LMFDB - Embedded newform 930.2.bg.f.691.2

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:	16.0.1669788916259765625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 16x^{14} + 90x^{12} + 239x^{10} + 329x^{8} + 239x^{6} + 90x^{4} + 16x^{2} + 1 $ x^16 + 16x^14 + 90x^12 + 239x^10 + 329x^8 + 239x^6 + 90x^4 + 16*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			691.2
Root			$0.718661i$ of defining polynomial
Character	$\chi$	$=$	930.691
Dual form			930.2.bg.f.751.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.897334 + 0.399519i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.897334 + 0.399519i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +(0.978148 - 0.207912i) q^{10} +(0.250286 - 2.38131i) q^{11} +(0.669131 + 0.743145i) q^{12} +(-0.151760 + 0.168547i) q^{13} +(-0.102674 - 0.976874i) q^{14} +(0.309017 + 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.443529 + 4.21990i) q^{17} +(-0.669131 + 0.743145i) q^{18} +(-1.63168 - 1.81216i) q^{19} +(-0.104528 + 0.994522i) q^{20} +(0.960790 - 0.204222i) q^{21} +(2.18742 + 0.973903i) q^{22} +(-2.11975 + 1.54009i) q^{23} +(-0.913545 + 0.406737i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.113401 - 0.196417i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.960790 + 0.204222i) q^{28} +(-0.494138 + 1.52080i) q^{29} -1.00000 q^{30} +(5.35516 + 1.52390i) q^{31} -1.00000 q^{32} +(-0.739920 + 2.27724i) q^{33} +(-4.15042 - 0.882198i) q^{34} +(0.794661 + 0.577355i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-4.86545 + 8.42720i) q^{37} +(2.22768 - 0.991829i) q^{38} +(0.183487 - 0.133311i) q^{39} +(-0.913545 - 0.406737i) q^{40} +(-11.6094 + 2.46766i) q^{41} +(-0.102674 + 0.976874i) q^{42} +(1.56406 + 1.73707i) q^{43} +(-1.60219 + 1.77941i) q^{44} +(-0.104528 - 0.994522i) q^{45} +(-0.809671 - 2.49191i) q^{46} +(-0.265962 - 0.818547i) q^{47} +(-0.104528 - 0.994522i) q^{48} +(-4.03832 + 4.48501i) q^{49} +(-0.669131 - 0.743145i) q^{50} +(0.443529 - 4.21990i) q^{51} +(0.221846 - 0.0471549i) q^{52} +(-10.0348 - 4.46780i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-2.18742 + 0.973903i) q^{55} +(-0.491127 + 0.850657i) q^{56} +(1.21925 + 2.11181i) q^{57} +(-1.29367 - 0.939906i) q^{58} +(-6.52581 - 1.38710i) q^{59} +(0.309017 - 0.951057i) q^{60} +3.26813 q^{61} +(-3.10415 + 4.62215i) q^{62} -0.982255 q^{63} +(0.309017 - 0.951057i) q^{64} +(0.221846 + 0.0471549i) q^{65} +(-1.93714 - 1.40741i) q^{66} +(4.50357 + 7.80041i) q^{67} +(2.12157 - 3.67467i) q^{68} +(2.39363 - 1.06571i) q^{69} +(-0.794661 + 0.577355i) q^{70} +(-3.43393 - 1.52888i) q^{71} +(0.978148 - 0.207912i) q^{72} +(-0.974607 + 9.27277i) q^{73} +(-6.51124 - 7.23146i) q^{74} +(0.669131 - 0.743145i) q^{75} +(0.254893 + 2.42515i) q^{76} +(0.726790 + 2.23683i) q^{77} +(0.0700858 + 0.215702i) q^{78} +(0.770886 + 7.33449i) q^{79} +(0.669131 - 0.743145i) q^{80} +(0.669131 + 0.743145i) q^{81} +(1.24062 - 11.8038i) q^{82} +(1.65830 - 0.352482i) q^{83} +(-0.897334 - 0.399519i) q^{84} +(3.43277 - 2.49405i) q^{85} +(-2.13537 + 0.950730i) q^{86} +(0.799532 - 1.38483i) q^{87} +(-1.19722 - 2.07364i) q^{88} +(-10.0283 - 7.28596i) q^{89} +(0.978148 + 0.207912i) q^{90} +(0.0688421 - 0.211874i) q^{91} +2.62015 q^{92} +(-4.92130 - 2.60400i) q^{93} +0.860671 q^{94} +(-0.753539 + 2.31916i) q^{95} +(0.978148 + 0.207912i) q^{96} +(10.2161 + 7.42240i) q^{97} +(-3.01759 - 5.22662i) q^{98} +(1.19722 - 2.07364i) 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} - 13 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 - 13 * q^7 + 4 * q^8 + 2 * q^9	\( 16 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} - 13 q^{7} + 4 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{12} - 6 q^{13} - 2 q^{14} - 4 q^{15} - 4 q^{16} + 6 q^{17} - 2 q^{18} + 9 q^{19} + 2 q^{20} + 2 q^{21} - 13 q^{22} - 3 q^{23} - 2 q^{24} - 8 q^{25} + q^{26} - 4 q^{27} + 2 q^{28} - q^{29} - 16 q^{30} - 19 q^{31} - 16 q^{32} + 14 q^{33} + 4 q^{34} + 11 q^{35} - 8 q^{36} - 3 q^{37} + 6 q^{38} - 13 q^{39} - 2 q^{40} - 2 q^{42} + 2 q^{43} - 7 q^{44} + 2 q^{45} - 7 q^{46} - q^{47} + 2 q^{48} + 3 q^{49} - 2 q^{50} + 6 q^{51} - 6 q^{52} - 14 q^{53} + 4 q^{54} + 13 q^{55} - 7 q^{56} - 6 q^{57} - 4 q^{58} + 16 q^{59} - 4 q^{60} - 28 q^{61} - 21 q^{62} - 14 q^{63} - 4 q^{64} - 6 q^{65} + 11 q^{66} + 47 q^{67} - 4 q^{68} + 9 q^{69} - 11 q^{70} + 3 q^{71} - 2 q^{72} - 27 q^{73} + 8 q^{74} + 2 q^{75} - 6 q^{76} + 14 q^{77} - 12 q^{78} + 4 q^{79} + 2 q^{80} + 2 q^{81} + 30 q^{82} + 66 q^{83} - 13 q^{84} + 18 q^{85} + 13 q^{86} + 3 q^{87} - 3 q^{88} - 45 q^{89} - 2 q^{90} + 12 q^{91} - 8 q^{92} - 26 q^{93} + 36 q^{94} - 18 q^{95} - 2 q^{96} + 5 q^{97} - 13 q^{98} + 3 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 - 13 * q^7 + 4 * q^8 + 2 * q^9 - 2 * q^10 - 2 * q^11 + 2 * q^12 - 6 * q^13 - 2 * q^14 - 4 * q^15 - 4 * q^16 + 6 * q^17 - 2 * q^18 + 9 * q^19 + 2 * q^20 + 2 * q^21 - 13 * q^22 - 3 * q^23 - 2 * q^24 - 8 * q^25 + q^26 - 4 * q^27 + 2 * q^28 - q^29 - 16 * q^30 - 19 * q^31 - 16 * q^32 + 14 * q^33 + 4 * q^34 + 11 * q^35 - 8 * q^36 - 3 * q^37 + 6 * q^38 - 13 * q^39 - 2 * q^40 - 2 * q^42 + 2 * q^43 - 7 * q^44 + 2 * q^45 - 7 * q^46 - q^47 + 2 * q^48 + 3 * q^49 - 2 * q^50 + 6 * q^51 - 6 * q^52 - 14 * q^53 + 4 * q^54 + 13 * q^55 - 7 * q^56 - 6 * q^57 - 4 * q^58 + 16 * q^59 - 4 * q^60 - 28 * q^61 - 21 * q^62 - 14 * q^63 - 4 * q^64 - 6 * q^65 + 11 * q^66 + 47 * q^67 - 4 * q^68 + 9 * q^69 - 11 * q^70 + 3 * q^71 - 2 * q^72 - 27 * q^73 + 8 * q^74 + 2 * q^75 - 6 * q^76 + 14 * q^77 - 12 * q^78 + 4 * q^79 + 2 * q^80 + 2 * q^81 + 30 * q^82 + 66 * q^83 - 13 * q^84 + 18 * q^85 + 13 * q^86 + 3 * q^87 - 3 * q^88 - 45 * q^89 - 2 * q^90 + 12 * q^91 - 8 * q^92 - 26 * q^93 + 36 * q^94 - 18 * q^95 - 2 * q^96 + 5 * q^97 - 13 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	−0.978148	−	0.207912i	−0.564734	−	0.120038i
$3$	−0.978148	−	0.207912i	−0.564734	−	0.120038i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−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
$7$	−0.897334	+	0.399519i	−0.339160	+	0.151004i	−0.569248	−	0.822166i	$-0.692765\pi$
$7$	−0.897334	+	0.399519i	−0.339160	+	0.151004i	0.230087	+	0.973170i	$0.426099\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	0.913545	+	0.406737i	0.304515	+	0.135579i
$10$	0.978148	−	0.207912i	0.309317	−	0.0657474i
$11$	0.250286	−	2.38131i	0.0754642	−	0.717993i	−0.889735	−	0.456477i	$-0.849111\pi$
$11$	0.250286	−	2.38131i	0.0754642	−	0.717993i	0.965199	−	0.261516i	$-0.0842224\pi$
$12$	0.669131	+	0.743145i	0.193161	+	0.214527i
$13$	−0.151760	+	0.168547i	−0.0420908	+	0.0467465i	−0.763823	−	0.645426i	$-0.776680\pi$
$13$	−0.151760	+	0.168547i	−0.0420908	+	0.0467465i	0.721732	+	0.692173i	$0.243346\pi$
$14$	−0.102674	−	0.976874i	−0.0274407	−	0.261080i
$15$	0.309017	+	0.951057i	0.0797878	+	0.245562i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	0.443529	+	4.21990i	0.107572	+	1.02347i	0.906545	+	0.422109i	$0.138710\pi$
$17$	0.443529	+	4.21990i	0.107572	+	1.02347i	−0.798974	+	0.601366i	$0.794623\pi$
$18$	−0.669131	+	0.743145i	−0.157716	+	0.175161i
$19$	−1.63168	−	1.81216i	−0.374333	−	0.415738i	0.526314	−	0.850290i	$-0.323574\pi$
$19$	−1.63168	−	1.81216i	−0.374333	−	0.415738i	−0.900647	+	0.434552i	$0.856907\pi$
$20$	−0.104528	+	0.994522i	−0.0233733	+	0.222382i
$21$	0.960790	−	0.204222i	0.209662	−	0.0445649i
$22$	2.18742	+	0.973903i	0.466360	+	0.207637i
$23$	−2.11975	+	1.54009i	−0.441998	+	0.321130i	−0.786428	−	0.617682i	$-0.788072\pi$
$23$	−2.11975	+	1.54009i	−0.441998	+	0.321130i	0.344431	+	0.938812i	$0.388072\pi$
$24$	−0.913545	+	0.406737i	−0.186477	+	0.0830248i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.113401	−	0.196417i	−0.0222398	−	0.0385205i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	0.960790	+	0.204222i	0.181572	+	0.0385944i
$29$	−0.494138	+	1.52080i	−0.0917591	+	0.282406i	−0.986396	−	0.164389i	$-0.947435\pi$
$29$	−0.494138	+	1.52080i	−0.0917591	+	0.282406i	0.894636	+	0.446795i	$0.147435\pi$
$30$	−1.00000			−0.182574
$31$	5.35516	+	1.52390i	0.961815	+	0.273700i
$31$	5.35516	+	1.52390i	0.961815	+	0.273700i
$32$	−1.00000			−0.176777
$33$	−0.739920	+	2.27724i	−0.128804	+	0.396417i
$34$	−4.15042	−	0.882198i	−0.711791	−	0.151296i
$35$	0.794661	+	0.577355i	0.134322	+	0.0975908i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−4.86545	+	8.42720i	−0.799874	+	1.38542i	0.119823	+	0.992795i	$0.461767\pi$
$37$	−4.86545	+	8.42720i	−0.799874	+	1.38542i	−0.919698	+	0.392628i	$0.871566\pi$
$38$	2.22768	−	0.991829i	0.361378	−	0.160896i
$39$	0.183487	−	0.133311i	0.0293814	−	0.0213469i
$40$	−0.913545	−	0.406737i	−0.144444	−	0.0643107i
$41$	−11.6094	+	2.46766i	−1.81308	+	0.385383i	−0.984627	−	0.174669i	$-0.944115\pi$
$41$	−11.6094	+	2.46766i	−1.81308	+	0.385383i	−0.828458	+	0.560052i	$0.810781\pi$
$42$	−0.102674	+	0.976874i	−0.0158429	+	0.150735i
$43$	1.56406	+	1.73707i	0.238518	+	0.264901i	0.850505	−	0.525967i	$-0.176296\pi$
$43$	1.56406	+	1.73707i	0.238518	+	0.264901i	−0.611988	+	0.790867i	$0.709630\pi$
$44$	−1.60219	+	1.77941i	−0.241539	+	0.268256i
$45$	−0.104528	−	0.994522i	−0.0155822	−	0.148255i
$46$	−0.809671	−	2.49191i	−0.119379	−	0.367412i
$47$	−0.265962	−	0.818547i	−0.0387945	−	0.119397i	0.929784	−	0.368106i	$-0.119994\pi$
$47$	−0.265962	−	0.818547i	−0.0387945	−	0.119397i	−0.968578	+	0.248709i	$0.919994\pi$
$48$	−0.104528	−	0.994522i	−0.0150874	−	0.143547i
$49$	−4.03832	+	4.48501i	−0.576903	+	0.640716i
$50$	−0.669131	−	0.743145i	−0.0946294	−	0.105097i
$51$	0.443529	−	4.21990i	0.0621065	−	0.590904i
$52$	0.221846	−	0.0471549i	0.0307645	−	0.00653920i
$53$	−10.0348	−	4.46780i	−1.37839	−	0.613700i	−0.422217	−	0.906495i	$-0.638748\pi$
$53$	−10.0348	−	4.46780i	−1.37839	−	0.613700i	−0.956175	+	0.292795i	$0.905415\pi$
$54$	0.809017	−	0.587785i	0.110093	−	0.0799874i
$55$	−2.18742	+	0.973903i	−0.294952	+	0.131321i
