LMFDB - Embedded newform 891.2.f.f.82.9

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			82.9
Character	$\chi$	$=$	891.82
Dual form			891.2.f.f.163.9

$q$-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	$0.207941\pi$
$2$	0.719701	+	2.21501i	0.508906	+	1.56625i	−0.285198	+	0.958469i	$0.592059\pi$
$3$		0			0
$3$		0			0
$4$	−2.77028	+	2.01272i	−1.38514	+	1.00636i
$5$	−0.0979645	+	0.301504i	−0.0438111	+	0.134837i	−0.970569	−	0.240821i	$-0.922583\pi$
$5$	−0.0979645	+	0.301504i	−0.0438111	+	0.134837i	0.926758	+	0.375658i	$0.122583\pi$
$6$		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	$0.373444\pi$
$17$	−1.92957	+	5.93860i	−0.467989	+	1.44032i	−0.855184	+	0.518325i	$0.826556\pi$
$18$		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	$-0.656213\pi$
$23$	−4.52050			−0.942589			−0.471295	+	0.881976i	$0.656213\pi$
$24$		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	−0.785612	−	0.618719i	$-0.787652\pi$
$29$	−2.36916	+	1.72130i	−0.439942	+	0.319637i	0.345670	+	0.938356i	$0.387652\pi$
$30$		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	0.804767	−	0.593591i	$-0.202290\pi$
$41$	3.13058	+	2.27450i	0.488914	+	0.355217i	−0.315852	+	0.948808i	$0.602290\pi$
$42$		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	0.933059	−	0.359724i	$-0.117129\pi$
$47$	6.02798	+	4.37959i	0.879272	+	0.638828i	−0.0537868	+	0.998552i	$0.517129\pi$
$48$		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	$0.0517898\pi$
$53$	2.06517	+	6.35595i	0.283673	+	0.873057i	−0.703120	+	0.711071i	$0.748210\pi$
$54$		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	0.272504	−	0.962155i	$-0.412148\pi$
$59$	9.76870	−	7.09737i	1.27178	−	0.923999i	0.999272	+	0.0381555i	$0.0121482\pi$
$60$		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	−0.882826	−	0.469701i	$-0.844362\pi$
$71$	0.905630	−	2.78724i	0.107479	−	0.330785i	0.990304	+	0.138916i	$0.0443618\pi$
$72$		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	$0.365279\pi$
$83$	−4.16786	+	12.8273i	−0.457482	+	1.40798i	−0.868196	+	0.496221i	$0.834721\pi$
$84$		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	$-0.454336\pi$
$89$	2.69745			0.285929			0.142965	+	0.989728i	$0.454336\pi$
$90$		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	$-0.942765\pi$
$101$	−2.94485	−	9.06333i	−0.293024	−	0.901835i	0.690854	−	0.722994i	$-0.257235\pi$
$102$		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	0.366840	−	0.930284i	$-0.380440\pi$
$107$	−4.18472	−	3.04038i	−0.404552	−	0.293924i	−0.771393	+	0.636359i	$0.780440\pi$
$108$		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	0.833500	−	0.552519i	$-0.186333\pi$
$113$	6.01230	+	4.36819i	0.565589	+	0.410925i	−0.267911	+	0.963444i	$0.586333\pi$
$114$		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	$-0.603320\pi$
$131$	−7.30043			−0.637841			−0.318921	+	0.947781i	$0.603320\pi$
$132$		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	$-0.762399\pi$
$137$	3.03063	−	9.32733i	0.258924	−	0.796887i	0.993031	−	0.117853i	$-0.0376012\pi$
$138$		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	−0.989610	−	0.143776i	$-0.954075\pi$
$149$	−1.27545	+	3.92544i	−0.104489	+	0.321584i	0.885121	+	0.465361i	$0.154075\pi$
$150$		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	$0.101982\pi$
$167$	4.73464	+	14.5717i	0.366378	+	1.12759i	−0.582736	+	0.812661i	$0.698018\pi$
$168$		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	0.617697	−	0.786416i	$-0.288066\pi$
$173$	0.797722	+	0.579579i	0.0606497	+	0.0440646i	−0.557047	+	0.830481i	$0.688066\pi$
$174$		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	0.872963	−	0.487787i	$-0.162196\pi$
$179$	9.08186	+	6.59836i	0.678810	+	0.493185i	−0.194153	+	0.980971i	$0.562196\pi$
$180$		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	−0.897200	−	0.441625i	$-0.854402\pi$
$191$	−10.4266	+	7.57534i	−0.754440	+	0.548133i	0.142760	+	0.989757i	$0.454402\pi$
$192$		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	$-0.487777\pi$
$197$	1.07766			0.0767801			0.0383900	+	0.999263i	$0.487777\pi$
