LMFDB - Embedded newform 207.4.m.a.4.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(207, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([22, 12])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("207.4"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	207.m (of order $33$, 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 $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			4.10
Character	$\chi$	$=$	207.4
Dual form			207.4.m.a.52.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.46695 + 3.46434i) q^{2} +(-4.27108 + 2.95937i) q^{3} +(-3.29930 - 9.53272i) q^{4} +(-2.65977 + 1.37121i) q^{5} +(0.284244 - 22.0971i) q^{6} +(-16.6811 + 13.1182i) q^{7} +(8.51848 + 2.50125i) q^{8} +(9.48422 - 25.2794i) q^{9} +(1.81118 - 12.5970i) q^{10} +(-3.79715 + 0.362584i) q^{11} +(42.3024 + 30.9511i) q^{12} +(-56.1716 - 44.1738i) q^{13} +(-4.29442 - 90.1509i) q^{14} +(7.30217 - 13.7278i) q^{15} +(33.7548 - 26.5450i) q^{16} +(57.2427 + 66.0616i) q^{17} +(64.1796 + 95.2197i) q^{18} +(22.2958 - 25.7307i) q^{19} +(21.8467 + 20.8308i) q^{20} +(32.4247 - 105.394i) q^{21} +(8.11126 - 14.0491i) q^{22} +(5.96969 - 110.142i) q^{23} +(-43.7852 + 14.5263i) q^{24} +(-67.3130 + 94.5278i) q^{25} +(291.606 - 85.6232i) q^{26} +(34.3034 + 136.038i) q^{27} +(180.088 + 115.735i) q^{28} +(20.2562 - 58.5265i) q^{29} +(29.5437 + 59.1629i) q^{30} +(-161.452 + 153.944i) q^{31} +(12.0694 + 253.368i) q^{32} +(15.1449 - 12.7858i) q^{33} +(-370.075 + 35.3379i) q^{34} +(26.3801 - 57.7644i) q^{35} +(-272.273 - 7.00588i) q^{36} +(-240.948 + 154.848i) q^{37} +(34.1375 + 140.717i) q^{38} +(370.640 + 22.4372i) q^{39} +(-26.0869 + 5.02784i) q^{40} +(260.495 - 134.294i) q^{41} +(285.132 + 372.333i) q^{42} +(143.831 + 137.142i) q^{43} +(15.9844 + 35.0009i) q^{44} +(9.43745 + 80.2422i) q^{45} +(366.845 + 292.397i) q^{46} +(96.5673 + 167.260i) q^{47} +(-65.6126 + 213.269i) q^{48} +(25.3075 - 104.319i) q^{49} +(-161.419 - 466.391i) q^{50} +(-439.989 - 112.752i) q^{51} +(-235.769 + 681.211i) q^{52} +(-46.0020 - 319.951i) q^{53} +(-555.906 - 216.759i) q^{54} +(9.60236 - 6.17106i) q^{55} +(-174.909 + 70.0231i) q^{56} +(-19.0803 + 175.879i) q^{57} +(152.785 + 214.556i) q^{58} +(504.835 + 397.007i) q^{59} +(-154.955 - 24.3174i) q^{60} +(-205.893 - 848.703i) q^{61} +(-135.022 - 939.095i) q^{62} +(173.412 + 546.104i) q^{63} +(-618.526 - 397.503i) q^{64} +(209.975 + 40.4693i) q^{65} +(6.93274 + 84.0091i) q^{66} +(403.674 + 38.5461i) q^{67} +(440.885 - 763.635i) q^{68} +(300.456 + 488.094i) q^{69} +(135.038 + 233.892i) q^{70} +(-129.075 - 282.635i) q^{71} +(144.021 - 191.620i) q^{72} +(483.454 - 557.936i) q^{73} +(57.9599 - 1216.73i) q^{74} +(7.75586 - 602.940i) q^{75} +(-318.844 - 127.646i) q^{76} +(58.5842 - 55.8599i) q^{77} +(-992.081 + 1228.67i) q^{78} +(782.052 - 313.087i) q^{79} +(-53.3811 + 116.888i) q^{80} +(-549.099 - 479.512i) q^{81} +(-177.385 + 1233.74i) q^{82} +(-188.729 - 97.2965i) q^{83} +(-1111.67 + 38.6319i) q^{84} +(-242.836 - 97.2169i) q^{85} +(-829.932 + 159.956i) q^{86} +(86.6858 + 309.917i) q^{87} +(-33.2529 - 6.40896i) q^{88} +(1094.57 - 321.396i) q^{89} +(-301.268 - 165.259i) q^{90} +1516.48 q^{91} +(-1069.65 + 306.486i) q^{92} +(233.995 - 1135.30i) q^{93} +(-817.671 - 78.0781i) q^{94} +(-24.0195 + 99.0098i) q^{95} +(-801.359 - 1046.44i) q^{96} +(-4.11629 + 86.4116i) q^{97} +(298.965 + 345.024i) q^{98} +(-26.8471 + 99.4286i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1400 q - 9 q^{2} - 14 q^{3} + 263 q^{4} + 19 q^{5} - 35 q^{6} - 9 q^{7} - 74 q^{8} - 78 q^{9} - 68 q^{10} + 79 q^{11} + 54 q^{12} - 9 q^{13} + 159 q^{14} - 868 q^{15} + 1031 q^{16} - 308 q^{17} - 87 q^{18}+ \cdots + 7484 q^{99}+O(q^{100}) $ 1400 * q - 9 * q^2 - 14 * q^3 + 263 * q^4 + 19 * q^5 - 35 * q^6 - 9 * q^7 - 74 * q^8 - 78 * q^9 - 68 * q^10 + 79 * q^11 + 54 * q^12 - 9 * q^13 + 159 * q^14 - 868 * q^15 + 1031 * q^16 - 308 * q^17 - 87 * q^18 - 36 * q^19 + 119 * q^20 - 660 * q^21 - 52 * q^22 - 116 * q^23 + 2420 * q^24 + 1397 * q^25 + 432 * q^26 + 274 * q^27 - 324 * q^28 - 45 * q^29 + 768 * q^30 - 45 * q^31 + 111 * q^32 - 1664 * q^33 + 403 * q^34 - 536 * q^35 - 121 * q^36 - 180 * q^37 - 117 * q^38 - 46 * q^39 - 473 * q^40 - 333 * q^41 - 332 * q^42 - 9 * q^43 - 1908 * q^44 + 1762 * q^45 + 484 * q^46 + 216 * q^47 + 1072 * q^48 + 4615 * q^49 - 105 * q^50 + 1298 * q^51 - 708 * q^52 - 1380 * q^53 + 4116 * q^54 - 1328 * q^55 - 3971 * q^56 + 2154 * q^57 - 338 * q^58 + 1917 * q^59 + 154 * q^60 + 27 * q^61 - 3854 * q^62 - 4850 * q^63 - 5854 * q^64 + 3363 * q^65 - 2017 * q^66 + 603 * q^67 - 18454 * q^68 - 4653 * q^69 + 542 * q^70 - 5296 * q^71 - 8044 * q^72 - 36 * q^73 + 3243 * q^74 + 5140 * q^75 - 1029 * q^76 - 1661 * q^77 + 14687 * q^78 - 9 * q^79 + 10312 * q^80 - 294 * q^81 - 770 * q^82 - 2735 * q^83 + 2298 * q^84 + 241 * q^85 + 10507 * q^86 - 10268 * q^87 + 2183 * q^88 - 2980 * q^89 + 33928 * q^90 - 1452 * q^91 - 1973 * q^92 - 11406 * q^93 + 2034 * q^94 - 3339 * q^95 - 4446 * q^96 - 5193 * q^97 + 14820 * q^98 + 7484 * q^99

Character values

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

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−2.46695	+	3.46434i	−0.872198	+	1.22483i	0.101006	+	0.994886i	$0.467794\pi$
$2$	−2.46695	+	3.46434i	−0.872198	+	1.22483i	−0.973204	+	0.229945i	$0.926145\pi$
$3$	−4.27108	+	2.95937i	−0.821969	+	0.569532i
$3$	−4.27108	+	2.95937i	−0.821969	+	0.569532i
$4$	−3.29930	−	9.53272i	−0.412413	−	1.19159i
$5$	−2.65977	+	1.37121i	−0.237897	+	0.122644i	−0.573053	−	0.819518i	$-0.694241\pi$
$5$	−2.65977	+	1.37121i	−0.237897	+	0.122644i	0.335156	+	0.942163i	$0.391211\pi$
$6$	0.284244	−	22.0971i	0.0193404	−	1.50352i
$7$	−16.6811	+	13.1182i	−0.900694	+	0.708314i	−0.956996	−	0.290100i	$-0.906311\pi$
$7$	−16.6811	+	13.1182i	−0.900694	+	0.708314i	0.0563020	+	0.998414i	$0.482069\pi$
$8$	8.51848	+	2.50125i	0.376467	+	0.110541i
$9$	9.48422	−	25.2794i	0.351268	−	0.936275i
$10$	1.81118	−	12.5970i	0.0572746	−	0.398353i
$11$	−3.79715	+	0.362584i	−0.104080	+	0.00993847i	−0.146966	−	0.989142i	$-0.546951\pi$
$11$	−3.79715	+	0.362584i	−0.104080	+	0.00993847i	0.0428859	+	0.999080i	$0.486345\pi$
$12$	42.3024	+	30.9511i	1.01764	+	0.744568i
$13$	−56.1716	−	44.1738i	−1.19840	−	0.942432i	−0.199105	−	0.979978i	$-0.563804\pi$
$13$	−56.1716	−	44.1738i	−1.19840	−	0.942432i	−0.999295	+	0.0375457i	$0.988046\pi$
$14$	−4.29442	−	90.1509i	−0.0819808	−	1.72099i
$15$	7.30217	−	13.7278i	0.125694	−	0.236300i
$16$	33.7548	−	26.5450i	0.527418	−	0.414766i
$17$	57.2427	+	66.0616i	0.816670	+	0.942487i	0.999171	−	0.0407185i	$-0.0129647\pi$
$17$	57.2427	+	66.0616i	0.816670	+	0.942487i	−0.182501	+	0.983206i	$0.558419\pi$
$18$	64.1796	+	95.2197i	0.840404	+	1.24686i
$19$	22.2958	−	25.7307i	0.269211	−	0.310686i	−0.605007	−	0.796220i	$-0.706830\pi$
$19$	22.2958	−	25.7307i	0.269211	−	0.310686i	0.874217	+	0.485535i	$0.161375\pi$
$20$	21.8467	+	20.8308i	0.244253	+	0.232895i
$21$	32.4247	−	105.394i	0.336936	−	1.09519i
$22$	8.11126	−	14.0491i	0.0786058	−	0.136149i
$23$	5.96969	−	110.142i	0.0541203	−	0.998534i
$23$	5.96969	−	110.142i	0.0541203	−	0.998534i
$24$	−43.7852	+	14.5263i	−0.372401	+	0.123549i
$25$	−67.3130	+	94.5278i	−0.538504	+	0.756223i
$26$	291.606	−	85.6232i	2.19956	−	0.645850i
$27$	34.3034	+	136.038i	0.244507	+	0.969648i
$28$	180.088	+	115.735i	1.21548	+	0.781140i
$29$	20.2562	−	58.5265i	0.129706	−	0.374762i	−0.861384	−	0.507955i	$-0.830402\pi$
$29$	20.2562	−	58.5265i	0.129706	−	0.374762i	0.991090	+	0.133193i	$0.0425229\pi$
$30$	29.5437	+	59.1629i	0.179797	+	0.360054i
$31$	−161.452	+	153.944i	−0.935405	+	0.891907i	−0.994328	−	0.106355i	$-0.966082\pi$
$31$	−161.452	+	153.944i	−0.935405	+	0.891907i	0.0589229	+	0.998263i	$0.481233\pi$
$32$	12.0694	+	253.368i	0.0666746	+	1.39967i
$33$	15.1449	−	12.7858i	0.0798906	−	0.0674462i
$34$	−370.075	+	35.3379i	−1.86669	+	0.178247i
$35$	26.3801	−	57.7644i	0.127402	−	0.278971i
$36$	−272.273	−	7.00588i	−1.26052	−	0.0324346i
$37$	−240.948	+	154.848i	−1.07058	+	0.688023i	−0.952364	−	0.304965i	$-0.901355\pi$
$37$	−240.948	+	154.848i	−1.07058	+	0.688023i	−0.118221	+	0.992987i	$0.537719\pi$
$38$	34.1375	+	140.717i	0.145732	+	0.600717i
$39$	370.640	+	22.4372i	1.52179	+	0.0921239i
$40$	−26.0869	+	5.02784i	−0.103118	+	0.0198743i
$41$	260.495	−	134.294i	0.992254	−	0.511543i	0.115926	−	0.993258i	$-0.463016\pi$
$41$	260.495	−	134.294i	0.992254	−	0.511543i	0.876328	+	0.481715i	$0.159986\pi$
$42$	285.132	+	372.333i	1.04754	+	1.36791i
$43$	143.831	+	137.142i	0.510093	+	0.486372i	0.900856	−	0.434119i	$-0.142940\pi$
$43$	143.831	+	137.142i	0.510093	+	0.486372i	−0.390763	+	0.920491i	$0.627789\pi$
$44$	15.9844	+	35.0009i	0.0547667	+	0.119922i
$45$	9.43745	+	80.2422i	0.0312634	+	0.265818i
$46$	366.845	+	292.397i	1.17583	+	0.937208i
$47$	96.5673	+	167.260i	0.299698	+	0.519092i	0.976067	−	0.217471i	$-0.0697808\pi$
$47$	96.5673	+	167.260i	0.299698	+	0.519092i	−0.676369	+	0.736563i	$0.736448\pi$
$48$	−65.6126	+	213.269i	−0.197299	+	0.641306i
$49$	25.3075	−	104.319i	0.0737829	−	0.304137i
$50$	−161.419	−	466.391i	−0.456563	−	1.31915i
$51$	−439.989	−	112.752i	−1.20805	−	0.309576i
$52$	−235.769	+	681.211i	−0.628756	+	1.81667i
$53$	−46.0020	−	319.951i	−0.119224	−	0.829220i	−0.958414	−	0.285382i	$-0.907880\pi$
$53$	−46.0020	−	319.951i	−0.119224	−	0.829220i	0.839190	−	0.543838i	$-0.183029\pi$
$54$	−555.906	−	216.759i	−1.40091	−	0.546245i
$55$	9.60236	−	6.17106i	0.0235415	−	0.0151292i
$56$	−174.909	+	70.0231i	−0.417379	+	0.167094i
$57$	−19.0803	+	175.879i	−0.0443377	+	0.408698i
$58$	152.785	+	214.556i	0.345890	+	0.485735i
$59$	504.835	+	397.007i	1.11397	+	0.876032i	0.993174	−	0.116645i	$-0.0372141\pi$
