LMFDB - Embedded newform 306.2.l.d.127.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [306,2,Mod(19,306)]

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

lf = mfeigenbasis(mf)

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")

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

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

Self dual:	no
Analytic conductor:	$2.44342230185$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{8})$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 102)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			127.2
Root			$0.923880 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	306.127
Dual form			306.2.l.d.253.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.400544 - 0.165911i) q^{5} +(3.15432 - 1.30656i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.400544 - 0.165911i) q^{5} +(3.15432 - 1.30656i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.400544 + 0.165911i) q^{10} +(-0.648847 - 1.56645i) q^{11} -0.331821i q^{13} +(1.30656 - 3.15432i) q^{14} -1.00000 q^{16} +(3.94495 - 1.19891i) q^{17} +(-1.51594 + 1.51594i) q^{19} +(-0.165911 + 0.400544i) q^{20} +(-1.56645 - 0.648847i) q^{22} +(-0.720777 - 1.74011i) q^{23} +(-3.40262 - 3.40262i) q^{25} +(-0.234633 - 0.234633i) q^{26} +(-1.30656 - 3.15432i) q^{28} +(7.88877 + 3.26763i) q^{29} +(-0.989538 + 2.38896i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(1.94174 - 3.63726i) q^{34} -1.48022 q^{35} +(-4.06193 + 9.80638i) q^{37} +2.14386i q^{38} +(0.165911 + 0.400544i) q^{40} +(-11.1953 + 4.63726i) q^{41} +(7.13707 + 7.13707i) q^{43} +(-1.56645 + 0.648847i) q^{44} +(-1.74011 - 0.720777i) q^{46} -2.38009i q^{47} +(3.29289 - 3.29289i) q^{49} -4.81204 q^{50} -0.331821 q^{52} +(-2.21371 + 2.21371i) q^{53} +0.735084i q^{55} +(-3.15432 - 1.30656i) q^{56} +(7.88877 - 3.26763i) q^{58} +(5.42676 + 5.42676i) q^{59} +(-7.42788 + 3.07673i) q^{61} +(0.989538 + 2.38896i) q^{62} +1.00000i q^{64} +(-0.0550527 + 0.132909i) q^{65} +15.7711 q^{67} +(-1.19891 - 3.94495i) q^{68} +(-1.04667 + 1.04667i) q^{70} +(-0.0867259 + 0.209375i) q^{71} +(-11.2147 - 4.64527i) q^{73} +(4.06193 + 9.80638i) q^{74} +(1.51594 + 1.51594i) q^{76} +(-4.09334 - 4.09334i) q^{77} +(-4.79863 - 11.5849i) q^{79} +(0.400544 + 0.165911i) q^{80} +(-4.63726 + 11.1953i) q^{82} +(0.738027 - 0.738027i) q^{83} +(-1.77904 - 0.174292i) q^{85} +10.0933 q^{86} +(-0.648847 + 1.56645i) q^{88} +13.8281i q^{89} +(-0.433546 - 1.04667i) q^{91} +(-1.74011 + 0.720777i) q^{92} +(-1.68297 - 1.68297i) q^{94} +(0.858710 - 0.355689i) q^{95} +(3.46953 + 1.43713i) q^{97} -4.65685i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{5}+O(q^{10}) $ 8 * q - 8 * q^5	$ 8 q - 8 q^{5} - 8 q^{10} - 8 q^{16} + 8 q^{17} - 16 q^{22} + 16 q^{23} + 8 q^{25} - 8 q^{26} + 16 q^{34} + 16 q^{35} - 16 q^{41} - 16 q^{43} - 16 q^{44} + 32 q^{49} - 8 q^{50} - 8 q^{53} - 32 q^{61} - 24 q^{65} + 48 q^{67} + 16 q^{70} + 16 q^{71} - 24 q^{73} + 16 q^{77} + 8 q^{80} - 8 q^{82} + 32 q^{83} + 8 q^{85} + 32 q^{86} - 16 q^{94} - 48 q^{95} + 16 q^{97}+O(q^{100}) $ 8 * q - 8 * q^5 - 8 * q^10 - 8 * q^16 + 8 * q^17 - 16 * q^22 + 16 * q^23 + 8 * q^25 - 8 * q^26 + 16 * q^34 + 16 * q^35 - 16 * q^41 - 16 * q^43 - 16 * q^44 + 32 * q^49 - 8 * q^50 - 8 * q^53 - 32 * q^61 - 24 * q^65 + 48 * q^67 + 16 * q^70 + 16 * q^71 - 24 * q^73 + 16 * q^77 + 8 * q^80 - 8 * q^82 + 32 * q^83 + 8 * q^85 + 32 * q^86 - 16 * q^94 - 48 * q^95 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$

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
$5$	−0.400544	−	0.165911i	−0.179129	−	0.0741975i	0.291317	−	0.956627i	$-0.405907\pi$
$5$	−0.400544	−	0.165911i	−0.179129	−	0.0741975i	−0.470445	+	0.882429i	$0.655907\pi$
$6$		0			0
$7$	3.15432	−	1.30656i	1.19222	−	0.493834i	0.303744	−	0.952754i	$-0.401763\pi$
$7$	3.15432	−	1.30656i	1.19222	−	0.493834i	0.888478	+	0.458919i	$0.151763\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	−0.400544	+	0.165911i	−0.126663	+	0.0524656i
$11$	−0.648847	−	1.56645i	−0.195635	−	0.472304i	0.795371	−	0.606123i	$-0.207276\pi$
$11$	−0.648847	−	1.56645i	−0.195635	−	0.472304i	−0.991006	+	0.133819i	$0.957276\pi$
$12$		0			0
$13$		−	0.331821i		−	0.0920307i	−0.998941	−	0.0460153i	$-0.985348\pi$
$13$		−	0.331821i		−	0.0920307i	0.998941	−	0.0460153i	$-0.0146523\pi$
$14$	1.30656	−	3.15432i	0.349194	−	0.843028i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	3.94495	−	1.19891i	0.956790	−	0.290779i
$17$	3.94495	−	1.19891i	0.956790	−	0.290779i
$18$		0			0
$19$	−1.51594	+	1.51594i	−0.347780	+	0.347780i	−0.859282	−	0.511502i	$-0.829089\pi$
$19$	−1.51594	+	1.51594i	−0.347780	+	0.347780i	0.511502	+	0.859282i	$0.329089\pi$
$20$	−0.165911	+	0.400544i	−0.0370988	+	0.0895643i
$21$		0			0
$22$	−1.56645	−	0.648847i	−0.333969	−	0.138335i
$23$	−0.720777	−	1.74011i	−0.150292	−	0.362838i	0.830746	−	0.556652i	$-0.187914\pi$
$23$	−0.720777	−	1.74011i	−0.150292	−	0.362838i	−0.981038	+	0.193814i	$0.937914\pi$
$24$		0			0
$25$	−3.40262	−	3.40262i	−0.680525	−	0.680525i
$26$	−0.234633	−	0.234633i	−0.0460153	−	0.0460153i
$27$		0			0
$28$	−1.30656	−	3.15432i	−0.246917	−	0.596111i
$29$	7.88877	+	3.26763i	1.46491	+	0.606785i	0.965691	−	0.259693i	$-0.0836213\pi$
$29$	7.88877	+	3.26763i	1.46491	+	0.606785i	0.499216	+	0.866477i	$0.333621\pi$
$30$		0			0
$31$	−0.989538	+	2.38896i	−0.177726	+	0.429069i	−0.987489	−	0.157688i	$-0.949596\pi$
$31$	−0.989538	+	2.38896i	−0.177726	+	0.429069i	0.809763	+	0.586758i	$0.199596\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$	1.94174	−	3.63726i	0.333006	−	0.623785i
$35$	−1.48022			−0.250202
$36$		0			0
$37$	−4.06193	+	9.80638i	−0.667778	+	1.61216i	0.117542	+	0.993068i	$0.462499\pi$
$37$	−4.06193	+	9.80638i	−0.667778	+	1.61216i	−0.785320	+	0.619090i	$0.787501\pi$
$38$			2.14386i			0.347780i
$39$		0			0
$40$	0.165911	+	0.400544i	0.0262328	+	0.0633315i
$41$	−11.1953	+	4.63726i	−1.74842	+	0.724218i	−0.750420	+	0.660962i	$0.770149\pi$
$41$	−11.1953	+	4.63726i	−1.74842	+	0.724218i	−0.997997	+	0.0632564i	$0.979851\pi$
$42$		0			0
$43$	7.13707	+	7.13707i	1.08839	+	1.08839i	0.995694	+	0.0926990i	$0.0295494\pi$
$43$	7.13707	+	7.13707i	1.08839	+	1.08839i	0.0926990	+	0.995694i	$0.470451\pi$
$44$	−1.56645	+	0.648847i	−0.236152	+	0.0978173i
$45$		0			0
$46$	−1.74011	−	0.720777i	−0.256565	−	0.106273i
$47$		−	2.38009i		−	0.347171i	−0.984819	−	0.173586i	$-0.944465\pi$
$47$		−	2.38009i		−	0.347171i	0.984819	−	0.173586i	$-0.0555353\pi$
$48$		0			0
$49$	3.29289	−	3.29289i	0.470413	−	0.470413i
$50$	−4.81204			−0.680525
$51$		0			0
$52$	−0.331821			−0.0460153
$53$	−2.21371	+	2.21371i	−0.304076	+	0.304076i	−0.842606	−	0.538530i	$-0.818980\pi$
$53$	−2.21371	+	2.21371i	−0.304076	+	0.304076i	0.538530	+	0.842606i	$0.318980\pi$
$54$		0			0
$55$			0.735084i			0.0991187i
$56$	−3.15432	−	1.30656i	−0.421514	−	0.174597i
$57$		0			0
$58$	7.88877	−	3.26763i	1.03585	−	0.429061i
$59$	5.42676	+	5.42676i	0.706504	+	0.706504i	0.965798	−	0.259295i	$-0.0834901\pi$
$59$	5.42676	+	5.42676i	0.706504	+	0.706504i	−0.259295	+	0.965798i	$0.583490\pi$
$60$		0			0
$61$	−7.42788	+	3.07673i	−0.951043	+	0.393935i	−0.803623	−	0.595139i	$-0.797097\pi$
$61$	−7.42788	+	3.07673i	−0.951043	+	0.393935i	−0.147420	+	0.989074i	$0.547097\pi$
$62$	0.989538	+	2.38896i	0.125671	+	0.303398i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−0.0550527	+	0.132909i	−0.00682845	+	0.0164853i
$66$		0			0
$67$	15.7711			1.92675			0.963375	−	0.268159i	$-0.0864153\pi$
$67$	15.7711			1.92675			0.963375	+	0.268159i	$0.0864153\pi$
