LMFDB - Embedded newform 930.2.br.a.761.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(11,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 0, 23]))

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

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

chi := DirichletCharacter("930.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.br (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			761.7
Character	$\chi$	$=$	930.761
Dual form			930.2.br.a.11.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(0.821805 - 1.52468i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.25273 + 1.19610i) q^{6} +(0.122441 - 1.16495i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-1.64927 - 2.50597i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{2} +(0.821805 - 1.52468i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.25273 + 1.19610i) q^{6} +(0.122441 - 1.16495i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-1.64927 - 2.50597i) q^{9} +(-0.669131 - 0.743145i) q^{10} +(0.519826 - 0.231441i) q^{11} +(1.56104 - 0.750444i) q^{12} +(0.447115 - 2.10351i) q^{13} +(-0.476438 + 1.07010i) q^{14} +(1.47404 - 0.909505i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-5.00147 - 2.22680i) q^{17} +(0.794163 + 2.89298i) q^{18} +(3.58590 - 0.762207i) q^{19} +(0.406737 + 0.913545i) q^{20} +(-1.67555 - 1.14404i) q^{21} +(-0.565903 + 0.0594788i) q^{22} +(-5.52033 + 4.01076i) q^{23} +(-1.71653 + 0.231328i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-1.07525 + 1.86239i) q^{26} +(-5.17618 + 0.455184i) q^{27} +(0.783797 - 0.870495i) q^{28} +(3.19081 - 9.82031i) q^{29} +(-1.68295 + 0.409487i) q^{30} +(4.19859 - 3.65676i) q^{31} -1.00000i q^{32} +(0.0743226 - 0.982766i) q^{33} +(4.06856 + 3.66335i) q^{34} +(0.688512 - 0.947655i) q^{35} +(0.138685 - 2.99679i) q^{36} +(-1.33670 + 0.771745i) q^{37} +(-3.64593 - 0.383203i) q^{38} +(-2.83973 - 2.41038i) q^{39} +(-0.104528 - 0.994522i) q^{40} +(1.22627 - 1.10414i) q^{41} +(1.24001 + 1.60582i) q^{42} +(-1.07851 - 5.07399i) q^{43} +(0.556586 + 0.118306i) q^{44} +(-0.175325 - 2.99487i) q^{45} +(6.48954 - 2.10858i) q^{46} +(0.408277 - 0.132657i) q^{47} +(1.70400 + 0.310432i) q^{48} +(5.50492 + 1.17011i) q^{49} +(-0.207912 - 0.978148i) q^{50} +(-7.50538 + 5.79563i) q^{51} +(1.59814 - 1.43897i) q^{52} +(0.499825 + 4.75551i) q^{53} +(5.06350 + 1.16662i) q^{54} +(0.565903 + 0.0594788i) q^{55} +(-1.01443 + 0.585683i) q^{56} +(1.78480 - 6.09373i) q^{57} +(-6.06929 + 8.35366i) q^{58} +(-2.81688 - 2.53633i) q^{59} +(1.72712 + 0.130615i) q^{60} +5.66315i q^{61} +(-5.12309 + 2.18035i) q^{62} +(-3.12127 + 1.61448i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(1.43897 - 1.59814i) q^{65} +(-0.374376 + 0.911699i) q^{66} +(6.10033 - 10.5661i) q^{67} +(-2.73740 - 4.74131i) q^{68} +(1.57846 + 11.7128i) q^{69} +(-0.947655 + 0.688512i) q^{70} +(-10.1259 + 1.06427i) q^{71} +(-1.05796 + 2.80726i) q^{72} +(1.02323 + 2.29822i) q^{73} +(1.50976 - 0.320909i) q^{74} +(1.73131 - 0.0506337i) q^{75} +(3.34907 + 1.49110i) q^{76} +(-0.205970 - 0.633909i) q^{77} +(1.95589 + 3.16993i) q^{78} +(0.346214 - 0.777609i) q^{79} +(-0.207912 + 0.978148i) q^{80} +(-3.55980 + 8.26606i) q^{81} +(-1.50745 + 0.671159i) q^{82} +(-2.23296 - 2.47995i) q^{83} +(-0.683094 - 1.91041i) q^{84} +(-3.21800 - 4.42920i) q^{85} +(-0.542226 + 5.15893i) q^{86} +(-12.3506 - 12.9353i) q^{87} +(-0.492786 - 0.284510i) q^{88} +(-10.6012 - 7.70220i) q^{89} +(-0.758722 + 2.90247i) q^{90} +(-2.39574 - 0.778422i) q^{91} -6.82351 q^{92} +(-2.12495 - 9.40662i) q^{93} -0.429288 q^{94} +(3.48659 + 1.13286i) q^{95} +(-1.52468 - 0.821805i) q^{96} +(0.672915 + 0.488901i) q^{97} +(-4.87391 - 2.81395i) q^{98} +(-1.43732 - 0.920960i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9	$ 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9} - 22 q^{10} - 38 q^{13} - 44 q^{16} + 12 q^{18} + 8 q^{19} - 18 q^{21} - 4 q^{22} + 88 q^{25} - 90 q^{27} + 36 q^{28} + 24 q^{31} + 18 q^{33} + 14 q^{34} + 4 q^{36} - 42 q^{37} - 42 q^{39} + 22 q^{40} - 12 q^{42} - 34 q^{43} - 8 q^{45} + 10 q^{46} + 22 q^{49} + 26 q^{51} - 2 q^{52} + 4 q^{55} + 114 q^{57} + 32 q^{63} + 44 q^{64} - 42 q^{66} + 20 q^{67} + 16 q^{69} + 8 q^{70} - 12 q^{72} - 28 q^{73} + 12 q^{76} - 92 q^{78} - 56 q^{79} - 124 q^{81} - 32 q^{82} - 12 q^{84} - 36 q^{87} - 6 q^{88} + 24 q^{90} - 140 q^{91} - 104 q^{93} - 36 q^{94} + 88 q^{97} - 60 q^{99}+O(q^{100}) $ 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9 - 22 * q^10 - 38 * q^13 - 44 * q^16 + 12 * q^18 + 8 * q^19 - 18 * q^21 - 4 * q^22 + 88 * q^25 - 90 * q^27 + 36 * q^28 + 24 * q^31 + 18 * q^33 + 14 * q^34 + 4 * q^36 - 42 * q^37 - 42 * q^39 + 22 * q^40 - 12 * q^42 - 34 * q^43 - 8 * q^45 + 10 * q^46 + 22 * q^49 + 26 * q^51 - 2 * q^52 + 4 * q^55 + 114 * q^57 + 32 * q^63 + 44 * q^64 - 42 * q^66 + 20 * q^67 + 16 * q^69 + 8 * q^70 - 12 * q^72 - 28 * q^73 + 12 * q^76 - 92 * q^78 - 56 * q^79 - 124 * q^81 - 32 * q^82 - 12 * q^84 - 36 * q^87 - 6 * q^88 + 24 * q^90 - 140 * q^91 - 104 * q^93 - 36 * q^94 + 88 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{30}\right)$

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 $

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$	0.821805	−	1.52468i	0.474469	−	0.880272i
$3$	0.821805	−	1.52468i	0.474469	−	0.880272i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	−1.25273	+	1.19610i	−0.511426	+	0.488306i
$7$	0.122441	−	1.16495i	0.0462784	−	0.440310i	−0.946709	−	0.322090i	$-0.895615\pi$
$7$	0.122441	−	1.16495i	0.0462784	−	0.440310i	0.992987	−	0.118220i	$-0.0377187\pi$
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	−1.64927	−	2.50597i	−0.549757	−	0.835324i
$10$	−0.669131	−	0.743145i	−0.211598	−	0.235003i
$11$	0.519826	−	0.231441i	0.156733	−	0.0697822i	−0.326871	−	0.945069i	$-0.605994\pi$
$11$	0.519826	−	0.231441i	0.156733	−	0.0697822i	0.483604	+	0.875287i	$0.339327\pi$
$12$	1.56104	−	0.750444i	0.450632	−	0.216634i
$13$	0.447115	−	2.10351i	0.124007	−	0.583409i	−0.871635	−	0.490155i	$-0.836940\pi$
$13$	0.447115	−	2.10351i	0.124007	−	0.583409i	0.995642	−	0.0932532i	$-0.0297266\pi$
$14$	−0.476438	+	1.07010i	−0.127333	+	0.285995i
$15$	1.47404	−	0.909505i	0.380596	−	0.234833i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−5.00147	−	2.22680i	−1.21304	−	0.540078i	−0.302357	−	0.953195i	$-0.597774\pi$
$17$	−5.00147	−	2.22680i	−1.21304	−	0.540078i	−0.910678	+	0.413117i	$0.864440\pi$
$18$	0.794163	+	2.89298i	0.187186	+	0.681881i
$19$	3.58590	−	0.762207i	0.822663	−	0.174862i	0.222697	−	0.974888i	$-0.428514\pi$
$19$	3.58590	−	0.762207i	0.822663	−	0.174862i	0.599966	+	0.800025i	$0.295181\pi$
$20$	0.406737	+	0.913545i	0.0909491	+	0.204275i
$21$	−1.67555	−	1.14404i	−0.365634	−	0.249651i
$22$	−0.565903	+	0.0594788i	−0.120651	+	0.0126809i
$23$	−5.52033	+	4.01076i	−1.15107	+	0.836300i	−0.988623	−	0.150417i	$-0.951938\pi$
$23$	−5.52033	+	4.01076i	−1.15107	+	0.836300i	−0.162446	+	0.986717i	$0.551938\pi$
$24$	−1.71653	+	0.231328i	−0.350386	+	0.0472195i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−1.07525	+	1.86239i	−0.210874	+	0.365245i
$27$	−5.17618	+	0.455184i	−0.996156	+	0.0876002i
$28$	0.783797	−	0.870495i	0.148124	−	0.164508i
$29$	3.19081	−	9.82031i	0.592519	−	1.82359i	0.0258119	−	0.999667i	$-0.491783\pi$
$29$	3.19081	−	9.82031i	0.592519	−	1.82359i	0.566707	−	0.823919i	$-0.308217\pi$
$30$	−1.68295	+	0.409487i	−0.307263	+	0.0747617i
$31$	4.19859	−	3.65676i	0.754088	−	0.656773i
$31$	4.19859	−	3.65676i	0.754088	−	0.656773i
$32$		−	1.00000i		−	0.176777i
$33$	0.0743226	−	0.982766i	0.0129379	−	0.171078i
$34$	4.06856	+	3.66335i	0.697753	+	0.628260i
$35$	0.688512	−	0.947655i	0.116380	−	0.160183i
$36$	0.138685	−	2.99679i	0.0231141	−	0.499465i
$37$	−1.33670	+	0.771745i	−0.219752	+	0.126874i	−0.605836	−	0.795590i	$-0.707161\pi$
$37$	−1.33670	+	0.771745i	−0.219752	+	0.126874i	0.386083	+	0.922464i	$0.373828\pi$
$38$	−3.64593	−	0.383203i	−0.591448	−	0.0621637i
$39$	−2.83973	−	2.41038i	−0.454720	−	0.385970i
$40$	−0.104528	−	0.994522i	−0.0165274	−	0.157248i
$41$	1.22627	−	1.10414i	0.191511	−	0.172437i	−0.567797	−	0.823169i	$-0.692204\pi$
$41$	1.22627	−	1.10414i	0.191511	−	0.172437i	0.759308	+	0.650731i	$0.225538\pi$
$42$	1.24001	+	1.60582i	0.191338	+	0.247784i
$43$	−1.07851	−	5.07399i	−0.164471	−	0.773777i	−0.980618	−	0.195931i	$-0.937227\pi$
$43$	−1.07851	−	5.07399i	−0.164471	−	0.773777i	0.816146	−	0.577845i	$-0.196106\pi$
$44$	0.556586	+	0.118306i	0.0839085	+	0.0178353i
$45$	−0.175325	−	2.99487i	−0.0261360	−	0.446449i
$46$	6.48954	−	2.10858i	0.956830	−	0.310893i
$47$	0.408277	−	0.132657i	0.0595533	−	0.0193500i	−0.279089	−	0.960265i	$-0.590032\pi$
$47$	0.408277	−	0.132657i	0.0595533	−	0.0193500i	0.338642	+	0.940915i	$0.390032\pi$
$48$	1.70400	+	0.310432i	0.245952	+	0.0448071i
$49$	5.50492	+	1.17011i	0.786417	+	0.167158i
$50$	−0.207912	−	0.978148i	−0.0294032	−	0.138331i
$51$	−7.50538	+	5.79563i	−1.05096	+	0.811550i
$52$	1.59814	−	1.43897i	0.221621	−	0.199549i
$53$	0.499825	+	4.75551i	0.0686562	+	0.653220i	0.973689	+	0.227879i	$0.0731791\pi$
$53$	0.499825	+	4.75551i	0.0686562	+	0.653220i	−0.905033	+	0.425341i	$0.860154\pi$
$54$	5.06350	+	1.16662i	0.689055	+	0.158757i
$55$	0.565903	+	0.0594788i	0.0763064	+	0.00802012i
$56$	−1.01443	+	0.585683i	−0.135559	+	0.0782652i
$57$	1.78480	−	6.09373i	0.236402	−	0.807134i
$58$	−6.06929	+	8.35366i	−0.796936	+	1.09689i
$59$	−2.81688	−	2.53633i	−0.366727	−	0.330202i	0.465079	−	0.885269i	$-0.346026\pi$
$59$	−2.81688	−	2.53633i	−0.366727	−	0.330202i	−0.831806	+	0.555067i	$0.812693\pi$
$60$	1.72712	+	0.130615i	0.222970	+	0.0168623i
$61$			5.66315i			0.725092i	0.931966	+	0.362546i	$0.118092\pi$
$61$			5.66315i			0.725092i	−0.931966	+	0.362546i	$0.881908\pi$
