LMFDB - Embedded newform 409.3.p.a.21.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [409,3,Mod(21,409)] 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("409.21"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(409, base_ring=CyclotomicField(408)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 409 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	409.p (of order $408$, degree $128$, 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:	$11.1444428123$
Analytic rank:	$0$
Dimension:	$8576$
Relative dimension:	$67$ over $\Q(\zeta_{408})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{408}]$

Embedding invariants

Embedding label			21.20
Character	$\chi$	$=$	409.21
Dual form			409.3.p.a.39.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.59279 - 1.16475i) q^{2} +(-2.07047 - 1.61421i) q^{3} +(-0.0322475 - 0.101368i) q^{4} +(-2.55276 - 0.477193i) q^{5} +(1.41770 + 4.98268i) q^{6} +(-6.76777 + 5.19309i) q^{7} +(-2.57500 + 7.68276i) q^{8} +(-0.514037 - 2.04380i) q^{9} +(3.51021 + 3.73338i) q^{10} +(1.98127 + 17.0775i) q^{11} +(-0.0968619 + 0.261935i) q^{12} +(10.7557 - 8.51950i) q^{13} +(16.8283 - 0.388802i) q^{14} +(4.51513 + 5.10870i) q^{15} +(12.7026 - 8.99200i) q^{16} +(7.61063 - 11.4856i) q^{17} +(-1.56175 + 3.85408i) q^{18} +(-3.86841 + 3.69369i) q^{19} +(0.0339479 + 0.274156i) q^{20} +(22.3952 + 0.172446i) q^{21} +(16.7352 - 29.5087i) q^{22} +(1.81958 + 8.96709i) q^{23} +(17.7331 - 11.7504i) q^{24} +(-17.0230 - 6.59473i) q^{25} +(-27.0547 + 1.04212i) q^{26} +(-11.7788 + 26.6764i) q^{27} +(0.744657 + 0.518571i) q^{28} +(-5.57007 + 6.81386i) q^{29} +(-1.24133 - 13.3961i) q^{30} +(-33.6298 - 13.9299i) q^{31} +(1.70132 + 0.0262024i) q^{32} +(23.4646 - 38.5568i) q^{33} +(-25.5000 + 9.42975i) q^{34} +(19.7546 - 10.0272i) q^{35} +(-0.190600 + 0.118015i) q^{36} +(12.8392 + 11.8868i) q^{37} +(10.4638 - 1.37758i) q^{38} +(-36.0218 + 0.277373i) q^{39} +(10.2395 - 18.3834i) q^{40} +(48.9415 - 52.0531i) q^{41} +(-35.4701 - 26.3594i) q^{42} +(-25.6237 + 26.8357i) q^{43} +(1.66723 - 0.751545i) q^{44} +(0.336923 + 5.46262i) q^{45} +(7.54615 - 16.4021i) q^{46} +(2.49999 - 11.0090i) q^{47} +(-40.8155 - 1.88701i) q^{48} +(6.15234 - 22.9609i) q^{49} +(19.4329 + 30.3315i) q^{50} +(-34.2978 + 11.4955i) q^{51} +(-1.21045 - 0.815557i) q^{52} +(-5.79916 + 10.0444i) q^{53} +(49.8324 - 28.7708i) q^{54} +(3.09158 - 44.5402i) q^{55} +(-22.4703 - 65.3674i) q^{56} +(13.9719 - 1.40327i) q^{57} +(16.8084 - 4.36536i) q^{58} +(38.6395 - 107.015i) q^{59} +(0.372258 - 0.622433i) q^{60} +(53.0477 - 31.1742i) q^{61} +(37.3406 + 61.3577i) q^{62} +(14.0925 + 11.1625i) q^{63} +(-52.3581 - 39.5390i) q^{64} +(-31.5222 + 16.6157i) q^{65} +(-82.2831 + 34.0828i) q^{66} +(72.8648 - 28.8752i) q^{67} +(-1.40970 - 0.401094i) q^{68} +(10.7074 - 21.5033i) q^{69} +(-43.1440 - 7.03782i) q^{70} +(-50.6266 - 59.0916i) q^{71} +(17.0257 + 1.31357i) q^{72} +(80.4313 + 115.498i) q^{73} +(-6.60515 - 33.8877i) q^{74} +(24.6003 + 41.1329i) q^{75} +(0.499170 + 0.273021i) q^{76} +(-102.094 - 105.288i) q^{77} +(57.6984 + 41.5144i) q^{78} +(21.8713 + 103.681i) q^{79} +(-36.7176 + 16.8928i) q^{80} +(50.7389 - 27.2462i) q^{81} +(-138.582 + 25.9055i) q^{82} +(50.4584 + 101.334i) q^{83} +(-0.704710 - 2.27572i) q^{84} +(-24.9089 + 25.6882i) q^{85} +(72.0699 - 12.8987i) q^{86} +(22.5317 - 5.11665i) q^{87} +(-136.304 - 28.7531i) q^{88} +(128.920 - 117.526i) q^{89} +(5.82592 - 9.09327i) q^{90} +(-28.5498 + 113.514i) q^{91} +(0.850300 - 0.473614i) q^{92} +(47.1438 + 83.1272i) q^{93} +(-16.8046 + 14.6232i) q^{94} +(11.6377 - 7.58312i) q^{95} +(-3.48025 - 2.80055i) q^{96} +(-174.489 - 56.9923i) q^{97} +(-36.5430 + 29.4060i) q^{98} +(33.8847 - 12.8278i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8576 q - 124 q^{2} - 112 q^{3} - 124 q^{4} - 120 q^{5} - 120 q^{6} - 144 q^{7} + 8 q^{8} - 292 q^{9} - 96 q^{10} - 160 q^{11} + 36 q^{12} - 164 q^{13} - 16 q^{14} - 80 q^{15} - 204 q^{16} - 148 q^{17} - 148 q^{18}+ \cdots + 1180 q^{99}+O(q^{100}) $ 8576 * q - 124 * q^2 - 112 * q^3 - 124 * q^4 - 120 * q^5 - 120 * q^6 - 144 * q^7 + 8 * q^8 - 292 * q^9 - 96 * q^10 - 160 * q^11 + 36 * q^12 - 164 * q^13 - 16 * q^14 - 80 * q^15 - 204 * q^16 - 148 * q^17 - 148 * q^18 - 96 * q^19 + 68 * q^20 - 144 * q^21 - 256 * q^22 - 128 * q^23 - 1156 * q^24 - 2496 * q^25 - 280 * q^26 - 100 * q^27 - 92 * q^28 - 80 * q^29 + 672 * q^30 - 168 * q^31 + 2112 * q^32 - 96 * q^33 + 92 * q^34 + 64 * q^35 - 2344 * q^36 - 152 * q^37 - 2972 * q^39 + 112 * q^40 - 196 * q^41 + 488 * q^42 - 452 * q^43 + 92 * q^44 - 244 * q^45 - 124 * q^46 + 16 * q^47 - 188 * q^48 + 16 * q^49 + 96 * q^50 + 8 * q^51 - 828 * q^52 - 256 * q^53 + 240 * q^54 - 1016 * q^55 + 76 * q^56 - 92 * q^57 - 800 * q^58 + 48 * q^59 - 64 * q^60 + 428 * q^61 - 52 * q^62 + 1604 * q^63 - 136 * q^64 + 136 * q^65 + 224 * q^66 + 600 * q^67 - 136 * q^68 + 2808 * q^69 - 20 * q^70 - 188 * q^71 + 560 * q^72 + 144 * q^73 - 996 * q^74 + 1152 * q^75 + 992 * q^76 - 3084 * q^77 - 4900 * q^78 - 560 * q^79 - 292 * q^80 - 3128 * q^81 + 1488 * q^82 + 120 * q^83 + 6560 * q^84 + 288 * q^85 + 3248 * q^86 - 632 * q^87 + 144 * q^88 + 608 * q^89 + 268 * q^90 + 404 * q^91 - 5128 * q^92 - 104 * q^93 - 624 * q^94 + 84 * q^95 + 140 * q^96 - 840 * q^97 - 72 * q^98 + 1180 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/409\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{408}\right)$

Coefficient data

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

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

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

$2$	−1.59279	−	1.16475i	−0.796397	−	0.582373i	0.115255	−	0.993336i	$-0.463232\pi$
$2$	−1.59279	−	1.16475i	−0.796397	−	0.582373i	−0.911652	+	0.410963i	$0.865192\pi$
$3$	−2.07047	−	1.61421i	−0.690158	−	0.538071i	0.207789	−	0.978174i	$-0.433373\pi$
$3$	−2.07047	−	1.61421i	−0.690158	−	0.538071i	−0.897947	+	0.440103i	$0.854942\pi$
$4$	−0.0322475	−	0.101368i	−0.00806188	−	0.0253420i
$5$	−2.55276	−	0.477193i	−0.510551	−	0.0954385i	−0.0778305	−	0.996967i	$-0.524799\pi$
$5$	−2.55276	−	0.477193i	−0.510551	−	0.0954385i	−0.432721	+	0.901528i	$0.642446\pi$
$6$	1.41770	+	4.98268i	0.236283	+	0.830447i
$7$	−6.76777	+	5.19309i	−0.966824	+	0.741870i	−0.966110	−	0.258130i	$-0.916894\pi$
$7$	−6.76777	+	5.19309i	−0.966824	+	0.741870i	−0.000713405		1.00000i	$0.500227\pi$
$8$	−2.57500	+	7.68276i	−0.321875	+	0.960346i
$9$	−0.514037	−	2.04380i	−0.0571152	−	0.227089i
$10$	3.51021	+	3.73338i	0.351021	+	0.373338i
$11$	1.98127	+	17.0775i	0.180115	+	1.55250i	0.709859	+	0.704344i	$0.248759\pi$
$11$	1.98127	+	17.0775i	0.180115	+	1.55250i	−0.529743	+	0.848158i	$0.677712\pi$
$12$	−0.0968619	+	0.261935i	−0.00807183	+	0.0218279i
$13$	10.7557	−	8.51950i	0.827365	−	0.655346i	−0.113722	−	0.993513i	$-0.536277\pi$
$13$	10.7557	−	8.51950i	0.827365	−	0.655346i	0.941086	+	0.338166i	$0.109807\pi$
$14$	16.8283	−	0.388802i	1.20202	−	0.0277715i
$15$	4.51513	+	5.10870i	0.301008	+	0.340580i
$16$	12.7026	−	8.99200i	0.793914	−	0.562000i
$17$	7.61063	−	11.4856i	0.447684	−	0.675623i	−0.538245	−	0.842789i	$-0.680912\pi$
$17$	7.61063	−	11.4856i	0.447684	−	0.675623i	0.985929	+	0.167165i	$0.0534614\pi$
$18$	−1.56175	+	3.85408i	−0.0867641	+	0.214116i
$19$	−3.86841	+	3.69369i	−0.203601	+	0.194405i	−0.785511	−	0.618848i	$-0.787600\pi$
$19$	−3.86841	+	3.69369i	−0.203601	+	0.194405i	0.581910	+	0.813253i	$0.302306\pi$
$20$	0.0339479	+	0.274156i	0.00169740	+	0.0137078i
$21$	22.3952	+	0.172446i	1.06644	+	0.00821173i
$22$	16.7352	−	29.5087i	0.760691	−	1.34130i
$23$	1.81958	+	8.96709i	0.0791122	+	0.389873i	1.00000		4.55133e-5i	$1.44873e-5\pi$
$23$	1.81958	+	8.96709i	0.0791122	+	0.389873i	−0.920888	+	0.389828i	$0.872535\pi$
$24$	17.7331	−	11.7504i	0.738879	−	0.489599i
$25$	−17.0230	−	6.59473i	−0.680918	−	0.263789i
$26$	−27.0547	+	1.04212i	−1.04057	+	0.0400815i
$27$	−11.7788	+	26.6764i	−0.436252	+	0.988016i
$28$	0.744657	+	0.518571i	0.0265949	+	0.0185204i
$29$	−5.57007	+	6.81386i	−0.192071	+	0.234961i	−0.861301	−	0.508095i	$-0.830350\pi$
$29$	−5.57007	+	6.81386i	−0.192071	+	0.234961i	0.669229	+	0.743056i	$0.266624\pi$
$30$	−1.24133	−	13.3961i	−0.0413777	−	0.446536i
$31$	−33.6298	−	13.9299i	−1.08483	−	0.449352i	−0.232631	−	0.972565i	$-0.574733\pi$
$31$	−33.6298	−	13.9299i	−1.08483	−	0.449352i	−0.852202	+	0.523213i	$0.824733\pi$
$32$	1.70132	+	0.0262024i	0.0531664	+	0.000818825i
$33$	23.4646	−	38.5568i	0.711048	−	1.16839i
$34$	−25.5000	+	9.42975i	−0.749999	+	0.277346i
$35$	19.7546	−	10.0272i	0.564416	−	0.286490i
$36$	−0.190600	+	0.118015i	−0.00529445	+	0.00327818i
$37$	12.8392	+	11.8868i	0.347006	+	0.321265i	0.833606	−	0.552360i	$-0.186273\pi$
$37$	12.8392	+	11.8868i	0.347006	+	0.321265i	−0.486599	+	0.873625i	$0.661763\pi$
$38$	10.4638	−	1.37758i	0.275363	−	0.0362522i
$39$	−36.0218	+	0.277373i	−0.923635	+	0.00711212i
$40$	10.2395	−	18.3834i	0.255988	−	0.459586i
$41$	48.9415	−	52.0531i	1.19369	−	1.26959i	0.239331	−	0.970938i	$-0.423072\pi$
$41$	48.9415	−	52.0531i	1.19369	−	1.26959i	0.954363	−	0.298649i	$-0.0965361\pi$
$42$	−35.4701	−	26.3594i	−0.844527	−	0.627605i
$43$	−25.6237	+	26.8357i	−0.595899	+	0.624086i	−0.950422	−	0.310962i	$-0.899349\pi$
$43$	−25.6237	+	26.8357i	−0.595899	+	0.624086i	0.354524	+	0.935047i	$0.384643\pi$
$44$	1.66723	−	0.751545i	0.0378915	−	0.0170806i
$45$	0.336923	+	5.46262i	0.00748718	+	0.121392i
$46$	7.54615	−	16.4021i	0.164047	−	0.356567i
$47$	2.49999	−	11.0090i	0.0531913	−	0.234234i	−0.941518	−	0.336962i	$-0.890600\pi$
$47$	2.49999	−	11.0090i	0.0531913	−	0.234234i	0.994709	+	0.102729i	$0.0327573\pi$
$48$	−40.8155	−	1.88701i	−0.850322	−	0.0393128i
$49$	6.15234	−	22.9609i	0.125558	−	0.468589i
$50$	19.4329	+	30.3315i	0.388658	+	0.606629i
$51$	−34.2978	+	11.4955i	−0.672506	+	0.225401i
$52$	−1.21045	−	0.815557i	−0.0232779	−	0.0156838i
