LMFDB - Embedded newform 900.2.bj.f.127.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(127,900)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("900.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.bj (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			127.16
Character	$\chi$	$=$	900.127
Dual form			900.2.bj.f.163.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0475977 + 1.41341i) q^{2} +(-1.99547 + 0.134550i) q^{4} +(-2.23568 + 0.0415918i) q^{5} +(1.15642 - 1.15642i) q^{7} +(-0.285155 - 2.81402i) q^{8} +O(q^{10})$	\(q+(0.0475977 + 1.41341i) q^{2} +(-1.99547 + 0.134550i) q^{4} +(-2.23568 + 0.0415918i) q^{5} +(1.15642 - 1.15642i) q^{7} +(-0.285155 - 2.81402i) q^{8} +(-0.165200 - 3.15796i) q^{10} +(0.574557 + 0.790810i) q^{11} +(3.66677 - 0.580759i) q^{13} +(1.68954 + 1.57946i) q^{14} +(3.96379 - 0.536982i) q^{16} +(-1.54304 + 3.02838i) q^{17} +(-1.54393 - 4.75171i) q^{19} +(4.45564 - 0.383807i) q^{20} +(-1.09039 + 0.849726i) q^{22} +(1.65652 + 0.262367i) q^{23} +(4.99654 - 0.185972i) q^{25} +(0.995382 + 5.15501i) q^{26} +(-2.15201 + 2.46320i) q^{28} +(6.16400 + 2.00281i) q^{29} +(3.69657 - 1.20109i) q^{31} +(0.947644 + 5.57691i) q^{32} +(-4.35379 - 2.03680i) q^{34} +(-2.53729 + 2.63349i) q^{35} +(1.23176 + 7.77702i) q^{37} +(6.64264 - 2.40837i) q^{38} +(0.754555 + 6.27938i) q^{40} +(2.58309 + 1.87673i) q^{41} +(6.18535 + 6.18535i) q^{43} +(-1.25291 - 1.50073i) q^{44} +(-0.291986 + 2.35384i) q^{46} +(-4.67720 - 9.17952i) q^{47} +4.32538i q^{49} +(0.500679 + 7.05332i) q^{50} +(-7.23878 + 1.65225i) q^{52} +(0.989011 + 1.94104i) q^{53} +(-1.31742 - 1.74410i) q^{55} +(-3.58395 - 2.92443i) q^{56} +(-2.53740 + 8.80760i) q^{58} +(2.96719 + 2.15579i) q^{59} +(-3.48146 + 2.52943i) q^{61} +(1.87358 + 5.16761i) q^{62} +(-7.83737 + 1.60486i) q^{64} +(-8.17357 + 1.45090i) q^{65} +(6.00029 + 3.05730i) q^{67} +(2.67161 - 6.25065i) q^{68} +(-3.84297 - 3.46089i) q^{70} +(2.89032 + 0.939123i) q^{71} +(2.20940 - 13.9496i) q^{73} +(-10.9335 + 2.11115i) q^{74} +(3.72020 + 9.27416i) q^{76} +(1.57894 + 0.250079i) q^{77} +(0.430746 - 1.32570i) q^{79} +(-8.83944 + 1.36538i) q^{80} +(-2.52964 + 3.74030i) q^{82} +(7.43080 - 14.5838i) q^{83} +(3.32378 - 6.83466i) q^{85} +(-8.44804 + 9.03686i) q^{86} +(2.06151 - 1.84231i) q^{88} +(-1.66905 - 2.29725i) q^{89} +(3.56873 - 4.91193i) q^{91} +(-3.34084 - 0.300660i) q^{92} +(12.7518 - 7.04774i) q^{94} +(3.64936 + 10.5591i) q^{95} +(-12.3696 + 6.30263i) q^{97} +(-6.11354 + 0.205878i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 12 q^{8}+O(q^{10}) $ 240 * q - 12 * q^8	$ 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58} + 44 q^{62} - 60 q^{64} + 20 q^{65} - 16 q^{68} - 44 q^{70} - 44 q^{73} + 48 q^{77} + 4 q^{80} + 24 q^{82} - 64 q^{85} + 60 q^{88} + 260 q^{89} - 144 q^{92} + 40 q^{94} - 180 q^{97} - 256 q^{98}+O(q^{100}) $ 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{20}\right)$

Coefficient data

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

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

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

$2$	0.0475977	+	1.41341i	0.0336566	+	0.999433i
$2$	0.0475977	+	1.41341i	0.0336566	+	0.999433i
$3$		0			0
$3$		0			0
$4$	−1.99547	+	0.134550i	−0.997734	+	0.0672751i
$5$	−2.23568	+	0.0415918i	−0.999827	+	0.0186004i
$5$	−2.23568	+	0.0415918i	−0.999827	+	0.0186004i
$6$		0			0
$7$	1.15642	−	1.15642i	0.437086	−	0.437086i	−0.453944	−	0.891030i	$-0.649983\pi$
$7$	1.15642	−	1.15642i	0.437086	−	0.437086i	0.891030	+	0.453944i	$0.149983\pi$
$8$	−0.285155	−	2.81402i	−0.100817	−	0.994905i
$9$		0			0
$10$	−0.165200	−	3.15796i	−0.0522407	−	0.998635i
$11$	0.574557	+	0.790810i	0.173235	+	0.238438i	0.886802	−	0.462149i	$-0.152922\pi$
$11$	0.574557	+	0.790810i	0.173235	+	0.238438i	−0.713567	+	0.700587i	$0.752922\pi$
$12$		0			0
$13$	3.66677	−	0.580759i	1.01698	−	0.161074i	0.374379	−	0.927276i	$-0.377856\pi$
$13$	3.66677	−	0.580759i	1.01698	−	0.161074i	0.642600	+	0.766202i	$0.277856\pi$
$14$	1.68954	+	1.57946i	0.451549	+	0.422128i
$15$		0			0
$16$	3.96379	−	0.536982i	0.990948	−	0.134245i
$17$	−1.54304	+	3.02838i	−0.374241	+	0.734489i	−0.998923	−	0.0463896i	$-0.985228\pi$
$17$	−1.54304	+	3.02838i	−0.374241	+	0.734489i	0.624682	+	0.780879i	$0.285228\pi$
$18$		0			0
$19$	−1.54393	−	4.75171i	−0.354201	−	1.09012i	−0.956471	−	0.291826i	$-0.905737\pi$
$19$	−1.54393	−	4.75171i	−0.354201	−	1.09012i	0.602271	−	0.798292i	$-0.294263\pi$
$20$	4.45564	−	0.383807i	0.996311	−	0.0858218i
$21$		0			0
$22$	−1.09039	+	0.849726i	−0.232472	+	0.181162i
$23$	1.65652	+	0.262367i	0.345409	+	0.0547073i	0.326729	−	0.945118i	$-0.394054\pi$
$23$	1.65652	+	0.262367i	0.345409	+	0.0547073i	0.0186799	+	0.999826i	$0.494054\pi$
$24$		0			0
$25$	4.99654	−	0.185972i	0.999308	−	0.0371944i
$26$	0.995382	+	5.15501i	0.195210	+	1.01098i
$27$		0			0
$28$	−2.15201	+	2.46320i	−0.406691	+	0.465501i
$29$	6.16400	+	2.00281i	1.14463	+	0.371912i	0.819117	−	0.573627i	$-0.194464\pi$
$29$	6.16400	+	2.00281i	1.14463	+	0.371912i	0.325510	+	0.945539i	$0.394464\pi$
$30$		0			0
$31$	3.69657	−	1.20109i	0.663924	−	0.215722i	0.0423804	−	0.999102i	$-0.486506\pi$
$31$	3.69657	−	1.20109i	0.663924	−	0.215722i	0.621544	+	0.783380i	$0.286506\pi$
$32$	0.947644	+	5.57691i	0.167521	+	0.985868i
$33$		0			0
$34$	−4.35379	−	2.03680i	−0.746669	−	0.349309i
$35$	−2.53729	+	2.63349i	−0.428881	+	0.445141i
$36$		0			0
$37$	1.23176	+	7.77702i	0.202500	+	1.27853i	0.854155	+	0.520019i	$0.174075\pi$
$37$	1.23176	+	7.77702i	0.202500	+	1.27853i	−0.651655	+	0.758516i	$0.725925\pi$
$38$	6.64264	−	2.40837i	1.07758	−	0.390690i
$39$		0			0
$40$	0.754555	+	6.27938i	0.119306	+	0.992858i
$41$	2.58309	+	1.87673i	0.403411	+	0.293095i	0.770929	−	0.636921i	$-0.219792\pi$
$41$	2.58309	+	1.87673i	0.403411	+	0.293095i	−0.367518	+	0.930016i	$0.619792\pi$
$42$		0			0
$43$	6.18535	+	6.18535i	0.943257	+	0.943257i	0.998474	−	0.0552173i	$-0.0175852\pi$
$43$	6.18535	+	6.18535i	0.943257	+	0.943257i	−0.0552173	+	0.998474i	$0.517585\pi$
$44$	−1.25291	−	1.50073i	−0.188884	−	0.226243i
$45$		0			0
$46$	−0.291986	+	2.35384i	−0.0430511	+	0.347054i
$47$	−4.67720	−	9.17952i	−0.682240	−	1.33897i	−0.929067	−	0.369911i	$-0.879388\pi$
$47$	−4.67720	−	9.17952i	−0.682240	−	1.33897i	0.246827	−	0.969059i	$-0.420612\pi$
$48$		0			0
$49$			4.32538i			0.617911i
$50$	0.500679	+	7.05332i	0.0708067	+	0.997490i
$51$		0			0
$52$	−7.23878	+	1.65225i	−1.00384	+	0.229126i
$53$	0.989011	+	1.94104i	0.135851	+	0.266623i	0.948903	−	0.315569i	$-0.102195\pi$
$53$	0.989011	+	1.94104i	0.135851	+	0.266623i	−0.813052	+	0.582192i	$0.802195\pi$
$54$		0			0
$55$	−1.31742	−	1.74410i	−0.177640	−	0.235175i
$56$	−3.58395	−	2.92443i	−0.478925	−	0.390793i
$57$		0			0
$58$	−2.53740	+	8.80760i	−0.333177	+	1.15649i
$59$	2.96719	+	2.15579i	0.386295	+	0.280659i	0.763935	−	0.645293i	$-0.223265\pi$
$59$	2.96719	+	2.15579i	0.386295	+	0.280659i	−0.377641	+	0.925952i	$0.623265\pi$
$60$		0			0
$61$	−3.48146	+	2.52943i	−0.445755	+	0.323860i	−0.787918	−	0.615781i	$-0.788841\pi$
$61$	−3.48146	+	2.52943i	−0.445755	+	0.323860i	0.342162	+	0.939641i	$0.388841\pi$
$62$	1.87358	+	5.16761i	0.237945	+	0.656287i
$63$		0			0
$64$	−7.83737	+	1.60486i	−0.979672	+	0.200607i
$65$	−8.17357	+	1.45090i	−1.01381	+	0.179962i
$66$		0			0
$67$	6.00029	+	3.05730i	0.733052	+	0.373509i	0.780326	−	0.625373i	$-0.215053\pi$
$67$	6.00029	+	3.05730i	0.733052	+	0.373509i	−0.0472734	+	0.998882i	$0.515053\pi$
$68$	2.67161	−	6.25065i	0.323980	−	0.758002i
$69$		0			0
$70$	−3.84297	−	3.46089i	−0.459323	−	0.413656i
$71$	2.89032	+	0.939123i	0.343018	+	0.111453i	0.475460	−	0.879737i	$-0.342282\pi$
$71$	2.89032	+	0.939123i	0.343018	+	0.111453i	−0.132442	+	0.991191i	$0.542282\pi$
$72$		0			0
