LMFDB - Embedded newform 76.7.b.a.39.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,7,Mod(39,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("76.39");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	76.b (of order $2$, degree $1$, 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:	$17.4841103551$
Analytic rank:	$0$
Dimension:	$54$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.20
Character	$\chi$	$=$	76.39
Dual form			76.7.b.a.39.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.60097 + 6.54454i) q^{2} -21.0346i q^{3} +(-21.6621 - 60.2225i) q^{4} -46.6232 q^{5} +(137.662 + 96.7797i) q^{6} -184.040i q^{7} +(493.796 + 135.314i) q^{8} +286.545 q^{9} +O(q^{10})$	\(q+(-4.60097 + 6.54454i) q^{2} -21.0346i q^{3} +(-21.6621 - 60.2225i) q^{4} -46.6232 q^{5} +(137.662 + 96.7797i) q^{6} -184.040i q^{7} +(493.796 + 135.314i) q^{8} +286.545 q^{9} +(214.512 - 305.128i) q^{10} -790.519i q^{11} +(-1266.76 + 455.654i) q^{12} +775.625 q^{13} +(1204.46 + 846.765i) q^{14} +980.702i q^{15} +(-3157.51 + 2609.09i) q^{16} -6841.14 q^{17} +(-1318.39 + 1875.31i) q^{18} +1573.56i q^{19} +(1009.96 + 2807.77i) q^{20} -3871.22 q^{21} +(5173.59 + 3637.16i) q^{22} +8630.01i q^{23} +(2846.27 - 10386.8i) q^{24} -13451.3 q^{25} +(-3568.63 + 5076.11i) q^{26} -21361.6i q^{27} +(-11083.4 + 3986.70i) q^{28} -25149.9 q^{29} +(-6418.25 - 4512.18i) q^{30} -18917.2i q^{31} +(-2547.73 - 32668.8i) q^{32} -16628.3 q^{33} +(31475.9 - 44772.1i) q^{34} +8580.56i q^{35} +(-6207.16 - 17256.5i) q^{36} -17259.5 q^{37} +(-10298.2 - 7239.92i) q^{38} -16315.0i q^{39} +(-23022.4 - 6308.76i) q^{40} -100532. q^{41} +(17811.4 - 25335.4i) q^{42} -29182.4i q^{43} +(-47607.1 + 17124.3i) q^{44} -13359.6 q^{45} +(-56479.5 - 39706.5i) q^{46} +156598. i q^{47} +(54881.3 + 66416.9i) q^{48} +83778.1 q^{49} +(61888.9 - 88032.5i) q^{50} +143901. i q^{51} +(-16801.7 - 46710.1i) q^{52} -8209.91 q^{53} +(139802. + 98284.1i) q^{54} +36856.6i q^{55} +(24903.2 - 90878.3i) q^{56} +33099.3 q^{57} +(115714. - 164595. i) q^{58} +296739. i q^{59} +(59060.3 - 21244.1i) q^{60} -233354. q^{61} +(123805. + 87037.7i) q^{62} -52735.8i q^{63} +(225524. + 133635. i) q^{64} -36162.2 q^{65} +(76506.2 - 108824. i) q^{66} +188870. i q^{67} +(148193. + 411991. i) q^{68} +181529. q^{69} +(-56155.8 - 39478.9i) q^{70} -153617. i q^{71} +(141495. + 38773.4i) q^{72} -306135. q^{73} +(79410.6 - 112956. i) q^{74} +282942. i q^{75} +(94763.9 - 34086.7i) q^{76} -145487. q^{77} +(106774. + 75064.8i) q^{78} -447677. i q^{79} +(147213. - 121644. i) q^{80} -240442. q^{81} +(462546. - 657938. i) q^{82} -356959. i q^{83} +(83858.7 + 233135. i) q^{84} +318956. q^{85} +(190985. + 134267. i) q^{86} +529019. i q^{87} +(106968. - 390355. i) q^{88} +167074. q^{89} +(61467.4 - 87432.8i) q^{90} -142746. i q^{91} +(519721. - 186944. i) q^{92} -397917. q^{93} +(-1.02486e6 - 720504. i) q^{94} -73364.6i q^{95} +(-687176. + 53590.4i) q^{96} +61902.8 q^{97} +(-385461. + 548290. i) q^{98} -226519. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9}+O(q^{10}) $ 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9	\( 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9} - 2088 q^{10} - 2384 q^{12} - 828 q^{13} + 4116 q^{14} - 7782 q^{16} + 12220 q^{17} + 15790 q^{18} - 7000 q^{20} - 16048 q^{21} - 51864 q^{22} + 19294 q^{24} + 218346 q^{25} - 18110 q^{26} + 97926 q^{28} - 101996 q^{29} + 50076 q^{30} - 235160 q^{32} + 9072 q^{33} - 51156 q^{34} - 48028 q^{36} - 63420 q^{37} + 157260 q^{40} - 135700 q^{41} + 302290 q^{42} + 137784 q^{44} - 50348 q^{45} - 177084 q^{46} + 111320 q^{48} - 1099338 q^{49} + 485770 q^{50} + 232980 q^{52} + 892932 q^{53} - 730010 q^{54} - 298644 q^{56} - 702534 q^{58} + 1231628 q^{60} + 323700 q^{61} + 1573116 q^{62} - 1065942 q^{64} + 587512 q^{65} - 74604 q^{66} - 1235974 q^{68} + 217376 q^{69} + 1163796 q^{70} - 1228320 q^{72} - 739428 q^{73} - 1852264 q^{74} - 563144 q^{77} - 2516852 q^{78} - 1597436 q^{80} + 4660886 q^{81} - 919236 q^{82} + 4928476 q^{84} - 737904 q^{85} - 1444124 q^{86} + 2679960 q^{88} - 3415940 q^{89} + 4702636 q^{90} - 3230670 q^{92} - 5021584 q^{93} + 1881960 q^{94} + 1838870 q^{96} + 3483660 q^{97} - 3419858 q^{98}+O(q^{100}) \) 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9 - 2088 * q^10 - 2384 * q^12 - 828 * q^13 + 4116 * q^14 - 7782 * q^16 + 12220 * q^17 + 15790 * q^18 - 7000 * q^20 - 16048 * q^21 - 51864 * q^22 + 19294 * q^24 + 218346 * q^25 - 18110 * q^26 + 97926 * q^28 - 101996 * q^29 + 50076 * q^30 - 235160 * q^32 + 9072 * q^33 - 51156 * q^34 - 48028 * q^36 - 63420 * q^37 + 157260 * q^40 - 135700 * q^41 + 302290 * q^42 + 137784 * q^44 - 50348 * q^45 - 177084 * q^46 + 111320 * q^48 - 1099338 * q^49 + 485770 * q^50 + 232980 * q^52 + 892932 * q^53 - 730010 * q^54 - 298644 * q^56 - 702534 * q^58 + 1231628 * q^60 + 323700 * q^61 + 1573116 * q^62 - 1065942 * q^64 + 587512 * q^65 - 74604 * q^66 - 1235974 * q^68 + 217376 * q^69 + 1163796 * q^70 - 1228320 * q^72 - 739428 * q^73 - 1852264 * q^74 - 563144 * q^77 - 2516852 * q^78 - 1597436 * q^80 + 4660886 * q^81 - 919236 * q^82 + 4928476 * q^84 - 737904 * q^85 - 1444124 * q^86 + 2679960 * q^88 - 3415940 * q^89 + 4702636 * q^90 - 3230670 * q^92 - 5021584 * q^93 + 1881960 * q^94 + 1838870 * q^96 + 3483660 * q^97 - 3419858 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$1$	$-1$

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 $

$2$	−4.60097	+	6.54454i	−0.575122	+	0.818068i
$2$	−4.60097	+	6.54454i	−0.575122	+	0.818068i
$3$		−	21.0346i		−	0.779060i	−0.921014	−	0.389530i	$-0.872637\pi$
$3$		−	21.0346i		−	0.779060i	0.921014	−	0.389530i	$-0.127363\pi$
$4$	−21.6621	−	60.2225i	−0.338470	−	0.940977i
$5$	−46.6232			−0.372986			−0.186493	−	0.982456i	$-0.559712\pi$
$5$	−46.6232			−0.372986			−0.186493	+	0.982456i	$0.559712\pi$
$6$	137.662	+	96.7797i	0.637324	+	0.448054i
$7$		−	184.040i		−	0.536561i	−0.963341	−	0.268280i	$-0.913545\pi$
$7$		−	184.040i		−	0.536561i	0.963341	−	0.268280i	$-0.0864554\pi$
$8$	493.796	+	135.314i	0.964445	+	0.264284i
$9$	286.545			0.393066
$10$	214.512	−	305.128i	0.214512	−	0.305128i
$11$		−	790.519i		−	0.593929i	−0.954889	−	0.296964i	$-0.904026\pi$
$11$		−	790.519i		−	0.593929i	0.954889	−	0.296964i	$-0.0959743\pi$
$12$	−1266.76	+	455.654i	−0.733077	+	0.263689i
$13$	775.625			0.353038			0.176519	−	0.984297i	$-0.443516\pi$
$13$	775.625			0.353038			0.176519	+	0.984297i	$0.443516\pi$
$14$	1204.46	+	846.765i	0.438943	+	0.308588i
$15$			980.702i			0.290578i
$16$	−3157.51	+	2609.09i	−0.770876	+	0.636986i
$17$	−6841.14			−1.39246			−0.696228	−	0.717820i	$-0.745140\pi$
$17$	−6841.14			−1.39246			−0.696228	+	0.717820i	$0.745140\pi$
$18$	−1318.39	+	1875.31i	−0.226061	+	0.321554i
$19$			1573.56i			0.229416i
$19$			1573.56i			0.229416i
$20$	1009.96	+	2807.77i	0.126245	+	0.350971i
$21$	−3871.22			−0.418013
$22$	5173.59	+	3637.16i	0.485874	+	0.341581i
$23$			8630.01i			0.709297i	0.935000	+	0.354648i	$0.115399\pi$
$23$			8630.01i			0.709297i	−0.935000	+	0.354648i	$0.884601\pi$
$24$	2846.27	−	10386.8i	0.205893	−	0.751360i
$25$	−13451.3			−0.860882
$26$	−3568.63	+	5076.11i	−0.203040	+	0.288809i
$27$		−	21361.6i		−	1.08528i
$28$	−11083.4	+	3986.70i	−0.504891	+	0.181610i
$29$	−25149.9			−1.03120			−0.515600	−	0.856830i	$-0.672431\pi$
$29$	−25149.9			−1.03120			−0.515600	+	0.856830i	$0.672431\pi$
$30$	−6418.25	−	4512.18i	−0.237713	−	0.167118i
$31$		−	18917.2i		−	0.634999i	−0.948258	−	0.317499i	$-0.897157\pi$
$31$		−	18917.2i		−	0.634999i	0.948258	−	0.317499i	$-0.102843\pi$
$32$	−2547.73	−	32668.8i	−0.0777504	−	0.996973i
$33$	−16628.3			−0.462706
$34$	31475.9	−	44772.1i	0.800832	−	1.13912i
$35$			8580.56i			0.200130i
$36$	−6207.16	−	17256.5i	−0.133041	−	0.369866i
$37$	−17259.5			−0.340740			−0.170370	−	0.985380i	$-0.554496\pi$
$37$	−17259.5			−0.340740			−0.170370	+	0.985380i	$0.554496\pi$
$38$	−10298.2	−	7239.92i	−0.187678	−	0.131942i
$39$		−	16315.0i		−	0.275038i
$40$	−23022.4	−	6308.76i	−0.359724	−	0.0985743i
$41$	−100532.			−1.45866			−0.729330	−	0.684162i	$-0.760168\pi$
$41$	−100532.			−1.45866			−0.729330	+	0.684162i	$0.760168\pi$
$42$	17811.4	−	25335.4i	0.240408	−	0.341963i
$43$		−	29182.4i		−	0.367041i	−0.983016	−	0.183521i	$-0.941251\pi$
$43$		−	29182.4i		−	0.367041i	0.983016	−	0.183521i	$-0.0587494\pi$
$44$	−47607.1	+	17124.3i	−0.558874	+	0.201027i
$45$	−13359.6			−0.146608
$46$	−56479.5	−	39706.5i	−0.580253	−	0.407932i
$47$			156598.i			1.50832i	0.656691	+	0.754160i	$0.271955\pi$
$47$			156598.i			1.50832i	−0.656691	+	0.754160i	$0.728045\pi$
$48$	54881.3	+	66416.9i	0.496250	+	0.600558i
