LMFDB - Embedded newform 138.2.f.a.5.6

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			5.6
Character	$\chi$	$=$	138.5
Dual form			138.2.f.a.83.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.281733 - 0.959493i) q^{2} +(0.0873233 + 1.72985i) q^{3} +(-0.841254 - 0.540641i) q^{4} +(-0.591943 + 4.11706i) q^{5} +(1.68438 + 0.403568i) q^{6} +(0.656690 - 0.299900i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(-2.98475 + 0.302112i) q^{9} +O(q^{10})$	\(q+(0.281733 - 0.959493i) q^{2} +(0.0873233 + 1.72985i) q^{3} +(-0.841254 - 0.540641i) q^{4} +(-0.591943 + 4.11706i) q^{5} +(1.68438 + 0.403568i) q^{6} +(0.656690 - 0.299900i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(-2.98475 + 0.302112i) q^{9} +(3.78352 + 1.72787i) q^{10} +(2.11016 - 0.619599i) q^{11} +(0.861765 - 1.50245i) q^{12} +(1.65446 - 3.62275i) q^{13} +(-0.102741 - 0.714581i) q^{14} +(-7.17357 - 0.664457i) q^{15} +(0.415415 + 0.909632i) q^{16} +(1.67303 - 1.07519i) q^{17} +(-0.551026 + 2.94896i) q^{18} +(2.25954 - 3.51591i) q^{19} +(2.72382 - 3.14346i) q^{20} +(0.576126 + 1.10979i) 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} +(-0.783247 - 5.13678i) q^{27} +(-0.714581 - 0.102741i) q^{28} +(-2.17993 - 3.39204i) q^{29} +(-2.65857 + 6.69579i) q^{30} +(6.72079 + 7.75621i) q^{31} +(0.989821 - 0.142315i) q^{32} +(1.25608 + 3.59615i) q^{33} +(-0.560292 - 1.90818i) q^{34} +(0.845983 + 2.88115i) q^{35} +(2.67427 + 1.35952i) q^{36} +(-1.56573 + 0.225118i) q^{37} +(-2.73690 - 3.15855i) q^{38} +(6.41128 + 2.54561i) q^{39} +(-2.24874 - 3.49910i) q^{40} +(-7.04547 - 1.01299i) q^{41} +(1.22715 - 0.240126i) 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} +(-1.53725 + 0.798037i) q^{48} +(-4.24272 + 4.89636i) q^{49} +(-6.65018 + 10.3479i) q^{50} +(2.00602 + 2.80020i) q^{51} +(-3.35042 + 2.15319i) q^{52} +(-1.52719 - 3.34409i) q^{53} +(-5.14937 - 0.695679i) q^{54} +(1.30183 + 9.05442i) q^{55} +(-0.299900 + 0.656690i) q^{56} +(6.27929 + 3.60163i) q^{57} +(-3.86880 + 1.13598i) q^{58} +(0.0270675 + 0.0123613i) q^{59} +(5.67556 + 4.43730i) q^{60} +(8.55934 - 7.41671i) q^{61} +(9.33549 - 4.26338i) q^{62} +(-1.86945 + 1.09352i) q^{63} +(0.142315 - 0.989821i) q^{64} +(13.9357 + 8.95595i) q^{65} +(3.80436 - 0.192045i) q^{66} +(1.78438 - 6.07703i) q^{67} -1.98874 q^{68} +(-7.39069 + 3.79180i) q^{69} +3.00279 q^{70} +(-1.83181 + 6.23857i) q^{71} +(2.05788 - 2.18292i) q^{72} +(3.72319 + 2.39275i) q^{73} +(-0.225118 + 1.56573i) q^{74} +(4.96412 - 20.7188i) q^{75} +(-3.80168 + 1.73617i) q^{76} +(1.19990 - 1.03972i) q^{77} +(4.24876 - 5.43440i) q^{78} +(4.07232 + 1.85977i) q^{79} +(-3.99091 + 1.17184i) q^{80} +(8.81746 - 1.80346i) q^{81} +(-2.95689 + 6.47469i) q^{82} +(-0.309844 - 2.15501i) q^{83} +(0.115327 - 1.24509i) q^{84} +(3.43629 + 7.52443i) q^{85} +(0.163614 - 0.105148i) q^{86} +(5.67736 - 4.06716i) q^{87} +(-1.18900 + 1.85012i) q^{88} +(-0.817699 + 0.943675i) q^{89} +(-11.8149 - 4.01423i) 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} +(0.332618 + 1.69981i) q^{96} +(-12.7924 - 1.83926i) q^{97} +(3.50271 + 5.45033i) q^{98} +(-6.11111 + 2.48685i) 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 $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

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

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
$3$	0.0873233	+	1.72985i	0.0504162	+	0.998728i
$3$	0.0873233	+	1.72985i	0.0504162	+	0.998728i
$4$	−0.841254	−	0.540641i	−0.420627	−	0.270320i
$5$	−0.591943	+	4.11706i	−0.264725	+	1.84120i	0.231284	+	0.972886i	$0.425707\pi$
$5$	−0.591943	+	4.11706i	−0.264725	+	1.84120i	−0.496009	+	0.868318i	$0.665202\pi$
$6$	1.68438	+	0.403568i	0.687645	+	0.164756i
$7$	0.656690	−	0.299900i	0.248205	−	0.113352i	−0.287428	−	0.957802i	$-0.592800\pi$
$7$	0.656690	−	0.299900i	0.248205	−	0.113352i	0.535633	+	0.844451i	$0.320073\pi$
$8$	−0.755750	+	0.654861i	−0.267198	+	0.231528i
$9$	−2.98475	+	0.302112i	−0.994916	+	0.100704i
$10$	3.78352	+	1.72787i	1.19645	+	0.546402i
$11$	2.11016	−	0.619599i	0.636237	−	0.186816i	0.0523215	−	0.998630i	$-0.483338\pi$
$11$	2.11016	−	0.619599i	0.636237	−	0.186816i	0.583916	+	0.811814i	$0.301520\pi$
$12$	0.861765	−	1.50245i	0.248770	−	0.433720i
$13$	1.65446	−	3.62275i	0.458863	−	1.00477i	−0.528882	−	0.848695i	$-0.677389\pi$
$13$	1.65446	−	3.62275i	0.458863	−	1.00477i	0.987745	−	0.156075i	$-0.0498842\pi$
$14$	−0.102741	−	0.714581i	−0.0274588	−	0.190980i
$15$	−7.17357	−	0.664457i	−1.85221	−	0.171562i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	1.67303	−	1.07519i	0.405770	−	0.260773i	−0.321798	−	0.946808i	$-0.604287\pi$
$17$	1.67303	−	1.07519i	0.405770	−	0.260773i	0.727568	+	0.686036i	$0.240651\pi$
$18$	−0.551026	+	2.94896i	−0.129878	+	0.695077i
$19$	2.25954	−	3.51591i	0.518373	−	0.806604i	−0.479092	−	0.877765i	$-0.659034\pi$
$19$	2.25954	−	3.51591i	0.518373	−	0.806604i	0.997465	+	0.0711606i	$0.0226703\pi$
$20$	2.72382	−	3.14346i	0.609065	−	0.702899i
$21$	0.576126	+	1.10979i	0.125721	+	0.242175i
$22$		−	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
$27$	−0.783247	−	5.13678i	−0.150736	−	0.988574i
$28$	−0.714581	−	0.102741i	−0.135043	−	0.0194163i
$29$	−2.17993	−	3.39204i	−0.404804	−	0.629887i	0.577674	−	0.816268i	$-0.303961\pi$
$29$	−2.17993	−	3.39204i	−0.404804	−	0.629887i	−0.982478	+	0.186381i	$0.940324\pi$
$30$	−2.65857	+	6.69579i	−0.485386	+	1.22248i
$31$	6.72079	+	7.75621i	1.20709	+	1.39306i	0.896813	+	0.442410i	$0.145876\pi$
$31$	6.72079	+	7.75621i	1.20709	+	1.39306i	0.310277	+	0.950646i	$0.399578\pi$
$32$	0.989821	−	0.142315i	0.174977	−	0.0251579i
$33$	1.25608	+	3.59615i	0.218655	+	0.626010i
$34$	−0.560292	−	1.90818i	−0.0960894	−	0.327250i
$35$	0.845983	+	2.88115i	0.142997	+	0.487004i
$36$	2.67427	+	1.35952i	0.445711	+	0.226587i
$37$	−1.56573	+	0.225118i	−0.257405	+	0.0370092i	−0.269809	−	0.962914i	$-0.586961\pi$
$37$	−1.56573	+	0.225118i	−0.257405	+	0.0370092i	0.0124043	+	0.999923i	$0.496051\pi$
$38$	−2.73690	−	3.15855i	−0.443984	−	0.512385i
$39$	6.41128	+	2.54561i	1.02663	+	0.407623i
$40$	−2.24874	−	3.49910i	−0.355557	−	0.553257i
$41$	−7.04547	−	1.01299i	−1.10032	−	0.158202i	−0.431852	−	0.901944i	$-0.642140\pi$
$41$	−7.04547	−	1.01299i	−1.10032	−	0.158202i	−0.668466	+	0.743743i	$0.733049\pi$
$42$	1.22715	−	0.240126i	0.189353	−	0.0370523i
$43$	0.146984	+	0.127363i	0.0224149	+	0.0194226i	0.665996	−	0.745955i	$-0.268007\pi$
$43$	0.146984	+	0.127363i	0.0224149	+	0.0194226i	−0.643581	+	0.765378i	$0.722552\pi$
$44$	−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	$-0.207836\pi$
$48$	−1.53725	+	0.798037i	−0.221883	+	0.115187i
$49$	−4.24272	+	4.89636i	−0.606103	+	0.699481i
$50$	−6.65018	+	10.3479i	−0.940478	+	1.46341i
$51$	2.00602	+	2.80020i	0.280898	+	0.392107i
$52$	−3.35042	+	2.15319i	−0.464620	+	0.298593i
$53$	−1.52719	−	3.34409i	−0.209776	−	0.459346i	0.775271	−	0.631628i	$-0.217613\pi$
$53$	−1.52719	−	3.34409i	−0.209776	−	0.459346i	−0.985048	+	0.172282i	$0.944886\pi$
$54$	−5.14937	−	0.695679i	−0.700741	−	0.0946699i
$55$	1.30183	+	9.05442i	0.175539	+	1.22090i
$56$	−0.299900	+	0.656690i	−0.0400759	+	0.0877539i
$57$	6.27929	+	3.60163i	0.831713	+	0.477048i
$58$	−3.86880	+	1.13598i	−0.507998	+	0.149162i
$59$	0.0270675	+	0.0123613i	0.00352389	+	0.00160931i	0.417176	−	0.908826i	$-0.363020\pi$
$59$	0.0270675	+	0.0123613i	0.00352389	+	0.00160931i	−0.413652	+	0.910435i	$0.635747\pi$
$60$	5.67556	+	4.43730i	0.732712	+	0.572853i
$61$	8.55934	−	7.41671i	1.09591	−	0.949613i	0.0969550	−	0.995289i	$-0.469090\pi$
$61$	8.55934	−	7.41671i	1.09591	−	0.949613i	0.998956	+	0.0456762i	$0.0145443\pi$
$62$	9.33549	−	4.26338i	1.18561	−	0.541449i
$63$	−1.86945	+	1.09352i	−0.235529	+	0.137771i
$64$	0.142315	−	0.989821i	0.0177894	−	0.123728i
$65$	13.9357	+	8.95595i	1.72851	+	1.11085i
$66$	3.80436	−	0.192045i	0.468284	−	0.0236392i
$67$	1.78438	−	6.07703i	0.217996	−	0.742427i	−0.775777	−	0.631007i	$-0.782642\pi$
$67$	1.78438	−	6.07703i	0.217996	−	0.742427i	0.993773	−	0.111420i	$-0.0355399\pi$
$68$	−1.98874			−0.241170
$69$	−7.39069	+	3.79180i	−0.889734	+	0.456479i
$70$	3.00279			0.358902
$71$	−1.83181	+	6.23857i	−0.217396	+	0.740381i	0.776506	+	0.630110i	$0.216990\pi$
$71$	−1.83181	+	6.23857i	−0.217396	+	0.740381i	−0.993902	+	0.110271i	$0.964828\pi$
$72$	2.05788	−	2.18292i	0.242524	−	0.257259i
$73$	3.72319	+	2.39275i	0.435767	+	0.280050i	0.740076	−	0.672523i	$-0.234789\pi$
$73$	3.72319	+	2.39275i	0.435767	+	0.280050i	−0.304310	+	0.952573i	$0.598426\pi$
$74$	−0.225118	+	1.56573i	−0.0261695	+	0.182013i
$75$	4.96412	−	20.7188i	0.573207	−	2.39240i
$76$	−3.80168	+	1.73617i	−0.436083	+	0.199152i
$77$	1.19990	−	1.03972i	0.136742	−	0.118487i
