LMFDB - Embedded newform 97.3.l.a.5.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [97,3,Mod(5,97)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(97, base_ring=CyclotomicField(96)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("97.5"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 97 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	97.l (of order $96$, degree $32$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.64305856429$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$15$ over $\Q(\zeta_{96})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{96}]$

Embedding invariants

Embedding label			5.8
Character	$\chi$	$=$	97.5
Dual form			97.3.l.a.39.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.294635 - 0.597460i) q^{2} +(2.48200 - 2.83018i) q^{3} +(2.16490 - 2.82135i) q^{4} +(-0.576421 - 0.0188701i) q^{5} +(-2.42220 - 0.649027i) q^{6} +(1.69403 + 2.72423i) q^{7} +(-4.93693 - 0.982017i) q^{8} +(-0.674853 - 5.12602i) q^{9} +(0.158559 + 0.349948i) q^{10} +(-10.5723 + 3.58880i) q^{11} +(-2.61165 - 13.1296i) q^{12} +(7.61363 + 8.12899i) q^{13} +(1.12850 - 1.81477i) q^{14} +(-1.48408 + 1.58454i) q^{15} +(-2.81381 - 10.5013i) q^{16} +(6.79034 - 1.58328i) q^{17} +(-2.86375 + 1.91350i) q^{18} +(18.6904 - 9.99020i) q^{19} +(-1.30113 + 1.58543i) q^{20} +(11.9147 + 1.96712i) q^{21} +(5.25912 + 5.25912i) q^{22} +(-2.62842 + 1.88350i) q^{23} +(-15.0328 + 11.5350i) q^{24} +(-24.6146 - 1.61332i) q^{25} +(2.61351 - 6.94392i) q^{26} +(11.9869 + 8.00937i) q^{27} +(11.3534 + 1.11821i) q^{28} +(2.42412 + 1.09836i) q^{29} +(1.38396 + 0.419820i) q^{30} +(3.66257 + 55.8800i) q^{31} +(-20.5830 + 18.0508i) q^{32} +(-16.0834 + 38.8288i) q^{33} +(-2.94662 - 3.59046i) q^{34} +(-0.925071 - 1.60227i) q^{35} +(-15.9233 - 9.19330i) q^{36} +(15.9136 - 2.62735i) q^{37} +(-11.4756 - 8.22328i) q^{38} +(41.9036 - 1.37178i) q^{39} +(2.82722 + 0.659215i) q^{40} +(-10.7481 + 4.04531i) q^{41} +(-2.33519 - 7.69810i) q^{42} +(-9.59864 - 1.26369i) q^{43} +(-12.7626 + 37.5974i) q^{44} +(0.292271 + 2.96748i) q^{45} +(1.89974 + 1.01543i) q^{46} +(20.8607 - 8.64079i) q^{47} +(-36.7044 - 18.1006i) q^{48} +(17.1205 - 34.7169i) q^{49} +(6.28841 + 15.1816i) q^{50} +(12.3726 - 23.1476i) q^{51} +(39.4175 - 3.88228i) q^{52} +(-44.2260 - 15.0127i) q^{53} +(1.25353 - 9.52151i) q^{54} +(6.16180 - 1.86916i) q^{55} +(-5.68809 - 15.1129i) q^{56} +(18.1154 - 77.6928i) q^{57} +(-0.0580070 - 1.77193i) q^{58} +(-41.6658 + 58.1446i) q^{59} +(1.25765 + 7.61748i) q^{60} +(34.2040 - 59.2430i) q^{61} +(32.3070 - 18.6524i) q^{62} +(12.8212 - 10.5221i) q^{63} +(-23.3275 - 9.66257i) q^{64} +(-4.23527 - 4.82939i) q^{65} +(27.9374 - 1.83111i) q^{66} +(-4.64850 + 15.3241i) q^{67} +(10.2334 - 22.5856i) q^{68} +(-1.19310 + 12.1137i) q^{69} +(-0.684734 + 1.02478i) q^{70} +(-33.9696 - 12.7852i) q^{71} +(-1.70213 + 25.9695i) q^{72} +(-14.5252 - 18.9295i) q^{73} +(-6.25843 - 8.73363i) q^{74} +(-65.6594 + 65.6594i) q^{75} +(12.2768 - 74.3598i) q^{76} +(-27.6865 - 22.7217i) q^{77} +(-13.1658 - 24.6315i) q^{78} +(20.7020 + 30.9827i) q^{79} +(1.42378 + 6.10625i) q^{80} +(97.3661 - 26.0892i) q^{81} +(5.58368 + 5.22969i) q^{82} +(-105.909 - 65.8582i) q^{83} +(31.3439 - 29.3568i) q^{84} +(-3.94397 + 0.784504i) q^{85} +(2.07309 + 6.10713i) q^{86} +(9.12522 - 4.13459i) q^{87} +(55.7188 - 7.33552i) q^{88} +(-23.2154 + 116.712i) q^{89} +(1.68684 - 1.04894i) q^{90} +(-9.24748 + 34.5121i) q^{91} +(-0.376251 + 11.4933i) q^{92} +(167.241 + 128.329i) q^{93} +(-11.3088 - 9.91756i) q^{94} +(-10.9620 + 5.40588i) q^{95} +103.056i q^{96} +(-6.81000 - 96.7607i) q^{97} -25.7862 q^{98} +(25.5310 + 51.7717i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} + 64 q^{9} - 32 q^{10} - 32 q^{11} - 224 q^{12} - 32 q^{13} - 32 q^{14} + 224 q^{15} - 32 q^{16} + 48 q^{17} - 32 q^{18}+ \cdots - 512 q^{99}+O(q^{100}) $ 480 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 + 64 * q^9 - 32 * q^10 - 32 * q^11 - 224 * q^12 - 32 * q^13 - 32 * q^14 + 224 * q^15 - 32 * q^16 + 48 * q^17 - 32 * q^18 - 32 * q^19 - 416 * q^20 - 32 * q^21 - 32 * q^22 - 144 * q^23 - 32 * q^24 + 288 * q^25 + 48 * q^26 - 32 * q^27 - 272 * q^28 + 256 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 + 144 * q^33 - 432 * q^34 - 16 * q^35 - 48 * q^36 - 272 * q^37 - 32 * q^38 - 384 * q^39 + 544 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 + 496 * q^44 - 240 * q^45 - 32 * q^46 - 800 * q^47 - 912 * q^48 - 32 * q^49 - 32 * q^50 + 160 * q^51 + 352 * q^52 - 32 * q^53 + 1376 * q^54 - 352 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 544 * q^59 + 1408 * q^60 - 16 * q^61 - 48 * q^62 - 288 * q^63 - 32 * q^64 + 544 * q^65 - 1696 * q^66 - 32 * q^67 + 1696 * q^68 - 32 * q^69 - 1728 * q^70 + 16 * q^71 - 96 * q^72 - 176 * q^73 - 752 * q^74 - 32 * q^75 + 2368 * q^76 - 32 * q^77 - 32 * q^78 + 1776 * q^79 + 1760 * q^80 - 160 * q^81 + 80 * q^82 + 384 * q^83 + 2272 * q^84 + 944 * q^85 + 1888 * q^86 + 1760 * q^87 + 2272 * q^88 + 640 * q^89 + 2240 * q^90 + 928 * q^91 - 624 * q^92 + 784 * q^93 + 224 * q^94 - 448 * q^95 - 192 * q^97 - 768 * q^98 - 512 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/97\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{1}{96}\right)$

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 $

$2$	−0.294635	−	0.597460i	−0.147317	−	0.298730i	0.810689	−	0.585477i	$-0.199093\pi$
$2$	−0.294635	−	0.597460i	−0.147317	−	0.298730i	−0.958006	+	0.286747i	$0.907426\pi$
$3$	2.48200	−	2.83018i	0.827334	−	0.943393i	−0.171795	−	0.985133i	$-0.554957\pi$
$3$	2.48200	−	2.83018i	0.827334	−	0.943393i	0.999129	+	0.0417395i	$0.0132899\pi$
$4$	2.16490	−	2.82135i	0.541224	−	0.705337i
$5$	−0.576421	−	0.0188701i	−0.115284	−	0.00377402i	−0.0249775	−	0.999688i	$-0.507951\pi$
$5$	−0.576421	−	0.0188701i	−0.115284	−	0.00377402i	−0.0903067	+	0.995914i	$0.528785\pi$
$6$	−2.42220	−	0.649027i	−0.403700	−	0.108171i
$7$	1.69403	+	2.72423i	0.242005	+	0.389176i	0.947610	−	0.319430i	$-0.103491\pi$
$7$	1.69403	+	2.72423i	0.242005	+	0.389176i	−0.705605	+	0.708605i	$0.749325\pi$
$8$	−4.93693	−	0.982017i	−0.617116	−	0.122752i
$9$	−0.674853	−	5.12602i	−0.0749836	−	0.569557i
$10$	0.158559	+	0.349948i	0.0158559	+	0.0349948i
$11$	−10.5723	+	3.58880i	−0.961115	+	0.326254i	−0.757528	−	0.652803i	$-0.773593\pi$
$11$	−10.5723	+	3.58880i	−0.961115	+	0.326254i	−0.203586	+	0.979057i	$0.565260\pi$
$12$	−2.61165	−	13.1296i	−0.217637	−	1.09414i
$13$	7.61363	+	8.12899i	0.585664	+	0.625307i	0.952339	−	0.305042i	$-0.0986705\pi$
$13$	7.61363	+	8.12899i	0.585664	+	0.625307i	−0.366675	+	0.930349i	$0.619504\pi$
$14$	1.12850	−	1.81477i	0.0806068	−	0.129626i
$15$	−1.48408	+	1.58454i	−0.0989389	+	0.105636i
$16$	−2.81381	−	10.5013i	−0.175863	−	0.656330i
$17$	6.79034	−	1.58328i	0.399432	−	0.0931344i	−0.0225344	−	0.999746i	$-0.507174\pi$
$17$	6.79034	−	1.58328i	0.399432	−	0.0931344i	0.421966	+	0.906612i	$0.361340\pi$
$18$	−2.86375	+	1.91350i	−0.159097	+	0.106305i
$19$	18.6904	−	9.99020i	0.983703	−	0.525800i	0.100574	−	0.994930i	$-0.467932\pi$
$19$	18.6904	−	9.99020i	0.983703	−	0.525800i	0.883129	+	0.469129i	$0.155432\pi$
$20$	−1.30113	+	1.58543i	−0.0650566	+	0.0792717i
$21$	11.9147	+	1.96712i	0.567364	+	0.0936722i
$22$	5.25912	+	5.25912i	0.239051	+	0.239051i
$23$	−2.62842	+	1.88350i	−0.114279	+	0.0818912i	−0.638176	−	0.769890i	$-0.720311\pi$
$23$	−2.62842	+	1.88350i	−0.114279	+	0.0818912i	0.523897	+	0.851781i	$0.324478\pi$
$24$	−15.0328	+	11.5350i	−0.626365	+	0.480626i
$25$	−24.6146	−	1.61332i	−0.984583	−	0.0645330i
$26$	2.61351	−	6.94392i	0.100520	−	0.267074i
$27$	11.9869	+	8.00937i	0.443958	+	0.296643i
$28$	11.3534	+	1.11821i	0.405479	+	0.0399362i
$29$	2.42412	+	1.09836i	0.0835905	+	0.0378744i	0.454068	−	0.890967i	$-0.349972\pi$
$29$	2.42412	+	1.09836i	0.0835905	+	0.0378744i	−0.370477	+	0.928842i	$0.620806\pi$
$30$	1.38396	+	0.419820i	0.0461320	+	0.0139940i
$31$	3.66257	+	55.8800i	0.118147	+	1.80258i	0.487322	+	0.873222i	$0.337974\pi$
$31$	3.66257	+	55.8800i	0.118147	+	1.80258i	−0.369175	+	0.929360i	$0.620360\pi$
$32$	−20.5830	+	18.0508i	−0.643220	+	0.564089i
$33$	−16.0834	+	38.8288i	−0.487376	+	1.17663i
$34$	−2.94662	−	3.59046i	−0.0866652	−	0.105602i
$35$	−0.925071	−	1.60227i	−0.0264306	−	0.0457791i
$36$	−15.9233	−	9.19330i	−0.442313	−	0.255369i
$37$	15.9136	−	2.62735i	0.430097	−	0.0710094i	0.0560696	−	0.998427i	$-0.482143\pi$
$37$	15.9136	−	2.62735i	0.430097	−	0.0710094i	0.374028	+	0.927418i	$0.377976\pi$
$38$	−11.4756	−	8.22328i	−0.301989	−	0.216402i
$39$	41.9036	−	1.37178i	1.07445	−	0.0351739i
$40$	2.82722	+	0.659215i	0.0706805	+	0.0164804i
$41$	−10.7481	+	4.04531i	−0.262150	+	0.0986662i	−0.479853	−	0.877349i	$-0.659310\pi$
$41$	−10.7481	+	4.04531i	−0.262150	+	0.0986662i	0.217704	+	0.976015i	$0.430143\pi$
$42$	−2.33519	−	7.69810i	−0.0555999	−	0.183288i
$43$	−9.59864	−	1.26369i	−0.223224	−	0.0293880i	0.0180843	−	0.999836i	$-0.494243\pi$
$43$	−9.59864	−	1.26369i	−0.223224	−	0.0293880i	−0.241309	+	0.970448i	$0.577577\pi$
$44$	−12.7626	+	37.5974i	−0.290059	+	0.854487i
$45$	0.292271	+	2.96748i	0.00649491	+	0.0659440i
$46$	1.89974	+	1.01543i	0.0412986	+	0.0220746i
$47$	20.8607	−	8.64079i	0.443845	−	0.183847i	−0.149557	−	0.988753i	$-0.547785\pi$
$47$	20.8607	−	8.64079i	0.443845	−	0.183847i	0.593402	+	0.804907i	$0.297785\pi$
$48$	−36.7044	−	18.1006i	−0.764674	−	0.377096i
$49$	17.1205	−	34.7169i	0.349397	−	0.708508i
$50$	6.28841	+	15.1816i	0.125768	+	0.303631i
$51$	12.3726	−	23.1476i	0.242601	−	0.453874i
$52$	39.4175	−	3.88228i	0.758028	−	0.0746593i
$53$	−44.2260	−	15.0127i	−0.834452	−	0.283258i	−0.128670	−	0.991687i	$-0.541071\pi$
$53$	−44.2260	−	15.0127i	−0.834452	−	0.283258i	−0.705782	+	0.708429i	$0.749404\pi$
$54$	1.25353	−	9.52151i	0.0232135	−	0.176324i
$55$	6.16180	−	1.86916i	0.112033	−	0.0339847i