$56$	−0.491127	+	0.850657i	−0.0656296	+	0.113674i
$57$	1.21925	+	2.11181i	0.161494	+	0.279716i
$58$	−1.29367	−	0.939906i	−0.169867	−	0.123416i
$59$	−6.52581	−	1.38710i	−0.849588	−	0.180586i	−0.237512	−	0.971385i	$-0.576332\pi$
$59$	−6.52581	−	1.38710i	−0.849588	−	0.180586i	−0.612076	+	0.790799i	$0.709665\pi$
$60$	0.309017	−	0.951057i	0.0398939	−	0.122781i
$61$	3.26813			0.418441			0.209220	−	0.977869i	$-0.432907\pi$
$61$	3.26813			0.418441			0.209220	+	0.977869i	$0.432907\pi$
$62$	−3.10415	+	4.62215i	−0.394227	+	0.587013i
$63$	−0.982255			−0.123752
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	0.221846	+	0.0471549i	0.0275166	+	0.00584884i
$66$	−1.93714	−	1.40741i	−0.238445	−	0.173240i
$67$	4.50357	+	7.80041i	0.550199	+	0.952972i	0.998260	+	0.0589689i	$0.0187813\pi$
$67$	4.50357	+	7.80041i	0.550199	+	0.952972i	−0.448061	+	0.894003i	$0.647885\pi$
$68$	2.12157	−	3.67467i	0.257278	−	0.445619i
$69$	2.39363	−	1.06571i	0.288159	−	0.128297i
$70$	−0.794661	+	0.577355i	−0.0949801	+	0.0690071i
$71$	−3.43393	−	1.52888i	−0.407532	−	0.181445i	0.192723	−	0.981253i	$-0.438268\pi$
$71$	−3.43393	−	1.52888i	−0.407532	−	0.181445i	−0.600256	+	0.799808i	$0.704935\pi$
$72$	0.978148	−	0.207912i	0.115276	−	0.0245026i
$73$	−0.974607	+	9.27277i	−0.114069	+	1.08530i	0.776396	+	0.630245i	$0.217045\pi$
$73$	−0.974607	+	9.27277i	−0.114069	+	1.08530i	−0.890466	+	0.455051i	$0.849621\pi$
$74$	−6.51124	−	7.23146i	−0.756916	−	0.840640i
$75$	0.669131	−	0.743145i	0.0772645	−	0.0858110i
$76$	0.254893	+	2.42515i	0.0292382	+	0.278183i
$77$	0.726790	+	2.23683i	0.0828254	+	0.254910i
$78$	0.0700858	+	0.215702i	0.00793565	+	0.0244234i
$79$	0.770886	+	7.33449i	0.0867314	+	0.825195i	0.948262	+	0.317489i	$0.102840\pi$
$79$	0.770886	+	7.33449i	0.0867314	+	0.825195i	−0.861531	+	0.507706i	$0.830494\pi$
$80$	0.669131	−	0.743145i	0.0748111	−	0.0830861i
$81$	0.669131	+	0.743145i	0.0743478	+	0.0825716i
$82$	1.24062	−	11.8038i	0.137004	−	1.30351i
$83$	1.65830	−	0.352482i	0.182022	−	0.0386899i	−0.115999	−	0.993249i	$-0.537007\pi$
$83$	1.65830	−	0.352482i	0.182022	−	0.0386899i	0.298021	+	0.954559i	$0.403674\pi$
$84$	−0.897334	−	0.399519i	−0.0979072	−	0.0435911i
$85$	3.43277	−	2.49405i	0.372336	−	0.270518i
$86$	−2.13537	+	0.950730i	−0.230263	+	0.102520i
$87$	0.799532	−	1.38483i	0.0857188	−	0.148469i
$88$	−1.19722	−	2.07364i	−0.127624	−	0.221051i
$89$	−10.0283	−	7.28596i	−1.06299	−	0.772311i	−0.0883544	−	0.996089i	$-0.528161\pi$
$89$	−10.0283	−	7.28596i	−1.06299	−	0.772311i	−0.974640	+	0.223778i	$0.928161\pi$
$90$	0.978148	+	0.207912i	0.103106	+	0.0219158i
$91$	0.0688421	−	0.211874i	0.00721661	−	0.0222104i
$92$	2.62015			0.273170
$93$	−4.92130	−	2.60400i	−0.510315	−	0.270022i
$94$	0.860671			0.0887714
$95$	−0.753539	+	2.31916i	−0.0773115	+	0.237940i
$96$	0.978148	+	0.207912i	0.0998318	+	0.0212199i
$97$	10.2161	+	7.42240i	1.03728	+	0.753630i	0.969753	−	0.244087i	$-0.0784883\pi$
$97$	10.2161	+	7.42240i	1.03728	+	0.753630i	0.0675297	+	0.997717i	$0.478488\pi$
$98$	−3.01759	−	5.22662i	−0.304822	−	0.527968i
$99$	1.19722	−	2.07364i	0.120325	−	0.208409i
$100$	0.913545	−	0.406737i	0.0913545	−	0.0406737i
$101$	−0.655993	+	0.476607i	−0.0652737	+	0.0474242i	−0.619944	−	0.784646i	$-0.712845\pi$
$101$	−0.655993	+	0.476607i	−0.0652737	+	0.0474242i	0.554670	+	0.832070i	$0.312845\pi$
$102$	3.87630	+	1.72584i	0.383811	+	0.170884i
$103$	−13.2643	+	2.81942i	−1.30697	+	0.277805i	−0.808190	−	0.588922i	$-0.799553\pi$
$103$	−13.2643	+	2.81942i	−1.30697	+	0.277805i	−0.498782	+	0.866727i	$0.666219\pi$
$104$	−0.0237073	+	0.225560i	−0.00232469	+	0.0221180i
$105$	−0.657257	−	0.729957i	−0.0641417	−	0.0712365i
$106$	7.35007	−	8.16308i	0.713902	−	0.792868i
$107$	0.290684	+	2.76567i	0.0281014	+	0.267367i	0.999547	+	0.0301039i	$0.00958381\pi$
$107$	0.290684	+	2.76567i	0.0281014	+	0.267367i	−0.971445	+	0.237263i	$0.923750\pi$
$108$	0.309017	+	0.951057i	0.0297352	+	0.0915155i
$109$	−4.15509	−	12.7880i	−0.397985	−	1.22487i	−0.926612	−	0.376018i	$-0.877293\pi$
$109$	−4.15509	−	12.7880i	−0.397985	−	1.22487i	0.528627	−	0.848854i	$-0.322707\pi$
$110$	−0.250286	−	2.38131i	−0.0238639	−	0.227049i
$111$	6.51124	−	7.23146i	0.618019	−	0.686380i
$112$	−0.657257	−	0.729957i	−0.0621049	−	0.0689745i
$113$	−0.107684	+	1.02454i	−0.0101300	+	0.0963810i	−0.998419	−	0.0562152i	$-0.982097\pi$
$113$	−0.107684	+	1.02454i	−0.0101300	+	0.0963810i	0.988289	+	0.152596i	$0.0487634\pi$
$114$	−2.38522	+	0.506994i	−0.223396	+	0.0474843i
$115$	2.39363	+	1.06571i	0.223207	+	0.0993781i
$116$	1.29367	−	0.939906i	0.120114	−	0.0872681i
$117$	−0.207194	+	0.0922488i	−0.0191551	+	0.00852841i
$118$	3.33580	−	5.77778i	0.307085	−	0.531888i
$119$	−2.08392	−	3.60946i	−0.191033	−	0.330878i
$120$	0.809017	+	0.587785i	0.0738528	+	0.0536572i
$121$	5.15161	+	1.09501i	0.468328	+	0.0995462i
$122$	−1.00991	+	3.10817i	−0.0914327	+	0.281401i
$123$	11.8688			1.07017
$124$	−3.43669	−	4.38054i	−0.308624	−	0.393384i
$125$	1.00000			0.0894427
$126$	0.303533	−	0.934180i	0.0270409	−	0.0832233i
$127$	1.37147	+	0.291515i	0.121698	+	0.0258678i	0.268358	−	0.963319i	$-0.413519\pi$
$127$	1.37147	+	0.291515i	0.121698	+	0.0258678i	−0.146660	+	0.989187i	$0.546852\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	−1.16873	−	2.02430i	−0.102901	−	0.178229i
$130$	−0.113401	+	0.196417i	−0.00994594	+	0.0172269i
$131$	8.39511	−	3.73774i	0.733484	−	0.326568i	−0.00578054	−	0.999983i	$-0.501840\pi$
$131$	8.39511	−	3.73774i	0.733484	−	0.326568i	0.739264	+	0.673415i	$0.235173\pi$
$132$	1.93714	−	1.40741i	0.168606	−	0.122499i
$133$	2.18815	+	0.974229i	0.189737	+	0.0844763i
$134$	−8.81031	+	1.87269i	−0.761095	+	0.161776i
$135$	−0.104528	+	0.994522i	−0.00899638	+	0.0855948i
$136$	2.83921	+	3.15327i	0.243461	+	0.270390i
$137$	−4.61112	+	5.12117i	−0.393955	+	0.437531i	−0.907193	−	0.420715i	$-0.861779\pi$
$137$	−4.61112	+	5.12117i	−0.393955	+	0.437531i	0.513238	+	0.858246i	$0.328446\pi$
$138$	0.273880	+	2.60580i	0.0233142	+	0.221820i
$139$	−4.90190	−	15.0865i	−0.415774	−	1.27962i	−0.911557	−	0.411173i	$-0.865119\pi$
$139$	−4.90190	−	15.0865i	−0.415774	−	1.27962i	0.495784	−	0.868446i	$-0.334881\pi$
$140$	−0.303533	−	0.934180i	−0.0256532	−	0.0789526i
$141$	0.0899646	+	0.855956i	0.00757639	+	0.0720845i
$142$	2.51520	−	2.79341i	0.211071	−	0.234418i
$143$	0.363380	+	0.403574i	0.0303874	+	0.0337486i
$144$	−0.104528	+	0.994522i	−0.00871071	+	0.0828768i
$145$	1.56412	−	0.332464i	0.129893	−	0.0276096i
$146$	−8.51776	−	3.79235i	−0.704934	−	0.313857i
$147$	4.88256	−	3.54739i	0.402707	−	0.292584i
$148$	8.88961	−	3.95791i	0.730721	−	0.325338i
$149$	−2.84310	+	4.92439i	−0.232916	+	0.403422i	−0.958665	−	0.284537i	$-0.908160\pi$
$149$	−2.84310	+	4.92439i	−0.232916	+	0.403422i	0.725749	+	0.687960i	$0.241493\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	11.2000	+	8.13728i	0.911443	+	0.662202i	0.941379	−	0.337350i	$-0.109530\pi$
$151$	11.2000	+	8.13728i	0.911443	+	0.662202i	−0.0299363	+	0.999552i	$0.509530\pi$
$152$	−2.38522	−	0.506994i	−0.193467	−	0.0411226i
$153$	−1.31120	+	4.03547i	−0.106004	+	0.326248i
$154$	−2.35194			−0.189525
$155$	−1.35784	−	5.39965i	−0.109065	−	0.433711i
$156$	−0.226802			−0.0181587
$157$	0.493934	−	1.52017i	0.0394202	−	0.121323i	−0.929410	−	0.369049i	$-0.879683\pi$
$157$	0.493934	−	1.52017i	0.0394202	−	0.121323i	0.968830	+	0.247726i	$0.0796834\pi$
$158$	−7.21373	−	1.53333i	−0.573894	−	0.121985i
$159$	8.88665	+	6.45653i	0.704757	+	0.512036i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	1.28683	−	2.22885i	0.101416	−	0.175658i
$162$	−0.913545	+	0.406737i	−0.0717749	+	0.0319562i
$163$	4.05225	−	2.94413i	0.317397	−	0.230602i	−0.417667	−	0.908600i	$-0.637152\pi$
$163$	4.05225	−	2.94413i	0.317397	−	0.230602i	0.735064	+	0.677998i	$0.237152\pi$
$164$	10.8427	+	4.82746i	0.846670	+	0.376962i
$165$	2.34211	−	0.497830i	0.182333	−	0.0387560i
$166$	−0.177212	+	1.68606i	−0.0137543	+	0.130863i
$167$	6.96270	+	7.73286i	0.538790	+	0.598387i	0.949650	−	0.313311i	$-0.101438\pi$
$167$	6.96270	+	7.73286i	0.538790	+	0.598387i	−0.410860	+	0.911698i	$0.634772\pi$
$168$	0.657257	−	0.729957i	0.0507084	−	0.0563174i
$169$	1.35349	+	12.8776i	0.104115	+	0.990587i
$170$	1.31120	+	4.03547i	0.100565	+	0.309506i
$171$	−0.753539	−	2.31916i	−0.0576246	−	0.177350i
$172$	−0.244331	−	2.32465i	−0.0186301	−	0.177253i
$173$	−9.41796	+	10.4597i	−0.716035	+	0.795237i	−0.985842	−	0.167677i	$-0.946373\pi$
$173$	−9.41796	+	10.4597i	−0.716035	+	0.795237i	0.269807	+	0.962914i	$0.413040\pi$
$174$	1.06998	+	1.18834i	0.0811152	+	0.0900875i
$175$	0.102674	−	0.976874i	0.00776139	−	0.0738447i
$176$	2.34211	−	0.497830i	0.176543	−	0.0375254i
$177$	6.09481	+	2.71359i	0.458114	+	0.203966i
$178$	10.0283	−	7.28596i	0.751651	−	0.546106i
$179$	20.7007	−	9.21653i	1.54724	−	0.688876i	0.557293	−	0.830316i	$-0.311840\pi$
$179$	20.7007	−	9.21653i	1.54724	−	0.688876i	0.989947	+	0.141440i	$0.0451733\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	0.909792	+	1.57581i	0.0676243	+	0.117129i	0.897855	−	0.440291i	$-0.145125\pi$
$181$	0.909792	+	1.57581i	0.0676243	+	0.117129i	−0.830231	+	0.557420i	$0.811791\pi$
$182$	0.180231	+	0.130945i	0.0133596	+	0.00970632i
$183$	−3.19671	−	0.679482i	−0.236308	−	0.0502287i
$184$	−0.809671	+	2.49191i	−0.0596897	+	0.183706i
$185$	9.73089			0.715429
$186$	3.99732	−	3.87575i	0.293097	−	0.284184i
$187$	10.1599			0.742966
$188$	−0.265962	+	0.818547i	−0.0193973	+	0.0596987i
$189$	0.960790	+	0.204222i	0.0698872	+	0.0148550i
$190$	−1.97279	−	1.43332i	−0.143121	−	0.103984i
$191$	−5.30998	−	9.19715i	−0.384216	−	0.665482i	0.607444	−	0.794363i	$-0.292195\pi$
$191$	−5.30998	−	9.19715i	−0.384216	−	0.665482i	−0.991660	+	0.128880i	$0.958862\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−3.10960	+	1.38448i	−0.223834	+	0.0996571i	−0.515590	−	0.856836i	$-0.672427\pi$
