LMFDB - Embedded newform 306.2.l.c.253.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [306,2,Mod(19,306)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(306, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("306.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 306 = 2 \cdot 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	306.l (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,8,0,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$2.44342230185$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 34)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			253.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	306.253
Dual form			306.2.l.c.127.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(3.41421 - 1.41421i) q^{5} +(1.41421 + 0.585786i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-3.41421 - 1.41421i) q^{10} +(-1.70711 + 4.12132i) q^{11} +0.828427i q^{13} +(-0.585786 - 1.41421i) q^{14} -1.00000 q^{16} +(2.12132 - 3.53553i) q^{17} +(0.585786 + 0.585786i) q^{19} +(1.41421 + 3.41421i) q^{20} +(4.12132 - 1.70711i) q^{22} +(1.17157 - 2.82843i) q^{23} +(6.12132 - 6.12132i) q^{25} +(0.585786 - 0.585786i) q^{26} +(-0.585786 + 1.41421i) q^{28} +(1.41421 - 0.585786i) q^{29} +(-1.41421 - 3.41421i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-4.00000 + 1.00000i) q^{34} +5.65685 q^{35} +(0.828427 + 2.00000i) q^{37} -0.828427i q^{38} +(1.41421 - 3.41421i) q^{40} +(-10.3640 - 4.29289i) q^{41} +(-1.24264 + 1.24264i) q^{43} +(-4.12132 - 1.70711i) q^{44} +(-2.82843 + 1.17157i) q^{46} +9.65685i q^{47} +(-3.29289 - 3.29289i) q^{49} -8.65685 q^{50} -0.828427 q^{52} +(-0.585786 - 0.585786i) q^{53} +16.4853i q^{55} +(1.41421 - 0.585786i) q^{56} +(-1.41421 - 0.585786i) q^{58} +(-0.414214 + 0.414214i) q^{59} +(6.82843 + 2.82843i) q^{61} +(-1.41421 + 3.41421i) q^{62} -1.00000i q^{64} +(1.17157 + 2.82843i) q^{65} -7.41421 q^{67} +(3.53553 + 2.12132i) q^{68} +(-4.00000 - 4.00000i) q^{70} +(-0.828427 - 2.00000i) q^{71} +(-4.94975 + 2.05025i) q^{73} +(0.828427 - 2.00000i) q^{74} +(-0.585786 + 0.585786i) q^{76} +(-4.82843 + 4.82843i) q^{77} +(-2.00000 + 4.82843i) q^{79} +(-3.41421 + 1.41421i) q^{80} +(4.29289 + 10.3640i) q^{82} +(-4.41421 - 4.41421i) q^{83} +(2.24264 - 15.0711i) q^{85} +1.75736 q^{86} +(1.70711 + 4.12132i) q^{88} +15.0711i q^{89} +(-0.485281 + 1.17157i) q^{91} +(2.82843 + 1.17157i) q^{92} +(6.82843 - 6.82843i) q^{94} +(2.82843 + 1.17157i) q^{95} +(-5.12132 + 2.12132i) q^{97} +4.65685i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{5} - 8 q^{10} - 4 q^{11} - 8 q^{14} - 4 q^{16} + 8 q^{19} + 8 q^{22} + 16 q^{23} + 16 q^{25} + 8 q^{26} - 8 q^{28} - 16 q^{34} - 8 q^{37} - 16 q^{41} + 12 q^{43} - 8 q^{44} - 16 q^{49} - 12 q^{50}+ \cdots - 12 q^{97}+O(q^{100}) $ 4 * q + 8 * q^5 - 8 * q^10 - 4 * q^11 - 8 * q^14 - 4 * q^16 + 8 * q^19 + 8 * q^22 + 16 * q^23 + 16 * q^25 + 8 * q^26 - 8 * q^28 - 16 * q^34 - 8 * q^37 - 16 * q^41 + 12 * q^43 - 8 * q^44 - 16 * q^49 - 12 * q^50 + 8 * q^52 - 8 * q^53 + 4 * q^59 + 16 * q^61 + 16 * q^65 - 24 * q^67 - 16 * q^70 + 8 * q^71 - 8 * q^74 - 8 * q^76 - 8 * q^77 - 8 * q^79 - 8 * q^80 + 20 * q^82 - 12 * q^83 - 8 * q^85 + 24 * q^86 + 4 * q^88 + 32 * q^91 + 16 * q^94 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/306\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	3.41421	−	1.41421i	1.52688	−	0.632456i	0.547927	−	0.836526i	$-0.315417\pi$
$5$	3.41421	−	1.41421i	1.52688	−	0.632456i	0.978956	+	0.204071i	$0.0654173\pi$
$6$		0			0
$7$	1.41421	+	0.585786i	0.534522	+	0.221406i	0.633583	−	0.773675i	$-0.281584\pi$
$7$	1.41421	+	0.585786i	0.534522	+	0.221406i	−0.0990602	+	0.995081i	$0.531584\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	−3.41421	−	1.41421i	−1.07967	−	0.447214i
$11$	−1.70711	+	4.12132i	−0.514712	+	1.24262i	0.426401	+	0.904534i	$0.359781\pi$
$11$	−1.70711	+	4.12132i	−0.514712	+	1.24262i	−0.941113	+	0.338091i	$0.890219\pi$
$12$		0			0
$13$			0.828427i			0.229764i	0.993379	+	0.114882i	$0.0366490\pi$
$13$			0.828427i			0.229764i	−0.993379	+	0.114882i	$0.963351\pi$
$14$	−0.585786	−	1.41421i	−0.156558	−	0.377964i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	2.12132	−	3.53553i	0.514496	−	0.857493i
$17$	2.12132	−	3.53553i	0.514496	−	0.857493i
$18$		0			0
$19$	0.585786	+	0.585786i	0.134389	+	0.134389i	0.771101	−	0.636713i	$-0.219706\pi$
$19$	0.585786	+	0.585786i	0.134389	+	0.134389i	−0.636713	+	0.771101i	$0.719706\pi$
$20$	1.41421	+	3.41421i	0.316228	+	0.763441i
$21$		0			0
$22$	4.12132	−	1.70711i	0.878668	−	0.363956i
$23$	1.17157	−	2.82843i	0.244290	−	0.589768i	−0.753410	−	0.657551i	$-0.771593\pi$
$23$	1.17157	−	2.82843i	0.244290	−	0.589768i	0.997700	+	0.0677829i	$0.0215925\pi$
$24$		0			0
$25$	6.12132	−	6.12132i	1.22426	−	1.22426i
$26$	0.585786	−	0.585786i	0.114882	−	0.114882i
$27$		0			0
$28$	−0.585786	+	1.41421i	−0.110703	+	0.267261i
$29$	1.41421	−	0.585786i	0.262613	−	0.108778i	−0.247492	−	0.968890i	$-0.579606\pi$
$29$	1.41421	−	0.585786i	0.262613	−	0.108778i	0.510105	+	0.860112i	$0.329606\pi$
$30$		0			0
$31$	−1.41421	−	3.41421i	−0.254000	−	0.613211i	0.744520	−	0.667601i	$-0.232679\pi$
$31$	−1.41421	−	3.41421i	−0.254000	−	0.613211i	−0.998520	+	0.0543898i	$0.982679\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$	−4.00000	+	1.00000i	−0.685994	+	0.171499i
$35$	5.65685			0.956183
$36$		0			0
$37$	0.828427	+	2.00000i	0.136193	+	0.328798i	0.977231	−	0.212177i	$-0.0680553\pi$
$37$	0.828427	+	2.00000i	0.136193	+	0.328798i	−0.841039	+	0.540975i	$0.818055\pi$
$38$		−	0.828427i		−	0.134389i
$39$		0			0
$40$	1.41421	−	3.41421i	0.223607	−	0.539835i
$41$	−10.3640	−	4.29289i	−1.61858	−	0.670437i	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	−10.3640	−	4.29289i	−1.61858	−	0.670437i	−0.993884	+	0.110432i	$0.964777\pi$
$42$		0			0
$43$	−1.24264	+	1.24264i	−0.189501	+	0.189501i	−0.795480	−	0.605979i	$-0.792781\pi$
$43$	−1.24264	+	1.24264i	−0.189501	+	0.189501i	0.605979	+	0.795480i	$0.292781\pi$
$44$	−4.12132	−	1.70711i	−0.621312	−	0.257356i
$45$		0			0
$46$	−2.82843	+	1.17157i	−0.417029	+	0.172739i
$47$			9.65685i			1.40860i	0.709904	+	0.704298i	$0.248738\pi$
$47$			9.65685i			1.40860i	−0.709904	+	0.704298i	$0.751262\pi$
$48$		0			0
$49$	−3.29289	−	3.29289i	−0.470413	−	0.470413i
$50$	−8.65685			−1.22426
$51$		0			0
$52$	−0.828427			−0.114882
$53$	−0.585786	−	0.585786i	−0.0804640	−	0.0804640i	0.665729	−	0.746193i	$-0.268121\pi$
$53$	−0.585786	−	0.585786i	−0.0804640	−	0.0804640i	−0.746193	+	0.665729i	$0.768121\pi$
$54$		0			0
$55$			16.4853i			2.22287i
$56$	1.41421	−	0.585786i	0.188982	−	0.0782790i
$57$		0			0
$58$	−1.41421	−	0.585786i	−0.185695	−	0.0769175i
$59$	−0.414214	+	0.414214i	−0.0539260	+	0.0539260i	−0.733556	−	0.679630i	$-0.762141\pi$
$59$	−0.414214	+	0.414214i	−0.0539260	+	0.0539260i	0.679630	+	0.733556i	$0.262141\pi$
$60$		0			0
$61$	6.82843	+	2.82843i	0.874291	+	0.362143i	0.774280	−	0.632843i	$-0.218112\pi$
$61$	6.82843	+	2.82843i	0.874291	+	0.362143i	0.100011	+	0.994986i	$0.468112\pi$
$62$	−1.41421	+	3.41421i	−0.179605	+	0.433606i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	1.17157	+	2.82843i	0.145316	+	0.350823i
$66$		0			0
$67$	−7.41421			−0.905790			−0.452895	−	0.891564i	$-0.649609\pi$
$67$	−7.41421			−0.905790			−0.452895	+	0.891564i	$0.649609\pi$
$68$	3.53553	+	2.12132i	0.428746	+	0.257248i
$69$		0			0
$70$	−4.00000	−	4.00000i	−0.478091	−	0.478091i
$71$	−0.828427	−	2.00000i	−0.0983162	−	0.237356i	0.867067	−	0.498191i	$-0.166002\pi$
$71$	−0.828427	−	2.00000i	−0.0983162	−	0.237356i	−0.965383	+	0.260835i	$0.916002\pi$
