LMFDB - Embedded newform 1674.2.q.a.1115.27

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1674,2,Mod(557,1674)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1674.557"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1674, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1674 = 2 \cdot 3^{3} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1674.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.3669572984$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 558)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1115.27
Character	$\chi$	$=$	1674.1115
Dual form			1674.2.q.a.557.27

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(2.42613 - 1.40073i) q^{5} +(-0.855855 + 1.48238i) q^{7} +1.00000i q^{8} +2.80145 q^{10} +(0.733565 - 1.27057i) q^{11} +(3.07658 - 1.77627i) q^{13} +(-1.48238 + 0.855855i) q^{14} +(-0.500000 + 0.866025i) q^{16} -1.55277 q^{17} +7.16077 q^{19} +(2.42613 + 1.40073i) q^{20} +(1.27057 - 0.733565i) q^{22} +(-3.83599 - 6.64412i) q^{23} +(1.42407 - 2.46656i) q^{25} +3.55253 q^{26} -1.71171 q^{28} +(0.755499 - 1.30856i) q^{29} +(5.54699 - 0.480466i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.34474 - 0.776384i) q^{34} +4.79527i q^{35} +10.5948i q^{37} +(6.20141 + 3.58039i) q^{38} +(1.40073 + 2.42613i) q^{40} +(-4.73504 + 2.73378i) q^{41} +(-3.01033 - 1.73802i) q^{43} +1.46713 q^{44} -7.67197i q^{46} +(8.53055 + 4.92512i) q^{47} +(2.03502 + 3.52477i) q^{49} +(2.46656 - 1.42407i) q^{50} +(3.07658 + 1.77627i) q^{52} -7.26920 q^{53} -4.11009i q^{55} +(-1.48238 - 0.855855i) q^{56} +(1.30856 - 0.755499i) q^{58} +(9.52695 - 5.50039i) q^{59} +(0.811064 + 0.468268i) q^{61} +(5.04407 + 2.35740i) q^{62} -1.00000 q^{64} +(4.97612 - 8.61890i) q^{65} +(-6.03957 - 10.4608i) q^{67} +(-0.776384 - 1.34474i) q^{68} +(-2.39764 + 4.15283i) q^{70} -11.1071i q^{71} +0.138072i q^{73} +(-5.29741 + 9.17538i) q^{74} +(3.58039 + 6.20141i) q^{76} +(1.25565 + 2.17485i) q^{77} +(10.6375 + 6.14158i) q^{79} +2.80145i q^{80} -5.46756 q^{82} +(-3.12049 + 5.40484i) q^{83} +(-3.76721 + 2.17500i) q^{85} +(-1.73802 - 3.01033i) q^{86} +(1.27057 + 0.733565i) q^{88} -1.01069 q^{89} +6.08090i q^{91} +(3.83599 - 6.64412i) q^{92} +(4.92512 + 8.53055i) q^{94} +(17.3730 - 10.0303i) q^{95} +(-5.03375 + 8.71871i) q^{97} +4.07005i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} - 12 q^{5} - 4 q^{7} - 32 q^{16} - 8 q^{19} - 12 q^{20} + 44 q^{25} - 8 q^{28} + 8 q^{31} - 36 q^{38} - 24 q^{41} + 48 q^{47} - 36 q^{49} + 12 q^{59} - 64 q^{64} + 16 q^{67} - 12 q^{70}+ \cdots - 16 q^{97}+O(q^{100}) $ 64 * q + 32 * q^4 - 12 * q^5 - 4 * q^7 - 32 * q^16 - 8 * q^19 - 12 * q^20 + 44 * q^25 - 8 * q^28 + 8 * q^31 - 36 * q^38 - 24 * q^41 + 48 * q^47 - 36 * q^49 + 12 * q^59 - 64 * q^64 + 16 * q^67 - 12 * q^70 - 4 * q^76 + 180 * q^95 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1674\mathbb{Z}\right)^\times$.

$n$	$1055$	$1243$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	2.42613	−	1.40073i	1.08500	−	0.626424i	0.152757	−	0.988264i	$-0.451185\pi$
$5$	2.42613	−	1.40073i	1.08500	−	0.626424i	0.932240	+	0.361840i	$0.117851\pi$
$6$		0			0
$7$	−0.855855	+	1.48238i	−0.323483	+	0.560289i	−0.981204	−	0.192973i	$-0.938187\pi$
$7$	−0.855855	+	1.48238i	−0.323483	+	0.560289i	0.657721	+	0.753261i	$0.271520\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	2.80145			0.885897
$11$	0.733565	−	1.27057i	0.221178	−	0.383092i	−0.733988	−	0.679163i	$-0.762343\pi$
$11$	0.733565	−	1.27057i	0.221178	−	0.383092i	0.955166	+	0.296071i	$0.0956765\pi$
$12$		0			0
$13$	3.07658	−	1.77627i	0.853290	−	0.492647i	−0.00846930	−	0.999964i	$-0.502696\pi$
$13$	3.07658	−	1.77627i	0.853290	−	0.492647i	0.861760	+	0.507317i	$0.169363\pi$
$14$	−1.48238	+	0.855855i	−0.396184	+	0.228737i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.55277			−0.376601			−0.188301	−	0.982111i	$-0.560298\pi$
$17$	−1.55277			−0.376601			−0.188301	+	0.982111i	$0.560298\pi$
$18$		0			0
$19$	7.16077			1.64279			0.821397	−	0.570357i	$-0.193195\pi$
$19$	7.16077			1.64279			0.821397	+	0.570357i	$0.193195\pi$
$20$	2.42613	+	1.40073i	0.542499	+	0.313212i
$21$		0			0
$22$	1.27057	−	0.733565i	0.270887	−	0.156396i
$23$	−3.83599	−	6.64412i	−0.799859	−	1.38540i	−0.919708	−	0.392604i	$-0.871574\pi$
$23$	−3.83599	−	6.64412i	−0.799859	−	1.38540i	0.119849	−	0.992792i	$-0.461759\pi$
$24$		0			0
$25$	1.42407	−	2.46656i	0.284813	−	0.493311i
$26$	3.55253			0.696709
$27$		0			0
$28$	−1.71171			−0.323483
$29$	0.755499	−	1.30856i	0.140293	−	0.242994i	−0.787314	−	0.616552i	$-0.788529\pi$
$29$	0.755499	−	1.30856i	0.140293	−	0.242994i	0.927607	+	0.373558i	$0.121862\pi$
$30$		0			0
$31$	5.54699	−	0.480466i	0.996270	−	0.0862943i
$31$	5.54699	−	0.480466i	0.996270	−	0.0862943i
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	−1.34474	−	0.776384i	−0.230620	−	0.133149i
$35$			4.79527i			0.810549i
$36$		0			0
$37$			10.5948i			1.74178i	0.491480	+	0.870889i	$0.336456\pi$
$37$			10.5948i			1.74178i	−0.491480	+	0.870889i	$0.663544\pi$
$38$	6.20141	+	3.58039i	1.00600	+	0.580816i
$39$		0			0
$40$	1.40073	+	2.42613i	0.221474	+	0.383605i
$41$	−4.73504	+	2.73378i	−0.739489	+	0.426944i	−0.821884	−	0.569655i	$-0.807077\pi$
$41$	−4.73504	+	2.73378i	−0.739489	+	0.426944i	0.0823943	+	0.996600i	$0.473743\pi$
$42$		0			0
$43$	−3.01033	−	1.73802i	−0.459072	−	0.265045i	0.252582	−	0.967575i	$-0.418720\pi$
$43$	−3.01033	−	1.73802i	−0.459072	−	0.265045i	−0.711654	+	0.702530i	$0.752054\pi$
$44$	1.46713			0.221178
$45$		0			0
$46$		−	7.67197i		−	1.13117i
$47$	8.53055	+	4.92512i	1.24431	+	0.718402i	0.969968	−	0.243231i	$-0.0782073\pi$
$47$	8.53055	+	4.92512i	1.24431	+	0.718402i	0.274340	+	0.961633i	$0.411541\pi$
$48$		0			0
$49$	2.03502	+	3.52477i	0.290718	+	0.503538i
$50$	2.46656	−	1.42407i	0.348824	−	0.201393i
$51$		0			0
$52$	3.07658	+	1.77627i	0.426645	+	0.246324i
$53$	−7.26920			−0.998501			−0.499251	−	0.866458i	$-0.666391\pi$
$53$	−7.26920			−0.998501			−0.499251	+	0.866458i	$0.666391\pi$
$54$		0			0
$55$		−	4.11009i		−	0.554205i
$56$	−1.48238	−	0.855855i	−0.198092	−	0.114368i
$57$		0			0
$58$	1.30856	−	0.755499i	0.171823	−	0.0992018i
$59$	9.52695	−	5.50039i	1.24030	−	0.716089i	0.271147	−	0.962538i	$-0.412597\pi$
$59$	9.52695	−	5.50039i	1.24030	−	0.716089i	0.969156	+	0.246449i	$0.0792637\pi$
$60$		0			0
$61$	0.811064	+	0.468268i	0.103846	+	0.0599556i	0.551024	−	0.834490i	$-0.314237\pi$
$61$	0.811064	+	0.468268i	0.103846	+	0.0599556i	−0.447177	+	0.894445i	$0.647571\pi$
$62$	5.04407	+	2.35740i	0.640598	+	0.299390i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	4.97612	−	8.61890i	0.617212	−	1.06904i
$66$		0			0
$67$	−6.03957	−	10.4608i	−0.737851	−	1.27799i	−0.953461	−	0.301515i	$-0.902508\pi$
$67$	−6.03957	−	10.4608i	−0.737851	−	1.27799i	0.215611	−	0.976479i	$-0.430826\pi$
$68$	−0.776384	−	1.34474i	−0.0941504	−	0.163073i
$69$		0			0
$70$	−2.39764	+	4.15283i	−0.286572	+	0.496358i
$71$		−	11.1071i		−	1.31817i	−0.752070	−	0.659084i	$-0.770944\pi$
$71$		−	11.1071i		−	1.31817i	0.752070	−	0.659084i	$-0.229056\pi$
$72$		0			0
$73$			0.138072i			0.0161601i	0.999967	+	0.00808004i	$0.00257198\pi$