$53$	−5.79916	+	10.0444i	−0.109418	+	0.189518i	−0.915535	−	0.402239i	$-0.868232\pi$
$53$	−5.79916	+	10.0444i	−0.109418	+	0.189518i	0.806117	+	0.591757i	$0.201565\pi$
$54$	49.8324	−	28.7708i	0.922823	−	0.532792i
$55$	3.09158	−	44.5402i	0.0562105	−	0.809822i
$56$	−22.4703	−	65.3674i	−0.401255	−	1.16727i
$57$	13.9719	−	1.40327i	0.245120	−	0.0246188i
$58$	16.8084	−	4.36536i	0.289800	−	0.0752648i
$59$	38.6395	−	107.015i	0.654907	−	1.81381i	0.0780782	−	0.996947i	$-0.475122\pi$
$59$	38.6395	−	107.015i	0.654907	−	1.81381i	0.576828	−	0.816865i	$-0.304290\pi$
$60$	0.372258	−	0.622433i	0.00620430	−	0.0103739i
$61$	53.0477	−	31.1742i	0.869635	−	0.511052i	−0.00267997	−	0.999996i	$-0.500853\pi$
$61$	53.0477	−	31.1742i	0.869635	−	0.511052i	0.872315	+	0.488944i	$0.162618\pi$
$62$	37.3406	+	61.3577i	0.602267	+	0.989640i
$63$	14.0925	+	11.1625i	0.223691	+	0.177183i
$64$	−52.3581	−	39.5390i	−0.818096	−	0.617797i
$65$	−31.5222	+	16.6157i	−0.484957	+	0.255625i
$66$	−82.2831	+	34.0828i	−1.24671	+	0.516405i
$67$	72.8648	−	28.8752i	1.08753	−	0.430973i	0.244950	−	0.969536i	$-0.421229\pi$
$67$	72.8648	−	28.8752i	1.08753	−	0.430973i	0.842585	+	0.538563i	$0.181033\pi$
$68$	−1.40970	−	0.401094i	−0.0207308	−	0.00589843i
$69$	10.7074	−	21.5033i	0.155179	−	0.311642i
$70$	−43.1440	−	7.03782i	−0.616343	−	0.100540i
$71$	−50.6266	−	59.0916i	−0.713050	−	0.832276i	0.278711	−	0.960375i	$-0.410093\pi$
$71$	−50.6266	−	59.0916i	−0.713050	−	0.832276i	−0.991761	+	0.128099i	$0.959112\pi$
$72$	17.0257	+	1.31357i	0.236468	+	0.0182441i
$73$	80.4313	+	115.498i	1.10180	+	1.58216i	0.769102	+	0.639126i	$0.220704\pi$
$73$	80.4313	+	115.498i	1.10180	+	1.58216i	0.332697	+	0.943034i	$0.392041\pi$
$74$	−6.60515	−	33.8877i	−0.0892588	−	0.457942i
$75$	24.6003	+	41.1329i	0.328004	+	0.548438i
$76$	0.499170	+	0.273021i	0.00656802	+	0.00359238i
$77$	−102.094	−	105.288i	−1.32589	−	1.36737i
$78$	57.6984	+	41.5144i	0.739723	+	0.532236i
$79$	21.8713	+	103.681i	0.276852	+	1.31242i	0.864225	+	0.503106i	$0.167809\pi$
$79$	21.8713	+	103.681i	0.276852	+	1.31242i	−0.587373	+	0.809317i	$0.699838\pi$
$80$	−36.7176	+	16.8928i	−0.458970	+	0.211160i
$81$	50.7389	−	27.2462i	0.626406	−	0.336373i
$82$	−138.582	+	25.9055i	−1.69003	+	0.315921i
$83$	50.4584	+	101.334i	0.607933	+	1.22089i	0.958697	+	0.284430i	$0.0918042\pi$
$83$	50.4584	+	101.334i	0.607933	+	1.22089i	−0.350764	+	0.936464i	$0.614078\pi$
$84$	−0.704710	−	2.27572i	−0.00838941	−	0.0270920i
$85$	−24.9089	+	25.6882i	−0.293046	+	0.302214i
$86$	72.0699	−	12.8987i	0.838023	−	0.149985i
$87$	22.5317	−	5.11665i	0.258985	−	0.0588120i
$88$	−136.304	−	28.7531i	−1.54891	−	0.326739i
$89$	128.920	−	117.526i	1.44854	−	1.32051i	0.590380	−	0.807125i	$-0.298978\pi$
$89$	128.920	−	117.526i	1.44854	−	1.32051i	0.858156	−	0.513389i	$-0.171610\pi$
$90$	5.82592	−	9.09327i	0.0647324	−	0.101036i
$91$	−28.5498	+	113.514i	−0.313734	+	1.24740i
$92$	0.850300	−	0.473614i	0.00924239	−	0.00514798i
$93$	47.1438	+	83.1272i	0.506923	+	0.893841i
$94$	−16.8046	+	14.6232i	−0.178773	+	0.155566i
$95$	11.6377	−	7.58312i	0.122502	−	0.0798223i
$96$	−3.48025	−	2.80055i	−0.0362526	−	0.0291724i
$97$	−174.489	−	56.9923i	−1.79886	−	0.587549i	−0.798955	−	0.601391i	$-0.794614\pi$
$97$	−174.489	−	56.9923i	−1.79886	−	0.587549i	−0.999904	+	0.0138417i	$0.995594\pi$
$98$	−36.5430	+	29.4060i	−0.372887	+	0.300061i
$99$	33.8847	−	12.8278i	0.342269	−	0.129574i
$100$	−0.119547	+	1.93825i	−0.00119547	+	0.0193825i
$101$	90.8820	+	48.8026i	0.899822	+	0.483194i	0.856664	−	0.515874i	$-0.172533\pi$
$101$	90.8820	+	48.8026i	0.899822	+	0.483194i	0.0431574	+	0.999068i	$0.486258\pi$
$102$	68.0187	+	21.6383i	0.666850	+	0.212140i
$103$	144.413	−	98.9255i	1.40207	−	0.960442i	0.403098	−	0.915157i	$-0.367933\pi$
$103$	144.413	−	98.9255i	1.40207	−	0.960442i	0.998974	−	0.0452847i	$-0.0144195\pi$
$104$	37.7573	+	104.572i	0.363051	+	1.00550i
$105$	−57.0873	−	11.1271i	−0.543688	−	0.105972i
$106$	20.9361	−	9.24419i	0.197510	−	0.0872093i
$107$	25.9525	+	53.1412i	0.242546	+	0.496647i	0.984848	−	0.173419i	$-0.0554816\pi$
$107$	25.9525	+	53.1412i	0.242546	+	0.496647i	−0.742302	+	0.670066i	$0.766266\pi$
$108$	3.08398	+	0.333746i	0.0285553	+	0.00309024i
$109$	−21.7564	−	19.2285i	−0.199600	−	0.176408i	0.556535	−	0.830824i	$-0.312130\pi$
$109$	−21.7564	−	19.2285i	−0.199600	−	0.176408i	−0.756135	+	0.654416i	$0.772915\pi$
$110$	−56.8022	+	67.3425i	−0.516384	+	0.612204i
$111$	−7.39548	−	45.3366i	−0.0666259	−	0.408438i
$112$	−39.2721	+	126.822i	−0.350644	+	1.13234i
$113$	13.7812	+	25.1964i	0.121957	+	0.222977i	0.931209	−	0.364485i	$-0.118755\pi$
$113$	13.7812	+	25.1964i	0.121957	+	0.222977i	−0.809252	+	0.587461i	$0.800127\pi$
$114$	−23.8887	−	14.0385i	−0.209550	−	0.123145i
$115$	−0.365918	−	23.7591i	−0.00318189	−	0.206601i
$116$	0.870329	+	0.344898i	0.00750284	+	0.00297326i
$117$	−22.9410	−	17.6033i	−0.196077	−	0.150455i
$118$	−186.190	+	125.448i	−1.57788	+	1.06312i
$119$	8.13875	+	117.255i	0.0683929	+	0.985332i
$120$	−50.8754	+	21.5337i	−0.423962	+	0.179448i
$121$	−169.930	+	39.9673i	−1.40438	+	0.330308i
$122$	−120.804	−	12.1330i	−0.990198	−	0.0994510i
$123$	−185.357	+	28.7727i	−1.50697	+	0.233924i
$124$	−0.327572	+	3.85820i	−0.00264171	+	0.0311145i
$125$	95.5083	+	59.1362i	0.764066	+	0.473090i
$126$	−9.44500	−	34.1938i	−0.0749603	−	0.271380i
$127$	−5.22213	−	96.7919i	−0.0411191	−	0.762141i	−0.943535	−	0.331274i	$-0.892522\pi$
$127$	−5.22213	−	96.7919i	−0.0411191	−	0.762141i	0.902416	−	0.430867i	$-0.141792\pi$
$128$	35.3797	+	117.445i	0.276404	+	0.917536i
$129$	96.3716	−	14.2006i	0.747067	−	0.110082i
$130$	69.5614	+	10.2500i	0.535088	+	0.0788465i
$131$	25.5330	+	7.69171i	0.194908	+	0.0587153i	0.384398	−	0.923167i	$-0.374409\pi$
$131$	25.5330	+	7.69171i	0.194908	+	0.0587153i	−0.189490	+	0.981883i	$0.560683\pi$
$132$	−4.66510	−	1.13520i	−0.0353417	−	0.00860000i
$133$	6.99881	−	45.0871i	0.0526226	−	0.339000i
$134$	−149.691	−	38.8767i	−1.11710	−	0.290125i
$135$	42.7982	−	62.4776i	0.317024	−	0.462797i
$136$	68.6437	+	88.0462i	0.504733	+	0.647398i
$137$	148.686	−	4.58096i	1.08530	−	0.0334376i	0.516787	−	0.856114i	$-0.327128\pi$
$137$	148.686	−	4.58096i	1.08530	−	0.0334376i	0.568510	+	0.822676i	$0.307520\pi$
$138$	−42.1005	+	21.7790i	−0.305076	+	0.157819i
$139$	64.6912	+	183.580i	0.465405	+	1.32072i	0.906099	+	0.423065i	$0.139046\pi$
$139$	64.6912	+	183.580i	0.465405	+	1.32072i	−0.440695	+	0.897657i	$0.645268\pi$
$140$	−1.65347	−	1.67913i	−0.0118105	−	0.0119938i
$141$	−22.9470	+	18.7583i	−0.162745	+	0.133038i
$142$	11.8111	+	153.088i	0.0831766	+	1.07808i
$143$	166.802	+	166.802i	1.16645	+	1.16645i
$144$	−24.9075	−	21.3394i	−0.172969	−	0.148191i
$145$	17.4706	−	14.7361i	0.120487	−	0.101628i
$146$	6.41475	−	277.646i	0.0439366	−	1.90169i
$147$	−49.8019	+	37.6087i	−0.338789	+	0.255841i
$148$	0.790910	−	1.68481i	0.00534399	−	0.0113838i
$149$	131.720	−	133.765i	0.884029	−	0.897749i	−0.111349	−	0.993781i	$-0.535517\pi$
$149$	131.720	−	133.765i	0.884029	−	0.897749i	0.995378	+	0.0960322i	$0.0306152\pi$
$150$	8.72607	−	94.1693i	0.0581738	−	0.627795i
$151$	−36.5501	+	69.3407i	−0.242054	+	0.459210i	−0.975339	−	0.220711i	$-0.929162\pi$
$151$	−36.5501	+	69.3407i	−0.242054	+	0.459210i	0.733286	+	0.679921i	$0.237986\pi$
$152$	−18.4166	−	39.2314i	−0.121162	−	0.258101i
$153$	−27.3864	−	9.65061i	−0.178996	−	0.0630759i
$154$	39.9811	+	286.615i	0.259618	+	1.86114i
$155$	79.2014	+	51.6076i	0.510977	+	0.332952i
$156$	1.18973	+	3.64252i	0.00762647	+	0.0233495i
$157$	26.2541	+	9.93909i	0.167224	+	0.0633063i	0.436245	−	0.899828i	$-0.356308\pi$
$157$	26.2541	+	9.93909i	0.167224	+	0.0633063i	−0.269021	+	0.963134i	$0.586700\pi$
$158$	85.9258	−	190.618i	0.543834	−	1.20644i
$159$	28.2209	−	11.4357i	0.177490	−	0.0719226i
$160$	−4.33056	−	0.878748i	−0.0270660	−	0.00549218i
$161$	−58.8814	−	51.2379i	−0.365723	−	0.318248i
$162$	−112.551	−	15.7003i	−0.694762	−	0.0969152i
$163$	39.3573	−	76.0808i	0.241456	−	0.466753i	−0.736257	−	0.676702i	$-0.763408\pi$
$163$	39.3573	−	76.0808i	0.241456	−	0.466753i	0.977712	+	0.209949i	$0.0673299\pi$
$164$	−6.85476	−	3.28252i	−0.0417973	−	0.0200154i
$165$	−78.2983	+	87.2289i	−0.474535	+	0.528660i
$166$	37.6586	−	220.176i	0.226859	−	1.32636i
$167$	−38.1108	+	90.0403i	−0.228208	+	0.539164i	−0.994668	−	0.103129i	$-0.967115\pi$
$167$	−38.1108	+	90.0403i	−0.228208	+	0.539164i	0.766460	+	0.642293i	$0.222017\pi$
$168$	−58.9927	+	171.613i	−0.351147	+	1.02151i
$169$	4.41141	−	18.7562i	0.0261030	−	0.110983i
$170$	69.5950	−	11.9034i	0.409382	−	0.0700203i
$171$	9.53769	+	6.00757i	0.0557760	+	0.0351320i
$172$	3.54658	+	1.73204i	0.0206197	+	0.0100700i
$173$	−12.1081	+	314.342i	−0.0699891	+	1.81701i	0.381108	+	0.924531i	$0.375543\pi$
$173$	−12.1081	+	314.342i	−0.0699891	+	1.81701i	−0.451097	+	0.892475i	$0.648967\pi$
$174$	−41.8480	−	18.0939i	−0.240506	−	0.103988i
$175$	149.454	−	43.7702i	0.854025	−	0.250115i
$176$	178.728	+	199.114i	1.01550	+	1.13133i
$177$	−252.747	+	159.199i	−1.42795	+	0.899432i
$178$	−342.230	+	37.0359i	−1.92264	+	0.208067i
$179$	−39.6107	−	28.0398i	−0.221289	−	0.156647i	0.461796	−	0.886986i	$-0.347205\pi$
$179$	−39.6107	−	28.0398i	−0.221289	−	0.156647i	−0.683085	+	0.730339i	$0.739362\pi$
$180$	0.542871	−	0.210309i	0.00301595	−	0.00116839i
$181$	−140.425	+	60.7160i	−0.775829	+	0.335447i	−0.747596	−	0.664154i	$-0.768792\pi$
$181$	−140.425	+	60.7160i	−0.775829	+	0.335447i	−0.0282329	+	0.999601i	$0.508988\pi$
$182$	177.688	−	147.551i	0.976309	−	0.810717i
$183$	−160.156	−	21.0849i	−0.875168	−	0.115218i
$184$	−73.5774	−	9.11086i	−0.399877	−	0.0495156i
$185$	−27.1031	−	36.4709i	−0.146503	−	0.197140i
$186$	21.7316	−	187.315i	0.116836	−	1.00707i
$187$	211.224	+	107.215i	1.12954	+	0.573341i
$188$	−1.19658	+	0.101593i	−0.00636478	+	0.000540389i
$189$	−58.8169	−	241.708i	−0.311201	−	1.27888i
$190$	−27.3689	−	1.47661i	−0.144047	−	0.00777163i
$191$	173.049	−	37.8983i	0.906015	−	0.198420i	0.263469	−	0.964668i	$-0.415133\pi$
