LMFDB - Embedded newform 207.4.o.a.149.30

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [207,4,Mod(5,207)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("207.5"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(207, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([55, 3])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	207.o (of order $66$, degree $20$, 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:	$12.2133953712$
Analytic rank:	$0$
Dimension:	$1400$
Relative dimension:	$70$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			149.30
Character	$\chi$	$=$	207.149
Dual form			207.4.o.a.182.30

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.553250 + 1.07316i) q^{2} +(1.90721 + 4.83348i) q^{3} +(3.79488 + 5.32916i) q^{4} +(3.34944 - 13.8066i) q^{5} +(-6.24225 - 0.627386i) q^{6} +(4.72700 + 1.63603i) q^{7} +(-17.3792 + 2.49875i) q^{8} +(-19.7251 + 18.4370i) q^{9} +(12.9636 + 11.2330i) q^{10} +(-0.374829 + 7.86864i) q^{11} +(-18.5207 + 28.5063i) q^{12} +(26.1038 + 75.4221i) q^{13} +(-4.37093 + 4.16767i) q^{14} +(73.1220 - 10.1427i) q^{15} +(-10.1846 + 29.4264i) q^{16} +(1.14356 + 2.50405i) q^{17} +(-8.87285 - 31.3683i) q^{18} +(29.7207 + 13.5730i) q^{19} +(86.2883 - 34.5446i) q^{20} +(1.10768 + 25.9681i) q^{21} +(-8.23690 - 4.75558i) q^{22} +(-85.6257 + 69.5359i) q^{23} +(-45.2236 - 79.2364i) q^{24} +(-68.2989 - 35.2105i) q^{25} +(-95.3817 - 13.7138i) q^{26} +(-126.735 - 60.1774i) q^{27} +(9.21971 + 31.3995i) q^{28} +(86.9471 + 61.9148i) q^{29} +(-29.5701 + 84.0828i) q^{30} +(14.9164 + 5.97163i) q^{31} +(-122.875 - 128.868i) q^{32} +(-38.7478 + 13.1954i) q^{33} +(-3.31991 - 0.158147i) q^{34} +(38.4208 - 59.7840i) q^{35} +(-173.108 - 35.1520i) q^{36} +(-4.93156 + 16.7953i) q^{37} +(-31.0089 + 24.3857i) q^{38} +(-314.766 + 270.019i) q^{39} +(-23.7114 + 248.317i) q^{40} +(-159.169 - 38.6140i) q^{41} +(-28.4807 - 13.1782i) q^{42} +(-2.57877 - 6.44146i) q^{43} +(-43.3556 + 27.8630i) q^{44} +(188.484 + 334.090i) q^{45} +(-27.2504 - 130.361i) q^{46} +(547.319 - 315.995i) q^{47} +(-161.656 + 6.89552i) q^{48} +(-249.948 - 196.562i) q^{49} +(75.5728 - 53.8151i) q^{50} +(-9.92227 + 10.3032i) q^{51} +(-302.876 + 425.329i) q^{52} +(228.695 + 263.928i) q^{53} +(134.696 - 102.713i) q^{54} +(107.384 + 31.5307i) q^{55} +(-86.2395 - 16.6213i) q^{56} +(-8.92100 + 169.541i) q^{57} +(-114.548 + 59.0535i) q^{58} +(332.169 - 114.965i) q^{59} +(331.541 + 351.189i) q^{60} +(278.194 + 353.752i) q^{61} +(-14.6610 + 12.7038i) q^{62} +(-123.404 + 54.8807i) q^{63} +(-32.7452 + 9.61485i) q^{64} +(1128.76 - 107.783i) q^{65} +(7.27645 - 48.8828i) q^{66} +(-696.728 + 33.1893i) q^{67} +(-9.00481 + 15.5968i) q^{68} +(-499.407 - 281.250i) q^{69} +(42.9012 + 74.3070i) q^{70} +(-322.328 - 501.552i) q^{71} +(296.737 - 369.708i) q^{72} +(243.951 - 534.178i) q^{73} +(-15.2956 - 14.5844i) q^{74} +(39.9287 - 397.275i) q^{75} +(40.4537 + 209.894i) q^{76} +(-14.6451 + 36.5818i) q^{77} +(-115.628 - 487.181i) q^{78} +(-36.4522 + 189.132i) q^{79} +(372.166 + 239.176i) q^{80} +(49.1562 - 727.341i) q^{81} +(129.499 - 149.450i) q^{82} +(15.1688 + 62.5267i) q^{83} +(-134.185 + 104.449i) q^{84} +(38.4027 - 7.40152i) q^{85} +(8.33940 + 0.796316i) q^{86} +(-133.437 + 538.342i) q^{87} +(-13.1475 - 137.687i) q^{88} +(194.868 - 1355.34i) q^{89} +(-462.809 + 17.4374i) q^{90} +399.227i q^{91} +(-695.507 - 192.433i) q^{92} +(-0.414956 + 83.4874i) q^{93} +(36.3072 + 762.183i) q^{94} +(286.944 - 364.879i) q^{95} +(388.531 - 839.694i) q^{96} +(910.726 - 955.142i) q^{97} +(349.225 - 159.486i) q^{98} +(-137.680 - 162.120i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1400 q - 27 q^{2} - 22 q^{3} - 281 q^{4} - 33 q^{5} + 29 q^{6} - 11 q^{7} - 22 q^{9} - 44 q^{10} - 33 q^{11} + 86 q^{12} - 9 q^{13} - 33 q^{14} + 726 q^{15} + 999 q^{16} + 51 q^{18} - 44 q^{19} - 33 q^{20}+ \cdots - 9262 q^{99}+O(q^{100}) $ 1400 * q - 27 * q^2 - 22 * q^3 - 281 * q^4 - 33 * q^5 + 29 * q^6 - 11 * q^7 - 22 * q^9 - 44 * q^10 - 33 * q^11 + 86 * q^12 - 9 * q^13 - 33 * q^14 + 726 * q^15 + 999 * q^16 + 51 * q^18 - 44 * q^19 - 33 * q^20 + 638 * q^21 + 252 * q^23 - 2564 * q^24 + 1397 * q^25 - 178 * q^27 - 44 * q^28 - 135 * q^29 - 1518 * q^30 - 45 * q^31 - 339 * q^32 + 1914 * q^33 - 11 * q^34 - 2137 * q^36 - 44 * q^37 - 33 * q^38 + 374 * q^39 + 979 * q^40 + 441 * q^41 - 22 * q^42 - 11 * q^43 + 516 * q^46 - 1992 * q^47 - 20 * q^48 - 4633 * q^49 - 6231 * q^50 - 22 * q^51 + 178 * q^52 + 2640 * q^54 + 256 * q^55 + 17391 * q^56 + 2090 * q^57 + 320 * q^58 - 2061 * q^59 + 418 * q^60 - 11 * q^61 - 2112 * q^63 + 8546 * q^64 - 12969 * q^65 - 5775 * q^66 - 11 * q^67 - 519 * q^69 - 1582 * q^70 - 4156 * q^72 - 36 * q^73 - 10065 * q^74 - 7876 * q^75 - 11 * q^76 + 1317 * q^77 - 10053 * q^78 - 11 * q^79 + 12442 * q^81 + 698 * q^82 + 14025 * q^83 + 16720 * q^84 + 241 * q^85 - 33 * q^86 + 11672 * q^87 - 1419 * q^88 - 37136 * q^90 + 3141 * q^92 + 1138 * q^93 + 396 * q^94 + 5883 * q^95 + 9218 * q^96 + 6325 * q^97 - 9262 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.553250	+	1.07316i	−0.195604	+	0.379418i	−0.966156	−	0.257959i	$-0.916950\pi$
$2$	−0.553250	+	1.07316i	−0.195604	+	0.379418i	0.770552	+	0.637377i	$0.219980\pi$
$3$	1.90721	+	4.83348i	0.367044	+	0.930204i
$3$	1.90721	+	4.83348i	0.367044	+	0.930204i
$4$	3.79488	+	5.32916i	0.474360	+	0.666145i
$5$	3.34944	−	13.8066i	0.299583	−	1.23490i	−0.600657	−	0.799507i	$-0.705094\pi$
$5$	3.34944	−	13.8066i	0.299583	−	1.23490i	0.900241	−	0.435393i	$-0.143390\pi$
$6$	−6.24225	−	0.627386i	−0.424731	−	0.0426882i
$7$	4.72700	+	1.63603i	0.255234	+	0.0883373i	0.451689	−	0.892176i	$-0.350822\pi$
$7$	4.72700	+	1.63603i	0.255234	+	0.0883373i	−0.196455	+	0.980513i	$0.562943\pi$
$8$	−17.3792	+	2.49875i	−0.768060	+	0.110430i
$9$	−19.7251	+	18.4370i	−0.730558	+	0.682851i
$10$	12.9636	+	11.2330i	0.409943	+	0.355218i
$11$	−0.374829	+	7.86864i	−0.0102741	+	0.215680i	0.987892	+	0.155144i	$0.0495841\pi$
$11$	−0.374829	+	7.86864i	−0.0102741	+	0.215680i	−0.998166	+	0.0605363i	$0.980719\pi$
$12$	−18.5207	+	28.5063i	−0.445540	+	0.685755i
$13$	26.1038	+	75.4221i	0.556916	+	1.60910i	0.774163	+	0.632986i	$0.218171\pi$
$13$	26.1038	+	75.4221i	0.556916	+	1.60910i	−0.217247	+	0.976117i	$0.569708\pi$
$14$	−4.37093	+	4.16767i	−0.0834414	+	0.0795612i
$15$	73.1220	−	10.1427i	1.25867	−	0.174588i
$16$	−10.1846	+	29.4264i	−0.159134	+	0.459788i
$17$	1.14356	+	2.50405i	0.0163150	+	0.0357248i	0.917614	−	0.397473i	$-0.130113\pi$
$17$	1.14356	+	2.50405i	0.0163150	+	0.0357248i	−0.901299	+	0.433197i	$0.857385\pi$
$18$	−8.87285	−	31.3683i	−0.116186	−	0.410755i
$19$	29.7207	+	13.5730i	0.358862	+	0.163887i	0.586684	−	0.809816i	$-0.300433\pi$
$19$	29.7207	+	13.5730i	0.358862	+	0.163887i	−0.227822	+	0.973703i	$0.573160\pi$
$20$	86.2883	−	34.5446i	0.964732	−	0.386221i
$21$	1.10768	+	25.9681i	0.0115103	+	0.269843i
$22$	−8.23690	−	4.75558i	−0.0798233	−	0.0460860i
$23$	−85.6257	+	69.5359i	−0.776269	+	0.630401i
$23$	−85.6257	+	69.5359i	−0.776269	+	0.630401i
$24$	−45.2236	−	79.2364i	−0.384634	−	0.673919i
$25$	−68.2989	−	35.2105i	−0.546391	−	0.281684i
$26$	−95.3817	−	13.7138i	−0.719457	−	0.103442i
$27$	−126.735	−	60.1774i	−0.903337	−	0.428932i
$28$	9.21971	+	31.3995i	0.0622272	+	0.211926i
$29$	86.9471	+	61.9148i	0.556747	+	0.396458i	0.823508	−	0.567305i	$-0.192014\pi$
$29$	86.9471	+	61.9148i	0.556747	+	0.396458i	−0.266761	+	0.963763i	$0.585953\pi$
$30$	−29.5701	+	84.0828i	−0.179958	+	0.511711i
$31$	14.9164	+	5.97163i	0.0864215	+	0.0345980i	0.414470	−	0.910063i	$-0.363967\pi$
$31$	14.9164	+	5.97163i	0.0864215	+	0.0345980i	−0.328049	+	0.944661i	$0.606391\pi$
$32$	−122.875	−	128.868i	−0.678797	−	0.711902i
$33$	−38.7478	+	13.1954i	−0.204398	+	0.0696071i
$34$	−3.31991	−	0.158147i	−0.0167459	−	0.000797706i
$35$	38.4208	−	59.7840i	0.185552	−	0.288724i
$36$	−173.108	−	35.1520i	−0.801425	−	0.162741i
$37$	−4.93156	+	16.7953i	−0.0219120	+	0.0746253i	−0.969723	−	0.244207i	$-0.921472\pi$
$37$	−4.93156	+	16.7953i	−0.0219120	+	0.0746253i	0.947811	+	0.318832i	$0.103291\pi$
$38$	−31.0089	+	24.3857i	−0.132376	+	0.104102i
$39$	−314.766	+	270.019i	−1.29238	+	1.10866i
$40$	−23.7114	+	248.317i	−0.0937276	+	0.981560i
$41$	−159.169	−	38.6140i	−0.606293	−	0.147085i	−0.0791515	−	0.996863i	$-0.525221\pi$
$41$	−159.169	−	38.6140i	−0.606293	−	0.147085i	−0.527142	+	0.849777i	$0.676736\pi$
$42$	−28.4807	−	13.1782i	−0.104635	−	0.0484151i
$43$	−2.57877	−	6.44146i	−0.00914556	−	0.0228445i	0.923725	−	0.383057i	$-0.125129\pi$
$43$	−2.57877	−	6.44146i	−0.00914556	−	0.0228445i	−0.932870	+	0.360212i	$0.882704\pi$
$44$	−43.3556	+	27.8630i	−0.148548	+	0.0954660i
$45$	188.484	+	334.090i	0.624389	+	1.10674i
$46$	−27.2504	−	130.361i	−0.0873445	−	0.417839i
$47$	547.319	−	315.995i	1.69861	−	0.980692i	0.751526	−	0.659703i	$-0.229318\pi$
$47$	547.319	−	315.995i	1.69861	−	0.980692i	0.947083	−	0.320989i	$-0.104015\pi$
$48$	−161.656	+	6.89552i	−0.486105	+	0.0207351i
$49$	−249.948	−	196.562i	−0.728712	−	0.573066i
$50$	75.5728	−	53.8151i	0.213752	−	0.152212i
$51$	−9.92227	+	10.3032i	−0.0272430	+	0.0282888i
$52$	−302.876	+	425.329i	−0.807717	+	1.13428i
$53$	228.695	+	263.928i	0.592711	+	0.684025i	0.970288	−	0.241954i	$-0.0777882\pi$
$53$	228.695	+	263.928i	0.592711	+	0.684025i	−0.377577	+	0.925978i	$0.623243\pi$
$54$	134.696	−	102.713i	0.339440	−	0.258842i
$55$	107.384	+	31.5307i	0.263265	+	0.0773017i
$56$	−86.2395	−	16.6213i	−0.205790	−	0.0396628i
$57$	−8.92100	+	169.541i	−0.0207301	+	0.393969i
$58$	−114.548	+	59.0535i	−0.259325	+	0.133691i
$59$	332.169	−	114.965i	0.732960	−	0.253680i	0.0650087	−	0.997885i	$-0.479292\pi$
$59$	332.169	−	114.965i	0.732960	−	0.253680i	0.667952	+	0.744205i	$0.267171\pi$
$60$	331.541	+	351.189i	0.713363	+	0.755638i