$72$		0			0
$73$	−4.94975	+	2.05025i	−0.579324	+	0.239964i	−0.653050	−	0.757315i	$-0.726511\pi$
$73$	−4.94975	+	2.05025i	−0.579324	+	0.239964i	0.0737261	+	0.997279i	$0.476511\pi$
$74$	0.828427	−	2.00000i	0.0963027	−	0.232495i
$75$		0			0
$76$	−0.585786	+	0.585786i	−0.0671943	+	0.0671943i
$77$	−4.82843	+	4.82843i	−0.550250	+	0.550250i
$78$		0			0
$79$	−2.00000	+	4.82843i	−0.225018	+	0.543240i	−0.995558	−	0.0941507i	$-0.969986\pi$
$79$	−2.00000	+	4.82843i	−0.225018	+	0.543240i	0.770540	+	0.637391i	$0.219986\pi$
$80$	−3.41421	+	1.41421i	−0.381721	+	0.158114i
$81$		0			0
$82$	4.29289	+	10.3640i	0.474071	+	1.14451i
$83$	−4.41421	−	4.41421i	−0.484523	−	0.484523i	0.422050	−	0.906573i	$-0.361311\pi$
$83$	−4.41421	−	4.41421i	−0.484523	−	0.484523i	−0.906573	+	0.422050i	$0.861311\pi$
$84$		0			0
$85$	2.24264	−	15.0711i	0.243249	−	1.63469i
$86$	1.75736			0.189501
$87$		0			0
$88$	1.70711	+	4.12132i	0.181978	+	0.439334i
$89$			15.0711i			1.59753i	0.601643	+	0.798765i	$0.294513\pi$
$89$			15.0711i			1.59753i	−0.601643	+	0.798765i	$0.705487\pi$
$90$		0			0
$91$	−0.485281	+	1.17157i	−0.0508713	+	0.122814i
$92$	2.82843	+	1.17157i	0.294884	+	0.122145i
$93$		0			0
$94$	6.82843	−	6.82843i	0.704298	−	0.704298i
$95$	2.82843	+	1.17157i	0.290191	+	0.120201i
$96$		0			0
$97$	−5.12132	+	2.12132i	−0.519991	+	0.215387i	−0.627213	−	0.778848i	$-0.715804\pi$
$97$	−5.12132	+	2.12132i	−0.519991	+	0.215387i	0.107222	+	0.994235i	$0.465804\pi$
$98$			4.65685i			0.470413i
$99$		0			0
$100$	6.12132	+	6.12132i	0.612132	+	0.612132i
$101$	−4.34315			−0.432159			−0.216080	−	0.976376i	$-0.569327\pi$
$101$	−4.34315			−0.432159			−0.216080	+	0.976376i	$0.569327\pi$
$102$		0			0
$103$	12.4853			1.23021			0.615106	−	0.788445i	$-0.289113\pi$
$103$	12.4853			1.23021			0.615106	+	0.788445i	$0.289113\pi$
$104$	0.585786	+	0.585786i	0.0574411	+	0.0574411i
$105$		0			0
$106$			0.828427i			0.0804640i
$107$	−10.7782	+	4.46447i	−1.04197	+	0.431596i	−0.837017	−	0.547177i	$-0.815703\pi$
$107$	−10.7782	+	4.46447i	−1.04197	+	0.431596i	−0.204948	+	0.978773i	$0.565703\pi$
$108$		0			0
$109$	−9.07107	−	3.75736i	−0.868851	−	0.359890i	−0.0966881	−	0.995315i	$-0.530825\pi$
$109$	−9.07107	−	3.75736i	−0.868851	−	0.359890i	−0.772163	+	0.635425i	$0.780825\pi$
$110$	11.6569	−	11.6569i	1.11144	−	1.11144i
$111$		0			0
$112$	−1.41421	−	0.585786i	−0.133631	−	0.0553516i
$113$	3.53553	−	8.53553i	0.332595	−	0.802955i	−0.665790	−	0.746140i	$-0.731905\pi$
$113$	3.53553	−	8.53553i	0.332595	−	0.802955i	0.998385	−	0.0568160i	$-0.0180948\pi$
$114$		0			0
$115$		−	11.3137i		−	1.05501i
$116$	0.585786	+	1.41421i	0.0543889	+	0.131306i
$117$		0			0
$118$	0.585786			0.0539260
$119$	5.07107	−	3.75736i	0.464864	−	0.344437i
$120$		0			0
$121$	−6.29289	−	6.29289i	−0.572081	−	0.572081i
$122$	−2.82843	−	6.82843i	−0.256074	−	0.618217i
$123$		0			0
$124$	3.41421	−	1.41421i	0.306605	−	0.127000i
$125$	5.17157	−	12.4853i	0.462560	−	1.11672i
$126$		0			0
$127$	−9.17157	+	9.17157i	−0.813845	+	0.813845i	−0.985208	−	0.171363i	$-0.945183\pi$
$127$	−9.17157	+	9.17157i	−0.813845	+	0.813845i	0.171363	+	0.985208i	$0.445183\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	1.17157	−	2.82843i	0.102754	−	0.248069i
$131$	−0.121320	+	0.0502525i	−0.0105998	+	0.00439058i	−0.387977	−	0.921669i	$-0.626826\pi$
$131$	−0.121320	+	0.0502525i	−0.0105998	+	0.00439058i	0.377377	+	0.926060i	$0.376826\pi$
$132$		0			0
$133$	0.485281	+	1.17157i	0.0420792	+	0.101588i
$134$	5.24264	+	5.24264i	0.452895	+	0.452895i
$135$		0			0
$136$	−1.00000	−	4.00000i	−0.0857493	−	0.342997i
$137$	2.34315			0.200188			0.100094	−	0.994978i	$-0.468086\pi$
$137$	2.34315			0.200188			0.100094	+	0.994978i	$0.468086\pi$
$138$		0			0
$139$	−0.707107	−	1.70711i	−0.0599760	−	0.144795i	0.891051	−	0.453904i	$-0.149969\pi$
$139$	−0.707107	−	1.70711i	−0.0599760	−	0.144795i	−0.951027	+	0.309109i	$0.899969\pi$
$140$			5.65685i			0.478091i
$141$		0			0
$142$	−0.828427	+	2.00000i	−0.0695201	+	0.167836i
$143$	−3.41421	−	1.41421i	−0.285511	−	0.118262i
$144$		0			0
$145$	4.00000	−	4.00000i	0.332182	−	0.332182i
$146$	4.94975	+	2.05025i	0.409644	+	0.169680i
$147$		0			0
$148$	−2.00000	+	0.828427i	−0.164399	+	0.0680963i
$149$		−	15.6569i		−	1.28266i	−0.767265	−	0.641330i	$-0.778383\pi$
$149$		−	15.6569i		−	1.28266i	0.767265	−	0.641330i	$-0.221617\pi$
$150$		0			0
$151$	−15.6569	−	15.6569i	−1.27414	−	1.27414i	−0.943897	−	0.330240i	$-0.892870\pi$
$151$	−15.6569	−	15.6569i	−1.27414	−	1.27414i	−0.330240	−	0.943897i	$-0.607130\pi$
$152$	0.828427			0.0671943
$153$		0			0
$154$	6.82843			0.550250
$155$	−9.65685	−	9.65685i	−0.775657	−	0.775657i
$156$		0			0
$157$			13.3137i			1.06255i	0.847200	+	0.531275i	$0.178287\pi$
$157$			13.3137i			1.06255i	−0.847200	+	0.531275i	$0.821713\pi$
$158$	4.82843	−	2.00000i	0.384129	−	0.159111i
$159$		0			0
$160$	3.41421	+	1.41421i	0.269917	+	0.111803i
$161$	3.31371	−	3.31371i	0.261157	−	0.261157i
$162$		0			0
$163$	21.0208	+	8.70711i	1.64648	+	0.681993i	0.996928	−	0.0783260i	$-0.0249575\pi$
$163$	21.0208	+	8.70711i	1.64648	+	0.681993i	0.649550	+	0.760319i	$0.274958\pi$
$164$	4.29289	−	10.3640i	0.335219	−	0.809289i
$165$		0			0
$166$			6.24264i			0.484523i
$167$	7.55635	+	18.2426i	0.584728	+	1.41166i	0.888484	+	0.458908i	$0.151759\pi$
$167$	7.55635	+	18.2426i	0.584728	+	1.41166i	−0.303756	+	0.952750i	$0.598241\pi$
$168$		0			0
$169$	12.3137			0.947208
$170$	−12.2426	+	9.07107i	−0.938968	+	0.695719i
$171$		0			0
$172$	−1.24264	−	1.24264i	−0.0947505	−	0.0947505i
$173$	2.24264	+	5.41421i	0.170505	+	0.411635i	0.985915	−	0.167249i	$-0.0534884\pi$
$173$	2.24264	+	5.41421i	0.170505	+	0.411635i	−0.815410	+	0.578884i	$0.803488\pi$
$174$		0			0
$175$	12.2426	−	5.07107i	0.925457	−	0.383337i
$176$	1.70711	−	4.12132i	0.128678	−	0.310656i
$177$		0			0
$178$	10.6569	−	10.6569i	0.798765	−	0.798765i
$179$	18.2426	−	18.2426i	1.36352	−	1.36352i	0.494132	−	0.869387i	$-0.335486\pi$
$179$	18.2426	−	18.2426i	1.36352	−	1.36352i	0.869387	−	0.494132i	$-0.164514\pi$
$180$		0			0
$181$	2.34315	−	5.65685i	0.174165	−	0.420471i	−0.812559	−	0.582879i	$-0.801926\pi$
$181$	2.34315	−	5.65685i	0.174165	−	0.420471i	0.986724	+	0.162408i	$0.0519262\pi$
$182$	1.17157	−	0.485281i	0.0868428	−	0.0359714i
$183$		0			0
$184$	−1.17157	−	2.82843i	−0.0863695	−	0.208514i
$185$	5.65685	+	5.65685i	0.415900	+	0.415900i
$186$		0			0
$187$	10.9497	+	14.7782i	0.800725	+	1.08069i
$188$	−9.65685			−0.704298
$189$		0			0
$190$	−1.17157	−	2.82843i	−0.0849948	−	0.205196i
$191$		−	2.82843i		−	0.204658i	−0.994751	−	0.102329i	$-0.967371\pi$
$191$		−	2.82843i		−	0.204658i	0.994751	−	0.102329i	$-0.0326294\pi$
$192$		0			0
$193$	4.70711	−	11.3640i	0.338825	−	0.817996i	−0.659004	−	0.752139i	$-0.729022\pi$
$193$	4.70711	−	11.3640i	0.338825	−	0.817996i	0.997829	−	0.0658565i	$-0.0209780\pi$
$194$	5.12132	+	2.12132i	0.367689	+	0.152302i
$195$		0			0
$196$	3.29289	−	3.29289i	0.235207	−	0.235207i
$197$	18.4853	+	7.65685i	1.31702	+	0.545528i	0.926925	−	0.375246i	$-0.122442\pi$
$197$	18.4853	+	7.65685i	1.31702	+	0.545528i	0.390096	+	0.920774i	$0.372442\pi$
$198$		0			0
$199$	−19.3137	+	8.00000i	−1.36911	+	0.567105i	−0.941548	−	0.336880i	$-0.890628\pi$
$199$	−19.3137	+	8.00000i	−1.36911	+	0.567105i	−0.427565	+	0.903985i	$0.640628\pi$
$200$		−	8.65685i		−	0.612132i
$201$		0			0
$202$	3.07107	+	3.07107i	0.216080	+	0.216080i
$203$	2.34315			0.164457
$204$		0			0
$205$	−41.4558			−2.89540
$206$	−8.82843	−	8.82843i	−0.615106	−	0.615106i
$207$		0			0
$208$		−	0.828427i		−	0.0574411i
$209$	−3.41421	+	1.41421i	−0.236166	+	0.0978232i
$210$		0			0