$56$	−5.68809	−	15.1129i	−0.101573	−	0.269873i
$57$	18.1154	−	77.6928i	0.317814	−	1.36303i
$58$	−0.0580070	−	1.77193i	−0.00100012	−	0.0305505i
$59$	−41.6658	+	58.1446i	−0.706200	+	0.985501i	0.293365	+	0.956001i	$0.405225\pi$
$59$	−41.6658	+	58.1446i	−0.706200	+	0.985501i	−0.999565	+	0.0295005i	$0.990608\pi$
$60$	1.25765	+	7.61748i	0.0209609	+	0.126958i
$61$	34.2040	−	59.2430i	0.560721	−	0.971197i	−0.436713	−	0.899601i	$-0.643857\pi$
$61$	34.2040	−	59.2430i	0.560721	−	0.971197i	0.997434	−	0.0715961i	$-0.0228093\pi$
$62$	32.3070	−	18.6524i	0.521080	−	0.300846i
$63$	12.8212	−	10.5221i	0.203511	−	0.167017i
$64$	−23.3275	−	9.66257i	−0.364492	−	0.150978i
$65$	−4.23527	−	4.82939i	−0.0651579	−	0.0742984i
$66$	27.9374	−	1.83111i	0.423294	−	0.0277441i
$67$	−4.64850	+	15.3241i	−0.0693806	+	0.228717i	−0.984773	−	0.173846i	$-0.944381\pi$
$67$	−4.64850	+	15.3241i	−0.0693806	+	0.228717i	0.915392	+	0.402563i	$0.131881\pi$
$68$	10.2334	−	22.5856i	0.150491	−	0.332141i
$69$	−1.19310	+	12.1137i	−0.0172913	+	0.175561i
$70$	−0.684734	+	1.02478i	−0.00978191	+	0.0146397i
$71$	−33.9696	−	12.7852i	−0.478445	−	0.180074i	0.101326	−	0.994853i	$-0.467691\pi$
$71$	−33.9696	−	12.7852i	−0.478445	−	0.180074i	−0.579771	+	0.814779i	$0.696858\pi$
$72$	−1.70213	+	25.9695i	−0.0236407	+	0.360688i
$73$	−14.5252	−	18.9295i	−0.198975	−	0.259309i	0.683200	−	0.730231i	$-0.260588\pi$
$73$	−14.5252	−	18.9295i	−0.198975	−	0.259309i	−0.882175	+	0.470923i	$0.843921\pi$
$74$	−6.25843	−	8.73363i	−0.0845734	−	0.118022i
$75$	−65.6594	+	65.6594i	−0.875458	+	0.875458i
$76$	12.2768	−	74.3598i	0.161537	−	0.978418i
$77$	−27.6865	−	22.7217i	−0.359565	−	0.295087i
$78$	−13.1658	−	24.6315i	−0.168793	−	0.315789i
$79$	20.7020	+	30.9827i	0.262050	+	0.392186i	0.939041	−	0.343806i	$-0.111716\pi$
$79$	20.7020	+	30.9827i	0.262050	+	0.392186i	−0.676990	+	0.735992i	$0.736716\pi$
$80$	1.42378	+	6.10625i	0.0177972	+	0.0763282i
$81$	97.3661	−	26.0892i	1.20205	−	0.322088i
$82$	5.58368	+	5.22969i	0.0680937	+	0.0637767i
$83$	−105.909	−	65.8582i	−1.27601	−	0.793473i	−0.289499	−	0.957178i	$-0.593489\pi$
$83$	−105.909	−	65.8582i	−1.27601	−	0.793473i	−0.986509	+	0.163706i	$0.947655\pi$
$84$	31.3439	−	29.3568i	0.373142	−	0.349486i
$85$	−3.94397	+	0.784504i	−0.0463997	+	0.00922946i
$86$	2.07309	+	6.10713i	0.0241057	+	0.0710131i
$87$	9.12522	−	4.13459i	0.104888	−	0.0475240i
$88$	55.7188	−	7.33552i	0.633168	−	0.0833581i
$89$	−23.2154	+	116.712i	−0.260847	+	1.31137i	0.598972	+	0.800770i	$0.295576\pi$
$89$	−23.2154	+	116.712i	−0.260847	+	1.31137i	−0.859819	+	0.510598i	$0.829424\pi$
$90$	1.68684	−	1.04894i	0.0187426	−	0.0116549i
$91$	−9.24748	+	34.5121i	−0.101621	+	0.379254i
$92$	−0.376251	+	11.4933i	−0.00408968	+	0.124927i
$93$	167.241	+	128.329i	1.79829	+	1.37988i
$94$	−11.3088	−	9.91756i	−0.120306	−	0.105506i
$95$	−10.9620	+	5.40588i	−0.115390	+	0.0569040i
$96$			103.056i			1.07350i
$97$	−6.81000	−	96.7607i	−0.0702062	−	0.997533i
$97$	−6.81000	−	96.7607i	−0.0702062	−	0.997533i
$98$	−25.7862			−0.263125
$99$	25.5310	+	51.7717i	0.257888	+	0.522946i
$100$	−57.8398	+	65.9536i	−0.578398	+	0.659536i
$101$	9.46758	−	12.3384i	0.0937384	−	0.122162i	−0.744129	−	0.668036i	$-0.767135\pi$
$101$	9.46758	−	12.3384i	0.0937384	−	0.122162i	0.837868	+	0.545873i	$0.183802\pi$
$102$	−17.4752	−	0.572077i	−0.171325	−	0.00560860i
$103$	−140.327	−	37.6005i	−1.36240	−	0.365054i	−0.497702	−	0.867348i	$-0.665823\pi$
$103$	−140.327	−	37.6005i	−1.36240	−	0.365054i	−0.864697	+	0.502294i	$0.832489\pi$
$104$	−29.6052	−	47.6090i	−0.284665	−	0.457779i
$105$	−6.83074	−	1.35872i	−0.0650546	−	0.0129402i
$106$	4.06102	+	30.8465i	0.0383115	+	0.291005i
$107$	−6.07359	−	13.4047i	−0.0567625	−	0.125278i	0.880326	−	0.474369i	$-0.157324\pi$
$107$	−6.07359	−	13.4047i	−0.0567625	−	0.125278i	−0.937089	+	0.349091i	$0.886490\pi$
$108$	48.5476	−	16.4797i	0.449515	−	0.152590i
$109$	13.5575	+	68.1581i	0.124381	+	0.625304i	0.991808	+	0.127740i	$0.0407722\pi$
$109$	13.5575	+	68.1581i	0.124381	+	0.625304i	−0.867427	+	0.497564i	$0.834228\pi$
$110$	−2.93223	−	3.13071i	−0.0266566	−	0.0284610i
$111$	32.0617	−	51.5594i	0.288844	−	0.464499i
$112$	23.8412	−	25.4550i	0.212868	−	0.227277i
$113$	9.50088	+	35.4577i	0.0840785	+	0.313785i	0.995138	−	0.0984894i	$-0.0314010\pi$
$113$	9.50088	+	35.4577i	0.0840785	+	0.313785i	−0.911060	+	0.412275i	$0.864734\pi$
$114$	−51.7557	+	12.0677i	−0.453998	+	0.105857i
$115$	1.55062	−	1.03609i	0.0134836	−	0.00900948i
$116$	8.34682	−	4.46147i	0.0719554	−	0.0384610i
$117$	36.5313	−	44.5135i	0.312233	−	0.380457i
$118$	47.0152	+	7.76224i	0.398434	+	0.0657817i
$119$	15.8163	+	15.8163i	0.132910	+	0.132910i
$120$	8.88286	−	6.36537i	0.0740239	−	0.0530447i
$121$	2.89745	−	2.22329i	0.0239459	−	0.0183743i
$122$	−45.4730	−	2.98046i	−0.372729	−	0.0244300i
$123$	−15.2279	+	40.4596i	−0.123804	+	0.328940i
$124$	165.586	+	110.641i	1.33537	+	0.892267i
$125$	28.5067	+	2.80767i	0.228054	+	0.0224613i
$126$	−10.0641	−	4.55999i	−0.0798738	−	0.0361904i
$127$	−161.949	−	49.1268i	−1.27519	−	0.386825i	−0.421131	−	0.907000i	$-0.638367\pi$
$127$	−161.949	−	49.1268i	−1.27519	−	0.386825i	−0.854060	+	0.520175i	$0.825867\pi$
$128$	8.26223	+	126.057i	0.0645487	+	0.984823i
$129$	−27.4003	+	24.0294i	−0.212405	+	0.186275i
$130$	−1.63751	+	3.95331i	−0.0125963	+	0.0304101i
$131$	−85.3511	−	104.001i	−0.651535	−	0.793898i	0.337540	−	0.941311i	$-0.390405\pi$
$131$	−85.3511	−	104.001i	−0.651535	−	0.793898i	−0.989075	+	0.147414i	$0.952905\pi$
$132$	74.7307	+	129.437i	0.566141	+	0.980585i
$133$	58.8777	+	33.9931i	0.442690	+	0.255587i
$134$	10.5251	−	1.73770i	0.0785457	−	0.0129679i
$135$	−6.75835	−	4.84296i	−0.0500618	−	0.0358738i
$136$	−35.0782	+	1.14834i	−0.257928	+	0.00844369i
$137$	−172.446	−	40.2087i	−1.25873	−	0.293494i	−0.456076	−	0.889941i	$-0.650745\pi$
$137$	−172.446	−	40.2087i	−1.25873	−	0.293494i	−0.802653	+	0.596447i	$0.796579\pi$
$138$	7.58900	−	2.85630i	0.0549928	−	0.0206978i
$139$	41.5821	+	137.078i	0.299152	+	0.986172i	0.969699	+	0.244304i	$0.0785596\pi$
$139$	41.5821	+	137.078i	0.299152	+	0.986172i	−0.670547	+	0.741867i	$0.733940\pi$
$140$	−6.52324	−	0.858801i	−0.0465946	−	0.00613430i
$141$	27.3213	−	80.4860i	0.193768	−	0.570823i
$142$	2.36994	+	24.0624i	0.0166897	+	0.169454i
$143$	−109.667	−	58.6180i	−0.766900	−	0.409916i
$144$	−51.9308	+	21.5104i	−0.360630	+	0.149378i
$145$	−1.37659	−	0.678859i	−0.00949373	−	0.00468179i
$146$	−7.03003	+	14.2555i	−0.0481509	+	0.0976403i
$147$	−55.7620	−	134.621i	−0.379333	−	0.915792i
$148$	27.0387	−	50.5858i	0.182694	−	0.341796i
$149$	193.690	−	19.0768i	1.29993	−	0.128032i	0.575742	−	0.817632i	$-0.304713\pi$
$149$	193.690	−	19.0768i	1.29993	−	0.128032i	0.724191	+	0.689600i	$0.242213\pi$
$150$	58.5744	+	19.8833i	0.390496	+	0.132555i
$151$	12.1484	−	92.2761i	0.0804529	−	0.611100i	−0.902961	−	0.429723i	$-0.858611\pi$
$151$	12.1484	−	92.2761i	0.0804529	−	0.611100i	0.983414	−	0.181377i	$-0.0580555\pi$
$152$	−102.084	+	30.9667i	−0.671602	+	0.203728i
$153$	−12.6984	−	33.7389i	−0.0829962	−	0.220516i
$154$	−5.41791	+	23.2362i	−0.0351812	+	0.150884i
$155$	−1.05672	−	32.2796i	−0.00681757	−	0.208255i
$156$	86.8466	−	121.194i	0.556709	−	0.776887i
$157$	26.8543	+	162.654i	0.171046	+	1.03601i	0.925246	+	0.379368i	$0.123858\pi$
$157$	26.8543	+	162.654i	0.171046	+	1.03601i	−0.754200	+	0.656645i	$0.771975\pi$
$158$	12.4114	−	21.4972i	0.0785531	−	0.136058i
$159$	−152.258	+	87.9059i	−0.957595	+	0.552867i
$160$	12.2051	−	10.0165i	0.0762820	−	0.0626030i
$161$	−9.58371	−	3.96970i	−0.0595261	−	0.0246565i
$162$	−44.2746	−	50.4855i	−0.273300	−	0.311639i
$163$	60.6122	−	3.97273i	0.371854	−	0.0243726i	0.121669	−	0.992571i	$-0.461175\pi$
$163$	60.6122	−	3.97273i	0.371854	−	0.0243726i	0.250185	+	0.968198i	$0.419509\pi$
$164$	−11.8554	+	39.0819i	−0.0722889	+	0.238304i
$165$	10.0035	−	22.0782i	0.0606274	−	0.133808i
$166$	−8.14329	+	82.6803i	−0.0490560	+	0.498074i
$167$	139.452	−	208.704i	0.835041	−	1.24973i	−0.131011	−	0.991381i	$-0.541822\pi$
$167$	139.452	−	208.704i	0.835041	−	1.24973i	0.966052	−	0.258346i	$-0.0831776\pi$
$168$	−56.8901	−	21.4119i	−0.338631	−	0.127452i
$169$	2.94000	−	44.8558i	0.0173965	−	0.265419i
$170$	1.63074	+	2.12522i	0.00959259	+	0.0125013i
$171$	−63.8232	−	89.0651i	−0.373235	−	0.520849i
$172$	−24.3454	+	24.3454i	−0.141543	+	0.141543i
$173$	53.1512	−	321.932i	0.307232	−	1.86088i	−0.174633	−	0.984634i	$-0.555874\pi$
$173$	53.1512	−	321.932i	0.307232	−	1.86088i	0.481865	−	0.876245i	$-0.339959\pi$
$174$	−5.15885	−	4.23376i	−0.0296486	−	0.0243320i
$175$	−37.3029	−	69.7887i	−0.213159	−	0.398793i
$176$	67.4353	+	100.924i	0.383155	+	0.573432i
$177$	61.1450	+	262.237i	0.345452	+	1.48156i
$178$	76.5706	−	20.5170i	0.430172	−	0.115264i
$179$	102.180	+	95.7017i	0.570836	+	0.534646i	0.914574	−	0.404420i	$-0.132526\pi$
$179$	102.180	+	95.7017i	0.570836	+	0.534646i	−0.343738	+	0.939066i	$0.611693\pi$
$180$	9.00503	+	5.59969i	0.0500279	+	0.0311094i
$181$	146.492	−	137.204i	0.809345	−	0.758035i	−0.164225	−	0.986423i	$-0.552512\pi$
$181$	146.492	−	137.204i	0.809345	−	0.758035i	0.973570	+	0.228388i	$0.0733456\pi$
$182$	23.3442	−	4.64345i	0.128265	−	0.0255135i
$183$	−82.7741	−	243.845i	−0.452318	−	1.33248i
$184$	14.8259	−	6.71755i	0.0805758	−	0.0365084i
$185$	−9.22252	+	1.21417i	−0.0498514	+	0.00656307i
$186$	27.3962	−	137.730i	0.147291	−	0.740483i
$187$	−66.1071	+	41.1080i	−0.353514	+	0.219829i
$188$	20.7826	−	77.5618i	0.110546	−	0.412563i
$189$	−1.51319	+	46.2231i	−0.00800629	+	0.244567i
$190$	6.45959	+	4.95662i	0.0339978	+	0.0260875i
$191$	153.143	+	134.303i	0.801794	+	0.703155i	0.958688	−	0.284461i	$-0.0918146\pi$
$191$	153.143	+	134.303i	0.801794	+	0.703155i	−0.156893	+	0.987616i	$0.550148\pi$
$192$	−85.2457	+	42.0385i	−0.443988	+	0.218951i
$193$			1.10990i			0.00575077i	0.999996	+	0.00287539i	$0.000915265\pi$