$73$			0.138072i			0.0161601i	−0.999967	+	0.00808004i	$0.997428\pi$
$74$	−5.29741	+	9.17538i	−0.615811	+	1.06662i
$75$		0			0
$76$	3.58039	+	6.20141i	0.410699	+	0.711351i
$77$	1.25565	+	2.17485i	0.143095	+	0.247847i
$78$		0			0
$79$	10.6375	+	6.14158i	1.19681	+	0.690981i	0.959844	−	0.280535i	$-0.0905120\pi$
$79$	10.6375	+	6.14158i	1.19681	+	0.690981i	0.236971	+	0.971517i	$0.423845\pi$
$80$			2.80145i			0.313212i
$81$		0			0
$82$	−5.46756			−0.603790
$83$	−3.12049	+	5.40484i	−0.342518	+	0.593258i	−0.984900	−	0.173126i	$-0.944613\pi$
$83$	−3.12049	+	5.40484i	−0.342518	+	0.593258i	0.642382	+	0.766385i	$0.277946\pi$
$84$		0			0
$85$	−3.76721	+	2.17500i	−0.408612	+	0.235912i
$86$	−1.73802	−	3.01033i	−0.187415	−	0.324613i
$87$		0			0
$88$	1.27057	+	0.733565i	0.135443	+	0.0781982i
$89$	−1.01069			−0.107133			−0.0535664	−	0.998564i	$-0.517059\pi$
$89$	−1.01069			−0.107133			−0.0535664	+	0.998564i	$0.517059\pi$
$90$		0			0
$91$			6.08090i			0.637452i
$92$	3.83599	−	6.64412i	0.399929	−	0.692698i
$93$		0			0
$94$	4.92512	+	8.53055i	0.507987	+	0.879859i
$95$	17.3730	−	10.0303i	1.78243	−	1.02909i
$96$		0			0
$97$	−5.03375	+	8.71871i	−0.511100	+	0.885251i	0.488817	+	0.872386i	$0.337428\pi$
$97$	−5.03375	+	8.71871i	−0.511100	+	0.885251i	−0.999917	+	0.0128649i	$0.995905\pi$
$98$			4.07005i			0.411137i
$99$		0			0
$100$	2.84813			0.284813
$101$	−5.14898	−	2.97276i	−0.512343	−	0.295801i	0.221453	−	0.975171i	$-0.428920\pi$
$101$	−5.14898	−	2.97276i	−0.512343	−	0.295801i	−0.733796	+	0.679370i	$0.762253\pi$
$102$		0			0
$103$	−0.186316	−	0.322708i	−0.0183582	−	0.0317974i	0.856700	−	0.515814i	$-0.172511\pi$
$103$	−0.186316	−	0.322708i	−0.0183582	−	0.0317974i	−0.875059	+	0.484017i	$0.839177\pi$
$104$	1.77627	+	3.07658i	0.174177	+	0.301684i
$105$		0			0
$106$	−6.29531	−	3.63460i	−0.611455	−	0.353024i
$107$			4.45522i			0.430702i	0.976537	+	0.215351i	$0.0690896\pi$
$107$			4.45522i			0.430702i	−0.976537	+	0.215351i	$0.930910\pi$
$108$		0			0
$109$	−9.27511			−0.888395			−0.444197	−	0.895929i	$-0.646511\pi$
$109$	−9.27511			−0.888395			−0.444197	+	0.895929i	$0.646511\pi$
$110$	2.05505	−	3.55944i	0.195941	−	0.339380i
$111$		0			0
$112$	−0.855855	−	1.48238i	−0.0808707	−	0.140072i
$113$	−0.738545	+	0.426399i	−0.0694764	+	0.0401122i	−0.534336	−	0.845272i	$-0.679438\pi$
$113$	−0.738545	+	0.426399i	−0.0694764	+	0.0401122i	0.464859	+	0.885385i	$0.346105\pi$
$114$		0			0
$115$	−18.6132	−	10.7463i	−1.73569	−	1.00210i
$116$	1.51100			0.140293
$117$		0			0
$118$	11.0008			1.01270
$119$	1.32894	−	2.30180i	0.121824	−	0.211005i
$120$		0			0
$121$	4.42377	+	7.66219i	0.402161	+	0.696563i
$122$	0.468268	+	0.811064i	0.0423950	+	0.0734303i
$123$		0			0
$124$	3.18959	+	4.56361i	0.286434	+	0.409824i
$125$			6.02835i			0.539192i
$126$		0			0
$127$			1.27925i			0.113515i	0.998388	+	0.0567577i	$0.0180762\pi$
$127$			1.27925i			0.113515i	−0.998388	+	0.0567577i	$0.981924\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	8.61890	−	4.97612i	0.755927	−	0.436435i
$131$	3.33518	−	1.92557i	0.291396	−	0.168238i	−0.347175	−	0.937800i	$-0.612859\pi$
$131$	3.33518	−	1.92557i	0.291396	−	0.168238i	0.638571	+	0.769563i	$0.279526\pi$
$132$		0			0
$133$	−6.12858	+	10.6150i	−0.531416	+	0.920439i
$134$		−	12.0791i		−	1.04348i
$135$		0			0
$136$		−	1.55277i		−	0.133149i
$137$	3.18244	−	5.51214i	0.271894	−	0.470934i	−0.697453	−	0.716631i	$-0.745683\pi$
$137$	3.18244	−	5.51214i	0.271894	−	0.470934i	0.969347	+	0.245697i	$0.0790167\pi$
$138$		0			0
$139$	12.2227	−	7.05676i	1.03671	−	0.598546i	0.117812	−	0.993036i	$-0.462412\pi$
$139$	12.2227	−	7.05676i	1.03671	−	0.598546i	0.918900	+	0.394490i	$0.129079\pi$
$140$	−4.15283	+	2.39764i	−0.350978	+	0.202637i
$141$		0			0
$142$	5.55354	−	9.61901i	0.466042	−	0.807209i
$143$		−	5.21202i		−	0.435851i
$144$		0			0
$145$		−	4.23299i		−	0.351530i
$146$	−0.0690359	+	0.119574i	−0.00571345	+	0.00989599i
$147$		0			0
$148$	−9.17538	+	5.29741i	−0.754212	+	0.435444i
$149$	−3.45276	+	1.99345i	−0.282861	+	0.163310i	−0.634718	−	0.772744i	$-0.718884\pi$
$149$	−3.45276	+	1.99345i	−0.282861	+	0.163310i	0.351857	+	0.936054i	$0.385550\pi$
$150$		0			0
$151$	−19.7926	−	11.4273i	−1.61070	−	0.929939i	−0.989208	−	0.146519i	$-0.953193\pi$
$151$	−19.7926	−	11.4273i	−1.61070	−	0.929939i	−0.621493	−	0.783420i	$-0.713474\pi$
$152$			7.16077i			0.580816i
$153$		0			0
$154$			2.51130i			0.202366i
$155$	12.7847	−	8.93549i	1.02689	−	0.717716i
$156$		0			0
$157$	−3.75070	−	6.49641i	−0.299339	−	0.518470i	0.676646	−	0.736308i	$-0.263433\pi$
$157$	−3.75070	−	6.49641i	−0.299339	−	0.518470i	−0.975985	+	0.217839i	$0.930099\pi$
$158$	6.14158	+	10.6375i	0.488598	+	0.846276i
$159$		0			0
$160$	−1.40073	+	2.42613i	−0.110737	+	0.191802i
$161$	13.1322			1.03496
$162$		0			0
$163$	−7.62392			−0.597151			−0.298576	−	0.954386i	$-0.596512\pi$
$163$	−7.62392			−0.597151			−0.298576	+	0.954386i	$0.596512\pi$
$164$	−4.73504	−	2.73378i	−0.369745	−	0.213472i
$165$		0			0
$166$	−5.40484	+	3.12049i	−0.419497	+	0.242197i
$167$	9.90418	+	17.1545i	0.766408	+	1.32746i	0.939499	+	0.342552i	$0.111291\pi$
$167$	9.90418	+	17.1545i	0.766408	+	1.32746i	−0.173090	+	0.984906i	$0.555375\pi$
$168$		0			0
$169$	−0.189761	+	0.328676i	−0.0145970	+	0.0252827i
$170$	−4.35000			−0.333630
$171$		0			0
$172$		−	3.47603i		−	0.265045i
$173$	−21.7443	−	12.5541i	−1.65319	−	0.954468i	−0.975750	−	0.218886i	$-0.929758\pi$
$173$	−21.7443	−	12.5541i	−1.65319	−	0.954468i	−0.677436	−	0.735582i	$-0.736909\pi$
$174$		0			0
$175$	2.43759	+	4.22203i	0.184264	+	0.319155i
$176$	0.733565	+	1.27057i	0.0552945	+	0.0957729i
$177$		0			0
$178$	−0.875282	−	0.505344i	−0.0656052	−	0.0378772i
$179$	−15.3162			−1.14478			−0.572392	−	0.819980i	$-0.693984\pi$
$179$	−15.3162			−1.14478			−0.572392	+	0.819980i	$0.693984\pi$
$180$		0			0
$181$			17.1311i			1.27335i	0.771133	+	0.636674i	$0.219690\pi$
$181$			17.1311i			1.27335i	−0.771133	+	0.636674i	$0.780310\pi$
$182$	−3.04045	+	5.26622i	−0.225373	+	0.390358i
$183$		0			0
$184$	6.64412	−	3.83599i	0.489811	−	0.282793i
$185$	14.8404	+	25.7044i	1.09109	+	1.88982i
$186$		0			0
$187$	−1.13906	+	1.97290i	−0.0832960	+	0.144273i
$188$			9.85023i			0.718402i
$189$		0			0
$190$	20.0606			1.45535
$191$	1.58477	+	0.914970i	0.114670	+	0.0662049i	0.556238	−	0.831023i	$-0.312244\pi$
$191$	1.58477	+	0.914970i	0.114670	+	0.0662049i	−0.441568	+	0.897228i	$0.645578\pi$
$192$		0			0
$193$	−2.95915	−	5.12540i	−0.213004	−	0.368934i	0.739649	−	0.672993i	$-0.234991\pi$
$193$	−2.95915	−	5.12540i	−0.213004	−	0.368934i	−0.952653	+	0.304059i	$0.901658\pi$
$194$	−8.71871	+	5.03375i	−0.625967	+	0.361402i
$195$		0			0
$196$	−2.03502	+	3.52477i	−0.145359	+	0.251769i
$197$	−12.4301			−0.885606			−0.442803	−	0.896619i	$-0.646016\pi$
$197$	−12.4301			−0.885606			−0.442803	+	0.896619i	$0.646016\pi$
$198$		0			0
$199$			3.47989i			0.246683i	0.992364	+	0.123342i	$0.0393611\pi$
$199$			3.47989i			0.246683i	−0.992364	+	0.123342i	$0.960639\pi$
$200$	2.46656	+	1.42407i	0.174412	+	0.100697i
$201$		0			0
$202$	−2.97276	−	5.14898i	−0.209163	−	0.362281i
$203$	1.29319	+	2.23988i	0.0907645	+	0.157209i
$204$		0			0
