LMFDB - Embedded newform 945.2.bj.h.26.1

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			26.1
Root			$0.500000 - 2.05195i$ of defining polynomial
Character	$\chi$	$=$	945.26
Dual form			945.2.bj.h.836.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02704 - 0.592963i) q^{2} +(-0.296790 - 0.514055i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.0665372 + 2.64491i) q^{7} +3.07579i q^{8} +O(q^{10})$	\(q+(-1.02704 - 0.592963i) q^{2} +(-0.296790 - 0.514055i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.0665372 + 2.64491i) q^{7} +3.07579i q^{8} +(-1.02704 + 0.592963i) q^{10} +(-1.36333 + 0.787117i) q^{11} -2.52967i q^{13} +(1.63667 - 2.67698i) q^{14} +(1.23025 - 2.13086i) q^{16} +(-3.55408 - 6.15585i) q^{17} +(6.69076 + 3.86291i) q^{19} -0.593579 q^{20} +1.86693 q^{22} +(-2.52704 - 1.45899i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-1.50000 + 2.59808i) q^{26} +(1.37938 - 0.750780i) q^{28} -9.86718i q^{29} +(2.39037 - 1.38008i) q^{31} +(2.80039 - 1.61680i) q^{32} +8.42976i q^{34} +(2.25729 + 1.38008i) q^{35} +(5.39397 - 9.34263i) q^{37} +(-4.58113 - 7.93474i) q^{38} +(2.66372 + 1.53790i) q^{40} -0.945916 q^{41} -9.84202 q^{43} +(0.809243 + 0.467216i) q^{44} +(1.73025 + 2.99689i) q^{46} +(-1.97296 + 3.41726i) q^{47} +(-6.99115 - 0.351971i) q^{49} +1.18593i q^{50} +(-1.30039 + 0.750780i) q^{52} +(0.217799 - 0.125747i) q^{53} +1.57423i q^{55} +(-8.13521 - 0.204655i) q^{56} +(-5.85087 + 10.1340i) q^{58} +(1.30039 + 2.25234i) q^{59} +(2.27188 + 1.31167i) q^{61} -3.27335 q^{62} -8.75583 q^{64} +(-2.19076 - 1.26483i) q^{65} +(1.74484 + 3.02215i) q^{67} +(-2.10963 + 3.65399i) q^{68} +(-1.50000 - 2.75589i) q^{70} -11.3563i q^{71} +(-0.199612 + 0.115246i) q^{73} +(-11.0797 + 6.39685i) q^{74} -4.58589i q^{76} +(-1.99115 - 3.65826i) q^{77} +(6.44445 - 11.1621i) q^{79} +(-1.23025 - 2.13086i) q^{80} +(0.971495 + 0.560893i) q^{82} -16.1082 q^{83} -7.10817 q^{85} +(10.1082 + 5.83595i) q^{86} +(-2.42101 - 4.19331i) q^{88} +(5.46410 - 9.46410i) q^{89} +(6.69076 + 0.168317i) q^{91} +1.73205i q^{92} +(4.05262 - 2.33978i) q^{94} +(6.69076 - 3.86291i) q^{95} -14.8414i q^{97} +(6.97150 + 4.50698i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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	$-0.471054\pi$
$2$	−1.02704	−	0.592963i	−0.726228	−	0.419288i	−0.817041	+	0.576580i	$0.804387\pi$
$3$		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	$-0.742937\pi$
$11$	−1.36333	+	0.787117i	−0.411059	+	0.237325i	0.280186	+	0.959946i	$0.409604\pi$
$12$		0			0
$13$		−	2.52967i		−	0.701604i	−0.936450	−	0.350802i	$-0.885909\pi$
$13$		−	2.52967i		−	0.701604i	0.936450	−	0.350802i	$-0.114091\pi$
$14$	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	−0.870003	−	0.493046i	$-0.835883\pi$
$17$	−3.55408	−	6.15585i	−0.861992	−	1.49301i	0.00801115	−	0.999968i	$-0.497450\pi$
$18$		0			0
$19$	6.69076	+	3.86291i	1.53496	+	0.886212i	0.999122	+	0.0418948i	$0.0133394\pi$
$19$	6.69076	+	3.86291i	1.53496	+	0.886212i	0.535843	+	0.844318i	$0.319994\pi$
$20$	−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	$-0.431729\pi$
$23$	−2.52704	−	1.45899i	−0.526925	−	0.304220i	−0.739763	+	0.672867i	$0.765063\pi$
