LMFDB - Embedded newform 900.2.bj.f.127.18

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			127.18
Character	$\chi$	$=$	900.127
Dual form			900.2.bj.f.163.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.482036 - 1.32953i) q^{2} +(-1.53528 - 1.28176i) q^{4} +(-2.23568 + 0.0415918i) q^{5} +(-1.15642 + 1.15642i) q^{7} +(-2.44420 + 1.42334i) q^{8} +O(q^{10})$	\(q+(0.482036 - 1.32953i) q^{2} +(-1.53528 - 1.28176i) q^{4} +(-2.23568 + 0.0415918i) q^{5} +(-1.15642 + 1.15642i) q^{7} +(-2.44420 + 1.42334i) q^{8} +(-1.02238 + 2.99245i) q^{10} +(-0.574557 - 0.790810i) q^{11} +(3.66677 - 0.580759i) q^{13} +(0.980056 + 2.09493i) q^{14} +(0.714179 + 3.93573i) q^{16} +(-1.54304 + 3.02838i) q^{17} +(1.54393 + 4.75171i) q^{19} +(3.48571 + 2.80175i) q^{20} +(-1.32836 + 0.382689i) q^{22} +(-1.65652 - 0.262367i) q^{23} +(4.99654 - 0.185972i) q^{25} +(0.995382 - 5.15501i) q^{26} +(3.25769 - 0.293177i) q^{28} +(6.16400 + 2.00281i) q^{29} +(-3.69657 + 1.20109i) q^{31} +(5.57691 + 0.947644i) q^{32} +(3.28251 + 3.51129i) q^{34} +(2.53729 - 2.63349i) q^{35} +(1.23176 + 7.77702i) q^{37} +(7.06176 + 0.237810i) q^{38} +(5.40524 - 3.28380i) q^{40} +(2.58309 + 1.87673i) q^{41} +(-6.18535 - 6.18535i) q^{43} +(-0.131522 + 1.95056i) q^{44} +(-1.14733 + 2.07592i) q^{46} +(4.67720 + 9.17952i) q^{47} +4.32538i q^{49} +(2.16126 - 6.73268i) q^{50} +(-6.37392 - 3.80829i) q^{52} +(0.989011 + 1.94104i) q^{53} +(1.31742 + 1.74410i) q^{55} +(1.18054 - 4.47250i) q^{56} +(5.63406 - 7.22978i) q^{58} +(-2.96719 - 2.15579i) q^{59} +(-3.48146 + 2.52943i) q^{61} +(-0.185003 + 5.49366i) q^{62} +(3.94819 - 6.95786i) q^{64} +(-8.17357 + 1.45090i) q^{65} +(-6.00029 - 3.05730i) q^{67} +(6.25065 - 2.67161i) q^{68} +(-2.27822 - 4.64283i) q^{70} +(-2.89032 - 0.939123i) q^{71} +(2.20940 - 13.9496i) q^{73} +(10.9335 + 2.11115i) q^{74} +(3.72020 - 9.27416i) q^{76} +(1.57894 + 0.250079i) q^{77} +(-0.430746 + 1.32570i) q^{79} +(-1.76037 - 8.76933i) q^{80} +(3.74030 - 2.52964i) q^{82} +(-7.43080 + 14.5838i) q^{83} +(3.32378 - 6.83466i) q^{85} +(-11.2052 + 5.24202i) q^{86} +(2.52992 + 1.11510i) q^{88} +(-1.66905 - 2.29725i) q^{89} +(-3.56873 + 4.91193i) q^{91} +(2.20693 + 2.52607i) q^{92} +(14.4590 - 1.79360i) q^{94} +(-3.64936 - 10.5591i) q^{95} +(-12.3696 + 6.30263i) q^{97} +(5.75071 + 2.08499i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.482036	−	1.32953i	0.340851	−	0.940117i
$2$	0.482036	−	1.32953i	0.340851	−	0.940117i
$3$		0			0
$3$		0			0
$4$	−1.53528	−	1.28176i	−0.767641	−	0.640880i
$5$	−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	−0.891030	−	0.453944i	$-0.850017\pi$
$7$	−1.15642	+	1.15642i	−0.437086	+	0.437086i	0.453944	+	0.891030i	$0.350017\pi$
$8$	−2.44420	+	1.42334i	−0.864154	+	0.503227i
$9$		0			0
$10$	−1.02238	+	2.99245i	−0.323306	+	0.946295i
$11$	−0.574557	−	0.790810i	−0.173235	−	0.238438i	0.713567	−	0.700587i	$-0.247078\pi$
$11$	−0.574557	−	0.790810i	−0.173235	−	0.238438i	−0.886802	+	0.462149i	$0.847078\pi$
$12$		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	$0.277856\pi$
$14$	0.980056	+	2.09493i	0.261931	+	0.559894i
$15$		0			0
$16$	0.714179	+	3.93573i	0.178545	+	0.983932i
$17$	−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	$0.0942628\pi$
$19$	1.54393	+	4.75171i	0.354201	+	1.09012i	−0.602271	+	0.798292i	$0.705737\pi$
$20$	3.48571	+	2.80175i	0.779429	+	0.626491i
$21$		0			0
$22$	−1.32836	+	0.382689i	−0.283207	+	0.0815897i
$23$	−1.65652	−	0.262367i	−0.345409	−	0.0547073i	−0.0186799	−	0.999826i	$-0.505946\pi$
$23$	−1.65652	−	0.262367i	−0.345409	−	0.0547073i	−0.326729	+	0.945118i	$0.605946\pi$
$24$		0			0
$25$	4.99654	−	0.185972i	0.999308	−	0.0371944i
$26$	0.995382	−	5.15501i	0.195210	−	1.01098i
$27$		0			0
$28$	3.25769	−	0.293177i	0.615645	−	0.0554053i
$29$	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	−0.621544	−	0.783380i	$-0.713494\pi$
$31$	−3.69657	+	1.20109i	−0.663924	+	0.215722i	−0.0423804	+	0.999102i	$0.513494\pi$
$32$	5.57691	+	0.947644i	0.985868	+	0.167521i
$33$		0			0
$34$	3.28251	+	3.51129i	0.562946	+	0.602182i
$35$	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	$0.725925\pi$
$38$	7.06176	+	0.237810i	1.14557	+	0.0385778i
$39$		0			0
$40$	5.40524	−	3.28380i	0.854644	−	0.519214i
$41$	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	0.0552173	−	0.998474i	$-0.482415\pi$
$43$	−6.18535	−	6.18535i	−0.943257	−	0.943257i	−0.998474	+	0.0552173i	$0.982415\pi$
$44$	−0.131522	+	1.95056i	−0.0198277	+	0.294058i
$45$		0			0
$46$	−1.14733	+	2.07592i	−0.169164	+	0.306077i
$47$	4.67720	+	9.17952i	0.682240	+	1.33897i	0.929067	+	0.369911i	$0.120612\pi$
$47$	4.67720	+	9.17952i	0.682240	+	1.33897i	−0.246827	+	0.969059i	$0.579388\pi$
$48$		0			0
$49$			4.32538i			0.617911i
$50$	2.16126	−	6.73268i	0.305648	−	0.952144i
$51$		0			0
$52$	−6.37392	−	3.80829i	−0.883903	−	0.528115i
$53$	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
$56$	1.18054	−	4.47250i	0.157756	−	0.597664i
$57$		0			0
$58$	5.63406	−	7.22978i	0.739788	−	0.949316i
$59$	−2.96719	−	2.15579i	−0.386295	−	0.280659i	0.377641	−	0.925952i	$-0.376735\pi$
$59$	−2.96719	−	2.15579i	−0.386295	−	0.280659i	−0.763935	+	0.645293i	$0.776735\pi$
$60$		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	$0.388841\pi$
$62$	−0.185003	+	5.49366i	−0.0234954	+	0.697695i
$63$		0			0
$64$	3.94819	−	6.95786i	0.493524	−	0.869732i
$65$	−8.17357	+	1.45090i	−1.01381	+	0.179962i
$66$		0			0
$67$	−6.00029	−	3.05730i	−0.733052	−	0.373509i	0.0472734	−	0.998882i	$-0.484947\pi$
$67$	−6.00029	−	3.05730i	−0.733052	−	0.373509i	−0.780326	+	0.625373i	$0.784947\pi$
$68$	6.25065	−	2.67161i	0.758002	−	0.323980i
$69$		0			0
$70$	−2.27822	−	4.64283i	−0.272300	−	0.554925i
$71$	−2.89032	−	0.939123i	−0.343018	−	0.111453i	0.132442	−	0.991191i	$-0.457718\pi$