$59$	504.835	+	397.007i	1.11397	+	0.876032i	0.120792	+	0.992678i	$0.461457\pi$
$60$	−154.955	−	24.3174i	−0.333410	−	0.0523227i
$61$	−205.893	−	848.703i	−0.432162	−	1.78140i	−0.604762	−	0.796406i	$-0.706732\pi$
$61$	−205.893	−	848.703i	−0.432162	−	1.78140i	0.172600	−	0.984992i	$-0.444783\pi$
$62$	−135.022	−	939.095i	−0.276577	−	1.92363i
$63$	173.412	+	546.104i	0.346792	+	1.09211i
$64$	−618.526	−	397.503i	−1.20806	−	0.776373i
$65$	209.975	+	40.4693i	0.400680	+	0.0772247i
$66$	6.93274	+	84.0091i	0.0129297	+	0.156679i
$67$	403.674	+	38.5461i	0.736068	+	0.0702860i	0.456355	−	0.889798i	$-0.349155\pi$
$67$	403.674	+	38.5461i	0.736068	+	0.0702860i	0.279713	+	0.960084i	$0.409761\pi$
$68$	440.885	−	763.635i	0.786252	−	1.36183i
$69$	300.456	+	488.094i	0.524212	+	0.851588i
$70$	135.038	+	233.892i	0.230572	+	0.399363i
$71$	−129.075	−	282.635i	−0.215752	−	0.472432i	0.770550	−	0.637380i	$-0.219982\pi$
$71$	−129.075	−	282.635i	−0.215752	−	0.472432i	−0.986302	+	0.164948i	$0.947254\pi$
$72$	144.021	−	191.620i	0.235737	−	0.313647i
$73$	483.454	−	557.936i	0.775123	−	0.894540i	−0.221624	−	0.975132i	$-0.571136\pi$
$73$	483.454	−	557.936i	0.775123	−	0.894540i	0.996747	+	0.0805923i	$0.0256812\pi$
$74$	57.9599	−	1216.73i	0.0910501	−	1.91138i
$75$	7.75586	−	602.940i	0.0119409	−	0.928287i
$76$	−318.844	−	127.646i	−0.481236	−	0.192658i
$77$	58.5842	−	55.8599i	0.0867050	−	0.0826731i
$78$	−992.081	+	1228.67i	−1.44014	+	1.78359i
$79$	782.052	−	313.087i	1.11377	−	0.445886i	0.259514	−	0.965739i	$-0.416438\pi$
$79$	782.052	−	313.087i	1.11377	−	0.445886i	0.854255	+	0.519854i	$0.174013\pi$
$80$	−53.3811	+	116.888i	−0.0746024	+	0.163356i
$81$	−549.099	−	479.512i	−0.753222	−	0.657766i
$82$	−177.385	+	1233.74i	−0.238889	+	1.66151i
$83$	−188.729	−	97.2965i	−0.249587	−	0.128671i	0.328894	−	0.944367i	$-0.393324\pi$
$83$	−188.729	−	97.2965i	−0.249587	−	0.128671i	−0.578481	+	0.815696i	$0.696354\pi$
$84$	−1111.67	+	38.6319i	−1.44397	+	0.0501796i
$85$	−242.836	−	97.2169i	−0.309874	−	0.124055i
$86$	−829.932	+	159.956i	−1.04063	+	0.200564i
$87$	86.6858	+	309.917i	0.106824	+	0.381915i
$88$	−33.2529	−	6.40896i	−0.0402814	−	0.00776361i
$89$	1094.57	−	321.396i	1.30365	−	0.382786i	0.445083	−	0.895490i	$-0.353174\pi$
$89$	1094.57	−	321.396i	1.30365	−	0.382786i	0.858565	+	0.512704i	$0.171356\pi$
$90$	−301.268	−	165.259i	−0.352850	−	0.193553i
$91$	1516.48			1.74693
$92$	−1069.65	+	306.486i	−1.21216	+	0.347320i
$93$	233.995	−	1135.30i	0.260905	−	1.26586i
$94$	−817.671	−	78.0781i	−0.897195	−	0.0856718i
$95$	−24.0195	+	99.0098i	−0.0259405	+	0.106928i
$96$	−801.359	−	1046.44i	−0.851962	−	1.11251i
$97$	−4.11629	+	86.4116i	−0.00430872	+	0.0904512i	−0.999997	−	0.00230753i	$-0.999265\pi$
$97$	−4.11629	+	86.4116i	−0.00430872	+	0.0904512i	0.995689	+	0.0927587i	$0.0295685\pi$
$98$	298.965	+	345.024i	0.308163	+	0.355639i
$99$	−26.8471	+	99.4286i	−0.0272549	+	0.100939i
$100$	1123.19	+	329.799i	1.12319	+	0.329799i
$101$	−1411.83	−	727.847i	−1.39091	−	0.717065i	−0.410103	−	0.912039i	$-0.634507\pi$
$101$	−1411.83	−	727.847i	−1.39091	−	0.717065i	−0.980808	+	0.194975i	$0.937538\pi$
$102$	1476.04	−	1246.12i	1.43284	−	1.20965i
$103$	−598.210	−	840.069i	−0.572266	−	0.803635i	0.422441	−	0.906391i	$-0.361173\pi$
$103$	−598.210	−	840.069i	−0.572266	−	0.803635i	−0.994707	+	0.102755i	$0.967234\pi$
$104$	−368.007	−	516.793i	−0.346981	−	0.487267i
$105$	58.2749	+	324.785i	0.0541623	+	0.301865i
$106$	1221.91	+	629.936i	1.11964	+	0.577215i
$107$	593.964	+	174.403i	0.536641	+	0.157572i	0.538813	−	0.842426i	$-0.318873\pi$
$107$	593.964	+	174.403i	0.536641	+	0.157572i	−0.00217148	+	0.999998i	$0.500691\pi$
$108$	1183.63	−	775.834i	1.05458	−	0.691247i
$109$	−861.335	−	994.034i	−0.756889	−	0.873497i	0.238328	−	0.971185i	$-0.423401\pi$
$109$	−861.335	−	994.034i	−0.756889	−	0.873497i	−0.995217	+	0.0976879i	$0.968855\pi$
$110$	−2.30984	+	48.4896i	−0.00200214	+	0.0420300i
$111$	570.855	−	1374.42i	0.488137	−	1.17527i
$112$	−214.844	+	885.601i	−0.181258	+	0.747155i
$113$	806.677	+	77.0283i	0.671555	+	0.0641258i	0.425263	−	0.905070i	$-0.360182\pi$
$113$	806.677	+	77.0283i	0.671555	+	0.0641258i	0.246292	+	0.969196i	$0.420788\pi$
$114$	−562.237	−	499.986i	−0.461915	−	0.410772i
$115$	135.150	+	301.139i	0.109590	+	0.244186i
$116$	−624.748			−0.500055
$117$	−1649.43	+	1001.03i	−1.30334	+	0.790986i
$118$	−2620.77	+	769.528i	−2.04459	+	0.600346i
$119$	−1821.48	−	351.061i	−1.40315	−	0.270434i
$120$	96.5400	−	98.6752i	0.0734404	−	0.0750647i
$121$	−1292.66	+	249.140i	−0.971195	+	0.187182i
$122$	3448.13	+	1380.42i	2.55884	+	1.02441i
$123$	−715.166	+	1344.48i	−0.524263	+	0.985592i
$124$	2000.18	+	1031.16i	1.44856	+	0.746785i
$125$	102.653	−	713.967i	0.0734525	−	0.510873i
$126$	−2319.69	−	746.451i	−1.64012	−	0.527771i
$127$	−253.258	+	554.557i	−0.176953	+	0.387472i	−0.977238	−	0.212147i	$-0.931954\pi$
$127$	−253.258	+	554.557i	−0.176953	+	0.387472i	0.800285	+	0.599620i	$0.204682\pi$
$128$	1019.08	−	407.977i	0.703708	−	0.281722i
$129$	−1020.17	−	160.097i	−0.696285	−	0.109269i
$130$	−658.197	+	627.589i	−0.444059	+	0.423410i
$131$	1508.84	+	604.049i	1.00632	+	0.402870i	0.815502	−	0.578755i	$-0.196461\pi$
$131$	1508.84	+	604.049i	1.00632	+	0.402870i	0.190820	+	0.981625i	$0.438885\pi$
$132$	−171.851	−	102.188i	−0.113316	−	0.0673811i
$133$	−34.3786	+	721.696i	−0.0224136	+	0.470519i
$134$	−1129.38	+	1303.37i	−0.728086	+	0.840256i
$135$	−277.775	−	314.792i	−0.177089	−	0.200689i
$136$	322.384	+	705.922i	0.203266	+	0.445091i
$137$	−322.703	−	558.938i	−0.201244	−	0.348564i	0.747686	−	0.664053i	$-0.231165\pi$
$137$	−322.703	−	558.938i	−0.201244	−	0.348564i	−0.948929	+	0.315489i	$0.897832\pi$
$138$	−2432.13	−	163.220i	−1.50027	−	0.100683i
$139$	653.842	−	1132.49i	0.398980	−	0.691053i	−0.594621	−	0.804006i	$-0.702698\pi$
$139$	653.842	−	1132.49i	0.398980	−	0.691053i	0.993600	+	0.112953i	$0.0360311\pi$
$140$	−637.688	−	60.8918i	−0.384961	−	0.0367593i
$141$	−907.430	−	428.600i	−0.541981	−	0.255990i
$142$	1297.57	+	250.086i	0.766828	+	0.147794i
$143$	229.309	+	147.368i	0.134096	+	0.0861784i
$144$	−350.906	−	1105.06i	−0.203070	−	0.639502i
$145$	26.3750	+	183.442i	0.0151057	+	0.105062i
$146$	740.225	+	3051.25i	0.419599	+	1.72961i
$147$	200.628	+	520.449i	0.112568	+	0.292013i
$148$	2271.08	+	1786.00i	1.26136	+	0.991947i
$149$	645.131	+	905.960i	0.354706	+	0.498115i	0.952920	−	0.303221i	$-0.0980622\pi$
$149$	645.131	+	905.960i	0.354706	+	0.498115i	−0.598214	+	0.801336i	$0.704123\pi$
$150$	2069.66	+	1514.29i	1.12658	+	0.824275i
$151$	2521.04	−	1009.27i	1.35867	−	0.543930i	0.426021	−	0.904713i	$-0.359915\pi$
$151$	2521.04	−	1009.27i	1.35867	−	0.543930i	0.932650	+	0.360784i	$0.117491\pi$
$152$	254.285	−	163.419i	0.135692	−	0.0872043i
$153$	2212.90	−	820.519i	1.16930	−	0.433562i
$154$	48.9938	+	340.759i	0.0256366	+	0.178306i
$155$	218.335	−	630.838i	0.113143	−	0.326904i
$156$	−1008.97	−	3607.24i	−0.517834	−	1.85135i
$157$	122.911	+	355.128i	0.0624800	+	0.180524i	0.971920	−	0.235310i	$-0.0756107\pi$
$157$	122.911	+	355.128i	0.0624800	+	0.180524i	−0.909440	+	0.415835i	$0.863489\pi$
$158$	−844.643	+	3481.67i	−0.425293	+	1.75308i
$159$	1143.33	+	1230.40i	0.570265	+	0.613692i
$160$	−379.521	−	657.350i	−0.187524	−	0.324800i
$161$	1345.29	+	1915.61i	0.658530	+	0.937709i
$162$	3015.79	−	719.338i	1.46261	−	0.348867i
$163$	−915.231	−	2004.08i	−0.439794	−	0.963015i	−0.991636	−	0.129066i	$-0.958802\pi$
$163$	−915.231	−	2004.08i	−0.439794	−	0.963015i	0.551842	−	0.833949i	$-0.313925\pi$
$164$	−2139.64	−	2040.14i	−1.01877	−	0.971393i
$165$	−22.7500	+	54.7741i	−0.0107338	+	0.0258434i
$166$	802.653	−	413.797i	0.375289	−	0.193475i
$167$	1788.62	−	344.728i	0.828787	−	0.159736i	0.242821	−	0.970071i	$-0.421927\pi$
$167$	1788.62	−	344.728i	0.828787	−	0.159736i	0.585966	+	0.810336i	$0.300715\pi$
$168$	539.827	−	816.696i	0.247908	−	0.375057i
$169$	685.959	+	2827.56i	0.312225	+	1.28701i
$170$	935.857	−	601.439i	0.422218	−	0.271343i
$171$	−438.999	−	807.661i	−0.196322	−	0.361189i
$172$	832.798	−	1823.57i	0.369187	−	0.808407i
$173$	−2013.32	+	192.248i	−0.884795	+	0.0844877i	−0.527551	−	0.849523i	$-0.676890\pi$
$173$	−2013.32	+	192.248i	−0.884795	+	0.0844877i	−0.357244	+	0.934011i	$0.616284\pi$
$174$	−1287.51	−	464.240i	−0.560953	−	0.202264i
$175$	−117.177	−	2459.85i	−0.0506157	−	1.06256i
$176$	−118.547	+	113.034i	−0.0507717	+	0.0484108i
$177$	−3331.08	−	201.652i	−1.41457	−	0.0856332i
$178$	−1586.83	+	4584.85i	−0.668192	+	1.93061i
$179$	−3002.29	−	1929.45i	−1.25364	−	0.805665i	−0.266239	−	0.963907i	$-0.585781\pi$
$179$	−3002.29	−	1929.45i	−1.25364	−	0.805665i	−0.987400	+	0.158242i	$0.949417\pi$
$180$	733.789	−	354.708i	0.303852	−	0.146880i
$181$	3245.19	−	952.873i	1.33267	−	0.391307i	0.463620	−	0.886034i	$-0.346550\pi$
$181$	3245.19	−	952.873i	1.33267	−	0.391307i	0.869048	+	0.494728i	$0.164732\pi$
$182$	−3741.09	+	5253.62i	−1.52367	+	2.13969i
$183$	3391.01	+	3015.56i	1.36979	+	1.21812i
$184$	326.347	−	923.315i	0.130753	−	0.369933i
$185$	428.537	−	742.249i	0.170306	−	0.294979i
$186$	3355.82	+	3611.37i	1.32291	+	1.42365i
$187$	−241.312	−	230.090i	−0.0943662	−	0.0899780i
$188$	1275.83	−	1472.39i	0.494945	−	0.571197i
$189$	−2356.78	−	1819.26i	−0.907041	−	0.700168i
$190$	−283.749	−	327.464i	−0.108344	−	0.125035i
$191$	−860.340	+	676.579i	−0.325927	+	0.256312i	−0.767692	−	0.640819i	$-0.778595\pi$
$191$	−860.340	+	676.579i	−0.325927	+	0.256312i	0.441765	+	0.897131i	$0.354352\pi$
$192$	3818.13	−	132.685i	1.43516	−	0.0498734i
$193$	62.1958	+	1305.65i	0.0231966	+	0.486957i	0.980337	+	0.197332i	$0.0632276\pi$
$193$	62.1958	+	1305.65i	0.0231966	+	0.486957i	−0.957140	+	0.289625i	$0.906469\pi$
$194$	−289.205	−	227.433i	−0.107029	−	0.0841688i
$195$	−1016.58	+	448.546i	−0.373328	+	0.164723i
