LMFDB - Embedded newform 891.2.f.e.82.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(82,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("891.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.f (of order $5$, degree $4$, 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			82.1
Character	$\chi$	$=$	891.82
Dual form			891.2.f.e.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.719701 - 2.21501i) q^{2} +(-2.77028 + 2.01272i) q^{4} +(0.0979645 - 0.301504i) q^{5} +(1.14758 - 0.833769i) q^{7} +(2.68358 + 1.94973i) q^{8} -0.738340 q^{10} +(3.24416 - 0.689532i) q^{11} +(1.29696 + 3.99162i) q^{13} +(-2.67273 - 1.94185i) q^{14} +(0.271005 - 0.834068i) q^{16} +(1.92957 - 5.93860i) q^{17} +(-2.50622 - 1.82087i) q^{19} +(0.335455 + 1.03242i) q^{20} +(-3.86214 - 6.68959i) q^{22} +4.52050 q^{23} +(3.96378 + 2.87985i) q^{25} +(7.90807 - 5.74555i) q^{26} +(-1.50098 + 4.61954i) q^{28} +(2.36916 - 1.72130i) q^{29} +(-2.94857 - 9.07476i) q^{31} +4.59165 q^{32} -14.5428 q^{34} +(-0.138962 - 0.427681i) q^{35} +(-0.685637 + 0.498145i) q^{37} +(-2.22953 + 6.86179i) q^{38} +(0.850747 - 0.618104i) q^{40} +(-3.13058 - 2.27450i) q^{41} +3.55302 q^{43} +(-7.59937 + 8.43978i) q^{44} +(-3.25341 - 10.0130i) q^{46} +(-6.02798 - 4.37959i) q^{47} +(-1.54134 + 4.74375i) q^{49} +(3.52617 - 10.8525i) q^{50} +(-11.6270 - 8.44748i) q^{52} +(-2.06517 - 6.35595i) q^{53} +(0.109916 - 1.04568i) q^{55} +4.70526 q^{56} +(-5.51778 - 4.00890i) q^{58} +(-9.76870 + 7.09737i) q^{59} +(1.42776 - 4.39418i) q^{61} +(-17.9786 + 13.0622i) q^{62} +(-3.84663 - 11.8387i) q^{64} +1.33054 q^{65} +9.96771 q^{67} +(6.60733 + 20.3353i) q^{68} +(-0.847308 + 0.615605i) q^{70} +(-0.905630 + 2.78724i) q^{71} +(-3.43158 + 2.49319i) q^{73} +(1.59685 + 1.16018i) q^{74} +10.6078 q^{76} +(3.14803 - 3.49617i) q^{77} +(-1.04509 - 3.21646i) q^{79} +(-0.224926 - 0.163418i) q^{80} +(-2.78496 + 8.57123i) q^{82} +(4.16786 - 12.8273i) q^{83} +(-1.60148 - 1.16355i) q^{85} +(-2.55711 - 7.86998i) q^{86} +(10.0503 + 4.47482i) q^{88} -2.69745 q^{89} +(4.81645 + 3.49936i) q^{91} +(-12.5230 + 9.09852i) q^{92} +(-5.36249 + 16.5041i) q^{94} +(-0.794521 + 0.577253i) q^{95} +(-1.62464 - 5.00013i) q^{97} +11.6168 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{2} - 11 q^{4} - 8 q^{5} + 2 q^{7} - 3 q^{8} - 4 q^{10} - 2 q^{11} + 11 q^{13} - 10 q^{14} + 9 q^{16} + 10 q^{17} + 4 q^{19} - 45 q^{20} + 16 q^{22} + 20 q^{23} - 11 q^{25} + 6 q^{26} - 27 q^{28}+ \cdots + 164 q^{98}+O(q^{100}) $ 36 * q - q^2 - 11 * q^4 - 8 * q^5 + 2 * q^7 - 3 * q^8 - 4 * q^10 - 2 * q^11 + 11 * q^13 - 10 * q^14 + 9 * q^16 + 10 * q^17 + 4 * q^19 - 45 * q^20 + 16 * q^22 + 20 * q^23 - 11 * q^25 + 6 * q^26 - 27 * q^28 - 23 * q^29 - 3 * q^31 + 18 * q^32 - 8 * q^34 - 9 * q^35 - 21 * q^37 - q^38 + 25 * q^40 + 10 * q^41 + 8 * q^43 - 19 * q^44 - 9 * q^46 - 34 * q^47 - q^49 + 27 * q^52 - 2 * q^53 + 9 * q^55 + 114 * q^56 - q^58 - 16 * q^59 + 3 * q^61 - 92 * q^62 + 13 * q^64 + 84 * q^65 - 10 * q^67 - 23 * q^68 + 46 * q^70 + 24 * q^71 - 20 * q^73 + 68 * q^74 - 16 * q^76 - 26 * q^77 - 19 * q^79 + 28 * q^80 + 47 * q^82 + 7 * q^83 - 25 * q^85 - 77 * q^86 - 18 * q^88 + 28 * q^89 + 10 * q^91 + 50 * q^92 + 63 * q^94 - 77 * q^95 + 33 * q^97 + 164 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	−0.719701	−	2.21501i	−0.508906	−	1.56625i	−0.794104	−	0.607782i	$-0.792059\pi$
$2$	−0.719701	−	2.21501i	−0.508906	−	1.56625i	0.285198	−	0.958469i	$-0.407941\pi$
$3$		0			0
$3$		0			0
$4$	−2.77028	+	2.01272i	−1.38514	+	1.00636i
$5$	0.0979645	−	0.301504i	0.0438111	−	0.134837i	−0.926758	−	0.375658i	$-0.877417\pi$
$5$	0.0979645	−	0.301504i	0.0438111	−	0.134837i	0.970569	+	0.240821i	$0.0774168\pi$
$6$		0			0
$7$	1.14758	−	0.833769i	0.433746	−	0.315135i	−0.349399	−	0.936974i	$-0.613614\pi$
$7$	1.14758	−	0.833769i	0.433746	−	0.315135i	0.783145	+	0.621839i	$0.213614\pi$
$8$	2.68358	+	1.94973i	0.948787	+	0.689334i
$9$		0			0
$10$	−0.738340			−0.233484
$11$	3.24416	−	0.689532i	0.978150	−	0.207902i
$11$	3.24416	−	0.689532i	0.978150	−	0.207902i
$12$		0			0
$13$	1.29696	+	3.99162i	0.359711	+	1.10708i	0.953227	+	0.302254i	$0.0977391\pi$
$13$	1.29696	+	3.99162i	0.359711	+	1.10708i	−0.593517	+	0.804822i	$0.702261\pi$
$14$	−2.67273	−	1.94185i	−0.714316	−	0.518981i
$15$		0			0
$16$	0.271005	−	0.834068i	0.0677513	−	0.208517i
$17$	1.92957	−	5.93860i	0.467989	−	1.44032i	−0.387195	−	0.921998i	$-0.626556\pi$
$17$	1.92957	−	5.93860i	0.467989	−	1.44032i	0.855184	−	0.518325i	$-0.173444\pi$
$18$		0			0
$19$	−2.50622	−	1.82087i	−0.574966	−	0.417737i	0.261940	−	0.965084i	$-0.415638\pi$
$19$	−2.50622	−	1.82087i	−0.574966	−	0.417737i	−0.836906	+	0.547347i	$0.815638\pi$
$20$	0.335455	+	1.03242i	0.0750101	+	0.230857i
$21$		0			0
$22$	−3.86214	−	6.68959i	−0.823412	−	1.42623i
$23$	4.52050			0.942589			0.471295	−	0.881976i	$-0.343787\pi$
$23$	4.52050			0.942589			0.471295	+	0.881976i	$0.343787\pi$
$24$		0			0
$25$	3.96378	+	2.87985i	0.792755	+	0.575971i
$26$	7.90807	−	5.74555i	1.55090	−	1.12679i
$27$		0			0
$28$	−1.50098	+	4.61954i	−0.283659	+	0.873011i
$29$	2.36916	−	1.72130i	0.439942	−	0.319637i	−0.345670	−	0.938356i	$-0.612348\pi$
$29$	2.36916	−	1.72130i	0.439942	−	0.319637i	0.785612	+	0.618719i	$0.212348\pi$
$30$		0			0
$31$	−2.94857	−	9.07476i	−0.529578	−	1.62987i	−0.755081	−	0.655632i	$-0.772402\pi$
$31$	−2.94857	−	9.07476i	−0.529578	−	1.62987i	0.225503	−	0.974243i	$-0.427598\pi$
$32$	4.59165			0.811697
$33$		0			0
$34$	−14.5428			−2.49407
$35$	−0.138962	−	0.427681i	−0.0234889	−	0.0722913i
$36$		0			0
$37$	−0.685637	+	0.498145i	−0.112718	+	0.0818945i	−0.642716	−	0.766104i	$-0.722193\pi$
$37$	−0.685637	+	0.498145i	−0.112718	+	0.0818945i	0.529998	+	0.847999i	$0.322193\pi$
$38$	−2.22953	+	6.86179i	−0.361678	+	1.11313i
$39$		0			0
$40$	0.850747	−	0.618104i	0.134515	−	0.0977308i
$41$	−3.13058	−	2.27450i	−0.488914	−	0.355217i	0.315852	−	0.948808i	$-0.397710\pi$
$41$	−3.13058	−	2.27450i	−0.488914	−	0.355217i	−0.804767	+	0.593591i	$0.797710\pi$
$42$		0			0
$43$	3.55302			0.541830			0.270915	−	0.962603i	$-0.412674\pi$
$43$	3.55302			0.541830			0.270915	+	0.962603i	$0.412674\pi$
$44$	−7.59937	+	8.43978i	−1.14565	+	1.27235i
$45$		0			0
$46$	−3.25341	−	10.0130i	−0.479689	−	1.47633i
$47$	−6.02798	−	4.37959i	−0.879272	−	0.638828i	0.0537868	−	0.998552i	$-0.482871\pi$
$47$	−6.02798	−	4.37959i	−0.879272	−	0.638828i	−0.933059	+	0.359724i	$0.882871\pi$
$48$		0			0
$49$	−1.54134	+	4.74375i	−0.220191	+	0.677679i
$50$	3.52617	−	10.8525i	0.498676	−	1.53477i
$51$		0			0
$52$	−11.6270	−	8.44748i	−1.61237	−	1.17145i
$53$	−2.06517	−	6.35595i	−0.283673	−	0.873057i	−0.986793	−	0.161986i	$-0.948210\pi$
$53$	−2.06517	−	6.35595i	−0.283673	−	0.873057i	0.703120	−	0.711071i	$-0.251790\pi$
$54$		0			0
$55$	0.109916	−	1.04568i	0.0148210	−	0.140999i
$56$	4.70526			0.628766
$57$		0			0
$58$	−5.51778	−	4.00890i	−0.724520	−	0.526395i
$59$	−9.76870	+	7.09737i	−1.27178	+	0.923999i	−0.999272	−	0.0381555i	$-0.987852\pi$
$59$	−9.76870	+	7.09737i	−1.27178	+	0.923999i	−0.272504	+	0.962155i	$0.587852\pi$
$60$		0			0
$61$	1.42776	−	4.39418i	0.182806	−	0.562618i	−0.817098	−	0.576499i	$-0.804419\pi$
$61$	1.42776	−	4.39418i	0.182806	−	0.562618i	0.999904	+	0.0138810i	$0.00441859\pi$
$62$	−17.9786	+	13.0622i	−2.28329	+	1.65890i
$63$		0			0
$64$	−3.84663	−	11.8387i	−0.480828	−	1.47984i
$65$	1.33054			0.165034
$66$		0			0
$67$	9.96771			1.21775			0.608875	−	0.793266i	$-0.291621\pi$
$67$	9.96771			1.21775			0.608875	+	0.793266i	$0.291621\pi$
$68$	6.60733	+	20.3353i	0.801256	+	2.46601i
$69$		0			0
$70$	−0.847308	+	0.615605i	−0.101273	+	0.0735789i
