LMFDB - Embedded newform 930.2.bg.e.421.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(121,930)]

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([0, 0, 16]))

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bg (of order $15$, 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:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 27x^{14} + 345x^{12} - 2652x^{10} + 13244x^{8} - 43398x^{6} + 89940x^{4} - 107433x^{2} + 58081 $ x^16 - 27x^14 + 345x^12 - 2652x^10 + 13244x^8 - 43398x^6 + 89940x^4 - 107433*x^2 + 58081
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			421.1
Root			$1.37050 + 0.406737i$ of defining polynomial
Character	$\chi$	$=$	930.421
Dual form			930.2.bg.e.391.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(-0.913545 + 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.80375 - 2.00327i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(-0.913545 + 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.80375 - 2.00327i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +(0.913545 + 0.406737i) q^{10} +(-3.30831 + 0.703202i) q^{11} +(0.104528 + 0.994522i) q^{12} +(-0.0272435 + 0.259204i) q^{13} +(-2.63676 - 0.560460i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-6.17732 - 1.31303i) q^{17} +(0.104528 - 0.994522i) q^{18} +(0.114514 + 1.08953i) q^{19} +(0.978148 - 0.207912i) q^{20} +(2.46261 + 1.09642i) q^{21} +(-2.26314 + 2.51348i) q^{22} +(-1.53548 - 4.72573i) q^{23} +(0.669131 + 0.743145i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.130316 + 0.225714i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-2.46261 + 1.09642i) q^{28} +(-0.0165861 + 0.0120505i) q^{29} -1.00000 q^{30} +(0.423540 - 5.55163i) q^{31} -1.00000 q^{32} +(2.73627 - 1.98802i) q^{33} +(-5.76934 + 2.56868i) q^{34} +(0.833006 - 2.56373i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-5.17056 + 8.95567i) q^{37} +(0.733052 + 0.814137i) q^{38} +(-0.0805398 - 0.247876i) q^{39} +(0.669131 - 0.743145i) q^{40} +(0.831317 + 0.370126i) q^{41} +(2.63676 - 0.560460i) q^{42} +(-0.399217 - 3.79830i) q^{43} +(-0.353538 + 3.36369i) q^{44} +(0.978148 + 0.207912i) q^{45} +(-4.01995 - 2.92066i) q^{46} +(-5.27939 - 3.83570i) q^{47} +(0.978148 + 0.207912i) q^{48} +(-0.0278672 + 0.265139i) q^{49} +(0.104528 + 0.994522i) q^{50} +(6.17732 - 1.31303i) q^{51} +(0.238099 + 0.106009i) q^{52} +(-0.960500 + 1.06674i) q^{53} +(0.309017 + 0.951057i) q^{54} +(-2.26314 - 2.51348i) q^{55} +(-1.34783 + 2.33451i) q^{56} +(-0.547765 - 0.948756i) q^{57} +(-0.00633532 + 0.0194981i) q^{58} +(-5.48469 + 2.44194i) q^{59} +(-0.809017 + 0.587785i) q^{60} -13.5780 q^{61} +(-2.92052 - 4.74031i) q^{62} -2.69566 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-0.238099 + 0.106009i) q^{65} +(1.04516 - 3.21668i) q^{66} +(-2.25178 - 3.90020i) q^{67} +(-3.15766 + 5.46924i) q^{68} +(3.32486 + 3.69263i) q^{69} +(-0.833006 - 2.56373i) q^{70} +(4.08617 - 4.53815i) q^{71} +(-0.913545 - 0.406737i) q^{72} +(13.4190 - 2.85230i) q^{73} +(1.08094 + 10.2845i) q^{74} +(0.104528 - 0.994522i) q^{75} +(1.07159 + 0.227773i) q^{76} +(7.37606 + 5.35902i) q^{77} +(-0.210856 - 0.153196i) q^{78} +(13.3408 + 2.83568i) q^{79} +(0.104528 - 0.994522i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(0.890104 - 0.189197i) q^{82} +(-12.4475 - 5.54197i) q^{83} +(1.80375 - 2.00327i) q^{84} +(-1.95154 - 6.00623i) q^{85} +(-2.55556 - 2.83823i) q^{86} +(0.0102508 - 0.0177548i) q^{87} +(1.69111 + 2.92908i) q^{88} +(-2.76036 + 8.49553i) q^{89} +(0.913545 - 0.406737i) q^{90} +(0.568396 - 0.412964i) q^{91} -4.96893 q^{92} +(1.87113 + 5.24394i) q^{93} -6.52568 q^{94} +(-0.886302 + 0.643936i) q^{95} +(0.913545 - 0.406737i) q^{96} +(4.95656 - 15.2547i) q^{97} +(0.133300 + 0.230882i) q^{98} +(-1.69111 + 2.92908i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} - 5 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 - 5 * q^7 + 4 * q^8 + 2 * q^9	\( 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} - 5 q^{7} + 4 q^{8} + 2 q^{9} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 4 q^{13} - 10 q^{14} - 4 q^{15} - 4 q^{16} - 22 q^{17} - 2 q^{18} - 3 q^{19} - 2 q^{20} - 11 q^{22} + 9 q^{23} + 2 q^{24} - 8 q^{25} + 11 q^{26} + 4 q^{27} - 3 q^{29} - 16 q^{30} - 15 q^{31} - 16 q^{32} - 8 q^{33} - 8 q^{34} + 5 q^{35} - 8 q^{36} - 17 q^{37} - 2 q^{38} + 3 q^{39} + 2 q^{40} + 28 q^{41} + 10 q^{42} - 28 q^{43} - 19 q^{44} - 2 q^{45} - 9 q^{46} + 9 q^{47} - 2 q^{48} + 19 q^{49} - 2 q^{50} + 22 q^{51} + 4 q^{52} + 2 q^{53} - 4 q^{54} - 11 q^{55} + 5 q^{56} - 2 q^{57} - 12 q^{58} + 24 q^{59} - 4 q^{60} - 40 q^{61} - 25 q^{62} + 10 q^{63} - 4 q^{64} - 4 q^{65} - 7 q^{66} - q^{67} - 2 q^{68} - 3 q^{69} - 5 q^{70} + 39 q^{71} - 2 q^{72} + 81 q^{73} - 8 q^{74} - 2 q^{75} + 2 q^{76} + 28 q^{77} - 8 q^{78} + 64 q^{79} - 2 q^{80} + 2 q^{81} + 32 q^{82} - 40 q^{83} + 5 q^{84} - 14 q^{85} + 13 q^{86} - 9 q^{87} - q^{88} - 7 q^{89} + 2 q^{90} - 46 q^{91} - 36 q^{92} - 20 q^{93} - 4 q^{94} - 6 q^{95} + 2 q^{96} - 17 q^{97} - 9 q^{98} + q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 - 5 * q^7 + 4 * q^8 + 2 * q^9 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 4 * q^13 - 10 * q^14 - 4 * q^15 - 4 * q^16 - 22 * q^17 - 2 * q^18 - 3 * q^19 - 2 * q^20 - 11 * q^22 + 9 * q^23 + 2 * q^24 - 8 * q^25 + 11 * q^26 + 4 * q^27 - 3 * q^29 - 16 * q^30 - 15 * q^31 - 16 * q^32 - 8 * q^33 - 8 * q^34 + 5 * q^35 - 8 * q^36 - 17 * q^37 - 2 * q^38 + 3 * q^39 + 2 * q^40 + 28 * q^41 + 10 * q^42 - 28 * q^43 - 19 * q^44 - 2 * q^45 - 9 * q^46 + 9 * q^47 - 2 * q^48 + 19 * q^49 - 2 * q^50 + 22 * q^51 + 4 * q^52 + 2 * q^53 - 4 * q^54 - 11 * q^55 + 5 * q^56 - 2 * q^57 - 12 * q^58 + 24 * q^59 - 4 * q^60 - 40 * q^61 - 25 * q^62 + 10 * q^63 - 4 * q^64 - 4 * q^65 - 7 * q^66 - q^67 - 2 * q^68 - 3 * q^69 - 5 * q^70 + 39 * q^71 - 2 * q^72 + 81 * q^73 - 8 * q^74 - 2 * q^75 + 2 * q^76 + 28 * q^77 - 8 * q^78 + 64 * q^79 - 2 * q^80 + 2 * q^81 + 32 * q^82 - 40 * q^83 + 5 * q^84 - 14 * q^85 + 13 * q^86 - 9 * q^87 - q^88 - 7 * q^89 + 2 * q^90 - 46 * q^91 - 36 * q^92 - 20 * q^93 - 4 * q^94 - 6 * q^95 + 2 * q^96 - 17 * q^97 - 9 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{13}{15}\right)$

Coefficient data

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

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

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

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	−0.913545	+	0.406737i	−0.527436	+	0.234830i
$3$	−0.913545	+	0.406737i	−0.527436	+	0.234830i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−1.80375	−	2.00327i	−0.681754	−	0.757164i	0.298607	−	0.954376i	$-0.403478\pi$
$7$	−1.80375	−	2.00327i	−0.681754	−	0.757164i	−0.980361	+	0.197212i	$0.936811\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	0.669131	−	0.743145i	0.223044	−	0.247715i
$10$	0.913545	+	0.406737i	0.288888	+	0.128621i
$11$	−3.30831	+	0.703202i	−0.997492	+	0.212023i	−0.677600	−	0.735431i	$-0.736980\pi$
$11$	−3.30831	+	0.703202i	−0.997492	+	0.212023i	−0.319892	+	0.947454i	$0.603647\pi$
$12$	0.104528	+	0.994522i	0.0301748	+	0.287094i
$13$	−0.0272435	+	0.259204i	−0.00755598	+	0.0718903i	−0.997650	−	0.0685150i	$-0.978174\pi$
$13$	−0.0272435	+	0.259204i	−0.00755598	+	0.0718903i	0.990094	+	0.140405i	$0.0448406\pi$
$14$	−2.63676	−	0.560460i	−0.704703	−	0.149789i
$15$	−0.809017	−	0.587785i	−0.208887	−	0.151765i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−6.17732	−	1.31303i	−1.49822	−	0.318457i	−0.615418	−	0.788201i	$-0.711013\pi$
$17$	−6.17732	−	1.31303i	−1.49822	−	0.318457i	−0.882803	+	0.469744i	$0.844346\pi$
$18$	0.104528	−	0.994522i	0.0246376	−	0.234411i
$19$	0.114514	+	1.08953i	0.0262713	+	0.249955i	0.999774	+	0.0212776i	$0.00677339\pi$
$19$	0.114514	+	1.08953i	0.0262713	+	0.249955i	−0.973502	+	0.228677i	$0.926560\pi$
$20$	0.978148	−	0.207912i	0.218720	−	0.0464905i
$21$	2.46261	+	1.09642i	0.537386	+	0.239260i
$22$	−2.26314	+	2.51348i	−0.482504	+	0.535875i
$23$	−1.53548	−	4.72573i	−0.320170	−	0.985383i	−0.973574	−	0.228373i	$-0.926659\pi$
$23$	−1.53548	−	4.72573i	−0.320170	−	0.985383i	0.653403	−	0.757010i	$-0.273341\pi$
$24$	0.669131	+	0.743145i	0.136586	+	0.151694i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.130316	+	0.225714i	0.0255571	+	0.0442662i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	−2.46261	+	1.09642i	−0.465390	+	0.207205i
$29$	−0.0165861	+	0.0120505i	−0.00307996	+	0.00223772i	−0.589324	−	0.807897i	$-0.700606\pi$
$29$	−0.0165861	+	0.0120505i	−0.00307996	+	0.00223772i	0.586244	+	0.810134i	$0.300606\pi$
$30$	−1.00000			−0.182574
$31$	0.423540	−	5.55163i	0.0760700	−	0.997102i
$31$	0.423540	−	5.55163i	0.0760700	−	0.997102i
$32$	−1.00000			−0.176777
$33$	2.73627	−	1.98802i	0.476323	−	0.346069i
$34$	−5.76934	+	2.56868i	−0.989434	+	0.440524i
$35$	0.833006	−	2.56373i	0.140804	−	0.433349i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−5.17056	+	8.95567i	−0.850034	+	1.47230i	0.0311424	+	0.999515i	$0.490085\pi$
$37$	−5.17056	+	8.95567i	−0.850034	+	1.47230i	−0.881177	+	0.472787i	$0.843248\pi$
$38$	0.733052	+	0.814137i	0.118917	+	0.132070i
$39$	−0.0805398	−	0.247876i	−0.0128967	−	0.0396919i
$40$	0.669131	−	0.743145i	0.105799	−	0.117502i
$41$	0.831317	+	0.370126i	0.129830	+	0.0578040i	0.470623	−	0.882334i	$-0.344029\pi$
$41$	0.831317	+	0.370126i	0.129830	+	0.0578040i	−0.340794	+	0.940138i	$0.610696\pi$
$42$	2.63676	−	0.560460i	0.406860	−	0.0864808i
$43$	−0.399217	−	3.79830i	−0.0608801	−	0.579235i	−0.981858	−	0.189620i	$-0.939275\pi$
$43$	−0.399217	−	3.79830i	−0.0608801	−	0.579235i	0.920978	−	0.389616i	$-0.127392\pi$
$44$	−0.353538	+	3.36369i	−0.0532978	+	0.507095i
$45$	0.978148	+	0.207912i	0.145814	+	0.0309936i
$46$	−4.01995	−	2.92066i	−0.592709	−	0.430628i
$47$	−5.27939	−	3.83570i	−0.770078	−	0.559494i	0.131907	−	0.991262i	$-0.457890\pi$
$47$	−5.27939	−	3.83570i	−0.770078	−	0.559494i	−0.901985	+	0.431768i	$0.857890\pi$
