LMFDB - Embedded newform 946.2.t.a.7.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [946,2,Mod(7,946)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(946, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([21, 25]))

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

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

chi := DirichletCharacter("946.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 946 = 2 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	946.t (of order $30$, degree $8$, 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:	$7.55384803121$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			7.10
Character	$\chi$	$=$	946.7
Dual form			946.2.t.a.811.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-0.122515 - 0.576387i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.58246 + 3.55426i) q^{5} +(-0.239675 + 0.538319i) q^{6} +(4.84535 + 1.02991i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.42342 - 1.07898i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.122515 - 0.576387i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.58246 + 3.55426i) q^{5} +(-0.239675 + 0.538319i) q^{6} +(4.84535 + 1.02991i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.42342 - 1.07898i) q^{9} +(3.36938 - 1.94531i) q^{10} +(0.187163 - 3.31134i) q^{11} +(0.510318 - 0.294632i) q^{12} +(1.77450 + 3.98560i) q^{13} +(-3.31460 - 3.68124i) q^{14} +(2.24250 + 0.476659i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-7.24359 + 0.761332i) q^{17} +(-2.59480 - 0.551541i) q^{18} +(2.46260 - 0.523442i) q^{19} +(-3.86931 - 0.406681i) q^{20} -2.91898i q^{21} +(-2.09777 + 2.56892i) q^{22} +(3.42438 + 5.93119i) q^{23} +(-0.586036 - 0.0615949i) q^{24} +(-6.78293 - 7.53321i) q^{25} +(0.907073 - 4.26744i) q^{26} +(-1.95790 - 2.69481i) q^{27} +(0.517792 + 4.92646i) q^{28} +(5.71008 + 1.21372i) q^{29} +(-1.53405 - 1.70374i) q^{30} +(0.353510 - 3.36342i) q^{31} +1.00000 q^{32} +(-1.93154 + 0.297810i) q^{33} +(6.30768 + 3.64174i) q^{34} +(-11.3281 + 15.5918i) q^{35} +(1.77505 + 1.97139i) q^{36} +(-1.58350 - 1.42579i) q^{37} +(-2.29996 - 1.02401i) q^{38} +(2.07985 - 1.51110i) q^{39} +(2.89129 + 2.60333i) q^{40} +(-7.75459 - 2.51962i) q^{41} +(-1.71573 + 2.36150i) q^{42} +(4.25802 + 4.98691i) q^{43} +(3.20711 - 0.845257i) q^{44} +10.3209i q^{45} +(0.715890 - 6.81123i) q^{46} +(0.546846 - 1.68302i) q^{47} +(0.437908 + 0.394295i) q^{48} +(16.0219 + 7.13340i) q^{49} +(1.05960 + 10.0814i) q^{50} +(1.32627 + 4.08184i) q^{51} +(-3.24218 + 2.91927i) q^{52} +(-0.767602 + 7.30324i) q^{53} +3.33097i q^{54} +(11.4732 + 5.90528i) q^{55} +(2.47680 - 4.28994i) q^{56} +(-0.603410 - 1.35528i) q^{57} +(-3.90615 - 4.33822i) q^{58} +(1.46100 + 4.49650i) q^{59} +(0.239642 + 2.28004i) q^{60} +(0.490765 + 4.66932i) q^{61} +(-2.26297 + 2.51328i) q^{62} +(12.8536 - 2.73212i) q^{63} +(-0.809017 - 0.587785i) q^{64} -16.9739 q^{65} +(1.73770 + 0.894400i) q^{66} +(2.21331 + 3.83357i) q^{67} +(-2.96246 - 6.65380i) q^{68} +(2.99913 - 2.70043i) q^{69} +(18.3293 - 5.95555i) q^{70} +(6.28617 - 0.660704i) q^{71} +(-0.277290 - 2.63824i) q^{72} +(-12.5234 - 2.66194i) q^{73} +(0.443020 + 2.08425i) q^{74} +(-3.51103 + 4.83252i) q^{75} +(1.25881 + 2.18032i) q^{76} +(4.31726 - 15.8518i) q^{77} -2.57083 q^{78} +(-2.06092 - 4.62889i) q^{79} +(-0.808906 - 3.80560i) q^{80} +(4.01176 - 4.45551i) q^{81} +(4.79260 + 6.59645i) q^{82} +(2.20433 - 4.95100i) q^{83} +(2.77611 - 0.902014i) q^{84} +(8.75670 - 26.9504i) q^{85} +(-0.513582 - 6.53730i) q^{86} -3.43992i q^{87} +(-3.09143 - 1.20126i) q^{88} +(0.484178 - 0.279540i) q^{89} +(6.06648 - 8.34979i) q^{90} +(4.49328 + 21.1392i) q^{91} +(-4.58271 + 5.08961i) q^{92} +(-1.98194 + 0.208311i) q^{93} +(-1.43166 + 1.04016i) q^{94} +(-2.03651 + 9.58105i) q^{95} +(-0.122515 - 0.576387i) q^{96} +(11.4006 + 8.28299i) q^{97} +(-8.76907 - 15.1885i) q^{98} +(-3.11929 - 8.22673i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 44 q^{2} - 44 q^{4} - 5 q^{6} - 15 q^{7} - 44 q^{8} - 20 q^{9}+O(q^{10}) $ 176 * q - 44 * q^2 - 44 * q^4 - 5 * q^6 - 15 * q^7 - 44 * q^8 - 20 * q^9	$ 176 q - 44 q^{2} - 44 q^{4} - 5 q^{6} - 15 q^{7} - 44 q^{8} - 20 q^{9} - 5 q^{11} - 5 q^{13} + 15 q^{14} + 41 q^{15} - 44 q^{16} - 2 q^{17} - 25 q^{18} + 34 q^{19} + 5 q^{22} - 4 q^{23} + 5 q^{24} - 24 q^{25} + 20 q^{26} - 60 q^{27} - 3 q^{29} - 49 q^{30} + 40 q^{31} + 176 q^{32} - 47 q^{33} + 3 q^{34} - 60 q^{35} - 25 q^{36} - 8 q^{37} + 14 q^{38} + 12 q^{39} - 19 q^{43} - 10 q^{44} + 26 q^{46} - 4 q^{47} - 21 q^{49} + 6 q^{50} + 45 q^{51} - 20 q^{52} - 27 q^{53} + 68 q^{55} + 71 q^{57} - 3 q^{58} - 21 q^{59} + 6 q^{60} + 30 q^{61} + 71 q^{63} - 44 q^{64} - 16 q^{65} + 43 q^{66} - 3 q^{67} + 8 q^{68} - 42 q^{69} + 3 q^{71} - 20 q^{72} - 19 q^{73} - 28 q^{74} + 9 q^{76} + 38 q^{77} + 92 q^{78} + 32 q^{79} - 23 q^{81} - 5 q^{82} - 26 q^{83} + 2 q^{85} + 36 q^{86} + 5 q^{88} + 57 q^{89} + 30 q^{91} + 6 q^{92} - 10 q^{93} + 6 q^{94} - 58 q^{95} - 37 q^{97} - 106 q^{98} - 119 q^{99}+O(q^{100}) $ 176 * q - 44 * q^2 - 44 * q^4 - 5 * q^6 - 15 * q^7 - 44 * q^8 - 20 * q^9 - 5 * q^11 - 5 * q^13 + 15 * q^14 + 41 * q^15 - 44 * q^16 - 2 * q^17 - 25 * q^18 + 34 * q^19 + 5 * q^22 - 4 * q^23 + 5 * q^24 - 24 * q^25 + 20 * q^26 - 60 * q^27 - 3 * q^29 - 49 * q^30 + 40 * q^31 + 176 * q^32 - 47 * q^33 + 3 * q^34 - 60 * q^35 - 25 * q^36 - 8 * q^37 + 14 * q^38 + 12 * q^39 - 19 * q^43 - 10 * q^44 + 26 * q^46 - 4 * q^47 - 21 * q^49 + 6 * q^50 + 45 * q^51 - 20 * q^52 - 27 * q^53 + 68 * q^55 + 71 * q^57 - 3 * q^58 - 21 * q^59 + 6 * q^60 + 30 * q^61 + 71 * q^63 - 44 * q^64 - 16 * q^65 + 43 * q^66 - 3 * q^67 + 8 * q^68 - 42 * q^69 + 3 * q^71 - 20 * q^72 - 19 * q^73 - 28 * q^74 + 9 * q^76 + 38 * q^77 + 92 * q^78 + 32 * q^79 - 23 * q^81 - 5 * q^82 - 26 * q^83 + 2 * q^85 + 36 * q^86 + 5 * q^88 + 57 * q^89 + 30 * q^91 + 6 * q^92 - 10 * q^93 + 6 * q^94 - 58 * q^95 - 37 * q^97 - 106 * q^98 - 119 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/946\mathbb{Z}\right)^\times$.

$n$	$89$	$431$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−0.122515	−	0.576387i	−0.0707340	−	0.332777i	0.928525	−	0.371270i	$-0.121078\pi$
$3$	−0.122515	−	0.576387i	−0.0707340	−	0.332777i	−0.999259	+	0.0384929i	$0.987744\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−1.58246	+	3.55426i	−0.707697	+	1.58951i	0.0966264	+	0.995321i	$0.469195\pi$
$5$	−1.58246	+	3.55426i	−0.707697	+	1.58951i	−0.804323	+	0.594192i	$0.797472\pi$
$6$	−0.239675	+	0.538319i	−0.0978470	+	0.219768i
$7$	4.84535	+	1.02991i	1.83137	+	0.389270i	0.988791	−	0.149303i	$-0.0477030\pi$
$7$	4.84535	+	1.02991i	1.83137	+	0.389270i	0.842579	+	0.538573i	$0.181036\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	2.42342	−	1.07898i	0.807808	−	0.359659i
$10$	3.36938	−	1.94531i	1.06549	−	0.615161i
$11$	0.187163	−	3.31134i	0.0564318	−	0.998406i
$11$	0.187163	−	3.31134i	0.0564318	−	0.998406i
$12$	0.510318	−	0.294632i	0.147316	−	0.0850529i
$13$	1.77450	+	3.98560i	0.492159	+	1.10541i	0.973461	+	0.228852i	$0.0734972\pi$
$13$	1.77450	+	3.98560i	0.492159	+	1.10541i	−0.481303	+	0.876555i	$0.659836\pi$
$14$	−3.31460	−	3.68124i	−0.885865	−	0.983853i
$15$	2.24250	+	0.476659i	0.579012	+	0.123073i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−7.24359	+	0.761332i	−1.75683	+	0.184650i	−0.927427	−	0.374004i	$-0.877985\pi$
$17$	−7.24359	+	0.761332i	−1.75683	+	0.184650i	−0.829401	+	0.558654i	$0.811318\pi$
$18$	−2.59480	−	0.551541i	−0.611600	−	0.130000i
$19$	2.46260	−	0.523442i	0.564959	−	0.120086i	0.0834267	−	0.996514i	$-0.473414\pi$
$19$	2.46260	−	0.523442i	0.564959	−	0.120086i	0.481533	+	0.876428i	$0.340080\pi$
$20$	−3.86931	−	0.406681i	−0.865203	−	0.0909365i
$21$		−	2.91898i		−	0.636973i
$22$	−2.09777	+	2.56892i	−0.447247	+	0.547695i
$23$	3.42438	+	5.93119i	0.714032	+	1.23674i	0.963332	+	0.268313i	$0.0864661\pi$
$23$	3.42438	+	5.93119i	0.714032	+	1.23674i	−0.249300	+	0.968426i	$0.580201\pi$
$24$	−0.586036	−	0.0615949i	−0.119624	−	0.0125730i
$25$	−6.78293	−	7.53321i	−1.35659	−	1.50664i
$26$	0.907073	−	4.26744i	0.177892	−	0.836915i
$27$	−1.95790	−	2.69481i	−0.376797	−	0.518617i
$28$	0.517792	+	4.92646i	0.0978535	+	0.931014i
$29$	5.71008	+	1.21372i	1.06034	+	0.225381i	0.704891	−	0.709316i	$-0.250996\pi$
$29$	5.71008	+	1.21372i	1.06034	+	0.225381i	0.355445	+	0.934697i	$0.384329\pi$
$30$	−1.53405	−	1.70374i	−0.280078	−	0.311058i
$31$	0.353510	−	3.36342i	0.0634923	−	0.604089i	−0.915800	−	0.401635i	$-0.868442\pi$
$31$	0.353510	−	3.36342i	0.0634923	−	0.604089i	0.979292	−	0.202453i	$-0.0648914\pi$
$32$	1.00000			0.176777
$33$	−1.93154	+	0.297810i	−0.336239	+	0.0518420i
$34$	6.30768	+	3.64174i	1.08176	+	0.624554i
$35$	−11.3281	+	15.5918i	−1.91480	+	2.63550i
$36$	1.77505	+	1.97139i	0.295841	+	0.328565i
$37$	−1.58350	−	1.42579i	−0.260326	−	0.234398i	0.528624	−	0.848856i	$-0.322708\pi$
$37$	−1.58350	−	1.42579i	−0.260326	−	0.234398i	−0.788950	+	0.614458i	$0.789375\pi$
$38$	−2.29996	−	1.02401i	−0.373102	−	0.166116i
$39$	2.07985	−	1.51110i	0.333042	−	0.241969i
$40$	2.89129	+	2.60333i	0.457154	+	0.411623i
$41$	−7.75459	−	2.51962i	−1.21106	−	0.393499i	−0.367244	−	0.930125i	$-0.619699\pi$
$41$	−7.75459	−	2.51962i	−1.21106	−	0.393499i	−0.843820	+	0.536626i	$0.819699\pi$
$42$	−1.71573	+	2.36150i	−0.264743	+	0.364388i
$43$	4.25802	+	4.98691i	0.649342	+	0.760496i
$43$	4.25802	+	4.98691i	0.649342	+	0.760496i
$44$	3.20711	−	0.845257i	0.483490	−	0.127427i
$45$			10.3209i			1.53855i
$46$	0.715890	−	6.81123i	0.105552	−	1.00426i
$47$	0.546846	−	1.68302i	0.0797658	−	0.245494i	−0.903219	−	0.429179i	$-0.858803\pi$
$47$	0.546846	−	1.68302i	0.0797658	−	0.245494i	0.982985	+	0.183686i	$0.0588028\pi$
$48$	0.437908	+	0.394295i	0.0632066	+	0.0569115i
$49$	16.0219	+	7.13340i	2.28884	+	1.01906i
$50$	1.05960	+	10.0814i	0.149850	+	1.42572i