$211$	−0.121320	−	0.0502525i	−0.00835204	−	0.00345953i	0.378504	−	0.925600i	$-0.376439\pi$
$211$	−0.121320	−	0.0502525i	−0.00835204	−	0.00345953i	−0.386856	+	0.922140i	$0.626439\pi$
$212$	0.585786	−	0.585786i	0.0402320	−	0.0402320i
$213$		0			0
$214$	10.7782	+	4.46447i	0.736781	+	0.305185i
$215$	−2.48528	+	6.00000i	−0.169495	+	0.409197i
$216$		0			0
$217$		−	5.65685i		−	0.384012i
$218$	3.75736	+	9.07107i	0.254480	+	0.614370i
$219$		0			0
$220$	−16.4853			−1.11144
$221$	2.92893	+	1.75736i	0.197021	+	0.118213i
$222$		0			0
$223$	−17.3137	−	17.3137i	−1.15941	−	1.15941i	−0.984602	−	0.174809i	$-0.944069\pi$
$223$	−17.3137	−	17.3137i	−1.15941	−	1.15941i	−0.174809	−	0.984602i	$-0.555931\pi$
$224$	0.585786	+	1.41421i	0.0391395	+	0.0944911i
$225$		0			0
$226$	−8.53553	+	3.53553i	−0.567775	+	0.235180i
$227$	−7.77817	+	18.7782i	−0.516256	+	1.24635i	0.423932	+	0.905694i	$0.360650\pi$
$227$	−7.77817	+	18.7782i	−0.516256	+	1.24635i	−0.940188	+	0.340657i	$0.889350\pi$
$228$		0			0
$229$	13.0711	−	13.0711i	0.863760	−	0.863760i	−0.128012	−	0.991773i	$-0.540860\pi$
$229$	13.0711	−	13.0711i	0.863760	−	0.863760i	0.991773	+	0.128012i	$0.0408596\pi$
$230$	−8.00000	+	8.00000i	−0.527504	+	0.527504i
$231$		0			0
$232$	0.585786	−	1.41421i	0.0384588	−	0.0928477i
$233$	−9.70711	+	4.02082i	−0.635934	+	0.263412i	−0.677272	−	0.735733i	$-0.736838\pi$
$233$	−9.70711	+	4.02082i	−0.635934	+	0.263412i	0.0413382	+	0.999145i	$0.486838\pi$
$234$		0			0
$235$	13.6569	+	32.9706i	0.890875	+	2.15076i
$236$	−0.414214	−	0.414214i	−0.0269630	−	0.0269630i
$237$		0			0
$238$	−6.24264	−	0.928932i	−0.404650	−	0.0602137i
$239$	−21.1716			−1.36948			−0.684738	−	0.728790i	$-0.740083\pi$
$239$	−21.1716			−1.36948			−0.684738	+	0.728790i	$0.740083\pi$
$240$		0			0
$241$	7.60660	+	18.3640i	0.489984	+	1.18293i	0.954728	+	0.297481i	$0.0961466\pi$
$241$	7.60660	+	18.3640i	0.489984	+	1.18293i	−0.464743	+	0.885445i	$0.653853\pi$
$242$			8.89949i			0.572081i
$243$		0			0
$244$	−2.82843	+	6.82843i	−0.181071	+	0.437145i
$245$	−15.8995	−	6.58579i	−1.01578	−	0.420750i
$246$		0			0
$247$	−0.485281	+	0.485281i	−0.0308777	+	0.0308777i
$248$	−3.41421	−	1.41421i	−0.216803	−	0.0898027i
$249$		0			0
$250$	−12.4853	+	5.17157i	−0.789639	+	0.327079i
$251$		−	18.7279i		−	1.18210i	−0.806636	−	0.591048i	$-0.798714\pi$
$251$		−	18.7279i		−	1.18210i	0.806636	−	0.591048i	$-0.201286\pi$
$252$		0			0
$253$	9.65685	+	9.65685i	0.607121	+	0.607121i
$254$	12.9706			0.813845
$255$		0			0
$256$	1.00000			0.0625000
$257$	−5.82843	−	5.82843i	−0.363567	−	0.363567i	0.501557	−	0.865124i	$-0.332761\pi$
$257$	−5.82843	−	5.82843i	−0.363567	−	0.363567i	−0.865124	+	0.501557i	$0.832761\pi$
$258$		0			0
$259$			3.31371i			0.205904i
$260$	−2.82843	+	1.17157i	−0.175412	+	0.0726579i
$261$		0			0
$262$	0.121320	+	0.0502525i	0.00749520	+	0.00310461i
$263$	−5.65685	+	5.65685i	−0.348817	+	0.348817i	−0.859669	−	0.510852i	$-0.829330\pi$
$263$	−5.65685	+	5.65685i	−0.348817	+	0.348817i	0.510852	+	0.859669i	$0.329330\pi$
$264$		0			0
$265$	−2.82843	−	1.17157i	−0.173749	−	0.0719691i
$266$	0.485281	−	1.17157i	0.0297545	−	0.0718337i
$267$		0			0
$268$		−	7.41421i		−	0.452895i
$269$	−2.92893	−	7.07107i	−0.178580	−	0.431131i	0.809089	−	0.587686i	$-0.199961\pi$
$269$	−2.92893	−	7.07107i	−0.178580	−	0.431131i	−0.987669	+	0.156555i	$0.949961\pi$
$270$		0			0
$271$	−14.8284			−0.900763			−0.450381	−	0.892836i	$-0.648712\pi$
$271$	−14.8284			−0.900763			−0.450381	+	0.892836i	$0.648712\pi$
$272$	−2.12132	+	3.53553i	−0.128624	+	0.214373i
$273$		0			0
$274$	−1.65685	−	1.65685i	−0.100094	−	0.100094i
$275$	14.7782	+	35.6777i	0.891157	+	2.15144i
$276$		0			0
$277$	21.8995	−	9.07107i	1.31581	−	0.545028i	0.389238	−	0.921137i	$-0.372738\pi$
$277$	21.8995	−	9.07107i	1.31581	−	0.545028i	0.926575	+	0.376110i	$0.122738\pi$
$278$	−0.707107	+	1.70711i	−0.0424094	+	0.102385i
$279$		0			0
$280$	4.00000	−	4.00000i	0.239046	−	0.239046i
$281$	−10.1421	+	10.1421i	−0.605029	+	0.605029i	−0.941643	−	0.336614i	$-0.890718\pi$
$281$	−10.1421	+	10.1421i	−0.605029	+	0.605029i	0.336614	+	0.941643i	$0.390718\pi$
$282$		0			0
$283$	0.435029	−	1.05025i	0.0258598	−	0.0624310i	−0.910422	−	0.413680i	$-0.864243\pi$
$283$	0.435029	−	1.05025i	0.0258598	−	0.0624310i	0.936282	+	0.351249i	$0.114243\pi$
$284$	2.00000	−	0.828427i	0.118678	−	0.0491581i
$285$		0			0
$286$	1.41421	+	3.41421i	0.0836242	+	0.201887i
$287$	−12.1421	−	12.1421i	−0.716728	−	0.716728i
$288$		0			0
$289$	−8.00000	−	15.0000i	−0.470588	−	0.882353i
$290$	−5.65685			−0.332182
$291$		0			0
$292$	−2.05025	−	4.94975i	−0.119982	−	0.289662i
$293$		−	22.0000i		−	1.28525i	−0.766179	−	0.642627i	$-0.777845\pi$
$293$		−	22.0000i		−	1.28525i	0.766179	−	0.642627i	$-0.222155\pi$
$294$		0			0
$295$	−0.828427	+	2.00000i	−0.0482329	+	0.116445i
$296$	2.00000	+	0.828427i	0.116248	+	0.0481513i
$297$		0			0
$298$	−11.0711	+	11.0711i	−0.641330	+	0.641330i
$299$	2.34315	+	0.970563i	0.135508	+	0.0561291i
$300$		0			0
$301$	−2.48528	+	1.02944i	−0.143249	+	0.0593358i
$302$			22.1421i			1.27414i
$303$		0			0
$304$	−0.585786	−	0.585786i	−0.0335972	−	0.0335972i
$305$	27.3137			1.56398
$306$		0			0
$307$	6.34315			0.362022			0.181011	−	0.983481i	$-0.442063\pi$
$307$	6.34315			0.362022			0.181011	+	0.983481i	$0.442063\pi$
$308$	−4.82843	−	4.82843i	−0.275125	−	0.275125i
$309$		0			0
$310$			13.6569i			0.775657i
$311$	13.8995	−	5.75736i	0.788168	−	0.326470i	0.0479613	−	0.998849i	$-0.484728\pi$
$311$	13.8995	−	5.75736i	0.788168	−	0.326470i	0.740207	+	0.672379i	$0.234728\pi$
$312$		0			0
$313$	12.5355	+	5.19239i	0.708550	+	0.293491i	0.707705	−	0.706509i	$-0.249731\pi$
$313$	12.5355	+	5.19239i	0.708550	+	0.293491i	0.000845724		1.00000i	$0.499731\pi$
$314$	9.41421	−	9.41421i	0.531275	−	0.531275i
$315$		0			0
$316$	−4.82843	−	2.00000i	−0.271620	−	0.112509i
$317$	−8.48528	+	20.4853i	−0.476581	+	1.15057i	0.484622	+	0.874724i	$0.338957\pi$
$317$	−8.48528	+	20.4853i	−0.476581	+	1.15057i	−0.961202	+	0.275844i	$0.911043\pi$
$318$		0			0
$319$			6.82843i			0.382319i
$320$	−1.41421	−	3.41421i	−0.0790569	−	0.190860i
$321$		0			0
$322$	−4.68629			−0.261157
$323$	3.31371	−	0.828427i	0.184380	−	0.0460949i
$324$		0			0
$325$	5.07107	+	5.07107i	0.281292	+	0.281292i
$326$	−8.70711	−	21.0208i	−0.482242	−	1.16424i
$327$		0			0
$328$	−10.3640	+	4.29289i	−0.572254	+	0.237035i
$329$	−5.65685	+	13.6569i	−0.311872	+	0.752927i
$330$		0			0
$331$	19.5858	−	19.5858i	1.07653	−	1.07653i	0.0797144	−	0.996818i	$-0.474599\pi$
$331$	19.5858	−	19.5858i	1.07653	−	1.07653i	0.996818	−	0.0797144i	$-0.0254008\pi$
$332$	4.41421	−	4.41421i	0.242261	−	0.242261i
$333$		0			0
$334$	7.55635	−	18.2426i	0.413465	−	0.998193i
$335$	−25.3137	+	10.4853i	−1.38304	+	0.572872i
$336$		0			0
$337$	4.46447	+	10.7782i	0.243195	+	0.587125i	0.997597	−	0.0692885i	$-0.0220729\pi$
$337$	4.46447	+	10.7782i	0.243195	+	0.587125i	−0.754402	+	0.656413i	$0.772073\pi$
$338$	−8.70711	−	8.70711i	−0.473604	−	0.473604i
$339$		0			0
$340$	15.0711	+	2.24264i	0.817343	+	0.121624i
$341$	16.4853			0.892728
$342$		0			0
$343$	−6.82843	−	16.4853i	−0.368700	−	0.890122i
$344$			1.75736i			0.0947505i
$345$		0			0
$346$	2.24264	−	5.41421i	0.120565	−	0.291070i
$347$	14.9497	+	6.19239i	0.802544	+	0.332425i	0.745975	−	0.665974i	$-0.231984\pi$
$347$	14.9497	+	6.19239i	0.802544	+	0.332425i	0.0565694	+	0.998399i	$0.481984\pi$
$348$		0			0
$349$	−13.8995	+	13.8995i	−0.744023	+	0.744023i	−0.973350	−	0.229327i	$-0.926348\pi$
$349$	−13.8995	+	13.8995i	−0.744023	+	0.744023i	0.229327	+	0.973350i	$0.426348\pi$
$350$	−12.2426	−	5.07107i	−0.654397	−	0.271060i
$351$		0			0