$62$	−5.12309	+	2.18035i	−0.650633	+	0.276904i
$63$	−3.12127	+	1.61448i	−0.393243	+	0.203406i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	1.43897	−	1.59814i	0.178482	−	0.198224i
$66$	−0.374376	+	0.911699i	−0.0460825	+	0.112222i
$67$	6.10033	−	10.5661i	0.745274	−	1.29085i	−0.204792	−	0.978805i	$-0.565652\pi$
$67$	6.10033	−	10.5661i	0.745274	−	1.29085i	0.950067	−	0.312047i	$-0.101015\pi$
$68$	−2.73740	−	4.74131i	−0.331958	−	0.574968i
$69$	1.57846	+	11.7128i	0.190025	+	1.41005i
$70$	−0.947655	+	0.688512i	−0.113266	+	0.0822929i
$71$	−10.1259	+	1.06427i	−1.20172	+	0.126306i	−0.684155	−	0.729336i	$-0.739829\pi$
$71$	−10.1259	+	1.06427i	−1.20172	+	0.126306i	−0.517567	+	0.855643i	$0.673162\pi$
$72$	−1.05796	+	2.80726i	−0.124681	+	0.330839i
$73$	1.02323	+	2.29822i	0.119760	+	0.268986i	0.963471	−	0.267812i	$-0.0863005\pi$
$73$	1.02323	+	2.29822i	0.119760	+	0.268986i	−0.843711	+	0.536798i	$0.819634\pi$
$74$	1.50976	−	0.320909i	0.175506	−	0.0373050i
$75$	1.73131	−	0.0506337i	0.199915	−	0.00584668i
$76$	3.34907	+	1.49110i	0.384165	+	0.171041i
$77$	−0.205970	−	0.633909i	−0.0234724	−	0.0722406i
$78$	1.95589	+	3.16993i	0.221461	+	0.358924i
$79$	0.346214	−	0.777609i	0.0389521	−	0.0874878i	−0.893022	−	0.450014i	$-0.851419\pi$
$79$	0.346214	−	0.777609i	0.0389521	−	0.0874878i	0.931974	+	0.362526i	$0.118086\pi$
$80$	−0.207912	+	0.978148i	−0.0232452	+	0.109360i
$81$	−3.55980	+	8.26606i	−0.395533	+	0.918452i
$82$	−1.50745	+	0.671159i	−0.166470	+	0.0741171i
$83$	−2.23296	−	2.47995i	−0.245099	−	0.272210i	0.608025	−	0.793918i	$-0.291962\pi$
$83$	−2.23296	−	2.47995i	−0.245099	−	0.272210i	−0.853125	+	0.521707i	$0.825295\pi$
$84$	−0.683094	−	1.91041i	−0.0745317	−	0.208443i
$85$	−3.21800	−	4.42920i	−0.349041	−	0.480414i
$86$	−0.542226	+	5.15893i	−0.0584697	+	0.556302i
$87$	−12.3506	−	12.9353i	−1.32412	−	1.38681i
$88$	−0.492786	−	0.284510i	−0.0525312	−	0.0303289i
$89$	−10.6012	−	7.70220i	−1.12372	−	0.816431i	−0.138952	−	0.990299i	$-0.544374\pi$
$89$	−10.6012	−	7.70220i	−1.12372	−	0.816431i	−0.984769	+	0.173868i	$0.944374\pi$
$90$	−0.758722	+	2.90247i	−0.0799763	+	0.305947i
$91$	−2.39574	−	0.778422i	−0.251141	−	0.0816008i
$92$	−6.82351			−0.711400
$93$	−2.12495	−	9.40662i	−0.220347	−	0.975422i
$94$	−0.429288			−0.0442776
$95$	3.48659	+	1.13286i	0.357716	+	0.116229i
$96$	−1.52468	−	0.821805i	−0.155612	−	0.0838751i
$97$	0.672915	+	0.488901i	0.0683242	+	0.0496404i	0.621423	−	0.783475i	$-0.286555\pi$
$97$	0.672915	+	0.488901i	0.0683242	+	0.0496404i	−0.553099	+	0.833116i	$0.686555\pi$
$98$	−4.87391	−	2.81395i	−0.492339	−	0.284252i
$99$	−1.43732	−	0.920960i	−0.144456	−	0.0925600i
$100$	−0.104528	+	0.994522i	−0.0104528	+	0.0994522i
$101$	9.35065	+	12.8701i	0.930424	+	1.28062i	0.959694	+	0.281047i	$0.0906818\pi$
$101$	9.35065	+	12.8701i	0.930424	+	1.28062i	−0.0292699	+	0.999572i	$0.509318\pi$
$102$	8.92899	−	3.19268i	0.884102	−	0.316122i
$103$	−2.88696	−	3.20629i	−0.284460	−	0.315925i	0.583932	−	0.811802i	$-0.301513\pi$
$103$	−2.88696	−	3.20629i	−0.284460	−	0.315925i	−0.868393	+	0.495877i	$0.834847\pi$
$104$	−1.96458	+	0.874688i	−0.192643	+	0.0857703i
$105$	−0.879044	−	1.82855i	−0.0857860	−	0.178448i
$106$	0.994173	−	4.67722i	0.0965626	−	0.454291i
$107$	1.88572	−	4.23539i	0.182299	−	0.409450i	−0.799161	−	0.601117i	$-0.794723\pi$
$107$	1.88572	−	4.23539i	0.182299	−	0.409450i	0.981460	+	0.191667i	$0.0613893\pi$
$108$	−4.45517	−	2.67423i	−0.428699	−	0.257328i
$109$	0.311319	+	0.958142i	0.0298190	+	0.0917734i	0.964858	−	0.262770i	$-0.0846362\pi$
$109$	0.311319	+	0.958142i	0.0298190	+	0.0917734i	−0.935039	+	0.354544i	$0.884636\pi$
$110$	−0.519826	−	0.231441i	−0.0495635	−	0.0220671i
$111$	0.0781526	+	2.67226i	0.00741791	+	0.253640i
$112$	1.14577	−	0.243541i	0.108265	−	0.0230124i
$113$	6.93779	+	15.5825i	0.652653	+	1.46588i	0.871636	+	0.490154i	$0.163059\pi$
$113$	6.93779	+	15.5825i	0.652653	+	1.46588i	−0.218983	+	0.975729i	$0.570274\pi$
$114$	−3.58051	+	5.24395i	−0.335345	+	0.491141i
$115$	−6.78613	+	0.713251i	−0.632809	+	0.0665110i
$116$	8.35366	−	6.06929i	0.775618	−	0.563519i
$117$	−6.00875	+	2.34880i	−0.555509	+	0.217147i
$118$	1.89524	+	3.28266i	0.174471	+	0.302193i
$119$	−3.20649	+	5.55381i	−0.293939	+	0.509117i
$120$	−1.60223	−	0.657931i	−0.146263	−	0.0600606i
$121$	−7.14378	+	7.93397i	−0.649435	+	0.721270i
$122$	1.75001	−	5.38598i	0.158438	−	0.487623i
$123$	−0.675698	−	2.77705i	−0.0609256	−	0.250398i
$124$	5.54612	−	0.490512i	0.498056	−	0.0440492i
$125$			1.00000i			0.0894427i
$126$	3.46741	−	0.570941i	0.308901	−	0.0508634i
$127$	−11.2462	−	10.1261i	−0.997937	−	0.898547i	−0.00309626	−	0.999995i	$-0.500986\pi$
$127$	−11.2462	−	10.1261i	−0.997937	−	0.898547i	−0.994841	+	0.101449i	$0.967652\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	−8.62252	−	2.52546i	−0.759171	−	0.222354i
$130$	−1.86239	+	1.07525i	−0.163342	+	0.0943058i
$131$	12.4646	+	1.31008i	1.08904	+	0.114463i	0.631988	−	0.774978i	$-0.282239\pi$
$131$	12.4646	+	1.31008i	1.08904	+	0.114463i	0.457051	+	0.889441i	$0.348906\pi$
$132$	0.637784	−	0.751389i	0.0555119	−	0.0654000i
$133$	−0.448871	−	4.27072i	−0.0389221	−	0.370319i
$134$	−9.06686	+	8.16384i	−0.783257	+	0.705248i
$135$	−4.71029	−	2.19389i	−0.405397	−	0.188820i
$136$	1.13827	+	5.35516i	0.0976062	+	0.459201i
$137$	−4.64789	−	0.987941i	−0.397096	−	0.0844055i	0.00503517	−	0.999987i	$-0.498397\pi$
$137$	−4.64789	−	0.987941i	−0.397096	−	0.0844055i	−0.402132	+	0.915582i	$0.631731\pi$
$138$	2.11824	−	11.6273i	0.180316	−	0.989780i
$139$	4.27398	−	1.38870i	0.362514	−	0.117788i	−0.122096	−	0.992518i	$-0.538961\pi$
$139$	4.27398	−	1.38870i	0.362514	−	0.117788i	0.484610	+	0.874730i	$0.338961\pi$
$140$	1.11404	−	0.361972i	0.0941532	−	0.0305922i
$141$	0.133265	−	0.731508i	0.0112229	−	0.0616041i
$142$	9.95918	+	2.11689i	0.835756	+	0.177645i
$143$	−0.254417	−	1.19694i	−0.0212755	−	0.100093i
$144$	1.87367	−	2.34294i	0.156139	−	0.195245i
$145$	7.67348	−	6.90923i	0.637248	−	0.573781i
$146$	−0.262964	−	2.50193i	−0.0217630	−	0.207061i
$147$	6.30800	−	7.43162i	0.520275	−	0.612949i
$148$	−1.53503	−	0.161339i	−0.126179	−	0.0132619i
$149$	15.4834	−	8.93935i	1.26845	−	0.732340i	0.293756	−	0.955880i	$-0.405095\pi$
$149$	15.4834	−	8.93935i	1.26845	−	0.732340i	0.974695	+	0.223540i	$0.0717613\pi$
$150$	−1.66222	−	0.486849i	−0.135720	−	0.0397510i
$151$	0.434637	−	0.598227i	0.0353703	−	0.0486830i	−0.790966	−	0.611861i	$-0.790421\pi$
$151$	0.434637	−	0.598227i	0.0353703	−	0.0486830i	0.826336	+	0.563178i	$0.190421\pi$
$152$	−2.72438	−	2.45304i	−0.220976	−	0.198968i
$153$	2.66849	+	16.2062i	0.215735	+	1.31019i
$154$			0.666531i			0.0537106i
$155$	5.46446	−	1.06755i	0.438916	−	0.0857478i
$156$	−0.880603	−	3.61919i	−0.0705047	−	0.289767i
$157$	4.49248	−	13.8264i	0.358539	−	1.10347i	−0.595390	−	0.803437i	$-0.703002\pi$
$157$	4.49248	−	13.8264i	0.358539	−	1.10347i	0.953929	−	0.300033i	$-0.0969976\pi$
$158$	−0.569563	+	0.632564i	−0.0453120	+	0.0503241i
$159$	7.66137	+	3.14603i	0.607586	+	0.249497i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	3.99641	+	6.92199i	0.314961	+	0.545529i
$162$	5.93993	−	6.76146i	0.466685	−	0.531230i
$163$	−1.48950	+	1.08219i	−0.116667	+	0.0847633i	−0.644589	−	0.764530i	$-0.722971\pi$
$163$	−1.48950	+	1.08219i	−0.116667	+	0.0847633i	0.527922	+	0.849293i	$0.322971\pi$
$164$	1.64107	−	0.172483i	0.128146	−	0.0134687i
$165$	0.555748	−	0.813939i	0.0432649	−	0.0633651i
$166$	1.35732	+	3.04860i	0.105349	+	0.236617i
$167$	8.07631	−	1.71667i	0.624964	−	0.132840i	0.115465	−	0.993312i	$-0.463164\pi$
$167$	8.07631	−	1.71667i	0.624964	−	0.132840i	0.509499	+	0.860471i	$0.329831\pi$
$168$	0.0593106	+	2.02800i	0.00457591	+	0.156464i
$169$	7.65125	+	3.40656i	0.588558	+	0.262043i
$170$	1.69180	+	5.20684i	0.129755	+	0.399346i
$171$	−7.82420	−	7.72909i	−0.598332	−	0.591058i
$172$	2.10989	−	4.73888i	0.160877	−	0.361336i
$173$	−2.62903	+	12.3686i	−0.199881	+	0.940368i	0.757789	+	0.652500i	$0.226280\pi$
$173$	−2.62903	+	12.3686i	−0.199881	+	0.940368i	−0.957670	+	0.287868i	$0.907054\pi$
$174$	7.74885	+	16.1188i	0.587439	+	1.22196i
$175$	1.07010	−	0.476438i	0.0808917	−	0.0360153i
$176$	0.380749	+	0.422865i	0.0287000	+	0.0318746i
$177$	−6.18201	+	2.21046i	−0.464669	+	0.166148i
$178$	7.70220	+	10.6012i	0.577304	+	0.794591i
$179$	0.510614	−	4.85816i	0.0381651	−	0.363116i	−0.958726	−	0.284330i	$-0.908229\pi$
$179$	0.510614	−	4.85816i	0.0381651	−	0.363116i	0.996892	−	0.0787862i	$-0.0251045\pi$
$180$	1.61850	−	2.52596i	0.120636	−	0.188274i
$181$	10.9043	+	6.29562i	0.810513	+	0.467950i	0.847134	−	0.531380i	$-0.178326\pi$
$181$	10.9043	+	6.29562i	0.810513	+	0.467950i	−0.0366213	+	0.999329i	$0.511660\pi$
$182$	2.03794	+	1.48065i	0.151062	+	0.109753i
$183$	8.63447	+	4.65401i	0.638278	+	0.344034i
$184$	6.48954	+	2.10858i	0.478415	+	0.155447i
$185$	−1.54349			−0.113480
$186$	−0.885860	+	9.60288i	−0.0649544	+	0.704117i
$187$	−3.11527			−0.227811
$188$	0.408277	+	0.132657i	0.0297766	+	0.00967502i
$189$	−0.103510	+	6.08572i	−0.00752927	+	0.442671i
$190$	−2.96587	−	2.15483i	−0.215167	−	0.156328i
$191$	15.8368	+	9.14337i	1.14591	+	0.661591i	0.947887	−	0.318606i	$-0.103215\pi$
$191$	15.8368	+	9.14337i	1.14591	+	0.661591i	0.198022	+	0.980198i	$0.436548\pi$
$192$	1.19610	+	1.25273i	0.0863212	+	0.0904083i
$193$	−1.65439	+	15.7405i	−0.119086	+	1.13303i	0.757854	+	0.652425i	$0.226248\pi$
$193$	−1.65439	+	15.7405i	−0.119086	+	1.13303i	−0.876939	+	0.480601i	$0.840419\pi$
$194$	−0.488901	−	0.672915i	−0.0351011	−	0.0483125i
$195$	−1.25409	−	3.50731i	−0.0898070	−	0.251164i
$196$	3.76580	+	4.18235i	0.268986	+	0.298739i
$197$	16.5671	−	7.37615i	1.18036	−	0.525529i	0.279712	−	0.960084i	$-0.409761\pi$