$51$	1.32627	+	4.08184i	0.185715	+	0.571571i
$52$	−3.24218	+	2.91927i	−0.449609	+	0.404830i
$53$	−0.767602	+	7.30324i	−0.105438	+	1.00318i	0.806049	+	0.591849i	$0.201602\pi$
$53$	−0.767602	+	7.30324i	−0.105438	+	1.00318i	−0.911487	+	0.411329i	$0.865065\pi$
$54$			3.33097i			0.453288i
$55$	11.4732	+	5.90528i	1.54704	+	0.796268i
$56$	2.47680	−	4.28994i	0.330976	−	0.573268i
$57$	−0.603410	−	1.35528i	−0.0799237	−	0.179511i
$58$	−3.90615	−	4.33822i	−0.512903	−	0.569636i
$59$	1.46100	+	4.49650i	0.190206	+	0.585394i	0.999999	−	0.00132140i	$-0.000420614\pi$
$59$	1.46100	+	4.49650i	0.190206	+	0.585394i	−0.809793	+	0.586716i	$0.800421\pi$
$60$	0.239642	+	2.28004i	0.0309377	+	0.294352i
$61$	0.490765	+	4.66932i	0.0628361	+	0.597845i	0.979953	+	0.199228i	$0.0638433\pi$
$61$	0.490765	+	4.66932i	0.0628361	+	0.597845i	−0.917117	+	0.398618i	$0.869490\pi$
$62$	−2.26297	+	2.51328i	−0.287397	+	0.319187i
$63$	12.8536	−	2.73212i	1.61940	−	0.344214i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−16.9739			−2.10536
$66$	1.73770	+	0.894400i	0.213896	+	0.110093i
$67$	2.21331	+	3.83357i	0.270399	+	0.468345i	0.968964	−	0.247202i	$-0.0795111\pi$
$67$	2.21331	+	3.83357i	0.270399	+	0.468345i	−0.698565	+	0.715546i	$0.746178\pi$
$68$	−2.96246	−	6.65380i	−0.359251	−	0.806891i
$69$	2.99913	−	2.70043i	0.361052	−	0.325093i
$70$	18.3293	−	5.95555i	2.19077	−	0.711825i
$71$	6.28617	−	0.660704i	0.746032	−	0.0784111i	0.276118	−	0.961124i	$-0.410952\pi$
$71$	6.28617	−	0.660704i	0.746032	−	0.0784111i	0.469913	+	0.882713i	$0.344285\pi$
$72$	−0.277290	−	2.63824i	−0.0326789	−	0.310919i
$73$	−12.5234	−	2.66194i	−1.46576	−	0.311556i	−0.595181	−	0.803591i	$-0.702920\pi$
$73$	−12.5234	−	2.66194i	−1.46576	−	0.311556i	−0.870575	+	0.492035i	$0.836253\pi$
$74$	0.443020	+	2.08425i	0.0515001	+	0.242289i
$75$	−3.51103	+	4.83252i	−0.405419	+	0.558012i
$76$	1.25881	+	2.18032i	0.144395	+	0.250100i
$77$	4.31726	−	15.8518i	0.491997	−	1.80648i
$78$	−2.57083			−0.291089
$79$	−2.06092	−	4.62889i	−0.231871	−	0.520791i	0.759712	−	0.650259i	$-0.225340\pi$
$79$	−2.06092	−	4.62889i	−0.231871	−	0.520791i	−0.991584	+	0.129468i	$0.958673\pi$
$80$	−0.808906	−	3.80560i	−0.0904384	−	0.425479i
$81$	4.01176	−	4.45551i	0.445751	−	0.495057i
$82$	4.79260	+	6.59645i	0.529254	+	0.728456i
$83$	2.20433	−	4.95100i	0.241956	−	0.543443i	−0.751222	−	0.660050i	$-0.770535\pi$
$83$	2.20433	−	4.95100i	0.241956	−	0.543443i	0.993178	+	0.116607i	$0.0372018\pi$
$84$	2.77611	−	0.902014i	0.302899	−	0.0984177i
$85$	8.75670	−	26.9504i	0.949798	−	2.92318i
$86$	−0.513582	−	6.53730i	−0.0553810	−	0.704935i
$87$		−	3.43992i		−	0.368798i
$88$	−3.09143	−	1.20126i	−0.329548	−	0.128055i
$89$	0.484178	−	0.279540i	0.0513228	−	0.0296312i	−0.474119	−	0.880461i	$-0.657233\pi$
$89$	0.484178	−	0.279540i	0.0513228	−	0.0296312i	0.525442	+	0.850830i	$0.323900\pi$
$90$	6.06648	−	8.34979i	0.639463	−	0.880146i
$91$	4.49328	+	21.1392i	0.471023	+	2.21599i
$92$	−4.58271	+	5.08961i	−0.477781	+	0.530629i
$93$	−1.98194	+	0.208311i	−0.205518	+	0.0216008i
$94$	−1.43166	+	1.04016i	−0.147665	+	0.107285i
$95$	−2.03651	+	9.58105i	−0.208942	+	0.982995i
$96$	−0.122515	−	0.576387i	−0.0125041	−	0.0588273i
$97$	11.4006	+	8.28299i	1.15755	+	0.841010i	0.989466	−	0.144762i	$-0.0462417\pi$
$97$	11.4006	+	8.28299i	1.15755	+	0.841010i	0.168085	+	0.985773i	$0.446242\pi$
$98$	−8.76907	−	15.1885i	−0.885810	−	1.53427i
$99$	−3.11929	−	8.22673i	−0.313500	−	0.826817i
$100$	5.06846	−	8.77884i	0.506846	−	0.877884i
$101$	2.77412	+	6.23078i	0.276036	+	0.619986i	0.997360	−	0.0726109i	$-0.0231331\pi$
$101$	2.77412	+	6.23078i	0.276036	+	0.619986i	−0.721325	+	0.692597i	$0.756466\pi$
$102$	1.32627	−	4.08184i	0.131320	−	0.404162i
$103$	−6.37258	−	1.35453i	−0.627909	−	0.133466i	−0.117043	−	0.993127i	$-0.537342\pi$
$103$	−6.37258	−	1.35453i	−0.627909	−	0.133466i	−0.510865	+	0.859661i	$0.670675\pi$
$104$	4.33888	−	0.456035i	0.425462	−	0.0447179i
$105$	10.3748	+	4.61916i	1.01248	+	0.450784i
$106$	4.91374	−	5.45726i	0.477265	−	0.530056i
$107$	−2.51450	−	0.817011i	−0.243086	−	0.0789835i	0.184940	−	0.982750i	$-0.440791\pi$
$107$	−2.51450	−	0.817011i	−0.243086	−	0.0789835i	−0.428026	+	0.903766i	$0.640791\pi$
$108$	1.95790	−	2.69481i	0.188399	−	0.259309i
$109$	1.82943	−	1.05622i	0.175228	−	0.101168i	−0.409821	−	0.912166i	$-0.634409\pi$
$109$	1.82943	−	1.05622i	0.175228	−	0.101168i	0.585049	+	0.810998i	$0.301075\pi$
$110$	−5.81096	−	11.5212i	−0.554053	−	1.09851i
$111$	−0.627805	+	1.08739i	−0.0595886	+	0.103210i
$112$	−4.52534	+	2.01481i	−0.427604	+	0.190382i
$113$	5.99985	+	1.94947i	0.564419	+	0.183391i	0.577308	−	0.816526i	$-0.304103\pi$
$113$	5.99985	+	1.94947i	0.564419	+	0.183391i	−0.0128897	+	0.999917i	$0.504103\pi$
$114$	−0.308446	+	1.45112i	−0.0288886	+	0.135910i
$115$	−26.4999	+	2.78525i	−2.47113	+	0.259726i
$116$	0.610201	+	5.80567i	0.0566557	+	0.539043i
$117$	8.60075	+	7.74415i	0.795140	+	0.715947i
$118$	1.46100	−	4.49650i	0.134496	−	0.413936i
$119$	−35.8818	−	3.77133i	−3.28928	−	0.345717i
$120$	1.14630	−	1.98545i	0.104643	−	0.181246i
$121$	−10.9299	−	1.23952i	−0.993631	−	0.112684i
$122$	2.34752	−	4.06602i	0.212534	−	0.368121i
$123$	−0.502224	+	4.77834i	−0.0452840	+	0.430848i
$124$	3.30805	−	0.703147i	0.297071	−	0.0631445i
$125$	19.0077	−	6.17596i	1.70010	−	0.552395i
$126$	−12.0047	−	5.34482i	−1.06946	−	0.476155i
$127$	7.77339	+	10.6992i	0.689777	+	0.949397i	0.999999	−	0.00126731i	$-0.000403397\pi$
$127$	7.77339	+	10.6992i	0.689777	+	0.949397i	−0.310222	+	0.950664i	$0.600403\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	2.35272	−	3.06524i	0.207145	−	0.269879i
$130$	13.7322	+	9.97703i	1.20439	+	0.875043i
$131$	11.9471			1.04382			0.521912	−	0.852999i	$-0.325219\pi$
$131$	11.9471			1.04382			0.521912	+	0.852999i	$0.325219\pi$
$132$	−0.880114	−	1.74498i	−0.0766041	−	0.151881i
$133$	12.4713			1.08140
$134$	0.462708	−	4.40237i	0.0399719	−	0.380307i
$135$	12.6764	−	2.69444i	1.09101	−	0.231901i
$136$	−1.51432	+	7.12433i	−0.129852	+	0.610906i
$137$	−8.73821	−	12.0271i	−0.746556	−	1.02755i	−0.998215	−	0.0597300i	$-0.980976\pi$
$137$	−8.73821	−	12.0271i	−0.746556	−	1.02755i	0.251659	−	0.967816i	$-0.419024\pi$
$138$	−4.01361	+	0.421848i	−0.341662	+	0.0359101i
$139$	−9.80960	−	8.83261i	−0.832040	−	0.749172i	0.138436	−	0.990371i	$-0.455793\pi$
$139$	−9.80960	−	8.83261i	−0.832040	−	0.749172i	−0.970476	+	0.241199i	$0.922459\pi$
$140$	−18.3293	−	5.95555i	−1.54911	−	0.503336i
$141$	−1.03707	−	0.109000i	−0.0873369	−	0.00917948i
$142$	−5.47397	−	3.16040i	−0.459366	−	0.265215i
$143$	13.5298	−	5.13003i	1.13142	−	0.428994i
$144$	−1.32638	+	2.29736i	−0.110532	+	0.191447i
$145$	−13.3498	+	18.3745i	−1.10864	+	1.52592i
$146$	8.56702	+	9.51464i	0.709012	+	0.787437i
$147$	2.14868	−	10.1088i	0.177220	−	0.833756i
$148$	0.866678	−	1.94659i	0.0712405	−	0.160009i
$149$	−1.41013	−	0.627828i	−0.115522	−	0.0514337i	0.348162	−	0.937434i	$-0.386806\pi$
$149$	−1.41013	−	0.627828i	−0.115522	−	0.0514337i	−0.463684	+	0.886001i	$0.653473\pi$
$150$	5.68097	−	1.84586i	0.463849	−	0.150714i
$151$	−0.886398	+	2.72805i	−0.0721340	+	0.222006i	−0.980623	−	0.195902i	$-0.937237\pi$
$151$	−0.886398	+	2.72805i	−0.0721340	+	0.222006i	0.908489	+	0.417908i	$0.137237\pi$
$152$	0.263163	−	2.50383i	0.0213453	−	0.203087i
$153$	−16.7328	+	9.66070i	−1.35277	+	0.781021i
$154$	−12.8102	+	10.2868i	−1.03228	+	0.828933i
$155$	11.3951	+	6.57894i	0.915274	+	0.528434i
$156$	2.07985	+	1.51110i	0.166521	+	0.120985i
$157$	−11.2900	+	10.1656i	−0.901040	+	0.811300i	−0.982670	−	0.185363i	$-0.940654\pi$
$157$	−11.2900	+	10.1656i	−0.901040	+	0.811300i	0.0816305	+	0.996663i	$0.473987\pi$
$158$	−1.05348	+	4.95623i	−0.0838103	+	0.394296i
$159$	4.30354	−	0.452320i	0.341293	−	0.0358713i
$160$	−1.58246	+	3.55426i	−0.125104	+	0.280989i
$161$	10.4837	+	32.2655i	0.826231	+	2.54288i
$162$	−5.86447	+	1.24653i	−0.460756	+	0.0979367i
$163$	−0.366055	−	0.822173i	−0.0286716	−	0.0643976i	0.898642	−	0.438683i	$-0.144555\pi$
$163$	−0.366055	−	0.822173i	−0.0286716	−	0.0643976i	−0.927314	+	0.374285i	$0.877888\pi$
$164$		−	8.15366i		−	0.636694i
$165$	1.99809	−	7.33648i	0.155551	−	0.571144i
$166$	−4.69346	+	2.70977i	−0.364283	+	0.210319i
$167$	−7.22328	−	0.759197i	−0.558954	−	0.0587485i	−0.179161	−	0.983820i	$-0.557338\pi$
$167$	−7.22328	−	0.759197i	−0.558954	−	0.0587485i	−0.379793	+	0.925071i	$0.624005\pi$
$168$	−2.77611	−	0.902014i	−0.214182	−	0.0695919i
$169$	−4.03745	+	4.48404i	−0.310573	+	0.344926i
$170$	−22.9253	+	16.6562i	−1.75829	+	1.27748i
$171$	5.40314	−	3.92561i	0.413189	−	0.300199i
$172$	−3.42703	+	5.59066i	−0.261309	+	0.426284i
$173$	4.59225	+	1.49211i	0.349142	+	0.113443i	0.478338	−	0.878176i	$-0.341240\pi$
$173$	4.59225	+	1.49211i	0.349142	+	0.113443i	−0.129196	+	0.991619i	$0.541240\pi$
$174$	−2.02193	+	2.78295i	−0.153282	+	0.210975i
$175$	−25.1071	−	43.4868i	−1.89792	−	3.28730i
$176$	1.79494	+	2.78894i	0.135299	+	0.210224i
$177$	2.41273	−	1.39299i	0.181352	−	0.104704i
$178$	−0.556018	−	0.0584399i	−0.0416753	−	0.00438025i
$179$	−10.4852	+	9.44092i	−0.783701	+	0.705648i	−0.960402	−	0.278617i	$-0.910124\pi$
$179$	−10.4852	+	9.44092i	−0.783701	+	0.705648i	0.176701	+	0.984265i	$0.443457\pi$
$180$	−9.81577	+	3.18934i	−0.731624	+	0.237719i
$181$	0.464582	+	4.42020i	0.0345321	+	0.328551i	0.998127	+	0.0611829i	$0.0194873\pi$
$181$	0.464582	+	4.42020i	0.0345321	+	0.328551i	−0.963594	+	0.267368i	$0.913846\pi$
$182$	8.79018	−	19.7431i	0.651571	−	1.46345i
$183$	2.63121	−	0.854932i	0.194505	−	0.0631984i
$184$	6.69909	−	1.42394i	0.493863	−	0.104974i
$185$	7.57345	−	3.37192i	0.556811	−	0.247908i
$186$	1.72587	+	0.996431i	0.126547	+	0.0730619i
$187$	1.16529	+	24.1285i	0.0852148	+	1.76445i
$188$	1.76963			0.129064
$189$	−6.71128	−	15.0738i	−0.488174	−	1.09646i
$190$	7.27917	−	6.55420i	0.528087	−	0.475491i