$352$	−4.12132	+	1.70711i	−0.219667	+	0.0909891i
$353$		−	14.3848i		−	0.765624i	−0.923826	−	0.382812i	$-0.874956\pi$
$353$		−	14.3848i		−	0.765624i	0.923826	−	0.382812i	$-0.125044\pi$
$354$		0			0
$355$	−5.65685	−	5.65685i	−0.300235	−	0.300235i
$356$	−15.0711			−0.798765
$357$		0			0
$358$	−25.7990			−1.36352
$359$	−8.00000	−	8.00000i	−0.422224	−	0.422224i	0.463745	−	0.885969i	$-0.346505\pi$
$359$	−8.00000	−	8.00000i	−0.422224	−	0.422224i	−0.885969	+	0.463745i	$0.846505\pi$
$360$		0			0
$361$		−	18.3137i		−	0.963879i
$362$	−5.65685	+	2.34315i	−0.297318	+	0.123153i
$363$		0			0
$364$	−1.17157	−	0.485281i	−0.0614071	−	0.0254357i
$365$	−14.0000	+	14.0000i	−0.732793	+	0.732793i
$366$		0			0
$367$	17.3137	+	7.17157i	0.903768	+	0.374353i	0.785668	−	0.618649i	$-0.212320\pi$
$367$	17.3137	+	7.17157i	0.903768	+	0.374353i	0.118100	+	0.993002i	$0.462320\pi$
$368$	−1.17157	+	2.82843i	−0.0610725	+	0.147442i
$369$		0			0
$370$		−	8.00000i		−	0.415900i
$371$	−0.485281	−	1.17157i	−0.0251946	−	0.0608250i
$372$		0			0
$373$	−10.4853			−0.542907			−0.271454	−	0.962452i	$-0.587504\pi$
$373$	−10.4853			−0.542907			−0.271454	+	0.962452i	$0.587504\pi$
$374$	2.70711	−	18.1924i	0.139981	−	0.940706i
$375$		0			0
$376$	6.82843	+	6.82843i	0.352149	+	0.352149i
$377$	0.485281	+	1.17157i	0.0249933	+	0.0603391i
$378$		0			0
$379$	8.60660	−	3.56497i	0.442091	−	0.183120i	−0.150523	−	0.988606i	$-0.548096\pi$
$379$	8.60660	−	3.56497i	0.442091	−	0.183120i	0.592614	+	0.805486i	$0.298096\pi$
$380$	−1.17157	+	2.82843i	−0.0601004	+	0.145095i
$381$		0			0
$382$	−2.00000	+	2.00000i	−0.102329	+	0.102329i
$383$	21.3137	−	21.3137i	1.08908	−	1.08908i	0.0934562	−	0.995623i	$-0.470208\pi$
$383$	21.3137	−	21.3137i	1.08908	−	1.08908i	0.995623	−	0.0934562i	$-0.0297915\pi$
$384$		0			0
$385$	−9.65685	+	23.3137i	−0.492159	+	1.18818i
$386$	−11.3640	+	4.70711i	−0.578410	+	0.239585i
$387$		0			0
$388$	−2.12132	−	5.12132i	−0.107694	−	0.259996i
$389$	−2.24264	−	2.24264i	−0.113706	−	0.113706i	0.647964	−	0.761671i	$-0.275621\pi$
$389$	−2.24264	−	2.24264i	−0.113706	−	0.113706i	−0.761671	+	0.647964i	$0.775621\pi$
$390$		0			0
$391$	−7.51472	−	10.1421i	−0.380036	−	0.512910i
$392$	−4.65685			−0.235207
$393$		0			0
$394$	−7.65685	−	18.4853i	−0.385747	−	0.931275i
$395$			19.3137i			0.971778i
$396$		0			0
$397$	3.17157	−	7.65685i	0.159177	−	0.384286i	−0.824090	−	0.566459i	$-0.808313\pi$
$397$	3.17157	−	7.65685i	0.159177	−	0.384286i	0.983267	+	0.182173i	$0.0583129\pi$
$398$	19.3137	+	8.00000i	0.968109	+	0.401004i
$399$		0			0
$400$	−6.12132	+	6.12132i	−0.306066	+	0.306066i
$401$	22.1924	+	9.19239i	1.10823	+	0.459046i	0.860330	−	0.509738i	$-0.170258\pi$
$401$	22.1924	+	9.19239i	1.10823	+	0.459046i	0.247905	+	0.968784i	$0.420258\pi$
$402$		0			0
$403$	2.82843	−	1.17157i	0.140894	−	0.0583602i
$404$		−	4.34315i		−	0.216080i
$405$		0			0
$406$	−1.65685	−	1.65685i	−0.0822283	−	0.0822283i
$407$	−9.65685			−0.478672
$408$		0			0
$409$	15.5563			0.769212			0.384606	−	0.923081i	$-0.374337\pi$
$409$	15.5563			0.769212			0.384606	+	0.923081i	$0.374337\pi$
$410$	29.3137	+	29.3137i	1.44770	+	1.44770i
$411$		0			0
$412$			12.4853i			0.615106i
$413$	−0.828427	+	0.343146i	−0.0407642	+	0.0168851i
$414$		0			0
$415$	−21.3137	−	8.82843i	−1.04625	−	0.433370i
$416$	−0.585786	+	0.585786i	−0.0287205	+	0.0287205i
$417$		0			0
$418$	3.41421	+	1.41421i	0.166995	+	0.0691714i
$419$	6.60660	−	15.9497i	0.322754	−	0.779196i	−0.676338	−	0.736591i	$-0.736434\pi$
$419$	6.60660	−	15.9497i	0.322754	−	0.779196i	0.999092	−	0.0426051i	$-0.0135657\pi$
$420$		0			0
$421$			15.6569i			0.763068i	0.924355	+	0.381534i	$0.124604\pi$
$421$			15.6569i			0.763068i	−0.924355	+	0.381534i	$0.875396\pi$
$422$	0.0502525	+	0.121320i	0.00244625	+	0.00590578i
$423$		0			0
$424$	−0.828427			−0.0402320
$425$	−8.65685	−	34.6274i	−0.419919	−	1.67968i
$426$		0			0
$427$	8.00000	+	8.00000i	0.387147	+	0.387147i
$428$	−4.46447	−	10.7782i	−0.215798	−	0.520983i
$429$		0			0
$430$	6.00000	−	2.48528i	0.289346	−	0.119851i
$431$	5.51472	−	13.3137i	0.265635	−	0.641299i	−0.733634	−	0.679545i	$-0.762177\pi$
$431$	5.51472	−	13.3137i	0.265635	−	0.641299i	0.999268	+	0.0382464i	$0.0121772\pi$
$432$		0			0
$433$	−9.17157	+	9.17157i	−0.440758	+	0.440758i	−0.892267	−	0.451509i	$-0.850886\pi$
$433$	−9.17157	+	9.17157i	−0.440758	+	0.440758i	0.451509	+	0.892267i	$0.350886\pi$
$434$	−4.00000	+	4.00000i	−0.192006	+	0.192006i
$435$		0			0
$436$	3.75736	−	9.07107i	0.179945	−	0.434425i
$437$	2.34315	−	0.970563i	0.112088	−	0.0464283i
$438$		0			0
$439$	−8.82843	−	21.3137i	−0.421358	−	1.01725i	−0.981947	−	0.189154i	$-0.939425\pi$
$439$	−8.82843	−	21.3137i	−0.421358	−	1.01725i	0.560590	−	0.828094i	$-0.310575\pi$
$440$	11.6569	+	11.6569i	0.555719	+	0.555719i
$441$		0			0
$442$	−0.828427	−	3.31371i	−0.0394043	−	0.157617i
$443$	36.8701			1.75175			0.875875	−	0.482539i	$-0.160285\pi$
$443$	36.8701			1.75175			0.875875	+	0.482539i	$0.160285\pi$
$444$		0			0
$445$	21.3137	+	51.4558i	1.01037	+	2.43924i
$446$			24.4853i			1.15941i
$447$		0			0
$448$	0.585786	−	1.41421i	0.0276758	−	0.0668153i
$449$	−5.12132	−	2.12132i	−0.241690	−	0.100111i	0.258551	−	0.965998i	$-0.416755\pi$
$449$	−5.12132	−	2.12132i	−0.241690	−	0.100111i	−0.500241	+	0.865886i	$0.666755\pi$
$450$		0			0
$451$	35.3848	−	35.3848i	1.66620	−	1.66620i
$452$	8.53553	+	3.53553i	0.401478	+	0.166298i
$453$		0			0
$454$	18.7782	−	7.77817i	0.881303	−	0.365048i
$455$			4.68629i			0.219697i
$456$		0			0
$457$	3.51472	+	3.51472i	0.164412	+	0.164412i	0.784518	−	0.620106i	$-0.212911\pi$
$457$	3.51472	+	3.51472i	0.164412	+	0.164412i	−0.620106	+	0.784518i	$0.712911\pi$
$458$	−18.4853			−0.863760
$459$		0			0
$460$	11.3137			0.527504
$461$	24.7279	+	24.7279i	1.15169	+	1.15169i	0.986213	+	0.165481i	$0.0529177\pi$
$461$	24.7279	+	24.7279i	1.15169	+	1.15169i	0.165481	+	0.986213i	$0.447082\pi$
$462$		0			0
$463$		−	3.31371i		−	0.154001i	−0.997031	−	0.0770005i	$-0.975466\pi$
$463$		−	3.31371i		−	0.154001i	0.997031	−	0.0770005i	$-0.0245343\pi$
$464$	−1.41421	+	0.585786i	−0.0656532	+	0.0271945i
$465$		0			0
$466$	9.70711	+	4.02082i	0.449673	+	0.186261i
$467$	1.75736	−	1.75736i	0.0813209	−	0.0813209i	−0.665276	−	0.746597i	$-0.731686\pi$
$467$	1.75736	−	1.75736i	0.0813209	−	0.0813209i	0.746597	+	0.665276i	$0.231686\pi$
$468$		0			0
$469$	−10.4853	−	4.34315i	−0.484165	−	0.200548i
$470$	13.6569	−	32.9706i	0.629944	−	1.52082i
$471$		0			0
$472$			0.585786i			0.0269630i
$473$	−3.00000	−	7.24264i	−0.137940	−	0.333017i
$474$		0			0
$475$	7.17157			0.329054
$476$	3.75736	+	5.07107i	0.172218	+	0.232432i
$477$		0			0
$478$	14.9706	+	14.9706i	0.684738	+	0.684738i
$479$	−9.51472	−	22.9706i	−0.434739	−	1.04955i	−0.977740	−	0.209820i	$-0.932712\pi$
$479$	−9.51472	−	22.9706i	−0.434739	−	1.04955i	0.543001	−	0.839732i	$-0.317288\pi$
$480$		0			0
$481$	−1.65685	+	0.686292i	−0.0755461	+	0.0312922i
$482$	7.60660	−	18.3640i	0.346471	−	0.836456i
$483$		0			0
$484$	6.29289	−	6.29289i	0.286041	−	0.286041i
$485$	−14.4853	+	14.4853i	−0.657743	+	0.657743i
$486$		0			0
$487$	8.48528	−	20.4853i	0.384505	−	0.928277i	−0.606577	−	0.795024i	$-0.707458\pi$
$487$	8.48528	−	20.4853i	0.384505	−	0.928277i	0.991082	−	0.133252i	$-0.0425420\pi$
$488$	6.82843	−	2.82843i	0.309108	−	0.128037i
$489$		0			0
$490$	6.58579	+	15.8995i	0.297516	+	0.718266i
$491$	−10.9289	−	10.9289i	−0.493216	−	0.493216i	0.416102	−	0.909318i	$-0.363396\pi$
$491$	−10.9289	−	10.9289i	−0.493216	−	0.493216i	−0.909318	+	0.416102i	$0.863396\pi$
$492$		0			0
$493$	0.928932	−	6.24264i	0.0418370	−	0.281154i
$494$	0.686292			0.0308777