$49$	83778.1			0.712102
$50$	61888.9	−	88032.5i	0.495112	−	0.704260i
$51$			143901.i			1.08481i
$52$	−16801.7	−	46710.1i	−0.119493	−	0.332201i
$53$	−8209.91			−0.0551456			−0.0275728	−	0.999620i	$-0.508778\pi$
$53$	−8209.91			−0.0551456			−0.0275728	+	0.999620i	$0.508778\pi$
$54$	139802.	+	98284.1i	0.887834	+	0.624169i
$55$			36856.6i			0.221527i
$56$	24903.2	−	90878.3i	0.141805	−	0.517483i
$57$	33099.3			0.178729
$58$	115714.	−	164595.i	0.593065	−	0.843591i
$59$			296739.i			1.44484i	0.691456	+	0.722418i	$0.256970\pi$
$59$			296739.i			1.44484i	−0.691456	+	0.722418i	$0.743030\pi$
$60$	59060.3	−	21244.1i	0.273428	−	0.0983521i
$61$	−233354.			−1.02808			−0.514038	−	0.857767i	$-0.671851\pi$
$61$	−233354.			−1.02808			−0.514038	+	0.857767i	$0.671851\pi$
$62$	123805.	+	87037.7i	0.519472	+	0.365201i
$63$		−	52735.8i		−	0.210904i
$64$	225524.	+	133635.i	0.860307	+	0.509775i
$65$	−36162.2			−0.131678
$66$	76506.2	−	108824.i	0.266112	−	0.378525i
$67$			188870.i			0.627969i	0.949428	+	0.313985i	$0.101664\pi$
$67$			188870.i			0.627969i	−0.949428	+	0.313985i	$0.898336\pi$
$68$	148193.	+	411991.i	0.471305	+	1.31027i
$69$	181529.			0.552585
$70$	−56155.8	−	39478.9i	−0.163720	−	0.115099i
$71$		−	153617.i		−	0.429205i	−0.976702	−	0.214602i	$-0.931154\pi$
$71$		−	153617.i		−	0.429205i	0.976702	−	0.214602i	$-0.0688455\pi$
$72$	141495.	+	38773.4i	0.379090	+	0.103881i
$73$	−306135.			−0.786946			−0.393473	−	0.919336i	$-0.628726\pi$
$73$	−306135.			−0.786946			−0.393473	+	0.919336i	$0.628726\pi$
$74$	79410.6	−	112956.i	0.195967	−	0.278749i
$75$			282942.i			0.670678i
$76$	94763.9	−	34086.7i	0.215875	−	0.0776504i
$77$	−145487.			−0.318679
$78$	106774.	+	75064.8i	0.225000	+	0.158180i
$79$		−	447677.i		−	0.907994i	−0.891003	−	0.453997i	$-0.849998\pi$
$79$		−	447677.i		−	0.907994i	0.891003	−	0.453997i	$-0.150002\pi$
$80$	147213.	−	121644.i	0.287526	−	0.237587i
$81$	−240442.			−0.452434
$82$	462546.	−	657938.i	0.838907	−	1.19328i
$83$		−	356959.i		−	0.624287i	−0.950035	−	0.312143i	$-0.898953\pi$
$83$		−	356959.i		−	0.624287i	0.950035	−	0.312143i	$-0.101047\pi$
$84$	83858.7	+	233135.i	0.141485	+	0.393341i
$85$	318956.			0.519367
$86$	190985.	+	134267.i	0.300265	+	0.211093i
$87$			529019.i			0.803366i
$88$	106968.	−	390355.i	0.156966	−	0.572812i
$89$	167074.			0.236995			0.118497	−	0.992954i	$-0.462192\pi$
$89$	167074.			0.236995			0.118497	+	0.992954i	$0.462192\pi$
$90$	61467.4	−	87432.8i	0.0843174	−	0.119935i
$91$		−	142746.i		−	0.189427i
$92$	519721.	−	186944.i	0.667432	−	0.240076i
$93$	−397917.			−0.494702
$94$	−1.02486e6	−	720504.i	−1.23391	−	0.867467i
$95$		−	73364.6i		−	0.0855688i
$96$	−687176.	+	53590.4i	−0.776702	+	0.0605722i
$97$	61902.8			0.0678258			0.0339129	−	0.999425i	$-0.489203\pi$
$97$	61902.8			0.0678258			0.0339129	+	0.999425i	$0.489203\pi$
$98$	−385461.	+	548290.i	−0.409545	+	0.582548i
$99$		−	226519.i		−	0.233453i
$100$	291383.	+	810070.i	0.291383	+	0.810070i
$101$	−217585.			−0.211185			−0.105593	−	0.994409i	$-0.533674\pi$
$101$	−217585.			−0.211185			−0.105593	+	0.994409i	$0.533674\pi$
$102$	−941765.	−	662083.i	−0.887446	−	0.623896i
$103$		−	479972.i		−	0.439242i	−0.975585	−	0.219621i	$-0.929518\pi$
$103$		−	479972.i		−	0.439242i	0.975585	−	0.219621i	$-0.0704822\pi$
$104$	383000.	+	104953.i	0.340486	+	0.0933025i
$105$	180489.			0.155913
$106$	37773.6	−	53730.1i	0.0317154	−	0.0451128i
$107$			242954.i			0.198323i	0.995071	+	0.0991614i	$0.0316160\pi$
$107$			242954.i			0.198323i	−0.995071	+	0.0991614i	$0.968384\pi$
$108$	−1.28645e6	+	462737.i	−1.02123	+	0.367336i
$109$	−615978.			−0.475648			−0.237824	−	0.971308i	$-0.576434\pi$
$109$	−615978.			−0.475648			−0.237824	+	0.971308i	$0.576434\pi$
$110$	−241209.	−	169576.i	−0.181224	−	0.127405i
$111$			363048.i			0.265457i
$112$	480179.	+	581109.i	0.341782	+	0.413622i
$113$	16570.1			0.0114839			0.00574197	−	0.999984i	$-0.498172\pi$
$113$	16570.1			0.0114839			0.00574197	+	0.999984i	$0.498172\pi$
$114$	−152289.	+	216620.i	−0.102791	+	0.146212i
$115$		−	402359.i		−	0.264558i
$116$	544800.	+	1.51459e6i	0.349031	+	0.970335i
$117$	222251.			0.138767
$118$	−1.94202e6	−	1.36529e6i	−1.18197	−	0.830957i
$119$			1.25905e6i			0.747138i
$120$	−132702.	+	484266.i	−0.0767953	+	0.280247i
$121$	1.14664e6			0.647248
$122$	1.07365e6	−	1.52719e6i	0.591269	−	0.841036i
$123$			2.11466e6i			1.13638i
$124$	−1.13924e6	+	409787.i	−0.597519	+	0.214928i
$125$	1.35563e6			0.694082
$126$	345132.	+	242636.i	0.172534	+	0.121295i
$127$		−	2.17917e6i		−	1.06385i	−0.846792	−	0.531924i	$-0.821469\pi$
$127$		−	2.17917e6i		−	1.06385i	0.846792	−	0.531924i	$-0.178531\pi$
$128$	−1.91221e6	+	861106.i	−0.911812	+	0.410607i
$129$	−613840.			−0.285947
$130$	166381.	−	236665.i	0.0757310	−	0.107722i
$131$		−	1.94960e6i		−	0.867226i	−0.901099	−	0.433613i	$-0.857239\pi$
$131$		−	1.94960e6i		−	0.867226i	0.901099	−	0.433613i	$-0.142761\pi$
$132$	360203.	+	1.00140e6i	0.156612	+	0.435396i
$133$	289599.			0.123095
$134$	−1.23607e6	−	868985.i	−0.513721	−	0.361159i
$135$			995947.i			0.404795i
$136$	−3.37813e6	−	925699.i	−1.34295	−	0.368005i
$137$	−3.69369e6			−1.43648			−0.718238	−	0.695797i	$-0.755051\pi$
$137$	−3.69369e6			−1.43648			−0.718238	+	0.695797i	$0.755051\pi$
$138$	−835210.	+	1.18802e6i	−0.317803	+	0.452052i
$139$		−	1.27664e6i		−	0.475360i	−0.971344	−	0.237680i	$-0.923613\pi$
$139$		−	1.27664e6i		−	0.475360i	0.971344	−	0.237680i	$-0.0763869\pi$
$140$	516743.	−	185873.i	0.188317	−	0.0677379i
$141$	3.29398e6			1.17507
$142$	1.00535e6	+	706788.i	0.351119	+	0.246845i
$143$		−	613147.i		−	0.209680i
$144$	−904767.	+	747622.i	−0.303005	+	0.250377i
$145$	1.17257e6			0.384623
$146$	1.40852e6	−	2.00352e6i	0.452590	−	0.643775i
$147$		−	1.76224e6i		−	0.554770i
$148$	373878.	+	1.03941e6i	0.115331	+	0.320629i
$149$	3.94418e6			1.19233			0.596166	−	0.802861i	$-0.296690\pi$
$149$	3.94418e6			1.19233			0.596166	+	0.802861i	$0.296690\pi$
$150$	−1.85173e6	−	1.30181e6i	−0.548660	−	0.385722i
$151$		−	4.79389e6i		−	1.39238i	−0.717858	−	0.696190i	$-0.754877\pi$
$151$		−	4.79389e6i		−	1.39238i	0.717858	−	0.696190i	$-0.245123\pi$
$152$	−212924.	+	777018.i	−0.0606310	+	0.221259i
$153$	−1.96029e6			−0.547327
$154$	669384.	−	952149.i	0.183279	−	0.260701i
$155$			881983.i			0.236846i
$156$	−982529.	+	353417.i	−0.258804	+	0.0930922i
$157$	4.30231e6			1.11174			0.555870	−	0.831270i	$-0.312385\pi$
$157$	4.30231e6			1.11174			0.555870	+	0.831270i	$0.312385\pi$
$158$	2.92984e6	+	2.05975e6i	0.742801	+	0.522207i
$159$			172692.i			0.0429617i
$160$	118783.	+	1.52313e6i	0.0289998	+	0.371857i
$161$	1.58827e6			0.380581
$162$	1.10627e6	−	1.57358e6i	0.260204	−	0.370122i
$163$		−	5.38798e6i		−	1.24412i	−0.782969	−	0.622061i	$-0.786296\pi$
$163$		−	5.38798e6i		−	1.24412i	0.782969	−	0.622061i	$-0.213704\pi$
$164$	2.17774e6	+	6.05431e6i	0.493713	+	1.37257i
$165$	775264.			0.172583
$166$	2.33613e6	+	1.64236e6i	0.510709	+	0.359041i
$167$		−	3.29435e6i		−	0.707327i	−0.935373	−	0.353664i	$-0.884936\pi$
$167$		−	3.29435e6i		−	0.707327i	0.935373	−	0.353664i	$-0.115064\pi$
$168$	−1.91159e6	−	523829.i	−0.403150	−	0.110474i
$169$	−4.22521e6			−0.875364
$170$	−1.46751e6	+	2.08742e6i	−0.298699	+	0.424877i
$171$			450896.i			0.0901754i
$172$	−1.75744e6	+	632151.i	−0.345378	+	0.124233i
$173$	5.24468e6			1.01293			0.506467	−	0.862260i	$-0.330951\pi$
$173$	5.24468e6			1.01293			0.506467	+	0.862260i	$0.330951\pi$
$174$	−3.46219e6	−	2.43400e6i	−0.657208	−	0.462033i
$175$			2.47558e6i			0.461915i
$176$	2.06254e6	+	2.49607e6i	0.378324	+	0.457845i
$177$	6.24179e6			1.12561
$178$	−768703.	+	1.09342e6i	−0.136301	+	0.193878i
$179$			8.28153e6i			1.44395i	0.691920	+	0.721974i	$0.256765\pi$
$179$			8.28153e6i			1.44395i	−0.691920	+	0.721974i	$0.743235\pi$
$180$	289398.	+	804552.i	0.0496224	+	0.137955i
$181$	−7.95450e6			−1.34146			−0.670729	−	0.741702i	$-0.734019\pi$
$181$	−7.95450e6			−1.34146			−0.670729	+	0.741702i	$0.734019\pi$
$182$	934210.	+	656772.i	0.154964	+	0.108943i
$183$			4.90851e6i			0.800933i
$184$	−1.16776e6	+	4.26146e6i	−0.187456	+	0.684078i
$185$	804695.			0.127091
$186$	1.83081e6	−	2.60419e6i	0.284514	−	0.404700i
$187$			5.40805e6i			0.827020i
$188$	9.43074e6	−	3.39225e6i	1.41929	−	0.510521i
$189$	−3.93140e6			−0.582320
$190$	480138.	+	337548.i	0.0700011	+	0.0492125i
$191$		−	4.53876e6i		−	0.651383i	−0.945476	−	0.325692i	$-0.894403\pi$
$191$		−	4.53876e6i		−	0.651383i	0.945476	−	0.325692i	$-0.105597\pi$
$192$	2.81095e6	−	4.74382e6i	0.397146	−	0.670231i
$193$	−9.49200e6			−1.32034			−0.660170	−	0.751116i	$-0.729516\pi$
