LMFDB - Embedded newform 525.2.j.b.218.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(218,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("525.218");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.j (of order $4$, degree $2$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			218.8
Character	$\chi$	$=$	525.218
Dual form			525.2.j.b.407.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.347054 + 0.347054i) q^{2} +(-1.72305 - 0.176396i) q^{3} -1.75911i q^{4} +(-0.536770 - 0.659208i) q^{6} +(0.707107 - 0.707107i) q^{7} +(1.30461 - 1.30461i) q^{8} +(2.93777 + 0.607876i) q^{9} +O(q^{10})$	\(q+(0.347054 + 0.347054i) q^{2} +(-1.72305 - 0.176396i) q^{3} -1.75911i q^{4} +(-0.536770 - 0.659208i) q^{6} +(0.707107 - 0.707107i) q^{7} +(1.30461 - 1.30461i) q^{8} +(2.93777 + 0.607876i) q^{9} +2.67137i q^{11} +(-0.310299 + 3.03102i) q^{12} +(-2.14945 - 2.14945i) q^{13} +0.490808 q^{14} -2.61267 q^{16} +(-3.26719 - 3.26719i) q^{17} +(0.808598 + 1.23053i) q^{18} -5.24329i q^{19} +(-1.34311 + 1.09365i) q^{21} +(-0.927108 + 0.927108i) q^{22} +(2.54815 - 2.54815i) q^{23} +(-2.47803 + 2.01778i) q^{24} -1.49195i q^{26} +(-4.95468 - 1.56561i) q^{27} +(-1.24388 - 1.24388i) q^{28} -2.86924 q^{29} -5.28599 q^{31} +(-3.51596 - 3.51596i) q^{32} +(0.471218 - 4.60289i) q^{33} -2.26778i q^{34} +(1.06932 - 5.16785i) q^{36} +(2.14286 - 2.14286i) q^{37} +(1.81970 - 1.81970i) q^{38} +(3.32444 + 4.08274i) q^{39} -11.5768i q^{41} +(-0.845684 - 0.0865765i) q^{42} +(-0.759108 - 0.759108i) q^{43} +4.69922 q^{44} +1.76869 q^{46} +(7.66034 + 7.66034i) q^{47} +(4.50176 + 0.460865i) q^{48} -1.00000i q^{49} +(5.05320 + 6.20584i) q^{51} +(-3.78111 + 3.78111i) q^{52} +(-4.43577 + 4.43577i) q^{53} +(-1.17619 - 2.26289i) q^{54} -1.84500i q^{56} +(-0.924894 + 9.03442i) q^{57} +(-0.995779 - 0.995779i) q^{58} +0.159437 q^{59} +4.72534 q^{61} +(-1.83452 - 1.83452i) q^{62} +(2.50715 - 1.64748i) q^{63} +2.78490i q^{64} +(1.76099 - 1.43391i) q^{66} +(5.41156 - 5.41156i) q^{67} +(-5.74734 + 5.74734i) q^{68} +(-4.84006 + 3.94109i) q^{69} +13.5880i q^{71} +(4.62569 - 3.03961i) q^{72} +(-4.16486 - 4.16486i) q^{73} +1.48737 q^{74} -9.22351 q^{76} +(1.88894 + 1.88894i) q^{77} +(-0.263173 + 2.57069i) q^{78} -3.89710i q^{79} +(8.26097 + 3.57160i) q^{81} +(4.01778 - 4.01778i) q^{82} +(-4.03778 + 4.03778i) q^{83} +(1.92384 + 2.36267i) q^{84} -0.526902i q^{86} +(4.94383 + 0.506122i) q^{87} +(3.48510 + 3.48510i) q^{88} +3.95125 q^{89} -3.03977 q^{91} +(-4.48247 - 4.48247i) q^{92} +(9.10800 + 0.932426i) q^{93} +5.31710i q^{94} +(5.43796 + 6.67836i) q^{96} +(1.86878 - 1.86878i) q^{97} +(0.347054 - 0.347054i) q^{98} +(-1.62386 + 7.84786i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3}+O(q^{10}) $ 24 * q + 4 * q^3	$ 24 q + 4 q^{3} - 16 q^{12} + 8 q^{13} - 16 q^{16} + 20 q^{18} + 4 q^{21} - 8 q^{22} + 16 q^{27} - 28 q^{33} + 16 q^{36} + 16 q^{37} + 20 q^{42} + 40 q^{43} - 64 q^{46} - 16 q^{48} - 20 q^{51} - 4 q^{57} - 40 q^{58} + 32 q^{61} + 8 q^{63} - 16 q^{66} - 24 q^{67} + 8 q^{72} - 32 q^{73} + 32 q^{76} - 60 q^{78} + 52 q^{81} + 80 q^{82} - 4 q^{87} - 96 q^{88} - 24 q^{91} + 76 q^{93} - 96 q^{96} - 24 q^{97}+O(q^{100}) $ 24 * q + 4 * q^3 - 16 * q^12 + 8 * q^13 - 16 * q^16 + 20 * q^18 + 4 * q^21 - 8 * q^22 + 16 * q^27 - 28 * q^33 + 16 * q^36 + 16 * q^37 + 20 * q^42 + 40 * q^43 - 64 * q^46 - 16 * q^48 - 20 * q^51 - 4 * q^57 - 40 * q^58 + 32 * q^61 + 8 * q^63 - 16 * q^66 - 24 * q^67 + 8 * q^72 - 32 * q^73 + 32 * q^76 - 60 * q^78 + 52 * q^81 + 80 * q^82 - 4 * q^87 - 96 * q^88 - 24 * q^91 + 76 * q^93 - 96 * q^96 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	0.347054	+	0.347054i	0.245404	+	0.245404i	0.819081	−	0.573677i	$-0.194484\pi$
$2$	0.347054	+	0.347054i	0.245404	+	0.245404i	−0.573677	+	0.819081i	$0.694484\pi$
$3$	−1.72305	−	0.176396i	−0.994801	−	0.101842i
$3$	−1.72305	−	0.176396i	−0.994801	−	0.101842i
$4$		−	1.75911i		−	0.879554i
$5$		0			0
$5$		0			0
$6$	−0.536770	−	0.659208i	−0.219135	−	0.269120i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	1.30461	−	1.30461i	0.461250	−	0.461250i
$9$	2.93777	+	0.607876i	0.979256	+	0.202625i
$10$		0			0
$11$			2.67137i			0.805448i	0.915322	+	0.402724i	$0.131936\pi$
$11$			2.67137i			0.805448i	−0.915322	+	0.402724i	$0.868064\pi$
$12$	−0.310299	+	3.03102i	−0.0895757	+	0.874981i
$13$	−2.14945	−	2.14945i	−0.596149	−	0.596149i	0.343137	−	0.939285i	$-0.388511\pi$
$13$	−2.14945	−	2.14945i	−0.596149	−	0.596149i	−0.939285	+	0.343137i	$0.888511\pi$
$14$	0.490808			0.131174
$15$		0			0
$16$	−2.61267			−0.653169
$17$	−3.26719	−	3.26719i	−0.792410	−	0.792410i	0.189475	−	0.981886i	$-0.439321\pi$
$17$	−3.26719	−	3.26719i	−0.792410	−	0.792410i	−0.981886	+	0.189475i	$0.939321\pi$
$18$	0.808598	+	1.23053i	0.190588	+	0.290038i
$19$		−	5.24329i		−	1.20289i	−0.798913	−	0.601446i	$-0.794591\pi$
$19$		−	5.24329i		−	1.20289i	0.798913	−	0.601446i	$-0.205409\pi$
$20$		0			0
$21$	−1.34311	+	1.09365i	−0.293090	+	0.238653i
$22$	−0.927108	+	0.927108i	−0.197660	+	0.197660i
$23$	2.54815	−	2.54815i	0.531326	−	0.531326i	−0.389641	−	0.920967i	$-0.627401\pi$
$23$	2.54815	−	2.54815i	0.531326	−	0.531326i	0.920967	+	0.389641i	$0.127401\pi$
$24$	−2.47803	+	2.01778i	−0.505826	+	0.411877i
$25$		0			0
$26$		−	1.49195i		−	0.292595i
$27$	−4.95468	−	1.56561i	−0.953529	−	0.301301i
$28$	−1.24388	−	1.24388i	−0.235071	−	0.235071i
$29$	−2.86924			−0.532804			−0.266402	−	0.963862i	$-0.585835\pi$
$29$	−2.86924			−0.532804			−0.266402	+	0.963862i	$0.585835\pi$
$30$		0			0
$31$	−5.28599			−0.949391			−0.474696	−	0.880150i	$-0.657442\pi$
$31$	−5.28599			−0.949391			−0.474696	+	0.880150i	$0.657442\pi$
$32$	−3.51596	−	3.51596i	−0.621540	−	0.621540i
$33$	0.471218	−	4.60289i	0.0820286	−	0.801260i
$34$		−	2.26778i		−	0.388921i
$35$		0			0
$36$	1.06932	−	5.16785i	0.178220	−	0.861309i
$37$	2.14286	−	2.14286i	0.352284	−	0.352284i	−0.508675	−	0.860959i	$-0.669864\pi$
$37$	2.14286	−	2.14286i	0.352284	−	0.352284i	0.860959	+	0.508675i	$0.169864\pi$
$38$	1.81970	−	1.81970i	0.295195	−	0.295195i
$39$	3.32444	+	4.08274i	0.532336	+	0.653762i
$40$		0			0
$41$		−	11.5768i		−	1.80800i	−0.427537	−	0.903998i	$-0.640619\pi$
$41$		−	11.5768i		−	1.80800i	0.427537	−	0.903998i	$-0.359381\pi$
$42$	−0.845684	−	0.0865765i	−0.130492	−	0.0133590i
$43$	−0.759108	−	0.759108i	−0.115763	−	0.115763i	0.646852	−	0.762615i	$-0.276085\pi$
$43$	−0.759108	−	0.759108i	−0.115763	−	0.115763i	−0.762615	+	0.646852i	$0.776085\pi$
$44$	4.69922			0.708434
$45$		0			0
$46$	1.76869			0.260779
$47$	7.66034	+	7.66034i	1.11738	+	1.11738i	0.992125	+	0.125250i	$0.0399734\pi$
$47$	7.66034	+	7.66034i	1.11738	+	1.11738i	0.125250	+	0.992125i	$0.460027\pi$
$48$	4.50176	+	0.460865i	0.649773	+	0.0665201i
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$	5.05320	+	6.20584i	0.707589	+	0.868991i
$52$	−3.78111	+	3.78111i	−0.524345	+	0.524345i
$53$	−4.43577	+	4.43577i	−0.609300	+	0.609300i	−0.942763	−	0.333463i	$-0.891783\pi$
$53$	−4.43577	+	4.43577i	−0.609300	+	0.609300i	0.333463	+	0.942763i	$0.391783\pi$
$54$	−1.17619	−	2.26289i	−0.160059	−	0.307940i
$55$		0			0
$56$		−	1.84500i		−	0.246548i
$57$	−0.924894	+	9.03442i	−0.122505	+	1.19664i
$58$	−0.995779	−	0.995779i	−0.130752	−	0.130752i
$59$	0.159437			0.0207569			0.0103785	−	0.999946i	$-0.496696\pi$
$59$	0.159437			0.0207569			0.0103785	+	0.999946i	$0.496696\pi$
$60$		0			0
$61$	4.72534			0.605018			0.302509	−	0.953147i	$-0.402176\pi$
$61$	4.72534			0.605018			0.302509	+	0.953147i	$0.402176\pi$
$62$	−1.83452	−	1.83452i	−0.232984	−	0.232984i
$63$	2.50715	−	1.64748i	0.315871	−	0.207563i
$64$			2.78490i			0.348112i
$65$		0			0
$66$	1.76099	−	1.43391i	0.216762	−	0.176502i
$67$	5.41156	−	5.41156i	0.661127	−	0.661127i	−0.294519	−	0.955646i	$-0.595159\pi$
$67$	5.41156	−	5.41156i	0.661127	−	0.661127i	0.955646	+	0.294519i	$0.0951594\pi$
$68$	−5.74734	+	5.74734i	−0.696967	+	0.696967i
$69$	−4.84006	+	3.94109i	−0.582675	+	0.474452i
