LMFDB - Embedded newform 930.2.bg.h.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:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			421.1
Character	$\chi$	$=$	930.421
Dual form			930.2.bg.h.391.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(-0.913545 + 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-2.71613 - 3.01657i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +O(q^{10})$	\(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} +(-2.71613 - 3.01657i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +(-0.913545 - 0.406737i) q^{10} +(-3.78332 + 0.804170i) q^{11} +(0.104528 + 0.994522i) q^{12} +(-0.578028 + 5.49957i) q^{13} +(-3.97049 - 0.843955i) q^{14} +(0.809017 + 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(2.13677 + 0.454184i) q^{17} +(0.104528 - 0.994522i) q^{18} +(0.0679048 + 0.646071i) q^{19} +(-0.978148 + 0.207912i) q^{20} +(3.70826 + 1.65102i) q^{21} +(-2.58809 + 2.87437i) q^{22} +(2.60689 + 8.02317i) q^{23} +(0.669131 + 0.743145i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.76493 + 4.78900i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-3.70826 + 1.65102i) q^{28} +(-4.53963 + 3.29823i) q^{29} +1.00000 q^{30} +(-5.20908 + 1.96607i) q^{31} -1.00000 q^{32} +(3.12915 - 2.27346i) q^{33} +(1.99564 - 0.888517i) q^{34} +(-1.25436 + 3.86053i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(2.93175 - 5.07794i) q^{37} +(0.434687 + 0.482769i) q^{38} +(-1.70882 - 5.25921i) q^{39} +(-0.669131 + 0.743145i) q^{40} +(-4.03346 - 1.79581i) q^{41} +(3.97049 - 0.843955i) q^{42} +(-0.0588338 - 0.559766i) q^{43} +(-0.404300 + 3.84666i) q^{44} +(-0.978148 - 0.207912i) q^{45} +(6.82492 + 4.95859i) q^{46} +(-6.13829 - 4.45973i) q^{47} +(0.978148 + 0.207912i) q^{48} +(-0.990625 + 9.42517i) q^{49} +(0.104528 + 0.994522i) q^{50} +(-2.13677 + 0.454184i) q^{51} +(5.05178 + 2.24920i) q^{52} +(7.93261 - 8.81005i) q^{53} +(0.309017 + 0.951057i) q^{54} +(2.58809 + 2.87437i) q^{55} +(-2.02960 + 3.51537i) q^{56} +(-0.324815 - 0.562596i) q^{57} +(-1.73398 + 5.33665i) q^{58} +(-4.15517 + 1.85000i) q^{59} +(0.809017 - 0.587785i) q^{60} +1.37824 q^{61} +(-3.05861 + 4.65241i) q^{62} -4.05920 q^{63} +(-0.809017 + 0.587785i) q^{64} +(5.05178 - 2.24920i) q^{65} +(1.19523 - 3.67854i) q^{66} +(-6.75507 - 11.7001i) q^{67} +(1.09225 - 1.89183i) q^{68} +(-5.64483 - 6.26921i) q^{69} +(1.25436 + 3.86053i) q^{70} +(-9.99861 + 11.1046i) q^{71} +(-0.913545 - 0.406737i) q^{72} +(-9.99467 + 2.12443i) q^{73} +(-0.612903 - 5.83138i) q^{74} +(0.104528 - 0.994522i) q^{75} +(0.635434 + 0.135066i) q^{76} +(12.7018 + 9.22843i) q^{77} +(-4.47375 - 3.25037i) q^{78} +(-16.9439 - 3.60154i) q^{79} +(-0.104528 + 0.994522i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(-4.31869 + 0.917967i) q^{82} +(3.33457 + 1.48465i) q^{83} +(2.71613 - 3.01657i) q^{84} +(-0.675048 - 2.07759i) q^{85} +(-0.376620 - 0.418279i) q^{86} +(2.80565 - 4.85952i) q^{87} +(1.93392 + 3.34965i) q^{88} +(-2.72174 + 8.37665i) q^{89} +(-0.913545 + 0.406737i) q^{90} +(18.1598 - 13.1939i) q^{91} +8.43606 q^{92} +(3.95906 - 3.91482i) q^{93} -7.58734 q^{94} +(0.525562 - 0.381843i) q^{95} +(0.913545 - 0.406737i) q^{96} +(2.64905 - 8.15292i) q^{97} +(4.73854 + 8.20739i) q^{98} +(-1.93392 + 3.34965i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} - 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 11 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 - 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 - 11 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q + 6 q^{2} - 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 11 q^{7} + 6 q^{8} + 3 q^{9} - 3 q^{10} - 5 q^{11} - 3 q^{12} - 13 q^{13} - 4 q^{14} + 6 q^{15} - 6 q^{16} + 31 q^{17} - 3 q^{18} - 3 q^{19} + 3 q^{20} - 4 q^{21} + 5 q^{22} - 9 q^{23} + 3 q^{24} - 12 q^{25} + 3 q^{26} + 6 q^{27} + 4 q^{28} + 11 q^{29} + 24 q^{30} + 17 q^{31} - 24 q^{32} + 10 q^{33} + 9 q^{34} + 7 q^{35} - 12 q^{36} + 8 q^{37} - 2 q^{38} - q^{39} - 3 q^{40} + 12 q^{41} + 4 q^{42} - 7 q^{43} - 10 q^{44} + 3 q^{45} - 6 q^{46} - 46 q^{47} - 3 q^{48} + 20 q^{49} - 3 q^{50} - 31 q^{51} + 17 q^{52} + 48 q^{53} - 6 q^{54} - 5 q^{55} + q^{56} - 2 q^{57} + 14 q^{58} + 12 q^{59} + 6 q^{60} - 4 q^{61} + 13 q^{62} + 2 q^{63} - 6 q^{64} + 17 q^{65} + 10 q^{66} - 33 q^{67} + q^{68} - 12 q^{69} - 7 q^{70} - 35 q^{71} - 3 q^{72} + 19 q^{73} + 7 q^{74} - 3 q^{75} + 2 q^{76} + 26 q^{77} - 4 q^{78} - 12 q^{79} + 3 q^{80} + 3 q^{81} - 12 q^{82} + 11 q^{84} - 2 q^{85} - 48 q^{86} + 3 q^{87} + 21 q^{89} - 3 q^{90} + 72 q^{91} + 6 q^{92} + 19 q^{93} - 14 q^{94} + 6 q^{95} + 3 q^{96} - 35 q^{97} - 5 q^{98}+O(q^{100}) \) 24 * q + 6 * q^2 - 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 - 11 * q^7 + 6 * q^8 + 3 * q^9 - 3 * q^10 - 5 * q^11 - 3 * q^12 - 13 * q^13 - 4 * q^14 + 6 * q^15 - 6 * q^16 + 31 * q^17 - 3 * q^18 - 3 * q^19 + 3 * q^20 - 4 * q^21 + 5 * q^22 - 9 * q^23 + 3 * q^24 - 12 * q^25 + 3 * q^26 + 6 * q^27 + 4 * q^28 + 11 * q^29 + 24 * q^30 + 17 * q^31 - 24 * q^32 + 10 * q^33 + 9 * q^34 + 7 * q^35 - 12 * q^36 + 8 * q^37 - 2 * q^38 - q^39 - 3 * q^40 + 12 * q^41 + 4 * q^42 - 7 * q^43 - 10 * q^44 + 3 * q^45 - 6 * q^46 - 46 * q^47 - 3 * q^48 + 20 * q^49 - 3 * q^50 - 31 * q^51 + 17 * q^52 + 48 * q^53 - 6 * q^54 - 5 * q^55 + q^56 - 2 * q^57 + 14 * q^58 + 12 * q^59 + 6 * q^60 - 4 * q^61 + 13 * q^62 + 2 * q^63 - 6 * q^64 + 17 * q^65 + 10 * q^66 - 33 * q^67 + q^68 - 12 * q^69 - 7 * q^70 - 35 * q^71 - 3 * q^72 + 19 * q^73 + 7 * q^74 - 3 * q^75 + 2 * q^76 + 26 * q^77 - 4 * q^78 - 12 * q^79 + 3 * q^80 + 3 * q^81 - 12 * q^82 + 11 * q^84 - 2 * q^85 - 48 * q^86 + 3 * q^87 + 21 * q^89 - 3 * q^90 + 72 * q^91 + 6 * q^92 + 19 * q^93 - 14 * q^94 + 6 * q^95 + 3 * q^96 - 35 * q^97 - 5 * q^98

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
$7$	−2.71613	−	3.01657i	−1.02660	−	1.14016i	−0.990034	−	0.140826i	$-0.955024\pi$