$191$	173.049	−	37.8983i	0.906015	−	0.198420i	0.642546	+	0.766247i	$0.277878\pi$
$192$	44.5818	+	166.382i	0.232197	+	0.866571i
$193$	−181.331	+	198.911i	−0.939541	+	1.03063i	0.0599328	+	0.998202i	$0.480911\pi$
$193$	−181.331	+	198.911i	−0.939541	+	1.03063i	−0.999474	+	0.0324254i	$0.989677\pi$
$194$	211.544	+	294.013i	1.09043	+	1.51553i
$195$	92.0872	+	16.4813i	0.472242	+	0.0845193i
$196$	−2.52590	+	0.116779i	−0.0128872	+	0.000595812i
$197$	24.6228	−	112.431i	0.124989	−	0.570717i	−0.871745	−	0.489960i	$-0.837011\pi$
$197$	24.6228	−	112.431i	0.124989	−	0.570717i	0.996734	−	0.0807571i	$-0.0257338\pi$
$198$	−68.9124	−	19.0349i	−0.348042	−	0.0961360i
$199$	177.998	−	164.794i	0.894461	−	0.828109i	−0.0913761	−	0.995816i	$-0.529127\pi$
$199$	177.998	−	164.794i	0.894461	−	0.828109i	0.985837	+	0.167707i	$0.0536364\pi$
$200$	94.4999	−	113.802i	0.472500	−	0.569010i
$201$	−197.475	−	57.8339i	−0.982465	−	0.287731i
$202$	−87.9138	−	183.587i	−0.435217	−	0.908846i
$203$	2.31197	−	75.0405i	0.0113890	−	0.369658i
$204$	2.27129	+	3.10600i	0.0111338	+	0.0152255i
$205$	−149.775	+	109.524i	−0.730610	+	0.534265i
$206$	−345.244	−	10.6369i	−1.67594	−	0.0516352i
$207$	17.3916	−	8.32828i	0.0840175	−	0.0402332i
$208$	60.0188	−	204.936i	0.288552	−	0.985268i
$209$	−70.7435	−	58.7447i	−0.338486	−	0.281075i
$210$	77.9681	+	84.2152i	0.371277	+	0.401025i
$211$	15.1959	−	55.0140i	0.0720186	−	0.260730i	−0.919039	−	0.394168i	$-0.871033\pi$
$211$	15.1959	−	55.0140i	0.0720186	−	0.260730i	0.991057	+	0.133438i	$0.0426016\pi$
$212$	1.20520	+	0.263942i	0.00568488	+	0.00124501i
$213$	9.43471	+	204.070i	0.0442944	+	0.958073i
$214$	20.5590	−	114.871i	0.0960701	−	0.536780i
$215$	78.2167	−	56.2775i	0.363799	−	0.261756i
$216$	−174.618	−	159.186i	−0.808418	−	0.736970i
$217$	299.938	−	80.3682i	1.38220	−	0.370360i
$218$	12.2571	+	55.9676i	0.0562252	+	0.256732i
$219$	19.9066	−	368.968i	0.0908978	−	1.68479i
$220$	−4.61465	+	1.12292i	−0.0209757	+	0.00510420i
$221$	−15.9936	−	188.375i	−0.0723692	−	0.852375i
$222$	−41.0261	+	80.8257i	−0.184802	+	0.364080i
$223$	−165.977	−	19.2560i	−0.744292	−	0.0863498i	−0.265296	−	0.964167i	$-0.585470\pi$
$223$	−165.977	−	19.2560i	−0.744292	−	0.0863498i	−0.478996	+	0.877817i	$0.658999\pi$
$224$	−11.6502	+	8.65780i	−0.0520100	+	0.0386509i
$225$	−4.72790	+	38.1815i	−0.0210129	+	0.169696i
$226$	7.39679	−	56.1842i	0.0327292	−	0.248603i
$227$	−140.154	−	168.781i	−0.617420	−	0.743530i	0.364837	−	0.931071i	$-0.381125\pi$
$227$	−140.154	−	168.781i	−0.617420	−	0.743530i	−0.982257	+	0.187541i	$0.939948\pi$
$228$	−0.592804	−	1.37105i	−0.00260002	−	0.00601337i
$229$	−144.272	−	372.409i	−0.630009	−	1.62624i	−0.771447	−	0.636294i	$-0.780467\pi$
$229$	−144.272	−	372.409i	−0.630009	−	1.62624i	0.141438	−	0.989947i	$-0.454828\pi$
$230$	−27.0904	+	38.2695i	−0.117784	+	0.166389i
$231$	41.4260	+	382.797i	0.179333	+	1.65713i
$232$	−38.0063	−	60.3393i	−0.163820	−	0.260083i
$233$	−81.8577	+	73.4771i	−0.351321	+	0.315352i	−0.824770	−	0.565469i	$-0.808695\pi$
$233$	−81.8577	+	73.4771i	−0.351321	+	0.315352i	0.473449	+	0.880821i	$0.343009\pi$
$234$	16.0370	+	54.7589i	0.0685343	+	0.234012i
$235$	−11.6353	+	26.9103i	−0.0495118	+	0.114512i
$236$	−12.0939	−	0.465846i	−0.0512455	−	0.00197392i
$237$	122.080	−	249.975i	0.515104	−	1.05474i
$238$	123.608	−	196.242i	0.519363	−	0.824546i
$239$	53.8180	+	314.654i	0.225180	+	1.31654i	0.846249	+	0.532788i	$0.178856\pi$
$239$	53.8180	+	314.654i	0.225180	+	1.31654i	−0.621069	+	0.783756i	$0.713301\pi$
$240$	103.291	+	24.2939i	0.430381	+	0.101225i
$241$	61.7972	+	21.2430i	0.256420	+	0.0881453i	0.450291	−	0.892882i	$-0.351320\pi$
$241$	61.7972	+	21.2430i	0.256420	+	0.0881453i	−0.193871	+	0.981027i	$0.562104\pi$
$242$	317.216	+	134.266i	1.31081	+	0.554818i
$243$	109.659	+	18.7559i	0.451271	+	0.0771849i
$244$	−4.87073	−	4.37206i	−0.0199620	−	0.0179183i
$245$	−26.6622	+	55.6776i	−0.108825	+	0.227255i
$246$	328.748	+	170.064i	1.33637	+	0.691319i
$247$	−10.1392	+	72.6854i	−0.0410493	+	0.294273i
$248$	193.617	−	222.500i	0.780715	−	0.897179i
$249$	59.1019	−	291.260i	0.237357	−	1.16972i
$250$	−83.2464	−	205.435i	−0.332986	−	0.821739i
$251$	−46.4638	−	20.9448i	−0.185115	−	0.0834453i	0.316272	−	0.948669i	$-0.397569\pi$
$251$	−46.4638	−	20.9448i	−0.185115	−	0.0834453i	−0.501387	+	0.865223i	$0.667177\pi$
$252$	0.677076	−	1.78850i	0.00268681	−	0.00709722i
$253$	−149.531	+	48.8401i	−0.591030	+	0.193044i
$254$	−104.420	+	160.252i	−0.411103	+	0.630913i
$255$	93.0395	−	12.9785i	0.364861	−	0.0508959i
$256$	−6.78310	+	19.2490i	−0.0264965	+	0.0751916i
$257$	317.986	−	149.274i	1.23730	−	0.580832i	0.308431	−	0.951247i	$-0.400196\pi$
$257$	317.986	−	149.274i	1.23730	−	0.580832i	0.928867	+	0.370414i	$0.120784\pi$
$258$	−170.040	−	89.6297i	−0.659071	−	0.347402i
$259$	−148.622	−	13.7719i	−0.573831	−	0.0531732i
$260$	2.70081	+	2.65954i	0.0103877	+	0.0102290i
$261$	16.7894	+	7.88156i	0.0643272	+	0.0301975i
$262$	−31.7099	−	41.9908i	−0.121030	−	0.160270i
$263$	390.085	+	9.01254i	1.48321	+	0.0342682i	0.757096	−	0.653304i	$-0.226618\pi$
$263$	390.085	+	9.01254i	1.48321	+	0.0342682i	0.726116	+	0.687572i	$0.241324\pi$
$264$	235.801	+	279.557i	0.893186	+	1.05893i
$265$	19.5970	−	22.8737i	0.0739509	−	0.0863158i
$266$	−63.6626	+	63.6626i	−0.239333	+	0.239333i
$267$	−456.637	+	35.2306i	−1.71025	+	0.131950i
$268$	−5.27674	−	6.45502i	−0.0196893	−	0.0240859i
$269$	89.4419	−	88.0750i	0.332498	−	0.327416i	−0.516027	−	0.856572i	$-0.672589\pi$
$269$	89.4419	−	88.0750i	0.332498	−	0.327416i	0.848524	+	0.529156i	$0.177491\pi$
$270$	−140.939	+	49.6651i	−0.521997	+	0.183945i
$271$	−17.3501	−	33.5391i	−0.0640225	−	0.123761i	0.854024	−	0.520234i	$-0.174155\pi$
$271$	−17.3501	−	33.5391i	−0.0640225	−	0.123761i	−0.918046	+	0.396474i	$0.870234\pi$
$272$	−6.60350	−	214.332i	−0.0242776	−	0.787986i
$273$	242.347	−	188.941i	0.887716	−	0.692093i
$274$	−242.161	−	165.884i	−0.883801	−	0.605418i
$275$	78.8946	−	303.776i	0.286889	−	1.10464i
$276$	−2.52504	−	0.391958i	−0.00914869	−	0.00142014i
$277$	−20.9776	+	86.2074i	−0.0757314	+	0.311218i	−0.996971	−	0.0777783i	$-0.975217\pi$
$277$	−20.9776	+	86.2074i	−0.0757314	+	0.311218i	0.921239	+	0.388996i	$0.127178\pi$
$278$	110.785	−	367.755i	0.398506	−	1.32286i
$279$	−11.1831	+	75.8932i	−0.0400826	+	0.272019i
$280$	26.1683	+	177.590i	0.0934581	+	0.634248i
$281$	332.440	−	100.146i	1.18306	−	0.356392i	0.364715	−	0.931119i	$-0.381166\pi$
$281$	332.440	−	100.146i	1.18306	−	0.356392i	0.818345	+	0.574728i	$0.194892\pi$
$282$	58.3985	−	3.15072i	0.207087	−	0.0111728i
$283$	153.595	−	42.4260i	0.542740	−	0.149915i	0.0158904	−	0.999874i	$-0.494942\pi$
$283$	153.595	−	42.4260i	0.542740	−	0.149915i	0.526850	+	0.849959i	$0.323373\pi$
$284$	−4.35742	+	7.03748i	−0.0153430	+	0.0247798i
$285$	−36.3363	−	3.08506i	−0.127496	−	0.0108248i
$286$	−71.3995	−	459.963i	−0.249649	−	1.60826i
$287$	−60.9081	+	606.440i	−0.212223	+	2.11303i
$288$	−0.820992	−	3.49064i	−0.00285067	−	0.0121203i
$289$	38.6509	+	91.3164i	0.133740	+	0.315974i
$290$	−44.9908	+	3.12286i	−0.155141	+	0.0107685i
$291$	269.278	+	399.664i	0.925355	+	1.37342i
$292$	9.11407	−	11.8777i	0.0312126	−	0.0406770i
$293$	−81.0788	+	204.598i	−0.276720	+	0.698285i	0.723251	+	0.690585i	$0.242647\pi$
$293$	−81.0788	+	204.598i	−0.276720	+	0.698285i	−0.999970	+	0.00769991i	$0.997549\pi$
$294$	123.129	−	1.89633i	0.418805	−	0.00645010i
$295$	−149.704	+	254.745i	−0.507471	+	0.863541i
$296$	−124.385	+	68.0322i	−0.420218	+	0.229839i
$297$	−478.904	−	148.299i	−1.61247	−	0.499325i
$298$	−365.605	+	59.6389i	−1.22686	+	0.200131i
$299$	95.9661	+	80.9457i	0.320957	+	0.270722i
$300$	3.37626	−	3.82012i	0.0112542	−	0.0127337i
$301$	34.0548	−	314.684i	0.113139	−	1.04546i
$302$	138.981	−	67.8739i	0.460202	−	0.224748i
$303$	−109.391	−	247.747i	−0.361027	−	0.817648i
$304$	−15.9253	+	81.7044i	−0.0523857	+	0.268764i
$305$	−150.294	+	54.2661i	−0.492767	+	0.177922i
$306$	32.3805	+	47.2697i	0.105819	+	0.154476i
$307$	15.9870	−	50.2542i	0.0520750	−	0.163695i	−0.923383	−	0.383880i	$-0.874588\pi$
$307$	15.9870	−	50.2542i	0.0520750	−	0.163695i	0.975458	+	0.220185i	$0.0706662\pi$
$308$	−7.38055	+	13.7443i	−0.0239628	+	0.0446245i
$309$	−458.691	−	28.2911i	−1.48444	−	0.0915569i
$310$	−66.0419	−	174.450i	−0.213038	−	0.562741i
$311$	−133.033	−	165.321i	−0.427759	−	0.531578i	0.518461	−	0.855101i	$-0.326505\pi$
$311$	−133.033	−	165.321i	−0.427759	−	0.531578i	−0.946220	+	0.323524i	$0.895132\pi$
$312$	90.6252	−	277.461i	0.290465	−	0.889298i
$313$	17.3511	−	21.5622i	0.0554347	−	0.0688889i	−0.750601	−	0.660755i	$-0.770236\pi$
$313$	17.3511	−	21.5622i	0.0554347	−	0.0688889i	0.806036	+	0.591866i	$0.201609\pi$
$314$	−30.2409	−	46.4103i	−0.0963087	−	0.147804i
$315$	−30.6481	−	35.2201i	−0.0972956	−	0.111810i
$316$	9.80469	−	5.56052i	0.0310275	−	0.0175966i
$317$	−27.4881	−	49.3506i	−0.0867133	−	0.155680i	0.826791	−	0.562509i	$-0.190164\pi$
$317$	−27.4881	−	49.3506i	−0.0867133	−	0.155680i	−0.913504	+	0.406829i	$0.866634\pi$
$318$	−58.2697	−	14.6554i	−0.183238	−	0.0460862i
$319$	−127.400	−	81.6230i	−0.399372	−	0.255871i
$320$	114.790	+	125.918i	0.358718	+	0.393495i
$321$	32.0472	−	151.920i	0.0998355	−	0.473272i
$322$	34.1068	+	150.193i	0.105922	+	0.466439i
$323$	12.9832	+	72.5423i	0.0401958	+	0.224589i
$324$	−4.39810	−	4.26468i	−0.0135744	−	0.0131626i
$325$	−239.278	+	74.0959i	−0.736241	+	0.227988i
$326$	−151.303	+	75.3398i	−0.464119	+	0.231104i
$327$	14.0071	+	74.9315i	0.0428352	+	0.229148i
$328$	273.887	+	510.043i	0.835022	+	1.55501i
$329$	40.2513	+	87.4889i	0.122344	+	0.265924i
$330$	226.313	−	47.7401i	0.685796	−	0.144667i
$331$	204.275	−	283.909i	0.617145	−	0.857732i	−0.380608	−	0.924737i	$-0.624285\pi$
$331$	204.275	−	283.909i	0.617145	−	0.857732i	0.997753	+	0.0670041i	$0.0213441\pi$
$332$	8.64490	−	8.38265i	0.0260388	−	0.0252489i
$333$	17.6945	−	32.3511i	0.0531365	−	0.0971505i
