LMFDB - Embedded newform 945.2.bj.g.836.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(26,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("945.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.bj (of order $6$, degree $2$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			836.3
Root			$0.500000 + 2.05195i$ of defining polynomial
Character	$\chi$	$=$	945.836
Dual form			945.2.bj.g.26.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02704 - 0.592963i) q^{2} +(-0.296790 + 0.514055i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0665372 - 2.64491i) q^{7} +3.07579i q^{8} +O(q^{10})$	\(q+(1.02704 - 0.592963i) q^{2} +(-0.296790 + 0.514055i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0665372 - 2.64491i) q^{7} +3.07579i q^{8} +(-1.02704 - 0.592963i) q^{10} +(1.36333 + 0.787117i) q^{11} +2.52967i q^{13} +(-1.63667 - 2.67698i) q^{14} +(1.23025 + 2.13086i) q^{16} +(3.55408 - 6.15585i) q^{17} +(6.69076 - 3.86291i) q^{19} +0.593579 q^{20} +1.86693 q^{22} +(2.52704 - 1.45899i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(1.50000 + 2.59808i) q^{26} +(1.37938 + 0.750780i) q^{28} -9.86718i q^{29} +(2.39037 + 1.38008i) q^{31} +(-2.80039 - 1.61680i) q^{32} -8.42976i q^{34} +(-2.25729 + 1.38008i) q^{35} +(5.39397 + 9.34263i) q^{37} +(4.58113 - 7.93474i) q^{38} +(2.66372 - 1.53790i) q^{40} +0.945916 q^{41} -9.84202 q^{43} +(-0.809243 + 0.467216i) q^{44} +(1.73025 - 2.99689i) q^{46} +(1.97296 + 3.41726i) q^{47} +(-6.99115 + 0.351971i) q^{49} +1.18593i q^{50} +(-1.30039 - 0.750780i) q^{52} +(-0.217799 - 0.125747i) q^{53} -1.57423i q^{55} +(8.13521 - 0.204655i) q^{56} +(-5.85087 - 10.1340i) q^{58} +(-1.30039 + 2.25234i) q^{59} +(2.27188 - 1.31167i) q^{61} +3.27335 q^{62} -8.75583 q^{64} +(2.19076 - 1.26483i) q^{65} +(1.74484 - 3.02215i) q^{67} +(2.10963 + 3.65399i) q^{68} +(-1.50000 + 2.75589i) q^{70} -11.3563i q^{71} +(-0.199612 - 0.115246i) q^{73} +(11.0797 + 6.39685i) q^{74} +4.58589i q^{76} +(1.99115 - 3.65826i) q^{77} +(6.44445 + 11.1621i) q^{79} +(1.23025 - 2.13086i) q^{80} +(0.971495 - 0.560893i) q^{82} +16.1082 q^{83} -7.10817 q^{85} +(-10.1082 + 5.83595i) q^{86} +(-2.42101 + 4.19331i) q^{88} +(-5.46410 - 9.46410i) q^{89} +(6.69076 - 0.168317i) q^{91} +1.73205i q^{92} +(4.05262 + 2.33978i) q^{94} +(-6.69076 - 3.86291i) q^{95} +14.8414i q^{97} +(-6.97150 + 4.50698i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + q^{4} - 3 q^{5} - 4 q^{7}+O(q^{10}) $ 6 * q - 3 * q^2 + q^4 - 3 * q^5 - 4 * q^7	$ 6 q - 3 q^{2} + q^{4} - 3 q^{5} - 4 q^{7} + 3 q^{10} + 9 q^{11} - 9 q^{14} + q^{16} + 3 q^{17} + 21 q^{19} - 2 q^{20} + 4 q^{22} + 6 q^{23} - 3 q^{25} + 9 q^{26} + 23 q^{28} + 6 q^{31} - 6 q^{32} + 2 q^{35} + 16 q^{37} + 6 q^{40} + 24 q^{41} - 8 q^{43} - 24 q^{44} + 4 q^{46} + 21 q^{47} - 12 q^{49} + 3 q^{52} + 27 q^{53} + 3 q^{56} - 14 q^{58} + 3 q^{59} - 33 q^{61} + 18 q^{62} + 8 q^{64} - 6 q^{65} - 27 q^{67} + 21 q^{68} - 9 q^{70} - 12 q^{73} - 6 q^{74} - 18 q^{77} + 12 q^{79} + q^{80} - 30 q^{82} + 60 q^{83} - 6 q^{85} - 24 q^{86} + 11 q^{88} - 12 q^{89} + 21 q^{91} - 39 q^{94} - 21 q^{95} - 6 q^{98}+O(q^{100}) $ 6 * q - 3 * q^2 + q^4 - 3 * q^5 - 4 * q^7 + 3 * q^10 + 9 * q^11 - 9 * q^14 + q^16 + 3 * q^17 + 21 * q^19 - 2 * q^20 + 4 * q^22 + 6 * q^23 - 3 * q^25 + 9 * q^26 + 23 * q^28 + 6 * q^31 - 6 * q^32 + 2 * q^35 + 16 * q^37 + 6 * q^40 + 24 * q^41 - 8 * q^43 - 24 * q^44 + 4 * q^46 + 21 * q^47 - 12 * q^49 + 3 * q^52 + 27 * q^53 + 3 * q^56 - 14 * q^58 + 3 * q^59 - 33 * q^61 + 18 * q^62 + 8 * q^64 - 6 * q^65 - 27 * q^67 + 21 * q^68 - 9 * q^70 - 12 * q^73 - 6 * q^74 - 18 * q^77 + 12 * q^79 + q^80 - 30 * q^82 + 60 * q^83 - 6 * q^85 - 24 * q^86 + 11 * q^88 - 12 * q^89 + 21 * q^91 - 39 * q^94 - 21 * q^95 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

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 $

$2$	1.02704	−	0.592963i	0.726228	−	0.419288i	−0.0908124	−	0.995868i	$-0.528946\pi$
$2$	1.02704	−	0.592963i	0.726228	−	0.419288i	0.817041	+	0.576580i	$0.195613\pi$
$3$		0			0
$3$		0			0
$4$	−0.296790	+	0.514055i	−0.148395	+	0.257027i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−0.0665372	−	2.64491i	−0.0251487	−	0.999684i
$7$	−0.0665372	−	2.64491i	−0.0251487	−	0.999684i
$8$			3.07579i			1.08746i
$9$		0			0
$10$	−1.02704	−	0.592963i	−0.324779	−	0.187511i
$11$	1.36333	+	0.787117i	0.411059	+	0.237325i	0.691244	−	0.722621i	$-0.257063\pi$
$11$	1.36333	+	0.787117i	0.411059	+	0.237325i	−0.280186	+	0.959946i	$0.590396\pi$
$12$		0			0
$13$			2.52967i			0.701604i	0.936450	+	0.350802i	$0.114091\pi$
$13$			2.52967i			0.701604i	−0.936450	+	0.350802i	$0.885909\pi$
$14$	−1.63667	−	2.67698i	−0.437419	−	0.715454i
$15$		0			0
$16$	1.23025	+	2.13086i	0.307563	+	0.532715i
$17$	3.55408	−	6.15585i	0.861992	−	1.49301i	−0.00801115	−	0.999968i	$-0.502550\pi$
$17$	3.55408	−	6.15585i	0.861992	−	1.49301i	0.870003	−	0.493046i	$-0.164117\pi$
$18$		0			0
$19$	6.69076	−	3.86291i	1.53496	−	0.886212i	0.535843	−	0.844318i	$-0.319994\pi$
$19$	6.69076	−	3.86291i	1.53496	−	0.886212i	0.999122	−	0.0418948i	$-0.0133394\pi$
$20$	0.593579			0.132728
$21$		0			0
$22$	1.86693			0.398030
$23$	2.52704	−	1.45899i	0.526925	−	0.304220i	−0.212839	−	0.977087i	$-0.568271\pi$
$23$	2.52704	−	1.45899i	0.526925	−	0.304220i	0.739763	+	0.672867i	$0.234937\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.50000	+	2.59808i	0.294174	+	0.509525i
$27$		0			0
$28$	1.37938	+	0.750780i	0.260678	+	0.141884i
$29$		−	9.86718i		−	1.83229i	−0.400847	−	0.916145i	$-0.631284\pi$
$29$		−	9.86718i		−	1.83229i	0.400847	−	0.916145i	$-0.368716\pi$
$30$		0			0
$31$	2.39037	+	1.38008i	0.429323	+	0.247870i	0.699058	−	0.715065i	$-0.253603\pi$
$31$	2.39037	+	1.38008i	0.429323	+	0.247870i	−0.269735	+	0.962935i	$0.586936\pi$
$32$	−2.80039	−	1.61680i	−0.495043	−	0.285813i
$33$		0			0
$34$		−	8.42976i		−	1.44569i
$35$	−2.25729	+	1.38008i	−0.381552	+	0.233276i
$36$		0			0
$37$	5.39397	+	9.34263i	0.886763	+	1.53592i	0.843680	+	0.536847i	$0.180385\pi$
$37$	5.39397	+	9.34263i	0.886763	+	1.53592i	0.0430830	+	0.999071i	$0.486282\pi$
$38$	4.58113	−	7.93474i	0.743157	−	1.28719i
$39$		0			0
$40$	2.66372	−	1.53790i	0.421170	−	0.243163i
$41$	0.945916			0.147727			0.0738636	−	0.997268i	$-0.476467\pi$
$41$	0.945916			0.147727			0.0738636	+	0.997268i	$0.476467\pi$
$42$		0			0
$43$	−9.84202			−1.50089			−0.750447	−	0.660931i	$-0.770162\pi$
$43$	−9.84202			−1.50089			−0.750447	+	0.660931i	$0.770162\pi$
$44$	−0.809243	+	0.467216i	−0.121998	+	0.0704355i
$45$		0			0
$46$	1.73025	−	2.99689i	0.255112	−	0.441867i
$47$	1.97296	+	3.41726i	0.287785	+	0.498459i	0.973281	−	0.229618i	$-0.0737477\pi$
$47$	1.97296	+	3.41726i	0.287785	+	0.498459i	−0.685495	+	0.728077i	$0.740414\pi$
$48$		0			0
$49$	−6.99115	+	0.351971i	−0.998735	+	0.0502815i
$50$			1.18593i			0.167715i
$51$		0			0
$52$	−1.30039	−	0.750780i	−0.180331	−	0.104114i
$53$	−0.217799	−	0.125747i	−0.0299171	−	0.0172726i	0.484967	−	0.874533i	$-0.338832\pi$
$53$	−0.217799	−	0.125747i	−0.0299171	−	0.0172726i	−0.514884	+	0.857260i	$0.672165\pi$
$54$		0			0
$55$		−	1.57423i		−	0.212270i
$56$	8.13521	−	0.204655i	1.08711	−	0.0273481i
$57$		0			0
$58$	−5.85087	−	10.1340i	−0.768257	−	1.33066i
$59$	−1.30039	+	2.25234i	−0.169296	+	0.293230i	−0.938173	−	0.346168i	$-0.887483\pi$
$59$	−1.30039	+	2.25234i	−0.169296	+	0.293230i	0.768876	+	0.639397i	$0.220816\pi$
$60$		0			0