$71$	−2.89032	−	0.939123i	−0.343018	−	0.111453i	−0.475460	+	0.879737i	$0.657718\pi$
$72$		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	−0.972359	−	0.233489i	$-0.924986\pi$
$79$	−0.430746	+	1.32570i	−0.0484628	+	0.149153i	0.923897	+	0.382642i	$0.124986\pi$
$80$	−1.76037	−	8.76933i	−0.196816	−	0.980441i
$81$		0			0
$82$	3.74030	−	2.52964i	0.413047	−	0.279352i
$83$	−7.43080	+	14.5838i	−0.815636	+	1.60078i	−0.0163181	+	0.999867i	$0.505194\pi$
$83$	−7.43080	+	14.5838i	−0.815636	+	1.60078i	−0.799318	+	0.600909i	$0.794806\pi$
$84$		0			0
$85$	3.32378	−	6.83466i	0.360514	−	0.741323i
$86$	−11.2052	+	5.24202i	−1.20828	+	0.565262i
$87$		0			0
$88$	2.52992	+	1.11510i	0.269691	+	0.118870i
$89$	−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
$92$	2.20693	+	2.52607i	0.230089	+	0.263361i
$93$		0			0
$94$	14.4590	−	1.79360i	1.49133	−	0.184995i
$95$	−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	$0.598958\pi$
$98$	5.75071	+	2.08499i	0.580909	+	0.210616i
$99$		0			0
$100$	−7.90947	−	6.11885i	−0.790947	−	0.611885i
$101$	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	−0.883025	−	0.469327i	$-0.844497\pi$
$103$	−10.3758	+	5.28675i	−1.02236	+	0.520919i	−0.139336	+	0.990245i	$0.544497\pi$
$104$	−8.13569	+	6.63856i	−0.797770	+	0.650964i
$105$		0			0
$106$	3.05741	−	0.379263i	0.296962	−	0.0368372i
$107$	−10.7876	+	10.7876i	−1.04287	+	1.04287i	−0.0438342	+	0.999039i	$0.513957\pi$
$107$	−10.7876	+	10.7876i	−1.04287	+	1.04287i	−0.999039	+	0.0438342i	$0.986043\pi$
$108$		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	$0.888898\pi$
$110$	2.95387	−	0.910820i	0.281641	−	0.0868433i
$111$		0			0
$112$	−5.37725	−	3.72547i	−0.508103	−	0.352024i
$113$	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
$116$	−6.89636	−	10.9756i	−0.640311	−	1.01906i
$117$		0			0
$118$	−4.29647	+	2.90578i	−0.395522	+	0.267499i
$119$	−1.71768	−	5.28648i	−0.157460	−	0.484611i
$120$		0			0
$121$	3.10392	−	9.55289i	0.282175	−	0.868445i
$122$	1.68475	+	5.84797i	0.152530	+	0.529450i
$123$		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	$0.271061\pi$
$127$	−2.25651	+	14.2470i	−0.200233	+	1.26422i	−0.859040	+	0.511908i	$0.828939\pi$
$128$	−7.34748	−	8.60317i	−0.649432	−	0.760420i
$129$		0			0
$130$	−2.01095	+	11.5664i	−0.176372	+	1.01444i
$131$	15.8689	−	5.15611i	1.38647	−	0.450491i	0.481679	−	0.876348i	$-0.340027\pi$
$131$	15.8689	−	5.15611i	1.38647	−	0.450491i	0.904791	+	0.425857i	$0.140027\pi$
$132$		0			0
$133$	−7.28041	−	3.70956i	−0.631292	−	0.321659i
$134$	−6.95712	+	6.50382i	−0.601004	+	0.561844i
$135$		0			0
$136$	−0.538936	−	9.59822i	−0.0462134	−	0.823040i
$137$	−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	$-0.270251\pi$
$139$	18.6136	−	13.5236i	1.57879	−	1.14706i	0.918067	−	0.396425i	$-0.129749\pi$
$140$	−7.27096	+	0.790944i	−0.614508	+	0.0668469i
$141$		0			0
$142$	−2.64183	+	3.39007i	−0.221697	+	0.284488i
$143$	−2.56604	−	2.56604i	−0.214583	−	0.214583i
$144$		0			0
$145$	−13.8640	−	4.22126i	−1.15135	−	0.350557i
$146$	−17.4813	−	9.66166i	−1.44677	−	0.799605i
$147$		0			0
$148$	8.07718	−	13.5187i	0.663940	−	1.11123i
$149$		−	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	$-0.975228\pi$
$151$		−	1.91070i		−	0.155490i	0.996973	−	0.0777451i	$-0.0247720\pi$
$152$	−10.5370	−	9.41659i	−0.854661	−	0.763786i
$153$		0			0
$154$	1.09359	−	1.97869i	0.0881243	−	0.159448i
$155$	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	$0.421845\pi$
$158$	1.55492	+	1.21173i	0.123703	+	0.0963997i
$159$		0			0
$160$	−12.5076	−	1.88668i	−0.988814	−	0.149155i
$161$	2.21904	−	1.61223i	0.174885	−	0.127061i
$162$		0			0
$163$	2.32827	+	14.7001i	0.182364	+	1.15140i	0.893738	+	0.448589i	$0.148073\pi$
$163$	2.32827	+	14.7001i	0.182364	+	1.15140i	−0.711374	+	0.702814i	$0.751927\pi$
$164$	−1.56026	−	6.19221i	−0.121836	−	0.483530i
$165$		0			0
$166$	15.8076	+	16.9093i	1.22691	+	1.31242i
$167$	−13.6609	−	6.96060i	−1.05712	−	0.538627i	−0.163075	−	0.986614i	$-0.552141\pi$
$167$	−13.6609	−	6.96060i	−1.05712	−	0.538627i	−0.894040	+	0.447986i	$0.852141\pi$
$168$		0			0
$169$	0.744179	−	0.241798i	0.0572445	−	0.0185999i
$170$	−7.48468	−	7.71361i	−0.574049	−	0.591607i
$171$		0			0
$172$	1.56812	+	17.4244i	0.119568	+	1.32860i
$173$	−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
$178$	−3.85880	+	1.11169i	−0.289229	+	0.0833246i
$179$	2.12634	−	6.54421i	0.158930	−	0.489137i	−0.839608	−	0.543193i	$-0.817215\pi$
$179$	2.12634	−	6.54421i	0.158930	−	0.489137i	0.998538	+	0.0540563i	$0.0172150\pi$
$180$		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	$0.860633\pi$
$182$	4.81029	+	7.11245i	0.356562	+	0.527210i
$183$		0			0
$184$	4.42230	−	1.71652i	0.326016	−	0.126544i
$185$	−3.07728	−	17.3357i	−0.226246	−	1.27455i
$186$		0			0
$187$	3.28143	−	0.519728i	0.239962	−	0.0380062i
$188$	4.58513	−	20.0882i	0.334405	−	1.46508i
$189$		0			0
$190$	−15.7977	−	0.237955i	−1.14609	−	0.0172631i
$191$	4.95656	−	6.82212i	0.358644	−	0.493631i	−0.591126	−	0.806579i	$-0.701317\pi$
$191$	4.95656	−	6.82212i	0.358644	−	0.493631i	0.949770	+	0.312948i	$0.101317\pi$
$192$		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	$0.0872163\pi$
$194$	2.41691	+	19.4838i	0.173524	+	1.39886i
$195$		0			0
$196$	5.54410	−	6.64067i	0.396007	−	0.474334i
$197$	−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	$-0.663578\pi$
$199$	−13.8690			−0.983146			−0.491573	+	0.870836i	$0.663578\pi$
$200$	−11.9478	+	7.56634i	−0.844839	+	0.535021i
$201$		0			0
$202$	6.20399	−	17.1115i	0.436511	−	1.20396i
$203$	−9.44427	+	4.81210i	−0.662858	+	0.337743i
$204$		0			0
$205$	−5.85303	−	4.08833i	−0.408793	−	0.285541i
$206$	2.02734	+	16.3433i	0.141252	+	1.13869i
$207$		0			0
$208$	4.90444	+	14.0166i	0.340062	+	0.971879i
