LMFDB - Embedded newform 256.2.i.a.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(17,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("256.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.i (of order $16$, degree $8$, 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:	$2.04417029174$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			17.2
Character	$\chi$	$=$	256.17
Dual form			256.2.i.a.241.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25103 - 1.87230i) q^{3} +(0.509835 + 2.56311i) q^{5} +(1.78664 + 4.31333i) q^{7} +(-0.792379 + 1.91297i) q^{9} +O(q^{10})$	\(q+(-1.25103 - 1.87230i) q^{3} +(0.509835 + 2.56311i) q^{5} +(1.78664 + 4.31333i) q^{7} +(-0.792379 + 1.91297i) q^{9} +(0.337256 + 0.225347i) q^{11} +(0.558477 - 2.80765i) q^{13} +(4.16110 - 4.16110i) q^{15} +(2.50296 + 2.50296i) q^{17} +(2.54690 + 0.506609i) q^{19} +(5.84071 - 8.74124i) q^{21} +(2.78551 + 1.15380i) q^{23} +(-1.69022 + 0.700112i) q^{25} +(-2.05264 + 0.408295i) q^{27} +(-4.40189 + 2.94125i) q^{29} -0.289905i q^{31} -0.913360i q^{33} +(-10.1447 + 6.77845i) q^{35} +(1.93303 - 0.384503i) q^{37} +(-5.95544 + 2.46682i) q^{39} +(-5.97284 - 2.47403i) q^{41} +(3.47301 - 5.19772i) q^{43} +(-5.30715 - 1.05566i) q^{45} +(-0.140633 - 0.140633i) q^{47} +(-10.4630 + 10.4630i) q^{49} +(1.55501 - 7.81758i) q^{51} +(0.438386 + 0.292920i) q^{53} +(-0.405645 + 0.979314i) q^{55} +(-2.23772 - 5.40234i) q^{57} +(1.05758 + 5.31680i) q^{59} +(4.77369 + 7.14433i) q^{61} -9.66698 q^{63} +7.48106 q^{65} +(-2.53466 - 3.79339i) q^{67} +(-1.32451 - 6.65875i) q^{69} +(-5.35506 - 12.9282i) q^{71} +(5.89360 - 14.2284i) q^{73} +(3.42534 + 2.28874i) q^{75} +(-0.369442 + 1.85731i) q^{77} +(4.17941 - 4.17941i) q^{79} +(7.72474 + 7.72474i) q^{81} +(-7.83362 - 1.55820i) q^{83} +(-5.13928 + 7.69148i) q^{85} +(11.0138 + 4.56206i) q^{87} +(-6.46701 + 2.67872i) q^{89} +(13.1081 - 2.60737i) q^{91} +(-0.542790 + 0.362680i) q^{93} +6.78627i q^{95} -16.2429i q^{97} +(-0.698317 + 0.466600i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) $ 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9	$ 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9} + 8 q^{11} - 8 q^{13} + 8 q^{15} - 8 q^{17} + 8 q^{19} - 8 q^{21} + 8 q^{23} - 8 q^{25} + 8 q^{27} - 8 q^{29} + 8 q^{35} - 8 q^{37} + 8 q^{39} - 8 q^{41} + 8 q^{43} - 8 q^{45} + 8 q^{47} - 8 q^{49} - 24 q^{51} - 8 q^{53} - 56 q^{55} - 8 q^{57} - 56 q^{59} - 8 q^{61} - 64 q^{63} - 16 q^{65} - 72 q^{67} - 8 q^{69} - 56 q^{71} - 8 q^{73} - 56 q^{75} - 8 q^{77} - 24 q^{79} - 8 q^{81} + 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{89} + 8 q^{91} + 16 q^{93} - 16 q^{99}+O(q^{100}) $ 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9 + 8 * q^11 - 8 * q^13 + 8 * q^15 - 8 * q^17 + 8 * q^19 - 8 * q^21 + 8 * q^23 - 8 * q^25 + 8 * q^27 - 8 * q^29 + 8 * q^35 - 8 * q^37 + 8 * q^39 - 8 * q^41 + 8 * q^43 - 8 * q^45 + 8 * q^47 - 8 * q^49 - 24 * q^51 - 8 * q^53 - 56 * q^55 - 8 * q^57 - 56 * q^59 - 8 * q^61 - 64 * q^63 - 16 * q^65 - 72 * q^67 - 8 * q^69 - 56 * q^71 - 8 * q^73 - 56 * q^75 - 8 * q^77 - 24 * q^79 - 8 * q^81 + 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^89 + 8 * q^91 + 16 * q^93 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{7}{16}\right)$	$1$

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
$3$	−1.25103	−	1.87230i	−0.722283	−	1.08097i	−0.992977	−	0.118308i	$-0.962253\pi$
$3$	−1.25103	−	1.87230i	−0.722283	−	1.08097i	0.270694	−	0.962665i	$-0.412747\pi$
$4$		0			0
$5$	0.509835	+	2.56311i	0.228005	+	1.14626i	0.909906	+	0.414814i	$0.136154\pi$
$5$	0.509835	+	2.56311i	0.228005	+	1.14626i	−0.681901	+	0.731445i	$0.738846\pi$
$6$		0			0
$7$	1.78664	+	4.31333i	0.675287	+	1.63029i	0.772494	+	0.635022i	$0.219009\pi$
$7$	1.78664	+	4.31333i	0.675287	+	1.63029i	−0.0972076	+	0.995264i	$0.530991\pi$
$8$		0			0
$9$	−0.792379	+	1.91297i	−0.264126	+	0.637657i
$10$		0			0
$11$	0.337256	+	0.225347i	0.101686	+	0.0679447i	0.605374	−	0.795941i	$-0.293024\pi$
$11$	0.337256	+	0.225347i	0.101686	+	0.0679447i	−0.503687	+	0.863886i	$0.668024\pi$
$12$		0			0
$13$	0.558477	−	2.80765i	0.154894	−	0.778703i	−0.822745	−	0.568411i	$-0.807559\pi$
$13$	0.558477	−	2.80765i	0.154894	−	0.778703i	0.977639	−	0.210292i	$-0.0674415\pi$
$14$		0			0
$15$	4.16110	−	4.16110i	1.07439	−	1.07439i
$16$		0			0
$17$	2.50296	+	2.50296i	0.607058	+	0.607058i	0.942176	−	0.335118i	$-0.108776\pi$
$17$	2.50296	+	2.50296i	0.607058	+	0.607058i	−0.335118	+	0.942176i	$0.608776\pi$
$18$		0			0
$19$	2.54690	+	0.506609i	0.584298	+	0.116224i	0.478384	−	0.878151i	$-0.341223\pi$
$19$	2.54690	+	0.506609i	0.584298	+	0.116224i	0.105915	+	0.994375i	$0.466223\pi$
$20$		0			0
$21$	5.84071	−	8.74124i	1.27455	−	1.90749i
$22$		0			0
$23$	2.78551	+	1.15380i	0.580820	+	0.240583i	0.653696	−	0.756758i	$-0.273218\pi$
$23$	2.78551	+	1.15380i	0.580820	+	0.240583i	−0.0728759	+	0.997341i	$0.523218\pi$
$24$		0			0
$25$	−1.69022	+	0.700112i	−0.338044	+	0.140022i
$26$		0			0
$27$	−2.05264	+	0.408295i	−0.395030	+	0.0785764i
$28$		0			0
$29$	−4.40189	+	2.94125i	−0.817410	+	0.546176i	−0.892525	−	0.450999i	$-0.851068\pi$
$29$	−4.40189	+	2.94125i	−0.817410	+	0.546176i	0.0751143	+	0.997175i	$0.476068\pi$
$30$		0			0
$31$		−	0.289905i		−	0.0520685i	−0.999661	−	0.0260343i	$-0.991712\pi$
$31$		−	0.289905i		−	0.0520685i	0.999661	−	0.0260343i	$-0.00828790\pi$
$32$		0			0
$33$		−	0.913360i		−	0.158995i
$34$		0			0
$35$	−10.1447	+	6.77845i	−1.71476	+	1.14577i
$36$		0			0
$37$	1.93303	−	0.384503i	0.317787	−	0.0632119i	−0.0336194	−	0.999435i	$-0.510703\pi$
$37$	1.93303	−	0.384503i	0.317787	−	0.0632119i	0.351407	+	0.936223i	$0.385703\pi$
$38$		0			0
$39$	−5.95544	+	2.46682i	−0.953634	+	0.395008i
$40$		0			0
$41$	−5.97284	−	2.47403i	−0.932801	−	0.386379i	−0.136061	−	0.990700i	$-0.543444\pi$
$41$	−5.97284	−	2.47403i	−0.932801	−	0.386379i	−0.796741	+	0.604321i	$0.793444\pi$
$42$		0			0
$43$	3.47301	−	5.19772i	0.529628	−	0.792645i	−0.466124	−	0.884720i	$-0.654350\pi$
$43$	3.47301	−	5.19772i	0.529628	−	0.792645i	0.995752	+	0.0920747i	$0.0293499\pi$
$44$		0			0
$45$	−5.30715	−	1.05566i	−0.791143	−	0.157368i
$46$		0			0
$47$	−0.140633	−	0.140633i	−0.0205135	−	0.0205135i	0.696776	−	0.717289i	$-0.254617\pi$
$47$	−0.140633	−	0.140633i	−0.0205135	−	0.0205135i	−0.717289	+	0.696776i	$0.754617\pi$
$48$		0			0
$49$	−10.4630	+	10.4630i	−1.49471	+	1.49471i
$50$		0			0
$51$	1.55501	−	7.81758i	0.217746	−	1.09468i
$52$		0			0
$53$	0.438386	+	0.292920i	0.0602169	+	0.0402356i	0.585314	−	0.810806i	$-0.300971\pi$
$53$	0.438386	+	0.292920i	0.0602169	+	0.0402356i	−0.525097	+	0.851042i	$0.675971\pi$
$54$		0			0
$55$	−0.405645	+	0.979314i	−0.0546972	+	0.132051i
$56$		0			0
$57$	−2.23772	−	5.40234i	−0.296394	−	0.715558i
$58$		0			0
$59$	1.05758	+	5.31680i	0.137685	+	0.692189i	0.986534	+	0.163554i	$0.0522958\pi$
$59$	1.05758	+	5.31680i	0.137685	+	0.692189i	−0.848850	+	0.528635i	$0.822704\pi$
$60$		0			0
$61$	4.77369	+	7.14433i	0.611209	+	0.914738i	0.999978	−	0.00659665i	$-0.00209980\pi$
