LMFDB - Embedded newform 925.2.o.d.174.11

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			174.11
Character	$\chi$	$=$	925.174
Dual form			925.2.o.d.824.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.348412 + 0.201156i) q^{2} +(0.227139 + 0.131139i) q^{3} +(-0.919073 + 1.59188i) q^{4} -0.105517 q^{6} +(1.99551 + 1.15211i) q^{7} -1.54413i q^{8} +(-1.46561 - 2.53850i) q^{9} +O(q^{10})$	\(q+(-0.348412 + 0.201156i) q^{2} +(0.227139 + 0.131139i) q^{3} +(-0.919073 + 1.59188i) q^{4} -0.105517 q^{6} +(1.99551 + 1.15211i) q^{7} -1.54413i q^{8} +(-1.46561 - 2.53850i) q^{9} +4.73598 q^{11} +(-0.417515 + 0.241052i) q^{12} +(0.756262 + 0.436628i) q^{13} -0.927014 q^{14} +(-1.52754 - 2.64577i) q^{16} +(3.04159 - 1.75607i) q^{17} +(1.02127 + 0.589630i) q^{18} +(1.46980 - 2.54576i) q^{19} +(0.302173 + 0.523378i) q^{21} +(-1.65007 + 0.952670i) q^{22} +4.66022i q^{23} +(0.202495 - 0.350732i) q^{24} -0.351321 q^{26} -1.55562i q^{27} +(-3.66804 + 2.11775i) q^{28} -1.38961 q^{29} +4.55390 q^{31} +(3.73893 + 2.15867i) q^{32} +(1.07573 + 0.621071i) q^{33} +(-0.706485 + 1.22367i) q^{34} +5.38799 q^{36} +(-1.28176 + 5.94618i) q^{37} +1.18263i q^{38} +(0.114518 + 0.198351i) q^{39} +(4.21111 - 7.29385i) q^{41} +(-0.210561 - 0.121567i) q^{42} +8.27070i q^{43} +(-4.35271 + 7.53912i) q^{44} +(-0.937429 - 1.62367i) q^{46} +9.58509i q^{47} -0.801277i q^{48} +(-0.845285 - 1.46408i) q^{49} +0.921153 q^{51} +(-1.39012 + 0.802586i) q^{52} +(-0.0727132 + 0.0419810i) q^{53} +(0.312922 + 0.541998i) q^{54} +(1.77901 - 3.08133i) q^{56} +(0.667696 - 0.385495i) q^{57} +(0.484158 - 0.279529i) q^{58} +(3.55942 + 6.16510i) q^{59} +(2.42564 - 4.20133i) q^{61} +(-1.58663 + 0.916042i) q^{62} -6.75415i q^{63} +4.37322 q^{64} -0.499728 q^{66} +(-4.47062 - 2.58111i) q^{67} +6.45581i q^{68} +(-0.611135 + 1.05852i) q^{69} +(-3.82640 + 6.62753i) q^{71} +(-3.91978 + 2.26308i) q^{72} +2.22328i q^{73} +(-0.749528 - 2.32955i) q^{74} +(2.70170 + 4.67948i) q^{76} +(9.45072 + 5.45637i) q^{77} +(-0.0797987 - 0.0460718i) q^{78} +(-0.514848 + 0.891742i) q^{79} +(-4.19281 + 7.26217i) q^{81} +3.38835i q^{82} +(11.9970 - 6.92650i) q^{83} -1.11087 q^{84} +(-1.66370 - 2.88161i) q^{86} +(-0.315635 - 0.182232i) q^{87} -7.31297i q^{88} +(4.27032 + 7.39642i) q^{89} +(1.00609 + 1.74259i) q^{91} +(-7.41851 - 4.28308i) q^{92} +(1.03437 + 0.597193i) q^{93} +(-1.92809 - 3.33956i) q^{94} +(0.566172 + 0.980638i) q^{96} -17.7844i q^{97} +(0.589015 + 0.340068i) q^{98} +(-6.94108 - 12.0223i) 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 $

$2$	−0.348412	+	0.201156i	−0.246364	+	0.142239i	−0.618098	−	0.786101i	$-0.712097\pi$
$2$	−0.348412	+	0.201156i	−0.246364	+	0.142239i	0.371734	+	0.928339i	$0.378763\pi$
$3$	0.227139	+	0.131139i	0.131139	+	0.0757130i	0.564134	−	0.825683i	$-0.309210\pi$
$3$	0.227139	+	0.131139i	0.131139	+	0.0757130i	−0.432995	+	0.901396i	$0.642543\pi$
$4$	−0.919073	+	1.59188i	−0.459536	+	0.795940i
$5$		0			0
$5$		0			0
$6$	−0.105517			−0.0430772
$7$	1.99551	+	1.15211i	0.754233	+	0.435457i	0.827221	−	0.561876i	$-0.189920\pi$
$7$	1.99551	+	1.15211i	0.754233	+	0.435457i	−0.0729883	+	0.997333i	$0.523254\pi$
$8$		−	1.54413i		−	0.545932i
$9$	−1.46561	−	2.53850i	−0.488535	−	0.846168i
$10$		0			0
$11$	4.73598			1.42795			0.713976	−	0.700170i	$-0.246892\pi$
$11$	4.73598			1.42795			0.713976	+	0.700170i	$0.246892\pi$
$12$	−0.417515	+	0.241052i	−0.120526	+	0.0695858i
$13$	0.756262	+	0.436628i	0.209749	+	0.121099i	0.601195	−	0.799102i	$-0.294692\pi$
$13$	0.756262	+	0.436628i	0.209749	+	0.121099i	−0.391446	+	0.920201i	$0.628025\pi$
$14$	−0.927014			−0.247755
$15$		0			0
$16$	−1.52754	−	2.64577i	−0.381884	−	0.661442i
$17$	3.04159	−	1.75607i	0.737695	−	0.425908i	−0.0835356	−	0.996505i	$-0.526621\pi$
$17$	3.04159	−	1.75607i	0.737695	−	0.425908i	0.821231	+	0.570596i	$0.193288\pi$
$18$	1.02127	+	0.589630i	0.240715	+	0.138977i
$19$	1.46980	−	2.54576i	0.337194	−	0.584038i	−0.646710	−	0.762736i	$-0.723855\pi$
$19$	1.46980	−	2.54576i	0.337194	−	0.584038i	0.983904	+	0.178699i	$0.0571887\pi$
$20$		0			0
$21$	0.302173	+	0.523378i	0.0659395	+	0.114211i
$22$	−1.65007	+	0.952670i	−0.351797	+	0.203110i
$23$			4.66022i			0.971722i	0.874036	+	0.485861i	$0.161494\pi$
$23$			4.66022i			0.971722i	−0.874036	+	0.485861i	$0.838506\pi$
$24$	0.202495	−	0.350732i	0.0413342	−	0.0715929i
$25$		0			0
$26$	−0.351321			−0.0688997
$27$		−	1.55562i		−	0.299380i
$28$	−3.66804	+	2.11775i	−0.693195	+	0.400216i
$29$	−1.38961			−0.258045			−0.129022	−	0.991642i	$-0.541184\pi$
$29$	−1.38961			−0.258045			−0.129022	+	0.991642i	$0.541184\pi$
$30$		0			0
$31$	4.55390			0.817904			0.408952	−	0.912556i	$-0.365894\pi$
$31$	4.55390			0.817904			0.408952	+	0.912556i	$0.365894\pi$
$32$	3.73893	+	2.15867i	0.660956	+	0.381603i
$33$	1.07573	+	0.621071i	0.187260	+	0.108115i
$34$	−0.706485	+	1.22367i	−0.121161	+	0.209857i
$35$		0			0
$36$	5.38799			0.897999
$37$	−1.28176	+	5.94618i	−0.210720	+	0.977546i
$37$	−1.28176	+	5.94618i	−0.210720	+	0.977546i
$38$			1.18263i			0.191848i
$39$	0.114518	+	0.198351i	0.0183375	+	0.0317615i
$40$		0			0
$41$	4.21111	−	7.29385i	0.657665	−	1.13911i	−0.323554	−	0.946210i	$-0.604878\pi$
$41$	4.21111	−	7.29385i	0.657665	−	1.13911i	0.981219	−	0.192899i	$-0.0617890\pi$
$42$	−0.210561	−	0.121567i	−0.0324903	−	0.0187583i
$43$			8.27070i			1.26127i	0.776080	+	0.630635i	$0.217205\pi$
$43$			8.27070i			1.26127i	−0.776080	+	0.630635i	$0.782795\pi$
$44$	−4.35271	+	7.53912i	−0.656196	+	1.13657i
$45$		0			0
$46$	−0.937429	−	1.62367i	−0.138216	−	0.239398i
$47$			9.58509i			1.39813i	0.715059	+	0.699064i	$0.246400\pi$
$47$			9.58509i			1.39813i	−0.715059	+	0.699064i	$0.753600\pi$
$48$		−	0.801277i		−	0.115654i
$49$	−0.845285	−	1.46408i	−0.120755	−	0.209154i
$50$		0			0
$51$	0.921153			0.128987
$52$	−1.39012	+	0.802586i	−0.192775	+	0.111299i
$53$	−0.0727132	+	0.0419810i	−0.00998792	+	0.00576653i	−0.504986	−	0.863128i	$-0.668502\pi$
$53$	−0.0727132	+	0.0419810i	−0.00998792	+	0.00576653i	0.494998	+	0.868894i	$0.335169\pi$
$54$	0.312922	+	0.541998i	0.0425834	+	0.0737565i
$55$		0			0
$56$	1.77901	−	3.08133i	0.237730	−	0.411760i
$57$	0.667696	−	0.385495i	0.0884385	−	0.0510600i
$58$	0.484158	−	0.279529i	0.0635730	−	0.0367039i
$59$	3.55942	+	6.16510i	0.463398	+	0.802628i	0.999128	−	0.0417611i	$-0.0132968\pi$
$59$	3.55942	+	6.16510i	0.463398	+	0.802628i	−0.535730	+	0.844389i	$0.679964\pi$
$60$		0			0
$61$	2.42564	−	4.20133i	0.310571	−	0.537925i	−0.667915	−	0.744238i	$-0.732813\pi$
$61$	2.42564	−	4.20133i	0.310571	−	0.537925i	0.978486	+	0.206312i	$0.0661463\pi$
$62$	−1.58663	+	0.916042i	−0.201502	+	0.116338i
$63$		−	6.75415i		−	0.850943i
$64$	4.37322			0.546653
$65$		0			0
$66$	−0.499728			−0.0615123
$67$	−4.47062	−	2.58111i	−0.546173	−	0.315333i	0.201404	−	0.979508i	$-0.435449\pi$
$67$	−4.47062	−	2.58111i	−0.546173	−	0.315333i	−0.747577	+	0.664175i	$0.768783\pi$
$68$			6.45581i			0.782882i
$69$	−0.611135	+	1.05852i	−0.0735720	+	0.127430i
$70$		0			0
$71$	−3.82640	+	6.62753i	−0.454111	+	0.786543i	−0.998637	−	0.0522014i	$-0.983376\pi$
$71$	−3.82640	+	6.62753i	−0.454111	+	0.786543i	0.544526	+	0.838744i	$0.316710\pi$
$72$	−3.91978	+	2.26308i	−0.461950	+	0.266707i
$73$			2.22328i			0.260215i	0.991500	+	0.130108i	$0.0415323\pi$
$73$			2.22328i			0.260215i	−0.991500	+	0.130108i	$0.958468\pi$
$74$	−0.749528	−	2.32955i	−0.0871309	−	0.270805i
$75$		0			0
$76$	2.70170	+	4.67948i	0.309906	+	0.536773i
$77$	9.45072	+	5.45637i	1.07701	+	0.621812i
$78$	−0.0797987	−	0.0460718i	−0.00903542	−	0.00521660i
$79$	−0.514848	+	0.891742i	−0.0579249	+	0.100329i	−0.893534	−	0.448996i	$-0.851782\pi$
