LMFDB - Embedded newform 456.2.e.a.379.21

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [456,2,Mod(379,456)] 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("456.379"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(456, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.e (of order $2$, degree $1$, 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:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.21
Character	$\chi$	$=$	456.379
Dual form			456.2.e.a.379.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.134537 - 1.40780i) q^{2} +1.00000i q^{3} +(-1.96380 - 0.378802i) q^{4} +2.61555i q^{5} +(1.40780 + 0.134537i) q^{6} -4.81248i q^{7} +(-0.797481 + 2.71367i) q^{8} -1.00000 q^{9} +(3.68217 + 0.351888i) q^{10} +3.49434 q^{11} +(0.378802 - 1.96380i) q^{12} +1.50149 q^{13} +(-6.77501 - 0.647456i) q^{14} -2.61555 q^{15} +(3.71302 + 1.48778i) q^{16} +5.31012 q^{17} +(-0.134537 + 1.40780i) q^{18} +(3.83470 + 2.07245i) q^{19} +(0.990775 - 5.13641i) q^{20} +4.81248 q^{21} +(0.470118 - 4.91934i) q^{22} -2.26423i q^{23} +(-2.71367 - 0.797481i) q^{24} -1.84109 q^{25} +(0.202006 - 2.11379i) q^{26} -1.00000i q^{27} +(-1.82298 + 9.45075i) q^{28} +5.12817 q^{29} +(-0.351888 + 3.68217i) q^{30} +1.72573 q^{31} +(2.59404 - 5.02702i) q^{32} +3.49434i q^{33} +(0.714407 - 7.47558i) q^{34} +12.5873 q^{35} +(1.96380 + 0.378802i) q^{36} -10.2996 q^{37} +(3.43350 - 5.11967i) q^{38} +1.50149i q^{39} +(-7.09774 - 2.08585i) q^{40} +3.90666i q^{41} +(0.647456 - 6.77501i) q^{42} +0.342152 q^{43} +(-6.86219 - 1.32366i) q^{44} -2.61555i q^{45} +(-3.18759 - 0.304623i) q^{46} -0.679062i q^{47} +(-1.48778 + 3.71302i) q^{48} -16.1600 q^{49} +(-0.247695 + 2.59189i) q^{50} +5.31012i q^{51} +(-2.94862 - 0.568767i) q^{52} -10.0708 q^{53} +(-1.40780 - 0.134537i) q^{54} +9.13962i q^{55} +(13.0595 + 3.83786i) q^{56} +(-2.07245 + 3.83470i) q^{57} +(0.689928 - 7.21944i) q^{58} -9.15071i q^{59} +(5.13641 + 0.990775i) q^{60} -2.65473i q^{61} +(0.232175 - 2.42948i) q^{62} +4.81248i q^{63} +(-6.72805 - 4.32821i) q^{64} +3.92721i q^{65} +(4.91934 + 0.470118i) q^{66} +7.37340i q^{67} +(-10.4280 - 2.01148i) q^{68} +2.26423 q^{69} +(1.69345 - 17.7204i) q^{70} +9.74773 q^{71} +(0.797481 - 2.71367i) q^{72} -7.16085 q^{73} +(-1.38568 + 14.4998i) q^{74} -1.84109i q^{75} +(-6.74554 - 5.52247i) q^{76} -16.8165i q^{77} +(2.11379 + 0.202006i) q^{78} -5.21007 q^{79} +(-3.89137 + 9.71158i) q^{80} +1.00000 q^{81} +(5.49980 + 0.525590i) q^{82} -4.80051 q^{83} +(-9.45075 - 1.82298i) q^{84} +13.8889i q^{85} +(0.0460321 - 0.481681i) q^{86} +5.12817i q^{87} +(-2.78667 + 9.48251i) q^{88} +14.0944i q^{89} +(-3.68217 - 0.351888i) q^{90} -7.22588i q^{91} +(-0.857696 + 4.44650i) q^{92} +1.72573i q^{93} +(-0.955984 - 0.0913590i) q^{94} +(-5.42059 + 10.0299i) q^{95} +(5.02702 + 2.59404i) q^{96} -13.2574i q^{97} +(-2.17411 + 22.7500i) q^{98} -3.49434 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{4} + 4 q^{6} - 40 q^{9} + 4 q^{16} + 8 q^{19} + 32 q^{20} - 4 q^{24} - 40 q^{25} + 40 q^{26} - 8 q^{28} - 48 q^{35} + 4 q^{36} - 8 q^{44} - 56 q^{49} - 4 q^{54} - 8 q^{57} + 16 q^{58} + 40 q^{62}+ \cdots + 44 q^{96}+O(q^{100}) $ 40 * q - 4 * q^4 + 4 * q^6 - 40 * q^9 + 4 * q^16 + 8 * q^19 + 32 * q^20 - 4 * q^24 - 40 * q^25 + 40 * q^26 - 8 * q^28 - 48 * q^35 + 4 * q^36 - 8 * q^44 - 56 * q^49 - 4 * q^54 - 8 * q^57 + 16 * q^58 + 40 * q^62 + 68 * q^64 + 8 * q^66 - 88 * q^68 - 16 * q^73 - 40 * q^74 - 12 * q^76 - 32 * q^80 + 40 * q^81 - 64 * q^82 + 80 * q^83 - 48 * q^92 + 44 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	0.134537	−	1.40780i	0.0951320	−	0.995465i
$2$	0.134537	−	1.40780i	0.0951320	−	0.995465i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.96380	−	0.378802i	−0.981900	−	0.189401i
$5$			2.61555i			1.16971i	0.811138	+	0.584854i	$0.198848\pi$
$5$			2.61555i			1.16971i	−0.811138	+	0.584854i	$0.801152\pi$
$6$	1.40780	+	0.134537i	0.574732	+	0.0549245i
$7$		−	4.81248i		−	1.81895i	−0.415763	−	0.909473i	$-0.636485\pi$
$7$		−	4.81248i		−	1.81895i	0.415763	−	0.909473i	$-0.363515\pi$
$8$	−0.797481	+	2.71367i	−0.281952	+	0.959428i
$9$	−1.00000			−0.333333
$10$	3.68217	+	0.351888i	1.16440	+	0.111277i
$11$	3.49434			1.05358			0.526792	−	0.849994i	$-0.323395\pi$
$11$	3.49434			1.05358			0.526792	+	0.849994i	$0.323395\pi$
$12$	0.378802	−	1.96380i	0.109351	−	0.566900i
$13$	1.50149			0.416438			0.208219	−	0.978082i	$-0.433233\pi$
$13$	1.50149			0.416438			0.208219	+	0.978082i	$0.433233\pi$
$14$	−6.77501	−	0.647456i	−1.81070	−	0.173040i
$15$	−2.61555			−0.675332
$16$	3.71302	+	1.48778i	0.928254	+	0.371946i
$17$	5.31012			1.28789			0.643947	−	0.765071i	$-0.277296\pi$
$17$	5.31012			1.28789			0.643947	+	0.765071i	$0.277296\pi$
$18$	−0.134537	+	1.40780i	−0.0317107	+	0.331822i
$19$	3.83470	+	2.07245i	0.879742	+	0.475452i
$19$	3.83470	+	2.07245i	0.879742	+	0.475452i
$20$	0.990775	−	5.13641i	0.221544	−	1.14854i
$21$	4.81248			1.05017
$22$	0.470118	−	4.91934i	0.100230	−	1.04881i
$23$		−	2.26423i		−	0.472125i	−0.971738	−	0.236063i	$-0.924143\pi$
$23$		−	2.26423i		−	0.472125i	0.971738	−	0.236063i	$-0.0758570\pi$
$24$	−2.71367	−	0.797481i	−0.553926	−	0.162785i
$25$	−1.84109			−0.368219
$26$	0.202006	−	2.11379i	0.0396165	−	0.414549i
$27$		−	1.00000i		−	0.192450i
$28$	−1.82298	+	9.45075i	−0.344510	+	1.78602i
$29$	5.12817			0.952277			0.476139	−	0.879370i	$-0.342036\pi$
$29$	5.12817			0.952277			0.476139	+	0.879370i	$0.342036\pi$
$30$	−0.351888	+	3.68217i	−0.0642457	+	0.672269i
$31$	1.72573			0.309950			0.154975	−	0.987918i	$-0.450470\pi$
$31$	1.72573			0.309950			0.154975	+	0.987918i	$0.450470\pi$
$32$	2.59404	−	5.02702i	0.458566	−	0.888661i
$33$			3.49434i			0.608287i
$34$	0.714407	−	7.47558i	0.122520	−	1.28205i
$35$	12.5873			2.12764
$36$	1.96380	+	0.378802i	0.327300	+	0.0631337i
$37$	−10.2996			−1.69324			−0.846622	−	0.532195i	$-0.821367\pi$
$37$	−10.2996			−1.69324			−0.846622	+	0.532195i	$0.821367\pi$
$38$	3.43350	−	5.11967i	0.556987	−	0.830521i
$39$			1.50149i			0.240430i
$40$	−7.09774	−	2.08585i	−1.12225	−	0.329802i
$41$			3.90666i			0.610118i	0.952333	+	0.305059i	$0.0986762\pi$
$41$			3.90666i			0.610118i	−0.952333	+	0.305059i	$0.901324\pi$
$42$	0.647456	−	6.77501i	0.0999047	−	1.04541i
$43$	0.342152			0.0521777			0.0260888	−	0.999660i	$-0.491695\pi$
$43$	0.342152			0.0521777			0.0260888	+	0.999660i	$0.491695\pi$
$44$	−6.86219	−	1.32366i	−1.03451	−	0.199550i
$45$		−	2.61555i		−	0.389903i
$46$	−3.18759	−	0.304623i	−0.469984	−	0.0449142i
$47$		−	0.679062i		−	0.0990514i	−0.998773	−	0.0495257i	$-0.984229\pi$
$47$		−	0.679062i		−	0.0990514i	0.998773	−	0.0495257i	$-0.0157710\pi$
$48$	−1.48778	+	3.71302i	−0.214743	+	0.535928i
$49$	−16.1600			−2.30857
$50$	−0.247695	+	2.59189i	−0.0350294	+	0.366549i
$51$			5.31012i			0.743565i
$52$	−2.94862	−	0.568767i	−0.408900	−	0.0788737i
$53$	−10.0708			−1.38333			−0.691667	−	0.722216i	$-0.743124\pi$
$53$	−10.0708			−1.38333			−0.691667	+	0.722216i	$0.743124\pi$
$54$	−1.40780	−	0.134537i	−0.191577	−	0.0183082i
$55$			9.13962i			1.23239i
$56$	13.0595	+	3.83786i	1.74515	+	0.512856i
$57$	−2.07245	+	3.83470i	−0.274502	+	0.507919i
$58$	0.689928	−	7.21944i	0.0905920	−	0.947958i
$59$		−	9.15071i		−	1.19132i	−0.803236	−	0.595660i	$-0.796890\pi$
$59$		−	9.15071i		−	1.19132i	0.803236	−	0.595660i	$-0.203110\pi$
$60$	5.13641	+	0.990775i	0.663108	+	0.127909i
$61$		−	2.65473i		−	0.339904i	−0.985452	−	0.169952i	$-0.945639\pi$
$61$		−	2.65473i		−	0.339904i	0.985452	−	0.169952i	$-0.0543613\pi$
$62$	0.232175	−	2.42948i	0.0294862	−	0.308545i
$63$			4.81248i			0.606315i
$64$	−6.72805	−	4.32821i	−0.841006	−	0.541026i
$65$			3.92721i			0.487111i
$66$	4.91934	+	0.470118i	0.605528	+	0.0578676i
$67$			7.37340i			0.900804i	0.892826	+	0.450402i	$0.148719\pi$
$67$			7.37340i			0.900804i	−0.892826	+	0.450402i	$0.851281\pi$
$68$	−10.4280	−	2.01148i	−1.26458	−	0.243928i
$69$	2.26423			0.272582
$70$	1.69345	−	17.7204i	0.202406	−	2.11799i
$71$	9.74773			1.15684			0.578421	−	0.815738i	$-0.303669\pi$