$78$	4.24876	−	5.43440i	0.481077	−	0.615325i
$79$	4.07232	+	1.85977i	0.458172	+	0.209240i	0.631111	−	0.775692i	$-0.282599\pi$
$79$	4.07232	+	1.85977i	0.458172	+	0.209240i	−0.172939	+	0.984933i	$0.555326\pi$
$80$	−3.99091	+	1.17184i	−0.446197	+	0.131015i
$81$	8.81746	−	1.80346i	0.979717	−	0.200384i
$82$	−2.95689	+	6.47469i	−0.326534	+	0.715010i
$83$	−0.309844	−	2.15501i	−0.0340098	−	0.236544i	0.965725	−	0.259567i	$-0.0835799\pi$
$83$	−0.309844	−	2.15501i	−0.0340098	−	0.236544i	−0.999735	+	0.0230234i	$0.992671\pi$
$84$	0.115327	−	1.24509i	0.0125832	−	0.135850i
$85$	3.43629	+	7.52443i	0.372718	+	0.816139i
$86$	0.163614	−	0.105148i	0.0176429	−	0.0113384i
$87$	5.67736	−	4.06716i	0.608677	−	0.436045i
$88$	−1.18900	+	1.85012i	−0.126748	+	0.197224i
$89$	−0.817699	+	0.943675i	−0.0866759	+	0.100029i	−0.797431	−	0.603410i	$-0.793808\pi$
$89$	−0.817699	+	0.943675i	−0.0866759	+	0.100029i	0.710755	+	0.703440i	$0.248354\pi$
$90$	−11.8149	−	4.01423i	−1.24540	−	0.423137i
$91$		−	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
$96$	0.332618	+	1.69981i	0.0339476	+	0.173486i
$97$	−12.7924	−	1.83926i	−1.29887	−	0.186749i	−0.542034	−	0.840357i	$-0.682346\pi$
$97$	−12.7924	−	1.83926i	−1.29887	−	0.186749i	−0.756834	+	0.653608i	$0.773255\pi$
$98$	3.50271	+	5.45033i	0.353827	+	0.550566i
$99$	−6.11111	+	2.48685i	−0.614190	+	0.249938i
$100$	8.05515	+	9.29614i	0.805515	+	0.929614i
$101$	−13.1575	+	1.89177i	−1.30922	+	0.188238i	−0.761360	−	0.648329i	$-0.775468\pi$
$101$	−13.1575	+	1.89177i	−1.30922	+	0.188238i	−0.547864	+	0.836567i	$0.684559\pi$
$102$	3.25194	−	1.13585i	0.321990	−	0.112466i
$103$	−3.32884	−	11.3370i	−0.328000	−	1.11707i	−0.944172	−	0.329453i	$-0.893136\pi$
$103$	−3.32884	−	11.3370i	−0.328000	−	1.11707i	0.616172	−	0.787612i	$-0.288683\pi$
$104$	1.12204	+	3.82133i	0.110025	+	0.374712i
$105$	−4.91009	+	1.71501i	−0.479175	+	0.167368i
$106$	−3.63889	+	0.523194i	−0.353440	+	0.0508171i
$107$	0.439642	+	0.507374i	0.0425018	+	0.0490497i	0.776602	−	0.629991i	$-0.216941\pi$
$107$	0.439642	+	0.507374i	0.0425018	+	0.0490497i	−0.734101	+	0.679041i	$0.762396\pi$
$108$	−2.11824	+	4.74479i	−0.203828	+	0.456568i
$109$	5.20638	+	8.10129i	0.498681	+	0.775963i	0.995784	−	0.0917289i	$-0.0292393\pi$
$109$	5.20638	+	8.10129i	0.498681	+	0.775963i	−0.497103	+	0.867691i	$0.665603\pi$
$110$	9.05442	+	1.30183i	0.863305	+	0.124125i
$111$	−0.526145	−	2.68882i	−0.0499395	−	0.255211i
$112$	0.545598	+	0.472763i	0.0515541	+	0.0446719i
$113$	−14.2038	−	4.17060i	−1.33618	−	0.392337i	−0.465874	−	0.884851i	$-0.654260\pi$
$113$	−14.2038	−	4.17060i	−1.33618	−	0.392337i	−0.870305	+	0.492514i	$0.836078\pi$
$114$	5.22482	−	5.01024i	0.489349	−	0.469252i
$115$	−19.1665	+	5.52794i	−1.78729	+	0.515483i
$116$			4.03213i			0.374374i
$117$	−3.84366	+	11.3128i	−0.355346	+	1.04587i
$118$	0.0194864	−	0.0224885i	0.00179387	−	0.00207024i
$119$	0.776214	−	1.20781i	0.0711554	−	0.110720i
$120$	5.85655	−	4.19553i	0.534628	−	0.382998i
$121$	−5.18491	+	3.33214i	−0.471356	+	0.302922i
$122$	−4.70484	−	10.3022i	−0.425956	−	0.932713i
$123$	1.13708	−	12.2761i	0.102527	−	1.10689i
$124$	−1.46057	−	10.1585i	−0.131163	−	0.912258i
$125$	12.6144	−	27.6218i	1.12827	−	2.47057i
$126$	0.522541	+	2.10181i	0.0465516	+	0.187244i
$127$	−14.2195	+	4.17523i	−1.26178	+	0.370491i	−0.843156	−	0.537669i	$-0.819305\pi$
$127$	−14.2195	+	4.17523i	−1.26178	+	0.370491i	−0.418622	+	0.908161i	$0.637487\pi$
$128$	−0.909632	−	0.415415i	−0.0804009	−	0.0367178i
$129$	−0.207483	+	0.265382i	−0.0182679	+	0.0233656i
$130$	12.5193	−	10.8481i	1.09802	−	0.951437i
$131$	4.70731	−	2.14976i	0.411280	−	0.187825i	−0.199020	−	0.979995i	$-0.563776\pi$
$131$	4.70731	−	2.14976i	0.411280	−	0.187825i	0.610300	+	0.792170i	$0.291049\pi$
$132$	0.887546	−	3.70436i	0.0772510	−	0.322423i
$133$	0.429393	−	2.98650i	0.0372331	−	0.258962i
$134$	−5.32815	−	3.42419i	−0.460282	−	0.295805i
$135$	21.6121	−	0.183986i	1.86007	−	0.0158350i
$136$	−0.560292	+	1.90818i	−0.0480447	+	0.163625i
$137$	−10.7206			−0.915925			−0.457962	−	0.888972i	$-0.651421\pi$
$137$	−10.7206			−0.915925			−0.457962	+	0.888972i	$0.651421\pi$
$138$	1.55601	+	8.15959i	0.132456	+	0.694590i
$139$	−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
$141$	14.4095	−	0.727395i	1.21350	−	0.0612577i
$142$	5.46978	+	3.51521i	0.459014	+	0.294990i
$143$	1.24651	−	8.66969i	0.104239	−	0.724996i
$144$	−1.51472	−	2.58952i	−0.126227	−	0.215793i
$145$	15.2556	−	6.96701i	1.26691	−	0.578579i
$146$	3.34477	−	2.89826i	0.276815	−	0.239862i
$147$	−8.84046	−	6.91170i	−0.729148	−	0.570067i
$148$	1.43889	+	0.657117i	0.118276	+	0.0540147i
$149$	20.3556	−	5.97694i	1.66759	−	0.489650i	0.694391	−	0.719598i	$-0.255674\pi$
$149$	20.3556	−	5.97694i	1.66759	−	0.489650i	0.973203	+	0.229949i	$0.0738558\pi$
$150$	−18.4810	−	10.6002i	−1.50897	−	0.865502i
$151$	−2.43114	+	5.32345i	−0.197843	+	0.433216i	−0.982387	−	0.186857i	$-0.940170\pi$
$151$	−2.43114	+	5.32345i	−0.197843	+	0.433216i	0.784544	+	0.620073i	$0.212897\pi$
$152$	0.594786	+	4.13683i	0.0482435	+	0.335541i
$153$	−4.66876	+	3.71463i	−0.377447	+	0.300310i
$154$	−0.659554	−	1.44422i	−0.0531484	−	0.116379i
$155$	−35.9111	+	23.0786i	−2.88445	+	1.85372i
$156$	−4.01726	−	5.60770i	−0.321638	−	0.448975i
$157$	−3.13288	+	4.87486i	−0.250031	+	0.389056i	−0.943469	−	0.331460i	$-0.892459\pi$
$157$	−3.13288	+	4.87486i	−0.250031	+	0.389056i	0.693438	+	0.720516i	$0.256095\pi$
$158$	2.93174	−	3.38341i	0.233237	−	0.269170i
$159$	5.65141	−	2.93383i	0.448186	−	0.232668i
$160$			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	0.441182	−	0.897418i	$-0.354559\pi$
$163$	4.17674	+	1.22640i	0.327148	+	0.0960592i	−0.114034	+	0.993477i	$0.536377\pi$
$164$	5.37937	+	4.66125i	0.420058	+	0.363982i
$165$	−15.5491	+	3.04263i	−1.21050	+	0.236868i
$166$	−2.15501	−	0.309844i	−0.167262	−	0.0240486i
$167$	−4.39447	−	6.83794i	−0.340055	−	0.529135i	0.628541	−	0.777776i	$-0.283652\pi$
$167$	−4.39447	−	6.83794i	−0.340055	−	0.529135i	−0.968596	+	0.248641i	$0.920016\pi$
$168$	−1.16216	−	0.461438i	−0.0896628	−	0.0356007i
$169$	−1.87392	−	2.16262i	−0.144148	−	0.166355i
$170$	8.18775	−	1.17722i	0.627972	−	0.0902887i
$171$	−5.68195	+	11.1767i	−0.434509	+	0.854706i
$172$	−0.0547937	−	0.186610i	−0.00417798	−	0.0142289i
$173$	4.51163	+	15.3652i	0.343013	+	1.16819i	0.932727	+	0.360582i	$0.117422\pi$
$173$	4.51163	+	15.3652i	0.343013	+	1.16819i	−0.589715	+	0.807612i	$0.700760\pi$
$174$	−2.30291	−	6.59324i	−0.174583	−	0.499832i
$175$	−8.78975	+	1.26377i	−0.664442	+	0.0955324i
$176$	1.44020	+	1.66208i	0.108559	+	0.125284i
$177$	−0.0190196	+	0.0479022i	−0.00142960	+	0.00360055i
$178$	0.675077	+	1.05044i	0.0505991	+	0.0787338i
$179$	−7.07616	−	1.01740i	−0.528897	−	0.0760439i	−0.127307	−	0.991863i	$-0.540633\pi$
$179$	−7.07616	−	1.01740i	−0.528897	−	0.0760439i	−0.401590	+	0.915819i	$0.631542\pi$
$180$	−7.18025	+	10.2053i	−0.535184	+	0.760661i
$181$	13.1684	+	11.4105i	0.978801	+	0.848136i	0.988409	−	0.151818i	$-0.0485127\pi$
$181$	13.1684	+	11.4105i	0.978801	+	0.848136i	−0.00960722	+	0.999954i	$0.503058\pi$
$182$	−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
$186$	8.19020	+	15.7767i	0.600535	+	1.15680i
$187$	2.86418	−	3.30544i	0.209450	−	0.241718i
$188$	−4.50348	+	7.00756i	−0.328450	+	0.511079i
$189$	−2.05487	−	3.13838i	−0.149470	−	0.228283i
$190$	14.6240	−	9.39830i	1.06094	−	0.681824i
$191$	8.26623	+	18.1005i	0.598124	+	1.30971i	0.930407	+	0.366529i	$0.119454\pi$
$191$	8.26623	+	18.1005i	0.598124	+	1.30971i	−0.332283	+	0.943180i	$0.607819\pi$
$192$	1.72467	+	0.159749i	0.124467	+	0.0115289i
$193$	−2.21480	−	15.4043i	−0.159425	−	1.10883i	−0.899696	−	0.436517i	$-0.856212\pi$
$193$	−2.21480	−	15.4043i	−0.159425	−	1.10883i	0.740271	−	0.672309i	$-0.234697\pi$
$194$	−5.36879	+	11.7560i	−0.385456	+	0.844032i
$195$	−14.2755	+	24.8888i	−1.02229	+	1.78232i
$196$	6.21638	−	1.82529i	0.444027	−	0.130378i
$197$	3.90627	+	1.78394i	0.278310	+	0.127100i	0.549681	−	0.835375i	$-0.314749\pi$
$197$	3.90627	+	1.78394i	0.278310	+	0.127100i	−0.271370	+	0.962475i	$0.587477\pi$
$198$	0.664419	+	6.56420i	0.0472182	+	0.466497i
$199$	15.9996	−	13.8637i	1.13418	−	0.982774i	0.134215	−	0.990952i	$-0.457149\pi$
$199$	15.9996	−	13.8637i	1.13418	−	0.982774i	0.999967	+	0.00817869i	$0.00260339\pi$
$200$	11.1890	−	5.10984i	0.791180	−	0.361320i
$201$	10.6681	+	2.55603i	0.752473	+	0.180289i
$202$	−1.89177	+	13.1575i	−0.133104	+	0.925761i
$203$	−2.44882	−	1.57376i	−0.171873	−	0.110456i
$204$	−0.173663	−	3.44022i	−0.0121589	−	0.240863i
$205$	8.34104	−	28.4070i	0.582564	−	1.98403i
$206$	−11.8156			−0.823231
$207$	−7.20462	−	12.4537i	−0.500755	−	0.865589i
$208$	3.98266			0.276148