$73$	2.20940	−	13.9496i	0.258590	−	1.63268i	−0.426691	−	0.904397i	$-0.640321\pi$
$73$	2.20940	−	13.9496i	0.258590	−	1.63268i	0.685282	−	0.728278i	$-0.259679\pi$
$74$	−10.9335	+	2.11115i	−1.27099	+	0.245416i
$75$		0			0
$76$	3.72020	+	9.27416i	0.426736	+	1.06382i
$77$	1.57894	+	0.250079i	0.179937	+	0.0284992i
$78$		0			0
$79$	0.430746	−	1.32570i	0.0484628	−	0.149153i	−0.923897	−	0.382642i	$-0.875014\pi$
$79$	0.430746	−	1.32570i	0.0484628	−	0.149153i	0.972359	+	0.233489i	$0.0750143\pi$
$80$	−8.83944	+	1.36538i	−0.988280	+	0.152654i
$81$		0			0
$82$	−2.52964	+	3.74030i	−0.279352	+	0.413047i
$83$	7.43080	−	14.5838i	0.815636	−	1.60078i	0.0163181	−	0.999867i	$-0.494806\pi$
$83$	7.43080	−	14.5838i	0.815636	−	1.60078i	0.799318	−	0.600909i	$-0.205194\pi$
$84$		0			0
$85$	3.32378	−	6.83466i	0.360514	−	0.741323i
$86$	−8.44804	+	9.03686i	−0.910976	+	0.974470i
$87$		0			0
$88$	2.06151	−	1.84231i	0.219758	−	0.196391i
$89$	−1.66905	−	2.29725i	−0.176919	−	0.243508i	0.711343	−	0.702845i	$-0.248087\pi$
$89$	−1.66905	−	2.29725i	−0.176919	−	0.243508i	−0.888262	+	0.459337i	$0.848087\pi$
$90$		0			0
$91$	3.56873	−	4.91193i	0.374104	−	0.514910i
$92$	−3.34084	−	0.300660i	−0.348306	−	0.0313460i
$93$		0			0
$94$	12.7518	−	7.04774i	1.31525	−	0.726918i
$95$	3.64936	+	10.5591i	0.374416	+	1.08334i
$96$		0			0
$97$	−12.3696	+	6.30263i	−1.25594	+	0.639935i	−0.950040	−	0.312128i	$-0.898958\pi$
$97$	−12.3696	+	6.30263i	−1.25594	+	0.639935i	−0.305903	+	0.952063i	$0.598958\pi$
$98$	−6.11354	+	0.205878i	−0.617561	+	0.0207968i
$99$		0			0
$100$	−9.94542	+	1.04339i	−0.994542	+	0.104339i
$101$	12.8704			1.28065			0.640325	−	0.768104i	$-0.278800\pi$
$101$	12.8704			1.28065			0.640325	+	0.768104i	$0.278800\pi$
$102$		0			0
$103$	10.3758	−	5.28675i	1.02236	−	0.520919i	0.139336	−	0.990245i	$-0.455503\pi$
$103$	10.3758	−	5.28675i	1.02236	−	0.520919i	0.883025	+	0.469327i	$0.155503\pi$
$104$	−2.67986	−	10.1527i	−0.262782	−	0.995558i
$105$		0			0
$106$	−2.69642	+	1.49027i	−0.261899	+	0.144748i
$107$	10.7876	−	10.7876i	1.04287	−	1.04287i	0.0438342	−	0.999039i	$-0.486043\pi$
$107$	10.7876	−	10.7876i	1.04287	−	1.04287i	0.999039	−	0.0438342i	$-0.0139573\pi$
$108$		0			0
$109$	−10.1748	+	14.0045i	−0.974573	+	1.34138i	−0.0348708	+	0.999392i	$0.511102\pi$
$109$	−10.1748	+	14.0045i	−0.974573	+	1.34138i	−0.939702	+	0.341993i	$0.888898\pi$
$110$	2.40243	−	1.94507i	0.229063	−	0.185455i
$111$		0			0
$112$	3.96284	−	5.20479i	0.374453	−	0.491807i
$113$	13.6135	−	2.15616i	1.28065	−	0.202835i	0.521218	−	0.853424i	$-0.325478\pi$
$113$	13.6135	−	2.15616i	1.28065	−	0.202835i	0.759430	+	0.650589i	$0.225478\pi$
$114$		0			0
$115$	−3.71437	−	0.517672i	−0.346366	−	0.0482731i
$116$	−12.5695	−	3.16717i	−1.16705	−	0.294064i
$117$		0			0
$118$	−2.90578	+	4.29647i	−0.267499	+	0.395522i
$119$	1.71768	+	5.28648i	0.157460	+	0.484611i
$120$		0			0
$121$	3.10392	−	9.55289i	0.282175	−	0.868445i
$122$	−3.74083	−	4.80034i	−0.338679	−	0.434603i
$123$		0			0
$124$	−7.21479	+	2.89411i	−0.647907	+	0.259899i
$125$	−11.1629	+	0.623590i	−0.998443	+	0.0557756i
$126$		0			0
$127$	2.25651	−	14.2470i	0.200233	−	1.26422i	−0.658807	−	0.752312i	$-0.728939\pi$
$127$	2.25651	−	14.2470i	0.200233	−	1.26422i	0.859040	−	0.511908i	$-0.171061\pi$
$128$	−2.64137	−	11.0011i	−0.233466	−	0.972365i
$129$		0			0
$130$	−2.43976	−	11.4836i	−0.213981	−	1.00718i
$131$	−15.8689	+	5.15611i	−1.38647	+	0.450491i	−0.904791	−	0.425857i	$-0.859973\pi$
$131$	−15.8689	+	5.15611i	−1.38647	+	0.450491i	−0.481679	+	0.876348i	$0.659973\pi$
$132$		0			0
$133$	−7.28041	−	3.70956i	−0.631292	−	0.321659i
$134$	−4.03563	+	8.62641i	−0.348625	+	0.745208i
$135$		0			0
$136$	8.96191	+	3.47857i	0.768477	+	0.298285i
$137$	−2.25985	−	14.2681i	−0.193072	−	1.21901i	−0.873731	−	0.486409i	$-0.838306\pi$
$137$	−2.25985	−	14.2681i	−0.193072	−	1.21901i	0.680659	−	0.732601i	$-0.261694\pi$
$138$		0			0
$139$	−18.6136	+	13.5236i	−1.57879	+	1.14706i	−0.660721	+	0.750632i	$0.729749\pi$
$139$	−18.6136	+	13.5236i	−1.57879	+	1.14706i	−0.918067	+	0.396425i	$0.870251\pi$
$140$	4.70875	−	5.59644i	0.397962	−	0.472985i
$141$		0			0
$142$	−1.18979	+	4.12992i	−0.0998454	+	0.346575i
$143$	2.56604	+	2.56604i	0.214583	+	0.214583i
$144$		0			0
$145$	−13.8640	−	4.22126i	−1.15135	−	0.350557i
$146$	19.8217	+	2.45882i	1.64045	+	0.203494i
$147$		0			0
$148$	−3.50434	−	15.3531i	−0.288055	−	1.26201i
$149$		−	4.23779i		−	0.347173i	−0.984819	−	0.173586i	$-0.944464\pi$
$149$		−	4.23779i		−	0.347173i	0.984819	−	0.173586i	$-0.0555356\pi$
$150$		0			0
$151$			1.91070i			0.155490i	0.996973	+	0.0777451i	$0.0247720\pi$
$151$			1.91070i			0.155490i	−0.996973	+	0.0777451i	$0.975228\pi$
$152$	−12.9311	+	5.69960i	−1.04885	+	0.462299i
$153$		0			0
$154$	−0.278311	+	2.24359i	−0.0224270	+	0.180794i
$155$	−8.21440	+	2.83900i	−0.659797	+	0.228034i
$156$		0			0
$157$	15.1998	+	15.1998i	1.21308	+	1.21308i	0.970009	+	0.243071i	$0.0781547\pi$
$157$	15.1998	+	15.1998i	1.21308	+	1.21308i	0.243071	+	0.970009i	$0.421845\pi$
$158$	1.89426	+	0.545722i	0.150700	+	0.0434153i
$159$		0			0
$160$	−2.35058	−	12.4288i	−0.185830	−	0.982582i
$161$	2.21904	−	1.61223i	0.174885	−	0.127061i
$162$		0			0
$163$	−2.32827	−	14.7001i	−0.182364	−	1.15140i	−0.893738	−	0.448589i	$-0.851927\pi$
$163$	−2.32827	−	14.7001i	−0.182364	−	1.15140i	0.711374	−	0.702814i	$-0.248073\pi$
$164$	−5.40699	−	3.39739i	−0.422215	−	0.265292i
$165$		0			0
$166$	20.9666	+	9.80863i	1.62732	+	0.761297i
$167$	13.6609	+	6.96060i	1.05712	+	0.538627i	0.894040	−	0.447986i	$-0.147859\pi$
$167$	13.6609	+	6.96060i	1.05712	+	0.538627i	0.163075	+	0.986614i	$0.447859\pi$
$168$		0			0
$169$	0.744179	−	0.241798i	0.0572445	−	0.0185999i
$170$	9.81840	+	4.37256i	0.753037	+	0.335360i
$171$		0			0
$172$	−13.1749	−	11.5104i	−1.00458	−	0.877662i
$173$	−3.15268	+	19.9053i	−0.239694	+	1.51337i	0.514942	+	0.857225i	$0.327814\pi$
$173$	−3.15268	+	19.9053i	−0.239694	+	1.51337i	−0.754636	+	0.656144i	$0.772186\pi$
$174$		0			0
$175$	5.56304	−	5.99317i	0.420527	−	0.453041i
$176$	2.70207	+	2.82608i	0.203676	+	0.213024i
$177$		0			0
$178$	3.16752	−	2.46840i	0.237416	−	0.185014i
$179$	−2.12634	+	6.54421i	−0.158930	+	0.489137i	−0.998538	−	0.0540563i	$-0.982785\pi$
$179$	−2.12634	+	6.54421i	−0.158930	+	0.489137i	0.839608	+	0.543193i	$0.182785\pi$
$180$		0			0
$181$	1.02571	+	3.15681i	0.0762404	+	0.234644i	0.981913	−	0.189335i	$-0.0606331\pi$
$181$	1.02571	+	3.15681i	0.0762404	+	0.234644i	−0.905672	+	0.423979i	$0.860633\pi$
$182$	7.11245	+	4.81029i	0.527210	+	0.356562i
$183$		0			0
$184$	0.265941	−	4.73629i	0.0196054	−	0.349164i
$185$	−3.07728	−	17.3357i	−0.226246	−	1.27455i
$186$		0			0
$187$	−3.28143	+	0.519728i	−0.239962	+	0.0380062i
$188$	10.5683	+	17.6881i	0.770773	+	1.29004i
$189$		0			0
$190$	−14.7507	+	5.66064i	−1.07013	+	0.410666i
$191$	−4.95656	+	6.82212i	−0.358644	+	0.493631i	−0.949770	−	0.312948i	$-0.898683\pi$
$191$	−4.95656	+	6.82212i	−0.358644	+	0.493631i	0.591126	+	0.806579i	$0.298683\pi$
$192$		0			0
$193$	9.61516	−	9.61516i	0.692114	−	0.692114i	−0.270583	−	0.962697i	$-0.587216\pi$
$193$	9.61516	−	9.61516i	0.692114	−	0.692114i	0.962697	+	0.270583i	$0.0872163\pi$
$194$	−9.49697	−	17.1834i	−0.681843	−	1.23369i
$195$		0			0
$196$	−0.581981	−	8.63116i	−0.0415701	−	0.616511i
$197$	−6.82019	+	3.47506i	−0.485918	+	0.247588i	−0.679746	−	0.733448i	$-0.737910\pi$
$197$	−6.82019	+	3.47506i	−0.485918	+	0.247588i	0.193827	+	0.981036i	$0.437910\pi$
$198$		0			0
$199$	13.8690			0.983146			0.491573	−	0.870836i	$-0.336422\pi$
$199$	13.8690			0.983146			0.491573	+	0.870836i	$0.336422\pi$
$200$	−1.94812	−	14.0073i	−0.137753	−	0.990467i
$201$		0			0
$202$	0.612599	+	18.1911i	0.0431023	+	1.27992i
$203$	9.44427	−	4.81210i	0.662858	−	0.337743i
$204$		0			0