$209$	2.87063	−	3.95108i	0.198566	−	0.273302i
$210$		0			0
$211$	−5.56295	−	7.65675i	−0.382970	−	0.527112i	0.573399	−	0.819277i	$-0.305625\pi$
$211$	−5.56295	−	7.65675i	−0.382970	−	0.527112i	−0.956368	+	0.292164i	$0.905625\pi$
$212$	0.969542	−	4.24772i	0.0665884	−	0.291735i
$213$		0			0
$214$	9.14235	+	19.5423i	0.624958	+	1.33589i
$215$	14.0857	+	13.5712i	0.960639	+	0.925549i
$216$		0			0
$217$	2.88583	−	5.66376i	0.195903	−	0.384481i
$218$	13.7147	+	20.2784i	0.928875	+	1.37343i
$219$		0			0
$220$	0.212914	−	4.36630i	0.0143547	−	0.294376i
$221$	−3.89920	+	12.0005i	−0.262288	+	0.807240i
$222$		0			0
$223$	−2.66635	−	0.422309i	−0.178552	−	0.0282799i	0.0665180	−	0.997785i	$-0.478811\pi$
$223$	−2.66635	−	0.422309i	−0.178552	−	0.0282799i	−0.245070	+	0.969505i	$0.578811\pi$
$224$	−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	$0.177890\pi$
$227$	−1.84338	+	11.6386i	−0.122349	+	0.772482i	−0.970210	+	0.242264i	$0.922110\pi$
$228$		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	$0.556735\pi$
$230$	2.47872	−	4.68881i	0.163442	−	0.309171i
$231$		0			0
$232$	−17.9167	+	3.87823i	−1.17629	+	0.254618i
$233$	−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
$236$	1.79226	+	7.11296i	0.116666	+	0.463014i
$237$		0			0
$238$	−7.85650	−	0.264573i	−0.509261	−	0.0171497i
$239$	8.99618	−	6.53610i	0.581914	−	0.422785i	−0.257499	−	0.966278i	$-0.582899\pi$
$239$	8.99618	−	6.53610i	0.581914	−	0.422785i	0.839414	+	0.543493i	$0.182899\pi$
$240$		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	$0.688792\pi$
$242$	−11.2046	−	8.73159i	−0.720260	−	0.561288i
$243$		0			0
$244$	8.58714	+	0.579013i	0.549735	+	0.0370675i
$245$	−0.179900	−	9.67017i	−0.0114934	−	0.617804i
$246$		0			0
$247$	8.42082	+	16.5268i	0.535804	+	1.05157i
$248$	7.32559	−	8.19719i	0.465175	−	0.520522i
$249$		0			0
$250$	−4.55186	+	15.1420i	−0.287885	+	0.957665i
$251$			27.5973i			1.74193i	0.491348	+	0.870964i	$0.336504\pi$
$251$			27.5973i			1.74193i	−0.491348	+	0.870964i	$0.663496\pi$
$252$		0			0
$253$	0.744283	+	1.46074i	0.0467927	+	0.0918358i
$254$	17.8541	+	9.86768i	1.12027	+	0.619153i
$255$		0			0
$256$	−14.9799	+	5.62163i	−0.936243	+	0.351352i
$257$	−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
$260$	14.4084	+	8.24902i	0.893574	+	0.511583i
$261$		0			0
$262$	0.794191	−	23.5835i	0.0490653	−	1.45699i
$263$	−2.64700	−	16.7125i	−0.163221	−	1.03054i	−0.924241	−	0.381810i	$-0.875301\pi$
$263$	−2.64700	−	16.7125i	−0.163221	−	1.03054i	0.761020	−	0.648729i	$-0.224699\pi$
$264$		0			0
$265$	−2.29184	−	4.29842i	−0.140787	−	0.264050i
$266$	−8.44138	+	7.89136i	−0.517574	+	0.483850i
$267$		0			0
$268$	5.29341	+	12.3848i	0.323347	+	0.756520i
$269$	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	0.972846	−	0.231451i	$-0.0743474\pi$
$271$	26.7320	+	8.68575i	1.62385	+	0.527622i	0.651006	+	0.759073i	$0.274347\pi$
$272$	−13.0209	−	3.91016i	−0.789506	−	0.237088i
$273$		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	$0.846505\pi$
$278$	−9.00753	−	31.2662i	−0.540236	−	1.87522i
$279$		0			0
$280$	−2.45329	+	10.0482i	−0.146612	+	0.600495i
$281$	−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	$-0.682937\pi$
$283$	7.65378	−	15.0214i	0.454970	−	0.892929i	0.998564	−	0.0535804i	$-0.0170633\pi$
$284$	3.23373	+	5.14652i	0.191886	+	0.305390i
$285$		0			0
$286$	−4.64854	+	2.17469i	−0.274874	+	0.128592i
$287$	−5.15743	+	0.816856i	−0.304433	+	0.0482175i
$288$		0			0
$289$	3.20224	+	4.40750i	0.188367	+	0.259265i
$290$	−12.2953	+	16.3978i	−0.722002	+	0.962912i
$291$		0			0
$292$	−21.2721	+	18.5846i	−1.24485	+	1.08758i
$293$	−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
$296$	−14.0800	−	17.2554i	−0.818385	−	1.00295i
$297$		0			0
$298$	−5.63425	−	2.04277i	−0.326383	−	0.118334i
$299$	−6.22645			−0.360085
$300$		0			0
$301$	14.3057			0.824569
$302$	−2.54032	−	0.921025i	−0.146179	−	0.0529990i
$303$		0			0
$304$	−17.5988	+	9.47005i	−1.00936	+	0.543144i
$305$	7.67823	−	5.79979i	0.439654	−	0.332095i
$306$		0			0
$307$	1.88086	−	1.88086i	0.107346	−	0.107346i	−0.651394	−	0.758740i	$-0.725815\pi$
$307$	1.88086	−	1.88086i	0.107346	−	0.107346i	0.758740	+	0.651394i	$0.225815\pi$
$308$	−2.10357	−	2.40776i	−0.119862	−	0.137195i
$309$		0			0
$310$	0.185116	−	12.2898i	0.0105139	−	0.698012i
$311$	7.58700	+	10.4426i	0.430219	+	0.592146i	0.968004	−	0.250937i	$-0.0807386\pi$
$311$	7.58700	+	10.4426i	0.430219	+	0.592146i	−0.537784	+	0.843082i	$0.680739\pi$
$312$		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	$0.373440\pi$
$314$	27.5355	−	12.8817i	1.55392	−	0.726957i
$315$		0			0
$316$	2.36055	−	1.48321i	0.132791	−	0.0834371i
$317$	−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
$320$	−8.53751	+	15.7198i	−0.477261	+	0.878761i
$321$		0			0
$322$	−1.07384	−	3.72743i	−0.0598429	−	0.207722i
$323$	−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
$328$	−8.98481	−	0.910464i	−0.496103	−	0.0502719i
$329$	−16.0242	−	5.20658i	−0.883443	−	0.287048i
$330$		0			0
$331$	28.4519	−	9.24458i	1.56386	−	0.508128i	0.606022	−	0.795448i	$-0.292764\pi$
$331$	28.4519	−	9.24458i	1.56386	−	0.508128i	0.957835	+	0.287320i	$0.0927642\pi$
$332$	30.1013	−	12.8657i	1.65202	−	0.706096i
$333$		0			0
$334$	−15.8394	+	14.8073i	−0.866692	+	0.810221i
$335$	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	$-0.144161\pi$
$338$	0.0372440	−	1.10596i	0.00202581	−	0.0601564i
$339$		0			0
$340$	−13.8633	+	6.23284i	−0.751845	+	0.338023i
$341$	3.07372	+	2.23319i	0.166451	+	0.120934i
$342$		0			0
$343$	−13.0969	−	13.0969i	−0.707167	−	0.707167i
$344$	23.9221	+	6.31434i	1.28979	+	0.340446i
$345$		0			0
$346$	24.9449	+	13.7866i	1.34104	+	0.741174i
$347$	6.08901	+	11.9504i	0.326875	+	0.641529i	0.994703	−	0.102786i	$-0.0327758\pi$