$209$	2.58953	−	8.81913i	0.179122	−	0.610032i
$210$	0.262213	+	5.19437i	0.0180944	+	0.358445i
$211$	−13.4413	−	8.63822i	−0.925340	−	0.594680i	−0.0111376	−	0.999938i	$-0.503545\pi$
$211$	−13.4413	−	8.63822i	−0.925340	−	0.594680i	−0.914202	+	0.405258i	$0.867182\pi$
$212$	−0.523194	+	3.63889i	−0.0359331	+	0.249920i
$213$	−10.9517	−	2.62398i	−0.750400	−	0.179792i
$214$	0.610683	−	0.278890i	0.0417455	−	0.0190645i
$215$	−0.611366	+	0.529752i	−0.0416948	+	0.0361288i
$216$	3.95581	+	3.36920i	0.269159	+	0.229245i
$217$	6.73957	+	3.07786i	0.457512	+	0.208939i
$218$	9.23994	−	2.71309i	0.625807	−	0.183754i
$219$	−3.81397	+	6.64950i	−0.257724	+	0.449332i
$220$	3.80002	−	8.32088i	0.256197	−	0.560994i
$221$	−1.12720	−	7.83984i	−0.0758236	−	0.527365i
$222$	−2.72814	−	0.252695i	−0.183100	−	0.0169598i
$223$	4.40157	+	9.63809i	0.294751	+	0.645414i	0.997840	−	0.0656871i	$-0.0209239\pi$
$223$	4.40157	+	9.63809i	0.294751	+	0.645414i	−0.703089	+	0.711101i	$0.748197\pi$
$224$	0.607326	−	0.390304i	0.0405786	−	0.0260783i
$225$	36.2739	+	6.77793i	2.41826	+	0.451862i
$226$	−8.00333	+	12.4534i	−0.532373	+	0.828389i
$227$	−6.03474	+	6.96446i	−0.400540	+	0.462248i	−0.919811	−	0.392362i	$-0.871658\pi$
$227$	−6.03474	+	6.96446i	−0.400540	+	0.462248i	0.519271	+	0.854610i	$0.326203\pi$
$228$	−3.33529	−	6.42473i	−0.220885	−	0.425488i
$229$			11.4148i			0.754309i	0.926150	+	0.377155i	$0.123097\pi$
$229$			11.4148i			0.754309i	−0.926150	+	0.377155i	$0.876903\pi$
$230$	−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	$-0.465981\pi$
$233$	−13.1628	−	11.4056i	−0.862323	−	0.747207i	−0.968993	+	0.247087i	$0.920527\pi$
$234$	9.77170	+	6.87516i	0.638796	+	0.449443i
$235$	34.2947	+	4.93083i	2.23714	+	0.321652i
$236$	−0.0160876	−	0.0250328i	−0.00104721	−	0.00162950i
$237$	−2.86151	+	7.20690i	−0.185875	+	0.468139i
$238$	−0.940202	−	1.08505i	−0.0609443	−	0.0703334i
$239$	14.9668	−	2.15190i	0.968122	−	0.139195i	0.359925	−	0.932981i	$-0.382802\pi$
$239$	14.9668	−	2.15190i	0.968122	−	0.139195i	0.608197	+	0.793786i	$0.291893\pi$
$240$	−2.37560	−	6.80134i	−0.153344	−	0.439024i
$241$	−0.800955	−	2.72780i	−0.0515941	−	0.175713i	0.929665	−	0.368406i	$-0.120096\pi$
$241$	−0.800955	−	2.72780i	−0.0515941	−	0.175713i	−0.981259	+	0.192692i	$0.938278\pi$
$242$	1.73641	+	5.91366i	0.111621	+	0.380145i
$243$	3.88968	+	15.0954i	0.249523	+	0.968369i
$244$	−11.2104	+	1.61181i	−0.717669	+	0.103185i
$245$	−17.6472	−	20.3659i	−1.12744	−	1.30113i
$246$	−11.4584	−	4.54958i	−0.730563	−	0.290071i
$247$	−8.99895	−	14.0026i	−0.572590	−	0.890967i
$248$	−10.1585	−	1.46057i	−0.645064	−	0.0927461i
$249$	3.70079	−	0.724167i	0.234528	−	0.0458922i
$250$	−22.9490	−	19.8854i	−1.45142	−	1.25766i
$251$	2.55586	+	0.750469i	0.161325	+	0.0473692i	0.361398	−	0.932412i	$-0.382300\pi$
$251$	2.55586	+	0.750469i	0.161325	+	0.0473692i	−0.200073	+	0.979781i	$0.564118\pi$
$252$	2.16388	+	0.0907732i	0.136312	+	0.00571817i
$253$	6.86859	+	8.00413i	0.431825	+	0.503215i
$254$			14.8198i			0.929878i
$255$	−12.7160	+	6.60132i	−0.796310	+	0.413391i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	5.36966	−	8.35536i	0.334950	−	0.521193i	−0.632398	−	0.774644i	$-0.717929\pi$
$257$	5.36966	−	8.35536i	0.334950	−	0.521193i	0.967348	+	0.253451i	$0.0815656\pi$
$258$	0.196178	+	0.273845i	0.0122135	+	0.0170489i
$259$	−0.960687	+	0.617396i	−0.0596942	+	0.0383631i
$260$	−6.88153	−	15.0685i	−0.426774	−	0.934506i
$261$	7.53133	+	9.46581i	0.466178	+	0.585919i
$262$	−0.736474	−	5.12229i	−0.0454995	−	0.316456i
$263$	4.09666	−	8.97043i	0.252611	−	0.553141i	−0.740262	−	0.672318i	$-0.765299\pi$
$263$	4.09666	−	8.97043i	0.252611	−	0.553141i	0.992873	+	0.119178i	$0.0380259\pi$
$264$	−3.30426	−	1.89523i	−0.203363	−	0.116644i
$265$	14.6718	−	4.30804i	0.901283	−	0.264641i
$266$	−2.74455	−	1.25339i	−0.168279	−	0.0768504i
$267$	−1.70382	−	1.33209i	−0.104272	−	0.0815226i
$268$	−4.78660	+	4.14761i	−0.292388	+	0.253356i
$269$	3.07146	−	1.40269i	0.187270	−	0.0855235i	−0.319573	−	0.947562i	$-0.603540\pi$
$269$	3.07146	−	1.40269i	0.187270	−	0.0855235i	0.506843	+	0.862038i	$0.330812\pi$
$270$	5.91229	−	20.7885i	0.359810	−	1.26515i
$271$	−2.04708	+	14.2377i	−0.124351	+	0.864880i	0.828185	+	0.560455i	$0.189374\pi$
$271$	−2.04708	+	14.2377i	−0.124351	+	0.864880i	−0.952536	+	0.304426i	$0.901536\pi$
$272$	1.67303	+	1.07519i	0.101443	+	0.0651932i
$273$	4.97365	−	0.251072i	0.301019	−	0.0151956i
$274$	−3.02035	+	10.2864i	−0.182466	+	0.621422i
$275$	−27.0519			−1.63129
$276$	8.26744	+	0.805842i	0.497642	+	0.0485060i
$277$	−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
$279$	−22.4031	−	21.1199i	−1.34124	−	1.26442i
$280$	−2.52611	−	1.62343i	−0.150964	−	0.0970185i
$281$	−0.0418767	+	0.291259i	−0.00249815	+	0.0173750i	−0.991032	−	0.133622i	$-0.957339\pi$
$281$	−0.0418767	+	0.291259i	−0.00249815	+	0.0173750i	0.988534	+	0.150997i	$0.0482483\pi$
$282$	3.36168	−	14.0307i	0.200185	−	0.835517i
$283$	16.0458	−	7.32785i	0.953821	−	0.435596i	0.123168	−	0.992386i	$-0.460695\pi$
$283$	16.0458	−	7.32785i	0.953821	−	0.435596i	0.830653	+	0.556790i	$0.187967\pi$
$284$	4.91384	−	4.25786i	0.291583	−	0.252658i
$285$	−18.5451	+	23.7202i	−1.09852	+	1.40507i
$286$	−7.96732	−	3.63855i	−0.471118	−	0.215152i
$287$	−4.93049	+	1.44772i	−0.291037	+	0.0854563i
$288$	−2.91137	+	0.723811i	−0.171554	+	0.0426510i
$289$	−5.41906	+	11.8661i	−0.318768	+	0.698004i
$290$	−2.38679	−	16.6005i	−0.140157	−	0.974815i
$291$	2.06458	−	22.2895i	0.121028	−	1.30663i
$292$	−1.83853	−	4.02582i	−0.107592	−	0.235593i
$293$	22.4214	−	14.4094i	1.30987	−	0.841804i	0.315623	−	0.948885i	$-0.397787\pi$
$293$	22.4214	−	14.4094i	1.30987	−	0.841804i	0.994250	+	0.107080i	$0.0341502\pi$
$294$	−9.12237	+	6.53510i	−0.532028	+	0.381135i
$295$	−0.0669147	+	0.104121i	−0.00389593	+	0.00606218i
$296$	1.03588	−	1.19547i	0.0602093	−	0.0694852i
$297$	−4.83552	−	10.3541i	−0.280585	−	0.600808i
$298$		−	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
$303$	−4.42143	−	22.5953i	−0.254005	−	1.29807i
$304$	4.13683	+	0.594786i	0.237263	+	0.0341133i
$305$	25.4684	+	39.6296i	1.45832	+	2.26918i
$306$	2.24882	+	5.52617i	0.128556	+	0.315910i
$307$	−22.8736	−	26.3975i	−1.30546	−	1.50658i	−0.713625	−	0.700528i	$-0.752948\pi$
$307$	−22.8736	−	26.3975i	−1.30546	−	1.50658i	−0.591839	−	0.806056i	$-0.701598\pi$
$308$	−1.57154	+	0.225953i	−0.0895468	+	0.0128749i
$309$	19.3206	−	6.74836i	1.09911	−	0.383901i
$310$	12.0265	+	40.9584i	0.683058	+	2.32628i
$311$	0.262167	+	0.892860i	0.0148661	+	0.0506294i	0.966592	−	0.256320i	$-0.0825100\pi$
$311$	0.262167	+	0.892860i	0.0148661	+	0.0506294i	−0.951726	+	0.306949i	$0.900692\pi$
$312$	−6.51234	+	2.27466i	−0.368689	+	0.128777i
$313$	18.4209	−	2.64853i	1.04121	−	0.149704i	0.399565	−	0.916705i	$-0.369161\pi$
$313$	18.4209	−	2.64853i	1.04121	−	0.149704i	0.641646	+	0.767001i	$0.278252\pi$
$314$	3.79476	+	4.37938i	0.214150	+	0.247143i
$315$	−3.39548	−	8.34394i	−0.191314	−	0.470128i
$316$	−2.42039	−	3.76620i	−0.136158	−	0.211865i
$317$	−16.7469	−	2.40784i	−0.940601	−	0.135238i	−0.345076	−	0.938575i	$-0.612147\pi$
$317$	−16.7469	−	2.40784i	−0.940601	−	0.135238i	−0.595525	+	0.803337i	$0.703056\pi$
$318$	−1.22281	−	6.24904i	−0.0685715	−	0.350429i
$319$	−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
$324$	−8.39274	−	3.24991i	−0.466263	−	0.180551i
$325$	−32.0809	+	37.0233i	−1.77953	+	2.05368i
$326$	2.35345	−	3.66204i	0.130345	−	0.202821i
$327$	−13.5594	+	9.71368i	−0.749834	+	0.537168i
$328$	5.98798	−	3.84824i	0.330631	−	0.212484i
$329$	−2.49814	−	5.47016i	−0.137727	−	0.301580i
$330$	−1.46130	+	15.7765i	−0.0804422	+	0.868465i
$331$	0.117484	+	0.817121i	0.00645752	+	0.0449130i	0.992795	−	0.119822i	$-0.0382323\pi$
$331$	0.117484	+	0.817121i	0.00645752	+	0.0449130i	−0.986338	+	0.164735i	$0.947323\pi$
$332$	−0.904431	+	1.98043i	−0.0496371	+	0.108690i
$333$	4.60530	−	1.14495i	0.252369	−	0.0627428i
$334$	−7.79902	+	2.29000i	−0.426743	+	0.125303i
$335$	23.9632	+	10.9436i	1.30925	+	0.597915i
$336$	−0.770165	+	0.985085i	−0.0420159	+	0.0537408i
$337$	−21.5178	+	18.6453i	−1.17215	+	1.01567i	−0.172620	+	0.984988i	$0.555223\pi$
$337$	−21.5178	+	18.6453i	−1.17215	+	1.01567i	−0.999529	+	0.0306850i	$0.990231\pi$
$338$	−2.60296	+	1.18873i	−0.141582	+	0.0646585i
$339$	5.97419	−	24.9346i	0.324473	−	1.35426i
$340$	1.17722	−	8.18775i	0.0638438	−	0.444043i
$341$	18.9877	+	12.2026i	1.02824	+	0.660810i
$342$	9.12320	+	8.60064i	0.493326	+	0.465069i
$343$	−2.74147	+	9.33659i	−0.148025	+	0.504128i
$344$	−0.194488			−0.0104861
$345$	−11.2362	−	32.6724i	−0.604936	−	1.75902i
$346$	16.0139			0.860911
$347$	−0.0175599	+	0.0598036i	−0.000942666	+	0.00321043i	−0.959963	−	0.280127i	$-0.909623\pi$
