LMFDB - Embedded newform 864.2.bf.a.49.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(49,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 14]))

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

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

chi := DirichletCharacter("864.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bf (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			49.10
Character	$\chi$	$=$	864.49
Dual form			864.2.bf.a.529.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09709 - 1.34029i) q^{3} +(0.0373388 + 0.102588i) q^{5} +(-0.639213 - 3.62515i) q^{7} +(-0.592777 + 2.94085i) q^{9} +O(q^{10})$	\(q+(-1.09709 - 1.34029i) q^{3} +(0.0373388 + 0.102588i) q^{5} +(-0.639213 - 3.62515i) q^{7} +(-0.592777 + 2.94085i) q^{9} +(-2.11447 + 5.80945i) q^{11} +(-1.73216 + 2.06430i) q^{13} +(0.0965334 - 0.162593i) q^{15} +(-2.10194 + 3.64068i) q^{17} +(-0.833027 + 0.480948i) q^{19} +(-4.15750 + 4.83386i) q^{21} +(0.836159 - 4.74209i) q^{23} +(3.82109 - 3.20628i) q^{25} +(4.59194 - 2.43189i) q^{27} +(2.99914 + 3.57423i) q^{29} +(-0.606649 + 3.44048i) q^{31} +(10.1061 - 3.53950i) q^{33} +(0.348028 - 0.200934i) q^{35} +(-0.956350 - 0.552149i) q^{37} +(4.66711 + 0.0568675i) q^{39} +(3.46816 + 2.91013i) q^{41} +(-3.40344 + 9.35087i) q^{43} +(-0.323828 + 0.0489964i) q^{45} +(1.97444 + 11.1976i) q^{47} +(-6.15530 + 2.24035i) q^{49} +(7.18560 - 1.17693i) q^{51} -7.58112i q^{53} -0.674929 q^{55} +(1.55852 + 0.588856i) q^{57} +(-0.408327 - 1.12187i) q^{59} +(-6.15378 + 1.08508i) q^{61} +(11.0400 + 0.269078i) q^{63} +(-0.276449 - 0.100619i) q^{65} +(-2.84467 + 3.39015i) q^{67} +(-7.27314 + 4.08181i) q^{69} +(-4.37202 + 7.57257i) q^{71} +(-2.24888 - 3.89517i) q^{73} +(-8.48945 - 1.60381i) q^{75} +(22.4118 + 3.95180i) q^{77} +(-10.6416 + 8.92932i) q^{79} +(-8.29723 - 3.48654i) q^{81} +(-0.946192 - 1.12763i) q^{83} +(-0.451972 - 0.0796949i) q^{85} +(1.50019 - 7.94099i) q^{87} +(5.28564 + 9.15500i) q^{89} +(8.59064 + 4.95981i) q^{91} +(5.27680 - 2.96143i) q^{93} +(-0.0804435 - 0.0675001i) q^{95} +(3.71478 + 1.35207i) q^{97} +(-15.8313 - 9.66205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 12 q^{7} - 12 q^{9}+O(q^{10}) $ 204 * q + 12 * q^7 - 12 * q^9	$ 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73} + 12 q^{79} - 12 q^{81} + 48 q^{87} - 6 q^{89} + 42 q^{95} - 12 q^{97}+O(q^{100}) $ 204 * q + 12 * q^7 - 12 * q^9 + 12 * q^15 - 6 * q^17 + 12 * q^23 - 12 * q^25 + 12 * q^31 + 12 * q^39 - 24 * q^41 + 12 * q^47 - 12 * q^49 + 24 * q^55 - 30 * q^57 + 72 * q^63 - 12 * q^65 + 90 * q^71 - 6 * q^73 + 12 * q^79 - 12 * q^81 + 48 * q^87 - 6 * q^89 + 42 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$-1$	$e\left(\frac{7}{9}\right)$	$1$

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			0
$2$		0			0
$3$	−1.09709	−	1.34029i	−0.633407	−	0.773819i
$3$	−1.09709	−	1.34029i	−0.633407	−	0.773819i
$4$		0			0
$5$	0.0373388	+	0.102588i	0.0166984	+	0.0458785i	0.947762	−	0.318979i	$-0.103340\pi$
$5$	0.0373388	+	0.102588i	0.0166984	+	0.0458785i	−0.931063	+	0.364857i	$0.881118\pi$
$6$		0			0
$7$	−0.639213	−	3.62515i	−0.241600	−	1.37018i	−0.828259	−	0.560346i	$-0.810668\pi$
$7$	−0.639213	−	3.62515i	−0.241600	−	1.37018i	0.586659	−	0.809834i	$-0.300443\pi$
$8$		0			0
$9$	−0.592777	+	2.94085i	−0.197592	+	0.980284i
$10$		0			0
$11$	−2.11447	+	5.80945i	−0.637536	+	1.75162i	0.0217946	+	0.999762i	$0.493062\pi$
$11$	−2.11447	+	5.80945i	−0.637536	+	1.75162i	−0.659331	+	0.751853i	$0.729160\pi$
$12$		0			0
$13$	−1.73216	+	2.06430i	−0.480414	+	0.572535i	−0.950753	−	0.309951i	$-0.899687\pi$
$13$	−1.73216	+	2.06430i	−0.480414	+	0.572535i	0.470339	+	0.882486i	$0.344132\pi$
$14$		0			0
$15$	0.0965334	−	0.162593i	0.0249248	−	0.0419813i
$16$		0			0
$17$	−2.10194	+	3.64068i	−0.509797	+	0.882993i	0.490139	+	0.871644i	$0.336946\pi$
$17$	−2.10194	+	3.64068i	−0.509797	+	0.882993i	−0.999936	+	0.0113492i	$0.996387\pi$
$18$		0			0
$19$	−0.833027	+	0.480948i	−0.191109	+	0.110337i	−0.592502	−	0.805569i	$-0.701860\pi$
$19$	−0.833027	+	0.480948i	−0.191109	+	0.110337i	0.401392	+	0.915906i	$0.368526\pi$
$20$		0			0
$21$	−4.15750	+	4.83386i	−0.907241	+	1.05484i
$22$		0			0
$23$	0.836159	−	4.74209i	0.174351	−	0.988795i	−0.764539	−	0.644578i	$-0.777033\pi$
$23$	0.836159	−	4.74209i	0.174351	−	0.988795i	0.938890	−	0.344217i	$-0.111856\pi$
$24$		0			0
$25$	3.82109	−	3.20628i	0.764218	−	0.641255i
$26$		0			0
$27$	4.59194	−	2.43189i	0.883719	−	0.468018i
$28$		0			0
$29$	2.99914	+	3.57423i	0.556926	+	0.663718i	0.968893	−	0.247480i	$-0.0796026\pi$
$29$	2.99914	+	3.57423i	0.556926	+	0.663718i	−0.411967	+	0.911199i	$0.635158\pi$
$30$		0			0
$31$	−0.606649	+	3.44048i	−0.108957	+	0.617928i	0.880608	+	0.473845i	$0.157134\pi$
$31$	−0.606649	+	3.44048i	−0.108957	+	0.617928i	−0.989566	+	0.144083i	$0.953977\pi$
$32$		0			0
$33$	10.1061	−	3.53950i	1.75925	−	0.616147i
$34$		0			0
$35$	0.348028	−	0.200934i	0.0588275	−	0.0339641i
$36$		0			0
$37$	−0.956350	−	0.552149i	−0.157223	−	0.0907727i	0.419324	−	0.907836i	$-0.362267\pi$
$37$	−0.956350	−	0.552149i	−0.157223	−	0.0907727i	−0.576547	+	0.817064i	$0.695600\pi$
$38$		0			0
$39$	4.66711	+	0.0568675i	0.747336	+	0.00910608i
$40$		0			0
$41$	3.46816	+	2.91013i	0.541636	+	0.454487i	0.872097	−	0.489333i	$-0.162760\pi$
$41$	3.46816	+	2.91013i	0.541636	+	0.454487i	−0.330461	+	0.943820i	$0.607204\pi$
$42$		0			0
$43$	−3.40344	+	9.35087i	−0.519020	+	1.42599i	0.352583	+	0.935781i	$0.385304\pi$
$43$	−3.40344	+	9.35087i	−0.519020	+	1.42599i	−0.871602	+	0.490214i	$0.836919\pi$
$44$		0			0
$45$	−0.323828	+	0.0489964i	−0.0482735	+	0.00730396i
$46$		0			0
$47$	1.97444	+	11.1976i	0.288002	+	1.63334i	0.694360	+	0.719628i	$0.255687\pi$
$47$	1.97444	+	11.1976i	0.288002	+	1.63334i	−0.406358	+	0.913714i	$0.633201\pi$
$48$		0			0
$49$	−6.15530	+	2.24035i	−0.879329	+	0.320050i
$50$		0			0
$51$	7.18560	−	1.17693i	1.00619	−	0.164804i
$52$		0			0
$53$		−	7.58112i		−	1.04135i	−0.853756	−	0.520673i	$-0.825681\pi$
$53$		−	7.58112i		−	1.04135i	0.853756	−	0.520673i	$-0.174319\pi$
$54$		0			0
$55$	−0.674929			−0.0910074
$56$		0			0
$57$	1.55852	+	0.588856i	0.206431	+	0.0779959i
$58$		0			0
$59$	−0.408327	−	1.12187i	−0.0531597	−	0.146055i	0.910271	−	0.414013i	$-0.135873\pi$
$59$	−0.408327	−	1.12187i	−0.0531597	−	0.146055i	−0.963431	+	0.267958i	$0.913651\pi$
$60$		0			0
$61$	−6.15378	+	1.08508i	−0.787910	+	0.138930i	−0.553104	−	0.833112i	$-0.686557\pi$
$61$	−6.15378	+	1.08508i	−0.787910	+	0.138930i	−0.234806	+	0.972042i	$0.575446\pi$
$62$		0			0
$63$	11.0400	+	0.269078i	1.39090	+	0.0339006i
$64$		0			0
$65$	−0.276449	−	0.100619i	−0.0342892	−	0.0124803i
$66$		0			0
$67$	−2.84467	+	3.39015i	−0.347532	+	0.414173i	−0.911289	−	0.411768i	$-0.864911\pi$
$67$	−2.84467	+	3.39015i	−0.347532	+	0.414173i	0.563756	+	0.825941i	$0.309356\pi$
$68$		0			0
$69$	−7.27314	+	4.08181i	−0.875583	+	0.491393i
$70$		0			0
$71$	−4.37202	+	7.57257i	−0.518864	+	0.898698i	0.480896	+	0.876778i	$0.340311\pi$
