LMFDB - Embedded newform 138.2.f.a.83.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,2,Mod(5,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 1]))

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

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

chi := DirichletCharacter("138.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	138.f (of order $22$, degree $10$, 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:	$1.10193554789$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			83.1
Character	$\chi$	$=$	138.83
Dual form			138.2.f.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.281733 - 0.959493i) q^{2} +(-1.72467 - 0.159749i) q^{3} +(-0.841254 + 0.540641i) q^{4} +(0.591943 + 4.11706i) q^{5} +(0.332618 + 1.69981i) q^{6} +(0.656690 + 0.299900i) q^{7} +(0.755750 + 0.654861i) q^{8} +(2.94896 + 0.551026i) q^{9} +O(q^{10})$	\(q+(-0.281733 - 0.959493i) q^{2} +(-1.72467 - 0.159749i) q^{3} +(-0.841254 + 0.540641i) q^{4} +(0.591943 + 4.11706i) q^{5} +(0.332618 + 1.69981i) q^{6} +(0.656690 + 0.299900i) q^{7} +(0.755750 + 0.654861i) q^{8} +(2.94896 + 0.551026i) q^{9} +(3.78352 - 1.72787i) q^{10} +(-2.11016 - 0.619599i) q^{11} +(1.53725 - 0.798037i) q^{12} +(1.65446 + 3.62275i) q^{13} +(0.102741 - 0.714581i) q^{14} +(-0.363212 - 7.19512i) q^{15} +(0.415415 - 0.909632i) q^{16} +(-1.67303 - 1.07519i) q^{17} +(-0.302112 - 2.98475i) q^{18} +(2.25954 + 3.51591i) q^{19} +(-2.72382 - 3.14346i) q^{20} +(-1.08466 - 0.622134i) q^{21} +2.19925i q^{22} +(-1.97129 + 4.37196i) q^{23} +(-1.19880 - 1.25015i) q^{24} +(-11.8023 + 3.46547i) q^{25} +(3.00989 - 2.60809i) q^{26} +(-4.99795 - 1.42143i) q^{27} +(-0.714581 + 0.102741i) q^{28} +(2.17993 - 3.39204i) q^{29} +(-6.80134 + 2.37560i) q^{30} +(6.72079 - 7.75621i) q^{31} +(-0.989821 - 0.142315i) q^{32} +(3.54035 + 1.40570i) q^{33} +(-0.560292 + 1.90818i) q^{34} +(-0.845983 + 2.88115i) q^{35} +(-2.77873 + 1.13078i) q^{36} +(-1.56573 - 0.225118i) q^{37} +(2.73690 - 3.15855i) q^{38} +(-2.27466 - 6.51234i) q^{39} +(-2.24874 + 3.49910i) q^{40} +(7.04547 - 1.01299i) q^{41} +(-0.291348 + 1.21600i) q^{42} +(0.146984 - 0.127363i) q^{43} +(2.11016 - 0.619599i) q^{44} +(-0.522990 + 12.4672i) q^{45} +(4.75024 + 0.659712i) q^{46} -8.32990i q^{47} +(-0.861765 + 1.50245i) q^{48} +(-4.24272 - 4.89636i) q^{49} +(6.65018 + 10.3479i) q^{50} +(2.71367 + 2.12162i) q^{51} +(-3.35042 - 2.15319i) q^{52} +(1.52719 - 3.34409i) q^{53} +(0.0442340 + 5.19596i) q^{54} +(1.30183 - 9.05442i) q^{55} +(0.299900 + 0.656690i) q^{56} +(-3.33529 - 6.42473i) q^{57} +(-3.86880 - 1.13598i) q^{58} +(-0.0270675 + 0.0123613i) q^{59} +(4.19553 + 5.85655i) q^{60} +(8.55934 + 7.41671i) q^{61} +(-9.33549 - 4.26338i) q^{62} +(1.77130 + 1.24625i) q^{63} +(0.142315 + 0.989821i) q^{64} +(-13.9357 + 8.95595i) q^{65} +(0.351326 - 3.79297i) q^{66} +(1.78438 + 6.07703i) q^{67} +1.98874 q^{68} +(4.09823 - 7.22527i) q^{69} +3.00279 q^{70} +(1.83181 + 6.23857i) q^{71} +(1.86783 + 2.34760i) q^{72} +(3.72319 - 2.39275i) q^{73} +(0.225118 + 1.56573i) q^{74} +(20.9087 - 4.09138i) q^{75} +(-3.80168 - 1.73617i) q^{76} +(-1.19990 - 1.03972i) q^{77} +(-5.60770 + 4.01726i) q^{78} +(4.07232 - 1.85977i) q^{79} +(3.99091 + 1.17184i) q^{80} +(8.39274 + 3.24991i) q^{81} +(-2.95689 - 6.47469i) q^{82} +(0.309844 - 2.15501i) q^{83} +(1.24883 - 0.0630413i) q^{84} +(3.43629 - 7.52443i) q^{85} +(-0.163614 - 0.105148i) q^{86} +(-4.30154 + 5.50191i) q^{87} +(-1.18900 - 1.85012i) q^{88} +(0.817699 + 0.943675i) q^{89} +(12.1095 - 3.01062i) q^{90} +2.87520i q^{91} +(-0.705309 - 4.74368i) q^{92} +(-12.8302 + 12.3032i) q^{93} +(-7.99248 + 2.34680i) q^{94} +(-13.1377 + 11.3839i) q^{95} +(1.68438 + 0.403568i) q^{96} +(-12.7924 + 1.83926i) q^{97} +(-3.50271 + 5.45033i) q^{98} +(-5.88137 - 2.98993i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6}+O(q^{10}) $ 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6	$ 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6} - 4 q^{12} + 8 q^{13} - 22 q^{15} - 8 q^{16} - 28 q^{18} - 66 q^{21} - 4 q^{24} - 48 q^{25} - 38 q^{27} - 44 q^{30} - 16 q^{31} - 22 q^{33} - 44 q^{37} - 24 q^{39} - 44 q^{43} - 16 q^{46} + 4 q^{48} - 76 q^{49} - 8 q^{52} - 6 q^{54} + 64 q^{55} + 66 q^{57} + 36 q^{58} + 22 q^{60} + 88 q^{61} + 110 q^{63} + 8 q^{64} + 88 q^{66} + 44 q^{67} + 82 q^{69} + 112 q^{70} + 28 q^{72} + 52 q^{73} + 136 q^{75} + 82 q^{78} + 88 q^{79} + 36 q^{81} + 44 q^{82} + 22 q^{84} + 20 q^{85} - 10 q^{87} + 8 q^{93} - 56 q^{94} + 4 q^{96} - 132 q^{97} - 66 q^{99}+O(q^{100}) $ 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6 - 4 * q^12 + 8 * q^13 - 22 * q^15 - 8 * q^16 - 28 * q^18 - 66 * q^21 - 4 * q^24 - 48 * q^25 - 38 * q^27 - 44 * q^30 - 16 * q^31 - 22 * q^33 - 44 * q^37 - 24 * q^39 - 44 * q^43 - 16 * q^46 + 4 * q^48 - 76 * q^49 - 8 * q^52 - 6 * q^54 + 64 * q^55 + 66 * q^57 + 36 * q^58 + 22 * q^60 + 88 * q^61 + 110 * q^63 + 8 * q^64 + 88 * q^66 + 44 * q^67 + 82 * q^69 + 112 * q^70 + 28 * q^72 + 52 * q^73 + 136 * q^75 + 82 * q^78 + 88 * q^79 + 36 * q^81 + 44 * q^82 + 22 * q^84 + 20 * q^85 - 10 * q^87 + 8 * q^93 - 56 * q^94 + 4 * q^96 - 132 * q^97 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$-1$	$e\left(\frac{21}{22}\right)$

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 $

$2$	−0.281733	−	0.959493i	−0.199215	−	0.678464i
$2$	−0.281733	−	0.959493i	−0.199215	−	0.678464i
$3$	−1.72467	−	0.159749i	−0.995738	−	0.0922309i
$3$	−1.72467	−	0.159749i	−0.995738	−	0.0922309i
$4$	−0.841254	+	0.540641i	−0.420627	+	0.270320i
$5$	0.591943	+	4.11706i	0.264725	+	1.84120i	0.496009	+	0.868318i	$0.334798\pi$
$5$	0.591943	+	4.11706i	0.264725	+	1.84120i	−0.231284	+	0.972886i	$0.574293\pi$
$6$	0.332618	+	1.69981i	0.135791	+	0.693946i
$7$	0.656690	+	0.299900i	0.248205	+	0.113352i	0.535633	−	0.844451i	$-0.320073\pi$
$7$	0.656690	+	0.299900i	0.248205	+	0.113352i	−0.287428	+	0.957802i	$0.592800\pi$
$8$	0.755750	+	0.654861i	0.267198	+	0.231528i
$9$	2.94896	+	0.551026i	0.982987	+	0.183675i
$10$	3.78352	−	1.72787i	1.19645	−	0.546402i
$11$	−2.11016	−	0.619599i	−0.636237	−	0.186816i	−0.0523215	−	0.998630i	$-0.516662\pi$
$11$	−2.11016	−	0.619599i	−0.636237	−	0.186816i	−0.583916	+	0.811814i	$0.698480\pi$
$12$	1.53725	−	0.798037i	0.443766	−	0.230373i
$13$	1.65446	+	3.62275i	0.458863	+	1.00477i	0.987745	+	0.156075i	$0.0498842\pi$
$13$	1.65446	+	3.62275i	0.458863	+	1.00477i	−0.528882	+	0.848695i	$0.677389\pi$
$14$	0.102741	−	0.714581i	0.0274588	−	0.190980i
$15$	−0.363212	−	7.19512i	−0.0937810	−	1.85777i
$16$	0.415415	−	0.909632i	0.103854	−	0.227408i
$17$	−1.67303	−	1.07519i	−0.405770	−	0.260773i	0.321798	−	0.946808i	$-0.395713\pi$
$17$	−1.67303	−	1.07519i	−0.405770	−	0.260773i	−0.727568	+	0.686036i	$0.759349\pi$
$18$	−0.302112	−	2.98475i	−0.0712085	−	0.703512i
$19$	2.25954	+	3.51591i	0.518373	+	0.806604i	0.997465	−	0.0711606i	$-0.0226703\pi$
$19$	2.25954	+	3.51591i	0.518373	+	0.806604i	−0.479092	+	0.877765i	$0.659034\pi$
$20$	−2.72382	−	3.14346i	−0.609065	−	0.702899i
$21$	−1.08466	−	0.622134i	−0.236693	−	0.135761i
$22$			2.19925i			0.468881i
$23$	−1.97129	+	4.37196i	−0.411042	+	0.911617i
$23$	−1.97129	+	4.37196i	−0.411042	+	0.911617i
$24$	−1.19880	−	1.25015i	−0.244705	−	0.255185i
$25$	−11.8023	+	3.46547i	−2.36046	+	0.693093i
$26$	3.00989	−	2.60809i	0.590288	−	0.511488i
$27$	−4.99795	−	1.42143i	−0.961857	−	0.273554i
$28$	−0.714581	+	0.102741i	−0.135043	+	0.0194163i
$29$	2.17993	−	3.39204i	0.404804	−	0.629887i	−0.577674	−	0.816268i	$-0.696039\pi$
$29$	2.17993	−	3.39204i	0.404804	−	0.629887i	0.982478	+	0.186381i	$0.0596759\pi$
$30$	−6.80134	+	2.37560i	−1.24175	+	0.433723i
$31$	6.72079	−	7.75621i	1.20709	−	1.39306i	0.310277	−	0.950646i	$-0.399578\pi$
$31$	6.72079	−	7.75621i	1.20709	−	1.39306i	0.896813	−	0.442410i	$-0.145876\pi$
$32$	−0.989821	−	0.142315i	−0.174977	−	0.0251579i
$33$	3.54035	+	1.40570i	0.616295	+	0.244701i
$34$	−0.560292	+	1.90818i	−0.0960894	+	0.327250i
$35$	−0.845983	+	2.88115i	−0.142997	+	0.487004i
$36$	−2.77873	+	1.13078i	−0.463122	+	0.188463i
$37$	−1.56573	−	0.225118i	−0.257405	−	0.0370092i	0.0124043	−	0.999923i	$-0.496051\pi$
$37$	−1.56573	−	0.225118i	−0.257405	−	0.0370092i	−0.269809	+	0.962914i	$0.586961\pi$
$38$	2.73690	−	3.15855i	0.443984	−	0.512385i
$39$	−2.27466	−	6.51234i	−0.364237	−	1.04281i
$40$	−2.24874	+	3.49910i	−0.355557	+	0.553257i
$41$	7.04547	−	1.01299i	1.10032	−	0.158202i	0.431852	−	0.901944i	$-0.357860\pi$
$41$	7.04547	−	1.01299i	1.10032	−	0.158202i	0.668466	+	0.743743i	$0.266951\pi$
$42$	−0.291348	+	1.21600i	−0.0449560	+	0.187633i
$43$	0.146984	−	0.127363i	0.0224149	−	0.0194226i	−0.643581	−	0.765378i	$-0.722552\pi$
$43$	0.146984	−	0.127363i	0.0224149	−	0.0194226i	0.665996	+	0.745955i	$0.268007\pi$
$44$	2.11016	−	0.619599i	0.318119	−	0.0934081i
$45$	−0.522990	+	12.4672i	−0.0779627	+	1.85850i
$46$	4.75024	+	0.659712i	0.700385	+	0.0972692i
$47$		−	8.32990i		−	1.21504i	−0.794304	−	0.607520i	$-0.792164\pi$
$47$		−	8.32990i		−	1.21504i	0.794304	−	0.607520i	$-0.207836\pi$
$48$	−0.861765	+	1.50245i	−0.124385	+	0.216860i
$49$	−4.24272	−	4.89636i	−0.606103	−	0.699481i
$50$	6.65018	+	10.3479i	0.940478	+	1.46341i
$51$	2.71367	+	2.12162i	0.379989	+	0.297086i
$52$	−3.35042	−	2.15319i	−0.464620	−	0.298593i
$53$	1.52719	−	3.34409i	0.209776	−	0.459346i	−0.775271	−	0.631628i	$-0.782387\pi$
$53$	1.52719	−	3.34409i	0.209776	−	0.459346i	0.985048	+	0.172282i	$0.0551141\pi$
$54$	0.0442340	+	5.19596i	0.00601948	+	0.707081i
$55$	1.30183	−	9.05442i	0.175539	−	1.22090i
$56$	0.299900	+	0.656690i	0.0400759	+	0.0877539i
$57$	−3.33529	−	6.42473i	−0.441770	−	0.850976i
$58$	−3.86880	−	1.13598i	−0.507998	−	0.149162i
$59$	−0.0270675	+	0.0123613i	−0.00352389	+	0.00160931i	−0.417176	−	0.908826i	$-0.636980\pi$
