LMFDB - Embedded newform 900.2.bj.f.127.1

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			127.1
Character	$\chi$	$=$	900.127
Dual form			900.2.bj.f.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41129 + 0.0909451i) q^{2} +(1.98346 - 0.256699i) q^{4} +(1.83309 - 1.28054i) q^{5} +(1.46352 - 1.46352i) q^{7} +(-2.77588 + 0.542662i) q^{8} +O(q^{10})$	\(q+(-1.41129 + 0.0909451i) q^{2} +(1.98346 - 0.256699i) q^{4} +(1.83309 - 1.28054i) q^{5} +(1.46352 - 1.46352i) q^{7} +(-2.77588 + 0.542662i) q^{8} +(-2.47056 + 1.97391i) q^{10} +(0.716610 + 0.986329i) q^{11} +(0.610002 - 0.0966148i) q^{13} +(-1.93235 + 2.19855i) q^{14} +(3.86821 - 1.01830i) q^{16} +(2.23367 - 4.38383i) q^{17} +(1.11648 + 3.43617i) q^{19} +(3.30715 - 3.01044i) q^{20} +(-1.10104 - 1.32682i) q^{22} +(6.81819 + 1.07989i) q^{23} +(1.72046 - 4.69468i) q^{25} +(-0.852100 + 0.191828i) q^{26} +(2.52715 - 3.27852i) q^{28} +(-0.953684 - 0.309871i) q^{29} +(-10.1146 + 3.28642i) q^{31} +(-5.36654 + 1.78891i) q^{32} +(-2.75367 + 6.38999i) q^{34} +(0.808681 - 4.55687i) q^{35} +(-0.749924 - 4.73483i) q^{37} +(-1.88818 - 4.74789i) q^{38} +(-4.39355 + 4.54936i) q^{40} +(4.46659 + 3.24517i) q^{41} +(-2.74571 - 2.74571i) q^{43} +(1.67455 + 1.77239i) q^{44} +(-9.72062 - 0.903960i) q^{46} +(0.593032 + 1.16389i) q^{47} +2.71620i q^{49} +(-2.00110 + 6.78200i) q^{50} +(1.18511 - 0.348218i) q^{52} +(-2.82569 - 5.54573i) q^{53} +(2.57664 + 0.890388i) q^{55} +(-3.26837 + 4.85677i) q^{56} +(1.37410 + 0.350583i) q^{58} +(-10.5976 - 7.69958i) q^{59} +(7.64473 - 5.55422i) q^{61} +(13.9757 - 5.55795i) q^{62} +(7.41104 - 3.01273i) q^{64} +(0.994471 - 0.958232i) q^{65} +(7.24032 + 3.68913i) q^{67} +(3.30507 - 9.26853i) q^{68} +(-0.726856 + 6.50459i) q^{70} +(12.8093 + 4.16201i) q^{71} +(1.08745 - 6.86590i) q^{73} +(1.48897 + 6.61400i) q^{74} +(3.09656 + 6.52891i) q^{76} +(2.49229 + 0.394740i) q^{77} +(-2.17258 + 6.68651i) q^{79} +(5.78682 - 6.82003i) q^{80} +(-6.59877 - 4.17364i) q^{82} +(-3.19885 + 6.27810i) q^{83} +(-1.51912 - 10.8963i) q^{85} +(4.12469 + 3.62528i) q^{86} +(-2.52447 - 2.34905i) q^{88} +(-8.41934 - 11.5882i) q^{89} +(0.751354 - 1.03415i) q^{91} +(13.8008 + 0.391703i) q^{92} +(-0.942788 - 1.58865i) q^{94} +(6.44675 + 4.86913i) q^{95} +(3.66823 - 1.86906i) q^{97} +(-0.247025 - 3.83333i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.41129	+	0.0909451i	−0.997930	+	0.0643079i
$2$	−1.41129	+	0.0909451i	−0.997930	+	0.0643079i
$3$		0			0
$3$		0			0
$4$	1.98346	−	0.256699i	0.991729	−	0.128350i
$5$	1.83309	−	1.28054i	0.819784	−	0.572673i
$5$	1.83309	−	1.28054i	0.819784	−	0.572673i
$6$		0			0
$7$	1.46352	−	1.46352i	0.553160	−	0.553160i	−0.374192	−	0.927351i	$-0.622080\pi$
$7$	1.46352	−	1.46352i	0.553160	−	0.553160i	0.927351	+	0.374192i	$0.122080\pi$
$8$	−2.77588	+	0.542662i	−0.981422	+	0.191860i
$9$		0			0
$10$	−2.47056	+	1.97391i	−0.781260	+	0.624206i
$11$	0.716610	+	0.986329i	0.216066	+	0.297389i	0.903268	−	0.429077i	$-0.141161\pi$
$11$	0.716610	+	0.986329i	0.216066	+	0.297389i	−0.687202	+	0.726467i	$0.741161\pi$
$12$		0			0
$13$	0.610002	−	0.0966148i	0.169184	−	0.0267961i	−0.0712677	−	0.997457i	$-0.522704\pi$
$13$	0.610002	−	0.0966148i	0.169184	−	0.0267961i	0.240452	+	0.970661i	$0.422704\pi$
$14$	−1.93235	+	2.19855i	−0.516442	+	0.587587i
$15$		0			0
$16$	3.86821	−	1.01830i	0.967053	−	0.254576i
$17$	2.23367	−	4.38383i	0.541746	−	1.06324i	−0.444162	−	0.895946i	$-0.646499\pi$
$17$	2.23367	−	4.38383i	0.541746	−	1.06324i	0.985908	−	0.167289i	$-0.0535014\pi$
$18$		0			0
$19$	1.11648	+	3.43617i	0.256138	+	0.788312i	0.993603	+	0.112927i	$0.0360227\pi$
$19$	1.11648	+	3.43617i	0.256138	+	0.788312i	−0.737465	+	0.675385i	$0.763977\pi$
$20$	3.30715	−	3.01044i	0.739501	−	0.673155i
$21$		0			0
$22$	−1.10104	−	1.32682i	−0.234743	−	0.282879i
$23$	6.81819	+	1.07989i	1.42169	+	0.225174i	0.819454	−	0.573145i	$-0.194277\pi$
$23$	6.81819	+	1.07989i	1.42169	+	0.225174i	0.602236	+	0.798318i	$0.294277\pi$
$24$		0			0
$25$	1.72046	−	4.69468i	0.344092	−	0.938936i
$26$	−0.852100	+	0.191828i	−0.167111	+	0.0376205i
$27$		0			0
$28$	2.52715	−	3.27852i	0.477587	−	0.619582i
$29$	−0.953684	−	0.309871i	−0.177095	−	0.0575416i	0.219127	−	0.975696i	$-0.429679\pi$
$29$	−0.953684	−	0.309871i	−0.177095	−	0.0575416i	−0.396222	+	0.918155i	$0.629679\pi$
$30$		0			0
$31$	−10.1146	+	3.28642i	−1.81663	+	0.590259i	−0.816717	+	0.577038i	$0.804209\pi$
$31$	−10.1146	+	3.28642i	−1.81663	+	0.590259i	−0.999913	+	0.0132212i	$0.995791\pi$
$32$	−5.36654	+	1.78891i	−0.948680	+	0.316238i
$33$		0			0
$34$	−2.75367	+	6.38999i	−0.472250	+	1.09587i
$35$	0.808681	−	4.55687i	0.136692	−	0.770251i
$36$		0			0
$37$	−0.749924	−	4.73483i	−0.123287	−	0.778402i	−0.969416	−	0.245424i	$-0.921073\pi$
$37$	−0.749924	−	4.73483i	−0.123287	−	0.778402i	0.846129	−	0.532978i	$-0.178927\pi$
$38$	−1.88818	−	4.74789i	−0.306303	−	0.770209i
$39$		0			0
$40$	−4.39355	+	4.54936i	−0.694681	+	0.719317i
$41$	4.46659	+	3.24517i	0.697564	+	0.506810i	0.879138	−	0.476568i	$-0.158119\pi$
$41$	4.46659	+	3.24517i	0.697564	+	0.506810i	−0.181574	+	0.983377i	$0.558119\pi$
$42$		0			0
$43$	−2.74571	−	2.74571i	−0.418717	−	0.418717i	0.466044	−	0.884761i	$-0.345679\pi$
$43$	−2.74571	−	2.74571i	−0.418717	−	0.418717i	−0.884761	+	0.466044i	$0.845679\pi$
$44$	1.67455	+	1.77239i	0.252449	+	0.267198i
$45$		0			0
$46$	−9.72062	−	0.903960i	−1.43323	−	0.133282i
$47$	0.593032	+	1.16389i	0.0865026	+	0.169771i	0.930205	−	0.367040i	$-0.119629\pi$
$47$	0.593032	+	1.16389i	0.0865026	+	0.169771i	−0.843703	+	0.536811i	$0.819629\pi$
$48$		0			0
$49$			2.71620i			0.388028i
$50$	−2.00110	+	6.78200i	−0.282999	+	0.959120i
$51$		0			0
$52$	1.18511	−	0.348218i	0.164345	−	0.0482892i
$53$	−2.82569	−	5.54573i	−0.388139	−	0.761765i	0.611425	−	0.791302i	$-0.290597\pi$
$53$	−2.82569	−	5.54573i	−0.388139	−	0.761765i	−0.999564	+	0.0295374i	$0.990597\pi$
$54$		0			0
$55$	2.57664	+	0.890388i	0.347434	+	0.120060i
$56$	−3.26837	+	4.85677i	−0.436754	+	0.649013i
$57$		0			0
$58$	1.37410	+	0.350583i	0.180429	+	0.0460339i
$59$	−10.5976	−	7.69958i	−1.37969	−	1.00240i	−0.996909	−	0.0785588i	$-0.974968\pi$
$59$	−10.5976	−	7.69958i	−1.37969	−	1.00240i	−0.382776	−	0.923841i	$-0.625032\pi$
$60$		0			0
$61$	7.64473	−	5.55422i	0.978807	−	0.711145i	0.0213655	−	0.999772i	$-0.493199\pi$
$61$	7.64473	−	5.55422i	0.978807	−	0.711145i	0.957442	+	0.288627i	$0.0931986\pi$
$62$	13.9757	−	5.55795i	1.77491	−	0.705861i
$63$		0			0
$64$	7.41104	−	3.01273i	0.926380	−	0.376591i
$65$	0.994471	−	0.958232i	0.123349	−	0.118854i
$66$		0			0
$67$	7.24032	+	3.68913i	0.884546	+	0.450699i	0.836386	−	0.548141i	$-0.184664\pi$
$67$	7.24032	+	3.68913i	0.884546	+	0.450699i	0.0481602	+	0.998840i	$0.484664\pi$
$68$	3.30507	−	9.26853i	0.400799	−	1.12397i
$69$		0			0
$70$	−0.726856	+	6.50459i	−0.0868759	+	0.777447i
$71$	12.8093	+	4.16201i	1.52019	+	0.493940i	0.945830	−	0.324663i	$-0.105251\pi$
$71$	12.8093	+	4.16201i	1.52019	+	0.493940i	0.574360	+	0.818603i	$0.305251\pi$
$72$		0			0
$73$	1.08745	−	6.86590i	0.127277	−	0.803592i	−0.838630	−	0.544701i	$-0.816643\pi$
$73$	1.08745	−	6.86590i	0.127277	−	0.803592i	0.965907	−	0.258891i	$-0.0833570\pi$
$74$	1.48897	+	6.61400i	0.173089	+	0.768862i
$75$		0			0
$76$	3.09656	+	6.52891i	0.355199	+	0.748917i
$77$	2.49229	+	0.394740i	0.284023	+	0.0449848i
$78$		0			0
$79$	−2.17258	+	6.68651i	−0.244434	+	0.752291i	0.751295	+	0.659967i	$0.229430\pi$
$79$	−2.17258	+	6.68651i	−0.244434	+	0.752291i	−0.995729	+	0.0923241i	$0.970570\pi$
$80$	5.78682	−	6.82003i	0.646986	−	0.762502i
$81$		0			0
$82$	−6.59877	−	4.17364i	−0.728712	−	0.460902i