$205$	−7.65855	+	13.2650i	−0.534896	+	0.926467i
$206$		−	0.372631i		−	0.0259624i
$207$		0			0
$208$			3.55253i			0.246324i
$209$	5.25289	−	9.09827i	0.363350	−	0.629341i
$210$		0			0
$211$	−6.02815	−	10.4411i	−0.414995	−	0.718792i	0.580433	−	0.814308i	$-0.302883\pi$
$211$	−6.02815	−	10.4411i	−0.414995	−	0.718792i	−0.995428	+	0.0955160i	$0.969550\pi$
$212$	−3.63460	−	6.29531i	−0.249625	−	0.432364i
$213$		0			0
$214$	−2.22761	+	3.85833i	−0.152276	+	0.263750i
$215$	−9.73794			−0.664122
$216$		0			0
$217$	−4.03519	+	8.63399i	−0.273926	+	0.586113i
$218$	−8.03248	−	4.63756i	−0.544028	−	0.314095i
$219$		0			0
$220$	3.55944	−	2.05505i	0.239978	−	0.138551i
$221$	−4.77722	+	2.75813i	−0.321350	+	0.185532i
$222$		0			0
$223$	21.6565	+	12.5034i	1.45023	+	0.837288i	0.998494	−	0.0548651i	$-0.0174729\pi$
$223$	21.6565	+	12.5034i	1.45023	+	0.837288i	0.451732	+	0.892154i	$0.350806\pi$
$224$		−	1.71171i		−	0.114368i
$225$		0			0
$226$	−0.852798			−0.0567273
$227$	2.95339	+	1.70514i	0.196023	+	0.113174i	0.594799	−	0.803874i	$-0.297232\pi$
$227$	2.95339	+	1.70514i	0.196023	+	0.113174i	−0.398776	+	0.917048i	$0.630565\pi$
$228$		0			0
$229$	7.49557	−	4.32757i	0.495321	−	0.285974i	−0.231458	−	0.972845i	$-0.574350\pi$
$229$	7.49557	−	4.32757i	0.495321	−	0.285974i	0.726779	+	0.686871i	$0.241016\pi$
$230$	−10.7463	−	18.6132i	−0.708592	−	1.22732i
$231$		0			0
$232$	1.30856	+	0.755499i	0.0859113	+	0.0496009i
$233$		−	11.0476i		−	0.723749i	−0.932227	−	0.361875i	$-0.882137\pi$
$233$		−	11.0476i		−	0.723749i	0.932227	−	0.361875i	$-0.117863\pi$
$234$		0			0
$235$	27.5949			1.80010
$236$	9.52695	+	5.50039i	0.620151	+	0.358045i
$237$		0			0
$238$	2.30180	−	1.32894i	0.149203	−	0.0861426i
$239$	−10.6056	−	18.3695i	−0.686022	−	1.18822i	−0.973115	−	0.230322i	$-0.926022\pi$
$239$	−10.6056	−	18.3695i	−0.686022	−	1.18822i	0.287093	−	0.957903i	$-0.407311\pi$
$240$		0			0
$241$	1.62450	+	0.937906i	0.104643	+	0.0604158i	0.551408	−	0.834236i	$-0.314091\pi$
$241$	1.62450	+	0.937906i	0.104643	+	0.0604158i	−0.446765	+	0.894651i	$0.647424\pi$
$242$			8.84753i			0.568741i
$243$		0			0
$244$			0.936536i			0.0599556i
$245$	9.87446	+	5.70102i	0.630856	+	0.364225i
$246$		0			0
$247$	22.0307	−	12.7194i	1.40178	−	0.809318i
$248$	0.480466	+	5.54699i	0.0305096	+	0.352235i
$249$		0			0
$250$	−3.01418	+	5.22070i	−0.190633	+	0.330186i
$251$	−23.3528			−1.47402			−0.737008	−	0.675884i	$-0.763762\pi$
$251$	−23.3528			−1.47402			−0.737008	+	0.675884i	$0.763762\pi$
$252$		0			0
$253$	−11.2558			−0.707645
$254$	−0.639627	+	1.10787i	−0.0401337	+	0.0695137i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.266405	+	0.153809i	−0.0166179	+	0.00959436i	−0.508286	−	0.861188i	$-0.669721\pi$
$257$	−0.266405	+	0.153809i	−0.0166179	+	0.00959436i	0.491668	+	0.870783i	$0.336387\pi$
$258$		0			0
$259$	−15.7056	−	9.06763i	−0.975898	−	0.563435i
$260$	9.95225			0.617212
$261$		0			0
$262$	3.85114			0.237924
$263$	−12.4680	+	21.5952i	−0.768810	+	1.33162i	0.169399	+	0.985548i	$0.445817\pi$
$263$	−12.4680	+	21.5952i	−0.768810	+	1.33162i	−0.938209	+	0.346070i	$0.887516\pi$
$264$		0			0
$265$	−17.6360	+	10.1822i	−1.08337	+	0.625485i
$266$	−10.6150	+	6.12858i	−0.650849	+	0.375768i
$267$		0			0
$268$	6.03957	−	10.4608i	0.368925	−	0.638997i
$269$	−5.85961			−0.357267			−0.178633	−	0.983916i	$-0.557168\pi$
$269$	−5.85961			−0.357267			−0.178633	+	0.983916i	$0.557168\pi$
$270$		0			0
$271$			18.2115i			1.10627i	0.833091	+	0.553136i	$0.186569\pi$
$271$			18.2115i			1.10627i	−0.833091	+	0.553136i	$0.813431\pi$
$272$	0.776384	−	1.34474i	0.0470752	−	0.0815366i
$273$		0			0
$274$	5.51214	−	3.18244i	0.333001	−	0.192258i
$275$	−2.08929	−	3.61876i	−0.125989	−	0.218219i
$276$		0			0
$277$	9.65869	+	5.57645i	0.580334	+	0.335056i	0.761266	−	0.648439i	$-0.224578\pi$
$277$	9.65869	+	5.57645i	0.580334	+	0.335056i	−0.180932	+	0.983496i	$0.557911\pi$
$278$	14.1135			0.846472
$279$		0			0
$280$	−4.79527			−0.286572
$281$	1.20286	+	0.694470i	0.0717564	+	0.0414286i	0.535449	−	0.844568i	$-0.320142\pi$
$281$	1.20286	+	0.694470i	0.0717564	+	0.0414286i	−0.463693	+	0.885996i	$0.653476\pi$
$282$		0			0
$283$	−12.9929	−	22.5044i	−0.772348	−	1.33775i	−0.936273	−	0.351273i	$-0.885749\pi$
$283$	−12.9929	−	22.5044i	−0.772348	−	1.33775i	0.163925	−	0.986473i	$-0.447585\pi$
$284$	9.61901	−	5.55354i	0.570783	−	0.329542i
$285$		0			0
$286$	2.60601	−	4.51374i	0.154097	−	0.266903i
$287$		−	9.35887i		−	0.552437i
$288$		0			0
$289$	−14.5889			−0.858171
$290$	2.11649	−	3.66587i	0.124285	−	0.215268i
$291$		0			0
$292$	−0.119574	+	0.0690359i	−0.00699752	+	0.00404002i
$293$	1.52102	−	0.878162i	0.0888591	−	0.0513028i	−0.454912	−	0.890536i	$-0.650329\pi$
$293$	1.52102	−	0.878162i	0.0888591	−	0.0513028i	0.543771	+	0.839234i	$0.316996\pi$
$294$		0			0
$295$	15.4091	−	26.6893i	0.897150	−	1.55391i
$296$	−10.5948			−0.615811
$297$		0			0
$298$	−3.98691			−0.230955
$299$	−23.6035	−	13.6275i	−1.36502	−	0.788097i
$300$		0			0
$301$	5.15282	−	2.97498i	0.297003	−	0.171475i
$302$	−11.4273	−	19.7926i	−0.657566	−	1.13894i
$303$		0			0
$304$	−3.58039	+	6.20141i	−0.205349	+	0.355675i
$305$	2.62366			0.150230
$306$		0			0
$307$	−19.6057			−1.11895			−0.559477	−	0.828846i	$-0.688998\pi$
$307$	−19.6057			−1.11895			−0.559477	+	0.828846i	$0.688998\pi$
$308$	−1.25565	+	2.17485i	−0.0715473	+	0.123924i
$309$		0			0
$310$	15.5396	−	1.34600i	0.882592	−	0.0764478i
$311$	14.9268	−	8.61798i	0.846420	−	0.488681i	−0.0130214	−	0.999915i	$-0.504145\pi$
$311$	14.9268	−	8.61798i	0.846420	−	0.488681i	0.859441	+	0.511234i	$0.170812\pi$
$312$		0			0
$313$	−22.5106	−	12.9965i	−1.27238	−	0.734607i	−0.296942	−	0.954895i	$-0.595967\pi$
$313$	−22.5106	−	12.9965i	−1.27238	−	0.734607i	−0.975435	+	0.220288i	$0.929300\pi$
$314$		−	7.50140i		−	0.423329i
$315$		0			0
$316$			12.2832i			0.690981i
$317$	−16.6768	−	9.62837i	−0.936664	−	0.540783i	−0.0477510	−	0.998859i	$-0.515205\pi$
$317$	−16.6768	−	9.62837i	−0.936664	−	0.540783i	−0.888913	+	0.458076i	$0.848539\pi$
$318$		0			0
$319$	−1.10841	−	1.91983i	−0.0620593	−	0.107490i
$320$	−2.42613	+	1.40073i	−0.135625	+	0.0783030i
$321$		0			0
$322$	11.3728	+	6.56610i	0.633782	+	0.365914i
$323$	−11.1190			−0.618679
$324$		0			0
$325$		−	10.1181i		−	0.561250i
$326$	−6.60251	−	3.81196i	−0.365679	−	0.211125i
$327$		0			0
$328$	−2.73378	−	4.73504i	−0.150948	−	0.261449i
$329$	−14.6018	+	8.43037i	−0.805025	+	0.464781i
$330$		0			0
$331$	−17.2573	−	9.96350i	−0.948546	−	0.547643i	−0.0559171	−	0.998435i	$-0.517808\pi$
$331$	−17.2573	−	9.96350i	−0.948546	−	0.547643i	−0.892629	+	0.450792i	$0.851142\pi$
$332$	−6.24097			−0.342518
$333$		0			0
$334$			19.8084i			1.08387i
$335$	−29.3055	−	16.9196i	−1.60113	−	0.924414i
$336$		0			0
$337$	−11.4177	+	6.59199i	−0.621960	+	0.359089i	−0.777632	−	0.628720i	$-0.783579\pi$
$337$	−11.4177	+	6.59199i	−0.621960	+	0.359089i	0.155672	+	0.987809i	$0.450246\pi$
$338$	−0.328676	+	0.189761i	−0.0178776	+	0.0103216i
$339$		0			0
$340$	−3.76721	−	2.17500i	−0.204306	−	0.117956i
$341$	3.45861	−	7.40030i	0.187294	−	0.400749i
$342$		0			0
$343$	−18.9487			−1.02313
$344$	1.73802	−	3.01033i	0.0937076	−	0.162306i
$345$		0			0