$61$	4.77369	+	7.14433i	0.611209	+	0.914738i	−0.388770	+	0.921335i	$0.627100\pi$
$62$		0			0
$63$	−9.66698			−1.21792
$64$		0			0
$65$	7.48106			0.927912
$66$		0			0
$67$	−2.53466	−	3.79339i	−0.309658	−	0.463436i	0.643700	−	0.765278i	$-0.277399\pi$
$67$	−2.53466	−	3.79339i	−0.309658	−	0.463436i	−0.953358	+	0.301842i	$0.902399\pi$
$68$		0			0
$69$	−1.32451	−	6.65875i	−0.159452	−	0.801620i
$70$		0			0
$71$	−5.35506	−	12.9282i	−0.635528	−	1.53430i	−0.832578	−	0.553907i	$-0.813136\pi$
$71$	−5.35506	−	12.9282i	−0.635528	−	1.53430i	0.197050	−	0.980393i	$-0.436864\pi$
$72$		0			0
$73$	5.89360	−	14.2284i	0.689794	−	1.66531i	−0.0554020	−	0.998464i	$-0.517644\pi$
$73$	5.89360	−	14.2284i	0.689794	−	1.66531i	0.745196	−	0.666846i	$-0.232356\pi$
$74$		0			0
$75$	3.42534	+	2.28874i	0.395524	+	0.264280i
$76$		0			0
$77$	−0.369442	+	1.85731i	−0.0421018	+	0.211660i
$78$		0			0
$79$	4.17941	−	4.17941i	0.470220	−	0.470220i	−0.431765	−	0.901986i	$-0.642109\pi$
$79$	4.17941	−	4.17941i	0.470220	−	0.470220i	0.901986	+	0.431765i	$0.142109\pi$
$80$		0			0
$81$	7.72474	+	7.72474i	0.858304	+	0.858304i
$82$		0			0
$83$	−7.83362	−	1.55820i	−0.859851	−	0.171035i	−0.254578	−	0.967052i	$-0.581936\pi$
$83$	−7.83362	−	1.55820i	−0.859851	−	0.171035i	−0.605274	+	0.796017i	$0.706936\pi$
$84$		0			0
$85$	−5.13928	+	7.69148i	−0.557433	+	0.834258i
$86$		0			0
$87$	11.0138	+	4.56206i	1.18080	+	0.489105i
$88$		0			0
$89$	−6.46701	+	2.67872i	−0.685501	+	0.283944i	−0.698125	−	0.715976i	$-0.745982\pi$
$89$	−6.46701	+	2.67872i	−0.685501	+	0.283944i	0.0126231	+	0.999920i	$0.495982\pi$
$90$		0			0
$91$	13.1081	−	2.60737i	1.37411	−	0.273327i
$92$		0			0
$93$	−0.542790	+	0.362680i	−0.0562847	+	0.0376082i
$94$		0			0
$95$			6.78627i			0.696257i
$96$		0			0
$97$		−	16.2429i		−	1.64922i	−0.565702	−	0.824610i	$-0.691395\pi$
$97$		−	16.2429i		−	1.64922i	0.565702	−	0.824610i	$-0.308605\pi$
$98$		0			0
$99$	−0.698317	+	0.466600i	−0.0701835	+	0.0468951i
$100$		0			0
$101$	−15.3251	+	3.04834i	−1.52490	+	0.303321i	−0.885166	−	0.465275i	$-0.845955\pi$
$101$	−15.3251	+	3.04834i	−1.52490	+	0.303321i	−0.639734	+	0.768597i	$0.720955\pi$
$102$		0			0
$103$	−1.43693	+	0.595196i	−0.141585	+	0.0586464i	−0.452351	−	0.891840i	$-0.649414\pi$
$103$	−1.43693	+	0.595196i	−0.141585	+	0.0586464i	0.310766	+	0.950486i	$0.399414\pi$
$104$		0			0
$105$	25.3826	+	10.5138i	2.47709	+	1.02604i
$106$		0			0
$107$	2.12845	−	3.18545i	0.205765	−	0.307949i	−0.714206	−	0.699936i	$-0.753212\pi$
$107$	2.12845	−	3.18545i	0.205765	−	0.307949i	0.919971	+	0.391986i	$0.128212\pi$
$108$		0			0
$109$	−2.80639	−	0.558226i	−0.268803	−	0.0534683i	0.0588482	−	0.998267i	$-0.481257\pi$
$109$	−2.80639	−	0.558226i	−0.268803	−	0.0534683i	−0.327652	+	0.944799i	$0.606257\pi$
$110$		0			0
$111$	−3.13818	−	3.13818i	−0.297863	−	0.297863i
$112$		0			0
$113$	8.29968	−	8.29968i	0.780769	−	0.780769i	−0.199192	−	0.979960i	$-0.563832\pi$
$113$	8.29968	−	8.29968i	0.780769	−	0.780769i	0.979960	+	0.199192i	$0.0638317\pi$
$114$		0			0
$115$	−1.53716	+	7.72783i	−0.143341	+	0.720624i
$116$		0			0
$117$	4.92844	+	3.29308i	0.455634	+	0.304445i
$118$		0			0
$119$	−6.32421	+	15.2680i	−0.579740	+	1.39962i
$120$		0			0
$121$	−4.14656	−	10.0107i	−0.376960	−	0.910061i
$122$		0			0
$123$	2.84008	+	14.2780i	0.256081	+	1.28741i
$124$		0			0
$125$	4.60324	+	6.88923i	0.411726	+	0.616191i
$126$		0			0
$127$	7.21464			0.640196			0.320098	−	0.947384i	$-0.396284\pi$
$127$	7.21464			0.640196			0.320098	+	0.947384i	$0.396284\pi$
$128$		0			0
$129$	−14.0765			−1.23937
$130$		0			0
$131$	6.24500	+	9.34631i	0.545628	+	0.816591i	0.997132	−	0.0756785i	$-0.0241123\pi$
$131$	6.24500	+	9.34631i	0.545628	+	0.816591i	−0.451504	+	0.892269i	$0.649112\pi$
$132$		0			0
$133$	2.36522	+	11.8907i	0.205090	+	1.03106i
$134$		0			0
$135$	−2.09301	−	5.05298i	−0.180138	−	0.434891i
$136$		0			0
$137$	−4.59287	+	11.0882i	−0.392395	+	0.947326i	0.597022	+	0.802225i	$0.296351\pi$
$137$	−4.59287	+	11.0882i	−0.392395	+	0.947326i	−0.989417	+	0.145101i	$0.953649\pi$
$138$		0			0
$139$	−13.1247	−	8.76967i	−1.11323	−	0.743834i	−0.143895	−	0.989593i	$-0.545963\pi$
$139$	−13.1247	−	8.76967i	−1.11323	−	0.743834i	−0.969331	+	0.245759i	$0.920963\pi$
$140$		0			0
$141$	−0.0873711	+	0.439244i	−0.00735797	+	0.0369910i
$142$		0			0
$143$	0.821045	−	0.821045i	0.0686593	−	0.0686593i
$144$		0			0
$145$	−9.78299	−	9.78299i	−0.812433	−	0.812433i
$146$		0			0
$147$	32.6794	+	6.50034i	2.69535	+	0.536139i
$148$		0			0
$149$	10.8556	−	16.2465i	0.889324	−	1.33097i	−0.0538088	−	0.998551i	$-0.517136\pi$
$149$	10.8556	−	16.2465i	0.889324	−	1.33097i	0.943133	−	0.332416i	$-0.107864\pi$
$150$		0			0
$151$	−12.4999	−	5.17764i	−1.01723	−	0.421351i	−0.189143	−	0.981950i	$-0.560571\pi$
$151$	−12.4999	−	5.17764i	−1.01723	−	0.421351i	−0.828087	+	0.560599i	$0.810571\pi$
$152$		0			0
$153$	−6.77140	+	2.80480i	−0.547435	+	0.226755i
$154$		0			0
$155$	0.743060	−	0.147804i	0.0596840	−	0.0118719i
$156$		0			0
$157$	8.26557	−	5.52287i	0.659664	−	0.440773i	−0.180156	−	0.983638i	$-0.557660\pi$
$157$	8.26557	−	5.52287i	0.659664	−	0.440773i	0.839820	+	0.542865i	$0.182660\pi$
$158$		0			0
$159$		−	1.18724i		−	0.0941544i
$160$		0			0
$161$			14.0763i			1.10936i
$162$		0			0
$163$	16.9295	−	11.3119i	1.32602	−	0.886017i	0.327746	−	0.944766i	$-0.393711\pi$
$163$	16.9295	−	11.3119i	1.32602	−	0.886017i	0.998273	+	0.0587489i	$0.0187111\pi$
$164$		0			0
$165$	2.34104	−	0.465663i	0.182250	−	0.0362518i
$166$		0			0
$167$	6.10786	−	2.52996i	0.472640	−	0.195774i	−0.133632	−	0.991031i	$-0.542664\pi$
$167$	6.10786	−	2.52996i	0.472640	−	0.195774i	0.606272	+	0.795257i	$0.292664\pi$
$168$		0			0
$169$	4.43942	+	1.83887i	0.341494	+	0.141451i
$170$		0			0
$171$	−2.98724	+	4.47072i	−0.228440	+	0.341884i
$172$		0			0
$173$	−2.36420	−	0.470269i	−0.179747	−	0.0357539i	0.104396	−	0.994536i	$-0.466709\pi$
$173$	−2.36420	−	0.470269i	−0.179747	−	0.0357539i	−0.284143	+	0.958782i	$0.591709\pi$
$174$		0			0
$175$	−6.03963	−	6.03963i	−0.456553	−	0.456553i
$176$		0			0
$177$	8.63159	−	8.63159i	0.648790	−	0.648790i
$178$		0			0
$179$	−2.21659	+	11.1436i	−0.165676	+	0.832910i	0.805140	+	0.593085i	$0.202090\pi$
$179$	−2.21659	+	11.1436i	−0.165676	+	0.832910i	−0.970816	+	0.239825i	$0.922910\pi$
$180$		0			0
$181$	16.6040	+	11.0944i	1.23417	+	0.824644i	0.989439	−	0.144948i	$-0.0463016\pi$
$181$	16.6040	+	11.0944i	1.23417	+	0.824644i	0.244727	+	0.969592i	$0.421302\pi$
$182$		0			0
$183$	7.40430	−	17.8756i	0.547342	−	1.32140i
$184$		0			0
$185$	1.97105	+	4.75853i	0.144914	+	0.349854i
$186$		0			0
$187$	0.280103	+	1.40817i	0.0204832	+	0.102976i
$188$		0			0
$189$	−5.42843	−	8.12423i	−0.394860	−	0.590950i
$190$		0			0
$191$	−6.26580			−0.453378			−0.226689	−	0.973967i	$-0.572790\pi$
$191$	−6.26580			−0.453378			−0.226689	+	0.973967i	$0.572790\pi$
$192$		0			0
$193$	10.7005			0.770241			0.385120	−	0.922866i	$-0.374160\pi$
$193$	10.7005			0.770241			0.385120	+	0.922866i	$0.374160\pi$
$194$		0			0
$195$	−9.35904	−	14.0068i	−0.670215	−	1.00305i
$196$		0			0