$495$		0			0
$496$	1.41421	+	3.41421i	0.0635001	+	0.153303i
$497$		−	3.31371i		−	0.148640i
$498$		0			0
$499$	−14.0919	+	34.0208i	−0.630839	+	1.52298i	0.207730	+	0.978186i	$0.433392\pi$
$499$	−14.0919	+	34.0208i	−0.630839	+	1.52298i	−0.838569	+	0.544795i	$0.816608\pi$
$500$	12.4853	+	5.17157i	0.558359	+	0.231280i
$501$		0			0
$502$	−13.2426	+	13.2426i	−0.591048	+	0.591048i
$503$	−11.1716	−	4.62742i	−0.498116	−	0.206326i	0.119458	−	0.992839i	$-0.461884\pi$
$503$	−11.1716	−	4.62742i	−0.498116	−	0.206326i	−0.617574	+	0.786513i	$0.711884\pi$
$504$		0			0
$505$	−14.8284	+	6.14214i	−0.659856	+	0.273321i
$506$		−	13.6569i		−	0.607121i
$507$		0			0
$508$	−9.17157	−	9.17157i	−0.406923	−	0.406923i
$509$	−16.6274			−0.736997			−0.368499	−	0.929628i	$-0.620128\pi$
$509$	−16.6274			−0.736997			−0.368499	+	0.929628i	$0.620128\pi$
$510$		0			0
$511$	−8.20101			−0.362791
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$			8.24264i			0.363567i
$515$	42.6274	−	17.6569i	1.87839	−	0.778054i
$516$		0			0
$517$	−39.7990	−	16.4853i	−1.75036	−	0.725022i
$518$	2.34315	−	2.34315i	0.102952	−	0.102952i
$519$		0			0
$520$	2.82843	+	1.17157i	0.124035	+	0.0513769i
$521$	−13.4645	+	32.5061i	−0.589889	+	1.42412i	0.293720	+	0.955892i	$0.405107\pi$
$521$	−13.4645	+	32.5061i	−0.589889	+	1.42412i	−0.883609	+	0.468226i	$0.844893\pi$
$522$		0			0
$523$		−	23.2132i		−	1.01504i	−0.861639	−	0.507521i	$-0.830562\pi$
$523$		−	23.2132i		−	1.01504i	0.861639	−	0.507521i	$-0.169438\pi$
$524$	−0.0502525	−	0.121320i	−0.00219529	−	0.00529990i
$525$		0			0
$526$	8.00000			0.348817
$527$	−15.0711	−	2.24264i	−0.656506	−	0.0976910i
$528$		0			0
$529$	9.63604	+	9.63604i	0.418958	+	0.418958i
$530$	1.17157	+	2.82843i	0.0508899	+	0.122859i
$531$		0			0
$532$	−1.17157	+	0.485281i	−0.0507941	+	0.0210396i
$533$	3.55635	−	8.58579i	0.154043	−	0.371892i
$534$		0			0
$535$	−30.4853	+	30.4853i	−1.31799	+	1.31799i
$536$	−5.24264	+	5.24264i	−0.226448	+	0.226448i
$537$		0			0
$538$	−2.92893	+	7.07107i	−0.126275	+	0.304855i
$539$	19.1924	−	7.94975i	0.826675	−	0.342420i
$540$		0			0
$541$	7.79899	+	18.8284i	0.335305	+	0.809497i	0.998153	+	0.0607439i	$0.0193473\pi$
$541$	7.79899	+	18.8284i	0.335305	+	0.809497i	−0.662849	+	0.748753i	$0.730653\pi$
$542$	10.4853	+	10.4853i	0.450381	+	0.450381i
$543$		0			0
$544$	4.00000	−	1.00000i	0.171499	−	0.0428746i
$545$	−36.2843			−1.55425
$546$		0			0
$547$	−9.39340	−	22.6777i	−0.401633	−	0.969627i	−0.987270	−	0.159054i	$-0.949156\pi$
$547$	−9.39340	−	22.6777i	−0.401633	−	0.969627i	0.585637	−	0.810573i	$-0.300844\pi$
$548$			2.34315i			0.100094i
$549$		0			0
$550$	14.7782	−	35.6777i	0.630143	−	1.52130i
$551$	1.17157	+	0.485281i	0.0499107	+	0.0206737i
$552$		0			0
$553$	−5.65685	+	5.65685i	−0.240554	+	0.240554i
$554$	−21.8995	−	9.07107i	−0.930420	−	0.385393i
$555$		0			0
$556$	1.70711	−	0.707107i	0.0723975	−	0.0299880i
$557$			41.1127i			1.74200i	0.491282	+	0.871000i	$0.336528\pi$
$557$			41.1127i			1.74200i	−0.491282	+	0.871000i	$0.663472\pi$
$558$		0			0
$559$	−1.02944	−	1.02944i	−0.0435406	−	0.0435406i
$560$	−5.65685			−0.239046
$561$		0			0
$562$	14.3431			0.605029
$563$	5.92893	+	5.92893i	0.249875	+	0.249875i	0.820919	−	0.571044i	$-0.193462\pi$
$563$	5.92893	+	5.92893i	0.249875	+	0.249875i	−0.571044	+	0.820919i	$0.693462\pi$
$564$		0			0
$565$		−	34.1421i		−	1.43637i
$566$	−1.05025	+	0.435029i	−0.0441454	+	0.0182856i
$567$		0			0
$568$	−2.00000	−	0.828427i	−0.0839181	−	0.0347600i
$569$	−3.48528	+	3.48528i	−0.146111	+	0.146111i	−0.776378	−	0.630267i	$-0.782945\pi$
$569$	−3.48528	+	3.48528i	−0.146111	+	0.146111i	0.630267	+	0.776378i	$0.282945\pi$
$570$		0			0
$571$	2.22183	+	0.920310i	0.0929805	+	0.0385138i	0.428689	−	0.903452i	$-0.358976\pi$
$571$	2.22183	+	0.920310i	0.0929805	+	0.0385138i	−0.335708	+	0.941966i	$0.608976\pi$
$572$	1.41421	−	3.41421i	0.0591312	−	0.142755i
$573$		0			0
$574$			17.1716i			0.716728i
$575$	−10.1421	−	24.4853i	−0.422956	−	1.02111i
$576$		0			0
$577$	−16.6274			−0.692208			−0.346104	−	0.938196i	$-0.612496\pi$
$577$	−16.6274			−0.692208			−0.346104	+	0.938196i	$0.612496\pi$
$578$	−4.94975	+	16.2635i	−0.205882	+	0.676471i
$579$		0			0
$580$	4.00000	+	4.00000i	0.166091	+	0.166091i
$581$	−3.65685	−	8.82843i	−0.151712	−	0.366265i
$582$		0			0
$583$	3.41421	−	1.41421i	0.141402	−	0.0585707i
$584$	−2.05025	+	4.94975i	−0.0848401	+	0.204822i
$585$		0			0
$586$	−15.5563	+	15.5563i	−0.642627	+	0.642627i
$587$	2.14214	−	2.14214i	0.0884154	−	0.0884154i	−0.661516	−	0.749931i	$-0.730087\pi$
$587$	2.14214	−	2.14214i	0.0884154	−	0.0884154i	0.749931	+	0.661516i	$0.230087\pi$
$588$		0			0
$589$	1.17157	−	2.82843i	0.0482738	−	0.116543i
$590$	2.00000	−	0.828427i	0.0823387	−	0.0341058i
$591$		0			0
$592$	−0.828427	−	2.00000i	−0.0340481	−	0.0821995i
$593$	3.00000	+	3.00000i	0.123195	+	0.123195i	0.766016	−	0.642821i	$-0.222236\pi$
$593$	3.00000	+	3.00000i	0.123195	+	0.123195i	−0.642821	+	0.766016i	$0.722236\pi$
$594$		0			0
$595$	12.0000	−	20.0000i	0.491952	−	0.819920i
$596$	15.6569			0.641330
$597$		0			0
$598$	−0.970563	−	2.34315i	−0.0396893	−	0.0958184i
$599$		−	26.3431i		−	1.07635i	−0.842833	−	0.538176i	$-0.819114\pi$
$599$		−	26.3431i		−	1.07635i	0.842833	−	0.538176i	$-0.180886\pi$
$600$		0			0
$601$	−7.05025	+	17.0208i	−0.287586	+	0.694294i	−0.999972	−	0.00749419i	$-0.997615\pi$
$601$	−7.05025	+	17.0208i	−0.287586	+	0.694294i	0.712386	+	0.701788i	$0.247615\pi$
$602$	2.48528	+	1.02944i	0.101293	+	0.0419567i
$603$		0			0
$604$	15.6569	−	15.6569i	0.637068	−	0.637068i
$605$	−30.3848	−	12.5858i	−1.23532	−	0.511685i
$606$		0			0
$607$	9.07107	−	3.75736i	0.368183	−	0.152507i	−0.190918	−	0.981606i	$-0.561146\pi$
$607$	9.07107	−	3.75736i	0.368183	−	0.152507i	0.559101	+	0.829100i	$0.311146\pi$
$608$			0.828427i			0.0335972i
$609$		0			0
$610$	−19.3137	−	19.3137i	−0.781989	−	0.781989i
$611$	−8.00000			−0.323645
$612$		0			0
$613$	37.7990			1.52669			0.763343	−	0.645993i	$-0.223556\pi$
$613$	37.7990			1.52669			0.763343	+	0.645993i	$0.223556\pi$
$614$	−4.48528	−	4.48528i	−0.181011	−	0.181011i
$615$		0			0
$616$			6.82843i			0.275125i
$617$	16.7071	−	6.92031i	0.672603	−	0.278601i	−0.0201281	−	0.999797i	$-0.506407\pi$
$617$	16.7071	−	6.92031i	0.672603	−	0.278601i	0.692731	+	0.721196i	$0.256407\pi$
$618$		0			0
$619$	5.12132	+	2.12132i	0.205843	+	0.0852631i	0.483223	−	0.875497i	$-0.339466\pi$
$619$	5.12132	+	2.12132i	0.205843	+	0.0852631i	−0.277380	+	0.960760i	$0.589466\pi$
$620$	9.65685	−	9.65685i	0.387829	−	0.387829i
$621$		0			0
$622$	−13.8995	−	5.75736i	−0.557319	−	0.230849i
$623$	−8.82843	+	21.3137i	−0.353703	+	0.853916i
$624$		0			0
$625$		−	6.65685i		−	0.266274i
$626$	−5.19239	−	12.5355i	−0.207530	−	0.501021i
$627$		0			0
$628$	−13.3137			−0.531275
$629$	8.82843	+	1.31371i	0.352012	+	0.0523810i
$630$		0			0
$631$	−21.6569	−	21.6569i	−0.862146	−	0.862146i	0.129441	−	0.991587i	$-0.458682\pi$
$631$	−21.6569	−	21.6569i	−0.862146	−	0.862146i	−0.991587	+	0.129441i	$0.958682\pi$
$632$	2.00000	+	4.82843i	0.0795557	+	0.192065i
$633$		0			0
$634$	20.4853	−	8.48528i	0.813574	−	0.336994i
$635$	−18.3431	+	44.2843i	−0.727926	+	1.75737i
$636$		0			0
$637$	2.72792	−	2.72792i	0.108084	−	0.108084i
$638$	4.82843	−	4.82843i	0.191159	−	0.191159i
$639$		0			0
$640$	−1.41421	+	3.41421i	−0.0559017	+	0.134959i
$641$	13.4350	−	5.56497i	0.530652	−	0.219803i	−0.101237	−	0.994862i	$-0.532280\pi$
$641$	13.4350	−	5.56497i	0.530652	−	0.219803i	0.631889	+	0.775059i	$0.282280\pi$
$642$		0			0
$643$	−5.12132	−	12.3640i	−0.201965	−	0.487587i	0.790150	−	0.612913i	$-0.210002\pi$