$347$	−0.0175599	+	0.0598036i	−0.000942666	+	0.00321043i	0.959020	+	0.283337i	$0.0914416\pi$
$348$	−6.97497	+	0.352099i	−0.373898	+	0.0188745i
$349$	−17.9464	−	11.5334i	−0.960647	−	0.617370i	−0.0364699	−	0.999335i	$-0.511611\pi$
$349$	−17.9464	−	11.5334i	−0.960647	−	0.617370i	−0.924177	+	0.381964i	$0.875248\pi$
$350$	−1.26377	+	8.78975i	−0.0675516	+	0.469832i
$351$	−19.9051	−	5.66107i	−1.06246	−	0.302165i
$352$	2.00050	−	0.913600i	0.106627	−	0.0486950i
$353$	−0.167102	+	0.144794i	−0.00889393	+	0.00770663i	−0.659296	−	0.751883i	$-0.729146\pi$
$353$	−0.167102	+	0.144794i	−0.00889393	+	0.00770663i	0.650402	+	0.759590i	$0.274600\pi$
$354$	0.0406033	+	0.0317448i	0.00215804	+	0.00168722i
$355$	−24.6002	−	11.2345i	−1.30564	−	0.596267i
$356$	1.19808	−	0.351788i	0.0634982	−	0.0186447i
$357$	2.15711	+	1.23726i	0.114167	+	0.0654828i
$358$	−2.96977	+	6.50289i	−0.156957	+	0.343688i
$359$	−0.583737	−	4.05998i	−0.0308085	−	0.214278i	0.968602	−	0.248618i	$-0.0799762\pi$
$359$	−0.583737	−	4.05998i	−0.0308085	−	0.214278i	−0.999410	+	0.0343399i	$0.989067\pi$
$360$	7.76904	+	9.76458i	0.409464	+	0.514638i
$361$	0.636792	+	1.39438i	0.0335154	+	0.0733884i
$362$	14.6583	−	9.42030i	0.770422	−	0.495120i
$363$	−6.21686	−	8.67814i	−0.326301	−	0.455484i
$364$	−1.55445	+	2.41877i	−0.0814752	+	0.126778i
$365$	−12.0550	+	13.9122i	−0.630988	+	0.728199i
$366$	17.4103	−	9.03827i	0.910052	−	0.472438i
$367$			31.2246i			1.62991i	0.579523	+	0.814956i	$0.303239\pi$
$367$			31.2246i			1.62991i	−0.579523	+	0.814956i	$0.696761\pi$
$368$	−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
$372$	17.4451	−	3.41363i	0.904485	−	0.176989i
$373$	0.330235	+	0.0474807i	0.0170989	+	0.00245846i	0.150859	−	0.988555i	$-0.451796\pi$
$373$	0.330235	+	0.0474807i	0.0170989	+	0.00245846i	−0.133760	+	0.991014i	$0.542705\pi$
$374$	−2.36461	−	3.67941i	−0.122271	−	0.190258i
$375$	48.8830	+	19.4091i	2.52431	+	1.00228i
$376$	5.45492	+	6.29532i	0.281316	+	0.324656i
$377$	−15.8951	+	2.28538i	−0.818641	+	0.117703i
$378$	−3.59018	+	1.08745i	−0.184659	+	0.0559325i
$379$	−3.18337	−	10.8416i	−0.163519	−	0.556894i	−0.999961	−	0.00883868i	$-0.997187\pi$
$379$	−3.18337	−	10.8416i	−0.163519	−	0.556894i	0.836442	−	0.548055i	$-0.184632\pi$
$380$	−4.89753	−	16.6795i	−0.251238	−	0.855639i
$381$	−8.46420	−	24.2330i	−0.433634	−	1.24149i
$382$	19.6962	−	2.83189i	1.00775	−	0.144892i
$383$	−4.46062	−	5.14783i	−0.227927	−	0.263042i	0.630254	−	0.776389i	$-0.282951\pi$
$383$	−4.46062	−	5.14783i	−0.227927	−	0.263042i	−0.858181	+	0.513347i	$0.828405\pi$
$384$	0.639173	−	1.60980i	0.0326177	−	0.0821498i
$385$	3.57032	+	5.55553i	0.181960	+	0.283136i
$386$	−15.4043	−	2.21480i	−0.784058	−	0.112731i
$387$	−0.477189	−	0.335740i	−0.0242569	−	0.0170666i
$388$	9.76724	+	8.46336i	0.495856	+	0.429662i
$389$	9.89092	+	2.90423i	0.501489	+	0.147251i	0.522687	−	0.852525i	$-0.324930\pi$
$389$	9.89092	+	2.90423i	0.501489	+	0.147251i	−0.0211975	+	0.999775i	$0.506748\pi$
$390$	19.8587	+	20.7092i	1.00559	+	1.04865i
$391$	7.99873	+	5.19492i	0.404513	+	0.262718i
$392$		−	6.47882i		−	0.327230i
$393$	4.12981	+	7.95521i	0.208322	+	0.401287i
$394$	2.81220	−	3.24545i	0.141676	−	0.163503i
$395$	−10.0674	+	15.6651i	−0.506544	+	0.788198i
$396$	6.48549	+	1.21184i	0.325908	+	0.0608974i
$397$	9.82670	−	6.31524i	0.493188	−	0.316953i	−0.270298	−	0.962777i	$-0.587122\pi$
$397$	9.82670	−	6.31524i	0.493188	−	0.316953i	0.763486	+	0.645824i	$0.223486\pi$
$398$	−8.79454	−	19.2574i	−0.440831	−	0.965284i
$399$	5.20368	+	0.481994i	0.260510	+	0.0241299i
$400$	−1.75055	−	12.1754i	−0.0875276	−	0.608768i
$401$	−5.88936	+	12.8959i	−0.294100	+	0.643990i	−0.997785	−	0.0665224i	$-0.978810\pi$
$401$	−5.88936	+	12.8959i	−0.294100	+	0.643990i	0.703684	+	0.710513i	$0.251537\pi$
$402$	5.45806	−	9.51590i	0.272223	−	0.474610i
$403$	39.2181	−	11.5155i	1.95359	−	0.573626i
$404$	12.0916	+	5.52205i	0.601579	+	0.274732i
$405$	2.20551	+	37.3695i	0.109592	+	1.85691i
$406$	−2.19992	+	1.90624i	−0.109180	+	0.0946052i
$407$	−3.16446	+	1.44516i	−0.156857	+	0.0716340i
$408$	−3.34979	−	0.802592i	−0.165839	−	0.0397342i
$409$	−0.919748	+	6.39699i	−0.0454786	+	0.316311i	0.954365	+	0.298642i	$0.0965336\pi$
$409$	−0.919748	+	6.39699i	−0.0454786	+	0.316311i	−0.999844	+	0.0176689i	$0.994376\pi$
$410$	−24.9064	−	16.0063i	−1.23004	−	0.790497i
$411$	−0.936160	−	18.5450i	−0.0461774	−	0.914760i
$412$	−3.32884	+	11.3370i	−0.164000	+	0.558533i
$413$	0.0214821			0.00105707
$414$	−13.9790	+	3.40418i	−0.687029	+	0.167306i
$415$	9.05573			0.444528
$416$	1.12204	−	3.82133i	0.0550127	−	0.187356i
$417$	−0.0459556	−	0.910365i	−0.00225045	−	0.0445808i
$418$	−7.73234	−	4.96927i	−0.378201	−	0.243055i
$419$	−1.23696	+	8.60326i	−0.0604295	+	0.420297i	0.937041	+	0.349219i	$0.113553\pi$
$419$	−1.23696	+	8.60326i	−0.0604295	+	0.420297i	−0.997471	+	0.0710778i	$0.977356\pi$
$420$	5.05783	+	1.21183i	0.246797	+	0.0591313i
$421$	−26.5913	+	12.1439i	−1.29598	+	0.591856i	−0.939533	−	0.342459i	$-0.888740\pi$
$421$	−26.5913	+	12.1439i	−1.29598	+	0.591856i	−0.356450	+	0.934314i	$0.616013\pi$
$422$	−12.0752	+	10.4632i	−0.587810	+	0.509341i
$423$	2.51656	+	24.8627i	0.122360	+	1.20886i
$424$	3.34409	+	1.52719i	0.162403	+	0.0741671i
$425$	−23.4717	+	6.89191i	−1.13854	+	0.334307i
$426$	−5.60315	+	9.76885i	−0.271473	+	0.473302i
$427$	3.39656	−	7.43743i	0.164371	−	0.359922i
$428$	−0.0955434	−	0.664519i	−0.00461826	−	0.0321207i
$429$	15.1061	+	1.39921i	0.729329	+	0.0675546i
$430$	0.336051	+	0.735850i	0.0162058	+	0.0354858i
$431$	−25.7588	+	16.5542i	−1.24076	+	0.797387i	−0.985531	−	0.169494i	$-0.945787\pi$
$431$	−25.7588	+	16.5542i	−1.24076	+	0.797387i	−0.255228	+	0.966881i	$0.582150\pi$
$432$	4.34721	−	2.84636i	0.209155	−	0.136946i
$433$	9.94612	−	15.4765i	0.477980	−	0.743751i	−0.515607	−	0.856825i	$-0.672433\pi$
$433$	9.94612	−	15.4765i	0.477980	−	0.743751i	0.993587	+	0.113074i	$0.0360698\pi$
$434$	4.85194	−	5.59943i	0.232900	−	0.268781i
$435$	13.3841	+	25.7815i	0.641716	+	1.23613i
$436$		−	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	0.511119	−	0.859510i	$-0.329231\pi$
$439$	9.98198	+	2.93097i	0.476414	+	0.139888i	−0.0347053	+	0.999398i	$0.511049\pi$
$440$	−6.91324	−	5.99036i	−0.329576	−	0.285579i
$441$	11.1842	−	15.8962i	0.532582	−	0.756962i
$442$	−7.83984	−	1.12720i	−0.372903	−	0.0536154i
$443$	0.575214	+	0.895050i	0.0273292	+	0.0425251i	0.854649	−	0.519206i	$-0.173772\pi$
$443$	0.575214	+	0.895050i	0.0273292	+	0.0425251i	−0.827320	+	0.561731i	$0.810136\pi$
$444$	−1.01106	+	2.54643i	−0.0479830	+	0.120848i
$445$	−3.40113	−	3.92511i	−0.161229	−	0.186068i
$446$	10.4877	−	1.50791i	0.496609	−	0.0714016i
$447$	12.1167	+	34.6901i	0.573101	+	1.64079i
$448$	−0.203391	−	0.692686i	−0.00960932	−	0.0327263i
$449$	3.39728	+	11.5701i	0.160327	+	0.546025i	0.999996	+	0.00292531i	$0.000931156\pi$
$449$	3.39728	+	11.5701i	0.160327	+	0.546025i	−0.839668	+	0.543099i	$0.817251\pi$
$450$	16.7229	−	32.8949i	0.788325	−	1.55068i
$451$	−15.4947	+	2.22781i	−0.729618	+	0.104903i
$452$	9.69417	+	11.1877i	0.455976	+	0.526224i
$453$	−9.42106	−	3.74064i	−0.442640	−	0.175751i
$454$	4.98217	+	7.75241i	0.233825	+	0.363838i
$455$	11.8373	+	1.70195i	0.554943	+	0.0797888i
$456$	−7.10414	+	1.39013i	−0.332682	+	0.0650988i
$457$	4.86845	+	4.21854i	0.227737	+	0.197335i	0.761253	−	0.648455i	$-0.224584\pi$
$457$	4.86845	+	4.21854i	0.227737	+	0.197335i	−0.533517	+	0.845790i	$0.679130\pi$
$458$	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	$0.942487\pi$
$462$	2.44069	−	1.26704i	0.113551	−	0.0589482i
$463$	10.2702	−	11.8525i	0.477299	−	0.550832i	−0.465129	−	0.885243i	$-0.653992\pi$
$463$	10.2702	−	11.8525i	0.477299	−	0.550832i	0.942427	+	0.334411i	$0.108537\pi$
$464$	2.17993	−	3.39204i	0.101201	−	0.157472i
$465$	−43.0584	−	60.1054i	−1.99679	−	2.78732i
$466$	−14.6520	+	9.41627i	−0.678741	+	0.436200i
$467$	−0.130816	−	0.286446i	−0.00605343	−	0.0132552i	0.906581	−	0.422032i	$-0.138683\pi$
$467$	−0.130816	−	0.286446i	−0.00605343	−	0.0132552i	−0.912635	+	0.408776i	$0.865956\pi$
$468$	9.34967	−	7.43893i	0.432189	−	0.343864i
$469$	−0.650720	−	4.52586i	−0.0300475	−	0.208985i
$470$	14.3930	−	31.5163i	0.663901	−	1.45374i
$471$	−8.70633	−	4.99372i	−0.401167	−	0.230098i
$472$	−0.0285512	+	0.00838340i	−0.00131418	+	0.000385877i
$473$	0.389075	+	0.177684i	0.0178897	+	0.00816994i
$474$	6.10879	+	4.77602i	0.280586	+	0.219370i
$475$	−38.8520	+	33.6654i	−1.78265	+	1.54468i
$476$	−1.30598	+	0.596423i	−0.0598597	+	0.0273370i
$477$	5.56858	+	9.51989i	0.254968	+	0.435886i
$478$	2.15190	−	14.9668i	0.0984257	−	0.684566i
$479$	−23.8946	−	15.3561i	−1.09177	−	0.701639i	−0.134525	−	0.990910i	$-0.542951\pi$