$61$	2.27188	−	1.31167i	0.290885	−	0.167942i	−0.347456	−	0.937696i	$-0.612954\pi$
$61$	2.27188	−	1.31167i	0.290885	−	0.167942i	0.638341	+	0.769754i	$0.279621\pi$
$62$	3.27335			0.415715
$63$		0			0
$64$	−8.75583			−1.09448
$65$	2.19076	−	1.26483i	0.271730	−	0.156883i
$66$		0			0
$67$	1.74484	−	3.02215i	0.213166	−	0.369215i	−0.739537	−	0.673115i	$-0.764956\pi$
$67$	1.74484	−	3.02215i	0.213166	−	0.369215i	0.952704	+	0.303901i	$0.0982890\pi$
$68$	2.10963	+	3.65399i	0.255830	+	0.443111i
$69$		0			0
$70$	−1.50000	+	2.75589i	−0.179284	+	0.329392i
$71$		−	11.3563i		−	1.34774i	−0.738849	−	0.673871i	$-0.764630\pi$
$71$		−	11.3563i		−	1.34774i	0.738849	−	0.673871i	$-0.235370\pi$
$72$		0			0
$73$	−0.199612	−	0.115246i	−0.0233628	−	0.0134885i	0.488273	−	0.872691i	$-0.337627\pi$
$73$	−0.199612	−	0.115246i	−0.0233628	−	0.0134885i	−0.511636	+	0.859202i	$0.670960\pi$
$74$	11.0797	+	6.39685i	1.28798	+	0.743618i
$75$		0			0
$76$			4.58589i			0.526037i
$77$	1.99115	−	3.65826i	0.226912	−	0.416897i
$78$		0			0
$79$	6.44445	+	11.1621i	0.725058	+	1.25584i	0.958950	+	0.283574i	$0.0915202\pi$
$79$	6.44445	+	11.1621i	0.725058	+	1.25584i	−0.233893	+	0.972262i	$0.575146\pi$
$80$	1.23025	−	2.13086i	0.137546	−	0.238237i
$81$		0			0
$82$	0.971495	−	0.560893i	0.107284	−	0.0619403i
$83$	16.1082			1.76810			0.884051	−	0.467391i	$-0.154806\pi$
$83$	16.1082			1.76810			0.884051	+	0.467391i	$0.154806\pi$
$84$		0			0
$85$	−7.10817			−0.770989
$86$	−10.1082	+	5.83595i	−1.08999	+	0.629307i
$87$		0			0
$88$	−2.42101	+	4.19331i	−0.258081	+	0.447009i
$89$	−5.46410	−	9.46410i	−0.579194	−	1.00319i	−0.995572	−	0.0940016i	$-0.970034\pi$
$89$	−5.46410	−	9.46410i	−0.579194	−	1.00319i	0.416378	−	0.909191i	$-0.363299\pi$
$90$		0			0
$91$	6.69076	−	0.168317i	0.701382	−	0.0176444i
$92$			1.73205i			0.180579i
$93$		0			0
$94$	4.05262	+	2.33978i	0.417996	+	0.241330i
$95$	−6.69076	−	3.86291i	−0.686457	−	0.396326i
$96$		0			0
$97$			14.8414i			1.50691i	0.657497	+	0.753457i	$0.271615\pi$
$97$			14.8414i			1.50691i	−0.657497	+	0.753457i	$0.728385\pi$
$98$	−6.97150	+	4.50698i	−0.704227	+	0.455274i
$99$		0			0
$100$	−0.296790	−	0.514055i	−0.0296790	−	0.0514055i
$101$	2.39037	−	4.14024i	0.237851	−	0.411969i	−0.722247	−	0.691636i	$-0.756890\pi$
$101$	2.39037	−	4.14024i	0.237851	−	0.411969i	0.960097	+	0.279666i	$0.0902238\pi$
$102$		0			0
$103$	−11.6819	+	6.74455i	−1.15105	+	0.664560i	−0.949143	−	0.314844i	$-0.898048\pi$
$103$	−11.6819	+	6.74455i	−1.15105	+	0.664560i	−0.201909	+	0.979404i	$0.564714\pi$
$104$	−7.78074			−0.762964
$105$		0			0
$106$	−0.298252			−0.0289688
$107$	−14.3456	+	8.28245i	−1.38684	+	0.800694i	−0.992958	−	0.118465i	$-0.962203\pi$
$107$	−14.3456	+	8.28245i	−1.38684	+	0.800694i	−0.393885	+	0.919160i	$0.628869\pi$
$108$		0			0
$109$	0.956906	−	1.65741i	0.0916550	−	0.158751i	−0.816553	−	0.577271i	$-0.804118\pi$
$109$	0.956906	−	1.65741i	0.0916550	−	0.158751i	0.908208	+	0.418520i	$0.137451\pi$
$110$	−0.933463	−	1.61680i	−0.0890022	−	0.154156i
$111$		0			0
$112$	5.55408	−	3.39569i	0.524812	−	0.320863i
$113$			5.35397i			0.503659i	0.967772	+	0.251830i	$0.0810322\pi$
$113$			5.35397i			0.503659i	−0.967772	+	0.251830i	$0.918968\pi$
$114$		0			0
$115$	−2.52704	−	1.45899i	−0.235648	−	0.136051i
$116$	5.07227	+	2.92848i	0.470949	+	0.271902i
$117$		0			0
$118$			3.08433i			0.283935i
$119$	−16.5182	−	8.99066i	−1.51422	−	0.824172i
$120$		0			0
$121$	−4.26089	−	7.38008i	−0.387354	−	0.670917i
$122$	1.55555	−	2.69429i	0.140833	−	0.243929i
$123$		0			0
$124$	−1.41887	+	0.819187i	−0.127419	+	0.0735652i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−7.43560			−0.659803			−0.329901	−	0.944015i	$-0.607015\pi$
$127$	−7.43560			−0.659803			−0.329901	+	0.944015i	$0.607015\pi$
$128$	−3.39183	+	1.95827i	−0.299798	+	0.173089i
$129$		0			0
$130$	1.50000	−	2.59808i	0.131559	−	0.227866i
$131$	2.24630	+	3.89071i	0.196260	+	0.339933i	0.947313	−	0.320309i	$-0.103787\pi$
$131$	2.24630	+	3.89071i	0.196260	+	0.339933i	−0.751053	+	0.660242i	$0.770454\pi$
$132$		0			0
$133$	−10.6623	−	17.4395i	−0.924535	−	1.51219i
$134$		−	4.13851i		−	0.357512i
$135$		0			0
$136$	18.9341	+	10.9316i	1.62359	+	0.937379i
$137$	5.53443	+	3.19531i	0.472839	+	0.272993i	0.717427	−	0.696633i	$-0.245320\pi$
$137$	5.53443	+	3.19531i	0.472839	+	0.272993i	−0.244589	+	0.969627i	$0.578653\pi$
$138$		0			0
$139$			13.3954i			1.13618i	0.822965	+	0.568092i	$0.192318\pi$
$139$			13.3954i			1.13618i	−0.822965	+	0.568092i	$0.807682\pi$
$140$	−0.0394951	−	1.56997i	−0.00333795	−	0.132686i
$141$		0			0
$142$	−6.73385	−	11.6634i	−0.565092	−	0.978768i
$143$	−1.99115	+	3.44877i	−0.166508	+	0.288400i
$144$		0			0
$145$	−8.54523	+	4.93359i	−0.709643	+	0.409712i
$146$	−0.273346			−0.0226223
$147$		0			0
$148$	−6.40350			−0.526364
$149$	−9.63521	+	5.56289i	−0.789347	+	0.455730i	−0.839733	−	0.543000i	$-0.817288\pi$
$149$	−9.63521	+	5.56289i	−0.789347	+	0.455730i	0.0503855	+	0.998730i	$0.483955\pi$
$150$		0			0
$151$	0.620621	−	1.07495i	0.0505055	−	0.0874780i	−0.839667	−	0.543101i	$-0.817250\pi$
$151$	0.620621	−	1.07495i	0.0505055	−	0.0874780i	0.890173	+	0.455623i	$0.150583\pi$
$152$	11.8815	+	20.5794i	0.963718	+	1.66921i
$153$		0			0
$154$	−0.124220	−	4.93786i	−0.0100099	−	0.397904i
$155$		−	2.76016i		−	0.221701i
$156$		0			0
$157$	1.99115	+	1.14959i	0.158911	+	0.0917471i	0.577347	−	0.816499i	$-0.304088\pi$
$157$	1.99115	+	1.14959i	0.158911	+	0.0917471i	−0.418436	+	0.908246i	$0.637422\pi$
$158$	13.2374	+	7.64265i	1.05311	+	0.608016i
$159$		0			0
$160$			3.23361i			0.255639i
$161$	−4.02704	−	6.58673i	−0.317375	−	0.519107i
$162$		0			0
$163$	−1.89037	−	3.27422i	−0.148065	−	0.256456i	0.782447	−	0.622717i	$-0.213971\pi$
$163$	−1.89037	−	3.27422i	−0.148065	−	0.256456i	−0.930512	+	0.366261i	$0.880638\pi$
$164$	−0.280738	+	0.486253i	−0.0219220	+	0.0379699i
$165$		0			0
$166$	16.5438	−	9.55155i	1.28405	−	0.741344i
$167$	−23.2163			−1.79653			−0.898267	−	0.439450i	$-0.855173\pi$
$167$	−23.2163			−1.79653			−0.898267	+	0.439450i	$0.855173\pi$
$168$		0			0
$169$	6.60078			0.507752
$170$	−7.30039	+	4.21488i	−0.559914	+	0.323267i
$171$		0			0
$172$	2.92101	−	5.05934i	0.222725	−	0.385771i
$173$	7.71780	+	13.3676i	0.586773	+	1.01632i	0.994652	+	0.103285i	$0.0329354\pi$
$173$	7.71780	+	13.3676i	0.586773	+	1.01632i	−0.407878	+	0.913036i	$0.633731\pi$
$174$		0			0
$175$	2.32383	+	1.26483i	0.175665	+	0.0956125i
$176$			3.87341i			0.291969i
$177$		0			0
$178$	−11.2237	−	6.48002i	−0.841254	−	0.485698i
$179$	−16.3889	−	9.46214i	−1.22496	−	0.707234i	−0.258992	−	0.965879i	$-0.583390\pi$
$179$	−16.3889	−	9.46214i	−1.22496	−	0.707234i	−0.965972	+	0.258646i	$0.916724\pi$
$180$		0			0
$181$			8.60465i			0.639579i	0.947489	+	0.319789i	$0.103612\pi$
$181$			8.60465i			0.639579i	−0.947489	+	0.319789i	$0.896388\pi$
$182$	6.77188	−	4.14024i	0.501965	−	0.306895i
$183$		0			0
$184$	4.48755	+	7.77266i	0.330826	+	0.573008i
$185$	5.39397	−	9.34263i	0.396572	−	0.686884i
$186$		0			0
$187$	9.69076	−	5.59496i	0.708658	−	0.409144i
$188$	−2.34221			−0.170824
$189$		0			0
$190$	−9.16225			−0.664700
$191$	−5.12441	+	2.95858i	−0.370790	+	0.214075i	−0.673803	−	0.738911i	$-0.735341\pi$
$191$	−5.12441	+	2.95858i	−0.370790	+	0.214075i	0.303014	+	0.952986i	$0.402007\pi$
$192$		0			0
$193$	1.84728	−	3.19957i	0.132970	−	0.230310i	−0.791850	−	0.610715i	$-0.790882\pi$
$193$	1.84728	−	3.19957i	0.132970	−	0.230310i	0.924820	+	0.380405i	$0.124215\pi$