$48$	0.978148	+	0.207912i	0.141183	+	0.0300095i
$49$	−0.0278672	+	0.265139i	−0.00398103	+	0.0378770i
$50$	0.104528	+	0.994522i	0.0147826	+	0.140647i
$51$	6.17732	−	1.31303i	0.864998	−	0.183861i
$52$	0.238099	+	0.106009i	0.0330184	+	0.0147008i
$53$	−0.960500	+	1.06674i	−0.131935	+	0.146528i	−0.805492	−	0.592607i	$-0.798099\pi$
$53$	−0.960500	+	1.06674i	−0.131935	+	0.146528i	0.673557	+	0.739135i	$0.264766\pi$
$54$	0.309017	+	0.951057i	0.0420519	+	0.129422i
$55$	−2.26314	−	2.51348i	−0.305162	−	0.338917i
$56$	−1.34783	+	2.33451i	−0.180112	+	0.311962i
$57$	−0.547765	−	0.948756i	−0.0725532	−	0.125666i
$58$	−0.00633532	+	0.0194981i	−0.000831868	+	0.00256023i
$59$	−5.48469	+	2.44194i	−0.714046	+	0.317914i	−0.731412	−	0.681935i	$-0.761139\pi$
$59$	−5.48469	+	2.44194i	−0.714046	+	0.317914i	0.0173663	+	0.999849i	$0.494472\pi$
$60$	−0.809017	+	0.587785i	−0.104444	+	0.0758827i
$61$	−13.5780			−1.73849			−0.869244	−	0.494384i	$-0.835394\pi$
$61$	−13.5780			−1.73849			−0.869244	+	0.494384i	$0.835394\pi$
$62$	−2.92052	−	4.74031i	−0.370906	−	0.602021i
$63$	−2.69566			−0.339622
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−0.238099	+	0.106009i	−0.0295326	+	0.0131488i
$66$	1.04516	−	3.21668i	0.128651	−	0.395946i
$67$	−2.25178	−	3.90020i	−0.275099	−	0.476485i	0.695061	−	0.718951i	$-0.255377\pi$
$67$	−2.25178	−	3.90020i	−0.275099	−	0.476485i	−0.970160	+	0.242465i	$0.922044\pi$
$68$	−3.15766	+	5.46924i	−0.382923	+	0.663242i
$69$	3.32486	+	3.69263i	0.400266	+	0.444541i
$70$	−0.833006	−	2.56373i	−0.0995632	−	0.306424i
$71$	4.08617	−	4.53815i	0.484939	−	0.538580i	−0.450168	−	0.892944i	$-0.648636\pi$
$71$	4.08617	−	4.53815i	0.484939	−	0.538580i	0.935108	+	0.354364i	$0.115303\pi$
$72$	−0.913545	−	0.406737i	−0.107662	−	0.0479344i
$73$	13.4190	−	2.85230i	1.57058	−	0.333836i	0.661330	−	0.750095i	$-0.269992\pi$
$73$	13.4190	−	2.85230i	1.57058	−	0.333836i	0.909246	+	0.416259i	$0.136659\pi$
$74$	1.08094	+	10.2845i	0.125657	+	1.19554i
$75$	0.104528	−	0.994522i	0.0120699	−	0.114837i
$76$	1.07159	+	0.227773i	0.122920	+	0.0261274i
$77$	7.37606	+	5.35902i	0.840580	+	0.610717i
$78$	−0.210856	−	0.153196i	−0.0238747	−	0.0173460i
$79$	13.3408	+	2.83568i	1.50096	+	0.319038i	0.883824	−	0.467820i	$-0.154960\pi$
$79$	13.3408	+	2.83568i	1.50096	+	0.319038i	0.617134	+	0.786858i	$0.288294\pi$
$80$	0.104528	−	0.994522i	0.0116866	−	0.111191i
$81$	−0.104528	−	0.994522i	−0.0116143	−	0.110502i
$82$	0.890104	−	0.189197i	0.0982955	−	0.0208934i
$83$	−12.4475	−	5.54197i	−1.36629	−	0.608310i	−0.413098	−	0.910687i	$-0.635553\pi$
$83$	−12.4475	−	5.54197i	−1.36629	−	0.608310i	−0.953189	+	0.302376i	$0.902220\pi$
$84$	1.80375	−	2.00327i	0.196805	−	0.218574i
$85$	−1.95154	−	6.00623i	−0.211675	−	0.651468i
$86$	−2.55556	−	2.83823i	−0.275573	−	0.306055i
$87$	0.0102508	−	0.0177548i	0.00109900	−	0.00190352i
$88$	1.69111	+	2.92908i	0.180273	+	0.312241i
$89$	−2.76036	+	8.49553i	−0.292598	+	0.900524i	0.691420	+	0.722453i	$0.256986\pi$
$89$	−2.76036	+	8.49553i	−0.292598	+	0.900524i	−0.984018	+	0.178071i	$0.943014\pi$
$90$	0.913545	−	0.406737i	0.0962961	−	0.0428738i
$91$	0.568396	−	0.412964i	0.0595841	−	0.0432904i
$92$	−4.96893			−0.518046
$93$	1.87113	+	5.24394i	0.194027	+	0.543771i
$94$	−6.52568			−0.673073
$95$	−0.886302	+	0.643936i	−0.0909327	+	0.0660664i
$96$	0.913545	−	0.406737i	0.0932383	−	0.0415124i
$97$	4.95656	−	15.2547i	0.503263	−	1.54888i	−0.300410	−	0.953810i	$-0.597123\pi$
$97$	4.95656	−	15.2547i	0.503263	−	1.54888i	0.803672	−	0.595072i	$-0.202877\pi$
$98$	0.133300	+	0.230882i	0.0134653	+	0.0233226i
$99$	−1.69111	+	2.92908i	−0.169963	+	0.294384i
$100$	0.669131	+	0.743145i	0.0669131	+	0.0743145i
$101$	4.51382	+	13.8921i	0.449142	+	1.38232i	0.877877	+	0.478886i	$0.158959\pi$
$101$	4.51382	+	13.8921i	0.449142	+	1.38232i	−0.428735	+	0.903430i	$0.641041\pi$
$102$	4.22578	−	4.69320i	0.418415	−	0.464696i
$103$	5.64634	+	2.51391i	0.556350	+	0.247703i	0.665597	−	0.746312i	$-0.268177\pi$
$103$	5.64634	+	2.51391i	0.556350	+	0.247703i	−0.109246	+	0.994015i	$0.534844\pi$
$104$	0.254937	−	0.0541885i	0.0249986	−	0.00531362i
$105$	0.281774	+	2.68090i	0.0274983	+	0.261629i
$106$	−0.150045	+	1.42758i	−0.0145736	+	0.138659i
$107$	−2.15561	−	0.458189i	−0.208391	−	0.0442948i	0.102533	−	0.994730i	$-0.467305\pi$
$107$	−2.15561	−	0.458189i	−0.208391	−	0.0442948i	−0.310924	+	0.950435i	$0.600638\pi$
$108$	0.809017	+	0.587785i	0.0778477	+	0.0565597i
$109$	14.8446	+	10.7852i	1.42186	+	1.03304i	0.991462	+	0.130397i	$0.0416253\pi$
$109$	14.8446	+	10.7852i	1.42186	+	1.03304i	0.430394	+	0.902641i	$0.358375\pi$
$110$	−3.30831	−	0.703202i	−0.315435	−	0.0670477i
$111$	1.08094	−	10.2845i	0.102598	−	0.976158i
$112$	0.281774	+	2.68090i	0.0266251	+	0.253321i
$113$	−1.00444	+	0.213500i	−0.0944895	+	0.0200844i	−0.254914	−	0.966964i	$-0.582047\pi$
$113$	−1.00444	+	0.213500i	−0.0944895	+	0.0200844i	0.160424	+	0.987048i	$0.448714\pi$
$114$	−1.00082	−	0.445592i	−0.0937350	−	0.0417335i
$115$	3.32486	−	3.69263i	0.310045	−	0.344340i
$116$	0.00633532	+	0.0194981i	0.000588220	+	0.00181035i
$117$	0.174397	+	0.193687i	0.0161230	+	0.0179064i
$118$	−3.00187	+	5.19939i	−0.276345	+	0.478643i
$119$	8.51200	+	14.7432i	0.780294	+	1.35151i
$120$	−0.309017	+	0.951057i	−0.0282093	+	0.0868192i
$121$	0.401395	−	0.178713i	0.0364905	−	0.0162466i
$122$	−10.9848	+	7.98096i	−0.994522	+	0.722562i
$123$	−0.909989			−0.0820510
$124$	−5.14903	−	2.11836i	−0.462397	−	0.190234i
$125$	−1.00000			−0.0894427
$126$	−2.18084	+	1.58447i	−0.194284	+	0.141156i
$127$	−7.03065	+	3.13025i	−0.623870	+	0.277765i	−0.694226	−	0.719757i	$-0.744253\pi$
$127$	−7.03065	+	3.13025i	−0.623870	+	0.277765i	0.0703561	+	0.997522i	$0.477586\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	1.90961	+	3.30754i	0.168132	+	0.291213i
$130$	−0.130316	+	0.225714i	−0.0114295	+	0.0197964i
$131$	1.33289	+	1.48032i	0.116455	+	0.129336i	0.798553	−	0.601924i	$-0.205599\pi$
$131$	1.33289	+	1.48032i	0.116455	+	0.129336i	−0.682098	+	0.731261i	$0.738932\pi$
$132$	−1.04516	−	3.21668i	−0.0909697	−	0.279976i
$133$	1.97606	−	2.19464i	0.171346	−	0.190299i
$134$	−4.11421	−	1.83176i	−0.355414	−	0.158240i
$135$	−0.978148	+	0.207912i	−0.0841855	+	0.0178942i
$136$	0.660132	+	6.28073i	0.0566058	+	0.538568i
$137$	0.316529	−	3.01157i	0.0270429	−	0.257296i	−0.972645	−	0.232298i	$-0.925375\pi$
$137$	0.316529	−	3.01157i	0.0270429	−	0.257296i	0.999688	−	0.0249979i	$-0.00795790\pi$
$138$	4.86034	+	1.03310i	0.413740	+	0.0879431i
$139$	−2.27520	−	1.65303i	−0.192980	−	0.140208i	0.487100	−	0.873346i	$-0.338055\pi$
$139$	−2.27520	−	1.65303i	−0.192980	−	0.140208i	−0.680080	+	0.733138i	$0.738055\pi$
$140$	−2.18084	−	1.58447i	−0.184314	−	0.133912i
$141$	6.38308	+	1.35677i	0.537552	+	0.114260i
$142$	0.638323	−	6.07324i	0.0535669	−	0.509655i
$143$	−0.0921433	−	0.876685i	−0.00770541	−	0.0733121i
$144$	−0.978148	+	0.207912i	−0.0815123	+	0.0173260i
$145$	−0.0187291	−	0.00833872i	−0.00155537	−	0.000692493i
$146$	9.17967	−	10.1951i	0.759715	−	0.843749i
$147$	−0.0823838	−	0.253551i	−0.00679490	−	0.0209126i
$148$	6.91955	+	7.68494i	0.568784	+	0.631698i
$149$	−0.308225	+	0.533862i	−0.0252508	+	0.0437357i	−0.878375	−	0.477973i	$-0.841372\pi$
$149$	−0.308225	+	0.533862i	−0.0252508	+	0.0437357i	0.853124	+	0.521708i	$0.174705\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	7.18376	−	22.1093i	0.584606	−	1.79923i	−0.0162392	−	0.999868i	$-0.505169\pi$
$151$	7.18376	−	22.1093i	0.584606	−	1.79923i	0.600846	−	0.799365i	$-0.294831\pi$
$152$	1.00082	−	0.445592i	0.0811769	−	0.0361423i
$153$	−5.10921	+	3.71206i	−0.413055	+	0.300102i
$154$	9.11731			0.734694
$155$	5.01962	−	2.40902i	0.403186	−	0.193497i
$156$	−0.260632			−0.0208673
$157$	14.1364	−	10.2707i	1.12821	−	0.819692i	0.142776	−	0.989755i	$-0.454397\pi$
$157$	14.1364	−	10.2707i	1.12821	−	0.819692i	0.985433	+	0.170064i	$0.0543973\pi$
$158$	12.4597	−	5.54742i	0.991241	−	0.441329i
$159$	0.443577	−	1.36519i	0.0351779	−	0.108267i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−6.69728	+	11.6000i	−0.527819	+	0.914210i
$162$	−0.669131	−	0.743145i	−0.0525719	−	0.0583870i
$163$	2.31707	+	7.13121i	0.181487	+	0.558560i	0.999870	−	0.0161134i	$-0.00512926\pi$
$163$	2.31707	+	7.13121i	0.181487	+	0.558560i	−0.818383	+	0.574673i	$0.805129\pi$
$164$	0.608902	−	0.676254i	0.0475472	−	0.0528066i
$165$	3.08981	+	1.37567i	0.240541	+	0.107096i
$166$	−13.3277	+	2.83289i	−1.03443	+	0.219875i
$167$	−0.951729	−	9.05510i	−0.0736470	−	0.700704i	−0.967590	−	0.252525i	$-0.918739\pi$
$167$	−0.951729	−	9.05510i	−0.0736470	−	0.700704i	0.893943	−	0.448180i	$-0.147928\pi$
$168$	0.281774	−	2.68090i	0.0217393	−	0.206836i
$169$	12.6495	+	2.68873i	0.973036	+	0.206825i
$170$	−5.10921	−	3.71206i	−0.391858	−	0.284702i
$171$	0.886302	+	0.643936i	0.0677772	+	0.0492430i
$172$	−3.73576	−	0.794061i	−0.284849	−	0.0605466i
$173$	−0.357745	+	3.40371i	−0.0271988	+	0.258780i	0.972470	+	0.233030i	$0.0748640\pi$
$173$	−0.357745	+	3.40371i	−0.0271988	+	0.258780i	−0.999668	+	0.0257498i	$0.991803\pi$
$174$	−0.00214299	−	0.0203892i	−0.000162460	−	0.00154570i
$175$	2.63676	−	0.560460i	0.199320	−	0.0423668i
$176$	3.08981	+	1.37567i	0.232903	+	0.103695i
$177$	4.01729	−	4.46165i	0.301958	−	0.335358i
$178$	2.76036	+	8.49553i	0.206898	+	0.636767i
$179$	7.98177	+	8.86466i	0.596586	+	0.662575i	0.963509	−	0.267676i	$-0.0862556\pi$
$179$	7.98177	+	8.86466i	0.596586	+	0.662575i	−0.366923	+	0.930251i	$0.619589\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	−7.19740	−	12.4663i	−0.534979	−	0.926610i	−0.999164	−	0.0408722i	$-0.986986\pi$
$181$	−7.19740	−	12.4663i	−0.534979	−	0.926610i	0.464186	−	0.885738i	$-0.346347\pi$
$182$	0.217108	−	0.668190i	0.0160931	−	0.0495295i
$183$	12.4041	−	5.52268i	0.916940	−	0.408248i
$184$	−4.01995	+	2.92066i	−0.296354	+	0.215314i
$185$	−10.3411			−0.760294
$186$	4.59608	+	3.14261i	0.337001	+	0.230428i
$187$	21.3598			1.56198
$188$	−5.27939	+	3.83570i	−0.385039	+	0.279747i
$189$	2.46261	−	1.09642i	0.179129	−	0.0797532i
