LMFDB - Embedded newform 925.2.o.d.174.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [925,2,Mod(174,925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(925, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("925.174");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.o (of order $6$, degree $2$, not 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:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			174.17
Character	$\chi$	$=$	925.174
Dual form			925.2.o.d.824.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06320 - 0.613840i) q^{2} +(-0.819784 - 0.473302i) q^{3} +(-0.246400 + 0.426778i) q^{4} -1.16213 q^{6} +(-1.74824 - 1.00935i) q^{7} +3.06036i q^{8} +(-1.05197 - 1.82207i) q^{9} +O(q^{10})$	\(q+(1.06320 - 0.613840i) q^{2} +(-0.819784 - 0.473302i) q^{3} +(-0.246400 + 0.426778i) q^{4} -1.16213 q^{6} +(-1.74824 - 1.00935i) q^{7} +3.06036i q^{8} +(-1.05197 - 1.82207i) q^{9} -0.974618 q^{11} +(0.403990 - 0.233244i) q^{12} +(4.65421 + 2.68711i) q^{13} -2.47831 q^{14} +(1.38577 + 2.40023i) q^{16} +(-6.57089 + 3.79371i) q^{17} +(-2.23691 - 1.29148i) q^{18} +(0.489261 - 0.847425i) q^{19} +(0.955452 + 1.65489i) q^{21} +(-1.03622 + 0.598260i) q^{22} +7.57635i q^{23} +(1.44848 - 2.50883i) q^{24} +6.59783 q^{26} +4.83141i q^{27} +(0.861533 - 0.497406i) q^{28} -3.68974 q^{29} -1.02277 q^{31} +(-2.35399 - 1.35908i) q^{32} +(0.798976 + 0.461289i) q^{33} +(-4.65746 + 8.06696i) q^{34} +1.03682 q^{36} +(3.81892 + 4.73453i) q^{37} -1.20131i q^{38} +(-2.54363 - 4.40570i) q^{39} +(-4.57221 + 7.91929i) q^{41} +(2.03168 + 1.17299i) q^{42} +4.36348i q^{43} +(0.240146 - 0.415945i) q^{44} +(4.65067 + 8.05519i) q^{46} -8.32046i q^{47} -2.62356i q^{48} +(-1.46244 - 2.53302i) q^{49} +7.18228 q^{51} +(-2.29360 + 1.32421i) q^{52} +(-10.9316 + 6.31138i) q^{53} +(2.96572 + 5.13677i) q^{54} +(3.08897 - 5.35025i) q^{56} +(-0.802176 + 0.463137i) q^{57} +(-3.92294 + 2.26491i) q^{58} +(5.00242 + 8.66445i) q^{59} +(-0.168170 + 0.291280i) q^{61} +(-1.08741 + 0.627818i) q^{62} +4.24721i q^{63} -8.88011 q^{64} +1.13263 q^{66} +(-0.817291 - 0.471863i) q^{67} -3.73908i q^{68} +(3.58590 - 6.21096i) q^{69} +(5.32054 - 9.21545i) q^{71} +(5.57618 - 3.21941i) q^{72} -10.8928i q^{73} +(6.96654 + 2.68956i) q^{74} +(0.241108 + 0.417611i) q^{76} +(1.70387 + 0.983727i) q^{77} +(-5.40879 - 3.12277i) q^{78} +(8.73059 - 15.1218i) q^{79} +(-0.869192 + 1.50548i) q^{81} +11.2264i q^{82} +(0.992674 - 0.573121i) q^{83} -0.941694 q^{84} +(2.67848 + 4.63927i) q^{86} +(3.02479 + 1.74636i) q^{87} -2.98269i q^{88} +(-1.34021 - 2.32130i) q^{89} +(-5.42445 - 9.39543i) q^{91} +(-3.23342 - 1.86681i) q^{92} +(0.838451 + 0.484080i) q^{93} +(-5.10743 - 8.84633i) q^{94} +(1.28651 + 2.22830i) q^{96} +12.0269i q^{97} +(-3.10974 - 1.79541i) q^{98} +(1.02527 + 1.77582i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 22 q^{4} + 20 q^{9}+O(q^{10}) $ 48 * q + 22 * q^4 + 20 * q^9	$ 48 q + 22 q^{4} + 20 q^{9} - 40 q^{14} - 26 q^{16} - 10 q^{19} - 12 q^{21} + 42 q^{24} - 40 q^{26} - 12 q^{29} + 76 q^{31} + 10 q^{34} - 4 q^{36} - 28 q^{39} - 26 q^{41} + 30 q^{44} - 26 q^{46} + 52 q^{49} - 92 q^{51} + 74 q^{54} + 14 q^{59} + 32 q^{61} - 40 q^{64} + 164 q^{66} - 42 q^{69} - 4 q^{71} - 96 q^{74} + 34 q^{76} + 42 q^{79} - 32 q^{81} - 152 q^{84} - 32 q^{86} - 58 q^{89} + 64 q^{91} + 26 q^{94} + 52 q^{96} + 30 q^{99}+O(q^{100}) $ 48 * q + 22 * q^4 + 20 * q^9 - 40 * q^14 - 26 * q^16 - 10 * q^19 - 12 * q^21 + 42 * q^24 - 40 * q^26 - 12 * q^29 + 76 * q^31 + 10 * q^34 - 4 * q^36 - 28 * q^39 - 26 * q^41 + 30 * q^44 - 26 * q^46 + 52 * q^49 - 92 * q^51 + 74 * q^54 + 14 * q^59 + 32 * q^61 - 40 * q^64 + 164 * q^66 - 42 * q^69 - 4 * q^71 - 96 * q^74 + 34 * q^76 + 42 * q^79 - 32 * q^81 - 152 * q^84 - 32 * q^86 - 58 * q^89 + 64 * q^91 + 26 * q^94 + 52 * q^96 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.06320	−	0.613840i	0.751798	−	0.434051i	−0.0745454	−	0.997218i	$-0.523751\pi$
$2$	1.06320	−	0.613840i	0.751798	−	0.434051i	0.826343	+	0.563167i	$0.190417\pi$
$3$	−0.819784	−	0.473302i	−0.473302	−	0.273261i	0.244319	−	0.969695i	$-0.421436\pi$
$3$	−0.819784	−	0.473302i	−0.473302	−	0.273261i	−0.717621	+	0.696434i	$0.754769\pi$
$4$	−0.246400	+	0.426778i	−0.123200	+	0.213389i
$5$		0			0
$5$		0			0
$6$	−1.16213			−0.474437
$7$	−1.74824	−	1.00935i	−0.660772	−	0.381497i	0.131799	−	0.991276i	$-0.457925\pi$
$7$	−1.74824	−	1.00935i	−0.660772	−	0.381497i	−0.792571	+	0.609779i	$0.791258\pi$
$8$			3.06036i			1.08200i
$9$	−1.05197	−	1.82207i	−0.350657	−	0.607355i
$10$		0			0
$11$	−0.974618			−0.293858			−0.146929	−	0.989147i	$-0.546939\pi$
$11$	−0.974618			−0.293858			−0.146929	+	0.989147i	$0.546939\pi$
$12$	0.403990	−	0.233244i	0.116622	−	0.0673316i
$13$	4.65421	+	2.68711i	1.29085	+	0.745271i	0.978804	−	0.204798i	$-0.0656537\pi$
$13$	4.65421	+	2.68711i	1.29085	+	0.745271i	0.312042	+	0.950068i	$0.398987\pi$
$14$	−2.47831			−0.662356
$15$		0			0
$16$	1.38577	+	2.40023i	0.346443	+	0.600057i
$17$	−6.57089	+	3.79371i	−1.59368	+	0.920109i	−0.601007	+	0.799244i	$0.705234\pi$
$17$	−6.57089	+	3.79371i	−1.59368	+	0.920109i	−0.992669	+	0.120866i	$0.961433\pi$
$18$	−2.23691	−	1.29148i	−0.527246	−	0.304405i
$19$	0.489261	−	0.847425i	0.112244	−	0.194413i	−0.804431	−	0.594047i	$-0.797529\pi$
$19$	0.489261	−	0.847425i	0.112244	−	0.194413i	0.916675	+	0.399634i	$0.130863\pi$
$20$		0			0
$21$	0.955452	+	1.65489i	0.208497	+	0.361127i
$22$	−1.03622	+	0.598260i	−0.220922	+	0.127549i
$23$			7.57635i			1.57978i	0.613250	+	0.789889i	$0.289862\pi$
$23$			7.57635i			1.57978i	−0.613250	+	0.789889i	$0.710138\pi$
$24$	1.44848	−	2.50883i	0.295669	−	0.512114i
$25$		0			0
$26$	6.59783			1.29394
$27$			4.83141i			0.929806i
$28$	0.861533	−	0.497406i	0.162814	−	0.0940010i
$29$	−3.68974			−0.685167			−0.342583	−	0.939487i	$-0.611302\pi$
$29$	−3.68974			−0.685167			−0.342583	+	0.939487i	$0.611302\pi$
$30$		0			0
$31$	−1.02277			−0.183695			−0.0918476	−	0.995773i	$-0.529277\pi$
$31$	−1.02277			−0.183695			−0.0918476	+	0.995773i	$0.529277\pi$
$32$	−2.35399	−	1.35908i	−0.416130	−	0.240253i
$33$	0.798976	+	0.461289i	0.139084	+	0.0803001i
$34$	−4.65746	+	8.06696i	−0.798748	+	1.38347i
$35$		0			0
$36$	1.03682			0.172804
$37$	3.81892	+	4.73453i	0.627827	+	0.778353i
$37$	3.81892	+	4.73453i	0.627827	+	0.778353i
$38$		−	1.20131i		−	0.194879i
$39$	−2.54363	−	4.40570i	−0.407307	−	0.705476i
$40$		0			0
$41$	−4.57221	+	7.91929i	−0.714059	+	1.23679i	0.249263	+	0.968436i	$0.419812\pi$
$41$	−4.57221	+	7.91929i	−0.714059	+	1.23679i	−0.963321	+	0.268350i	$0.913522\pi$
$42$	2.03168	+	1.17299i	0.313495	+	0.180996i
$43$			4.36348i			0.665425i	0.943028	+	0.332712i	$0.107964\pi$
$43$			4.36348i			0.665425i	−0.943028	+	0.332712i	$0.892036\pi$
$44$	0.240146	−	0.415945i	0.0362034	−	0.0627061i
$45$		0			0
$46$	4.65067	+	8.05519i	0.685703	+	1.18767i
$47$		−	8.32046i		−	1.21366i	−0.794830	−	0.606832i	$-0.792440\pi$
$47$		−	8.32046i		−	1.21366i	0.794830	−	0.606832i	$-0.207560\pi$
$48$		−	2.62356i		−	0.378678i
$49$	−1.46244	−	2.53302i	−0.208920	−	0.361860i
$50$		0			0
$51$	7.18228			1.00572
$52$	−2.29360	+	1.32421i	−0.318065	+	0.183635i
$53$	−10.9316	+	6.31138i	−1.50157	+	0.866934i	−0.501576	+	0.865114i	$0.667246\pi$
$53$	−10.9316	+	6.31138i	−1.50157	+	0.866934i	−0.999998	+	0.00182090i	$0.999420\pi$
$54$	2.96572	+	5.13677i	0.403583	+	0.699026i
$55$		0			0
$56$	3.08897	−	5.35025i	0.412780	−	0.714957i
$57$	−0.802176	+	0.463137i	−0.106251	+	0.0613439i
$58$	−3.92294	+	2.26491i	−0.515107	+	0.297397i
$59$	5.00242	+	8.66445i	0.651260	+	1.12801i	0.982817	+	0.184580i	$0.0590925\pi$
$59$	5.00242	+	8.66445i	0.651260	+	1.12801i	−0.331558	+	0.943435i	$0.607574\pi$
$60$		0			0
$61$	−0.168170	+	0.291280i	−0.0215320	+	0.0372946i	−0.876591	−	0.481237i	$-0.840188\pi$
$61$	−0.168170	+	0.291280i	−0.0215320	+	0.0372946i	0.855059	+	0.518531i	$0.173521\pi$
$62$	−1.08741	+	0.627818i	−0.138102	+	0.0797330i