$68$	−1.19891	−	3.94495i	−0.145389	−	0.478395i
$69$		0			0
$70$	−1.04667	+	1.04667i	−0.125101	+	0.125101i
$71$	−0.0867259	+	0.209375i	−0.0102925	+	0.0248482i	−0.928942	−	0.370225i	$-0.879281\pi$
$71$	−0.0867259	+	0.209375i	−0.0102925	+	0.0248482i	0.918650	+	0.395073i	$0.129281\pi$
$72$		0			0
$73$	−11.2147	−	4.64527i	−1.31258	−	0.543687i	−0.386942	−	0.922104i	$-0.626469\pi$
$73$	−11.2147	−	4.64527i	−1.31258	−	0.543687i	−0.925635	+	0.378417i	$0.876469\pi$
$74$	4.06193	+	9.80638i	0.472190	+	1.13997i
$75$		0			0
$76$	1.51594	+	1.51594i	0.173890	+	0.173890i
$77$	−4.09334	−	4.09334i	−0.466480	−	0.466480i
$78$		0			0
$79$	−4.79863	−	11.5849i	−0.539888	−	1.30341i	−0.924800	−	0.380453i	$-0.875768\pi$
$79$	−4.79863	−	11.5849i	−0.539888	−	1.30341i	0.384912	−	0.922953i	$-0.374232\pi$
$80$	0.400544	+	0.165911i	0.0447822	+	0.0185494i
$81$		0			0
$82$	−4.63726	+	11.1953i	−0.512099	+	1.23632i
$83$	0.738027	−	0.738027i	0.0810090	−	0.0810090i	−0.665441	−	0.746450i	$-0.731757\pi$
$83$	0.738027	−	0.738027i	0.0810090	−	0.0810090i	0.746450	+	0.665441i	$0.231757\pi$
$84$		0			0
$85$	−1.77904	−	0.174292i	−0.192964	−	0.0189046i
$86$	10.0933			1.08839
$87$		0			0
$88$	−0.648847	+	1.56645i	−0.0691673	+	0.166985i
$89$			13.8281i			1.46577i	0.680352	+	0.732885i	$0.261827\pi$
$89$			13.8281i			1.46577i	−0.680352	+	0.732885i	$0.738173\pi$
$90$		0			0
$91$	−0.433546	−	1.04667i	−0.0454479	−	0.109721i
$92$	−1.74011	+	0.720777i	−0.181419	+	0.0751461i
$93$		0			0
$94$	−1.68297	−	1.68297i	−0.173586	−	0.173586i
$95$	0.858710	−	0.355689i	0.0881018	−	0.0364929i
$96$		0			0
$97$	3.46953	+	1.43713i	0.352277	+	0.145918i	0.551803	−	0.833975i	$-0.313940\pi$
$97$	3.46953	+	1.43713i	0.352277	+	0.145918i	−0.199525	+	0.979893i	$0.563940\pi$
$98$		−	4.65685i		−	0.470413i
$99$		0			0
$100$	−3.40262	+	3.40262i	−0.340262	+	0.340262i
$101$	0.636303			0.0633145			0.0316573	−	0.999499i	$-0.489921\pi$
$101$	0.636303			0.0633145			0.0316573	+	0.999499i	$0.489921\pi$
$102$		0			0
$103$	8.59955			0.847339			0.423669	−	0.905817i	$-0.360742\pi$
$103$	8.59955			0.847339			0.423669	+	0.905817i	$0.360742\pi$
$104$	−0.234633	+	0.234633i	−0.0230077	+	0.0230077i
$105$		0			0
$106$			3.13066i			0.304076i
$107$	−2.00000	−	0.828427i	−0.193347	−	0.0800871i	0.283909	−	0.958851i	$-0.408369\pi$
$107$	−2.00000	−	0.828427i	−0.193347	−	0.0800871i	−0.477256	+	0.878764i	$0.658369\pi$
$108$		0			0
$109$	−7.31136	+	3.02847i	−0.700302	+	0.290074i	−0.704285	−	0.709918i	$-0.748732\pi$
$109$	−7.31136	+	3.02847i	−0.700302	+	0.290074i	0.00398311	+	0.999992i	$0.498732\pi$
$110$	0.519783	+	0.519783i	0.0495594	+	0.0495594i
$111$		0			0
$112$	−3.15432	+	1.30656i	−0.298055	+	0.123459i
$113$	−3.51620	−	8.48886i	−0.330776	−	0.798565i	−0.998531	−	0.0541835i	$-0.982744\pi$
$113$	−3.51620	−	8.48886i	−0.330776	−	0.798565i	0.667755	−	0.744382i	$-0.267256\pi$
$114$		0			0
$115$			0.816574i			0.0761459i
$116$	3.26763	−	7.88877i	0.303392	−	0.732454i
$117$		0			0
$118$	7.67459			0.706504
$119$	10.8772	−	8.93608i	0.997109	−	0.819169i
$120$		0			0
$121$	5.74540	−	5.74540i	0.522309	−	0.522309i
$122$	−3.07673	+	7.42788i	−0.278554	+	0.672489i
$123$		0			0
$124$	2.38896	+	0.989538i	0.214535	+	0.0888631i
$125$	1.62792	+	3.93015i	0.145606	+	0.351523i
$126$		0			0
$127$	−8.54487	−	8.54487i	−0.758235	−	0.758235i	0.217766	−	0.976001i	$-0.430123\pi$
$127$	−8.54487	−	8.54487i	−0.758235	−	0.758235i	−0.976001	+	0.217766i	$0.930123\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	0.0550527	+	0.132909i	0.00482844	+	0.0116569i
$131$	0.828427	+	0.343146i	0.0723800	+	0.0299808i	0.418580	−	0.908180i	$-0.362528\pi$
$131$	0.828427	+	0.343146i	0.0723800	+	0.0299808i	−0.346200	+	0.938161i	$0.612528\pi$
$132$		0			0
$133$	−2.80109	+	6.76242i	−0.242885	+	0.586377i
$134$	11.1519	−	11.1519i	0.963375	−	0.963375i
$135$		0			0
$136$	−3.63726	−	1.94174i	−0.311892	−	0.166503i
$137$	−12.6109			−1.07742			−0.538710	−	0.842491i	$-0.681088\pi$
$137$	−12.6109			−1.07742			−0.538710	+	0.842491i	$0.681088\pi$
$138$		0			0
$139$	6.52273	−	15.7473i	0.553250	−	1.33566i	−0.361774	−	0.932266i	$-0.617829\pi$
$139$	6.52273	−	15.7473i	0.553250	−	1.33566i	0.915024	−	0.403399i	$-0.132171\pi$
$140$			1.48022i			0.125101i
$141$		0			0
$142$	0.0867259	+	0.209375i	0.00727787	+	0.0175703i
$143$	−0.519783	+	0.215301i	−0.0434664	+	0.0180044i
$144$		0			0
$145$	−2.61766	−	2.61766i	−0.217385	−	0.217385i
$146$	−11.2147	+	4.64527i	−0.928132	+	0.384445i
$147$		0			0
$148$	9.80638	+	4.06193i	0.806079	+	0.333889i
$149$		−	17.5004i		−	1.43369i	−0.697234	−	0.716844i	$-0.745586\pi$
$149$		−	17.5004i		−	1.43369i	0.697234	−	0.716844i	$-0.254414\pi$
$150$		0			0
$151$	6.81657	−	6.81657i	0.554725	−	0.554725i	−0.373076	−	0.927801i	$-0.621697\pi$
$151$	6.81657	−	6.81657i	0.554725	−	0.554725i	0.927801	+	0.373076i	$0.121697\pi$
$152$	2.14386			0.173890
$153$		0			0
$154$	−5.78886			−0.466480
$155$	0.792706	−	0.792706i	0.0636717	−	0.0636717i
$156$		0			0
$157$			4.78976i			0.382265i	0.981564	+	0.191132i	$0.0612160\pi$
$157$			4.78976i			0.382265i	−0.981564	+	0.191132i	$0.938784\pi$
$158$	−11.5849	−	4.79863i	−0.921647	−	0.381759i
$159$		0			0
$160$	0.400544	−	0.165911i	0.0316658	−	0.0131164i
$161$	−4.54712	−	4.54712i	−0.358363	−	0.358363i
$162$		0			0
$163$	−16.4496	+	6.81363i	−1.28843	+	0.533685i	−0.918517	−	0.395382i	$-0.870612\pi$
$163$	−16.4496	+	6.81363i	−1.28843	+	0.533685i	−0.369912	+	0.929067i	$0.620612\pi$
$164$	4.63726	+	11.1953i	0.362109	+	0.874208i
$165$		0			0
$166$		−	1.04373i		−	0.0810090i
$167$	−6.73332	+	16.2557i	−0.521040	+	1.25790i	0.416218	+	0.909265i	$0.363355\pi$
$167$	−6.73332	+	16.2557i	−0.521040	+	1.25790i	−0.937258	+	0.348637i	$0.886645\pi$
$168$		0			0
$169$	12.8899			0.991530
$170$	−1.38121	+	1.13473i	−0.105934	+	0.0870295i
$171$		0			0
$172$	7.13707	−	7.13707i	0.544197	−	0.544197i
$173$	7.40349	−	17.8736i	0.562877	−	1.35890i	−0.344579	−	0.938757i	$-0.611978\pi$
$173$	7.40349	−	17.8736i	0.562877	−	1.35890i	0.907456	−	0.420147i	$-0.138022\pi$
$174$		0			0
$175$	−15.1787	−	6.28723i	−1.14740	−	0.475270i
$176$	0.648847	+	1.56645i	0.0489087	+	0.118076i
$177$		0			0
$178$	9.77791	+	9.77791i	0.732885	+	0.732885i
$179$	−6.44834	−	6.44834i	−0.481972	−	0.481972i	0.423789	−	0.905761i	$-0.360700\pi$
$179$	−6.44834	−	6.44834i	−0.481972	−	0.481972i	−0.905761	+	0.423789i	$0.860700\pi$
$180$		0			0
$181$	0.297227	+	0.717569i	0.0220927	+	0.0533365i	0.934541	−	0.355856i	$-0.115811\pi$
$181$	0.297227	+	0.717569i	0.0220927	+	0.0533365i	−0.912448	+	0.409192i	$0.865811\pi$
$182$	−1.04667	−	0.433546i	−0.0775844	−	0.0321365i
$183$		0			0
$184$	−0.720777	+	1.74011i	−0.0531364	+	0.128282i
$185$	3.25397	−	3.25397i	0.239236	−	0.239236i
$186$		0			0
$187$	−4.43771	−	5.40167i	−0.324517	−	0.395009i
$188$	−2.38009			−0.173586
$189$		0			0
$190$	0.355689	−	0.858710i	0.0258044	−	0.0622974i
$191$		−	13.4248i		−	0.971384i	−0.874130	−	0.485692i	$-0.838568\pi$
$191$		−	13.4248i		−	0.971384i	0.874130	−	0.485692i	$-0.161432\pi$
$192$		0			0
$193$	1.94749	+	4.70167i	0.140184	+	0.338434i	0.978342	−	0.206993i	$-0.0663677\pi$
$193$	1.94749	+	4.70167i	0.140184	+	0.338434i	−0.838159	+	0.545426i	$0.816368\pi$
$194$	3.46953	−	1.43713i	0.249098	−	0.103180i
$195$		0			0
$196$	−3.29289	−	3.29289i	−0.235207	−	0.235207i
$197$	−3.83825	+	1.58986i	−0.273464	+	0.113273i	−0.515201	−	0.857069i	$-0.672283\pi$
$197$	−3.83825	+	1.58986i	−0.273464	+	0.113273i	0.241737	+	0.970342i	$0.422283\pi$
$198$		0			0
$199$	9.89357	+	4.09805i	0.701336	+	0.290503i	0.704714	−	0.709491i	$-0.251075\pi$
