817	−	0.116894i
$591$	8.63903e7	−	1.41593e8i	0.418507	−	0.685927i
$592$	4.00124e7	−	1.14279e8i	0.192854	−	0.550809i
$593$	3.64704e8			1.74895			0.874473	−	0.485074i	$-0.161207\pi$
$593$	3.64704e8			1.74895			0.874473	+	0.485074i	$0.161207\pi$
$594$	−1.77413e6	−	1.68524e7i	−0.00846497	−	0.0804084i
$595$	3.03686e6			0.0144170
$596$	1.21029e8	+	3.26278e8i	0.571676	+	1.54117i
$597$	−6.17613e7	+	1.01226e8i	−0.290264	+	0.475740i
$598$	−7.87916e7	+	1.41426e7i	−0.368448	+	0.0661339i
$599$	2.17084e8	−	1.25334e8i	1.01006	−	0.583159i	0.0988516	−	0.995102i	$-0.468483\pi$
$599$	2.17084e8	−	1.25334e8i	1.01006	−	0.583159i	0.911210	+	0.411943i	$0.135150\pi$
$600$	−9.22202e7	+	1.54326e8i	−0.426945	+	0.714471i
$601$	−8.40160e7	+	1.45520e8i	−0.387025	+	0.670347i	−0.992048	−	0.125861i	$-0.959831\pi$
$601$	−8.40160e7	+	1.45520e8i	−0.387025	+	0.670347i	0.605023	+	0.796208i	$0.293164\pi$
$602$	2.31801e6	+	835638.i	0.0106249	+	0.00383026i
$603$	1.30535e8	−	2.02726e8i	0.595355	−	0.924609i
$604$	−2.07516e8	+	2.50413e8i	−0.941761	+	1.13644i
$605$	−7.80177e7	−	4.50435e7i	−0.352312	−	0.203407i
$606$	−1.43881e8	+	3.70700e8i	−0.646525	+	1.66573i
$607$	9.85662e7	−	5.69072e7i	0.440719	−	0.254449i	−0.263183	−	0.964746i	$-0.584772\pi$
$607$	9.85662e7	−	5.69072e7i	0.440719	−	0.254449i	0.703903	+	0.710296i	$0.251439\pi$
$608$	−7.06341e7	−	1.85174e8i	−0.314271	−	0.823891i
$609$	−471273.	+	1.94399e7i	−0.00208651	+	0.0860679i
$610$	−1.59922e7	−	1.89404e7i	−0.0704561	−	0.0834449i
$611$	−8.79608e7			−0.385625
$612$	9.67663e7	−	3.06482e7i	0.422153	−	0.133706i
$613$			1.74045e8i			0.755581i	0.925891	+	0.377790i	$0.123316\pi$
$613$			1.74045e8i			0.755581i	−0.925891	+	0.377790i	$0.876684\pi$
$614$	3.82077e6	+	4.52514e6i	0.0165061	+	0.0195491i
$615$	−1.01203e7	−	1.85533e7i	−0.0435080	−	0.0797620i
$616$	739278.	−	1.30814e6i	0.00316276	−	0.00559642i
$617$	1.25627e8	+	2.17593e8i	0.534845	+	0.926379i	0.999171	+	0.0407142i	$0.0129633\pi$
$617$	1.25627e8	+	2.17593e8i	0.534845	+	0.926379i	−0.464326	+	0.885664i	$0.653703\pi$
$618$	−1.74490e8	−	2.17121e8i	−0.739272	−	0.919893i
$619$	4.41787e6	−	7.65197e6i	0.0186269	−	0.0322627i	−0.856562	−	0.516045i	$-0.827404\pi$
$619$	4.41787e6	−	7.65197e6i	0.0186269	−	0.0322627i	0.875189	+	0.483782i	$0.160737\pi$
$620$	9.16205e7	+	7.59253e7i	0.384430	+	0.318575i
$621$	−5.60479e7	−	1.15766e8i	−0.234037	−	0.483400i
$622$	2.32654e8	+	8.38713e7i	0.966805	+	0.348532i
$623$	1.25002e7	+	7.21698e6i	0.0516954	+	0.0298464i
$624$	1.58431e8	+	5.98200e7i	0.652060	+	0.246203i
$625$	−6.40952e7	−	1.11016e8i	−0.262534	−	0.454722i
$626$	−3.72746e8	+	6.69054e7i	−1.51946	+	0.272733i
$627$	−1.54278e7	+	8.41546e6i	−0.0625895	+	0.0341409i
$628$	−2.14439e7	−	5.78102e7i	−0.0865816	−	0.233413i
$629$		−	6.43120e7i		−	0.258428i
$630$	−3.12868e6	+	7.51558e6i	−0.0125124	+	0.0300567i
$631$		−	2.47969e8i		−	0.986983i	−0.869751	−	0.493491i	$-0.835720\pi$
$631$		−	2.47969e8i		−	0.986983i	0.869751	−	0.493491i	$-0.164280\pi$
$632$	4.39072e8	−	4.04264e6i	1.73934	−	0.0160145i
$633$	−5.44817e6	+	2.24736e8i	−0.0214803	+	0.886055i
$634$	−7.08308e7	−	3.94615e8i	−0.277942	−	1.54848i
$635$	−2.30446e7	−	3.99144e7i	−0.0900011	−	0.155886i
$636$	−2.68074e7	−	2.33338e7i	−0.104204	−	0.0907012i
$637$	1.55032e8	+	8.95080e7i	0.599797	+	0.346293i
$638$	−2.13892e7	−	7.71076e6i	−0.0823629	−	0.0296917i
$639$	−3.21350e8	+	1.65311e8i	−1.23162	+	0.633578i
$640$	8.07304e7	−	7.07510e7i	0.307962	−	0.269894i
$641$	1.63794e8	−	2.83700e8i	0.621905	−	1.07717i	−0.367225	−	0.930132i	$-0.619692\pi$
$641$	1.63794e8	−	2.83700e8i	0.621905	−	1.07717i	0.989131	−	0.147039i	$-0.0469744\pi$
$642$	−6.34922e7	−	4.10746e8i	−0.239947	−	1.55227i
$643$	8.41297e6	+	1.45717e7i	0.0316458	+	0.0548122i	0.881415	−	0.472343i	$-0.156592\pi$
$643$	8.41297e6	+	1.45717e7i	0.0316458	+	0.0548122i	−0.849769	+	0.527156i	$0.823258\pi$
$644$	1.91147e6	−	1.12436e7i	0.00715665	−	0.0420967i
$645$	8.12990e6	−	1.33248e7i	0.0302974	−	0.0496571i
$646$	−6.79116e7	−	8.04313e7i	−0.251911	−	0.298351i
$647$		−	2.54824e8i		−	0.940867i	−0.882436	−	0.470433i	$-0.844098\pi$
$647$		−	2.54824e8i		−	0.940867i	0.882436	−	0.470433i	$-0.155902\pi$
$648$	−2.38444e7	+	2.71051e8i	−0.0876319	+	0.996153i
$649$	−6.41008e6			−0.0234493