$63$			4.24721i			0.535098i
$64$	−8.88011			−1.11001
$65$		0			0
$66$	1.13263			0.139417
$67$	−0.817291	−	0.471863i	−0.0998479	−	0.0576472i	0.449245	−	0.893409i	$-0.351693\pi$
$67$	−0.817291	−	0.471863i	−0.0998479	−	0.0576472i	−0.549092	+	0.835762i	$0.685027\pi$
$68$		−	3.73908i		−	0.453430i
$69$	3.58590	−	6.21096i	0.431692	−	0.747712i
$70$		0			0
$71$	5.32054	−	9.21545i	0.631432	−	1.09367i	−0.355827	−	0.934552i	$-0.615801\pi$
$71$	5.32054	−	9.21545i	0.631432	−	1.09367i	0.987259	−	0.159121i	$-0.0508659\pi$
$72$	5.57618	−	3.21941i	0.657159	−	0.379411i
$73$		−	10.8928i		−	1.27490i	−0.770490	−	0.637452i	$-0.779989\pi$
$73$		−	10.8928i		−	1.27490i	0.770490	−	0.637452i	$-0.220011\pi$
$74$	6.96654	+	2.68956i	0.809844	+	0.312655i
$75$		0			0
$76$	0.241108	+	0.417611i	0.0276570	+	0.0479033i
$77$	1.70387	+	0.983727i	0.194174	+	0.112106i
$78$	−5.40879	−	3.12277i	−0.612425	−	0.353584i
$79$	8.73059	−	15.1218i	0.982269	−	1.70134i	0.328772	−	0.944409i	$-0.393365\pi$
$79$	8.73059	−	15.1218i	0.982269	−	1.70134i	0.653496	−	0.756930i	$-0.273302\pi$
$80$		0			0
$81$	−0.869192	+	1.50548i	−0.0965769	+	0.167276i
$82$			11.2264i			1.23975i
$83$	0.992674	−	0.573121i	0.108960	−	0.0629082i	−0.444530	−	0.895764i	$-0.646629\pi$
$83$	0.992674	−	0.573121i	0.108960	−	0.0629082i	0.553490	+	0.832856i	$0.313296\pi$
$84$	−0.941694			−0.102747
$85$		0			0
$86$	2.67848	+	4.63927i	0.288828	+	0.500265i
$87$	3.02479	+	1.74636i	0.324291	+	0.187230i
$88$		−	2.98269i		−	0.317955i
$89$	−1.34021	−	2.32130i	−0.142062	−	0.246058i	0.786211	−	0.617958i	$-0.212040\pi$
$89$	−1.34021	−	2.32130i	−0.142062	−	0.246058i	−0.928273	+	0.371900i	$0.878706\pi$
$90$		0			0
$91$	−5.42445	−	9.39543i	−0.568637	−	0.984908i
$92$	−3.23342	−	1.86681i	−0.337107	−	0.194629i
$93$	0.838451	+	0.484080i	0.0869433	+	0.0501967i
$94$	−5.10743	−	8.84633i	−0.526791	−	0.912429i
$95$		0			0
$96$	1.28651	+	2.22830i	0.131304	+	0.227424i
$97$			12.0269i			1.22115i	0.791958	+	0.610575i	$0.209062\pi$
$97$			12.0269i			1.22115i	−0.791958	+	0.610575i	$0.790938\pi$
$98$	−3.10974	−	1.79541i	−0.314131	−	0.181364i
$99$	1.02527	+	1.77582i	0.103043	+	0.178476i
$100$		0			0
$101$	7.82346			0.778464			0.389232	−	0.921140i	$-0.372741\pi$
$101$	7.82346			0.778464			0.389232	+	0.921140i	$0.372741\pi$
$102$	7.63622	−	4.40877i	0.756098	−	0.436534i
$103$		−	4.79163i		−	0.472133i	−0.971737	−	0.236067i	$-0.924142\pi$
$103$		−	4.79163i		−	0.472133i	0.971737	−	0.236067i	$-0.0758584\pi$
$104$	−8.22353	+	14.2436i	−0.806384	+	1.39670i
$105$		0			0
$106$	−7.74836	+	13.4205i	−0.752587	+	1.30352i
$107$	7.21431	+	4.16518i	0.697433	+	0.402663i	0.806391	−	0.591383i	$-0.201418\pi$
$107$	7.21431	+	4.16518i	0.697433	+	0.402663i	−0.108957	+	0.994046i	$0.534751\pi$
$108$	−2.06194	−	1.19046i	−0.198410	−	0.114552i
$109$	3.21608	+	5.57042i	0.308045	+	0.533549i	0.977935	−	0.208911i	$-0.0669920\pi$
$109$	3.21608	+	5.57042i	0.308045	+	0.533549i	−0.669890	+	0.742461i	$0.733659\pi$
$110$		0			0
$111$	−0.889825	−	5.68880i	−0.0844584	−	0.539957i
$112$		−	5.59490i		−	0.528668i
$113$	4.95732	−	2.86211i	0.466345	−	0.269245i	−0.248363	−	0.968667i	$-0.579893\pi$
$113$	4.95732	−	2.86211i	0.466345	−	0.269245i	0.714709	+	0.699422i	$0.246559\pi$
$114$	−0.568584	+	0.984816i	−0.0532527	+	0.0922365i
$115$		0			0
$116$	0.909152	−	1.57470i	0.0844126	−	0.146207i
$117$		−	11.3070i		−	1.04534i
$118$	10.6372	+	6.14137i	0.979231	+	0.565359i
$119$	15.3167			1.40408
$120$		0			0
$121$	−10.0501			−0.913647
$122$			0.412919i			0.0373840i
$123$	7.49644	−	4.32807i	0.675931	−	0.390249i
$124$	0.252011	−	0.436496i	0.0226313	−	0.0391985i
$125$		0			0
$126$	2.60711	+	4.51564i	0.232260	+	0.402285i
$127$	−16.5642	+	9.56337i	−1.46984	+	0.848612i	−0.999427	−	0.0338354i	$-0.989228\pi$
$127$	−16.5642	+	9.56337i	−1.46984	+	0.848612i	−0.470411	+	0.882447i	$0.655894\pi$
$128$	−4.73338	+	2.73282i	−0.418376	+	0.241550i
$129$	2.06525	−	3.57711i	0.181835	−	0.314947i
$130$		0			0
$131$	4.27980	+	7.41283i	0.373928	+	0.647662i	0.990166	−	0.139898i	$-0.0446774\pi$
$131$	4.27980	+	7.41283i	0.373928	+	0.647662i	−0.616238	+	0.787560i	$0.711344\pi$
$132$	−0.393736	+	0.227323i	−0.0342703	+	0.0197860i
$133$	−1.71069	+	0.987667i	−0.148336	+	0.0856416i
$134$	−1.15859			−0.100087
$135$		0			0
$136$	−11.6101	−	20.1093i	−0.995560	−	1.72436i
$137$		−	4.04835i		−	0.345874i	−0.984933	−	0.172937i	$-0.944674\pi$
$137$		−	4.04835i		−	0.345874i	0.984933	−	0.172937i	$-0.0553256\pi$
$138$		−	8.80468i		−	0.749504i
$139$	−5.04282	−	8.73443i	−0.427727	−	0.740844i	0.568944	−	0.822376i	$-0.307352\pi$
$139$	−5.04282	−	8.73443i	−0.427727	−	0.740844i	−0.996671	+	0.0815318i	$0.974019\pi$
$140$		0			0
$141$	−3.93809	+	6.82097i	−0.331647	+	0.574430i
$142$		−	13.0639i		−	1.09629i
$143$	−4.53608	−	2.61891i	−0.379326	−	0.219004i
$144$	2.91558	−	5.04994i	0.242965	−	0.420828i
$145$		0			0
$146$	−6.68643	−	11.5812i	−0.553373	−	0.958469i
$147$			2.76870i			0.228359i
$148$	−2.96158	+	0.463241i	−0.243440	+	0.0380782i
$149$	−11.1636			−0.914555			−0.457278	−	0.889324i	$-0.651175\pi$
$149$	−11.1636			−0.914555			−0.457278	+	0.889324i	$0.651175\pi$
$150$		0			0
$151$	6.05075	−	10.4802i	0.492403	−	0.852867i	−0.507559	−	0.861617i	$-0.669452\pi$
$151$	6.05075	−	10.4802i	0.492403	−	0.852867i	0.999962	+	0.00874999i	$0.00278524\pi$
$152$	2.59343	+	1.49732i	0.210355	+	0.121448i
$153$	13.8248	+	7.98173i	1.11767	+	0.645285i
$154$	2.41541			0.194639
$155$		0			0
$156$	2.50701			0.200721
$157$	−3.80029	+	2.19410i	−0.303297	+	0.175108i	−0.643923	−	0.765090i	$-0.722694\pi$
$157$	−3.80029	+	2.19410i	−0.303297	+	0.175108i	0.340626	+	0.940199i	$0.389361\pi$
$158$		−	21.4368i		−	1.70542i
$159$	11.9488			0.947598
$160$		0			0
$161$	7.64716	−	13.2453i	0.602680	−	1.04387i
$162$			2.13418i			0.167677i
$163$	10.4330	−	6.02349i	0.817175	−	0.471796i	−0.0322664	−	0.999479i	$-0.510272\pi$
$163$	10.4330	−	6.02349i	0.817175	−	0.471796i	0.849441	+	0.527683i	$0.176939\pi$
$164$	−2.25319	−	3.90263i	−0.175944	−	0.304744i
$165$		0			0
$166$	0.703609	−	1.21869i	0.0546107	−	0.0945884i
$167$	−7.26507	−	4.19449i	−0.562188	−	0.324580i	0.191835	−	0.981427i	$-0.438556\pi$
$167$	−7.26507	−	4.19449i	−0.562188	−	0.324580i	−0.754023	+	0.656848i	$0.771889\pi$
$168$	−5.06457	+	2.92403i	−0.390740	+	0.225594i
$169$	7.94113	+	13.7544i	0.610856	+	1.05803i
$170$		0			0
$171$	−2.05875			−0.157437
$172$	−1.86224	−	1.07516i	−0.141994	−	0.0819804i
$173$	−8.81636	+	5.09013i	−0.670296	+	0.386995i	−0.796189	−	0.605049i	$-0.793154\pi$
$173$	−8.81636	+	5.09013i	−0.670296	+	0.386995i	0.125893	+	0.992044i	$0.459820\pi$
$174$	4.28795			0.325068
$175$		0			0
$176$	−1.35060	−	2.33931i	−0.101805	−	0.176332i
$177$		−	9.47063i		−	0.711856i
$178$	−2.84982	−	1.64534i	−0.213603	−	0.123324i
$179$	8.25324			0.616876			0.308438	−	0.951244i	$-0.400194\pi$
$179$	8.25324			0.616876			0.308438	+	0.951244i	$0.400194\pi$
$180$		0			0
$181$	−7.97151	+	13.8071i	−0.592518	+	1.02627i	0.401374	+	0.915914i	$0.368533\pi$
$181$	−7.97151	+	13.8071i	−0.592518	+	1.02627i	−0.993892	+	0.110357i	$0.964801\pi$
$182$	−11.5346	−	6.65949i	−0.855000	−	0.493634i
$183$	0.275727	−	0.159191i	0.0203823	−	0.0117677i
$184$	−23.1864			−1.70932
$185$		0			0
$186$	1.18859			0.0871517
$187$	6.40411	−	3.69742i	0.468315	−	0.270382i
$188$	3.55099	+	2.05016i	0.258982	+	0.149523i
$189$	4.87657	−	8.44646i	0.354718	−	0.614390i
$190$		0			0
$191$	−4.31793			−0.312434			−0.156217	−	0.987723i	$-0.549930\pi$
$191$	−4.31793			−0.312434			−0.156217	+	0.987723i	$0.549930\pi$
$192$	7.27977	+	4.20298i	0.525372	+	0.303324i
$193$			1.22144i			0.0879212i	0.999033	+	0.0439606i	$0.0139976\pi$
$193$			1.22144i			0.0879212i	−0.999033	+	0.0439606i	$0.986002\pi$
$194$	7.38262	+	12.7871i	0.530041	+	0.918058i
$195$		0			0
$196$	1.44138			0.102956
$197$	18.8221	−	10.8669i	1.34102	−	0.774237i	0.354061	−	0.935222i	$-0.384800\pi$