$61$	278.194	+	353.752i	0.583920	+	0.742514i	0.984815	−	0.173610i	$-0.0555432\pi$
$61$	278.194	+	353.752i	0.583920	+	0.742514i	−0.400895	+	0.916124i	$0.631301\pi$
$62$	−14.6610	+	12.7038i	−0.0300314	+	0.0260224i
$63$	−123.404	+	54.8807i	−0.246784	+	0.109751i
$64$	−32.7452	+	9.61485i	−0.0639554	+	0.0187790i
$65$	1128.76	−	107.783i	2.15392	−	0.205675i
$66$	7.27645	−	48.8828i	0.0135707	−	0.0911675i
$67$	−696.728	+	33.1893i	−1.27043	+	0.0605181i	−0.671937	−	0.740609i	$-0.734537\pi$
$67$	−696.728	+	33.1893i	−1.27043	+	0.0605181i	−0.598495	+	0.801127i	$0.704234\pi$
$68$	−9.00481	+	15.5968i	−0.0160587	+	0.0278145i
$69$	−499.407	−	281.250i	−0.871326	−	0.490704i
$70$	42.9012	+	74.3070i	0.0732525	+	0.126877i
$71$	−322.328	−	501.552i	−0.538779	−	0.838356i	0.459992	−	0.887923i	$-0.347852\pi$
$71$	−322.328	−	501.552i	−0.538779	−	0.838356i	−0.998771	+	0.0495669i	$0.984216\pi$
$72$	296.737	−	369.708i	0.485705	−	0.605146i
$73$	243.951	−	534.178i	0.391127	−	0.856449i	−0.606966	−	0.794728i	$-0.707614\pi$
$73$	243.951	−	534.178i	0.391127	−	0.856449i	0.998093	−	0.0617217i	$-0.0196591\pi$
$74$	−15.2956	−	14.5844i	−0.0240281	−	0.0229108i
$75$	39.9287	−	397.275i	0.0614743	−	0.611645i
$76$	40.4537	+	209.894i	0.0610574	+	0.316796i
$77$	−14.6451	+	36.5818i	−0.0216749	+	0.0541413i
$78$	−115.628	−	487.181i	−0.167850	−	0.707210i
$79$	−36.4522	+	189.132i	−0.0519138	+	0.269354i	−0.998606	−	0.0527856i	$-0.983190\pi$
$79$	−36.4522	+	189.132i	−0.0519138	+	0.269354i	0.946692	+	0.322140i	$0.104402\pi$
$80$	372.166	+	239.176i	0.520118	+	0.334259i
$81$	49.1562	−	727.341i	0.0674296	−	0.997724i
$82$	129.499	−	149.450i	0.174400	−	0.201268i
$83$	15.1688	+	62.5267i	0.0200602	+	0.0826891i	0.980962	−	0.194201i	$-0.0622114\pi$
$83$	15.1688	+	62.5267i	0.0200602	+	0.0826891i	−0.960902	+	0.276890i	$0.910696\pi$
$84$	−134.185	+	104.449i	−0.174295	+	0.135670i
$85$	38.4027	−	7.40152i	0.0490042	−	0.00944479i
$86$	8.33940	+	0.796316i	0.0104565	+	0.000998477i
$87$	−133.437	+	538.342i	−0.164436	+	0.663406i
$88$	−13.1475	−	137.687i	−0.0159265	−	0.166790i
$89$	194.868	−	1355.34i	0.232090	−	1.61422i	−0.456947	−	0.889494i	$-0.651057\pi$
$89$	194.868	−	1355.34i	0.232090	−	1.61422i	0.689037	−	0.724726i	$-0.258034\pi$
$90$	−462.809	+	17.4374i	−0.542048	+	0.0204229i
$91$			399.227i			0.459894i
$92$	−695.507	−	192.433i	−0.788169	−	0.218071i
$93$	−0.414956	+	83.4874i	−0.000462676	+	0.0930886i
$94$	36.3072	+	762.183i	0.0398383	+	0.836310i
$95$	286.944	−	364.879i	0.309893	−	0.394061i
$96$	388.531	−	839.694i	0.413065	−	0.892718i
$97$	910.726	−	955.142i	0.953301	−	0.999794i	−0.0466984	−	0.998909i	$-0.514870\pi$
$97$	910.726	−	955.142i	0.953301	−	0.999794i	1.00000		0.000884502i	$-0.000281546\pi$
$98$	349.225	−	159.486i	0.359970	−	0.164393i
$99$	−137.680	−	162.120i	−0.139772	−	0.164583i
$100$	−71.5434	−	497.595i	−0.0715434	−	0.497595i
$101$	791.184	−	191.939i	0.779463	−	0.189096i	0.173762	−	0.984788i	$-0.444408\pi$
$101$	791.184	−	191.939i	0.779463	−	0.189096i	0.605701	+	0.795692i	$0.292893\pi$
$102$	−5.56739	−	16.3484i	−0.00540445	−	0.0158699i
$103$	745.757	+	1446.57i	0.713414	+	1.38383i	0.914634	+	0.404284i	$0.132479\pi$
$103$	745.757	+	1446.57i	0.713414	+	1.38383i	−0.201220	+	0.979546i	$0.564490\pi$
$104$	−642.126	−	1245.55i	−0.605438	−	1.17439i
$105$	362.241	+	71.6854i	0.336677	+	0.0666265i
$106$	−409.762	+	99.4071i	−0.375468	+	0.0910874i
$107$	34.7485	+	241.681i	0.0313950	+	0.218357i	0.999479	−	0.0322681i	$-0.0102730\pi$
$107$	34.7485	+	241.681i	0.0313950	+	0.218357i	−0.968084	+	0.250625i	$0.919364\pi$
$108$	−160.247	−	903.755i	−0.142776	−	0.805221i
$109$	1896.08	−	865.912i	1.66616	−	0.760911i	0.666279	−	0.745703i	$-0.267886\pi$
$109$	1896.08	−	865.912i	1.66616	−	0.760911i	0.999884	−	0.0152085i	$-0.00484121\pi$
$110$	−93.2474	+	97.7950i	−0.0808253	+	0.0847672i
$111$	−90.5855	+	8.19574i	−0.0774594	+	0.00700816i
$112$	−96.2850	+	122.436i	−0.0812328	+	0.103296i
$113$	99.3431	+	2085.47i	0.0827028	+	1.73615i	0.535503	+	0.844533i	$0.320122\pi$
$113$	99.3431	+	2085.47i	0.0827028	+	1.73615i	−0.452800	+	0.891612i	$0.649575\pi$
$114$	−177.008	−	103.372i	−0.145424	−	0.0849271i
$115$	673.255	+	1415.11i	0.545925	+	1.14747i
$116$			698.314i			0.558938i
$117$	−1905.46	−	1006.43i	−1.50564	−	0.795252i
$118$	−60.3974	+	420.073i	−0.0471189	+	0.327719i
$119$	1.30891	+	13.7075i	0.00100830	+	0.0105594i
$120$	−1245.46	+	358.986i	−0.947453	+	0.273090i
$121$	1263.20	+	120.621i	0.949060	+	0.0906242i
$122$	−533.543	+	102.832i	−0.395940	+	0.0763112i
$123$	−116.930	−	842.985i	−0.0857169	−	0.617963i
$124$	24.7822	+	102.154i	0.0179476	+	0.0739811i
$125$	448.056	−	517.084i	0.320603	−	0.369995i
$126$	9.37760	−	162.794i	0.00663034	−	0.115102i
$127$	379.357	+	243.798i	0.265059	+	0.170343i	0.666419	−	0.745577i	$-0.267826\pi$
$127$	379.357	+	243.798i	0.265059	+	0.170343i	−0.401360	+	0.915920i	$0.631462\pi$
$128$	277.382	−	1439.20i	0.191542	−	0.993814i
$129$	26.2164	−	24.7497i	0.0178932	−	0.0168922i
$130$	−508.817	+	1270.96i	−0.343278	+	0.857468i
$131$	231.293	+	1200.06i	0.154261	+	0.800381i	0.973808	+	0.227370i	$0.0730127\pi$
$131$	231.293	+	1200.06i	0.154261	+	0.800381i	−0.819548	+	0.573011i	$0.805775\pi$
$132$	−217.364	−	156.418i	−0.143326	−	0.103140i
$133$	118.284	+	112.783i	0.0771165	+	0.0735305i
$134$	349.848	−	766.060i	0.225539	−	0.493862i
$135$	−1255.34	+	1548.21i	−0.800312	+	0.987030i
$136$	−26.1312	−	40.6610i	−0.0164760	−	0.0256371i
$137$	−486.274	−	842.252i	−0.303250	−	0.525244i	0.673620	−	0.739078i	$-0.264738\pi$
$137$	−486.274	−	842.252i	−0.303250	−	0.525244i	−0.976870	+	0.213833i	$0.931405\pi$
$138$	578.123	−	380.340i	0.356616	−	0.234613i
$139$	−376.602	+	652.293i	−0.229805	+	0.398034i	−0.957750	−	0.287601i	$-0.907142\pi$
$139$	−376.602	+	652.293i	−0.229805	+	0.398034i	0.727945	+	0.685635i	$0.240476\pi$
$140$	464.400	−	22.1221i	0.280350	−	0.0133547i
$141$	2571.21	+	2042.78i	1.53571	+	1.22010i
$142$	716.572	−	68.4243i	0.423474	−	0.0404369i
$143$	−603.254	+	177.131i	−0.352773	+	0.103584i
$144$	−341.642	−	768.211i	−0.197710	−	0.444566i
$145$	1146.06	−	993.063i	0.656378	−	0.568755i
$146$	438.291	+	557.332i	0.248446	+	0.315925i
$147$	473.371	−	1583.01i	0.265599	−	0.888191i
$148$	−108.220	+	37.4552i	−0.0601055	+	0.0208027i
$149$	157.155	−	81.0188i	0.0864067	−	0.0445458i	−0.414482	−	0.910058i	$-0.636037\pi$
$149$	157.155	−	81.0188i	0.0864067	−	0.0445458i	0.500888	+	0.865512i	$0.333007\pi$
$150$	404.248	+	262.642i	0.220045	+	0.142964i
$151$	−2989.12	−	576.105i	−1.61093	−	0.310482i	−0.697225	−	0.716852i	$-0.745582\pi$
$151$	−2989.12	−	576.105i	−1.61093	−	0.310482i	−0.913709	+	0.406370i	$0.866794\pi$
$152$	−550.437	−	161.623i	−0.293726	−	0.0862457i
$153$	−68.7240	−	28.3088i	−0.0363137	−	0.0149583i
$154$	−31.1555	−	35.9554i	−0.0163025	−	0.0188141i
$155$	132.410	−	185.943i	0.0686154	−	0.0963569i
$156$	−2633.47	−	652.749i	−1.35158	−	0.335011i
$157$	1742.66	−	1240.94i	0.885856	−	0.630815i	−0.0438823	−	0.999037i	$-0.513973\pi$
$157$	1742.66	−	1240.94i	0.885856	−	0.630815i	0.929738	+	0.368222i	$0.120033\pi$
$158$	−182.801	−	143.756i	−0.0920433	−	0.0723837i
$159$	−839.521	+	1608.76i	−0.418731	+	0.802409i
$160$	−2190.79	+	1264.85i	−1.08248	+	0.624972i
$161$	−518.515	+	188.610i	−0.253818	+	0.0923262i
$162$	753.355	+	455.154i	0.365365	+	0.220742i
$163$	−1260.95	+	810.365i	−0.605923	+	0.389403i	−0.807326	−	0.590106i	$-0.799086\pi$
$163$	−1260.95	+	810.365i	−0.605923	+	0.389403i	0.201404	+	0.979508i	$0.435450\pi$
$164$	−398.247	−	994.772i	−0.189621	−	0.473650i
$165$	52.4007	+	579.172i	0.0247236	+	0.273264i
$166$	−75.4931	−	18.3144i	−0.0352976	−	0.00856310i
$167$	55.3695	−	579.856i	0.0256564	−	0.268686i	−0.973537	−	0.228530i	$-0.926608\pi$
$167$	55.3695	−	579.856i	0.0256564	−	0.268686i	0.999193	−	0.0401567i	$-0.0127857\pi$
$168$	−84.1385	−	448.537i	−0.0386395	−	0.205985i
$169$	−3280.13	+	2579.52i	−1.49300	+	1.17411i
$170$	−13.3033	+	45.3070i	−0.00600188	+	0.0204405i
$171$	−836.486	+	280.231i	−0.374080	+	0.125321i
$172$	24.5415	−	38.1872i	0.0108795	−	0.0169288i
$173$	−2852.35	−	135.874i	−1.25353	−	0.0597129i	−0.589715	−	0.807612i	$-0.700760\pi$
$173$	−2852.35	−	135.874i	−1.25353	−	0.0597129i	−0.663813	+	0.747899i	$0.731063\pi$
$174$	−503.901	−	441.037i	−0.219544	−	0.192155i
$175$	−265.243	−	278.179i	−0.114574	−	0.120162i
$176$	−227.728	−	91.1686i	−0.0975322	−	0.0390460i
$177$	1189.20	+	1386.27i	0.505003	+	0.588691i
$178$	1346.68	+	958.966i	0.567067	+	0.403806i
$179$	−76.3266	−	259.944i	−0.0318710	−	0.108543i	0.942021	−	0.335553i	$-0.108923\pi$
$179$	−76.3266	−	259.944i	−0.0318710	−	0.108543i	−0.973892	+	0.227010i	$0.927105\pi$
$180$	−1065.14	+	2272.29i	−0.441062	+	0.940925i
$181$	−1760.10	−	253.064i	−0.722801	−	0.103923i	−0.228911	−	0.973447i	$-0.573516\pi$
$181$	−1760.10	−	253.064i	−0.722801	−	0.103923i	−0.493890	+	0.869524i	$0.664425\pi$
$182$	−428.433	−	220.872i	−0.174492	−	0.0899569i
$183$	−1179.28	+	2019.33i	−0.476365	+	0.815699i
$184$	1314.35	−	1422.44i	0.526606	−	0.569910i
$185$	215.369	+	124.343i	0.0855903	+	0.0494156i
$186$	−89.3654	−	46.6347i	−0.0352290	−	0.0183840i
$187$	−20.1321	+	8.05968i	−0.00787276	+	0.00315178i
$188$	3760.99	+	1717.59i	1.45903	+	0.666319i
$189$	−500.622	−	491.800i	−0.192672	−	0.189276i
$190$	232.820	+	509.805i	0.0888977	+	0.194659i
$191$	−477.965	+	1380.99i	−0.181070	+	0.523167i	−0.998610	−	0.0527045i	$-0.983216\pi$
$191$	−477.965	+	1380.99i	−0.181070	+	0.523167i	0.817540	+	0.575871i	$0.195337\pi$
$192$	−108.925	−	139.936i	−0.0409427	−	0.0525988i
$193$	2673.11	−	2548.80i	0.996966	−	0.950605i	−0.00181324	−	0.999998i	$-0.500577\pi$
$193$	2673.11	−	2548.80i	0.996966	−	0.950605i	0.998779	+	0.0493930i	$0.0157287\pi$
$194$	521.157	+	1505.78i	0.192871	+	0.557263i
$195$	2673.75	+	5250.25i	0.981903	+	1.92810i
$196$	98.9845	−	2077.94i	0.0360731	−	0.757267i