$650$	−1.21727e8	+	1.02780e8i	−0.443250	+	0.374255i
$651$	−2.28308e7	−	1.39298e7i	−0.0827520	−	0.0504897i
$652$	3.91669e7	−	2.30387e8i	0.141311	−	0.831219i
$653$	−3.58115e7	+	2.06758e7i	−0.128612	+	0.0742544i	−0.562926	−	0.826507i	$-0.690324\pi$
$653$	−3.58115e7	+	2.06758e7i	−0.128612	+	0.0742544i	0.434313	+	0.900762i	$0.356991\pi$
$654$	−3.99699e8	+	6.17847e7i	−1.42889	+	0.220876i
$655$	−7.51967e7	−	4.34149e7i	−0.267593	−	0.154495i
$656$	−1.16330e7	−	6.15462e7i	−0.0412079	−	0.218017i
$657$	−1.82945e8	−	3.55628e8i	−0.645095	−	1.25401i
$658$	4.25000e6	−	1.17892e7i	0.0149180	−	0.0413816i
$659$	6.46411e6	−	1.11962e7i	0.0225867	−	0.0391213i	−0.854511	−	0.519433i	$-0.826143\pi$
$659$	6.46411e6	−	1.11962e7i	0.0225867	−	0.0391213i	0.877098	+	0.480312i	$0.159476\pi$
$660$	−7.17971e6	−	6.24938e6i	−0.0249733	−	0.0217373i
$661$	3.77950e8	−	2.18209e8i	1.30867	−	0.755560i	0.326795	−	0.945095i	$-0.394031\pi$
$661$	3.77950e8	−	2.18209e8i	1.30867	−	0.755560i	0.981874	+	0.189535i	$0.0606981\pi$
$662$	−4.51106e8	+	8.09704e7i	−1.55491	+	0.279095i
$663$	8.99226e7	+	2.17996e6i	0.308552	+	0.00748010i
$664$	−2.87637e6	−	3.12402e8i	−0.00982517	−	1.06711i
$665$	8.44263e6			0.0287087
$666$	1.59159e8	+	6.62566e7i	0.538775	+	0.224288i
$667$	−1.72576e8			−0.581571
$668$	4.46269e7	+	1.20309e8i	0.149716	+	0.403615i
$669$	1.73402e8	+	3.17893e8i	0.579129	+	1.06170i
$670$	−2.39280e7	−	1.33309e8i	−0.0795578	−	0.443236i
$671$	−5.64178e6	+	3.25728e6i	−0.0186745	+	0.0107817i
$672$	−1.56725e7	+	1.83439e7i	−0.0516452	+	0.0604484i
$673$	1.01506e8	−	1.75814e8i	0.333003	−	0.576779i	−0.650096	−	0.759852i	$-0.725271\pi$
$673$	1.01506e8	−	1.75814e8i	0.333003	−	0.576779i	0.983099	+	0.183073i	$0.0586046\pi$
$674$	6.96595e7	−	1.93231e8i	0.227510	−	0.631098i
$675$	−2.11798e8	−	1.43755e8i	−0.688669	−	0.467425i
$676$	−1.22307e8	−	1.01355e8i	−0.395923	−	0.328099i
$677$	−5.79528e6	−	3.34591e6i	−0.0186771	−	0.0107832i	0.490632	−	0.871367i	$-0.336766\pi$
$677$	−5.79528e6	−	3.34591e6i	−0.0186771	−	0.0107832i	−0.509309	+	0.860583i	$0.670099\pi$
$678$	2.06722e8	−	1.66133e8i	0.663283	−	0.533047i
$679$	−9.16939e6	+	5.29395e6i	−0.0292908	+	0.0169111i
$680$	2.80524e7	−	4.96380e7i	0.0892160	−	0.157866i
$681$	−1.50761e8	+	8.22359e7i	−0.477361	+	0.260388i
$682$	2.38933e7	−	2.01741e7i	0.0753222	−	0.0635978i
$683$	4.64772e8			1.45874			0.729370	−	0.684119i	$-0.239813\pi$
$683$	4.64772e8			1.45874			0.729370	+	0.684119i	$0.239813\pi$
$684$	2.69016e8	−	8.52036e7i	0.840638	−	0.266250i
$685$			1.35893e8i			0.422792i
$686$	−3.90985e7	+	3.30126e7i	−0.121112	+	0.102260i
$687$	−2.73029e8	−	6.61892e6i	−0.842050	−	0.0204135i
$688$	3.50707e7	−	3.01692e7i	0.107691	−	0.0926399i
$689$	−1.57472e7	−	2.72749e7i	−0.0481443	−	0.0833884i
$690$	−6.73528e7	−	2.61418e7i	−0.205026	−	0.0795772i
$691$	−1.94299e8	+	3.36535e8i	−0.588892	+	1.01999i	0.405486	+	0.914101i	$0.367102\pi$
$691$	−1.94299e8	+	3.36535e8i	−0.588892	+	1.01999i	−0.994378	+	0.105889i	$0.966231\pi$
$692$	1.43271e8	−	1.72887e8i	0.432354	−	0.521729i
$693$	1.79878e6	+	1.15823e6i	0.00540478	+	0.00348013i
$694$	1.84020e8	−	5.10460e8i	0.550538	−	1.52716i
$695$	−1.53171e8	−	8.84335e7i	−0.456271	−	0.263428i
$696$	3.13395e8	+	1.87275e8i	0.929531	+	0.555459i
$697$	−1.66344e7	−	2.88117e7i	−0.0491258	−	0.0850884i
$698$	1.04242e8	+	5.80759e8i	0.306533	+	1.70777i
$699$	−1.80241e8	−	1.09971e8i	−0.527741	−	0.321992i
$700$	−7.89387e6	−	2.12809e7i	−0.0230142	−	0.0620434i
$701$			4.46343e8i			1.29573i	0.761755	+	0.647865i	$0.224338\pi$
$701$			4.46343e8i			1.29573i	−0.761755	+	0.647865i	$0.775662\pi$
$702$	−9.80365e7	+	2.20294e8i	−0.283385	+	0.636782i
$703$		−	1.78791e8i		−	0.514611i
$704$	−1.45528e7	−	2.41673e7i	−0.0417088	−	0.0692643i
$705$	−6.77691e7	−	4.13481e7i	−0.193403	−	0.118002i
$706$	2.71157e8	−	4.86708e7i	0.770560	−	0.138310i
$707$	−2.51018e7	−	4.34776e7i	−0.0710308	−	0.123029i
$708$	1.01024e8	+	1.97049e7i	0.284660	+	0.0555233i
$709$	3.41563e8	+	1.97202e8i	0.958369	+	0.553314i	0.895671	−	0.444718i	$-0.146696\pi$
$709$	3.41563e8	+	1.97202e8i	0.958369	+	0.553314i	0.0626982	+	0.998033i	$0.480029\pi$
$710$	−6.88415e7	+	1.90962e8i	−0.192343	+	0.533546i
$711$	−3.02946e7	+	6.24455e8i	−0.0842863	+	1.73737i
$712$	2.33431e8	−	1.37652e8i	0.646723	−	0.381367i