$198$		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	−0.0680764	−	0.997680i	$-0.521686\pi$
$227$	12.9532	−	9.41108i	0.859737	−	0.624635i	0.927813	+	0.373045i	$0.121686\pi$
$228$		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	$-0.990982\pi$
$233$	−3.16820	−	9.75073i	−0.207556	−	0.638792i	0.792043	−	0.610466i	$-0.209018\pi$
$234$		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	0.810743	−	0.585403i	$-0.199064\pi$
$239$	7.79977	+	5.66686i	0.504525	+	0.366559i	−0.306218	+	0.951962i	$0.599064\pi$
$240$		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	0.984894	−	0.173159i	$-0.0553975\pi$
$251$	1.36753	+	4.20881i	0.0863175	+	0.265658i	−0.898576	+	0.438817i	$0.855398\pi$
$252$		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	−0.676168	−	0.736748i	$-0.736360\pi$
$257$	−2.95657	+	2.14807i	−0.184426	+	0.133993i	0.491742	+	0.870741i	$0.336360\pi$
$258$		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	$-0.647005\pi$
$263$	−14.4524			−0.891174			−0.445587	+	0.895239i	$0.647005\pi$
$264$		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	−0.942039	−	0.335505i	$-0.891093\pi$
$269$	0.283600	−	0.872830i	0.0172914	−	0.0532174i	0.959330	+	0.282287i	$0.0910931\pi$
$270$		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	−0.837569	−	0.546331i	$-0.816024\pi$
$281$	2.70160	−	8.31468i	0.161164	−	0.496012i	0.998733	+	0.0503194i	$0.0160239\pi$
$282$		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	0.0311460	−	0.999515i	$-0.490084\pi$
$293$	16.9694	−	12.3290i	0.991366	−	0.720269i	0.960220	+	0.279245i	$0.0900843\pi$
$294$		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	0.0110507	−	0.999939i	$-0.496482\pi$
$311$	−16.5159	−	11.9995i	−0.936533	−	0.680431i	−0.947584	+	0.319508i	$0.896482\pi$
$312$		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	$-0.820235\pi$
$317$	−8.47337	−	26.0784i	−0.475912	−	1.46471i	0.368812	−	0.929504i	$-0.379765\pi$
$318$		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	$-0.697879\pi$
$347$	6.82891	−	21.0172i	0.366595	−	1.12826i	0.948976	−	0.315348i	$-0.102121\pi$
$348$		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	$-0.157483\pi$
$353$	33.0708			1.76018			0.880089	+	0.474808i	$0.157483\pi$
$354$		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	−0.649960	−	0.759968i	$-0.725215\pi$
$359$	−2.42595	+	1.76256i	−0.128037	+	0.0930242i	0.521924	+	0.852992i	$0.325215\pi$
$360$		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	0.957171	−	0.289522i	$-0.0934962\pi$
$383$	0.247114	+	0.760538i	0.0126269	+	0.0388617i	−0.944545	+	0.328383i	$0.893496\pi$
$384$		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	−0.551597	−	0.834111i	$-0.685981\pi$
$389$	1.40501	−	1.02080i	0.0712367	−	0.0517565i	0.622834	+	0.782354i	$0.285981\pi$
$390$		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	$-0.716292\pi$
$401$	6.75274	−	20.7828i	0.337216	−	1.03784i	0.965620	−	0.259957i	$-0.0837084\pi$
$402$		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	$-0.543653\pi$
$419$	−5.59681			−0.273422			−0.136711	+	0.990611i	$0.543653\pi$
$420$		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	$-0.845363\pi$
$431$	−9.20389	−	28.3267i	−0.443336	−	1.36445i	0.440963	−	0.897525i	$-0.354637\pi$
$432$		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	0.273146	−	0.961973i	$-0.411936\pi$
$443$	−11.7306	−	8.52278i	−0.557337	−	0.404929i	−0.830483	+	0.557043i	$0.811936\pi$
$444$		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	$-0.933055\pi$
$449$	−6.55787	−	20.1830i	−0.309485	−	0.952497i	0.668481	−	0.743730i	$-0.266945\pi$
$450$		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	$-0.289942\pi$
$461$	26.3256			1.22610			0.613052	+	0.790042i	$0.289942\pi$
$462$		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	$0.240756\pi$
$467$	−5.71532	+	17.5899i	−0.264473	+	0.813965i	−0.991814	+	0.127689i	$0.959244\pi$
$468$		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	−0.952159	−	0.305604i	$-0.901142\pi$
$479$	−0.0485151	+	0.149314i	−0.00221671	+	0.00682234i	0.949942	+	0.312426i	$0.101142\pi$