$70$		0			0
$71$			13.5880i			1.61260i	0.591508	+	0.806299i	$0.298533\pi$
$71$			13.5880i			1.61260i	−0.591508	+	0.806299i	$0.701467\pi$
$72$	4.62569	−	3.03961i	0.545143	−	0.358221i
$73$	−4.16486	−	4.16486i	−0.487460	−	0.487460i	0.420044	−	0.907504i	$-0.362015\pi$
$73$	−4.16486	−	4.16486i	−0.487460	−	0.487460i	−0.907504	+	0.420044i	$0.862015\pi$
$74$	1.48737			0.172904
$75$		0			0
$76$	−9.22351			−1.05801
$77$	1.88894	+	1.88894i	0.215265	+	0.215265i
$78$	−0.263173	+	2.57069i	−0.0297985	+	0.291073i
$79$		−	3.89710i		−	0.438458i	−0.975673	−	0.219229i	$-0.929646\pi$
$79$		−	3.89710i		−	0.438458i	0.975673	−	0.219229i	$-0.0703542\pi$
$80$		0			0
$81$	8.26097	+	3.57160i	0.917886	+	0.396844i
$82$	4.01778	−	4.01778i	0.443689	−	0.443689i
$83$	−4.03778	+	4.03778i	−0.443204	+	0.443204i	−0.893087	−	0.449883i	$-0.851466\pi$
$83$	−4.03778	+	4.03778i	−0.443204	+	0.443204i	0.449883	+	0.893087i	$0.351466\pi$
$84$	1.92384	+	2.36267i	0.209908	+	0.257789i
$85$		0			0
$86$		−	0.526902i		−	0.0568173i
$87$	4.94383	+	0.506122i	0.530034	+	0.0542619i
$88$	3.48510	+	3.48510i	0.371513	+	0.371513i
$89$	3.95125			0.418832			0.209416	−	0.977827i	$-0.432844\pi$
$89$	3.95125			0.418832			0.209416	+	0.977827i	$0.432844\pi$
$90$		0			0
$91$	−3.03977			−0.318655
$92$	−4.48247	−	4.48247i	−0.467330	−	0.467330i
$93$	9.10800	+	0.932426i	0.944455	+	0.0966881i
$94$			5.31710i			0.548417i
$95$		0			0
$96$	5.43796	+	6.67836i	0.555009	+	0.681607i
$97$	1.86878	−	1.86878i	0.189746	−	0.189746i	−0.605840	−	0.795586i	$-0.707163\pi$
$97$	1.86878	−	1.86878i	0.189746	−	0.189746i	0.795586	+	0.605840i	$0.207163\pi$
$98$	0.347054	−	0.347054i	0.0350577	−	0.0350577i
$99$	−1.62386	+	7.84786i	−0.163204	+	0.788740i
$100$		0			0
$101$		−	3.76115i		−	0.374249i	−0.982336	−	0.187124i	$-0.940083\pi$
$101$		−	3.76115i		−	0.374249i	0.982336	−	0.187124i	$-0.0599167\pi$
$102$	−0.400027	+	3.90749i	−0.0396086	+	0.386899i
$103$	8.85701	+	8.85701i	0.872707	+	0.872707i	0.992767	−	0.120060i	$-0.0383086\pi$
$103$	8.85701	+	8.85701i	0.872707	+	0.872707i	−0.120060	+	0.992767i	$0.538309\pi$
$104$	−5.60838			−0.549947
$105$		0			0
$106$	−3.07890			−0.299049
$107$	0.710397	+	0.710397i	0.0686766	+	0.0686766i	0.740611	−	0.671934i	$-0.234536\pi$
$107$	0.710397	+	0.710397i	0.0686766	+	0.0686766i	−0.671934	+	0.740611i	$0.734536\pi$
$108$	−2.75407	+	8.71582i	−0.265011	+	0.838680i
$109$		−	19.0144i		−	1.82125i	−0.413237	−	0.910623i	$-0.635602\pi$
$109$		−	19.0144i		−	1.82125i	0.413237	−	0.910623i	$-0.364398\pi$
$110$		0			0
$111$	−4.07024	+	3.31425i	−0.386330	+	0.314575i
$112$	−1.84744	+	1.84744i	−0.174567	+	0.174567i
$113$	5.69132	−	5.69132i	0.535394	−	0.535394i	−0.386779	−	0.922173i	$-0.626412\pi$
$113$	5.69132	−	5.69132i	0.535394	−	0.535394i	0.922173	+	0.386779i	$0.126412\pi$
$114$	−3.45642	+	2.81444i	−0.323723	+	0.263597i
$115$		0			0
$116$			5.04730i			0.468630i
$117$	−5.00798	−	7.62117i	−0.462988	−	0.704577i
$118$	0.0553332	+	0.0553332i	0.00509383	+	0.00509383i
$119$	−4.62051			−0.423561
$120$		0			0
$121$	3.86380			0.351254
$122$	1.63995	+	1.63995i	0.148474	+	0.148474i
$123$	−2.04210	+	19.9474i	−0.184130	+	1.79859i
$124$			9.29862i			0.835041i
$125$		0			0
$126$	1.44188	+	0.298350i	0.128453	+	0.0265792i
$127$	12.1366	−	12.1366i	1.07695	−	1.07695i	0.0801668	−	0.996781i	$-0.474455\pi$
$127$	12.1366	−	12.1366i	1.07695	−	1.07695i	0.996781	−	0.0801668i	$-0.0255453\pi$
$128$	−7.99843	+	7.99843i	−0.706968	+	0.706968i
$129$	1.17407	+	1.44188i	0.103371	+	0.126950i
$130$		0			0
$131$			9.94280i			0.868706i	0.900743	+	0.434353i	$0.143023\pi$
$131$			9.94280i			0.868706i	−0.900743	+	0.434353i	$0.856977\pi$
$132$	−8.09697	−	0.828923i	−0.704751	−	0.0721485i
$133$	−3.70756	−	3.70756i	−0.321487	−	0.321487i
$134$	3.75620			0.324486
$135$		0			0
$136$	−8.52483			−0.730998
$137$	13.6645	+	13.6645i	1.16744	+	1.16744i	0.982808	+	0.184630i	$0.0591086\pi$
$137$	13.6645	+	13.6645i	1.16744	+	1.16744i	0.184630	+	0.982808i	$0.440891\pi$
$138$	−3.04753	−	0.311989i	−0.259423	−	0.0265583i
$139$			16.7933i			1.42439i	0.701982	+	0.712195i	$0.252299\pi$
$139$			16.7933i			1.42439i	−0.701982	+	0.712195i	$0.747701\pi$
$140$		0			0
$141$	−11.8479	−	14.5504i	−0.997770	−	1.22536i
$142$	−4.71576	+	4.71576i	−0.395738	+	0.395738i
$143$	5.74196	−	5.74196i	0.480167	−	0.480167i
$144$	−7.67544	−	1.58818i	−0.639620	−	0.132349i
$145$		0			0
$146$		−	2.89086i		−	0.239249i
$147$	−0.176396	+	1.72305i	−0.0145489	+	0.142114i
$148$	−3.76952	−	3.76952i	−0.309853	−	0.309853i
$149$	−9.31256			−0.762915			−0.381458	−	0.924386i	$-0.624578\pi$
$149$	−9.31256			−0.762915			−0.381458	+	0.924386i	$0.624578\pi$
$150$		0			0
$151$	20.3868			1.65905			0.829527	−	0.558466i	$-0.188610\pi$
$151$	20.3868			1.65905			0.829527	+	0.558466i	$0.188610\pi$
$152$	−6.84046	−	6.84046i	−0.554834	−	0.554834i
$153$	−7.61221	−	11.5843i	−0.615410	−	0.936535i
$154$			1.31113i			0.105654i
$155$		0			0
$156$	7.18199	−	5.84804i	0.575019	−	0.468218i
$157$	−6.32887	+	6.32887i	−0.505098	+	0.505098i	−0.913018	−	0.407919i	$-0.866254\pi$
$157$	−6.32887	+	6.32887i	−0.505098	+	0.505098i	0.407919	+	0.913018i	$0.366254\pi$
$158$	1.35250	−	1.35250i	0.107599	−	0.107599i
$159$	8.42549	−	6.86058i	0.668185	−	0.544080i
$160$		0			0
$161$		−	3.60363i		−	0.284006i
$162$	1.62746	+	4.10654i	0.127866	+	0.322640i
$163$	6.45638	+	6.45638i	0.505703	+	0.505703i	0.913205	−	0.407502i	$-0.133600\pi$
$163$	6.45638	+	6.45638i	0.505703	+	0.505703i	−0.407502	+	0.913205i	$0.633600\pi$
$164$	−20.3649			−1.59023
$165$		0			0
$166$	−2.80266			−0.217528
$167$	1.58004	+	1.58004i	0.122268	+	0.122268i	0.765593	−	0.643325i	$-0.222446\pi$
$167$	1.58004	+	1.58004i	0.122268	+	0.122268i	−0.643325	+	0.765593i	$0.722446\pi$
$168$	−0.325450	+	3.17902i	−0.0251090	+	0.245267i
$169$		−	3.75977i		−	0.289213i
$170$		0			0
$171$	3.18727	−	15.4036i	0.243737	−	1.17794i
$172$	−1.33535	+	1.33535i	−0.101820	+	0.101820i
$173$	−1.69970	+	1.69970i	−0.129226	+	0.129226i	−0.768761	−	0.639536i	$-0.779127\pi$
$173$	−1.69970	+	1.69970i	−0.129226	+	0.129226i	0.639536	+	0.768761i	$0.279127\pi$
$174$	1.54012	+	1.89142i	0.116756	+	0.143388i
$175$		0			0
$176$		−	6.97941i		−	0.526093i
$177$	−0.274717	−	0.0281240i	−0.0206490	−	0.00211393i
$178$	1.37130	+	1.37130i	0.102783	+	0.102783i
$179$	8.44380			0.631119			0.315560	−	0.948906i	$-0.397808\pi$
$179$	8.44380			0.631119			0.315560	+	0.948906i	$0.397808\pi$
$180$		0			0
$181$	5.51483			0.409914			0.204957	−	0.978771i	$-0.434295\pi$
$181$	5.51483			0.409914			0.204957	+	0.978771i	$0.434295\pi$
$182$	−1.05496	−	1.05496i	−0.0781992	−	0.0781992i
$183$	−8.14198	−	0.833531i	−0.601872	−	0.0616164i
$184$		−	6.64869i		−	0.490148i
$185$		0			0
$186$	2.83736	+	3.48456i	0.208045	+	0.255501i
$187$	8.72787	−	8.72787i	0.638245	−	0.638245i
$188$	13.4754	−	13.4754i	0.982792	−	0.982792i
$189$	−4.61054	+	2.39644i	−0.335368	+	0.174315i
$190$		0			0
$191$			0.559524i			0.0404858i	0.999795	+	0.0202429i	$0.00644395\pi$
$191$			0.559524i			0.0404858i	−0.999795	+	0.0202429i	$0.993556\pi$
$192$	0.491244	−	4.79850i	0.0354525	−	0.346302i
$193$	−7.05199	−	7.05199i	−0.507613	−	0.507613i	0.406180	−	0.913793i	$-0.366861\pi$
$193$	−7.05199	−	7.05199i	−0.507613	−	0.507613i	−0.913793	+	0.406180i	$0.866861\pi$
$194$	1.29713			0.0931287
$195$		0			0
$196$	−1.75911			−0.125651
$197$	−10.1505	−	10.1505i	−0.723190	−	0.723190i	0.246064	−	0.969254i	$-0.420863\pi$
$197$	−10.1505	−	10.1505i	−0.723190	−	0.723190i	−0.969254	+	0.246064i	$0.920863\pi$
$198$	−3.28719	+	2.16006i	−0.233611	+	0.153509i
$199$		−	11.6748i		−	0.827604i	−0.910367	−	0.413802i	$-0.864201\pi$
$199$		−	11.6748i		−	0.827604i	0.910367	−	0.413802i	$-0.135799\pi$
$200$		0			0
$201$	−10.2789	+	8.36978i	−0.725020	+	0.590359i
$202$	1.30532	−	1.30532i	0.0918421	−	0.0918421i
$203$	−2.02886	+	2.02886i	−0.142398	+	0.142398i
$204$	10.9167	−	8.88912i	0.764324	−	0.622363i
$205$		0			0
$206$			6.14771i			0.428332i
$207$	9.03483	−	5.93692i	0.627964	−	0.412644i