$71$	−4.37202	+	7.57257i	−0.518864	+	0.898698i	−0.999760	+	0.0219206i	$0.993022\pi$
$72$		0			0
$73$	−2.24888	−	3.89517i	−0.263211	−	0.455895i	0.703882	−	0.710317i	$-0.251448\pi$
$73$	−2.24888	−	3.89517i	−0.263211	−	0.455895i	−0.967093	+	0.254421i	$0.918115\pi$
$74$		0			0
$75$	−8.48945	−	1.60381i	−0.980277	−	0.185192i
$76$		0			0
$77$	22.4118	+	3.95180i	2.55406	+	0.450349i
$78$		0			0
$79$	−10.6416	+	8.92932i	−1.19727	+	1.00463i	−0.197565	+	0.980290i	$0.563303\pi$
$79$	−10.6416	+	8.92932i	−1.19727	+	1.00463i	−0.999704	+	0.0243375i	$0.992252\pi$
$80$		0			0
$81$	−8.29723	−	3.48654i	−0.921915	−	0.387393i
$82$		0			0
$83$	−0.946192	−	1.12763i	−0.103858	−	0.123773i	0.711611	−	0.702573i	$-0.247966\pi$
$83$	−0.946192	−	1.12763i	−0.103858	−	0.123773i	−0.815470	+	0.578800i	$0.803521\pi$
$84$		0			0
$85$	−0.451972	−	0.0796949i	−0.0490233	−	0.00864412i
$86$		0			0
$87$	1.50019	−	7.94099i	0.160838	−	0.851363i
$88$		0			0
$89$	5.28564	+	9.15500i	0.560277	+	0.970429i	0.997472	+	0.0710617i	$0.0226387\pi$
$89$	5.28564	+	9.15500i	0.560277	+	0.970429i	−0.437195	+	0.899367i	$0.644028\pi$
$90$		0			0
$91$	8.59064	+	4.95981i	0.900544	+	0.519929i
$92$		0			0
$93$	5.27680	−	2.96143i	0.547179	−	0.307086i
$94$		0			0
$95$	−0.0804435	−	0.0675001i	−0.00825333	−	0.00692537i
$96$		0			0
$97$	3.71478	+	1.35207i	0.377179	+	0.137282i	0.523651	−	0.851933i	$-0.324570\pi$
$97$	3.71478	+	1.35207i	0.377179	+	0.137282i	−0.146472	+	0.989215i	$0.546792\pi$
$98$		0			0
$99$	−15.8313	−	9.66205i	−1.59111	−	0.971072i
$100$		0			0
$101$	−3.91572	+	0.690446i	−0.389628	+	0.0687020i	−0.365031	−	0.930995i	$-0.618942\pi$
$101$	−3.91572	+	0.690446i	−0.389628	+	0.0687020i	−0.0245975	+	0.999697i	$0.507830\pi$
$102$		0			0
$103$	13.9248	−	5.06822i	1.37205	−	0.499386i	0.452293	−	0.891869i	$-0.350606\pi$
$103$	13.9248	−	5.06822i	1.37205	−	0.499386i	0.919759	+	0.392483i	$0.128384\pi$
$104$		0			0
$105$	−0.651130	−	0.246017i	−0.0635438	−	0.0240088i
$106$		0			0
$107$		−	1.60153i		−	0.154826i	−0.996999	−	0.0774131i	$-0.975334\pi$
$107$		−	1.60153i		−	0.154826i	0.996999	−	0.0774131i	$-0.0246660\pi$
$108$		0			0
$109$			1.89967i			0.181955i	0.995853	+	0.0909777i	$0.0289992\pi$
$109$			1.89967i			0.181955i	−0.995853	+	0.0909777i	$0.971001\pi$
$110$		0			0
$111$	0.309162	+	1.88755i	0.0293444	+	0.179158i
$112$		0			0
$113$	−1.79471	+	0.653223i	−0.168833	+	0.0614500i	−0.425054	−	0.905168i	$-0.639745\pi$
$113$	−1.79471	+	0.653223i	−0.168833	+	0.0614500i	0.256221	+	0.966618i	$0.417523\pi$
$114$		0			0
$115$	0.517701	−	0.0912846i	0.0482758	−	0.00851233i
$116$		0			0
$117$	−5.04403	−	6.31769i	−0.466321	−	0.584071i
$118$		0			0
$119$	14.5416	+	5.29271i	1.33303	+	0.485182i
$120$		0			0
$121$	−20.8523	−	17.4971i	−1.89566	−	1.59065i
$122$		0			0
$123$	0.0955410	−	7.84105i	0.00861464	−	0.707003i
$124$		0			0
$125$	0.944325	+	0.545206i	0.0844630	+	0.0487647i
$126$		0			0
$127$	−9.53211	−	16.5101i	−0.845838	−	1.46503i	−0.884892	−	0.465797i	$-0.845768\pi$
$127$	−9.53211	−	16.5101i	−0.845838	−	1.46503i	0.0390542	−	0.999237i	$-0.487565\pi$
$128$		0			0
$129$	16.2668	−	5.69716i	1.43221	−	0.501607i
$130$		0			0
$131$	11.3676	+	2.00441i	0.993189	+	0.175126i	0.646549	−	0.762872i	$-0.276212\pi$
$131$	11.3676	+	2.00441i	0.993189	+	0.175126i	0.346640	+	0.937998i	$0.387323\pi$
$132$		0			0
$133$	2.27599	+	2.71242i	0.197354	+	0.235197i
$134$		0			0
$135$	0.420939	+	0.380272i	0.0362287	+	0.0327286i
$136$		0			0
$137$	−0.577991	+	0.484992i	−0.0493811	+	0.0414357i	−0.667144	−	0.744929i	$-0.732484\pi$
$137$	−0.577991	+	0.484992i	−0.0493811	+	0.0414357i	0.617763	+	0.786364i	$0.288039\pi$
$138$		0			0
$139$	6.41973	+	1.13197i	0.544515	+	0.0960126i	0.439138	−	0.898420i	$-0.355284\pi$
$139$	6.41973	+	1.13197i	0.544515	+	0.0960126i	0.105377	+	0.994432i	$0.466395\pi$
$140$		0			0
$141$	12.8420	−	14.9312i	1.08149	−	1.25743i
$142$		0			0
$143$	−8.32989	−	14.4278i	−0.696580	−	1.20651i
$144$		0			0
$145$	−0.254688	+	0.441132i	−0.0211506	+	0.0366340i
$146$		0			0
$147$	9.75566	+	5.79205i	0.804633	+	0.477720i
$148$		0			0
$149$	−8.06261	+	9.60865i	−0.660515	+	0.787171i	−0.987459	−	0.157873i	$-0.949536\pi$
$149$	−8.06261	+	9.60865i	−0.660515	+	0.787171i	0.326945	+	0.945043i	$0.393981\pi$
$150$		0			0
$151$	−7.96834	−	2.90024i	−0.648454	−	0.236018i	−0.00321042	−	0.999995i	$-0.501022\pi$
$151$	−7.96834	−	2.90024i	−0.648454	−	0.236018i	−0.645244	+	0.763977i	$0.723244\pi$
$152$		0			0
$153$	−9.46071	−	8.33962i	−0.764853	−	0.674218i
$154$		0			0
$155$	−0.375602	+	0.0662287i	−0.0301691	+	0.00531962i
$156$		0			0
$157$	−5.59650	−	15.3763i	−0.446649	−	1.22716i	−0.935043	−	0.354535i	$-0.884639\pi$
$157$	−5.59650	−	15.3763i	−0.446649	−	1.22716i	0.488394	−	0.872623i	$-0.337583\pi$
$158$		0			0
$159$	−10.1609	+	8.31719i	−0.805814	+	0.659596i
$160$		0			0
$161$	−17.7253			−1.39695
$162$		0			0
$163$			11.1426i			0.872757i	0.899763	+	0.436379i	$0.143739\pi$
$163$			11.1426i			0.872757i	−0.899763	+	0.436379i	$0.856261\pi$
$164$		0			0
$165$	0.740460	+	0.904603i	0.0576447	+	0.0704233i
$166$		0			0
$167$	−19.5111	+	7.10145i	−1.50981	+	0.549527i	−0.958579	−	0.284825i	$-0.908064\pi$
$167$	−19.5111	+	7.10145i	−1.50981	+	0.549527i	−0.551232	+	0.834352i	$0.685842\pi$
$168$		0			0
$169$	0.996442	+	5.65110i	0.0766494	+	0.434700i
$170$		0			0
$171$	−0.920599	−	2.73490i	−0.0704000	−	0.209143i
$172$		0			0
$173$	−0.672403	+	1.84741i	−0.0511219	+	0.140456i	−0.962626	−	0.270836i	$-0.912700\pi$
$173$	−0.672403	+	1.84741i	−0.0511219	+	0.140456i	0.911504	+	0.411292i	$0.134922\pi$
$174$		0			0
$175$	−14.0657	−	11.8026i	−1.06327	−	0.892189i
$176$		0			0
$177$	−1.05566	+	1.77807i	−0.0793485	+	0.133648i
$178$		0			0
$179$	−4.80402	−	2.77360i	−0.359070	−	0.207309i	0.309603	−	0.950866i	$-0.399804\pi$
$179$	−4.80402	−	2.77360i	−0.359070	−	0.207309i	−0.668673	+	0.743557i	$0.733137\pi$
$180$		0			0
$181$	−17.5709	+	10.1445i	−1.30603	+	0.754038i	−0.981432	−	0.191813i	$-0.938563\pi$
$181$	−17.5709	+	10.1445i	−1.30603	+	0.754038i	−0.324601	+	0.945851i	$0.605230\pi$
$182$		0			0
$183$	8.20558	+	7.05744i	0.606574	+	0.521701i
$184$		0			0
$185$	0.0209346	−	0.118726i	0.00153914	−	0.00872892i
$186$		0			0
$187$	−16.7058	−	19.9092i	−1.22165	−	1.45591i
$188$		0			0
$189$	−11.7512	−	15.0920i	−0.854775	−	1.09778i
$190$		0			0
$191$	−6.49421	+	5.44929i	−0.469904	+	0.394297i	−0.846760	−	0.531976i	$-0.821450\pi$
$191$	−6.49421	+	5.44929i	−0.469904	+	0.394297i	0.376855	+	0.926272i	$0.377005\pi$
$192$		0			0
$193$	−0.621885	+	3.52689i	−0.0447643	+	0.253871i	−0.998975	−	0.0452643i	$-0.985587\pi$
$193$	−0.621885	+	3.52689i	−0.0447643	+	0.253871i	0.954211	+	0.299135i	$0.0966981\pi$
$194$		0			0
$195$	0.168430	+	0.480911i	0.0120616	+	0.0344387i
$196$		0			0
$197$	2.48369	−	1.43396i	0.176955	−	0.102165i	−0.408906	−	0.912577i	$-0.634090\pi$
$197$	2.48369	−	1.43396i	0.176955	−	0.102165i	0.585861	+	0.810411i	$0.300756\pi$
$198$		0			0
$199$	3.96119	−	6.86098i	0.280801	−	0.486362i	−0.690781	−	0.723064i	$-0.742733\pi$