$205$	−5.85303	−	4.08833i	−0.408793	−	0.285541i
$206$	7.96622	+	14.4137i	0.555033	+	1.00425i
$207$		0			0
$208$	14.2225	−	4.27100i	0.986150	−	0.296140i
$209$	2.87063	−	3.95108i	0.198566	−	0.273302i
$210$		0			0
$211$	5.56295	+	7.65675i	0.382970	+	0.527112i	0.956368	−	0.292164i	$-0.0943754\pi$
$211$	5.56295	+	7.65675i	0.382970	+	0.527112i	−0.573399	+	0.819277i	$0.694375\pi$
$212$	−2.23471	−	3.74022i	−0.153480	−	0.256879i
$213$		0			0
$214$	15.7607	+	14.7338i	1.07738	+	1.00718i
$215$	−14.0857	−	13.5712i	−0.960639	−	0.925549i
$216$		0			0
$217$	2.88583	−	5.66376i	0.195903	−	0.384481i
$218$	−20.2784	−	13.7147i	−1.37343	−	0.928875i
$219$		0			0
$220$	2.86353	+	3.30304i	0.193059	+	0.222691i
$221$	−3.89920	+	12.0005i	−0.262288	+	0.807240i
$222$		0			0
$223$	2.66635	+	0.422309i	0.178552	+	0.0282799i	0.245070	−	0.969505i	$-0.421189\pi$
$223$	2.66635	+	0.422309i	0.178552	+	0.0282799i	−0.0665180	+	0.997785i	$0.521189\pi$
$224$	7.54514	+	5.35339i	0.504131	+	0.357688i
$225$		0			0
$226$	3.69552	+	19.1388i	0.245822	+	1.27310i
$227$	1.84338	−	11.6386i	0.122349	−	0.772482i	−0.847861	−	0.530218i	$-0.822110\pi$
$227$	1.84338	−	11.6386i	0.122349	−	0.772482i	0.970210	−	0.242264i	$-0.0778900\pi$
$228$		0			0
$229$	3.90033	+	1.26729i	0.257741	+	0.0837451i	0.435037	−	0.900412i	$-0.356735\pi$
$229$	3.90033	+	1.26729i	0.257741	+	0.0837451i	−0.177297	+	0.984157i	$0.556735\pi$
$230$	0.554888	−	5.27457i	0.0365883	−	0.347795i
$231$		0			0
$232$	3.87823	−	17.9167i	0.254618	−	1.17629i
$233$	−7.40542	−	3.77325i	−0.485145	−	0.247194i	0.194270	−	0.980948i	$-0.437766\pi$
$233$	−7.40542	−	3.77325i	−0.485145	−	0.247194i	−0.679415	+	0.733754i	$0.737766\pi$
$234$		0			0
$235$	10.8385	+	20.3279i	0.707027	+	1.32605i
$236$	−6.21099	−	3.90257i	−0.404301	−	0.254036i
$237$		0			0
$238$	−7.39022	+	2.67942i	−0.479037	+	0.173681i
$239$	−8.99618	+	6.53610i	−0.581914	+	0.422785i	−0.839414	−	0.543493i	$-0.817101\pi$
$239$	−8.99618	+	6.53610i	−0.581914	+	0.422785i	0.257499	+	0.966278i	$0.417101\pi$
$240$		0			0
$241$	0.884285	+	0.642471i	0.0569618	+	0.0413852i	0.615902	−	0.787823i	$-0.288792\pi$
$241$	0.884285	+	0.642471i	0.0569618	+	0.0413852i	−0.558940	+	0.829208i	$0.688792\pi$
$242$	13.6499	+	3.93243i	0.877450	+	0.252786i
$243$		0			0
$244$	6.60681	−	5.51583i	0.422957	−	0.353115i
$245$	−0.179900	−	9.67017i	−0.0114934	−	0.617804i
$246$		0			0
$247$	−8.42082	−	16.5268i	−0.535804	−	1.05157i
$248$	−4.43398	−	10.0597i	−0.281558	−	0.638793i
$249$		0			0
$250$	−1.41272	−	15.7481i	−0.0893482	−	0.996000i
$251$		−	27.5973i		−	1.74193i	−0.491348	−	0.870964i	$-0.663496\pi$
$251$		−	27.5973i		−	1.74193i	0.491348	−	0.870964i	$-0.336504\pi$
$252$		0			0
$253$	0.744283	+	1.46074i	0.0467927	+	0.0918358i
$254$	20.2443	+	2.51125i	1.27024	+	0.157570i
$255$		0			0
$256$	15.4233	−	4.25697i	0.963956	−	0.266060i
$257$	−8.15087	−	8.15087i	−0.508437	−	0.508437i	0.405609	−	0.914047i	$-0.367059\pi$
$257$	−8.15087	−	8.15087i	−0.508437	−	0.508437i	−0.914047	+	0.405609i	$0.867059\pi$
$258$		0			0
$259$	10.4179	+	7.56908i	0.647340	+	0.470320i
$260$	16.1149	−	3.99498i	0.999403	−	0.247758i
$261$		0			0
$262$	−8.04303	−	22.1838i	−0.496900	−	1.37052i
$263$	2.64700	+	16.7125i	0.163221	+	1.03054i	0.924241	+	0.381810i	$0.124699\pi$
$263$	2.64700	+	16.7125i	0.163221	+	1.03054i	−0.761020	+	0.648729i	$0.775301\pi$
$264$		0			0
$265$	−2.29184	−	4.29842i	−0.140787	−	0.264050i
$266$	4.89660	−	10.4668i	0.300230	−	0.641760i
$267$		0			0
$268$	−12.3848	−	5.29341i	−0.756520	−	0.323347i
$269$	4.74451	−	1.54159i	0.289278	−	0.0939922i	−0.160783	−	0.986990i	$-0.551402\pi$
$269$	4.74451	−	1.54159i	0.289278	−	0.0939922i	0.450061	+	0.892998i	$0.351402\pi$
$270$		0			0
$271$	−26.7320	−	8.68575i	−1.62385	−	0.527622i	−0.651006	−	0.759073i	$-0.725653\pi$
$271$	−26.7320	−	8.68575i	−1.62385	−	0.527622i	−0.972846	+	0.231451i	$0.925653\pi$
$272$	−4.49009	+	12.8324i	−0.272252	+	0.778081i
$273$		0			0
$274$	20.0592	−	3.87323i	1.21182	−	0.233991i
$275$	3.01786	+	3.84446i	0.181984	+	0.231830i
$276$		0			0
$277$	−26.3841	−	4.17884i	−1.58527	−	0.251082i	−0.699301	−	0.714827i	$-0.746505\pi$
$277$	−26.3841	−	4.17884i	−1.58527	−	0.251082i	−0.885969	+	0.463745i	$0.846505\pi$
$278$	−20.0004	−	25.6651i	−1.19954	−	1.53929i
$279$		0			0
$280$	8.13420	+	6.38903i	0.486111	+	0.381818i
$281$	−0.691214	−	2.12734i	−0.0412344	−	0.126906i	0.928320	−	0.371782i	$-0.121253\pi$
$281$	−0.691214	−	2.12734i	−0.0412344	−	0.126906i	−0.969555	+	0.244875i	$0.921253\pi$
$282$		0			0
$283$	−7.65378	+	15.0214i	−0.454970	+	0.892929i	0.543593	+	0.839349i	$0.317063\pi$
$283$	−7.65378	+	15.0214i	−0.454970	+	0.892929i	−0.998564	+	0.0535804i	$0.982937\pi$
$284$	−5.89391	−	1.48510i	−0.349739	−	0.0881243i
$285$		0			0
$286$	−3.50473	+	3.74901i	−0.207239	+	0.221683i
$287$	5.15743	−	0.816856i	0.304433	−	0.0482175i
$288$		0			0
$289$	3.20224	+	4.40750i	0.188367	+	0.259265i
$290$	5.30649	−	19.7965i	0.311608	−	1.16249i
$291$		0			0
$292$	−2.53186	+	28.1332i	−0.148166	+	1.64637i
$293$	−7.35935	+	7.35935i	−0.429938	+	0.429938i	−0.888607	−	0.458669i	$-0.848326\pi$
$293$	−7.35935	+	7.35935i	−0.429938	+	0.429938i	0.458669	+	0.888607i	$0.348326\pi$
$294$		0			0
$295$	−6.72334	−	4.69624i	−0.391448	−	0.273426i
$296$	21.5334	−	5.68384i	1.25160	−	0.330367i
$297$		0			0
$298$	5.98974	−	0.201709i	0.346976	−	0.0116847i
$299$	6.22645			0.360085
$300$		0			0
$301$	14.3057			0.824569
$302$	−2.70060	+	0.0909447i	−0.155402	+	0.00523328i
$303$		0			0
$304$	−8.67138	−	18.0058i	−0.497338	−	1.03270i
$305$	7.67823	−	5.79979i	0.439654	−	0.332095i
$306$		0			0
$307$	−1.88086	+	1.88086i	−0.107346	+	0.107346i	−0.758740	−	0.651394i	$-0.774185\pi$
$307$	−1.88086	+	1.88086i	−0.107346	+	0.107346i	0.651394	+	0.758740i	$0.274185\pi$
$308$	−3.18437	−	0.286579i	−0.181446	−	0.0163294i
$309$		0			0
$310$	−4.40366	−	11.4752i	−0.250111	−	0.651748i
$311$	−7.58700	−	10.4426i	−0.430219	−	0.592146i	0.537784	−	0.843082i	$-0.319261\pi$
$311$	−7.58700	−	10.4426i	−0.430219	−	0.592146i	−0.968004	+	0.250937i	$0.919261\pi$
$312$		0			0
$313$	8.32486	−	1.31853i	0.470549	−	0.0745276i	0.0833429	−	0.996521i	$-0.473440\pi$
$313$	8.32486	−	1.31853i	0.470549	−	0.0745276i	0.387206	+	0.921993i	$0.373440\pi$
$314$	−20.7602	+	22.2071i	−1.17156	+	1.25322i
$315$		0			0
$316$	−0.681168	+	2.70335i	−0.0383187	+	0.152075i
$317$	−8.53106	+	16.7431i	−0.479152	+	0.940389i	0.517266	+	0.855825i	$0.326950\pi$
$317$	−8.53106	+	16.7431i	−0.479152	+	0.940389i	−0.996418	+	0.0845641i	$0.973050\pi$
$318$		0			0
$319$	1.95773	+	6.02528i	0.109612	+	0.337351i
$320$	17.4551	−	3.91392i	0.975771	−	0.218795i
$321$		0			0
$322$	2.38437	+	3.05969i	0.132876	+	0.170510i
$323$	16.7723	+	2.65647i	0.933237	+	0.147810i
$324$		0			0
$325$	18.2132	−	3.58370i	1.01028	−	0.198788i
$326$	20.6665	−	3.99050i	1.14461	−	0.221013i
$327$		0			0
$328$	4.54456	−	7.80402i	0.250931	−	0.430905i
$329$	−16.0242	−	5.20658i	−0.883443	−	0.287048i
$330$		0			0
$331$	−28.4519	+	9.24458i	−1.56386	+	0.508128i	−0.957835	−	0.287320i	$-0.907236\pi$
$331$	−28.4519	+	9.24458i	−1.56386	+	0.508128i	−0.606022	+	0.795448i	$0.707236\pi$
$332$	−12.8657	+	30.1013i	−0.706096	+	1.65202i
$333$		0			0
$334$	−9.18797	+	19.6399i	−0.502743	+	1.07465i
$335$	−13.5419	−	6.58559i	−0.739873	−	0.359809i
$336$		0			0
$337$	−1.67435	−	10.5714i	−0.0912078	−	0.575863i	−0.990392	−	0.138292i	$-0.955839\pi$
$337$	−1.67435	−	10.5714i	−0.0912078	−	0.575863i	0.899184	−	0.437571i	$-0.144161\pi$
$338$	0.377182	+	1.04032i	0.0205160	+	0.0565861i
$339$		0			0
$340$	−5.71289	+	14.0856i	−0.309825	+	0.763897i
$341$	3.07372	+	2.23319i	0.166451	+	0.120934i
$342$		0			0
$343$	13.0969	+	13.0969i	0.707167	+	0.707167i
$344$	15.6419	−	19.1695i	0.843354	−	1.03355i
$345$		0			0
$346$	−28.2844	−	3.50860i	−1.52058	−	0.188623i