$197$	18.8221	−	10.8669i	1.34102	−	0.774237i	0.986957	+	0.160985i	$0.0514671\pi$
$198$	2.18014	+	1.25870i	0.154936	+	0.0894521i
$199$	−9.02547			−0.639799			−0.319899	−	0.947452i	$-0.603649\pi$
$199$	−9.02547			−0.639799			−0.319899	+	0.947452i	$0.603649\pi$
$200$		0			0
$201$	0.446668	+	0.773651i	0.0315055	+	0.0545691i
$202$	8.31792	−	4.80236i	0.585247	−	0.337893i
$203$	6.45054	+	3.72422i	0.452739	+	0.261389i
$204$	−1.76972	+	3.06524i	−0.123905	+	0.214610i
$205$		0			0
$206$	−2.94130	−	5.09447i	−0.204930	−	0.354949i
$207$	13.8046	−	7.97009i	0.959486	−	0.553959i
$208$			14.8949i			1.03278i
$209$	−0.476843	+	0.825916i	−0.0329839	+	0.0571298i
$210$		0			0
$211$	−16.5240			−1.13756			−0.568781	−	0.822489i	$-0.692585\pi$
$211$	−16.5240			−1.13756			−0.568781	+	0.822489i	$0.692585\pi$
$212$		−	6.22050i		−	0.427226i
$213$	−8.72338	+	5.03645i	−0.597716	+	0.345092i
$214$	10.2270			0.699105
$215$		0			0
$216$	−14.7859			−1.00605
$217$	1.78805	+	1.03233i	0.121381	+	0.0700792i
$218$	6.83869	+	3.94832i	0.463175	+	0.267414i
$219$	−5.15558	+	8.92972i	−0.348382	+	0.603415i
$220$		0			0
$221$	−40.7765			−2.74292
$222$	−4.43808	−	5.50213i	−0.297864	−	0.369279i
$223$		−	11.4544i		−	0.767043i	−0.923532	−	0.383521i	$-0.874711\pi$
$223$		−	11.4544i		−	0.767043i	0.923532	−	0.383521i	$-0.125289\pi$
$224$	2.74356	+	4.75198i	0.183312	+	0.317505i
$225$		0			0
$226$	3.51376	−	6.08601i	0.233732	−	0.404835i
$227$	9.99862	+	5.77271i	0.663632	+	0.383148i	0.793659	−	0.608362i	$-0.208173\pi$
$227$	9.99862	+	5.77271i	0.663632	+	0.383148i	−0.130028	+	0.991510i	$0.541507\pi$
$228$		−	0.456468i		−	0.0302303i
$229$	1.63928	−	2.83931i	0.108327	−	0.187627i	−0.806766	−	0.590871i	$-0.798784\pi$
$229$	1.63928	−	2.83931i	0.108327	−	0.187627i	0.915092	+	0.403244i	$0.132117\pi$
$230$		0			0
$231$	−0.931201	−	1.61289i	−0.0612685	−	0.106120i
$232$		−	11.2919i		−	0.741352i
$233$			9.25482i			0.606304i	0.952942	+	0.303152i	$0.0980389\pi$
$233$			9.25482i			0.606304i	−0.952942	+	0.303152i	$0.901961\pi$
$234$	−6.94072	−	12.0217i	−0.453729	−	0.785881i
$235$		0			0
$236$	−4.93039			−0.320941
$237$	−14.3144	+	8.26442i	−0.929820	+	0.536832i
$238$	16.2847	−	9.40198i	1.05558	−	0.609440i
$239$	7.56902	+	13.1099i	0.489599	+	0.848010i	0.999928	−	0.0119687i	$-0.00380985\pi$
$239$	7.56902	+	13.1099i	0.489599	+	0.848010i	−0.510329	+	0.859979i	$0.670477\pi$
$240$		0			0
$241$	−3.07747	+	5.33033i	−0.198237	+	0.343357i	−0.947957	−	0.318399i	$-0.896855\pi$
$241$	−3.07747	+	5.33033i	−0.198237	+	0.343357i	0.749720	+	0.661755i	$0.230188\pi$
$242$	−10.6853	+	6.16917i	−0.686878	+	0.396569i
$243$	13.9775	−	8.06990i	0.896655	−	0.517684i
$244$	−0.0828745	−	0.143543i	−0.00530550	−	0.00918939i
$245$		0			0
$246$	5.31349	−	9.20323i	0.338776	−	0.586777i
$247$	4.55425	−	2.62940i	0.289780	−	0.167305i
$248$		−	3.13005i		−	0.198758i
$249$	−1.08504			−0.0687614
$250$		0			0
$251$	−12.2776			−0.774953			−0.387476	−	0.921880i	$-0.626653\pi$
$251$	−12.2776			−0.774953			−0.387476	+	0.921880i	$0.626653\pi$
$252$	−1.81261	−	1.04651i	−0.114184	−	0.0659241i
$253$		−	7.38404i		−	0.464231i
$254$	−11.7408	+	20.3356i	−0.736681	+	1.27597i
$255$		0			0
$256$	5.52508	−	9.56973i	0.345318	−	0.598108i
$257$	−26.0549	+	15.0428i	−1.62526	+	0.938343i	−0.639776	+	0.768562i	$0.720973\pi$
$257$	−26.0549	+	15.0428i	−1.62526	+	0.938343i	−0.985482	+	0.169781i	$0.945694\pi$
$258$		−	5.07093i		−	0.315702i
$259$	−1.89761	−	12.1317i	−0.117912	−	0.753828i
$260$		0			0
$261$	3.88149	+	6.72294i	0.240258	+	0.416140i
$262$	9.10059	+	5.25423i	0.562236	+	0.324607i
$263$	−5.13884	−	2.96691i	−0.316874	−	0.182947i	0.333124	−	0.942883i	$-0.391897\pi$
$263$	−5.13884	−	2.96691i	−0.316874	−	0.182947i	−0.649998	+	0.759936i	$0.725230\pi$
$264$	−1.41171	+	2.44516i	−0.0868848	+	0.150489i
$265$		0			0
$266$	−1.21254	+	2.10018i	−0.0743456	+	0.128770i
$267$			2.53729i			0.155280i
$268$	0.402761	−	0.232534i	0.0246026	−	0.0142043i
$269$	1.92752			0.117523			0.0587615	−	0.998272i	$-0.481285\pi$
$269$	1.92752			0.117523			0.0587615	+	0.998272i	$0.481285\pi$
$270$		0			0
$271$	−4.09226	−	7.08800i	−0.248587	−	0.430565i	0.714547	−	0.699587i	$-0.246633\pi$
$271$	−4.09226	−	7.08800i	−0.248587	−	0.430565i	−0.963134	+	0.269022i	$0.913300\pi$
$272$	−18.2115	−	10.5144i	−1.10424	−	0.637531i
$273$			10.2696i			0.621546i
$274$	−2.48504	−	4.30421i	−0.150127	−	0.260027i
$275$		0			0
$276$	1.76713	+	3.06077i	0.106369	+	0.184236i
$277$	10.9163	+	6.30251i	0.655895	+	0.378681i	0.790711	−	0.612189i	$-0.209711\pi$
$277$	10.9163	+	6.30251i	0.655895	+	0.378681i	−0.134816	+	0.990871i	$0.543044\pi$
$278$	−10.7231	−	6.19098i	−0.643128	−	0.371310i
$279$	1.07592	+	1.86356i	0.0644139	+	0.111568i
$280$		0			0
$281$	6.83855	+	11.8447i	0.407954	+	0.706597i	0.994660	−	0.103203i	$-0.0329091\pi$
$281$	6.83855	+	11.8447i	0.407954	+	0.706597i	−0.586706	+	0.809800i	$0.699576\pi$
$282$			9.66944i			0.575807i
$283$	28.1220	+	16.2362i	1.67168	+	0.965144i	0.966699	+	0.255917i	$0.0823772\pi$
$283$	28.1220	+	16.2362i	1.67168	+	0.965144i	0.704980	+	0.709227i	$0.250956\pi$
$284$	2.62197	+	4.54138i	0.155585	+	0.269481i
$285$		0			0
$286$	−6.43036			−0.380235
$287$	15.9866	−	9.22988i	0.943660	−	0.544823i
$288$			5.71883i			0.336985i
$289$	20.2844	−	35.1337i	1.19320	−	2.06669i
$290$		0			0
$291$	5.69238	−	9.85949i	0.333693	−	0.577973i
$292$	4.64880	+	2.68398i	0.272050	+	0.157068i
$293$	1.08171	+	0.624528i	0.0631944	+	0.0364853i	0.531264	−	0.847206i	$-0.321717\pi$
$293$	1.08171	+	0.624528i	0.0631944	+	0.0364853i	−0.468070	+	0.883691i	$0.655050\pi$
$294$	1.69954	+	2.94369i	0.0991193	+	0.171680i
$295$		0			0
$296$	−14.4894	+	11.6873i	−0.842179	+	0.679310i
$297$		−	4.70878i		−	0.273231i
$298$	−11.8691	+	6.85265i	−0.687560	+	0.396963i
$299$	−20.3585	+	35.2619i	−1.17736	+	2.03925i
$300$		0			0
$301$	4.40427	−	7.62841i	0.253858	−	0.439694i
$302$		−	14.8568i		−	0.854912i
$303$	−6.41354	−	3.70286i	−0.368449	−	0.212724i
$304$	2.71202			0.155545
$305$		0			0
$306$	19.5980			1.12035
$307$		−	5.33090i		−	0.304251i	−0.988361	−	0.152125i	$-0.951388\pi$
$307$		−	5.33090i		−	0.304251i	0.988361	−	0.152125i	$-0.0486118\pi$
$308$	−0.839666	+	0.484781i	−0.0478444	+	0.0276230i
$309$	−2.26789	+	3.92810i	−0.129016	+	0.223462i
$310$		0			0
$311$	9.78903	+	16.9551i	0.555085	+	0.961435i	0.997897	+	0.0648209i	$0.0206476\pi$
$311$	9.78903	+	16.9551i	0.555085	+	0.961435i	−0.442812	+	0.896615i	$0.646019\pi$
$312$	13.4830	−	7.78443i	0.763327	−	0.440707i
$313$	−1.93445	+	1.11685i	−0.109341	+	0.0631283i	−0.553673	−	0.832734i	$-0.686774\pi$
$313$	−1.93445	+	1.11685i	−0.109341	+	0.0631283i	0.444332	+	0.895862i	$0.353441\pi$
$314$	−2.69366	+	4.66555i	−0.152012	+	0.263292i
$315$		0			0
$316$	4.30244	+	7.45205i	0.242031	+	0.419210i
$317$	1.52442	−	0.880122i	0.0856198	−	0.0494326i	−0.456579	−	0.889683i	$-0.650925\pi$
$317$	1.52442	−	0.880122i	0.0856198	−	0.0494326i	0.542199	+	0.840250i	$0.317592\pi$
$318$	12.7039	−	7.33463i	0.712402	−	0.411306i
$319$	3.59608			0.201342
$320$		0			0
$321$	−3.94278	−	6.82910i	−0.220065	−	0.381163i
$322$		−	18.7765i		−	1.04638i
$323$			7.42445i			0.413108i
$324$	−0.428338	−	0.741903i	−0.0237966	−	0.0412169i
$325$		0			0
$326$	7.39492	−	12.8084i	0.409567	−	0.709391i
$327$		−	6.08872i		−	0.336707i
$328$	−24.2359	−	13.9926i	−1.33820	−	0.772613i
$329$	−8.39822	+	14.5462i	−0.463009	+	0.801955i
$330$		0			0
$331$	8.90506	+	15.4240i	0.489466	+	0.847780i	0.999927	−	0.0121210i	$-0.00385832\pi$
$331$	8.90506	+	15.4240i	0.489466	+	0.847780i	−0.510460	+	0.859901i	$0.670525\pi$
$332$			0.564868i			0.0310012i
$333$	4.60924	−	11.9389i	0.252585	−	0.654249i
$334$	−10.2990			−0.563536
$335$		0			0
$336$	−2.64808	+	4.58661i	−0.144465	+	0.250220i
$337$	14.4201	+	8.32543i	0.785511	+	0.453515i	0.838380	−	0.545087i	$-0.183503\pi$
$337$	14.4201	+	8.32543i	0.785511	+	0.453515i	−0.0528689	+	0.998601i	$0.516837\pi$
$338$	16.8861	+	9.74917i	0.918481	+	0.530285i
$339$	−5.41857			−0.294296