$71$	−0.905630	+	2.78724i	−0.107479	+	0.330785i	−0.990304	−	0.138916i	$-0.955638\pi$
$71$	−0.905630	+	2.78724i	−0.107479	+	0.330785i	0.882826	+	0.469701i	$0.155638\pi$
$72$		0			0
$73$	−3.43158	+	2.49319i	−0.401636	+	0.291806i	−0.770207	−	0.637794i	$-0.779847\pi$
$73$	−3.43158	+	2.49319i	−0.401636	+	0.291806i	0.368571	+	0.929600i	$0.379847\pi$
$74$	1.59685	+	1.16018i	0.185630	+	0.134868i
$75$		0			0
$76$	10.6078			1.21680
$77$	3.14803	−	3.49617i	0.358752	−	0.398426i
$78$		0			0
$79$	−1.04509	−	3.21646i	−0.117582	−	0.361880i	0.874895	−	0.484313i	$-0.160930\pi$
$79$	−1.04509	−	3.21646i	−0.117582	−	0.361880i	−0.992477	+	0.122433i	$0.960930\pi$
$80$	−0.224926	−	0.163418i	−0.0251475	−	0.0182707i
$81$		0			0
$82$	−2.78496	+	8.57123i	−0.307548	+	0.946534i
$83$	4.16786	−	12.8273i	0.457482	−	1.40798i	−0.410715	−	0.911764i	$-0.634721\pi$
$83$	4.16786	−	12.8273i	0.457482	−	1.40798i	0.868196	−	0.496221i	$-0.165279\pi$
$84$		0			0
$85$	−1.60148	−	1.16355i	−0.173705	−	0.126204i
$86$	−2.55711	−	7.86998i	−0.275740	−	0.848642i
$87$		0			0
$88$	10.0503	+	4.47482i	1.07137	+	0.477018i
$89$	−2.69745			−0.285929			−0.142965	−	0.989728i	$-0.545664\pi$
$89$	−2.69745			−0.285929			−0.142965	+	0.989728i	$0.545664\pi$
$90$		0			0
$91$	4.81645	+	3.49936i	0.504902	+	0.366833i
$92$	−12.5230	+	9.09852i	−1.30562	+	0.948586i
$93$		0			0
$94$	−5.36249	+	16.5041i	−0.553099	+	1.70226i
$95$	−0.794521	+	0.577253i	−0.0815161	+	0.0592249i
$96$		0			0
$97$	−1.62464	−	5.00013i	−0.164957	−	0.507686i	0.834076	−	0.551650i	$-0.186001\pi$
$97$	−1.62464	−	5.00013i	−0.164957	−	0.507686i	−0.999033	+	0.0439637i	$0.986001\pi$
$98$	11.6168			1.17347
$99$		0			0
$100$	−16.7771			−1.67771
$101$	2.94485	+	9.06333i	0.293024	+	0.901835i	0.983878	+	0.178841i	$0.0572346\pi$
$101$	2.94485	+	9.06333i	0.293024	+	0.901835i	−0.690854	+	0.722994i	$0.742765\pi$
$102$		0			0
$103$	−7.71449	+	5.60490i	−0.760131	+	0.552267i	−0.898951	−	0.438050i	$-0.855669\pi$
$103$	−7.71449	+	5.60490i	−0.760131	+	0.552267i	0.138820	+	0.990318i	$0.455669\pi$
$104$	−4.30211	+	13.2405i	−0.421857	+	1.29834i
$105$		0			0
$106$	−12.5922	+	9.14877i	−1.22306	+	0.888607i
$107$	4.18472	+	3.04038i	0.404552	+	0.293924i	0.771393	−	0.636359i	$-0.219560\pi$
$107$	4.18472	+	3.04038i	0.404552	+	0.293924i	−0.366840	+	0.930284i	$0.619560\pi$
$108$		0			0
$109$	14.4767			1.38661			0.693307	−	0.720643i	$-0.256153\pi$
$109$	14.4767			1.38661			0.693307	+	0.720643i	$0.256153\pi$
$110$	−2.39529	+	0.509109i	−0.228382	+	0.0485416i
$111$		0			0
$112$	−0.384419	−	1.18312i	−0.0363242	−	0.111794i
$113$	−6.01230	−	4.36819i	−0.565589	−	0.410925i	0.267911	−	0.963444i	$-0.413667\pi$
$113$	−6.01230	−	4.36819i	−0.565589	−	0.410925i	−0.833500	+	0.552519i	$0.813667\pi$
$114$		0			0
$115$	0.442849	−	1.36295i	0.0412958	−	0.127096i
$116$	−3.09874	+	9.53694i	−0.287711	+	0.885482i
$117$		0			0
$118$	22.7513	+	16.5298i	2.09443	+	1.52169i
$119$	−2.73708	−	8.42386i	−0.250908	−	0.772214i
$120$		0			0
$121$	10.0491	−	4.47390i	0.913554	−	0.406718i
$122$	−10.7607			−0.974231
$123$		0			0
$124$	26.4333	+	19.2049i	2.37378	+	1.72465i
$125$	2.53897	−	1.84467i	0.227092	−	0.164992i
$126$		0			0
$127$	−4.08040	+	12.5582i	−0.362077	+	1.11436i	0.589715	+	0.807612i	$0.299240\pi$
$127$	−4.08040	+	12.5582i	−0.362077	+	1.11436i	−0.951791	+	0.306746i	$0.900760\pi$
$128$	−16.0250	+	11.6428i	−1.41642	+	1.02909i
$129$		0			0
$130$	−0.957594	−	2.94717i	−0.0839866	−	0.258484i
$131$	7.30043			0.637841			0.318921	−	0.947781i	$-0.396680\pi$
$131$	7.30043			0.637841			0.318921	+	0.947781i	$0.396680\pi$
$132$		0			0
$133$	−4.39429			−0.381033
$134$	−7.17377	−	22.0786i	−0.619719	−	1.90730i
$135$		0			0
$136$	16.7568	−	12.1746i	1.43689	−	1.04396i
$137$	−3.03063	+	9.32733i	−0.258924	+	0.796887i	0.734107	+	0.679034i	$0.237601\pi$
$137$	−3.03063	+	9.32733i	−0.258924	+	0.796887i	−0.993031	+	0.117853i	$0.962399\pi$
$138$		0			0
$139$	7.66697	−	5.57038i	0.650304	−	0.472473i	−0.213071	−	0.977037i	$-0.568347\pi$
$139$	7.66697	−	5.57038i	0.650304	−	0.472473i	0.863375	+	0.504563i	$0.168347\pi$
$140$	1.24577	+	0.905103i	0.105287	+	0.0764951i
$141$		0			0
$142$	6.82556			0.572789
$143$	6.95987	+	12.0551i	0.582014	+	1.00810i
$144$		0			0
$145$	−0.286884	−	0.882938i	−0.0238244	−	0.0733240i
$146$	7.99216	+	5.80665i	0.661436	+	0.480562i
$147$		0			0
$148$	0.896778	−	2.76000i	0.0737147	−	0.226870i
$149$	1.27545	−	3.92544i	0.104489	−	0.321584i	−0.885121	−	0.465361i	$-0.845925\pi$
$149$	1.27545	−	3.92544i	0.104489	−	0.321584i	0.989610	+	0.143776i	$0.0459246\pi$
$150$		0			0
$151$	14.3805	+	10.4480i	1.17027	+	0.850249i	0.991041	−	0.133559i	$-0.0426404\pi$
$151$	14.3805	+	10.4480i	1.17027	+	0.850249i	0.179227	+	0.983808i	$0.442640\pi$
$152$	−3.17541	−	9.77291i	−0.257560	−	0.792688i
$153$		0			0
$154$	−10.0097	−	4.45673i	−0.806605	−	0.359134i
$155$	−3.02493			−0.242968
$156$		0			0
$157$	1.63200	+	1.18571i	0.130247	+	0.0946303i	0.651002	−	0.759076i	$-0.274349\pi$
$157$	1.63200	+	1.18571i	0.130247	+	0.0946303i	−0.520754	+	0.853707i	$0.674349\pi$
$158$	−6.37235	+	4.62978i	−0.506957	+	0.368326i
$159$		0			0
$160$	0.449819	−	1.38440i	0.0355613	−	0.109446i
$161$	5.18765	−	3.76905i	0.408844	−	0.297043i
$162$		0			0
$163$	−0.488377	−	1.50307i	−0.0382526	−	0.117729i	0.930107	−	0.367289i	$-0.119714\pi$
$163$	−0.488377	−	1.50307i	−0.0382526	−	0.117729i	−0.968359	+	0.249560i	$0.919714\pi$
$164$	13.2505			1.03469
$165$		0			0
$166$	−31.4124			−2.43807
$167$	−4.73464	−	14.5717i	−0.366378	−	1.12759i	−0.949114	−	0.314933i	$-0.898018\pi$
$167$	−4.73464	−	14.5717i	−0.366378	−	1.12759i	0.582736	−	0.812661i	$-0.301982\pi$
$168$		0			0
$169$	−3.73371	+	2.71270i	−0.287208	+	0.208669i
$170$	−1.42468	+	4.38471i	−0.109268	+	0.336292i
$171$		0			0
$172$	−9.84284	+	7.15124i	−0.750510	+	0.545277i
$173$	−0.797722	−	0.579579i	−0.0606497	−	0.0440646i	0.557047	−	0.830481i	$-0.311934\pi$
$173$	−0.797722	−	0.579579i	−0.0606497	−	0.0440646i	−0.617697	+	0.786416i	$0.711934\pi$
$174$		0			0
$175$	6.94990			0.525363
$176$	0.304067	−	2.89271i	0.0229199	−	0.218046i
$177$		0			0
$178$	1.94136	+	5.97489i	0.145511	+	0.447837i
$179$	−9.08186	−	6.59836i	−0.678810	−	0.493185i	0.194153	−	0.980971i	$-0.437804\pi$
$179$	−9.08186	−	6.59836i	−0.678810	−	0.493185i	−0.872963	+	0.487787i	$0.837804\pi$
$180$		0			0
$181$	5.53932	−	17.0483i	0.411735	−	1.26719i	−0.503405	−	0.864051i	$-0.667919\pi$
$181$	5.53932	−	17.0483i	0.411735	−	1.26719i	0.915139	−	0.403138i	$-0.132081\pi$
$182$	4.28472	−	13.1870i	0.317604	−	0.977486i
$183$		0			0
$184$	12.1311	+	8.81376i	0.894317	+	0.649759i
$185$	0.0830244	+	0.255523i	0.00610408	+	0.0187864i
$186$		0			0
$187$	2.16497	−	20.5963i	0.158318	−	1.50615i
$188$	25.5141			1.86081
$189$		0			0
$190$	1.85044	+	1.34442i	0.134245	+	0.0975348i
$191$	10.4266	−	7.57534i	0.754440	−	0.548133i	−0.142760	−	0.989757i	$-0.545598\pi$
$191$	10.4266	−	7.57534i	0.754440	−	0.548133i	0.897200	+	0.441625i	$0.145598\pi$
$192$		0			0
$193$	−7.15406	+	22.0179i	−0.514960	+	1.58489i	0.268393	+	0.963309i	$0.413507\pi$
$193$	−7.15406	+	22.0179i	−0.514960	+	1.58489i	−0.783354	+	0.621576i	$0.786493\pi$
$194$	−9.90609	+	7.19719i	−0.711216	+	0.516728i
$195$		0			0
$196$	−5.27793	−	16.2438i	−0.376995	−	1.16027i
$197$	−1.07766			−0.0767801			−0.0383900	−	0.999263i	$-0.512223\pi$
$197$	−1.07766			−0.0767801			−0.0383900	+	0.999263i	$0.512223\pi$
$198$		0			0
$199$	16.4307			1.16474			0.582371	−	0.812923i	$-0.302125\pi$
$199$	16.4307			1.16474			0.582371	+	0.812923i	$0.302125\pi$
$200$	5.02216	+	15.4566i	0.355120	+	1.09295i
$201$		0			0
$202$	17.9560	−	13.0458i	1.26338	−	0.917897i