$79$	−0.514848	+	0.891742i	−0.0579249	+	0.100329i	0.835609	+	0.549325i	$0.185115\pi$
$80$		0			0
$81$	−4.19281	+	7.26217i	−0.465868	+	0.806907i
$82$			3.38835i			0.374181i
$83$	11.9970	−	6.92650i	1.31685	−	0.760282i	0.333627	−	0.942705i	$-0.391728\pi$
$83$	11.9970	−	6.92650i	1.31685	−	0.760282i	0.983220	+	0.182424i	$0.0583942\pi$
$84$	−1.11087			−0.121206
$85$		0			0
$86$	−1.66370	−	2.88161i	−0.179401	−	0.310732i
$87$	−0.315635	−	0.182232i	−0.0338397	−	0.0195373i
$88$		−	7.31297i		−	0.779565i
$89$	4.27032	+	7.39642i	0.452653	+	0.784019i	0.998550	−	0.0538339i	$-0.0171441\pi$
$89$	4.27032	+	7.39642i	0.452653	+	0.784019i	−0.545896	+	0.837853i	$0.683811\pi$
$90$		0			0
$91$	1.00609	+	1.74259i	0.105467	+	0.182674i
$92$	−7.41851	−	4.28308i	−0.773433	−	0.446542i
$93$	1.03437	+	0.597193i	0.107259	+	0.0619260i
$94$	−1.92809	−	3.33956i	−0.198868	−	0.344449i
$95$		0			0
$96$	0.566172	+	0.980638i	0.0577847	+	0.100086i
$97$		−	17.7844i		−	1.80573i	−0.429921	−	0.902867i	$-0.641459\pi$
$97$		−	17.7844i		−	1.80573i	0.429921	−	0.902867i	$-0.358541\pi$
$98$	0.589015	+	0.340068i	0.0594995	+	0.0343520i
$99$	−6.94108	−	12.0223i	−0.697605	−	1.20829i
$100$		0			0
$101$	−0.551934			−0.0549194			−0.0274597	−	0.999623i	$-0.508742\pi$
$101$	−0.551934			−0.0549194			−0.0274597	+	0.999623i	$0.508742\pi$
$102$	−0.320941	+	0.185295i	−0.0317779	+	0.0183470i
$103$			6.56940i			0.647303i	0.946176	+	0.323651i	$0.104910\pi$
$103$			6.56940i			0.647303i	−0.946176	+	0.323651i	$0.895090\pi$
$104$	0.674210	−	1.16777i	0.0661118	−	0.114509i
$105$		0			0
$106$	0.0168894	−	0.0292533i	0.00164045	−	0.00284133i
$107$	10.4922	+	6.05770i	1.01432	+	0.585620i	0.912455	−	0.409178i	$-0.134184\pi$
$107$	10.4922	+	6.05770i	1.01432	+	0.585620i	0.101869	+	0.994798i	$0.467518\pi$
$108$	2.47637	+	1.42973i	0.238289	+	0.137576i
$109$	−8.73835	−	15.1353i	−0.836982	−	1.44969i	−0.892407	−	0.451232i	$-0.850985\pi$
$109$	−8.73835	−	15.1353i	−0.836982	−	1.44969i	0.0554249	−	0.998463i	$-0.482349\pi$
$110$		0			0
$111$	−1.07091	+	1.18252i	−0.101647	+	0.112240i
$112$		−	7.03955i		−	0.665175i
$113$	−2.46551	+	1.42346i	−0.231935	+	0.133908i	−0.611465	−	0.791272i	$-0.709419\pi$
$113$	−2.46551	+	1.42346i	−0.231935	+	0.133908i	0.379529	+	0.925180i	$0.376086\pi$
$114$	−0.155089	+	0.268622i	−0.0145254	+	0.0251587i
$115$		0			0
$116$	1.27716	−	2.21210i	0.118581	−	0.205388i
$117$		−	2.55970i		−	0.236644i
$118$	−2.48029	−	1.43200i	−0.228329	−	0.131826i
$119$	8.09272			0.741859
$120$		0			0
$121$	11.4295			1.03905
$122$			1.95172i			0.176701i
$123$	1.91301	−	1.10448i	0.172491	−	0.0995876i
$124$	−4.18536	+	7.24926i	−0.375857	+	0.651003i
$125$		0			0
$126$	1.35864	+	2.35323i	0.121037	+	0.209642i
$127$	8.14930	−	4.70500i	0.723133	−	0.417501i	−0.0927717	−	0.995687i	$-0.529573\pi$
$127$	8.14930	−	4.70500i	0.723133	−	0.417501i	0.815905	+	0.578186i	$0.196239\pi$
$128$	−9.00155	+	5.19705i	−0.795632	+	0.459358i
$129$	−1.08461	+	1.87860i	−0.0954945	+	0.165401i
$130$		0			0
$131$	−8.48318	−	14.6933i	−0.741179	−	1.28376i	−0.951959	−	0.306226i	$-0.900934\pi$
$131$	−8.48318	−	14.6933i	−0.741179	−	1.28376i	0.210780	−	0.977534i	$-0.432400\pi$
$132$	−1.97734	+	1.14162i	−0.172106	+	0.0993652i
$133$	5.86599	−	3.38673i	0.508646	−	0.293667i
$134$	2.07682			0.179410
$135$		0			0
$136$	−2.71159	−	4.69662i	−0.232517	−	0.402732i
$137$			2.58830i			0.221133i	0.993869	+	0.110566i	$0.0352665\pi$
$137$			2.58830i			0.221133i	−0.993869	+	0.110566i	$0.964733\pi$
$138$		−	0.491733i		−	0.0418591i
$139$	−1.50849	−	2.61277i	−0.127948	−	0.221613i	0.794933	−	0.606697i	$-0.207506\pi$
$139$	−1.50849	−	2.61277i	−0.127948	−	0.221613i	−0.922881	+	0.385084i	$0.874172\pi$
$140$		0			0
$141$	−1.25698	+	2.17715i	−0.105857	+	0.183349i
$142$		−	3.07881i		−	0.258368i
$143$	3.58165	+	2.06786i	0.299512	+	0.172923i
$144$	−4.47753	+	7.75530i	−0.373127	+	0.646275i
$145$		0			0
$146$	−0.447225	−	0.774617i	−0.0370126	−	0.0641078i
$147$		−	0.443399i		−	0.0365709i
$148$	−8.28758	−	7.50538i	−0.681235	−	0.616939i
$149$	7.81283			0.640052			0.320026	−	0.947409i	$-0.396308\pi$
$149$	7.81283			0.640052			0.320026	+	0.947409i	$0.396308\pi$
$150$		0			0
$151$	−11.4699	+	19.8664i	−0.933405	+	1.61671i	−0.155953	+	0.987765i	$0.549845\pi$
$151$	−11.4699	+	19.8664i	−0.933405	+	1.61671i	−0.777453	+	0.628941i	$0.783489\pi$
$152$	−3.93098	−	2.26956i	−0.318845	−	0.184085i
$153$	−8.91555	−	5.14740i	−0.720780	−	0.416142i
$154$	−4.39032			−0.353782
$155$		0			0
$156$	−0.421001			−0.0337070
$157$	−5.09745	+	2.94302i	−0.406821	+	0.234878i	−0.689423	−	0.724359i	$-0.742136\pi$
$157$	−5.09745	+	2.94302i	−0.406821	+	0.234878i	0.282602	+	0.959237i	$0.408802\pi$
$158$		−	0.414258i		−	0.0329566i
$159$	−0.0220213			−0.00174641
$160$		0			0
$161$	−5.36908	+	9.29952i	−0.423143	+	0.732905i
$162$		−	3.37363i		−	0.265058i
$163$	20.2605	−	11.6974i	1.58692	−	0.916210i	0.593112	−	0.805120i	$-0.297899\pi$
$163$	20.2605	−	11.6974i	1.58692	−	0.916210i	0.993810	−	0.111090i	$-0.0354340\pi$
$164$	7.74063	+	13.4072i	0.604442	+	1.04692i
$165$		0			0
$166$	−2.78661	+	4.82655i	−0.216283	+	0.374613i
$167$	−9.48382	−	5.47549i	−0.733880	−	0.423706i	0.0859598	−	0.996299i	$-0.472604\pi$
$167$	−9.48382	−	5.47549i	−0.733880	−	0.423706i	−0.819840	+	0.572593i	$0.805938\pi$
$168$	0.808164	−	0.466594i	0.0623512	−	0.0359985i
$169$	−6.11871	−	10.5979i	−0.470670	−	0.815225i
$170$		0			0
$171$	−8.61656			−0.658925
$172$	−13.1660	−	7.60137i	−1.00390	−	0.579599i
$173$	−14.9540	+	8.63370i	−1.13693	+	0.656408i	−0.945669	−	0.325130i	$-0.894592\pi$
$173$	−14.9540	+	8.63370i	−1.13693	+	0.656408i	−0.191263	+	0.981539i	$0.561258\pi$
$174$	0.146628			0.0111159
$175$		0			0
$176$	−7.23438	−	12.5303i	−0.545312	−	0.944508i
$177$			1.86711i			0.140341i
$178$	−2.97566	−	1.71800i	−0.223035	−	0.128770i
$179$	7.65491			0.572155			0.286077	−	0.958207i	$-0.407649\pi$
$179$	7.65491			0.572155			0.286077	+	0.958207i	$0.407649\pi$
$180$		0			0
$181$	−9.48385	+	16.4265i	−0.704929	+	1.22097i	0.261788	+	0.965125i	$0.415688\pi$
$181$	−9.48385	+	16.4265i	−0.704929	+	1.22097i	−0.966717	+	0.255848i	$0.917645\pi$
$182$	−0.701065	−	0.404760i	−0.0519664	−	0.0300028i
$183$	1.10191	−	0.636191i	0.0814559	−	0.0470286i
$184$	7.19598			0.530494
$185$		0			0
$186$	−0.480515			−0.0352331
$187$	14.4049	−	8.31670i	1.05339	−	0.608177i
$188$	−15.2583	−	8.80939i	−1.11283	−	0.642491i
$189$	1.79225	−	3.10427i	0.130367	−	0.225802i
$190$		0			0
$191$	−13.4094			−0.970267			−0.485134	−	0.874440i	$-0.661229\pi$
$191$	−13.4094			−0.970267			−0.485134	+	0.874440i	$0.661229\pi$
$192$	0.993330	+	0.573499i	0.0716874	+	0.0413887i
$193$		−	26.5994i		−	1.91467i	−0.288981	−	0.957335i	$-0.593316\pi$
$193$		−	26.5994i		−	1.91467i	0.288981	−	0.957335i	$-0.406684\pi$
$194$	3.57743	+	6.19630i	0.256845	+	0.444868i
$195$		0			0
$196$	3.10751			0.221965
$197$	−11.5723	+	6.68125i	−0.824489	+	0.476019i	−0.851962	−	0.523603i	$-0.824587\pi$
$197$	−11.5723	+	6.68125i	−0.824489	+	0.476019i	0.0274727	+	0.999623i	$0.491254\pi$
$198$	4.83671	+	2.79248i	0.343730	+	0.198453i
$199$	17.5369			1.24316			0.621579	−	0.783351i	$-0.286491\pi$
$199$	17.5369			1.24316			0.621579	+	0.783351i	$0.286491\pi$
$200$		0			0
$201$	−0.676968	−	1.17254i	−0.0477496	−	0.0827047i
$202$	0.192300	−	0.111025i	0.0135302	−	0.00781166i
$203$	−2.77299	−	1.60099i	−0.194626	−	0.112367i
$204$	−0.846607	+	1.46637i	−0.0592743	+	0.102666i
$205$		0			0
$206$	−1.32147	−	2.28886i	−0.0920714	−	0.159472i
$207$	11.8300	−	6.83004i	0.822240	−	0.474720i
$208$		−	2.66786i		−	0.184983i
$209$	6.96093	−	12.0567i	0.481498	−	0.833978i
$210$		0			0
$211$	4.22883			0.291125			0.145562	−	0.989349i	$-0.453501\pi$
$211$	4.22883			0.291125			0.145562	+	0.989349i	$0.453501\pi$