$347$	−6.08901	−	11.9504i	−0.326875	−	0.641529i	0.667828	−	0.744316i	$-0.267224\pi$
$347$	−6.08901	−	11.9504i	−0.326875	−	0.641529i	−0.994703	+	0.102786i	$0.967224\pi$
$348$		0			0
$349$			11.8463i			0.634116i	0.948406	+	0.317058i	$0.102695\pi$
$349$			11.8463i			0.634116i	−0.948406	+	0.317058i	$0.897305\pi$
$350$	8.73561	+	7.57761i	0.466938	+	0.405041i
$351$		0			0
$352$	−3.86580	+	3.95366i	−0.206048	+	0.210731i
$353$	−14.3565	−	28.1762i	−0.764120	−	1.49967i	−0.863350	−	0.504606i	$-0.831638\pi$
$353$	−14.3565	−	28.1762i	−0.764120	−	1.49967i	0.0992300	−	0.995065i	$-0.468362\pi$
$354$		0			0
$355$	−6.50090	−	1.97936i	−0.345032	−	0.105054i
$356$	3.63963	+	4.35952i	0.192900	+	0.231054i
$357$		0			0
$358$	−9.35087	−	2.69391i	−0.494209	−	0.142378i
$359$	0.764560	+	0.555486i	0.0403520	+	0.0293174i	0.607778	−	0.794107i	$-0.292061\pi$
$359$	0.764560	+	0.555486i	0.0403520	+	0.0293174i	−0.567426	+	0.823424i	$0.692061\pi$
$360$		0			0
$361$	−4.82376	+	3.50467i	−0.253882	+	0.184456i
$362$	−4.41305	+	1.60001i	−0.231945	+	0.0840945i
$363$		0			0
$364$	−6.46038	+	10.2818i	−0.338616	+	0.538912i
$365$	−4.35932	+	31.2787i	−0.228177	+	1.63720i
$366$		0			0
$367$	−3.97266	−	2.02417i	−0.207371	−	0.105661i	0.347221	−	0.937783i	$-0.387125\pi$
$367$	−3.97266	−	2.02417i	−0.207371	−	0.105661i	−0.554592	+	0.832123i	$0.687125\pi$
$368$	6.70699	+	0.150448i	0.349626	+	0.00784262i
$369$		0			0
$370$	24.3560	−	5.17461i	1.26621	−	0.269015i
$371$	3.38838	+	1.10095i	0.175916	+	0.0571585i
$372$		0			0
$373$	−1.49600	+	9.44535i	−0.0774598	+	0.489062i	0.918209	+	0.396095i	$0.129635\pi$
$373$	−1.49600	+	9.44535i	−0.0774598	+	0.489062i	−0.995669	+	0.0929666i	$0.970365\pi$
$374$	−0.890778	−	4.61328i	−0.0460610	−	0.238547i
$375$		0			0
$376$	−24.4976	+	15.7793i	−1.26337	+	0.813755i
$377$	23.7651	+	3.76402i	1.22397	+	0.193857i
$378$		0			0
$379$	−0.907685	+	2.79357i	−0.0466246	+	0.143496i	−0.971659	−	0.236388i	$-0.924036\pi$
$379$	−0.907685	+	2.79357i	−0.0466246	+	0.143496i	0.925034	+	0.379884i	$0.124036\pi$
$380$	−8.70291	−	20.5793i	−0.446450	−	1.05570i
$381$		0			0
$382$	−9.87838	−	6.68094i	−0.505422	−	0.341827i
$383$	−11.7564	+	23.0732i	−0.600723	+	1.17898i	0.367764	+	0.929919i	$0.380124\pi$
$383$	−11.7564	+	23.0732i	−0.600723	+	1.17898i	−0.968487	+	0.249066i	$0.919876\pi$
$384$		0			0
$385$	−3.54041	−	0.493427i	−0.180436	−	0.0251474i
$386$	14.0478	+	13.1325i	0.715016	+	0.668428i
$387$		0			0
$388$	23.8351	−	14.2410i	1.21005	−	0.722979i
$389$	5.82961	+	8.02377i	0.295573	+	0.406821i	0.930814	−	0.365492i	$-0.119099\pi$
$389$	5.82961	+	8.02377i	0.295573	+	0.406821i	−0.635241	+	0.772314i	$0.719099\pi$
$390$		0			0
$391$	−3.35062	+	4.61173i	−0.169448	+	0.233225i
$392$	12.1717	−	1.23340i	0.614763	−	0.0622962i
$393$		0			0
$394$	−5.23631	−	9.47433i	−0.263802	−	0.477310i
$395$	−0.907873	+	2.98176i	−0.0456801	+	0.150029i
$396$		0			0
$397$	21.3376	−	10.8721i	1.07090	−	0.545653i	0.172585	−	0.984995i	$-0.444788\pi$
$397$	21.3376	−	10.8721i	1.07090	−	0.545653i	0.898320	+	0.439341i	$0.144788\pi$
$398$	0.660131	+	19.6026i	0.0330894	+	0.982589i
$399$		0			0
$400$	19.7054	−	3.42021i	0.985269	−	0.171010i
$401$	−6.16472			−0.307851			−0.153926	−	0.988082i	$-0.549192\pi$
$401$	−6.16472			−0.307851			−0.153926	+	0.988082i	$0.549192\pi$
$402$		0			0
$403$	12.8569	−	6.55093i	0.640449	−	0.326325i
$404$	−25.6824	+	1.73171i	−1.27775	+	0.0861558i
$405$		0			0
$406$	7.25100	+	13.1196i	0.359861	+	0.651115i
$407$	−5.44243	+	5.44243i	−0.269771	+	0.269771i
$408$		0			0
$409$	−0.203968	+	0.280737i	−0.0100855	+	0.0138816i	−0.814030	−	0.580823i	$-0.802731\pi$
$409$	−0.203968	+	0.280737i	−0.0100855	+	0.0138816i	0.803944	+	0.594704i	$0.202731\pi$
$410$	5.49990	−	8.46733i	0.271621	−	0.418172i
$411$		0			0
$412$	−19.9933	+	11.9456i	−0.984999	+	0.588518i
$413$	5.92431	−	0.938319i	0.291516	−	0.0461717i
$414$		0			0
$415$	−16.0063	+	32.9137i	−0.785720	+	1.61567i
$416$	6.71363	+	19.8989i	0.329163	+	0.975624i
$417$		0			0
$418$	5.72114	+	3.86932i	0.279830	+	0.189255i
$419$	8.61814	+	26.5239i	0.421024	+	1.29578i	0.906751	+	0.421668i	$0.138555\pi$
$419$	8.61814	+	26.5239i	0.421024	+	1.29578i	−0.485727	+	0.874111i	$0.661445\pi$
$420$		0			0
$421$	4.87173	−	14.9936i	0.237433	−	0.730745i	−0.759356	−	0.650676i	$-0.774486\pi$
$421$	4.87173	−	14.9936i	0.237433	−	0.730745i	0.996789	−	0.0800694i	$-0.0255142\pi$
$422$	−10.5574	+	8.22719i	−0.513924	+	0.400493i
$423$		0			0
$424$	5.18011	−	3.33659i	0.251568	−	0.162039i
$425$	−7.14664	+	15.4184i	−0.346663	+	0.747901i
$426$		0			0
$427$	−1.10095	+	6.95112i	−0.0532787	+	0.336388i
$428$	−20.0748	+	22.9777i	−0.970351	+	1.11067i
$429$		0			0
$430$	18.5113	−	20.5549i	0.892693	−	0.991245i
$431$	−11.2786	+	3.66463i	−0.543269	+	0.176519i	−0.567779	−	0.823181i	$-0.692197\pi$
$431$	−11.2786	+	3.66463i	−0.543269	+	0.176519i	0.0245103	+	0.999700i	$0.492197\pi$
$432$		0			0
$433$	3.48035	+	1.77333i	0.167255	+	0.0852207i	0.535614	−	0.844463i	$-0.320080\pi$
$433$	3.48035	+	1.77333i	0.167255	+	0.0852207i	−0.368359	+	0.929684i	$0.620080\pi$
$434$	8.14259	+	3.80929i	0.390857	+	0.182852i
$435$		0			0
$436$	18.4193	−	29.3145i	0.882123	−	1.40391i
$437$	−1.31085	−	8.27639i	−0.0627065	−	0.395913i
$438$		0			0
$439$	−5.00770	+	3.63831i	−0.239005	+	0.173647i	−0.700840	−	0.713319i	$-0.747191\pi$
$439$	−5.00770	+	3.63831i	−0.239005	+	0.173647i	0.461835	+	0.886966i	$0.347191\pi$
$440$	−4.53226	+	4.20457i	−0.216067	+	0.200445i
$441$		0			0
$442$	−17.1472	−	4.93998i	−0.815611	−	0.234971i
$443$	4.96290	+	4.96290i	0.235794	+	0.235794i	0.815106	−	0.579312i	$-0.196679\pi$
$443$	4.96290	+	4.96290i	0.235794	+	0.235794i	−0.579312	+	0.815106i	$0.696679\pi$
$444$		0			0
$445$	3.82701	+	5.06650i	0.181418	+	0.240175i
$446$	−0.469984	+	3.78876i	−0.0222544	+	0.179403i
$447$		0			0
$448$	−7.20741	+	10.9192i	−0.340518	+	0.515884i
$449$			22.5446i			1.06395i	0.846761	+	0.531973i	$0.178549\pi$
$449$			22.5446i			1.06395i	−0.846761	+	0.531973i	$0.821451\pi$
$450$		0			0
$451$			3.12102i			0.146963i
$452$	−26.8752	+	6.13425i	−1.26410	+	0.288531i
$453$		0			0
$454$	16.5379	+	2.05148i	0.776163	+	0.0962807i
$455$	−7.77424	+	11.1299i	−0.364462	+	0.521780i
$456$		0			0
$457$	−3.08538	−	3.08538i	−0.144328	−	0.144328i	0.631251	−	0.775579i	$-0.282542\pi$
$457$	−3.08538	−	3.08538i	−0.144328	−	0.144328i	−0.775579	+	0.631251i	$0.782542\pi$
$458$	−1.60556	+	5.57309i	−0.0750229	+	0.260413i
$459$		0			0
$460$	7.48155	+	0.533229i	0.348829	+	0.0248619i
$461$	28.0983	−	20.4146i	1.30867	−	0.950804i	0.308670	−	0.951169i	$-0.400116\pi$
$461$	28.0983	−	20.4146i	1.30867	−	0.950804i	1.00000		0.000364875i	$0.000116143\pi$
$462$		0			0
$463$	0.272846	+	1.72268i	0.0126802	+	0.0800597i	0.993217	−	0.116276i	$-0.0370957\pi$
$463$	0.272846	+	1.72268i	0.0126802	+	0.0800597i	−0.980537	+	0.196336i	$0.937096\pi$
$464$	25.5083	+	4.62875i	1.18419	+	0.214884i
$465$		0			0
$466$	4.98068	−	10.6465i	0.230725	−	0.493190i
$467$	−31.3897	−	15.9938i	−1.45254	−	0.740107i	−0.463272	−	0.886216i	$-0.653325\pi$
$467$	−31.3897	−	15.9938i	−1.45254	−	0.740107i	−0.989268	+	0.146109i	$0.953325\pi$
$468$		0			0
$469$	10.4744	−	3.40334i	0.483663	−	0.157152i
$470$	−28.2159	+	16.2869i	−1.30150	+	0.751257i
$471$		0			0
$472$	5.22031	−	8.96444i	0.240284	−	0.412622i
$473$	−1.33760	+	8.44527i	−0.0615029	+	0.388314i
$474$		0			0
$475$	−8.59797	−	23.4550i	−0.394502	−	1.07619i
$476$	−4.13888	−	10.3179i	−0.189705	−	0.472920i
$477$		0			0
$478$	−9.66641	−	12.4042i	−0.442131	−	0.567355i
$479$	−8.73304	+	26.8775i	−0.399023	+	1.22807i	0.526761	+	0.850013i	$0.323406\pi$
$479$	−8.73304	+	26.8775i	−0.399023	+	1.22807i	−0.925784	+	0.378053i	$0.876594\pi$
$480$		0			0
$481$	9.03315	+	27.8012i	0.411876	+	1.26762i
$482$	−0.865987	+	1.28044i	−0.0394446	+	0.0583224i