$7$	−2.71613	−	3.01657i	−1.02660	−	1.14016i	−0.0365674	−	0.999331i	$-0.511642\pi$
$8$	−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
$11$	−3.78332	+	0.804170i	−1.14071	+	0.242466i	−0.739265	−	0.673415i	$-0.764827\pi$
$11$	−3.78332	+	0.804170i	−1.14071	+	0.242466i	−0.401450	+	0.915881i	$0.631494\pi$
$12$	0.104528	+	0.994522i	0.0301748	+	0.287094i
$13$	−0.578028	+	5.49957i	−0.160316	+	1.52531i	0.558148	+	0.829741i	$0.311512\pi$
$13$	−0.578028	+	5.49957i	−0.160316	+	1.52531i	−0.718464	+	0.695564i	$0.755155\pi$
$14$	−3.97049	−	0.843955i	−1.06116	−	0.225556i
$15$	0.809017	+	0.587785i	0.208887	+	0.151765i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	2.13677	+	0.454184i	0.518242	+	0.110156i	0.459605	−	0.888124i	$-0.347991\pi$
$17$	2.13677	+	0.454184i	0.518242	+	0.110156i	0.0586373	+	0.998279i	$0.481324\pi$
$18$	0.104528	−	0.994522i	0.0246376	−	0.234411i
$19$	0.0679048	+	0.646071i	0.0155784	+	0.148219i	0.999546	−	0.0301284i	$-0.00959161\pi$
$19$	0.0679048	+	0.646071i	0.0155784	+	0.148219i	−0.983968	+	0.178347i	$0.942925\pi$
$20$	−0.978148	+	0.207912i	−0.218720	+	0.0464905i
$21$	3.70826	+	1.65102i	0.809209	+	0.360283i
$22$	−2.58809	+	2.87437i	−0.551783	+	0.612817i
$23$	2.60689	+	8.02317i	0.543573	+	1.67295i	0.724358	+	0.689424i	$0.242136\pi$
$23$	2.60689	+	8.02317i	0.543573	+	1.67295i	−0.180785	+	0.983523i	$0.557864\pi$
$24$	0.669131	+	0.743145i	0.136586	+	0.151694i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.76493	+	4.78900i	0.542247	+	0.939200i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	−3.70826	+	1.65102i	−0.700795	+	0.312014i
$29$	−4.53963	+	3.29823i	−0.842988	+	0.612467i	−0.923204	−	0.384311i	$-0.874439\pi$
$29$	−4.53963	+	3.29823i	−0.842988	+	0.612467i	0.0802158	+	0.996778i	$0.474439\pi$
$30$	1.00000			0.182574
$31$	−5.20908	+	1.96607i	−0.935579	+	0.353117i
$31$	−5.20908	+	1.96607i	−0.935579	+	0.353117i
$32$	−1.00000			−0.176777
$33$	3.12915	−	2.27346i	0.544715	−	0.395759i
$34$	1.99564	−	0.888517i	0.342250	−	0.152379i
$35$	−1.25436	+	3.86053i	−0.212026	+	0.652548i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	2.93175	−	5.07794i	0.481977	−	0.834809i	−0.517809	−	0.855496i	$-0.673252\pi$
$37$	2.93175	−	5.07794i	0.481977	−	0.834809i	0.999786	+	0.0206876i	$0.00658552\pi$
$38$	0.434687	+	0.482769i	0.0705156	+	0.0783155i
$39$	−1.70882	−	5.25921i	−0.273630	−	0.842147i
$40$	−0.669131	+	0.743145i	−0.105799	+	0.117502i
$41$	−4.03346	−	1.79581i	−0.629921	−	0.280459i	0.0668383	−	0.997764i	$-0.478709\pi$
$41$	−4.03346	−	1.79581i	−0.629921	−	0.280459i	−0.696759	+	0.717305i	$0.745376\pi$
$42$	3.97049	−	0.843955i	0.612661	−	0.130225i
$43$	−0.0588338	−	0.559766i	−0.00897207	−	0.0853636i	0.989120	−	0.147114i	$-0.0469984\pi$
$43$	−0.0588338	−	0.559766i	−0.00897207	−	0.0853636i	−0.998092	+	0.0617504i	$0.980332\pi$
$44$	−0.404300	+	3.84666i	−0.0609505	+	0.579905i
$45$	−0.978148	−	0.207912i	−0.145814	−	0.0309936i
$46$	6.82492	+	4.95859i	1.00628	+	0.731104i
$47$	−6.13829	−	4.45973i	−0.895361	−	0.650518i	0.0419089	−	0.999121i	$-0.486656\pi$
$47$	−6.13829	−	4.45973i	−0.895361	−	0.650518i	−0.937270	+	0.348603i	$0.886656\pi$
$48$	0.978148	+	0.207912i	0.141183	+	0.0300095i
$49$	−0.990625	+	9.42517i	−0.141518	+	1.34645i
$50$	0.104528	+	0.994522i	0.0147826	+	0.140647i
$51$	−2.13677	+	0.454184i	−0.299207	+	0.0635984i
$52$	5.05178	+	2.24920i	0.700556	+	0.311907i
$53$	7.93261	−	8.81005i	1.08963	−	1.21015i	0.113367	−	0.993553i	$-0.463836\pi$
$53$	7.93261	−	8.81005i	1.08963	−	1.21015i	0.976260	−	0.216601i	$-0.0694969\pi$
$54$	0.309017	+	0.951057i	0.0420519	+	0.129422i
$55$	2.58809	+	2.87437i	0.348978	+	0.387580i
$56$	−2.02960	+	3.51537i	−0.271217	+	0.469761i
$57$	−0.324815	−	0.562596i	−0.0430228	−	0.0745177i
$58$	−1.73398	+	5.33665i	−0.227683	+	0.700737i
$59$	−4.15517	+	1.85000i	−0.540957	+	0.240850i	−0.658979	−	0.752161i	$-0.729011\pi$
$59$	−4.15517	+	1.85000i	−0.540957	+	0.240850i	0.118022	+	0.993011i	$0.462345\pi$
$60$	0.809017	−	0.587785i	0.104444	−	0.0758827i
$61$	1.37824			0.176466			0.0882328	−	0.996100i	$-0.471878\pi$
$61$	1.37824			0.176466			0.0882328	+	0.996100i	$0.471878\pi$
$62$	−3.05861	+	4.65241i	−0.388444	+	0.590857i
$63$	−4.05920			−0.511411
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	5.05178	−	2.24920i	0.626596	−	0.278979i
$66$	1.19523	−	3.67854i	0.147123	−	0.452797i
$67$	−6.75507	−	11.7001i	−0.825264	−	1.42940i	−0.901718	−	0.432325i	$-0.857693\pi$
$67$	−6.75507	−	11.7001i	−0.825264	−	1.42940i	0.0764541	−	0.997073i	$-0.475640\pi$
$68$	1.09225	−	1.89183i	0.132455	−	0.229419i
$69$	−5.64483	−	6.26921i	−0.679557	−	0.754725i
$70$	1.25436	+	3.86053i	0.149925	+	0.461421i
$71$	−9.99861	+	11.1046i	−1.18662	+	1.31787i	−0.249698	+	0.968324i	$0.580331\pi$
$71$	−9.99861	+	11.1046i	−1.18662	+	1.31787i	−0.936919	+	0.349547i	$0.886335\pi$
$72$	−0.913545	−	0.406737i	−0.107662	−	0.0479344i
$73$	−9.99467	+	2.12443i	−1.16979	+	0.248646i	−0.751540	−	0.659687i	$-0.770689\pi$
$73$	−9.99467	+	2.12443i	−1.16979	+	0.248646i	−0.418247	+	0.908333i	$0.637355\pi$
$74$	−0.612903	−	5.83138i	−0.0712485	−	0.677884i
$75$	0.104528	−	0.994522i	0.0120699	−	0.114837i
$76$	0.635434	+	0.135066i	0.0728893	+	0.0154931i
$77$	12.7018	+	9.22843i	1.44751	+	1.05168i
$78$	−4.47375	−	3.25037i	−0.506553	−	0.368032i
$79$	−16.9439	−	3.60154i	−1.90634	−	0.405205i	−0.906484	−	0.422240i	$-0.861244\pi$
$79$	−16.9439	−	3.60154i	−1.90634	−	0.405205i	−0.999855	+	0.0170351i	$0.994577\pi$
$80$	−0.104528	+	0.994522i	−0.0116866	+	0.111191i
$81$	−0.104528	−	0.994522i	−0.0116143	−	0.110502i
$82$	−4.31869	+	0.917967i	−0.476920	+	0.101372i
$83$	3.33457	+	1.48465i	0.366016	+	0.162961i	0.581500	−	0.813546i	$-0.302466\pi$
$83$	3.33457	+	1.48465i	0.366016	+	0.162961i	−0.215483	+	0.976507i	$0.569133\pi$
$84$	2.71613	−	3.01657i	0.296354	−	0.329135i
$85$	−0.675048	−	2.07759i	−0.0732193	−	0.225346i
$86$	−0.376620	−	0.418279i	−0.0406120	−	0.0451042i
$87$	2.80565	−	4.85952i	0.300797	−	0.520995i