$193$	−9.49200e6			−1.32034			−0.660170	+	0.751116i	$0.729516\pi$
$194$	−284813.	+	405125.i	−0.0390081	+	0.0554861i
$195$			760657.i			0.102585i
$196$	−1.81481e6	−	5.04533e6i	−0.241026	−	0.670072i
$197$	1.43544e7			1.87752			0.938761	−	0.344569i	$-0.111975\pi$
$197$	1.43544e7			1.87752			0.938761	+	0.344569i	$0.111975\pi$
$198$	1.48247e6	+	1.04221e6i	0.190980	+	0.134264i
$199$		−	2.03059e6i		−	0.257670i	−0.991666	−	0.128835i	$-0.958876\pi$
$199$		−	2.03059e6i		−	0.257670i	0.991666	−	0.128835i	$-0.0411237\pi$
$200$	−6.64218e6	−	1.82014e6i	−0.830273	−	0.227518i
$201$	3.97281e6			0.489226
$202$	1.00110e6	−	1.42399e6i	0.121457	−	0.172764i
$203$			4.62860e6i			0.553301i
$204$	8.66607e6	−	3.11719e6i	1.02078	−	0.367175i
$205$	4.68714e6			0.544060
$206$	3.14120e6	+	2.20834e6i	0.359330	+	0.252618i
$207$			2.47289e6i			0.278800i
$208$	−2.44904e6	+	2.02368e6i	−0.272149	+	0.224880i
$209$	1.24393e6			0.136257
$210$	−830424.	+	1.18122e6i	−0.0896689	+	0.127547i
$211$		−	4.59589e6i		−	0.489241i	−0.969619	−	0.244620i	$-0.921337\pi$
$211$		−	4.59589e6i		−	0.489241i	0.969619	−	0.244620i	$-0.0786633\pi$
$212$	177844.	+	494422.i	0.0186651	+	0.0518907i
$213$	−3.23128e6			−0.334376
$214$	−1.59002e6	−	1.11782e6i	−0.162241	−	0.114060i
$215$			1.36058e6i			0.136901i
$216$	2.89052e6	−	1.05483e7i	0.286823	−	1.04669i
$217$	−3.48154e6			−0.340715
$218$	2.83410e6	−	4.03129e6i	0.273555	−	0.389112i
$219$			6.43944e6i			0.613078i
$220$	2.21960e6	−	798391.i	0.208452	−	0.0749804i
$221$	−5.30616e6			−0.491591
$222$	−2.37598e6	−	1.67037e6i	−0.217162	−	0.152670i
$223$			4.53610e6i			0.409042i	0.978862	+	0.204521i	$0.0655636\pi$
$223$			4.53610e6i			0.409042i	−0.978862	+	0.204521i	$0.934436\pi$
$224$	−6.01238e6	+	468884.i	−0.534937	+	0.0417178i
$225$	−3.85439e6			−0.338383
$226$	−76238.8	+	108444.i	−0.00660466	+	0.00939464i
$227$			1.42284e7i			1.21641i	0.793780	+	0.608204i	$0.208110\pi$
$227$			1.42284e7i			1.21641i	−0.793780	+	0.608204i	$0.791890\pi$
$228$	−717000.	−	1.99332e6i	−0.0604943	−	0.168180i
$229$	−2.05799e7			−1.71371			−0.856856	−	0.515556i	$-0.827585\pi$
$229$	−2.05799e7			−1.71371			−0.856856	+	0.515556i	$0.827585\pi$
$230$	2.63326e6	+	1.85124e6i	0.216426	+	0.152153i
$231$			3.06027e6i			0.248270i
$232$	−1.24189e7	−	3.40313e6i	−0.994535	−	0.272530i
$233$	−1.57338e7			−1.24384			−0.621922	−	0.783079i	$-0.713648\pi$
$233$	−1.57338e7			−1.24384			−0.621922	+	0.783079i	$0.713648\pi$
$234$	−1.02257e6	+	1.45453e6i	−0.0798080	+	0.113521i
$235$		−	7.30111e6i		−	0.562582i
$236$	1.78704e7	−	6.42799e6i	1.35956	−	0.489034i
$237$	−9.41671e6			−0.707382
$238$	−8.23988e6	−	5.79284e6i	−0.611209	−	0.429695i
$239$			1.15354e6i			0.0844967i	0.999107	+	0.0422484i	$0.0134521\pi$
$239$			1.15354e6i			0.0844967i	−0.999107	+	0.0422484i	$0.986548\pi$
$240$	−2.55874e6	−	3.09657e6i	−0.185094	−	0.224000i
$241$	980922.			0.0700782			0.0350391	−	0.999386i	$-0.488844\pi$
$241$	980922.			0.0700782			0.0350391	+	0.999386i	$0.488844\pi$
$242$	−5.27566e6	+	7.50424e6i	−0.372246	+	0.529493i
$243$		−	1.05150e7i		−	0.732809i
$244$	5.05493e6	+	1.40531e7i	0.347973	+	0.967396i
$245$	−3.90601e6			−0.265604
$246$	−1.38395e7	−	9.72949e6i	−0.929639	−	0.653559i
$247$			1.22049e6i			0.0809926i
$248$	2.55976e6	−	9.34126e6i	0.167820	−	0.612421i
$249$	−7.50850e6			−0.486357
$250$	−6.23722e6	+	8.87198e6i	−0.399182	+	0.567807i
$251$		−	1.37549e7i		−	0.869831i	−0.900471	−	0.434915i	$-0.856778\pi$
$251$		−	1.37549e7i		−	0.869831i	0.900471	−	0.434915i	$-0.143222\pi$
$252$	−3.17588e6	+	1.14237e6i	−0.198455	+	0.0713846i
$253$	6.82219e6			0.421272
$254$	1.42616e7	+	1.00263e7i	0.870299	+	0.611841i
$255$		−	6.70912e6i		−	0.404618i
$256$	3.16248e6	−	1.64765e7i	0.188498	−	0.982073i
$257$	−1.62126e7			−0.955109			−0.477554	−	0.878602i	$-0.658477\pi$
$257$	−1.62126e7			−0.955109			−0.477554	+	0.878602i	$0.658477\pi$
$258$	2.82426e6	−	4.01730e6i	0.164454	−	0.233924i
$259$			3.17645e6i			0.182828i
$260$	783348.	+	2.17778e6i	0.0445692	+	0.123906i
$261$	−7.20658e6			−0.405329
$262$	1.27593e7	+	8.97007e6i	0.709449	+	0.498760i
$263$			4.62826e6i			0.254420i	0.991876	+	0.127210i	$0.0406022\pi$
$263$			4.62826e6i			0.254420i	−0.991876	+	0.127210i	$0.959398\pi$
$264$	−8.21097e6	−	2.25003e6i	−0.446255	−	0.122286i
$265$	382773.			0.0205685
$266$	−1.33244e6	+	1.89529e6i	−0.0707949	+	0.100700i
$267$		−	3.51434e6i		−	0.184633i
$268$	1.13742e7	−	4.09132e6i	0.590905	−	0.212549i
$269$	−1.96403e7			−1.00900			−0.504501	−	0.863411i	$-0.668323\pi$
$269$	−1.96403e7			−1.00900			−0.504501	+	0.863411i	$0.668323\pi$
$270$	−6.51802e6	−	4.58232e6i	−0.331150	−	0.232806i
$271$		−	2.71295e7i		−	1.36312i	−0.731762	−	0.681560i	$-0.761302\pi$
$271$		−	2.71295e7i		−	1.36312i	0.731762	−	0.681560i	$-0.238698\pi$
$272$	2.16009e7	−	1.78492e7i	1.07341	−	0.886975i
$273$	−3.00262e6			−0.147575
$274$	1.69946e7	−	2.41735e7i	0.826149	−	1.17514i
$275$			1.06335e7i			0.511303i
$276$	−3.93230e6	−	1.09321e7i	−0.187034	−	0.519970i
$277$	9.32068e6			0.438539			0.219269	−	0.975664i	$-0.429633\pi$
$277$	9.32068e6			0.438539			0.219269	+	0.975664i	$0.429633\pi$
$278$	8.35500e6	+	5.87377e6i	0.388877	+	0.273390i
$279$		−	5.42064e6i		−	0.249596i
$280$	−1.16107e6	+	4.23704e6i	−0.0528911	+	0.193014i
$281$	2.95862e7			1.33343			0.666714	−	0.745313i	$-0.267700\pi$
$281$	2.95862e7			1.33343			0.666714	+	0.745313i	$0.267700\pi$
$282$	−1.51555e7	+	2.15576e7i	−0.675809	+	0.961288i
$283$			2.39922e7i			1.05855i	0.848450	+	0.529275i	$0.177536\pi$
$283$			2.39922e7i			1.05855i	−0.848450	+	0.529275i	$0.822464\pi$
$284$	−9.25121e6	+	3.32767e6i	−0.403872	+	0.145273i
$285$	−1.54320e6			−0.0666632
$286$	4.01277e6	+	2.82107e6i	0.171532	+	0.120591i
$287$			1.85020e7i			0.782660i
$288$	−730038.	−	9.36108e6i	−0.0305610	−	0.391876i
$289$	2.26636e7			0.938936
$290$	−5.39497e6	+	7.67394e6i	−0.221205	+	0.314648i
$291$		−	1.30210e6i		−	0.0528404i
$292$	6.63154e6	+	1.84362e7i	0.266358	+	0.740498i
$293$	2.48324e7			0.987222			0.493611	−	0.869683i	$-0.335677\pi$
$293$	2.48324e7			0.987222			0.493611	+	0.869683i	$0.335677\pi$
$294$	1.15331e7	+	8.10802e6i	0.453840	+	0.319060i
$295$		−	1.38349e7i		−	0.538904i
$296$	−8.52268e6	−	2.33545e6i	−0.328625	−	0.0900524i
$297$	−1.68868e7			−0.644580
$298$	−1.81470e7	+	2.58128e7i	−0.685736	+	0.975409i
$299$			6.69366e6i			0.250409i
$300$	1.70395e7	−	6.12913e6i	0.631093	−	0.227005i
$301$	−5.37073e6			−0.196940
$302$	3.13738e7	+	2.20566e7i	1.13906	+	0.800787i
$303$			4.57681e6i			0.164526i
$304$	−4.10557e6	−	4.96853e6i	−0.146135	−	0.176851i
$305$	1.08797e7			0.383458
$306$	9.01926e6	−	1.28292e7i	0.314780	−	0.447751i
$307$			5.04876e7i			1.74490i	0.488707	+	0.872448i	$0.337469\pi$
$307$			5.04876e7i			1.74490i	−0.488707	+	0.872448i	$0.662531\pi$
$308$	3.15157e6	+	8.76163e6i	0.107863	+	0.299870i
$309$	−1.00960e7			−0.342196
$310$	−5.77218e6	−	4.05798e6i	−0.193756	−	0.136215i
$311$		−	3.95162e7i		−	1.31369i	−0.754024	−	0.656847i	$-0.771890\pi$
$311$		−	3.95162e7i		−	1.31369i	0.754024	−	0.656847i	$-0.228110\pi$
$312$	2.20764e6	−	8.05627e6i	0.0726883	−	0.265259i
$313$	3.76092e7			1.22648			0.613241	−	0.789896i	$-0.289865\pi$
$313$	3.76092e7			1.22648			0.613241	+	0.789896i	$0.289865\pi$
$314$	−1.97948e7	+	2.81567e7i	−0.639385	+	0.909478i
$315$			2.45871e6i			0.0786641i
$316$	−2.69602e7	+	9.69762e6i	−0.854402	+	0.307329i
$317$	2.67605e7			0.840072			0.420036	−	0.907507i	$-0.362017\pi$
$317$	2.67605e7			0.840072			0.420036	+	0.907507i	$0.362017\pi$
$318$	−1.13019e6	−	794553.i	−0.0351456	−	0.0247082i
$319$			1.98815e7i			0.612459i
$320$	−1.05147e7	−	6.23048e6i	−0.320882	−	0.190139i
$321$	5.11044e6			0.154505
$322$	−7.30759e6	+	1.03945e7i	−0.218880	+	0.311341i
$323$		−	1.07650e7i		−	0.319451i
$324$	5.20848e6	+	1.44800e7i	0.153135	+	0.425730i
$325$	−1.04331e7			−0.303924
$326$	3.52618e7	+	2.47899e7i	1.01778	+	0.715521i
$327$			1.29569e7i			0.370558i
$328$	−4.96424e7	−	1.36034e7i	−1.40680	−	0.385501i
$329$	2.88204e7			0.809305
$330$	−3.56697e6	+	5.07375e6i	−0.0992561	+	0.141185i
$331$			3.90986e6i			0.107815i	0.998546	+	0.0539073i	$0.0171675\pi$
$331$			3.90986e6i			0.107815i	−0.998546	+	0.0539073i	$0.982832\pi$
$332$	−2.14970e7	+	7.73248e6i	−0.587439	+	0.211303i
$333$	−4.94563e6			−0.133933
$334$	2.15600e7	+	1.51572e7i	0.578642	+	0.406799i
$335$		−	8.80572e6i		−	0.234224i
$336$	1.22234e7	−	1.01004e7i	0.322236	−	0.266268i
$337$	1.97548e7			0.516158			0.258079	−	0.966124i	$-0.416910\pi$
$337$	1.97548e7			0.516158			0.258079	+	0.966124i	$0.416910\pi$
$338$	1.94401e7	−	2.76521e7i	0.503441	−	0.716107i
$339$		−	348547.i		−	0.00894668i
$340$	−6.90926e6	−	1.92083e7i	−0.175790	−	0.488712i