$193$			1.10990i			0.00575077i	−0.999996	+	0.00287539i	$0.999085\pi$
$194$	−55.8041	+	32.5777i	−0.287650	+	0.167926i
$195$	−24.1800			−0.124000
$196$	−60.8844	−	123.461i	−0.310635	−	0.629905i
$197$	256.752	−	292.769i	1.30331	−	1.48614i	0.537148	−	0.843488i	$-0.319502\pi$
$197$	256.752	−	292.769i	1.30331	−	1.48614i	0.766160	−	0.642650i	$-0.222165\pi$
$198$	23.4092	−	30.5074i	0.118228	−	0.154078i
$199$	−131.096	−	4.29163i	−0.658772	−	0.0215660i	−0.298495	−	0.954411i	$-0.596485\pi$
$199$	−131.096	−	4.29163i	−0.658772	−	0.0215660i	−0.360277	+	0.932845i	$0.617318\pi$
$200$	119.936	+	32.1368i	0.599681	+	0.160684i
$201$	31.8323	+	51.1904i	0.158369	+	0.254679i
$202$	−10.1612	−	2.02118i	−0.0503028	−	0.0100059i
$203$	1.11438	+	8.46452i	0.00548953	+	0.0416971i
$204$	−38.5219	−	85.0197i	−0.188833	−	0.416763i
$205$	6.27179	−	2.12899i	0.0305941	−	0.0103853i
$206$	18.8804	+	94.9182i	0.0916525	+	0.460768i
$207$	11.4286	+	12.2022i	0.0552108	+	0.0589480i
$208$	63.9415	−	102.826i	0.307411	−	0.494357i
$209$	−161.746	+	172.695i	−0.773907	+	0.826292i
$210$	1.20079	+	4.48142i	0.00571806	+	0.0213401i
$211$	−350.386	+	81.6986i	−1.66060	+	0.387197i	−0.948972	−	0.315361i	$-0.897875\pi$
$211$	−350.386	+	81.6986i	−1.66060	+	0.387197i	−0.711627	+	0.702558i	$0.752041\pi$
$212$	−138.101	+	92.2760i	−0.651419	+	0.435264i
$213$	−120.497	+	64.4070i	−0.565714	+	0.302380i
$214$	−6.21928	+	7.57821i	−0.0290620	+	0.0354122i
$215$	5.50902	+	0.909542i	0.0256233	+	0.00423043i
$216$	−51.3130	−	51.3130i	−0.237560	−	0.237560i
$217$	−146.025	+	104.640i	−0.672928	+	0.482214i
$218$	36.7272	−	28.1818i	0.168474	−	0.129274i
$219$	−89.6255	−	5.87436i	−0.409249	−	0.0268236i
$220$	8.06610	−	21.4311i	0.0366641	−	0.0974142i
$221$	64.5696	+	43.1441i	0.292170	+	0.195222i
$222$	−40.2512	−	3.96439i	−0.181312	−	0.0178576i
$223$	149.423	+	67.7028i	0.670059	+	0.303600i	0.718806	−	0.695211i	$-0.244689\pi$
$223$	149.423	+	67.7028i	0.670059	+	0.303600i	−0.0487460	+	0.998811i	$0.515523\pi$
$224$	−84.0430	−	25.4942i	−0.375192	−	0.113813i
$225$	8.34128	+	127.263i	0.0370724	+	0.565615i
$226$	18.3853	−	16.1235i	0.0813508	−	0.0713428i
$227$	−163.146	+	393.870i	−0.718706	+	1.73511i	−0.0417017	+	0.999130i	$0.513278\pi$
$227$	−163.146	+	393.870i	−0.718706	+	1.73511i	−0.677004	+	0.735979i	$0.736722\pi$
$228$	−179.980	−	219.307i	−0.789388	−	0.961872i
$229$	165.942	+	287.420i	0.724637	+	1.25511i	0.959123	+	0.282989i	$0.0913258\pi$
$229$	165.942	+	287.420i	0.724637	+	1.25511i	−0.234486	+	0.972119i	$0.575341\pi$
$230$	−1.07589	−	0.621164i	−0.00467777	−	0.00270071i
$231$	−133.024	+	21.9624i	−0.575863	+	0.0950754i
$232$	−10.8891	−	7.80304i	−0.0469359	−	0.0336338i
$233$	270.606	−	8.85873i	1.16140	−	0.0380203i	0.554070	−	0.832470i	$-0.313074\pi$
$233$	270.606	−	8.85873i	1.16140	−	0.0380203i	0.607330	+	0.794450i	$0.292241\pi$
$234$	−37.3584	−	8.71075i	−0.159651	−	0.0372254i
$235$	−12.1876	+	4.58709i	−0.0518622	+	0.0195195i
$236$	73.8439	+	243.431i	0.312898	+	1.03149i
$237$	139.069	+	18.3088i	0.586789	+	0.0772522i
$238$	4.78957	−	14.1096i	0.0201242	−	0.0592841i
$239$	41.7950	+	424.351i	0.174874	+	1.77553i	0.537178	+	0.843469i	$0.319490\pi$
$239$	41.7950	+	424.351i	0.174874	+	1.77553i	−0.362304	+	0.932060i	$0.618010\pi$
$240$	20.8156	+	11.1262i	0.0867317	+	0.0463591i
$241$	−10.1176	+	4.19084i	−0.0419816	+	0.0173894i	−0.403575	−	0.914946i	$-0.632233\pi$
$241$	−10.1176	+	4.19084i	−0.0419816	+	0.0173894i	0.361594	+	0.932336i	$0.382233\pi$
$242$	−2.18202	−	1.07605i	−0.00901660	−	0.00444649i
$243$	110.439	−	223.949i	0.454483	−	0.921601i
$244$	−93.0971	−	224.756i	−0.381546	−	0.921133i
$245$	−10.5237	+	19.6885i	−0.0429539	+	0.0803612i
$246$	28.6597	−	2.82273i	0.116503	−	0.0114745i
$247$	223.512	+	75.8721i	0.904906	+	0.307174i
$248$	36.7933	−	279.473i	0.148360	−	1.12691i
$249$	−449.256	+	136.280i	−1.80424	+	0.547311i
$250$	−6.72160	−	17.8589i	−0.0268864	−	0.0714354i
$251$	−109.456	+	469.431i	−0.436079	+	1.87024i	0.0539625	+	0.998543i	$0.482815\pi$
$251$	−109.456	+	469.431i	−0.436079	+	1.87024i	−0.490042	+	0.871699i	$0.663018\pi$
$252$	−1.92990	−	58.9524i	−0.00765834	−	0.233938i
$253$	21.0288	−	29.3457i	0.0831179	−	0.115991i
$254$	18.3646	+	111.233i	0.0723015	+	0.437924i
$255$	−7.56865	+	13.1093i	−0.0296810	+	0.0514090i
$256$	−14.5871	+	8.42185i	−0.0569807	+	0.0328978i
$257$	298.729	−	245.160i	1.16237	−	0.953931i	0.162904	−	0.986642i	$-0.447914\pi$
$257$	298.729	−	245.160i	1.16237	−	0.953931i	0.999465	+	0.0327108i	$0.0104140\pi$
$258$	22.4297	+	9.29068i	0.0869368	+	0.0360104i
$259$	34.1157	+	38.9015i	0.131721	+	0.150199i
$260$	−22.7943	+	1.49402i	−0.0876705	+	0.00574623i
$261$	3.99426	−	13.1673i	0.0153037	−	0.0504495i
$262$	−36.9888	+	81.6360i	−0.141179	+	0.311588i
$263$	33.9806	−	345.011i	0.129204	−	1.31183i	−0.683843	−	0.729629i	$-0.739693\pi$
$263$	33.9806	−	345.011i	0.129204	−	1.31183i	0.813047	−	0.582198i	$-0.197807\pi$
$264$	117.533	−	175.901i	0.445202	−	0.666291i
$265$	25.2095	+	9.48818i	0.0951302	+	0.0358045i
$266$	2.96208	−	45.1926i	0.0111356	−	0.169897i
$267$	272.695	+	355.382i	1.02133	+	1.33102i
$268$	33.1710	+	46.2901i	0.123772	+	0.172724i
$269$	151.075	−	151.075i	0.561617	−	0.561617i	−0.368150	−	0.929767i	$-0.620009\pi$
$269$	151.075	−	151.075i	0.561617	−	0.561617i	0.929767	+	0.368150i	$0.120009\pi$
$270$	−0.902233	+	5.46475i	−0.00334160	+	0.0202398i
$271$	−336.024	−	275.767i	−1.23994	−	1.01759i	−0.998891	−	0.0470790i	$-0.985009\pi$
$271$	−336.024	−	275.767i	−1.23994	−	1.01759i	−0.241048	−	0.970513i	$-0.577491\pi$
$272$	−35.7332	−	66.8521i	−0.131372	−	0.245780i
$273$	74.7231	+	111.831i	0.273711	+	0.409638i
$274$	26.7854	+	114.876i	0.0977569	+	0.419257i
$275$	266.022	−	71.2802i	0.967351	−	0.259201i
$276$	31.5942	+	29.5912i	0.114472	+	0.107214i
$277$	−123.916	−	77.0559i	−0.447350	−	0.278180i	0.285746	−	0.958305i	$-0.407759\pi$
$277$	−123.916	−	77.0559i	−0.447350	−	0.278180i	−0.733096	+	0.680125i	$0.761925\pi$
$278$	69.6470	−	65.2315i	0.250529	−	0.234646i
$279$	283.970	−	56.4852i	1.01781	−	0.202456i
$280$	2.99356	+	8.81873i	0.0106913	+	0.0314955i
$281$	324.643	−	147.094i	1.15531	−	0.523465i	0.258559	−	0.965996i	$-0.416752\pi$
$281$	324.643	−	147.094i	1.15531	−	0.523465i	0.896754	+	0.442530i	$0.145919\pi$
$282$	−56.1370	+	7.39057i	−0.199067	+	0.0262077i
$283$	−25.3606	+	127.496i	−0.0896133	+	0.450516i	0.909761	+	0.415133i	$0.136265\pi$
$283$	−25.3606	+	127.496i	−0.0896133	+	0.450516i	−0.999374	+	0.0353830i	$0.988735\pi$
$284$	−109.612	+	68.1613i	−0.385959	+	0.240004i
$285$	−11.9082	+	44.4419i	−0.0417831	+	0.155937i
$286$	−2.71034	+	82.7923i	−0.00947671	+	0.289484i
$287$	−29.2281	−	22.4275i	−0.101840	−	0.0781445i
$288$	106.419	+	93.3273i	0.369512	+	0.324053i
$289$	−215.594	+	106.319i	−0.746001	+	0.367887i
$290$			1.02247i			0.00352577i
$291$	−290.752	−	220.887i	−0.999149	−	0.759060i
$292$	−84.8523			−0.290590
$293$	150.207	+	304.590i	0.512652	+	1.03956i	0.987224	+	0.159339i	$0.0509363\pi$
$293$	150.207	+	304.590i	0.512652	+	1.03956i	−0.474572	+	0.880217i	$0.657397\pi$
$294$	−64.0014	+	72.9797i	−0.217692	+	0.248230i
$295$	25.1142	−	32.7295i	0.0851330	−	0.110948i
$296$	−81.1444	−	2.65639i	−0.274137	−	0.00897430i
$297$	−155.472	−	41.6587i	−0.523476	−	0.140265i
$298$	−68.4654	−	110.101i	−0.229750	−	0.369467i
$299$	−35.3228	−	7.02613i	−0.118136	−	0.0234988i
$300$	43.1022	+	327.394i	0.143674	+	1.09131i
$301$	−12.8179	−	28.2896i	−0.0425843	−	0.0939855i
$302$	−58.7106	+	19.9296i	−0.194406	+	0.0659919i
$303$	−11.4213	−	57.4189i	−0.0376941	−	0.189501i
$304$	−157.501	−	168.162i	−0.518095	−	0.553165i
$305$	−20.8338	+	33.5035i	−0.0683076	+	0.109848i
$306$	−16.4162	+	17.5274i	−0.0536478	+	0.0572792i
$307$	−39.1349	−	146.053i	−0.127475	−	0.475744i	0.872441	−	0.488720i	$-0.162536\pi$
$307$	−39.1349	−	146.053i	−0.127475	−	0.475744i	−0.999916	+	0.0129762i	$0.995869\pi$
$308$	−124.044	+	28.9231i	−0.402741	+	0.0939060i
$309$	−454.708	+	303.826i	−1.47155	+	0.983257i
$310$	−18.9744	+	10.1420i	−0.0612077	+	0.0327162i
$311$	253.479	−	308.865i	0.815046	−	0.993136i	−0.184900	−	0.982757i	$-0.559196\pi$
$311$	253.479	−	308.865i	0.815046	−	0.993136i	0.999946	−	0.0103788i	$-0.00330373\pi$
$312$	−208.222	−	34.3776i	−0.667379	−	0.110185i
$313$	−221.078	−	221.078i	−0.706321	−	0.706321i	0.259439	−	0.965760i	$-0.416462\pi$
$313$	−221.078	−	221.078i	−0.706321	−	0.706321i	−0.965760	+	0.259439i	$0.916462\pi$
$314$	89.2670	−	63.9679i	0.284290	−	0.203719i
$315$	−7.58897	+	5.82322i	−0.0240920	+	0.0184864i
$316$	132.231	+	8.66686i	0.418451	+	0.0274268i
$317$	49.7156	−	132.091i	0.156831	−	0.416691i	−0.834005	−	0.551756i	$-0.813958\pi$
$317$	49.7156	−	132.091i	0.156831	−	0.416691i	0.990837	+	0.135065i	$0.0431245\pi$
$318$	97.3806	+	65.0676i	0.306228	+	0.204615i
$319$	−29.5702	−	2.91242i	−0.0926967	−	0.00912983i
$320$	13.2641	+	6.00990i	0.0414504	+	0.0187809i
$321$	−53.0123	−	16.0811i	−0.165148	−	0.0500969i
$322$	0.451954	+	6.89549i	0.00140359	+	0.0214146i
$323$	111.096	−	97.4290i	0.343952	−	0.301638i
$324$	137.181	−	331.184i	0.423398	−	1.02217i
$325$	−174.292	−	212.375i	−0.536282	−	0.653461i
$326$	−20.2320	−	35.0428i	−0.0620613	−	0.107493i
$327$	226.549	+	130.798i	0.692812	+	0.399995i
$328$	57.0354	−	9.41658i	0.173888	−	0.0287091i
$329$	58.8782	+	42.1916i	0.178961	+	0.128242i
$330$	−16.1382	+	0.528311i	−0.0489038	+	0.00160094i
$331$	475.515	+	110.875i	1.43660	+	0.334968i	0.871639	−	0.490148i	$-0.163057\pi$
$331$	475.515	+	110.875i	1.43660	+	0.334968i	0.564962	+	0.825117i	$0.308891\pi$
$332$	−415.090	+	156.229i	−1.25027	+	0.470569i
$333$	−24.2072	−	79.8003i	−0.0726942	−	0.239641i
$334$	−165.780	−	21.8253i	−0.496347	−	0.0653453i
$335$	2.96866	−	8.74540i	0.00886168	−	0.0261057i
$336$	−12.8683	−	130.654i	−0.0382985	−	0.388852i
$337$	−285.522	−	152.615i	−0.847246	−	0.452862i	−0.0101695	−	0.999948i	$-0.503237\pi$