$334$	165.577	−	99.0264i	0.495739	−	0.296486i
$335$	−199.785	+	38.9407i	−0.596374	+	0.116241i
$336$	286.029	−	199.187i	0.851277	−	0.592820i
$337$	−37.0573	+	480.313i	−0.109962	+	1.42526i	0.642328	+	0.766430i	$0.277969\pi$
$337$	−37.0573	+	480.313i	−0.109962	+	1.42526i	−0.752290	+	0.658832i	$0.771051\pi$
$338$	−28.8726	+	24.7365i	−0.0854220	+	0.0731850i
$339$	12.1387	−	74.4142i	0.0358075	−	0.219511i
$340$	3.40721	+	1.69659i	0.0100212	+	0.00498997i
$341$	171.259	−	601.913i	0.502226	−	1.76514i
$342$	−8.19429	−	20.6778i	−0.0239599	−	0.0604614i
$343$	−82.3610	−	198.837i	−0.240119	−	0.579700i
$344$	−140.191	−	265.962i	−0.407533	−	0.773147i
$345$	−37.5945	+	49.7832i	−0.108970	+	0.144299i
$346$	385.414	−	486.579i	1.11391	−	1.40630i
$347$	70.6189	−	42.9767i	0.203513	−	0.123852i	−0.414412	−	0.910089i	$-0.636013\pi$
$347$	70.6189	−	42.9767i	0.203513	−	0.123852i	0.617925	+	0.786237i	$0.287974\pi$
$348$	−1.24526	−	2.11900i	−0.00357832	−	0.00608907i
$349$	292.005	+	174.639i	0.836690	+	0.500399i	0.866512	−	0.499156i	$-0.166357\pi$
$349$	292.005	+	174.639i	0.836690	+	0.500399i	−0.0298217	+	0.999555i	$0.509494\pi$
$350$	−289.031	−	104.359i	−0.825804	−	0.298170i
$351$	100.580	+	387.274i	0.286553	+	1.10335i
$352$	2.92331	+	29.1063i	0.00830485	+	0.0826884i
$353$	−315.883	+	108.586i	−0.894852	+	0.307608i	−0.733823	−	0.679341i	$-0.762266\pi$
$353$	−315.883	+	108.586i	−0.894852	+	0.307608i	−0.161029	+	0.986950i	$0.551481\pi$
$354$	588.001	+	40.8137i	1.66102	+	0.115293i
$355$	101.039	+	175.005i	0.284617	+	0.492972i
$356$	−16.0707	−	9.27843i	−0.0451425	−	0.0260630i
$357$	172.423	−	255.910i	0.482976	−	0.716835i
$358$	30.4324	+	90.7980i	0.0850067	+	0.253626i
$359$	343.487	−	220.067i	0.956788	−	0.612999i	0.0344593	−	0.999406i	$-0.489029\pi$
$359$	343.487	−	220.067i	0.956788	−	0.612999i	0.922328	+	0.386407i	$0.126284\pi$
$360$	−42.8356	−	11.4778i	−0.118988	−	0.0318827i
$361$	−15.3510	+	332.037i	−0.0425236	+	0.919771i
$362$	294.387	+	66.8513i	0.813223	+	0.184672i
$363$	416.352	+	191.552i	1.14698	+	0.527692i
$364$	12.4273	−	0.766491i	0.0341410	−	0.00210574i
$365$	−150.207	−	333.219i	−0.411526	−	0.912927i
$366$	230.537	+	220.125i	0.629882	+	0.601433i
$367$	−306.355	+	412.242i	−0.834754	+	1.12327i	0.156020	+	0.987754i	$0.450133\pi$
$367$	−306.355	+	412.242i	−0.834754	+	1.12327i	−0.990775	+	0.135521i	$0.956729\pi$
$368$	103.746	+	97.5439i	0.281917	+	0.265065i
$369$	−131.544	−	73.2695i	−0.356488	−	0.198562i
$370$	0.690386	+	89.6589i	0.00186591	+	0.242321i
$371$	−12.9143	−	98.0940i	−0.0348095	−	0.264404i
$372$	6.90618	−	7.45953i	0.0185650	−	0.0200525i
$373$	−88.2014	−	142.450i	−0.236465	−	0.381904i	0.710264	−	0.703935i	$-0.248576\pi$
$373$	−88.2014	−	142.450i	−0.236465	−	0.381904i	−0.946729	+	0.322031i	$0.895634\pi$
$374$	−211.559	−	416.793i	−0.565666	−	1.11442i
$375$	−102.289	−	276.611i	−0.272771	−	0.737628i
$376$	78.1420	+	47.5550i	0.207824	+	0.126476i
$377$	−1.85958	+	120.742i	−0.00493256	+	0.320272i
$378$	−187.845	+	453.498i	−0.496945	+	1.19973i
$379$	−384.403	+	35.6202i	−1.01426	+	0.0939848i	−0.586534	−	0.809925i	$-0.699508\pi$
$379$	−384.403	+	35.6202i	−1.01426	+	0.0939848i	−0.427723	+	0.903910i	$0.640684\pi$
$380$	−1.14397	−	0.935156i	−0.00301046	−	0.00246094i
$381$	−145.430	+	208.835i	−0.381707	+	0.548123i
$382$	−319.773	−	141.194i	−0.837103	−	0.369617i
$383$	15.5495	+	403.684i	0.0405992	+	1.05401i	0.869291	+	0.494301i	$0.164576\pi$
$383$	15.5495	+	403.684i	0.0405992	+	1.05401i	−0.828692	+	0.559705i	$0.810914\pi$
$384$	116.328	−	300.276i	0.302937	−	0.781970i
$385$	210.378	+	317.492i	0.546437	+	0.824656i
$386$	520.505	−	105.620i	1.34846	−	0.273626i
$387$	68.0184	+	38.5752i	0.175758	+	0.0996775i
$388$	−0.150349	+	19.5255i	−0.000387498	+	0.0503235i
$389$	−379.628	+	47.0081i	−0.975907	+	0.120843i	−0.594962	−	0.803754i	$-0.702833\pi$
$389$	−379.628	+	47.0081i	−0.975907	+	0.120843i	−0.380945	+	0.924598i	$0.624401\pi$
$390$	−127.479	−	133.509i	−0.326870	−	0.342332i
$391$	116.840	+	47.3462i	0.298825	+	0.121090i
$392$	160.561	+	106.391i	0.409593	+	0.271406i
$393$	−40.4494	−	57.1412i	−0.102925	−	0.145397i
$394$	−170.173	+	150.401i	−0.431911	+	0.381728i
$395$	−6.35616	−	275.110i	−0.0160915	−	0.696481i
$396$	−2.39303	−	3.02116i	−0.00604300	−	0.00762919i
$397$	226.379	+	83.7137i	0.570224	+	0.210866i	0.615538	−	0.788107i	$-0.288939\pi$
$397$	226.379	+	83.7137i	0.570224	+	0.210866i	−0.0453142	+	0.998973i	$0.514429\pi$
$398$	−475.456	+	55.1606i	−1.19461	+	0.138594i
$399$	−87.2709	+	82.0541i	−0.218724	+	0.205649i
$400$	−275.536	+	69.3001i	−0.688840	+	0.173250i
$401$	241.223	+	80.8497i	0.601553	+	0.201620i	0.602154	−	0.798380i	$-0.294309\pi$
$401$	241.223	+	80.8497i	0.601553	+	0.201620i	−0.000601718		1.00000i	$0.500192\pi$
$402$	247.176	+	322.126i	0.614866	+	0.801309i
$403$	−480.390	+	136.683i	−1.19203	+	0.339163i
$404$	2.01631	−	10.7863i	0.00499086	−	0.0266988i
$405$	−142.526	+	45.3406i	−0.351915	+	0.111952i
$406$	−91.0855	+	116.831i	−0.224349	+	0.287762i
$407$	−177.559	+	242.813i	−0.436264	+	0.596593i
$408$		−	293.103i		−	0.718389i
$409$	−208.094	−	352.105i	−0.508787	−	0.860893i
$409$	−208.094	−	352.105i	−0.508787	−	0.860893i
$410$	366.129			0.892997
$411$	−315.245	−	230.525i	−0.767018	−	0.560889i
$412$	−14.6849	−	11.4488i	−0.0356429	−	0.0277884i
$413$	294.235	+	924.910i	0.712434	+	2.23949i
$414$	−37.4016	−	6.99157i	−0.0903421	−	0.0168879i
$415$	−80.4521	−	282.760i	−0.193860	−	0.681349i
$416$	18.5222	−	14.2126i	0.0445246	−	0.0341649i
$417$	162.396	−	484.524i	0.389439	−	1.16193i
$418$	44.2573	+	175.966i	0.105879	+	0.420972i
$419$	154.955	+	164.807i	0.369821	+	0.393333i	0.886411	−	0.462900i	$-0.153191\pi$
$419$	154.955	+	164.807i	0.369821	+	0.393333i	−0.516590	+	0.856233i	$0.672799\pi$
$420$	0.712994	+	6.14565i	0.00169761	+	0.0146325i
$421$	204.895	−	554.079i	0.486687	−	1.31610i	−0.424991	−	0.905197i	$-0.639723\pi$
$421$	204.895	−	554.079i	0.486687	−	1.31610i	0.911678	−	0.410904i	$-0.134787\pi$
$422$	−88.2813	+	69.9266i	−0.209197	+	0.165703i
$423$	−23.7853	+	0.549537i	−0.0562300	+	0.00129914i
$424$	−62.2362	−	70.4181i	−0.146784	−	0.166080i
$425$	−205.300	+	145.329i	−0.483059	+	0.341950i
$426$	222.662	−	336.030i	0.522680	−	0.788803i
$427$	−197.124	+	486.461i	−0.461649	+	1.13925i
$428$	4.54992	−	4.34442i	0.0106307	−	0.0101505i
$429$	−76.1056	−	614.613i	−0.177402	−	1.43266i
$430$	−190.132	−	1.46404i	−0.442168	−	0.00340475i
$431$	−238.285	+	420.161i	−0.552866	+	0.974850i	0.444022	+	0.896016i	$0.353551\pi$
$431$	−238.285	+	420.161i	−0.552866	+	0.974850i	−0.996888	+	0.0788345i	$0.974880\pi$
$432$	90.2529	+	444.776i	0.208919	+	1.02957i
$433$	−399.457	+	264.690i	−0.922533	+	0.611292i	−0.921361	−	0.388707i	$-0.872922\pi$
$433$	−399.457	+	264.690i	−0.922533	+	0.611292i	−0.00117124	+	0.999999i	$0.500373\pi$
$434$	−571.348	−	221.341i	−1.31647	−	0.510003i
$435$	−59.9596	+	2.30958i	−0.137838	+	0.00530938i
$436$	−1.24757	+	2.82547i	−0.00286139	+	0.00648044i
$437$	−40.1606	−	27.9674i	−0.0919006	−	0.0639986i
$438$	−461.461	+	564.504i	−1.05356	+	1.28882i
$439$	−33.9783	−	366.684i	−0.0773993	−	0.835271i	−0.942617	−	0.333875i	$-0.891644\pi$
$439$	−33.9783	−	366.684i	−0.0773993	−	0.835271i	0.865218	−	0.501396i	$-0.167180\pi$
$440$	334.231	+	138.443i	0.759616	+	0.314643i
$441$	−50.0900	−	0.771445i	−0.113583	−	0.00174931i
$442$	−193.934	+	318.671i	−0.438765	+	0.720975i
$443$	−415.830	+	153.772i	−0.938669	+	0.347115i	−0.769627	−	0.638494i	$-0.779558\pi$
$443$	−415.830	+	153.772i	−0.938669	+	0.347115i	−0.169042	+	0.985609i	$0.554067\pi$
$444$	−4.35720	+	2.21166i	−0.00981351	+	0.00498121i
$445$	−385.183	+	238.495i	−0.865580	+	0.535944i
$446$	241.939	+	223.992i	0.542464	+	0.502224i
$447$	−488.648	+	64.3317i	−1.09317	+	0.143919i
$448$	559.677	−	4.30959i	1.24928	−	0.00961962i
$449$	227.197	−	407.896i	0.506006	−	0.908455i	−0.493250	−	0.869888i	$-0.664191\pi$
$449$	227.197	−	407.896i	0.506006	−	0.908455i	0.999256	−	0.0385675i	$-0.0122795\pi$
$450$	52.0023	−	55.3085i	0.115561	−	0.122908i
$451$	985.904	+	732.668i	2.18604	+	1.62454i
$452$	2.10970	−	2.20949i	0.00466748	−	0.00488826i
$453$	187.607	−	84.5685i	0.414142	−	0.186685i
$454$	26.6497	+	432.078i	0.0586997	+	0.951714i
$455$	127.048	−	276.149i	0.279227	−	0.606920i
$456$	−25.1966	+	110.956i	−0.0552556	+	0.243324i
$457$	772.718	+	35.7249i	1.69085	+	0.0781727i	0.870025	−	0.493008i	$-0.164103\pi$
$457$	772.718	+	35.7249i	1.69085	+	0.0781727i	0.820824	+	0.571181i	$0.193514\pi$
$458$	−203.966	+	761.212i	−0.445341	+	1.66203i
$459$	216.751	+	338.311i	0.472224	+	0.737061i
$460$	−2.39661	+	0.803264i	−0.00521003	+	0.00174623i
$461$	88.4065	+	59.5650i	0.191771	+	0.129208i	0.650906	−	0.759159i	$-0.274389\pi$
$461$	88.4065	+	59.5650i	0.191771	+	0.129208i	−0.459134	+	0.888367i	$0.651840\pi$
$462$	379.878	−	657.967i	0.822246	−	1.42417i
$463$	22.3204	−	12.8867i	0.0482081	−	0.0278330i	−0.475702	−	0.879606i	$-0.657806\pi$
$463$	22.3204	−	12.8867i	0.0482081	−	0.0278330i	0.523910	+	0.851773i	$0.324473\pi$
$464$	−9.48432	+	136.640i	−0.0204403	+	0.294483i
$465$	−80.6790	−	234.700i	−0.173503	−	0.504731i
$466$	215.965	−	21.6905i	0.463443	−	0.0465462i
$467$	383.479	−	99.5944i	0.821153	−	0.213264i	0.182940	−	0.983124i	$-0.441439\pi$
$467$	383.479	−	99.5944i	0.821153	−	0.213264i	0.638213	+	0.769860i	$0.279674\pi$
$468$	−1.04462	+	2.89315i	−0.00223209	+	0.00618195i
$469$	−343.181	+	573.814i	−0.731729	+	1.22348i
$470$	49.8762	−	29.3104i	0.106120	−	0.0623626i
$471$	−38.3147	−	62.9584i	−0.0813476	−	0.133670i
$472$	722.674	+	572.422i	1.53109	+	1.21276i
$473$	−509.054	−	384.420i	−1.07622	−	0.812727i
$474$	−485.604	+	255.966i	−1.02448	+	0.540014i
$475$	90.2107	−	37.3665i	0.189917	−	0.0786663i
$476$	11.6234	−	4.60618i	0.0244189	−	0.00967685i
$477$	23.5099	+	6.68913i	0.0492869	+	0.0140233i
$478$	280.771	−	563.863i	0.587386	−	1.17963i
$479$	−350.360	−	57.1521i	−0.731441	−	0.119315i	−0.216186	−	0.976352i	$-0.569362\pi$