$340$		0			0
$341$	0.996811			0.0539804
$342$	−2.18887	+	1.26374i	−0.118361	+	0.0683355i
$343$			20.0353i			1.08180i
$344$	−13.3538			−0.719991
$345$		0			0
$346$	−6.24905	+	10.8237i	−0.335951	+	0.581884i
$347$			34.5760i			1.85614i	0.372412	+	0.928068i	$0.378531\pi$
$347$			34.5760i			1.85614i	−0.372412	+	0.928068i	$0.621469\pi$
$348$	−1.49062	+	0.860607i	−0.0799054	+	0.0461334i
$349$	−8.67319	−	15.0224i	−0.464265	−	0.804131i	0.534903	−	0.844914i	$-0.320348\pi$
$349$	−8.67319	−	15.0224i	−0.464265	−	0.804131i	−0.999168	+	0.0407826i	$0.987015\pi$
$350$		0			0
$351$	−12.9825	+	22.4864i	−0.692957	+	1.20024i
$352$	2.29424	+	1.32458i	0.122283	+	0.0706003i
$353$	−19.5011	+	11.2590i	−1.03794	+	0.599254i	−0.919248	−	0.393678i	$-0.871203\pi$
$353$	−19.5011	+	11.2590i	−1.03794	+	0.599254i	−0.118689	+	0.992931i	$0.537869\pi$
$354$	−5.81345	−	10.0692i	−0.308982	−	0.535172i
$355$		0			0
$356$	1.32091			0.0700080
$357$	−12.5563	−	7.24941i	−0.664552	−	0.383679i
$358$	8.77487	−	5.06617i	0.463766	−	0.267755i
$359$	22.2676			1.17524			0.587620	−	0.809137i	$-0.300065\pi$
$359$	22.2676			1.17524			0.587620	+	0.809137i	$0.300065\pi$
$360$		0			0
$361$	9.02125	+	15.6253i	0.474803	+	0.822382i
$362$			19.5729i			1.02873i
$363$	8.23892	+	4.75674i	0.432431	+	0.249664i
$364$	5.34634			0.280225
$365$		0			0
$366$	0.195436	−	0.338504i	0.0102156	−	0.0176939i
$367$	14.2838	+	8.24676i	0.745609	+	0.430477i	0.824105	−	0.566437i	$-0.191679\pi$
$367$	14.2838	+	8.24676i	0.745609	+	0.430477i	−0.0784963	+	0.996914i	$0.525012\pi$
$368$	−18.1850	+	10.4991i	−0.947957	+	0.547303i
$369$	19.2393			1.00156
$370$		0			0
$371$	25.4815			1.32293
$372$	−0.413189	+	0.238555i	−0.0214229	+	0.0123685i
$373$	−21.3859	−	12.3471i	−1.10732	−	0.639310i	−0.169184	−	0.985584i	$-0.554113\pi$
$373$	−21.3859	−	12.3471i	−1.10732	−	0.639310i	−0.938133	+	0.346274i	$0.887447\pi$
$374$	4.53925	−	7.86221i	0.234719	−	0.406545i
$375$		0			0
$376$	25.4636			1.31319
$377$	−17.1728	−	9.91473i	−0.884445	−	0.510635i
$378$		−	11.9737i		−	0.615863i
$379$	−2.09399	−	3.62689i	−0.107561	−	0.186301i	0.807221	−	0.590250i	$-0.200971\pi$
$379$	−2.09399	−	3.62689i	−0.107561	−	0.186301i	−0.914782	+	0.403949i	$0.867637\pi$
$380$		0			0
$381$	18.1055			0.927571
$382$	−4.59083	+	2.65052i	−0.234888	+	0.135612i
$383$	−0.311090	−	0.179608i	−0.0158960	−	0.00917754i	0.492031	−	0.870578i	$-0.336255\pi$
$383$	−0.311090	−	0.179608i	−0.0158960	−	0.00917754i	−0.507927	+	0.861400i	$0.669588\pi$
$384$	5.17380			0.264024
$385$		0			0
$386$	0.749769	+	1.29864i	0.0381622	+	0.0660989i
$387$	7.95055	−	4.59025i	0.404149	−	0.233336i
$388$	−5.13283	−	2.96344i	−0.260580	−	0.150446i
$389$	6.91639	−	11.9795i	0.350675	−	0.607387i	−0.635693	−	0.771942i	$-0.719286\pi$
$389$	6.91639	−	11.9795i	0.350675	−	0.607387i	0.986368	+	0.164555i	$0.0526189\pi$
$390$		0			0
$391$	−28.7424	−	49.7834i	−1.45357	−	2.51765i
$392$	7.75196	−	4.47560i	0.391533	−	0.226052i
$393$		−	8.10256i		−	0.408720i
$394$	13.3411	−	23.1075i	0.672116	−	1.16414i
$395$		0			0
$396$	−1.01051			−0.0507798
$397$			19.8419i			0.995836i	0.867224	+	0.497918i	$0.165902\pi$
$397$			19.8419i			0.995836i	−0.867224	+	0.497918i	$0.834098\pi$
$398$	−9.59590	+	5.54020i	−0.480999	+	0.277705i
$399$	1.86986			0.0936101
$400$		0			0
$401$	8.31660			0.415311			0.207656	−	0.978202i	$-0.433417\pi$
$401$	8.31660			0.415311			0.207656	+	0.978202i	$0.433417\pi$
$402$	0.949796	+	0.548365i	0.0473715	+	0.0273500i
$403$	−4.76019	−	2.74830i	−0.237122	−	0.136903i
$404$	−1.92770	+	3.33888i	−0.0959068	+	0.166115i
$405$		0			0
$406$	9.14431			0.453825
$407$	−3.72199	−	4.61436i	−0.184492	−	0.228726i
$408$			21.9804i			1.08819i
$409$	12.2024	+	21.1351i	0.603368	+	1.04506i	0.992307	+	0.123801i	$0.0395084\pi$
$409$	12.2024	+	21.1351i	0.603368	+	1.04506i	−0.388939	+	0.921264i	$0.627158\pi$
$410$		0			0
$411$	−1.91609	+	3.31877i	−0.0945138	+	0.163703i
$412$	2.04496	+	1.18066i	0.100748	+	0.0581669i
$413$		−	20.1967i		−	0.993815i
$414$	9.78472	−	16.9476i	0.480893	−	0.832931i
$415$		0			0
$416$	−7.30397	−	12.6509i	−0.358107	−	0.620259i
$417$			9.54712i			0.467524i
$418$			1.17082i			0.0572667i
$419$	−4.24803	−	7.35781i	−0.207530	−	0.359452i	0.743406	−	0.668841i	$-0.233209\pi$
$419$	−4.24803	−	7.35781i	−0.207530	−	0.359452i	−0.950936	+	0.309388i	$0.899876\pi$
$420$		0			0
$421$	25.0577			1.22124			0.610619	−	0.791924i	$-0.290921\pi$
$421$	25.0577			1.22124			0.610619	+	0.791924i	$0.290921\pi$
$422$	−17.5684	+	10.1431i	−0.855216	+	0.493759i
$423$	−15.1604	+	8.75287i	−0.737125	+	0.425579i
$424$	−19.3151	−	33.4547i	−0.938024	−	1.62471i
$425$		0			0
$426$	−6.18315	+	10.7095i	−0.299575	+	0.518878i
$427$	0.588004	−	0.339485i	0.0284555	−	0.0164288i
$428$	−3.55521	+	2.05260i	−0.171848	+	0.0992163i
$429$	2.47907	+	4.29387i	0.119691	+	0.207310i
$430$		0			0
$431$	18.5632	−	32.1525i	0.894160	−	1.54873i	0.0593182	−	0.998239i	$-0.481107\pi$
$431$	18.5632	−	32.1525i	0.894160	−	1.54873i	0.834841	−	0.550491i	$-0.185559\pi$
$432$	−11.5965	+	6.69524i	−0.557937	+	0.322125i
$433$		−	32.6089i		−	1.56708i	−0.621338	−	0.783542i	$-0.713411\pi$
$433$		−	32.6089i		−	1.56708i	0.621338	−	0.783542i	$-0.286589\pi$
$434$	2.53474			0.121672
$435$		0			0
$436$	−3.16977			−0.151805
$437$	6.42038	+	3.70681i	0.307129	+	0.177321i
$438$			12.6588i			0.604861i
$439$	−18.1894	+	31.5049i	−0.868132	+	1.50365i	−0.00422870	+	0.999991i	$0.501346\pi$
$439$	−18.1894	+	31.5049i	−0.868132	+	1.50365i	−0.863903	+	0.503658i	$0.831987\pi$
$440$		0			0
$441$	−3.07689	+	5.32932i	−0.146518	+	0.253777i
$442$	−43.3536	+	25.0302i	−2.06212	+	1.19057i
$443$		−	25.4499i		−	1.20916i	−0.796544	−	0.604580i	$-0.793341\pi$
$443$		−	25.4499i		−	1.20916i	0.796544	−	0.604580i	$-0.206659\pi$
$444$	2.64711	+	1.02196i	0.125626	+	0.0485003i
$445$		0			0
$446$	−7.03117	−	12.1783i	−0.332935	−	0.576661i
$447$	9.15171	+	5.28374i	0.432861	+	0.249912i
$448$	15.5246	+	8.96311i	0.733467	+	0.423467i
$449$	0.762421	−	1.32055i	0.0359809	−	0.0623207i	−0.847474	−	0.530837i	$-0.821878\pi$
$449$	0.762421	−	1.32055i	0.0359809	−	0.0623207i	0.883455	+	0.468516i	$0.155211\pi$
$450$		0			0
$451$	4.45616	−	7.71829i	0.209832	−	0.363440i
$452$			2.82090i			0.132684i
$453$	−9.92061	+	5.72767i	−0.466111	+	0.269109i
$454$	14.1741			0.665223
$455$		0			0
$456$	−1.41737	−	2.45495i	−0.0663742	−	0.114964i
$457$	−2.60114	−	1.50177i	−0.121676	−	0.0702499i	0.437927	−	0.899011i	$-0.355713\pi$
$457$	−2.60114	−	1.50177i	−0.121676	−	0.0702499i	−0.559603	+	0.828761i	$0.689046\pi$
$458$		−	4.02502i		−	0.188077i
$459$	−18.3290	−	31.7467i	−0.855523	−	1.48181i
$460$		0			0
$461$	14.3453	+	24.8467i	0.668125	+	1.15723i	0.978428	+	0.206589i	$0.0662363\pi$
$461$	14.3453	+	24.8467i	0.668125	+	1.15723i	−0.310303	+	0.950638i	$0.600430\pi$
$462$	−1.98011	−	1.14322i	−0.0921230	−	0.0531873i
$463$	20.0329	+	11.5660i	0.931010	+	0.537519i	0.887131	−	0.461518i	$-0.152695\pi$
$463$	20.0329	+	11.5660i	0.931010	+	0.537519i	0.0438792	+	0.999037i	$0.486028\pi$
$464$	−5.11314	−	8.85622i	−0.237372	−	0.411140i
$465$		0			0
$466$	5.68098	+	9.83975i	0.263167	+	0.455818i
$467$		−	33.7320i		−	1.56093i	−0.625198	−	0.780466i	$-0.714982\pi$
$467$		−	33.7320i		−	1.56093i	0.625198	−	0.780466i	$-0.285018\pi$
$468$	4.82559	+	2.78606i	0.223063	+	0.128786i
$469$	0.952546	+	1.64986i	0.0439845	+	0.0761834i
$470$		0			0
$471$	4.15389			0.191401
$472$	−26.5163	+	15.3092i	−1.22051	+	0.704664i
$473$		−	4.25273i		−	0.195541i
$474$	−10.1461	+	17.5735i	−0.466024	+	0.807178i
$475$		0			0
$476$	−3.77403	+	6.53681i	−0.172982	+	0.299614i
$477$	22.9995	+	13.2788i	1.05307	+	0.607993i
$478$	16.0948	+	9.29233i	0.736159	+	0.425021i
$479$	−11.1817	−	19.3673i	−0.510906	−	0.884916i	−0.999920	−	0.0126396i	$-0.995977\pi$
$479$	−11.1817	−	19.3673i	−0.510906	−	0.884916i	0.489014	−	0.872276i	$-0.337357\pi$
$480$		0			0
$481$	5.05186	+	32.2974i	0.230345	+	1.47263i
$482$			7.55629i			0.344180i