$83$	−3.19885	+	6.27810i	−0.351119	+	0.689111i	−0.997250	−	0.0741166i	$-0.976386\pi$
$83$	−3.19885	+	6.27810i	−0.351119	+	0.689111i	0.646130	+	0.763227i	$0.276386\pi$
$84$		0			0
$85$	−1.51912	−	10.8963i	−0.164772	−	1.18187i
$86$	4.12469	+	3.62528i	0.444777	+	0.390924i
$87$		0			0
$88$	−2.52447	−	2.34905i	−0.269109	−	0.250410i
$89$	−8.41934	−	11.5882i	−0.892448	−	1.22835i	−0.972815	−	0.231585i	$-0.925609\pi$
$89$	−8.41934	−	11.5882i	−0.892448	−	1.22835i	0.0803663	−	0.996765i	$-0.474391\pi$
$90$		0			0
$91$	0.751354	−	1.03415i	0.0787633	−	0.108408i
$92$	13.8008	+	0.391703i	1.43883	+	0.0408378i
$93$		0			0
$94$	−0.942788	−	1.58865i	−0.0972412	−	0.163857i
$95$	6.44675	+	4.86913i	0.661423	+	0.499563i
$96$		0			0
$97$	3.66823	−	1.86906i	0.372453	−	0.189774i	−0.257737	−	0.966215i	$-0.582977\pi$
$97$	3.66823	−	1.86906i	0.372453	−	0.189774i	0.630190	+	0.776441i	$0.282977\pi$
$98$	−0.247025	−	3.83333i	−0.0249533	−	0.387225i
$99$		0			0
$100$	2.20734	−	9.75334i	0.220734	−	0.975334i
$101$	14.2792			1.42083			0.710417	−	0.703781i	$-0.248506\pi$
$101$	14.2792			1.42083			0.710417	+	0.703781i	$0.248506\pi$
$102$		0			0
$103$	11.1840	−	5.69852i	1.10199	−	0.561492i	0.194219	−	0.980958i	$-0.437783\pi$
$103$	11.1840	−	5.69852i	1.10199	−	0.561492i	0.907771	+	0.419467i	$0.137783\pi$
$104$	−1.64086	+	0.599216i	−0.160900	+	0.0587579i
$105$		0			0
$106$	4.49222	+	7.56963i	0.436323	+	0.735228i
$107$	−3.88843	+	3.88843i	−0.375909	+	0.375909i	−0.869624	−	0.493715i	$-0.835639\pi$
$107$	−3.88843	+	3.88843i	−0.375909	+	0.375909i	0.493715	+	0.869624i	$0.335639\pi$
$108$		0			0
$109$	−3.30533	+	4.54940i	−0.316593	+	0.435753i	−0.937423	−	0.348192i	$-0.886796\pi$
$109$	−3.30533	+	4.54940i	−0.316593	+	0.435753i	0.620830	+	0.783945i	$0.286796\pi$
$110$	−3.71735	−	1.02226i	−0.354436	−	0.0974686i
$111$		0			0
$112$	4.17091	−	7.15153i	0.394114	−	0.675756i
$113$	−6.70930	+	1.06265i	−0.631158	+	0.0999656i	−0.463813	−	0.885933i	$-0.653519\pi$
$113$	−6.70930	+	1.06265i	−0.631158	+	0.0999656i	−0.167345	+	0.985898i	$0.553519\pi$
$114$		0			0
$115$	13.8812	−	6.75138i	1.29443	−	0.629569i
$116$	−1.97114	−	0.369806i	−0.183015	−	0.0343356i
$117$		0			0
$118$	15.6564	+	9.90252i	1.44129	+	0.911601i
$119$	−3.14681	−	9.68488i	−0.288467	−	0.887811i
$120$		0			0
$121$	2.93987	−	9.04800i	0.267261	−	0.822545i
$122$	−10.2838	+	8.53385i	−0.931049	+	0.772618i
$123$		0			0
$124$	−19.2182	+	9.11488i	−1.72585	+	0.818541i
$125$	−2.85794	−	10.8089i	−0.255622	−	0.966777i
$126$		0			0
$127$	2.16580	−	13.6743i	0.192183	−	1.21340i	−0.683296	−	0.730142i	$-0.739454\pi$
$127$	2.16580	−	13.6743i	0.192183	−	1.21340i	0.875479	−	0.483256i	$-0.160546\pi$
$128$	−10.1851	+	4.92582i	−0.900244	+	0.435385i
$129$		0			0
$130$	−1.31634	+	1.44278i	−0.115450	+	0.126540i
$131$	−1.62756	+	0.528826i	−0.142201	+	0.0462038i	−0.379253	−	0.925293i	$-0.623819\pi$
$131$	−1.62756	+	0.528826i	−0.142201	+	0.0462038i	0.237052	+	0.971497i	$0.423819\pi$
$132$		0			0
$133$	6.66292	+	3.39493i	0.577748	+	0.294377i
$134$	−10.5537	−	4.54795i	−0.911699	−	0.392883i
$135$		0			0
$136$	−3.82148	+	13.3811i	−0.327689	+	1.14742i
$137$	0.0719242	+	0.454112i	0.00614490	+	0.0387974i	0.990570	−	0.137006i	$-0.0437478\pi$
$137$	0.0719242	+	0.454112i	0.00614490	+	0.0387974i	−0.984425	+	0.175803i	$0.943748\pi$
$138$		0			0
$139$	3.76808	−	2.73767i	0.319604	−	0.232206i	−0.416402	−	0.909180i	$-0.636709\pi$
$139$	3.76808	−	2.73767i	0.319604	−	0.232206i	0.736007	+	0.676974i	$0.236709\pi$
$140$	0.434241	−	9.24594i	0.0367001	−	0.781425i
$141$		0			0
$142$	−18.4562	−	4.70884i	−1.54881	−	0.395157i
$143$	0.532427	+	0.532427i	0.0445238	+	0.0445238i
$144$		0			0
$145$	−2.14499	+	0.653204i	−0.178132	+	0.0542456i
$146$	−0.910285	+	9.78864i	−0.0753357	+	0.810114i
$147$		0			0
$148$	−2.70287	−	9.19884i	−0.222175	−	0.756140i
$149$			19.6344i			1.60852i	0.594281	+	0.804258i	$0.297437\pi$
$149$			19.6344i			1.60852i	−0.594281	+	0.804258i	$0.702563\pi$
$150$		0			0
$151$			23.7781i			1.93504i	0.252799	+	0.967519i	$0.418649\pi$
$151$			23.7781i			1.93504i	−0.252799	+	0.967519i	$0.581351\pi$
$152$	−4.96390	−	8.93254i	−0.402625	−	0.724525i
$153$		0			0
$154$	−3.55323	−	0.330429i	−0.286328	−	0.0266268i
$155$	−14.3326	+	18.9764i	−1.15122	+	1.52422i
$156$		0			0
$157$	2.38350	+	2.38350i	0.190224	+	0.190224i	0.795793	−	0.605569i	$-0.207054\pi$
$157$	2.38350	+	2.38350i	0.190224	+	0.190224i	−0.605569	+	0.795793i	$0.707054\pi$
$158$	2.45802	−	9.63416i	0.195550	−	0.766453i
$159$		0			0
$160$	−7.54661	+	10.1513i	−0.596612	+	0.802530i
$161$	11.5590	−	8.39812i	0.910979	−	0.661865i
$162$		0			0
$163$	−0.927372	−	5.85520i	−0.0726374	−	0.458614i	−0.997020	−	0.0771471i	$-0.975419\pi$
$163$	−0.927372	−	5.85520i	−0.0726374	−	0.458614i	0.924382	−	0.381467i	$-0.124581\pi$
$164$	9.69232	+	5.29008i	0.756843	+	0.413086i
$165$		0			0
$166$	3.94353	−	9.15111i	0.306077	−	0.710264i
$167$	−11.9576	−	6.09269i	−0.925305	−	0.471467i	−0.0746615	−	0.997209i	$-0.523788\pi$
$167$	−11.9576	−	6.09269i	−0.925305	−	0.471467i	−0.850644	+	0.525742i	$0.823788\pi$
$168$		0			0
$169$	−12.0010	+	3.89935i	−0.923151	+	0.299950i
$170$	3.13487	+	15.2396i	0.240434	+	1.16882i
$171$		0			0
$172$	−6.15083	−	4.74118i	−0.468996	−	0.361512i
$173$	−2.52253	+	15.9266i	−0.191785	+	1.21088i	0.684473	+	0.729038i	$0.260032\pi$
$173$	−2.52253	+	15.9266i	−0.191785	+	1.21088i	−0.876258	+	0.481842i	$0.839968\pi$
$174$		0			0
$175$	−4.35284	−	9.38871i	−0.329044	−	0.709720i
$176$	3.77638	+	3.08560i	0.284655	+	0.232586i
$177$		0			0
$178$	12.9360	+	15.5886i	0.969594	+	1.16842i
$179$	1.87266	−	5.76347i	0.139970	−	0.430782i	−0.856360	−	0.516379i	$-0.827280\pi$
$179$	1.87266	−	5.76347i	0.139970	−	0.430782i	0.996330	+	0.0855968i	$0.0272797\pi$
$180$		0			0
$181$	7.06640	+	21.7482i	0.525242	+	1.61653i	0.763837	+	0.645409i	$0.223313\pi$
$181$	7.06640	+	21.7482i	0.525242	+	1.61653i	−0.238596	+	0.971119i	$0.576687\pi$
$182$	−0.966324	+	1.52781i	−0.0716287	+	0.113249i
$183$		0			0
$184$	−19.5125	+	0.702310i	−1.43848	+	0.0517750i
$185$	−7.43780	−	7.71909i	−0.546838	−	0.567518i
$186$		0			0
$187$	5.92457	−	0.938360i	0.433248	−	0.0686197i
$188$	1.47502	+	2.15630i	0.107577	+	0.157264i
$189$		0			0
$190$	−9.54104	−	6.28544i	−0.692180	−	0.455994i
$191$	−4.71698	+	6.49237i	−0.341309	+	0.469771i	−0.944823	−	0.327581i	$-0.893767\pi$
$191$	−4.71698	+	6.49237i	−0.341309	+	0.469771i	0.603514	+	0.797352i	$0.293767\pi$
$192$		0			0
$193$	7.12358	−	7.12358i	0.512767	−	0.512767i	−0.402606	−	0.915373i	$-0.631896\pi$
$193$	7.12358	−	7.12358i	0.512767	−	0.512767i	0.915373	+	0.402606i	$0.131896\pi$
$194$	−5.00695	+	2.97139i	−0.359478	+	0.213333i
$195$		0			0
$196$	0.697246	+	5.38747i	0.0498033	+	0.384819i
$197$	−13.3419	+	6.79803i	−0.950570	+	0.484339i	−0.859292	−	0.511486i	$-0.829095\pi$
$197$	−13.3419	+	6.79803i	−0.950570	+	0.484339i	−0.0912781	+	0.995825i	$0.529095\pi$
$198$		0			0
$199$	−4.76131			−0.337520			−0.168760	−	0.985657i	$-0.553976\pi$
$199$	−4.76131			−0.337520			−0.168760	+	0.985657i	$0.553976\pi$
$200$	−2.22817	+	13.9655i	−0.157555	+	0.987510i
$201$		0			0
$202$	−20.1520	+	1.29862i	−1.41789	+	0.0913709i
$203$	−1.84924	+	0.942236i	−0.129791	+	0.0661320i
$204$		0			0
$205$	12.3432	+	0.229069i	0.862088	+	0.0159988i
$206$	−15.2655	+	9.05937i	−1.06360	+	0.631196i
$207$		0			0
$208$	2.26123	−	0.994893i	0.156788	−	0.0689834i
$209$	−2.58912	+	3.56361i	−0.179093	+	0.246500i
$210$		0			0
$211$	−0.683337	−	0.940532i	−0.0470428	−	0.0647489i	0.784848	−	0.619689i	$-0.212741\pi$
$211$	−0.683337	−	0.940532i	−0.0470428	−	0.0647489i	−0.831890	+	0.554940i	$0.812741\pi$
$212$	−7.02823	−	10.2744i	−0.482701	−	0.705647i
$213$		0			0