$59$	−0.0270675	+	0.0123613i	−0.00352389	+	0.00160931i	0.413652	+	0.910435i	$0.364253\pi$
$60$	4.19553	+	5.85655i	0.541640	+	0.756078i
$61$	8.55934	+	7.41671i	1.09591	+	0.949613i	0.998956	−	0.0456762i	$-0.0145443\pi$
$61$	8.55934	+	7.41671i	1.09591	+	0.949613i	0.0969550	+	0.995289i	$0.469090\pi$
$62$	−9.33549	−	4.26338i	−1.18561	−	0.541449i
$63$	1.77130	+	1.24625i	0.223163	+	0.157012i
$64$	0.142315	+	0.989821i	0.0177894	+	0.123728i
$65$	−13.9357	+	8.95595i	−1.72851	+	1.11085i
$66$	0.351326	−	3.79297i	0.0432453	−	0.466882i
$67$	1.78438	+	6.07703i	0.217996	+	0.742427i	0.993773	+	0.111420i	$0.0355399\pi$
$67$	1.78438	+	6.07703i	0.217996	+	0.742427i	−0.775777	+	0.631007i	$0.782642\pi$
$68$	1.98874			0.241170
$69$	4.09823	−	7.22527i	0.493369	−	0.869820i
$70$	3.00279			0.358902
$71$	1.83181	+	6.23857i	0.217396	+	0.740381i	0.993902	+	0.110271i	$0.0351720\pi$
$71$	1.83181	+	6.23857i	0.217396	+	0.740381i	−0.776506	+	0.630110i	$0.783010\pi$
$72$	1.86783	+	2.34760i	0.220126	+	0.276667i
$73$	3.72319	−	2.39275i	0.435767	−	0.280050i	−0.304310	−	0.952573i	$-0.598426\pi$
$73$	3.72319	−	2.39275i	0.435767	−	0.280050i	0.740076	+	0.672523i	$0.234789\pi$
$74$	0.225118	+	1.56573i	0.0261695	+	0.182013i
$75$	20.9087	−	4.09138i	2.41432	−	0.472432i
$76$	−3.80168	−	1.73617i	−0.436083	−	0.199152i
$77$	−1.19990	−	1.03972i	−0.136742	−	0.118487i
$78$	−5.60770	+	4.01726i	−0.634947	+	0.454865i
$79$	4.07232	−	1.85977i	0.458172	−	0.209240i	−0.172939	−	0.984933i	$-0.555326\pi$
$79$	4.07232	−	1.85977i	0.458172	−	0.209240i	0.631111	+	0.775692i	$0.282599\pi$
$80$	3.99091	+	1.17184i	0.446197	+	0.131015i
$81$	8.39274	+	3.24991i	0.932527	+	0.361101i
$82$	−2.95689	−	6.47469i	−0.326534	−	0.715010i
$83$	0.309844	−	2.15501i	0.0340098	−	0.236544i	−0.965725	−	0.259567i	$-0.916420\pi$
$83$	0.309844	−	2.15501i	0.0340098	−	0.236544i	0.999735	+	0.0230234i	$0.00732924\pi$
$84$	1.24883	−	0.0630413i	0.136258	−	0.00687837i
$85$	3.43629	−	7.52443i	0.372718	−	0.816139i
$86$	−0.163614	−	0.105148i	−0.0176429	−	0.0113384i
$87$	−4.30154	+	5.50191i	−0.461173	+	0.589866i
$88$	−1.18900	−	1.85012i	−0.126748	−	0.197224i
$89$	0.817699	+	0.943675i	0.0866759	+	0.100029i	0.797431	−	0.603410i	$-0.206192\pi$
$89$	0.817699	+	0.943675i	0.0866759	+	0.100029i	−0.710755	+	0.703440i	$0.751646\pi$
$90$	12.1095	−	3.01062i	1.27646	−	0.317347i
$91$			2.87520i			0.301402i
$92$	−0.705309	−	4.74368i	−0.0735335	−	0.494563i
$93$	−12.8302	+	12.3032i	−1.33043	+	1.27579i
$94$	−7.99248	+	2.34680i	−0.824361	+	0.242054i
$95$	−13.1377	+	11.3839i	−1.34790	+	1.16796i
$96$	1.68438	+	0.403568i	0.171911	+	0.0411890i
$97$	−12.7924	+	1.83926i	−1.29887	+	0.186749i	−0.756834	−	0.653608i	$-0.773255\pi$
$97$	−12.7924	+	1.83926i	−1.29887	+	0.186749i	−0.542034	+	0.840357i	$0.682346\pi$
$98$	−3.50271	+	5.45033i	−0.353827	+	0.550566i
$99$	−5.88137	−	2.98993i	−0.591099	−	0.300499i
$100$	8.05515	−	9.29614i	0.805515	−	0.929614i
$101$	13.1575	+	1.89177i	1.30922	+	0.188238i	0.761360	−	0.648329i	$-0.224532\pi$
$101$	13.1575	+	1.89177i	1.30922	+	0.188238i	0.547864	+	0.836567i	$0.315441\pi$
$102$	1.27115	−	3.20147i	0.125862	−	0.316993i
$103$	−3.32884	+	11.3370i	−0.328000	+	1.11707i	0.616172	+	0.787612i	$0.288683\pi$
$103$	−3.32884	+	11.3370i	−0.328000	+	1.11707i	−0.944172	+	0.329453i	$0.893136\pi$
$104$	−1.12204	+	3.82133i	−0.110025	+	0.374712i
$105$	1.91930	−	4.83389i	0.187305	−	0.471739i
$106$	−3.63889	−	0.523194i	−0.353440	−	0.0508171i
$107$	−0.439642	+	0.507374i	−0.0425018	+	0.0490497i	−0.776602	−	0.629991i	$-0.783059\pi$
$107$	−0.439642	+	0.507374i	−0.0425018	+	0.0490497i	0.734101	+	0.679041i	$0.237604\pi$
$108$	4.97303	−	1.50631i	0.478530	−	0.144945i
$109$	5.20638	−	8.10129i	0.498681	−	0.775963i	−0.497103	−	0.867691i	$-0.665603\pi$
$109$	5.20638	−	8.10129i	0.498681	−	0.775963i	0.995784	+	0.0917289i	$0.0292393\pi$
$110$	−9.05442	+	1.30183i	−0.863305	+	0.124125i
$111$	2.66440	+	0.638378i	0.252894	+	0.0605921i
$112$	0.545598	−	0.472763i	0.0515541	−	0.0446719i
$113$	14.2038	−	4.17060i	1.33618	−	0.392337i	0.465874	−	0.884851i	$-0.345740\pi$
$113$	14.2038	−	4.17060i	1.33618	−	0.392337i	0.870305	+	0.492514i	$0.163922\pi$
$114$	−5.22482	+	5.01024i	−0.489349	+	0.469252i
$115$	−19.1665	−	5.52794i	−1.78729	−	0.515483i
$116$			4.03213i			0.374374i
$117$	2.88269	+	11.5950i	0.266505	+	1.07196i
$118$	0.0194864	+	0.0224885i	0.00179387	+	0.00207024i
$119$	−0.776214	−	1.20781i	−0.0711554	−	0.110720i
$120$	4.43730	−	5.67556i	0.405069	−	0.518106i
$121$	−5.18491	−	3.33214i	−0.471356	−	0.302922i
$122$	4.70484	−	10.3022i	0.425956	−	0.932713i
$123$	−12.3129	+	0.621561i	−1.11022	+	0.0560443i
$124$	−1.46057	+	10.1585i	−0.131163	+	0.912258i
$125$	−12.6144	−	27.6218i	−1.12827	−	2.47057i
$126$	0.696733	−	2.05066i	0.0620699	−	0.182687i
$127$	−14.2195	−	4.17523i	−1.26178	−	0.370491i	−0.418622	−	0.908161i	$-0.637487\pi$
$127$	−14.2195	−	4.17523i	−1.26178	−	0.370491i	−0.843156	+	0.537669i	$0.819305\pi$
$128$	0.909632	−	0.415415i	0.0804009	−	0.0367178i
$129$	−0.273845	+	0.196178i	−0.0241107	+	0.0172725i
$130$	12.5193	+	10.8481i	1.09802	+	0.951437i
$131$	−4.70731	−	2.14976i	−0.411280	−	0.187825i	0.199020	−	0.979995i	$-0.436224\pi$
$131$	−4.70731	−	2.14976i	−0.411280	−	0.187825i	−0.610300	+	0.792170i	$0.708951\pi$
$132$	−3.73831	+	0.731508i	−0.325378	+	0.0636696i
$133$	0.429393	+	2.98650i	0.0372331	+	0.258962i
$134$	5.32815	−	3.42419i	0.460282	−	0.295805i
$135$	2.89360	−	21.4183i	0.249042	−	1.84339i
$136$	−0.560292	−	1.90818i	−0.0480447	−	0.163625i
$137$	10.7206			0.915925			0.457962	−	0.888972i	$-0.348579\pi$
$137$	10.7206			0.915925			0.457962	+	0.888972i	$0.348579\pi$
$138$	−8.08720	−	1.89663i	−0.688428	−	0.161452i
$139$	−0.526269			−0.0446375			−0.0223188	−	0.999751i	$-0.507105\pi$
$139$	−0.526269			−0.0446375			−0.0223188	+	0.999751i	$0.507105\pi$
$140$	−0.845983	−	2.88115i	−0.0714986	−	0.243502i
$141$	−1.33069	+	14.3663i	−0.112064	+	1.20986i
$142$	5.46978	−	3.51521i	0.459014	−	0.294990i
$143$	−1.24651	−	8.66969i	−0.104239	−	0.724996i
$144$	1.72627	−	2.45356i	0.143856	−	0.204464i
$145$	15.2556	+	6.96701i	1.26691	+	0.578579i
$146$	−3.34477	−	2.89826i	−0.276815	−	0.239862i
$147$	6.53510	+	9.12237i	0.539006	+	0.752401i
$148$	1.43889	−	0.657117i	0.118276	−	0.0540147i
$149$	−20.3556	−	5.97694i	−1.66759	−	0.489650i	−0.694391	−	0.719598i	$-0.744326\pi$
$149$	−20.3556	−	5.97694i	−1.66759	−	0.489650i	−0.973203	+	0.229949i	$0.926144\pi$
$150$	−9.81630	−	18.9090i	−0.801497	−	1.54392i
$151$	−2.43114	−	5.32345i	−0.197843	−	0.433216i	0.784544	−	0.620073i	$-0.212897\pi$
$151$	−2.43114	−	5.32345i	−0.197843	−	0.433216i	−0.982387	+	0.186857i	$0.940170\pi$
$152$	−0.594786	+	4.13683i	−0.0482435	+	0.335541i
$153$	−4.34125	−	4.09259i	−0.350969	−	0.330866i
$154$	−0.659554	+	1.44422i	−0.0531484	+	0.116379i
$155$	35.9111	+	23.0786i	2.88445	+	1.85372i
$156$	5.43440	+	4.24876i	0.435100	+	0.340173i
$157$	−3.13288	−	4.87486i	−0.250031	−	0.389056i	0.693438	−	0.720516i	$-0.256095\pi$
$157$	−3.13288	−	4.87486i	−0.250031	−	0.389056i	−0.943469	+	0.331460i	$0.892459\pi$
$158$	−2.93174	−	3.38341i	−0.233237	−	0.269170i
$159$	−3.16812	+	5.52348i	−0.251248	+	0.438040i
$160$		−	4.15939i		−	0.328829i
$161$	−2.60568	+	2.27983i	−0.205356	+	0.179676i
$162$	0.753759	−	8.96838i	0.0592209	−	0.704623i
$163$	4.17674	−	1.22640i	0.327148	−	0.0960592i	−0.114034	−	0.993477i	$-0.536377\pi$
$163$	4.17674	−	1.22640i	0.327148	−	0.0960592i	0.441182	+	0.897418i	$0.354559\pi$
$164$	−5.37937	+	4.66125i	−0.420058	+	0.363982i
$165$	−3.69165	+	15.4079i	−0.287395	+	1.19950i
$166$	−2.15501	+	0.309844i	−0.167262	+	0.0240486i
$167$	4.39447	−	6.83794i	0.340055	−	0.529135i	−0.628541	−	0.777776i	$-0.716348\pi$
$167$	4.39447	−	6.83794i	0.340055	−	0.529135i	0.968596	+	0.248641i	$0.0799840\pi$
$168$	−0.412323	−	1.18048i	−0.0318114	−	0.0910761i
$169$	−1.87392	+	2.16262i	−0.144148	+	0.166355i
$170$	−8.18775	−	1.17722i	−0.627972	−	0.0902887i
$171$	4.72592	+	11.6133i	0.361400	+	0.888094i
$172$	−0.0547937	+	0.186610i	−0.00417798	+	0.0142289i
$173$	−4.51163	+	15.3652i	−0.343013	+	1.16819i	0.589715	+	0.807612i	$0.299240\pi$
$173$	−4.51163	+	15.3652i	−0.343013	+	1.16819i	−0.932727	+	0.360582i	$0.882578\pi$
$174$	6.49093	+	2.57723i	0.492076	+	0.195379i
$175$	−8.78975	−	1.26377i	−0.664442	−	0.0955324i
$176$	−1.44020	+	1.66208i	−0.108559	+	0.125284i
$177$	0.0486572	−	0.0169952i	0.00365730	−	0.00127744i
$178$	0.675077	−	1.05044i	0.0505991	−	0.0787338i
$179$	7.07616	−	1.01740i	0.528897	−	0.0760439i	0.127307	−	0.991863i	$-0.459367\pi$
$179$	7.07616	−	1.01740i	0.528897	−	0.0760439i	0.401590	+	0.915819i	$0.368458\pi$
$180$	−6.30032	−	10.7708i	−0.469598	−	0.802811i
$181$	13.1684	−	11.4105i	0.978801	−	0.848136i	−0.00960722	−	0.999954i	$-0.503058\pi$
$181$	13.1684	−	11.4105i	0.978801	−	0.848136i	0.988409	+	0.151818i	$0.0485127\pi$
$182$	2.75873	−	0.810036i	0.204491	−	0.0600439i
$183$	−13.5772	−	14.1587i	−1.00366	−	1.04664i
$184$	−4.35282	+	2.01319i	−0.320894	+	0.148414i
$185$		−	6.57946i		−	0.483732i
$186$	15.4196	+	8.84424i	1.13062	+	0.648491i
$187$	2.86418	+	3.30544i	0.209450	+	0.241718i
$188$	4.50348	+	7.00756i	0.328450	+	0.511079i
$189$	−2.85582	−	2.43233i	−0.207730	−	0.176926i
$190$	14.6240	+	9.39830i	1.06094	+	0.681824i
$191$	−8.26623	+	18.1005i	−0.598124	+	1.30971i	0.332283	+	0.943180i	$0.392181\pi$
$191$	−8.26623	+	18.1005i	−0.598124	+	1.30971i	−0.930407	+	0.366529i	$0.880546\pi$
$192$	−0.0873233	−	1.72985i	−0.00630202	−	0.124841i
$193$	−2.21480	+	15.4043i	−0.159425	+	1.10883i	0.740271	+	0.672309i	$0.234697\pi$
$193$	−2.21480	+	15.4043i	−0.159425	+	1.10883i	−0.899696	+	0.436517i	$0.856212\pi$
$194$	5.36879	+	11.7560i	0.385456	+	0.844032i