$212$		−	0.154334i		−	0.0105997i
$213$	−1.73825	+	1.00358i	−0.119103	+	0.0687642i
$214$	−4.87416			−0.333191
$215$		0			0
$216$	−2.40208			−0.163441
$217$	9.08736	+	5.24659i	0.616890	+	0.356162i
$218$	6.08909	+	3.51554i	0.412405	+	0.238102i
$219$	−0.291558	+	0.504994i	−0.0197017	+	0.0341243i
$220$		0			0
$221$	3.06699			0.206308
$222$	0.135248	−	0.627425i	0.00907723	−	0.0421100i
$223$			0.954338i			0.0639072i	0.999489	+	0.0319536i	$0.0101729\pi$
$223$			0.954338i			0.0639072i	−0.999489	+	0.0319536i	$0.989827\pi$
$224$	4.97406	+	8.61532i	0.332343	+	0.575636i
$225$		0			0
$226$	0.572675	−	0.991902i	0.0380938	−	0.0659803i
$227$	−15.7265	−	9.07973i	−1.04381	−	0.602643i	−0.122898	−	0.992419i	$-0.539219\pi$
$227$	−15.7265	−	9.07973i	−1.04381	−	0.602643i	−0.920909	+	0.389777i	$0.872552\pi$
$228$			1.41719i			0.0938557i
$229$	8.03886	−	13.9237i	0.531223	−	0.920105i	−0.468113	−	0.883669i	$-0.655066\pi$
$229$	8.03886	−	13.9237i	0.531223	−	0.920105i	0.999336	−	0.0364366i	$-0.0116007\pi$
$230$		0			0
$231$	1.43108	+	2.47871i	0.0941585	+	0.163087i
$232$			2.14574i			0.140875i
$233$			9.37991i			0.614498i	0.951629	+	0.307249i	$0.0994085\pi$
$233$			9.37991i			0.614498i	−0.951629	+	0.307249i	$0.900592\pi$
$234$	0.514898	+	0.891829i	0.0336599	+	0.0583007i
$235$		0			0
$236$	−13.0855			−0.851792
$237$	−0.233884	+	0.135033i	−0.0151924	+	0.00877133i
$238$	−2.81960	+	1.62790i	−0.182768	+	0.105521i
$239$	−4.42692	−	7.66765i	−0.286354	−	0.495979i	0.686583	−	0.727052i	$-0.259110\pi$
$239$	−4.42692	−	7.66765i	−0.286354	−	0.495979i	−0.972937	+	0.231072i	$0.925777\pi$
$240$		0			0
$241$	9.48942	−	16.4362i	0.611267	−	1.05875i	−0.379760	−	0.925085i	$-0.623993\pi$
$241$	9.48942	−	16.4362i	0.611267	−	1.05875i	0.991027	−	0.133661i	$-0.0426733\pi$
$242$	−3.98219	+	2.29912i	−0.255985	+	0.147793i
$243$	−5.94633	+	3.43312i	−0.381457	+	0.220235i
$244$	4.45868	+	7.72266i	0.285438	+	0.494392i
$245$		0			0
$246$	−0.444345	+	0.769627i	−0.0283304	+	0.0490697i
$247$	2.22310	−	1.28351i	0.141453	−	0.0816677i
$248$		−	7.03181i		−	0.446520i
$249$	3.63333			0.230253
$250$		0			0
$251$	−12.5875			−0.794514			−0.397257	−	0.917707i	$-0.630038\pi$
$251$	−12.5875			−0.794514			−0.397257	+	0.917707i	$0.630038\pi$
$252$	10.7518	+	6.20756i	0.677300	+	0.391039i
$253$			22.0707i			1.38757i
$254$	−1.89287	+	3.27855i	−0.118769	+	0.205715i
$255$		0			0
$256$	−2.28239	+	3.95322i	−0.142650	+	0.247076i
$257$	−11.2823	+	6.51386i	−0.703773	+	0.406323i	−0.808751	−	0.588151i	$-0.799856\pi$
$257$	−11.2823	+	6.51386i	−0.703773	+	0.406323i	0.104978	+	0.994475i	$0.466523\pi$
$258$		−	0.872701i		−	0.0543320i
$259$	−9.40842	+	10.3890i	−0.584611	+	0.645538i
$260$		0			0
$261$	2.03662	+	3.52754i	0.126064	+	0.218349i
$262$	5.91128	+	3.41288i	0.365200	+	0.210848i
$263$	−12.7745	−	7.37535i	−0.787709	−	0.454784i	0.0514467	−	0.998676i	$-0.483617\pi$
$263$	−12.7745	−	7.37535i	−0.787709	−	0.454784i	−0.839155	+	0.543892i	$0.816950\pi$
$264$	0.959014	−	1.66106i	0.0590232	−	0.102231i
$265$		0			0
$266$	−1.36252	+	2.35996i	−0.0835415	+	0.144698i
$267$			2.24002i			0.137087i
$268$	8.21764	−	4.74446i	0.501972	−	0.289814i
$269$	11.8049			0.719757			0.359879	−	0.932999i	$-0.382818\pi$
$269$	11.8049			0.719757			0.359879	+	0.932999i	$0.382818\pi$
$270$		0			0
$271$	−9.12973	−	15.8132i	−0.554592	−	0.960581i	−0.997935	−	0.0642292i	$-0.979541\pi$
$271$	−9.12973	−	15.8132i	−0.554592	−	0.960581i	0.443343	−	0.896352i	$-0.353792\pi$
$272$	−9.29229	−	5.36490i	−0.563428	−	0.325295i
$273$			0.527748i			0.0319408i
$274$	−0.520650	−	0.901793i	−0.0314536	−	0.0544793i
$275$		0			0
$276$	−1.12336	−	1.94571i	−0.0676180	−	0.117118i
$277$	−9.55253	−	5.51516i	−0.573956	−	0.331374i	0.184772	−	0.982781i	$-0.440845\pi$
$277$	−9.55253	−	5.51516i	−0.573956	−	0.331374i	−0.758728	+	0.651408i	$0.774179\pi$
$278$	1.05115	+	0.606881i	0.0630437	+	0.0363983i
$279$	−6.67422	−	11.5601i	−0.399575	−	0.692084i
$280$		0			0
$281$	10.2346	+	17.7269i	0.610546	+	1.05750i	0.991148	+	0.132759i	$0.0423835\pi$
$281$	10.2346	+	17.7269i	0.610546	+	1.05750i	−0.380602	+	0.924739i	$0.624283\pi$
$282$		−	1.01139i		−	0.0602275i
$283$	−7.24477	−	4.18277i	−0.430657	−	0.248640i	0.268970	−	0.963149i	$-0.413317\pi$
$283$	−7.24477	−	4.18277i	−0.430657	−	0.248640i	−0.699626	+	0.714509i	$0.746650\pi$
$284$	−7.03349	−	12.1824i	−0.417361	−	0.722890i
$285$		0			0
$286$	−1.66385			−0.0983855
$287$	16.8066	−	9.70332i	0.992065	−	0.572769i
$288$		−	12.6551i		−	0.745706i
$289$	−2.33247	+	4.03995i	−0.137204	+	0.237644i
$290$		0			0
$291$	2.33223	−	4.03953i	0.136718	−	0.236802i
$292$	−3.53920	−	2.04336i	−0.207116	−	0.119578i
$293$	10.9259	+	6.30806i	0.638297	+	0.368521i	0.783958	−	0.620814i	$-0.213198\pi$
$293$	10.9259	+	6.30806i	0.638297	+	0.368521i	−0.145661	+	0.989335i	$0.546531\pi$
$294$	0.0891922	+	0.154485i	0.00520179	+	0.00900977i
$295$		0			0
$296$	9.18168	+	1.97920i	0.533674	+	0.115039i
$297$		−	7.36741i		−	0.427500i
$298$	−2.72208	+	1.57160i	−0.157686	+	0.0910401i
$299$	−2.03478	+	3.52434i	−0.117674	+	0.203818i
$300$		0			0
$301$	−9.52876	+	16.5043i	−0.549228	+	0.951291i
$302$		−	9.22892i		−	0.531065i
$303$	−0.125366	−	0.0723799i	−0.00720207	−	0.00415812i
$304$	−8.98066			−0.515076
$305$		0			0
$306$	4.14171			0.236766
$307$		−	10.0118i		−	0.571404i	−0.958318	−	0.285702i	$-0.907773\pi$
$307$		−	10.0118i		−	0.571404i	0.958318	−	0.285702i	$-0.0922268\pi$
$308$	−17.3718	+	10.0296i	−0.989850	+	0.571490i
$309$	−0.861504	+	1.49217i	−0.0490092	+	0.0848865i
$310$		0			0
$311$	−11.0837	−	19.1976i	−0.628500	−	1.08859i	−0.987853	−	0.155392i	$-0.950336\pi$
$311$	−11.0837	−	19.1976i	−0.628500	−	1.08859i	0.359353	−	0.933202i	$-0.382997\pi$
$312$	0.306279	−	0.176830i	0.0173396	−	0.0100110i
$313$	−2.82211	+	1.62935i	−0.159515	+	0.0920961i	−0.577633	−	0.816297i	$-0.696023\pi$
$313$	−2.82211	+	1.62935i	−0.159515	+	0.0920961i	0.418118	+	0.908393i	$0.362690\pi$
$314$	1.18401	−	2.05076i	0.0668175	−	0.115731i
$315$		0			0
$316$	−0.946365	−	1.63915i	−0.0532372	−	0.0922095i
$317$	−16.6988	+	9.64103i	−0.937896	+	0.541494i	−0.889300	−	0.457324i	$-0.848808\pi$
$317$	−16.6988	+	9.64103i	−0.937896	+	0.541494i	−0.0485957	+	0.998819i	$0.515475\pi$
$318$	0.00767249	−	0.00442972i	0.000430252	−	0.000248406i
$319$	−6.58118			−0.368476
$320$		0			0
$321$	1.58880	+	2.75188i	0.0886781	+	0.153595i
$322$		−	4.32008i		−	0.240749i
$323$		−	10.3242i		−	0.574456i
$324$	−7.70700	−	13.3489i	−0.428167	−	0.741607i
$325$		0			0
$326$	−4.70599	+	8.15101i	−0.260641	+	0.451443i
$327$		−	4.58374i		−	0.253482i
$328$	−11.2627	−	6.50250i	−0.621876	−	0.359040i
$329$	−11.0431	+	19.1272i	−0.608825	+	1.05451i
$330$		0			0
$331$	−8.57889	−	14.8591i	−0.471539	−	0.816729i	0.527931	−	0.849287i	$-0.322968\pi$
$331$	−8.57889	−	14.8591i	−0.471539	−	0.816729i	−0.999470	+	0.0325584i	$0.989635\pi$
$332$			25.4638i			1.39751i
$333$	16.9730	−	5.46101i	0.930112	−	0.299261i
$334$	4.40570			0.241069
$335$		0			0
$336$	0.923159	−	1.59896i	0.0503624	−	0.0872303i
$337$	14.8132	+	8.55240i	0.806926	+	0.465879i	0.845887	−	0.533362i	$-0.179072\pi$
$337$	14.8132	+	8.55240i	0.806926	+	0.465879i	−0.0389614	+	0.999241i	$0.512405\pi$
$338$	4.26366	+	2.46163i	0.231913	+	0.133895i
$339$	−0.746684			−0.0405543
$340$		0			0
$341$	21.5672			1.16793
$342$	3.00211	−	1.73327i	0.162336	−	0.0937245i
$343$		−	20.0250i		−	1.08125i
$344$	12.7710			0.688568
$345$		0			0
$346$	3.47344	−	6.01617i	0.186733	−	0.323431i
$347$		−	2.86901i		−	0.154016i	−0.997030	−	0.0770082i	$-0.975463\pi$
$347$		−	2.86901i		−	0.154016i	0.997030	−	0.0770082i	$-0.0245368\pi$
$348$	0.580184	−	0.334969i	0.0311011	−	0.0179562i