$196$	−1077.94	+	102.931i	−0.392836	+	0.0375112i
$197$	−255.099	+	1774.25i	−0.0922592	+	0.641677i	0.890251	+	0.455470i	$0.150529\pi$
$197$	−255.099	+	1774.25i	−0.0922592	+	0.641677i	−0.982510	+	0.186207i	$0.940380\pi$
$198$	−278.225	−	338.293i	−0.0998614	−	0.121421i
$199$	−2304.58	−	676.686i	−0.820942	−	0.241050i	−0.155820	−	0.987785i	$-0.549802\pi$
$199$	−2304.58	−	676.686i	−0.820942	−	0.241050i	−0.665122	+	0.746735i	$0.731620\pi$
$200$	−809.842	+	636.867i	−0.286322	+	0.225166i
$201$	−1838.19	+	1029.99i	−0.645056	+	0.361441i
$202$	6004.42	−	3095.49i	2.09143	−	1.07821i
$203$	429.864	+	1242.01i	0.148623	+	0.429419i
$204$	376.827	+	4566.29i	0.129329	+	1.56718i
$205$	−508.710	+	714.383i	−0.173316	+	0.243389i
$206$	4386.04			1.48345
$207$	−2727.72	−	1195.53i	−0.915892	−	0.401424i
$208$	−3068.66			−1.02295
$209$	−75.3309	+	105.787i	−0.0249318	+	0.0350118i
$210$	−1268.93	−	599.344i	−0.416973	−	0.196946i
$211$	413.542	+	1194.85i	0.134926	+	0.389843i	0.992142	−	0.125113i	$-0.0399294\pi$
$211$	413.542	+	1194.85i	0.134926	+	0.389843i	−0.857216	+	0.514956i	$0.827808\pi$
$212$	−2898.23	+	1494.14i	−0.938920	+	0.484047i
$213$	1387.71	+	825.176i	0.446407	+	0.265447i
$214$	−2069.47	+	1627.45i	−0.661057	+	0.519861i
$215$	−570.607	−	167.545i	−0.181000	−	0.0531465i
$216$	−48.0520	+	1244.64i	−0.0151367	+	0.392068i
$217$	673.730	−	4685.90i	0.210764	−	1.46590i
$218$	5568.54	−	531.732i	1.73004	−	0.165199i
$219$	−413.730	+	3813.71i	−0.127659	+	1.17674i
$220$	−90.5081	−	71.1763i	−0.0277366	−	0.0218123i
$221$	−297.220	−	6239.41i	−0.0904669	−	1.89913i
$222$	3353.20	+	5368.27i	1.01375	+	1.62295i
$223$	818.678	−	643.815i	0.245842	−	0.193332i	−0.487633	−	0.873049i	$-0.662140\pi$
$223$	818.678	−	643.815i	0.245842	−	0.193332i	0.733475	+	0.679717i	$0.237897\pi$
$224$	−3525.05	−	4068.12i	−1.05146	−	1.21345i
$225$	1751.20	+	2598.16i	0.518873	+	0.769824i
$226$	−2256.88	+	2604.58i	−0.664273	+	0.766611i
$227$	3293.33	+	3140.18i	0.962933	+	0.918155i	0.996692	−	0.0812754i	$-0.0258993\pi$
$227$	3293.33	+	3140.18i	0.962933	+	0.918155i	−0.0337588	+	0.999430i	$0.510748\pi$
$228$	1739.56	−	398.393i	0.505286	−	0.115720i
$229$	3115.67	−	5396.50i	0.899080	−	1.55725i	0.0704069	−	0.997518i	$-0.477570\pi$
$229$	3115.67	−	5396.50i	0.899080	−	1.55725i	0.828673	−	0.559733i	$-0.189096\pi$
$230$	−1376.66	−	274.688i	−0.394670	−	0.0787497i
$231$	−84.9074	+	411.955i	−0.0241840	+	0.117336i
$232$	318.942	−	447.891i	0.0902567	−	0.126748i
$233$	−2391.92	+	702.333i	−0.672533	+	0.197474i	−0.600131	−	0.799902i	$-0.704885\pi$
$233$	−2391.92	+	702.333i	−0.672533	+	0.197474i	−0.0724024	+	0.997376i	$0.523067\pi$
$234$	601.150	−	8183.70i	0.167942	−	2.28626i
$235$	−486.194	−	312.458i	−0.134961	−	0.0867340i
$236$	2118.95	−	6122.30i	0.584457	−	1.68868i
$237$	−2413.67	+	3651.60i	−0.661538	+	1.00083i
$238$	5709.68	−	5444.17i	1.55506	−	1.48275i
$239$	84.6178	+	1776.35i	0.0229015	+	0.480762i	0.980962	+	0.194198i	$0.0622103\pi$
$239$	84.6178	+	1776.35i	0.0229015	+	0.480762i	−0.958061	+	0.286565i	$0.907487\pi$
$240$	−117.921	−	657.214i	−0.0317158	−	0.176762i
$241$	−5957.87	+	568.908i	−1.59245	+	0.152060i	−0.853278	−	0.521457i	$-0.825389\pi$
$241$	−5957.87	+	568.908i	−1.59245	+	0.152060i	−0.739171	+	0.673517i	$0.764783\pi$
$242$	2325.82	−	5092.84i	0.617807	−	1.35281i
$243$	3764.30	+	423.043i	0.993744	+	0.111680i
$244$	−7411.14	+	4762.85i	−1.94447	+	1.24963i
$245$	75.7307	+	312.166i	0.0197480	+	0.0814023i
$246$	−2893.47	−	5794.35i	−0.749923	−	1.50177i
$247$	−2389.02	+	460.445i	−0.615423	+	0.118613i
$248$	−1760.37	+	907.536i	−0.450741	+	0.232373i
$249$	1094.01	−	142.958i	0.278435	−	0.0363840i
$250$	2220.19	+	2116.94i	0.561668	+	0.535549i
$251$	−1488.25	−	3258.80i	−0.374252	−	0.819497i	−0.999244	−	0.0388664i	$-0.987625\pi$
$251$	−1488.25	−	3258.80i	−0.374252	−	0.819497i	0.624993	−	0.780631i	$-0.285102\pi$
$252$	4633.71	−	3454.85i	1.15832	−	0.863632i
$253$	17.2681	+	420.392i	0.00429104	+	0.104466i
$254$	−1296.40	−	2245.44i	−0.320250	−	0.554690i
$255$	1324.87	−	303.422i	0.325360	−	0.0745137i
$256$	286.083	−	1179.25i	0.0698446	−	0.287903i
$257$	−63.9971	−	184.908i	−0.0155332	−	0.0448802i	0.936968	−	0.349416i	$-0.113620\pi$
$257$	−63.9971	−	184.908i	−0.0155332	−	0.0448802i	−0.952501	+	0.304536i	$0.901499\pi$
$258$	3071.33	−	3139.26i	0.741135	−	0.757527i
$259$	1987.96	−	5743.83i	0.476933	−	1.37801i
$260$	−306.988	−	2135.15i	−0.0732254	−	0.509294i
$261$	−1287.40	−	1067.14i	−0.305319	−	0.253083i
$262$	−5814.87	+	3736.99i	−1.37116	+	0.881191i
$263$	3672.52	−	1470.25i	0.861054	−	0.344714i	0.101246	−	0.994861i	$-0.467717\pi$
$263$	3672.52	−	1470.25i	0.861054	−	0.344714i	0.759808	+	0.650147i	$0.225293\pi$
$264$	160.992	−	71.0344i	0.0375317	−	0.0165601i
$265$	561.073	+	787.917i	0.130062	+	0.182647i
$266$	−2415.39	−	1899.49i	−0.556757	−	0.437838i
$267$	−3723.88	+	4611.96i	−0.853550	+	1.05711i
$268$	−964.393	−	3975.28i	−0.219812	−	0.906078i
$269$	−699.572	−	4865.63i	−0.158564	−	1.10283i	−0.901283	−	0.433231i	$-0.857373\pi$
$269$	−699.572	−	4865.63i	−0.158564	−	1.10283i	0.742719	−	0.669603i	$-0.233536\pi$
$270$	1775.80	−	185.732i	0.400267	−	0.0418641i
$271$	−523.294	−	336.301i	−0.117298	−	0.0753831i	0.480676	−	0.876898i	$-0.340391\pi$
$271$	−523.294	−	336.301i	−0.117298	−	0.0753831i	−0.597975	+	0.801515i	$0.704028\pi$
$272$	3685.82	+	710.384i	0.821638	+	0.158358i
$273$	−6477.02	+	4487.84i	−1.43592	+	0.994932i
$274$	2732.44	+	260.917i	0.602456	+	0.0575276i
$275$	221.323	−	383.343i	0.0485320	−	0.0840598i
$276$	3661.56	−	4474.53i	0.798552	−	0.975851i
$277$	−1076.79	−	1865.05i	−0.233567	−	0.404550i	0.725288	−	0.688445i	$-0.241706\pi$
$277$	−1076.79	−	1865.05i	−0.233567	−	0.404550i	−0.958855	+	0.283896i	$0.908373\pi$
$278$	2310.33	+	5058.93i	0.498434	+	1.09142i
$279$	2360.37	+	5541.44i	0.506493	+	1.18909i
$280$	369.202	−	426.082i	0.0788002	−	0.0909402i
$281$	−204.919	+	4301.77i	−0.0435033	+	0.913247i	0.866635	+	0.498942i	$0.166278\pi$
$281$	−204.919	+	4301.77i	−0.0435033	+	0.913247i	−0.910138	+	0.414304i	$0.864025\pi$
$282$	3723.40	−	2086.32i	0.786260	−	0.440561i
$283$	−3476.60	−	1391.82i	−0.730256	−	0.292350i	−0.0234180	−	0.999726i	$-0.507455\pi$
$283$	−3476.60	−	1391.82i	−0.730256	−	0.292350i	−0.706838	+	0.707375i	$0.749879\pi$
$284$	−2268.42	+	2162.94i	−0.473966	+	0.451925i
$285$	−190.418	−	493.961i	−0.0395767	−	0.102666i
$286$	−1076.23	+	430.856i	−0.222513	+	0.0890806i
$287$	−2583.64	+	5657.38i	−0.531385	+	1.16357i
$288$	6519.46	+	2097.89i	1.33390	+	0.429234i
$289$	−388.214	+	2700.09i	−0.0790177	+	0.549580i
$290$	−700.573	−	361.171i	−0.141859	−	0.0731333i
$291$	−238.143	−	381.252i	−0.0479732	−	0.0768021i
$292$	−6913.70	−	2767.83i	−1.38560	−	0.554709i
$293$	−2495.65	+	480.998i	−0.497603	+	0.0959051i	−0.431877	−	0.901933i	$-0.642148\pi$
$293$	−2495.65	+	480.998i	−0.497603	+	0.0959051i	−0.0657261	+	0.997838i	$0.520936\pi$
$294$	−2297.96	−	588.875i	−0.455849	−	0.116816i
$295$	−1887.12	−	363.713i	−0.372449	−	0.0717837i
$296$	−2439.82	+	716.397i	−0.479094	+	0.140675i
$297$	−179.580	−	504.118i	−0.0350852	−	0.0984912i
$298$	−4730.06			−0.919480
$299$	−5200.74	+	5923.18i	−1.00591	+	1.14564i
$300$	−5773.24	+	1915.35i	−1.11106	+	0.368609i
$301$	−4198.31	−	400.890i	−0.803942	−	0.0767672i
$302$	−2722.81	+	11223.6i	−0.518808	+	2.13856i
$303$	8184.00	−	1069.43i	1.55168	−	0.202763i
$304$	69.5663	−	1460.38i	0.0131247	−	0.275521i
$305$	1711.37	+	1975.03i	0.321288	+	0.370787i
$306$	−2616.55	+	9690.43i	−0.488818	+	1.81034i
$307$	−4190.46	−	1230.43i	−0.779029	−	0.228744i	−0.132042	−	0.991244i	$-0.542153\pi$
$307$	−4190.46	−	1230.43i	−0.779029	−	0.228744i	−0.646988	+	0.762500i	$0.723971\pi$
$308$	−725.784	−	374.168i	−0.134271	−	0.0692213i
$309$	5041.08	+	1817.67i	0.928081	+	0.334640i
$310$	1646.82	+	2312.63i	0.301719	+	0.423706i
$311$	2126.67	+	2986.49i	0.387756	+	0.544528i	0.961606	−	0.274433i	$-0.0884901\pi$
$311$	2126.67	+	2986.49i	0.387756	+	0.544528i	−0.573850	+	0.818960i	$0.694551\pi$
$312$	3101.17	+	1118.20i	0.562722	+	0.202902i
$313$	−4320.34	−	2227.29i	−0.780191	−	0.402217i	0.0216408	−	0.999766i	$-0.493111\pi$
$313$	−4320.34	−	2227.29i	−0.780191	−	0.402217i	−0.801832	+	0.597549i	$0.796141\pi$
$314$	−1533.50	−	450.276i	−0.275607	−	0.0809254i
$315$	−1210.06	−	1214.73i	−0.216441	−	0.217276i
$316$	−5564.79	−	6422.11i	−0.990646	−	1.14327i
$317$	437.058	−	9174.98i	0.0774374	−	1.62561i	−0.541870	−	0.840462i	$-0.682284\pi$
$317$	437.058	−	9174.98i	0.0774374	−	1.62561i	0.619308	−	0.785148i	$-0.287413\pi$
$318$	−7083.07	+	925.567i	−1.24905	+	0.163218i
$319$	−55.6951	+	229.578i	−0.00977533	+	0.0402944i
$320$	2190.19	+	209.138i	0.382611	+	0.0365349i
$321$	−3052.99	+	1012.87i	−0.530845	+	0.176115i
$322$	−9955.08	−	65.1755i	−1.72290	−	0.0112798i
$323$	2976.08			0.512674
$324$	−2759.40	+	6816.46i	−0.473149	+	1.16880i
$325$	7956.73	−	2336.31i	1.35803	−	0.398754i
$326$	9200.64	+	1773.28i	1.56312	+	0.301266i
$327$	6620.55	+	1696.58i	1.11962	+	0.286915i
$328$	2554.92	−	492.421i	0.430097	−	0.0828945i
$329$	−3804.99	−	1523.29i	−0.637616	−	0.255263i
$330$	−133.633	−	213.938i	−0.0222917	−	0.0356877i
$331$	2147.55	+	1107.14i	0.356617	+	0.183849i	0.627220	−	0.778842i	$-0.284193\pi$
$331$	2147.55	+	1107.14i	0.356617	+	0.183849i	−0.270603	+	0.962691i	$0.587223\pi$
$332$	−304.826	+	2120.11i	−0.0503900	+	0.350470i
$333$	1629.26	+	7559.64i	0.268117	+	1.24404i
$334$	−3218.17	+	7046.81i	−0.527217	+	1.15444i
$335$	−1126.53	+	450.995i	−0.183728	+	0.0735538i
$336$	−1703.21	−	4418.27i	−0.276540	−	0.717371i
$337$	−6894.78	+	6574.16i	−1.11449	+	1.06266i	−0.116907	+	0.993143i	$0.537298\pi$
$337$	−6894.78	+	6574.16i	−1.11449	+	1.06266i	−0.997581	+	0.0695191i	$0.977854\pi$
$338$	−11487.9	−	4599.05i	−1.84869	−	0.740105i