$197$	252.471	+	218.767i	0.0913086	+	0.0791193i	0.699319	−	0.714810i	$-0.253487\pi$
$197$	252.471	+	218.767i	0.0913086	+	0.0791193i	−0.608010	+	0.793929i	$0.708032\pi$
$198$	250.152	−	58.0594i	0.0897854	−	0.0208389i
$199$	1998.88	−	287.395i	0.712043	−	0.102376i	0.223231	−	0.974765i	$-0.428339\pi$
$199$	1998.88	−	287.395i	0.712043	−	0.102376i	0.488812	+	0.872389i	$0.337430\pi$
$200$	1274.96	+	441.269i	0.450767	+	0.156012i
$201$	−1489.23	−	3304.32i	−0.522598	−	1.15955i
$202$	−231.742	+	955.254i	−0.0807194	+	0.332730i
$203$	309.704	+	434.919i	0.107079	+	0.150371i
$204$	−92.5609	−	13.7781i	−0.0317675	−	0.00472874i
$205$	−1066.25	+	2068.25i	−0.363271	+	0.704647i
$206$	−1964.98			−0.664596
$207$	406.942	−	2950.28i	0.136640	−	0.990621i
$208$	−2485.26			−0.828470
$209$	−117.941	+	228.773i	−0.0390342	+	0.0757157i
$210$	−277.340	+	349.082i	−0.0911346	+	0.114709i
$211$	−414.546	−	582.148i	−0.135254	−	0.189937i	0.741394	−	0.671070i	$-0.234165\pi$
$211$	−414.546	−	582.148i	−0.135254	−	0.189937i	−0.876648	+	0.481133i	$0.840226\pi$
$212$	−538.645	+	2220.33i	−0.174501	+	0.719305i
$213$	1809.49	−	2514.53i	0.582087	−	0.808887i
$214$	−278.586	−	96.4195i	−0.0889894	−	0.0307995i
$215$	−97.5721	+	14.0288i	−0.0309505	+	0.00445001i
$216$	2352.92	+	729.158i	0.741184	+	0.229689i
$217$	60.7401	+	52.6316i	0.0190014	+	0.0164648i
$218$	−119.750	+	2513.86i	−0.0372041	+	0.781009i
$219$	3047.21	+	160.340i	0.940233	+	0.0494738i
$220$	239.476	+	691.919i	0.0733884	+	0.212042i
$221$	−159.010	+	151.615i	−0.0483988	+	0.0461482i
$222$	41.3212	−	101.747i	0.0124923	−	0.0307603i
$223$	442.707	−	1279.12i	0.132941	−	0.384108i	−0.858809	−	0.512296i	$-0.828795\pi$
$223$	442.707	−	1279.12i	0.132941	−	0.384108i	0.991750	+	0.128188i	$0.0409162\pi$
$224$	−370.000	−	810.186i	−0.110364	−	0.241664i
$225$	1996.37	−	564.695i	0.591518	−	0.167317i
$226$	−2293.00	−	1047.18i	−0.674902	−	0.308217i
$227$	3429.77	−	1373.07i	1.00283	−	0.401471i	0.188622	−	0.982050i	$-0.439598\pi$
$227$	3429.77	−	1373.07i	1.00283	−	0.401471i	0.814204	+	0.580579i	$0.197174\pi$
$228$	−937.364	+	595.845i	−0.272274	+	0.173074i
$229$	−3133.11	−	1808.90i	−0.904113	−	0.521990i	−0.0255809	−	0.999673i	$-0.508144\pi$
$229$	−3133.11	−	1808.90i	−0.904113	−	0.521990i	−0.878532	+	0.477683i	$0.841477\pi$
$230$	−1891.11	−	60.4004i	−0.542157	−	0.0173160i
$231$	−204.749	−	1.01766i	−0.0583181	−	0.000289857i
$232$	−1665.78	−	858.770i	−0.471396	−	0.243022i
$233$	−2055.42	−	295.525i	−0.577920	−	0.0830924i	−0.152844	−	0.988250i	$-0.548843\pi$
$233$	−2055.42	−	295.525i	−0.577920	−	0.0830924i	−0.425075	+	0.905158i	$0.639752\pi$
$234$	2134.25	−	1488.04i	0.596241	−	0.415711i
$235$	−2529.60	−	8615.01i	−0.702182	−	2.39141i
$236$	1873.20	+	1333.90i	0.516674	+	0.367922i
$237$	−983.687	+	184.524i	−0.269609	+	0.0505744i
$238$	−15.4345	−	6.17904i	−0.00420365	−	0.00168289i
$239$	−2245.97	−	2355.51i	−0.607865	−	0.637511i	0.345826	−	0.938299i	$-0.387599\pi$
$239$	−2245.97	−	2355.51i	−0.607865	−	0.637511i	−0.953691	+	0.300788i	$0.902750\pi$
$240$	−446.254	+	2255.02i	−0.120023	+	0.606503i
$241$	5302.72	+	252.600i	1.41734	+	0.0675161i	0.742201	−	0.670177i	$-0.233782\pi$
$241$	5302.72	+	252.600i	1.41734	+	0.0675161i	0.675136	+	0.737693i	$0.264085\pi$
$242$	−828.310	+	1288.88i	−0.220024	+	0.342364i
$243$	3609.34	−	1149.60i	0.952836	−	0.303485i
$244$	−829.491	+	2824.99i	−0.217634	+	0.741194i
$245$	−3551.03	+	2792.56i	−0.925988	+	0.728205i
$246$	969.346	+	340.898i	0.251233	+	0.0883532i
$247$	−247.879	+	2595.90i	−0.0638548	+	0.668718i
$248$	−274.157	−	66.5098i	−0.0701976	−	0.0170297i
$249$	−273.291	+	192.570i	−0.0695548	+	0.0490106i
$250$	307.025	+	766.911i	0.0776718	+	0.194015i
$251$	−1767.00	+	1135.58i	−0.444352	+	0.285568i	−0.743621	−	0.668601i	$-0.766893\pi$
$251$	−1767.00	+	1135.58i	−0.444352	+	0.285568i	0.299269	+	0.954169i	$0.403257\pi$
$252$	−760.770	−	449.373i	−0.190175	−	0.112333i
$253$	−515.057	−	699.822i	−0.127990	−	0.173903i
$254$	−471.513	+	272.228i	−0.116478	+	0.0672485i
$255$	109.017	+	171.503i	0.0267723	+	0.0421173i
$256$	1176.41	+	925.141i	0.287210	+	0.225864i
$257$	−930.017	+	662.262i	−0.225731	+	0.160742i	−0.687327	−	0.726348i	$-0.741216\pi$
$257$	−930.017	+	662.262i	−0.225731	+	0.160742i	0.461596	+	0.887090i	$0.347277\pi$
$258$	12.0561	+	41.8271i	0.00290921	+	0.0100932i
$259$	−50.7892	+	71.3234i	−0.0121849	+	0.0171113i
$260$	4857.88	+	5606.30i	1.15874	+	1.33726i
$261$	−2856.56	+	381.769i	−0.677458	+	0.0905398i
$262$	−1415.82	−	415.722i	−0.333853	−	0.0980281i
$263$	−877.786	−	169.179i	−0.205805	−	0.0396656i	0.0853068	−	0.996355i	$-0.472813\pi$
$263$	−877.786	−	169.179i	−0.205805	−	0.0396656i	−0.291112	+	0.956689i	$0.594025\pi$
$264$	640.434	−	326.148i	0.149303	−	0.0760341i
$265$	4409.95	−	2273.49i	1.02227	−	0.527016i
$266$	−186.475	+	64.5395i	−0.0429830	+	0.0148766i
$267$	6922.66	−	1643.03i	1.58674	−	0.376599i
$268$	−2820.87	−	3587.03i	−0.642955	−	0.817584i
$269$	−1481.12	+	1283.40i	−0.335708	+	0.290893i	−0.806358	−	0.591427i	$-0.798565\pi$
$269$	−1481.12	+	1283.40i	−0.335708	+	0.290893i	0.470650	+	0.882320i	$0.344019\pi$
$270$	−966.959	−	2203.72i	−0.217953	−	0.496719i
$271$	4618.49	−	1356.11i	1.03525	−	0.303978i	0.280408	−	0.959881i	$-0.409530\pi$
$271$	4618.49	−	1356.11i	1.03525	−	0.303978i	0.754845	+	0.655903i	$0.227712\pi$
$272$	−85.3320	+	8.14821i	−0.0190221	+	0.00181639i
$273$	−1929.66	+	761.411i	−0.427795	+	0.168801i
$274$	1172.90	−	55.8721i	0.258604	−	0.0123188i
$275$	302.659	−	524.221i	0.0663674	−	0.114952i
$276$	−396.359	−	3728.73i	−0.0864422	−	0.813200i
$277$	−3115.77	−	5396.67i	−0.675842	−	1.17059i	−0.976222	−	0.216774i	$-0.930447\pi$
$277$	−3115.77	−	5396.67i	−0.675842	−	1.17059i	0.300380	−	0.953820i	$-0.402887\pi$
$278$	−491.657	−	765.034i	−0.106071	−	0.165049i
$279$	−404.326	+	157.223i	−0.0867612	+	0.0337372i
$280$	−518.338	+	1135.00i	−0.110631	+	0.242248i
$281$	−3197.83	−	3049.12i	−0.678884	−	0.647314i	0.270029	−	0.962852i	$-0.412967\pi$
$281$	−3197.83	−	3049.12i	−0.678884	−	0.647314i	−0.948913	+	0.315538i	$0.897815\pi$
$282$	−3614.75	+	1629.14i	−0.763316	+	0.344020i
$283$	1742.37	+	9040.27i	0.365983	+	1.89890i	0.433452	+	0.901176i	$0.357295\pi$
$283$	1742.37	+	9040.27i	0.365983	+	1.89890i	−0.0674699	+	0.997721i	$0.521493\pi$
$284$	1449.66	−	3621.07i	0.302892	−	0.756587i
$285$	2310.90	+	691.036i	0.480302	+	0.143626i
$286$	143.661	−	745.383i	0.0297023	−	0.154110i
$287$	−689.218	−	442.933i	−0.141753	−	0.0910994i
$288$	4799.66	+	276.479i	0.982023	+	0.0565684i
$289$	3212.37	−	3707.27i	0.653851	−	0.754584i
$290$	431.656	+	1779.31i	0.0874059	+	0.360292i
$291$	6353.61	+	2580.32i	1.27991	+	0.519796i
$292$	3772.48	−	727.087i	0.756055	−	0.145718i
$293$	−822.913	−	78.5787i	−0.164079	−	0.0156676i	0.0126933	−	0.999919i	$-0.495959\pi$
$293$	−822.913	−	78.5787i	−0.164079	−	0.0156676i	−0.176772	+	0.984252i	$0.556566\pi$
$294$	1436.92	+	1383.80i	0.285044	+	0.274506i
$295$	−474.691	−	4971.18i	−0.0936866	−	0.981131i
$296$	43.7392	−	304.213i	0.00858881	−	0.0597365i
$297$	521.018	−	974.673i	0.101793	−	0.190425i
$298$			213.475i			0.0414976i
$299$	−7479.70	−	4642.92i	−1.44670	−	0.898017i
$300$	2268.67	−	1294.82i	0.436605	−	0.249189i
$301$	−1.65143	−	34.6677i	−0.000316235	−	0.00663859i
$302$	2271.98	−	2889.06i	0.432907	−	0.550486i
$303$	2436.69	+	3458.10i	0.461994	+	0.655653i
$304$	−702.096	+	736.337i	−0.132460	+	0.138921i
$305$	5815.91	−	2656.04i	1.09186	−	0.498637i
$306$	68.4013	−	58.0897i	0.0127786	−	0.0108522i
$307$	137.662	+	957.459i	0.0255921	+	0.177997i	0.998608	−	0.0527399i	$-0.0167954\pi$
$307$	137.662	+	957.459i	0.0255921	+	0.177997i	−0.973016	+	0.230737i	$0.925886\pi$
$308$	−250.527	+	60.7771i	−0.0463477	+	0.0112438i
$309$	−5569.63	+	6363.52i	−1.02539	+	1.17155i
$310$	126.290	+	244.969i	0.0231381	+	0.0448817i
$311$	−771.552	−	1496.60i	−0.140677	−	0.272876i	0.807963	−	0.589234i	$-0.200570\pi$
$311$	−771.552	−	1496.60i	−0.140677	−	0.272876i	−0.948640	+	0.316358i	$0.897540\pi$
$312$	4795.67	−	5479.23i	0.870196	−	0.994232i
$313$	−7188.05	+	1743.80i	−1.29806	+	0.314906i	−0.824503	−	0.565858i	$-0.808545\pi$
$313$	−7188.05	+	1743.80i	−1.29806	+	0.314906i	−0.473556	+	0.880764i	$0.657030\pi$
$314$	367.598	+	2556.70i	0.0660660	+	0.459499i
$315$	344.382	+	1887.61i	0.0615991	+	0.337633i
$316$	−1146.24	+	523.472i	−0.204055	+	0.0931887i
$317$	1375.84	−	1442.94i	0.243770	−	0.255659i	−0.590471	−	0.807059i	$-0.701058\pi$
$317$	1375.84	−	1442.94i	0.243770	−	0.255659i	0.834241	+	0.551400i	$0.185906\pi$
$318$	−1261.99	−	1790.98i	−0.222543	−	0.315828i
$319$	−519.775	+	660.948i	−0.0912282	+	0.116006i
$320$	23.0702	+	484.304i	0.00403020	+	0.0846044i
$321$	−1101.89	+	628.893i	−0.191593	+	0.109350i
$322$	84.4613	−	660.796i	0.0146175	−	0.114363i
$323$			89.9436i			0.0154941i
$324$	4062.66	−	2498.21i	0.696615	−	0.428362i
$325$	872.788	−	6070.38i	0.148965	−	1.03607i
$326$	−172.026	−	1801.53i	−0.0292258	−	0.306067i
$327$	7801.61	+	7513.20i	1.31936	+	1.27058i
$328$	2862.72	+	273.356i	0.481912	+	0.0460170i
$329$	3104.15	−	598.276i	0.520174	−	0.100255i
$330$	−650.533	−	264.193i	−0.108517	−	0.0440708i
$331$	−1041.36	−	4292.55i	−0.172926	−	0.712810i	−0.990561	−	0.137073i	$-0.956231\pi$
$331$	−1041.36	−	4292.55i	−0.172926	−	0.712810i	0.817635	−	0.575737i	$-0.195285\pi$
$332$	−275.651	+	318.118i	−0.0455672	+	0.0525874i
$333$	−212.380	−	422.212i	−0.0349500	−	0.0694807i
$334$	591.643	+	380.226i	0.0969259	+	0.0622905i
$335$	−1875.42	+	9730.61i	−0.305866	+	1.58699i
$336$	−775.430	−	231.879i	−0.125902	−	0.0376489i
$337$	1821.82	−	4550.68i	0.294483	−	0.735582i	−0.705165	−	0.709043i	$-0.749127\pi$
$337$	1821.82	−	4550.68i	0.294483	−	0.735582i	0.999648	−	0.0265390i	$-0.00844862\pi$
$338$	−953.496	−	4947.21i	−0.153442	−	0.796132i
$339$	−9890.61	+	4457.61i	−1.58461	+	0.714172i