$71$	9.74773			1.15684			0.578421	+	0.815738i	$0.303669\pi$
$72$	0.797481	−	2.71367i	0.0939841	−	0.319809i
$73$	−7.16085			−0.838114			−0.419057	−	0.907960i	$-0.637639\pi$
$73$	−7.16085			−0.838114			−0.419057	+	0.907960i	$0.637639\pi$
$74$	−1.38568	+	14.4998i	−0.161082	+	1.68556i
$75$		−	1.84109i		−	0.212591i
$76$	−6.74554	−	5.52247i	−0.773767	−	0.633470i
$77$		−	16.8165i		−	1.91641i
$78$	2.11379	+	0.202006i	0.239340	+	0.0228726i
$79$	−5.21007			−0.586178			−0.293089	−	0.956085i	$-0.594683\pi$
$79$	−5.21007			−0.586178			−0.293089	+	0.956085i	$0.594683\pi$
$80$	−3.89137	+	9.71158i	−0.435068	+	1.08579i
$81$	1.00000			0.111111
$82$	5.49980	+	0.525590i	0.607351	+	0.0580417i
$83$	−4.80051			−0.526925			−0.263462	−	0.964670i	$-0.584865\pi$
$83$	−4.80051			−0.526925			−0.263462	+	0.964670i	$0.584865\pi$
$84$	−9.45075	−	1.82298i	−1.03116	−	0.198903i
$85$			13.8889i			1.50646i
$86$	0.0460321	−	0.481681i	0.00496377	−	0.0519410i
$87$			5.12817i			0.549798i
$88$	−2.78667	+	9.48251i	−0.297060	+	1.01084i
$89$			14.0944i			1.49400i	0.664823	+	0.747001i	$0.268507\pi$
$89$			14.0944i			1.49400i	−0.664823	+	0.747001i	$0.731493\pi$
$90$	−3.68217	−	0.351888i	−0.388135	−	0.0370922i
$91$		−	7.22588i		−	0.757478i
$92$	−0.857696	+	4.44650i	−0.0894210	+	0.463579i
$93$			1.72573i			0.178950i
$94$	−0.955984	−	0.0913590i	−0.0986022	−	0.00942296i
$95$	−5.42059	+	10.0299i	−0.556141	+	1.02904i
$96$	5.02702	+	2.59404i	0.513068	+	0.264753i
$97$		−	13.2574i		−	1.34608i	−0.739604	−	0.673042i	$-0.764987\pi$
$97$		−	13.2574i		−	1.34608i	0.739604	−	0.673042i	$-0.235013\pi$
$98$	−2.17411	+	22.7500i	−0.219618	+	2.29810i
$99$	−3.49434			−0.351195
$100$	3.61554	+	0.697410i	0.361554	+	0.0697410i
$101$		−	0.101742i		−	0.0101237i	−0.999987	−	0.00506187i	$-0.998389\pi$
$101$		−	0.101742i		−	0.0101237i	0.999987	−	0.00506187i	$-0.00161125\pi$
$102$	7.47558	+	0.714407i	0.740193	+	0.0707369i
$103$	19.3937			1.91092			0.955460	−	0.295120i	$-0.0953597\pi$
$103$	19.3937			1.91092			0.955460	+	0.295120i	$0.0953597\pi$
$104$	−1.19741	+	4.07455i	−0.117415	+	0.399542i
$105$			12.5873i			1.22839i
$106$	−1.35490	+	14.1777i	−0.131599	+	1.37706i
$107$			2.03827i			0.197047i	0.995135	+	0.0985235i	$0.0314120\pi$
$107$			2.03827i			0.197047i	−0.995135	+	0.0985235i	$0.968588\pi$
$108$	−0.378802	+	1.96380i	−0.0364503	+	0.188967i
$109$	18.0323			1.72718			0.863589	−	0.504197i	$-0.168212\pi$
$109$	18.0323			1.72718			0.863589	+	0.504197i	$0.168212\pi$
$110$	12.8668	+	1.22962i	1.22680	+	0.117239i
$111$		−	10.2996i		−	0.977595i
$112$	7.15993	−	17.8688i	0.676549	−	1.68845i
$113$		−	5.54322i		−	0.521462i	−0.965412	−	0.260731i	$-0.916036\pi$
$113$		−	5.54322i		−	0.521462i	0.965412	−	0.260731i	$-0.0839635\pi$
$114$	5.11967	+	3.43350i	0.479501	+	0.321577i
$115$	5.92221			0.552249
$116$	−10.0707	−	1.94256i	−0.935041	−	0.180362i
$117$	−1.50149			−0.138813
$118$	−12.8824	−	1.23111i	−1.18592	−	0.113333i
$119$		−	25.5548i		−	2.34261i
$120$	2.08585	−	7.09774i	0.190411	−	0.647932i
$121$	1.21043			0.110039
$122$	−3.73733	−	0.357160i	−0.338362	−	0.0323357i
$123$	−3.90666			−0.352252
$124$	−3.38899	−	0.653711i	−0.304340	−	0.0587050i
$125$			8.26227i			0.739000i
$126$	6.77501	+	0.647456i	0.603566	+	0.0576800i
$127$	−12.4962			−1.10886			−0.554430	−	0.832231i	$-0.687064\pi$
$127$	−12.4962			−1.10886			−0.554430	+	0.832231i	$0.687064\pi$
$128$	−6.99842	+	8.88944i	−0.618579	+	0.785723i
$129$			0.342152i			0.0301248i
$130$	5.52873	+	0.528355i	0.484901	+	0.0463398i
$131$	12.5819			1.09928			0.549642	−	0.835400i	$-0.314764\pi$
$131$	12.5819			1.09928			0.549642	+	0.835400i	$0.314764\pi$
$132$	1.32366	−	6.86219i	0.115210	−	0.597277i
$133$	9.97362	−	18.4544i	0.864822	−	1.60020i
$134$	10.3803	+	0.991994i	0.896718	+	0.0856952i
$135$	2.61555			0.225111
$136$	−4.23472	+	14.4099i	−0.363124	+	1.23564i
$137$	−1.32093			−0.112855			−0.0564273	−	0.998407i	$-0.517971\pi$
$137$	−1.32093			−0.112855			−0.0564273	+	0.998407i	$0.517971\pi$
$138$	0.304623	−	3.18759i	0.0259312	−	0.271345i
$139$	1.41682			0.120173			0.0600864	−	0.998193i	$-0.480862\pi$
$139$	1.41682			0.120173			0.0600864	+	0.998193i	$0.480862\pi$
$140$	−24.7189	−	4.76809i	−2.08913	−	0.402977i
$141$	0.679062			0.0571874
$142$	1.31143	−	13.7229i	0.110053	−	1.15160i
$143$	5.24671			0.438752
$144$	−3.71302	−	1.48778i	−0.309418	−	0.123982i
$145$			13.4130i			1.11389i
$146$	−0.963399	+	10.0810i	−0.0797315	+	0.834313i
$147$		−	16.1600i		−	1.33285i
$148$	20.2264	+	3.90151i	1.66260	+	0.320702i
$149$			13.2785i			1.08782i	0.839144	+	0.543909i	$0.183057\pi$
$149$			13.2785i			1.08782i	−0.839144	+	0.543909i	$0.816943\pi$
$150$	−2.59189	−	0.247695i	−0.211627	−	0.0202242i
$151$	−16.2778			−1.32467			−0.662334	−	0.749208i	$-0.730434\pi$
$151$	−16.2778			−1.32467			−0.662334	+	0.749208i	$0.730434\pi$
$152$	−8.68205	+	8.75340i	−0.704207	+	0.709994i
$153$	−5.31012			−0.429298
$154$	−23.6742	−	2.26243i	−1.90772	−	0.182312i
$155$			4.51373i			0.362552i
$156$	0.568767	−	2.94862i	0.0455378	−	0.236079i
$157$			18.3793i			1.46683i	0.679783	+	0.733413i	$0.262074\pi$
$157$			18.3793i			1.46683i	−0.679783	+	0.733413i	$0.737926\pi$
$158$	−0.700946	+	7.33473i	−0.0557643	+	0.583520i
$159$		−	10.0708i		−	0.798669i
$160$	13.1484	+	6.78483i	1.03947	+	0.536388i
$161$	−10.8966			−0.858770
$162$	0.134537	−	1.40780i	0.0105702	−	0.110607i
$163$	−12.3413			−0.966649			−0.483325	−	0.875441i	$-0.660571\pi$
$163$	−12.3413			−0.966649			−0.483325	+	0.875441i	$0.660571\pi$
$164$	1.47985	−	7.67190i	0.115557	−	0.599075i
$165$	−9.13962			−0.711519
$166$	−0.645847	+	6.75816i	−0.0501274	+	0.524535i
$167$	−20.7583			−1.60632			−0.803161	−	0.595762i	$-0.796850\pi$
$167$	−20.7583			−1.60632			−0.803161	+	0.595762i	$0.796850\pi$
$168$	−3.83786	+	13.0595i	−0.296097	+	1.00756i
$169$	−10.7455			−0.826580
$170$	19.5527	+	1.86857i	1.49963	+	0.143313i
$171$	−3.83470	−	2.07245i	−0.293247	−	0.158484i
$172$	−0.671918	−	0.129608i	−0.0512333	−	0.00988251i
$173$	−0.684931			−0.0520743			−0.0260372	−	0.999661i	$-0.508289\pi$
$173$	−0.684931			−0.0520743			−0.0260372	+	0.999661i	$0.508289\pi$
$174$	7.21944	+	0.689928i	0.547304	+	0.0523033i
$175$			8.86022i			0.669770i
$176$	12.9746	+	5.19882i	0.977994	+	0.391876i
$177$	9.15071			0.687809
$178$	19.8421	+	1.89622i	1.48723	+	0.142127i
$179$		−	18.7464i		−	1.40117i	−0.713568	−	0.700586i	$-0.752922\pi$
$179$		−	18.7464i		−	1.40117i	0.713568	−	0.700586i	$-0.247078\pi$
$180$	−0.990775	+	5.13641i	−0.0738480	+	0.382846i
$181$	−11.8359			−0.879758			−0.439879	−	0.898057i	$-0.644979\pi$
$181$	−11.8359			−0.879758			−0.439879	+	0.898057i	$0.644979\pi$
$182$	−10.1726	−	0.972147i	−0.754042	−	0.0720604i
$183$	2.65473			0.196244
$184$	6.14439	+	1.80568i	0.452970	+	0.133117i
$185$		−	26.9391i		−	1.98060i
$186$	2.42948	+	0.232175i	0.178138	+	0.0170239i
$187$	18.5554			1.35690
$188$	−0.257230	+	1.33354i	−0.0187604	+	0.0972586i
$189$	−4.81248			−0.350056
$190$	13.3908	+	8.98049i	0.971468	+	0.651513i
$191$			17.4611i			1.26344i	0.775197	+	0.631720i	$0.217651\pi$
$191$			17.4611i			1.26344i	−0.775197	+	0.631720i	$0.782349\pi$
$192$	4.32821	−	6.72805i	0.312361	−	0.485555i
$193$		−	11.0743i		−	0.797149i	−0.917136	−	0.398574i	$-0.869505\pi$
$193$		−	11.0743i		−	0.797149i	0.917136	−	0.398574i	$-0.130495\pi$
$194$	−18.6638	−	1.78361i	−1.33998	−	0.128056i
$195$	−3.92721			−0.281233
$196$	31.7349	+	6.12143i	2.26678	+	0.437245i
$197$			20.2434i			1.44228i	0.692788	+	0.721141i	$0.256382\pi$
$197$			20.2434i			1.44228i	−0.692788	+	0.721141i	$0.743618\pi$
$198$	−0.470118	+	4.91934i	−0.0334099	+	0.349602i
$199$		−	12.1969i		−	0.864613i	−0.901727	−	0.432307i	$-0.857700\pi$
$199$		−	12.1969i		−	0.864613i	0.901727	−	0.432307i	$-0.142300\pi$
$200$	1.46824	−	4.99613i	0.103820	−	0.353279i
$201$	−7.37340			−0.520079
$202$	−0.143233	−	0.0136881i	−0.0100778	−	0.000963092i
$203$		−	24.6792i		−	1.73214i
$204$	2.01148	−	10.4280i	0.140832	−	0.730107i
$205$	−10.2181			−0.713660
$206$	2.60917	−	27.3025i	0.181790	−	1.90225i