$347$	6.08901	+	11.9504i	0.326875	+	0.641529i	−0.667828	+	0.744316i	$0.732776\pi$
$348$		0			0
$349$			11.8463i			0.634116i	0.948406	+	0.317058i	$0.102695\pi$
$349$			11.8463i			0.634116i	−0.948406	+	0.317058i	$0.897305\pi$
$350$	5.28649	+	10.2851i	0.282575	+	0.549764i
$351$		0			0
$352$	−2.45485	−	4.95475i	−0.130844	−	0.264089i
$353$	−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
$356$	−0.382063	+	5.66625i	−0.0202493	+	0.300311i
$357$		0			0
$358$	−7.67572	−	5.98158i	−0.405675	−	0.316136i
$359$	−0.764560	−	0.555486i	−0.0403520	−	0.0293174i	0.567426	−	0.823424i	$-0.307939\pi$
$359$	−0.764560	−	0.555486i	−0.0403520	−	0.0293174i	−0.607778	+	0.794107i	$0.707939\pi$
$360$		0			0
$361$	−4.82376	+	3.50467i	−0.253882	+	0.184456i
$362$	4.69149	+	0.157989i	0.246579	+	0.00830374i
$363$		0			0
$364$	11.7749	−	2.96694i	0.617174	−	0.155510i
$365$	−4.35932	+	31.2787i	−0.228177	+	1.63720i
$366$		0			0
$367$	3.97266	+	2.02417i	0.207371	+	0.105661i	0.554592	−	0.832123i	$-0.312875\pi$
$367$	3.97266	+	2.02417i	0.207371	+	0.105661i	−0.347221	+	0.937783i	$0.612875\pi$
$368$	−0.150448	−	6.70699i	−0.00784262	−	0.349626i
$369$		0			0
$370$	−24.5316	−	4.26512i	−1.27534	−	0.221733i
$371$	−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	−0.925034	−	0.379884i	$-0.875964\pi$
$379$	0.907685	−	2.79357i	0.0466246	−	0.143496i	0.971659	+	0.236388i	$0.0759638\pi$
$380$	−7.93145	+	20.8888i	−0.406875	+	1.07157i
$381$		0			0
$382$	−6.68094	−	9.87838i	−0.341827	−	0.505422i
$383$	11.7564	−	23.0732i	0.600723	−	1.17898i	−0.367764	−	0.929919i	$-0.619876\pi$
$383$	11.7564	−	23.0732i	0.600723	−	1.17898i	0.968487	−	0.249066i	$-0.0801235\pi$
$384$		0			0
$385$	−3.54041	−	0.493427i	−0.180436	−	0.0251474i
$386$	−8.14875	−	17.4185i	−0.414760	−	0.886576i
$387$		0			0
$388$	27.0693	+	6.17856i	1.37423	+	0.313669i
$389$	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
$392$	−6.15649	−	10.5721i	−0.310950	−	0.533970i
$393$		0			0
$394$	1.33260	+	10.7427i	0.0671356	+	0.541211i
$395$	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	$0.144788\pi$
$398$	−6.68535	+	18.4392i	−0.335106	+	0.924272i
$399$		0			0
$400$	4.30036	+	19.5322i	0.215018	+	0.976610i
$401$	−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
$404$	−19.7596	−	16.4967i	−0.983079	−	0.820743i
$405$		0			0
$406$	1.84533	+	14.8760i	0.0915820	+	0.738284i
$407$	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	$0.202731\pi$
$410$	−8.25691	+	5.81103i	−0.407780	+	0.286986i
$411$		0			0
$412$	22.7062	+	5.18268i	1.11865	+	0.255332i
$413$	5.92431	−	0.938319i	0.291516	−	0.0461717i
$414$		0			0
$415$	16.0063	−	32.9137i	0.785720	−	1.61567i
$416$	20.9996	+	0.235947i	1.02959	+	0.0115682i
$417$		0			0
$418$	−3.86932	−	5.72114i	−0.189255	−	0.279830i
$419$	−8.61814	−	26.5239i	−0.421024	−	1.29578i	−0.906751	−	0.421668i	$-0.861445\pi$
$419$	−8.61814	−	26.5239i	−0.421024	−	1.29578i	0.485727	−	0.874111i	$-0.338555\pi$
$420$		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	$-0.0255142\pi$
$422$	−12.8614	+	3.70526i	−0.626083	+	0.180369i
$423$		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
$428$	30.3890	−	2.73487i	1.46891	−	0.132195i
$429$		0			0
$430$	24.8331	−	12.1855i	1.19756	−	0.587639i
$431$	11.2786	−	3.66463i	0.543269	−	0.176519i	−0.0245103	−	0.999700i	$-0.507803\pi$
$431$	11.2786	−	3.66463i	0.543269	−	0.176519i	0.567779	+	0.823181i	$0.307803\pi$
$432$		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	$0.620080\pi$
$434$	−6.13904	−	6.56693i	−0.294684	−	0.315223i
$435$		0			0
$436$	33.5716	−	8.45909i	1.60779	−	0.405117i
$437$	−1.31085	−	8.27639i	−0.0627065	−	0.395913i
$438$		0			0
$439$	5.00770	−	3.63831i	0.239005	−	0.173647i	−0.461835	−	0.886966i	$-0.652809\pi$
$439$	5.00770	−	3.63831i	0.239005	−	0.173647i	0.700840	+	0.713319i	$0.252809\pi$
$440$	−5.70248	−	2.38779i	−0.271855	−	0.113833i
$441$		0			0
$442$	14.0754	+	10.9688i	0.669499	+	0.521731i
$443$	−4.96290	−	4.96290i	−0.235794	−	0.235794i	0.579312	−	0.815106i	$-0.303321\pi$
$443$	−4.96290	−	4.96290i	−0.235794	−	0.235794i	−0.815106	+	0.579312i	$0.803321\pi$
$444$		0			0
$445$	3.82701	+	5.06650i	0.181418	+	0.240175i
$446$	−1.84675	+	3.34142i	−0.0874461	+	0.158221i
$447$		0			0
$448$	3.48044	+	12.6120i	0.164435	+	0.595861i
$449$			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
$452$	−23.6642	−	14.1389i	−1.11307	−	0.665038i
$453$		0			0
$454$	14.5853	+	8.06106i	0.684521	+	0.378324i
$455$	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	$0.782542\pi$
$458$	3.56500	−	4.57470i	0.166581	−	0.213762i
$459$		0			0
$460$	−5.03907	−	5.55570i	−0.234948	−	0.259036i
$461$	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	0.980537	−	0.196336i	$-0.0629043\pi$
$463$	−0.272846	−	1.72268i	−0.0126802	−	0.0800597i	−0.993217	+	0.116276i	$0.962904\pi$
$464$	−3.48029	+	25.6902i	−0.161569	+	1.19264i
$465$		0			0
$466$	−8.58632	+	8.02686i	−0.397753	+	0.371837i
$467$	31.3897	+	15.9938i	1.45254	+	0.740107i	0.989268	−	0.146109i	$-0.0466751\pi$
$467$	31.3897	+	15.9938i	1.45254	+	0.740107i	0.463272	+	0.886216i	$0.346675\pi$
$468$		0			0
$469$	10.4744	−	3.40334i	0.483663	−	0.157152i
$470$	−32.2511	+	4.61129i	−1.48763	+	0.212703i
$471$		0			0
$472$	10.3208	+	1.04585i	0.475054	+	0.0481389i
$473$	−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
$478$	−4.35344	−	15.1113i	−0.199122	−	0.691175i
$479$	8.73304	−	26.8775i	0.399023	−	1.22807i	−0.526761	−	0.850013i	$-0.676594\pi$
$479$	8.73304	−	26.8775i	0.399023	−	1.22807i	0.925784	−	0.378053i	$-0.123406\pi$
$480$		0			0
$481$	9.03315	+	27.8012i	0.411876	+	1.26762i
$482$	1.28044	−	0.865987i	0.0583224	−	0.0394446i
$483$		0			0
$484$	−17.0099	+	10.6879i	−0.773178	+	0.485813i
$485$	27.3923	−	14.6051i	1.24382	−	0.663185i
$486$		0			0
$487$	20.4192	−	3.23409i	0.925283	−	0.146550i	0.324430	−	0.945910i	$-0.394828\pi$
