LMFDB - Embedded newform 900.2.bj.f.523.28

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			523.28
Character	$\chi$	$=$	900.523
Dual form			900.2.bj.f.487.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35338 - 0.410309i) q^{2} +(1.66329 - 1.11061i) q^{4} +(-2.17065 - 0.536923i) q^{5} +(0.403183 + 0.403183i) q^{7} +(1.79538 - 2.18554i) q^{8} +O(q^{10})$	\(q+(1.35338 - 0.410309i) q^{2} +(1.66329 - 1.11061i) q^{4} +(-2.17065 - 0.536923i) q^{5} +(0.403183 + 0.403183i) q^{7} +(1.79538 - 2.18554i) q^{8} +(-3.15802 + 0.163973i) q^{10} +(-2.68322 - 3.69314i) q^{11} +(-0.669605 - 4.22772i) q^{13} +(0.711090 + 0.380232i) q^{14} +(1.53309 - 3.69454i) q^{16} +(-1.13184 - 0.576699i) q^{17} +(0.214045 + 0.658762i) q^{19} +(-4.20674 + 1.51768i) q^{20} +(-5.14676 - 3.89729i) q^{22} +(-0.103651 + 0.654427i) q^{23} +(4.42343 + 2.33094i) q^{25} +(-2.64090 - 5.44698i) q^{26} +(1.11839 + 0.222833i) q^{28} +(-5.48448 - 1.78201i) q^{29} +(7.87705 - 2.55941i) q^{31} +(0.558959 - 5.62917i) q^{32} +(-1.76843 - 0.316093i) q^{34} +(-0.658690 - 1.09165i) q^{35} +(-0.551102 + 0.0872860i) q^{37} +(0.559981 + 0.803734i) q^{38} +(-5.07061 + 3.78007i) q^{40} +(3.58374 + 2.60374i) q^{41} +(2.72923 - 2.72923i) q^{43} +(-8.56463 - 3.16276i) q^{44} +(0.128237 + 0.928219i) q^{46} +(9.06571 - 4.61921i) q^{47} -6.67489i q^{49} +(6.94300 + 1.33969i) q^{50} +(-5.80910 - 6.28827i) q^{52} +(-7.66275 + 3.90436i) q^{53} +(3.84140 + 9.45719i) q^{55} +(1.60504 - 0.157307i) q^{56} +(-8.15378 - 0.161421i) q^{58} +(5.72938 + 4.16264i) q^{59} +(-10.7384 + 7.80192i) q^{61} +(9.61052 - 6.69588i) q^{62} +(-1.55321 - 7.84777i) q^{64} +(-0.816485 + 9.53642i) q^{65} +(-4.20759 + 8.25787i) q^{67} +(-2.52306 + 0.297808i) q^{68} +(-1.33937 - 1.20715i) q^{70} +(-1.71079 - 0.555870i) q^{71} +(-6.95389 - 1.10139i) q^{73} +(-0.710038 + 0.344253i) q^{74} +(1.08765 + 0.857995i) q^{76} +(0.407181 - 2.57084i) q^{77} +(2.36601 - 7.28182i) q^{79} +(-5.31149 + 7.19640i) q^{80} +(5.91851 + 2.05342i) q^{82} +(7.97834 + 4.06517i) q^{83} +(2.14717 + 1.85952i) q^{85} +(2.57387 - 4.81352i) q^{86} +(-12.8889 - 0.766290i) q^{88} +(-3.05003 - 4.19801i) q^{89} +(1.43457 - 1.97452i) q^{91} +(0.554411 + 1.20362i) q^{92} +(10.3741 - 9.97131i) q^{94} +(-0.110911 - 1.54487i) q^{95} +(5.74169 + 11.2687i) q^{97} +(-2.73876 - 9.03368i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

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 $

$2$	1.35338	−	0.410309i	0.956987	−	0.290132i
$2$	1.35338	−	0.410309i	0.956987	−	0.290132i
$3$		0			0
$3$		0			0
$4$	1.66329	−	1.11061i	0.831647	−	0.555305i
$5$	−2.17065	−	0.536923i	−0.970743	−	0.240119i
$5$	−2.17065	−	0.536923i	−0.970743	−	0.240119i
$6$		0			0
$7$	0.403183	+	0.403183i	0.152389	+	0.152389i	0.779184	−	0.626795i	$-0.215634\pi$
$7$	0.403183	+	0.403183i	0.152389	+	0.152389i	−0.626795	+	0.779184i	$0.715634\pi$
$8$	1.79538	−	2.18554i	0.634763	−	0.772707i
$9$		0			0
$10$	−3.15802	+	0.163973i	−0.998655	+	0.0518527i
$11$	−2.68322	−	3.69314i	−0.809022	−	1.11352i	−0.991473	−	0.130309i	$-0.958403\pi$
$11$	−2.68322	−	3.69314i	−0.809022	−	1.11352i	0.182451	−	0.983215i	$-0.441597\pi$
$12$		0			0
$13$	−0.669605	−	4.22772i	−0.185715	−	1.17256i	−0.887719	−	0.460386i	$-0.847711\pi$
$13$	−0.669605	−	4.22772i	−0.185715	−	1.17256i	0.702004	−	0.712173i	$-0.252289\pi$
$14$	0.711090	+	0.380232i	0.190047	+	0.101621i
$15$		0			0
$16$	1.53309	−	3.69454i	0.383273	−	0.923635i
$17$	−1.13184	−	0.576699i	−0.274511	−	0.139870i	0.311316	−	0.950306i	$-0.399230\pi$
$17$	−1.13184	−	0.576699i	−0.274511	−	0.139870i	−0.585827	+	0.810436i	$0.699230\pi$
$18$		0			0
$19$	0.214045	+	0.658762i	0.0491053	+	0.151130i	0.972602	−	0.232475i	$-0.0746823\pi$
$19$	0.214045	+	0.658762i	0.0491053	+	0.151130i	−0.923497	+	0.383605i	$0.874682\pi$
$20$	−4.20674	+	1.51768i	−0.940655	+	0.339364i
$21$		0			0
$22$	−5.14676	−	3.89729i	−1.09729	−	0.830904i
$23$	−0.103651	+	0.654427i	−0.0216127	+	0.136457i	−0.996135	−	0.0878321i	$-0.972006\pi$
$23$	−0.103651	+	0.654427i	−0.0216127	+	0.136457i	0.974523	+	0.224289i	$0.0720061\pi$
$24$		0			0
$25$	4.42343	+	2.33094i	0.884685	+	0.466189i
$26$	−2.64090	−	5.44698i	−0.517924	−	1.06824i
$27$		0			0
$28$	1.11839	+	0.222833i	0.211356	+	0.0421114i
$29$	−5.48448	−	1.78201i	−1.01844	−	0.330912i	−0.248231	−	0.968701i	$-0.579849\pi$
$29$	−5.48448	−	1.78201i	−1.01844	−	0.330912i	−0.770211	+	0.637789i	$0.779849\pi$
$30$		0			0
$31$	7.87705	−	2.55941i	1.41476	−	0.459683i	0.500826	−	0.865548i	$-0.333030\pi$
$31$	7.87705	−	2.55941i	1.41476	−	0.459683i	0.913933	+	0.405865i	$0.133030\pi$
$32$	0.558959	−	5.62917i	0.0988109	−	0.995106i
$33$		0			0
$34$	−1.76843	−	0.316093i	−0.303284	−	0.0542095i
$35$	−0.658690	−	1.09165i	−0.111339	−	0.184522i
$36$		0			0
$37$	−0.551102	+	0.0872860i	−0.0906006	+	0.0143497i	−0.201570	−	0.979474i	$-0.564604\pi$
$37$	−0.551102	+	0.0872860i	−0.0906006	+	0.0143497i	0.110970	+	0.993824i	$0.464604\pi$
$38$	0.559981	+	0.803734i	0.0908409	+	0.130383i
$39$		0			0
$40$	−5.07061	+	3.78007i	−0.801734	+	0.597681i
$41$	3.58374	+	2.60374i	0.559686	+	0.406636i	0.831344	−	0.555758i	$-0.187572\pi$
$41$	3.58374	+	2.60374i	0.559686	+	0.406636i	−0.271658	+	0.962394i	$0.587572\pi$
$42$		0			0
$43$	2.72923	−	2.72923i	0.416204	−	0.416204i	−0.467689	−	0.883893i	$-0.654913\pi$
$43$	2.72923	−	2.72923i	0.416204	−	0.416204i	0.883893	+	0.467689i	$0.154913\pi$
$44$	−8.56463	−	3.16276i	−1.29117	−	0.476804i
$45$		0			0
$46$	0.128237	+	0.928219i	0.0189076	+	0.136858i
$47$	9.06571	−	4.61921i	1.32237	−	0.673781i	0.356863	−	0.934157i	$-0.383846\pi$
$47$	9.06571	−	4.61921i	1.32237	−	0.673781i	0.965507	+	0.260375i	$0.0838463\pi$
$48$		0			0
$49$		−	6.67489i		−	0.953555i
$50$	6.94300	+	1.33969i	0.981888	+	0.189461i
$51$		0			0
$52$	−5.80910	−	6.28827i	−0.805577	−	0.872027i
$53$	−7.66275	+	3.90436i	−1.05256	+	0.536306i	−0.892615	−	0.450820i	$-0.851132\pi$
$53$	−7.66275	+	3.90436i	−1.05256	+	0.536306i	−0.159944	+	0.987126i	$0.551132\pi$
$54$		0			0
$55$	3.84140	+	9.45719i	0.517974	+	1.27521i
$56$	1.60504	−	0.157307i	0.214483	−	0.0210211i
$57$		0			0
$58$	−8.15378	−	0.161421i	−1.07064	−	0.0211956i
$59$	5.72938	+	4.16264i	0.745902	+	0.541929i	0.894554	−	0.446960i	$-0.147493\pi$
$59$	5.72938	+	4.16264i	0.745902	+	0.541929i	−0.148652	+	0.988890i	$0.547493\pi$
$60$		0			0
$61$	−10.7384	+	7.80192i	−1.37491	+	0.998934i	−0.377579	+	0.925977i	$0.623243\pi$
$61$	−10.7384	+	7.80192i	−1.37491	+	0.998934i	−0.997335	+	0.0729561i	$0.976757\pi$
$62$	9.61052	−	6.69588i	1.22054	−	0.850378i
$63$		0			0
$64$	−1.55321	−	7.84777i	−0.194151	−	0.980972i
$65$	−0.816485	+	9.53642i	−0.101272	+	1.18285i
$66$		0			0
$67$	−4.20759	+	8.25787i	−0.514039	+	1.00886i	0.477448	+	0.878660i	$0.341562\pi$
$67$	−4.20759	+	8.25787i	−0.514039	+	1.00886i	−0.991488	+	0.130199i	$0.958438\pi$
$68$	−2.52306	+	0.297808i	−0.305966	+	0.0361145i
$69$		0			0
$70$	−1.33937	−	1.20715i	−0.160086	−	0.144282i
$71$	−1.71079	−	0.555870i	−0.203034	−	0.0659696i	0.205735	−	0.978608i	$-0.434042\pi$
$71$	−1.71079	−	0.555870i	−0.203034	−	0.0659696i	−0.408768	+	0.912638i	$0.634042\pi$
$72$		0			0
$73$	−6.95389	−	1.10139i	−0.813892	−	0.128908i	−0.264407	−	0.964411i	$-0.585176\pi$
$73$	−6.95389	−	1.10139i	−0.813892	−	0.128908i	−0.549485	+	0.835504i	$0.685176\pi$
$74$	−0.710038	+	0.344253i	−0.0825402	+	0.0400186i
$75$		0			0
$76$	1.08765	+	0.857995i	0.124762	+	0.0984188i
$77$	0.407181	−	2.57084i	0.0464026	−	0.292974i
$78$		0			0
$79$	2.36601	−	7.28182i	0.266197	−	0.819269i	−0.725219	−	0.688518i	$-0.758261\pi$
$79$	2.36601	−	7.28182i	0.266197	−	0.819269i	0.991415	−	0.130750i	$-0.0417386\pi$
$80$	−5.31149	+	7.19640i	−0.593842	+	0.804581i