$199$	9.89357	+	4.09805i	0.701336	+	0.290503i	−0.00337780	+	0.999994i	$0.501075\pi$
$200$			4.81204i			0.340262i
$201$		0			0
$202$	0.449934	−	0.449934i	0.0316573	−	0.0316573i
$203$	29.1531			2.04615
$204$		0			0
$205$	5.25359			0.366927
$206$	6.08080	−	6.08080i	0.423669	−	0.423669i
$207$		0			0
$208$			0.331821i			0.0230077i
$209$	3.35826	+	1.39104i	0.232296	+	0.0962200i
$210$		0			0
$211$	−4.36210	+	1.80684i	−0.300300	+	0.124388i	−0.527746	−	0.849403i	$-0.676963\pi$
$211$	−4.36210	+	1.80684i	−0.300300	+	0.124388i	0.227446	+	0.973791i	$0.426963\pi$
$212$	2.21371	+	2.21371i	0.152038	+	0.152038i
$213$		0			0
$214$	−2.00000	+	0.828427i	−0.136717	+	0.0566301i
$215$	−1.67459	−	4.04283i	−0.114206	−	0.275718i
$216$		0			0
$217$			8.82843i			0.599313i
$218$	−3.02847	+	7.31136i	−0.205114	+	0.495188i
$219$		0			0
$220$	0.735084			0.0495594
$221$	−0.397825	−	1.30902i	−0.0267606	−	0.0880541i
$222$		0			0
$223$	11.0563	−	11.0563i	0.740383	−	0.740383i	−0.232269	−	0.972652i	$-0.574615\pi$
$223$	11.0563	−	11.0563i	0.740383	−	0.740383i	0.972652	+	0.232269i	$0.0746149\pi$
$224$	−1.30656	+	3.15432i	−0.0872984	+	0.210757i
$225$		0			0
$226$	−8.48886	−	3.51620i	−0.564671	−	0.233894i
$227$	4.23304	+	10.2195i	0.280957	+	0.678290i	0.999858	−	0.0168221i	$-0.00535489\pi$
$227$	4.23304	+	10.2195i	0.280957	+	0.678290i	−0.718902	+	0.695112i	$0.755355\pi$
$228$		0			0
$229$	−10.8789	−	10.8789i	−0.718901	−	0.718901i	0.249479	−	0.968380i	$-0.419741\pi$
$229$	−10.8789	−	10.8789i	−0.718901	−	0.718901i	−0.968380	+	0.249479i	$0.919741\pi$
$230$	0.577405	+	0.577405i	0.0380730	+	0.0380730i
$231$		0			0
$232$	−3.26763	−	7.88877i	−0.214531	−	0.517923i
$233$	9.58764	+	3.97133i	0.628107	+	0.260171i	0.673949	−	0.738778i	$-0.264597\pi$
$233$	9.58764	+	3.97133i	0.628107	+	0.260171i	−0.0458413	+	0.998949i	$0.514597\pi$
$234$		0			0
$235$	−0.394882	+	0.953329i	−0.0257592	+	0.0621883i
$236$	5.42676	−	5.42676i	0.353252	−	0.353252i
$237$		0			0
$238$	1.37257	−	14.0101i	0.0889703	−	0.908139i
$239$	24.7803			1.60291			0.801454	−	0.598057i	$-0.204060\pi$
$239$	24.7803			1.60291			0.801454	+	0.598057i	$0.204060\pi$
$240$		0			0
$241$	−1.64752	+	3.97746i	−0.106126	+	0.256211i	−0.968018	−	0.250881i	$-0.919280\pi$
$241$	−1.64752	+	3.97746i	−0.106126	+	0.256211i	0.861892	+	0.507092i	$0.169280\pi$
$242$		−	8.12522i		−	0.522309i
$243$		0			0
$244$	3.07673	+	7.42788i	0.196967	+	0.475522i
$245$	−1.86527	+	0.772622i	−0.119168	+	0.0493610i
$246$		0			0
$247$	0.503021	+	0.503021i	0.0320064	+	0.0320064i
$248$	2.38896	−	0.989538i	0.151699	−	0.0628357i
$249$		0			0
$250$	3.93015	+	1.62792i	0.248565	+	0.102959i
$251$			19.0639i			1.20330i	0.798759	+	0.601652i	$0.205490\pi$
$251$			19.0639i			1.20330i	−0.798759	+	0.601652i	$0.794510\pi$
$252$		0			0
$253$	−2.25813	+	2.25813i	−0.141967	+	0.141967i
$254$	−12.0843			−0.758235
$255$		0			0
$256$	1.00000			0.0625000
$257$	−18.9218	+	18.9218i	−1.18031	+	1.18031i	−0.200643	+	0.979664i	$0.564303\pi$
$257$	−18.9218	+	18.9218i	−1.18031	+	1.18031i	−0.979664	+	0.200643i	$0.935697\pi$
$258$		0			0
$259$			36.2396i			2.25182i
$260$	0.132909	+	0.0550527i	0.00824267	+	0.00341422i
$261$		0			0
$262$	0.828427	−	0.343146i	0.0511804	−	0.0211996i
$263$	−19.4541	−	19.4541i	−1.19959	−	1.19959i	−0.974289	−	0.225302i	$-0.927663\pi$
$263$	−19.4541	−	19.4541i	−1.19959	−	1.19959i	−0.225302	−	0.974289i	$-0.572337\pi$
$264$		0			0
$265$	1.25397	−	0.519409i	0.0770305	−	0.0319071i
$266$	2.80109	+	6.76242i	0.171746	+	0.414631i
$267$		0			0
$268$		−	15.7711i		−	0.963375i
$269$	−3.83250	+	9.25247i	−0.233671	+	0.564133i	−0.996604	−	0.0823455i	$-0.973759\pi$
$269$	−3.83250	+	9.25247i	−0.233671	+	0.564133i	0.762932	+	0.646478i	$0.223759\pi$
$270$		0			0
$271$	−9.20949			−0.559437			−0.279718	−	0.960082i	$-0.590241\pi$
$271$	−9.20949			−0.559437			−0.279718	+	0.960082i	$0.590241\pi$
$272$	−3.94495	+	1.19891i	−0.239198	+	0.0726947i
$273$		0			0
$274$	−8.91723	+	8.91723i	−0.538710	+	0.538710i
$275$	−3.12228	+	7.53784i	−0.188280	+	0.454549i
$276$		0			0
$277$	−7.72852	−	3.20126i	−0.464362	−	0.192345i	0.138221	−	0.990401i	$-0.455862\pi$
$277$	−7.72852	−	3.20126i	−0.464362	−	0.192345i	−0.602583	+	0.798056i	$0.705862\pi$
$278$	−6.52273	−	15.7473i	−0.391207	−	0.944458i
$279$		0			0
$280$	1.04667	+	1.04667i	0.0625506	+	0.0625506i
$281$	7.77791	+	7.77791i	0.463991	+	0.463991i	0.899961	−	0.435970i	$-0.143595\pi$
$281$	7.77791	+	7.77791i	0.463991	+	0.463991i	−0.435970	+	0.899961i	$0.643595\pi$
$282$		0			0
$283$	8.08918	+	19.5290i	0.480852	+	1.16088i	0.959205	+	0.282712i	$0.0912339\pi$
$283$	8.08918	+	19.5290i	0.480852	+	1.16088i	−0.478353	+	0.878168i	$0.658766\pi$
$284$	0.209375	+	0.0867259i	0.0124241	+	0.00514623i
$285$		0			0
$286$	−0.215301	+	0.519783i	−0.0127310	+	0.0307354i
$287$	−29.2548	+	29.2548i	−1.72686	+	1.72686i
$288$		0			0
$289$	14.1252	−	9.45929i	0.830895	−	0.556429i
$290$	−3.70193			−0.217385
$291$		0			0
$292$	−4.64527	+	11.2147i	−0.271844	+	0.656289i
$293$			25.1277i			1.46797i	0.679164	+	0.733987i	$0.262343\pi$
$293$			25.1277i			1.46797i	−0.679164	+	0.733987i	$0.737657\pi$
$294$		0			0
$295$	−1.27330	−	3.07401i	−0.0741342	−	0.178976i
$296$	9.80638	−	4.06193i	0.569984	−	0.236095i
$297$		0			0
$298$	−12.3746	−	12.3746i	−0.716844	−	0.716844i
$299$	−0.577405	+	0.239169i	−0.0333922	+	0.0138315i
$300$		0			0
$301$	31.8377	+	13.1876i	1.83509	+	0.760120i
$302$		−	9.64009i		−	0.554725i
$303$		0			0
$304$	1.51594	−	1.51594i	0.0869450	−	0.0869450i
$305$	3.48566			0.199588
$306$		0			0
$307$	15.3433			0.875688			0.437844	−	0.899051i	$-0.355742\pi$
$307$	15.3433			0.875688			0.437844	+	0.899051i	$0.355742\pi$
$308$	−4.09334	+	4.09334i	−0.233240	+	0.233240i
$309$		0			0
$310$		−	1.12106i		−	0.0636717i
$311$	−20.0320	−	8.29752i	−1.13591	−	0.470509i	−0.266124	−	0.963939i	$-0.585743\pi$
$311$	−20.0320	−	8.29752i	−1.13591	−	0.470509i	−0.869786	+	0.493429i	$0.835743\pi$
$312$		0			0
$313$	−7.74993	+	3.21013i	−0.438052	+	0.181447i	−0.590800	−	0.806818i	$-0.701188\pi$
$313$	−7.74993	+	3.21013i	−0.438052	+	0.181447i	0.152748	+	0.988265i	$0.451188\pi$
$314$	3.38687	+	3.38687i	0.191132	+	0.191132i
$315$		0			0
$316$	−11.5849	+	4.79863i	−0.651703	+	0.269944i
$317$	−9.17686	−	22.1549i	−0.515424	−	1.24434i	−0.940688	−	0.339274i	$-0.889819\pi$
$317$	−9.17686	−	22.1549i	−0.515424	−	1.24434i	0.425264	−	0.905069i	$-0.360181\pi$
$318$		0			0
$319$		−	14.4776i		−	0.810589i
$320$	0.165911	−	0.400544i	0.00927469	−	0.0223911i
$321$		0			0
$322$	−6.43060			−0.358363
$323$	−4.16282	+	7.79777i	−0.231625	+	0.433880i
$324$		0			0
$325$	−1.12906	+	1.12906i	−0.0626292	+	0.0626292i
$326$	−6.81363	+	16.4496i	−0.377372	+	0.911057i
$327$		0			0
$328$	11.1953	+	4.63726i	0.618159	+	0.256050i
$329$	−3.10973	−	7.50756i	−0.171445	−	0.413905i
$330$		0			0
$331$	−2.88311	−	2.88311i	−0.158470	−	0.158470i	0.623418	−	0.781888i	$-0.285743\pi$
$331$	−2.88311	−	2.88311i	−0.158470	−	0.158470i	−0.781888	+	0.623418i	$0.785743\pi$
$332$	−0.738027	−	0.738027i	−0.0405045	−	0.0405045i
$333$		0			0
$334$	6.73332	+	16.2557i	0.368431	+	0.889471i
$335$	−6.31703	−	2.61660i	−0.345136	−	0.142960i
$336$		0			0
$337$	−3.83323	+	9.25423i	−0.208809	+	0.504110i	−0.993236	−	0.116111i	$-0.962957\pi$
$337$	−3.83323	+	9.25423i	−0.208809	+	0.504110i	0.784427	+	0.620221i	$0.212957\pi$
$338$	9.11453	−	9.11453i	0.495765	−	0.495765i
$339$		0			0
$340$	−0.174292	+	1.77904i	−0.00945231	+	0.0964818i
$341$	4.38425			0.237420
$342$		0			0
$343$	−3.06147	+	7.39104i	−0.165304	+	0.399078i
$344$		−	10.0933i		−	0.544197i
$345$		0			0