$337$	−285.522	−	152.615i	−0.847246	−	0.452862i	−0.837077	+	0.547086i	$0.815737\pi$
$338$	−27.6657	+	11.4595i	−0.0818513	+	0.0339039i
$339$	123.933	+	61.1170i	0.365584	+	0.180286i
$340$	−6.32493	+	12.8257i	−0.0186027	+	0.0377226i
$341$	−239.264	−	577.634i	−0.701654	−	1.69394i
$342$	−34.4083	+	64.3734i	−0.100609	+	0.188226i
$343$	280.014	−	27.5790i	0.816367	−	0.0804051i
$344$	46.1469	+	15.6648i	0.134148	+	0.0455371i
$345$	0.916315	−	6.96010i	0.00265599	−	0.0201742i
$346$	−208.002	+	63.0966i	−0.601161	+	0.182360i
$347$	−55.0724	−	146.324i	−0.158710	−	0.421683i	0.832492	−	0.554036i	$-0.186913\pi$
$347$	−55.0724	−	146.324i	−0.158710	−	0.421683i	−0.991203	+	0.132354i	$0.957747\pi$
$348$	8.09006	−	34.6964i	0.0232473	−	0.0997023i
$349$	−6.51434	−	198.993i	−0.0186657	−	0.570179i	−0.967275	−	0.253730i	$-0.918343\pi$
$349$	−6.51434	−	198.993i	−0.0186657	−	0.570179i	0.948609	−	0.316449i	$-0.102491\pi$
$350$	−30.7052	+	42.8491i	−0.0877293	+	0.122426i
$351$	26.1555	+	158.422i	0.0745171	+	0.451344i
$352$	152.828	−	264.707i	0.434172	−	0.752007i
$353$	313.129	−	180.785i	0.887052	−	0.512140i	0.0140749	−	0.999901i	$-0.495520\pi$
$353$	313.129	−	180.785i	0.887052	−	0.512140i	0.872977	+	0.487761i	$0.162186\pi$
$354$	138.660	−	113.796i	0.391696	−	0.321457i
$355$	19.3395	+	8.01069i	0.0544775	+	0.0225653i
$356$	279.026	+	318.168i	0.783780	+	0.893730i
$357$	84.0190	−	5.50690i	0.235347	−	0.0154255i
$358$	27.0722	−	89.2452i	0.0756208	−	0.249288i
$359$	51.4663	−	113.589i	0.143360	−	0.316403i	−0.825340	−	0.564636i	$-0.809017\pi$
$359$	51.4663	−	113.589i	0.143360	−	0.316403i	0.968700	+	0.248233i	$0.0798500\pi$
$360$	1.47119	−	14.9373i	0.00408664	−	0.0414924i
$361$	48.9644	−	73.2804i	0.135636	−	0.202993i
$362$	−125.135	−	47.0977i	−0.345678	−	0.130104i
$363$	0.899160	−	13.7185i	0.00247702	−	0.0377921i
$364$	77.3508	+	100.805i	0.212502	+	0.276938i
$365$	8.01540	+	11.1855i	0.0219600	+	0.0306452i
$366$	−121.299	+	121.299i	−0.331419	+	0.331419i
$367$	16.7210	−	101.278i	0.0455613	−	0.275961i	−0.954167	−	0.299275i	$-0.903255\pi$
$367$	16.7210	−	101.278i	0.0455613	−	0.275961i	0.999728	+	0.0233144i	$0.00742187\pi$
$368$	27.1750	+	22.3019i	0.0738451	+	0.0606031i
$369$	27.9897	+	52.3651i	0.0758530	+	0.141911i
$370$	3.44269	+	5.15235i	0.00930456	+	0.0139253i
$371$	−34.0223	−	145.914i	−0.0917043	−	0.393298i
$372$	724.119	−	194.027i	1.94656	−	0.521579i
$373$	472.826	+	442.850i	1.26763	+	1.18726i	0.972782	+	0.231720i	$0.0744354\pi$
$373$	472.826	+	442.850i	1.26763	+	1.18726i	0.294847	+	0.955544i	$0.404731\pi$
$374$	44.0378	+	27.3845i	0.117748	+	0.0732206i
$375$	78.7000	−	73.7106i	0.209867	−	0.196561i
$376$	−111.473	+	22.1734i	−0.296471	+	0.0589718i
$377$	9.52786	+	28.0682i	0.0252728	+	0.0744514i
$378$	28.0623	−	12.7149i	0.0742389	−	0.0336372i
$379$	238.404	−	31.3864i	0.629033	−	0.0828138i	0.190732	−	0.981642i	$-0.438914\pi$
$379$	238.404	−	31.3864i	0.629033	−	0.0828138i	0.438301	+	0.898828i	$0.355580\pi$
$380$	−8.47981	+	42.6309i	−0.0223153	+	0.112187i
$381$	−540.996	+	336.413i	−1.41994	+	0.882974i
$382$	35.1192	−	131.067i	0.0919352	−	0.343107i
$383$	−5.26442	+	160.811i	−0.0137452	+	0.419873i	0.970295	+	0.241926i	$0.0777790\pi$
$383$	−5.26442	+	160.811i	−0.0137452	+	0.419873i	−0.984040	+	0.177947i	$0.943054\pi$
$384$	377.272	+	289.491i	0.982478	+	0.753882i
$385$	15.5303	+	13.6197i	0.0403385	+	0.0353759i
$386$	0.663120	−	0.327015i	0.00171793	−	0.000847188i
$387$			50.0556i			0.129343i
$388$	−287.739	−	190.263i	−0.741594	−	0.490370i
$389$	−148.954			−0.382914			−0.191457	−	0.981501i	$-0.561321\pi$
$389$	−148.954			−0.382914			−0.191457	+	0.981501i	$0.561321\pi$
$390$	7.12426	+	14.4466i	0.0182673	+	0.0370425i
$391$	−14.8657	+	16.9511i	−0.0380198	+	0.0433532i
$392$	−118.615	+	154.582i	−0.302590	+	0.394343i
$393$	−506.182	−	16.5707i	−1.28799	−	0.0421646i
$394$	−250.566	−	67.1389i	−0.635953	−	0.170403i
$395$	−11.3484	−	18.2497i	−0.0287302	−	0.0462019i
$396$	201.338	+	40.0486i	0.508429	+	0.101133i
$397$	−11.2888	−	85.7472i	−0.0284354	−	0.215988i	0.971328	−	0.237744i	$-0.0764078\pi$
$397$	−11.2888	−	85.7472i	−0.0284354	−	0.215988i	−0.999763	+	0.0217555i	$0.993074\pi$
$398$	36.0612	+	79.5888i	0.0906061	+	0.199972i
$399$	242.341	−	82.2637i	0.607371	−	0.206175i
$400$	52.3187	+	263.024i	0.130797	+	0.657560i
$401$	−397.659	−	424.576i	−0.991668	−	1.05879i	−0.998269	−	0.0588147i	$-0.981268\pi$
$401$	−397.659	−	424.576i	−0.991668	−	1.05879i	0.00660117	−	0.999978i	$-0.497899\pi$
$402$	21.2053	−	34.1010i	0.0527496	−	0.0848283i
$403$	−426.363	+	455.223i	−1.05797	+	1.12959i
$404$	−14.3146	−	53.4227i	−0.0354321	−	0.132234i
$405$	−56.6162	+	13.2010i	−0.139793	+	0.0325952i
$406$	4.72888	−	3.15973i	0.0116475	−	0.00778260i
$407$	−158.814	+	84.8877i	−0.390206	+	0.208569i
$408$	−83.8142	+	102.128i	−0.205427	+	0.250313i
$409$	228.590	+	37.7403i	0.558899	+	0.0922747i	0.435675	−	0.900104i	$-0.356510\pi$
$409$	228.590	+	37.7403i	0.558899	+	0.0922747i	0.123225	+	0.992379i	$0.460676\pi$
$410$	−3.11987	−	3.11987i	−0.00760944	−	0.00760944i
$411$	−541.809	+	388.255i	−1.31827	+	0.944658i
$412$	−409.878	+	314.510i	−0.994849	+	0.763375i
$413$	−228.982	−	15.0083i	−0.554437	−	0.0363397i
$414$	3.92307	−	10.4233i	0.00947602	−	0.0251772i
$415$	59.8052	+	39.9606i	0.144109	+	0.0962906i
$416$	−303.447	−	29.8869i	−0.729440	−	0.0718435i
$417$	491.162	+	222.543i	1.17785	+	0.533675i
$418$	150.834	+	45.7551i	0.360848	+	0.109462i
$419$	48.2115	+	735.566i	0.115063	+	1.75553i	0.532140	+	0.846656i	$0.321388\pi$
$419$	48.2115	+	735.566i	0.115063	+	1.75553i	−0.417077	+	0.908871i	$0.636945\pi$
$420$	−18.6213	+	16.3304i	−0.0443363	+	0.0388819i
$421$	−189.641	+	457.834i	−0.450454	+	1.08749i	0.521696	+	0.853131i	$0.325299\pi$
$421$	−189.641	+	457.834i	−0.450454	+	1.08749i	−0.972150	+	0.234360i	$0.924701\pi$
$422$	152.048	+	185.270i	0.360302	+	0.439030i
$423$	−58.3707	−	101.101i	−0.137992	−	0.239010i
$424$	203.598	+	117.547i	0.480184	+	0.277234i
$425$	−169.696	+	28.0168i	−0.399284	+	0.0659220i
$426$	73.9832	+	53.0156i	0.173669	+	0.124450i
$427$	219.334	−	7.18026i	0.513663	−	0.0168156i
$428$	−50.9680	−	11.8841i	−0.119084	−	0.0277665i
$429$	−438.092	+	164.886i	−1.02119	+	0.384350i
$430$	−1.07973	−	3.55940i	−0.00251100	−	0.00827767i
$431$	540.669	+	71.1804i	1.25445	+	0.165152i	0.728312	−	0.685246i	$-0.240305\pi$
$431$	540.669	+	71.1804i	1.25445	+	0.165152i	0.526140	+	0.850398i	$0.323639\pi$
$432$	50.3798	−	148.414i	0.116620	−	0.343551i
$433$	−13.8847	−	140.974i	−0.0320663	−	0.325574i	−0.997814	−	0.0660903i	$-0.978947\pi$
$433$	−13.8847	−	140.974i	−0.0320663	−	0.325574i	0.965747	−	0.259484i	$-0.0835525\pi$
$434$	105.543	+	56.4137i	0.243186	+	0.129985i
$435$	−5.33799	+	2.21107i	−0.0122712	+	0.00508292i
$436$	221.648	+	109.305i	0.508368	+	0.250699i
$437$	−30.3096	+	61.4617i	−0.0693582	+	0.140645i
$438$	22.8971	+	55.2784i	0.0522764	+	0.126206i
$439$	59.2572	−	110.862i	0.134982	−	0.252534i	−0.805344	−	0.592807i	$-0.798020\pi$
$439$	59.2572	−	110.862i	0.134982	−	0.252534i	0.940327	+	0.340273i	$0.110520\pi$
$440$	−32.2559	+	3.17693i	−0.0733089	+	0.00722029i
$441$	−189.513	−	64.3310i	−0.429735	−	0.145875i
$442$	6.75239	−	51.2895i	0.0152769	−	0.116040i
$443$	48.0129	−	14.5646i	0.108381	−	0.0328771i	−0.235628	−	0.971843i	$-0.575715\pi$
$443$	48.0129	−	14.5646i	0.108381	−	0.0328771i	0.344010	+	0.938966i	$0.388215\pi$
$444$	−76.0568	−	202.078i	−0.171299	−	0.455131i
$445$	15.5842	−	66.8371i	0.0350207	−	0.150196i
$446$	−3.57556	−	109.222i	−0.00801694	−	0.244892i
$447$	426.748	−	595.526i	0.954693	−	1.33227i
$448$	−13.1945	−	79.9182i	−0.0294521	−	0.178389i
$449$	−95.1643	+	164.829i	−0.211947	+	0.367103i	−0.952324	−	0.305089i	$-0.901314\pi$
$449$	−95.1643	+	164.829i	−0.211947	+	0.367103i	0.740377	+	0.672192i	$0.234647\pi$
$450$	73.5771	−	42.4798i	0.163505	−	0.0943995i
$451$	99.1143	−	81.3410i	0.219766	−	0.180357i
$452$	120.607	+	49.9571i	0.266830	+	0.110525i
$453$	−231.006	−	263.412i	−0.509946	−	0.581482i
$454$	283.390	−	18.5744i	0.624207	−	0.0409127i
$455$	5.98169	−	19.7190i	0.0131466	−	0.0433384i
$456$	−165.730	+	365.774i	−0.363443	+	0.802136i
$457$	−17.9914	+	182.670i	−0.0393686	+	0.399716i	0.955226	+	0.295878i	$0.0956122\pi$
$457$	−17.9914	+	182.670i	−0.0393686	+	0.399716i	−0.994594	+	0.103838i	$0.966888\pi$
$458$	122.830	−	183.827i	0.268187	−	0.401370i
$459$	94.0760	+	35.4077i	0.204959	+	0.0771409i
$460$	0.433758	−	6.61786i	0.000942951	−	0.0143867i
$461$	−91.6462	−	119.436i	−0.198799	−	0.259079i	0.683307	−	0.730131i	$-0.260541\pi$
$461$	−91.6462	−	119.436i	−0.198799	−	0.259079i	−0.882105	+	0.471052i	$0.843874\pi$
$462$	52.3152	+	73.0058i	0.113236	+	0.158021i
$463$	−528.912	+	528.912i	−1.14236	+	1.14236i	−0.154342	+	0.988018i	$0.549326\pi$
$463$	−528.912	+	528.912i	−1.14236	+	1.14236i	−0.988018	+	0.154342i	$0.950674\pi$
$464$	4.71312	−	28.5470i	0.0101576	−	0.0615236i
$465$	−93.9797	−	77.1272i	−0.202107	−	0.165865i
$466$	−85.0226	−	159.066i	−0.182452	−	0.341344i
$467$	−321.743	−	481.522i	−0.688956	−	1.03110i	−0.996822	−	0.0796660i	$-0.974615\pi$
$467$	−321.743	−	481.522i	−0.688956	−	1.03110i	0.307865	−	0.951430i	$-0.400385\pi$
$468$	−46.5016	−	199.435i	−0.0993624	−	0.426142i
$469$	−49.6210	+	13.2959i	−0.105802	+	0.0283495i
$470$	6.33149	+	5.93009i	0.0134713	+	0.0126172i
$471$	526.993	+	327.705i	1.11888	+	0.695764i
$472$	262.800	−	246.139i	0.556780	−	0.521481i
$473$	106.014	−	21.0876i	0.224132	−	0.0445826i
$474$	−30.0358	−	88.4825i	−0.0633666	−	0.186672i
$475$	−476.173	+	215.751i	−1.00247	+	0.454213i
$476$	78.8639	−	10.3826i	0.165680	−	0.0218123i
$477$	−47.1093	+	236.834i	−0.0987616	+	0.496508i
$478$	241.219	−	149.999i	0.504641	−	0.313806i
$479$	151.694	−	566.131i	0.316690	−	1.18190i	−0.605717	−	0.795680i	$-0.707114\pi$
$479$	151.694	−	566.131i	0.316690	−	1.18190i	0.922406	−	0.386221i	$-0.126220\pi$