$195$	25.4652	−	13.2198i	1.82360	−	0.946692i
$196$	6.21638	+	1.82529i	0.444027	+	0.130378i
$197$	−3.90627	+	1.78394i	−0.278310	+	0.127100i	−0.549681	−	0.835375i	$-0.685251\pi$
$197$	−3.90627	+	1.78394i	−0.278310	+	0.127100i	0.271370	+	0.962475i	$0.412523\pi$
$198$	−1.21184	+	6.48549i	−0.0861219	+	0.460904i
$199$	15.9996	+	13.8637i	1.13418	+	0.982774i	0.999967	−	0.00817869i	$-0.00260339\pi$
$199$	15.9996	+	13.8637i	1.13418	+	0.982774i	0.134215	+	0.990952i	$0.457149\pi$
$200$	−11.1890	−	5.10984i	−0.791180	−	0.361320i
$201$	−2.10666	−	10.7659i	−0.148592	−	0.759368i
$202$	−1.89177	−	13.1575i	−0.133104	−	0.925761i
$203$	2.44882	−	1.57376i	0.171873	−	0.110456i
$204$	−3.42991	−	0.317698i	−0.240142	−	0.0222433i
$205$	8.34104	+	28.4070i	0.582564	+	1.98403i
$206$	11.8156			0.823231
$207$	−8.22231	+	11.8065i	−0.571490	+	0.820609i
$208$	3.98266			0.276148
$209$	−2.58953	−	8.81913i	−0.179122	−	0.610032i
$210$	−5.17881	−	0.479691i	−0.357372	−	0.0331018i
$211$	−13.4413	+	8.63822i	−0.925340	+	0.594680i	−0.914202	−	0.405258i	$-0.867182\pi$
$211$	−13.4413	+	8.63822i	−0.925340	+	0.594680i	−0.0111376	+	0.999938i	$0.503545\pi$
$212$	0.523194	+	3.63889i	0.0359331	+	0.249920i
$213$	−2.16266	−	11.0521i	−0.148183	−	0.757276i
$214$	0.610683	+	0.278890i	0.0417455	+	0.0190645i
$215$	0.611366	+	0.529752i	0.0416948	+	0.0361288i
$216$	−2.84636	−	4.34721i	−0.193670	−	0.295790i
$217$	6.73957	−	3.07786i	0.457512	−	0.208939i
$218$	−9.23994	−	2.71309i	−0.625807	−	0.183754i
$219$	−6.80351	+	3.53193i	−0.459739	+	0.238665i
$220$	3.80002	+	8.32088i	0.256197	+	0.560994i
$221$	1.12720	−	7.83984i	0.0758236	−	0.527365i
$222$	−0.138131	−	2.73633i	−0.00927074	−	0.183650i
$223$	4.40157	−	9.63809i	0.294751	−	0.645414i	−0.703089	−	0.711101i	$-0.748197\pi$
$223$	4.40157	−	9.63809i	0.294751	−	0.645414i	0.997840	+	0.0656871i	$0.0209239\pi$
$224$	−0.607326	−	0.390304i	−0.0405786	−	0.0260783i
$225$	−36.7141	+	3.71615i	−2.44761	+	0.247743i
$226$	−8.00333	−	12.4534i	−0.532373	−	0.828389i
$227$	6.03474	+	6.96446i	0.400540	+	0.462248i	0.919811	−	0.392362i	$-0.128342\pi$
$227$	6.03474	+	6.96446i	0.400540	+	0.462248i	−0.519271	+	0.854610i	$0.673797\pi$
$228$	6.27929	+	3.60163i	0.415856	+	0.238524i
$229$		−	11.4148i		−	0.754309i	−0.926150	−	0.377155i	$-0.876903\pi$
$229$		−	11.4148i		−	0.754309i	0.926150	−	0.377155i	$-0.123097\pi$
$230$	0.0958026	+	19.9475i	0.00631704	+	1.31530i
$231$	1.90334	+	1.98486i	0.125231	+	0.130594i
$232$	3.86880	−	1.13598i	0.253999	−	0.0745809i
$233$	13.1628	−	11.4056i	0.862323	−	0.747207i	−0.106670	−	0.994294i	$-0.534019\pi$
$233$	13.1628	−	11.4056i	0.862323	−	0.747207i	0.968993	+	0.247087i	$0.0794735\pi$
$234$	10.3132	−	6.03261i	0.674193	−	0.394364i
$235$	34.2947	−	4.93083i	2.23714	−	0.321652i
$236$	0.0160876	−	0.0250328i	0.00104721	−	0.00162950i
$237$	−7.32050	+	2.55694i	−0.475518	+	0.166091i
$238$	−0.940202	+	1.08505i	−0.0609443	+	0.0703334i
$239$	−14.9668	−	2.15190i	−0.968122	−	0.139195i	−0.359925	−	0.932981i	$-0.617198\pi$
$239$	−14.9668	−	2.15190i	−0.968122	−	0.139195i	−0.608197	+	0.793786i	$0.708107\pi$
$240$	−6.69579	−	2.65857i	−0.432212	−	0.171610i
$241$	−0.800955	+	2.72780i	−0.0515941	+	0.175713i	−0.981259	−	0.192692i	$-0.938278\pi$
$241$	−0.800955	+	2.72780i	−0.0515941	+	0.175713i	0.929665	+	0.368406i	$0.120096\pi$
$242$	−1.73641	+	5.91366i	−0.111621	+	0.380145i
$243$	−13.9555	−	6.94575i	−0.895247	−	0.445570i
$244$	−11.2104	−	1.61181i	−0.717669	−	0.103185i
$245$	17.6472	−	20.3659i	1.12744	−	1.30113i
$246$	4.06534	+	11.6391i	0.259196	+	0.742079i
$247$	−8.99895	+	14.0026i	−0.572590	+	0.890967i
$248$	10.1585	−	1.46057i	0.645064	−	0.0927461i
$249$	−0.878639	+	3.66719i	−0.0556815	+	0.232399i
$250$	−22.9490	+	19.8854i	−1.45142	+	1.25766i
$251$	−2.55586	+	0.750469i	−0.161325	+	0.0473692i	−0.361398	−	0.932412i	$-0.617700\pi$
$251$	−2.55586	+	0.750469i	−0.161325	+	0.0473692i	0.200073	+	0.979781i	$0.435882\pi$
$252$	−2.16388	−	0.0907732i	−0.136312	−	0.00571817i
$253$	6.86859	−	8.00413i	0.431825	−	0.503215i
$254$			14.8198i			0.929878i
$255$	−7.12848	+	12.4282i	−0.446403	+	0.778284i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	−5.36966	−	8.35536i	−0.334950	−	0.521193i	0.632398	−	0.774644i	$-0.282071\pi$
$257$	−5.36966	−	8.35536i	−0.334950	−	0.521193i	−0.967348	+	0.253451i	$0.918434\pi$
$258$	0.265382	+	0.207483i	0.0165220	+	0.0129173i
$259$	−0.960687	−	0.617396i	−0.0596942	−	0.0383631i
$260$	6.88153	−	15.0685i	0.426774	−	0.934506i
$261$	8.29765	−	8.80180i	0.513611	−	0.544818i
$262$	−0.736474	+	5.12229i	−0.0454995	+	0.316456i
$263$	−4.09666	−	8.97043i	−0.252611	−	0.553141i	0.740262	−	0.672318i	$-0.234701\pi$
$263$	−4.09666	−	8.97043i	−0.252611	−	0.553141i	−0.992873	+	0.119178i	$0.961974\pi$
$264$	1.75508	+	3.38079i	0.108018	+	0.208073i
$265$	14.6718	+	4.30804i	0.901283	+	0.264641i
$266$	2.74455	−	1.25339i	0.168279	−	0.0768504i
$267$	−1.25951	−	1.75815i	−0.0770807	−	0.107597i
$268$	−4.78660	−	4.14761i	−0.292388	−	0.253356i
$269$	−3.07146	−	1.40269i	−0.187270	−	0.0855235i	0.319573	−	0.947562i	$-0.396460\pi$
$269$	−3.07146	−	1.40269i	−0.187270	−	0.0855235i	−0.506843	+	0.862038i	$0.669188\pi$
$270$	−21.3659	+	3.25783i	−1.30029	+	0.198265i
$271$	−2.04708	−	14.2377i	−0.124351	−	0.864880i	−0.952536	−	0.304426i	$-0.901536\pi$
$271$	−2.04708	−	14.2377i	−0.124351	−	0.864880i	0.828185	−	0.560455i	$-0.189374\pi$
$272$	−1.67303	+	1.07519i	−0.101443	+	0.0651932i
$273$	0.459308	−	4.95876i	0.0277986	−	0.300118i
$274$	−3.02035	−	10.2864i	−0.182466	−	0.621422i
$275$	27.0519			1.63129
$276$	0.458626	+	8.29395i	0.0276061	+	0.499237i
$277$	−9.51013			−0.571408			−0.285704	−	0.958318i	$-0.592227\pi$
$277$	−9.51013			−0.571408			−0.285704	+	0.958318i	$0.592227\pi$
$278$	0.148267	+	0.504951i	0.00889247	+	0.0302850i
$279$	24.0932	−	19.1694i	1.44242	−	1.14764i
$280$	−2.52611	+	1.62343i	−0.150964	+	0.0970185i
$281$	0.0418767	+	0.291259i	0.00249815	+	0.0173750i	0.991032	−	0.133622i	$-0.0426608\pi$
$281$	0.0418767	+	0.291259i	0.00249815	+	0.0173750i	−0.988534	+	0.150997i	$0.951752\pi$
$282$	14.1593	−	2.77067i	0.843173	−	0.164991i
$283$	16.0458	+	7.32785i	0.953821	+	0.435596i	0.830653	−	0.556790i	$-0.187967\pi$
$283$	16.0458	+	7.32785i	0.953821	+	0.435596i	0.123168	+	0.992386i	$0.460695\pi$
$284$	−4.91384	−	4.25786i	−0.291583	−	0.252658i
$285$	24.4767	−	17.5346i	1.44987	−	1.03866i
$286$	−7.96732	+	3.63855i	−0.471118	+	0.215152i
$287$	4.93049	+	1.44772i	0.291037	+	0.0854563i
$288$	−2.84053	−	0.965099i	−0.167380	−	0.0568690i
$289$	−5.41906	−	11.8661i	−0.318768	−	0.698004i
$290$	2.38679	−	16.6005i	0.140157	−	0.974815i
$291$	22.3564	−	1.12856i	1.31056	−	0.0661573i
$292$	−1.83853	+	4.02582i	−0.107592	+	0.235593i
$293$	−22.4214	−	14.4094i	−1.30987	−	0.841804i	−0.315623	−	0.948885i	$-0.602213\pi$
$293$	−22.4214	−	14.4094i	−1.30987	−	0.841804i	−0.994250	+	0.107080i	$0.965850\pi$
$294$	6.91170	−	8.84046i	0.403099	−	0.515586i
$295$	−0.0669147	−	0.104121i	−0.00389593	−	0.00606218i
$296$	−1.03588	−	1.19547i	−0.0602093	−	0.0694852i
$297$	9.66577	+	6.09617i	0.560865	+	0.353736i
$298$			21.2149i			1.22895i
$299$	−19.0999	+	0.0917319i	−1.10458	+	0.00530499i
$300$	−15.3775	+	14.7460i	−0.887821	+	0.851358i
$301$	0.134719	−	0.0395572i	0.00776509	−	0.00228004i
$302$	−4.42288	+	3.83245i	−0.254508	+	0.220533i
$303$	−22.3902	−	5.36457i	−1.28628	−	0.308187i
$304$	4.13683	−	0.594786i	0.237263	−	0.0341133i
$305$	−25.4684	+	39.6296i	−1.45832	+	2.26918i
$306$	−2.70374	+	5.31841i	−0.154562	+	0.304034i
$307$	−22.8736	+	26.3975i	−1.30546	+	1.50658i	−0.591839	+	0.806056i	$0.701598\pi$
$307$	−22.8736	+	26.3975i	−1.30546	+	1.50658i	−0.713625	+	0.700528i	$0.752948\pi$
$308$	1.57154	+	0.225953i	0.0895468	+	0.0128749i
$309$	7.55220	−	19.0207i	0.429630	−	1.08205i
$310$	12.0265	−	40.9584i	0.683058	−	2.32628i
$311$	−0.262167	+	0.892860i	−0.0148661	+	0.0506294i	−0.966592	−	0.256320i	$-0.917490\pi$
$311$	−0.262167	+	0.892860i	−0.0148661	+	0.0506294i	0.951726	+	0.306949i	$0.0993082\pi$
$312$	2.54561	−	6.41128i	0.144117	−	0.362967i
$313$	18.4209	+	2.64853i	1.04121	+	0.149704i	0.641646	−	0.767001i	$-0.278252\pi$
$313$	18.4209	+	2.64853i	1.04121	+	0.149704i	0.399565	+	0.916705i	$0.369161\pi$
$314$	−3.79476	+	4.37938i	−0.214150	+	0.247143i
$315$	−4.08236	+	8.03025i	−0.230015	+	0.452453i
$316$	−2.42039	+	3.76620i	−0.136158	+	0.211865i
$317$	16.7469	−	2.40784i	0.940601	−	0.135238i	0.345076	−	0.938575i	$-0.387853\pi$
$317$	16.7469	−	2.40784i	0.940601	−	0.135238i	0.595525	+	0.803337i	$0.296944\pi$
$318$	6.19230	+	1.48364i	0.347247	+	0.0831986i
$319$	−6.70172	+	5.80707i	−0.375224	+	0.325134i
$320$	−3.99091	+	1.17184i	−0.223099	+	0.0655077i
$321$	0.839289	−	0.804820i	0.0468446	−	0.0449207i
$322$	2.92159	+	1.85782i	0.162814	+	0.103533i
$323$		−	8.31167i		−	0.462473i
$324$	−8.81746	+	1.80346i	−0.489859	+	0.100192i
$325$	−32.0809	−	37.0233i	−1.77953	−	2.05368i
$326$	−2.35345	−	3.66204i	−0.130345	−	0.202821i
$327$	−10.2734	+	13.1403i	−0.568123	+	0.726661i
$328$	5.98798	+	3.84824i	0.330631	+	0.212484i
$329$	2.49814	−	5.47016i	0.137727	−	0.301580i
$330$	15.8238	−	0.798793i	0.871073	−	0.0439721i
$331$	0.117484	−	0.817121i	0.00645752	−	0.0449130i	−0.986338	−	0.164735i	$-0.947323\pi$
$331$	0.117484	−	0.817121i	0.00645752	−	0.0449130i	0.992795	+	0.119822i	$0.0382323\pi$
$332$	0.904431	+	1.98043i	0.0496371	+	0.108690i
$333$	−4.49323	−	1.52662i	−0.246228	−	0.0836585i
$334$	−7.79902	−	2.29000i	−0.426743	−	0.125303i
$335$	−23.9632	+	10.9436i	−1.30925	+	0.597915i
$336$	−1.01650	+	0.728201i	−0.0554545	+	0.0397266i
$337$	−21.5178	−	18.6453i	−1.17215	−	1.01567i	−0.999529	−	0.0306850i	$-0.990231\pi$
$337$	−21.5178	−	18.6453i	−1.17215	−	1.01567i	−0.172620	−	0.984988i	$-0.555223\pi$