$339$	−3673.34	+	2058.26i	−0.588520	+	0.329763i
$340$	−125.551	+	2635.64i	−0.0200263	+	0.420404i
$341$	557.239	−	643.088i	0.0884931	−	0.102127i
$342$	3881.00	+	471.612i	0.613628	+	0.0745669i
$343$	−2077.46	−	4548.99i	−0.327032	−	0.716101i
$344$	882.192	+	1528.00i	0.138269	+	0.239489i
$345$	−1468.42	−	886.229i	−0.229151	−	0.138298i
$346$	4300.73	−	7449.09i	0.668233	−	1.15741i
$347$	10798.6	+	1031.14i	1.67061	+	0.159524i	0.887012	−	0.461747i	$-0.152777\pi$
$347$	10798.6	+	1031.14i	1.67061	+	0.159524i	0.783596	+	0.621271i	$0.213383\pi$
$348$	2668.35	−	1848.86i	0.411030	−	0.284797i
$349$	9681.21	+	1865.90i	1.48488	+	0.286187i	0.866296	−	0.499531i	$-0.166494\pi$
$349$	9681.21	+	1865.90i	1.48488	+	0.286187i	0.618584	+	0.785718i	$0.287707\pi$
$350$	8810.84	+	5662.38i	1.34560	+	0.864763i
$351$	4082.44	−	9156.77i	0.620810	−	1.39246i
$352$	−137.696	−	957.700i	−0.0208501	−	0.145016i
$353$	−2623.78	−	10815.4i	−0.395608	−	1.63072i	−0.726584	−	0.687078i	$-0.758893\pi$
$353$	−2623.78	−	10815.4i	−0.395608	−	1.63072i	0.330976	−	0.943639i	$-0.392622\pi$
$354$	8916.20	−	11042.6i	1.33867	−	1.65792i
$355$	730.861	+	574.756i	0.109268	+	0.0859292i
$356$	−6675.11	−	9373.88i	−0.993765	−	1.39555i
$357$	8818.59	−	3891.02i	1.30736	−	0.576848i
$358$	14090.8	−	5641.10i	2.08023	−	0.832797i
$359$	−3712.39	+	2385.81i	−0.545772	+	0.350747i	−0.784293	−	0.620391i	$-0.786974\pi$
$359$	−3712.39	+	2385.81i	−0.545772	+	0.350747i	0.238520	+	0.971137i	$0.423338\pi$
$360$	−120.313	+	707.147i	−0.0176141	+	0.103528i
$361$	811.170	+	5641.81i	0.118264	+	0.822541i
$362$	−4704.63	+	13593.1i	−0.683066	+	1.97359i
$363$	4783.76	−	4889.56i	0.691686	−	0.706984i
$364$	−5003.34	−	14456.2i	−0.720457	−	2.08162i
$365$	−520.831	+	2146.89i	−0.0746891	+	0.307873i
$366$	−18812.4	+	4308.40i	−2.68672	+	0.615311i
$367$	2882.11	+	4991.95i	0.409931	+	0.710021i	0.994882	−	0.101048i	$-0.0322194\pi$
$367$	2882.11	+	4991.95i	0.409931	+	0.710021i	−0.584951	+	0.811069i	$0.698886\pi$
$368$	−2722.23	−	3876.30i	−0.385614	−	0.549092i
$369$	−924.294	−	7858.83i	−0.130398	−	1.10871i
$370$	1514.23	+	3315.69i	0.212759	+	0.465877i
$371$	4964.53	+	4733.67i	0.694732	+	0.662426i
$372$	−11594.5	+	1515.09i	−1.61599	+	0.211167i
$373$	−2959.83	+	1525.90i	−0.410869	+	0.211818i	−0.651254	−	0.758860i	$-0.725757\pi$
$373$	−2959.83	+	1525.90i	−0.410869	+	0.211818i	0.240385	+	0.970678i	$0.422726\pi$
$374$	1392.42	−	268.366i	0.192514	−	0.0371040i
$375$	1674.46	+	3353.20i	0.230583	+	0.461756i
$376$	404.249	+	1666.34i	0.0554456	+	0.228550i
$377$	−3723.16	+	2392.73i	−0.508628	+	0.326875i
$378$	12116.6	−	3676.68i	1.64871	−	0.500286i
$379$	781.730	−	1711.75i	0.105949	−	0.231997i	−0.849231	−	0.528022i	$-0.822934\pi$
$379$	781.730	−	1711.75i	0.105949	−	0.231997i	0.955180	+	0.296025i	$0.0956612\pi$
$380$	1023.08	−	97.6923i	0.138113	−	0.0131882i
$381$	−559.458	−	3118.04i	−0.0752280	−	0.419271i
$382$	−221.488	−	4649.60i	−0.0296657	−	0.622760i
$383$	7702.75	−	7344.56i	1.02766	−	0.979868i	0.0278506	−	0.999612i	$-0.491134\pi$
$383$	7702.75	−	7344.56i	1.02766	−	0.979868i	0.999805	+	0.0197444i	$0.00628525\pi$
$384$	−3145.20	+	4758.33i	−0.417977	+	0.632351i
$385$	−79.2249	+	228.905i	−0.0104875	+	0.0303015i
$386$	−4676.65	−	3005.50i	−0.616672	−	0.396311i
$387$	4831.00	−	2335.27i	0.634557	−	0.306740i
$388$	837.318	−	245.859i	0.109558	−	0.0321690i
$389$	−5644.43	+	7926.49i	−0.735691	+	1.03313i	0.261990	+	0.965071i	$0.415621\pi$
$389$	−5644.43	+	7926.49i	−0.735691	+	1.03313i	−0.997681	+	0.0680626i	$0.978318\pi$
$390$	953.939	−	4628.33i	0.123858	−	0.600935i
$391$	7617.90	−	5910.48i	0.985304	−	0.764465i
$392$	476.510	−	825.339i	0.0613964	−	0.106342i
$393$	−8231.99	+	1885.28i	−1.05661	+	0.241985i
$394$	−5517.31	−	5260.75i	−0.705478	−	0.672671i
$395$	−1650.77	+	1905.09i	−0.210277	+	0.242672i
$396$	1036.40	−	72.1194i	0.131518	−	0.00915186i
$397$	4909.14	+	5665.45i	0.620611	+	0.716224i	0.975823	−	0.218562i	$-0.0701367\pi$
$397$	4909.14	+	5665.45i	0.620611	+	0.716224i	−0.355212	+	0.934786i	$0.615591\pi$
$398$	8029.56	−	6314.51i	1.01127	−	0.795271i
$399$	−1988.93	−	3184.16i	−0.249552	−	0.399517i
$400$	237.112	+	4977.59i	0.0296390	+	0.622199i
$401$	1545.43	+	1215.34i	0.192457	+	0.151350i	0.709738	−	0.704466i	$-0.248813\pi$
$401$	1545.43	+	1215.34i	0.192457	+	0.151350i	−0.517281	+	0.855816i	$0.673056\pi$
$402$	966.500	−	8909.06i	0.119912	−	1.10533i
$403$	15869.3	−	1515.33i	1.96155	−	0.187306i
$404$	−2280.31	+	15859.9i	−0.280817	+	1.95312i
$405$	2117.98	+	522.462i	0.259860	+	0.0641021i
$406$	−5363.20	−	1574.78i	−0.655594	−	0.192500i
$407$	858.771	−	675.345i	0.104589	−	0.0822496i
$408$	−3466.01	−	2061.00i	−0.420572	−	0.250085i
$409$	520.546	−	268.360i	0.0629324	−	0.0324439i	−0.426473	−	0.904500i	$-0.640244\pi$
$409$	520.546	−	268.360i	0.0629324	−	0.0324439i	0.489405	+	0.872056i	$0.337214\pi$
$410$	−1219.91	−	3524.69i	−0.146944	−	0.424566i
$411$	3032.39	+	1432.27i	0.363934	+	0.171894i
$412$	−6034.46	+	8474.21i	−0.721593	+	1.01334i
$413$	−13629.2			−1.62385
$414$	10870.9	−	6500.46i	1.29052	−	0.771692i
$415$	635.389			0.0751566
$416$	10514.3	−	14765.2i	1.23919	−	1.74020i
$417$	558.843	+	6771.91i	0.0656274	+	0.795256i
$418$	−180.647	−	521.945i	−0.0211381	−	0.0610745i
$419$	−2729.34	+	1407.08i	−0.318227	+	0.164058i	−0.609938	−	0.792449i	$-0.708806\pi$
$419$	−2729.34	+	1407.08i	−0.318227	+	0.164058i	0.291711	+	0.956507i	$0.405775\pi$
$420$	2903.82	−	1627.08i	0.337361	−	0.189032i
$421$	5042.92	−	3965.80i	0.583793	−	0.459100i	−0.282061	−	0.959396i	$-0.591018\pi$
$421$	5042.92	−	3965.80i	0.583793	−	0.459100i	0.865854	+	0.500296i	$0.166776\pi$
$422$	−5159.56	−	1514.98i	−0.595174	−	0.174759i
$423$	5144.09	−	854.840i	0.591287	−	0.0982594i
$424$	408.411	−	2840.56i	0.0467787	−	0.325353i
$425$	−10097.8	+	964.226i	−1.15251	+	0.110051i
$426$	−6282.12	+	2771.85i	−0.714482	+	0.315251i
$427$	14567.9	+	11456.4i	1.65104	+	1.29839i
$428$	−297.129	−	6237.50i	−0.0335567	−	0.704441i
$429$	−1415.51	+	49.1907i	−0.159304	+	0.00553601i
$430$	1988.09	−	1563.45i	0.222964	−	0.175340i
$431$	7169.36	+	8273.88i	0.801244	+	0.924684i	0.998449	−	0.0556778i	$-0.0177320\pi$
$431$	7169.36	+	8273.88i	0.801244	+	0.924684i	−0.197205	+	0.980362i	$0.563187\pi$
$432$	4769.03	+	3681.34i	0.531135	+	0.409996i
$433$	10004.8	−	11546.1i	1.11039	−	1.28146i	0.154419	−	0.988005i	$-0.450650\pi$
$433$	10004.8	−	11546.1i	1.11039	−	1.28146i	0.955973	−	0.293455i	$-0.0948050\pi$
$434$	14571.5	+	13893.9i	1.61165	+	1.53670i
$435$	−655.524	−	705.443i	−0.0722528	−	0.0777549i
$436$	−6634.03	+	11490.5i	−0.728699	+	1.26214i
$437$	−2700.95	−	2609.32i	−0.295661	−	0.285631i
$438$	−12191.3	−	10841.5i	−1.32997	−	1.18271i
$439$	−10219.3	+	14351.1i	−1.11103	+	1.56022i	−0.321082	+	0.947051i	$0.604047\pi$
$439$	−10219.3	+	14351.1i	−1.11103	+	1.56022i	−0.789948	+	0.613173i	$0.789893\pi$
$440$	97.2329	−	28.5502i	0.0105350	−	0.00309335i
$441$	−2397.10	−	1629.14i	−0.258838	−	0.175915i
$442$	22348.7	+	14362.6i	2.40502	+	1.54561i
$443$	818.217	−	2364.08i	0.0877532	−	0.253546i	−0.892582	−	0.450885i	$-0.851109\pi$
$443$	818.217	−	2364.08i	0.0877532	−	0.253546i	0.980335	+	0.197338i	$0.0632298\pi$
$444$	−14985.4	−	907.162i	−1.60175	−	0.0969640i
$445$	−2470.61	+	2355.73i	−0.263187	+	0.250949i
$446$	210.762	+	4424.44i	0.0223764	+	0.469738i
$447$	−5436.48	−	1960.24i	−0.575250	−	0.207419i
$448$	15532.2	−	1483.15i	1.63801	−	0.156411i
$449$	4767.91	−	10440.3i	0.501140	−	1.09734i	−0.474957	−	0.880009i	$-0.657536\pi$
$449$	4767.91	−	10440.3i	0.501140	−	1.09734i	0.976097	−	0.217334i	$-0.0697362\pi$
$450$	−13321.0	−	342.764i	−1.39546	−	0.0359068i
$451$	−940.444	+	604.387i	−0.0981902	+	0.0631030i
$452$	−1927.18	−	7943.96i	−0.200547	−	0.826665i
$453$	−7780.74	+	11771.4i	−0.807001	+	1.22090i
$454$	−19003.1	+	3662.55i	−1.96445	+	0.378617i
$455$	−4033.49	+	2079.41i	−0.415589	+	0.214251i
$456$	−602.454	+	1450.50i	−0.0618695	+	0.148960i
$457$	−8698.51	−	8294.01i	−0.890370	−	0.848966i	0.0988949	−	0.995098i	$-0.468469\pi$
$457$	−8698.51	−	8294.01i	−0.890370	−	0.848966i	−0.989265	+	0.146132i	$0.953318\pi$
$458$	11009.1	+	24106.6i	1.12319	+	2.45945i
$459$	−7023.25	+	10053.3i	−0.714199	+	1.02233i
$460$	2424.77	−	2281.90i	0.245773	−	0.231291i
$461$	2737.52	+	4741.53i	0.276571	+	0.479035i	0.970530	−	0.240979i	$-0.0774686\pi$
$461$	2737.52	+	4741.53i	0.276571	+	0.479035i	−0.693959	+	0.720014i	$0.744135\pi$
$462$	−1217.69	−	1310.42i	−0.122624	−	0.131962i
$463$	3001.65	−	12373.0i	0.301292	−	1.24194i	−0.596891	−	0.802322i	$-0.703597\pi$
$463$	3001.65	−	12373.0i	0.301292	−	1.24194i	0.898183	−	0.439621i	$-0.144887\pi$
$464$	−869.844	−	2513.25i	−0.0870291	−	0.251454i
$465$	934.358	+	3340.49i	0.0931824	+	0.333143i
$466$	3467.63	−	10019.1i	0.344710	−	0.995975i
$467$	−2501.41	−	17397.7i	−0.247861	−	1.72391i	−0.610527	−	0.791995i	$-0.709042\pi$
$467$	−2501.41	−	17397.7i	−0.247861	−	1.72391i	0.362666	−	0.931919i	$-0.381867\pi$
$468$	14984.5	+	12420.9i	1.48004	+	1.22683i
$469$	−7239.37	+	4652.46i	−0.712757	+	0.458061i
$470$	2281.88	−	913.525i	0.223947	−	0.0896549i
$471$	−1575.92	−	1153.04i	−0.154171	−	0.112801i
$472$	3307.42	+	4644.62i	0.322534	+	0.452936i
$473$	−595.873	−	468.599i	−0.0579244	−	0.0455523i
$474$	−6696.01	−	17370.1i	−0.648857	−	1.68320i
$475$	931.473	+	3839.58i	0.0899766	+	0.370889i
$476$	2663.04	+	18521.9i	0.256429	+	1.78351i
$477$	−8524.47	−	1871.58i	−0.818257	−	0.179652i
$478$	−6362.62	−	4089.01i	−0.608827	−	0.391270i
$479$	−12298.9	−	2370.42i	−1.17318	−	0.226112i	−0.434818	−	0.900518i	$-0.643187\pi$
$479$	−12298.9	−	2370.42i	−1.17318	−	0.226112i	−0.738360	+	0.674407i	$0.764400\pi$
$480$	3566.31	+	1684.45i	0.339123	+	0.160175i
$481$	20374.7	+	1945.54i	1.93140	+	0.184427i
$482$	12726.9	−	22043.6i	1.20268	−	2.08311i