$193$	−3.10960	+	1.38448i	−0.223834	+	0.0996571i	0.291756	+	0.956493i	$0.405760\pi$
$194$	−10.2161	+	7.42240i	−0.733470	+	0.532897i
$195$	−0.207194	−	0.0922488i	−0.0148375	−	0.00660608i
$196$	5.90329	−	1.25478i	0.421664	−	0.0896274i
$197$	−1.95349	+	18.5863i	−0.139181	+	1.32422i	0.672492	+	0.740104i	$0.265224\pi$
$197$	−1.95349	+	18.5863i	−0.139181	+	1.32422i	−0.811673	+	0.584112i	$0.801443\pi$
$198$	1.60219	+	1.77941i	0.113863	+	0.126457i
$199$	9.91935	−	11.0166i	0.703164	−	0.780943i	−0.280712	−	0.959792i	$-0.590571\pi$
$199$	9.91935	−	11.0166i	0.703164	−	0.780943i	0.983877	+	0.178849i	$0.0572374\pi$
$200$	0.104528	+	0.994522i	0.00739128	+	0.0703233i
$201$	−2.78336	−	8.56630i	−0.196323	−	0.604220i
$202$	−0.250567	−	0.771166i	−0.0176298	−	0.0542591i
$203$	−0.164182	−	1.56208i	−0.0115233	−	0.109637i
$204$	−2.83921	+	3.15327i	−0.198785	+	0.220773i
$205$	7.94176	+	8.82021i	0.554676	+	0.616030i
$206$	1.41747	−	13.4864i	0.0987601	−	0.939640i
$207$	−2.56289	+	0.544760i	−0.178133	+	0.0378634i
$208$	−0.207194	−	0.0922488i	−0.0143663	−	0.00639631i
$209$	−4.72371	+	3.43198i	−0.326746	+	0.237395i
$210$	0.897334	−	0.399519i	0.0619219	−	0.0275694i
$211$	−7.40799	+	12.8310i	−0.509987	+	0.883324i	0.489946	+	0.871753i	$0.337017\pi$
$211$	−7.40799	+	12.8310i	−0.509987	+	0.883324i	−0.999933	+	0.0115711i	$0.996317\pi$
$212$	5.49225	+	9.51286i	0.377209	+	0.653346i
$213$	3.04102	+	2.20943i	0.208367	+	0.151388i
$214$	−2.72013	−	0.578182i	−0.185945	−	0.0395237i
$215$	0.722314	−	2.22305i	0.0492614	−	0.151611i
$216$	−1.00000			−0.0680414
$217$	−5.41419	+	0.772041i	−0.367539	+	0.0524095i
$218$	13.4461			0.910687
$219$	2.88123	−	8.86750i	0.194695	−	0.599210i
$220$	2.34211	+	0.497830i	0.157905	+	0.0335637i
$221$	−0.778561	−	0.565658i	−0.0523717	−	0.0380503i
$222$	4.86545	+	8.42720i	0.326547	+	0.565597i
$223$	−0.661401	+	1.14558i	−0.0442907	+	0.0767137i	−0.887321	−	0.461152i	$-0.847436\pi$
$223$	−0.661401	+	1.14558i	−0.0442907	+	0.0767137i	0.843030	+	0.537866i	$0.180769\pi$
$224$	0.897334	−	0.399519i	0.0599557	−	0.0266940i
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$	−0.941123	−	0.419015i	−0.0626026	−	0.0278725i
$227$	18.8303	−	4.00249i	1.24981	−	0.265655i	0.464954	−	0.885335i	$-0.346071\pi$
$227$	18.8303	−	4.00249i	1.24981	−	0.265655i	0.784854	+	0.619680i	$0.212738\pi$
$228$	0.254893	−	2.42515i	0.0168807	−	0.160609i
$229$	−8.80183	−	9.77543i	−0.581642	−	0.645978i	0.378464	−	0.925616i	$-0.376452\pi$
$229$	−8.80183	−	9.77543i	−0.581642	−	0.645978i	−0.960106	+	0.279638i	$0.909786\pi$
$230$	−1.75322	+	1.94715i	−0.115604	+	0.128391i
$231$	−0.245845	−	2.33906i	−0.0161754	−	0.153899i
$232$	0.494138	+	1.52080i	0.0324417	+	0.0998454i
$233$	−4.06027	−	12.4962i	−0.265997	−	0.818655i	−0.991462	−	0.130396i	$-0.958375\pi$
$233$	−4.06027	−	12.4962i	−0.265997	−	0.818655i	0.725465	−	0.688259i	$-0.241625\pi$
$234$	−0.0237073	−	0.225560i	−0.00154980	−	0.0147453i
$235$	−0.575901	+	0.639603i	−0.0375677	+	0.0417231i
$236$	4.46417	+	4.95797i	0.290593	+	0.322736i
$237$	0.770886	−	7.33449i	0.0500744	−	0.476426i
$238$	4.07677	−	0.866543i	0.264257	−	0.0561697i
$239$	−6.98021	−	3.10779i	−0.451512	−	0.201026i	0.168365	−	0.985725i	$-0.446151\pi$
$239$	−6.98021	−	3.10779i	−0.451512	−	0.201026i	−0.619878	+	0.784698i	$0.712818\pi$
$240$	−0.809017	+	0.587785i	−0.0522218	+	0.0379414i
$241$	12.9904	−	5.78368i	0.836783	−	0.372560i	0.0568191	−	0.998384i	$-0.481904\pi$
$241$	12.9904	−	5.78368i	0.836783	−	0.372560i	0.779964	+	0.625825i	$0.215237\pi$
$242$	−2.63335	+	4.56109i	−0.169278	+	0.293198i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−2.64397	−	1.92096i	−0.169263	−	0.122977i
$245$	5.90329	+	1.25478i	0.377148	+	0.0801652i
$246$	−3.66765	+	11.2879i	−0.233841	+	0.719688i
$247$	0.553059			0.0351903
$248$	5.22814	−	1.91482i	0.331987	−	0.121591i
$249$	−1.69535			−0.107438
$250$	−0.309017	+	0.951057i	−0.0195440	+	0.0601501i
$251$	−13.3028	−	2.82759i	−0.839665	−	0.178476i	−0.232046	−	0.972705i	$-0.574542\pi$
$251$	−13.3028	−	2.82759i	−0.839665	−	0.178476i	−0.607619	+	0.794229i	$0.707875\pi$
$252$	0.794661	+	0.577355i	0.0500589	+	0.0363699i
$253$	3.13689	+	5.43325i	0.197214	+	0.341585i
$254$	−0.701054	+	1.21426i	−0.0439881	+	0.0761895i
$255$	−3.87630	+	1.72584i	−0.242743	+	0.108076i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	9.77748	+	4.35321i	0.609902	+	0.271546i	0.688357	−	0.725372i	$-0.258332\pi$
$257$	9.77748	+	4.35321i	0.609902	+	0.271546i	−0.0784551	+	0.996918i	$0.524999\pi$
$258$	2.28638	−	0.485985i	0.142344	−	0.0302561i
$259$	0.999105	−	9.50585i	0.0620814	−	0.590665i
$260$	−0.151760	−	0.168547i	−0.00941178	−	0.0104528i
$261$	−1.06998	+	1.18834i	−0.0662303	+	0.0735562i
$262$	0.960574	+	9.13925i	0.0593444	+	0.564625i
$263$	−3.92079	−	12.0670i	−0.241766	−	0.744080i	−0.996151	−	0.0876483i	$-0.972065\pi$
$263$	−3.92079	−	12.0670i	−0.241766	−	0.744080i	0.754385	−	0.656432i	$-0.227935\pi$
$264$	0.739920	+	2.27724i	0.0455389	+	0.140154i
$265$	1.14819	+	10.9243i	0.0705330	+	0.671076i
$266$	−1.60272	+	1.78000i	−0.0982692	+	0.109139i
$267$	8.29429	+	9.21174i	0.507602	+	0.563750i
$268$	0.941502	−	8.95780i	0.0575114	−	0.547184i
$269$	8.65106	−	1.83884i	0.527464	−	0.112116i	0.0635203	−	0.997981i	$-0.479767\pi$
$269$	8.65106	−	1.83884i	0.527464	−	0.112116i	0.463944	+	0.885865i	$0.346434\pi$
$270$	−0.913545	−	0.406737i	−0.0555966	−	0.0247532i
$271$	−18.6531	+	13.5523i	−1.13309	+	0.823241i	−0.986142	−	0.165903i	$-0.946946\pi$
$271$	−18.6531	+	13.5523i	−1.13309	+	0.823241i	−0.146951	+	0.989144i	$0.546946\pi$
$272$	−3.87630	+	1.72584i	−0.235035	+	0.104644i
$273$	−0.111389	+	0.192931i	−0.00674156	+	0.0116767i
$274$	−3.44561	−	5.96797i	−0.208157	−	0.360538i
$275$	1.93714	+	1.40741i	0.116814	+	0.0848701i
$276$	−2.56289	−	0.544760i	−0.154268	−	0.0327907i
$277$	5.69524	−	17.5282i	0.342194	−	1.05316i	−0.620875	−	0.783910i	$-0.713223\pi$
$277$	5.69524	−	17.5282i	0.342194	−	1.05316i	0.963069	−	0.269255i	$-0.0867775\pi$
$278$	15.8629			0.951392
$279$	4.27236	+	3.57029i	0.255779	+	0.213748i
$280$	0.982255			0.0587009
$281$	−7.19356	+	22.1395i	−0.429132	+	1.32073i	0.469850	+	0.882746i	$0.344308\pi$
$281$	−7.19356	+	22.1395i	−0.429132	+	1.32073i	−0.898982	+	0.437986i	$0.855692\pi$
$282$	−0.841863	−	0.178944i	−0.0501322	−	0.0106559i
$283$	−6.72397	−	4.88525i	−0.399698	−	0.290398i	0.369720	−	0.929143i	$-0.379454\pi$
$283$	−6.72397	−	4.88525i	−0.399698	−	0.290398i	−0.769418	+	0.638745i	$0.779454\pi$
$284$	1.87945	+	3.25531i	0.111525	+	0.193167i
$285$	1.21925	−	2.11181i	0.0722223	−	0.125093i
$286$	−0.496113	+	0.220884i	−0.0293358	+	0.0130611i
$287$	9.43164	−	6.85249i	0.556732	−	0.404490i
$288$	−0.913545	−	0.406737i	−0.0538312	−	0.0239672i
$289$	−0.982290	+	0.208792i	−0.0577818	+	0.0122819i
$290$	−0.167148	+	1.59030i	−0.00981525	+	0.0933859i
$291$	−8.44960	−	9.38424i	−0.495325	−	0.550114i
$292$	6.23887	−	6.92897i	0.365102	−	0.405487i
$293$	0.827254	+	7.87080i	0.0483287	+	0.459817i	0.991747	+	0.128211i	$0.0409236\pi$
$293$	0.827254	+	7.87080i	0.0483287	+	0.459817i	−0.943418	+	0.331605i	$0.892410\pi$
$294$	1.86497	+	5.73979i	0.108767	+	0.334752i
$295$	2.06164	+	6.34507i	0.120033	+	0.369424i
$296$	1.01716	+	9.67758i	0.0591209	+	0.562498i
$297$	−1.60219	+	1.77941i	−0.0929684	+	0.103252i
$298$	−3.80481	−	4.22567i	−0.220407	−	0.244787i
$299$	0.0621167	−	0.591001i	0.00359230	−	0.0341785i
$300$	−0.978148	+	0.207912i	−0.0564734	+	0.0120038i
$301$	−2.09748	−	0.933858i	−0.120897	−	0.0538267i
$302$	−11.2000	+	8.13728i	−0.644488	+	0.468248i
$303$	0.740750	−	0.329803i	0.0425550	−	0.0189467i
$304$	1.21925	−	2.11181i	0.0699289	−	0.121120i
$305$	−1.63406	−	2.83028i	−0.0935662	−	0.162061i
$306$	−3.43277	−	2.49405i	−0.196239	−	0.142576i
$307$	−14.3240	−	3.04465i	−0.817511	−	0.173767i	−0.219868	−	0.975530i	$-0.570563\pi$
$307$	−14.3240	−	3.04465i	−0.817511	−	0.173767i	−0.597643	+	0.801762i	$0.703896\pi$
$308$	0.726790	−	2.23683i	0.0414127	−	0.127455i
$309$	13.5607			0.771438
$310$	5.55497	+	0.377198i	0.315501	+	0.0214234i
$311$	−25.2612			−1.43243			−0.716217	−	0.697878i	$-0.754128\pi$
$311$	−25.2612			−1.43243			−0.716217	+	0.697878i	$0.754128\pi$
$312$	0.0700858	−	0.215702i	0.00396783	−	0.0122117i
$313$	6.47936	+	1.37723i	0.366235	+	0.0778457i	0.387353	−	0.921931i	$-0.373389\pi$
$313$	6.47936	+	1.37723i	0.366235	+	0.0778457i	−0.0211183	+	0.999777i	$0.506723\pi$
$314$	1.29314	+	0.939518i	0.0729759	+	0.0530201i
$315$	0.491127	+	0.850657i	0.0276719	+	0.0479291i
$316$	3.68745	−	6.38684i	0.207435	−	0.359288i
$317$	−12.1528	+	5.41078i	−0.682570	+	0.303900i	−0.718573	−	0.695452i	$-0.755204\pi$
$317$	−12.1528	+	5.41078i	−0.682570	+	0.303900i	0.0360024	+	0.999352i	$0.488538\pi$
$318$	−8.88665	+	6.45653i	−0.498339	+	0.362064i
$319$	3.49783	+	1.55733i	0.195841	+	0.0871939i
$320$	−0.978148	+	0.207912i	−0.0546801	+	0.0116226i
$321$	0.290684	−	2.76567i	0.0162244	−	0.154365i
$322$	1.72211	+	1.91260i	0.0959695	+	0.106585i
$323$	6.92344	−	7.68926i	0.385230	−	0.427842i
$324$	−0.104528	−	0.994522i	−0.00580714	−	0.0552512i
$325$	−0.0700858	−	0.215702i	−0.00388766	−	0.0119650i
$326$	1.54782	+	4.76371i	0.0857260	+	0.263837i
$327$	1.40550	+	13.3725i	0.0777246	+	0.739500i
$328$	−7.94176	+	8.82021i	−0.438510	+	0.487015i
$329$	0.565682	+	0.628253i	0.0311870	+	0.0346367i
$330$	−0.250286	+	2.38131i	−0.0137778	+	0.131087i
$331$	23.9194	−	5.08423i	1.31473	−	0.279454i	0.503405	−	0.864051i	$-0.332080\pi$
$331$	23.9194	−	5.08423i	1.31473	−	0.279454i	0.811324	+	0.584596i	$0.198747\pi$
$332$	−1.54877	−	0.689559i	−0.0850001	−	0.0378445i
$333$	−7.87246	+	5.71967i	−0.431408	+	0.313436i
$334$	−9.50598	+	4.23234i	−0.520144	+	0.231583i
$335$	4.50357	−	7.80041i	0.246056	−	0.426182i
$336$	0.491127	+	0.850657i	0.0267932	+	0.0464072i
$337$	−10.8230	−	7.86339i	−0.589568	−	0.428346i	0.252593	−	0.967573i	$-0.418717\pi$
$337$	−10.8230	−	7.86339i	−0.589568	−	0.428346i	−0.842161	+	0.539227i	$0.818717\pi$