$191$	−14.7365	−	13.2688i	−1.06630	−	0.960100i	−0.0670077	−	0.997752i	$-0.521345\pi$
$191$	−14.7365	−	13.2688i	−1.06630	−	0.960100i	−0.999291	+	0.0376529i	$0.988012\pi$
$192$	−0.239675	+	0.538319i	−0.0172971	+	0.0388499i
$193$	−6.48046	−	8.91959i	−0.466474	−	0.642046i	0.509362	−	0.860552i	$-0.329881\pi$
$193$	−6.48046	−	8.91959i	−0.466474	−	0.642046i	−0.975835	+	0.218507i	$0.929881\pi$
$194$	−4.35463	−	13.4022i	−0.312644	−	0.962219i
$195$	2.07956	+	9.78355i	0.148920	+	0.700615i
$196$	−1.83323	+	17.4421i	−0.130945	+	1.24586i
$197$	15.5159	+	8.95809i	1.10546	+	0.638237i	0.937650	−	0.347582i	$-0.112997\pi$
$197$	15.5159	+	8.95809i	1.10546	+	0.638237i	0.167810	+	0.985819i	$0.446331\pi$
$198$	−2.31199	+	8.48903i	−0.164306	+	0.603289i
$199$			5.08586i			0.360527i	0.983618	+	0.180263i	$0.0576950\pi$
$199$			5.08586i			0.360527i	−0.983618	+	0.180263i	$0.942305\pi$
$200$	−9.26054	+	4.12306i	−0.654819	+	0.291544i
$201$	1.93845	−	1.74539i	0.136728	−	0.123110i
$202$	1.41805	−	6.67140i	0.0997736	−	0.469398i
$203$	26.4173	+	11.7618i	1.85413	+	0.825513i
$204$	−3.47222	+	2.52271i	−0.243104	+	0.176625i
$205$	21.2267	−	23.5746i	1.48254	−	1.64652i
$206$	4.35935	+	4.84155i	0.303730	+	0.337327i
$207$	14.6983	+	10.6790i	1.02161	+	0.742240i
$208$	−3.77828	−	2.18139i	−0.261977	−	0.151252i
$209$	−1.27239	−	8.25248i	−0.0880128	−	0.570836i
$210$	−5.67832	−	9.83513i	−0.391841	−	0.678689i
$211$	−13.0209	−	9.46027i	−0.896399	−	0.651272i	0.0411396	−	0.999153i	$-0.486901\pi$
$211$	−13.0209	−	9.46027i	−0.896399	−	0.651272i	−0.937539	+	0.347881i	$0.886901\pi$
$212$	−7.18300	+	1.52679i	−0.493330	+	0.104861i
$213$	−1.15097	−	3.54232i	−0.0788632	−	0.242716i
$214$	1.55405	+	2.13896i	0.106233	+	0.146217i
$215$	−24.4629	+	7.24254i	−1.66836	+	0.493937i
$216$	−3.16794	+	1.02933i	−0.215551	+	0.0700368i
$217$	5.17691	−	15.9329i	0.351431	−	1.08159i
$218$	−2.10087	−	0.220811i	−0.142289	−	0.0149552i
$219$			7.54447i			0.509808i
$220$	−2.07085	+	12.7365i	−0.139617	+	0.858693i
$221$	−15.8881	−	27.5191i	−1.06875	−	1.85113i
$222$	1.14706	−	0.510702i	0.0769854	−	0.0342761i
$223$	1.65524	+	0.537819i	0.110843	+	0.0360150i	0.363913	−	0.931433i	$-0.381440\pi$
$223$	1.65524	+	0.537819i	0.110843	+	0.0360150i	−0.253070	+	0.967448i	$0.581440\pi$
$224$	4.84535	+	1.02991i	0.323744	+	0.0688138i
$225$	−24.5661	−	10.9375i	−1.63774	−	0.729168i
$226$	−3.70811	−	5.10378i	−0.246660	−	0.339498i
$227$	12.1008	−	13.4393i	0.803160	−	0.892000i	−0.192851	−	0.981228i	$-0.561773\pi$
$227$	12.1008	−	13.4393i	0.803160	−	0.892000i	0.996011	+	0.0892280i	$0.0284400\pi$
$228$	1.10249	−	0.992683i	0.0730139	−	0.0657420i
$229$	−8.06710	+	3.59170i	−0.533089	+	0.237346i	−0.655583	−	0.755123i	$-0.727577\pi$
$229$	−8.06710	+	3.59170i	−0.533089	+	0.237346i	0.122495	+	0.992469i	$0.460911\pi$
$230$	23.0760	+	13.3229i	1.52159	+	0.878489i
$231$	−9.66572	−	0.546325i	−0.635958	−	0.0359456i
$232$	2.91883	−	5.05555i	0.191630	−	0.331913i
$233$	19.2603	−	8.57524i	1.26178	−	0.561782i	0.336724	−	0.941603i	$-0.390681\pi$
$233$	19.2603	−	8.57524i	1.26178	−	0.561782i	0.925060	+	0.379821i	$0.124014\pi$
$234$	−2.40626	−	11.3205i	−0.157302	−	0.740047i
$235$	5.11653	+	4.60694i	0.333766	+	0.300524i
$236$	−3.82495	+	2.77899i	−0.248983	+	0.180897i
$237$	−2.41554	+	1.75499i	−0.156906	+	0.113999i
$238$	26.8123	+	24.1419i	1.73798	+	1.56489i
$239$	−1.06005	−	4.98715i	−0.0685690	−	0.322592i	0.930473	−	0.366361i	$-0.119397\pi$
$239$	−1.06005	−	4.98715i	−0.0685690	−	0.322592i	−0.999042	+	0.0437695i	$0.986063\pi$
$240$	−2.09440	+	0.932485i	−0.135193	+	0.0601917i
$241$	4.38275	−	7.59114i	0.282317	−	0.488988i	−0.689638	−	0.724155i	$-0.742230\pi$
$241$	4.38275	−	7.59114i	0.282317	−	0.488988i	0.971955	+	0.235166i	$0.0755635\pi$
$242$	8.11393	+	7.42725i	0.521583	+	0.477442i
$243$	−11.7137	−	6.76292i	−0.751435	−	0.433841i
$244$	−4.28913	+	1.90964i	−0.274584	+	0.122252i
$245$	−50.7079	+	45.6576i	−3.23961	+	2.91696i
$246$	3.21494	−	3.57056i	0.204977	−	0.227650i
$247$	6.45612	+	8.88609i	0.410793	+	0.565409i
$248$	−3.08957	−	1.37556i	−0.196188	−	0.0873484i
$249$	−3.12376	−	0.663975i	−0.197960	−	0.0420777i
$250$	−19.0077	−	6.17596i	−1.20215	−	0.390602i
$251$	−4.39423	+	1.95644i	−0.277362	+	0.123489i	−0.540704	−	0.841213i	$-0.681842\pi$
$251$	−4.39423	+	1.95644i	−0.277362	+	0.123489i	0.263342	+	0.964703i	$0.415175\pi$
$252$	6.57037	+	11.3802i	0.413895	+	0.716887i
$253$	20.2811	−	10.2292i	1.27506	−	0.643102i
$254$		−	13.2249i		−	0.829803i
$255$	−16.6067	−	1.74543i	−1.03995	−	0.109303i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−11.6384	+	3.78153i	−0.725981	+	0.235886i	−0.648615	−	0.761117i	$-0.724651\pi$
$257$	−11.6384	+	3.78153i	−0.725981	+	0.235886i	−0.0773668	+	0.997003i	$0.524651\pi$
$258$	−3.70509	+	1.09694i	−0.230669	+	0.0682924i
$259$	−6.20418	−	8.53932i	−0.385509	−	0.530607i
$260$	−5.24523	−	16.1432i	−0.325296	−	1.00116i
$261$	15.1475	−	3.21971i	0.937608	−	0.199295i
$262$	−9.66542	−	7.02234i	−0.597132	−	0.433842i
$263$	−11.2052	−	19.4080i	−0.690943	−	1.19675i	−0.971529	−	0.236919i	$-0.923862\pi$
$263$	−11.2052	−	19.4080i	−0.690943	−	1.19675i	0.280587	−	0.959829i	$-0.409471\pi$
$264$	−0.313646	+	1.92904i	−0.0193036	+	0.118724i
$265$	−24.7429	−	14.2853i	−1.51995	−	0.877541i
$266$	−10.0895	−	7.33043i	−0.618625	−	0.449457i
$267$	−0.220443	−	0.244826i	−0.0134909	−	0.0149831i
$268$	−2.96199	+	3.28962i	−0.180932	+	0.200945i
$269$	17.7760	−	12.9150i	1.08382	−	0.787442i	0.105476	−	0.994422i	$-0.466363\pi$
$269$	17.7760	−	12.9150i	1.08382	−	0.787442i	0.978345	+	0.206980i	$0.0663634\pi$
$270$	−11.8391	−	5.27112i	−0.720507	−	0.320790i
$271$	3.23410	−	15.2152i	0.196457	−	0.924260i	−0.763867	−	0.645374i	$-0.776702\pi$
$271$	3.23410	−	15.2152i	0.196457	−	0.924260i	0.960324	−	0.278886i	$-0.0899651\pi$
$272$	5.41269	−	4.87360i	0.328192	−	0.295506i
$273$	11.6339	−	5.17973i	0.704114	−	0.313492i
$274$			14.8663i			0.898108i
$275$	−26.2145	+	21.0506i	−1.58079	+	1.26940i
$276$	3.49504	+	2.01786i	0.210377	+	0.121461i
$277$	1.56196	−	14.8611i	0.0938491	−	0.892915i	−0.841754	−	0.539861i	$-0.818477\pi$
$277$	1.56196	−	14.8611i	0.0938491	−	0.892915i	0.935603	−	0.353053i	$-0.114857\pi$
$278$	2.74446	+	12.9117i	0.164602	+	0.774391i
$279$	−2.77236	−	8.53243i	−0.165977	−	0.510823i
$280$	11.3281	+	15.5918i	0.676985	+	0.931791i
$281$	5.67033	−	12.7358i	0.338264	−	0.759753i	−0.661687	−	0.749781i	$-0.730159\pi$
$281$	5.67033	−	12.7358i	0.338264	−	0.759753i	0.999950	−	0.00997225i	$-0.00317432\pi$
$282$	0.774937	+	0.697756i	0.0461468	+	0.0415508i
$283$	17.5894	−	15.8376i	1.04558	−	0.941448i	0.0472344	−	0.998884i	$-0.484959\pi$
$283$	17.5894	−	15.8376i	1.04558	−	0.941448i	0.998349	+	0.0574361i	$0.0182926\pi$
$284$	2.57090	+	5.77434i	0.152555	+	0.342644i
$285$	5.77189			0.341898
$286$	−13.9612	−	3.80234i	−0.825542	−	0.224837i
$287$	−34.9787	−	20.1950i	−2.06473	−	1.19207i
$288$	2.42342	−	1.07898i	0.142802	−	0.0635794i
$289$	35.2614	−	7.49505i	2.07420	−	0.440885i
$290$	21.6005	−	7.01842i	1.26842	−	0.412136i
$291$	3.37747	−	7.58592i	0.197991	−	0.444695i
$292$	−1.33830	−	12.7331i	−0.0783181	−	0.745147i
$293$	−20.2958	+	6.59451i	−1.18569	+	0.385256i	−0.834479	−	0.551039i	$-0.814231\pi$
$293$	−20.2958	+	6.59451i	−1.18569	+	0.385256i	−0.351215	+	0.936295i	$0.614231\pi$
$294$	−7.68010	+	6.91519i	−0.447913	+	0.403302i
$295$	−18.2937	−	1.92274i	−1.06510	−	0.111947i
$296$	−1.84534	+	1.06540i	−0.107258	+	0.0619254i
$297$	−9.28989	+	5.97889i	−0.539054	+	0.346930i
$298$	0.771787	+	1.33677i	0.0447084	+	0.0774373i
$299$	−17.5628	+	24.1731i	−1.01568	+	1.39797i
$300$	−5.68097	−	1.84586i	−0.327991	−	0.106571i
$301$	15.4955	+	28.5487i	0.893148	+	1.64552i
$302$	2.32062	−	1.68603i	0.133537	−	0.0970201i
$303$	3.25147	−	2.36233i	0.186792	−	0.135712i
$304$	−1.68461	+	1.87095i	−0.0966193	+	0.107307i
$305$	−17.3726	−	5.64470i	−0.994752	−	0.323214i
$306$	19.2156	+	2.01964i	1.09848	+	0.115455i
$307$	1.57211	−	0.907659i	0.0897251	−	0.0518028i	−0.454466	−	0.890764i	$-0.650170\pi$
$307$	1.57211	−	0.907659i	0.0897251	−	0.0518028i	0.544191	+	0.838961i	$0.316837\pi$
$308$	16.4101	−	0.792533i	0.935052	−	0.0451587i
$309$			3.83902i			0.218394i
$310$	−5.35180	−	12.0203i	−0.303962	−	0.682709i
$311$	−21.3630	+	4.54085i	−1.21139	+	0.257488i	−0.768948	−	0.639311i	$-0.779220\pi$
$311$	−21.3630	+	4.54085i	−1.21139	+	0.257488i	−0.442438	+	0.896799i	$0.645886\pi$
$312$	−0.794430	−	2.44500i	−0.0449758	−	0.138421i
$313$	7.93897	−	17.8312i	0.448737	−	1.00788i	−0.537609	−	0.843194i	$-0.680672\pi$
$313$	7.93897	−	17.8312i	0.448737	−	1.00788i	0.986346	−	0.164685i	$-0.0526609\pi$
$314$	15.1090	−	1.58802i	0.852648	−	0.0896169i
$315$	−10.6296	+	50.0084i	−0.598911	+	2.81766i
$316$	3.76548	−	3.39045i	0.211825	−	0.190728i
$317$	23.1640	+	16.8297i	1.30102	+	0.945248i	0.999965	−	0.00835830i	$-0.00266056\pi$
$317$	23.1640	+	16.8297i	1.30102	+	0.945248i	0.301057	+	0.953606i	$0.402661\pi$
$318$	−3.74750	−	2.16362i	−0.210150	−	0.121330i
$319$	5.08774	−	18.6809i	0.284859	−	1.04593i
$320$	3.36938	−	1.94531i	0.188354	−	0.108746i
$321$	−0.162851	+	1.54942i	−0.00908945	+	0.0864804i
$322$	10.4837	−	32.2655i	0.584234	−	1.79809i
$323$	−17.4396	+	5.66645i	−0.970363	+	0.315290i
$324$	5.47715	+	2.43858i	0.304286	+	0.135477i
$325$	17.9880	−	40.4017i	0.997795	−	2.24109i
$326$	−0.187116	+	0.880314i	−0.0103634	+	0.0487561i
$327$	−0.832925	−	0.925057i	−0.0460609	−	0.0511558i
$328$	−4.79260	+	6.59645i	−0.264627	+	0.364228i
$329$	4.38302	−	7.59162i	0.241644	−	0.418540i
$330$	−5.92877	+	4.76089i	−0.326368	+	0.262078i
$331$	20.5540	+	11.8669i	1.12975	+	0.652262i	0.943872	−	0.330310i	$-0.107153\pi$
$331$	20.5540	+	11.8669i	1.12975	+	0.652262i	0.185879	+	0.982573i	$0.440487\pi$
$332$	5.38986	+	0.566497i	0.295807	+	0.0310905i
$333$	−5.37589	−	1.74673i	−0.294597	−	0.0957203i
$334$	5.39751	+	4.85994i	0.295339	+	0.265924i