$483$	−11414.8	−	4200.51i	−1.07535	−	0.395714i
$484$	6639.86	+	11500.6i	0.623578	+	1.08007i
$485$	−107.540	−	235.479i	−0.0100683	−	0.0220465i
$486$	−10751.9	+	11997.2i	−1.00353	+	1.11976i
$487$	821.298	−	947.828i	0.0764200	−	0.0881934i	−0.716252	−	0.697842i	$-0.754144\pi$
$487$	821.298	−	947.828i	0.0764200	−	0.0881934i	0.792672	+	0.609648i	$0.208689\pi$
$488$	368.923	−	7744.65i	0.0342221	−	0.718409i
$489$	9839.84	+	5851.06i	0.909965	+	0.541092i
$490$	−1268.27	−	507.741i	−0.116928	−	0.0468110i
$491$	−2156.51	+	2056.22i	−0.198211	+	0.188994i	−0.782684	−	0.622419i	$-0.786150\pi$
$491$	−2156.51	+	2056.22i	−0.198211	+	0.188994i	0.584473	+	0.811413i	$0.301301\pi$
$492$	15176.1	+	2381.62i	1.39063	+	0.218235i
$493$	5025.87	−	2012.06i	0.459136	−	0.183810i
$494$	4298.44	−	9412.27i	0.391490	−	0.857243i
$495$	−64.9300	−	301.270i	−0.00589573	−	0.0273557i
$496$	−1363.32	+	9482.08i	−0.123417	+	0.858383i
$497$	5860.77	+	3021.44i	0.528957	+	0.272696i
$498$	−2203.62	+	4142.71i	−0.198286	+	0.372769i
$499$	5935.70	+	2376.29i	0.532501	+	0.213181i	0.622300	−	0.782778i	$-0.286198\pi$
$499$	5935.70	+	2376.29i	0.532501	+	0.213181i	−0.0897990	+	0.995960i	$0.528622\pi$
$500$	−7144.73	+	1377.03i	−0.639044	+	0.123166i
$501$	−6619.15	+	6765.55i	−0.590263	+	0.603318i
$502$	14961.0	+	2883.50i	1.33017	+	0.256369i
$503$	−18909.5	+	5552.32i	−1.67621	+	0.492178i	−0.975264	−	0.221041i	$-0.929054\pi$
$503$	−18909.5	+	5552.32i	−1.67621	+	0.492178i	−0.700941	+	0.713220i	$0.747236\pi$
$504$	111.265	+	5085.72i	0.00983363	+	0.449476i
$505$	4753.16			0.418837
$506$	−1498.98	−	977.263i	−0.131695	−	0.0858590i
$507$	−11297.6	−	10046.7i	−0.989633	−	0.880061i
$508$	6122.01	+	584.581i	0.534686	+	0.0510563i
$509$	−1380.71	+	5691.38i	−0.120234	+	0.495611i	0.879569	+	0.475771i	$0.157831\pi$
$509$	−1380.71	+	5691.38i	−0.120234	+	0.495611i	−0.999803	+	0.0198402i	$0.993684\pi$
$510$	−2217.24	+	5338.34i	−0.192512	+	0.463502i
$511$	−745.454	+	15649.0i	−0.0645341	+	1.35474i
$512$	9130.35	+	10537.0i	0.788102	+	0.909519i
$513$	4265.17	+	2150.42i	0.367080	+	0.185075i
$514$	798.461	+	234.449i	0.0685187	+	0.0201189i
$515$	2743.01	+	1414.12i	0.234702	+	0.120997i
$516$	1839.69	+	10253.2i	0.156953	+	0.874750i
$517$	−427.326	−	600.096i	−0.0363516	−	0.0510487i
$518$	14994.4	+	21056.7i	1.27185	+	1.78606i
$519$	8030.09	−	6779.26i	0.679156	−	0.573365i
$520$	1687.44	+	869.937i	0.142306	+	0.0733640i
$521$	446.632	+	131.143i	0.0375572	+	0.0110278i	0.300457	−	0.953795i	$-0.402861\pi$
$521$	446.632	+	131.143i	0.0375572	+	0.0110278i	−0.262900	+	0.964823i	$0.584679\pi$
$522$	6872.91	−	1827.41i	0.576282	−	0.153226i
$523$	1820.17	+	2100.59i	0.152181	+	0.175626i	0.826721	−	0.562612i	$-0.190204\pi$
$523$	1820.17	+	2100.59i	0.152181	+	0.175626i	−0.674540	+	0.738238i	$0.735658\pi$
$524$	780.100	−	16376.3i	0.0650359	−	1.36527i
$525$	7780.08	+	10159.4i	0.646763	+	0.844561i
$526$	−3966.45	+	16349.9i	−0.328793	+	1.35530i
$527$	−19411.7	−	1853.59i	−1.60453	−	0.153214i
$528$	171.813	−	833.604i	0.0141614	−	0.0687083i
$529$	−12095.7	−	1315.03i	−0.994142	−	0.108082i
$530$	−4113.76			−0.337151
$531$	14824.1	−	8996.65i	1.21151	−	0.735257i
$532$	6993.15	−	2053.37i	0.569909	−	0.167340i
$533$	−20564.7	−	3963.52i	−1.67121	−	0.322100i
$534$	−6790.80	−	24278.3i	−0.550312	−	1.96746i
$535$	−1818.95	+	350.573i	−0.146991	+	0.0283301i
$536$	3342.27	+	1338.04i	0.269336	+	0.107826i
$537$	18533.0	−	644.042i	1.48931	−	0.0517551i
$538$	18582.0	+	9579.70i	1.48908	+	0.767677i
$539$	−58.2721	+	405.291i	−0.00465669	+	0.0323880i
$540$	−2084.36	+	3686.54i	−0.166105	+	0.293784i
$541$	−1564.50	+	3425.77i	−0.124331	+	0.272247i	−0.961555	−	0.274614i	$-0.911450\pi$
$541$	−1564.50	+	3425.77i	−0.124331	+	0.272247i	0.837224	+	0.546861i	$0.184177\pi$
$542$	2456.00	−	983.234i	0.194639	−	0.0779217i
$543$	−11040.5	+	13673.5i	−0.872551	+	1.08064i
$544$	−16047.0	+	15300.8i	−1.26472	+	1.20591i
$545$	3653.97	+	1462.83i	0.287191	+	0.114974i
$546$	431.052	−	33509.9i	0.0337863	−	2.62654i
$547$	−304.855	+	6399.70i	−0.0238294	+	0.500240i	0.955130	+	0.296186i	$0.0957149\pi$
$547$	−304.855	+	6399.70i	−0.0238294	+	0.500240i	−0.978960	+	0.204054i	$0.934588\pi$
$548$	−4263.50	+	4920.34i	−0.332350	+	0.383552i
$549$	−23407.5	−	2844.43i	−1.81968	−	0.221124i
$550$	782.039	+	1712.43i	0.0606296	+	0.132760i
$551$	−1054.30	−	1826.10i	−0.0815149	−	0.141188i
$552$	1338.58	+	4909.33i	0.103213	+	0.378542i
$553$	−8938.37	+	15481.7i	−0.687338	+	1.19051i
$554$	9117.58	+	870.623i	0.699222	+	0.0667676i
$555$	366.273	+	4438.40i	0.0280134	+	0.339459i
$556$	−12952.9	−	2496.47i	−0.987996	−	0.190421i
$557$	13347.3	+	8577.80i	1.01534	+	0.652519i	0.938770	−	0.344545i	$-0.111967\pi$
$557$	13347.3	+	8577.80i	1.01534	+	0.652519i	0.0765695	+	0.997064i	$0.475603\pi$
$558$	−25020.4	−	5493.33i	−1.89820	−	0.416758i
$559$	−2021.10	−	14057.1i	−0.152922	−	1.06360i
$560$	−642.904	−	2650.09i	−0.0485137	−	0.199976i
$561$	1711.59	+	268.602i	0.128811	+	0.0202146i
$562$	−14397.3	−	11322.2i	−1.08063	−	0.849816i
$563$	−9805.23	−	13769.5i	−0.733999	−	1.03076i	−0.997808	−	0.0661818i	$-0.978918\pi$
$563$	−9805.23	−	13769.5i	−0.733999	−	1.03076i	0.263809	−	0.964575i	$-0.415021\pi$
$564$	−1091.83	+	10064.4i	−0.0815149	+	0.751393i
$565$	−2251.19	+	901.242i	−0.167626	+	0.0671071i
$566$	13398.3	−	8610.59i	0.995008	−	0.639453i
$567$	15449.9	+	795.611i	1.14433	+	0.0589286i
$568$	−392.583	−	2730.47i	−0.0290007	−	0.201704i
$569$	−3247.90	+	9384.19i	−0.239295	+	0.691398i	0.759852	+	0.650097i	$0.225272\pi$
$569$	−3247.90	+	9384.19i	−0.239295	+	0.691398i	−0.999147	+	0.0413015i	$0.986850\pi$
$570$	2181.00	+	558.905i	0.160267	+	0.0410701i
$571$	−7650.42	−	22104.4i	−0.560701	−	1.62004i	−0.767069	−	0.641564i	$-0.778286\pi$
$571$	−7650.42	−	22104.4i	−0.560701	−	1.62004i	0.206368	−	0.978474i	$-0.433836\pi$
$572$	648.256	−	2672.15i	0.0473863	−	0.195329i
$573$	1672.33	−	5435.79i	0.121924	−	0.396306i
$574$	−13225.4	−	22907.1i	−0.961704	−	1.66572i
$575$	10009.7	+	7978.32i	0.725970	+	0.578641i
$576$	−15914.9	+	11866.0i	−1.15125	+	0.858361i
$577$	263.786	+	577.610i	0.0190321	+	0.0416746i	0.918909	−	0.394469i	$-0.129071\pi$
$577$	263.786	+	577.610i	0.0190321	+	0.0416746i	−0.899877	+	0.436143i	$0.856344\pi$
$578$	−8396.33	−	8005.89i	−0.604224	−	0.576126i
$579$	−4129.55	−	5392.47i	−0.296404	−	0.387053i
$580$	1661.68	−	856.657i	0.118961	−	0.0613289i
$581$	4424.56	−	852.763i	0.315941	−	0.0608926i
$582$	1908.28	+	115.520i	0.135912	+	0.00822760i
$583$	290.686	+	1198.22i	0.0206500	+	0.0851206i
$584$	5513.83	−	3543.52i	0.390692	−	0.251082i
$585$	3014.49	−	4924.22i	0.213049	−	0.348020i
$586$	4490.31	−	9832.40i	0.316541	−	0.693128i
$587$	4776.78	−	456.128i	0.335876	−	0.0320722i	0.0742442	−	0.997240i	$-0.476346\pi$
$587$	4776.78	−	456.128i	0.335876	−	0.0320722i	0.261631	+	0.965168i	$0.415740\pi$
$588$	4299.36	−	3629.65i	0.301535	−	0.254565i
$589$	361.393	+	7586.56i	0.0252817	+	0.530728i
$590$	5915.46	−	5640.38i	0.412773	−	0.393578i
$591$	−4161.13	−	8332.91i	−0.289621	−	0.579983i
$592$	−4022.70	+	11622.8i	−0.279277	+	0.806918i
$593$	−10490.6	−	6741.93i	−0.726474	−	0.466876i	0.124410	−	0.992231i	$-0.460296\pi$
$593$	−10490.6	−	6741.93i	−0.726474	−	0.466876i	−0.850883	+	0.525355i	$0.823933\pi$
$594$	2189.45	+	621.506i	0.151236	+	0.0429305i
$595$	5326.08	−	1563.88i	0.366971	−	0.107753i
$596$	6507.77	−	9138.89i	0.447263	−	0.628093i
$597$	11845.6	−	3929.94i	0.812075	−	0.269416i
$598$	−7689.96	−	32629.3i	−0.525862	−	2.23129i
$599$	4823.54	−	8354.62i	0.329023	−	0.569884i	−0.653296	−	0.757103i	$-0.726614\pi$
$599$	4823.54	−	8354.62i	0.329023	−	0.569884i	0.982318	+	0.187219i	$0.0599475\pi$
$600$	1574.17	−	5116.73i	0.107109	−	0.348150i
$601$	−8166.06	−	7786.33i	−0.554244	−	0.528471i	0.360364	−	0.932812i	$-0.382652\pi$
$601$	−8166.06	−	7786.33i	−0.554244	−	0.528471i	−0.914608	+	0.404341i	$0.867501\pi$
$602$	11745.8	−	13555.4i	0.795223	−	0.917737i
$603$	4802.96	−	9839.06i	0.324364	−	0.664473i
$604$	−17938.8	−	20702.5i	−1.20847	−	1.39465i
$605$	3096.55	−	2435.16i	0.208087	−	0.163642i
$606$	−16484.6	+	30990.4i	−1.10502	+	2.07739i
$607$	−38.7131	−	812.688i	−0.00258866	−	0.0543426i	0.997203	−	0.0747356i	$-0.0238113\pi$
$607$	−38.7131	−	812.688i	−0.00258866	−	0.0543426i	−0.999792	+	0.0203930i	$0.993508\pi$
$608$	6788.43	+	5338.48i	0.452808	+	0.356092i
$609$	−5511.55	−	4032.60i	−0.366731	−	0.268323i
$610$	−11064.1	+	1056.49i	−0.734378	+	0.0701246i
$611$	1964.15	−	13661.0i	0.130051	−	0.904524i
$612$	−15122.8	−	18387.8i	−0.998862	−	1.21452i
$613$	−1908.53	−	560.394i	−0.125750	−	0.0369235i	0.218252	−	0.975892i	$-0.429965\pi$
$613$	−1908.53	−	560.394i	−0.125750	−	0.0369235i	−0.344002	+	0.938969i	$0.611783\pi$
$614$	14600.3	−	11481.8i	0.959640	−	0.754669i
$615$	58.6140	−	4556.65i	0.00384317	−	0.298767i
$616$	638.768	−	329.308i	0.0417803	−	0.0215393i
$617$	−4919.31	−	14213.4i	−0.320979	−	0.927408i	−0.983900	−	0.178719i	$-0.942805\pi$
$617$	−4919.31	−	14213.4i	−0.320979	−	0.927408i	0.662921	−	0.748689i	$-0.269317\pi$
$618$	−18733.1	+	12979.9i	−1.21935	+	0.844870i
$619$	−8071.12	+	11334.3i	−0.524080	+	0.735968i	−0.988760	−	0.149511i	$-0.952230\pi$
$619$	−8071.12	+	11334.3i	−0.524080	+	0.735968i	0.464680	+	0.885479i	$0.346169\pi$
$620$	−6733.95			−0.436197
$621$	15188.3	−	2966.16i	0.981459	−	0.191671i
$622$	−15592.6			−1.00515
$623$	−14042.6	+	19720.0i	−0.903056	+	1.26816i
$624$	13106.5	−	9081.30i	0.840831	−	0.582601i
$625$	−4038.38	−	11668.1i	−0.258456	−	0.746761i
$626$	18374.1	−	9472.53i	1.17313	−	0.604790i
$627$	8.67970	−	674.759i	0.000552845	−	0.0429781i
$628$	2979.81	−	2343.35i	0.189343	−	0.148901i
$629$	−24022.0	−	7053.50i	−1.52277	−	0.447125i
$630$	7193.38	−	1195.39i	0.454906	−	0.0755959i