$480$		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	−0.459774	−	0.888036i	$-0.652070\pi$
$491$	5.37832	−	3.90758i	0.242720	−	0.176347i	0.702494	+	0.711689i	$0.252070\pi$
$492$		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	0.529761	−	0.848147i	$-0.322282\pi$
$503$	−2.53812	−	1.84405i	−0.113169	−	0.0822222i	−0.642930	+	0.765925i	$0.722282\pi$
$504$		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	0.0983444	−	0.995152i	$-0.468645\pi$
$509$	−18.4484	−	13.4036i	−0.817712	−	0.594102i	−0.916056	+	0.401050i	$0.868645\pi$
$510$		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	−0.677219	−	0.735781i	$-0.736815\pi$
$521$	−4.26200	+	3.09653i	−0.186722	+	0.135661i	0.490497	+	0.871443i	$0.336815\pi$
$522$		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	−0.474800	−	0.880093i	$-0.657480\pi$
$557$	5.08590	−	3.69513i	0.215497	−	0.156568i	0.690297	+	0.723526i	$0.257480\pi$
$558$		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	$-0.983621\pi$
$563$	−5.24291	−	16.1360i	−0.220962	−	0.680052i	0.777714	−	0.628618i	$-0.216379\pi$
$564$		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	0.142620	−	0.989778i	$-0.454447\pi$
$569$	−18.0010	−	13.0785i	−0.754643	−	0.548280i	−0.897262	+	0.441498i	$0.854447\pi$
$570$		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	−0.361391	−	0.932414i	$-0.617698\pi$
$587$	10.0234	−	7.28245i	0.413711	−	0.300579i	0.775103	+	0.631835i	$0.217698\pi$
$588$		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	$-0.472645\pi$
$593$	4.18039			0.171668			0.0858340	+	0.996309i	$0.472645\pi$
$594$		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	$0.456803\pi$
$599$	−13.6211	+	41.9214i	−0.556542	+	1.71286i	−0.691835	+	0.722056i	$0.743197\pi$
$600$		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	$-0.474368\pi$
$617$	3.99611			0.160877			0.0804386	+	0.996760i	$0.474368\pi$
$618$		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	−0.192368	−	0.981323i	$-0.561617\pi$
$641$	−30.0045	−	21.7995i	−1.18511	−	0.861030i	−0.992738	+	0.120292i	$0.961617\pi$
$642$		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	0.947541	−	0.319634i	$-0.103560\pi$
$647$	−0.175813	−	0.541098i	−0.00691193	−	0.0212727i	−0.954453	+	0.298361i	$0.903560\pi$
$648$		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	0.167114	−	0.985938i	$-0.446555\pi$
$653$	29.5514	−	21.4704i	1.15644	−	0.840201i	0.989323	+	0.145737i	$0.0465552\pi$
$654$		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	$-0.654877\pi$
$659$	−24.0070			−0.935179			−0.467590	+	0.883946i	$0.654877\pi$
$660$		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	$0.338400\pi$
$677$	−10.9490	+	33.6975i	−0.420803	+	1.29510i	−0.906956	+	0.421226i	$0.861600\pi$
$678$		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	$-0.348856\pi$
$683$	23.8967			0.914381			0.457191	+	0.889369i	$0.348856\pi$
$684$		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	0.904054	−	0.427419i	$-0.140577\pi$
$701$	20.5701	+	14.9451i	0.776922	+	0.564467i	−0.127131	+	0.991886i	$0.540577\pi$
$702$		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	−0.754446	−	0.656362i	$-0.772094\pi$
$719$	−9.74281	+	7.07857i	−0.363345	+	0.263986i	0.391101	+	0.920348i	$0.372094\pi$
$720$		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	−0.897150	−	0.441725i	$-0.854367\pi$
$743$	2.40686	−	7.40756i	0.0882992	−	0.271757i	0.985450	+	0.169968i	$0.0543666\pi$
$744$		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	$0.198777\pi$
$761$	13.7545	+	42.3320i	0.498601	+	1.53454i	−0.312668	+	0.949862i	$0.601223\pi$
$762$		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	0.0903152	−	0.995913i	$-0.471213\pi$
$773$	−23.0471	−	16.7447i	−0.828946	−	0.602264i	−0.919261	+	0.393649i	$0.871213\pi$
$774$		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	$-0.551668\pi$
$797$	15.5044	−	47.7177i	0.549195	−	1.69025i	0.710802	−	0.703392i	$-0.248332\pi$
$798$		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	$0.312022\pi$
$809$	−10.8621	+	33.4301i	−0.381892	+	1.17534i	−0.938710	+	0.344707i	$0.887978\pi$