$480$	1.94467	−	59.4036i	0.00405140	−	0.123758i
$481$	142.518	+	109.358i	0.296295	+	0.227355i
$482$	5.48484	+	4.81008i	0.0113793	+	0.00997941i
$483$	−35.0218	+	17.2708i	−0.0725088	+	0.0357574i
$484$		−	12.9879i		−	0.0268345i
$485$	2.09955	+	55.9034i	0.00432896	+	0.115265i
$486$	−166.340			−0.342263
$487$	96.3263	+	195.330i	0.197795	+	0.401089i	0.973062	−	0.230545i	$-0.0740510\pi$
$487$	96.3263	+	195.330i	0.197795	+	0.401089i	−0.775266	+	0.631635i	$0.782384\pi$
$488$	−227.040	+	258.890i	−0.465246	+	0.530512i
$489$	139.196	−	181.404i	0.284654	−	0.370969i
$490$	14.8637	+	0.486588i	0.0303341	+	0.000993037i
$491$	181.567	+	48.6507i	0.369790	+	0.0990850i	0.438928	−	0.898522i	$-0.355358\pi$
$491$	181.567	+	48.6507i	0.369790	+	0.0990850i	−0.0691380	+	0.997607i	$0.522025\pi$
$492$	81.1838	+	130.554i	0.165008	+	0.265354i
$493$	18.1996	+	3.62013i	0.0369161	+	0.00734306i
$494$	−20.5238	−	155.894i	−0.0415462	−	0.315575i
$495$	−13.7396	−	30.3241i	−0.0277569	−	0.0612607i
$496$	576.506	−	195.697i	1.16231	−	0.394551i
$497$	−22.7157	−	114.199i	−0.0457056	−	0.229778i
$498$	213.788	+	228.259i	0.429294	+	0.458352i
$499$	392.900	−	631.834i	0.787374	−	1.26620i	−0.172288	−	0.985047i	$-0.555116\pi$
$499$	392.900	−	631.834i	0.787374	−	1.26620i	0.959663	−	0.281154i	$-0.0907173\pi$
$500$	69.6356	−	74.3491i	0.139271	−	0.148698i
$501$	−244.551	−	912.679i	−0.488127	−	1.82171i
$502$	312.715	−	72.9150i	0.622939	−	0.145249i
$503$	−37.0278	+	24.7412i	−0.0736140	+	0.0491873i	−0.591833	−	0.806061i	$-0.701595\pi$
$503$	−37.0278	+	24.7412i	−0.0736140	+	0.0491873i	0.518219	+	0.855248i	$0.326595\pi$
$504$	−73.6303	+	39.3562i	−0.146092	+	0.0780878i
$505$	−5.69014	+	6.93346i	−0.0112676	+	0.0137296i
$506$	−23.7287	−	3.91762i	−0.0468946	−	0.00774234i
$507$	−119.653	−	119.653i	−0.236002	−	0.236002i
$508$	−489.207	+	350.561i	−0.963007	+	0.690081i
$509$	−219.673	+	168.561i	−0.431578	+	0.331161i	−0.801599	−	0.597862i	$-0.796017\pi$
$509$	−219.673	+	168.561i	−0.431578	+	0.331161i	0.370021	+	0.929023i	$0.379350\pi$
$510$	10.0623	+	0.659515i	0.0197299	+	0.00129317i
$511$	26.9623	−	71.6371i	0.0527638	−	0.140190i
$512$	429.480	+	286.970i	0.838829	+	0.560488i
$513$	304.054	+	29.9467i	0.592698	+	0.0583757i
$514$	−234.489	−	106.246i	−0.456205	−	0.206704i
$515$	80.1780	+	24.3217i	0.155685	+	0.0472267i
$516$	8.47654	+	129.327i	0.0164274	+	0.250634i
$517$	−189.535	+	166.218i	−0.366605	+	0.321504i
$518$	13.1904	−	31.8445i	0.0254641	−	0.0614758i
$519$	−779.204	−	949.463i	−1.50136	−	1.82941i
$520$	16.1667	+	28.0015i	0.0310897	+	0.0538490i
$521$	−129.622	−	74.8370i	−0.248794	−	0.143641i	0.370418	−	0.928865i	$-0.379214\pi$
$521$	−129.622	−	74.8370i	−0.248794	−	0.143641i	−0.619212	+	0.785224i	$0.712548\pi$
$522$	−9.04379	+	1.49314i	−0.0173253	+	0.00286041i
$523$	−631.084	−	452.228i	−1.20666	−	0.864681i	−0.212995	−	0.977053i	$-0.568322\pi$
$523$	−631.084	−	452.228i	−1.20666	−	0.864681i	−0.993666	+	0.112372i	$0.964155\pi$
$524$	−478.198	+	15.6546i	−0.912592	+	0.0298752i
$525$	−290.100	−	67.6419i	−0.552572	−	0.128842i
$526$	−216.142	+	81.3500i	−0.410916	+	0.154658i
$527$	113.344	+	373.645i	0.215074	+	0.709005i
$528$	453.007	+	59.6396i	0.857969	+	0.112954i
$529$	−166.680	+	491.025i	−0.315086	+	0.928213i
$530$	−1.75878	−	17.8572i	−0.00331845	−	0.0336928i
$531$	326.168	+	174.341i	0.614253	+	0.328325i
$532$	223.370	−	92.5231i	0.419869	−	0.173916i
$533$	−114.717	−	56.5720i	−0.215228	−	0.106139i
$534$	131.981	−	267.632i	0.247156	−	0.501183i
$535$	3.24800	+	7.84136i	0.00607102	+	0.0146567i
$536$	37.9978	−	71.0889i	0.0708915	−	0.132629i
$537$	524.463	−	51.6551i	0.976653	−	0.0961920i
$538$	−134.773	−	45.7493i	−0.250508	−	0.0850358i
$539$	−56.4102	+	428.478i	−0.104657	+	0.794950i
$540$	−28.2948	+	8.58314i	−0.0523978	+	0.0158947i
$541$	−40.0488	−	106.407i	−0.0740273	−	0.196686i	0.893711	−	0.448643i	$-0.148092\pi$
$541$	−40.0488	−	106.407i	−0.0740273	−	0.196686i	−0.967738	+	0.251957i	$0.918926\pi$
$542$	−65.7558	+	282.011i	−0.121321	+	0.520316i
$543$	−24.7207	−	755.139i	−0.0455261	−	1.39068i
$544$	−111.186	+	155.160i	−0.204386	+	0.285221i
$545$	−6.52868	−	39.5436i	−0.0119792	−	0.0725571i
$546$	44.7985	−	77.5933i	0.0820486	−	0.142112i
$547$	620.675	−	358.347i	1.13469	−	0.655113i	0.189579	−	0.981866i	$-0.439288\pi$
$547$	620.675	−	358.347i	1.13469	−	0.655113i	0.945110	+	0.326753i	$0.105954\pi$
$548$	−486.770	+	399.482i	−0.888267	+	0.728982i
$549$	−326.763	−	135.350i	−0.595197	−	0.246539i
$550$	−120.966	−	137.936i	−0.219939	−	0.250792i
$551$	56.2805	−	3.68882i	0.102143	−	0.00669478i
$552$	17.7861	−	58.6331i	0.0322213	−	0.106219i
$553$	−49.3341	+	108.883i	−0.0892117	+	0.196895i
$554$	−9.52788	+	96.7382i	−0.0171983	+	0.174618i
$555$	−19.4540	+	29.1149i	−0.0350522	+	0.0524594i
$556$	476.765	+	179.442i	0.857492	+	0.322737i
$557$	−35.1371	+	536.088i	−0.0630827	+	0.962457i	0.842611	+	0.538523i	$0.181018\pi$
$557$	−35.1371	+	536.088i	−0.0630827	+	0.962457i	−0.905693	+	0.423933i	$0.860649\pi$
$558$	−117.415	−	153.018i	−0.210421	−	0.274226i
$559$	−62.8081	−	87.6486i	−0.112358	−	0.156795i
$560$	−14.2229	+	14.2229i	−0.0253980	+	0.0253980i
$561$	−47.7348	+	289.125i	−0.0850887	+	0.515375i
$562$	−183.534	−	150.622i	−0.326572	−	0.268011i
$563$	−169.427	−	316.976i	−0.300937	−	0.563013i	0.685318	−	0.728244i	$-0.259663\pi$
$563$	−169.427	−	316.976i	−0.300937	−	0.563013i	−0.986255	+	0.165231i	$0.947163\pi$
$564$	−167.931	−	251.327i	−0.297750	−	0.445615i
$565$	−4.80742	−	20.6179i	−0.00850870	−	0.0364918i
$566$	83.6459	−	22.4129i	0.147784	−	0.0395987i
$567$	236.014	+	221.051i	0.416251	+	0.389862i
$568$	155.150	+	96.4785i	0.273152	+	0.169857i
$569$	454.736	−	425.907i	0.799185	−	0.748519i	−0.172446	−	0.985019i	$-0.555167\pi$
$569$	454.736	−	425.907i	0.799185	−	0.748519i	0.971631	+	0.236500i	$0.0760004\pi$
$570$	30.0608	−	5.97947i	0.0527383	−	0.0104903i
$571$	173.489	+	511.082i	0.303834	+	0.895065i	0.986417	+	0.164258i	$0.0525229\pi$
$571$	173.489	+	511.082i	0.303834	+	0.895065i	−0.682584	+	0.730807i	$0.739144\pi$
$572$	−402.799	+	182.506i	−0.704194	+	0.319066i
$573$	760.201	−	100.082i	1.32670	−	0.174664i
$574$	−4.78792	+	24.0705i	−0.00834133	+	0.0419347i
$575$	67.7361	−	42.1210i	0.117802	−	0.0732539i
$576$	−33.7879	+	126.098i	−0.0586595	+	0.218920i
$577$	22.9200	−	700.133i	0.0397227	−	1.21340i	−0.774395	−	0.632702i	$-0.781946\pi$
$577$	22.9200	−	700.133i	0.0397227	−	1.21340i	0.814118	−	0.580700i	$-0.197221\pi$
$578$	127.043	+	97.4836i	0.219798	+	0.168657i
$579$	3.14121	+	2.75477i	0.00542524	+	0.00475781i
$580$	−4.89547	+	2.41418i	−0.00844047	+	0.00416238i
$581$		−	400.085i		−	0.688615i
$582$	−46.3051	+	238.794i	−0.0795620	+	0.410298i
$583$	521.446			0.894419
$584$	53.1205	+	107.718i	0.0909598	+	0.184448i
$585$	−21.8974	+	24.9692i	−0.0374314	+	0.0426823i
$586$	137.724	−	179.485i	0.235024	−	0.306289i
$587$	−302.589	−	9.90575i	−0.515484	−	0.0168752i	−0.226130	−	0.974097i	$-0.572607\pi$
$587$	−302.589	−	9.90575i	−0.515484	−	0.0168752i	−0.289355	+	0.957222i	$0.593441\pi$
$588$	−500.533	−	134.117i	−0.851246	−	0.228091i
$589$	626.708	+	1007.83i	1.06402	+	1.71108i
$590$	−26.9541	−	5.36150i	−0.0456849	−	0.00908729i
$591$	−191.331	−	1453.31i	−0.323742	−	2.45906i
$592$	−72.3683	−	159.720i	−0.122244	−	0.269798i
$593$	−404.379	+	137.268i	−0.681920	+	0.231481i	−0.640839	−	0.767675i	$-0.721413\pi$
$593$	−404.379	+	137.268i	−0.681920	+	0.231481i	−0.0410808	+	0.999156i	$0.513080\pi$
$594$	20.9181	+	105.163i	0.0352157	+	0.177041i
$595$	−8.81839	−	9.41530i	−0.0148208	−	0.0158240i
$596$	365.497	−	587.766i	0.613249	−	0.986185i
$597$	−337.526	+	360.372i	−0.565369	+	0.603639i
$598$	6.20947	+	23.1741i	0.0103837	+	0.0387526i
$599$	399.508	−	93.1521i	0.666958	−	0.155513i	0.120130	−	0.992758i	$-0.461669\pi$
$599$	399.508	−	93.1521i	0.666958	−	0.155513i	0.546827	+	0.837245i	$0.315835\pi$
$600$	388.634	−	259.677i	0.647724	−	0.432795i
$601$	168.855	−	90.2547i	0.280956	−	0.150174i	−0.324900	−	0.945748i	$-0.605331\pi$
$601$	168.855	−	90.2547i	0.280956	−	0.150174i	0.605856	+	0.795574i	$0.292831\pi$
$602$	−13.1253	+	15.9933i	−0.0218029	+	0.0265669i
$603$	81.6884	+	13.4868i	0.135470	+	0.0223662i
$604$	−234.043	−	234.043i	−0.387489	−	0.387489i
$605$	−1.71211	+	1.22688i	−0.00282993	+	0.00202790i
$606$	−30.9403	+	23.7414i	−0.0510567	+	0.0391772i
$607$	−209.547	−	13.7344i	−0.345218	−	0.0226268i	−0.108192	−	0.994130i	$-0.534506\pi$
$607$	−209.547	−	13.7344i	−0.345218	−	0.0226268i	−0.237026	+	0.971503i	$0.576173\pi$
$608$	−204.373	+	543.005i	−0.336139	+	0.893101i
$609$	26.7220	+	17.8551i	0.0438785	+	0.0293187i
$610$	26.1554	+	2.57608i	0.0428776	+	0.00422308i
$611$	229.067	+	103.789i	0.374905	+	0.169867i
$612$	−122.680	−	37.2146i	−0.200457	−	0.0608081i
$613$	45.7154	+	697.482i	0.0745765	+	1.13782i	0.857084	+	0.515176i	$0.172274\pi$
$613$	45.7154	+	697.482i	0.0745765	+	1.13782i	−0.782508	+	0.622641i	$0.786060\pi$
$614$	−75.7305	+	66.4139i	−0.123340	+	0.108166i
$615$	9.54118	−	23.0344i	0.0155141	−	0.0374544i
$616$	114.373	+	139.364i	0.185671	+	0.226240i
$617$	−389.474	−	674.589i	−0.631238	−	1.09334i	−0.987299	−	0.158874i	$-0.949214\pi$
$617$	−389.474	−	674.589i	−0.631238	−	1.09334i	0.356060	−	0.934463i	$-0.384120\pi$
$618$	315.497	+	182.152i	0.510513	+	0.294745i
$619$	−598.047	+	98.7379i	−0.966150	+	0.159512i	−0.625110	−	0.780537i	$-0.714946\pi$
$619$	−598.047	+	98.7379i	−0.966150	+	0.159512i	−0.341040	+	0.940049i	$0.610779\pi$
$620$	−93.3596	−	66.9005i	−0.150580	−	0.107904i
$621$	−46.5921	+	1.52527i	−0.0750276	+	0.00245615i
$622$	−259.218	−	60.4412i	−0.416750	−	0.0971724i
$623$	−357.277	+	134.470i	−0.573479	+	0.215842i
$624$	−132.314	−	436.181i	−0.212042	−	0.699008i
$625$	595.030	+	78.3372i	0.952048	+	0.125339i
$626$	−66.9481	+	197.223i	−0.106946	+	0.315052i