$88$	1.93392	+	3.34965i	0.206157	+	0.357074i
$89$	−2.72174	+	8.37665i	−0.288504	+	0.887923i	0.696823	+	0.717243i	$0.254596\pi$
$89$	−2.72174	+	8.37665i	−0.288504	+	0.887923i	−0.985327	+	0.170680i	$0.945404\pi$
$90$	−0.913545	+	0.406737i	−0.0962961	+	0.0428738i
$91$	18.1598	−	13.1939i	1.90367	−	1.38310i
$92$	8.43606			0.879520
$93$	3.95906	−	3.91482i	0.410536	−	0.405948i
$94$	−7.58734			−0.782575
$95$	0.525562	−	0.381843i	0.0539215	−	0.0391763i
$96$	0.913545	−	0.406737i	0.0932383	−	0.0415124i
$97$	2.64905	−	8.15292i	0.268970	−	0.827804i	−0.721782	−	0.692120i	$-0.756677\pi$
$97$	2.64905	−	8.15292i	0.268970	−	0.827804i	0.990752	−	0.135684i	$-0.0433231\pi$
$98$	4.73854	+	8.20739i	0.478665	+	0.829072i
$99$	−1.93392	+	3.34965i	−0.194366	+	0.336653i
$100$	0.669131	+	0.743145i	0.0669131	+	0.0743145i
$101$	0.0204627	+	0.0629778i	0.00203612	+	0.00626653i	0.952069	−	0.305882i	$-0.0989513\pi$
$101$	0.0204627	+	0.0629778i	0.00203612	+	0.00626653i	−0.950033	+	0.312149i	$0.898951\pi$
$102$	−1.46172	+	1.62340i	−0.144732	+	0.160741i
$103$	−1.68065	−	0.748275i	−0.165600	−	0.0737298i	0.322263	−	0.946650i	$-0.395557\pi$
$103$	−1.68065	−	0.748275i	−0.165600	−	0.0737298i	−0.487862	+	0.872921i	$0.662223\pi$
$104$	5.40902	−	1.14972i	0.530398	−	0.112740i
$105$	−0.424302	−	4.03696i	−0.0414076	−	0.393967i
$106$	1.23919	−	11.7902i	0.120361	−	1.14516i
$107$	15.3354	+	3.25964i	1.48253	+	0.315121i	0.876919	−	0.480639i	$-0.159595\pi$
$107$	15.3354	+	3.25964i	1.48253	+	0.315121i	0.605611	+	0.795761i	$0.292929\pi$
$108$	0.809017	+	0.587785i	0.0778477	+	0.0565597i
$109$	4.51571	+	3.28086i	0.432527	+	0.314249i	0.782658	−	0.622451i	$-0.213863\pi$
$109$	4.51571	+	3.28086i	0.432527	+	0.314249i	−0.350132	+	0.936700i	$0.613863\pi$
$110$	3.78332	+	0.804170i	0.360726	+	0.0766746i
$111$	−0.612903	+	5.83138i	−0.0581742	+	0.553490i
$112$	0.424302	+	4.03696i	0.0400927	+	0.381457i
$113$	−5.65665	+	1.20236i	−0.532133	+	0.113108i	−0.466139	−	0.884712i	$-0.654355\pi$
$113$	−5.65665	+	1.20236i	−0.532133	+	0.113108i	−0.0659940	+	0.997820i	$0.521022\pi$
$114$	−0.593467	−	0.264228i	−0.0555832	−	0.0247473i
$115$	5.64483	−	6.26921i	0.526383	−	0.584607i
$116$	1.73398	+	5.33665i	0.160996	+	0.495496i
$117$	3.70020	+	4.10949i	0.342083	+	0.379922i
$118$	−2.27420	+	3.93903i	−0.209357	+	0.362617i
$119$	−4.43366	−	7.67933i	−0.406433	−	0.703963i
$120$	0.309017	−	0.951057i	0.0282093	−	0.0868192i
$121$	3.61784	−	1.61077i	0.328895	−	0.146433i
$122$	1.11502	−	0.810110i	0.100949	−	0.0733439i
$123$	4.41518			0.398103
$124$	0.260151	+	5.56168i	0.0233622	+	0.499454i
$125$	1.00000			0.0894427
$126$	−3.28396	+	2.38594i	−0.292558	+	0.212556i
$127$	9.72385	−	4.32933i	0.862852	−	0.384166i	0.0729029	−	0.997339i	$-0.476774\pi$
$127$	9.72385	−	4.32933i	0.862852	−	0.384166i	0.789949	+	0.613173i	$0.210107\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	0.281425	+	0.487442i	0.0247781	+	0.0429169i
$130$	2.76493	−	4.78900i	0.242500	−	0.420023i
$131$	9.67185	+	10.7417i	0.845034	+	0.938505i	0.998769	−	0.0496071i	$-0.0157969\pi$
$131$	9.67185	+	10.7417i	0.845034	+	0.938505i	−0.153735	+	0.988112i	$0.549130\pi$
$132$	−1.19523	−	3.67854i	−0.104031	−	0.320176i
$133$	1.76448	−	1.95966i	0.153000	−	0.169924i
$134$	−12.3421	−	5.49507i	−1.06620	−	0.474702i
$135$	0.978148	−	0.207912i	0.0841855	−	0.0178942i
$136$	−0.228343	−	2.17254i	−0.0195802	−	0.186293i
$137$	−1.85776	+	17.6754i	−0.158719	+	1.51011i	0.567916	+	0.823086i	$0.307750\pi$
$137$	−1.85776	+	17.6754i	−0.158719	+	1.51011i	−0.726635	+	0.687023i	$0.758917\pi$
$138$	−8.25171	−	1.75396i	−0.702432	−	0.149307i
$139$	−18.5781	−	13.4978i	−1.57578	−	1.14487i	−0.921345	−	0.388746i	$-0.872908\pi$
$139$	−18.5781	−	13.4978i	−1.57578	−	1.14487i	−0.654431	−	0.756122i	$-0.727092\pi$
$140$	3.28396	+	2.38594i	0.277545	+	0.201648i
$141$	7.42154	+	1.57750i	0.625006	+	0.132849i
$142$	−1.56194	+	14.8608i	−0.131075	+	1.24709i
$143$	−2.23572	−	21.2715i	−0.186960	−	1.77881i
$144$	−0.978148	+	0.207912i	−0.0815123	+	0.0173260i
$145$	5.12617	+	2.28232i	0.425705	+	0.189536i
$146$	−6.83715	+	7.59342i	−0.565846	+	0.628436i
$147$	−2.92858	−	9.01324i	−0.241545	−	0.743400i
$148$	−3.92345	−	4.35743i	−0.322506	−	0.358179i
$149$	7.23664	−	12.5342i	0.592849	−	1.02684i	−0.400998	−	0.916079i	$-0.631336\pi$
$149$	7.23664	−	12.5342i	0.592849	−	1.02684i	0.993847	−	0.110766i	$-0.0353303\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	3.48137	−	10.7145i	0.283309	−	0.871937i	−0.703591	−	0.710605i	$-0.748421\pi$
$151$	3.48137	−	10.7145i	0.283309	−	0.871937i	0.986900	−	0.161332i	$-0.0515788\pi$
$152$	0.593467	−	0.264228i	0.0481365	−	0.0214317i
$153$	1.76730	−	1.28402i	0.142878	−	0.103807i
$154$	15.7003			1.26517
$155$	4.30721	+	3.52816i	0.345964	+	0.283389i
$156$	−5.52986			−0.442743
$157$	−1.61242	+	1.17149i	−0.128685	+	0.0934951i	−0.650266	−	0.759707i	$-0.725342\pi$
$157$	−1.61242	+	1.17149i	−0.128685	+	0.0934951i	0.521581	+	0.853202i	$0.325342\pi$
$158$	−15.8248	+	7.04567i	−1.25896	+	0.560524i
$159$	−3.66343	+	11.2749i	−0.290529	+	0.894155i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	17.1218	−	29.6559i	1.34939	−	2.33721i
$162$	−0.669131	−	0.743145i	−0.0525719	−	0.0583870i
$163$	−4.25328	−	13.0903i	−0.333143	−	1.02531i	−0.967630	−	0.252375i	$-0.918788\pi$
$163$	−4.25328	−	13.0903i	−0.333143	−	1.02531i	0.634487	−	0.772934i	$-0.281212\pi$
$164$	−2.95433	+	3.28111i	−0.230694	+	0.256212i
$165$	−3.53345	−	1.57319i	−0.275079	−	0.122473i
$166$	3.57038	−	0.758907i	0.277115	−	0.0589026i
$167$	0.00752452	+	0.0715911i	0.000582265	+	0.00553988i	0.994809	−	0.101758i	$-0.0324468\pi$
$167$	0.00752452	+	0.0715911i	0.000582265	+	0.00553988i	−0.994227	+	0.107298i	$0.965780\pi$
$168$	0.424302	−	4.03696i	0.0327356	−	0.311458i
$169$	−17.1952	−	3.65495i	−1.32271	−	0.281150i
$170$	−1.76730	−	1.28402i	−0.135546	−	0.0984797i
$171$	0.525562	+	0.381843i	0.0401907	+	0.0292003i
$172$	−0.550550	−	0.117023i	−0.0419790	−	0.00892292i