$194$	8.80039	+	15.2427i	0.631831	+	1.09436i
$195$		0			0
$196$	1.89397	−	3.69829i	0.135283	−	0.264164i
$197$			12.8493i			0.915475i	0.889087	+	0.457737i	$0.151340\pi$
$197$			12.8493i			0.915475i	−0.889087	+	0.457737i	$0.848660\pi$
$198$		0			0
$199$	−12.9715	−	7.48910i	−0.919525	−	0.530888i	−0.0360415	−	0.999350i	$-0.511475\pi$
$199$	−12.9715	−	7.48910i	−0.919525	−	0.530888i	−0.883483	+	0.468462i	$0.844808\pi$
$200$	−2.66372	−	1.53790i	−0.188353	−	0.108746i
$201$		0			0
$202$		−	5.66960i		−	0.398912i
$203$	−26.0979	+	0.656535i	−1.83171	+	0.0460797i
$204$		0			0
$205$	−0.472958	−	0.819187i	−0.0330328	−	0.0572145i
$206$	−7.99854	+	13.8539i	−0.557285	+	0.965245i
$207$		0			0
$208$	−5.39037	+	3.11213i	−0.373755	+	0.215787i
$209$	12.1623			0.841281
$210$		0			0
$211$	1.48541			0.102260			0.0511300	−	0.998692i	$-0.483718\pi$
$211$	1.48541			0.102260			0.0511300	+	0.998692i	$0.483718\pi$
$212$	0.129281	−	0.0746406i	0.00887907	−	0.00512633i
$213$		0			0
$214$	−9.82237	+	17.0128i	−0.671443	+	1.16297i
$215$	4.92101	+	8.52344i	0.335610	+	0.581294i
$216$		0			0
$217$	3.49115	−	6.41415i	0.236994	−	0.435421i
$218$		−	2.26964i		−	0.153719i
$219$		0			0
$220$	0.809243	+	0.467216i	0.0545591	+	0.0314997i
$221$	15.5723	+	8.99066i	1.04750	+	0.604777i
$222$		0			0
$223$		−	3.50724i		−	0.234862i	−0.993081	−	0.117431i	$-0.962534\pi$
$223$		−	3.50724i		−	0.234862i	0.993081	−	0.117431i	$-0.0374659\pi$
$224$	−4.08998	+	7.51437i	−0.273273	+	0.502075i
$225$		0			0
$226$	3.17471	+	5.49875i	0.211178	+	0.365772i
$227$	9.21780	−	15.9657i	0.611807	−	1.05968i	−0.379129	−	0.925344i	$-0.623776\pi$
$227$	9.21780	−	15.9657i	0.611807	−	1.05968i	0.990936	−	0.134337i	$-0.0428904\pi$
$228$		0			0
$229$	11.9626	−	6.90663i	0.790514	−	0.456403i	−0.0496297	−	0.998768i	$-0.515804\pi$
$229$	11.9626	−	6.90663i	0.790514	−	0.456403i	0.840143	+	0.542364i	$0.182471\pi$
$230$	−3.46050			−0.228179
$231$		0			0
$232$	30.3494			1.99254
$233$	4.07081	−	2.35028i	0.266688	−	0.153972i	−0.360694	−	0.932684i	$-0.617460\pi$
$233$	4.07081	−	2.35028i	0.266688	−	0.153972i	0.627381	+	0.778712i	$0.284127\pi$
$234$		0			0
$235$	1.97296	−	3.41726i	0.128702	−	0.222918i
$236$	−0.771884	−	1.33694i	−0.0502453	−	0.0870275i
$237$		0			0
$238$	−22.2960	+	0.560893i	−1.44524	+	0.0363573i
$239$			21.0361i			1.36071i	0.732882	+	0.680356i	$0.238175\pi$
$239$			21.0361i			1.36071i	−0.732882	+	0.680356i	$0.761825\pi$
$240$		0			0
$241$	13.4189	+	7.74739i	0.864386	+	0.499053i	0.865478	−	0.500946i	$-0.167015\pi$
$241$	13.4189	+	7.74739i	0.864386	+	0.499053i	−0.00109283	+	0.999999i	$0.500348\pi$
$242$	−8.75223	−	5.05310i	−0.562615	−	0.324826i
$243$		0			0
$244$			1.55716i			0.0996872i
$245$	3.80039	+	5.87852i	0.242798	+	0.375565i
$246$		0			0
$247$	9.77188	+	16.9254i	0.621770	+	1.07694i
$248$	−4.24484	+	7.35228i	−0.269548	+	0.466870i
$249$		0			0
$250$	1.02704	−	0.592963i	0.0649558	−	0.0375023i
$251$	18.6726			1.17860			0.589301	−	0.807914i	$-0.299403\pi$
$251$	18.6726			1.17860			0.589301	+	0.807914i	$0.299403\pi$
$252$		0			0
$253$	4.59358			0.288796
$254$	−7.63667	+	4.40904i	−0.479167	+	0.276647i
$255$		0			0
$256$	6.43346	−	11.1431i	0.402091	−	0.696443i
$257$	−10.5182	−	18.2180i	−0.656107	−	1.13641i	−0.981615	−	0.190871i	$-0.938869\pi$
$257$	−10.5182	−	18.2180i	−0.656107	−	1.13641i	0.325509	−	0.945539i	$-0.394464\pi$
$258$		0			0
$259$	24.3515	−	14.8882i	1.51313	−	0.925109i
$260$			1.50156i			0.0931227i
$261$		0			0
$262$	4.61410	+	2.66395i	0.285060	+	0.164579i
$263$	−19.5512	−	11.2879i	−1.20558	−	0.696040i	−0.243786	−	0.969829i	$-0.578390\pi$
$263$	−19.5512	−	11.2879i	−1.20558	−	0.696040i	−0.961790	+	0.273789i	$0.911723\pi$
$264$		0			0
$265$			0.251493i			0.0154491i
$266$	−21.2915	−	11.5887i	−1.30547	−	0.710551i
$267$		0			0
$268$	1.03570	+	1.79389i	0.0632656	+	0.109579i
$269$	5.39037	−	9.33639i	0.328657	−	0.569250i	−0.653589	−	0.756850i	$-0.726737\pi$
$269$	5.39037	−	9.33639i	0.328657	−	0.569250i	0.982246	+	0.187600i	$0.0600708\pi$
$270$		0			0
$271$	8.96264	−	5.17458i	0.544442	−	0.314334i	−0.202435	−	0.979296i	$-0.564886\pi$
$271$	8.96264	−	5.17458i	0.544442	−	0.314334i	0.746877	+	0.664962i	$0.231552\pi$
$272$	17.4897			1.06047
$273$		0			0
$274$	7.57880			0.457852
$275$	−1.36333	+	0.787117i	−0.0822117	+	0.0474650i
$276$		0			0
$277$	−5.86186	+	10.1530i	−0.352205	+	0.610037i	−0.986636	−	0.162943i	$-0.947901\pi$
$277$	−5.86186	+	10.1530i	−0.352205	+	0.610037i	0.634430	+	0.772980i	$0.281235\pi$
$278$	7.94299	+	13.7577i	0.476389	+	0.825130i
$279$		0			0
$280$	−4.24484	−	6.94297i	−0.253678	−	0.414922i
$281$			11.6288i			0.693714i	0.937918	+	0.346857i	$0.112751\pi$
$281$			11.6288i			0.693714i	−0.937918	+	0.346857i	$0.887249\pi$
$282$		0			0
$283$	−3.89037	−	2.24611i	−0.231258	−	0.133517i	0.379894	−	0.925030i	$-0.375960\pi$
$283$	−3.89037	−	2.24611i	−0.231258	−	0.133517i	−0.611152	+	0.791513i	$0.709294\pi$
$284$	5.83775	+	3.37043i	0.346407	+	0.199998i
$285$		0			0
$286$			4.72270i			0.279259i
$287$	−0.0629386	−	2.50187i	−0.00371515	−	0.147681i
$288$		0			0
$289$	−16.7630	−	29.0344i	−0.986061	−	1.70791i
$290$	−5.85087	+	10.1340i	−0.343575	+	0.595090i
$291$		0			0
$292$	0.118485	−	0.0684076i	0.00693383	−	0.00400325i
$293$	−6.27335			−0.366493			−0.183246	−	0.983067i	$-0.558661\pi$
$293$	−6.27335			−0.366493			−0.183246	+	0.983067i	$0.558661\pi$
$294$		0			0
$295$	2.60078			0.151423
$296$	−28.7360	+	16.5907i	−1.67025	+	0.964317i
$297$		0			0
$298$	−6.59718	+	11.4266i	−0.382164	+	0.661928i
$299$	3.69076	+	6.39258i	0.213442	+	0.369692i
$300$		0			0
$301$	0.654861	+	26.0313i	0.0377455	+	1.50042i
$302$		−	1.47202i		−	0.0847054i
$303$		0			0
$304$	16.4626	+	9.50471i	0.944197	+	0.545133i
$305$	−2.27188	−	1.31167i	−0.130088	−	0.0751062i
$306$		0			0
$307$			7.11556i			0.406106i	0.979168	+	0.203053i	$0.0650864\pi$
$307$			7.11556i			0.406106i	−0.979168	+	0.203053i	$0.934914\pi$
$308$	1.28959	+	2.10929i	0.0734813	+	0.120188i
$309$		0			0
$310$	−1.63667	−	2.83480i	−0.0929568	−	0.161006i
$311$	8.58259	−	14.8655i	0.486674	−	0.842944i	−0.513209	−	0.858264i	$-0.671543\pi$
$311$	8.58259	−	14.8655i	0.486674	−	0.842944i	0.999883	+	0.0153198i	$0.00487664\pi$
$312$		0			0
$313$	10.0089	−	5.77861i	0.565734	−	0.326627i	−0.189710	−	0.981840i	$-0.560755\pi$
$313$	10.0089	−	5.77861i	0.565734	−	0.326627i	0.755444	+	0.655214i	$0.227421\pi$
$314$	2.72665			0.153874
$315$		0			0
$316$	−7.65059			−0.430379
$317$	−28.7360	+	16.5907i	−1.61397	+	0.931828i	−0.625537	+	0.780194i	$0.715120\pi$
$317$	−28.7360	+	16.5907i	−1.61397	+	0.931828i	−0.988437	+	0.151634i	$0.951547\pi$
$318$		0			0
$319$	7.76663	−	13.4522i	0.434848	−	0.753178i
$320$	4.37792	+	7.58277i	0.244733	+	0.423890i
$321$		0			0
$322$	−8.04163	−	4.37697i	−0.448143	−	0.243919i
$323$		−	54.9164i		−	3.05563i
$324$		0			0
$325$	−2.19076	−	1.26483i	−0.121521	−	0.0701604i
$326$	−3.88298	−	2.24184i	−0.215058	−	0.124164i
$327$		0			0
$328$			2.90944i			0.160647i
$329$	8.90709	−	5.44568i	0.491064	−	0.300230i
$330$		0			0
$331$	1.24844	+	2.16236i	0.0686205	+	0.118854i	0.898294	−	0.439394i	$-0.144807\pi$
$331$	1.24844	+	2.16236i	0.0686205	+	0.118854i	−0.829674	+	0.558248i	$0.811474\pi$
$332$	−4.78074	+	8.28048i	−0.262377	+	0.454450i
$333$		0			0
$334$	−23.8442	+	13.7664i	−1.30469	+	0.753266i
$335$	−3.48968			−0.190662
$336$		0			0
$337$	−11.8961			−0.648022			−0.324011	−	0.946053i	$-0.605031\pi$