$627$	87.3029	+	886.401i	0.139239	+	1.41372i
$628$	517.041	+	276.364i	0.823313	+	0.440070i
$629$	103.899	−	43.0363i	0.165181	−	0.0684202i
$630$	5.71511	+	2.81838i	0.00907161	+	0.00447362i
$631$	411.903	−	835.256i	0.652778	−	1.32370i	−0.278866	−	0.960330i	$-0.589959\pi$
$631$	411.903	−	835.256i	0.652778	−	1.32370i	0.931644	−	0.363373i	$-0.118375\pi$
$632$	−71.7787	−	173.289i	−0.113574	−	0.274192i
$633$	−638.437	+	1194.43i	−1.00859	+	1.88694i
$634$	−93.5670	+	9.21554i	−0.147582	+	0.0145356i
$635$	92.4240	+	31.3737i	0.145550	+	0.0494074i
$636$	−81.6086	+	619.879i	−0.128315	+	0.974652i
$637$	412.562	−	125.149i	0.647665	−	0.196467i
$638$	6.97236	+	18.5251i	0.0109285	+	0.0290363i
$639$	−42.6129	+	182.757i	−0.0666868	+	0.286004i
$640$	−2.38381	−	72.8180i	−0.00372471	−	0.113778i
$641$	−292.230	+	407.807i	−0.455898	+	0.636205i	−0.975967	−	0.217920i	$-0.930073\pi$
$641$	−292.230	+	407.807i	−0.455898	+	0.636205i	0.520069	+	0.854124i	$0.325906\pi$
$642$	6.01145	+	36.4108i	0.00936362	+	0.0567146i
$643$	−454.898	+	787.907i	−0.707462	+	1.22536i	0.258334	+	0.966056i	$0.416827\pi$
$643$	−454.898	+	787.907i	−0.707462	+	1.22536i	−0.965796	+	0.259304i	$0.916507\pi$
$644$	−31.9477	+	18.4450i	−0.0496082	+	0.0286413i
$645$	16.2476	−	13.3340i	0.0251900	−	0.0206729i
$646$	−90.9428	−	37.6697i	−0.140778	−	0.0583123i
$647$	−228.572	−	260.636i	−0.353279	−	0.402838i	0.547718	−	0.836663i	$-0.315497\pi$
$647$	−228.572	−	260.636i	−0.353279	−	0.402838i	−0.900997	+	0.433825i	$0.857163\pi$
$648$	−506.310	+	33.1853i	−0.781342	+	0.0512118i
$649$	231.833	−	764.250i	0.357215	−	1.17758i
$650$	−75.5331	+	166.705i	−0.116205	+	0.256470i
$651$	−66.2843	+	672.996i	−0.101819	+	1.03379i
$652$	120.011	−	179.609i	0.184065	−	0.275473i
$653$	−361.793	−	136.169i	−0.554048	−	0.208529i	0.0594414	−	0.998232i	$-0.481068\pi$
$653$	−361.793	−	136.169i	−0.554048	−	0.208529i	−0.613490	+	0.789703i	$0.710235\pi$
$654$	11.3975	−	173.892i	0.0174273	−	0.265890i
$655$	47.2357	+	61.5587i	0.0721155	+	0.0939828i
$656$	72.7241	+	101.486i	0.110860	+	0.154705i
$657$	−87.2308	+	87.2308i	−0.132771	+	0.132771i
$658$	7.86019	−	47.6085i	0.0119456	−	0.0723533i
$659$	744.463	+	610.965i	1.12969	+	0.927109i	0.997939	−	0.0641747i	$-0.0204415\pi$
$659$	744.463	+	610.965i	1.12969	+	0.927109i	0.131747	+	0.991283i	$0.457942\pi$
$660$	−40.6338	−	76.0206i	−0.0615664	−	0.115183i
$661$	−250.960	−	375.589i	−0.379668	−	0.568213i	0.591591	−	0.806238i	$-0.298500\pi$
$661$	−250.960	−	375.589i	−0.379668	−	0.568213i	−0.971259	+	0.238025i	$0.923500\pi$
$662$	−73.8601	−	316.769i	−0.111571	−	0.478502i
$663$	282.367	−	75.6601i	0.425893	−	0.114118i
$664$	458.190	+	429.142i	0.690045	+	0.646298i
$665$	−33.2969	−	20.7053i	−0.0500705	−	0.0311359i
$666$	−40.5452	+	37.9747i	−0.0608787	+	0.0570191i
$667$	−8.44036	+	1.67889i	−0.0126542	+	0.00251708i
$668$	−286.929	−	845.266i	−0.429535	−	1.26537i
$669$	562.480	−	254.856i	0.840777	−	0.380951i
$670$	−6.09969	+	0.803040i	−0.00910402	+	0.00119857i
$671$	−149.002	+	749.084i	−0.222060	+	1.11637i
$672$	−280.748	+	174.580i	−0.417780	+	0.259792i
$673$	−137.066	+	511.539i	−0.203665	+	0.760088i	0.786188	+	0.617988i	$0.212052\pi$
$673$	−137.066	+	511.539i	−0.203665	+	0.760088i	−0.989852	+	0.142100i	$0.954615\pi$
$674$	−7.05649	+	215.553i	−0.0104696	+	0.319812i
$675$	−282.130	−	216.486i	−0.417970	−	0.320720i
$676$	−120.189	−	105.403i	−0.177794	−	0.155921i
$677$	−866.910	+	427.512i	−1.28052	+	0.631481i	−0.949979	−	0.312312i	$-0.898896\pi$
$677$	−866.910	+	427.512i	−1.28052	+	0.631481i	−0.330537	+	0.943793i	$0.607230\pi$
$678$		−	92.0521i		−	0.135770i
$679$	252.062	−	182.468i	0.371225	−	0.268730i
$680$	20.2415			0.0297669
$681$	709.793	+	1439.32i	1.04228	+	2.11354i
$682$	−274.618	+	313.141i	−0.402665	+	0.459152i
$683$	−597.579	+	778.781i	−0.874933	+	1.14024i	0.114236	+	0.993454i	$0.463558\pi$
$683$	−597.579	+	778.781i	−0.874933	+	1.14024i	−0.989169	+	0.146782i	$0.953109\pi$
$684$	−389.454	−	12.7494i	−0.569378	−	0.0186395i
$685$	98.6427	+	26.4312i	0.144004	+	0.0385857i
$686$	−98.9790	−	159.171i	−0.144284	−	0.232028i
$687$	1225.32	+	243.731i	1.78358	+	0.354776i
$688$	13.7384	+	104.354i	0.0199687	+	0.151677i
$689$	−214.682	−	473.814i	−0.311585	−	0.687683i
$690$	−4.42836	+	1.50323i	−0.00641791	+	0.00217859i
$691$	157.767	+	793.146i	0.228316	+	1.14782i	0.909498	+	0.415709i	$0.136467\pi$
$691$	157.767	+	793.146i	0.228316	+	1.14782i	−0.681181	+	0.732115i	$0.738533\pi$
$692$	−793.216	−	846.908i	−1.14627	−	1.22386i
$693$	−97.7875	+	157.255i	−0.141108	+	0.226919i
$694$	−71.1964	+	76.0156i	−0.102588	+	0.109533i
$695$	−21.3821	−	79.7992i	−0.0307657	−	0.114819i
$696$	−49.1108	+	11.4510i	−0.0705615	+	0.0164526i
$697$	−66.5786	+	44.4864i	−0.0955216	+	0.0638255i
$698$	−116.971	+	62.5221i	−0.167580	+	0.0895733i
$699$	646.573	−	787.851i	0.924997	−	1.12711i
$700$	−277.655	−	45.8411i	−0.396650	−	0.0654872i
$701$	−234.676	−	234.676i	−0.334773	−	0.334773i	0.519623	−	0.854396i	$-0.326073\pi$
$701$	−234.676	−	234.676i	−0.334773	−	0.334773i	−0.854396	+	0.519623i	$0.826073\pi$
$702$	86.9442	−	62.3033i	0.123852	−	0.0887512i
$703$	271.183	−	208.086i	0.385751	−	0.295997i
$704$	281.302	+	18.4375i	0.399576	+	0.0261896i
$705$	−17.2674	+	45.8783i	−0.0244927	+	0.0650756i
$706$	−200.271	−	133.817i	−0.283669	−	0.189542i
$707$	49.6510	+	4.89020i	0.0702277	+	0.00691683i
$708$	872.234	+	395.204i	1.23197	+	0.558198i
$709$	−186.425	−	56.5513i	−0.262940	−	0.0797621i	0.156062	−	0.987747i	$-0.450120\pi$
$709$	−186.425	−	56.5513i	−0.262940	−	0.0797621i	−0.419002	+	0.907985i	$0.637620\pi$
$710$	−0.912025	−	13.9148i	−0.00128454	−	0.0195983i
$711$	144.847	−	127.027i	0.203723	−	0.178660i
$712$	229.226	−	553.400i	0.321946	−	0.777247i
$713$	−114.877	−	139.978i	−0.161117	−	0.196322i
$714$	−28.0450	−	48.5754i	−0.0392788	−	0.0680328i
$715$	62.1080	+	35.8581i	0.0868644	+	0.0501512i
$716$	491.216	−	81.1001i	0.686056	−	0.113268i
$717$	1304.73	+	934.953i	1.81970	+	1.30398i
$718$	−83.0283	+	2.71807i	−0.115638	+	0.00378561i
$719$	−138.825	−	32.3694i	−0.193080	−	0.0450200i	0.129418	−	0.991590i	$-0.458689\pi$
$719$	−138.825	−	32.3694i	−0.193080	−	0.0450200i	−0.322498	+	0.946570i	$0.604523\pi$
$720$	30.3399	−	11.4191i	0.0421388	−	0.0158599i
$721$	−135.286	−	445.980i	−0.187637	−	0.618557i
$722$	−58.2087	−	7.66332i	−0.0806215	−	0.0106140i
$723$	−13.2510	+	39.0362i	−0.0183278	+	0.0539920i
$724$	−69.9621	−	710.337i	−0.0966327	−	0.981128i
$725$	−57.8968	−	30.9465i	−0.0798576	−	0.0426848i
$726$	−8.46119	+	3.50474i	−0.0116545	+	0.00482746i
$727$	−332.597	−	164.019i	−0.457493	−	0.225611i	0.198915	−	0.980017i	$-0.436258\pi$
$727$	−332.597	−	164.019i	−0.457493	−	0.225611i	−0.656408	+	0.754406i	$0.727925\pi$
$728$	79.5456	−	161.303i	0.109266	−	0.221569i
$729$	−12.5321	−	30.2553i	−0.0171909	−	0.0415024i
$730$	4.32126	−	8.08451i	0.00591953	−	0.0110747i
$731$	−67.1788	+	6.61653i	−0.0918999	+	0.00905135i
$732$	−867.168	−	294.364i	−1.18466	−	0.402137i
$733$	−37.9188	+	288.022i	−0.0517310	+	0.392936i	0.945918	+	0.324406i	$0.105164\pi$
$733$	−37.9188	+	288.022i	−0.0517310	+	0.392936i	−0.997649	+	0.0685301i	$0.978169\pi$
$734$	−65.4358	+	19.8497i	−0.0891496	+	0.0270432i
$735$	29.6021	+	78.6509i	0.0402749	+	0.107008i
$736$	20.1021	−	86.2133i	0.0273127	−	0.117138i
$737$	−5.84979	−	178.693i	−0.00793730	−	0.242459i
$738$	23.0393	−	32.1513i	0.0312186	−	0.0435655i
$739$	−194.792	−	1179.84i	−0.263589	−	1.59653i	−0.711652	−	0.702532i	$-0.752053\pi$
$739$	−194.792	−	1179.84i	−0.263589	−	1.59653i	0.448063	−	0.894002i	$-0.352114\pi$
$740$	−16.5402	+	28.6485i	−0.0223516	+	0.0387142i
$741$	769.488	−	444.264i	1.03845	−	0.599547i
$742$	−77.1534	+	63.3182i	−0.103980	+	0.0853344i
$743$	275.549	+	114.136i	0.370859	+	0.153615i	0.560326	−	0.828272i	$-0.310676\pi$
$743$	275.549	+	114.136i	0.370859	+	0.153615i	−0.189467	+	0.981887i	$0.560676\pi$
$744$	−699.637	−	797.783i	−0.940372	−	1.07229i
$745$	−112.007	+	7.34132i	−0.150345	+	0.00985413i
$746$	125.274	−	412.973i	0.167928	−	0.553583i
$747$	−266.118	+	587.334i	−0.356248	+	0.786257i
$748$	−27.1350	+	275.506i	−0.0362767	+	0.368323i
$749$	26.2286	−	39.2539i	0.0350181	−	0.0524083i
$750$	−67.2268	−	25.3024i	−0.0896357	−	0.0337365i
$751$	−49.4971	+	755.180i	−0.0659082	+	1.00557i	0.828981	+	0.559277i	$0.188921\pi$
$751$	−49.4971	+	755.180i	−0.0659082	+	1.00557i	−0.894889	+	0.446289i	$0.852745\pi$
$752$	−149.437	−	194.751i	−0.198720	−	0.258977i
$753$	1056.90	+	1474.91i	1.40359	+	1.95871i
$754$	13.9624	−	13.9624i	0.0185177	−	0.0185177i
$755$	−8.74384	+	52.9607i	−0.0115812	+	0.0701466i
$756$	127.136	+	104.338i	0.168169	+	0.138013i
$757$	−192.380	−	359.917i	−0.254134	−	0.475452i	0.722210	−	0.691674i	$-0.243127\pi$
$757$	−192.380	−	359.917i	−0.254134	−	0.475452i	−0.976344	+	0.216222i	$0.930627\pi$
$758$	−88.9941	−	133.189i	−0.117406	−	0.175711i
$759$	−30.8600	−	132.351i	−0.0406588	−	0.174376i
$760$	59.4275	−	15.9235i	0.0781940	−	0.0209520i
$761$	−213.949	−	200.385i	−0.281142	−	0.263318i	0.530223	−	0.847858i	$-0.322108\pi$
$761$	−213.949	−	200.385i	−0.281142	−	0.263318i	−0.811365	+	0.584540i	$0.801275\pi$
$762$	360.389	+	224.104i	0.472952	+	0.294100i
$763$	−162.711	+	152.396i	−0.213252	+	0.199733i
$764$	710.453	−	141.318i	0.929912	−	0.184971i
$765$	6.68298	+	19.6874i	0.00873592	+	0.0257352i
$766$	97.6294	−	44.2353i	0.127453	−	0.0577484i
$767$	−789.885	+	103.990i	−1.02984	+	0.135581i
$768$	−12.3698	+	62.1871i	−0.0161065	+	0.0809727i
$769$	572.542	−	356.029i	0.744528	−	0.462977i	−0.102361	−	0.994747i	$-0.532640\pi$
$769$	572.542	−	356.029i	0.744528	−	0.462977i	0.846889	+	0.531770i	$0.178473\pi$
$770$	3.56147	−	13.2916i	0.00462528	−	0.0172618i
$771$	47.5972	−	1453.94i	0.0617344	−	1.88579i
$772$	3.13141	+	2.40282i	0.00405623	+	0.00311246i
$773$	845.150	+	741.177i	1.09334	+	0.958831i	0.999325	−	0.0367397i	$-0.0116972\pi$