$203$	1.28365	−	3.95067i	0.0900945	−	0.277282i
$204$		0			0
$205$	−0.992456	+	0.721062i	−0.0693161	+	0.0503611i
$206$	17.9671	+	13.0538i	1.25182	+	0.909503i
$207$		0			0
$208$	3.68076			0.255215
$209$	−9.38611	−	4.17908i	−0.649251	−	0.289073i
$210$		0			0
$211$	−4.61974	−	14.2181i	−0.318036	−	0.978814i	−0.974487	−	0.224445i	$-0.927943\pi$
$211$	−4.61974	−	14.2181i	−0.318036	−	0.978814i	0.656451	−	0.754369i	$-0.272057\pi$
$212$	18.5139	+	13.4511i	1.27154	+	0.923827i
$213$		0			0
$214$	3.72273	−	11.4574i	0.254480	−	0.783210i
$215$	0.348070	−	1.07125i	0.0237382	−	0.0730585i
$216$		0			0
$217$	−10.9500	−	7.95563i	−0.743333	−	0.540063i
$218$	−10.4189	−	32.0660i	−0.705655	−	2.17178i
$219$		0			0
$220$	1.80016	+	3.11804i	0.121367	+	0.210218i
$221$	26.2072			1.76289
$222$		0			0
$223$	−1.55839	−	1.13224i	−0.104358	−	0.0758203i	0.534383	−	0.845243i	$-0.320544\pi$
$223$	−1.55839	−	1.13224i	−0.104358	−	0.0758203i	−0.638740	+	0.769422i	$0.720544\pi$
$224$	5.26931	−	3.82838i	0.352070	−	0.255794i
$225$		0			0
$226$	−5.34854	+	16.4611i	−0.355779	+	1.09498i
$227$	−12.9532	+	9.41108i	−0.859737	+	0.624635i	−0.927813	−	0.373045i	$-0.878314\pi$
$227$	−12.9532	+	9.41108i	−0.859737	+	0.624635i	0.0680764	+	0.997680i	$0.478314\pi$
$228$		0			0
$229$	−0.161593	−	0.497332i	−0.0106784	−	0.0328646i	0.945575	−	0.325403i	$-0.105500\pi$
$229$	−0.161593	−	0.497332i	−0.0106784	−	0.0328646i	−0.956254	+	0.292539i	$0.905500\pi$
$230$	−3.33766			−0.220079
$231$		0			0
$232$	9.71389			0.637748
$233$	3.16820	+	9.75073i	0.207556	+	0.638792i	0.999599	+	0.0283260i	$0.00901764\pi$
$233$	3.16820	+	9.75073i	0.207556	+	0.638792i	−0.792043	+	0.610466i	$0.790982\pi$
$234$		0			0
$235$	−1.91099	+	1.38842i	−0.124659	+	0.0905703i
$236$	12.7769	−	39.3234i	0.831708	−	2.55973i
$237$		0			0
$238$	−16.6891	+	12.1253i	−1.08179	+	0.785969i
$239$	−7.79977	−	5.66686i	−0.504525	−	0.366559i	0.306218	−	0.951962i	$-0.400936\pi$
$239$	−7.79977	−	5.66686i	−0.504525	−	0.366559i	−0.810743	+	0.585403i	$0.800936\pi$
$240$		0			0
$241$	−0.278731			−0.0179547			−0.00897733	−	0.999960i	$-0.502858\pi$
$241$	−0.278731			−0.0179547			−0.00897733	+	0.999960i	$0.502858\pi$
$242$	−17.1421	−	19.0390i	−1.10193	−	1.22387i
$243$		0			0
$244$	4.88900	+	15.0468i	0.312986	+	0.963272i
$245$	1.27926	+	0.929440i	0.0817292	+	0.0593797i
$246$		0			0
$247$	4.01778	−	12.3655i	0.255645	−	0.786795i
$248$	9.78064	−	30.1017i	0.621071	−	1.91146i
$249$		0			0
$250$	−5.91326	−	4.29624i	−0.373988	−	0.271718i
$251$	−1.36753	−	4.20881i	−0.0863175	−	0.265658i	0.898576	−	0.438817i	$-0.144602\pi$
$251$	−1.36753	−	4.20881i	−0.0863175	−	0.265658i	−0.984894	+	0.173159i	$0.944602\pi$
$252$		0			0
$253$	14.6652	−	3.11703i	0.921993	−	0.195966i
$254$	30.7532			1.92963
$255$		0			0
$256$	17.1811	+	12.4828i	1.07382	+	0.780173i
$257$	2.95657	−	2.14807i	0.184426	−	0.133993i	−0.491742	−	0.870741i	$-0.663640\pi$
$257$	2.95657	−	2.14807i	0.184426	−	0.133993i	0.676168	+	0.736748i	$0.263640\pi$
$258$		0			0
$259$	−0.371489	+	1.14333i	−0.0230832	+	0.0710429i
$260$	−3.68598	+	2.67802i	−0.228595	+	0.166084i
$261$		0			0
$262$	−5.25413	−	16.1705i	−0.324601	−	0.999019i
$263$	14.4524			0.891174			0.445587	−	0.895239i	$-0.352995\pi$
$263$	14.4524			0.891174			0.445587	+	0.895239i	$0.352995\pi$
$264$		0			0
$265$	−2.11866			−0.130148
$266$	3.16257	+	9.73340i	0.193910	+	0.596793i
$267$		0			0
$268$	−27.6133	+	20.0622i	−1.68675	+	1.22550i
$269$	−0.283600	+	0.872830i	−0.0172914	+	0.0532174i	−0.959330	−	0.282287i	$-0.908907\pi$
$269$	−0.283600	+	0.872830i	−0.0172914	+	0.0532174i	0.942039	+	0.335505i	$0.108907\pi$
$270$		0			0
$271$	2.13921	−	1.55422i	0.129948	−	0.0944124i	−0.520913	−	0.853610i	$-0.674408\pi$
$271$	2.13921	−	1.55422i	0.129948	−	0.0944124i	0.650860	+	0.759197i	$0.274408\pi$
$272$	−4.43028	−	3.21878i	−0.268625	−	0.195167i
$273$		0			0
$274$	22.8413			1.37989
$275$	14.8449	+	6.60954i	0.895179	+	0.398570i
$276$		0			0
$277$	8.93198	+	27.4898i	0.536671	+	1.65170i	0.740011	+	0.672594i	$0.234820\pi$
$277$	8.93198	+	27.4898i	0.536671	+	1.65170i	−0.203341	+	0.979108i	$0.565180\pi$
$278$	−17.8564	−	12.9734i	−1.07095	−	0.778094i
$279$		0			0
$280$	0.460948	−	1.41865i	0.0275469	−	0.0847807i
$281$	−2.70160	+	8.31468i	−0.161164	+	0.496012i	−0.998733	−	0.0503194i	$-0.983976\pi$
$281$	−2.70160	+	8.31468i	−0.161164	+	0.496012i	0.837569	+	0.546331i	$0.183976\pi$
$282$		0			0
$283$	18.7832	+	13.6468i	1.11654	+	0.811216i	0.983681	−	0.179919i	$-0.0575835\pi$
$283$	18.7832	+	13.6468i	1.11654	+	0.811216i	0.132861	+	0.991135i	$0.457583\pi$
$284$	−3.10111	−	9.54422i	−0.184017	−	0.566345i
$285$		0			0
$286$	21.6933	−	24.0923i	1.28275	−	1.42461i
$287$	−5.48901			−0.324006
$288$		0			0
$289$	−17.7905	−	12.9255i	−1.04650	−	0.760326i
$290$	−1.74925	+	1.27090i	−0.102719	+	0.0746300i
$291$		0			0
$292$	4.48833	−	13.8137i	0.262660	−	0.808383i
$293$	−16.9694	+	12.3290i	−0.991366	+	0.720269i	−0.960220	−	0.279245i	$-0.909916\pi$
$293$	−16.9694	+	12.3290i	−0.991366	+	0.720269i	−0.0311460	+	0.999515i	$0.509916\pi$
$294$		0			0
$295$	1.18290	+	3.64059i	0.0688711	+	0.211963i
$296$	−2.81121			−0.163398
$297$		0			0
$298$	−9.61284			−0.556857
$299$	5.86289	+	18.0441i	0.339059	+	1.04352i
$300$		0			0
$301$	4.07739	−	2.96240i	0.235017	−	0.170750i
$302$	12.7929	−	39.3724i	0.736147	−	2.26563i
$303$		0			0
$304$	−2.19793	+	1.59689i	−0.126060	+	0.0915879i
$305$	−1.18499	−	0.860949i	−0.0678526	−	0.0492978i
$306$		0			0
$307$	23.1324			1.32024			0.660118	−	0.751162i	$-0.270506\pi$
$307$	23.1324			1.32024			0.660118	+	0.751162i	$0.270506\pi$
$308$	−1.68409	+	16.0215i	−0.0959601	+	0.912909i
$309$		0			0
$310$	2.17704	+	6.70026i	0.123648	+	0.380549i
$311$	16.5159	+	11.9995i	0.936533	+	0.680431i	0.947584	−	0.319508i	$-0.103518\pi$
$311$	16.5159	+	11.9995i	0.936533	+	0.680431i	−0.0110507	+	0.999939i	$0.503518\pi$
$312$		0			0
$313$	−10.5187	+	32.3733i	−0.594554	+	1.82985i	−0.0376200	+	0.999292i	$0.511978\pi$
$313$	−10.5187	+	32.3733i	−0.594554	+	1.82985i	−0.556934	+	0.830557i	$0.688022\pi$
$314$	1.45182	−	4.46825i	0.0819311	−	0.252158i
$315$		0			0
$316$	9.36904	+	6.80701i	0.527050	+	0.382924i
$317$	8.47337	+	26.0784i	0.475912	+	1.46471i	0.844724	+	0.535203i	$0.179765\pi$
$317$	8.47337	+	26.0784i	0.475912	+	1.46471i	−0.368812	+	0.929504i	$0.620235\pi$
$318$		0			0
$319$	6.49904	−	7.21777i	0.363876	−	0.404117i
$320$	−3.94625			−0.220602
$321$		0			0
$322$	−12.0821	−	8.77813i	−0.673307	−	0.489186i
$323$	−15.6494	+	11.3699i	−0.870754	+	0.632640i
$324$		0			0
$325$	−6.35443	+	19.5569i	−0.352480	+	1.08482i
$326$	−2.97783	+	2.16352i	−0.164927	+	0.119826i
$327$		0			0
$328$	−3.96648	−	12.2076i	−0.219012	−	0.674051i
$329$	−10.5692			−0.582698
$330$		0			0
$331$	−17.9724			−0.987854			−0.493927	−	0.869503i	$-0.664439\pi$
$331$	−17.9724			−0.987854			−0.493927	+	0.869503i	$0.664439\pi$
$332$	14.2718	+	43.9241i	0.783266	+	2.41065i
$333$		0			0
$334$	−28.8690	+	20.9746i	−1.57964	+	1.14768i
$335$	0.976482	−	3.00530i	0.0533509	−	0.164197i
$336$		0			0
$337$	−8.87665	+	6.44927i	−0.483542	+	0.351314i	−0.802695	−	0.596389i	$-0.796601\pi$
$337$	−8.87665	+	6.44927i	−0.483542	+	0.351314i	0.319153	+	0.947703i	$0.396601\pi$
$338$	8.69581	+	6.31788i	0.472990	+	0.343647i
$339$		0			0
$340$	6.77845			0.367613
$341$	−15.8229	−	27.4068i	−0.856860	−	1.48416i
$342$		0			0
$343$	5.25475	+	16.1724i	0.283730	+	0.873230i
$344$	9.53479	+	6.92743i	0.514082	+	0.373502i
$345$		0			0
$346$	−0.709654	+	2.18409i	−0.0381512	+	0.117417i
$347$	−6.82891	+	21.0172i	−0.366595	+	1.12826i	0.582381	+	0.812916i	$0.302121\pi$
$347$	−6.82891	+	21.0172i	−0.366595	+	1.12826i	−0.948976	+	0.315348i	$0.897879\pi$