$24$		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	−0.269735	−	0.962935i	$-0.586936\pi$
$31$	2.39037	−	1.38008i	0.429323	−	0.247870i	0.699058	+	0.715065i	$0.253603\pi$
$32$	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	0.0430830	−	0.999071i	$-0.486282\pi$
$37$	5.39397	−	9.34263i	0.886763	−	1.53592i	0.843680	−	0.536847i	$-0.180385\pi$
$38$	−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	$-0.523533\pi$
$41$	−0.945916			−0.147727			−0.0738636	+	0.997268i	$0.523533\pi$
$42$		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	$-0.926252\pi$
$47$	−1.97296	+	3.41726i	−0.287785	+	0.498459i	0.685495	+	0.728077i	$0.259586\pi$
$48$		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	$-0.661168\pi$
$53$	0.217799	−	0.125747i	0.0299171	−	0.0172726i	0.514884	+	0.857260i	$0.327835\pi$
$54$		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	$-0.112517\pi$
$59$	1.30039	+	2.25234i	0.169296	+	0.293230i	−0.768876	+	0.639397i	$0.779184\pi$
$60$		0			0
$61$	2.27188	+	1.31167i	0.290885	+	0.167942i	0.638341	−	0.769754i	$-0.279621\pi$
$61$	2.27188	+	1.31167i	0.290885	+	0.167942i	−0.347456	+	0.937696i	$0.612954\pi$
$62$	−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	0.952704	−	0.303901i	$-0.0982890\pi$
$67$	1.74484	+	3.02215i	0.213166	+	0.369215i	−0.739537	+	0.673115i	$0.764956\pi$
$68$	−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	−0.511636	−	0.859202i	$-0.670960\pi$
$73$	−0.199612	+	0.115246i	−0.0233628	+	0.0134885i	0.488273	+	0.872691i	$0.337627\pi$
$74$	−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	−0.233893	−	0.972262i	$-0.575146\pi$
$79$	6.44445	−	11.1621i	0.725058	−	1.25584i	0.958950	−	0.283574i	$-0.0915202\pi$
$80$	−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	$-0.845194\pi$
$83$	−16.1082			−1.76810			−0.884051	+	0.467391i	$0.845194\pi$
$84$		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	−0.416378	−	0.909191i	$-0.636701\pi$
$89$	5.46410	−	9.46410i	0.579194	−	1.00319i	0.995572	−	0.0940016i	$-0.0299659\pi$
$90$		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	$-0.728385\pi$
$97$		−	14.8414i		−	1.50691i	0.657497	−	0.753457i	$-0.271615\pi$
$98$	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	$-0.243110\pi$
$101$	−2.39037	−	4.14024i	−0.237851	−	0.411969i	−0.960097	+	0.279666i	$0.909776\pi$
$102$		0			0
$103$	−11.6819	−	6.74455i	−1.15105	−	0.664560i	−0.201909	−	0.979404i	$-0.564714\pi$
$103$	−11.6819	−	6.74455i	−1.15105	−	0.664560i	−0.949143	+	0.314844i	$0.898048\pi$
$104$	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	$-0.0377975\pi$
$107$	14.3456	+	8.28245i	1.38684	+	0.800694i	0.393885	+	0.919160i	$0.371131\pi$
$108$		0			0
$109$	0.956906	+	1.65741i	0.0916550	+	0.158751i	0.908208	−	0.418520i	$-0.137451\pi$
$109$	0.956906	+	1.65741i	0.0916550	+	0.158751i	−0.816553	+	0.577271i	$0.804118\pi$
$110$	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	$-0.896213\pi$
$131$	−2.24630	+	3.89071i	−0.196260	+	0.339933i	0.751053	+	0.660242i	$0.229546\pi$
$132$		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	$-0.754680\pi$
$137$	−5.53443	+	3.19531i	−0.472839	+	0.272993i	0.244589	+	0.969627i	$0.421347\pi$
$138$		0			0
$139$		−	13.3954i		−	1.13618i	−0.822965	−	0.568092i	$-0.807682\pi$