$773$	845.150	+	741.177i	1.09334	+	0.958831i	0.0940127	+	0.995571i	$0.470031\pi$
$774$	29.9062	−	14.7481i	0.0386385	−	0.0190544i
$775$		−	1381.37i		−	1.78242i
$776$	−61.4001	+	484.388i	−0.0791238	+	0.624212i
$777$	194.773			0.250674
$778$	43.8869	+	88.9938i	0.0564099	+	0.114388i
$779$	−160.473	+	182.984i	−0.205999	+	0.234897i
$780$	−52.3472	+	68.2202i	−0.0671118	+	0.0874618i
$781$	405.019	+	13.2589i	0.518590	+	0.0169769i
$782$	14.5076	+	3.88729i	0.0185519	+	0.00497096i
$783$	20.2605	+	32.5816i	0.0258755	+	0.0416112i
$784$	−412.745	−	82.1001i	−0.526461	−	0.104720i
$785$	−12.4101	−	94.2640i	−0.0158090	−	0.120081i
$786$	139.238	+	307.306i	0.177148	+	0.390974i
$787$	−622.945	+	211.461i	−0.791544	+	0.268693i	−0.687790	−	0.725910i	$-0.741419\pi$
$787$	−622.945	+	211.461i	−0.791544	+	0.268693i	−0.103754	+	0.994603i	$0.533086\pi$
$788$	−270.163	−	1358.20i	−0.342846	−	1.72361i
$789$	−892.102	−	952.488i	−1.13067	−	1.20721i
$790$	−7.55985	+	12.1572i	−0.00956942	+	0.0153889i
$791$	−80.5002	+	85.9492i	−0.101770	+	0.108659i
$792$	−75.2039	−	280.665i	−0.0949545	−	0.354375i
$793$	742.003	−	173.011i	0.935691	−	0.218172i
$794$	−47.9044	+	32.0087i	−0.0603330	+	0.0403133i
$795$	89.4233	−	47.7977i	0.112482	−	0.0601229i
$796$	−295.917	+	360.576i	−0.371755	+	0.452984i
$797$	−734.843	−	121.323i	−0.922011	−	0.152225i	−0.316985	−	0.948430i	$-0.602671\pi$
$797$	−734.843	−	121.323i	−0.922011	−	0.152225i	−0.605026	+	0.796206i	$0.706837\pi$
$798$	−120.551	−	120.551i	−0.151067	−	0.151067i
$799$	127.970	−	91.7023i	0.160163	−	0.114771i
$800$	535.764	−	411.107i	0.669706	−	0.513883i
$801$	613.933	+	40.2393i	0.766458	+	0.0502363i
$802$	−136.503	+	362.680i	−0.170203	+	0.452219i
$803$	221.498	+	148.000i	0.275838	+	0.184309i
$804$	213.340	+	21.0121i	0.265348	+	0.0261345i
$805$	5.44934	+	2.46907i	0.00676937	+	0.00306716i
$806$	397.599	+	120.610i	0.493299	+	0.149641i
$807$	−52.6011	−	802.537i	−0.0651810	−	0.994470i
$808$	−58.8573	+	51.6165i	−0.0728432	+	0.0638818i
$809$	438.054	−	1057.56i	0.541477	−	1.30724i	−0.382205	−	0.924078i	$-0.624835\pi$
$809$	438.054	−	1057.56i	0.541477	−	1.30724i	0.923681	−	0.383162i	$-0.125165\pi$
$810$	24.5682	+	29.9364i	0.0303311	+	0.0369585i
$811$	−9.38801	−	16.2605i	−0.0115758	−	0.0200500i	0.860179	−	0.509991i	$-0.170351\pi$
$811$	−9.38801	−	16.2605i	−0.0115758	−	0.0200500i	−0.871755	+	0.489942i	$0.837018\pi$
$812$	26.2939	+	15.1808i	0.0323816	+	0.0186955i
$813$	−1614.48	+	266.552i	−1.98583	+	0.327862i
$814$	97.5090	+	69.8740i	0.119790	+	0.0858402i
$815$	−35.0131	+	1.14621i	−0.0429609	+	0.00140639i
$816$	−277.893	−	64.7956i	−0.340556	−	0.0794064i
$817$	−192.027	+	72.2737i	−0.235039	+	0.0884623i
$818$	−44.8021	−	147.693i	−0.0547703	−	0.180554i
$819$	183.150	+	24.1122i	0.223627	+	0.0294410i
$820$	7.57117	−	22.3039i	0.00923313	−	0.0271999i
$821$	−63.6319	−	646.065i	−0.0775053	−	0.786925i	−0.952853	−	0.303431i	$-0.901868\pi$
$821$	−63.6319	−	646.065i	−0.0775053	−	0.786925i	0.875348	−	0.483494i	$-0.160632\pi$
$822$	391.602	+	209.316i	0.476401	+	0.254642i
$823$	−319.921	+	132.516i	−0.388726	+	0.161015i	−0.568482	−	0.822696i	$-0.692469\pi$
$823$	−319.921	+	132.516i	−0.388726	+	0.161015i	0.179756	+	0.983711i	$0.442469\pi$
$824$	655.861	+	323.435i	0.795948	+	0.392518i
$825$	458.530	−	929.806i	0.555794	−	1.12704i
$826$	58.4993	+	141.230i	0.0708223	+	0.170980i
$827$	−354.956	+	664.076i	−0.429209	+	0.802994i	−0.999834	−	0.0182169i	$-0.994201\pi$
$827$	−354.956	+	664.076i	−0.429209	+	0.802994i	0.570625	+	0.821211i	$0.306701\pi$
$828$	59.1686	−	5.82760i	0.0714596	−	0.00703816i
$829$	−971.358	−	329.731i	−1.17172	−	0.397746i	−0.333328	−	0.942811i	$-0.608172\pi$
$829$	−971.358	−	329.731i	−1.17172	−	0.397746i	−0.838394	+	0.545065i	$0.816505\pi$
$830$	6.25415	−	47.5050i	0.00753512	−	0.0572349i
$831$	−525.642	+	159.452i	−0.632541	+	0.191879i
$832$	−99.0601	−	263.196i	−0.119063	−	0.316342i
$833$	61.2871	−	262.846i	0.0735739	−	0.315541i
$834$	−11.7530	−	359.018i	−0.0140924	−	0.430477i
$835$	−84.3213	+	117.670i	−0.100984	+	0.140922i
$836$	137.068	+	830.210i	0.163957	+	0.993074i
$837$	−403.661	+	699.162i	−0.482271	+	0.835319i
$838$	425.266	−	245.528i	0.507478	−	0.292992i
$839$	−632.982	+	519.475i	−0.754448	+	0.619159i	−0.930952	−	0.365140i	$-0.881021\pi$
$839$	−632.982	+	519.475i	−0.754448	+	0.619159i	0.176505	+	0.984300i	$0.443521\pi$
$840$	32.3886	+	13.4158i	0.0385579	+	0.0159712i
$841$	−549.840	−	626.972i	−0.653793	−	0.745508i
$842$	329.412	−	21.5908i	0.391226	−	0.0256423i
$843$	389.462	−	1283.88i	0.461995	−	1.52299i
$844$	−528.050	+	1165.43i	−0.625652	+	1.38084i
$845$	−2.54111	+	25.8003i	−0.00300723	+	0.0305330i
$846$	−43.2058	+	64.6620i	−0.0510707	+	0.0764326i
$847$	10.9651	+	4.12699i	0.0129459	+	0.00487247i
$848$	−33.2090	+	506.672i	−0.0391616	+	0.597490i
$849$	297.892	+	388.221i	0.350874	+	0.457268i
$850$	66.7371	+	93.1315i	0.0785142	+	0.109566i
$851$	−36.8790	+	36.8790i	−0.0433361	+	0.0433361i
$852$	−79.1490	+	479.399i	−0.0928979	+	0.562674i
$853$	563.927	+	462.803i	0.661111	+	0.542560i	0.904020	−	0.427489i	$-0.140602\pi$
$853$	563.927	+	462.803i	0.661111	+	0.542560i	−0.242910	+	0.970049i	$0.578102\pi$
$854$	−68.9134	−	128.928i	−0.0806948	−	0.150969i
$855$	35.1084	+	52.5434i	0.0410624	+	0.0614543i
$856$	16.8213	+	72.1424i	0.0196510	+	0.0842785i
$857$	1134.87	−	304.088i	1.32424	−	0.354829i	0.473675	−	0.880700i	$-0.342927\pi$
$857$	1134.87	−	304.088i	1.32424	−	0.354829i	0.850565	+	0.525871i	$0.176260\pi$
$858$	227.590	+	213.161i	0.265256	+	0.248440i
$859$	968.951	+	602.533i	1.12800	+	0.701435i	0.958782	−	0.284144i	$-0.0917093\pi$
$859$	968.951	+	602.533i	1.12800	+	0.701435i	0.169217	+	0.985579i	$0.445876\pi$
$860$	14.4926	−	13.5738i	0.0168518	−	0.0157835i
$861$	−136.018	+	27.0556i	−0.157977	+	0.0314235i
$862$	−116.772	−	344.000i	−0.135467	−	0.399072i
$863$	−373.888	+	169.407i	−0.433243	+	0.196300i	−0.617488	−	0.786581i	$-0.711849\pi$
$863$	−373.888	+	169.407i	−0.433243	+	0.196300i	0.184245	+	0.982880i	$0.441016\pi$
$864$	−391.302	+	51.5159i	−0.452896	+	0.0596249i
$865$	−36.7124	+	184.565i	−0.0424420	+	0.213371i
$866$	−80.1352	+	49.8313i	−0.0925349	+	0.0575419i
$867$	−234.202	+	874.056i	−0.270130	+	1.00814i
$868$	−20.9031	+	638.524i	−0.0240819	+	0.735627i
$869$	−330.057	−	253.262i	−0.379813	−	0.291441i
$870$	2.89378	+	2.53778i	0.00332619	+	0.00291699i
$871$	−159.961	+	78.8841i	−0.183652	+	0.0905673i
$872$		−	349.806i		−	0.401153i
$873$	−491.401	+	100.207i	−0.562888	+	0.114785i
$874$	45.6511			0.0522324
$875$	40.6427	+	82.4152i	0.0464487	+	0.0941887i
$876$	−210.604	+	240.147i	−0.240415	+	0.274141i
$877$	−228.060	+	297.214i	−0.260046	+	0.338899i	−0.905069	−	0.425264i	$-0.860181\pi$
$877$	−228.060	+	297.214i	−0.260046	+	0.338899i	0.645023	+	0.764163i	$0.276848\pi$
$878$	−83.6951	−	2.73989i	−0.0953247	−	0.00312061i
$879$	1234.86	+	330.879i	1.40484	+	0.376427i
$880$	−36.9667	−	59.4472i	−0.0420076	−	0.0675537i
$881$	−1279.56	−	254.521i	−1.45240	−	0.288900i	−0.595071	−	0.803673i	$-0.702876\pi$
$881$	−1279.56	−	254.521i	−1.45240	−	0.288900i	−0.857326	+	0.514773i	$0.827876\pi$
$882$	17.4019	+	132.181i	0.0197301	+	0.149865i
$883$	−213.655	−	471.547i	−0.241965	−	0.534028i	0.749866	−	0.661590i	$-0.230118\pi$
$883$	−213.655	−	471.547i	−0.241965	−	0.534028i	−0.991831	+	0.127562i	$0.959285\pi$
$884$	261.511	−	88.7710i	0.295827	−	0.100420i
$885$	−30.2968	−	152.313i	−0.0342337	−	0.172105i
$886$	−22.8480	−	24.3946i	−0.0257878	−	0.0275334i
$887$	484.599	−	779.299i	0.546335	−	0.878579i	−0.453585	−	0.891213i	$-0.649855\pi$
$887$	484.599	−	779.299i	0.546335	−	0.878579i	0.999920	+	0.0126345i	$0.00402180\pi$
$888$	−208.919	+	223.060i	−0.235269	+	0.251194i
$889$	−140.515	−	524.409i	−0.158060	−	0.589887i
$890$	−44.5241	+	10.3816i	−0.0500271	+	0.0116647i
$891$	−935.751	+	625.249i	−1.05023	+	0.701738i
$892$	514.499	−	275.006i	0.576793	−	0.308302i
$893$	303.571	−	369.902i	0.339945	−	0.414224i
$894$	−481.537	−	79.5022i	−0.538633	−	0.0889286i
$895$	−57.0926	−	57.0926i	−0.0637906	−	0.0637906i
$896$	−329.412	+	236.054i	−0.367648	+	0.263453i
$897$	−107.556	+	82.5309i	−0.119907	+	0.0920077i
$898$	126.518	+	8.29241i	0.140888	+	0.00923430i
$899$	−52.4977	+	139.483i	−0.0583956	+	0.155153i
$900$	377.113	+	251.979i	0.419014	+	0.279976i
$901$	−324.079	−	31.9190i	−0.359688	−	0.0354261i
$902$	−77.8005	−	35.2509i	−0.0862533	−	0.0390809i
$903$	−111.879	−	33.9380i	−0.123897	−	0.0375836i
$904$	−12.0851	−	184.382i	−0.0133684	−	0.203963i
$905$	−87.0299	+	76.3231i	−0.0961656	+	0.0843350i
$906$	−89.3155	+	215.627i	−0.0985823	+	0.237999i
$907$	3.63801	+	4.43293i	0.00401103	+	0.00488746i	0.775012	−	0.631946i	$-0.217744\pi$
$907$	3.63801	+	4.43293i	0.00401103	+	0.00488746i	−0.771001	+	0.636834i	$0.780244\pi$
$908$	758.049	+	1312.98i	0.834856	+	1.44601i
$909$	−69.6360	−	40.2044i	−0.0766073	−	0.0442292i
$910$	−13.5437	+	2.23608i	−0.0148832	+	0.00245723i
$911$	990.990	+	710.133i	1.08780	+	0.779510i	0.976767	−	0.214306i	$-0.0687491\pi$
$911$	990.990	+	710.133i	1.08780	+	0.779510i	0.111038	+	0.993816i	$0.464582\pi$
$912$	−866.846	+	28.3776i	−0.950489	+	0.0311158i
$913$	1356.05	+	316.186i	1.48526	+	0.346315i
$914$	114.439	−	43.0718i	0.125207	−	0.0471245i
$915$	43.1114	+	142.119i	0.0471163	+	0.155322i
$916$	1170.16	+	154.054i	1.27747	+	0.168182i
$917$	138.734	−	408.696i	0.151291	−	0.445689i
$918$	−6.56336	−	66.6389i	−0.00714963	−	0.0725914i
$919$	741.618	+	396.403i	0.806983	+	0.431342i	0.822659	−	0.568536i	$-0.192490\pi$
$919$	741.618	+	396.403i	0.806983	+	0.431342i	−0.0156754	+	0.999877i	$0.504990\pi$
$920$	−8.67275	+	3.59237i	−0.00942690	+	0.00390475i
$921$	−510.490	−	251.746i	−0.554278	−	0.273340i
$922$	−44.3558	+	89.9447i	−0.0481083	+	0.0975539i
$923$	−154.701	−	373.481i	−0.167606	−	0.404638i
$924$	−226.020	+	422.855i	−0.244611	+	0.457635i