$197$	−0.0517041	−	0.259934i	−0.00368377	−	0.0185195i	0.978900	−	0.204341i	$-0.0655053\pi$
$197$	−0.0517041	−	0.259934i	−0.00368377	−	0.0185195i	−0.982583	+	0.185822i	$0.940505\pi$
$198$		0			0
$199$	−0.892313	−	2.15423i	−0.0632544	−	0.152710i	0.889092	−	0.457729i	$-0.151337\pi$
$199$	−0.892313	−	2.15423i	−0.0632544	−	0.152710i	−0.952346	+	0.305019i	$0.901337\pi$
$200$		0			0
$201$	−3.93142	+	9.49130i	−0.277301	+	0.669465i
$202$		0			0
$203$	−20.5512	−	13.7319i	−1.44241	−	0.963787i
$204$		0			0
$205$	3.29606	−	16.5704i	0.230207	−	1.15733i
$206$		0			0
$207$	−4.41436	+	4.41436i	−0.306820	+	0.306820i
$208$		0			0
$209$	0.744792	+	0.744792i	0.0515184	+	0.0515184i
$210$		0			0
$211$	−13.1481	−	2.61531i	−0.905149	−	0.180045i	−0.279496	−	0.960147i	$-0.590167\pi$
$211$	−13.1481	−	2.61531i	−0.905149	−	0.180045i	−0.625653	+	0.780101i	$0.715167\pi$
$212$		0			0
$213$	−17.5062	+	26.1999i	−1.19951	+	1.79519i
$214$		0			0
$215$	15.0930	+	6.25173i	1.02933	+	0.426364i
$216$		0			0
$217$	1.25046	−	0.517956i	0.0848866	−	0.0351612i
$218$		0			0
$219$	−34.0129	+	6.76559i	−2.29838	+	0.457176i
$220$		0			0
$221$	8.42530	−	5.62960i	0.566747	−	0.378688i
$222$		0			0
$223$			26.8359i			1.79706i	0.438907	+	0.898532i	$0.355366\pi$
$223$			26.8359i			1.79706i	−0.438907	+	0.898532i	$0.644634\pi$
$224$		0			0
$225$		−	3.78810i		−	0.252540i
$226$		0			0
$227$	1.92112	−	1.28365i	0.127509	−	0.0851989i	−0.490180	−	0.871621i	$-0.663069\pi$
$227$	1.92112	−	1.28365i	0.127509	−	0.0851989i	0.617689	+	0.786422i	$0.288069\pi$
$228$		0			0
$229$	−9.00910	+	1.79202i	−0.595338	+	0.118420i	−0.483557	−	0.875313i	$-0.660656\pi$
$229$	−9.00910	+	1.79202i	−0.595338	+	0.118420i	−0.111781	+	0.993733i	$0.535656\pi$
$230$		0			0
$231$	3.93962	−	1.63185i	0.259208	−	0.107368i
$232$		0			0
$233$	−16.3550	−	6.77448i	−1.07145	−	0.443811i	−0.223951	−	0.974600i	$-0.571896\pi$
$233$	−16.3550	−	6.77448i	−1.07145	−	0.443811i	−0.847504	+	0.530789i	$0.821896\pi$
$234$		0			0
$235$	0.288759	−	0.432158i	0.0188366	−	0.0281909i
$236$		0			0
$237$	−13.0537	−	2.59654i	−0.847928	−	0.168663i
$238$		0			0
$239$	2.35012	+	2.35012i	0.152017	+	0.152017i	0.779018	−	0.627001i	$-0.215718\pi$
$239$	2.35012	+	2.35012i	0.152017	+	0.152017i	−0.627001	+	0.779018i	$0.715718\pi$
$240$		0			0
$241$	−8.40368	+	8.40368i	−0.541329	+	0.541329i	−0.923918	−	0.382590i	$-0.875032\pi$
$241$	−8.40368	+	8.40368i	−0.541329	+	0.541329i	0.382590	+	0.923918i	$0.375032\pi$
$242$		0			0
$243$	3.57426	−	17.9690i	0.229289	−	1.15271i
$244$		0			0
$245$	−32.1522	−	21.4834i	−2.05413	−	1.37253i
$246$		0			0
$247$	2.84477	−	6.86787i	0.181008	−	0.436992i
$248$		0			0
$249$	6.88268	+	16.6162i	0.436172	+	1.05301i
$250$		0			0
$251$	−2.69294	−	13.5383i	−0.169977	−	0.854531i	−0.967816	−	0.251660i	$-0.919023\pi$
$251$	−2.69294	−	13.5383i	−0.169977	−	0.854531i	0.797839	−	0.602871i	$-0.205977\pi$
$252$		0			0
$253$	0.679425	+	1.01683i	0.0427151	+	0.0639276i
$254$		0			0
$255$	20.8301			1.30443
$256$		0			0
$257$	−8.71882			−0.543865			−0.271933	−	0.962316i	$-0.587663\pi$
$257$	−8.71882			−0.543865			−0.271933	+	0.962316i	$0.587663\pi$
$258$		0			0
$259$	5.11211	+	7.65081i	0.317651	+	0.475398i
$260$		0			0
$261$	−2.13856	−	10.7513i	−0.132374	−	0.665487i
$262$		0			0
$263$	2.14234	+	5.17205i	0.132102	+	0.318923i	0.976065	−	0.217479i	$-0.0697833\pi$
$263$	2.14234	+	5.17205i	0.132102	+	0.318923i	−0.843963	+	0.536401i	$0.819783\pi$
$264$		0			0
$265$	−0.527283	+	1.27297i	−0.0323907	+	0.0781981i
$266$		0			0
$267$	13.1058	+	8.75701i	0.802062	+	0.535921i
$268$		0			0
$269$	−0.259937	+	1.30679i	−0.0158487	+	0.0796766i	−0.987900	−	0.155091i	$-0.950433\pi$
$269$	−0.259937	+	1.30679i	−0.0158487	+	0.0796766i	0.972052	+	0.234768i	$0.0754329\pi$
$270$		0			0
$271$	−21.0223	+	21.0223i	−1.27701	+	1.27701i	−0.334682	+	0.942331i	$0.608629\pi$
$271$	−21.0223	+	21.0223i	−1.27701	+	1.27701i	−0.942331	+	0.334682i	$0.891371\pi$
$272$		0			0
$273$	−21.2805	−	21.2805i	−1.28795	−	1.28795i
$274$		0			0
$275$	−0.727804	−	0.144769i	−0.0438882	−	0.00872991i
$276$		0			0
$277$	7.36491	−	11.0224i	0.442515	−	0.662270i	−0.541430	−	0.840746i	$-0.682117\pi$
$277$	7.36491	−	11.0224i	0.442515	−	0.662270i	0.983944	+	0.178476i	$0.0571167\pi$
$278$		0			0
$279$	0.554581	+	0.229715i	0.0332019	+	0.0137527i
$280$		0			0
$281$	16.4892	−	6.83006i	0.983664	−	0.407447i	0.167883	−	0.985807i	$-0.446307\pi$
$281$	16.4892	−	6.83006i	0.983664	−	0.407447i	0.815782	+	0.578360i	$0.196307\pi$
$282$		0			0
$283$	−5.71735	+	1.13725i	−0.339861	+	0.0676026i	−0.362070	−	0.932151i	$-0.617930\pi$
$283$	−5.71735	+	1.13725i	−0.339861	+	0.0676026i	0.0222092	+	0.999753i	$0.492930\pi$
$284$		0			0
$285$	12.7059	−	8.48984i	0.752635	−	0.502895i
$286$		0			0
$287$		−	30.1831i		−	1.78165i
$288$		0			0
$289$		−	4.47035i		−	0.262962i
$290$		0			0
$291$	−30.4116	+	20.3204i	−1.78276	+	1.19120i
$292$		0			0
$293$	−0.815583	+	0.162230i	−0.0476469	+	0.00947755i	−0.218856	−	0.975757i	$-0.570233\pi$
$293$	−0.815583	+	0.162230i	−0.0476469	+	0.00947755i	0.171209	+	0.985235i	$0.445233\pi$
$294$		0			0
$295$	−13.0884	+	5.42138i	−0.762035	+	0.315645i
$296$		0			0
$297$	−0.784271	−	0.324856i	−0.0455080	−	0.0188500i
$298$		0			0
$299$	4.79511	−	7.17638i	0.277308	−	0.415021i
$300$		0			0
$301$	28.6245	+	5.69377i	1.64989	+	0.328183i
$302$		0			0
$303$	24.8795	+	24.8795i	1.42929	+	1.42929i
$304$		0			0
$305$	−15.8779	+	15.8779i	−0.909168	+	0.909168i
$306$		0			0
$307$	1.18896	−	5.97730i	0.0678574	−	0.341142i	−0.931910	−	0.362688i	$-0.881859\pi$
$307$	1.18896	−	5.97730i	0.0678574	−	0.341142i	0.999768	+	0.0215462i	$0.00685891\pi$
$308$		0			0
$309$	2.91203	+	1.94576i	0.165660	+	0.110690i
$310$		0			0
$311$	−0.557543	+	1.34603i	−0.0316154	+	0.0763262i	−0.938899	−	0.344194i	$-0.888152\pi$
$311$	−0.557543	+	1.34603i	−0.0316154	+	0.0763262i	0.907283	+	0.420520i	$0.138152\pi$
$312$		0			0
$313$	6.66243	+	16.0845i	0.376583	+	0.909151i	0.992601	+	0.121419i	$0.0387446\pi$
$313$	6.66243	+	16.0845i	0.376583	+	0.909151i	−0.616019	+	0.787732i	$0.711255\pi$
$314$		0			0
$315$	−4.92856	−	24.7776i	−0.277693	−	1.39606i
$316$		0			0
$317$	−0.843312	−	1.26210i	−0.0473651	−	0.0708869i	0.807031	−	0.590509i	$-0.201073\pi$
$317$	−0.843312	−	1.26210i	−0.0473651	−	0.0708869i	−0.854396	+	0.519622i	$0.826073\pi$
$318$		0			0
$319$	−2.14736			−0.120229
$320$		0			0
$321$	−8.62688			−0.481505
$322$		0			0
$323$	5.10677	+	7.64282i	0.284148	+	0.425258i
$324$		0			0
$325$	1.02172	+	5.13654i	0.0566749	+	0.284924i
$326$		0			0
$327$	2.46572	+	5.95276i	0.136354	+	0.329189i
$328$		0			0
$329$	0.355337	−	0.857858i	0.0195903	−	0.0472953i
$330$		0			0
$331$	27.1506	+	18.1415i	1.49233	+	0.997145i	0.991286	+	0.131726i	$0.0420518\pi$
$331$	27.1506	+	18.1415i	1.49233	+	0.997145i	0.501047	+	0.865420i	$0.332948\pi$
$332$		0			0
$333$	−0.796146	+	4.00250i	−0.0436285	+	0.219335i
$334$		0			0
$335$	8.43063	−	8.43063i	0.460615	−	0.460615i
$336$		0			0
$337$	16.9423	+	16.9423i	0.922905	+	0.922905i	0.997234	−	0.0743291i	$-0.0236815\pi$
$337$	16.9423	+	16.9423i	0.922905	+	0.922905i	−0.0743291	+	0.997234i	$0.523682\pi$