$479$	−350.360	−	57.1521i	−0.731441	−	0.119315i	−0.515255	+	0.857037i	$0.672303\pi$
$480$	7.54784	+	8.80987i	0.0157247	+	0.0183539i
$481$	239.365	+	18.4676i	0.497641	+	0.0383942i
$482$	−73.6876	−	105.814i	−0.152879	−	0.219531i
$483$	39.2036	+	201.134i	0.0811669	+	0.416426i
$484$	9.53124	+	15.9367i	0.0196926	+	0.0329270i
$485$	418.232	+	228.752i	0.862335	+	0.471654i
$486$	−152.818	−	157.599i	−0.314441	−	0.324278i
$487$	−215.186	−	154.828i	−0.441860	−	0.317922i	0.341062	−	0.940041i	$-0.389213\pi$
$487$	−215.186	−	154.828i	−0.441860	−	0.317922i	−0.782923	+	0.622119i	$0.786272\pi$
$488$	102.906	+	487.827i	0.210873	+	0.999646i
$489$	−204.299	+	93.9923i	−0.417789	+	0.192213i
$490$	107.318	−	57.6283i	0.219015	−	0.117609i
$491$	−105.869	+	19.7904i	−0.215619	+	0.0403062i	−0.290451	−	0.956890i	$-0.593805\pi$
$491$	−105.869	+	19.7904i	−0.215619	+	0.0403062i	0.0748314	+	0.997196i	$0.476158\pi$
$492$	8.89393	+	17.8614i	0.0180771	+	0.0363037i
$493$	35.8695	+	115.833i	0.0727575	+	0.234956i
$494$	100.810	−	103.963i	0.204068	−	0.210452i
$495$	−92.6206	+	16.5767i	−0.187112	+	0.0334883i
$496$	−552.445	+	125.453i	−1.11380	+	0.252929i
$497$	649.496	+	137.010i	1.30683	+	0.275673i
$498$	−433.381	+	395.079i	−0.870244	+	0.793332i
$499$	78.1509	−	121.980i	0.156615	−	0.244449i	−0.754784	−	0.655973i	$-0.772258\pi$
$499$	78.1509	−	121.980i	0.156615	−	0.244449i	0.911399	+	0.411524i	$0.135003\pi$
$500$	2.91462	−	11.5885i	0.00582925	−	0.0231770i
$501$	224.252	−	124.907i	0.447608	−	0.249316i
$502$	49.6120	+	87.4792i	0.0988286	+	0.174261i
$503$	−519.462	+	452.029i	−1.03273	+	0.898667i	−0.994925	−	0.100618i	$-0.967918\pi$
$503$	−519.462	+	452.029i	−1.03273	+	0.898667i	−0.0378017	+	0.999285i	$0.512036\pi$
$504$	−122.047	+	79.5261i	−0.242158	+	0.157790i
$505$	−208.711	−	167.949i	−0.413290	−	0.332573i
$506$	295.058	+	96.3727i	0.583118	+	0.190460i
$507$	−39.4101	+	31.7132i	−0.0777320	+	0.0625507i
$508$	−9.64321	+	3.65066i	−0.0189827	+	0.00718633i
$509$	−32.2745	+	523.274i	−0.0634076	+	1.02804i	0.823861	+	0.566791i	$0.191815\pi$
$509$	−32.2745	+	523.274i	−0.0634076	+	1.02804i	−0.887269	+	0.461252i	$0.847400\pi$
$510$	−163.309	−	87.6953i	−0.320214	−	0.171952i
$511$	−1144.13	−	363.974i	−2.23900	−	0.712278i
$512$	437.994	−	300.033i	0.855457	−	0.586002i
$513$	−52.9694	−	146.703i	−0.103254	−	0.285970i
$514$	−680.352	−	132.609i	−1.32364	−	0.257995i
$515$	−415.859	+	183.620i	−0.807493	+	0.356543i
$516$	−4.54723	−	9.31108i	−0.00881247	−	0.0180447i
$517$	192.959	+	20.8819i	0.373229	+	0.0403906i
$518$	220.684	+	195.043i	0.426031	+	0.376530i
$519$	532.484	−	631.292i	1.02598	−	1.21636i
$520$	−46.4843	−	284.963i	−0.0893929	−	0.548006i
$521$	−104.873	+	338.668i	−0.201292	+	0.650034i	0.797609	+	0.603174i	$0.206098\pi$
$521$	−104.873	+	338.668i	−0.201292	+	0.650034i	−0.998902	+	0.0468592i	$0.985079\pi$
$522$	−17.5621	−	32.1091i	−0.0336438	−	0.0615117i
$523$	421.981	+	247.983i	0.806847	+	0.474154i	0.851187	−	0.524862i	$-0.175883\pi$
$523$	421.981	+	247.983i	0.806847	+	0.474154i	−0.0443399	+	0.999017i	$0.514118\pi$
$524$	−0.0436819	−	2.83627i	−8.33625e−5	−	0.00541273i
$525$	−380.096	−	150.626i	−0.723992	−	0.286907i
$526$	−610.827	−	468.704i	−1.16127	−	0.891073i
$527$	−415.938	+	280.243i	−0.789256	+	0.531770i
$528$	−48.6408	−	700.766i	−0.0921228	−	1.32721i
$529$	410.061	−	173.564i	0.775163	−	0.328098i
$530$	−57.8560	+	13.6076i	−0.109162	+	0.0256747i
$531$	−238.580	−	23.9618i	−0.449302	−	0.0451259i
$532$	−4.79608	+	0.744490i	−0.00901520	+	0.00139942i
$533$	82.9354	−	976.827i	0.155601	−	1.83270i
$534$	768.363	+	475.750i	1.43888	+	0.890918i
$535$	−40.8917	−	148.041i	−0.0764331	−	0.276712i
$536$	34.2141	+	634.157i	0.0638323	+	1.18313i
$537$	36.7507	+	121.996i	0.0684370	+	0.227180i
$538$	−245.047	+	36.1083i	−0.455479	+	0.0671159i
$539$	404.304	+	59.5752i	0.750100	+	0.110529i
$540$	−7.71338	−	2.32362i	−0.0142840	−	0.00430300i
$541$	−582.442	−	141.731i	−1.07660	−	0.261979i	−0.341463	−	0.939895i	$-0.610922\pi$
$541$	−582.442	−	141.731i	−1.07660	−	0.261979i	−0.735139	+	0.677916i	$0.762883\pi$
$542$	−11.4294	+	73.6294i	−0.0210874	+	0.135848i
$543$	388.755	+	100.965i	0.715939	+	0.185939i
$544$	13.2491	−	19.3413i	0.0243550	−	0.0355539i
$545$	46.3630	+	59.4676i	0.0850696	+	0.109115i
$546$	−606.077	+	18.6730i	−1.11003	+	0.0341997i
$547$	829.783	−	429.255i	1.51697	−	0.784743i	0.519409	−	0.854526i	$-0.326152\pi$
$547$	829.783	−	429.255i	1.51697	−	0.784743i	0.997562	+	0.0697823i	$0.0222305\pi$
$548$	−5.25911	−	14.9243i	−0.00959691	−	0.0272341i
$549$	−90.9824	−	92.3945i	−0.165724	−	0.168296i
$550$	−479.484	+	391.960i	−0.871790	+	0.712655i
$551$	−3.62099	−	46.9329i	−0.00657166	−	0.0851778i
$552$	137.633	+	137.633i	0.249336	+	0.249336i
$553$	−686.446	−	588.111i	−1.24131	−	1.06349i
$554$	133.823	−	112.877i	0.241557	−	0.203749i
$555$	−2.75544	+	119.262i	−0.00496476	+	0.214887i
$556$	16.5231	−	12.4776i	0.0297178	−	0.0224418i
$557$	407.498	−	868.058i	0.731594	−	1.55845i	−0.0948863	−	0.995488i	$-0.530249\pi$
$557$	407.498	−	868.058i	0.731594	−	1.55845i	0.826481	−	0.562965i	$-0.190339\pi$
$558$	106.209	−	107.857i	0.190338	−	0.193292i
$559$	−46.9748	+	506.939i	−0.0840336	+	0.906867i
$560$	160.771	−	305.004i	0.287090	−	0.544651i
$561$	−264.267	−	562.946i	−0.471065	−	1.00347i
$562$	−646.153	−	227.696i	−1.14974	−	0.405152i
$563$	−27.9575	−	200.421i	−0.0496580	−	0.355987i	−0.999114	−	0.0420864i	$-0.986600\pi$
$563$	−27.9575	−	200.421i	−0.0496580	−	0.355987i	0.949456	−	0.313900i	$-0.101636\pi$
$564$	2.64148	+	1.72119i	0.00468347	+	0.00305175i
$565$	−23.1564	−	70.8965i	−0.0409848	−	0.125481i
$566$	−294.061	−	111.324i	−0.519543	−	0.196685i
$567$	−201.897	+	447.887i	−0.356079	+	0.789924i
$568$	584.350	−	236.791i	1.02879	−	0.416885i
$569$	−147.400	−	29.9102i	−0.259052	−	0.0525662i	0.0675945	−	0.997713i	$-0.478468\pi$
$569$	−147.400	−	29.9102i	−0.259052	−	0.0525662i	−0.326646	+	0.945147i	$0.605919\pi$
$570$	54.2830	+	47.2365i	0.0952334	+	0.0828710i
$571$	186.333	+	25.9924i	0.326328	+	0.0455208i	0.299433	−	0.954117i	$-0.403203\pi$
$571$	186.333	+	25.9924i	0.326328	+	0.0455208i	0.0268953	+	0.999638i	$0.491438\pi$
$572$	11.5295	−	22.2874i	0.0201564	−	0.0389639i
$573$	−419.469	−	200.870i	−0.732058	−	0.350559i
$574$	803.363	−	894.993i	1.39959	−	1.55922i
$575$	28.1608	−	164.646i	0.0489754	−	0.286341i
$576$	−53.8959	+	127.334i	−0.0935693	+	0.221066i
$577$	−235.305	+	684.518i	−0.407808	+	1.18634i	0.532622	+	0.846353i	$0.321207\pi$
$577$	−235.305	+	684.518i	−0.407808	+	1.18634i	−0.940430	+	0.339986i	$0.889578\pi$
$578$	44.7974	−	190.467i	0.0775041	−	0.329527i
$579$	696.527	−	119.133i	1.20298	−	0.205757i
$580$	−2.05715	−	1.29575i	−0.00354682	−	0.00223406i
$581$	−867.728	−	423.771i	−1.49351	−	0.729382i
$582$	36.6016	−	950.223i	0.0628893	−	1.63269i
$583$	−183.024	−	79.1346i	−0.313935	−	0.135737i
$584$	−1094.45	+	320.528i	−1.87406	+	0.548850i
$585$	50.1627	+	55.8842i	0.0857482	+	0.0955285i
$586$	367.446	−	231.446i	0.627041	−	0.394959i
$587$	508.946	−	55.0778i	0.867030	−	0.0938293i	0.336691	−	0.941615i	$-0.390692\pi$
$587$	508.946	−	55.0778i	0.867030	−	0.0938293i	0.530339	+	0.847786i	$0.322065\pi$
$588$	5.41831	+	3.83554i	0.00921482	+	0.00652303i
$589$	181.547	−	70.3316i	0.308229	−	0.119409i
$590$	535.160	−	231.389i	0.907051	−	0.392184i
$591$	−232.469	+	193.040i	−0.393348	+	0.326632i
$592$	269.978	+	35.5433i	0.456044	+	0.0600394i
$593$	766.278	+	94.8858i	1.29221	+	0.160010i	0.739381	−	0.673288i	$-0.235118\pi$
$593$	766.278	+	94.8858i	1.29221	+	0.160010i	0.552825	+	0.833297i	$0.313550\pi$
$594$	590.065	+	794.012i	0.993375	+	1.33672i
$595$	35.1768	−	303.206i	0.0591206	−	0.509590i
$596$	−17.8071	−	9.03867i	−0.0298777	−	0.0151656i
$597$	−634.552	+	53.8753i	−1.06290	+	0.0902434i
$598$	−58.5731	−	240.706i	−0.0979483	−	0.402518i
$599$	−310.168	−	16.7342i	−0.517810	−	0.0279370i	−0.206874	−	0.978368i	$-0.566329\pi$
$599$	−310.168	−	16.7342i	−0.517810	−	0.0279370i	−0.310936	+	0.950431i	$0.600643\pi$
$600$	−379.360	+	83.0811i	−0.632267	+	0.138469i
$601$	−237.746	−	887.280i	−0.395584	−	1.47634i	−0.820783	−	0.571240i	$-0.806463\pi$
$601$	−237.746	−	887.280i	−0.395584	−	1.47634i	0.425199	−	0.905100i	$-0.360204\pi$
$602$	−420.768	+	461.561i	−0.698951	+	0.766713i
$603$	−96.4705	−	134.078i	−0.159984	−	0.222352i
$604$	8.20758	+	1.46895i	0.0135887	+	0.00243204i
$605$	452.863	−	20.9371i	0.748533	−	0.0346068i
$606$	−114.325	+	522.023i	−0.188655	+	0.861425i
$607$	−68.0732	−	18.8031i	−0.112147	−	0.0309772i	0.209725	−	0.977761i	$-0.432743\pi$
$607$	−68.0732	−	18.8031i	−0.112147	−	0.0309772i	−0.321872	+	0.946783i	$0.604312\pi$
$608$	−6.67821	+	6.18281i	−0.0109839	+	0.0101691i
$609$	−125.918	+	151.637i	−0.206762	+	0.248994i
$610$	302.594	+	88.6195i	0.496055	+	0.145278i
$611$	−66.9018	−	139.709i	−0.109496	−	0.228656i
$612$	−0.0951194	+	3.08732i	−0.000155424	+	0.00504464i
$613$	−78.4644	−	107.300i	−0.128001	−	0.175041i	0.738444	−	0.674315i	$-0.235561\pi$
$613$	−78.4644	−	107.300i	−0.128001	−	0.175041i	−0.866444	+	0.499274i	$0.833600\pi$
$614$	−83.9974	+	61.4238i	−0.136804	+	0.100039i
$615$	486.901	+	15.0012i	0.791708	+	0.0243923i
$616$	1071.79	−	513.247i	1.73992	−	0.833193i
$617$	134.734	−	460.052i	0.218369	−	0.745628i	−0.775131	−	0.631800i	$-0.782316\pi$
$617$	134.734	−	460.052i	0.218369	−	0.745628i	0.993501	−	0.113828i	$-0.0363111\pi$
$618$	697.649	+	579.320i	1.12888	+	0.937411i
$619$	−489.746	−	528.986i	−0.791189	−	0.854582i	0.200966	−	0.979598i	$-0.435592\pi$
$619$	−489.746	−	528.986i	−0.791189	−	0.854582i	−0.992155	+	0.125016i	$0.960102\pi$
$620$	2.67732	−	9.69272i	0.00431825	−	0.0156334i
$621$	−260.642	−	57.0815i	−0.419714	−	0.0919187i
$622$	19.3379	+	418.271i	0.0310898	+	0.672462i
$623$	−262.176	+	1464.88i	−0.420828	+	2.35133i
$624$	−455.077	+	327.431i	−0.729290	+	0.524730i
$625$	121.689	+	110.934i	0.194702	+	0.177494i
$626$	−52.7512	+	14.1346i	−0.0842670	+	0.0225793i