$631$	−2250.90	+	15655.3i	−0.142008	+	0.987685i	0.786822	+	0.617179i	$0.211725\pi$
$631$	−2250.90	+	15655.3i	−0.142008	+	0.987685i	−0.928830	+	0.370506i	$0.879184\pi$
$632$	7445.01	−	710.912i	0.468586	−	0.0447445i
$633$	−5302.28	−	3879.48i	−0.332933	−	0.243594i
$634$	30707.1	+	24148.3i	1.92356	+	1.51270i
$635$	−86.8050	−	1822.26i	−0.00542481	−	0.113881i
$636$	7956.84	−	14958.5i	0.496084	−	0.932617i
$637$	−6029.74	+	4741.84i	−0.375050	+	0.294943i
$638$	−657.942	−	759.306i	−0.0408279	−	0.0471179i
$639$	−8369.04	+	582.371i	−0.518113	+	0.0360536i
$640$	−2151.09	+	2482.49i	−0.132858	+	0.153327i
$641$	18107.8	+	17265.7i	1.11578	+	1.06389i	0.997482	+	0.0709145i	$0.0225917\pi$
$641$	18107.8	+	17265.7i	1.11578	+	1.06389i	0.118296	+	0.992978i	$0.462257\pi$
$642$	4022.64	−	13075.3i	0.247291	−	0.803802i
$643$	−2522.51	+	4369.12i	−0.154709	+	0.267965i	−0.932953	−	0.359998i	$-0.882777\pi$
$643$	−2522.51	+	4369.12i	−0.154709	+	0.267965i	0.778244	+	0.627962i	$0.216111\pi$
$644$	13822.4	−	19144.4i	0.845777	−	1.17142i
$645$	2932.93	−	973.039i	0.179045	−	0.0594006i
$646$	−7341.84	+	10310.2i	−0.447153	+	0.627939i
$647$	11910.4	−	3497.21i	0.723718	−	0.212503i	0.100930	−	0.994894i	$-0.467818\pi$
$647$	11910.4	−	3497.21i	0.723718	−	0.212503i	0.622788	+	0.782391i	$0.286000\pi$
$648$	−3478.11	−	5458.14i	−0.210853	−	0.330889i
$649$	−2060.88	−	1324.45i	−0.124648	−	0.0801067i
$650$	−11535.1	+	33328.4i	−0.696066	+	2.01115i
$651$	10989.8	+	22007.7i	0.661633	+	1.32496i
$652$	−16084.7	+	15336.7i	−0.966142	+	0.921214i
$653$	−1533.47	−	32191.5i	−0.0918978	−	1.92917i	−0.305389	−	0.952228i	$-0.598786\pi$
$653$	−1533.47	−	32191.5i	−0.0918978	−	1.92917i	0.213491	−	0.976945i	$-0.431517\pi$
$654$	−22210.1	+	18750.5i	−1.32796	+	1.12110i
$655$	−4841.44	+	462.302i	−0.288810	+	0.0275781i
$656$	5228.09	−	11447.9i	0.311162	−	0.681350i
$657$	−9519.11	−	17513.0i	−0.565260	−	1.03995i
$658$	14663.9	−	9423.91i	0.868781	−	0.558332i
$659$	−6774.23	−	27923.7i	−0.400435	−	1.65061i	−0.713331	−	0.700827i	$-0.752814\pi$
$659$	−6774.23	−	27923.7i	−0.400435	−	1.65061i	0.312897	−	0.949787i	$-0.398701\pi$
$660$	597.205	+	36.1526i	0.0352214	+	0.00213218i
$661$	1543.46	−	297.478i	0.0908226	−	0.0175046i	−0.143637	−	0.989630i	$-0.545880\pi$
$661$	1543.46	−	297.478i	0.0908226	−	0.0175046i	0.234460	+	0.972126i	$0.424668\pi$
$662$	−9133.41	+	4708.60i	−0.536224	+	0.276443i
$663$	19734.2	+	25769.4i	1.15598	+	1.50951i
$664$	−1364.32	−	1300.88i	−0.0797378	−	0.0760299i
$665$	−898.154	−	1966.68i	−0.0523743	−	0.114684i
$666$	−30208.5	−	13004.9i	−1.75759	−	0.756653i
$667$	−6325.33	−	2580.45i	−0.367193	−	0.149799i
$668$	−9187.39	−	15913.0i	−0.532142	−	0.921697i
$669$	−1591.35	+	5172.56i	−0.0919657	+	0.298928i
$670$	1216.69	−	5015.28i	0.0701567	−	0.289190i
$671$	1089.53	+	3148.00i	0.0626840	+	0.181114i
$672$	27094.9	+	6943.34i	1.55537	+	0.398579i
$673$	−6926.46	+	20012.7i	−0.396724	+	1.14626i	0.553002	+	0.833180i	$0.313482\pi$
$673$	−6926.46	+	20012.7i	−0.396724	+	1.14626i	−0.949727	+	0.313080i	$0.898639\pi$
$674$	−5766.08	−	40104.0i	−0.329527	−	2.29191i
$675$	−15168.4	−	5914.48i	−0.864937	−	0.337257i
$676$	24691.2	−	15868.0i	1.40482	−	0.902825i
$677$	1501.53	−	601.124i	0.0852418	−	0.0341256i	−0.328650	−	0.944452i	$-0.606594\pi$
$677$	1501.53	−	601.124i	0.0852418	−	0.0341256i	0.413891	+	0.910326i	$0.364169\pi$
$678$	1931.40	−	17803.3i	0.109402	−	1.00846i
$679$	−1064.90	−	1495.44i	−0.0601870	−	0.0845208i
$680$	−1825.43	−	1435.53i	−0.102944	−	0.0809562i
$681$	−23359.0	−	3665.78i	−1.31442	−	0.206274i
$682$	853.198	+	3516.93i	0.0479042	+	0.197464i
$683$	−611.514	−	4253.18i	−0.0342591	−	0.238277i	0.965496	−	0.260419i	$-0.0838606\pi$
$683$	−611.514	−	4253.18i	−0.0342591	−	0.238277i	−0.999755	+	0.0221416i	$0.992952\pi$
$684$	−6250.81	+	6849.58i	−0.349423	+	0.382895i
$685$	1624.73	+	1044.15i	0.0906246	+	0.0582409i
$686$	20884.3	+	4025.11i	1.16234	+	0.224022i
$687$	2662.98	+	32269.3i	0.147888	+	1.79207i
$688$	8495.42	+	811.215i	0.470763	+	0.0449524i
$689$	−11549.5	+	20004.3i	−0.638606	+	1.10610i
$690$	6692.72	−	2900.83i	0.369257	−	0.160047i
$691$	−15607.6	−	27033.1i	−0.859248	−	1.48826i	−0.872647	−	0.488351i	$-0.837599\pi$
$691$	−15607.6	−	27033.1i	−0.859248	−	1.48826i	0.0133992	−	0.999910i	$-0.495735\pi$
$692$	8475.19	+	18558.1i	0.465576	+	1.01947i
$693$	−856.481	−	2010.76i	−0.0469481	−	0.110220i
$694$	−30211.9	+	34866.4i	−1.65249	+	1.90708i
$695$	−186.195	+	3908.71i	−0.0101623	+	0.213332i
$696$	−36.7488	+	2856.84i	−0.00200138	+	0.155587i
$697$	23783.1	+	9521.32i	1.29247	+	0.517425i
$698$	−30347.2	+	28936.0i	−1.64564	+	1.56912i
$699$	8137.64	−	10078.3i	0.440334	−	0.545346i
$700$	−23062.4	+	9232.81i	−1.24525	+	0.498525i
$701$	8063.78	−	17657.2i	0.434472	−	0.951361i	−0.558108	−	0.829768i	$-0.688473\pi$
$701$	8063.78	−	17657.2i	0.434472	−	0.951361i	0.992580	−	0.121593i	$-0.0388002\pi$
$702$	21651.1	+	36732.3i	1.16406	+	1.97489i
$703$	−1387.78	+	9652.22i	−0.0744539	+	0.517838i
$704$	2492.77	+	1285.11i	0.133451	+	0.0687989i
$705$	3001.25	−	104.297i	0.160331	−	0.00557170i
$706$	43940.8	+	17591.3i	2.34240	+	0.937756i
$707$	33098.8	−	6379.28i	1.76069	−	0.339346i
$708$	9067.97	+	32419.6i	0.481349	+	1.72091i
$709$	−26070.0	−	5024.58i	−1.38093	−	0.266152i	−0.555904	−	0.831247i	$-0.687628\pi$
$709$	−26070.0	−	5024.58i	−1.38093	−	0.266152i	−0.825026	+	0.565094i	$0.808840\pi$
$710$	−3794.15	+	1114.06i	−0.200552	+	0.0588874i
$711$	−497.488	−	22739.2i	−0.0262409	−	1.19942i
$712$	10128.0			0.533094
$713$	15991.9	+	18701.7i	0.839976	+	0.982305i
$714$	−8275.17	+	40149.6i	−0.433740	+	2.10443i
$715$	−811.980	−	77.5347i	−0.0424704	−	0.00405543i
$716$	−8487.46	+	34985.8i	−0.443005	+	1.82609i
$717$	−5618.28	−	7336.49i	−0.292634	−	0.382129i
$718$	893.013	−	18746.6i	0.0464164	−	0.974399i
$719$	3488.49	+	4025.93i	0.180944	+	0.208821i	0.838974	−	0.544171i	$-0.183156\pi$
$719$	3488.49	+	4025.93i	0.180944	+	0.208821i	−0.658030	+	0.752991i	$0.728610\pi$
$720$	2448.59	+	2458.04i	0.126741	+	0.127230i
$721$	20999.0	+	6165.85i	1.08466	+	0.318486i
$722$	−21546.3	−	11107.9i	−1.11062	−	0.572566i
$723$	23762.9	−	20061.4i	1.22234	−	1.03194i
$724$	−19790.3	−	27791.6i	−1.01589	−	1.42661i
$725$	4168.88	+	5854.37i	0.213556	+	0.299898i
$726$	5137.84	+	28634.9i	0.262649	+	1.46383i
$727$	6220.10	+	3206.69i	0.317319	+	0.163589i	0.609527	−	0.792766i	$-0.291360\pi$
$727$	6220.10	+	3206.69i	0.317319	+	0.163589i	−0.292208	+	0.956355i	$0.594390\pi$
$728$	12918.1	+	3793.11i	0.657662	+	0.193107i
$729$	−17329.6	+	9333.11i	−0.880433	+	0.474171i
$730$	−6152.72	−	7100.61i	−0.311948	−	0.360007i
$731$	−826.581	+	17352.1i	−0.0418225	+	0.877962i
$732$	17558.5	−	42274.8i	0.886586	−	2.13459i
$733$	3376.46	−	13918.0i	0.170140	−	0.701325i	−0.821271	−	0.570538i	$-0.806735\pi$
$733$	3376.46	−	13918.0i	0.170140	−	0.701325i	0.991411	−	0.130787i	$-0.0417503\pi$
$734$	−24403.9	−	2330.29i	−1.22720	−	0.117183i
$735$	−1247.27	−	1109.17i	−0.0625934	−	0.0556631i
$736$	27978.6	+	183.175i	1.40123	+	0.00917380i
$737$	−1546.79			−0.0773088
$738$	29505.9	+	16185.3i	1.47172	+	0.807300i
$739$	30296.6	−	8895.89i	1.50809	−	0.442815i	0.579827	−	0.814740i	$-0.303120\pi$
$739$	30296.6	−	8895.89i	1.50809	−	0.442815i	0.928263	+	0.371924i	$0.121302\pi$
$740$	−8489.52	−	1636.22i	−0.421731	−	0.0812820i
$741$	8841.04	−	9036.58i	0.438305	−	0.447999i
$742$	−28646.3	+	5521.13i	−1.41730	+	0.273163i
$743$	24674.4	+	9878.14i	1.21833	+	0.487744i	0.889626	−	0.456690i	$-0.150965\pi$
$743$	24674.4	+	9878.14i	1.21833	+	0.487744i	0.328700	+	0.944434i	$0.393389\pi$
$744$	4832.96	−	9085.76i	0.238152	−	0.447715i
$745$	−2958.15	−	1525.03i	−0.145474	−	0.0749972i
$746$	2015.51	−	14018.2i	0.0989184	−	0.687993i
$747$	−4249.55	+	3848.18i	−0.208143	+	0.188484i
$748$	−1397.23	+	3059.50i	−0.0682989	+	0.149554i
$749$	−12195.8	+	4882.47i	−0.594960	+	0.238186i
$750$	−15747.4	−	2471.27i	−0.766686	−	0.120318i
$751$	−2465.02	+	2350.40i	−0.119774	+	0.114204i	−0.747599	−	0.664150i	$-0.768794\pi$
$751$	−2465.02	+	2350.40i	−0.119774	+	0.114204i	0.627826	+	0.778354i	$0.283945\pi$
$752$	7699.52	+	3082.42i	0.373368	+	0.149474i
$753$	16000.4	+	9514.33i	0.774353	+	0.460453i
$754$	895.606	−	18801.1i	0.0432573	−	0.908083i
$755$	−5321.46	+	6141.29i	−0.256513	+	0.296032i
$756$	−9566.76	+	28468.8i	−0.460238	+	1.36958i
$757$	−15080.1	−	33020.8i	−0.724036	−	1.58542i	−0.808160	−	0.588963i	$-0.799537\pi$
$757$	−15080.1	−	33020.8i	−0.724036	−	1.58542i	0.0841241	−	0.996455i	$-0.473191\pi$
$758$	4001.61	+	6930.99i	0.191748	+	0.332117i
$759$	−1317.85	−	1744.42i	−0.0630236	−	0.0834237i
$760$	−452.258	+	783.334i	−0.0215857	+	0.0373875i
$761$	−9484.15	−	905.626i	−0.451774	−	0.0431392i	−0.133311	−	0.991074i	$-0.542561\pi$
$761$	−9484.15	−	905.626i	−0.451774	−	0.0431392i	−0.318463	+	0.947935i	$0.603167\pi$
$762$	12182.1	+	5753.90i	0.579149	+	0.273545i
$763$	27407.9	+	5282.44i	1.30044	+	0.250638i
$764$	9288.16	+	5969.14i	0.439835	+	0.282665i
$765$	−4760.70	+	5216.73i	−0.224998	+	0.246551i
$766$	6441.79	+	44803.6i	0.303853	+	2.11334i
$767$	−10820.1	−	44601.1i	−0.509376	−	2.09967i
$768$	2267.96	+	5883.30i	0.106560	+	0.276426i
$769$	20606.2	+	16204.9i	0.966290	+	0.759899i	0.970750	−	0.240091i	$-0.0771773\pi$
$769$	20606.2	+	16204.9i	0.966290	+	0.759899i	−0.00446029	+	0.999990i	$0.501420\pi$
$770$	−597.563	−	839.160i	−0.0279671	−	0.0392743i
$771$	820.547	+	600.364i	0.0383285	+	0.0280435i
$772$	12241.2	−	4900.63i	0.570686	−	0.228468i
$773$	19589.6	−	12589.4i	0.911497	−	0.585784i	0.00131850	−	0.999999i	$-0.499580\pi$
$773$	19589.6	−	12589.4i	0.911497	−	0.585784i	0.910179	+	0.414215i	$0.135944\pi$
$774$	−3827.66	+	22497.3i	−0.177755	+	1.04476i
$775$	−3684.19	−	25624.1i	−0.170761	−	1.18767i
$776$	−251.202	+	725.799i	−0.0116206	+	0.0335756i