$214$	5.13406	−	5.84132i	0.350957	−	0.399305i
$215$	−8.54912	−	1.51716i	−0.583045	−	0.103470i
$216$		0			0
$217$	−9.99315	+	19.6127i	−0.678379	+	1.33139i
$218$	4.25102	−	6.72110i	0.287916	−	0.455211i
$219$		0			0
$220$	5.33922	+	1.10463i	0.359970	+	0.0744739i
$221$	0.939002	−	2.88995i	0.0631641	−	0.194399i
$222$		0			0
$223$	−21.2551	−	3.36648i	−1.42335	−	0.225436i	−0.603202	−	0.797589i	$-0.706109\pi$
$223$	−21.2551	−	3.36648i	−1.42335	−	0.225436i	−0.820147	+	0.572152i	$0.806109\pi$
$224$	−5.23595	+	10.4722i	−0.349841	+	0.699702i
$225$		0			0
$226$	9.37210	−	2.10988i	0.623423	−	0.140347i
$227$	−1.05635	+	6.66952i	−0.0701123	+	0.442672i	0.927513	+	0.373792i	$0.121943\pi$
$227$	−1.05635	+	6.66952i	−0.0701123	+	0.442672i	−0.997625	+	0.0688800i	$0.978057\pi$
$228$		0			0
$229$	−19.0806	−	6.19967i	−1.26088	−	0.409686i	−0.399075	−	0.916918i	$-0.630669\pi$
$229$	−19.0806	−	6.19967i	−1.26088	−	0.409686i	−0.861809	+	0.507232i	$0.830669\pi$
$230$	−18.9764	+	10.7906i	−1.25126	+	0.711508i
$231$		0			0
$232$	2.81547	+	0.342637i	0.184845	+	0.0224952i
$233$	4.84966	+	2.47103i	0.317712	+	0.161882i	0.605573	−	0.795790i	$-0.292944\pi$
$233$	4.84966	+	2.47103i	0.317712	+	0.161882i	−0.287861	+	0.957672i	$0.592944\pi$
$234$		0			0
$235$	2.57749	+	1.37412i	0.168137	+	0.0896378i
$236$	−22.9963	−	12.5514i	−1.49693	−	0.817027i
$237$		0			0
$238$	5.32184	+	13.3819i	0.344964	+	0.867423i
$239$	11.2896	−	8.20235i	0.730261	−	0.530566i	−0.159385	−	0.987217i	$-0.550951\pi$
$239$	11.2896	−	8.20235i	0.730261	−	0.530566i	0.889646	+	0.456651i	$0.150951\pi$
$240$		0			0
$241$	13.3980	+	9.73420i	0.863040	+	0.627035i	0.928710	−	0.370806i	$-0.120919\pi$
$241$	13.3980	+	9.73420i	0.863040	+	0.627035i	−0.0656704	+	0.997841i	$0.520919\pi$
$242$	−3.32613	+	13.0367i	−0.213812	+	0.838030i
$243$		0			0
$244$	13.7372	−	12.9790i	0.879436	−	0.830893i
$245$	3.47819	+	4.97904i	0.222213	+	0.318099i
$246$		0			0
$247$	1.01304	+	1.98820i	0.0644582	+	0.126506i
$248$	26.2934	−	14.6115i	1.66963	−	0.927832i
$249$		0			0
$250$	5.01639	+	14.9945i	0.317264	+	0.948337i
$251$		−	22.8681i		−	1.44342i	−0.692195	−	0.721711i	$-0.743356\pi$
$251$		−	22.8681i		−	1.44342i	0.692195	−	0.721711i	$-0.256644\pi$
$252$		0			0
$253$	3.82085	+	7.49883i	0.240215	+	0.471448i
$254$	−1.81295	+	19.4953i	−0.113754	+	1.22325i
$255$		0			0
$256$	13.9261	−	7.87803i	0.870382	−	0.492377i
$257$	17.5555	+	17.5555i	1.09508	+	1.09508i	0.994977	+	0.100106i	$0.0319182\pi$
$257$	17.5555	+	17.5555i	1.09508	+	1.09508i	0.100106	+	0.994977i	$0.468082\pi$
$258$		0			0
$259$	−8.02707	−	5.83201i	−0.498778	−	0.362383i
$260$	1.72651	−	2.15589i	0.107074	−	0.133703i
$261$		0			0
$262$	2.24886	−	0.894344i	0.138935	−	0.0552528i
$263$	−1.08432	−	6.84611i	−0.0668619	−	0.422149i	−0.998302	−	0.0582542i	$-0.981447\pi$
$263$	−1.08432	−	6.84611i	−0.0668619	−	0.422149i	0.931440	−	0.363895i	$-0.118553\pi$
$264$		0			0
$265$	−12.2813	−	6.54745i	−0.754432	−	0.402206i
$266$	−9.71204	−	4.18525i	−0.595483	−	0.256614i
$267$		0			0
$268$	15.3079	+	5.45865i	0.935077	+	0.333440i
$269$	−26.2916	+	8.54266i	−1.60303	+	0.520855i	−0.967854	−	0.251514i	$-0.919072\pi$
$269$	−26.2916	+	8.54266i	−1.60303	+	0.520855i	−0.635174	+	0.772369i	$0.719072\pi$
$270$		0			0
$271$	−14.4397	−	4.69173i	−0.877147	−	0.285002i	−0.164375	−	0.986398i	$-0.552561\pi$
$271$	−14.4397	−	4.69173i	−0.877147	−	0.285002i	−0.712772	+	0.701396i	$0.752561\pi$
$272$	4.17625	−	19.2322i	0.253222	−	1.16612i
$273$		0			0
$274$	−0.142805	−	0.634340i	−0.00862716	−	0.0383219i
$275$	5.86339	−	1.66731i	0.353576	−	0.100543i
$276$		0			0
$277$	−18.0952	−	2.86600i	−1.08723	−	0.172201i	−0.413009	−	0.910727i	$-0.635522\pi$
$277$	−18.0952	−	2.86600i	−1.08723	−	0.172201i	−0.674225	+	0.738526i	$0.735522\pi$
$278$	−5.06886	+	4.20632i	−0.304010	+	0.252278i
$279$		0			0
$280$	0.228034	+	13.0882i	0.0136277	+	0.782167i
$281$	4.45191	+	13.7016i	0.265579	+	0.817368i	0.991559	+	0.129653i	$0.0413863\pi$
$281$	4.45191	+	13.7016i	0.265579	+	0.817368i	−0.725980	+	0.687715i	$0.758614\pi$
$282$		0			0
$283$	−13.2557	+	26.0158i	−0.787971	+	1.54648i	0.0487251	+	0.998812i	$0.484484\pi$
$283$	−13.2557	+	26.0158i	−0.787971	+	1.54648i	−0.836696	+	0.547668i	$0.815516\pi$
$284$	26.4752	+	4.96702i	1.57101	+	0.294738i
$285$		0			0
$286$	−0.799828	−	0.702985i	−0.0472948	−	0.0415684i
$287$	11.2863	−	1.78758i	0.666211	−	0.105517i
$288$		0			0
$289$	−4.23634	−	5.83082i	−0.249197	−	0.342990i
$290$	2.96779	−	1.11693i	0.174275	−	0.0655887i
$291$		0			0
$292$	0.394444	−	13.8974i	0.0230831	−	0.813282i
$293$	−3.00790	+	3.00790i	−0.175723	+	0.175723i	−0.789489	−	0.613765i	$-0.789654\pi$
$293$	−3.00790	+	3.00790i	−0.175723	+	0.175723i	0.613765	+	0.789489i	$0.289654\pi$
$294$		0			0
$295$	−29.2859	−	0.543495i	−1.70509	−	0.0316435i
$296$	4.65111	+	12.7364i	0.270340	+	0.740287i
$297$		0			0
$298$	−1.78566	−	27.7098i	−0.103440	−	1.60519i
$299$	4.26344			0.246561
$300$		0			0
$301$	−8.03683			−0.463235
$302$	−2.16251	−	33.5578i	−0.124438	−	1.93103i
$303$		0			0
$304$	7.81785	+	12.1549i	0.448385	+	0.697133i
$305$	6.90112	−	19.9707i	0.395157	−	1.14352i
$306$		0			0
$307$	−22.9222	+	22.9222i	−1.30824	+	1.30824i	−0.385554	+	0.922685i	$0.625990\pi$
$307$	−22.9222	+	22.9222i	−1.30824	+	1.30824i	−0.922685	+	0.385554i	$0.874010\pi$
$308$	5.04468	+	0.143181i	0.287447	+	0.00815851i
$309$		0			0
$310$	18.5015	−	28.0846i	1.05082	−	1.59510i
$311$	5.82470	+	8.01702i	0.330289	+	0.454603i	0.941574	−	0.336807i	$-0.109347\pi$
$311$	5.82470	+	8.01702i	0.330289	+	0.454603i	−0.611285	+	0.791411i	$0.709347\pi$
$312$		0			0
$313$	−12.2798	+	1.94493i	−0.694097	+	0.109934i	−0.493508	−	0.869741i	$-0.664286\pi$
$313$	−12.2798	+	1.94493i	−0.694097	+	0.109934i	−0.200589	+	0.979675i	$0.564286\pi$
$314$	−3.58057	−	3.14703i	−0.202063	−	0.177597i
$315$		0			0
$316$	−2.59280	+	13.8201i	−0.145856	+	0.777441i
$317$	−1.92273	+	3.77356i	−0.107991	+	0.211944i	−0.938678	−	0.344796i	$-0.887948\pi$
$317$	−1.92273	+	3.77356i	−0.107991	+	0.211944i	0.830687	+	0.556740i	$0.187948\pi$
$318$		0			0
$319$	−0.377785	−	1.16270i	−0.0211519	−	0.0650988i
$320$	9.72721	−	15.0127i	0.543768	−	0.839236i
$321$		0			0
$322$	−15.5493	+	12.9034i	−0.866530	+	0.719078i
$323$	17.5575	+	2.78083i	0.976924	+	0.154730i
$324$		0			0
$325$	0.595908	−	3.02998i	0.0330550	−	0.168073i
$326$	1.84129	+	8.17902i	0.101980	+	0.452994i
$327$		0			0
$328$	−14.1597	−	6.58435i	−0.781841	−	0.363560i
$329$	2.57130	+	0.835465i	0.141760	+	0.0460607i
$330$		0			0
$331$	8.18304	−	2.65883i	0.449781	−	0.146143i	−0.0753630	−	0.997156i	$-0.524012\pi$
$331$	8.18304	−	2.65883i	0.449781	−	0.146143i	0.525144	+	0.851014i	$0.324012\pi$
$332$	−4.73320	+	13.2735i	−0.259768	+	0.728477i
$333$		0			0
$334$	17.4297	+	7.51105i	0.953709	+	0.410986i
$335$	17.9962	−	2.50897i	0.983240	−	0.137080i
$336$		0			0
$337$	0.107869	+	0.681059i	0.00587601	+	0.0370997i	0.990452	−	0.137857i	$-0.0440215\pi$
$337$	0.107869	+	0.681059i	0.00587601	+	0.0370997i	−0.984576	+	0.174957i	$0.944021\pi$
$338$	16.5822	−	6.59453i	0.901951	−	0.358695i
$339$		0			0
$340$	−5.81017	−	21.2223i	−0.315101	−	1.15094i
$341$	−10.4897	−	7.62121i	−0.568049	−	0.412711i
$342$		0			0
$343$	14.2199	+	14.2199i	0.767802	+	0.767802i
$344$	9.11176	+	6.13178i	0.491273	+	0.330603i
$345$		0			0
$346$	2.11156	−	22.7065i	0.113518	−	1.22071i
$347$	−11.6804	−	22.9240i	−0.627035	−	1.23063i	−0.957942	−	0.286962i	$-0.907355\pi$
$347$	−11.6804	−	22.9240i	−0.627035	−	1.23063i	0.330907	−	0.943663i	$-0.392645\pi$
$348$		0			0
$349$			29.6548i			1.58739i	0.608318	+	0.793694i	$0.291845\pi$
$349$			29.6548i			1.58739i	−0.608318	+	0.793694i	$0.708155\pi$