$199$	3.96119	−	6.86098i	0.280801	−	0.486362i	0.971582	+	0.236702i	$0.0760664\pi$
$200$		0			0
$201$	7.66467	+	0.0933919i	0.540624	+	0.00658736i
$202$		0			0
$203$	11.0401	−	13.1570i	0.774860	−	0.923443i
$204$		0			0
$205$	−0.169046	+	0.464451i	−0.0118067	+	0.0324387i
$206$		0			0
$207$	13.4501	+	5.27002i	0.934849	+	0.366292i
$208$		0			0
$209$	−1.03264	−	5.85638i	−0.0714290	−	0.405094i
$210$		0			0
$211$	−8.06208	−	22.1504i	−0.555016	−	1.52489i	−0.826777	−	0.562530i	$-0.809828\pi$
$211$	−8.06208	−	22.1504i	−0.555016	−	1.52489i	0.271761	−	0.962365i	$-0.412394\pi$
$212$		0			0
$213$	14.9460	−	2.44801i	1.02408	−	0.167735i
$214$		0			0
$215$	−1.08636			−0.0740894
$216$		0			0
$217$	12.8600			0.872997
$218$		0			0
$219$	−2.75345	+	7.28752i	−0.186061	+	0.492445i
$220$		0			0
$221$	−3.87456	−	10.6453i	−0.260631	−	0.716079i
$222$		0			0
$223$	2.89828	+	16.4370i	0.194083	+	1.10070i	0.913719	+	0.406348i	$0.133198\pi$
$223$	2.89828	+	16.4370i	0.194083	+	1.10070i	−0.719635	+	0.694352i	$0.755691\pi$
$224$		0			0
$225$	7.16413	+	13.1379i	0.477609	+	0.875858i
$226$		0			0
$227$	2.76059	−	7.58467i	0.183227	−	0.503412i	−0.813741	−	0.581228i	$-0.802572\pi$
$227$	2.76059	−	7.58467i	0.183227	−	0.503412i	0.996968	+	0.0778158i	$0.0247946\pi$
$228$		0			0
$229$	10.1015	−	12.0385i	0.667525	−	0.795525i	−0.320920	−	0.947106i	$-0.603992\pi$
$229$	10.1015	−	12.0385i	0.667525	−	0.795525i	0.988445	+	0.151581i	$0.0484364\pi$
$230$		0			0
$231$	−19.2912	−	34.3738i	−1.26927	−	2.26163i
$232$		0			0
$233$	−5.19699	+	9.00144i	−0.340466	+	0.589704i	−0.984519	−	0.175276i	$-0.943918\pi$
$233$	−5.19699	+	9.00144i	−0.340466	+	0.589704i	0.644053	+	0.764981i	$0.277251\pi$
$234$		0			0
$235$	−1.07501	+	0.620659i	−0.0701261	+	0.0404873i
$236$		0			0
$237$	23.6427	+	4.46652i	1.53576	+	0.290132i
$238$		0			0
$239$	0.826042	−	4.68472i	0.0534322	−	0.303029i	−0.946366	−	0.323095i	$-0.895277\pi$
$239$	0.826042	−	4.68472i	0.0534322	−	0.303029i	0.999799	+	0.0200662i	$0.00638769\pi$
$240$		0			0
$241$	−5.35622	+	4.49440i	−0.345024	+	0.289510i	−0.798788	−	0.601612i	$-0.794525\pi$
$241$	−5.35622	+	4.49440i	−0.345024	+	0.289510i	0.453764	+	0.891122i	$0.350081\pi$
$242$		0			0
$243$	4.42984	+	14.9458i	0.284174	+	0.958773i
$244$		0			0
$245$	−0.459664	−	0.547806i	−0.0293668	−	0.0349980i
$246$		0			0
$247$	0.450110	−	2.55270i	0.0286398	−	0.162424i
$248$		0			0
$249$	−0.473293	+	2.50529i	−0.0299937	+	0.158766i
$250$		0			0
$251$	17.5816	−	10.1507i	1.10974	−	0.640708i	0.170976	−	0.985275i	$-0.445308\pi$
$251$	17.5816	−	10.1507i	1.10974	−	0.640708i	0.938762	+	0.344568i	$0.111974\pi$
$252$		0			0
$253$	25.7809	+	14.8846i	1.62083	+	0.935788i
$254$		0			0
$255$	0.389041	+	0.693208i	0.0243627	+	0.0434104i
$256$		0			0
$257$	5.58805	+	4.68893i	0.348573	+	0.292487i	0.800217	−	0.599711i	$-0.204718\pi$
$257$	5.58805	+	4.68893i	0.348573	+	0.292487i	−0.451644	+	0.892198i	$0.649162\pi$
$258$		0			0
$259$	−1.39031	+	3.81986i	−0.0863899	+	0.237354i
$260$		0			0
$261$	−12.2891	+	6.70130i	−0.760677	+	0.414800i
$262$		0			0
$263$	2.52683	+	14.3304i	0.155811	+	0.883648i	0.958041	+	0.286632i	$0.0925358\pi$
$263$	2.52683	+	14.3304i	0.155811	+	0.883648i	−0.802230	+	0.597015i	$0.796353\pi$
$264$		0			0
$265$	0.777728	−	0.283070i	0.0477755	−	0.0173888i
$266$		0			0
$267$	6.47156	−	17.1282i	0.396053	−	1.04823i
$268$		0			0
$269$		−	8.64560i		−	0.527131i	−0.964641	−	0.263566i	$-0.915101\pi$
$269$		−	8.64560i		−	0.527131i	0.964641	−	0.263566i	$-0.0848986\pi$
$270$		0			0
$271$	23.7009			1.43972			0.719862	−	0.694117i	$-0.244205\pi$
$271$	23.7009			1.43972			0.719862	+	0.694117i	$0.244205\pi$
$272$		0			0
$273$	−2.77712	−	16.9554i	−0.168079	−	1.02618i
$274$		0			0
$275$	10.5471	+	28.9780i	0.636016	+	1.74744i
$276$		0			0
$277$	−26.8073	+	4.72686i	−1.61070	+	0.284009i	−0.905290	−	0.424793i	$-0.860347\pi$
$277$	−26.8073	+	4.72686i	−1.61070	+	0.284009i	−0.705407	+	0.708803i	$0.749236\pi$
$278$		0			0
$279$	−9.75833	−	3.82350i	−0.584216	−	0.228907i
$280$		0			0
$281$	−4.65683	−	1.69495i	−0.277803	−	0.101112i	0.199361	−	0.979926i	$-0.436113\pi$
$281$	−4.65683	−	1.69495i	−0.277803	−	0.101112i	−0.477165	+	0.878814i	$0.658335\pi$
$282$		0			0
$283$	7.00402	−	8.34706i	0.416346	−	0.496181i	−0.516586	−	0.856235i	$-0.672797\pi$
$283$	7.00402	−	8.34706i	0.416346	−	0.496181i	0.932931	+	0.360054i	$0.117242\pi$
$284$		0			0
$285$	−0.00221606	+	0.181872i	−0.000131268	+	0.0107732i
$286$		0			0
$287$	8.33279	−	14.4328i	0.491869	−	0.851943i
$288$		0			0
$289$	−0.336345	−	0.582567i	−0.0197850	−	0.0342686i
$290$		0			0
$291$	−2.26329	−	6.46225i	−0.132676	−	0.378824i
$292$		0			0
$293$	−2.82925	−	0.498873i	−0.165286	−	0.0291445i	0.0903925	−	0.995906i	$-0.471188\pi$
$293$	−2.82925	−	0.498873i	−0.165286	−	0.0291445i	−0.255679	+	0.966762i	$0.582299\pi$
$294$		0			0
$295$	0.0998434	−	0.0837786i	0.00581311	−	0.00487778i
$296$		0			0
$297$	4.41845	+	31.8188i	0.256385	+	1.84631i
$298$		0			0
$299$	8.34076	+	9.94014i	0.482359	+	0.574853i
$300$		0			0
$301$	36.0739	+	6.36080i	2.07926	+	0.366630i
$302$		0			0
$303$	5.22130	+	4.49073i	0.299956	+	0.257986i
$304$		0			0
$305$	−0.341090	−	0.590785i	−0.0195308	−	0.0338283i
$306$		0			0
$307$	16.5294	+	9.54326i	0.943384	+	0.544663i	0.891019	−	0.453965i	$-0.149991\pi$
$307$	16.5294	+	9.54326i	0.943384	+	0.544663i	0.0523642	+	0.998628i	$0.483324\pi$
$308$		0			0
$309$	−22.0697	−	13.1030i	−1.25550	−	0.745406i
$310$		0			0
$311$	−5.97952	−	5.01742i	−0.339068	−	0.284512i	0.457315	−	0.889305i	$-0.348811\pi$
$311$	−5.97952	−	5.01742i	−0.339068	−	0.284512i	−0.796382	+	0.604793i	$0.793256\pi$
$312$		0			0
$313$	−3.49186	−	1.27093i	−0.197372	−	0.0718374i	0.241443	−	0.970415i	$-0.422379\pi$
$313$	−3.49186	−	1.27093i	−0.197372	−	0.0718374i	−0.438815	+	0.898578i	$0.644602\pi$
$314$		0			0
$315$	0.384615	+	1.14261i	0.0216706	+	0.0643787i
$316$		0			0
$317$	−2.42721	+	0.427982i	−0.136325	+	0.0240379i	−0.241394	−	0.970427i	$-0.577605\pi$
$317$	−2.42721	+	0.427982i	−0.136325	+	0.0240379i	0.105069	+	0.994465i	$0.466494\pi$
$318$		0			0
$319$	−27.1059	+	9.86574i	−1.51764	+	0.552376i
$320$		0			0
$321$	−2.14653	+	1.75703i	−0.119807	+	0.0980679i
$322$		0			0
$323$		−	4.04371i		−	0.224998i
$324$		0			0
$325$			13.4417i			0.745610i
$326$		0			0
$327$	2.54612	−	2.08411i	0.140801	−	0.115252i
$328$		0			0
$329$	39.3310	−	14.3153i	2.16839	−	0.789229i
$330$		0			0
$331$	−24.1981	+	4.26677i	−1.33005	+	0.234523i	−0.793099	−	0.609093i	$-0.791534\pi$
$331$	−24.1981	+	4.26677i	−1.33005	+	0.234523i	−0.536947	+	0.843616i	$0.680423\pi$
$332$		0			0
$333$	2.19069	−	2.48518i	0.120049	−	0.136187i
$334$		0			0
$335$	−0.454004	−	0.165244i	−0.0248049	−	0.00902824i
$336$		0			0
$337$	−8.84802	−	7.42437i	−0.481982	−	0.404431i	0.369160	−	0.929366i	$-0.379645\pi$
$337$	−8.84802	−	7.42437i	−0.481982	−	0.404431i	−0.851143	+	0.524935i	$0.824090\pi$
$338$		0			0
$339$	2.84448	+	1.68880i	0.154491	+	0.0917230i
$340$		0			0
$341$	−18.7046	−	10.7991i	−1.01291	−	0.584803i
$342$		0			0
$343$	−0.827619	−	1.43348i	−0.0446873	−	0.0774006i