$346$	−12.5541	−	21.7443i	−0.674911	−	1.16898i
$347$	15.8053	+	27.3756i	0.848474	+	1.46960i	0.882570	+	0.470182i	$0.155812\pi$
$347$	15.8053	+	27.3756i	0.848474	+	1.46960i	−0.0340955	+	0.999419i	$0.510855\pi$
$348$		0			0
$349$	14.7463	−	25.5413i	0.789349	−	1.36719i	−0.137017	−	0.990569i	$-0.543751\pi$
$349$	14.7463	−	25.5413i	0.789349	−	1.36719i	0.926366	−	0.376624i	$-0.122915\pi$
$350$			4.87518i			0.260589i
$351$		0			0
$352$			1.46713i			0.0781982i
$353$	−2.19529	+	3.80236i	−0.116844	+	0.202379i	−0.918515	−	0.395386i	$-0.870611\pi$
$353$	−2.19529	+	3.80236i	−0.116844	+	0.202379i	0.801672	+	0.597765i	$0.203944\pi$
$354$		0			0
$355$	−15.5580	−	26.9472i	−0.825731	−	1.43021i
$356$	−0.505344	−	0.875282i	−0.0267832	−	0.0463899i
$357$		0			0
$358$	−13.2642	−	7.65808i	−0.701034	−	0.404742i
$359$			15.9884i			0.843836i	0.906634	+	0.421918i	$0.138643\pi$
$359$			15.9884i			0.843836i	−0.906634	+	0.421918i	$0.861357\pi$
$360$		0			0
$361$	32.2767			1.69877
$362$	−8.56557	+	14.8360i	−0.450196	+	0.779763i
$363$		0			0
$364$	−5.26622	+	3.04045i	−0.276025	+	0.159363i
$365$	0.193401	+	0.334980i	0.0101231	+	0.0175336i
$366$		0			0
$367$	−26.6166	−	15.3671i	−1.38937	−	0.802155i	−0.396129	−	0.918195i	$-0.629647\pi$
$367$	−26.6166	−	15.3671i	−1.38937	−	0.802155i	−0.993245	+	0.116040i	$0.962980\pi$
$368$	7.67197			0.399929
$369$		0			0
$370$			29.6809i			1.54304i
$371$	6.22138	−	10.7757i	0.322998	−	0.559449i
$372$		0			0
$373$	−13.4906	−	23.3664i	−0.698516	−	1.20987i	−0.968981	−	0.247136i	$-0.920511\pi$
$373$	−13.4906	−	23.3664i	−0.698516	−	1.20987i	0.270465	−	0.962730i	$-0.412823\pi$
$374$	−1.97290	+	1.13906i	−0.102016	+	0.0588991i
$375$		0			0
$376$	−4.92512	+	8.53055i	−0.253993	+	0.439930i
$377$		−	5.36787i		−	0.276459i
$378$		0			0
$379$	19.1216			0.982211			0.491106	−	0.871100i	$-0.336593\pi$
$379$	19.1216			0.982211			0.491106	+	0.871100i	$0.336593\pi$
$380$	17.3730	+	10.0303i	0.891214	+	0.514543i
$381$		0			0
$382$	0.914970	+	1.58477i	0.0468139	+	0.0810841i
$383$	−0.976928	−	1.69209i	−0.0499187	−	0.0864617i	0.839986	−	0.542607i	$-0.182563\pi$
$383$	−0.976928	−	1.69209i	−0.0499187	−	0.0864617i	−0.889905	+	0.456146i	$0.849230\pi$
$384$		0			0
$385$	6.09274	+	3.51764i	0.310515	+	0.179276i
$386$		−	5.91830i		−	0.301234i
$387$		0			0
$388$	−10.0675			−0.511100
$389$	−15.7084	+	27.2077i	−0.796447	+	1.37949i	0.125470	+	0.992097i	$0.459956\pi$
$389$	−15.7084	+	27.2077i	−0.796447	+	1.37949i	−0.921916	+	0.387389i	$0.873377\pi$
$390$		0			0
$391$	5.95640	+	10.3168i	0.301228	+	0.521742i
$392$	−3.52477	+	2.03502i	−0.178028	+	0.102784i
$393$		0			0
$394$	−10.7648	−	6.21503i	−0.542320	−	0.313109i
$395$	34.4107			1.73139
$396$		0			0
$397$	18.7186			0.939458			0.469729	−	0.882811i	$-0.344352\pi$
$397$	18.7186			0.939458			0.469729	+	0.882811i	$0.344352\pi$
$398$	−1.73995	+	3.01368i	−0.0872157	+	0.151062i
$399$		0			0
$400$	1.42407	+	2.46656i	0.0712033	+	0.123328i
$401$	1.80742	+	3.13054i	0.0902583	+	0.156332i	0.907620	−	0.419793i	$-0.137897\pi$
$401$	1.80742	+	3.13054i	0.0902583	+	0.156332i	−0.817361	+	0.576125i	$0.804564\pi$
$402$		0			0
$403$	16.2124	−	11.3311i	0.807595	−	0.564444i
$404$		−	5.94553i		−	0.295801i
$405$		0			0
$406$			2.58639i			0.128360i
$407$	13.4615	+	7.77198i	0.667260	+	0.385243i
$408$		0			0
$409$	−3.08139	+	1.77904i	−0.152365	+	0.0879679i	−0.574244	−	0.818684i	$-0.694704\pi$
$409$	−3.08139	+	1.77904i	−0.152365	+	0.0879679i	0.421879	+	0.906652i	$0.361371\pi$
$410$	−13.2650	+	7.65855i	−0.655111	+	0.378229i
$411$		0			0
$412$	0.186316	−	0.322708i	0.00917911	−	0.0158987i
$413$			18.8301i			0.926570i
$414$		0			0
$415$			17.4838i			0.858245i
$416$	−1.77627	+	3.07658i	−0.0870886	+	0.150842i
$417$		0			0
$418$	9.09827	−	5.25289i	0.445011	−	0.256927i
$419$	−29.1162	+	16.8102i	−1.42242	+	0.821233i	−0.996505	−	0.0835308i	$-0.973380\pi$
$419$	−29.1162	+	16.8102i	−1.42242	+	0.821233i	−0.425913	+	0.904764i	$0.640047\pi$
$420$		0			0
$421$	3.44737	−	5.97103i	0.168015	−	0.291010i	−0.769707	−	0.638397i	$-0.779598\pi$
$421$	3.44737	−	5.97103i	0.168015	−	0.291010i	0.937722	+	0.347387i	$0.112931\pi$
$422$		−	12.0563i		−	0.586891i
$423$		0			0
$424$		−	7.26920i		−	0.353024i
$425$	−2.21124	+	3.82999i	−0.107261	+	0.185782i
$426$		0			0
$427$	−1.38831	+	0.801539i	−0.0671848	+	0.0387892i
$428$	−3.85833	+	2.22761i	−0.186500	+	0.107676i
$429$		0			0
$430$	−8.43331	−	4.86897i	−0.406690	−	0.234803i
$431$			1.48642i			0.0715984i	0.999359	+	0.0357992i	$0.0113977\pi$
$431$			1.48642i			0.0715984i	−0.999359	+	0.0357992i	$0.988602\pi$
$432$		0			0
$433$		−	16.5728i		−	0.796440i	−0.917290	−	0.398220i	$-0.869628\pi$
$433$		−	16.5728i		−	0.796440i	0.917290	−	0.398220i	$-0.130372\pi$
$434$	−7.81157	+	5.45966i	−0.374967	+	0.262072i
$435$		0			0
$436$	−4.63756	−	8.03248i	−0.222099	−	0.384686i
$437$	−27.4686	−	47.5771i	−1.31400	−	2.27592i
$438$		0			0
$439$	−17.8947	+	30.9945i	−0.854065	+	1.47928i	0.0234440	+	0.999725i	$0.492537\pi$
$439$	−17.8947	+	30.9945i	−0.854065	+	1.47928i	−0.877509	+	0.479559i	$0.840796\pi$
$440$	4.11009			0.195941
$441$		0			0
$442$	−5.51626			−0.262381
$443$	16.1237	+	9.30903i	0.766061	+	0.442286i	0.831468	−	0.555573i	$-0.187501\pi$
$443$	16.1237	+	9.30903i	0.766061	+	0.442286i	−0.0654066	+	0.997859i	$0.520834\pi$
$444$		0			0
$445$	−2.45206	+	1.41570i	−0.116239	+	0.0671105i
$446$	12.5034	+	21.6565i	0.592052	+	1.02546i
$447$		0			0
$448$	0.855855	−	1.48238i	0.0404353	−	0.0700361i
$449$	37.5508			1.77213			0.886065	−	0.463560i	$-0.153428\pi$
$449$	37.5508			1.77213			0.886065	+	0.463560i	$0.153428\pi$
$450$		0			0
$451$			8.02161i			0.377723i
$452$	−0.738545	−	0.426399i	−0.0347382	−	0.0200561i
$453$		0			0
$454$	1.70514	+	2.95339i	0.0800262	+	0.138609i
$455$	8.51768	+	14.7531i	0.399315	+	0.691634i
$456$		0			0
$457$	15.3789	+	8.87898i	0.719392	+	0.415341i	0.814529	−	0.580123i	$-0.196995\pi$
$457$	15.3789	+	8.87898i	0.719392	+	0.415341i	−0.0951366	+	0.995464i	$0.530329\pi$
$458$	8.65514			0.404428
$459$		0			0
$460$		−	21.4927i		−	1.00210i
$461$	16.6185	−	28.7841i	0.774000	−	1.34061i	−0.161355	−	0.986896i	$-0.551586\pi$
$461$	16.6185	−	28.7841i	0.774000	−	1.34061i	0.935355	−	0.353711i	$-0.115080\pi$
$462$		0			0
$463$	13.2832	−	7.66907i	0.617323	−	0.356412i	−0.158503	−	0.987359i	$-0.550667\pi$
$463$	13.2832	−	7.66907i	0.617323	−	0.356412i	0.775826	+	0.630947i	$0.217333\pi$
$464$	0.755499	+	1.30856i	0.0350731	+	0.0607485i
$465$		0			0
$466$	5.52378	−	9.56746i	0.255884	−	0.443204i
$467$		−	7.95169i		−	0.367960i	−0.982930	−	0.183980i	$-0.941102\pi$
$467$		−	7.95169i		−	0.367960i	0.982930	−	0.183980i	$-0.0588982\pi$
$468$		0			0
$469$	20.6760			0.954728
$470$	23.8979	+	13.7975i	1.10233	+	0.636430i
$471$		0			0
$472$	5.50039	+	9.52695i	0.253176	+	0.438513i
$473$	−4.41655	+	2.54989i	−0.203073	+	0.117244i
$474$		0			0
$475$	10.1974	−	17.6625i	0.467890	−	0.810409i
$476$	2.65789			0.121824
$477$		0			0
$478$		−	21.2113i		−	0.970181i
$479$	−0.289339	−	0.167050i	−0.0132202	−	0.00763271i	0.493375	−	0.869817i	$-0.335763\pi$
$479$	−0.289339	−	0.167050i	−0.0132202	−	0.00763271i	−0.506596	+	0.862184i	$0.669096\pi$
$480$		0			0
$481$	18.8192	+	32.5958i	0.858082	+	1.48624i