$349$	−10.1209	−	17.5300i	−0.541761	−	0.938358i	−0.998803	−	0.0489125i	$-0.984424\pi$
$349$	−10.1209	−	17.5300i	−0.541761	−	0.938358i	0.457042	−	0.889445i	$-0.348909\pi$
$350$		0			0
$351$	0.679229	−	1.17646i	0.0362546	−	0.0627947i
$352$	17.7075	+	10.2234i	0.943814	+	0.544911i
$353$	−5.98135	+	3.45333i	−0.318355	+	0.183802i	−0.650659	−	0.759370i	$-0.725507\pi$
$353$	−5.98135	+	3.45333i	−0.318355	+	0.183802i	0.332304	+	0.943172i	$0.392174\pi$
$354$	−0.375581	−	0.650525i	−0.0199619	−	0.0345750i
$355$		0			0
$356$	−15.6990			−0.832043
$357$	1.83817	+	1.06127i	0.0972865	+	0.0561684i
$358$	−2.66706	+	1.53983i	−0.140959	+	0.0813825i
$359$	9.60626			0.506999			0.253500	−	0.967335i	$-0.418418\pi$
$359$	9.60626			0.506999			0.253500	+	0.967335i	$0.418418\pi$
$360$		0			0
$361$	5.17940	+	8.97098i	0.272600	+	0.472157i
$362$		−	7.63092i		−	0.401072i
$363$	2.59609	+	1.49886i	0.136260	+	0.0786695i
$364$	−3.69867			−0.193863
$365$		0			0
$366$	−0.255947	+	0.443313i	−0.0133785	+	0.0231723i
$367$	−7.54739	−	4.35749i	−0.393970	−	0.227459i	0.289909	−	0.957054i	$-0.406375\pi$
$367$	−7.54739	−	4.35749i	−0.393970	−	0.227459i	−0.683879	+	0.729595i	$0.739708\pi$
$368$	12.3299	−	7.11864i	0.642738	−	0.371085i
$369$	−24.6873			−1.28517
$370$		0			0
$371$	−0.193467			−0.0100443
$372$	−1.90132	+	1.09773i	−0.0985788	+	0.0569145i
$373$	11.7561	+	6.78741i	0.608710	+	0.351439i	0.772460	−	0.635063i	$-0.219026\pi$
$373$	11.7561	+	6.78741i	0.608710	+	0.351439i	−0.163751	+	0.986502i	$0.552359\pi$
$374$	−3.34590	+	5.79527i	−0.173012	+	0.299666i
$375$		0			0
$376$	14.8006			0.763284
$377$	−1.05091	−	0.606744i	−0.0541247	−	0.0312489i
$378$			1.44208i			0.0741728i
$379$	10.8111	+	18.7253i	0.555327	+	0.961854i	0.997878	+	0.0651108i	$0.0207401\pi$
$379$	10.8111	+	18.7253i	0.555327	+	0.961854i	−0.442551	+	0.896743i	$0.645927\pi$
$380$		0			0
$381$	2.46803			0.126441
$382$	4.67198	−	2.69737i	0.239039	−	0.138009i
$383$	19.9971	+	11.5454i	1.02181	+	0.589940i	0.914627	−	0.404299i	$-0.132485\pi$
$383$	19.9971	+	11.5454i	1.02181	+	0.589940i	0.107180	+	0.994240i	$0.465818\pi$
$384$	−2.72614			−0.139118
$385$		0			0
$386$	5.35063	+	9.26756i	0.272340	+	0.471706i
$387$	20.9952	−	12.1216i	1.06725	−	0.616175i
$388$	28.3107	+	16.3452i	1.43726	+	0.829800i
$389$	3.19678	−	5.53698i	0.162083	−	0.280736i	−0.773533	−	0.633757i	$-0.781512\pi$
$389$	3.19678	−	5.53698i	0.162083	−	0.280736i	0.935616	+	0.353021i	$0.114845\pi$
$390$		0			0
$391$	8.18364	+	14.1745i	0.413865	+	0.716835i
$392$	−2.26072	+	1.30523i	−0.114184	+	0.0659240i
$393$		−	4.44990i		−	0.224468i
$394$	2.68794	−	4.65565i	0.135417	−	0.234548i
$395$		0			0
$396$	25.5174			1.28230
$397$			35.3078i			1.77205i	0.463642	+	0.886023i	$0.346542\pi$
$397$			35.3078i			1.77205i	−0.463642	+	0.886023i	$0.653458\pi$
$398$	−6.11007	+	3.52765i	−0.306270	+	0.176825i
$399$	1.77653			0.0889377
$400$		0			0
$401$	25.6866			1.28273			0.641363	−	0.767237i	$-0.278369\pi$
$401$	25.6866			1.28273			0.641363	+	0.767237i	$0.278369\pi$
$402$	0.471727	+	0.272352i	0.0235276	+	0.0135837i
$403$	3.44394	+	1.98836i	0.171555	+	0.0990473i
$404$	0.507267	−	0.878613i	0.0252375	−	0.0437126i
$405$		0			0
$406$	1.28819			0.0639318
$407$	−6.07039	+	28.1610i	−0.300898	+	1.39589i
$408$		−	1.42238i		−	0.0704183i
$409$	−5.16123	−	8.93951i	−0.255206	−	0.442030i	0.709745	−	0.704459i	$-0.248810\pi$
$409$	−5.16123	−	8.93951i	−0.255206	−	0.442030i	−0.964952	+	0.262428i	$0.915477\pi$
$410$		0			0
$411$	−0.339426	+	0.587903i	−0.0167426	+	0.0289991i
$412$	−10.4577	−	6.03776i	−0.515214	−	0.297459i
$413$			16.4034i			0.807158i
$414$	−2.74780	+	4.75933i	−0.135047	+	0.233908i
$415$		0			0
$416$	1.88508	+	3.26505i	0.0924234	+	0.160082i
$417$		−	0.791284i		−	0.0387493i
$418$			5.60092i			0.273950i
$419$	6.40784	+	11.0987i	0.313043	+	0.542207i	0.979020	−	0.203766i	$-0.0653181\pi$
$419$	6.40784	+	11.0987i	0.313043	+	0.542207i	−0.665976	+	0.745973i	$0.731985\pi$
$420$		0			0
$421$	−4.06415			−0.198074			−0.0990372	−	0.995084i	$-0.531576\pi$
$421$	−4.06415			−0.198074			−0.0990372	+	0.995084i	$0.531576\pi$
$422$	−1.47338	+	0.850654i	−0.0717228	+	0.0414092i
$423$	24.3318	−	14.0480i	1.18305	−	0.683035i
$424$	0.0648240	+	0.112279i	0.00314813	+	0.00545273i
$425$		0			0
$426$	0.403752	−	0.699318i	0.0195618	−	0.0338821i
$427$	9.68079	−	5.58921i	0.468486	−	0.270481i
$428$	−19.2863	+	11.1349i	−0.932237	+	0.538227i
$429$	0.542354	+	0.939385i	0.0261851	+	0.0453539i
$430$		0			0
$431$	5.62924	−	9.75013i	0.271151	−	0.469647i	−0.698006	−	0.716092i	$-0.745929\pi$
$431$	5.62924	−	9.75013i	0.271151	−	0.469647i	0.969157	+	0.246445i	$0.0792624\pi$
$432$	−4.11582	+	2.37627i	−0.198022	+	0.114328i
$433$			25.3426i			1.21789i	0.793214	+	0.608944i	$0.208406\pi$
$433$			25.3426i			1.21789i	−0.793214	+	0.608944i	$0.791594\pi$
$434$	−4.22153			−0.202640
$435$		0			0
$436$	32.1247			1.53849
$437$	11.8638	+	6.84957i	0.567522	+	0.327659i
$438$		−	0.234594i		−	0.0112094i
$439$	−0.0491244	+	0.0850859i	−0.00234458	+	0.00406093i	−0.867195	−	0.497968i	$-0.834080\pi$
$439$	−0.0491244	+	0.0850859i	−0.00234458	+	0.00406093i	0.864851	+	0.502029i	$0.167413\pi$
$440$		0			0
$441$	−2.47771	+	4.29152i	−0.117986	+	0.204358i
$442$	−1.06858	+	0.616943i	−0.0508270	+	0.0293450i
$443$		−	27.3663i		−	1.30021i	−0.759843	−	0.650107i	$-0.774724\pi$
$443$		−	27.3663i		−	1.30021i	0.759843	−	0.650107i	$-0.225276\pi$
$444$	−0.898187	−	2.79159i	−0.0426261	−	0.132483i
$445$		0			0
$446$	−0.191971	−	0.332503i	−0.00909007	−	0.0157445i
$447$	1.77460	+	1.02457i	0.0839357	+	0.0484603i
$448$	8.72682	+	5.03843i	0.412304	+	0.238044i
$449$	−1.82022	+	3.15272i	−0.0859017	+	0.148786i	−0.905775	−	0.423759i	$-0.860710\pi$
$449$	−1.82022	+	3.15272i	−0.0859017	+	0.148786i	0.819873	+	0.572545i	$0.194044\pi$
$450$		0			0
$451$	19.9437	−	34.5436i	0.939114	−	1.62659i
$452$		−	5.23306i		−	0.246142i
$453$	−5.21051	+	3.00829i	−0.244811	+	0.141342i
$454$	7.30575			0.342876
$455$		0			0
$456$	−0.595253	−	1.03101i	−0.0278753	−	0.0482814i
$457$	−24.4186	−	14.0981i	−1.14226	−	0.659482i	−0.195268	−	0.980750i	$-0.562558\pi$
$457$	−24.4186	−	14.0981i	−1.14226	−	0.659482i	−0.946988	+	0.321268i	$0.895891\pi$
$458$			6.46825i			0.302242i
$459$	−2.73178	−	4.73158i	−0.127508	−	0.220851i
$460$		0			0
$461$	−6.68865	−	11.5851i	−0.311521	−	0.539571i	0.667171	−	0.744905i	$-0.267505\pi$
$461$	−6.68865	−	11.5851i	−0.311521	−	0.539571i	−0.978692	+	0.205334i	$0.934172\pi$
$462$	−0.997214	−	0.575742i	−0.0463946	−	0.0267859i
$463$	−11.9314	−	6.88862i	−0.554501	−	0.320141i	0.196434	−	0.980517i	$-0.437064\pi$
$463$	−11.9314	−	6.88862i	−0.554501	−	0.320141i	−0.750935	+	0.660376i	$0.770397\pi$
$464$	2.12268	+	3.67659i	0.0985431	+	0.170682i
$465$		0			0
$466$	−1.88682	−	3.26807i	−0.0874053	−	0.151390i
$467$			39.5661i			1.83090i	0.402431	+	0.915450i	$0.368165\pi$
$467$			39.5661i			1.83090i	−0.402431	+	0.915450i	$0.631835\pi$
$468$	4.07473	+	2.35255i	0.188355	+	0.108747i
$469$	−5.94745	−	10.3013i	−0.274628	−	0.475669i
$470$		0			0
$471$	−1.54377			−0.0711334
$472$	9.51972	−	5.49621i	0.438181	−	0.252984i
$473$			39.1699i			1.80103i
$474$	0.0543253	−	0.0940942i	0.00249524	−	0.00432189i
$475$		0			0
$476$	−7.43780	+	12.8827i	−0.340911	+	0.590475i
$477$	0.213138	+	0.123055i	0.00975890	+	0.00563430i
$478$	3.08478	+	1.78100i	0.141095	+	0.0814611i
$479$	2.65439	+	4.59754i	0.121282	+	0.210067i	0.920274	−	0.391275i	$-0.127966\pi$
$479$	2.65439	+	4.59754i	0.121282	+	0.210067i	−0.798991	+	0.601343i	$0.794633\pi$
$480$		0			0
$481$	−3.56562	+	3.93722i	−0.162578	+	0.179522i
$482$			7.63540i			0.347783i
$483$	−2.43906	+	1.40819i	−0.110981	+	0.0640748i
$484$	−10.5046	+	18.1945i	−0.477481	+	0.827021i