$344$		0			0
$345$	−0.690314	−	0.593724i	−0.0371652	−	0.0319650i
$346$		0			0
$347$	−23.5421	−	4.15110i	−1.26381	−	0.222843i	−0.498715	−	0.866766i	$-0.666195\pi$
$347$	−23.5421	−	4.15110i	−1.26381	−	0.222843i	−0.765090	+	0.643923i	$0.777306\pi$
$348$		0			0
$349$	7.09323	+	8.45338i	0.379692	+	0.452499i	0.921717	−	0.387863i	$-0.126787\pi$
$349$	7.09323	+	8.45338i	0.379692	+	0.452499i	−0.542025	+	0.840362i	$0.682342\pi$
$350$		0			0
$351$	−2.93379	+	13.6916i	−0.156594	+	0.730802i
$352$		0			0
$353$	0.0385822	−	0.0323743i	0.00205352	−	0.00172311i	−0.641760	−	0.766905i	$-0.721796\pi$
$353$	0.0385822	−	0.0323743i	0.00205352	−	0.00172311i	0.643814	+	0.765182i	$0.277351\pi$
$354$		0			0
$355$	−0.940097	−	0.165764i	−0.0498952	−	0.00879786i
$356$		0			0
$357$	−8.85969	−	25.2966i	−0.468905	−	1.33884i
$358$		0			0
$359$	15.2923	+	26.4870i	0.807095	+	1.39793i	0.914867	+	0.403755i	$0.132295\pi$
$359$	15.2923	+	26.4870i	0.807095	+	1.39793i	−0.107772	+	0.994176i	$0.534372\pi$
$360$		0			0
$361$	−9.03738	+	15.6532i	−0.475651	+	0.823852i
$362$		0			0
$363$	−0.574439	+	47.1441i	−0.0301502	+	2.47443i
$364$		0			0
$365$	0.315626	−	0.376148i	0.0165206	−	0.0196885i
$366$		0			0
$367$	17.2857	+	6.29149i	0.902308	+	0.328413i	0.751177	−	0.660101i	$-0.229486\pi$
$367$	17.2857	+	6.29149i	0.902308	+	0.328413i	0.151131	+	0.988514i	$0.451709\pi$
$368$		0			0
$369$	−10.6141	+	8.47430i	−0.552549	+	0.441154i
$370$		0			0
$371$	−27.4827	+	4.84595i	−1.42683	+	0.251589i
$372$		0			0
$373$	0.534148	+	1.46756i	0.0276571	+	0.0759874i	0.952753	−	0.303747i	$-0.0982377\pi$
$373$	0.534148	+	1.46756i	0.0276571	+	0.0759874i	−0.925096	+	0.379734i	$0.876015\pi$
$374$		0			0
$375$	−0.305275	−	1.86382i	−0.0157643	−	0.0962470i
$376$		0			0
$377$	−12.5733			−0.647557
$378$		0			0
$379$		−	24.0773i		−	1.23677i	−0.785875	−	0.618385i	$-0.787787\pi$
$379$		−	24.0773i		−	1.23677i	0.785875	−	0.618385i	$-0.212213\pi$
$380$		0			0
$381$	−11.6708	+	30.8889i	−0.597912	+	1.58249i
$382$		0			0
$383$	30.3027	−	11.0293i	1.54839	−	0.563569i	0.580353	−	0.814365i	$-0.302914\pi$
$383$	30.3027	−	11.0293i	1.54839	−	0.563569i	0.968040	+	0.250796i	$0.0806922\pi$
$384$		0			0
$385$	0.431423	+	2.44672i	0.0219874	+	0.124697i
$386$		0			0
$387$	−25.4821	−	15.5520i	−1.29533	−	0.790552i
$388$		0			0
$389$	−10.1599	+	27.9140i	−0.515125	+	1.41529i	0.360707	+	0.932679i	$0.382535\pi$
$389$	−10.1599	+	27.9140i	−0.515125	+	1.41529i	−0.875832	+	0.482615i	$0.839687\pi$
$390$		0			0
$391$	15.5069	+	13.0118i	0.784216	+	0.658035i
$392$		0			0
$393$	−9.78477	−	17.4349i	−0.493576	−	0.879475i
$394$		0			0
$395$	−1.31338	−	0.758280i	−0.0660833	−	0.0381532i
$396$		0			0
$397$	20.3311	−	11.7382i	1.02039	−	0.589123i	0.106173	−	0.994348i	$-0.466140\pi$
$397$	20.3311	−	11.7382i	1.02039	−	0.589123i	0.914217	+	0.405225i	$0.132807\pi$
$398$		0			0
$399$	1.13847	−	6.02628i	0.0569948	−	0.301691i
$400$		0			0
$401$	4.04375	−	22.9332i	0.201935	−	1.14523i	−0.700255	−	0.713892i	$-0.746931\pi$
$401$	4.04375	−	22.9332i	0.201935	−	1.14523i	0.902190	−	0.431338i	$-0.141958\pi$
$402$		0			0
$403$	−6.05138	−	7.21176i	−0.301441	−	0.359243i
$404$		0			0
$405$	0.0478667	−	0.981376i	0.00237852	−	0.0487650i
$406$		0			0
$407$	5.22985	−	4.38837i	0.259234	−	0.217523i
$408$		0			0
$409$	−0.197458	+	1.11984i	−0.00976365	+	0.0553724i	−0.989300	−	0.145893i	$-0.953394\pi$
$409$	−0.197458	+	1.11984i	−0.00976365	+	0.0553724i	0.979537	+	0.201266i	$0.0645055\pi$
$410$		0			0
$411$	1.28414	+	0.242597i	0.0633421	+	0.0119664i
$412$		0			0
$413$	−3.80594	+	2.19736i	−0.187278	+	0.108125i
$414$		0			0
$415$	0.0803509	−	0.139172i	0.00394427	−	0.00683168i
$416$		0			0
$417$	−5.52586	−	9.84621i	−0.270603	−	0.482171i
$418$		0			0
$419$	24.6678	−	29.3979i	1.20510	−	1.43618i	0.335777	−	0.941941i	$-0.391001\pi$
$419$	24.6678	−	29.3979i	1.20510	−	1.43618i	0.869324	−	0.494242i	$-0.164554\pi$
$420$		0			0
$421$	1.98516	−	5.45419i	0.0967509	−	0.265821i	−0.881870	−	0.471492i	$-0.843716\pi$
$421$	1.98516	−	5.45419i	0.0967509	−	0.265821i	0.978621	+	0.205671i	$0.0659378\pi$
$422$		0			0
$423$	−34.1010	−	0.831146i	−1.65805	−	0.0404117i
$424$		0			0
$425$	3.64129	+	20.6508i	0.176628	+	1.00171i
$426$		0			0
$427$	7.86714	+	21.6148i	0.380718	+	1.04601i
$428$		0			0
$429$	−10.1988	+	26.9931i	−0.492404	+	1.30324i
$430$		0			0
$431$	1.73147			0.0834018			0.0417009	−	0.999130i	$-0.486722\pi$
$431$	1.73147			0.0834018			0.0417009	+	0.999130i	$0.486722\pi$
$432$		0			0
$433$	35.2171			1.69242			0.846212	−	0.532846i	$-0.178878\pi$
$433$	35.2171			1.69242			0.846212	+	0.532846i	$0.178878\pi$
$434$		0			0
$435$	0.870662	−	0.142606i	0.0417450	−	0.00683744i
$436$		0			0
$437$	1.58416	+	4.35244i	0.0757806	+	0.208205i
$438$		0			0
$439$	1.39618	+	7.91812i	0.0666359	+	0.377911i	0.999828	+	0.0185338i	$0.00589983\pi$
$439$	1.39618	+	7.91812i	0.0666359	+	0.377911i	−0.933192	+	0.359377i	$0.882989\pi$
$440$		0			0
$441$	−2.93981	−	19.4299i	−0.139991	−	0.925232i
$442$		0			0
$443$	−13.3548	+	36.6920i	−0.634506	+	1.74329i	0.0338267	+	0.999428i	$0.489231\pi$
$443$	−13.3548	+	36.6920i	−0.634506	+	1.74329i	−0.668333	+	0.743863i	$0.732992\pi$
$444$		0			0
$445$	−0.741830	+	0.884078i	−0.0351661	+	0.0419093i
$446$		0			0
$447$	21.7238	+	0.264699i	1.02750	+	0.0125198i
$448$		0			0
$449$	−1.45938	+	2.52773i	−0.0688726	+	0.119291i	−0.898405	−	0.439167i	$-0.855274\pi$
$449$	−1.45938	+	2.52773i	−0.0688726	+	0.119291i	0.829533	+	0.558458i	$0.188607\pi$
$450$		0			0
$451$	−24.2396	+	13.9947i	−1.14140	+	0.658987i
$452$		0			0
$453$	4.85483	+	13.8617i	0.228100	+	0.651282i
$454$		0			0
$455$	−0.188050	+	1.06649i	−0.00881593	+	0.0499976i
$456$		0			0
$457$	16.1748	−	13.5723i	0.756625	−	0.634884i	−0.180621	−	0.983553i	$-0.557811\pi$
$457$	16.1748	−	13.5723i	0.756625	−	0.634884i	0.937246	+	0.348669i	$0.113366\pi$
$458$		0			0
$459$	−0.798274	+	21.8295i	−0.0372602	+	1.01891i
$460$		0			0
$461$	−13.2762	−	15.8219i	−0.618334	−	0.736901i	0.362449	−	0.932003i	$-0.381941\pi$
$461$	−13.2762	−	15.8219i	−0.618334	−	0.736901i	−0.980783	+	0.195102i	$0.937496\pi$
$462$		0			0
$463$	−0.664092	+	3.76626i	−0.0308630	+	0.175033i	−0.996343	−	0.0854448i	$-0.972769\pi$
$463$	−0.664092	+	3.76626i	−0.0308630	+	0.175033i	0.965480	+	0.260478i	$0.0838800\pi$
$464$		0			0
$465$	0.500836	+	0.430758i	0.0232257	+	0.0199759i
$466$		0			0
$467$	−20.8197	+	12.0203i	−0.963422	+	0.556232i	−0.897225	−	0.441574i	$-0.854420\pi$
$467$	−20.8197	+	12.0203i	−0.963422	+	0.556232i	−0.0661978	+	0.997807i	$0.521087\pi$
$468$		0			0
$469$	14.1082	+	8.14536i	0.651455	+	0.376118i
$470$		0			0
$471$	−14.4688	+	24.3701i	−0.666688	+	1.12292i
$472$		0			0
$473$	−47.1270	−	39.5442i	−2.16690	−	1.81825i
$474$		0			0
$475$	−1.64102	+	4.50866i	−0.0752951	+	0.206872i
$476$		0			0
$477$	22.2950	+	4.49391i	1.02082	+	0.205762i
$478$		0			0
$479$	−5.14233	−	29.1636i	−0.234959	−	1.33252i	−0.842700	−	0.538384i	$-0.819035\pi$
$479$	−5.14233	−	29.1636i	−0.234959	−	1.33252i	0.607741	−	0.794136i	$-0.292076\pi$