$81$		0			0
$82$	5.91851	+	2.05342i	0.653590	+	0.226762i
$83$	7.97834	+	4.06517i	0.875737	+	0.446210i	0.833256	−	0.552887i	$-0.186474\pi$
$83$	7.97834	+	4.06517i	0.875737	+	0.446210i	0.0424806	+	0.999097i	$0.486474\pi$
$84$		0			0
$85$	2.14717	+	1.85952i	0.232894	+	0.201693i
$86$	2.57387	−	4.81352i	0.277547	−	0.519055i
$87$		0			0
$88$	−12.8889	−	0.766290i	−1.37397	−	0.0816868i
$89$	−3.05003	−	4.19801i	−0.323303	−	0.444988i	0.616169	−	0.787614i	$-0.288684\pi$
$89$	−3.05003	−	4.19801i	−0.323303	−	0.444988i	−0.939472	+	0.342626i	$0.888684\pi$
$90$		0			0
$91$	1.43457	−	1.97452i	0.150384	−	0.206986i
$92$	0.554411	+	1.20362i	0.0578013	+	0.125486i
$93$		0			0
$94$	10.3741	−	9.97131i	1.07001	−	1.02846i
$95$	−0.110911	−	1.54487i	−0.0113793	−	0.158500i
$96$		0			0
$97$	5.74169	+	11.2687i	0.582981	+	1.14416i	0.974582	+	0.224029i	$0.0719210\pi$
$97$	5.74169	+	11.2687i	0.582981	+	1.14416i	−0.391602	+	0.920135i	$0.628079\pi$
$98$	−2.73876	−	9.03368i	−0.276657	−	0.912540i
$99$		0			0
$100$	9.94623	−	1.03566i	0.994623	−	0.103566i
$101$	18.5684			1.84763			0.923813	−	0.382845i	$-0.125055\pi$
$101$	18.5684			1.84763			0.923813	+	0.382845i	$0.125055\pi$
$102$		0			0
$103$	3.40490	+	6.68249i	0.335495	+	0.658445i	0.995700	−	0.0926401i	$-0.0295306\pi$
$103$	3.40490	+	6.68249i	0.335495	+	0.658445i	−0.660205	+	0.751085i	$0.729531\pi$
$104$	−10.4421	−	6.12692i	−1.02393	−	0.600794i
$105$		0			0
$106$	−8.76864	+	8.42819i	−0.851686	+	0.818618i
$107$	0.808322	+	0.808322i	0.0781434	+	0.0781434i	0.745098	−	0.666955i	$-0.232403\pi$
$107$	0.808322	+	0.808322i	0.0781434	+	0.0781434i	−0.666955	+	0.745098i	$0.732403\pi$
$108$		0			0
$109$	−10.5714	+	14.5503i	−1.01256	+	1.39367i	−0.0952690	+	0.995452i	$0.530371\pi$
$109$	−10.5714	+	14.5503i	−1.01256	+	1.39367i	−0.917291	+	0.398218i	$0.869629\pi$
$110$	9.07926	+	11.2231i	0.865673	+	1.07008i
$111$		0			0
$112$	2.10769	−	0.871459i	0.199158	−	0.0823451i
$113$	1.84765	+	11.6656i	0.173813	+	1.09741i	0.908156	+	0.418632i	$0.137490\pi$
$113$	1.84765	+	11.6656i	0.173813	+	1.09741i	−0.734343	+	0.678778i	$0.762510\pi$
$114$		0			0
$115$	0.576367	−	1.36488i	0.0537465	−	0.127276i
$116$	−11.1014	+	3.12710i	−1.03074	+	0.290344i
$117$		0			0
$118$	9.46201	+	3.28283i	0.871049	+	0.302209i
$119$	−0.223822	−	0.688852i	−0.0205177	−	0.0631469i
$120$		0			0
$121$	−3.04041	+	9.35742i	−0.276401	+	0.850675i
$122$	−11.3320	+	14.9651i	−1.02595	+	1.35487i
$123$		0			0
$124$	10.2593	−	13.0054i	0.921316	−	1.16792i
$125$	−8.35017	−	7.43470i	−0.746862	−	0.664980i
$126$		0			0
$127$	19.6106	+	3.10602i	1.74016	+	0.275614i	0.944113	−	0.329621i	$-0.106921\pi$
$127$	19.6106	+	3.10602i	1.74016	+	0.275614i	0.796047	+	0.605235i	$0.206921\pi$
$128$	−5.32210	−	9.98375i	−0.470412	−	0.882447i
$129$		0			0
$130$	2.80786	+	13.2415i	0.246266	+	1.16135i
$131$	21.6599	−	7.03773i	1.89243	−	0.614889i	0.915083	−	0.403264i	$-0.132125\pi$
$131$	21.6599	−	7.03773i	1.89243	−	0.614889i	0.977351	−	0.211625i	$-0.0678755\pi$
$132$		0			0
$133$	−0.179302	+	0.351901i	−0.0155475	+	0.0305137i
$134$	−2.30621	+	12.9025i	−0.199227	+	1.11460i
$135$		0			0
$136$	−3.29248	+	1.43828i	−0.282328	+	0.123332i
$137$	16.5163	−	2.61593i	1.41109	−	0.223494i	0.596070	−	0.802932i	$-0.296728\pi$
$137$	16.5163	−	2.61593i	1.41109	−	0.223494i	0.815016	+	0.579438i	$0.196728\pi$
$138$		0			0
$139$	−0.991605	+	0.720443i	−0.0841068	+	0.0611072i	−0.629044	−	0.777370i	$-0.716553\pi$
$139$	−0.991605	+	0.720443i	−0.0841068	+	0.0611072i	0.544937	+	0.838477i	$0.316553\pi$
$140$	−2.30799	−	1.08418i	−0.195061	−	0.0916300i
$141$		0			0
$142$	−2.54343	−	0.0503525i	−0.213440	−	0.00422549i
$143$	−13.8169	+	13.8169i	−1.15542	+	1.15542i
$144$		0			0
$145$	10.9481	+	6.81287i	0.909187	+	0.565778i
$146$	−9.86319	+	1.36264i	−0.816284	+	0.112773i
$147$		0			0
$148$	−0.819704	+	0.757241i	−0.0673792	+	0.0622449i
$149$		−	13.9644i		−	1.14401i	−0.820251	−	0.572003i	$-0.806166\pi$
$149$		−	13.9644i		−	1.14401i	0.820251	−	0.572003i	$-0.193834\pi$
$150$		0			0
$151$		−	19.3040i		−	1.57094i	−0.618901	−	0.785469i	$-0.712422\pi$
$151$		−	19.3040i		−	1.57094i	0.618901	−	0.785469i	$-0.287578\pi$
$152$	1.82405	+	0.714925i	0.147950	+	0.0579881i
$153$		0			0
$154$	−0.503766	−	3.64640i	−0.0405946	−	0.293836i
$155$	−18.4725	+	1.32620i	−1.48375	+	0.106523i
$156$		0			0
$157$	11.6248	−	11.6248i	0.927763	−	0.927763i	−0.0697978	−	0.997561i	$-0.522235\pi$
$157$	11.6248	−	11.6248i	0.927763	−	0.927763i	0.997561	+	0.0697978i	$0.0222354\pi$
$158$	0.214321	−	10.8259i	0.0170504	−	0.861261i
$159$		0			0
$160$	−4.23574	+	11.9188i	−0.334864	+	0.942266i
$161$	−0.305644	+	0.222063i	−0.0240881	+	0.0175010i
$162$		0			0
$163$	−17.3839	+	2.75333i	−1.36161	+	0.215658i	−0.794139	−	0.607736i	$-0.792078\pi$
$163$	−17.3839	+	2.75333i	−1.36161	+	0.215658i	−0.567470	+	0.823394i	$0.692078\pi$
$164$	8.85255	+	0.350646i	0.691268	+	0.0273809i
$165$		0			0
$166$	12.4657	+	2.22815i	0.967528	+	0.172938i
$167$	−3.04644	+	5.97897i	−0.235741	+	0.462667i	−0.978322	−	0.207089i	$-0.933601\pi$
$167$	−3.04644	+	5.97897i	−0.235741	+	0.462667i	0.742582	+	0.669756i	$0.233601\pi$
$168$		0			0
$169$	−5.06153	+	1.64459i	−0.389349	+	0.126507i
$170$	3.66893	+	1.63564i	0.281394	+	0.125448i
$171$		0			0
$172$	1.50840	−	7.57062i	0.115015	−	0.577254i
$173$	0.974029	+	0.154271i	0.0740540	+	0.0117290i	0.193352	−	0.981130i	$-0.438064\pi$
$173$	0.974029	+	0.154271i	0.0740540	+	0.0117290i	−0.119297	+	0.992859i	$0.538064\pi$
$174$		0			0
$175$	0.843653	+	2.72325i	0.0637742	+	0.205858i
$176$	−17.7581	+	4.25136i	−1.33857	+	0.320458i
$177$		0			0
$178$	−5.85034	−	4.43006i	−0.438502	−	0.332047i
$179$	−5.08238	+	15.6420i	−0.379875	+	1.16914i	0.560255	+	0.828320i	$0.310703\pi$
$179$	−5.08238	+	15.6420i	−0.379875	+	1.16914i	−0.940130	+	0.340815i	$0.889297\pi$
$180$		0			0
$181$	−7.05393	−	21.7098i	−0.524314	−	1.61367i	−0.765668	−	0.643236i	$-0.777591\pi$
$181$	−7.05393	−	21.7098i	−0.524314	−	1.61367i	0.241353	−	0.970437i	$-0.422409\pi$
$182$	1.13136	−	3.26090i	0.0838622	−	0.241714i
$183$		0			0
$184$	1.24419	+	1.40148i	0.0917226	+	0.103318i
$185$	1.24311	+	0.106432i	0.0913956	+	0.00782506i
$186$		0			0
$187$	0.907138	+	5.72744i	0.0663365	+	0.418832i
$188$	9.94880	−	17.7516i	0.725591	−	1.29467i
$189$		0			0
$190$	−0.783978	−	2.04529i	−0.0568757	−	0.148381i
$191$	−5.09993	+	7.01945i	−0.369018	+	0.507910i	−0.952634	−	0.304120i	$-0.901638\pi$
$191$	−5.09993	+	7.01945i	−0.369018	+	0.507910i	0.583616	+	0.812030i	$0.301638\pi$
$192$		0			0
$193$	3.60845	+	3.60845i	0.259742	+	0.259742i	0.824949	−	0.565207i	$-0.191204\pi$
$193$	3.60845	+	3.60845i	0.259742	+	0.259742i	−0.565207	+	0.824949i	$0.691204\pi$
$194$	12.3944	+	12.8950i	0.889863	+	0.925808i
$195$		0			0
$196$	−7.41320	−	11.1023i	−0.529514	−	0.793021i
$197$	−5.27204	−	10.3470i	−0.375617	−	0.737190i	0.623382	−	0.781917i	$-0.285758\pi$
$197$	−5.27204	−	10.3470i	−0.375617	−	0.737190i	−0.998999	+	0.0447274i	$0.985758\pi$
$198$		0			0
$199$	−1.27147			−0.0901321			−0.0450661	−	0.998984i	$-0.514350\pi$
$199$	−1.27147			−0.0901321			−0.0450661	+	0.998984i	$0.514350\pi$
$200$	13.0361	−	5.48267i	0.921793	−	0.387683i
$201$		0			0
$202$	25.1302	−	7.61878i	1.76815	−	0.536055i
$203$	−1.49277	−	2.92972i	−0.104772	−	0.205626i
$204$		0			0
$205$	−6.38103	−	7.57599i	−0.445670	−	0.529130i
$206$	7.35002	+	7.64691i	0.512100	+	0.532786i
$207$		0			0
$208$	−16.6461	−	4.00760i	−1.15420	−	0.277877i
$209$	1.85857	−	2.55811i	0.128560	−	0.176948i
$210$		0			0
$211$	−2.56831	−	3.53497i	−0.176810	−	0.243358i	0.711409	−	0.702778i	$-0.248057\pi$
$211$	−2.56831	−	3.53497i	−0.176810	−	0.243358i	−0.888219	+	0.459420i	$0.848057\pi$