$139$		−	13.3954i		−	1.13618i	0.822965	−	0.568092i	$-0.192318\pi$
$140$	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	$-0.182712\pi$
$149$	9.63521	+	5.56289i	0.789347	+	0.455730i	−0.0503855	+	0.998730i	$0.516045\pi$
$150$		0			0
$151$	0.620621	+	1.07495i	0.0505055	+	0.0874780i	0.890173	−	0.455623i	$-0.150583\pi$
$151$	0.620621	+	1.07495i	0.0505055	+	0.0874780i	−0.839667	+	0.543101i	$0.817250\pi$
$152$	−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	−0.418436	−	0.908246i	$-0.637422\pi$
$157$	1.99115	−	1.14959i	0.158911	−	0.0917471i	0.577347	+	0.816499i	$0.304088\pi$
$158$	−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	−0.930512	−	0.366261i	$-0.880638\pi$
$163$	−1.89037	+	3.27422i	−0.148065	+	0.256456i	0.782447	+	0.622717i	$0.213971\pi$
$164$	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	$-0.144827\pi$
$167$	23.2163			1.79653			0.898267	+	0.439450i	$0.144827\pi$
$168$		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	0.407878	+	0.913036i	$0.366269\pi$
$173$	−7.71780	+	13.3676i	−0.586773	+	1.01632i	−0.994652	+	0.103285i	$0.967065\pi$
$174$		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	$-0.416610\pi$
$179$	16.3889	−	9.46214i	1.22496	−	0.707234i	0.965972	+	0.258646i	$0.0832763\pi$
$180$		0			0
$181$		−	8.60465i		−	0.639579i	−0.947489	−	0.319789i	$-0.896388\pi$
$181$		−	8.60465i		−	0.639579i	0.947489	−	0.319789i	$-0.103612\pi$
$182$	−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	$-0.264659\pi$
$191$	5.12441	+	2.95858i	0.370790	+	0.214075i	−0.303014	+	0.952986i	$0.597993\pi$
$192$		0			0
$193$	1.84728	+	3.19957i	0.132970	+	0.230310i	0.924820	−	0.380405i	$-0.124215\pi$
$193$	1.84728	+	3.19957i	0.132970	+	0.230310i	−0.791850	+	0.610715i	$0.790882\pi$
$194$	−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	−0.883483	−	0.468462i	$-0.844808\pi$
$199$	−12.9715	+	7.48910i	−0.919525	+	0.530888i	−0.0360415	+	0.999350i	$0.511475\pi$
$200$	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	$0.0374659\pi$
$223$			3.50724i			0.234862i	−0.993081	+	0.117431i	$0.962534\pi$
$224$	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	−0.990936	−	0.134337i	$-0.957110\pi$
$227$	−9.21780	−	15.9657i	−0.611807	−	1.05968i	0.379129	−	0.925344i	$-0.376224\pi$
$228$		0			0
$229$	11.9626	+	6.90663i	0.790514	+	0.456403i	0.840143	−	0.542364i	$-0.182471\pi$
$229$	11.9626	+	6.90663i	0.790514	+	0.456403i	−0.0496297	+	0.998768i	$0.515804\pi$
$230$	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	$-0.382540\pi$
$233$	−4.07081	−	2.35028i	−0.266688	−	0.153972i	−0.627381	+	0.778712i	$0.715873\pi$
$234$		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	−0.00109283	−	0.999999i	$-0.500348\pi$
$241$	13.4189	−	7.74739i	0.864386	−	0.499053i	0.865478	+	0.500946i	$0.167015\pi$
$242$	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	$-0.700597\pi$
$251$	−18.6726			−1.17860			−0.589301	+	0.807914i	$0.700597\pi$
$252$		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	−0.325509	−	0.945539i	$-0.605536\pi$
$257$	10.5182	−	18.2180i	0.656107	−	1.13641i	0.981615	−	0.190871i	$-0.0611311\pi$
$258$		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	$-0.421610\pi$