$713$	1.18678e8	−	2.05556e8i	0.327417	−	0.567102i
$714$	−4.63696e6	+	1.19468e7i	−0.0127391	+	0.0328214i
$715$	−4.21750e6	−	7.30493e6i	−0.0115382	−	0.0199847i
$716$	−2.80308e7	+	1.64882e8i	−0.0763653	+	0.449195i
$717$	−5.16143e8	−	1.25126e7i	−1.40027	−	0.0339462i
$718$	4.99437e8	−	4.21696e8i	1.34930	−	1.13927i
$719$		−	4.54243e8i		−	1.22209i	−0.791598	−	0.611043i	$-0.790750\pi$
$719$		−	4.54243e8i		−	1.22209i	0.791598	−	0.611043i	$-0.209250\pi$
$720$	9.39430e7	+	1.20563e8i	0.251691	+	0.323009i
$721$	3.51674e7			0.0938283
$722$	5.40098e7	+	6.39666e7i	0.143503	+	0.169958i
$723$	−3.17134e8	+	1.72988e8i	−0.839126	+	0.457721i
$724$	−1.28645e8	−	2.18703e7i	−0.338982	−	0.0576286i
$725$	−2.97441e8	+	1.71728e8i	−0.780526	+	0.450637i
$726$	2.96323e8	−	2.38140e8i	0.774383	−	0.622333i
$727$	2.61670e7	+	1.51075e7i	0.0681006	+	0.0393179i	0.533664	−	0.845697i	$-0.320815\pi$
$727$	2.61670e7	+	1.51075e7i	0.0681006	+	0.0393179i	−0.465563	+	0.885015i	$0.654148\pi$
$728$	−1.84171e7	+	1.08604e7i	−0.0477338	+	0.0281483i
$729$	−3.83331e8	−	5.61431e7i	−0.989444	−	0.144915i
$730$	−2.11331e8	−	7.61846e7i	−0.543245	−	0.195839i
$731$	1.22859e7	−	2.12797e7i	0.0314524	−	0.0544771i
$732$	9.89289e7	−	3.39924e7i	0.252226	−	0.0866660i
$733$	6.54391e8	−	3.77813e8i	1.66160	−	0.959323i	0.689644	−	0.724149i	$-0.257767\pi$
$733$	6.54391e8	−	3.77813e8i	1.66160	−	0.959323i	0.971953	−	0.235175i	$-0.0755663\pi$
$734$	−1.05781e8	−	5.89329e8i	−0.267496	−	1.49029i
$735$	7.73687e7	+	1.41838e8i	0.194851	+	0.357215i
$736$	−1.66122e8	−	1.35104e8i	−0.416672	−	0.338871i
$737$	−3.55937e7			−0.0889141
$738$	8.84403e7	−	1.14839e7i	0.220030	−	0.0285706i
$739$	−6.65319e8			−1.64853			−0.824264	−	0.566205i	$-0.808411\pi$
$739$	−6.65319e8			−1.64853			−0.824264	+	0.566205i	$0.808411\pi$
$740$	9.07942e7	−	3.36789e7i	0.224059	−	0.0831119i
$741$	2.49990e8	+	6.06040e6i	0.614423	+	0.0148952i
$742$	4.41646e6	−	792724.i	0.0108109	−	0.00194049i
$743$	1.08727e8	−	6.27737e7i	0.265077	−	0.153042i	−0.361571	−	0.932344i	$-0.617760\pi$
$743$	1.08727e8	−	6.27737e7i	0.265077	−	0.153042i	0.626648	+	0.779302i	$0.284426\pi$
$744$	−4.38580e8	+	2.44500e8i	−1.06495	+	0.593690i
$745$	−1.39164e8	+	2.41039e8i	−0.336557	+	0.582933i
$746$	5.24394e8	+	1.89043e8i	1.26311	+	0.455349i
$747$	4.44304e8	+	2.15548e7i	1.06590	+	0.0517110i
$748$	−1.15373e7	−	9.56089e6i	−0.0275676	−	0.0228451i
$749$	4.54436e7	+	2.62369e7i	0.108150	+	0.0624405i
$750$	−3.12825e8	+	4.83558e7i	−0.741511	+	0.114621i
$751$	−5.22936e8	+	3.01917e8i	−1.23461	+	0.712800i	−0.967987	−	0.251002i	$-0.919240\pi$
$751$	−5.22936e8	+	3.01917e8i	−1.23461	+	0.712800i	−0.266619	+	0.963802i	$0.585907\pi$
$752$	−1.53438e8	−	1.78367e8i	−0.360812	−	0.419433i
$753$	−6.37343e7	−	3.88864e7i	−0.149275	−	0.0910777i
$754$	2.08718e8	+	2.47196e8i	0.486908	+	0.576671i
$755$	−2.60109e8			−0.604386
$756$	−2.47887e7	−	2.37836e7i	−0.0573705	−	0.0550442i
$757$			8.22632e8i			1.89635i	0.317753	+	0.948174i	$0.397072\pi$
$757$			8.22632e8i			1.89635i	−0.317753	+	0.948174i	$0.602928\pi$
$758$	1.02076e8	+	1.20894e8i	0.234378	+	0.277586i
$759$	−9.88918e6	+	1.62083e7i	−0.0226170	+	0.0370690i
$760$	7.79871e7	−	1.37996e8i	0.177657	−	0.314360i
$761$	1.04209e8	+	1.80495e8i	0.236457	+	0.409555i	0.959695	−	0.281044i	$-0.0906805\pi$
$761$	1.04209e8	+	1.80495e8i	0.236457	+	0.409555i	−0.723238	+	0.690598i	$0.757347\pi$
$762$	1.92208e8	−	2.97110e7i	0.434416	−	0.0671511i
$763$	2.55313e7	−	4.42215e7i	0.0574776	−	0.0995542i
$764$	2.65322e8	−	3.20169e8i	0.594967	−	0.717958i
$765$	6.82557e7	+	4.39498e7i	0.152460	+	0.0981686i
$766$	2.05020e8	+	7.39093e7i	0.456152	+	0.164442i
$767$	7.89912e7	+	4.56056e7i	0.175062	+	0.101072i
$768$	1.55064e8	+	4.25618e8i	0.342315	+	0.939585i
$769$	−1.98853e8	−	3.44424e8i	−0.437274	−	0.757381i	0.560204	−	0.828355i	$-0.310723\pi$
$769$	−1.98853e8	−	3.44424e8i	−0.437274	−	0.757381i	−0.997478	+	0.0709736i	$0.977389\pi$
$770$	1.18284e6	−	212312.i	0.00259092	−	0.000465053i
$771$	−3.29598e6	+	1.35958e8i	−0.00719153	+	0.296648i
$772$	−5.81004e8	+	2.15516e8i	−1.26278	+	0.468411i
$773$			7.20951e7i			0.156087i	0.996950	+	0.0780436i	$0.0248673\pi$
$773$			7.20951e7i			0.156087i	−0.996950	+	0.0780436i	$0.975133\pi$