$479$	−23.8946	−	15.3561i	−1.09177	−	0.701639i	−0.957247	+	0.289271i	$0.906587\pi$
$480$	−7.19512	+	0.363212i	−0.328411	+	0.0165783i
$481$	−1.77489	+	6.04470i	−0.0809278	+	0.275615i
$482$	−2.84296			−0.129493
$483$	−3.71623	+	4.70651i	−0.169094	+	0.214153i
$484$	6.16332			0.280151
$485$	15.1447	−	51.5781i	0.687686	−	2.34204i
$486$	15.5798	+	0.520739i	0.706712	+	0.0236212i
$487$	12.9391	+	8.31544i	0.586326	+	0.376809i	0.799914	−	0.600115i	$-0.204879\pi$
$487$	12.9391	+	8.31544i	0.586326	+	0.376809i	−0.213588	+	0.976924i	$0.568515\pi$
$488$	−1.61181	+	11.2104i	−0.0729630	+	0.507469i
$489$	−1.75676	+	7.33222i	−0.0794435	+	0.331575i
$490$	−24.5127	+	11.1946i	−1.10737	+	0.505720i
$491$	27.6389	−	23.9493i	1.24733	−	1.08082i	0.253796	−	0.967258i	$-0.418321\pi$
$491$	27.6389	−	23.9493i	1.24733	−	1.08082i	0.993531	−	0.113557i	$-0.0362246\pi$
$492$	−7.59351	+	9.71253i	−0.342342	+	0.437874i
$493$	−7.29420	−	3.33115i	−0.328514	−	0.150028i
$494$	−15.9707	+	4.68943i	−0.718557	+	0.210988i
$495$	−6.62108	−	26.6319i	−0.297596	−	1.19701i
$496$	−4.26338	+	9.33549i	−0.191431	+	0.419176i
$497$	0.668017	+	4.64616i	0.0299647	+	0.208409i
$498$	0.347801	−	3.75490i	0.0155853	−	0.168261i
$499$	6.50748	+	14.2494i	0.291315	+	0.637890i	0.997540	−	0.0700968i	$-0.0223308\pi$
$499$	6.50748	+	14.2494i	0.291315	+	0.637890i	−0.706226	+	0.707987i	$0.749604\pi$
$500$	−25.5454	+	16.4170i	−1.14243	+	0.734192i
$501$	11.4448	−	8.19888i	0.511318	−	0.366299i
$502$	1.44014	−	2.24090i	0.0642766	−	0.100016i
$503$	−5.98194	+	6.90353i	−0.266722	+	0.307813i	−0.873273	−	0.487231i	$-0.838007\pi$
$503$	−5.98194	+	6.90353i	−0.266722	+	0.307813i	0.606552	+	0.795044i	$0.292552\pi$
$504$	0.696733	−	2.05066i	0.0310350	−	0.0913436i
$505$		−	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	$-0.429215\pi$
$509$	−16.0975	−	13.9486i	−0.713510	−	0.618260i	−0.934060	+	0.357116i	$0.883760\pi$
$510$	2.75139	+	14.0608i	0.121834	+	0.622621i
$511$	3.16257	+	0.454709i	0.139904	+	0.0201151i
$512$	0.540641	+	0.841254i	0.0238932	+	0.0371785i
$513$	−19.8302	−	8.85292i	−0.875525	−	0.390866i
$514$	−6.50410	−	7.50613i	−0.286884	−	0.331081i
$515$	48.6454	−	6.99416i	2.14357	−	0.308199i
$516$	0.318022	−	0.111080i	0.0140002	−	0.00489003i
$517$	−5.16120	−	17.5774i	−0.226989	−	0.773054i
$518$	0.321730	+	1.09571i	0.0141360	+	0.0481429i
$519$	−26.1855	+	9.14617i	−1.14942	+	0.401472i
$520$	−16.3968	+	2.35751i	−0.719048	+	0.103384i
$521$	27.4746	+	31.7074i	1.20368	+	1.38913i	0.899735	+	0.436437i	$0.143760\pi$
$521$	27.4746	+	31.7074i	1.20368	+	1.38913i	0.303949	+	0.952688i	$0.401695\pi$
$522$	11.2042	−	4.55943i	0.490395	−	0.199561i
$523$	18.6310	+	28.9904i	0.814677	+	1.26766i	0.960480	+	0.278348i	$0.0897870\pi$
$523$	18.6310	+	28.9904i	0.814677	+	1.26766i	−0.145803	+	0.989314i	$0.546577\pi$
$524$	−5.12229	−	0.736474i	−0.223768	−	0.0321730i
$525$	−2.95369	−	15.0946i	−0.128910	−	0.658781i
$526$	−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
$531$	−0.0845243	−	0.0287180i	−0.00366804	−	0.00124626i
$532$	−1.97585	+	2.28025i	−0.0856640	+	0.0988615i
$533$	−15.3262	+	23.8481i	−0.663852	+	1.03297i
$534$	−1.75815	+	1.25951i	−0.0760827	+	0.0545043i
$535$	−2.34913	+	1.50970i	−0.101562	+	0.0652698i
$536$	2.63106	+	5.76123i	0.113645	+	0.248847i
$537$	1.14203	−	12.3295i	0.0492823	−	0.532058i
$538$	−0.480540	−	3.34223i	−0.0207175	−	0.144094i
$539$	−5.91905	+	12.9609i	−0.254951	+	0.558266i
$540$	−18.2807	−	11.5296i	−0.786676	−	0.496154i
$541$	−34.2915	+	10.0689i	−1.47431	+	0.432895i	−0.917496	−	0.397744i	$-0.869793\pi$
$541$	−34.2915	+	10.0689i	−1.47431	+	0.432895i	−0.556810	+	0.830640i	$0.687975\pi$
$542$	13.0843	+	5.97539i	0.562017	+	0.256665i
$543$	−18.5885	+	23.7758i	−0.797710	+	1.02032i
$544$	1.50299	−	1.30235i	0.0644401	−	0.0558377i
$545$	−36.4353	+	16.6395i	−1.56072	+	0.712756i
$546$	1.16034	−	4.84292i	0.0496579	−	0.207258i
$547$	2.55106	−	17.7430i	0.109076	−	0.758638i	−0.859718	−	0.510769i	$-0.829361\pi$
$547$	2.55106	−	17.7430i	0.109076	−	0.758638i	0.968794	−	0.247869i	$-0.0797301\pi$
$548$	9.01876	+	5.79601i	0.385262	+	0.247593i
$549$	−23.3068	+	24.7229i	−0.994710	+	1.05515i
$550$	−7.62141	+	25.9561i	−0.324978	+	1.10677i
$551$	−16.8517			−0.717908
$552$	3.10241	−	7.70552i	0.132047	−	0.327969i
$553$	3.23200			0.137439
$554$	−2.67931	+	9.12490i	−0.113833	+	0.387680i
$555$	11.3815	−	0.574541i	0.483117	−	0.0243879i
$556$	0.442726	+	0.284522i	0.0187757	+	0.0120664i
$557$	−0.449193	+	3.12421i	−0.0190329	+	0.132377i	−0.997122	−	0.0758078i	$-0.975846\pi$
$557$	−0.449193	+	3.12421i	−0.0190329	+	0.132377i	0.978090	+	0.208185i	$0.0667555\pi$
$558$	−26.5761	+	15.5455i	−1.12506	+	0.658093i
$559$	0.704583	−	0.321772i	0.0298007	−	0.0136095i
$560$	−2.26936	+	1.96641i	−0.0958978	+	0.0830959i
$561$	5.96802	+	4.66596i	0.251970	+	0.196997i
$562$	0.267663	+	0.122237i	0.0112907	+	0.00515627i
$563$	45.3508	−	13.3162i	1.91131	−	0.561211i	0.930482	−	0.366338i	$-0.119389\pi$
$563$	45.3508	−	13.3162i	1.91131	−	0.561211i	0.980828	−	0.194874i	$-0.0624296\pi$
$564$	−12.5153	−	7.17842i	−0.526988	−	0.302266i
$565$	25.5784	−	56.0090i	1.07609	−	2.35631i
$566$	−2.51041	−	17.4603i	−0.105520	−	0.733910i
$567$	5.24948	−	3.82867i	0.220457	−	0.160789i
$568$	−2.70100	−	5.91437i	−0.113332	−	0.248162i
$569$	−17.1815	+	11.0419i	−0.720285	+	0.462899i	−0.848736	−	0.528817i	$-0.822636\pi$
$569$	−17.1815	+	11.0419i	−0.720285	+	0.462899i	0.128451	+	0.991716i	$0.458999\pi$
$570$	17.5346	+	24.4767i	0.734446	+	1.02522i
$571$	−6.38883	+	9.94122i	−0.267364	+	0.416027i	−0.948813	−	0.315839i	$-0.897714\pi$
$571$	−6.38883	+	9.94122i	−0.267364	+	0.416027i	0.681448	+	0.731866i	$0.261350\pi$
$572$	−5.73582	+	6.61949i	−0.239827	+	0.276775i
$573$	−30.5893	+	15.8799i	−1.27789	+	0.663394i
$574$			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	0.396174	−	0.918176i	$-0.370338\pi$
$577$	5.59812	+	1.64376i	0.233053	+	0.0684304i	−0.163121	+	0.986606i	$0.552156\pi$
$578$	9.85869	+	8.54260i	0.410068	+	0.355326i
$579$	26.4537	−	5.17643i	1.09938	−	0.215125i
$580$	−16.6005	−	2.38679i	−0.689299	−	0.0991062i
$581$	−0.849761	−	1.32225i	−0.0352540	−	0.0548563i
$582$	−20.8049	−	8.26061i	−0.862391	−	0.342413i
$583$	−5.29462	−	6.11032i	−0.219281	−	0.253064i
$584$	−4.38072	+	0.629852i	−0.181275	+	0.0260635i
$585$	−44.3004	−	22.5211i	−1.83159	−	0.931133i
$586$	−7.50885	−	25.5728i	−0.310188	−	1.05640i
$587$	−4.90768	−	16.7140i	−0.202562	−	0.689861i	−0.996630	−	0.0820325i	$-0.973859\pi$
$587$	−4.90768	−	16.7140i	−0.202562	−	0.689861i	0.794068	−	0.607829i	$-0.207959\pi$
$588$	3.70032	+	10.5940i	0.152598	+	0.436889i
$589$	42.4560	−	6.10425i	1.74937	−	0.251521i
$590$	0.0810517	+	0.0935386i	0.00333684	+	0.00385092i
$591$	−2.74483	+	6.91304i	−0.112907	+	0.284364i
$592$	−0.855203	−	1.33072i	−0.0351486	−	0.0546923i
$593$	−1.69315	−	0.243438i	−0.0695293	−	0.00999681i	0.107462	−	0.994209i	$-0.465727\pi$
$593$	−1.69315	−	0.243438i	−0.0695293	−	0.00999681i	−0.176992	+	0.984212i	$0.556637\pi$
$594$	−11.2970	+	1.72255i	−0.463523	+	0.0706771i
$595$	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	$-0.00542348\pi$
$600$	9.81630	+	18.9090i	0.400749	+	0.771958i
$601$	26.6742	−	30.7837i	1.08806	−	1.25569i	0.123360	−	0.992362i	$-0.460633\pi$
$601$	26.6742	−	30.7837i	1.08806	−	1.25569i	0.964705	−	0.263332i	$-0.0848214\pi$
$602$	0.0759096	−	0.118118i	0.00309385	−	0.00481412i
$603$	−3.48997	+	18.6775i	−0.142123	+	0.760606i
$604$	4.92328	−	3.16400i	0.200325	−	0.128741i
$605$	−10.6494	−	23.3190i	−0.432961	−	0.948053i
$606$	−22.9257	−	2.12351i	−0.931294	−	0.0862618i
$607$	−1.03026	−	7.16565i	−0.0418171	−	0.290845i	−0.999989	−	0.00465177i	$-0.998519\pi$
$607$	−1.03026	−	7.16565i	−0.0418171	−	0.290845i	0.958172	−	0.286193i	$-0.0923898\pi$
$608$	1.73617	−	3.80168i	0.0704110	−	0.154179i
$609$	2.50852	−	4.37350i	0.101651	−	0.177223i
$610$	45.1996	−	13.2718i	1.83008	−	0.537359i
$611$	−30.1772	−	13.7814i	−1.22084	−	0.557538i
$612$	5.93589	−	0.600822i	0.239944	−	0.0242868i
$613$	−1.67864	+	1.45455i	−0.0677995	+	0.0587486i	−0.688101	−	0.725615i	$-0.741556\pi$
$613$	−1.67864	+	1.45455i	−0.0677995	+	0.0587486i	0.620302	+	0.784363i	$0.287010\pi$
$614$	−31.7724	+	14.5100i	−1.28223	+	0.585575i
$615$	49.8681	+	11.9481i	2.01088	+	0.481796i
$616$	−0.225953	+	1.57154i	−0.00910392	+	0.0633191i
$617$	25.2102	+	16.2016i	1.01492	+	0.652252i	0.938663	−	0.344836i	$-0.112066\pi$
$617$	25.2102	+	16.2016i	1.01492	+	0.652252i	0.0762604	+	0.997088i	$0.475702\pi$
$618$	−1.03178	−	20.4392i	−0.0415041	−	0.822184i
$619$	1.36024	−	4.63255i	0.0546726	−	0.186198i	−0.927629	−	0.373502i	$-0.878157\pi$
$619$	1.36024	−	4.63255i	0.0546726	−	0.186198i	0.982302	+	0.187304i	$0.0599751\pi$