$338$	2.60296	+	1.18873i	0.141582	+	0.0646585i
$339$	−25.1630	+	4.92387i	−1.36667	+	0.267428i
$340$	1.17722	+	8.18775i	0.0638438	+	0.444043i
$341$	−18.9877	+	12.2026i	−1.02824	+	0.660810i
$342$	9.81146	−	7.80635i	0.530543	−	0.422119i
$343$	−2.74147	−	9.33659i	−0.148025	−	0.504128i
$344$	0.194488			0.0104861
$345$	32.1728	+	12.5957i	1.73212	+	0.678129i
$346$	16.0139			0.860911
$347$	0.0175599	+	0.0598036i	0.000942666	+	0.00321043i	0.959963	−	0.280127i	$-0.0903766\pi$
$347$	0.0175599	+	0.0598036i	0.000942666	+	0.00321043i	−0.959020	+	0.283337i	$0.908558\pi$
$348$	0.644127	−	6.95409i	0.0345288	−	0.372778i
$349$	−17.9464	+	11.5334i	−0.960647	+	0.617370i	−0.924177	−	0.381964i	$-0.875248\pi$
$349$	−17.9464	+	11.5334i	−0.960647	+	0.617370i	−0.0364699	+	0.999335i	$0.511611\pi$
$350$	1.26377	+	8.78975i	0.0675516	+	0.469832i
$351$	−3.11940	−	20.4580i	−0.166501	−	1.09197i
$352$	2.00050	+	0.913600i	0.106627	+	0.0486950i
$353$	0.167102	+	0.144794i	0.00889393	+	0.00770663i	0.659296	−	0.751883i	$-0.270854\pi$
$353$	0.167102	+	0.144794i	0.00889393	+	0.00770663i	−0.650402	+	0.759590i	$0.725400\pi$
$354$	−0.0300151	−	0.0418982i	−0.00159528	−	0.00222686i
$355$	−24.6002	+	11.2345i	−1.30564	+	0.596267i
$356$	−1.19808	−	0.351788i	−0.0634982	−	0.0186447i
$357$	1.14576	+	2.20707i	0.0606403	+	0.116811i
$358$	−2.96977	−	6.50289i	−0.156957	−	0.343688i
$359$	0.583737	−	4.05998i	0.0308085	−	0.214278i	−0.968602	−	0.248618i	$-0.920024\pi$
$359$	0.583737	−	4.05998i	0.0308085	−	0.214278i	0.999410	+	0.0343399i	$0.0109329\pi$
$360$	−8.55954	+	9.07961i	−0.451127	+	0.478537i
$361$	0.636792	−	1.39438i	0.0335154	−	0.0733884i
$362$	−14.6583	−	9.42030i	−0.770422	−	0.495120i
$363$	8.40995	+	6.57512i	0.441408	+	0.345104i
$364$	−1.55445	−	2.41877i	−0.0814752	−	0.126778i
$365$	12.0550	+	13.9122i	0.630988	+	0.728199i
$366$	−9.76004	+	17.0162i	−0.510165	+	0.889452i
$367$		−	31.2246i		−	1.62991i	−0.579523	−	0.814956i	$-0.696761\pi$
$367$		−	31.2246i		−	1.62991i	0.579523	−	0.814956i	$-0.303239\pi$
$368$	3.15797	+	3.60932i	0.164621	+	0.188149i
$369$	21.3350	+	0.894986i	1.11066	+	0.0465911i
$370$	−6.31295	+	1.85365i	−0.328195	+	0.0963666i
$371$	2.00579	−	1.73802i	0.104135	−	0.0902337i
$372$	4.14180	−	17.2867i	0.214742	−	0.896272i
$373$	0.330235	−	0.0474807i	0.0170989	−	0.00245846i	−0.133760	−	0.991014i	$-0.542705\pi$
$373$	0.330235	−	0.0474807i	0.0170989	−	0.00245846i	0.150859	+	0.988555i	$0.451796\pi$
$374$	2.36461	−	3.67941i	0.122271	−	0.190258i
$375$	17.3432	+	49.6536i	0.895599	+	2.56410i
$376$	5.45492	−	6.29532i	0.281316	−	0.324656i
$377$	15.8951	+	2.28538i	0.818641	+	0.117703i
$378$	−1.52922	+	3.42540i	−0.0786547	+	0.176184i
$379$	−3.18337	+	10.8416i	−0.163519	+	0.556894i	0.836442	+	0.548055i	$0.184632\pi$
$379$	−3.18337	+	10.8416i	−0.163519	+	0.556894i	−0.999961	+	0.00883868i	$0.997187\pi$
$380$	4.89753	−	16.6795i	0.251238	−	0.855639i
$381$	23.8570	+	9.47243i	1.22223	+	0.485287i
$382$	19.6962	+	2.83189i	1.00775	+	0.144892i
$383$	4.46062	−	5.14783i	0.227927	−	0.263042i	−0.630254	−	0.776389i	$-0.717049\pi$
$383$	4.46062	−	5.14783i	0.227927	−	0.263042i	0.858181	+	0.513347i	$0.171595\pi$
$384$	−1.63518	+	0.571141i	−0.0834447	+	0.0291459i
$385$	3.57032	−	5.55553i	0.181960	−	0.283136i
$386$	15.4043	−	2.21480i	0.784058	−	0.112731i
$387$	0.503631	−	0.294595i	0.0256010	−	0.0149751i
$388$	9.76724	−	8.46336i	0.495856	−	0.429662i
$389$	−9.89092	+	2.90423i	−0.501489	+	0.147251i	−0.522687	−	0.852525i	$-0.675070\pi$
$389$	−9.89092	+	2.90423i	−0.501489	+	0.147251i	0.0211975	+	0.999775i	$0.493252\pi$
$390$	−19.8587	−	20.7092i	−1.00559	−	1.04865i
$391$	7.99873	−	5.19492i	0.404513	−	0.262718i
$392$		−	6.47882i		−	0.327230i
$393$	7.77513	+	4.45961i	0.392204	+	0.224957i
$394$	2.81220	+	3.24545i	0.141676	+	0.163503i
$395$	10.0674	+	15.6651i	0.506544	+	0.788198i
$396$	6.56420	−	0.664419i	0.329863	−	0.0333883i
$397$	9.82670	+	6.31524i	0.493188	+	0.316953i	0.763486	−	0.645824i	$-0.223486\pi$
$397$	9.82670	+	6.31524i	0.493188	+	0.316953i	−0.270298	+	0.962777i	$0.587122\pi$
$398$	8.79454	−	19.2574i	0.440831	−	0.965284i
$399$	−0.263473	−	5.21931i	−0.0131901	−	0.261292i
$400$	−1.75055	+	12.1754i	−0.0875276	+	0.608768i
$401$	5.88936	+	12.8959i	0.294100	+	0.643990i	0.997785	−	0.0665224i	$-0.0211904\pi$
$401$	5.88936	+	12.8959i	0.294100	+	0.643990i	−0.703684	+	0.710513i	$0.748463\pi$
$402$	−9.73630	+	5.05443i	−0.485602	+	0.252092i
$403$	39.2181	+	11.5155i	1.95359	+	0.573626i
$404$	−12.0916	+	5.52205i	−0.601579	+	0.274732i
$405$	−8.41204	+	36.4772i	−0.417998	+	1.81256i
$406$	−2.19992	−	1.90624i	−0.109180	−	0.0946052i
$407$	3.16446	+	1.44516i	0.156857	+	0.0716340i
$408$	0.661489	+	3.38048i	0.0327486	+	0.167359i
$409$	−0.919748	−	6.39699i	−0.0454786	−	0.316311i	−0.999844	−	0.0176689i	$-0.994376\pi$
$409$	−0.919748	−	6.39699i	−0.0454786	−	0.316311i	0.954365	−	0.298642i	$-0.0965336\pi$
$410$	24.9064	−	16.0063i	1.23004	−	0.790497i
$411$	−18.4895	−	1.71260i	−0.912021	−	0.0844765i
$412$	−3.32884	−	11.3370i	−0.164000	−	0.558533i
$413$	−0.0214821			−0.00105707
$414$	13.6448	+	4.56297i	0.670603	+	0.224258i
$415$	9.05573			0.444528
$416$	−1.12204	−	3.82133i	−0.0550127	−	0.187356i
$417$	0.907639	+	0.0840707i	0.0444473	+	0.00411696i
$418$	−7.73234	+	4.96927i	−0.378201	+	0.243055i
$419$	1.23696	+	8.60326i	0.0604295	+	0.420297i	0.997471	+	0.0710778i	$0.0226439\pi$
$419$	1.23696	+	8.60326i	0.0604295	+	0.420297i	−0.937041	+	0.349219i	$0.886447\pi$
$420$	0.998780	+	5.10418i	0.0487355	+	0.249058i
$421$	−26.5913	−	12.1439i	−1.29598	−	0.591856i	−0.356450	−	0.934314i	$-0.616013\pi$
$421$	−26.5913	−	12.1439i	−1.29598	−	0.591856i	−0.939533	+	0.342459i	$0.888740\pi$
$422$	12.0752	+	10.4632i	0.587810	+	0.509341i
$423$	4.59000	−	24.5645i	0.223173	−	1.19437i
$424$	3.34409	−	1.52719i	0.162403	−	0.0741671i
$425$	23.4717	+	6.89191i	1.13854	+	0.334307i
$426$	−9.99511	+	5.18879i	−0.484264	+	0.251398i
$427$	3.39656	+	7.43743i	0.164371	+	0.359922i
$428$	0.0955434	−	0.664519i	0.00461826	−	0.0321207i
$429$	0.764851	+	15.1515i	0.0369274	+	0.731519i
$430$	0.336051	−	0.735850i	0.0162058	−	0.0354858i
$431$	25.7588	+	16.5542i	1.24076	+	0.797387i	0.985531	−	0.169494i	$-0.0542133\pi$
$431$	25.7588	+	16.5542i	1.24076	+	0.797387i	0.255228	+	0.966881i	$0.417850\pi$
$432$	−3.36920	+	3.95581i	−0.162101	+	0.190324i
$433$	9.94612	+	15.4765i	0.477980	+	0.743751i	0.993587	−	0.113074i	$-0.0360698\pi$
$433$	9.94612	+	15.4765i	0.477980	+	0.743751i	−0.515607	+	0.856825i	$0.672433\pi$
$434$	−4.85194	−	5.59943i	−0.232900	−	0.268781i
$435$	−25.1979	−	14.4529i	−1.20815	−	0.692961i
$436$			9.63002i			0.461194i
$437$	−19.8256	+	2.94774i	−0.948387	+	0.141010i
$438$	5.30563	+	5.53286i	0.253513	+	0.264370i
$439$	9.98198	−	2.93097i	0.476414	−	0.139888i	−0.0347053	−	0.999398i	$-0.511049\pi$
$439$	9.98198	−	2.93097i	0.476414	−	0.139888i	0.511119	+	0.859510i	$0.329231\pi$
$440$	6.91324	−	5.99036i	0.329576	−	0.285579i
$441$	−9.81360	−	16.7770i	−0.467314	−	0.798907i
$442$	−7.83984	+	1.12720i	−0.372903	+	0.0536154i
$443$	−0.575214	+	0.895050i	−0.0273292	+	0.0425251i	−0.854649	−	0.519206i	$-0.826228\pi$
$443$	−0.575214	+	0.895050i	−0.0273292	+	0.0425251i	0.827320	+	0.561731i	$0.189864\pi$
$444$	−2.58657	+	0.903449i	−0.122753	+	0.0428758i
$445$	−3.40113	+	3.92511i	−0.161229	+	0.186068i
$446$	−10.4877	−	1.50791i	−0.496609	−	0.0714016i
$447$	34.1518	+	13.5600i	1.61532	+	0.641366i
$448$	−0.203391	+	0.692686i	−0.00960932	+	0.0327263i
$449$	−3.39728	+	11.5701i	−0.160327	+	0.546025i	0.839668	+	0.543099i	$0.182749\pi$
$449$	−3.39728	+	11.5701i	−0.160327	+	0.546025i	−0.999996	+	0.00292531i	$0.999069\pi$
$450$	13.9092	+	34.1799i	0.655685	+	1.61126i
$451$	−15.4947	−	2.22781i	−0.729618	−	0.104903i
$452$	−9.69417	+	11.1877i	−0.455976	+	0.526224i
$453$	3.34249	+	9.56956i	0.157044	+	0.449617i
$454$	4.98217	−	7.75241i	0.233825	−	0.363838i
$455$	−11.8373	+	1.70195i	−0.554943	+	0.0797888i
$456$	1.68666	−	7.03964i	0.0789851	−	0.329661i
$457$	4.86845	−	4.21854i	0.227737	−	0.197335i	−0.533517	−	0.845790i	$-0.679130\pi$
$457$	4.86845	−	4.21854i	0.227737	−	0.197335i	0.761253	+	0.648455i	$0.224584\pi$
$458$	−10.9524	+	3.21591i	−0.511772	+	0.150270i
$459$	6.83343	+	7.75187i	0.318957	+	0.361826i
$460$	19.1125	−	5.71179i	0.891126	−	0.266314i
$461$			7.71670i			0.359403i	0.983721	+	0.179701i	$0.0575131\pi$
$461$			7.71670i			0.359403i	−0.983721	+	0.179701i	$0.942487\pi$
$462$	1.36822	−	2.38544i	0.0636556	−	0.110981i
$463$	10.2702	+	11.8525i	0.477299	+	0.550832i	0.942427	−	0.334411i	$-0.108537\pi$
$463$	10.2702	+	11.8525i	0.477299	+	0.550832i	−0.465129	+	0.885243i	$0.653992\pi$
$464$	−2.17993	−	3.39204i	−0.101201	−	0.157472i
$465$	−58.2479	−	45.5398i	−2.70118	−	2.11186i
$466$	−14.6520	−	9.41627i	−0.678741	−	0.436200i
$467$	0.130816	−	0.286446i	0.00605343	−	0.0132552i	−0.906581	−	0.422032i	$-0.861317\pi$
$467$	0.130816	−	0.286446i	0.00605343	−	0.0132552i	0.912635	+	0.408776i	$0.134044\pi$
$468$	−8.69381	−	8.19584i	−0.401871	−	0.378853i
$469$	−0.650720	+	4.52586i	−0.0300475	+	0.208985i
$470$	−14.3930	−	31.5163i	−0.663901	−	1.45374i
$471$	4.62443	+	8.90798i	0.213082	+	0.410458i
$472$	−0.0285512	−	0.00838340i	−0.00131418	−	0.000385877i
$473$	−0.389075	+	0.177684i	−0.0178897	+	0.00816994i
$474$	4.51579	+	6.30360i	0.207417	+	0.289534i
$475$	−38.8520	−	33.6654i	−1.78265	−	1.54468i
$476$	1.30598	+	0.596423i	0.0598597	+	0.0273370i
$477$	6.34632	−	9.02007i	0.290578	−	0.413000i
$478$	2.15190	+	14.9668i	0.0984257	+	0.684566i
$479$	23.8946	−	15.3561i	1.09177	−	0.701639i	0.134525	−	0.990910i	$-0.457049\pi$
$479$	23.8946	−	15.3561i	1.09177	−	0.701639i	0.957247	+	0.289271i	$0.0934129\pi$
$480$	−0.664457	+	7.17357i	−0.0303282	+	0.327427i
$481$	−1.77489	−	6.04470i	−0.0809278	−	0.275615i