$173$	−1.50882	+	14.3555i	−0.114714	+	1.09143i	0.774069	+	0.633101i	$0.218218\pi$
$173$	−1.50882	+	14.3555i	−0.114714	+	1.09143i	−0.888783	+	0.458328i	$0.848448\pi$
$174$	−0.586540	−	5.58055i	−0.0444654	−	0.423060i
$175$	3.97049	−	0.843955i	0.300141	−	0.0637970i
$176$	3.53345	+	1.57319i	0.266344	+	0.118584i
$177$	3.04347	−	3.38012i	0.228762	−	0.254065i
$178$	2.72174	+	8.37665i	0.204003	+	0.627857i
$179$	−2.45441	−	2.72590i	−0.183451	−	0.203743i	0.644404	−	0.764685i	$-0.277106\pi$
$179$	−2.45441	−	2.72590i	−0.183451	−	0.203743i	−0.827855	+	0.560942i	$0.810439\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	5.64922	+	9.78473i	0.419903	+	0.727293i	0.995929	−	0.0901378i	$-0.0287308\pi$
$181$	5.64922	+	9.78473i	0.419903	+	0.727293i	−0.576026	+	0.817431i	$0.695397\pi$
$182$	6.93644	−	21.3482i	0.514163	−	1.58243i
$183$	−1.25909	+	0.560581i	−0.0930743	+	0.0414393i
$184$	6.82492	−	4.95859i	0.503139	−	0.365552i
$185$	−5.86350			−0.431093
$186$	0.901873	−	5.49424i	0.0661286	−	0.402857i
$187$	−8.44932			−0.617875
$188$	−6.13829	+	4.45973i	−0.447681	+	0.325259i
$189$	3.70826	−	1.65102i	0.269736	−	0.120094i
$190$	0.200747	−	0.617835i	0.0145637	−	0.0448225i
$191$	−2.95101	−	5.11129i	−0.213527	−	0.369840i	0.739289	−	0.673389i	$-0.235162\pi$
$191$	−2.95101	−	5.11129i	−0.213527	−	0.369840i	−0.952816	+	0.303548i	$0.901829\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	0.845993	+	0.939570i	0.0608959	+	0.0676317i	0.772823	−	0.634622i	$-0.218844\pi$
$193$	0.845993	+	0.939570i	0.0608959	+	0.0676317i	−0.711927	+	0.702253i	$0.752177\pi$
$194$	−2.64905	−	8.15292i	−0.190190	−	0.585346i
$195$	−3.70020	+	4.10949i	−0.264977	+	0.294286i
$196$	8.65775	+	3.85468i	0.618410	+	0.275334i
$197$	−23.1841	+	4.92793i	−1.65180	+	0.351101i	−0.937297	−	0.348532i	$-0.886680\pi$
$197$	−23.1841	+	4.92793i	−1.65180	+	0.351101i	−0.714502	+	0.699633i	$0.753347\pi$
$198$	0.404300	+	3.84666i	0.0287323	+	0.273370i
$199$	−0.659390	+	6.27368i	−0.0467429	+	0.444729i	0.945973	+	0.324247i	$0.105111\pi$
$199$	−0.659390	+	6.27368i	−0.0467429	+	0.444729i	−0.992715	+	0.120482i	$0.961556\pi$
$200$	0.978148	+	0.207912i	0.0691655	+	0.0147016i
$201$	10.9299	+	7.94106i	0.770938	+	0.560120i
$202$	0.0535721	+	0.0389224i	0.00376932	+	0.00273857i
$203$	22.2796	+	4.73567i	1.56372	+	0.332379i
$204$	−0.228343	+	2.17254i	−0.0159872	+	0.152108i
$205$	0.461512	+	4.39099i	0.0322334	+	0.306680i
$206$	−1.79950	+	0.382496i	−0.125377	+	0.0266498i
$207$	7.70672	+	3.43125i	0.535654	+	0.238489i
$208$	3.70020	−	4.10949i	0.256563	−	0.284942i
$209$	−0.776457	−	2.38969i	−0.0537087	−	0.165298i
$210$	−2.71613	−	3.01657i	−0.187431	−	0.208163i
$211$	13.0751	−	22.6467i	0.900125	−	1.55906i	0.0727951	−	0.997347i	$-0.476808\pi$
$211$	13.0751	−	22.6467i	0.900125	−	1.55906i	0.827330	−	0.561716i	$-0.189859\pi$
$212$	−5.92755	−	10.2668i	−0.407106	−	0.705128i
$213$	4.61754	−	14.2113i	0.316389	−	0.973745i
$214$	14.3226	−	6.37682i	0.979071	−	0.435911i
$215$	−0.455355	+	0.330835i	−0.0310550	+	0.0225627i
$216$	1.00000			0.0680414
$217$	20.0794	+	10.3735i	1.36308	+	0.704196i
$218$	5.58172			0.378042
$219$	8.26650	−	6.00596i	0.558598	−	0.405845i
$220$	3.53345	−	1.57319i	0.238225	−	0.106065i
$221$	−3.73292	+	11.4888i	−0.251104	+	0.772817i
$222$	2.93175	+	5.07794i	0.196766	+	0.340809i
$223$	3.25292	−	5.63423i	0.217832	−	0.377296i	−0.736313	−	0.676641i	$-0.763435\pi$
$223$	3.25292	−	5.63423i	0.217832	−	0.377296i	0.954145	+	0.299345i	$0.0967683\pi$
$224$	2.71613	+	3.01657i	0.181479	+	0.201553i
$225$	0.309017	+	0.951057i	0.0206011	+	0.0634038i
$226$	−3.86960	+	4.29762i	−0.257402	+	0.285873i
$227$	−6.61790	−	2.94648i	−0.439246	−	0.195565i	0.175185	−	0.984536i	$-0.443948\pi$
$227$	−6.61790	−	2.94648i	−0.439246	−	0.195565i	−0.614431	+	0.788971i	$0.710614\pi$
$228$	−0.635434	+	0.135066i	−0.0420827	+	0.00894494i
$229$	−0.318483	−	3.03017i	−0.0210460	−	0.200239i	0.978947	−	0.204117i	$-0.0654323\pi$
$229$	−0.318483	−	3.03017i	−0.0210460	−	0.200239i	−0.999992	+	0.00387797i	$0.998766\pi$
$230$	0.881808	−	8.38985i	0.0581447	−	0.553210i
$231$	−15.3573	−	3.26428i	−1.01043	−	0.214774i
$232$	4.53963	+	3.29823i	0.298041	+	0.216540i
$233$	−7.40626	−	5.38096i	−0.485200	−	0.352519i	0.318135	−	0.948045i	$-0.396943\pi$
$233$	−7.40626	−	5.38096i	−0.485200	−	0.352519i	−0.803336	+	0.595527i	$0.796943\pi$
$234$	5.40902	+	1.14972i	0.353599	+	0.0751597i
$235$	−0.793093	+	7.54578i	−0.0517357	+	0.492232i
$236$	0.475437	+	4.52349i	0.0309483	+	0.294454i
$237$	16.9439	−	3.60154i	1.10063	−	0.233945i
$238$	−8.10071	−	3.60667i	−0.525091	−	0.233786i
$239$	−10.4649	+	11.6224i	−0.676918	+	0.751794i	−0.979525	−	0.201322i	$-0.935476\pi$
$239$	−10.4649	+	11.6224i	−0.676918	+	0.751794i	0.302607	+	0.953115i	$0.402143\pi$
$240$	−0.309017	−	0.951057i	−0.0199470	−	0.0613904i
$241$	−10.4077	−	11.5590i	−0.670421	−	0.744578i	0.307957	−	0.951400i	$-0.400355\pi$
$241$	−10.4077	−	11.5590i	−0.670421	−	0.744578i	−0.978379	+	0.206822i	$0.933688\pi$
$242$	1.98011	−	3.42965i	0.127286	−	0.220466i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	0.425900	−	1.31078i	0.0272654	−	0.0839144i
$245$	8.65775	−	3.85468i	0.553123	−	0.246266i
$246$	3.57195	−	2.59518i	0.227739	−	0.165462i
$247$	−3.59236			−0.228577
$248$	3.47954	+	4.34658i	0.220951	+	0.276008i
$249$	−3.65014			−0.231318
$250$	0.809017	−	0.587785i	0.0511667	−	0.0371748i
$251$	−20.7459	+	9.23667i	−1.30947	+	0.583013i	−0.938387	−	0.345587i	$-0.887680\pi$
$251$	−20.7459	+	9.23667i	−1.30947	+	0.583013i	−0.371082	+	0.928600i	$0.621013\pi$
$252$	−1.25436	+	3.86053i	−0.0790173	+	0.243190i
$253$	−16.3147	−	28.2579i	−1.02570	−	1.77656i
$254$	5.32204	−	9.21804i	0.333934	−	0.578391i
$255$	1.46172	+	1.62340i	0.0915363	+	0.101661i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	9.16620	−	10.1801i	0.571772	−	0.635017i	−0.386016	−	0.922492i	$-0.626149\pi$
$257$	9.16620	−	10.1801i	0.571772	−	0.635017i	0.957788	+	0.287475i	$0.0928158\pi$