$350$	6.99696	+	12.8543i	0.374003	+	0.687090i
$351$		0			0
$352$	−5.61017	−	4.01122i	−0.299023	−	0.213799i
$353$	15.1420	+	29.7179i	0.805928	+	1.58172i	0.813368	+	0.581750i	$0.197632\pi$
$353$	15.1420	+	29.7179i	0.805928	+	1.58172i	−0.00744012	+	0.999972i	$0.502368\pi$
$354$		0			0
$355$	28.8103	−	8.77347i	1.52909	−	0.465647i
$356$	−19.6741	−	20.8235i	−1.04273	−	1.10364i
$357$		0			0
$358$	−2.11871	+	8.30421i	−0.111977	+	0.438891i
$359$	5.20850	+	3.78419i	0.274894	+	0.199722i	0.716687	−	0.697395i	$-0.245658\pi$
$359$	5.20850	+	3.78419i	0.274894	+	0.199722i	−0.441793	+	0.897117i	$0.645658\pi$
$360$		0			0
$361$	4.81056	−	3.49508i	0.253187	−	0.183951i
$362$	−11.9506	−	30.0502i	−0.628110	−	1.57940i
$363$		0			0
$364$	1.22481	−	2.24406i	0.0641976	−	0.117621i
$365$	−6.79862	−	13.9783i	−0.355856	−	0.731660i
$366$		0			0
$367$	8.78476	+	4.47606i	0.458561	+	0.233648i	0.667982	−	0.744177i	$-0.267158\pi$
$367$	8.78476	+	4.47606i	0.458561	+	0.233648i	−0.209422	+	0.977825i	$0.567158\pi$
$368$	27.4738	−	2.76573i	1.43217	−	0.144173i
$369$		0			0
$370$	11.1989	+	10.2174i	0.582202	+	0.531178i
$371$	−12.2518	−	3.98084i	−0.636081	−	0.206675i
$372$		0			0
$373$	−1.58263	+	9.99236i	−0.0819457	+	0.517385i	0.912236	+	0.409666i	$0.134355\pi$
$373$	−1.58263	+	9.99236i	−0.0819457	+	0.517385i	−0.994181	+	0.107719i	$0.965645\pi$
$374$	−8.27593	+	1.86311i	−0.427938	+	0.0963389i
$375$		0			0
$376$	−2.27779	−	2.90901i	−0.117468	−	0.150021i
$377$	−0.611687	−	0.0968817i	−0.0315035	−	0.00498966i
$378$		0			0
$379$	5.72788	−	17.6286i	0.294221	−	0.905521i	−0.689260	−	0.724514i	$-0.742064\pi$
$379$	5.72788	−	17.6286i	0.294221	−	0.905521i	0.983482	−	0.181007i	$-0.0579356\pi$
$380$	14.0368	+	8.00285i	0.720071	+	0.410537i
$381$		0			0
$382$	6.06656	−	9.59158i	0.310392	−	0.490748i
$383$	4.71055	−	9.24497i	0.240698	−	0.472396i	−0.738781	−	0.673946i	$-0.764598\pi$
$383$	4.71055	−	9.24497i	0.240698	−	0.472396i	0.979478	+	0.201550i	$0.0645980\pi$
$384$		0			0
$385$	5.07408	−	2.46787i	0.258599	−	0.125774i
$386$	−9.40556	+	10.7013i	−0.478730	+	0.544680i
$387$		0			0
$388$	6.79600	−	4.64883i	0.345015	−	0.236009i
$389$	−16.6111	−	22.8633i	−0.842217	−	1.15921i	−0.985524	−	0.169535i	$-0.945774\pi$
$389$	−16.6111	−	22.8633i	−0.842217	−	1.15921i	0.143307	−	0.989678i	$-0.454226\pi$
$390$		0			0
$391$	19.9637	−	27.4777i	1.00961	−	1.38960i
$392$	−1.47398	−	7.53985i	−0.0744471	−	0.380820i
$393$		0			0
$394$	18.2110	−	10.8073i	0.917455	−	0.544466i
$395$	4.57977	+	15.0390i	0.230433	+	0.756697i
$396$		0			0
$397$	−13.0371	+	6.64271i	−0.654311	+	0.333388i	−0.749436	−	0.662077i	$-0.769675\pi$
$397$	−13.0371	+	6.64271i	−0.654311	+	0.333388i	0.0951247	+	0.995465i	$0.469675\pi$
$398$	6.71957	−	0.433018i	0.336822	−	0.0217052i
$399$		0			0
$400$	1.87449	−	19.9120i	0.0937245	−	0.995598i
$401$	18.3995			0.918829			0.459415	−	0.888222i	$-0.348059\pi$
$401$	18.3995			0.918829			0.459415	+	0.888222i	$0.348059\pi$
$402$		0			0
$403$	−5.85239	+	2.98194i	−0.291528	+	0.148541i
$404$	28.3222	−	3.66546i	1.40908	−	0.182363i
$405$		0			0
$406$	2.52412	−	1.49794i	0.125270	−	0.0743417i
$407$	4.13270	−	4.13270i	0.204850	−	0.204850i
$408$		0			0
$409$	1.04712	−	1.44123i	0.0517766	−	0.0712643i	−0.782344	−	0.622847i	$-0.785976\pi$
$409$	1.04712	−	1.44123i	0.0517766	−	0.0712643i	0.834120	+	0.551583i	$0.185976\pi$
$410$	−17.4406	+	0.799274i	−0.861332	+	0.0394733i
$411$		0			0
$412$	20.7201	−	14.1737i	1.02081	−	0.698287i
$413$	−26.7783	+	4.24127i	−1.31767	+	0.208699i
$414$		0			0
$415$	2.17553	+	15.6046i	0.106793	+	0.765998i
$416$	−3.10076	+	1.60973i	−0.152027	+	0.0789234i
$417$		0			0
$418$	3.32989	−	5.26474i	0.162870	−	0.257507i
$419$	12.5557	+	38.6425i	0.613386	+	1.88781i	0.423108	+	0.906079i	$0.360939\pi$
$419$	12.5557	+	38.6425i	0.613386	+	1.88781i	0.190279	+	0.981730i	$0.439061\pi$
$420$		0			0
$421$	2.89797	−	8.91902i	0.141238	−	0.434687i	−0.855270	−	0.518183i	$-0.826609\pi$
$421$	2.89797	−	8.91902i	0.141238	−	0.434687i	0.996508	+	0.0834962i	$0.0266087\pi$
$422$	1.04992	+	1.26521i	0.0511093	+	0.0615897i
$423$		0			0
$424$	10.8532	+	13.8609i	0.527080	+	0.673145i
$425$	−16.7377	−	18.0286i	−0.811900	−	0.874515i
$426$		0			0
$427$	3.05951	−	19.3170i	0.148060	−	0.934814i
$428$	−6.71438	+	8.71070i	−0.324552	+	0.421047i
$429$		0			0
$430$	12.2032	+	1.36365i	0.588493	+	0.0657612i
$431$	3.54339	−	1.15132i	0.170679	−	0.0554571i	−0.222431	−	0.974948i	$-0.571399\pi$
$431$	3.54339	−	1.15132i	0.170679	−	0.0554571i	0.393110	+	0.919491i	$0.371399\pi$
$432$		0			0
$433$	−5.53878	−	2.82215i	−0.266177	−	0.135624i	0.315809	−	0.948823i	$-0.397724\pi$
$433$	−5.53878	−	2.82215i	−0.266177	−	0.135624i	−0.581986	+	0.813199i	$0.697724\pi$
$434$	12.3195	−	28.5879i	0.591356	−	1.37226i
$435$		0			0
$436$	−5.38816	+	9.87201i	−0.258046	+	0.472784i
$437$	3.90167	+	24.6342i	0.186642	+	1.17841i
$438$		0			0
$439$	0.813614	−	0.591125i	0.0388317	−	0.0282129i	−0.568200	−	0.822890i	$-0.692360\pi$
$439$	0.813614	−	0.591125i	0.0388317	−	0.0282129i	0.607032	+	0.794678i	$0.292360\pi$
$440$	−7.63563	−	1.07337i	−0.364014	−	0.0511708i
$441$		0			0
$442$	−1.06237	+	4.16395i	−0.0505320	+	0.198059i
$443$	−10.2940	−	10.2940i	−0.489083	−	0.489083i	0.418934	−	0.908017i	$-0.362404\pi$
$443$	−10.2940	−	10.2940i	−0.489083	−	0.489083i	−0.908017	+	0.418934i	$0.862404\pi$
$444$		0			0
$445$	−30.2726	−	10.4610i	−1.43506	−	0.495901i
$446$	30.3032	+	2.81802i	1.43490	+	0.133437i
$447$		0			0
$448$	6.43702	−	15.2554i	0.304121	−	0.720751i
$449$		−	18.2346i		−	0.860542i	−0.902700	−	0.430271i	$-0.858418\pi$
$449$		−	18.2346i		−	0.860542i	0.902700	−	0.430271i	$-0.141582\pi$
$450$		0			0
$451$			6.73104i			0.316952i
$452$	−13.0348	+	3.82999i	−0.613107	+	0.180148i
$453$		0			0
$454$	0.884250	−	9.50868i	0.0414999	−	0.446264i
$455$	0.0530363	−	2.85783i	0.00248638	−	0.133977i
$456$		0			0
$457$	20.4576	+	20.4576i	0.956967	+	0.956967i	0.999112	−	0.0421448i	$-0.0134191\pi$
$457$	20.4576	+	20.4576i	0.956967	+	0.956967i	−0.0421448	+	0.999112i	$0.513419\pi$
$458$	27.4921	+	7.01422i	1.28462	+	0.327753i
$459$		0			0
$460$	25.7997	−	16.9544i	1.20292	−	0.790502i
$461$	−1.26163	+	0.916631i	−0.0587602	+	0.0426918i	−0.616778	−	0.787137i	$-0.711562\pi$
$461$	−1.26163	+	0.916631i	−0.0587602	+	0.0426918i	0.558017	+	0.829829i	$0.311562\pi$
$462$		0			0
$463$	−1.78849	−	11.2921i	−0.0831181	−	0.524787i	−0.993755	−	0.111581i	$-0.964409\pi$
$463$	−1.78849	−	11.2921i	−0.0831181	−	0.524787i	0.910637	−	0.413207i	$-0.135591\pi$
$464$	−4.00459	−	0.227505i	−0.185909	−	0.0105617i
$465$		0			0
$466$	−7.06899	−	3.04627i	−0.327465	−	0.141116i
$467$	−24.5198	−	12.4935i	−1.13464	−	0.578129i	−0.217251	−	0.976116i	$-0.569709\pi$
$467$	−24.5198	−	12.4935i	−1.13464	−	0.578129i	−0.917391	+	0.397987i	$0.869709\pi$
$468$		0			0
$469$	15.9955	−	5.19726i	0.738604	−	0.239987i
$470$	−3.76254	−	1.70487i	−0.173553	−	0.0786398i
$471$		0			0
$472$	33.5959	+	15.6222i	1.54637	+	0.719071i
$473$	0.740570	−	4.67578i	0.0340515	−	0.214992i
$474$		0			0
$475$	18.0526	+	0.670280i	0.828310	+	0.0307546i
$476$	−8.72766	−	18.4018i	−0.400032	−	0.843443i
$477$		0			0
$478$	−15.1868	+	12.6026i	−0.694630	+	0.576429i
$479$	−0.100925	+	0.310615i	−0.00461137	+	0.0141923i	−0.953336	−	0.301912i	$-0.902375\pi$
$479$	−0.100925	+	0.310615i	−0.00461137	+	0.0141923i	0.948724	+	0.316105i	$0.102375\pi$
$480$		0			0
$481$	−0.914910	−	2.81580i	−0.0417163	−	0.128390i
$482$	−19.7937	−	12.5193i	−0.901577	−	0.570237i
$483$		0			0
$484$	3.50850	−	18.7010i	0.159477	−	0.850045i
$485$	4.33082	−	8.12346i	0.196652	−	0.368867i
$486$		0			0
$487$	−5.27724	+	0.835833i	−0.239135	+	0.0378752i	−0.274851	−	0.961487i	$-0.588629\pi$