$335$	−17.1280	+	1.80022i	−0.935800	+	0.0983565i
$336$	1.71573	+	2.36150i	0.0936008	+	0.128830i
$337$	6.54023	−	30.7694i	0.356269	−	1.67611i	−0.326279	−	0.945274i	$-0.605795\pi$
$337$	6.54023	−	30.7694i	0.356269	−	1.67611i	0.682548	−	0.730841i	$-0.260872\pi$
$338$	5.90201	−	1.25451i	0.321027	−	0.0682364i
$339$	0.388578	−	3.69708i	0.0211047	−	0.200798i
$340$	28.3373			1.53681
$341$	−11.0713	−	1.80010i	−0.599543	−	0.0974810i
$342$	−6.67865			−0.361140
$343$	42.2321	+	30.6834i	2.28032	+	1.65675i
$344$	6.05863	−	2.50858i	0.326660	−	0.135254i
$345$	4.85202	+	14.9330i	0.261224	+	0.803965i
$346$	−2.83816	−	3.90640i	−0.152581	−	0.210009i
$347$	−10.5230	−	4.68515i	−0.564906	−	0.251512i	0.104355	−	0.994540i	$-0.466722\pi$
$347$	−10.5230	−	4.68515i	−0.564906	−	0.251512i	−0.669260	+	0.743028i	$0.733389\pi$
$348$	3.27156	−	1.06299i	0.175374	−	0.0569824i
$349$	−18.1461	+	3.85707i	−0.971339	+	0.206464i	−0.666142	−	0.745825i	$-0.732056\pi$
$349$	−18.1461	+	3.85707i	−0.971339	+	0.206464i	−0.305197	+	0.952289i	$0.598722\pi$
$350$	−5.24882	+	49.9392i	−0.280561	+	2.66936i
$351$	7.26615	−	12.5853i	0.387839	−	0.671756i
$352$	0.187163	−	3.31134i	0.00997583	−	0.176495i
$353$	4.41436	−	7.64589i	0.234952	−	0.406950i	−0.724306	−	0.689478i	$-0.757840\pi$
$353$	4.41436	−	7.64589i	0.234952	−	0.406950i	0.959259	+	0.282529i	$0.0911732\pi$
$354$	−2.77072	−	0.291214i	−0.147262	−	0.0154779i
$355$	−7.59930	+	23.3882i	−0.403329	+	1.24132i
$356$	0.415478	+	0.374098i	0.0220203	+	0.0198272i
$357$	2.22231	+	21.1439i	0.117617	+	1.11905i
$358$	14.0319	−	1.47482i	0.741611	−	0.0779465i
$359$	4.34137	−	20.4245i	0.229129	−	1.07797i	−0.701690	−	0.712483i	$-0.747571\pi$
$359$	4.34137	−	20.4245i	0.229129	−	1.07797i	0.930818	−	0.365483i	$-0.119096\pi$
$360$	9.81577	+	3.18934i	0.517337	+	0.168093i
$361$	−11.5670	+	5.14994i	−0.608787	+	0.271049i
$362$	2.22227	−	3.84909i	0.116800	−	0.202304i
$363$	0.624635	+	6.45174i	0.0327849	+	0.338628i
$364$	−18.7161	+	10.8057i	−0.980989	+	0.566374i
$365$	29.2790	−	40.2991i	1.53253	−	2.10935i
$366$	−2.63121	−	0.854932i	−0.137536	−	0.0446880i
$367$	−2.82709	+	3.13980i	−0.147573	+	0.163896i	−0.812399	−	0.583102i	$-0.801839\pi$
$367$	−2.82709	+	3.13980i	−0.147573	+	0.163896i	0.664826	+	0.746998i	$0.268506\pi$
$368$	−6.25665	−	2.78564i	−0.326150	−	0.145211i
$369$	−21.5113	+	2.26093i	−1.11983	+	0.117699i
$370$	−8.10901	−	1.72362i	−0.421567	−	0.0896069i
$371$	−11.2410	+	34.5962i	−0.583603	+	1.79615i
$372$	−0.810570	−	1.82057i	−0.0420261	−	0.0943921i
$373$	4.10215	−	7.10512i	0.212401	−	0.367889i	−0.740064	−	0.672536i	$-0.765205\pi$
$373$	4.10215	−	7.10512i	0.212401	−	0.367889i	0.952465	+	0.304647i	$0.0985384\pi$
$374$	13.2396	−	20.2053i	0.684604	−	1.04479i
$375$	−5.88847	−	10.1991i	−0.304079	−	0.526681i
$376$	−1.43166	−	1.04016i	−0.0738324	−	0.0536424i
$377$	5.29518	+	24.9119i	0.272715	+	1.28303i
$378$	−3.43061	+	16.1397i	−0.176451	+	0.830138i
$379$	7.31170	−	5.31226i	0.375577	−	0.272872i	−0.383943	−	0.923357i	$-0.625434\pi$
$379$	7.31170	−	5.31226i	0.375577	−	0.272872i	0.759520	+	0.650484i	$0.225434\pi$
$380$	−9.74143	+	1.02387i	−0.499725	+	0.0525232i
$381$	5.21450	−	5.79129i	0.267147	−	0.296697i
$382$	4.12288	+	19.3966i	0.210945	+	0.992418i
$383$	−7.88608	+	10.8543i	−0.402960	+	0.554627i	−0.961484	−	0.274862i	$-0.911368\pi$
$383$	−7.88608	+	10.8543i	−0.402960	+	0.554627i	0.558524	+	0.829488i	$0.311368\pi$
$384$	0.510318	−	0.294632i	0.0260420	−	0.0150354i
$385$	49.5097	+	40.4295i	2.52325	+	2.06048i
$386$			11.0252i			0.561169i
$387$	15.6998	+	7.49108i	0.798064	+	0.380793i
$388$	−4.35463	+	13.4022i	−0.221073	+	0.680392i
$389$	7.18802	−	2.33553i	0.364447	−	0.118416i	−0.121068	−	0.992644i	$-0.538632\pi$
$389$	7.18802	−	2.33553i	0.364447	−	0.118416i	0.485515	+	0.874228i	$0.338632\pi$
$390$	4.06823	−	9.13740i	0.206003	−	0.462690i
$391$	−29.3204	−	40.3560i	−1.48279	−	2.04089i
$392$	11.7353	−	13.0334i	0.592722	−	0.658285i
$393$	−1.46370	−	6.88617i	−0.0738339	−	0.347361i
$394$	−7.28716	−	16.3672i	−0.367122	−	0.824570i
$395$	19.7136			0.991899
$396$	6.86017	−	5.50882i	0.344736	−	0.276828i
$397$	11.7712	+	20.3883i	0.590780	+	1.02326i	0.994128	+	0.108214i	$0.0345131\pi$
$397$	11.7712	+	20.3883i	0.590780	+	1.02326i	−0.403348	+	0.915047i	$0.632154\pi$
$398$	2.98939	−	4.11455i	0.149845	−	0.206244i
$399$	−1.52792	−	7.18828i	−0.0764914	−	0.359864i
$400$	9.91541	+	2.10759i	0.495771	+	0.105379i
$401$	−3.65368	−	34.7624i	−0.182456	−	1.73595i	−0.576709	−	0.816950i	$-0.695663\pi$
$401$	−3.65368	−	34.7624i	−0.182456	−	1.73595i	0.394253	−	0.919002i	$-0.371003\pi$
$402$	−2.59416	+	0.272657i	−0.129385	+	0.0135989i
$403$	14.0326	−	4.55946i	0.699012	−	0.227123i
$404$	−5.06858	+	4.56377i	−0.252171	+	0.227056i
$405$	9.48760	+	21.3095i	0.471443	+	1.05888i
$406$	−14.4587	−	25.0432i	−0.717573	−	1.24287i
$407$	−5.01765	+	4.97665i	−0.248716	+	0.246683i
$408$	4.29190			0.212481
$409$	−29.7404	−	21.6077i	−1.47057	−	1.06843i	−0.980449	−	0.196774i	$-0.936954\pi$
$409$	−29.7404	−	21.6077i	−1.47057	−	1.06843i	−0.490118	−	0.871656i	$-0.663046\pi$
$410$	−31.0296	+	6.59554i	−1.53244	+	0.325731i
$411$	−5.86172	+	6.51009i	−0.289137	+	0.321119i
$412$	−0.680997	−	6.47926i	−0.0335503	−	0.319210i
$413$	2.44807	+	23.2918i	0.120462	+	1.14612i
$414$	−5.61427	−	17.2789i	−0.275926	−	0.849213i
$415$	14.1089	+	15.6695i	0.692578	+	0.769186i
$416$	1.77450	+	3.98560i	0.0870022	+	0.195410i
$417$	−3.88918	+	6.73626i	−0.190454	+	0.329876i
$418$	−3.82130	+	7.42428i	−0.186906	+	0.363134i
$419$		−	19.3370i		−	0.944673i	−0.881418	−	0.472337i	$-0.843411\pi$
$419$		−	19.3370i		−	0.944673i	0.881418	−	0.472337i	$-0.156589\pi$
$420$	−1.18709	+	11.2944i	−0.0579241	+	0.551111i
$421$	0.280240	−	0.252329i	0.0136580	−	0.0122978i	−0.662273	−	0.749262i	$-0.730408\pi$
$421$	0.280240	−	0.252329i	0.0136580	−	0.0122978i	0.675931	+	0.736965i	$0.263742\pi$
$422$	4.97356	+	15.3070i	0.242109	+	0.745135i
$423$	−0.490701	−	4.66871i	−0.0238587	−	0.227000i
$424$	6.70860	+	2.98686i	0.325798	+	0.145055i
$425$	54.8680	+	49.4034i	2.66149	+	2.39642i
$426$	−1.15097	+	3.54232i	−0.0557647	+	0.171626i
$427$	−2.43105	+	23.1299i	−0.117647	+	1.11934i
$428$		−	2.64390i		−	0.127798i
$429$	−4.61448	−	7.16990i	−0.222789	−	0.346166i
$430$	24.0480	+	8.51959i	1.15970	+	0.410851i
$431$	−16.0958	+	22.1540i	−0.775307	+	1.06712i	0.220477	+	0.975392i	$0.429239\pi$
$431$	−16.0958	+	22.1540i	−0.775307	+	1.06712i	−0.995784	+	0.0917268i	$0.970761\pi$
$432$	3.16794	+	1.02933i	0.152418	+	0.0495235i
$433$	−20.4085	−	18.3759i	−0.980768	−	0.883088i	0.0123831	−	0.999923i	$-0.496058\pi$
$433$	−20.4085	−	18.3759i	−0.980768	−	0.883088i	−0.993151	+	0.116836i	$0.962725\pi$
$434$	−13.5533	+	9.84707i	−0.650580	+	0.472674i
$435$	12.2264	+	5.44352i	0.586209	+	0.260997i
$436$	1.56985	+	1.41350i	0.0751823	+	0.0676944i
$437$	11.5375	+	12.8137i	0.551914	+	0.612962i
$438$	4.43453	−	6.10361i	0.211890	−	0.291642i
$439$	15.5297	+	8.96606i	0.741191	+	0.427927i	0.822502	−	0.568762i	$-0.192577\pi$
$439$	15.5297	+	8.96606i	0.741191	+	0.427927i	−0.0813112	+	0.996689i	$0.525911\pi$
$440$	9.16166	−	9.08681i	0.436765	−	0.433197i
$441$	46.5246			2.21546
$442$	−3.32152	+	31.6022i	−0.157989	+	1.50316i
$443$	10.2864	+	11.4242i	0.488723	+	0.542782i	0.936179	−	0.351524i	$-0.114336\pi$
$443$	10.2864	+	11.4242i	0.488723	+	0.542782i	−0.447456	+	0.894306i	$0.647670\pi$
$444$	−1.22817	−	0.261056i	−0.0582864	−	0.0123892i
$445$	0.227367	+	2.16326i	0.0107782	+	0.102548i
$446$	−1.02299	−	1.40803i	−0.0484401	−	0.0666720i
$447$	−0.189111	+	0.889697i	−0.00894464	+	0.0420812i
$448$	−3.31460	−	3.68124i	−0.156600	−	0.173922i
$449$	34.8955	+	3.66766i	1.64682	+	0.173088i	0.882030	−	0.471193i	$-0.156176\pi$
$449$	34.8955	+	3.66766i	1.64682	+	0.173088i	0.764789	+	0.644281i	$0.222843\pi$
$450$	13.4455	+	23.2882i	0.633825	+	1.09782i
$451$	−9.79469	+	25.2065i	−0.461214	+	1.18693i
$452$			6.30862i			0.296732i
$453$	1.68101	+	0.176681i	0.0789808	+	0.00830121i
$454$	−17.6892	+	3.75996i	−0.830196	+	0.176464i
$455$	−82.2446	−	17.4816i	−3.85569	−	0.819552i
$456$	−1.47541	+	0.155072i	−0.0690926	+	0.00726192i
$457$	5.12852	−	3.72609i	0.239902	−	0.174299i	−0.461338	−	0.887225i	$-0.652630\pi$
$457$	5.12852	−	3.72609i	0.239902	−	0.174299i	0.701240	+	0.712926i	$0.252630\pi$
$458$	8.63757	+	1.83597i	0.403607	+	0.0857893i
$459$	16.2338	+	18.0295i	0.757731	+	0.841545i
$460$	−10.8379	−	24.3422i	−0.505318	−	1.13496i
$461$	30.5380	−	17.6311i	1.42230	−	0.821163i	0.425801	−	0.904817i	$-0.359992\pi$
$461$	30.5380	−	17.6311i	1.42230	−	0.821163i	0.996495	+	0.0836534i	$0.0266589\pi$
$462$	7.49861	+	6.12336i	0.348867	+	0.284884i
$463$	17.4364	−	10.0669i	0.810338	−	0.467849i	−0.0367351	−	0.999325i	$-0.511696\pi$
$463$	17.4364	−	10.0669i	0.810338	−	0.467849i	0.847073	+	0.531476i	$0.178362\pi$
$464$	−5.33296	+	2.37439i	−0.247576	+	0.110228i
$465$	2.39595	−	7.37399i	0.111110	−	0.341960i
$466$	−20.6223	−	4.38341i	−0.955310	−	0.203057i
$467$	0.0437196	−	0.0981959i	0.00202310	−	0.00454397i	−0.912531	−	0.409007i	$-0.865875\pi$
$467$	0.0437196	−	0.0981959i	0.00202310	−	0.00454397i	0.914554	+	0.404463i	$0.132542\pi$
$468$	−4.70735	+	10.5729i	−0.217597	+	0.488731i
$469$	6.77603	+	20.8545i	0.312888	+	0.962970i
$470$	−1.43147	−	6.73452i	−0.0660286	−	0.310640i
$471$	7.24249	+	5.26198i	0.333716	+	0.242459i
$472$	4.72790			0.217619
$473$	17.3103	−	13.1664i	0.795928	−	0.605391i
$474$	2.98577			0.137141
$475$	−20.6468	−	15.0008i	−0.947342	−	0.688284i
$476$	−7.50134	−	35.2910i	−0.343824	−	1.61756i
$477$	6.01981	+	18.5271i	0.275628	+	0.848297i
$478$	−2.07377	+	4.65777i	−0.0948522	+	0.213042i
$479$	0.587177	−	1.31882i	0.0268288	−	0.0602585i	−0.899634	−	0.436645i	$-0.856167\pi$
$479$	0.587177	−	1.31882i	0.0268288	−	0.0602585i	0.926463	+	0.376386i	$0.122833\pi$
$480$	2.24250	+	0.476659i	0.102356	+	0.0217564i
$481$	2.87270	−	8.84127i	0.130984	−	0.403127i