$208$	5.61580	+	5.61580i	0.389386	+	0.389386i
$209$	14.0067			0.968867
$210$		0			0
$211$	−0.777102			−0.0534979			−0.0267490	−	0.999642i	$-0.508515\pi$
$211$	−0.777102			−0.0534979			−0.0267490	+	0.999642i	$0.508515\pi$
$212$	7.80300	+	7.80300i	0.535912	+	0.535912i
$213$	2.39687	−	23.4127i	0.164231	−	1.60421i
$214$			0.493091i			0.0337070i
$215$		0			0
$216$	−8.50645	+	4.42142i	−0.578790	+	0.300840i
$217$	−3.73776	+	3.73776i	−0.253736	+	0.253736i
$218$	6.59901	−	6.59901i	0.446941	−	0.446941i
$219$	6.44157	+	7.91090i	0.435281	+	0.534569i
$220$		0			0
$221$			14.0453i			0.944789i
$222$	−2.56281	−	0.262367i	−0.172005	−	0.0176089i
$223$	3.33811	+	3.33811i	0.223536	+	0.223536i	0.809986	−	0.586450i	$-0.199475\pi$
$223$	3.33811	+	3.33811i	0.223536	+	0.223536i	−0.586450	+	0.809986i	$0.699475\pi$
$224$	−4.97232			−0.332227
$225$		0			0
$226$	3.95038			0.262776
$227$	0.242326	+	0.242326i	0.0160838	+	0.0160838i	0.715103	−	0.699019i	$-0.246380\pi$
$227$	0.242326	+	0.242326i	0.0160838	+	0.0160838i	−0.699019	+	0.715103i	$0.746380\pi$
$228$	15.8925	+	1.62699i	1.05251	+	0.107750i
$229$			13.4793i			0.890735i	0.895348	+	0.445368i	$0.146927\pi$
$229$			13.4793i			0.890735i	−0.895348	+	0.445368i	$0.853073\pi$
$230$		0			0
$231$	−2.92153	−	3.58793i	−0.192223	−	0.236069i
$232$	−3.74324	+	3.74324i	−0.245756	+	0.245756i
$233$	1.19260	−	1.19260i	0.0781301	−	0.0781301i	−0.666962	−	0.745092i	$-0.732406\pi$
$233$	1.19260	−	1.19260i	0.0781301	−	0.0781301i	0.745092	+	0.666962i	$0.232406\pi$
$234$	0.906918	−	4.38299i	0.0592871	−	0.286525i
$235$		0			0
$236$		−	0.280467i		−	0.0182568i
$237$	−0.687432	+	6.71488i	−0.0446535	+	0.436178i
$238$	−1.60356	−	1.60356i	−0.103944	−	0.103944i
$239$	−5.15325			−0.333336			−0.166668	−	0.986013i	$-0.553301\pi$
$239$	−5.15325			−0.333336			−0.166668	+	0.986013i	$0.553301\pi$
$240$		0			0
$241$	−14.9174			−0.960914			−0.480457	−	0.877018i	$-0.659529\pi$
$241$	−14.9174			−0.960914			−0.480457	+	0.877018i	$0.659529\pi$
$242$	1.34094	+	1.34094i	0.0861992	+	0.0861992i
$243$	−13.6040	−	7.61123i	−0.872698	−	0.488261i
$244$		−	8.31238i		−	0.532146i
$245$		0			0
$246$	−7.63153	+	6.21409i	−0.486569	+	0.396196i
$247$	−11.2702	+	11.2702i	−0.717103	+	0.717103i
$248$	−6.89616	+	6.89616i	−0.437907	+	0.437907i
$249$	7.66953	−	6.24504i	0.486037	−	0.395763i
$250$		0			0
$251$			4.30303i			0.271605i	0.990736	+	0.135802i	$0.0433613\pi$
$251$			4.30303i			0.271605i	−0.990736	+	0.135802i	$0.956639\pi$
$252$	−2.89810	−	4.41035i	−0.182563	−	0.277826i
$253$	6.80704	+	6.80704i	0.427955	+	0.427955i
$254$	8.42409			0.528575
$255$		0			0
$256$	0.0180230			0.00112644
$257$	−5.82885	−	5.82885i	−0.363594	−	0.363594i	0.501540	−	0.865134i	$-0.332767\pi$
$257$	−5.82885	−	5.82885i	−0.363594	−	0.363594i	−0.865134	+	0.501540i	$0.832767\pi$
$258$	−0.0929433	+	0.907876i	−0.00578640	+	0.0565219i
$259$		−	3.03046i		−	0.188304i
$260$		0			0
$261$	−8.42916	−	1.74414i	−0.521752	−	0.107960i
$262$	−3.45068	+	3.45068i	−0.213184	+	0.213184i
$263$	−0.0624909	+	0.0624909i	−0.00385335	+	0.00385335i	−0.709031	−	0.705177i	$-0.750867\pi$
$263$	−0.0624909	+	0.0624909i	−0.00385335	+	0.00385335i	0.705177	+	0.709031i	$0.250867\pi$
$264$	−5.39022	−	6.61974i	−0.331745	−	0.407417i
$265$		0			0
$266$		−	2.57345i		−	0.157788i
$267$	−6.80819	−	0.696985i	−0.416654	−	0.0426548i
$268$	−9.51951	−	9.51951i	−0.581497	−	0.581497i
$269$	29.6699			1.80901			0.904504	−	0.426465i	$-0.140241\pi$
$269$	29.6699			1.80901			0.904504	+	0.426465i	$0.140241\pi$
$270$		0			0
$271$	22.6377			1.37514			0.687571	−	0.726117i	$-0.258677\pi$
$271$	22.6377			1.37514			0.687571	+	0.726117i	$0.258677\pi$
$272$	8.53611	+	8.53611i	0.517578	+	0.517578i
$273$	5.23767	+	0.536204i	0.316998	+	0.0324525i
$274$			9.48463i			0.572988i
$275$		0			0
$276$	6.93281	+	8.51419i	0.417306	+	0.512494i
$277$	−4.21136	+	4.21136i	−0.253036	+	0.253036i	−0.822214	−	0.569178i	$-0.807262\pi$
$277$	−4.21136	+	4.21136i	−0.253036	+	0.253036i	0.569178	+	0.822214i	$0.307262\pi$
$278$	−5.82817	+	5.82817i	−0.349551	+	0.349551i
$279$	−15.5290	−	3.21323i	−0.929698	−	0.192371i
$280$		0			0
$281$		−	22.0093i		−	1.31297i	−0.754341	−	0.656483i	$-0.772043\pi$
$281$		−	22.0093i		−	1.31297i	0.754341	−	0.656483i	$-0.227957\pi$
$282$	0.937914	−	9.16160i	0.0558520	−	0.545565i
$283$	−9.59899	−	9.59899i	−0.570601	−	0.570601i	0.361695	−	0.932296i	$-0.382198\pi$
$283$	−9.59899	−	9.59899i	−0.570601	−	0.570601i	−0.932296	+	0.361695i	$0.882198\pi$
$284$	23.9027			1.41837
$285$		0			0
$286$	3.98553			0.235670
$287$	−8.18605	−	8.18605i	−0.483207	−	0.483207i
$288$	−8.19181	−	12.4664i	−0.482707	−	0.734587i
$289$			4.34908i			0.255828i
$290$		0			0
$291$	−3.54963	+	2.89034i	−0.208083	+	0.169435i
$292$	−7.32643	+	7.32643i	−0.428747	+	0.428747i
$293$	3.56359	−	3.56359i	0.208187	−	0.208187i	−0.595309	−	0.803497i	$-0.702970\pi$
$293$	3.56359	−	3.56359i	0.208187	−	0.208187i	0.803497	+	0.595309i	$0.202970\pi$
$294$	−0.659208	+	0.536770i	−0.0384458	+	0.0313051i
$295$		0			0
$296$		−	5.59120i		−	0.324982i
$297$	4.18231	−	13.2358i	0.242683	−	0.768018i
$298$	−3.23196	−	3.23196i	−0.187222	−	0.187222i
$299$	−10.9542			−0.633499
$300$		0			0
$301$	−1.07354			−0.0618778
$302$	7.07531	+	7.07531i	0.407139	+	0.407139i
$303$	−0.663452	+	6.48063i	−0.0381143	+	0.372303i
$304$			13.6990i			0.785692i
$305$		0			0
$306$	1.37853	−	6.66222i	0.0788053	−	0.380854i
$307$	−10.4746	+	10.4746i	−0.597814	+	0.597814i	−0.939730	−	0.341916i	$-0.888924\pi$
$307$	−10.4746	+	10.4746i	−0.597814	+	0.597814i	0.341916	+	0.939730i	$0.388924\pi$
$308$	3.32285	−	3.32285i	0.189337	−	0.189337i
$309$	−13.6987	−	16.8234i	−0.779291	−	0.957048i
$310$		0			0
$311$		−	20.4344i		−	1.15873i	−0.815068	−	0.579365i	$-0.803301\pi$
$311$		−	20.4344i		−	1.15873i	0.815068	−	0.579365i	$-0.196699\pi$
$312$	9.66350	+	0.989296i	0.547088	+	0.0560078i
$313$	16.4829	+	16.4829i	0.931670	+	0.931670i	0.997810	−	0.0661408i	$-0.0210686\pi$
$313$	16.4829	+	16.4829i	0.931670	+	0.931670i	−0.0661408	+	0.997810i	$0.521069\pi$
$314$	−4.39291			−0.247906
$315$		0			0
$316$	−6.85542			−0.385647
$317$	−22.9540	−	22.9540i	−1.28922	−	1.28922i	−0.935259	−	0.353965i	$-0.884833\pi$
$317$	−22.9540	−	22.9540i	−1.28922	−	1.28922i	−0.353965	−	0.935259i	$-0.615167\pi$
$318$	5.30509	+	0.543105i	0.297494	+	0.0304558i
$319$		−	7.66479i		−	0.429146i
$320$		0			0
$321$	−1.09873	−	1.34936i	−0.0613254	−	0.0753137i
$322$	1.25065	−	1.25065i	0.0696961	−	0.0696961i
$323$	−17.1308	+	17.1308i	−0.953185	+	0.953185i
$324$	6.28283	−	14.5319i	0.349046	−	0.807330i
$325$		0			0
$326$			4.48142i			0.248203i
$327$	−3.35406	+	32.7626i	−0.185480	+	1.81178i
$328$	−15.1033	−	15.1033i	−0.833938	−	0.833938i
$329$	10.8334			0.597262
$330$		0			0
$331$	−2.21461			−0.121726			−0.0608631	−	0.998146i	$-0.519385\pi$
$331$	−2.21461			−0.121726			−0.0608631	+	0.998146i	$0.519385\pi$
$332$	7.10290	+	7.10290i	0.389822	+	0.389822i
$333$	7.59782	−	4.99263i	0.416358	−	0.273595i
$334$			1.09672i			0.0600099i
$335$		0			0
$336$	3.50910	−	2.85734i	0.191437	−	0.155881i
$337$	−10.8541	+	10.8541i	−0.591263	+	0.591263i	−0.937972	−	0.346710i	$-0.887299\pi$
$337$	−10.8541	+	10.8541i	−0.591263	+	0.591263i	0.346710	+	0.937972i	$0.387299\pi$
$338$	1.30484	−	1.30484i	0.0709741	−	0.0709741i
$339$	−10.8103	+	8.80247i	−0.587136	+	0.478085i
$340$		0			0
$341$		−	14.1208i		−	0.764685i
$342$	6.45202	−	4.23971i	0.348885	−	0.229257i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−1.98068			−0.106791
$345$		0			0
$346$	−1.17977			−0.0634251
$347$	−5.06341	−	5.06341i	−0.271818	−	0.271818i	0.558014	−	0.829832i	$-0.311564\pi$
$347$	−5.06341	−	5.06341i	−0.271818	−	0.271818i	−0.829832	+	0.558014i	$0.811564\pi$
$348$	0.890323	−	8.69672i	0.0477263	−	0.466193i
$349$			7.42733i			0.397576i	0.980043	+	0.198788i	$0.0637005\pi$
$349$			7.42733i			0.397576i	−0.980043	+	0.198788i	$0.936300\pi$
$350$		0			0
$351$	7.28463	+	14.0150i	0.388825	+	0.748066i