$212$	−8.40917	+	15.0044i	−0.577544	+	1.03051i
$213$		0			0
$214$	1.42563	+	0.762308i	0.0974541	+	0.0521103i
$215$	−7.38958	+	4.45881i	−0.503965	+	0.304088i
$216$		0			0
$217$	4.20780	+	2.14398i	0.285644	+	0.145543i
$218$	−8.33708	+	24.0297i	−0.564658	+	1.62750i
$219$		0			0
$220$	16.8926	+	11.4638i	1.13890	+	0.772889i
$221$	−1.68024	+	5.17125i	−0.113025	+	0.347856i
$222$		0			0
$223$	−1.79466	+	11.3311i	−0.120180	+	0.758784i	0.851826	+	0.523825i	$0.175496\pi$
$223$	−1.79466	+	11.3311i	−0.120180	+	0.758784i	−0.972005	+	0.234959i	$0.924504\pi$
$224$	2.49495	−	2.04422i	0.166701	−	0.136585i
$225$		0			0
$226$	7.28709	+	15.0300i	0.484730	+	0.999778i
$227$	29.6086	+	4.68955i	1.96519	+	0.311256i	0.998460	+	0.0554697i	$0.0176656\pi$
$227$	29.6086	+	4.68955i	1.96519	+	0.311256i	0.966733	+	0.255786i	$0.0823344\pi$
$228$		0			0
$229$	0.824628	+	0.267938i	0.0544929	+	0.0177058i	0.336137	−	0.941813i	$-0.390880\pi$
$229$	0.824628	+	0.267938i	0.0544929	+	0.0177058i	−0.281644	+	0.959519i	$0.590880\pi$
$230$	0.220024	−	2.08369i	0.0145080	−	0.137395i
$231$		0			0
$232$	−13.7414	+	8.78718i	−0.902167	+	0.576906i
$233$	4.29817	−	8.43563i	0.281582	−	0.552637i	−0.706287	−	0.707926i	$-0.749631\pi$
$233$	4.29817	−	8.43563i	0.281582	−	0.552637i	0.987869	+	0.155289i	$0.0496310\pi$
$234$		0			0
$235$	−22.1586	+	5.15909i	−1.44547	+	0.336542i
$236$	14.1527	+	0.560584i	0.921263	+	0.0364909i
$237$		0			0
$238$	−0.585558	−	0.840445i	−0.0379561	−	0.0544779i
$239$	−8.95405	+	6.50550i	−0.579190	+	0.420806i	−0.838432	−	0.545006i	$-0.816527\pi$
$239$	−8.95405	+	6.50550i	−0.579190	+	0.420806i	0.259242	+	0.965812i	$0.416527\pi$
$240$		0			0
$241$	−0.593499	−	0.431202i	−0.0382306	−	0.0277762i	0.568506	−	0.822679i	$-0.307522\pi$
$241$	−0.593499	−	0.431202i	−0.0382306	−	0.0277762i	−0.606736	+	0.794903i	$0.707522\pi$
$242$	−0.275411	+	13.9117i	−0.0177041	+	0.894277i
$243$		0			0
$244$	−9.19626	+	24.9031i	−0.588730	+	1.59426i
$245$	−3.58390	+	14.4888i	−0.228967	+	0.925658i
$246$		0			0
$247$	2.64174	−	1.34603i	0.168090	−	0.0856461i
$248$	8.54860	−	21.8107i	0.542837	−	1.38498i
$249$		0			0
$250$	−14.3515	−	6.63585i	−0.907668	−	0.419688i
$251$		−	13.1418i		−	0.829505i	−0.909934	−	0.414753i	$-0.863868\pi$
$251$		−	13.1418i		−	0.829505i	0.909934	−	0.414753i	$-0.136132\pi$
$252$		0			0
$253$	2.69501	−	1.37318i	0.169434	−	0.0863308i
$254$	27.8151	−	3.84277i	1.74527	−	0.241117i
$255$		0			0
$256$	−11.2993	−	11.3281i	−0.706204	−	0.708009i
$257$	−11.0515	+	11.0515i	−0.689375	+	0.689375i	−0.962094	−	0.272719i	$-0.912077\pi$
$257$	−11.0515	+	11.0515i	−0.689375	+	0.689375i	0.272719	+	0.962094i	$0.412077\pi$
$258$		0			0
$259$	−0.257387	−	0.187003i	−0.0159932	−	0.0116198i
$260$	9.23319	+	16.7687i	0.572618	+	1.03995i
$261$		0			0
$262$	26.4265	−	18.4120i	1.63264	−	1.13750i
$263$	−13.8057	+	2.18660i	−0.851294	+	0.134832i	−0.566810	−	0.823849i	$-0.691822\pi$
$263$	−13.8057	+	2.18660i	−0.851294	+	0.134832i	−0.284485	+	0.958681i	$0.591822\pi$
$264$		0			0
$265$	18.7295	−	4.36069i	1.15054	−	0.267875i
$266$	−0.0982770	+	0.549826i	−0.00602575	+	0.0337120i
$267$		0			0
$268$	2.17281	+	18.4083i	0.132725	+	1.12446i
$269$	5.95656	−	1.93540i	0.363178	−	0.118004i	−0.121743	−	0.992562i	$-0.538848\pi$
$269$	5.95656	−	1.93540i	0.363178	−	0.118004i	0.484921	+	0.874558i	$0.338848\pi$
$270$		0			0
$271$	−19.0797	−	6.19936i	−1.15901	−	0.376584i	−0.334478	−	0.942404i	$-0.608560\pi$
$271$	−19.0797	−	6.19936i	−1.15901	−	0.376584i	−0.824529	+	0.565820i	$0.808560\pi$
$272$	−3.86585	+	3.29748i	−0.234401	+	0.199939i
$273$		0			0
$274$	21.2796	−	10.3172i	1.28555	−	0.623282i
$275$	−3.26054	−	22.5908i	−0.196618	−	1.36228i
$276$		0			0
$277$	1.56268	−	9.86635i	0.0938922	−	0.592812i	−0.895217	−	0.445630i	$-0.852980\pi$
$277$	1.56268	−	9.86635i	0.0938922	−	0.592812i	0.989109	−	0.147182i	$-0.0470203\pi$
$278$	−1.04642	+	1.38190i	−0.0627600	+	0.0828809i
$279$		0			0
$280$	−3.56844	−	0.520325i	−0.213255	−	0.0310954i
$281$	8.65459	+	26.6361i	0.516290	+	1.58898i	0.780923	+	0.624627i	$0.214749\pi$
$281$	8.65459	+	26.6361i	0.516290	+	1.58898i	−0.264633	+	0.964349i	$0.585251\pi$
$282$		0			0
$283$	8.54906	+	4.35596i	0.508189	+	0.258935i	0.689233	−	0.724540i	$-0.257948\pi$
$283$	8.54906	+	4.35596i	0.508189	+	0.258935i	−0.181044	+	0.983475i	$0.557948\pi$
$284$	−3.46290	+	0.975447i	−0.205485	+	0.0578821i
$285$		0			0
$286$	−13.0303	+	24.3687i	−0.770500	+	1.44095i
$287$	0.395119	+	2.49468i	0.0233232	+	0.147257i
$288$		0			0
$289$	−9.04388	−	12.4478i	−0.531993	−	0.732225i
$290$	17.6123	+	4.72834i	1.03423	+	0.277658i
$291$		0			0
$292$	−12.7896	+	5.89113i	−0.748454	+	0.344752i
$293$	0.365499	+	0.365499i	0.0213527	+	0.0213527i	0.717703	−	0.696350i	$-0.245194\pi$
$293$	0.365499	+	0.365499i	0.0213527	+	0.0213527i	−0.696350	+	0.717703i	$0.745194\pi$
$294$		0			0
$295$	−10.2014	−	12.1119i	−0.593951	−	0.705180i
$296$	−0.798671	+	1.36117i	−0.0464218	+	0.0791164i
$297$		0			0
$298$	−5.72970	−	18.8992i	−0.331913	−	1.09480i
$299$	2.83614			0.164018
$300$		0			0
$301$	2.20076			0.126850
$302$	−7.92060	−	26.1257i	−0.455780	−	1.50337i
$303$		0			0
$304$	2.76198	+	0.219146i	0.158410	+	0.0125689i
$305$	27.4984	−	11.1695i	1.57455	−	0.639565i
$306$		0			0
$307$	7.86266	+	7.86266i	0.448745	+	0.448745i	0.894937	−	0.446192i	$-0.147220\pi$
$307$	7.86266	+	7.86266i	0.448745	+	0.448745i	−0.446192	+	0.894937i	$0.647220\pi$
$308$	−2.17794	−	4.72828i	−0.124100	−	0.269419i
$309$		0			0
$310$	−24.4562	+	9.37429i	−1.38902	+	0.532424i
$311$	−11.2964	−	15.5482i	−0.640562	−	0.881658i	0.358084	−	0.933689i	$-0.383430\pi$
$311$	−11.2964	−	15.5482i	−0.640562	−	0.881658i	−0.998645	+	0.0520319i	$0.983430\pi$
$312$		0			0
$313$	1.18066	+	7.45438i	0.0667347	+	0.421346i	0.998326	+	0.0578387i	$0.0184209\pi$
$313$	1.18066	+	7.45438i	0.0667347	+	0.421346i	−0.931591	+	0.363508i	$0.881579\pi$
$314$	10.9631	−	20.5026i	0.618683	−	1.15703i
$315$		0			0
$316$	−4.15190	−	14.7395i	−0.233562	−	0.829162i
$317$	−10.8062	−	5.50604i	−0.606937	−	0.309250i	0.123379	−	0.992360i	$-0.460627\pi$
$317$	−10.8062	−	5.50604i	−0.606937	−	0.309250i	−0.730316	+	0.683110i	$0.760627\pi$
$318$		0			0
$319$	8.13485	+	25.0365i	0.455464	+	1.40177i
$320$	−0.842175	+	17.8687i	−0.0470790	+	0.998891i
$321$		0			0
$322$	−0.322539	+	0.425945i	−0.0179744	+	0.0237370i
$323$	0.137644	−	0.869050i	0.00765872	−	0.0483553i
$324$		0			0
$325$	6.89263	−	20.2618i	0.382334	−	1.12392i
$326$	−22.3973	+	10.8591i	−1.24047	+	0.601428i
$327$		0			0
$328$	12.1248	−	3.15772i	0.669478	−	0.174356i
$329$	5.51753	+	1.79275i	0.304191	+	0.0988377i
$330$		0			0
$331$	−1.45790	+	0.473702i	−0.0801336	+	0.0260370i	−0.348809	−	0.937194i	$-0.613414\pi$
$331$	−1.45790	+	0.473702i	−0.0801336	+	0.0260370i	0.268676	+	0.963231i	$0.413414\pi$
$332$	17.7851	−	2.09926i	0.976086	−	0.115212i
$333$		0			0
$334$	−1.66978	+	9.34182i	−0.0913661	+	0.511162i
$335$	13.5670	−	15.6658i	0.741247	−	0.855913i
$336$		0			0
$337$	1.08031	−	0.171104i	0.0588481	−	0.00932062i	−0.126941	−	0.991910i	$-0.540516\pi$
$337$	1.08031	−	0.171104i	0.0588481	−	0.00932062i	0.185789	+	0.982590i	$0.440516\pi$
$338$	−6.17540	+	4.30255i	−0.335898	+	0.234028i
$339$		0			0
$340$	5.63658	+	0.708255i	0.305687	+	0.0384105i
$341$	−30.5881	−	22.2236i	−1.65644	−	1.20347i
$342$		0			0
$343$	5.51348	−	5.51348i	0.297700	−	0.297700i
$344$	−1.06485	−	10.8649i	−0.0574126	−	0.585794i
$345$		0			0
$346$	1.38153	−	0.190865i	0.0742717	−	0.0102609i
$347$	20.4311	−	10.4102i	1.09680	−	0.558846i	0.190586	−	0.981670i	$-0.438961\pi$
$347$	20.4311	−	10.4102i	1.09680	−	0.558846i	0.906212	+	0.422824i	$0.138961\pi$
$348$		0			0
$349$		−	20.7955i		−	1.11316i	−0.830795	−	0.556578i	$-0.812114\pi$