$483$	−12.5380	+	7.23883i	−0.570500	+	0.329378i
$484$	2.47635	−	4.28917i	0.112561	−	0.194962i
$485$		0			0
$486$	9.90726	−	17.1599i	0.449402	−	0.778388i
$487$			16.9964i			0.770180i	0.922879	+	0.385090i	$0.125830\pi$
$487$			16.9964i			0.770180i	−0.922879	+	0.385090i	$0.874170\pi$
$488$	−0.891422	−	0.514663i	−0.0403528	−	0.0232977i
$489$	−11.4037			−0.515694
$490$		0			0
$491$	21.6542			0.977240			0.488620	−	0.872497i	$-0.337500\pi$
$491$	21.6542			0.977240			0.488620	+	0.872497i	$0.337500\pi$
$492$			4.26575i			0.192315i
$493$	24.2449	−	13.9978i	1.09193	−	0.630428i
$494$	3.22806	−	5.59116i	0.145237	−	0.251558i
$495$		0			0
$496$	−1.41733	−	2.45489i	−0.0636400	−	0.110228i
$497$	−18.6032	+	10.7405i	−0.834466	+	0.481779i
$498$	−1.15361	+	0.666039i	−0.0516947	+	0.0298459i
$499$	5.65525	−	9.79517i	0.253164	−	0.438492i	−0.711232	−	0.702958i	$-0.751862\pi$
$499$	5.65525	−	9.79517i	0.253164	−	0.438492i	0.964395	+	0.264466i	$0.0851956\pi$
$500$		0			0
$501$	3.97052	+	6.87715i	0.177390	+	0.307248i
$502$	−13.0535	+	7.53646i	−0.582608	+	0.336369i
$503$	−28.2131	+	16.2888i	−1.25796	+	0.726283i	−0.972678	−	0.232160i	$-0.925421\pi$
$503$	−28.2131	+	16.2888i	−1.25796	+	0.726283i	−0.285282	+	0.958444i	$0.592087\pi$
$504$	−12.9980			−0.578977
$505$		0			0
$506$	−4.53262	−	7.85074i	−0.201500	−	0.349008i
$507$		−	15.0342i		−	0.667693i
$508$		−	9.42567i		−	0.418196i
$509$	18.3004	+	31.6972i	0.811151	+	1.40496i	0.912059	+	0.410059i	$0.134492\pi$
$509$	18.3004	+	31.6972i	0.811151	+	1.40496i	−0.100908	+	0.994896i	$0.532175\pi$
$510$		0			0
$511$	−10.9946	+	19.0432i	−0.486372	+	0.842421i
$512$		−	24.4974i		−	1.08264i
$513$	4.09426	+	2.36382i	0.180766	+	0.104365i
$514$	−18.4677	+	31.9870i	−0.814577	+	1.41089i
$515$		0			0
$516$	1.01775	+	1.76280i	0.0448041	+	0.0776030i
$517$			8.10927i			0.356645i
$518$	−9.46448	−	11.7336i	−0.415845	−	0.515547i
$519$	9.63668			0.423003
$520$		0			0
$521$	−6.86678	+	11.8936i	−0.300839	+	0.521068i	−0.976326	−	0.216303i	$-0.930600\pi$
$521$	−6.86678	+	11.8936i	−0.300839	+	0.521068i	0.675487	+	0.737372i	$0.263933\pi$
$522$	8.25363	+	4.76523i	0.361251	+	0.208569i
$523$	−8.47593	−	4.89358i	−0.370626	−	0.213981i	0.303106	−	0.952957i	$-0.401976\pi$
$523$	−8.47593	−	4.89358i	−0.370626	−	0.213981i	−0.673732	+	0.738976i	$0.735310\pi$
$524$	−4.21818			−0.184272
$525$		0			0
$526$	−7.28483			−0.317634
$527$	6.72052	−	3.88010i	0.292751	−	0.169020i
$528$			2.55697i			0.111278i
$529$	−34.4010			−1.49570
$530$		0			0
$531$	10.5248	−	18.2295i	0.456737	−	0.791092i
$532$		−	0.973446i		−	0.0422042i
$533$	−42.5600	+	24.5721i	−1.84348	+	1.06433i
$534$	1.55749	+	2.69765i	0.0673992	+	0.116739i
$535$		0			0
$536$	1.44407	−	2.50121i	0.0623744	−	0.108036i
$537$	−6.76587	−	3.90628i	−0.291969	−	0.168568i
$538$	2.04934	−	1.18319i	0.0883535	−	0.0510109i
$539$	1.42532	+	2.46873i	0.0613929	+	0.106336i
$540$		0			0
$541$	19.1337			0.822623			0.411311	−	0.911495i	$-0.365071\pi$
$541$	19.1337			0.822623			0.411311	+	0.911495i	$0.365071\pi$
$542$	−8.70180	−	5.02399i	−0.373774	−	0.215799i
$543$	13.0698	−	7.54587i	0.560880	−	0.323824i
$544$	20.6237			0.884236
$545$		0			0
$546$	6.30391	+	10.9187i	0.269782	+	0.467277i
$547$		−	36.0238i		−	1.54027i	−0.637884	−	0.770133i	$-0.720190\pi$
$547$		−	36.0238i		−	1.54027i	0.637884	−	0.770133i	$-0.279810\pi$
$548$	1.72774	+	0.997513i	0.0738056	+	0.0426117i
$549$	0.707641			0.0302014
$550$		0			0
$551$	−1.80524	+	3.12677i	−0.0769060	+	0.133205i
$552$	19.0078	+	10.9742i	0.809026	+	0.467091i
$553$	−30.5263	+	17.6244i	−1.29811	+	0.749465i
$554$	15.4749			0.657468
$555$		0			0
$556$	4.97021			0.210784
$557$	−29.8983	+	17.2618i	−1.26683	+	0.731406i	−0.974387	−	0.224877i	$-0.927802\pi$
$557$	−29.8983	+	17.2618i	−1.26683	+	0.731406i	−0.292445	+	0.956282i	$0.594469\pi$
$558$	2.28785	+	1.32089i	0.0968525	+	0.0559178i
$559$	−11.7252	+	20.3086i	−0.495922	+	0.858961i
$560$		0			0
$561$	−6.99998			−0.295539
$562$	14.5415	+	8.39556i	0.613398	+	0.354145i
$563$			7.10033i			0.299243i	0.988743	+	0.149622i	$0.0478056\pi$
$563$			7.10033i			0.299243i	−0.988743	+	0.149622i	$0.952194\pi$
$564$	−1.94069	−	3.36138i	−0.0817179	−	0.141540i
$565$		0			0
$566$	39.8658			1.67569
$567$	3.03911	−	1.75463i	0.127631	−	0.0736876i
$568$	28.2026	+	16.2828i	1.18336	+	0.683211i
$569$	14.3253			0.600547			0.300273	−	0.953853i	$-0.402922\pi$
$569$	14.3253			0.600547			0.300273	+	0.953853i	$0.402922\pi$
$570$		0			0
$571$	13.2864	+	23.0127i	0.556018	+	0.963052i	0.997824	+	0.0659410i	$0.0210049\pi$
$571$	13.2864	+	23.0127i	0.556018	+	0.963052i	−0.441805	+	0.897111i	$0.645662\pi$
$572$	2.23538	−	1.29060i	0.0934660	−	0.0539626i
$573$	3.53977	+	2.04369i	0.147876	+	0.0853762i
$574$	11.3313	−	19.6265i	0.472961	−	0.819193i
$575$		0			0
$576$	9.34161	+	16.1802i	0.389234	+	0.674173i
$577$	32.2901	−	18.6427i	1.34425	−	0.776106i	0.356826	−	0.934171i	$-0.383859\pi$
$577$	32.2901	−	18.6427i	1.34425	−	0.776106i	0.987429	+	0.158065i	$0.0505256\pi$
$578$		−	49.8056i		−	2.07164i
$579$	0.578110	−	1.00132i	0.0240254	−	0.0416133i
$580$		0			0
$581$	−2.31391			−0.0959971
$582$		−	13.9768i		−	0.579359i
$583$	10.6542	−	6.15118i	0.441250	−	0.254756i
$584$	33.3359			1.37945
$585$		0			0
$586$	1.53344			0.0633458
$587$	15.4785	+	8.93653i	0.638867	+	0.368850i	0.784178	−	0.620536i	$-0.213085\pi$
$587$	15.4785	+	8.93653i	0.638867	+	0.368850i	−0.145311	+	0.989386i	$0.546418\pi$
$588$	−1.18162	−	0.682209i	−0.0487292	−	0.0281338i
$589$	−0.500402	+	0.866722i	−0.0206187	+	0.0357126i
$590$		0			0
$591$	−20.5734			−0.846276
$592$	−6.07181	+	15.7273i	−0.249550	+	0.646388i
$593$			14.2027i			0.583237i	0.956535	+	0.291618i	$0.0941937\pi$
$593$			14.2027i			0.583237i	−0.956535	+	0.291618i	$0.905806\pi$
$594$	−2.89044	−	5.00639i	−0.118596	−	0.205415i
$595$		0			0
$596$	2.75071	−	4.76436i	0.112673	−	0.195156i
$597$	7.39893	+	4.27177i	0.302818	+	0.174832i
$598$			49.9874i			2.04414i
$599$	−4.87768	+	8.44840i	−0.199297	+	0.345192i	−0.948301	−	0.317373i	$-0.897199\pi$
$599$	−4.87768	+	8.44840i	−0.199297	+	0.345192i	0.749004	+	0.662566i	$0.230532\pi$
$600$		0			0
$601$	12.8644	+	22.2818i	0.524749	+	0.908892i	0.999585	+	0.0288177i	$0.00917422\pi$
$601$	12.8644	+	22.2818i	0.524749	+	0.908892i	−0.474836	+	0.880075i	$0.657492\pi$
$602$		−	10.8141i		−	0.440748i
$603$			1.98554i			0.0808576i
$604$	2.98181	+	5.16465i	0.121328	+	0.210147i
$605$		0			0
$606$	−9.09186			−0.369332
$607$	−16.2452	+	9.37916i	−0.659371	+	0.380688i	−0.792037	−	0.610473i	$-0.790980\pi$
$607$	−16.2452	+	9.37916i	−0.659371	+	0.380688i	0.132666	+	0.991161i	$0.457646\pi$
$608$	−2.30343	+	1.32989i	−0.0934164	+	0.0539340i
$609$	−3.52537	−	6.10611i	−0.142855	−	0.247432i
$610$		0			0
$611$	22.3580	−	38.7252i	0.904508	−	1.56665i
$612$	−6.81285	+	3.93340i	−0.275393	+	0.158998i
$613$	−3.87562	+	2.23759i	−0.156535	+	0.0903753i	−0.576221	−	0.817294i	$-0.695473\pi$
$613$	−3.87562	+	2.23759i	−0.156535	+	0.0903753i	0.419687	+	0.907669i	$0.362140\pi$
$614$	−3.27232	−	5.66783i	−0.132060	−	0.228735i
$615$		0			0
$616$	−3.01056	+	5.21445i	−0.121299	+	0.210096i
$617$	−28.0198	+	16.1772i	−1.12803	+	0.651271i	−0.943440	−	0.331544i	$-0.892430\pi$
$617$	−28.0198	+	16.1772i	−1.12803	+	0.651271i	−0.184594	+	0.982815i	$0.559097\pi$
$618$			5.56849i			0.223997i
$619$	−3.98890			−0.160328			−0.0801638	−	0.996782i	$-0.525544\pi$
$619$	−3.98890			−0.160328			−0.0801638	+	0.996782i	$0.525544\pi$
$620$		0			0
$621$	−36.6045			−1.46889
$622$	20.8154	+	12.0178i	0.834623	+	0.481870i
$623$			5.41093i			0.216784i
$624$	7.04979	−	12.2106i	0.282218	−	0.488815i
$625$		0			0
$626$	−1.37114	+	2.37488i	−0.0548017	+	0.0949194i
$627$	0.781815	−	0.451381i	0.0312227	−	0.0180264i
$628$		−	2.16251i		−	0.0862935i
$629$	−43.0552	−	16.6222i	−1.71672	−	0.662772i
$630$		0			0
$631$	2.19418	+	3.80044i	0.0873491	+	0.151293i	0.906390	−	0.422442i	$-0.138827\pi$