$352$	9.39243	−	9.39243i	0.500618	−	0.500618i
$353$	9.09032	−	9.09032i	0.483829	−	0.483829i	−0.422523	−	0.906352i	$-0.638856\pi$
$353$	9.09032	−	9.09032i	0.483829	−	0.483829i	0.906352	+	0.422523i	$0.138856\pi$
$354$	−0.0855810	−	0.105102i	−0.00454858	−	0.00558611i
$355$		0			0
$356$		−	6.95068i		−	0.368385i
$357$	7.96134	+	0.815038i	0.421359	+	0.0431364i
$358$	2.93045	+	2.93045i	0.154879	+	0.154879i
$359$	−25.2640			−1.33338			−0.666692	−	0.745333i	$-0.732290\pi$
$359$	−25.2640			−1.33338			−0.666692	+	0.745333i	$0.732290\pi$
$360$		0			0
$361$	−8.49208			−0.446951
$362$	1.91394	+	1.91394i	0.100594	+	0.100594i
$363$	−6.65750	−	0.681558i	−0.349428	−	0.0357725i
$364$			5.34729i			0.280274i
$365$		0			0
$366$	−2.53642	−	3.11498i	−0.132581	−	0.162823i
$367$	−1.61189	+	1.61189i	−0.0841399	+	0.0841399i	−0.747924	−	0.663784i	$-0.768949\pi$
$367$	−1.61189	+	1.61189i	−0.0841399	+	0.0841399i	0.663784	+	0.747924i	$0.268949\pi$
$368$	−6.65749	+	6.65749i	−0.347045	+	0.347045i
$369$	7.03727	−	34.0100i	0.366346	−	1.77049i
$370$		0			0
$371$			6.27313i			0.325685i
$372$	1.64024	−	16.0219i	0.0850424	−	0.830699i
$373$	−13.0455	−	13.0455i	−0.675469	−	0.675469i	0.283502	−	0.958972i	$-0.408504\pi$
$373$	−13.0455	−	13.0455i	−0.675469	−	0.675469i	−0.958972	+	0.283502i	$0.908504\pi$
$374$	6.05808			0.313256
$375$		0			0
$376$	19.9875			1.03078
$377$	6.16727	+	6.16727i	0.317630	+	0.317630i
$378$	−2.43180	−	0.768413i	−0.125078	−	0.0395229i
$379$			19.0635i			0.979228i	0.871939	+	0.489614i	$0.162862\pi$
$379$			19.0635i			0.979228i	−0.871939	+	0.489614i	$0.837138\pi$
$380$		0			0
$381$	−23.0527	+	18.7710i	−1.18103	+	0.961670i
$382$	−0.194185	+	0.194185i	−0.00993537	+	0.00993537i
$383$	17.7244	−	17.7244i	0.905673	−	0.905673i	−0.0902463	−	0.995919i	$-0.528765\pi$
$383$	17.7244	−	17.7244i	0.905673	−	0.905673i	0.995919	+	0.0902463i	$0.0287654\pi$
$384$	15.1925	−	12.3708i	0.775291	−	0.631293i
$385$		0			0
$386$		−	4.89484i		−	0.249141i
$387$	−1.76864	−	2.69153i	−0.0899050	−	0.136818i
$388$	−3.28738	−	3.28738i	−0.166892	−	0.166892i
$389$	−18.3513			−0.930446			−0.465223	−	0.885193i	$-0.654026\pi$
$389$	−18.3513			−0.930446			−0.465223	+	0.885193i	$0.654026\pi$
$390$		0			0
$391$	−16.6506			−0.842056
$392$	−1.30461	−	1.30461i	−0.0658928	−	0.0658928i
$393$	1.75387	−	17.1319i	0.0884710	−	0.864189i
$394$		−	7.04550i		−	0.354947i
$395$		0			0
$396$	13.8052	+	2.85655i	0.693739	+	0.143547i
$397$	10.9124	−	10.9124i	0.547679	−	0.547679i	−0.378090	−	0.925769i	$-0.623419\pi$
$397$	10.9124	−	10.9124i	0.547679	−	0.547679i	0.925769	+	0.378090i	$0.123419\pi$
$398$	4.05178	−	4.05178i	0.203097	−	0.203097i
$399$	5.73430	+	7.04230i	0.287074	+	0.352556i
$400$		0			0
$401$			34.4243i			1.71907i	0.511079	+	0.859534i	$0.329246\pi$
$401$			34.4243i			1.71907i	−0.511079	+	0.859534i	$0.670754\pi$
$402$	−6.47210	−	0.662578i	−0.322799	−	0.0330464i
$403$	11.3619	+	11.3619i	0.565979	+	0.565979i
$404$	−6.61627			−0.329172
$405$		0			0
$406$	−1.40824			−0.0698900
$407$	5.72437	+	5.72437i	0.283746	+	0.283746i
$408$	14.6887	+	1.50375i	0.727198	+	0.0744465i
$409$			7.59254i			0.375427i	0.982224	+	0.187714i	$0.0601077\pi$
$409$			7.59254i			0.375427i	−0.982224	+	0.187714i	$0.939892\pi$
$410$		0			0
$411$	−21.1342	−	25.9549i	−1.04247	−	1.28026i
$412$	15.5804	−	15.5804i	0.767593	−	0.767593i
$413$	0.112739	−	0.112739i	0.00554752	−	0.00554752i
$414$	5.19600	+	1.07514i	0.255369	+	0.0528404i
$415$		0			0
$416$			15.1147i			0.741061i
$417$	2.96227	−	28.9356i	0.145063	−	1.41698i
$418$	4.86109	+	4.86109i	0.237764	+	0.237764i
$419$	−6.20644			−0.303204			−0.151602	−	0.988442i	$-0.548443\pi$
$419$	−6.20644			−0.303204			−0.151602	+	0.988442i	$0.548443\pi$
$420$		0			0
$421$	25.1339			1.22495			0.612474	−	0.790490i	$-0.290174\pi$
$421$	25.1339			1.22495			0.612474	+	0.790490i	$0.290174\pi$
$422$	−0.269696	−	0.269696i	−0.0131286	−	0.0131286i
$423$	17.8478	+	27.1608i	0.867788	+	1.32061i
$424$			11.5739i			0.562079i
$425$		0			0
$426$	8.95731	−	7.29363i	0.433983	−	0.353377i
$427$	3.34132	−	3.34132i	0.161698	−	0.161698i
$428$	1.24966	−	1.24966i	0.0604048	−	0.0604048i
$429$	−10.9065	+	8.88079i	−0.526571	+	0.428769i
$430$		0			0
$431$		−	8.43225i		−	0.406167i	−0.979161	−	0.203084i	$-0.934904\pi$
$431$		−	8.43225i		−	0.406167i	0.979161	−	0.203084i	$-0.0650963\pi$
$432$	12.9450	+	4.09043i	0.622815	+	0.196801i
$433$	18.8277	+	18.8277i	0.904802	+	0.904802i	0.995847	−	0.0910444i	$-0.0290205\pi$
$433$	18.8277	+	18.8277i	0.904802	+	0.904802i	−0.0910444	+	0.995847i	$0.529021\pi$
$434$	−2.59440			−0.124535
$435$		0			0
$436$	−33.4483			−1.60188
$437$	−13.3607	−	13.3607i	−0.639128	−	0.639128i
$438$	−0.509935	+	4.98108i	−0.0243657	+	0.238005i
$439$			4.88270i			0.233039i	0.993188	+	0.116519i	$0.0371737\pi$
$439$			4.88270i			0.233039i	−0.993188	+	0.116519i	$0.962826\pi$
$440$		0			0
$441$	0.607876	−	2.93777i	0.0289465	−	0.139894i
$442$	−4.87447	+	4.87447i	−0.231855	+	0.231855i
$443$	−23.8960	+	23.8960i	−1.13534	+	1.13534i	−0.146059	+	0.989276i	$0.546659\pi$
$443$	−23.8960	+	23.8960i	−1.13534	+	1.13534i	−0.989276	+	0.146059i	$0.953341\pi$
$444$	5.83013	+	7.15998i	0.276686	+	0.339798i
$445$		0			0
$446$			2.31700i			0.109713i
$447$	16.0460	+	1.64270i	0.758948	+	0.0776970i
$448$	1.96922	+	1.96922i	0.0930368	+	0.0930368i
$449$	−23.6736			−1.11723			−0.558613	−	0.829428i	$-0.688666\pi$
$449$	−23.6736			−1.11723			−0.558613	+	0.829428i	$0.688666\pi$
$450$		0			0
$451$	30.9259			1.45625
$452$	−10.0116	−	10.0116i	−0.470908	−	0.470908i
$453$	−35.1274	−	3.59615i	−1.65043	−	0.168962i
$454$			0.168200i			0.00789404i
$455$		0			0
$456$	10.5798	+	12.9930i	0.495444	+	0.608455i
$457$	−10.2580	+	10.2580i	−0.479849	+	0.479849i	−0.905083	−	0.425234i	$-0.860192\pi$
$457$	−10.2580	+	10.2580i	−0.479849	+	0.479849i	0.425234	+	0.905083i	$0.360192\pi$
$458$	−4.67803	+	4.67803i	−0.218590	+	0.218590i
$459$	11.0728	+	21.3030i	0.516832	+	0.994341i
$460$		0			0
$461$			23.3153i			1.08590i	0.839764	+	0.542951i	$0.182693\pi$
$461$			23.3153i			1.08590i	−0.839764	+	0.542951i	$0.817307\pi$
$462$	0.231278	−	2.25913i	0.0107600	−	0.105104i
$463$	17.0563	+	17.0563i	0.792672	+	0.792672i	0.981928	−	0.189256i	$-0.0606077\pi$
$463$	17.0563	+	17.0563i	0.792672	+	0.792672i	−0.189256	+	0.981928i	$0.560608\pi$
$464$	7.49639			0.348011
$465$		0			0
$466$	0.827796			0.0383469
$467$	8.00621	+	8.00621i	0.370483	+	0.370483i	0.867653	−	0.497170i	$-0.165627\pi$
$467$	8.00621	+	8.00621i	0.370483	+	0.370483i	−0.497170	+	0.867653i	$0.665627\pi$
$468$	−13.4065	+	8.80957i	−0.619714	+	0.407223i
$469$		−	7.65310i		−	0.353387i
$470$		0			0
$471$	12.0213	−	9.78854i	0.553913	−	0.451032i
$472$	0.208003	−	0.208003i	0.00957413	−	0.00957413i
$473$	2.02786	−	2.02786i	0.0932409	−	0.0932409i
$474$	−2.56900	+	2.09185i	−0.117998	+	0.0960817i
$475$		0			0
$476$			8.12797i			0.372545i
$477$	−15.7277	+	10.3349i	−0.720121	+	0.473201i
$478$	−1.78845	−	1.78845i	−0.0818019	−	0.0818019i
$479$	−20.1199			−0.919304			−0.459652	−	0.888099i	$-0.652026\pi$
$479$	−20.1199			−0.919304			−0.459652	+	0.888099i	$0.652026\pi$
$480$		0			0
$481$	−9.21192			−0.420027
$482$	−5.17713	−	5.17713i	−0.235812	−	0.235812i
$483$	−0.635665	+	6.20921i	−0.0289238	+	0.282529i
$484$		−	6.79683i		−	0.308947i
$485$		0			0
$486$	−2.07982	−	7.36283i	−0.0943425	−	0.333985i
$487$	−7.77959	+	7.77959i	−0.352527	+	0.352527i	−0.861049	−	0.508522i	$-0.830192\pi$
$487$	−7.77959	+	7.77959i	−0.352527	+	0.352527i	0.508522	+	0.861049i	$0.330192\pi$
$488$	6.16474	−	6.16474i	0.279064	−	0.279064i
$489$	−9.98576	−	12.2635i	−0.451572	−	0.554576i
$490$		0			0
$491$		−	2.29546i		−	0.103593i	−0.998658	−	0.0517963i	$-0.983505\pi$
$491$		−	2.29546i		−	0.103593i	0.998658	−	0.0517963i	$-0.0164947\pi$
$492$	35.0896	+	3.59228i	1.58196	+	0.161952i
$493$	9.37435	+	9.37435i	0.422199	+	0.422199i
$494$	−7.82270			−0.351960
$495$		0			0
$496$	13.8106			0.620113
$497$	9.60816	+	9.60816i	0.430985	+	0.430985i
$498$	4.82910	+	0.494377i	0.216397	+	0.0221536i