$337$	−11.8961			−0.648022			−0.324011	+	0.946053i	$0.605031\pi$
$338$	6.77928	−	3.91402i	0.368744	−	0.212894i
$339$		0			0
$340$	2.10963	−	3.65399i	0.114411	−	0.198165i
$341$	2.17257	+	3.76300i	0.117651	+	0.203778i
$342$		0			0
$343$	1.39610	+	18.4676i	0.0753825	+	0.997155i
$344$		−	30.2720i		−	1.63216i
$345$		0			0
$346$	15.8530	+	9.15274i	0.852263	+	0.492054i
$347$	−0.584051	−	0.337202i	−0.0313535	−	0.0181020i	0.484241	−	0.874934i	$-0.339096\pi$
$347$	−0.584051	−	0.337202i	−0.0313535	−	0.0181020i	−0.515595	+	0.856833i	$0.672429\pi$
$348$		0			0
$349$			7.95631i			0.425892i	0.977064	+	0.212946i	$0.0683058\pi$
$349$			7.95631i			0.425892i	−0.977064	+	0.212946i	$0.931694\pi$
$350$	3.13667	−	0.0789082i	0.167662	−	0.00421782i
$351$		0			0
$352$	−2.54523	−	4.40847i	−0.135661	−	0.234972i
$353$	2.60078	−	4.50468i	0.138425	−	0.239760i	−0.788475	−	0.615066i	$-0.789129\pi$
$353$	2.60078	−	4.50468i	0.138425	−	0.239760i	0.926901	+	0.375307i	$0.122463\pi$
$354$		0			0
$355$	−9.83482	+	5.67814i	−0.521978	+	0.301364i
$356$	6.48676			0.343797
$357$		0			0
$358$	−22.4428			−1.18614
$359$	−1.28220	+	0.740279i	−0.0676720	+	0.0390704i	−0.533454	−	0.845829i	$-0.679106\pi$
$359$	−1.28220	+	0.740279i	−0.0676720	+	0.0390704i	0.465782	+	0.884899i	$0.345773\pi$
$360$		0			0
$361$	20.3442	−	35.2371i	1.07075	−	1.85458i
$362$	5.10224	+	8.83734i	0.268168	+	0.464480i
$363$		0			0
$364$	−1.89922	+	3.48937i	−0.0995464	+	0.182893i
$365$			0.230492i			0.0120645i
$366$		0			0
$367$	−26.5153	−	15.3086i	−1.38409	−	0.799102i	−0.391445	−	0.920201i	$-0.628025\pi$
$367$	−26.5153	−	15.3086i	−1.38409	−	0.799102i	−0.992640	+	0.121099i	$0.961358\pi$
$368$	6.21780	+	3.58985i	0.324125	+	0.187134i
$369$		0			0
$370$		−	12.7937i		−	0.665112i
$371$	−0.318097	+	0.584428i	−0.0165148	+	0.0303420i
$372$		0			0
$373$	−4.69815	−	8.13743i	−0.243261	−	0.421340i	0.718380	−	0.695651i	$-0.244884\pi$
$373$	−4.69815	−	8.13743i	−0.243261	−	0.421340i	−0.961641	+	0.274310i	$0.911550\pi$
$374$	6.63521	−	11.4925i	0.343099	−	0.594264i
$375$		0			0
$376$	−10.5108	+	6.06841i	−0.542053	+	0.312954i
$377$	24.9607			1.28554
$378$		0			0
$379$	−13.1665			−0.676319			−0.338159	−	0.941089i	$-0.609804\pi$
$379$	−13.1665			−0.676319			−0.338159	+	0.941089i	$0.609804\pi$
$380$	3.97150	−	2.29294i	0.203733	−	0.117626i
$381$		0			0
$382$	−3.50866	+	6.07718i	−0.179519	+	0.310935i
$383$	14.9700	+	25.9289i	0.764933	+	1.32490i	0.940282	+	0.340396i	$0.110561\pi$
$383$	14.9700	+	25.9289i	0.764933	+	1.32490i	−0.175349	+	0.984506i	$0.556105\pi$
$384$		0			0
$385$	−4.16372	+	0.104745i	−0.212203	+	0.00533831i
$386$		−	4.38146i		−	0.223011i
$387$		0			0
$388$	−7.62928	−	4.40477i	−0.387318	−	0.223618i
$389$	12.1549	+	7.01761i	0.616276	+	0.355807i	0.775418	−	0.631449i	$-0.217539\pi$
$389$	12.1549	+	7.01761i	0.616276	+	0.355807i	−0.159142	+	0.987256i	$0.550873\pi$
$390$		0			0
$391$		−	20.7415i		−	1.04894i
$392$	−1.08259	−	21.5033i	−0.0546790	−	1.08608i
$393$		0			0
$394$	7.61916	+	13.1968i	0.383848	+	0.664844i
$395$	6.44445	−	11.1621i	0.324256	−	0.561627i
$396$		0			0
$397$	11.4823	−	6.62930i	0.576280	−	0.332715i	−0.183374	−	0.983043i	$-0.558702\pi$
$397$	11.4823	−	6.62930i	0.576280	−	0.332715i	0.759654	+	0.650328i	$0.225369\pi$
$398$	−17.7630			−0.890380
$399$		0			0
$400$	−2.46050			−0.123025
$401$	−5.42674	+	3.13313i	−0.270999	+	0.156461i	−0.629341	−	0.777129i	$-0.716675\pi$
$401$	−5.42674	+	3.13313i	−0.270999	+	0.156461i	0.358343	+	0.933590i	$0.383342\pi$
$402$		0			0
$403$	−3.49115	+	6.04684i	−0.173906	+	0.301215i
$404$	1.41887	+	2.45756i	0.0705916	+	0.122268i
$405$		0			0
$406$	−26.4143	+	16.1494i	−1.31092	+	0.801479i
$407$			16.9827i			0.841803i
$408$		0			0
$409$	13.7326	+	7.92851i	0.679033	+	0.392040i	0.799490	−	0.600679i	$-0.205103\pi$
$409$	13.7326	+	7.92851i	0.679033	+	0.392040i	−0.120458	+	0.992718i	$0.538436\pi$
$410$	−0.971495	−	0.560893i	−0.0479787	−	0.0277005i
$411$		0			0
$412$		−	8.00685i		−	0.394469i
$413$	6.04377	+	3.28955i	0.297394	+	0.161868i
$414$		0			0
$415$	−8.05408	−	13.9501i	−0.395359	−	0.684783i
$416$	4.08998	−	7.08405i	0.200528	−	0.347324i
$417$		0			0
$418$	12.4911	−	7.21177i	0.610962	−	0.352739i
$419$	6.39922			0.312623			0.156311	−	0.987708i	$-0.450040\pi$
$419$	6.39922			0.312623			0.156311	+	0.987708i	$0.450040\pi$
$420$		0			0
$421$	13.6519			0.665355			0.332677	−	0.943041i	$-0.392048\pi$
$421$	13.6519			0.665355			0.332677	+	0.943041i	$0.392048\pi$
$422$	1.52558	−	0.880794i	0.0742641	−	0.0428764i
$423$		0			0
$424$	0.386770	−	0.669906i	0.0187832	−	0.0325335i
$425$	3.55408	+	6.15585i	0.172398	+	0.298603i
$426$		0			0
$427$	−3.62043	−	5.92166i	−0.175205	−	0.286569i
$428$		−	9.83258i		−	0.475276i
$429$		0			0
$430$	10.1082	+	5.83595i	0.487459	+	0.281435i
$431$	−8.39776	−	4.84845i	−0.404506	−	0.233542i	0.283920	−	0.958848i	$-0.408365\pi$
$431$	−8.39776	−	4.84845i	−0.404506	−	0.233542i	−0.688426	+	0.725306i	$0.741698\pi$
$432$		0			0
$433$			18.9970i			0.912935i	0.889740	+	0.456468i	$0.150886\pi$
$433$			18.9970i			0.912935i	−0.889740	+	0.456468i	$0.849114\pi$
$434$	−0.217799	−	8.65772i	−0.0104547	−	0.415584i
$435$		0			0
$436$	0.568000	+	0.983804i	0.0272023	+	0.0471157i
$437$	11.2719	−	19.5235i	0.539207	−	0.933934i
$438$		0			0
$439$	9.90116	−	5.71644i	0.472557	−	0.272831i	−0.244753	−	0.969586i	$-0.578707\pi$
$439$	9.90116	−	5.71644i	0.472557	−	0.272831i	0.717309	+	0.696755i	$0.245373\pi$
$440$	4.84202			0.230834
$441$		0			0
$442$	21.3245			1.01430
$443$	−2.86333	+	1.65314i	−0.136041	+	0.0785432i	−0.566476	−	0.824078i	$-0.691694\pi$
$443$	−2.86333	+	1.65314i	−0.136041	+	0.0785432i	0.430435	+	0.902622i	$0.358360\pi$
$444$		0			0
$445$	−5.46410	+	9.46410i	−0.259023	+	0.448642i
$446$	−2.07966	−	3.60208i	−0.0984749	−	0.170564i
$447$		0			0
$448$	0.582589	+	23.1584i	0.0275247	+	1.09413i
$449$			6.38208i			0.301189i	0.988596	+	0.150594i	$0.0481188\pi$
$449$			6.38208i			0.301189i	−0.988596	+	0.150594i	$0.951881\pi$
$450$		0			0
$451$	1.28959	+	0.744547i	0.0607245	+	0.0350593i
$452$	−2.75223	−	1.58900i	−0.129454	−	0.0747404i
$453$		0			0
$454$		−	21.8633i		−	1.02609i
$455$	−3.49115	−	5.71021i	−0.163667	−	0.267699i
$456$		0			0
$457$	6.22140	+	10.7758i	0.291025	+	0.504070i	0.974052	−	0.226323i	$-0.0726705\pi$
$457$	6.22140	+	10.7758i	0.291025	+	0.504070i	−0.683028	+	0.730393i	$0.739337\pi$
$458$	8.19076	−	14.1868i	0.382729	−	0.662906i
$459$		0			0
$460$	1.50000	−	0.866025i	0.0699379	−	0.0403786i
$461$	17.6519			0.822133			0.411066	−	0.911605i	$-0.365156\pi$
$461$	17.6519			0.822133			0.411066	+	0.911605i	$0.365156\pi$
$462$		0			0
$463$	−14.8023			−0.687923			−0.343961	−	0.938984i	$-0.611769\pi$
$463$	−14.8023			−0.687923			−0.343961	+	0.938984i	$0.611769\pi$
$464$	21.0256	−	12.1391i	0.976088	−	0.563545i
$465$		0			0
$466$	2.78726	−	4.82768i	0.129117	−	0.223638i
$467$	−13.4808	−	23.3495i	−0.623818	−	1.08049i	−0.988768	−	0.149458i	$-0.952247\pi$
$467$	−13.4808	−	23.3495i	−0.623818	−	1.08049i	0.364950	−	0.931027i	$-0.381086\pi$
$468$		0			0
$469$	−8.10944	−	4.41387i	−0.374459	−	0.203814i
$470$		−	4.67956i		−	0.215852i
$471$		0			0
$472$	−6.92773	−	3.99973i	−0.318875	−	0.184102i
$473$	−13.4179	−	7.74682i	−0.616955	−	0.356199i
$474$		0			0
$475$			7.72582i			0.354485i
$476$	9.52412	−	5.82292i	0.436537	−	0.266893i
$477$		0			0
$478$	12.4736	+	21.6050i	0.570531	+	0.988188i
$479$	−11.0167	+	19.0815i	−0.503367	+	0.871857i	0.496625	+	0.867965i	$0.334572\pi$