$263$	19.5512	−	11.2879i	1.20558	−	0.696040i	0.961790	+	0.273789i	$0.0882771\pi$
$264$		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	$-0.273263\pi$
$269$	−5.39037	−	9.33639i	−0.328657	−	0.569250i	−0.982246	+	0.187600i	$0.939929\pi$
$270$		0			0
$271$	8.96264	+	5.17458i	0.544442	+	0.314334i	0.746877	−	0.664962i	$-0.231552\pi$
$271$	8.96264	+	5.17458i	0.544442	+	0.314334i	−0.202435	+	0.979296i	$0.564886\pi$
$272$	−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	0.634430	−	0.772980i	$-0.281235\pi$
$277$	−5.86186	−	10.1530i	−0.352205	−	0.610037i	−0.986636	+	0.162943i	$0.947901\pi$
$278$	−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	−0.611152	−	0.791513i	$-0.709294\pi$
$283$	−3.89037	+	2.24611i	−0.231258	+	0.133517i	0.379894	+	0.925030i	$0.375960\pi$
$284$	−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	$-0.441339\pi$
$293$	6.27335			0.366493			0.183246	+	0.983067i	$0.441339\pi$
$294$		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	$-0.934914\pi$
$307$		−	7.11556i		−	0.406106i	0.979168	−	0.203053i	$-0.0650864\pi$
$308$	−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	$-0.328457\pi$
$311$	−8.58259	−	14.8655i	−0.486674	−	0.842944i	−0.999883	+	0.0153198i	$0.995123\pi$
$312$		0			0
$313$	10.0089	+	5.77861i	0.565734	+	0.326627i	0.755444	−	0.655214i	$-0.227421\pi$
$313$	10.0089	+	5.77861i	0.565734	+	0.326627i	−0.189710	+	0.981840i	$0.560755\pi$
$314$	−2.72665			−0.153874
$315$		0			0
$316$	−7.65059			−0.430379
$317$	28.7360	+	16.5907i	1.61397	+	0.931828i	0.988437	+	0.151634i	$0.0484534\pi$
$317$	28.7360	+	16.5907i	1.61397	+	0.931828i	0.625537	+	0.780194i	$0.284880\pi$
$318$		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	−0.829674	−	0.558248i	$-0.811474\pi$
$331$	1.24844	−	2.16236i	0.0686205	−	0.118854i	0.898294	+	0.439394i	$0.144807\pi$
$332$	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	$-0.660904\pi$
$347$	0.584051	−	0.337202i	0.0313535	−	0.0181020i	0.515595	+	0.856833i	$0.327571\pi$
$348$		0			0
$349$		−	7.95631i		−	0.425892i	−0.977064	−	0.212946i	$-0.931694\pi$
$349$		−	7.95631i		−	0.425892i	0.977064	−	0.212946i	$-0.0683058\pi$
$350$	−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	$-0.210871\pi$
$353$	−2.60078	−	4.50468i	−0.138425	−	0.239760i	−0.926901	+	0.375307i	$0.877537\pi$
$354$		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	$-0.320894\pi$
$359$	1.28220	+	0.740279i	0.0676720	+	0.0390704i	−0.465782	+	0.884899i	$0.654227\pi$
$360$		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	−0.992640	−	0.121099i	$-0.961358\pi$
$367$	−26.5153	+	15.3086i	−1.38409	+	0.799102i	−0.391445	+	0.920201i	$0.628025\pi$
$368$	−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	−0.961641	−	0.274310i	$-0.911550\pi$
$373$	−4.69815	+	8.13743i	−0.243261	+	0.421340i	0.718380	+	0.695651i	$0.244884\pi$
$374$	−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	0.175349	+	0.984506i	$0.443895\pi$
$383$	−14.9700	+	25.9289i	−0.764933	+	1.32490i	−0.940282	+	0.340396i	$0.889439\pi$
$384$		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	$-0.782461\pi$
$389$	−12.1549	+	7.01761i	−0.616276	+	0.355807i	0.159142	+	0.987256i	$0.449127\pi$
$390$		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	0.759654	−	0.650328i	$-0.225369\pi$