$346$	−7.40349	−	17.8736i	−0.398014	−	0.960891i
$347$	7.98618	−	3.30798i	0.428721	−	0.177582i	−0.157880	−	0.987458i	$-0.550466\pi$
$347$	7.98618	−	3.30798i	0.428721	−	0.177582i	0.586601	+	0.809876i	$0.300466\pi$
$348$		0			0
$349$	−14.7167	−	14.7167i	−0.787768	−	0.787768i	0.193360	−	0.981128i	$-0.438062\pi$
$349$	−14.7167	−	14.7167i	−0.787768	−	0.787768i	−0.981128	+	0.193360i	$0.938062\pi$
$350$	−15.1787	+	6.28723i	−0.811337	+	0.336067i
$351$		0			0
$352$	1.56645	+	0.648847i	0.0834923	+	0.0345836i
$353$			20.1049i			1.07007i	0.844829	+	0.535037i	$0.179702\pi$
$353$			20.1049i			1.07007i	−0.844829	+	0.535037i	$0.820298\pi$
$354$		0			0
$355$	0.0694750	−	0.0694750i	0.00368735	−	0.00368735i
$356$	13.8281			0.732885
$357$		0			0
$358$	−9.11933			−0.481972
$359$	17.8899	−	17.8899i	0.944193	−	0.944193i	−0.0543305	−	0.998523i	$-0.517302\pi$
$359$	17.8899	−	17.8899i	0.944193	−	0.944193i	0.998523	+	0.0543305i	$0.0173024\pi$
$360$		0			0
$361$			14.4039i			0.758098i
$362$	0.717569	+	0.297227i	0.0377146	+	0.0156219i
$363$		0			0
$364$	−1.04667	+	0.433546i	−0.0548605	+	0.0227240i
$365$	3.72126	+	3.72126i	0.194780	+	0.194780i
$366$		0			0
$367$	−9.53441	+	3.94928i	−0.497692	+	0.206151i	−0.617386	−	0.786660i	$-0.711809\pi$
$367$	−9.53441	+	3.94928i	−0.497692	+	0.206151i	0.119694	+	0.992811i	$0.461809\pi$
$368$	0.720777	+	1.74011i	0.0375731	+	0.0907094i
$369$		0			0
$370$		−	4.60180i		−	0.239236i
$371$	−4.09040	+	9.87510i	−0.212363	+	0.512690i
$372$		0			0
$373$	−18.2719			−0.946083			−0.473041	−	0.881040i	$-0.656844\pi$
$373$	−18.2719			−0.946083			−0.473041	+	0.881040i	$0.656844\pi$
$374$	−6.95749	−	0.681624i	−0.359763	−	0.0352460i
$375$		0			0
$376$	−1.68297	+	1.68297i	−0.0867928	+	0.0867928i
$377$	1.08427	−	2.61766i	0.0558428	−	0.134816i
$378$		0			0
$379$	19.3386	+	8.01029i	0.993355	+	0.411461i	0.819356	−	0.573285i	$-0.194331\pi$
$379$	19.3386	+	8.01029i	0.993355	+	0.411461i	0.173999	+	0.984746i	$0.444331\pi$
$380$	−0.355689	−	0.858710i	−0.0182465	−	0.0440509i
$381$		0			0
$382$	−9.49276	−	9.49276i	−0.485692	−	0.485692i
$383$	16.2616	+	16.2616i	0.830929	+	0.830929i	0.987644	−	0.156715i	$-0.0500904\pi$
$383$	16.2616	+	16.2616i	0.830929	+	0.830929i	−0.156715	+	0.987644i	$0.550090\pi$
$384$		0			0
$385$	0.960434	+	2.31869i	0.0489482	+	0.118172i
$386$	4.70167	+	1.94749i	0.239309	+	0.0991249i
$387$		0			0
$388$	1.43713	−	3.46953i	0.0729590	−	0.176139i
$389$	6.41875	−	6.41875i	0.325444	−	0.325444i	−0.525407	−	0.850851i	$-0.676087\pi$
$389$	6.41875	−	6.41875i	0.325444	−	0.325444i	0.850851	+	0.525407i	$0.176087\pi$
$390$		0			0
$391$	−4.92966	−	6.00049i	−0.249304	−	0.303458i
$392$	−4.65685			−0.235207
$393$		0			0
$394$	−1.58986	+	3.83825i	−0.0800958	+	0.193368i
$395$			5.43641i			0.273536i
$396$		0			0
$397$	−2.98821	−	7.21417i	−0.149974	−	0.362069i	0.830982	−	0.556299i	$-0.187779\pi$
$397$	−2.98821	−	7.21417i	−0.149974	−	0.362069i	−0.980956	+	0.194230i	$0.937779\pi$
$398$	9.89357	−	4.09805i	0.495920	−	0.205417i
$399$		0			0
$400$	3.40262	+	3.40262i	0.170131	+	0.170131i
$401$	16.0392	−	6.64367i	0.800962	−	0.331769i	0.0556201	−	0.998452i	$-0.482286\pi$
$401$	16.0392	−	6.64367i	0.800962	−	0.331769i	0.745342	+	0.666683i	$0.232286\pi$
$402$		0			0
$403$	0.792706	+	0.328350i	0.0394875	+	0.0163563i
$404$		−	0.636303i		−	0.0316573i
$405$		0			0
$406$	20.6143	−	20.6143i	1.02307	−	1.02307i
$407$	17.9968			0.892069
$408$		0			0
$409$	4.42153			0.218631			0.109315	−	0.994007i	$-0.465134\pi$
$409$	4.42153			0.218631			0.109315	+	0.994007i	$0.465134\pi$
$410$	3.71485	−	3.71485i	0.183463	−	0.183463i
$411$		0			0
$412$		−	8.59955i		−	0.423669i
$413$	24.2081	+	10.0273i	1.19120	+	0.493413i
$414$		0			0
$415$	−0.418059	+	0.173166i	−0.0205217	+	0.00850037i
$416$	0.234633	+	0.234633i	0.0115038	+	0.0115038i
$417$		0			0
$418$	3.35826	−	1.39104i	0.164258	−	0.0680378i
$419$	−8.86537	−	21.4029i	−0.433102	−	1.04560i	−0.978282	−	0.207281i	$-0.933539\pi$
$419$	−8.86537	−	21.4029i	−0.433102	−	1.04560i	0.545180	−	0.838319i	$-0.316461\pi$
$420$		0			0
$421$		−	20.0524i		−	0.977295i	−0.872481	−	0.488648i	$-0.837490\pi$
$421$		−	20.0524i		−	0.977295i	0.872481	−	0.488648i	$-0.162510\pi$
$422$	−1.80684	+	4.36210i	−0.0879557	+	0.212344i
$423$		0			0
$424$	3.13066			0.152038
$425$	−17.5026	−	9.34373i	−0.849002	−	0.453237i
$426$		0			0
$427$	−19.4100	+	19.4100i	−0.939315	+	0.939315i
$428$	−0.828427	+	2.00000i	−0.0400435	+	0.0966736i
$429$		0			0
$430$	−4.04283	−	1.67459i	−0.194962	−	0.0807561i
$431$	−15.3635	−	37.0908i	−0.740033	−	1.78660i	−0.605749	−	0.795656i	$-0.707126\pi$
$431$	−15.3635	−	37.0908i	−0.740033	−	1.78660i	−0.134285	−	0.990943i	$-0.542874\pi$
$432$		0			0
$433$	−15.4502	−	15.4502i	−0.742490	−	0.742490i	0.230566	−	0.973057i	$-0.425942\pi$
$433$	−15.4502	−	15.4502i	−0.742490	−	0.742490i	−0.973057	+	0.230566i	$0.925942\pi$
$434$	6.24264	+	6.24264i	0.299656	+	0.299656i
$435$		0			0
$436$	3.02847	+	7.31136i	0.145037	+	0.350151i
$437$	3.73055	+	1.54524i	0.178456	+	0.0739190i
$438$		0			0
$439$	0.320985	−	0.774927i	0.0153198	−	0.0369852i	−0.916035	−	0.401099i	$-0.868628\pi$
$439$	0.320985	−	0.774927i	0.0153198	−	0.0369852i	0.931354	+	0.364114i	$0.118628\pi$
$440$	0.519783	−	0.519783i	0.0247797	−	0.0247797i
$441$		0			0
$442$	−1.20692	−	0.644311i	−0.0574073	−	0.0306467i
$443$	3.21267			0.152639			0.0763194	−	0.997083i	$-0.475683\pi$
$443$	3.21267			0.152639			0.0763194	+	0.997083i	$0.475683\pi$
$444$		0			0
$445$	2.29422	−	5.53874i	0.108757	−	0.262562i
$446$		−	15.6359i		−	0.740383i
$447$		0			0
$448$	1.30656	+	3.15432i	0.0617293	+	0.149028i
$449$	26.5599	−	11.0015i	1.25344	−	0.519192i	0.345550	−	0.938400i	$-0.387692\pi$
$449$	26.5599	−	11.0015i	1.25344	−	0.519192i	0.907890	+	0.419208i	$0.137692\pi$
$450$		0			0
$451$	14.5281	+	14.5281i	0.684102	+	0.684102i
$452$	−8.48886	+	3.51620i	−0.399283	+	0.165388i
$453$		0			0
$454$	10.2195	+	4.23304i	0.479623	+	0.198666i
$455$			0.491168i			0.0230263i
$456$		0			0
$457$	−5.26863	+	5.26863i	−0.246456	+	0.246456i	−0.819515	−	0.573058i	$-0.805757\pi$
$457$	−5.26863	+	5.26863i	−0.246456	+	0.246456i	0.573058	+	0.819515i	$0.305757\pi$
$458$	−15.3852			−0.718901
$459$		0			0
$460$	0.816574			0.0380730
$461$	18.1287	−	18.1287i	0.844337	−	0.844337i	−0.145082	−	0.989420i	$-0.546345\pi$
$461$	18.1287	−	18.1287i	0.844337	−	0.844337i	0.989420	+	0.145082i	$0.0463447\pi$
$462$		0			0
$463$			10.7747i			0.500744i	0.968150	+	0.250372i	$0.0805529\pi$
$463$			10.7747i			0.500744i	−0.968150	+	0.250372i	$0.919447\pi$
$464$	−7.88877	−	3.26763i	−0.366227	−	0.151696i
$465$		0			0
$466$	9.58764	−	3.97133i	0.444139	−	0.183968i
$467$	−25.2078	−	25.2078i	−1.16648	−	1.16648i	−0.983030	−	0.183447i	$-0.941275\pi$
$467$	−25.2078	−	25.2078i	−1.16648	−	1.16648i	−0.183447	−	0.983030i	$-0.558725\pi$
$468$		0			0
$469$	49.7472	−	20.6060i	2.29711	−	0.951495i
$470$	0.394882	+	0.953329i	0.0182145	+	0.0439738i
$471$		0			0
$472$		−	7.67459i		−	0.353252i
$473$	6.54903	−	15.8108i	0.301125	−	0.726980i
$474$		0			0
$475$	10.3163			0.473346
$476$	−8.93608	−	10.8772i	−0.409584	−	0.498555i
$477$		0			0
$478$	17.5224	−	17.5224i	0.801454	−	0.801454i
$479$	5.38442	−	12.9991i	0.246020	−	0.593946i	−0.751839	−	0.659347i	$-0.770833\pi$
$479$	5.38442	−	12.9991i	0.246020	−	0.593946i	0.997859	+	0.0654014i	$0.0208328\pi$
$480$		0			0
$481$	3.25397	+	1.34784i	0.148368	+	0.0614561i
$482$	1.64752	+	3.97746i	0.0750424	+	0.181168i
$483$		0			0
$484$	−5.74540	−	5.74540i	−0.261154	−	0.261154i
$485$	−1.15126	−	1.15126i	−0.0522762	−	0.0522762i
$486$		0			0