$207$			2.26423i			0.157375i
$208$	5.57505	+	2.23389i	0.386560	+	0.154892i
$209$	13.3998	+	7.24185i	0.926882	+	0.500929i
$210$	17.7204	+	1.69345i	1.22282	+	0.116859i
$211$			11.2304i			0.773136i	0.922261	+	0.386568i	$0.126339\pi$
$211$			11.2304i			0.773136i	−0.922261	+	0.386568i	$0.873661\pi$
$212$	19.7771	+	3.81485i	1.35830	+	0.262005i
$213$			9.74773i			0.667904i
$214$	2.86948	+	0.274223i	0.196153	+	0.0187455i
$215$			0.894915i			0.0610327i
$216$	2.71367	+	0.797481i	0.184642	+	0.0542617i
$217$		−	8.30505i		−	0.563783i
$218$	2.42601	−	25.3858i	0.164310	−	1.71934i
$219$		−	7.16085i		−	0.483885i
$220$	3.46211	−	17.9484i	0.233415	−	1.21008i
$221$	7.97308			0.536327
$222$	−14.4998	−	1.38568i	−0.973161	−	0.0930006i
$223$	−5.86592			−0.392811			−0.196406	−	0.980523i	$-0.562927\pi$
$223$	−5.86592			−0.392811			−0.196406	+	0.980523i	$0.562927\pi$
$224$	−24.1924	−	12.4838i	−1.61643	−	0.834106i
$225$	1.84109			0.122740
$226$	−7.80374	−	0.745767i	−0.519097	−	0.0496077i
$227$		−	13.7884i		−	0.915168i	−0.889166	−	0.457584i	$-0.848715\pi$
$227$		−	13.7884i		−	0.915168i	0.889166	−	0.457584i	$-0.151285\pi$
$228$	5.52247	−	6.74554i	0.365734	−	0.446735i
$229$		−	7.75918i		−	0.512741i	−0.966579	−	0.256371i	$-0.917473\pi$
$229$		−	7.75918i		−	0.512741i	0.966579	−	0.256371i	$-0.0825268\pi$
$230$	0.796756	−	8.33728i	0.0525365	−	0.549744i
$231$	16.8165			1.10644
$232$	−4.08962	+	13.9162i	−0.268497	+	0.913642i
$233$	23.5694			1.54408			0.772041	−	0.635573i	$-0.219236\pi$
$233$	23.5694			1.54408			0.772041	+	0.635573i	$0.219236\pi$
$234$	−0.202006	+	2.11379i	−0.0132055	+	0.138183i
$235$	1.77612			0.115861
$236$	−3.46631	+	17.9702i	−0.225637	+	1.16976i
$237$		−	5.21007i		−	0.338430i
$238$	−35.9761	−	3.43807i	−2.33198	−	0.222857i
$239$			13.3670i			0.864640i	0.901720	+	0.432320i	$0.142305\pi$
$239$			13.3670i			0.864640i	−0.901720	+	0.432320i	$0.857695\pi$
$240$	−9.71158	−	3.89137i	−0.626880	−	0.251187i
$241$		−	19.9602i		−	1.28575i	−0.765972	−	0.642873i	$-0.777742\pi$
$241$		−	19.9602i		−	1.28575i	0.765972	−	0.642873i	$-0.222258\pi$
$242$	0.162848	−	1.70405i	0.0104683	−	0.109540i
$243$			1.00000i			0.0641500i
$244$	−1.00562	+	5.21337i	−0.0643782	+	0.333752i
$245$		−	42.2672i		−	2.70035i
$246$	−0.525590	+	5.49980i	−0.0335104	+	0.350654i
$247$	5.75776	+	3.11175i	0.366357	+	0.197996i
$248$	−1.37624	+	4.68307i	−0.0873912	+	0.297375i
$249$		−	4.80051i		−	0.304220i
$250$	11.6316	+	1.11158i	0.735649	+	0.0703026i
$251$	−29.8620			−1.88487			−0.942435	−	0.334388i	$-0.891470\pi$
$251$	−29.8620			−1.88487			−0.942435	+	0.334388i	$0.891470\pi$
$252$	1.82298	−	9.45075i	0.114837	−	0.595341i
$253$		−	7.91200i		−	0.497423i
$254$	−1.68120	+	17.5922i	−0.105488	+	1.10383i
$255$	−13.8889			−0.869755
$256$	11.5730	+	11.0483i	0.723313	+	0.690521i
$257$			0.677951i			0.0422894i	0.999776	+	0.0211447i	$0.00673108\pi$
$257$			0.677951i			0.0422894i	−0.999776	+	0.0211447i	$0.993269\pi$
$258$	0.481681	+	0.0460321i	0.0299882	+	0.00286583i
$259$			49.5666i			3.07992i
$260$	1.48764	−	7.71226i	0.0922593	−	0.478294i
$261$	−5.12817			−0.317426
$262$	1.69273	−	17.7128i	0.104577	−	1.09430i
$263$		−	3.00903i		−	0.185545i	−0.995687	−	0.0927723i	$-0.970427\pi$
$263$		−	3.00903i		−	0.185545i	0.995687	−	0.0927723i	$-0.0295729\pi$
$264$	−9.48251	−	2.78667i	−0.583608	−	0.171508i
$265$		−	26.3407i		−	1.61810i
$266$	−24.6383	−	16.5237i	−1.51067	−	1.01313i
$267$	−14.0944			−0.862563
$268$	2.79306	−	14.4799i	0.170613	−	0.884499i
$269$	7.04041			0.429261			0.214631	−	0.976695i	$-0.431145\pi$
$269$	7.04041			0.429261			0.214631	+	0.976695i	$0.431145\pi$
$270$	0.351888	−	3.68217i	0.0214152	−	0.224090i
$271$		−	22.8229i		−	1.38639i	−0.720750	−	0.693195i	$-0.756202\pi$
$271$		−	22.8229i		−	1.38639i	0.720750	−	0.693195i	$-0.243798\pi$
$272$	19.7166	+	7.90031i	1.19549	+	0.479026i
$273$	7.22588			0.437330
$274$	−0.177714	+	1.85960i	−0.0107361	+	0.112343i
$275$	−6.43341			−0.387949
$276$	−4.44650	−	0.857696i	−0.267648	−	0.0516272i
$277$		−	20.9985i		−	1.26168i	−0.775913	−	0.630840i	$-0.782710\pi$
$277$		−	20.9985i		−	1.26168i	0.775913	−	0.630840i	$-0.217290\pi$
$278$	0.190614	−	1.99459i	0.0114323	−	0.119628i
$279$	−1.72573			−0.103317
$280$	−10.0381	+	34.1577i	−0.599892	+	2.04132i
$281$			5.03139i			0.300148i	0.988675	+	0.150074i	$0.0479511\pi$
$281$			5.03139i			0.300148i	−0.988675	+	0.150074i	$0.952049\pi$
$282$	0.0913590	−	0.955984i	0.00544035	−	0.0569280i
$283$	−1.25113			−0.0743719			−0.0371860	−	0.999308i	$-0.511839\pi$
$283$	−1.25113			−0.0743719			−0.0371860	+	0.999308i	$0.511839\pi$
$284$	−19.1426	−	3.69246i	−1.13590	−	0.219107i
$285$	−10.0299	−	5.42059i	−0.594117	−	0.321088i
$286$	0.705877	−	7.38632i	0.0417394	−	0.436762i
$287$	18.8007			1.10977
$288$	−2.59404	+	5.02702i	−0.152855	+	0.296220i
$289$	11.1974			0.658668
$290$	18.8828	+	1.80454i	1.10884	+	0.105966i
$291$	13.2574			0.777162
$292$	14.0625	+	2.71255i	0.822944	+	0.158740i
$293$	18.5789			1.08539			0.542695	−	0.839930i	$-0.317404\pi$
$293$	18.5789			1.08539			0.542695	+	0.839930i	$0.317404\pi$
$294$	−22.7500	−	2.17411i	−1.32681	−	0.126797i
$295$	23.9341			1.39350
$296$	8.21374	−	27.9498i	0.477414	−	1.62455i
$297$		−	3.49434i		−	0.202762i
$298$	18.6935	+	1.78645i	1.08289	+	0.103486i
$299$		−	3.39972i		−	0.196611i
$300$	−0.697410	+	3.61554i	−0.0402650	+	0.208743i
$301$		−	1.64660i		−	0.0949084i
$302$	−2.18997	+	22.9159i	−0.126018	+	1.31866i
$303$	0.101742			0.00584495
$304$	11.1550	+	13.4002i	0.639782	+	0.768557i
$305$	6.94359			0.397589
$306$	−0.714407	+	7.47558i	−0.0408399	+	0.427351i
$307$		−	10.7076i		−	0.611115i	−0.952174	−	0.305557i	$-0.901157\pi$
$307$		−	10.7076i		−	0.611115i	0.952174	−	0.305557i	$-0.0988428\pi$
$308$	−6.37011	+	33.0241i	−0.362971	+	1.88173i
$309$			19.3937i			1.10327i
$310$	6.35443	+	0.607264i	0.360907	+	0.0344903i
$311$			13.2171i			0.749472i	0.927132	+	0.374736i	$0.122267\pi$
$311$			13.2171i			0.749472i	−0.927132	+	0.374736i	$0.877733\pi$
$312$	−4.07455	−	1.19741i	−0.230676	−	0.0677899i
$313$	−32.4175			−1.83235			−0.916174	−	0.400781i	$-0.868739\pi$
$313$	−32.4175			−1.83235			−0.916174	+	0.400781i	$0.868739\pi$
$314$	25.8743	+	2.47269i	1.46017	+	0.139542i
$315$	−12.5873			−0.709212
$316$	10.2315	+	1.97358i	0.575568	+	0.111023i
$317$	−14.4866			−0.813650			−0.406825	−	0.913506i	$-0.633364\pi$
$317$	−14.4866			−0.813650			−0.406825	+	0.913506i	$0.633364\pi$
$318$	−14.1777	−	1.35490i	−0.795046	−	0.0759789i
$319$	17.9196			1.00330
$320$	11.3206	−	17.5975i	0.632843	−	0.983732i
$321$	−2.03827			−0.113765
$322$	−1.46599	+	15.3402i	−0.0816965	+	0.854875i
$323$	20.3627	+	11.0049i	1.13301	+	0.612332i
$324$	−1.96380	−	0.378802i	−0.109100	−	0.0210446i
$325$	−2.76438			−0.153340
$326$	−1.66037	+	17.3741i	−0.0919593	+	0.962265i
$327$			18.0323i			0.997186i
$328$	−10.6014	−	3.11549i	−0.585364	−	0.172024i
$329$	−3.26797			−0.180169
$330$	−1.22962	+	12.8668i	−0.0676882	+	0.708292i
$331$		−	5.22689i		−	0.287296i	−0.989629	−	0.143648i	$-0.954117\pi$
$331$		−	5.22689i		−	0.287296i	0.989629	−	0.143648i	$-0.0458832\pi$
$332$	9.42725	+	1.81845i	0.517387	+	0.0998001i
$333$	10.2996			0.564415
$334$	−2.79275	+	29.2235i	−0.152813	+	1.59904i
$335$	−19.2855			−1.05368
$336$	17.8688	+	7.15993i	0.974824	+	0.390606i
$337$			18.1981i			0.991312i	0.868519	+	0.495656i	$0.165072\pi$
$337$			18.1981i			0.991312i	−0.868519	+	0.495656i	$0.834928\pi$
$338$	−1.44567	+	15.1276i	−0.0786342	+	0.822831i
$339$	5.54322			0.301066
$340$	5.26114	−	27.2750i	0.285325	−	1.47919i
$341$	6.03030			0.326559
$342$	−3.43350	+	5.11967i	−0.185662	+	0.276840i
$343$			44.0821i			2.38021i
$344$	−0.272860	+	0.928489i	−0.0147116	+	0.0500608i
$345$			5.92221i			0.318841i
$346$	−0.0921485	+	0.964245i	−0.00495393	+	0.0518381i
$347$	−16.9154			−0.908066			−0.454033	−	0.890985i	$-0.650015\pi$
$347$	−16.9154			−0.908066			−0.454033	+	0.890985i	$0.650015\pi$
$348$	1.94256	−	10.0707i	0.104132	−	0.539846i
$349$			28.3766i			1.51896i	0.650528	+	0.759482i	$0.274547\pi$