$499$			12.3264i			0.551806i	0.961185	+	0.275903i	$0.0889769\pi$
$499$			12.3264i			0.551806i	−0.961185	+	0.275903i	$0.911023\pi$
$500$		0			0
$501$	−2.44378	−	3.00120i	−0.109180	−	0.134084i
$502$	−1.49338	+	1.49338i	−0.0666529	+	0.0666529i
$503$	−4.62523	+	4.62523i	−0.206229	+	0.206229i	−0.802662	−	0.596434i	$-0.796584\pi$
$503$	−4.62523	+	4.62523i	−0.206229	+	0.206229i	0.596434	+	0.802662i	$0.296584\pi$
$504$	1.12153	−	5.42018i	0.0499570	−	0.241434i
$505$		0			0
$506$			4.72482i			0.210044i
$507$	−0.663208	+	6.47826i	−0.0294541	+	0.287709i
$508$	−21.3496	−	21.3496i	−0.947234	−	0.947234i
$509$	13.6161			0.603525			0.301762	−	0.953383i	$-0.402425\pi$
$509$	13.6161			0.603525			0.301762	+	0.953383i	$0.402425\pi$
$510$		0			0
$511$	−5.89000			−0.260558
$512$	16.0031	+	16.0031i	0.707245	+	0.707245i
$513$	−8.20894	+	25.9788i	−0.362433	+	1.14699i
$514$		−	4.04585i		−	0.178455i
$515$		0			0
$516$	2.53642	−	2.06532i	0.111660	−	0.0909207i
$517$	−20.4636	+	20.4636i	−0.899987	+	0.899987i
$518$	1.05173	−	1.05173i	0.0462105	−	0.0462105i
$519$	3.22848	−	2.62884i	0.141715	−	0.115393i
$520$		0			0
$521$		−	18.3870i		−	0.805550i	−0.915299	−	0.402775i	$-0.868046\pi$
$521$		−	18.3870i		−	0.805550i	0.915299	−	0.402775i	$-0.131954\pi$
$522$	−2.32006	−	3.53068i	−0.101546	−	0.154534i
$523$	8.91043	+	8.91043i	0.389626	+	0.389626i	0.874554	−	0.484928i	$-0.161154\pi$
$523$	8.91043	+	8.91043i	0.389626	+	0.389626i	−0.484928	+	0.874554i	$0.661154\pi$
$524$	17.4905			0.764074
$525$		0			0
$526$	−0.0433754			−0.00189126
$527$	17.2703	+	17.2703i	0.752308	+	0.752308i
$528$	−1.23114	+	12.0258i	−0.0535785	+	0.523358i
$529$			10.0139i			0.435385i
$530$		0			0
$531$	0.468389	+	0.0969179i	0.0203264	+	0.00420588i
$532$	−6.52201	+	6.52201i	−0.282765	+	0.282765i
$533$	−24.8837	+	24.8837i	−1.07783	+	1.07783i
$534$	−2.12091	−	2.60470i	−0.0917810	−	0.112716i
$535$		0			0
$536$		−	14.1200i		−	0.609889i
$537$	−14.5491	−	1.48945i	−0.627838	−	0.0642746i
$538$	10.2971	+	10.2971i	0.443938	+	0.443938i
$539$	2.67137			0.115064
$540$		0			0
$541$	27.8258			1.19632			0.598162	−	0.801375i	$-0.295898\pi$
$541$	27.8258			1.19632			0.598162	+	0.801375i	$0.295898\pi$
$542$	7.85649	+	7.85649i	0.337465	+	0.337465i
$543$	−9.50229	−	0.972793i	−0.407783	−	0.0417465i
$544$			22.9746i			0.985030i
$545$		0			0
$546$	1.63166	+	2.00384i	0.0698286	+	0.0857566i
$547$	13.2773	−	13.2773i	0.567695	−	0.567695i	−0.363787	−	0.931482i	$-0.618517\pi$
$547$	13.2773	−	13.2773i	0.567695	−	0.567695i	0.931482	+	0.363787i	$0.118517\pi$
$548$	24.0373	−	24.0373i	1.02682	−	1.02682i
$549$	13.8820	+	2.87242i	0.592468	+	0.122592i
$550$		0			0
$551$			15.0442i			0.640906i
$552$	−1.17280	+	11.4560i	−0.0499178	+	0.487600i
$553$	−2.75566	−	2.75566i	−0.117183	−	0.117183i
$554$	−2.92314			−0.124192
$555$		0			0
$556$	29.5412			1.25283
$557$	10.4002	+	10.4002i	0.440672	+	0.440672i	0.892238	−	0.451566i	$-0.149134\pi$
$557$	10.4002	+	10.4002i	0.440672	+	0.440672i	−0.451566	+	0.892238i	$0.649134\pi$
$558$	−4.27424	−	6.50456i	−0.180943	−	0.275360i
$559$			3.26332i			0.138024i
$560$		0			0
$561$	−16.5781	+	13.4990i	−0.699927	+	0.569926i
$562$	7.63842	−	7.63842i	0.322207	−	0.322207i
$563$	−10.1623	+	10.1623i	−0.428291	+	0.428291i	−0.888046	−	0.459755i	$-0.847937\pi$
$563$	−10.1623	+	10.1623i	−0.428291	+	0.428291i	0.459755	+	0.888046i	$0.347937\pi$
$564$	−25.5957	+	20.8417i	−1.07777	+	0.877592i
$565$		0			0
$566$		−	6.66273i		−	0.280055i
$567$	8.36689	−	3.31589i	0.351376	−	0.139254i
$568$	17.7271	+	17.7271i	0.743811	+	0.743811i
$569$	39.8275			1.66965			0.834827	−	0.550512i	$-0.185567\pi$
$569$	39.8275			1.66965			0.834827	+	0.550512i	$0.185567\pi$
$570$		0			0
$571$	−43.8314			−1.83429			−0.917143	−	0.398558i	$-0.869511\pi$
$571$	−43.8314			−1.83429			−0.917143	+	0.398558i	$0.869511\pi$
$572$	−10.1007	−	10.1007i	−0.422332	−	0.422332i
$573$	0.0986978	−	0.964086i	0.00412316	−	0.0402753i
$574$		−	5.68199i		−	0.237162i
$575$		0			0
$576$	−1.69287	+	8.18138i	−0.0705363	+	0.340891i
$577$	27.8182	−	27.8182i	1.15809	−	1.15809i	0.173202	−	0.984886i	$-0.444589\pi$
$577$	27.8182	−	27.8182i	1.15809	−	1.15809i	0.984886	−	0.173202i	$-0.0554114\pi$
$578$	−1.50936	+	1.50936i	−0.0627812	+	0.0627812i
$579$	10.9070	+	13.3948i	0.453278	+	0.556670i
$580$		0			0
$581$			5.71029i			0.236903i
$582$	−2.23502	−	0.228809i	−0.0926445	−	0.00948443i
$583$	−11.8496	−	11.8496i	−0.490759	−	0.490759i
$584$	−10.8670			−0.449681
$585$		0			0
$586$	2.47352			0.102180
$587$	−27.2778	−	27.2778i	−1.12588	−	1.12588i	−0.990841	−	0.135034i	$-0.956886\pi$
$587$	−27.2778	−	27.2778i	−1.12588	−	1.12588i	−0.135034	−	0.990841i	$-0.543114\pi$
$588$	3.03102	+	0.310299i	0.124997	+	0.0127965i
$589$			27.7160i			1.14202i
$590$		0			0
$591$	15.6992	+	19.2802i	0.645779	+	0.793081i
$592$	−5.59860	+	5.59860i	−0.230101	+	0.230101i
$593$	1.21000	−	1.21000i	0.0496886	−	0.0496886i	−0.681826	−	0.731515i	$-0.738814\pi$
$593$	1.21000	−	1.21000i	0.0496886	−	0.0496886i	0.731515	+	0.681826i	$0.238814\pi$
$594$	6.04501	−	3.14204i	0.248030	−	0.128919i
$595$		0			0
$596$			16.3818i			0.671025i
$597$	−2.05939	+	20.1162i	−0.0842850	+	0.823301i
$598$	−3.80170	−	3.80170i	−0.155463	−	0.155463i
$599$	−15.6005			−0.637421			−0.318710	−	0.947852i	$-0.603250\pi$
$599$	−15.6005			−0.637421			−0.318710	+	0.947852i	$0.603250\pi$
$600$		0			0
$601$	14.2954			0.583122			0.291561	−	0.956552i	$-0.405825\pi$
$601$	14.2954			0.583122			0.291561	+	0.956552i	$0.405825\pi$
$602$	−0.372576	−	0.372576i	−0.0151851	−	0.0151851i
$603$	19.1875	−	12.6083i	0.781374	−	0.513452i
$604$		−	35.8626i		−	1.45923i
$605$		0			0
$606$	−2.47938	+	2.01887i	−0.100718	+	0.0820111i
$607$	26.8784	−	26.8784i	1.09096	−	1.09096i	0.0955365	−	0.995426i	$-0.469543\pi$
$607$	26.8784	−	26.8784i	1.09096	−	1.09096i	0.995426	−	0.0955365i	$-0.0304567\pi$
$608$	−18.4352	+	18.4352i	−0.747646	+	0.747646i
$609$	3.85369	−	3.13793i	0.156160	−	0.127155i
$610$		0			0
$611$		−	32.9310i		−	1.33224i
$612$	−20.3780	+	13.3907i	−0.823733	+	0.541287i
$613$	−2.77744	−	2.77744i	−0.112180	−	0.112180i	0.648789	−	0.760969i	$-0.275276\pi$
$613$	−2.77744	−	2.77744i	−0.112180	−	0.112180i	−0.760969	+	0.648789i	$0.775276\pi$
$614$	−7.27046			−0.293412
$615$		0			0
$616$	4.92867			0.198582
$617$	3.21465	+	3.21465i	0.129417	+	0.129417i	0.768848	−	0.639431i	$-0.220830\pi$
$617$	3.21465	+	3.21465i	0.129417	+	0.129417i	−0.639431	+	0.768848i	$0.720830\pi$
$618$	1.08443	−	10.5928i	0.0436222	−	0.426104i
$619$		−	48.7011i		−	1.95746i	−0.205146	−	0.978731i	$-0.565767\pi$
$619$		−	48.7011i		−	1.95746i	0.205146	−	0.978731i	$-0.434233\pi$
$620$		0			0
$621$	−16.6147	+	8.63587i	−0.666724	+	0.346545i
$622$	7.09184	−	7.09184i	0.284357	−	0.284357i
$623$	2.79396	−	2.79396i	0.111938	−	0.111938i
$624$	−8.68567	−	10.6669i	−0.347705	−	0.427017i
$625$		0			0
$626$			11.4409i			0.457271i
$627$	−24.1343	−	2.47073i	−0.963830	−	0.0986716i
$628$	11.1332	+	11.1332i	0.444261	+	0.444261i
$629$	−14.0023			−0.558307
$630$		0			0
$631$	15.0588			0.599480			0.299740	−	0.954021i	$-0.403100\pi$
$631$	15.0588			0.599480			0.299740	+	0.954021i	$0.403100\pi$
$632$	−5.08420	−	5.08420i	−0.202239	−	0.202239i
$633$	1.33898	+	0.137078i	0.0532197	+	0.00544834i
$634$		−	15.9325i		−	0.632761i
$635$		0			0
$636$	−12.0685	−	14.8213i	−0.478547	−	0.587704i
$637$	−2.14945	+	2.14945i	−0.0851641	+	0.0851641i
$638$	2.66009	−	2.66009i	0.105314	−	0.105314i
$639$	−8.25981	+	39.9184i	−0.326753	+	1.57915i
$640$		0			0
$641$		−	45.9720i		−	1.81578i	−0.419204	−	0.907892i	$-0.637691\pi$
$641$		−	45.9720i		−	1.81578i	0.419204	−	0.907892i	$-0.362309\pi$
$642$	0.0869793	−	0.849619i	0.00343280	−	0.0335318i
$643$	5.91991	+	5.91991i	0.233458	+	0.233458i	0.814135	−	0.580676i	$-0.197212\pi$
$643$	5.91991	+	5.91991i	0.233458	+	0.233458i	−0.580676	+	0.814135i	$0.697212\pi$
$644$	−6.33917			−0.249798
$645$		0			0
$646$	−11.8906			−0.467831