$482$	−8.00768	+	3.56525i	−0.364740	+	0.162393i
$483$	17.3130	−	9.99568i	0.787770	−	0.454819i
$484$	−2.19868	−	10.7780i	−0.0999401	−	0.489910i
$485$	−47.4808	+	27.4131i	−2.15599	+	1.24476i
$486$	5.50145	+	12.3565i	0.249551	+	0.560501i
$487$	−1.59068	−	1.76663i	−0.0720805	−	0.0800535i	0.706026	−	0.708186i	$-0.250486\pi$
$487$	−1.59068	−	1.76663i	−0.0720805	−	0.0800535i	−0.778106	+	0.628133i	$0.783820\pi$
$488$	4.59244	+	0.976154i	0.207890	+	0.0441884i
$489$	−0.429043	+	0.311718i	−0.0194020	+	0.0140964i
$490$	67.8605	−	7.13242i	3.06562	−	0.322210i
$491$	−17.2549	−	3.66763i	−0.778701	−	0.165518i	−0.198620	−	0.980077i	$-0.563646\pi$
$491$	−17.2549	−	3.66763i	−0.778701	−	0.165518i	−0.580081	+	0.814559i	$0.696979\pi$
$492$	−4.69967	+	0.998945i	−0.211877	+	0.0450359i
$493$	−42.2855	−	4.44439i	−1.90444	−	0.200165i
$494$		−	10.9838i		−	0.494185i
$495$	34.1761	+	1.93170i	1.53610	+	0.0868233i
$496$	1.69098	+	2.92886i	0.0759270	+	0.131509i
$497$	31.1392	+	3.27286i	1.39678	+	0.146808i
$498$	2.13690	+	2.37326i	0.0957566	+	0.106349i
$499$	1.61986	−	7.62085i	0.0725150	−	0.341156i	−0.926902	−	0.375304i	$-0.877538\pi$
$499$	1.61986	−	7.62085i	0.0725150	−	0.341156i	0.999417	+	0.0341478i	$0.0108717\pi$
$500$	11.7474	+	16.1689i	0.525359	+	0.723094i
$501$	0.447368	+	4.25642i	0.0199869	+	0.190163i
$502$	4.70497	+	1.00007i	0.209993	+	0.0446355i
$503$	4.53506	+	5.03670i	0.202209	+	0.224575i	0.835717	−	0.549161i	$-0.185052\pi$
$503$	4.53506	+	5.03670i	0.202209	+	0.224575i	−0.633508	+	0.773736i	$0.718386\pi$
$504$	1.37358	−	13.0688i	0.0611842	−	0.582129i
$505$	−26.5358			−1.18083
$506$	−22.4203	−	3.64537i	−0.996705	−	0.162056i
$507$	3.07919	+	1.77777i	0.136752	+	0.0789536i
$508$	−7.77339	+	10.6992i	−0.344889	+	0.474698i
$509$	1.65729	+	1.84061i	0.0734581	+	0.0815834i	0.778753	−	0.627330i	$-0.215852\pi$
$509$	1.65729	+	1.84061i	0.0734581	+	0.0815834i	−0.705295	+	0.708914i	$0.749186\pi$
$510$	12.4091	+	11.1732i	0.549486	+	0.494759i
$511$	−57.9389	−	25.7960i	−2.56306	−	1.14115i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−6.23210	−	5.61140i	−0.275154	−	0.247750i
$514$	11.6384	+	3.78153i	0.513346	+	0.166796i
$515$	14.8987	−	20.5063i	0.656515	−	0.903615i
$516$	3.64225	+	1.29036i	0.160341	+	0.0568048i
$517$	−5.47070	−	2.12579i	−0.240601	−	0.0934923i
$518$			10.5552i			0.463768i
$519$	0.297415	−	2.82972i	0.0130551	−	0.124211i
$520$	−5.24523	+	16.1432i	−0.230019	+	0.707925i
$521$	−0.197544	−	0.177869i	−0.00865456	−	0.00779260i	0.664792	−	0.747029i	$-0.268520\pi$
$521$	−0.197544	−	0.177869i	−0.00865456	−	0.00779260i	−0.673447	+	0.739236i	$0.735187\pi$
$522$	−14.1471	−	6.29870i	−0.619202	−	0.275686i
$523$	−3.32077	−	31.5950i	−0.145207	−	1.38155i	−0.788077	−	0.615577i	$-0.788923\pi$
$523$	−3.32077	−	31.5950i	−0.145207	−	1.38155i	0.642870	−	0.765975i	$-0.277744\pi$
$524$	3.69186	+	11.3624i	0.161280	+	0.496368i
$525$	−21.9893	+	19.7992i	−0.959690	+	0.864109i
$526$	−2.34253	+	22.2877i	−0.102139	+	0.971788i
$527$			24.6324i			1.07300i
$528$	1.38760	−	1.37627i	0.0603877	−	0.0598943i
$529$	−11.9527	+	20.7027i	−0.519683	+	0.900117i
$530$	11.6207	+	26.1006i	0.504773	+	1.13374i
$531$	8.39225	+	9.32054i	0.364193	+	0.404477i
$532$	3.85383	+	11.8609i	0.167085	+	0.514234i
$533$	−3.71836	−	35.3778i	−0.161060	−	1.53238i
$534$	0.0344365	+	0.327641i	0.00149021	+	0.0141784i
$535$	6.88296	−	7.64431i	0.297577	−	0.330492i
$536$	4.32989	−	0.920346i	0.187023	−	0.0397529i
$537$	6.72622	+	4.88689i	0.290258	+	0.210885i
$538$	−21.9723			−0.947294
$539$	26.6198	−	51.7188i	1.14660	−	2.22769i
$540$	6.47977	+	11.2233i	0.278845	+	0.482974i
$541$	−8.35022	−	18.7549i	−0.359004	−	0.806336i	−0.999271	−	0.0381834i	$-0.987843\pi$
$541$	−8.35022	−	18.7549i	−0.359004	−	0.806336i	0.640267	−	0.768153i	$-0.278824\pi$
$542$	−11.5597	+	10.4084i	−0.496533	+	0.447080i
$543$	2.49083	−	0.809319i	0.106892	−	0.0347312i
$544$	−7.24359	+	0.761332i	−0.310566	+	0.0326418i
$545$	0.859090	+	8.17370i	0.0367994	+	0.350123i
$546$	−12.4566	−	2.64773i	−0.533092	−	0.113312i
$547$	1.16274	+	5.47028i	0.0497153	+	0.233892i	0.995989	−	0.0894743i	$-0.0285187\pi$
$547$	1.16274	+	5.47028i	0.0497153	+	0.233892i	−0.946274	+	0.323366i	$0.895185\pi$
$548$	8.73821	−	12.0271i	0.373278	−	0.513773i
$549$	6.22743	+	10.7862i	0.265780	+	0.460345i
$550$	33.5812	−	1.62182i	1.43191	−	0.0691546i
$551$	14.6970			0.626112
$552$	−1.64148	−	3.68682i	−0.0698659	−	0.156921i
$553$	−5.21851	−	24.5512i	−0.221914	−	1.04402i
$554$	−9.99876	+	11.1048i	−0.424807	+	0.471796i
$555$	−2.87139	−	3.95213i	−0.121884	−	0.167759i
$556$	5.36897	−	12.0589i	0.227695	−	0.511412i
$557$	−19.5469	+	6.35116i	−0.828227	+	0.269107i	−0.692298	−	0.721611i	$-0.743402\pi$
$557$	−19.5469	+	6.35116i	−0.828227	+	0.269107i	−0.135929	+	0.990719i	$0.543402\pi$
$558$	−2.77236	+	8.53243i	−0.117363	+	0.361207i
$559$	−12.3199	+	25.8201i	−0.521078	+	1.09207i
$560$		−	19.2726i		−	0.814415i
$561$	13.7646	−	3.62776i	0.581141	−	0.153164i
$562$	−12.0733	+	6.97052i	−0.509281	+	0.294034i
$563$	18.3122	−	25.2046i	0.771768	−	1.06225i	−0.224375	−	0.974503i	$-0.572034\pi$
$563$	18.3122	−	25.2046i	0.771768	−	1.06225i	0.996143	−	0.0877441i	$-0.0279658\pi$
$564$	−0.216806	−	1.01999i	−0.00912919	−	0.0429495i
$565$	−16.4234	+	18.2401i	−0.690939	+	0.767366i
$566$	−23.5393	+	2.47408i	−0.989429	+	0.103993i
$567$	24.0272	−	17.4568i	1.00905	−	0.733115i
$568$	1.31417	−	6.18268i	0.0551413	−	0.259419i
$569$	−5.29745	−	24.9225i	−0.222080	−	1.04481i	−0.938003	−	0.346627i	$-0.887327\pi$
$569$	−5.29745	−	24.9225i	−0.222080	−	1.04481i	0.715923	−	0.698180i	$-0.246006\pi$
$570$	−4.66956	−	3.39263i	−0.195586	−	0.142102i
$571$	−20.0163	−	34.6692i	−0.837654	−	1.45086i	−0.891851	−	0.452329i	$-0.850593\pi$
$571$	−20.0163	−	34.6692i	−0.837654	−	1.45086i	0.0541970	−	0.998530i	$-0.482740\pi$
$572$	9.05988	+	11.2823i	0.378813	+	0.471738i
$573$	−5.84254	+	10.1196i	−0.244076	+	0.422752i
$574$	16.4281	+	36.8981i	0.685695	+	1.54010i
$575$	21.4536	−	66.0274i	0.894677	−	2.75353i
$576$	−2.59480	−	0.551541i	−0.108117	−	0.0229809i
$577$	−10.8632	+	1.14177i	−0.452241	+	0.0475324i	−0.327911	−	0.944709i	$-0.606345\pi$
$577$	−10.8632	+	1.14177i	−0.452241	+	0.0475324i	−0.124330	+	0.992241i	$0.539678\pi$
$578$	−32.9326	−	14.6625i	−1.36981	−	0.609881i
$579$	−4.34718	+	4.82803i	−0.180663	+	0.200646i
$580$	−21.6005	−	7.01842i	−0.896911	−	0.291424i
$581$	15.7798	−	21.7191i	0.654658	−	0.901059i
$582$	−7.19133	+	4.15191i	−0.298090	+	0.172102i
$583$	24.0399	+	3.90869i	0.995629	+	0.161881i
$584$	−6.40161	+	11.0879i	−0.264900	+	0.458821i
$585$	−41.1350	+	18.3145i	−1.70072	+	0.757211i
$586$	20.2958	+	6.59451i	0.838413	+	0.272417i
$587$	−0.210384	+	0.989779i	−0.00868348	+	0.0408526i	−0.982276	−	0.187440i	$-0.939981\pi$
$587$	−0.210384	+	0.989779i	−0.00868348	+	0.0408526i	0.973593	+	0.228293i	$0.0733143\pi$
$588$	10.2780	−	1.08026i	0.423857	−	0.0445491i
$589$	−0.890003	−	8.46781i	−0.0366719	−	0.348910i
$590$	13.6697	+	12.3083i	0.562775	+	0.506725i
$591$	3.26240	−	10.0406i	0.134197	−	0.413017i
$592$	2.11914	+	0.222730i	0.0870960	+	0.00915416i
$593$	−4.01819	+	6.95971i	−0.165007	+	0.285801i	−0.936658	−	0.350246i	$-0.886098\pi$
$593$	−4.01819	+	6.95971i	−0.165007	+	0.285801i	0.771651	+	0.636047i	$0.219431\pi$
$594$	11.0300	+	0.623436i	0.452566	+	0.0255799i
$595$	70.1858	−	121.565i	2.87734	−	4.98369i
$596$	0.161347	−	1.53512i	0.00660905	−	0.0628809i
$597$	2.93142	−	0.623093i	0.119975	−	0.0255015i
$598$	28.4172	−	9.23331i	1.16207	−	0.377578i
$599$	18.4543	+	8.21639i	0.754023	+	0.335713i	0.747496	−	0.664266i	$-0.231256\pi$
$599$	18.4543	+	8.21639i	0.754023	+	0.335713i	0.00652678	+	0.999979i	$0.497922\pi$
$600$	3.51103	+	4.83252i	0.143337	+	0.197287i
$601$	7.08521	+	21.8060i	0.289012	+	0.889487i	0.985167	+	0.171596i	$0.0548924\pi$
$601$	7.08521	+	21.8060i	0.289012	+	0.889487i	−0.696156	+	0.717891i	$0.745108\pi$
$602$	4.24435	−	32.2044i	0.172987	−	1.31255i
$603$	9.50012	+	6.90224i	0.386875	+	0.281081i
$604$	−2.86844			−0.116715
$605$	21.7018	−	36.8863i	0.882302	−	1.49964i
$606$	−4.01904			−0.163262
$607$	−3.49993	+	33.2996i	−0.142058	+	1.35159i	0.658611	+	0.752483i	$0.271144\pi$
$607$	−3.49993	+	33.2996i	−0.142058	+	1.35159i	−0.800669	+	0.599107i	$0.795523\pi$
$608$	2.46260	−	0.523442i	0.0998717	−	0.0212284i
$609$	3.54281	−	16.6676i	0.143562	−	0.675405i
$610$	10.7369	+	14.7780i	0.434722	+	0.598344i
$611$	7.67823	−	0.807014i	0.310628	−	0.0326483i
$612$	−14.3586	−	12.9285i	−0.580412	−	0.522605i
$613$	23.8010	+	7.73341i	0.961312	+	0.312349i	0.747304	−	0.664482i	$-0.231348\pi$
$613$	23.8010	+	7.73341i	0.961312	+	0.312349i	0.214009	+	0.976832i	$0.431348\pi$
$614$	−1.80537	−	0.189752i	−0.0728589	−	0.00765778i
$615$	−16.1887	−	9.34655i	−0.652792	−	0.376889i
$616$	−13.7419	−	9.00444i	−0.553677	−	0.362799i
$617$	−2.55598	+	4.42709i	−0.102900	+	0.178228i	−0.912878	−	0.408232i	$-0.866146\pi$
$617$	−2.55598	+	4.42709i	−0.102900	+	0.178228i	0.809978	+	0.586460i	$0.199479\pi$
$618$	2.25652	−	3.10583i	0.0907706	−	0.124935i
$619$	−10.2290	−	11.3605i	−0.411138	−	0.456616i	0.501636	−	0.865079i	$-0.332732\pi$
$619$	−10.2290	−	11.3605i	−0.411138	−	0.456616i	−0.912775	+	0.408463i	$0.866065\pi$
$620$	−2.73568	+	12.8704i	−0.109868	+	0.516886i
$621$	9.27888	−	20.8407i	0.372349	−	0.836309i
$622$	19.9521	+	8.88325i	0.800007	+	0.356186i
$623$	2.63392	−	0.855811i	0.105526	−	0.0342873i
$624$	−0.794430	+	2.44500i	−0.0318027	+	0.0978785i
$625$	−2.82987	+	26.9244i	−0.113195	+	1.07697i
$626$	−16.9037	+	9.75934i	−0.675607	+	0.390062i
$627$	−4.60074	+	1.74444i	−0.183736	+	0.0696661i
$628$	−13.1568	−	7.59609i	−0.525014	−	0.303117i
$629$	12.5557	+	9.12227i	0.500629	+	0.363729i
$630$	37.9938	−	34.2097i	1.51371	−	1.36295i
$631$	2.43358	−	11.4491i	0.0968791	−	0.455780i	−0.902791	−	0.430080i	$-0.858485\pi$