$348$		0			0
$349$	14.8889	+	10.8174i	0.796986	+	0.579044i	0.910028	−	0.414546i	$-0.136060\pi$
$349$	14.8889	+	10.8174i	0.796986	+	0.579044i	−0.113042	+	0.993590i	$0.536060\pi$
$350$	−5.00185	−	15.3941i	−0.267360	−	0.822850i
$351$		0			0
$352$	14.8960	−	3.16609i	0.793961	−	0.168753i
$353$	−33.0708			−1.76018			−0.880089	−	0.474808i	$-0.842517\pi$
$353$	−33.0708			−1.76018			−0.880089	+	0.474808i	$0.842517\pi$
$354$		0			0
$355$	0.751645	+	0.546102i	0.0398932	+	0.0289841i
$356$	7.47269	−	5.42923i	0.396052	−	0.287749i
$357$		0			0
$358$	−8.07922	+	24.8653i	−0.427000	+	1.31417i
$359$	2.42595	−	1.76256i	0.128037	−	0.0930242i	−0.521924	−	0.852992i	$-0.674785\pi$
$359$	2.42595	−	1.76256i	0.128037	−	0.0930242i	0.649960	+	0.759968i	$0.274785\pi$
$360$		0			0
$361$	−2.90578	−	8.94306i	−0.152936	−	0.470687i
$362$	−41.7488			−2.19427
$363$		0			0
$364$	−20.3862			−1.06852
$365$	0.415533	+	1.27888i	0.0217500	+	0.0669396i
$366$		0			0
$367$	−1.34496	+	0.977170i	−0.0702063	+	0.0510078i	−0.622335	−	0.782751i	$-0.713816\pi$
$367$	−1.34496	+	0.977170i	−0.0702063	+	0.0510078i	0.552129	+	0.833759i	$0.313816\pi$
$368$	1.22508	−	3.77040i	0.0638616	−	0.196546i
$369$		0			0
$370$	0.506234	−	0.367800i	0.0263178	−	0.0191210i
$371$	−7.66936	−	5.57211i	−0.398173	−	0.289290i
$372$		0			0
$373$	−21.5087			−1.11368			−0.556839	−	0.830621i	$-0.687986\pi$
$373$	−21.5087			−1.11368			−0.556839	+	0.830621i	$0.687986\pi$
$374$	−47.1791	+	10.0277i	−2.43957	+	0.518521i
$375$		0			0
$376$	−7.63753	−	23.5059i	−0.393876	−	1.21222i
$377$	9.94346	+	7.22435i	0.512114	+	0.372073i
$378$		0			0
$379$	3.83779	−	11.8115i	0.197134	−	0.606715i	−0.802811	−	0.596233i	$-0.796663\pi$
$379$	3.83779	−	11.8115i	0.197134	−	0.606715i	0.999945	−	0.0104822i	$-0.00333665\pi$
$380$	1.03919	−	3.19830i	0.0533094	−	0.164069i
$381$		0			0
$382$	−24.2835	−	17.6430i	−1.24245	−	0.902694i
$383$	−0.247114	−	0.760538i	−0.0126269	−	0.0388617i	0.944545	−	0.328383i	$-0.106504\pi$
$383$	−0.247114	−	0.760538i	−0.0126269	−	0.0388617i	−0.957171	+	0.289522i	$0.906504\pi$
$384$		0			0
$385$	−0.745714	−	1.29165i	−0.0380051	−	0.0658283i
$386$	53.9188			2.74439
$387$		0			0
$388$	14.5646	+	10.5818i	0.739404	+	0.537209i
$389$	−1.40501	+	1.02080i	−0.0712367	+	0.0517565i	−0.622834	−	0.782354i	$-0.714019\pi$
$389$	−1.40501	+	1.02080i	−0.0712367	+	0.0517565i	0.551597	+	0.834111i	$0.314019\pi$
$390$		0			0
$391$	8.72261	−	26.8454i	0.441122	−	1.35763i
$392$	−13.3854	+	9.72503i	−0.676062	+	0.491188i
$393$		0			0
$394$	0.775593	+	2.38703i	0.0390738	+	0.120257i
$395$	−1.07216			−0.0539461
$396$		0			0
$397$	−24.7599			−1.24267			−0.621333	−	0.783547i	$-0.713409\pi$
$397$	−24.7599			−1.24267			−0.621333	+	0.783547i	$0.713409\pi$
$398$	−11.8252	−	36.3942i	−0.592744	−	1.82428i
$399$		0			0
$400$	3.47620	−	2.52561i	0.173810	−	0.126280i
$401$	−6.75274	+	20.7828i	−0.337216	+	1.03784i	0.628404	+	0.777887i	$0.283708\pi$
$401$	−6.75274	+	20.7828i	−0.337216	+	1.03784i	−0.965620	+	0.259957i	$0.916292\pi$
$402$		0			0
$403$	32.3988	−	23.5391i	1.61390	−	1.17257i
$404$	−26.4000	−	19.1807i	−1.31345	−	0.954278i
$405$		0			0
$406$	−9.67462			−0.480143
$407$	−1.88083	+	2.08883i	−0.0932292	+	0.103539i
$408$		0			0
$409$	2.48288	+	7.64152i	0.122771	+	0.377849i	0.993488	−	0.113934i	$-0.0363453\pi$
$409$	2.48288	+	7.64152i	0.122771	+	0.377849i	−0.870718	+	0.491783i	$0.836345\pi$
$410$	2.31143	+	1.67935i	0.114154	+	0.0829374i
$411$		0			0
$412$	10.0901	−	31.0543i	0.497106	−	1.52993i
$413$	−5.29283	+	16.2897i	−0.260443	+	0.801562i
$414$		0			0
$415$	−3.45919	−	2.51325i	−0.169805	−	0.123371i
$416$	5.95517	+	18.3281i	0.291976	+	0.898610i
$417$		0			0
$418$	−2.50152	+	23.7980i	−0.122354	+	1.16400i
$419$	5.59681			0.273422			0.136711	−	0.990611i	$-0.456347\pi$
$419$	5.59681			0.273422			0.136711	+	0.990611i	$0.456347\pi$
$420$		0			0
$421$	−30.6248	−	22.2502i	−1.49256	−	1.08441i	−0.973228	−	0.229840i	$-0.926180\pi$
$421$	−30.6248	−	22.2502i	−1.49256	−	1.08441i	−0.519335	−	0.854571i	$-0.673820\pi$
$422$	−28.1684	+	20.4656i	−1.37122	+	0.996248i
$423$		0			0
$424$	6.85035	−	21.0832i	0.332682	−	1.02389i
$425$	24.7507	−	17.9824i	1.20058	−	0.872276i
$426$		0			0
$427$	−2.02526	−	6.23312i	−0.0980093	−	0.301642i
$428$	−17.7123			−0.856155
$429$		0			0
$430$	−2.62333			−0.126508
$431$	9.20389	+	28.3267i	0.443336	+	1.36445i	0.884299	+	0.466922i	$0.154637\pi$
$431$	9.20389	+	28.3267i	0.443336	+	1.36445i	−0.440963	+	0.897525i	$0.645363\pi$
$432$		0			0
$433$	0.225935	−	0.164152i	0.0108578	−	0.00788862i	−0.582343	−	0.812943i	$-0.697864\pi$
$433$	0.225935	−	0.164152i	0.0108578	−	0.00788862i	0.593201	+	0.805054i	$0.297864\pi$
$434$	−9.74110	+	29.9800i	−0.467588	+	1.43909i
$435$		0			0
$436$	−40.1044	+	29.1375i	−1.92065	+	1.39543i
$437$	−11.3294	−	8.23126i	−0.541957	−	0.393754i
$438$		0			0
$439$	14.9965			0.715746			0.357873	−	0.933770i	$-0.383502\pi$
$439$	14.9965			0.715746			0.357873	+	0.933770i	$0.383502\pi$
$440$	2.33375	−	2.59184i	0.111257	−	0.123561i
$441$		0			0
$442$	−18.8614	−	58.0493i	−0.897143	−	2.76112i
$443$	11.7306	+	8.52278i	0.557337	+	0.404929i	0.830483	−	0.557043i	$-0.188064\pi$
$443$	11.7306	+	8.52278i	0.557337	+	0.404929i	−0.273146	+	0.961973i	$0.588064\pi$
$444$		0			0
$445$	−0.264255	+	0.813293i	−0.0125269	+	0.0385538i
$446$	−1.38634	+	4.26673i	−0.0656453	+	0.202036i
$447$		0			0
$448$	−14.2851	−	10.3787i	−0.674906	−	0.490348i
$449$	6.55787	+	20.1830i	0.309485	+	0.952497i	0.977965	+	0.208767i	$0.0669450\pi$
$449$	6.55787	+	20.1830i	0.309485	+	0.952497i	−0.668481	+	0.743730i	$0.733055\pi$
$450$		0			0
$451$	−11.7244	−	5.22020i	−0.552082	−	0.245809i
$452$	25.4477			1.19696
$453$		0			0
$454$	30.1681	+	21.9184i	1.41586	+	1.02868i
$455$	1.52691	−	1.10937i	0.0715827	−	0.0520079i
$456$		0			0
$457$	−0.991791	+	3.05242i	−0.0463940	+	0.142786i	−0.971570	−	0.236752i	$-0.923917\pi$
$457$	−0.991791	+	3.05242i	−0.0463940	+	0.142786i	0.925176	+	0.379538i	$0.123917\pi$
$458$	−0.985297	+	0.715860i	−0.0460399	+	0.0334499i
$459$		0			0
$460$	1.51642	+	4.66707i	0.0707037	+	0.217603i
$461$	−26.3256			−1.22610			−0.613052	−	0.790042i	$-0.710058\pi$
$461$	−26.3256			−1.22610			−0.613052	+	0.790042i	$0.710058\pi$
$462$		0			0
$463$	3.62824			0.168619			0.0843093	−	0.996440i	$-0.473132\pi$
$463$	3.62824			0.168619			0.0843093	+	0.996440i	$0.473132\pi$
$464$	−0.793624	−	2.44252i	−0.0368431	−	0.113391i
$465$		0			0
$466$	19.3178	−	14.0352i	0.894881	−	0.650169i
$467$	5.71532	−	17.5899i	0.264473	−	0.813965i	−0.727341	−	0.686276i	$-0.759244\pi$
$467$	5.71532	−	17.5899i	0.264473	−	0.813965i	0.991814	−	0.127689i	$-0.0407559\pi$
$468$		0			0
$469$	11.4388	−	8.31077i	0.528194	−	0.383756i
$470$	4.45070	+	3.23362i	0.205296	+	0.149156i
$471$		0			0
$472$	−40.0530			−1.84359
$473$	11.5265	−	2.44992i	0.529991	−	0.112647i
$474$		0			0
$475$	−4.69024	−	14.4351i	−0.215203	−	0.662327i
$476$	24.5374	+	17.8275i	1.12467	+	0.817120i
$477$		0			0
$478$	−6.93867	+	21.3550i	−0.317367	+	0.976756i
$479$	0.0485151	−	0.149314i	0.00221671	−	0.00682234i	−0.949942	−	0.312426i	$-0.898858\pi$
$479$	0.0485151	−	0.149314i	0.00221671	−	0.00682234i	0.952159	+	0.305604i	$0.0988583\pi$
$480$		0			0
$481$	−2.87765	−	2.09073i	−0.131209	−	0.0953292i
$482$	0.200603	+	0.617393i	0.00913722	+	0.0281215i
$483$		0			0
$484$	−18.8341	+	32.6200i	−0.856093	+	1.48273i
$485$	−1.66671			−0.0756816
$486$		0			0
$487$	−14.5028	−	10.5369i	−0.657187	−	0.477474i	0.208525	−	0.978017i	$-0.433134\pi$
$487$	−14.5028	−	10.5369i	−0.657187	−	0.477474i	−0.865712	+	0.500543i	$0.833134\pi$
$488$	12.3990	−	9.00839i	0.561275	−	0.407790i