$190$	−0.338537	+	1.04191i	−0.0245601	+	0.0755881i
$191$	4.56072	+	7.89941i	0.330002	+	0.571581i	0.982512	−	0.186200i	$-0.0596171\pi$
$191$	4.56072	+	7.89941i	0.330002	+	0.571581i	−0.652509	+	0.757781i	$0.726284\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−6.96562	−	7.73610i	−0.501396	−	0.556857i	0.438317	−	0.898820i	$-0.355575\pi$
$193$	−6.96562	−	7.73610i	−0.501396	−	0.556857i	−0.939713	+	0.341964i	$0.888908\pi$
$194$	−4.95656	−	15.2547i	−0.355860	−	1.09523i
$195$	0.174397	−	0.193687i	0.0124888	−	0.0138702i
$196$	0.243551	+	0.108436i	0.0173965	+	0.00774541i
$197$	18.0162	−	3.82946i	1.28360	−	0.272838i	0.484902	−	0.874568i	$-0.338855\pi$
$197$	18.0162	−	3.82946i	1.28360	−	0.272838i	0.798699	+	0.601730i	$0.205522\pi$
$198$	0.353538	+	3.36369i	0.0251248	+	0.239047i
$199$	0.294480	−	2.80179i	0.0208751	−	0.198613i	−0.979114	−	0.203313i	$-0.934829\pi$
$199$	0.294480	−	2.80179i	0.0208751	−	0.198613i	0.999989	+	0.00469933i	$0.00149585\pi$
$200$	0.978148	+	0.207912i	0.0691655	+	0.0147016i
$201$	3.64346	+	2.64713i	0.256990	+	0.186714i
$202$	11.8173	+	8.58579i	0.831465	+	0.604094i
$203$	0.0540575	+	0.0114903i	0.00379410	+	0.000806460i
$204$	0.660132	−	6.28073i	0.0462185	−	0.439739i
$205$	0.0951198	+	0.905004i	0.00664345	+	0.0632082i
$206$	6.04562	−	1.28504i	0.421219	−	0.0895328i
$207$	−4.53934	−	2.02104i	−0.315506	−	0.140472i
$208$	0.174397	−	0.193687i	0.0120923	−	0.0134298i
$209$	−1.14501	−	3.52397i	−0.0792017	−	0.243758i
$210$	1.80375	+	2.00327i	0.124471	+	0.138239i
$211$	9.10227	−	15.7656i	0.626626	−	1.08535i	−0.361598	−	0.932334i	$-0.617769\pi$
$211$	9.10227	−	15.7656i	0.626626	−	1.08535i	0.988224	−	0.153014i	$-0.0488979\pi$
$212$	0.717722	+	1.24313i	0.0492934	+	0.0853786i
$213$	−1.88707	+	5.80781i	−0.129300	+	0.397944i
$214$	−2.01324	+	0.896353i	−0.137622	+	0.0612734i
$215$	3.08981	−	2.24488i	0.210724	−	0.153100i
$216$	1.00000			0.0680414
$217$	−11.8854	+	9.16530i	−0.806831	+	0.622181i
$218$	18.3489			1.24275
$219$	−11.0987	+	8.06371i	−0.749983	+	0.544895i
$220$	−3.08981	+	1.37567i	−0.208315	+	0.0927477i
$221$	0.508635	−	1.56542i	0.0342145	−	0.105301i
$222$	−5.17056	−	8.95567i	−0.347025	−	0.601065i
$223$	−6.01720	+	10.4221i	−0.402941	+	0.697915i	−0.994079	−	0.108656i	$-0.965345\pi$
$223$	−6.01720	+	10.4221i	−0.402941	+	0.697915i	0.591138	+	0.806570i	$0.298679\pi$
$224$	1.80375	+	2.00327i	0.120518	+	0.133849i
$225$	0.309017	+	0.951057i	0.0206011	+	0.0634038i
$226$	−0.687115	+	0.763118i	−0.0457062	+	0.0507619i
$227$	−0.660992	−	0.294293i	−0.0438716	−	0.0195329i	0.384684	−	0.923049i	$-0.374311\pi$
$227$	−0.660992	−	0.294293i	−0.0438716	−	0.0195329i	−0.428555	+	0.903516i	$0.640977\pi$
$228$	−1.07159	+	0.227773i	−0.0709678	+	0.0150847i
$229$	0.619126	+	5.89059i	0.0409130	+	0.389261i	0.995748	+	0.0921234i	$0.0293654\pi$
$229$	0.619126	+	5.89059i	0.0409130	+	0.389261i	−0.954835	+	0.297138i	$0.903968\pi$
$230$	0.519394	−	4.94171i	0.0342478	−	0.325846i
$231$	−8.91808	−	1.89560i	−0.586766	−	0.124721i
$232$	0.0165861	+	0.0120505i	0.00108893	+	0.000791154i
$233$	0.0235404	+	0.0171031i	0.00154218	+	0.00112046i	0.588556	−	0.808456i	$-0.299697\pi$
$233$	0.0235404	+	0.0171031i	0.00154218	+	0.00112046i	−0.587014	+	0.809577i	$0.699697\pi$
$234$	0.254937	+	0.0541885i	0.0166657	+	0.00354241i
$235$	0.682120	−	6.48993i	0.0444966	−	0.423357i
$236$	0.627562	+	5.97085i	0.0408508	+	0.388670i
$237$	−13.3408	+	2.83568i	−0.866578	+	0.184197i
$238$	15.5522	+	6.92428i	1.00810	+	0.448835i
$239$	−7.68325	+	8.53311i	−0.496988	+	0.551961i	−0.938493	−	0.345297i	$-0.887778\pi$
$239$	−7.68325	+	8.53311i	−0.496988	+	0.551961i	0.441505	+	0.897259i	$0.354445\pi$
$240$	0.309017	+	0.951057i	0.0199470	+	0.0613904i
$241$	−14.8927	−	16.5400i	−0.959321	−	1.06543i	−0.997808	−	0.0661743i	$-0.978921\pi$
$241$	−14.8927	−	16.5400i	−0.959321	−	1.06543i	0.0384875	−	0.999259i	$-0.487746\pi$
$242$	0.219691	−	0.380516i	0.0141223	−	0.0244605i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−4.19584	+	12.9135i	−0.268611	+	0.826700i
$245$	−0.243551	+	0.108436i	−0.0155599	+	0.00692771i
$246$	−0.736197	+	0.534878i	−0.0469382	+	0.0341026i
$247$	−0.285530			−0.0181678
$248$	−5.41080	+	1.31274i	−0.343586	+	0.0833590i
$249$	13.6254			0.863478
$250$	−0.809017	+	0.587785i	−0.0511667	+	0.0371748i
$251$	−0.127314	+	0.0566839i	−0.00803600	+	0.00357786i	−0.410751	−	0.911748i	$-0.634733\pi$
$251$	−0.127314	+	0.0566839i	−0.00803600	+	0.00357786i	0.402715	+	0.915326i	$0.368067\pi$
$252$	−0.833006	+	2.56373i	−0.0524744	+	0.161500i
$253$	8.40299	+	14.5544i	0.528291	+	0.915028i
$254$	−3.84800	+	6.66494i	−0.241445	+	0.418196i
$255$	4.22578	+	4.69320i	0.264629	+	0.293900i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−7.14725	+	7.93783i	−0.445833	+	0.495148i	−0.923610	−	0.383333i	$-0.874776\pi$
$257$	−7.14725	+	7.93783i	−0.445833	+	0.495148i	0.477777	+	0.878481i	$0.341443\pi$
$258$	3.48903	+	1.55342i	0.217218	+	0.0967115i
$259$	27.2670	−	5.79578i	1.69429	−	0.360132i
$260$	0.0272435	+	0.259204i	0.00168957	+	0.0160752i
$261$	−0.00214299	+	0.0203892i	−0.000132648	+	0.00126206i
$262$	1.94844	+	0.414154i	0.120375	+	0.0255865i
$263$	−23.1969	−	16.8535i	−1.43038	−	1.03923i	−0.989946	−	0.141449i	$-0.954824\pi$
$263$	−23.1969	−	16.8535i	−1.43038	−	1.03923i	−0.440436	−	0.897784i	$-0.645176\pi$
$264$	−2.73627	−	1.98802i	−0.168406	−	0.122354i
$265$	−1.40408	−	0.298446i	−0.0862517	−	0.0183334i
$266$	0.308691	−	2.93700i	0.0189271	−	0.180079i
$267$	−0.933724	−	8.88379i	−0.0571430	−	0.543679i
$268$	−4.40515	+	0.936343i	−0.269087	+	0.0571963i
$269$	0.713493	+	0.317668i	0.0435024	+	0.0193685i	0.428373	−	0.903602i	$-0.359087\pi$
$269$	0.713493	+	0.317668i	0.0435024	+	0.0193685i	−0.384870	+	0.922971i	$0.625754\pi$
$270$	−0.669131	+	0.743145i	−0.0407220	+	0.0452264i
$271$	7.87756	+	24.2446i	0.478527	+	1.47276i	0.841141	+	0.540816i	$0.181885\pi$
$271$	7.87756	+	24.2446i	0.478527	+	1.47276i	−0.362613	+	0.931940i	$0.618115\pi$
$272$	4.22578	+	4.69320i	0.256226	+	0.284567i
$273$	−0.351288	+	0.608449i	−0.0212609	+	0.0368250i
$274$	−1.51408	−	2.62247i	−0.0914690	−	0.158429i
$275$	1.04516	−	3.21668i	0.0630256	−	0.193973i
$276$	4.53934	−	2.02104i	0.273236	−	0.121653i
$277$	−10.7187	+	7.78763i	−0.644027	+	0.467913i	−0.861231	−	0.508213i	$-0.830306\pi$
$277$	−10.7187	+	7.78763i	−0.644027	+	0.467913i	0.217204	+	0.976126i	$0.430306\pi$
$278$	−2.81230			−0.168670
$279$	−3.84226	−	4.02952i	−0.230030	−	0.241241i
$280$	−2.69566			−0.161097
$281$	6.28352	−	4.56525i	0.374843	−	0.272340i	−0.384373	−	0.923178i	$-0.625582\pi$
$281$	6.28352	−	4.56525i	0.374843	−	0.272340i	0.759217	+	0.650838i	$0.225582\pi$
$282$	5.96151	−	2.65423i	0.355003	−	0.158057i
$283$	3.26348	−	10.0440i	0.193994	−	0.597051i	−0.805993	−	0.591925i	$-0.798368\pi$
$283$	3.26348	−	10.0440i	0.193994	−	0.597051i	0.999987	−	0.00512625i	$-0.00163174\pi$
$284$	−3.05334	−	5.28855i	−0.181183	−	0.313818i
$285$	0.547765	−	0.948756i	0.0324468	−	0.0561995i
$286$	−0.589848	−	0.655093i	−0.0348784	−	0.0387364i
$287$	−0.758026	−	2.33296i	−0.0447449	−	0.137711i
$288$	−0.669131	+	0.743145i	−0.0394289	+	0.0437902i
$289$	20.9050	+	9.30751i	1.22971	+	0.547501i
$290$	−0.0200535	+	0.00426251i	−0.00117758	+	0.000250303i
$291$	1.67661	+	15.9519i	0.0982848	+	0.935117i
$292$	1.43400	−	13.6436i	0.0839188	−	0.798434i
$293$	−24.7343	−	5.25744i	−1.44499	−	0.307143i	−0.582344	−	0.812943i	$-0.697864\pi$
$293$	−24.7343	−	5.25744i	−1.44499	−	0.307143i	−0.862651	+	0.505800i	$0.831198\pi$
$294$	−0.215684	−	0.156703i	−0.0125789	−	0.00913912i
$295$	−4.85713	−	3.52891i	−0.282793	−	0.205461i
$296$	10.1151	+	2.15004i	0.587930	+	0.124968i
$297$	0.353538	−	3.36369i	0.0205143	−	0.195181i
$298$	0.0644366	+	0.613074i	0.00373271	+	0.0355144i
$299$	1.26676	−	0.269258i	0.0732587	−	0.0155716i
$300$	−0.913545	−	0.406737i	−0.0527436	−	0.0234830i
$301$	−6.88892	+	7.65092i	−0.397071	+	0.440992i
$302$	−7.18376	−	22.1093i	−0.413379	−	1.27225i
$303$	−9.77401	−	10.8551i	−0.561502	−	0.623611i
$304$	0.547765	−	0.948756i	0.0314165	−	0.0544149i
$305$	−6.78901	−	11.7589i	−0.388738	−	0.673313i
$306$	−1.95154	+	6.00623i	−0.111562	+	0.343354i
$307$	1.26560	−	0.563481i	0.0722316	−	0.0321596i	−0.370303	−	0.928911i	$-0.620746\pi$
$307$	1.26560	−	0.563481i	0.0722316	−	0.0321596i	0.442534	+	0.896752i	$0.354079\pi$
$308$	7.37606	−	5.35902i	0.420290	−	0.305359i
$309$	−6.18069			−0.351607
$310$	2.64498	−	4.89940i	0.150224	−	0.278267i
$311$	−24.8670			−1.41008			−0.705039	−	0.709168i	$-0.749071\pi$
$311$	−24.8670			−1.41008			−0.705039	+	0.709168i	$0.749071\pi$
$312$	−0.210856	+	0.153196i	−0.0119374	+	0.00867300i
$313$	−27.6306	+	12.3019i	−1.56177	+	0.695346i	−0.991974	−	0.126438i	$-0.959645\pi$
$313$	−27.6306	+	12.3019i	−1.56177	+	0.695346i	−0.569799	+	0.821784i	$0.692979\pi$
$314$	5.39963	−	16.6184i	0.304719	−	0.937828i
$315$	−1.34783	−	2.33451i	−0.0759417	−	0.131535i
$316$	6.81942	−	11.8116i	0.383623	−	0.664454i
$317$	−16.1049	−	17.8863i	−0.904540	−	1.00459i	−0.999958	−	0.00915628i	$-0.997085\pi$
$317$	−16.1049	−	17.8863i	−0.904540	−	1.00459i	0.0954180	−	0.995437i	$-0.469581\pi$
$318$	−0.443577	−	1.36519i	−0.0248745	−	0.0765560i
$319$	0.0463979	−	0.0515301i	0.00259778	−	0.00288513i
$320$	−0.913545	−	0.406737i	−0.0510687	−	0.0227373i
$321$	2.15561	−	0.458189i	0.120314	−	0.0255736i
$322$	1.40011	+	13.3212i	0.0780252	+	0.742360i
$323$	0.723194	−	6.88073i	0.0402396	−	0.382854i
$324$	−0.978148	−	0.207912i	−0.0543415	−	0.0115506i
$325$	−0.210856	−	0.153196i	−0.0116962	−	0.00849777i
$326$	6.06617	+	4.40733i	0.335974	+	0.244100i
$327$	−17.9480	−	3.81496i	−0.992525	−	0.210968i
$328$	0.0951198	−	0.905004i	0.00525211	−	0.0499705i
$329$	1.83876	+	17.4947i	0.101374	+	0.964513i
$330$	3.30831	−	0.703202i	0.182116	−	0.0387100i
$331$	2.08669	+	0.929054i	0.114695	+	0.0510654i	0.463282	−	0.886211i	$-0.346672\pi$
$331$	2.08669	+	0.929054i	0.114695	+	0.0510654i	−0.348587	+	0.937276i	$0.613338\pi$
$332$	−9.11720	+	10.1257i	−0.500372	+	0.555719i