$341$	−1.49545e7			−0.377144
$342$	−2.95091e6	−	2.07456e6i	−0.0737696	−	0.0518618i
$343$		−	3.70707e7i		−	0.918647i
$344$	3.94877e6	−	1.44101e7i	0.0970033	−	0.353991i
$345$	−8.46347e6			−0.206106
$346$	−2.41306e7	+	3.43241e7i	−0.582560	+	0.828648i
$347$			6.53911e6i			0.156506i	0.996934	+	0.0782528i	$0.0249341\pi$
$347$			6.53911e6i			0.156506i	−0.996934	+	0.0782528i	$0.975066\pi$
$348$	3.18589e7	−	1.14597e7i	0.755949	−	0.271916i
$349$	8.10847e7			1.90749			0.953746	−	0.300613i	$-0.0971912\pi$
$349$	8.10847e7			1.90749			0.953746	+	0.300613i	$0.0971912\pi$
$350$	−1.62015e7	−	1.13901e7i	−0.377878	−	0.265657i
$351$		−	1.65686e7i		−	0.383146i
$352$	−2.58253e7	+	2.01403e6i	−0.592131	+	0.0461782i
$353$	6.22241e7			1.41460			0.707302	−	0.706912i	$-0.249912\pi$
$353$	6.22241e7			1.41460			0.707302	+	0.706912i	$0.249912\pi$
$354$	−2.87183e7	+	4.08497e7i	−0.647365	+	0.920829i
$355$			7.16212e6i			0.160087i
$356$	−3.61917e6	−	1.00616e7i	−0.0802157	−	0.223007i
$357$	2.64835e7			0.582065
$358$	−5.41989e7	−	3.81031e7i	−1.18125	−	0.830446i
$359$		−	4.53790e7i		−	0.980779i	−0.871503	−	0.490390i	$-0.836854\pi$
$359$		−	4.53790e7i		−	0.980779i	0.871503	−	0.490390i	$-0.163146\pi$
$360$	−6.59694e6	−	1.80774e6i	−0.141395	−	0.0387462i
$361$	−2.47610e6			−0.0526316
$362$	3.65985e7	−	5.20586e7i	0.771502	−	1.09740i
$363$		−	2.41191e7i		−	0.504245i
$364$	−8.59655e6	+	3.09219e6i	−0.178246	+	0.0641153i
$365$	1.42730e7			0.293520
$366$	−3.21239e7	−	2.25839e7i	−0.655217	−	0.460634i
$367$		−	8.51540e7i		−	1.72269i	−0.508021	−	0.861345i	$-0.669623\pi$
$367$		−	8.51540e7i		−	1.72269i	0.508021	−	0.861345i	$-0.330377\pi$
$368$	−2.25165e7	−	2.72493e7i	−0.451812	−	0.546780i
$369$	−2.88070e7			−0.573349
$370$	−3.70238e6	+	5.26636e6i	−0.0730930	+	0.103969i
$371$			1.51095e6i			0.0295890i
$372$	8.61972e6	+	2.39636e7i	0.167442	+	0.465503i
$373$	−4.61806e7			−0.889883			−0.444941	−	0.895560i	$-0.646776\pi$
$373$	−4.61806e7			−0.889883			−0.444941	+	0.895560i	$0.646776\pi$
$374$	−3.53932e7	−	2.48823e7i	−0.676559	−	0.475637i
$375$		−	2.85152e7i		−	0.540732i
$376$	−2.11899e7	+	7.73275e7i	−0.398625	+	1.45469i
$377$	−1.95069e7			−0.364053
$378$	1.80882e7	−	2.57292e7i	0.334905	−	0.476377i
$379$		−	4.25418e6i		−	0.0781445i	−0.999236	−	0.0390723i	$-0.987560\pi$
$379$		−	4.25418e6i		−	0.0781445i	0.999236	−	0.0390723i	$-0.0124403\pi$
$380$	−4.41820e6	+	1.58923e6i	−0.0805183	+	0.0289625i
$381$	−4.58379e7			−0.828801
$382$	2.97041e7	+	2.08827e7i	0.532876	+	0.374625i
$383$			8.21742e7i			1.46265i	0.682031	+	0.731323i	$0.261097\pi$
$383$			8.21742e7i			1.46265i	−0.682031	+	0.731323i	$0.738903\pi$
$384$	1.81130e7	+	4.02226e7i	0.319888	+	0.710356i
$385$	6.78310e6			0.118863
$386$	4.36724e7	−	6.21208e7i	0.759356	−	1.08013i
$387$		−	8.36206e6i		−	0.144271i
$388$	−1.34094e6	−	3.72794e6i	−0.0229570	−	0.0638225i
$389$	−3.26067e7			−0.553934			−0.276967	−	0.960879i	$-0.589329\pi$
$389$	−3.26067e7			−0.553934			−0.276967	+	0.960879i	$0.589329\pi$
$390$	−4.97815e6	−	3.49976e6i	−0.0839217	−	0.0589990i
$391$		−	5.90391e7i		−	0.987665i
$392$	4.13693e7	+	1.13363e7i	0.686784	+	0.188198i
$393$	−4.10091e7			−0.675621
$394$	−6.60440e7	+	9.39427e7i	−1.07980	+	1.53594i
$395$			2.08721e7i			0.338669i
$396$	−1.36416e7	+	4.90688e6i	−0.219674	+	0.0790170i
$397$	−1.56492e7			−0.250104			−0.125052	−	0.992150i	$-0.539910\pi$
$397$	−1.56492e7			−0.250104			−0.125052	+	0.992150i	$0.539910\pi$
$398$	1.32893e7	+	9.34270e6i	0.210791	+	0.148191i
$399$		−	6.09160e6i		−	0.0958988i
$400$	4.24725e7	−	3.50956e7i	0.663633	−	0.548369i
$401$	−1.19804e8			−1.85797			−0.928987	−	0.370112i	$-0.879319\pi$
$401$	−1.19804e8			−1.85797			−0.928987	+	0.370112i	$0.879319\pi$
$402$	−1.82788e7	+	2.60002e7i	−0.281364	+	0.400220i
$403$		−	1.46727e7i		−	0.224179i
$404$	4.71334e6	+	1.31035e7i	0.0714800	+	0.198721i
$405$	1.12102e7			0.168751
$406$	−3.02921e7	−	2.12961e7i	−0.452638	−	0.318216i
$407$			1.36440e7i			0.202376i
$408$	−1.94717e7	+	7.10576e7i	−0.286698	+	1.04624i
$409$	4.27283e7			0.624519			0.312259	−	0.949997i	$-0.398914\pi$
$409$	4.27283e7			0.624519			0.312259	+	0.949997i	$0.398914\pi$
$410$	−2.15654e7	+	3.06752e7i	−0.312900	+	0.445078i
$411$			7.76953e7i			1.11910i
$412$	−2.89051e7	+	1.03972e7i	−0.413317	+	0.148671i
$413$	5.46120e7			0.775243
$414$	−1.61839e7	−	1.13777e7i	−0.228078	−	0.160344i
$415$			1.66426e7i			0.232850i
$416$	−1.97608e6	−	2.53388e7i	−0.0274489	−	0.351970i
$417$	−2.68535e7			−0.370334
$418$	−5.72330e6	+	8.14097e6i	−0.0783641	+	0.111467i
$419$		−	1.83025e7i		−	0.248810i	−0.992232	−	0.124405i	$-0.960298\pi$
$419$		−	1.83025e7i		−	0.248810i	0.992232	−	0.124405i	$-0.0397022\pi$
$420$	−3.90977e6	−	1.08695e7i	−0.0527719	−	0.146710i
$421$	−8.97845e7			−1.20325			−0.601624	−	0.798779i	$-0.705479\pi$
$421$	−8.97845e7			−1.20325			−0.601624	+	0.798779i	$0.705479\pi$
$422$	3.00780e7	+	2.11456e7i	0.400232	+	0.281373i
$423$			4.48724e7i			0.592868i
$424$	−4.05402e6	−	1.11091e6i	−0.0531849	−	0.0145741i
$425$	9.20221e7			1.19874
$426$	1.48670e7	−	2.11472e7i	0.192307	−	0.273542i
$427$			4.29465e7i			0.551625i
$428$	1.46313e7	−	5.26289e6i	0.186617	−	0.0671264i
$429$	−1.28973e7			−0.163353
$430$	−8.90435e6	−	6.25997e6i	−0.111995	−	0.0787348i
$431$		−	1.07911e8i		−	1.34783i	−0.738808	−	0.673916i	$-0.764611\pi$
$431$		−	1.07911e8i		−	1.34783i	0.738808	−	0.673916i	$-0.235389\pi$
$432$	5.57344e7	+	6.74494e7i	0.691309	+	0.836617i
$433$	1.35906e7			0.167407			0.0837036	−	0.996491i	$-0.473325\pi$
$433$	1.35906e7			0.167407			0.0837036	+	0.996491i	$0.473325\pi$
$434$	1.60185e7	−	2.27851e7i	0.195953	−	0.278728i
$435$		−	2.46646e7i		−	0.299644i
$436$	1.33434e7	+	3.70957e7i	0.160993	+	0.447574i
$437$	−1.35799e7			−0.162724
$438$	−4.21432e7	−	2.96277e7i	−0.501539	−	0.352594i
$439$		−	2.82075e6i		−	0.0333404i	−0.999861	−	0.0166702i	$-0.994693\pi$
$439$		−	2.82075e6i		−	0.0333404i	0.999861	−	0.0166702i	$-0.00530654\pi$
$440$	−4.98720e6	+	1.81996e7i	−0.0585462	+	0.213651i
$441$	2.40062e7			0.279903
$442$	2.44135e7	−	3.47264e7i	0.282724	−	0.402155i
$443$			1.48199e8i			1.70464i	0.523020	+	0.852320i	$0.324805\pi$
$443$			1.48199e8i			1.70464i	−0.523020	+	0.852320i	$0.675195\pi$
$444$	2.18636e7	−	7.86437e6i	0.249789	−	0.0898494i
$445$	−7.78953e6			−0.0883957
$446$	−2.96867e7	−	2.08705e7i	−0.334624	−	0.235249i
$447$		−	8.29642e7i		−	0.928899i
$448$	2.45942e7	−	4.15056e7i	0.273526	−	0.461607i
$449$	−8.77824e7			−0.969770			−0.484885	−	0.874578i	$-0.661138\pi$
$449$	−8.77824e7			−0.969770			−0.484885	+	0.874578i	$0.661138\pi$
$450$	1.77340e7	−	2.52252e7i	0.194611	−	0.276820i
$451$			7.94728e7i			0.866341i
$452$	−358944.	−	997896.i	−0.00388697	−	0.0108061i
$453$	−1.00838e8			−1.08475
$454$	−9.31186e7	−	6.54646e7i	−0.995105	−	0.699583i
$455$			6.65530e6i			0.0706534i
$456$	1.63443e7	+	4.47878e6i	0.172374	+	0.0472352i
$457$	1.42771e8			1.49586			0.747932	−	0.663775i	$-0.231047\pi$
$457$	1.42771e8			1.49586			0.747932	+	0.663775i	$0.231047\pi$
$458$	9.46878e7	−	1.34686e8i	0.985593	−	1.40193i
$459$			1.46138e8i			1.51121i
$460$	−2.42311e7	+	8.71595e6i	−0.248943	+	0.0895449i
$461$	1.10553e7			0.112841			0.0564204	−	0.998407i	$-0.482031\pi$
$461$	1.10553e7			0.112841			0.0564204	+	0.998407i	$0.482031\pi$
$462$	−2.00281e7	−	1.40802e7i	−0.203102	−	0.142785i
$463$		−	1.64073e8i		−	1.65309i	−0.562874	−	0.826543i	$-0.690304\pi$
$463$		−	1.64073e8i		−	1.65309i	0.562874	−	0.826543i	$-0.309696\pi$
$464$	7.94111e7	−	6.56185e7i	0.794927	−	0.656859i
$465$	1.85522e7			0.184517
$466$	7.23908e7	−	1.02971e8i	0.715361	−	1.01755i
$467$			1.37689e8i			1.35191i	0.736943	+	0.675955i	$0.236269\pi$
$467$			1.37689e8i			1.35191i	−0.736943	+	0.675955i	$0.763731\pi$
$468$	−4.81443e6	−	1.33845e7i	−0.0469686	−	0.130577i
$469$	3.47597e7			0.336944
$470$	4.77825e7	+	3.35922e7i	0.460230	+	0.323553i
$471$		−	9.04975e7i		−	0.866111i
$472$	−4.01528e7	+	1.46529e8i	−0.381848	+	1.39347i
$473$	−2.30692e7			−0.217997
$474$	4.33260e7	−	6.16281e7i	0.406831	−	0.578687i
$475$		−	2.11664e7i		−	0.197500i
$476$	7.58229e7	−	2.72736e7i	0.703039	−	0.252884i
$477$	−2.35251e6			−0.0216758
$478$	−7.54941e6	−	5.30742e6i	−0.0691241	−	0.0485959i
$479$			1.79988e7i			0.163771i	0.996642	+	0.0818853i	$0.0260941\pi$
$479$			1.79988e7i			0.163771i	−0.996642	+	0.0818853i	$0.973906\pi$
$480$	3.20384e7	−	2.49856e6i	0.289699	−	0.0225926i
$481$	−1.33869e7			−0.120294
$482$	−4.51319e6	+	6.41969e6i	−0.0403035	+	0.0573288i
$483$		−	3.34087e7i		−	0.296495i
$484$	−2.48386e7	−	6.90536e7i	−0.219074	−	0.609046i
$485$	−2.88611e6			−0.0252981
$486$	6.88159e7	+	4.83792e7i	0.599487	+	0.421454i