$489$		0			0
$490$	1.13803	−	3.50250i	0.0514111	−	0.158227i
$491$	−5.37832	+	3.90758i	−0.242720	+	0.176347i	−0.702494	−	0.711689i	$-0.747930\pi$
$491$	−5.37832	+	3.90758i	−0.242720	+	0.176347i	0.459774	+	0.888036i	$0.347930\pi$
$492$		0			0
$493$	−5.65064	−	17.3909i	−0.254492	−	0.783246i
$494$	−30.2813			−1.36242
$495$		0			0
$496$	−8.36804			−0.375736
$497$	1.28463	+	3.95368i	0.0576235	+	0.177347i
$498$		0			0
$499$	−27.4640	+	19.9537i	−1.22946	+	0.893252i	−0.996849	−	0.0793185i	$-0.974726\pi$
$499$	−27.4640	+	19.9537i	−1.22946	+	0.893252i	−0.232607	+	0.972571i	$0.574726\pi$
$500$	−3.32084	+	10.2205i	−0.148512	+	0.457074i
$501$		0			0
$502$	−8.33837	+	6.05818i	−0.372159	+	0.270390i
$503$	2.53812	+	1.84405i	0.113169	+	0.0822222i	0.642930	−	0.765925i	$-0.277718\pi$
$503$	2.53812	+	1.84405i	0.113169	+	0.0822222i	−0.529761	+	0.848147i	$0.677718\pi$
$504$		0			0
$505$	3.02112			0.134438
$506$	−17.4588	−	30.2403i	−0.776139	−	1.34434i
$507$		0			0
$508$	−13.9723	−	43.0023i	−0.619921	−	1.90792i
$509$	18.4484	+	13.4036i	0.817712	+	0.594102i	0.916056	−	0.401050i	$-0.131355\pi$
$509$	18.4484	+	13.4036i	0.817712	+	0.594102i	−0.0983444	+	0.995152i	$0.531355\pi$
$510$		0			0
$511$	−1.85929	+	5.72230i	−0.0822500	+	0.253139i
$512$	3.04225	−	9.36310i	0.134450	−	0.413794i
$513$		0			0
$514$	−6.88586	−	5.00287i	−0.303722	−	0.220667i
$515$	0.934154	+	2.87503i	0.0411637	+	0.126689i
$516$		0			0
$517$	−22.5756	−	10.0516i	−0.992873	−	0.442068i
$518$	2.79984			0.123018
$519$		0			0
$520$	3.57062	+	2.59421i	0.156582	+	0.113763i
$521$	4.26200	−	3.09653i	0.186722	−	0.135661i	−0.490497	−	0.871443i	$-0.663185\pi$
$521$	4.26200	−	3.09653i	0.186722	−	0.135661i	0.677219	+	0.735781i	$0.263185\pi$
$522$		0			0
$523$	3.67595	−	11.3134i	0.160738	−	0.494701i	−0.837959	−	0.545733i	$-0.816251\pi$
$523$	3.67595	−	11.3134i	0.160738	−	0.494701i	0.998697	+	0.0510325i	$0.0162512\pi$
$524$	−20.2242	+	14.6937i	−0.883499	+	0.641899i
$525$		0			0
$526$	−10.4014	−	32.0123i	−0.453524	−	1.39580i
$527$	−59.5808			−2.59538
$528$		0			0
$529$	−2.56510			−0.111526
$530$	1.52480	+	4.69285i	0.0662331	+	0.203845i
$531$		0			0
$532$	12.1734	−	8.84448i	0.527783	−	0.383457i
$533$	5.01871	−	15.4460i	0.217385	−	0.669041i
$534$		0			0
$535$	1.32664	−	0.963860i	0.0573557	−	0.0416713i
$536$	26.7491	+	19.4344i	1.15539	+	0.839437i
$537$		0			0
$538$	2.13744			0.0921515
$539$	−1.72938	+	16.4523i	−0.0744895	+	0.708650i
$540$		0			0
$541$	12.5401	+	38.5945i	0.539142	+	1.65931i	0.734525	+	0.678581i	$0.237405\pi$
$541$	12.5401	+	38.5945i	0.539142	+	1.65931i	−0.195383	+	0.980727i	$0.562595\pi$
$542$	−4.98222	−	3.61979i	−0.214005	−	0.155483i
$543$		0			0
$544$	8.85991	−	27.2680i	0.379865	−	1.16911i
$545$	1.41820	−	4.36477i	0.0607490	−	0.186966i
$546$		0			0
$547$	−19.0397	−	13.8331i	−0.814077	−	0.591461i	0.100933	−	0.994893i	$-0.467817\pi$
$547$	−19.0397	−	13.8331i	−0.814077	−	0.591461i	−0.915010	+	0.403432i	$0.867817\pi$
$548$	−10.3776	−	31.9391i	−0.443311	−	1.36437i
$549$		0			0
$550$	3.95635	−	37.6384i	0.168699	−	1.60491i
$551$	−9.07190			−0.386476
$552$		0			0
$553$	−3.88112	−	2.81980i	−0.165042	−	0.119910i
$554$	54.4619	−	39.5689i	2.31386	−	1.68112i
$555$		0			0
$556$	−10.0280	+	30.8630i	−0.425282	+	1.30888i
$557$	−5.08590	+	3.69513i	−0.215497	+	0.156568i	−0.690297	−	0.723526i	$-0.742520\pi$
$557$	−5.08590	+	3.69513i	−0.215497	+	0.156568i	0.474800	+	0.880093i	$0.342520\pi$
$558$		0			0
$559$	4.60811	+	14.1823i	0.194902	+	0.599847i
$560$	−0.394374			−0.0166654
$561$		0			0
$562$	20.3615			0.858896
$563$	5.24291	+	16.1360i	0.220962	+	0.680052i	0.998676	+	0.0514336i	$0.0163791\pi$
$563$	5.24291	+	16.1360i	0.220962	+	0.680052i	−0.777714	+	0.628618i	$0.783621\pi$
$564$		0			0
$565$	−1.90602	+	1.38480i	−0.0801868	+	0.0582591i
$566$	16.7095	−	51.4265i	0.702352	−	2.16162i
$567$		0			0
$568$	−7.86471	+	5.71404i	−0.329996	+	0.239756i
$569$	18.0010	+	13.0785i	0.754643	+	0.548280i	0.897262	−	0.441498i	$-0.145553\pi$
$569$	18.0010	+	13.0785i	0.754643	+	0.548280i	−0.142620	+	0.989778i	$0.545553\pi$
$570$		0			0
$571$	35.3152			1.47789			0.738947	−	0.673763i	$-0.235323\pi$
$571$	35.3152			1.47789			0.738947	+	0.673763i	$0.235323\pi$
$572$	−43.5445	−	19.3878i	−1.82068	−	0.810644i
$573$		0			0
$574$	3.95045	+	12.1582i	0.164889	+	0.507475i
$575$	17.9182	+	13.0184i	0.747243	+	0.542904i
$576$		0			0
$577$	−11.8156	+	36.3646i	−0.491889	+	1.51388i	0.329859	+	0.944030i	$0.392999\pi$
$577$	−11.8156	+	36.3646i	−0.491889	+	1.51388i	−0.821749	+	0.569850i	$0.807001\pi$
$578$	−15.8264	+	48.7087i	−0.658292	+	2.02601i
$579$		0			0
$580$	2.57186	+	1.86856i	0.106791	+	0.0775879i
$581$	−5.91208	−	18.1955i	−0.245274	−	0.754877i
$582$		0			0
$583$	−11.0824	−	19.1957i	−0.458985	−	0.795004i
$584$	−14.0700			−0.582219
$585$		0			0
$586$	39.5219	+	28.7143i	1.63263	+	1.18618i
$587$	−10.0234	+	7.28245i	−0.413711	+	0.300579i	−0.775103	−	0.631835i	$-0.782302\pi$
$587$	−10.0234	+	7.28245i	−0.413711	+	0.300579i	0.361391	+	0.932414i	$0.382302\pi$
$588$		0			0
$589$	−9.13423	+	28.1123i	−0.376370	+	1.15835i
$590$	7.21262	−	5.24027i	0.296939	−	0.215739i
$591$		0			0
$592$	0.229675	+	0.706868i	0.00943960	+	0.0290521i
$593$	−4.18039			−0.171668			−0.0858340	−	0.996309i	$-0.527355\pi$
$593$	−4.18039			−0.171668			−0.0858340	+	0.996309i	$0.527355\pi$
$594$		0			0
$595$	−2.80796			−0.115115
$596$	4.36747	+	13.4417i	0.178898	+	0.550593i
$597$		0			0
$598$	35.7484	−	25.9727i	1.46186	−	1.06210i
$599$	13.6211	−	41.9214i	0.556542	−	1.71286i	−0.135292	−	0.990806i	$-0.543197\pi$
$599$	13.6211	−	41.9214i	0.556542	−	1.71286i	0.691835	−	0.722056i	$-0.256803\pi$
$600$		0			0
$601$	1.41684	−	1.02940i	0.0577943	−	0.0419900i	−0.558513	−	0.829496i	$-0.688628\pi$
$601$	1.41684	−	1.02940i	0.0577943	−	0.0419900i	0.616307	+	0.787506i	$0.288628\pi$
$602$	−9.49624	−	6.89943i	−0.387038	−	0.281200i
$603$		0			0
$604$	−60.8670			−2.47664
$605$	−0.364442	−	3.46812i	−0.0148167	−	0.140999i
$606$		0			0
$607$	−3.35875	−	10.3372i	−0.136327	−	0.419573i	0.859467	−	0.511192i	$-0.170796\pi$
$607$	−3.35875	−	10.3372i	−0.136327	−	0.419573i	−0.995794	+	0.0916189i	$0.970796\pi$
$608$	−11.5077	−	8.36082i	−0.466698	−	0.339076i
$609$		0			0
$610$	−1.05417	+	3.24440i	−0.0426821	+	0.131362i
$611$	9.66362	−	29.7416i	0.390948	−	1.20321i
$612$		0			0
$613$	−14.3951	−	10.4586i	−0.581412	−	0.422421i	0.257821	−	0.966193i	$-0.416996\pi$
$613$	−14.3951	−	10.4586i	−0.581412	−	0.422421i	−0.839233	+	0.543772i	$0.816996\pi$
$614$	−16.6484	−	51.2385i	−0.671875	−	2.06782i
$615$		0			0
$616$	15.2646	−	3.24442i	0.615028	−	0.130722i
$617$	−3.99611			−0.160877			−0.0804386	−	0.996760i	$-0.525632\pi$
$617$	−3.99611			−0.160877			−0.0804386	+	0.996760i	$0.525632\pi$
$618$		0			0
$619$	8.87927	+	6.45117i	0.356888	+	0.259294i	0.751753	−	0.659445i	$-0.229209\pi$
$619$	8.87927	+	6.45117i	0.356888	+	0.259294i	−0.394865	+	0.918739i	$0.629209\pi$
$620$	8.37989	−	6.08835i	0.336544	−	0.244514i
$621$		0			0
$622$	14.6926	−	45.2191i	0.589118	−	1.81312i
$623$	−3.09556	+	2.24905i	−0.124021	+	0.0901064i
$624$		0			0
$625$	7.26270	+	22.3523i	0.290508	+	0.894091i
$626$	79.2777			3.16857
$627$		0			0
$628$	−6.90760			−0.275643
$629$	1.63530	+	5.03293i	0.0652037	+	0.200676i
$630$		0			0
$631$	−6.99735	+	5.08388i	−0.278560	+	0.202386i	−0.718289	−	0.695745i	$-0.755075\pi$
$631$	−6.99735	+	5.08388i	−0.278560	+	0.202386i	0.439729	+	0.898131i	$0.355075\pi$
$632$	3.46666	−	10.6693i	0.137896	−	0.424401i
$633$		0			0
$634$	51.6656	−	37.5373i	2.05190	−	1.49079i
$635$	3.38660	+	2.46051i	0.134393	+	0.0976424i
$636$		0			0
$637$	−20.9343			−0.829448