$482$	0.937906	+	1.62450i	0.0427204	+	0.0739940i
$483$		0			0
$484$	−4.42377	+	7.66219i	−0.201080	+	0.348281i
$485$			28.2036i			1.28066i
$486$		0			0
$487$		−	26.5619i		−	1.20363i	−0.798634	−	0.601817i	$-0.794444\pi$
$487$		−	26.5619i		−	1.20363i	0.798634	−	0.601817i	$-0.205556\pi$
$488$	−0.468268	+	0.811064i	−0.0211975	+	0.0367151i
$489$		0			0
$490$	5.70102	+	9.87446i	0.257546	+	0.446083i
$491$	−0.293876	−	0.509009i	−0.0132625	−	0.0229712i	0.859318	−	0.511442i	$-0.170888\pi$
$491$	−0.293876	−	0.509009i	−0.0132625	−	0.0229712i	−0.872580	+	0.488470i	$0.837555\pi$
$492$		0			0
$493$	−1.17311	+	2.03189i	−0.0528344	+	0.0915118i
$494$	25.4389			1.14455
$495$		0			0
$496$	−2.35740	+	5.04407i	−0.105850	+	0.226486i
$497$	16.4650	+	9.50604i	0.738554	+	0.426404i
$498$		0			0
$499$	−24.6683	+	14.2422i	−1.10430	+	0.637571i	−0.937348	−	0.348394i	$-0.886727\pi$
$499$	−24.6683	+	14.2422i	−1.10430	+	0.637571i	−0.166956	+	0.985964i	$0.553394\pi$
$500$	−5.22070	+	3.01418i	−0.233477	+	0.134798i
$501$		0			0
$502$	−20.2241	−	11.6764i	−0.902647	−	0.521144i
$503$			1.68247i			0.0750177i	0.999296	+	0.0375088i	$0.0119422\pi$
$503$			1.68247i			0.0750177i	−0.999296	+	0.0375088i	$0.988058\pi$
$504$		0			0
$505$	−16.6561			−0.741187
$506$	−9.74779	−	5.62789i	−0.433342	−	0.250190i
$507$		0			0
$508$	−1.10787	+	0.639627i	−0.0491536	+	0.0283788i
$509$	3.73041	+	6.46126i	0.165347	+	0.286390i	0.936779	−	0.349923i	$-0.113792\pi$
$509$	3.73041	+	6.46126i	0.165347	+	0.286390i	−0.771431	+	0.636313i	$0.780459\pi$
$510$		0			0
$511$	−0.204675	−	0.118169i	−0.00905431	−	0.00522751i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−0.307619			−0.0135685
$515$	−0.904051	−	0.521954i	−0.0398373	−	0.0230001i
$516$		0			0
$517$	12.5154	−	7.22578i	0.550427	−	0.317789i
$518$	−9.06763	−	15.7056i	−0.398409	−	0.690064i
$519$		0			0
$520$	8.61890	+	4.97612i	0.377964	+	0.218217i
$521$		−	5.59532i		−	0.245136i	−0.992460	−	0.122568i	$-0.960887\pi$
$521$		−	5.59532i		−	0.245136i	0.992460	−	0.122568i	$-0.0391129\pi$
$522$		0			0
$523$		−	1.73661i		−	0.0759367i	−0.999279	−	0.0379684i	$-0.987911\pi$
$523$		−	1.73661i		−	0.0759367i	0.999279	−	0.0379684i	$-0.0120886\pi$
$524$	3.33518	+	1.92557i	0.145698	+	0.0841188i
$525$		0			0
$526$	−21.5952	+	12.4680i	−0.941596	+	0.543630i
$527$	−8.61319	+	0.746052i	−0.375197	+	0.0324986i
$528$		0			0
$529$	−17.9296	+	31.0550i	−0.779548	+	1.35022i
$530$	−20.3643			−0.884569
$531$		0			0
$532$	−12.2572			−0.531416
$533$	−9.71183	+	16.8214i	−0.420666	+	0.728615i
$534$		0			0
$535$	6.24054	+	10.8089i	0.269802	+	0.467311i
$536$	10.4608	−	6.03957i	0.451839	−	0.260870i
$537$		0			0
$538$	−5.07457	−	2.92980i	−0.218780	−	0.126313i
$539$	5.97129			0.257202
$540$		0			0
$541$	−8.04805			−0.346013			−0.173006	−	0.984921i	$-0.555348\pi$
$541$	−8.04805			−0.346013			−0.173006	+	0.984921i	$0.555348\pi$
$542$	−9.10576	+	15.7716i	−0.391126	+	0.677450i
$543$		0			0
$544$	1.34474	−	0.776384i	0.0576551	−	0.0332872i
$545$	−22.5026	+	12.9919i	−0.963906	+	0.556511i
$546$		0			0
$547$	6.72268	−	11.6440i	0.287441	−	0.497863i	−0.685757	−	0.727831i	$-0.740529\pi$
$547$	6.72268	−	11.6440i	0.287441	−	0.497863i	0.973198	+	0.229968i	$0.0738621\pi$
$548$	6.36487			0.271894
$549$		0			0
$550$		−	4.17858i		−	0.178175i
$551$	5.40996	−	9.37032i	0.230472	−	0.399189i
$552$		0			0
$553$	−18.2084	+	10.5126i	−0.774298	+	0.447041i
$554$	5.57645	+	9.65869i	0.236920	+	0.410358i
$555$		0			0
$556$	12.2227	+	7.05676i	0.518356	+	0.299273i
$557$	0.933781			0.0395656			0.0197828	−	0.999804i	$-0.493703\pi$
$557$	0.933781			0.0395656			0.0197828	+	0.999804i	$0.493703\pi$
$558$		0			0
$559$	−12.3487			−0.522295
$560$	−4.15283	−	2.39764i	−0.175489	−	0.101319i
$561$		0			0
$562$	0.694470	+	1.20286i	0.0292944	+	0.0507394i
$563$	10.9266	−	6.30846i	0.460500	−	0.265870i	−0.251754	−	0.967791i	$-0.581008\pi$
$563$	10.9266	−	6.30846i	0.460500	−	0.265870i	0.712254	+	0.701921i	$0.247674\pi$
$564$		0			0
$565$	−1.19454	+	2.06900i	−0.0502545	+	0.0870434i
$566$		−	25.9858i		−	1.09227i
$567$		0			0
$568$	11.1071			0.466042
$569$	−21.0010	+	36.3748i	−0.880407	+	1.52491i	−0.0295185	+	0.999564i	$0.509397\pi$
$569$	−21.0010	+	36.3748i	−0.880407	+	1.52491i	−0.850889	+	0.525346i	$0.823936\pi$
$570$		0			0
$571$	−22.8546	+	13.1951i	−0.956435	+	0.552198i	−0.895074	−	0.445917i	$-0.852877\pi$
$571$	−22.8546	+	13.1951i	−0.956435	+	0.552198i	−0.0613612	+	0.998116i	$0.519544\pi$
$572$	4.51374	−	2.60601i	0.188729	−	0.108963i
$573$		0			0
$574$	4.67943	−	8.10502i	0.195316	−	0.338297i
$575$	−21.8508			−0.911242
$576$		0			0
$577$	11.6642			0.485586			0.242793	−	0.970078i	$-0.421936\pi$
$577$	11.6642			0.485586			0.242793	+	0.970078i	$0.421936\pi$
$578$	−12.6344	−	7.29446i	−0.525520	−	0.303409i
$579$		0			0
$580$	3.66587	−	2.11649i	0.152217	−	0.0878826i
$581$	−5.34137	−	9.25152i	−0.221597	−	0.383818i
$582$		0			0
$583$	−5.33243	+	9.23603i	−0.220847	+	0.382517i
$584$	−0.138072			−0.00571345
$585$		0			0
$586$	1.75632			0.0725531
$587$	15.8654	−	27.4797i	0.654835	−	1.13421i	−0.327101	−	0.944990i	$-0.606072\pi$
$587$	15.8654	−	27.4797i	0.654835	−	1.13421i	0.981935	−	0.189217i	$-0.0605951\pi$
$588$		0			0
$589$	39.7208	−	3.44051i	1.63667	−	0.141764i
$590$	26.6893	−	15.4091i	1.09878	−	0.634381i
$591$		0			0
$592$	−9.17538	−	5.29741i	−0.377106	−	0.217722i
$593$		−	14.9623i		−	0.614426i	−0.951641	−	0.307213i	$-0.900604\pi$
$593$		−	14.9623i		−	0.614426i	0.951641	−	0.307213i	$-0.0993964\pi$
$594$		0			0
$595$		−	7.44594i		−	0.305254i
$596$	−3.45276	−	1.99345i	−0.141431	−	0.0816550i
$597$		0			0
$598$	−13.6275	−	23.6035i	−0.557268	−	0.965217i
$599$	32.4012	−	18.7068i	1.32388	−	0.764341i	0.339532	−	0.940594i	$-0.389731\pi$
$599$	32.4012	−	18.7068i	1.32388	−	0.764341i	0.984345	+	0.176254i	$0.0563979\pi$
$600$		0			0
$601$	29.9367	+	17.2840i	1.22115	+	0.705028i	0.965162	−	0.261653i	$-0.0842675\pi$
$601$	29.9367	+	17.2840i	1.22115	+	0.705028i	0.255983	+	0.966681i	$0.417601\pi$
$602$	5.94996			0.242502
$603$		0			0
$604$		−	22.8546i		−	0.929939i
$605$	21.4653	+	12.3930i	0.872687	+	0.503846i
$606$		0			0
$607$	6.70104	+	11.6065i	0.271987	+	0.471095i	0.969371	−	0.245603i	$-0.0789859\pi$
$607$	6.70104	+	11.6065i	0.271987	+	0.471095i	−0.697384	+	0.716698i	$0.745653\pi$
$608$	−6.20141	+	3.58039i	−0.251500	+	0.145204i
$609$		0			0
$610$	2.27216	+	1.31183i	0.0919969	+	0.0531144i
$611$	34.9933			1.41568
$612$		0			0
$613$		−	22.6537i		−	0.914975i	−0.889216	−	0.457488i	$-0.848749\pi$
$613$		−	22.6537i		−	0.914975i	0.889216	−	0.457488i	$-0.151251\pi$
$614$	−16.9790	−	9.80284i	−0.685217	−	0.395610i
$615$		0			0
$616$	−2.17485	+	1.25565i	−0.0876272	+	0.0505916i
$617$	19.6767	−	11.3604i	0.792155	−	0.457351i	−0.0485657	−	0.998820i	$-0.515465\pi$
$617$	19.6767	−	11.3604i	0.792155	−	0.457351i	0.840721	+	0.541469i	$0.182132\pi$
$618$		0			0
$619$	29.8488	+	17.2332i	1.19973	+	0.692662i	0.960494	−	0.278300i	$-0.0897709\pi$
$619$	29.8488	+	17.2332i	1.19973	+	0.692662i	0.239232	+	0.970962i	$0.423104\pi$
$620$	14.1307	+	6.60415i	0.567504	+	0.265229i
$621$		0			0
$622$	17.2360			0.691099
$623$	0.865003	−	1.49823i	0.0346556	−	0.0600253i