$479$	−11.0167	+	19.0815i	−0.503367	+	0.871857i	−0.999992	+	0.00389227i	$0.998761\pi$
$480$		0			0
$481$	−23.6337	+	13.6450i	−1.07761	+	0.622156i
$482$	18.3757			0.836989
$483$		0			0
$484$	5.05836			0.229925
$485$	12.8530	−	7.42069i	0.583625	−	0.336956i
$486$		0			0
$487$	−21.0402	+	36.4426i	−0.953421	+	1.65137i	−0.215480	+	0.976508i	$0.569132\pi$
$487$	−21.0402	+	36.4426i	−0.953421	+	1.65137i	−0.737941	+	0.674866i	$0.764202\pi$
$488$	4.03443	+	6.98784i	0.182630	+	0.316325i
$489$		0			0
$490$	7.38891	+	3.78400i	0.333797	+	0.170944i
$491$			22.7557i			1.02695i	0.858105	+	0.513475i	$0.171642\pi$
$491$			22.7557i			1.02695i	−0.858105	+	0.513475i	$0.828358\pi$
$492$		0			0
$493$	−60.7409	−	35.0688i	−2.73563	−	1.57942i
$494$	20.0723	+	11.5887i	0.903094	+	0.521402i
$495$		0			0
$496$			6.79139i			0.304942i
$497$	−30.0364	+	0.755615i	−1.34732	+	0.0338940i
$498$		0			0
$499$	−1.15272	−	1.99658i	−0.0516030	−	0.0893791i	0.839070	−	0.544023i	$-0.183100\pi$
$499$	−1.15272	−	1.99658i	−0.0516030	−	0.0893791i	−0.890673	+	0.454644i	$0.849766\pi$
$500$	−0.296790	+	0.514055i	−0.0132728	+	0.0229892i
$501$		0			0
$502$	19.1775	−	11.0721i	0.855934	−	0.494174i
$503$	−19.5801			−0.873035			−0.436518	−	0.899696i	$-0.643788\pi$
$503$	−19.5801			−0.873035			−0.436518	+	0.899696i	$0.643788\pi$
$504$		0			0
$505$	−4.78074			−0.212740
$506$	4.71780	−	2.72382i	0.209732	−	0.121089i
$507$		0			0
$508$	2.20681	−	3.82231i	0.0979113	−	0.169587i
$509$	12.8904	+	22.3268i	0.571356	+	0.989617i	0.996427	+	0.0844571i	$0.0269156\pi$
$509$	12.8904	+	22.3268i	0.571356	+	0.989617i	−0.425072	+	0.905160i	$0.639751\pi$
$510$		0			0
$511$	−0.291534	+	0.535624i	−0.0128967	+	0.0236946i
$512$		−	23.0923i		−	1.02055i
$513$		0			0
$514$	−21.6052	−	12.4738i	−0.952966	−	0.550195i
$515$	11.6819	+	6.74455i	0.514766	+	0.297200i
$516$		0			0
$517$			6.21180i			0.273194i
$518$	16.1819	−	29.7304i	0.710992	−	1.30628i
$519$		0			0
$520$	3.89037	+	6.73832i	0.170604	+	0.295495i
$521$	16.3997	−	28.4051i	0.718484	−	1.24445i	−0.243116	−	0.969997i	$-0.578170\pi$
$521$	16.3997	−	28.4051i	0.718484	−	1.24445i	0.961600	−	0.274454i	$-0.0884970\pi$
$522$		0			0
$523$	1.79153	−	1.03434i	0.0783383	−	0.0452286i	−0.460319	−	0.887753i	$-0.652265\pi$
$523$	1.79153	−	1.03434i	0.0783383	−	0.0452286i	0.538657	+	0.842525i	$0.318932\pi$
$524$	−2.66672			−0.116496
$525$		0			0
$526$	−26.7732			−1.16736
$527$	16.9911	−	9.80984i	0.740146	−	0.427323i
$528$		0			0
$529$	−7.24271	+	12.5447i	−0.314900	+	0.545423i
$530$	0.149126	+	0.258294i	0.00647762	+	0.0112196i
$531$		0			0
$532$	12.1293	−	0.305132i	0.525871	−	0.0132292i
$533$			2.39285i			0.103646i
$534$		0			0
$535$	14.3456	+	8.28245i	0.620215	+	0.358081i
$536$	9.29552	+	5.36677i	0.401505	+	0.231809i
$537$		0			0
$538$		−	12.7852i		−	0.551207i
$539$	−9.80826	−	5.02300i	−0.422472	−	0.216356i
$540$		0			0
$541$	21.3997	+	37.0654i	0.920045	+	1.59356i	0.799342	+	0.600876i	$0.205182\pi$
$541$	21.3997	+	37.0654i	0.920045	+	1.59356i	0.120703	+	0.992689i	$0.461485\pi$
$542$	6.13667	−	10.6290i	0.263593	−	0.456556i
$543$		0			0
$544$	−19.9056	+	11.4925i	−0.853447	+	0.492738i
$545$	−1.91381			−0.0819787
$546$		0			0
$547$	17.4720			0.747048			0.373524	−	0.927621i	$-0.378149\pi$
$547$	17.4720			0.747048			0.373524	+	0.927621i	$0.378149\pi$
$548$	−3.28513	+	1.89667i	−0.140334	+	0.0810217i
$549$		0			0
$550$	−0.933463	+	1.61680i	−0.0398030	+	0.0689408i
$551$	−38.1160	−	66.0189i	−1.62380	−	2.81250i
$552$		0			0
$553$	29.0941	−	17.7877i	1.23721	−	0.756411i
$554$			13.9035i			0.590702i
$555$		0			0
$556$	−6.88598	−	3.97562i	−0.292031	−	0.168604i
$557$	27.3501	+	15.7906i	1.15886	+	0.669068i	0.951031	−	0.309097i	$-0.100027\pi$
$557$	27.3501	+	15.7906i	1.15886	+	0.669068i	0.207830	+	0.978165i	$0.433360\pi$
$558$		0			0
$559$		−	24.8970i		−	1.05303i
$560$	−5.71780	−	3.11213i	−0.241621	−	0.131512i
$561$		0			0
$562$	6.89543	+	11.9432i	0.290866	+	0.503795i
$563$	7.59931	−	13.1624i	0.320273	−	0.554729i	−0.660271	−	0.751027i	$-0.729559\pi$
$563$	7.59931	−	13.1624i	0.320273	−	0.554729i	0.980544	+	0.196298i	$0.0628921\pi$
$564$		0			0
$565$	4.63667	−	2.67698i	0.195066	−	0.112622i
$566$	−5.32743			−0.223929
$567$		0			0
$568$	34.9296			1.46561
$569$	−19.5256	+	11.2731i	−0.818555	+	0.472593i	−0.849918	−	0.526915i	$-0.823349\pi$
$569$	−19.5256	+	11.2731i	−0.818555	+	0.472593i	0.0313630	+	0.999508i	$0.490015\pi$
$570$		0			0
$571$	10.8707	−	18.8286i	0.454925	−	0.787954i	−0.543758	−	0.839242i	$-0.682999\pi$
$571$	10.8707	−	18.8286i	0.454925	−	0.787954i	0.998684	+	0.0512878i	$0.0163326\pi$
$572$	−1.18190	−	2.04712i	−0.0494178	−	0.0855942i
$573$		0			0
$574$	−1.54815	−	2.53220i	−0.0646187	−	0.105692i
$575$			2.91798i			0.121688i
$576$		0			0
$577$	−9.87957	−	5.70397i	−0.411292	−	0.237460i	0.280053	−	0.959985i	$-0.409648\pi$
$577$	−9.87957	−	5.70397i	−0.411292	−	0.237460i	−0.691345	+	0.722525i	$0.742981\pi$
$578$	−34.4327	−	19.8797i	−1.43221	−	0.826887i
$579$		0			0
$580$		−	5.85696i		−	0.243197i
$581$	−1.07179	−	42.6047i	−0.0444655	−	1.76754i
$582$		0			0
$583$	−0.197955	−	0.342867i	−0.00819844	−	0.0142001i
$584$	0.354473	−	0.613964i	0.0146682	−	0.0254060i
$585$		0			0
$586$	−6.44299	+	3.71986i	−0.266157	+	0.153666i
$587$	5.83775			0.240950			0.120475	−	0.992716i	$-0.461558\pi$
$587$	5.83775			0.240950			0.120475	+	0.992716i	$0.461558\pi$
$588$		0			0
$589$	21.3245			0.878661
$590$	2.67111	−	1.54216i	0.109968	−	0.0634899i
$591$		0			0
$592$	−13.2719	+	22.9876i	−0.545471	+	0.944784i
$593$	6.73452	+	11.6645i	0.276554	+	0.479005i	0.970526	−	0.240997i	$-0.0774743\pi$
$593$	6.73452	+	11.6645i	0.276554	+	0.479005i	−0.693972	+	0.720002i	$0.744141\pi$
$594$		0			0
$595$	0.472958	+	18.8005i	0.0193894	+	0.770745i
$596$		−	6.60403i		−	0.270512i
$597$		0			0
$598$	7.58113	+	4.37697i	0.310015	+	0.178987i
$599$	21.1175	+	12.1922i	0.862838	+	0.498160i	0.864962	−	0.501838i	$-0.167343\pi$
$599$	21.1175	+	12.1922i	0.862838	+	0.498160i	−0.00212381	+	0.999998i	$0.500676\pi$
$600$		0			0
$601$		−	26.8721i		−	1.09613i	−0.836434	−	0.548067i	$-0.815364\pi$
$601$		−	26.8721i		−	1.09613i	0.836434	−	0.548067i	$-0.184636\pi$
$602$	16.1082	+	26.3469i	0.656520	+	1.07382i
$603$		0			0
$604$	0.368388	+	0.638067i	0.0149895	+	0.0259626i
$605$	−4.26089	+	7.38008i	−0.173230	+	0.300043i
$606$		0			0
$607$	−21.4868	+	12.4054i	−0.872121	+	0.503519i	−0.868052	−	0.496473i	$-0.834628\pi$
$607$	−21.4868	+	12.4054i	−0.872121	+	0.503519i	−0.00406824	+	0.999992i	$0.501295\pi$
$608$	−24.9823			−1.01317
$609$		0			0
$610$	−3.11109			−0.125964
$611$	−8.64454	+	4.99093i	−0.349721	+	0.201911i
$612$		0			0
$613$	17.3171	−	29.9941i	0.699432	−	1.21145i	−0.269232	−	0.963075i	$-0.586770\pi$
$613$	17.3171	−	29.9941i	0.699432	−	1.21145i	0.968664	−	0.248376i	$-0.0798968\pi$
$614$	4.21926	+	7.30798i	0.170276	+	0.294926i
$615$		0			0
$616$	11.2520	+	6.12435i	0.453358	+	0.246757i
$617$			17.5595i			0.706920i	0.935450	+	0.353460i	$0.114995\pi$
$617$			17.5595i			0.706920i	−0.935450	+	0.353460i	$0.885005\pi$
$618$		0			0
$619$	−19.6249	−	11.3304i	−0.788791	−	0.455409i	0.0507457	−	0.998712i	$-0.483840\pi$
$619$	−19.6249	−	11.3304i	−0.788791	−	0.455409i	−0.839537	+	0.543303i	$0.817174\pi$
$620$	1.41887	+	0.819187i	0.0569833	+	0.0328993i
$621$		0			0
$622$		−	20.3566i		−	0.816227i
$623$	−24.6682	+	15.0818i	−0.988310	+	0.604240i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	6.85301	−	11.8698i	0.273901	−	0.474411i