$333$	3.19558	+	9.83498i	0.175117	+	0.538954i
$334$	−6.09242	−	6.76632i	−0.333362	−	0.370236i
$335$	2.25178	−	3.90020i	0.123028	−	0.213091i
$336$	−1.34783	−	2.33451i	−0.0735302	−	0.127358i
$337$	5.85298	−	18.0136i	0.318832	−	0.981265i	−0.655316	−	0.755355i	$-0.727464\pi$
$337$	5.85298	−	18.0136i	0.318832	−	0.981265i	0.974148	−	0.225910i	$-0.0725356\pi$
$338$	11.8140	−	5.25995i	0.642599	−	0.286103i
$339$	0.830761	−	0.603583i	0.0451207	−	0.0327821i
$340$	−6.31533			−0.342497
$341$	2.50272	+	18.6643i	0.135530	+	1.01073i
$342$	1.09553			0.0592395
$343$	−14.6845	+	10.6689i	−0.792886	+	0.576065i
$344$	−3.48903	+	1.55342i	−0.188116	+	0.0837546i
$345$	−1.53548	+	4.72573i	−0.0826676	+	0.254425i
$346$	1.71123	+	2.96394i	0.0919964	+	0.159342i
$347$	−7.32731	+	12.6913i	−0.393351	+	0.681304i	−0.992889	−	0.119042i	$-0.962018\pi$
$347$	−7.32731	+	12.6913i	−0.393351	+	0.681304i	0.599538	+	0.800346i	$0.295351\pi$
$348$	−0.0137182	−	0.0152356i	−0.000735373	−	0.000816714i
$349$	−2.62558	−	8.08069i	−0.140544	−	0.432550i	0.855867	−	0.517196i	$-0.173024\pi$
$349$	−2.62558	−	8.08069i	−0.140544	−	0.432550i	−0.996411	+	0.0846461i	$0.973024\pi$
$350$	1.80375	−	2.00327i	0.0964145	−	0.107079i
$351$	−0.238099	−	0.106009i	−0.0127088	−	0.00565832i
$352$	3.30831	−	0.703202i	0.176333	−	0.0374808i
$353$	2.91715	+	27.7548i	0.155264	+	1.47724i	0.743601	+	0.668624i	$0.233116\pi$
$353$	2.91715	+	27.7548i	0.155264	+	1.47724i	−0.588337	+	0.808616i	$0.700217\pi$
$354$	0.627562	−	5.97085i	0.0333546	−	0.317347i
$355$	5.97324	+	1.26965i	0.317027	+	0.0673861i
$356$	7.22673	+	5.25052i	0.383016	+	0.278277i
$357$	−13.7727	−	10.0065i	−0.728929	−	0.529598i
$358$	11.6679	+	2.48009i	0.616668	+	0.131077i
$359$	1.06046	−	10.0896i	0.0559691	−	0.532510i	−0.930234	−	0.366968i	$-0.880396\pi$
$359$	1.06046	−	10.0896i	0.0559691	−	0.532510i	0.986203	−	0.165542i	$-0.0529375\pi$
$360$	−0.104528	−	0.994522i	−0.00550913	−	0.0524159i
$361$	17.4108	−	3.70079i	0.916360	−	0.194778i
$362$	−13.1503	−	5.85489i	−0.691165	−	0.307726i
$363$	−0.294004	+	0.326524i	−0.0154312	+	0.0171381i
$364$	−0.217108	−	0.668190i	−0.0113796	−	0.0350227i
$365$	9.17967	+	10.1951i	0.480486	+	0.533634i
$366$	6.78901	−	11.7589i	0.354867	−	0.614648i
$367$	−18.5687	−	32.1620i	−0.969280	−	1.67884i	−0.697646	−	0.716442i	$-0.745769\pi$
$367$	−18.5687	−	32.1620i	−0.969280	−	1.67884i	−0.271634	−	0.962401i	$-0.587564\pi$
$368$	−1.53548	+	4.72573i	−0.0800426	+	0.246346i
$369$	0.831317	−	0.370126i	0.0432766	−	0.0192680i
$370$	−8.36614	+	6.07835i	−0.434935	+	0.315999i
$371$	3.86947			0.200893
$372$	5.56549	−	0.159084i	0.288557	−	0.00824811i
$373$	11.9090			0.616627			0.308313	−	0.951285i	$-0.400236\pi$
$373$	11.9090			0.616627			0.308313	+	0.951285i	$0.400236\pi$
$374$	17.2804	−	12.5550i	0.893551	−	0.649202i
$375$	0.913545	−	0.406737i	0.0471753	−	0.0210038i
$376$	−2.01655	+	6.20629i	−0.103995	+	0.320065i
$377$	−0.00267168	−	0.00462748i	−0.000137598	−	0.000238327i
$378$	1.34783	−	2.33451i	0.0693250	−	0.120074i
$379$	−9.16321	−	10.1768i	−0.470682	−	0.522746i	0.460323	−	0.887752i	$-0.347734\pi$
$379$	−9.16321	−	10.1768i	−0.470682	−	0.522746i	−0.931005	+	0.365006i	$0.881067\pi$
$380$	0.338537	+	1.04191i	0.0173666	+	0.0534489i
$381$	5.14964	−	5.71925i	0.263824	−	0.293006i
$382$	8.33286	+	3.71003i	0.426346	+	0.189822i
$383$	16.9517	−	3.60320i	0.866193	−	0.184115i	0.246676	−	0.969098i	$-0.420662\pi$
$383$	16.9517	−	3.60320i	0.866193	−	0.184115i	0.619517	+	0.784983i	$0.287328\pi$
$384$	−0.104528	−	0.994522i	−0.00533420	−	0.0507515i
$385$	−0.953019	+	9.06737i	−0.0485703	+	0.462116i
$386$	−10.1825	−	2.16435i	−0.518274	−	0.110163i
$387$	−3.08981	−	2.24488i	−0.157064	−	0.114114i
$388$	−12.9764	−	9.42794i	−0.658779	−	0.478631i
$389$	−15.2853	−	3.24899i	−0.774995	−	0.164730i	−0.196596	−	0.980485i	$-0.562989\pi$
$389$	−15.2853	−	3.24899i	−0.774995	−	0.164730i	−0.578399	+	0.815754i	$0.696322\pi$
$390$	0.0272435	−	0.259204i	0.00137953	−	0.0131253i
$391$	3.28015	+	31.2085i	0.165884	+	1.57828i
$392$	0.260774	−	0.0554292i	0.0131711	−	0.00279960i
$393$	−1.81976	−	0.810208i	−0.0917945	−	0.0408696i
$394$	12.3245	−	13.6878i	0.620900	−	0.689580i
$395$	4.21464	+	12.9713i	0.212061	+	0.652658i
$396$	2.26314	+	2.51348i	0.113727	+	0.126307i
$397$	−2.96338	+	5.13273i	−0.148728	+	0.257604i	−0.930758	−	0.365637i	$-0.880851\pi$
$397$	−2.96338	+	5.13273i	−0.148728	+	0.257604i	0.782030	+	0.623241i	$0.214185\pi$
$398$	−1.40861	−	2.43978i	−0.0706072	−	0.122295i
$399$	−0.912582	+	2.80864i	−0.0456863	+	0.140608i
$400$	0.913545	−	0.406737i	0.0456773	−	0.0203368i
$401$	−19.2536	+	13.9886i	−0.961480	+	0.698556i	−0.953494	−	0.301412i	$-0.902542\pi$
$401$	−19.2536	+	13.9886i	−0.961480	+	0.698556i	−0.00798610	+	0.999968i	$0.502542\pi$
$402$	4.50356			0.224617
$403$	1.42747	+	0.261029i	0.0711073	+	0.0130028i
$404$	14.6070			0.726727
$405$	0.809017	−	0.587785i	0.0402004	−	0.0292073i
$406$	0.0504873	−	0.0224784i	0.00250564	−	0.00111558i
$407$	10.8081	−	33.2640i	0.535740	−	1.64884i
$408$	−3.15766	−	5.46924i	−0.156328	−	0.270768i
$409$	−10.6000	+	18.3597i	−0.524136	+	0.907830i	0.475470	+	0.879732i	$0.342278\pi$
$409$	−10.6000	+	18.3597i	−0.524136	+	0.907830i	−0.999605	+	0.0280974i	$0.991055\pi$
$410$	0.608902	+	0.676254i	0.0300715	+	0.0333978i
$411$	0.935754	+	2.87995i	0.0461573	+	0.142058i
$412$	4.13569	−	4.59315i	0.203751	−	0.226288i
$413$	14.7849	+	6.58265i	0.727517	+	0.323911i
$414$	−4.86034	+	1.03310i	−0.238873	+	0.0507740i
$415$	−1.42425	−	13.5508i	−0.0699135	−	0.665183i
$416$	0.0272435	−	0.259204i	0.00133572	−	0.0127085i
$417$	2.75084	+	0.584710i	0.134709	+	0.0286333i
$418$	−2.99766	−	2.17793i	−0.146621	−	0.106526i
$419$	−1.86125	−	1.35228i	−0.0909281	−	0.0660632i	0.541392	−	0.840770i	$-0.317897\pi$
$419$	−1.86125	−	1.35228i	−0.0909281	−	0.0660632i	−0.632320	+	0.774707i	$0.717897\pi$
$420$	2.63676	+	0.560460i	0.128661	+	0.0273476i
$421$	0.875154	−	8.32653i	0.0426524	−	0.405810i	−0.952277	−	0.305235i	$-0.901265\pi$
$421$	0.875154	−	8.32653i	0.0426524	−	0.405810i	0.994929	−	0.100575i	$-0.0320684\pi$
$422$	−1.90289	−	18.1048i	−0.0926313	−	0.881328i
$423$	−6.38308	+	1.35677i	−0.310356	+	0.0659682i
$424$	1.31134	+	0.583848i	0.0636845	+	0.0283542i
$425$	4.22578	−	4.69320i	0.204980	−	0.227654i
$426$	1.88707	+	5.80781i	0.0914289	+	0.281389i
$427$	24.4914	+	27.2004i	1.18522	+	1.31632i
$428$	−1.10188	+	1.90852i	−0.0532616	+	0.0922517i
$429$	0.440757	+	0.763413i	0.0212799	+	0.0368580i
$430$	1.18020	−	3.63229i	0.0569145	−	0.175165i
$431$	12.0794	−	5.37809i	0.581844	−	0.259054i	−0.0946392	−	0.995512i	$-0.530170\pi$
$431$	12.0794	−	5.37809i	0.581844	−	0.259054i	0.676483	+	0.736458i	$0.263503\pi$
$432$	0.809017	−	0.587785i	0.0389238	−	0.0282798i
$433$	11.6682			0.560737			0.280368	−	0.959893i	$-0.409543\pi$
$433$	11.6682			0.560737			0.280368	+	0.959893i	$0.409543\pi$
$434$	−4.22824	+	14.4009i	−0.202962	+	0.691266i
$435$	0.0205015			0.000982973
$436$	14.8446	−	10.7852i	0.710928	−	0.516519i
$437$	4.97298	−	2.21411i	0.237890	−	0.105915i
$438$	−4.23934	+	13.0474i	−0.202564	+	0.623427i
$439$	1.37783	+	2.38647i	0.0657603	+	0.113900i	0.897031	−	0.441968i	$-0.145719\pi$
$439$	1.37783	+	2.38647i	0.0657603	+	0.113900i	−0.831271	+	0.555868i	$0.812386\pi$
$440$	−1.69111	+	2.92908i	−0.0806204	+	0.139639i
$441$	0.178390	+	0.198122i	0.00849476	+	0.00943438i
$442$	−0.508635	−	1.56542i	−0.0241933	−	0.0744593i
$443$	10.1522	−	11.2752i	0.482346	−	0.535699i	−0.452023	−	0.892006i	$-0.649298\pi$
$443$	10.1522	−	11.2752i	0.482346	−	0.535699i	0.934369	+	0.356307i	$0.115964\pi$
$444$	−9.44708	−	4.20611i	−0.448338	−	0.199613i
$445$	−8.73752	+	1.85722i	−0.414198	+	0.0880406i
$446$	1.25794	+	11.9685i	0.0595650	+	0.566723i
$447$	0.0644366	−	0.613074i	0.00304775	−	0.0289974i
$448$	2.63676	+	0.560460i	0.124575	+	0.0264792i
$449$	13.0666	+	9.49342i	0.616650	+	0.448022i	0.851750	−	0.523949i	$-0.175542\pi$
$449$	13.0666	+	9.49342i	0.616650	+	0.448022i	−0.235100	+	0.971971i	$0.575542\pi$
$450$	0.809017	+	0.587785i	0.0381374	+	0.0277085i
$451$	−3.01052	−	0.639906i	−0.141760	−	0.0301320i
$452$	−0.107338	+	1.02125i	−0.00504875	+	0.0480356i
$453$	2.42999	+	23.1198i	0.114171	+	1.08626i
$454$	−0.707735	+	0.150434i	−0.0332156	+	0.00706020i
$455$	0.641835	+	0.285764i	0.0300897	+	0.0133968i
$456$	−0.733052	+	0.814137i	−0.0343283	+	0.0381255i
$457$	−2.05130	−	6.31326i	−0.0959559	−	0.295322i	0.891546	−	0.452931i	$-0.149622\pi$
$457$	−2.05130	−	6.31326i	−0.0959559	−	0.295322i	−0.987502	+	0.157609i	$0.949622\pi$
$458$	3.96329	+	4.40168i	0.185192	+	0.205677i
$459$	3.15766	−	5.46924i	0.147387	−	0.255282i
$460$	−2.48446	−	4.30322i	−0.115839	−	0.200639i
$461$	−11.2373	+	34.5849i	−0.523374	+	1.61078i	0.244136	+	0.969741i	$0.421496\pi$
$461$	−11.2373	+	34.5849i	−0.523374	+	1.61078i	−0.767510	+	0.641037i	$0.778504\pi$
$462$	−8.32908	+	3.70835i	−0.387504	+	0.172528i
$463$	−19.3608	+	14.0665i	−0.899773	+	0.653723i	−0.938408	−	0.345530i	$-0.887699\pi$
$463$	−19.3608	+	14.0665i	−0.899773	+	0.653723i	0.0386346	+	0.999253i	$0.487699\pi$
$464$	0.0205015			0.000951760
$465$	−3.60582	+	4.24241i	−0.167216	+	0.196737i
$466$	0.0290976			0.00134792
$467$	−14.7476	+	10.7148i	−0.682437	+	0.495820i	−0.874165	−	0.485628i	$-0.838591\pi$
$467$	−14.7476	+	10.7148i	−0.682437	+	0.495820i	0.191728	+	0.981448i	$0.438591\pi$
$468$	0.238099	−	0.106009i	0.0110061	−	0.00490025i
$469$	−3.75149	+	11.5459i	−0.173228	+	0.533141i
$470$	−3.26284	−	5.65141i	−0.150504	−	0.260680i
$471$	−8.73678	+	15.1326i	−0.402570	+	0.697271i
$472$	4.01729	+	4.46165i	0.184911	+	0.205364i
$473$	3.99170	+	12.2852i	0.183539	+	0.564874i
$474$	−9.12617	+	10.1356i	−0.419179	+	0.465545i
$475$	−1.00082	−	0.445592i	−0.0459206	−	0.0204452i
$476$	16.6520	−	3.53949i	0.763242	−	0.162232i
$477$	0.150045	+	1.42758i	0.00687008	+	0.0653644i
$478$	−1.20024	+	11.4195i	−0.0548978	+	0.522317i
$479$	−32.4284	−	6.89286i	−1.48169	−	0.314943i	−0.605087	−	0.796159i	$-0.706862\pi$