$631$	2.43358	−	11.4491i	0.0968791	−	0.455780i	0.999670	−	0.0257000i	$-0.00818146\pi$
$632$	−5.03920	+	0.529641i	−0.200449	+	0.0210680i
$633$	−3.85752	+	8.66413i	−0.153323	+	0.344368i
$634$	−8.84788	−	27.2310i	−0.351394	−	1.08148i
$635$	−50.3286	+	10.6977i	−1.99723	+	0.424525i
$636$	1.76005	+	3.95313i	0.0697905	+	0.156752i
$637$			76.5151i			3.03164i
$638$	−15.0964	+	12.1226i	−0.597672	+	0.479940i
$639$	14.5212	−	8.38381i	0.574449	−	0.331658i
$640$	−3.86931	−	0.406681i	−0.152948	−	0.0160755i
$641$	8.47857	+	2.75486i	0.334883	+	0.108810i	0.471632	−	0.881796i	$-0.343665\pi$
$641$	8.47857	+	2.75486i	0.334883	+	0.108810i	−0.136748	+	0.990606i	$0.543665\pi$
$642$	1.04248	−	1.15779i	0.0411433	−	0.0456943i
$643$	−30.5836	+	22.2203i	−1.20610	+	0.876282i	−0.994871	−	0.101155i	$-0.967746\pi$
$643$	−30.5836	+	22.2203i	−1.20610	+	0.876282i	−0.211227	+	0.977437i	$0.567746\pi$
$644$	−27.4467	+	19.9412i	−1.08155	+	0.785793i
$645$	7.17158	+	13.2128i	0.282381	+	0.520253i
$646$	17.4396	+	5.66645i	0.686150	+	0.222944i
$647$	−23.5042	+	32.3507i	−0.924045	+	1.27184i	0.0380923	+	0.999274i	$0.487872\pi$
$647$	−23.5042	+	32.3507i	−0.924045	+	1.27184i	−0.962137	+	0.272565i	$0.912128\pi$
$648$	−2.99774	−	5.19224i	−0.117762	−	0.203970i
$649$	15.1629	−	3.99629i	0.595195	−	0.156868i
$650$	−38.3002	+	22.1126i	−1.50226	+	0.867328i
$651$	−9.81776	−	1.03189i	−0.384788	−	0.0404429i
$652$	0.668816	−	0.602205i	0.0261929	−	0.0235841i
$653$	4.86894	−	1.58201i	0.190536	−	0.0619090i	−0.212195	−	0.977227i	$-0.568061\pi$
$653$	4.86894	−	1.58201i	0.190536	−	0.0619090i	0.402731	+	0.915318i	$0.368061\pi$
$654$	0.130116	+	1.23797i	0.00508793	+	0.0484084i
$655$	−18.9058	+	42.4632i	−0.738711	+	1.65917i
$656$	7.75459	−	2.51962i	0.302766	−	0.0983747i
$657$	−33.2218	+	7.06150i	−1.29610	+	0.275495i
$658$	−8.00818	+	3.56547i	−0.312192	+	0.138997i
$659$	−23.4838	−	13.5584i	−0.914800	−	0.528160i	−0.0328273	−	0.999461i	$-0.510451\pi$
$659$	−23.4838	−	13.5584i	−0.914800	−	0.528160i	−0.881972	+	0.471301i	$0.843784\pi$
$660$	7.59485	−	0.366796i	0.295629	−	0.0142775i
$661$	20.3923			0.793167			0.396583	−	0.917999i	$-0.370196\pi$
$661$	20.3923			0.793167			0.396583	+	0.917999i	$0.370196\pi$
$662$	−9.65338	−	21.6819i	−0.375189	−	0.842689i
$663$	−13.9151	+	12.5292i	−0.540418	+	0.486594i
$664$	−4.02751	−	3.62638i	−0.156298	−	0.140731i
$665$	−19.7353	+	44.3261i	−0.765300	+	1.71889i
$666$	3.32248	+	4.57300i	0.128744	+	0.177200i
$667$	12.3547	+	38.0238i	0.478376	+	1.47229i
$668$	−1.51008	−	7.10435i	−0.0584266	−	0.274876i
$669$	0.107201	−	1.01995i	0.00414462	−	0.0394334i
$670$	14.9149	+	8.61115i	0.576215	+	0.332678i
$671$	15.5536	−	0.751166i	0.600438	−	0.0289984i
$672$		−	2.91898i		−	0.112602i
$673$	−38.4670	+	17.1266i	−1.48279	+	0.660183i	−0.979041	−	0.203665i	$-0.934715\pi$
$673$	−38.4670	+	17.1266i	−1.48279	+	0.660183i	−0.503754	+	0.863847i	$0.668048\pi$
$674$	−23.3769	+	21.0487i	−0.900446	+	0.810765i
$675$	−7.02031	+	33.0280i	−0.270212	+	1.27125i
$676$	−5.51221	−	2.45420i	−0.212008	−	0.0943921i
$677$	−26.3350	+	19.1335i	−1.01214	+	0.735361i	−0.964656	−	0.263511i	$-0.915119\pi$
$677$	−26.3350	+	19.1335i	−1.01214	+	0.735361i	−0.0474812	+	0.998872i	$0.515119\pi$
$678$	−2.48745	+	2.76260i	−0.0955301	+	0.106097i
$679$	46.7090	+	51.8756i	1.79253	+	1.99080i
$680$	−22.9253	−	16.6562i	−0.879147	−	0.638738i
$681$	−9.22879	−	5.32825i	−0.353648	−	0.204179i
$682$	7.89878	+	7.96385i	0.302460	+	0.304951i
$683$	−4.89313	−	8.47516i	−0.187231	−	0.324293i	0.757095	−	0.653304i	$-0.226618\pi$
$683$	−4.89313	−	8.47516i	−0.187231	−	0.324293i	−0.944326	+	0.329012i	$0.893284\pi$
$684$	5.40314	+	3.92561i	0.206594	+	0.150100i
$685$	56.5753	−	12.0255i	2.16163	−	0.459469i
$686$	−16.1312	−	49.6468i	−0.615893	−	1.89552i
$687$	3.05855	+	4.20973i	0.116691	+	0.160611i
$688$	−6.37604	−	1.53169i	−0.243084	−	0.0583951i
$689$	−30.4699	+	9.90028i	−1.16081	+	0.377171i
$690$	4.85202	−	14.9330i	0.184713	−	0.568489i
$691$	33.1528	+	3.48450i	1.26119	+	0.132557i	0.711426	−	0.702761i	$-0.248050\pi$
$691$	33.1528	+	3.48450i	1.26119	+	0.132557i	0.549767	+	0.835318i	$0.314716\pi$
$692$			4.82857i			0.183555i
$693$	−6.64124	−	43.0740i	−0.252280	−	1.63624i
$694$	5.75944	+	9.97565i	0.218625	+	0.378670i
$695$	46.9167	−	20.8886i	1.77965	−	0.792351i
$696$	−3.27156	−	1.06299i	−0.124008	−	0.0402926i
$697$	58.0893	+	12.3473i	2.20029	+	0.467686i
$698$	16.9476	+	7.54557i	0.641477	+	0.285604i
$699$	−7.30233	−	10.0508i	−0.276199	−	0.380156i
$700$	33.5999	−	37.3165i	1.26996	−	1.41043i
$701$	6.41984	−	5.78045i	0.242474	−	0.218325i	−0.538929	−	0.842351i	$-0.681171\pi$
$701$	6.41984	−	5.78045i	0.242474	−	0.218325i	0.781403	+	0.624027i	$0.214504\pi$
$702$	−13.2759	+	5.91082i	−0.501067	+	0.223090i
$703$	−4.64585	−	2.68228i	−0.175221	−	0.101164i
$704$	−2.09777	+	2.56892i	−0.0790629	+	0.0968197i
$705$	2.02853	−	3.51352i	0.0763989	−	0.132327i
$706$	−8.06543	+	3.59096i	−0.303546	+	0.135148i
$707$	7.02445	+	33.0474i	0.264182	+	1.24288i
$708$	2.07039	+	1.86418i	0.0778099	+	0.0700604i
$709$	−27.3349	+	19.8600i	−1.02659	+	0.745858i	−0.967622	−	0.252402i	$-0.918779\pi$
$709$	−27.3349	+	19.8600i	−1.02659	+	0.745858i	−0.0589628	+	0.998260i	$0.518779\pi$
$710$	19.8952	−	14.4547i	0.746654	−	0.542476i
$711$	−9.98895	−	8.99409i	−0.374615	−	0.337305i
$712$	−0.116239	−	0.546864i	−0.00435626	−	0.0204946i
$713$	21.1597	−	9.42089i	0.792436	−	0.352815i
$714$	10.6302	−	18.4120i	0.397824	−	0.689051i
$715$	−3.17690	+	56.2064i	−0.118809	+	2.10200i
$716$	−12.2190	−	7.05462i	−0.456644	−	0.263644i
$717$	−2.74466	+	1.22200i	−0.102501	+	0.0456364i
$718$	−15.5175	+	13.9720i	−0.579107	+	0.521430i
$719$	15.8591	−	17.6133i	0.591445	−	0.656867i	−0.370908	−	0.928670i	$-0.620953\pi$
$719$	15.8591	−	17.6133i	0.591445	−	0.656867i	0.962353	+	0.271803i	$0.0876200\pi$
$720$	−6.06648	−	8.34979i	−0.226084	−	0.311178i
$721$	−29.4823	−	13.1264i	−1.09798	−	0.488852i
$722$	12.3849	+	2.63250i	0.460919	+	0.0979713i
$723$	−4.91239	−	1.59613i	−0.182694	−	0.0593608i
$724$	−4.06030	+	1.80776i	−0.150900	+	0.0671849i
$725$	−29.5879	−	51.2478i	−1.09887	−	1.90329i
$726$	3.28689	−	5.58672i	0.121988	−	0.207342i
$727$			12.6278i			0.468339i	0.972196	+	0.234170i	$0.0752371\pi$
$727$			12.6278i			0.468339i	−0.972196	+	0.234170i	$0.924763\pi$
$728$	21.4931	+	2.25901i	0.796587	+	0.0837246i
$729$	3.09516	−	9.52593i	0.114636	−	0.352812i
$730$	−47.3744	+	15.3929i	−1.75341	+	0.569716i
$731$	−34.6400	−	32.8813i	−1.28121	−	1.21616i
$732$	1.62618	+	2.23824i	0.0601052	+	0.0827278i
$733$	−11.2879	−	34.7405i	−0.416928	−	1.28317i	−0.910515	−	0.413475i	$-0.864315\pi$
$733$	−11.2879	−	34.7405i	−0.416928	−	1.28317i	0.493588	−	0.869696i	$-0.335685\pi$
$734$	4.13269	−	0.878430i	0.152540	−	0.0324234i
$735$	32.5289	+	23.6337i	1.19985	+	0.871741i
$736$	3.42438	+	5.93119i	0.126224	+	0.218627i
$737$	13.1085	−	6.61152i	0.482857	−	0.243538i
$738$	18.7319	+	10.8149i	0.689532	+	0.398102i
$739$	11.4202	+	8.29725i	0.420098	+	0.305219i	0.777677	−	0.628664i	$-0.216398\pi$
$739$	11.4202	+	8.29725i	0.420098	+	0.305219i	−0.357579	+	0.933883i	$0.616398\pi$
$740$	5.54721	+	6.16080i	0.203919	+	0.226475i
$741$	4.33086	−	4.80991i	0.159098	−	0.176696i
$742$	29.4293	−	21.3816i	1.08038	−	0.784945i
$743$	24.9874	+	11.1251i	0.916700	+	0.408141i	0.810188	−	0.586170i	$-0.199365\pi$
$743$	24.9874	+	11.1251i	0.916700	+	0.408141i	0.106512	+	0.994311i	$0.466032\pi$
$744$	−0.414339	+	1.94931i	−0.0151904	+	0.0714653i
$745$	4.46293	−	4.01844i	0.163509	−	0.147224i
$746$	−7.49499	+	3.33699i	−0.274411	+	0.122176i
$747$		−	14.3768i		−	0.526019i
$748$	−22.5874	+	8.56437i	−0.825879	+	0.313144i
$749$	−11.3422	−	6.54842i	−0.414435	−	0.239274i
$750$	−1.23102	+	11.7124i	−0.0449507	+	0.427677i
$751$	1.48888	+	7.00462i	0.0543299	+	0.255602i	0.996928	−	0.0783283i	$-0.0249582\pi$
$751$	1.48888	+	7.00462i	0.0543299	+	0.255602i	−0.942598	+	0.333931i	$0.891625\pi$
$752$	0.546846	+	1.68302i	0.0199414	+	0.0613734i
$753$	1.66602	+	2.29309i	0.0607133	+	0.0835647i
$754$	10.3589	−	23.2665i	0.377250	−	0.847317i
$755$	−8.29351	−	7.46751i	−0.301832	−	0.271771i
$756$	12.2621	−	11.0409i	0.445969	−	0.401552i
$757$	7.28139	+	16.3543i	0.264647	+	0.594406i	0.996173	−	0.0874076i	$-0.0278583\pi$
$757$	7.28139	+	16.3543i	0.264647	+	0.594406i	−0.731526	+	0.681813i	$0.761192\pi$
$758$	−9.03775			−0.328266
$759$	−8.38070	−	10.4365i	−0.304200	−	0.378823i
$760$	8.48280	+	4.89755i	0.307703	+	0.177653i
$761$	−10.2150	+	4.54801i	−0.370293	+	0.164865i	−0.583442	−	0.812155i	$-0.698295\pi$
$761$	−10.2150	+	4.54801i	−0.370293	+	0.164865i	0.213149	+	0.977020i	$0.431628\pi$
$762$	−7.62265	+	1.62025i	−0.276140	+	0.0586953i
$763$	9.95205	−	3.23362i	0.360288	−	0.117065i
$764$	8.06558	−	18.1156i	0.291802	−	0.655399i
$765$	−7.85764	−	74.7604i	−0.284094	−	2.70297i
$766$	12.7599	−	4.14596i	0.461036	−	0.149800i
$767$	−15.3287	+	13.8020i	−0.553487	+	0.498362i
$768$	−0.586036	−	0.0615949i	−0.0211467	−	0.00222261i
$769$	19.7187	−	11.3846i	0.711076	−	0.410540i	−0.100384	−	0.994949i	$-0.532007\pi$
$769$	19.7187	−	11.3846i	0.711076	−	0.410540i	0.811459	+	0.584409i	$0.198674\pi$
$770$	−16.2903	−	61.8092i	−0.587061	−	2.22745i
$771$	3.60550	+	6.24491i	0.129849	+	0.224905i
$772$	6.48046	−	8.91959i	0.233237	−	0.321023i
$773$	37.1627	+	12.0749i	1.33665	+	0.434304i	0.888181	−	0.459494i	$-0.151969\pi$
$773$	37.1627	+	12.0749i	1.33665	+	0.434304i	0.448469	+	0.893798i	$0.351969\pi$
$774$	−8.29822	−	15.2885i	−0.298274	−	0.549534i
$775$	−27.7352	+	20.1508i	−0.996278	+	0.723838i
$776$	11.4006	−	8.28299i	0.409256	−	0.297342i
$777$	−4.16185	+	4.62220i	−0.149305	+	0.165821i
$778$	−7.18802	−	2.33553i	−0.257703	−	0.0837327i
$779$	−20.4153	−	2.14574i	−0.731456	−	0.0768791i
$780$	−8.66209	+	5.00106i	−0.310153	+	0.179067i
$781$	−1.01127	−	20.9393i	−0.0361862	−	0.749268i
$782$			49.8828i			1.78381i
$783$	−7.90901	−	17.7639i	−0.282645	−	0.634831i