$620$	42.6876			1.71437
$621$	20.9138	−	13.5504i	0.839242	−	0.543758i
$622$	0.930554			0.0373118
$623$	−0.253966	+	0.864930i	−0.0101749	+	0.0346527i
$624$	0.347779	+	6.88939i	0.0139223	+	0.275796i
$625$	54.5140	+	35.0340i	2.18056	+	1.40136i
$626$	2.64853	−	18.4209i	0.105856	−	0.736247i
$627$	15.4819	+	3.70938i	0.618287	+	0.148138i
$628$	5.27109	−	2.40723i	0.210339	−	0.0960588i
$629$	−2.37748	+	2.06009i	−0.0947962	+	0.0821413i
$630$	−8.96257	+	0.907179i	−0.357077	+	0.0361429i
$631$	−35.4292	−	16.1800i	−1.41041	−	0.644115i	−0.442817	−	0.896612i	$-0.646021\pi$
$631$	−35.4292	−	16.1800i	−1.41041	−	0.644115i	−0.967598	+	0.252498i	$0.918748\pi$
$632$	−4.29555	+	1.26129i	−0.170868	+	0.0501713i
$633$	13.7691	−	24.0058i	0.547272	−	0.954145i
$634$	−7.02846	+	15.3902i	−0.279136	+	0.611222i
$635$	−8.77250	−	61.0141i	−0.348126	−	2.42127i
$636$	−6.34042	−	0.587285i	−0.251414	−	0.0232874i
$637$	10.7189	+	23.4711i	0.424699	+	0.929961i
$638$	−7.45994	+	4.79421i	−0.295342	+	0.189805i
$639$	3.58274	−	19.1740i	0.141731	−	0.758510i
$640$	2.24874	−	3.49910i	0.0888892	−	0.138314i
$641$	−1.82236	+	2.10312i	−0.0719789	+	0.0830681i	−0.790597	−	0.612337i	$-0.790230\pi$
$641$	−1.82236	+	2.10312i	−0.0719789	+	0.0830681i	0.718618	+	0.695405i	$0.244775\pi$
$642$	0.535764	+	1.03204i	0.0211449	+	0.0407312i
$643$			24.1796i			0.953551i	0.879025	+	0.476775i	$0.158194\pi$
$643$			24.1796i			0.953551i	−0.879025	+	0.476775i	$0.841806\pi$
$644$	−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	$-0.0251034\pi$
$647$	26.9823	+	23.3803i	1.06078	+	0.919174i	0.0638914	+	0.997957i	$0.479649\pi$
$648$	−5.48277	+	7.13717i	−0.215384	+	0.280374i
$649$	0.0647759	+	0.00931337i	0.00254268	+	0.000365582i
$650$	26.4854	+	41.2121i	1.03884	+	1.61647i
$651$	−4.73570	+	11.9272i	−0.185607	+	0.467464i
$652$	−2.85066	−	3.28983i	−0.111640	−	0.128840i
$653$	2.27969	−	0.327771i	0.0892113	−	0.0128267i	−0.0975646	−	0.995229i	$-0.531105\pi$
$653$	2.27969	−	0.327771i	0.0892113	−	0.0128267i	0.186776	+	0.982403i	$0.440196\pi$
$654$	5.50010	+	15.7468i	0.215071	+	0.615747i
$655$	6.06421	+	20.6528i	0.236948	+	0.806972i
$656$	−2.00535	−	6.82960i	−0.0782958	−	0.266651i
$657$	−11.8357	−	6.01694i	−0.461754	−	0.234743i
$658$	−5.95239	+	0.855824i	−0.232048	+	0.0333635i
$659$	25.4420	+	29.3616i	0.991080	+	1.14377i	0.989611	+	0.143768i	$0.0459220\pi$
$659$	25.4420	+	29.3616i	0.991080	+	1.14377i	0.00146862	+	0.999999i	$0.499533\pi$
$660$	14.7257	+	5.84685i	0.573197	+	0.227588i
$661$	−8.92799	−	13.8922i	−0.347258	−	0.540345i	0.623060	−	0.782174i	$-0.285889\pi$
$661$	−8.92799	−	13.8922i	−0.347258	−	0.540345i	−0.970319	+	0.241829i	$0.922253\pi$
$662$	0.817121	+	0.117484i	0.0317583	+	0.00456615i
$663$	13.4633	−	2.63448i	0.522872	−	0.102315i
$664$	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
$669$	−16.2881	+	8.45568i	−0.629733	+	0.326915i
$670$	17.2516	−	19.9094i	0.666486	−	0.769166i
$671$	13.4662	−	20.9538i	0.519857	−	0.808913i
$672$	0.728201	+	1.01650i	0.0280910	+	0.0392123i
$673$	−20.1151	+	12.9272i	−0.775381	+	0.498307i	−0.867498	−	0.497441i	$-0.834273\pi$
$673$	−20.1151	+	12.9272i	−0.775381	+	0.498307i	0.0921168	+	0.995748i	$0.470637\pi$
$674$	11.8278	+	25.8992i	0.455588	+	0.997599i
$675$	−8.55724	+	63.3401i	−0.329368	+	2.43796i
$676$	0.407241	+	2.83243i	0.0156631	+	0.108939i
$677$	−15.5663	+	34.0854i	−0.598262	+	1.31001i	0.332058	+	0.943259i	$0.392257\pi$
$677$	−15.5663	+	34.0854i	−0.598262	+	1.31001i	−0.930319	+	0.366751i	$0.880470\pi$
$678$	−22.2414	−	12.7571i	−0.854176	−	0.489932i
$679$	−8.95221	+	2.62861i	−0.343554	+	0.100877i
$680$	−7.52443	−	3.43629i	−0.288549	−	0.131776i
$681$	−12.5744	−	9.83102i	−0.481853	−	0.376726i
$682$	17.0578	−	14.7807i	0.653177	−	0.565981i
$683$	−2.46051	+	1.12368i	−0.0941488	+	0.0429963i	−0.461933	−	0.886915i	$-0.652844\pi$
$683$	−2.46051	+	1.12368i	−0.0941488	+	0.0429963i	0.367784	+	0.929911i	$0.380117\pi$
$684$	10.8226	−	6.33057i	0.413811	−	0.242055i
$685$	6.34600	−	44.1374i	0.242468	−	1.68640i
$686$	8.18603	+	5.26084i	0.312544	+	0.200860i
$687$	−19.7458	+	0.996776i	−0.753350	+	0.0380294i
$688$	−0.0547937	+	0.186610i	−0.00208899	+	0.00711444i
$689$	−14.6415			−0.557796
$690$	−34.5145	+	1.57616i	−1.31395	+	0.0600034i
$691$	−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
$693$	−3.26730	+	3.46582i	−0.124114	+	0.131655i
$694$	0.0524339	+	0.0336972i	0.00199037	+	0.00127913i
$695$	0.311521	−	2.16668i	0.0118167	−	0.0821868i
$696$	−1.62724	+	6.79163i	−0.0616804	+	0.257436i
$697$	−12.8765	+	5.88049i	−0.487731	+	0.222739i
$698$	−16.1223	+	13.9701i	−0.610239	+	0.528775i
$699$	18.5806	−	23.7656i	0.702782	−	0.898898i
$700$	8.07765	+	3.68894i	0.305307	+	0.139429i
$701$	3.55633	−	1.04423i	0.134321	−	0.0394401i	−0.213881	−	0.976860i	$-0.568611\pi$
$701$	3.55633	−	1.04423i	0.134321	−	0.0394401i	0.348202	+	0.937420i	$0.386792\pi$
$702$	−11.0397	+	17.5039i	−0.416666	+	0.660643i
$703$	−2.74633	+	6.01363i	−0.103580	+	0.226808i
$704$	−0.312985	−	2.17686i	−0.0117961	−	0.0820435i
$705$	−5.53486	+	59.7552i	−0.208455	+	2.25051i
$706$	0.0918513	+	0.201126i	0.00345687	+	0.00756949i
$707$	−8.07308	+	5.18825i	−0.303619	+	0.195124i
$708$	0.0418982	−	0.0300151i	0.00157463	−	0.00112804i
$709$	15.5346	−	24.1722i	0.583413	−	0.907808i	−0.416587	−	0.909096i	$-0.636774\pi$
$709$	15.5346	−	24.1722i	0.583413	−	0.907808i	0.999999	+	0.00128839i	$0.000410109\pi$
$710$	−17.7101	+	20.4386i	−0.664650	+	0.767046i
$711$	−12.7167	−	4.32064i	−0.476915	−	0.162037i
$712$		−	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
$717$	5.02941	+	25.7024i	0.187827	+	0.959873i
$718$	−4.05998	−	0.583737i	−0.151517	−	0.0217849i
$719$	2.49443	+	3.88140i	0.0930264	+	0.144752i	0.884648	−	0.466260i	$-0.154399\pi$
$719$	2.49443	+	3.88140i	0.0930264	+	0.144752i	−0.791621	+	0.611012i	$0.790763\pi$
$720$	11.5578	−	4.70334i	0.430735	−	0.175283i
$721$	−5.58597	−	6.44656i	−0.208033	−	0.240082i
$722$	1.51730	−	0.218155i	0.0564681	−	0.00811889i
$723$	4.64874	−	1.62373i	0.172889	−	0.0603872i
$724$	−4.90900	−	16.7185i	−0.182442	−	0.621339i
$725$	13.9732	+	47.5884i	0.518952	+	1.76739i
$726$	−10.0781	+	3.52012i	−0.374034	+	0.130644i
$727$	50.7325	−	7.29423i	1.88156	−	0.270528i	0.896543	−	0.442957i	$-0.146071\pi$
$727$	50.7325	−	7.29423i	1.88156	−	0.270528i	0.985022	+	0.172429i	$0.0551615\pi$
$728$	1.88285	+	2.17293i	0.0697832	+	0.0805341i
$729$	−25.7730	+	8.04673i	−0.954557	+	0.298027i
$730$	9.95239	+	15.4862i	0.368354	+	0.573171i
$731$	0.382849	+	0.0550454i	0.0141602	+	0.00203593i
$732$	−3.76710	−	19.2515i	−0.139236	−	0.711554i
$733$	−12.9779	−	11.2454i	−0.479351	−	0.415360i	0.381382	−	0.924418i	$-0.375448\pi$
$733$	−12.9779	−	11.2454i	−0.479351	−	0.415360i	−0.860732	+	0.509058i	$0.829994\pi$
$734$	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
$738$	6.86950	−	20.2186i	0.252870	−	0.744259i
$739$	−9.77783	+	11.2842i	−0.359683	+	0.415097i	−0.906534	−	0.422134i	$-0.861281\pi$
$739$	−9.77783	+	11.2842i	−0.359683	+	0.415097i	0.546850	+	0.837230i	$0.315827\pi$
$740$	−3.55713	+	5.53500i	−0.130763	+	0.203471i
$741$	23.4366	−	16.7896i	0.860966	−	0.616781i
$742$	−2.23272	+	1.43488i	−0.0819656	+	0.0526761i
$743$	−11.1515	−	24.4184i	−0.409109	−	0.895825i	−0.996265	−	0.0863505i	$-0.972479\pi$
$743$	−11.1515	−	24.4184i	−0.409109	−	0.895825i	0.587155	−	0.809474i	$-0.300248\pi$
$744$	1.63949	−	17.7002i	0.0601066	−	0.648919i
$745$	12.5580	+	87.3431i	0.460091	+	3.20000i
$746$	0.138595	−	0.303482i	0.00507434	−	0.0111113i
$747$	1.57586	+	6.33857i	0.0576578	+	0.231916i
$748$	−4.19656	+	1.23222i	−0.153441	+	0.0450544i
$749$	0.440870	+	0.201339i	0.0161090	+	0.00735676i
$750$	32.3948	−	41.4348i	1.18289	−	1.51298i
$751$	5.53673	−	4.79760i	0.202038	−	0.175067i	−0.547965	−	0.836501i	$-0.684597\pi$
$751$	5.53673	−	4.79760i	0.202038	−	0.175067i	0.750003	+	0.661434i	$0.230052\pi$
$752$	7.57714	−	3.46037i	0.276310	−	0.126187i
$753$	−1.07501	+	4.48679i	−0.0391756	+	0.163508i
$754$	−2.28538	+	15.8951i	−0.0832285	+	0.578867i
$755$	−20.4779	−	13.1603i	−0.745266	−	0.478953i
$756$	0.0319338	+	3.75112i	0.00116142	+	0.136427i
$757$	−12.7459	+	43.4086i	−0.463258	+	1.57771i	0.314569	+	0.949235i	$0.398140\pi$
$757$	−12.7459	+	43.4086i	−0.463258	+	1.57771i	−0.777827	+	0.628478i	$0.783678\pi$
$758$	−11.2993			−0.410408
$759$	−13.2461	+	12.5806i	−0.480804	+	0.456646i
$760$	−17.3836			−0.630570
$761$	7.11988	−	24.2481i	0.258095	−	0.878993i	−0.723871	−	0.689936i	$-0.757639\pi$
$761$	7.11988	−	24.2481i	0.258095	−	0.878993i	0.981966	−	0.189057i	$-0.0605430\pi$
$762$	−25.6360	+	1.29412i	−0.928696	+	0.0468809i
$763$	5.84856	+	3.75864i	0.211732	+	0.136072i
$764$	2.83189	−	19.6962i	0.102454	−	0.712583i