$487$	−9.23512	−	22.2956i	−0.418483	−	1.01031i	−0.982787	−	0.184741i	$-0.940855\pi$
$487$	−9.23512	−	22.2956i	−0.418483	−	1.01031i	0.564304	−	0.825567i	$-0.309145\pi$
$488$	7.42788	+	3.07673i	0.336244	+	0.139277i
$489$		0			0
$490$	−0.772622	+	1.86527i	−0.0349035	+	0.0842645i
$491$	−18.7525	+	18.7525i	−0.846288	+	0.846288i	−0.989668	−	0.143380i	$-0.954203\pi$
$491$	−18.7525	+	18.7525i	−0.846288	+	0.846288i	0.143380	+	0.989668i	$0.454203\pi$
$492$		0			0
$493$	35.0384	+	3.43271i	1.57805	+	0.154601i
$494$	0.711378			0.0320064
$495$		0			0
$496$	0.989538	−	2.38896i	0.0444316	−	0.107267i
$497$			0.773748i			0.0347073i
$498$		0			0
$499$	−1.73737	−	4.19438i	−0.0777753	−	0.187766i	0.880209	−	0.474585i	$-0.157402\pi$
$499$	−1.73737	−	4.19438i	−0.0777753	−	0.187766i	−0.957985	+	0.286819i	$0.907402\pi$
$500$	3.93015	−	1.62792i	0.175762	−	0.0728029i
$501$		0			0
$502$	13.4802	+	13.4802i	0.601652	+	0.601652i
$503$	−3.69306	+	1.52972i	−0.164666	+	0.0682067i	−0.463494	−	0.886100i	$-0.653404\pi$
$503$	−3.69306	+	1.52972i	−0.164666	+	0.0682067i	0.298828	+	0.954307i	$0.403404\pi$
$504$		0			0
$505$	−0.254867	−	0.105570i	−0.0113414	−	0.00469778i
$506$			3.19347i			0.141967i
$507$		0			0
$508$	−8.54487	+	8.54487i	−0.379117	+	0.379117i
$509$	−22.9751			−1.01835			−0.509176	−	0.860662i	$-0.670050\pi$
$509$	−22.9751			−1.01835			−0.509176	+	0.860662i	$0.670050\pi$
$510$		0			0
$511$	−41.4440			−1.83337
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$			26.7594i			1.18031i
$515$	−3.44450	−	1.42676i	−0.151783	−	0.0628704i
$516$		0			0
$517$	−3.72830	+	1.54431i	−0.163970	+	0.0679187i
$518$	25.6253	+	25.6253i	1.12591	+	1.12591i
$519$		0			0
$520$	0.132909	−	0.0550527i	0.00582844	−	0.00241422i
$521$	6.46078	+	15.5977i	0.283052	+	0.683347i	0.999904	−	0.0138781i	$-0.00441768\pi$
$521$	6.46078	+	15.5977i	0.283052	+	0.683347i	−0.716852	+	0.697225i	$0.754418\pi$
$522$		0			0
$523$		−	15.5903i		−	0.681717i	−0.940115	−	0.340859i	$-0.889282\pi$
$523$		−	15.5903i		−	0.681717i	0.940115	−	0.340859i	$-0.110718\pi$
$524$	0.343146	−	0.828427i	0.0149904	−	0.0361900i
$525$		0			0
$526$	−27.5122			−1.19959
$527$	−1.03953	+	10.6107i	−0.0452825	+	0.462208i
$528$		0			0
$529$	13.7550	−	13.7550i	0.598043	−	0.598043i
$530$	0.519409	−	1.25397i	0.0225617	−	0.0544688i
$531$		0			0
$532$	6.76242	+	2.80109i	0.293188	+	0.121443i
$533$	1.53874	+	3.71485i	0.0666503	+	0.160908i
$534$		0			0
$535$	0.663643	+	0.663643i	0.0286918	+	0.0286918i
$536$	−11.1519	−	11.1519i	−0.481687	−	0.481687i
$537$		0			0
$538$	3.83250	+	9.25247i	0.165231	+	0.398902i
$539$	−7.29475	−	3.02158i	−0.314207	−	0.130149i
$540$		0			0
$541$	5.79023	−	13.9789i	0.248941	−	0.600998i	−0.749173	−	0.662374i	$-0.769549\pi$
$541$	5.79023	−	13.9789i	0.248941	−	0.600998i	0.998115	+	0.0613763i	$0.0195490\pi$
$542$	−6.51209	+	6.51209i	−0.279718	+	0.279718i
$543$		0			0
$544$	−1.94174	+	3.63726i	−0.0832514	+	0.155946i
$545$	3.43098			0.146967
$546$		0			0
$547$	−1.01292	+	2.44540i	−0.0433092	+	0.104558i	−0.944054	−	0.329791i	$-0.893022\pi$
$547$	−1.01292	+	2.44540i	−0.0433092	+	0.104558i	0.900745	+	0.434349i	$0.143022\pi$
$548$			12.6109i			0.538710i
$549$		0			0
$550$	3.12228	+	7.53784i	0.133134	+	0.321415i
$551$	−16.9124	+	7.00535i	−0.720493	+	0.298438i
$552$		0			0
$553$	−30.2729	−	30.2729i	−1.28733	−	1.28733i
$554$	−7.72852	+	3.20126i	−0.328353	+	0.136008i
$555$		0			0
$556$	−15.7473	−	6.52273i	−0.667832	−	0.276625i
$557$			12.4900i			0.529217i	0.964356	+	0.264609i	$0.0852427\pi$
$557$			12.4900i			0.529217i	−0.964356	+	0.264609i	$0.914757\pi$
$558$		0			0
$559$	2.36823	−	2.36823i	0.100166	−	0.100166i
$560$	1.48022			0.0625506
$561$		0			0
$562$	10.9996			0.463991
$563$	1.40167	−	1.40167i	0.0590734	−	0.0590734i	−0.676953	−	0.736026i	$-0.736700\pi$
$563$	1.40167	−	1.40167i	0.0590734	−	0.0590734i	0.736026	+	0.676953i	$0.236700\pi$
$564$		0			0
$565$			3.98354i			0.167589i
$566$	19.5290	+	8.08918i	0.820866	+	0.340014i
$567$		0			0
$568$	0.209375	−	0.0867259i	0.00878517	−	0.00363894i
$569$	−11.8558	−	11.8558i	−0.497020	−	0.497020i	0.413489	−	0.910509i	$-0.364310\pi$
$569$	−11.8558	−	11.8558i	−0.497020	−	0.497020i	−0.910509	+	0.413489i	$0.864310\pi$
$570$		0			0
$571$	−27.8300	+	11.5275i	−1.16465	+	0.482413i	−0.879420	−	0.476047i	$-0.842069\pi$
$571$	−27.8300	+	11.5275i	−1.16465	+	0.482413i	−0.285228	+	0.958460i	$0.592069\pi$
$572$	0.215301	+	0.519783i	0.00900220	+	0.0217332i
$573$		0			0
$574$			41.3725i			1.72686i
$575$	−3.46840	+	8.37347i	−0.144642	+	0.349198i
$576$		0			0
$577$	19.8204			0.825132			0.412566	−	0.910928i	$-0.364633\pi$
$577$	19.8204			0.825132			0.412566	+	0.910928i	$0.364633\pi$
$578$	3.29931	−	16.6768i	0.137233	−	0.693662i
$579$		0			0
$580$	−2.61766	+	2.61766i	−0.108692	+	0.108692i
$581$	1.36370	−	3.29226i	0.0565757	−	0.136586i
$582$		0			0
$583$	4.90403	+	2.03132i	0.203104	+	0.0841285i
$584$	4.64527	+	11.2147i	0.192222	+	0.464066i
$585$		0			0
$586$	17.7679	+	17.7679i	0.733987	+	0.733987i
$587$	9.09425	+	9.09425i	0.375360	+	0.375360i	0.869425	−	0.494065i	$-0.164490\pi$
$587$	9.09425	+	9.09425i	0.375360	+	0.375360i	−0.494065	+	0.869425i	$0.664490\pi$
$588$		0			0
$589$	−2.12143	−	5.12158i	−0.0874120	−	0.211031i
$590$	−3.07401	−	1.27330i	−0.126555	−	0.0524208i
$591$		0			0
$592$	4.06193	−	9.80638i	0.166944	−	0.403040i
$593$	25.3356	−	25.3356i	1.04041	−	1.04041i	0.0412617	−	0.999148i	$-0.486862\pi$
$593$	25.3356	−	25.3356i	1.04041	−	1.04041i	0.999148	−	0.0412617i	$-0.0131377\pi$
$594$		0			0
$595$	−5.83938	+	1.77465i	−0.239391	+	0.0727536i
$596$	−17.5004			−0.716844
$597$		0			0
$598$	−0.239169	+	0.577405i	−0.00978035	+	0.0236119i
$599$		−	21.1148i		−	0.862728i	−0.902178	−	0.431364i	$-0.858032\pi$
$599$		−	21.1148i		−	0.862728i	0.902178	−	0.431364i	$-0.141968\pi$
$600$		0			0
$601$	5.83004	+	14.0750i	0.237812	+	0.574130i	0.997056	−	0.0766767i	$-0.0244309\pi$
$601$	5.83004	+	14.0750i	0.237812	+	0.574130i	−0.759244	+	0.650806i	$0.774431\pi$
$602$	31.8377	−	13.1876i	1.29761	−	0.537486i
$603$		0			0
$604$	−6.81657	−	6.81657i	−0.277362	−	0.277362i
$605$	−3.25451	+	1.34806i	−0.132314	+	0.0548065i
$606$		0			0
$607$	−35.4629	−	14.6892i	−1.43940	−	0.596217i	−0.479743	−	0.877409i	$-0.659270\pi$
$607$	−35.4629	−	14.6892i	−1.43940	−	0.596217i	−0.959652	+	0.281192i	$0.909270\pi$
$608$		−	2.14386i		−	0.0869450i
$609$		0			0
$610$	2.46473	−	2.46473i	0.0997940	−	0.0997940i
$611$	−0.789763			−0.0319504
$612$		0			0
$613$	−1.39554			−0.0563654			−0.0281827	−	0.999603i	$-0.508972\pi$
$613$	−1.39554			−0.0563654			−0.0281827	+	0.999603i	$0.508972\pi$
$614$	10.8494	−	10.8494i	0.437844	−	0.437844i
$615$		0			0
$616$			5.78886i			0.233240i
$617$	−7.77433	−	3.22023i	−0.312983	−	0.129642i	0.220662	−	0.975350i	$-0.429178\pi$
$617$	−7.77433	−	3.22023i	−0.312983	−	0.129642i	−0.533645	+	0.845709i	$0.679178\pi$
$618$		0			0
$619$	−4.93657	+	2.04479i	−0.198417	+	0.0821872i	−0.479679	−	0.877444i	$-0.659247\pi$
$619$	−4.93657	+	2.04479i	−0.198417	+	0.0821872i	0.281262	+	0.959631i	$0.409247\pi$
$620$	−0.792706	−	0.792706i	−0.0318359	−	0.0318359i
$621$		0			0
$622$	−20.0320	+	8.29752i	−0.803210	+	0.332700i
$623$	18.0672	+	43.6181i	0.723848	+	1.74752i
$624$		0			0
$625$			22.2159i			0.888636i
$626$	−3.21013	+	7.74993i	−0.128302	+	0.309750i
$627$		0			0
$628$	4.78976			0.191132
$629$	−4.26713	+	43.5555i	−0.170142	+	1.73667i
$630$		0			0
$631$	1.03437	−	1.03437i	0.0411776	−	0.0411776i	−0.686218	−	0.727396i	$-0.740730\pi$
$631$	1.03437	−	1.03437i	0.0411776	−	0.0411776i	0.727396	+	0.686218i	$0.240730\pi$