$482$	2.84296			0.129493
$483$	4.85813	−	3.51570i	0.221052	−	0.159970i
$484$	6.16332			0.280151
$485$	−15.1447	−	51.5781i	−0.687686	−	2.34204i
$486$	−2.73267	+	15.3471i	−0.123956	+	0.696157i
$487$	12.9391	−	8.31544i	0.586326	−	0.376809i	−0.213588	−	0.976924i	$-0.568515\pi$
$487$	12.9391	−	8.31544i	0.586326	−	0.376809i	0.799914	+	0.600115i	$0.204879\pi$
$488$	1.61181	+	11.2104i	0.0729630	+	0.507469i
$489$	−7.39941	+	1.44791i	−0.334613	+	0.0654767i
$490$	−24.5127	−	11.1946i	−1.10737	−	0.505720i
$491$	−27.6389	−	23.9493i	−1.24733	−	1.08082i	−0.993531	−	0.113557i	$-0.963775\pi$
$491$	−27.6389	−	23.9493i	−1.24733	−	1.08082i	−0.253796	−	0.967258i	$-0.581679\pi$
$492$	10.0223	−	7.17976i	0.451838	−	0.323689i
$493$	−7.29420	+	3.33115i	−0.328514	+	0.150028i
$494$	15.9707	+	4.68943i	0.718557	+	0.210988i
$495$	8.82827	−	25.9838i	0.396801	−	1.16788i
$496$	−4.26338	−	9.33549i	−0.191431	−	0.419176i
$497$	−0.668017	+	4.64616i	−0.0299647	+	0.208409i
$498$	3.76618	−	0.190118i	0.168767	−	0.00851940i
$499$	6.50748	−	14.2494i	0.291315	−	0.637890i	−0.706226	−	0.707987i	$-0.749604\pi$
$499$	6.50748	−	14.2494i	0.291315	−	0.637890i	0.997540	+	0.0700968i	$0.0223308\pi$
$500$	25.5454	+	16.4170i	1.14243	+	0.734192i
$501$	−8.67136	+	11.0912i	−0.387408	+	0.495516i
$502$	1.44014	+	2.24090i	0.0642766	+	0.100016i
$503$	5.98194	+	6.90353i	0.266722	+	0.307813i	0.873273	−	0.487231i	$-0.161993\pi$
$503$	5.98194	+	6.90353i	0.266722	+	0.307813i	−0.606552	+	0.795044i	$0.707448\pi$
$504$	0.522541	+	2.10181i	0.0232758	+	0.0936219i
$505$			55.2902i			2.46038i
$506$	−9.61501	−	4.33534i	−0.427439	−	0.192729i
$507$	3.57736	−	3.43044i	0.158876	−	0.152351i
$508$	14.2195	−	4.17523i	0.630889	−	0.185246i
$509$	16.0975	−	13.9486i	0.713510	−	0.618260i	−0.220550	−	0.975376i	$-0.570785\pi$
$509$	16.0975	−	13.9486i	0.713510	−	0.618260i	0.934060	+	0.357116i	$0.116240\pi$
$510$	13.9331	+	3.33830i	0.616968	+	0.147822i
$511$	3.16257	−	0.454709i	0.139904	−	0.0201151i
$512$	−0.540641	+	0.841254i	−0.0238932	+	0.0371785i
$513$	−6.29544	−	20.7841i	−0.277950	−	0.917641i
$514$	−6.50410	+	7.50613i	−0.286884	+	0.331081i
$515$	−48.6454	−	6.99416i	−2.14357	−	0.308199i
$516$	0.124312	−	0.313087i	0.00547251	−	0.0137829i
$517$	−5.16120	+	17.5774i	−0.226989	+	0.773054i
$518$	−0.321730	+	1.09571i	−0.0141360	+	0.0481429i
$519$	10.2356	−	25.7791i	0.449294	−	1.13158i
$520$	−16.3968	−	2.35751i	−0.719048	−	0.103384i
$521$	−27.4746	+	31.7074i	−1.20368	+	1.38913i	−0.303949	+	0.952688i	$0.598305\pi$
$521$	−27.4746	+	31.7074i	−1.20368	+	1.38913i	−0.899735	+	0.436437i	$0.856240\pi$
$522$	−10.7830	−	5.48178i	−0.471958	−	0.239931i
$523$	18.6310	−	28.9904i	0.814677	−	1.26766i	−0.145803	−	0.989314i	$-0.546577\pi$
$523$	18.6310	−	28.9904i	0.814677	−	1.26766i	0.960480	−	0.278348i	$-0.0897870\pi$
$524$	5.12229	−	0.736474i	0.223768	−	0.0321730i
$525$	14.9575	+	3.58374i	0.652799	+	0.156407i
$526$	−7.45290	+	6.45798i	−0.324962	+	0.281581i
$527$	−19.5835	+	5.75024i	−0.853072	+	0.250485i
$528$	2.74938	−	2.63646i	0.119651	−	0.114737i
$529$	−15.2281	−	17.2368i	−0.662090	−	0.749425i
$530$		−	15.2912i		−	0.664208i
$531$	−0.0866325	+	0.0215381i	−0.00375953	+	0.000934676i
$532$	−1.97585	−	2.28025i	−0.0856640	−	0.0988615i
$533$	15.3262	+	23.8481i	0.663852	+	1.03297i
$534$	−1.33209	+	1.70382i	−0.0576452	+	0.0737314i
$535$	−2.34913	−	1.50970i	−0.101562	−	0.0652698i
$536$	−2.63106	+	5.76123i	−0.113645	+	0.248847i
$537$	−12.3666	+	0.624268i	−0.533656	+	0.0269392i
$538$	−0.480540	+	3.34223i	−0.0207175	+	0.144094i
$539$	5.91905	+	12.9609i	0.254951	+	0.558266i
$540$	9.14533	+	19.5826i	0.393553	+	0.842701i
$541$	−34.2915	−	10.0689i	−1.47431	−	0.432895i	−0.556810	−	0.830640i	$-0.687975\pi$
$541$	−34.2915	−	10.0689i	−1.47431	−	0.432895i	−0.917496	+	0.397744i	$0.869793\pi$
$542$	−13.0843	+	5.97539i	−0.562017	+	0.256665i
$543$	−24.5340	+	17.5757i	−1.05285	+	0.754245i
$544$	1.50299	+	1.30235i	0.0644401	+	0.0558377i
$545$	36.4353	+	16.6395i	1.56072	+	0.712756i
$546$	−4.88730	+	0.956341i	−0.209157	+	0.0409276i
$547$	2.55106	+	17.7430i	0.109076	+	0.758638i	0.968794	+	0.247869i	$0.0797301\pi$
$547$	2.55106	+	17.7430i	0.109076	+	0.758638i	−0.859718	+	0.510769i	$0.829361\pi$
$548$	−9.01876	+	5.79601i	−0.385262	+	0.247593i
$549$	21.1544	+	26.5880i	0.902846	+	1.13475i
$550$	−7.62141	−	25.9561i	−0.324978	−	1.10677i
$551$	16.8517			0.717908
$552$	7.82878	−	2.77673i	0.333215	−	0.118185i
$553$	3.23200			0.137439
$554$	2.67931	+	9.12490i	0.113833	+	0.387680i
$555$	−1.05106	+	11.3474i	−0.0446150	+	0.481670i
$556$	0.442726	−	0.284522i	0.0187757	−	0.0120664i
$557$	0.449193	+	3.12421i	0.0190329	+	0.132377i	0.997122	−	0.0758078i	$-0.0241536\pi$
$557$	0.449193	+	3.12421i	0.0190329	+	0.132377i	−0.978090	+	0.208185i	$0.933244\pi$
$558$	−25.1808	−	17.7166i	−1.06599	−	0.750005i
$559$	0.704583	+	0.321772i	0.0298007	+	0.0136095i
$560$	2.26936	+	1.96641i	0.0958978	+	0.0830959i
$561$	−4.41172	−	6.15834i	−0.186263	−	0.260005i
$562$	0.267663	−	0.122237i	0.0112907	−	0.00515627i
$563$	−45.3508	−	13.3162i	−1.91131	−	0.561211i	−0.980828	−	0.194874i	$-0.937570\pi$
$563$	−45.3508	−	13.3162i	−1.91131	−	0.561211i	−0.930482	−	0.366338i	$-0.880611\pi$
$564$	−6.64757	−	12.8051i	−0.279913	−	0.539194i
$565$	25.5784	+	56.0090i	1.07609	+	2.35631i
$566$	2.51041	−	17.4603i	0.105520	−	0.733910i
$567$	4.53678	+	4.65117i	0.190527	+	0.195331i
$568$	−2.70100	+	5.91437i	−0.113332	+	0.248162i
$569$	17.1815	+	11.0419i	0.720285	+	0.462899i	0.848736	−	0.528817i	$-0.177364\pi$
$569$	17.1815	+	11.0419i	0.720285	+	0.462899i	−0.128451	+	0.991716i	$0.541001\pi$
$570$	−23.7202	−	18.5451i	−0.993532	−	0.776769i
$571$	−6.38883	−	9.94122i	−0.267364	−	0.416027i	0.681448	−	0.731866i	$-0.261350\pi$
$571$	−6.38883	−	9.94122i	−0.267364	−	0.416027i	−0.948813	+	0.315839i	$0.897714\pi$
$572$	5.73582	+	6.61949i	0.239827	+	0.276775i
$573$	17.1480	−	29.8969i	0.716370	−	1.24896i
$574$		−	5.13864i		−	0.214483i
$575$	8.11482	−	58.4306i	0.338411	−	2.43672i
$576$	−0.125737	+	2.99736i	−0.00523904	+	0.124890i
$577$	5.59812	−	1.64376i	0.233053	−	0.0684304i	−0.163121	−	0.986606i	$-0.552156\pi$
$577$	5.59812	−	1.64376i	0.233053	−	0.0684304i	0.396174	+	0.918176i	$0.370338\pi$
$578$	−9.85869	+	8.54260i	−0.410068	+	0.355326i
$579$	6.28061	−	26.2135i	0.261013	−	1.08940i
$580$	−16.6005	+	2.38679i	−0.689299	+	0.0991062i
$581$	0.849761	−	1.32225i	0.0352540	−	0.0548563i
$582$	−7.38137	−	21.1329i	−0.305968	−	0.875985i
$583$	−5.29462	+	6.11032i	−0.219281	+	0.253064i
$584$	4.38072	+	0.629852i	0.181275	+	0.0260635i
$585$	−46.0309	+	18.7318i	−1.90314	+	0.774464i
$586$	−7.50885	+	25.5728i	−0.310188	+	1.05640i
$587$	4.90768	−	16.7140i	0.202562	−	0.689861i	−0.794068	−	0.607829i	$-0.792041\pi$
$587$	4.90768	−	16.7140i	0.202562	−	0.689861i	0.996630	−	0.0820325i	$-0.0261411\pi$
$588$	−10.4296	−	4.14108i	−0.430110	−	0.170775i
$589$	42.4560	+	6.10425i	1.74937	+	0.251521i
$590$	−0.0810517	+	0.0935386i	−0.00333684	+	0.00385092i
$591$	7.02201	−	2.45267i	0.288847	−	0.100890i
$592$	−0.855203	+	1.33072i	−0.0351486	+	0.0546923i
$593$	1.69315	−	0.243438i	0.0695293	−	0.00999681i	−0.107462	−	0.994209i	$-0.534273\pi$
$593$	1.69315	−	0.243438i	0.0695293	−	0.00999681i	0.176992	+	0.984212i	$0.443363\pi$
$594$	3.12607	−	10.9917i	0.128264	−	0.450996i
$595$	4.51316	−	3.91067i	0.185021	−	0.160322i
$596$	20.3556	−	5.97694i	0.833797	−	0.244825i
$597$	−25.3793	−	26.4662i	−1.03870	−	1.08319i
$598$	5.46909	+	18.3004i	0.223648	+	0.748359i
$599$		−	0.833970i		−	0.0340751i	−0.999855	−	0.0170376i	$-0.994577\pi$
$599$		−	0.833970i		−	0.0340751i	0.999855	−	0.0170376i	$-0.00542348\pi$
$600$	18.4810	+	10.6002i	0.754483	+	0.432751i
$601$	26.6742	+	30.7837i	1.08806	+	1.25569i	0.964705	+	0.263332i	$0.0848214\pi$
$601$	26.6742	+	30.7837i	1.08806	+	1.25569i	0.123360	+	0.992362i	$0.460633\pi$
$602$	−0.0759096	−	0.118118i	−0.00309385	−	0.00481412i
$603$	1.91345	+	18.9041i	0.0779218	+	0.769836i
$604$	4.92328	+	3.16400i	0.200325	+	0.128741i
$605$	10.6494	−	23.3190i	0.432961	−	0.948053i
$606$	1.16078	+	22.9946i	0.0471533	+	0.934092i
$607$	−1.03026	+	7.16565i	−0.0418171	+	0.290845i	0.958172	+	0.286193i	$0.0923898\pi$
$607$	−1.03026	+	7.16565i	−0.0418171	+	0.290845i	−0.999989	+	0.00465177i	$0.998519\pi$
$608$	−1.73617	−	3.80168i	−0.0704110	−	0.154179i
$609$	−4.47480	+	2.32302i	−0.181328	+	0.0941334i
$610$	45.1996	+	13.2718i	1.83008	+	0.537359i
$611$	30.1772	−	13.7814i	1.22084	−	0.557538i
$612$	5.86471	+	1.09585i	0.237067	+	0.0442970i
$613$	−1.67864	−	1.45455i	−0.0677995	−	0.0587486i	0.620302	−	0.784363i	$-0.287010\pi$
$613$	−1.67864	−	1.45455i	−0.0677995	−	0.0587486i	−0.688101	+	0.725615i	$0.741556\pi$
$614$	31.7724	+	14.5100i	1.28223	+	0.585575i
$615$	−9.84756	−	50.3251i	−0.397092	−	2.02930i
$616$	−0.225953	−	1.57154i	−0.00910392	−	0.0633191i
$617$	−25.2102	+	16.2016i	−1.01492	+	0.652252i	−0.938663	−	0.344836i	$-0.887934\pi$
$617$	−25.2102	+	16.2016i	−1.01492	+	0.652252i	−0.0762604	+	0.997088i	$0.524298\pi$
$618$	−20.3780	−	1.88752i	−0.819722	−	0.0759273i
$619$	1.36024	+	4.63255i	0.0546726	+	0.186198i	0.982302	−	0.187304i	$-0.0599751\pi$
$619$	1.36024	+	4.63255i	0.0546726	+	0.186198i	−0.927629	+	0.373502i	$0.878157\pi$
$620$	−42.6876			−1.71437
$621$	16.0668	−	19.0488i	0.644740	−	0.764402i
$622$	0.930554			0.0373118
$623$	0.253966	+	0.864930i	0.0101749	+	0.0346527i
$624$	−6.86876	−	0.636224i	−0.274970	−	0.0254693i
$625$	54.5140	−	35.0340i	2.18056	−	1.40136i
$626$	−2.64853	−	18.4209i	−0.105856	−	0.736247i
$627$	3.05724	+	15.6238i	0.122094	+	0.623953i
$628$	5.27109	+	2.40723i	0.210339	+	0.0960588i
$629$	2.37748	+	2.06009i	0.0947962	+	0.0821413i
$630$	8.85510	+	1.65462i	0.352796	+	0.0659215i