$487$	−5.27724	+	0.835833i	−0.239135	+	0.0378752i	0.0357166	+	0.999362i	$0.488629\pi$
$488$	−18.2068	+	19.5664i	−0.824183	+	0.885727i
$489$		0			0
$490$	−5.36154	−	6.71053i	−0.242210	−	0.303151i
$491$	−21.9210	+	30.1717i	−0.989282	+	1.36163i	−0.0576063	+	0.998339i	$0.518347\pi$
$491$	−21.9210	+	30.1717i	−0.989282	+	1.36163i	−0.931676	+	0.363291i	$0.881653\pi$
$492$		0			0
$493$	−3.48864	+	3.48864i	−0.157121	+	0.157121i
$494$	−1.61051	−	2.71379i	−0.0724601	−	0.122099i
$495$		0			0
$496$	−35.7787	+	23.0123i	−1.60651	+	1.03328i
$497$	24.8380	−	12.6556i	1.11414	−	0.567680i
$498$		0			0
$499$	−13.5542			−0.606769			−0.303385	−	0.952868i	$-0.598117\pi$
$499$	−13.5542			−0.606769			−0.303385	+	0.952868i	$0.598117\pi$
$500$	−8.44324	−	20.7054i	−0.377593	−	0.925972i
$501$		0			0
$502$	2.07974	+	32.2734i	0.0928234	+	1.44043i
$503$	−31.6307	+	16.1167i	−1.41034	+	0.718606i	−0.982676	−	0.185330i	$-0.940665\pi$
$503$	−31.6307	+	16.1167i	−1.41034	+	0.718606i	−0.427668	+	0.903936i	$0.640665\pi$
$504$		0			0
$505$	26.1751	−	18.2850i	1.16478	−	0.813673i
$506$	−6.07429	−	10.2355i	−0.270035	−	0.455024i
$507$		0			0
$508$	0.785584	−	27.6784i	0.0348547	−	1.22803i
$509$	−5.94794	+	8.18664i	−0.263638	+	0.362866i	−0.920229	−	0.391380i	$-0.871998\pi$
$509$	−5.94794	+	8.18664i	−0.263638	+	0.362866i	0.656591	+	0.754247i	$0.271998\pi$
$510$		0			0
$511$	−8.45689	−	11.6399i	−0.374111	−	0.514919i
$512$	−18.9373	+	12.3847i	−0.836917	+	0.547330i
$513$		0			0
$514$	−26.3724	−	23.1793i	−1.16324	−	1.02239i
$515$	13.2041	−	24.7674i	0.581842	−	1.09138i
$516$		0			0
$517$	−0.723006	+	1.41898i	−0.0317978	+	0.0624067i
$518$	11.8589	+	7.50061i	0.521050	+	0.329558i
$519$		0			0
$520$	−2.24054	+	3.19960i	−0.0982541	+	0.140312i
$521$	11.1158	−	34.2110i	0.486994	−	1.49881i	−0.342079	−	0.939671i	$-0.611131\pi$
$521$	11.1158	−	34.2110i	0.486994	−	1.49881i	0.829072	−	0.559141i	$-0.188869\pi$
$522$		0			0
$523$	22.2065	+	3.51717i	0.971023	+	0.153795i	0.621741	−	0.783223i	$-0.286426\pi$
$523$	22.2065	+	3.51717i	0.971023	+	0.153795i	0.349282	+	0.937018i	$0.386426\pi$
$524$	−3.09245	+	1.46670i	−0.135094	+	0.0640730i
$525$		0			0
$526$	2.15290	+	9.56321i	0.0938710	+	0.416976i
$527$	−8.18553	+	51.6814i	−0.356567	+	2.25128i
$528$		0			0
$529$	23.4472	+	7.61845i	1.01944	+	0.331237i
$530$	17.9278	+	8.12340i	0.778735	+	0.352858i
$531$		0			0
$532$	14.0871	+	5.02333i	0.610753	+	0.217789i
$533$	3.03816	+	1.54802i	0.131597	+	0.0670521i
$534$		0			0
$535$	−2.14858	+	12.1071i	−0.0928914	+	0.523437i
$536$	−22.1002	−	6.31154i	−0.954585	−	0.272617i
$537$		0			0
$538$	36.3281	−	14.4472i	1.56621	−	0.622865i
$539$	−2.67906	+	1.94645i	−0.115395	+	0.0838397i
$540$		0			0
$541$	16.8088	+	12.2123i	0.722666	+	0.525048i	0.887235	−	0.461318i	$-0.152623\pi$
$541$	16.8088	+	12.2123i	0.722666	+	0.525048i	−0.164569	+	0.986366i	$0.552623\pi$
$542$	20.8052	+	5.30816i	0.893659	+	0.228005i
$543$		0			0
$544$	−4.14481	+	27.5219i	−0.177707	+	1.17999i
$545$	−0.233316	+	12.5721i	−0.00999414	+	0.538528i
$546$		0			0
$547$	−1.88617	−	3.70181i	−0.0806466	−	0.158278i	0.847162	−	0.531335i	$-0.178310\pi$
$547$	−1.88617	−	3.70181i	−0.0806466	−	0.158278i	−0.927808	+	0.373057i	$0.878310\pi$
$548$	0.259229	+	0.882248i	0.0110737	+	0.0376878i
$549$		0			0
$550$	−8.12329	+	2.88630i	−0.346378	+	0.123072i
$551$		−	3.62299i		−	0.154345i
$552$		0			0
$553$	6.60624	+	12.9655i	0.280926	+	0.551348i
$554$	25.7981	+	2.39907i	1.09606	+	0.101927i
$555$		0			0
$556$	6.77107	−	6.39731i	0.287157	−	0.271306i
$557$	12.9204	+	12.9204i	0.547455	+	0.547455i	0.925704	−	0.378249i	$-0.123474\pi$
$557$	12.9204	+	12.9204i	0.547455	+	0.547455i	−0.378249	+	0.925704i	$0.623474\pi$
$558$		0			0
$559$	−1.94016	−	1.40961i	−0.0820602	−	0.0596202i
$560$	−1.51213	−	18.4504i	−0.0638990	−	0.779672i
$561$		0			0
$562$	−7.52902	−	18.9320i	−0.317592	−	0.798597i
$563$	0.508973	+	3.21353i	0.0214506	+	0.135434i	0.996090	−	0.0883493i	$-0.0281592\pi$
$563$	0.508973	+	3.21353i	0.0214506	+	0.135434i	−0.974639	+	0.223783i	$0.928159\pi$
$564$		0			0
$565$	−10.9380	+	10.5394i	−0.460166	+	0.443397i
$566$	16.3416	−	37.9213i	0.686889	−	1.59395i
$567$		0			0
$568$	−37.8158	−	4.60210i	−1.58672	−	0.193100i
$569$	18.5217	−	6.01805i	0.776468	−	0.252290i	0.106137	−	0.994352i	$-0.466152\pi$
$569$	18.5217	−	6.01805i	0.776468	−	0.252290i	0.670332	+	0.742062i	$0.266152\pi$
$570$		0			0
$571$	39.3841	+	12.7967i	1.64817	+	0.535525i	0.978343	−	0.206989i	$-0.0663663\pi$
$571$	39.3841	+	12.7967i	1.64817	+	0.535525i	0.669832	+	0.742513i	$0.266366\pi$
$572$	1.19272	+	0.919373i	0.0498701	+	0.0384409i
$573$		0			0
$574$	−15.7657	+	3.54922i	−0.658046	+	0.148142i
$575$	16.8002	−	30.1513i	0.700616	−	1.25740i
$576$		0			0
$577$	24.3357	+	3.85440i	1.01311	+	0.160461i	0.640849	−	0.767667i	$-0.278583\pi$
$577$	24.3357	+	3.85440i	1.01311	+	0.160461i	0.372261	+	0.928128i	$0.378583\pi$
$578$	6.50898	+	7.84369i	0.270738	+	0.326254i
$579$		0			0
$580$	−4.08682	+	1.84622i	−0.169696	+	0.0766601i
$581$	4.50655	+	13.8697i	0.186963	+	0.575413i
$582$		0			0
$583$	3.44500	−	6.76119i	0.142677	−	0.280020i
$584$	0.707225	+	19.6490i	0.0292652	+	0.813083i
$585$		0			0
$586$	3.97145	−	4.51856i	0.164059	−	0.186660i
$587$	38.9053	−	6.16199i	1.60579	−	0.254333i	0.711789	−	0.702393i	$-0.247885\pi$
$587$	38.9053	−	6.16199i	1.60579	−	0.254333i	0.894003	+	0.448060i	$0.147885\pi$
$588$		0			0
$589$	−22.5854	−	31.0862i	−0.930617	−	1.28088i
$590$	41.3802	−	1.89638i	1.70360	−	0.0780728i
$591$		0			0
$592$	−7.72236	−	17.5517i	−0.317387	−	0.721370i
$593$	22.6547	−	22.6547i	0.930317	−	0.930317i	−0.0674081	−	0.997725i	$-0.521473\pi$
$593$	22.6547	−	22.6547i	0.930317	−	0.930317i	0.997725	+	0.0674081i	$0.0214730\pi$
$594$		0			0
$595$	−18.1702	−	13.7237i	−0.744906	−	0.562616i
$596$	5.04014	+	38.9441i	0.206452	+	1.59521i
$597$		0			0
$598$	−6.01693	+	0.387739i	−0.246051	+	0.0158558i
$599$	−33.3301			−1.36183			−0.680916	−	0.732361i	$-0.738418\pi$
$599$	−33.3301			−1.36183			−0.680916	+	0.732361i	$0.738418\pi$
$600$		0			0
$601$	−30.1376			−1.22934			−0.614669	−	0.788785i	$-0.710710\pi$
$601$	−30.1376			−1.22934			−0.614669	+	0.788785i	$0.710710\pi$
$602$	11.3423	−	0.730910i	0.462276	−	0.0297897i
$603$		0			0
$604$	6.10383	+	47.1629i	0.248361	+	1.91903i
$605$	−6.19722	−	20.3504i	−0.251953	−	0.827363i
$606$		0			0
$607$	−16.1185	+	16.1185i	−0.654230	+	0.654230i	−0.954009	−	0.299779i	$-0.903087\pi$
$607$	−16.1185	+	16.1185i	−0.654230	+	0.654230i	0.299779	+	0.954009i	$0.403087\pi$
$608$	−12.1387	−	16.4431i	−0.492288	−	0.666855i
$609$		0			0
$610$	−7.92322	+	28.8121i	−0.320802	+	1.16657i
$611$	0.474199	+	0.652680i	0.0191841	+	0.0264046i
$612$		0			0
$613$	−41.4745	+	6.56892i	−1.67514	+	0.265316i	−0.920478	−	0.390795i	$-0.872200\pi$
$613$	−41.4745	+	6.56892i	−1.67514	+	0.265316i	−0.754664	+	0.656112i	$0.772200\pi$
$614$	30.2651	−	34.4345i	1.22140	−	1.38966i
$615$		0			0
$616$	−7.13251	+	0.256719i	−0.287377	+	0.0103435i
$617$	−10.3229	+	20.2599i	−0.415585	+	0.815632i	0.584406	+	0.811461i	$0.301327\pi$
$617$	−10.3229	+	20.2599i	−0.415585	+	0.815632i	−0.999991	+	0.00417035i	$0.998673\pi$
$618$		0			0
$619$	4.80555	+	14.7900i	0.193151	+	0.594459i	0.999993	+	0.00369144i	$0.00117503\pi$
$619$	4.80555	+	14.7900i	0.193151	+	0.594459i	−0.806842	+	0.590768i	$0.798825\pi$
$620$	−23.5568	+	41.3180i	−0.946065	+	1.65937i
$621$		0			0
$622$	−8.94943	−	10.7846i	−0.358840	−	0.432422i
$623$	−29.2815	−	4.63774i	−1.17314	−	0.185807i
$624$		0			0
$625$	−19.0800	−	16.1540i	−0.763201	−	0.646161i
$626$	17.1535	−	3.86165i	0.685591	−	0.154343i
$627$		0			0
$628$	5.33942	+	4.11573i	0.213066	+	0.164236i