$338$		0			0
$339$	−25.9227	−	5.15634i	−1.40793	−	0.280054i
$340$		0			0
$341$	0.0653293	−	0.0977721i	0.00353778	−	0.00529466i
$342$		0			0
$343$	−33.6307	−	13.9303i	−1.81588	−	0.752164i
$344$		0			0
$345$	16.3919	−	6.78973i	0.882508	−	0.365547i
$346$		0			0
$347$	18.8803	−	3.75552i	1.01355	−	0.201607i	0.339744	−	0.940518i	$-0.389660\pi$
$347$	18.8803	−	3.75552i	1.01355	−	0.201607i	0.673803	+	0.738911i	$0.264660\pi$
$348$		0			0
$349$	−19.9458	+	13.3274i	−1.06768	+	0.713398i	−0.959777	−	0.280764i	$-0.909412\pi$
$349$	−19.9458	+	13.3274i	−1.06768	+	0.713398i	−0.107899	+	0.994162i	$0.534412\pi$
$350$		0			0
$351$			5.99111i			0.319782i
$352$		0			0
$353$		−	5.30693i		−	0.282459i	−0.989977	−	0.141230i	$-0.954894\pi$
$353$		−	5.30693i		−	0.282459i	0.989977	−	0.141230i	$-0.0451056\pi$
$354$		0			0
$355$	30.4064	−	20.3169i	1.61380	−	1.07831i
$356$		0			0
$357$	36.4981	−	7.25992i	1.93168	−	0.384236i
$358$		0			0
$359$	29.2567	−	12.1185i	1.54411	−	0.639591i	0.561871	−	0.827225i	$-0.310082\pi$
$359$	29.2567	−	12.1185i	1.54411	−	0.639591i	0.982239	+	0.187634i	$0.0600819\pi$
$360$		0			0
$361$	−11.3237	−	4.69042i	−0.595983	−	0.246864i
$362$		0			0
$363$	−13.5555	+	20.2873i	−0.711480	+	1.06481i
$364$		0			0
$365$	39.4738	+	7.85183i	2.06615	+	0.410983i
$366$		0			0
$367$	10.7708	+	10.7708i	0.562232	+	0.562232i	0.929941	−	0.367709i	$-0.119858\pi$
$367$	10.7708	+	10.7708i	0.562232	+	0.562232i	−0.367709	+	0.929941i	$0.619858\pi$
$368$		0			0
$369$	9.46551	−	9.46551i	0.492755	−	0.492755i
$370$		0			0
$371$	−0.480223	+	2.41425i	−0.0249319	+	0.125341i
$372$		0			0
$373$	−7.80692	−	5.21641i	−0.404227	−	0.270096i	0.336793	−	0.941579i	$-0.390658\pi$
$373$	−7.80692	−	5.21641i	−0.404227	−	0.270096i	−0.741020	+	0.671483i	$0.765658\pi$
$374$		0			0
$375$	7.13992	−	17.2373i	0.368704	−	0.890129i
$376$		0			0
$377$	5.79965	+	14.0016i	0.298697	+	0.721119i
$378$		0			0
$379$	−2.74905	−	13.8204i	−0.141209	−	0.709906i	−0.984907	−	0.173087i	$-0.944626\pi$
$379$	−2.74905	−	13.8204i	−0.141209	−	0.709906i	0.843697	−	0.536819i	$-0.180374\pi$
$380$		0			0
$381$	−9.02574	−	13.5080i	−0.462403	−	0.692035i
$382$		0			0
$383$	−15.8956			−0.812226			−0.406113	−	0.913823i	$-0.633116\pi$
$383$	−15.8956			−0.812226			−0.406113	+	0.913823i	$0.633116\pi$
$384$		0			0
$385$	−4.94885			−0.252217
$386$		0			0
$387$	7.19116	+	10.7623i	0.365547	+	0.547080i
$388$		0			0
$389$	−2.40830	−	12.1074i	−0.122106	−	0.613867i	−0.992574	−	0.121643i	$-0.961184\pi$
$389$	−2.40830	−	12.1074i	−0.122106	−	0.613867i	0.870468	−	0.492225i	$-0.163816\pi$
$390$		0			0
$391$	4.08412	+	9.85995i	0.206543	+	0.498639i
$392$		0			0
$393$	9.68640	−	23.3850i	0.488614	−	1.17962i
$394$		0			0
$395$	12.8431	+	8.58149i	0.646207	+	0.431782i
$396$		0			0
$397$	−0.557626	+	2.80338i	−0.0279864	+	0.140697i	−0.992252	−	0.124239i	$-0.960351\pi$
$397$	−0.557626	+	2.80338i	−0.0279864	+	0.140697i	0.964266	+	0.264937i	$0.0853510\pi$
$398$		0			0
$399$	19.3041	−	19.3041i	0.966413	−	0.966413i
$400$		0			0
$401$	12.5125	+	12.5125i	0.624843	+	0.624843i	0.946766	−	0.321923i	$-0.104329\pi$
$401$	12.5125	+	12.5125i	0.624843	+	0.624843i	−0.321923	+	0.946766i	$0.604329\pi$
$402$		0			0
$403$	−0.813953	−	0.161905i	−0.0405459	−	0.00806508i
$404$		0			0
$405$	−15.8610	+	23.7377i	−0.788141	+	1.17954i
$406$		0			0
$407$	0.738570	+	0.305926i	0.0366096	+	0.0151642i
$408$		0			0
$409$	−9.49266	+	3.93199i	−0.469382	+	0.194424i	−0.604821	−	0.796361i	$-0.706755\pi$
$409$	−9.49266	+	3.93199i	−0.469382	+	0.194424i	0.135439	+	0.990786i	$0.456755\pi$
$410$		0			0
$411$	26.5062	−	5.27241i	1.30745	−	0.260069i
$412$		0			0
$413$	−21.0436	+	14.0609i	−1.03549	+	0.691891i
$414$		0			0
$415$		−	20.8729i		−	1.02461i
$416$		0			0
$417$			35.5446i			1.74063i
$418$		0			0
$419$	−7.10316	+	4.74618i	−0.347012	+	0.231866i	−0.716846	−	0.697232i	$-0.754415\pi$
$419$	−7.10316	+	4.74618i	−0.347012	+	0.231866i	0.369834	+	0.929098i	$0.379415\pi$
$420$		0			0
$421$	−5.75098	+	1.14394i	−0.280286	+	0.0557523i	−0.333231	−	0.942845i	$-0.608139\pi$
$421$	−5.75098	+	1.14394i	−0.280286	+	0.0557523i	0.0529457	+	0.998597i	$0.483139\pi$
$422$		0			0
$423$	0.380462	−	0.157593i	0.0184987	−	0.00766241i
$424$		0			0
$425$	−5.98291	−	2.47820i	−0.290214	−	0.120210i
$426$		0			0
$427$	−22.2870	+	33.3549i	−1.07854	+	1.61416i
$428$		0			0
$429$	−2.56440	−	0.510090i	−0.123810	−	0.0246274i
$430$		0			0
$431$	−26.6006	−	26.6006i	−1.28131	−	1.28131i	−0.939924	−	0.341384i	$-0.889104\pi$
$431$	−26.6006	−	26.6006i	−1.28131	−	1.28131i	−0.341384	−	0.939924i	$-0.610896\pi$
$432$		0			0
$433$	1.87012	−	1.87012i	0.0898724	−	0.0898724i	−0.660741	−	0.750614i	$-0.729758\pi$
$433$	1.87012	−	1.87012i	0.0898724	−	0.0898724i	0.750614	+	0.660741i	$0.229758\pi$
$434$		0			0
$435$	−6.07787	+	30.5555i	−0.291412	+	1.46502i
$436$		0			0
$437$	6.50989	+	4.34977i	0.311410	+	0.208078i
$438$		0			0
$439$	−3.81047	+	9.19929i	−0.181864	+	0.439058i	−0.988351	−	0.152194i	$-0.951366\pi$
$439$	−3.81047	+	9.19929i	−0.181864	+	0.439058i	0.806487	+	0.591252i	$0.201366\pi$
$440$		0			0
$441$	−11.7248	−	28.3061i	−0.558322	−	1.34791i
$442$		0			0
$443$	2.30288	+	11.5774i	0.109413	+	0.550057i	0.996141	+	0.0877657i	$0.0279727\pi$
$443$	2.30288	+	11.5774i	0.109413	+	0.550057i	−0.886728	+	0.462292i	$0.847027\pi$
$444$		0			0
$445$	−10.1630	−	15.2100i	−0.481771	−	0.721021i
$446$		0			0
$447$	−43.9990			−2.08108
$448$		0			0
$449$	34.7985			1.64224			0.821122	−	0.570753i	$-0.193349\pi$
$449$	34.7985			1.64224			0.821122	+	0.570753i	$0.193349\pi$
$450$		0			0
$451$	−1.45686	−	2.18034i	−0.0686008	−	0.102668i
$452$		0			0
$453$	5.94370	+	29.8810i	0.279260	+	1.40393i
$454$		0			0
$455$	13.3660	+	32.2683i	0.626606	+	1.51276i
$456$		0			0
$457$	−9.80367	+	23.6682i	−0.458596	+	1.10715i	0.510369	+	0.859955i	$0.329509\pi$
$457$	−9.80367	+	23.6682i	−0.458596	+	1.10715i	−0.968966	+	0.247195i	$0.920491\pi$
$458$		0			0
$459$	−6.15962	−	4.11573i	−0.287506	−	0.192106i
$460$		0			0
$461$	−7.22385	+	36.3168i	−0.336448	+	1.69144i	0.328463	+	0.944517i	$0.393470\pi$
$461$	−7.22385	+	36.3168i	−0.336448	+	1.69144i	−0.664911	+	0.746923i	$0.731530\pi$
$462$		0			0
$463$	−20.4267	+	20.4267i	−0.949309	+	0.949309i	−0.998776	−	0.0494671i	$-0.984248\pi$
$463$	−20.4267	+	20.4267i	−0.949309	+	0.949309i	0.0494671	+	0.998776i	$0.484248\pi$
$464$		0			0
$465$	−1.20632	−	1.20632i	−0.0559419	−	0.0559419i
$466$		0			0
$467$	13.6740	+	2.71993i	0.632758	+	0.125863i	0.501041	−	0.865424i	$-0.332951\pi$
$467$	13.6740	+	2.71993i	0.632758	+	0.125863i	0.131718	+	0.991287i	$0.457951\pi$
$468$		0			0
$469$	11.8336	−	17.7103i	0.546426	−	0.817784i
$470$		0			0
$471$	−20.6810	−	8.56633i	−0.952928	−	0.394716i
$472$		0			0
$473$	2.34258	−	0.970329i	0.107712	−	0.0446158i
$474$		0			0
$475$	−4.65950	+	0.926832i	−0.213792	+	0.0425260i
$476$		0			0
$477$	−0.907715	+	0.606516i	−0.0415614	+	0.0277705i
$478$		0			0
$479$			12.6579i			0.578354i	0.957276	+	0.289177i	$0.0933816\pi$
$479$			12.6579i			0.578354i	−0.957276	+	0.289177i	$0.906618\pi$