$631$	−35.4292	+	16.1800i	−1.41041	+	0.644115i	−0.967598	−	0.252498i	$-0.918748\pi$
$631$	−35.4292	+	16.1800i	−1.41041	+	0.644115i	−0.442817	+	0.896612i	$0.646021\pi$
$632$	4.29555	+	1.26129i	0.170868	+	0.0501713i
$633$	24.5618	−	12.7508i	0.976244	−	0.506800i
$634$	−7.02846	−	15.3902i	−0.279136	−	0.611222i
$635$	8.77250	−	61.0141i	0.348126	−	2.42127i
$636$	−0.321028	−	6.35946i	−0.0127296	−	0.252169i
$637$	10.7189	−	23.4711i	0.424699	−	0.929961i
$638$	7.45994	+	4.79421i	0.295342	+	0.189805i
$639$	1.96432	+	19.4067i	0.0777071	+	0.767716i
$640$	2.24874	+	3.49910i	0.0888892	+	0.138314i
$641$	1.82236	+	2.10312i	0.0719789	+	0.0830681i	0.790597	−	0.612337i	$-0.209770\pi$
$641$	1.82236	+	2.10312i	0.0719789	+	0.0830681i	−0.718618	+	0.695405i	$0.755225\pi$
$642$	−1.00867	−	0.578548i	−0.0398092	−	0.0228335i
$643$		−	24.1796i		−	0.953551i	−0.879025	−	0.476775i	$-0.841806\pi$
$643$		−	24.1796i		−	0.953551i	0.879025	−	0.476775i	$-0.158194\pi$
$644$	0.959463	−	3.32665i	0.0378081	−	0.131088i
$645$	−0.969776	−	1.01131i	−0.0381849	−	0.0398203i
$646$	−7.97498	+	2.34167i	−0.313772	+	0.0921316i
$647$	−26.9823	+	23.3803i	−1.06078	+	0.919174i	−0.996892	−	0.0787830i	$-0.974897\pi$
$647$	−26.9823	+	23.3803i	−1.06078	+	0.919174i	−0.0638914	+	0.997957i	$0.520351\pi$
$648$	4.21457	+	7.95219i	0.165564	+	0.312392i
$649$	0.0647759	−	0.00931337i	0.00254268	−	0.000365582i
$650$	−26.4854	+	41.2121i	−1.03884	+	1.61647i
$651$	−12.1152	+	4.23165i	−0.474832	+	0.165851i
$652$	−2.85066	+	3.28983i	−0.111640	+	0.128840i
$653$	−2.27969	−	0.327771i	−0.0892113	−	0.0128267i	0.0975646	−	0.995229i	$-0.468895\pi$
$653$	−2.27969	−	0.327771i	−0.0892113	−	0.0128267i	−0.186776	+	0.982403i	$0.559804\pi$
$654$	15.5024	+	6.15525i	0.606192	+	0.240689i
$655$	6.06421	−	20.6528i	0.236948	−	0.806972i
$656$	2.00535	−	6.82960i	0.0782958	−	0.266651i
$657$	12.2980	−	5.00455i	0.479791	−	0.195246i
$658$	−5.95239	−	0.855824i	−0.232048	−	0.0333635i
$659$	−25.4420	+	29.3616i	−0.991080	+	1.14377i	−0.00146862	+	0.999999i	$0.500467\pi$
$659$	−25.4420	+	29.3616i	−0.991080	+	1.14377i	−0.989611	+	0.143768i	$0.954078\pi$
$660$	−5.22453	−	14.9578i	−0.203364	−	0.582232i
$661$	−8.92799	+	13.8922i	−0.347258	+	0.540345i	−0.970319	−	0.241829i	$-0.922253\pi$
$661$	−8.92799	+	13.8922i	−0.347258	+	0.540345i	0.623060	+	0.782174i	$0.285889\pi$
$662$	−0.817121	+	0.117484i	−0.0317583	+	0.00456615i
$663$	−3.19645	+	13.3411i	−0.124140	+	0.518124i
$664$	1.64540	−	1.42575i	0.0638539	−	0.0553297i
$665$	−12.0414	+	3.53567i	−0.466945	+	0.137108i
$666$	−0.198895	+	4.74133i	−0.00770702	+	0.183723i
$667$	10.5326	+	16.2173i	0.407824	+	0.627935i
$668$			8.12827i			0.314492i
$669$	−9.13092	+	15.9194i	−0.353022	+	0.615478i
$670$	17.2516	+	19.9094i	0.666486	+	0.769166i
$671$	−13.4662	−	20.9538i	−0.519857	−	0.808913i
$672$	0.985085	+	0.770165i	0.0380005	+	0.0297098i
$673$	−20.1151	−	12.9272i	−0.775381	−	0.498307i	0.0921168	−	0.995748i	$-0.470637\pi$
$673$	−20.1151	−	12.9272i	−0.775381	−	0.498307i	−0.867498	+	0.497441i	$0.834273\pi$
$674$	−11.8278	+	25.8992i	−0.455588	+	0.997599i
$675$	63.9133	−	0.544102i	2.46002	−	0.0209425i
$676$	0.407241	−	2.83243i	0.0156631	−	0.108939i
$677$	15.5663	+	34.0854i	0.598262	+	1.31001i	0.930319	+	0.366751i	$0.119530\pi$
$677$	15.5663	+	34.0854i	0.598262	+	1.31001i	−0.332058	+	0.943259i	$0.607743\pi$
$678$	11.8137	+	22.7565i	0.453701	+	0.873960i
$679$	−8.95221	−	2.62861i	−0.343554	−	0.100877i
$680$	7.52443	−	3.43629i	0.288549	−	0.131776i
$681$	−9.29536	−	12.9754i	−0.356199	−	0.497219i
$682$	17.0578	+	14.7807i	0.653177	+	0.565981i
$683$	2.46051	+	1.12368i	0.0941488	+	0.0429963i	0.461933	−	0.886915i	$-0.347156\pi$
$683$	2.46051	+	1.12368i	0.0941488	+	0.0429963i	−0.367784	+	0.929911i	$0.619883\pi$
$684$	−10.2543	−	7.21473i	−0.392085	−	0.275862i
$685$	6.34600	+	44.1374i	0.242468	+	1.68640i
$686$	−8.18603	+	5.26084i	−0.312544	+	0.200860i
$687$	−1.82349	+	19.6867i	−0.0695706	+	0.751094i
$688$	−0.0547937	−	0.186610i	−0.00208899	−	0.00711444i
$689$	14.6415			0.557796
$690$	3.02136	−	34.4182i	0.115021	−	1.31028i
$691$	−27.2153			−1.03532			−0.517660	−	0.855586i	$-0.673197\pi$
$691$	−27.2153			−1.03532			−0.517660	+	0.855586i	$0.673197\pi$
$692$	−4.51163	−	15.3652i	−0.171506	−	0.584097i
$693$	−2.96555	−	3.72728i	−0.112652	−	0.141588i
$694$	0.0524339	−	0.0336972i	0.00199037	−	0.00127913i
$695$	−0.311521	−	2.16668i	−0.0118167	−	0.0821868i
$696$	−6.85387	+	1.34116i	−0.259795	+	0.0508364i
$697$	−12.8765	−	5.88049i	−0.487731	−	0.222739i
$698$	16.1223	+	13.9701i	0.610239	+	0.528775i
$699$	−24.5235	+	17.5682i	−0.927563	+	0.664489i
$700$	8.07765	−	3.68894i	0.305307	−	0.139429i
$701$	−3.55633	−	1.04423i	−0.134321	−	0.0394401i	0.213881	−	0.976860i	$-0.431389\pi$
$701$	−3.55633	−	1.04423i	−0.134321	−	0.0394401i	−0.348202	+	0.937420i	$0.613208\pi$
$702$	−18.7505	+	8.75674i	−0.707692	+	0.330502i
$703$	−2.74633	−	6.01363i	−0.103580	−	0.226808i
$704$	0.312985	−	2.17686i	0.0117961	−	0.0820435i
$705$	−59.9346	+	3.02552i	−2.25727	+	0.113948i
$706$	0.0918513	−	0.201126i	0.00345687	−	0.00756949i
$707$	8.07308	+	5.18825i	0.303619	+	0.195124i
$708$	−0.0317448	+	0.0406033i	−0.00119304	+	0.00152597i
$709$	15.5346	+	24.1722i	0.583413	+	0.907808i	0.999999	−	0.00128839i	$-0.000410109\pi$
$709$	15.5346	+	24.1722i	0.583413	+	0.907808i	−0.416587	+	0.909096i	$0.636774\pi$
$710$	17.7101	+	20.4386i	0.664650	+	0.767046i
$711$	13.0339	−	3.24043i	0.488810	−	0.121525i
$712$			1.24866i			0.0467955i
$713$	20.6612	+	44.6727i	0.773769	+	1.67301i
$714$	1.79487	−	1.72116i	0.0671714	−	0.0644127i
$715$	34.9557	−	10.2639i	1.30727	−	0.383849i
$716$	−5.40280	+	4.68155i	−0.201912	+	0.174958i
$717$	25.4690	+	6.10224i	0.951158	+	0.227892i
$718$	−4.05998	+	0.583737i	−0.151517	+	0.0217849i
$719$	−2.49443	+	3.88140i	−0.0930264	+	0.144752i	−0.884648	−	0.466260i	$-0.845601\pi$
$719$	−2.49443	+	3.88140i	−0.0930264	+	0.144752i	0.791621	+	0.611012i	$0.209237\pi$
$720$	11.1233	+	5.65480i	0.414542	+	0.210742i
$721$	−5.58597	+	6.44656i	−0.208033	+	0.240082i
$722$	−1.51730	−	0.218155i	−0.0564681	−	0.00811889i
$723$	1.81714	−	4.57660i	0.0675803	−	0.170206i
$724$	−4.90900	+	16.7185i	−0.182442	+	0.621339i
$725$	−13.9732	+	47.5884i	−0.518952	+	1.76739i
$726$	3.93943	−	9.92172i	0.146206	−	0.368229i
$727$	50.7325	+	7.29423i	1.88156	+	0.270528i	0.985022	−	0.172429i	$-0.0551615\pi$
$727$	50.7325	+	7.29423i	1.88156	+	0.270528i	0.896543	+	0.442957i	$0.146071\pi$
$728$	−1.88285	+	2.17293i	−0.0697832	+	0.0805341i
$729$	22.9591	+	14.2085i	0.850336	+	0.526240i
$730$	9.95239	−	15.4862i	0.368354	−	0.573171i
$731$	−0.382849	+	0.0550454i	−0.0141602	+	0.00203593i
$732$	19.0767	+	4.57067i	0.705093	+	0.168937i
$733$	−12.9779	+	11.2454i	−0.479351	+	0.415360i	−0.860732	−	0.509058i	$-0.829994\pi$
$733$	−12.9779	+	11.2454i	−0.479351	+	0.415360i	0.381382	+	0.924418i	$0.375448\pi$
$734$	−29.9598	+	8.79699i	−1.10584	+	0.324703i
$735$	−33.6889	+	32.3053i	−1.24263	+	1.19160i
$736$	2.57342	−	4.04692i	0.0948574	−	0.149171i
$737$		−	13.9291i		−	0.513085i
$738$	−5.15203	−	20.7229i	−0.189649	−	0.762822i
$739$	−9.77783	−	11.2842i	−0.359683	−	0.415097i	0.546850	−	0.837230i	$-0.315827\pi$
$739$	−9.77783	−	11.2842i	−0.359683	−	0.415097i	−0.906534	+	0.422134i	$0.861281\pi$
$740$	3.55713	+	5.53500i	0.130763	+	0.203471i
$741$	17.7571	−	22.7123i	0.652324	−	0.834359i
$742$	−2.23272	−	1.43488i	−0.0819656	−	0.0526761i
$743$	11.1515	−	24.4184i	0.409109	−	0.895825i	−0.587155	−	0.809474i	$-0.699752\pi$
$743$	11.1515	−	24.4184i	0.409109	−	0.895825i	0.996265	−	0.0863505i	$-0.0275205\pi$
$744$	−17.7533	+	0.896194i	−0.650868	+	0.0328561i
$745$	12.5580	−	87.3431i	0.460091	−	3.20000i
$746$	−0.138595	−	0.303482i	−0.00507434	−	0.0111113i
$747$	2.10119	−	6.18432i	0.0768785	−	0.226272i
$748$	−4.19656	−	1.23222i	−0.153441	−	0.0450544i
$749$	−0.440870	+	0.201339i	−0.0161090	+	0.00735676i
$750$	42.7561	−	30.6297i	1.56123	−	1.11844i
$751$	5.53673	+	4.79760i	0.202038	+	0.175067i	0.750003	−	0.661434i	$-0.230052\pi$
$751$	5.53673	+	4.79760i	0.202038	+	0.175067i	−0.547965	+	0.836501i	$0.684597\pi$
$752$	−7.57714	−	3.46037i	−0.276310	−	0.126187i
$753$	4.52790	−	0.886015i	0.165006	−	0.0322882i
$754$	−2.28538	−	15.8951i	−0.0832285	−	0.578867i
$755$	20.4779	−	13.1603i	0.745266	−	0.478953i
$756$	3.71748	+	0.502231i	0.135204	+	0.0182660i
$757$	−12.7459	−	43.4086i	−0.463258	−	1.57771i	−0.777827	−	0.628478i	$-0.783678\pi$
$757$	−12.7459	−	43.4086i	−0.463258	−	1.57771i	0.314569	−	0.949235i	$-0.398140\pi$
$758$	11.2993			0.410408
$759$	−13.1247	+	12.7072i	−0.476396	+	0.461243i
$760$	−17.3836			−0.630570
$761$	−7.11988	−	24.2481i	−0.258095	−	0.878993i	−0.981966	−	0.189057i	$-0.939457\pi$
$761$	−7.11988	−	24.2481i	−0.258095	−	0.878993i	0.723871	−	0.689936i	$-0.242361\pi$
$762$	2.36745	−	25.5593i	0.0857635	−	0.925915i
$763$	5.84856	−	3.75864i	0.211732	−	0.136072i
$764$	−2.83189	−	19.6962i	−0.102454	−	0.712583i
$765$	14.2796	−	20.2958i	0.516282	−	0.733795i
$766$	−6.19601	−	2.82962i	−0.223871	−	0.102238i
$767$	−0.0895640	−	0.0776077i	−0.00323397	−	0.00280225i
$768$	1.00869	+	1.40803i	0.0363979	+	0.0508079i
$769$	15.0249	−	6.86164i	0.541812	−	0.247437i	−0.125659	−	0.992074i	$-0.540104\pi$
$769$	15.0249	−	6.86164i	0.541812	−	0.247437i	0.667470	+	0.744636i	$0.267377\pi$
$770$	−6.33637	−	1.86052i	−0.228347	−	0.0670487i
$771$	7.92613	+	15.2680i	0.285453	+	0.549864i
$772$	−6.46498	−	14.1563i	−0.232680	−	0.509497i
$773$	−1.49875	+	10.4240i	−0.0539062	+	0.374926i	0.944954	+	0.327202i	$0.106106\pi$
$773$	−1.49875	+	10.4240i	−0.0539062	+	0.374926i	−0.998861	+	0.0477236i	$0.984803\pi$
$774$	−0.424552	−	0.400234i	−0.0152602	−	0.0143861i
$775$	−52.4419	+	114.832i	−1.88377	+	4.12488i
$776$	−10.8723	−	6.98719i	−0.390292	−	0.250826i