$777$	8507.40	+	30415.4i	0.392794	+	1.40431i
$778$	−13535.6	−	39108.5i	−0.623745	−	1.80219i
$779$	2352.44	−	9696.91i	0.108197	−	0.445992i
$780$	7629.88	+	8210.90i	0.350248	+	0.376920i
$781$	592.597	+	1026.41i	0.0271508	+	0.0470266i
$782$	1682.97	+	40971.9i	0.0769600	+	1.87360i
$783$	8656.67	+	747.954i	0.395101	+	0.0341375i
$784$	−1914.90	−	4193.05i	−0.0872314	−	0.191010i
$785$	−813.868	−	776.022i	−0.0370041	−	0.0352833i
$786$	13776.6	−	33169.4i	0.625186	−	1.50523i
$787$	−30679.3	+	15816.3i	−1.38958	+	0.716377i	−0.980573	−	0.196155i	$-0.937154\pi$
$787$	−30679.3	+	15816.3i	−1.38958	+	0.716377i	−0.409005	+	0.912532i	$0.634124\pi$
$788$	17755.1	−	3422.02i	0.802665	−	0.154701i
$789$	−11334.6	+	17147.9i	−0.511434	+	0.773742i
$790$	−2527.53	−	10418.6i	−0.113830	−	0.469212i
$791$	−14466.7	+	9297.20i	−0.650287	+	0.417914i
$792$	−477.393	+	779.829i	−0.0214184	+	0.0349874i
$793$	−25925.1	+	56768.1i	−1.16094	+	2.54211i
$794$	−31737.7	+	3030.58i	−1.41855	+	0.135455i
$795$	−4728.13	−	1704.83i	−0.210930	−	0.0760555i
$796$	1152.86	+	24201.5i	0.0513342	+	1.07764i
$797$	−7695.83	+	7337.95i	−0.342033	+	0.326128i	−0.841553	−	0.540175i	$-0.818358\pi$
$797$	−7695.83	+	7337.95i	−0.342033	+	0.326128i	0.499520	+	0.866302i	$0.333510\pi$
$798$	15937.6	+	964.806i	0.707000	+	0.0427992i
$799$	−5521.65	+	15953.8i	−0.244483	+	0.706388i
$800$	−24762.7	−	15914.0i	−1.09437	−	0.703308i
$801$	2256.48	−	30718.4i	0.0995367	−	1.35503i
$802$	−8022.86	+	2355.72i	−0.353238	+	0.103720i
$803$	−1633.45	+	2293.86i	−0.0717848	+	0.100808i
$804$	15883.3	+	14124.7i	0.696719	+	0.619578i
$805$	−6204.84	−	3250.41i	−0.271667	−	0.142313i
$806$	−33899.1	+	58714.9i	−1.48144	+	2.56594i
$807$	17387.1	+	18711.2i	0.758434	+	0.816189i
$808$	−10206.1	−	9731.49i	−0.444368	−	0.423704i
$809$	24824.2	−	28648.6i	1.07883	−	1.24503i	0.110891	−	0.993833i	$-0.464629\pi$
$809$	24824.2	−	28648.6i	1.07883	−	1.24503i	0.967935	−	0.251200i	$-0.0808251\pi$
$810$	−7034.95	+	6048.54i	−0.305164	+	0.262375i
$811$	4006.62	+	4623.89i	0.173479	+	0.200206i	0.835830	−	0.548988i	$-0.184987\pi$
$811$	4006.62	+	4623.89i	0.173479	+	0.200206i	−0.662351	+	0.749194i	$0.730441\pi$
$812$	10421.5	−	8195.54i	0.450397	−	0.354196i
$813$	3230.27	−	112.256i	0.139349	−	0.00484253i
$814$	221.084	+	4641.12i	0.00951963	+	0.199842i
$815$	5182.30	+	4075.41i	0.222734	+	0.175160i
$816$	−17844.7	+	7873.61i	−0.765551	+	0.337784i
$817$	6735.59	−	643.171i	0.288431	−	0.0275419i
$818$	−354.468	+	2465.38i	−0.0151512	+	0.105379i
$819$	14382.7	−	38335.8i	0.613640	−	1.63561i
$820$	8488.40	+	2492.42i	0.361497	+	0.106145i
$821$	−30270.8	+	23805.3i	−1.28680	+	1.01195i	−0.288277	+	0.957547i	$0.593082\pi$
$821$	−30270.8	+	23805.3i	−1.28680	+	1.01195i	−0.998519	+	0.0544006i	$0.982675\pi$
$822$	−12442.6	+	6971.92i	−0.527964	+	0.295832i
$823$	341.500	−	176.055i	0.0144641	−	0.00745675i	−0.450979	−	0.892534i	$-0.648925\pi$
$823$	341.500	−	176.055i	0.0144641	−	0.00745675i	0.465443	+	0.885078i	$0.345895\pi$
$824$	−2994.62	−	8652.38i	−0.126605	−	0.365801i
$825$	189.166	+	2292.27i	0.00798293	+	0.0967351i
$826$	33622.6	−	47216.3i	1.41632	−	1.98894i
$827$	8505.21			0.357624			0.178812	−	0.983883i	$-0.442775\pi$
$827$	8505.21			0.357624			0.178812	+	0.983883i	$0.442775\pi$
$828$	−2397.03	+	29947.0i	−0.100607	+	1.25692i
$829$	29553.5			1.23816			0.619081	−	0.785328i	$-0.287505\pi$
$829$	29553.5			1.23816			0.619081	+	0.785328i	$0.287505\pi$
$830$	−1567.47	+	2201.20i	−0.0655515	+	0.0920541i
$831$	10118.4	+	4779.17i	0.422389	+	0.199504i
$832$	17184.4	+	49651.1i	0.716060	+	2.06892i
$833$	8340.15	−	4299.65i	0.346902	−	0.178840i
$834$	−24838.9	−	14769.9i	−1.03129	−	0.613238i
$835$	−4284.61	+	3369.46i	−0.177575	+	0.139647i
$836$	1256.98	+	369.083i	0.0520019	+	0.0152691i
$837$	−26480.5	−	16682.7i	−1.09355	−	0.688936i
$838$	1858.56	−	12926.6i	0.0766145	−	0.532865i
$839$	9227.11	−	881.082i	0.379684	−	0.0362555i	0.0965307	−	0.995330i	$-0.469225\pi$
$839$	9227.11	−	881.082i	0.379684	−	0.0362555i	0.283154	+	0.959075i	$0.408619\pi$
$840$	−315.956	+	2912.44i	−0.0129780	+	0.119629i
$841$	16156.0	+	12705.2i	0.662430	+	0.520941i
$842$	1298.26	+	27253.8i	0.0531366	+	1.11547i
$843$	−11855.3	−	18979.6i	−0.484364	−	0.775437i
$844$	10025.8	−	7884.35i	0.408888	−	0.321553i
$845$	−5701.66	−	6580.07i	−0.232122	−	0.267883i
$846$	−9728.75	+	19929.8i	−0.395368	+	0.809928i
$847$	18294.7	−	21113.2i	0.742166	−	0.856505i
$848$	−10045.9	−	9578.75i	−0.406813	−	0.387896i
$849$	18967.8	−	4343.98i	0.766751	−	0.175601i
$850$	21570.4	−	37361.1i	0.870423	−	1.50762i
$851$	15616.9	+	27463.0i	0.629074	+	1.10625i
$852$	3287.68	−	15951.2i	0.132200	−	0.641407i
$853$	26618.6	−	37380.6i	1.06847	−	1.50046i	0.216915	−	0.976190i	$-0.430401\pi$
$853$	26618.6	−	37380.6i	1.06847	−	1.50046i	0.851555	−	0.524266i	$-0.175660\pi$
$854$	−75627.1	+	22206.1i	−3.03034	+	0.889787i
$855$	2275.10	+	1546.23i	0.0910023	+	0.0618479i
$856$	4623.44	+	2971.30i	0.184610	+	0.118641i
$857$	4026.32	−	11633.3i	0.160486	−	0.463694i	−0.835876	−	0.548919i	$-0.815040\pi$
$857$	4026.32	−	11633.3i	0.160486	−	0.463694i	0.996362	+	0.0852249i	$0.0271609\pi$
$858$	3321.58	−	5025.17i	0.132164	−	0.199949i
$859$	6176.82	−	5889.59i	0.245344	−	0.233935i	−0.557422	−	0.830229i	$-0.688209\pi$
$859$	6176.82	−	5889.59i	0.245344	−	0.233935i	0.802766	+	0.596294i	$0.203361\pi$
$860$	285.444	+	5992.21i	0.0113181	+	0.237596i
$861$	−5707.38	−	31809.1i	−0.225908	−	1.25906i
$862$	−46350.0	+	4425.89i	−1.83143	+	0.174880i
$863$	−2311.59	+	5061.67i	−0.0911788	+	0.199654i	−0.949727	−	0.313079i	$-0.898640\pi$
$863$	−2311.59	+	5061.67i	−0.0911788	+	0.199654i	0.858548	+	0.512733i	$0.171367\pi$
$864$	−34053.6	+	10333.3i	−1.34089	+	0.406881i
$865$	5091.34	−	3272.00i	0.200128	−	0.128614i
$866$	15318.5	+	63143.8i	0.601091	+	2.47773i
$867$	−6332.47	−	12681.2i	−0.248053	−	0.496741i
$868$	−46892.2	+	9037.73i	−1.83367	+	0.353411i
$869$	−2856.05	+	1472.40i	−0.111490	+	0.0574771i
$870$	4061.04	−	530.669i	0.158255	−	0.0206797i
$871$	−20972.3	−	19997.0i	−0.815865	−	0.777925i
$872$	−4850.94	−	10622.1i	−0.188387	−	0.412510i
$873$	2145.39	+	923.604i	0.0831737	+	0.0358067i
$874$	15702.7	−	2919.95i	0.607724	−	0.113008i
$875$	7653.57	+	13256.4i	0.295700	+	0.512168i
$876$	37720.0	−	8638.61i	1.45484	−	0.333187i
$877$	1885.65	−	7772.76i	0.0726042	−	0.299279i	−0.923920	−	0.382587i	$-0.875033\pi$
$877$	1885.65	−	7772.76i	0.0726042	−	0.299279i	0.996524	+	0.0833080i	$0.0265485\pi$
$878$	−24506.4	−	70806.6i	−0.941972	−	2.72165i
$879$	9235.68	−	9439.95i	0.354393	−	0.362232i
$880$	160.314	−	463.198i	0.00614113	−	0.0177436i
$881$	−1141.48	−	7939.19i	−0.0436521	−	0.303607i	−0.999938	−	0.0111724i	$-0.996444\pi$
$881$	−1141.48	−	7939.19i	−0.0436521	−	0.303607i	0.956285	−	0.292435i	$-0.0944655\pi$
$882$	11557.4	−	4285.37i	0.441224	−	0.163601i
$883$	12531.0	−	8053.20i	0.477579	−	0.306922i	−0.279614	−	0.960113i	$-0.590206\pi$
$883$	12531.0	−	8053.20i	0.477579	−	0.306922i	0.757193	+	0.653191i	$0.226570\pi$
$884$	−58497.9	+	23419.0i	−2.22568	+	0.891027i
$885$	9136.41	−	4031.25i	0.347025	−	0.153118i
$886$	6171.50	+	8666.66i	0.234013	+	0.328625i
$887$	8115.49	+	6382.09i	0.307206	+	0.241589i	0.759845	−	0.650105i	$-0.225275\pi$
$887$	8115.49	+	6382.09i	0.307206	+	0.241589i	−0.452639	+	0.891694i	$0.649517\pi$
$888$	8300.60	−	10280.1i	0.313682	−	0.388490i
$889$	−3050.15	−	12572.9i	−0.115072	−	0.474332i
$890$	−2066.17	−	14370.5i	−0.0778181	−	0.541237i
$891$	2258.87	+	1621.68i	0.0849328	+	0.0609747i
$892$	−8838.37	−	5680.08i	−0.331761	−	0.213210i
$893$	6456.75	+	1244.44i	0.241956	+	0.0466332i
$894$	20202.5	−	13998.0i	0.755785	−	0.523673i
$895$	10631.1	+	1015.14i	0.397047	+	0.0379134i
$896$	−11647.4	+	20173.9i	−0.434278	+	0.752192i
$897$	4683.90	−	40689.3i	0.174349	−	1.51458i
$898$	24406.5	+	42273.3i	0.906967	+	1.57091i
$899$	5739.39	+	12567.5i	0.212925	+	0.466240i
$900$	18989.7	−	25265.8i	0.703324	−	0.935770i
$901$	18503.2	−	21353.8i	0.684163	−	0.789566i
$902$	226.223	−	4749.01i	0.00835079	−	0.175305i
$903$	19117.7	−	10712.1i	0.704537	−	0.394770i
$904$	6678.99	+	2673.87i	0.245730	+	0.0983755i
$905$	−7324.86	+	6984.24i	−0.269046	+	0.256535i
$906$	−21585.4	−	55994.6i	−0.791531	−	2.05331i
$907$	8203.51	−	3284.19i	0.300323	−	0.120231i	−0.216607	−	0.976259i	$-0.569499\pi$
$907$	8203.51	−	3284.19i	0.300323	−	0.120231i	0.516930	+	0.856028i	$0.327075\pi$
$908$	19068.8	−	41754.8i	0.696937	−	1.52608i
$909$	−31789.7	+	28787.1i	−1.15995	+	1.05039i
$910$	2746.63	−	19103.2i	0.100055	−	0.695896i
$911$	36027.4	+	18573.4i	1.31026	+	0.675484i	0.964808	−	0.262955i	$-0.0846970\pi$
$911$	36027.4	+	18573.4i	1.31026	+	0.675484i	0.345447	+	0.938438i	$0.387727\pi$
$912$	4024.68	+	6443.26i	0.146130	+	0.233945i
$913$	751.910	+	301.020i	0.0272559	+	0.0109116i
$914$	50192.1	−	9673.74i	1.81642	−	0.350086i
$915$	−13154.3	−	3370.92i	−0.475264	−	0.121791i
$916$	−61722.8	−	11896.1i	−2.22640	−	0.429103i
$917$	−33093.1	+	9717.02i	−1.19175	+	0.349928i
$918$	−17502.1	−	49131.9i	−0.629254	−	1.76644i
$919$	−3455.02			−0.124016			−0.0620079	−	0.998076i	$-0.519750\pi$
$919$	−3455.02			−0.124016			−0.0620079	+	0.998076i	$0.519750\pi$
$920$	398.048	+	2903.29i	0.0142644	+	0.104042i
$921$	21539.1	−	7145.87i	0.770615	−	0.255662i
$922$	−23179.6	−	2213.39i	−0.827961	−	0.0790607i
$923$	−5234.73	+	21577.8i	−0.186677	+	0.769494i
$924$	4207.18	−	549.766i	0.149790	−	0.0195736i
$925$	1581.49	−	33199.6i	0.0562152	−	1.18010i
$926$	35459.3	+	40922.2i	1.25838	+	1.45225i
$927$	−26910.0	+	7155.01i	−0.953442	+	0.253507i
$928$	15073.2	+	4425.89i	0.533192	+	0.156559i
$929$	−2552.13	−	1315.71i	−0.0901320	−	0.0464663i	0.412571	−	0.910925i	$-0.364631\pi$
$929$	−2552.13	−	1315.71i	−0.0901320	−	0.0464663i	−0.502703	+	0.864459i	$0.667661\pi$