$638$	−20.6648	−	9.20082i	−0.818128	−	0.364264i
$639$		0			0
$640$	1.94048	+	5.97219i	0.0767042	+	0.236071i
$641$	30.0045	+	21.7995i	1.18511	+	0.861030i	0.992738	−	0.120292i	$-0.0383832\pi$
$641$	30.0045	+	21.7995i	1.18511	+	0.861030i	0.192368	+	0.981323i	$0.438383\pi$
$642$		0			0
$643$	−12.5871	+	38.7390i	−0.496385	+	1.52772i	0.318402	+	0.947956i	$0.396854\pi$
$643$	−12.5871	+	38.7390i	−0.496385	+	1.52772i	−0.814787	+	0.579761i	$0.803146\pi$
$644$	−6.78518	+	20.8826i	−0.267373	+	0.822891i
$645$		0			0
$646$	36.4474	+	26.4806i	1.43400	+	1.04187i
$647$	0.175813	+	0.541098i	0.00691193	+	0.0212727i	0.954453	−	0.298361i	$-0.0964400\pi$
$647$	0.175813	+	0.541098i	0.00691193	+	0.0212727i	−0.947541	+	0.319634i	$0.896440\pi$
$648$		0			0
$649$	−26.7973	+	29.7608i	−1.05189	+	1.16821i
$650$	47.8921			1.87848
$651$		0			0
$652$	4.37820	+	3.18095i	0.171464	+	0.124576i
$653$	−29.5514	+	21.4704i	−1.15644	+	0.840201i	−0.989323	−	0.145737i	$-0.953445\pi$
$653$	−29.5514	+	21.4704i	−1.15644	+	0.840201i	−0.167114	+	0.985938i	$0.553445\pi$
$654$		0			0
$655$	0.715183	−	2.20111i	0.0279445	−	0.0860044i
$656$	−2.74549	+	1.99472i	−0.107193	+	0.0778806i
$657$		0			0
$658$	7.60666	+	23.4109i	0.296538	+	0.912651i
$659$	24.0070			0.935179			0.467590	−	0.883946i	$-0.345123\pi$
$659$	24.0070			0.935179			0.467590	+	0.883946i	$0.345123\pi$
$660$		0			0
$661$	12.9833			0.504992			0.252496	−	0.967598i	$-0.418749\pi$
$661$	12.9833			0.504992			0.252496	+	0.967598i	$0.418749\pi$
$662$	12.9348	+	39.8092i	0.502725	+	1.54723i
$663$		0			0
$664$	36.1947	−	26.2970i	1.40463	−	1.02052i
$665$	−0.430484	+	1.32489i	−0.0166935	+	0.0513772i
$666$		0			0
$667$	10.7098	−	7.78112i	0.414685	−	0.301286i
$668$	42.4452	+	30.8382i	1.64225	+	1.19317i
$669$		0			0
$670$	−7.35956			−0.284325
$671$	1.60194	−	15.2399i	0.0618421	−	0.588330i
$672$		0			0
$673$	5.26122	+	16.1924i	0.202805	+	0.624170i	0.999796	+	0.0201790i	$0.00642360\pi$
$673$	5.26122	+	16.1924i	0.202805	+	0.624170i	−0.796991	+	0.603991i	$0.793576\pi$
$674$	20.6737	+	15.0204i	0.796323	+	0.578562i
$675$		0			0
$676$	4.88349	−	15.0298i	0.187827	−	0.578071i
$677$	10.9490	−	33.6975i	0.420803	−	1.29510i	−0.486153	−	0.873874i	$-0.661600\pi$
$677$	10.9490	−	33.6975i	0.420803	−	1.29510i	0.906956	−	0.421226i	$-0.138400\pi$
$678$		0			0
$679$	−6.03336	−	4.38349i	−0.231539	−	0.168223i
$680$	−2.02910	−	6.24492i	−0.0778124	−	0.239482i
$681$		0			0
$682$	−49.3186	+	54.7727i	−1.88851	+	2.09736i
$683$	−23.8967			−0.914381			−0.457191	−	0.889369i	$-0.651144\pi$
$683$	−23.8967			−0.914381			−0.457191	+	0.889369i	$0.651144\pi$
$684$		0			0
$685$	2.51533	+	1.82749i	0.0961058	+	0.0698250i
$686$	32.0403	−	23.2787i	1.22331	−	0.888783i
$687$		0			0
$688$	0.962886	−	2.96346i	0.0367097	−	0.112981i
$689$	22.6921	−	16.4868i	0.864500	−	0.628096i
$690$		0			0
$691$	−0.183128	−	0.563610i	−0.00696652	−	0.0214407i	0.947513	−	0.319718i	$-0.103588\pi$
$691$	−0.183128	−	0.563610i	−0.00696652	−	0.0214407i	−0.954479	+	0.298277i	$0.903588\pi$
$692$	3.37645			0.128353
$693$		0			0
$694$	51.4682			1.95371
$695$	−0.928400	−	2.85732i	−0.0352162	−	0.108384i
$696$		0			0
$697$	−19.5480	+	14.2025i	−0.740434	+	0.537957i
$698$	13.2452	−	40.7645i	0.501338	−	1.54296i
$699$		0			0
$700$	−19.2532	+	13.9882i	−0.727701	+	0.528706i
$701$	−20.5701	−	14.9451i	−0.776922	−	0.564467i	0.127131	−	0.991886i	$-0.459423\pi$
$701$	−20.5701	−	14.9451i	−0.776922	−	0.564467i	−0.904054	+	0.427419i	$0.859423\pi$
$702$		0			0
$703$	2.62542			0.0990194
$704$	−20.6422	−	35.7542i	−0.777983	−	1.34754i
$705$		0			0
$706$	23.8011	+	73.2521i	0.895765	+	2.75688i
$707$	10.9362	+	7.94561i	0.411298	+	0.298825i
$708$		0			0
$709$	4.66760	−	14.3654i	0.175295	−	0.539503i	−0.824352	−	0.566078i	$-0.808460\pi$
$709$	4.66760	−	14.3654i	0.175295	−	0.539503i	0.999647	+	0.0265748i	$0.00846000\pi$
$710$	0.668663	−	2.05793i	0.0250945	−	0.0772329i
$711$		0			0
$712$	−7.23882	−	5.25931i	−0.271286	−	0.197101i
$713$	−13.3290	−	41.0224i	−0.499175	−	1.53630i
$714$		0			0
$715$	4.31649	−	0.917452i	0.161428	−	0.0343108i
$716$	38.4399			1.43657
$717$		0			0
$718$	−5.65004	−	4.10500i	−0.210858	−	0.153197i
$719$	9.74281	−	7.07857i	0.363345	−	0.263986i	−0.391101	−	0.920348i	$-0.627906\pi$
$719$	9.74281	−	7.07857i	0.363345	−	0.263986i	0.754446	+	0.656362i	$0.227906\pi$
$720$		0			0
$721$	−4.17983	+	12.8642i	−0.155665	+	0.479088i
$722$	−17.7177	+	12.8727i	−0.659384	+	0.479071i
$723$		0			0
$724$	18.9680	+	58.3776i	0.704941	+	2.16959i
$725$	14.3479			0.532868
$726$		0			0
$727$	49.5932			1.83931			0.919654	−	0.392729i	$-0.128469\pi$
$727$	49.5932			1.83931			0.919654	+	0.392729i	$0.128469\pi$
$728$	6.10251	+	18.7816i	0.226174	+	0.696092i
$729$		0			0
$730$	2.53368	−	1.84082i	0.0937755	−	0.0681319i
$731$	6.85579	−	21.1000i	0.253571	−	0.780410i
$732$		0			0
$733$	26.1032	−	18.9651i	0.964145	−	0.700493i	0.0100355	−	0.999950i	$-0.496806\pi$
$733$	26.1032	−	18.9651i	0.964145	−	0.700493i	0.954110	+	0.299457i	$0.0968055\pi$
$734$	3.13241	+	2.27583i	0.115619	+	0.0840024i
$735$		0			0
$736$	20.7566			0.765097
$737$	32.3368	−	6.87305i	1.19114	−	0.253172i
$738$		0			0
$739$	−0.968005	−	2.97921i	−0.0356086	−	0.109592i	0.931672	−	0.363300i	$-0.118350\pi$
$739$	−0.968005	−	2.97921i	−0.0356086	−	0.109592i	−0.967281	+	0.253708i	$0.918350\pi$
$740$	−0.744298	−	0.540764i	−0.0273609	−	0.0198789i
$741$		0			0
$742$	−6.82266	+	20.9980i	−0.250468	+	0.770860i
$743$	−2.40686	+	7.40756i	−0.0882992	+	0.271757i	−0.985450	−	0.169968i	$-0.945633\pi$
$743$	−2.40686	+	7.40756i	−0.0882992	+	0.271757i	0.897150	+	0.441725i	$0.145633\pi$
$744$		0			0
$745$	−1.05859	−	0.769107i	−0.0387836	−	0.0281779i
$746$	15.4798	+	47.6420i	0.566756	+	1.74430i
$747$		0			0
$748$	35.4570	+	61.4148i	1.29644	+	2.24555i
$749$	7.33730			0.268099
$750$		0			0
$751$	−40.1993	−	29.2065i	−1.46689	−	1.06576i	−0.981500	−	0.191463i	$-0.938677\pi$
$751$	−40.1993	−	29.2065i	−1.46689	−	1.06576i	−0.485392	−	0.874297i	$-0.661323\pi$
$752$	−5.28649	+	3.84086i	−0.192778	+	0.140062i
$753$		0			0
$754$	8.84570	−	27.2243i	0.322141	−	0.991449i
$755$	4.55890	−	3.31224i	0.165915	−	0.120545i
$756$		0			0
$757$	−8.35296	−	25.7078i	−0.303594	−	0.934365i	−0.980198	−	0.198018i	$-0.936549\pi$
$757$	−8.35296	−	25.7078i	−0.303594	−	0.934365i	0.676605	−	0.736346i	$-0.263451\pi$
$758$	−28.9247			−1.05059
$759$		0			0
$760$	−3.25765			−0.118167
$761$	−13.7545	−	42.3320i	−0.498601	−	1.53454i	−0.811269	−	0.584673i	$-0.801223\pi$
$761$	−13.7545	−	42.3320i	−0.498601	−	1.53454i	0.312668	−	0.949862i	$-0.398777\pi$
$762$		0			0
$763$	16.6132	−	12.0702i	0.601438	−	0.436970i
$764$	−13.6374	+	41.9716i	−0.493384	+	1.51848i
$765$		0			0
$766$	−1.50675	+	1.09472i	−0.0544412	+	0.0395538i
$767$	−40.9996	−	29.7879i	−1.48041	−	1.07558i
$768$		0			0
$769$	−3.31905			−0.119688			−0.0598440	−	0.998208i	$-0.519060\pi$
$769$	−3.31905			−0.119688			−0.0598440	+	0.998208i	$0.519060\pi$
$770$	−2.32432	+	2.58136i	−0.0837626	+	0.0930259i
$771$		0			0
$772$	−24.4973	−	75.3949i	−0.881677	−	2.71352i
$773$	23.0471	+	16.7447i	0.828946	+	0.602264i	0.919261	−	0.393649i	$-0.128787\pi$
$773$	23.0471	+	16.7447i	0.828946	+	0.602264i	−0.0903152	+	0.995913i	$0.528787\pi$
$774$		0			0
$775$	14.4465	−	44.4617i	0.518934	−	1.59711i
$776$	5.38906	−	16.5858i	0.193456	−	0.595397i
$777$		0			0
$778$	3.27227	+	2.37744i	0.117316	+	0.0852354i
$779$	3.70434	+	11.4008i	0.132722	+	0.408475i
$780$		0			0
$781$	−1.01611	+	9.66671i	−0.0363594	+	0.345902i
$782$	−65.7407			−2.35088
$783$		0			0
$784$	3.53890	+	2.57116i	0.126389	+	0.0918273i
$785$	0.517375	−	0.375895i	0.0184659	−	0.0134163i