$197$	16.5671	−	7.37615i	1.18036	−	0.525529i	0.900645	+	0.434555i	$0.143094\pi$
$198$	1.08238	+	1.32004i	0.0769215	+	0.0938113i
$199$	−4.21524	+	19.8311i	−0.298810	+	1.40579i	0.530823	+	0.847483i	$0.321883\pi$
$199$	−4.21524	+	19.8311i	−0.298810	+	1.40579i	−0.829633	+	0.558309i	$0.811451\pi$
$200$	0.406737	−	0.913545i	0.0287606	−	0.0645974i
$201$	−11.0966	−	17.9843i	−0.782692	−	1.26851i
$202$	−4.91593	−	15.1297i	−0.345883	−	1.06452i
$203$	−11.0495	−	4.91955i	−0.775521	−	0.345284i
$204$	−9.47857	+	0.277209i	−0.663632	+	0.0194085i
$205$	1.61405	−	0.343077i	0.112730	−	0.0239615i
$206$	1.75486	+	3.94148i	0.122267	+	0.274616i
$207$	19.1554	+	7.21897i	1.33139	+	0.501753i
$208$	2.13872	−	0.224789i	0.148294	−	0.0155863i
$209$	1.68764	−	1.22614i	0.116736	−	0.0848140i
$210$	0.270969	+	2.01069i	0.0186987	+	0.138751i
$211$	−8.73743	−	15.1337i	−0.601510	−	1.04185i	−0.992593	−	0.121490i	$-0.961233\pi$
$211$	−8.73743	−	15.1337i	−0.601510	−	1.04185i	0.391083	−	0.920355i	$-0.372101\pi$
$212$	−2.39085	+	4.14108i	−0.164205	+	0.284411i
$213$	−6.69884	+	16.3133i	−0.458997	+	1.11777i
$214$	−3.10223	+	3.44537i	−0.212064	+	0.235521i
$215$	1.60298	−	4.93346i	0.109322	−	0.336459i
$216$	3.41073	+	3.92006i	0.232071	+	0.266727i
$217$	−3.74586	−	5.33888i	−0.254285	−	0.362427i
$218$		−	1.00745i		−	0.0682331i
$219$	4.34494	+	0.328590i	0.293604	+	0.0222040i
$220$	0.422865	+	0.380749i	0.0285095	+	0.0256701i
$221$	−6.92032	+	9.52501i	−0.465511	+	0.640722i
$222$	0.751446	−	2.56562i	0.0504337	−	0.172193i
$223$	11.8538	−	6.84380i	0.793790	−	0.458295i	−0.0475051	−	0.998871i	$-0.515127\pi$
$223$	11.8538	−	6.84380i	0.793790	−	0.458295i	0.841295	+	0.540576i	$0.181794\pi$
$224$	−1.16495	−	0.122441i	−0.0778365	−	0.00818094i
$225$	1.34560	−	2.68130i	0.0897067	−	0.178753i
$226$	−1.78296	−	16.9638i	−0.118601	−	1.12841i
$227$	−12.8460	+	11.5666i	−0.852620	+	0.767703i	−0.974392	−	0.224856i	$-0.927809\pi$
$227$	−12.8460	+	11.5666i	−0.852620	+	0.767703i	0.121772	+	0.992558i	$0.461142\pi$
$228$	5.02573	−	3.88085i	0.332837	−	0.257016i
$229$	3.74095	+	17.5998i	0.247209	+	1.16303i	0.910126	+	0.414332i	$0.135985\pi$
$229$	3.74095	+	17.5998i	0.247209	+	1.16303i	−0.662917	+	0.748693i	$0.730682\pi$
$230$	6.67440	+	1.41869i	0.440097	+	0.0935454i
$231$	−1.13577	−	0.206913i	−0.0747284	−	0.0136139i
$232$	−9.82031	+	3.19081i	−0.644735	+	0.209487i
$233$	24.9434	−	8.10459i	1.63409	−	0.530949i	0.658887	−	0.752242i	$-0.271028\pi$
$233$	24.9434	−	8.10459i	1.63409	−	0.530949i	0.975207	+	0.221293i	$0.0710277\pi$
$234$	6.44048	−	0.377038i	0.421027	−	0.0246477i
$235$	0.419907	+	0.0892539i	0.0273917	+	0.00582228i
$236$	−0.788087	−	3.70766i	−0.0513001	−	0.241348i
$237$	−0.901081	−	1.16691i	−0.0585315	−	0.0757987i
$238$	4.76578	−	4.29113i	0.308920	−	0.278152i
$239$	1.54501	+	14.6997i	0.0999381	+	0.950848i	0.923494	+	0.383613i	$0.125320\pi$
$239$	1.54501	+	14.6997i	0.0999381	+	0.950848i	−0.823556	+	0.567235i	$0.808013\pi$
$240$	1.32050	+	1.12084i	0.0852376	+	0.0723502i
$241$	−3.01041	−	0.316407i	−0.193918	−	0.0203816i	0.00707169	−	0.999975i	$-0.497749\pi$
$241$	−3.01041	−	0.316407i	−0.193918	−	0.0203816i	−0.200989	+	0.979593i	$0.564416\pi$
$242$	9.24587	−	5.33811i	0.594347	−	0.343147i
$243$	9.67761	+	12.2206i	0.620819	+	0.783954i
$244$	−3.32872	+	4.58159i	−0.213099	+	0.293306i
$245$	4.18235	+	3.76580i	0.267200	+	0.240588i
$246$	−0.215529	+	2.84993i	−0.0137416	+	0.181705i
$247$		−	7.88378i		−	0.501633i
$248$	−5.42625	−	1.24734i	−0.344567	−	0.0792062i
$249$	−5.61619	+	1.36650i	−0.355911	+	0.0865986i
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	8.51058	−	9.45196i	0.537183	−	0.596602i	−0.412056	−	0.911159i	$-0.635189\pi$
$251$	8.51058	−	9.45196i	0.537183	−	0.596602i	0.949239	+	0.314556i	$0.101856\pi$
$252$	−3.47413	−	0.528491i	−0.218850	−	0.0332918i
$253$	−1.94136	+	3.36253i	−0.122052	+	0.211400i
$254$	7.56661	+	13.1058i	0.474772	+	0.822328i
$255$	−9.39767	+	1.26647i	−0.588505	+	0.0793095i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−9.15701	+	0.962441i	−0.571199	+	0.0600354i	−0.385725	−	0.922614i	$-0.626049\pi$
$257$	−9.15701	+	0.962441i	−0.571199	+	0.0600354i	−0.185474	+	0.982649i	$0.559382\pi$
$258$	7.42010	+	5.06636i	0.461955	+	0.315418i
$259$	0.735376	+	1.65168i	0.0456941	+	0.102631i
$260$	2.10351	−	0.447115i	0.130454	−	0.0277289i
$261$	−29.8720	+	8.20028i	−1.84903	+	0.507585i
$262$	−11.4497	−	5.09775i	−0.707366	−	0.314940i
$263$	8.49185	+	26.1352i	0.523630	+	1.61157i	0.767009	+	0.641637i	$0.221744\pi$
$263$	8.49185	+	26.1352i	0.523630	+	1.61157i	−0.243379	+	0.969931i	$0.578256\pi$
$264$	−0.838760	+	0.517527i	−0.0516221	+	0.0318516i
$265$	−1.94490	+	4.36831i	−0.119474	+	0.268343i
$266$	−0.892824	+	4.20041i	−0.0547426	+	0.257544i
$267$	−20.4555	+	9.83364i	−1.25185	+	0.601809i
$268$	11.1459	−	4.96246i	0.680842	−	0.303130i
$269$	−3.12757	−	3.47352i	−0.190692	−	0.211784i	0.640216	−	0.768195i	$-0.278845\pi$
$269$	−3.12757	−	3.47352i	−0.190692	−	0.211784i	−0.830908	+	0.556411i	$0.812178\pi$
$270$	3.80181	+	3.54207i	0.231371	+	0.215564i
$271$	12.0604	+	16.5997i	0.732618	+	1.00836i	0.999010	+	0.0444972i	$0.0141686\pi$
$271$	12.0604	+	16.5997i	0.732618	+	1.00836i	−0.266392	+	0.963865i	$0.585831\pi$
$272$	0.572272	−	5.44480i	0.0346991	−	0.330140i
$273$	−3.15567	+	3.01301i	−0.190990	+	0.182356i
$274$	4.11512	+	2.37587i	0.248604	+	0.143531i
$275$	0.460347	+	0.334462i	0.0277600	+	0.0201688i
$276$	−5.60759	+	10.4036i	−0.337537	+	0.626225i
$277$	28.9704	+	9.41307i	1.74067	+	0.565576i	0.994921	−	0.100656i	$-0.0320942\pi$
$277$	28.9704	+	9.41307i	1.74067	+	0.565576i	0.745744	+	0.666233i	$0.232094\pi$
$278$	−4.49393			−0.269528
$279$	−16.0883	−	4.49056i	−0.963184	−	0.268843i
$280$	−1.17137			−0.0700025
$281$	6.09864	+	1.98157i	0.363815	+	0.118211i	0.485219	−	0.874393i	$-0.338740\pi$
$281$	6.09864	+	1.98157i	0.363815	+	0.118211i	−0.121405	+	0.992603i	$0.538740\pi$
$282$	−0.352791	+	0.654524i	−0.0210084	+	0.0389764i
$283$	12.5885	+	9.14610i	0.748310	+	0.543679i	0.895303	−	0.445459i	$-0.146959\pi$
$283$	12.5885	+	9.14610i	0.748310	+	0.543679i	−0.146993	+	0.989138i	$0.546959\pi$
$284$	−8.81759	−	5.09084i	−0.523227	−	0.302085i
$285$	4.59254	−	4.38492i	0.272039	−	0.259741i
$286$	−0.127909	+	1.21698i	−0.00756344	+	0.0719613i
$287$	−1.13612	−	1.56373i	−0.0670630	−	0.0923042i
$288$	−2.50597	+	1.64927i	−0.147666	+	0.0971843i
$289$	8.68088	+	9.64109i	0.510640	+	0.567123i
$290$	−9.43298	+	4.19984i	−0.553924	+	0.246623i
$291$	1.29842	−	0.624195i	0.0761148	−	0.0365910i
$292$	−0.523046	+	2.46074i	−0.0306090	+	0.144004i
$293$	12.2895	−	27.6027i	0.717960	−	1.61257i	−0.0705235	−	0.997510i	$-0.522467\pi$
$293$	12.2895	−	27.6027i	0.717960	−	1.61257i	0.788484	−	0.615055i	$-0.210866\pi$
$294$	−8.29576	+	5.11861i	−0.483819	+	0.298523i
$295$	−1.17133	−	3.60497i	−0.0681972	−	0.209889i
$296$	1.41005	+	0.627794i	0.0819573	+	0.0364898i
$297$	−2.58536	+	1.43460i	−0.150018	+	0.0832439i
$298$	−17.4880	+	3.71719i	−1.01305	+	0.215331i
$299$	5.96844	+	13.4053i	0.345164	+	0.775251i
$300$	1.43042	+	0.976675i	0.0825854	+	0.0563884i
$301$	−6.04300	+	0.635145i	−0.348313	+	0.0366091i
$302$	−0.598227	+	0.434637i	−0.0344241	+	0.0250106i
$303$	27.3071	−	3.68002i	1.56875	−	0.211412i
$304$	1.83301	+	3.17486i	0.105130	+	0.182091i
$305$	−2.83158	+	4.90443i	−0.162136	+	0.280827i
$306$	2.47009	−	16.2376i	0.141206	−	0.928241i
$307$	−13.6916	+	15.2061i	−0.781421	+	0.867856i	−0.994010	−	0.109286i	$-0.965144\pi$
$307$	−13.6916	+	15.2061i	−0.781421	+	0.867856i	0.212590	+	0.977142i	$0.431810\pi$
$308$	0.205970	−	0.633909i	0.0117362	−	0.0361203i
$309$	−7.26107	+	1.76673i	−0.413068	+	0.100506i
$310$	−5.52690	−	0.673310i	−0.313907	−	0.0382414i
$311$		−	32.8476i		−	1.86262i	−0.364230	−	0.931309i	$-0.618668\pi$
$311$		−	32.8476i		−	1.86262i	0.364230	−	0.931309i	$-0.381332\pi$
$312$	−0.280888	+	3.71417i	−0.0159021	+	0.210274i
$313$	13.2534	+	11.9334i	0.749125	+	0.674515i	0.952484	−	0.304589i	$-0.0985192\pi$
$313$	13.2534	+	11.9334i	0.749125	+	0.674515i	−0.203359	+	0.979104i	$0.565186\pi$
$314$	−8.54521	+	11.7615i	−0.482234	+	0.663738i
$315$	−3.51034	−	0.162450i	−0.197785	−	0.00915304i
$316$	0.737160	−	0.425599i	0.0414685	−	0.0239418i
$317$	27.4340	+	2.88343i	1.54085	+	0.161950i	0.836524	−	0.547930i	$-0.184584\pi$
$317$	27.4340	+	2.88343i	1.54085	+	0.161950i	0.704323	+	0.709880i	$0.251251\pi$
$318$	−6.31422	−	5.35955i	−0.354084	−	0.300549i
$319$	−0.614160	−	5.84334i	−0.0343863	−	0.327164i
$320$	−0.743145	+	0.669131i	−0.0415431	+	0.0374055i
$321$	−4.90790	−	6.35577i	−0.273932	−	0.354744i
$322$	−1.66180	−	7.81816i	−0.0926086	−	0.435689i
$323$	−19.6321	−	4.17293i	−1.09236	−	0.232188i
$324$	−7.73861	+	4.59499i	−0.429923	+	0.255277i
$325$	2.04525	−	0.664542i	0.113450	−	0.0368622i
$326$	1.75101	−	0.568938i	0.0969796	−	0.0315106i
$327$	1.71670	+	0.312745i	0.0949337	+	0.0172948i
$328$	−1.61405	−	0.343077i	−0.0891209	−	0.0189432i
$329$	−0.104549	−	0.491865i	−0.00576398	−	0.0271174i
$330$	−0.780069	+	0.602366i	−0.0429414	+	0.0331592i
$331$	2.86711	−	2.58156i	0.157591	−	0.141895i	−0.586563	−	0.809903i	$-0.699519\pi$
$331$	2.86711	−	2.58156i	0.157591	−	0.141895i	0.744154	+	0.668008i	$0.232853\pi$
$332$	−0.348823	−	3.31883i	−0.0191441	−	0.182144i
$333$	4.13855	+	2.07692i	0.226791	+	0.113814i
$334$	−8.21151	−	0.863065i	−0.449314	−	0.0472248i
$335$	10.5661	−	6.10033i	0.577287	−	0.333297i
$336$	0.570278	−	1.94707i	0.0311112	−	0.106221i
$337$	6.05519	−	8.33426i	0.329847	−	0.453996i	−0.611594	−	0.791171i	$-0.709472\pi$
$337$	6.05519	−	8.33426i	0.329847	−	0.453996i	0.941442	+	0.337175i	$0.109472\pi$
$338$	−6.22409	−	5.60419i	−0.338546	−	0.304828i
$339$	29.4598	+	2.22793i	1.60004	+	0.121004i
$340$		−	5.47479i		−	0.296912i
$341$	1.33621	−	2.87260i	0.0723598	−	0.155560i