$338$	−12.6656	−	2.69216i	−0.688918	−	0.146434i
$339$	0.318345	−	0.979766i	0.0172901	−	0.0532136i
$340$	−4.24314			−0.230117
$341$	4.96921	−	12.3709i	0.269098	−	0.669922i
$342$	2.43850			0.131859
$343$	3.95661	−	12.1772i	0.213637	−	0.657507i
$344$	2.28638	+	0.485985i	0.123273	+	0.0262025i
$345$	−2.11975	−	1.54009i	−0.114123	−	0.0829154i
$346$	−7.03746	−	12.1892i	−0.378336	−	0.655298i
$347$	7.50310	−	12.9957i	0.402787	−	0.697648i	−0.591274	−	0.806471i	$-0.701375\pi$
$347$	7.50310	−	12.9957i	0.402787	−	0.697648i	0.994061	+	0.108823i	$0.0347081\pi$
$348$	−1.46082	+	0.650398i	−0.0783080	+	0.0348650i
$349$	4.95187	−	3.59774i	0.265068	−	0.192583i	−0.447311	−	0.894379i	$-0.647618\pi$
$349$	4.95187	−	3.59774i	0.265068	−	0.192583i	0.712378	+	0.701796i	$0.247618\pi$
$350$	0.897334	+	0.399519i	0.0479645	+	0.0213552i
$351$	0.221846	−	0.0471549i	0.0118413	−	0.00251694i
$352$	−0.250286	+	2.38131i	−0.0133403	+	0.126925i
$353$	−0.505948	−	0.561913i	−0.0269289	−	0.0299076i	0.729530	−	0.683949i	$-0.239739\pi$
$353$	−0.505948	−	0.561913i	−0.0269289	−	0.0299076i	−0.756459	+	0.654041i	$0.773072\pi$
$354$	−4.46417	+	4.95797i	−0.237268	+	0.263513i
$355$	0.392912	+	3.73831i	0.0208536	+	0.198409i
$356$	3.83046	+	11.7889i	0.203014	+	0.624812i
$357$	1.28793	+	3.96385i	0.0681647	+	0.209789i
$358$	2.36858	+	22.5356i	0.125184	+	1.19104i
$359$	2.80895	−	3.11965i	0.148250	−	0.164649i	−0.664446	−	0.747337i	$-0.731332\pi$
$359$	2.80895	−	3.11965i	0.148250	−	0.164649i	0.812696	+	0.582688i	$0.197999\pi$
$360$	−0.669131	−	0.743145i	−0.0352663	−	0.0391672i
$361$	1.36448	−	12.9822i	0.0718149	−	0.683273i
$362$	−1.77982	+	0.378313i	−0.0935453	+	0.0198837i
$363$	−4.81137	−	2.14216i	−0.252531	−	0.112434i
$364$	−0.180231	+	0.130945i	−0.00944667	+	0.00686341i
$365$	8.51776	−	3.79235i	0.445840	−	0.198501i
$366$	1.63406	−	2.83028i	0.0854139	−	0.147941i
$367$	−8.40026	−	14.5497i	−0.438490	−	0.759487i	0.559083	−	0.829111i	$-0.311153\pi$
$367$	−8.40026	−	14.5497i	−0.438490	−	0.759487i	−0.997573	+	0.0696246i	$0.977820\pi$
$368$	−2.11975	−	1.54009i	−0.110499	−	0.0802825i
$369$	−11.6094	−	2.46766i	−0.604362	−	0.128461i
$370$	−3.00701	+	9.25463i	−0.156327	+	0.481125i
$371$	10.7896			0.560167
$372$	2.45082	+	4.99935i	0.127069	+	0.259204i
$373$	−17.0471			−0.882663			−0.441332	−	0.897344i	$-0.645494\pi$
$373$	−17.0471			−0.882663			−0.441332	+	0.897344i	$0.645494\pi$
$374$	−3.13958	+	9.66265i	−0.162344	+	0.499644i
$375$	−0.978148	−	0.207912i	−0.0505113	−	0.0107365i
$376$	−0.696297	−	0.505890i	−0.0359088	−	0.0260893i
$377$	−0.181336	−	0.314083i	−0.00933927	−	0.0161761i
$378$	−0.491127	+	0.850657i	−0.0252609	+	0.0437531i
$379$	0.000736261	0	0.000327805i	3.78192e−5	0	1.68382e-5i	−0.406718	−	0.913554i	$-0.633327\pi$
$379$	0.000736261	0	0.000327805i	3.78192e−5	0	1.68382e-5i	0.406756	+	0.913537i	$0.366660\pi$
$380$	1.97279	−	1.43332i	0.101202	−	0.0735276i
$381$	−1.28089	−	0.570289i	−0.0656220	−	0.0292168i
$382$	10.3879	−	2.20801i	0.531490	−	0.112972i
$383$	2.32994	−	22.1679i	0.119054	−	1.13273i	−0.757973	−	0.652285i	$-0.773810\pi$
$383$	2.32994	−	22.1679i	0.119054	−	1.13273i	0.877028	−	0.480440i	$-0.159523\pi$
$384$	−0.669131	−	0.743145i	−0.0341464	−	0.0379235i
$385$	1.57376	−	1.74783i	0.0802060	−	0.0890778i
$386$	−0.355802	−	3.38523i	−0.0181098	−	0.172304i
$387$	0.722314	+	2.22305i	0.0367173	+	0.113004i
$388$	−3.90219	−	12.0097i	−0.198103	−	0.609700i
$389$	3.11633	+	29.6499i	0.158004	+	1.50331i	0.730223	+	0.683209i	$0.239416\pi$
$389$	3.11633	+	29.6499i	0.158004	+	1.50331i	−0.572219	+	0.820101i	$0.693917\pi$
$390$	0.151760	−	0.168547i	0.00768469	−	0.00853471i
$391$	−7.43917	−	8.26204i	−0.376215	−	0.417829i
$392$	−0.630848	+	6.00211i	−0.0318626	+	0.303153i
$393$	−8.98877	+	1.91062i	−0.453424	+	0.0963782i
$394$	−17.0729	−	7.60135i	−0.860121	−	0.382951i
$395$	5.96641	−	4.33485i	0.300203	−	0.218110i
$396$	−2.18742	+	0.973903i	−0.109922	+	0.0489405i
$397$	2.23112	−	3.86441i	0.111977	−	0.193949i	−0.804591	−	0.593830i	$-0.797615\pi$
$397$	2.23112	−	3.86441i	0.111977	−	0.193949i	0.916567	+	0.399881i	$0.130949\pi$
$398$	7.41212	+	12.8382i	0.371536	+	0.643519i
$399$	−1.93778	−	1.40788i	−0.0970105	−	0.0704823i
$400$	−0.978148	−	0.207912i	−0.0489074	−	0.0103956i
$401$	1.48347	−	4.56566i	0.0740811	−	0.227998i	−0.907159	−	0.420788i	$-0.861754\pi$
$401$	1.48347	−	4.56566i	0.0740811	−	0.227998i	0.981240	+	0.192790i	$0.0617536\pi$
$402$	9.00714			0.449235
$403$	−1.06955	+	0.671329i	−0.0532781	+	0.0334413i
$404$	0.810852			0.0403414
$405$	0.309017	−	0.951057i	0.0153552	−	0.0472584i
$406$	1.53636	+	0.326564i	0.0762485	+	0.0162071i
$407$	18.8501	+	13.6954i	0.934363	+	0.678854i
$408$	−2.12157	−	3.67467i	−0.105033	−	0.181923i
$409$	11.6405	−	20.1619i	0.575584	−	0.996941i	−0.420394	−	0.907342i	$-0.638108\pi$
$409$	11.6405	−	20.1619i	0.575584	−	0.996941i	0.995978	−	0.0895992i	$-0.0285586\pi$
$410$	−10.8427	+	4.82746i	−0.535481	+	0.238411i
$411$	5.57511	−	4.05055i	0.275000	−	0.199799i
$412$	12.3883	+	5.51561i	0.610326	+	0.271735i
$413$	6.41001	−	1.36249i	0.315416	−	0.0670437i
$414$	0.273880	−	2.60580i	0.0134605	−	0.128068i
$415$	−1.13441	−	1.25989i	−0.0556859	−	0.0618454i
$416$	0.151760	−	0.168547i	0.00744067	−	0.00826370i
$417$	1.65812	+	15.7760i	0.0811986	+	0.772553i
$418$	−1.80430	−	5.55306i	−0.0882511	−	0.271609i
$419$	3.86965	+	11.9096i	0.189045	+	0.581820i	0.999995	−	0.00329593i	$-0.00104913\pi$
$419$	3.86965	+	11.9096i	0.189045	+	0.581820i	−0.810950	+	0.585116i	$0.801049\pi$
$420$	0.102674	+	0.976874i	0.00500996	+	0.0476666i
$421$	−19.1169	+	21.2315i	−0.931702	+	1.03476i	0.0676110	+	0.997712i	$0.478462\pi$
$421$	−19.1169	+	21.2315i	−0.931702	+	1.03476i	−0.999313	+	0.0370487i	$0.988204\pi$
$422$	−9.91383	−	11.0104i	−0.482598	−	0.535979i
$423$	0.0899646	−	0.855956i	0.00437423	−	0.0416180i
$424$	−10.7445	+	2.28381i	−0.521797	+	0.110911i
$425$	−3.87630	−	1.72584i	−0.188028	−	0.0837156i
$426$	−3.04102	+	2.20943i	−0.147338	+	0.107047i
$427$	−2.93260	+	1.30568i	−0.141919	+	0.0631862i
$428$	1.39045	−	2.40833i	0.0672100	−	0.116411i
$429$	−0.271531	−	0.470306i	−0.0131097	−	0.0227066i
$430$	1.89104	+	1.37392i	0.0911942	+	0.0662565i
$431$	−22.5929	−	4.80226i	−1.08826	−	0.231317i	−0.371357	−	0.928490i	$-0.621107\pi$
$431$	−22.5929	−	4.80226i	−1.08826	−	0.231317i	−0.716902	+	0.697174i	$0.754441\pi$
$432$	0.309017	−	0.951057i	0.0148676	−	0.0457577i
$433$	−38.0801			−1.83001			−0.915007	−	0.403439i	$-0.867815\pi$
$433$	−38.0801			−1.83001			−0.915007	+	0.403439i	$0.867815\pi$
$434$	0.938824	−	5.38778i	0.0450650	−	0.258622i
$435$	−1.59906			−0.0766692
$436$	−4.15509	+	12.7880i	−0.198992	+	0.612436i
$437$	6.24963	+	1.32840i	0.298960	+	0.0635460i
$438$	7.54315	+	5.48042i	0.360426	+	0.261865i
$439$	−12.4176	−	21.5080i	−0.592661	−	1.02652i	−0.993872	−	0.110534i	$-0.964744\pi$
$439$	−12.4176	−	21.5080i	−0.592661	−	1.02652i	0.401211	−	0.915986i	$-0.368589\pi$
$440$	−1.19722	+	2.07364i	−0.0570750	+	0.0988569i
$441$	−5.51341	+	2.45473i	−0.262543	+	0.116892i
$442$	0.778561	−	0.565658i	0.0370324	−	0.0269056i
$443$	−21.7062	−	9.66420i	−1.03129	−	0.459160i	−0.179896	−	0.983686i	$-0.557576\pi$
$443$	−21.7062	−	9.66420i	−1.03129	−	0.459160i	−0.851395	+	0.524525i	$0.824243\pi$
$444$	−9.51825	+	2.02317i	−0.451716	+	0.0960152i
$445$	−1.29570	+	12.3277i	−0.0614219	+	0.584390i
$446$	−0.885128	−	0.983034i	−0.0419120	−	0.0465480i
$447$	3.80481	−	4.22567i	0.179961	−	0.199867i
$448$	0.102674	+	0.976874i	0.00485087	+	0.0461529i
$449$	−11.5321	−	35.4922i	−0.544234	−	1.67498i	−0.722803	−	0.691054i	$-0.757147\pi$
$449$	−11.5321	−	35.4922i	−0.544234	−	1.67498i	0.178569	−	0.983927i	$-0.442853\pi$
$450$	−0.309017	−	0.951057i	−0.0145672	−	0.0448332i
$451$	2.97059	+	28.2633i	0.139880	+	1.33087i
$452$	0.689330	−	0.765578i	0.0324233	−	0.0360098i
$453$	−9.26342	−	10.2881i	−0.435233	−	0.483376i
$454$	−2.01227	+	19.1455i	−0.0944405	+	0.898542i
$455$	−0.217909	+	0.0463181i	−0.0102158	+	0.00217143i
$456$	2.22768	+	0.991829i	0.104321	+	0.0464466i
$457$	−0.837368	+	0.608384i	−0.0391704	+	0.0284590i	−0.607198	−	0.794550i	$-0.707707\pi$
$457$	−0.837368	+	0.608384i	−0.0391704	+	0.0284590i	0.568028	+	0.823009i	$0.307707\pi$
$458$	12.0169	−	5.35027i	0.561513	−	0.250002i
$459$	2.12157	−	3.67467i	0.0990264	−	0.171519i
$460$	−1.31008	−	2.26912i	−0.0610826	−	0.105798i
$461$	−10.3565	−	7.52445i	−0.482351	−	0.350448i	0.319884	−	0.947457i	$-0.396356\pi$
$461$	−10.3565	−	7.52445i	−0.482351	−	0.350448i	−0.802235	+	0.597008i	$0.796356\pi$
$462$	2.30055	+	0.488996i	0.107031	+	0.0227502i
$463$	−9.58016	+	29.4847i	−0.445228	+	1.37027i	0.437006	+	0.899459i	$0.356039\pi$
$463$	−9.58016	+	29.4847i	−0.445228	+	1.37027i	−0.882234	+	0.470812i	$0.843961\pi$
$464$	−1.59906			−0.0742347
$465$	0.205521	+	5.56397i	0.00953081	+	0.258023i
$466$	13.1393			0.608667
$467$	5.25993	−	16.1884i	0.243401	−	0.749110i	−0.752495	−	0.658598i	$-0.771150\pi$
$467$	5.25993	−	16.1884i	0.243401	−	0.749110i	0.995895	−	0.0905118i	$-0.0288503\pi$
$468$	0.221846	+	0.0471549i	0.0102548	+	0.00217973i
$469$	−7.15762	−	5.20031i	−0.330508	−	0.240128i
$470$	−0.430335	−	0.745363i	−0.0198499	−	0.0343810i
$471$	−0.799202	+	1.38426i	−0.0368253	+	0.0637832i
$472$	−6.09481	+	2.71359i	−0.280536	+	0.124903i
$473$	4.52797	−	3.28977i	0.208196	−	0.151264i
$474$	6.73730	+	2.99964i	0.309454	+	0.137778i
$475$	2.38522	−	0.506994i	0.109441	−	0.0232625i
$476$	−0.435658	+	4.14501i	−0.0199684	+	0.189986i
$477$	−7.35007	−	8.16308i	−0.336537	−	0.373762i
$478$	5.11269	−	5.67821i	0.233849	−	0.259715i
$479$	−1.54431	−	14.6931i	−0.0705614	−	0.671347i	−0.971442	−	0.237279i	$-0.923744\pi$
$479$	−1.54431	−	14.6931i	−0.0705614	−	0.671347i	0.900880	−	0.434068i	$-0.142922\pi$
$480$	−0.309017	−	0.951057i	−0.0141046	−	0.0434096i
$481$	−0.681997	−	2.09897i	−0.0310964	−	0.0957049i
$482$	1.48637	+	14.1418i	0.0677021	+	0.644143i