$258$	0.514189	+	0.228932i	0.0320120	+	0.0142527i
$259$	−23.2810	+	4.94853i	−1.44661	+	0.307487i
$260$	−0.578028	−	5.49957i	−0.0358478	−	0.341069i
$261$	−0.586540	+	5.58055i	−0.0363059	+	0.345427i
$262$	14.1385	+	3.00523i	0.873479	+	0.185664i
$263$	3.98775	+	2.89727i	0.245895	+	0.178653i	0.703906	−	0.710294i	$-0.251438\pi$
$263$	3.98775	+	2.89727i	0.245895	+	0.178653i	−0.458011	+	0.888947i	$0.651438\pi$
$264$	−3.12915	−	2.27346i	−0.192586	−	0.139922i
$265$	−11.5960	−	2.46481i	−0.712339	−	0.151412i
$266$	0.275639	−	2.62253i	0.0169005	−	0.160798i
$267$	−0.920659	−	8.75948i	−0.0563434	−	0.536072i
$268$	−13.2149	+	2.80892i	−0.807230	+	0.171582i
$269$	24.7132	+	11.0030i	1.50679	+	0.670865i	0.983437	−	0.181252i	$-0.0580151\pi$
$269$	24.7132	+	11.0030i	1.50679	+	0.670865i	0.523351	+	0.852117i	$0.324682\pi$
$270$	0.669131	−	0.743145i	0.0407220	−	0.0452264i
$271$	8.86978	+	27.2984i	0.538801	+	1.65826i	0.735290	+	0.677753i	$0.237046\pi$
$271$	8.86978	+	27.2984i	0.538801	+	1.65826i	−0.196489	+	0.980506i	$0.562954\pi$
$272$	−1.46172	−	1.62340i	−0.0886297	−	0.0984332i
$273$	−11.2234	+	19.4395i	−0.679271	+	1.17653i
$274$	8.88637	+	15.3916i	0.536845	+	0.929843i
$275$	1.19523	−	3.67854i	0.0720751	−	0.221824i
$276$	−7.70672	+	3.43125i	−0.463890	+	0.206537i
$277$	−1.17890	+	0.856522i	−0.0708333	+	0.0514634i	−0.622638	−	0.782510i	$-0.713939\pi$
$277$	−1.17890	+	0.856522i	−0.0708333	+	0.0514634i	0.551805	+	0.833973i	$0.313939\pi$
$278$	−22.9638			−1.37728
$279$	−2.02448	+	5.18666i	−0.121203	+	0.310517i
$280$	4.05920			0.242583
$281$	−2.67607	+	1.94428i	−0.159641	+	0.115986i	−0.664738	−	0.747077i	$-0.731457\pi$
$281$	−2.67607	+	1.94428i	−0.159641	+	0.115986i	0.505097	+	0.863063i	$0.331457\pi$
$282$	6.93138	−	3.08605i	0.412758	−	0.183772i
$283$	1.49725	−	4.60806i	0.0890022	−	0.273921i	−0.896642	−	0.442756i	$-0.854001\pi$
$283$	1.49725	−	4.60806i	0.0890022	−	0.273921i	0.985644	+	0.168836i	$0.0540007\pi$
$284$	7.47134	+	12.9407i	0.443343	+	0.767892i
$285$	−0.324815	+	0.562596i	−0.0192404	+	0.0333253i
$286$	−14.3118	−	15.8949i	−0.846274	−	0.939883i
$287$	5.53822	+	17.0449i	0.326911	+	1.00613i
$288$	−0.669131	+	0.743145i	−0.0394289	+	0.0437902i
$289$	−11.1708	−	4.97355i	−0.657105	−	0.292562i
$290$	5.48867	−	1.16665i	0.322306	−	0.0685082i
$291$	0.896069	+	8.52553i	0.0525285	+	0.499775i
$292$	−1.06807	+	10.1620i	−0.0625039	+	0.594685i
$293$	21.0538	+	4.47512i	1.22998	+	0.261439i	0.776665	−	0.629913i	$-0.216910\pi$
$293$	21.0538	+	4.47512i	1.22998	+	0.261439i	0.453310	+	0.891353i	$0.350243\pi$
$294$	−7.66712	−	5.57049i	−0.447156	−	0.324878i
$295$	3.67973	+	2.67348i	0.214242	+	0.155656i
$296$	−5.73537	−	1.21909i	−0.333362	−	0.0708582i
$297$	0.404300	−	3.84666i	0.0234599	−	0.223206i
$298$	−1.51287	−	14.3940i	−0.0876383	−	0.833822i
$299$	−45.6308	+	9.69913i	−2.63890	+	0.560915i
$300$	−0.913545	−	0.406737i	−0.0527436	−	0.0234830i
$301$	−1.52877	+	1.69788i	−0.0881171	+	0.0978640i
$302$	−3.48137	−	10.7145i	−0.200330	−	0.616552i
$303$	−0.0443090	−	0.0492102i	−0.00254549	−	0.00282705i
$304$	0.324815	−	0.562596i	0.0186294	−	0.0322671i
$305$	−0.689120	−	1.19359i	−0.0394589	−	0.0683448i
$306$	0.675048	−	2.07759i	0.0385900	−	0.118768i
$307$	8.06943	−	3.59274i	0.460547	−	0.205049i	−0.163330	−	0.986572i	$-0.552223\pi$
$307$	8.06943	−	3.59274i	0.460547	−	0.205049i	0.623877	+	0.781523i	$0.285557\pi$
$308$	12.7018	−	9.22843i	0.723755	−	0.525839i
$309$	1.83970			0.104657
$310$	5.55841	+	0.322629i	0.315696	+	0.0183241i
$311$	−22.6211			−1.28273			−0.641364	−	0.767237i	$-0.721631\pi$
$311$	−22.6211			−1.28273			−0.641364	+	0.767237i	$0.721631\pi$
$312$	−4.47375	+	3.25037i	−0.253276	+	0.184016i
$313$	2.25039	−	1.00194i	0.127200	−	0.0566329i	−0.342150	−	0.939645i	$-0.611155\pi$
$313$	2.25039	−	1.00194i	0.127200	−	0.0566329i	0.469350	+	0.883012i	$0.344488\pi$
$314$	−0.615889	+	1.89551i	−0.0347566	+	0.106970i
$315$	2.02960	+	3.51537i	0.114355	+	0.198069i
$316$	−8.66122	+	15.0017i	−0.487232	+	0.843910i
$317$	21.6235	+	24.0153i	1.21449	+	1.34883i	0.919380	+	0.393371i	$0.128691\pi$
$317$	21.6235	+	24.0153i	1.21449	+	1.34883i	0.295115	+	0.955462i	$0.404642\pi$
$318$	3.66343	+	11.2749i	0.205435	+	0.632263i
$319$	14.5225	−	16.1289i	0.813106	−	0.903046i
$320$	0.913545	+	0.406737i	0.0510687	+	0.0227373i
$321$	−15.3354	+	3.25964i	−0.855939	+	0.181935i
$322$	−3.57943	−	34.0560i	−0.199474	−	1.89787i
$323$	−0.148338	+	1.41134i	−0.00825376	+	0.0785293i
$324$	−0.978148	−	0.207912i	−0.0543415	−	0.0115506i
$325$	−4.47375	−	3.25037i	−0.248159	−	0.180298i
$326$	−11.1352	−	8.09023i	−0.616724	−	0.448076i
$327$	−5.45975	−	1.16051i	−0.301925	−	0.0641761i
$328$	−0.461512	+	4.39099i	−0.0254827	+	0.242452i
$329$	3.21932	+	30.6298i	0.177487	+	1.68868i
$330$	−3.78332	+	0.804170i	−0.208265	+	0.0442681i
$331$	−19.8701	−	8.84672i	−1.09216	−	0.486260i	−0.220007	−	0.975498i	$-0.570608\pi$
$331$	−19.8701	−	8.84672i	−1.09216	−	0.486260i	−0.872150	+	0.489239i	$0.837275\pi$
$332$	2.44242	−	2.71258i	0.134045	−	0.148872i
$333$	−1.81192	−	5.57652i	−0.0992927	−	0.305592i
$334$	0.0481676	+	0.0534956i	0.00263562	+	0.00292715i
$335$	−6.75507	+	11.7001i	−0.369069	+	0.639246i
$336$	−2.02960	−	3.51537i	−0.110724	−	0.191779i
$337$	1.17868	−	3.62761i	0.0642068	−	0.197608i	−0.913807	−	0.406149i	$-0.866871\pi$
$337$	1.17868	−	3.62761i	0.0642068	−	0.197608i	0.978014	+	0.208541i	$0.0668714\pi$
$338$	−16.0595	+	7.15017i	−0.873524	+	0.388918i
$339$	4.67856	−	3.39917i	0.254105	−	0.184618i
$340$	−2.18450			−0.118471
$341$	18.1266	−	11.6273i	0.981610	−	0.629652i
$342$	0.649630			0.0351280
$343$	8.13464	−	5.91016i	0.439229	−	0.319119i
$344$	−0.514189	+	0.228932i	−0.0277232	+	0.0123432i
$345$	−2.60689	+	8.02317i	−0.140350	+	0.431953i
$346$	7.21729	+	12.5007i	0.388004	+	0.672043i
$347$	12.8688	−	22.2893i	0.690831	−	1.19655i	−0.280735	−	0.959785i	$-0.590578\pi$
$347$	12.8688	−	22.2893i	0.690831	−	1.19655i	0.971566	−	0.236769i	$-0.0760885\pi$