$342$	5.05284	+	9.76861i	0.273226	+	0.528226i
$343$	4.57095	−	14.0679i	0.246808	−	0.759597i
$344$	−3.47101	+	3.85495i	−0.187145	+	0.207845i
$345$	−4.48940	+	10.9328i	−0.241701	+	0.588602i
$346$	6.32246	−	10.9508i	0.339898	−	0.588720i
$347$	−14.3911	−	24.9261i	−0.772554	−	1.33810i	−0.936159	−	0.351577i	$-0.885646\pi$
$347$	−14.3911	−	24.9261i	−0.772554	−	1.33810i	0.163605	−	0.986526i	$-0.447688\pi$
$348$	−2.38862	−	17.7244i	−0.128043	−	0.950127i
$349$	−12.5161	+	9.09349i	−0.669973	+	0.486764i	−0.870016	−	0.493023i	$-0.835892\pi$
$349$	−12.5161	+	9.09349i	−0.669973	+	0.486764i	0.200043	+	0.979787i	$0.435892\pi$
$350$	−1.16495	+	0.122441i	−0.0622692	+	0.00654475i
$351$	−1.35686	+	11.0917i	−0.0724239	+	0.592029i
$352$	−0.231441	−	0.519826i	−0.0123359	−	0.0277068i
$353$	−7.48355	+	1.59068i	−0.398309	+	0.0846632i	−0.402711	−	0.915327i	$-0.631932\pi$
$353$	−7.48355	+	1.59068i	−0.398309	+	0.0846632i	0.00440211	+	0.999990i	$0.498599\pi$
$354$	6.56251	−	0.191927i	0.348794	−	0.0102008i
$355$	−9.30142	−	4.14126i	−0.493668	−	0.219795i
$356$	−4.04929	−	12.4624i	−0.214612	−	0.660507i
$357$	5.83265	+	9.45302i	0.308696	+	0.500307i
$358$	−1.98688	+	4.46260i	−0.105010	+	0.235856i
$359$	1.09807	−	5.16601i	0.0579539	−	0.272652i	−0.939624	−	0.342208i	$-0.888825\pi$
$359$	1.09807	−	5.16601i	0.0579539	−	0.272652i	0.997578	+	0.0695567i	$0.0221585\pi$
$360$	−2.31985	+	1.90218i	−0.122267	+	0.100254i
$361$	−5.07962	+	2.26159i	−0.267348	+	0.119031i
$362$	−8.42518	−	9.35711i	−0.442818	−	0.491799i
$363$	6.22594	+	17.4121i	0.326777	+	0.913900i
$364$	−1.48065	−	2.03794i	−0.0776070	−	0.106817i
$365$	−0.262964	+	2.50193i	−0.0137641	+	0.130957i
$366$	−6.77370	−	7.09442i	−0.354067	−	0.370831i
$367$	−4.30266	−	2.48414i	−0.224597	−	0.129671i	0.383480	−	0.923549i	$-0.374725\pi$
$367$	−4.30266	−	2.48414i	−0.224597	−	0.129671i	−0.608077	+	0.793878i	$0.708059\pi$
$368$	−5.52033	−	4.01076i	−0.287767	−	0.209075i
$369$	−4.78939	−	1.25197i	−0.249326	−	0.0651751i
$370$	1.46795	+	0.476964i	0.0763148	+	0.0247962i
$371$	5.60113			0.290796
$372$	3.80996	−	8.85913i	0.197537	−	0.459325i
$373$	−33.1963			−1.71884			−0.859419	−	0.511271i	$-0.829175\pi$
$373$	−33.1963			−1.71884			−0.859419	+	0.511271i	$0.829175\pi$
$374$	2.96280	+	0.962671i	0.153203	+	0.0497785i
$375$	1.52468	+	0.821805i	0.0787339	+	0.0424378i
$376$	−0.347301	−	0.252329i	−0.0179107	−	0.0130129i
$377$	−19.2305	−	11.1027i	−0.990419	−	0.571819i
$378$	1.97903	−	5.75588i	0.101791	−	0.296050i
$379$	2.07737	−	19.7648i	0.106707	−	1.01525i	−0.801860	−	0.597512i	$-0.796156\pi$
$379$	2.07737	−	19.7648i	0.106707	−	1.01525i	0.908567	−	0.417739i	$-0.137177\pi$
$380$	2.15483	+	2.96587i	0.110540	+	0.152146i
$381$	−24.6812	+	8.82509i	−1.26446	+	0.452123i
$382$	−12.2362	−	13.5897i	−0.626059	−	0.695309i
$383$	15.2225	−	6.77751i	0.777835	−	0.346315i	0.0208806	−	0.999782i	$-0.493353\pi$
$383$	15.2225	−	6.77751i	0.777835	−	0.346315i	0.756955	+	0.653467i	$0.226686\pi$
$384$	−0.750444	−	1.56104i	−0.0382959	−	0.0796613i
$385$	0.138580	−	0.651966i	0.00706267	−	0.0332273i
$386$	6.43750	−	14.4589i	0.327660	−	0.735937i
$387$	−10.9365	+	11.0711i	−0.555935	+	0.562776i
$388$	0.257031	+	0.791059i	0.0130488	+	0.0401599i
$389$	−18.9726	−	8.44715i	−0.961950	−	0.428288i	−0.135176	−	0.990822i	$-0.543160\pi$
$389$	−18.9726	−	8.44715i	−0.961950	−	0.428288i	−0.826774	+	0.562534i	$0.809826\pi$
$390$	0.108888	+	3.72319i	0.00551376	+	0.188531i
$391$	36.5409	−	7.76702i	1.84795	−	0.392795i
$392$	−2.28907	−	5.14134i	−0.115616	−	0.259677i
$393$	12.2409	−	17.9279i	0.617474	−	0.904342i
$394$	−18.0356	+	1.89562i	−0.908621	+	0.0954999i
$395$	0.688634	−	0.500322i	0.0346490	−	0.0251739i
$396$	−0.621490	−	1.58991i	−0.0312311	−	0.0798959i
$397$	2.36809	+	4.10165i	0.118851	+	0.205856i	0.919313	−	0.393528i	$-0.128746\pi$
$397$	2.36809	+	4.10165i	0.118851	+	0.205856i	−0.800462	+	0.599384i	$0.795412\pi$
$398$	10.1371	−	17.5579i	0.508126	−	0.880100i
$399$	−6.88035	−	2.82532i	−0.344448	−	0.141443i
$400$	−0.669131	+	0.743145i	−0.0334565	+	0.0371572i
$401$	−5.38252	+	16.5657i	−0.268790	+	0.827251i	0.722006	+	0.691887i	$0.243220\pi$
$401$	−5.38252	+	16.5657i	−0.268790	+	0.827251i	−0.990796	+	0.135364i	$0.956780\pi$
$402$	4.99601	+	20.5331i	0.249178	+	1.02410i
$403$	−5.81477	−	10.4668i	−0.289654	−	0.521386i
$404$			15.9083i			0.791466i
$405$	−7.21591	+	5.37872i	−0.358561	+	0.267271i
$406$	8.98846	+	8.09324i	0.446090	+	0.401661i
$407$	−0.516238	+	0.710541i	−0.0255890	+	0.0352202i
$408$	9.10032	+	2.66540i	0.450533	+	0.131957i
$409$	−22.7494	+	13.1343i	−1.12488	+	0.649452i	−0.942643	−	0.333802i	$-0.891668\pi$
$409$	−22.7494	+	13.1343i	−1.12488	+	0.649452i	−0.182240	+	0.983254i	$0.558335\pi$
$410$	−1.64107	−	0.172483i	−0.0810466	−	0.00851834i
$411$	−5.32595	+	6.27464i	−0.262710	+	0.309505i
$412$	−0.450987	−	4.29085i	−0.0222185	−	0.211395i
$413$	−3.29960	+	2.97097i	−0.162363	+	0.146192i
$414$	−15.9871	−	12.7850i	−0.785721	−	0.628348i
$415$	−0.693824	−	3.26418i	−0.0340585	−	0.160233i
$416$	−2.10351	−	0.447115i	−0.103133	−	0.0219216i
$417$	1.39506	−	7.65768i	0.0683165	−	0.374998i
$418$	−1.98394	+	0.644621i	−0.0970377	+	0.0315294i
$419$	−5.07827	+	1.65003i	−0.248090	+	0.0806092i	−0.430422	−	0.902628i	$-0.641635\pi$
$419$	−5.07827	+	1.65003i	−0.248090	+	0.0806092i	0.182333	+	0.983237i	$0.441635\pi$
$420$	0.363630	−	1.99601i	0.0177433	−	0.0973955i
$421$	8.11085	+	1.72401i	0.395299	+	0.0840233i	0.401272	−	0.915959i	$-0.368568\pi$
$421$	8.11085	+	1.72401i	0.395299	+	0.0840233i	−0.00597357	+	0.999982i	$0.501901\pi$
$422$	3.63323	+	17.0930i	0.176863	+	0.832074i
$423$	−1.00580	−	0.804343i	−0.0489034	−	0.0391085i
$424$	3.55350	−	3.19959i	0.172573	−	0.155386i
$425$	−0.572272	−	5.44480i	−0.0277593	−	0.264112i
$426$	11.4121	−	13.4448i	0.552917	−	0.651405i
$427$	6.59729	+	0.693403i	0.319265	+	0.0335561i
$428$	4.01507	−	2.31810i	0.194076	−	0.112050i
$429$	−2.03403	−	0.595747i	−0.0982037	−	0.0287630i
$430$	−3.04905	+	4.19665i	−0.147038	+	0.202381i
$431$	19.2853	+	17.3645i	0.928938	+	0.836420i	0.986806	−	0.161904i	$-0.0517636\pi$
$431$	19.2853	+	17.3645i	0.928938	+	0.836420i	−0.0578680	+	0.998324i	$0.518430\pi$
$432$	−2.03243	−	4.78218i	−0.0977855	−	0.230083i
$433$			5.55549i			0.266980i	0.991050	+	0.133490i	$0.0426184\pi$
$433$			5.55549i			0.266980i	−0.991050	+	0.133490i	$0.957382\pi$
$434$	1.91272	+	6.23511i	0.0918134	+	0.299295i
$435$	−4.22823	−	17.3776i	−0.202728	−	0.833193i
$436$	−0.311319	+	0.958142i	−0.0149095	+	0.0458867i
$437$	−16.7384	+	18.5898i	−0.800704	+	0.889272i
$438$	−4.03074	−	1.65517i	−0.192596	−	0.0790869i
$439$	19.1175	−	33.1126i	0.912430	−	1.58038i	0.101810	−	0.994804i	$-0.467537\pi$
$439$	19.1175	−	33.1126i	0.912430	−	1.58038i	0.810620	−	0.585572i	$-0.199130\pi$
$440$	−0.284510	−	0.492786i	−0.0135635	−	0.0234927i
$441$	−6.14685	−	15.7250i	−0.292707	−	0.748809i
$442$	9.52501	−	6.92032i	0.453059	−	0.329166i
$443$	13.1871	−	1.38602i	0.626537	−	0.0658517i	0.214061	−	0.976820i	$-0.431331\pi$
$443$	13.1871	−	1.38602i	0.626537	−	0.0658517i	0.412476	+	0.910969i	$0.364664\pi$
$444$	−1.50749	+	2.20784i	−0.0715422	+	0.104779i
$445$	−5.32978	−	11.9709i	−0.252656	−	0.567474i
$446$	−13.3885	+	2.84581i	−0.633964	+	0.134753i
$447$	−0.905265	−	30.9536i	−0.0428176	−	1.46405i
$448$	1.07010	+	0.476438i	0.0505573	+	0.0225096i
$449$	−6.03767	−	18.5820i	−0.284935	−	0.876940i	−0.986418	−	0.164254i	$-0.947478\pi$
$449$	−6.03767	−	18.5820i	−0.284935	−	0.876940i	0.701483	−	0.712686i	$-0.252522\pi$
$450$	−2.10831	+	2.13425i	−0.0993866	+	0.100610i
$451$	0.381903	−	0.857769i	0.0179831	−	0.0403908i
$452$	−3.54639	+	16.6845i	−0.166808	+	0.784772i
$453$	−0.554915	−	1.15431i	−0.0260722	−	0.0542341i
$454$	15.7916	−	7.03086i	0.741135	−	0.329975i
$455$	−1.68556	−	1.87200i	−0.0790202	−	0.0877608i
$456$	−5.97901	+	2.13787i	−0.279993	+	0.100115i
$457$	8.32696	+	11.4611i	0.389519	+	0.536126i	0.958075	−	0.286518i	$-0.0924978\pi$
$457$	8.32696	+	11.4611i	0.389519	+	0.536126i	−0.568556	+	0.822644i	$0.692498\pi$
$458$	1.88078	−	17.8944i	0.0878829	−	0.836150i
$459$	26.9021	+	9.24972i	1.25568	+	0.431740i
$460$	−5.90933	−	3.41175i	−0.275524	−	0.159074i
$461$	23.3216	+	16.9441i	1.08619	+	0.789166i	0.978752	−	0.205045i	$-0.0657341\pi$
$461$	23.3216	+	16.9441i	1.08619	+	0.789166i	0.107442	+	0.994211i	$0.465734\pi$
$462$	1.01624	+	0.547759i	0.0472800	+	0.0254841i
$463$	−30.0461	−	9.76257i	−1.39636	−	0.453705i	−0.488349	−	0.872649i	$-0.662401\pi$
$463$	−30.0461	−	9.76257i	−1.39636	−	0.453705i	−0.908012	+	0.418943i	$0.862401\pi$
$464$	10.3257			0.479358
$465$	2.86305	−	9.20885i	0.132771	−	0.427050i
$466$	−26.2270			−1.21494
$467$	−2.95370	−	0.959715i	−0.136681	−	0.0444103i	0.239878	−	0.970803i	$-0.422893\pi$
$467$	−2.95370	−	0.959715i	−0.136681	−	0.0444103i	−0.376559	+	0.926393i	$0.622893\pi$
$468$	−6.24177	−	1.63163i	−0.288526	−	0.0754223i
$469$	−11.5620	−	8.40030i	−0.533885	−	0.387890i
$470$	−0.371774	−	0.214644i	−0.0171487	−	0.00990078i
$471$	−17.3889	−	18.2122i	−0.801238	−	0.839175i
$472$	−0.396214	+	3.76972i	−0.0182372	+	0.173516i
$473$	−1.73497	−	2.38798i	−0.0797740	−	0.109800i
$474$	0.496385	+	1.38824i	0.0227997	+	0.0637641i
$475$	2.45304	+	2.72438i	0.112553	+	0.125003i
$476$	−5.85856	+	2.60840i	−0.268527	+	0.119556i
$477$	11.0928	−	9.09568i	0.507906	−	0.416463i
$478$	3.07308	−	14.4577i	0.140560	−	0.661281i
$479$	8.08892	−	18.1680i	0.369592	−	0.830118i	−0.629017	−	0.777392i	$-0.716542\pi$
$479$	8.08892	−	18.1680i	0.369592	−	0.830118i	0.998609	−	0.0527261i	$-0.0167910\pi$
$480$	−0.909505	−	1.47404i	−0.0415130	−	0.0672805i
$481$	1.02571	+	3.15682i	0.0467685	+	0.143939i
$482$	2.76530	+	1.23119i	0.125956	+	0.0560791i
$483$	13.8381	−	0.404706i	0.629654	−	0.0184148i
$484$	−10.4429	+	2.21971i	−0.474678	+	0.100896i