$627$	51.6463	+	235.824i	0.0823705	+	0.376115i
$628$	0.160877	−	2.98184i	0.000256173	−	0.00474816i
$629$	234.242	−	57.0001i	0.372403	−	0.0906202i
$630$	7.79372	+	91.7956i	0.0123710	+	0.145707i
$631$	−22.9323	+	45.1791i	−0.0363428	+	0.0715991i	−0.909157	−	0.416453i	$-0.863273\pi$
$631$	−22.9323	+	45.1791i	−0.0363428	+	0.0715991i	0.872814	+	0.488052i	$0.162293\pi$
$632$	−852.878	−	98.9476i	−1.34949	−	0.156563i
$633$	−120.267	+	89.3756i	−0.189995	+	0.141194i
$634$	−13.6980	+	110.622i	−0.0216056	+	0.174483i
$635$	−32.8576	+	249.578i	−0.0517442	+	0.393036i
$636$	−2.06927	−	2.49193i	−0.00325357	−	0.00391812i
$637$	−129.442	−	299.376i	−0.203206	−	0.469978i
$638$	107.851	+	278.397i	0.169046	+	0.436359i
$639$	−94.7476	+	133.846i	−0.148275	+	0.209462i
$640$	−34.2720	−	316.690i	−0.0535500	−	0.494828i
$641$	528.145	+	838.489i	0.823939	+	1.30809i	0.948786	+	0.315919i	$0.102313\pi$
$641$	528.145	+	838.489i	0.823939	+	1.30809i	−0.124847	+	0.992176i	$0.539844\pi$
$642$	−227.993	+	204.651i	−0.355129	+	0.318771i
$643$	32.1216	+	109.680i	0.0499558	+	0.170575i	0.980871	−	0.194661i	$-0.0623607\pi$
$643$	32.1216	+	109.680i	0.0499558	+	0.170575i	−0.930915	+	0.365236i	$0.880988\pi$
$644$	−3.29511	+	7.62099i	−0.00511663	+	0.0118338i
$645$	−252.790	−	9.73719i	−0.391922	−	0.0150964i
$646$	63.8137	−	130.667i	0.0987828	−	0.202271i
$647$	−221.725	+	352.013i	−0.342697	+	0.544070i	−0.972565	−	0.232633i	$-0.925266\pi$
$647$	−221.725	+	352.013i	−0.342697	+	0.544070i	0.629868	+	0.776702i	$0.283109\pi$
$648$	78.6733	+	459.974i	0.121409	+	0.709836i
$649$	1904.11	+	447.841i	2.93391	+	0.690049i
$650$	467.424	+	160.679i	0.719114	+	0.247198i
$651$	−750.745	−	317.763i	−1.15322	−	0.488116i
$652$	−8.98134	−	1.53616i	−0.0137751	−	0.00235607i
$653$	732.514	+	657.519i	1.12177	+	1.00692i	0.999897	+	0.0143736i	$0.00457543\pi$
$653$	732.514	+	657.519i	1.12177	+	1.00692i	0.121870	+	0.992546i	$0.461111\pi$
$654$	64.9656	−	135.665i	0.0993358	−	0.207439i
$655$	−61.5091	−	31.8192i	−0.0939070	−	0.0485790i
$656$	153.624	−	1101.29i	0.234183	−	1.67880i
$657$	194.710	−	223.756i	0.296362	−	0.340572i
$658$	37.7903	−	186.234i	0.0574320	−	0.283031i
$659$	−369.312	−	911.384i	−0.560413	−	1.38298i	−0.897294	−	0.441433i	$-0.854470\pi$
$659$	−369.312	−	911.384i	−0.560413	−	1.38298i	0.336881	−	0.941547i	$-0.390628\pi$
$660$	11.3672	+	5.12404i	0.0172230	+	0.00776370i
$661$	105.130	−	277.701i	0.159047	−	0.420122i	−0.831806	−	0.555066i	$-0.812693\pi$
$661$	105.130	−	277.701i	0.159047	−	0.420122i	0.990853	+	0.134943i	$0.0430852\pi$
$662$	−656.050	+	214.281i	−0.991012	+	0.323688i
$663$	−270.963	+	415.843i	−0.408692	+	0.627214i
$664$	−908.457	+	126.724i	−1.36816	+	0.190850i
$665$	−39.3815	+	111.756i	−0.0592202	+	0.168055i
$666$	−65.8645	+	30.9192i	−0.0988956	+	0.0464252i
$667$	−71.2357	−	37.5490i	−0.106800	−	0.0562953i
$668$	10.3562	+	0.959643i	0.0155033	+	0.00143659i
$669$	312.568	+	307.791i	0.467217	+	0.460076i
$670$	363.573	+	170.674i	0.542646	+	0.254738i
$671$	637.480	+	844.160i	0.950044	+	1.25806i
$672$	38.0970	+	0.880196i	0.0566920	+	0.00130982i
$673$	−538.867	−	638.859i	−0.800694	−	0.949271i	0.198833	−	0.980033i	$-0.436285\pi$
$673$	−538.867	−	638.859i	−0.800694	−	0.949271i	−0.999527	+	0.0307626i	$0.990206\pi$
$674$	618.467	−	721.878i	0.917607	−	1.07104i
$675$	376.434	−	376.434i	0.557680	−	0.557680i
$676$	−2.04353	+	0.157663i	−0.00302298	+	0.000233230i
$677$	−436.025	−	533.388i	−0.644055	−	0.787871i	0.344492	−	0.938789i	$-0.388051\pi$
$677$	−436.025	−	533.388i	−0.644055	−	0.787871i	−0.988546	+	0.150919i	$0.951777\pi$
$678$	−106.008	+	104.388i	−0.156354	+	0.153965i
$679$	1476.87	−	520.428i	2.17506	−	0.766463i
$680$	−133.216	−	257.517i	−0.195905	−	0.378701i
$681$	17.7370	+	575.696i	0.0260455	+	0.845369i
$682$	−973.856	+	759.251i	−1.42794	+	1.11327i
$683$	745.282	+	510.530i	1.09119	+	0.747482i	0.969501	−	0.245087i	$-0.0788164\pi$
$683$	745.282	+	510.530i	1.09119	+	0.747482i	0.121688	+	0.992568i	$0.461169\pi$
$684$	0.301409	−	1.16055i	0.000440657	−	0.00169671i
$685$	−381.744	−	59.2577i	−0.557291	−	0.0865075i
$686$	−100.410	+	412.636i	−0.146371	+	0.601510i
$687$	−302.436	+	1003.95i	−0.440226	+	1.46135i
$688$	−84.1812	+	571.292i	−0.122356	+	0.830366i
$689$	23.1994	+	157.441i	0.0336711	+	0.228507i
$690$	117.865	−	35.5064i	0.170819	−	0.0514585i
$691$	1178.88	−	63.6033i	1.70606	−	0.0920454i	0.825023	−	0.565100i	$-0.191162\pi$
$691$	1178.88	−	63.6033i	1.70606	−	0.0920454i	0.881033	+	0.473054i	$0.156849\pi$
$692$	32.2547	−	8.90937i	0.0466109	−	0.0128748i
$693$	−162.707	+	262.782i	−0.234787	+	0.379194i
$694$	−162.538	−	13.8000i	−0.234205	−	0.0198847i
$695$	−77.5377	−	499.506i	−0.111565	−	0.718714i
$696$	−18.7092	+	186.281i	−0.0268811	+	0.267645i
$697$	−225.385	−	958.279i	−0.323365	−	1.37486i
$698$	−261.694	−	618.276i	−0.374919	−	0.885782i
$699$	288.092	−	19.9967i	0.412149	−	0.0286077i
$700$	−9.25643	−	13.7384i	−0.0132235	−	0.0196263i
$701$	−276.118	+	359.844i	−0.393892	+	0.513330i	−0.947634	−	0.319358i	$-0.896533\pi$
$701$	−276.118	+	359.844i	−0.393892	+	0.513330i	0.553742	+	0.832688i	$0.313199\pi$
$702$	290.872	−	733.999i	0.414348	−	1.04558i
$703$	−93.5737	+	1.44114i	−0.133106	+	0.00204999i
$704$	571.493	−	972.484i	0.811780	−	1.38137i
$705$	67.5294	−	36.9352i	0.0957864	−	0.0523904i
$706$	629.611	+	194.968i	0.891800	+	0.276159i
$707$	−868.504	+	141.674i	−1.22844	+	0.200387i
$708$	24.2882	+	20.4867i	0.0343054	+	0.0289360i
$709$	258.014	−	291.934i	0.363913	−	0.411755i	−0.538501	−	0.842625i	$-0.681009\pi$
$709$	258.014	−	291.934i	0.363913	−	0.411755i	0.902414	+	0.430870i	$0.141793\pi$
$710$	42.9016	−	396.432i	0.0604247	−	0.558355i
$711$	200.662	−	97.9967i	0.282224	−	0.137829i
$712$	570.955	+	1293.09i	0.801903	+	1.81614i
$713$	63.7187	−	326.908i	0.0893670	−	0.458497i
$714$	−572.704	+	206.784i	−0.802106	+	0.289614i
$715$	−346.208	−	505.402i	−0.484207	−	0.706855i
$716$	−1.56500	+	4.91947i	−0.00218575	+	0.00687077i
$717$	396.489	−	738.357i	0.552983	−	1.02979i
$718$	−803.425	−	49.5536i	−1.11898	−	0.0690161i
$719$	−102.177	−	269.902i	−0.142110	−	0.375385i	0.845143	−	0.534540i	$-0.179515\pi$
$719$	−102.177	−	269.902i	−0.142110	−	0.375385i	−0.987254	+	0.159155i	$0.949123\pi$
$720$	53.3998	+	66.3601i	0.0741663	+	0.0921668i
$721$	−463.627	+	1419.46i	−0.643034	+	1.96873i
$722$	411.190	−	510.987i	0.569515	−	0.707739i
$723$	−93.6589	−	143.737i	−0.129542	−	0.198806i
$724$	10.6830	+	12.2767i	0.0147556	+	0.0169567i
$725$	139.755	−	79.2589i	0.192765	−	0.109323i
$726$	−440.054	−	790.048i	−0.606135	−	1.08822i
$727$	910.586	+	229.021i	1.25252	+	0.315023i	0.812499	−	0.582962i	$-0.198107\pi$
$727$	910.586	+	229.021i	1.25252	+	0.315023i	0.440026	+	0.897985i	$0.354969\pi$
$728$	−798.582	−	511.639i	−1.09695	−	0.702801i
$729$	−545.962	−	598.892i	−0.748920	−	0.821526i
$730$	−148.866	+	705.701i	−0.203926	+	0.966714i
$731$	113.212	+	498.539i	0.154872	+	0.681997i
$732$	3.02729	+	16.9146i	0.00413564	+	0.0231074i
$733$	75.4131	+	73.1254i	0.102883	+	0.0997618i	0.745786	−	0.666186i	$-0.232074\pi$
$733$	75.4131	+	73.1254i	0.102883	+	0.0997618i	−0.642903	+	0.765947i	$0.722270\pi$
$734$	968.117	−	299.791i	1.31896	−	0.408435i
$735$	145.079	−	72.2406i	0.197386	−	0.0982866i
$736$	2.86074	+	15.3036i	0.00388687	+	0.0207929i
$737$	637.482	+	1187.14i	0.864968	+	1.61078i
$738$	124.182	+	269.919i	0.168269	+	0.365743i
$739$	−279.100	+	58.8755i	−0.377673	+	0.0796691i	−0.391361	−	0.920237i	$-0.627996\pi$
$739$	−279.100	+	58.8755i	−0.377673	+	0.0796691i	0.0136884	+	0.999906i	$0.495643\pi$
$740$	−2.82298	+	3.92349i	−0.00381484	+	0.00530201i
$741$	138.322	−	134.126i	0.186670	−	0.181007i
$742$	−93.6847	+	171.286i	−0.126260	+	0.230843i
$743$	111.490	−	66.6785i	0.150053	−	0.0897422i	−0.436285	−	0.899808i	$-0.643706\pi$
$743$	111.490	−	66.6785i	0.150053	−	0.0897422i	0.586338	+	0.810066i	$0.300569\pi$
$744$	−760.042	+	148.142i	−1.02156	+	0.199116i
$745$	−400.081	+	278.612i	−0.537022	+	0.373976i
$746$	−25.4314	+	329.626i	−0.0340904	+	0.441858i
$747$	181.170	−	155.217i	0.242530	−	0.207787i
$748$	4.05670	−	24.8688i	0.00542339	−	0.0332471i
$749$	−451.607	−	224.874i	−0.602947	−	0.300232i
$750$	−159.255	+	559.725i	−0.212341	+	0.746300i
$751$	124.497	+	314.162i	0.165776	+	0.418325i	0.988716	−	0.149803i	$-0.0478640\pi$
$751$	124.497	+	314.162i	0.165776	+	0.418325i	−0.822940	+	0.568128i	$0.807668\pi$
$752$	−67.2364	−	162.323i	−0.0894101	−	0.215855i
$753$	62.3928	+	118.368i	0.0828590	+	0.157195i
$754$	143.596	−	190.152i	0.190446	−	0.252191i
$755$	126.392	−	159.568i	0.167407	−	0.211349i
$756$	−22.6048	+	13.7567i	−0.0299005	+	0.0181966i
$757$	33.7379	+	57.4104i	0.0445680	+	0.0758393i	0.883599	−	0.468244i	$-0.155113\pi$
$757$	33.7379	+	57.4104i	0.0445680	+	0.0758393i	−0.839031	+	0.544083i	$0.816878\pi$
$758$	653.764	+	390.996i	0.862486	+	0.515826i
$759$	388.438	+	140.252i	0.511775	+	0.184785i
$760$	28.2922	+	108.936i	0.0372266	+	0.143337i
$761$	54.7795	+	545.420i	0.0719836	+	0.716715i	0.964212	+	0.265131i	$0.0854153\pi$
$761$	54.7795	+	545.420i	0.0719836	+	0.716715i	−0.892229	+	0.451584i	$0.850859\pi$
$762$	474.880	−	163.242i	0.623202	−	0.214228i
$763$	247.097	+	17.1513i	0.323849	+	0.0224787i
$764$	−9.42208	−	16.3195i	−0.0123326	−	0.0213606i
$765$	65.3057	+	37.7043i	0.0853669	+	0.0492866i
$766$	445.422	−	661.097i	0.581491	−	0.863051i
$767$	−496.118	−	1480.21i	−0.646829	−	1.92988i
$768$	45.1163	−	28.9053i	0.0587451	−	0.0376371i
$769$	−657.088	−	176.066i	−0.854470	−	0.228955i	−0.195110	−	0.980781i	$-0.562506\pi$
$769$	−657.088	−	176.066i	−0.854470	−	0.228955i	−0.659361	+	0.751827i	$0.729173\pi$
$770$	34.7087	−	750.737i	0.0450762	−	0.974983i
$771$	−899.341	−	204.228i	−1.16646	−	0.264887i
$772$	26.0107	+	11.9668i	0.0336927	+	0.0155011i
$773$	260.899	−	16.0917i	0.337515	−	0.0208172i	0.108083	−	0.994142i	$-0.465529\pi$
$773$	260.899	−	16.0917i	0.337515	−	0.0208172i	0.229432	+	0.973325i	$0.426313\pi$