$480$		0			0
$481$	2.79635	−	1.01779i	0.127503	−	0.0464072i
$482$		0			0
$483$	19.4463	+	23.7571i	0.884837	+	1.08099i
$484$		0			0
$485$			0.431575i			0.0195968i
$486$		0			0
$487$	29.6797			1.34492			0.672459	−	0.740135i	$-0.265238\pi$
$487$	29.6797			1.34492			0.672459	+	0.740135i	$0.265238\pi$
$488$		0			0
$489$	14.9344	−	12.2245i	0.675356	−	0.552810i
$490$		0			0
$491$	9.14025	+	25.1126i	0.412494	+	1.13332i	0.955860	+	0.293822i	$0.0949272\pi$
$491$	9.14025	+	25.1126i	0.412494	+	1.13332i	−0.543366	+	0.839496i	$0.682851\pi$
$492$		0			0
$493$	−19.3166	+	3.40605i	−0.869978	+	0.153401i
$494$		0			0
$495$	0.400082	−	1.98487i	0.0179824	−	0.0892131i
$496$		0			0
$497$	30.2464	+	11.0088i	1.35674	+	0.493811i
$498$		0			0
$499$	17.3765	−	20.7085i	0.777881	−	0.927042i	−0.220955	−	0.975284i	$-0.570917\pi$
$499$	17.3765	−	20.7085i	0.777881	−	0.927042i	0.998836	+	0.0482420i	$0.0153619\pi$
$500$		0			0
$501$	30.9235	+	18.3596i	1.38156	+	0.820248i
$502$		0			0
$503$	−6.23622	+	10.8014i	−0.278059	+	0.481613i	−0.970902	−	0.239476i	$-0.923025\pi$
$503$	−6.23622	+	10.8014i	−0.278059	+	0.481613i	0.692843	+	0.721088i	$0.256358\pi$
$504$		0			0
$505$	−0.217039	−	0.375923i	−0.00965813	−	0.0167284i
$506$		0			0
$507$	6.48095	−	7.53531i	0.287829	−	0.334655i
$508$		0			0
$509$	24.9223	+	4.39448i	1.10466	+	0.194782i	0.696098	−	0.717947i	$-0.254918\pi$
$509$	24.9223	+	4.39448i	1.10466	+	0.194782i	0.408565	+	0.912729i	$0.366029\pi$
$510$		0			0
$511$	−12.6831	+	10.6424i	−0.561067	+	0.470791i
$512$		0			0
$513$	−2.65559	+	4.23432i	−0.117247	+	0.186950i
$514$		0			0
$515$	1.03987	+	1.23927i	0.0458222	+	0.0546088i
$516$		0			0
$517$	−69.2270	−	12.2066i	−3.04460	−	0.536845i
$518$		0			0
$519$	3.21377	−	1.12556i	0.141069	−	0.0494068i
$520$		0			0
$521$	−15.2055	−	26.3367i	−0.666166	−	1.15383i	−0.978968	−	0.204015i	$-0.934601\pi$
$521$	−15.2055	−	26.3367i	−0.666166	−	1.15383i	0.312802	−	0.949819i	$-0.398733\pi$
$522$		0			0
$523$	10.2289	+	5.90567i	0.447280	+	0.258237i	0.706681	−	0.707533i	$-0.250192\pi$
$523$	10.2289	+	5.90567i	0.447280	+	0.258237i	−0.259401	+	0.965770i	$0.583525\pi$
$524$		0			0
$525$	−0.387483	+	31.8007i	−0.0169112	+	1.38790i
$526$		0			0
$527$	−11.2505	−	9.44031i	−0.490080	−	0.411226i
$528$		0			0
$529$	−0.175352	−	0.0638229i	−0.00762400	−	0.00277491i
$530$		0			0
$531$	3.54130	−	0.535812i	0.153679	−	0.0232523i
$532$		0			0
$533$	−12.0148	+	2.11853i	−0.520419	+	0.0917639i
$534$		0			0
$535$	0.164297	−	0.0597994i	0.00710320	−	0.00258535i
$536$		0			0
$537$	1.55301	+	9.48171i	0.0670174	+	0.409166i
$538$		0			0
$539$		−	40.4961i		−	1.74429i
$540$		0			0
$541$		−	31.2536i		−	1.34370i	−0.740688	−	0.671849i	$-0.765500\pi$
$541$		−	31.2536i		−	1.34370i	0.740688	−	0.671849i	$-0.234500\pi$
$542$		0			0
$543$	32.8735	+	12.4206i	1.41074	+	0.533020i
$544$		0			0
$545$	−0.194882	+	0.0709314i	−0.00834784	+	0.00303837i
$546$		0			0
$547$	36.3415	−	6.40799i	1.55385	−	0.273986i	0.670217	−	0.742165i	$-0.266201\pi$
$547$	36.3415	−	6.40799i	1.55385	−	0.273986i	0.883633	+	0.468180i	$0.155090\pi$
$548$		0			0
$549$	0.456765	−	18.7406i	0.0194943	−	0.799828i
$550$		0			0
$551$	−4.21738	−	1.53500i	−0.179667	−	0.0653933i
$552$		0			0
$553$	39.1724	+	32.8695i	1.66578	+	1.39776i
$554$		0			0
$555$	−0.182095	+	0.102195i	−0.00772951	+	0.00433794i
$556$		0			0
$557$	−10.7370	−	6.19900i	−0.454940	−	0.262660i	0.254974	−	0.966948i	$-0.417933\pi$
$557$	−10.7370	−	6.19900i	−0.454940	−	0.262660i	−0.709914	+	0.704288i	$0.751266\pi$
$558$		0			0
$559$	−13.4078	−	23.2229i	−0.567088	−	0.982225i
$560$		0			0
$561$	−8.35639	+	44.2330i	−0.352807	+	1.86752i
$562$		0			0
$563$	−17.6008	−	3.10349i	−0.741784	−	0.130796i	−0.210029	−	0.977695i	$-0.567356\pi$
$563$	−17.6008	−	3.10349i	−0.741784	−	0.130796i	−0.531754	+	0.846899i	$0.678467\pi$
$564$		0			0
$565$	−0.134025	−	0.159725i	−0.00563847	−	0.00671967i
$566$		0			0
$567$	−7.33555	+	32.3074i	−0.308064	+	1.35678i
$568$		0			0
$569$	16.5929	−	13.9231i	0.695612	−	0.583688i	−0.224909	−	0.974380i	$-0.572209\pi$
$569$	16.5929	−	13.9231i	0.695612	−	0.583688i	0.920522	+	0.390692i	$0.127764\pi$
$570$		0			0
$571$	−1.61867	−	0.285415i	−0.0677393	−	0.0119443i	0.139676	−	0.990197i	$-0.455394\pi$
$571$	−1.61867	−	0.285415i	−0.0677393	−	0.0119443i	−0.207415	+	0.978253i	$0.566505\pi$
$572$		0			0
$573$	14.4284	+	2.72578i	0.602755	+	0.113871i
$574$		0			0
$575$	−12.0094	−	20.8009i	−0.500828	−	0.867459i
$576$		0			0
$577$	−8.78675	+	15.2191i	−0.365797	+	0.633579i	−0.988904	−	0.148558i	$-0.952537\pi$
$577$	−8.78675	+	15.2191i	−0.365797	+	0.633579i	0.623107	+	0.782137i	$0.285870\pi$
$578$		0			0
$579$	5.40933	−	3.03581i	0.224804	−	0.126164i
$580$		0			0
$581$	−3.48301	+	4.15089i	−0.144499	+	0.172208i
$582$		0			0
$583$	44.0421	+	16.0300i	1.82404	+	0.663896i
$584$		0			0
$585$	0.459778	−	0.753350i	0.0190095	−	0.0311472i
$586$		0			0
$587$	−18.5694	+	3.27428i	−0.766439	+	0.135144i	−0.543181	−	0.839615i	$-0.682780\pi$
$587$	−18.5694	+	3.27428i	−0.766439	+	0.135144i	−0.223258	+	0.974759i	$0.571669\pi$
$588$		0			0
$589$	−1.14934	−	3.15778i	−0.0473576	−	0.130114i
$590$		0			0
$591$	−4.64676	−	1.75569i	−0.191142	−	0.0722194i
$592$		0			0
$593$	24.1750			0.992749			0.496375	−	0.868108i	$-0.334664\pi$
$593$	24.1750			0.992749			0.496375	+	0.868108i	$0.334664\pi$
$594$		0			0
$595$			1.68941i			0.0692591i
$596$		0			0
$597$	−13.5415	+	2.21797i	−0.554218	+	0.0907755i
$598$		0			0
$599$	−3.55960	+	1.29559i	−0.145441	+	0.0529363i	−0.413715	−	0.910406i	$-0.635769\pi$
$599$	−3.55960	+	1.29559i	−0.145441	+	0.0529363i	0.268274	+	0.963343i	$0.413547\pi$
$600$		0			0
$601$	7.56976	+	42.9302i	0.308777	+	1.75116i	0.605171	+	0.796095i	$0.293105\pi$
$601$	7.56976	+	42.9302i	0.308777	+	1.75116i	−0.296394	+	0.955066i	$0.595784\pi$
$602$		0			0
$603$	−8.28368	−	10.3754i	−0.337337	−	0.422518i
$604$		0			0
$605$	1.01639	−	2.79251i	0.0413221	−	0.113531i
$606$		0			0
$607$	−1.07415	−	0.901320i	−0.0435985	−	0.0365835i	0.620728	−	0.784026i	$-0.286837\pi$
$607$	−1.07415	−	0.901320i	−0.0435985	−	0.0365835i	−0.664327	+	0.747442i	$0.731282\pi$
$608$		0			0
$609$	−29.7463	−	0.362450i	−1.20538	−	0.0146872i
$610$		0			0
$611$	−26.5354	−	15.3202i	−1.07351	−	0.619789i
$612$		0			0
$613$	−15.1900	+	8.76998i	−0.613520	+	0.354216i	−0.774342	−	0.632767i	$-0.781919\pi$
$613$	−15.1900	+	8.76998i	−0.613520	+	0.354216i	0.160822	+	0.986983i	$0.448586\pi$
$614$		0			0
$615$	0.807961	−	0.282974i	0.0325801	−	0.0114106i
$616$		0			0
$617$	−4.28526	+	24.3029i	−0.172518	+	0.978400i	0.768451	+	0.639908i	$0.221028\pi$
$617$	−4.28526	+	24.3029i	−0.172518	+	0.978400i	−0.940970	+	0.338491i	$0.890083\pi$
$618$		0			0
$619$	23.2298	+	27.6842i	0.933683	+	1.11272i	0.993423	+	0.114506i	$0.0365286\pi$
$619$	23.2298	+	27.6842i	0.933683	+	1.11272i	−0.0597395	+	0.998214i	$0.519027\pi$
$620$		0			0
$621$	−7.69267	−	23.8088i	−0.308696	−	0.955416i
$622$		0			0
$623$	29.8097	−	25.0133i	1.19430	−	1.00214i
$624$		0			0
$625$	4.31019	−	24.4443i	0.172407	−	0.977771i