$624$		0			0
$625$	15.5644	+	26.9583i	0.622576	+	1.07833i
$626$	−12.9965	−	22.5106i	−0.519446	−	0.899706i
$627$		0			0
$628$	3.75070	−	6.49641i	0.149669	−	0.259235i
$629$		−	16.4513i		−	0.655956i
$630$		0			0
$631$		−	22.1803i		−	0.882983i	−0.897265	−	0.441492i	$-0.854449\pi$
$631$		−	22.1803i		−	0.882983i	0.897265	−	0.441492i	$-0.145551\pi$
$632$	−6.14158	+	10.6375i	−0.244299	+	0.423138i
$633$		0			0
$634$	−9.62837	−	16.6768i	−0.382391	−	0.662321i
$635$	1.79188	+	3.10363i	0.0711087	+	0.123164i
$636$		0			0
$637$	12.5218	+	7.22949i	0.496133	+	0.286443i
$638$		−	2.21683i		−	0.0877651i
$639$		0			0
$640$	−2.80145			−0.110737
$641$	4.64820	−	8.05092i	0.183593	−	0.317992i	−0.759509	−	0.650497i	$-0.774560\pi$
$641$	4.64820	−	8.05092i	0.183593	−	0.317992i	0.943101	+	0.332505i	$0.107894\pi$
$642$		0			0
$643$	−31.8796	+	18.4057i	−1.25721	+	0.725849i	−0.972531	−	0.232775i	$-0.925220\pi$
$643$	−31.8796	+	18.4057i	−1.25721	+	0.725849i	−0.284677	+	0.958624i	$0.591886\pi$
$644$	6.56610	+	11.3728i	0.258740	+	0.448152i
$645$		0			0
$646$	−9.62935	−	5.55951i	−0.378862	−	0.218736i
$647$	−0.908098			−0.0357010			−0.0178505	−	0.999841i	$-0.505682\pi$
$647$	−0.908098			−0.0357010			−0.0178505	+	0.999841i	$0.505682\pi$
$648$		0			0
$649$		−	16.1395i		−	0.633533i
$650$	5.05904	−	8.76252i	0.198432	−	0.343694i
$651$		0			0
$652$	−3.81196	−	6.60251i	−0.149288	−	0.258574i
$653$	−20.6816	+	11.9405i	−0.809335	+	0.467270i	−0.846725	−	0.532031i	$-0.821429\pi$
$653$	−20.6816	+	11.9405i	−0.809335	+	0.467270i	0.0373900	+	0.999301i	$0.488096\pi$
$654$		0			0
$655$	5.39439	−	9.34335i	0.210776	−	0.365075i
$656$		−	5.46756i		−	0.213472i
$657$		0			0
$658$	−16.8607			−0.657300
$659$	28.4514	+	16.4264i	1.10831	+	0.639883i	0.938391	−	0.345575i	$-0.112316\pi$
$659$	28.4514	+	16.4264i	1.10831	+	0.639883i	0.169919	+	0.985458i	$0.445649\pi$
$660$		0			0
$661$	12.3834	+	21.4487i	0.481659	+	0.834258i	0.999778	−	0.0210506i	$-0.00670112\pi$
$661$	12.3834	+	21.4487i	0.481659	+	0.834258i	−0.518120	+	0.855308i	$0.673368\pi$
$662$	−9.96350	−	17.2573i	−0.387242	−	0.670723i
$663$		0			0
$664$	−5.40484	−	3.12049i	−0.209749	−	0.121098i
$665$			34.3379i			1.33157i
$666$		0			0
$667$	−11.5923			−0.448857
$668$	−9.90418	+	17.1545i	−0.383204	+	0.663729i
$669$		0			0
$670$	−16.9196	−	29.3055i	−0.653660	−	1.13217i
$671$	1.18994	−	0.687009i	0.0459369	−	0.0265217i
$672$		0			0
$673$	7.04262	+	4.06606i	0.271473	+	0.156735i	0.629557	−	0.776954i	$-0.283236\pi$
$673$	7.04262	+	4.06606i	0.271473	+	0.156735i	−0.358084	+	0.933689i	$0.616570\pi$
$674$	−13.1840			−0.507828
$675$		0			0
$676$	−0.379522			−0.0145970
$677$	−25.5772	+	44.3010i	−0.983012	+	1.70263i	−0.332556	+	0.943084i	$0.607911\pi$
$677$	−25.5772	+	44.3010i	−0.983012	+	1.70263i	−0.650456	+	0.759544i	$0.725422\pi$
$678$		0			0
$679$	−8.61632	−	14.9239i	−0.330664	−	0.572727i
$680$	−2.17500	−	3.76721i	−0.0834075	−	0.144466i
$681$		0			0
$682$	6.69540	−	4.67955i	0.256380	−	0.179189i
$683$			37.0300i			1.41691i	0.705755	+	0.708456i	$0.250608\pi$
$683$			37.0300i			1.41691i	−0.705755	+	0.708456i	$0.749392\pi$
$684$		0			0
$685$		−	17.8309i		−	0.681283i
$686$	−16.4101	−	9.47436i	−0.626539	−	0.361733i
$687$		0			0
$688$	3.01033	−	1.73802i	0.114768	−	0.0662613i
$689$	−22.3643	+	12.9120i	−0.852012	+	0.491909i
$690$		0			0
$691$	18.9242	−	32.7776i	0.719909	−	1.24692i	−0.241127	−	0.970494i	$-0.577517\pi$
$691$	18.9242	−	32.7776i	0.719909	−	1.24692i	0.961035	−	0.276425i	$-0.0891498\pi$
$692$		−	25.1081i		−	0.954468i
$693$		0			0
$694$			31.6106i			1.19992i
$695$	19.7692	−	34.2412i	0.749887	−	1.29884i
$696$		0			0
$697$	7.35242	−	4.24492i	0.278493	−	0.160788i
$698$	25.5413	−	14.7463i	0.966751	−	0.558154i
$699$		0			0
$700$	−2.43759	+	4.22203i	−0.0921322	+	0.159578i
$701$		−	11.1960i		−	0.422866i	−0.977392	−	0.211433i	$-0.932187\pi$
$701$		−	11.1960i		−	0.422866i	0.977392	−	0.211433i	$-0.0678130\pi$
$702$		0			0
$703$			75.8671i			2.86138i
$704$	−0.733565	+	1.27057i	−0.0276473	+	0.0478864i
$705$		0			0
$706$	−3.80236	+	2.19529i	−0.143104	+	0.0826210i
$707$	8.81356	−	5.08851i	0.331468	−	0.191373i
$708$		0			0
$709$	14.6470	+	8.45643i	0.550078	+	0.317588i	0.749154	−	0.662396i	$-0.230460\pi$
$709$	14.6470	+	8.45643i	0.550078	+	0.317588i	−0.199075	+	0.979984i	$0.563794\pi$
$710$		−	31.1159i		−	1.16776i
$711$		0			0
$712$		−	1.01069i		−	0.0378772i
$713$	−24.4705	−	35.0119i	−0.916427	−	1.31120i
$714$		0			0
$715$	−7.30061	−	12.6450i	−0.273027	−	0.472897i
$716$	−7.65808	−	13.2642i	−0.286196	−	0.495706i
$717$		0			0
$718$	−7.99421	+	13.8464i	−0.298341	+	0.516742i
$719$	−19.5121			−0.727680			−0.363840	−	0.931461i	$-0.618535\pi$
$719$	−19.5121			−0.727680			−0.363840	+	0.931461i	$0.618535\pi$
$720$		0			0
$721$	0.637837			0.0237543
$722$	27.9524	+	16.1383i	1.04028	+	0.600607i
$723$		0			0
$724$	−14.8360	+	8.56557i	−0.551376	+	0.318337i
$725$	−2.15176	−	3.72696i	−0.0799144	−	0.138416i
$726$		0			0
$727$	−21.7893	+	37.7402i	−0.808121	+	1.39971i	0.106043	+	0.994362i	$0.466182\pi$
$727$	−21.7893	+	37.7402i	−0.808121	+	1.39971i	−0.914164	+	0.405345i	$0.867151\pi$
$728$	−6.08090			−0.225373
$729$		0			0
$730$			0.386801i			0.0143162i
$731$	4.67435	+	2.69874i	0.172887	+	0.0998164i
$732$		0			0
$733$	7.07522	+	12.2546i	0.261329	+	0.452635i	0.966595	−	0.256307i	$-0.0825059\pi$
$733$	7.07522	+	12.2546i	0.261329	+	0.452635i	−0.705266	+	0.708943i	$0.749173\pi$
$734$	−15.3671	−	26.6166i	−0.567209	−	0.982435i
$735$		0			0
$736$	6.64412	+	3.83599i	0.244906	+	0.141396i
$737$	−17.7217			−0.652785
$738$		0			0
$739$		−	9.47332i		−	0.348482i	−0.984703	−	0.174241i	$-0.944253\pi$
$739$		−	9.47332i		−	0.348482i	0.984703	−	0.174241i	$-0.0557471\pi$
$740$	−14.8404	+	25.7044i	−0.545545	+	0.944912i
$741$		0			0
$742$	10.7757	−	6.22138i	0.395590	−	0.228394i
$743$	0.971636	+	1.68292i	0.0356459	+	0.0617404i	0.883298	−	0.468812i	$-0.155318\pi$
$743$	0.971636	+	1.68292i	0.0356459	+	0.0617404i	−0.847652	+	0.530552i	$0.821984\pi$
$744$		0			0
$745$	−5.58457	+	9.67275i	−0.204603	+	0.354382i
$746$		−	26.9812i		−	0.987851i
$747$		0			0
$748$	−2.27811			−0.0832960
$749$	−6.60435	−	3.81302i	−0.241318	−	0.139325i
$750$		0			0
$751$	2.74754	+	4.75887i	0.100259	+	0.173654i	0.911791	−	0.410654i	$-0.134700\pi$
$751$	2.74754	+	4.75887i	0.100259	+	0.173654i	−0.811532	+	0.584308i	$0.801366\pi$
$752$	−8.53055	+	4.92512i	−0.311077	+	0.179600i
$753$		0			0
$754$	2.68393	−	4.64871i	0.0977431	−	0.169296i
$755$	−64.0259			−2.33014
$756$		0			0
$757$		−	1.41065i		−	0.0512710i	−0.999671	−	0.0256355i	$-0.991839\pi$
$757$		−	1.41065i		−	0.0512710i	0.999671	−	0.0256355i	$-0.00816093\pi$
$758$	16.5598	+	9.56081i	0.601479	+	0.347264i
$759$		0			0
$760$	10.0303	+	17.3730i	0.363837	+	0.630184i
$761$	−2.55571	−	4.42662i	−0.0926445	−	0.160465i	0.815979	−	0.578082i	$-0.196199\pi$
$761$	−2.55571	−	4.42662i	−0.0926445	−	0.160465i	−0.908623	+	0.417617i	$0.862865\pi$
$762$		0			0
$763$	7.93815	−	13.7493i	0.287380	−	0.497757i
$764$			1.82994i			0.0662049i
$765$		0			0
$766$		−	1.95386i		−	0.0705957i
$767$	19.5403	−	33.8448i	0.705559	−	1.22206i
$768$		0			0