$480$		0			0
$481$		−	5.64200i		−	0.257253i
$482$		0			0
$483$	26.3550	−	17.6098i	1.19919	−	0.801275i
$484$		0			0
$485$	41.6325	−	8.28121i	1.89043	−	0.376030i
$486$		0			0
$487$	−11.3843	+	4.71555i	−0.515874	+	0.213682i	−0.625404	−	0.780302i	$-0.715066\pi$
$487$	−11.3843	+	4.71555i	−0.515874	+	0.213682i	0.109529	+	0.993984i	$0.465066\pi$
$488$		0			0
$489$	−42.3586	−	17.5455i	−1.91552	−	0.793435i
$490$		0			0
$491$	17.7122	−	26.5081i	0.799339	−	1.19629i	−0.177878	−	0.984052i	$-0.556923\pi$
$491$	17.7122	−	26.5081i	0.799339	−	1.19629i	0.977217	−	0.212242i	$-0.0680767\pi$
$492$		0			0
$493$	−18.3796	−	3.65593i	−0.827776	−	0.164655i
$494$		0			0
$495$	−1.55198	−	1.55198i	−0.0697561	−	0.0697561i
$496$		0			0
$497$	46.1963	−	46.1963i	2.07219	−	2.07219i
$498$		0			0
$499$	7.59034	−	38.1592i	0.339790	−	1.70824i	−0.312202	−	0.950016i	$-0.601067\pi$
$499$	7.59034	−	38.1592i	0.339790	−	1.70824i	0.651992	−	0.758226i	$-0.273933\pi$
$500$		0			0
$501$	−12.3780	−	8.27069i	−0.553006	−	0.369507i
$502$		0			0
$503$	−2.13613	+	5.15707i	−0.0952452	+	0.229942i	−0.964320	−	0.264738i	$-0.914715\pi$
$503$	−2.13613	+	5.15707i	−0.0952452	+	0.229942i	0.869075	+	0.494680i	$0.164715\pi$
$504$		0			0
$505$	−15.6265	−	37.7257i	−0.695370	−	1.67877i
$506$		0			0
$507$	−2.11094	−	10.6124i	−0.0937500	−	0.471313i
$508$		0			0
$509$	−18.2483	−	27.3106i	−0.808843	−	1.21052i	−0.974511	−	0.224338i	$-0.927978\pi$
$509$	−18.2483	−	27.3106i	−0.808843	−	1.21052i	0.165668	−	0.986182i	$-0.447022\pi$
$510$		0			0
$511$	71.9016			3.18074
$512$		0			0
$513$	−5.43470			−0.239948
$514$		0			0
$515$	−2.25815	−	3.37956i	−0.0995061	−	0.148921i
$516$		0			0
$517$	−0.0157381	−	0.0791206i	−0.000692159	−	0.00347972i
$518$		0			0
$519$	2.07720	+	5.01481i	0.0911791	+	0.220126i
$520$		0			0
$521$	8.78528	−	21.2095i	0.384890	−	0.929207i	−0.606114	−	0.795378i	$-0.707273\pi$
$521$	8.78528	−	21.2095i	0.384890	−	0.929207i	0.991004	−	0.133829i	$-0.0427274\pi$
$522$		0			0
$523$	6.37316	+	4.25841i	0.278679	+	0.186207i	0.687053	−	0.726607i	$-0.258904\pi$
$523$	6.37316	+	4.25841i	0.278679	+	0.186207i	−0.408374	+	0.912815i	$0.633904\pi$
$524$		0			0
$525$	−3.75223	+	18.8638i	−0.163761	+	0.823282i
$526$		0			0
$527$	0.725622	−	0.725622i	0.0316086	−	0.0316086i
$528$		0			0
$529$	−9.83562	−	9.83562i	−0.427636	−	0.427636i
$530$		0			0
$531$	−11.0089	−	2.18981i	−0.477745	−	0.0950295i
$532$		0			0
$533$	−10.2819	+	15.3880i	−0.445359	+	0.666527i
$534$		0			0
$535$	9.24983	+	3.83140i	0.399905	+	0.165646i
$536$		0			0
$537$	23.6371	−	9.79083i	1.02002	−	0.422505i
$538$		0			0
$539$	−5.88651	+	1.17090i	−0.253550	+	0.0504342i
$540$		0			0
$541$	−30.0903	+	20.1057i	−1.29368	+	0.864412i	−0.995921	−	0.0902276i	$-0.971241\pi$
$541$	−30.0903	+	20.1057i	−1.29368	+	0.864412i	−0.297763	+	0.954640i	$0.596241\pi$
$542$		0			0
$543$		−	44.9672i		−	1.92973i
$544$		0			0
$545$		−	7.47770i		−	0.320309i
$546$		0			0
$547$	−9.47625	+	6.33183i	−0.405175	+	0.270729i	−0.741415	−	0.671047i	$-0.765845\pi$
$547$	−9.47625	+	6.33183i	−0.405175	+	0.270729i	0.336239	+	0.941777i	$0.390845\pi$
$548$		0			0
$549$	−17.4495	+	3.47092i	−0.744726	+	0.148135i
$550$		0			0
$551$	−12.7012	+	5.26102i	−0.541090	+	0.224127i
$552$		0			0
$553$	25.4943	+	10.5601i	1.08413	+	0.449060i
$554$		0			0
$555$	6.44356	−	9.64346i	0.273514	−	0.409342i
$556$		0			0
$557$	−31.7111	−	6.30773i	−1.34364	−	0.267267i	−0.529686	−	0.848194i	$-0.677690\pi$
$557$	−31.7111	−	6.30773i	−1.34364	−	0.267267i	−0.813956	+	0.580927i	$0.802690\pi$
$558$		0			0
$559$	−12.6538	−	12.6538i	−0.535199	−	0.535199i
$560$		0			0
$561$	2.28611	−	2.28611i	0.0965194	−	0.0965194i
$562$		0			0
$563$	−8.24892	+	41.4701i	−0.347650	+	1.74776i	0.271457	+	0.962451i	$0.412494\pi$
$563$	−8.24892	+	41.4701i	−0.347650	+	1.74776i	−0.619108	+	0.785306i	$0.712506\pi$
$564$		0			0
$565$	25.5045	+	17.0416i	1.07298	+	0.716944i
$566$		0			0
$567$	−19.5180	+	47.1207i	−0.819680	+	1.97888i
$568$		0			0
$569$	12.0106	+	28.9961i	0.503509	+	1.21558i	0.947560	+	0.319577i	$0.103541\pi$
$569$	12.0106	+	28.9961i	0.503509	+	1.21558i	−0.444051	+	0.896001i	$0.646459\pi$
$570$		0			0
$571$	−0.546501	−	2.74744i	−0.0228703	−	0.114977i	0.967664	−	0.252243i	$-0.0811684\pi$
$571$	−0.546501	−	2.74744i	−0.0228703	−	0.114977i	−0.990534	+	0.137266i	$0.956168\pi$
$572$		0			0
$573$	7.83871	+	11.7315i	0.327467	+	0.490089i
$574$		0			0
$575$	−5.51591			−0.230030
$576$		0			0
$577$	−24.8273			−1.03357			−0.516787	−	0.856114i	$-0.672872\pi$
$577$	−24.8273			−1.03357			−0.516787	+	0.856114i	$0.672872\pi$
$578$		0			0
$579$	−13.3867	−	20.0346i	−0.556332	−	0.832609i
$580$		0			0
$581$	−7.27481	−	36.5729i	−0.301810	−	1.51730i
$582$		0			0
$583$	0.0818394	+	0.197578i	0.00338944	+	0.00818283i
$584$		0			0
$585$	−5.92784	+	14.3111i	−0.245086	+	0.591690i
$586$		0			0
$587$	8.37191	+	5.59393i	0.345546	+	0.230886i	0.716217	−	0.697878i	$-0.245872\pi$
$587$	8.37191	+	5.59393i	0.345546	+	0.230886i	−0.370671	+	0.928764i	$0.620872\pi$
$588$		0			0
$589$	0.146869	−	0.738359i	0.00605162	−	0.0304236i
$590$		0			0
$591$	−0.421991	+	0.421991i	−0.0173584	+	0.0173584i
$592$		0			0
$593$	−28.3397	−	28.3397i	−1.16377	−	1.16377i	−0.983643	−	0.180131i	$-0.942348\pi$
$593$	−28.3397	−	28.3397i	−1.16377	−	1.16377i	−0.180131	−	0.983643i	$-0.557652\pi$
$594$		0			0
$595$	−42.3579	−	8.42552i	−1.73651	−	0.345412i
$596$		0			0
$597$	−2.91706	+	4.36569i	−0.119387	+	0.178676i
$598$		0			0
$599$	4.40247	+	1.82356i	0.179880	+	0.0745087i	0.470806	−	0.882237i	$-0.343963\pi$
$599$	4.40247	+	1.82356i	0.179880	+	0.0745087i	−0.290926	+	0.956746i	$0.593963\pi$
$600$		0			0
$601$	−2.66779	+	1.10504i	−0.108822	+	0.0450754i	−0.436430	−	0.899738i	$-0.643757\pi$
$601$	−2.66779	+	1.10504i	−0.108822	+	0.0450754i	0.327608	+	0.944814i	$0.393757\pi$
$602$		0			0
$603$	9.26507	−	1.84294i	0.377303	−	0.0750502i
$604$		0			0
$605$	23.5444	−	15.7319i	0.957217	−	0.639592i
$606$		0			0
$607$		−	46.5933i		−	1.89116i	−0.325386	−	0.945581i	$-0.605494\pi$
$607$		−	46.5933i		−	1.89116i	0.325386	−	0.945581i	$-0.394506\pi$
$608$		0			0
$609$			55.6569i			2.25533i
$610$		0			0
$611$	−0.473389	+	0.316309i	−0.0191513	+	0.0127965i
$612$		0			0
$613$	−18.2485	+	3.62984i	−0.737048	+	0.146608i	−0.549319	−	0.835613i	$-0.685113\pi$
$613$	−18.2485	+	3.62984i	−0.737048	+	0.146608i	−0.187729	+	0.982221i	$0.560113\pi$
$614$		0			0
$615$	−35.1483	+	14.5589i	−1.41732	+	0.587071i
$616$		0			0
$617$	−26.6169	−	11.0251i	−1.07155	−	0.443852i	−0.224016	−	0.974586i	$-0.571917\pi$
$617$	−26.6169	−	11.0251i	−1.07155	−	0.443852i	−0.847539	+	0.530733i	$0.821917\pi$
$618$		0			0
$619$	−6.76585	+	10.1258i	−0.271942	+	0.406990i	−0.942154	−	0.335179i	$-0.891203\pi$
$619$	−6.76585	+	10.1258i	−0.271942	+	0.406990i	0.670212	+	0.742170i	$0.266203\pi$
$620$		0			0
$621$	−6.18874	−	1.23102i	−0.248345	−	0.0493990i
$622$		0			0
$623$	−23.1084	−	23.1084i	−0.925820	−	0.925820i
$624$		0			0
$625$	−21.7792	+	21.7792i	−0.871167	+	0.871167i
$626$		0			0
$627$	0.462717	−	2.32623i	0.0184791	−	0.0929008i
$628$		0			0