$631$	2.19418	+	3.80044i	0.0873491	+	0.151293i	−0.819041	+	0.573735i	$0.805494\pi$
$632$	46.2783	+	26.7188i	1.84085	+	1.06282i
$633$	13.5461	+	7.82087i	0.538411	+	0.310852i
$634$	1.08051	−	1.87150i	0.0429125	−	0.0743266i
$635$		0			0
$636$	−2.94418	+	5.09946i	−0.116744	+	0.202207i
$637$		−	15.7190i		−	0.622808i
$638$	3.82337	−	2.20742i	0.151369	−	0.0873927i
$639$	−22.3882			−0.885664
$640$		0			0
$641$	−17.3536	−	30.0573i	−0.685425	−	1.18719i	−0.973303	−	0.229523i	$-0.926283\pi$
$641$	−17.3536	−	30.0573i	−0.685425	−	1.18719i	0.287878	−	0.957667i	$-0.407050\pi$
$642$	−8.38395	−	4.84047i	−0.330888	−	0.191038i
$643$			16.4675i			0.649414i	0.945815	+	0.324707i	$0.105266\pi$
$643$			16.4675i			0.649414i	−0.945815	+	0.324707i	$0.894734\pi$
$644$	3.76852	+	6.52727i	0.148501	+	0.257211i
$645$		0			0
$646$	4.55743	+	7.89370i	0.179310	+	0.310573i
$647$	−36.4821	−	21.0629i	−1.43426	−	0.828069i	−0.436816	−	0.899551i	$-0.643894\pi$
$647$	−36.4821	−	21.0629i	−1.43426	−	0.828069i	−0.997442	+	0.0714813i	$0.977227\pi$
$648$	−4.60733	−	2.66004i	−0.180993	−	0.104496i
$649$	−4.87545	−	8.44453i	−0.191378	−	0.331477i
$650$		0			0
$651$	−0.977209	−	1.69257i	−0.0382998	−	0.0663372i
$652$			5.93676i			0.232501i
$653$	0.955506	+	0.551662i	0.0373918	+	0.0215882i	0.518579	−	0.855029i	$-0.326461\pi$
$653$	0.955506	+	0.551662i	0.0373918	+	0.0215882i	−0.481188	+	0.876618i	$0.659794\pi$
$654$	−3.73750	−	6.47354i	−0.146148	−	0.253135i
$655$		0			0
$656$	−25.3442			−0.989524
$657$	−19.8474	+	11.4589i	−0.774319	+	0.447053i
$658$			20.6207i			0.803877i
$659$	−14.5631	+	25.2241i	−0.567299	+	0.982591i	0.429533	+	0.903051i	$0.358678\pi$
$659$	−14.5631	+	25.2241i	−0.567299	+	0.982591i	−0.996832	+	0.0795396i	$0.974655\pi$
$660$		0			0
$661$	−18.2698	+	31.6443i	−0.710614	+	1.23082i	0.254013	+	0.967201i	$0.418249\pi$
$661$	−18.2698	+	31.6443i	−0.710614	+	1.23082i	−0.964627	+	0.263619i	$0.915084\pi$
$662$	18.9358	+	10.9326i	0.735959	+	0.424906i
$663$	33.4279	+	19.2996i	1.29823	+	0.749534i
$664$	1.75396	+	3.03794i	0.0680667	+	0.117895i
$665$		0			0
$666$	−2.42803	−	15.5228i	−0.0940844	−	0.601497i
$667$		−	27.9547i		−	1.08241i
$668$	3.58023	−	2.06705i	0.138523	−	0.0799765i
$669$	−5.42139	+	9.39012i	−0.209603	+	0.363043i
$670$		0			0
$671$	0.163902	−	0.283887i	0.00632737	−	0.0109593i
$672$		−	5.19412i		−	0.200368i
$673$	−24.1476	−	13.9417i	−0.930823	−	0.537411i	−0.0437515	−	0.999042i	$-0.513931\pi$
$673$	−24.1476	−	13.9417i	−0.930823	−	0.537411i	−0.887072	+	0.461631i	$0.847264\pi$
$674$	20.4419			0.787394
$675$		0			0
$676$	−7.82679			−0.301030
$677$		−	3.14537i		−	0.120886i	−0.998172	−	0.0604431i	$-0.980749\pi$
$677$		−	3.14537i		−	0.120886i	0.998172	−	0.0604431i	$-0.0192514\pi$
$678$	−5.76104	+	3.32614i	−0.221251	+	0.127740i
$679$	12.1393	−	21.0260i	0.465865	−	0.806903i
$680$		0			0
$681$	−5.46447	−	9.46474i	−0.209399	−	0.362690i
$682$	1.05981	−	0.611883i	0.0405823	−	0.0234302i
$683$	7.85637	−	4.53587i	0.300615	−	0.173560i	−0.342104	−	0.939662i	$-0.611139\pi$
$683$	7.85637	−	4.53587i	0.300615	−	0.173560i	0.642719	+	0.766102i	$0.277806\pi$
$684$	0.507277	−	0.878629i	0.0193962	−	0.0335952i
$685$		0			0
$686$	12.2985	+	21.3016i	0.469558	+	0.813297i
$687$	−2.68771	+	1.55175i	−0.102542	+	0.0592029i
$688$	−10.4734	+	6.04680i	−0.399293	+	0.230532i
$689$	−67.8375			−2.58440
$690$		0			0
$691$	−22.6684	−	39.2628i	−0.862347	−	1.49363i	−0.869657	−	0.493656i	$-0.835660\pi$
$691$	−22.6684	−	39.2628i	−0.862347	−	1.49363i	0.00731011	−	0.999973i	$-0.497673\pi$
$692$		−	5.01684i		−	0.190711i
$693$		−	4.13941i		−	0.157243i
$694$	21.2241	+	36.7613i	0.805657	+	1.39544i
$695$		0			0
$696$	−5.34450	+	9.25694i	−0.202583	+	0.350883i
$697$		−	69.3825i		−	2.62805i
$698$	−18.4427	−	10.6479i	−0.698067	−	0.403029i
$699$	4.38033	−	7.58695i	0.165679	−	0.286965i
$700$		0			0
$701$	11.0905	+	19.2093i	0.418882	+	0.725525i	0.995827	−	0.0912579i	$-0.0290888\pi$
$701$	11.0905	+	19.2093i	0.418882	+	0.725525i	−0.576945	+	0.816783i	$0.695755\pi$
$702$			31.8768i			1.20311i
$703$	5.88061	−	0.919828i	0.221791	−	0.0346920i
$704$	8.65472			0.326187
$705$		0			0
$706$	−13.8224	+	23.9411i	−0.520213	+	0.901035i
$707$	−13.6773	−	7.89658i	−0.514387	−	0.296982i
$708$	4.04185	+	2.33356i	0.151902	+	0.0877007i
$709$	33.1688			1.24568			0.622840	−	0.782349i	$-0.285979\pi$
$709$	33.1688			1.24568			0.622840	+	0.782349i	$0.285979\pi$
$710$		0			0
$711$	−36.7373			−1.37776
$712$	7.10403	−	4.10152i	0.266235	−	0.153711i
$713$		−	7.74887i		−	0.290197i
$714$	−17.7999			−0.666145
$715$		0			0
$716$	−2.03360	+	3.52230i	−0.0759992	+	0.131635i
$717$		−	14.3297i		−	0.535154i
$718$	23.6750	−	13.6688i	0.883543	−	0.510114i
$719$	14.3574	+	24.8678i	0.535441	+	0.927411i	0.999142	+	0.0414190i	$0.0131878\pi$
$719$	14.3574	+	24.8678i	0.535441	+	0.927411i	−0.463701	+	0.885992i	$0.653479\pi$
$720$		0			0
$721$	−4.83641	+	8.37692i	−0.180117	+	0.311973i
$722$	19.1828	+	11.0752i	0.713911	+	0.412177i
$723$	5.04571	−	2.91314i	0.187652	−	0.108341i
$724$	−3.92837	−	6.80413i	−0.145997	−	0.252873i
$725$		0			0
$726$	11.6795			0.433468
$727$	30.4246	+	17.5657i	1.12839	+	0.651475i	0.943529	−	0.331291i	$-0.107484\pi$
$727$	30.4246	+	17.5657i	1.12839	+	0.651475i	0.184858	+	0.982765i	$0.440817\pi$
$728$	28.7534	−	16.6008i	1.06567	−	0.615266i
$729$	−10.0629			−0.372698
$730$		0			0
$731$	−16.5538	−	28.6720i	−0.612264	−	1.06047i
$732$			0.156899i			0.00579914i
$733$	−36.5201	−	21.0849i	−1.34890	−	0.778788i	−0.360807	−	0.932641i	$-0.617499\pi$
$733$	−36.5201	−	21.0849i	−1.34890	−	0.778788i	−0.988094	+	0.153853i	$0.950832\pi$
$734$	20.2488			0.747396
$735$		0			0
$736$	10.2968	−	17.8346i	0.379546	−	0.657393i
$737$	0.796546	+	0.459886i	0.0293412	+	0.0169401i
$738$	20.4553	−	11.8099i	0.752969	−	0.434727i
$739$	−2.08985			−0.0768765			−0.0384382	−	0.999261i	$-0.512238\pi$
$739$	−2.08985			−0.0768765			−0.0384382	+	0.999261i	$0.512238\pi$
$740$		0			0
$741$	−4.97800			−0.182871
$742$	27.0920	−	15.6415i	0.994577	−	0.574219i
$743$	14.2640	+	8.23530i	0.523294	+	0.302124i	0.738281	−	0.674493i	$-0.235638\pi$
$743$	14.2640	+	8.23530i	0.523294	+	0.302124i	−0.214987	+	0.976617i	$0.568971\pi$
$744$	−1.48146	+	2.56596i	−0.0543130	+	0.0940728i
$745$		0			0
$746$	−30.3167			−1.10997
$747$	−2.08853	−	1.20581i	−0.0764152	−	0.0441183i
$748$			3.64418i			0.133244i
$749$	−8.40822	−	14.5635i	−0.307230	−	0.532138i
$750$		0			0
$751$	25.3537			0.925170			0.462585	−	0.886575i	$-0.346922\pi$
$751$	25.3537			0.925170			0.462585	+	0.886575i	$0.346922\pi$
$752$	19.9710	−	11.5303i	0.728268	−	0.420466i
$753$	10.0649	+	5.81100i	0.366787	+	0.211765i
$754$	−24.3442			−0.886565
$755$		0			0
$756$	2.40318	+	4.16242i	0.0874026	+	0.151386i
$757$	24.6946	−	14.2575i	0.897542	−	0.518196i	0.0211398	−	0.999777i	$-0.493270\pi$
$757$	24.6946	−	14.2575i	0.897542	−	0.518196i	0.876402	+	0.481581i	$0.159937\pi$
$758$	−4.45267	−	2.57075i	−0.161728	−	0.0933738i
$759$	−3.49488	+	6.05332i	−0.126856	+	0.219722i
$760$		0			0
$761$	−1.78657	−	3.09442i	−0.0647630	−	0.112173i	0.831826	−	0.555037i	$-0.187296\pi$
$761$	−1.78657	−	3.09442i	−0.0647630	−	0.112173i	−0.896589	+	0.442864i	$0.853962\pi$
$762$	19.2498	−	11.1139i	0.697346	−	0.402613i
$763$		−	12.9846i		−	0.470073i
$764$	1.06394	−	1.84280i	0.0384920	−	0.0666700i
$765$		0			0
$766$	−0.441002			−0.0159341
$767$			53.7682i			1.94146i
$768$	−9.05875	+	5.23007i	−0.326879	+	0.188724i
$769$	−11.8163			−0.426105			−0.213053	−	0.977041i	$-0.568341\pi$
$769$	−11.8163			−0.426105			−0.213053	+	0.977041i	$0.568341\pi$
$770$		0			0
$771$	28.4791			1.02565
$772$	−0.521283	−	0.300963i	−0.0187614	−	0.0108319i
$773$	−11.0235	−	6.36443i	−0.396488	−	0.228913i	0.288479	−	0.957486i	$-0.406850\pi$
$773$	−11.0235	−	6.36443i	−0.396488	−	0.228913i	−0.684968	+	0.728574i	$0.740184\pi$
$774$	5.63536	−	9.76074i	0.202559	−	0.350842i
$775$		0			0
$776$	−36.8068			−1.32129
$777$	−4.18634	+	10.8435i	−0.150184	+	0.389009i