$647$	11.1176	+	11.1176i	0.437079	+	0.437079i	0.891028	−	0.453949i	$-0.149985\pi$
$647$	11.1176	+	11.1176i	0.437079	+	0.437079i	−0.453949	+	0.891028i	$0.649985\pi$
$648$	15.4369	−	6.11781i	0.606419	−	0.240330i
$649$			0.425915i			0.0167186i
$650$		0			0
$651$	7.09965	−	5.78100i	0.278257	−	0.226575i
$652$	11.3575	−	11.3575i	0.444793	−	0.444793i
$653$	30.6500	−	30.6500i	1.19943	−	1.19943i	0.225088	−	0.974339i	$-0.427733\pi$
$653$	30.6500	−	30.6500i	1.19943	−	1.19943i	0.974339	−	0.225088i	$-0.0722669\pi$
$654$	−12.5344	+	10.2063i	−0.490135	+	0.399100i
$655$		0			0
$656$			30.2465i			1.18093i
$657$	−9.70367	−	14.7671i	−0.378576	−	0.576120i
$658$	3.75976	+	3.75976i	0.146571	+	0.146571i
$659$	50.9397			1.98433			0.992165	−	0.124933i	$-0.0398714\pi$
$659$	50.9397			1.98433			0.992165	+	0.124933i	$0.0398714\pi$
$660$		0			0
$661$	−20.5394			−0.798889			−0.399445	−	0.916757i	$-0.630797\pi$
$661$	−20.5394			−0.798889			−0.399445	+	0.916757i	$0.630797\pi$
$662$	−0.768589	−	0.768589i	−0.0298721	−	0.0298721i
$663$	2.47753	−	24.2007i	0.0962194	−	0.939877i
$664$			10.5355i			0.408856i
$665$		0			0
$666$	4.36956	+	0.904139i	0.169317	+	0.0350347i
$667$	−7.31125	+	7.31125i	−0.283093	+	0.283093i
$668$	2.77947	−	2.77947i	0.107541	−	0.107541i
$669$	−5.16288	−	6.34054i	−0.199609	−	0.245139i
$670$		0			0
$671$			12.6231i			0.487310i
$672$	8.56753	+	0.877097i	0.330500	+	0.0338347i
$673$	−25.4635	−	25.4635i	−0.981544	−	0.981544i	0.0182887	−	0.999833i	$-0.494178\pi$
$673$	−25.4635	−	25.4635i	−0.981544	−	0.981544i	−0.999833	+	0.0182887i	$0.994178\pi$
$674$	−7.53394			−0.290196
$675$		0			0
$676$	−6.61384			−0.254379
$677$	−8.67613	−	8.67613i	−0.333451	−	0.333451i	0.520445	−	0.853895i	$-0.325766\pi$
$677$	−8.67613	−	8.67613i	−0.333451	−	0.333451i	−0.853895	+	0.520445i	$0.825766\pi$
$678$	−6.80669	−	0.696831i	−0.261409	−	0.0267616i
$679$		−	2.64285i		−	0.101423i
$680$		0			0
$681$	−0.374794	−	0.460284i	−0.0143621	−	0.0176381i
$682$	4.90068	−	4.90068i	0.187657	−	0.187657i
$683$	24.0010	−	24.0010i	0.918373	−	0.918373i	−0.0785378	−	0.996911i	$-0.525025\pi$
$683$	24.0010	−	24.0010i	0.918373	−	0.918373i	0.996911	+	0.0785378i	$0.0250251\pi$
$684$	−27.0965	−	5.60675i	−1.03606	−	0.214379i
$685$		0			0
$686$		−	0.490808i		−	0.0187391i
$687$	2.37769	−	23.2254i	0.0907145	−	0.886104i
$688$	1.98330	+	1.98330i	0.0756127	+	0.0756127i
$689$	19.0689			0.726467
$690$		0			0
$691$	−32.5680			−1.23894			−0.619472	−	0.785019i	$-0.712653\pi$
$691$	−32.5680			−1.23894			−0.619472	+	0.785019i	$0.712653\pi$
$692$	2.98996	+	2.98996i	0.113661	+	0.113661i
$693$	4.40103	+	6.69752i	0.167181	+	0.254418i
$694$		−	3.51455i		−	0.133410i
$695$		0			0
$696$	7.11007	−	5.78948i	0.269506	−	0.219450i
$697$	−37.8237	+	37.8237i	−1.43267	+	1.43267i
$698$	−2.57768	+	2.57768i	−0.0975667	+	0.0975667i
$699$	−2.26528	+	1.84454i	−0.0856808	+	0.0697670i
$700$		0			0
$701$			2.43359i			0.0919155i	0.998943	+	0.0459577i	$0.0146340\pi$
$701$			2.43359i			0.0919155i	−0.998943	+	0.0459577i	$0.985366\pi$
$702$	−2.33580	+	7.39211i	−0.0881592	+	0.278997i
$703$	−11.2356	−	11.2356i	−0.423760	−	0.423760i
$704$	−7.43948			−0.280386
$705$		0			0
$706$	6.30965			0.237467
$707$	−2.65954	−	2.65954i	−0.100022	−	0.100022i
$708$	−0.0494732	+	0.483257i	−0.00185932	+	0.0181619i
$709$		−	12.3477i		−	0.463728i	−0.972748	−	0.231864i	$-0.925518\pi$
$709$		−	12.3477i		−	0.463728i	0.972748	−	0.231864i	$-0.0744825\pi$
$710$		0			0
$711$	2.36895	−	11.4488i	0.0888427	−	0.429363i
$712$	5.15485	−	5.15485i	0.193186	−	0.193186i
$713$	−13.4695	+	13.4695i	−0.504436	+	0.504436i
$714$	2.48015	+	3.04587i	0.0928173	+	0.113989i
$715$		0			0
$716$		−	14.8536i		−	0.555103i
$717$	8.87927	+	0.909011i	0.331603	+	0.0339476i
$718$	−8.76797	−	8.76797i	−0.327218	−	0.327218i
$719$	24.2165			0.903125			0.451562	−	0.892240i	$-0.350867\pi$
$719$	24.2165			0.903125			0.451562	+	0.892240i	$0.350867\pi$
$720$		0			0
$721$	12.5257			0.466482
$722$	−2.94721	−	2.94721i	−0.109684	−	0.109684i
$723$	25.7033	+	2.63137i	0.955917	+	0.0978616i
$724$		−	9.70117i		−	0.360541i
$725$		0			0
$726$	−2.07397	−	2.54704i	−0.0769723	−	0.0945297i
$727$	25.8923	−	25.8923i	0.960293	−	0.960293i	−0.0389483	−	0.999241i	$-0.512401\pi$
$727$	25.8923	−	25.8923i	0.960293	−	0.960293i	0.999241	+	0.0389483i	$0.0124008\pi$
$728$	−3.96573	+	3.96573i	−0.146980	+	0.146980i
$729$	22.0977	+	15.5142i	0.818435	+	0.574599i
$730$		0			0
$731$			4.96030i			0.183463i
$732$	−1.46627	+	14.3226i	−0.0541949	+	0.529379i
$733$	−13.4535	−	13.4535i	−0.496918	−	0.496918i	0.413559	−	0.910477i	$-0.364285\pi$
$733$	−13.4535	−	13.4535i	−0.496918	−	0.496918i	−0.910477	+	0.413559i	$0.864285\pi$
$734$	−1.11882			−0.0412965
$735$		0			0
$736$	−17.9184			−0.660481
$737$	14.4563	+	14.4563i	0.532503	+	0.532503i
$738$	14.2456	−	9.36099i	0.524388	−	0.344583i
$739$		−	1.96813i		−	0.0723987i	−0.999345	−	0.0361994i	$-0.988475\pi$
$739$		−	1.96813i		−	0.0723987i	0.999345	−	0.0361994i	$-0.0115251\pi$
$740$		0			0
$741$	21.4070	−	17.4310i	0.786406	−	0.640343i
$742$	−2.17711	+	2.17711i	−0.0799243	+	0.0799243i
$743$	4.54680	−	4.54680i	0.166806	−	0.166806i	−0.618768	−	0.785574i	$-0.712368\pi$
$743$	4.54680	−	4.54680i	0.166806	−	0.166806i	0.785574	+	0.618768i	$0.212368\pi$
$744$	13.0989	−	10.6659i	0.480227	−	0.391032i
$745$		0			0
$746$		−	9.05496i		−	0.331526i
$747$	−14.3166	+	9.40761i	−0.523815	+	0.344206i
$748$	−15.3533	−	15.3533i	−0.561371	−	0.561371i
$749$	1.00465			0.0367092
$750$		0			0
$751$	−0.491718			−0.0179430			−0.00897152	−	0.999960i	$-0.502856\pi$
$751$	−0.491718			−0.0179430			−0.00897152	+	0.999960i	$0.502856\pi$
$752$	−20.0140	−	20.0140i	−0.729835	−	0.729835i
$753$	0.759037	−	7.41432i	0.0276609	−	0.270193i
$754$			4.28075i			0.155896i
$755$		0			0
$756$	4.21559	+	8.11044i	0.153320	+	0.294974i
$757$	−3.50957	+	3.50957i	−0.127558	+	0.127558i	−0.768003	−	0.640446i	$-0.778750\pi$
$757$	−3.50957	+	3.50957i	−0.127558	+	0.127558i	0.640446	+	0.768003i	$0.278750\pi$
$758$	−6.61607	+	6.61607i	−0.240306	+	0.240306i
$759$	−10.5281	−	12.9296i	−0.382146	−	0.469314i
$760$		0			0
$761$		−	26.9220i		−	0.975922i	−0.872865	−	0.487961i	$-0.837741\pi$
$761$		−	26.9220i		−	0.975922i	0.872865	−	0.487961i	$-0.162259\pi$
$762$	−14.5151	−	1.48598i	−0.525826	−	0.0538312i
$763$	−13.4452	−	13.4452i	−0.486749	−	0.486749i
$764$	0.984264			0.0356094
$765$		0			0
$766$	12.3026			0.444512
$767$	−0.342701	−	0.342701i	−0.0123742	−	0.0123742i
$768$	−0.0310544	−	0.00317918i	−0.00112058	−	0.000114719i
$769$		−	31.3935i		−	1.13208i	−0.824378	−	0.566040i	$-0.808475\pi$
$769$		−	31.3935i		−	1.13208i	0.824378	−	0.566040i	$-0.191525\pi$
$770$		0			0
$771$	9.01519	+	11.0716i	0.324674	+	0.398733i
$772$	−12.4052	+	12.4052i	−0.446473	+	0.446473i
$773$	−13.3925	+	13.3925i	−0.481693	+	0.481693i	−0.905672	−	0.423979i	$-0.860633\pi$
$773$	−13.3925	+	13.3925i	−0.481693	+	0.481693i	0.423979	+	0.905672i	$0.360633\pi$
$774$	0.320291	−	1.54792i	0.0115126	−	0.0556387i
$775$		0			0
$776$		−	4.87606i		−	0.175040i
$777$	−0.534561	+	5.22162i	−0.0191773	+	0.187325i
$778$	−6.36887	−	6.36887i	−0.228335	−	0.228335i
$779$	−60.7006			−2.17482
$780$		0			0
$781$	−36.2985			−1.29886
$782$	−5.77865	−	5.77865i	−0.206644	−	0.206644i
$783$	14.2162	+	4.49210i	0.508044	+	0.160535i
$784$			2.61267i			0.0933098i
$785$		0			0
$786$	6.55437	−	5.33700i	0.233787	−	0.190364i
$787$	−22.4712	+	22.4712i	−0.801011	+	0.801011i	−0.983254	−	0.182243i	$-0.941664\pi$
$787$	−22.4712	+	22.4712i	−0.801011	+	0.801011i	0.182243	+	0.983254i	$0.441664\pi$
$788$	−17.8557	+	17.8557i	−0.636085	+	0.636085i
$789$	0.118698	−	0.0966515i	0.00422575	−	0.00344088i
$790$		0			0
$791$		−	8.04874i		−	0.286180i
$792$	8.11990	+	12.3569i	0.288528	+	0.439084i
$793$	−10.1569	−	10.1569i	−0.360681	−	0.360681i
$794$	7.57440			0.268805
$795$		0			0
$796$	−20.5372			−0.727922
$797$	−7.83907	−	7.83907i	−0.277674	−	0.277674i	0.554506	−	0.832180i	$-0.312907\pi$
$797$	−7.83907	−	7.83907i	−0.277674	−	0.277674i	−0.832180	+	0.554506i	$0.812907\pi$