$774$	4.00055e7	+	5.23281e7i	0.0862774	+	0.112853i
$775$		−	4.72378e8i		−	1.01481i
$776$	1.83019e6	+	1.98777e8i	0.00391662	+	0.425384i
$777$	−1.91080e7	+	1.04229e7i	−0.0407336	+	0.0222191i
$778$	6.64027e7	+	3.69946e8i	0.141009	+	0.785596i
$779$	−4.62447e7	−	8.00981e7i	−0.0978249	−	0.169438i
$780$	4.40131e7	+	1.28092e8i	0.0927466	+	0.269923i
$781$	4.61995e7	+	2.66733e7i	0.0969804	+	0.0559917i
$782$	−1.06992e8	−	3.85705e7i	−0.223734	−	0.0806556i
$783$	−2.91929e8	+	4.30106e8i	−0.608123	+	0.895963i
$784$	8.89330e7	+	4.70513e8i	0.184550	+	0.976391i
$785$	2.46571e7	−	4.27074e7i	0.0509722	−	0.0882865i
$786$	2.85609e8	−	2.29530e8i	0.588172	−	0.472684i
$787$	2.08093e8	+	3.60428e8i	0.426908	+	0.739426i	0.996596	−	0.0824346i	$-0.0262696\pi$
$787$	2.08093e8	+	3.60428e8i	0.426908	+	0.739426i	−0.569689	+	0.821861i	$0.692936\pi$
$788$	3.87604e8	+	6.58946e7i	0.792154	+	0.134670i
$789$	−2.67540e8	−	4.90473e8i	−0.544700	−	0.998582i
$790$	2.26558e8	+	2.68325e8i	0.459514	+	0.544226i
$791$			3.34830e7i			0.0676543i
$792$	3.55474e7	−	1.87024e7i	0.0715537	−	0.0376463i
$793$	9.26980e7			0.185888
$794$	−2.85449e8	+	2.41016e8i	−0.570251	+	0.481488i
$795$	688882.	−	2.84162e7i	0.00137102	−	0.0565542i
$796$	−2.77102e8	−	4.71088e7i	−0.549416	−	0.0934034i
$797$	−5.30088e8	+	3.06046e8i	−1.04706	+	0.604522i	−0.921826	−	0.387605i	$-0.873303\pi$
$797$	−5.30088e8	+	3.06046e8i	−1.04706	+	0.604522i	−0.125238	+	0.992127i	$0.539969\pi$
$798$	−1.28910e7	+	3.32128e7i	−0.0253675	+	0.0653578i
$799$	−1.08227e8	−	6.24851e7i	−0.212176	−	0.122500i
$800$	−4.20758e8	−	6.75512e7i	−0.821793	−	0.131936i
$801$	1.76506e8	+	3.43112e8i	0.343449	+	0.667633i
$802$	−9.05179e7	+	2.51091e8i	−0.175473	+	0.486752i
$803$	−2.95185e7	+	5.11275e7i	−0.0570095	+	0.0987433i
$804$	5.60965e8	+	1.09417e8i	1.07936	+	0.210531i
$805$	7.89948e6	−	4.56077e6i	0.0151430	−	0.00874279i
$806$	−4.37969e8	+	7.86124e7i	−0.836446	+	0.150136i
$807$	7.47152e7	−	1.22457e8i	0.142163	−	0.233004i
$808$	−9.42522e8	+	8.67803e6i	−1.78672	+	0.0164508i
$809$	1.53184e8			0.289313			0.144657	−	0.989482i	$-0.453792\pi$
$809$	1.53184e8			0.289313			0.144657	+	0.989482i	$0.453792\pi$
$810$	−1.79086e8	+	1.23640e8i	−0.336982	+	0.232650i
$811$	3.89278e8			0.729788			0.364894	−	0.931049i	$-0.381105\pi$
$811$	3.89278e8			0.729788			0.364894	+	0.931049i	$0.381105\pi$
$812$	−4.32159e7	+	1.60304e7i	−0.0807189	+	0.0299416i
$813$	2.51763e8	−	4.12637e8i	0.468512	−	0.767886i
$814$	−4.49617e6	−	2.50492e7i	−0.00833622	−	0.0464431i
$815$	1.61864e8	−	9.34522e7i	0.299004	−	0.172630i
$816$	1.52440e8	+	1.86148e8i	0.280562	+	0.342601i
$817$	3.41554e7	−	5.91588e7i	0.0626315	−	0.108481i
$818$	−8.06101e7	+	2.23607e8i	−0.147275	+	0.408532i
$819$	−1.39259e7	−	2.70706e7i	−0.0253496	−	0.0492772i
$820$	3.19646e7	−	3.85723e7i	0.0579732	−	0.0699574i
$821$	−2.07173e8	−	1.19611e8i	−0.374372	−	0.216144i	0.300995	−	0.953626i	$-0.402681\pi$
$821$	−2.07173e8	−	1.19611e8i	−0.374372	−	0.216144i	−0.675367	+	0.737482i	$0.736015\pi$
$822$	−5.34597e8	−	2.07495e8i	−0.962522	−	0.373587i
$823$	−8.73327e8	+	5.04216e8i	−1.56667	+	0.904517i	−0.570116	+	0.821564i	$0.693102\pi$
$823$	−8.73327e8	+	5.04216e8i	−1.56667	+	0.904517i	−0.996553	+	0.0829529i	$0.973565\pi$
$824$	3.24851e8	−	5.74817e8i	0.580635	−	1.02742i
$825$	−915792.	+	3.77762e7i	−0.00163093	+	0.0672754i
$826$	−9.92904e6	+	8.38352e6i	−0.0176184	+	0.0148760i
$827$	−7.94548e7			−0.140476			−0.0702382	−	0.997530i	$-0.522376\pi$
$827$	−7.94548e7			−0.140476			−0.0702382	+	0.997530i	$0.522376\pi$
$828$	2.05681e8	−	2.25046e8i	0.362329	−	0.396443i
$829$		−	1.65239e8i		−	0.290034i	−0.989429	−	0.145017i	$-0.953676\pi$
$829$		−	1.65239e8i		−	0.290034i	0.989429	−	0.145017i	$-0.0463237\pi$
$830$	1.90915e8	−	1.61198e8i	0.333892	−	0.281919i
$831$	4.98724e7	+	9.14297e7i	0.0869076	+	0.159325i
$832$	7.39130e6	+	4.01351e8i	0.0128337	+	0.696874i
$833$	1.27168e8	+	2.20262e8i	0.220011	+	0.381070i
$834$	5.81768e8	−	4.67538e8i	1.00289	−	0.805971i
$835$	−5.13139e7	+	8.88783e7i	−0.0881405	+	0.152664i
$836$	−3.20744e7	−	2.65798e7i	−0.0548958	−	0.0454918i
$837$	−3.11546e8	−	6.43494e8i	−0.531307	−	1.09741i
$838$	−2.97360e6	+	8.24858e6i	−0.00505302	+	0.0140167i
$839$	4.51925e8	+	2.60919e8i	0.765210	+	0.441794i	0.831163	−	0.556028i	$-0.187675\pi$