$774$	−63.4090	−	140.666i	−0.0819238	−	0.181740i
$775$	480.615	+	458.908i	0.620148	+	0.592139i
$776$	887.169	−	1193.81i	1.14326	−	1.53841i
$777$	285.488	+	268.422i	0.367423	+	0.345459i
$778$	659.422	+	367.295i	0.847586	+	0.472102i
$779$	2.94251	+	382.137i	0.00377729	+	0.490549i
$780$	−1.29891	−	9.86618i	−0.00166527	−	0.0126490i
$781$	908.833	−	981.652i	1.16368	−	1.25692i
$782$	−130.957	−	211.502i	−0.167464	−	0.270463i
$783$	−116.161	−	228.849i	−0.148353	−	0.292272i
$784$	−128.313	−	346.985i	−0.163665	−	0.442583i
$785$	−62.2775	−	37.9004i	−0.0793344	−	0.0482807i
$786$	−2.12732	+	138.127i	−0.00270652	+	0.175735i
$787$	316.698	−	764.577i	0.402412	−	0.971508i	−0.584667	−	0.811273i	$-0.698775\pi$
$787$	316.698	−	764.577i	0.402412	−	0.971508i	0.987079	−	0.160235i	$-0.0512251\pi$
$788$	−12.1910	+	1.12966i	−0.0154708	+	0.00143358i
$789$	−793.112	−	648.339i	−1.00521	−	0.821723i
$790$	−310.309	+	445.597i	−0.392796	+	0.564047i
$791$	−224.115	−	98.9564i	−0.283331	−	0.125103i
$792$	11.2999	+	293.359i	0.0142675	+	0.370403i
$793$	304.979	−	787.242i	0.384589	−	0.992739i
$794$	−263.070	−	397.012i	−0.331322	−	0.500016i
$795$	−77.4980	+	15.7257i	−0.0974818	+	0.0197808i
$796$	−22.4448	−	12.7291i	−0.0281970	−	0.0159913i
$797$	11.5812	−	1504.03i	0.0145310	−	1.88712i	−0.323853	−	0.946107i	$-0.604978\pi$
$797$	11.5812	−	1504.03i	0.0145310	−	1.88712i	0.338384	−	0.941008i	$-0.390120\pi$
$798$	234.577	−	29.0469i	0.293956	−	0.0363996i
$799$	−107.418	−	112.499i	−0.134441	−	0.140800i
$800$	−28.7888	−	11.6658i	−0.0359860	−	0.0145823i
$801$	−306.469	−	203.074i	−0.382608	−	0.253525i
$802$	−290.049	−	409.740i	−0.361657	−	0.510897i
$803$	−1813.06	+	1602.40i	−2.25786	+	1.99552i
$804$	0.505580	+	21.8827i	0.000628830	+	0.0272173i
$805$	125.859	+	158.896i	0.156347	+	0.197386i
$806$	924.363	+	341.824i	1.14685	+	0.424100i
$807$	−327.359	+	37.9789i	−0.405649	+	0.0470618i
$808$	−608.960	+	572.558i	−0.753664	+	0.708612i
$809$	784.573	−	197.328i	0.969806	−	0.243916i	0.273668	−	0.961824i	$-0.411763\pi$
$809$	784.573	−	197.328i	0.969806	−	0.243916i	0.696138	+	0.717908i	$0.254900\pi$
$810$	279.824	+	93.7876i	0.345462	+	0.115787i
$811$	403.355	+	525.663i	0.497355	+	0.648166i	0.972818	−	0.231570i	$-0.0743861\pi$
$811$	403.355	+	525.663i	0.497355	+	0.648166i	−0.475463	+	0.879736i	$0.657719\pi$
$812$	−7.68127	+	2.18551i	−0.00945969	+	0.00269151i
$813$	−18.2163	+	97.4486i	−0.0224063	+	0.119863i
$814$	565.631	−	179.940i	0.694878	−	0.221057i
$815$	−136.775	+	175.435i	−0.167822	+	0.215257i
$816$	−332.305	+	454.429i	−0.407237	+	0.556898i
$817$		−	198.457i		−	0.242910i
$818$	−78.6620	+	803.207i	−0.0961638	+	0.981916i
$819$	246.675			0.301190
$820$	15.9321	+	11.6505i	0.0194294	+	0.0142080i
$821$	519.349	+	404.902i	0.632581	+	0.493182i	0.879528	−	0.475848i	$-0.157859\pi$
$821$	519.349	+	404.902i	0.632581	+	0.493182i	−0.246947	+	0.969029i	$0.579427\pi$
$822$	233.617	+	734.359i	0.284205	+	0.893381i
$823$	−304.042	−	56.8353i	−0.369431	−	0.0690587i	−0.00423954	−	0.999991i	$-0.501349\pi$
$823$	−304.042	−	56.8353i	−0.369431	−	0.0690587i	−0.365192	+	0.930932i	$0.618997\pi$
$824$	388.156	+	1364.23i	0.471063	+	1.65562i
$825$	−653.708	+	501.608i	−0.792373	+	0.608009i
$826$	608.629	−	1815.90i	0.736839	−	2.19843i
$827$	−316.567	−	1258.67i	−0.382790	−	1.52197i	−0.792570	−	0.609781i	$-0.791257\pi$
$827$	−316.567	−	1258.67i	−0.382790	−	1.52197i	0.409780	−	0.912184i	$-0.365605\pi$
$828$	−1.40506	−	1.49439i	−0.00169693	−	0.00180482i
$829$	9.54289	+	82.2549i	0.0115113	+	0.0992218i	0.997853	−	0.0654884i	$-0.0208605\pi$
$829$	9.54289	+	82.2549i	0.0115113	+	0.0992218i	−0.986342	+	0.164710i	$0.947331\pi$
$830$	−201.199	+	544.084i	−0.242409	+	0.655523i
$831$	182.591	−	144.628i	0.219724	−	0.174041i
$832$	−900.003	+	20.7937i	−1.08173	+	0.0249925i
$833$	−216.896	−	245.410i	−0.260379	−	0.294610i
$834$	−823.011	+	582.597i	−0.986823	+	0.698558i
$835$	140.254	−	211.665i	0.167969	−	0.253491i
$836$	−3.67353	+	9.06551i	−0.00439418	+	0.0108439i
$837$	767.719	−	733.046i	0.917227	−	0.875801i
$838$	−54.8536	−	442.986i	−0.0654577	−	0.528623i
$839$	−1210.95	−	9.32447i	−1.44332	−	0.0111138i	−0.716332	−	0.697760i	$-0.754180\pi$
$839$	−1210.95	−	9.32447i	−1.44332	−	0.0111138i	−0.726992	+	0.686646i	$0.759082\pi$
$840$	232.486	−	409.936i	0.276770	−	0.488019i
$841$	151.842	+	748.295i	0.180550	+	0.889768i
$842$	−971.717	+	643.883i	−1.15406	+	0.764707i
$843$	−849.965	−	329.278i	−1.00826	−	0.390603i
$844$	−6.06670	+	0.233683i	−0.00718803	+	0.000276875i
$845$	−20.2116	+	45.7748i	−0.0239190	+	0.0541714i
$846$	38.5252	+	26.8285i	0.0455380	+	0.0317122i
$847$	942.495	−	1152.95i	1.11275	−	1.36122i
$848$	16.6551	+	179.737i	0.0196404	+	0.211954i
$849$	−386.500	−	160.094i	−0.455241	−	0.188567i
$850$	496.272	+	7.64317i	0.583849	+	0.00899196i
$851$	−83.2280	+	136.759i	−0.0978003	+	0.160704i
$852$	20.3819	−	7.53712i	0.0239224	−	0.00884638i
$853$	1013.45	−	514.413i	1.18810	−	0.603063i	0.256497	−	0.966545i	$-0.417432\pi$
$853$	1013.45	−	514.413i	1.18810	−	0.603063i	0.931601	+	0.363482i	$0.118412\pi$
$854$	880.582	−	545.233i	1.03113	−	0.638447i
$855$	−21.4806	−	19.8872i	−0.0251235	−	0.0232599i
$856$	−475.099	+	62.5480i	−0.555022	+	0.0730700i
$857$	−922.138	+	7.10058i	−1.07601	+	0.00828539i	−0.544494	−	0.838765i	$-0.683278\pi$
$857$	−922.138	+	7.10058i	−1.07601	+	0.00828539i	−0.531513	+	0.847050i	$0.678376\pi$
$858$	−594.647	+	1067.60i	−0.693062	+	1.24428i
$859$	−576.434	+	613.083i	−0.671053	+	0.713717i	−0.970690	−	0.240336i	$-0.922742\pi$
$859$	−576.434	+	613.083i	−0.671053	+	0.713717i	0.299637	+	0.954053i	$0.403134\pi$
$860$	−8.22704	−	6.11387i	−0.00956633	−	0.00710915i
$861$	1105.03	−	1157.30i	1.28343	−	1.34414i
$862$	868.919	−	391.688i	1.00803	−	0.454394i
$863$	47.8606	+	775.977i	0.0554584	+	0.899162i	0.918845	+	0.394619i	$0.129123\pi$
$863$	47.8606	+	775.977i	0.0554584	+	0.899162i	−0.863386	+	0.504543i	$0.831661\pi$
$864$	−20.7385	+	45.0766i	−0.0240029	+	0.0521720i
$865$	180.911	−	796.660i	0.209145	−	0.920995i
$866$	944.548	+	43.6691i	1.09070	+	0.0504262i
$867$	67.3782	−	251.459i	0.0777142	−	0.290033i
$868$	−17.8190	−	27.8125i	−0.0205288	−	0.0320420i
$869$	−1727.29	+	578.928i	−1.98767	+	0.666201i
$870$	98.1933	+	66.1589i	0.112866	+	0.0760447i
$871$	537.713	−	931.346i	0.617351	−	1.06928i
$872$	203.751	−	117.636i	0.233659	−	0.134903i
$873$	−26.7870	+	385.918i	−0.0306838	+	0.442060i
$874$	31.3926	+	91.3231i	0.0359184	+	0.104489i
$875$	−953.477	+	95.7629i	−1.08969	+	0.109443i
$876$	−38.0436	+	9.88041i	−0.0434287	+	0.0112790i
$877$	−32.3117	+	89.4896i	−0.0368434	+	0.102041i	−0.957604	−	0.288087i	$-0.906981\pi$
$877$	−32.3117	+	89.4896i	−0.0368434	+	0.102041i	0.920761	+	0.390127i	$0.127569\pi$
$878$	−372.973	+	623.629i	−0.424799	+	0.710283i
$879$	498.136	−	292.736i	0.566707	−	0.333033i
$880$	−361.234	−	593.577i	−0.410494	−	0.674519i
$881$	536.117	+	424.652i	0.608532	+	0.482012i	0.876491	−	0.481419i	$-0.159878\pi$
$881$	536.117	+	424.652i	0.608532	+	0.482012i	−0.267958	+	0.963431i	$0.586349\pi$
$882$	78.8845	+	59.5708i	0.0894382	+	0.0675406i
$883$	648.162	−	341.652i	0.734045	−	0.386922i	−0.0572470	−	0.998360i	$-0.518232\pi$
$883$	648.162	−	341.652i	0.734045	−	0.386922i	0.791292	+	0.611438i	$0.209409\pi$
$884$	−18.5795	+	7.69587i	−0.0210175	+	0.00870573i
$885$	721.170	−	285.788i	0.814881	−	0.322925i
$886$	841.437	+	239.409i	0.949703	+	0.270214i
$887$	247.054	−	496.151i	0.278527	−	0.559359i	−0.711087	−	0.703104i	$-0.751797\pi$
$887$	247.054	−	496.151i	0.278527	−	0.559359i	0.989615	+	0.143745i	$0.0459146\pi$
$888$	367.354	+	59.9241i	0.413687	+	0.0674821i
$889$	537.991	+	627.946i	0.605164	+	0.706351i
$890$	891.303	+	68.7662i	1.00146	+	0.0772653i
$891$	565.825	+	812.512i	0.635044	+	0.911910i
$892$	3.40040	+	17.4457i	0.00381211	+	0.0195580i
$893$	30.9928	+	51.8215i	0.0347064	+	0.0580308i
$894$	853.246	+	466.683i	0.954414	+	0.522017i
$895$	87.7359	+	90.4807i	0.0980290	+	0.101096i
$896$	−849.341	−	611.107i	−0.947926	−	0.682040i
$897$	−68.0318	−	322.506i	−0.0758437	−	0.359538i
$898$	−836.973	+	385.069i	−0.932042	+	0.428807i
$899$	282.237	−	151.558i	0.313946	−	0.168585i
$900$	4.02285	−	0.752001i	0.00446983	−	0.000835557i
$901$	71.2312	+	143.051i	0.0790579	+	0.158770i
$902$	−716.971	−	2315.32i	−0.794868	−	2.56687i
$903$	−578.475	+	596.573i	−0.640615	+	0.660656i
$904$	−229.064	+	40.9967i	−0.253390	+	0.0453504i
$905$	387.444	−	87.9833i	0.428115	−	0.0972191i
$906$	−397.319	−	83.8135i	−0.438542	−	0.0925094i
$907$	−751.636	+	685.207i	−0.828706	+	0.755465i	−0.972192	−	0.234187i	$-0.924757\pi$
$907$	−751.636	+	685.207i	−0.828706	+	0.755465i	0.143485	+	0.989652i	$0.454169\pi$
$908$	−12.5894	+	19.6500i	−0.0138650	+	0.0216409i
$909$	53.0262	−	210.831i	0.0583346	−	0.231938i
$910$	−524.005	+	291.869i	−0.575830	+	0.320735i
$911$	−384.216	−	677.475i	−0.421751	−	0.743661i	0.575496	−	0.817804i	$-0.304809\pi$
$911$	−384.216	−	677.475i	−0.421751	−	0.743661i	−0.997248	+	0.0741439i	$0.976378\pi$
$912$	164.861	−	143.460i	0.180769	−	0.157303i
$913$	−1630.56	+	1062.47i	−1.78594	+	1.16372i
$914$	−1189.17	−	956.922i	−1.30106	−	1.04696i
$915$	398.777	+	130.250i	0.435822	+	0.142349i
$916$	−33.0980	+	26.6339i	−0.0361332	+	0.0290763i
$917$	−212.745	+	80.5395i	−0.232001	+	0.0878293i
$918$	48.8069	−	791.319i	0.0531665	−	0.862003i
$919$	−755.095	−	405.477i	−0.821648	−	0.441216i	0.00768478	−	0.999970i	$-0.497554\pi$
$919$	−755.095	−	405.477i	−0.821648	−	0.441216i	−0.829333	+	0.558755i	$0.811279\pi$
$920$	183.478	+	58.3684i	0.199432	+	0.0634439i
$921$	−114.222	+	78.2437i	−0.124019	+	0.0849551i
$922$	−71.4355	−	197.846i	−0.0774788	−	0.214583i
$923$	−1047.96	−	204.261i	−1.13538	−	0.221301i
$924$	37.4675	−	16.5435i	0.0405493	−	0.0179042i
$925$	−140.171	−	287.020i	−0.151537	−	0.310292i
$926$	−50.5614	−	5.47172i	−0.0546020	−	0.00590899i
$927$	−276.418	−	244.301i	−0.298186	−	0.263540i
$928$	−9.65504	+	11.4466i	−0.0104041	+	0.0123347i