$483$		0			0
$484$	−4.90844	+	19.4801i	−0.223111	+	0.885461i
$485$	27.3923	−	14.6051i	1.24382	−	0.663185i
$486$		0			0
$487$	−20.4192	+	3.23409i	−0.925283	+	0.146550i	−0.600853	−	0.799359i	$-0.705172\pi$
$487$	−20.4192	+	3.23409i	−0.925283	+	0.146550i	−0.324430	+	0.945910i	$0.605172\pi$
$488$	8.11060	+	9.07560i	0.367150	+	0.410833i
$489$		0			0
$490$	13.6594	−	0.714551i	0.617068	−	0.0322801i
$491$	−8.93859	+	12.3029i	−0.403393	+	0.555223i	−0.961591	−	0.274485i	$-0.911493\pi$
$491$	−8.93859	+	12.3029i	−0.403393	+	0.555223i	0.558199	+	0.829707i	$0.311493\pi$
$492$		0			0
$493$	−15.5765	+	15.5765i	−0.701531	+	0.701531i
$494$	22.9584	−	12.6887i	1.03295	−	0.570893i
$495$		0			0
$496$	14.0075	−	6.74586i	0.628955	−	0.302898i
$497$	4.42845	−	2.25641i	0.198643	−	0.101214i
$498$		0			0
$499$	−12.1532			−0.544051			−0.272025	−	0.962290i	$-0.587693\pi$
$499$	−12.1532			−0.544051			−0.272025	+	0.962290i	$0.587693\pi$
$500$	22.1914	−	2.74633i	0.992429	−	0.122820i
$501$		0			0
$502$	39.0064	−	1.31357i	1.74094	−	0.0586274i
$503$	20.2930	−	10.3398i	0.904820	−	0.461029i	0.0612957	−	0.998120i	$-0.480477\pi$
$503$	20.2930	−	10.3398i	0.904820	−	0.461029i	0.843524	+	0.537091i	$0.180477\pi$
$504$		0			0
$505$	−28.7740	+	0.535302i	−1.28043	+	0.0238206i
$506$	−2.02920	+	1.12151i	−0.0902089	+	0.0498570i
$507$		0			0
$508$	−2.58585	+	28.7331i	−0.114729	+	1.27483i
$509$	−23.4284	+	32.2465i	−1.03845	+	1.42930i	−0.140036	+	0.990146i	$0.544722\pi$
$509$	−23.4284	+	32.2465i	−1.03845	+	1.42930i	−0.898412	+	0.439154i	$0.855278\pi$
$510$		0			0
$511$	−13.5766	−	18.6866i	−0.600594	−	0.826646i
$512$	6.75096	+	21.5969i	0.298353	+	0.954456i
$513$		0			0
$514$	11.1326	−	11.9085i	0.491037	−	0.525261i
$515$	−22.9771	+	12.2510i	−1.01249	+	0.539845i
$516$		0			0
$517$	4.57194	−	8.97293i	0.201074	−	0.394629i
$518$	−10.2024	+	15.0851i	−0.448266	+	0.662802i
$519$		0			0
$520$	6.41359	+	22.5868i	0.281254	+	0.990498i
$521$	2.01724	−	6.20841i	0.0883767	−	0.271996i	−0.897094	−	0.441839i	$-0.854326\pi$
$521$	2.01724	−	6.20841i	0.0883767	−	0.271996i	0.985471	+	0.169844i	$0.0543262\pi$
$522$		0			0
$523$	−20.1531	−	3.19194i	−0.881234	−	0.139574i	−0.300612	−	0.953747i	$-0.597191\pi$
$523$	−20.1531	−	3.19194i	−0.881234	−	0.139574i	−0.580622	+	0.814173i	$0.697191\pi$
$524$	30.9721	−	12.4240i	1.35302	−	0.542745i
$525$		0			0
$526$	−23.4957	+	4.53678i	−1.02446	+	0.197813i
$527$	−2.06659	+	13.0479i	−0.0900221	+	0.568377i
$528$		0			0
$529$	−19.1991	−	6.23816i	−0.834742	−	0.271224i
$530$	5.96635	−	3.44392i	0.259162	−	0.149594i
$531$		0			0
$532$	15.0270	+	6.42272i	0.651501	+	0.278460i
$533$	10.5615	+	5.38137i	0.457470	+	0.233093i
$534$		0			0
$535$	−23.6689	+	24.5662i	−1.02329	+	1.06209i
$536$	6.89229	−	17.7567i	0.297701	−	0.766974i
$537$		0			0
$538$	2.40472	+	6.63258i	0.103675	+	0.285951i
$539$	−3.42055	+	2.48518i	−0.147334	+	0.107044i
$540$		0			0
$541$	−21.6765	−	15.7489i	−0.931945	−	0.677097i	0.0145235	−	0.999895i	$-0.495377\pi$
$541$	−21.6765	−	15.7489i	−0.931945	−	0.677097i	−0.946468	+	0.322797i	$0.895377\pi$
$542$	11.0042	−	38.1967i	0.472669	−	1.64069i
$543$		0			0
$544$	−18.3512	−	5.73555i	−0.786803	−	0.245910i
$545$	22.1652	−	31.7327i	0.949454	−	1.35928i
$546$		0			0
$547$	−1.09113	−	2.14147i	−0.0466534	−	0.0915625i	0.866503	−	0.499172i	$-0.166362\pi$
$547$	−1.09113	−	2.14147i	−0.0466534	−	0.0915625i	−0.913156	+	0.407610i	$0.866362\pi$
$548$	6.42925	+	28.1676i	0.274644	+	1.20326i
$549$		0			0
$550$	−5.29016	+	4.44847i	−0.225573	+	0.189684i
$551$		−	32.3818i		−	1.37951i
$552$		0			0
$553$	−1.03494	−	2.03119i	−0.0440103	−	0.0863751i
$554$	4.65060	−	37.4906i	0.197585	−	1.59282i
$555$		0			0
$556$	35.3233	−	29.4904i	1.49804	−	1.25067i
$557$	17.1440	+	17.1440i	0.726416	+	0.726416i	0.969904	−	0.243488i	$-0.0782915\pi$
$557$	17.1440	+	17.1440i	0.726416	+	0.726416i	−0.243488	+	0.969904i	$0.578292\pi$
$558$		0			0
$559$	26.2724	+	19.0881i	1.11121	+	0.807339i
$560$	−8.64316	+	11.8011i	−0.365240	+	0.498686i
$561$		0			0
$562$	2.97391	−	1.07823i	0.125447	−	0.0454822i
$563$	3.26270	+	20.5999i	0.137506	+	0.868181i	0.955936	+	0.293574i	$0.0948449\pi$
$563$	3.26270	+	20.5999i	0.137506	+	0.868181i	−0.818430	+	0.574606i	$0.805155\pi$
$564$		0			0
$565$	−30.3457	+	5.38670i	−1.27665	+	0.226620i
$566$	−21.5957	−	10.1030i	−0.907736	−	0.424659i
$567$		0			0
$568$	1.81852	−	8.40121i	0.0763033	−	0.352507i
$569$	14.5574	−	4.72997i	0.610276	−	0.198291i	0.0124579	−	0.999922i	$-0.496034\pi$
$569$	14.5574	−	4.72997i	0.610276	−	0.198291i	0.597818	+	0.801632i	$0.296034\pi$
$570$		0			0
$571$	36.1142	+	11.7342i	1.51133	+	0.491062i	0.943299	−	0.331943i	$-0.107704\pi$
$571$	36.1142	+	11.7342i	1.51133	+	0.491062i	0.568034	+	0.823005i	$0.307704\pi$
$572$	−5.46571	−	4.77519i	−0.228533	−	0.199661i
$573$		0			0
$574$	1.40004	+	7.25069i	0.0584364	+	0.302638i
$575$	8.32567	+	1.00286i	0.347204	+	0.0418222i
$576$		0			0
$577$	−29.1734	−	4.62061i	−1.21451	−	0.192359i	−0.483878	−	0.875135i	$-0.660772\pi$
$577$	−29.1734	−	4.62061i	−1.21451	−	0.192359i	−0.730627	+	0.682777i	$0.760772\pi$
$578$	−6.07720	+	4.73587i	−0.252778	+	0.196986i
$579$		0			0
$580$	28.2332	+	6.55799i	1.17232	+	0.272306i
$581$	−8.27184	−	25.4581i	−0.343174	−	1.05618i
$582$		0			0
$583$	−0.966752	+	1.89736i	−0.0400388	+	0.0785806i
$584$	−39.8844	−	2.23949i	−1.65043	−	0.0926708i
$585$		0			0
$586$	−10.7521	−	10.0515i	−0.444165	−	0.415224i
$587$	8.67609	−	1.37416i	0.358100	−	0.0567175i	0.0252077	−	0.999682i	$-0.491975\pi$
$587$	8.67609	−	1.37416i	0.358100	−	0.0567175i	0.332893	+	0.942965i	$0.391975\pi$
$588$		0			0
$589$	−11.4145	−	15.7107i	−0.470325	−	0.647347i
$590$	6.31771	−	9.72639i	0.260096	−	0.400429i
$591$		0			0
$592$	9.05856	+	30.1651i	0.372304	+	1.23978i
$593$	16.2759	−	16.2759i	0.668372	−	0.668372i	−0.288967	−	0.957339i	$-0.593312\pi$
$593$	16.2759	−	16.2759i	0.668372	−	0.668372i	0.957339	+	0.288967i	$0.0933118\pi$
$594$		0			0
$595$	−4.06006	−	11.7474i	−0.166446	−	0.481598i
$596$	0.570195	+	8.45637i	0.0233561	+	0.346386i
$597$		0			0
$598$	0.296365	+	8.80055i	0.0121192	+	0.359881i
$599$	22.8730			0.934566			0.467283	−	0.884108i	$-0.345233\pi$
$599$	22.8730			0.934566			0.467283	+	0.884108i	$0.345233\pi$
$600$		0			0
$601$	28.0770			1.14529			0.572643	−	0.819805i	$-0.305918\pi$
$601$	28.0770			1.14529			0.572643	+	0.819805i	$0.305918\pi$
$602$	0.680920	+	20.2199i	0.0277522	+	0.824102i
$603$		0			0
$604$	−0.257085	−	3.81273i	−0.0104606	−	0.155138i
$605$	−6.54206	+	21.4863i	−0.265973	+	0.873543i
$606$		0			0
$607$	16.1309	−	16.1309i	0.654732	−	0.654732i	−0.299397	−	0.954129i	$-0.596786\pi$
$607$	16.1309	−	16.1309i	0.654732	−	0.654732i	0.954129	+	0.299397i	$0.0967855\pi$
$608$	25.0368	−	13.1133i	1.01538	−	0.531813i
$609$		0			0
$610$	8.56297	+	10.5764i	0.346704	+	0.428228i
$611$	−22.4813	−	30.9429i	−0.909496	−	1.25181i
$612$		0			0
$613$	8.76640	−	1.38846i	0.354071	−	0.0560794i	0.0231347	−	0.999732i	$-0.492635\pi$
$613$	8.76640	−	1.38846i	0.354071	−	0.0560794i	0.330937	+	0.943653i	$0.392635\pi$
$614$	−2.74795	−	2.56891i	−0.110898	−	0.103673i
$615$		0			0
$616$	0.253486	−	4.51447i	0.0102132	−	0.181893i
$617$	−9.82315	+	19.2790i	−0.395465	+	0.776144i	−0.999788	−	0.0205955i	$-0.993444\pi$
$617$	−9.82315	+	19.2790i	−0.395465	+	0.776144i	0.604323	+	0.796740i	$0.293444\pi$
$618$		0			0
$619$	−7.47376	−	23.0019i	−0.300396	−	0.924524i	−0.981355	−	0.192202i	$-0.938437\pi$
$619$	−7.47376	−	23.0019i	−0.300396	−	0.924524i	0.680959	−	0.732321i	$-0.261563\pi$
$620$	16.0096	−	6.77038i	0.642961	−	0.271905i
$621$		0			0
$622$	14.3986	−	11.2206i	0.577331	−	0.449905i
$623$	−4.58672	−	0.726464i	−0.183763	−	0.0291052i
$624$		0			0
$625$	24.9308	−	1.85843i	0.997233	−	0.0743374i
$626$	2.25987	+	11.7037i	0.0903224	+	0.467774i