$483$	−1.72211	+	1.91260i	−0.0783588	+	0.0870262i
$484$	−3.52411	−	3.91392i	−0.160187	−	0.177905i
$485$	1.31996	−	12.5586i	0.0599362	−	0.570255i
$486$	0.978148	−	0.207912i	0.0443697	−	0.00943107i
$487$	−33.5230	−	14.9254i	−1.51907	−	0.676334i	−0.533531	−	0.845780i	$-0.679135\pi$
$487$	−33.5230	−	14.9254i	−1.51907	−	0.676334i	−0.985539	+	0.169447i	$0.945802\pi$
$488$	2.64397	−	1.92096i	0.119687	−	0.0869576i
$489$	−4.57582	+	2.03729i	−0.206926	+	0.0921293i
$490$	−3.01759	+	5.22662i	−0.136321	+	0.236114i
$491$	−3.59427	−	6.22545i	−0.162207	−	0.280951i	0.773453	−	0.633854i	$-0.218528\pi$
$491$	−3.59427	−	6.22545i	−0.162207	−	0.280951i	−0.935660	+	0.352903i	$0.885195\pi$
$492$	−9.60204	−	6.97629i	−0.432893	−	0.314515i
$493$	−6.63678	−	1.41069i	−0.298906	−	0.0635344i
$494$	−0.170905	+	0.525990i	−0.00768936	+	0.0236654i
$495$	−2.39443			−0.107622
$496$	0.205521	+	5.56397i	0.00922817	+	0.249830i
$497$	3.69220			0.165618
$498$	0.523890	−	1.61237i	0.0234761	−	0.0722520i
$499$	29.1661	+	6.19944i	1.30565	+	0.277525i	0.807656	−	0.589653i	$-0.200736\pi$
$499$	29.1661	+	6.19944i	1.30565	+	0.277525i	0.497997	+	0.867179i	$0.334069\pi$
$500$	−0.809017	−	0.587785i	−0.0361803	−	0.0262866i
$501$	−5.20280	−	9.01151i	−0.232444	−	0.402605i
$502$	6.79999	−	11.7779i	0.303498	−	0.525675i
$503$	7.09361	−	3.15828i	0.316289	−	0.140821i	−0.242452	−	0.970164i	$-0.577952\pi$
$503$	7.09361	−	3.15828i	0.316289	−	0.140821i	0.558740	+	0.829343i	$0.311285\pi$
$504$	−0.794661	+	0.577355i	−0.0353970	+	0.0257174i
$505$	0.740750	+	0.329803i	0.0329629	+	0.0146760i
$506$	−6.13668	+	1.30439i	−0.272808	+	0.0579872i
$507$	1.35349	−	12.8776i	0.0601107	−	0.571915i
$508$	−0.938194	−	1.04197i	−0.0416256	−	0.0462299i
$509$	3.99733	−	4.43948i	0.177178	−	0.196777i	−0.648014	−	0.761629i	$-0.724400\pi$
$509$	3.99733	−	4.43948i	0.177178	−	0.196777i	0.825192	+	0.564852i	$0.191067\pi$
$510$	−0.443529	−	4.21990i	−0.0196398	−	0.186860i
$511$	−2.83010	−	8.71015i	−0.125196	−	0.385314i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	0.254893	+	2.42515i	0.0112538	+	0.107073i
$514$	−7.16156	+	7.95372i	−0.315883	+	0.350823i
$515$	9.07385	+	10.0775i	0.399841	+	0.444069i
$516$	−0.244331	+	2.32465i	−0.0107561	+	0.102337i
$517$	−2.01578	+	0.428468i	−0.0886541	+	0.0188440i
$518$	8.73186	+	3.88767i	0.383656	+	0.170815i
$519$	11.3869	−	8.27303i	0.499827	−	0.363146i
$520$	0.207194	−	0.0922488i	0.00908607	−	0.00404538i
$521$	−15.4742	+	26.8021i	−0.677938	+	1.17422i	0.297663	+	0.954671i	$0.403793\pi$
$521$	−15.4742	+	26.8021i	−0.677938	+	1.17422i	−0.975601	+	0.219552i	$0.929541\pi$
$522$	−0.799532	−	1.38483i	−0.0349946	−	0.0606124i
$523$	−20.8942	−	15.1805i	−0.913638	−	0.663797i	0.0282946	−	0.999600i	$-0.490992\pi$
$523$	−20.8942	−	15.1805i	−0.913638	−	0.663797i	−0.941932	+	0.335803i	$0.890992\pi$
$524$	−8.98877	−	1.91062i	−0.392676	−	0.0834660i
$525$	−0.303533	+	0.934180i	−0.0132473	+	0.0407709i
$526$	12.6879			0.553221
$527$	−4.05553	+	23.2741i	−0.176662	+	1.01384i
$528$	−2.39443			−0.104204
$529$	−4.98593	+	15.3451i	−0.216780	+	0.667179i
$530$	−10.7445	−	2.28381i	−0.466710	−	0.0992022i
$531$	−5.39744	−	3.92147i	−0.234229	−	0.170177i
$532$	−1.19762	−	2.07433i	−0.0519232	−	0.0899337i
$533$	1.34593	−	2.33122i	0.0582988	−	0.100977i
$534$	−11.3240	+	5.04175i	−0.490036	+	0.218178i
$535$	2.24980	−	1.63457i	0.0972673	−	0.0706688i
$536$	8.22843	+	3.66353i	0.355414	+	0.158241i
$537$	−22.1645	+	4.71122i	−0.956470	+	0.203304i
$538$	−0.924484	+	8.79588i	−0.0398573	+	0.379217i
$539$	9.66948	+	10.7391i	0.416494	+	0.462564i
$540$	0.669131	−	0.743145i	0.0287948	−	0.0319799i
$541$	2.90327	+	27.6228i	0.124821	+	1.18760i	0.860206	+	0.509947i	$0.170335\pi$
$541$	2.90327	+	27.6228i	0.124821	+	1.18760i	−0.735384	+	0.677650i	$0.762998\pi$
$542$	−7.12484	−	21.9280i	−0.306038	−	0.941888i
$543$	−0.562282	−	1.73053i	−0.0241298	−	0.0742640i
$544$	−0.443529	−	4.21990i	−0.0190161	−	0.180927i
$545$	−8.99722	+	9.99243i	−0.385399	+	0.428029i
$546$	−0.149067	−	0.165556i	−0.00637949	−	0.00708515i
$547$	0.945170	−	8.99269i	0.0404125	−	0.384500i	−0.955557	−	0.294807i	$-0.904745\pi$
$547$	0.945170	−	8.99269i	0.0404125	−	0.384500i	0.995969	−	0.0896930i	$-0.0285886\pi$
$548$	6.74063	−	1.43276i	0.287945	−	0.0612047i
$549$	2.98558	+	1.32927i	0.127422	+	0.0567317i
$550$	−1.93714	+	1.40741i	−0.0825998	+	0.0600122i
$551$	3.56221	−	1.58600i	0.151755	−	0.0675658i
$552$	1.31008	−	2.26912i	0.0557605	−	0.0965800i
$553$	−3.62201	−	6.27350i	−0.154024	−	0.266777i
$554$	14.9103	+	10.8330i	0.633480	+	0.460250i
$555$	−9.51825	−	2.02317i	−0.404027	−	0.0858786i
$556$	−4.90190	+	15.0865i	−0.207887	+	0.639810i
$557$	39.5094			1.67407			0.837033	−	0.547152i	$-0.184288\pi$
$557$	39.5094			1.67407			0.837033	+	0.547152i	$0.184288\pi$
$558$	−4.71578	+	2.95997i	−0.199635	+	0.125306i
$559$	−0.530141			−0.0224226
$560$	−0.303533	+	0.934180i	−0.0128266	+	0.0394763i
$561$	−9.93789	−	2.11236i	−0.419578	−	0.0891841i
$562$	−18.8330	−	13.6830i	−0.794421	−	0.577181i
$563$	6.83523	+	11.8390i	0.288071	+	0.498953i	0.973349	−	0.229328i	$-0.0736529\pi$
$563$	6.83523	+	11.8390i	0.288071	+	0.498953i	−0.685279	+	0.728281i	$0.740320\pi$
$564$	0.430335	−	0.745363i	0.0181204	−	0.0313854i
$565$	0.941123	−	0.419015i	0.0395933	−	0.0176281i
$566$	6.72397	−	4.88525i	0.282629	−	0.205342i
$567$	−0.897334	−	0.399519i	−0.0376845	−	0.0167782i
$568$	−3.67676	+	0.781520i	−0.154274	+	0.0327919i
$569$	−1.82699	+	17.3826i	−0.0765913	+	0.728718i	0.887078	+	0.461619i	$0.152731\pi$
$569$	−1.82699	+	17.3826i	−0.0765913	+	0.728718i	−0.963669	+	0.267098i	$0.913935\pi$
$570$	1.63168	+	1.81216i	0.0683435	+	0.0759031i
$571$	−8.75966	+	9.72859i	−0.366580	+	0.407129i	−0.898011	−	0.439973i	$-0.854988\pi$
$571$	−8.75966	+	9.72859i	−0.366580	+	0.407129i	0.531431	+	0.847102i	$0.321655\pi$
$572$	−0.0567655	−	0.540088i	−0.00237349	−	0.0225822i
$573$	3.28175	+	10.1002i	0.137097	+	0.421941i
$574$	3.60257	+	11.0876i	0.150368	+	0.462786i
$575$	−0.273880	−	2.60580i	−0.0114216	−	0.108669i
$576$	0.669131	−	0.743145i	0.0278804	−	0.0309644i
$577$	−14.8137	−	16.4522i	−0.616701	−	0.684916i	0.351185	−	0.936306i	$-0.385779\pi$
$577$	−14.8137	−	16.4522i	−0.616701	−	0.684916i	−0.967886	+	0.251390i	$0.919112\pi$
$578$	0.104971	−	0.998734i	0.00436622	−	0.0415419i
$579$	3.32949	−	0.707706i	0.138369	−	0.0294112i
$580$	−1.46082	−	0.650398i	−0.0606571	−	0.0270063i
$581$	−1.34722	+	0.978816i	−0.0558923	+	0.0406081i
$582$	11.5360	−	5.13616i	0.478183	−	0.212901i
$583$	−13.1508	+	22.7779i	−0.544652	+	0.943364i
$584$	4.66192	+	8.07469i	0.192912	+	0.334133i
$585$	0.183487	+	0.133311i	0.00758625	+	0.00551174i
$586$	−7.74121	−	1.64544i	−0.319786	−	0.0679727i
$587$	−2.46500	+	7.58648i	−0.101741	+	0.313127i	−0.988952	−	0.148237i	$-0.952640\pi$
$587$	−2.46500	+	7.58648i	−0.101741	+	0.313127i	0.887211	+	0.461365i	$0.152640\pi$
$588$	−6.03518			−0.248886
$589$	−5.97634	−	12.1909i	−0.246251	−	0.502318i
$590$	−6.67160			−0.274666
$591$	5.77511	−	17.7739i	0.237556	−	0.731123i
$592$	−9.51825	−	2.02317i	−0.391198	−	0.0831516i
$593$	−1.83325	−	1.33193i	−0.0752824	−	0.0546959i	0.549507	−	0.835489i	$-0.314815\pi$
$593$	−1.83325	−	1.33193i	−0.0752824	−	0.0546959i	−0.624790	+	0.780793i	$0.714815\pi$
$594$	−1.19722	−	2.07364i	−0.0491224	−	0.0850824i
$595$	−2.08392	+	3.60946i	−0.0854325	+	0.147973i
$596$	5.19460	−	2.31279i	0.212779	−	0.0947354i
$597$	−11.9931	+	8.71347i	−0.490843	+	0.356619i
$598$	0.542880	+	0.241706i	0.0222000	+	0.00988409i
$599$	30.4661	−	6.47577i	1.24481	−	0.264593i	0.462016	−	0.886872i	$-0.347126\pi$
$599$	30.4661	−	6.47577i	1.24481	−	0.264593i	0.782796	+	0.622279i	$0.213793\pi$
$600$	0.104528	−	0.994522i	0.00426736	−	0.0406012i
$601$	19.8175	+	22.0096i	0.808373	+	0.897789i	0.996435	−	0.0843682i	$-0.0268872\pi$
$601$	19.8175	+	22.0096i	0.808373	+	0.897789i	−0.188062	+	0.982157i	$0.560221\pi$
$602$	1.53631	−	1.70624i	0.0626153	−	0.0695413i
$603$	0.941502	+	8.95780i	0.0383409	+	0.364790i
$604$	−4.27802	−	13.1664i	−0.174070	−	0.535733i
$605$	−1.62750	−	5.00893i	−0.0661672	−	0.203642i
$606$	0.0847571	+	0.806410i	0.00344302	+	0.0327582i
$607$	−19.9749	+	22.1844i	−0.810756	+	0.900436i	−0.996621	−	0.0821394i	$-0.973825\pi$
$607$	−19.9749	+	22.1844i	−0.810756	+	0.900436i	0.185865	+	0.982575i	$0.440491\pi$
$608$	1.63168	+	1.81216i	0.0661733	+	0.0734929i
$609$	−0.164182	+	1.56208i	−0.00665297	+	0.0632988i
$610$	3.19671	−	0.679482i	0.129431	−	0.0275114i
$611$	0.178326	+	0.0793959i	0.00721430	+	0.00321201i
$612$	3.43277	−	2.49405i	0.138762	−	0.100816i
$613$	22.1865	−	9.87808i	0.896106	−	0.398972i	0.0935954	−	0.995610i	$-0.470164\pi$
$613$	22.1865	−	9.87808i	0.896106	−	0.398972i	0.802510	+	0.596638i	$0.203497\pi$
$614$	7.32198	−	12.6820i	0.295491	−	0.511805i
$615$	−5.93438	−	10.2787i	−0.239297	−	0.414475i
$616$	1.90276	+	1.38244i	0.0766644	+	0.0557000i
$617$	13.0292	+	2.76945i	0.524537	+	0.111494i	0.462567	−	0.886584i	$-0.346928\pi$
$617$	13.0292	+	2.76945i	0.524537	+	0.111494i	0.0619699	+	0.998078i	$0.480262\pi$
$618$	−4.19047	+	12.8969i	−0.168565	+	0.518791i
$619$	7.12186			0.286252			0.143126	−	0.989705i	$-0.454285\pi$
$619$	7.12186			0.286252			0.143126	+	0.989705i	$0.454285\pi$
$620$	−2.07532	+	5.16653i	−0.0833468	+	0.207493i
$621$	2.62015			0.105143
$622$	7.80615	−	24.0249i	0.312998	−	0.963309i
$623$	11.9096	+	2.53146i	0.477148	+	0.101421i
$624$	0.183487	+	0.133311i	0.00734536	+	0.00533672i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−3.31206	+	5.73665i	−0.132376	+	0.229283i
$627$	5.33404	−	2.37487i	0.213021	−	0.0948431i
$628$	−1.29314	+	0.939518i	−0.0516017	+	0.0374908i
$629$	−37.7199	−	16.7940i	−1.50399	−	0.669619i
$630$	−0.960790	+	0.204222i	−0.0382788	+	0.00813641i
$631$	−4.65557	+	44.2948i	−0.185335	+	1.76335i	0.367468	+	0.930036i	$0.380225\pi$
$631$	−4.65557	+	44.2948i	−0.185335	+	1.76335i	−0.552804	+	0.833312i	$0.686442\pi$