$786$		0			0
$787$	4.03227	−	12.4101i	0.143735	−	0.442371i	−0.853111	−	0.521729i	$-0.825287\pi$
$787$	4.03227	−	12.4101i	0.143735	−	0.442371i	0.996846	+	0.0793585i	$0.0252872\pi$
$788$	2.98542	−	2.16903i	0.106351	−	0.0772685i
$789$		0			0
$790$	0.771633	+	2.37484i	0.0274535	+	0.0844931i
$791$	−10.5417			−0.374819
$792$		0			0
$793$	19.3917			0.688618
$794$	17.8198	+	54.8436i	0.632400	+	1.94633i
$795$		0			0
$796$	−45.5176	+	33.0705i	−1.61333	+	1.17215i
$797$	−15.5044	+	47.7177i	−0.549195	+	1.69025i	0.161607	+	0.986855i	$0.448332\pi$
$797$	−15.5044	+	47.7177i	−0.549195	+	1.69025i	−0.710802	+	0.703392i	$0.751668\pi$
$798$		0			0
$799$	−37.6400	+	27.3471i	−1.33161	+	0.967471i
$800$	18.2003	+	13.2233i	0.643477	+	0.467514i
$801$		0			0
$802$	50.8941			1.79713
$803$	−9.41346	+	10.4545i	−0.332194	+	0.368931i
$804$		0			0
$805$	−0.628177	−	1.93333i	−0.0221403	−	0.0681410i
$806$	−75.4569	−	54.8226i	−2.65786	−	1.93104i
$807$		0			0
$808$	−9.76832	+	30.0638i	−0.343648	+	1.05764i
$809$	10.8621	−	33.4301i	0.381892	−	1.17534i	−0.556819	−	0.830634i	$-0.687978\pi$
$809$	10.8621	−	33.4301i	0.381892	−	1.17534i	0.938710	−	0.344707i	$-0.112022\pi$
$810$		0			0
$811$	−17.8837	−	12.9933i	−0.627981	−	0.456255i	0.227719	−	0.973727i	$-0.426873\pi$
$811$	−17.8837	−	12.9933i	−0.627981	−	0.456255i	−0.855700	+	0.517472i	$0.826873\pi$
$812$	4.39554	+	13.5281i	0.154253	+	0.474742i
$813$		0			0
$814$	5.98041	+	2.66273i	0.209613	+	0.0933285i
$815$	−0.501025			−0.0175501
$816$		0			0
$817$	−8.90464	−	6.46960i	−0.311534	−	0.226343i
$818$	15.1391	−	10.9992i	0.529327	−	0.384579i
$819$		0			0
$820$	1.29808	−	3.99508i	0.0453309	−	0.139514i
$821$	2.05264	−	1.49133i	0.0716375	−	0.0520477i	−0.551390	−	0.834248i	$-0.685902\pi$
$821$	2.05264	−	1.49133i	0.0716375	−	0.0520477i	0.623028	+	0.782200i	$0.285902\pi$
$822$		0			0
$823$	−3.20534	−	9.86502i	−0.111731	−	0.343873i	0.879520	−	0.475862i	$-0.157864\pi$
$823$	−3.20534	−	9.86502i	−0.111731	−	0.343873i	−0.991251	+	0.131989i	$0.957864\pi$
$824$	−31.6305			−1.10190
$825$		0			0
$826$	39.8911			1.38799
$827$	−16.2925	−	50.1431i	−0.566546	−	1.74365i	−0.663314	−	0.748341i	$-0.730851\pi$
$827$	−16.2925	−	50.1431i	−0.566546	−	1.74365i	0.0967683	−	0.995307i	$-0.469149\pi$
$828$		0			0
$829$	−30.6163	+	22.2440i	−1.06335	+	0.772566i	−0.974705	−	0.223497i	$-0.928253\pi$
$829$	−30.6163	+	22.2440i	−1.06335	+	0.772566i	−0.0886419	+	0.996064i	$0.528253\pi$
$830$	−3.07730	+	9.47095i	−0.106815	+	0.328741i
$831$		0			0
$832$	42.2667	−	30.7085i	1.46533	−	1.06463i
$833$	25.1972	+	18.3068i	0.873030	+	0.634293i
$834$		0			0
$835$	−4.85726			−0.168092
$836$	34.4135	−	7.31444i	1.19021	−	0.252975i
$837$		0			0
$838$	−4.02803	−	12.3970i	−0.139146	−	0.428247i
$839$	−16.2738	−	11.8236i	−0.561835	−	0.408197i	0.270295	−	0.962778i	$-0.412879\pi$
$839$	−16.2738	−	11.8236i	−0.561835	−	0.408197i	−0.832130	+	0.554581i	$0.812879\pi$
$840$		0			0
$841$	−6.31143	+	19.4246i	−0.217635	+	0.669813i
$842$	−27.2438	+	83.8479i	−0.938885	+	2.88959i
$843$		0			0
$844$	41.4150	+	30.0898i	1.42556	+	1.03573i
$845$	0.452118	+	1.39148i	0.0155533	+	0.0478682i
$846$		0			0
$847$	7.80199	−	13.5128i	0.268079	−	0.464305i
$848$	−5.86097			−0.201266
$849$		0			0
$850$	−57.6444	−	41.8811i	−1.97719	−	1.43651i
$851$	−3.09942	+	2.25186i	−0.106247	+	0.0771929i
$852$		0			0
$853$	2.81829	−	8.67382i	0.0964966	−	0.296986i	−0.891144	−	0.453720i	$-0.850097\pi$
$853$	2.81829	−	8.67382i	0.0964966	−	0.296986i	0.987641	+	0.156734i	$0.0500966\pi$
$854$	−12.3489	+	8.97197i	−0.422569	+	0.307014i
$855$		0			0
$856$	5.30210	+	16.3182i	0.181222	+	0.557744i
$857$	1.84536			0.0630362			0.0315181	−	0.999503i	$-0.489966\pi$
$857$	1.84536			0.0630362			0.0315181	+	0.999503i	$0.489966\pi$
$858$		0			0
$859$	28.5111			0.972785			0.486392	−	0.873741i	$-0.338313\pi$
$859$	28.5111			0.972785			0.486392	+	0.873741i	$0.338313\pi$
$860$	1.19188	+	3.66822i	0.0406427	+	0.125085i
$861$		0			0
$862$	56.1199	−	40.7735i	1.91145	−	1.38875i
$863$	3.30628	−	10.1757i	0.112547	−	0.346385i	−0.878880	−	0.477042i	$-0.841709\pi$
$863$	3.30628	−	10.1757i	0.112547	−	0.346385i	0.991428	+	0.130658i	$0.0417089\pi$
$864$		0			0
$865$	−0.252894	+	0.183738i	−0.00859865	+	0.00624729i
$866$	−0.526204	−	0.382309i	−0.0178811	−	0.0129914i
$867$		0			0
$868$	46.3470			1.57312
$869$	−5.60829	−	9.71408i	−0.190248	−	0.329528i
$870$		0			0
$871$	12.9277	+	39.7873i	0.438038	+	1.34814i
$872$	38.8492	+	28.2256i	1.31560	+	0.955840i
$873$		0			0
$874$	−10.0786	+	31.0187i	−0.340913	+	1.04922i
$875$	1.37565	−	4.23383i	0.0465056	−	0.143129i
$876$		0			0
$877$	−33.0340	−	24.0006i	−1.11548	−	0.810442i	−0.131961	−	0.991255i	$-0.542127\pi$
$877$	−33.0340	−	24.0006i	−1.11548	−	0.810442i	−0.983518	+	0.180812i	$0.942127\pi$
$878$	−10.7930	−	33.2175i	−0.364247	−	1.12104i
$879$		0			0
$880$	−0.842377	−	0.375061i	−0.0283965	−	0.0126433i
$881$	−21.0458			−0.709050			−0.354525	−	0.935047i	$-0.615357\pi$
$881$	−21.0458			−0.709050			−0.354525	+	0.935047i	$0.615357\pi$
$882$		0			0
$883$	−10.2973	−	7.48145i	−0.346533	−	0.251771i	0.400880	−	0.916130i	$-0.368704\pi$
$883$	−10.2973	−	7.48145i	−0.346533	−	0.251771i	−0.747413	+	0.664360i	$0.768704\pi$
$884$	−72.6012	+	52.7479i	−2.44184	+	1.77410i
$885$		0			0
$886$	10.4355	−	32.1173i	0.350589	−	1.07900i
$887$	8.67670	−	6.30399i	0.291335	−	0.211667i	−0.432511	−	0.901628i	$-0.642372\pi$
$887$	8.67670	−	6.30399i	0.291335	−	0.211667i	0.723846	+	0.689961i	$0.242372\pi$
$888$		0			0
$889$	5.78801	+	17.8137i	0.194124	+	0.597452i
$890$	1.99164			0.0667599
$891$		0			0
$892$	6.59606			0.220852
$893$	7.13277	+	21.9524i	0.238689	+	0.734609i
$894$		0			0
$895$	−2.87913	+	2.09181i	−0.0962387	+	0.0699215i
$896$	−8.68260	+	26.7223i	−0.290065	+	0.892729i
$897$		0			0
$898$	39.9860	−	29.0515i	1.33435	−	0.969462i
$899$	−22.6060	−	16.4242i	−0.753952	−	0.547778i
$900$		0			0
$901$	−41.7304			−1.39024
$902$	−3.12472	+	29.7267i	−0.104042	+	0.989792i
$903$		0			0
$904$	−7.61766	−	23.4447i	−0.253360	−	0.779761i
$905$	−4.59747	−	3.34025i	−0.152825	−	0.111034i
$906$		0			0
$907$	−4.09311	+	12.5973i	−0.135909	+	0.418286i	−0.995730	−	0.0923094i	$-0.970575\pi$
$907$	−4.09311	+	12.5973i	−0.135909	+	0.418286i	0.859821	+	0.510596i	$0.170575\pi$
$908$	16.9422	−	52.1426i	0.562245	−	1.73041i
$909$		0			0
$910$	−3.55618	−	2.58372i	−0.117886	−	0.0856494i
$911$	17.6524	+	54.3286i	0.584851	+	1.79999i	0.599867	+	0.800099i	$0.295220\pi$
$911$	17.6524	+	54.3286i	0.584851	+	1.79999i	−0.0150163	+	0.999887i	$0.504780\pi$
$912$		0			0
$913$	4.67632	−	44.4878i	0.154764	−	1.47233i
$914$	7.47494			0.247249
$915$		0			0
$916$	1.44865	+	1.05250i	0.0478647	+	0.0347757i
$917$	8.37786	−	6.08687i	0.276661	−	0.201006i
$918$		0			0
$919$	5.12287	−	15.7666i	0.168988	−	0.520091i	−0.830320	−	0.557287i	$-0.811842\pi$
$919$	5.12287	−	15.7666i	0.168988	−	0.520091i	0.999308	+	0.0371955i	$0.0118424\pi$
$920$	3.84580	−	2.79414i	0.126792	−	0.0921200i
$921$		0			0
$922$	18.9465	+	58.3115i	0.623971	+	1.92039i
$923$	−12.3002			−0.404865
$924$		0			0
$925$	−4.15230			−0.136527
$926$	−2.61125	−	8.03660i	−0.0858109	−	0.264099i
$927$		0			0
$928$	10.8784	−	7.90359i	0.357100	−	0.259448i
$929$	2.27554	−	7.00338i	0.0746580	−	0.229774i	−0.906763	−	0.421641i	$-0.861454\pi$
$929$	2.27554	−	7.00338i	0.0746580	−	0.229774i	0.981421	+	0.191867i	$0.0614543\pi$
$930$		0			0
$931$	12.5007	−	9.08230i	0.409694	−	0.297660i
$932$	−28.4023	−	20.6355i	−0.930349	−	0.675938i
$933$		0			0
$934$	−43.0753			−1.40947
$935$	−5.99776	−	2.67045i	−0.196148	−	0.0873330i
$936$		0			0
$937$	14.6033	+	44.9444i	0.477069	+	1.46827i	0.843147	+	0.537684i	$0.180701\pi$