$629$	−22.4318	−	7.28854i	−0.894415	−	0.290613i
$630$		0			0
$631$	−9.56990	+	3.10945i	−0.380972	+	0.123785i	−0.493241	−	0.869893i	$-0.664188\pi$
$631$	−9.56990	+	3.10945i	−0.380972	+	0.123785i	0.112270	+	0.993678i	$0.464188\pi$
$632$	2.40231	−	19.7399i	0.0955586	−	0.785212i
$633$		0			0
$634$	2.37033	−	5.50044i	0.0941379	−	0.218450i
$635$	−13.5403	−	27.8396i	−0.537331	−	1.10478i
$636$		0			0
$637$	0.262425	+	1.65689i	0.0103977	+	0.0656482i
$638$	0.638905	+	1.60655i	0.0252945	+	0.0636038i
$639$		0			0
$640$	−12.3625	+	22.0719i	−0.488673	+	0.872467i
$641$	2.79699	+	2.03213i	0.110474	+	0.0802644i	0.641651	−	0.766997i	$-0.278250\pi$
$641$	2.79699	+	2.03213i	0.110474	+	0.0802644i	−0.531176	+	0.847261i	$0.678250\pi$
$642$		0			0
$643$	−17.1130	−	17.1130i	−0.674871	−	0.674871i	0.283964	−	0.958835i	$-0.408350\pi$
$643$	−17.1130	−	17.1130i	−0.674871	−	0.674871i	−0.958835	+	0.283964i	$0.908350\pi$
$644$	20.7710	−	19.6245i	0.818494	−	0.773314i
$645$		0			0
$646$	−25.0315	−	2.32778i	−0.984852	−	0.0915853i
$647$	16.5566	+	32.4942i	0.650909	+	1.27748i	0.946666	+	0.322217i	$0.104428\pi$
$647$	16.5566	+	32.4942i	0.650909	+	1.27748i	−0.295757	+	0.955263i	$0.595572\pi$
$648$		0			0
$649$		−	15.9703i		−	0.626888i
$650$	−0.565434	+	4.33037i	−0.0221782	+	0.169851i
$651$		0			0
$652$	−3.34243	−	11.3755i	−0.130900	−	0.445498i
$653$	18.6301	+	36.5636i	0.729051	+	1.43084i	0.895623	+	0.444813i	$0.146730\pi$
$653$	18.6301	+	36.5636i	0.729051	+	1.43084i	−0.166573	+	0.986029i	$0.553270\pi$
$654$		0			0
$655$	−2.30629	+	3.05354i	−0.0901141	+	0.119312i
$656$	20.5823	+	8.00464i	0.803603	+	0.312529i
$657$		0			0
$658$	−3.70482	−	0.945234i	−0.144429	−	0.0368490i
$659$	25.5515	+	18.5642i	0.995344	+	0.723160i	0.961085	−	0.276253i	$-0.0890929\pi$
$659$	25.5515	+	18.5642i	0.995344	+	0.723160i	0.0342591	+	0.999413i	$0.489093\pi$
$660$		0			0
$661$	−6.57518	+	4.77715i	−0.255745	+	0.185810i	−0.708269	−	0.705943i	$-0.750524\pi$
$661$	−6.57518	+	4.77715i	−0.255745	+	0.185810i	0.452524	+	0.891752i	$0.350524\pi$
$662$	−11.3068	+	4.49658i	−0.439452	+	0.174765i
$663$		0			0
$664$	5.47274	−	19.1631i	0.212384	−	0.743674i
$665$	16.5611	−	2.30888i	0.642211	−	0.0895347i
$666$		0			0
$667$	−6.16777	−	3.14263i	−0.238817	−	0.121683i
$668$	−25.2813	−	9.01510i	−0.978165	−	0.348805i
$669$		0			0
$670$	−25.1697	+	5.17755i	−0.972389	+	0.200026i
$671$	10.9566	+	3.56001i	0.422974	+	0.137433i
$672$		0			0
$673$	−4.92681	+	31.1067i	−0.189915	+	1.19907i	0.689952	+	0.723855i	$0.257631\pi$
$673$	−4.92681	+	31.1067i	−0.189915	+	1.19907i	−0.879867	+	0.475220i	$0.842369\pi$
$674$	−0.214173	−	0.951360i	−0.00824965	−	0.0366450i
$675$		0			0
$676$	−22.8025	+	10.8148i	−0.877017	+	0.415955i
$677$	4.81004	+	0.761836i	0.184865	+	0.0292797i	0.248180	−	0.968714i	$-0.420167\pi$
$677$	4.81004	+	0.761836i	0.184865	+	0.0292797i	−0.0633155	+	0.997994i	$0.520167\pi$
$678$		0			0
$679$	2.63314	−	8.10396i	0.101050	−	0.311001i
$680$	10.1299	+	29.4224i	0.388463	+	1.12830i
$681$		0			0
$682$	15.4971	+	9.80172i	0.593413	+	0.375327i
$683$	3.12436	−	6.13190i	0.119550	−	0.234631i	−0.823474	−	0.567353i	$-0.807967\pi$
$683$	3.12436	−	6.13190i	0.119550	−	0.234631i	0.943025	+	0.332723i	$0.107967\pi$
$684$		0			0
$685$	0.713350	+	0.740327i	0.0272557	+	0.0282865i
$686$	−21.3616	−	18.7751i	−0.815588	−	0.716837i
$687$		0			0
$688$	−13.4170	−	7.82502i	−0.511517	−	0.298326i
$689$	−2.25948	−	3.10990i	−0.0860792	−	0.118478i
$690$		0			0
$691$	−6.99922	+	9.63360i	−0.266263	+	0.366480i	−0.921124	−	0.389270i	$-0.872727\pi$
$691$	−6.99922	+	9.63360i	−0.266263	+	0.366480i	0.654861	+	0.755750i	$0.272727\pi$
$692$	−0.914981	+	32.2374i	−0.0347823	+	1.22548i
$693$		0			0
$694$	18.5692	+	31.2901i	0.704876	+	1.18776i
$695$	3.40156	−	9.84356i	0.129028	−	0.373387i
$696$		0			0
$697$	24.2032	−	12.3321i	0.916760	−	0.467113i
$698$	−2.69696	−	41.8515i	−0.102082	−	1.58410i
$699$		0			0
$700$	−11.0437	−	17.5047i	−0.417414	−	0.661617i
$701$	−33.9745			−1.28320			−0.641600	−	0.767040i	$-0.721729\pi$
$701$	−33.9745			−1.28320			−0.641600	+	0.767040i	$0.721729\pi$
$702$		0			0
$703$	15.4324	−	7.86322i	0.582045	−	0.296567i
$704$	8.28236	+	5.15077i	0.312153	+	0.194127i
$705$		0			0
$706$	−24.0724	−	40.5633i	−0.905977	−	1.52662i
$707$	20.8979	−	20.8979i	0.785948	−	0.785948i
$708$		0			0
$709$	−9.76306	+	13.4377i	−0.366659	+	0.504663i	−0.951989	−	0.306132i	$-0.900965\pi$
$709$	−9.76306	+	13.4377i	−0.366659	+	0.504663i	0.585330	+	0.810795i	$0.300965\pi$
$710$	−39.8617	+	15.0020i	−1.49598	+	0.563016i
$711$		0			0
$712$	29.6596	+	27.5987i	1.11154	+	1.03430i
$713$	−72.5120	+	11.4848i	−2.71560	+	0.430108i
$714$		0			0
$715$	1.65778	+	0.294197i	0.0619974	+	0.0110023i
$716$	2.23487	−	11.9123i	0.0835211	−	0.445184i
$717$		0			0
$718$	−7.69483	−	4.86689i	−0.287169	−	0.181631i
$719$	−11.5947	−	35.6849i	−0.432410	−	1.33082i	−0.895717	−	0.444624i	$-0.853337\pi$
$719$	−11.5947	−	35.6849i	−0.432410	−	1.33082i	0.463307	−	0.886198i	$-0.346663\pi$
$720$		0			0
$721$	8.02809	−	24.7079i	0.298982	−	0.920171i
$722$	−6.47122	+	5.37005i	−0.240834	+	0.199853i
$723$		0			0
$724$	19.5987	+	41.3226i	0.728378	+	1.53574i
$725$	−3.09552	+	3.94412i	−0.114965	+	0.146481i
$726$		0			0
$727$	5.20051	−	32.8348i	0.192876	−	1.21777i	−0.681241	−	0.732059i	$-0.738559\pi$
$727$	5.20051	−	32.8348i	0.192876	−	1.21777i	0.874118	−	0.485715i	$-0.161441\pi$
$728$	−1.52448	+	3.27841i	−0.0565008	+	0.121506i
$729$		0			0
$730$	10.8661	+	19.1091i	0.402171	+	0.707261i
$731$	−18.1698	+	5.90372i	−0.672033	+	0.218357i
$732$		0			0
$733$	28.4963	+	14.5196i	1.05254	+	0.536294i	0.892607	−	0.450835i	$-0.148874\pi$
$733$	28.4963	+	14.5196i	1.05254	+	0.536294i	0.159928	+	0.987129i	$0.448874\pi$
$734$	−12.8049	−	5.51807i	−0.472637	−	0.203676i
$735$		0			0
$736$	−38.5219	+	6.40184i	−1.41994	+	0.235975i
$737$	1.54979	+	9.78500i	0.0570873	+	0.360435i
$738$		0			0
$739$	14.5373	−	10.5619i	0.534762	−	0.388527i	−0.287374	−	0.957818i	$-0.592782\pi$
$739$	14.5373	−	10.5619i	0.534762	−	0.388527i	0.822136	+	0.569291i	$0.192782\pi$
$740$	−16.7340	−	13.4012i	−0.615156	−	0.492638i
$741$		0			0
$742$	17.6528	+	4.50387i	0.648055	+	0.165342i
$743$	−13.7539	−	13.7539i	−0.504581	−	0.504581i	0.408277	−	0.912858i	$-0.366130\pi$
$743$	−13.7539	−	13.7539i	−0.504581	−	0.504581i	−0.912858	+	0.408277i	$0.866130\pi$
$744$		0			0
$745$	25.1426	+	35.9917i	0.921153	+	1.31864i
$746$	1.32479	−	14.2460i	0.0485041	−	0.521584i
$747$		0			0
$748$	11.5103	−	3.38203i	0.420857	−	0.123659i
$749$			11.3816i			0.415875i
$750$		0			0
$751$		−	1.95838i		−	0.0714623i	−0.999361	−	0.0357311i	$-0.988624\pi$
$751$		−	1.95838i		−	0.0714623i	0.999361	−	0.0357311i	$-0.0113760\pi$
$752$	3.47917	+	3.89829i	0.126872	+	0.142156i
$753$		0			0
$754$	0.872076	+	0.0810979i	0.0317591	+	0.00295341i
$755$	30.4487	+	43.5875i	1.10814	+	1.58631i
$756$		0			0
$757$	−17.8464	−	17.8464i	−0.648640	−	0.648640i	0.304025	−	0.952664i	$-0.401670\pi$
$757$	−17.8464	−	17.8464i	−0.648640	−	0.648640i	−0.952664	+	0.304025i	$0.901670\pi$
$758$	−6.48044	+	25.3999i	−0.235380	+	0.922567i
$759$		0			0
$760$	−20.5377	−	10.0177i	−0.744981	−	0.363381i
$761$	9.56396	−	6.94862i	0.346693	−	0.251887i	−0.400787	−	0.916171i	$-0.631263\pi$
$761$	9.56396	−	6.94862i	0.346693	−	0.251887i	0.747481	+	0.664284i	$0.231263\pi$
$762$		0			0
$763$	1.82072	+	11.4956i	0.0659145	+	0.416168i
$764$	−7.68935	+	14.0882i	−0.278191	+	0.509693i
$765$		0			0
$766$	−5.80714	+	13.4757i	−0.209821	+	0.486897i
$767$	−7.20842	−	3.67288i	−0.260281	−	0.132620i
$768$		0			0
$769$	19.4145	−	6.30814i	0.700103	−	0.227477i	0.0627276	−	0.998031i	$-0.480020\pi$