$839$	4.51925e8	+	2.60919e8i	0.765210	+	0.441794i	−0.0659531	+	0.997823i	$0.521009\pi$
$840$	−1.92945e7	−	290035.i	−0.0325534	−	0.000489343i
$841$	5.13223e7	+	8.88928e7i	0.0862816	+	0.149444i
$842$	2.04448e8	+	1.13903e9i	0.342489	+	1.90809i
$843$	8.84257e8	−	4.82338e8i	1.47603	−	0.805135i
$844$	−4.99599e8	+	1.85320e8i	−0.830987	+	0.308244i
$845$		−	1.27042e8i		−	0.210561i
$846$	2.66137e8	−	2.03465e8i	0.439536	−	0.336031i
$847$			4.79957e7i			0.0789864i
$848$	2.78389e7	−	7.95105e7i	0.0456526	−	0.130388i
$849$	4.90092e6	−	2.02162e8i	0.00800857	−	0.330351i
$850$	−2.22786e8	+	3.99885e7i	−0.362770	+	0.0651147i
$851$	−9.65840e7	−	1.67288e8i	−0.156717	−	0.271442i
$852$	−6.46119e8	−	5.62397e8i	−1.04471	−	0.909336i
$853$	−3.57290e8	−	2.06281e8i	−0.575670	−	0.332363i	0.183741	−	0.982975i	$-0.441179\pi$
$853$	−3.57290e8	−	2.06281e8i	−0.575670	−	0.332363i	−0.759411	+	0.650612i	$0.774513\pi$
$854$	−4.47888e6	+	1.24241e7i	−0.00719111	+	0.0199477i
$855$	1.89755e8	+	1.22183e8i	0.303595	+	0.195484i
$856$	8.48622e8	−	5.00426e8i	1.35298	−	0.797844i
$857$	−3.59237e8	+	6.22216e8i	−0.570740	+	0.988550i	0.425750	+	0.904841i	$0.360010\pi$
$857$	−3.59237e8	+	6.22216e8i	−0.570740	+	0.988550i	−0.996490	+	0.0837096i	$0.973323\pi$
$858$	3.51768e7	−	5.43756e6i	0.0556923	−	0.00860880i
$859$	6.88024e7	+	1.19169e8i	0.108549	+	0.188012i	0.915182	−	0.403040i	$-0.132046\pi$
$859$	6.88024e7	+	1.19169e8i	0.108549	+	0.188012i	−0.806634	+	0.591051i	$0.798713\pi$
$860$	3.64761e7	+	6.20112e6i	0.0573473	+	0.00974933i
$861$	−5.86446e6	+	9.61178e6i	−0.00918795	+	0.0150589i
$862$	7.60258e8	−	6.41918e8i	1.18697	−	1.00221i
$863$			3.76010e7i			0.0585015i	0.999572	+	0.0292508i	$0.00931213\pi$
$863$			3.76010e7i			0.0585015i	−0.999572	+	0.0292508i	$0.990688\pi$
$864$	−6.17727e8	+	1.85480e8i	−0.957757	+	0.287578i
$865$	1.79581e8			0.277468
$866$	−7.32731e7	−	8.67812e7i	−0.112821	−	0.133620i
$867$	−4.47246e8	−	2.72879e8i	−0.686260	−	0.418710i
$868$	1.06250e7	−	6.24984e7i	0.0162469	−	0.0955675i
$869$	7.99259e7	−	4.61453e7i	0.121795	−	0.0703182i
$870$	4.46057e7	+	2.88565e8i	0.0677380	+	0.438213i
$871$	4.38620e8	+	2.53238e8i	0.663795	+	0.383242i
$872$	−4.86968e8	−	8.25800e8i	−0.734430	−	1.24545i
$873$	−2.82704e8	−	1.37150e7i	−0.424903	−	0.0206136i
$874$	−2.97444e8	−	1.07228e8i	−0.445523	−	0.160611i
$875$	1.99821e7	−	3.46100e7i	0.0298275	−	0.0516627i
$876$	6.22386e8	−	7.15039e8i	0.925865	−	1.06370i
$877$	−4.53514e8	+	2.61836e8i	−0.672345	+	0.388178i	−0.796964	−	0.604026i	$-0.793562\pi$
$877$	−4.53514e8	+	2.61836e8i	−0.672345	+	0.388178i	0.124620	+	0.992205i	$0.460229\pi$
$878$	−1.22995e8	−	6.85233e8i	−0.181720	−	1.01241i
$879$	1.13706e9	+	2.75652e7i	1.67423	+	0.0405878i
$880$	7.45599e6	−	2.12950e7i	0.0109410	−	0.0312485i
$881$	−6.85895e8			−1.00307			−0.501534	−	0.865138i	$-0.667231\pi$
$881$	−6.85895e8			−1.00307			−0.501534	+	0.865138i	$0.667231\pi$
$882$	−6.76116e8	+	8.77928e7i	−0.985406	+	0.127954i
$883$	9.09790e7			0.132148			0.0660738	−	0.997815i	$-0.478953\pi$
$883$	9.09790e7			0.132148			0.0660738	+	0.997815i	$0.478953\pi$
$884$	7.41513e7	+	1.99903e8i	0.107340	+	0.289376i
$885$	3.94204e7	+	7.22684e7i	0.0568711	+	0.104260i
$886$	−3.86646e8	+	6.94002e7i	−0.555920	+	0.0997837i
$887$	9.70116e8	−	5.60097e8i	1.39012	−	0.802587i	0.396794	−	0.917908i	$-0.370123\pi$
$887$	9.70116e8	−	5.60097e8i	1.39012	−	0.802587i	0.993328	+	0.115321i	$0.0367896\pi$
$888$	−6.14212e6	+	4.08603e8i	−0.00877162	+	0.583530i
$889$	−1.22775e7	+	2.12652e7i	−0.0174745	+	0.0302667i
$890$	2.03894e8	+	7.35034e7i	0.289224	+	0.104265i
$891$	2.36669e7	+	5.20643e7i	0.0334586	+	0.0736050i
$892$	−5.47682e8	+	6.60898e8i	−0.771674	+	0.931193i
$893$	−3.00878e8	−	1.73712e8i	−0.422509	−	0.243936i
$894$	−7.35745e8	−	9.15504e8i	−1.02971	−	1.28129i
$895$	−1.15842e8	+	6.68814e7i	−0.161583	+	0.0932902i
$896$	−5.41494e7	−	1.84014e7i	−0.0752783	−	0.0255815i
$897$	2.37181e8	−	1.29376e8i	0.328626	−	0.179257i
$898$	8.97288e8	+	1.06271e9i	1.23909	+	1.46752i
$899$	−9.59275e8			−1.32027
$900$	1.30559e8	−	5.92546e8i	0.179093	−	0.812820i
$901$		−	4.47455e7i		−	0.0611752i
$902$	−8.49332e6	−	1.00591e7i	−0.0115733	−	0.0137069i
$903$	−8.31366e6	−	201545.i	−0.0112909	−	0.000273721i