$485$		0			0
$486$	1.38118	−	2.39228i	0.0626517	−	0.108516i
$487$		−	25.9029i		−	1.17377i	−0.809670	−	0.586886i	$-0.800354\pi$
$487$		−	25.9029i		−	1.17377i	0.809670	−	0.586886i	$-0.199646\pi$
$488$	−6.48740	−	3.74550i	−0.293671	−	0.169551i
$489$	6.13592			0.277476
$490$		0			0
$491$	3.32604			0.150102			0.0750510	−	0.997180i	$-0.476088\pi$
$491$	3.32604			0.150102			0.0750510	+	0.997180i	$0.476088\pi$
$492$			4.06039i			0.183056i
$493$	−4.22664	+	2.44025i	−0.190358	+	0.109903i
$494$	−0.516370	+	0.894379i	−0.0232326	+	0.0402400i
$495$		0			0
$496$	−6.95624	−	12.0486i	−0.312344	−	0.540996i
$497$	−15.2713	+	8.81688i	−0.685010	+	0.395491i
$498$	−1.26589	+	0.730865i	−0.0567261	+	0.0327508i
$499$	−15.5649	+	26.9592i	−0.696780	+	1.20686i	0.272797	+	0.962072i	$0.412051\pi$
$499$	−15.5649	+	26.9592i	−0.696780	+	1.20686i	−0.969577	+	0.244787i	$0.921282\pi$
$500$		0			0
$501$	−1.43610	−	2.48739i	−0.0641601	−	0.111129i
$502$	4.38562	−	2.53204i	0.195740	−	0.113011i
$503$	−25.8888	+	14.9469i	−1.15433	+	0.666451i	−0.949938	−	0.312439i	$-0.898854\pi$
$503$	−25.8888	+	14.9469i	−1.15433	+	0.666451i	−0.204389	+	0.978890i	$0.565521\pi$
$504$	−10.4293			−0.464557
$505$		0			0
$506$	−4.43965	−	7.68969i	−0.197366	−	0.341849i
$507$		−	3.20960i		−	0.142543i
$508$			17.2969i			0.767428i
$509$	21.2285	+	36.7688i	0.940936	+	1.62975i	0.763691	+	0.645583i	$0.223385\pi$
$509$	21.2285	+	36.7688i	0.940936	+	1.62975i	0.177246	+	0.984167i	$0.443281\pi$
$510$		0			0
$511$	−2.56146	+	4.43659i	−0.113312	+	0.196263i
$512$		−	22.6247i		−	0.999878i
$513$	−3.96025	−	2.28645i	−0.174849	−	0.100949i
$514$	2.62060	−	4.53901i	0.115590	−	0.200207i
$515$		0			0
$516$	−1.99367	−	3.45314i	−0.0877664	−	0.152016i
$517$			45.3948i			1.99646i
$518$	1.18821	−	5.51219i	0.0522069	−	0.242192i
$519$	−4.52885			−0.198795
$520$		0			0
$521$	−4.40062	+	7.62209i	−0.192795	+	0.333930i	−0.946175	−	0.323655i	$-0.895088\pi$
$521$	−4.40062	+	7.62209i	−0.192795	+	0.333930i	0.753381	+	0.657585i	$0.228422\pi$
$522$	−1.41917	−	0.819357i	−0.0621153	−	0.0358623i
$523$	3.62916	+	2.09530i	0.158692	+	0.0916209i	0.577243	−	0.816572i	$-0.304129\pi$
$523$	3.62916	+	2.09530i	0.158692	+	0.0916209i	−0.418551	+	0.908193i	$0.637462\pi$
$524$	31.1867			1.36240
$525$		0			0
$526$	5.93438			0.258751
$527$	13.8511	−	7.99694i	0.603364	−	0.348352i
$528$		−	3.79483i		−	0.165149i
$529$	1.28239			0.0557561
$530$		0			0
$531$	10.4334	−	18.0712i	0.452772	−	0.784224i
$532$			12.4506i			0.539803i
$533$	6.36940	−	3.67738i	0.275890	−	0.159285i
$534$	−0.450593	−	0.780450i	−0.0194991	−	0.0337734i
$535$		0			0
$536$	−3.98557	+	6.90321i	−0.172150	+	0.298173i
$537$	1.73873	+	1.00386i	0.0750317	+	0.0433196i
$538$	−4.11297	+	2.37462i	−0.177323	+	0.102377i
$539$	−4.00326	−	6.93384i	−0.172432	−	0.298662i
$540$		0			0
$541$	10.4351			0.448640			0.224320	−	0.974516i	$-0.427984\pi$
$541$	10.4351			0.448640			0.224320	+	0.974516i	$0.427984\pi$
$542$	6.36181	+	3.67299i	0.273263	+	0.157769i
$543$	−4.30831	+	2.48740i	−0.184887	+	0.106745i
$544$	15.1631			0.650112
$545$		0			0
$546$	−0.106160	−	0.183874i	−0.00454321	−	0.00786907i
$547$		−	8.80876i		−	0.376635i	−0.982108	−	0.188318i	$-0.939697\pi$
$547$		−	8.80876i		−	0.376635i	0.982108	−	0.188318i	$-0.0603035\pi$
$548$	−4.12026	−	2.37883i	−0.176009	−	0.101619i
$549$	−14.2201			−0.606900
$550$		0			0
$551$	−2.04245	+	3.53762i	−0.0870112	+	0.150708i
$552$	1.63449	+	0.943672i	0.0695684	+	0.0401653i
$553$	−2.05477	+	1.18632i	−0.0873777	+	0.0504475i
$554$	4.43762			0.188536
$555$		0			0
$556$	5.54563			0.235187
$557$	−17.8555	+	10.3089i	−0.756561	+	0.436800i	−0.828060	−	0.560640i	$-0.810555\pi$
$557$	−17.8555	+	10.3089i	−0.756561	+	0.436800i	0.0714989	+	0.997441i	$0.477222\pi$
$558$	4.65075	+	2.68511i	0.196882	+	0.113670i
$559$	−3.61122	+	6.25482i	−0.152738	+	0.264551i
$560$		0			0
$561$	4.36257			0.184188
$562$	−7.13173	−	4.11750i	−0.300834	−	0.173686i
$563$			1.74811i			0.0736740i	0.999321	+	0.0368370i	$0.0117282\pi$
$563$			1.74811i			0.0736740i	−0.999321	+	0.0368370i	$0.988272\pi$
$564$	−2.31051	−	4.00192i	−0.0972899	−	0.168511i
$565$		0			0
$566$	3.36555			0.141465
$567$	−16.7336	+	9.66116i	−0.702746	+	0.405731i
$568$	10.2338	+	5.90846i	0.429399	+	0.247914i
$569$	−39.2910			−1.64716			−0.823582	−	0.567198i	$-0.808028\pi$
$569$	−39.2910			−1.64716			−0.823582	+	0.567198i	$0.808028\pi$
$570$		0			0
$571$	−10.2664	−	17.7819i	−0.429635	−	0.744149i	0.567206	−	0.823576i	$-0.308024\pi$
$571$	−10.2664	−	17.7819i	−0.429635	−	0.744149i	−0.996841	+	0.0794269i	$0.974691\pi$
$572$	−6.58359	+	3.80103i	−0.275274	+	0.158929i
$573$	−3.04579	−	1.75849i	−0.127240	−	0.0734618i
$574$	−3.90376	+	6.76150i	−0.162940	+	0.282220i
$575$		0			0
$576$	−6.40942	−	11.1014i	−0.267059	−	0.462560i
$577$	37.7833	−	21.8142i	1.57294	−	0.908138i	0.577135	−	0.816649i	$-0.304171\pi$
$577$	37.7833	−	21.8142i	1.57294	−	0.908138i	0.995806	−	0.0914896i	$-0.0291628\pi$
$578$		−	1.87676i		−	0.0780627i
$579$	3.48822	−	6.04177i	0.144965	−	0.251087i
$580$		0			0
$581$	31.9203			1.32428
$582$			1.87656i			0.0777860i
$583$	−0.344368	+	0.198821i	−0.0142623	+	0.00823433i
$584$	3.43303			0.142060
$585$		0			0
$586$	−5.07561			−0.209672
$587$	16.6133	+	9.59172i	0.685706	+	0.395893i	0.802001	−	0.597322i	$-0.203769\pi$
$587$	16.6133	+	9.59172i	0.685706	+	0.395893i	−0.116295	+	0.993215i	$0.537102\pi$
$588$	0.705838	+	0.407516i	0.0291083	+	0.0168057i
$589$	6.69330	−	11.5931i	0.275793	−	0.477687i
$590$		0			0
$591$	−3.50468			−0.144163
$592$	17.6902	−	5.69177i	0.727061	−	0.233930i
$593$			7.87377i			0.323337i	0.986845	+	0.161668i	$0.0516875\pi$
$593$			7.87377i			0.323337i	−0.986845	+	0.161668i	$0.948312\pi$
$594$	1.48200	+	2.56689i	0.0608070	+	0.105321i
$595$		0			0
$596$	−7.18056	+	12.4371i	−0.294127	+	0.509443i
$597$	3.98332	+	2.29977i	0.163026	+	0.0941233i
$598$		−	1.63723i		−	0.0669514i
$599$	16.8040	−	29.1055i	0.686594	−	1.18922i	−0.286338	−	0.958129i	$-0.592438\pi$
$599$	16.8040	−	29.1055i	0.686594	−	1.18922i	0.972933	−	0.231088i	$-0.0742285\pi$
$600$		0			0
$601$	15.4364	+	26.7366i	0.629663	+	1.09061i	0.987619	+	0.156870i	$0.0501403\pi$
$601$	15.4364	+	26.7366i	0.629663	+	1.09061i	−0.357956	+	0.933738i	$0.616526\pi$
$602$		−	7.66705i		−	0.312486i
$603$			15.1316i			0.616205i
$604$	−21.0833	−	36.5174i	−0.857868	−	1.48587i
$605$		0			0
$606$	0.0582385			0.00236578
$607$	−36.1752	+	20.8857i	−1.46830	+	0.847726i	−0.999369	−	0.0355065i	$-0.988696\pi$
$607$	−36.1752	+	20.8857i	−1.46830	+	0.847726i	−0.468935	+	0.883233i	$0.655362\pi$
$608$	10.9909	−	6.34562i	0.445741	−	0.257349i
$609$	−0.419903	−	0.727293i	−0.0170153	−	0.0294714i
$610$		0			0
$611$	−4.18512	+	7.24884i	−0.169312	+	0.293257i
$612$	16.3881	−	9.46167i	0.662449	−	0.382465i
$613$	26.7385	−	15.4375i	1.07996	−	0.623513i	0.149072	−	0.988826i	$-0.452372\pi$
$613$	26.7385	−	15.4375i	1.07996	−	0.623513i	0.930885	+	0.365313i	$0.119038\pi$
$614$	2.01393	+	3.48823i	0.0812757	+	0.140774i
$615$		0			0
$616$	8.42535	−	14.5931i	0.339467	−	0.587974i
$617$	−31.7473	+	18.3293i	−1.27810	+	0.737910i	−0.976498	−	0.215525i	$-0.930854\pi$
$617$	−31.7473	+	18.3293i	−1.27810	+	0.737910i	−0.301599	+	0.953435i	$0.597520\pi$
$618$		−	0.693185i		−	0.0278840i
$619$	−44.9409			−1.80633			−0.903164	−	0.429295i	$-0.858762\pi$
$619$	−44.9409			−1.80633			−0.903164	+	0.429295i	$0.858762\pi$
$620$		0			0
$621$	7.24954			0.290914
$622$	7.72339	+	4.45910i	0.309680	+	0.178794i
$623$			19.6795i			0.788444i
$624$	0.349860	−	0.605975i	0.0140056	−	0.0242584i
$625$		0			0
$626$	0.655504	−	1.13537i	0.0261992	−	0.0453784i
$627$	3.16220	−	1.82570i	0.126286	−	0.0729113i
$628$		−	10.8194i		−	0.431740i