$349$		−	20.7955i		−	1.11316i	0.830795	−	0.556578i	$-0.187886\pi$
$350$	2.25916	+	3.33944i	0.120757	+	0.178500i
$351$		0			0
$352$	−22.2891	+	13.0400i	−1.18801	+	0.695035i
$353$	−20.9677	+	10.6836i	−1.11600	+	0.568628i	−0.911937	−	0.410330i	$-0.865413\pi$
$353$	−20.9677	+	10.6836i	−1.11600	+	0.568628i	−0.204059	+	0.978959i	$0.565413\pi$
$354$		0			0
$355$	3.41507	+	2.12516i	0.181253	+	0.112792i
$356$	−9.73545	−	3.59513i	−0.515978	−	0.190541i
$357$		0			0
$358$	−0.460379	+	23.2549i	−0.0243318	+	1.22906i
$359$	−28.2460	−	20.5219i	−1.49077	−	1.08311i	−0.973883	−	0.227051i	$-0.927092\pi$
$359$	−28.2460	−	20.5219i	−1.49077	−	1.08311i	−0.516885	−	0.856055i	$-0.672908\pi$
$360$		0			0
$361$	14.9832	−	10.8859i	0.788588	−	0.572943i
$362$	−18.4544	−	26.4873i	−0.969940	−	1.39214i
$363$		0			0
$364$	0.193194	−	4.87745i	0.0101261	−	0.255648i
$365$	14.5031	+	6.12443i	0.759127	+	0.320568i
$366$		0			0
$367$	7.31720	−	14.3608i	0.381955	−	0.749628i	−0.617359	−	0.786682i	$-0.711797\pi$
$367$	7.31720	−	14.3608i	0.381955	−	0.749628i	0.999313	+	0.0370536i	$0.0117972\pi$
$368$	2.25890	+	1.38624i	0.117753	+	0.0722627i
$369$		0			0
$370$	1.72608	−	0.366017i	0.0897346	−	0.0190283i
$371$	−4.66366	−	1.51531i	−0.242125	−	0.0786712i
$372$		0			0
$373$	−11.3634	−	1.79978i	−0.588373	−	0.0931891i	−0.144852	−	0.989453i	$-0.546271\pi$
$373$	−11.3634	−	1.79978i	−0.588373	−	0.0931891i	−0.443520	+	0.896264i	$0.646271\pi$
$374$	3.57772	+	7.37922i	0.185000	+	0.381570i
$375$		0			0
$376$	6.18092	−	28.1068i	0.318757	−	1.44950i
$377$	−3.86143	+	24.3801i	−0.198874	+	1.25564i
$378$		0			0
$379$	3.02441	−	9.30816i	0.155353	−	0.478128i	−0.842843	−	0.538159i	$-0.819120\pi$
$379$	3.02441	−	9.30816i	0.155353	−	0.478128i	0.998197	+	0.0600309i	$0.0191199\pi$
$380$	−1.90022	−	2.44639i	−0.0974794	−	0.125497i
$381$		0			0
$382$	−4.02202	+	11.5926i	−0.205784	+	0.593127i
$383$	14.8289	+	7.55569i	0.757720	+	0.386078i	0.789766	−	0.613409i	$-0.210202\pi$
$383$	14.8289	+	7.55569i	0.757720	+	0.386078i	−0.0320454	+	0.999486i	$0.510202\pi$
$384$		0			0
$385$	−2.26419	+	5.36176i	−0.115394	+	0.273261i
$386$	6.36419	+	3.40304i	0.323929	+	0.173210i
$387$		0			0
$388$	22.0653	+	12.3664i	1.12019	+	0.627808i
$389$	−8.71062	−	11.9891i	−0.441646	−	0.607873i	0.528931	−	0.848665i	$-0.322593\pi$
$389$	−8.71062	−	11.9891i	−0.441646	−	0.607873i	−0.970577	+	0.240792i	$0.922593\pi$
$390$		0			0
$391$	0.494723	−	0.680928i	0.0250192	−	0.0344360i
$392$	−14.5883	−	11.9840i	−0.736819	−	0.605282i
$393$		0			0
$394$	−11.3805	−	11.8402i	−0.573343	−	0.596502i
$395$	−9.04555	+	14.5359i	−0.455131	+	0.731381i
$396$		0			0
$397$	16.9966	+	33.3577i	0.853034	+	1.67417i	0.731768	+	0.681554i	$0.238696\pi$
$397$	16.9966	+	33.3577i	0.853034	+	1.67417i	0.121267	+	0.992620i	$0.461304\pi$
$398$	−1.72079	+	0.521695i	−0.0862552	+	0.0261502i
$399$		0			0
$400$	15.3933	−	12.7690i	0.769664	−	0.638449i
$401$	−6.38092			−0.318648			−0.159324	−	0.987226i	$-0.550931\pi$
$401$	−6.38092			−0.318648			−0.159324	+	0.987226i	$0.550931\pi$
$402$		0			0
$403$	−16.0950	−	31.5882i	−0.801748	−	1.57352i
$404$	30.8847	−	20.6223i	1.53657	−	1.02600i
$405$		0			0
$406$	−3.22238	−	3.35254i	−0.159924	−	0.166384i
$407$	1.80109	+	1.80109i	0.0892767	+	0.0892767i
$408$		0			0
$409$	7.75145	−	10.6690i	0.383285	−	0.527546i	−0.573166	−	0.819439i	$-0.694285\pi$
$409$	7.75145	−	10.6690i	0.383285	−	0.527546i	0.956451	+	0.291893i	$0.0942851\pi$
$410$	−11.7445	−	7.63503i	−0.580018	−	0.377067i
$411$		0			0
$412$	13.0850	+	7.33343i	0.644651	+	0.361292i
$413$	0.631683	+	3.98829i	0.0310831	+	0.196251i
$414$		0			0
$415$	−15.1355	−	13.1078i	−0.742972	−	0.643437i
$416$	−24.1729	+	1.40620i	−1.18517	+	0.0689447i
$417$		0			0
$418$	1.46575	−	4.22469i	0.0716921	−	0.206636i
$419$	1.32767	+	4.08615i	0.0648610	+	0.199622i	0.978235	−	0.207500i	$-0.0665326\pi$
$419$	1.32767	+	4.08615i	0.0648610	+	0.199622i	−0.913374	+	0.407121i	$0.866533\pi$
$420$		0			0
$421$	−1.80550	+	5.55676i	−0.0879948	+	0.270820i	−0.985365	−	0.170459i	$-0.945475\pi$
$421$	−1.80550	+	5.55676i	−0.0879948	+	0.270820i	0.897370	+	0.441279i	$0.145475\pi$
$422$	−4.92634	−	3.73038i	−0.239810	−	0.181592i
$423$		0			0
$424$	−5.22439	+	23.7571i	−0.253719	+	1.15375i
$425$	−3.66234	−	5.18923i	−0.177650	−	0.251715i
$426$		0			0
$427$	−7.47515	−	1.18395i	−0.361748	−	0.0572952i
$428$	2.24221	+	0.446746i	0.108381	+	0.0215943i
$429$		0			0
$430$	−8.17145	+	9.06649i	−0.394062	+	0.437225i
$431$	2.92353	−	0.949912i	0.140821	−	0.0457556i	−0.237758	−	0.971324i	$-0.576413\pi$
$431$	2.92353	−	0.949912i	0.140821	−	0.0457556i	0.378580	+	0.925569i	$0.376413\pi$
$432$		0			0
$433$	−12.4138	+	24.3634i	−0.596568	+	1.17083i	0.373416	+	0.927664i	$0.378186\pi$
$433$	−12.4138	+	24.3634i	−0.596568	+	1.17083i	−0.969984	+	0.243167i	$0.921814\pi$
$434$	6.57446	+	1.17513i	0.315584	+	0.0564081i
$435$		0			0
$436$	−1.42366	+	35.9422i	−0.0681809	+	1.72132i
$437$	−0.453298	+	0.0717953i	−0.0216842	+	0.00343444i
$438$		0			0
$439$	−19.5015	+	14.1687i	−0.930757	+	0.676235i	−0.946178	−	0.323646i	$-0.895091\pi$
$439$	−19.5015	+	14.1687i	−0.930757	+	0.676235i	0.0154210	+	0.999881i	$0.495091\pi$
$440$	27.5659	+	8.58372i	1.31415	+	0.409213i
$441$		0			0
$442$	−0.152202	+	7.68810i	−0.00723950	+	0.365686i
$443$	−17.8280	+	17.8280i	−0.847032	+	0.847032i	−0.989762	−	0.142730i	$-0.954412\pi$
$443$	−17.8280	+	17.8280i	−0.847032	+	0.847032i	0.142730	+	0.989762i	$0.454412\pi$
$444$		0			0
$445$	4.36654	+	10.7500i	0.206994	+	0.509601i
$446$	2.22036	+	16.0716i	0.105137	+	0.761014i
$447$		0			0
$448$	2.53786	−	3.79031i	0.119903	−	0.179076i
$449$		−	10.8433i		−	0.511725i	−0.966713	−	0.255862i	$-0.917641\pi$
$449$		−	10.8433i		−	0.511725i	0.966713	−	0.255862i	$-0.0823594\pi$
$450$		0			0
$451$		−	20.2217i		−	0.952201i
$452$	16.0291	+	17.3513i	0.753948	+	0.816138i
$453$		0			0
$454$	41.9960	−	5.80192i	1.97097	−	0.272298i
$455$	−4.17411	+	3.51573i	−0.195686	+	0.164820i
$456$		0			0
$457$	−10.7529	+	10.7529i	−0.502999	+	0.502999i	−0.912369	−	0.409369i	$-0.865749\pi$
$457$	−10.7529	+	10.7529i	−0.502999	+	0.502999i	0.409369	+	0.912369i	$0.365749\pi$
$458$	1.22597	+	0.0242707i	0.0572860	+	0.00113410i
$459$		0			0
$460$	−0.557179	−	2.91031i	−0.0259786	−	0.135694i
$461$	6.99954	−	5.08547i	0.326001	−	0.236854i	−0.412731	−	0.910853i	$-0.635425\pi$
$461$	6.99954	−	5.08547i	0.326001	−	0.236854i	0.738732	+	0.673999i	$0.235425\pi$
$462$		0			0
$463$	−6.98414	+	1.10618i	−0.324581	+	0.0514085i	−0.316599	−	0.948560i	$-0.602541\pi$
$463$	−6.98414	+	1.10618i	−0.324581	+	0.0514085i	−0.00798209	+	0.999968i	$0.502541\pi$
$464$	−14.9919	+	17.5306i	−0.695983	+	0.813839i
$465$		0			0
$466$	2.35586	−	13.1802i	0.109133	−	0.610562i
$467$	−8.40547	+	16.4967i	−0.388959	+	0.763374i	−0.999593	−	0.0285385i	$-0.990915\pi$
$467$	−8.40547	+	16.4967i	−0.388959	+	0.763374i	0.610634	+	0.791913i	$0.290915\pi$
$468$		0			0
$469$	−5.02586	+	1.63300i	−0.232073	+	0.0754050i
$470$	−27.8723	+	16.0741i	−1.28565	+	0.741443i
$471$		0			0
$472$	19.3841	−	5.04829i	0.892223	−	0.232367i
$473$	−17.4026	−	2.75630i	−0.800171	−	0.126735i
$474$		0			0
$475$	−0.588726	+	3.41291i	−0.0270126	+	0.156595i
$476$	−1.13733	−	0.897185i	−0.0521293	−	0.0411224i
$477$		0			0
$478$	−9.44901	+	12.4784i	−0.432187	+	0.570747i
$479$	7.81425	−	24.0498i	0.357042	−	1.09886i	−0.597774	−	0.801665i	$-0.703948\pi$
$479$	7.81425	−	24.0498i	0.357042	−	1.09886i	0.954816	−	0.297198i	$-0.0960521\pi$
$480$		0			0
$481$	0.738042	+	2.27146i	0.0336518	+	0.103570i
$482$	−0.980158	−	0.340064i	−0.0446450	−	0.0154895i
$483$		0			0
$484$	5.33535	+	18.9409i	0.242516	+	0.860948i
$485$	−6.41276	−	27.5432i	−0.291189	−	1.25067i