$485$	0.338311	+	0.759858i	0.0153619	+	0.0345034i
$486$	−5.42756	−	14.6131i	−0.246199	−	0.662862i
$487$	−17.9348	+	1.88503i	−0.812705	+	0.0854188i	−0.501758	−	0.865008i	$-0.667313\pi$
$487$	−17.9348	+	1.88503i	−0.812705	+	0.0854188i	−0.310948	+	0.950427i	$0.600646\pi$
$488$	4.58159	−	3.32872i	0.207399	−	0.150684i
$489$	0.425903	+	3.16035i	0.0192600	+	0.142916i
$490$	−2.81395	−	4.87391i	−0.127121	−	0.220181i
$491$	0.426512	−	0.738741i	0.0192482	−	0.0333389i	−0.856241	−	0.516577i	$-0.827206\pi$
$491$	0.426512	−	0.738741i	0.0192482	−	0.0333389i	0.875489	+	0.483238i	$0.160539\pi$
$492$	1.08566	−	2.64384i	0.0489452	−	0.119194i
$493$	−37.8266	+	42.0107i	−1.70363	+	1.89207i
$494$	−2.43622	+	7.49792i	−0.109611	+	0.337347i
$495$	−0.784276	−	1.51624i	−0.0352506	−	0.0681497i
$496$	4.77522	+	2.86309i	0.214414	+	0.128557i
$497$			11.9265i			0.534975i
$498$	5.76358	+	0.435876i	0.258272	+	0.0195321i
$499$	−7.37273	−	6.63843i	−0.330049	−	0.297177i	0.487400	−	0.873179i	$-0.337945\pi$
$499$	−7.37273	−	6.63843i	−0.330049	−	0.297177i	−0.817448	+	0.576002i	$0.804612\pi$
$500$	−0.587785	+	0.809017i	−0.0262866	+	0.0361803i
$501$	4.01979	−	13.7245i	0.179591	−	0.613167i
$502$	−11.0149	+	6.35943i	−0.491617	+	0.283835i
$503$	−32.0836	−	3.37213i	−1.43054	−	0.150356i	−0.642644	−	0.766165i	$-0.722162\pi$
$503$	−32.0836	−	3.37213i	−1.43054	−	0.150356i	−0.787895	+	0.615810i	$0.788829\pi$
$504$	3.14078	+	1.57619i	0.139902	+	0.0702091i
$505$	1.66287	+	15.8211i	0.0739966	+	0.704031i
$506$	2.88542	−	2.59804i	0.128273	−	0.115497i
$507$	11.4817	−	8.86615i	0.509922	−	0.393760i
$508$	−3.14637	−	14.8025i	−0.139598	−	0.656756i
$509$	−6.94827	−	1.47690i	−0.307977	−	0.0654625i	0.0513307	−	0.998682i	$-0.483654\pi$
$509$	−6.94827	−	1.47690i	−0.307977	−	0.0654625i	−0.359307	+	0.933219i	$0.616987\pi$
$510$	9.32907	+	1.69955i	0.413098	+	0.0752575i
$511$	2.80259	−	0.910618i	0.123979	−	0.0402834i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	−18.2143	+	5.57757i	−0.804182	+	0.246256i
$514$	9.00625	+	1.91434i	0.397248	+	0.0844378i
$515$	−0.897032	−	4.22021i	−0.0395280	−	0.185964i
$516$	−5.49134	−	7.11133i	−0.241743	−	0.313059i
$517$	0.181531	−	0.163451i	0.00798370	−	0.00718856i
$518$	−0.188987	−	1.79809i	−0.00830359	−	0.0790034i
$519$	16.6976	+	14.1730i	0.732942	+	0.622126i
$520$	−2.13872	−	0.224789i	−0.0937892	−	0.00985764i
$521$	−5.15742	+	2.97764i	−0.225951	+	0.130453i	−0.608703	−	0.793398i	$-0.708310\pi$
$521$	−5.15742	+	2.97764i	−0.225951	+	0.130453i	0.382752	+	0.923851i	$0.374976\pi$
$522$	30.9439	+	1.43201i	1.35438	+	0.0626775i
$523$	−11.8967	+	16.3744i	−0.520207	+	0.716004i	−0.985599	−	0.169101i	$-0.945914\pi$
$523$	−11.8967	+	16.3744i	−0.520207	+	0.716004i	0.465392	+	0.885105i	$0.345914\pi$
$524$	9.31404	+	8.38640i	0.406886	+	0.366362i
$525$	0.152998	−	2.02309i	0.00667738	−	0.0882948i
$526$		−	27.4802i		−	1.19819i
$527$	−29.1420	+	8.93976i	−1.26944	+	0.389422i
$528$	0.957633	−	0.233006i	0.0416756	−	0.0101403i
$529$	7.28051	−	22.4071i	0.316544	−	0.974222i
$530$	3.19959	−	3.55350i	0.138981	−	0.154354i
$531$	−1.71017	+	11.2421i	−0.0742152	+	0.487867i
$532$	2.14712	−	3.71893i	0.0930896	−	0.161236i
$533$	−1.77428	−	3.07314i	−0.0768526	−	0.133113i
$534$	22.4931	−	3.03126i	0.973369	−	0.131176i
$535$	3.75077	−	2.72509i	0.162160	−	0.117816i
$536$	−12.1338	+	1.27532i	−0.524102	+	0.0550853i
$537$	−6.98750	−	4.77098i	−0.301533	−	0.205883i
$538$	1.90112	+	4.26999i	0.0819632	+	0.184092i
$539$	3.13241	−	0.665814i	0.134922	−	0.0286787i
$540$	−2.52117	−	4.54353i	−0.108494	−	0.195523i
$541$	0.527913	+	0.235042i	0.0226967	+	0.0101052i	0.418054	−	0.908422i	$-0.362712\pi$
$541$	0.527913	+	0.235042i	0.0226967	+	0.0101052i	−0.395357	+	0.918528i	$0.629379\pi$
$542$	−6.34053	−	19.5142i	−0.272349	−	0.838205i
$543$	18.5600	−	11.4518i	0.796486	−	0.491444i
$544$	−2.22680	+	5.00147i	−0.0954732	+	0.214436i
$545$	−0.209461	+	0.985435i	−0.00897231	+	0.0422114i
$546$	3.93229	−	1.89039i	0.168287	−	0.0809011i
$547$	−16.0945	+	7.16573i	−0.688151	+	0.306384i	−0.720860	−	0.693081i	$-0.756253\pi$
$547$	−16.0945	+	7.16573i	−0.688151	+	0.306384i	0.0327096	+	0.999465i	$0.489586\pi$
$548$	−3.17953	−	3.53122i	−0.135823	−	0.150846i
$549$	14.1917	−	9.34008i	0.605687	−	0.398625i
$550$	−0.334462	−	0.460347i	−0.0142615	−	0.0196293i
$551$	3.95683	−	37.6468i	0.168567	−	1.60381i
$552$	8.54804	−	8.16160i	0.363829	−	0.347381i
$553$	−0.863484	−	0.498533i	−0.0367191	−	0.0211998i
$554$	−24.6437	−	17.9047i	−1.04701	−	0.760699i
$555$	−1.26845	+	2.35332i	−0.0538426	+	0.0998929i
$556$	4.27398	+	1.38870i	0.181257	+	0.0588940i
$557$	18.8652			0.799343			0.399672	−	0.916658i	$-0.369124\pi$
$557$	18.8652			0.799343			0.399672	+	0.916658i	$0.369124\pi$
$558$	13.9133	+	9.24234i	0.588996	+	0.391260i
$559$	−11.1554			−0.471824
$560$	1.11404	+	0.361972i	0.0470766	+	0.0152961i
$561$	−2.56014	+	4.74978i	−0.108089	+	0.200536i
$562$	−5.18782	−	3.76917i	−0.218835	−	0.158993i
$563$	9.19574	+	5.30916i	0.387554	+	0.223755i	0.681100	−	0.732191i	$-0.261502\pi$
$563$	9.19574	+	5.30916i	0.387554	+	0.223755i	−0.293546	+	0.955945i	$0.594835\pi$
$564$	0.537783	−	0.513471i	0.0226448	−	0.0216210i
$565$	−1.78296	+	16.9638i	−0.0750099	+	0.713671i
$566$	−9.14610	−	12.5885i	−0.384439	−	0.529135i
$567$	9.19368	+	5.15909i	0.386098	+	0.216662i
$568$	6.81287	+	7.56646i	0.285862	+	0.317481i
$569$	−26.4747	+	11.7873i	−1.10988	+	0.494149i	−0.878031	−	0.478604i	$-0.841143\pi$
$569$	−26.4747	+	11.7873i	−1.10988	+	0.494149i	−0.231846	+	0.972753i	$0.574476\pi$
$570$	−5.72278	+	2.75114i	−0.239701	+	0.115232i
$571$	−5.05028	+	23.7597i	−0.211348	+	0.994312i	0.736709	+	0.676210i	$0.236379\pi$
$571$	−5.05028	+	23.7597i	−0.211348	+	0.994312i	−0.948056	+	0.318102i	$0.896954\pi$
$572$	0.497716	−	1.11789i	0.0208105	−	0.0467412i
$573$	26.9554	−	16.6319i	1.12608	−	0.694807i
$574$	0.597293	+	1.83828i	0.0249305	+	0.0767283i
$575$	−6.23358	−	2.77537i	−0.259958	−	0.115741i
$576$	2.89298	−	0.794163i	0.120541	−	0.0330901i
$577$	31.4854	−	6.69244i	1.31076	−	0.278610i	0.501036	−	0.865426i	$-0.332952\pi$
$577$	31.4854	−	6.69244i	1.31076	−	0.278610i	0.809720	+	0.586816i	$0.199619\pi$
$578$	−5.27674	−	11.8518i	−0.219484	−	0.492968i
$579$	22.6396	+	15.4580i	0.940868	+	0.642414i
$580$	10.2691	−	1.07933i	0.426402	−	0.0448167i
$581$	−3.16243	+	2.29764i	−0.131200	+	0.0953221i
$582$	−1.42776	+	0.192411i	−0.0591825	+	0.00797569i
$583$	1.36044	+	2.35636i	0.0563439	+	0.0975904i
$584$	1.25786	−	2.17867i	0.0520505	−	0.0901541i
$585$	−6.37813	−	0.970253i	−0.263703	−	0.0401150i
$586$	−20.2177	+	22.4540i	−0.835186	+	0.927568i
$587$	−9.02095	+	27.7636i	−0.372335	+	1.14593i	0.572925	+	0.819608i	$0.305809\pi$
$587$	−9.02095	+	27.7636i	−0.372335	+	1.14593i	−0.945259	+	0.326320i	$0.894191\pi$
$588$	9.47148	−	2.30455i	0.390597	−	0.0950381i
$589$	12.2685	−	16.3130i	0.505516	−	0.672164i
$590$			3.79049i			0.156052i
$591$	2.36870	−	31.3212i	0.0974351	−	1.28838i
$592$	−1.14704	−	1.03280i	−0.0471429	−	0.0424476i
$593$	−19.6006	+	26.9779i	−0.804900	+	1.10785i	0.187191	+	0.982324i	$0.440062\pi$
$593$	−19.6006	+	26.9779i	−0.804900	+	1.10785i	−0.992090	+	0.125526i	$0.959938\pi$
$594$	2.90214	−	0.565463i	0.119076	−	0.0232012i
$595$	−5.55381	+	3.20649i	−0.227684	+	0.131453i
$596$	17.7808	+	1.86883i	0.728329	+	0.0765504i
$597$	26.7719	+	22.7242i	1.09570	+	0.930039i
$598$	−1.53385	−	14.5936i	−0.0627237	−	0.596776i
$599$	−17.3303	+	15.6043i	−0.708097	+	0.637574i	−0.942360	−	0.334599i	$-0.891399\pi$
$599$	−17.3303	+	15.6043i	−0.708097	+	0.637574i	0.234263	+	0.972173i	$0.424732\pi$
$600$	−1.05860	−	1.37090i	−0.0432173	−	0.0559667i
$601$	−4.22756	−	19.8891i	−0.172446	−	0.811293i	−0.976292	−	0.216457i	$-0.930550\pi$
$601$	−4.22756	−	19.8891i	−0.172446	−	0.811293i	0.803846	−	0.594837i	$-0.202783\pi$
$602$	5.94351	+	1.26333i	0.242239	+	0.0514895i
$603$	−36.5394	+	2.13909i	−1.48800	+	0.0871103i
$604$	0.703258	−	0.228502i	0.0286152	−	0.00929763i
$605$	−10.1537	+	3.29913i	−0.412806	+	0.134129i
$606$	−27.1078	−	4.93844i	−1.10118	−	0.200611i
$607$	14.7869	+	3.14305i	0.600181	+	0.127572i	0.497976	−	0.867191i	$-0.334077\pi$
$607$	14.7869	+	3.14305i	0.600181	+	0.127572i	0.102205	+	0.994763i	$0.467410\pi$
$608$	−0.762207	−	3.58590i	−0.0309116	−	0.145428i
$609$	−16.5812	+	12.8040i	−0.671905	+	0.518843i
$610$	4.20854	−	3.78939i	0.170399	−	0.153428i
$611$	−0.0964990	−	0.918127i	−0.00390393	−	0.0371434i
$612$	−7.36688	+	14.6796i	−0.297789	+	0.593386i
$613$	−5.40291	−	0.567868i	−0.218221	−	0.0229360i	−0.00521317	−	0.999986i	$-0.501659\pi$
$613$	−5.40291	−	0.567868i	−0.218221	−	0.0229360i	−0.213008	+	0.977050i	$0.568326\pi$
$614$	17.7204	−	10.2309i	0.715138	−	0.412885i
$615$	0.803353	−	2.74284i	0.0323943	−	0.110602i
$616$	−0.391777	+	0.539235i	−0.0157852	+	0.0217264i
$617$	−6.79995	−	6.12270i	−0.273756	−	0.246491i	0.520805	−	0.853676i	$-0.325632\pi$
$617$	−6.79995	−	6.12270i	−0.273756	−	0.246491i	−0.794560	+	0.607185i	$0.792299\pi$
$618$	7.45163	+	0.563536i	0.299749	+	0.0226688i
$619$			26.6125i			1.06965i	0.844963	+	0.534824i	$0.179622\pi$
$619$			26.6125i			1.06965i	−0.844963	+	0.534824i	$0.820378\pi$
$620$	5.04833	+	2.34826i	0.202746	+	0.0943085i
$621$	26.7486	−	23.2731i	1.07338	−	0.933919i
$622$	−10.1505	+	31.2400i	−0.406997	+	1.25261i
$623$	−10.2707	+	11.4068i	−0.411487	+	0.457002i
$624$	1.41488	−	3.44559i	0.0566407	−	0.137934i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−8.91708	−	15.4448i	−0.356398	−	0.617300i
$627$	−0.482558	−	3.58075i	−0.0192715	−	0.143002i
$628$	11.7615	−	8.54521i	0.469334	−	0.340991i
$629$	8.40399	−	0.883295i	0.335089	−	0.0352193i
$630$	3.28833	+	1.23925i	0.131010	+	0.0493731i
$631$	−4.89230	−	10.9883i	−0.194759	−	0.437437i	0.789597	−	0.613626i	$-0.210290\pi$