$765$	−12.5297	−	21.4204i	−0.453012	−	0.774456i
$766$	−6.19601	+	2.82962i	−0.223871	+	0.102238i
$767$	0.0895640	−	0.0776077i	0.00323397	−	0.00280225i
$768$	−1.36452	−	1.06682i	−0.0492378	−	0.0384954i
$769$	15.0249	+	6.86164i	0.541812	+	0.247437i	0.667470	−	0.744636i	$-0.267377\pi$
$769$	15.0249	+	6.86164i	0.541812	+	0.247437i	−0.125659	+	0.992074i	$0.540104\pi$
$770$	6.33637	−	1.86052i	0.228347	−	0.0670487i
$771$	14.9224	+	8.55909i	0.537417	+	0.308248i
$772$	−6.46498	+	14.1563i	−0.232680	+	0.509497i
$773$	1.49875	+	10.4240i	0.0539062	+	0.374926i	0.998861	+	0.0477236i	$0.0151967\pi$
$773$	1.49875	+	10.4240i	0.0539062	+	0.374926i	−0.944954	+	0.327202i	$0.893894\pi$
$774$	−0.456580	+	0.363271i	−0.0164114	+	0.0130575i
$775$	−52.4419	−	114.832i	−1.88377	−	4.12488i
$776$	10.8723	−	6.98719i	0.390292	−	0.250826i
$777$	−1.15189	−	1.60793i	−0.0413239	−	0.0576842i
$778$	5.57319	−	8.67205i	0.199808	−	0.310908i
$779$	−19.4811	+	22.4823i	−0.697981	+	0.805514i
$780$	25.4652	−	13.2198i	0.911801	−	0.473346i
$781$			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
$786$	8.79647	−	1.72128i	0.313760	−	0.0613962i
$787$	−5.59262	−	0.804097i	−0.199355	−	0.0286630i	0.0419138	−	0.999121i	$-0.486655\pi$
$787$	−5.59262	−	0.804097i	−0.199355	−	0.0286630i	−0.241269	+	0.970458i	$0.577564\pi$
$788$	−2.32170	−	3.61263i	−0.0827071	−	0.128695i
$789$	15.8752	+	6.30327i	0.565173	+	0.224402i
$790$	12.1943	+	14.0729i	0.433853	+	0.500692i
$791$	−10.5782	+	1.52092i	−0.376119	+	0.0540777i
$792$	2.98993	−	5.88137i	0.106242	−	0.208985i
$793$	−12.7079	−	43.2790i	−0.451269	−	1.53688i
$794$	−3.29092	−	11.2079i	−0.116791	−	0.397752i
$795$	8.73344	+	25.0038i	0.309743	+	0.886795i
$796$	−20.9550	+	3.01288i	−0.742731	+	0.106789i
$797$	−31.8424	−	36.7480i	−1.12791	−	1.30168i	−0.948097	−	0.317983i	$-0.896995\pi$
$797$	−31.8424	−	36.7480i	−1.12791	−	1.30168i	−0.179818	−	0.983700i	$-0.557551\pi$
$798$	1.92852	−	4.85710i	0.0682687	−	0.171939i
$799$	−8.95625	−	13.9362i	−0.316849	−	0.493027i
$800$	−12.1754	−	1.75055i	−0.430464	−	0.0618913i
$801$	2.15553	−	3.06367i	0.0761619	−	0.108249i
$802$	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
$807$	2.69465	+	5.19067i	0.0948562	+	0.182720i
$808$	8.70496	−	10.0461i	0.306239	−	0.353419i
$809$	26.8673	−	41.8063i	0.944602	−	1.46983i	0.0629022	−	0.998020i	$-0.479964\pi$
$809$	26.8673	−	41.8063i	0.944602	−	1.46983i	0.881700	−	0.471810i	$-0.156399\pi$
$810$	36.4772	+	8.41204i	1.28168	+	0.295569i
$811$	−24.3906	+	15.6749i	−0.856471	+	0.550420i	−0.893587	−	0.448891i	$-0.851819\pi$
$811$	−24.3906	+	15.6749i	−0.856471	+	0.550420i	0.0371160	+	0.999311i	$0.488183\pi$
$812$	1.20924	+	2.64786i	0.0424359	+	0.0929216i
$813$	−24.8079	−	2.29784i	−0.870050	−	0.0805889i
$814$	0.495090	+	3.44343i	0.0173529	+	0.120692i
$815$	−7.52156	+	16.4699i	−0.263469	+	0.576916i
$816$	−1.71383	+	2.98798i	−0.0599959	+	0.104600i
$817$	0.779912	−	0.229003i	0.0272857	−	0.00801179i
$818$	5.87874	+	2.68473i	0.205545	+	0.0938694i
$819$	0.868632	+	8.58174i	0.0303525	+	0.299870i
$820$	−22.3749	+	19.3880i	−0.781366	+	0.677057i
$821$	51.9920	−	23.7439i	1.81453	−	0.828669i	0.877326	−	0.479894i	$-0.159325\pi$
$821$	51.9920	−	23.7439i	1.81453	−	0.828669i	0.937206	−	0.348775i	$-0.113402\pi$
$822$	−18.0576	−	4.32650i	−0.629831	−	0.150904i
$823$	−6.26314	+	43.5611i	−0.218319	+	1.51844i	0.525922	+	0.850533i	$0.323720\pi$
$823$	−6.26314	+	43.5611i	−0.218319	+	1.51844i	−0.744241	+	0.667911i	$0.767189\pi$
$824$	9.93990	+	6.38799i	0.346273	+	0.222536i
$825$	−2.36227	−	46.7958i	−0.0822435	−	1.62922i
$826$	0.00605222	−	0.0206120i	0.000210584	−	0.000717182i
$827$	0.0645061			0.00224310			0.00112155	−	0.999999i	$-0.499643\pi$
$827$	0.0645061			0.00224310			0.00112155	+	0.999999i	$0.499643\pi$
$828$	−0.672044	+	14.3718i	−0.0233551	+	0.499454i
$829$	−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
$831$	−0.830456	−	16.4511i	−0.0288082	−	0.570682i
$832$	−3.35042	−	2.15319i	−0.116155	−	0.0746483i
$833$	−1.83368	+	12.7535i	−0.0635333	+	0.441884i
$834$	−0.886436	−	0.212386i	−0.0306948	−	0.00735431i
$835$	30.7535	−	14.0446i	1.06427	−	0.486034i
$836$	−6.94643	+	6.01912i	−0.240247	+	0.208176i
$837$	34.5779	−	40.5983i	1.19519	−	1.40328i
$838$	7.90627	+	3.61067i	0.273118	+	0.124729i
$839$	−34.8953	+	10.2462i	−1.20472	+	0.353738i	−0.821656	−	0.569983i	$-0.806950\pi$
$839$	−34.8953	+	10.2462i	−1.20472	+	0.353738i	−0.383065	+	0.923721i	$0.625131\pi$
$840$	2.58770	−	4.51154i	0.0892841	−	0.155663i
$841$	5.29319	−	11.5905i	0.182524	−	0.399671i
$842$	4.16030	+	28.9355i	0.143373	+	0.997184i
$843$	−0.507490	−	0.0470066i	−0.0174789	−	0.00161899i
$844$	6.63740	+	14.5339i	0.228469	+	0.500277i
$845$	10.0129	−	6.43488i	0.344453	−	0.221367i
$846$	24.5645	+	4.59000i	0.844547	+	0.157807i
$847$	−2.40557	+	3.74314i	−0.0826564	+	0.128616i
$848$	2.40747	−	2.77837i	0.0826729	−	0.0954096i
$849$	14.0772	+	27.1168i	0.483130	+	0.930647i
$850$			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	0.0906080	−	0.995887i	$-0.471119\pi$
$853$	−10.8526	−	3.18660i	−0.371585	−	0.109107i	−0.462193	+	0.886780i	$0.652937\pi$
$854$	−6.17924	−	5.35434i	−0.211449	−	0.183222i
$855$	−42.6518	−	30.0089i	−1.45866	−	1.02628i
$856$	−0.664519	−	0.0955434i	−0.0227128	−	0.00326561i
$857$	−2.88250	−	4.48526i	−0.0984643	−	0.153213i	0.788526	−	0.615001i	$-0.210845\pi$
$857$	−2.88250	−	4.48526i	−0.0984643	−	0.153213i	−0.886990	+	0.461788i	$0.847208\pi$
$858$	5.59841	−	14.1000i	0.191127	−	0.481366i
$859$	21.0275	+	24.2670i	0.717448	+	0.827979i	0.990998	−	0.133879i	$-0.0427433\pi$
$859$	21.0275	+	24.2670i	0.717448	+	0.827979i	−0.273550	+	0.961858i	$0.588198\pi$
$860$	0.800719	−	0.115126i	0.0273043	−	0.00392577i
$861$	−2.93488	−	8.40257i	−0.100021	−	0.286359i
$862$	8.62653	+	29.3793i	0.293821	+	1.00066i
$863$	−9.34922	−	31.8405i	−0.318251	−	1.08386i	−0.950919	−	0.309440i	$-0.899858\pi$
$863$	−9.34922	−	31.8405i	−0.318251	−	1.08386i	0.632668	−	0.774423i	$-0.281960\pi$
$864$	−1.50631	−	4.97303i	−0.0512459	−	0.169186i
$865$	−65.9300	+	9.47931i	−2.24169	+	0.322306i
$866$	−12.0474	−	13.9035i	−0.409388	−	0.472458i
$867$	−20.9997	−	8.33796i	−0.713188	−	0.283172i
$868$	−4.00567	−	6.23294i	−0.135961	−	0.211560i
$869$	9.74557	+	1.40120i	0.330596	+	0.0475325i
$870$	28.5079	−	5.57840i	0.966510	−	0.189126i
$871$	−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
$876$	6.80351	−	3.53193i	0.229869	−	0.119333i
$877$	−2.59283	+	2.99228i	−0.0875535	+	0.101042i	−0.797836	−	0.602875i	$-0.794022\pi$
$877$	−2.59283	+	2.99228i	−0.0875535	+	0.101042i	0.710282	+	0.703917i	$0.248567\pi$
$878$	5.62450	−	8.75189i	0.189818	−	0.295362i
$879$	26.8839	+	37.5274i	0.906773	+	1.26577i
$880$	−7.69539	+	4.94553i	−0.259412	+	0.166714i
$881$	−7.00372	−	15.3360i	−0.235961	−	0.516683i	0.754195	−	0.656651i	$-0.228027\pi$
$881$	−7.00372	−	15.3360i	−0.235961	−	0.516683i	−0.990156	+	0.139967i	$0.955300\pi$
$882$	−12.1013	−	15.2097i	−0.407473	−	0.512136i
$883$	1.93605	+	13.4655i	0.0651533	+	0.453151i	0.996117	+	0.0880394i	$0.0280601\pi$
$883$	1.93605	+	13.4655i	0.0651533	+	0.453151i	−0.930964	+	0.365112i	$0.881031\pi$
$884$	−3.29028	+	7.20471i	−0.110664	+	0.242320i
$885$	−0.185957	−	0.106660i	−0.00625089	−	0.00358534i
$886$	1.02085	−	0.299749i	0.0342962	−	0.0100703i
$887$	−44.8662	−	20.4897i	−1.50646	−	0.687977i	−0.520332	−	0.853964i	$-0.674192\pi$
$887$	−44.8662	−	20.4897i	−1.50646	−	0.687977i	−0.986128	+	0.165987i	$0.946919\pi$
$888$	2.15844	+	1.68752i	0.0724324	+	0.0566295i
$889$	−8.08566	+	7.00627i	−0.271184	+	0.234983i
$890$	−4.72433	+	2.15753i	−0.158360	+	0.0723205i
$891$	17.4888	−	9.26887i	0.585898	−	0.310519i
$892$	1.50791	−	10.4877i	0.0504886	−	0.351156i
$893$	−29.2871	−	18.8217i	−0.980057	−	0.629844i
$894$	36.6986	−	1.85256i	1.22738	−	0.0619588i
$895$	8.37737	−	28.5307i	0.280025	−	0.953677i
$896$	−0.721929			−0.0241180
$897$	1.50919	+	33.0480i	0.0503903	+	1.10344i
$898$	12.0585			0.402398
$899$	11.6585	−	39.7052i	0.388833	−	1.32424i
$900$	−26.8511	−	25.3131i	−0.895036	−	0.843770i
$901$	−6.15059	−	3.95274i	−0.204906	−	0.131685i
$902$	−2.22781	+	15.4947i	−0.0741778	+	0.515918i
$903$	−0.0566637	+	0.236498i	−0.00188565	+	0.00787017i
$904$	13.4657	−	6.14956i	0.447861	−	0.204531i
$905$	−54.7727	+	47.4608i	−1.82070	+	1.57765i
$906$	−6.24334	+	7.98558i	−0.207421	+	0.265303i
$907$	31.8531	+	14.5468i	1.05766	+	0.483019i	0.866830	−	0.498603i	$-0.166153\pi$
$907$	31.8531	+	14.5468i	1.05766	+	0.483019i	0.190834	+	0.981622i	$0.438881\pi$
$908$	8.84202	−	2.59625i	0.293433	−	0.0861596i
$909$	38.7004	−	9.62151i	1.28361	−	0.319125i
$910$	4.96798	−	10.8784i	0.164687	−	0.360614i
$911$	3.99792	+	27.8061i	0.132457	+	0.921259i	0.942338	+	0.334664i	$0.108623\pi$