$632$	−4.79863	+	11.5849i	−0.190879	+	0.460824i
$633$		0			0
$634$	−22.1549	−	9.17686i	−0.879884	−	0.364460i
$635$	2.00491	+	4.84028i	0.0795624	+	0.192081i
$636$		0			0
$637$	−1.09265	−	1.09265i	−0.0432925	−	0.0432925i
$638$	−10.2372	−	10.2372i	−0.405295	−	0.405295i
$639$		0			0
$640$	−0.165911	−	0.400544i	−0.00655820	−	0.0158329i
$641$	0.442882	+	0.183448i	0.0174928	+	0.00724574i	0.391413	−	0.920215i	$-0.371987\pi$
$641$	0.442882	+	0.183448i	0.0174928	+	0.00724574i	−0.373920	+	0.927461i	$0.621987\pi$
$642$		0			0
$643$	−12.2860	+	29.6610i	−0.484512	+	1.16972i	0.472932	+	0.881099i	$0.343196\pi$
$643$	−12.2860	+	29.6610i	−0.484512	+	1.16972i	−0.957444	+	0.288617i	$0.906804\pi$
$644$	−4.54712	+	4.54712i	−0.179182	+	0.179182i
$645$		0			0
$646$	2.57030	+	8.45741i	0.101127	+	0.332752i
$647$	−23.4802			−0.923103			−0.461551	−	0.887114i	$-0.652707\pi$
$647$	−23.4802			−0.923103			−0.461551	+	0.887114i	$0.652707\pi$
$648$		0			0
$649$	4.97963	−	12.0219i	0.195468	−	0.471901i
$650$			1.59674i			0.0626292i
$651$		0			0
$652$	6.81363	+	16.4496i	0.266842	+	0.644215i
$653$	−41.9154	+	17.3619i	−1.64027	+	0.679424i	−0.996326	−	0.0856443i	$-0.972705\pi$
$653$	−41.9154	+	17.3619i	−1.64027	+	0.679424i	−0.643949	+	0.765068i	$0.722705\pi$
$654$		0			0
$655$	−0.274890	−	0.274890i	−0.0107408	−	0.0107408i
$656$	11.1953	−	4.63726i	0.437104	−	0.181055i
$657$		0			0
$658$	−7.50756	−	3.10973i	−0.292675	−	0.121230i
$659$		−	12.8417i		−	0.500240i	−0.968215	−	0.250120i	$-0.919530\pi$
$659$		−	12.8417i		−	0.500240i	0.968215	−	0.250120i	$-0.0804701\pi$
$660$		0			0
$661$	−19.2247	+	19.2247i	−0.747753	+	0.747753i	−0.974057	−	0.226304i	$-0.927336\pi$
$661$	−19.2247	+	19.2247i	−0.747753	+	0.747753i	0.226304	+	0.974057i	$0.427336\pi$
$662$	−4.07733			−0.158470
$663$		0			0
$664$	−1.04373			−0.0405045
$665$	2.24392	−	2.24392i	0.0870154	−	0.0870154i
$666$		0			0
$667$		−	16.0825i		−	0.622719i
$668$	16.2557	+	6.73332i	0.628951	+	0.260520i
$669$		0			0
$670$	−6.31703	+	2.61660i	−0.244048	+	0.101088i
$671$	9.63912	+	9.63912i	0.372114	+	0.372114i
$672$		0			0
$673$	15.4077	−	6.38207i	0.593923	−	0.246011i	−0.0654145	−	0.997858i	$-0.520837\pi$
$673$	15.4077	−	6.38207i	0.593923	−	0.246011i	0.659337	+	0.751847i	$0.270837\pi$
$674$	3.83323	+	9.25423i	0.147650	+	0.356460i
$675$		0			0
$676$		−	12.8899i		−	0.495765i
$677$	−0.996062	+	2.40471i	−0.0382818	+	0.0924204i	−0.941864	−	0.335994i	$-0.890928\pi$
$677$	−0.996062	+	2.40471i	−0.0382818	+	0.0924204i	0.903582	+	0.428415i	$0.140928\pi$
$678$		0			0
$679$	12.8217			0.492052
$680$	1.13473	+	1.38121i	0.0435147	+	0.0529671i
$681$		0			0
$682$	3.10013	−	3.10013i	0.118710	−	0.118710i
$683$	−4.68507	+	11.3108i	−0.179269	+	0.432794i	−0.987814	−	0.155641i	$-0.950256\pi$
$683$	−4.68507	+	11.3108i	−0.179269	+	0.432794i	0.808544	+	0.588435i	$0.200256\pi$
$684$		0			0
$685$	5.05121	+	2.09228i	0.192997	+	0.0799419i
$686$	3.06147	+	7.39104i	0.116887	+	0.282191i
$687$		0			0
$688$	−7.13707	−	7.13707i	−0.272098	−	0.272098i
$689$	0.734556	+	0.734556i	0.0279843	+	0.0279843i
$690$		0			0
$691$	−5.99803	−	14.4805i	−0.228176	−	0.550865i	0.767779	−	0.640714i	$-0.221362\pi$
$691$	−5.99803	−	14.4805i	−0.228176	−	0.550865i	−0.995955	+	0.0898487i	$0.971362\pi$
$692$	−17.8736	−	7.40349i	−0.679452	−	0.281438i
$693$		0			0
$694$	3.30798	−	7.98618i	0.125569	−	0.303151i
$695$	−5.22528	+	5.22528i	−0.198206	+	0.198206i
$696$		0			0
$697$	−38.6053	+	31.7160i	−1.46228	+	1.20133i
$698$	−20.8126			−0.787768
$699$		0			0
$700$	−6.28723	+	15.1787i	−0.237635	+	0.573702i
$701$			30.8222i			1.16414i	0.813139	+	0.582070i	$0.197757\pi$
$701$			30.8222i			1.16414i	−0.813139	+	0.582070i	$0.802243\pi$
$702$		0			0
$703$	−8.70822	−	21.0235i	−0.328437	−	0.792916i
$704$	1.56645	−	0.648847i	0.0590380	−	0.0244543i
$705$		0			0
$706$	14.2163	+	14.2163i	0.535037	+	0.535037i
$707$	2.00711	−	0.831370i	0.0754850	−	0.0312669i
$708$		0			0
$709$	0.364823	+	0.151115i	0.0137012	+	0.00567523i	0.389524	−	0.921017i	$-0.372640\pi$
$709$	0.364823	+	0.151115i	0.0137012	+	0.00567523i	−0.375822	+	0.926692i	$0.622640\pi$
$710$		−	0.0982525i		−	0.00368735i
$711$		0			0
$712$	9.77791	−	9.77791i	0.366443	−	0.366443i
$713$	4.87028			0.182393
$714$		0			0
$715$	0.243917			0.00912197
$716$	−6.44834	+	6.44834i	−0.240986	+	0.240986i
$717$		0			0
$718$		−	25.3001i		−	0.944193i
$719$	10.2515	+	4.24631i	0.382317	+	0.158361i	0.565561	−	0.824707i	$-0.308660\pi$
$719$	10.2515	+	4.24631i	0.382317	+	0.158361i	−0.183244	+	0.983067i	$0.558660\pi$
$720$		0			0
$721$	27.1257	−	11.2359i	1.01022	−	0.418445i
$722$	10.1851	+	10.1851i	0.379049	+	0.379049i
$723$		0			0
$724$	0.717569	−	0.297227i	0.0266682	−	0.0110463i
$725$	−15.7240	−	37.9611i	−0.583974	−	1.40984i
$726$		0			0
$727$			27.2866i			1.01200i	0.862533	+	0.506001i	$0.168877\pi$
$727$			27.2866i			1.01200i	−0.862533	+	0.506001i	$0.831123\pi$
$728$	−0.433546	+	1.04667i	−0.0160683	+	0.0387922i
$729$		0			0
$730$	5.26266			0.194780
$731$	36.7121	+	19.5986i	1.35785	+	0.724882i
$732$		0			0
$733$	20.7090	−	20.7090i	0.764906	−	0.764906i	−0.212299	−	0.977205i	$-0.568095\pi$
$733$	20.7090	−	20.7090i	0.764906	−	0.764906i	0.977205	+	0.212299i	$0.0680951\pi$
$734$	−3.94928	+	9.53441i	−0.145771	+	0.351921i
$735$		0			0
$736$	1.74011	+	0.720777i	0.0641412	+	0.0265682i
$737$	−10.2330	−	24.7047i	−0.376939	−	0.910011i
$738$		0			0
$739$	26.2007	+	26.2007i	0.963810	+	0.963810i	0.999368	−	0.0355580i	$-0.0113209\pi$
$739$	26.2007	+	26.2007i	0.963810	+	0.963810i	−0.0355580	+	0.999368i	$0.511321\pi$
$740$	−3.25397	−	3.25397i	−0.119618	−	0.119618i
$741$		0			0
$742$	4.09040	+	9.87510i	0.150163	+	0.362526i
$743$	−13.3844	−	5.54401i	−0.491027	−	0.203390i	0.123410	−	0.992356i	$-0.460617\pi$
$743$	−13.3844	−	5.54401i	−0.491027	−	0.203390i	−0.614437	+	0.788966i	$0.710617\pi$
$744$		0			0
$745$	−2.90350	+	7.00967i	−0.106376	+	0.256815i
$746$	−12.9202	+	12.9202i	−0.473041	+	0.473041i
$747$		0			0
$748$	−5.40167	+	4.43771i	−0.197505	+	0.162259i
$749$	−7.39104			−0.270063
$750$		0			0
$751$	16.8240	−	40.6167i	0.613917	−	1.48213i	−0.244747	−	0.969587i	$-0.578705\pi$
$751$	16.8240	−	40.6167i	0.613917	−	1.48213i	0.858664	−	0.512539i	$-0.171295\pi$
$752$			2.38009i			0.0867928i
$753$		0			0
$754$	−1.08427	−	2.61766i	−0.0394868	−	0.0953296i
$755$	−3.86128	+	1.59939i	−0.140526	+	0.0582079i
$756$		0			0
$757$	26.7702	+	26.7702i	0.972980	+	0.972980i	0.999644	−	0.0266643i	$-0.00848850\pi$
$757$	26.7702	+	26.7702i	0.972980	+	0.972980i	−0.0266643	+	0.999644i	$0.508489\pi$
$758$	19.3386	−	8.01029i	0.702408	−	0.290947i
$759$		0			0
$760$	−0.858710	−	0.355689i	−0.0311487	−	0.0129022i
$761$			9.82880i			0.356294i	0.984004	+	0.178147i	$0.0570102\pi$
$761$			9.82880i			0.356294i	−0.984004	+	0.178147i	$0.942990\pi$
$762$		0			0
$763$	−19.1055	+	19.1055i	−0.691666	+	0.691666i
$764$	−13.4248			−0.485692
$765$		0			0
$766$	22.9974			0.830929
$767$	1.80071	−	1.80071i	0.0650200	−	0.0650200i
$768$		0			0
$769$		−	41.1522i		−	1.48398i	−0.670408	−	0.741992i	$-0.733881\pi$
$769$		−	41.1522i		−	1.48398i	0.670408	−	0.741992i	$-0.266119\pi$
$770$	2.31869	+	0.960434i	0.0835599	+	0.0346116i
$771$		0			0
$772$	4.70167	−	1.94749i	0.169217	−	0.0700919i
$773$	−15.3765	−	15.3765i	−0.553054	−	0.553054i	0.374267	−	0.927321i	$-0.377894\pi$
$773$	−15.3765	−	15.3765i	−0.553054	−	0.553054i	−0.927321	+	0.374267i	$0.877894\pi$
$774$		0			0
$775$	11.4957	−	4.76169i	0.412939	−	0.171045i
$776$	−1.43713	−	3.46953i	−0.0515898	−	0.124549i
$777$		0			0
$778$		−	9.07748i		−	0.325444i