$340$	185.178	+	176.566i	0.0295372	+	0.0281637i
$341$	−52.5797	+	115.133i	−0.00835000	+	0.0182840i
$342$	162.055	−	1052.72i	0.0256225	−	0.166446i
$343$	−1787.51	−	2781.43i	−0.281390	−	0.437851i
$344$	60.9127	+	105.504i	0.00954706	+	0.0165360i
$345$	−5555.85	+	5953.08i	−0.867005	+	0.928994i
$346$	1723.88	−	2985.85i	0.267851	−	0.463931i
$347$	2195.76	−	104.597i	0.339696	−	0.0161817i	0.122959	−	0.992412i	$-0.460762\pi$
$347$	2195.76	−	104.597i	0.339696	−	0.0161817i	0.216737	+	0.976230i	$0.430459\pi$
$348$	−3375.29	+	1331.83i	−0.519926	+	0.205155i
$349$	−10611.2	+	1013.25i	−1.62752	+	0.155409i	−0.868511	−	0.495669i	$-0.834923\pi$
$349$	−10611.2	+	1013.25i	−1.62752	+	0.155409i	−0.759010	+	0.651079i	$0.774317\pi$
$350$	445.275	−	130.745i	0.0680028	−	0.0199674i
$351$	1230.45	−	11129.5i	0.187112	−	1.69244i
$352$	1060.07	−	918.558i	0.160517	−	0.139089i
$353$	3995.28	+	5080.42i	0.602401	+	0.766015i	0.987629	−	0.156806i	$-0.0501198\pi$
$353$	3995.28	+	5080.42i	0.602401	+	0.766015i	−0.385229	+	0.922821i	$0.625877\pi$
$354$	−2145.61	+	509.240i	−0.322140	+	0.0764570i
$355$	−8004.35	+	2770.33i	−1.19669	+	0.414180i
$356$	7962.32	−	4104.86i	1.18540	−	0.611116i
$357$	−63.7588	+	32.4698i	−0.00945231	+	0.00481369i
$358$	321.189	+	61.9040i	0.0474172	+	0.00913891i
$359$	−9029.39	−	2651.27i	−1.32745	−	0.389773i	−0.460272	−	0.887778i	$-0.652248\pi$
$359$	−9029.39	−	2651.27i	−1.32745	−	0.389773i	−0.867174	+	0.498005i	$0.834066\pi$
$360$	−4110.51	−	5335.24i	−0.601785	−	0.781088i
$361$	−3792.60	−	4376.89i	−0.552937	−	0.638124i
$362$	1245.35	−	1748.85i	0.180813	−	0.253916i
$363$	1826.17	+	6335.69i	0.264047	+	0.916082i
$364$	−2127.54	+	1515.02i	−0.306356	+	0.218155i
$365$	−6558.08	−	5157.33i	−0.940454	−	0.739581i
$366$	−1514.62	−	2382.75i	−0.216312	−	0.340295i
$367$	10315.9	−	5955.90i	1.46727	−	0.847127i	0.467938	−	0.883761i	$-0.344997\pi$
$367$	10315.9	−	5955.90i	1.46727	−	0.847127i	0.999329	+	0.0366345i	$0.0116637\pi$
$368$	−1174.13	−	3227.85i	−0.166320	−	0.457237i
$369$	3851.54	−	2172.93i	0.543369	−	0.306554i
$370$	−252.592	+	162.331i	−0.0354909	+	0.0228086i
$371$	649.246	+	1621.74i	0.0908550	+	0.226945i
$372$	−446.492	+	314.613i	−0.0622300	+	0.0438493i
$373$	11163.7	+	2708.29i	1.54969	+	0.375951i	0.917140	−	0.398566i	$-0.130492\pi$
$373$	11163.7	+	2708.29i	1.54969	+	0.375951i	0.632553	+	0.774517i	$0.282007\pi$
$374$	2.48880	−	26.0639i	0.000344099	−	0.00360357i
$375$	3353.86	+	1179.48i	0.461846	+	0.162421i
$376$	−8722.37	+	6859.35i	−1.19634	+	0.940808i
$377$	−2400.09	+	8173.95i	−0.327880	+	1.11666i
$378$	804.748	−	265.157i	0.109502	−	0.0360799i
$379$	836.441	−	1301.53i	0.113364	−	0.176398i	−0.779935	−	0.625860i	$-0.784748\pi$
$379$	836.441	−	1301.53i	0.113364	−	0.176398i	0.893299	+	0.449462i	$0.148384\pi$
$380$	3033.42	+	144.499i	0.409503	+	0.0195070i
$381$	−454.878	+	2298.59i	−0.0611656	+	0.309082i
$382$	−1217.58	−	1276.96i	−0.163081	−	0.171034i
$383$	−4914.91	−	1967.63i	−0.655719	−	0.262510i	0.0198547	−	0.999803i	$-0.493680\pi$
$383$	−4914.91	−	1967.63i	−0.655719	−	0.262510i	−0.675573	+	0.737293i	$0.736104\pi$
$384$	7485.36	−	1404.13i	0.994754	−	0.186600i
$385$	456.017	+	324.728i	0.0603656	+	0.0429862i
$386$	1256.37	+	4278.79i	0.165667	+	0.564209i
$387$	169.628	+	79.5135i	0.0222808	+	0.0104442i
$388$	8546.20	+	1228.76i	1.11822	+	0.160775i
$389$	−5999.10	−	3092.75i	−0.781918	−	0.403107i	0.0205597	−	0.999789i	$-0.493455\pi$
$389$	−5999.10	−	3092.75i	−0.781918	−	0.403107i	−0.802478	+	0.596682i	$0.796485\pi$
$390$	−7113.60	−	35.3566i	−0.923618	−	0.00459064i
$391$	−272.040	−	134.893i	−0.0351858	−	0.0174471i
$392$	4835.06	+	2791.52i	0.622978	+	0.359677i
$393$	−5359.35	+	3406.73i	−0.687897	+	0.437269i
$394$	−374.451	+	149.907i	−0.0478796	+	0.0191681i
$395$	2489.17	+	1136.77i	0.317073	+	0.144802i
$396$	341.484	−	1348.95i	0.0433339	−	0.171179i
$397$	1220.19	+	2671.84i	0.154256	+	0.337773i	0.970944	−	0.239306i	$-0.0769199\pi$
$397$	1220.19	+	2671.84i	0.154256	+	0.337773i	−0.816689	+	0.577079i	$0.804193\pi$
$398$	−797.460	+	2304.11i	−0.100435	+	0.290187i
$399$	−319.543	+	786.824i	−0.0400932	+	0.0987230i
$400$	1731.71	−	1651.19i	0.216464	−	0.206398i
$401$	3488.81	+	10080.2i	0.434470	+	1.25532i	0.923684	+	0.383156i	$0.125163\pi$
$401$	3488.81	+	10080.2i	0.434470	+	1.25532i	−0.489213	+	0.872164i	$0.662716\pi$
$402$	4369.97	+	229.942i	0.542175	+	0.0285285i
$403$	−61.0173	+	1280.91i	−0.00754215	+	0.158329i
$404$	4025.32	+	3487.96i	0.495711	+	0.429536i
$405$	−9877.45	−	3114.87i	−1.21189	−	0.382170i
$406$	−638.080	+	91.7421i	−0.0779985	+	0.0112145i
$407$	−130.308	−	45.1000i	−0.0158701	−	0.00549269i
$408$	146.696	−	203.854i	0.0178003	−	0.0247360i
$409$	−1052.35	+	4337.86i	−0.127226	+	0.524433i	0.872154	+	0.489231i	$0.162723\pi$
$409$	−1052.35	+	4337.86i	−0.127226	+	0.524433i	−0.999380	+	0.0352020i	$0.988793\pi$
$410$	−1629.65	−	2288.52i	−0.196299	−	0.275663i
$411$	3143.58	−	3956.75i	0.377278	−	0.474872i
$412$	−4878.93	+	9463.80i	−0.583417	+	1.13167i
$413$	1758.25			0.209486
$414$	2940.97	+	2068.96i	0.349132	+	0.245613i
$415$	914.088			0.108122
$416$	6511.97	−	12631.5i	0.767490	−	1.48872i
$417$	−3871.11	−	576.233i	−0.454602	−	0.0676697i
$418$	−180.259	−	253.138i	−0.0210927	−	0.0296205i
$419$	−2574.03	+	10610.3i	−0.300118	+	1.23710i	0.599482	+	0.800388i	$0.295373\pi$
$419$	−2574.03	+	10610.3i	−0.300118	+	1.23710i	−0.899600	+	0.436715i	$0.856142\pi$
$420$	992.638	+	2202.48i	0.115323	+	0.255881i
$421$	−1121.71	−	388.226i	−0.129854	−	0.0449430i	0.261368	−	0.965239i	$-0.415826\pi$
$421$	−1121.71	−	388.226i	−0.129854	−	0.0449430i	−0.391222	+	0.920296i	$0.627948\pi$
$422$	854.084	−	122.799i	0.0985217	−	0.0141653i
$423$	−4969.91	+	16323.9i	−0.571266	+	1.87635i
$424$	−4634.03	−	4015.41i	−0.530774	−	0.459919i
$425$	10.0650	−	211.289i	0.00114876	−	0.0241154i
$426$	1697.38	+	3333.04i	0.193048	+	0.379075i
$427$	736.273	+	2127.32i	0.0834444	+	0.241097i
$428$	−1156.09	+	1102.33i	−0.130565	+	0.124493i
$429$	−2006.69	−	2577.99i	−0.225837	−	0.290131i
$430$	38.9268	−	112.472i	0.00436562	−	0.0126136i
$431$	−6261.70	−	13711.2i	−0.699804	−	1.53236i	−0.840208	−	0.542264i	$-0.817567\pi$
$431$	−6261.70	−	13711.2i	−0.699804	−	1.53236i	0.140404	−	0.990094i	$-0.455160\pi$
$432$	3061.55	−	3116.46i	0.340969	−	0.347086i
$433$	14498.7	+	6621.35i	1.60916	+	0.734877i	0.998378	−	0.0569258i	$-0.0181299\pi$
$433$	14498.7	+	6621.35i	1.60916	+	0.734877i	0.610777	+	0.791803i	$0.290857\pi$
$434$	−90.0864	+	36.0651i	−0.00996379	+	0.00398890i
$435$	6985.73	+	3645.46i	0.769977	+	0.401807i
$436$	11810.0	+	6818.50i	1.29724	+	0.748961i
$437$	−3488.66	+	904.456i	−0.381888	+	0.0990069i
$438$	−1857.94	+	3181.42i	−0.202684	+	0.347064i
$439$	−208.958	−	107.725i	−0.0227175	−	0.0117117i	0.446830	−	0.894619i	$-0.352553\pi$
$439$	−208.958	−	107.725i	−0.0227175	−	0.0117117i	−0.469548	+	0.882907i	$0.655583\pi$
$440$	−1945.03	−	279.653i	−0.210740	−	0.0302998i
$441$	8554.24	−	731.101i	0.923685	−	0.0789441i
$442$	−74.7348	−	254.523i	−0.00804247	−	0.0273901i
$443$	12321.9	+	8774.42i	1.32152	+	0.941050i	0.999983	−	0.00584683i	$-0.00186112\pi$
$443$	12321.9	+	8774.42i	1.32152	+	0.941050i	0.321537	+	0.946897i	$0.395801\pi$
$444$	−387.437	−	451.643i	−0.0414121	−	0.0482748i
$445$	−18059.9	−	7230.10i	−1.92387	−	0.770201i
$446$	1127.77	+	1182.77i	0.119734	+	0.125573i
$447$	691.330	+	605.083i	0.0731517	+	0.0640256i
$448$	−170.516	−	8.12270i	−0.0179825	−	0.000856611i
$449$	−9480.26	+	14751.6i	−0.996439	+	1.55049i	−0.171564	+	0.985173i	$0.554882\pi$
$449$	−9480.26	+	14751.6i	−0.996439	+	1.55049i	−0.824874	+	0.565316i	$0.808754\pi$
$450$	−498.490	+	2454.84i	−0.0522201	+	0.257161i
$451$	363.500	−	1237.97i	0.0379525	−	0.129254i
$452$	−10736.8	+	8443.52i	−1.11729	+	0.878649i
$453$	−2916.30	−	15546.6i	−0.302472	−	1.61246i
$454$	−424.000	+	4440.33i	−0.0438311	+	0.459020i
$455$	5511.96	+	1337.19i	0.567923	+	0.137777i
$456$	−268.601	−	2968.78i	−0.0275842	−	0.304881i
$457$	4363.65	+	10899.9i	0.446659	+	1.11570i	0.965401	+	0.260769i	$0.0839762\pi$
$457$	4363.65	+	10899.9i	0.446659	+	1.11570i	−0.518742	+	0.854931i	$0.673600\pi$
$458$	3674.63	−	2361.54i	0.374900	−	0.240934i
$459$	5.75845	−	386.167i	0.000585580	−	0.0392696i
$460$	−4986.41	+	8958.04i	−0.505418	+	0.907980i
$461$	−5510.15	+	3181.28i	−0.556688	+	0.321404i	−0.751815	−	0.659374i	$-0.770821\pi$
$461$	−5510.15	+	3181.28i	−0.556688	+	0.321404i	0.195127	+	0.980778i	$0.437488\pi$
$462$	114.369	−	219.164i	0.0115172	−	0.0220702i
$463$	6930.55	+	5450.25i	0.695659	+	0.547072i	0.902175	−	0.431371i	$-0.141970\pi$
$463$	6930.55	+	5450.25i	0.695659	+	0.547072i	−0.206515	+	0.978443i	$0.566212\pi$
$464$	−2707.45	+	1927.97i	−0.270884	+	0.192896i
$465$	1151.29	+	285.365i	0.114816	+	0.0284591i
$466$	1454.31	−	2042.29i	0.144570	−	0.203020i
$467$	−1957.93	−	2259.57i	−0.194009	−	0.223898i	0.650408	−	0.759585i	$-0.274598\pi$
$467$	−1957.93	−	2259.57i	−0.194009	−	0.223898i	−0.844417	+	0.535687i	$0.820053\pi$
$468$	−1867.54	−	13973.8i	−0.184460	−	1.38021i
$469$	−3347.73	−	982.983i	−0.329603	−	0.0967802i
$470$	10644.8	+	2051.61i	1.04469	+	0.201348i
$471$	9321.70	+	6056.37i	0.911934	+	0.592490i
$472$	−5485.56	+	2828.00i	−0.534943	+	0.275783i
$473$	51.6521	−	17.8770i	0.00502107	−	0.00173781i
$474$	346.202	−	1157.74i	0.0335476	−	0.112187i
$475$	−1551.98	−	1973.50i	−0.149915	−	0.190632i
$476$	−68.0826	+	58.9939i	−0.00655580	+	0.00568063i
$477$	−9377.06	−	989.555i	−0.900096	−	0.0949866i
$478$	3770.41	−	1107.09i	0.360784	−	0.105936i
$479$	−5333.50	+	509.287i	−0.508755	+	0.0485802i	−0.346278	−	0.938132i	$-0.612555\pi$
$479$	−5333.50	+	509.287i	−0.508755	+	0.0485802i	−0.162478	+	0.986712i	$0.551948\pi$
$480$	−10292.0	−	8176.80i	−0.978670	−	0.777538i
$481$	−1395.47	+	66.4746i	−0.132283	+	0.00630141i