$348$	−3.75469	−	4.17000i	−0.201272	−	0.223536i
$349$	3.55478	+	10.9405i	0.190283	+	0.585630i	0.999999	−	0.00119102i	$-0.000379113\pi$
$349$	3.55478	+	10.9405i	0.190283	+	0.585630i	−0.809716	+	0.586821i	$0.800379\pi$
$350$	2.71613	−	3.01657i	0.145183	−	0.161243i
$351$	−5.05178	−	2.24920i	−0.269644	−	0.120053i
$352$	3.78332	−	0.804170i	0.201652	−	0.0428624i
$353$	0.824700	+	7.84649i	0.0438943	+	0.417627i	0.994300	+	0.106615i	$0.0340012\pi$
$353$	0.824700	+	7.84649i	0.0438943	+	0.417627i	−0.950406	+	0.311012i	$0.899332\pi$
$354$	0.475437	−	4.52349i	0.0252692	−	0.240421i
$355$	14.6162	+	3.10676i	0.775745	+	0.164890i
$356$	7.12561	+	5.17706i	0.377656	+	0.274383i
$357$	7.17382	+	5.21208i	0.379679	+	0.275853i
$358$	−3.58790	−	0.762631i	−0.189626	−	0.0403063i
$359$	1.54531	−	14.7027i	0.0815585	−	0.775978i	−0.874938	−	0.484235i	$-0.839098\pi$
$359$	1.54531	−	14.7027i	0.0815585	−	0.775978i	0.956497	−	0.291743i	$-0.0942352\pi$
$360$	0.104528	+	0.994522i	0.00550913	+	0.0524159i
$361$	18.1720	−	3.86258i	0.956421	−	0.203294i
$362$	10.3216	+	4.59549i	0.542493	+	0.241533i
$363$	−2.64990	+	2.94302i	−0.139084	+	0.154468i
$364$	−6.93644	−	21.3482i	−0.363568	−	1.11895i
$365$	6.83715	+	7.59342i	0.357873	+	0.397458i
$366$	−0.689120	+	1.19359i	−0.0360209	+	0.0623900i
$367$	18.4533	+	31.9621i	0.963255	+	1.66841i	0.714232	+	0.699909i	$0.246776\pi$
$367$	18.4533	+	31.9621i	0.963255	+	1.66841i	0.249024	+	0.968497i	$0.419890\pi$
$368$	2.60689	−	8.02317i	0.135893	−	0.418237i
$369$	−4.03346	+	1.79581i	−0.209974	+	0.0934863i
$370$	−4.74367	+	3.44648i	−0.246612	+	0.179174i
$371$	−48.1222			−2.49838
$372$	−2.49980	−	4.97504i	−0.129609	−	0.257944i
$373$	−10.6012			−0.548911			−0.274456	−	0.961600i	$-0.588498\pi$
$373$	−10.6012			−0.548911			−0.274456	+	0.961600i	$0.588498\pi$
$374$	−6.83564	+	4.96638i	−0.353463	+	0.256806i
$375$	−0.913545	+	0.406737i	−0.0471753	+	0.0210038i
$376$	−2.34462	+	7.21599i	−0.120914	+	0.372136i
$377$	−15.5148	−	26.8725i	−0.799054	−	1.38400i
$378$	2.02960	−	3.51537i	0.104391	−	0.180811i
$379$	5.53637	+	6.14876i	0.284384	+	0.315840i	0.868364	−	0.495928i	$-0.165172\pi$
$379$	5.53637	+	6.14876i	0.284384	+	0.315840i	−0.583980	+	0.811768i	$0.698505\pi$
$380$	−0.200747	−	0.617835i	−0.0102981	−	0.0316943i
$381$	−7.12228	+	7.91009i	−0.364885	+	0.405246i
$382$	−5.39176	−	2.40057i	−0.275866	−	0.122824i
$383$	−6.96307	+	1.48005i	−0.355796	+	0.0756268i	−0.382342	−	0.924021i	$-0.624882\pi$
$383$	−6.96307	+	1.48005i	−0.355796	+	0.0756268i	0.0265460	+	0.999648i	$0.491549\pi$
$384$	−0.104528	−	0.994522i	−0.00533420	−	0.0507515i
$385$	1.64113	−	15.6143i	0.0836399	−	0.795780i
$386$	1.23669	+	0.262866i	0.0629458	+	0.0133795i
$387$	−0.455355	−	0.330835i	−0.0231470	−	0.0168173i
$388$	−6.93529	−	5.03878i	−0.352086	−	0.255805i
$389$	15.9445	+	3.38912i	0.808420	+	0.171835i	0.593539	−	0.804805i	$-0.297730\pi$
$389$	15.9445	+	3.38912i	0.808420	+	0.171835i	0.214881	+	0.976640i	$0.431064\pi$
$390$	−0.578028	+	5.49957i	−0.0292696	+	0.278481i
$391$	1.92631	+	18.3276i	0.0974178	+	0.926869i
$392$	9.26998	−	1.97040i	0.468205	−	0.0995200i
$393$	−13.2047	−	5.87912i	−0.666090	−	0.296562i
$394$	−15.8598	+	17.6141i	−0.799004	+	0.887383i
$395$	5.35293	+	16.4746i	0.269335	+	0.828928i
$396$	2.58809	+	2.87437i	0.130057	+	0.144442i
$397$	−14.1290	+	24.4722i	−0.709116	+	1.22822i	0.256070	+	0.966658i	$0.417572\pi$
$397$	−14.1290	+	24.4722i	−0.709116	+	1.22822i	−0.965185	+	0.261566i	$0.915761\pi$
$398$	3.15412	+	5.46309i	0.158102	+	0.273840i
$399$	−0.814871	+	2.50791i	−0.0407946	+	0.125553i
$400$	0.913545	−	0.406737i	0.0456773	−	0.0203368i
$401$	−6.68643	+	4.85798i	−0.333905	+	0.242596i	−0.742086	−	0.670305i	$-0.766163\pi$
$401$	−6.68643	+	4.85798i	−0.333905	+	0.242596i	0.408181	+	0.912901i	$0.366163\pi$
$402$	13.5101			0.673825
$403$	−7.80155	−	29.7842i	−0.388623	−	1.48365i
$404$	0.0662188			0.00329451
$405$	−0.809017	+	0.587785i	−0.0402004	+	0.0292073i
$406$	20.8081	−	9.26438i	1.03269	−	0.459783i
$407$	−7.00823	+	21.5691i	−0.347385	+	1.06914i
$408$	1.09225	+	1.89183i	0.0540745	+	0.0936598i
$409$	10.1668	−	17.6094i	0.502717	−	0.870731i	−0.497278	−	0.867591i	$-0.665667\pi$
$409$	10.1668	−	17.6094i	0.502717	−	0.870731i	0.999995	−	0.00313991i	$-0.000999467\pi$
$410$	2.95433	+	3.28111i	0.145904	+	0.162043i
$411$	−5.49208	−	16.9029i	−0.270904	−	0.833758i
$412$	−1.23100	+	1.36717i	−0.0606471	+	0.0673555i
$413$	16.8667	+	7.50952i	0.829954	+	0.369519i
$414$	8.25171	−	1.75396i	0.405549	−	0.0862022i
$415$	−0.381544	−	3.63014i	−0.0187292	−	0.178197i
$416$	0.578028	−	5.49957i	0.0283401	−	0.269638i
$417$	22.4620	+	4.77445i	1.09997	+	0.233806i
$418$	−2.03279	−	1.47691i	−0.0994271	−	0.0722380i
$419$	13.9055	+	10.1029i	0.679328	+	0.493561i	0.873135	−	0.487479i	$-0.162083\pi$
$419$	13.9055	+	10.1029i	0.679328	+	0.493561i	−0.193807	+	0.981040i	$0.562083\pi$
$420$	−3.97049	−	0.843955i	−0.193740	−	0.0411808i
$421$	1.77059	−	16.8461i	0.0862933	−	0.821026i	−0.862697	−	0.505721i	$-0.831226\pi$
$421$	1.77059	−	16.8461i	0.0862933	−	0.821026i	0.948990	−	0.315305i	$-0.102107\pi$
$422$	−2.73344	−	26.0069i	−0.133062	−	1.26600i
$423$	−7.42154	+	1.57750i	−0.360848	+	0.0767005i
$424$	−10.8302	−	4.82190i	−0.525959	−	0.234172i
$425$	−1.46172	+	1.62340i	−0.0709037	+	0.0787466i
$426$	−4.61754	−	14.2113i	−0.223721	−	0.688542i
$427$	−3.74349	−	4.15756i	−0.181160	−	0.201199i
$428$	7.83901	−	13.5776i	0.378913	−	0.656296i
$429$	10.6943	+	18.5231i	0.516327	+	0.894304i
$430$	−0.173930	+	0.535302i	−0.00838766	+	0.0258145i
$431$	11.8282	−	5.26624i	0.569743	−	0.253666i	−0.101584	−	0.994827i	$-0.532391\pi$
$431$	11.8282	−	5.26624i	0.569743	−	0.253666i	0.671327	+	0.741161i	$0.265724\pi$
$432$	0.809017	−	0.587785i	0.0389238	−	0.0282798i
$433$	20.4159			0.981124			0.490562	−	0.871406i	$-0.336792\pi$
$433$	20.4159			0.981124			0.490562	+	0.871406i	$0.336792\pi$
$434$	22.3419	−	3.41005i	1.07245	−	0.163688i