$487$	20.4192	−	3.23409i	0.925283	−	0.146550i	0.600853	+	0.799359i	$0.294828\pi$
$488$	4.90913	−	11.1377i	0.222226	−	0.504181i
$489$		0			0
$490$	−12.9435	−	4.42219i	−0.584726	−	0.199774i
$491$	8.93859	−	12.3029i	0.403393	−	0.555223i	−0.558199	−	0.829707i	$-0.688507\pi$
$491$	8.93859	−	12.3029i	0.403393	−	0.555223i	0.961591	+	0.274485i	$0.0885073\pi$
$492$		0			0
$493$	−15.5765	+	15.5765i	−0.701531	+	0.701531i
$494$	26.0319	−	3.22919i	1.17123	−	0.145288i
$495$		0			0
$496$	−7.36717	−	13.6909i	−0.330796	−	0.614740i
$497$	4.42845	−	2.25641i	0.198643	−	0.101214i
$498$		0			0
$499$	12.1532			0.544051			0.272025	−	0.962290i	$-0.412307\pi$
$499$	12.1532			0.544051			0.272025	+	0.962290i	$0.412307\pi$
$500$	17.9375	+	13.3508i	0.802191	+	0.597067i
$501$		0			0
$502$	36.6914	+	13.3029i	1.63762	+	0.593738i
$503$	−20.2930	+	10.3398i	−0.904820	+	0.461029i	−0.843524	−	0.537091i	$-0.819523\pi$
$503$	−20.2930	+	10.3398i	−0.904820	+	0.461029i	−0.0612957	+	0.998120i	$0.519523\pi$
$504$		0			0
$505$	−28.7740	+	0.535302i	−1.28043	+	0.0238206i
$506$	2.30086	−	0.285415i	0.102286	−	0.0126883i
$507$		0			0
$508$	21.7257	−	18.9809i	0.963921	−	0.842142i
$509$	−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
$512$	0.253250	+	22.6260i	0.0111922	+	0.999937i
$513$		0			0
$514$	−14.7658	+	6.90778i	−0.651292	+	0.304689i
$515$	22.9771	−	12.2510i	1.01249	−	0.539845i
$516$		0			0
$517$	4.57194	−	8.97293i	0.201074	−	0.394629i
$518$	−15.0851	+	10.2024i	−0.662802	+	0.448266i
$519$		0			0
$520$	17.9127	−	15.1801i	0.785523	−	0.665690i
$521$	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	0.580622	−	0.814173i	$-0.302809\pi$
$523$	20.1531	+	3.19194i	0.881234	+	0.139574i	0.300612	+	0.953747i	$0.402809\pi$
$524$	−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
$530$	−6.81961	+	0.975073i	−0.296225	+	0.0423545i
$531$		0			0
$532$	6.42272	+	15.0270i	0.278460	+	0.651501i
$533$	10.5615	+	5.38137i	0.457470	+	0.233093i
$534$		0			0
$535$	23.6689	−	24.5662i	1.02329	−	1.06209i
$536$	19.0175	−	1.06782i	0.821430	−	0.0461230i
$537$		0			0
$538$	0.237449	−	7.05106i	0.0102372	−	0.303993i
$539$	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	$0.895377\pi$
$542$	24.4337	−	31.3540i	1.04952	−	1.34677i
$543$		0			0
$544$	−11.4752	+	15.4268i	−0.491995	+	0.661417i
$545$	22.1652	−	31.7327i	0.949454	−	1.35928i
$546$		0			0
$547$	1.09113	+	2.14147i	0.0466534	+	0.0915625i	0.913156	−	0.407610i	$-0.133638\pi$
$547$	1.09113	+	2.14147i	0.0466534	+	0.0915625i	−0.866503	+	0.499172i	$0.833638\pi$
$548$	−14.8188	+	24.8022i	−0.633029	+	1.05950i
$549$		0			0
$550$	−6.56603	+	2.15916i	−0.279977	+	0.0920669i
$551$			32.3818i			1.37951i
$552$		0			0
$553$	−1.03494	−	2.03119i	−0.0440103	−	0.0863751i
$554$	−18.2740	+	33.0641i	−0.776388	+	1.40476i
$555$		0			0
$556$	−45.9112	−	3.09569i	−1.94707	−	0.131287i
$557$	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
$560$	12.1768	+	8.10531i	0.514562	+	0.342512i
$561$		0			0
$562$	−3.16154	−	0.106467i	−0.133362	−	0.00449105i
$563$	−3.26270	−	20.5999i	−0.137506	−	0.868181i	−0.955936	−	0.293574i	$-0.905155\pi$
$563$	−3.26270	−	20.5999i	−0.137506	−	0.868181i	0.818430	−	0.574606i	$-0.194845\pi$
$564$		0			0
$565$	−30.3457	+	5.38670i	−1.27665	+	0.226620i
$566$	−16.2819	−	17.4168i	−0.684381	−	0.732081i
$567$		0			0
$568$	8.40121	−	1.81852i	0.352507	−	0.0763033i
$569$	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	−0.568034	−	0.823005i	$-0.692296\pi$
$571$	−36.1142	−	11.7342i	−1.51133	−	0.491062i	−0.943299	+	0.331943i	$0.892296\pi$
$572$	0.650544	+	7.22863i	0.0272006	+	0.302244i
$573$		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	$0.760772\pi$
$578$	7.40349	−	2.13288i	0.307945	−	0.0887163i
$579$		0			0
$580$	15.8746	+	24.2512i	0.659155	+	1.00698i
$581$	−8.27184	−	25.4581i	−0.343174	−	1.05618i
$582$		0			0
$583$	0.966752	−	1.89736i	0.0400388	−	0.0785806i
$584$	14.4548	+	37.2403i	0.598145	+	1.54101i
$585$		0			0
$586$	6.23698	+	13.3319i	0.257647	+	0.550737i
$587$	−8.67609	+	1.37416i	−0.358100	+	0.0567175i	−0.332893	−	0.942965i	$-0.608025\pi$
$587$	−8.67609	+	1.37416i	−0.358100	+	0.0567175i	−0.0252077	+	0.999682i	$0.508025\pi$
$588$		0			0
$589$	−11.4145	−	15.7107i	−0.470325	−	0.647347i
$590$	9.48467	−	6.67510i	0.390478	−	0.274810i
$591$		0			0
$592$	−29.7285	+	10.4021i	−1.22184	+	0.427522i
$593$	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
$596$	−5.43183	+	6.50619i	−0.222496	+	0.266504i
$597$		0			0
$598$	−3.00138	+	8.27823i	−0.122735	+	0.338522i
$599$	−22.8730			−0.934566			−0.467283	−	0.884108i	$-0.654767\pi$
$599$	−22.8730			−0.934566			−0.467283	+	0.884108i	$0.654767\pi$
$600$		0			0
$601$	28.0770			1.14529			0.572643	−	0.819805i	$-0.305918\pi$
$601$	28.0770			1.14529			0.572643	+	0.819805i	$0.305918\pi$
$602$	6.89589	−	19.0199i	0.281056	−	0.775192i
$603$		0			0
$604$	−2.44906	+	2.93346i	−0.0996506	+	0.119361i
$605$	−6.54206	+	21.4863i	−0.265973	+	0.873543i
$606$		0			0
$607$	−16.1309	+	16.1309i	−0.654732	+	0.654732i	−0.954129	−	0.299397i	$-0.903214\pi$
$607$	−16.1309	+	16.1309i	−0.654732	+	0.654732i	0.299397	+	0.954129i	$0.403214\pi$
$608$	4.10741	+	27.9630i	0.166577	+	1.13405i
$609$		0			0
$610$	−4.00979	−	13.0041i	−0.162352	−	0.526521i
$611$	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	$0.392635\pi$
$614$	−1.59401	−	3.40729i	−0.0643290	−	0.137507i
$615$		0			0
$616$	−4.21519	+	1.63613i	−0.169835	+	0.0659214i
$617$	−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	$0.0615630\pi$
$619$	7.47376	+	23.0019i	0.300396	+	0.924524i	−0.680959	+	0.732321i	$0.738437\pi$
$620$	−16.2503	−	6.17023i	−0.652629	−	0.247802i
$621$		0			0
$622$	17.5409	−	5.05340i	0.703327	−	0.202623i
$623$	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