$487$			5.51546e7i			0.477523i	0.971078	+	0.238762i	$0.0767415\pi$
$487$			5.51546e7i			0.477523i	−0.971078	+	0.238762i	$0.923259\pi$
$488$	−1.15229e8	−	3.15759e7i	−0.991522	−	0.271704i
$489$	−1.13334e8			−0.969245
$490$	1.79714e7	−	2.55630e7i	0.152755	−	0.217282i
$491$			5.60530e7i			0.473538i	0.971566	+	0.236769i	$0.0760884\pi$
$491$			5.60530e7i			0.473538i	−0.971566	+	0.236769i	$0.923912\pi$
$492$	1.27350e8	−	4.58080e7i	1.06931	−	0.384632i
$493$	1.72054e8			1.43590
$494$	−7.98758e6	−	5.61546e6i	−0.0662574	−	0.0465806i
$495$			1.05611e7i			0.0870747i
$496$	4.93569e7	+	5.97313e7i	0.404485	+	0.489505i
$497$	−2.82717e7			−0.230294
$498$	3.45464e7	−	4.91397e7i	0.279714	−	0.397873i
$499$			3.33630e7i			0.268512i	0.990947	+	0.134256i	$0.0428645\pi$
$499$			3.33630e7i			0.268512i	−0.990947	+	0.134256i	$0.957136\pi$
$500$	−2.93658e7	−	8.16395e7i	−0.234926	−	0.653116i
$501$	−6.92954e7			−0.551050
$502$	9.00192e7	+	6.32857e7i	0.711581	+	0.500258i
$503$			6.56486e7i			0.515848i	0.966165	+	0.257924i	$0.0830384\pi$
$503$			6.56486e7i			0.515848i	−0.966165	+	0.257924i	$0.916962\pi$
$504$	7.13588e6	−	2.60407e7i	0.0557385	−	0.203405i
$505$	1.01445e7			0.0787692
$506$	−3.13887e7	+	4.46482e7i	−0.242283	+	0.344629i
$507$			8.88758e7i			0.681961i
$508$	−1.31235e8	+	4.72053e7i	−1.00106	+	0.360081i
$509$	−2.39636e8			−1.81718			−0.908592	−	0.417686i	$-0.862841\pi$
$509$	−2.39636e8			−1.81718			−0.908592	+	0.417686i	$0.862841\pi$
$510$	4.39081e7	+	3.08685e7i	0.331005	+	0.232704i
$511$			5.63413e7i			0.422244i
$512$	9.32804e7	+	9.65047e7i	0.694993	+	0.719016i
$513$	3.36138e7			0.248981
$514$	7.45936e7	−	1.06104e8i	0.549304	−	0.781344i
$515$			2.23778e7i			0.163831i
$516$	1.32971e7	+	3.69670e7i	0.0967847	+	0.269070i
$517$	1.23794e8			0.895834
$518$	−2.07884e7	−	1.46148e7i	−0.149566	−	0.105148i
$519$		−	1.10320e8i		−	0.789136i
$520$	−1.78567e7	−	4.89323e6i	−0.126996	−	0.0348005i
$521$	−1.41796e8			−1.00265			−0.501326	−	0.865259i	$-0.667154\pi$
$521$	−1.41796e8			−1.00265			−0.501326	+	0.865259i	$0.667154\pi$
$522$	3.31573e7	−	4.71638e7i	0.233114	−	0.331587i
$523$		−	1.25526e8i		−	0.877466i	−0.898618	−	0.438733i	$-0.855427\pi$
$523$		−	1.25526e8i		−	0.877466i	0.898618	−	0.438733i	$-0.144573\pi$
$524$	−1.17410e8	+	4.22325e7i	−0.816039	+	0.293530i
$525$	5.20728e7			0.359860
$526$	−3.02899e7	−	2.12945e7i	−0.208133	−	0.146322i
$527$			1.29416e8i			0.884208i
$528$	5.25039e7	−	4.33847e7i	0.356689	−	0.294737i
$529$	7.35587e7			0.496898
$530$	−1.76113e6	+	2.50507e6i	−0.0118294	+	0.0168265i
$531$			8.50291e7i			0.567916i
$532$	−6.27332e6	−	1.74404e7i	−0.0416642	−	0.115830i
$533$	−7.79754e7			−0.514963
$534$	2.29997e7	+	1.61694e7i	0.151042	+	0.106186i
$535$		−	1.13273e7i		−	0.0739716i
$536$	−2.55567e7	+	9.32631e7i	−0.165962	+	0.605642i
$537$	1.74199e8			1.12492
$538$	9.03646e7	−	1.28537e8i	0.580298	−	0.825432i
$539$		−	6.62283e7i		−	0.422938i
$540$	5.99784e7	−	2.15743e7i	0.380902	−	0.137011i
$541$	1.61470e6			0.0101976			0.00509882	−	0.999987i	$-0.498377\pi$
$541$	1.61470e6			0.0101976			0.00509882	+	0.999987i	$0.498377\pi$
$542$	1.77550e8	+	1.24822e8i	1.11513	+	0.783960i
$543$			1.67320e8i			1.04508i
$544$	1.74293e7	+	2.23492e8i	0.108264	+	1.38824i
$545$	2.87189e7			0.177410
$546$	1.38149e7	−	1.96507e7i	0.0848734	−	0.120726i
$547$		−	2.46031e8i		−	1.50324i	−0.659599	−	0.751618i	$-0.729274\pi$
$547$		−	2.46031e8i		−	1.50324i	0.659599	−	0.751618i	$-0.270726\pi$
$548$	8.00131e7	+	2.22443e8i	0.486205	+	1.35169i
$549$	−6.68663e7			−0.404101
$550$	−6.95914e7	−	4.89244e7i	−0.418280	−	0.294061i
$551$		−	3.95750e7i		−	0.236573i
$552$	8.96383e7	+	2.45634e7i	0.532937	+	0.146040i
$553$	−8.23906e7			−0.487194
$554$	−4.28842e7	+	6.09996e7i	−0.252213	+	0.358755i
$555$		−	1.69264e7i		−	0.0990118i
$556$	−7.68822e7	+	2.76546e7i	−0.447303	+	0.160895i
$557$	1.91348e8			1.10728			0.553642	−	0.832755i	$-0.313238\pi$
$557$	1.91348e8			1.10728			0.553642	+	0.832755i	$0.313238\pi$
$558$	3.54756e7	+	2.49402e7i	0.204187	+	0.143548i
$559$		−	2.26346e7i		−	0.129580i
$560$	−2.23875e7	−	2.70932e7i	−0.127480	−	0.154275i
$561$	1.13756e8			0.644298
$562$	−1.36125e8	+	1.93628e8i	−0.766884	+	1.09084i
$563$			2.18743e8i			1.22577i	0.790172	+	0.612885i	$0.209991\pi$
$563$			2.18743e8i			1.22577i	−0.790172	+	0.612885i	$0.790009\pi$
$564$	−7.13546e7	−	1.98372e8i	−0.397727	−	1.10571i
$565$	−772553.			−0.00428335
$566$	−1.57018e8	−	1.10388e8i	−0.865966	−	0.608795i
$567$			4.42510e7i			0.242758i
$568$	2.07865e7	−	7.58555e7i	0.113432	−	0.413944i
$569$	−5.50261e7			−0.298698			−0.149349	−	0.988785i	$-0.547718\pi$
$569$	−5.50261e7			−0.298698			−0.149349	+	0.988785i	$0.547718\pi$
$570$	7.10020e6	−	1.00995e7i	0.0383395	−	0.0545351i
$571$		−	2.81053e8i		−	1.50966i	−0.655920	−	0.754831i	$-0.727719\pi$
$571$		−	2.81053e8i		−	1.50966i	0.655920	−	0.754831i	$-0.272281\pi$
$572$	−3.69253e7	+	1.32821e7i	−0.197304	+	0.0709704i
$573$	−9.54710e7			−0.507467
$574$	−1.21087e8	−	8.51272e7i	−0.640269	−	0.450125i
$575$		−	1.16085e8i		−	0.610621i
$576$	6.46229e7	+	3.82923e7i	0.338157	+	0.200375i
$577$	−1.88729e8			−0.982453			−0.491226	−	0.871032i	$-0.663451\pi$
$577$	−1.88729e8			−0.982453			−0.491226	+	0.871032i	$0.663451\pi$
$578$	−1.04275e8	+	1.48323e8i	−0.540002	+	0.768113i
$579$			1.99661e8i			1.02862i
$580$	−2.54003e7	−	7.06152e7i	−0.130183	−	0.361921i
$581$	−6.56949e7			−0.334968
$582$	8.52166e6	+	5.99093e6i	0.0432270	+	0.0303896i
$583$			6.49009e6i			0.0327526i
$584$	−1.51168e8	−	4.14243e7i	−0.758966	−	0.207978i
$585$	−1.03621e7			−0.0517582
$586$	−1.14253e8	+	1.62516e8i	−0.567773	+	0.807615i
$587$			3.09526e7i			0.153032i	0.997068	+	0.0765161i	$0.0243797\pi$
$587$			3.09526e7i			0.153032i	−0.997068	+	0.0765161i	$0.975620\pi$
$588$	−1.06127e8	+	3.81739e7i	−0.522026	+	0.187773i
$589$	2.97675e7			0.145679
$590$	9.05433e7	+	6.36542e7i	0.440860	+	0.309935i
$591$		−	3.01938e8i		−	1.46270i
$592$	5.44971e7	−	4.50317e7i	0.262669	−	0.217047i
$593$	−3.20132e8			−1.53520			−0.767601	−	0.640928i	$-0.778550\pi$
$593$	−3.20132e8			−1.53520			−0.767601	+	0.640928i	$0.778550\pi$
$594$	7.76955e7	−	1.10516e8i	0.370712	−	0.527310i
$595$		−	5.87008e7i		−	0.278672i
$596$	−8.54392e7	−	2.37528e8i	−0.403569	−	1.12196i
$597$	−4.27127e7			−0.200740
$598$	−4.38069e7	−	3.07973e7i	−0.204852	−	0.144016i
$599$		−	3.38491e8i		−	1.57495i	−0.616347	−	0.787475i	$-0.711388\pi$
$599$		−	3.38491e8i		−	1.57495i	0.616347	−	0.787475i	$-0.288612\pi$
$600$	−3.82860e7	+	1.39716e8i	−0.177250	+	0.646832i
$601$	1.12162e8			0.516682			0.258341	−	0.966054i	$-0.416824\pi$
$601$	1.12162e8			0.516682			0.258341	+	0.966054i	$0.416824\pi$
$602$	2.47106e7	−	3.51490e7i	0.113264	−	0.161110i
$603$			5.41197e7i			0.246833i
$604$	−2.88700e8	+	1.03846e8i	−1.31020	+	0.471279i
$605$	−5.34601e7			−0.241414
$606$	−2.99531e7	−	2.10578e7i	−0.134594	−	0.0946225i
$607$			5.34945e7i			0.239190i	0.992823	+	0.119595i	$0.0381596\pi$
$607$			5.34945e7i			0.239190i	−0.992823	+	0.119595i	$0.961840\pi$
$608$	5.14064e7	−	4.00901e6i	0.228721	−	0.0178372i
$609$	9.73609e7			0.431055
$610$	−5.00572e7	+	7.12027e7i	−0.220535	+	0.313694i
$611$			1.21462e8i			0.532494i
$612$	4.24641e7	+	1.18054e8i	0.185254	+	0.515022i
$613$	4.29793e8			1.86585			0.932927	−	0.360065i	$-0.117246\pi$
$613$	4.29793e8			1.86585			0.932927	+	0.360065i	$0.117246\pi$
$614$	−3.30418e8	−	2.32292e8i	−1.42744	−	1.00353i
$615$		−	9.85922e7i		−	0.423855i
$616$	−7.18411e7	−	1.96864e7i	−0.307348	−	0.0842219i
$617$	−422369.			−0.00179820			−0.000899098	−	1.00000i	$-0.500286\pi$
$617$	−422369.			−0.00179820			−0.000899098		1.00000i	$0.500286\pi$
$618$	4.64516e7	−	6.60739e7i	0.196804	−	0.279940i
$619$		−	5.53231e7i		−	0.233257i	−0.993176	−	0.116628i	$-0.962791\pi$
$619$		−	5.53231e7i		−	0.233257i	0.993176	−	0.116628i	$-0.0372087\pi$
$620$	5.31153e7	−	1.91056e7i	0.222866	−	0.0801652i
$621$	1.84351e8			0.769787
$622$	2.58615e8	+	1.81813e8i	1.07469	+	0.755533i
$623$		−	3.07483e7i		−	0.127162i
$624$	4.25673e7	+	5.15147e7i	0.175195	+	0.212020i
$625$	1.46972e8			0.601999
$626$	−1.73039e8	+	2.46135e8i	−0.705377	+	1.00335i
$627$		−	2.61656e7i		−	0.106152i
$628$	−9.31971e7	−	2.59096e8i	−0.376291	−	1.04612i
$629$	1.18075e8			0.474466
$630$	−1.60912e7	−	1.13125e7i	−0.0643526	−	0.0452414i
$631$		−	3.51832e8i		−	1.40039i	−0.713954	−	0.700193i	$-0.753097\pi$
$631$		−	3.51832e8i		−	1.40039i	0.713954	−	0.700193i	$-0.246903\pi$
$632$	6.05768e7	−	2.21061e8i	0.239969	−	0.875711i
$633$	−9.66728e7			−0.381148
$634$	−1.23124e8	+	1.75135e8i	−0.483144	+	0.687236i
$635$			1.01600e8i			0.396800i
$636$	1.04000e7	−	3.74088e6i	0.0404260	−	0.0145413i