$482$	−3204.81	+	5550.89i	−0.302853	+	0.524557i
$483$	−1900.56	−	2146.51i	−0.179045	−	0.202215i
$484$	4150.87	+	7189.53i	0.389827	+	0.675200i
$485$	−10136.8	−	15773.2i	−0.949051	−	1.47675i
$486$	−763.168	+	4509.40i	−0.0712305	+	0.420886i
$487$	−6454.10	+	14132.5i	−0.600540	+	1.31500i	0.328319	+	0.944567i	$0.393518\pi$
$487$	−6454.10	+	14132.5i	−0.600540	+	1.31500i	−0.928859	+	0.370433i	$0.879209\pi$
$488$	−5718.73	−	5452.80i	−0.530481	−	0.505813i
$489$	−6321.79	−	4549.25i	−0.584624	−	0.420704i
$490$	−1032.25	−	5355.80i	−0.0951676	−	0.493776i
$491$	−7212.94	+	18017.0i	−0.662964	+	1.65600i	0.0883748	+	0.996087i	$0.471833\pi$
$491$	−7212.94	+	18017.0i	−0.662964	+	1.65600i	−0.751339	+	0.659917i	$0.770592\pi$
$492$	4048.67	−	3822.16i	0.370992	−	0.350236i
$493$	−55.6083	+	288.523i	−0.00508007	+	0.0263579i
$494$	−2648.67	−	1702.20i	−0.241233	−	0.155031i
$495$	−2699.48	+	1357.88i	−0.245116	+	0.123298i
$496$	−327.641	+	378.118i	−0.0296603	+	0.0342298i
$497$	−703.089	−	2898.17i	−0.0634565	−	0.261571i
$498$	−55.4591	−	399.824i	−0.00499033	−	0.0359770i
$499$	−15124.8	+	2915.06i	−1.35687	+	0.261515i	−0.815251	−	0.579108i	$-0.803401\pi$
$499$	−15124.8	+	2915.06i	−1.35687	+	0.261515i	−0.541620	+	0.840623i	$0.682189\pi$
$500$	4455.94	+	425.491i	0.398552	+	0.0380571i
$501$	2908.32	−	838.283i	0.259350	−	0.0747539i
$502$	−241.064	−	2524.53i	−0.0214327	−	0.224453i
$503$	832.036	−	5786.94i	0.0737548	−	0.512976i	−0.919135	−	0.393942i	$-0.871111\pi$
$503$	832.036	−	5786.94i	0.0737548	−	0.512976i	0.992890	−	0.119034i	$-0.0379798\pi$
$504$	2007.53	−	1262.14i	0.177425	−	0.111548i
$505$		−	11566.4i		−	1.01921i
$506$	1035.97	−	165.560i	0.0910171	−	0.0145456i
$507$	−18724.0	−	10934.7i	−1.64016	−	0.957847i
$508$	140.375	+	2946.84i	0.0122601	+	0.257372i
$509$	−3384.43	+	4303.66i	−0.294720	+	0.374767i	−0.910752	−	0.412955i	$-0.864497\pi$
$509$	−3384.43	+	4303.66i	−0.294720	+	0.374767i	0.616032	+	0.787721i	$0.288739\pi$
$510$	−244.363	+	22.1088i	−0.0212168	+	0.00191959i
$511$	2027.09	−	2125.95i	0.175485	−	0.184044i
$512$	9022.19	−	4120.30i	0.778766	−	0.355650i
$513$	−2949.85	−	3508.68i	−0.253877	−	0.301973i
$514$	−196.178	−	1364.45i	−0.0168347	−	0.117088i
$515$	22470.0	−	5451.17i	1.92262	−	0.466422i
$516$	231.383	+	45.7893i	0.0197405	+	0.00390652i
$517$	2281.30	+	4425.10i	0.194064	+	0.376432i
$518$	−48.4420	−	93.9644i	−0.00410892	−	0.00797019i
$519$	−4783.30	−	14045.9i	−0.404554	−	1.18795i
$520$	−19347.6	+	4693.67i	−1.63163	+	0.395829i
$521$	−2958.36	−	20575.8i	−0.248768	−	1.73022i	−0.605354	−	0.795956i	$-0.706968\pi$
$521$	−2958.36	−	20575.8i	−0.248768	−	1.73022i	0.356586	−	0.934262i	$-0.383941\pi$
$522$	1170.69	−	3276.75i	0.0981607	−	0.274750i
$523$	17788.8	−	8123.86i	1.48728	−	0.679220i	0.504404	−	0.863468i	$-0.331712\pi$
$523$	17788.8	−	8123.86i	1.48728	−	0.679220i	0.982880	+	0.184248i	$0.0589851\pi$
$524$	−5517.60	+	5786.69i	−0.459995	+	0.482429i
$525$	838.697	−	1812.59i	0.0697214	−	0.150682i
$526$	667.192	−	848.403i	0.0553060	−	0.0703273i
$527$	2.10457	+	44.1804i	0.000173959	+	0.00365186i
$528$	6.33511	−	1274.60i	0.000522159	−	0.105056i
$529$	2496.53	−	11908.1i	0.205189	−	0.978722i
$530$			5990.37i			0.490953i
$531$	−4432.45	+	8391.87i	−0.362244	+	0.685831i
$532$	−152.168	+	1058.35i	−0.0124010	+	0.0862507i
$533$	−1242.58	−	13012.8i	−0.100979	−	1.05750i
$534$	−2066.74	+	8338.10i	−0.167484	+	0.675702i
$535$	3453.18	+	329.739i	0.279054	+	0.0266464i
$536$	12025.7	−	2317.76i	0.969084	−	0.186776i
$537$	1110.86	−	864.693i	0.0892688	−	0.0694865i
$538$	−557.856	−	2299.51i	−0.0447042	−	0.184273i
$539$	1640.36	−	1893.08i	0.131086	−	0.151281i
$540$	−13014.5	−	814.607i	−1.03714	−	0.0649169i
$541$	3621.68	+	2327.51i	0.287816	+	0.184968i	0.676580	−	0.736370i	$-0.263461\pi$
$541$	3621.68	+	2327.51i	0.287816	+	0.184968i	−0.388764	+	0.921337i	$0.627098\pi$
$542$	−1099.86	+	5706.63i	−0.0871645	+	0.452253i
$543$	−2133.70	−	8990.04i	−0.168630	−	0.710496i
$544$	182.176	−	455.055i	0.0143580	−	0.0358645i
$545$	−5604.47	−	29078.8i	−0.440494	−	2.28550i
$546$	250.469	−	2492.07i	0.0196320	−	0.195331i
$547$	14919.3	+	14225.5i	1.16619	+	1.11196i	0.991868	+	0.127268i	$0.0406207\pi$
$547$	14919.3	+	14225.5i	1.16619	+	1.11196i	0.174318	+	0.984689i	$0.444228\pi$
$548$	2643.14	−	5787.68i	0.206039	−	0.451163i
$549$	−12009.5	−	1848.73i	−0.933613	−	0.143720i
$550$	395.125	+	614.826i	0.0306330	+	0.0476659i
$551$	1743.76	+	3020.28i	0.134821	+	0.233517i
$552$	9382.07	+	3640.02i	0.723419	+	0.280669i
$553$	−481.734	+	834.388i	−0.0370442	+	0.0641624i
$554$	7515.27	−	357.996i	0.576341	−	0.0274545i
$555$	−190.256	+	1278.13i	−0.0145512	+	0.0977541i
$556$	−4905.33	+	468.402i	−0.374159	+	0.0357278i
$557$	16887.2	−	4958.52i	1.28462	−	0.377198i	0.433016	−	0.901386i	$-0.357449\pi$
$557$	16887.2	−	4958.52i	1.28462	−	0.377198i	0.851602	+	0.524188i	$0.175631\pi$
$558$	54.9690	−	520.888i	0.00417030	−	0.0395179i
$559$	418.513	−	362.643i	0.0316658	−	0.0274386i
$560$	1367.93	+	1739.46i	0.103224	+	0.131260i
$561$	−77.3526	−	81.9366i	−0.00582144	−	0.00616643i
$562$	5041.38	−	1744.84i	0.378395	−	0.130964i
$563$	18000.9	−	9280.13i	1.34751	−	0.694691i	0.374887	−	0.927070i	$-0.377681\pi$
$563$	18000.9	−	9280.13i	1.34751	−	0.694691i	0.972625	+	0.232379i	$0.0746511\pi$
$564$	−1128.91	+	21454.5i	−0.0842828	+	1.60177i
$565$	29126.0	+	5613.57i	2.16874	+	0.417991i
$566$	−10665.6	−	3131.70i	−0.792063	−	0.232571i
$567$	1422.31	−	3357.72i	0.105347	−	0.248696i
$568$	6855.06	+	7911.16i	0.506394	+	0.584410i
$569$	8033.19	−	11281.0i	0.591861	−	0.831152i	−0.404663	−	0.914466i	$-0.632611\pi$
$569$	8033.19	−	11281.0i	0.591861	−	0.831152i	0.996523	+	0.0833141i	$0.0265505\pi$
$570$	−2020.10	+	2097.64i	−0.148443	+	0.154141i
$571$	−7293.81	+	5193.90i	−0.534565	+	0.380662i	−0.815224	−	0.579146i	$-0.803386\pi$
$571$	−7293.81	+	5193.90i	−0.534565	+	0.380662i	0.280659	+	0.959807i	$0.409447\pi$
$572$	−3233.23	−	2542.64i	−0.236343	−	0.185862i
$573$	−7586.57	+	323.609i	−0.553112	+	0.0235933i
$574$	856.647	−	494.585i	0.0622922	−	0.0359644i
$575$	8296.53	−	1734.29i	0.601721	−	0.125783i
$576$	468.632	−	793.375i	0.0338999	−	0.0573911i
$577$	−9305.15	+	5980.06i	−0.671367	+	0.431461i	−0.831418	−	0.555648i	$-0.812470\pi$
$577$	−9305.15	+	5980.06i	−0.671367	+	0.431461i	0.160051	+	0.987109i	$0.448834\pi$
$578$	2201.24	+	5498.42i	0.158407	+	0.395682i
$579$	17417.8	+	8059.30i	1.25019	+	0.578468i
$580$	9641.34	+	2338.96i	0.690232	+	0.167449i
$581$	−30.5926	+	320.380i	−0.00218450	+	0.0228771i
$582$	−6284.22	+	5390.86i	−0.447576	+	0.383949i
$583$	−2162.47	+	1700.59i	−0.153620	+	0.120808i
$584$	−2904.90	+	9893.17i	−0.205831	+	0.700997i
$585$	−20277.6	+	22936.9i	−1.43312	+	1.62106i
$586$	539.604	−	839.640i	0.0380390	−	0.0591898i
$587$	−17689.6	−	842.661i	−1.24383	−	0.0592510i	−0.584682	−	0.811263i	$-0.698781\pi$
$587$	−17689.6	−	842.661i	−1.24383	−	0.0592510i	−0.659150	+	0.752011i	$0.729084\pi$
$588$	10232.5	−	3484.64i	0.717653	−	0.244395i
$589$	362.273	+	379.941i	0.0253433	+	0.0265793i
$590$	5597.48	+	2240.89i	0.390584	+	0.156366i
$591$	−575.891	+	1637.55i	−0.0400829	+	0.113976i
$592$	−444.001	−	316.172i	−0.0308249	−	0.0219503i
$593$	−4266.71	−	14531.1i	−0.295468	−	1.00627i	−0.964729	−	0.263245i	$-0.915207\pi$
$593$	−4266.71	−	14531.1i	−0.295468	−	1.00627i	0.669260	−	0.743028i	$-0.266611\pi$
$594$	757.722	+	1098.37i	0.0523396	+	0.0758699i
$595$	193.639	+	27.8410i	0.0133419	+	0.00191827i
$596$	1028.14	+	530.045i	0.0706618	+	0.0364287i
$597$	5201.41	+	9113.41i	0.356582	+	0.624769i
$598$	9120.73	−	5458.19i	0.623703	−	0.373248i
$599$	−1625.30	−	938.369i	−0.110865	−	0.0640079i	0.443542	−	0.896253i	$-0.353722\pi$
$599$	−1625.30	−	938.369i	−0.110865	−	0.0640079i	−0.554407	+	0.832246i	$0.687055\pi$
$600$	298.763	+	7004.10i	0.0203283	+	0.476569i
$601$	14952.1	−	5985.91i	1.01482	−	0.406273i	0.196174	−	0.980569i	$-0.437148\pi$
$601$	14952.1	−	5985.91i	1.01482	−	0.406273i	0.818648	+	0.574296i	$0.194724\pi$
$602$	38.1175	+	17.4077i	0.00258066	+	0.00117855i
$603$	13131.1	−	13500.2i	0.886799	−	0.911727i
$604$	−8273.18	−	18115.7i	−0.557336	−	1.22040i
$605$	5896.37	−	17036.5i	0.396234	−	1.14484i
$606$	−5059.18	+	701.754i	−0.339134	+	0.0470409i
$607$	−8895.26	+	8481.61i	−0.594806	+	0.567147i	−0.926526	−	0.376231i	$-0.877220\pi$
$607$	−8895.26	+	8481.61i	−0.594806	+	0.567147i	0.331719	+	0.943378i	$0.392371\pi$
$608$	−1902.82	−	5497.82i	−0.126923	−	0.366721i
$609$	−1511.50	+	2326.43i	−0.100573	+	0.154798i
$610$	−367.312	+	7710.84i	−0.0243804	+	0.511808i
$611$	38120.1	+	33031.3i	2.52402	+	2.18707i
$612$	−109.937	−	473.669i	−0.00726135	−	0.0312859i
$613$	5983.94	−	860.361i	0.394273	−	0.0566879i	0.0576727	−	0.998336i	$-0.481632\pi$
$613$	5983.94	−	860.361i	0.394273	−	0.0566879i	0.336600	+	0.941648i	$0.390723\pi$
$614$	−1103.66	−	381.982i	−0.0725412	−	0.0251067i
$615$	−12030.4	−	1209.13i	−0.788801	−	0.0792796i
$616$	163.112	−	672.357i	0.0106688	−	0.0439773i
$617$	11145.5	+	15651.6i	0.727227	+	1.02125i	0.998277	+	0.0586824i	$0.0186899\pi$
$617$	11145.5	+	15651.6i	0.727227	+	1.02125i	−0.271049	+	0.962565i	$0.587371\pi$
$618$	−3747.64	−	9497.71i	−0.243936	−	0.618210i
$619$	−11094.4	+	21520.1i	−0.720389	+	1.39736i	0.189238	+	0.981931i	$0.439398\pi$
$619$	−11094.4	+	21520.1i	−0.720389	+	1.39736i	−0.909626	+	0.415428i	$0.863632\pi$
$620$	1493.40			0.0967361
$621$	15036.2	−	3659.87i	0.971632	−	0.236498i
$622$	2032.95			0.131051
$623$	3138.52	−	6087.87i	0.201833	−	0.391502i
$624$	−4739.92	−	12012.4i	−0.304085	−	0.770646i
$625$	−11209.9	−	15742.2i	−0.717436	−	1.00750i
$626$	2105.42	−	8678.66i	0.134424	−	0.554104i
$627$	−1330.71	−	133.745i	−0.0847583	−	0.00851875i
$628$	13226.4	+	4577.69i	0.840428	+	0.290875i
$629$	−47.6960	+	6.85764i	−0.00302347	+	0.000434709i
$630$	−2216.23	−	674.743i	−0.140153	−	0.0426705i