$349$			28.3766i			1.51896i	−0.650528	+	0.759482i	$0.725453\pi$
$350$	12.4734	+	1.19203i	0.666732	+	0.0637165i
$351$		−	1.50149i		−	0.0801435i
$352$	9.06446	−	17.5661i	0.483137	−	0.936279i
$353$	2.43957			0.129845			0.0649227	−	0.997890i	$-0.479320\pi$
$353$	2.43957			0.129845			0.0649227	+	0.997890i	$0.479320\pi$
$354$	1.23111	−	12.8824i	0.0654327	−	0.684690i
$355$			25.4957i			1.35317i
$356$	5.33899	−	27.6786i	0.282966	−	1.46696i
$357$	25.5548			1.35251
$358$	−26.3912	−	2.52209i	−1.39482	−	0.133296i
$359$		−	24.6073i		−	1.29872i	−0.760479	−	0.649362i	$-0.775036\pi$
$359$		−	24.6073i		−	1.29872i	0.760479	−	0.649362i	$-0.224964\pi$
$360$	7.09774	+	2.08585i	0.374084	+	0.109934i
$361$	10.4099	+	15.8945i	0.547890	+	0.836550i
$362$	−1.59237	+	16.6626i	−0.0836931	+	0.875768i
$363$			1.21043i			0.0635313i
$364$	−2.73718	+	14.1902i	−0.143467	+	0.743767i
$365$		−	18.7295i		−	0.980349i
$366$	0.357160	−	3.73733i	0.0186691	−	0.195354i
$367$		−	18.9695i		−	0.990201i	−0.868836	−	0.495100i	$-0.835131\pi$
$367$		−	18.9695i		−	0.990201i	0.868836	−	0.495100i	$-0.164869\pi$
$368$	3.36869	−	8.40713i	0.175605	−	0.438252i
$369$		−	3.90666i		−	0.203373i
$370$	−37.9249	−	3.62431i	−1.97162	−	0.188419i
$371$			48.4657i			2.51621i
$372$	0.653711	−	3.38899i	0.0338933	−	0.175711i
$373$	−20.4231			−1.05747			−0.528734	−	0.848788i	$-0.677333\pi$
$373$	−20.4231			−1.05747			−0.528734	+	0.848788i	$0.677333\pi$
$374$	2.49638	−	26.1223i	0.129085	−	1.35075i
$375$	−8.26227			−0.426662
$376$	1.84275	+	0.541540i	0.0950328	+	0.0279278i
$377$	7.69988			0.396564
$378$	−0.647456	+	6.77501i	−0.0333016	+	0.348469i
$379$			26.0452i			1.33785i	0.743330	+	0.668925i	$0.233245\pi$
$379$			26.0452i			1.33785i	−0.743330	+	0.668925i	$0.766755\pi$
$380$	14.4443	−	17.6433i	0.740976	−	0.905082i
$381$		−	12.4962i		−	0.640200i
$382$	24.5817	+	2.34916i	1.25771	+	0.120194i
$383$	−23.1300			−1.18189			−0.590944	−	0.806712i	$-0.701245\pi$
$383$	−23.1300			−1.18189			−0.590944	+	0.806712i	$0.701245\pi$
$384$	−8.88944	−	6.99842i	−0.453637	−	0.357137i
$385$	43.9843			2.24165
$386$	−15.5905	−	1.48991i	−0.793534	−	0.0758344i
$387$	−0.342152			−0.0173926
$388$	−5.02193	+	26.0349i	−0.254950	+	1.32172i
$389$			17.1821i			0.871166i	0.900148	+	0.435583i	$0.143458\pi$
$389$			17.1821i			0.871166i	−0.900148	+	0.435583i	$0.856542\pi$
$390$	−0.528355	+	5.52873i	−0.0267543	+	0.279958i
$391$		−	12.0233i		−	0.608047i
$392$	12.8873	−	43.8529i	0.650905	−	2.21490i
$393$			12.5819i			0.634672i
$394$	28.4986	+	2.72349i	1.43574	+	0.137207i
$395$		−	13.6272i		−	0.685658i
$396$	6.86219	+	1.32366i	0.344838	+	0.0665167i
$397$			28.3706i			1.42388i	0.702242	+	0.711939i	$0.252183\pi$
$397$			28.3706i			1.42388i	−0.702242	+	0.711939i	$0.747817\pi$
$398$	−17.1708	−	1.64093i	−0.860692	−	0.0822524i
$399$	18.4544	+	9.97362i	0.923877	+	0.499305i
$400$	−6.83601	−	2.73915i	−0.341801	−	0.136957i
$401$		−	6.28011i		−	0.313614i	−0.987629	−	0.156807i	$-0.949880\pi$
$401$		−	6.28011i		−	0.313614i	0.987629	−	0.156807i	$-0.0501200\pi$
$402$	−0.991994	+	10.3803i	−0.0494762	+	0.517720i
$403$	2.59116			0.129075
$404$	−0.0385402	+	0.199802i	−0.00191745	+	0.00994050i
$405$			2.61555i			0.129968i
$406$	−34.7434	−	3.32027i	−1.72429	−	0.164782i
$407$	−35.9903			−1.78398
$408$	−14.4099	−	4.23472i	−0.713398	−	0.209650i
$409$			2.75238i			0.136097i	0.997682	+	0.0680483i	$0.0216772\pi$
$409$			2.75238i			0.136097i	−0.997682	+	0.0680483i	$0.978323\pi$
$410$	−1.37471	+	14.3850i	−0.0678919	+	0.710424i
$411$		−	1.32093i		−	0.0651566i
$412$	−38.0854	−	7.34638i	−1.87633	−	0.361930i
$413$	−44.0376			−2.16695
$414$	3.18759	+	0.304623i	0.156661	+	0.0149714i
$415$		−	12.5560i		−	0.616349i
$416$	3.89492	−	7.54801i	0.190964	−	0.370072i
$417$			1.41682i			0.0693818i
$418$	11.9978	−	17.8899i	0.586833	−	0.875024i
$419$	−33.3577			−1.62963			−0.814816	−	0.579719i	$-0.803162\pi$
$419$	−33.3577			−1.62963			−0.814816	+	0.579719i	$0.803162\pi$
$420$	4.76809	−	24.7189i	0.232659	−	1.20616i
$421$	0.929028			0.0452781			0.0226390	−	0.999744i	$-0.492793\pi$
$421$	0.929028			0.0452781			0.0226390	+	0.999744i	$0.492793\pi$
$422$	15.8102	+	1.51091i	0.769629	+	0.0735499i
$423$			0.679062i			0.0330171i
$424$	8.03130	−	27.3289i	0.390034	−	1.32721i
$425$	−9.77642			−0.474226
$426$	13.7229	+	1.31143i	0.664874	+	0.0635390i
$427$	−12.7759			−0.618267
$428$	0.772101	−	4.00275i	0.0373209	−	0.193480i
$429$			5.24671i			0.253314i
$430$	1.25986	+	0.120399i	0.0607559	+	0.00580616i
$431$	34.4951			1.66157			0.830786	−	0.556592i	$-0.187891\pi$
$431$	34.4951			1.66157			0.830786	+	0.556592i	$0.187891\pi$
$432$	1.48778	−	3.71302i	0.0715810	−	0.178643i
$433$		−	24.9055i		−	1.19688i	−0.801166	−	0.598442i	$-0.795787\pi$
$433$		−	24.9055i		−	1.19688i	0.801166	−	0.598442i	$-0.204213\pi$
$434$	−11.6918	−	1.11734i	−0.561226	−	0.0536338i
$435$	−13.4130			−0.643103
$436$	−35.4117	−	6.83066i	−1.69591	−	0.327129i
$437$	4.69250	−	8.68266i	0.224473	−	0.415348i
$438$	−10.0810	−	0.963399i	−0.481691	−	0.0460330i
$439$	−20.5120			−0.978984			−0.489492	−	0.872008i	$-0.662818\pi$
$439$	−20.5120			−0.978984			−0.489492	+	0.872008i	$0.662818\pi$
$440$	−24.8020	−	7.28868i	−1.18239	−	0.347474i
$441$	16.1600			0.769522
$442$	1.07267	−	11.2245i	0.0510219	−	0.533895i
$443$	25.9849			1.23458			0.617289	−	0.786736i	$-0.288231\pi$
$443$	25.9849			1.23458			0.617289	+	0.786736i	$0.288231\pi$
$444$	−3.90151	+	20.2264i	−0.185158	+	0.959900i
$445$	−36.8646			−1.74755
$446$	−0.789184	+	8.25805i	−0.0373689	+	0.391030i
$447$	−13.2785			−0.628053
$448$	−20.8294	+	32.3786i	−0.984097	+	1.52974i
$449$			36.4806i			1.72163i	0.508920	+	0.860814i	$0.330045\pi$
$449$			36.4806i			1.72163i	−0.508920	+	0.860814i	$0.669955\pi$
$450$	0.247695	−	2.59189i	0.0116765	−	0.122183i
$451$			13.6512i			0.642810i
$452$	−2.09978	+	10.8858i	−0.0987654	+	0.512023i
$453$		−	16.2778i		−	0.764798i
$454$	−19.4113	−	1.85505i	−0.911018	−	0.0870618i
$455$	18.8996			0.886028
$456$	−8.75340	−	8.68205i	−0.409915	−	0.406574i
$457$	23.2770			1.08885			0.544425	−	0.838809i	$-0.316748\pi$
$457$	23.2770			1.08885			0.544425	+	0.838809i	$0.316748\pi$
$458$	−10.9234	−	1.04390i	−0.510416	−	0.0487781i
$459$		−	5.31012i		−	0.247855i
$460$	−11.6300	−	2.24335i	−0.542253	−	0.104597i
$461$			14.2845i			0.665298i	0.943051	+	0.332649i	$0.107942\pi$
$461$			14.2845i			0.665298i	−0.943051	+	0.332649i	$0.892058\pi$
$462$	2.26243	−	23.6742i	0.105258	−	1.10142i
$463$		−	15.6276i		−	0.726275i	−0.931736	−	0.363137i	$-0.881706\pi$
$463$		−	15.6276i		−	0.726275i	0.931736	−	0.363137i	$-0.118294\pi$
$464$	19.0410	+	7.62961i	0.883956	+	0.354196i
$465$	−4.51373			−0.209319
$466$	3.17095	−	33.1810i	0.146892	−	1.53708i
$467$	−8.66870			−0.401140			−0.200570	−	0.979679i	$-0.564279\pi$
$467$	−8.66870			−0.401140			−0.200570	+	0.979679i	$0.564279\pi$
$468$	2.94862	+	0.568767i	0.136300	+	0.0262912i
$469$	35.4843			1.63851
$470$	0.238954	−	2.50042i	0.0110221	−	0.115336i
$471$	−18.3793			−0.846873
$472$	24.8320	+	7.29752i	1.14299	+	0.335895i
$473$	1.19560			0.0549736
$474$	−7.33473	−	0.700946i	−0.336895	−	0.0321955i
$475$	−7.06005	−	3.81557i	−0.323937	−	0.175070i
$476$	−9.68023	+	50.1846i	−0.443693	+	2.30021i
$477$	10.0708			0.461112
$478$	18.8181	+	1.79836i	0.860719	+	0.0822549i
$479$		−	3.41248i		−	0.155920i	−0.996956	−	0.0779602i	$-0.975159\pi$
$479$		−	3.41248i		−	0.155920i	0.996956	−	0.0779602i	$-0.0248407\pi$
$480$	−6.78483	+	13.1484i	−0.309684	+	0.600141i
$481$	−15.4647			−0.705130
$482$	−28.0999	−	2.68538i	−1.27992	−	0.122316i
$483$		−	10.8966i		−	0.495811i
$484$	−2.37705	−	0.458515i	−0.108048	−	0.0208416i
$485$	34.6754			1.57453
$486$	1.40780	+	0.134537i	0.0638591	+	0.00610272i
$487$	41.8116			1.89467			0.947333	−	0.320250i	$-0.103767\pi$
$487$	41.8116			1.89467			0.947333	+	0.320250i	$0.103767\pi$
$488$	7.20408	+	2.11710i	0.326114	+	0.0958367i
$489$		−	12.3413i		−	0.558095i
$490$	−59.5037	−	5.68650i	−2.68810	−	0.256890i
$491$	−13.0613			−0.589448			−0.294724	−	0.955582i	$-0.595228\pi$