$637$	6.49804e7			0.251399
$638$	−1.30115e8	−	9.14743e7i	−0.501033	−	0.352239i
$639$		−	4.40182e7i		−	0.168706i
$640$	8.91534e7	−	4.01475e7i	0.340093	−	0.153151i
$641$	−4.66445e8			−1.77103			−0.885515	−	0.464611i	$-0.846194\pi$
$641$	−4.66445e8			−1.77103			−0.885515	+	0.464611i	$0.846194\pi$
$642$	−2.35130e7	+	3.34455e7i	−0.0888593	+	0.126396i
$643$			5.04498e8i			1.89770i	0.315732	+	0.948849i	$0.397750\pi$
$643$			5.04498e8i			1.89770i	−0.315732	+	0.948849i	$0.602250\pi$
$644$	−3.44053e7	−	9.56497e7i	−0.128815	−	0.358118i
$645$	2.86192e7			0.106654
$646$	7.04518e7	+	4.95293e7i	0.261333	+	0.183723i
$647$		−	4.91604e8i		−	1.81511i	−0.419933	−	0.907555i	$-0.637946\pi$
$647$		−	4.91604e8i		−	1.81511i	0.419933	−	0.907555i	$-0.362054\pi$
$648$	−1.18729e8	−	3.25351e7i	−0.436347	−	0.119571i
$649$	2.34578e8			0.858130
$650$	4.80026e7	−	6.82802e7i	0.174793	−	0.248631i
$651$			7.32328e7i			0.265438i
$652$	−3.24478e8	+	1.16715e8i	−1.17069	+	0.421098i
$653$	1.28322e8			0.460851			0.230425	−	0.973090i	$-0.425988\pi$
$653$	1.28322e8			0.460851			0.230425	+	0.973090i	$0.425988\pi$
$654$	−8.47967e7	−	5.96141e7i	−0.303142	−	0.213116i
$655$			9.08967e7i			0.323463i
$656$	3.17431e8	−	2.62298e8i	1.12445	−	0.929146i
$657$	−8.77215e7			−0.309321
$658$	−1.32602e8	+	1.88616e8i	−0.465449	+	0.662066i
$659$		−	2.71006e8i		−	0.946941i	−0.880810	−	0.473471i	$-0.843001\pi$
$659$		−	2.71006e8i		−	0.946941i	0.880810	−	0.473471i	$-0.156999\pi$
$660$	−1.67938e7	−	4.66883e7i	−0.0584142	−	0.162397i
$661$	1.40824e8			0.487609			0.243804	−	0.969824i	$-0.421605\pi$
$661$	1.40824e8			0.487609			0.243804	+	0.969824i	$0.421605\pi$
$662$	−2.55882e7	−	1.79892e7i	−0.0881996	−	0.0620064i
$663$			1.11613e8i			0.382979i
$664$	4.83014e7	−	1.76265e8i	0.164989	−	0.602090i
$665$	−1.35020e7			−0.0459129
$666$	2.27547e7	−	3.23669e7i	0.0770280	−	0.109567i
$667$		−	2.17044e8i		−	0.731427i
$668$	−1.98394e8	+	7.13625e7i	−0.665579	+	0.239409i
$669$	9.54151e7			0.318668
$670$	5.76294e7	+	4.05149e7i	0.191611	+	0.134707i
$671$			1.84471e8i			0.610604i
$672$	9.86280e6	+	1.26468e8i	0.0325007	+	0.416748i
$673$	5.04359e7			0.165461			0.0827303	−	0.996572i	$-0.473636\pi$
$673$	5.04359e7			0.165461			0.0827303	+	0.996572i	$0.473636\pi$
$674$	−9.08913e7	+	1.29286e8i	−0.296854	+	0.422253i
$675$			2.87341e8i			0.934299i
$676$	9.15270e7	+	2.54453e8i	0.296285	+	0.823697i
$677$	−2.71022e8			−0.873452			−0.436726	−	0.899594i	$-0.643862\pi$
$677$	−2.71022e8			−0.873452			−0.436726	+	0.899594i	$0.643862\pi$
$678$	2.28108e6	+	1.60365e6i	0.00731899	+	0.00514543i
$679$		−	1.13926e7i		−	0.0363927i
$680$	1.57499e8	+	4.31591e7i	0.500900	+	0.137260i
$681$	2.99290e8			0.947655
$682$	6.88050e7	−	9.78701e7i	0.216904	−	0.308530i
$683$			1.66132e7i			0.0521425i	0.999660	+	0.0260713i	$0.00829968\pi$
$683$			1.66132e7i			0.0521425i	−0.999660	+	0.0260713i	$0.991700\pi$
$684$	2.71541e7	−	9.76736e6i	0.0848530	−	0.0305217i
$685$	1.72212e8			0.535785
$686$	2.42611e8	+	1.70561e8i	0.751516	+	0.528334i
$687$			4.32891e8i			1.33508i
$688$	7.61395e7	+	9.21435e7i	0.233800	+	0.282943i
$689$	−6.36781e6			−0.0194685
$690$	3.89402e7	−	5.53896e7i	0.118536	−	0.168609i
$691$		−	6.71702e7i		−	0.203583i	−0.994806	−	0.101792i	$-0.967542\pi$
$691$		−	6.71702e7i		−	0.203583i	0.994806	−	0.101792i	$-0.0324575\pi$
$692$	−1.13611e8	−	3.15848e8i	−0.342848	−	0.953147i
$693$	−4.16887e7			−0.125262
$694$	−4.27955e7	−	3.00863e7i	−0.128032	−	0.0900098i
$695$			5.95209e7i			0.177303i
$696$	−7.15835e7	+	2.61227e8i	−0.212317	+	0.774802i
$697$	6.87756e8			2.03112
$698$	−3.73069e8	+	5.30663e8i	−1.09704	+	1.56046i
$699$			3.30954e8i			0.969029i
$700$	1.49086e8	−	5.36262e7i	0.434652	−	0.156345i
$701$	1.39571e8			0.405173			0.202586	−	0.979264i	$-0.435065\pi$
$701$	1.39571e8			0.405173			0.202586	+	0.979264i	$0.435065\pi$
$702$	1.08434e8	+	7.62316e7i	0.313439	+	0.220356i
$703$		−	2.71589e7i		−	0.0781712i
$704$	1.05641e8	−	1.78281e8i	0.302770	−	0.510962i
$705$	−1.53576e8			−0.438285
$706$	−2.86292e8	+	4.07229e8i	−0.813569	+	1.15724i
$707$			4.00443e7i			0.113314i
$708$	−1.35210e8	−	3.75897e8i	−0.380987	−	1.05918i
$709$	7.51108e7			0.210748			0.105374	−	0.994433i	$-0.466396\pi$
$709$	7.51108e7			0.210748			0.105374	+	0.994433i	$0.466396\pi$
$710$	−4.68728e7	−	3.29527e7i	−0.130962	−	0.0920696i
$711$		−	1.28279e8i		−	0.356901i
$712$	8.25004e7	+	2.26074e7i	0.228568	+	0.0626340i
$713$	1.63256e8			0.450403
$714$	−1.21850e8	+	1.73323e8i	−0.334758	+	0.476169i
$715$			2.85869e7i			0.0782076i
$716$	4.98735e8	−	1.79395e8i	1.35872	−	0.488734i
$717$	2.42643e7			0.0658280
$718$	2.96985e8	+	2.08787e8i	0.802344	+	0.564067i
$719$		−	3.96575e8i		−	1.06694i	−0.845820	−	0.533468i	$-0.820888\pi$
$719$		−	3.96575e8i		−	1.06694i	0.845820	−	0.533468i	$-0.179112\pi$
$720$	4.21832e7	−	3.48566e7i	0.113016	−	0.0933871i
$721$	−8.83342e7			−0.235680
$722$	1.13925e7	−	1.62049e7i	0.0302696	−	0.0430562i
$723$		−	2.06333e7i		−	0.0545952i
$724$	1.72311e8	+	4.79040e8i	0.454044	+	1.26228i
$725$	3.38299e8			0.887741
$726$	1.57849e8	+	1.10971e8i	0.412507	+	0.290002i
$727$			5.28973e8i			1.37667i	0.725392	+	0.688336i	$0.241658\pi$
$727$			5.28973e8i			1.37667i	−0.725392	+	0.688336i	$0.758342\pi$
$728$	1.93155e7	−	7.04875e7i	0.0500625	−	0.182691i
$729$	−3.96461e8			−1.02334
$730$	−6.56698e7	+	9.34104e7i	−0.168809	+	0.240119i
$731$			1.99641e8i			0.511089i
$732$	2.95603e8	−	1.06329e8i	0.753659	−	0.271092i
$733$	−5.41561e8			−1.37510			−0.687551	−	0.726136i	$-0.741314\pi$
$733$	−5.41561e8			−1.37510			−0.687551	+	0.726136i	$0.741314\pi$
$734$	5.57294e8	+	3.91791e8i	1.40928	+	0.990756i
$735$			8.21614e7i			0.206922i
$736$	2.81932e8	−	2.19869e7i	0.707150	−	0.0551481i
$737$	1.49305e8			0.372969
$738$	1.32540e8	−	1.88529e8i	0.329745	−	0.469039i
$739$		−	6.74728e8i		−	1.67184i	−0.548848	−	0.835922i	$-0.684934\pi$
$739$		−	6.74728e8i		−	1.67184i	0.548848	−	0.835922i	$-0.315066\pi$
$740$	−1.74314e7	−	4.84608e7i	−0.0430167	−	0.119590i
$741$	2.56726e7			0.0630981
$742$	−9.88851e6	−	6.95186e6i	−0.0242058	−	0.0170173i
$743$		−	5.91590e8i		−	1.44230i	−0.692781	−	0.721148i	$-0.743615\pi$
$743$		−	5.91590e8i		−	1.44230i	0.692781	−	0.721148i	$-0.256385\pi$
$744$	−1.96490e8	−	5.38436e7i	−0.477113	−	0.130742i
$745$	−1.83890e8			−0.444723
$746$	2.12476e8	−	3.02231e8i	0.511791	−	0.727985i
$747$		−	1.02285e8i		−	0.245386i
$748$	3.25687e8	−	1.17150e8i	0.778207	−	0.279922i
$749$	4.47133e7			0.106412
$750$	1.86619e8	+	1.31197e8i	0.442355	+	0.310987i
$751$		−	2.10445e8i		−	0.496842i	−0.968652	−	0.248421i	$-0.920088\pi$
$751$		−	2.10445e8i		−	0.496842i	0.968652	−	0.248421i	$-0.0799116\pi$
$752$	−4.08579e8	−	4.94460e8i	−0.960778	−	1.16273i
$753$	−2.89328e8			−0.677650
$754$	8.97508e7	−	1.27664e8i	0.209375	−	0.297820i
$755$			2.23507e8i			0.519338i
$756$	8.51623e7	+	2.36759e8i	0.197098	+	0.547949i
$757$	−2.20837e8			−0.509078			−0.254539	−	0.967063i	$-0.581924\pi$
$757$	−2.20837e8			−0.509078			−0.254539	+	0.967063i	$0.581924\pi$
$758$	2.78417e7	+	1.95734e7i	0.0639275	+	0.0449426i
$759$		−	1.43502e8i		−	0.328196i
$760$	9.92722e6	−	3.62271e7i	0.0226145	−	0.0825264i
$761$	−2.53245e8			−0.574627			−0.287314	−	0.957837i	$-0.592762\pi$
$761$	−2.53245e8			−0.574627			−0.287314	+	0.957837i	$0.592762\pi$
$762$	2.10899e8	−	2.99988e8i	0.476661	−	0.678015i
$763$			1.13365e8i			0.255214i
$764$	−2.73335e8	+	9.83190e7i	−0.612937	+	0.220474i
$765$	9.13952e7			0.204145
$766$	−5.37793e8	−	3.78081e8i	−1.19654	−	0.841199i
$767$			2.30158e8i			0.510083i
$768$	−3.46576e8	−	6.65215e7i	−0.765094	−	0.146852i
$769$	9.07521e7			0.199562			0.0997809	−	0.995009i	$-0.468186\pi$
$769$	9.07521e7			0.199562			0.0997809	+	0.995009i	$0.468186\pi$
$770$	−3.12088e7	+	4.43923e7i	−0.0683605	+	0.0972378i
$771$			3.41025e8i			0.744087i
$772$	2.05617e8	+	5.71632e8i	0.446896	+	1.24241i
$773$	−3.93346e8			−0.851602			−0.425801	−	0.904817i	$-0.640008\pi$
$773$	−3.93346e8			−0.851602			−0.425801	+	0.904817i	$0.640008\pi$
$774$	5.47258e7	+	3.84736e7i	0.118024	+	0.0829736i
$775$			2.54461e8i			0.546659i
$776$	3.05673e7	+	8.37629e6i	0.0654142	+	0.0179253i
$777$	6.68154e7			0.142434
$778$	1.50023e8	−	2.13396e8i	0.318580	−	0.453156i
$779$		−	1.58194e8i		−	0.334640i
$780$	4.58087e7	−	1.64774e7i	0.0965304	−	0.0347221i
$781$	−1.21437e8			−0.254917
$782$	3.86384e8	+	2.71637e8i	0.807977	+	0.568028i
$783$			5.37243e8i			1.11914i
$784$	−2.64530e8	+	2.18585e8i	−0.548942	+	0.453599i
$785$	−2.00588e8			−0.414663
$786$	1.88682e8	−	2.68386e8i	0.388564	−	0.552704i
$787$			4.00467e7i			0.0821565i	0.999156	+	0.0410783i	$0.0130793\pi$