$632$	4.93476	+	5.48061i	0.196294	+	0.218007i
$633$	9.91383	−	11.0104i	0.394039	−	0.437625i
$634$	−1.39053	−	13.2300i	−0.0552251	−	0.525432i
$635$	−0.433275	−	1.33348i	−0.0171940	−	0.0529177i
$636$	−3.39440	−	10.4469i	−0.134597	−	0.414246i
$637$	−0.143078	−	1.36129i	−0.00566895	−	0.0539364i
$638$	−2.56200	+	2.84539i	−0.101431	+	0.112650i
$639$	−2.51520	−	2.79341i	−0.0994997	−	0.110506i
$640$	0.104528	−	0.994522i	0.00413185	−	0.0393119i
$641$	13.4179	−	2.85206i	0.529975	−	0.112650i	0.0648506	−	0.997895i	$-0.479343\pi$
$641$	13.4179	−	2.85206i	0.529975	−	0.112650i	0.465124	+	0.885245i	$0.346010\pi$
$642$	2.54048	+	1.13110i	0.100265	+	0.0446408i
$643$	9.97158	−	7.24478i	0.393241	−	0.285706i	−0.373541	−	0.927613i	$-0.621857\pi$
$643$	9.97158	−	7.24478i	0.393241	−	0.285706i	0.766782	+	0.641907i	$0.221857\pi$
$644$	−2.35115	+	1.04680i	−0.0926483	+	0.0412497i
$645$	−1.16873	+	2.02430i	−0.0460186	+	0.0797066i
$646$	5.17346	+	8.96069i	0.203547	+	0.352554i
$647$	−13.5941	−	9.87668i	−0.534439	−	0.388292i	0.287577	−	0.957758i	$-0.407150\pi$
$647$	−13.5941	−	9.87668i	−0.534439	−	0.388292i	−0.822015	+	0.569465i	$0.807150\pi$
$648$	0.978148	+	0.207912i	0.0384253	+	0.00816754i
$649$	−4.93645	+	15.1928i	−0.193773	+	0.596371i
$650$	0.226802			0.00889592
$651$	5.45640	+	0.370505i	0.213853	+	0.0145212i
$652$	−5.00886			−0.196162
$653$	−5.64291	+	17.3671i	−0.220824	+	0.679627i	0.777865	+	0.628432i	$0.216303\pi$
$653$	−5.64291	+	17.3671i	−0.220824	+	0.679627i	−0.998689	+	0.0511947i	$0.983697\pi$
$654$	−13.1523	−	2.79561i	−0.514296	−	0.109317i
$655$	−7.43453	−	5.40150i	−0.290491	−	0.211054i
$656$	−5.93438	−	10.2787i	−0.231699	−	0.401314i
$657$	−4.66192	+	8.07469i	−0.181879	+	0.315024i
$658$	−0.772309	+	0.343854i	−0.0301078	+	0.0134048i
$659$	11.7640	−	8.54703i	0.458259	−	0.332945i	−0.334589	−	0.942364i	$-0.608597\pi$
$659$	11.7640	−	8.54703i	0.458259	−	0.332945i	0.792848	+	0.609419i	$0.208597\pi$
$660$	−2.18742	−	0.973903i	−0.0851453	−	0.0379091i
$661$	29.1469	−	6.19536i	1.13368	−	0.240972i	0.397399	−	0.917646i	$-0.369913\pi$
$661$	29.1469	−	6.19536i	1.13368	−	0.240972i	0.736283	+	0.676674i	$0.236579\pi$
$662$	−2.55612	+	24.3198i	−0.0993462	+	0.945216i
$663$	0.643941	+	0.715169i	0.0250086	+	0.0277748i
$664$	1.13441	−	1.25989i	0.0440235	−	0.0488931i
$665$	−0.250370	−	2.38211i	−0.00970893	−	0.0923743i
$666$	−3.00701	−	9.25463i	−0.116519	−	0.358609i
$667$	−1.29472	−	3.98473i	−0.0501316	−	0.154289i
$668$	−1.08768	−	10.3486i	−0.0420836	−	0.400399i
$669$	0.885128	−	0.983034i	0.0342210	−	0.0380063i
$670$	6.02695	+	6.69361i	0.232841	+	0.258597i
$671$	0.817967	−	7.78244i	0.0315773	−	0.300438i
$672$	−0.960790	+	0.204222i	−0.0370633	+	0.00787804i
$673$	10.9709	+	4.88458i	0.422899	+	0.188287i	0.607141	−	0.794594i	$-0.292316\pi$
$673$	10.9709	+	4.88458i	0.422899	+	0.188287i	−0.184242	+	0.982881i	$0.558983\pi$
$674$	10.8230	−	7.86339i	0.416887	−	0.302886i
$675$	0.913545	−	0.406737i	0.0351624	−	0.0156553i
$676$	6.47428	−	11.2138i	0.249011	−	0.431299i
$677$	−15.8697	−	27.4872i	−0.609923	−	1.05642i	−0.991253	−	0.131978i	$-0.957867\pi$
$677$	−15.8697	−	27.4872i	−0.609923	−	1.05642i	0.381330	−	0.924439i	$-0.375466\pi$
$678$	0.833439	+	0.605529i	0.0320080	+	0.0232552i
$679$	−12.1326	−	2.57886i	−0.465607	−	0.0989677i
$680$	1.31120	−	4.03547i	0.0502823	−	0.154753i
$681$	−19.2509			−0.737697
$682$	10.2299	+	8.54882i	0.391722	+	0.327351i
$683$	0.141639			0.00541967			0.00270984	−	0.999996i	$-0.499137\pi$
$683$	0.141639			0.00541967			0.00270984	+	0.999996i	$0.499137\pi$
$684$	−0.753539	+	2.31916i	−0.0288123	+	0.0886751i
$685$	6.74063	+	1.43276i	0.257546	+	0.0547431i
$686$	10.3585	+	7.52592i	0.395491	+	0.287341i
$687$	6.57707	+	11.3918i	0.250931	+	0.434625i
$688$	−1.16873	+	2.02430i	−0.0445574	+	0.0771756i
$689$	2.27593	−	1.01331i	0.0867059	−	0.0386040i
$690$	2.11975	−	1.54009i	0.0806974	−	0.0586301i
$691$	18.4966	+	8.23520i	0.703643	+	0.313282i	0.727186	−	0.686441i	$-0.240828\pi$
$691$	18.4966	+	8.23520i	0.703643	+	0.313282i	−0.0235430	+	0.999723i	$0.507495\pi$
$692$	13.7674	−	2.92634i	0.523356	−	0.111243i
$693$	−0.245845	+	2.33906i	−0.00933887	+	0.0888534i
$694$	10.0411	+	11.1518i	0.381155	+	0.423316i
$695$	−10.6143	+	11.7884i	−0.402625	+	0.447160i
$696$	−0.167148	−	1.59030i	−0.00633572	−	0.0602803i
$697$	−15.5624	−	47.8960i	−0.589466	−	1.81419i
$698$	1.89145	+	5.82127i	0.0715923	+	0.220338i
$699$	1.37343	+	13.0673i	0.0519479	+	0.494252i
$700$	−0.657257	+	0.729957i	−0.0248420	+	0.0275898i
$701$	34.8261	+	38.6783i	1.31536	+	1.46086i	0.794568	+	0.607175i	$0.207697\pi$
$701$	34.8261	+	38.6783i	1.31536	+	1.46086i	0.520794	+	0.853682i	$0.325636\pi$
$702$	−0.0237073	+	0.225560i	−0.000894775	+	0.00851321i
$703$	23.2103	−	4.93350i	0.875392	−	0.186070i
$704$	−2.18742	−	0.973903i	−0.0824416	−	0.0367054i
$705$	0.696297	−	0.505890i	0.0262241	−	0.0190529i
$706$	0.690757	−	0.307545i	0.0259970	−	0.0115746i
$707$	0.398231	−	0.689757i	0.0149770	−	0.0259410i
$708$	−3.33580	−	5.77778i	−0.125367	−	0.217142i
$709$	19.7154	+	14.3241i	0.740429	+	0.537953i	0.892845	−	0.450363i	$-0.148706\pi$
$709$	19.7154	+	14.3241i	0.740429	+	0.537953i	−0.152417	+	0.988316i	$0.548706\pi$
$710$	−3.67676	−	0.781520i	−0.137986	−	0.0293299i
$711$	−2.27897	+	7.01394i	−0.0854679	+	0.263043i
$712$	−12.3956			−0.464546
$713$	−13.6985	+	5.01713i	−0.513013	+	0.187893i
$714$	−4.16784			−0.155978
$715$	0.167816	−	0.516484i	0.00627595	−	0.0193154i
$716$	−22.1645	−	4.71122i	−0.828327	−	0.176066i
$717$	6.18153	+	4.49114i	0.230853	+	0.167725i
$718$	2.09895	+	3.63549i	0.0783322	+	0.135675i
$719$	1.57914	−	2.73516i	0.0588922	−	0.102004i	−0.835076	−	0.550134i	$-0.814577\pi$
$719$	1.57914	−	2.73516i	0.0588922	−	0.102004i	0.893968	+	0.448130i	$0.147910\pi$
$720$	0.913545	−	0.406737i	0.0340458	−	0.0151582i
$721$	10.7761	−	7.82931i	0.401324	−	0.291579i
$722$	11.9251	+	5.30942i	0.443808	+	0.197596i
$723$	−13.9090	+	2.95645i	−0.517281	+	0.109951i
$724$	0.190198	−	1.80962i	0.00706866	−	0.0672538i
$725$	−1.06998	−	1.18834i	−0.0397382	−	0.0441337i
$726$	3.52411	−	3.91392i	0.130792	−	0.145259i
$727$	3.43355	+	32.6681i	0.127343	+	1.21159i	0.852395	+	0.522898i	$0.175149\pi$
$727$	3.43355	+	32.6681i	0.127343	+	1.21159i	−0.725052	+	0.688694i	$0.758184\pi$
$728$	−0.0688421	−	0.211874i	−0.00255146	−	0.00785258i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	0.974607	+	9.27277i	0.0360718	+	0.343201i
$731$	−6.63654	+	7.37063i	−0.245461	+	0.272613i
$732$	2.18680	+	2.42869i	0.0808266	+	0.0897670i
$733$	−0.0975533	+	0.928158i	−0.00360321	+	0.0342823i	−0.996176	−	0.0873718i	$-0.972153\pi$
$733$	−0.0975533	+	0.928158i	−0.00360321	+	0.0342823i	0.992573	+	0.121654i	$0.0388199\pi$
$734$	16.4334	−	3.49302i	0.606567	−	0.128930i
$735$	−5.51341	−	2.45473i	−0.203365	−	0.0905440i
$736$	2.11975	−	1.54009i	0.0781349	−	0.0567683i
$737$	19.7024	−	8.77208i	0.725748	−	0.323124i
$738$	5.93438	−	10.2787i	0.218448	−	0.378363i
$739$	11.9160	+	20.6390i	0.438335	+	0.759219i	0.997561	−	0.0697961i	$-0.0222349\pi$
$739$	11.9160	+	20.6390i	0.438335	+	0.759219i	−0.559226	+	0.829015i	$0.688902\pi$
$740$	−7.87246	−	5.71967i	−0.289397	−	0.210259i
$741$	−0.540973	−	0.114987i	−0.0198731	−	0.00422417i
$742$	−3.33416	+	10.2615i	−0.122401	+	0.376712i
$743$	29.5313			1.08340			0.541699	−	0.840572i	$-0.317781\pi$
$743$	29.5313			1.08340			0.541699	+	0.840572i	$0.317781\pi$
$744$	−5.51201	+	0.785988i	−0.202080	+	0.0288157i
$745$	5.68620			0.208326
$746$	5.26783	−	16.2127i	0.192869	−	0.593590i
$747$	1.65830	+	0.352482i	0.0606739	+	0.0128966i
$748$	−8.21954	−	5.97184i	−0.300536	−	0.218352i
$749$	−1.36578	−	2.36560i	−0.0499044	−	0.0864370i
$750$	0.500000	−	0.866025i	0.0182574	−	0.0316228i
$751$	−27.4990	+	12.2434i	−1.00345	+	0.446766i	−0.841631	−	0.540053i	$-0.818404\pi$
$751$	−27.4990	+	12.2434i	−1.00345	+	0.446766i	−0.161823	+	0.986820i	$0.551737\pi$
$752$	0.696297	−	0.505890i	0.0253914	−	0.0184479i
$753$	12.4242	+	5.53161i	0.452763	+	0.201583i
$754$	0.354746	−	0.0754037i	0.0129191	−	0.00274604i
$755$	1.44709	−	13.7681i	0.0526649	−	0.501073i
$756$	−0.657257	−	0.729957i	−0.0239042	−	0.0265483i
$757$	10.9124	−	12.1195i	0.396619	−	0.440490i	−0.511449	−	0.859314i	$-0.670891\pi$
$757$	10.9124	−	12.1195i	0.396619	−	0.440490i	0.908067	+	0.418824i	$0.137558\pi$
$758$	8.42435e−5	0	0.000801523i	3.05986e−6	0	2.91126e-5i
$759$	−1.93870	−	5.96671i	−0.0703704	−	0.216578i
$760$	0.753539	+	2.31916i	0.0273337	+	0.0841246i
$761$	2.20086	+	20.9398i	0.0797811	+	0.759067i	0.959145	+	0.282916i	$0.0913017\pi$
$761$	2.20086	+	20.9398i	0.0797811	+	0.759067i	−0.879364	+	0.476151i	$0.842032\pi$
$762$	0.938194	−	1.04197i	0.0339872	−	0.0377466i
$763$	8.83756	+	9.81511i	0.319941	+	0.355331i
$764$	−1.11009	+	10.5618i	−0.0401615	+	0.382112i
$765$	4.15042	−	0.882198i	0.150059	−	0.0318959i
$766$	20.3629	+	9.06615i	0.735742	+	0.327573i
$767$	1.22415	−	0.889399i	0.0442016	−	0.0321143i
$768$	0.913545	−	0.406737i	0.0329647	−	0.0146768i
$769$	5.87364	−	10.1734i	0.211809	−	0.366864i	−0.740472	−	0.672087i	$-0.765398\pi$
$769$	5.87364	−	10.1734i	0.211809	−	0.366864i	0.952281	+	0.305224i	$0.0987313\pi$
$770$	1.17597	+	2.03684i	0.0423790	+	0.0734027i
$771$	−8.65873	−	6.29094i	−0.311837	−	0.226563i
$772$	3.32949	+	0.707706i	0.119831	+	0.0254709i
$773$	−7.23989	+	22.2821i	−0.260401	+	0.801431i	0.732317	+	0.680964i	$0.238439\pi$
$773$	−7.23989	+	22.2821i	−0.260401	+	0.801431i	−0.992717	+	0.120466i	$0.961561\pi$
$774$	−2.33746			−0.0840182
$775$	−3.99732	+	3.87575i	−0.143588	+	0.139221i
$776$	12.6277			0.453309
$777$	−2.95365	+	9.09040i	−0.105962	+	0.326116i
$778$	−29.1617	−	6.19852i	−1.04550	−	0.222228i
$779$	23.4146	+	17.0117i	0.838915	+	0.609508i
$780$	0.113401	+	0.196417i	0.00406041	+	0.00703284i
$781$	−4.50022	+	7.79461i	−0.161031	+	0.278913i
$782$	10.1565	−	4.52196i	0.363195	−	0.161705i