$491$	−13.0613			−0.589448			−0.294724	+	0.955582i	$0.595228\pi$
$492$	7.67190	+	1.47985i	0.345876	+	0.0667169i
$493$	27.2312			1.22643
$494$	5.15536	−	7.68713i	0.231951	−	0.345860i
$495$		−	9.13962i		−	0.410796i
$496$	6.40767	+	2.56751i	0.287713	+	0.115285i
$497$		−	46.9108i		−	2.10424i
$498$	−6.75816	−	0.645847i	−0.302840	−	0.0289411i
$499$	7.12405			0.318916			0.159458	−	0.987205i	$-0.449025\pi$
$499$	7.12405			0.318916			0.159458	+	0.987205i	$0.449025\pi$
$500$	3.12977	−	16.2255i	0.139967	−	0.725624i
$501$		−	20.7583i		−	0.927411i
$502$	−4.01754	+	42.0397i	−0.179312	+	1.87632i
$503$			6.92730i			0.308873i	0.988003	+	0.154437i	$0.0493562\pi$
$503$			6.92730i			0.308873i	−0.988003	+	0.154437i	$0.950644\pi$
$504$	−13.0595	−	3.83786i	−0.581716	−	0.170952i
$505$	0.266112			0.0118418
$506$	−11.1385	−	1.06446i	−0.495167	−	0.0473209i
$507$		−	10.7455i		−	0.477226i
$508$	24.5400	+	4.73359i	1.08879	+	0.210019i
$509$	5.92205			0.262490			0.131245	−	0.991350i	$-0.458103\pi$
$509$	5.92205			0.262490			0.131245	+	0.991350i	$0.458103\pi$
$510$	−1.86857	+	19.5527i	−0.0827415	+	0.865810i
$511$			34.4614i			1.52448i
$512$	17.1108	−	14.8061i	0.756199	−	0.654342i
$513$	2.07245	−	3.83470i	0.0915008	−	0.169306i
$514$	0.954420	+	0.0912095i	0.0420977	+	0.00402308i
$515$			50.7252i			2.23522i
$516$	0.129608	−	0.671918i	0.00570567	−	0.0295795i
$517$		−	2.37288i		−	0.104359i
$518$	69.7799	+	6.66854i	3.06595	+	0.292999i
$519$		−	0.684931i		−	0.0300651i
$520$	−10.6572	−	3.13188i	−0.467348	−	0.137342i
$521$		−	16.9113i		−	0.740898i	−0.928853	−	0.370449i	$-0.879204\pi$
$521$		−	16.9113i		−	0.740898i	0.928853	−	0.370449i	$-0.120796\pi$
$522$	−0.689928	+	7.21944i	−0.0301973	+	0.315986i
$523$		−	20.3406i		−	0.889434i	−0.895671	−	0.444717i	$-0.853304\pi$
$523$		−	20.3406i		−	0.889434i	0.895671	−	0.444717i	$-0.146696\pi$
$524$	−24.7083	−	4.76604i	−1.07939	−	0.208206i
$525$	−8.86022			−0.386692
$526$	−4.23611	−	0.404826i	−0.184703	−	0.0176512i
$527$	9.16384			0.399183
$528$	−5.19882	+	12.9746i	−0.226250	+	0.564645i
$529$	17.8733			0.777098
$530$	−37.0825	−	3.54380i	−1.61076	−	0.153933i
$531$			9.15071i			0.397107i
$532$	−26.5768	+	32.4628i	−1.15225	+	1.40744i
$533$			5.86580i			0.254076i
$534$	−1.89622	+	19.8421i	−0.0820573	+	0.858651i
$535$	−5.33119			−0.230488
$536$	−20.0090	−	5.88014i	−0.864257	−	0.253984i
$537$	18.7464			0.808967
$538$	0.947196	−	9.91149i	0.0408365	−	0.427315i
$539$	−56.4684			−2.43227
$540$	−5.13641	−	0.990775i	−0.221036	−	0.0426362i
$541$		−	24.8364i		−	1.06780i	−0.845548	−	0.533900i	$-0.820726\pi$
$541$		−	24.8364i		−	1.06780i	0.845548	−	0.533900i	$-0.179274\pi$
$542$	−32.1300	−	3.07052i	−1.38010	−	0.131890i
$543$		−	11.8359i		−	0.507928i
$544$	13.7747	−	26.6941i	0.590583	−	1.14450i
$545$			47.1642i			2.02029i
$546$	0.972147	−	10.1726i	0.0416041	−	0.435346i
$547$		−	22.8518i		−	0.977071i	−0.872544	−	0.488535i	$-0.837531\pi$
$547$		−	22.8518i		−	0.977071i	0.872544	−	0.488535i	$-0.162469\pi$
$548$	2.59404	+	0.500370i	0.110812	+	0.0213748i
$549$			2.65473i			0.113301i
$550$	−0.865532	+	9.05695i	−0.0369064	+	0.386190i
$551$	19.6650	+	10.6279i	0.837758	+	0.452762i
$552$	−1.80568	+	6.14439i	−0.0768550	+	0.261522i
$553$			25.0733i			1.06623i
$554$	−29.5617	−	2.82508i	−1.25596	−	0.120026i
$555$	26.9391			1.14350
$556$	−2.78234	−	0.536693i	−0.117998	−	0.0227609i
$557$		−	5.88751i		−	0.249462i	−0.992191	−	0.124731i	$-0.960193\pi$
$557$		−	5.88751i		−	0.249462i	0.992191	−	0.124731i	$-0.0398067\pi$
$558$	−0.232175	+	2.42948i	−0.00982874	+	0.102848i
$559$	0.513737			0.0217288
$560$	46.7368	+	18.7271i	1.97499	+	0.791366i
$561$			18.5554i			0.783409i
$562$	7.08319	+	0.676908i	0.298786	+	0.0285536i
$563$			6.33319i			0.266912i	0.991055	+	0.133456i	$0.0426075\pi$
$563$			6.33319i			0.266912i	−0.991055	+	0.133456i	$0.957393\pi$
$564$	−1.33354	−	0.257230i	−0.0561523	−	0.0108314i
$565$	14.4985			0.609959
$566$	−0.168323	+	1.76134i	−0.00707515	+	0.0740346i
$567$		−	4.81248i		−	0.202105i
$568$	−7.77363	+	26.4522i	−0.326174	+	1.10991i
$569$			19.8209i			0.830937i	0.909607	+	0.415469i	$0.136382\pi$
$569$			19.8209i			0.830937i	−0.909607	+	0.415469i	$0.863618\pi$
$570$	−8.98049	+	13.3908i	−0.376151	+	0.560877i
$571$	−35.3004			−1.47728			−0.738639	−	0.674101i	$-0.764531\pi$
$571$	−35.3004			−1.47728			−0.738639	+	0.674101i	$0.764531\pi$
$572$	−10.3035	−	1.98747i	−0.430811	−	0.0831001i
$573$	−17.4611			−0.729448
$574$	2.52939	−	26.4677i	0.105575	−	1.10474i
$575$			4.16866i			0.173845i
$576$	6.72805	+	4.32821i	0.280335	+	0.180342i
$577$	28.4776			1.18554			0.592769	−	0.805373i	$-0.298035\pi$
$577$	28.4776			1.18554			0.592769	+	0.805373i	$0.298035\pi$
$578$	1.50646	−	15.7636i	0.0626604	−	0.655681i
$579$	11.0743			0.460234
$580$	5.08087	−	26.3404i	0.210971	−	1.09373i
$581$			23.1024i			0.958448i
$582$	1.78361	−	18.6638i	0.0739330	−	0.773637i
$583$	−35.1909			−1.45746
$584$	5.71064	−	19.4322i	0.236308	−	0.804111i
$585$		−	3.92721i		−	0.162370i
$586$	2.49955	−	26.1554i	0.103255	−	1.08047i
$587$	28.0180			1.15643			0.578214	−	0.815885i	$-0.303750\pi$
$587$	28.0180			1.15643			0.578214	+	0.815885i	$0.303750\pi$
$588$	−6.12143	+	31.7349i	−0.252443	+	1.30873i
$589$	6.61767	+	3.57649i	0.272676	+	0.147367i
$590$	3.22002	−	33.6944i	0.132566	−	1.38718i
$591$	−20.2434			−0.832702
$592$	−38.2426	−	15.3236i	−1.57176	−	0.629795i
$593$	−45.6450			−1.87442			−0.937208	−	0.348771i	$-0.886599\pi$
$593$	−45.6450			−1.87442			−0.937208	+	0.348771i	$0.886599\pi$
$594$	−4.91934	−	0.470118i	−0.201843	−	0.0192892i
$595$	66.8399			2.74017
$596$	5.02993	−	26.0764i	0.206034	−	1.06813i
$597$	12.1969			0.499185
$598$	−4.78612	−	0.457387i	−0.195719	−	0.0187040i
$599$	−20.9807			−0.857248			−0.428624	−	0.903483i	$-0.641002\pi$
$599$	−20.9807			−0.857248			−0.428624	+	0.903483i	$0.641002\pi$
$600$	4.99613	+	1.46824i	0.203966	+	0.0599405i
$601$		−	0.458660i		−	0.0187091i	−0.999956	−	0.00935456i	$-0.997022\pi$
$601$		−	0.458660i		−	0.0187091i	0.999956	−	0.00935456i	$-0.00297769\pi$
$602$	−2.31808	−	0.221528i	−0.0944780	−	0.00902883i
$603$		−	7.37340i		−	0.300268i
$604$	31.9663	+	6.16607i	1.30069	+	0.250894i
$605$			3.16595i			0.128714i
$606$	0.0136881	−	0.143233i	0.000556041	−	0.00581844i
$607$	30.1779			1.22488			0.612441	−	0.790516i	$-0.290188\pi$
$607$	30.1779			1.22488			0.612441	+	0.790516i	$0.290188\pi$
$608$	20.3656	−	13.9011i	0.825935	−	0.563766i
$609$	24.6792			1.00005
$610$	0.934169	−	9.77518i	0.0378234	−	0.395785i
$611$		−	1.01960i		−	0.0412487i
$612$	10.4280	+	2.01148i	0.421527	+	0.0813094i
$613$		−	15.1288i		−	0.611045i	−0.952185	−	0.305523i	$-0.901169\pi$
$613$		−	15.1288i		−	0.611045i	0.952185	−	0.305523i	$-0.0988311\pi$
$614$	−15.0742	−	1.44057i	−0.608343	−	0.0581366i
$615$		−	10.2181i		−	0.412032i
$616$	45.6344	+	13.4108i	1.83866	+	0.540337i
$617$	−3.05065			−0.122815			−0.0614073	−	0.998113i	$-0.519559\pi$
$617$	−3.05065			−0.122815			−0.0614073	+	0.998113i	$0.519559\pi$
$618$	27.3025	+	2.60917i	1.09827	+	0.104956i
$619$	−14.3298			−0.575962			−0.287981	−	0.957636i	$-0.592984\pi$
$619$	−14.3298			−0.575962			−0.287981	+	0.957636i	$0.592984\pi$
$620$	1.70981	−	8.86407i	0.0686677	−	0.355990i
$621$	−2.26423			−0.0908605
$622$	18.6070	+	1.77819i	0.746073	+	0.0712987i
$623$	67.8290			2.71751
$624$	−2.23389	+	5.57505i	−0.0894271	+	0.223181i
$625$	−30.8158			−1.23263
$626$	−4.36136	+	45.6374i	−0.174315	+	1.82404i
$627$	−7.24185	+	13.3998i	−0.289211	+	0.535135i
$628$	6.96211	−	36.0932i	0.277818	−	1.44028i
$629$	−54.6921			−2.18072
$630$	−1.69345	+	17.7204i	−0.0674688	+	0.705996i
$631$		−	11.4416i		−	0.455482i	−0.973722	−	0.227741i	$-0.926866\pi$
$631$		−	11.4416i		−	0.455482i	0.973722	−	0.227741i	$-0.0731340\pi$
$632$	4.15493	−	14.1384i	0.165274	−	0.562396i
$633$	−11.2304			−0.446370
$634$	−1.94899	+	20.3943i	−0.0774041	+	0.809960i
$635$		−	32.6844i		−	1.29704i
$636$	−3.81485	+	19.7771i	−0.151269	+	0.784213i
$637$	−24.2640			−0.961374
$638$	2.41085	−	25.2272i	0.0954463	−	0.998754i