$930$	−13877.6	−	5003.89i	−0.489318	−	0.176434i
$931$	−2119.95	−	2977.06i	−0.0746279	−	0.104800i
$932$	14586.8	+	20484.3i	0.512669	+	0.719943i
$933$	−17921.3	−	6461.92i	−0.628849	−	0.226746i
$934$	66442.4	+	34253.4i	2.32769	+	1.20001i
$935$	957.335	+	281.099i	0.0334847	+	0.00983200i
$936$	−16554.5	+	4401.62i	−0.578099	+	0.153709i
$937$	−25874.8	−	29861.1i	−0.902127	−	1.04111i	−0.998950	−	0.0458089i	$-0.985413\pi$
$937$	−25874.8	−	29861.1i	−0.902127	−	1.04111i	0.0968228	−	0.995302i	$-0.469132\pi$
$938$	1741.43	−	36557.1i	0.0606179	−	1.27253i
$939$	25043.9	−	3272.56i	0.870369	−	0.113734i
$940$	−1374.47	+	5665.64i	−0.0476918	+	0.196588i
$941$	34453.7	+	3289.93i	1.19358	+	0.113973i	0.672870	−	0.739761i	$-0.265061\pi$
$941$	34453.7	+	3289.93i	1.19358	+	0.113973i	0.520710	+	0.853734i	$0.325667\pi$
$942$	7882.24	−	2615.03i	0.272630	−	0.0904484i
$943$	−13236.4	−	29493.2i	−0.457092	−	1.01848i
$944$	27579.2			0.950875
$945$	8763.08	+	1607.18i	0.301654	+	0.0553244i
$946$	3093.38	−	908.298i	0.106315	−	0.0312170i
$947$	2656.88	+	512.072i	0.0911690	+	0.0175714i	0.234632	−	0.972084i	$-0.424612\pi$
$947$	2656.88	+	512.072i	0.0911690	+	0.0175714i	−0.143463	+	0.989656i	$0.545824\pi$
$948$	42773.1	+	10961.1i	1.46541	+	0.375526i
$949$	−51802.5	+	9984.12i	−1.77195	+	0.341516i
$950$	−15599.5	−	6245.11i	−0.532753	−	0.213282i
$951$	25285.5	+	40480.5i	0.862185	+	1.38031i
$952$	−14638.1	−	7546.47i	−0.498345	−	0.256915i
$953$	2461.91	−	17122.9i	0.0836821	−	0.582022i	−0.904235	−	0.427036i	$-0.859558\pi$
$953$	2461.91	−	17122.9i	0.0836821	−	0.582022i	0.987917	−	0.154986i	$-0.0495332\pi$
$954$	27513.2	−	24914.6i	0.933726	−	0.845535i
$955$	1360.58	−	2979.24i	0.0461018	−	0.100949i
$956$	16654.2	−	6667.34i	0.563427	−	0.225562i
$957$	−441.530	−	1145.37i	−0.0149139	−	0.0386882i
$958$	38552.8	−	36760.0i	1.30019	−	1.23973i
$959$	12715.3	+	5090.43i	0.428152	+	0.171406i
$960$	−9973.41	+	5588.36i	−0.335303	+	0.187879i
$961$	950.416	−	19951.7i	0.0319028	−	0.669722i
$962$	−57003.3	+	65785.3i	−1.91046	+	2.20479i
$963$	10042.1	−	13361.0i	0.336036	−	0.447094i
$964$	25080.1	+	54917.7i	0.837941	+	1.83483i
$965$	−1955.74	−	3387.44i	−0.0652409	−	0.113001i
$966$	42711.8	−	29182.4i	1.42260	−	0.971976i
$967$	−24478.3	+	42397.6i	−0.814031	+	1.40994i	0.0959899	+	0.995382i	$0.469398\pi$
$967$	−24478.3	+	42397.6i	−0.814031	+	1.40994i	−0.910021	+	0.414561i	$0.863935\pi$
$968$	−11634.7	−	1110.98i	−0.386314	−	0.0368885i
$969$	−12711.1	+	8807.34i	−0.421402	+	0.291984i
$970$	1081.07	+	208.360i	0.0357848	+	0.00689695i
$971$	9221.08	+	5926.03i	0.304757	+	0.195855i	0.684076	−	0.729411i	$-0.260206\pi$
$971$	9221.08	+	5926.03i	0.304757	+	0.195855i	−0.379320	+	0.925266i	$0.623842\pi$
$972$	−8386.82	−	37279.7i	−0.276757	−	1.23019i
$973$	3949.35	+	27468.3i	0.130124	+	0.905031i
$974$	1257.50	+	5183.50i	0.0413686	+	0.170524i
$975$	−27069.8	+	33525.5i	−0.889157	+	1.10121i
$976$	−29478.7	−	23182.3i	−0.966794	−	0.760295i
$977$	22104.3	+	31041.2i	0.723829	+	1.01648i	0.998490	+	0.0549340i	$0.0174948\pi$
$977$	22104.3	+	31041.2i	0.723829	+	1.01648i	−0.274661	+	0.961541i	$0.588566\pi$
$978$	−44544.5	+	19654.3i	−1.45642	+	0.642613i
$979$	−4039.73	+	1617.26i	−0.131880	+	0.0527967i
$980$	2725.93	−	1751.85i	0.0888538	−	0.0571029i
$981$	−33297.7	+	12346.4i	−1.08370	+	0.401826i
$982$	−1803.48	−	12543.5i	−0.0586063	−	0.407616i
$983$	−18202.9	+	52593.7i	−0.590622	+	1.70649i	0.110890	+	0.993833i	$0.464630\pi$
$983$	−18202.9	+	52593.7i	−0.590622	+	1.70649i	−0.701512	+	0.712657i	$0.747491\pi$
$984$	−9455.01	+	9664.13i	−0.306316	+	0.313091i
$985$	−1754.36	−	5068.90i	−0.0567499	−	0.163968i
$986$	−5428.11	+	22375.0i	−0.175321	+	0.722682i
$987$	20759.4	−	4754.29i	0.669481	−	0.153324i
$988$	12271.4	+	21254.7i	0.395146	+	0.684414i
$989$	15963.8	−	15023.2i	0.513266	−	0.483023i
$990$	1203.88	+	518.278i	0.0386484	+	0.0166383i
$991$	8839.96	+	19356.8i	0.283361	+	0.620474i	0.996773	−	0.0802707i	$-0.0255785\pi$
$991$	8839.96	+	19356.8i	0.283361	+	0.620474i	−0.713412	+	0.700745i	$0.752851\pi$
$992$	−40953.0	−	39048.6i	−1.31075	−	1.24979i
$993$	−12448.8	+	1626.72i	−0.397836	+	0.0519865i
$994$	−24925.5	+	12850.0i	−0.795362	+	0.410038i
$995$	7057.53	−	1360.23i	0.224863	−	0.0433388i
$996$	−4972.26	−	9957.25i	−0.158185	−	0.316775i
$997$	−8413.86	−	34682.4i	−0.267271	−	1.10171i	−0.934247	−	0.356628i	$-0.883926\pi$
$997$	−8413.86	−	34682.4i	−0.267271	−	1.10171i	0.666975	−	0.745080i	$-0.267589\pi$
$998$	−22875.4	+	14701.1i	−0.725558	+	0.466288i
$999$	−29330.5	−	27466.2i	−0.928905	−	0.869863i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.4.m.a.4.10	✓	1400
9.7	even	3	inner	207.4.m.a.142.61	yes	1400
23.6	even	11	inner	207.4.m.a.121.61	yes	1400
207.52	even	33	inner	207.4.m.a.52.10	yes	1400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.4.m.a.4.10	✓	1400	1.1	even	1	trivial
207.4.m.a.52.10	yes	1400	207.52	even	33	inner
207.4.m.a.121.61	yes	1400	23.6	even	11	inner
207.4.m.a.142.61	yes	1400	9.7	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	207.m (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.46695 + 3.46434i) q^{2} +(-4.27108 + 2.95937i) q^{3} +(-3.29930 - 9.53272i) q^{4} +(-2.65977 + 1.37121i) q^{5} +(0.284244 - 22.0971i) q^{6} +(-16.6811 + 13.1182i) q^{7} +(8.51848 + 2.50125i) q^{8} +(9.48422 - 25.2794i) q^{9} +(1.81118 - 12.5970i) q^{10} +(-3.79715 + 0.362584i) q^{11} +(42.3024 + 30.9511i) q^{12} +(-56.1716 - 44.1738i) q^{13} +(-4.29442 - 90.1509i) q^{14} +(7.30217 - 13.7278i) q^{15} +(33.7548 - 26.5450i) q^{16} +(57.2427 + 66.0616i) q^{17} +(64.1796 + 95.2197i) q^{18} +(22.2958 - 25.7307i) q^{19} +(21.8467 + 20.8308i) q^{20} +(32.4247 - 105.394i) q^{21} +(8.11126 - 14.0491i) q^{22} +(5.96969 - 110.142i) q^{23} +(-43.7852 + 14.5263i) q^{24} +(-67.3130 + 94.5278i) q^{25} +(291.606 - 85.6232i) q^{26} +(34.3034 + 136.038i) q^{27} +(180.088 + 115.735i) q^{28} +(20.2562 - 58.5265i) q^{29} +(29.5437 + 59.1629i) q^{30} +(-161.452 + 153.944i) q^{31} +(12.0694 + 253.368i) q^{32} +(15.1449 - 12.7858i) q^{33} +(-370.075 + 35.3379i) q^{34} +(26.3801 - 57.7644i) q^{35} +(-272.273 - 7.00588i) q^{36} +(-240.948 + 154.848i) q^{37} +(34.1375 + 140.717i) q^{38} +(370.640 + 22.4372i) q^{39} +(-26.0869 + 5.02784i) q^{40} +(260.495 - 134.294i) q^{41} +(285.132 + 372.333i) q^{42} +(143.831 + 137.142i) q^{43} +(15.9844 + 35.0009i) q^{44} +(9.43745 + 80.2422i) q^{45} +(366.845 + 292.397i) q^{46} +(96.5673 + 167.260i) q^{47} +(-65.6126 + 213.269i) q^{48} +(25.3075 - 104.319i) q^{49} +(-161.419 - 466.391i) q^{50} +(-439.989 - 112.752i) q^{51} +(-235.769 + 681.211i) q^{52} +(-46.0020 - 319.951i) q^{53} +(-555.906 - 216.759i) q^{54} +(9.60236 - 6.17106i) q^{55} +(-174.909 + 70.0231i) q^{56} +(-19.0803 + 175.879i) q^{57} +(152.785 + 214.556i) q^{58} +(504.835 + 397.007i) q^{59} +(-154.955 - 24.3174i) q^{60} +(-205.893 - 848.703i) q^{61} +(-135.022 - 939.095i) q^{62} +(173.412 + 546.104i) q^{63} +(-618.526 - 397.503i) q^{64} +(209.975 + 40.4693i) q^{65} +(6.93274 + 84.0091i) q^{66} +(403.674 + 38.5461i) q^{67} +(440.885 - 763.635i) q^{68} +(300.456 + 488.094i) q^{69} +(135.038 + 233.892i) q^{70} +(-129.075 - 282.635i) q^{71} +(144.021 - 191.620i) q^{72} +(483.454 - 557.936i) q^{73} +(57.9599 - 1216.73i) q^{74} +(7.75586 - 602.940i) q^{75} +(-318.844 - 127.646i) q^{76} +(58.5842 - 55.8599i) q^{77} +(-992.081 + 1228.67i) q^{78} +(782.052 - 313.087i) q^{79} +(-53.3811 + 116.888i) q^{80} +(-549.099 - 479.512i) q^{81} +(-177.385 + 1233.74i) q^{82} +(-188.729 - 97.2965i) q^{83} +(-1111.67 + 38.6319i) q^{84} +(-242.836 - 97.2169i) q^{85} +(-829.932 + 159.956i) q^{86} +(86.6858 + 309.917i) q^{87} +(-33.2529 - 6.40896i) q^{88} +(1094.57 - 321.396i) q^{89} +(-301.268 - 165.259i) q^{90} +1516.48 q^{91} +(-1069.65 + 306.486i) q^{92} +(233.995 - 1135.30i) q^{93} +(-817.671 - 78.0781i) q^{94} +(-24.0195 + 99.0098i) q^{95} +(-801.359 - 1046.44i) q^{96} +(-4.11629 + 86.4116i) q^{97} +(298.965 + 345.024i) q^{98} +(-26.8471 + 99.4286i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1400 q - 9 q^{2} - 14 q^{3} + 263 q^{4} + 19 q^{5} - 35 q^{6} - 9 q^{7} - 74 q^{8} - 78 q^{9} - 68 q^{10} + 79 q^{11} + 54 q^{12} - 9 q^{13} + 159 q^{14} - 868 q^{15} + 1031 q^{16} - 308 q^{17} - 87 q^{18}+ \cdots + 7484 q^{99}+O(q^{100}) \) 1400 * q - 9 * q^2 - 14 * q^3 + 263 * q^4 + 19 * q^5 - 35 * q^6 - 9 * q^7 - 74 * q^8 - 78 * q^9 - 68 * q^10 + 79 * q^11 + 54 * q^12 - 9 * q^13 + 159 * q^14 - 868 * q^15 + 1031 * q^16 - 308 * q^17 - 87 * q^18 - 36 * q^19 + 119 * q^20 - 660 * q^21 - 52 * q^22 - 116 * q^23 + 2420 * q^24 + 1397 * q^25 + 432 * q^26 + 274 * q^27 - 324 * q^28 - 45 * q^29 + 768 * q^30 - 45 * q^31 + 111 * q^32 - 1664 * q^33 + 403 * q^34 - 536 * q^35 - 121 * q^36 - 180 * q^37 - 117 * q^38 - 46 * q^39 - 473 * q^40 - 333 * q^41 - 332 * q^42 - 9 * q^43 - 1908 * q^44 + 1762 * q^45 + 484 * q^46 + 216 * q^47 + 1072 * q^48 + 4615 * q^49 - 105 * q^50 + 1298 * q^51 - 708 * q^52 - 1380 * q^53 + 4116 * q^54 - 1328 * q^55 - 3971 * q^56 + 2154 * q^57 - 338 * q^58 + 1917 * q^59 + 154 * q^60 + 27 * q^61 - 3854 * q^62 - 4850 * q^63 - 5854 * q^64 + 3363 * q^65 - 2017 * q^66 + 603 * q^67 - 18454 * q^68 - 4653 * q^69 + 542 * q^70 - 5296 * q^71 - 8044 * q^72 - 36 * q^73 + 3243 * q^74 + 5140 * q^75 - 1029 * q^76 - 1661 * q^77 + 14687 * q^78 - 9 * q^79 + 10312 * q^80 - 294 * q^81 - 770 * q^82 - 2735 * q^83 + 2298 * q^84 + 241 * q^85 + 10507 * q^86 - 10268 * q^87 + 2183 * q^88 - 2980 * q^89 + 33928 * q^90 - 1452 * q^91 - 1973 * q^92 - 11406 * q^93 + 2034 * q^94 - 3339 * q^95 - 4446 * q^96 - 5193 * q^97 + 14820 * q^98 + 7484 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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