$631$	10737.8	+	9304.34i	0.677439	+	0.587005i	0.924125	−	0.382091i	$-0.124796\pi$
$631$	10737.8	+	9304.34i	0.677439	+	0.587005i	−0.246685	+	0.969096i	$0.579341\pi$
$632$	160.916	−	3378.04i	0.0101280	−	0.212613i
$633$	2023.17	−	3113.98i	0.127036	−	0.195529i
$634$	787.318	+	2274.81i	0.0493192	+	0.142499i
$635$	4636.66	−	4421.04i	0.289764	−	0.276289i
$636$	−11759.2	+	1631.11i	−0.733150	+	0.101694i
$637$	8300.47	−	23982.6i	0.516290	−	1.49172i
$638$	−421.734	−	923.469i	−0.0261702	−	0.0573049i
$639$	15605.0	+	3950.40i	0.966081	+	0.244562i
$640$	−18941.3	−	8650.21i	−1.16988	−	0.534265i
$641$	−5855.78	+	2344.30i	−0.360826	+	0.144453i	−0.544990	−	0.838443i	$-0.683467\pi$
$641$	−5855.78	+	2344.30i	−0.360826	+	0.144453i	0.184164	+	0.982896i	$0.441042\pi$
$642$	−65.2813	−	1530.43i	−0.00401316	−	0.0940831i
$643$	−12059.1	−	6962.32i	−0.739602	−	0.427010i	0.0823224	−	0.996606i	$-0.473766\pi$
$643$	−12059.1	−	6962.32i	−0.739602	−	0.427010i	−0.821925	+	0.569596i	$0.807100\pi$
$644$	−2972.83	−	2047.50i	−0.181904	−	0.125284i
$645$	−253.899	−	444.857i	−0.0154996	−	0.0271569i
$646$	−96.5235	−	49.7613i	−0.00587874	−	0.00303070i
$647$	183.410	+	26.3704i	0.0111447	+	0.00160236i	0.147885	−	0.989005i	$-0.452753\pi$
$647$	183.410	+	26.3704i	0.0111447	+	0.00160236i	−0.136740	+	0.990607i	$0.543663\pi$
$648$	963.149	+	12763.4i	0.0583890	+	0.773758i
$649$	780.108	+	2656.81i	0.0471833	+	0.160691i
$650$	6031.59	+	4295.08i	0.363967	+	0.259180i
$651$	−138.549	+	393.966i	−0.00834128	+	0.0237185i
$652$	−9103.72	−	3644.58i	−0.546824	−	0.218915i
$653$	−8436.57	−	8848.02i	−0.505587	−	0.530245i	0.420631	−	0.907232i	$-0.361809\pi$
$653$	−8436.57	−	8848.02i	−0.505587	−	0.530245i	−0.926219	+	0.376987i	$0.876960\pi$
$654$	−12379.1	+	4215.66i	−0.740153	+	0.252057i
$655$	17343.5	+	826.172i	1.03460	+	0.0492843i
$656$	2757.34	−	4290.50i	0.164110	−	0.255360i
$657$	5036.68	+	15034.4i	0.299086	+	0.892768i
$658$	−1075.33	+	3662.23i	−0.0637093	+	0.216974i
$659$	3932.24	−	3092.35i	0.232441	−	0.182793i	−0.495145	−	0.868810i	$-0.664885\pi$
$659$	3932.24	−	3092.35i	0.232441	−	0.182793i	0.727585	+	0.686017i	$0.240643\pi$
$660$	−2887.65	+	2477.14i	−0.170305	+	0.146095i
$661$	99.6389	−	1043.47i	0.00586309	−	0.0614011i	−0.992067	−	0.125711i	$-0.959879\pi$
$661$	99.6389	−	1043.47i	0.00586309	−	0.0614011i	0.997930	+	0.0643103i	$0.0204847\pi$
$662$	5182.71	+	1257.31i	0.304278	+	0.0738170i
$663$	−1036.09	−	479.406i	−0.0606917	−	0.0280824i
$664$	−419.861	−	1048.76i	−0.0245388	−	0.0612949i
$665$	1953.34	−	1255.33i	0.113906	−	0.0732026i
$666$	570.599	+	5.67221i	0.0331986	+	0.000330021i
$667$	−11750.2	+	744.446i	−0.682113	+	0.0432160i
$668$	3300.27	−	1905.41i	0.191154	−	0.110363i
$669$	7026.93	−	299.737i	0.406094	−	0.0173221i
$670$	−9404.89	−	7396.09i	−0.542302	−	0.426471i
$671$	−2887.82	+	2056.41i	−0.166145	+	0.118311i
$672$	3210.35	−	3333.59i	0.184289	−	0.191363i
$673$	−11342.1	+	15927.8i	−0.649638	+	0.912288i	−0.999701	−	0.0244376i	$-0.992221\pi$
$673$	−11342.1	+	15927.8i	−0.649638	+	0.912288i	0.350064	+	0.936726i	$0.386160\pi$
$674$	3875.67	+	4472.76i	0.221491	+	0.255615i
$675$	6536.96	+	8572.44i	0.372752	+	0.488820i
$676$	−26194.4	−	7691.36i	−1.49035	−	0.437606i
$677$	−11529.7	−	2222.17i	−0.654539	−	0.126152i	−0.148839	−	0.988861i	$-0.547554\pi$
$677$	−11529.7	−	2222.17i	−0.654539	−	0.126152i	−0.505700	+	0.862709i	$0.668766\pi$
$678$	688.269	−	13080.3i	0.0389865	−	0.740925i
$679$	5867.64	−	3024.98i	0.331634	−	0.170969i
$680$	−648.914	+	224.591i	−0.0365952	+	0.0126657i
$681$	13178.0	+	13959.0i	0.741531	+	0.785475i
$682$	−94.4665	−	120.124i	−0.00530397	−	0.00674455i
$683$	18923.3	−	16397.2i	1.06015	−	0.918623i	0.0633027	−	0.997994i	$-0.479837\pi$
$683$	18923.3	−	16397.2i	1.06015	−	0.918623i	0.996845	+	0.0793710i	$0.0252912\pi$
$684$	−4667.76	−	3394.33i	−0.260930	−	0.189745i
$685$	−13257.4	+	3892.72i	−0.739472	+	0.217129i
$686$	3973.85	−	379.457i	0.221169	−	0.0211191i
$687$	2767.78	−	18593.8i	0.153708	−	1.03260i
$688$	215.813	−	10.2804i	0.0119590	−	0.000569677i
$689$	−13936.2	+	24138.2i	−0.770576	+	1.33468i
$690$	−3314.81	−	9255.83i	−0.182888	−	0.510672i
$691$	−2474.22	−	4285.47i	−0.136214	−	0.235929i	0.789847	−	0.613304i	$-0.210160\pi$
$691$	−2474.22	−	4285.47i	−0.136214	−	0.235929i	−0.926060	+	0.377375i	$0.876827\pi$
$692$	−10100.2	−	15716.3i	−0.554845	−	0.863356i
$693$	−385.581	−	991.590i	−0.0211357	−	0.0543541i
$694$	−1102.55	+	2414.26i	−0.0603060	+	0.132052i
$695$	7744.54	+	7384.40i	0.422687	+	0.403031i
$696$	973.845	−	9689.38i	0.0530366	−	0.527694i
$697$	−85.3282	−	442.725i	−0.00463707	−	0.0240594i
$698$	4783.28	−	11948.1i	0.259384	−	0.647910i
$699$	−2491.72	−	10498.5i	−0.134829	−	0.568082i
$700$	475.895	−	2469.18i	0.0256959	−	0.133323i
$701$	−15109.2	−	9710.09i	−0.814075	−	0.523174i	0.0661062	−	0.997813i	$-0.478942\pi$
$701$	−15109.2	−	9710.09i	−0.814075	−	0.523174i	−0.880181	+	0.474639i	$0.842579\pi$
$702$	11262.9	+	7477.84i	0.605543	+	0.402041i
$703$	−374.532	+	432.233i	−0.0200935	+	0.0231891i
$704$	−63.3819	−	261.264i	−0.00339317	−	0.0139869i
$705$	36816.0	−	28657.4i	1.96677	−	1.53092i
$706$	−7662.47	+	1476.82i	−0.408472	+	0.0787265i
$707$	4053.94	+	387.105i	0.215650	+	0.0205920i
$708$	−2874.79	+	11598.1i	−0.152601	+	0.615656i
$709$	−377.621	−	3954.63i	−0.0200026	−	0.209477i	−0.999948	−	0.0102101i	$-0.996750\pi$
$709$	−377.621	−	3954.63i	−0.0200026	−	0.209477i	0.979945	−	0.199267i	$-0.0638561\pi$
$710$	1455.41	−	10122.6i	0.0769304	−	0.535063i
$711$	−2768.00	−	4402.70i	−0.146003	−	0.232228i
$712$			24041.6i			1.26545i
$713$	−1692.47	+	525.900i	−0.0888970	+	0.0276229i
$714$	0.429368	−	86.3871i	2.25052e−5	−	0.00452795i
$715$	425.015	+	8922.17i	0.0222303	+	0.466672i
$716$	1095.64	−	1393.21i	0.0571869	−	0.0727190i
$717$	7101.74	−	15348.3i	0.369902	−	0.799433i
$718$	7840.74	−	8223.13i	0.407540	−	0.427416i
$719$	−26357.3	+	12037.0i	−1.36712	+	0.624344i	−0.957638	−	0.287973i	$-0.907019\pi$
$719$	−26357.3	+	12037.0i	−1.36712	+	0.624344i	−0.409484	+	0.912317i	$0.634291\pi$
$720$	−11750.7	+	2143.84i	−0.608225	+	0.110967i
$721$	1158.57	+	8058.00i	0.0598436	+	0.416221i
$722$	6795.34	−	1648.53i	0.350272	−	0.0849751i
$723$	8892.49	+	26112.3i	0.457421	+	1.34319i
$724$	−5330.73	−	10340.2i	−0.273640	−	0.530787i
$725$	−3758.34	−	7290.16i	−0.192526	−	0.373448i
$726$	−7809.52	−	1545.46i	−0.399226	−	0.0790045i
$727$	−14995.5	+	3637.86i	−0.764994	+	0.185585i	−0.599227	−	0.800579i	$-0.704525\pi$
$727$	−14995.5	+	3637.86i	−0.764994	+	0.185585i	−0.165767	+	0.986165i	$0.553010\pi$
$728$	−997.569	−	6938.25i	−0.0507862	−	0.353226i
$729$	12440.4	+	15253.1i	0.632035	+	0.774940i
$730$	9162.88	−	4184.55i	0.464566	−	0.212160i
$731$	13.1808	−	13.8236i	0.000666906	−	0.000699431i
$732$	−15236.5	+	1378.53i	−0.769343	+	0.0696064i
$733$	21437.4	−	27259.9i	1.08023	−	1.37362i	0.157796	−	0.987472i	$-0.449561\pi$
$733$	21437.4	−	27259.9i	1.08023	−	1.37362i	0.922435	−	0.386153i	$-0.126196\pi$
$734$	684.323	+	14365.7i	0.0344126	+	0.722408i
$735$	−20270.4	−	11837.8i	−1.01726	−	0.594075i
$736$	19482.2	+	2490.17i	0.975713	+	0.124713i
$737$		−	5494.74i		−	0.274629i
$738$	201.026	+	5335.48i	0.0100269	+	0.266127i
$739$	−2361.77	+	16426.5i	−0.117563	+	0.817670i	0.842662	+	0.538443i	$0.180987\pi$
$739$	−2361.77	+	16426.5i	−0.117563	+	0.817670i	−0.960225	+	0.279227i	$0.909922\pi$
$740$	154.653	+	1619.60i	0.00768265	+	0.0804563i
$741$	−13020.0	+	3752.83i	−0.645481	+	0.186051i
$742$	−2099.57	−	200.485i	−0.103878	−	0.00991919i
$743$	−35199.1	+	6784.07i	−1.73799	+	0.334971i	−0.957114	−	0.289711i	$-0.906441\pi$
$743$	−35199.1	+	6784.07i	−1.73799	+	0.334971i	−0.780879	+	0.624682i	$0.785229\pi$
$744$	−201.403	−	1451.98i	−0.00992444	−	0.0715487i
$745$	−592.214	−	2441.14i	−0.0291235	−	0.120049i
$746$	−9082.75	+	10482.1i	−0.445768	+	0.514444i
$747$	−1452.01	−	953.676i	−0.0711195	−	0.0467111i
$748$	−119.350	−	76.7017i	−0.00583406	−	0.00374932i
$749$	−231.141	+	1199.27i	−0.0112760	+	0.0585054i
$750$	−3121.29	+	2946.66i	−0.151964	+	0.143463i
$751$	10607.8	−	26497.0i	0.515425	−	1.28747i	−0.411221	−	0.911536i	$-0.634897\pi$
$751$	10607.8	−	26497.0i	0.515425	−	1.28747i	0.926646	−	0.375935i	$-0.122678\pi$
$752$	3724.38	+	19323.9i	0.180604	+	0.937061i
$753$	−8858.88	−	6374.97i	−0.428733	−	0.308522i
$754$	−7444.07	−	7097.91i	−0.359545	−	0.342826i
$755$	−17965.9	+	39339.9i	−0.866023	+	1.89633i
$756$	721.082	−	4534.22i	0.0346898	−	0.218132i
$757$	8267.02	+	12863.7i	0.396922	+	0.617623i	0.980985	−	0.194086i	$-0.0621741\pi$
$757$	8267.02	+	12863.7i	0.396922	+	0.617623i	−0.584062	+	0.811709i	$0.698538\pi$
$758$	933.981	+	1617.70i	0.0447542	+	0.0775166i
$759$	2400.25	−	3824.23i	0.114787	−	0.182886i
$760$	−4075.12	+	7058.31i	−0.194500	+	0.336884i
$761$	−19425.3	+	925.342i	−0.925318	+	0.0440783i	−0.504829	−	0.863219i	$-0.668444\pi$
$761$	−19425.3	+	925.342i	−0.925318	+	0.0440783i	−0.420489	+	0.907298i	$0.638141\pi$
$762$	−2215.09	−	1759.85i	−0.105307	−	0.0836649i
$763$	10379.4	−	991.116i	0.492478	−	0.0470260i
$764$	−9173.33	+	2693.53i	−0.434397	+	0.127551i
$765$	−621.035	+	854.025i	−0.0293511	+	0.0403626i
$766$	4830.76	−	4185.87i	0.227862	−	0.197444i
$767$	17341.8	+	22051.8i	0.816394	+	1.03813i
$768$	−2227.98	+	7450.61i	−0.104681	+	0.350066i
$769$	−15575.6	+	5390.76i	−0.730390	+	0.252790i	−0.666853	−	0.745189i	$-0.732359\pi$
$769$	−15575.6	+	5390.76i	−0.730390	+	0.252790i	−0.0635368	+	0.997979i	$0.520238\pi$
$770$	−600.776	+	309.721i	−0.0281175	+	0.0144956i
$771$	−4974.77	−	3232.14i	−0.232376	−	0.150976i
$772$	23727.1	+	4573.02i	1.10616	+	0.213195i
$773$	12563.4	+	3688.94i	0.584571	+	0.171645i	0.560628	−	0.828068i	$-0.310560\pi$
$773$	12563.4	+	3688.94i	0.584571	+	0.171645i	0.0239429	+	0.999713i	$0.492378\pi$
$774$	−179.177	+	138.046i	−0.00832091	+	0.00641080i