$435$	−5.61129			−0.269041
$436$	4.51571	−	3.28086i	0.216263	−	0.157124i
$437$	−5.00652	+	2.22905i	−0.239494	+	0.106630i
$438$	3.15752	−	9.71785i	0.150872	−	0.464337i
$439$	14.5970	+	25.2828i	0.696678	+	1.20668i	0.969612	+	0.244649i	$0.0786726\pi$
$439$	14.5970	+	25.2828i	0.696678	+	1.20668i	−0.272934	+	0.962033i	$0.587994\pi$
$440$	1.93392	−	3.34965i	0.0921961	−	0.159688i
$441$	6.34141	+	7.04284i	0.301972	+	0.335374i
$442$	3.73292	+	11.4888i	0.177557	+	0.546464i
$443$	−5.60926	+	6.22972i	−0.266504	+	0.295983i	−0.861512	−	0.507737i	$-0.830482\pi$
$443$	−5.60926	+	6.22972i	−0.266504	+	0.295983i	0.595008	+	0.803720i	$0.297149\pi$
$444$	5.35658	+	2.38490i	0.254212	+	0.113182i
$445$	8.61526	−	1.83123i	0.408403	−	0.0868087i
$446$	−0.680046	−	6.47020i	−0.0322011	−	0.306373i
$447$	−1.51287	+	14.3940i	−0.0715563	+	0.680813i
$448$	3.97049	+	0.843955i	0.187588	+	0.0398731i
$449$	−24.5491	−	17.8360i	−1.15854	−	0.841732i	−0.168951	−	0.985624i	$-0.554038\pi$
$449$	−24.5491	−	17.8360i	−1.15854	−	0.841732i	−0.989593	+	0.143893i	$0.954038\pi$
$450$	0.809017	+	0.587785i	0.0381374	+	0.0277085i
$451$	16.7040	+	3.55055i	0.786562	+	0.167189i
$452$	−0.604490	+	5.75134i	−0.0284328	+	0.270520i
$453$	1.17761	+	11.2042i	0.0553290	+	0.526420i
$454$	−7.08589	+	1.50615i	−0.332558	+	0.0706873i
$455$	−20.5062	−	9.12993i	−0.961344	−	0.428018i
$456$	−0.434687	+	0.482769i	−0.0203561	+	0.0226077i
$457$	−10.0163	−	30.8271i	−0.468544	−	1.44203i	−0.854471	−	0.519500i	$-0.826118\pi$
$457$	−10.0163	−	30.8271i	−0.468544	−	1.44203i	0.385927	−	0.922529i	$-0.373882\pi$
$458$	−2.03874	−	2.26426i	−0.0952643	−	0.105802i
$459$	−1.09225	+	1.89183i	−0.0509819	+	0.0883033i
$460$	−4.21803	−	7.30584i	−0.196667	−	0.340637i
$461$	1.11670	−	3.43684i	0.0520098	−	0.160070i	−0.921678	−	0.387956i	$-0.873181\pi$
$461$	1.11670	−	3.43684i	0.0520098	−	0.160070i	0.973688	+	0.227886i	$0.0731814\pi$
$462$	−14.3430	+	6.38590i	−0.667296	+	0.297099i
$463$	−0.757416	+	0.550295i	−0.0352001	+	0.0255744i	−0.605246	−	0.796038i	$-0.706925\pi$
$463$	−0.757416	+	0.550295i	−0.0352001	+	0.0255744i	0.570046	+	0.821613i	$0.306925\pi$
$464$	5.61129			0.260498
$465$	−5.36987	−	1.47124i	−0.249022	−	0.0682270i
$466$	−9.15464			−0.424081
$467$	19.1931	−	13.9446i	0.888151	−	0.645280i	−0.0472440	−	0.998883i	$-0.515044\pi$
$467$	19.1931	−	13.9446i	0.888151	−	0.645280i	0.935395	+	0.353604i	$0.115044\pi$
$468$	5.05178	−	2.24920i	0.233519	−	0.103969i
$469$	−16.9466	+	52.1563i	−0.782521	+	2.40835i
$470$	3.79367	+	6.57083i	0.174989	+	0.303090i
$471$	0.996529	−	1.72604i	0.0459176	−	0.0795317i
$472$	3.04347	+	3.38012i	0.140087	+	0.155583i
$473$	0.672735	+	2.07046i	0.0309324	+	0.0952000i
$474$	11.5910	−	12.8731i	0.532391	−	0.591281i
$475$	−0.593467	−	0.264228i	−0.0272301	−	0.0121236i
$476$	−8.67356	+	1.84362i	−0.397552	+	0.0845022i
$477$	−1.23919	−	11.7902i	−0.0567388	−	0.539834i
$478$	−1.63478	+	15.5539i	−0.0747730	+	0.711418i
$479$	−3.97432	−	0.844769i	−0.181592	−	0.0385985i	0.116218	−	0.993224i	$-0.462923\pi$
$479$	−3.97432	−	0.844769i	−0.181592	−	0.0385985i	−0.297810	+	0.954625i	$0.596256\pi$
$480$	−0.809017	−	0.587785i	−0.0369264	−	0.0268286i
$481$	26.2319	+	19.0586i	1.19607	+	0.868995i
$482$	−15.2142	−	3.23388i	−0.692989	−	0.147299i
$483$	−3.57943	+	34.0560i	−0.162870	+	1.54960i
$484$	−0.413956	−	3.93853i	−0.0188162	−	0.179024i
$485$	−8.38516	+	1.78232i	−0.380751	+	0.0809310i
$486$	0.913545	+	0.406737i	0.0414393	+	0.0184499i
$487$	−24.7862	+	27.5278i	−1.12317	+	1.24741i	−0.157531	+	0.987514i	$0.550353\pi$
$487$	−24.7862	+	27.5278i	−1.12317	+	1.24741i	−0.965638	+	0.259891i	$0.916313\pi$
$488$	−0.425900	−	1.31078i	−0.0192796	−	0.0593364i
$489$	9.20986	+	10.2286i	0.416484	+	0.462552i
$490$	4.73854	−	8.20739i	0.214065	−	0.370772i
$491$	5.92146	+	10.2563i	0.267232	+	0.462859i	0.968146	−	0.250386i	$-0.0805577\pi$
$491$	5.92146	+	10.2563i	0.267232	+	0.462859i	−0.700914	+	0.713246i	$0.747224\pi$
$492$	1.36436	−	4.19908i	0.0615103	−	0.189309i
$493$	−11.1981	+	4.98573i	−0.504338	+	0.224546i
$494$	−2.90628	+	2.11154i	−0.130760	+	0.0950026i
$495$	3.86784			0.173847
$496$	5.36987	+	1.47124i	0.241114	+	0.0660605i
$497$	60.6553			2.72076
$498$	−2.95303	+	2.14550i	−0.132328	+	0.0961421i
$499$	22.0899	−	9.83505i	0.988879	−	0.440277i	0.152425	−	0.988315i	$-0.451292\pi$
$499$	22.0899	−	9.83505i	0.988879	−	0.440277i	0.836454	+	0.548038i	$0.184625\pi$
$500$	0.309017	−	0.951057i	0.0138197	−	0.0425325i
$501$	−0.0359927	−	0.0623412i	−0.00160804	−	0.00278520i
$502$	−11.3546	+	19.6668i	−0.506781	+	0.877770i
$503$	−17.3638	−	19.2844i	−0.774213	−	0.859851i	0.219052	−	0.975713i	$-0.429704\pi$
$503$	−17.3638	−	19.2844i	−0.774213	−	0.859851i	−0.993265	+	0.115862i	$0.963037\pi$
$504$	1.25436	+	3.86053i	0.0558737	+	0.171961i
$505$	0.0443090	−	0.0492102i	0.00197173	−	0.00218982i
$506$	−29.8084	−	13.2716i	−1.32515	−	0.589993i
$507$	17.1952	−	3.65495i	0.763666	−	0.162322i
$508$	−1.11261	−	10.5858i	−0.0493640	−	0.469667i
$509$	2.35336	−	22.3908i	0.104311	−	0.992453i	−0.809722	−	0.586813i	$-0.800382\pi$
$509$	2.35336	−	22.3908i	0.104311	−	0.992453i	0.914033	−	0.405639i	$-0.132951\pi$
$510$	2.13677	+	0.454184i	0.0946176	+	0.0201116i
$511$	33.5554	+	24.3794i	1.48440	+	1.07848i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−0.635434	−	0.135066i	−0.0280551	−	0.00596330i
$514$	1.43190	−	13.6236i	0.0631585	−	0.600913i
$515$	0.192301	+	1.82963i	0.00847382	+	0.0806230i
$516$	0.550550	−	0.117023i	0.0242366	−	0.00515165i
$517$	26.8095	+	11.9364i	1.17908	+	0.524961i
$518$	−15.9261	+	17.6877i	−0.699751	+	0.777152i
$519$	−4.46053	−	13.7281i	−0.195796	−	0.602597i
$520$	−3.70020	−	4.10949i	−0.162264	−	0.180213i
$521$	−4.71838	+	8.17247i	−0.206716	+	0.358042i	−0.950678	−	0.310179i	$-0.899611\pi$
$521$	−4.71838	+	8.17247i	−0.206716	+	0.358042i	0.743962	+	0.668222i	$0.232944\pi$
$522$	2.80565	+	4.85952i	0.122800	+	0.212695i