$397$	11.4823	+	6.62930i	0.576280	+	0.332715i	−0.183374	+	0.983043i	$0.558702\pi$
$398$	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	$-0.283325\pi$
$401$	5.42674	+	3.13313i	0.270999	+	0.156461i	−0.358343	+	0.933590i	$0.616658\pi$
$402$		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	−0.120458	−	0.992718i	$-0.538436\pi$
$409$	13.7326	−	7.92851i	0.679033	−	0.392040i	0.799490	+	0.600679i	$0.205103\pi$
$410$	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	$-0.549960\pi$
$419$	−6.39922			−0.312623			−0.156311	+	0.987708i	$0.549960\pi$
$420$		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	$-0.591635\pi$
$431$	8.39776	−	4.84845i	0.404506	−	0.233542i	0.688426	+	0.725306i	$0.258302\pi$
$432$		0			0
$433$		−	18.9970i		−	0.912935i	−0.889740	−	0.456468i	$-0.849114\pi$
$433$		−	18.9970i		−	0.912935i	0.889740	−	0.456468i	$-0.150886\pi$
$434$	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	0.717309	−	0.696755i	$-0.245373\pi$
$439$	9.90116	+	5.71644i	0.472557	+	0.272831i	−0.244753	+	0.969586i	$0.578707\pi$
$440$	−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	$-0.308306\pi$
$443$	2.86333	+	1.65314i	0.136041	+	0.0785432i	−0.430435	+	0.902622i	$0.641640\pi$
$444$		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	−0.683028	−	0.730393i	$-0.739337\pi$
$457$	6.22140	−	10.7758i	0.291025	−	0.504070i	0.974052	+	0.226323i	$0.0726705\pi$
$458$	−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	$-0.634844\pi$
$461$	−17.6519			−0.822133			−0.411066	+	0.911605i	$0.634844\pi$
$462$		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	−0.364950	−	0.931027i	$-0.618914\pi$
$467$	13.4808	−	23.3495i	0.623818	−	1.08049i	0.988768	−	0.149458i	$-0.0477528\pi$
$468$		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	0.999992	+	0.00389227i	$0.00123895\pi$
$479$	11.0167	+	19.0815i	0.503367	+	0.871857i	−0.496625	+	0.867965i	$0.665428\pi$
$480$		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	−0.737941	−	0.674866i	$-0.764202\pi$
$487$	−21.0402	−	36.4426i	−0.953421	−	1.65137i	−0.215480	−	0.976508i	$-0.569132\pi$
$488$	−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	−0.890673	−	0.454644i	$-0.849766\pi$
$499$	−1.15272	+	1.99658i	−0.0516030	+	0.0893791i	0.839070	+	0.544023i	$0.183100\pi$
$500$	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	$-0.356212\pi$
$503$	19.5801			0.873035			0.436518	+	0.899696i	$0.356212\pi$
$504$		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	0.425072	+	0.905160i	$0.360249\pi$
$509$	−12.8904	+	22.3268i	−0.571356	+	0.989617i	−0.996427	+	0.0844571i	$0.973084\pi$
$510$		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	−0.961600	−	0.274454i	$-0.911503\pi$
$521$	−16.3997	−	28.4051i	−0.718484	−	1.24445i	0.243116	−	0.969997i	$-0.421830\pi$
$522$		0			0
$523$	1.79153	+	1.03434i	0.0783383	+	0.0452286i	0.538657	−	0.842525i	$-0.318932\pi$
$523$	1.79153	+	1.03434i	0.0783383	+	0.0452286i	−0.460319	+	0.887753i	$0.652265\pi$
$524$	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	0.120703	−	0.992689i	$-0.461485\pi$
$541$	21.3997	−	37.0654i	0.920045	−	1.59356i	0.799342	−	0.600876i	$-0.205182\pi$