$479$	−32.4284	−	6.89286i	−1.48169	−	0.314943i	−0.876602	+	0.481216i	$0.840195\pi$
$480$	0.809017	+	0.587785i	0.0369264	+	0.0268286i
$481$	−2.18048	−	1.58421i	−0.0994215	−	0.0722339i
$482$	−21.7704	−	4.62743i	−0.991613	−	0.210774i
$483$	1.40011	−	13.3212i	0.0637073	−	0.606134i
$484$	−0.0459279	−	0.436975i	−0.00208763	−	0.0198625i
$485$	15.6893	−	3.33486i	0.712413	−	0.151428i
$486$	0.913545	+	0.406737i	0.0414393	+	0.0184499i
$487$	−3.75658	+	4.17211i	−0.170227	+	0.189056i	−0.822222	−	0.569167i	$-0.807266\pi$
$487$	−3.75658	+	4.17211i	−0.170227	+	0.189056i	0.651995	+	0.758223i	$0.273932\pi$
$488$	4.19584	+	12.9135i	0.189937	+	0.584565i
$489$	−5.01727	−	5.57225i	−0.226889	−	0.251986i
$490$	−0.133300	+	0.230882i	−0.00602187	+	0.0104302i
$491$	−10.5964	−	18.3536i	−0.478210	−	0.828284i	0.521478	−	0.853265i	$-0.325381\pi$
$491$	−10.5964	−	18.3536i	−0.478210	−	0.828284i	−0.999688	+	0.0249805i	$0.992048\pi$
$492$	−0.281202	+	0.865451i	−0.0126776	+	0.0390176i
$493$	0.118280	−	0.0526618i	0.00532708	−	0.00237177i
$494$	−0.230999	+	0.167830i	−0.0103931	+	0.00755105i
$495$	−3.38222			−0.152019
$496$	−3.60582	+	4.24241i	−0.161906	+	0.190490i
$497$	−16.4616			−0.738403
$498$	11.0232	−	8.00884i	0.493962	−	0.358885i
$499$	−23.3791	+	10.4090i	−1.04659	+	0.465973i	−0.856691	−	0.515830i	$-0.827483\pi$
$499$	−23.3791	+	10.4090i	−1.04659	+	0.465973i	−0.189901	+	0.981803i	$0.560817\pi$
$500$	−0.309017	+	0.951057i	−0.0138197	+	0.0425325i
$501$	4.55249	+	7.88514i	0.203390	+	0.352282i
$502$	−0.0696814	+	0.120692i	−0.00311003	+	0.00538673i
$503$	−26.0366	−	28.9165i	−1.16091	−	1.28932i	−0.950152	−	0.311787i	$-0.899072\pi$
$503$	−26.0366	−	28.9165i	−1.16091	−	1.28932i	−0.210761	−	0.977538i	$-0.567594\pi$
$504$	0.833006	+	2.56373i	0.0371050	+	0.114198i
$505$	−9.77401	+	10.8551i	−0.434938	+	0.483047i
$506$	15.3530	+	6.83561i	0.682525	+	0.303880i
$507$	−12.6495	+	2.68873i	−0.561783	+	0.119411i
$508$	0.804452	+	7.65385i	0.0356918	+	0.339585i
$509$	2.78667	−	26.5134i	0.123517	−	1.17519i	−0.740618	−	0.671926i	$-0.765467\pi$
$509$	2.78667	−	26.5134i	0.123517	−	1.17519i	0.864135	−	0.503260i	$-0.167866\pi$
$510$	6.17732	+	1.31303i	0.273537	+	0.0581420i
$511$	−29.9185	−	21.7370i	−1.32352	−	0.961590i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−1.07159	−	0.227773i	−0.0473118	−	0.0100564i
$514$	−1.11651	+	10.6229i	−0.0492472	+	0.468556i
$515$	0.646058	+	6.14683i	0.0284687	+	0.270862i
$516$	3.73576	−	0.794061i	0.164458	−	0.0349566i
$517$	20.1631	+	8.97719i	0.886772	+	0.394816i
$518$	18.6528	−	20.7160i	0.819556	−	0.910210i
$519$	−1.05760	−	3.25496i	−0.0464234	−	0.142877i
$520$	0.174397	+	0.193687i	0.00764781	+	0.00849375i
$521$	7.66167	−	13.2704i	0.335664	−	0.581387i	−0.647948	−	0.761684i	$-0.724373\pi$
$521$	7.66167	−	13.2704i	0.335664	−	0.581387i	0.983612	+	0.180297i	$0.0577060\pi$
$522$	0.0102508	+	0.0177548i	0.000448664	+	0.000777108i
$523$	−4.87772	+	15.0121i	−0.213288	+	0.656432i	0.785983	+	0.618248i	$0.212157\pi$
$523$	−4.87772	+	15.0121i	−0.213288	+	0.656432i	−0.999271	+	0.0381842i	$0.987843\pi$
$524$	1.81976	−	0.810208i	0.0794964	−	0.0353941i
$525$	−2.18084	+	1.58447i	−0.0951795	+	0.0691520i
$526$	−28.6729			−1.25020
$527$	−9.90581	+	33.7381i	−0.431504	+	1.46965i
$528$	−3.38222			−0.147192
$529$	−1.36742	+	0.993492i	−0.0594532	+	0.0431953i
$530$	−1.31134	+	0.583848i	−0.0569611	+	0.0253607i
$531$	−1.85526	+	5.70990i	−0.0805114	+	0.247789i
$532$	−1.47659	−	2.55753i	−0.0640183	−	0.110883i
$533$	−0.118586	+	0.205397i	−0.00513654	+	0.00889675i
$534$	−5.97716	−	6.63831i	−0.258657	−	0.287268i
$535$	−0.681002	−	2.09591i	−0.0294423	−	0.0906140i
$536$	−3.01347	+	3.34680i	−0.130162	+	0.144560i
$537$	−10.8973	−	4.85179i	−0.470253	−	0.209370i
$538$	0.763948	−	0.162382i	0.0329362	−	0.00700080i
$539$	−0.0942530	−	0.896757i	−0.00405976	−	0.0386261i
$540$	−0.104528	+	0.994522i	−0.00449819	+	0.0427974i
$541$	−31.5999	−	6.71677i	−1.35859	−	0.288776i	−0.529696	−	0.848188i	$-0.677694\pi$
$541$	−31.5999	−	6.71677i	−1.35859	−	0.288776i	−0.828890	+	0.559411i	$0.811027\pi$
$542$	20.6237	+	14.9840i	0.885864	+	0.643618i
$543$	11.6456	+	8.46105i	0.499762	+	0.363098i
$544$	6.17732	+	1.31303i	0.264851	+	0.0562957i
$545$	−1.91799	+	18.2484i	−0.0821575	+	0.781677i
$546$	0.0734392	+	0.698728i	0.00314291	+	0.0299028i
$547$	8.03298	−	1.70746i	0.343465	−	0.0730058i	−0.0329496	−	0.999457i	$-0.510490\pi$
$547$	8.03298	−	1.70746i	0.343465	−	0.0730058i	0.376415	+	0.926451i	$0.377157\pi$
$548$	−2.76636	−	1.23166i	−0.118173	−	0.0526141i
$549$	−9.08547	+	10.0904i	−0.387758	+	0.430649i
$550$	−1.04516	−	3.21668i	−0.0445659	−	0.137160i
$551$	−0.0150287	−	0.0166911i	−0.000640244	−	0.000711063i
$552$	2.48446	−	4.30322i	0.105746	−	0.183157i
$553$	−18.3829	−	31.8401i	−0.781719	−	1.35398i
$554$	−4.09420	+	12.6006i	−0.173946	+	0.535350i
$555$	9.44708	−	4.20611i	0.401006	−	0.178539i
$556$	−2.27520	+	1.65303i	−0.0964898	+	0.0701040i
$557$	42.0327			1.78098			0.890492	−	0.454999i	$-0.150360\pi$
$557$	42.0327			1.78098			0.890492	+	0.454999i	$0.150360\pi$
$558$	−5.47695	−	1.00152i	−0.231858	−	0.0423979i
$559$	0.995411			0.0421014
$560$	−2.18084	+	1.58447i	−0.0921572	+	0.0669561i
$561$	−19.5132	+	8.68782i	−0.823846	+	0.366800i
$562$	2.40009	−	7.38672i	0.101242	−	0.311590i
$563$	−3.59728	−	6.23068i	−0.151607	−	0.262592i	0.780211	−	0.625516i	$-0.215112\pi$
$563$	−3.59728	−	6.23068i	−0.151607	−	0.262592i	−0.931819	+	0.362924i	$0.881778\pi$
$564$	3.26284	−	5.65141i	0.137390	−	0.237967i
$565$	−0.687115	−	0.763118i	−0.0289071	−	0.0321046i
$566$	−3.26348	−	10.0440i	−0.137174	−	0.422179i
$567$	−1.80375	+	2.00327i	−0.0757504	+	0.0841294i
$568$	−5.57874	−	2.48381i	−0.234079	−	0.104219i
$569$	25.8293	−	5.49020i	1.08282	−	0.230161i	0.368253	−	0.929726i	$-0.379956\pi$
$569$	25.8293	−	5.49020i	1.08282	−	0.230161i	0.714569	+	0.699565i	$0.246623\pi$
$570$	−0.114514	−	1.08953i	−0.00479646	−	0.0456353i
$571$	3.05875	−	29.1021i	0.128005	−	1.21788i	−0.722295	−	0.691586i	$-0.756913\pi$
$571$	3.05875	−	29.1021i	0.128005	−	1.21788i	0.850299	−	0.526299i	$-0.176421\pi$
$572$	−0.862251	−	0.183277i	−0.0360525	−	0.00766320i
$573$	−7.37941	−	5.36145i	−0.308279	−	0.223978i
$574$	−1.98454	−	1.44185i	−0.0828330	−	0.0601817i
$575$	4.86034	+	1.03310i	0.202690	+	0.0430832i
$576$	−0.104528	+	0.994522i	−0.00435535	+	0.0414384i
$577$	−1.06754	−	10.1570i	−0.0444424	−	0.422841i	−0.994011	−	0.109281i	$-0.965145\pi$
$577$	−1.06754	−	10.1570i	−0.0444424	−	0.422841i	0.949568	−	0.313560i	$-0.101522\pi$
$578$	22.3833	−	4.75772i	0.931024	−	0.197895i
$579$	9.50996	+	4.23411i	0.395221	+	0.175964i
$580$	−0.0137182	+	0.0152356i	−0.000569617	+	0.000632624i
$581$	11.3501	+	34.9319i	0.470880	+	1.44922i
$582$	10.7327	+	11.9199i	0.444885	+	0.494095i
$583$	2.42749	−	4.20454i	0.100536	−	0.174134i
$584$	−6.85940	−	11.8808i	−0.283844	−	0.491632i
$585$	−0.0805398	+	0.247876i	−0.00332991	+	0.0102484i
$586$	−23.1007	+	10.2851i	−0.954283	+	0.424874i
$587$	13.4492	−	9.77142i	0.555108	−	0.403309i	−0.274557	−	0.961571i	$-0.588531\pi$
$587$	13.4492	−	9.77142i	0.555108	−	0.403309i	0.829665	+	0.558261i	$0.188531\pi$
$588$	−0.266600			−0.0109944
$589$	6.09716	−	0.174281i	0.251229	−	0.00718112i
$590$	−6.00374			−0.247170
$591$	−14.9010	+	10.8262i	−0.612947	+	0.445332i
$592$	9.44708	−	4.20611i	0.388272	−	0.172870i
$593$	6.03365	−	18.5697i	0.247772	−	0.762565i	−0.747396	−	0.664379i	$-0.768696\pi$
$593$	6.03365	−	18.5697i	0.247772	−	0.762565i	0.995168	−	0.0981859i	$-0.0313040\pi$
$594$	−1.69111	−	2.92908i	−0.0693870	−	0.120182i
$595$	−8.51200	+	14.7432i	−0.348958	+	0.604413i
$596$	0.412486	+	0.458112i	0.0168961	+	0.0187650i
$597$	0.870569	+	2.67934i	0.0356300	+	0.109658i
$598$	0.866565	−	0.962418i	0.0354365	−	0.0393562i
$599$	17.6030	+	7.83735i	0.719238	+	0.320225i	0.733516	−	0.679673i	$-0.237878\pi$
$599$	17.6030	+	7.83735i	0.719238	+	0.320225i	−0.0142776	+	0.999898i	$0.504545\pi$
$600$	−0.978148	+	0.207912i	−0.0399327	+	0.00848796i
$601$	−2.15376	−	20.4916i	−0.0878535	−	0.835871i	−0.946370	−	0.323085i	$-0.895280\pi$
$601$	−2.15376	−	20.4916i	−0.0878535	−	0.835871i	0.858517	−	0.512786i	$-0.171387\pi$
$602$	−1.07616	+	10.2389i	−0.0438608	+	0.417308i
$603$	−4.40515	−	0.936343i	−0.179392	−	0.0381308i
$604$	−18.8073	−	13.6643i	−0.765260	−	0.555994i
$605$	0.355467	+	0.258262i	0.0144518	+	0.0104999i
$606$	−14.2878	−	3.03697i	−0.580403	−	0.123369i
$607$	−3.98473	+	37.9122i	−0.161735	+	1.53881i	0.549284	+	0.835636i	$0.314901\pi$
$607$	−3.98473	+	37.9122i	−0.161735	+	1.53881i	−0.711019	+	0.703173i	$0.751766\pi$
$608$	−0.114514	−	1.08953i	−0.00464416	−	0.0441862i
$609$	−0.0540575	+	0.0114903i	−0.00219052	+	0.000465610i
$610$	−12.4041	−	5.52268i	−0.502229	−	0.223607i
$611$	1.13806	−	1.26394i	0.0460409	−	0.0511336i
$612$	1.95154	+	6.00623i	0.0788865	+	0.242788i
$613$	−17.8105	−	19.7806i	−0.719360	−	0.798930i	0.266971	−	0.963704i	$-0.413977\pi$
$613$	−17.8105	−	19.7806i	−0.719360	−	0.798930i	−0.986331	+	0.164774i	$0.947310\pi$
$614$	0.692685	−	1.19977i	0.0279545	−	0.0484186i
$615$	−0.454995	−	0.788074i	−0.0183472	−	0.0317782i
$616$	2.81740	−	8.67108i	0.113516	−	0.349368i
$617$	−13.4209	+	5.97535i	−0.540303	+	0.240559i	−0.658697	−	0.752408i	$-0.728892\pi$
$617$	−13.4209	+	5.97535i	−0.540303	+	0.240559i	0.118394	+	0.992967i	$0.462225\pi$
$618$	−5.00028	+	3.63292i	−0.201141	+	0.146137i
$619$	22.2062			0.892544			0.446272	−	0.894897i	$-0.352751\pi$
$619$	22.2062			0.892544			0.446272	+	0.894897i	$0.352751\pi$
$620$	−0.739965	−	5.51837i	−0.0297177	−	0.221623i
$621$	4.96893			0.199396
$622$	−20.1178	+	14.6165i	−0.806651	+	0.586067i
$623$	21.9978	−	9.79406i	0.881324	−	0.392391i
$624$	−0.0805398	+	0.247876i	−0.00322417	+	0.00992298i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−15.1227	+	26.1933i	−0.604426	+	1.04690i
$627$	2.47934	+	2.75359i	0.0990153	+	0.109968i
$628$	−5.39963	−	16.6184i	−0.215469	−	0.663144i
$629$	43.6993	−	48.5329i	1.74240	−	1.93514i
$630$	−2.46261	−	1.09642i	−0.0981128	−	0.0436826i