$627$		0			0
$628$	−1.18190	+	0.682372i	−0.0471631	+	0.0272296i
$629$	76.6825			3.05753
$630$		0			0
$631$	4.76303			0.189613			0.0948066	−	0.995496i	$-0.469777\pi$
$631$	4.76303			0.189613			0.0948066	+	0.995496i	$0.469777\pi$
$632$	−34.3324	+	19.8218i	−1.36567	+	0.788469i
$633$		0			0
$634$	−19.6754	+	34.0788i	−0.781409	+	1.35344i
$635$	3.71780	+	6.43942i	0.147536	+	0.255540i
$636$		0			0
$637$	−0.890369	−	17.6853i	−0.0352777	−	0.700716i
$638$		−	18.4213i		−	0.729306i
$639$		0			0
$640$	3.39183	+	1.95827i	0.134074	+	0.0774076i
$641$	13.9686	+	8.06476i	0.551725	+	0.318539i	0.749818	−	0.661645i	$-0.230141\pi$
$641$	13.9686	+	8.06476i	0.551725	+	0.318539i	−0.198092	+	0.980183i	$0.563475\pi$
$642$		0			0
$643$		−	18.2243i		−	0.718695i	−0.933204	−	0.359347i	$-0.882999\pi$
$643$		−	18.2243i		−	0.718695i	0.933204	−	0.359347i	$-0.117001\pi$
$644$	4.58113	−	0.115246i	0.180522	−	0.00454132i
$645$		0			0
$646$	−32.5634	−	56.4015i	−1.28119	−	2.21909i
$647$	−17.1460	+	29.6978i	−0.674079	+	1.16754i	0.302658	+	0.953099i	$0.402126\pi$
$647$	−17.1460	+	29.6978i	−0.674079	+	1.16754i	−0.976737	+	0.214440i	$0.931207\pi$
$648$		0			0
$649$	−3.54571	+	2.04712i	−0.139181	+	0.0803563i
$650$	−3.00000			−0.117670
$651$		0			0
$652$	2.24417			0.0878884
$653$	39.1868	−	22.6245i	1.53350	−	0.885367i	0.534303	−	0.845293i	$-0.320574\pi$
$653$	39.1868	−	22.6245i	1.53350	−	0.885367i	0.999197	−	0.0400736i	$-0.0127593\pi$
$654$		0			0
$655$	2.24630	−	3.89071i	0.0877704	−	0.152023i
$656$	1.16372	+	2.01561i	0.0454354	+	0.0786965i
$657$		0			0
$658$	5.91887	−	10.8745i	0.230742	−	0.423933i
$659$		−	6.39061i		−	0.248943i	−0.992223	−	0.124471i	$-0.960276\pi$
$659$		−	6.39061i		−	0.248943i	0.992223	−	0.124471i	$-0.0397235\pi$
$660$		0			0
$661$	3.03736	+	1.75362i	0.118140	+	0.0682079i	0.557905	−	0.829905i	$-0.311605\pi$
$661$	3.03736	+	1.75362i	0.118140	+	0.0682079i	−0.439766	+	0.898112i	$0.644939\pi$
$662$	2.56440	+	1.48056i	0.0996683	+	0.0575435i
$663$		0			0
$664$			49.5454i			1.92273i
$665$	−9.77188	+	17.9535i	−0.378937	+	0.696207i
$666$		0			0
$667$	−14.3961	−	24.9348i	−0.557419	−	0.965479i
$668$	6.89037	−	11.9345i	0.266596	−	0.461758i
$669$		0			0
$670$	−3.58405	+	2.06925i	−0.138464	+	0.0799422i
$671$	4.12976			0.159428
$672$		0			0
$673$	48.1167			1.85476			0.927381	−	0.374117i	$-0.122054\pi$
$673$	48.1167			1.85476			0.927381	+	0.374117i	$0.122054\pi$
$674$	−12.2178	+	7.05395i	−0.470612	+	0.271708i
$675$		0			0
$676$	−1.95904	+	3.39316i	−0.0753478	+	0.130506i
$677$	12.5349	+	21.7111i	0.481756	+	0.834426i	0.999781	−	0.0209400i	$-0.00666588\pi$
$677$	12.5349	+	21.7111i	0.481756	+	0.834426i	−0.518025	+	0.855366i	$0.673333\pi$
$678$		0			0
$679$	39.2542	−	0.987504i	1.50644	−	0.0378969i
$680$		−	21.8633i		−	0.838418i
$681$		0			0
$682$	4.46264	+	2.57651i	0.170883	+	0.0986595i
$683$	−26.6298	−	15.3747i	−1.01896	−	0.588297i	−0.105157	−	0.994456i	$-0.533535\pi$
$683$	−26.6298	−	15.3747i	−1.01896	−	0.588297i	−0.913802	+	0.406159i	$0.866868\pi$
$684$		0			0
$685$		−	6.39061i		−	0.244173i
$686$	12.3844	+	18.1391i	0.472840	+	0.692555i
$687$		0			0
$688$	−12.1082	−	20.9720i	−0.461620	−	0.799549i
$689$	0.318097	−	0.550960i	0.0121185	−	0.0209899i
$690$		0			0
$691$	−38.9583	+	22.4926i	−1.48204	+	0.855657i	−0.999792	−	0.0203767i	$-0.993513\pi$
$691$	−38.9583	+	22.4926i	−1.48204	+	0.855657i	−0.482249	+	0.876034i	$0.660180\pi$
$692$	−9.16225			−0.348297
$693$		0			0
$694$	−0.799794			−0.0303598
$695$	11.6008	−	6.69771i	0.440043	−	0.254059i
$696$		0			0
$697$	3.36186	−	5.82292i	0.127340	−	0.220559i
$698$	4.71780	+	8.17147i	0.178571	+	0.309295i
$699$		0			0
$700$	−1.33988	+	0.819187i	−0.0506428	+	0.0309624i
$701$			7.08602i			0.267635i	0.991006	+	0.133818i	$0.0427236\pi$
$701$			7.08602i			0.267635i	−0.991006	+	0.133818i	$0.957276\pi$
$702$		0			0
$703$	72.1795	+	41.6728i	2.72230	+	1.57172i
$704$	−11.9371	−	6.89187i	−0.449895	−	0.259747i
$705$		0			0
$706$		−	6.16866i		−	0.232160i
$707$	−11.1096	−	6.04684i	−0.417821	−	0.227415i
$708$		0			0
$709$	11.7003	+	20.2655i	0.439413	+	0.761086i	0.997644	−	0.0685993i	$-0.0218530\pi$
$709$	11.7003	+	20.2655i	0.439413	+	0.761086i	−0.558231	+	0.829686i	$0.688520\pi$
$710$	−6.73385	+	11.6634i	−0.252717	+	0.437719i
$711$		0			0
$712$	29.1096	−	16.8065i	1.09093	−	0.629848i
$713$	8.05408			0.301628
$714$		0			0
$715$	3.98229			0.148929
$716$	9.72812	−	5.61653i	0.363557	−	0.209900i
$717$		0			0
$718$	−0.877916	+	1.52060i	−0.0327635	+	0.0567481i
$719$	−9.16964	−	15.8823i	−0.341970	−	0.592309i	0.642828	−	0.766010i	$-0.277761\pi$
$719$	−9.16964	−	15.8823i	−0.341970	−	0.592309i	−0.984798	+	0.173701i	$0.944427\pi$
$720$		0			0
$721$	18.6160	+	30.4489i	0.693298	+	1.13398i
$722$		−	48.2533i		−	1.79580i
$723$		0			0
$724$	−4.42326	−	2.55377i	−0.164389	−	0.0949102i
$725$	8.54523	+	4.93359i	0.317362	+	0.183229i
$726$		0			0
$727$			10.6353i			0.394440i	0.980359	+	0.197220i	$0.0631913\pi$
$727$			10.6353i			0.394440i	−0.980359	+	0.197220i	$0.936809\pi$
$728$	0.517709	+	20.5794i	0.0191876	+	0.762723i
$729$		0			0
$730$	0.136673	+	0.236725i	0.00505850	+	0.00876158i
$731$	−34.9794	+	60.5860i	−1.29376	+	2.24086i
$732$		0			0
$733$	−27.4538	+	15.8505i	−1.01403	+	0.585450i	−0.912369	−	0.409369i	$-0.865749\pi$
$733$	−27.4538	+	15.8505i	−1.01403	+	0.585450i	−0.101660	+	0.994819i	$0.532415\pi$
$734$	−36.3097			−1.34022
$735$		0			0
$736$	−9.43560			−0.347801
$737$	4.75758	−	2.74679i	0.175248	−	0.101179i
$738$		0			0
$739$	2.14406	−	3.71363i	0.0788707	−	0.136608i	−0.823892	−	0.566746i	$-0.808202\pi$
$739$	2.14406	−	3.71363i	0.0788707	−	0.136608i	0.902763	+	0.430138i	$0.141535\pi$
$740$	3.20175	+	5.54559i	0.117699	+	0.203860i
$741$		0			0
$742$	0.0198449	+	0.788852i	0.000728528	+	0.0289597i
$743$			43.7401i			1.60467i	0.596874	+	0.802335i	$0.296409\pi$
$743$			43.7401i			1.60467i	−0.596874	+	0.802335i	$0.703591\pi$
$744$		0			0
$745$	9.63521	+	5.56289i	0.353007	+	0.203809i
$746$	−9.65039	−	5.57166i	−0.353326	−	0.203993i
$747$		0			0
$748$			6.64211i			0.242859i
$749$	22.8609	+	37.3918i	0.835318	+	1.36627i
$750$		0			0
$751$	−12.6946	−	21.9876i	−0.463231	−	0.802339i	0.535889	−	0.844288i	$-0.319977\pi$
$751$	−12.6946	−	21.9876i	−0.463231	−	0.802339i	−0.999120	+	0.0419493i	$0.986643\pi$
$752$	−4.85447	+	8.40819i	−0.177024	+	0.306615i
$753$		0			0
$754$	25.6357	−	14.8008i	0.933597	−	0.539012i
$755$	−1.24124			−0.0451735
$756$		0			0
$757$	14.7047			0.534450			0.267225	−	0.963634i	$-0.413893\pi$
$757$	14.7047			0.534450			0.267225	+	0.963634i	$0.413893\pi$
$758$	−13.5226	+	7.80726i	−0.491162	+	0.283573i
$759$		0			0
$760$	11.8815	−	20.5794i	0.430988	−	0.746493i
$761$	8.19076	+	14.1868i	0.296915	+	0.514271i	0.975428	−	0.220316i	$-0.0707090\pi$
$761$	8.19076	+	14.1868i	0.296915	+	0.514271i	−0.678514	+	0.734588i	$0.737376\pi$
$762$		0			0
$763$	−4.44738	−	2.42066i	−0.161006	−	0.0876336i
$764$		−	3.51231i		−	0.127071i
$765$		0			0
$766$	30.7497	+	17.7534i	1.11103	+	0.641455i
$767$	−5.69767	−	3.28955i	−0.205731	−	0.118779i
$768$		0			0
$769$		−	16.1937i		−	0.583958i	−0.956425	−	0.291979i	$-0.905686\pi$
$769$		−	16.1937i		−	0.583958i	0.956425	−	0.291979i	$-0.0943138\pi$
$770$	−4.21420	+	2.57651i	−0.151869	+	0.0928509i
$771$		0			0
$772$	1.09650	+	1.89920i	0.0394641	+	0.0683538i
$773$	6.21041	−	10.7567i	0.223373	−	0.386893i	−0.732457	−	0.680813i	$-0.761627\pi$