$783$	1.29367	−	0.939906i	0.0462320	−	0.0335895i
$784$	−5.51341	−	2.45473i	−0.196907	−	0.0876688i
$785$	−1.56347	+	0.332327i	−0.0558028	+	0.0118613i
$786$	0.960574	−	9.13925i	0.0342625	−	0.325986i
$787$	−15.1750	−	16.8536i	−0.540931	−	0.600764i	0.409266	−	0.912415i	$-0.365785\pi$
$787$	−15.1750	−	16.8536i	−0.540931	−	0.600764i	−0.950197	+	0.311651i	$0.899118\pi$
$788$	12.5051	−	13.8884i	0.445477	−	0.494752i
$789$	1.32625	+	12.6184i	0.0472158	+	0.449228i
$790$	2.27897	+	7.01394i	0.0810820	+	0.249545i
$791$	−0.312696	−	0.962380i	−0.0111182	−	0.0342183i
$792$	−0.250286	−	2.38131i	−0.00889354	−	0.0846163i
$793$	−0.495972	+	0.550833i	−0.0176125	+	0.0195607i
$794$	2.98582	+	3.31609i	0.105963	+	0.117684i
$795$	1.14819	−	10.9243i	0.0407222	−	0.387446i
$796$	−14.5003	+	3.08213i	−0.513949	+	0.109243i
$797$	−43.8912	−	19.5416i	−1.55471	−	0.692200i	−0.563696	−	0.825982i	$-0.690621\pi$
$797$	−43.8912	−	19.5416i	−1.55471	−	0.692200i	−0.991011	+	0.133782i	$0.957288\pi$
$798$	1.93778	−	1.40788i	0.0685968	−	0.0498385i
$799$	3.33622	−	1.48538i	0.118027	−	0.0525490i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−6.19781	−	10.7349i	−0.218989	−	0.379300i
$802$	3.88378	+	2.82173i	0.137141	+	0.0996389i
$803$	21.8374	+	4.64169i	0.770627	+	0.163802i
$804$	−2.78336	+	8.56630i	−0.0981615	+	0.302110i
$805$	−2.57365			−0.0907094
$806$	−0.307962	−	1.22465i	−0.0108475	−	0.0431366i
$807$	−8.84433			−0.311335
$808$	−0.250567	+	0.771166i	−0.00881492	+	0.0271295i
$809$	−5.43525	−	1.15530i	−0.191093	−	0.0406181i	0.111371	−	0.993779i	$-0.464476\pi$
$809$	−5.43525	−	1.15530i	−0.191093	−	0.0406181i	−0.302464	+	0.953161i	$0.597809\pi$
$810$	0.809017	+	0.587785i	0.0284260	+	0.0206527i
$811$	−18.4209	−	31.9059i	−0.646844	−	1.12037i	−0.983872	−	0.178872i	$-0.942755\pi$
$811$	−18.4209	−	31.9059i	−0.646844	−	1.12037i	0.337029	−	0.941494i	$-0.390578\pi$
$812$	−0.785344	+	1.36026i	−0.0275602	+	0.0477356i
$813$	21.0631	−	9.37791i	0.738716	−	0.328898i
$814$	−18.8501	+	13.6954i	−0.660694	+	0.480022i
$815$	−4.57582	−	2.03729i	−0.160284	−	0.0713630i
$816$	4.15042	−	0.882198i	0.145294	−	0.0308831i
$817$	0.595802	−	5.66868i	0.0208445	−	0.198322i
$818$	15.5780	+	17.3011i	0.544672	+	0.604919i
$819$	0.149067	−	0.165556i	0.00520884	−	0.00578500i
$820$	−1.24062	−	11.8038i	−0.0433245	−	0.412205i
$821$	2.02612	+	6.23576i	0.0707122	+	0.217630i	0.980167	−	0.198173i	$-0.0635007\pi$
$821$	2.02612	+	6.23576i	0.0707122	+	0.217630i	−0.909455	+	0.415803i	$0.863501\pi$
$822$	2.12950	+	6.55393i	0.0742749	+	0.228595i
$823$	4.06830	+	38.7073i	0.141812	+	1.34925i	0.801627	+	0.597825i	$0.203968\pi$
$823$	4.06830	+	38.7073i	0.141812	+	1.34925i	−0.659815	+	0.751428i	$0.729365\pi$
$824$	−9.07385	+	10.0775i	−0.316102	+	0.351067i
$825$	−1.60219	−	1.77941i	−0.0557810	−	0.0619511i
$826$	−0.684997	+	6.51731i	−0.0238341	+	0.226766i
$827$	33.5048	−	7.12167i	1.16508	−	0.247645i	0.415520	−	0.909584i	$-0.363600\pi$
$827$	33.5048	−	7.12167i	1.16508	−	0.247645i	0.749558	+	0.661939i	$0.230266\pi$
$828$	2.39363	+	1.06571i	0.0831843	+	0.0370360i
$829$	18.3217	−	13.3115i	0.636341	−	0.462329i	−0.222250	−	0.974990i	$-0.571340\pi$
$829$	18.3217	−	13.3115i	0.636341	−	0.462329i	0.858591	+	0.512661i	$0.171340\pi$
$830$	1.54877	−	0.689559i	0.0537588	−	0.0239349i
$831$	−9.21510	+	15.9610i	−0.319668	+	0.553681i
$832$	0.113401	+	0.196417i	0.00393148	+	0.00680952i
$833$	−20.7174	−	15.0521i	−0.717815	−	0.521523i
$834$	−15.5162	−	3.29808i	−0.537283	−	0.114203i
$835$	3.21551	−	9.89631i	0.111277	−	0.342476i
$836$	5.83883			0.201940
$837$	−3.43669	−	4.38054i	−0.118789	−	0.151414i
$838$	−12.5224			−0.432581
$839$	−15.9538	+	49.1008i	−0.550787	+	1.69515i	0.156030	+	0.987752i	$0.450130\pi$
$839$	−15.9538	+	49.1008i	−0.550787	+	1.69515i	−0.706817	+	0.707396i	$0.749870\pi$
$840$	−0.960790	−	0.204222i	−0.0331504	−	0.00704634i
$841$	21.3928	+	15.5428i	0.737684	+	0.535959i
$842$	−14.2849	−	24.7422i	−0.492290	−	0.852672i
$843$	11.6394	−	20.1601i	0.400883	−	0.694350i
$844$	13.5351	−	6.02621i	0.465897	−	0.207431i
$845$	10.4756	−	7.61097i	0.360372	−	0.261825i
$846$	0.786262	+	0.350066i	0.0270322	+	0.0120355i
$847$	−5.06019	+	1.07558i	−0.173870	+	0.0369572i
$848$	1.14819	−	10.9243i	0.0394291	−	0.375143i
$849$	5.56133	+	6.17649i	0.190864	+	0.211976i
$850$	2.83921	−	3.15327i	0.0973843	−	0.108156i
$851$	−2.66510	−	25.3567i	−0.0913584	−	0.869217i
$852$	−1.16157	−	3.57493i	−0.0397946	−	0.122475i
$853$	−2.52956	−	7.78518i	−0.0866105	−	0.266560i	0.898366	−	0.439247i	$-0.144755\pi$
$853$	−2.52956	−	7.78518i	−0.0866105	−	0.266560i	−0.984977	+	0.172688i	$0.944755\pi$
$854$	−0.335550	−	3.19255i	−0.0114823	−	0.109247i
$855$	−1.63168	+	1.81216i	−0.0558022	+	0.0619746i
$856$	1.86079	+	2.06661i	0.0636004	+	0.0706354i
$857$	4.68981	−	44.6206i	0.160201	−	1.52421i	−0.558859	−	0.829263i	$-0.688761\pi$
$857$	4.68981	−	44.6206i	0.160201	−	1.52421i	0.719060	−	0.694948i	$-0.244573\pi$
$858$	0.531196	−	0.112909i	0.0181347	−	0.00385465i
$859$	49.7779	+	22.1626i	1.69840	+	0.756176i	0.999147	+	0.0413027i	$0.0131508\pi$
$859$	49.7779	+	22.1626i	1.69840	+	0.756176i	0.699253	+	0.714874i	$0.253516\pi$
$860$	−1.89104	+	1.37392i	−0.0644840	+	0.0468504i
$861$	−10.6503	+	4.74180i	−0.362960	+	0.161600i
$862$	11.5488	−	20.0031i	0.393353	−	0.681308i
$863$	21.2650	+	36.8321i	0.723870	+	1.25378i	0.959438	+	0.281921i	$0.0909717\pi$
$863$	21.2650	+	36.8321i	0.723870	+	1.25378i	−0.235568	+	0.971858i	$0.575695\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	13.7674	+	2.92634i	0.468104	+	0.0994986i
$866$	11.7674	−	36.2163i	0.399873	−	1.23068i
$867$	1.00424			0.0341056
$868$	4.83397	+	2.55779i	0.164076	+	0.0868170i
$869$	17.6587			0.599029
$870$	0.494138	−	1.52080i	0.0167528	−	0.0515600i
$871$	−1.99820	−	0.424730i	−0.0677064	−	0.0143914i
$872$	−10.8782	−	7.90344i	−0.368381	−	0.267644i
$873$	6.31387	+	10.9359i	0.213692	+	0.370126i
$874$	−3.19462	+	5.53325i	−0.108060	+	0.187165i
$875$	−0.897334	+	0.399519i	−0.0303354	+	0.0135062i
$876$	−7.54315	+	5.48042i	−0.254859	+	0.185166i
$877$	−10.4073	−	4.63365i	−0.351431	−	0.156467i	0.223426	−	0.974721i	$-0.428276\pi$
$877$	−10.4073	−	4.63365i	−0.351431	−	0.156467i	−0.574857	+	0.818254i	$0.694942\pi$
$878$	24.2925	−	5.16354i	0.819834	−	0.174261i
$879$	0.827254	−	7.87080i	0.0279026	−	0.265475i
$880$	−1.60219	−	1.77941i	−0.0540097	−	0.0599839i
$881$	28.2155	−	31.3365i	0.950606	−	1.05575i	−0.0477744	−	0.998858i	$-0.515213\pi$
$881$	28.2155	−	31.3365i	0.950606	−	1.05575i	0.998380	−	0.0568964i	$-0.0181205\pi$
$882$	−0.630848	−	6.00211i	−0.0212417	−	0.202102i
$883$	0.328334	+	1.01051i	0.0110493	+	0.0340063i	0.956429	−	0.291964i	$-0.0943089\pi$
$883$	0.328334	+	1.01051i	0.0110493	+	0.0340063i	−0.945380	+	0.325971i	$0.894309\pi$
$884$	0.297384	+	0.915253i	0.0100021	+	0.0307833i
$885$	−0.697372	−	6.63506i	−0.0234419	−	0.223035i
$886$	15.8988	−	17.6574i	0.534130	−	0.593211i
$887$	0.839967	+	0.932878i	0.0282033	+	0.0313230i	0.757081	−	0.653321i	$-0.226625\pi$
$887$	0.839967	+	0.932878i	0.0282033	+	0.0313230i	−0.728878	+	0.684643i	$0.759958\pi$
$888$	1.01716	−	9.67758i	0.0341335	−	0.324758i
$889$	−1.34713	+	0.286342i	−0.0451813	+	0.00960359i
$890$	−11.3240	−	5.04175i	−0.379580	−	0.169000i
$891$	1.93714	−	1.40741i	0.0648965	−	0.0471501i
$892$	1.20844	−	0.538032i	0.0404616	−	0.0180147i
$893$	−1.04937	+	1.81757i	−0.0351160	+	0.0608227i
$894$	2.84310	+	4.92439i	0.0950875	+	0.164696i
$895$	−18.3321	−	13.3190i	−0.612774	−	0.445206i
$896$	−0.960790	−	0.204222i	−0.0320977	−	0.00682258i
$897$	−0.183635	+	0.565171i	−0.00613141	+	0.0188705i
$898$	37.3187			1.24534
$899$	−4.96373	+	7.39111i	−0.165550	+	0.246507i
$900$	1.00000			0.0333333
$901$	14.4029	−	44.3276i	0.479830	−	1.47677i
$902$	−27.7979	−	5.90863i	−0.925570	−	0.196736i
$903$	1.85749	+	1.34954i	0.0618132	+	0.0449099i
$904$	0.515094	+	0.892168i	0.0171318	+	0.0296731i
$905$	0.909792	−	1.57581i	0.0302425	−	0.0523816i
$906$	12.6471	−	5.63085i	0.420171	−	0.187072i
$907$	26.9942	−	19.6124i	0.896326	−	0.651219i	−0.0411934	−	0.999151i	$-0.513116\pi$
$907$	26.9942	−	19.6124i	0.896326	−	0.651219i	0.937520	+	0.347932i	$0.113116\pi$
$908$	−17.5866	−	7.83006i	−0.583632	−	0.259850i
$909$	−0.793133	+	0.168586i	−0.0263066	+	0.00559163i
$910$	0.0232866	−	0.221557i	0.000771944	−	0.00734455i
$911$	−0.900576	−	1.00019i	−0.0298374	−	0.0331378i	0.728041	−	0.685533i	$-0.240431\pi$
$911$	−0.900576	−	1.00019i	−0.0298374	−	0.0331378i	−0.757879	+	0.652395i	$0.773764\pi$
$912$	−1.63168	+	1.81216i	−0.0540303	+	0.0600067i
$913$	−0.424322	−	4.03715i	−0.0140430	−	0.133610i
$914$	−0.319846	−	0.984385i	−0.0105796	−	0.0325606i
$915$	1.00991	+	3.10817i	0.0333865	+	0.102753i
$916$	1.37498	+	13.0821i	0.0454307	+	0.432244i
$917$	−6.03992	+	6.70801i	−0.199456	+	0.221518i
$918$	2.83921	+	3.15327i	0.0937080	+	0.104073i
$919$	0.784948	−	7.46828i	0.0258930	−	0.246356i	−0.973918	−	0.226902i	$-0.927140\pi$
$919$	0.784948	−	7.46828i	0.0258930	−	0.246356i	0.999811	−	0.0194543i	$-0.00619290\pi$
$920$	2.56289	−	0.544760i	0.0844961	−	0.0179602i
$921$	13.3779	+	5.95623i	0.440817	+	0.196265i
$922$	10.3565	−	7.52445i	0.341074	−	0.247804i
$923$	0.778823	−	0.346755i	0.0256353	−	0.0114136i
$924$	−1.17597	+	2.03684i	−0.0386866	+	0.0670072i
$925$	−4.86545	−	8.42720i	−0.159975	−	0.277085i
$926$	−25.0812	−	18.2225i	−0.824219	−	0.598830i
$927$	−13.2643	−	2.81942i	−0.435657	−	0.0926018i
$928$	0.494138	−	1.52080i	0.0162209	−	0.0499227i
$929$	2.40759			0.0789906			0.0394953	−	0.999220i	$-0.487425\pi$
$929$	2.40759			0.0789906			0.0394953	+	0.999220i	$0.487425\pi$
$930$	−5.35516	−	1.52390i	−0.175603	−	0.0499706i
$931$	14.7168			0.482324
$932$	−4.06027	+	12.4962i	−0.132999	+	0.409327i
$933$	24.7092	+	5.25211i	0.808943	+	0.171946i
$934$	13.7707	+	10.0050i	0.450590	+	0.327373i
$935$	−5.07995	−	8.79874i	−0.166132	−	0.287750i
$936$	−0.113401	+	0.196417i	−0.00370663	+	0.00642008i