$787$			4.00467e7i			0.0821565i	−0.999156	+	0.0410783i	$0.986921\pi$
$788$	−3.10946e8	−	8.64456e8i	−0.635486	−	1.76671i
$789$	9.73537e7			0.198208
$790$	−1.36599e8	−	9.60321e7i	−0.277054	−	0.194776i
$791$		−	3.04957e6i		−	0.00616183i
$792$	3.06511e7	−	1.11854e8i	0.0616980	−	0.225153i
$793$	−1.80995e8			−0.362950
$794$	7.20016e7	−	1.02417e8i	0.143840	−	0.204602i
$795$		−	8.05147e6i		−	0.0160241i
$796$	−1.22287e8	+	4.39869e7i	−0.242461	+	0.0872136i
$797$	5.42316e7			0.107122			0.0535608	−	0.998565i	$-0.482943\pi$
$797$	5.42316e7			0.107122			0.0535608	+	0.998565i	$0.482943\pi$
$798$	3.98668e7	+	2.80273e7i	0.0784517	+	0.0551534i
$799$		−	1.07131e9i		−	2.10027i
$800$	3.42702e7	+	4.39437e8i	0.0669339	+	0.858276i
$801$	4.78742e7			0.0931545
$802$	5.51217e8	−	7.84065e8i	1.06856	−	1.51995i
$803$			2.42006e8i			0.467390i
$804$	−8.60593e7	−	2.39252e8i	−0.165588	−	0.460350i
$805$	−7.40503e7			−0.141951
$806$	9.60261e7	+	6.75087e7i	0.183394	+	0.128930i
$807$			4.13127e8i			0.786072i
$808$	−1.07442e8	−	2.94422e7i	−0.203677	−	0.0558130i
$809$	−7.90659e8			−1.49329			−0.746644	−	0.665223i	$-0.768336\pi$
$809$	−7.90659e8			−1.49329			−0.746644	+	0.665223i	$0.768336\pi$
$810$	−5.15777e7	+	7.33655e7i	−0.0970525	+	0.138050i
$811$			1.04890e9i			1.96640i	0.182525	+	0.983201i	$0.441573\pi$
$811$			1.04890e9i			1.96640i	−0.182525	+	0.983201i	$0.558427\pi$
$812$	2.78746e8	−	1.00265e8i	0.520644	−	0.187276i
$813$	−5.70659e8			−1.06195
$814$	−8.92937e7	−	6.27756e7i	−0.165557	−	0.116391i
$815$			2.51205e8i			0.464040i
$816$	−3.75451e8	−	4.54368e8i	−0.691007	−	0.836251i
$817$	4.59203e7			0.0842051
$818$	−1.96592e8	+	2.79637e8i	−0.359174	+	0.510899i
$819$		−	4.09032e7i		−	0.0744571i
$820$	−1.01533e8	−	2.82271e8i	−0.184148	−	0.511948i
$821$	−5.47461e8			−0.989290			−0.494645	−	0.869095i	$-0.664702\pi$
$821$	−5.47461e8			−0.989290			−0.494645	+	0.869095i	$0.664702\pi$
$822$	−5.08481e8	−	3.57474e8i	−0.915501	−	0.643619i
$823$			5.77332e8i			1.03568i	0.855477	+	0.517841i	$0.173264\pi$
$823$			5.77332e8i			1.03568i	−0.855477	+	0.517841i	$0.826736\pi$
$824$	6.49468e7	−	2.37008e8i	0.116085	−	0.423625i
$825$	2.23671e8			0.398335
$826$	−2.51268e8	+	3.57410e8i	−0.445859	+	0.634201i
$827$		−	7.17000e8i		−	1.26766i	−0.773473	−	0.633830i	$-0.781482\pi$
$827$		−	7.17000e8i		−	1.26766i	0.773473	−	0.633830i	$-0.218518\pi$
$828$	1.48923e8	−	5.35679e7i	0.262345	−	0.0943656i
$829$	−3.64346e8			−0.639514			−0.319757	−	0.947500i	$-0.603601\pi$
$829$	−3.64346e8			−0.639514			−0.319757	+	0.947500i	$0.603601\pi$
$830$	−1.08918e8	−	7.65720e7i	−0.190487	−	0.133917i
$831$		−	1.96057e8i		−	0.341648i
$832$	1.74922e8	+	1.03650e8i	0.303722	+	0.179970i
$833$	−5.73138e8			−0.991572
$834$	1.23552e8	−	1.75744e8i	0.212987	−	0.302958i
$835$			1.53593e8i			0.263823i
$836$	−2.69462e7	−	7.49127e7i	−0.0461188	−	0.128214i
$837$	−4.04103e8			−0.689153
$838$	1.19781e8	+	8.42093e7i	0.203544	+	0.143096i
$839$			6.25953e8i			1.05988i	0.848036	+	0.529939i	$0.177785\pi$
$839$			6.25953e8i			1.05988i	−0.848036	+	0.529939i	$0.822215\pi$
$840$	8.91246e7	+	2.44226e7i	0.150369	+	0.0412054i
$841$	3.76955e7			0.0633726
$842$	4.13096e8	−	5.87599e8i	0.692014	−	0.984339i
$843$		−	6.22334e8i		−	1.03882i
$844$	−2.76776e8	+	9.95567e7i	−0.460364	+	0.165593i
$845$	1.96993e8			0.326498
$846$	−2.93669e8	−	2.06457e8i	−0.485007	−	0.340971i
$847$		−	2.11028e8i		−	0.347288i
$848$	2.59228e7	−	2.14204e7i	0.0425104	−	0.0351270i
$849$	5.04667e8			0.824674
$850$	−4.23391e8	+	6.02242e8i	−0.689421	+	0.980651i
$851$		−	1.48950e8i		−	0.241686i
$852$	6.99962e7	+	1.94596e8i	0.113176	+	0.314640i
$853$	4.97529e8			0.801625			0.400812	−	0.916160i	$-0.368728\pi$
$853$	4.97529e8			0.801625			0.400812	+	0.916160i	$0.368728\pi$
$854$	−2.81065e8	−	1.97596e8i	−0.451267	−	0.317252i
$855$		−	2.10222e7i		−	0.0336342i
$856$	−3.28750e7	+	1.19970e8i	−0.0524136	+	0.191271i
$857$	7.64394e8			1.21444			0.607218	−	0.794535i	$-0.292285\pi$
$857$	7.64394e8			1.21444			0.607218	+	0.794535i	$0.292285\pi$
$858$	5.93402e7	−	8.44070e7i	0.0939479	−	0.133634i
$859$			3.81161e7i			0.0601352i	0.999548	+	0.0300676i	$0.00957226\pi$
$859$			3.81161e7i			0.0601352i	−0.999548	+	0.0300676i	$0.990428\pi$
$860$	8.19373e7	−	2.94729e7i	0.128821	−	0.0463370i
$861$	3.89183e8			0.609739
$862$	7.06231e8	+	4.96497e8i	1.10262	+	0.775167i
$863$			5.14459e7i			0.0800421i	0.999199	+	0.0400210i	$0.0127425\pi$
$863$			5.14459e7i			0.0800421i	−0.999199	+	0.0400210i	$0.987258\pi$
$864$	−6.97858e8	+	5.44235e7i	−1.08200	+	0.0843811i
$865$	−2.44524e8			−0.377810
$866$	−6.25299e7	+	8.89442e7i	−0.0962795	+	0.136951i
$867$		−	4.76721e8i		−	0.731487i
$868$	7.54174e7	+	2.09667e8i	0.115322	+	0.320605i
$869$	−3.53897e8			−0.539284
$870$	1.61418e8	+	1.13481e8i	0.245129	+	0.172332i
$871$			1.46492e8i			0.221697i
$872$	−3.04167e8	−	8.33502e7i	−0.458736	−	0.125706i
$873$	1.77379e7			0.0266600
$874$	6.24806e7	−	8.88740e7i	0.0935860	−	0.133119i
$875$		−	2.49491e8i		−	0.372417i
$876$	3.87799e8	−	1.39492e8i	0.576892	−	0.207509i
$877$	8.20835e8			1.21691			0.608453	−	0.793590i	$-0.291790\pi$
$877$	8.20835e8			1.21691			0.608453	+	0.793590i	$0.291790\pi$
$878$	1.84605e7	+	1.29782e7i	0.0272747	+	0.0191748i
$879$		−	5.22339e8i		−	0.769105i
$880$	−9.61622e7	−	1.16375e8i	−0.141110	−	0.170770i
$881$	−6.47450e8			−0.946844			−0.473422	−	0.880836i	$-0.656981\pi$
$881$	−6.47450e8			−0.946844			−0.473422	+	0.880836i	$0.656981\pi$
$882$	−1.10452e8	+	1.57110e8i	−0.160978	+	0.228980i
$883$			1.73373e8i			0.251826i	0.992041	+	0.125913i	$0.0401860\pi$
$883$			1.73373e8i			0.251826i	−0.992041	+	0.125913i	$0.959814\pi$
$884$	1.14943e8	+	3.19550e8i	0.166389	+	0.462576i
$885$	−2.91013e8			−0.419838
$886$	−9.69892e8	−	6.81858e8i	−1.39451	−	0.980376i
$887$			5.63804e8i			0.807900i	0.914781	+	0.403950i	$0.132363\pi$
$887$			5.63804e8i			0.807900i	−0.914781	+	0.403950i	$0.867637\pi$
$888$	−4.91253e7	+	1.79271e8i	−0.0701562	+	0.256019i
$889$	−4.01055e8			−0.570819
$890$	3.58394e7	−	5.09789e7i	0.0508383	−	0.0723137i
$891$			1.90074e8i			0.268714i
$892$	2.73175e8	−	9.82614e7i	0.384899	−	0.138449i
$893$	−2.46417e8			−0.346032
$894$	5.42963e8	+	3.81716e8i	0.759902	+	0.534230i
$895$		−	3.86112e8i		−	0.538572i
$896$	1.58478e8	+	3.51924e8i	0.220316	+	0.489243i
$897$	1.40799e8			0.195084
$898$	4.03885e8	−	5.74496e8i	0.557735	−	0.793337i
$899$			4.75767e8i			0.654810i
$900$	8.34943e7	+	2.32121e8i	0.114533	+	0.318411i
$901$	5.61651e7			0.0767879
$902$	−5.20113e8	−	3.65652e8i	−0.708725	−	0.498251i
$903$			1.12971e8i			0.153428i
$904$	8.18227e6	+	2.24217e6i	0.0110756	+	0.00303503i
$905$	3.70865e8			0.500345
$906$	4.63952e8	−	6.59937e8i	0.623861	−	0.887397i
$907$		−	7.10297e7i		−	0.0951959i	−0.998867	−	0.0475980i	$-0.984843\pi$
$907$		−	7.10297e7i		−	0.0951959i	0.998867	−	0.0475980i	$-0.0151566\pi$
$908$	8.56872e8	−	3.08218e8i	1.14461	−	0.411718i
$909$	−6.23477e7			−0.0830097
$910$	−4.35559e7	−	3.06208e7i	−0.0577993	−	0.0406343i
$911$			1.31086e9i			1.73382i	0.498469	+	0.866908i	$0.333896\pi$
$911$			1.31086e9i			1.73382i	−0.498469	+	0.866908i	$0.666104\pi$
$912$	−1.04511e8	+	8.63591e7i	−0.137778	+	0.113848i
$913$	−2.82183e8			−0.370782
$914$	−6.56887e8	+	9.34373e8i	−0.860304	+	1.22372i
$915$		−	2.28850e8i		−	0.298737i
$916$	4.45805e8	+	1.23938e9i	0.580041	+	1.61256i
$917$	−3.58805e8			−0.465319
$918$	−9.56404e8	−	6.72375e8i	−1.23627	−	0.869128i
$919$			2.11036e8i			0.271901i	0.990716	+	0.135950i	$0.0434088\pi$
$919$			2.11036e8i			0.271901i	−0.990716	+	0.135950i	$0.956591\pi$
$920$	5.44447e7	−	1.98683e8i	0.0699185	−	0.255151i
$921$	1.06199e9			1.35938
$922$	−5.08649e7	+	7.23516e7i	−0.0648971	+	0.0923114i
$923$		−	1.19149e8i		−	0.151526i
$924$	1.84297e8	−	6.62920e7i	0.233616	−	0.0840321i
$925$	2.32163e8			0.293337
$926$	1.07379e9	+	7.54898e8i	1.35234	+	0.950725i
$927$		−	1.37534e8i		−	0.172651i
$928$	6.40751e7	+	8.21618e8i	0.0801762	+	1.02808i
$929$	1.07162e9			1.33657			0.668285	−	0.743905i	$-0.267029\pi$
$929$	1.07162e9			1.33657			0.668285	+	0.743905i	$0.267029\pi$
$930$	−8.53581e7	+	1.21416e8i	−0.106120	+	0.150947i
$931$			1.31830e8i			0.163368i
$932$	3.40827e8	+	9.47529e8i	0.421004	+	1.17043i
$933$	−8.31208e8			−1.02345
$934$	−9.01110e8	−	6.33502e8i	−1.10595	−	0.777512i
$935$		−	2.52141e8i		−	0.308467i
$936$	1.09747e8	+	3.00736e7i	0.133833	+	0.0366740i
$937$	1.02180e9			1.24208			0.621039	−	0.783779i	$-0.286711\pi$
$937$	1.02180e9			1.24208			0.621039	+	0.783779i	$0.286711\pi$
$938$	−1.59928e8	+	2.27486e8i	−0.193784	+	0.275643i
$939$		−	7.91096e8i		−	0.955504i
$940$	−4.39692e8	+	1.58157e8i	−0.529376	+	0.190417i