$486$		0			0
$487$	−3.69540	−	23.3318i	−0.167455	−	1.05727i	−0.918038	−	0.396491i	$-0.870228\pi$
$487$	−3.69540	−	23.3318i	−0.167455	−	1.05727i	0.750584	−	0.660775i	$-0.229772\pi$
$488$	−2.22812	+	37.4767i	−0.100862	+	1.69649i
$489$		0			0
$490$	1.09450	+	21.0795i	0.0494444	+	0.952273i
$491$	14.0618	−	19.3544i	0.634599	−	0.873451i	−0.363714	−	0.931511i	$-0.618491\pi$
$491$	14.0618	−	19.3544i	0.634599	−	0.873451i	0.998313	+	0.0580598i	$0.0184914\pi$
$492$		0			0
$493$	5.17984	+	5.17984i	0.233288	+	0.233288i
$494$	3.02300	−	2.90563i	0.136011	−	0.130730i
$495$		0			0
$496$	2.62040	−	33.0259i	0.117659	−	1.48291i
$497$	−0.465644	−	0.913879i	−0.0208870	−	0.0409931i
$498$		0			0
$499$	−3.20194			−0.143339			−0.0716693	−	0.997428i	$-0.522833\pi$
$499$	−3.20194			−0.143339			−0.0716693	+	0.997428i	$0.522833\pi$
$500$	−22.1458	−	3.09231i	−0.990391	−	0.138292i
$501$		0			0
$502$	−5.39221	−	17.7859i	−0.240666	−	0.793825i
$503$	5.20750	+	10.2203i	0.232191	+	0.455701i	0.977476	−	0.211045i	$-0.0676867\pi$
$503$	5.20750	+	10.2203i	0.232191	+	0.455701i	−0.745285	+	0.666746i	$0.767687\pi$
$504$		0			0
$505$	−40.3055	−	9.96981i	−1.79357	−	0.443651i
$506$	3.08396	−	2.96422i	0.137099	−	0.131776i
$507$		0			0
$508$	36.0678	−	16.6135i	1.60025	−	0.737106i
$509$	−13.6267	+	18.7556i	−0.603994	+	0.831327i	−0.996067	−	0.0886075i	$-0.971758\pi$
$509$	−13.6267	+	18.7556i	−0.603994	+	0.831327i	0.392072	+	0.919934i	$0.371758\pi$
$510$		0			0
$511$	−2.35963	−	3.24775i	−0.104384	−	0.143672i
$512$	−19.9403	−	10.6951i	−0.881244	−	0.472662i
$513$		0			0
$514$	−10.4224	+	19.4915i	−0.459713	+	0.859732i
$515$	−3.80285	−	16.3335i	−0.167574	−	0.719740i
$516$		0			0
$517$	−41.3847	−	21.0866i	−1.82010	−	0.927387i
$518$	−0.425072	−	0.147478i	−0.0186766	−	0.00647982i
$519$		0			0
$520$	19.3764	+	18.9060i	0.849711	+	0.829082i
$521$	4.78400	−	14.7236i	0.209591	−	0.645054i	−0.789903	−	0.613232i	$-0.789869\pi$
$521$	4.78400	−	14.7236i	0.209591	−	0.645054i	0.999494	−	0.0318218i	$-0.0101309\pi$
$522$		0			0
$523$	−1.35911	+	8.58111i	−0.0594299	+	0.375226i	0.939991	+	0.341199i	$0.110833\pi$
$523$	−1.35911	+	8.58111i	−0.0594299	+	0.375226i	−0.999421	+	0.0340265i	$0.989167\pi$
$524$	28.2106	−	35.7615i	1.23239	−	1.56225i
$525$		0			0
$526$	−17.7872	+	8.62390i	−0.775558	+	0.376020i
$527$	−10.3915	−	1.64586i	−0.452662	−	0.0716946i
$528$		0			0
$529$	21.4568	+	6.97173i	0.932903	+	0.303119i
$530$	23.5589	−	13.5866i	1.02333	−	0.590162i
$531$		0			0
$532$	0.0925920	+	0.784450i	0.00401437	+	0.0340102i
$533$	8.60819	−	16.8945i	0.372862	−	0.731783i
$534$		0			0
$535$	−1.32058	−	2.18859i	−0.0570935	−	0.0946210i
$536$	10.4937	+	24.0219i	0.453259	+	1.03759i
$537$		0			0
$538$	7.26739	−	5.06337i	0.313319	−	0.218297i
$539$	−24.6513	+	17.9102i	−1.06181	+	0.771448i
$540$		0			0
$541$	30.7034	+	22.3073i	1.32004	+	0.959067i	0.999932	+	0.0116875i	$0.00372033\pi$
$541$	30.7034	+	22.3073i	1.32004	+	0.959067i	0.320111	+	0.947380i	$0.396280\pi$
$542$	−28.3657	−	0.561559i	−1.21841	−	0.0241210i
$543$		0			0
$544$	−3.87899	+	6.04895i	−0.166310	+	0.259346i
$545$	30.7593	−	25.9076i	1.31758	−	1.10976i
$546$		0			0
$547$	−12.8211	+	6.53267i	−0.548190	+	0.279317i	−0.706071	−	0.708141i	$-0.749534\pi$
$547$	−12.8211	+	6.53267i	−0.548190	+	0.279317i	0.157881	+	0.987458i	$0.449534\pi$
$548$	24.5662	−	22.6943i	1.04942	−	0.969451i
$549$		0			0
$550$	−13.6820	−	29.2362i	−0.583401	−	1.24663i
$551$		−	3.99440i		−	0.170167i
$552$		0			0
$553$	3.88984	−	1.98197i	0.165413	−	0.0842820i
$554$	−1.93335	−	13.9941i	−0.0821401	−	0.594554i
$555$		0			0
$556$	−0.849199	+	2.29960i	−0.0360141	+	0.0975246i
$557$	−22.6217	+	22.6217i	−0.958513	+	0.958513i	−0.999173	−	0.0406596i	$-0.987054\pi$
$557$	−22.6217	+	22.6217i	−0.958513	+	0.958513i	0.0406596	+	0.999173i	$0.487054\pi$
$558$		0			0
$559$	−13.3659	−	9.71092i	−0.565319	−	0.410728i
$560$	−5.04296	+	0.759962i	−0.213104	+	0.0321143i
$561$		0			0
$562$	22.6420	+	32.4978i	0.955095	+	1.37084i
$563$	33.9090	−	5.37066i	1.42909	−	0.226346i	0.606549	−	0.795046i	$-0.292553\pi$
$563$	33.9090	−	5.37066i	1.42909	−	0.226346i	0.822545	+	0.568700i	$0.192553\pi$
$564$		0			0
$565$	2.25294	−	26.3140i	0.0947819	−	1.10704i
$566$	13.3574	+	2.38754i	0.561455	+	0.100356i
$567$		0			0
$568$	−4.28640	+	2.74101i	−0.179853	+	0.115010i
$569$	13.8272	−	4.49274i	0.579667	−	0.188345i	−0.00448435	−	0.999990i	$-0.501427\pi$
$569$	13.8272	−	4.49274i	0.579667	−	0.188345i	0.584151	+	0.811645i	$0.301427\pi$
$570$		0			0
$571$	32.5728	+	10.5835i	1.36313	+	0.442908i	0.897087	−	0.441854i	$-0.145679\pi$
$571$	32.5728	+	10.5835i	1.36313	+	0.442908i	0.466043	+	0.884762i	$0.345679\pi$
$572$	−7.63636	+	38.3267i	−0.319292	+	1.60252i
$573$		0			0
$574$	1.55834	+	3.21414i	0.0650438	+	0.134156i
$575$	−1.98392	+	2.65320i	−0.0827354	+	0.110646i
$576$		0			0
$577$	4.65814	−	29.4103i	0.193921	−	1.22437i	−0.678126	−	0.734945i	$-0.737208\pi$
$577$	4.65814	−	29.4103i	0.193921	−	1.22437i	0.872047	−	0.489422i	$-0.162792\pi$
$578$	−17.3473	−	13.1359i	−0.721552	−	0.546382i
$579$		0			0
$580$	25.7763	−	0.827225i	1.07030	−	0.0343487i
$581$	1.57772	+	4.85574i	0.0654550	+	0.201450i
$582$		0			0
$583$	34.9802	+	17.8233i	1.44873	+	0.738166i
$584$	−14.8920	+	13.2206i	−0.616236	+	0.547074i
$585$		0			0
$586$	0.644627	+	0.344693i	0.0266293	+	0.0142391i
$587$	−0.417161	−	2.63385i	−0.0172181	−	0.108711i	0.977583	−	0.210553i	$-0.0675264\pi$
$587$	−0.417161	−	2.63385i	−0.0172181	−	0.108711i	−0.994801	+	0.101842i	$0.967526\pi$
$588$		0			0
$589$	3.37208	+	4.64127i	0.138944	+	0.191240i
$590$	−18.7761	−	12.2062i	−0.772999	−	0.502523i
$591$		0			0
$592$	−0.522408	+	2.16989i	−0.0214708	+	0.0891817i
$593$	4.29407	+	4.29407i	0.176336	+	0.176336i	0.789757	−	0.613420i	$-0.210207\pi$
$593$	4.29407	+	4.29407i	0.176336	+	0.176336i	−0.613420	+	0.789757i	$0.710207\pi$
$594$		0			0
$595$	0.115977	+	1.61543i	0.00475460	+	0.0662262i
$596$	−15.5090	−	23.2269i	−0.635272	−	0.951409i
$597$		0			0
$598$	3.83839	−	1.16369i	0.156963	−	0.0475869i
$599$	1.90922			0.0780086			0.0390043	−	0.999239i	$-0.487581\pi$
$599$	1.90922			0.0780086			0.0390043	+	0.999239i	$0.487581\pi$
$600$		0			0
$601$	−19.9000			−0.811739			−0.405869	−	0.913931i	$-0.633031\pi$
$601$	−19.9000			−0.811739			−0.405869	+	0.913931i	$0.633031\pi$
$602$	2.97847	−	0.902990i	0.121393	−	0.0368031i
$603$		0			0
$604$	−21.4392	−	32.1082i	−0.872350	−	1.30647i
$605$	11.6239	−	18.6792i	0.472578	−	0.759418i
$606$		0			0
$607$	6.68008	+	6.68008i	0.271136	+	0.271136i	0.829557	−	0.558421i	$-0.188593\pi$
$607$	6.68008	+	6.68008i	0.271136	+	0.271136i	−0.558421	+	0.829557i	$0.688593\pi$
$608$	3.82793	−	0.836674i	0.155243	−	0.0339316i
$609$		0			0
$610$	32.6329	−	26.3995i	1.32127	−	1.06888i
$611$	−25.5992	−	35.2343i	−1.03563	−	1.42543i
$612$		0			0
$613$	1.64882	+	10.4102i	0.0665950	+	0.420465i	0.998352	+	0.0573826i	$0.0182755\pi$
$613$	1.64882	+	10.4102i	0.0665950	+	0.420465i	−0.931757	+	0.363082i	$0.881725\pi$
$614$	13.8673	+	7.41507i	0.559639	+	0.299248i
$615$		0			0
$616$	−4.88764	−	5.50555i	−0.196929	−	0.221825i
$617$	33.5664	+	17.1029i	1.35133	+	0.688538i	0.971616	−	0.236564i	$-0.0760214\pi$
$617$	33.5664	+	17.1029i	1.35133	+	0.688538i	0.379717	+	0.925103i	$0.376021\pi$
$618$		0			0
$619$	−11.4354	−	35.1945i	−0.459627	−	1.41459i	−0.865616	−	0.500708i	$-0.833073\pi$
$619$	−11.4354	−	35.1945i	−0.459627	−	1.41459i	0.405989	−	0.913878i	$-0.366927\pi$
$620$	−29.2523	+	22.7216i	−1.17480	+	0.912522i
$621$		0			0
$622$	−21.6680	−	16.4077i	−0.868806	−	0.657887i
$623$	0.462845	−	2.92229i	0.0185435	−	0.117079i
$624$		0			0
$625$	14.1334	+	20.6215i	0.565336	+	0.824860i