$773$	6.21041	−	10.7567i	0.223373	−	0.386893i	0.955830	+	0.293920i	$0.0949599\pi$
$774$		0			0
$775$	−2.39037	+	1.38008i	−0.0858646	+	0.0495739i
$776$	−45.6490			−1.63870
$777$		0			0
$778$	16.6447			0.596743
$779$	6.32889	−	3.65399i	0.226756	−	0.130918i
$780$		0			0
$781$	8.93872	−	15.4823i	0.319852	−	0.554001i
$782$	−12.2989	−	21.3024i	−0.439809	−	0.761771i
$783$		0			0
$784$	−9.35087	−	14.4641i	−0.333960	−	0.516576i
$785$		−	2.29918i		−	0.0820611i
$786$		0			0
$787$	−23.2941	−	13.4488i	−0.830344	−	0.479399i	0.0236267	−	0.999721i	$-0.492479\pi$
$787$	−23.2941	−	13.4488i	−0.830344	−	0.479399i	−0.853970	+	0.520322i	$0.825812\pi$
$788$	−6.60524	−	3.81354i	−0.235302	−	0.135852i
$789$		0			0
$790$		−	15.2853i		−	0.543826i
$791$	14.1608	−	0.356238i	0.503500	−	0.0126664i
$792$		0			0
$793$	3.31810	+	5.74711i	0.117829	+	0.204086i
$794$	7.86186	−	13.6171i	0.279007	−	0.483255i
$795$		0			0
$796$	7.69961	−	4.44537i	0.272906	−	0.157562i
$797$	−29.1052			−1.03096			−0.515480	−	0.856901i	$-0.672386\pi$
$797$	−29.1052			−1.03096			−0.515480	+	0.856901i	$0.672386\pi$
$798$		0			0
$799$	28.0482			0.992275
$800$	2.80039	−	1.61680i	0.0990087	−	0.0571627i
$801$		0			0
$802$	−3.71566	+	6.43572i	−0.131205	+	0.227253i
$803$	−0.181424	−	0.314236i	−0.00640231	−	0.0110891i
$804$		0			0
$805$	−3.69076	+	6.78089i	−0.130082	+	0.238995i
$806$			8.28048i			0.291668i
$807$		0			0
$808$	12.7345	+	7.35228i	0.447999	+	0.258652i
$809$	−36.8820	−	21.2938i	−1.29670	−	0.748651i	−0.316869	−	0.948469i	$-0.602632\pi$
$809$	−36.8820	−	21.2938i	−1.29670	−	0.748651i	−0.979833	+	0.199818i	$0.935965\pi$
$810$		0			0
$811$		−	26.4491i		−	0.928755i	−0.885637	−	0.464378i	$-0.846278\pi$
$811$		−	26.4491i		−	0.928755i	0.885637	−	0.464378i	$-0.153722\pi$
$812$	7.40808	−	13.6106i	0.259973	−	0.477638i
$813$		0			0
$814$	10.0701	+	17.4420i	0.352958	+	0.611341i
$815$	−1.89037	+	3.27422i	−0.0662167	+	0.114691i
$816$		0			0
$817$	−65.8506	+	38.0188i	−2.30382	+	1.33011i
$818$	18.8053			0.657510
$819$		0			0
$820$	0.561476			0.0196076
$821$	−19.9312	+	11.5073i	−0.695604	+	0.401607i	−0.805708	−	0.592313i	$-0.798215\pi$
$821$	−19.9312	+	11.5073i	−0.695604	+	0.401607i	0.110104	+	0.993920i	$0.464882\pi$
$822$		0			0
$823$	−5.20847	+	9.02133i	−0.181556	+	0.314464i	−0.942410	−	0.334458i	$-0.891447\pi$
$823$	−5.20847	+	9.02133i	−0.181556	+	0.314464i	0.760855	+	0.648922i	$0.224780\pi$
$824$	−20.7448	−	35.9311i	−0.722681	−	1.25172i
$825$		0			0
$826$	8.15779	−	0.205223i	0.283846	−	0.00714061i
$827$		−	13.6049i		−	0.473089i	−0.971621	−	0.236545i	$-0.923985\pi$
$827$		−	13.6049i		−	0.473089i	0.971621	−	0.236545i	$-0.0760149\pi$
$828$		0			0
$829$	−40.7124	−	23.5053i	−1.41400	−	0.816374i	−0.418239	−	0.908337i	$-0.637352\pi$
$829$	−40.7124	−	23.5053i	−1.41400	−	0.816374i	−0.995762	+	0.0919633i	$0.970686\pi$
$830$	−16.5438	−	9.55155i	−0.574243	−	0.331539i
$831$		0			0
$832$		−	22.1494i		−	0.767891i
$833$	−22.6804	+	44.2874i	−0.785831	+	1.53447i
$834$		0			0
$835$	11.6082	+	20.1059i	0.401717	+	0.695795i
$836$	−3.60963	+	6.25206i	−0.124842	+	0.216232i
$837$		0			0
$838$	6.57227	−	3.79450i	0.227035	−	0.131079i
$839$	−31.8683			−1.10021			−0.550107	−	0.835094i	$-0.685413\pi$
$839$	−31.8683			−1.10021			−0.550107	+	0.835094i	$0.685413\pi$
$840$		0			0
$841$	−68.3613			−2.35729
$842$	14.0211	−	8.09509i	0.483199	−	0.278975i
$843$		0			0
$844$	−0.440855	+	0.763583i	−0.0151748	+	0.0262836i
$845$	−3.30039	−	5.71644i	−0.113537	−	0.196652i
$846$		0			0
$847$	−19.2362	+	11.7607i	−0.660963	+	0.404104i
$848$		−	0.618800i		−	0.0212497i
$849$		0			0
$850$	7.30039	+	4.21488i	0.250401	+	0.144569i
$851$	27.2616	+	15.7395i	0.934514	+	0.539542i
$852$		0			0
$853$		−	22.1874i		−	0.759683i	−0.925052	−	0.379841i	$-0.875979\pi$
$853$		−	22.1874i		−	0.759683i	0.925052	−	0.379841i	$-0.124021\pi$
$854$	−7.22966	−	3.93502i	−0.247394	−	0.134654i
$855$		0			0
$856$	−25.4751	−	44.1242i	−0.870721	−	1.50813i
$857$	−16.5811	+	28.7194i	−0.566400	+	0.981034i	0.430517	+	0.902582i	$0.358331\pi$
$857$	−16.5811	+	28.7194i	−0.566400	+	0.981034i	−0.996918	+	0.0784521i	$0.975002\pi$
$858$		0			0
$859$	10.8511	−	6.26487i	0.370234	−	0.213755i	−0.303327	−	0.952887i	$-0.598097\pi$
$859$	10.8511	−	6.26487i	0.370234	−	0.213755i	0.673561	+	0.739132i	$0.264764\pi$
$860$	−5.84202			−0.199211
$861$		0			0
$862$	−11.4998			−0.391685
$863$	−27.8412	+	16.0741i	−0.947727	+	0.547170i	−0.892374	−	0.451297i	$-0.850962\pi$
$863$	−27.8412	+	16.0741i	−0.947727	+	0.547170i	−0.0553526	+	0.998467i	$0.517628\pi$
$864$		0			0
$865$	7.71780	−	13.3676i	0.262413	−	0.454513i
$866$	11.2645	+	19.5107i	0.382783	+	0.663000i
$867$		0			0
$868$	2.26109	+	3.69829i	0.0767463	+	0.125528i
$869$			20.2902i			0.688296i
$870$		0			0
$871$	7.64505	+	4.41387i	0.259043	+	0.149558i
$872$	5.09785	+	2.94325i	0.172635	+	0.0996709i
$873$		0			0
$874$		−	26.7352i		−	0.904333i
$875$	−0.0665372	−	2.64491i	−0.00224937	−	0.0894144i
$876$		0			0
$877$	−3.23891	−	5.60996i	−0.109370	−	0.189435i	0.806145	−	0.591718i	$-0.201550\pi$
$877$	−3.23891	−	5.60996i	−0.109370	−	0.189435i	−0.915515	+	0.402283i	$0.868217\pi$
$878$	6.77928	−	11.7420i	0.228789	−	0.396275i
$879$		0			0
$880$	3.35447	−	1.93671i	0.113079	−	0.0652863i
$881$	29.3638			0.989292			0.494646	−	0.869095i	$-0.335298\pi$
$881$	29.3638			0.989292			0.494646	+	0.869095i	$0.335298\pi$
$882$		0			0
$883$	22.2996			0.750441			0.375221	−	0.926936i	$-0.377567\pi$
$883$	22.2996			0.750441			0.375221	+	0.926936i	$0.377567\pi$
$884$	−9.24338	+	5.33667i	−0.310888	+	0.179492i
$885$		0			0
$886$	−1.96050	+	3.39569i	−0.0658644	+	0.114081i
$887$	5.34562	+	9.25888i	0.179488	+	0.310883i	0.941705	−	0.336439i	$-0.109222\pi$
$887$	5.34562	+	9.25888i	0.179488	+	0.310883i	−0.762217	+	0.647321i	$0.775889\pi$
$888$		0			0
$889$	0.494744	+	19.6665i	0.0165932	+	0.659594i
$890$			12.9600i			0.434422i
$891$		0			0
$892$	1.80291	+	1.04091i	0.0603660	+	0.0348523i
$893$	26.4012	+	15.2427i	0.883481	+	0.510078i
$894$		0			0
$895$			18.9243i			0.632569i
$896$	5.40515	+	8.84081i	0.180573	+	0.295351i
$897$		0			0
$898$	3.78434	+	6.55466i	0.126285	+	0.218732i
$899$	13.6175	−	23.5862i	0.454169	−	0.786644i
$900$		0			0
$901$	−1.54815	+	0.893828i	−0.0515765	+	0.0297777i
$902$	1.76595			0.0587998
$903$		0			0
$904$	−16.4677			−0.547708
$905$	7.45185	−	4.30232i	0.247708	−	0.143014i
$906$		0			0
$907$	−19.3150	+	33.4545i	−0.641343	+	1.11084i	0.343790	+	0.939047i	$0.388289\pi$
$907$	−19.3150	+	33.4545i	−0.641343	+	1.11084i	−0.985133	+	0.171793i	$0.945044\pi$
$908$	5.47150	+	9.47691i	0.181578	+	0.314502i
$909$		0			0
$910$	−6.97150	−	3.79450i	−0.231103	−	0.125787i
$911$			33.5476i			1.11148i	0.831355	+	0.555741i	$0.187565\pi$
$911$			33.5476i			1.11148i	−0.831355	+	0.555741i	$0.812435\pi$
$912$		0			0
$913$	21.9607	+	12.6790i	0.726793	+	0.419614i
$914$	12.7793	+	7.37812i	0.422701	+	0.244046i
$915$		0			0
$916$			8.19927i			0.270912i
$917$	10.1411	−	6.20016i	0.334890	−	0.204747i
$918$		0			0
$919$	1.83249	+	3.17397i	0.0604483	+	0.104700i	0.894666	−	0.446736i	$-0.147414\pi$
$919$	1.83249	+	3.17397i	0.0604483	+	0.104700i	−0.834218	+	0.551435i	$0.814080\pi$
$920$	4.48755	−	7.77266i	0.147950	−	0.256257i
$921$		0			0
$922$	18.1293	−	10.4669i	0.597056	−	0.344710i
$923$	28.7276			0.945581
$924$		0			0
$925$	−10.7879			−0.354705
$926$	−15.2026	+	8.77723i	−0.499589	+	0.288438i
$927$		0			0