$798$	−0.453945	+	4.43417i	−0.0160695	+	0.156968i
$799$		−	50.0556i		−	1.77084i
$800$		0			0
$801$	11.6079	+	2.40187i	0.410144	+	0.0848660i
$802$	−11.9471	+	11.9471i	−0.421866	+	0.421866i
$803$	11.1259	−	11.1259i	0.392623	−	0.392623i
$804$	14.7233	+	18.0817i	0.519252	+	0.637694i
$805$		0			0
$806$			7.88640i			0.277787i
$807$	−51.1227	−	5.23366i	−1.79960	−	0.184233i
$808$	−4.90684	−	4.90684i	−0.172622	−	0.172622i
$809$	−6.27026			−0.220451			−0.110225	−	0.993907i	$-0.535157\pi$
$809$	−6.27026			−0.220451			−0.110225	+	0.993907i	$0.535157\pi$
$810$		0			0
$811$	−8.90138			−0.312570			−0.156285	−	0.987712i	$-0.549952\pi$
$811$	−8.90138			−0.312570			−0.156285	+	0.987712i	$0.549952\pi$
$812$	3.56898	+	3.56898i	0.125247	+	0.125247i
$813$	−39.0058	−	3.99320i	−1.36799	−	0.140048i
$814$			3.97332i			0.139265i
$815$		0			0
$816$	−13.2024	−	16.2138i	−0.462175	−	0.567598i
$817$	−3.98022	+	3.98022i	−0.139250	+	0.139250i
$818$	−2.63502	+	2.63502i	−0.0921313	+	0.0921313i
$819$	−8.93015	−	1.84781i	−0.312045	−	0.0645676i
$820$		0			0
$821$			16.8442i			0.587867i	0.955826	+	0.293934i	$0.0949645\pi$
$821$			16.8442i			0.587867i	−0.955826	+	0.293934i	$0.905036\pi$
$822$	1.67305	−	16.3425i	0.0583543	−	0.570008i
$823$	−32.4880	−	32.4880i	−1.13246	−	1.13246i	−0.989767	−	0.142695i	$-0.954423\pi$
$823$	−32.4880	−	32.4880i	−1.13246	−	1.13246i	−0.142695	−	0.989767i	$-0.545577\pi$
$824$	23.1099			0.805072
$825$		0			0
$826$	0.0782529			0.00272277
$827$	4.87454	+	4.87454i	0.169504	+	0.169504i	0.786762	−	0.617257i	$-0.211756\pi$
$827$	4.87454	+	4.87454i	0.169504	+	0.169504i	−0.617257	+	0.786762i	$0.711756\pi$
$828$	−10.4437	−	15.8932i	−0.362943	−	0.552329i
$829$		−	9.82522i		−	0.341244i	−0.985337	−	0.170622i	$-0.945422\pi$
$829$		−	9.82522i		−	0.341244i	0.985337	−	0.170622i	$-0.0545777\pi$
$830$		0			0
$831$	7.99924	−	6.51350i	0.277490	−	0.225951i
$832$	5.98598	−	5.98598i	0.207527	−	0.207527i
$833$	−3.26719	+	3.26719i	−0.113201	+	0.113201i
$834$	11.0703	−	9.01414i	0.383332	−	0.312134i
$835$		0			0
$836$		−	24.6394i		−	0.852171i
$837$	26.1904	+	8.27579i	0.905272	+	0.286053i
$838$	−2.15397	−	2.15397i	−0.0744075	−	0.0744075i
$839$	13.0314			0.449893			0.224947	−	0.974371i	$-0.427779\pi$
$839$	13.0314			0.449893			0.224947	+	0.974371i	$0.427779\pi$
$840$		0			0
$841$	−20.7675			−0.716120
$842$	8.72279	+	8.72279i	0.300607	+	0.300607i
$843$	−3.88235	+	37.9231i	−0.133715	+	1.30614i
$844$			1.36701i			0.0470543i
$845$		0			0
$846$	−3.23214	+	15.6204i	−0.111123	+	0.537041i
$847$	2.73212	−	2.73212i	0.0938766	−	0.0938766i
$848$	11.5892	−	11.5892i	0.397976	−	0.397976i
$849$	14.8463	+	18.2327i	0.509523	+	0.625745i
$850$		0			0
$851$		−	10.9207i		−	0.374355i
$852$	−41.1855	−	4.21634i	−1.41099	−	0.144450i
$853$	36.7177	+	36.7177i	1.25719	+	1.25719i	0.952429	+	0.304761i	$0.0985765\pi$
$853$	36.7177	+	36.7177i	1.25719	+	1.25719i	0.304761	+	0.952429i	$0.401424\pi$
$854$	2.31923			0.0793626
$855$		0			0
$856$	1.85358			0.0633542
$857$	25.5867	+	25.5867i	0.874024	+	0.874024i	0.992908	−	0.118884i	$-0.0379318\pi$
$857$	25.5867	+	25.5867i	0.874024	+	0.874024i	−0.118884	+	0.992908i	$0.537932\pi$
$858$	−6.86725	−	0.703032i	−0.234444	−	0.0240011i
$859$			15.7133i			0.536132i	0.963401	+	0.268066i	$0.0863845\pi$
$859$			15.7133i			0.536132i	−0.963401	+	0.268066i	$0.913615\pi$
$860$		0			0
$861$	12.6609	+	15.5489i	0.431484	+	0.529906i
$862$	2.92644	−	2.92644i	0.0996751	−	0.0996751i
$863$	−11.1088	+	11.1088i	−0.378147	+	0.378147i	−0.870433	−	0.492286i	$-0.836161\pi$
$863$	−11.1088	+	11.1088i	−0.378147	+	0.378147i	0.492286	+	0.870433i	$0.336161\pi$
$864$	11.9159	+	22.9251i	0.405386	+	0.779927i
$865$		0			0
$866$			13.0685i			0.444084i
$867$	0.767159	−	7.49366i	0.0260541	−	0.254498i
$868$	6.57512	+	6.57512i	0.223174	+	0.223174i
$869$	10.4106			0.353155
$870$		0			0
$871$	−23.2637			−0.788260
$872$	−24.8064	−	24.8064i	−0.840050	−	0.840050i
$873$	6.62602	−	4.35405i	0.224257	−	0.147362i
$874$		−	9.27375i		−	0.313689i
$875$		0			0
$876$	13.9161	−	11.3314i	0.470182	−	0.382853i
$877$	20.7301	−	20.7301i	0.700006	−	0.700006i	−0.264405	−	0.964412i	$-0.585176\pi$
$877$	20.7301	−	20.7301i	0.700006	−	0.700006i	0.964412	+	0.264405i	$0.0851757\pi$
$878$	−1.69456	+	1.69456i	−0.0571886	+	0.0571886i
$879$	−6.76884	+	5.51163i	−0.228307	+	0.185903i
$880$		0			0
$881$			26.4774i			0.892045i	0.895022	+	0.446023i	$0.147160\pi$
$881$			26.4774i			0.892045i	−0.895022	+	0.446023i	$0.852840\pi$
$882$	1.23053	−	0.808598i	0.0414341	−	0.0272269i
$883$	26.9720	+	26.9720i	0.907681	+	0.907681i	0.996085	−	0.0884037i	$-0.0281766\pi$
$883$	26.9720	+	26.9720i	0.907681	+	0.907681i	−0.0884037	+	0.996085i	$0.528177\pi$
$884$	24.7072			0.830993
$885$		0			0
$886$	−16.5864			−0.557231
$887$	1.34997	+	1.34997i	0.0453275	+	0.0453275i	0.729407	−	0.684080i	$-0.239796\pi$
$887$	1.34997	+	1.34997i	0.0453275	+	0.0453275i	−0.684080	+	0.729407i	$0.739796\pi$
$888$	−0.986265	+	9.63389i	−0.0330969	+	0.323292i
$889$		−	17.1637i		−	0.575653i
$890$		0			0
$891$	−9.54105	+	22.0681i	−0.319637	+	0.739309i
$892$	5.87209	−	5.87209i	0.196612	−	0.196612i
$893$	40.1654	−	40.1654i	1.34408	−	1.34408i
$894$	4.99871	+	6.13892i	0.167182	+	0.205316i
$895$		0			0
$896$			11.3115i			0.377890i
$897$	18.8746	+	1.93228i	0.630205	+	0.0645169i
$898$	−8.21601	−	8.21601i	−0.274172	−	0.274172i
$899$	15.1668			0.505840
$900$		0			0
$901$	28.9850			0.965631
$902$	10.7330	+	10.7330i	0.357368	+	0.357368i
$903$	1.84976	+	0.189368i	0.0615561	+	0.00630178i
$904$		−	14.8499i		−	0.493901i
$905$		0			0
$906$	−10.9430	−	13.4391i	−0.363558	−	0.446486i
$907$	28.6846	−	28.6846i	0.952456	−	0.952456i	−0.0464640	−	0.998920i	$-0.514795\pi$
$907$	28.6846	−	28.6846i	0.952456	−	0.952456i	0.998920	+	0.0464640i	$0.0147953\pi$
$908$	0.426278	−	0.426278i	0.0141465	−	0.0141465i
$909$	2.28631	−	11.0494i	0.0758322	−	0.366485i
$910$		0			0
$911$			34.0874i			1.12937i	0.825307	+	0.564684i	$0.191002\pi$
$911$			34.0874i			1.12937i	−0.825307	+	0.564684i	$0.808998\pi$
$912$	2.41645	−	23.6040i	0.0800166	−	0.781607i
$913$	−10.7864	−	10.7864i	−0.356978	−	0.356978i
$914$	−7.12016			−0.235514
$915$		0			0
$916$	23.7115			0.783450
$917$	7.03062	+	7.03062i	0.232172	+	0.232172i
$918$	−3.55046	+	11.2361i	−0.117183	+	0.370848i
$919$		−	2.19661i		−	0.0724593i	−0.999343	−	0.0362297i	$-0.988465\pi$
$919$		−	2.19661i		−	0.0724593i	0.999343	−	0.0362297i	$-0.0115348\pi$
$920$		0			0
$921$	19.8958	−	16.2005i	0.655589	−	0.533823i
$922$	−8.09166	+	8.09166i	−0.266485	+	0.266485i
$923$	29.2066	−	29.2066i	0.961348	−	0.961348i
$924$	−6.31156	+	5.13929i	−0.207635	+	0.169070i
$925$		0			0
$926$			11.8389i			0.389049i
$927$	20.6359	+	31.4038i	0.677771	+	1.03144i
$928$	10.0881	+	10.0881i	0.331159	+	0.331159i
$929$	−51.2981			−1.68304			−0.841518	−	0.540230i	$-0.818337\pi$
$929$	−51.2981			−1.68304			−0.841518	+	0.540230i	$0.818337\pi$
$930$		0			0
$931$	−5.24329			−0.171842
$932$	−2.09792	−	2.09792i	−0.0687197	−	0.0687197i
$933$	−3.60455	+	35.2094i	−0.118008	+	1.15271i
$934$			5.55717i			0.181836i
$935$		0			0
$936$	−16.4761	−	3.40920i	−0.538539	−	0.111433i
$937$	−16.4279	+	16.4279i	−0.536675	+	0.536675i	−0.922551	−	0.385876i	$-0.873899\pi$
$937$	−16.4279	+	16.4279i	−0.536675	+	0.536675i	0.385876	+	0.922551i	$0.373899\pi$
$938$	2.65603	−	2.65603i	0.0867226	−	0.0867226i
$939$	−25.4933	−	31.3083i	−0.831942	−	1.02171i
$940$		0			0
$941$			57.2870i			1.86750i	0.357922	+	0.933752i	$0.383485\pi$
$941$			57.2870i			1.86750i	−0.357922	+	0.933752i	$0.616515\pi$
$942$	7.56918	+	0.774891i	0.246617	+	0.0252473i
$943$	−29.4995	−	29.4995i	−0.960635	−	0.960635i
$944$	−0.416557			−0.0135578
$945$		0			0
$946$	1.40755			0.0457634
$947$	−35.8300	−	35.8300i	−1.16432	−	1.16432i	−0.983520	−	0.180799i	$-0.942132\pi$
$947$	−35.8300	−	35.8300i	−1.16432	−	1.16432i	−0.180799	−	0.983520i	$-0.557868\pi$
$948$	11.8122	+	1.20927i	0.383642	+	0.0392752i
$949$			17.9043i			0.581197i