$626$	4.65648	+	9.60420i	0.186110	+	0.383861i
$627$		0			0
$628$	6.42486	−	32.2462i	0.256380	−	1.28676i
$629$	0.674095	+	0.219027i	0.0268779	+	0.00873316i
$630$		0			0
$631$	11.9182	−	3.87246i	0.474456	−	0.154160i	−0.0620213	−	0.998075i	$-0.519755\pi$
$631$	11.9182	−	3.87246i	0.474456	−	0.154160i	0.536477	+	0.843915i	$0.319755\pi$
$632$	−11.6669	−	18.2447i	−0.464083	−	0.725733i
$633$		0			0
$634$	−16.8841	−	3.01790i	−0.670554	−	0.119856i
$635$	−40.9000	−	17.2715i	−1.62307	−	0.685397i
$636$		0			0
$637$	−28.2196	+	4.46954i	−1.11810	+	0.177090i
$638$	21.2823	+	30.5462i	0.842573	+	1.20933i
$639$		0			0
$640$	6.19190	+	24.5288i	0.244756	+	0.969585i
$641$	−12.9136	−	9.38230i	−0.510058	−	0.370579i	0.302788	−	0.953058i	$-0.402083\pi$
$641$	−12.9136	−	9.38230i	−0.510058	−	0.370579i	−0.812845	+	0.582479i	$0.802083\pi$
$642$		0			0
$643$	−18.8472	+	18.8472i	−0.743260	+	0.743260i	−0.973204	−	0.229944i	$-0.926146\pi$
$643$	−18.8472	+	18.8472i	−0.743260	+	0.743260i	0.229944	+	0.973204i	$0.426146\pi$
$644$	−0.261750	+	0.708808i	−0.0103144	+	0.0279309i
$645$		0			0
$646$	−0.170294	−	1.23264i	−0.00670012	−	0.0484974i
$647$	−9.13665	+	4.65536i	−0.359199	+	0.183021i	−0.624271	−	0.781207i	$-0.714604\pi$
$647$	−9.13665	+	4.65536i	−0.359199	+	0.183021i	0.265073	+	0.964228i	$0.414604\pi$
$648$		0			0
$649$		−	32.3287i		−	1.26901i
$650$	1.01477	−	30.2501i	0.0398024	−	1.18651i
$651$		0			0
$652$	−25.8566	+	23.8863i	−1.01262	+	0.935459i
$653$	16.6573	−	8.48730i	0.651849	−	0.332134i	−0.0966028	−	0.995323i	$-0.530798\pi$
$653$	16.6573	−	8.48730i	0.651849	−	0.332134i	0.748452	+	0.663189i	$0.230798\pi$
$654$		0			0
$655$	−50.7947	+	3.64673i	−1.98472	+	0.142489i
$656$	15.1138	−	9.24850i	0.590096	−	0.361093i
$657$		0			0
$658$	8.20291	+	0.162394i	0.319783	+	0.00633076i
$659$	−2.98224	−	2.16672i	−0.116171	−	0.0844035i	0.528183	−	0.849131i	$-0.322874\pi$
$659$	−2.98224	−	2.16672i	−0.116171	−	0.0844035i	−0.644354	+	0.764727i	$0.722874\pi$
$660$		0			0
$661$	19.7563	−	14.3538i	0.768432	−	0.558299i	−0.133053	−	0.991109i	$-0.542478\pi$
$661$	19.7563	−	14.3538i	0.768432	−	0.558299i	0.901485	+	0.432810i	$0.142478\pi$
$662$	−1.77874	+	1.23929i	−0.0691327	+	0.0481664i
$663$		0			0
$664$	23.2088	−	10.1385i	0.900675	−	0.393450i
$665$	0.578146	−	0.667581i	0.0224196	−	0.0258877i
$666$		0			0
$667$	1.73467	−	3.40448i	0.0671667	−	0.131822i
$668$	1.57318	+	13.3282i	0.0608683	+	0.515683i
$669$		0			0
$670$	11.9336	−	26.7685i	0.461036	−	1.03416i
$671$	57.6272	+	18.7242i	2.22467	+	0.722840i
$672$		0			0
$673$	−23.5644	−	3.73224i	−0.908342	−	0.143867i	−0.315256	−	0.949007i	$-0.602090\pi$
$673$	−23.5644	−	3.73224i	−0.908342	−	0.143867i	−0.593086	+	0.805139i	$0.702090\pi$
$674$	1.39186	−	0.674828i	0.0536126	−	0.0259934i
$675$		0			0
$676$	−6.59231	+	8.35682i	−0.253550	+	0.321416i
$677$	−1.26062	+	7.95924i	−0.0484495	+	0.305898i	−0.999999	−	0.00159823i	$-0.999491\pi$
$677$	−1.26062	+	7.95924i	−0.0484495	+	0.305898i	0.951549	+	0.307497i	$0.0994913\pi$
$678$		0			0
$679$	−2.22840	+	6.85830i	−0.0855180	+	0.263197i
$680$	7.91906	−	1.35420i	0.303682	−	0.0519311i
$681$		0			0
$682$	−50.5160	−	17.5264i	−1.93436	−	0.671122i
$683$	35.5849	+	18.1314i	1.36162	+	0.693780i	0.973683	−	0.227906i	$-0.0731880\pi$
$683$	35.5849	+	18.1314i	1.36162	+	0.693780i	0.387937	+	0.921686i	$0.373188\pi$
$684$		0			0
$685$	−37.2557	−	3.18974i	−1.42347	−	0.121874i
$686$	5.19962	−	9.72408i	0.198523	−	0.371267i
$687$		0			0
$688$	−5.89909	−	14.2674i	−0.224901	−	0.543940i
$689$	21.6376	+	29.7816i	0.824326	+	1.13459i
$690$		0			0
$691$	−28.5593	+	39.3084i	−1.08645	+	1.49536i	−0.234223	+	0.972183i	$0.575255\pi$
$691$	−28.5593	+	39.3084i	−1.08645	+	1.49536i	−0.852222	+	0.523181i	$0.824745\pi$
$692$	1.79143	−	0.825168i	0.0681000	−	0.0313682i
$693$		0			0
$694$	23.3797	−	22.4720i	0.887482	−	0.853025i
$695$	2.53925	−	1.03141i	0.0963192	−	0.0391237i
$696$		0			0
$697$	−2.55463	−	5.01374i	−0.0967635	−	0.189909i
$698$	−8.53257	−	28.1443i	−0.322962	−	1.06528i
$699$		0			0
$700$	4.42771	+	3.59259i	0.167352	+	0.135787i
$701$	0.239240			0.00903597			0.00451799	−	0.999990i	$-0.498562\pi$
$701$	0.239240			0.00903597			0.00451799	+	0.999990i	$0.498562\pi$
$702$		0			0
$703$	−0.175461	−	0.344362i	−0.00661765	−	0.0129879i
$704$	−24.8153	+	26.7936i	−0.935262	+	1.00982i
$705$		0			0
$706$	−23.9937	+	23.0622i	−0.903016	+	0.867956i
$707$	7.48646	+	7.48646i	0.281557	+	0.281557i
$708$		0			0
$709$	−8.43241	+	11.6062i	−0.316686	+	0.435881i	−0.937452	−	0.348115i	$-0.886822\pi$
$709$	−8.43241	+	11.6062i	−0.316686	+	0.435881i	0.620766	+	0.783996i	$0.286822\pi$
$710$	5.49387	+	1.47493i	0.206181	+	0.0553530i
$711$		0			0
$712$	−14.6509	−	0.871046i	−0.549066	−	0.0326438i
$713$	0.858481	+	5.42024i	0.0321504	+	0.202989i
$714$		0			0
$715$	37.4102	−	22.5730i	1.39906	−	0.844181i
$716$	8.91863	+	31.6617i	0.333305	+	1.18325i
$717$		0			0
$718$	−46.6480	−	16.1845i	−1.74089	−	0.603999i
$719$	9.40688	+	28.9514i	0.350818	+	1.07971i	0.958395	+	0.285445i	$0.0921414\pi$
$719$	9.40688	+	28.9514i	0.350818	+	1.07971i	−0.607578	+	0.794260i	$0.707859\pi$
$720$		0			0
$721$	−1.32147	+	4.06706i	−0.0492141	+	0.151465i
$722$	15.8114	−	20.8805i	0.588439	−	0.777093i
$723$		0			0
$724$	−35.8438	−	28.2755i	−1.33213	−	1.05085i
$725$	−20.1064	−	20.6666i	−0.746733	−	0.767539i
$726$		0			0
$727$	21.2294	+	3.36240i	0.787354	+	0.124705i	0.537148	−	0.843488i	$-0.319502\pi$
$727$	21.2294	+	3.36240i	0.787354	+	0.124705i	0.250206	+	0.968193i	$0.419502\pi$
$728$	−1.73980	−	6.68033i	−0.0644811	−	0.247590i
$729$		0			0
$730$	22.1412	+	2.33796i	0.819481	+	0.0865319i
$731$	−4.66298	+	1.51510i	−0.172467	+	0.0560378i
$732$		0			0
$733$	14.4461	−	28.3522i	0.533581	−	1.04721i	−0.454133	−	0.890934i	$-0.650051\pi$
$733$	14.4461	−	28.3522i	0.533581	−	1.04721i	0.987713	−	0.156277i	$-0.0499492\pi$
$734$	4.01061	−	22.4380i	0.148034	−	0.828201i
$735$		0			0
$736$	3.62594	+	0.949267i	0.133654	+	0.0349904i
$737$	41.7874	−	6.61847i	1.53926	−	0.243795i
$738$		0			0
$739$	9.06553	−	6.58650i	0.333481	−	0.242288i	−0.408425	−	0.912792i	$-0.633922\pi$
$739$	9.06553	−	6.58650i	0.333481	−	0.242288i	0.741906	+	0.670504i	$0.233922\pi$
$740$	2.18587	−	1.20359i	0.0803541	−	0.0442447i
$741$		0			0
$742$	−6.93347	−	0.137262i	−0.254536	−	0.00503906i
$743$	22.0818	−	22.0818i	0.810104	−	0.810104i	−0.174545	−	0.984649i	$-0.555846\pi$
$743$	22.0818	−	22.0818i	0.810104	−	0.810104i	0.984649	+	0.174545i	$0.0558455\pi$
$744$		0			0
$745$	−7.49780	+	30.3118i	−0.274698	+	1.11054i
$746$	−16.1175	+	2.22669i	−0.590102	+	0.0815250i
$747$		0			0
$748$	7.86979	+	8.51894i	0.287748	+	0.311483i
$749$			0.651803i			0.0238164i
$750$		0			0
$751$		−	3.26645i		−	0.119194i	−0.998223	−	0.0595972i	$-0.981018\pi$
$751$		−	3.26645i		−	0.119194i	0.998223	−	0.0595972i	$-0.0189816\pi$
$752$	−3.16730	−	40.5753i	−0.115499	−	1.47963i
$753$		0			0
$754$	4.77737	+	34.5800i	0.173982	+	1.25933i
$755$	−10.3648	+	41.9022i	−0.377213	+	1.52498i
$756$		0			0
$757$	−1.58095	+	1.58095i	−0.0574608	+	0.0574608i	−0.735253	−	0.677792i	$-0.762937\pi$
$757$	−1.58095	+	1.58095i	−0.0574608	+	0.0574608i	0.677792	+	0.735253i	$0.262937\pi$
$758$	0.273961	−	13.8385i	0.00995070	−	0.502635i
$759$		0			0
$760$	−3.57550	−	2.53122i	−0.129697	−	0.0918172i
$761$	0.114145	−	0.0829313i	0.00413776	−	0.00300626i	−0.585714	−	0.810517i	$-0.699186\pi$
$761$	0.114145	−	0.0829313i	0.00413776	−	0.00300626i	0.589852	+	0.807511i	$0.299186\pi$
$762$		0			0
$763$	−10.1287	+	1.60422i	−0.366682	+	0.0580768i
$764$	−0.686809	+	17.3394i	−0.0248479	+	0.627319i
$765$		0			0
$766$	23.1693	+	4.14133i	0.837142	+	0.149632i
$767$	13.7621	−	27.0096i	0.496919	−	0.975258i
$768$		0			0