$643$	−5.12132	−	12.3640i	−0.201965	−	0.487587i	−0.992116	+	0.125326i	$0.960002\pi$
$644$	3.31371	+	3.31371i	0.130578	+	0.130578i
$645$		0			0
$646$	−2.92893	−	1.75736i	−0.115237	−	0.0691424i
$647$	−12.4853			−0.490847			−0.245424	−	0.969416i	$-0.578927\pi$
$647$	−12.4853			−0.490847			−0.245424	+	0.969416i	$0.578927\pi$
$648$		0			0
$649$	−1.00000	−	2.41421i	−0.0392534	−	0.0947662i
$650$		−	7.17157i		−	0.281292i
$651$		0			0
$652$	−8.70711	+	21.0208i	−0.340997	+	0.823239i
$653$	23.8995	+	9.89949i	0.935260	+	0.387397i	0.797671	−	0.603092i	$-0.206065\pi$
$653$	23.8995	+	9.89949i	0.935260	+	0.387397i	0.137588	+	0.990490i	$0.456065\pi$
$654$		0			0
$655$	−0.343146	+	0.343146i	−0.0134078	+	0.0134078i
$656$	10.3640	+	4.29289i	0.404645	+	0.167609i
$657$		0			0
$658$	13.6569	−	5.65685i	0.532400	−	0.220527i
$659$			39.3137i			1.53144i	0.643171	+	0.765722i	$0.277618\pi$
$659$			39.3137i			1.53144i	−0.643171	+	0.765722i	$0.722382\pi$
$660$		0			0
$661$	12.7279	+	12.7279i	0.495059	+	0.495059i	0.909896	−	0.414837i	$-0.136161\pi$
$661$	12.7279	+	12.7279i	0.495059	+	0.495059i	−0.414837	+	0.909896i	$0.636161\pi$
$662$	−27.6985			−1.07653
$663$		0			0
$664$	−6.24264			−0.242261
$665$	3.31371	+	3.31371i	0.128500	+	0.128500i
$666$		0			0
$667$		−	4.68629i		−	0.181454i
$668$	−18.2426	+	7.55635i	−0.705829	+	0.292364i
$669$		0			0
$670$	25.3137	+	10.4853i	0.977954	+	0.405082i
$671$	−23.3137	+	23.3137i	−0.900016	+	0.900016i
$672$		0			0
$673$	0.949747	+	0.393398i	0.0366101	+	0.0151644i	0.400913	−	0.916116i	$-0.368693\pi$
$673$	0.949747	+	0.393398i	0.0366101	+	0.0151644i	−0.364303	+	0.931280i	$0.618693\pi$
$674$	4.46447	−	10.7782i	0.171965	−	0.415160i
$675$		0			0
$676$			12.3137i			0.473604i
$677$	4.48528	+	10.8284i	0.172383	+	0.416170i	0.986333	−	0.164766i	$-0.0526867\pi$
$677$	4.48528	+	10.8284i	0.172383	+	0.416170i	−0.813949	+	0.580936i	$0.802687\pi$
$678$		0			0
$679$	−8.48528			−0.325635
$680$	−9.07107	−	12.2426i	−0.347860	−	0.469484i
$681$		0			0
$682$	−11.6569	−	11.6569i	−0.446364	−	0.446364i
$683$	4.15076	+	10.0208i	0.158824	+	0.383436i	0.983181	−	0.182635i	$-0.0584628\pi$
$683$	4.15076	+	10.0208i	0.158824	+	0.383436i	−0.824356	+	0.566071i	$0.808463\pi$
$684$		0			0
$685$	8.00000	−	3.31371i	0.305664	−	0.126610i
$686$	−6.82843	+	16.4853i	−0.260711	+	0.629411i
$687$		0			0
$688$	1.24264	−	1.24264i	0.0473752	−	0.0473752i
$689$	0.485281	−	0.485281i	0.0184877	−	0.0184877i
$690$		0			0
$691$	−17.9914	+	43.4350i	−0.684424	+	1.65235i	0.0712988	+	0.997455i	$0.477286\pi$
$691$	−17.9914	+	43.4350i	−0.684424	+	1.65235i	−0.755723	+	0.654891i	$0.772714\pi$
$692$	−5.41421	+	2.24264i	−0.205818	+	0.0852524i
$693$		0			0
$694$	−6.19239	−	14.9497i	−0.235060	−	0.567485i
$695$	−4.82843	−	4.82843i	−0.183153	−	0.183153i
$696$		0			0
$697$	−37.1630	+	27.5355i	−1.40765	+	1.04298i
$698$	19.6569			0.744023
$699$		0			0
$700$	5.07107	+	12.2426i	0.191668	+	0.462728i
$701$			1.51472i			0.0572101i	0.999591	+	0.0286051i	$0.00910652\pi$
$701$			1.51472i			0.0572101i	−0.999591	+	0.0286051i	$0.990893\pi$
$702$		0			0
$703$	−0.686292	+	1.65685i	−0.0258840	+	0.0624894i
$704$	4.12132	+	1.70711i	0.155328	+	0.0643390i
$705$		0			0
$706$	−10.1716	+	10.1716i	−0.382812	+	0.382812i
$707$	−6.14214	−	2.54416i	−0.230999	−	0.0956828i
$708$		0			0
$709$	−5.75736	+	2.38478i	−0.216222	+	0.0895622i	−0.488165	−	0.872751i	$-0.662334\pi$
$709$	−5.75736	+	2.38478i	−0.216222	+	0.0895622i	0.271943	+	0.962313i	$0.412334\pi$
$710$			8.00000i			0.300235i
$711$		0			0
$712$	10.6569	+	10.6569i	0.399382	+	0.399382i
$713$	−11.3137			−0.423702
$714$		0			0
$715$	−13.6569			−0.510737
$716$	18.2426	+	18.2426i	0.681759	+	0.681759i
$717$		0			0
$718$			11.3137i			0.422224i
$719$	−4.00000	+	1.65685i	−0.149175	+	0.0617902i	−0.456022	−	0.889969i	$-0.650726\pi$
$719$	−4.00000	+	1.65685i	−0.149175	+	0.0617902i	0.306847	+	0.951759i	$0.400726\pi$
$720$		0			0
$721$	17.6569	+	7.31371i	0.657576	+	0.272377i
$722$	−12.9497	+	12.9497i	−0.481940	+	0.481940i
$723$		0			0
$724$	5.65685	+	2.34315i	0.210235	+	0.0870823i
$725$	5.07107	−	12.2426i	0.188335	−	0.454680i
$726$		0			0
$727$			32.2843i			1.19736i	0.800989	+	0.598679i	$0.204307\pi$
$727$			32.2843i			1.19736i	−0.800989	+	0.598679i	$0.795693\pi$
$728$	0.485281	+	1.17157i	0.0179857	+	0.0434214i
$729$		0			0
$730$	19.7990			0.732793
$731$	1.75736	+	7.02944i	0.0649983	+	0.259993i
$732$		0			0
$733$	−9.89949	−	9.89949i	−0.365646	−	0.365646i	0.500240	−	0.865887i	$-0.333245\pi$
$733$	−9.89949	−	9.89949i	−0.365646	−	0.365646i	−0.865887	+	0.500240i	$0.833245\pi$
$734$	−7.17157	−	17.3137i	−0.264708	−	0.639061i
$735$		0			0
$736$	2.82843	−	1.17157i	0.104257	−	0.0431847i
$737$	12.6569	−	30.5563i	0.466221	−	1.12556i
$738$		0			0
$739$	−0.485281	+	0.485281i	−0.0178514	+	0.0178514i	−0.715976	−	0.698125i	$-0.754018\pi$
$739$	−0.485281	+	0.485281i	−0.0178514	+	0.0178514i	0.698125	+	0.715976i	$0.254018\pi$
$740$	−5.65685	+	5.65685i	−0.207950	+	0.207950i
$741$		0			0
$742$	−0.485281	+	1.17157i	−0.0178152	+	0.0430098i
$743$	−23.8995	+	9.89949i	−0.876787	+	0.363177i	−0.775250	−	0.631654i	$-0.782376\pi$
$743$	−23.8995	+	9.89949i	−0.876787	+	0.363177i	−0.101537	+	0.994832i	$0.532376\pi$
$744$		0			0
$745$	−22.1421	−	53.4558i	−0.811225	−	1.95847i
$746$	7.41421	+	7.41421i	0.271454	+	0.271454i
$747$		0			0
$748$	−14.7782	+	10.9497i	−0.540344	+	0.400362i
$749$	−17.8579			−0.652512
$750$		0			0
$751$	9.51472	+	22.9706i	0.347197	+	0.838208i	0.996949	+	0.0780611i	$0.0248729\pi$
$751$	9.51472	+	22.9706i	0.347197	+	0.838208i	−0.649752	+	0.760147i	$0.725127\pi$
$752$		−	9.65685i		−	0.352149i
$753$		0			0
$754$	0.485281	−	1.17157i	0.0176729	−	0.0426662i
$755$	−75.5980	−	31.3137i	−2.75129	−	1.13962i
$756$		0			0
$757$	−7.75736	+	7.75736i	−0.281946	+	0.281946i	−0.833885	−	0.551939i	$-0.813888\pi$
$757$	−7.75736	+	7.75736i	−0.281946	+	0.281946i	0.551939	+	0.833885i	$0.313888\pi$
$758$	−8.60660	−	3.56497i	−0.312606	−	0.129486i
$759$		0			0
$760$	2.82843	−	1.17157i	0.102598	−	0.0424974i
$761$		−	53.2548i		−	1.93049i	−0.261354	−	0.965243i	$-0.584169\pi$
$761$		−	53.2548i		−	1.93049i	0.261354	−	0.965243i	$-0.415831\pi$
$762$		0			0
$763$	−10.6274	−	10.6274i	−0.384738	−	0.384738i
$764$	2.82843			0.102329
$765$		0			0
$766$	−30.1421			−1.08908
$767$	−0.343146	−	0.343146i	−0.0123903	−	0.0123903i
$768$		0			0
$769$			26.3431i			0.949958i	0.879997	+	0.474979i	$0.157544\pi$
$769$			26.3431i			0.949958i	−0.879997	+	0.474979i	$0.842456\pi$
$770$	23.3137	−	9.65685i	0.840168	−	0.348009i
$771$		0			0
$772$	11.3640	+	4.70711i	0.408998	+	0.169412i
$773$	−2.58579	+	2.58579i	−0.0930043	+	0.0930043i	−0.752078	−	0.659074i	$-0.770948\pi$
$773$	−2.58579	+	2.58579i	−0.0930043	+	0.0930043i	0.659074	+	0.752078i	$0.270948\pi$
$774$		0			0
$775$	−29.5563	−	12.2426i	−1.06170	−	0.439769i
$776$	−2.12132	+	5.12132i	−0.0761510	+	0.183845i
$777$		0			0
$778$			3.17157i			0.113706i
$779$	−3.55635	−	8.58579i	−0.127419	−	0.307618i
$780$		0			0
$781$	9.65685			0.345549
$782$	−1.85786	+	12.4853i	−0.0664371	+	0.446473i
$783$		0			0
$784$	3.29289	+	3.29289i	0.117603	+	0.117603i
$785$	18.8284	+	45.4558i	0.672015	+	1.62239i
$786$		0			0
$787$	−17.6066	+	7.29289i	−0.627608	+	0.259964i	−0.673736	−	0.738972i	$-0.735312\pi$
$787$	−17.6066	+	7.29289i	−0.627608	+	0.259964i	0.0461286	+	0.998936i	$0.485312\pi$
$788$	−7.65685	+	18.4853i	−0.272764	+	0.658511i
$789$		0			0
$790$	13.6569	−	13.6569i	0.485889	−	0.485889i
$791$	10.0000	−	10.0000i	0.355559	−	0.355559i
$792$		0			0
$793$	−2.34315	+	5.65685i	−0.0832075	+	0.200881i
$794$	−7.65685	+	3.17157i	−0.271732	+	0.112555i