$769$	−0.0607588	−	0.105237i	−0.00219102	−	0.00379496i	0.864928	−	0.501896i	$-0.167364\pi$
$769$	−0.0607588	−	0.105237i	−0.00219102	−	0.00379496i	−0.867119	+	0.498101i	$0.834031\pi$
$770$	3.51764	+	6.09274i	0.126767	+	0.219567i
$771$		0			0
$772$	2.95915	−	5.12540i	0.106502	−	0.184467i
$773$	48.3540			1.73917			0.869585	−	0.493782i	$-0.164386\pi$
$773$	48.3540			1.73917			0.869585	+	0.493782i	$0.164386\pi$
$774$		0			0
$775$	6.71419	−	14.3662i	0.241181	−	0.516049i
$776$	−8.71871	−	5.03375i	−0.312984	−	0.180701i
$777$		0			0
$778$	−27.2077	+	15.7084i	−0.975444	+	0.563173i
$779$	−33.9066	+	19.5760i	−1.21483	+	0.701382i
$780$		0			0
$781$	−14.1123	−	8.14775i	−0.504979	−	0.291550i
$782$			11.9128i			0.426001i
$783$		0			0
$784$	−4.07005			−0.145359
$785$	−18.1994	−	10.5074i	−0.649563	−	0.375026i
$786$		0			0
$787$	27.9505	−	16.1372i	0.996326	−	0.575229i	0.0891668	−	0.996017i	$-0.471580\pi$
$787$	27.9505	−	16.1372i	0.996326	−	0.575229i	0.907159	+	0.420788i	$0.138246\pi$
$788$	−6.21503	−	10.7648i	−0.221401	−	0.383478i
$789$		0			0
$790$	29.8005	+	17.2053i	1.06025	+	0.612138i
$791$		−	1.45974i		−	0.0519025i
$792$		0			0
$793$	3.32707			0.118148
$794$	16.2108	+	9.35928i	0.575298	+	0.332148i
$795$		0			0
$796$	−3.01368	+	1.73995i	−0.106817	+	0.0616708i
$797$	22.9770	+	39.7974i	0.813888	+	1.40969i	0.910124	+	0.414336i	$0.135986\pi$
$797$	22.9770	+	39.7974i	0.813888	+	1.40969i	−0.0962361	+	0.995359i	$0.530680\pi$
$798$		0			0
$799$	−13.2460	−	7.64756i	−0.468608	−	0.270551i
$800$			2.84813i			0.100697i
$801$		0			0
$802$			3.61484i			0.127644i
$803$	0.175430	+	0.101285i	0.00619079	+	0.00357425i
$804$		0			0
$805$	31.8604	−	18.3946i	1.12293	−	0.648325i
$806$	19.7059	−	1.70687i	0.694110	−	0.0601220i
$807$		0			0
$808$	2.97276	−	5.14898i	0.104581	−	0.181140i
$809$	−39.8147			−1.39981			−0.699906	−	0.714235i	$-0.746775\pi$
$809$	−39.8147			−1.39981			−0.699906	+	0.714235i	$0.746775\pi$
$810$		0			0
$811$	30.5818			1.07387			0.536936	−	0.843623i	$-0.319582\pi$
$811$	30.5818			1.07387			0.536936	+	0.843623i	$0.319582\pi$
$812$	−1.29319	+	2.23988i	−0.0453822	+	0.0786043i
$813$		0			0
$814$	7.77198	+	13.4615i	0.272408	+	0.471824i
$815$	−18.4966	+	10.6790i	−0.647908	+	0.374070i
$816$		0			0
$817$	−21.5563	−	12.4455i	−0.754160	−	0.435415i
$818$	−3.55808			−0.124405
$819$		0			0
$820$	−15.3171			−0.534896
$821$	12.0397	−	20.8533i	0.420187	−	0.727786i	−0.575770	−	0.817612i	$-0.695298\pi$
$821$	12.0397	−	20.8533i	0.420187	−	0.727786i	0.995957	+	0.0898259i	$0.0286311\pi$
$822$		0			0
$823$	−0.553517	+	0.319573i	−0.0192944	+	0.0111396i	−0.509616	−	0.860402i	$-0.670213\pi$
$823$	−0.553517	+	0.319573i	−0.0192944	+	0.0111396i	0.490322	+	0.871541i	$0.336879\pi$
$824$	0.322708	−	0.186316i	0.0112421	−	0.00649061i
$825$		0			0
$826$	−9.41506	+	16.3074i	−0.327592	+	0.567406i
$827$	−25.0098			−0.869675			−0.434838	−	0.900509i	$-0.643194\pi$
$827$	−25.0098			−0.869675			−0.434838	+	0.900509i	$0.643194\pi$
$828$		0			0
$829$			25.9309i			0.900617i	0.892873	+	0.450308i	$0.148686\pi$
$829$			25.9309i			0.900617i	−0.892873	+	0.450308i	$0.851314\pi$
$830$	−8.74189	+	15.1414i	−0.303436	+	0.525566i
$831$		0			0
$832$	−3.07658	+	1.77627i	−0.106661	+	0.0615809i
$833$	−3.15992	−	5.47314i	−0.109485	−	0.189633i
$834$		0			0
$835$	48.0576	+	27.7461i	1.66310	+	0.960193i
$836$	10.5058			0.363350
$837$		0			0
$838$	−33.6205			−1.16140
$839$	40.3348	+	23.2873i	1.39251	+	0.803966i	0.993593	−	0.113020i	$-0.0360525\pi$
$839$	40.3348	+	23.2873i	1.39251	+	0.803966i	0.398918	+	0.916987i	$0.369386\pi$
$840$		0			0
$841$	13.3584	+	23.1375i	0.460636	+	0.797845i
$842$	5.97103	−	3.44737i	0.205775	−	0.118804i
$843$		0			0
$844$	6.02815	−	10.4411i	0.207497	−	0.359396i
$845$			1.06321i			0.0365756i
$846$		0			0
$847$	−15.1444			−0.520368
$848$	3.63460	−	6.29531i	0.124813	−	0.216182i
$849$		0			0
$850$	−3.82999	+	2.21124i	−0.131368	+	0.0758451i
$851$	70.3933	−	40.6416i	2.41305	−	1.39318i
$852$		0			0
$853$	−21.9940	+	38.0947i	−0.753061	+	1.30434i	0.193272	+	0.981145i	$0.438090\pi$
$853$	−21.9940	+	38.0947i	−0.753061	+	1.30434i	−0.946333	+	0.323194i	$0.895243\pi$
$854$	−1.60308			−0.0548562
$855$		0			0
$856$	−4.45522			−0.152276
$857$	−32.2115	−	18.5973i	−1.10033	−	0.635273i	−0.164019	−	0.986457i	$-0.552446\pi$
$857$	−32.2115	−	18.5973i	−1.10033	−	0.635273i	−0.936306	+	0.351184i	$0.885779\pi$
$858$		0			0
$859$	36.5777	−	21.1182i	1.24802	−	0.720542i	0.277302	−	0.960783i	$-0.410560\pi$
$859$	36.5777	−	21.1182i	1.24802	−	0.720542i	0.970713	+	0.240241i	$0.0772264\pi$
$860$	−4.86897	−	8.43331i	−0.166031	−	0.287573i
$861$		0			0
$862$	−0.743210	+	1.28728i	−0.0253138	+	0.0438449i
$863$	38.2498			1.30204			0.651019	−	0.759062i	$-0.274342\pi$
$863$	38.2498			1.30204			0.651019	+	0.759062i	$0.274342\pi$
$864$		0			0
$865$	−70.3392			−2.39160
$866$	8.28642	−	14.3525i	0.281584	−	0.487718i
$867$		0			0
$868$	−9.49485	+	0.822419i	−0.322276	+	0.0279147i
$869$	15.6066	−	9.01048i	0.529418	−	0.305660i
$870$		0			0
$871$	−37.1625	−	21.4558i	−1.25920	−	0.727000i
$872$		−	9.27511i		−	0.314095i
$873$		0			0
$874$		−	54.9373i		−	1.85828i
$875$	−8.93633	−	5.15939i	−0.302103	−	0.174419i
$876$		0			0
$877$	22.6974	+	39.3131i	0.766437	+	1.32751i	0.939483	+	0.342594i	$0.111306\pi$
$877$	22.6974	+	39.3131i	0.766437	+	1.32751i	−0.173046	+	0.984914i	$0.555361\pi$
$878$	−30.9945	+	17.8947i	−1.04601	+	0.603915i
$879$		0			0
$880$	3.55944	+	2.05505i	0.119989	+	0.0692756i
$881$	28.3421			0.954870			0.477435	−	0.878667i	$-0.341567\pi$
$881$	28.3421			0.954870			0.477435	+	0.878667i	$0.341567\pi$
$882$		0			0
$883$		−	30.2606i		−	1.01835i	−0.860663	−	0.509176i	$-0.829950\pi$
$883$		−	30.2606i		−	1.01835i	0.860663	−	0.509176i	$-0.170050\pi$
$884$	−4.77722	−	2.75813i	−0.160675	−	0.0927659i
$885$		0			0
$886$	9.30903	+	16.1237i	0.312743	+	0.541687i
$887$	−9.66606	+	5.58070i	−0.324554	+	0.187382i	−0.653421	−	0.756995i	$-0.726667\pi$
$887$	−9.66606	+	5.58070i	−0.324554	+	0.187382i	0.328866	+	0.944376i	$0.393333\pi$
$888$		0			0
$889$	−1.89634	−	1.09486i	−0.0636014	−	0.0367203i
$890$	−2.83140			−0.0949086
$891$		0			0
$892$			25.0068i			0.837288i
$893$	61.0853	+	35.2676i	2.04414	+	1.18019i
$894$		0			0
$895$	−37.1590	+	21.4537i	−1.24209	+	0.717119i
$896$	1.48238	−	0.855855i	0.0495230	−	0.0285921i
$897$		0			0
$898$	32.5199	+	18.7754i	1.08520	+	0.626543i
$899$	3.56203	−	7.62158i	0.118800	−	0.254194i
$900$		0			0
$901$	11.2874			0.376037
$902$	−4.01080	+	6.94692i	−0.133545	+	0.231307i
$903$		0			0
$904$	−0.426399	−	0.738545i	−0.0141818	−	0.0245636i
$905$	23.9960	+	41.5623i	0.797655	+	1.38158i
$906$		0			0
$907$	−21.7875	+	37.7371i	−0.723443	+	1.25304i	0.236169	+	0.971712i	$0.424108\pi$
$907$	−21.7875	+	37.7371i	−0.723443	+	1.25304i	−0.959612	+	0.281328i	$0.909225\pi$
$908$			3.41028i			0.113174i
$909$		0			0
$910$			17.0354i			0.564717i
$911$	15.0062	−	25.9915i	0.497178	−	0.861137i	−0.502817	−	0.864393i	$-0.667703\pi$
$911$	15.0062	−	25.9915i	0.497178	−	0.861137i	0.999995	+	0.00325559i	$0.00103629\pi$
$912$		0			0
$913$	4.57816	+	7.92960i	0.151515	+	0.262431i
$914$	8.87898	+	15.3789i	0.293691	+	0.508687i
$915$		0			0