$631$	−37.8549	+	8.04631i	−1.50698	+	0.320319i	−0.886066	−	0.463560i	$-0.846572\pi$
$631$	−37.8549	+	8.04631i	−1.50698	+	0.320319i	−0.620915	+	0.783878i	$0.713239\pi$
$632$	−1.42565	−	13.5641i	−0.0567092	−	0.539552i
$633$	−1.90289	+	18.1048i	−0.0756332	+	0.719602i
$634$	−23.5424	−	5.00409i	−0.934989	−	0.198738i
$635$	−6.22620	−	4.52360i	−0.247079	−	0.179514i
$636$	−1.16130	−	0.843733i	−0.0460485	−	0.0334562i
$637$	−0.0679660	−	0.0144466i	−0.00269291	−	0.000572396i
$638$	0.00724807	−	0.0689607i	0.000286954	−	0.00273018i
$639$	−0.638323	−	6.07324i	−0.0252517	−	0.240254i
$640$	−0.978148	+	0.207912i	−0.0386647	+	0.00821843i
$641$	−18.6966	−	8.32428i	−0.738473	−	0.328789i	0.00279750	−	0.999996i	$-0.499110\pi$
$641$	−18.6966	−	8.32428i	−0.738473	−	0.328789i	−0.741270	+	0.671207i	$0.765776\pi$
$642$	1.47461	−	1.63772i	0.0581981	−	0.0646356i
$643$	5.61584	+	17.2838i	0.221467	+	0.681606i	0.998631	+	0.0523078i	$0.0166577\pi$
$643$	5.61584	+	17.2838i	0.221467	+	0.681606i	−0.777164	+	0.629298i	$0.783342\pi$
$644$	8.96270	+	9.95409i	0.353180	+	0.392246i
$645$	−1.90961	+	3.30754i	−0.0751908	+	0.130234i
$646$	−3.45931	−	5.99171i	−0.136105	−	0.235741i
$647$	8.34092	−	25.6707i	0.327915	−	1.00922i	−0.642192	−	0.766544i	$-0.721975\pi$
$647$	8.34092	−	25.6707i	0.327915	−	1.00922i	0.970107	−	0.242676i	$-0.0780252\pi$
$648$	−0.913545	+	0.406737i	−0.0358875	+	0.0159781i
$649$	16.4279	−	11.9355i	0.644850	−	0.468511i
$650$	−0.260632			−0.0102228
$651$	7.12996	−	13.2071i	0.279445	−	0.517628i
$652$	7.49820			0.293652
$653$	4.00932	−	2.91294i	0.156897	−	0.113992i	−0.506567	−	0.862201i	$-0.669086\pi$
$653$	4.00932	−	2.91294i	0.156897	−	0.113992i	0.663464	+	0.748209i	$0.269086\pi$
$654$	−16.7626	+	7.46319i	−0.655469	+	0.291834i
$655$	−0.615553	+	1.89448i	−0.0240516	+	0.0740233i
$656$	−0.454995	−	0.788074i	−0.0177646	−	0.0307691i
$657$	6.85940	−	11.8808i	0.267611	−	0.463515i
$658$	11.7707	+	13.0727i	0.458870	+	0.509627i
$659$	−5.13129	−	15.7925i	−0.199887	−	0.615188i	−0.999885	−	0.0151851i	$-0.995166\pi$
$659$	−5.13129	−	15.7925i	−0.199887	−	0.615188i	0.799998	−	0.600003i	$-0.204834\pi$
$660$	2.26314	−	2.51348i	0.0880928	−	0.0978369i
$661$	−29.4451	−	13.1098i	−1.14528	−	0.509913i	−0.255731	−	0.966748i	$-0.582316\pi$
$661$	−29.4451	−	13.1098i	−1.14528	−	0.509913i	−0.889551	+	0.456835i	$0.848983\pi$
$662$	2.23425	−	0.474905i	0.0868366	−	0.0184577i
$663$	0.172052	+	1.63696i	0.00668193	+	0.0635743i
$664$	−1.42425	+	13.5508i	−0.0552715	+	0.525873i
$665$	2.88864	+	0.614000i	0.112017	+	0.0238099i
$666$	8.36614	+	6.07835i	0.324181	+	0.235531i
$667$	0.0824150	+	0.0598780i	0.00319112	+	0.00231849i
$668$	−8.90601	−	1.89303i	−0.344584	−	0.0732436i
$669$	1.25794	−	11.9685i	0.0486346	−	0.462728i
$670$	−0.470750	−	4.47889i	−0.0181867	−	0.173035i
$671$	44.9202	−	9.54809i	1.73413	−	0.368600i
$672$	−2.46261	−	1.09642i	−0.0949973	−	0.0422955i
$673$	27.3366	−	30.3604i	1.05375	−	1.17031i	0.0687707	−	0.997632i	$-0.478092\pi$
$673$	27.3366	−	30.3604i	1.05375	−	1.17031i	0.984979	−	0.172675i	$-0.0552410\pi$
$674$	−5.85298	−	18.0136i	−0.225449	−	0.693859i
$675$	−0.669131	−	0.743145i	−0.0257548	−	0.0286037i
$676$	6.46604	−	11.1995i	0.248694	−	0.430750i
$677$	−9.71830	−	16.8326i	−0.373505	−	0.646929i	0.616597	−	0.787279i	$-0.288511\pi$
$677$	−9.71830	−	16.8326i	−0.373505	−	0.646929i	−0.990102	+	0.140350i	$0.955177\pi$
$678$	0.317322	−	0.976618i	0.0121867	−	0.0375068i
$679$	−39.4997	+	17.5864i	−1.51586	+	0.674904i
$680$	−5.10921	+	3.71206i	−0.195929	+	0.142351i
$681$	0.723546			0.0277263
$682$	12.9954	+	13.6287i	0.497618	+	0.521870i
$683$	−16.6224			−0.636040			−0.318020	−	0.948084i	$-0.603018\pi$
$683$	−16.6224			−0.636040			−0.318020	+	0.948084i	$0.603018\pi$
$684$	0.886302	−	0.643936i	0.0338886	−	0.0246215i
$685$	2.76636	−	1.23166i	0.105697	−	0.0470595i
$686$	−5.60896	+	17.2626i	−0.214151	+	0.659089i
$687$	−2.96152	−	5.12950i	−0.112989	−	0.195703i
$688$	−1.90961	+	3.30754i	−0.0728032	+	0.126099i
$689$	−0.250337	−	0.278027i	−0.00953708	−	0.0105920i
$690$	1.53548	+	4.72573i	0.0584548	+	0.179905i
$691$	−10.5215	+	11.6853i	−0.400257	+	0.444530i	−0.909256	−	0.416236i	$-0.863349\pi$
$691$	−10.5215	+	11.6853i	−0.400257	+	0.444530i	0.508999	+	0.860767i	$0.330016\pi$
$692$	3.12658	+	1.39204i	0.118855	+	0.0529175i
$693$	8.91808	−	1.89560i	0.338770	−	0.0720077i
$694$	1.53183	+	14.5743i	0.0581473	+	0.553235i
$695$	0.293965	−	2.79689i	0.0111507	−	0.106092i
$696$	−0.0200535	−	0.00426251i	−0.000760127	−	0.000161570i
$697$	−4.64932	−	3.37793i	−0.176106	−	0.127948i
$698$	−6.87385	−	4.99414i	−0.260179	−	0.189031i
$699$	−0.0284617	−	0.00604972i	−0.00107652	−	0.000228822i
$700$	0.281774	−	2.68090i	0.0106500	−	0.101328i
$701$	−0.739570	−	7.03654i	−0.0279332	−	0.265766i	−0.999571	−	0.0292920i	$-0.990675\pi$
$701$	−0.739570	−	7.03654i	−0.0279332	−	0.265766i	0.971638	−	0.236474i	$-0.0759919\pi$
$702$	−0.254937	+	0.0541885i	−0.00962196	+	0.00204521i
$703$	−10.3496	−	4.60792i	−0.390341	−	0.173791i
$704$	2.26314	−	2.51348i	0.0852954	−	0.0947302i
$705$	2.01655	+	6.20629i	0.0759476	+	0.233743i
$706$	18.6739	+	20.7395i	0.702801	+	0.780540i
$707$	19.6878	−	34.1003i	0.740436	−	1.28247i
$708$	−3.00187	−	5.19939i	−0.112817	−	0.195405i
$709$	2.81675	−	8.66906i	0.105785	−	0.325573i	−0.884129	−	0.467243i	$-0.845247\pi$
$709$	2.81675	−	8.66906i	0.105785	−	0.325573i	0.989914	+	0.141670i	$0.0452472\pi$
$710$	5.57874	−	2.48381i	0.209366	−	0.0932159i
$711$	11.0341	−	8.01671i	0.413810	−	0.300650i
$712$	8.93273			0.334768
$713$	−26.8858	+	6.52290i	−1.00688	+	0.244284i
$714$	−17.0240			−0.637107
$715$	0.713160	−	0.518141i	0.0266707	−	0.0193774i
$716$	10.8973	−	4.85179i	0.407251	−	0.181320i
$717$	3.54827	−	10.9204i	0.132513	−	0.407832i
$718$	−5.07260	−	8.78601i	−0.189308	−	0.327891i
$719$	−13.0408	+	22.5873i	−0.486339	+	0.842364i	−0.999877	−	0.0157028i	$-0.995001\pi$
$719$	−13.0408	+	22.5873i	−0.486339	+	0.842364i	0.513537	+	0.858067i	$0.328335\pi$
$720$	−0.669131	−	0.743145i	−0.0249370	−	0.0276954i
$721$	−5.14855	−	15.8456i	−0.191742	−	0.590121i
$722$	11.9104	−	13.2278i	0.443259	−	0.492289i
$723$	20.3325	+	9.05263i	0.756175	+	0.336671i
$724$	−14.0802	+	2.99285i	−0.523288	+	0.111228i
$725$	−0.00214299	−	0.0203892i	−7.95888e−5	−	0.000757237i
$726$	−0.0459279	+	0.436975i	−0.00170454	+	0.0162177i
$727$	19.3392	+	4.11068i	0.717253	+	0.152457i	0.552060	−	0.833805i	$-0.313842\pi$
$727$	19.3392	+	4.11068i	0.717253	+	0.152457i	0.165193	+	0.986261i	$0.447175\pi$
$728$	−0.568396	−	0.412964i	−0.0210662	−	0.0153055i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	13.4190	+	2.85230i	0.496660	+	0.105568i
$731$	−2.52119	+	23.9875i	−0.0932495	+	0.887210i
$732$	−1.41929	−	13.5036i	−0.0524585	−	0.499109i
$733$	−18.2570	+	3.88064i	−0.674337	+	0.143335i	−0.532338	−	0.846532i	$-0.678686\pi$
$733$	−18.2570	+	3.88064i	−0.674337	+	0.143335i	−0.141999	+	0.989867i	$0.545353\pi$
$734$	−33.9268	−	15.1052i	−1.25226	−	0.557542i
$735$	0.178390	−	0.198122i	0.00658001	−	0.00730784i
$736$	1.53548	+	4.72573i	0.0565986	+	0.174193i
$737$	10.1922	+	11.3196i	0.375435	+	0.416963i
$738$	0.454995	−	0.788074i	0.0167486	−	0.0290094i
$739$	3.87077	+	6.70437i	0.142388	+	0.246624i	0.928396	−	0.371593i	$-0.121188\pi$
$739$	3.87077	+	6.70437i	0.142388	+	0.246624i	−0.786007	+	0.618217i	$0.787855\pi$
$740$	−3.19558	+	9.83498i	−0.117472	+	0.361541i
$741$	0.260845	−	0.116136i	0.00958237	−	0.00426635i
$742$	3.13047	−	2.27442i	0.114923	−	0.0834966i
$743$	−0.684875			−0.0251256			−0.0125628	−	0.999921i	$-0.503999\pi$
$743$	−0.684875			−0.0251256			−0.0125628	+	0.999921i	$0.503999\pi$
$744$	4.40907	−	3.40002i	0.161644	−	0.124651i
$745$	−0.616451			−0.0225850
$746$	9.63461	−	6.99996i	0.352748	−	0.256287i
$747$	−12.4475	+	5.54197i	−0.455429	+	0.202770i
$748$	6.60054	−	20.3144i	0.241340	−	0.742767i
$749$	2.97031	+	5.14472i	0.108533	+	0.187984i
$750$	0.500000	−	0.866025i	0.0182574	−	0.0316228i
$751$	−12.1024	−	13.4411i	−0.441624	−	0.490473i	0.480703	−	0.876883i	$-0.340381\pi$
$751$	−12.1024	−	13.4411i	−0.441624	−	0.490473i	−0.922327	+	0.386411i	$0.873715\pi$
$752$	2.01655	+	6.20629i	0.0735359	+	0.226320i
$753$	0.0932519	−	0.103567i	0.00339829	−	0.00377418i
$754$	−0.00488140	−	0.00217334i	−0.000177770	−	7.91483e-5i
$755$	22.7391	−	4.83335i	0.827562	−	0.175904i
$756$	−0.281774	−	2.68090i	−0.0102480	−	0.0975032i
$757$	−3.71920	+	35.3858i	−0.135176	+	1.28612i	0.691061	+	0.722796i	$0.257144\pi$
$757$	−3.71920	+	35.3858i	−0.135176	+	1.28612i	−0.826237	+	0.563322i	$0.809523\pi$
$758$	−13.3949	−	2.84718i	−0.486526	−	0.103414i
$759$	−13.5963	−	9.87831i	−0.493515	−	0.358560i
$760$	0.886302	+	0.643936i	0.0321496	+	0.0233580i
$761$	49.7808	+	10.5812i	1.80455	+	0.383569i	0.982562	−	0.185934i	$-0.0595310\pi$
$761$	49.7808	+	10.5812i	1.80455	+	0.383569i	0.821989	+	0.569503i	$0.192864\pi$
$762$	0.804452	−	7.65385i	0.0291422	−	0.277270i
$763$	−5.17025	−	49.1916i	−0.187175	−	1.78086i
$764$	8.92212	−	1.89646i	0.322791	−	0.0686114i
$765$	−5.76934	−	2.56868i	−0.208591	−	0.0928707i
$766$	11.5963	−	12.8790i	0.418993	−	0.465338i
$767$	−0.483540	−	1.48818i	−0.0174596	−	0.0537352i
$768$	−0.669131	−	0.743145i	−0.0241452	−	0.0268159i
$769$	11.2363	−	19.4619i	0.405192	−	0.701814i	−0.589151	−	0.808023i	$-0.700538\pi$
$769$	11.2363	−	19.4619i	0.405192	−	0.701814i	0.994344	+	0.106209i	$0.0338712\pi$
$770$	4.55866	+	7.89583i	0.164283	+	0.284546i
$771$	3.30074	−	10.1586i	0.118873	−	0.365854i
$772$	−9.50996	+	4.23411i	−0.342271	+	0.152389i
$773$	39.6410	−	28.8009i	1.42579	−	1.03590i	0.435006	−	0.900427i	$-0.356746\pi$
$773$	39.6410	−	28.8009i	1.42579	−	1.03590i	0.990782	−	0.135468i	$-0.0432539\pi$
$774$	−3.81922			−0.137279
$775$	4.59608	+	3.14261i	0.165096	+	0.112886i
$776$	−16.0398			−0.575794
$777$	−22.5523	+	16.3852i	−0.809059	+	0.587815i
$778$	−14.2758	+	6.35598i	−0.511811	+	0.227873i
$779$	−0.308065	+	0.948127i	−0.0110376	+	0.0339702i
$780$	−0.130316	−	0.225714i	−0.00466606	−	0.00808186i