$810$		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	−0.623028	−	0.782200i	$-0.714098\pi$
$821$	−2.05264	+	1.49133i	−0.0716375	+	0.0520477i	0.551390	+	0.834248i	$0.314098\pi$
$822$		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	$0.269149\pi$
$827$	16.2925	+	50.1431i	0.566546	+	1.74365i	−0.0967683	+	0.995307i	$0.530851\pi$
$828$		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	0.832130	−	0.554581i	$-0.187121\pi$
$839$	16.2738	+	11.8236i	0.561835	+	0.408197i	−0.270295	+	0.962778i	$0.587121\pi$
$840$		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	$-0.510034\pi$
$857$	−1.84536			−0.0630362			−0.0315181	+	0.999503i	$0.510034\pi$
$858$		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	−0.991428	−	0.130658i	$-0.958291\pi$
$863$	−3.30628	+	10.1757i	−0.112547	+	0.346385i	0.878880	+	0.477042i	$0.158291\pi$
$864$		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	$-0.384643\pi$
$881$	21.0458			0.709050			0.354525	+	0.935047i	$0.384643\pi$
$882$		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	−0.723846	−	0.689961i	$-0.757628\pi$
$887$	−8.67670	+	6.30399i	−0.291335	+	0.211667i	0.432511	+	0.901628i	$0.357628\pi$
$888$		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	$-0.704780\pi$
$911$	−17.6524	−	54.3286i	−0.584851	−	1.79999i	0.0150163	−	0.999887i	$-0.495220\pi$
$912$		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	−0.981421	−	0.191867i	$-0.938546\pi$
$929$	−2.27554	+	7.00338i	−0.0746580	+	0.229774i	0.906763	+	0.421641i	$0.138546\pi$
$930$		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	$0.467709\pi$
$941$	−17.3447	+	53.3816i	−0.565422	+	1.74019i	−0.666695	+	0.745331i	$0.732291\pi$
$942$		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	$-0.566615\pi$
$947$	−12.7865			−0.415504			−0.207752	+	0.978182i	$0.566615\pi$
$948$		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	−0.239060	−	0.971005i	$-0.576839\pi$
$953$	18.8480	−	13.6939i	0.610547	−	0.443588i	0.849607	+	0.527417i	$0.176839\pi$
$954$		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	0.644916	−	0.764253i	$-0.276892\pi$
$971$	3.65698	+	2.65695i	0.117358	+	0.0852656i	−0.527558	+	0.849519i	$0.676892\pi$
$972$		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	$-0.957620\pi$
$977$	−8.35560	−	25.7159i	−0.267319	−	0.822724i	0.723831	−	0.689977i	$-0.242380\pi$
$978$		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	−0.716510	−	0.697577i	$-0.754262\pi$
$983$	−8.60599	+	6.25262i	−0.274489	+	0.199428i	0.442021	+	0.897005i	$0.354262\pi$
$984$		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.f.82.9		36
3.2	odd	2		891.2.f.e.82.1		36
9.2	odd	6		297.2.n.b.280.1		72
9.4	even	3		99.2.m.b.16.1	✓	72
9.5	odd	6		297.2.n.b.181.9		72
9.7	even	3		99.2.m.b.49.9	yes	72
11.3	even	5		9801.2.a.cm.1.18		18
11.8	odd	10		9801.2.a.co.1.1		18
11.9	even	5	inner	891.2.f.f.163.9		36
33.8	even	10		9801.2.a.cn.1.18		18
33.14	odd	10		9801.2.a.cp.1.1		18
33.20	odd	10		891.2.f.e.163.1		36
99.20	odd	30		297.2.n.b.64.9		72
99.25	even	15		1089.2.e.p.364.1		36
99.31	even	15		99.2.m.b.97.9	yes	72
99.52	odd	30		1089.2.e.o.364.18		36
99.58	even	15		1089.2.e.p.727.1		36
99.85	odd	30		1089.2.e.o.727.18		36
99.86	odd	30		297.2.n.b.262.1		72
99.97	even	15		99.2.m.b.31.1	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.16.1	✓	72	9.4	even	3
99.2.m.b.31.1	yes	72	99.97	even	15
99.2.m.b.49.9	yes	72	9.7	even	3
99.2.m.b.97.9	yes	72	99.31	even	15
297.2.n.b.64.9		72	99.20	odd	30
297.2.n.b.181.9		72	9.5	odd	6
297.2.n.b.262.1		72	99.86	odd	30
297.2.n.b.280.1		72	9.2	odd	6
891.2.f.e.82.1		36	3.2	odd	2
891.2.f.e.163.1		36	33.20	odd	10
891.2.f.f.82.9		36	1.1	even	1	trivial
891.2.f.f.163.9		36	11.9	even	5	inner
1089.2.e.o.364.18		36	99.52	odd	30
1089.2.e.o.727.18		36	99.85	odd	30
1089.2.e.p.364.1		36	99.25	even	15
1089.2.e.p.727.1		36	99.58	even	15
9801.2.a.cm.1.18		18	11.3	even	5
9801.2.a.cn.1.18		18	33.8	even	10
9801.2.a.co.1.1		18	11.8	odd	10
9801.2.a.cp.1.1		18	33.14	odd	10

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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