$639$	−9.74773			−0.385614
$640$	−23.2508	−	18.3047i	−0.919067	−	0.723557i
$641$			13.6910i			0.540760i	0.962754	+	0.270380i	$0.0871494\pi$
$641$			13.6910i			0.540760i	−0.962754	+	0.270380i	$0.912851\pi$
$642$	−0.274223	+	2.86948i	−0.0108227	+	0.113249i
$643$	7.58609			0.299166			0.149583	−	0.988749i	$-0.452207\pi$
$643$	7.58609			0.299166			0.149583	+	0.988749i	$0.452207\pi$
$644$	21.3987	+	4.12764i	0.843226	+	0.162652i
$645$	−0.894915			−0.0352372
$646$	18.2323	−	27.1861i	0.717340	−	1.06962i
$647$		−	27.2526i		−	1.07141i	−0.844405	−	0.535705i	$-0.820046\pi$
$647$		−	27.2526i		−	1.07141i	0.844405	−	0.535705i	$-0.179954\pi$
$648$	−0.797481	+	2.71367i	−0.0313280	+	0.106603i
$649$		−	31.9757i		−	1.25516i
$650$	−0.371911	+	3.89169i	−0.0145875	+	0.152645i
$651$	8.30505			0.325500
$652$	24.2359	+	4.67493i	0.949153	+	0.183084i
$653$		−	3.86565i		−	0.151274i	−0.997135	−	0.0756372i	$-0.975901\pi$
$653$		−	3.86565i		−	0.151274i	0.997135	−	0.0756372i	$-0.0240991\pi$
$654$	25.3858	+	2.42601i	0.992664	+	0.0948643i
$655$			32.9085i			1.28584i
$656$	−5.81226	+	14.5055i	−0.226931	+	0.566345i
$657$	7.16085			0.279371
$658$	−0.439663	+	4.60065i	−0.0171399	+	0.179352i
$659$			33.7642i			1.31527i	0.753338	+	0.657633i	$0.228442\pi$
$659$			33.7642i			1.31527i	−0.753338	+	0.657633i	$0.771558\pi$
$660$	17.9484	+	3.46211i	0.698640	+	0.134762i
$661$	−7.29497			−0.283741			−0.141871	−	0.989885i	$-0.545312\pi$
$661$	−7.29497			−0.283741			−0.141871	+	0.989885i	$0.545312\pi$
$662$	−7.35841	−	0.703209i	−0.285993	−	0.0273310i
$663$			7.97308i			0.309649i
$664$	3.82832	−	13.0270i	0.148568	−	0.505547i
$665$	48.2685	+	26.0865i	1.87177	+	1.01159i
$666$	1.38568	−	14.4998i	0.0536939	−	0.561855i
$667$		−	11.6114i		−	0.449594i
$668$	40.7651	+	7.86327i	1.57725	+	0.304239i
$669$		−	5.86592i		−	0.226790i
$670$	−2.59461	+	27.1501i	−0.100238	+	1.04890i
$671$		−	9.27655i		−	0.358117i
$672$	12.4838	−	24.1924i	0.481571	−	0.933244i
$673$			20.7118i			0.798380i	0.916868	+	0.399190i	$0.130709\pi$
$673$			20.7118i			0.798380i	−0.916868	+	0.399190i	$0.869291\pi$
$674$	25.6192	+	2.44831i	0.986816	+	0.0943055i
$675$			1.84109i			0.0708637i
$676$	21.1021	+	4.07043i	0.811618	+	0.156555i
$677$	22.9317			0.881336			0.440668	−	0.897670i	$-0.354742\pi$
$677$	22.9317			0.881336			0.440668	+	0.897670i	$0.354742\pi$
$678$	0.745767	−	7.80374i	0.0286410	−	0.299701i
$679$	−63.8009			−2.44846
$680$	−37.6899	−	11.0761i	−1.44534	−	0.424750i
$681$	13.7884			0.528373
$682$	0.811298	−	8.48945i	0.0310662	−	0.325078i
$683$		−	22.5142i		−	0.861483i	−0.902475	−	0.430741i	$-0.858252\pi$
$683$		−	22.5142i		−	0.861483i	0.902475	−	0.430741i	$-0.141748\pi$
$684$	6.74554	+	5.52247i	0.257922	+	0.211157i
$685$		−	3.45495i		−	0.132007i
$686$	62.0588	+	5.93068i	2.36942	+	0.226434i
$687$	7.75918			0.296031
$688$	1.27042	+	0.509048i	0.0484342	+	0.0194073i
$689$	−15.1212			−0.576073
$690$	8.33728	+	0.796756i	0.317395	+	0.0303320i
$691$	−13.4002			−0.509766			−0.254883	−	0.966972i	$-0.582037\pi$
$691$	−13.4002			−0.509766			−0.254883	+	0.966972i	$0.582037\pi$
$692$	1.34507	+	0.259453i	0.0511318	+	0.00986293i
$693$			16.8165i			0.638804i
$694$	−2.27575	+	23.8135i	−0.0863861	+	0.903948i
$695$			3.70575i			0.140567i
$696$	−13.9162	−	4.08962i	−0.527491	−	0.155017i
$697$			20.7448i			0.785767i
$698$	39.9485	+	3.81770i	1.51207	+	0.144502i
$699$			23.5694i			0.891476i
$700$	3.35627	−	17.3997i	0.126855	−	0.657647i
$701$			33.0858i			1.24963i	0.780772	+	0.624816i	$0.214826\pi$
$701$			33.0858i			1.24963i	−0.780772	+	0.624816i	$0.785174\pi$
$702$	−2.11379	−	0.202006i	−0.0797800	−	0.00762421i
$703$	−39.4959	−	21.3454i	−1.48962	−	0.805057i
$704$	−23.5101	−	15.1242i	−0.886070	−	0.570016i
$705$			1.77612i			0.0668926i
$706$	0.328213	−	3.43443i	0.0123525	−	0.129257i
$707$	−0.489633			−0.0184145
$708$	−17.9702	−	3.46631i	−0.675360	−	0.130272i
$709$		−	19.4606i		−	0.730858i	−0.930839	−	0.365429i	$-0.880922\pi$
$709$		−	19.4606i		−	0.730858i	0.930839	−	0.365429i	$-0.119078\pi$
$710$	35.8928	+	3.43011i	1.34703	+	0.128730i
$711$	5.21007			0.195393
$712$	−38.2476	−	11.2400i	−1.43339	−	0.421237i
$713$		−	3.90746i		−	0.146335i
$714$	3.43807	−	35.9761i	0.128667	−	1.34637i
$715$			13.7230i			0.513212i
$716$	−7.10118	+	36.8142i	−0.265384	+	1.37581i
$717$	−13.3670			−0.499200
$718$	−34.6422	−	3.31059i	−1.29283	−	0.123550i
$719$			32.5024i			1.21213i	0.795414	+	0.606067i	$0.207254\pi$
$719$			32.5024i			1.21213i	−0.795414	+	0.606067i	$0.792746\pi$
$720$	3.89137	−	9.71158i	0.145023	−	0.361929i
$721$		−	93.3319i		−	3.47586i
$722$	23.7767	−	12.5167i	0.884878	−	0.465823i
$723$	19.9602			0.742326
$724$	23.2434	+	4.48348i	0.863834	+	0.166627i
$725$	−9.44144			−0.350646
$726$	1.70405	+	0.162848i	0.0632432	+	0.00604386i
$727$			11.3190i			0.419800i	0.977723	+	0.209900i	$0.0673139\pi$
$727$			11.3190i			0.419800i	−0.977723	+	0.209900i	$0.932686\pi$
$728$	19.6087	+	5.76250i	0.726746	+	0.213572i
$729$	−1.00000			−0.0370370
$730$	−26.3675	−	2.51982i	−0.975903	−	0.0932626i
$731$	1.81687			0.0671993
$732$	−5.21337	−	1.00562i	−0.192692	−	0.0371688i
$733$			14.7845i			0.546079i	0.962003	+	0.273040i	$0.0880290\pi$
$733$			14.7845i			0.546079i	−0.962003	+	0.273040i	$0.911971\pi$
$734$	−26.7053	−	2.55210i	−0.985710	−	0.0941998i
$735$	42.2672			1.55905
$736$	−11.3823	−	5.87351i	−0.419559	−	0.216500i
$737$			25.7652i			0.949072i
$738$	−5.49980	−	0.525590i	−0.202450	−	0.0193472i
$739$	33.9300			1.24813			0.624067	−	0.781371i	$-0.285479\pi$
$739$	33.9300			1.24813			0.624067	+	0.781371i	$0.285479\pi$
$740$	−10.2046	+	52.9030i	−0.375128	+	1.94475i
$741$	−3.11175	+	5.75776i	−0.114313	+	0.211517i
$742$	68.2299	+	6.52042i	2.50480	+	0.239372i
$743$	−14.5846			−0.535056			−0.267528	−	0.963550i	$-0.586207\pi$
$743$	−14.5846			−0.535056			−0.267528	+	0.963550i	$0.586207\pi$
$744$	−4.68307	−	1.37624i	−0.171690	−	0.0504553i
$745$	−34.7306			−1.27243
$746$	−2.74766	+	28.7516i	−0.100599	+	1.05267i
$747$	4.80051			0.175642
$748$	−36.4390	−	7.02882i	−1.33234	−	0.256999i
$749$	9.80913			0.358418
$750$	−1.11158	+	11.6316i	−0.0405892	+	0.424727i
$751$	−13.8729			−0.506229			−0.253114	−	0.967436i	$-0.581455\pi$
$751$	−13.8729			−0.506229			−0.253114	+	0.967436i	$0.581455\pi$
$752$	1.01030	−	2.52137i	0.0368418	−	0.0919449i
$753$		−	29.8620i		−	1.08823i
$754$	1.03592	−	10.8399i	0.0377259	−	0.394766i
$755$		−	42.5754i		−	1.54948i
$756$	9.45075	+	1.82298i	0.343720	+	0.0663011i
$757$		−	13.4956i		−	0.490506i	−0.969459	−	0.245253i	$-0.921129\pi$
$757$		−	13.4956i		−	0.490506i	0.969459	−	0.245253i	$-0.0788710\pi$
$758$	36.6664	+	3.50404i	1.33178	+	0.127272i
$759$	7.91200			0.287188
$760$	−22.8949	−	22.7083i	−0.830487	−	0.823718i
$761$	19.7088			0.714442			0.357221	−	0.934020i	$-0.383724\pi$
$761$	19.7088			0.714442			0.357221	+	0.934020i	$0.383724\pi$
$762$	−17.5922	−	1.68120i	−0.637297	−	0.0609035i
$763$		−	86.7799i		−	3.14164i
$764$	6.61430	−	34.2901i	0.239297	−	1.24057i
$765$		−	13.8889i		−	0.502153i
$766$	−3.11184	+	32.5624i	−0.112435	+	1.17653i
$767$		−	13.7397i		−	0.496111i
$768$	−11.0483	+	11.5730i	−0.398672	+	0.417605i
$769$	18.8060			0.678163			0.339081	−	0.940757i	$-0.389884\pi$
$769$	18.8060			0.678163			0.339081	+	0.940757i	$0.389884\pi$
$770$	5.91751	−	61.9210i	0.213252	−	2.23148i
$771$	−0.677951			−0.0244158
$772$	−4.19499	+	21.7478i	−0.150981	+	0.782720i
$773$	0.638576			0.0229680			0.0114840	−	0.999934i	$-0.496344\pi$
$773$	0.638576			0.0229680			0.0114840	+	0.999934i	$0.496344\pi$
$774$	−0.0460321	+	0.481681i	−0.00165459	+	0.0173137i
$775$	−3.17723			−0.114130
$776$	35.9762	+	10.5725i	1.29147	+	0.379531i
$777$	−49.5666			−1.77819
$778$	24.1889	+	2.31163i	0.867215	+	0.0828758i
$779$	−8.09635	+	14.9809i	−0.290082	+	0.536746i
$780$	7.71226	+	1.48764i	0.276143	+	0.0532659i
$781$	34.0619			1.21883
$782$	−16.9265	−	1.61758i	−0.605289	−	0.0578447i
$783$		−	5.12817i		−	0.183266i
$784$	−60.0022	−	24.0425i	−2.14294	−	0.858661i
$785$	−48.0719			−1.71576
$786$	17.7128	+	1.69273i	0.631793	+	0.0603776i