$778$		−	16.9822i		−	0.608842i
$779$	4.47400	+	7.74920i	0.160298	+	0.277644i
$780$		0			0
$781$	−5.18550	+	8.98154i	−0.185552	+	0.321385i
$782$	−61.1181	−	35.2865i	−2.18558	−	1.26184i
$783$		−	17.8266i		−	0.637072i
$784$	4.05322	−	7.02038i	0.144758	−	0.250728i
$785$		0			0
$786$	−4.97368	−	8.61466i	−0.177405	−	0.307275i
$787$		−	7.49137i		−	0.267039i	−0.991046	−	0.133519i	$-0.957372\pi$
$787$		−	7.49137i		−	0.267039i	0.991046	−	0.133519i	$-0.0426278\pi$
$788$			10.7105i			0.381544i
$789$	2.80849	+	4.86444i	0.0999848	+	0.173179i
$790$		0			0
$791$	−11.5554			−0.410864
$792$	−5.43465	+	3.13770i	−0.193112	+	0.111493i
$793$	−1.56540	+	0.903786i	−0.0555891	+	0.0320944i
$794$	12.1798	+	21.0960i	0.432243	+	0.748667i
$795$		0			0
$796$	2.22388	−	3.85187i	0.0788233	−	0.136526i
$797$	−29.6288	+	17.1062i	−1.04951	+	0.605933i	−0.922511	−	0.385971i	$-0.873867\pi$
$797$	−29.6288	+	17.1062i	−1.04951	+	0.605933i	−0.126995	+	0.991903i	$0.540533\pi$
$798$	1.98804	−	1.14780i	0.0703759	−	0.0406315i
$799$	31.5654	+	54.6729i	1.11670	+	1.93419i
$800$		0			0
$801$	−2.81971	+	4.88389i	−0.0996296	+	0.172564i
$802$	8.84223	−	5.10507i	0.312230	−	0.180266i
$803$			10.6163i			0.374641i
$804$	−0.440236			−0.0155259
$805$		0			0
$806$	−6.74807			−0.237691
$807$	−1.58015	−	0.912299i	−0.0556239	−	0.0321145i
$808$			23.9426i			0.842299i
$809$	8.52626	−	14.7679i	0.299767	−	0.519212i	−0.676315	−	0.736612i	$-0.736424\pi$
$809$	8.52626	−	14.7679i	0.299767	−	0.519212i	0.976083	+	0.217400i	$0.0697576\pi$
$810$		0			0
$811$	26.3835	−	45.6975i	0.926448	−	1.60466i	0.137233	−	0.990539i	$-0.456179\pi$
$811$	26.3835	−	45.6975i	0.926448	−	1.60466i	0.789215	−	0.614117i	$-0.210488\pi$
$812$	−3.17883	+	1.83530i	−0.111555	+	0.0644064i
$813$			7.74750i			0.271717i
$814$	−6.78971	−	2.62129i	−0.237979	−	0.0918763i
$815$		0			0
$816$	9.95301	+	17.2391i	0.348425	+	0.603490i
$817$	3.69772	+	2.13488i	0.129367	+	0.0746900i
$818$	25.9472	+	14.9806i	0.907222	+	0.523785i
$819$	−11.4127	+	19.7674i	−0.398793	+	0.690729i
$820$		0			0
$821$	7.87664	−	13.6427i	0.274897	−	0.476135i	−0.695212	−	0.718804i	$-0.744690\pi$
$821$	7.87664	−	13.6427i	0.274897	−	0.476135i	0.970109	+	0.242669i	$0.0780230\pi$
$822$			4.70470i			0.164095i
$823$	37.9759	−	21.9254i	1.32376	−	0.764272i	0.339432	−	0.940631i	$-0.389765\pi$
$823$	37.9759	−	21.9254i	1.32376	−	0.764272i	0.984326	+	0.176358i	$0.0564318\pi$
$824$	14.6641			0.510849
$825$		0			0
$826$	−12.3975	−	21.4732i	−0.431366	−	0.747148i
$827$	12.2859	+	7.09330i	0.427224	+	0.246658i	0.698163	−	0.715938i	$-0.254001\pi$
$827$	12.2859	+	7.09330i	0.427224	+	0.246658i	−0.270939	+	0.962596i	$0.587334\pi$
$828$			7.85533i			0.272991i
$829$	7.87183	+	13.6344i	0.273400	+	0.473542i	0.969730	−	0.244179i	$-0.0785185\pi$
$829$	7.87183	+	13.6344i	0.273400	+	0.473542i	−0.696330	+	0.717721i	$0.745185\pi$
$830$		0			0
$831$	−5.96599	−	10.3334i	−0.206958	−	0.358461i
$832$	−41.3299	−	23.8619i	−1.43286	−	0.827261i
$833$	19.2191	+	11.0961i	0.665902	+	0.384458i
$834$	5.86041	+	10.1505i	0.202929	+	0.351484i
$835$		0			0
$836$	−0.234988	−	0.407012i	−0.00812724	−	0.0140768i
$837$		−	4.94143i		−	0.170801i
$838$	−9.03304	−	5.21523i	−0.312041	−	0.180157i
$839$	−3.10619	−	5.38009i	−0.107238	−	0.185741i	0.807413	−	0.589987i	$-0.200867\pi$
$839$	−3.10619	−	5.38009i	−0.107238	−	0.185741i	−0.914650	+	0.404246i	$0.867534\pi$
$840$		0			0
$841$	−15.3858			−0.530546
$842$	26.6414	−	15.3814i	0.918124	−	0.530079i
$843$		−	12.9468i		−	0.445912i
$844$	4.07153	−	7.05209i	0.140148	−	0.242743i
$845$		0			0
$846$	−10.7457	+	18.6122i	−0.369446	+	0.639899i
$847$	17.5700	+	10.1441i	0.603713	+	0.348554i
$848$	−30.2975	−	17.4923i	−1.04042	−	0.600687i
$849$	−15.3693	−	26.6204i	−0.527473	−	0.913610i
$850$		0			0
$851$	−35.8705	+	28.9335i	−1.22962	+	0.991827i
$852$		−	4.96393i		−	0.170061i
$853$	7.36132	−	4.25006i	0.252047	−	0.145519i	−0.368654	−	0.929567i	$-0.620181\pi$
$853$	7.36132	−	4.25006i	0.252047	−	0.145519i	0.620701	+	0.784047i	$0.286848\pi$
$854$	0.416779	−	0.721882i	0.0142619	−	0.0247023i
$855$		0			0
$856$	−12.7470	+	22.0784i	−0.435682	+	0.754624i
$857$		−	41.2677i		−	1.40968i	−0.709368	−	0.704839i	$-0.751019\pi$
$857$		−	41.2677i		−	1.40968i	0.709368	−	0.704839i	$-0.248981\pi$
$858$	5.27151	+	3.04351i	0.179966	+	0.103904i
$859$	−18.0944			−0.617374			−0.308687	−	0.951164i	$-0.599889\pi$
$859$	−18.0944			−0.617374			−0.308687	+	0.951164i	$0.599889\pi$
$860$		0			0
$861$	−17.4741			−0.595515
$862$		−	45.5794i		−	1.55244i
$863$	28.1310	−	16.2414i	0.957589	−	0.552865i	0.0621592	−	0.998066i	$-0.480201\pi$
$863$	28.1310	−	16.2414i	0.957589	−	0.552865i	0.895430	+	0.445202i	$0.146868\pi$
$864$	6.56625	−	11.3731i	0.223389	−	0.386920i
$865$		0			0
$866$	−20.0167	−	34.6699i	−0.680194	−	1.17813i
$867$	−33.2577	+	19.2013i	−1.12949	+	0.652112i
$868$	−0.881151	+	0.508733i	−0.0299082	+	0.0172675i
$869$	−8.50900	+	14.7380i	−0.288648	+	0.499953i
$870$		0			0
$871$	−2.53590	−	4.39230i	−0.0859256	−	0.148827i
$872$	−17.0475	+	9.84238i	−0.577301	+	0.333305i
$873$	21.9139	−	12.6520i	0.741672	−	0.428205i
$874$	9.10156			0.307865
$875$		0			0
$876$	−2.54067	−	4.40057i	−0.0858413	−	0.148681i
$877$		−	56.5151i		−	1.90838i	−0.299205	−	0.954189i	$-0.596721\pi$
$877$		−	56.5151i		−	1.90838i	0.299205	−	0.954189i	$-0.403279\pi$
$878$			44.6615i			1.50725i
$879$	−0.591181	−	1.02395i	−0.0199400	−	0.0345371i
$880$		0			0
$881$	−2.47287	+	4.28314i	−0.0833131	+	0.144303i	−0.904671	−	0.426110i	$-0.859883\pi$
$881$	−2.47287	+	4.28314i	−0.0833131	+	0.144303i	0.821358	+	0.570413i	$0.193217\pi$
$882$			7.55487i			0.254386i
$883$	−22.6865	−	13.0981i	−0.763462	−	0.440785i	0.0670752	−	0.997748i	$-0.478633\pi$
$883$	−22.6865	−	13.0981i	−0.763462	−	0.440785i	−0.830537	+	0.556963i	$0.811967\pi$
$884$	10.0473	−	17.4025i	0.337928	−	0.585309i
$885$		0			0
$886$	−15.6222	−	27.0584i	−0.524837	−	0.909044i
$887$			10.6023i			0.355990i	0.984031	+	0.177995i	$0.0569611\pi$
$887$			10.6023i			0.355990i	−0.984031	+	0.177995i	$0.943039\pi$
$888$	17.4098	−	2.72319i	0.584234	−	0.0913842i
$889$	38.6110			1.29497
$890$		0			0
$891$	0.847130	−	1.46727i	0.0283799	−	0.0491555i
$892$	4.88848	+	2.82236i	0.163678	+	0.0944997i
$893$	−7.05096	−	4.07087i	−0.235951	−	0.136227i
$894$	12.9735			0.433899
$895$		0			0
$896$	11.0335			0.368602
$897$	33.3791	−	19.2714i	1.11450	−	0.643454i
$898$		−	1.87202i		−	0.0624701i
$899$	3.77376			0.125862
$900$		0			0
$901$	47.8870	−	82.9428i	1.59535	−	2.76323i
$902$		−	10.9415i		−	0.364311i
$903$	−7.22109	+	4.16910i	−0.240303	+	0.138739i
$904$	8.75910	+	15.1712i	0.291323	+	0.504587i
$905$		0			0
$906$	−7.03175	+	12.1793i	−0.233614	+	0.404632i
$907$	9.77315	+	5.64253i	0.324512	+	0.187357i	0.653402	−	0.757011i	$-0.273341\pi$
$907$	9.77315	+	5.64253i	0.324512	+	0.187357i	−0.328890	+	0.944368i	$0.606675\pi$
$908$	−4.92733	+	2.84479i	−0.163519	+	0.0944078i
$909$	−8.23005	−	14.2549i	−0.272973	−	0.472804i
$910$		0			0
$911$	−19.8632			−0.658096			−0.329048	−	0.944313i	$-0.606728\pi$
$911$	−19.8632			−0.658096			−0.329048	+	0.944313i	$0.606728\pi$
$912$	−2.22327	−	1.28360i	−0.0736198	−	0.0425044i
$913$	−0.967478	+	0.558574i	−0.0320189	+	0.0184861i
$914$	−3.68739			−0.121968
$915$		0			0
$916$	0.807837	+	1.39921i	0.0266917	+	0.0462314i
$917$		−	17.2792i		−	0.570610i
$918$	−38.9748	−	22.5021i	−1.28636	−	0.742681i
$919$	29.1194			0.960560			0.480280	−	0.877115i	$-0.340535\pi$
$919$	29.1194			0.960560			0.480280	+	0.877115i	$0.340535\pi$
$920$		0			0
$921$	−2.52313	+	4.37019i	−0.0831399	+	0.144003i
$922$	30.5038	+	17.6114i	1.00459	+	0.580000i
$923$	49.5259	−	28.5938i	1.63016	−	0.941175i
$924$	0.917792			0.0301931
$925$		0			0
$926$	28.3988			0.933242
$927$	−8.73066	+	5.04065i	−0.286753	+	0.165557i
$928$	8.68560	+	5.01463i	0.285119	+	0.164613i
$929$	17.1729	−	29.7444i	0.563425	−	0.975881i	−0.433769	−	0.901024i	$-0.642817\pi$