$769$	19.4145	−	6.30814i	0.700103	−	0.227477i	0.637375	+	0.770553i	$0.280020\pi$
$770$	−6.93654	+	3.94433i	−0.249975	+	0.142144i
$771$		0			0
$772$	12.3007	−	15.9579i	0.442712	−	0.574339i
$773$	3.16880	−	20.0070i	0.113974	−	0.719603i	−0.862834	−	0.505487i	$-0.831313\pi$
$773$	3.16880	−	20.0070i	0.113974	−	0.719603i	0.976808	−	0.214116i	$-0.0686870\pi$
$774$		0			0
$775$	−1.97301	+	53.1388i	−0.0708725	+	1.90880i
$776$	−9.16832	+	7.17890i	−0.329123	+	0.257707i
$777$		0			0
$778$	25.5224	+	30.7559i	0.915021	+	1.10265i
$779$	−6.16410	+	18.9711i	−0.220852	+	0.679711i
$780$		0			0
$781$	5.07419	+	15.6168i	0.181569	+	0.558812i
$782$	−25.6755	+	40.5944i	−0.918155	+	1.45165i
$783$		0			0
$784$	2.76592	+	10.5068i	0.0987827	+	0.375244i
$785$	7.42134	+	1.31702i	0.264879	+	0.0470065i
$786$		0			0
$787$	−49.0348	+	7.76635i	−1.74790	+	0.276841i	−0.946832	−	0.321729i	$-0.895736\pi$
$787$	−49.0348	+	7.76635i	−1.74790	+	0.276841i	−0.801071	+	0.598570i	$0.795736\pi$
$788$	−24.7180	+	16.9085i	−0.880543	+	0.602339i
$789$		0			0
$790$	−7.83109	−	20.8079i	−0.278618	−	0.740312i
$791$	−8.26401	+	11.3744i	−0.293834	+	0.404428i
$792$		0			0
$793$	4.12668	−	4.12668i	0.146543	−	0.146543i
$794$	17.7949	−	10.5604i	0.631517	−	0.374775i
$795$		0			0
$796$	−9.44386	+	1.22222i	−0.334729	+	0.0433206i
$797$	−10.0858	+	5.13896i	−0.357257	+	0.182031i	−0.623402	−	0.781902i	$-0.714250\pi$
$797$	−10.0858	+	5.13896i	−0.357257	+	0.182031i	0.266145	+	0.963933i	$0.414250\pi$
$798$		0			0
$799$	6.42694			0.227369
$800$	−0.834546	+	28.2720i	−0.0295057	+	0.999565i
$801$		0			0
$802$	−25.9670	+	1.67335i	−0.916927	+	0.0590880i
$803$	7.55131	−	3.84758i	0.266480	−	0.135778i
$804$		0			0
$805$	10.4347	−	30.1963i	0.367774	−	1.06428i
$806$	7.98820	−	4.74062i	0.281372	−	0.166981i
$807$		0			0
$808$	−39.6374	+	7.74878i	−1.39444	+	0.272601i
$809$	9.99015	−	13.7503i	0.351235	−	0.483434i	−0.596446	−	0.802653i	$-0.703421\pi$
$809$	9.99015	−	13.7503i	0.351235	−	0.483434i	0.947681	+	0.319220i	$0.103421\pi$
$810$		0			0
$811$	−13.4786	−	18.5517i	−0.473299	−	0.651440i	0.503901	−	0.863761i	$-0.331898\pi$
$811$	−13.4786	−	18.5517i	−0.473299	−	0.651440i	−0.977200	+	0.212322i	$0.931898\pi$
$812$	−3.42602	+	2.34358i	−0.120230	+	0.0822437i
$813$		0			0
$814$	−5.45657	+	6.20827i	−0.191253	+	0.217600i
$815$	−9.19774	−	9.54559i	−0.322183	−	0.334367i
$816$		0			0
$817$	6.36921	−	12.5003i	0.222830	−	0.437329i
$818$	−1.34671	+	2.12922i	−0.0470865	+	0.0744465i
$819$		0			0
$820$	24.5411	−	2.71415i	0.857011	−	0.0947821i
$821$	−6.99281	+	21.5217i	−0.244051	+	0.751111i	0.751740	+	0.659459i	$0.229215\pi$
$821$	−6.99281	+	21.5217i	−0.244051	+	0.751111i	−0.995791	+	0.0916520i	$0.970785\pi$
$822$		0			0
$823$	53.8434	+	8.52795i	1.87686	+	0.297266i	0.987216	−	0.159386i	$-0.0509514\pi$
$823$	53.8434	+	8.52795i	1.87686	+	0.297266i	0.889646	+	0.456652i	$0.150951\pi$
$824$	−27.9530	+	21.8875i	−0.973789	+	0.762488i
$825$		0			0
$826$	37.4061	−	8.42100i	1.30153	−	0.293004i
$827$	2.96544	−	18.7231i	0.103119	−	0.651065i	−0.880941	−	0.473226i	$-0.843089\pi$
$827$	2.96544	−	18.7231i	0.103119	−	0.651065i	0.984060	−	0.177839i	$-0.0569107\pi$
$828$		0			0
$829$	−3.94785	−	1.28273i	−0.137114	−	0.0445512i	0.239656	−	0.970858i	$-0.422965\pi$
$829$	−3.94785	−	1.28273i	−0.137114	−	0.0445512i	−0.376770	+	0.926307i	$0.622965\pi$
$830$	−4.48946	−	21.8247i	−0.155831	−	0.757545i
$831$		0			0
$832$	4.22967	−	2.55379i	0.146637	−	0.0885366i
$833$	11.9074	+	6.06710i	0.412566	+	0.210213i
$834$		0			0
$835$	−29.7213	+	4.14363i	−1.02855	+	0.143396i
$836$	−4.22063	+	7.73290i	−0.145973	+	0.267448i
$837$		0			0
$838$	−21.2340	−	53.3937i	−0.733518	−	1.84446i
$839$	−2.92007	+	2.12156i	−0.100812	+	0.0732443i	−0.637049	−	0.770823i	$-0.719845\pi$
$839$	−2.92007	+	2.12156i	−0.100812	+	0.0732443i	0.536237	+	0.844067i	$0.319845\pi$
$840$		0			0
$841$	−22.6480	−	16.4547i	−0.780965	−	0.567405i
$842$	−3.27872	+	12.8509i	−0.112992	+	0.442870i
$843$		0			0
$844$	−1.59680	−	1.69009i	−0.0549643	−	0.0581755i
$845$	−17.0056	+	22.5155i	−0.585012	+	0.774558i
$846$		0			0
$847$	−8.93938	−	17.5445i	−0.307161	−	0.602837i
$848$	−16.5776	−	18.5747i	−0.569278	−	0.637856i
$849$		0			0
$850$	25.2614	+	23.9213i	0.866458	+	0.820494i
$851$		−	33.0928i		−	1.13441i
$852$		0			0
$853$	−2.88314	−	5.65849i	−0.0987169	−	0.193743i	0.836366	−	0.548171i	$-0.184676\pi$
$853$	−2.88314	−	5.65849i	−0.0987169	−	0.193743i	−0.935083	+	0.354428i	$0.884676\pi$
$854$	−2.56106	+	27.5400i	−0.0876376	+	0.942400i
$855$		0			0
$856$	8.68372	−	12.9039i	0.296803	−	0.441047i
$857$	−0.669915	−	0.669915i	−0.0228838	−	0.0228838i	0.695572	−	0.718456i	$-0.255151\pi$
$857$	−0.669915	−	0.669915i	−0.0228838	−	0.0228838i	−0.718456	+	0.695572i	$0.755151\pi$
$858$		0			0
$859$	−6.89179	−	5.00718i	−0.235145	−	0.170843i	0.463973	−	0.885849i	$-0.346424\pi$
$859$	−6.89179	−	5.00718i	−0.235145	−	0.170843i	−0.699117	+	0.715007i	$0.746424\pi$
$860$	−17.3463	−	0.814679i	−0.591503	−	0.0277803i
$861$		0			0
$862$	−4.89604	+	1.94709i	−0.166760	+	0.0663183i
$863$	−1.83066	−	11.5583i	−0.0623164	−	0.393451i	−0.999057	−	0.0434252i	$-0.986173\pi$
$863$	−1.83066	−	11.5583i	−0.0623164	−	0.393451i	0.936740	−	0.350025i	$-0.113827\pi$
$864$		0			0
$865$	15.7706	+	32.4252i	0.536216	+	1.10249i
$866$	8.07346	+	3.47913i	0.274347	+	0.118226i
$867$		0			0
$868$	−14.7864	+	41.4661i	−0.501884	+	1.40745i
$869$	−8.15198	+	2.64874i	−0.276537	+	0.0898523i
$870$		0			0
$871$	4.77303	+	1.55085i	0.161728	+	0.0525486i
$872$	6.70642	−	14.4223i	0.227108	−	0.488399i
$873$		0			0
$874$	−7.74672	−	34.4110i	−0.262037	−	1.16397i
$875$	−20.0017	−	11.6364i	−0.676182	−	0.393382i
$876$		0			0
$877$	27.8979	+	4.41859i	0.942044	+	0.149205i	0.608522	−	0.793537i	$-0.291763\pi$
$877$	27.8979	+	4.41859i	0.942044	+	0.149205i	0.333522	+	0.942742i	$0.391763\pi$
$878$	−1.09448	+	0.908241i	−0.0369370	+	0.0306517i
$879$		0			0
$880$	10.8737	+	0.820406i	0.366552	+	0.0276559i
$881$	−7.87708	−	24.2432i	−0.265386	−	0.816773i	−0.991604	−	0.129309i	$-0.958724\pi$
$881$	−7.87708	−	24.2432i	−0.265386	−	0.816773i	0.726219	−	0.687464i	$-0.241276\pi$
$882$		0			0
$883$	7.98248	−	15.6665i	0.268632	−	0.527219i	−0.716803	−	0.697276i	$-0.754395\pi$
$883$	7.98248	−	15.6665i	0.268632	−	0.527219i	0.985434	+	0.170057i	$0.0543951\pi$
$884$	1.12062	−	5.97314i	0.0376906	−	0.200898i
$885$		0			0
$886$	15.4640	+	13.5916i	0.519522	+	0.456619i
$887$	−24.9107	+	3.94547i	−0.836421	+	0.132476i	−0.559929	−	0.828540i	$-0.689172\pi$
$887$	−24.9107	+	3.94547i	−0.836421	+	0.132476i	−0.276491	+	0.961016i	$0.589172\pi$
$888$		0			0
$889$	−16.8430	−	23.1823i	−0.564895	−	0.777511i
$890$	43.6746	+	12.0104i	1.46398	+	0.402589i
$891$		0			0
$892$	−43.0228	−	1.22110i	−1.44051	−	0.0408855i
$893$	−3.33722	+	3.33722i	−0.111676	+	0.111676i
$894$		0			0
$895$	−3.94756	−	12.9630i	−0.131952	−	0.433305i
$896$	−7.69708	+	22.1152i	−0.257141	+	0.738817i
$897$		0			0
$898$	1.65834	+	25.7342i	0.0553397	+	0.858761i
$899$	10.6645			0.355680
$900$		0			0
$901$	−30.6232			−1.02021
$902$	−0.612155	−	9.49942i	−0.0203825	−	0.316296i
$903$		0			0
$904$	18.0476	−	6.59067i	0.600253	−	0.219202i
$905$	40.8027	+	30.8176i	1.35633	+	1.02441i
$906$		0			0
$907$	−20.9210	+	20.9210i	−0.694669	+	0.694669i	−0.963256	−	0.268586i	$-0.913444\pi$
$907$	−20.9210	+	20.9210i	−0.694669	+	0.694669i	0.268586	+	0.963256i	$0.413444\pi$
$908$	−0.383162	+	13.4999i	−0.0127157	+	0.448009i
$909$		0			0
$910$	0.185056	+	4.03804i	0.00613455	+	0.133860i
$911$	16.8211	+	23.1523i	0.557309	+	0.767070i	0.990981	−	0.134000i	$-0.0427823\pi$
$911$	16.8211	+	23.1523i	0.557309	+	0.767070i	−0.433672	+	0.901071i	$0.642782\pi$