$787$		−	5.69613i		−	0.203045i	−0.994833	−	0.101522i	$-0.967629\pi$
$787$		−	5.69613i		−	0.203045i	0.994833	−	0.101522i	$-0.0323714\pi$
$788$	7.66824	−	39.7540i	0.273170	−	1.41618i
$789$	3.00903			0.107124
$790$	−19.1843	−	1.83336i	−0.682548	−	0.0652280i
$791$	−26.6766			−0.948511
$792$	2.78667	−	9.48251i	0.0990201	−	0.336946i
$793$		−	3.98605i		−	0.141549i
$794$	39.9401	+	3.81689i	1.41742	+	0.135456i
$795$	26.3407			0.934210
$796$	−4.62020	+	23.9522i	−0.163759	+	0.848964i
$797$	−0.349816			−0.0123911			−0.00619557	−	0.999981i	$-0.501972\pi$
$797$	−0.349816			−0.0123911			−0.00619557	+	0.999981i	$0.501972\pi$
$798$	16.5237	−	24.6383i	0.584931	−	0.872187i
$799$		−	3.60590i		−	0.127568i
$800$	−4.77587	+	9.25522i	−0.168852	+	0.327221i
$801$		−	14.0944i		−	0.498001i
$802$	−8.84114	−	0.844907i	−0.312191	−	0.0298347i
$803$	−25.0225			−0.883024
$804$	14.4799	+	2.79306i	0.510666	+	0.0985036i
$805$		−	28.5005i		−	1.00451i
$806$	0.348607	−	3.64784i	0.0122792	−	0.128490i
$807$			7.04041i			0.247834i
$808$	0.276096	+	0.0811376i	0.00971301	+	0.00285441i
$809$	11.1848			0.393236			0.196618	−	0.980480i	$-0.437004\pi$
$809$	11.1848			0.393236			0.196618	+	0.980480i	$0.437004\pi$
$810$	3.68217	+	0.351888i	0.129378	+	0.0123641i
$811$		−	11.3206i		−	0.397520i	−0.980048	−	0.198760i	$-0.936309\pi$
$811$		−	11.3206i		−	0.397520i	0.980048	−	0.198760i	$-0.0636914\pi$
$812$	−9.34854	+	48.4650i	−0.328069	+	1.70079i
$813$	22.8229			0.800433
$814$	−4.84203	+	50.6672i	−0.169713	+	1.77588i
$815$		−	32.2794i		−	1.13070i
$816$	−7.90031	+	19.7166i	−0.276566	+	0.690218i
$817$	1.31205	+	0.709092i	0.0459029	+	0.0248080i
$818$	3.87480	+	0.370297i	0.135479	+	0.0129471i
$819$			7.22588i			0.252493i
$820$	20.0662	+	3.87062i	0.700743	+	0.135168i
$821$			16.9782i			0.592542i	0.955104	+	0.296271i	$0.0957432\pi$
$821$			16.9782i			0.592542i	−0.955104	+	0.296271i	$0.904257\pi$
$822$	−1.85960	−	0.177714i	−0.0648611	−	0.00619848i
$823$		−	5.17146i		−	0.180266i	−0.995930	−	0.0901329i	$-0.971271\pi$
$823$		−	5.17146i		−	0.180266i	0.995930	−	0.0901329i	$-0.0287292\pi$
$824$	−15.4661	+	52.6282i	−0.538788	+	1.83339i
$825$		−	6.43341i		−	0.223983i
$826$	−5.92468	+	61.9961i	−0.206146	+	2.15712i
$827$			0.733529i			0.0255073i	0.999919	+	0.0127536i	$0.00405972\pi$
$827$			0.733529i			0.0255073i	−0.999919	+	0.0127536i	$0.995940\pi$
$828$	0.857696	−	4.44650i	0.0298070	−	0.154526i
$829$	18.3783			0.638304			0.319152	−	0.947703i	$-0.396602\pi$
$829$	18.3783			0.638304			0.319152	+	0.947703i	$0.396602\pi$
$830$	−17.6763	−	1.68924i	−0.613553	−	0.0586345i
$831$	20.9985			0.728431
$832$	−10.1021	−	6.49875i	−0.350226	−	0.225304i
$833$	−85.8113			−2.97319
$834$	1.99459	+	0.190614i	0.0690671	+	0.00660043i
$835$		−	54.2942i		−	1.87893i
$836$	−23.5712	−	19.2974i	−0.815228	−	0.667414i
$837$		−	1.72573i		−	0.0596500i
$838$	−4.48785	+	46.9610i	−0.155030	+	1.62224i
$839$	37.9165			1.30902			0.654511	−	0.756052i	$-0.272875\pi$
$839$	37.9165			1.30902			0.654511	+	0.756052i	$0.272875\pi$
$840$	−34.1577	−	10.0381i	−1.17855	−	0.346348i
$841$	−2.70187			−0.0931678
$842$	0.124989	−	1.30789i	0.00430739	−	0.0450727i
$843$	−5.03139			−0.173290
$844$	4.25412	−	22.0543i	0.146433	−	0.759142i
$845$		−	28.1055i		−	0.966858i
$846$	0.955984	+	0.0913590i	0.0328674	+	0.00314099i
$847$		−	5.82519i		−	0.200156i
$848$	−37.3932	−	14.9832i	−1.28409	−	0.514525i
$849$		−	1.25113i		−	0.0429386i
$850$	−1.31529	+	13.7632i	−0.0451141	+	0.472075i
$851$			23.3207i			0.799423i
$852$	3.69246	−	19.1426i	0.126502	−	0.655814i
$853$			46.5801i			1.59487i	0.603404	+	0.797436i	$0.293811\pi$
$853$			46.5801i			1.59487i	−0.603404	+	0.797436i	$0.706189\pi$
$854$	−1.71883	+	17.9858i	−0.0588170	+	0.615463i
$855$	5.42059	−	10.0299i	0.185380	−	0.343014i
$856$	−5.53120	−	1.62548i	−0.189053	−	0.0555578i
$857$		−	25.6585i		−	0.876477i	−0.898859	−	0.438238i	$-0.855603\pi$
$857$		−	25.6585i		−	0.876477i	0.898859	−	0.438238i	$-0.144397\pi$
$858$	7.38632	+	0.705877i	0.252165	+	0.0240982i
$859$	−15.5918			−0.531986			−0.265993	−	0.963975i	$-0.585700\pi$
$859$	−15.5918			−0.531986			−0.265993	+	0.963975i	$0.585700\pi$
$860$	0.338996	−	1.75743i	0.0115597	−	0.0599280i
$861$			18.8007i			0.640727i
$862$	4.64087	−	48.5622i	0.158069	−	1.65404i
$863$	−31.1083			−1.05894			−0.529470	−	0.848329i	$-0.677609\pi$
$863$	−31.1083			−1.05894			−0.529470	+	0.848329i	$0.677609\pi$
$864$	−5.02702	−	2.59404i	−0.171023	−	0.0882510i
$865$		−	1.79147i		−	0.0609118i
$866$	−35.0620	−	3.35072i	−1.19146	−	0.113862i
$867$			11.1974i			0.380282i
$868$	−3.14597	+	16.3094i	−0.106781	+	0.553579i
$869$	−18.2058			−0.617588
$870$	−1.80454	+	18.8828i	−0.0611797	+	0.640186i
$871$			11.0711i			0.375128i
$872$	−14.3804	+	48.9337i	−0.486981	+	1.65710i
$873$			13.2574i			0.448695i
$874$	−11.5921	−	7.77424i	−0.392110	−	0.262968i
$875$	39.7620			1.34420
$876$	−2.71255	+	14.0625i	−0.0916484	+	0.475127i
$877$	−0.487909			−0.0164755			−0.00823776	−	0.999966i	$-0.502622\pi$
$877$	−0.487909			−0.0164755			−0.00823776	+	0.999966i	$0.502622\pi$
$878$	−2.75962	+	28.8768i	−0.0931327	+	0.974544i
$879$			18.5789i			0.626651i
$880$	−13.5978	+	33.9356i	−0.458381	+	1.14397i
$881$	−13.5269			−0.455732			−0.227866	−	0.973693i	$-0.573175\pi$
$881$	−13.5269			−0.455732			−0.227866	+	0.973693i	$0.573175\pi$
$882$	2.17411	−	22.7500i	0.0732062	−	0.766032i
$883$	34.7988			1.17107			0.585537	−	0.810646i	$-0.300884\pi$
$883$	34.7988			1.17107			0.585537	+	0.810646i	$0.300884\pi$
$884$	−15.6575	−	3.02022i	−0.526619	−	0.101581i
$885$			23.9341i			0.804537i
$886$	3.49592	−	36.5815i	0.117448	−	1.22898i
$887$	18.9849			0.637449			0.318725	−	0.947847i	$-0.396745\pi$
$887$	18.9849			0.637449			0.318725	+	0.947847i	$0.396745\pi$
$888$	27.9498	+	8.21374i	0.937932	+	0.275635i
$889$			60.1377i			2.01696i
$890$	−4.95965	+	51.8979i	−0.166248	+	1.73962i
$891$	3.49434			0.117065
$892$	11.5195	+	2.22202i	0.385701	+	0.0743989i
$893$	1.40732	−	2.60400i	0.0470942	−	0.0871397i
$894$	−1.78645	+	18.6935i	−0.0597479	+	0.625204i
$895$	49.0321			1.63896
$896$	42.7802	+	33.6798i	1.42919	+	1.12516i
$897$	3.39972			0.113513
$898$	51.3574	+	4.90799i	1.71382	+	0.163782i
$899$	8.84984			0.295159
$900$	−3.61554	−	0.697410i	−0.120518	−	0.0232470i
$901$	−53.4773			−1.78159
$902$	19.2182	+	1.83659i	0.639895	+	0.0611518i
$903$	1.64660			0.0547954
$904$	15.0425	+	4.42061i	0.500305	+	0.147027i
$905$		−	30.9574i		−	1.02906i
$906$	−22.9159	−	2.18997i	−0.761329	−	0.0727567i
$907$			20.6905i			0.687016i	0.939150	+	0.343508i	$0.111615\pi$
$907$			20.6905i			0.687016i	−0.939150	+	0.343508i	$0.888385\pi$
$908$	−5.22308	+	27.0777i	−0.173334	+	0.898603i
$909$			0.101742i			0.00337458i
$910$	2.54270	−	26.6069i	0.0842896	−	0.882010i
$911$	−29.8333			−0.988420			−0.494210	−	0.869342i	$-0.664543\pi$
$911$	−29.8333			−0.988420			−0.494210	+	0.869342i	$0.664543\pi$
$912$	−13.4002	+	11.1550i	−0.443726	+	0.369378i
$913$	−16.7746			−0.555160
$914$	3.13161	−	32.7693i	0.103584	−	1.08391i
$915$			6.94359i			0.229548i
$916$	−2.93920	+	15.2375i	−0.0971138	+	0.503461i
$917$		−	60.5500i		−	1.99954i
$918$	−7.47558	−	0.714407i	−0.246731	−	0.0235790i
$919$			35.6710i			1.17668i	0.808615	+	0.588338i	$0.200218\pi$
$919$			35.6710i			1.17668i	−0.808615	+	0.588338i	$0.799782\pi$
$920$	−4.72285	+	16.0709i	−0.155708	+	0.529843i
$921$	10.7076			0.352827
$922$	20.1098	+	1.92180i	0.662280	+	0.0632911i
$923$	14.6361			0.481753
$924$	−33.0241	−	6.37011i	−1.08641	−	0.209561i
$925$	18.9625			0.623484
$926$	−22.0005	−	2.10249i	−0.722981	−	0.0690920i
$927$	−19.3937			−0.636973
$928$	13.3027	−	25.7794i	0.436682	−	0.846251i
$929$	−5.05272			−0.165774			−0.0828872	−	0.996559i	$-0.526414\pi$
$929$	−5.05272			−0.165774			−0.0828872	+	0.996559i	$0.526414\pi$
$930$	−0.607264	+	6.35443i	−0.0199130	+	0.208370i
$931$	−61.9687	−	33.4907i	−2.03094	−	1.09761i
$932$	−46.2856	−	8.92814i	−1.51613	−	0.292451i
$933$	−13.2171			−0.432708
$934$	−1.16626	+	12.2038i	−0.0381612	+	0.399320i