$769$	30.9057	−	10.0419i	1.11449	−	0.362120i	0.306828	−	0.951765i	$-0.400733\pi$
$769$	30.9057	−	10.0419i	1.11449	−	0.362120i	0.807662	+	0.589645i	$0.200733\pi$
$770$	−0.864340	+	8.18554i	−0.0311487	+	0.294986i
$771$		0			0
$772$	10.0095	+	1.99433i	0.360249	+	0.0717776i
$773$	−35.2942	−	5.59005i	−1.26944	−	0.201060i	−0.514866	−	0.857271i	$-0.672158\pi$
$773$	−35.2942	−	5.59005i	−1.26944	−	0.201060i	−0.754578	+	0.656210i	$0.772158\pi$
$774$		0			0
$775$	40.8094	+	7.03959i	1.46592	+	0.252870i
$776$	34.9368	+	7.68290i	1.25416	+	0.275800i
$777$		0			0
$778$	−16.7080	−	12.6519i	−0.599013	−	0.453591i
$779$	−0.948164	+	2.91815i	−0.0339715	+	0.104554i
$780$		0			0
$781$	2.53753	+	7.80972i	0.0908000	+	0.279454i
$782$	0.390160	−	1.12455i	0.0139521	−	0.0402137i
$783$		0			0
$784$	−24.6606	−	10.2332i	−0.880737	−	0.365472i
$785$	−31.4751	+	18.9918i	−1.12339	+	0.677846i
$786$		0			0
$787$	−2.87851	−	18.1742i	−0.102608	−	0.647841i	−0.984365	−	0.176138i	$-0.943639\pi$
$787$	−2.87851	−	18.1742i	−0.102608	−	0.647841i	0.881758	−	0.471703i	$-0.156361\pi$
$788$	−20.2604	−	11.3548i	−0.721746	−	0.404500i
$789$		0			0
$790$	−6.27789	+	23.3841i	−0.223357	+	0.831970i
$791$	−3.95844	+	5.44832i	−0.140746	+	0.193720i
$792$		0			0
$793$	40.1749	+	40.1749i	1.42665	+	1.42665i
$794$	36.6898	+	38.1719i	1.30207	+	1.35467i
$795$		0			0
$796$	−2.11483	+	1.41211i	−0.0749581	+	0.0500508i
$797$	0.180269	+	0.353797i	0.00638545	+	0.0125322i	0.894177	−	0.447713i	$-0.147761\pi$
$797$	0.180269	+	0.353797i	0.00638545	+	0.0125322i	−0.887792	+	0.460245i	$0.847761\pi$
$798$		0			0
$799$	−12.9248			−0.457246
$800$	15.5938	−	23.5973i	0.551324	−	0.834291i
$801$		0			0
$802$	−8.63583	+	2.61815i	−0.304942	+	0.0924500i
$803$	14.5913	+	28.6370i	0.514915	+	1.01058i
$804$		0			0
$805$	0.782676	−	0.317914i	0.0275857	−	0.0112050i
$806$	−34.7436	−	36.1470i	−1.22379	−	1.27322i
$807$		0			0
$808$	33.3374	−	40.5821i	1.17280	−	1.42767i
$809$	−27.2343	+	37.4848i	−0.957506	+	1.31789i	−0.00939488	+	0.999956i	$0.502991\pi$
$809$	−27.2343	+	37.4848i	−0.957506	+	1.31789i	−0.948111	+	0.317938i	$0.897009\pi$
$810$		0			0
$811$	10.0855	+	13.8814i	0.354148	+	0.487443i	0.948507	−	0.316757i	$-0.102594\pi$
$811$	10.0855	+	13.8814i	0.354148	+	0.487443i	−0.594358	+	0.804200i	$0.702594\pi$
$812$	−5.73669	−	3.21511i	−0.201319	−	0.112828i
$813$		0			0
$814$	3.17657	+	1.69856i	0.111339	+	0.0595346i
$815$	39.2126	+	3.35728i	1.37356	+	0.117600i
$816$		0			0
$817$	2.38209	+	1.21374i	0.0833388	+	0.0424633i
$818$	6.11312	−	17.6197i	0.213740	−	0.616058i
$819$		0			0
$820$	−19.0275	−	5.51427i	−0.664469	−	0.192567i
$821$	7.99259	−	24.5987i	0.278943	−	0.858499i	−0.709206	−	0.705002i	$-0.750946\pi$
$821$	7.99259	−	24.5987i	0.278943	−	0.858499i	0.988149	−	0.153498i	$-0.0490537\pi$
$822$		0			0
$823$	−4.34747	+	27.4488i	−0.151543	+	0.956806i	0.788323	+	0.615262i	$0.210950\pi$
$823$	−4.34747	+	27.4488i	−0.151543	+	0.956806i	−0.939866	+	0.341544i	$0.889050\pi$
$824$	20.7180	+	4.55606i	0.721745	+	0.158718i
$825$		0			0
$826$	2.49134	+	5.13850i	0.0866848	+	0.178791i
$827$	−27.6226	−	4.37499i	−0.960533	−	0.152133i	−0.343571	−	0.939127i	$-0.611637\pi$
$827$	−27.6226	−	4.37499i	−0.960533	−	0.152133i	−0.616962	+	0.786993i	$0.711637\pi$
$828$		0			0
$829$	26.8128	+	8.71201i	0.931248	+	0.302581i	0.735073	−	0.677988i	$-0.237148\pi$
$829$	26.8128	+	8.71201i	0.931248	+	0.302581i	0.196175	+	0.980569i	$0.437148\pi$
$830$	−25.8624	−	11.5297i	−0.897696	−	0.400201i
$831$		0			0
$832$	−32.1382	+	11.8215i	−1.11419	+	0.409835i
$833$	−3.84940	+	7.55488i	−0.133374	+	0.261761i
$834$		0			0
$835$	9.82300	−	11.3425i	0.339939	−	0.392525i
$836$	0.250295	−	6.31903i	0.00865662	−	0.218548i
$837$		0			0
$838$	3.47343	+	4.98538i	0.119988	+	0.172217i
$839$	−26.1157	+	18.9742i	−0.901615	+	0.655062i	−0.938880	−	0.344244i	$-0.888135\pi$
$839$	−26.1157	+	18.9742i	−0.901615	+	0.655062i	0.0372654	+	0.999305i	$0.488135\pi$
$840$		0			0
$841$	3.44243	+	2.50107i	0.118704	+	0.0862438i
$842$	−0.163548	+	8.26125i	−0.00563625	+	0.284701i
$843$		0			0
$844$	−8.19783	−	3.02731i	−0.282181	−	0.104204i
$845$	11.8698	−	0.852175i	0.408334	−	0.0293157i
$846$		0			0
$847$	−4.99859	+	2.54691i	−0.171754	+	0.0875129i
$848$	2.67714	+	34.2961i	0.0919334	+	1.17773i
$849$		0			0
$850$	−7.08574	−	5.52033i	−0.243039	−	0.189346i
$851$		−	0.369703i		−	0.0126733i
$852$		0			0
$853$	11.7252	−	5.97427i	0.401462	−	0.204555i	−0.241589	−	0.970379i	$-0.577668\pi$
$853$	11.7252	−	5.97427i	0.401462	−	0.204555i	0.643051	+	0.765824i	$0.277668\pi$
$854$	−10.6025	+	1.46478i	−0.362811	+	0.0501238i
$855$		0			0
$856$	3.21787	−	0.315378i	0.109985	−	0.0107794i
$857$	−17.3368	+	17.3368i	−0.592213	+	0.592213i	−0.938229	−	0.346015i	$-0.887534\pi$
$857$	−17.3368	+	17.3368i	−0.592213	+	0.592213i	0.346015	+	0.938229i	$0.387534\pi$
$858$		0			0
$859$	26.4354	+	19.2065i	0.901966	+	0.655317i	0.938970	−	0.343999i	$-0.111782\pi$
$859$	26.4354	+	19.2065i	0.901966	+	0.655317i	−0.0370044	+	0.999315i	$0.511782\pi$
$860$	−7.33905	+	15.6233i	−0.250260	+	0.532749i
$861$		0			0
$862$	3.56690	−	2.48514i	0.121489	−	0.0846443i
$863$	−25.5766	+	4.05093i	−0.870637	+	0.137895i	−0.575739	−	0.817634i	$-0.695286\pi$
$863$	−25.5766	+	4.05093i	−0.870637	+	0.137895i	−0.294898	+	0.955529i	$0.595286\pi$
$864$		0			0
$865$	−2.03144	−	0.857847i	−0.0690711	−	0.0291677i
$866$	−6.80408	+	38.0665i	−0.231212	+	1.29355i
$867$		0			0
$868$	9.37993	−	1.10715i	0.318376	−	0.0375792i
$869$	−33.2413	+	10.8008i	−1.12763	+	0.366391i
$870$		0			0
$871$	37.7294	+	12.2590i	1.27841	+	0.415381i
$872$	12.8206	+	49.2277i	0.434162	+	1.66706i
$873$		0			0
$874$	−0.584028	+	0.283159i	−0.0197550	+	0.00957798i
$875$	−0.369101	−	6.36419i	−0.0124779	−	0.215149i
$876$		0			0
$877$	−2.40885	+	15.2089i	−0.0813410	+	0.513567i	0.913054	+	0.407839i	$0.133717\pi$
$877$	−2.40885	+	15.2089i	−0.0813410	+	0.513567i	−0.994395	+	0.105728i	$0.966283\pi$
$878$	−20.5795	+	27.1773i	−0.694525	+	0.917190i
$879$		0			0
$880$	40.8292	+	0.306531i	1.37635	+	0.0103331i
$881$	6.30400	+	19.4017i	0.212387	+	0.653660i	0.999329	+	0.0366329i	$0.0116632\pi$
$881$	6.30400	+	19.4017i	0.212387	+	0.653660i	−0.786942	+	0.617027i	$0.788337\pi$
$882$		0			0
$883$	42.2974	+	21.5516i	1.42342	+	0.725270i	0.984847	−	0.173424i	$-0.0554833\pi$
$883$	42.2974	+	21.5516i	1.42342	+	0.725270i	0.438575	+	0.898694i	$0.355483\pi$
$884$	2.94851	+	10.4674i	0.0991690	+	0.352057i
$885$		0			0
$886$	−16.8131	+	31.4430i	−0.564847	+	1.05635i
$887$	5.53478	+	34.9452i	0.185840	+	1.17335i	0.887491	+	0.460825i	$0.152447\pi$
$887$	5.53478	+	34.9452i	0.185840	+	1.17335i	−0.701651	+	0.712521i	$0.747553\pi$
$888$		0			0
$889$	6.65437	+	9.15895i	0.223180	+	0.307181i
$890$	10.3204	+	12.7573i	0.345942	+	0.427625i
$891$		0			0
$892$	9.59934	+	20.8401i	0.321410	+	0.697777i
$893$	4.98343	+	4.98343i	0.166764	+	0.166764i
$894$		0			0
$895$	19.4306	−	31.2244i	0.649493	−	1.04372i
$896$	1.87950	−	6.17105i	0.0627896	−	0.206160i
$897$		0			0
$898$	−4.44908	−	14.6751i	−0.148468	−	0.489714i
$899$	−47.7624			−1.59296
$900$		0			0
$901$	10.9246			0.363952
$902$	−8.29713	−	27.3677i	−0.276264	−	0.911244i
$903$		0			0
$904$	28.8130	+	16.9061i	0.958306	+	0.562289i
$905$	3.65512	+	50.9117i	0.121500	+	1.69236i
$906$		0			0
$907$	25.9955	+	25.9955i	0.863166	+	0.863166i	0.991705	−	0.128538i	$-0.0410286\pi$
$907$	25.9955	+	25.9955i	0.863166	+	0.863166i	−0.128538	+	0.991705i	$0.541029\pi$
$908$	54.4561	−	25.0835i	1.80719	−	0.832427i
$909$		0			0
$910$	−4.20664	+	6.47081i	−0.139449	+	0.214505i
$911$	4.91355	+	6.76292i	0.162793	+	0.224065i	0.882619	−	0.470089i	$-0.155778\pi$
$911$	4.91355	+	6.76292i	0.162793	+	0.224065i	−0.719826	+	0.694155i	$0.755778\pi$