$629$	5.80069	+	3.87590i	0.231289	+	0.154542i
$630$		0			0
$631$	−0.364096	+	0.879005i	−0.0144944	+	0.0349926i	−0.930961	−	0.365118i	$-0.881028\pi$
$631$	−0.364096	+	0.879005i	−0.0144944	+	0.0349926i	0.916467	+	0.400111i	$0.131028\pi$
$632$		0			0
$633$	11.5520	+	27.8889i	0.459150	+	1.10849i
$634$		0			0
$635$	3.67828	+	18.4919i	0.145968	+	0.733831i
$636$		0			0
$637$	23.5331	+	35.2198i	0.932416	+	1.39546i
$638$		0			0
$639$	28.9746			1.14622
$640$		0			0
$641$	23.8243			0.941002			0.470501	−	0.882399i	$-0.344073\pi$
$641$	23.8243			0.941002			0.470501	+	0.882399i	$0.344073\pi$
$642$		0			0
$643$	25.7461	+	38.5318i	1.01533	+	1.51954i	0.845432	+	0.534083i	$0.179343\pi$
$643$	25.7461	+	38.5318i	1.01533	+	1.51954i	0.169895	+	0.985462i	$0.445657\pi$
$644$		0			0
$645$	−7.17670	−	36.0797i	−0.282582	−	1.42064i
$646$		0			0
$647$	−13.2165	−	31.9073i	−0.519592	−	1.25441i	−0.938154	−	0.346219i	$-0.887466\pi$
$647$	−13.2165	−	31.9073i	−0.519592	−	1.25441i	0.418561	−	0.908188i	$-0.362534\pi$
$648$		0			0
$649$	−0.841451	+	2.03144i	−0.0330298	+	0.0797411i
$650$		0			0
$651$	−2.53413	−	1.69325i	−0.0993204	−	0.0663638i
$652$		0			0
$653$	2.10914	−	10.6034i	0.0825371	−	0.414942i	−0.917322	−	0.398146i	$-0.869654\pi$
$653$	2.10914	−	10.6034i	0.0825371	−	0.414942i	0.999859	−	0.0167955i	$-0.00534643\pi$
$654$		0			0
$655$	−20.7717	+	20.7717i	−0.811618	+	0.811618i
$656$		0			0
$657$	22.5486	+	22.5486i	0.879704	+	0.879704i
$658$		0			0
$659$	−19.8824	−	3.95485i	−0.774508	−	0.154059i	−0.208015	−	0.978126i	$-0.566700\pi$
$659$	−19.8824	−	3.95485i	−0.774508	−	0.154059i	−0.566493	+	0.824067i	$0.691700\pi$
$660$		0			0
$661$	1.28231	−	1.91911i	0.0498760	−	0.0746447i	−0.805694	−	0.592333i	$-0.798207\pi$
$661$	1.28231	−	1.91911i	0.0498760	−	0.0746447i	0.855570	+	0.517688i	$0.173207\pi$
$662$		0			0
$663$	−21.0806	−	8.73188i	−0.818703	−	0.339118i
$664$		0			0
$665$	−29.2714	+	12.1246i	−1.13510	+	0.470173i
$666$		0			0
$667$	−15.6551	+	3.11400i	−0.606169	+	0.120574i
$668$		0			0
$669$	50.2449	−	33.5725i	1.94258	−	1.29799i
$670$		0			0
$671$			3.48520i			0.134545i
$672$		0			0
$673$			9.14126i			0.352370i	0.984357	+	0.176185i	$0.0563756\pi$
$673$			9.14126i			0.352370i	−0.984357	+	0.176185i	$0.943624\pi$
$674$		0			0
$675$	3.18355	−	2.12718i	0.122535	−	0.0818753i
$676$		0			0
$677$	41.3684	−	8.22868i	1.58992	−	0.316254i	0.680695	−	0.732567i	$-0.261678\pi$
$677$	41.3684	−	8.22868i	1.58992	−	0.316254i	0.909221	+	0.416313i	$0.136678\pi$
$678$		0			0
$679$	70.0611	−	29.0203i	2.68870	−	1.11370i
$680$		0			0
$681$	−4.80676	−	1.99103i	−0.184195	−	0.0762963i
$682$		0			0
$683$	17.8505	−	26.7151i	0.683029	−	1.02223i	−0.314310	−	0.949321i	$-0.601773\pi$
$683$	17.8505	−	26.7151i	0.683029	−	1.02223i	0.997339	−	0.0729051i	$-0.0232270\pi$
$684$		0			0
$685$	−30.7618	−	6.11891i	−1.17535	−	0.233791i
$686$		0			0
$687$	14.6259	+	14.6259i	0.558012	+	0.558012i
$688$		0			0
$689$	1.06725	−	1.06725i	0.0406588	−	0.0406588i
$690$		0			0
$691$	−3.87095	+	19.4606i	−0.147258	+	0.740315i	0.834624	+	0.550820i	$0.185685\pi$
$691$	−3.87095	+	19.4606i	−0.147258	+	0.740315i	−0.981882	+	0.189495i	$0.939315\pi$
$692$		0			0
$693$	−3.26024	−	2.17842i	−0.123846	−	0.0827515i
$694$		0			0
$695$	15.7862	−	38.1113i	0.598805	−	1.44564i
$696$		0			0
$697$	−8.75739	−	21.1422i	−0.331710	−	0.800819i
$698$		0			0
$699$	7.77681	+	39.0966i	0.294146	+	1.47877i
$700$		0			0
$701$	15.9568	+	23.8811i	0.602681	+	0.901976i	0.999876	−	0.0157585i	$-0.00501628\pi$
$701$	15.9568	+	23.8811i	0.602681	+	0.901976i	−0.397195	+	0.917734i	$0.630016\pi$
$702$		0			0
$703$	5.11801			0.193029
$704$		0			0
$705$	−1.17038			−0.0440789
$706$		0			0
$707$	−40.5289	−	60.6557i	−1.52424	−	2.28119i
$708$		0			0
$709$	3.15652	+	15.8689i	0.118546	+	0.595969i	0.993695	+	0.112116i	$0.0357629\pi$
$709$	3.15652	+	15.8689i	0.118546	+	0.595969i	−0.875149	+	0.483853i	$0.839237\pi$
$710$		0			0
$711$	4.68342	+	11.3068i	0.175642	+	0.424037i
$712$		0			0
$713$	0.334492	−	0.807535i	0.0125268	−	0.0302424i
$714$		0			0
$715$	2.52303	+	1.68583i	0.0943560	+	0.0630466i
$716$		0			0
$717$	1.46006	−	7.34021i	0.0545269	−	0.274125i
$718$		0			0
$719$	−15.3302	+	15.3302i	−0.571719	+	0.571719i	−0.932609	−	0.360889i	$-0.882473\pi$
$719$	−15.3302	+	15.3302i	−0.571719	+	0.571719i	0.360889	+	0.932609i	$0.382473\pi$
$720$		0			0
$721$	−5.13455	−	5.13455i	−0.191221	−	0.191221i
$722$		0			0
$723$	26.2475	+	5.22095i	0.976154	+	0.194169i
$724$		0			0
$725$	5.38095	−	8.05317i	0.199844	−	0.299087i
$726$		0			0
$727$	29.8242	+	12.3536i	1.10612	+	0.458169i	0.859599	−	0.510969i	$-0.170713\pi$
$727$	29.8242	+	12.3536i	1.10612	+	0.458169i	0.246519	+	0.969138i	$0.420713\pi$
$728$		0			0
$729$	−7.83631	+	3.24591i	−0.290234	+	0.120219i
$730$		0			0
$731$	21.7025	−	4.31690i	0.802696	−	0.159666i
$732$		0			0
$733$	25.9985	−	17.3717i	0.960278	−	0.641637i	0.0265602	−	0.999647i	$-0.491545\pi$
$733$	25.9985	−	17.3717i	0.960278	−	0.641637i	0.933718	+	0.358010i	$0.116545\pi$
$734$		0			0
$735$			87.0751i			3.21181i
$736$		0			0
$737$		−	1.85052i		−	0.0681648i
$738$		0			0
$739$	−2.73845	+	1.82977i	−0.100735	+	0.0673092i	−0.604918	−	0.796288i	$-0.706794\pi$
$739$	−2.73845	+	1.82977i	−0.100735	+	0.0673092i	0.504182	+	0.863597i	$0.331794\pi$
$740$		0			0
$741$	−16.4176	+	3.26567i	−0.603116	+	0.119967i
$742$		0			0
$743$	−2.57199	+	1.06535i	−0.0943570	+	0.0390840i	−0.429363	−	0.903132i	$-0.641262\pi$
$743$	−2.57199	+	1.06535i	−0.0943570	+	0.0390840i	0.335006	+	0.942216i	$0.391262\pi$
$744$		0			0
$745$	47.1762	+	19.5410i	1.72840	+	0.715928i
$746$		0			0
$747$	9.18800	−	13.7508i	0.336171	−	0.503116i
$748$		0			0
$749$	17.5427	+	3.48946i	0.640996	+	0.127502i
$750$		0			0
$751$	10.0944	+	10.0944i	0.368350	+	0.368350i	0.866875	−	0.498525i	$-0.166125\pi$
$751$	10.0944	+	10.0944i	0.368350	+	0.368350i	−0.498525	+	0.866875i	$0.666125\pi$
$752$		0			0
$753$	−21.9788	+	21.9788i	−0.800954	+	0.800954i
$754$		0			0
$755$	6.89798	−	34.6785i	0.251043	−	1.26208i
$756$		0			0
$757$	0.275639	+	0.184176i	0.0100183	+	0.00669400i	0.560569	−	0.828108i	$-0.310582\pi$
$757$	0.275639	+	0.184176i	0.0100183	+	0.00669400i	−0.550551	+	0.834802i	$0.685582\pi$
$758$		0			0
$759$	1.05383	−	2.54418i	0.0382517	−	0.0923477i
$760$		0			0
$761$	−14.0734	−	33.9761i	−0.510160	−	1.23163i	−0.943791	−	0.330544i	$-0.892768\pi$
$761$	−14.0734	−	33.9761i	−0.510160	−	1.23163i	0.433631	−	0.901091i	$-0.357232\pi$
$762$		0			0
$763$	−2.60620	−	13.1022i	−0.0943507	−	0.474333i
$764$		0			0
$765$	−10.6413	−	15.9259i	−0.384738	−	0.575801i
$766$		0			0
$767$	15.5184			0.560336
$768$		0			0
$769$	10.1509			0.366049			0.183025	−	0.983108i	$-0.441411\pi$
$769$	10.1509			0.366049			0.183025	+	0.983108i	$0.441411\pi$
$770$		0			0
$771$	10.9075	+	16.3243i	0.392825	+	0.587904i
$772$		0			0
$773$	1.32796	+	6.67611i	0.0477634	+	0.240123i	0.997291	−	0.0735616i	$-0.0234366\pi$
$773$	1.32796	+	6.67611i	0.0477634	+	0.240123i	−0.949527	+	0.313685i	$0.898437\pi$
$774$		0			0
$775$	0.202966	+	0.490003i	0.00729076	+	0.0176014i