$929$	126.494	+	775.449i	0.136162	+	0.834714i	0.962448	+	0.271464i	$0.0875079\pi$
$929$	126.494	+	775.449i	0.136162	+	0.834714i	−0.826287	+	0.563250i	$0.809551\pi$
$930$	−144.861	+	467.800i	−0.155764	+	0.503010i
$931$	61.0106	+	111.547i	0.0655323	+	0.119814i
$932$	10.0879	+	5.92831i	0.0108240	+	0.00636085i
$933$	8.57901	+	557.036i	0.00919508	+	0.597037i
$934$	−726.805	−	288.021i	−0.778164	−	0.308374i
$935$	−488.042	−	374.488i	−0.521970	−	0.400522i
$936$	194.315	−	130.922i	0.207602	−	0.139874i
$937$	38.6706	+	557.125i	0.0412707	+	0.594584i	0.972908	+	0.231194i	$0.0742631\pi$
$937$	38.6706	+	557.125i	0.0412707	+	0.594584i	−0.931637	+	0.363390i	$0.881619\pi$
$938$	1214.96	−	514.250i	1.29527	−	0.548241i
$939$	−70.7309	+	16.6358i	−0.0753258	+	0.0177165i
$940$	3.10305	+	0.311657i	0.00330112	+	0.000331550i
$941$	−918.079	+	142.512i	−0.975642	+	0.151448i	−0.621219	−	0.783637i	$-0.713362\pi$
$941$	−918.079	+	142.512i	−0.975642	+	0.151448i	−0.354424	+	0.935085i	$0.615323\pi$
$942$	−12.3030	+	144.907i	−0.0130605	+	0.153829i
$943$	555.817	+	344.148i	0.589414	+	0.364950i
$944$	−471.456	−	1706.82i	−0.499423	−	1.80807i
$945$	34.8039	+	645.089i	0.0368295	+	0.682634i
$946$	363.068	+	1205.22i	0.383792	+	1.27402i
$947$	722.452	−	106.455i	0.762885	−	0.112413i	0.246935	−	0.969032i	$-0.420577\pi$
$947$	722.452	−	106.455i	0.762885	−	0.112413i	0.515949	+	0.856619i	$0.327439\pi$
$948$	−29.2762	−	4.31392i	−0.0308821	−	0.00455055i
$949$	1849.08	+	557.028i	1.94845	+	0.586963i
$950$	−187.210	−	45.5553i	−0.197063	−	0.0479530i
$951$	−22.7489	+	146.551i	−0.0239210	+	0.154102i
$952$	−921.796	−	239.403i	−0.968273	−	0.251473i
$953$	−712.465	+	1040.07i	−0.747602	+	1.09136i	0.244949	+	0.969536i	$0.421229\pi$
$953$	−712.465	+	1040.07i	−0.747602	+	1.09136i	−0.992551	+	0.121829i	$0.961124\pi$
$954$	−29.6552	−	38.0374i	−0.0310852	−	0.0398715i
$955$	−459.836	+	14.1674i	−0.481504	+	0.0148350i
$956$	30.1604	−	15.6022i	0.0315485	−	0.0163203i
$957$	132.021	+	374.648i	0.137953	+	0.391482i
$958$	491.484	+	499.112i	0.513031	+	0.520994i
$959$	−982.481	+	803.141i	−1.02448	+	0.837477i
$960$	−34.4104	−	446.006i	−0.0358442	−	0.464589i
$961$	257.392	+	257.392i	0.267838	+	0.267838i
$962$	−359.750	−	308.215i	−0.373960	−	0.320389i
$963$	95.2696	−	80.3583i	0.0989300	−	0.0834458i
$964$	0.160557	−	6.94930i	0.000166553	−	0.00720882i
$965$	557.814	−	421.242i	0.578046	−	0.436520i
$966$	171.826	−	366.027i	0.177874	−	0.378910i
$967$	−569.530	+	578.369i	−0.588966	+	0.598107i	−0.941219	−	0.337798i	$-0.890318\pi$
$967$	−569.530	+	578.369i	−0.588966	+	0.598107i	0.352252	+	0.935905i	$0.385416\pi$
$968$	130.512	−	1408.45i	0.134827	−	1.45501i
$969$	90.2172	−	171.155i	0.0931034	−	0.176630i
$970$	−399.720	−	851.490i	−0.412083	−	0.877824i
$971$	1122.26	+	395.468i	1.15578	+	0.407279i	0.840548	−	0.541737i	$-0.182233\pi$
$971$	1122.26	+	395.468i	1.15578	+	0.407279i	0.315227	+	0.949016i	$0.397919\pi$
$972$	−1.63497	−	11.7207i	−0.00168207	−	0.0120584i
$973$	−1391.16	−	906.482i	−1.42977	−	0.931636i
$974$	162.412	+	497.246i	0.166747	+	0.510519i
$975$	615.026	+	232.832i	0.630796	+	0.238802i
$976$	393.527	−	873.000i	0.403204	−	0.894467i
$977$	190.133	−	77.0458i	0.194609	−	0.0788595i	−0.276178	−	0.961106i	$-0.589068\pi$
$977$	190.133	−	77.0458i	0.194609	−	0.0788595i	0.470787	+	0.882247i	$0.343970\pi$
$978$	434.883	+	88.2455i	0.444666	+	0.0902305i
$979$	2262.47	+	1968.78i	2.31101	+	2.01101i
$980$	6.50372	+	0.907231i	0.00663645	+	0.000925745i
$981$	−28.1157	+	54.3499i	−0.0286602	+	0.0554025i
$982$	191.678	+	91.7885i	0.195192	+	0.0934710i
$983$	−743.204	+	827.973i	−0.756057	+	0.842292i	−0.991569	−	0.129580i	$-0.958637\pi$
$983$	−743.204	+	827.973i	−0.756057	+	0.842292i	0.235512	+	0.971872i	$0.424323\pi$
$984$	256.240	−	1498.14i	0.260407	−	1.52250i
$985$	−116.508	+	275.260i	−0.118282	+	0.279452i
$986$	77.7837	−	226.278i	0.0788881	−	0.229490i
$987$	57.8864	−	246.118i	0.0586488	−	0.249359i
$988$	7.69494	−	1.31613i	0.00778840	−	0.00133212i
$989$	−287.262	−	180.940i	−0.290457	−	0.182952i
$990$	166.833	+	81.4760i	0.168518	+	0.0822990i
$991$	34.3768	−	892.465i	0.0346890	−	0.900570i	−0.874710	−	0.484646i	$-0.838948\pi$
$991$	34.3768	−	892.465i	0.0346890	−	0.900570i	0.909399	−	0.415924i	$-0.136542\pi$
$992$	−56.8502	−	24.5805i	−0.0573087	−	0.0247787i
$993$	−881.236	+	258.084i	−0.887448	+	0.259904i
$994$	−874.933	−	974.726i	−0.880214	−	0.980610i
$995$	−533.023	+	335.739i	−0.535701	+	0.337426i
$996$	−31.4304	+	3.40138i	−0.0315566	+	0.00341504i
$997$	1415.28	+	1001.85i	1.41954	+	1.00487i	0.995044	+	0.0994382i	$0.0317046\pi$
$997$	1415.28	+	1001.85i	1.41954	+	1.00487i	0.424493	+	0.905431i	$0.360452\pi$
$998$	−266.554	+	103.264i	−0.267088	+	0.103471i
$999$	−468.328	+	202.492i	−0.468797	+	0.202695i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	409.3.p.a.21.20	✓	8576
409.39	odd	408	inner	409.3.p.a.39.20	yes	8576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
409.3.p.a.21.20	✓	8576	1.1	even	1	trivial
409.3.p.a.39.20	yes	8576	409.39	odd	408	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:	\( N \)	\(=\)	\( 409 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	409.p (of order \(408\), degree \(128\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.59279 - 1.16475i) q^{2} +(-2.07047 - 1.61421i) q^{3} +(-0.0322475 - 0.101368i) q^{4} +(-2.55276 - 0.477193i) q^{5} +(1.41770 + 4.98268i) q^{6} +(-6.76777 + 5.19309i) q^{7} +(-2.57500 + 7.68276i) q^{8} +(-0.514037 - 2.04380i) q^{9} +(3.51021 + 3.73338i) q^{10} +(1.98127 + 17.0775i) q^{11} +(-0.0968619 + 0.261935i) q^{12} +(10.7557 - 8.51950i) q^{13} +(16.8283 - 0.388802i) q^{14} +(4.51513 + 5.10870i) q^{15} +(12.7026 - 8.99200i) q^{16} +(7.61063 - 11.4856i) q^{17} +(-1.56175 + 3.85408i) q^{18} +(-3.86841 + 3.69369i) q^{19} +(0.0339479 + 0.274156i) q^{20} +(22.3952 + 0.172446i) q^{21} +(16.7352 - 29.5087i) q^{22} +(1.81958 + 8.96709i) q^{23} +(17.7331 - 11.7504i) q^{24} +(-17.0230 - 6.59473i) q^{25} +(-27.0547 + 1.04212i) q^{26} +(-11.7788 + 26.6764i) q^{27} +(0.744657 + 0.518571i) q^{28} +(-5.57007 + 6.81386i) q^{29} +(-1.24133 - 13.3961i) q^{30} +(-33.6298 - 13.9299i) q^{31} +(1.70132 + 0.0262024i) q^{32} +(23.4646 - 38.5568i) q^{33} +(-25.5000 + 9.42975i) q^{34} +(19.7546 - 10.0272i) q^{35} +(-0.190600 + 0.118015i) q^{36} +(12.8392 + 11.8868i) q^{37} +(10.4638 - 1.37758i) q^{38} +(-36.0218 + 0.277373i) q^{39} +(10.2395 - 18.3834i) q^{40} +(48.9415 - 52.0531i) q^{41} +(-35.4701 - 26.3594i) q^{42} +(-25.6237 + 26.8357i) q^{43} +(1.66723 - 0.751545i) q^{44} +(0.336923 + 5.46262i) q^{45} +(7.54615 - 16.4021i) q^{46} +(2.49999 - 11.0090i) q^{47} +(-40.8155 - 1.88701i) q^{48} +(6.15234 - 22.9609i) q^{49} +(19.4329 + 30.3315i) q^{50} +(-34.2978 + 11.4955i) q^{51} +(-1.21045 - 0.815557i) q^{52} +(-5.79916 + 10.0444i) q^{53} +(49.8324 - 28.7708i) q^{54} +(3.09158 - 44.5402i) q^{55} +(-22.4703 - 65.3674i) q^{56} +(13.9719 - 1.40327i) q^{57} +(16.8084 - 4.36536i) q^{58} +(38.6395 - 107.015i) q^{59} +(0.372258 - 0.622433i) q^{60} +(53.0477 - 31.1742i) q^{61} +(37.3406 + 61.3577i) q^{62} +(14.0925 + 11.1625i) q^{63} +(-52.3581 - 39.5390i) q^{64} +(-31.5222 + 16.6157i) q^{65} +(-82.2831 + 34.0828i) q^{66} +(72.8648 - 28.8752i) q^{67} +(-1.40970 - 0.401094i) q^{68} +(10.7074 - 21.5033i) q^{69} +(-43.1440 - 7.03782i) q^{70} +(-50.6266 - 59.0916i) q^{71} +(17.0257 + 1.31357i) q^{72} +(80.4313 + 115.498i) q^{73} +(-6.60515 - 33.8877i) q^{74} +(24.6003 + 41.1329i) q^{75} +(0.499170 + 0.273021i) q^{76} +(-102.094 - 105.288i) q^{77} +(57.6984 + 41.5144i) q^{78} +(21.8713 + 103.681i) q^{79} +(-36.7176 + 16.8928i) q^{80} +(50.7389 - 27.2462i) q^{81} +(-138.582 + 25.9055i) q^{82} +(50.4584 + 101.334i) q^{83} +(-0.704710 - 2.27572i) q^{84} +(-24.9089 + 25.6882i) q^{85} +(72.0699 - 12.8987i) q^{86} +(22.5317 - 5.11665i) q^{87} +(-136.304 - 28.7531i) q^{88} +(128.920 - 117.526i) q^{89} +(5.82592 - 9.09327i) q^{90} +(-28.5498 + 113.514i) q^{91} +(0.850300 - 0.473614i) q^{92} +(47.1438 + 83.1272i) q^{93} +(-16.8046 + 14.6232i) q^{94} +(11.6377 - 7.58312i) q^{95} +(-3.48025 - 2.80055i) q^{96} +(-174.489 - 56.9923i) q^{97} +(-36.5430 + 29.4060i) q^{98} +(33.8847 - 12.8278i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8576 q - 124 q^{2} - 112 q^{3} - 124 q^{4} - 120 q^{5} - 120 q^{6} - 144 q^{7} + 8 q^{8} - 292 q^{9} - 96 q^{10} - 160 q^{11} + 36 q^{12} - 164 q^{13} - 16 q^{14} - 80 q^{15} - 204 q^{16} - 148 q^{17} - 148 q^{18}+ \cdots + 1180 q^{99}+O(q^{100}) \) 8576 * q - 124 * q^2 - 112 * q^3 - 124 * q^4 - 120 * q^5 - 120 * q^6 - 144 * q^7 + 8 * q^8 - 292 * q^9 - 96 * q^10 - 160 * q^11 + 36 * q^12 - 164 * q^13 - 16 * q^14 - 80 * q^15 - 204 * q^16 - 148 * q^17 - 148 * q^18 - 96 * q^19 + 68 * q^20 - 144 * q^21 - 256 * q^22 - 128 * q^23 - 1156 * q^24 - 2496 * q^25 - 280 * q^26 - 100 * q^27 - 92 * q^28 - 80 * q^29 + 672 * q^30 - 168 * q^31 + 2112 * q^32 - 96 * q^33 + 92 * q^34 + 64 * q^35 - 2344 * q^36 - 152 * q^37 - 2972 * q^39 + 112 * q^40 - 196 * q^41 + 488 * q^42 - 452 * q^43 + 92 * q^44 - 244 * q^45 - 124 * q^46 + 16 * q^47 - 188 * q^48 + 16 * q^49 + 96 * q^50 + 8 * q^51 - 828 * q^52 - 256 * q^53 + 240 * q^54 - 1016 * q^55 + 76 * q^56 - 92 * q^57 - 800 * q^58 + 48 * q^59 - 64 * q^60 + 428 * q^61 - 52 * q^62 + 1604 * q^63 - 136 * q^64 + 136 * q^65 + 224 * q^66 + 600 * q^67 - 136 * q^68 + 2808 * q^69 - 20 * q^70 - 188 * q^71 + 560 * q^72 + 144 * q^73 - 996 * q^74 + 1152 * q^75 + 992 * q^76 - 3084 * q^77 - 4900 * q^78 - 560 * q^79 - 292 * q^80 - 3128 * q^81 + 1488 * q^82 + 120 * q^83 + 6560 * q^84 + 288 * q^85 + 3248 * q^86 - 632 * q^87 + 144 * q^88 + 608 * q^89 + 268 * q^90 + 404 * q^91 - 5128 * q^92 - 104 * q^93 - 624 * q^94 + 84 * q^95 + 140 * q^96 - 840 * q^97 - 72 * q^98 + 1180 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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