$912$		0			0
$913$	−6.39444	−	40.3729i	−0.211625	−	1.33615i
$914$	−10.1408	+	18.9648i	−0.335427	+	0.627300i
$915$		0			0
$916$	1.66917	−	0.470180i	0.0551510	−	0.0155352i
$917$	11.5704	+	5.89541i	0.382088	+	0.194684i
$918$		0			0
$919$	12.4509	+	38.3200i	0.410718	+	1.26406i	0.916025	+	0.401121i	$0.131379\pi$
$919$	12.4509	+	38.3200i	0.410718	+	1.26406i	−0.505307	+	0.862940i	$0.668621\pi$
$920$	−1.94820	−	3.71015i	−0.0642304	−	0.122320i
$921$		0			0
$922$	7.38646	−	9.75456i	0.243260	−	0.321249i
$923$	−1.20451	+	7.60496i	−0.0396469	+	0.250320i
$924$		0			0
$925$	−2.64122	−	0.898484i	−0.0868427	−	0.0295420i
$926$	−8.99835	+	4.36274i	−0.295704	+	0.143369i
$927$		0			0
$928$	−13.0969	+	29.8770i	−0.429926	+	0.980760i
$929$	−15.1027	−	4.90715i	−0.495502	−	0.160998i	0.0505966	−	0.998719i	$-0.483888\pi$
$929$	−15.1027	−	4.90715i	−0.495502	−	0.160998i	−0.546099	+	0.837721i	$0.683888\pi$
$930$		0			0
$931$	4.39717	−	1.42873i	0.144111	−	0.0468246i
$932$	−2.21958	−	18.8045i	−0.0727047	−	0.615962i
$933$		0			0
$934$	−4.60710	+	25.7751i	−0.150749	+	0.843389i
$935$	1.10612	−	12.9193i	0.0361740	−	0.422507i
$936$		0			0
$937$	−2.53917	+	0.402165i	−0.0829512	+	0.0131382i	−0.197772	−	0.980248i	$-0.563371\pi$
$937$	−2.53917	+	0.402165i	−0.0829512	+	0.0131382i	0.114821	+	0.993386i	$0.463371\pi$
$938$	−6.13188	+	4.27223i	−0.200213	+	0.139493i
$939$		0			0
$940$	−31.1266	+	33.1907i	−1.01524	+	1.08256i
$941$	13.7615	+	9.99831i	0.448612	+	0.325935i	0.789047	−	0.614332i	$-0.210575\pi$
$941$	13.7615	+	9.99831i	0.448612	+	0.325935i	−0.340436	+	0.940268i	$0.610575\pi$
$942$		0			0
$943$	−2.07541	+	2.07541i	−0.0675848	+	0.0675848i
$944$	24.1627	−	14.7857i	0.786429	−	0.481234i
$945$		0			0
$946$	−24.6833	+	3.41010i	−0.802522	+	0.110872i
$947$	25.4121	−	12.9481i	0.825782	−	0.420757i	0.0105872	−	0.999944i	$-0.496630\pi$
$947$	25.4121	−	12.9481i	0.825782	−	0.420757i	0.815195	+	0.579187i	$0.196630\pi$
$948$		0			0
$949$			30.1366i			0.978276i
$950$	0.603576	+	4.86054i	0.0195826	+	0.157697i
$951$		0			0
$952$	−1.90736	−	0.747580i	−0.0618179	−	0.0242292i
$953$	13.9573	−	7.11160i	0.452121	−	0.230367i	−0.213075	−	0.977036i	$-0.568348\pi$
$953$	13.9573	−	7.11160i	0.452121	−	0.230367i	0.665196	+	0.746669i	$0.268348\pi$
$954$		0			0
$955$	14.8391	−	12.4985i	0.480181	−	0.404442i
$956$	−7.66815	+	20.7650i	−0.248006	+	0.671589i
$957$		0			0
$958$	0.707841	−	35.7548i	0.0228693	−	1.15519i
$959$	7.71380	+	5.60441i	0.249092	+	0.180976i
$960$		0			0
$961$	30.4178	−	22.0998i	0.981218	−	0.712897i
$962$	1.93085	+	2.77133i	0.0622532	+	0.0893513i
$963$		0			0
$964$	−1.46606	−	0.0580702i	−0.0472186	−	0.00187031i
$965$	−5.89521	−	9.77013i	−0.189774	−	0.314512i
$966$		0			0
$967$	1.53584	−	3.01425i	0.0493891	−	0.0969316i	−0.864993	−	0.501784i	$-0.832677\pi$
$967$	1.53584	−	3.01425i	0.0493891	−	0.0969316i	0.914382	+	0.404853i	$0.132677\pi$
$968$	14.9924	+	23.4451i	0.481873	+	0.753554i
$969$		0			0
$970$	−19.9802	−	34.6454i	−0.641524	−	1.11240i
$971$	−0.924449	−	0.300372i	−0.0296670	−	0.00963939i	0.294146	−	0.955761i	$-0.404965\pi$
$971$	−0.924449	−	0.300372i	−0.0296670	−	0.00963939i	−0.323813	+	0.946121i	$0.604965\pi$
$972$		0			0
$973$	−0.690268	−	0.109328i	−0.0221290	−	0.00350489i
$974$	−14.5746	−	30.0607i	−0.466999	−	0.963206i
$975$		0			0
$976$	12.3615	+	51.6346i	0.395683	+	1.65278i
$977$	1.61466	−	10.1946i	0.0516576	−	0.326153i	−0.948304	−	0.317364i	$-0.897202\pi$
$977$	1.61466	−	10.1946i	0.0516576	−	0.326153i	0.999961	−	0.00878920i	$-0.00279773\pi$
$978$		0			0
$979$	−7.31992	+	22.5284i	−0.233946	+	0.720011i
$980$	10.1304	+	28.0795i	0.323602	+	0.896967i
$981$		0			0
$982$	11.0897	−	31.9636i	0.353887	−	1.02000i
$983$	2.23630	+	1.13945i	0.0713268	+	0.0363428i	0.489290	−	0.872121i	$-0.337256\pi$
$983$	2.23630	+	1.13945i	0.0713268	+	0.0363428i	−0.417963	+	0.908464i	$0.637256\pi$
$984$		0			0
$985$	5.88821	+	25.2903i	0.187614	+	0.805815i
$986$	9.13565	+	4.88498i	0.290938	+	0.155569i
$987$		0			0
$988$	2.89907	−	5.17279i	0.0922317	−	0.164568i
$989$	1.50319	+	2.06897i	0.0477988	+	0.0657894i
$990$		0			0
$991$	−22.1826	+	30.5317i	−0.704653	+	0.969871i	0.295243	+	0.955422i	$0.404599\pi$
$991$	−22.1826	+	30.5317i	−0.704653	+	0.969871i	−0.999896	+	0.0144492i	$0.995401\pi$
$992$	−10.0044	−	45.7718i	−0.317640	−	1.45326i
$993$		0			0
$994$	−1.00517	−	1.04577i	−0.0318820	−	0.0331698i
$995$	2.75991	+	0.682682i	0.0874952	+	0.0216425i
$996$		0			0
$997$	3.03505	+	5.95663i	0.0961211	+	0.188648i	0.934060	−	0.357115i	$-0.116240\pi$
$997$	3.03505	+	5.95663i	0.0961211	+	0.188648i	−0.837939	+	0.545764i	$0.816240\pi$
$998$	−4.33345	+	1.31378i	−0.137173	+	0.0415871i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.bj.f.523.28		240
3.2	odd	2		300.2.w.a.223.3	yes	240
4.3	odd	2	inner	900.2.bj.f.523.6		240
12.11	even	2		300.2.w.a.223.25	yes	240
25.12	odd	20	inner	900.2.bj.f.487.6		240
75.62	even	20		300.2.w.a.187.25	yes	240
100.87	even	20	inner	900.2.bj.f.487.28		240
300.287	odd	20		300.2.w.a.187.3	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.187.3	✓	240	300.287	odd	20
300.2.w.a.187.25	yes	240	75.62	even	20
300.2.w.a.223.3	yes	240	3.2	odd	2
300.2.w.a.223.25	yes	240	12.11	even	2
900.2.bj.f.487.6		240	25.12	odd	20	inner
900.2.bj.f.487.28		240	100.87	even	20	inner
900.2.bj.f.523.6		240	4.3	odd	2	inner
900.2.bj.f.523.28		240	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(1.35338 - 0.410309i) q^{2} +(1.66329 - 1.11061i) q^{4} +(-2.17065 - 0.536923i) q^{5} +(0.403183 + 0.403183i) q^{7} +(1.79538 - 2.18554i) q^{8} +O(q^{10})\)	\(q+(1.35338 - 0.410309i) q^{2} +(1.66329 - 1.11061i) q^{4} +(-2.17065 - 0.536923i) q^{5} +(0.403183 + 0.403183i) q^{7} +(1.79538 - 2.18554i) q^{8} +(-3.15802 + 0.163973i) q^{10} +(-2.68322 - 3.69314i) q^{11} +(-0.669605 - 4.22772i) q^{13} +(0.711090 + 0.380232i) q^{14} +(1.53309 - 3.69454i) q^{16} +(-1.13184 - 0.576699i) q^{17} +(0.214045 + 0.658762i) q^{19} +(-4.20674 + 1.51768i) q^{20} +(-5.14676 - 3.89729i) q^{22} +(-0.103651 + 0.654427i) q^{23} +(4.42343 + 2.33094i) q^{25} +(-2.64090 - 5.44698i) q^{26} +(1.11839 + 0.222833i) q^{28} +(-5.48448 - 1.78201i) q^{29} +(7.87705 - 2.55941i) q^{31} +(0.558959 - 5.62917i) q^{32} +(-1.76843 - 0.316093i) q^{34} +(-0.658690 - 1.09165i) q^{35} +(-0.551102 + 0.0872860i) q^{37} +(0.559981 + 0.803734i) q^{38} +(-5.07061 + 3.78007i) q^{40} +(3.58374 + 2.60374i) q^{41} +(2.72923 - 2.72923i) q^{43} +(-8.56463 - 3.16276i) q^{44} +(0.128237 + 0.928219i) q^{46} +(9.06571 - 4.61921i) q^{47} -6.67489i q^{49} +(6.94300 + 1.33969i) q^{50} +(-5.80910 - 6.28827i) q^{52} +(-7.66275 + 3.90436i) q^{53} +(3.84140 + 9.45719i) q^{55} +(1.60504 - 0.157307i) q^{56} +(-8.15378 - 0.161421i) q^{58} +(5.72938 + 4.16264i) q^{59} +(-10.7384 + 7.80192i) q^{61} +(9.61052 - 6.69588i) q^{62} +(-1.55321 - 7.84777i) q^{64} +(-0.816485 + 9.53642i) q^{65} +(-4.20759 + 8.25787i) q^{67} +(-2.52306 + 0.297808i) q^{68} +(-1.33937 - 1.20715i) q^{70} +(-1.71079 - 0.555870i) q^{71} +(-6.95389 - 1.10139i) q^{73} +(-0.710038 + 0.344253i) q^{74} +(1.08765 + 0.857995i) q^{76} +(0.407181 - 2.57084i) q^{77} +(2.36601 - 7.28182i) q^{79} +(-5.31149 + 7.19640i) q^{80} +(5.91851 + 2.05342i) q^{82} +(7.97834 + 4.06517i) q^{83} +(2.14717 + 1.85952i) q^{85} +(2.57387 - 4.81352i) q^{86} +(-12.8889 - 0.766290i) q^{88} +(-3.05003 - 4.19801i) q^{89} +(1.43457 - 1.97452i) q^{91} +(0.554411 + 1.20362i) q^{92} +(10.3741 - 9.97131i) q^{94} +(-0.110911 - 1.54487i) q^{95} +(5.74169 + 11.2687i) q^{97} +(-2.73876 - 9.03368i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{8}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more