$629$	6.54330	+	20.3367i	0.260898	+	0.810879i
$630$		0			0
$631$	−7.54686	−	13.0715i	−0.300436	−	0.520370i	0.675799	−	0.737086i	$-0.263799\pi$
$631$	−7.54686	−	13.0715i	−0.300436	−	0.520370i	−0.976235	+	0.216716i	$0.930465\pi$
$632$	1.37697	+	0.794991i	0.0547727	+	0.0316231i
$633$	0.960533	+	0.554564i	0.0381778	+	0.0220419i
$634$	3.87870	−	6.71810i	0.154043	−	0.266810i
$635$		0			0
$636$	0.0202392	−	0.0350553i	0.000802537	−	0.00139003i
$637$		−	1.47630i		−	0.0584932i
$638$	2.29296	−	1.32384i	0.0907793	−	0.0524114i
$639$	22.4320			0.887396
$640$		0			0
$641$	17.6553	+	30.5798i	0.697341	+	1.20783i	0.969385	+	0.245545i	$0.0789670\pi$
$641$	17.6553	+	30.5798i	0.697341	+	1.20783i	−0.272044	+	0.962285i	$0.587700\pi$
$642$	−1.10711	−	0.639192i	−0.0436943	−	0.0252269i
$643$		−	26.4749i		−	1.04407i	−0.852925	−	0.522033i	$-0.825174\pi$
$643$		−	26.4749i		−	1.04407i	0.852925	−	0.522033i	$-0.174826\pi$
$644$	−9.86915	−	17.0939i	−0.388899	−	0.673593i
$645$		0			0
$646$	2.07678	+	3.59708i	0.0817097	+	0.141525i
$647$	35.2290	+	20.3395i	1.38499	+	0.799627i	0.992746	−	0.120232i	$-0.0383639\pi$
$647$	35.2290	+	20.3395i	1.38499	+	0.799627i	0.392249	+	0.919859i	$0.371697\pi$
$648$	11.2137	+	6.47425i	0.440517	+	0.254332i
$649$	16.8574	+	29.1978i	0.661710	+	1.14612i
$650$		0			0
$651$	1.37606	+	2.38341i	0.0539322	+	0.0934133i
$652$			43.0030i			1.68413i
$653$	−33.6959	−	19.4543i	−1.31862	−	0.761307i	−0.335116	−	0.942177i	$-0.608775\pi$
$653$	−33.6959	−	19.4543i	−1.31862	−	0.761307i	−0.983507	+	0.180870i	$0.942109\pi$
$654$	0.922046	+	1.59703i	0.0360549	+	0.0624488i
$655$		0			0
$656$	−25.7305			−1.00461
$657$	5.64380	−	3.25845i	0.220186	−	0.127124i
$658$		−	8.88551i		−	0.346393i
$659$	−9.10755	+	15.7747i	−0.354780	+	0.614496i	−0.987080	−	0.160227i	$-0.948777\pi$
$659$	−9.10755	+	15.7747i	−0.354780	+	0.614496i	0.632301	+	0.774723i	$0.282111\pi$
$660$		0			0
$661$	3.38484	−	5.86271i	0.131655	−	0.228033i	−0.792660	−	0.609664i	$-0.791304\pi$
$661$	3.38484	−	5.86271i	0.131655	−	0.228033i	0.924315	+	0.381631i	$0.124638\pi$
$662$	5.97797	+	3.45138i	0.232341	+	0.134142i
$663$	0.696633	+	0.402201i	0.0270550	+	0.0156202i
$664$	−10.6954	−	18.5250i	−0.415062	−	0.718909i
$665$		0			0
$666$	−4.81507	+	5.31689i	−0.186580	+	0.206025i
$667$		−	6.47590i		−	0.250748i
$668$	17.4326	−	10.0647i	0.674489	−	0.389417i
$669$	−0.125151	+	0.216768i	−0.00483861	+	0.00838072i
$670$		0			0
$671$	11.4878	−	19.8974i	0.443481	−	0.768132i
$672$			2.60917i			0.100651i
$673$	−6.38236	−	3.68486i	−0.246022	−	0.142041i	0.371920	−	0.928265i	$-0.378700\pi$
$673$	−6.38236	−	3.68486i	−0.246022	−	0.142041i	−0.617941	+	0.786224i	$0.712033\pi$
$674$	−6.88145			−0.265064
$675$		0			0
$676$	22.4942			0.865160
$677$		−	49.9703i		−	1.92051i	−0.279118	−	0.960257i	$-0.590042\pi$
$677$		−	49.9703i		−	1.92051i	0.279118	−	0.960257i	$-0.409958\pi$
$678$	0.260154	−	0.150200i	0.00999114	−	0.00576839i
$679$	20.4896	−	35.4890i	0.786319	−	1.36194i
$680$		0			0
$681$	−2.38141	−	4.12472i	−0.0912558	−	0.158060i
$682$	−7.51426	+	4.33836i	−0.287736	+	0.166124i
$683$	−18.0036	+	10.3944i	−0.688887	+	0.397729i	−0.803195	−	0.595716i	$-0.796868\pi$
$683$	−18.0036	+	10.3944i	−0.688887	+	0.397729i	0.114308	+	0.993445i	$0.463535\pi$
$684$	7.91925	−	13.7165i	0.302800	−	0.524465i
$685$		0			0
$686$	4.02814	+	6.97694i	0.153795	+	0.266381i
$687$	3.65188	−	2.10841i	0.139328	−	0.0804410i
$688$	21.8824	−	12.6338i	0.834257	−	0.481659i
$689$	−0.0733203			−0.00279328
$690$		0			0
$691$	−3.66239	−	6.34345i	−0.139324	−	0.241316i	0.787917	−	0.615782i	$-0.211160\pi$
$691$	−3.66239	−	6.34345i	−0.139324	−	0.241316i	−0.927241	+	0.374465i	$0.877826\pi$
$692$		−	31.7400i		−	1.20657i
$693$		−	31.9876i		−	1.21511i
$694$	0.577117	+	0.999596i	0.0219071	+	0.0379441i
$695$		0			0
$696$	−0.281390	+	0.487382i	−0.0106661	+	0.0184742i
$697$		−	29.5799i		−	1.12042i
$698$	7.05250	+	4.07176i	0.266941	+	0.154119i
$699$	−1.23007	+	2.13054i	−0.0465255	+	0.0805846i
$700$		0			0
$701$	−19.9178	−	34.4986i	−0.752283	−	1.30299i	−0.946714	−	0.322076i	$-0.895619\pi$
$701$	−19.9178	−	34.4986i	−0.752283	−	1.30299i	0.194431	−	0.980916i	$-0.437714\pi$
$702$			0.546523i			0.0206272i
$703$	13.2536	+	12.0027i	0.499870	+	0.452692i
$704$	20.7115			0.780595
$705$		0			0
$706$	1.38931	−	2.40636i	0.0522875	−	0.0905647i
$707$	−1.10139	−	0.635888i	−0.0414221	−	0.0239150i
$708$	−2.97222	−	1.71601i	−0.111703	−	0.0644918i
$709$	−41.1334			−1.54480			−0.772398	−	0.635139i	$-0.780943\pi$
$709$	−41.1334			−1.54480			−0.772398	+	0.635139i	$0.780943\pi$
$710$		0			0
$711$	3.01825			0.113193
$712$	11.4210	−	6.59393i	0.428021	−	0.247118i
$713$			21.2221i			0.794776i
$714$	−0.853922			−0.0319572
$715$		0			0
$716$	−7.03542	+	12.1857i	−0.262926	+	0.455401i
$717$		−	2.32216i		−	0.0867228i
$718$	−3.34694	+	1.93235i	−0.124907	+	0.0721148i
$719$	17.4791	+	30.2747i	0.651862	+	1.12906i	0.982671	+	0.185360i	$0.0593450\pi$
$719$	17.4791	+	30.2747i	0.651862	+	1.12906i	−0.330809	+	0.943698i	$0.607322\pi$
$720$		0			0
$721$	−7.56868	+	13.1093i	−0.281872	+	0.488217i
$722$	−3.60913	−	2.08373i	−0.134318	−	0.0775484i
$723$	4.31084	−	2.48886i	0.160322	−	0.0925618i
$724$	−17.4327	−	30.1943i	−0.647881	−	1.12216i
$725$		0			0
$726$	−1.20601			−0.0447594
$727$	−40.9935	−	23.6676i	−1.52037	−	0.877784i	−0.999712	−	0.0240160i	$-0.992355\pi$
$727$	−40.9935	−	23.6676i	−1.52037	−	0.877784i	−0.520654	−	0.853768i	$-0.674312\pi$
$728$	2.69079	−	1.55353i	0.0997274	−	0.0575776i
$729$	23.3560			0.865038
$730$		0			0
$731$	14.5239	+	25.1561i	0.537185	+	0.930433i
$732$			2.33882i			0.0864454i
$733$	−42.8601	−	24.7453i	−1.58307	−	0.913987i	−0.994408	−	0.105610i	$-0.966321\pi$
$733$	−42.8601	−	24.7453i	−1.58307	−	0.913987i	−0.588665	−	0.808377i	$-0.700346\pi$
$734$	3.50613			0.129414
$735$		0			0
$736$	−10.0599	+	17.4242i	−0.370812	+	0.642266i
$737$	−21.1728	−	12.2241i	−0.779909	−	0.450280i
$738$	8.60134	−	4.96599i	0.316620	−	0.182801i
$739$	−11.8433			−0.435665			−0.217832	−	0.975986i	$-0.569899\pi$
$739$	−11.8433			−0.435665			−0.217832	+	0.975986i	$0.569899\pi$
$740$		0			0
$741$	0.673271			0.0247332
$742$	0.0674061	−	0.0389169i	0.00247456	−	0.00142869i
$743$	−9.27749	−	5.35636i	−0.340358	−	0.196506i	0.320072	−	0.947393i	$-0.396293\pi$
$743$	−9.27749	−	5.35636i	−0.340358	−	0.196506i	−0.660430	+	0.750887i	$0.729626\pi$
$744$	0.922143	−	1.59720i	0.0338074	−	0.0585561i
$745$		0			0
$746$	−5.46130			−0.199952
$747$	−35.1659	−	20.3030i	−1.28665	−	0.742849i
$748$			30.5746i			1.11792i
$749$	13.9583	+	24.1764i	0.510024	+	0.883388i
$750$		0			0
$751$	−49.8425			−1.81878			−0.909390	−	0.415946i	$-0.863451\pi$
$751$	−49.8425			−1.81878			−0.909390	+	0.415946i	$0.863451\pi$
$752$	25.3599	−	14.6416i	0.924781	−	0.533923i
$753$	−2.85911	−	1.65071i	−0.104192	−	0.0601551i
$754$	0.488200			0.0177792
$755$		0			0
$756$	3.29442	+	5.70610i	0.119817	+	0.207529i
$757$	3.28784	−	1.89824i	0.119499	−	0.0689925i	−0.439059	−	0.898458i	$-0.644688\pi$
$757$	3.28784	−	1.89824i	0.119499	−	0.0689925i	0.558558	+	0.829466i	$0.311355\pi$
$758$	−7.53340	−	4.34941i	−0.273625	−	0.157978i
$759$	−2.89433	+	5.01312i	−0.105057	+	0.181965i
$760$		0			0
$761$	−17.9425	−	31.0772i	−0.650413	−	1.12655i	−0.983023	−	0.183484i	$-0.941262\pi$
$761$	−17.9425	−	31.0772i	−0.650413	−	1.12655i	0.332609	−	0.943065i	$-0.392071\pi$
$762$	−0.859891	+	0.496458i	−0.0311506	+	0.0179848i
$763$		−	40.2701i		−	1.45788i
$764$	12.3242	−	21.3461i	0.445873	−	0.772275i
$765$		0			0
$766$	−9.28966			−0.335649
$767$			6.21658i			0.224468i
$768$	−1.03684	+	0.598620i	−0.0374138	+	0.0216009i
$769$	9.51810			0.343232			0.171616	−	0.985164i	$-0.445101\pi$