$928$	−15.9533	+	27.6319i	−0.523693	+	0.907063i
$929$	6.12489	+	10.6086i	0.200951	+	0.348058i	0.948835	−	0.315772i	$-0.102263\pi$
$929$	6.12489	+	10.6086i	0.200951	+	0.348058i	−0.747884	+	0.663830i	$0.768930\pi$
$930$		0			0
$931$	−45.4164	+	29.3611i	−1.48846	+	0.962272i
$932$			2.79016i			0.0913947i
$933$		0			0
$934$	−27.6908	−	15.9873i	−0.906069	−	0.523119i
$935$	−9.69076	−	5.59496i	−0.316922	−	0.182975i
$936$		0			0
$937$			26.0006i			0.849403i	0.905333	+	0.424702i	$0.139621\pi$
$937$			26.0006i			0.849403i	−0.905333	+	0.424702i	$0.860379\pi$
$938$	−10.9460	+	0.275365i	−0.357399	+	0.00899098i
$939$		0			0
$940$	1.17111	+	2.02842i	0.0381973	+	0.0661597i
$941$	0.0373591	−	0.0647078i	0.00121787	−	0.00210941i	−0.865416	−	0.501054i	$-0.832946\pi$
$941$	0.0373591	−	0.0647078i	0.00121787	−	0.00210941i	0.866634	+	0.498945i	$0.166279\pi$
$942$		0			0
$943$	2.39037	−	1.38008i	0.0778411	−	0.0449416i
$944$	−6.39922			−0.208277
$945$		0			0
$946$	−18.3743			−0.597401
$947$	−2.02111	+	1.16689i	−0.0656773	+	0.0379188i	−0.532479	−	0.846443i	$-0.678739\pi$
$947$	−2.02111	+	1.16689i	−0.0656773	+	0.0379188i	0.466802	+	0.884362i	$0.345406\pi$
$948$		0			0
$949$	0.291534	−	0.504951i	0.00946359	−	0.0163914i
$950$	4.58113	+	7.93474i	0.148631	+	0.257437i
$951$		0			0
$952$	27.6534	−	50.8065i	0.896252	−	1.64665i
$953$			18.9169i			0.612778i	0.951906	+	0.306389i	$0.0991208\pi$
$953$			18.9169i			0.612778i	−0.951906	+	0.306389i	$0.900879\pi$
$954$		0			0
$955$	5.12441	+	2.95858i	0.165822	+	0.0957375i
$956$	−10.8137	−	6.24330i	−0.349740	−	0.201923i
$957$		0			0
$958$			26.1300i			0.844223i
$959$	8.08307	−	14.8507i	0.261016	−	0.479554i
$960$		0			0
$961$	−11.6908	−	20.2490i	−0.377121	−	0.653193i
$962$	−16.1819	+	28.0279i	−0.521725	+	0.903655i
$963$		0			0
$964$	−7.96517	+	4.59869i	−0.256541	+	0.148114i
$965$	−3.69455			−0.118932
$966$		0			0
$967$	57.3068			1.84286			0.921431	−	0.388542i	$-0.127021\pi$
$967$	57.3068			1.84286			0.921431	+	0.388542i	$0.127021\pi$
$968$	22.6996	−	13.1056i	0.729593	−	0.421231i
$969$		0			0
$970$	8.80039	−	15.2427i	0.282563	−	0.489414i
$971$	−7.92480	−	13.7262i	−0.254319	−	0.440493i	0.710391	−	0.703807i	$-0.248518\pi$
$971$	−7.92480	−	13.7262i	−0.254319	−	0.440493i	−0.964710	+	0.263313i	$0.915185\pi$
$972$		0			0
$973$	35.4297	−	0.891294i	1.13583	−	0.0285736i
$974$			49.9042i			1.59903i
$975$		0			0
$976$	5.58998	+	3.22738i	0.178931	+	0.103306i
$977$	35.3083	+	20.3852i	1.12961	+	0.652181i	0.943837	−	0.330411i	$-0.107187\pi$
$977$	35.3083	+	20.3852i	1.12961	+	0.652181i	0.185774	+	0.982592i	$0.440521\pi$
$978$		0			0
$979$		−	17.2036i		−	0.549828i
$980$	−4.14980	+	0.208922i	−0.132560	+	0.00667378i
$981$		0			0
$982$	13.4933	+	23.3710i	0.430588	+	0.745800i
$983$	−15.5467	+	26.9277i	−0.495862	+	0.858859i	−0.999989	−	0.00477103i	$-0.998481\pi$
$983$	−15.5467	+	26.9277i	−0.495862	+	0.858859i	0.504126	+	0.863630i	$0.331815\pi$
$984$		0			0
$985$	11.1278	−	6.42465i	0.354562	−	0.204706i
$986$	−83.1780			−2.64893
$987$		0			0
$988$	−11.6008			−0.369070
$989$	−24.8712	+	14.3594i	−0.790858	+	0.456602i
$990$		0			0
$991$	−13.2702	+	22.9847i	−0.421543	+	0.730133i	−0.996091	−	0.0883377i	$-0.971845\pi$
$991$	−13.2702	+	22.9847i	−0.421543	+	0.730133i	0.574548	+	0.818471i	$0.305178\pi$
$992$	−4.46264	−	7.72952i	−0.141689	−	0.245413i
$993$		0			0
$994$	−30.4006	+	18.5865i	−0.964248	+	0.589528i
$995$			14.9782i			0.474841i
$996$		0			0
$997$	−19.5811	−	11.3052i	−0.620140	−	0.358038i	0.156783	−	0.987633i	$-0.449888\pi$
$997$	−19.5811	−	11.3052i	−0.620140	−	0.358038i	−0.776924	+	0.629595i	$0.783221\pi$
$998$	−2.36779	−	1.36705i	−0.0749512	−	0.0432731i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.bj.g.836.3	yes	6
3.2	odd	2		945.2.bj.h.836.1	yes	6
7.5	odd	6		945.2.bj.h.26.1	yes	6
21.5	even	6	inner	945.2.bj.g.26.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.bj.g.26.3	✓	6	21.5	even	6	inner
945.2.bj.g.836.3	yes	6	1.1	even	1	trivial
945.2.bj.h.26.1	yes	6	7.5	odd	6
945.2.bj.h.836.1	yes	6	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.02704 - 0.592963i) q^{2} +(-0.296790 + 0.514055i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0665372 - 2.64491i) q^{7} +3.07579i q^{8} +O(q^{10})\)	\(q+(1.02704 - 0.592963i) q^{2} +(-0.296790 + 0.514055i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0665372 - 2.64491i) q^{7} +3.07579i q^{8} +(-1.02704 - 0.592963i) q^{10} +(1.36333 + 0.787117i) q^{11} +2.52967i q^{13} +(-1.63667 - 2.67698i) q^{14} +(1.23025 + 2.13086i) q^{16} +(3.55408 - 6.15585i) q^{17} +(6.69076 - 3.86291i) q^{19} +0.593579 q^{20} +1.86693 q^{22} +(2.52704 - 1.45899i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(1.50000 + 2.59808i) q^{26} +(1.37938 + 0.750780i) q^{28} -9.86718i q^{29} +(2.39037 + 1.38008i) q^{31} +(-2.80039 - 1.61680i) q^{32} -8.42976i q^{34} +(-2.25729 + 1.38008i) q^{35} +(5.39397 + 9.34263i) q^{37} +(4.58113 - 7.93474i) q^{38} +(2.66372 - 1.53790i) q^{40} +0.945916 q^{41} -9.84202 q^{43} +(-0.809243 + 0.467216i) q^{44} +(1.73025 - 2.99689i) q^{46} +(1.97296 + 3.41726i) q^{47} +(-6.99115 + 0.351971i) q^{49} +1.18593i q^{50} +(-1.30039 - 0.750780i) q^{52} +(-0.217799 - 0.125747i) q^{53} -1.57423i q^{55} +(8.13521 - 0.204655i) q^{56} +(-5.85087 - 10.1340i) q^{58} +(-1.30039 + 2.25234i) q^{59} +(2.27188 - 1.31167i) q^{61} +3.27335 q^{62} -8.75583 q^{64} +(2.19076 - 1.26483i) q^{65} +(1.74484 - 3.02215i) q^{67} +(2.10963 + 3.65399i) q^{68} +(-1.50000 + 2.75589i) q^{70} -11.3563i q^{71} +(-0.199612 - 0.115246i) q^{73} +(11.0797 + 6.39685i) q^{74} +4.58589i q^{76} +(1.99115 - 3.65826i) q^{77} +(6.44445 + 11.1621i) q^{79} +(1.23025 - 2.13086i) q^{80} +(0.971495 - 0.560893i) q^{82} +16.1082 q^{83} -7.10817 q^{85} +(-10.1082 + 5.83595i) q^{86} +(-2.42101 + 4.19331i) q^{88} +(-5.46410 - 9.46410i) q^{89} +(6.69076 - 0.168317i) q^{91} +1.73205i q^{92} +(4.05262 + 2.33978i) q^{94} +(-6.69076 - 3.86291i) q^{95} +14.8414i q^{97} +(-6.97150 + 4.50698i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + q^{4} - 3 q^{5} - 4 q^{7}+O(q^{10}) \) 6 * q - 3 * q^2 + q^4 - 3 * q^5 - 4 * q^7	\( 6 q - 3 q^{2} + q^{4} - 3 q^{5} - 4 q^{7} + 3 q^{10} + 9 q^{11} - 9 q^{14} + q^{16} + 3 q^{17} + 21 q^{19} - 2 q^{20} + 4 q^{22} + 6 q^{23} - 3 q^{25} + 9 q^{26} + 23 q^{28} + 6 q^{31} - 6 q^{32} + 2 q^{35} + 16 q^{37} + 6 q^{40} + 24 q^{41} - 8 q^{43} - 24 q^{44} + 4 q^{46} + 21 q^{47} - 12 q^{49} + 3 q^{52} + 27 q^{53} + 3 q^{56} - 14 q^{58} + 3 q^{59} - 33 q^{61} + 18 q^{62} + 8 q^{64} - 6 q^{65} - 27 q^{67} + 21 q^{68} - 9 q^{70} - 12 q^{73} - 6 q^{74} - 18 q^{77} + 12 q^{79} + q^{80} - 30 q^{82} + 60 q^{83} - 6 q^{85} - 24 q^{86} + 11 q^{88} - 12 q^{89} + 21 q^{91} - 39 q^{94} - 21 q^{95} - 6 q^{98}+O(q^{100}) \) 6 * q - 3 * q^2 + q^4 - 3 * q^5 - 4 * q^7 + 3 * q^10 + 9 * q^11 - 9 * q^14 + q^16 + 3 * q^17 + 21 * q^19 - 2 * q^20 + 4 * q^22 + 6 * q^23 - 3 * q^25 + 9 * q^26 + 23 * q^28 + 6 * q^31 - 6 * q^32 + 2 * q^35 + 16 * q^37 + 6 * q^40 + 24 * q^41 - 8 * q^43 - 24 * q^44 + 4 * q^46 + 21 * q^47 - 12 * q^49 + 3 * q^52 + 27 * q^53 + 3 * q^56 - 14 * q^58 + 3 * q^59 - 33 * q^61 + 18 * q^62 + 8 * q^64 - 6 * q^65 - 27 * q^67 + 21 * q^68 - 9 * q^70 - 12 * q^73 - 6 * q^74 - 18 * q^77 + 12 * q^79 + q^80 - 30 * q^82 + 60 * q^83 - 6 * q^85 - 24 * q^86 + 11 * q^88 - 12 * q^89 + 21 * q^91 - 39 * q^94 - 21 * q^95 - 6 * q^98

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