$542$	−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	$-0.899973\pi$
$557$	−27.3501	+	15.7906i	−1.15886	+	0.669068i	−0.207830	+	0.978165i	$0.566640\pi$
$558$		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	$-0.270441\pi$
$563$	−7.59931	−	13.1624i	−0.320273	−	0.554729i	−0.980544	+	0.196298i	$0.937108\pi$
$564$		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	$-0.176651\pi$
$569$	19.5256	+	11.2731i	0.818555	+	0.472593i	−0.0313630	+	0.999508i	$0.509985\pi$
$570$		0			0
$571$	10.8707	+	18.8286i	0.454925	+	0.787954i	0.998684	−	0.0512878i	$-0.0163326\pi$
$571$	10.8707	+	18.8286i	0.454925	+	0.787954i	−0.543758	+	0.839242i	$0.682999\pi$
$572$	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	−0.691345	−	0.722525i	$-0.742981\pi$
$577$	−9.87957	+	5.70397i	−0.411292	+	0.237460i	0.280053	+	0.959985i	$0.409648\pi$
$578$	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	$-0.538442\pi$
$587$	−5.83775			−0.240950			−0.120475	+	0.992716i	$0.538442\pi$
$588$		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	$-0.922526\pi$
$593$	−6.73452	+	11.6645i	−0.276554	+	0.479005i	0.693972	+	0.720002i	$0.255859\pi$
$594$		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	$-0.832657\pi$
$599$	−21.1175	+	12.1922i	−0.862838	+	0.498160i	0.00212381	+	0.999998i	$0.499324\pi$
$600$		0			0
$601$			26.8721i			1.09613i	0.836434	+	0.548067i	$0.184636\pi$
$601$			26.8721i			1.09613i	−0.836434	+	0.548067i	$0.815364\pi$
$602$	−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	−0.00406824	−	0.999992i	$-0.501295\pi$
$607$	−21.4868	−	12.4054i	−0.872121	−	0.503519i	−0.868052	+	0.496473i	$0.834628\pi$
$608$	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	0.968664	+	0.248376i	$0.0798968\pi$
$613$	17.3171	+	29.9941i	0.699432	+	1.21145i	−0.269232	+	0.963075i	$0.586770\pi$
$614$	−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	−0.839537	−	0.543303i	$-0.817174\pi$
$619$	−19.6249	+	11.3304i	−0.788791	+	0.455409i	0.0507457	+	0.998712i	$0.483840\pi$
$620$	−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	$-0.769859\pi$
$641$	−13.9686	+	8.06476i	−0.551725	+	0.318539i	0.198092	+	0.980183i	$0.436525\pi$
$642$		0			0
$643$			18.2243i			0.718695i	0.933204	+	0.359347i	$0.117001\pi$
$643$			18.2243i			0.718695i	−0.933204	+	0.359347i	$0.882999\pi$
$644$	−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	0.976737	+	0.214440i	$0.0687926\pi$
$647$	17.1460	+	29.6978i	0.674079	+	1.16754i	−0.302658	+	0.953099i	$0.597874\pi$
$648$		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	−0.999197	−	0.0400736i	$-0.987241\pi$
$653$	−39.1868	−	22.6245i	−1.53350	−	0.885367i	−0.534303	−	0.845293i	$-0.679426\pi$
$654$		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	−0.439766	−	0.898112i	$-0.644939\pi$
$661$	3.03736	−	1.75362i	0.118140	−	0.0682079i	0.557905	+	0.829905i	$0.311605\pi$
$662$	−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	$-0.993334\pi$
$677$	−12.5349	+	21.7111i	−0.481756	+	0.834426i	0.518025	+	0.855366i	$0.326667\pi$
$678$		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	$-0.466465\pi$
$683$	26.6298	−	15.3747i	1.01896	−	0.588297i	0.913802	+	0.406159i	$0.133132\pi$
$684$		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	−0.482249	−	0.876034i	$-0.660180\pi$