$628$	−3.85348	−	42.8186i	−0.153771	−	1.70865i
$629$	−25.4524	−	8.26999i	−1.01485	−	0.329746i
$630$		0			0
$631$	26.5940	−	8.64091i	1.05869	−	0.343989i	0.272616	−	0.962123i	$-0.412111\pi$
$631$	26.5940	−	8.64091i	1.05869	−	0.343989i	0.786073	+	0.618134i	$0.212111\pi$
$632$	−0.834098	−	3.85337i	−0.0331786	−	0.153279i
$633$		0			0
$634$	18.1482	+	19.4131i	0.720756	+	0.770992i
$635$	4.45227	−	31.9457i	0.176683	−	1.26773i
$636$		0			0
$637$	2.51200	+	15.8602i	0.0995292	+	0.628403i
$638$	−8.95446	−	0.301548i	−0.354511	−	0.0119384i
$639$		0			0
$640$	16.7844	+	18.9283i	0.663464	+	0.748209i
$641$	−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	0.677197	−	0.735802i	$-0.263194\pi$
$643$	−1.48607	−	1.48607i	−0.0586048	−	0.0586048i	−0.735802	+	0.677197i	$0.763194\pi$
$644$	−5.47335	−	0.369056i	−0.215680	−	0.0145429i
$645$		0			0
$646$	−11.6167	+	21.0187i	−0.457054	+	0.826971i
$647$	10.7848	+	21.1664i	0.423994	+	0.832135i	0.999893	+	0.0146144i	$0.00465208\pi$
$647$	10.7848	+	21.1664i	0.423994	+	0.832135i	−0.575899	+	0.817521i	$0.695348\pi$
$648$		0			0
$649$			3.58510i			0.140727i
$650$	4.01478	−	25.9423i	0.157472	−	1.01754i
$651$		0			0
$652$	15.2675	−	25.5531i	0.597921	−	1.00074i
$653$	−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
$656$	−5.54149	+	11.5067i	−0.216359	+	0.449260i
$657$		0			0
$658$	−14.6465	+	18.7948i	−0.570982	+	0.732700i
$659$	−26.9961	−	19.6138i	−1.05162	−	0.764046i	−0.0790990	−	0.996867i	$-0.525204\pi$
$659$	−26.9961	−	19.6138i	−1.05162	−	0.764046i	−0.972520	+	0.232821i	$0.925204\pi$
$660$		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	$0.324147\pi$
$662$	1.42394	−	42.2838i	0.0553428	−	1.64340i
$663$		0			0
$664$	−2.59535	−	46.2221i	−0.100719	−	1.79377i
$665$	16.4310	+	7.99058i	0.637166	+	0.309861i
$666$		0			0
$667$	−9.68533	−	4.93492i	−0.375017	−	0.191081i
$668$	12.0516	+	28.1965i	0.466290	+	1.09096i
$669$		0			0
$670$	15.2834	−	14.8298i	0.590449	−	0.572926i
$671$	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
$680$	1.60410	+	21.4361i	0.0615143	+	0.822038i
$681$		0			0
$682$	4.45073	−	3.01012i	0.170427	−	0.115263i
$683$	−17.9286	+	35.1869i	−0.686020	+	1.34639i	0.240685	+	0.970603i	$0.422628\pi$
$683$	−17.9286	+	35.1869i	−0.686020	+	1.34639i	−0.926706	+	0.375788i	$0.877372\pi$
$684$		0			0
$685$	5.64575	+	31.8050i	0.215713	+	1.21521i
$686$	−23.7259	+	11.0995i	−0.905858	+	0.423781i
$687$		0			0
$688$	19.9264	−	28.7613i	0.759687	−	1.09651i
$689$	4.75375	+	6.54298i	0.181104	+	0.249268i
$690$		0			0
$691$	−20.7179	+	28.5157i	−0.788146	+	1.08479i	0.206190	+	0.978512i	$0.433893\pi$
$691$	−20.7179	+	28.5157i	−0.788146	+	1.08479i	−0.994336	+	0.106278i	$0.966107\pi$
$692$	30.3540	−	26.5192i	1.15389	−	1.00811i
$693$		0			0
$694$	18.8235	−	2.33499i	0.714529	−	0.0886352i
$695$	−41.0517	+	31.0086i	−1.55718	+	1.17622i
$696$		0			0
$697$	−9.66924	+	4.92672i	−0.366248	+	0.186613i
$698$	15.7499	+	5.71033i	0.596144	+	0.216139i
$699$		0			0
$700$	16.2226	−	2.07071i	0.613158	−	0.0782655i
$701$	−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
$704$	−7.77080	+	0.875414i	−0.292873	+	0.0329934i
$705$		0			0
$706$	−44.3814	+	5.50539i	−1.67032	+	0.207198i
$707$	−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	$-0.0572470\pi$
$710$	5.76529	−	7.68899i	0.216367	−	0.288563i
$711$		0			0
$712$	7.34926	+	3.23930i	0.275425	+	0.121398i
$713$	6.43858	−	1.01977i	0.241127	−	0.0381907i
$714$		0			0
$715$	5.84357	+	5.63011i	0.218537	+	0.210554i
$716$	−11.6526	+	7.32174i	−0.435480	+	0.273626i
$717$		0			0
$718$	−1.10708	+	0.748739i	−0.0413158	+	0.0279427i
$719$	11.1156	+	34.2102i	0.414540	+	1.27582i	0.912661	+	0.408717i	$0.134024\pi$
$719$	11.1156	+	34.2102i	0.414540	+	1.27582i	−0.498121	+	0.867108i	$0.665976\pi$
$720$		0			0
$721$	5.88512	−	18.1125i	0.219173	−	0.674546i
$722$	2.33432	+	8.10270i	0.0868744	+	0.301551i
$723$		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	$-0.814261\pi$
$727$	3.48933	−	22.0307i	0.129412	−	0.817075i	0.963942	−	0.266113i	$-0.0857393\pi$
$728$	1.73131	−	17.0853i	0.0641667	−	0.633222i
$729$		0			0
$730$	39.4845	+	20.8733i	1.46139	+	0.772556i
$731$	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	$0.807484\pi$
$734$	4.60615	−	4.30603i	0.170016	−	0.158938i
$735$		0			0
$736$	−8.98965	−	3.03299i	−0.331363	−	0.111798i
$737$	1.02977	+	6.50168i	0.0379319	+	0.239493i
$738$		0			0
$739$	−6.76750	+	4.91688i	−0.248947	+	0.180870i	−0.705260	−	0.708949i	$-0.749170\pi$
$739$	−6.76750	+	4.91688i	−0.248947	+	0.180870i	0.456313	+	0.889819i	$0.349170\pi$
$740$	−17.4957	+	30.5595i	−0.643156	+	1.12339i
$741$		0			0
$742$	−3.09706	+	3.97424i	−0.113697	+	0.145899i
$743$	0.563949	+	0.563949i	0.0206893	+	0.0206893i	0.717376	−	0.696686i	$-0.245343\pi$
$743$	0.563949	+	0.563949i	0.0206893	+	0.0206893i	−0.696686	+	0.717376i	$0.745343\pi$
$744$		0			0
$745$	0.176257	+	9.47434i	0.00645757	+	0.347113i
$746$	11.8367	+	6.54197i	0.433373	+	0.239519i
$747$		0			0
$748$	−5.70409	−	3.40808i	−0.208562	−	0.124612i
$749$		−	24.9499i		−	0.911651i
$750$		0			0
$751$			41.2218i			1.50420i	0.659046	+	0.752102i	$0.270960\pi$
$751$			41.2218i			1.50420i	−0.659046	+	0.752102i	$0.729040\pi$
$752$	−32.7877	+	24.9640i	−1.19565	+	0.910344i
$753$		0			0
$754$	16.4600	−	29.7820i	0.599439	−	1.08459i
$755$	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	$0.569994\pi$
$758$	−3.27658	−	2.55339i	−0.119011	−	0.0927434i
$759$		0			0
$760$	23.9490	+	20.6142i	0.868720	+	0.747757i
$761$	−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
$764$	−16.3540	+	4.12075i	−0.591668	+	0.149083i
$765$		0			0
$766$	−25.0094	−	26.7525i	−0.903627	−	0.966608i
$767$	−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	$0.139500\pi$
$770$	−2.36263	+	4.46921i	−0.0851432	+	0.161059i