$950$		0			0
$951$	35.5017	+	43.5997i	1.15122	+	1.41382i
$952$	−6.02797	+	6.02797i	−0.195368	+	0.195368i
$953$	35.4764	−	35.4764i	1.14919	−	1.14919i	0.162481	−	0.986712i	$-0.448050\pi$
$953$	35.4764	−	35.4764i	1.14919	−	1.14919i	0.986712	−	0.162481i	$-0.0519496\pi$
$954$	−9.04510	−	1.87159i	−0.292846	−	0.0605950i
$955$		0			0
$956$			9.06511i			0.293187i
$957$	−1.35204	+	13.2068i	−0.0437051	+	0.426914i
$958$	−6.98270	−	6.98270i	−0.225601	−	0.225601i
$959$	19.3245			0.624022
$960$		0			0
$961$	−3.05833			−0.0986558
$962$	−3.19703	−	3.19703i	−0.103076	−	0.103076i
$963$	1.65515	+	2.51881i	0.0533364	+	0.0811677i
$964$			26.2413i			0.845175i
$965$		0			0
$966$	−2.37554	+	1.93432i	−0.0764317	+	0.0622357i
$967$	21.0372	−	21.0372i	0.676511	−	0.676511i	−0.282698	−	0.959209i	$-0.591229\pi$
$967$	21.0372	−	21.0372i	0.676511	−	0.676511i	0.959209	+	0.282698i	$0.0912293\pi$
$968$	5.04075	−	5.04075i	0.162016	−	0.162016i
$969$	32.5390	−	26.4954i	1.04530	−	0.851154i
$970$		0			0
$971$		−	23.4561i		−	0.752742i	−0.926469	−	0.376371i	$-0.877172\pi$
$971$		−	23.4561i		−	0.752742i	0.926469	−	0.376371i	$-0.122828\pi$
$972$	−13.3890	+	23.9309i	−0.429451	+	0.767585i
$973$	11.8747	+	11.8747i	0.380684	+	0.380684i
$974$	−5.39987			−0.173023
$975$		0			0
$976$	−12.3458			−0.395179
$977$	−9.03422	−	9.03422i	−0.289030	−	0.289030i	0.547666	−	0.836697i	$-0.315516\pi$
$977$	−9.03422	−	9.03422i	−0.289030	−	0.289030i	−0.836697	+	0.547666i	$0.815516\pi$
$978$	0.790504	−	7.72169i	0.0252775	−	0.246913i
$979$			10.5552i			0.337347i
$980$		0			0
$981$	11.5584	−	55.8598i	0.369031	−	1.78347i
$982$	0.796647	−	0.796647i	0.0254220	−	0.0254220i
$983$	3.13374	−	3.13374i	0.0999509	−	0.0999509i	−0.655363	−	0.755314i	$-0.727484\pi$
$983$	3.13374	−	3.13374i	0.0999509	−	0.0999509i	0.755314	+	0.655363i	$0.227484\pi$
$984$	23.3594	+	28.6877i	0.744672	+	0.914532i
$985$		0			0
$986$			6.50680i			0.207219i
$987$	−18.6664	−	1.91096i	−0.594157	−	0.0608265i
$988$	19.8254	+	19.8254i	0.630731	+	0.630731i
$989$	−3.86864			−0.123016
$990$		0			0
$991$	−29.2283			−0.928467			−0.464233	−	0.885713i	$-0.653670\pi$
$991$	−29.2283			−0.928467			−0.464233	+	0.885713i	$0.653670\pi$
$992$	18.5853	+	18.5853i	0.590085	+	0.590085i
$993$	3.81588	+	0.390649i	0.121093	+	0.0123969i
$994$			6.66909i			0.211531i
$995$		0			0
$996$	−10.9857	−	13.4915i	−0.348095	−	0.427496i
$997$	4.57510	−	4.57510i	0.144895	−	0.144895i	−0.630938	−	0.775833i	$-0.717330\pi$
$997$	4.57510	−	4.57510i	0.144895	−	0.144895i	0.775833	+	0.630938i	$0.217330\pi$
$998$	−4.27793	+	4.27793i	−0.135415	+	0.135415i
$999$	−13.9721	+	7.26231i	−0.442057	+	0.229769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.j.b.218.8		24
3.2	odd	2	inner	525.2.j.b.218.5		24
5.2	odd	4	inner	525.2.j.b.407.5		24
5.3	odd	4		105.2.j.a.92.8	yes	24
5.4	even	2		105.2.j.a.8.5	✓	24
15.2	even	4	inner	525.2.j.b.407.8		24
15.8	even	4		105.2.j.a.92.5	yes	24
15.14	odd	2		105.2.j.a.8.8	yes	24
35.3	even	12		735.2.y.g.422.8		48
35.4	even	6		735.2.y.j.128.8		48
35.9	even	6		735.2.y.j.263.5		48
35.13	even	4		735.2.j.h.197.8		24
35.18	odd	12		735.2.y.j.422.8		48
35.19	odd	6		735.2.y.g.263.5		48
35.23	odd	12		735.2.y.j.557.5		48
35.24	odd	6		735.2.y.g.128.8		48
35.33	even	12		735.2.y.g.557.5		48
35.34	odd	2		735.2.j.h.638.5		24
105.23	even	12		735.2.y.j.557.8		48
105.38	odd	12		735.2.y.g.422.5		48
105.44	odd	6		735.2.y.j.263.8		48
105.53	even	12		735.2.y.j.422.5		48
105.59	even	6		735.2.y.g.128.5		48
105.68	odd	12		735.2.y.g.557.8		48
105.74	odd	6		735.2.y.j.128.5		48
105.83	odd	4		735.2.j.h.197.5		24
105.89	even	6		735.2.y.g.263.8		48
105.104	even	2		735.2.j.h.638.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.j.a.8.5	✓	24	5.4	even	2
105.2.j.a.8.8	yes	24	15.14	odd	2
105.2.j.a.92.5	yes	24	15.8	even	4
105.2.j.a.92.8	yes	24	5.3	odd	4
525.2.j.b.218.5		24	3.2	odd	2	inner
525.2.j.b.218.8		24	1.1	even	1	trivial
525.2.j.b.407.5		24	5.2	odd	4	inner
525.2.j.b.407.8		24	15.2	even	4	inner
735.2.j.h.197.5		24	105.83	odd	4
735.2.j.h.197.8		24	35.13	even	4
735.2.j.h.638.5		24	35.34	odd	2
735.2.j.h.638.8		24	105.104	even	2
735.2.y.g.128.5		48	105.59	even	6
735.2.y.g.128.8		48	35.24	odd	6
735.2.y.g.263.5		48	35.19	odd	6
735.2.y.g.263.8		48	105.89	even	6
735.2.y.g.422.5		48	105.38	odd	12
735.2.y.g.422.8		48	35.3	even	12
735.2.y.g.557.5		48	35.33	even	12
735.2.y.g.557.8		48	105.68	odd	12
735.2.y.j.128.5		48	105.74	odd	6
735.2.y.j.128.8		48	35.4	even	6
735.2.y.j.263.5		48	35.9	even	6
735.2.y.j.263.8		48	105.44	odd	6
735.2.y.j.422.5		48	105.53	even	12
735.2.y.j.422.8		48	35.18	odd	12
735.2.y.j.557.5		48	35.23	odd	12
735.2.y.j.557.8		48	105.23	even	12

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.347054 + 0.347054i) q^{2} +(-1.72305 - 0.176396i) q^{3} -1.75911i q^{4} +(-0.536770 - 0.659208i) q^{6} +(0.707107 - 0.707107i) q^{7} +(1.30461 - 1.30461i) q^{8} +(2.93777 + 0.607876i) q^{9} +O(q^{10})\)	\(q+(0.347054 + 0.347054i) q^{2} +(-1.72305 - 0.176396i) q^{3} -1.75911i q^{4} +(-0.536770 - 0.659208i) q^{6} +(0.707107 - 0.707107i) q^{7} +(1.30461 - 1.30461i) q^{8} +(2.93777 + 0.607876i) q^{9} +2.67137i q^{11} +(-0.310299 + 3.03102i) q^{12} +(-2.14945 - 2.14945i) q^{13} +0.490808 q^{14} -2.61267 q^{16} +(-3.26719 - 3.26719i) q^{17} +(0.808598 + 1.23053i) q^{18} -5.24329i q^{19} +(-1.34311 + 1.09365i) q^{21} +(-0.927108 + 0.927108i) q^{22} +(2.54815 - 2.54815i) q^{23} +(-2.47803 + 2.01778i) q^{24} -1.49195i q^{26} +(-4.95468 - 1.56561i) q^{27} +(-1.24388 - 1.24388i) q^{28} -2.86924 q^{29} -5.28599 q^{31} +(-3.51596 - 3.51596i) q^{32} +(0.471218 - 4.60289i) q^{33} -2.26778i q^{34} +(1.06932 - 5.16785i) q^{36} +(2.14286 - 2.14286i) q^{37} +(1.81970 - 1.81970i) q^{38} +(3.32444 + 4.08274i) q^{39} -11.5768i q^{41} +(-0.845684 - 0.0865765i) q^{42} +(-0.759108 - 0.759108i) q^{43} +4.69922 q^{44} +1.76869 q^{46} +(7.66034 + 7.66034i) q^{47} +(4.50176 + 0.460865i) q^{48} -1.00000i q^{49} +(5.05320 + 6.20584i) q^{51} +(-3.78111 + 3.78111i) q^{52} +(-4.43577 + 4.43577i) q^{53} +(-1.17619 - 2.26289i) q^{54} -1.84500i q^{56} +(-0.924894 + 9.03442i) q^{57} +(-0.995779 - 0.995779i) q^{58} +0.159437 q^{59} +4.72534 q^{61} +(-1.83452 - 1.83452i) q^{62} +(2.50715 - 1.64748i) q^{63} +2.78490i q^{64} +(1.76099 - 1.43391i) q^{66} +(5.41156 - 5.41156i) q^{67} +(-5.74734 + 5.74734i) q^{68} +(-4.84006 + 3.94109i) q^{69} +13.5880i q^{71} +(4.62569 - 3.03961i) q^{72} +(-4.16486 - 4.16486i) q^{73} +1.48737 q^{74} -9.22351 q^{76} +(1.88894 + 1.88894i) q^{77} +(-0.263173 + 2.57069i) q^{78} -3.89710i q^{79} +(8.26097 + 3.57160i) q^{81} +(4.01778 - 4.01778i) q^{82} +(-4.03778 + 4.03778i) q^{83} +(1.92384 + 2.36267i) q^{84} -0.526902i q^{86} +(4.94383 + 0.506122i) q^{87} +(3.48510 + 3.48510i) q^{88} +3.95125 q^{89} -3.03977 q^{91} +(-4.48247 - 4.48247i) q^{92} +(9.10800 + 0.932426i) q^{93} +5.31710i q^{94} +(5.43796 + 6.67836i) q^{96} +(1.86878 - 1.86878i) q^{97} +(0.347054 - 0.347054i) q^{98} +(-1.62386 + 7.84786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3}+O(q^{10}) \) 24 * q + 4 * q^3	\( 24 q + 4 q^{3} - 16 q^{12} + 8 q^{13} - 16 q^{16} + 20 q^{18} + 4 q^{21} - 8 q^{22} + 16 q^{27} - 28 q^{33} + 16 q^{36} + 16 q^{37} + 20 q^{42} + 40 q^{43} - 64 q^{46} - 16 q^{48} - 20 q^{51} - 4 q^{57} - 40 q^{58} + 32 q^{61} + 8 q^{63} - 16 q^{66} - 24 q^{67} + 8 q^{72} - 32 q^{73} + 32 q^{76} - 60 q^{78} + 52 q^{81} + 80 q^{82} - 4 q^{87} - 96 q^{88} - 24 q^{91} + 76 q^{93} - 96 q^{96} - 24 q^{97}+O(q^{100}) \) 24 * q + 4 * q^3 - 16 * q^12 + 8 * q^13 - 16 * q^16 + 20 * q^18 + 4 * q^21 - 8 * q^22 + 16 * q^27 - 28 * q^33 + 16 * q^36 + 16 * q^37 + 20 * q^42 + 40 * q^43 - 64 * q^46 - 16 * q^48 - 20 * q^51 - 4 * q^57 - 40 * q^58 + 32 * q^61 + 8 * q^63 - 16 * q^66 - 24 * q^67 + 8 * q^72 - 32 * q^73 + 32 * q^76 - 60 * q^78 + 52 * q^81 + 80 * q^82 - 4 * q^87 - 96 * q^88 - 24 * q^91 + 76 * q^93 - 96 * q^96 - 24 * q^97

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