$929$	17.1729	−	29.7444i	0.563425	−	0.975881i	0.997194	−	0.0748570i	$-0.0238500\pi$
$930$		0			0
$931$	−2.86206			−0.0938002
$932$	−3.94975	−	2.28039i	−0.129378	−	0.0746967i
$933$		−	18.5327i		−	0.606733i
$934$	−20.7061	−	35.8640i	−0.677523	−	1.17350i
$935$		0			0
$936$	34.6036			1.13106
$937$	−43.3926	+	25.0527i	−1.41757	+	0.818436i	−0.996085	−	0.0883975i	$-0.971825\pi$
$937$	−43.3926	+	25.0527i	−1.41757	+	0.818436i	−0.421488	+	0.906834i	$0.638492\pi$
$938$	2.02550	+	1.16942i	0.0661349	+	0.0381830i
$939$	2.11444			0.0690020
$940$		0			0
$941$	10.1603	+	17.5981i	0.331216	+	0.573682i	0.982751	−	0.184936i	$-0.0592079\pi$
$941$	10.1603	+	17.5981i	0.331216	+	0.573682i	−0.651535	+	0.758619i	$0.725875\pi$
$942$	4.41643	−	2.54983i	0.143895	−	0.0830778i
$943$	−59.9993	−	34.6406i	−1.95385	−	1.12805i
$944$	−13.8644	+	24.0139i	−0.451249	+	0.781587i
$945$		0			0
$946$	−2.61050	−	4.52151i	−0.0848746	−	0.147007i
$947$	14.6158	−	8.43842i	0.474949	−	0.274212i	−0.243360	−	0.969936i	$-0.578250\pi$
$947$	14.6158	−	8.43842i	0.474949	−	0.274212i	0.718309	+	0.695724i	$0.244916\pi$
$948$		−	8.14542i		−	0.264551i
$949$	29.2701	−	50.6973i	0.950148	−	1.64570i
$950$		0			0
$951$	−1.66626			−0.0540320
$952$			46.8745i			1.51921i
$953$	−9.08795	+	5.24693i	−0.294387	+	0.169965i	−0.639919	−	0.768443i	$-0.721032\pi$
$953$	−9.08795	+	5.24693i	−0.294387	+	0.169965i	0.345531	+	0.938407i	$0.387699\pi$
$954$	32.6042			1.05560
$955$		0			0
$956$	−7.46003			−0.241275
$957$	−2.94801	−	1.70203i	−0.0952957	−	0.0550190i
$958$	−23.7769	−	13.7276i	−0.768196	−	0.443518i
$959$	−4.08618	+	7.07748i	−0.131950	+	0.228544i
$960$		0			0
$961$	−29.9539			−0.966256
$962$	25.1966	+	31.2376i	0.812371	+	1.00714i
$963$		−	17.5266i		−	0.564786i
$964$	−1.51658	−	2.62679i	−0.0488457	−	0.0846032i
$965$		0			0
$966$	−8.88697	+	15.3927i	−0.285934	+	0.495252i
$967$	−0.393275	−	0.227057i	−0.0126469	−	0.00730168i	0.493663	−	0.869653i	$-0.335658\pi$
$967$	−0.393275	−	0.227057i	−0.0126469	−	0.00730168i	−0.506310	+	0.862351i	$0.668991\pi$
$968$		−	30.7570i		−	0.988568i
$969$	3.51401	−	6.08644i	0.112886	−	0.195525i
$970$		0			0
$971$	3.45078	+	5.97693i	0.110741	+	0.191809i	0.916069	−	0.401020i	$-0.131344\pi$
$971$	3.45078	+	5.97693i	0.110741	+	0.191809i	−0.805328	+	0.592829i	$0.798011\pi$
$972$			7.95370i			0.255115i
$973$			20.3598i			0.652706i
$974$	10.4331	+	18.0706i	0.334297	+	0.579020i
$975$		0			0
$976$	−0.932185			−0.0298385
$977$	−28.4743	+	16.4397i	−0.910974	+	0.525951i	−0.880744	−	0.473592i	$-0.842957\pi$
$977$	−28.4743	+	16.4397i	−0.910974	+	0.525951i	−0.0302295	+	0.999543i	$0.509624\pi$
$978$	−12.1245	+	7.00007i	−0.387698	+	0.223837i
$979$	1.30619	+	2.26239i	0.0417460	+	0.0723062i
$980$		0			0
$981$	6.76644	−	11.7198i	0.216036	−	0.374185i
$982$	23.0228	−	13.2922i	0.734687	−	0.424172i
$983$	7.56741	−	4.36905i	0.241363	−	0.139351i	−0.374440	−	0.927251i	$-0.622165\pi$
$983$	7.56741	−	4.36905i	0.241363	−	0.139351i	0.615803	+	0.787900i	$0.288832\pi$
$984$	13.2455	+	22.9418i	0.422250	+	0.731359i
$985$		0			0
$986$	17.1848	−	29.7650i	0.547276	−	0.947909i
$987$	13.7695	−	7.94980i	0.438286	−	0.253045i
$988$			2.59154i			0.0824477i
$989$	−33.0593			−1.05122
$990$		0			0
$991$	50.9489			1.61844			0.809222	−	0.587503i	$-0.199889\pi$
$991$	50.9489			1.61844			0.809222	+	0.587503i	$0.199889\pi$
$992$	2.40759	+	1.39002i	0.0764411	+	0.0441333i
$993$		−	16.8591i		−	0.535008i
$994$	−13.1859	+	22.8387i	−0.418233	+	0.724401i
$995$		0			0
$996$	0.267353	−	0.463070i	0.00847142	−	0.0146729i
$997$	−50.5136	+	29.1640i	−1.59978	+	0.923634i	−0.608254	+	0.793743i	$0.708130\pi$
$997$	−50.5136	+	29.1640i	−1.59978	+	0.923634i	−0.991528	+	0.129892i	$0.958537\pi$
$998$		−	13.8857i		−	0.439543i
$999$	−22.8745	+	18.4508i	−0.723717	+	0.583757i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.o.d.174.17		48
5.2	odd	4		925.2.e.d.26.9	✓	24
5.3	odd	4		925.2.e.e.26.4	yes	24
5.4	even	2	inner	925.2.o.d.174.8		48
37.10	even	3	inner	925.2.o.d.824.8		48
185.47	odd	12		925.2.e.d.676.9	yes	24
185.84	even	6	inner	925.2.o.d.824.17		48
185.158	odd	12		925.2.e.e.676.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
925.2.e.d.26.9	✓	24	5.2	odd	4
925.2.e.d.676.9	yes	24	185.47	odd	12
925.2.e.e.26.4	yes	24	5.3	odd	4
925.2.e.e.676.4	yes	24	185.158	odd	12
925.2.o.d.174.8		48	5.4	even	2	inner
925.2.o.d.174.17		48	1.1	even	1	trivial
925.2.o.d.824.8		48	37.10	even	3	inner
925.2.o.d.824.17		48	185.84	even	6	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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.06320 - 0.613840i) q^{2} +(-0.819784 - 0.473302i) q^{3} +(-0.246400 + 0.426778i) q^{4} -1.16213 q^{6} +(-1.74824 - 1.00935i) q^{7} +3.06036i q^{8} +(-1.05197 - 1.82207i) q^{9} +O(q^{10})\)	\(q+(1.06320 - 0.613840i) q^{2} +(-0.819784 - 0.473302i) q^{3} +(-0.246400 + 0.426778i) q^{4} -1.16213 q^{6} +(-1.74824 - 1.00935i) q^{7} +3.06036i q^{8} +(-1.05197 - 1.82207i) q^{9} -0.974618 q^{11} +(0.403990 - 0.233244i) q^{12} +(4.65421 + 2.68711i) q^{13} -2.47831 q^{14} +(1.38577 + 2.40023i) q^{16} +(-6.57089 + 3.79371i) q^{17} +(-2.23691 - 1.29148i) q^{18} +(0.489261 - 0.847425i) q^{19} +(0.955452 + 1.65489i) q^{21} +(-1.03622 + 0.598260i) q^{22} +7.57635i q^{23} +(1.44848 - 2.50883i) q^{24} +6.59783 q^{26} +4.83141i q^{27} +(0.861533 - 0.497406i) q^{28} -3.68974 q^{29} -1.02277 q^{31} +(-2.35399 - 1.35908i) q^{32} +(0.798976 + 0.461289i) q^{33} +(-4.65746 + 8.06696i) q^{34} +1.03682 q^{36} +(3.81892 + 4.73453i) q^{37} -1.20131i q^{38} +(-2.54363 - 4.40570i) q^{39} +(-4.57221 + 7.91929i) q^{41} +(2.03168 + 1.17299i) q^{42} +4.36348i q^{43} +(0.240146 - 0.415945i) q^{44} +(4.65067 + 8.05519i) q^{46} -8.32046i q^{47} -2.62356i q^{48} +(-1.46244 - 2.53302i) q^{49} +7.18228 q^{51} +(-2.29360 + 1.32421i) q^{52} +(-10.9316 + 6.31138i) q^{53} +(2.96572 + 5.13677i) q^{54} +(3.08897 - 5.35025i) q^{56} +(-0.802176 + 0.463137i) q^{57} +(-3.92294 + 2.26491i) q^{58} +(5.00242 + 8.66445i) q^{59} +(-0.168170 + 0.291280i) q^{61} +(-1.08741 + 0.627818i) q^{62} +4.24721i q^{63} -8.88011 q^{64} +1.13263 q^{66} +(-0.817291 - 0.471863i) q^{67} -3.73908i q^{68} +(3.58590 - 6.21096i) q^{69} +(5.32054 - 9.21545i) q^{71} +(5.57618 - 3.21941i) q^{72} -10.8928i q^{73} +(6.96654 + 2.68956i) q^{74} +(0.241108 + 0.417611i) q^{76} +(1.70387 + 0.983727i) q^{77} +(-5.40879 - 3.12277i) q^{78} +(8.73059 - 15.1218i) q^{79} +(-0.869192 + 1.50548i) q^{81} +11.2264i q^{82} +(0.992674 - 0.573121i) q^{83} -0.941694 q^{84} +(2.67848 + 4.63927i) q^{86} +(3.02479 + 1.74636i) q^{87} -2.98269i q^{88} +(-1.34021 - 2.32130i) q^{89} +(-5.42445 - 9.39543i) q^{91} +(-3.23342 - 1.86681i) q^{92} +(0.838451 + 0.484080i) q^{93} +(-5.10743 - 8.84633i) q^{94} +(1.28651 + 2.22830i) q^{96} +12.0269i q^{97} +(-3.10974 - 1.79541i) q^{98} +(1.02527 + 1.77582i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 22 q^{4} + 20 q^{9}+O(q^{10}) \) 48 * q + 22 * q^4 + 20 * q^9	\( 48 q + 22 q^{4} + 20 q^{9} - 40 q^{14} - 26 q^{16} - 10 q^{19} - 12 q^{21} + 42 q^{24} - 40 q^{26} - 12 q^{29} + 76 q^{31} + 10 q^{34} - 4 q^{36} - 28 q^{39} - 26 q^{41} + 30 q^{44} - 26 q^{46} + 52 q^{49} - 92 q^{51} + 74 q^{54} + 14 q^{59} + 32 q^{61} - 40 q^{64} + 164 q^{66} - 42 q^{69} - 4 q^{71} - 96 q^{74} + 34 q^{76} + 42 q^{79} - 32 q^{81} - 152 q^{84} - 32 q^{86} - 58 q^{89} + 64 q^{91} + 26 q^{94} + 52 q^{96} + 30 q^{99}+O(q^{100}) \) 48 * q + 22 * q^4 + 20 * q^9 - 40 * q^14 - 26 * q^16 - 10 * q^19 - 12 * q^21 + 42 * q^24 - 40 * q^26 - 12 * q^29 + 76 * q^31 + 10 * q^34 - 4 * q^36 - 28 * q^39 - 26 * q^41 + 30 * q^44 - 26 * q^46 + 52 * q^49 - 92 * q^51 + 74 * q^54 + 14 * q^59 + 32 * q^61 - 40 * q^64 + 164 * q^66 - 42 * q^69 - 4 * q^71 - 96 * q^74 + 34 * q^76 + 42 * q^79 - 32 * q^81 - 152 * q^84 - 32 * q^86 - 58 * q^89 + 64 * q^91 + 26 * q^94 + 52 * q^96 + 30 * q^99

Introduction

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