$771$		0			0
$772$	−27.0863	+	2.43764i	−0.974857	+	0.0877327i
$773$	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
$778$	13.4779	−	3.88287i	0.483206	−	0.139208i
$779$	−4.92956	+	15.1716i	−0.176620	+	0.543580i
$780$		0			0
$781$	0.917987	+	2.82527i	0.0328482	+	0.101096i
$782$	−4.51630	−	6.67776i	−0.161502	−	0.238796i
$783$		0			0
$784$	−17.0235	+	3.08910i	−0.607983	+	0.110325i
$785$	−34.6142	−	33.3498i	−1.23543	−	1.19031i
$786$		0			0
$787$	−44.4189	+	7.03527i	−1.58336	+	0.250780i	−0.885219	−	0.465175i	$-0.845991\pi$
$787$	−44.4189	+	7.03527i	−1.58336	+	0.250780i	−0.698146	+	0.715956i	$0.745991\pi$
$788$	14.9251	+	3.40665i	0.531685	+	0.121357i
$789$		0			0
$790$	−3.52670	−	2.64436i	−0.125474	−	0.0940821i
$791$	−13.2495	+	18.2363i	−0.471097	+	0.648410i
$792$		0			0
$793$	−11.2967	+	11.2967i	−0.401158	+	0.401158i
$794$	−4.16918	−	33.6097i	−0.147959	−	1.19276i
$795$		0			0
$796$	21.2928	+	17.7767i	0.754703	+	0.630079i
$797$	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
$800$	28.0415	+	3.69779i	0.991417	+	0.130737i
$801$		0			0
$802$	−2.97162	+	8.19615i	−0.104931	+	0.289416i
$803$	−12.3009	+	6.26762i	−0.434089	+	0.221179i
$804$		0			0
$805$	−4.89402	+	3.69673i	−0.172491	+	0.130292i
$806$	2.51213	+	20.2514i	0.0884860	+	0.713326i
$807$		0			0
$808$	−31.4577	+	18.3189i	−1.10668	+	0.644458i
$809$	−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	0.637331	−	0.770590i	$-0.280038\pi$
$811$	−8.32953	−	11.4646i	−0.292489	−	0.402577i	−0.929821	+	0.368013i	$0.880038\pi$
$812$	20.6676	+	4.71737i	0.725289	+	0.165547i
$813$		0			0
$814$	−4.61240	−	9.85930i	−0.161665	−	0.345568i
$815$	−5.81668	−	32.7680i	−0.203749	−	1.14781i
$816$		0			0
$817$	19.8413	−	38.9407i	0.694159	−	1.36236i
$818$	0.274928	+	0.406506i	0.00961263	+	0.0142131i
$819$		0			0
$820$	3.74579	+	13.7789i	0.130809	+	0.481180i
$821$	−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	0.599225	−	0.800581i	$-0.295476\pi$
$823$	26.4425	+	4.18808i	0.921728	+	0.145987i	0.322503	+	0.946568i	$0.395476\pi$
$824$	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	$0.111386\pi$
$827$	−1.72439	+	10.8874i	−0.0599630	+	0.378591i	−0.999360	+	0.0357611i	$0.988614\pi$
$828$		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	$0.538312\pi$
$830$	−36.0440	−	37.1464i	−1.25111	−	1.28937i
$831$		0			0
$832$	10.4363	−	27.8058i	0.361813	−	0.963993i
$833$	−13.0989	−	6.67421i	−0.453849	−	0.231248i
$834$		0			0
$835$	30.8310	+	14.9935i	1.06695	+	0.518871i
$836$	−9.47156	+	2.38656i	−0.327581	+	0.0825410i
$837$		0			0
$838$	−39.4185	−	1.32745i	−1.36169	−	0.0458559i
$839$	5.75338	−	4.18007i	0.198629	−	0.144312i	−0.484025	−	0.875054i	$-0.660826\pi$
$839$	5.75338	−	4.18007i	0.198629	−	0.144312i	0.682654	+	0.730742i	$0.260826\pi$
$840$		0			0
$841$	10.5222	+	7.64481i	0.362834	+	0.263614i
$842$	−17.5861	−	13.7046i	−0.606056	−	0.472291i
$843$		0			0
$844$	−1.27342	+	18.8856i	−0.0438329	+	0.650071i
$845$	−1.65369	+	0.571536i	−0.0568887	+	0.0196614i
$846$		0			0
$847$	7.45773	+	14.6366i	0.256251	+	0.502920i
$848$	−6.93308	+	5.27873i	−0.238083	+	0.181272i
$849$		0			0
$850$	17.0542	+	16.9339i	0.584954	+	0.580827i
$851$		−	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	$0.896026\pi$
$854$	−8.71100	−	4.81443i	−0.298084	−	0.164747i
$855$		0			0
$856$	11.0125	−	41.7213i	0.376401	−	1.42601i
$857$	−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	0.992114	−	0.125340i	$-0.0400022\pi$
$859$	34.5693	+	25.1160i	1.17949	+	0.856948i	0.187374	+	0.982289i	$0.440002\pi$
$860$	−4.23052	−	38.8902i	−0.144260	−	1.32614i
$861$		0			0
$862$	0.564460	−	16.7616i	0.0192256	−	0.570903i
$863$	4.41919	+	27.9017i	0.150431	+	0.949785i	0.941244	+	0.337727i	$0.109658\pi$
$863$	4.41919	+	27.9017i	0.150431	+	0.949785i	−0.790813	+	0.612058i	$0.790342\pi$
$864$		0			0
$865$	6.22050	−	44.6329i	0.211503	−	1.51757i
$866$	4.03534	−	3.77241i	0.137127	−	0.128192i
$867$		0			0
$868$	−11.6901	+	4.99652i	−0.396789	+	0.169593i
$869$	1.29587	−	0.421052i	0.0439592	−	0.0142832i
$870$		0			0
$871$	−23.7772	−	7.72570i	−0.805661	−	0.261775i
$872$	4.93616	−	48.7120i	0.167160	−	1.64960i
$873$		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	$0.608880\pi$
$878$	−2.42333	−	8.41167i	−0.0817835	−	0.283880i
$879$		0			0
$880$	−5.92343	+	6.43059i	−0.199679	+	0.216775i
$881$	−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	−0.847537	−	0.530736i	$-0.821916\pi$
$883$	2.37742	−	4.66595i	0.0800066	−	0.157022i	0.927544	+	0.373714i	$0.121916\pi$
$884$	21.3681	−	13.4263i	0.718688	−	0.451575i
$885$		0			0
$886$	−8.99060	+	4.20601i	−0.302045	+	0.141304i
$887$	3.92752	−	0.622058i	0.131873	−	0.0208867i	−0.0901489	−	0.995928i	$-0.528734\pi$
$887$	3.92752	−	0.622058i	0.131873	−	0.0208867i	0.222022	+	0.975042i	$0.428734\pi$
$888$		0			0
$889$	−13.8661	−	19.0851i	−0.465054	−	0.640092i
$890$	8.58081	−	2.64587i	0.287629	−	0.0886899i
$891$		0			0
$892$	3.55230	+	4.06599i	0.118940	+	0.136139i
$893$	−36.3972	+	36.3972i	−1.21799	+	1.21799i
$894$		0			0
$895$	−4.48164	+	14.7192i	−0.149805	+	0.492009i
$896$	18.4457	+	1.45210i	0.616227	+	0.0485114i
$897$		0			0
$898$	29.9737	+	10.8673i	1.00023	+	0.362648i
$899$	−25.1912			−0.840174
$900$		0			0
$901$	−7.40429			−0.246673
$902$	−4.14948	−	1.50445i	−0.138162	−	0.0500925i
$903$		0			0
$904$	−30.2050	+	24.6467i	−1.00460	+	0.819738i
$905$	−2.42446	−	7.01496i	−0.0805917	−	0.233185i
$906$		0			0
$907$	−6.99767	+	6.99767i	−0.232354	+	0.232354i	−0.813675	−	0.581321i	$-0.802536\pi$
$907$	−6.99767	+	6.99767i	−0.232354	+	0.232354i	0.581321	+	0.813675i	$0.302536\pi$
$908$	17.7480	−	15.5058i	0.588989	−	0.514578i
$909$		0			0
$910$	−11.0501	−	15.7011i	−0.366307	−	0.520486i
$911$	−32.8488	−	45.2125i	−1.08833	−	1.49796i	−0.850007	−	0.526771i	$-0.823403\pi$