$937$	14.6033	+	44.9444i	0.477069	+	1.46827i	−0.366077	+	0.930584i	$0.619299\pi$
$938$	−26.6410	−	19.3558i	−0.869858	−	0.631989i
$939$		0			0
$940$	2.49948	−	7.69260i	0.0815239	−	0.250905i
$941$	17.3447	−	53.3816i	0.565422	−	1.74019i	−0.101273	−	0.994859i	$-0.532291\pi$
$941$	17.3447	−	53.3816i	0.565422	−	1.74019i	0.666695	−	0.745331i	$-0.267709\pi$
$942$		0			0
$943$	−14.1518	−	10.2819i	−0.460845	−	0.334824i
$944$	3.27233	+	10.0712i	0.106505	+	0.327789i
$945$		0			0
$946$	−13.7223	−	23.7682i	−0.446149	−	0.772772i
$947$	12.7865			0.415504			0.207752	−	0.978182i	$-0.433385\pi$
$947$	12.7865			0.415504			0.207752	+	0.978182i	$0.433385\pi$
$948$		0			0
$949$	−14.4025	−	10.4640i	−0.467524	−	0.339676i
$950$	−28.5983	+	20.7779i	−0.927852	+	0.674124i
$951$		0			0
$952$	9.07912	−	27.9427i	0.294256	−	0.905627i
$953$	−18.8480	+	13.6939i	−0.610547	+	0.443588i	−0.849607	−	0.527417i	$-0.823161\pi$
$953$	−18.8480	+	13.6939i	−0.610547	+	0.443588i	0.239060	+	0.971005i	$0.423161\pi$
$954$		0			0
$955$	−1.26256	−	3.88576i	−0.0408555	−	0.125740i
$956$	33.0133			1.06773
$957$		0			0
$958$	−0.365649			−0.0118136
$959$	4.29893	+	13.2307i	0.138820	+	0.427243i
$960$		0			0
$961$	−48.5776	+	35.2937i	−1.56702	+	1.13851i
$962$	−2.55995	+	7.87872i	−0.0825362	+	0.254020i
$963$		0			0
$964$	0.772163	−	0.561009i	0.0248697	−	0.0180689i
$965$	5.93765	+	4.31395i	0.191140	+	0.138871i
$966$		0			0
$967$	−55.5173			−1.78531			−0.892657	−	0.450736i	$-0.851162\pi$
$967$	−55.5173			−1.78531			−0.892657	+	0.450736i	$0.851162\pi$
$968$	35.6904	+	7.58700i	1.14713	+	0.243855i
$969$		0			0
$970$	1.19954	+	3.69179i	0.0385148	+	0.118536i
$971$	−3.65698	−	2.65695i	−0.117358	−	0.0852656i	0.527558	−	0.849519i	$-0.323108\pi$
$971$	−3.65698	−	2.65695i	−0.117358	−	0.0852656i	−0.644916	+	0.764253i	$0.723108\pi$
$972$		0			0
$973$	4.15409	−	12.7850i	0.133174	−	0.409867i
$974$	−12.9017	+	39.7074i	−0.413398	+	1.27231i
$975$		0			0
$976$	−3.27812	−	2.38169i	−0.104930	−	0.0762361i
$977$	8.35560	+	25.7159i	0.267319	+	0.822724i	0.991150	+	0.132746i	$0.0423796\pi$
$977$	8.35560	+	25.7159i	0.267319	+	0.822724i	−0.723831	+	0.689977i	$0.757620\pi$
$978$		0			0
$979$	−8.75096	+	1.85998i	−0.279682	+	0.0594452i
$980$	−5.41462			−0.172964
$981$		0			0
$982$	12.5261	+	9.10076i	0.399725	+	0.290417i
$983$	8.60599	−	6.25262i	0.274489	−	0.199428i	−0.442021	−	0.897005i	$-0.645738\pi$
$983$	8.60599	−	6.25262i	0.274489	−	0.199428i	0.716510	+	0.697577i	$0.245738\pi$
$984$		0			0
$985$	−0.105572	+	0.324919i	−0.00336382	+	0.0103528i
$986$	−34.4542	+	25.0325i	−1.09725	+	0.797196i
$987$		0			0
$988$	13.7579	+	42.3424i	0.437697	+	1.34709i
$989$	16.0614			0.510723
$990$		0			0
$991$	−18.7938			−0.597005			−0.298502	−	0.954409i	$-0.596487\pi$
$991$	−18.7938			−0.597005			−0.298502	+	0.954409i	$0.596487\pi$
$992$	−13.5388	−	41.6681i	−0.429857	−	1.32296i
$993$		0			0
$994$	7.83291	−	5.69094i	0.248445	−	0.180506i
$995$	1.60963	−	4.95392i	0.0510286	−	0.157050i
$996$		0			0
$997$	21.1375	−	15.3573i	0.669433	−	0.486371i	−0.200403	−	0.979714i	$-0.564225\pi$
$997$	21.1375	−	15.3573i	0.669433	−	0.486371i	0.869835	+	0.493342i	$0.164225\pi$
$998$	63.9637	+	46.4723i	2.02473	+	1.47106i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.f.e.82.1		36
3.2	odd	2		891.2.f.f.82.9		36
9.2	odd	6		99.2.m.b.49.9	yes	72
9.4	even	3		297.2.n.b.181.9		72
9.5	odd	6		99.2.m.b.16.1	✓	72
9.7	even	3		297.2.n.b.280.1		72
11.3	even	5		9801.2.a.cp.1.1		18
11.8	odd	10		9801.2.a.cn.1.18		18
11.9	even	5	inner	891.2.f.e.163.1		36
33.8	even	10		9801.2.a.co.1.1		18
33.14	odd	10		9801.2.a.cm.1.18		18
33.20	odd	10		891.2.f.f.163.9		36
99.14	odd	30		1089.2.e.p.727.1		36
99.20	odd	30		99.2.m.b.31.1	yes	72
99.31	even	15		297.2.n.b.262.1		72
99.41	even	30		1089.2.e.o.727.18		36
99.47	odd	30		1089.2.e.p.364.1		36
99.74	even	30		1089.2.e.o.364.18		36
99.86	odd	30		99.2.m.b.97.9	yes	72
99.97	even	15		297.2.n.b.64.9		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.16.1	✓	72	9.5	odd	6
99.2.m.b.31.1	yes	72	99.20	odd	30
99.2.m.b.49.9	yes	72	9.2	odd	6
99.2.m.b.97.9	yes	72	99.86	odd	30
297.2.n.b.64.9		72	99.97	even	15
297.2.n.b.181.9		72	9.4	even	3
297.2.n.b.262.1		72	99.31	even	15
297.2.n.b.280.1		72	9.7	even	3
891.2.f.e.82.1		36	1.1	even	1	trivial
891.2.f.e.163.1		36	11.9	even	5	inner
891.2.f.f.82.9		36	3.2	odd	2
891.2.f.f.163.9		36	33.20	odd	10
1089.2.e.o.364.18		36	99.74	even	30
1089.2.e.o.727.18		36	99.41	even	30
1089.2.e.p.364.1		36	99.47	odd	30
1089.2.e.p.727.1		36	99.14	odd	30
9801.2.a.cm.1.18		18	33.14	odd	10
9801.2.a.cn.1.18		18	11.8	odd	10
9801.2.a.co.1.1		18	33.8	even	10
9801.2.a.cp.1.1		18	11.3	even	5

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.719701 - 2.21501i) q^{2} +(-2.77028 + 2.01272i) q^{4} +(0.0979645 - 0.301504i) q^{5} +(1.14758 - 0.833769i) q^{7} +(2.68358 + 1.94973i) q^{8} -0.738340 q^{10} +(3.24416 - 0.689532i) q^{11} +(1.29696 + 3.99162i) q^{13} +(-2.67273 - 1.94185i) q^{14} +(0.271005 - 0.834068i) q^{16} +(1.92957 - 5.93860i) q^{17} +(-2.50622 - 1.82087i) q^{19} +(0.335455 + 1.03242i) q^{20} +(-3.86214 - 6.68959i) q^{22} +4.52050 q^{23} +(3.96378 + 2.87985i) q^{25} +(7.90807 - 5.74555i) q^{26} +(-1.50098 + 4.61954i) q^{28} +(2.36916 - 1.72130i) q^{29} +(-2.94857 - 9.07476i) q^{31} +4.59165 q^{32} -14.5428 q^{34} +(-0.138962 - 0.427681i) q^{35} +(-0.685637 + 0.498145i) q^{37} +(-2.22953 + 6.86179i) q^{38} +(0.850747 - 0.618104i) q^{40} +(-3.13058 - 2.27450i) q^{41} +3.55302 q^{43} +(-7.59937 + 8.43978i) q^{44} +(-3.25341 - 10.0130i) q^{46} +(-6.02798 - 4.37959i) q^{47} +(-1.54134 + 4.74375i) q^{49} +(3.52617 - 10.8525i) q^{50} +(-11.6270 - 8.44748i) q^{52} +(-2.06517 - 6.35595i) q^{53} +(0.109916 - 1.04568i) q^{55} +4.70526 q^{56} +(-5.51778 - 4.00890i) q^{58} +(-9.76870 + 7.09737i) q^{59} +(1.42776 - 4.39418i) q^{61} +(-17.9786 + 13.0622i) q^{62} +(-3.84663 - 11.8387i) q^{64} +1.33054 q^{65} +9.96771 q^{67} +(6.60733 + 20.3353i) q^{68} +(-0.847308 + 0.615605i) q^{70} +(-0.905630 + 2.78724i) q^{71} +(-3.43158 + 2.49319i) q^{73} +(1.59685 + 1.16018i) q^{74} +10.6078 q^{76} +(3.14803 - 3.49617i) q^{77} +(-1.04509 - 3.21646i) q^{79} +(-0.224926 - 0.163418i) q^{80} +(-2.78496 + 8.57123i) q^{82} +(4.16786 - 12.8273i) q^{83} +(-1.60148 - 1.16355i) q^{85} +(-2.55711 - 7.86998i) q^{86} +(10.0503 + 4.47482i) q^{88} -2.69745 q^{89} +(4.81645 + 3.49936i) q^{91} +(-12.5230 + 9.09852i) q^{92} +(-5.36249 + 16.5041i) q^{94} +(-0.794521 + 0.577253i) q^{95} +(-1.62464 - 5.00013i) q^{97} +11.6168 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{2} - 11 q^{4} - 8 q^{5} + 2 q^{7} - 3 q^{8} - 4 q^{10} - 2 q^{11} + 11 q^{13} - 10 q^{14} + 9 q^{16} + 10 q^{17} + 4 q^{19} - 45 q^{20} + 16 q^{22} + 20 q^{23} - 11 q^{25} + 6 q^{26} - 27 q^{28}+ \cdots + 164 q^{98}+O(q^{100}) \) 36 * q - q^2 - 11 * q^4 - 8 * q^5 + 2 * q^7 - 3 * q^8 - 4 * q^10 - 2 * q^11 + 11 * q^13 - 10 * q^14 + 9 * q^16 + 10 * q^17 + 4 * q^19 - 45 * q^20 + 16 * q^22 + 20 * q^23 - 11 * q^25 + 6 * q^26 - 27 * q^28 - 23 * q^29 - 3 * q^31 + 18 * q^32 - 8 * q^34 - 9 * q^35 - 21 * q^37 - q^38 + 25 * q^40 + 10 * q^41 + 8 * q^43 - 19 * q^44 - 9 * q^46 - 34 * q^47 - q^49 + 27 * q^52 - 2 * q^53 + 9 * q^55 + 114 * q^56 - q^58 - 16 * q^59 + 3 * q^61 - 92 * q^62 + 13 * q^64 + 84 * q^65 - 10 * q^67 - 23 * q^68 + 46 * q^70 + 24 * q^71 - 20 * q^73 + 68 * q^74 - 16 * q^76 - 26 * q^77 - 19 * q^79 + 28 * q^80 + 47 * q^82 + 7 * q^83 - 25 * q^85 - 77 * q^86 - 18 * q^88 + 28 * q^89 + 10 * q^91 + 50 * q^92 + 63 * q^94 - 77 * q^95 + 33 * q^97 + 164 * q^98

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