$779$	9.94163	−	24.0012i	0.356196	−	0.859933i
$780$		0			0
$781$	0.384248			0.0137495
$782$	−7.72878	−	0.757188i	−0.276381	−	0.0270770i
$783$		0			0
$784$	−3.29289	+	3.29289i	−0.117603	+	0.117603i
$785$	0.794673	−	1.91851i	0.0283631	−	0.0684746i
$786$		0			0
$787$	43.9786	+	18.2165i	1.56767	+	0.649349i	0.986400	−	0.164364i	$-0.0525572\pi$
$787$	43.9786	+	18.2165i	1.56767	+	0.649349i	0.581267	+	0.813713i	$0.302557\pi$
$788$	1.58986	+	3.83825i	0.0566363	+	0.136732i
$789$		0			0
$790$	3.84413	+	3.84413i	0.136768	+	0.136768i
$791$	−22.1825	−	22.1825i	−0.788718	−	0.788718i
$792$		0			0
$793$	1.02092	+	2.46473i	0.0362541	+	0.0875251i
$794$	−7.21417	−	2.98821i	−0.256021	−	0.106048i
$795$		0			0
$796$	4.09805	−	9.89357i	0.145252	−	0.350668i
$797$	26.7982	−	26.7982i	0.949242	−	0.949242i	−0.0495310	−	0.998773i	$-0.515773\pi$
$797$	26.7982	−	26.7982i	0.949242	−	0.949242i	0.998773	+	0.0495310i	$0.0157727\pi$
$798$		0			0
$799$	−2.85351	−	9.38931i	−0.100950	−	0.332170i
$800$	4.81204			0.170131
$801$		0			0
$802$	6.64367	−	16.0392i	0.234596	−	0.566365i
$803$			20.5813i			0.726299i
$804$		0			0
$805$	1.06691	+	2.57574i	0.0376035	+	0.0907828i
$806$	0.792706	−	0.328350i	0.0279219	−	0.0115656i
$807$		0			0
$808$	−0.449934	−	0.449934i	−0.0158286	−	0.0158286i
$809$	35.6369	−	14.7613i	1.25293	−	0.518979i	0.345195	−	0.938531i	$-0.387813\pi$
$809$	35.6369	−	14.7613i	1.25293	−	0.518979i	0.907731	+	0.419552i	$0.137813\pi$
$810$		0			0
$811$	−17.9596	−	7.43911i	−0.630647	−	0.261223i	0.0443808	−	0.999015i	$-0.485869\pi$
$811$	−17.9596	−	7.43911i	−0.630647	−	0.261223i	−0.675028	+	0.737792i	$0.735869\pi$
$812$		−	29.1531i		−	1.02307i
$813$		0			0
$814$	12.7257	−	12.7257i	0.446034	−	0.446034i
$815$	7.71922			0.270393
$816$		0			0
$817$	−21.6387			−0.757043
$818$	3.12649	−	3.12649i	0.109315	−	0.109315i
$819$		0			0
$820$		−	5.25359i		−	0.183463i
$821$	−0.214175	−	0.0887142i	−0.00747476	−	0.00309615i	0.378943	−	0.925420i	$-0.376288\pi$
$821$	−0.214175	−	0.0887142i	−0.00747476	−	0.00309615i	−0.386418	+	0.922324i	$0.626288\pi$
$822$		0			0
$823$	−20.7809	+	8.60773i	−0.724376	+	0.300047i	−0.714239	−	0.699902i	$-0.753227\pi$
$823$	−20.7809	+	8.60773i	−0.724376	+	0.300047i	−0.0101376	+	0.999949i	$0.503227\pi$
$824$	−6.08080	−	6.08080i	−0.211835	−	0.211835i
$825$		0			0
$826$	24.2081	−	10.0273i	0.842309	−	0.348896i
$827$	20.0190	+	48.3300i	0.696127	+	1.68060i	0.732055	+	0.681246i	$0.238561\pi$
$827$	20.0190	+	48.3300i	0.696127	+	1.68060i	−0.0359274	+	0.999354i	$0.511439\pi$
$828$		0			0
$829$			23.3260i			0.810144i	0.914285	+	0.405072i	$0.132754\pi$
$829$			23.3260i			0.810144i	−0.914285	+	0.405072i	$0.867246\pi$
$830$	−0.173166	+	0.418059i	−0.00601067	+	0.0145110i
$831$		0			0
$832$	0.331821			0.0115038
$833$	9.04240	−	16.9382i	0.313301	−	0.586873i
$834$		0			0
$835$	5.39398	−	5.39398i	0.186666	−	0.186666i
$836$	1.39104	−	3.35826i	0.0481100	−	0.116148i
$837$		0			0
$838$	−21.4029	−	8.86537i	−0.739351	−	0.306249i
$839$	5.13605	+	12.3995i	0.177316	+	0.428079i	0.987402	−	0.158232i	$-0.0505794\pi$
$839$	5.13605	+	12.3995i	0.177316	+	0.428079i	−0.810086	+	0.586312i	$0.800579\pi$
$840$		0			0
$841$	31.0491	+	31.0491i	1.07066	+	1.07066i
$842$	−14.1792	−	14.1792i	−0.488648	−	0.488648i
$843$		0			0
$844$	1.80684	+	4.36210i	0.0621941	+	0.150150i
$845$	−5.16297	−	2.13857i	−0.177611	−	0.0735691i
$846$		0			0
$847$	10.6161	−	25.6296i	0.364774	−	0.880642i
$848$	2.21371	−	2.21371i	0.0760191	−	0.0760191i
$849$		0			0
$850$	−18.9832	+	5.76921i	−0.651120	+	0.197882i
$851$	19.9919			0.685314
$852$		0			0
$853$	−19.1093	+	46.1339i	−0.654290	+	1.57960i	0.152202	+	0.988349i	$0.451364\pi$
$853$	−19.1093	+	46.1339i	−0.654290	+	1.57960i	−0.806491	+	0.591246i	$0.798636\pi$
$854$			27.4499i			0.939315i
$855$		0			0
$856$	0.828427	+	2.00000i	0.0283151	+	0.0683586i
$857$	−15.8686	+	6.57298i	−0.542060	+	0.224529i	−0.636876	−	0.770966i	$-0.719774\pi$
$857$	−15.8686	+	6.57298i	−0.542060	+	0.224529i	0.0948160	+	0.995495i	$0.469774\pi$
$858$		0			0
$859$	−6.19681	−	6.19681i	−0.211433	−	0.211433i	0.593443	−	0.804876i	$-0.297768\pi$
$859$	−6.19681	−	6.19681i	−0.211433	−	0.211433i	−0.804876	+	0.593443i	$0.797768\pi$
$860$	−4.04283	+	1.67459i	−0.137859	+	0.0571032i
$861$		0			0
$862$	−37.0908	−	15.3635i	−1.26332	−	0.523283i
$863$		−	35.9177i		−	1.22265i	−0.791379	−	0.611326i	$-0.790636\pi$
$863$		−	35.9177i		−	1.22265i	0.791379	−	0.611326i	$-0.209364\pi$
$864$		0			0
$865$	−5.93084	+	5.93084i	−0.201655	+	0.201655i
$866$	−21.8499			−0.742490
$867$		0			0
$868$	8.82843			0.299656
$869$	−15.0337	+	15.0337i	−0.509983	+	0.509983i
$870$		0			0
$871$		−	5.23320i		−	0.177320i
$872$	7.31136	+	3.02847i	0.247594	+	0.102557i
$873$		0			0
$874$	3.73055	−	1.54524i	0.126188	−	0.0522686i
$875$	10.2700	+	10.2700i	0.347189	+	0.347189i
$876$		0			0
$877$	−3.90356	+	1.61691i	−0.131814	+	0.0545991i	−0.447615	−	0.894226i	$-0.647727\pi$
$877$	−3.90356	+	1.61691i	−0.131814	+	0.0545991i	0.315801	+	0.948825i	$0.397727\pi$
$878$	−0.320985	−	0.774927i	−0.0108327	−	0.0261525i
$879$		0			0
$880$		−	0.735084i		−	0.0247797i
$881$	11.4789	−	27.7125i	0.386734	−	0.933657i	−0.603894	−	0.797065i	$-0.706385\pi$
$881$	11.4789	−	27.7125i	0.386734	−	0.933657i	0.990627	−	0.136593i	$-0.0436151\pi$
$882$		0			0
$883$	−13.9714			−0.470175			−0.235087	−	0.971974i	$-0.575538\pi$
$883$	−13.9714			−0.470175			−0.235087	+	0.971974i	$0.575538\pi$
$884$	−1.30902	+	0.397825i	−0.0440270	+	0.0133803i
$885$		0			0
$886$	2.27170	−	2.27170i	0.0763194	−	0.0763194i
$887$	8.42959	−	20.3508i	0.283038	−	0.683314i	−0.716866	−	0.697211i	$-0.754424\pi$
$887$	8.42959	−	20.3508i	0.283038	−	0.683314i	0.999903	+	0.0138977i	$0.00442391\pi$
$888$		0			0
$889$	−38.1177	−	15.7889i	−1.27843	−	0.529541i
$890$	−2.29422	−	5.53874i	−0.0769025	−	0.185659i
$891$		0			0
$892$	−11.0563	−	11.0563i	−0.370191	−	0.370191i
$893$	3.60806	+	3.60806i	0.120739	+	0.120739i
$894$		0			0
$895$	1.51299	+	3.65269i	0.0505738	+	0.122096i
$896$	3.15432	+	1.30656i	0.105379	+	0.0436492i
$897$		0			0
$898$	11.0015	−	26.5599i	0.367124	−	0.886316i
$899$	−15.6125	+	15.6125i	−0.520705	+	0.520705i
$900$		0			0
$901$	−6.07892	+	11.3870i	−0.202518	+	0.379356i
$902$	20.5458			0.684102
$903$		0			0
$904$	−3.51620	+	8.48886i	−0.116947	+	0.282335i
$905$		−	0.336731i		−	0.0111933i
$906$		0			0
$907$	−10.2983	−	24.8622i	−0.341948	−	0.825535i	−0.997519	−	0.0704015i	$-0.977572\pi$
$907$	−10.2983	−	24.8622i	−0.341948	−	0.825535i	0.655571	−	0.755134i	$-0.272428\pi$
$908$	10.2195	−	4.23304i	0.339145	−	0.140478i
$909$		0			0
$910$	0.347308	+	0.347308i	0.0115131	+	0.0115131i
$911$	32.7838	−	13.5795i	1.08618	−	0.449908i	0.233504	−	0.972356i	$-0.424981\pi$
$911$	32.7838	−	13.5795i	1.08618	−	0.449908i	0.852671	+	0.522447i	$0.174981\pi$
$912$		0			0
$913$	−1.63495	−	0.677220i	−0.0541090	−	0.0224127i
$914$			7.45097i			0.246456i
$915$		0			0
$916$	−10.8789	+	10.8789i	−0.359450	+	0.359450i
$917$	3.06147			0.101099
$918$		0			0
$919$	−38.6107			−1.27365			−0.636824	−	0.771009i	$-0.719752\pi$
$919$	−38.6107			−1.27365			−0.636824	+	0.771009i	$0.719752\pi$
$920$	0.577405	−	0.577405i	0.0190365	−	0.0190365i
$921$		0			0
$922$		−	25.6378i		−	0.844337i
$923$	0.0694750	+	0.0287775i	0.00228680	+	0.000947223i
$924$		0			0
$925$	47.1887	−	19.5462i	1.55155	−	0.642675i
$926$	7.61888	+	7.61888i	0.250372	+	0.250372i
$927$		0			0
$928$	−7.88877	+	3.26763i	−0.258962	+	0.107265i
$929$	−8.76150	−	21.1521i	−0.287455	−	0.693979i	0.712515	−	0.701657i	$-0.247556\pi$
$929$	−8.76150	−	21.1521i	−0.287455	−	0.693979i	−0.999971	+	0.00767791i	$0.997556\pi$