$795$		0			0
$796$	−8.00000	−	19.3137i	−0.283552	−	0.684556i
$797$	−18.8701	−	18.8701i	−0.668412	−	0.668412i	0.288937	−	0.957348i	$-0.406698\pi$
$797$	−18.8701	−	18.8701i	−0.668412	−	0.668412i	−0.957348	+	0.288937i	$0.906698\pi$
$798$		0			0
$799$	34.1421	+	20.4853i	1.20786	+	0.724717i
$800$	8.65685			0.306066
$801$		0			0
$802$	−9.19239	−	22.1924i	−0.324595	−	0.783640i
$803$		−	23.8995i		−	0.843395i
$804$		0			0
$805$	6.62742	−	16.0000i	0.233586	−	0.563926i
$806$	−2.82843	−	1.17157i	−0.0996271	−	0.0412669i
$807$		0			0
$808$	−3.07107	+	3.07107i	−0.108040	+	0.108040i
$809$	43.1630	+	17.8787i	1.51753	+	0.628581i	0.977095	−	0.212806i	$-0.0682601\pi$
$809$	43.1630	+	17.8787i	1.51753	+	0.628581i	0.540434	+	0.841386i	$0.318260\pi$
$810$		0			0
$811$	45.5061	−	18.8492i	1.59794	−	0.661886i	0.606813	−	0.794844i	$-0.292447\pi$
$811$	45.5061	−	18.8492i	1.59794	−	0.661886i	0.991122	+	0.132958i	$0.0424475\pi$
$812$			2.34315i			0.0822283i
$813$		0			0
$814$	6.82843	+	6.82843i	0.239336	+	0.239336i
$815$	84.0833			2.94531
$816$		0			0
$817$	−1.45584			−0.0509335
$818$	−11.0000	−	11.0000i	−0.384606	−	0.384606i
$819$		0			0
$820$		−	41.4558i		−	1.44770i
$821$	0.343146	−	0.142136i	0.0119759	−	0.00496057i	−0.376687	−	0.926340i	$-0.622937\pi$
$821$	0.343146	−	0.142136i	0.0119759	−	0.00496057i	0.388663	+	0.921380i	$0.372937\pi$
$822$		0			0
$823$	40.2843	+	16.6863i	1.40422	+	0.581648i	0.950844	−	0.309671i	$-0.100219\pi$
$823$	40.2843	+	16.6863i	1.40422	+	0.581648i	0.453378	+	0.891319i	$0.350219\pi$
$824$	8.82843	−	8.82843i	0.307553	−	0.307553i
$825$		0			0
$826$	0.828427	+	0.343146i	0.0288247	+	0.0119396i
$827$	9.15076	−	22.0919i	0.318203	−	0.768210i	−0.681147	−	0.732147i	$-0.738518\pi$
$827$	9.15076	−	22.0919i	0.318203	−	0.768210i	0.999350	−	0.0360629i	$-0.0114817\pi$
$828$		0			0
$829$		−	20.1421i		−	0.699565i	−0.936831	−	0.349783i	$-0.886255\pi$
$829$		−	20.1421i		−	0.699565i	0.936831	−	0.349783i	$-0.113745\pi$
$830$	8.82843	+	21.3137i	0.306439	+	0.739810i
$831$		0			0
$832$	0.828427			0.0287205
$833$	−18.6274	+	4.65685i	−0.645402	+	0.161350i
$834$		0			0
$835$	51.5980	+	51.5980i	1.78562	+	1.78562i
$836$	−1.41421	−	3.41421i	−0.0489116	−	0.118083i
$837$		0			0
$838$	−15.9497	+	6.60660i	−0.550975	+	0.228221i
$839$	−18.5269	+	44.7279i	−0.639620	+	1.54418i	0.187566	+	0.982252i	$0.439940\pi$
$839$	−18.5269	+	44.7279i	−0.639620	+	1.54418i	−0.827187	+	0.561927i	$0.810060\pi$
$840$		0			0
$841$	−18.8492	+	18.8492i	−0.649974	+	0.649974i
$842$	11.0711	−	11.0711i	0.381534	−	0.381534i
$843$		0			0
$844$	0.0502525	−	0.121320i	0.00172976	−	0.00417602i
$845$	42.0416	−	17.4142i	1.44628	−	0.599067i
$846$		0			0
$847$	−5.21320	−	12.5858i	−0.179128	−	0.432453i
$848$	0.585786	+	0.585786i	0.0201160	+	0.0201160i
$849$		0			0
$850$	−18.3640	+	30.6066i	−0.629879	+	1.04980i
$851$	6.62742			0.227185
$852$		0			0
$853$	−14.5269	−	35.0711i	−0.497392	−	1.20081i	−0.950883	−	0.309550i	$-0.899822\pi$
$853$	−14.5269	−	35.0711i	−0.497392	−	1.20081i	0.453491	−	0.891261i	$-0.350178\pi$
$854$		−	11.3137i		−	0.387147i
$855$		0			0
$856$	−4.46447	+	10.7782i	−0.152592	+	0.368390i
$857$	37.1924	+	15.4056i	1.27047	+	0.526245i	0.913106	−	0.407721i	$-0.133676\pi$
$857$	37.1924	+	15.4056i	1.27047	+	0.526245i	0.357361	+	0.933966i	$0.383676\pi$
$858$		0			0
$859$	0.556349	−	0.556349i	0.0189824	−	0.0189824i	−0.697552	−	0.716534i	$-0.745727\pi$
$859$	0.556349	−	0.556349i	0.0189824	−	0.0189824i	0.716534	+	0.697552i	$0.245727\pi$
$860$	−6.00000	−	2.48528i	−0.204598	−	0.0847474i
$861$		0			0
$862$	−13.3137	+	5.51472i	−0.453467	+	0.187832i
$863$			0.970563i			0.0330383i	0.999864	+	0.0165192i	$0.00525845\pi$
$863$			0.970563i			0.0330383i	−0.999864	+	0.0165192i	$0.994742\pi$
$864$		0			0
$865$	15.3137	+	15.3137i	0.520682	+	0.520682i
$866$	12.9706			0.440758
$867$		0			0
$868$	5.65685			0.192006
$869$	−16.4853	−	16.4853i	−0.559225	−	0.559225i
$870$		0			0
$871$		−	6.14214i		−	0.208118i
$872$	−9.07107	+	3.75736i	−0.307185	+	0.127240i
$873$		0			0
$874$	−2.34315	−	0.970563i	−0.0792581	−	0.0328298i
$875$	14.6274	−	14.6274i	0.494497	−	0.494497i
$876$		0			0
$877$	9.89949	+	4.10051i	0.334282	+	0.138464i	0.543510	−	0.839403i	$-0.317095\pi$
$877$	9.89949	+	4.10051i	0.334282	+	0.138464i	−0.209228	+	0.977867i	$0.567095\pi$
$878$	−8.82843	+	21.3137i	−0.297945	+	0.719303i
$879$		0			0
$880$		−	16.4853i		−	0.555719i
$881$	6.92031	+	16.7071i	0.233151	+	0.562877i	0.996545	−	0.0830568i	$-0.0264683\pi$
$881$	6.92031	+	16.7071i	0.233151	+	0.562877i	−0.763394	+	0.645934i	$0.776468\pi$
$882$		0			0
$883$	34.5269			1.16192			0.580962	−	0.813931i	$-0.302677\pi$
$883$	34.5269			1.16192			0.580962	+	0.813931i	$0.302677\pi$
$884$	−1.75736	+	2.92893i	−0.0591064	+	0.0985106i
$885$		0			0
$886$	−26.0711	−	26.0711i	−0.875875	−	0.875875i
$887$	0.970563	+	2.34315i	0.0325883	+	0.0786751i	0.939336	−	0.342999i	$-0.111443\pi$
$887$	0.970563	+	2.34315i	0.0325883	+	0.0786751i	−0.906748	+	0.421674i	$0.861443\pi$
$888$		0			0
$889$	−18.3431	+	7.59798i	−0.615209	+	0.254828i
$890$	21.3137	−	51.4558i	0.714437	−	1.72480i
$891$		0			0
$892$	17.3137	−	17.3137i	0.579706	−	0.579706i
$893$	−5.65685	+	5.65685i	−0.189299	+	0.189299i
$894$		0			0
$895$	36.4853	−	88.0833i	1.21957	−	2.94430i
$896$	−1.41421	+	0.585786i	−0.0472456	+	0.0195698i
$897$		0			0
$898$	2.12132	+	5.12132i	0.0707894	+	0.170901i
$899$	−4.00000	−	4.00000i	−0.133407	−	0.133407i
$900$		0			0
$901$	−3.31371	+	0.828427i	−0.110396	+	0.0275989i
$902$	−50.0416			−1.66620
$903$		0			0
$904$	−3.53553	−	8.53553i	−0.117590	−	0.283888i
$905$		−	22.6274i		−	0.752161i
$906$		0			0
$907$	5.60660	−	13.5355i	0.186164	−	0.449440i	−0.803051	−	0.595910i	$-0.796791\pi$
$907$	5.60660	−	13.5355i	0.186164	−	0.449440i	0.989215	+	0.146470i	$0.0467913\pi$
$908$	−18.7782	−	7.77817i	−0.623176	−	0.258128i
$909$		0			0
$910$	3.31371	−	3.31371i	0.109848	−	0.109848i
$911$	21.5563	+	8.92893i	0.714194	+	0.295829i	0.710039	−	0.704163i	$-0.248677\pi$
$911$	21.5563	+	8.92893i	0.714194	+	0.295829i	0.00415500	+	0.999991i	$0.498677\pi$
$912$		0			0
$913$	25.7279	−	10.6569i	0.851470	−	0.352690i
$914$		−	4.97056i		−	0.164412i
$915$		0			0
$916$	13.0711	+	13.0711i	0.431880	+	0.431880i
$917$	−0.201010			−0.00663794
$918$		0			0
$919$	−2.34315			−0.0772932			−0.0386466	−	0.999253i	$-0.512305\pi$
$919$	−2.34315			−0.0772932			−0.0386466	+	0.999253i	$0.512305\pi$
$920$	−8.00000	−	8.00000i	−0.263752	−	0.263752i
$921$		0			0
$922$		−	34.9706i		−	1.15169i
$923$	1.65685	−	0.686292i	0.0545360	−	0.0225896i
$924$		0			0
$925$	17.3137	+	7.17157i	0.569271	+	0.235800i
$926$	−2.34315	+	2.34315i	−0.0770005	+	0.0770005i
$927$		0			0
$928$	1.41421	+	0.585786i	0.0464238	+	0.0192294i
$929$	3.53553	−	8.53553i	0.115997	−	0.280042i	−0.855209	−	0.518284i	$-0.826571\pi$
$929$	3.53553	−	8.53553i	0.115997	−	0.280042i	0.971206	+	0.238242i	$0.0765711\pi$
$930$		0			0
$931$		−	3.85786i		−	0.126436i
$932$	−4.02082	−	9.70711i	−0.131706	−	0.317967i
$933$		0			0
$934$	−2.48528			−0.0813209
$935$	58.2843	+	34.9706i	1.90610	+	1.14366i
$936$		0			0
$937$	−3.75736	−	3.75736i	−0.122748	−	0.122748i	0.643064	−	0.765812i	$-0.277663\pi$
$937$	−3.75736	−	3.75736i	−0.122748	−	0.122748i	−0.765812	+	0.643064i	$0.777663\pi$
$938$	4.34315	+	10.4853i	0.141809	+	0.342357i
$939$		0			0
$940$	−32.9706	+	13.6569i	−1.07538	+	0.445437i
$941$	−7.51472	+	18.1421i	−0.244973	+	0.591417i	−0.997763	−	0.0668433i	$-0.978707\pi$
$941$	−7.51472	+	18.1421i	−0.244973	+	0.591417i	0.752791	+	0.658260i	$0.228707\pi$
$942$		0			0
$943$	−24.2843	+	24.2843i	−0.790805	+	0.790805i