$912$		0			0
$913$	−8.48459	+	1.34383i	−0.280799	+	0.0444742i
$914$	−30.7321	−	27.0110i	−1.01653	−	0.893445i
$915$		0			0
$916$	−39.4371	−	7.39881i	−1.30304	−	0.244464i
$917$	−1.60802	+	3.15592i	−0.0531016	+	0.104218i
$918$		0			0
$919$	7.46481	+	22.9743i	0.246241	+	0.757853i	0.995430	+	0.0954962i	$0.0304438\pi$
$919$	7.46481	+	22.9743i	0.246241	+	0.757853i	−0.749188	+	0.662357i	$0.769556\pi$
$920$	−34.8689	+	26.2738i	−1.14959	+	0.866222i
$921$		0			0
$922$	1.69716	−	1.40837i	0.0558931	−	0.0463821i
$923$	8.21583	+	1.30126i	0.270427	+	0.0428315i
$924$		0			0
$925$	−23.5187	−	4.62544i	−0.773291	−	0.152083i
$926$	3.55103	+	15.7737i	0.116694	+	0.518356i
$927$		0			0
$928$	5.67232	−	0.0431235i	0.186203	−	0.00141560i
$929$	29.1865	+	9.48327i	0.957579	+	0.311136i	0.745791	−	0.666180i	$-0.232072\pi$
$929$	29.1865	+	9.48327i	0.957579	+	0.311136i	0.211787	+	0.977316i	$0.432072\pi$
$930$		0			0
$931$	−9.33333	+	3.03258i	−0.305888	+	0.0993889i
$932$	10.2534	+	3.65627i	0.335862	+	0.119765i
$933$		0			0
$934$	35.7407	+	15.4019i	1.16947	+	0.503966i
$935$	9.65869	−	9.30672i	0.315873	−	0.304362i
$936$		0			0
$937$	−5.74987	−	36.3032i	−0.187840	−	1.18598i	−0.883790	−	0.467885i	$-0.845016\pi$
$937$	−5.74987	−	36.3032i	−0.187840	−	1.18598i	0.695950	−	0.718091i	$-0.254984\pi$
$938$	−22.1016	+	8.78953i	−0.721642	+	0.286988i
$939$		0			0
$940$	5.46507	+	2.06387i	0.178251	+	0.0673162i
$941$	17.5281	+	12.7349i	0.571401	+	0.415147i	0.835614	−	0.549317i	$-0.185112\pi$
$941$	17.5281	+	12.7349i	0.571401	+	0.415147i	−0.264213	+	0.964464i	$0.585112\pi$
$942$		0			0
$943$	26.9496	+	26.9496i	0.877599	+	0.877599i
$944$	−48.8341	−	18.9921i	−1.58942	−	0.618139i
$945$		0			0
$946$	−0.619918	+	6.66621i	−0.0201553	+	0.216737i
$947$	15.1008	+	29.6371i	0.490711	+	0.963075i	0.995032	+	0.0995587i	$0.0317431\pi$
$947$	15.1008	+	29.6371i	0.490711	+	0.963075i	−0.504320	+	0.863517i	$0.668257\pi$
$948$		0			0
$949$		−	4.29327i		−	0.139366i
$950$	−25.5383	+	0.695838i	−0.828573	+	0.0225760i
$951$		0			0
$952$	13.9908	+	25.1764i	0.453444	+	0.815972i
$953$	−12.4971	−	24.5269i	−0.404819	−	0.794503i	0.595139	−	0.803623i	$-0.297097\pi$
$953$	−12.4971	−	24.5269i	−0.404819	−	0.794503i	−0.999958	+	0.00911989i	$0.997097\pi$
$954$		0			0
$955$	−0.332961	+	17.9414i	−0.0107744	+	0.580569i
$956$	20.2868	−	19.1670i	0.656123	−	0.619906i
$957$		0			0
$958$	0.114185	−	0.447545i	0.00368915	−	0.0144595i
$959$	0.769866	+	0.559340i	0.0248603	+	0.0180620i
$960$		0			0
$961$	66.4244	−	48.2601i	2.14272	−	1.55678i
$962$	1.54728	+	3.89070i	0.0498864	+	0.125441i
$963$		0			0
$964$	29.0731	+	15.8681i	0.936381	+	0.511078i
$965$	3.93619	−	22.1802i	0.126711	−	0.714006i
$966$		0			0
$967$	35.2063	+	17.9385i	1.13216	+	0.576863i	0.916671	−	0.399644i	$-0.130866\pi$
$967$	35.2063	+	17.9385i	1.13216	+	0.576863i	0.215487	+	0.976507i	$0.430866\pi$
$968$	−3.25073	+	26.7115i	−0.104483	+	0.858541i
$969$		0			0
$970$	−5.37324	+	11.8584i	−0.172524	+	0.380750i
$971$	−15.6458	−	5.08364i	−0.502099	−	0.163142i	0.0470070	−	0.998895i	$-0.485032\pi$
$971$	−15.6458	−	5.08364i	−0.502099	−	0.163142i	−0.549106	+	0.835753i	$0.685032\pi$
$972$		0			0
$973$	1.50803	−	9.52131i	0.0483451	−	0.305239i
$974$	7.37169	−	1.65954i	0.236204	−	0.0531751i
$975$		0			0
$976$	23.9155	−	29.2696i	0.765518	−	0.936896i
$977$	1.13863	+	0.180341i	0.0364279	+	0.00576961i	0.174622	−	0.984636i	$-0.444130\pi$
$977$	1.13863	+	0.180341i	0.0364279	+	0.00576961i	−0.138194	+	0.990405i	$0.544130\pi$
$978$		0			0
$979$	5.39642	−	16.6085i	0.172470	−	0.530809i
$980$	8.17696	+	8.98288i	0.261203	+	0.286948i
$981$		0			0
$982$	28.1929	−	44.5745i	0.899671	−	1.42243i
$983$	−0.911754	+	1.78942i	−0.0290804	+	0.0570735i	−0.905090	−	0.425221i	$-0.860196\pi$
$983$	−0.911754	+	1.78942i	−0.0290804	+	0.0570735i	0.876009	+	0.482294i	$0.160196\pi$
$984$		0			0
$985$	−15.7518	+	29.5462i	−0.501894	+	0.941419i
$986$	4.60620	−	5.24075i	0.146691	−	0.166899i
$987$		0			0
$988$	2.51969	+	3.68347i	0.0801621	+	0.117187i
$989$	−15.7557	−	21.6858i	−0.501002	−	0.689570i
$990$		0			0
$991$	14.2213	−	19.5739i	0.451754	−	0.621786i	−0.521019	−	0.853545i	$-0.674448\pi$
$991$	14.2213	−	19.5739i	0.451754	−	0.621786i	0.972773	+	0.231759i	$0.0744480\pi$
$992$	48.4011	−	35.7308i	1.53674	−	1.13445i
$993$		0			0
$994$	−33.9025	+	20.1195i	−1.07532	+	0.638153i
$995$	−8.72793	+	6.09703i	−0.276694	+	0.193289i
$996$		0			0
$997$	38.9735	−	19.8580i	1.23430	−	0.628909i	0.289699	−	0.957118i	$-0.406445\pi$
$997$	38.9735	−	19.8580i	1.23430	−	0.628909i	0.944605	+	0.328209i	$0.106445\pi$
$998$	19.1288	−	1.23269i	0.605513	−	0.0390200i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.bj.f.127.1		240
3.2	odd	2		300.2.w.a.127.30	yes	240
4.3	odd	2	inner	900.2.bj.f.127.5		240
12.11	even	2		300.2.w.a.127.26	✓	240
25.13	odd	20	inner	900.2.bj.f.163.5		240
75.38	even	20		300.2.w.a.163.26	yes	240
100.63	even	20	inner	900.2.bj.f.163.1		240
300.263	odd	20		300.2.w.a.163.30	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.127.26	✓	240	12.11	even	2
300.2.w.a.127.30	yes	240	3.2	odd	2
300.2.w.a.163.26	yes	240	75.38	even	20
300.2.w.a.163.30	yes	240	300.263	odd	20
900.2.bj.f.127.1		240	1.1	even	1	trivial
900.2.bj.f.127.5		240	4.3	odd	2	inner
900.2.bj.f.163.1		240	100.63	even	20	inner
900.2.bj.f.163.5		240	25.13	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.41129 + 0.0909451i) q^{2} +(1.98346 - 0.256699i) q^{4} +(1.83309 - 1.28054i) q^{5} +(1.46352 - 1.46352i) q^{7} +(-2.77588 + 0.542662i) q^{8} +O(q^{10})\)	\(q+(-1.41129 + 0.0909451i) q^{2} +(1.98346 - 0.256699i) q^{4} +(1.83309 - 1.28054i) q^{5} +(1.46352 - 1.46352i) q^{7} +(-2.77588 + 0.542662i) q^{8} +(-2.47056 + 1.97391i) q^{10} +(0.716610 + 0.986329i) q^{11} +(0.610002 - 0.0966148i) q^{13} +(-1.93235 + 2.19855i) q^{14} +(3.86821 - 1.01830i) q^{16} +(2.23367 - 4.38383i) q^{17} +(1.11648 + 3.43617i) q^{19} +(3.30715 - 3.01044i) q^{20} +(-1.10104 - 1.32682i) q^{22} +(6.81819 + 1.07989i) q^{23} +(1.72046 - 4.69468i) q^{25} +(-0.852100 + 0.191828i) q^{26} +(2.52715 - 3.27852i) q^{28} +(-0.953684 - 0.309871i) q^{29} +(-10.1146 + 3.28642i) q^{31} +(-5.36654 + 1.78891i) q^{32} +(-2.75367 + 6.38999i) q^{34} +(0.808681 - 4.55687i) q^{35} +(-0.749924 - 4.73483i) q^{37} +(-1.88818 - 4.74789i) q^{38} +(-4.39355 + 4.54936i) q^{40} +(4.46659 + 3.24517i) q^{41} +(-2.74571 - 2.74571i) q^{43} +(1.67455 + 1.77239i) q^{44} +(-9.72062 - 0.903960i) q^{46} +(0.593032 + 1.16389i) q^{47} +2.71620i q^{49} +(-2.00110 + 6.78200i) q^{50} +(1.18511 - 0.348218i) q^{52} +(-2.82569 - 5.54573i) q^{53} +(2.57664 + 0.890388i) q^{55} +(-3.26837 + 4.85677i) q^{56} +(1.37410 + 0.350583i) q^{58} +(-10.5976 - 7.69958i) q^{59} +(7.64473 - 5.55422i) q^{61} +(13.9757 - 5.55795i) q^{62} +(7.41104 - 3.01273i) q^{64} +(0.994471 - 0.958232i) q^{65} +(7.24032 + 3.68913i) q^{67} +(3.30507 - 9.26853i) q^{68} +(-0.726856 + 6.50459i) q^{70} +(12.8093 + 4.16201i) q^{71} +(1.08745 - 6.86590i) q^{73} +(1.48897 + 6.61400i) q^{74} +(3.09656 + 6.52891i) q^{76} +(2.49229 + 0.394740i) q^{77} +(-2.17258 + 6.68651i) q^{79} +(5.78682 - 6.82003i) q^{80} +(-6.59877 - 4.17364i) q^{82} +(-3.19885 + 6.27810i) q^{83} +(-1.51912 - 10.8963i) q^{85} +(4.12469 + 3.62528i) q^{86} +(-2.52447 - 2.34905i) q^{88} +(-8.41934 - 11.5882i) q^{89} +(0.751354 - 1.03415i) q^{91} +(13.8008 + 0.391703i) q^{92} +(-0.942788 - 1.58865i) q^{94} +(6.44675 + 4.86913i) q^{95} +(3.66823 - 1.86906i) q^{97} +(-0.247025 - 3.83333i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{8}+O(q^{10}) \) 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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