$769$	9.51810			0.343232			0.171616	+	0.985164i	$0.445101\pi$
$770$		0			0
$771$	−3.41688			−0.123056
$772$	42.3431	+	24.4468i	1.52396	+	0.879860i
$773$	−31.9894	−	18.4691i	−1.15058	−	0.664287i	−0.201550	−	0.979478i	$-0.564598\pi$
$773$	−31.9894	−	18.4691i	−1.15058	−	0.664287i	−0.949028	+	0.315192i	$0.897931\pi$
$774$	−4.87665	+	8.44660i	−0.175288	+	0.303607i
$775$		0			0
$776$	−27.4614			−0.985808
$777$	−3.49942	+	1.12593i	−0.125541	+	0.0403925i
$778$			2.57220i			0.0922178i
$779$	−12.3789	−	21.4410i	−0.443522	−	0.768202i
$780$		0			0
$781$	−18.1218	+	31.3879i	−0.648448	+	1.12315i
$782$	−5.70256	−	3.29237i	−0.203923	−	0.117735i
$783$			2.16171i			0.0772534i
$784$	−2.58241	+	4.47286i	−0.0922288	+	0.159745i
$785$		0			0
$786$	0.895122	+	1.55040i	0.0319279	+	0.0553008i
$787$		−	44.5576i		−	1.58831i	−0.607717	−	0.794154i	$-0.707914\pi$
$787$		−	44.5576i		−	1.58831i	0.607717	−	0.794154i	$-0.292086\pi$
$788$		−	24.5622i		−	0.874993i
$789$	−1.93439	−	3.35046i	−0.0688661	−	0.119280i
$790$		0			0
$791$	−6.55994			−0.233245
$792$	−18.5640	+	10.7179i	−0.659643	+	0.380845i
$793$	3.66884	−	2.11820i	0.130284	−	0.0752196i
$794$	−7.10235	−	12.3016i	−0.252053	−	0.436569i
$795$		0			0
$796$	−16.1177	+	27.9167i	−0.571277	+	0.989480i
$797$	−13.1243	+	7.57730i	−0.464886	+	0.268402i	−0.714096	−	0.700047i	$-0.753162\pi$
$797$	−13.1243	+	7.57730i	−0.464886	+	0.268402i	0.249211	+	0.968449i	$0.419829\pi$
$798$	−0.618964	+	0.357359i	−0.0219111	+	0.0126504i
$799$	16.8320	+	29.1540i	0.595475	+	1.03139i
$800$		0			0
$801$	12.5172	−	21.6805i	0.442274	−	0.766041i
$802$	−8.94951	+	5.16700i	−0.316018	+	0.182453i
$803$			10.5294i			0.371575i
$804$	2.48873			0.0877707
$805$		0			0
$806$	−1.59988			−0.0563534
$807$	2.68135	+	1.54808i	0.0943881	+	0.0544950i
$808$			0.852257i			0.0299823i
$809$	−6.70996	+	11.6220i	−0.235910	+	0.408607i	−0.959537	−	0.281584i	$-0.909140\pi$
$809$	−6.70996	+	11.6220i	−0.235910	+	0.408607i	0.723627	+	0.690191i	$0.242474\pi$
$810$		0			0
$811$	−5.35178	+	9.26955i	−0.187926	+	0.325498i	−0.944559	−	0.328343i	$-0.893510\pi$
$811$	−5.35178	+	9.26955i	−0.187926	+	0.325498i	0.756632	+	0.653841i	$0.226843\pi$
$812$	5.09716	−	2.94285i	0.178875	−	0.103274i
$813$		−	4.78905i		−	0.167959i
$814$	−3.54975	−	11.0327i	−0.124419	−	0.386697i
$815$		0			0
$816$	−1.40709	−	2.43716i	−0.0492582	−	0.0853176i
$817$	21.0552	+	12.1562i	0.736629	+	0.425293i
$818$	3.59647	+	2.07642i	0.125748	+	0.0726004i
$819$	2.94905	−	5.10791i	0.103048	−	0.178485i
$820$		0			0
$821$	12.8441	−	22.2467i	0.448263	−	0.776414i	−0.550010	−	0.835158i	$-0.685376\pi$
$821$	12.8441	−	22.2467i	0.448263	−	0.776414i	0.998273	+	0.0587437i	$0.0187095\pi$
$822$		−	0.273110i		−	0.00952580i
$823$	−20.1170	+	11.6146i	−0.701235	+	0.404858i	−0.807807	−	0.589447i	$-0.799346\pi$
$823$	−20.1170	+	11.6146i	−0.701235	+	0.404858i	0.106572	+	0.994305i	$0.466013\pi$
$824$	10.1440			0.353383
$825$		0			0
$826$	−3.29964	−	5.71514i	−0.114809	−	0.198855i
$827$	−19.6117	−	11.3228i	−0.681966	−	0.393733i	0.118629	−	0.992939i	$-0.462150\pi$
$827$	−19.6117	−	11.3228i	−0.681966	−	0.393733i	−0.800595	+	0.599205i	$0.795483\pi$
$828$			25.1092i			0.872605i
$829$	−9.85476	−	17.0690i	−0.342270	−	0.592829i	0.642584	−	0.766215i	$-0.277862\pi$
$829$	−9.85476	−	17.0690i	−0.342270	−	0.592829i	−0.984854	+	0.173386i	$0.944529\pi$
$830$		0			0
$831$	−1.44650	−	2.50541i	−0.0501786	−	0.0869119i
$832$	3.30730	+	1.90947i	0.114660	+	0.0661990i
$833$	−5.14203	−	2.96875i	−0.178161	−	0.102861i
$834$	0.159171	+	0.275693i	0.00551165	+	0.00954646i
$835$		0			0
$836$	12.7952	+	22.1619i	0.442531	+	0.766487i
$837$		−	7.08415i		−	0.244864i
$838$	−4.46513	−	2.57795i	−0.154245	−	0.0890537i
$839$	7.51885	+	13.0230i	0.259579	+	0.449605i	0.966129	−	0.258058i	$-0.0830827\pi$
$839$	7.51885	+	13.0230i	0.259579	+	0.449605i	−0.706550	+	0.707663i	$0.749749\pi$
$840$		0			0
$841$	−27.0690			−0.933413
$842$	1.41600	−	0.817526i	0.0487985	−	0.0281738i
$843$			5.36862i			0.184905i
$844$	−3.88660	+	6.73180i	−0.133782	+	0.231718i
$845$		0			0
$846$	−5.65165	+	9.78895i	−0.194308	+	0.336551i
$847$	22.8078	+	13.1681i	0.783685	+	0.452461i
$848$	0.222144	+	0.128255i	0.00762845	+	0.00440429i
$849$	−1.09705	−	1.90014i	−0.0376505	−	0.0652126i
$850$		0			0
$851$	−27.7105	−	5.97327i	−0.949904	−	0.204761i
$852$		−	3.68945i		−	0.126399i
$853$	−5.67278	+	3.27518i	−0.194232	+	0.112140i	−0.593962	−	0.804493i	$-0.702437\pi$
$853$	−5.67278	+	3.27518i	−0.194232	+	0.112140i	0.399730	+	0.916633i	$0.369104\pi$
$854$	−2.24860	+	3.89469i	−0.0769455	+	0.133274i
$855$		0			0
$856$	9.35387	−	16.2014i	0.319709	−	0.553752i
$857$			30.4395i			1.03979i	0.854229	+	0.519897i	$0.174030\pi$
$857$			30.4395i			1.03979i	−0.854229	+	0.519897i	$0.825970\pi$
$858$	−0.377925	−	0.218195i	−0.0129022	−	0.00744906i
$859$	33.2301			1.13380			0.566898	−	0.823788i	$-0.308143\pi$
$859$	33.2301			1.13380			0.566898	+	0.823788i	$0.308143\pi$
$860$		0			0
$861$	5.08993			0.173464
$862$			4.52941i			0.154272i
$863$	23.6450	−	13.6514i	0.804884	−	0.464700i	−0.0402922	−	0.999188i	$-0.512829\pi$
$863$	23.6450	−	13.6514i	0.804884	−	0.464700i	0.845176	+	0.534488i	$0.179496\pi$
$864$	3.35808	−	5.81637i	0.114244	−	0.197877i
$865$		0			0
$866$	−5.09780	−	8.82966i	−0.173230	−	0.300044i
$867$	−1.05959	+	0.611754i	−0.0359855	+	0.0207762i
$868$	−16.7039	+	9.64400i	−0.566967	+	0.327339i
$869$	−2.43831	+	4.22328i	−0.0827140	+	0.143265i
$870$		0			0
$871$	−2.25397	−	3.90399i	−0.0763729	−	0.132282i
$872$	−23.3708	+	13.4931i	−0.791435	+	0.456935i
$873$	−45.1458	+	26.0649i	−1.52795	+	0.882164i
$874$	−5.51132			−0.186423
$875$		0			0
$876$	−0.535927	−	0.928252i	−0.0181073	−	0.0313627i
$877$		−	34.0836i		−	1.15092i	−0.817829	−	0.575461i	$-0.804823\pi$
$877$		−	34.0836i		−	1.15092i	0.817829	−	0.575461i	$-0.195177\pi$
$878$		−	0.0395266i		−	0.00133396i
$879$	1.65446	+	2.86561i	0.0558037	+	0.0966548i
$880$		0			0
$881$	15.1852	−	26.3015i	0.511602	−	0.886120i	−0.488308	−	0.872672i	$-0.662386\pi$
$881$	15.1852	−	26.3015i	0.511602	−	0.886120i	0.999910	−	0.0134489i	$-0.00428106\pi$
$882$		−	1.99362i		−	0.0671287i
$883$	−27.8344	−	16.0702i	−0.936703	−	0.540805i	−0.0477774	−	0.998858i	$-0.515214\pi$
$883$	−27.8344	−	16.0702i	−0.936703	−	0.540805i	−0.888925	+	0.458053i	$0.848547\pi$
$884$	−2.81879	+	4.88228i	−0.0948061	+	0.164209i
$885$		0			0
$886$	5.50489	+	9.53475i	0.184940	+	0.320326i
$887$			30.8686i			1.03647i	0.855239	+	0.518233i	$0.173410\pi$
$887$			30.8686i			1.03647i	−0.855239	+	0.518233i	$0.826590\pi$
$888$	1.82597	+	1.65363i	0.0612754	+	0.0554921i
$889$	21.6827			0.727214
$890$		0			0
$891$	−19.8571	+	34.3935i	−0.665238	+	1.15223i
$892$	−1.51919	−	0.877106i	−0.0508663	−	0.0293677i
$893$	24.4013	+	14.0881i	0.816560	+	0.471441i
$894$	−0.824389			−0.0275717
$895$		0			0
$896$	−23.9503			−0.800123
$897$	−0.924357	+	0.533678i	−0.0308634	+	0.0178190i
$898$		−	1.46459i		−	0.0488741i
$899$	−6.32816			−0.211056
$900$		0			0
$901$	−0.147443	+	0.255378i	−0.00491203	+	0.00850788i
$902$			16.0472i			0.534313i
$903$	−4.32870	+	2.49918i	−0.144050	+	0.0831675i
$904$	2.19801	+	3.80706i	0.0731047	+	0.126621i
$905$		0			0
$906$	1.21027	−	2.09625i	0.0402085	−	0.0696432i
$907$	−21.2940	−	12.2941i	−0.707055	−	0.408219i	0.102914	−	0.994690i	$-0.467183\pi$
$907$	−21.2940	−	12.2941i	−0.707055	−	0.408219i	−0.809970	+	0.586472i	$0.800517\pi$
$908$	28.9077	−	16.6899i	0.959335	−	0.553872i
$909$	0.808917	+	1.40109i	0.0268301	+	0.0464711i
$910$		0			0
$911$	−24.0710			−0.797508			−0.398754	−	0.917058i	$-0.630557\pi$
$911$	−24.0710			−0.797508			−0.398754	+	0.917058i	$0.630557\pi$
$912$	−2.03986	−	1.17771i	−0.0675465	−	0.0389980i