$691$	−38.9583	−	22.4926i	−1.48204	−	0.855657i	−0.999792	+	0.0203767i	$0.993513\pi$
$692$	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	−0.558231	−	0.829686i	$-0.688520\pi$
$709$	11.7003	−	20.2655i	0.439413	−	0.761086i	0.997644	+	0.0685993i	$0.0218530\pi$
$710$	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	$-0.722239\pi$
$719$	9.16964	−	15.8823i	0.341970	−	0.592309i	0.984798	+	0.173701i	$0.0555725\pi$
$720$		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	$-0.936809\pi$
$727$		−	10.6353i		−	0.394440i	0.980359	−	0.197220i	$-0.0631913\pi$
$728$	−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	−0.101660	−	0.994819i	$-0.532415\pi$
$733$	−27.4538	−	15.8505i	−1.01403	−	0.585450i	−0.912369	+	0.409369i	$0.865749\pi$
$734$	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	0.902763	−	0.430138i	$-0.141535\pi$
$739$	2.14406	+	3.71363i	0.0788707	+	0.136608i	−0.823892	+	0.566746i	$0.808202\pi$
$740$	−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	−0.999120	−	0.0419493i	$-0.986643\pi$
$751$	−12.6946	+	21.9876i	−0.463231	+	0.802339i	0.535889	+	0.844288i	$0.319977\pi$
$752$	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	$-0.929291\pi$
$761$	−8.19076	+	14.1868i	−0.296915	+	0.514271i	0.678514	+	0.734588i	$0.262624\pi$
$762$		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	$0.0943138\pi$
$769$			16.1937i			0.583958i	−0.956425	+	0.291979i	$0.905686\pi$
$770$	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	$-0.238373\pi$
$773$	−6.21041	−	10.7567i	−0.223373	−	0.386893i	−0.955830	+	0.293920i	$0.905040\pi$
$774$		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	−0.853970	−	0.520322i	$-0.825812\pi$
$787$	−23.2941	+	13.4488i	−0.830344	+	0.479399i	0.0236267	+	0.999721i	$0.492479\pi$
$788$	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	$-0.327614\pi$
$797$	29.1052			1.03096			0.515480	+	0.856901i	$0.327614\pi$
$798$		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	$-0.397368\pi$
$809$	36.8820	−	21.2938i	1.29670	−	0.748651i	0.979833	+	0.199818i	$0.0640352\pi$
$810$		0			0
$811$			26.4491i			0.928755i	0.885637	+	0.464378i	$0.153722\pi$
$811$			26.4491i			0.928755i	−0.885637	+	0.464378i	$0.846278\pi$
$812$	−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	$-0.201785\pi$
$821$	19.9312	+	11.5073i	0.695604	+	0.401607i	−0.110104	+	0.993920i	$0.535118\pi$
$822$		0			0
$823$	−5.20847	−	9.02133i	−0.181556	−	0.314464i	0.760855	−	0.648922i	$-0.224780\pi$
$823$	−5.20847	−	9.02133i	−0.181556	−	0.314464i	−0.942410	+	0.334458i	$0.891447\pi$
$824$	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	−0.995762	−	0.0919633i	$-0.970686\pi$
$829$	−40.7124	+	23.5053i	−1.41400	+	0.816374i	−0.418239	+	0.908337i	$0.637352\pi$
$830$	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	$-0.314587\pi$
$839$	31.8683			1.10021			0.550107	+	0.835094i	$0.314587\pi$
$840$		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	$0.124021\pi$
$853$			22.1874i			0.759683i	−0.925052	+	0.379841i	$0.875979\pi$
$854$	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	0.996918	+	0.0784521i	$0.0249978\pi$
$857$	16.5811	+	28.7194i	0.566400	+	0.981034i	−0.430517	+	0.902582i	$0.641669\pi$