$626$		0			0
$627$	−6.71637	+	7.80903i	−0.268226	+	0.311862i
$628$		0			0
$629$	4.02039	−	2.32117i	0.160303	−	0.0925512i
$630$		0			0
$631$	−7.65736	+	13.2629i	−0.304835	+	0.527989i	−0.977224	−	0.212208i	$-0.931935\pi$
$631$	−7.65736	+	13.2629i	−0.304835	+	0.527989i	0.672390	+	0.740197i	$0.265268\pi$
$632$		0			0
$633$	−20.8432	+	35.1066i	−0.828442	+	1.39536i
$634$		0			0
$635$	1.33781	−	1.59434i	0.0530895	−	0.0632696i
$636$		0			0
$637$	6.03719	−	16.5871i	0.239202	−	0.657203i
$638$		0			0
$639$	−19.6782	−	17.3463i	−0.778456	−	0.686210i
$640$		0			0
$641$	4.12099	+	23.3713i	0.162769	+	0.923110i	0.951335	+	0.308159i	$0.0997129\pi$
$641$	4.12099	+	23.3713i	0.162769	+	0.923110i	−0.788566	+	0.614951i	$0.789176\pi$
$642$		0			0
$643$	−4.31565	−	11.8571i	−0.170192	−	0.467600i	0.825047	−	0.565065i	$-0.191149\pi$
$643$	−4.31565	−	11.8571i	−0.170192	−	0.467600i	−0.995239	+	0.0974649i	$0.968927\pi$
$644$		0			0
$645$	1.19184	+	1.45605i	0.0469287	+	0.0573318i
$646$		0			0
$647$	−44.1777			−1.73680			−0.868402	−	0.495861i	$-0.834853\pi$
$647$	−44.1777			−1.73680			−0.868402	+	0.495861i	$0.834853\pi$
$648$		0			0
$649$	7.38085			0.289724
$650$		0			0
$651$	−14.1087	−	17.2362i	−0.552962	−	0.675542i
$652$		0			0
$653$	3.69830	+	10.1610i	0.144726	+	0.397630i	0.990782	−	0.135462i	$-0.0432520\pi$
$653$	3.69830	+	10.1610i	0.144726	+	0.397630i	−0.846057	+	0.533093i	$0.821030\pi$
$654$		0			0
$655$	0.218824	+	1.24101i	0.00855016	+	0.0484904i
$656$		0			0
$657$	12.7882	−	4.30465i	0.498916	−	0.167940i
$658$		0			0
$659$	4.30357	−	11.8240i	0.167643	−	0.460596i	−0.827213	−	0.561888i	$-0.810075\pi$
$659$	4.30357	−	11.8240i	0.167643	−	0.460596i	0.994857	+	0.101291i	$0.0322975\pi$
$660$		0			0
$661$	31.7560	−	37.8453i	1.23517	−	1.47201i	0.405172	−	0.914241i	$-0.367212\pi$
$661$	31.7560	−	37.8453i	1.23517	−	1.47201i	0.829994	−	0.557773i	$-0.188344\pi$
$662$		0			0
$663$	−10.0170	+	16.8719i	−0.389030	+	0.655250i
$664$		0			0
$665$	−0.193278	+	0.334767i	−0.00749500	+	0.0129817i
$666$		0			0
$667$	19.4571	−	11.2336i	0.753382	−	0.434965i
$668$		0			0
$669$	18.8507	−	21.9174i	0.728809	−	0.847376i
$670$		0			0
$671$	6.70826	−	38.0444i	0.258969	−	1.46869i
$672$		0			0
$673$	−7.57318	+	6.35465i	−0.291925	+	0.244954i	−0.776974	−	0.629533i	$-0.783246\pi$
$673$	−7.57318	+	6.35465i	−0.291925	+	0.244954i	0.485049	+	0.874487i	$0.338802\pi$
$674$		0			0
$675$	9.74890	−	24.0155i	0.375235	−	0.924357i
$676$		0			0
$677$	17.9741	+	21.4207i	0.690802	+	0.823266i	0.991452	−	0.130469i	$-0.0416482\pi$
$677$	17.9741	+	21.4207i	0.690802	+	0.823266i	−0.300651	+	0.953734i	$0.597204\pi$
$678$		0			0
$679$	2.52693	−	14.3309i	0.0969746	−	0.549970i
$680$		0			0
$681$	−13.1943	+	4.62108i	−0.505607	+	0.177080i
$682$		0			0
$683$	−6.31026	+	3.64323i	−0.241455	+	0.139404i	−0.615845	−	0.787867i	$-0.711185\pi$
$683$	−6.31026	+	3.64323i	−0.241455	+	0.139404i	0.374390	+	0.927271i	$0.377852\pi$
$684$		0			0
$685$	−0.0713357	−	0.0411857i	−0.00272560	−	0.00157362i
$686$		0			0
$687$	−27.2174	−	0.331636i	−1.03841	−	0.0126527i
$688$		0			0
$689$	15.6497	+	13.1317i	0.596207	+	0.500277i
$690$		0			0
$691$	−2.74709	+	7.54756i	−0.104504	+	0.287123i	−0.980914	−	0.194444i	$-0.937710\pi$
$691$	−2.74709	+	7.54756i	−0.104504	+	0.287123i	0.876410	+	0.481567i	$0.159932\pi$
$692$		0			0
$693$	−24.9068	+	63.5671i	−0.946132	+	2.41472i
$694$		0			0
$695$	0.123579	+	0.700851i	0.00468762	+	0.0265848i
$696$		0			0
$697$	−17.8847	+	6.50951i	−0.677433	+	0.246565i
$698$		0			0
$699$	17.7662	−	2.90992i	0.671978	−	0.110063i
$700$		0			0
$701$			3.17365i			0.119867i	0.998202	+	0.0599336i	$0.0190889\pi$
$701$			3.17365i			0.119867i	−0.998202	+	0.0599336i	$0.980911\pi$
$702$		0			0
$703$	1.06222			0.0400624
$704$		0			0
$705$	2.01126	+	0.759914i	0.0757482	+	0.0286200i
$706$		0			0
$707$	5.00595	+	13.7537i	0.188268	+	0.517262i
$708$		0			0
$709$	41.3021	−	7.28268i	1.55113	−	0.273507i	0.668552	−	0.743666i	$-0.266915\pi$
$709$	41.3021	−	7.28268i	1.55113	−	0.273507i	0.882582	+	0.470159i	$0.155803\pi$
$710$		0			0
$711$	−19.9518	−	36.5883i	−0.748249	−	1.37217i
$712$		0			0
$713$	15.8078	+	5.75357i	0.592007	+	0.215473i
$714$		0			0
$715$	1.16908	−	1.39326i	0.0437212	−	0.0521049i
$716$		0			0
$717$	−7.18514	+	4.03243i	−0.268334	+	0.150594i
$718$		0			0
$719$	−0.602069	+	1.04281i	−0.0224534	+	0.0388904i	−0.877034	−	0.480429i	$-0.840481\pi$
$719$	−0.602069	+	1.04281i	−0.0224534	+	0.0388904i	0.854580	+	0.519319i	$0.173814\pi$
$720$		0			0
$721$	−27.2740	−	47.2399i	−1.01574	−	1.75931i
$722$		0			0
$723$	11.9001	+	2.24813i	0.442569	+	0.0836090i
$724$		0			0
$725$	22.9200	+	4.04141i	0.851226	+	0.150094i
$726$		0			0
$727$	26.1080	−	21.9072i	0.968291	−	0.812492i	−0.0139910	−	0.999902i	$-0.504454\pi$
$727$	26.1080	−	21.9072i	0.968291	−	0.812492i	0.982282	+	0.187410i	$0.0600092\pi$
$728$		0			0
$729$	15.1718	−	22.3342i	0.561919	−	0.827192i
$730$		0			0
$731$	−26.8896	−	32.0458i	−0.994550	−	1.18526i
$732$		0			0
$733$	30.0080	+	5.29122i	1.10837	+	0.195436i	0.697730	−	0.716361i	$-0.254194\pi$
$733$	30.0080	+	5.29122i	1.10837	+	0.195436i	0.410642	+	0.911797i	$0.365305\pi$
$734$		0			0
$735$	−0.229927	+	1.21708i	−0.00848100	+	0.0448926i
$736$		0			0
$737$	−13.6799	−	23.6944i	−0.503907	−	0.872793i
$738$		0			0
$739$	20.0759	+	11.5908i	0.738502	+	0.426375i	0.821525	−	0.570173i	$-0.193124\pi$
$739$	20.0759	+	11.5908i	0.738502	+	0.426375i	−0.0830222	+	0.996548i	$0.526457\pi$
$740$		0			0
$741$	−3.91518	+	2.19727i	−0.143828	+	0.0807186i
$742$		0			0
$743$	25.6661	+	21.5364i	0.941598	+	0.790094i	0.977863	−	0.209248i	$-0.0671016\pi$
$743$	25.6661	+	21.5364i	0.941598	+	0.790094i	−0.0362650	+	0.999342i	$0.511546\pi$
$744$		0			0
$745$	−1.28678	−	0.468348i	−0.0471438	−	0.0171589i
$746$		0			0
$747$	3.87707	−	2.11418i	0.141855	−	0.0773538i
$748$		0			0
$749$	−5.80581	+	1.02372i	−0.212140	+	0.0374059i
$750$		0			0
$751$	−17.0344	+	6.20002i	−0.621594	+	0.226242i	−0.633569	−	0.773686i	$-0.718411\pi$
$751$	−17.0344	+	6.20002i	−0.621594	+	0.226242i	0.0119743	+	0.999928i	$0.496188\pi$
$752$		0			0
$753$	−32.8935	−	12.4282i	−1.19871	−	0.452908i
$754$		0			0
$755$		−	0.925743i		−	0.0336913i
$756$		0			0
$757$		−	20.0826i		−	0.729913i	−0.931025	−	0.364956i	$-0.881084\pi$
$757$		−	20.0826i		−	0.729913i	0.931025	−	0.364956i	$-0.118916\pi$
$758$		0			0
$759$	−8.33428	−	50.8838i	−0.302515	−	1.84697i
$760$		0			0
$761$	−18.7432	+	6.82198i	−0.679442	+	0.247297i	−0.658608	−	0.752486i	$-0.728854\pi$
$761$	−18.7432	+	6.82198i	−0.679442	+	0.247297i	−0.0208341	+	0.999783i	$0.506632\pi$
$762$		0			0
$763$	6.88659	−	1.21429i	0.249311	−	0.0439603i
$764$		0			0
$765$	0.502289	−	1.28194i	0.0181603	−	0.0463487i
$766$		0			0
$767$	3.02317	+	1.10034i	0.109160	+	0.0397311i
$768$		0			0
$769$	22.1684	+	18.6015i	0.799412	+	0.670786i	0.948056	−	0.318105i	$-0.103046\pi$
$769$	22.1684	+	18.6015i	0.799412	+	0.670786i	−0.148644	+	0.988891i	$0.547491\pi$
$770$		0			0
$771$	0.153940	−	12.6338i	0.00554400	−	0.454996i
$772$		0			0