$631$	−4.89230	−	10.9883i	−0.194759	−	0.437437i	−0.984356	+	0.176189i	$0.943623\pi$
$632$	−0.832598	+	0.176974i	−0.0331190	+	0.00703966i
$633$	−30.2544	+	0.884817i	−1.20251	+	0.0351683i
$634$	−25.2003	−	11.2199i	−1.00083	−	0.445598i
$635$	−4.67642	−	14.3926i	−0.185578	−	0.571151i
$636$	4.34899	+	7.04844i	0.172449	+	0.279489i
$637$	4.92266	−	11.0565i	0.195043	−	0.438073i
$638$	−1.22159	+	5.74713i	−0.0483632	+	0.227531i
$639$	19.3674	+	23.6199i	0.766163	+	0.934390i
$640$	0.913545	−	0.406737i	0.0361111	−	0.0160777i
$641$	−18.2043	−	20.2180i	−0.719028	−	0.798562i	0.267255	−	0.963626i	$-0.413884\pi$
$641$	−18.2043	−	20.2180i	−0.719028	−	0.798562i	−0.986283	+	0.165064i	$0.947217\pi$
$642$	2.70365	+	7.56132i	0.106705	+	0.298421i
$643$	−23.1182	−	31.8194i	−0.911692	−	1.25484i	−0.966586	−	0.256344i	$-0.917482\pi$
$643$	−23.1182	−	31.8194i	−0.911692	−	1.25484i	0.0548934	−	0.998492i	$-0.482518\pi$
$644$	−0.835478	+	7.94904i	−0.0329224	+	0.313236i
$645$	−6.20459	−	6.49837i	−0.244306	−	0.255873i
$646$	17.3817	+	10.0353i	0.683874	+	0.394835i
$647$	−0.346380	−	0.251660i	−0.0136176	−	0.00989376i	0.580956	−	0.813935i	$-0.302679\pi$
$647$	−0.346380	−	0.251660i	−0.0136176	−	0.00989376i	−0.594573	+	0.804041i	$0.702679\pi$
$648$	8.77978	−	1.97873i	0.344903	−	0.0777319i
$649$	−2.05130	−	0.666508i	−0.0805206	−	0.0261627i
$650$	−2.15050			−0.0843497
$651$	−11.2184	+	1.32370i	−0.439685	+	0.0518799i
$652$	−1.84112			−0.0721040
$653$	13.1871	+	4.28474i	0.516050	+	0.167675i	0.555452	−	0.831549i	$-0.312545\pi$
$653$	13.1871	+	4.28474i	0.516050	+	0.167675i	−0.0394022	+	0.999223i	$0.512545\pi$
$654$	−1.53603	−	0.827928i	−0.0600637	−	0.0323745i
$655$	10.1396	+	7.36688i	0.396188	+	0.287848i
$656$	1.42904	+	0.825054i	0.0557944	+	0.0322129i
$657$	4.07168	−	6.35458i	0.158851	−	0.247916i
$658$	−0.0525625	+	0.500098i	−0.00204910	+	0.0194959i
$659$	−18.8321	−	25.9202i	−0.733595	−	1.00971i	−0.998962	−	0.0455599i	$-0.985493\pi$
$659$	−18.8321	−	25.9202i	−0.733595	−	1.00971i	0.265366	−	0.964148i	$-0.414507\pi$
$660$	0.928031	−	0.331830i	0.0361236	−	0.0129165i
$661$	−0.371837	−	0.412966i	−0.0144628	−	0.0160625i	0.735870	−	0.677123i	$-0.236773\pi$
$661$	−0.371837	−	0.412966i	−0.0144628	−	0.0160625i	−0.750333	+	0.661060i	$0.770107\pi$
$662$	−3.52453	+	1.56922i	−0.136985	+	0.0609896i
$663$	8.83539	+	18.3790i	0.343138	+	0.713779i
$664$	−0.693824	+	3.26418i	−0.0269256	+	0.126675i
$665$	1.74663	−	3.92299i	0.0677313	−	0.152127i
$666$	−3.29420	−	3.25415i	−0.127648	−	0.126096i
$667$	21.7725	+	67.0089i	0.843036	+	2.59460i
$668$	7.54291	+	3.35832i	0.291844	+	0.129937i
$669$	−0.693054	−	23.6975i	−0.0267950	−	0.916198i
$670$	−11.9340	+	2.53666i	−0.461053	+	0.0979997i
$671$	1.31069	+	2.94385i	0.0505986	+	0.113646i
$672$	−1.14404	+	1.67555i	−0.0441325	+	0.0646356i
$673$	−15.2554	+	1.60341i	−0.588053	+	0.0618068i	−0.393882	−	0.919161i	$-0.628868\pi$
$673$	−15.2554	+	1.60341i	−0.588053	+	0.0618068i	−0.194170	+	0.980968i	$0.562202\pi$
$674$	−8.33426	+	6.05519i	−0.321024	+	0.233237i
$675$	−2.98229	−	4.25511i	−0.114788	−	0.163779i
$676$	4.18767	+	7.25325i	0.161064	+	0.278971i
$677$	−0.114376	+	0.198105i	−0.00439582	+	0.00761378i	−0.868215	−	0.496188i	$-0.834733\pi$
$677$	−0.114376	+	0.198105i	−0.00439582	+	0.00761378i	0.863819	+	0.503802i	$0.168066\pi$
$678$	−27.3295	−	11.2225i	−1.04958	−	0.430997i
$679$	0.651938	−	0.724050i	0.0250191	−	0.0277865i
$680$	−1.69180	+	5.20684i	−0.0648777	+	0.199673i
$681$	7.07840	+	29.0915i	0.271245	+	1.11479i
$682$	−2.15849	+	2.31910i	−0.0826530	+	0.0888029i
$683$		−	11.8167i		−	0.452154i	−0.974109	−	0.226077i	$-0.927410\pi$
$683$		−	11.8167i		−	0.452154i	0.974109	−	0.226077i	$-0.0725900\pi$
$684$	−1.78687	−	10.8519i	−0.0683226	−	0.414933i
$685$	−3.53122	−	3.17953i	−0.134921	−	0.121484i
$686$	−8.69446	+	11.9669i	−0.331956	+	0.456898i
$687$	29.9083	+	8.75985i	1.14107	+	0.334209i
$688$	4.49238	−	2.59367i	0.171270	−	0.0988829i
$689$	10.2267	+	1.07487i	0.389608	+	0.0409494i
$690$	7.64809	−	9.01040i	0.291158	−	0.343020i
$691$	2.30335	+	21.9149i	0.0876236	+	0.833683i	0.946761	+	0.321938i	$0.104334\pi$
$691$	2.30335	+	21.9149i	0.0876236	+	0.833683i	−0.859137	+	0.511745i	$0.828999\pi$
$692$	−9.39701	+	8.46111i	−0.357221	+	0.321643i
$693$	−1.24886	+	1.56164i	−0.0474402	+	0.0593219i
$694$	5.98415	+	28.1532i	0.227155	+	1.06868i
$695$	4.39573	+	0.934341i	0.166739	+	0.0354416i
$696$	−3.20543	+	17.5950i	−0.121501	+	0.666937i
$697$	−8.59184	+	2.79166i	−0.325439	+	0.105742i
$698$	14.7136	−	4.78073i	0.556917	−	0.180953i
$699$	8.14171	−	44.6909i	0.307948	−	1.69037i
$700$	1.14577	+	0.243541i	0.0433060	+	0.00920498i
$701$	8.94605	+	42.0878i	0.337888	+	1.58964i	0.739064	+	0.673635i	$0.235268\pi$
$701$	8.94605	+	42.0878i	0.337888	+	1.58964i	−0.401176	+	0.916001i	$0.631399\pi$
$702$	4.71796	−	10.1295i	0.178068	−	0.382313i
$703$	−4.20505	+	3.78624i	−0.158597	+	0.142801i
$704$	0.0594788	+	0.565903i	0.00224169	+	0.0213283i
$705$	0.481165	−	0.566872i	0.0181217	−	0.0213496i
$706$	7.60882	+	0.799720i	0.286362	+	0.0300978i
$707$	16.1379	−	9.31721i	0.606927	−	0.350410i
$708$	−6.30063	−	1.84540i	−0.236792	−	0.0693542i
$709$	−22.8863	+	31.5003i	−0.859512	+	1.18302i	0.122173	+	0.992509i	$0.461014\pi$
$709$	−22.8863	+	31.5003i	−0.859512	+	1.18302i	−0.981686	+	0.190508i	$0.938986\pi$
$710$	7.56646	+	6.81287i	0.283964	+	0.255682i
$711$	−2.51967	+	0.414886i	−0.0944949	+	0.0155595i
$712$			13.1038i			0.491084i
$713$	−8.51123	+	37.0260i	−0.318748	+	1.38664i
$714$	−2.62604	−	10.7927i	−0.0982769	−	0.403908i
$715$	0.378138	−	1.16379i	0.0141416	−	0.0435232i
$716$	3.26865	−	3.63021i	0.122155	−	0.135667i
$717$	23.6820	+	9.72470i	0.884422	+	0.363175i
$718$	−2.64071	+	4.57385i	−0.0985505	+	0.170694i
$719$	−20.4449	−	35.4115i	−0.762464	−	1.32063i	−0.941577	−	0.336798i	$-0.890656\pi$
$719$	−20.4449	−	35.4115i	−0.762464	−	1.32063i	0.179113	−	0.983829i	$-0.442677\pi$
$720$	2.79411	−	1.09221i	0.104130	−	0.0407043i
$721$	−4.08865	+	2.97058i	−0.152269	+	0.110630i
$722$	5.52987	−	0.581213i	0.205801	−	0.0216305i
$723$	−2.95639	+	4.32988i	−0.109949	+	0.161030i
$724$	5.12132	+	11.5027i	0.190332	+	0.427493i
$725$	10.1000	−	2.14683i	0.375106	−	0.0797313i
$726$	−0.540576	−	18.4838i	−0.0200627	−	0.686000i
$727$	4.72429	+	2.10339i	0.175214	+	0.0780104i	0.492469	−	0.870330i	$-0.336094\pi$
$727$	4.72429	+	2.10339i	0.175214	+	0.0780104i	−0.317255	+	0.948340i	$0.602761\pi$
$728$	0.778422	+	2.39574i	0.0288502	+	0.0887919i
$729$	26.5856	−	4.71223i	0.984652	−	0.174527i
$730$	1.02323	−	2.29822i	0.0378715	−	0.0850609i
$731$	−5.90462	+	27.7791i	−0.218390	+	1.02745i
$732$	4.24988	+	8.84039i	0.157080	+	0.326750i
$733$	24.7784	−	11.0320i	0.915209	−	0.407477i	0.105575	−	0.994411i	$-0.466332\pi$
$733$	24.7784	−	11.0320i	0.915209	−	0.407477i	0.809635	+	0.586934i	$0.199665\pi$
$734$	3.32443	+	3.69215i	0.122707	+	0.136280i
$735$	9.17870	−	3.28197i	0.338561	−	0.121057i
$736$	4.01076	+	5.52033i	0.147838	+	0.203482i
$737$	0.725681	−	6.90440i	0.0267308	−	0.254327i
$738$	4.16810	+	2.67070i	0.153430	+	0.0983098i
$739$	12.4505	+	7.18833i	0.458001	+	0.264427i	0.711203	−	0.702986i	$-0.248151\pi$
$739$	12.4505	+	7.18833i	0.458001	+	0.264427i	−0.253203	+	0.967413i	$0.581484\pi$
$740$	−1.24871	−	0.907240i	−0.0459034	−	0.0333508i
$741$	−12.0202	−	6.47893i	−0.441573	−	0.238009i
$742$	−5.32699	−	1.73084i	−0.195560	−	0.0635413i
$743$	35.0045			1.28419			0.642096	−	0.766624i	$-0.278065\pi$
$743$	35.0045			1.28419			0.642096	+	0.766624i	$0.278065\pi$
$744$	−6.36111	+	7.24820i	−0.233209	+	0.265732i
$745$	17.8787			0.655025
$746$	31.5715	+	10.2582i	1.15592	+	0.375580i
$747$	−2.53194	+	9.68586i	−0.0926388	+	0.354387i
$748$	−2.52031	−	1.83111i	−0.0921515	−	0.0669520i
$749$	−4.70312	−	2.71535i	−0.171848	−	0.0992167i
$750$	−1.19610	−	1.25273i	−0.0436754	−	0.0457434i
$751$	2.35946	−	22.4487i	0.0860978	−	0.819166i	−0.863216	−	0.504835i	$-0.831553\pi$
$751$	2.35946	−	22.4487i	0.0860978	−	0.819166i	0.949314	−	0.314331i	$-0.101780\pi$
$752$	0.252329	+	0.347301i	0.00920149	+	0.0126648i
$753$	−7.41713	−	20.7435i	−0.270295	−	0.755937i
$754$	14.8583	+	16.5018i	0.541108	+	0.600962i
$755$	0.675520	−	0.300761i	0.0245847	−	0.0109458i
$756$	−3.66084	+	4.86261i	−0.133143	+	0.176851i
$757$	−2.59886	+	12.2267i	−0.0944572	+	0.444386i	0.905348	+	0.424670i	$0.139610\pi$
$757$	−2.59886	+	12.2267i	−0.0944572	+	0.444386i	−0.999806	+	0.0197166i	$0.993724\pi$
$758$	−8.08336	+	18.1555i	−0.293601	+	0.659438i
$759$	3.53135	+	5.72328i	0.128180	+	0.207742i
$760$	−1.13286	−	3.48659i	−0.0410932	−	0.126472i
$761$	8.95391	+	3.98654i	0.324579	+	0.144512i	0.562557	−	0.826759i	$-0.309818\pi$
$761$	8.95391	+	3.98654i	0.324579	+	0.144512i	−0.237978	+	0.971271i	$0.576484\pi$
$762$	26.2003	−	0.766251i	0.949137	−	0.0277584i
$763$	1.15431	−	0.245355i	0.0417887	−	0.00888245i
$764$	7.43789	+	16.7058i	0.269093	+	0.604394i
$765$	−5.79209	+	15.3692i	−0.209414	+	0.555674i
$766$	−16.5719	+	1.74177i	−0.598766	+	0.0629328i
$767$	−6.59467	+	4.79131i	−0.238120	+	0.173004i
$768$	0.231328	+	1.71653i	0.00834731	+	0.0619401i
$769$	−10.5137	−	18.2102i	−0.379133	−	0.656678i	0.611803	−	0.791010i	$-0.290444\pi$
$769$	−10.5137	−	18.2102i	−0.379133	−	0.656678i	−0.990936	+	0.134332i	$0.957111\pi$
$770$	−0.333266	+	0.577233i	−0.0120101	+	0.0208020i
$771$	−6.05787	+	14.7524i	−0.218169	+	0.531295i
$772$	−10.5905	+	11.7619i	−0.381159	+	0.423320i
$773$	−11.0955	+	34.1484i	−0.399077	+	1.22823i	0.526664	+	0.850074i	$0.323443\pi$
$773$	−11.0955	+	34.1484i	−0.399077	+	1.22823i	−0.925741	+	0.378159i	$0.876557\pi$
$774$	13.8224	−	7.14968i	0.496837	−	0.256990i
$775$	5.26614	+	1.80770i	0.189165	+	0.0649346i
$776$		−	0.831769i		−	0.0298587i
$777$	3.12262	+	0.236151i	0.112023	+	0.00847185i