$627$		0			0
$628$	−32.3760	−	28.2857i	−1.29194	−	1.12872i
$629$	−25.4524	−	8.26999i	−1.01485	−	0.329746i
$630$		0			0
$631$	−26.5940	+	8.64091i	−1.05869	+	0.343989i	−0.786073	−	0.618134i	$-0.787889\pi$
$631$	−26.5940	+	8.64091i	−1.05869	+	0.343989i	−0.272616	+	0.962123i	$0.587889\pi$
$632$	−3.85337	−	0.834098i	−0.153279	−	0.0331786i
$633$		0			0
$634$	−24.0710	−	11.2610i	−0.955983	−	0.447230i
$635$	−4.45227	+	31.9457i	−0.176683	+	1.26773i
$636$		0			0
$637$	2.51200	+	15.8602i	0.0995292	+	0.628403i
$638$	−8.42302	+	3.05387i	−0.333470	+	0.120904i
$639$		0			0
$640$	6.36281	+	24.4850i	0.251512	+	0.967854i
$641$	−3.18368	−	2.31308i	−0.125748	−	0.0913611i	0.523134	−	0.852251i	$-0.324763\pi$
$641$	−3.18368	−	2.31308i	−0.125748	−	0.0913611i	−0.648881	+	0.760890i	$0.724763\pi$
$642$		0			0
$643$	1.48607	+	1.48607i	0.0586048	+	0.0586048i	0.735802	−	0.677197i	$-0.236806\pi$
$643$	1.48607	+	1.48607i	0.0586048	+	0.0586048i	−0.677197	+	0.735802i	$0.736806\pi$
$644$	−4.21111	+	3.51573i	−0.165941	+	0.138539i
$645$		0			0
$646$	−2.95637	+	23.8326i	−0.116317	+	0.937683i
$647$	−10.7848	−	21.1664i	−0.423994	−	0.832135i	−0.999893	−	0.0146144i	$-0.995348\pi$
$647$	−10.7848	−	21.1664i	−0.423994	−	0.832135i	0.575899	−	0.817521i	$-0.304652\pi$
$648$		0			0
$649$			3.58510i			0.140727i
$650$	5.93215	+	25.5721i	0.232678	+	1.00302i
$651$		0			0
$652$	6.62390	+	29.0204i	0.259412	+	1.13653i
$653$	−1.32509	−	2.60064i	−0.0518549	−	0.101771i	0.863625	−	0.504135i	$-0.168189\pi$
$653$	−1.32509	−	2.60064i	−0.0518549	−	0.101771i	−0.915480	+	0.402364i	$0.868189\pi$
$654$		0			0
$655$	35.2633	−	12.1874i	1.37785	−	0.476202i
$656$	11.2466	+	6.05188i	0.439106	+	0.236286i
$657$		0			0
$658$	6.59633	−	22.8966i	0.257152	−	0.892604i
$659$	26.9961	+	19.6138i	1.05162	+	0.764046i	0.972520	−	0.232821i	$-0.0747957\pi$
$659$	26.9961	+	19.6138i	1.05162	+	0.764046i	0.0790990	+	0.996867i	$0.474796\pi$
$660$		0			0
$661$	−3.15278	+	2.29063i	−0.122629	+	0.0890950i	−0.647409	−	0.762143i	$-0.724147\pi$
$661$	−3.15278	+	2.29063i	−0.122629	+	0.0890950i	0.524780	+	0.851238i	$0.324147\pi$
$662$	−14.4206	−	39.7742i	−0.560474	−	1.54587i
$663$		0			0
$664$	−43.1579	−	16.7518i	−1.67485	−	0.650094i
$665$	16.4310	+	7.99058i	0.637166	+	0.309861i
$666$		0			0
$667$	9.68533	+	4.93492i	0.375017	+	0.191081i
$668$	−28.1965	−	12.0516i	−1.09096	−	0.466290i
$669$		0			0
$670$	8.66359	−	19.4537i	0.334704	−	0.751564i
$671$	−4.00059	−	1.29987i	−0.154441	−	0.0501810i
$672$		0			0
$673$	−6.76456	+	42.7098i	−0.260755	+	1.64634i	0.415442	+	0.909619i	$0.363627\pi$
$673$	−6.76456	+	42.7098i	−0.260755	+	1.64634i	−0.676197	+	0.736721i	$0.736373\pi$
$674$	14.8621	−	2.86973i	0.572467	−	0.110538i
$675$		0			0
$676$	−1.45245	+	0.582631i	−0.0558635	+	0.0224089i
$677$	17.8725	+	2.83072i	0.686896	+	0.108794i	0.490120	−	0.871655i	$-0.336953\pi$
$677$	17.8725	+	2.83072i	0.686896	+	0.108794i	0.196776	+	0.980449i	$0.436953\pi$
$678$		0			0
$679$	−7.01598	+	21.5930i	−0.269249	+	0.828662i
$680$	−20.1806	−	7.40423i	−0.773892	−	0.283939i
$681$		0			0
$682$	−3.01012	+	4.45073i	−0.115263	+	0.170427i
$683$	17.9286	−	35.1869i	0.686020	−	1.34639i	−0.240685	−	0.970603i	$-0.577372\pi$
$683$	17.9286	−	35.1869i	0.686020	−	1.34639i	0.926706	−	0.375788i	$-0.122628\pi$
$684$		0			0
$685$	5.64575	+	31.8050i	0.215713	+	1.21521i
$686$	−17.8880	+	19.1347i	−0.682965	+	0.730567i
$687$		0			0
$688$	27.8389	+	21.1960i	1.06135	+	0.808091i
$689$	4.75375	+	6.54298i	0.181104	+	0.249268i
$690$		0			0
$691$	20.7179	−	28.5157i	0.788146	−	1.08479i	−0.206190	−	0.978512i	$-0.566107\pi$
$691$	20.7179	−	28.5157i	0.788146	−	1.08479i	0.994336	−	0.106278i	$-0.0338933\pi$
$692$	3.61282	−	40.1445i	0.137339	−	1.52607i
$693$		0			0
$694$	16.6010	−	9.17510i	0.630164	−	0.348282i
$695$	41.0517	−	31.0086i	1.55718	−	1.17622i
$696$		0			0
$697$	−9.66924	+	4.92672i	−0.366248	+	0.186613i
$698$	−16.7437	+	0.563855i	−0.633757	+	0.0213422i
$699$		0			0
$700$	−10.2945	+	12.7077i	−0.389096	+	0.480306i
$701$	−41.8330			−1.58001			−0.790005	−	0.613100i	$-0.789922\pi$
$701$	−41.8330			−1.58001			−0.790005	+	0.613100i	$0.789922\pi$
$702$		0			0
$703$	35.0524	−	17.8601i	1.32203	−	0.673607i
$704$	−5.77215	−	5.27579i	−0.217546	−	0.198839i
$705$		0			0
$706$	39.1413	−	21.6328i	1.47310	−	0.814161i
$707$	14.8836	−	14.8836i	0.559754	−	0.559754i
$708$		0			0
$709$	22.6320	−	31.1503i	0.849962	−	1.16987i	−0.133909	−	0.990994i	$-0.542753\pi$
$709$	22.6320	−	31.1503i	0.849962	−	1.16987i	0.983871	−	0.178879i	$-0.0572470\pi$
$710$	2.48823	−	9.28266i	0.0933817	−	0.348372i
$711$		0			0
$712$	−5.98856	+	5.35181i	−0.224431	+	0.200567i
$713$	6.43858	−	1.01977i	0.241127	−	0.0381907i
$714$		0			0
$715$	−5.84357	−	5.63011i	−0.218537	−	0.210554i
$716$	3.36253	−	13.3449i	0.125663	−	0.498721i
$717$		0			0
$718$	−0.748739	+	1.10708i	−0.0279427	+	0.0413158i
$719$	−11.1156	−	34.2102i	−0.414540	−	1.27582i	−0.912661	−	0.408717i	$-0.865976\pi$
$719$	−11.1156	−	34.2102i	−0.414540	−	1.27582i	0.498121	−	0.867108i	$-0.334024\pi$
$720$		0			0
$721$	5.88512	−	18.1125i	0.219173	−	0.674546i
$722$	−5.18314	−	6.65115i	−0.192896	−	0.247530i
$723$		0			0
$724$	−2.47152	−	6.16131i	−0.0918534	−	0.228983i
$725$	31.1711	+	8.86076i	1.15767	+	0.329081i
$726$		0			0
$727$	−3.48933	+	22.0307i	−0.129412	+	0.817075i	0.834530	+	0.550963i	$0.185739\pi$
$727$	−3.48933	+	22.0307i	−0.129412	+	0.817075i	−0.963942	+	0.266113i	$0.914261\pi$
$728$	−14.8399	−	8.64180i	−0.550003	−	0.320286i
$729$		0			0
$730$	−44.4172	−	4.67272i	−1.64396	−	0.172945i
$731$	−28.2758	+	9.18736i	−1.04582	+	0.339807i
$732$		0			0
$733$	−22.9079	−	11.6722i	−0.846124	−	0.431122i	−0.0235109	−	0.999724i	$-0.507484\pi$
$733$	−22.9079	−	11.6722i	−0.846124	−	0.431122i	−0.822613	+	0.568602i	$0.807484\pi$
$734$	2.67190	−	5.71135i	0.0986215	−	0.210810i
$735$		0			0
$736$	0.106593	+	9.48691i	0.00392906	+	0.349692i
$737$	1.02977	+	6.50168i	0.0379319	+	0.239493i
$738$		0			0
$739$	6.76750	−	4.91688i	0.248947	−	0.180870i	−0.456313	−	0.889819i	$-0.650830\pi$
$739$	6.76750	−	4.91688i	0.248947	−	0.180870i	0.705260	+	0.708949i	$0.250830\pi$
$740$	8.47314	+	34.1788i	0.311479	+	1.25644i
$741$		0			0
$742$	−1.39482	+	4.84158i	−0.0512054	+	0.177740i
$743$	−0.563949	−	0.563949i	−0.0206893	−	0.0206893i	0.696686	−	0.717376i	$-0.254657\pi$
$743$	−0.563949	−	0.563949i	−0.0206893	−	0.0206893i	−0.717376	+	0.696686i	$0.754657\pi$
$744$		0			0
$745$	0.176257	+	9.47434i	0.00645757	+	0.347113i
$746$	−13.4214	−	1.66488i	−0.491392	−	0.0609557i
$747$		0			0
$748$	6.47806	−	1.47862i	0.236861	−	0.0540636i
$749$		−	24.9499i		−	0.911651i
$750$		0			0
$751$		−	41.2218i		−	1.50420i	−0.659046	−	0.752102i	$-0.729040\pi$
$751$		−	41.2218i		−	1.50420i	0.659046	−	0.752102i	$-0.270960\pi$
$752$	−23.4687	−	33.8741i	−0.855815	−	1.23526i
$753$		0			0
$754$	−4.18895	+	33.7691i	−0.152553	+	1.22980i
$755$	−0.0794693	−	4.27171i	−0.00289219	−	0.155463i
$756$		0			0
$757$	20.8498	+	20.8498i	0.757797	+	0.757797i	0.975921	−	0.218124i	$-0.0699937\pi$
$757$	20.8498	+	20.8498i	0.757797	+	0.757797i	−0.218124	+	0.975921i	$0.569994\pi$
$758$	−3.99166	−	1.14997i	−0.144984	−	0.0417686i
$759$		0			0
$760$	28.6729	−	13.2803i	1.04007	−	0.481728i
$761$	−13.7177	+	9.96648i	−0.497266	+	0.361285i	−0.807972	−	0.589221i	$-0.799435\pi$
$761$	−13.7177	+	9.96648i	−0.497266	+	0.361285i	0.310706	+	0.950506i	$0.399435\pi$
$762$		0			0
$763$	4.42866	+	27.9615i	0.160328	+	1.01227i
$764$	8.97274	−	14.2802i	0.324622	−	0.516640i
$765$		0			0
$766$	−33.1715	−	15.5184i	−1.19854	−	0.560702i
$767$	12.1320	+	6.18155i	0.438060	+	0.223203i
$768$		0			0
$769$	38.5078	−	12.5119i	1.38863	−	0.451192i	0.483130	−	0.875549i	$-0.339500\pi$
$769$	38.5078	−	12.5119i	1.38863	−	0.451192i	0.905495	+	0.424357i	$0.139500\pi$