$916$	7.49557	+	4.32757i	0.247661	+	0.142987i
$917$			6.59203i			0.217688i
$918$		0			0
$919$	7.79709			0.257202			0.128601	−	0.991696i	$-0.458951\pi$
$919$	7.79709			0.257202			0.128601	+	0.991696i	$0.458951\pi$
$920$	10.7463	−	18.6132i	0.354296	−	0.613659i
$921$		0			0
$922$	28.7841	−	16.6185i	0.947953	−	0.547301i
$923$	−19.7291	−	34.1718i	−0.649392	−	1.12478i
$924$		0			0
$925$	26.1327	+	15.0877i	0.859238	+	0.496082i
$926$	15.3381			0.504042
$927$		0			0
$928$			1.51100i			0.0496009i
$929$	2.51238	−	4.35156i	0.0824284	−	0.142770i	−0.821864	−	0.569684i	$-0.807066\pi$
$929$	2.51238	−	4.35156i	0.0824284	−	0.142770i	0.904293	+	0.426913i	$0.140399\pi$
$930$		0			0
$931$	14.5724	+	25.2401i	0.477590	+	0.827209i
$932$	9.56746	−	5.52378i	0.313393	−	0.180937i
$933$		0			0
$934$	3.97584	−	6.88637i	0.130094	−	0.225329i
$935$			6.38202i			0.208714i
$936$		0			0
$937$	43.6734			1.42675			0.713373	−	0.700784i	$-0.247166\pi$
$937$	43.6734			1.42675			0.713373	+	0.700784i	$0.247166\pi$
$938$	17.9059	+	10.3380i	0.584649	+	0.337547i
$939$		0			0
$940$	13.7975	+	23.8979i	0.450024	+	0.779464i
$941$	−20.0254	−	34.6850i	−0.652810	−	1.13070i	−0.982438	−	0.186589i	$-0.940257\pi$
$941$	−20.0254	−	34.6850i	−0.652810	−	1.13070i	0.329628	−	0.944111i	$-0.393077\pi$
$942$		0			0
$943$	36.3271	+	20.9735i	1.18297	+	0.682990i
$944$			11.0008i			0.358045i
$945$		0			0
$946$	−5.09979			−0.165808
$947$	−11.7628	+	20.3738i	−0.382241	+	0.662061i	−0.991382	−	0.131001i	$-0.958181\pi$
$947$	−11.7628	+	20.3738i	−0.382241	+	0.662061i	0.609141	+	0.793062i	$0.291514\pi$
$948$		0			0
$949$	0.245252	+	0.424789i	0.00796122	+	0.0137892i
$950$	17.6625	−	10.1974i	0.573046	−	0.330848i
$951$		0			0
$952$	2.30180	+	1.32894i	0.0746017	+	0.0430713i
$953$	−21.2533			−0.688463			−0.344232	−	0.938885i	$-0.611861\pi$
$953$	−21.2533			−0.688463			−0.344232	+	0.938885i	$0.611861\pi$
$954$		0			0
$955$	5.12649			0.165889
$956$	10.6056	−	18.3695i	0.343011	−	0.594112i
$957$		0			0
$958$	−0.167050	−	0.289339i	−0.00539714	−	0.00934812i
$959$	5.44741	+	9.43519i	0.175906	+	0.304678i
$960$		0			0
$961$	30.5383	−	5.33029i	0.985107	−	0.171945i
$962$			37.6384i			1.21351i
$963$		0			0
$964$			1.87581i			0.0604158i
$965$	−14.3586	−	8.28992i	−0.462218	−	0.266862i
$966$		0			0
$967$	1.99596	−	1.15237i	0.0641858	−	0.0370577i	−0.467564	−	0.883959i	$-0.654868\pi$
$967$	1.99596	−	1.15237i	0.0641858	−	0.0370577i	0.531749	+	0.846902i	$0.321535\pi$
$968$	−7.66219	+	4.42377i	−0.246272	+	0.142185i
$969$		0			0
$970$	−14.1018	+	24.4251i	−0.452782	+	0.784241i
$971$			31.8838i			1.02320i	0.859224	+	0.511600i	$0.170947\pi$
$971$			31.8838i			1.02320i	−0.859224	+	0.511600i	$0.829053\pi$
$972$		0			0
$973$			24.1582i			0.774478i
$974$	13.2809	−	23.0033i	0.425549	−	0.737072i
$975$		0			0
$976$	−0.811064	+	0.468268i	−0.0259615	+	0.0149889i
$977$	7.76184	−	4.48130i	0.248323	−	0.143369i	−0.370673	−	0.928763i	$-0.620873\pi$
$977$	7.76184	−	4.48130i	0.248323	−	0.143369i	0.618996	+	0.785394i	$0.287540\pi$
$978$		0			0
$979$	−0.741405	+	1.28415i	−0.0236954	+	0.0410417i
$980$			11.4020i			0.364225i
$981$		0			0
$982$		−	0.587753i		−	0.0187559i
$983$	0.172770	−	0.299246i	0.00551050	−	0.00954446i	−0.863257	−	0.504765i	$-0.831579\pi$
$983$	0.172770	−	0.299246i	0.00551050	−	0.00954446i	0.868768	+	0.495220i	$0.164913\pi$
$984$		0			0
$985$	−30.1569	+	17.4111i	−0.960880	+	0.554764i
$986$	−2.03189	+	1.17311i	−0.0647086	+	0.0373596i
$987$		0			0
$988$	22.0307	+	12.7194i	0.700890	+	0.404659i
$989$			26.6680i			0.847994i
$990$		0			0
$991$		−	23.9983i		−	0.762333i	−0.924507	−	0.381166i	$-0.875523\pi$
$991$		−	23.9983i		−	0.762333i	0.924507	−	0.381166i	$-0.124477\pi$
$992$	−4.56361	+	3.18959i	−0.144895	+	0.101270i
$993$		0			0
$994$	9.50604	+	16.4650i	0.301513	+	0.522237i
$995$	4.87438	+	8.44267i	0.154528	+	0.267651i
$996$		0			0
$997$	12.7281	−	22.0457i	0.403102	−	0.698194i	−0.590996	−	0.806674i	$-0.701265\pi$
$997$	12.7281	−	22.0457i	0.403102	−	0.698194i	0.994099	+	0.108481i	$0.0345985\pi$
$998$	−28.4845			−0.901661
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1674.2.q.a.1115.27		64
3.2	odd	2		558.2.q.a.371.10	yes	64
9.4	even	3		558.2.q.a.185.7	✓	64
9.5	odd	6	inner	1674.2.q.a.557.24		64
31.30	odd	2	inner	1674.2.q.a.1115.24		64
93.92	even	2		558.2.q.a.371.7	yes	64
279.185	even	6	inner	1674.2.q.a.557.27		64
279.247	odd	6		558.2.q.a.185.10	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.q.a.185.7	✓	64	9.4	even	3
558.2.q.a.185.10	yes	64	279.247	odd	6
558.2.q.a.371.7	yes	64	93.92	even	2
558.2.q.a.371.10	yes	64	3.2	odd	2
1674.2.q.a.557.24		64	9.5	odd	6	inner
1674.2.q.a.557.27		64	279.185	even	6	inner
1674.2.q.a.1115.24		64	31.30	odd	2	inner
1674.2.q.a.1115.27		64	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1674 = 2 \cdot 3^{3} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1674.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(2.42613 - 1.40073i) q^{5} +(-0.855855 + 1.48238i) q^{7} +1.00000i q^{8} +2.80145 q^{10} +(0.733565 - 1.27057i) q^{11} +(3.07658 - 1.77627i) q^{13} +(-1.48238 + 0.855855i) q^{14} +(-0.500000 + 0.866025i) q^{16} -1.55277 q^{17} +7.16077 q^{19} +(2.42613 + 1.40073i) q^{20} +(1.27057 - 0.733565i) q^{22} +(-3.83599 - 6.64412i) q^{23} +(1.42407 - 2.46656i) q^{25} +3.55253 q^{26} -1.71171 q^{28} +(0.755499 - 1.30856i) q^{29} +(5.54699 - 0.480466i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.34474 - 0.776384i) q^{34} +4.79527i q^{35} +10.5948i q^{37} +(6.20141 + 3.58039i) q^{38} +(1.40073 + 2.42613i) q^{40} +(-4.73504 + 2.73378i) q^{41} +(-3.01033 - 1.73802i) q^{43} +1.46713 q^{44} -7.67197i q^{46} +(8.53055 + 4.92512i) q^{47} +(2.03502 + 3.52477i) q^{49} +(2.46656 - 1.42407i) q^{50} +(3.07658 + 1.77627i) q^{52} -7.26920 q^{53} -4.11009i q^{55} +(-1.48238 - 0.855855i) q^{56} +(1.30856 - 0.755499i) q^{58} +(9.52695 - 5.50039i) q^{59} +(0.811064 + 0.468268i) q^{61} +(5.04407 + 2.35740i) q^{62} -1.00000 q^{64} +(4.97612 - 8.61890i) q^{65} +(-6.03957 - 10.4608i) q^{67} +(-0.776384 - 1.34474i) q^{68} +(-2.39764 + 4.15283i) q^{70} -11.1071i q^{71} +0.138072i q^{73} +(-5.29741 + 9.17538i) q^{74} +(3.58039 + 6.20141i) q^{76} +(1.25565 + 2.17485i) q^{77} +(10.6375 + 6.14158i) q^{79} +2.80145i q^{80} -5.46756 q^{82} +(-3.12049 + 5.40484i) q^{83} +(-3.76721 + 2.17500i) q^{85} +(-1.73802 - 3.01033i) q^{86} +(1.27057 + 0.733565i) q^{88} -1.01069 q^{89} +6.08090i q^{91} +(3.83599 - 6.64412i) q^{92} +(4.92512 + 8.53055i) q^{94} +(17.3730 - 10.0303i) q^{95} +(-5.03375 + 8.71871i) q^{97} +4.07005i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} - 12 q^{5} - 4 q^{7} - 32 q^{16} - 8 q^{19} - 12 q^{20} + 44 q^{25} - 8 q^{28} + 8 q^{31} - 36 q^{38} - 24 q^{41} + 48 q^{47} - 36 q^{49} + 12 q^{59} - 64 q^{64} + 16 q^{67} - 12 q^{70}+ \cdots - 16 q^{97}+O(q^{100}) \) 64 * q + 32 * q^4 - 12 * q^5 - 4 * q^7 - 32 * q^16 - 8 * q^19 - 12 * q^20 + 44 * q^25 - 8 * q^28 + 8 * q^31 - 36 * q^38 - 24 * q^41 + 48 * q^47 - 36 * q^49 + 12 * q^59 - 64 * q^64 + 16 * q^67 - 12 * q^70 - 4 * q^76 + 180 * q^95 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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