$778$	15.4337	+	13.8966i	0.553325	+	0.498216i
$779$	3.55570	−	4.89400i	0.127396	−	0.175346i
$780$	1.04697	−	3.57461i	0.0374875	−	0.127992i
$781$	−5.01739	+	2.89679i	−0.179536	+	0.103655i
$782$	−37.1526	−	3.90490i	−1.32858	−	0.139639i
$783$	−12.0462	+	52.2841i	−0.430495	+	1.86848i
$784$	0.588276	+	5.59707i	0.0210099	+	0.199895i
$785$	10.8038	−	9.72780i	0.385605	−	0.347200i
$786$	−17.1819	+	13.2678i	−0.612856	+	0.473245i
$787$	−8.94421	−	42.0792i	−0.318827	−	1.49996i	−0.787348	−	0.616509i	$-0.788546\pi$
$787$	−8.94421	−	42.0792i	−0.318827	−	1.49996i	0.468521	−	0.883452i	$-0.344787\pi$
$788$	17.7387	+	3.77047i	0.631914	+	0.134317i
$789$	46.8264	+	8.53075i	1.66706	+	0.303703i
$790$	−0.809538	+	0.263035i	−0.0288021	+	0.00935836i
$791$	19.0023	−	6.17424i	0.675646	−	0.219531i
$792$	0.0997637	+	1.70414i	0.00354495	+	0.0605541i
$793$	11.9125	+	2.53208i	0.423025	+	0.0899167i
$794$	−0.984706	−	4.63268i	−0.0349459	−	0.164408i
$795$	5.06193	+	6.55523i	0.179528	+	0.232490i
$796$	−15.0666	+	13.5661i	−0.534023	+	0.480836i
$797$	1.13001	+	10.7514i	0.0400272	+	0.380833i	0.996136	+	0.0878219i	$0.0279906\pi$
$797$	1.13001	+	10.7514i	0.0400272	+	0.380833i	−0.956109	+	0.293011i	$0.905343\pi$
$798$	5.67053	+	4.81318i	0.200735	+	0.170385i
$799$	−2.33739	−	0.245669i	−0.0826908	−	0.00869115i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$	−1.81729	+	39.2693i	−0.0642108	+	1.38751i
$802$	10.2382	−	14.0916i	0.361522	−	0.497592i
$803$	1.06381	+	0.957855i	0.0375409	+	0.0338020i
$804$	1.59359	−	21.0720i	0.0562015	−	0.743152i
$805$			7.99282i			0.281710i
$806$	2.29577	+	11.7513i	0.0808651	+	0.413923i
$807$	−7.86625	+	1.91398i	−0.276905	+	0.0673752i
$808$	4.91593	−	15.1297i	0.172942	−	0.532260i
$809$	5.67230	−	6.29973i	0.199428	−	0.221487i	−0.635133	−	0.772403i	$-0.719055\pi$
$809$	5.67230	−	6.29973i	0.199428	−	0.221487i	0.834561	+	0.550916i	$0.185721\pi$
$810$	8.52485	−	2.88563i	0.299533	−	0.101391i
$811$	−15.9404	+	27.6097i	−0.559745	+	0.969506i	0.437773	+	0.899086i	$0.355767\pi$
$811$	−15.9404	+	27.6097i	−0.559745	+	0.969506i	−0.997517	+	0.0704205i	$0.977566\pi$
$812$	−6.04758	−	10.4747i	−0.212228	−	0.367591i
$813$	35.2205	−	4.74647i	1.23524	−	0.166466i
$814$	0.710541	−	0.516238i	0.0249044	−	0.0180941i
$815$	−1.83104	+	0.192450i	−0.0641385	+	0.00674122i
$816$	−7.83126	−	5.34710i	−0.274149	−	0.187186i
$817$	−7.73487	−	17.3728i	−0.270609	−	0.607798i
$818$	25.6947	−	5.46157i	0.898393	−	0.190959i
$819$	2.00052	+	7.28748i	0.0699038	+	0.254645i
$820$	1.50745	+	0.671159i	0.0526424	+	0.0234379i
$821$	16.4500	+	50.6278i	0.574108	+	1.76692i	0.639198	+	0.769042i	$0.279266\pi$
$821$	16.4500	+	50.6278i	0.574108	+	1.76692i	−0.0650903	+	0.997879i	$0.520734\pi$
$822$	7.00425	−	4.32173i	0.244301	−	0.150737i
$823$	17.3842	−	39.0455i	0.605975	−	1.36104i	−0.306485	−	0.951876i	$-0.599153\pi$
$823$	17.3842	−	39.0455i	0.605975	−	1.36104i	0.912460	−	0.409166i	$-0.134180\pi$
$824$	−0.897032	+	4.22021i	−0.0312496	+	0.147018i
$825$	0.888262	−	0.427018i	0.0309253	−	0.0148669i
$826$	4.05619	−	1.80593i	0.141133	−	0.0628364i
$827$	−15.9257	−	17.6873i	−0.553791	−	0.615048i	0.399635	−	0.916674i	$-0.369137\pi$
$827$	−15.9257	−	17.6873i	−0.553791	−	0.615048i	−0.953426	+	0.301627i	$0.902470\pi$
$828$	11.2538	+	17.0995i	0.391097	+	0.594249i
$829$	−29.4461	−	40.5290i	−1.02270	−	1.40763i	−0.910290	−	0.413971i	$-0.864142\pi$
$829$	−29.4461	−	40.5290i	−1.02270	−	1.40763i	−0.112414	−	0.993661i	$-0.535858\pi$
$830$	−0.348823	+	3.31883i	−0.0121078	+	0.115198i
$831$	38.1599	−	36.4348i	1.32375	−	1.26391i
$832$	1.86239	+	1.07525i	0.0645668	+	0.0372776i
$833$	−24.9271	−	18.1106i	−0.863673	−	0.627495i
$834$	−3.69314	+	6.85179i	−0.127883	+	0.237258i
$835$	7.85263	+	2.55147i	0.271751	+	0.0882974i
$836$	2.08604			0.0721471
$837$	−20.0681	+	20.8392i	−0.693656	+	0.720306i
$838$	5.33961			0.184454
$839$	32.9135	+	10.6942i	1.13630	+	0.369206i	0.815966	−	0.578099i	$-0.196205\pi$
$839$	32.9135	+	10.6942i	1.13630	+	0.369206i	0.320332	+	0.947305i	$0.396205\pi$
$840$	−0.962635	+	1.78595i	−0.0332141	+	0.0616213i
$841$	−62.7957	−	45.6238i	−2.16537	−	1.57323i
$842$	−7.18113	−	4.14603i	−0.247478	−	0.142881i
$843$	8.03315	−	7.66999i	0.276676	−	0.264169i
$844$	1.82662	−	17.3791i	0.0628749	−	0.598215i
$845$	4.92290	+	6.77579i	0.169353	+	0.233094i
$846$	0.708012	+	1.07578i	0.0243420	+	0.0369862i
$847$	8.36799	+	9.29359i	0.287527	+	0.319332i
$848$	−4.36831	+	1.94490i	−0.150008	+	0.0667880i
$849$	24.2901	−	11.6771i	0.833636	−	0.400757i
$850$	−1.13827	+	5.35516i	−0.0390425	+	0.183680i
$851$	4.28375	−	9.62147i	0.146845	−	0.329820i
$852$	−15.0082	+	9.26028i	−0.514173	+	0.317252i
$853$	−3.16720	−	9.74763i	−0.108443	−	0.333753i	0.882080	−	0.471099i	$-0.156143\pi$
$853$	−3.16720	−	9.74763i	−0.108443	−	0.333753i	−0.990523	+	0.137347i	$0.956143\pi$
$854$	−6.06012	−	2.69814i	−0.207373	−	0.0923284i
$855$	−2.91141	−	10.6057i	−0.0995683	−	0.362707i
$856$	−4.53490	+	0.963922i	−0.155000	+	0.0329462i
$857$	6.42592	+	14.4329i	0.219505	+	0.493017i	0.989411	−	0.145141i	$-0.0463635\pi$
$857$	6.42592	+	14.4329i	0.219505	+	0.493017i	−0.769906	+	0.638158i	$0.779697\pi$
$858$	1.75038	+	1.19514i	0.0597569	+	0.0408013i
$859$	−31.8293	+	3.34539i	−1.08600	+	0.114143i	−0.630573	−	0.776130i	$-0.717180\pi$
$859$	−31.8293	+	3.34539i	−1.08600	+	0.114143i	−0.455427	+	0.890273i	$0.650514\pi$
$860$	4.19665	−	3.04905i	0.143105	−	0.103972i
$861$	−3.31785	+	0.447129i	−0.113072	+	0.0152381i
$862$	−12.9754	−	22.4741i	−0.441945	−	0.765472i
$863$	12.9685	−	22.4621i	0.441453	−	0.764620i	−0.556344	−	0.830952i	$-0.687796\pi$
$863$	12.9685	−	22.4621i	0.441453	−	0.764620i	0.997798	+	0.0663323i	$0.0211297\pi$
$864$	0.455184	+	5.17618i	0.0154857	+	0.176097i
$865$	−8.46111	+	9.39701i	−0.287686	+	0.319508i
$866$	1.71674	−	5.28359i	0.0583372	−	0.179544i
$867$	21.8335	−	5.31242i	0.741505	−	0.180419i
$868$	0.107652	−	6.52100i	0.00365393	−	0.221337i
$869$		−	0.484350i		−	0.0164304i
$870$	−1.34869	+	17.8337i	−0.0457248	+	0.604619i
$871$	−19.4983	−	17.5564i	−0.660675	−	0.594874i
$872$	0.592164	−	0.815044i	0.0200532	−	0.0276009i
$873$	0.115353	−	2.49264i	0.00390412	−	0.0843630i
$874$	21.6637	−	12.5075i	0.732785	−	0.423074i
$875$	1.16495	+	0.122441i	0.0393825	+	0.00413927i
$876$	3.32199	+	2.81972i	0.112240	+	0.0952696i
$877$	3.21830	+	30.6201i	0.108674	+	1.03397i	0.903927	+	0.427687i	$0.140672\pi$
$877$	3.21830	+	30.6201i	0.108674	+	1.03397i	−0.795252	+	0.606278i	$0.792662\pi$
$878$	−28.4142	+	25.5843i	−0.958933	+	0.863427i
$879$	−31.9856	−	41.4215i	−1.07885	−	1.39711i
$880$	0.118306	+	0.556586i	0.00398809	+	0.0187625i
$881$	−0.934730	−	0.198683i	−0.0314919	−	0.00669380i	0.192139	−	0.981368i	$-0.438458\pi$
$881$	−0.934730	−	0.198683i	−0.0314919	−	0.00669380i	−0.223631	+	0.974674i	$0.571791\pi$
$882$	0.986714	+	16.8548i	0.0332244	+	0.567532i
$883$	−11.5802	+	3.76263i	−0.389704	+	0.126622i	−0.497314	−	0.867571i	$-0.665680\pi$
$883$	−11.5802	+	3.76263i	−0.389704	+	0.126622i	0.107610	+	0.994193i	$0.465680\pi$
$884$	−11.1973	+	3.63823i	−0.376607	+	0.122367i
$885$	−6.45901	−	1.17669i	−0.217117	−	0.0395540i
$886$	−12.9700	−	2.75685i	−0.435734	−	0.0926182i
$887$	1.45636	+	6.85163i	0.0488998	+	0.230055i	0.995810	−	0.0914414i	$-0.0291474\pi$
$887$	1.45636	+	6.85163i	0.0488998	+	0.230055i	−0.946911	+	0.321497i	$0.895814\pi$
$888$	2.11597	−	1.63394i	0.0710072	−	0.0548315i
$889$	−13.1734	+	11.8614i	−0.441822	+	0.397818i
$890$	1.36972	+	13.0320i	0.0459130	+	0.436833i
$891$	0.0626328	+	5.12080i	0.00209828	+	0.171553i
$892$	13.6126	+	1.43074i	0.455784	+	0.0479049i
$893$	1.36293	−	0.786888i	0.0456087	−	0.0263322i
$894$	−8.70423	+	29.7184i	−0.291113	+	0.993931i
$895$	2.87129	−	3.95199i	0.0959765	−	0.132100i
$896$	−0.870495	−	0.783797i	−0.0290812	−	0.0261848i
$897$	25.3437	+	1.91664i	0.846201	+	0.0639947i
$898$			19.5383i			0.652001i
$899$	−22.5136	−	52.8995i	−0.750870	−	1.76430i
$900$	2.66464	−	1.37829i	0.0888214	−	0.0459431i
$901$	8.08971	−	24.8976i	0.269507	−	0.829459i
$902$	−0.628277	+	0.697772i	−0.0209193	+	0.0232333i
$903$	−3.99778	+	9.73558i	−0.133038	+	0.323980i
$904$	8.52861	−	14.7720i	0.283657	−	0.491309i
$905$	6.29562	+	10.9043i	0.209273	+	0.362472i
$906$	0.171055	+	1.26929i	0.00568292	+	0.0421693i
$907$	−15.3537	+	11.1551i	−0.509812	+	0.370400i	−0.812752	−	0.582609i	$-0.802032\pi$
$907$	−15.3537	+	11.1551i	−0.509812	+	0.370400i	0.302940	+	0.953010i	$0.402032\pi$
$908$	−17.1913	+	1.80688i	−0.570514	+	0.0599635i
$909$	16.8303	−	44.6587i	0.558224	−	1.48124i
$910$	1.02458	+	2.30125i	0.0339645	+	0.0762855i
$911$	7.27352	−	1.54604i	0.240983	−	0.0512224i	−0.0858369	−	0.996309i	$-0.527356\pi$
$911$	7.27352	−	1.54604i	0.240983	−	0.0512224i	0.326820	+	0.945087i	$0.394023\pi$
$912$	6.34701	−	0.185624i	0.210171	−	0.00614662i
$913$	−1.73472	−	0.772345i	−0.0574107	−	0.0255609i
$914$	−4.37774	−	13.4733i	−0.144803	−	0.445657i
$915$	5.15067	+	8.34772i	0.170276	+	0.275967i
$916$	−7.31840	+	16.4374i	−0.241807	+	0.543106i
$917$	3.05237	−	14.3602i	0.100798	−	0.474217i
$918$	−22.7271	−	17.1102i	−0.750106	−	0.564721i
$919$	23.9374	−	10.6576i	0.789622	−	0.351562i	0.0280200	−	0.999607i	$-0.491080\pi$
$919$	23.9374	−	10.6576i	0.789622	−	0.351562i	0.761602	+	0.648045i	$0.224413\pi$
$920$	4.56582	+	5.07085i	0.150531	+	0.167181i
$921$	11.9325	+	33.3717i	0.393189	+	1.09963i
$922$	−16.9441	−	23.3216i	−0.558025	−	0.768055i
$923$	−2.28873	+	21.7758i	−0.0753343	+	0.716758i
$924$	−0.797239	−	0.834987i	−0.0262272	−	0.0274690i
$925$	−1.33670	−	0.771745i	−0.0439504	−	0.0253748i
$926$	25.5587	+	18.5695i	0.839913	+	0.610232i
$927$	−3.27350	+	12.5227i	−0.107516	+	0.411299i
$928$	−9.82031	−	3.19081i	−0.322368	−	0.104744i
$929$	40.2266			1.31979			0.659897	−	0.751356i	$-0.270600\pi$