$904$	5.47286e8	+	3.09293e8i	0.740814	+	0.418663i
$905$	−5.21824e7	−	9.03826e7i	−0.0704009	−	0.121938i
$906$	3.97159e8	−	1.02325e9i	0.534047	−	1.37594i
$907$	6.66041e8	−	1.15362e9i	0.892646	−	1.54611i	0.0559542	−	0.998433i	$-0.482180\pi$
$907$	6.66041e8	−	1.15362e9i	0.892646	−	1.54611i	0.836692	−	0.547674i	$-0.184487\pi$
$908$	−3.13431e8	−	2.59738e8i	−0.418682	−	0.346959i
$909$	6.50312e7	−	1.34047e9i	0.0865825	−	1.78470i
$910$	−1.60867e7	−	5.79922e6i	−0.0213473	−	0.00769565i
$911$	8.13615e8	+	4.69741e8i	1.07613	+	0.621302i	0.929849	−	0.367941i	$-0.119937\pi$
$911$	8.13615e8	+	4.69741e8i	1.07613	+	0.621302i	0.146278	+	0.989243i	$0.453271\pi$
$912$	4.23792e8	+	5.17502e8i	0.558686	+	0.682225i
$913$	−3.28326e7	−	5.68678e7i	−0.0431413	−	0.0747230i
$914$	5.31364e8	−	9.53761e7i	0.695910	−	0.124911i
$915$	7.14188e7	+	4.35750e7i	0.0932287	+	0.0568818i
$916$	−2.25143e8	−	6.06958e8i	−0.292936	−	0.789718i
$917$			4.62603e7i			0.0599930i
$918$	−2.77115e8	+	2.01407e8i	−0.358206	+	0.260344i
$919$		−	2.11931e8i		−	0.273054i	−0.990636	−	0.136527i	$-0.956406\pi$
$919$		−	2.11931e8i		−	0.273054i	0.990636	−	0.136527i	$-0.0435940\pi$
$920$	−1.57672e6	−	1.71248e8i	−0.00202484	−	0.219918i
$921$	−1.70630e7	−	1.04107e7i	−0.0218412	−	0.0133260i
$922$	1.08971e8	+	6.07103e8i	0.139033	+	0.774586i
$923$	−3.79543e8	−	6.57388e8i	−0.482677	−	0.836020i
$924$	−970851.	+	4.97741e6i	−0.00123066	+	0.00630939i
$925$	−3.32933e8	−	1.92219e8i	−0.420660	−	0.242868i
$926$	−6.27919e6	−	2.26364e6i	−0.00790807	−	0.00285085i
$927$	7.90414e8	+	5.08947e8i	0.992237	+	0.638900i
$928$	−1.37179e8	+	8.54449e8i	−0.171649	+	1.06916i
$929$	−2.48784e8	+	4.30907e8i	−0.310295	+	0.537447i	−0.978426	−	0.206596i	$-0.933761\pi$
$929$	−2.48784e8	+	4.30907e8i	−0.310295	+	0.537447i	0.668131	+	0.744044i	$0.267095\pi$
$930$	−3.74385e8	−	1.45311e8i	−0.465446	−	0.180655i
$931$	3.53535e8	+	6.12341e8i	0.438110	+	0.758829i
$932$	8.38807e7	−	4.93401e8i	0.103613	−	0.609470i
$933$	−8.34426e8	−	2.02286e7i	−1.02741	−	0.0249070i
$934$	7.53668e8	+	8.92609e8i	0.924995	+	1.09552i
$935$		−	1.19840e7i		−	0.0146611i
$936$	−5.71111e8	−	2.24383e7i	−0.696455	−	0.0273629i
$937$	5.16666e8			0.628045			0.314023	−	0.949416i	$-0.398323\pi$
$937$	5.16666e8			0.628045			0.314023	+	0.949416i	$0.398323\pi$
$938$	−5.51337e7	+	4.65518e7i	−0.0668050	+	0.0564063i
$939$	1.12205e9	−	6.12048e8i	1.35524	−	0.739246i
$940$	3.15385e7	−	1.85515e8i	0.0379714	−	0.223355i
$941$	−4.18866e8	+	2.41833e8i	−0.502697	+	0.290232i	−0.729827	−	0.683632i	$-0.760399\pi$
$941$	−4.18866e8	+	2.41833e8i	−0.502697	+	0.290232i	0.227129	+	0.973865i	$0.427066\pi$
$942$	1.30360e8	+	1.62209e8i	0.155952	+	0.194054i
$943$	−8.65391e7	−	4.99634e7i	−0.103199	−	0.0595822i
$944$	4.53126e7	+	2.39733e8i	0.0538645	+	0.284978i
$945$	1.99606e6	−	2.74026e7i	0.00236526	−	0.0324711i
$946$	3.29758e6	−	9.14729e6i	0.00389513	−	0.0108049i
$947$	−3.40556e8	+	5.89861e8i	−0.400995	+	0.694543i	−0.993846	−	0.110768i	$-0.964669\pi$
$947$	−3.40556e8	+	5.89861e8i	−0.400995	+	0.694543i	0.592851	+	0.805312i	$0.298002\pi$
$948$	−1.40150e9	+	4.81563e8i	−1.64501	+	0.565234i
$949$	7.27510e8	−	4.20028e8i	0.851217	−	0.491451i
$950$	−6.19357e8	+	1.11170e8i	−0.722388	+	0.129664i
$951$	6.47957e8	+	1.18788e9i	0.753364	+	1.38112i
$952$	−3.03754e7	+	279673.i	−0.0352055	+	0.000324146i
$953$	7.34562e7			0.0848691			0.0424346	−	0.999099i	$-0.486489\pi$
$953$	7.34562e7			0.0848691			0.0424346	+	0.999099i	$0.486489\pi$
$954$	1.10736e8	+	4.60985e7i	0.127539	+	0.0530936i
$955$	3.32565e8			0.381827
$956$	−4.25618e8	−	1.14741e9i	−0.487132	−	1.31325i
$957$	7.67134e7	+	1.85973e6i	0.0875257	+	0.00212185i
$958$	1.24980e8	+	6.96294e8i	0.142149	+	0.791947i
$959$	6.27002e7	−	3.62000e7i	0.0710908	−	0.0410443i
$960$	−1.82970e8	+	3.12694e8i	−0.206807	+	0.353431i
$961$	2.15927e8	−	3.73996e8i	0.243297	−	0.421402i
$962$	−1.22811e8	+	3.40670e8i	−0.137947	+	0.382656i
$963$	6.41676e8	+	1.24736e9i	0.718517	+	1.39673i
$964$	−6.59319e8	−	5.46374e8i	−0.735978	−	0.609900i
$965$	−4.29218e8	−	2.47809e8i	−0.477635	−	0.275763i
$966$	5.88013e6	+	3.80399e7i	0.00652312	+	0.0421996i
$967$	−4.70223e8	+	2.71484e8i	−0.520026	+	0.300237i	−0.736945	−	0.675953i	$-0.763732\pi$
$967$	−4.70223e8	+	2.71484e8i	−0.520026	+	0.300237i	0.216920	+	0.976189i	$0.430399\pi$