$777$	1.55824	+	1.21827i	0.0559015	+	0.0437053i
$778$	5.57319	+	8.67205i	0.199808	+	0.310908i
$779$	19.4811	+	22.4823i	0.697981	+	0.805514i
$780$	−14.2755	+	24.8888i	−0.511146	+	0.891161i
$781$		−	14.2994i		−	0.511671i
$782$	−7.23799	−	6.21115i	−0.258830	−	0.222110i
$783$	−15.7168	+	13.8547i	−0.561671	+	0.495125i
$784$	−6.21638	+	1.82529i	−0.222014	+	0.0651891i
$785$	18.2156	−	15.7839i	0.650142	−	0.563351i
$786$	2.08845	−	8.71660i	0.0744926	−	0.310911i
$787$	−5.59262	+	0.804097i	−0.199355	+	0.0286630i	−0.241269	−	0.970458i	$-0.577564\pi$
$787$	−5.59262	+	0.804097i	−0.199355	+	0.0286630i	0.0419138	+	0.999121i	$0.486655\pi$
$788$	2.32170	−	3.61263i	0.0827071	−	0.128695i
$789$	5.63236	+	16.1255i	0.200517	+	0.574081i
$790$	12.1943	−	14.0729i	0.433853	−	0.500692i
$791$	10.5782	+	1.52092i	0.376119	+	0.0540777i
$792$	−2.48685	−	6.11111i	−0.0883665	−	0.217149i
$793$	−12.7079	+	43.2790i	−0.451269	+	1.53688i
$794$	3.29092	−	11.2079i	0.116791	−	0.397752i
$795$	−24.6158	−	9.77373i	−0.873033	−	0.346639i
$796$	−20.9550	−	3.01288i	−0.742731	−	0.106789i
$797$	31.8424	−	36.7480i	1.12791	−	1.30168i	0.179818	−	0.983700i	$-0.442449\pi$
$797$	31.8424	−	36.7480i	1.12791	−	1.30168i	0.948097	−	0.317983i	$-0.103005\pi$
$798$	−4.93366	+	1.72325i	−0.174650	+	0.0610024i
$799$	−8.95625	+	13.9362i	−0.316849	+	0.493027i
$800$	12.1754	−	1.75055i	0.430464	−	0.0618913i
$801$	1.89137	+	3.23343i	0.0668283	+	0.114248i
$802$	10.7143	−	9.28399i	0.378335	−	0.327829i
$803$	−9.33908	+	2.74220i	−0.329569	+	0.0967702i
$804$	7.59272	+	7.91791i	0.267775	+	0.279243i
$805$	−10.9286	−	9.37818i	−0.385183	−	0.330538i
$806$		−	40.8737i		−	1.43972i
$807$	5.07317	+	2.90984i	0.178584	+	0.102431i
$808$	8.70496	+	10.0461i	0.306239	+	0.353419i
$809$	−26.8673	−	41.8063i	−0.944602	−	1.46983i	−0.881700	−	0.471810i	$-0.843601\pi$
$809$	−26.8673	−	41.8063i	−0.944602	−	1.46983i	−0.0629022	−	0.998020i	$-0.520036\pi$
$810$	37.3695	−	2.20551i	1.31303	−	0.0774936i
$811$	−24.3906	−	15.6749i	−0.856471	−	0.550420i	0.0371160	−	0.999311i	$-0.488183\pi$
$811$	−24.3906	−	15.6749i	−0.856471	−	0.550420i	−0.893587	+	0.448891i	$0.851819\pi$
$812$	−1.20924	+	2.64786i	−0.0424359	+	0.0929216i
$813$	1.25607	+	24.8824i	0.0440523	+	0.872663i
$814$	0.495090	−	3.44343i	0.0173529	−	0.120692i
$815$	7.52156	+	16.4699i	0.263469	+	0.576916i
$816$	3.05719	−	1.58709i	0.107023	−	0.0555592i
$817$	0.779912	+	0.229003i	0.0272857	+	0.00801179i
$818$	−5.87874	+	2.68473i	−0.205545	+	0.0938694i
$819$	−1.58431	+	8.47884i	−0.0553602	+	0.296275i
$820$	−22.3749	−	19.3880i	−0.781366	−	0.677057i
$821$	−51.9920	−	23.7439i	−1.81453	−	0.828669i	−0.937206	−	0.348775i	$-0.886598\pi$
$821$	−51.9920	−	23.7439i	−1.81453	−	0.828669i	−0.877326	−	0.479894i	$-0.840675\pi$
$822$	3.56587	+	18.2231i	0.124374	+	0.635602i
$823$	−6.26314	−	43.5611i	−0.218319	−	1.51844i	−0.744241	−	0.667911i	$-0.767189\pi$
$823$	−6.26314	−	43.5611i	−0.218319	−	1.51844i	0.525922	−	0.850533i	$-0.323720\pi$
$824$	−9.93990	+	6.38799i	−0.346273	+	0.222536i
$825$	−46.6556	−	4.32151i	−1.62434	−	0.150456i
$826$	0.00605222	+	0.0206120i	0.000210584	+	0.000717182i
$827$	−0.0645061			−0.00224310			−0.00112155	−	0.999999i	$-0.500357\pi$
$827$	−0.0645061			−0.00224310			−0.00112155	+	0.999999i	$0.500357\pi$
$828$	0.533969	−	14.3776i	0.0185567	−	0.499656i
$829$	−32.2724			−1.12087			−0.560433	−	0.828200i	$-0.689365\pi$
$829$	−32.2724			−1.12087			−0.560433	+	0.828200i	$0.689365\pi$
$830$	−2.55129	−	8.68891i	−0.0885567	−	0.301596i
$831$	16.4018	+	1.51923i	0.568973	+	0.0527015i
$832$	−3.35042	+	2.15319i	−0.116155	+	0.0746483i
$833$	1.83368	+	12.7535i	0.0635333	+	0.441884i
$834$	−0.175046	−	0.894559i	−0.00606136	−	0.0309760i
$835$	30.7535	+	14.0446i	1.06427	+	0.486034i
$836$	6.94643	+	6.01912i	0.240247	+	0.208176i
$837$	−44.6151	+	29.2120i	−1.54212	+	1.00972i
$838$	7.90627	−	3.61067i	0.273118	−	0.124729i
$839$	34.8953	+	10.2462i	1.20472	+	0.353738i	0.821656	−	0.569983i	$-0.193050\pi$
$839$	34.8953	+	10.2462i	1.20472	+	0.353738i	0.383065	+	0.923721i	$0.374869\pi$
$840$	4.61604	−	2.39634i	0.159268	−	0.0826814i
$841$	5.29319	+	11.5905i	0.182524	+	0.399671i
$842$	−4.16030	+	28.9355i	−0.143373	+	0.997184i
$843$	−0.0256952	−	0.509014i	−0.000884990	−	0.0175314i
$844$	6.63740	−	14.5339i	0.228469	−	0.500277i
$845$	−10.0129	−	6.43488i	−0.344453	−	0.221367i
$846$	−24.8627	+	2.51656i	−0.854796	+	0.0865213i
$847$	−2.40557	−	3.74314i	−0.0826564	−	0.128616i
$848$	−2.40747	−	2.77837i	−0.0826729	−	0.0954096i
$849$	−26.5030	−	15.2014i	−0.909580	−	0.521711i
$850$		−	24.4626i		−	0.839060i
$851$	4.07071	−	6.40154i	0.139542	−	0.219442i
$852$	7.79455	+	8.12838i	0.267037	+	0.278474i
$853$	−10.8526	+	3.18660i	−0.371585	+	0.109107i	−0.462193	−	0.886780i	$-0.652937\pi$
$853$	−10.8526	+	3.18660i	−0.371585	+	0.109107i	0.0906080	+	0.995887i	$0.471119\pi$
$854$	6.17924	−	5.35434i	0.211449	−	0.183222i
$855$	−45.0153	+	26.3313i	−1.53949	+	0.900513i
$856$	−0.664519	+	0.0955434i	−0.0227128	+	0.00326561i
$857$	2.88250	−	4.48526i	0.0984643	−	0.153213i	−0.788526	−	0.615001i	$-0.789155\pi$
$857$	2.88250	−	4.48526i	0.0984643	−	0.153213i	0.886990	+	0.461788i	$0.152792\pi$
$858$	14.3222	−	5.00253i	0.488953	−	0.170784i
$859$	21.0275	−	24.2670i	0.717448	−	0.827979i	−0.273550	−	0.961858i	$-0.588198\pi$
$859$	21.0275	−	24.2670i	0.717448	−	0.827979i	0.990998	+	0.133879i	$0.0427433\pi$
$860$	−0.800719	−	0.115126i	−0.0273043	−	0.00392577i
$861$	−8.27218	−	3.28448i	−0.281915	−	0.111935i
$862$	8.62653	−	29.3793i	0.293821	−	1.00066i
$863$	9.34922	−	31.8405i	0.318251	−	1.08386i	−0.632668	−	0.774423i	$-0.718040\pi$
$863$	9.34922	−	31.8405i	0.318251	−	1.08386i	0.950919	−	0.309440i	$-0.100142\pi$
$864$	4.74479	+	2.11824i	0.161421	+	0.0720642i
$865$	−65.9300	−	9.47931i	−2.24169	−	0.322306i
$866$	12.0474	−	13.9035i	0.409388	−	0.472458i
$867$	7.45048	+	21.3307i	0.253032	+	0.724430i
$868$	−4.00567	+	6.23294i	−0.135961	+	0.211560i
$869$	−9.74557	+	1.40120i	−0.330596	+	0.0475325i
$870$	−6.76833	+	28.2491i	−0.229468	+	0.957734i
$871$	−19.0634	+	16.5185i	−0.645938	+	0.559709i
$872$	9.23994	−	2.71309i	0.312904	−	0.0918768i
$873$	−38.7377	−	1.62501i	−1.31107	−	0.0549984i
$874$	8.41385	+	18.1920i	0.284603	+	0.615355i
$875$		−	21.9220i		−	0.741100i
$876$	3.81397	−	6.64950i	0.128862	−	0.224666i
$877$	−2.59283	−	2.99228i	−0.0875535	−	0.101042i	0.710282	−	0.703917i	$-0.248567\pi$
$877$	−2.59283	−	2.99228i	−0.0875535	−	0.101042i	−0.797836	+	0.602875i	$0.794022\pi$
$878$	−5.62450	−	8.75189i	−0.189818	−	0.295362i
$879$	36.3676	+	28.4332i	1.22665	+	0.959027i
$880$	−7.69539	−	4.94553i	−0.259412	−	0.166714i
$881$	7.00372	−	15.3360i	0.235961	−	0.516683i	−0.754195	−	0.656651i	$-0.771973\pi$
$881$	7.00372	−	15.3360i	0.235961	−	0.516683i	0.990156	+	0.139967i	$0.0446998\pi$
$882$	−13.3326	+	14.1427i	−0.448933	+	0.476210i
$883$	1.93605	−	13.4655i	0.0651533	−	0.453151i	−0.930964	−	0.365112i	$-0.881031\pi$
$883$	1.93605	−	13.4655i	0.0651533	−	0.453151i	0.996117	−	0.0880394i	$-0.0280601\pi$
$884$	3.29028	+	7.20471i	0.110664	+	0.242320i
$885$	0.0987725	+	0.190264i	0.00332020	+	0.00639567i
$886$	1.02085	+	0.299749i	0.0342962	+	0.0100703i
$887$	44.8662	−	20.4897i	1.50646	−	0.687977i	0.520332	−	0.853964i	$-0.325808\pi$
$887$	44.8662	−	20.4897i	1.50646	−	0.687977i	0.986128	+	0.165987i	$0.0530808\pi$
$888$	1.59557	+	2.22727i	0.0535440	+	0.0747422i
$889$	−8.08566	−	7.00627i	−0.271184	−	0.234983i
$890$	4.72433	+	2.15753i	0.158360	+	0.0723205i
$891$	−15.6964	−	12.0580i	−0.525849	−	0.403957i
$892$	1.50791	+	10.4877i	0.0504886	+	0.351156i
$893$	29.2871	−	18.8217i	0.980057	−	0.629844i
$894$	3.38905	−	36.5887i	0.113347	−	1.22371i
$895$	8.37737	+	28.5307i	0.280025	+	0.953677i
$896$	0.721929			0.0241180
$897$	32.9557	+	2.89298i	1.10036	+	0.0965938i
$898$	12.0585			0.402398
$899$	−11.6585	−	39.7052i	−0.388833	−	1.32424i
$900$	28.8767	−	22.9754i	0.962558	−	0.765845i
$901$	−6.15059	+	3.95274i	−0.204906	+	0.131685i
$902$	2.22781	+	15.4947i	0.0741778	+	0.515918i
$903$	−0.238665	+	0.0467018i	−0.00794228	+	0.00155414i
$904$	13.4657	+	6.14956i	0.447861	+	0.204531i
$905$	54.7727	+	47.4608i	1.82070	+	1.57765i
$906$	8.24024	−	5.90316i	0.273764	−	0.196119i
$907$	31.8531	−	14.5468i	1.05766	−	0.483019i	0.190834	−	0.981622i	$-0.438881\pi$
$907$	31.8531	−	14.5468i	1.05766	−	0.483019i	0.866830	+	0.498603i	$0.166153\pi$
$908$	−8.84202	−	2.59625i	−0.293433	−	0.0861596i
$909$	37.7586	+	12.8289i	1.25238	+	0.425508i
$910$	4.96798	+	10.8784i	0.164687	+	0.360614i
$911$	−3.99792	+	27.8061i	−0.132457	+	0.921259i	0.809881	+	0.586595i	$0.199532\pi$
$911$	−3.99792	+	27.8061i	−0.132457	+	0.921259i	−0.942338	+	0.334664i	$0.891377\pi$
$912$	−7.22967	+	0.364956i	−0.239398	+	0.0120849i
$913$	−1.98907	+	4.35545i	−0.0658285	+	0.144144i
$914$	−5.41926	−	3.48275i	−0.179253	−	0.115199i
$915$	50.2553	−	64.2793i	1.66139	−	2.12501i
$916$	6.17129	+	9.60272i	0.203905	+	0.317283i
$917$	−2.44653	−	2.82345i	−0.0807916	−	0.0932385i
$918$	5.51266	−	8.74058i	0.181945	−	0.288482i
$919$		−	9.32003i		−	0.307439i	−0.988115	−	0.153720i	$-0.950875\pi$
$919$		−	9.32003i		−	0.307439i	0.988115	−	0.153720i	$-0.0491253\pi$
$920$	−10.8650	−	16.7291i	−0.358210	−	0.551543i
$921$	43.6663	−	41.8729i	1.43885	−	1.37976i
$922$	7.40412	−	2.17405i	0.243842	−	0.0715984i
$923$	−19.5701	+	16.9576i	−0.644159	+	0.558167i
$924$	−2.67429	−	0.640745i	−0.0879776	−	0.0210790i
$925$	19.2594	−	2.76908i	0.633244	−	0.0910468i
$926$	8.47892	−	13.1935i	0.278635	−	0.433564i
$927$	−16.0636	+	31.5980i	−0.527597	+	1.03781i
$928$	−2.64048	+	3.04728i	−0.0866781	+	0.100032i
$929$	7.82580	+	1.12518i	0.256756	+	0.0369160i	0.269491	−	0.963003i	$-0.413145\pi$
$929$	7.82580	+	1.12518i	0.256756	+	0.0369160i	−0.0127347	+	0.999919i	$0.504054\pi$