$937$	−40.1896	+	17.8936i	−1.31294	+	0.584557i	−0.939325	−	0.343028i	$-0.888547\pi$
$937$	−40.1896	+	17.8936i	−1.31294	+	0.584557i	−0.373612	+	0.927585i	$0.621881\pi$
$938$	7.15762	−	5.20031i	0.233705	−	0.169796i
$939$	−6.05143	−	2.69427i	−0.197481	−	0.0879242i
$940$	0.841863	−	0.178944i	0.0274586	−	0.00583650i
$941$	2.69618	−	25.6525i	0.0878931	−	0.836247i	−0.858410	−	0.512965i	$-0.828547\pi$
$941$	2.69618	−	25.6525i	0.0878931	−	0.836247i	0.946303	−	0.323282i	$-0.104786\pi$
$942$	−1.06954	−	1.18785i	−0.0348475	−	0.0387021i
$943$	20.8086	−	23.1103i	0.677621	−	0.752575i
$944$	−0.697372	−	6.63506i	−0.0226975	−	0.215953i
$945$	−0.303533	−	0.934180i	−0.00987394	−	0.0303889i
$946$	1.72953	+	5.32295i	0.0562319	+	0.173064i
$947$	0.810650	+	7.71281i	0.0263426	+	0.250633i	0.999766	+	0.0216211i	$0.00688274\pi$
$947$	0.810650	+	7.71281i	0.0263426	+	0.250633i	−0.973424	+	0.229012i	$0.926451\pi$
$948$	−4.93476	+	5.48061i	−0.160274	+	0.178002i
$949$	−1.41499	−	1.57151i	−0.0459325	−	0.0510133i
$950$	−0.254893	+	2.42515i	−0.00826982	+	0.0786821i
$951$	13.0122	−	2.76583i	0.421950	−	0.0896883i
$952$	−3.80751	−	1.69521i	−0.123402	−	0.0549422i
$953$	−35.2979	+	25.6454i	−1.14341	+	0.830737i	−0.987591	−	0.157049i	$-0.949802\pi$
$953$	−35.2979	+	25.6454i	−1.14341	+	0.830737i	−0.155820	+	0.987785i	$0.549802\pi$
$954$	10.0348	−	4.46780i	0.324890	−	0.144650i
$955$	−5.30998	+	9.19715i	−0.171827	+	0.297613i
$956$	3.82040	+	6.61712i	0.123560	+	0.214013i
$957$	−3.09760	−	2.25054i	−0.100131	−	0.0727497i
$958$	14.4512	+	3.07170i	0.466898	+	0.0992422i
$959$	2.09171	−	6.43763i	0.0675450	−	0.207882i
$960$	1.00000			0.0322749
$961$	26.3555	+	16.3214i	0.850176	+	0.526498i
$962$	2.20699			0.0711562
$963$	−0.859346	+	2.64480i	−0.0276921	+	0.0852274i
$964$	−13.9090	−	2.95645i	−0.447978	−	0.0952207i
$965$	2.75379	+	2.00075i	0.0886478	+	0.0644064i
$966$	−1.28683	−	2.22885i	−0.0414030	−	0.0717121i
$967$	8.70015	−	15.0691i	0.279778	−	0.484590i	−0.691552	−	0.722327i	$-0.743073\pi$
$967$	8.70015	−	15.0691i	0.279778	−	0.484590i	0.971329	+	0.237738i	$0.0764058\pi$
$968$	4.81137	−	2.14216i	0.154643	−	0.0688516i
$969$	−8.37083	+	6.08176i	−0.268910	+	0.195374i
$970$	11.5360	+	5.13616i	0.370399	+	0.164912i
$971$	−38.7944	+	8.24600i	−1.24497	+	0.264627i	−0.782862	−	0.622196i	$-0.786241\pi$
$971$	−38.7944	+	8.24600i	−1.24497	+	0.264627i	−0.462110	+	0.886823i	$0.652907\pi$
$972$	−0.104528	+	0.994522i	−0.00335275	+	0.0318993i
$973$	10.4260	+	11.5792i	0.334242	+	0.371213i
$974$	24.5541	−	27.2700i	0.786763	−	0.873788i
$975$	0.0237073	+	0.225560i	0.000759241	+	0.00722370i
$976$	1.00991	+	3.10817i	0.0323263	+	0.0994902i
$977$	16.8295	+	51.7959i	0.538424	+	1.65710i	0.736132	+	0.676838i	$0.236650\pi$
$977$	16.8295	+	51.7959i	0.538424	+	1.65710i	−0.197708	+	0.980261i	$0.563350\pi$
$978$	−0.523568	−	4.98142i	−0.0167419	−	0.159288i
$979$	−19.8601	+	22.0569i	−0.634732	+	0.704941i
$980$	−4.03832	−	4.48501i	−0.128999	−	0.143268i
$981$	1.40550	−	13.3725i	0.0448743	−	0.426950i
$982$	7.03145	−	1.49458i	0.224382	−	0.0476940i
$983$	6.66516	+	2.96752i	0.212586	+	0.0946492i	0.510267	−	0.860016i	$-0.329547\pi$
$983$	6.66516	+	2.96752i	0.212586	+	0.0946492i	−0.297681	+	0.954665i	$0.596213\pi$
$984$	9.60204	−	6.97629i	0.306102	−	0.222396i
$985$	17.0729	−	7.60135i	0.543988	−	0.242199i
$986$	3.39253	−	5.87603i	0.108040	−	0.187131i
$987$	−0.422699	−	0.732136i	−0.0134547	−	0.0233041i
$988$	−0.447434	−	0.325080i	−0.0142348	−	0.0103422i
$989$	−5.99066	−	1.27335i	−0.190492	−	0.0404903i
$990$	0.739920	−	2.27724i	0.0235162	−	0.0723754i
$991$	−43.1438			−1.37051			−0.685255	−	0.728304i	$-0.740309\pi$
$991$	−43.1438			−1.37051			−0.685255	+	0.728304i	$0.740309\pi$
$992$	−5.35516	−	1.52390i	−0.170026	−	0.0483838i
$993$	−24.4538			−0.776017
$994$	−1.14095	+	3.51149i	−0.0361888	+	0.111378i
$995$	−14.5003	−	3.08213i	−0.459690	−	0.0977102i
$996$	1.37156	+	0.996499i	0.0434596	+	0.0315753i
$997$	−11.5374	−	19.9834i	−0.365394	−	0.632881i	0.623445	−	0.781867i	$-0.285732\pi$
$997$	−11.5374	−	19.9834i	−0.365394	−	0.632881i	−0.988839	+	0.148986i	$0.952399\pi$
$998$	−14.9088	+	25.8229i	−0.471931	+	0.817409i
$999$	8.88961	−	3.95791i	0.281255	−	0.125223i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.f.691.2	✓	16
31.7	even	15	inner	930.2.bg.f.751.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.f.691.2	✓	16	1.1	even	1	trivial
930.2.bg.f.751.2	yes	16	31.7	even	15	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.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.897334 + 0.399519i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.897334 + 0.399519i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +(0.978148 - 0.207912i) q^{10} +(0.250286 - 2.38131i) q^{11} +(0.669131 + 0.743145i) q^{12} +(-0.151760 + 0.168547i) q^{13} +(-0.102674 - 0.976874i) q^{14} +(0.309017 + 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.443529 + 4.21990i) q^{17} +(-0.669131 + 0.743145i) q^{18} +(-1.63168 - 1.81216i) q^{19} +(-0.104528 + 0.994522i) q^{20} +(0.960790 - 0.204222i) q^{21} +(2.18742 + 0.973903i) q^{22} +(-2.11975 + 1.54009i) q^{23} +(-0.913545 + 0.406737i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.113401 - 0.196417i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.960790 + 0.204222i) q^{28} +(-0.494138 + 1.52080i) q^{29} -1.00000 q^{30} +(5.35516 + 1.52390i) q^{31} -1.00000 q^{32} +(-0.739920 + 2.27724i) q^{33} +(-4.15042 - 0.882198i) q^{34} +(0.794661 + 0.577355i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-4.86545 + 8.42720i) q^{37} +(2.22768 - 0.991829i) q^{38} +(0.183487 - 0.133311i) q^{39} +(-0.913545 - 0.406737i) q^{40} +(-11.6094 + 2.46766i) q^{41} +(-0.102674 + 0.976874i) q^{42} +(1.56406 + 1.73707i) q^{43} +(-1.60219 + 1.77941i) q^{44} +(-0.104528 - 0.994522i) q^{45} +(-0.809671 - 2.49191i) q^{46} +(-0.265962 - 0.818547i) q^{47} +(-0.104528 - 0.994522i) q^{48} +(-4.03832 + 4.48501i) q^{49} +(-0.669131 - 0.743145i) q^{50} +(0.443529 - 4.21990i) q^{51} +(0.221846 - 0.0471549i) q^{52} +(-10.0348 - 4.46780i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-2.18742 + 0.973903i) q^{55} +(-0.491127 + 0.850657i) q^{56} +(1.21925 + 2.11181i) q^{57} +(-1.29367 - 0.939906i) q^{58} +(-6.52581 - 1.38710i) q^{59} +(0.309017 - 0.951057i) q^{60} +3.26813 q^{61} +(-3.10415 + 4.62215i) q^{62} -0.982255 q^{63} +(0.309017 - 0.951057i) q^{64} +(0.221846 + 0.0471549i) q^{65} +(-1.93714 - 1.40741i) q^{66} +(4.50357 + 7.80041i) q^{67} +(2.12157 - 3.67467i) q^{68} +(2.39363 - 1.06571i) q^{69} +(-0.794661 + 0.577355i) q^{70} +(-3.43393 - 1.52888i) q^{71} +(0.978148 - 0.207912i) q^{72} +(-0.974607 + 9.27277i) q^{73} +(-6.51124 - 7.23146i) q^{74} +(0.669131 - 0.743145i) q^{75} +(0.254893 + 2.42515i) q^{76} +(0.726790 + 2.23683i) q^{77} +(0.0700858 + 0.215702i) q^{78} +(0.770886 + 7.33449i) q^{79} +(0.669131 - 0.743145i) q^{80} +(0.669131 + 0.743145i) q^{81} +(1.24062 - 11.8038i) q^{82} +(1.65830 - 0.352482i) q^{83} +(-0.897334 - 0.399519i) q^{84} +(3.43277 - 2.49405i) q^{85} +(-2.13537 + 0.950730i) q^{86} +(0.799532 - 1.38483i) q^{87} +(-1.19722 - 2.07364i) q^{88} +(-10.0283 - 7.28596i) q^{89} +(0.978148 + 0.207912i) q^{90} +(0.0688421 - 0.211874i) q^{91} +2.62015 q^{92} +(-4.92130 - 2.60400i) q^{93} +0.860671 q^{94} +(-0.753539 + 2.31916i) q^{95} +(0.978148 + 0.207912i) q^{96} +(10.2161 + 7.42240i) q^{97} +(-3.01759 - 5.22662i) q^{98} +(1.19722 - 2.07364i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} - 13 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 - 13 * q^7 + 4 * q^8 + 2 * q^9	\( 16 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} - 13 q^{7} + 4 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{12} - 6 q^{13} - 2 q^{14} - 4 q^{15} - 4 q^{16} + 6 q^{17} - 2 q^{18} + 9 q^{19} + 2 q^{20} + 2 q^{21} - 13 q^{22} - 3 q^{23} - 2 q^{24} - 8 q^{25} + q^{26} - 4 q^{27} + 2 q^{28} - q^{29} - 16 q^{30} - 19 q^{31} - 16 q^{32} + 14 q^{33} + 4 q^{34} + 11 q^{35} - 8 q^{36} - 3 q^{37} + 6 q^{38} - 13 q^{39} - 2 q^{40} - 2 q^{42} + 2 q^{43} - 7 q^{44} + 2 q^{45} - 7 q^{46} - q^{47} + 2 q^{48} + 3 q^{49} - 2 q^{50} + 6 q^{51} - 6 q^{52} - 14 q^{53} + 4 q^{54} + 13 q^{55} - 7 q^{56} - 6 q^{57} - 4 q^{58} + 16 q^{59} - 4 q^{60} - 28 q^{61} - 21 q^{62} - 14 q^{63} - 4 q^{64} - 6 q^{65} + 11 q^{66} + 47 q^{67} - 4 q^{68} + 9 q^{69} - 11 q^{70} + 3 q^{71} - 2 q^{72} - 27 q^{73} + 8 q^{74} + 2 q^{75} - 6 q^{76} + 14 q^{77} - 12 q^{78} + 4 q^{79} + 2 q^{80} + 2 q^{81} + 30 q^{82} + 66 q^{83} - 13 q^{84} + 18 q^{85} + 13 q^{86} + 3 q^{87} - 3 q^{88} - 45 q^{89} - 2 q^{90} + 12 q^{91} - 8 q^{92} - 26 q^{93} + 36 q^{94} - 18 q^{95} - 2 q^{96} + 5 q^{97} - 13 q^{98} + 3 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 - 13 * q^7 + 4 * q^8 + 2 * q^9 - 2 * q^10 - 2 * q^11 + 2 * q^12 - 6 * q^13 - 2 * q^14 - 4 * q^15 - 4 * q^16 + 6 * q^17 - 2 * q^18 + 9 * q^19 + 2 * q^20 + 2 * q^21 - 13 * q^22 - 3 * q^23 - 2 * q^24 - 8 * q^25 + q^26 - 4 * q^27 + 2 * q^28 - q^29 - 16 * q^30 - 19 * q^31 - 16 * q^32 + 14 * q^33 + 4 * q^34 + 11 * q^35 - 8 * q^36 - 3 * q^37 + 6 * q^38 - 13 * q^39 - 2 * q^40 - 2 * q^42 + 2 * q^43 - 7 * q^44 + 2 * q^45 - 7 * q^46 - q^47 + 2 * q^48 + 3 * q^49 - 2 * q^50 + 6 * q^51 - 6 * q^52 - 14 * q^53 + 4 * q^54 + 13 * q^55 - 7 * q^56 - 6 * q^57 - 4 * q^58 + 16 * q^59 - 4 * q^60 - 28 * q^61 - 21 * q^62 - 14 * q^63 - 4 * q^64 - 6 * q^65 + 11 * q^66 + 47 * q^67 - 4 * q^68 + 9 * q^69 - 11 * q^70 + 3 * q^71 - 2 * q^72 - 27 * q^73 + 8 * q^74 + 2 * q^75 - 6 * q^76 + 14 * q^77 - 12 * q^78 + 4 * q^79 + 2 * q^80 + 2 * q^81 + 30 * q^82 + 66 * q^83 - 13 * q^84 + 18 * q^85 + 13 * q^86 + 3 * q^87 - 3 * q^88 - 45 * q^89 - 2 * q^90 + 12 * q^91 - 8 * q^92 - 26 * q^93 + 36 * q^94 - 18 * q^95 - 2 * q^96 + 5 * q^97 - 13 * q^98 + 3 * q^99

Introduction

L-functions

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