$858$		0			0
$859$	10.8511	+	6.26487i	0.370234	+	0.213755i	0.673561	−	0.739132i	$-0.264764\pi$
$859$	10.8511	+	6.26487i	0.370234	+	0.213755i	−0.303327	+	0.952887i	$0.598097\pi$
$860$	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	$-0.149038\pi$
$863$	27.8412	+	16.0741i	0.947727	+	0.547170i	0.0553526	+	0.998467i	$0.482372\pi$
$864$		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	−0.915515	−	0.402283i	$-0.868217\pi$
$877$	−3.23891	+	5.60996i	−0.109370	+	0.189435i	0.806145	+	0.591718i	$0.201550\pi$
$878$	−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	$-0.664702\pi$
$881$	−29.3638			−0.989292			−0.494646	+	0.869095i	$0.664702\pi$
$882$		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	$-0.890778\pi$
$887$	−5.34562	+	9.25888i	−0.179488	+	0.310883i	0.762217	+	0.647321i	$0.224111\pi$
$888$		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	−0.985133	−	0.171793i	$-0.945044\pi$
$907$	−19.3150	−	33.4545i	−0.641343	−	1.11084i	0.343790	−	0.939047i	$-0.388289\pi$
$908$	−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	−0.834218	−	0.551435i	$-0.814080\pi$
$919$	1.83249	−	3.17397i	0.0604483	−	0.104700i	0.894666	+	0.446736i	$0.147414\pi$
$920$	−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	$-0.897737\pi$
$929$	−6.12489	+	10.6086i	−0.200951	+	0.348058i	0.747884	+	0.663830i	$0.231070\pi$
$930$		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	$-0.860379\pi$
$937$		−	26.0006i		−	0.849403i	0.905333	−	0.424702i	$-0.139621\pi$
$938$	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	$-0.167054\pi$
$941$	−0.0373591	−	0.0647078i	−0.00121787	−	0.00210941i	−0.866634	+	0.498945i	$0.833721\pi$
$942$		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	$-0.321261\pi$
$947$	2.02111	+	1.16689i	0.0656773	+	0.0379188i	−0.466802	+	0.884362i	$0.654594\pi$
$948$		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	$-0.751482\pi$
$971$	7.92480	−	13.7262i	0.254319	−	0.440493i	0.964710	+	0.263313i	$0.0848153\pi$
$972$		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	$-0.892813\pi$
$977$	−35.3083	+	20.3852i	−1.12961	+	0.652181i	−0.185774	+	0.982592i	$0.559479\pi$
$978$		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	$-0.00151867\pi$
$983$	15.5467	+	26.9277i	0.495862	+	0.858859i	−0.504126	+	0.863630i	$0.668185\pi$
$984$		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	0.574548	−	0.818471i	$-0.305178\pi$
$991$	−13.2702	−	22.9847i	−0.421543	−	0.730133i	−0.996091	+	0.0883377i	$0.971845\pi$
$992$	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	−0.776924	−	0.629595i	$-0.783221\pi$
$997$	−19.5811	+	11.3052i	−0.620140	+	0.358038i	0.156783	+	0.987633i	$0.449888\pi$
$998$	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.h.26.1	yes	6
3.2	odd	2		945.2.bj.g.26.3	✓	6
7.3	odd	6		945.2.bj.g.836.3	yes	6
21.17	even	6	inner	945.2.bj.h.836.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.bj.g.26.3	✓	6	3.2	odd	2
945.2.bj.g.836.3	yes	6	7.3	odd	6
945.2.bj.h.26.1	yes	6	1.1	even	1	trivial
945.2.bj.h.836.1	yes	6	21.17	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
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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