$781$	−10.3271	+	17.8870i	−0.369532	+	0.640048i
$782$	20.9976	+	23.3202i	0.750872	+	0.833928i
$783$	−0.00633532	−	0.0194981i	−0.000226406	−	0.000696806i
$784$	0.178390	−	0.198122i	0.00637107	−	0.00707579i
$785$	15.9629	+	7.10714i	0.569740	+	0.253665i
$786$	−1.94844	+	0.414154i	−0.0694986	+	0.0147724i
$787$	3.80811	+	36.2317i	0.135744	+	1.29152i	0.824223	+	0.566265i	$0.191612\pi$
$787$	3.80811	+	36.2317i	0.135744	+	1.29152i	−0.688479	+	0.725256i	$0.741721\pi$
$788$	1.92528	−	18.3178i	0.0685852	−	0.652545i
$789$	28.0464	+	5.96144i	0.998477	+	0.212233i
$790$	11.0341	+	8.01671i	0.392574	+	0.285222i
$791$	2.23945	+	1.62706i	0.0796257	+	0.0578515i
$792$	3.30831	+	0.703202i	0.117556	+	0.0249872i
$793$	0.369912	−	3.51948i	0.0131360	−	0.124980i
$794$	0.619516	+	5.89430i	0.0219858	+	0.209181i
$795$	1.40408	−	0.298446i	0.0497975	−	0.0105848i
$796$	−2.57366	−	1.14587i	−0.0912209	−	0.0406142i
$797$	−34.5542	+	38.3763i	−1.22397	+	1.35936i	−0.311486	+	0.950251i	$0.600827\pi$
$797$	−34.5542	+	38.3763i	−1.22397	+	1.35936i	−0.912486	+	0.409108i	$0.865840\pi$
$798$	0.912582	+	2.80864i	0.0323051	+	0.0994248i
$799$	27.5761	+	30.6264i	0.975572	+	1.08348i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	4.46636	+	7.73597i	0.157811	+	0.273337i
$802$	−7.35423	+	22.6340i	−0.259687	+	0.799234i
$803$	−42.3884	+	18.8726i	−1.49586	+	0.665998i
$804$	3.64346	−	2.64713i	0.128495	−	0.0933570i
$805$	−13.3946			−0.472096
$806$	1.30828	−	0.627868i	0.0460820	−	0.0221157i
$807$	−0.781016			−0.0274930
$808$	11.8173	−	8.58579i	0.415732	−	0.302047i
$809$	−20.5011	+	9.12767i	−0.720779	+	0.320912i	−0.734139	−	0.678999i	$-0.762414\pi$
$809$	−20.5011	+	9.12767i	−0.720779	+	0.320912i	0.0133597	+	0.999911i	$0.495747\pi$
$810$	0.309017	−	0.951057i	0.0108578	−	0.0334167i
$811$	−21.3660	−	37.0069i	−0.750260	−	1.29949i	−0.947696	−	0.319173i	$-0.896595\pi$
$811$	−21.3660	−	37.0069i	−0.750260	−	1.29949i	0.197436	−	0.980316i	$-0.436739\pi$
$812$	0.0276326	−	0.0478611i	0.000969714	−	0.00167959i
$813$	−17.0577	−	18.9445i	−0.598239	−	0.664412i
$814$	−10.8081	−	33.2640i	−0.378825	−	1.16590i
$815$	−5.01727	+	5.57225i	−0.175747	+	0.195187i
$816$	−5.76934	−	2.56868i	−0.201967	−	0.0899216i
$817$	4.09264	−	0.869917i	0.143183	−	0.0304345i
$818$	2.21600	+	21.0838i	0.0774807	+	0.737179i
$819$	0.0734392	−	0.698728i	0.00256617	−	0.0244155i
$820$	0.890104	+	0.189197i	0.0310838	+	0.00660706i
$821$	23.0736	+	16.7640i	0.805276	+	0.585067i	0.912457	−	0.409173i	$-0.134183\pi$
$821$	23.0736	+	16.7640i	0.805276	+	0.585067i	−0.107181	+	0.994239i	$0.534183\pi$
$822$	2.44984	+	1.77991i	0.0854478	+	0.0620815i
$823$	29.2357	+	6.21423i	1.01909	+	0.216615i	0.687019	−	0.726639i	$-0.258919\pi$
$823$	29.2357	+	6.21423i	1.01909	+	0.216615i	0.332072	+	0.943254i	$0.392252\pi$
$824$	0.646058	−	6.14683i	0.0225065	−	0.214135i
$825$	0.353538	+	3.36369i	0.0123086	+	0.117109i
$826$	15.8304	−	3.36486i	0.550810	−	0.117078i
$827$	20.0467	+	8.92536i	0.697092	+	0.310365i	0.724515	−	0.689259i	$-0.242064\pi$
$827$	20.0467	+	8.92536i	0.697092	+	0.310365i	−0.0274236	+	0.999624i	$0.508730\pi$
$828$	−3.32486	+	3.69263i	−0.115547	+	0.128328i
$829$	3.49651	+	10.7612i	0.121439	+	0.373750i	0.993235	−	0.116118i	$-0.0370450\pi$
$829$	3.49651	+	10.7612i	0.121439	+	0.373750i	−0.871797	+	0.489868i	$0.837045\pi$
$830$	−9.11720	−	10.1257i	−0.316463	−	0.351467i
$831$	6.62455	−	11.4741i	0.229803	−	0.398031i
$832$	−0.130316	−	0.225714i	−0.00451790	−	0.00782523i
$833$	0.520281	−	1.60126i	0.0180267	−	0.0554803i
$834$	2.56916	−	1.14386i	0.0889628	−	0.0396088i
$835$	7.36608	−	5.35177i	0.254914	−	0.185206i
$836$	−3.70532			−0.128151
$837$	5.14903	+	2.11836i	0.177977	+	0.0732212i
$838$	−2.30063			−0.0794741
$839$	−25.7374	+	18.6993i	−0.888554	+	0.645572i	−0.935501	−	0.353325i	$-0.885051\pi$
$839$	−25.7374	+	18.6993i	−0.888554	+	0.645572i	0.0469468	+	0.998897i	$0.485051\pi$
$840$	2.46261	−	1.09642i	0.0849681	−	0.0378303i
$841$	−8.96136	+	27.5802i	−0.309013	+	0.951043i
$842$	−4.18620	−	7.25071i	−0.144266	−	0.249876i
$843$	−3.88343	+	6.72630i	−0.133752	+	0.231666i
$844$	−12.1812	−	13.5286i	−0.419295	−	0.465674i
$845$	3.99623	+	12.2991i	0.137474	+	0.423103i
$846$	−4.36653	+	4.84953i	−0.150125	+	0.166730i
$847$	−1.08203	−	0.481749i	−0.0371789	−	0.0165531i
$848$	1.40408	−	0.298446i	0.0482162	−	0.0102487i
$849$	1.10391	+	10.5030i	0.0378860	+	0.360461i
$850$	0.660132	−	6.28073i	0.0226423	−	0.215427i
$851$	50.2614	+	10.6834i	1.72294	+	0.366222i
$852$	4.94042	+	3.58942i	0.169256	+	0.122972i
$853$	−4.40788	−	3.20251i	−0.150923	−	0.109652i	0.509761	−	0.860316i	$-0.329734\pi$
$853$	−4.40788	−	3.20251i	−0.150923	−	0.109652i	−0.660684	+	0.750664i	$0.729734\pi$
$854$	35.8019	+	7.60994i	1.22512	+	0.260407i
$855$	−0.114514	+	1.08953i	−0.00391630	+	0.0372611i
$856$	0.230356	+	2.19169i	0.00787342	+	0.0749106i
$857$	32.0177	−	6.80557i	1.09370	−	0.232474i	0.374467	−	0.927240i	$-0.377826\pi$
$857$	32.0177	−	6.80557i	1.09370	−	0.232474i	0.719235	+	0.694766i	$0.244492\pi$
$858$	0.805303	+	0.358544i	0.0274926	+	0.0122405i
$859$	−7.77463	+	8.63460i	−0.265267	+	0.294609i	−0.861033	−	0.508549i	$-0.830182\pi$
$859$	−7.77463	+	8.63460i	−0.265267	+	0.294609i	0.595766	+	0.803158i	$0.296849\pi$
$860$	−1.18020	−	3.63229i	−0.0402446	−	0.123860i
$861$	1.64139	+	1.82295i	0.0559385	+	0.0621261i
$862$	6.61127	−	11.4511i	0.225181	−	0.390025i
$863$	5.36210	+	9.28743i	0.182528	+	0.316148i	0.942741	−	0.333527i	$-0.108239\pi$
$863$	5.36210	+	9.28743i	0.182528	+	0.316148i	−0.760213	+	0.649674i	$0.774905\pi$
$864$	0.309017	−	0.951057i	0.0105130	−	0.0323556i
$865$	−3.12658	+	1.39204i	−0.106307	+	0.0473308i
$866$	9.43975	−	6.85838i	0.320776	−	0.233057i
$867$	−22.8834			−0.777160
$868$	5.04393	+	14.1359i	0.171202	+	0.479803i
$869$	−46.1295			−1.56484
$870$	0.0165861	−	0.0120505i	0.000562321	−	0.000408550i
$871$	1.07230	−	0.477417i	0.0363333	−	0.0161766i
$872$	5.67014	−	17.4509i	0.192015	−	0.590961i
$873$	−8.01988	−	13.8908i	−0.271432	−	0.470134i
$874$	2.72180	−	4.71430i	0.0920663	−	0.159464i
$875$	1.80375	+	2.00327i	0.0609779	+	0.0677228i
$876$	4.23934	+	13.0474i	0.143234	+	0.440829i
$877$	16.8066	−	18.6656i	0.567518	−	0.630292i	−0.389255	−	0.921130i	$-0.627267\pi$
$877$	16.8066	−	18.6656i	0.567518	−	0.630292i	0.956772	+	0.290838i	$0.0939340\pi$
$878$	2.51742	+	1.12083i	0.0849589	+	0.0378261i
$879$	24.7343	−	5.25744i	0.834268	−	0.177329i
$880$	0.353538	+	3.36369i	0.0119178	+	0.113390i
$881$	0.890241	−	8.47008i	0.0299930	−	0.285364i	−0.969237	−	0.246129i	$-0.920841\pi$
$881$	0.890241	−	8.47008i	0.0299930	−	0.285364i	0.999230	−	0.0392350i	$-0.0124921\pi$
$882$	0.260774	+	0.0554292i	0.00878071	+	0.00186640i
$883$	32.9671	+	23.9520i	1.10943	+	0.806048i	0.982574	−	0.185873i	$-0.0595112\pi$
$883$	32.9671	+	23.9520i	1.10943	+	0.806048i	0.126857	+	0.991921i	$0.459511\pi$
$884$	−1.33162	−	0.967481i	−0.0447874	−	0.0325399i
$885$	5.87255	+	1.24825i	0.197404	+	0.0419594i
$886$	1.58593	−	15.0891i	0.0532804	−	0.506929i
$887$	0.374241	+	3.56066i	0.0125658	+	0.119555i	0.999007	−	0.0445618i	$-0.0141892\pi$
$887$	0.374241	+	3.56066i	0.0125658	+	0.119555i	−0.986441	+	0.164117i	$0.947522\pi$
$888$	−10.1151	+	2.15004i	−0.339442	+	0.0721506i
$889$	18.9523	+	8.43810i	0.635639	+	0.283005i
$890$	−5.97716	+	6.63831i	−0.200355	+	0.222517i
$891$	1.04516	+	3.21668i	0.0350142	+	0.107763i
$892$	8.05258	+	8.94330i	0.269620	+	0.299444i
$893$	3.57454	−	6.19128i	0.119617	−	0.207183i
$894$	−0.308225	−	0.533862i	−0.0103086	−	0.0178550i
$895$	−3.68613	+	11.3447i	−0.123214	+	0.379213i
$896$	2.46261	−	1.09642i	0.0822701	−	0.0366290i
$897$	−1.04773	+	0.761218i	−0.0349826	+	0.0254163i
$898$	16.1512			0.538972
$899$	0.0598750	+	0.0971837i	0.00199694	+	0.00324126i
$900$	1.00000			0.0333333
$901$	7.33398	−	5.32845i	0.244330	−	0.177516i
$902$	−2.81169	+	1.25185i	−0.0936191	+	0.0416819i
$903$	3.18143	−	9.79144i	0.105871	−	0.325839i
$904$	0.513439	+	0.889302i	0.0170767	+	0.0295777i
$905$	7.19740	−	12.4663i	0.239250	−	0.414393i
$906$	15.5554	+	17.2760i	0.516793	+	0.573957i
$907$	3.48133	+	10.7144i	0.115596	+	0.355767i	0.992071	−	0.125680i	$-0.0401113\pi$
$907$	3.48133	+	10.7144i	0.115596	+	0.355767i	−0.876475	+	0.481447i	$0.840111\pi$
$908$	−0.484147	+	0.537699i	−0.0160670	+	0.0178442i
$909$	13.3442	+	5.94121i	0.442599	+	0.197058i
$910$	0.687223	−	0.146074i	0.0227812	−	0.00484230i
$911$	−3.75986	−	35.7727i	−0.124570	−	1.18520i	−0.860970	−	0.508656i	$-0.830143\pi$
$911$	−3.75986	−	35.7727i	−0.124570	−	1.18520i	0.736400	−	0.676546i	$-0.236524\pi$
$912$	−0.114514	+	1.08953i	−0.00379194	+	0.0360779i
$913$	45.0771	+	9.58144i	1.49184	+	0.317099i
$914$	−5.37038	−	3.90181i	−0.177636	−	0.129060i
$915$	10.9848	+	7.98096i	0.363148	+	0.263842i
$916$	5.79361	+	1.23147i	0.191426	+	0.0406889i
$917$	0.561285	−	5.34027i	0.0185353	−	0.176351i
$918$	−0.660132	−	6.28073i	−0.0217876	−	0.207295i
$919$	34.4937	−	7.33187i	1.13784	−	0.241856i	0.399795	−	0.916605i	$-0.369081\pi$
$919$	34.4937	−	7.33187i	1.13784	−	0.241856i	0.738048	+	0.674749i	$0.235748\pi$
$920$	−4.53934	−	2.02104i	−0.149658	−	0.0666319i
$921$	−0.926994	+	1.02953i	−0.0305455	+	0.0339242i
$922$	11.2373	+	34.5849i	0.370081	+	1.13899i
$923$	1.06499	+	1.18279i	0.0350545	+	0.0389320i
$924$	−4.55866	+	7.89583i	−0.149969	+	0.259754i
$925$	−5.17056	−	8.95567i	−0.170007	−	0.294460i
$926$	−7.39517	+	22.7600i	−0.243020	+	0.747940i
$927$	5.64634	−	2.51391i	0.185450	−	0.0825677i
$928$	0.0165861	−	0.0120505i	0.000544465	−	0.000395577i
$929$	34.9050			1.14519			0.572597	−	0.819837i	$-0.305936\pi$
$929$	34.9050			1.14519			0.572597	+	0.819837i	$0.305936\pi$
$930$	−0.423540	+	5.55163i	−0.0138884	+	0.182045i
$931$	−0.292068			−0.00957213
$932$	0.0235404	−	0.0171031i	0.000771092	−	0.000560231i
$933$	22.7171	−	10.1143i	0.743726	−	0.331128i
$934$	−5.63308	+	17.3368i	−0.184320	+	0.567279i
$935$	10.6799	+	18.4981i	0.349270	+	0.604954i
$936$	0.130316	−	0.225714i	0.00425951	−	0.00737769i
$937$	−4.69373	−	5.21291i	−0.153337	−	0.170298i	0.661582	−	0.749873i	$-0.269885\pi$