$944$	0.414214	−	0.414214i	0.0134815	−	0.0134815i
$945$		0			0
$946$	−3.00000	+	7.24264i	−0.0975384	+	0.235479i
$947$	48.3345	−	20.0208i	1.57066	−	0.650589i	0.583761	−	0.811925i	$-0.301580\pi$
$947$	48.3345	−	20.0208i	1.57066	−	0.650589i	0.986900	+	0.161336i	$0.0515803\pi$
$948$		0			0
$949$	−1.69848	−	4.10051i	−0.0551352	−	0.133108i
$950$	−5.07107	−	5.07107i	−0.164527	−	0.164527i
$951$		0			0
$952$	0.928932	−	6.24264i	0.0301069	−	0.202325i
$953$	11.5563			0.374347			0.187173	−	0.982327i	$-0.440067\pi$
$953$	11.5563			0.374347			0.187173	+	0.982327i	$0.440067\pi$
$954$		0			0
$955$	−4.00000	−	9.65685i	−0.129437	−	0.312488i
$956$		−	21.1716i		−	0.684738i
$957$		0			0
$958$	−9.51472	+	22.9706i	−0.307407	+	0.742145i
$959$	3.31371	+	1.37258i	0.107005	+	0.0443230i
$960$		0			0
$961$	12.2635	−	12.2635i	0.395595	−	0.395595i
$962$	1.65685	+	0.686292i	0.0534191	+	0.0221269i
$963$		0			0
$964$	−18.3640	+	7.60660i	−0.591463	+	0.244992i
$965$		−	45.4558i		−	1.46328i
$966$		0			0
$967$	9.65685	+	9.65685i	0.310543	+	0.310543i	0.845120	−	0.534577i	$-0.179529\pi$
$967$	9.65685	+	9.65685i	0.310543	+	0.310543i	−0.534577	+	0.845120i	$0.679529\pi$
$968$	−8.89949			−0.286041
$969$		0			0
$970$	20.4853			0.657743
$971$	−15.0416	−	15.0416i	−0.482709	−	0.482709i	0.423287	−	0.905996i	$-0.360876\pi$
$971$	−15.0416	−	15.0416i	−0.482709	−	0.482709i	−0.905996	+	0.423287i	$0.860876\pi$
$972$		0			0
$973$		−	2.82843i		−	0.0906752i
$974$	−20.4853	+	8.48528i	−0.656391	+	0.271886i
$975$		0			0
$976$	−6.82843	−	2.82843i	−0.218573	−	0.0905357i
$977$	−20.1127	+	20.1127i	−0.643462	+	0.643462i	−0.951405	−	0.307943i	$-0.900359\pi$
$977$	−20.1127	+	20.1127i	−0.643462	+	0.643462i	0.307943	+	0.951405i	$0.400359\pi$
$978$		0			0
$979$	−62.1127	−	25.7279i	−1.98513	−	0.822268i
$980$	6.58579	−	15.8995i	0.210375	−	0.507891i
$981$		0			0
$982$			15.4558i			0.493216i
$983$	−10.3431	−	24.9706i	−0.329895	−	0.796437i	−0.998599	−	0.0529088i	$-0.983151\pi$
$983$	−10.3431	−	24.9706i	−0.329895	−	0.796437i	0.668704	−	0.743529i	$-0.266849\pi$
$984$		0			0
$985$	73.9411			2.35596
$986$	−5.07107	+	3.75736i	−0.161496	+	0.119659i
$987$		0			0
$988$	−0.485281	−	0.485281i	−0.0154389	−	0.0154389i
$989$	2.05887	+	4.97056i	0.0654684	+	0.158055i
$990$		0			0
$991$	−42.2843	+	17.5147i	−1.34320	+	0.556373i	−0.934392	−	0.356245i	$-0.884057\pi$
$991$	−42.2843	+	17.5147i	−1.34320	+	0.556373i	−0.408812	+	0.912619i	$0.634057\pi$
$992$	1.41421	−	3.41421i	0.0449013	−	0.108401i
$993$		0			0
$994$	−2.34315	+	2.34315i	−0.0743201	+	0.0743201i
$995$	−54.6274	+	54.6274i	−1.73181	+	1.73181i
$996$		0			0
$997$	−4.54416	+	10.9706i	−0.143915	+	0.347441i	−0.979357	−	0.202137i	$-0.935211\pi$
$997$	−4.54416	+	10.9706i	−0.143915	+	0.347441i	0.835442	+	0.549578i	$0.185211\pi$
$998$	34.0208	−	14.0919i	1.07691	−	0.446071i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	306.2.l.c.253.1		4
3.2	odd	2		34.2.d.a.15.1	✓	4
12.11	even	2		272.2.v.b.49.1		4
15.2	even	4		850.2.o.a.49.1		4
15.8	even	4		850.2.o.b.49.1		4
15.14	odd	2		850.2.l.a.151.1		4
17.5	odd	16		5202.2.a.bw.1.1		4
17.8	even	8	inner	306.2.l.c.127.1		4
17.12	odd	16		5202.2.a.bw.1.4		4
51.2	odd	8		578.2.d.a.179.1		4
51.5	even	16		578.2.a.i.1.4		4
51.8	odd	8		34.2.d.a.25.1	yes	4
51.11	even	16		578.2.c.f.251.4		8
51.14	even	16		578.2.b.d.577.4		4
51.20	even	16		578.2.b.d.577.1		4
51.23	even	16		578.2.c.f.251.1		8
51.26	odd	8		578.2.d.b.399.1		4
51.29	even	16		578.2.a.i.1.1		4
51.32	odd	8		578.2.d.c.179.1		4
51.38	odd	4		578.2.d.a.155.1		4
51.41	even	16		578.2.c.f.327.1		8
51.44	even	16		578.2.c.f.327.4		8
51.47	odd	4		578.2.d.c.155.1		4
51.50	odd	2		578.2.d.b.423.1		4
204.59	even	8		272.2.v.b.161.1		4
204.107	odd	16		4624.2.a.bn.1.1		4
204.131	odd	16		4624.2.a.bn.1.4		4
255.8	even	8		850.2.o.a.399.1		4
255.59	odd	8		850.2.l.a.501.1		4
255.212	even	8		850.2.o.b.399.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
34.2.d.a.15.1	✓	4	3.2	odd	2
34.2.d.a.25.1	yes	4	51.8	odd	8
272.2.v.b.49.1		4	12.11	even	2
272.2.v.b.161.1		4	204.59	even	8
306.2.l.c.127.1		4	17.8	even	8	inner
306.2.l.c.253.1		4	1.1	even	1	trivial
578.2.a.i.1.1		4	51.29	even	16
578.2.a.i.1.4		4	51.5	even	16
578.2.b.d.577.1		4	51.20	even	16
578.2.b.d.577.4		4	51.14	even	16
578.2.c.f.251.1		8	51.23	even	16
578.2.c.f.251.4		8	51.11	even	16
578.2.c.f.327.1		8	51.41	even	16
578.2.c.f.327.4		8	51.44	even	16
578.2.d.a.155.1		4	51.38	odd	4
578.2.d.a.179.1		4	51.2	odd	8
578.2.d.b.399.1		4	51.26	odd	8
578.2.d.b.423.1		4	51.50	odd	2
578.2.d.c.155.1		4	51.47	odd	4
578.2.d.c.179.1		4	51.32	odd	8
850.2.l.a.151.1		4	15.14	odd	2
850.2.l.a.501.1		4	255.59	odd	8
850.2.o.a.49.1		4	15.2	even	4
850.2.o.a.399.1		4	255.8	even	8
850.2.o.b.49.1		4	15.8	even	4
850.2.o.b.399.1		4	255.212	even	8
4624.2.a.bn.1.1		4	204.107	odd	16
4624.2.a.bn.1.4		4	204.131	odd	16
5202.2.a.bw.1.1		4	17.5	odd	16
5202.2.a.bw.1.4		4	17.12	odd	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 306 = 2 \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	306.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(3.41421 - 1.41421i) q^{5} +(1.41421 + 0.585786i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-3.41421 - 1.41421i) q^{10} +(-1.70711 + 4.12132i) q^{11} +0.828427i q^{13} +(-0.585786 - 1.41421i) q^{14} -1.00000 q^{16} +(2.12132 - 3.53553i) q^{17} +(0.585786 + 0.585786i) q^{19} +(1.41421 + 3.41421i) q^{20} +(4.12132 - 1.70711i) q^{22} +(1.17157 - 2.82843i) q^{23} +(6.12132 - 6.12132i) q^{25} +(0.585786 - 0.585786i) q^{26} +(-0.585786 + 1.41421i) q^{28} +(1.41421 - 0.585786i) q^{29} +(-1.41421 - 3.41421i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-4.00000 + 1.00000i) q^{34} +5.65685 q^{35} +(0.828427 + 2.00000i) q^{37} -0.828427i q^{38} +(1.41421 - 3.41421i) q^{40} +(-10.3640 - 4.29289i) q^{41} +(-1.24264 + 1.24264i) q^{43} +(-4.12132 - 1.70711i) q^{44} +(-2.82843 + 1.17157i) q^{46} +9.65685i q^{47} +(-3.29289 - 3.29289i) q^{49} -8.65685 q^{50} -0.828427 q^{52} +(-0.585786 - 0.585786i) q^{53} +16.4853i q^{55} +(1.41421 - 0.585786i) q^{56} +(-1.41421 - 0.585786i) q^{58} +(-0.414214 + 0.414214i) q^{59} +(6.82843 + 2.82843i) q^{61} +(-1.41421 + 3.41421i) q^{62} -1.00000i q^{64} +(1.17157 + 2.82843i) q^{65} -7.41421 q^{67} +(3.53553 + 2.12132i) q^{68} +(-4.00000 - 4.00000i) q^{70} +(-0.828427 - 2.00000i) q^{71} +(-4.94975 + 2.05025i) q^{73} +(0.828427 - 2.00000i) q^{74} +(-0.585786 + 0.585786i) q^{76} +(-4.82843 + 4.82843i) q^{77} +(-2.00000 + 4.82843i) q^{79} +(-3.41421 + 1.41421i) q^{80} +(4.29289 + 10.3640i) q^{82} +(-4.41421 - 4.41421i) q^{83} +(2.24264 - 15.0711i) q^{85} +1.75736 q^{86} +(1.70711 + 4.12132i) q^{88} +15.0711i q^{89} +(-0.485281 + 1.17157i) q^{91} +(2.82843 + 1.17157i) q^{92} +(6.82843 - 6.82843i) q^{94} +(2.82843 + 1.17157i) q^{95} +(-5.12132 + 2.12132i) q^{97} +4.65685i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{5} - 8 q^{10} - 4 q^{11} - 8 q^{14} - 4 q^{16} + 8 q^{19} + 8 q^{22} + 16 q^{23} + 16 q^{25} + 8 q^{26} - 8 q^{28} - 16 q^{34} - 8 q^{37} - 16 q^{41} + 12 q^{43} - 8 q^{44} - 16 q^{49} - 12 q^{50}+ \cdots - 12 q^{97}+O(q^{100}) \) 4 * q + 8 * q^5 - 8 * q^10 - 4 * q^11 - 8 * q^14 - 4 * q^16 + 8 * q^19 + 8 * q^22 + 16 * q^23 + 16 * q^25 + 8 * q^26 - 8 * q^28 - 16 * q^34 - 8 * q^37 - 16 * q^41 + 12 * q^43 - 8 * q^44 - 16 * q^49 - 12 * q^50 + 8 * q^52 - 8 * q^53 + 4 * q^59 + 16 * q^61 + 16 * q^65 - 24 * q^67 - 16 * q^70 + 8 * q^71 - 8 * q^74 - 8 * q^76 - 8 * q^77 - 8 * q^79 - 8 * q^80 + 20 * q^82 - 12 * q^83 - 8 * q^85 + 24 * q^86 + 4 * q^88 + 32 * q^91 + 16 * q^94 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more