$929$	40.2266			1.31979			0.659897	+	0.751356i	$0.270600\pi$
$930$	−5.56862	+	7.87341i	−0.182602	+	0.258179i
$931$	20.6320			0.676186
$932$	24.9434	+	8.10459i	0.817047	+	0.265475i
$933$	−50.0820	−	26.9944i	−1.63961	−	0.883755i
$934$	2.51257	+	1.82549i	0.0822137	+	0.0597317i
$935$	−2.69790	−	1.55763i	−0.0882309	−	0.0509401i
$936$	5.43208	+	3.48059i	0.177553	+	0.113767i
$937$	−4.68578	+	44.5822i	−0.153078	+	1.45644i	0.600787	+	0.799409i	$0.294854\pi$
$937$	−4.68578	+	44.5822i	−0.153078	+	1.45644i	−0.753865	+	0.657029i	$0.771813\pi$
$938$	8.40030	+	11.5620i	0.274280	+	0.377513i
$939$	29.0862	−	10.4002i	0.949193	−	0.339397i
$940$	0.287250	+	0.319023i	0.00936905	+	0.0104054i
$941$	31.3744	−	13.9688i	1.02278	−	0.455369i	0.174350	−	0.984684i	$-0.444218\pi$
$941$	31.3744	−	13.9688i	1.02278	−	0.455369i	0.848425	+	0.529315i	$0.177551\pi$
$942$	10.9099	+	22.6943i	0.355465	+	0.739421i
$943$	−2.34099	+	11.0135i	−0.0762330	+	0.358648i
$944$	1.54173	−	3.46278i	0.0501791	−	0.112704i
$945$	−3.13250	+	5.21863i	−0.101900	+	0.169762i
$946$	0.912128	+	2.80724i	0.0296558	+	0.0912713i
$947$	−47.4251	−	21.1150i	−1.54111	−	0.686145i	−0.552068	−	0.833799i	$-0.686161\pi$
$947$	−47.4251	−	21.1150i	−1.54111	−	0.686145i	−0.989039	+	0.147654i	$0.952828\pi$
$948$	−0.0430994	−	1.47369i	−0.00139980	−	0.0478632i
$949$	5.29183	−	1.12481i	0.171780	−	0.0365129i
$950$	−1.49110	−	3.34907i	−0.0483778	−	0.108658i
$951$	26.9417	−	39.4583i	0.873644	−	1.27952i
$952$	6.37786	−	0.670340i	0.206708	−	0.0217258i
$953$	39.1769	−	28.4637i	1.26906	−	0.922029i	0.269900	−	0.962888i	$-0.413009\pi$
$953$	39.1769	−	28.4637i	1.26906	−	0.922029i	0.999165	+	0.0408592i	$0.0130095\pi$
$954$	−13.3606	+	5.22263i	−0.432567	+	0.169089i
$955$	9.14337	+	15.8368i	0.295873	+	0.512466i
$956$	−7.39036	+	12.8005i	−0.239021	+	0.413997i
$957$	−9.41392	−	3.86569i	−0.304309	−	0.124960i
$958$	−13.3072	+	14.7792i	−0.429938	+	0.477494i
$959$	−1.71999	+	5.29360i	−0.0555415	+	0.170939i
$960$	0.409487	+	1.68295i	0.0132161	+	0.0543170i
$961$	4.25625	−	30.7064i	0.137299	−	0.990530i
$962$		−	3.31928i		−	0.107018i
$963$	−13.7238	+	2.25975i	−0.442244	+	0.0728196i
$964$	−2.24949	−	2.02545i	−0.0724513	−	0.0652355i
$965$	−9.30299	+	12.8045i	−0.299474	+	0.412191i
$966$	−13.2858	−	3.89130i	−0.427465	−	0.125200i
$967$	−3.54427	+	2.04629i	−0.113976	+	0.0658041i	−0.555904	−	0.831246i	$-0.687628\pi$
$967$	−3.54427	+	2.04629i	−0.113976	+	0.0658041i	0.441928	+	0.897050i	$0.354295\pi$
$968$	10.6177	+	1.11597i	0.341267	+	0.0358686i
$969$	−22.4961	+	26.5032i	−0.722679	+	0.851406i
$970$	−0.0869435	−	0.827212i	−0.00279159	−	0.0265602i
$971$	5.12260	−	4.61241i	0.164392	−	0.148019i	−0.582829	−	0.812595i	$-0.698054\pi$
$971$	5.12260	−	4.61241i	0.164392	−	0.148019i	0.747221	+	0.664576i	$0.231388\pi$
$972$	0.646237	+	15.5751i	0.0207281	+	0.499570i
$973$	−1.09446	−	5.14901i	−0.0350866	−	0.165070i
$974$	17.6396	+	3.74940i	0.565208	+	0.120139i
$975$	0.667586	−	3.66447i	0.0213799	−	0.117357i
$976$	−5.38598	+	1.75001i	−0.172401	+	0.0560165i
$977$	22.4794	−	7.30401i	0.719180	−	0.233676i	0.0735126	−	0.997294i	$-0.476579\pi$
$977$	22.4794	−	7.30401i	0.719180	−	0.233676i	0.645668	+	0.763618i	$0.276579\pi$
$978$	0.571545	−	3.13728i	0.0182760	−	0.100319i
$979$	−7.29337	−	1.55025i	−0.233097	−	0.0495463i
$980$	1.17011	+	5.50492i	0.0373777	+	0.175848i
$981$	1.88763	−	2.36039i	0.0602673	−	0.0753616i
$982$	−0.633921	+	0.570785i	−0.0202292	+	0.0182145i
$983$	2.49555	+	23.7435i	0.0795955	+	0.757301i	0.959416	+	0.281995i	$0.0909961\pi$
$983$	2.49555	+	23.7435i	0.0795955	+	0.757301i	−0.879820	+	0.475306i	$0.842337\pi$
$984$	−1.84951	+	2.17896i	−0.0589604	+	0.0694627i
$985$	18.0356	+	1.89562i	0.574662	+	0.0603994i
$986$	48.9573	−	28.2655i	1.55912	−	0.900157i
$987$	−0.835853	−	0.244813i	−0.0266055	−	0.00779250i
$988$	4.63397	−	6.37811i	0.147426	−	0.202915i
$989$	26.3043	+	23.6845i	0.836428	+	0.753123i
$990$	0.277349	+	1.68438i	0.00881472	+	0.0535331i
$991$		−	7.38263i		−	0.234517i	−0.993101	−	0.117259i	$-0.962589\pi$
$991$		−	7.38263i		−	0.234517i	0.993101	−	0.117259i	$-0.0374106\pi$
$992$	−3.65676	−	4.19859i	−0.116102	−	0.133305i
$993$	−1.57983	−	6.49296i	−0.0501345	−	0.206048i
$994$	3.68548	−	11.3427i	0.116896	−	0.359770i
$995$	−13.5661	+	15.0666i	−0.430073	+	0.477645i
$996$	−5.34680	−	2.19559i	−0.169420	−	0.0695699i
$997$	−18.3449	+	31.7743i	−0.580988	+	1.00630i	0.414374	+	0.910107i	$0.364000\pi$
$997$	−18.3449	+	31.7743i	−0.580988	+	1.00630i	−0.995363	+	0.0961947i	$0.969333\pi$
$998$	4.96049	+	8.59182i	0.157022	+	0.271969i
$999$	6.56771	−	4.60313i	0.207793	−	0.145637i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.br.a.761.7	yes	176
3.2	odd	2	inner	930.2.br.a.761.14	yes	176
31.11	odd	30	inner	930.2.br.a.11.14	yes	176
93.11	even	30	inner	930.2.br.a.11.7	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.br.a.11.7	✓	176	93.11	even	30	inner
930.2.br.a.11.14	yes	176	31.11	odd	30	inner
930.2.br.a.761.7	yes	176	1.1	even	1	trivial
930.2.br.a.761.14	yes	176	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.br (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(0.821805 - 1.52468i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.25273 + 1.19610i) q^{6} +(0.122441 - 1.16495i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-1.64927 - 2.50597i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{2} +(0.821805 - 1.52468i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.25273 + 1.19610i) q^{6} +(0.122441 - 1.16495i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(-1.64927 - 2.50597i) q^{9} +(-0.669131 - 0.743145i) q^{10} +(0.519826 - 0.231441i) q^{11} +(1.56104 - 0.750444i) q^{12} +(0.447115 - 2.10351i) q^{13} +(-0.476438 + 1.07010i) q^{14} +(1.47404 - 0.909505i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-5.00147 - 2.22680i) q^{17} +(0.794163 + 2.89298i) q^{18} +(3.58590 - 0.762207i) q^{19} +(0.406737 + 0.913545i) q^{20} +(-1.67555 - 1.14404i) q^{21} +(-0.565903 + 0.0594788i) q^{22} +(-5.52033 + 4.01076i) q^{23} +(-1.71653 + 0.231328i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-1.07525 + 1.86239i) q^{26} +(-5.17618 + 0.455184i) q^{27} +(0.783797 - 0.870495i) q^{28} +(3.19081 - 9.82031i) q^{29} +(-1.68295 + 0.409487i) q^{30} +(4.19859 - 3.65676i) q^{31} -1.00000i q^{32} +(0.0743226 - 0.982766i) q^{33} +(4.06856 + 3.66335i) q^{34} +(0.688512 - 0.947655i) q^{35} +(0.138685 - 2.99679i) q^{36} +(-1.33670 + 0.771745i) q^{37} +(-3.64593 - 0.383203i) q^{38} +(-2.83973 - 2.41038i) q^{39} +(-0.104528 - 0.994522i) q^{40} +(1.22627 - 1.10414i) q^{41} +(1.24001 + 1.60582i) q^{42} +(-1.07851 - 5.07399i) q^{43} +(0.556586 + 0.118306i) q^{44} +(-0.175325 - 2.99487i) q^{45} +(6.48954 - 2.10858i) q^{46} +(0.408277 - 0.132657i) q^{47} +(1.70400 + 0.310432i) q^{48} +(5.50492 + 1.17011i) q^{49} +(-0.207912 - 0.978148i) q^{50} +(-7.50538 + 5.79563i) q^{51} +(1.59814 - 1.43897i) q^{52} +(0.499825 + 4.75551i) q^{53} +(5.06350 + 1.16662i) q^{54} +(0.565903 + 0.0594788i) q^{55} +(-1.01443 + 0.585683i) q^{56} +(1.78480 - 6.09373i) q^{57} +(-6.06929 + 8.35366i) q^{58} +(-2.81688 - 2.53633i) q^{59} +(1.72712 + 0.130615i) q^{60} +5.66315i q^{61} +(-5.12309 + 2.18035i) q^{62} +(-3.12127 + 1.61448i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(1.43897 - 1.59814i) q^{65} +(-0.374376 + 0.911699i) q^{66} +(6.10033 - 10.5661i) q^{67} +(-2.73740 - 4.74131i) q^{68} +(1.57846 + 11.7128i) q^{69} +(-0.947655 + 0.688512i) q^{70} +(-10.1259 + 1.06427i) q^{71} +(-1.05796 + 2.80726i) q^{72} +(1.02323 + 2.29822i) q^{73} +(1.50976 - 0.320909i) q^{74} +(1.73131 - 0.0506337i) q^{75} +(3.34907 + 1.49110i) q^{76} +(-0.205970 - 0.633909i) q^{77} +(1.95589 + 3.16993i) q^{78} +(0.346214 - 0.777609i) q^{79} +(-0.207912 + 0.978148i) q^{80} +(-3.55980 + 8.26606i) q^{81} +(-1.50745 + 0.671159i) q^{82} +(-2.23296 - 2.47995i) q^{83} +(-0.683094 - 1.91041i) q^{84} +(-3.21800 - 4.42920i) q^{85} +(-0.542226 + 5.15893i) q^{86} +(-12.3506 - 12.9353i) q^{87} +(-0.492786 - 0.284510i) q^{88} +(-10.6012 - 7.70220i) q^{89} +(-0.758722 + 2.90247i) q^{90} +(-2.39574 - 0.778422i) q^{91} -6.82351 q^{92} +(-2.12495 - 9.40662i) q^{93} -0.429288 q^{94} +(3.48659 + 1.13286i) q^{95} +(-1.52468 - 0.821805i) q^{96} +(0.672915 + 0.488901i) q^{97} +(-4.87391 - 2.81395i) q^{98} +(-1.43732 - 0.920960i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9	\( 176 q + 44 q^{4} + 4 q^{7} - 4 q^{9} - 22 q^{10} - 38 q^{13} - 44 q^{16} + 12 q^{18} + 8 q^{19} - 18 q^{21} - 4 q^{22} + 88 q^{25} - 90 q^{27} + 36 q^{28} + 24 q^{31} + 18 q^{33} + 14 q^{34} + 4 q^{36} - 42 q^{37} - 42 q^{39} + 22 q^{40} - 12 q^{42} - 34 q^{43} - 8 q^{45} + 10 q^{46} + 22 q^{49} + 26 q^{51} - 2 q^{52} + 4 q^{55} + 114 q^{57} + 32 q^{63} + 44 q^{64} - 42 q^{66} + 20 q^{67} + 16 q^{69} + 8 q^{70} - 12 q^{72} - 28 q^{73} + 12 q^{76} - 92 q^{78} - 56 q^{79} - 124 q^{81} - 32 q^{82} - 12 q^{84} - 36 q^{87} - 6 q^{88} + 24 q^{90} - 140 q^{91} - 104 q^{93} - 36 q^{94} + 88 q^{97} - 60 q^{99}+O(q^{100}) \) 176 * q + 44 * q^4 + 4 * q^7 - 4 * q^9 - 22 * q^10 - 38 * q^13 - 44 * q^16 + 12 * q^18 + 8 * q^19 - 18 * q^21 - 4 * q^22 + 88 * q^25 - 90 * q^27 + 36 * q^28 + 24 * q^31 + 18 * q^33 + 14 * q^34 + 4 * q^36 - 42 * q^37 - 42 * q^39 + 22 * q^40 - 12 * q^42 - 34 * q^43 - 8 * q^45 + 10 * q^46 + 22 * q^49 + 26 * q^51 - 2 * q^52 + 4 * q^55 + 114 * q^57 + 32 * q^63 + 44 * q^64 - 42 * q^66 + 20 * q^67 + 16 * q^69 + 8 * q^70 - 12 * q^72 - 28 * q^73 + 12 * q^76 - 92 * q^78 - 56 * q^79 - 124 * q^81 - 32 * q^82 - 12 * q^84 - 36 * q^87 - 6 * q^88 + 24 * q^90 - 140 * q^91 - 104 * q^93 - 36 * q^94 + 88 * q^97 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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