$930$	−27.2847	+	68.7185i	−0.894702	+	2.25337i
$931$	7.62857	−	25.9805i	0.250016	−	0.851477i
$932$	−4.90690	+	16.7114i	−0.160731	+	0.547399i
$933$	0.594785	−	1.49801i	0.0194724	−	0.0490425i
$934$	−0.311698	−	0.0448154i	−0.0101991	−	0.00146641i
$935$	−11.9133	+	13.7486i	−0.389605	+	0.449628i
$936$	−5.41452	+	10.6507i	−0.176979	+	0.348128i
$937$	−22.5621	+	35.1073i	−0.737071	+	1.14691i	0.246980	+	0.969021i	$0.420562\pi$
$937$	−22.5621	+	35.1073i	−0.737071	+	1.14691i	−0.984051	+	0.177885i	$0.943075\pi$
$938$	4.52586	−	0.650720i	0.147774	−	0.0212468i
$939$	−31.3468	−	7.51054i	−1.02297	−	0.245097i
$940$	−26.1847	+	22.6892i	−0.854051	+	0.740039i
$941$	−19.1703	+	5.62891i	−0.624934	+	0.183497i	−0.578842	−	0.815440i	$-0.696495\pi$
$941$	−19.1703	+	5.62891i	−0.624934	+	0.183497i	−0.0460923	+	0.998937i	$0.514677\pi$
$942$	7.24429	−	6.94677i	0.236032	−	0.226338i
$943$	−9.45991	+	32.7994i	−0.308057	+	1.06810i
$944$			0.0297566i			0.000968494i
$945$	8.32354	−	13.1974i	0.270765	−	0.429310i
$946$	0.280102	+	0.323255i	0.00910690	+	0.0105099i
$947$	6.85830	+	10.6717i	0.222865	+	0.346785i	0.934623	−	0.355640i	$-0.115737\pi$
$947$	6.85830	+	10.6717i	0.222865	+	0.346785i	−0.711758	+	0.702425i	$0.752101\pi$
$948$	4.77602	−	6.10879i	0.155118	−	0.198404i
$949$	14.8282	+	9.52950i	0.481344	+	0.309341i
$950$	−21.3559	+	46.7628i	−0.692876	+	1.51719i
$951$	−29.2675	+	1.47744i	−0.949065	+	0.0479091i
$952$	0.204325	−	1.42112i	0.00662223	−	0.0460586i
$953$	15.4711	+	33.8771i	0.501159	+	1.09739i	0.976091	+	0.217363i	$0.0697456\pi$
$953$	15.4711	+	33.8771i	0.501159	+	1.09739i	−0.474931	+	0.880023i	$0.657527\pi$
$954$	−10.4427	−	3.54800i	−0.338093	−	0.114871i
$955$	−79.4141	−	23.3181i	−2.56978	−	0.754555i
$956$	13.7543	−	6.28137i	0.444845	−	0.203154i
$957$	12.4859	−	8.94468i	0.403612	−	0.289141i
$958$	−21.4660	−	18.6004i	−0.693534	−	0.600951i
$959$	7.04012	+	3.21512i	0.227337	+	0.103822i
$960$	7.07019	−	1.38349i	0.228190	−	0.0446519i
$961$	−10.5779	−	73.5713i	−0.341224	−	2.37327i
$962$	−5.29981	+	3.40598i	−0.170873	+	0.109813i
$963$	−1.57606	+	1.25397i	−0.0507880	+	0.0404087i
$964$	−0.800955	−	2.72780i	−0.0257970	−	0.0878566i
$965$	−64.7314			−2.08378
$966$	−4.74198	−	3.67085i	−0.152571	−	0.118108i
$967$	−3.55846			−0.114432			−0.0572162	−	0.998362i	$-0.518222\pi$
$967$	−3.55846			−0.114432			−0.0572162	+	0.998362i	$0.518222\pi$
$968$	−1.73641	−	5.91366i	−0.0558103	−	0.190072i
$969$	−1.32778	+	14.3349i	−0.0426543	+	0.460502i
$970$	−45.2221	+	29.0625i	−1.45199	+	0.933140i
$971$	6.95460	+	48.3703i	0.223184	+	1.55228i	0.725884	+	0.687817i	$0.241431\pi$
$971$	6.95460	+	48.3703i	0.223184	+	1.55228i	−0.502700	+	0.864461i	$0.667660\pi$
$972$	15.4953	−	1.70179i	0.497012	−	0.0545850i
$973$	−0.345596	−	0.157828i	−0.0110793	−	0.00505974i
$974$	−11.6240	−	10.0722i	−0.372456	−	0.322735i
$975$	49.4145	+	68.9778i	1.58253	+	2.20906i
$976$	10.3022	−	4.70484i	0.329764	−	0.150598i
$977$	−14.8350	−	4.35595i	−0.474614	−	0.139359i	0.0356727	−	0.999364i	$-0.488643\pi$
$977$	−14.8350	−	4.35595i	−0.474614	−	0.139359i	−0.510287	+	0.860004i	$0.670461\pi$
$978$	3.47391	+	6.69176i	0.111083	+	0.213979i
$979$	−1.14078	−	2.49795i	−0.0364593	−	0.0798348i
$980$	−3.83509	+	26.6737i	−0.122508	+	0.852059i
$981$	19.8174	−	21.0215i	0.632722	−	0.671166i
$982$	−15.1924	+	33.2666i	−0.484808	+	1.06158i
$983$	−31.5534	−	20.2782i	−1.00640	−	0.646773i	−0.0699398	−	0.997551i	$-0.522281\pi$
$983$	−31.5534	−	20.2782i	−1.00640	−	0.646773i	−0.936459	+	0.350778i	$0.885917\pi$
$984$	−9.71253	−	7.59351i	−0.309624	−	0.242072i
$985$	−9.65686	−	15.0264i	−0.307693	−	0.478780i
$986$	5.25123	+	6.06024i	0.167233	+	0.192997i
$987$	−5.18231	+	9.03514i	−0.164955	+	0.287592i
$988$		−	16.6450i		−	0.529547i
$989$	0.267076	+	0.893678i	0.00849253	+	0.0284173i
$990$	−27.4185	−	1.15018i	−0.871416	−	0.0365552i
$991$	51.2407	−	15.0456i	1.62771	−	0.477940i	0.664636	−	0.747167i	$-0.268586\pi$
$991$	51.2407	−	15.0456i	1.62771	−	0.477940i	0.963077	+	0.269227i	$0.0867683\pi$
$992$	−7.75621	+	6.72079i	−0.246260	+	0.213385i
$993$	−0.333155	+	1.39049i	−0.0105724	+	0.0441260i
$994$	4.64616	−	0.668017i	0.147367	−	0.0211882i
$995$	−47.6069	+	74.0778i	−1.50924	+	2.34842i
$996$	−1.24347	−	3.56006i	−0.0394010	−	0.112805i
$997$	29.6921	−	34.2665i	0.940358	−	1.08523i	−0.0558682	−	0.998438i	$-0.517793\pi$
$997$	29.6921	−	34.2665i	0.940358	−	1.08523i	0.996226	−	0.0867930i	$-0.0276619\pi$
$998$	−15.5056	−	2.22936i	−0.490820	−	0.0705692i
$999$	7.50546	+	3.35071i	0.237462	+	0.106012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.f.a.83.1	yes	80
3.2	odd	2	inner	138.2.f.a.83.6	yes	80
23.5	odd	22	inner	138.2.f.a.5.6	yes	80
69.5	even	22	inner	138.2.f.a.5.1	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.f.a.5.1	✓	80	69.5	even	22	inner
138.2.f.a.5.6	yes	80	23.5	odd	22	inner
138.2.f.a.83.1	yes	80	1.1	even	1	trivial
138.2.f.a.83.6	yes	80	3.2	odd	2	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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	138.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.281733 - 0.959493i) q^{2} +(-1.72467 - 0.159749i) q^{3} +(-0.841254 + 0.540641i) q^{4} +(0.591943 + 4.11706i) q^{5} +(0.332618 + 1.69981i) q^{6} +(0.656690 + 0.299900i) q^{7} +(0.755750 + 0.654861i) q^{8} +(2.94896 + 0.551026i) q^{9} +O(q^{10})\)	\(q+(-0.281733 - 0.959493i) q^{2} +(-1.72467 - 0.159749i) q^{3} +(-0.841254 + 0.540641i) q^{4} +(0.591943 + 4.11706i) q^{5} +(0.332618 + 1.69981i) q^{6} +(0.656690 + 0.299900i) q^{7} +(0.755750 + 0.654861i) q^{8} +(2.94896 + 0.551026i) q^{9} +(3.78352 - 1.72787i) q^{10} +(-2.11016 - 0.619599i) q^{11} +(1.53725 - 0.798037i) q^{12} +(1.65446 + 3.62275i) q^{13} +(0.102741 - 0.714581i) q^{14} +(-0.363212 - 7.19512i) q^{15} +(0.415415 - 0.909632i) q^{16} +(-1.67303 - 1.07519i) q^{17} +(-0.302112 - 2.98475i) q^{18} +(2.25954 + 3.51591i) q^{19} +(-2.72382 - 3.14346i) q^{20} +(-1.08466 - 0.622134i) q^{21} +2.19925i q^{22} +(-1.97129 + 4.37196i) q^{23} +(-1.19880 - 1.25015i) q^{24} +(-11.8023 + 3.46547i) q^{25} +(3.00989 - 2.60809i) q^{26} +(-4.99795 - 1.42143i) q^{27} +(-0.714581 + 0.102741i) q^{28} +(2.17993 - 3.39204i) q^{29} +(-6.80134 + 2.37560i) q^{30} +(6.72079 - 7.75621i) q^{31} +(-0.989821 - 0.142315i) q^{32} +(3.54035 + 1.40570i) q^{33} +(-0.560292 + 1.90818i) q^{34} +(-0.845983 + 2.88115i) q^{35} +(-2.77873 + 1.13078i) q^{36} +(-1.56573 - 0.225118i) q^{37} +(2.73690 - 3.15855i) q^{38} +(-2.27466 - 6.51234i) q^{39} +(-2.24874 + 3.49910i) q^{40} +(7.04547 - 1.01299i) q^{41} +(-0.291348 + 1.21600i) q^{42} +(0.146984 - 0.127363i) q^{43} +(2.11016 - 0.619599i) q^{44} +(-0.522990 + 12.4672i) q^{45} +(4.75024 + 0.659712i) q^{46} -8.32990i q^{47} +(-0.861765 + 1.50245i) q^{48} +(-4.24272 - 4.89636i) q^{49} +(6.65018 + 10.3479i) q^{50} +(2.71367 + 2.12162i) q^{51} +(-3.35042 - 2.15319i) q^{52} +(1.52719 - 3.34409i) q^{53} +(0.0442340 + 5.19596i) q^{54} +(1.30183 - 9.05442i) q^{55} +(0.299900 + 0.656690i) q^{56} +(-3.33529 - 6.42473i) q^{57} +(-3.86880 - 1.13598i) q^{58} +(-0.0270675 + 0.0123613i) q^{59} +(4.19553 + 5.85655i) q^{60} +(8.55934 + 7.41671i) q^{61} +(-9.33549 - 4.26338i) q^{62} +(1.77130 + 1.24625i) q^{63} +(0.142315 + 0.989821i) q^{64} +(-13.9357 + 8.95595i) q^{65} +(0.351326 - 3.79297i) q^{66} +(1.78438 + 6.07703i) q^{67} +1.98874 q^{68} +(4.09823 - 7.22527i) q^{69} +3.00279 q^{70} +(1.83181 + 6.23857i) q^{71} +(1.86783 + 2.34760i) q^{72} +(3.72319 - 2.39275i) q^{73} +(0.225118 + 1.56573i) q^{74} +(20.9087 - 4.09138i) q^{75} +(-3.80168 - 1.73617i) q^{76} +(-1.19990 - 1.03972i) q^{77} +(-5.60770 + 4.01726i) q^{78} +(4.07232 - 1.85977i) q^{79} +(3.99091 + 1.17184i) q^{80} +(8.39274 + 3.24991i) q^{81} +(-2.95689 - 6.47469i) q^{82} +(0.309844 - 2.15501i) q^{83} +(1.24883 - 0.0630413i) q^{84} +(3.43629 - 7.52443i) q^{85} +(-0.163614 - 0.105148i) q^{86} +(-4.30154 + 5.50191i) q^{87} +(-1.18900 - 1.85012i) q^{88} +(0.817699 + 0.943675i) q^{89} +(12.1095 - 3.01062i) q^{90} +2.87520i q^{91} +(-0.705309 - 4.74368i) q^{92} +(-12.8302 + 12.3032i) q^{93} +(-7.99248 + 2.34680i) q^{94} +(-13.1377 + 11.3839i) q^{95} +(1.68438 + 0.403568i) q^{96} +(-12.7924 + 1.83926i) q^{97} +(-3.50271 + 5.45033i) q^{98} +(-5.88137 - 2.98993i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6}+O(q^{10}) \) 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6	\( 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6} - 4 q^{12} + 8 q^{13} - 22 q^{15} - 8 q^{16} - 28 q^{18} - 66 q^{21} - 4 q^{24} - 48 q^{25} - 38 q^{27} - 44 q^{30} - 16 q^{31} - 22 q^{33} - 44 q^{37} - 24 q^{39} - 44 q^{43} - 16 q^{46} + 4 q^{48} - 76 q^{49} - 8 q^{52} - 6 q^{54} + 64 q^{55} + 66 q^{57} + 36 q^{58} + 22 q^{60} + 88 q^{61} + 110 q^{63} + 8 q^{64} + 88 q^{66} + 44 q^{67} + 82 q^{69} + 112 q^{70} + 28 q^{72} + 52 q^{73} + 136 q^{75} + 82 q^{78} + 88 q^{79} + 36 q^{81} + 44 q^{82} + 22 q^{84} + 20 q^{85} - 10 q^{87} + 8 q^{93} - 56 q^{94} + 4 q^{96} - 132 q^{97} - 66 q^{99}+O(q^{100}) \) 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6 - 4 * q^12 + 8 * q^13 - 22 * q^15 - 8 * q^16 - 28 * q^18 - 66 * q^21 - 4 * q^24 - 48 * q^25 - 38 * q^27 - 44 * q^30 - 16 * q^31 - 22 * q^33 - 44 * q^37 - 24 * q^39 - 44 * q^43 - 16 * q^46 + 4 * q^48 - 76 * q^49 - 8 * q^52 - 6 * q^54 + 64 * q^55 + 66 * q^57 + 36 * q^58 + 22 * q^60 + 88 * q^61 + 110 * q^63 + 8 * q^64 + 88 * q^66 + 44 * q^67 + 82 * q^69 + 112 * q^70 + 28 * q^72 + 52 * q^73 + 136 * q^75 + 82 * q^78 + 88 * q^79 + 36 * q^81 + 44 * q^82 + 22 * q^84 + 20 * q^85 - 10 * q^87 + 8 * q^93 - 56 * q^94 + 4 * q^96 - 132 * q^97 - 66 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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