$911$	−32.8488	−	45.2125i	−1.08833	−	1.49796i	−0.238322	−	0.971186i	$-0.576597\pi$
$912$		0			0
$913$	15.8024	−	2.50285i	0.522983	−	0.0828323i
$914$	−5.58935	+	2.61483i	−0.184879	+	0.0864907i
$915$		0			0
$916$	−4.36373	−	6.94493i	−0.144182	−	0.229467i
$917$	−12.3885	+	24.3137i	−0.409103	+	0.802910i
$918$		0			0
$919$	−1.90011	−	5.84793i	−0.0626788	−	0.192905i	0.914814	−	0.403876i	$-0.132337\pi$
$919$	−1.90011	−	5.84793i	−0.0626788	−	0.192905i	−0.977492	+	0.210971i	$0.932337\pi$
$920$	−9.81546	+	4.02152i	−0.323606	+	0.132586i
$921$		0			0
$922$	−13.5974	−	47.1981i	−0.447806	−	1.55439i
$923$	−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
$928$	32.4782	+	17.0107i	1.06615	+	0.558405i
$929$	−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
$932$	6.53300	+	15.2850i	0.213996	+	0.500676i
$933$		0			0
$934$	36.3952	−	34.0238i	1.19089	−	1.11329i
$935$	−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	$-0.104090\pi$
$938$	0.524214	−	15.5665i	0.0171162	−	0.508265i
$939$		0			0
$940$	−9.41538	+	45.1015i	−0.307096	+	1.47105i
$941$	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
$944$	6.36548	−	13.2176i	0.207179	−	0.430198i
$945$		0			0
$946$	10.5834	+	5.84930i	0.344097	+	0.190177i
$947$	−11.7110	−	22.9842i	−0.380557	−	0.746885i	0.618692	−	0.785633i	$-0.287663\pi$
$947$	−11.7110	−	22.9842i	−0.380557	−	0.746885i	−0.999249	+	0.0387487i	$0.987663\pi$
$948$		0			0
$949$		−	52.4330i		−	1.70205i
$950$	35.3286	−	0.125064i	1.14621	−	0.00405763i
$951$		0			0
$952$	11.7228	+	10.4763i	0.379939	+	0.339540i
$953$	−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
$956$	−22.1894	−	1.49618i	−0.717656	−	0.0483900i
$957$		0			0
$958$	−31.5248	−	24.5668i	−1.01852	−	0.793716i
$959$	19.1133	+	13.8866i	0.617202	+	0.448423i
$960$		0			0
$961$	−12.8575	+	9.34152i	−0.414758	+	0.301339i
$962$	41.3167	+	1.39137i	1.33210	+	0.0448596i
$963$		0			0
$964$	−0.534133	−	2.11982i	−0.0172033	−	0.0682747i
$965$	−21.0965	+	21.8963i	−0.679121	+	0.704868i
$966$		0			0
$967$	−23.2179	−	11.8301i	−0.746638	−	0.380431i	0.0389013	−	0.999243i	$-0.487614\pi$
$967$	−23.2179	−	11.8301i	−0.746638	−	0.380431i	−0.785539	+	0.618812i	$0.787614\pi$
$968$	6.01044	+	27.7671i	0.193183	+	0.892468i
$969$		0			0
$970$	−6.21381	−	43.4591i	−0.199513	−	1.39539i
$971$	−5.43069	−	1.76454i	−0.174279	−	0.0566268i	0.220578	−	0.975369i	$-0.429206\pi$
$971$	−5.43069	−	1.76454i	−0.174279	−	0.0566268i	−0.394857	+	0.918743i	$0.629206\pi$
$972$		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
$980$	−12.1186	+	15.0770i	−0.387116	+	0.481618i
$981$		0			0
$982$	−12.0483	−	17.8145i	−0.384477	−	0.568485i
$983$	7.50817	−	14.7356i	0.239473	−	0.469993i	−0.739722	−	0.672913i	$-0.765043\pi$
$983$	7.50817	−	14.7356i	0.239473	−	0.469993i	0.979195	+	0.202920i	$0.0650430\pi$
$984$		0			0
$985$	15.1032	−	8.05279i	0.481229	−	0.256583i
$986$	13.2009	+	28.2178i	0.420404	+	0.898639i
$987$		0			0
$988$	8.25506	−	36.1668i	0.262628	−	1.15062i
$989$	8.62333	+	11.8690i	0.274206	+	0.377412i
$990$		0			0
$991$	17.3344	−	23.8587i	0.550644	−	0.757896i	−0.439455	−	0.898264i	$-0.644829\pi$
$991$	17.3344	−	23.8587i	0.550644	−	0.757896i	0.990099	+	0.140368i	$0.0448286\pi$
$992$	−21.7537	+	3.19534i	−0.690680	+	0.101452i
$993$		0			0
$994$	−0.865280	−	6.97542i	−0.0274450	−	0.221247i
$995$	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	$0.165872\pi$
$998$	5.85827	−	16.1580i	0.185440	−	0.511472i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.482036 - 1.32953i) q^{2} +(-1.53528 - 1.28176i) q^{4} +(-2.23568 + 0.0415918i) q^{5} +(-1.15642 + 1.15642i) q^{7} +(-2.44420 + 1.42334i) q^{8} +O(q^{10})\)	\(q+(0.482036 - 1.32953i) q^{2} +(-1.53528 - 1.28176i) q^{4} +(-2.23568 + 0.0415918i) q^{5} +(-1.15642 + 1.15642i) q^{7} +(-2.44420 + 1.42334i) q^{8} +(-1.02238 + 2.99245i) q^{10} +(-0.574557 - 0.790810i) q^{11} +(3.66677 - 0.580759i) q^{13} +(0.980056 + 2.09493i) q^{14} +(0.714179 + 3.93573i) q^{16} +(-1.54304 + 3.02838i) q^{17} +(1.54393 + 4.75171i) q^{19} +(3.48571 + 2.80175i) q^{20} +(-1.32836 + 0.382689i) q^{22} +(-1.65652 - 0.262367i) q^{23} +(4.99654 - 0.185972i) q^{25} +(0.995382 - 5.15501i) q^{26} +(3.25769 - 0.293177i) q^{28} +(6.16400 + 2.00281i) q^{29} +(-3.69657 + 1.20109i) q^{31} +(5.57691 + 0.947644i) q^{32} +(3.28251 + 3.51129i) q^{34} +(2.53729 - 2.63349i) q^{35} +(1.23176 + 7.77702i) q^{37} +(7.06176 + 0.237810i) q^{38} +(5.40524 - 3.28380i) q^{40} +(2.58309 + 1.87673i) q^{41} +(-6.18535 - 6.18535i) q^{43} +(-0.131522 + 1.95056i) q^{44} +(-1.14733 + 2.07592i) q^{46} +(4.67720 + 9.17952i) q^{47} +4.32538i q^{49} +(2.16126 - 6.73268i) q^{50} +(-6.37392 - 3.80829i) q^{52} +(0.989011 + 1.94104i) q^{53} +(1.31742 + 1.74410i) q^{55} +(1.18054 - 4.47250i) q^{56} +(5.63406 - 7.22978i) q^{58} +(-2.96719 - 2.15579i) q^{59} +(-3.48146 + 2.52943i) q^{61} +(-0.185003 + 5.49366i) q^{62} +(3.94819 - 6.95786i) q^{64} +(-8.17357 + 1.45090i) q^{65} +(-6.00029 - 3.05730i) q^{67} +(6.25065 - 2.67161i) q^{68} +(-2.27822 - 4.64283i) q^{70} +(-2.89032 - 0.939123i) q^{71} +(2.20940 - 13.9496i) q^{73} +(10.9335 + 2.11115i) q^{74} +(3.72020 - 9.27416i) q^{76} +(1.57894 + 0.250079i) q^{77} +(-0.430746 + 1.32570i) q^{79} +(-1.76037 - 8.76933i) q^{80} +(3.74030 - 2.52964i) q^{82} +(-7.43080 + 14.5838i) q^{83} +(3.32378 - 6.83466i) q^{85} +(-11.2052 + 5.24202i) q^{86} +(2.52992 + 1.11510i) q^{88} +(-1.66905 - 2.29725i) q^{89} +(-3.56873 + 4.91193i) q^{91} +(2.20693 + 2.52607i) q^{92} +(14.4590 - 1.79360i) q^{94} +(-3.64936 - 10.5591i) q^{95} +(-12.3696 + 6.30263i) q^{97} +(5.75071 + 2.08499i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{8}+O(q^{10}) \) 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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