$773$	1.48732	+	0.858704i	0.0534951	+	0.0308854i	0.526509	−	0.850170i	$-0.323501\pi$
$773$	1.48732	+	0.858704i	0.0534951	+	0.0308854i	−0.473014	+	0.881055i	$0.656834\pi$
$774$		0			0
$775$	8.71306	+	15.0915i	0.312983	+	0.542102i
$776$		0			0
$777$	6.64503	−	2.32730i	0.238389	−	0.0834916i
$778$		0			0
$779$	−4.28870	−	0.756213i	−0.153659	−	0.0270941i
$780$		0			0
$781$	−34.7480	−	41.4110i	−1.24338	−	1.48180i
$782$		0			0
$783$	22.4640	+	9.11908i	0.802798	+	0.325889i
$784$		0			0
$785$	1.36845	−	1.14826i	0.0488419	−	0.0409832i
$786$		0			0
$787$	−3.69732	−	0.651937i	−0.131795	−	0.0232390i	0.107361	−	0.994220i	$-0.465760\pi$
$787$	−3.69732	−	0.651937i	−0.131795	−	0.0232390i	−0.239157	+	0.970981i	$0.576871\pi$
$788$		0			0
$789$	16.4347	−	19.1084i	0.585092	−	0.680278i
$790$		0			0
$791$	3.51524	+	6.08857i	0.124987	+	0.216485i
$792$		0			0
$793$	8.41938	−	14.5828i	0.298981	−	0.517850i
$794$		0			0
$795$	−1.23264	−	0.731831i	−0.0437171	−	0.0259554i
$796$		0			0
$797$	6.56329	−	7.82182i	0.232484	−	0.277063i	−0.637172	−	0.770721i	$-0.719896\pi$
$797$	6.56329	−	7.82182i	0.232484	−	0.277063i	0.869656	+	0.493658i	$0.164341\pi$
$798$		0			0
$799$	−44.9171	−	16.3485i	−1.58905	−	0.578368i
$800$		0			0
$801$	−30.0567	+	10.1174i	−1.06200	+	0.357482i
$802$		0			0
$803$	27.3840	−	4.82854i	0.966360	−	0.170395i
$804$		0			0
$805$	−0.661842	−	1.81840i	−0.0233269	−	0.0640900i
$806$		0			0
$807$	−11.5876	+	9.48502i	−0.407904	+	0.333889i
$808$		0			0
$809$	11.4285			0.401805			0.200903	−	0.979611i	$-0.435613\pi$
$809$	11.4285			0.401805			0.200903	+	0.979611i	$0.435613\pi$
$810$		0			0
$811$		−	1.59342i		−	0.0559527i	−0.999609	−	0.0279763i	$-0.991094\pi$
$811$		−	1.59342i		−	0.0559527i	0.999609	−	0.0279763i	$-0.00890631\pi$
$812$		0			0
$813$	−26.0020	−	31.7661i	−0.911931	−	1.11409i
$814$		0			0
$815$	−1.14309	+	0.416052i	−0.0400408	+	0.0145737i
$816$		0			0
$817$	−1.66213	−	9.42640i	−0.0581505	−	0.329788i
$818$		0			0
$819$	−19.6784	+	22.3237i	−0.687619	+	0.780055i
$820$		0			0
$821$	5.27490	−	14.4927i	0.184095	−	0.505798i	−0.812974	−	0.582300i	$-0.802153\pi$
$821$	5.27490	−	14.4927i	0.184095	−	0.505798i	0.997069	+	0.0765019i	$0.0243751\pi$
$822$		0			0
$823$	−17.8513	−	14.9790i	−0.622256	−	0.522135i	0.276256	−	0.961084i	$-0.410906\pi$
$823$	−17.8513	−	14.9790i	−0.622256	−	0.522135i	−0.898512	+	0.438949i	$0.855351\pi$
$824$		0			0
$825$	27.2679	−	45.9278i	0.949346	−	1.59900i
$826$		0			0
$827$	3.49415	+	2.01735i	0.121503	+	0.0701501i	0.559520	−	0.828817i	$-0.310986\pi$
$827$	3.49415	+	2.01735i	0.121503	+	0.0701501i	−0.438016	+	0.898967i	$0.644319\pi$
$828$		0			0
$829$	−26.0502	+	15.0401i	−0.904759	+	0.522363i	−0.878741	−	0.477298i	$-0.841616\pi$
$829$	−26.0502	+	15.0401i	−0.904759	+	0.522363i	−0.0260180	+	0.999661i	$0.508283\pi$
$830$		0			0
$831$	35.7455	+	30.7439i	1.24000	+	1.06650i
$832$		0			0
$833$	4.78173	−	27.1186i	0.165677	−	0.939602i
$834$		0			0
$835$	−1.45704	−	1.73643i	−0.0504230	−	0.0600917i
$836$		0			0
$837$	5.58118	+	17.2738i	0.192914	+	0.597069i
$838$		0			0
$839$	−29.3968	+	24.6668i	−1.01489	+	0.851593i	−0.988977	−	0.148071i	$-0.952694\pi$
$839$	−29.3968	+	24.6668i	−1.01489	+	0.851593i	−0.0259126	+	0.999664i	$0.508249\pi$
$840$		0			0
$841$	1.25548	−	7.12020i	0.0432925	−	0.245524i
$842$		0			0
$843$	2.83724	+	8.10103i	0.0977199	+	0.279014i
$844$		0			0
$845$	−0.542527	+	0.313228i	−0.0186635	+	0.0107754i
$846$		0			0
$847$	−50.1008	+	86.7771i	−1.72148	+	2.98170i
$848$		0			0
$849$	−18.8716	−	0.229945i	−0.647671	−	0.00789169i
$850$		0			0
$851$	−3.41800	+	4.07341i	−0.117168	+	0.139635i
$852$		0			0
$853$	−5.96240	+	16.3815i	−0.204149	+	0.560894i	−0.998942	−	0.0459864i	$-0.985357\pi$
$853$	−5.96240	+	16.3815i	−0.204149	+	0.560894i	0.794794	+	0.606880i	$0.207579\pi$
$854$		0			0
$855$	0.246193	−	0.196560i	0.00841962	−	0.00672221i
$856$		0			0
$857$	−6.71601	−	38.0884i	−0.229414	−	1.30107i	−0.854064	−	0.520168i	$-0.825869\pi$
$857$	−6.71601	−	38.0884i	−0.229414	−	1.30107i	0.624649	−	0.780905i	$-0.285242\pi$
$858$		0			0
$859$	−5.00399	−	13.7483i	−0.170734	−	0.469087i	0.824584	−	0.565739i	$-0.191409\pi$
$859$	−5.00399	−	13.7483i	−0.170734	−	0.469087i	−0.995318	+	0.0966515i	$0.969187\pi$
$860$		0			0
$861$	−28.4861	+	4.66574i	−0.970803	+	0.159008i
$862$		0			0
$863$	14.5060			0.493790			0.246895	−	0.969042i	$-0.420590\pi$
$863$	14.5060			0.493790			0.246895	+	0.969042i	$0.420590\pi$
$864$		0			0
$865$	−0.214628			−0.00729758
$866$		0			0
$867$	−0.411809	+	1.08993i	−0.0139858	+	0.0370160i
$868$		0			0
$869$	−29.3733	−	80.7024i	−0.996419	−	2.73764i
$870$		0			0
$871$	−2.07088	−	11.7445i	−0.0701691	−	0.397949i
$872$		0			0
$873$	−6.17828	+	10.1232i	−0.209103	+	0.342617i
$874$		0			0
$875$	1.37283	−	3.77183i	0.0464102	−	0.127511i
$876$		0			0
$877$	−29.8292	+	35.5490i	−1.00726	+	1.20041i	−0.0276255	+	0.999618i	$0.508795\pi$
$877$	−29.8292	+	35.5490i	−1.00726	+	1.20041i	−0.979635	+	0.200788i	$0.935650\pi$
$878$		0			0
$879$	2.43531	+	4.33933i	0.0821410	+	0.146362i
$880$		0			0
$881$	4.79898	−	8.31208i	0.161682	−	0.280041i	−0.773790	−	0.633442i	$-0.781641\pi$
$881$	4.79898	−	8.31208i	0.161682	−	0.280041i	0.935472	+	0.353401i	$0.114975\pi$
$882$		0			0
$883$	−13.6741	+	7.89474i	−0.460170	+	0.265679i	−0.712116	−	0.702062i	$-0.752263\pi$
$883$	−13.6741	+	7.89474i	−0.460170	+	0.265679i	0.251946	+	0.967741i	$0.418930\pi$
$884$		0			0
$885$	−0.221825	−	0.0419067i	−0.00745658	−	0.00140868i
$886$		0			0
$887$	−1.21381	+	6.88388i	−0.0407559	+	0.231138i	−0.998381	−	0.0568793i	$-0.981885\pi$
$887$	−1.21381	+	6.88388i	−0.0407559	+	0.231138i	0.957625	+	0.288017i	$0.0929961\pi$
$888$		0			0
$889$	−53.7586	+	45.1088i	−1.80301	+	1.51290i
$890$		0			0
$891$	37.7991	−	40.8302i	1.26632	−	1.36786i
$892$		0			0
$893$	−7.03024	−	8.37832i	−0.235258	−	0.280370i
$894$		0			0
$895$	0.105161	−	0.596396i	0.00351514	−	0.0199353i
$896$		0			0
$897$	4.17212	−	22.0843i	0.139303	−	0.737374i
$898$		0			0
$899$	−14.1165	+	8.15016i	−0.470811	+	0.271823i
$900$		0			0
$901$	27.6004	+	15.9351i	0.919502	+	0.530875i
$902$		0			0
$903$	−31.0510	−	55.3280i	−1.03331	−	1.84120i
$904$		0			0
$905$	−1.69678	−	1.42377i	−0.0564029	−	0.0473276i
$906$		0			0
$907$	6.06565	−	16.6652i	0.201407	−	0.553360i	−0.797334	−	0.603539i	$-0.793757\pi$
$907$	6.06565	−	16.6652i	0.201407	−	0.553360i	0.998740	+	0.0501785i	$0.0159790\pi$
$908$		0			0
$909$	0.290645	−	11.9248i	0.00964008	−	0.395522i
$910$		0			0
$911$	−2.42298	−	13.7414i	−0.0802769	−	0.455273i	−0.998276	−	0.0586910i	$-0.981307\pi$
$911$	−2.42298	−	13.7414i	−0.0802769	−	0.455273i	0.917999	−	0.396582i	$-0.129804\pi$
$912$		0			0
$913$	8.55159	−	3.11253i	0.283016	−	0.103010i
$914$		0			0
$915$	−0.417619	+	1.10531i	−0.0138061	+	0.0365403i
$916$		0			0
$917$		−	42.4904i		−	1.40316i
$918$		0			0
$919$	34.2100			1.12848			0.564242	−	0.825610i	$-0.309169\pi$
$919$	34.2100			1.12848			0.564242	+	0.825610i	$0.309169\pi$
$920$		0			0
$921$	−5.34352	−	32.6241i	−0.176075	−	1.07500i
$922$		0			0