$968$	7.84499e8	+	4.43351e8i	0.864901	+	0.488789i
$969$	3.03283e8	+	1.85043e8i	0.333332	+	0.203377i
$970$	−1.21476e8	+	1.02568e8i	−0.133100	+	0.112382i
$971$	8.13223e8			0.888285			0.444142	−	0.895956i	$-0.353508\pi$
$971$	8.13223e8			0.888285			0.444142	+	0.895956i	$0.353508\pi$
$972$	−2.12947e8	−	8.93299e8i	−0.231885	−	0.972743i
$973$			9.42295e7i			0.102294i
$974$	2.49767e8	−	2.10889e8i	0.270308	−	0.228232i
$975$	2.80050e8	−	4.58999e8i	0.302150	−	0.495220i
$976$	1.61702e8	+	1.87974e8i	0.173927	+	0.202184i
$977$	8.69795e7	+	1.50653e8i	0.0932681	+	0.161545i	0.908884	−	0.417048i	$-0.136935\pi$
$977$	8.69795e7	+	1.50653e8i	0.0932681	+	0.161545i	−0.815616	+	0.578593i	$0.803602\pi$
$978$	1.20487e8	+	7.79455e8i	0.128802	+	0.833249i
$979$	2.84796e7	−	4.93281e7i	0.0303519	−	0.0525710i
$980$	−2.44365e8	+	2.94880e8i	−0.259634	+	0.313305i
$981$	1.21381e9	−	6.24420e8i	1.28572	−	0.661408i
$982$	−2.15574e7	+	5.97988e7i	−0.0227647	+	0.0631478i
$983$	−3.58394e8	−	2.06919e8i	−0.377311	−	0.217841i	0.299337	−	0.954148i	$-0.403235\pi$
$983$	−3.58394e8	−	2.06919e8i	−0.377311	−	0.217841i	−0.676648	+	0.736307i	$0.736568\pi$
$984$	1.02935e8	+	1.84643e8i	0.108038	+	0.193797i
$985$	1.57224e8	+	2.72321e8i	0.164517	+	0.284952i
$986$	8.12062e7	+	4.52419e8i	0.0847146	+	0.471966i
$987$	−1.02504e6	+	4.22827e7i	−0.00106608	+	0.0439755i
$988$	2.06145e8	+	5.55741e8i	0.213748	+	0.576237i
$989$		−	7.38038e7i		−	0.0762939i
$990$	2.96579e7	+	1.23464e7i	0.0305658	+	0.0127243i
$991$		−	1.53139e9i		−	1.57349i	−0.617277	−	0.786746i	$-0.711764\pi$
$991$		−	1.53139e9i		−	1.57349i	0.617277	−	0.786746i	$-0.288236\pi$
$992$	−9.23402e8	−	7.50985e8i	−0.945923	−	0.769301i
$993$	1.35793e9	−	7.40714e8i	1.38685	−	0.756490i
$994$	1.06447e8	−	1.91065e7i	0.108386	−	0.0194546i
$995$	−1.12401e8	−	1.94685e8i	−0.114104	−	0.197635i
$996$	3.42635e8	+	9.97179e8i	0.346780	+	1.00924i
$997$	−8.38081e8	−	4.83866e8i	−0.845669	−	0.488248i	0.0135179	−	0.999909i	$-0.495697\pi$
$997$	−8.38081e8	−	4.83866e8i	−0.845669	−	0.488248i	−0.859187	+	0.511661i	$0.829030\pi$
$998$	−6.52098e7	+	1.80888e8i	−0.0656026	+	0.181977i
$999$	−5.80309e8	−	4.22709e7i	−0.582054	−	0.0423979i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.7.p.b.43.19	✓	136
8.3	odd	2	inner	72.7.p.b.43.64	yes	136
9.4	even	3	inner	72.7.p.b.67.64	yes	136
72.67	odd	6	inner	72.7.p.b.67.19	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.7.p.b.43.19	✓	136	1.1	even	1	trivial
72.7.p.b.43.64	yes	136	8.3	odd	2	inner
72.7.p.b.67.19	yes	136	72.67	odd	6	inner
72.7.p.b.67.64	yes	136	9.4	even	3	inner

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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	72.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.16108 - 6.11255i) q^{2} +(23.0486 + 14.0627i) q^{3} +(-10.7264 + 63.0947i) q^{4} +(-44.3287 + 25.5932i) q^{5} +(-32.9969 - 213.465i) q^{6} +(23.6171 + 13.6353i) q^{7} +(441.029 - 260.072i) q^{8} +(333.480 + 648.253i) q^{9} +O(q^{10})\)	\(q+(-5.16108 - 6.11255i) q^{2} +(23.0486 + 14.0627i) q^{3} +(-10.7264 + 63.0947i) q^{4} +(-44.3287 + 25.5932i) q^{5} +(-32.9969 - 213.465i) q^{6} +(23.6171 + 13.6353i) q^{7} +(441.029 - 260.072i) q^{8} +(333.480 + 648.253i) q^{9} +(385.224 + 138.873i) q^{10} +(53.8075 - 93.1973i) q^{11} +(-1134.51 + 1303.40i) q^{12} +(-1326.14 + 765.646i) q^{13} +(-38.5431 - 214.733i) q^{14} +(-1381.63 - 33.4942i) q^{15} +(-3865.89 - 1353.56i) q^{16} -2175.58 q^{17} +(2241.36 - 5384.10i) q^{18} -6048.23 q^{19} +(-1139.31 - 3071.43i) q^{20} +(352.591 + 646.395i) q^{21} +(-847.378 + 152.099i) q^{22} +(-5659.12 + 3267.29i) q^{23} +(13822.4 + 207.779i) q^{24} +(-6502.48 + 11262.6i) q^{25} +(11524.3 + 4154.51i) q^{26} +(-1429.96 + 19631.0i) q^{27} +(-1113.64 + 1343.85i) q^{28} +(22871.4 + 13204.8i) q^{29} +(6925.96 + 8618.13i) q^{30} +(-31456.6 + 18161.5i) q^{31} +(11678.5 + 30616.3i) q^{32} +(2550.80 - 1391.39i) q^{33} +(11228.3 + 13298.3i) q^{34} -1395.89 q^{35} +(-44478.4 + 14087.4i) q^{36} +29560.9i q^{37} +(31215.4 + 36970.1i) q^{38} +(-41332.7 - 1002.01i) q^{39} +(-12894.2 + 22816.0i) q^{40} +(7645.99 + 13243.2i) q^{41} +(2131.37 - 5491.33i) q^{42} +(-5647.17 + 9781.18i) q^{43} +(5303.10 + 4394.64i) q^{44} +(-31373.6 - 20201.4i) q^{45} +(49178.7 + 17728.8i) q^{46} +(49746.5 + 28721.1i) q^{47} +(-70068.7 - 85562.6i) q^{48} +(-58452.7 - 101243. i) q^{49} +(102403. - 18380.6i) q^{50} +(-50144.1 - 30594.6i) q^{51} +(-34083.5 - 91884.9i) q^{52} +20567.2i q^{53} +(127375. - 92576.5i) q^{54} +5508.43i q^{55} +(13962.0 - 128.551i) q^{56} +(-139403. - 85054.6i) q^{57} +(-37326.2 - 207954. i) q^{58} +(-29782.4 - 51584.7i) q^{59} +(16933.2 - 86814.1i) q^{60} +(-52425.6 - 30267.9i) q^{61} +(273363. + 98547.0i) q^{62} +(-963.333 + 19856.9i) q^{63} +(126870. - 229398. i) q^{64} +(39190.7 - 67880.2i) q^{65} +(-21669.8 - 8410.78i) q^{66} +(-165375. - 286438. i) q^{67} +(23336.2 - 137268. i) q^{68} +(-176382. - 4275.96i) q^{69} +(7204.28 + 8532.41i) q^{70} +495717. i q^{71} +(315666. + 199170. i) q^{72} -548593. q^{73} +(180692. - 152566. i) q^{74} +(-308256. + 168145. i) q^{75} +(64875.8 - 381611. i) q^{76} +(2541.55 - 1467.36i) q^{77} +(207197. + 257820. i) q^{78} +(742702. + 428799. i) q^{79} +(206012. - 38938.9i) q^{80} +(-309024. + 432358. i) q^{81} +(41488.3 - 115086. i) q^{82} +(305093. - 528437. i) q^{83} +(-44566.2 + 15313.1i) q^{84} +(96440.6 - 55680.0i) q^{85} +(88933.4 - 15962.9i) q^{86} +(341459. + 625987. i) q^{87} +(-507.287 - 55096.6i) q^{88} +529286. q^{89} +(38439.6 + 296034. i) q^{90} -41759.3 q^{91} +(-145447. - 392107. i) q^{92} +(-980432. - 23768.2i) q^{93} +(-81186.5 - 452310. i) q^{94} +(268110. - 154794. i) q^{95} +(-161375. + 869894. i) q^{96} +(-194127. + 336237. i) q^{97} +(-317173. + 879818. i) q^{98} +(78359.2 + 3801.50i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 17 q^{2} + 42 q^{3} + 127 q^{4} - 561 q^{6} + 1774 q^{8} + 654 q^{9}+O(q^{10}) \) 136 * q - 17 * q^2 + 42 * q^3 + 127 * q^4 - 561 * q^6 + 1774 * q^8 + 654 * q^9	\( 136 q - 17 q^{2} + 42 q^{3} + 127 q^{4} - 561 q^{6} + 1774 q^{8} + 654 q^{9} - 132 q^{10} + 2336 q^{11} - 2796 q^{12} + 2346 q^{14} + 8191 q^{16} - 3460 q^{17} + 6306 q^{18} - 4972 q^{19} + 3588 q^{20} - 18577 q^{22} - 50553 q^{24} + 224998 q^{25} + 38352 q^{26} - 27792 q^{27} - 8196 q^{28} - 107130 q^{30} - 191717 q^{32} - 42852 q^{33} + 6125 q^{34} - 62508 q^{35} + 87339 q^{36} + 250223 q^{38} - 27126 q^{40} - 145084 q^{41} - 107478 q^{42} + 74912 q^{43} - 1118662 q^{44} + 22296 q^{46} + 690903 q^{48} + 1210102 q^{49} - 844727 q^{50} + 830778 q^{51} + 62952 q^{52} + 860925 q^{54} - 587718 q^{56} + 748686 q^{57} + 221136 q^{58} + 98960 q^{59} - 960810 q^{60} - 1062312 q^{62} - 784646 q^{64} - 62502 q^{65} + 802866 q^{66} + 596624 q^{67} + 681953 q^{68} + 86334 q^{70} - 2246001 q^{72} - 1186276 q^{73} - 782586 q^{74} + 3451098 q^{75} - 273235 q^{76} - 3340578 q^{78} + 2446320 q^{80} - 621690 q^{81} - 3119398 q^{82} - 179350 q^{83} - 227136 q^{84} + 917117 q^{86} - 1184629 q^{88} + 253712 q^{89} - 4940256 q^{90} - 470604 q^{91} + 1731894 q^{92} + 2055426 q^{94} + 8439666 q^{96} - 1822756 q^{97} + 6531850 q^{98} + 2509818 q^{99}+O(q^{100}) \) 136 * q - 17 * q^2 + 42 * q^3 + 127 * q^4 - 561 * q^6 + 1774 * q^8 + 654 * q^9 - 132 * q^10 + 2336 * q^11 - 2796 * q^12 + 2346 * q^14 + 8191 * q^16 - 3460 * q^17 + 6306 * q^18 - 4972 * q^19 + 3588 * q^20 - 18577 * q^22 - 50553 * q^24 + 224998 * q^25 + 38352 * q^26 - 27792 * q^27 - 8196 * q^28 - 107130 * q^30 - 191717 * q^32 - 42852 * q^33 + 6125 * q^34 - 62508 * q^35 + 87339 * q^36 + 250223 * q^38 - 27126 * q^40 - 145084 * q^41 - 107478 * q^42 + 74912 * q^43 - 1118662 * q^44 + 22296 * q^46 + 690903 * q^48 + 1210102 * q^49 - 844727 * q^50 + 830778 * q^51 + 62952 * q^52 + 860925 * q^54 - 587718 * q^56 + 748686 * q^57 + 221136 * q^58 + 98960 * q^59 - 960810 * q^60 - 1062312 * q^62 - 784646 * q^64 - 62502 * q^65 + 802866 * q^66 + 596624 * q^67 + 681953 * q^68 + 86334 * q^70 - 2246001 * q^72 - 1186276 * q^73 - 782586 * q^74 + 3451098 * q^75 - 273235 * q^76 - 3340578 * q^78 + 2446320 * q^80 - 621690 * q^81 - 3119398 * q^82 - 179350 * q^83 - 227136 * q^84 + 917117 * q^86 - 1184629 * q^88 + 253712 * q^89 - 4940256 * q^90 - 470604 * q^91 + 1731894 * q^92 + 2055426 * q^94 + 8439666 * q^96 - 1822756 * q^97 + 6531850 * q^98 + 2509818 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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