$775$	−808.510	−	933.070i	−0.0374742	−	0.0432476i
$776$	−13441.0	+	18875.3i	−0.621785	+	0.873175i
$777$	−441.606	−	109.459i	−0.0203894	−	0.00505384i
$778$	6638.00	−	4726.90i	0.305892	−	0.217825i
$779$	−4206.50	−	3308.03i	−0.193470	−	0.152147i
$780$	−17832.9	+	34172.9i	−0.818616	+	1.56870i
$781$	4067.35	−	2348.28i	0.186352	−	0.107591i
$782$	295.267	−	217.312i	0.0135022	−	0.00993740i
$783$	−7293.34	−	13079.0i	−0.332877	−	0.596942i
$784$	8329.72	−	5353.18i	0.379451	−	0.243859i
$785$	−11296.2	−	28216.7i	−0.513605	−	1.28292i
$786$	−690.886	−	7636.20i	−0.0313525	−	0.346532i
$787$	−9304.02	−	2257.13i	−0.421414	−	0.102234i	0.0194439	−	0.999811i	$-0.493810\pi$
$787$	−9304.02	−	2257.13i	−0.421414	−	0.102234i	−0.440857	+	0.897577i	$0.645326\pi$
$788$	−207.749	+	2175.65i	−0.00939184	+	0.0983558i
$789$	−856.402	−	4565.43i	−0.0386422	−	0.205999i
$790$	−2597.06	+	2042.35i	−0.116961	+	0.0919793i
$791$	−2942.30	+	10020.5i	−0.132258	+	0.450429i
$792$	2797.87	+	2473.49i	0.125528	+	0.110974i
$793$	−19418.8	+	30216.3i	−0.869587	+	1.35310i
$794$	−3542.37	−	168.744i	−0.158330	−	0.00754219i
$795$	19399.6	+	16979.4i	0.865449	+	0.757480i
$796$	9117.07	+	9561.71i	0.405962	+	0.425761i
$797$	−15628.3	−	6256.64i	−0.694584	−	0.278070i	−0.00261515	−	0.999997i	$-0.500832\pi$
$797$	−15628.3	−	6256.64i	−0.694584	−	0.278070i	−0.691969	+	0.721927i	$0.743257\pi$
$798$	−667.597	−	778.231i	−0.0296149	−	0.0345226i
$799$	1417.16	+	1009.15i	0.0627478	+	0.0446825i
$800$	3854.74	+	13128.0i	0.170357	+	0.580183i
$801$	21144.6	+	30326.9i	0.932717	+	1.33776i
$802$	−12747.9	−	1832.86i	−0.561275	−	0.0806991i
$803$	4111.81	+	2119.79i	0.180701	+	0.0931577i
$804$	11957.8	−	20475.8i	0.524527	−	0.898169i
$805$	867.319	+	7790.67i	0.0379739	+	0.341099i
$806$	−1340.86	−	774.145i	−0.0585977	−	0.0338314i
$807$	−9028.09	−	4711.25i	−0.393809	−	0.205507i
$808$	−13270.5	+	5312.72i	−0.577792	+	0.231313i
$809$	−294.239	−	134.374i	−0.0127872	−	0.00583974i	0.409011	−	0.912529i	$-0.365874\pi$
$809$	−294.239	−	134.374i	−0.0127872	−	0.00583974i	−0.421798	+	0.906690i	$0.638601\pi$
$810$	8807.44	−	8876.75i	0.382052	−	0.385058i
$811$	−10361.1	−	22687.7i	−0.448616	−	0.982333i	−0.989936	−	0.141516i	$-0.954802\pi$
$811$	−10361.1	−	22687.7i	−0.448616	−	0.982333i	0.541319	−	0.840817i	$-0.317925\pi$
$812$	−1142.46	+	3300.93i	−0.0493751	+	0.142660i
$813$	15363.2	+	19737.0i	0.662744	+	0.851423i
$814$	120.492	−	114.889i	0.00518827	−	0.00494701i
$815$	6964.89	+	20123.7i	0.299349	+	0.864912i
$816$	−202.131	−	396.910i	−0.00867155	−	0.0170277i
$817$	10.7870	−	226.446i	0.000461919	−	0.00969687i
$818$	−4072.98	−	3529.26i	−0.174094	−	0.150853i
$819$	−7360.53	−	7874.78i	−0.314039	−	0.335979i
$820$	−15068.3	+	2166.50i	−0.641718	+	0.0922651i
$821$	31619.5	+	10943.6i	1.34413	+	0.465207i	0.901996	−	0.431743i	$-0.142101\pi$
$821$	31619.5	+	10943.6i	1.34413	+	0.465207i	0.442131	+	0.896950i	$0.354223\pi$
$822$	2507.03	+	5562.63i	0.106378	+	0.236033i
$823$	−1382.92	+	5700.48i	−0.0585730	+	0.241441i	−0.993571	−	0.113212i	$-0.963886\pi$
$823$	−1382.92	+	5700.48i	−0.0585730	+	0.241441i	0.934998	+	0.354653i	$0.115401\pi$
$824$	−16575.3	−	23276.7i	−0.700761	−	0.984082i
$825$	3111.05	+	463.095i	0.131288	+	0.0195429i
$826$	−972.750	+	1886.87i	−0.0409762	+	0.0794827i
$827$	−16484.6			−0.693138			−0.346569	−	0.938024i	$-0.612653\pi$
$827$	−16484.6			−0.693138			−0.346569	+	0.938024i	$0.612653\pi$
$828$	17266.8	−	9027.28i	0.724713	−	0.378889i
$829$	34480.1			1.44456			0.722282	−	0.691598i	$-0.243093\pi$
$829$	34480.1			1.44456			0.722282	+	0.691598i	$0.243093\pi$
$830$	−505.720	+	980.959i	−0.0211491	+	0.0410236i
$831$	20142.2	−	25352.6i	0.840827	−	1.05833i
$832$	−1579.95	−	2218.73i	−0.0658351	−	0.0924525i
$833$	206.369	−	850.664i	0.00858374	−	0.0353827i
$834$	2760.08	−	3835.50i	0.114597	−	0.159248i
$835$	−7820.38	−	2706.66i	−0.324114	−	0.112177i
$836$	−1666.74	+	239.641i	−0.0689539	+	0.00991407i
$837$	−1531.07	−	1654.44i	−0.0632276	−	0.0683225i
$838$	−9962.40	−	8632.47i	−0.410675	−	0.355852i
$839$	−1183.23	+	24839.0i	−0.0486884	+	1.02210i	0.833890	+	0.551931i	$0.186109\pi$
$839$	−1183.23	+	24839.0i	−0.0486884	+	1.02210i	−0.882578	+	0.470165i	$0.844194\pi$
$840$	−6474.59	−	340.684i	−0.265946	−	0.0139937i
$841$	−4250.50	−	12281.0i	−0.174279	−	0.503547i
$842$	1037.21	−	988.980i	0.0424521	−	0.0404780i
$843$	8638.93	−	21272.0i	0.352954	−	0.869093i
$844$	1529.21	−	4418.36i	0.0623668	−	0.180197i
$845$	24627.8	+	53927.3i	1.00263	+	2.19545i
$846$	−14768.5	−	14364.7i	−0.600179	−	0.583769i
$847$	5773.80	+	2636.80i	0.234227	+	0.106968i
$848$	−10095.6	+	4041.67i	−0.408826	+	0.163669i
$849$	−40372.9	+	25663.4i	−1.63203	+	1.03742i
$850$	221.178	+	127.697i	0.00892511	+	0.00515291i
$851$	−745.611	−	1781.03i	−0.0300343	−	0.0717427i
$852$	20267.2	+	100.733i	0.814955	+	0.00405055i
$853$	−36194.1	−	18659.4i	−1.45283	−	0.748985i	−0.462356	−	0.886694i	$-0.652996\pi$
$853$	−36194.1	−	18659.4i	−1.45283	−	0.748985i	−0.990473	+	0.137709i	$0.956026\pi$
$854$	−2690.29	−	386.805i	−0.107798	−	0.0154991i
$855$	1067.28	+	12487.6i	0.0426901	+	0.499495i
$856$	−1207.80	−	4113.39i	−0.0482264	−	0.164244i
$857$	−21249.0	−	15131.3i	−0.846969	−	0.603124i	0.0720220	−	0.997403i	$-0.477055\pi$
$857$	−21249.0	−	15131.3i	−0.846969	−	0.603124i	−0.918991	+	0.394279i	$0.870994\pi$
$858$	3876.79	−	727.224i	0.154256	−	0.0289359i
$859$	−28420.6	−	11377.9i	−1.12887	−	0.451932i	−0.269355	−	0.963041i	$-0.586810\pi$
$859$	−28420.6	−	11377.9i	−1.12887	−	0.451932i	−0.859516	+	0.511109i	$0.829235\pi$
$860$	−445.036	−	466.740i	−0.0176460	−	0.0185066i
$861$	826.423	−	4176.09i	0.0327113	−	0.165297i
$862$	18178.6	+	865.952i	0.718288	+	0.0342163i
$863$	−12745.2	+	19831.9i	−0.502724	+	0.782254i	−0.996162	−	0.0875271i	$-0.972104\pi$
$863$	−12745.2	+	19831.9i	−0.502724	+	0.782254i	0.493438	+	0.869781i	$0.335740\pi$
$864$	7817.62	+	23726.4i	0.307825	+	0.934244i
$865$	−11429.7	+	38926.2i	−0.449275	+	1.53009i
$866$	−15127.2	+	11896.1i	−0.593582	+	0.466798i
$867$	24045.7	+	8456.36i	0.941908	+	0.331249i
$868$	−49.9809	+	523.424i	−0.00195445	+	0.0204679i
$869$	−1474.55	−	357.721i	−0.0575610	−	0.0139642i
$870$	−7777.00	+	5479.93i	−0.303063	+	0.213548i
$871$	−20690.5	−	51682.4i	−0.804903	−	2.01055i
$872$	−30788.7	+	19786.7i	−1.19569	+	0.768420i
$873$	−354.203	+	35631.3i	−0.0137319	+	1.38137i
$874$	959.480	−	4244.27i	0.0371338	−	0.164261i
$875$	2963.93	−	1711.22i	0.114513	−	0.0661142i
$876$	10709.3	+	16847.5i	0.413052	+	0.649800i
$877$	22429.2	+	17638.6i	0.863605	+	0.679147i	0.948340	−	0.317257i	$-0.102762\pi$
$877$	22429.2	+	17638.6i	0.863605	+	0.679147i	−0.0847344	+	0.996404i	$0.527004\pi$
$878$	231.212	−	164.645i	0.00888727	−	0.00632859i
$879$	−1189.66	−	4127.40i	−0.0456500	−	0.158377i
$880$	−2021.49	+	2838.79i	−0.0774369	+	0.108745i
$881$	10889.2	+	12566.8i	0.416421	+	0.480576i	0.924743	−	0.380591i	$-0.124280\pi$
$881$	10889.2	+	12566.8i	0.416421	+	0.480576i	−0.508322	+	0.861167i	$0.669734\pi$
$882$	−3948.05	+	9584.52i	−0.150723	+	0.365904i
$883$	31689.5	+	9304.86i	1.20774	+	0.354625i	0.822808	−	0.568320i	$-0.192406\pi$
$883$	31689.5	+	9304.86i	1.20774	+	0.354625i	0.384933	+	0.922945i	$0.374225\pi$
$884$	−1411.40	−	272.026i	−0.0536998	−	0.0103498i
$885$	23122.8	−	11775.5i	0.878264	−	0.447265i
$886$	−16233.4	+	8368.92i	−0.615545	+	0.317336i
$887$	37800.8	−	13083.0i	1.43092	−	0.495247i	0.501788	−	0.864991i	$-0.332676\pi$
$887$	37800.8	−	13083.0i	1.43092	−	0.495247i	0.929134	+	0.369744i	$0.120555\pi$
$888$	1553.83	−	368.786i	0.0587196	−	0.0139366i
$889$	1394.36	+	1773.07i	0.0526044	+	0.0668920i
$890$	17750.7	−	15381.1i	0.668544	−	0.579297i
$891$	5704.75	+	659.421i	0.214497	+	0.0247940i
$892$	8496.65	−	2494.84i	0.318934	−	0.0936474i
$893$	20555.7	−	1962.83i	0.770290	−	0.0735538i
$894$	−1031.83	+	407.143i	−0.0386012	+	0.0152314i
$895$	−3844.60	+	183.141i	−0.143587	+	0.00683991i
$896$	3665.75	−	6349.27i	0.136679	−	0.236735i
$897$	8176.06	−	45008.0i	0.304337	−	1.67533i
$898$	−10585.8	−	18335.1i	−0.393376	−	0.681348i
$899$	927.207	+	1442.76i	0.0343983	+	0.0535248i
$900$	10585.3	+	8496.05i	0.392050	+	0.314669i
$901$	−399.363	+	874.482i	−0.0147666	+	0.0323343i
$902$	1127.43	+	1075.00i	0.0416178	+	0.0396825i
$903$	164.416	−	74.1009i	0.00605917	−	0.00273081i
$904$	−6937.58	−	35995.6i	−0.255244	−	1.32433i
$905$	−9389.29	+	23453.3i	−0.344874	+	0.861453i
$906$	18297.4	+	5471.52i	0.670960	+	0.200639i
$907$	580.578	−	3012.32i	0.0212544	−	0.110278i	−0.969752	−	0.244092i	$-0.921510\pi$
$907$	580.578	−	3012.32i	0.0212544	−	0.110278i	0.991007	+	0.133813i	$0.0427223\pi$
$908$	20332.9	+	13067.1i	0.743138	+	0.477586i
$909$	−12067.4	+	18373.0i	−0.440319	+	0.670402i
$910$	−4484.51	+	5175.40i	−0.163363	+	0.188531i
$911$	−8851.88	−	36488.0i	−0.321928	−	1.32700i	−0.871022	−	0.491243i	$-0.836543\pi$
$911$	−8851.88	−	36488.0i	−0.321928	−	1.32700i	0.549095	−	0.835760i	$-0.314973\pi$
$912$	−4898.12	−	1989.21i	−0.177843	−	0.0722253i
$913$	−497.686	+	95.9210i	−0.0180405	+	0.00347702i
$914$	−14111.5	−	1347.48i	−0.510685	−	0.0487645i
$915$	23930.1	+	23045.5i	0.864595	+	0.832633i
$916$	−2249.84	−	23561.4i	−0.0811538	−	0.849882i
$917$	−870.016	+	6051.09i	−0.0313309	+	0.217911i
$918$	411.231	+	219.827i	0.0147850	+	0.00790344i
$919$			18477.2i			0.663229i	0.943415	+	0.331614i	$0.107593\pi$
$919$			18477.2i			0.663229i	−0.943415	+	0.331614i	$0.892407\pi$
$920$	−15236.6	−	22911.1i	−0.546019	−	0.821041i
$921$	−4365.31	+	2491.47i	−0.156180	+	0.0891385i
$922$	−365.524	−	7673.30i	−0.0130563	−	0.274085i
$923$	29414.1	−	37403.1i	1.04895	−	1.33384i
$924$	−771.573	−	1095.00i	−0.0274707	−	0.0389858i
$925$	928.193	−	973.460i	0.0329933	−	0.0346024i
$926$	−9683.30	+	4422.22i	−0.343643	+	0.156936i
$927$	−41380.4	−	14784.1i	−1.46614	−	0.523813i
$928$	−2704.83	−	18812.5i	−0.0956792	−	0.665464i