$784$	−17.1549	+	3.64638i	−0.612675	+	0.130228i
$785$	−18.2651	−	56.2141i	−0.651909	−	2.00637i
$786$	−2.86343	+	6.43137i	−0.102135	+	0.229399i
$787$	31.7253	−	3.33446i	1.13089	−	0.118861i	0.479453	−	0.877568i	$-0.340835\pi$
$787$	31.7253	−	3.33446i	1.13089	−	0.118861i	0.651432	+	0.758707i	$0.274168\pi$
$788$	−3.72498	+	17.5247i	−0.132697	+	0.624290i
$789$	−9.81371	+	8.83631i	−0.349377	+	0.314581i
$790$	−15.9486	−	11.5874i	−0.567427	−	0.412260i
$791$	27.0636	+	15.6252i	0.962271	+	0.555568i
$792$	−8.78799	+	0.424420i	−0.312268	+	0.0150811i
$793$	−17.7392	+	10.2417i	−0.629937	+	0.363694i
$794$	2.46085	−	23.4134i	0.0873323	−	0.830912i
$795$	−5.20251	+	16.0117i	−0.184514	+	0.567875i
$796$	−4.83694	+	1.57162i	−0.171441	+	0.0557045i
$797$	9.79476	+	4.36091i	0.346948	+	0.154471i	0.572810	−	0.819688i	$-0.305853\pi$
$797$	9.79476	+	4.36091i	0.346948	+	0.154471i	−0.225862	+	0.974159i	$0.572520\pi$
$798$	−2.98905	+	6.71352i	−0.105811	+	0.237656i
$799$	−2.67979	+	12.6074i	−0.0948043	+	0.446019i
$800$	−6.78293	−	7.53321i	−0.239813	−	0.266339i
$801$	0.871751	−	1.19986i	0.0308018	−	0.0423951i
$802$	−17.4769	+	30.2710i	−0.617132	+	1.06890i
$803$	−11.1585	+	40.9711i	−0.393775	+	1.44584i
$804$	2.25898	+	1.30422i	0.0796681	+	0.0459964i
$805$	−131.270	−	13.7970i	−4.62666	−	0.486282i
$806$	−14.0326	−	4.55946i	−0.494276	−	0.160600i
$807$	−9.62187	−	8.66357i	−0.338706	−	0.304972i
$808$	6.78308	−	0.712930i	0.238628	−	0.0250808i
$809$	24.6375	+	33.9106i	0.866209	+	1.19223i	0.980053	+	0.198736i	$0.0636835\pi$
$809$	24.6375	+	33.9106i	0.866209	+	1.19223i	−0.113844	+	0.993499i	$0.536316\pi$
$810$	4.84978	−	22.8164i	0.170404	−	0.801687i
$811$	−36.1170	+	7.67691i	−1.26824	+	0.269573i	−0.792423	−	0.609971i	$-0.791181\pi$
$811$	−36.1170	+	7.67691i	−1.26824	+	0.269573i	−0.475817	+	0.879544i	$0.657848\pi$
$812$	−3.02269	+	28.7590i	−0.106076	+	1.00924i
$813$	−9.16609			−0.321469
$814$	6.98457	−	1.07690i	0.244809	−	0.0377452i
$815$	3.50148			0.122652
$816$	−3.47222	−	2.52271i	−0.121552	−	0.0883126i
$817$	13.0962	+	10.0519i	0.458177	+	0.351673i
$818$	11.3598	+	34.9619i	0.397187	+	1.22241i
$819$	33.6979	+	46.3811i	1.17750	+	1.62069i
$820$	28.9802	+	12.9028i	1.01203	+	0.450586i
$821$	−31.1591	+	10.1242i	−1.08746	+	0.353337i	−0.797265	−	0.603630i	$-0.793720\pi$
$821$	−31.1591	+	10.1242i	−1.08746	+	0.353337i	−0.290196	+	0.956967i	$0.593720\pi$
$822$	8.56876	−	1.82135i	0.298870	−	0.0635268i
$823$	4.03079	−	38.3504i	0.140505	−	1.33681i	−0.666163	−	0.745806i	$-0.732064\pi$
$823$	4.03079	−	38.3504i	0.140505	−	1.33681i	0.806667	−	0.591006i	$-0.201269\pi$
$824$	−3.25747	+	5.64211i	−0.113479	+	0.196552i
$825$	15.3450	+	12.5307i	0.534244	+	0.436263i
$826$	11.7101	−	20.2824i	0.407445	−	0.705715i
$827$	−5.16165	−	0.542511i	−0.179488	−	0.0188650i	0.0143580	−	0.999897i	$-0.495430\pi$
$827$	−5.16165	−	0.542511i	−0.179488	−	0.0188650i	−0.193846	+	0.981032i	$0.562096\pi$
$828$	−5.61427	+	17.2789i	−0.195109	+	0.600485i
$829$	−17.6499	−	15.8921i	−0.613007	−	0.551954i	0.303064	−	0.952970i	$-0.401990\pi$
$829$	−17.6499	−	15.8921i	−0.613007	−	0.551954i	−0.916071	+	0.401016i	$0.868657\pi$
$830$	−2.20402	−	20.9699i	−0.0765028	−	0.727875i
$831$	−8.75709	+	0.920407i	−0.303780	+	0.0319286i
$832$	0.907073	−	4.26744i	0.0314471	−	0.147947i
$833$	−121.487	−	39.4735i	−4.20927	−	1.36767i
$834$	7.10588	−	3.16374i	0.246057	−	0.109551i
$835$	14.1289	−	24.4720i	0.488951	−	0.846889i
$836$	7.45538	−	3.76027i	0.257850	−	0.130052i
$837$	−9.75594	+	5.63259i	−0.337215	+	0.194691i
$838$	−11.3660	+	15.6439i	−0.392632	+	0.540411i
$839$	−29.4319	−	9.56301i	−1.01610	−	0.330152i	−0.246820	−	0.969061i	$-0.579386\pi$
$839$	−29.4319	−	9.56301i	−1.01610	−	0.330152i	−0.769282	+	0.638910i	$0.779386\pi$
$840$	7.59907	−	8.43962i	0.262193	−	0.291195i
$841$	4.63913	+	2.06547i	0.159970	+	0.0712232i
$842$	−0.375034	+	0.0394176i	−0.0129245	+	0.00135842i
$843$	−8.03544	−	1.70799i	−0.276755	−	0.0588261i
$844$	4.97356	−	15.3070i	0.171197	−	0.526890i
$845$	−9.54834	−	21.4459i	−0.328473	−	0.737762i
$846$	−2.34721	+	4.06549i	−0.0806988	+	0.139774i
$847$	−51.6828	−	17.2628i	−1.77584	−	0.593156i
$848$	−3.67174	−	6.35963i	−0.126088	−	0.218391i
$849$	−11.2836	−	8.19798i	−0.387251	−	0.281354i
$850$	−15.3506	−	72.2188i	−0.526520	−	2.47708i
$851$	3.03414	−	14.2745i	0.104009	−	0.489323i
$852$	3.01328	−	2.18928i	0.103233	−	0.0750034i
$853$	−38.5666	+	4.05352i	−1.32050	+	0.138790i	−0.738418	−	0.674343i	$-0.764427\pi$
$853$	−38.5666	+	4.05352i	−1.32050	+	0.138790i	−0.582078	+	0.813133i	$0.697760\pi$
$854$	15.5622	−	17.2836i	0.532528	−	0.591432i
$855$	5.40240	+	25.4163i	0.184758	+	0.869219i
$856$	−1.55405	+	2.13896i	−0.0531163	+	0.0731083i
$857$	3.87793	−	2.23892i	0.132468	−	0.0764802i	−0.432302	−	0.901729i	$-0.642298\pi$
$857$	3.87793	−	2.23892i	0.132468	−	0.0764802i	0.564769	+	0.825249i	$0.308965\pi$
$858$	−0.481165	+	8.51289i	−0.0164267	+	0.290625i
$859$			55.7592i			1.90248i	0.308454	+	0.951239i	$0.400188\pi$
$859$			55.7592i			1.90248i	−0.308454	+	0.951239i	$0.599812\pi$
$860$	−14.4475	−	21.0275i	−0.492656	−	0.717033i
$861$	−7.35471	+	22.6355i	−0.250648	+	0.771415i
$862$	26.0435	−	8.46206i	0.887047	−	0.288219i
$863$	−10.4787	+	23.5356i	−0.356700	+	0.801162i	0.642686	+	0.766130i	$0.277820\pi$
$863$	−10.4787	+	23.5356i	−0.356700	+	0.801162i	−0.999386	+	0.0350325i	$0.988847\pi$
$864$	−1.95790	−	2.69481i	−0.0666090	−	0.0916794i
$865$	−12.5704	+	13.9608i	−0.427406	+	0.474682i
$866$	5.70973	+	26.8622i	0.194025	+	0.912814i
$867$	−8.64010	−	19.4060i	−0.293433	−	0.659061i
$868$	16.7528			0.568628
$869$	−15.7136	+	5.95803i	−0.533046	+	0.202112i
$870$	−6.69171	−	11.5904i	−0.226870	−	0.392950i
$871$	−11.3515	+	15.6240i	−0.384632	+	0.529400i
$872$	−0.439202	−	2.06628i	−0.0148733	−	0.0699732i
$873$	36.5656	+	7.77225i	1.23756	+	0.263051i
$874$	−1.80234	−	17.1481i	−0.0609649	−	0.580042i
$875$	98.4595	−	10.3485i	3.32854	−	0.349843i
$876$	−7.17522	+	2.33137i	−0.242428	+	0.0787697i
$877$	9.26334	−	8.34075i	0.312801	−	0.281647i	−0.497744	−	0.867324i	$-0.665838\pi$
$877$	9.26334	−	8.34075i	0.312801	−	0.281647i	0.810545	+	0.585677i	$0.199171\pi$
$878$	−7.29365	−	16.3818i	−0.246149	−	0.552859i
$879$	6.28753	+	10.8903i	0.212073	+	0.367322i
$880$	−12.7530	+	1.96629i	−0.429905	+	0.0662837i
$881$	1.38087			0.0465226			0.0232613	−	0.999729i	$-0.492595\pi$
$881$	1.38087			0.0465226			0.0232613	+	0.999729i	$0.492595\pi$
$882$	−37.6392	−	27.3465i	−1.26738	−	0.920804i
$883$	22.4471	−	4.77127i	0.755404	−	0.160566i	0.185916	−	0.982566i	$-0.440475\pi$
$883$	22.4471	−	4.77127i	0.755404	−	0.160566i	0.569488	+	0.822000i	$0.307141\pi$
$884$	21.2625	−	23.6144i	0.715134	−	0.794237i
$885$	1.13300	+	10.7798i	0.0380855	+	0.362359i
$886$	−1.60690	−	15.2886i	−0.0539848	−	0.513631i
$887$	4.65602	+	14.3297i	0.156334	+	0.481146i	0.998294	−	0.0583944i	$-0.0185981\pi$
$887$	4.65602	+	14.3297i	0.156334	+	0.481146i	−0.841960	+	0.539540i	$0.818598\pi$
$888$	0.840167	+	0.933100i	0.0281941	+	0.0313128i
$889$	26.6456	+	59.8471i	0.893666	+	2.00721i
$890$	1.08759	−	1.88375i	0.0364560	−	0.0631436i
$891$	−14.0029	−	14.1182i	−0.469113	−	0.472978i
$892$			1.74042i			0.0582735i
$893$	0.465701	−	4.43085i	0.0155841	−	0.148273i
$894$	0.675944	−	0.608623i	0.0226070	−	0.0203554i
$895$	−16.9631	−	52.2070i	−0.567013	−	1.74509i
$896$	0.517792	+	4.92646i	0.0172982	+	0.164582i
$897$	16.0848	+	7.16140i	0.537055	+	0.239112i
$898$	−26.0752	−	23.4782i	−0.870142	−	0.783479i
$899$	6.10081	−	18.7764i	0.203474	−	0.626227i
$900$	2.81087	−	26.7436i	0.0936955	−	0.891454i
$901$		−	53.4861i		−	1.78188i
$902$	22.7401	−	14.6353i	0.757162	−	0.487303i
$903$	14.5567	−	12.4291i	0.484416	−	0.413614i
$904$	3.70811	−	5.10378i	0.123330	−	0.169749i
$905$	−16.4457	−	5.34354i	−0.546674	−	0.177625i
$906$	−1.25612	−	1.13101i	−0.0417316	−	0.0375753i
$907$	−41.5617	+	30.1963i	−1.38003	+	1.00265i	−0.383155	+	0.923684i	$0.625163\pi$
$907$	−41.5617	+	30.1963i	−1.38003	+	1.00265i	−0.996877	+	0.0789683i	$0.974837\pi$
$908$	16.5209	+	7.35559i	0.548266	+	0.244104i
$909$	13.4458	+	12.1066i	0.445968	+	0.401551i
$910$	56.2619	+	62.4851i	1.86506	+	2.07136i
$911$	−14.2860	+	19.6630i	−0.473316	+	0.651463i	−0.977203	−	0.212306i	$-0.931903\pi$
$911$	−14.2860	+	19.6630i	−0.473316	+	0.651463i	0.503887	+	0.863769i	$0.331903\pi$
$912$	1.28478	+	0.741770i	0.0425435	+	0.0245625i
$913$	−15.9819	−	8.22592i	−0.528923	−	0.272238i
$914$	−6.33920			−0.209682
$915$	−1.12513	+	10.7049i	−0.0371956	+	0.353893i
$916$	−5.90878	−	6.56237i	−0.195232	−	0.216827i
$917$	57.8880	+	12.3045i	1.91163	+	0.406329i
$918$	−2.53597	−	24.1282i	−0.0836996	−	0.796349i
$919$	15.0976	+	20.7800i	0.498023	+	0.685470i	0.981842	−	0.189698i	$-0.0607509\pi$
$919$	15.0976	+	20.7800i	0.498023	+	0.685470i	−0.483820	+	0.875168i	$0.660751\pi$
$920$	−5.53999	+	26.0636i	−0.182648	+	0.859292i
$921$	−0.715770	−	0.794943i	−0.0235854	−	0.0261943i
$922$	−35.0691	−	3.68591i	−1.15494	−	0.121389i
$923$	13.7881	+	23.8818i	0.453842	+	0.786078i
$924$	−2.46729	−	9.36147i	−0.0811678	−	0.307970i
$925$			21.5999i			0.710199i
$926$	−20.0235	−	2.10456i	−0.658014	−	0.0691600i
$927$	−16.9050	+	3.59326i	−0.555232	+	0.118018i
$928$	5.71008	+	1.21372i	0.187443	+	0.0398422i
$929$	−20.4964	+	2.15426i	−0.672466	+	0.0706790i	−0.434606	−	0.900621i	$-0.643112\pi$
$929$	−20.4964	+	2.15426i	−0.672466	+	0.0706790i	−0.237859	+	0.971300i	$0.576446\pi$
$930$	−6.27269	+	4.55737i	−0.205690	+	0.149442i
$931$	43.1894	+	9.18020i	1.41548	+	0.300869i
$932$	14.1073	+	15.6677i	0.462100	+	0.513214i
$933$	5.23458	+	11.7571i	0.171372	+	0.384909i
$934$	−0.0930881	+	0.0537444i	−0.00304593	+	0.00175857i
$935$	−87.6029	−	34.0405i	−2.86492	−	1.11324i
$936$	10.0229	−	5.78672i	0.327609	−	0.189145i
$937$	−15.3658	+	6.84132i	−0.501980	+	0.223496i	−0.642075	−	0.766642i	$-0.721926\pi$