$937$	−4.69373	−	5.21291i	−0.153337	−	0.170298i	−0.814919	+	0.579575i	$0.803219\pi$
$938$	3.75149	+	11.5459i	0.122491	+	0.376987i
$939$	20.2382	−	22.4767i	0.660447	−	0.733501i
$940$	−5.96151	−	2.65423i	−0.194443	−	0.0865716i
$941$	36.1780	−	7.68987i	1.17937	−	0.250683i	0.423803	−	0.905754i	$-0.360695\pi$
$941$	36.1780	−	7.68987i	1.17937	−	0.250683i	0.755567	+	0.655072i	$0.227362\pi$
$942$	1.82649	+	17.3778i	0.0595101	+	0.566201i
$943$	0.472643	−	4.49690i	0.0153914	−	0.146439i
$944$	5.87255	+	1.24825i	0.191135	+	0.0406270i
$945$	2.18084	+	1.58447i	0.0709426	+	0.0515428i
$946$	10.4504	+	7.59267i	0.339772	+	0.246859i
$947$	−6.51989	−	1.38585i	−0.211868	−	0.0450339i	0.100755	−	0.994911i	$-0.467874\pi$
$947$	−6.51989	−	1.38585i	−0.211868	−	0.0450339i	−0.312623	+	0.949877i	$0.601208\pi$
$948$	−1.42565	+	13.5641i	−0.0463029	+	0.440543i
$949$	0.373748	+	3.55597i	0.0121324	+	0.115432i
$950$	−1.07159	+	0.227773i	−0.0347670	+	0.00738994i
$951$	21.9875	+	9.78949i	0.712995	+	0.317446i
$952$	11.3913	−	12.6513i	0.369193	−	0.410031i
$953$	−5.22284	−	16.0743i	−0.169185	−	0.520696i	0.830136	−	0.557561i	$-0.188263\pi$
$953$	−5.22284	−	16.0743i	−0.169185	−	0.520696i	−0.999320	+	0.0368649i	$0.988263\pi$
$954$	0.960500	+	1.06674i	0.0310973	+	0.0345371i
$955$	−4.56072	+	7.89941i	−0.147582	+	0.255619i
$956$	5.74122	+	9.94408i	0.185684	+	0.321615i
$957$	−0.0214274	+	0.0659468i	−0.000692650	+	0.00213176i
$958$	−30.2866	+	13.4845i	−0.978516	+	0.435663i
$959$	−6.60393	+	4.79804i	−0.213252	+	0.154937i
$960$	1.00000			0.0322749
$961$	−30.6412	−	4.70268i	−0.988427	−	0.151699i
$962$	−2.69523			−0.0868976
$963$	−1.78289	+	1.29534i	−0.0574527	+	0.0417418i
$964$	−20.3325	+	9.05263i	−0.654867	+	0.291566i
$965$	3.21685	−	9.90045i	0.103554	−	0.318707i
$966$	−6.69728	−	11.6000i	−0.215481	−	0.373225i
$967$	3.16982	−	5.49029i	0.101935	−	0.176556i	−0.810547	−	0.585673i	$-0.800830\pi$
$967$	3.16982	−	5.49029i	0.101935	−	0.176556i	0.912482	+	0.409118i	$0.134163\pi$
$968$	−0.294004	−	0.326524i	−0.00944964	−	0.0104949i
$969$	2.13797	+	6.58001i	0.0686816	+	0.211380i
$970$	10.7327	−	11.9199i	0.344606	−	0.382724i
$971$	−12.3586	−	5.50238i	−0.396605	−	0.176580i	0.198736	−	0.980053i	$-0.436316\pi$
$971$	−12.3586	−	5.50238i	−0.396605	−	0.176580i	−0.595341	+	0.803473i	$0.702983\pi$
$972$	0.978148	−	0.207912i	0.0313741	−	0.00666877i
$973$	0.792431	+	7.53948i	0.0254042	+	0.241705i
$974$	−0.586836	+	5.58337i	−0.0188034	+	0.178903i
$975$	0.254937	+	0.0541885i	0.00816451	+	0.00173542i
$976$	10.9848	+	7.98096i	0.351616	+	0.255464i
$977$	31.0339	+	22.5475i	0.992864	+	0.721358i	0.960546	−	0.278120i	$-0.0897113\pi$
$977$	31.0339	+	22.5475i	0.992864	+	0.721358i	0.0323172	+	0.999478i	$0.489711\pi$
$978$	−7.33435	−	1.55896i	−0.234527	−	0.0498502i
$979$	3.15806	−	30.0469i	0.100932	−	0.960303i
$980$	0.0278672	+	0.265139i	0.000890186	+	0.00846956i
$981$	17.9480	−	3.81496i	0.573035	−	0.121802i
$982$	−19.3606	−	8.61991i	−0.617823	−	0.275072i
$983$	−10.8892	+	12.0936i	−0.347310	+	0.385727i	−0.891337	−	0.453341i	$-0.850232\pi$
$983$	−10.8892	+	12.0936i	−0.347310	+	0.385727i	0.544027	+	0.839068i	$0.316899\pi$
$984$	0.281202	+	0.865451i	0.00896440	+	0.0275896i
$985$	12.3245	+	13.6878i	0.392692	+	0.436128i
$986$	0.0647370	−	0.112128i	0.00206164	−	0.00357087i
$987$	−8.79552	−	15.2343i	−0.279965	−	0.484913i
$988$	−0.0882337	+	0.271555i	−0.00280709	+	0.00863933i
$989$	−17.3367	+	7.71881i	−0.551276	+	0.245444i
$990$	−2.73627	+	1.98802i	−0.0869644	+	0.0631833i
$991$	15.6530			0.497235			0.248618	−	0.968602i	$-0.420024\pi$
$991$	15.6530			0.497235			0.248618	+	0.968602i	$0.420024\pi$
$992$	−0.423540	+	5.55163i	−0.0134474	+	0.176264i
$993$	−2.28417			−0.0724858
$994$	−13.3177	+	9.67587i	−0.422412	+	0.306900i
$995$	2.57366	−	1.14587i	0.0815905	−	0.0363264i
$996$	4.21049	−	12.9586i	0.133415	−	0.410608i
$997$	5.67643	+	9.83187i	0.179774	+	0.311378i	0.941803	−	0.336165i	$-0.109130\pi$
$997$	5.67643	+	9.83187i	0.179774	+	0.311378i	−0.762029	+	0.647543i	$0.775797\pi$
$998$	−12.7958	+	22.1630i	−0.405044	+	0.701557i
$999$	−6.91955	−	7.68494i	−0.218925	−	0.243141i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.e.421.1	yes	16
31.19	even	15	inner	930.2.bg.e.391.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.e.391.1	✓	16	31.19	even	15	inner
930.2.bg.e.421.1	yes	16	1.1	even	1	trivial

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.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.913545 + 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.80375 - 2.00327i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.913545 + 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.80375 - 2.00327i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +(0.913545 + 0.406737i) q^{10} +(-3.30831 + 0.703202i) q^{11} +(0.104528 + 0.994522i) q^{12} +(-0.0272435 + 0.259204i) q^{13} +(-2.63676 - 0.560460i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-6.17732 - 1.31303i) q^{17} +(0.104528 - 0.994522i) q^{18} +(0.114514 + 1.08953i) q^{19} +(0.978148 - 0.207912i) q^{20} +(2.46261 + 1.09642i) q^{21} +(-2.26314 + 2.51348i) q^{22} +(-1.53548 - 4.72573i) q^{23} +(0.669131 + 0.743145i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.130316 + 0.225714i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-2.46261 + 1.09642i) q^{28} +(-0.0165861 + 0.0120505i) q^{29} -1.00000 q^{30} +(0.423540 - 5.55163i) q^{31} -1.00000 q^{32} +(2.73627 - 1.98802i) q^{33} +(-5.76934 + 2.56868i) q^{34} +(0.833006 - 2.56373i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-5.17056 + 8.95567i) q^{37} +(0.733052 + 0.814137i) q^{38} +(-0.0805398 - 0.247876i) q^{39} +(0.669131 - 0.743145i) q^{40} +(0.831317 + 0.370126i) q^{41} +(2.63676 - 0.560460i) q^{42} +(-0.399217 - 3.79830i) q^{43} +(-0.353538 + 3.36369i) q^{44} +(0.978148 + 0.207912i) q^{45} +(-4.01995 - 2.92066i) q^{46} +(-5.27939 - 3.83570i) q^{47} +(0.978148 + 0.207912i) q^{48} +(-0.0278672 + 0.265139i) q^{49} +(0.104528 + 0.994522i) q^{50} +(6.17732 - 1.31303i) q^{51} +(0.238099 + 0.106009i) q^{52} +(-0.960500 + 1.06674i) q^{53} +(0.309017 + 0.951057i) q^{54} +(-2.26314 - 2.51348i) q^{55} +(-1.34783 + 2.33451i) q^{56} +(-0.547765 - 0.948756i) q^{57} +(-0.00633532 + 0.0194981i) q^{58} +(-5.48469 + 2.44194i) q^{59} +(-0.809017 + 0.587785i) q^{60} -13.5780 q^{61} +(-2.92052 - 4.74031i) q^{62} -2.69566 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-0.238099 + 0.106009i) q^{65} +(1.04516 - 3.21668i) q^{66} +(-2.25178 - 3.90020i) q^{67} +(-3.15766 + 5.46924i) q^{68} +(3.32486 + 3.69263i) q^{69} +(-0.833006 - 2.56373i) q^{70} +(4.08617 - 4.53815i) q^{71} +(-0.913545 - 0.406737i) q^{72} +(13.4190 - 2.85230i) q^{73} +(1.08094 + 10.2845i) q^{74} +(0.104528 - 0.994522i) q^{75} +(1.07159 + 0.227773i) q^{76} +(7.37606 + 5.35902i) q^{77} +(-0.210856 - 0.153196i) q^{78} +(13.3408 + 2.83568i) q^{79} +(0.104528 - 0.994522i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(0.890104 - 0.189197i) q^{82} +(-12.4475 - 5.54197i) q^{83} +(1.80375 - 2.00327i) q^{84} +(-1.95154 - 6.00623i) q^{85} +(-2.55556 - 2.83823i) q^{86} +(0.0102508 - 0.0177548i) q^{87} +(1.69111 + 2.92908i) q^{88} +(-2.76036 + 8.49553i) q^{89} +(0.913545 - 0.406737i) q^{90} +(0.568396 - 0.412964i) q^{91} -4.96893 q^{92} +(1.87113 + 5.24394i) q^{93} -6.52568 q^{94} +(-0.886302 + 0.643936i) q^{95} +(0.913545 - 0.406737i) q^{96} +(4.95656 - 15.2547i) q^{97} +(0.133300 + 0.230882i) q^{98} +(-1.69111 + 2.92908i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} - 5 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 - 5 * q^7 + 4 * q^8 + 2 * q^9	\( 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} - 5 q^{7} + 4 q^{8} + 2 q^{9} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 4 q^{13} - 10 q^{14} - 4 q^{15} - 4 q^{16} - 22 q^{17} - 2 q^{18} - 3 q^{19} - 2 q^{20} - 11 q^{22} + 9 q^{23} + 2 q^{24} - 8 q^{25} + 11 q^{26} + 4 q^{27} - 3 q^{29} - 16 q^{30} - 15 q^{31} - 16 q^{32} - 8 q^{33} - 8 q^{34} + 5 q^{35} - 8 q^{36} - 17 q^{37} - 2 q^{38} + 3 q^{39} + 2 q^{40} + 28 q^{41} + 10 q^{42} - 28 q^{43} - 19 q^{44} - 2 q^{45} - 9 q^{46} + 9 q^{47} - 2 q^{48} + 19 q^{49} - 2 q^{50} + 22 q^{51} + 4 q^{52} + 2 q^{53} - 4 q^{54} - 11 q^{55} + 5 q^{56} - 2 q^{57} - 12 q^{58} + 24 q^{59} - 4 q^{60} - 40 q^{61} - 25 q^{62} + 10 q^{63} - 4 q^{64} - 4 q^{65} - 7 q^{66} - q^{67} - 2 q^{68} - 3 q^{69} - 5 q^{70} + 39 q^{71} - 2 q^{72} + 81 q^{73} - 8 q^{74} - 2 q^{75} + 2 q^{76} + 28 q^{77} - 8 q^{78} + 64 q^{79} - 2 q^{80} + 2 q^{81} + 32 q^{82} - 40 q^{83} + 5 q^{84} - 14 q^{85} + 13 q^{86} - 9 q^{87} - q^{88} - 7 q^{89} + 2 q^{90} - 46 q^{91} - 36 q^{92} - 20 q^{93} - 4 q^{94} - 6 q^{95} + 2 q^{96} - 17 q^{97} - 9 q^{98} + q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 - 5 * q^7 + 4 * q^8 + 2 * q^9 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 4 * q^13 - 10 * q^14 - 4 * q^15 - 4 * q^16 - 22 * q^17 - 2 * q^18 - 3 * q^19 - 2 * q^20 - 11 * q^22 + 9 * q^23 + 2 * q^24 - 8 * q^25 + 11 * q^26 + 4 * q^27 - 3 * q^29 - 16 * q^30 - 15 * q^31 - 16 * q^32 - 8 * q^33 - 8 * q^34 + 5 * q^35 - 8 * q^36 - 17 * q^37 - 2 * q^38 + 3 * q^39 + 2 * q^40 + 28 * q^41 + 10 * q^42 - 28 * q^43 - 19 * q^44 - 2 * q^45 - 9 * q^46 + 9 * q^47 - 2 * q^48 + 19 * q^49 - 2 * q^50 + 22 * q^51 + 4 * q^52 + 2 * q^53 - 4 * q^54 - 11 * q^55 + 5 * q^56 - 2 * q^57 - 12 * q^58 + 24 * q^59 - 4 * q^60 - 40 * q^61 - 25 * q^62 + 10 * q^63 - 4 * q^64 - 4 * q^65 - 7 * q^66 - q^67 - 2 * q^68 - 3 * q^69 - 5 * q^70 + 39 * q^71 - 2 * q^72 + 81 * q^73 - 8 * q^74 - 2 * q^75 + 2 * q^76 + 28 * q^77 - 8 * q^78 + 64 * q^79 - 2 * q^80 + 2 * q^81 + 32 * q^82 - 40 * q^83 + 5 * q^84 - 14 * q^85 + 13 * q^86 - 9 * q^87 - q^88 - 7 * q^89 + 2 * q^90 - 46 * q^91 - 36 * q^92 - 20 * q^93 - 4 * q^94 - 6 * q^95 + 2 * q^96 - 17 * q^97 - 9 * q^98 + q^99

Introduction

L-functions

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