$935$			48.5325i			1.58718i
$936$	1.19741	−	4.07455i	0.0391385	−	0.133181i
$937$	5.91078			0.193097			0.0965484	−	0.995328i	$-0.469220\pi$
$937$	5.91078			0.193097			0.0965484	+	0.995328i	$0.469220\pi$
$938$	4.77395	−	49.9548i	0.155875	−	1.63108i
$939$		−	32.4175i		−	1.05791i
$940$	−3.48794	−	0.672798i	−0.113764	−	0.0219443i
$941$	−19.2287			−0.626837			−0.313418	−	0.949615i	$-0.601474\pi$
$941$	−19.2287			−0.626837			−0.313418	+	0.949615i	$0.601474\pi$
$942$	−2.47269	+	25.8743i	−0.0805647	+	0.843032i
$943$	8.84559			0.288052
$944$	13.6143	−	33.9767i	0.443107	−	1.10585i
$945$		−	12.5873i		−	0.409464i
$946$	0.160852	−	1.68316i	0.00522975	−	0.0547243i
$947$	26.5034			0.861245			0.430623	−	0.902532i	$-0.358294\pi$
$947$	26.5034			0.861245			0.430623	+	0.902532i	$0.358294\pi$
$948$	−1.97358	+	10.2315i	−0.0640990	+	0.332305i
$949$	−10.7519			−0.349022
$950$	−6.32140	+	9.42580i	−0.205093	+	0.305813i
$951$		−	14.4866i		−	0.469761i
$952$	69.3475	+	20.3795i	2.24757	+	0.660504i
$953$		−	37.0464i		−	1.20005i	−0.799981	−	0.600025i	$-0.795157\pi$
$953$		−	37.0464i		−	1.20005i	0.799981	−	0.600025i	$-0.204843\pi$
$954$	1.35490	−	14.1777i	0.0438665	−	0.459020i
$955$	−45.6703			−1.47786
$956$	5.06345	−	26.2501i	0.163764	−	0.848990i
$957$			17.9196i			0.579258i
$958$	−4.80409	−	0.459105i	−0.155213	−	0.0148330i
$959$			6.35694i			0.205276i
$960$	17.5975	+	11.3206i	0.567958	+	0.365372i
$961$	−28.0219			−0.903931
$962$	−2.08058	+	21.7712i	−0.0670805	+	0.701932i
$963$		−	2.03827i		−	0.0656823i
$964$	−7.56095	+	39.1978i	−0.243522	+	1.26247i
$965$	28.9655			0.932432
$966$	−15.3402	−	1.46599i	−0.493562	−	0.0471675i
$967$		−	49.4739i		−	1.59097i	−0.605970	−	0.795487i	$-0.707215\pi$
$967$		−	49.4739i		−	1.59097i	0.605970	−	0.795487i	$-0.292785\pi$
$968$	−0.965299	+	3.28472i	−0.0310259	+	0.105575i
$969$	−11.0049	+	20.3627i	−0.353530	+	0.654145i
$970$	4.66512	−	48.8159i	0.149788	−	1.56739i
$971$			13.1840i			0.423095i	0.977368	+	0.211548i	$0.0678503\pi$
$971$			13.1840i			0.423095i	−0.977368	+	0.211548i	$0.932150\pi$
$972$	0.378802	−	1.96380i	0.0121501	−	0.0629889i
$973$		−	6.81840i		−	0.218588i
$974$	5.62521	−	58.8624i	0.180243	−	1.88607i
$975$		−	2.76438i		−	0.0885309i
$976$	3.94967	−	9.85708i	0.126426	−	0.315517i
$977$		−	28.8518i		−	0.923049i	−0.887127	−	0.461525i	$-0.847303\pi$
$977$		−	28.8518i		−	0.923049i	0.887127	−	0.461525i	$-0.152697\pi$
$978$	−17.3741	−	1.66037i	−0.555564	−	0.0530927i
$979$			49.2506i			1.57406i
$980$	−16.0109	+	83.0042i	−0.511449	+	2.65147i
$981$	−18.0323			−0.575726
$982$	−1.75723	+	18.3877i	−0.0560754	+	0.586775i
$983$	9.02606			0.287887			0.143943	−	0.989586i	$-0.454022\pi$
$983$	9.02606			0.287887			0.143943	+	0.989586i	$0.454022\pi$
$984$	3.11549	−	10.6014i	0.0993181	−	0.337960i
$985$	−52.9476			−1.68705
$986$	3.66360	−	38.3361i	0.116673	−	1.22087i
$987$		−	3.26797i		−	0.104021i
$988$	−10.1283	−	8.29191i	−0.322226	−	0.263801i
$989$		−	0.774712i		−	0.0246344i
$990$	−12.8668	−	1.22962i	−0.408932	−	0.0390798i
$991$	−12.9609			−0.411717			−0.205858	−	0.978582i	$-0.565999\pi$
$991$	−12.9609			−0.411717			−0.205858	+	0.978582i	$0.565999\pi$
$992$	4.47661	−	8.67529i	0.142133	−	0.275441i
$993$	5.22689			0.165870
$994$	−66.0410	−	6.31123i	−2.09469	−	0.200180i
$995$	31.9015			1.01135
$996$	−1.81845	+	9.42725i	−0.0576196	+	0.298714i
$997$			5.01059i			0.158687i	0.996847	+	0.0793435i	$0.0252824\pi$
$997$			5.01059i			0.158687i	−0.996847	+	0.0793435i	$0.974718\pi$
$998$	0.958448	−	10.0292i	0.0303391	−	0.317470i
$999$			10.2996i			0.325865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.e.a.379.21	yes	40
3.2	odd	2		1368.2.e.g.379.20		40
4.3	odd	2		1824.2.e.a.1519.37		40
8.3	odd	2	inner	456.2.e.a.379.19	✓	40
8.5	even	2		1824.2.e.a.1519.7		40
12.11	even	2		5472.2.e.g.5167.33		40
19.18	odd	2	inner	456.2.e.a.379.20	yes	40
24.5	odd	2		5472.2.e.g.5167.4		40
24.11	even	2		1368.2.e.g.379.22		40
57.56	even	2		1368.2.e.g.379.21		40
76.75	even	2		1824.2.e.a.1519.8		40
152.37	odd	2		1824.2.e.a.1519.38		40
152.75	even	2	inner	456.2.e.a.379.22	yes	40
228.227	odd	2		5472.2.e.g.5167.3		40
456.227	odd	2		1368.2.e.g.379.19		40
456.341	even	2		5472.2.e.g.5167.34		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.e.a.379.19	✓	40	8.3	odd	2	inner
456.2.e.a.379.20	yes	40	19.18	odd	2	inner
456.2.e.a.379.21	yes	40	1.1	even	1	trivial
456.2.e.a.379.22	yes	40	152.75	even	2	inner
1368.2.e.g.379.19		40	456.227	odd	2
1368.2.e.g.379.20		40	3.2	odd	2
1368.2.e.g.379.21		40	57.56	even	2
1368.2.e.g.379.22		40	24.11	even	2
1824.2.e.a.1519.7		40	8.5	even	2
1824.2.e.a.1519.8		40	76.75	even	2
1824.2.e.a.1519.37		40	4.3	odd	2
1824.2.e.a.1519.38		40	152.37	odd	2
5472.2.e.g.5167.3		40	228.227	odd	2
5472.2.e.g.5167.4		40	24.5	odd	2
5472.2.e.g.5167.33		40	12.11	even	2
5472.2.e.g.5167.34		40	456.341	even	2

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:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.134537 - 1.40780i) q^{2} +1.00000i q^{3} +(-1.96380 - 0.378802i) q^{4} +2.61555i q^{5} +(1.40780 + 0.134537i) q^{6} -4.81248i q^{7} +(-0.797481 + 2.71367i) q^{8} -1.00000 q^{9} +(3.68217 + 0.351888i) q^{10} +3.49434 q^{11} +(0.378802 - 1.96380i) q^{12} +1.50149 q^{13} +(-6.77501 - 0.647456i) q^{14} -2.61555 q^{15} +(3.71302 + 1.48778i) q^{16} +5.31012 q^{17} +(-0.134537 + 1.40780i) q^{18} +(3.83470 + 2.07245i) q^{19} +(0.990775 - 5.13641i) q^{20} +4.81248 q^{21} +(0.470118 - 4.91934i) q^{22} -2.26423i q^{23} +(-2.71367 - 0.797481i) q^{24} -1.84109 q^{25} +(0.202006 - 2.11379i) q^{26} -1.00000i q^{27} +(-1.82298 + 9.45075i) q^{28} +5.12817 q^{29} +(-0.351888 + 3.68217i) q^{30} +1.72573 q^{31} +(2.59404 - 5.02702i) q^{32} +3.49434i q^{33} +(0.714407 - 7.47558i) q^{34} +12.5873 q^{35} +(1.96380 + 0.378802i) q^{36} -10.2996 q^{37} +(3.43350 - 5.11967i) q^{38} +1.50149i q^{39} +(-7.09774 - 2.08585i) q^{40} +3.90666i q^{41} +(0.647456 - 6.77501i) q^{42} +0.342152 q^{43} +(-6.86219 - 1.32366i) q^{44} -2.61555i q^{45} +(-3.18759 - 0.304623i) q^{46} -0.679062i q^{47} +(-1.48778 + 3.71302i) q^{48} -16.1600 q^{49} +(-0.247695 + 2.59189i) q^{50} +5.31012i q^{51} +(-2.94862 - 0.568767i) q^{52} -10.0708 q^{53} +(-1.40780 - 0.134537i) q^{54} +9.13962i q^{55} +(13.0595 + 3.83786i) q^{56} +(-2.07245 + 3.83470i) q^{57} +(0.689928 - 7.21944i) q^{58} -9.15071i q^{59} +(5.13641 + 0.990775i) q^{60} -2.65473i q^{61} +(0.232175 - 2.42948i) q^{62} +4.81248i q^{63} +(-6.72805 - 4.32821i) q^{64} +3.92721i q^{65} +(4.91934 + 0.470118i) q^{66} +7.37340i q^{67} +(-10.4280 - 2.01148i) q^{68} +2.26423 q^{69} +(1.69345 - 17.7204i) q^{70} +9.74773 q^{71} +(0.797481 - 2.71367i) q^{72} -7.16085 q^{73} +(-1.38568 + 14.4998i) q^{74} -1.84109i q^{75} +(-6.74554 - 5.52247i) q^{76} -16.8165i q^{77} +(2.11379 + 0.202006i) q^{78} -5.21007 q^{79} +(-3.89137 + 9.71158i) q^{80} +1.00000 q^{81} +(5.49980 + 0.525590i) q^{82} -4.80051 q^{83} +(-9.45075 - 1.82298i) q^{84} +13.8889i q^{85} +(0.0460321 - 0.481681i) q^{86} +5.12817i q^{87} +(-2.78667 + 9.48251i) q^{88} +14.0944i q^{89} +(-3.68217 - 0.351888i) q^{90} -7.22588i q^{91} +(-0.857696 + 4.44650i) q^{92} +1.72573i q^{93} +(-0.955984 - 0.0913590i) q^{94} +(-5.42059 + 10.0299i) q^{95} +(5.02702 + 2.59404i) q^{96} -13.2574i q^{97} +(-2.17411 + 22.7500i) q^{98} -3.49434 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{4} + 4 q^{6} - 40 q^{9} + 4 q^{16} + 8 q^{19} + 32 q^{20} - 4 q^{24} - 40 q^{25} + 40 q^{26} - 8 q^{28} - 48 q^{35} + 4 q^{36} - 8 q^{44} - 56 q^{49} - 4 q^{54} - 8 q^{57} + 16 q^{58} + 40 q^{62}+ \cdots + 44 q^{96}+O(q^{100}) \) 40 * q - 4 * q^4 + 4 * q^6 - 40 * q^9 + 4 * q^16 + 8 * q^19 + 32 * q^20 - 4 * q^24 - 40 * q^25 + 40 * q^26 - 8 * q^28 - 48 * q^35 + 4 * q^36 - 8 * q^44 - 56 * q^49 - 4 * q^54 - 8 * q^57 + 16 * q^58 + 40 * q^62 + 68 * q^64 + 8 * q^66 - 88 * q^68 - 16 * q^73 - 40 * q^74 - 12 * q^76 - 32 * q^80 + 40 * q^81 - 64 * q^82 + 80 * q^83 - 48 * q^92 + 44 * q^96

Introduction

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