$937$	−15.3658	+	6.84132i	−0.501980	+	0.223496i	0.140094	+	0.990138i	$0.455259\pi$
$938$	6.77603	−	20.8545i	0.221245	−	0.680923i
$939$	−11.2503	−	2.39133i	−0.367140	−	0.0780381i
$940$	−2.80037	+	6.28973i	−0.0913380	+	0.205148i
$941$	−10.4029	+	23.3653i	−0.339125	+	0.761687i	0.660813	+	0.750551i	$0.270212\pi$
$941$	−10.4029	+	23.3653i	−0.339125	+	0.761687i	−0.999938	+	0.0111368i	$0.996455\pi$
$942$	−2.76638	−	8.51405i	−0.0901337	−	0.277403i
$943$	−11.6103	−	54.6221i	−0.378083	−	1.77874i
$944$	−3.82495	−	2.77899i	−0.124492	−	0.0904484i
$945$	64.1964			2.08831
$946$	−21.7433	+	0.477103i	−0.706937	+	0.0155119i
$947$	23.2218			0.754608			0.377304	−	0.926089i	$-0.376851\pi$
$947$	23.2218			0.754608			0.377304	+	0.926089i	$0.376851\pi$
$948$	−2.41554	−	1.75499i	−0.0784531	−	0.0569995i
$949$	−11.6135	−	54.6370i	−0.376989	−	1.77359i
$950$	7.88639	+	24.2718i	0.255868	+	0.787482i
$951$	6.86246	−	15.4133i	0.222531	−	0.499812i
$952$	−14.6748	+	32.9602i	−0.475614	+	1.06825i
$953$	−28.0632	−	5.96502i	−0.909056	−	0.193226i	−0.270427	−	0.962740i	$-0.587165\pi$
$953$	−28.0632	−	5.96502i	−0.909056	−	0.193226i	−0.638629	+	0.769515i	$0.720498\pi$
$954$	6.01981	−	18.5271i	0.194899	−	0.599837i
$955$	70.4808	−	31.3801i	2.28071	−	1.01544i
$956$	4.41549	−	2.54928i	0.142807	−	0.0824497i
$957$	−11.3907	−	0.643826i	−0.368210	−	0.0208119i
$958$	−1.25022	+	0.721814i	−0.0403928	+	0.0233208i
$959$	−29.9528	−	67.2752i	−0.967228	−	2.17243i
$960$	−1.53405	−	1.70374i	−0.0495113	−	0.0549878i
$961$	19.1349	+	4.06725i	0.617256	+	0.131202i
$962$	−7.52083	+	5.46420i	−0.242481	+	0.176173i
$963$	−6.97524	+	0.733128i	−0.224774	+	0.0236247i
$964$	8.57394	+	1.82245i	0.276148	+	0.0586971i
$965$	41.9576	−	8.91836i	1.35066	−	0.287092i
$966$	−19.8818	−	2.08967i	−0.639688	−	0.0672339i
$967$			35.1269i			1.12960i	0.825226	+	0.564802i	$0.191047\pi$
$967$			35.1269i			1.12960i	−0.825226	+	0.564802i	$0.808953\pi$
$968$	−4.55639	+	10.0120i	−0.146448	+	0.321796i
$969$	5.40268	+	9.35771i	0.173559	+	0.300613i
$970$	54.5258	+	5.73089i	1.75072	+	0.184008i
$971$	38.2647	+	42.4973i	1.22797	+	1.36380i	0.909409	+	0.415902i	$0.136534\pi$
$971$	38.2647	+	42.4973i	1.22797	+	1.36380i	0.318564	+	0.947901i	$0.396799\pi$
$972$	2.81218	−	13.2303i	0.0902007	−	0.424361i
$973$	−38.4342	−	52.9001i	−1.23214	−	1.69590i
$974$	0.248488	+	2.36421i	0.00796207	+	0.0757541i
$975$	−25.4908	−	5.41825i	−0.816360	−	0.173523i
$976$	−3.14160	−	3.48909i	−0.100560	−	0.111683i
$977$	2.38663	−	22.7073i	0.0763551	−	0.726471i	−0.887638	−	0.460542i	$-0.847655\pi$
$977$	2.38663	−	22.7073i	0.0763551	−	0.726471i	0.963993	−	0.265928i	$-0.0856784\pi$
$978$	0.530326			0.0169580
$979$	−0.835033	−	1.65560i	−0.0266878	−	0.0529132i
$980$	−59.0926	−	34.1171i	−1.88764	−	1.08983i
$981$	3.29385	−	4.53359i	0.105164	−	0.144746i
$982$	11.8037	+	13.1093i	0.376671	+	0.418336i
$983$	38.1589	+	34.3584i	1.21708	+	1.09586i	0.992606	+	0.121384i	$0.0387332\pi$
$983$	38.1589	+	34.3584i	1.21708	+	1.09586i	0.224475	+	0.974480i	$0.427933\pi$
$984$	4.38927	+	1.95423i	0.139925	+	0.0622986i
$985$	−56.3926	+	40.9716i	−1.79682	+	1.30546i
$986$	31.5974	+	28.4504i	1.00627	+	0.906045i
$987$	−4.91270	−	1.59623i	−0.156373	−	0.0508086i
$988$	−6.45612	+	8.88609i	−0.205397	+	0.282704i
$989$	−14.9972	+	42.3322i	−0.476885	+	1.34609i
$990$	−26.5136	−	21.6510i	−0.842657	−	0.688112i
$991$		−	2.91345i		−	0.0925488i	−0.998929	−	0.0462744i	$-0.985265\pi$
$991$		−	2.91345i		−	0.0925488i	0.998929	−	0.0462744i	$-0.0147349\pi$
$992$	0.353510	−	3.36342i	0.0112240	−	0.106789i
$993$	4.32174	−	13.3009i	0.137146	−	0.422093i
$994$	−23.2684	−	20.9510i	−0.738029	−	0.664524i
$995$	−18.0765	−	8.04816i	−0.573062	−	0.255144i
$996$	−0.333816	−	3.17605i	−0.0105774	−	0.100637i
$997$	−16.8684	−	51.9156i	−0.534228	−	1.64418i	−0.745312	−	0.666716i	$-0.767700\pi$
$997$	−16.8684	−	51.9156i	−0.534228	−	1.64418i	0.211084	−	0.977468i	$-0.432300\pi$
$998$	−5.78992	+	5.21327i	−0.183277	+	0.165023i
$999$	−0.741908	+	7.05879i	−0.0234729	+	0.223330i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	946.2.t.a.7.10	✓	176
11.8	odd	10		946.2.t.b.437.13	yes	176
43.37	odd	6		946.2.t.b.381.13	yes	176
473.338	even	30	inner	946.2.t.a.811.10	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
946.2.t.a.7.10	✓	176	1.1	even	1	trivial
946.2.t.a.811.10	yes	176	473.338	even	30	inner
946.2.t.b.381.13	yes	176	43.37	odd	6
946.2.t.b.437.13	yes	176	11.8	odd	10

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:	\( N \)	\(=\)	\( 946 = 2 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	946.t (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.122515 - 0.576387i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.58246 + 3.55426i) q^{5} +(-0.239675 + 0.538319i) q^{6} +(4.84535 + 1.02991i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.42342 - 1.07898i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.122515 - 0.576387i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.58246 + 3.55426i) q^{5} +(-0.239675 + 0.538319i) q^{6} +(4.84535 + 1.02991i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.42342 - 1.07898i) q^{9} +(3.36938 - 1.94531i) q^{10} +(0.187163 - 3.31134i) q^{11} +(0.510318 - 0.294632i) q^{12} +(1.77450 + 3.98560i) q^{13} +(-3.31460 - 3.68124i) q^{14} +(2.24250 + 0.476659i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-7.24359 + 0.761332i) q^{17} +(-2.59480 - 0.551541i) q^{18} +(2.46260 - 0.523442i) q^{19} +(-3.86931 - 0.406681i) q^{20} -2.91898i q^{21} +(-2.09777 + 2.56892i) q^{22} +(3.42438 + 5.93119i) q^{23} +(-0.586036 - 0.0615949i) q^{24} +(-6.78293 - 7.53321i) q^{25} +(0.907073 - 4.26744i) q^{26} +(-1.95790 - 2.69481i) q^{27} +(0.517792 + 4.92646i) q^{28} +(5.71008 + 1.21372i) q^{29} +(-1.53405 - 1.70374i) q^{30} +(0.353510 - 3.36342i) q^{31} +1.00000 q^{32} +(-1.93154 + 0.297810i) q^{33} +(6.30768 + 3.64174i) q^{34} +(-11.3281 + 15.5918i) q^{35} +(1.77505 + 1.97139i) q^{36} +(-1.58350 - 1.42579i) q^{37} +(-2.29996 - 1.02401i) q^{38} +(2.07985 - 1.51110i) q^{39} +(2.89129 + 2.60333i) q^{40} +(-7.75459 - 2.51962i) q^{41} +(-1.71573 + 2.36150i) q^{42} +(4.25802 + 4.98691i) q^{43} +(3.20711 - 0.845257i) q^{44} +10.3209i q^{45} +(0.715890 - 6.81123i) q^{46} +(0.546846 - 1.68302i) q^{47} +(0.437908 + 0.394295i) q^{48} +(16.0219 + 7.13340i) q^{49} +(1.05960 + 10.0814i) q^{50} +(1.32627 + 4.08184i) q^{51} +(-3.24218 + 2.91927i) q^{52} +(-0.767602 + 7.30324i) q^{53} +3.33097i q^{54} +(11.4732 + 5.90528i) q^{55} +(2.47680 - 4.28994i) q^{56} +(-0.603410 - 1.35528i) q^{57} +(-3.90615 - 4.33822i) q^{58} +(1.46100 + 4.49650i) q^{59} +(0.239642 + 2.28004i) q^{60} +(0.490765 + 4.66932i) q^{61} +(-2.26297 + 2.51328i) q^{62} +(12.8536 - 2.73212i) q^{63} +(-0.809017 - 0.587785i) q^{64} -16.9739 q^{65} +(1.73770 + 0.894400i) q^{66} +(2.21331 + 3.83357i) q^{67} +(-2.96246 - 6.65380i) q^{68} +(2.99913 - 2.70043i) q^{69} +(18.3293 - 5.95555i) q^{70} +(6.28617 - 0.660704i) q^{71} +(-0.277290 - 2.63824i) q^{72} +(-12.5234 - 2.66194i) q^{73} +(0.443020 + 2.08425i) q^{74} +(-3.51103 + 4.83252i) q^{75} +(1.25881 + 2.18032i) q^{76} +(4.31726 - 15.8518i) q^{77} -2.57083 q^{78} +(-2.06092 - 4.62889i) q^{79} +(-0.808906 - 3.80560i) q^{80} +(4.01176 - 4.45551i) q^{81} +(4.79260 + 6.59645i) q^{82} +(2.20433 - 4.95100i) q^{83} +(2.77611 - 0.902014i) q^{84} +(8.75670 - 26.9504i) q^{85} +(-0.513582 - 6.53730i) q^{86} -3.43992i q^{87} +(-3.09143 - 1.20126i) q^{88} +(0.484178 - 0.279540i) q^{89} +(6.06648 - 8.34979i) q^{90} +(4.49328 + 21.1392i) q^{91} +(-4.58271 + 5.08961i) q^{92} +(-1.98194 + 0.208311i) q^{93} +(-1.43166 + 1.04016i) q^{94} +(-2.03651 + 9.58105i) q^{95} +(-0.122515 - 0.576387i) q^{96} +(11.4006 + 8.28299i) q^{97} +(-8.76907 - 15.1885i) q^{98} +(-3.11929 - 8.22673i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 44 q^{2} - 44 q^{4} - 5 q^{6} - 15 q^{7} - 44 q^{8} - 20 q^{9}+O(q^{10}) \) 176 * q - 44 * q^2 - 44 * q^4 - 5 * q^6 - 15 * q^7 - 44 * q^8 - 20 * q^9	\( 176 q - 44 q^{2} - 44 q^{4} - 5 q^{6} - 15 q^{7} - 44 q^{8} - 20 q^{9} - 5 q^{11} - 5 q^{13} + 15 q^{14} + 41 q^{15} - 44 q^{16} - 2 q^{17} - 25 q^{18} + 34 q^{19} + 5 q^{22} - 4 q^{23} + 5 q^{24} - 24 q^{25} + 20 q^{26} - 60 q^{27} - 3 q^{29} - 49 q^{30} + 40 q^{31} + 176 q^{32} - 47 q^{33} + 3 q^{34} - 60 q^{35} - 25 q^{36} - 8 q^{37} + 14 q^{38} + 12 q^{39} - 19 q^{43} - 10 q^{44} + 26 q^{46} - 4 q^{47} - 21 q^{49} + 6 q^{50} + 45 q^{51} - 20 q^{52} - 27 q^{53} + 68 q^{55} + 71 q^{57} - 3 q^{58} - 21 q^{59} + 6 q^{60} + 30 q^{61} + 71 q^{63} - 44 q^{64} - 16 q^{65} + 43 q^{66} - 3 q^{67} + 8 q^{68} - 42 q^{69} + 3 q^{71} - 20 q^{72} - 19 q^{73} - 28 q^{74} + 9 q^{76} + 38 q^{77} + 92 q^{78} + 32 q^{79} - 23 q^{81} - 5 q^{82} - 26 q^{83} + 2 q^{85} + 36 q^{86} + 5 q^{88} + 57 q^{89} + 30 q^{91} + 6 q^{92} - 10 q^{93} + 6 q^{94} - 58 q^{95} - 37 q^{97} - 106 q^{98} - 119 q^{99}+O(q^{100}) \) 176 * q - 44 * q^2 - 44 * q^4 - 5 * q^6 - 15 * q^7 - 44 * q^8 - 20 * q^9 - 5 * q^11 - 5 * q^13 + 15 * q^14 + 41 * q^15 - 44 * q^16 - 2 * q^17 - 25 * q^18 + 34 * q^19 + 5 * q^22 - 4 * q^23 + 5 * q^24 - 24 * q^25 + 20 * q^26 - 60 * q^27 - 3 * q^29 - 49 * q^30 + 40 * q^31 + 176 * q^32 - 47 * q^33 + 3 * q^34 - 60 * q^35 - 25 * q^36 - 8 * q^37 + 14 * q^38 + 12 * q^39 - 19 * q^43 - 10 * q^44 + 26 * q^46 - 4 * q^47 - 21 * q^49 + 6 * q^50 + 45 * q^51 - 20 * q^52 - 27 * q^53 + 68 * q^55 + 71 * q^57 - 3 * q^58 - 21 * q^59 + 6 * q^60 + 30 * q^61 + 71 * q^63 - 44 * q^64 - 16 * q^65 + 43 * q^66 - 3 * q^67 + 8 * q^68 - 42 * q^69 + 3 * q^71 - 20 * q^72 - 19 * q^73 - 28 * q^74 + 9 * q^76 + 38 * q^77 + 92 * q^78 + 32 * q^79 - 23 * q^81 - 5 * q^82 - 26 * q^83 + 2 * q^85 + 36 * q^86 + 5 * q^88 + 57 * q^89 + 30 * q^91 + 6 * q^92 - 10 * q^93 + 6 * q^94 - 58 * q^95 - 37 * q^97 - 106 * q^98 - 119 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more