$923$	−8.05905	−	22.1421i	−0.265267	−	0.728815i
$924$		0			0
$925$	−5.42464	+	0.956511i	−0.178361	+	0.0314499i
$926$		0			0
$927$	6.65058	+	43.9552i	0.218434	+	1.44368i
$928$		0			0
$929$	−37.9506	−	13.8129i	−1.24512	−	0.453186i	−0.366370	−	0.930469i	$-0.619399\pi$
$929$	−37.9506	−	13.8129i	−1.24512	−	0.453186i	−0.878750	+	0.477283i	$0.841622\pi$
$930$		0			0
$931$	4.05004	−	4.82665i	0.132735	−	0.158187i
$932$		0			0
$933$	−0.164724	+	13.5189i	−0.00539282	+	0.442588i
$934$		0			0
$935$	1.41866	−	2.45720i	0.0463953	−	0.0803590i
$936$		0			0
$937$	−21.7492	−	37.6708i	−0.710516	−	1.23065i	−0.964664	−	0.263485i	$-0.915128\pi$
$937$	−21.7492	−	37.6708i	−0.710516	−	1.23065i	0.254147	−	0.967165i	$-0.418205\pi$
$938$		0			0
$939$	2.12747	+	6.07445i	0.0694273	+	0.198232i
$940$		0			0
$941$	4.81142	+	0.848383i	0.156848	+	0.0276565i	0.251521	−	0.967852i	$-0.419069\pi$
$941$	4.81142	+	0.848383i	0.156848	+	0.0276565i	−0.0946728	+	0.995508i	$0.530180\pi$
$942$		0			0
$943$	16.7001	−	14.0130i	0.543829	−	0.456327i
$944$		0			0
$945$	1.10947	−	1.76904i	0.0360912	−	0.0575470i
$946$		0			0
$947$	7.65489	+	9.12274i	0.248751	+	0.296449i	0.875943	−	0.482415i	$-0.160240\pi$
$947$	7.65489	+	9.12274i	0.248751	+	0.296449i	−0.627192	+	0.778865i	$0.715796\pi$
$948$		0			0
$949$	11.9362	+	2.10468i	0.387466	+	0.0683208i
$950$		0			0
$951$	3.23649	+	2.78363i	0.104950	+	0.0902655i
$952$		0			0
$953$	5.14051	+	8.90362i	0.166517	+	0.288417i	0.937193	−	0.348811i	$-0.113414\pi$
$953$	5.14051	+	8.90362i	0.166517	+	0.288417i	−0.770676	+	0.637228i	$0.780081\pi$
$954$		0			0
$955$	−0.801515	−	0.462755i	−0.0259364	−	0.0149744i
$956$		0			0
$957$	42.9607	+	25.5063i	1.38872	+	0.824500i
$958$		0			0
$959$	2.12763	+	1.78529i	0.0687048	+	0.0576502i
$960$		0			0
$961$	17.6616	+	6.42830i	0.569729	+	0.207364i
$962$		0			0
$963$	4.70988	+	0.949352i	0.151774	+	0.0305925i
$964$		0			0
$965$	−0.385035	+	0.0678921i	−0.0123947	+	0.00218552i
$966$		0			0
$967$	−8.15321	+	2.96753i	−0.262190	+	0.0954292i	−0.469770	−	0.882789i	$-0.655663\pi$
$967$	−8.15321	+	2.96753i	−0.262190	+	0.0954292i	0.207581	+	0.978218i	$0.433441\pi$
$968$		0			0
$969$	−5.41976	+	4.43632i	−0.174108	+	0.142515i
$970$		0			0
$971$			42.3576i			1.35932i	0.733527	+	0.679661i	$0.237873\pi$
$971$			42.3576i			1.35932i	−0.733527	+	0.679661i	$0.762127\pi$
$972$		0			0
$973$		−	23.9961i		−	0.769280i
$974$		0			0
$975$	18.0158	−	14.7468i	0.576967	−	0.472274i
$976$		0			0
$977$	−50.4274	+	18.3541i	−1.61332	+	0.587199i	−0.982092	−	0.188401i	$-0.939670\pi$
$977$	−50.4274	+	18.3541i	−1.61332	+	0.587199i	−0.631225	+	0.775600i	$0.717447\pi$
$978$		0			0
$979$	−64.3619	+	11.3487i	−2.05701	+	0.362707i
$980$		0			0
$981$	−5.58665	−	1.12608i	−0.178368	−	0.0359530i
$982$		0			0
$983$	−22.6514	−	8.24445i	−0.722469	−	0.262957i	−0.0454953	−	0.998965i	$-0.514487\pi$
$983$	−22.6514	−	8.24445i	−0.722469	−	0.262957i	−0.676973	+	0.736007i	$0.736709\pi$
$984$		0			0
$985$	0.239844	+	0.201253i	0.00764207	+	0.00641246i
$986$		0			0
$987$	−62.3365	−	37.0099i	−1.98419	−	1.17804i
$988$		0			0
$989$	41.4969	+	23.9582i	1.31952	+	0.761828i
$990$		0			0
$991$	6.31916	+	10.9451i	0.200735	+	0.347683i	0.948765	−	0.315981i	$-0.102334\pi$
$991$	6.31916	+	10.9451i	0.200735	+	0.347683i	−0.748031	+	0.663664i	$0.769000\pi$
$992$		0			0
$993$	32.2663	+	27.7515i	1.02394	+	0.880667i
$994$		0			0
$995$	0.851758	+	0.150188i	0.0270025	+	0.00476128i
$996$		0			0
$997$	13.4876	+	16.0739i	0.427156	+	0.509065i	0.936100	−	0.351735i	$-0.114408\pi$
$997$	13.4876	+	16.0739i	0.427156	+	0.509065i	−0.508944	+	0.860800i	$0.669964\pi$
$998$		0			0
$999$	−5.73426	−	0.209694i	−0.181424	−	0.00663444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bf.a.49.10		204
4.3	odd	2		216.2.t.a.157.1	✓	204
8.3	odd	2		216.2.t.a.157.16	yes	204
8.5	even	2	inner	864.2.bf.a.49.25		204
12.11	even	2		648.2.t.a.37.34		204
24.11	even	2		648.2.t.a.37.19		204
27.16	even	9	inner	864.2.bf.a.529.25		204
108.11	even	18		648.2.t.a.613.19		204
108.43	odd	18		216.2.t.a.205.16	yes	204
216.11	even	18		648.2.t.a.613.34		204
216.43	odd	18		216.2.t.a.205.1	yes	204
216.205	even	18	inner	864.2.bf.a.529.10		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.1	✓	204	4.3	odd	2
216.2.t.a.157.16	yes	204	8.3	odd	2
216.2.t.a.205.1	yes	204	216.43	odd	18
216.2.t.a.205.16	yes	204	108.43	odd	18
648.2.t.a.37.19		204	24.11	even	2
648.2.t.a.37.34		204	12.11	even	2
648.2.t.a.613.19		204	108.11	even	18
648.2.t.a.613.34		204	216.11	even	18
864.2.bf.a.49.10		204	1.1	even	1	trivial
864.2.bf.a.49.25		204	8.5	even	2	inner
864.2.bf.a.529.10		204	216.205	even	18	inner
864.2.bf.a.529.25		204	27.16	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bf (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.09709 - 1.34029i) q^{3} +(0.0373388 + 0.102588i) q^{5} +(-0.639213 - 3.62515i) q^{7} +(-0.592777 + 2.94085i) q^{9} +O(q^{10})\)	\(q+(-1.09709 - 1.34029i) q^{3} +(0.0373388 + 0.102588i) q^{5} +(-0.639213 - 3.62515i) q^{7} +(-0.592777 + 2.94085i) q^{9} +(-2.11447 + 5.80945i) q^{11} +(-1.73216 + 2.06430i) q^{13} +(0.0965334 - 0.162593i) q^{15} +(-2.10194 + 3.64068i) q^{17} +(-0.833027 + 0.480948i) q^{19} +(-4.15750 + 4.83386i) q^{21} +(0.836159 - 4.74209i) q^{23} +(3.82109 - 3.20628i) q^{25} +(4.59194 - 2.43189i) q^{27} +(2.99914 + 3.57423i) q^{29} +(-0.606649 + 3.44048i) q^{31} +(10.1061 - 3.53950i) q^{33} +(0.348028 - 0.200934i) q^{35} +(-0.956350 - 0.552149i) q^{37} +(4.66711 + 0.0568675i) q^{39} +(3.46816 + 2.91013i) q^{41} +(-3.40344 + 9.35087i) q^{43} +(-0.323828 + 0.0489964i) q^{45} +(1.97444 + 11.1976i) q^{47} +(-6.15530 + 2.24035i) q^{49} +(7.18560 - 1.17693i) q^{51} -7.58112i q^{53} -0.674929 q^{55} +(1.55852 + 0.588856i) q^{57} +(-0.408327 - 1.12187i) q^{59} +(-6.15378 + 1.08508i) q^{61} +(11.0400 + 0.269078i) q^{63} +(-0.276449 - 0.100619i) q^{65} +(-2.84467 + 3.39015i) q^{67} +(-7.27314 + 4.08181i) q^{69} +(-4.37202 + 7.57257i) q^{71} +(-2.24888 - 3.89517i) q^{73} +(-8.48945 - 1.60381i) q^{75} +(22.4118 + 3.95180i) q^{77} +(-10.6416 + 8.92932i) q^{79} +(-8.29723 - 3.48654i) q^{81} +(-0.946192 - 1.12763i) q^{83} +(-0.451972 - 0.0796949i) q^{85} +(1.50019 - 7.94099i) q^{87} +(5.28564 + 9.15500i) q^{89} +(8.59064 + 4.95981i) q^{91} +(5.27680 - 2.96143i) q^{93} +(-0.0804435 - 0.0675001i) q^{95} +(3.71478 + 1.35207i) q^{97} +(-15.8313 - 9.66205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 12 q^{7} - 12 q^{9}+O(q^{10}) \) 204 * q + 12 * q^7 - 12 * q^9	\( 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73} + 12 q^{79} - 12 q^{81} + 48 q^{87} - 6 q^{89} + 42 q^{95} - 12 q^{97}+O(q^{100}) \) 204 * q + 12 * q^7 - 12 * q^9 + 12 * q^15 - 6 * q^17 + 12 * q^23 - 12 * q^25 + 12 * q^31 + 12 * q^39 - 24 * q^41 + 12 * q^47 - 12 * q^49 + 24 * q^55 - 30 * q^57 + 72 * q^63 - 12 * q^65 + 90 * q^71 - 6 * q^73 + 12 * q^79 - 12 * q^81 + 48 * q^87 - 6 * q^89 + 42 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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