$776$		0			0
$777$	7.92921	−	19.1428i	0.284459	−	0.686744i
$778$		0			0
$779$	−13.9589	−	9.32701i	−0.500128	−	0.334175i
$780$		0			0
$781$	1.10732	−	5.56687i	0.0396230	−	0.199198i
$782$		0			0
$783$	7.83458	−	7.83458i	0.279985	−	0.279985i
$784$		0			0
$785$	18.3698	+	18.3698i	0.655647	+	0.655647i
$786$		0			0
$787$	1.70358	+	0.338863i	0.0607260	+	0.0120792i	0.225360	−	0.974276i	$-0.427644\pi$
$787$	1.70358	+	0.338863i	0.0607260	+	0.0120792i	−0.164634	+	0.986355i	$0.552644\pi$
$788$		0			0
$789$	7.00351	−	10.4815i	0.249332	−	0.373151i
$790$		0			0
$791$	50.6278	+	20.9707i	1.80012	+	0.745633i
$792$		0			0
$793$	22.7248	−	9.41292i	0.806982	−	0.334263i
$794$		0			0
$795$	3.04303	−	0.605297i	0.107925	−	0.0214677i
$796$		0			0
$797$	−17.9770	+	12.0118i	−0.636777	+	0.425481i	−0.831613	−	0.555355i	$-0.812582\pi$
$797$	−17.9770	+	12.0118i	−0.636777	+	0.425481i	0.194837	+	0.980836i	$0.437582\pi$
$798$		0			0
$799$		−	0.703999i		−	0.0249057i
$800$		0			0
$801$		−	14.4938i		−	0.512112i
$802$		0			0
$803$	5.19398	−	3.47051i	0.183292	−	0.122471i
$804$		0			0
$805$	−36.0790	+	7.17657i	−1.27162	+	0.252941i
$806$		0			0
$807$	2.77190	−	1.14816i	0.0975755	−	0.0404171i
$808$		0			0
$809$	13.9376	+	5.77316i	0.490022	+	0.202974i	0.613992	−	0.789312i	$-0.289563\pi$
$809$	13.9376	+	5.77316i	0.490022	+	0.202974i	−0.123970	+	0.992286i	$0.539563\pi$
$810$		0			0
$811$	−18.5133	+	27.7071i	−0.650091	+	0.972929i	0.349265	+	0.937024i	$0.386431\pi$
$811$	−18.5133	+	27.7071i	−0.650091	+	0.972929i	−0.999355	+	0.0359051i	$0.988569\pi$
$812$		0			0
$813$	65.6596	+	13.0605i	2.30278	+	0.458052i
$814$		0			0
$815$	37.6249	+	37.6249i	1.31794	+	1.31794i
$816$		0			0
$817$	11.4786	−	11.4786i	0.401585	−	0.401585i
$818$		0			0
$819$	−5.39878	+	27.1415i	−0.188649	+	0.948401i
$820$		0			0
$821$	−19.6678	−	13.1416i	−0.686411	−	0.458645i	0.162828	−	0.986655i	$-0.447939\pi$
$821$	−19.6678	−	13.1416i	−0.686411	−	0.458645i	−0.849238	+	0.528010i	$0.822939\pi$
$822$		0			0
$823$	−2.61584	+	6.31520i	−0.0911825	+	0.220134i	−0.962891	−	0.269891i	$-0.913012\pi$
$823$	−2.61584	+	6.31520i	−0.0911825	+	0.220134i	0.871708	+	0.490025i	$0.163012\pi$
$824$		0			0
$825$	0.639454	+	1.54378i	0.0222629	+	0.0537474i
$826$		0			0
$827$	−6.84993	−	34.4369i	−0.238195	−	1.19749i	−0.895915	−	0.444226i	$-0.853479\pi$
$827$	−6.84993	−	34.4369i	−0.238195	−	1.19749i	0.657720	−	0.753263i	$-0.271521\pi$
$828$		0			0
$829$	−19.9509	−	29.8586i	−0.692922	−	1.03703i	−0.996448	−	0.0842078i	$-0.973164\pi$
$829$	−19.9509	−	29.8586i	−0.692922	−	1.03703i	0.303526	−	0.952823i	$-0.401836\pi$
$830$		0			0
$831$	−29.8509			−1.03552
$832$		0			0
$833$	−52.3770			−1.81475
$834$		0			0
$835$	9.59856	+	14.3653i	0.332172	+	0.497131i
$836$		0			0
$837$	0.118367	+	0.595070i	0.00409136	+	0.0205686i
$838$		0			0
$839$	−3.33667	−	8.05543i	−0.115195	−	0.278104i	0.855758	−	0.517376i	$-0.173091\pi$
$839$	−3.33667	−	8.05543i	−0.115195	−	0.278104i	−0.970953	+	0.239272i	$0.923091\pi$
$840$		0			0
$841$	−0.372134	+	0.898412i	−0.0128322	+	0.0309797i
$842$		0			0
$843$	−33.4164	−	22.3282i	−1.15092	−	0.769023i
$844$		0			0
$845$	−2.44985	+	12.3162i	−0.0842775	+	0.423692i
$846$		0			0
$847$	35.7710	−	35.7710i	1.22910	−	1.22910i
$848$		0			0
$849$	9.28186	+	9.28186i	0.318553	+	0.318553i
$850$		0			0
$851$	5.82811	+	1.15928i	0.199785	+	0.0397397i
$852$		0			0
$853$	24.2816	−	36.3400i	0.831387	−	1.24426i	−0.135938	−	0.990717i	$-0.543405\pi$
$853$	24.2816	−	36.3400i	0.831387	−	1.24426i	0.967325	−	0.253541i	$-0.0815952\pi$
$854$		0			0
$855$	−12.9820	−	5.37730i	−0.443973	−	0.183900i
$856$		0			0
$857$	−20.2153	+	8.37347i	−0.690543	+	0.286032i	−0.700226	−	0.713921i	$-0.746918\pi$
$857$	−20.2153	+	8.37347i	−0.690543	+	0.286032i	0.00968359	+	0.999953i	$0.496918\pi$
$858$		0			0
$859$	−4.64811	+	0.924566i	−0.158591	+	0.0315458i	−0.273747	−	0.961802i	$-0.588263\pi$
$859$	−4.64811	+	0.924566i	−0.158591	+	0.0315458i	0.115156	+	0.993347i	$0.463263\pi$
$860$		0			0
$861$	−56.5117	+	37.7599i	−1.92592	+	1.28686i
$862$		0			0
$863$			53.4875i			1.82074i	0.413799	+	0.910368i	$0.364202\pi$
$863$			53.4875i			1.82074i	−0.413799	+	0.910368i	$0.635798\pi$
$864$		0			0
$865$		−	6.29947i		−	0.214188i
$866$		0			0
$867$	−8.36984	+	5.59255i	−0.284255	+	0.189933i
$868$		0			0
$869$	2.35135	−	0.467712i	0.0797640	−	0.0158660i
$870$		0			0
$871$	−12.0661	+	4.99793i	−0.408843	+	0.169348i
$872$		0			0
$873$	31.0723	+	12.8706i	1.05164	+	0.435602i
$874$		0			0
$875$	−21.4912	+	32.1639i	−0.726535	+	1.08734i
$876$		0			0
$877$	−4.46786	−	0.888712i	−0.150869	−	0.0300097i	0.119078	−	0.992885i	$-0.462006\pi$
$877$	−4.46786	−	0.888712i	−0.150869	−	0.0300097i	−0.269947	+	0.962875i	$0.587006\pi$
$878$		0			0
$879$	1.32406	+	1.32406i	0.0446595	+	0.0446595i
$880$		0			0
$881$	−15.9270	+	15.9270i	−0.536595	+	0.536595i	−0.922527	−	0.385932i	$-0.873880\pi$
$881$	−15.9270	+	15.9270i	−0.536595	+	0.536595i	0.385932	+	0.922527i	$0.373880\pi$
$882$		0			0
$883$	6.68186	−	33.5920i	0.224863	−	1.13046i	−0.689101	−	0.724665i	$-0.741995\pi$
$883$	6.68186	−	33.5920i	0.224863	−	1.13046i	0.913964	−	0.405796i	$-0.133005\pi$
$884$		0			0
$885$	26.5244	+	17.7230i	0.891608	+	0.595754i
$886$		0			0
$887$	−3.81352	+	9.20665i	−0.128045	+	0.309129i	−0.974881	−	0.222725i	$-0.928505\pi$
$887$	−3.81352	+	9.20665i	−0.128045	+	0.309129i	0.846836	+	0.531854i	$0.178505\pi$
$888$		0			0
$889$	12.8900	+	31.1191i	0.432316	+	1.04370i
$890$		0			0
$891$	0.864465	+	4.34596i	0.0289607	+	0.145595i
$892$		0			0
$893$	−0.286932	−	0.429424i	−0.00960182	−	0.0143701i
$894$		0			0
$895$	−29.6923			−0.992505
$896$		0			0
$897$	−19.4352			−0.648921
$898$		0			0
$899$	0.852683	+	1.27613i	0.0284386	+	0.0425613i
$900$		0			0
$901$	0.364095	+	1.83043i	0.0121298	+	0.0609805i
$902$		0			0
$903$	−25.1497	−	60.7167i	−0.836929	−	2.02053i
$904$		0			0
$905$	−19.9710	+	48.2143i	−0.663859	+	1.60270i
$906$		0			0
$907$	−26.1119	−	17.4474i	−0.867033	−	0.579333i	0.0405634	−	0.999177i	$-0.487085\pi$
$907$	−26.1119	−	17.4474i	−0.867033	−	0.579333i	−0.907596	+	0.419844i	$0.862085\pi$
$908$		0			0
$909$	6.31186	−	31.7318i	0.209351	−	1.05248i
$910$		0			0
$911$	27.7728	−	27.7728i	0.920155	−	0.920155i	−0.0768847	−	0.997040i	$-0.524497\pi$
$911$	27.7728	−	27.7728i	0.920155	−	0.920155i	0.997040	+	0.0768847i	$0.0244973\pi$
$912$		0			0
$913$	−2.29080	−	2.29080i	−0.0758143	−	0.0758143i
$914$		0			0
$915$	49.5921	+	9.86448i	1.63946	+	0.326110i
$916$		0			0
$917$	−29.1561	+	43.6353i	−0.962821	+	1.44096i
$918$		0			0
$919$	−27.5012	−	11.3914i	−0.907180	−	0.375766i	−0.120204	−	0.992749i	$-0.538355\pi$
$919$	−27.5012	−	11.3914i	−0.907180	−	0.375766i	−0.786976	+	0.616983i	$0.788355\pi$
$920$		0			0
$921$	−12.6787	+	5.25170i	−0.417778	+	0.173049i
$922$		0			0
$923$	−39.2887	+	7.81501i	−1.29320	+	0.257234i
$924$		0			0
$925$	−2.99804	+	2.00323i	−0.0985750	+	0.0658657i
$926$		0			0
$927$		−	3.22043i		−	0.105773i
$928$		0			0
$929$		−	46.3862i		−	1.52188i	−0.648821	−	0.760941i	$-0.724738\pi$
$929$		−	46.3862i		−	1.52188i	0.648821	−	0.760941i	$-0.275262\pi$