$929$	−32233.1	+	7819.66i	−1.13836	+	0.276162i	−0.760270	−	0.649608i	$-0.774933\pi$
$929$	−32233.1	+	7819.66i	−1.13836	+	0.276162i	−0.378087	+	0.925770i	$0.623418\pi$
$930$	−943.191	+	1077.63i	−0.0332564	+	0.0379967i
$931$	−4760.70	−	9234.48i	−0.167589	−	0.325078i
$932$	−6225.18	−	12075.2i	−0.218790	−	0.424394i
$933$	5762.28	−	6583.62i	0.202196	−	0.231016i
$934$	3508.10	−	851.056i	0.122900	−	0.0298152i
$935$	43.8454	+	304.951i	0.00153358	+	0.0106663i
$936$	35630.1	+	12729.7i	1.24424	+	0.444533i
$937$	23263.1	−	10623.9i	0.811068	−	0.370403i	0.0336873	−	0.999432i	$-0.489275\pi$
$937$	23263.1	−	10623.9i	0.811068	−	0.370403i	0.777381	+	0.629030i	$0.216548\pi$
$938$	2907.03	−	3048.80i	0.101192	−	0.106127i
$939$	−22137.8	−	31417.5i	−0.769371	−	1.09188i
$940$	36311.3	−	46173.5i	1.25994	−	1.60214i
$941$	−781.048	−	16396.2i	−0.0270579	−	0.568015i	−0.971170	−	0.238389i	$-0.923381\pi$
$941$	−781.048	−	16396.2i	−0.0270579	−	0.568015i	0.944112	−	0.329625i	$-0.106922\pi$
$942$	−11656.7	+	6652.95i	−0.403179	+	0.230111i
$943$	16314.0	−	7761.60i	0.563369	−	0.268030i
$944$			10945.4i			0.377375i
$945$	−8466.89	+	5264.63i	−0.291458	+	0.181226i
$946$	−9.39178	+	65.3212i	−0.000322783	+	0.00224501i
$947$	1207.92	+	12649.9i	0.0414488	+	0.434071i	0.992249	+	0.124266i	$0.0396577\pi$
$947$	1207.92	+	12649.9i	0.0414488	+	0.434071i	−0.950800	+	0.309805i	$0.899736\pi$
$948$	−4716.33	−	4541.98i	−0.161581	−	0.155608i
$949$	46656.9	+	4455.19i	1.59594	+	0.152394i
$950$	2976.50	−	573.674i	0.101653	−	0.0195920i
$951$	9598.47	+	3898.11i	0.327289	+	0.132918i
$952$	−56.9996	−	234.956i	−0.00194051	−	0.00799891i
$953$	26041.0	−	30052.9i	0.885153	−	1.02152i	−0.114452	−	0.993429i	$-0.536511\pi$
$953$	26041.0	−	30052.9i	0.885153	−	1.02152i	0.999605	−	0.0280924i	$-0.00894326\pi$
$954$	6249.81	−	9515.57i	0.212102	−	0.322933i
$955$	17465.8	+	11224.6i	0.591813	+	0.380335i
$956$	4029.69	−	20908.0i	0.136328	−	0.707336i
$957$	−4186.00	−	1251.75i	−0.141394	−	0.0422815i
$958$	2404.22	−	6005.44i	0.0810822	−	0.202533i
$959$	−920.669	−	4776.88i	−0.0310010	−	0.160848i
$960$	−2296.87	+	1035.18i	−0.0772200	+	0.0348024i
$961$	−21373.9	−	20380.0i	−0.717462	−	0.684099i
$962$	700.709	−	1534.34i	0.0234841	−	0.0514231i
$963$	−5141.28	−	4126.51i	−0.172041	−	0.138084i
$964$	18777.0	+	29217.6i	0.627352	+	0.976179i
$965$	−26236.9	−	45443.6i	−0.875227	−	1.51594i
$966$	3355.03	−	852.039i	0.111746	−	0.0283788i
$967$	−11113.6	+	19249.2i	−0.369584	+	0.640138i	−0.989500	−	0.144529i	$-0.953833\pi$
$967$	−11113.6	+	19249.2i	−0.369584	+	0.640138i	0.619916	+	0.784668i	$0.287166\pi$
$968$	−22254.8	+	1060.13i	−0.738942	+	0.0352002i
$969$	−434.741	+	171.542i	−0.0144127	+	0.00568701i
$970$	22535.3	−	2151.86i	0.745944	−	0.0712290i
$971$	22824.3	−	6701.81i	0.754342	−	0.221495i	0.118118	−	0.993000i	$-0.462314\pi$
$971$	22824.3	−	6701.81i	0.754342	−	0.221495i	0.636223	+	0.771505i	$0.280496\pi$
$972$	19823.4	+	14872.2i	0.654152	+	0.490766i
$973$	−2847.37	+	2467.26i	−0.0938154	+	0.0812915i
$974$	−11595.7	−	14745.1i	−0.381467	−	0.485075i
$975$	31005.6	−	7358.91i	1.01844	−	0.241716i
$976$	−13243.0	+	4583.43i	−0.434320	+	0.150320i
$977$	34705.3	−	17891.8i	1.13646	−	0.585885i	0.215871	−	0.976422i	$-0.430741\pi$
$977$	34705.3	−	17891.8i	1.13646	−	0.585885i	0.920587	+	0.390537i	$0.127710\pi$
$978$	8379.58	−	4267.39i	0.273977	−	0.139526i
$979$	10591.6	+	2041.37i	0.345771	+	0.0666419i
$980$	−28357.7	−	8326.59i	−0.924342	−	0.271411i
$981$	−21435.6	+	52038.2i	−0.697640	+	1.69363i
$982$	−15344.5	−	17708.5i	−0.498640	−	0.575461i
$983$	−29739.7	+	41763.5i	−0.964953	+	1.35509i	−0.0302939	+	0.999541i	$0.509644\pi$
$983$	−29739.7	+	41763.5i	−0.964953	+	1.35509i	−0.934659	+	0.355546i	$0.884295\pi$
$984$	4138.55	+	14358.2i	0.134078	+	0.465167i
$985$	3866.06	−	2753.01i	0.125059	−	0.0890541i
$986$	−278.865	−	219.302i	−0.00900698	−	0.00708317i
$987$	8812.04	+	13862.8i	0.284185	+	0.447070i
$988$	−14774.6	+	8530.14i	−0.475753	+	0.274676i
$989$	668.722	+	372.238i	0.0215006	+	0.0119681i
$990$	36.2662	−	3648.21i	0.00116426	−	0.117119i
$991$	−30283.3	+	19461.9i	−0.970718	+	0.623843i	−0.926944	−	0.375199i	$-0.877575\pi$
$991$	−30283.3	+	19461.9i	−0.970718	+	0.623843i	−0.0437740	+	0.999041i	$0.513938\pi$
$992$	−1063.31	−	2656.01i	−0.0340323	−	0.0850086i
$993$	18761.9	−	13220.2i	0.599587	−	0.422488i
$994$	3499.18	+	848.891i	0.111657	+	0.0270877i
$995$	2727.18	−	28560.3i	0.0868918	−	0.909972i
$996$	−2063.34	−	725.634i	−0.0656421	−	0.0230849i
$997$	30102.5	−	23672.8i	0.956223	−	0.751982i	−0.0125526	−	0.999921i	$-0.503996\pi$
$997$	30102.5	−	23672.8i	0.956223	−	0.751982i	0.968776	+	0.247939i	$0.0797533\pi$
$998$	5239.48	−	17844.0i	0.166185	−	0.565975i
$999$	1635.70	−	1831.78i	0.0518031	−	0.0580131i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.4.o.a.149.30	yes	1400
9.2	odd	6	inner	207.4.o.a.11.30	✓	1400
23.21	odd	22	inner	207.4.o.a.113.30	yes	1400
207.182	even	66	inner	207.4.o.a.182.30	yes	1400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.4.o.a.11.30	✓	1400	9.2	odd	6	inner
207.4.o.a.113.30	yes	1400	23.21	odd	22	inner
207.4.o.a.149.30	yes	1400	1.1	even	1	trivial
207.4.o.a.182.30	yes	1400	207.182	even	66	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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	207.o (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.553250 + 1.07316i) q^{2} +(1.90721 + 4.83348i) q^{3} +(3.79488 + 5.32916i) q^{4} +(3.34944 - 13.8066i) q^{5} +(-6.24225 - 0.627386i) q^{6} +(4.72700 + 1.63603i) q^{7} +(-17.3792 + 2.49875i) q^{8} +(-19.7251 + 18.4370i) q^{9} +(12.9636 + 11.2330i) q^{10} +(-0.374829 + 7.86864i) q^{11} +(-18.5207 + 28.5063i) q^{12} +(26.1038 + 75.4221i) q^{13} +(-4.37093 + 4.16767i) q^{14} +(73.1220 - 10.1427i) q^{15} +(-10.1846 + 29.4264i) q^{16} +(1.14356 + 2.50405i) q^{17} +(-8.87285 - 31.3683i) q^{18} +(29.7207 + 13.5730i) q^{19} +(86.2883 - 34.5446i) q^{20} +(1.10768 + 25.9681i) q^{21} +(-8.23690 - 4.75558i) q^{22} +(-85.6257 + 69.5359i) q^{23} +(-45.2236 - 79.2364i) q^{24} +(-68.2989 - 35.2105i) q^{25} +(-95.3817 - 13.7138i) q^{26} +(-126.735 - 60.1774i) q^{27} +(9.21971 + 31.3995i) q^{28} +(86.9471 + 61.9148i) q^{29} +(-29.5701 + 84.0828i) q^{30} +(14.9164 + 5.97163i) q^{31} +(-122.875 - 128.868i) q^{32} +(-38.7478 + 13.1954i) q^{33} +(-3.31991 - 0.158147i) q^{34} +(38.4208 - 59.7840i) q^{35} +(-173.108 - 35.1520i) q^{36} +(-4.93156 + 16.7953i) q^{37} +(-31.0089 + 24.3857i) q^{38} +(-314.766 + 270.019i) q^{39} +(-23.7114 + 248.317i) q^{40} +(-159.169 - 38.6140i) q^{41} +(-28.4807 - 13.1782i) q^{42} +(-2.57877 - 6.44146i) q^{43} +(-43.3556 + 27.8630i) q^{44} +(188.484 + 334.090i) q^{45} +(-27.2504 - 130.361i) q^{46} +(547.319 - 315.995i) q^{47} +(-161.656 + 6.89552i) q^{48} +(-249.948 - 196.562i) q^{49} +(75.5728 - 53.8151i) q^{50} +(-9.92227 + 10.3032i) q^{51} +(-302.876 + 425.329i) q^{52} +(228.695 + 263.928i) q^{53} +(134.696 - 102.713i) q^{54} +(107.384 + 31.5307i) q^{55} +(-86.2395 - 16.6213i) q^{56} +(-8.92100 + 169.541i) q^{57} +(-114.548 + 59.0535i) q^{58} +(332.169 - 114.965i) q^{59} +(331.541 + 351.189i) q^{60} +(278.194 + 353.752i) q^{61} +(-14.6610 + 12.7038i) q^{62} +(-123.404 + 54.8807i) q^{63} +(-32.7452 + 9.61485i) q^{64} +(1128.76 - 107.783i) q^{65} +(7.27645 - 48.8828i) q^{66} +(-696.728 + 33.1893i) q^{67} +(-9.00481 + 15.5968i) q^{68} +(-499.407 - 281.250i) q^{69} +(42.9012 + 74.3070i) q^{70} +(-322.328 - 501.552i) q^{71} +(296.737 - 369.708i) q^{72} +(243.951 - 534.178i) q^{73} +(-15.2956 - 14.5844i) q^{74} +(39.9287 - 397.275i) q^{75} +(40.4537 + 209.894i) q^{76} +(-14.6451 + 36.5818i) q^{77} +(-115.628 - 487.181i) q^{78} +(-36.4522 + 189.132i) q^{79} +(372.166 + 239.176i) q^{80} +(49.1562 - 727.341i) q^{81} +(129.499 - 149.450i) q^{82} +(15.1688 + 62.5267i) q^{83} +(-134.185 + 104.449i) q^{84} +(38.4027 - 7.40152i) q^{85} +(8.33940 + 0.796316i) q^{86} +(-133.437 + 538.342i) q^{87} +(-13.1475 - 137.687i) q^{88} +(194.868 - 1355.34i) q^{89} +(-462.809 + 17.4374i) q^{90} +399.227i q^{91} +(-695.507 - 192.433i) q^{92} +(-0.414956 + 83.4874i) q^{93} +(36.3072 + 762.183i) q^{94} +(286.944 - 364.879i) q^{95} +(388.531 - 839.694i) q^{96} +(910.726 - 955.142i) q^{97} +(349.225 - 159.486i) q^{98} +(-137.680 - 162.120i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1400 q - 27 q^{2} - 22 q^{3} - 281 q^{4} - 33 q^{5} + 29 q^{6} - 11 q^{7} - 22 q^{9} - 44 q^{10} - 33 q^{11} + 86 q^{12} - 9 q^{13} - 33 q^{14} + 726 q^{15} + 999 q^{16} + 51 q^{18} - 44 q^{19} - 33 q^{20}+ \cdots - 9262 q^{99}+O(q^{100}) \) 1400 * q - 27 * q^2 - 22 * q^3 - 281 * q^4 - 33 * q^5 + 29 * q^6 - 11 * q^7 - 22 * q^9 - 44 * q^10 - 33 * q^11 + 86 * q^12 - 9 * q^13 - 33 * q^14 + 726 * q^15 + 999 * q^16 + 51 * q^18 - 44 * q^19 - 33 * q^20 + 638 * q^21 + 252 * q^23 - 2564 * q^24 + 1397 * q^25 - 178 * q^27 - 44 * q^28 - 135 * q^29 - 1518 * q^30 - 45 * q^31 - 339 * q^32 + 1914 * q^33 - 11 * q^34 - 2137 * q^36 - 44 * q^37 - 33 * q^38 + 374 * q^39 + 979 * q^40 + 441 * q^41 - 22 * q^42 - 11 * q^43 + 516 * q^46 - 1992 * q^47 - 20 * q^48 - 4633 * q^49 - 6231 * q^50 - 22 * q^51 + 178 * q^52 + 2640 * q^54 + 256 * q^55 + 17391 * q^56 + 2090 * q^57 + 320 * q^58 - 2061 * q^59 + 418 * q^60 - 11 * q^61 - 2112 * q^63 + 8546 * q^64 - 12969 * q^65 - 5775 * q^66 - 11 * q^67 - 519 * q^69 - 1582 * q^70 - 4156 * q^72 - 36 * q^73 - 10065 * q^74 - 7876 * q^75 - 11 * q^76 + 1317 * q^77 - 10053 * q^78 - 11 * q^79 + 12442 * q^81 + 698 * q^82 + 14025 * q^83 + 16720 * q^84 + 241 * q^85 - 33 * q^86 + 11672 * q^87 - 1419 * q^88 - 37136 * q^90 + 3141 * q^92 + 1138 * q^93 + 396 * q^94 + 5883 * q^95 + 9218 * q^96 + 6325 * q^97 - 9262 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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