$941$	−2.94539e8			−0.353488			−0.176744	−	0.984257i	$-0.556556\pi$
$941$	−2.94539e8			−0.353488			−0.176744	+	0.984257i	$0.556556\pi$
$942$	5.92265e8	+	4.16376e8i	0.708538	+	0.498119i
$943$		−	8.67595e8i		−	1.03462i
$944$	−7.74220e8	−	9.36956e8i	−0.920340	−	1.11379i
$945$	1.83294e8			0.217197
$946$	1.06141e8	−	1.50978e8i	0.125374	−	0.178336i
$947$		−	8.16992e7i		−	0.0961984i	−0.998843	−	0.0480992i	$-0.984684\pi$
$947$		−	8.16992e7i		−	0.0961984i	0.998843	−	0.0480992i	$-0.0153164\pi$
$948$	2.03986e8	+	5.67098e8i	0.239428	+	0.665630i
$949$	−2.37446e8			−0.277822
$950$	1.38525e8	+	9.73861e7i	0.161568	+	0.113586i
$951$		−	5.62897e8i		−	0.654467i
$952$	−1.70366e8	+	6.21711e8i	−0.197457	+	0.720573i
$953$	2.06256e8			0.238302			0.119151	−	0.992876i	$-0.461983\pi$
$953$	2.06256e8			0.238302			0.119151	+	0.992876i	$0.461983\pi$
$954$	1.08238e7	−	1.53961e7i	0.0124662	−	0.0177323i
$955$			2.11611e8i			0.242957i
$956$	6.94693e7	−	2.49882e7i	0.0795095	−	0.0285996i
$957$	4.18200e8			0.477143
$958$	−1.17794e8	−	8.28118e7i	−0.133975	−	0.0941880i
$959$			6.79788e8i			0.770757i
$960$	−1.31056e8	+	2.21172e8i	−0.148130	+	0.249987i
$961$	5.29641e8			0.596777
$962$	6.15929e7	−	8.76113e7i	0.0691839	−	0.0984090i
$963$			6.96172e7i			0.0779539i
$964$	−2.12488e7	−	5.90736e7i	−0.0237194	−	0.0659420i
$965$	4.42548e8			0.492468
$966$	2.18645e8	+	1.53712e8i	0.242553	+	0.170521i
$967$			9.87671e7i			0.109228i	0.998508	+	0.0546139i	$0.0173928\pi$
$967$			9.87671e7i			0.109228i	−0.998508	+	0.0546139i	$0.982607\pi$
$968$	5.66206e8	+	1.55156e8i	0.624235	+	0.171058i
$969$	−2.26437e8			−0.248872
$970$	1.32789e7	−	1.88883e7i	0.0145495	−	0.0206955i
$971$		−	8.01547e8i		−	0.875531i	−0.899089	−	0.437765i	$-0.855770\pi$
$971$		−	8.01547e8i		−	0.875531i	0.899089	−	0.437765i	$-0.144230\pi$
$972$	−6.33240e8	+	2.27777e8i	−0.689556	+	0.248034i
$973$	−2.34952e8			−0.255060
$974$	−3.60962e8	−	2.53765e8i	−0.390647	−	0.274634i
$975$			2.19457e8i			0.236775i
$976$	7.36816e8	−	6.08842e8i	0.792519	−	0.654870i
$977$	1.72774e9			1.85265			0.926326	−	0.376723i	$-0.122949\pi$
$977$	1.72774e9			1.85265			0.926326	+	0.376723i	$0.122949\pi$
$978$	5.21447e8	−	7.41719e8i	0.557434	−	0.792908i
$979$		−	1.32075e8i		−	0.140758i
$980$	8.46123e7	+	2.35230e8i	0.0898991	+	0.249927i
$981$	−1.76505e8			−0.186961
$982$	−3.66841e8	−	2.57898e8i	−0.387386	−	0.272342i
$983$		−	1.11905e9i		−	1.17812i	−0.808090	−	0.589059i	$-0.799499\pi$
$983$		−	1.11905e9i		−	1.17812i	0.808090	−	0.589059i	$-0.200501\pi$
$984$	−2.86142e8	+	1.04421e9i	−0.300328	+	1.09598i
$985$	−6.69246e8			−0.700289
$986$	−7.91617e8	+	1.12602e9i	−0.825818	+	1.17466i
$987$		−	6.06226e8i		−	0.630497i
$988$	7.35013e7	−	2.64385e7i	0.0762121	−	0.0274136i
$989$	2.51844e8			0.260341
$990$	−6.91173e7	−	4.85911e7i	−0.0712330	−	0.0500785i
$991$			5.35058e8i			0.549769i	0.961477	+	0.274885i	$0.0886396\pi$
$991$			5.35058e8i			0.549769i	−0.961477	+	0.274885i	$0.911360\pi$
$992$	−6.18004e8	+	4.81960e7i	−0.633077	+	0.0493714i
$993$	8.22424e7			0.0839940
$994$	1.30078e8	−	1.85026e8i	0.132447	−	0.188396i
$995$			9.46728e7i			0.0961072i
$996$	1.62650e8	+	4.52181e8i	0.164617	+	0.457650i
$997$	3.06306e8			0.309079			0.154539	−	0.987987i	$-0.450611\pi$
$997$	3.06306e8			0.309079			0.154539	+	0.987987i	$0.450611\pi$
$998$	−2.18346e8	−	1.53502e8i	−0.219661	−	0.154427i
$999$			3.68691e8i			0.369799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.b.a.39.20	yes	54
4.3	odd	2	inner	76.7.b.a.39.19	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.b.a.39.19	✓	54	4.3	odd	2	inner
76.7.b.a.39.20	yes	54	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	76.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.60097 + 6.54454i) q^{2} -21.0346i q^{3} +(-21.6621 - 60.2225i) q^{4} -46.6232 q^{5} +(137.662 + 96.7797i) q^{6} -184.040i q^{7} +(493.796 + 135.314i) q^{8} +286.545 q^{9} +O(q^{10})\)	\(q+(-4.60097 + 6.54454i) q^{2} -21.0346i q^{3} +(-21.6621 - 60.2225i) q^{4} -46.6232 q^{5} +(137.662 + 96.7797i) q^{6} -184.040i q^{7} +(493.796 + 135.314i) q^{8} +286.545 q^{9} +(214.512 - 305.128i) q^{10} -790.519i q^{11} +(-1266.76 + 455.654i) q^{12} +775.625 q^{13} +(1204.46 + 846.765i) q^{14} +980.702i q^{15} +(-3157.51 + 2609.09i) q^{16} -6841.14 q^{17} +(-1318.39 + 1875.31i) q^{18} +1573.56i q^{19} +(1009.96 + 2807.77i) q^{20} -3871.22 q^{21} +(5173.59 + 3637.16i) q^{22} +8630.01i q^{23} +(2846.27 - 10386.8i) q^{24} -13451.3 q^{25} +(-3568.63 + 5076.11i) q^{26} -21361.6i q^{27} +(-11083.4 + 3986.70i) q^{28} -25149.9 q^{29} +(-6418.25 - 4512.18i) q^{30} -18917.2i q^{31} +(-2547.73 - 32668.8i) q^{32} -16628.3 q^{33} +(31475.9 - 44772.1i) q^{34} +8580.56i q^{35} +(-6207.16 - 17256.5i) q^{36} -17259.5 q^{37} +(-10298.2 - 7239.92i) q^{38} -16315.0i q^{39} +(-23022.4 - 6308.76i) q^{40} -100532. q^{41} +(17811.4 - 25335.4i) q^{42} -29182.4i q^{43} +(-47607.1 + 17124.3i) q^{44} -13359.6 q^{45} +(-56479.5 - 39706.5i) q^{46} +156598. i q^{47} +(54881.3 + 66416.9i) q^{48} +83778.1 q^{49} +(61888.9 - 88032.5i) q^{50} +143901. i q^{51} +(-16801.7 - 46710.1i) q^{52} -8209.91 q^{53} +(139802. + 98284.1i) q^{54} +36856.6i q^{55} +(24903.2 - 90878.3i) q^{56} +33099.3 q^{57} +(115714. - 164595. i) q^{58} +296739. i q^{59} +(59060.3 - 21244.1i) q^{60} -233354. q^{61} +(123805. + 87037.7i) q^{62} -52735.8i q^{63} +(225524. + 133635. i) q^{64} -36162.2 q^{65} +(76506.2 - 108824. i) q^{66} +188870. i q^{67} +(148193. + 411991. i) q^{68} +181529. q^{69} +(-56155.8 - 39478.9i) q^{70} -153617. i q^{71} +(141495. + 38773.4i) q^{72} -306135. q^{73} +(79410.6 - 112956. i) q^{74} +282942. i q^{75} +(94763.9 - 34086.7i) q^{76} -145487. q^{77} +(106774. + 75064.8i) q^{78} -447677. i q^{79} +(147213. - 121644. i) q^{80} -240442. q^{81} +(462546. - 657938. i) q^{82} -356959. i q^{83} +(83858.7 + 233135. i) q^{84} +318956. q^{85} +(190985. + 134267. i) q^{86} +529019. i q^{87} +(106968. - 390355. i) q^{88} +167074. q^{89} +(61467.4 - 87432.8i) q^{90} -142746. i q^{91} +(519721. - 186944. i) q^{92} -397917. q^{93} +(-1.02486e6 - 720504. i) q^{94} -73364.6i q^{95} +(-687176. + 53590.4i) q^{96} +61902.8 q^{97} +(-385461. + 548290. i) q^{98} -226519. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9}+O(q^{10}) \) 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9	\( 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9} - 2088 q^{10} - 2384 q^{12} - 828 q^{13} + 4116 q^{14} - 7782 q^{16} + 12220 q^{17} + 15790 q^{18} - 7000 q^{20} - 16048 q^{21} - 51864 q^{22} + 19294 q^{24} + 218346 q^{25} - 18110 q^{26} + 97926 q^{28} - 101996 q^{29} + 50076 q^{30} - 235160 q^{32} + 9072 q^{33} - 51156 q^{34} - 48028 q^{36} - 63420 q^{37} + 157260 q^{40} - 135700 q^{41} + 302290 q^{42} + 137784 q^{44} - 50348 q^{45} - 177084 q^{46} + 111320 q^{48} - 1099338 q^{49} + 485770 q^{50} + 232980 q^{52} + 892932 q^{53} - 730010 q^{54} - 298644 q^{56} - 702534 q^{58} + 1231628 q^{60} + 323700 q^{61} + 1573116 q^{62} - 1065942 q^{64} + 587512 q^{65} - 74604 q^{66} - 1235974 q^{68} + 217376 q^{69} + 1163796 q^{70} - 1228320 q^{72} - 739428 q^{73} - 1852264 q^{74} - 563144 q^{77} - 2516852 q^{78} - 1597436 q^{80} + 4660886 q^{81} - 919236 q^{82} + 4928476 q^{84} - 737904 q^{85} - 1444124 q^{86} + 2679960 q^{88} - 3415940 q^{89} + 4702636 q^{90} - 3230670 q^{92} - 5021584 q^{93} + 1881960 q^{94} + 1838870 q^{96} + 3483660 q^{97} - 3419858 q^{98}+O(q^{100}) \) 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9 - 2088 * q^10 - 2384 * q^12 - 828 * q^13 + 4116 * q^14 - 7782 * q^16 + 12220 * q^17 + 15790 * q^18 - 7000 * q^20 - 16048 * q^21 - 51864 * q^22 + 19294 * q^24 + 218346 * q^25 - 18110 * q^26 + 97926 * q^28 - 101996 * q^29 + 50076 * q^30 - 235160 * q^32 + 9072 * q^33 - 51156 * q^34 - 48028 * q^36 - 63420 * q^37 + 157260 * q^40 - 135700 * q^41 + 302290 * q^42 + 137784 * q^44 - 50348 * q^45 - 177084 * q^46 + 111320 * q^48 - 1099338 * q^49 + 485770 * q^50 + 232980 * q^52 + 892932 * q^53 - 730010 * q^54 - 298644 * q^56 - 702534 * q^58 + 1231628 * q^60 + 323700 * q^61 + 1573116 * q^62 - 1065942 * q^64 + 587512 * q^65 - 74604 * q^66 - 1235974 * q^68 + 217376 * q^69 + 1163796 * q^70 - 1228320 * q^72 - 739428 * q^73 - 1852264 * q^74 - 563144 * q^77 - 2516852 * q^78 - 1597436 * q^80 + 4660886 * q^81 - 919236 * q^82 + 4928476 * q^84 - 737904 * q^85 - 1444124 * q^86 + 2679960 * q^88 - 3415940 * q^89 + 4702636 * q^90 - 3230670 * q^92 - 5021584 * q^93 + 1881960 * q^94 + 1838870 * q^96 + 3483660 * q^97 - 3419858 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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