$930$		0			0
$931$	−31.9488	+	21.3475i	−1.04708	+	0.699637i
$932$		0			0
$933$	3.21767	−	0.640034i	0.105342	−	0.0209538i
$934$		0			0
$935$	−3.46650	+	1.43587i	−0.113367	+	0.0469580i
$936$		0			0
$937$	18.9322	+	7.84197i	0.618488	+	0.256186i	0.669853	−	0.742494i	$-0.266357\pi$
$937$	18.9322	+	7.84197i	0.618488	+	0.256186i	−0.0513650	+	0.998680i	$0.516357\pi$
$938$		0			0
$939$	21.7802	−	32.5963i	0.710768	−	1.06374i
$940$		0			0
$941$	9.60036	+	1.90963i	0.312963	+	0.0622521i	0.349073	−	0.937096i	$-0.386497\pi$
$941$	9.60036	+	1.90963i	0.312963	+	0.0622521i	−0.0361100	+	0.999348i	$0.511497\pi$
$942$		0			0
$943$	−13.7829	−	13.7829i	−0.448833	−	0.448833i
$944$		0			0
$945$	18.0557	−	18.0557i	0.587352	−	0.587352i
$946$		0			0
$947$	−1.52160	+	7.64962i	−0.0494455	+	0.248579i	−0.997601	−	0.0692279i	$-0.977946\pi$
$947$	−1.52160	+	7.64962i	−0.0494455	+	0.248579i	0.948155	+	0.317807i	$0.102946\pi$
$948$		0			0
$949$	−36.6570	−	24.4934i	−1.18994	−	0.795090i
$950$		0			0
$951$	−1.30803	+	3.15786i	−0.0424158	+	0.102401i
$952$		0			0
$953$	3.26587	+	7.88452i	0.105792	+	0.255405i	0.967907	−	0.251308i	$-0.0808606\pi$
$953$	3.26587	+	7.88452i	0.105792	+	0.255405i	−0.862115	+	0.506712i	$0.830861\pi$
$954$		0			0
$955$	−3.19452	−	16.0600i	−0.103372	−	0.519688i
$956$		0			0
$957$	2.68642	+	4.02051i	0.0868395	+	0.129965i
$958$		0			0
$959$	−56.0327			−1.80939
$960$		0			0
$961$	30.9160			0.997289
$962$		0			0
$963$	4.40714	+	6.59575i	0.142018	+	0.212545i
$964$		0			0
$965$	5.45550	+	27.4267i	0.175619	+	0.882895i
$966$		0			0
$967$	7.63680	+	18.4369i	0.245583	+	0.592890i	0.997819	−	0.0660036i	$-0.0210249\pi$
$967$	7.63680	+	18.4369i	0.245583	+	0.592890i	−0.752236	+	0.658893i	$0.771025\pi$
$968$		0			0
$969$	7.92092	−	19.1228i	0.254457	−	0.614313i
$970$		0			0
$971$	−6.07191	−	4.05712i	−0.194857	−	0.130199i	0.454315	−	0.890841i	$-0.349884\pi$
$971$	−6.07191	−	4.05712i	−0.194857	−	0.130199i	−0.649171	+	0.760642i	$0.724884\pi$
$972$		0			0
$973$	14.3773	−	72.2796i	0.460915	−	2.31718i
$974$		0			0
$975$	8.33895	−	8.33895i	0.267060	−	0.267060i
$976$		0			0
$977$	−9.80496	−	9.80496i	−0.313689	−	0.313689i	0.532648	−	0.846337i	$-0.321197\pi$
$977$	−9.80496	−	9.80496i	−0.313689	−	0.313689i	−0.846337	+	0.532648i	$0.821197\pi$
$978$		0			0
$979$	−2.78468	−	0.553906i	−0.0889986	−	0.0177029i
$980$		0			0
$981$	3.29160	−	4.92622i	0.105093	−	0.157282i
$982$		0			0
$983$	−23.5837	−	9.76870i	−0.752204	−	0.311573i	−0.0265636	−	0.999647i	$-0.508456\pi$
$983$	−23.5837	−	9.76870i	−0.752204	−	0.311573i	−0.725641	+	0.688074i	$0.758456\pi$
$984$		0			0
$985$	0.639880	−	0.265047i	0.0203883	−	0.00844510i
$986$		0			0
$987$	−2.05071	+	0.407911i	−0.0652747	+	0.0129839i
$988$		0			0
$989$	15.6712	−	10.4712i	0.498316	−	0.332964i
$990$		0			0
$991$		−	12.5312i		−	0.398066i	−0.979993	−	0.199033i	$-0.936220\pi$
$991$		−	12.5312i		−	0.398066i	0.979993	−	0.199033i	$-0.0637801\pi$
$992$		0			0
$993$		−	73.5297i		−	2.33339i
$994$		0			0
$995$	5.06661	−	3.38540i	0.160622	−	0.107324i
$996$		0			0
$997$	−45.0321	+	8.95744i	−1.42618	+	0.283685i	−0.847034	−	0.531538i	$-0.821614\pi$
$997$	−45.0321	+	8.95744i	−1.42618	+	0.283685i	−0.579147	+	0.815223i	$0.696614\pi$
$998$		0			0
$999$	−3.81081	+	1.57849i	−0.120569	+	0.0499412i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.i.a.17.2		56
4.3	odd	2		64.2.i.a.45.2	yes	56
8.3	odd	2		512.2.i.b.289.2		56
8.5	even	2		512.2.i.a.289.6		56
12.11	even	2		576.2.bd.a.109.6		56
64.5	even	16		512.2.i.a.225.6		56
64.27	odd	16		64.2.i.a.37.2	✓	56
64.37	even	16	inner	256.2.i.a.241.2		56
64.59	odd	16		512.2.i.b.225.2		56
192.155	even	16		576.2.bd.a.37.6		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.37.2	✓	56	64.27	odd	16
64.2.i.a.45.2	yes	56	4.3	odd	2
256.2.i.a.17.2		56	1.1	even	1	trivial
256.2.i.a.241.2		56	64.37	even	16	inner
512.2.i.a.225.6		56	64.5	even	16
512.2.i.a.289.6		56	8.5	even	2
512.2.i.b.225.2		56	64.59	odd	16
512.2.i.b.289.2		56	8.3	odd	2
576.2.bd.a.37.6		56	192.155	even	16
576.2.bd.a.109.6		56	12.11	even	2

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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.i (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.25103 - 1.87230i) q^{3} +(0.509835 + 2.56311i) q^{5} +(1.78664 + 4.31333i) q^{7} +(-0.792379 + 1.91297i) q^{9} +O(q^{10})\)	\(q+(-1.25103 - 1.87230i) q^{3} +(0.509835 + 2.56311i) q^{5} +(1.78664 + 4.31333i) q^{7} +(-0.792379 + 1.91297i) q^{9} +(0.337256 + 0.225347i) q^{11} +(0.558477 - 2.80765i) q^{13} +(4.16110 - 4.16110i) q^{15} +(2.50296 + 2.50296i) q^{17} +(2.54690 + 0.506609i) q^{19} +(5.84071 - 8.74124i) q^{21} +(2.78551 + 1.15380i) q^{23} +(-1.69022 + 0.700112i) q^{25} +(-2.05264 + 0.408295i) q^{27} +(-4.40189 + 2.94125i) q^{29} -0.289905i q^{31} -0.913360i q^{33} +(-10.1447 + 6.77845i) q^{35} +(1.93303 - 0.384503i) q^{37} +(-5.95544 + 2.46682i) q^{39} +(-5.97284 - 2.47403i) q^{41} +(3.47301 - 5.19772i) q^{43} +(-5.30715 - 1.05566i) q^{45} +(-0.140633 - 0.140633i) q^{47} +(-10.4630 + 10.4630i) q^{49} +(1.55501 - 7.81758i) q^{51} +(0.438386 + 0.292920i) q^{53} +(-0.405645 + 0.979314i) q^{55} +(-2.23772 - 5.40234i) q^{57} +(1.05758 + 5.31680i) q^{59} +(4.77369 + 7.14433i) q^{61} -9.66698 q^{63} +7.48106 q^{65} +(-2.53466 - 3.79339i) q^{67} +(-1.32451 - 6.65875i) q^{69} +(-5.35506 - 12.9282i) q^{71} +(5.89360 - 14.2284i) q^{73} +(3.42534 + 2.28874i) q^{75} +(-0.369442 + 1.85731i) q^{77} +(4.17941 - 4.17941i) q^{79} +(7.72474 + 7.72474i) q^{81} +(-7.83362 - 1.55820i) q^{83} +(-5.13928 + 7.69148i) q^{85} +(11.0138 + 4.56206i) q^{87} +(-6.46701 + 2.67872i) q^{89} +(13.1081 - 2.60737i) q^{91} +(-0.542790 + 0.362680i) q^{93} +6.78627i q^{95} -16.2429i q^{97} +(-0.698317 + 0.466600i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9}+O(q^{10}) \) 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9	\( 56 q + 8 q^{3} - 8 q^{5} + 8 q^{7} - 8 q^{9} + 8 q^{11} - 8 q^{13} + 8 q^{15} - 8 q^{17} + 8 q^{19} - 8 q^{21} + 8 q^{23} - 8 q^{25} + 8 q^{27} - 8 q^{29} + 8 q^{35} - 8 q^{37} + 8 q^{39} - 8 q^{41} + 8 q^{43} - 8 q^{45} + 8 q^{47} - 8 q^{49} - 24 q^{51} - 8 q^{53} - 56 q^{55} - 8 q^{57} - 56 q^{59} - 8 q^{61} - 64 q^{63} - 16 q^{65} - 72 q^{67} - 8 q^{69} - 56 q^{71} - 8 q^{73} - 56 q^{75} - 8 q^{77} - 24 q^{79} - 8 q^{81} + 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{89} + 8 q^{91} + 16 q^{93} - 16 q^{99}+O(q^{100}) \) 56 * q + 8 * q^3 - 8 * q^5 + 8 * q^7 - 8 * q^9 + 8 * q^11 - 8 * q^13 + 8 * q^15 - 8 * q^17 + 8 * q^19 - 8 * q^21 + 8 * q^23 - 8 * q^25 + 8 * q^27 - 8 * q^29 + 8 * q^35 - 8 * q^37 + 8 * q^39 - 8 * q^41 + 8 * q^43 - 8 * q^45 + 8 * q^47 - 8 * q^49 - 24 * q^51 - 8 * q^53 - 56 * q^55 - 8 * q^57 - 56 * q^59 - 8 * q^61 - 64 * q^63 - 16 * q^65 - 72 * q^67 - 8 * q^69 - 56 * q^71 - 8 * q^73 - 56 * q^75 - 8 * q^77 - 24 * q^79 - 8 * q^81 + 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^89 + 8 * q^91 + 16 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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