$770$	0.528900	−	5.02754i	0.0190602	−	0.181180i
$771$		0			0
$772$	−17.8930	+	20.4805i	−0.643984	+	0.737108i
$773$	4.17413	−	26.3544i	0.150133	−	0.947902i	−0.791478	−	0.611198i	$-0.790688\pi$
$773$	4.17413	−	26.3544i	0.150133	−	0.947902i	0.941611	−	0.336704i	$-0.109312\pi$
$774$		0			0
$775$	18.2467	−	6.68875i	0.655441	−	0.240267i
$776$	21.2629	+	33.0110i	0.763295	+	1.18503i
$777$		0			0
$778$	−11.0634	+	8.62155i	−0.396643	+	0.309098i
$779$	4.92956	−	15.1716i	0.176620	−	0.543580i
$780$		0			0
$781$	0.917987	+	2.82527i	0.0328482	+	0.101096i
$782$	−6.67776	−	4.51630i	−0.238796	−	0.161502i
$783$		0			0
$784$	2.32265	+	17.1449i	0.0829518	+	0.612318i
$785$	−34.6142	−	33.3498i	−1.23543	−	1.19031i
$786$		0			0
$787$	44.4189	−	7.03527i	1.58336	−	0.250780i	0.698146	−	0.715956i	$-0.254009\pi$
$787$	44.4189	−	7.03527i	1.58336	−	0.250780i	0.885219	+	0.465175i	$0.154009\pi$
$788$	13.1419	−	7.85203i	0.468161	−	0.279717i
$789$		0			0
$790$	−4.25767	−	1.14127i	−0.151481	−	0.0406047i
$791$	13.2495	−	18.2363i	0.471097	−	0.648410i
$792$		0			0
$793$	−11.2967	+	11.2967i	−0.401158	+	0.401158i
$794$	16.3823	+	29.6414i	0.581387	+	1.05193i
$795$		0			0
$796$	−27.6751	+	1.86607i	−0.980918	+	0.0661412i
$797$	25.8044	−	13.1480i	0.914037	−	0.465725i	0.0672976	−	0.997733i	$-0.478562\pi$
$797$	25.8044	−	13.1480i	0.914037	−	0.465725i	0.846739	+	0.532008i	$0.178562\pi$
$798$		0			0
$799$	35.0161			1.23878
$800$	5.77209	+	27.6890i	0.204074	+	0.978955i
$801$		0			0
$802$	−0.293426	−	8.71329i	−0.0103612	−	0.307677i
$803$	12.3009	−	6.26762i	0.434089	−	0.221179i
$804$		0			0
$805$	−4.89402	+	3.69673i	−0.172491	+	0.130292i
$806$	9.87113	+	17.8603i	0.347696	+	0.629104i
$807$		0			0
$808$	−3.67004	−	36.2174i	−0.129112	−	1.27412i
$809$	−19.7275	+	27.1526i	−0.693584	+	0.954636i	0.306413	+	0.951899i	$0.400871\pi$
$809$	−19.7275	+	27.1526i	−0.693584	+	0.954636i	−0.999996	+	0.00273720i	$0.999129\pi$
$810$		0			0
$811$	8.32953	+	11.4646i	0.292489	+	0.402577i	0.929821	−	0.368013i	$-0.119962\pi$
$811$	8.32953	+	11.4646i	0.292489	+	0.402577i	−0.637331	+	0.770590i	$0.719962\pi$
$812$	−18.1983	+	10.8731i	−0.638634	+	0.381572i
$813$		0			0
$814$	−7.95144	−	7.43335i	−0.278698	−	0.260539i
$815$	5.81668	+	32.7680i	0.203749	+	1.14781i
$816$		0			0
$817$	19.8413	−	38.9407i	0.694159	−	1.36236i
$818$	−0.406506	−	0.274928i	−0.0142131	−	0.00961263i
$819$		0			0
$820$	12.2296	+	7.37060i	0.427077	+	0.257393i
$821$	−13.6386	+	41.9754i	−0.475992	+	1.46495i	0.368624	+	0.929579i	$0.379829\pi$
$821$	−13.6386	+	41.9754i	−0.475992	+	1.46495i	−0.844616	+	0.535373i	$0.820171\pi$
$822$		0			0
$823$	−26.4425	−	4.18808i	−0.921728	−	0.145987i	−0.322503	−	0.946568i	$-0.604524\pi$
$823$	−26.4425	−	4.18808i	−0.921728	−	0.145987i	−0.599225	+	0.800581i	$0.704524\pi$
$824$	−17.8357	−	27.6902i	−0.621336	−	0.964634i
$825$		0			0
$826$	1.60822	+	8.32884i	0.0559570	+	0.289797i
$827$	1.72439	−	10.8874i	0.0599630	−	0.378591i	−0.939397	−	0.342830i	$-0.888614\pi$
$827$	1.72439	−	10.8874i	0.0599630	−	0.378591i	0.999360	−	0.0357611i	$-0.0113855\pi$
$828$		0			0
$829$	10.5473	+	3.42701i	0.366321	+	0.119025i	0.486393	−	0.873740i	$-0.338312\pi$
$829$	10.5473	+	3.42701i	0.366321	+	0.119025i	−0.120071	+	0.992765i	$0.538312\pi$
$830$	−47.2825	−	21.0569i	−1.64120	−	0.730896i
$831$		0			0
$832$	−27.8058	+	10.4363i	−0.963993	+	0.361813i
$833$	−13.0989	−	6.67421i	−0.453849	−	0.231248i
$834$		0			0
$835$	−30.8310	−	14.9935i	−1.06695	−	0.518871i
$836$	−5.19663	+	8.27050i	−0.179729	+	0.286041i
$837$		0			0
$838$	−37.0790	+	13.4435i	−1.28087	+	0.464397i
$839$	−5.75338	+	4.18007i	−0.198629	+	0.144312i	−0.682654	−	0.730742i	$-0.739174\pi$
$839$	−5.75338	+	4.18007i	−0.198629	+	0.144312i	0.484025	+	0.875054i	$0.339174\pi$
$840$		0			0
$841$	10.5222	+	7.64481i	0.362834	+	0.263614i
$842$	21.4241	+	6.17210i	0.738322	+	0.212704i
$843$		0			0
$844$	−12.1309	−	14.5303i	−0.417563	−	0.500154i
$845$	−1.65369	+	0.571536i	−0.0568887	+	0.0196614i
$846$		0			0
$847$	−7.45773	−	14.6366i	−0.256251	−	0.502920i
$848$	4.96254	+	7.16281i	0.170414	+	0.245972i
$849$		0			0
$850$	−22.1327	−	9.36728i	−0.759145	−	0.321295i
$851$			13.2060i			0.452695i
$852$		0			0
$853$	−3.82112	−	7.49937i	−0.130833	−	0.256774i	0.816292	−	0.577640i	$-0.196026\pi$
$853$	−3.82112	−	7.49937i	−0.130833	−	0.256774i	−0.947125	+	0.320866i	$0.896026\pi$
$854$	−9.87720	−	1.22524i	−0.337991	−	0.0419268i
$855$		0			0
$856$	−33.4325	−	27.2803i	−1.14270	−	0.932420i
$857$	−27.4409	−	27.4409i	−0.937362	−	0.937362i	0.0607885	−	0.998151i	$-0.480638\pi$
$857$	−27.4409	−	27.4409i	−0.937362	−	0.937362i	−0.998151	+	0.0607885i	$0.980638\pi$
$858$		0			0
$859$	−34.5693	−	25.1160i	−1.17949	−	0.856948i	−0.187374	−	0.982289i	$-0.559998\pi$
$859$	−34.5693	−	25.1160i	−1.17949	−	0.856948i	−0.992114	+	0.125340i	$0.959998\pi$
$860$	29.9336	+	25.1857i	1.02073	+	0.858825i
$861$		0			0
$862$	−5.71646	−	15.7668i	−0.194703	−	0.537020i
$863$	−4.41919	−	27.9017i	−0.150431	−	0.949785i	−0.941244	−	0.337727i	$-0.890342\pi$
$863$	−4.41919	−	27.9017i	−0.150431	−	0.949785i	0.790813	−	0.612058i	$-0.209658\pi$
$864$		0			0
$865$	6.22050	−	44.6329i	0.211503	−	1.51757i
$866$	−2.34079	+	5.00358i	−0.0795432	+	0.170028i
$867$		0			0
$868$	−4.99652	+	11.6901i	−0.169593	+	0.396789i
$869$	1.29587	−	0.421052i	0.0439592	−	0.0142832i
$870$		0			0
$871$	23.7772	+	7.72570i	0.805661	+	0.261775i
$872$	42.3102	+	24.6387i	1.43280	+	0.834373i
$873$		0			0
$874$	11.6356	−	2.24671i	0.393579	−	0.0759961i
$875$	−12.1879	+	13.6302i	−0.412027	+	0.460785i
$876$		0			0
$877$	−10.7595	−	1.70413i	−0.363321	−	0.0575444i	−0.0278947	−	0.999611i	$-0.508880\pi$
$877$	−10.7595	−	1.70413i	−0.363321	−	0.0575444i	−0.335426	+	0.942067i	$0.608880\pi$
$878$	−5.38079	−	6.90477i	−0.181593	−	0.233025i
$879$		0			0
$880$	−6.15852	−	6.20583i	−0.207604	−	0.209198i
$881$	−17.5572	−	54.0356i	−0.591518	−	1.82051i	−0.571345	−	0.820710i	$-0.693578\pi$
$881$	−17.5572	−	54.0356i	−0.591518	−	1.82051i	−0.0201739	−	0.999796i	$-0.506422\pi$
$882$		0			0
$883$	−2.37742	+	4.66595i	−0.0800066	+	0.157022i	−0.927544	−	0.373714i	$-0.878084\pi$
$883$	−2.37742	+	4.66595i	−0.0800066	+	0.157022i	0.847537	+	0.530736i	$0.178084\pi$
$884$	6.16606	−	24.4712i	0.207387	−	0.823057i
$885$		0			0
$886$	−6.77840	+	7.25084i	−0.227725	+	0.243597i
$887$	−3.92752	+	0.622058i	−0.131873	+	0.0208867i	−0.222022	−	0.975042i	$-0.571266\pi$
$887$	−3.92752	+	0.622058i	−0.131873	+	0.0208867i	0.0901489	+	0.995928i	$0.471266\pi$
$888$		0			0
$889$	−13.8661	−	19.0851i	−0.465054	−	0.640092i
$890$	−6.97890	+	5.65030i	−0.233933	+	0.189398i
$891$		0			0
$892$	−5.37744	−	0.483946i	−0.180050	−	0.0162037i
$893$	−36.3972	+	36.3972i	−1.21799	+	1.21799i
$894$		0			0
$895$	4.48164	−	14.7192i	0.149805	−	0.492009i
$896$	−15.7764	−	9.66732i	−0.527052	−	0.322962i
$897$		0			0
$898$	−31.8649	+	1.07307i	−1.06334	+	0.0358089i
$899$	25.1912			0.840174
$900$		0			0
$901$	−7.40429			−0.246673
$902$	−4.41129	+	0.148553i	−0.146880	+	0.00494628i
$903$		0			0
$904$	−9.94942	−	37.6937i	−0.330913	−	1.25367i
$905$	−2.42446	−	7.01496i	−0.0805917	−	0.233185i
$906$		0			0
$907$	6.99767	−	6.99767i	0.232354	−	0.232354i	−0.581321	−	0.813675i	$-0.697464\pi$
$907$	6.99767	−	6.99767i	0.232354	−	0.232354i	0.813675	+	0.581321i	$0.197464\pi$
$908$	−2.11242	+	23.4725i	−0.0701032	+	0.778963i
$909$		0			0
$910$	−16.1012	−	10.4584i	−0.533751	−	0.346694i
$911$	32.8488	+	45.2125i	1.08833	+	1.49796i	0.850007	+	0.526771i	$0.176597\pi$
$911$	32.8488	+	45.2125i	1.08833	+	1.49796i	0.238322	+	0.971186i	$0.423403\pi$
$912$		0			0
$913$	15.8024	−	2.50285i	0.522983	−	0.0828323i
$914$	4.21405	−	4.50776i	0.139388	−	0.149104i
$915$		0			0
$916$	−7.95349	−	2.00405i	−0.262791	−	0.0662158i
$917$	−12.3885	+	24.3137i	−0.409103	+	0.802910i