$925$	−395.945	+	38.9972i	−0.428049	+	0.0421591i
$926$	471.840	+	160.168i	0.509546	+	0.172968i
$927$	−98.0408	+	744.694i	−0.105761	+	0.803337i
$928$	−69.7221	+	21.1500i	−0.0751316	+	0.0227909i
$929$	349.115	+	927.577i	0.375797	+	0.998469i	0.979533	+	0.201284i	$0.0645115\pi$
$929$	349.115	+	927.577i	0.375797	+	0.998469i	−0.603736	+	0.797184i	$0.706322\pi$
$930$	−18.3907	+	78.8734i	−0.0197749	+	0.0848101i
$931$	−26.8410	−	819.908i	−0.0288303	−	0.880675i
$932$	560.841	−	782.652i	0.601761	−	0.839756i
$933$	−245.009	−	1484.00i	−0.262603	−	1.59056i
$934$	−192.893	+	334.101i	−0.206524	+	0.357710i
$935$	38.8813	−	22.4481i	0.0415842	−	0.0240087i
$936$	−224.065	+	183.886i	−0.239386	+	0.196459i
$937$	1046.59	+	433.511i	1.11696	+	0.462659i	0.863328	−	0.504643i	$-0.168376\pi$
$937$	1046.59	+	433.511i	1.11696	+	0.462659i	0.253629	+	0.967302i	$0.418376\pi$
$938$	22.5638	+	25.7291i	0.0240552	+	0.0274297i
$939$	−1174.41	+	76.9748i	−1.25070	+	0.0819753i
$940$	−13.4431	+	44.3161i	−0.0143012	+	0.0471448i
$941$	−669.111	+	1476.76i	−0.711063	+	1.56935i	0.107024	+	0.994256i	$0.465868\pi$
$941$	−669.111	+	1476.76i	−0.711063	+	1.56935i	−0.818087	+	0.575094i	$0.804965\pi$
$942$	40.5204	−	411.410i	0.0430152	−	0.436741i
$943$	20.6313	−	30.8769i	0.0218783	−	0.0327432i
$944$	727.832	+	273.936i	0.771008	+	0.290187i
$945$	1.74447	−	26.6154i	0.00184600	−	0.0281645i
$946$	−43.8345	−	57.1262i	−0.0463367	−	0.0603871i
$947$	840.477	+	1172.88i	0.887516	+	1.23853i	0.970287	+	0.241958i	$0.0777896\pi$
$947$	840.477	+	1172.88i	0.887516	+	1.23853i	−0.0827711	+	0.996569i	$0.526377\pi$
$948$	352.725	−	352.725i	0.372073	−	0.372073i
$949$	43.2890	−	262.198i	0.0456154	−	0.276288i
$950$	269.199	+	220.926i	0.283368	+	0.232554i
$951$	−250.447	−	468.554i	−0.263352	−	0.492696i
$952$	−62.5521	−	93.6158i	−0.0657060	−	0.0983359i
$953$	−6.57951	−	28.2180i	−0.00690400	−	0.0296096i	0.970312	−	0.241855i	$-0.0777558\pi$
$953$	−6.57951	−	28.2180i	−0.00690400	−	0.0296096i	−0.977216	+	0.212245i	$0.931922\pi$
$954$	155.379	−	41.6337i	0.162871	−	0.0436412i
$955$	−85.7404	−	80.3047i	−0.0897805	−	0.0840886i
$956$	1287.73	+	800.759i	1.34699	+	0.837614i
$957$	−81.6360	+	76.4605i	−0.0853041	+	0.0798960i
$958$	−382.935	+	76.1704i	−0.399723	+	0.0795099i
$959$	−182.591	−	537.897i	−0.190398	−	0.560893i
$960$	49.9307	−	22.6233i	0.0520112	−	0.0235659i
$961$	−2156.39	+	283.894i	−2.24390	+	0.295415i
$962$	23.3462	−	117.369i	0.0242684	−	0.122006i
$963$	−64.6139	+	40.1795i	−0.0670965	+	0.0417233i
$964$	−10.0797	+	37.6179i	−0.0104561	+	0.0390228i
$965$	0.0209439	−	0.639769i	2.17035e−5	−	0.000662973i
$966$	20.6372	+	15.8355i	0.0213636	+	0.0163929i
$967$	1095.43	+	960.662i	1.13281	+	0.993446i	0.999997	+	0.00230433i	$0.000733491\pi$
$967$	1095.43	+	960.662i	1.13281	+	0.993446i	0.132810	+	0.991141i	$0.457600\pi$
$968$	−16.4878	+	8.13090i	−0.0170329	+	0.00839969i
$969$		−	556.242i		−	0.574037i
$970$	32.7814	−	17.7255i	0.0337953	−	0.0182737i
$971$	1253.41			1.29084			0.645421	−	0.763827i	$-0.276682\pi$
$971$	1253.41			1.29084			0.645421	+	0.763827i	$0.276682\pi$
$972$	−392.748	−	796.415i	−0.404062	−	0.819357i
$973$	−302.990	+	345.494i	−0.311398	+	0.355081i
$974$	88.3210	−	115.102i	0.0906787	−	0.118175i
$975$	−1033.65	−	33.8382i	−1.06016	−	0.0347059i
$976$	−718.371	−	192.487i	−0.736035	−	0.197220i
$977$	383.260	+	616.332i	0.392283	+	0.630842i	0.984592	−	0.174869i	$-0.0559502\pi$
$977$	383.260	+	616.332i	0.392283	+	0.630842i	−0.592309	+	0.805711i	$0.701784\pi$
$978$	−149.393	−	29.7162i	−0.152754	−	0.0303846i
$979$	−173.416	−	1317.22i	−0.177135	−	1.34548i
$980$	32.7653	+	72.3146i	0.0334340	+	0.0737904i
$981$	340.230	−	115.493i	0.346820	−	0.117729i
$982$	−24.4291	−	122.813i	−0.0248768	−	0.125064i
$983$	670.318	+	715.691i	0.681910	+	0.728068i	0.973554	−	0.228459i	$-0.0733687\pi$
$983$	670.318	+	715.691i	0.681910	+	0.728068i	−0.291643	+	0.956527i	$0.594202\pi$
$984$	114.911	−	184.792i	0.116780	−	0.187797i
$985$	−153.522	+	163.913i	−0.155860	+	0.166410i
$986$	−3.19936	−	11.9402i	−0.00324478	−	0.0121097i
$987$	265.546	−	61.9165i	0.269043	−	0.0627321i
$988$	697.942	−	466.350i	0.706419	−	0.472014i
$989$	27.6094	−	14.7575i	0.0279165	−	0.0149217i
$990$	−14.0692	+	17.1434i	−0.0142113	+	0.0173166i
$991$	−1506.71	−	248.759i	−1.52039	−	0.251018i	−0.656358	−	0.754450i	$-0.727904\pi$
$991$	−1506.71	−	248.759i	−1.52039	−	0.251018i	−0.864035	+	0.503432i	$0.832071\pi$
$992$	−1084.07	−	1084.07i	−1.09281	−	1.09281i
$993$	1494.02	−	1070.60i	1.50456	−	1.07815i
$994$	−61.5368	+	47.2188i	−0.0619082	+	0.0475038i
$995$	75.4853	+	4.94757i	0.0758646	+	0.00497243i
$996$	−588.099	+	1562.54i	−0.590461	+	1.56882i
$997$	−655.870	−	438.238i	−0.657843	−	0.439557i	0.181329	−	0.983422i	$-0.441960\pi$
$997$	−655.870	−	438.238i	−0.657843	−	0.439557i	−0.839172	+	0.543866i	$0.816960\pi$
$998$	−493.257	−	48.5816i	−0.494246	−	0.0486790i
$999$	211.798	+	95.9643i	0.212010	+	0.0960603i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	97.3.l.a.5.8	✓	480
97.39	odd	96	inner	97.3.l.a.39.8	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
97.3.l.a.5.8	✓	480	1.1	even	1	trivial
97.3.l.a.39.8	yes	480	97.39	odd	96	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 97 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	97.l (of order \(96\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.294635 - 0.597460i) q^{2} +(2.48200 - 2.83018i) q^{3} +(2.16490 - 2.82135i) q^{4} +(-0.576421 - 0.0188701i) q^{5} +(-2.42220 - 0.649027i) q^{6} +(1.69403 + 2.72423i) q^{7} +(-4.93693 - 0.982017i) q^{8} +(-0.674853 - 5.12602i) q^{9} +(0.158559 + 0.349948i) q^{10} +(-10.5723 + 3.58880i) q^{11} +(-2.61165 - 13.1296i) q^{12} +(7.61363 + 8.12899i) q^{13} +(1.12850 - 1.81477i) q^{14} +(-1.48408 + 1.58454i) q^{15} +(-2.81381 - 10.5013i) q^{16} +(6.79034 - 1.58328i) q^{17} +(-2.86375 + 1.91350i) q^{18} +(18.6904 - 9.99020i) q^{19} +(-1.30113 + 1.58543i) q^{20} +(11.9147 + 1.96712i) q^{21} +(5.25912 + 5.25912i) q^{22} +(-2.62842 + 1.88350i) q^{23} +(-15.0328 + 11.5350i) q^{24} +(-24.6146 - 1.61332i) q^{25} +(2.61351 - 6.94392i) q^{26} +(11.9869 + 8.00937i) q^{27} +(11.3534 + 1.11821i) q^{28} +(2.42412 + 1.09836i) q^{29} +(1.38396 + 0.419820i) q^{30} +(3.66257 + 55.8800i) q^{31} +(-20.5830 + 18.0508i) q^{32} +(-16.0834 + 38.8288i) q^{33} +(-2.94662 - 3.59046i) q^{34} +(-0.925071 - 1.60227i) q^{35} +(-15.9233 - 9.19330i) q^{36} +(15.9136 - 2.62735i) q^{37} +(-11.4756 - 8.22328i) q^{38} +(41.9036 - 1.37178i) q^{39} +(2.82722 + 0.659215i) q^{40} +(-10.7481 + 4.04531i) q^{41} +(-2.33519 - 7.69810i) q^{42} +(-9.59864 - 1.26369i) q^{43} +(-12.7626 + 37.5974i) q^{44} +(0.292271 + 2.96748i) q^{45} +(1.89974 + 1.01543i) q^{46} +(20.8607 - 8.64079i) q^{47} +(-36.7044 - 18.1006i) q^{48} +(17.1205 - 34.7169i) q^{49} +(6.28841 + 15.1816i) q^{50} +(12.3726 - 23.1476i) q^{51} +(39.4175 - 3.88228i) q^{52} +(-44.2260 - 15.0127i) q^{53} +(1.25353 - 9.52151i) q^{54} +(6.16180 - 1.86916i) q^{55} +(-5.68809 - 15.1129i) q^{56} +(18.1154 - 77.6928i) q^{57} +(-0.0580070 - 1.77193i) q^{58} +(-41.6658 + 58.1446i) q^{59} +(1.25765 + 7.61748i) q^{60} +(34.2040 - 59.2430i) q^{61} +(32.3070 - 18.6524i) q^{62} +(12.8212 - 10.5221i) q^{63} +(-23.3275 - 9.66257i) q^{64} +(-4.23527 - 4.82939i) q^{65} +(27.9374 - 1.83111i) q^{66} +(-4.64850 + 15.3241i) q^{67} +(10.2334 - 22.5856i) q^{68} +(-1.19310 + 12.1137i) q^{69} +(-0.684734 + 1.02478i) q^{70} +(-33.9696 - 12.7852i) q^{71} +(-1.70213 + 25.9695i) q^{72} +(-14.5252 - 18.9295i) q^{73} +(-6.25843 - 8.73363i) q^{74} +(-65.6594 + 65.6594i) q^{75} +(12.2768 - 74.3598i) q^{76} +(-27.6865 - 22.7217i) q^{77} +(-13.1658 - 24.6315i) q^{78} +(20.7020 + 30.9827i) q^{79} +(1.42378 + 6.10625i) q^{80} +(97.3661 - 26.0892i) q^{81} +(5.58368 + 5.22969i) q^{82} +(-105.909 - 65.8582i) q^{83} +(31.3439 - 29.3568i) q^{84} +(-3.94397 + 0.784504i) q^{85} +(2.07309 + 6.10713i) q^{86} +(9.12522 - 4.13459i) q^{87} +(55.7188 - 7.33552i) q^{88} +(-23.2154 + 116.712i) q^{89} +(1.68684 - 1.04894i) q^{90} +(-9.24748 + 34.5121i) q^{91} +(-0.376251 + 11.4933i) q^{92} +(167.241 + 128.329i) q^{93} +(-11.3088 - 9.91756i) q^{94} +(-10.9620 + 5.40588i) q^{95} +103.056i q^{96} +(-6.81000 - 96.7607i) q^{97} -25.7862 q^{98} +(25.5310 + 51.7717i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} + 64 q^{9} - 32 q^{10} - 32 q^{11} - 224 q^{12} - 32 q^{13} - 32 q^{14} + 224 q^{15} - 32 q^{16} + 48 q^{17} - 32 q^{18}+ \cdots - 512 q^{99}+O(q^{100}) \) 480 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 + 64 * q^9 - 32 * q^10 - 32 * q^11 - 224 * q^12 - 32 * q^13 - 32 * q^14 + 224 * q^15 - 32 * q^16 + 48 * q^17 - 32 * q^18 - 32 * q^19 - 416 * q^20 - 32 * q^21 - 32 * q^22 - 144 * q^23 - 32 * q^24 + 288 * q^25 + 48 * q^26 - 32 * q^27 - 272 * q^28 + 256 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 + 144 * q^33 - 432 * q^34 - 16 * q^35 - 48 * q^36 - 272 * q^37 - 32 * q^38 - 384 * q^39 + 544 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 + 496 * q^44 - 240 * q^45 - 32 * q^46 - 800 * q^47 - 912 * q^48 - 32 * q^49 - 32 * q^50 + 160 * q^51 + 352 * q^52 - 32 * q^53 + 1376 * q^54 - 352 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 544 * q^59 + 1408 * q^60 - 16 * q^61 - 48 * q^62 - 288 * q^63 - 32 * q^64 + 544 * q^65 - 1696 * q^66 - 32 * q^67 + 1696 * q^68 - 32 * q^69 - 1728 * q^70 + 16 * q^71 - 96 * q^72 - 176 * q^73 - 752 * q^74 - 32 * q^75 + 2368 * q^76 - 32 * q^77 - 32 * q^78 + 1776 * q^79 + 1760 * q^80 - 160 * q^81 + 80 * q^82 + 384 * q^83 + 2272 * q^84 + 944 * q^85 + 1888 * q^86 + 1760 * q^87 + 2272 * q^88 + 640 * q^89 + 2240 * q^90 + 928 * q^91 - 624 * q^92 + 784 * q^93 + 224 * q^94 - 448 * q^95 - 192 * q^97 - 768 * q^98 - 512 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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