$913$	56.8178	−	32.8038i	1.88039	−	1.08565i
$914$	11.3437			0.375215
$915$		0			0
$916$	14.7766	+	25.5938i	0.488233	+	0.845644i
$917$		−	39.0942i		−	1.29101i
$918$	1.90357	+	1.09902i	0.0628271	+	0.0362732i
$919$	49.2679			1.62520			0.812599	−	0.582823i	$-0.198052\pi$
$919$	49.2679			1.62520			0.812599	+	0.582823i	$0.198052\pi$
$920$		0			0
$921$	1.31294	−	2.27407i	0.0432627	−	0.0749333i
$922$	4.66081	+	2.69092i	0.153495	+	0.0886207i
$923$	−5.78753	+	3.34143i	−0.190499	+	0.109985i
$924$	−5.26108			−0.173077
$925$		0			0
$926$	5.54274			0.182146
$927$	16.6764	−	9.62815i	0.547726	−	0.316230i
$928$	−5.19567	−	2.99972i	−0.170556	−	0.0984707i
$929$	−3.75243	+	6.49941i	−0.123113	+	0.213239i	−0.920994	−	0.389577i	$-0.872621\pi$
$929$	−3.75243	+	6.49941i	−0.123113	+	0.213239i	0.797881	+	0.602816i	$0.205955\pi$
$930$		0			0
$931$	−4.96959			−0.162872
$932$	−14.9317	−	8.62082i	−0.489104	−	0.282384i
$933$		−	5.81402i		−	0.190342i
$934$	−7.95894	−	13.7853i	−0.260425	−	0.451069i
$935$		0			0
$936$	−3.95250			−0.129192
$937$	−13.4522	+	7.76664i	−0.439465	+	0.253725i	−0.703371	−	0.710823i	$-0.748323\pi$
$937$	−13.4522	+	7.76664i	−0.439465	+	0.253725i	0.263906	+	0.964548i	$0.414989\pi$
$938$	4.14432	+	2.39273i	0.135317	+	0.0781252i
$939$	−0.854682			−0.0278915
$940$		0			0
$941$	11.0247	+	19.0953i	0.359395	+	0.622490i	0.987860	−	0.155348i	$-0.0496499\pi$
$941$	11.0247	+	19.0953i	0.359395	+	0.622490i	−0.628465	+	0.777838i	$0.716317\pi$
$942$	0.537869	−	0.310539i	0.0175247	−	0.0101179i
$943$	33.9909	+	19.6247i	1.10690	+	0.639067i
$944$	10.8743	−	18.8348i	0.353928	−	0.613021i
$945$		0			0
$946$	−7.87925	−	13.6473i	−0.256176	−	0.443710i
$947$	45.8540	−	26.4738i	1.49006	−	0.860284i	0.490120	−	0.871655i	$-0.336953\pi$
$947$	45.8540	−	26.4738i	1.49006	−	0.860284i	0.999935	+	0.0113714i	$0.00361972\pi$
$948$		−	0.496421i		−	0.0161230i
$949$	−0.970747	+	1.68138i	−0.0315118	+	0.0545800i
$950$		0			0
$951$	−5.05725			−0.163993
$952$		−	12.4962i		−	0.405005i
$953$	−30.3117	+	17.5005i	−0.981892	+	0.566896i	−0.902841	−	0.429975i	$-0.858522\pi$
$953$	−30.3117	+	17.5005i	−0.981892	+	0.566896i	−0.0790512	+	0.996871i	$0.525189\pi$
$954$	−0.0990129			−0.00320566
$955$		0			0
$956$	16.2747			0.526360
$957$	−1.49484	−	0.863049i	−0.0483214	−	0.0278984i
$958$	−1.84964	−	1.06789i	−0.0597593	−	0.0345020i
$959$	−2.98200	+	5.16498i	−0.0962938	+	0.166786i
$960$		0			0
$961$	−10.2620			−0.331033
$962$	0.450309	−	2.08902i	0.0145185	−	0.0673527i
$963$		−	35.5128i		−	1.14438i
$964$	17.4429	+	30.2120i	0.561799	+	0.973065i
$965$		0			0
$966$	0.566531	−	0.981260i	0.0182278	−	0.0315715i
$967$	3.82800	+	2.21010i	0.123100	+	0.0710719i	0.560286	−	0.828299i	$-0.310691\pi$
$967$	3.82800	+	2.21010i	0.123100	+	0.0710719i	−0.437186	+	0.899371i	$0.644025\pi$
$968$		−	17.6487i		−	0.567250i
$969$	1.35391	−	2.34504i	0.0434938	−	0.0753334i
$970$		0			0
$971$	0.798468	+	1.38299i	0.0256240	+	0.0443822i	0.878553	−	0.477645i	$-0.158509\pi$
$971$	0.798468	+	1.38299i	0.0256240	+	0.0443822i	−0.852929	+	0.522027i	$0.825176\pi$
$972$		−	12.6211i		−	0.404823i
$973$		−	6.95177i		−	0.222863i
$974$	5.21051	+	9.02487i	0.166956	+	0.289176i
$975$		0			0
$976$	−14.8210			−0.474408
$977$	−12.8796	+	7.43602i	−0.412054	+	0.237899i	−0.691672	−	0.722212i	$-0.743125\pi$
$977$	−12.8796	+	7.43602i	−0.412054	+	0.237899i	0.279618	+	0.960111i	$0.409792\pi$
$978$	−2.13783	+	1.23428i	−0.0683602	+	0.0394678i
$979$	20.2242	+	35.0293i	0.646368	+	1.11954i
$980$		0			0
$981$	−25.6139	+	44.3646i	−0.817790	+	1.41645i
$982$	−1.15883	+	0.669051i	−0.0369798	+	0.0213503i
$983$	37.4336	−	21.6123i	1.19395	−	0.689326i	0.234748	−	0.972056i	$-0.424573\pi$
$983$	37.4336	−	21.6123i	1.19395	−	0.689326i	0.959200	+	0.282730i	$0.0912401\pi$
$984$	−1.70546	−	2.95394i	−0.0543681	−	0.0941682i
$985$		0			0
$986$	0.981741	−	1.70043i	0.0312650	−	0.0541526i
$987$	−5.01663	+	2.89635i	−0.159681	+	0.0921919i
$988$			4.71855i			0.150117i
$989$	−38.5432			−1.22560
$990$		0			0
$991$	−7.31087			−0.232237			−0.116119	−	0.993235i	$-0.537045\pi$
$991$	−7.31087			−0.232237			−0.116119	+	0.993235i	$0.537045\pi$
$992$	17.0267	+	9.83038i	0.540599	+	0.312115i
$993$		−	4.50010i		−	0.142806i
$994$	3.54713	−	6.14381i	0.112508	−	0.194870i
$995$		0			0
$996$	−3.33929	+	5.78383i	−0.105810	+	0.183268i
$997$	−47.3711	+	27.3497i	−1.50026	+	0.866174i	−0.500257	+	0.865877i	$0.666761\pi$
$997$	−47.3711	+	27.3497i	−1.50026	+	0.866174i	−1.00000		0.000297334i	$0.999905\pi$
$998$		−	12.5239i		−	0.396436i
$999$	9.25002	+	1.99393i	0.292658	+	0.0630853i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.o.d.174.11		48
5.2	odd	4		925.2.e.d.26.6	✓	24
5.3	odd	4		925.2.e.e.26.7	yes	24
5.4	even	2	inner	925.2.o.d.174.14		48
37.10	even	3	inner	925.2.o.d.824.14		48
185.47	odd	12		925.2.e.d.676.6	yes	24
185.84	even	6	inner	925.2.o.d.824.11		48
185.158	odd	12		925.2.e.e.676.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
925.2.e.d.26.6	✓	24	5.2	odd	4
925.2.e.d.676.6	yes	24	185.47	odd	12
925.2.e.e.26.7	yes	24	5.3	odd	4
925.2.e.e.676.7	yes	24	185.158	odd	12
925.2.o.d.174.11		48	1.1	even	1	trivial
925.2.o.d.174.14		48	5.4	even	2	inner
925.2.o.d.824.11		48	185.84	even	6	inner
925.2.o.d.824.14		48	37.10	even	3	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)

\(f(q)\)	\(=\)	\(q+(-0.348412 + 0.201156i) q^{2} +(0.227139 + 0.131139i) q^{3} +(-0.919073 + 1.59188i) q^{4} -0.105517 q^{6} +(1.99551 + 1.15211i) q^{7} -1.54413i q^{8} +(-1.46561 - 2.53850i) q^{9} +O(q^{10})\)	\(q+(-0.348412 + 0.201156i) q^{2} +(0.227139 + 0.131139i) q^{3} +(-0.919073 + 1.59188i) q^{4} -0.105517 q^{6} +(1.99551 + 1.15211i) q^{7} -1.54413i q^{8} +(-1.46561 - 2.53850i) q^{9} +4.73598 q^{11} +(-0.417515 + 0.241052i) q^{12} +(0.756262 + 0.436628i) q^{13} -0.927014 q^{14} +(-1.52754 - 2.64577i) q^{16} +(3.04159 - 1.75607i) q^{17} +(1.02127 + 0.589630i) q^{18} +(1.46980 - 2.54576i) q^{19} +(0.302173 + 0.523378i) q^{21} +(-1.65007 + 0.952670i) q^{22} +4.66022i q^{23} +(0.202495 - 0.350732i) q^{24} -0.351321 q^{26} -1.55562i q^{27} +(-3.66804 + 2.11775i) q^{28} -1.38961 q^{29} +4.55390 q^{31} +(3.73893 + 2.15867i) q^{32} +(1.07573 + 0.621071i) q^{33} +(-0.706485 + 1.22367i) q^{34} +5.38799 q^{36} +(-1.28176 + 5.94618i) q^{37} +1.18263i q^{38} +(0.114518 + 0.198351i) q^{39} +(4.21111 - 7.29385i) q^{41} +(-0.210561 - 0.121567i) q^{42} +8.27070i q^{43} +(-4.35271 + 7.53912i) q^{44} +(-0.937429 - 1.62367i) q^{46} +9.58509i q^{47} -0.801277i q^{48} +(-0.845285 - 1.46408i) q^{49} +0.921153 q^{51} +(-1.39012 + 0.802586i) q^{52} +(-0.0727132 + 0.0419810i) q^{53} +(0.312922 + 0.541998i) q^{54} +(1.77901 - 3.08133i) q^{56} +(0.667696 - 0.385495i) q^{57} +(0.484158 - 0.279529i) q^{58} +(3.55942 + 6.16510i) q^{59} +(2.42564 - 4.20133i) q^{61} +(-1.58663 + 0.916042i) q^{62} -6.75415i q^{63} +4.37322 q^{64} -0.499728 q^{66} +(-4.47062 - 2.58111i) q^{67} +6.45581i q^{68} +(-0.611135 + 1.05852i) q^{69} +(-3.82640 + 6.62753i) q^{71} +(-3.91978 + 2.26308i) q^{72} +2.22328i q^{73} +(-0.749528 - 2.32955i) q^{74} +(2.70170 + 4.67948i) q^{76} +(9.45072 + 5.45637i) q^{77} +(-0.0797987 - 0.0460718i) q^{78} +(-0.514848 + 0.891742i) q^{79} +(-4.19281 + 7.26217i) q^{81} +3.38835i q^{82} +(11.9970 - 6.92650i) q^{83} -1.11087 q^{84} +(-1.66370 - 2.88161i) q^{86} +(-0.315635 - 0.182232i) q^{87} -7.31297i q^{88} +(4.27032 + 7.39642i) q^{89} +(1.00609 + 1.74259i) q^{91} +(-7.41851 - 4.28308i) q^{92} +(1.03437 + 0.597193i) q^{93} +(-1.92809 - 3.33956i) q^{94} +(0.566172 + 0.980638i) q^{96} -17.7844i q^{97} +(0.589015 + 0.340068i) q^{98} +(-6.94108 - 12.0223i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more