$930$		0			0
$931$			9.98364i			0.327201i
$932$	3.97133	−	9.58764i	0.130085	−	0.314054i
$933$		0			0
$934$	−35.6492			−1.16648
$935$	0.881302	+	2.89987i	0.0288216	+	0.0948358i
$936$		0			0
$937$	−28.0575	+	28.0575i	−0.916598	+	0.916598i	−0.996780	−	0.0801820i	$-0.974450\pi$
$937$	−28.0575	+	28.0575i	−0.916598	+	0.916598i	0.0801820	+	0.996780i	$0.474450\pi$
$938$	20.6060	−	49.7472i	0.672809	−	1.62430i
$939$		0			0
$940$	0.953329	+	0.394882i	0.0310941	+	0.0128796i
$941$	20.1541	+	48.6562i	0.657004	+	1.58615i	0.802409	+	0.596775i	$0.203551\pi$
$941$	20.1541	+	48.6562i	0.657004	+	1.58615i	−0.145405	+	0.989372i	$0.546449\pi$
$942$		0			0
$943$	16.1387	+	16.1387i	0.525547	+	0.525547i
$944$	−5.42676	−	5.42676i	−0.176626	−	0.176626i
$945$		0			0
$946$	−6.54903	−	15.8108i	−0.212927	−	0.514052i
$947$	1.41074	+	0.584348i	0.0458430	+	0.0189888i	0.405487	−	0.914101i	$-0.367102\pi$
$947$	1.41074	+	0.584348i	0.0458430	+	0.0189888i	−0.359644	+	0.933090i	$0.617102\pi$
$948$		0			0
$949$	−1.54140	+	3.72126i	−0.0500359	+	0.120797i
$950$	7.29475	−	7.29475i	0.236673	−	0.236673i
$951$		0			0
$952$	−14.0101	−	1.37257i	−0.454070	−	0.0444851i
$953$	−9.95360			−0.322429			−0.161214	−	0.986919i	$-0.551541\pi$
$953$	−9.95360			−0.322429			−0.161214	+	0.986919i	$0.551541\pi$
$954$		0			0
$955$	−2.22732	+	5.37722i	−0.0720743	+	0.174003i
$956$		−	24.7803i		−	0.801454i
$957$		0			0
$958$	−5.38442	−	12.9991i	−0.173963	−	0.419983i
$959$	−39.7788	+	16.4769i	−1.28452	+	0.532067i
$960$		0			0
$961$	17.1924	+	17.1924i	0.554593	+	0.554593i
$962$	3.25397	−	1.34784i	0.104912	−	0.0434560i
$963$		0			0
$964$	3.97746	+	1.64752i	0.128105	+	0.0530630i
$965$		−	2.20633i		−	0.0710244i
$966$		0			0
$967$	4.16375	−	4.16375i	0.133897	−	0.133897i	−0.636982	−	0.770879i	$-0.719817\pi$
$967$	4.16375	−	4.16375i	0.133897	−	0.133897i	0.770879	+	0.636982i	$0.219817\pi$
$968$	−8.12522			−0.261154
$969$		0			0
$970$	−1.62813			−0.0522762
$971$	13.4117	−	13.4117i	0.430403	−	0.430403i	−0.458363	−	0.888765i	$-0.651564\pi$
$971$	13.4117	−	13.4117i	0.430403	−	0.430403i	0.888765	+	0.458363i	$0.151564\pi$
$972$		0			0
$973$		−	58.1943i		−	1.86562i
$974$	−22.2956	−	9.23512i	−0.714396	−	0.295912i
$975$		0			0
$976$	7.42788	−	3.07673i	0.237761	−	0.0984837i
$977$	−22.8517	−	22.8517i	−0.731090	−	0.731090i	0.239746	−	0.970836i	$-0.422936\pi$
$977$	−22.8517	−	22.8517i	−0.731090	−	0.731090i	−0.970836	+	0.239746i	$0.922936\pi$
$978$		0			0
$979$	21.6610	−	8.97229i	0.692289	−	0.286756i
$980$	0.772622	+	1.86527i	0.0246805	+	0.0595840i
$981$		0			0
$982$			26.5200i			0.846288i
$983$	12.4128	−	29.9672i	0.395908	−	0.955805i	−0.592718	−	0.805410i	$-0.701945\pi$
$983$	12.4128	−	29.9672i	0.395908	−	0.955805i	0.988626	−	0.150396i	$-0.0480547\pi$
$984$		0			0
$985$	1.80116			0.0573898
$986$	27.2032	−	22.3486i	0.866325	−	0.711724i
$987$		0			0
$988$	0.503021	−	0.503021i	0.0160032	−	0.0160032i
$989$	7.27504	−	17.5635i	0.231333	−	0.558487i
$990$		0			0
$991$	43.3309	+	17.9482i	1.37645	+	0.570145i	0.943530	−	0.331287i	$-0.107483\pi$
$991$	43.3309	+	17.9482i	1.37645	+	0.570145i	0.432921	+	0.901432i	$0.357483\pi$
$992$	−0.989538	−	2.38896i	−0.0314179	−	0.0758494i
$993$		0			0
$994$	0.547123	+	0.547123i	0.0173537	+	0.0173537i
$995$	−3.28290	−	3.28290i	−0.104075	−	0.104075i
$996$		0			0
$997$	−18.1610	−	43.8446i	−0.575166	−	1.38857i	−0.897107	−	0.441813i	$-0.854335\pi$
$997$	−18.1610	−	43.8446i	−0.575166	−	1.38857i	0.321941	−	0.946760i	$-0.395665\pi$
$998$	−4.19438	−	1.73737i	−0.132771	−	0.0549954i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	306.2.l.d.127.2		8
3.2	odd	2		102.2.h.a.25.2	✓	8
12.11	even	2		816.2.bq.b.433.1		8
17.7	odd	16		5202.2.a.br.1.2		4
17.10	odd	16		5202.2.a.bt.1.3		4
17.15	even	8	inner	306.2.l.d.253.2		8
51.5	even	16		1734.2.f.m.829.3		8
51.11	even	16		1734.2.b.k.577.6		8
51.14	even	16		1734.2.f.j.1483.2		8
51.20	even	16		1734.2.f.m.1483.3		8
51.23	even	16		1734.2.b.k.577.3		8
51.29	even	16		1734.2.f.j.829.2		8
51.32	odd	8		102.2.h.a.49.2	yes	8
51.41	even	16		1734.2.a.v.1.3		4
51.44	even	16		1734.2.a.w.1.2		4
204.83	even	8		816.2.bq.b.49.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
102.2.h.a.25.2	✓	8	3.2	odd	2
102.2.h.a.49.2	yes	8	51.32	odd	8
306.2.l.d.127.2		8	1.1	even	1	trivial
306.2.l.d.253.2		8	17.15	even	8	inner
816.2.bq.b.49.1		8	204.83	even	8
816.2.bq.b.433.1		8	12.11	even	2
1734.2.a.v.1.3		4	51.41	even	16
1734.2.a.w.1.2		4	51.44	even	16
1734.2.b.k.577.3		8	51.23	even	16
1734.2.b.k.577.6		8	51.11	even	16
1734.2.f.j.829.2		8	51.29	even	16
1734.2.f.j.1483.2		8	51.14	even	16
1734.2.f.m.829.3		8	51.5	even	16
1734.2.f.m.1483.3		8	51.20	even	16
5202.2.a.br.1.2		4	17.7	odd	16
5202.2.a.bt.1.3		4	17.10	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.400544 - 0.165911i) q^{5} +(3.15432 - 1.30656i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.400544 - 0.165911i) q^{5} +(3.15432 - 1.30656i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.400544 + 0.165911i) q^{10} +(-0.648847 - 1.56645i) q^{11} -0.331821i q^{13} +(1.30656 - 3.15432i) q^{14} -1.00000 q^{16} +(3.94495 - 1.19891i) q^{17} +(-1.51594 + 1.51594i) q^{19} +(-0.165911 + 0.400544i) q^{20} +(-1.56645 - 0.648847i) q^{22} +(-0.720777 - 1.74011i) q^{23} +(-3.40262 - 3.40262i) q^{25} +(-0.234633 - 0.234633i) q^{26} +(-1.30656 - 3.15432i) q^{28} +(7.88877 + 3.26763i) q^{29} +(-0.989538 + 2.38896i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(1.94174 - 3.63726i) q^{34} -1.48022 q^{35} +(-4.06193 + 9.80638i) q^{37} +2.14386i q^{38} +(0.165911 + 0.400544i) q^{40} +(-11.1953 + 4.63726i) q^{41} +(7.13707 + 7.13707i) q^{43} +(-1.56645 + 0.648847i) q^{44} +(-1.74011 - 0.720777i) q^{46} -2.38009i q^{47} +(3.29289 - 3.29289i) q^{49} -4.81204 q^{50} -0.331821 q^{52} +(-2.21371 + 2.21371i) q^{53} +0.735084i q^{55} +(-3.15432 - 1.30656i) q^{56} +(7.88877 - 3.26763i) q^{58} +(5.42676 + 5.42676i) q^{59} +(-7.42788 + 3.07673i) q^{61} +(0.989538 + 2.38896i) q^{62} +1.00000i q^{64} +(-0.0550527 + 0.132909i) q^{65} +15.7711 q^{67} +(-1.19891 - 3.94495i) q^{68} +(-1.04667 + 1.04667i) q^{70} +(-0.0867259 + 0.209375i) q^{71} +(-11.2147 - 4.64527i) q^{73} +(4.06193 + 9.80638i) q^{74} +(1.51594 + 1.51594i) q^{76} +(-4.09334 - 4.09334i) q^{77} +(-4.79863 - 11.5849i) q^{79} +(0.400544 + 0.165911i) q^{80} +(-4.63726 + 11.1953i) q^{82} +(0.738027 - 0.738027i) q^{83} +(-1.77904 - 0.174292i) q^{85} +10.0933 q^{86} +(-0.648847 + 1.56645i) q^{88} +13.8281i q^{89} +(-0.433546 - 1.04667i) q^{91} +(-1.74011 + 0.720777i) q^{92} +(-1.68297 - 1.68297i) q^{94} +(0.858710 - 0.355689i) q^{95} +(3.46953 + 1.43713i) q^{97} -4.65685i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{5}+O(q^{10}) \) 8 * q - 8 * q^5	\( 8 q - 8 q^{5} - 8 q^{10} - 8 q^{16} + 8 q^{17} - 16 q^{22} + 16 q^{23} + 8 q^{25} - 8 q^{26} + 16 q^{34} + 16 q^{35} - 16 q^{41} - 16 q^{43} - 16 q^{44} + 32 q^{49} - 8 q^{50} - 8 q^{53} - 32 q^{61} - 24 q^{65} + 48 q^{67} + 16 q^{70} + 16 q^{71} - 24 q^{73} + 16 q^{77} + 8 q^{80} - 8 q^{82} + 32 q^{83} + 8 q^{85} + 32 q^{86} - 16 q^{94} - 48 q^{95} + 16 q^{97}+O(q^{100}) \) 8 * q - 8 * q^5 - 8 * q^10 - 8 * q^16 + 8 * q^17 - 16 * q^22 + 16 * q^23 + 8 * q^25 - 8 * q^26 + 16 * q^34 + 16 * q^35 - 16 * q^41 - 16 * q^43 - 16 * q^44 + 32 * q^49 - 8 * q^50 - 8 * q^53 - 32 * q^61 - 24 * q^65 + 48 * q^67 + 16 * q^70 + 16 * q^71 - 24 * q^73 + 16 * q^77 + 8 * q^80 - 8 * q^82 + 32 * q^83 + 8 * q^85 + 32 * q^86 - 16 * q^94 - 48 * q^95 + 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more