$918$		0			0
$919$	1.90011	+	5.84793i	0.0626788	+	0.192905i	0.977492	−	0.210971i	$-0.0676626\pi$
$919$	1.90011	+	5.84793i	0.0626788	+	0.192905i	−0.914814	+	0.403876i	$0.867663\pi$
$920$	−0.397568	+	10.5999i	−0.0131074	+	0.349468i
$921$		0			0
$922$	30.1917	+	38.7428i	0.994311	+	1.27593i
$923$	11.1435	+	1.76496i	0.366794	+	0.0580945i
$924$		0			0
$925$	7.60084	+	38.6291i	0.249914	+	1.27012i
$926$	−2.42187	+	0.467639i	−0.0795876	+	0.0153676i
$927$		0			0
$928$	−5.32820	+	36.2740i	−0.174907	+	1.19075i
$929$	−20.9750	−	6.81520i	−0.688168	−	0.223599i	−0.0560003	−	0.998431i	$-0.517835\pi$
$929$	−20.9750	−	6.81520i	−0.688168	−	0.223599i	−0.632168	+	0.774831i	$0.717835\pi$
$930$		0			0
$931$	20.5530	−	6.67806i	0.673596	−	0.218865i
$932$	15.2850	+	6.53300i	0.500676	+	0.213996i
$933$		0			0
$934$	21.1118	−	45.1278i	0.690800	−	1.47663i
$935$	7.31462	−	1.29843i	0.239214	−	0.0424631i
$936$		0			0
$937$	−1.61961	−	10.2258i	−0.0529102	−	0.334062i	−0.999917	−	0.0128498i	$-0.995910\pi$
$937$	−1.61961	−	10.2258i	−0.0529102	−	0.334062i	0.947007	−	0.321212i	$-0.104090\pi$
$938$	5.30888	+	14.6427i	0.173341	+	0.478100i
$939$		0			0
$940$	−24.3631	−	39.1055i	−0.794635	−	1.27548i
$941$	1.46640	+	1.06540i	0.0478034	+	0.0347312i	0.611430	−	0.791298i	$-0.290594\pi$
$941$	1.46640	+	1.06540i	0.0478034	+	0.0347312i	−0.563627	+	0.826029i	$0.690594\pi$
$942$		0			0
$943$	3.78655	+	3.78655i	0.123307	+	0.123307i
$944$	12.9189	+	6.95177i	0.420475	+	0.226261i
$945$		0			0
$946$	−12.0003	−	1.48860i	−0.390164	−	0.0483987i
$947$	11.7110	+	22.9842i	0.380557	+	0.746885i	0.999249	−	0.0387487i	$-0.0123372\pi$
$947$	11.7110	+	22.9842i	0.380557	+	0.746885i	−0.618692	+	0.785633i	$0.712337\pi$
$948$		0			0
$949$		−	52.4330i		−	1.70205i
$950$	32.7424	−	13.2689i	1.06230	−	0.430499i
$951$		0			0
$952$	14.3864	−	6.34105i	0.466267	−	0.205515i
$953$	−10.9366	−	21.4643i	−0.354271	−	0.695296i	0.643251	−	0.765656i	$-0.277585\pi$
$953$	−10.9366	−	21.4643i	−0.354271	−	0.695296i	−0.997522	+	0.0703598i	$0.977585\pi$
$954$		0			0
$955$	10.7975	−	15.4582i	0.349400	−	0.500217i
$956$	17.0722	−	14.2530i	0.552153	−	0.460976i
$957$		0			0
$958$	−38.4047	−	11.0641i	−1.24080	−	0.357464i
$959$	−19.1133	−	13.8866i	−0.617202	−	0.448423i
$960$		0			0
$961$	−12.8575	+	9.34152i	−0.414758	+	0.301339i
$962$	−38.8646	+	14.0908i	−1.25304	+	0.454307i
$963$		0			0
$964$	−1.85101	−	1.16305i	−0.0596170	−	0.0374593i
$965$	−21.0965	+	21.8963i	−0.679121	+	0.704868i
$966$		0			0
$967$	23.2179	+	11.8301i	0.746638	+	0.380431i	0.785539	−	0.618812i	$-0.212386\pi$
$967$	23.2179	+	11.8301i	0.746638	+	0.380431i	−0.0389013	+	0.999243i	$0.512386\pi$
$968$	−27.7671	−	6.01044i	−0.892468	−	0.193183i
$969$		0			0
$970$	21.9469	+	38.0215i	0.704672	+	1.22080i
$971$	5.43069	+	1.76454i	0.174279	+	0.0566268i	0.394857	−	0.918743i	$-0.370794\pi$
$971$	5.43069	+	1.76454i	0.174279	+	0.0566268i	−0.220578	+	0.975369i	$0.570794\pi$
$972$		0			0
$973$	−5.88623	+	37.1642i	−0.188704	+	1.19143i
$974$	−5.54300	−	28.7068i	−0.177609	−	0.919826i
$975$		0			0
$976$	−12.4415	+	11.8956i	−0.398243	+	0.380769i
$977$	13.2231	+	2.09434i	0.423045	+	0.0670038i	0.364328	−	0.931271i	$-0.381299\pi$
$977$	13.2231	+	2.09434i	0.423045	+	0.0670038i	0.0587177	+	0.998275i	$0.481299\pi$
$978$		0			0
$979$	0.857724	−	2.63980i	0.0274130	−	0.0843684i
$980$	1.66011	+	19.2723i	0.0530302	+	0.615631i
$981$		0			0
$982$	−17.8145	−	12.0483i	−0.568485	−	0.384477i
$983$	−7.50817	+	14.7356i	−0.239473	+	0.469993i	−0.979195	−	0.202920i	$-0.934957\pi$
$983$	−7.50817	+	14.7356i	−0.239473	+	0.469993i	0.739722	+	0.672913i	$0.234957\pi$
$984$		0			0
$985$	15.1032	−	8.05279i	0.481229	−	0.256583i
$986$	−22.7574	−	21.2746i	−0.724745	−	0.677523i
$987$		0			0
$988$	19.0272	+	31.8457i	0.605335	+	1.01315i
$989$	8.62333	+	11.8690i	0.274206	+	0.377412i
$990$		0			0
$991$	−17.3344	+	23.8587i	−0.550644	+	0.757896i	−0.990099	−	0.140368i	$-0.955171\pi$
$991$	−17.3344	+	23.8587i	−0.550644	+	0.757896i	0.439455	+	0.898264i	$0.355171\pi$
$992$	10.2014	+	19.4773i	0.323895	+	0.618404i
$993$		0			0
$994$	3.40002	+	6.15183i	0.107842	+	0.195124i
$995$	−31.0066	+	0.576836i	−0.982976	+	0.0182869i
$996$		0			0
$997$	30.7633	−	15.6747i	0.974284	−	0.496423i	0.107013	−	0.994258i	$-0.465872\pi$
$997$	30.7633	−	15.6747i	0.974284	−	0.496423i	0.867272	+	0.497835i	$0.165872\pi$
$998$	−0.578463	−	17.1774i	−0.0183109	−	0.543743i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.bj.f.127.16		240
3.2	odd	2		300.2.w.a.127.15	yes	240
4.3	odd	2	inner	900.2.bj.f.127.18		240
12.11	even	2		300.2.w.a.127.13	✓	240
25.13	odd	20	inner	900.2.bj.f.163.18		240
75.38	even	20		300.2.w.a.163.13	yes	240
100.63	even	20	inner	900.2.bj.f.163.16		240
300.263	odd	20		300.2.w.a.163.15	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.127.13	✓	240	12.11	even	2
300.2.w.a.127.15	yes	240	3.2	odd	2
300.2.w.a.163.13	yes	240	75.38	even	20
300.2.w.a.163.15	yes	240	300.263	odd	20
900.2.bj.f.127.16		240	1.1	even	1	trivial
900.2.bj.f.127.18		240	4.3	odd	2	inner
900.2.bj.f.163.16		240	100.63	even	20	inner
900.2.bj.f.163.18		240	25.13	odd	20	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0475977 + 1.41341i) q^{2} +(-1.99547 + 0.134550i) q^{4} +(-2.23568 + 0.0415918i) q^{5} +(1.15642 - 1.15642i) q^{7} +(-0.285155 - 2.81402i) q^{8} +O(q^{10})\)	\(q+(0.0475977 + 1.41341i) q^{2} +(-1.99547 + 0.134550i) q^{4} +(-2.23568 + 0.0415918i) q^{5} +(1.15642 - 1.15642i) q^{7} +(-0.285155 - 2.81402i) q^{8} +(-0.165200 - 3.15796i) q^{10} +(0.574557 + 0.790810i) q^{11} +(3.66677 - 0.580759i) q^{13} +(1.68954 + 1.57946i) q^{14} +(3.96379 - 0.536982i) q^{16} +(-1.54304 + 3.02838i) q^{17} +(-1.54393 - 4.75171i) q^{19} +(4.45564 - 0.383807i) q^{20} +(-1.09039 + 0.849726i) q^{22} +(1.65652 + 0.262367i) q^{23} +(4.99654 - 0.185972i) q^{25} +(0.995382 + 5.15501i) q^{26} +(-2.15201 + 2.46320i) q^{28} +(6.16400 + 2.00281i) q^{29} +(3.69657 - 1.20109i) q^{31} +(0.947644 + 5.57691i) q^{32} +(-4.35379 - 2.03680i) q^{34} +(-2.53729 + 2.63349i) q^{35} +(1.23176 + 7.77702i) q^{37} +(6.64264 - 2.40837i) q^{38} +(0.754555 + 6.27938i) q^{40} +(2.58309 + 1.87673i) q^{41} +(6.18535 + 6.18535i) q^{43} +(-1.25291 - 1.50073i) q^{44} +(-0.291986 + 2.35384i) q^{46} +(-4.67720 - 9.17952i) q^{47} +4.32538i q^{49} +(0.500679 + 7.05332i) q^{50} +(-7.23878 + 1.65225i) q^{52} +(0.989011 + 1.94104i) q^{53} +(-1.31742 - 1.74410i) q^{55} +(-3.58395 - 2.92443i) q^{56} +(-2.53740 + 8.80760i) q^{58} +(2.96719 + 2.15579i) q^{59} +(-3.48146 + 2.52943i) q^{61} +(1.87358 + 5.16761i) q^{62} +(-7.83737 + 1.60486i) q^{64} +(-8.17357 + 1.45090i) q^{65} +(6.00029 + 3.05730i) q^{67} +(2.67161 - 6.25065i) q^{68} +(-3.84297 - 3.46089i) q^{70} +(2.89032 + 0.939123i) q^{71} +(2.20940 - 13.9496i) q^{73} +(-10.9335 + 2.11115i) q^{74} +(3.72020 + 9.27416i) q^{76} +(1.57894 + 0.250079i) q^{77} +(0.430746 - 1.32570i) q^{79} +(-8.83944 + 1.36538i) q^{80} +(-2.52964 + 3.74030i) q^{82} +(7.43080 - 14.5838i) q^{83} +(3.32378 - 6.83466i) q^{85} +(-8.44804 + 9.03686i) q^{86} +(2.06151 - 1.84231i) q^{88} +(-1.66905 - 2.29725i) q^{89} +(3.56873 - 4.91193i) q^{91} +(-3.34084 - 0.300660i) q^{92} +(12.7518 - 7.04774i) q^{94} +(3.64936 + 10.5591i) q^{95} +(-12.3696 + 6.30263i) q^{97} +(-6.11354 + 0.205878i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{8}+O(q^{10}) \) 240 * q - 12 * q^8	\( 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58} + 44 q^{62} - 60 q^{64} + 20 q^{65} - 16 q^{68} - 44 q^{70} - 44 q^{73} + 48 q^{77} + 4 q^{80} + 24 q^{82} - 64 q^{85} + 60 q^{88} + 260 q^{89} - 144 q^{92} + 40 q^{94} - 180 q^{97} - 256 q^{98}+O(q^{100}) \) 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

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