$911$	3.99792	+	27.8061i	0.132457	+	0.921259i	−0.809881	+	0.586595i	$0.800468\pi$
$912$	−0.667648	+	7.20802i	−0.0221080	+	0.238681i
$913$	−1.98907	−	4.35545i	−0.0658285	−	0.144144i
$914$	5.41926	−	3.48275i	0.179253	−	0.115199i
$915$	−66.3292	+	47.5170i	−2.19277	+	1.57086i
$916$	6.17129	−	9.60272i	0.203905	−	0.317283i
$917$	2.44653	−	2.82345i	0.0807916	−	0.0932385i
$918$	−9.36306	+	4.37268i	−0.309027	+	0.144320i
$919$			9.32003i			0.307439i	0.988115	+	0.153720i	$0.0491253\pi$
$919$			9.32003i			0.307439i	−0.988115	+	0.153720i	$0.950875\pi$
$920$	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
$924$	−0.528097	−	2.69879i	−0.0173731	−	0.0887838i
$925$	19.2594	+	2.76908i	0.633244	+	0.0910468i
$926$	−8.47892	−	13.1935i	−0.278635	−	0.433564i
$927$	13.3608	+	32.8323i	0.438826	+	1.07836i
$928$	−2.64048	−	3.04728i	−0.0866781	−	0.100032i
$929$	−7.82580	+	1.12518i	−0.256756	+	0.0369160i	−0.269491	−	0.963003i	$-0.586855\pi$
$929$	−7.82580	+	1.12518i	−0.256756	+	0.0369160i	0.0127347	+	0.999919i	$0.495946\pi$
$930$	−69.8017	+	24.3806i	−2.28889	+	0.799472i
$931$	7.62857	+	25.9805i	0.250016	+	0.851477i
$932$	4.90690	+	16.7114i	0.160731	+	0.547399i
$933$	−1.52162	+	0.531477i	−0.0498156	+	0.0173998i
$934$	−0.311698	+	0.0448154i	−0.0101991	+	0.00146641i
$935$	11.9133	+	13.7486i	0.389605	+	0.449628i
$936$	−4.50349	−	11.0667i	−0.147201	−	0.361727i
$937$	−22.5621	−	35.1073i	−0.737071	−	1.14691i	−0.984051	−	0.177885i	$-0.943075\pi$
$937$	−22.5621	−	35.1073i	−0.737071	−	1.14691i	0.246980	−	0.969021i	$-0.420562\pi$
$938$	−4.52586	−	0.650720i	−0.147774	−	0.0212468i
$939$	6.19012	+	31.6341i	0.202007	+	1.03234i
$940$	−26.1847	−	22.6892i	−0.854051	−	0.740039i
$941$	19.1703	+	5.62891i	0.624934	+	0.183497i	0.578842	−	0.815440i	$-0.303505\pi$
$941$	19.1703	+	5.62891i	0.624934	+	0.183497i	0.0460923	+	0.998937i	$0.485323\pi$
$942$	−7.24429	+	6.94677i	−0.236032	+	0.226338i
$943$	−9.45991	−	32.7994i	−0.308057	−	1.06810i
$944$			0.0297566i			0.000968494i
$945$	14.1372	−	6.60228i	0.459885	−	0.214772i
$946$	0.280102	−	0.323255i	0.00910690	−	0.0105099i
$947$	−6.85830	+	10.6717i	−0.222865	+	0.346785i	−0.934623	−	0.355640i	$-0.884263\pi$
$947$	−6.85830	+	10.6717i	−0.222865	+	0.346785i	0.711758	+	0.702425i	$0.247899\pi$
$948$	6.30360	−	4.51579i	0.204731	−	0.146666i
$949$	14.8282	−	9.52950i	0.481344	−	0.309341i
$950$	21.3559	+	46.7628i	0.692876	+	1.51719i
$951$	2.70281	−	29.1799i	0.0876445	−	0.946223i
$952$	0.204325	+	1.42112i	0.00662223	+	0.0460586i
$953$	−15.4711	+	33.8771i	−0.501159	+	1.09739i	0.474931	+	0.880023i	$0.342473\pi$
$953$	−15.4711	+	33.8771i	−0.501159	+	1.09739i	−0.976091	+	0.217363i	$0.930254\pi$
$954$	10.7031	−	2.66096i	0.346526	−	0.0861516i
$955$	−79.4141	+	23.3181i	−2.56978	+	0.754555i
$956$	−13.7543	−	6.28137i	−0.444845	−	0.203154i
$957$	9.46014	−	12.1000i	0.305803	−	0.391139i
$958$	−21.4660	+	18.6004i	−0.693534	+	0.600951i
$959$	−7.04012	+	3.21512i	−0.227337	+	0.103822i
$960$	−1.67860	+	7.00600i	−0.0541766	+	0.226118i
$961$	−10.5779	+	73.5713i	−0.341224	+	2.37327i
$962$	5.29981	+	3.40598i	0.170873	+	0.109813i
$963$	−1.46551	−	1.38156i	−0.0472253	−	0.0445203i
$964$	−0.800955	+	2.72780i	−0.0257970	+	0.0878566i
$965$	64.7314			2.08378
$966$	3.46888	+	4.89167i	0.111609	+	0.157387i
$967$	−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
$969$	14.3779	−	0.725802i	0.461885	−	0.0233161i
$970$	−45.2221	−	29.0625i	−1.45199	−	0.933140i
$971$	−6.95460	+	48.3703i	−0.223184	+	1.55228i	0.502700	+	0.864461i	$0.332340\pi$
$971$	−6.95460	+	48.3703i	−0.223184	+	1.55228i	−0.725884	+	0.687817i	$0.758569\pi$
$972$	4.88897	−	14.8020i	0.156814	−	0.474773i
$973$	−0.345596	+	0.157828i	−0.0110793	+	0.00505974i
$974$	11.6240	−	10.0722i	0.372456	−	0.322735i
$975$	−66.8462	−	52.2621i	−2.14079	−	1.67373i
$976$	10.3022	+	4.70484i	0.329764	+	0.150598i
$977$	14.8350	−	4.35595i	0.474614	−	0.139359i	−0.0356727	−	0.999364i	$-0.511357\pi$
$977$	14.8350	−	4.35595i	0.474614	−	0.139359i	0.510287	+	0.860004i	$0.329539\pi$
$978$	6.54028	+	3.75133i	0.209135	+	0.119954i
$979$	−1.14078	+	2.49795i	−0.0364593	+	0.0798348i
$980$	3.83509	+	26.6737i	0.122508	+	0.852059i
$981$	−17.9872	−	22.6074i	−0.574288	−	0.721799i
$982$	−15.1924	−	33.2666i	−0.484808	−	1.06158i
$983$	31.5534	−	20.2782i	1.00640	−	0.646773i	0.0699398	−	0.997551i	$-0.477719\pi$
$983$	31.5534	−	20.2782i	1.00640	−	0.646773i	0.936459	+	0.350778i	$0.114083\pi$
$984$	7.17976	+	10.0223i	0.228882	+	0.319498i
$985$	−9.65686	+	15.0264i	−0.307693	+	0.478780i
$986$	−5.25123	+	6.06024i	−0.167233	+	0.192997i
$987$	9.24440	−	4.79907i	0.294253	−	0.152756i
$988$			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	0.963077	−	0.269227i	$-0.0867683\pi$
$991$	51.2407	+	15.0456i	1.62771	+	0.477940i	0.664636	+	0.747167i	$0.268586\pi$
$992$	7.75621	+	6.72079i	0.246260	+	0.213385i
$993$	−1.40324	+	0.274584i	−0.0445303	+	0.00871364i
$994$	4.64616	+	0.668017i	0.147367	+	0.0211882i
$995$	47.6069	+	74.0778i	1.50924	+	2.34842i
$996$	−3.50482	−	1.39159i	−0.111054	−	0.0440943i
$997$	29.6921	+	34.2665i	0.940358	+	1.08523i	0.996226	+	0.0867930i	$0.0276619\pi$
$997$	29.6921	+	34.2665i	0.940358	+	1.08523i	−0.0558682	+	0.998438i	$0.517793\pi$
$998$	15.5056	−	2.22936i	0.490820	−	0.0705692i
$999$	2.38274	+	7.86650i	0.0753865	+	0.248885i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.f.a.5.1	✓	80	3.2	odd	2	inner
138.2.f.a.5.6	yes	80	1.1	even	1	trivial
138.2.f.a.83.1	yes	80	23.14	odd	22	inner
138.2.f.a.83.6	yes	80	69.14	even	22	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)

\(f(q)\)	\(=\)	\(q+(0.281733 - 0.959493i) q^{2} +(0.0873233 + 1.72985i) q^{3} +(-0.841254 - 0.540641i) q^{4} +(-0.591943 + 4.11706i) q^{5} +(1.68438 + 0.403568i) q^{6} +(0.656690 - 0.299900i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(-2.98475 + 0.302112i) q^{9} +O(q^{10})\)	\(q+(0.281733 - 0.959493i) q^{2} +(0.0873233 + 1.72985i) q^{3} +(-0.841254 - 0.540641i) q^{4} +(-0.591943 + 4.11706i) q^{5} +(1.68438 + 0.403568i) q^{6} +(0.656690 - 0.299900i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(-2.98475 + 0.302112i) q^{9} +(3.78352 + 1.72787i) q^{10} +(2.11016 - 0.619599i) q^{11} +(0.861765 - 1.50245i) q^{12} +(1.65446 - 3.62275i) q^{13} +(-0.102741 - 0.714581i) q^{14} +(-7.17357 - 0.664457i) q^{15} +(0.415415 + 0.909632i) q^{16} +(1.67303 - 1.07519i) q^{17} +(-0.551026 + 2.94896i) q^{18} +(2.25954 - 3.51591i) q^{19} +(2.72382 - 3.14346i) q^{20} +(0.576126 + 1.10979i) 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} +(-0.783247 - 5.13678i) q^{27} +(-0.714581 - 0.102741i) q^{28} +(-2.17993 - 3.39204i) q^{29} +(-2.65857 + 6.69579i) q^{30} +(6.72079 + 7.75621i) q^{31} +(0.989821 - 0.142315i) q^{32} +(1.25608 + 3.59615i) q^{33} +(-0.560292 - 1.90818i) q^{34} +(0.845983 + 2.88115i) q^{35} +(2.67427 + 1.35952i) q^{36} +(-1.56573 + 0.225118i) q^{37} +(-2.73690 - 3.15855i) q^{38} +(6.41128 + 2.54561i) q^{39} +(-2.24874 - 3.49910i) q^{40} +(-7.04547 - 1.01299i) q^{41} +(1.22715 - 0.240126i) 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} +(-1.53725 + 0.798037i) q^{48} +(-4.24272 + 4.89636i) q^{49} +(-6.65018 + 10.3479i) q^{50} +(2.00602 + 2.80020i) q^{51} +(-3.35042 + 2.15319i) q^{52} +(-1.52719 - 3.34409i) q^{53} +(-5.14937 - 0.695679i) q^{54} +(1.30183 + 9.05442i) q^{55} +(-0.299900 + 0.656690i) q^{56} +(6.27929 + 3.60163i) q^{57} +(-3.86880 + 1.13598i) q^{58} +(0.0270675 + 0.0123613i) q^{59} +(5.67556 + 4.43730i) q^{60} +(8.55934 - 7.41671i) q^{61} +(9.33549 - 4.26338i) q^{62} +(-1.86945 + 1.09352i) q^{63} +(0.142315 - 0.989821i) q^{64} +(13.9357 + 8.95595i) q^{65} +(3.80436 - 0.192045i) q^{66} +(1.78438 - 6.07703i) q^{67} -1.98874 q^{68} +(-7.39069 + 3.79180i) q^{69} +3.00279 q^{70} +(-1.83181 + 6.23857i) q^{71} +(2.05788 - 2.18292i) q^{72} +(3.72319 + 2.39275i) q^{73} +(-0.225118 + 1.56573i) q^{74} +(4.96412 - 20.7188i) q^{75} +(-3.80168 + 1.73617i) q^{76} +(1.19990 - 1.03972i) q^{77} +(4.24876 - 5.43440i) q^{78} +(4.07232 + 1.85977i) q^{79} +(-3.99091 + 1.17184i) q^{80} +(8.81746 - 1.80346i) q^{81} +(-2.95689 + 6.47469i) q^{82} +(-0.309844 - 2.15501i) q^{83} +(0.115327 - 1.24509i) q^{84} +(3.43629 + 7.52443i) q^{85} +(0.163614 - 0.105148i) q^{86} +(5.67736 - 4.06716i) q^{87} +(-1.18900 + 1.85012i) q^{88} +(-0.817699 + 0.943675i) q^{89} +(-11.8149 - 4.01423i) 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} +(0.332618 + 1.69981i) q^{96} +(-12.7924 - 1.83926i) q^{97} +(3.50271 + 5.45033i) q^{98} +(-6.11111 + 2.48685i) 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

Fields

Representations

Groups

Database

Properties

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