$523$	−10.4569	+	32.1831i	−0.457249	+	1.40727i	0.411226	+	0.911533i	$0.365101\pi$
$523$	−10.4569	+	32.1831i	−0.457249	+	1.40727i	−0.868475	+	0.495733i	$0.834899\pi$
$524$	13.2047	−	5.87912i	0.576851	−	0.256830i
$525$	−3.28396	+	2.38594i	−0.143324	+	0.104131i
$526$	4.92913			0.214920
$527$	−12.0236	+	1.83516i	−0.523754	+	0.0799407i
$528$	−3.86784			−0.168326
$529$	−38.9680	+	28.3119i	−1.69426	+	1.23095i
$530$	−10.8302	+	4.82190i	−0.470432	+	0.209450i
$531$	−1.40553	+	4.32579i	−0.0609950	+	0.187723i
$532$	−1.31849	−	2.28369i	−0.0571637	−	0.0990105i
$533$	12.2077	−	21.1443i	0.528772	−	0.915860i
$534$	−5.89352	−	6.54542i	−0.255038	−	0.283248i
$535$	−4.84477	−	14.9107i	−0.209458	−	0.644645i
$536$	−9.04005	+	10.0400i	−0.390471	+	0.433662i
$537$	3.35093	+	1.49193i	0.144603	+	0.0643816i
$538$	26.4608	−	5.62441i	1.14080	−	0.242485i
$539$	−3.83158	−	36.4551i	−0.165038	−	1.57023i
$540$	0.104528	−	0.994522i	0.00449819	−	0.0427974i
$541$	−30.6955	−	6.52453i	−1.31970	−	0.280512i	−0.506374	−	0.862314i	$-0.669014\pi$
$541$	−30.6955	−	6.52453i	−1.31970	−	0.280512i	−0.813330	+	0.581803i	$0.802348\pi$
$542$	23.2214	+	16.8713i	0.997444	+	0.724686i
$543$	−9.14063	−	6.64105i	−0.392262	−	0.284995i
$544$	−2.13677	−	0.454184i	−0.0916131	−	0.0194730i
$545$	0.583449	−	5.55115i	0.0249922	−	0.237785i
$546$	2.34633	+	22.3238i	0.100414	+	0.955372i
$547$	−28.1587	+	5.98531i	−1.20398	+	0.255913i	−0.765862	−	0.643005i	$-0.777687\pi$
$547$	−28.1587	+	5.98531i	−1.20398	+	0.255913i	−0.438116	+	0.898919i	$0.644354\pi$
$548$	16.2362	+	7.22882i	0.693576	+	0.308800i
$549$	0.922223	−	1.02423i	0.0393595	−	0.0437132i
$550$	−1.19523	−	3.67854i	−0.0509648	−	0.156853i
$551$	−2.43916	−	2.70896i	−0.103912	−	0.115405i
$552$	−4.21803	+	7.30584i	−0.179531	+	0.310957i
$553$	35.1576	+	60.8948i	1.49505	+	2.58951i
$554$	−0.450300	+	1.38588i	−0.0191314	+	0.0588805i
$555$	5.35658	−	2.38490i	0.227374	−	0.101233i
$556$	−18.5781	+	13.4978i	−0.787888	+	0.572434i
$557$	−18.2847			−0.774748			−0.387374	−	0.921923i	$-0.626618\pi$
$557$	−18.2847			−0.774748			−0.387374	+	0.921923i	$0.626618\pi$
$558$	1.41080	+	5.38606i	0.0597241	+	0.228010i
$559$	3.11248			0.131644
$560$	3.28396	−	2.38594i	0.138773	−	0.100824i
$561$	7.71883	−	3.43665i	0.325889	−	0.145095i
$562$	−1.02217	+	3.14590i	−0.0431175	+	0.132702i
$563$	11.7923	+	20.4249i	0.496988	+	0.860808i	0.999994	−	0.00347490i	$-0.00110610\pi$
$563$	11.7923	+	20.4249i	0.496988	+	0.860808i	−0.503006	+	0.864283i	$0.667773\pi$
$564$	3.79367	−	6.57083i	0.159742	−	0.276682i
$565$	3.86960	+	4.29762i	0.162795	+	0.180802i
$566$	−1.49725	−	4.60806i	−0.0629341	−	0.193691i
$567$	−2.71613	+	3.01657i	−0.114067	+	0.126684i
$568$	13.6508	+	6.07774i	0.572776	+	0.255016i
$569$	−2.65576	+	0.564500i	−0.111335	+	0.0236651i	−0.263242	−	0.964730i	$-0.584792\pi$
$569$	−2.65576	+	0.564500i	−0.111335	+	0.0236651i	0.151907	+	0.988395i	$0.451459\pi$
$570$	0.0679048	+	0.646071i	0.00284422	+	0.0270609i
$571$	3.07518	−	29.2584i	0.128692	−	1.22443i	−0.719406	−	0.694589i	$-0.755586\pi$
$571$	3.07518	−	29.2584i	0.128692	−	1.22443i	0.848099	−	0.529838i	$-0.177747\pi$
$572$	−20.9212	−	4.44695i	−0.874761	−	0.185936i
$573$	4.77483	+	3.46912i	0.199471	+	0.144924i
$574$	14.4993	+	10.5343i	0.605187	+	0.439694i
$575$	−8.25171	−	1.75396i	−0.344120	−	0.0731450i
$576$	−0.104528	+	0.994522i	−0.00435535	+	0.0414384i
$577$	−0.0699192	−	0.665237i	−0.00291077	−	0.0276942i	0.992970	−	0.118365i	$-0.0377654\pi$
$577$	−0.0699192	−	0.665237i	−0.00291077	−	0.0276942i	−0.995881	+	0.0906712i	$0.971099\pi$
$578$	−11.9607	+	2.54233i	−0.497501	+	0.105747i
$579$	−1.15501	−	0.514244i	−0.0480006	−	0.0213712i
$580$	3.75469	−	4.17000i	0.155905	−	0.173150i
$581$	−4.57859	−	14.0915i	−0.189952	−	0.584612i
$582$	5.73612	+	6.37060i	0.237770	+	0.264070i
$583$	−22.9268	+	39.7104i	−0.949532	+	1.64464i
$584$	5.10898	+	8.84901i	0.211411	+	0.366175i
$585$	1.70882	−	5.25921i	0.0706510	−	0.217442i
$586$	19.6633	−	8.75466i	0.812283	−	0.361652i
$587$	−15.5302	+	11.2834i	−0.641001	+	0.465715i	−0.860194	−	0.509967i	$-0.829658\pi$
$587$	−15.5302	+	11.2834i	−0.641001	+	0.465715i	0.219193	+	0.975682i	$0.429658\pi$
$588$	−9.47708			−0.390828
$589$	−1.62395	−	3.23193i	−0.0669135	−	0.133170i
$590$	4.54840			0.187255
$591$	19.1754	−	13.9317i	0.788769	−	0.573074i
$592$	−5.35658	+	2.38490i	−0.220154	+	0.0980189i
$593$	1.93296	−	5.94902i	0.0793770	−	0.244297i	−0.903491	−	0.428606i	$-0.859005\pi$
$593$	1.93296	−	5.94902i	0.0793770	−	0.244297i	0.982868	+	0.184309i	$0.0590048\pi$
$594$	−1.93392	−	3.34965i	−0.0793498	−	0.137438i
$595$	−4.43366	+	7.67933i	−0.181762	+	0.314822i
$596$	−9.68452	−	10.7558i	−0.396693	−	0.440573i
$597$	−1.94935	−	5.99949i	−0.0797816	−	0.245543i
$598$	−31.2151	+	34.6679i	−1.27648	+	1.41767i
$599$	2.93715	+	1.30770i	0.120009	+	0.0534312i	0.465863	−	0.884857i	$-0.345744\pi$
$599$	2.93715	+	1.30770i	0.120009	+	0.0534312i	−0.345854	+	0.938288i	$0.612411\pi$
$600$	−0.978148	+	0.207912i	−0.0399327	+	0.00848796i
$601$	−3.01189	−	28.6562i	−0.122858	−	1.16891i	−0.866093	−	0.499883i	$-0.833376\pi$
$601$	−3.01189	−	28.6562i	−0.122858	−	1.16891i	0.743236	−	0.669030i	$-0.233290\pi$
$602$	−0.238818	+	2.27220i	−0.00973350	+	0.0926080i
$603$	−13.2149	−	2.80892i	−0.538153	−	0.114388i
$604$	−9.11433	−	6.62195i	−0.370857	−	0.269443i
$605$	−3.20389	−	2.32776i	−0.130256	−	0.0946369i
$606$	−0.0647718	−	0.0137677i	−0.00263117	−	0.000559273i
$607$	−1.79736	+	17.1008i	−0.0729527	+	0.694099i	0.895527	+	0.445007i	$0.146799\pi$
$607$	−1.79736	+	17.1008i	−0.0729527	+	0.694099i	−0.968480	+	0.249092i	$0.919868\pi$
$608$	−0.0679048	−	0.646071i	−0.00275390	−	0.0262017i
$609$	−22.2796	+	4.73567i	−0.902815	+	0.191899i
$610$	−1.25909	−	0.560581i	−0.0509789	−	0.0226973i
$611$	28.0747	−	31.1801i	1.13578	−	1.26141i
$612$	−0.675048	−	2.07759i	−0.0272872	−	0.0839814i
$613$	−13.7578	−	15.2795i	−0.555670	−	0.617134i	0.398220	−	0.917290i	$-0.369628\pi$
$613$	−13.7578	−	15.2795i	−0.555670	−	0.617134i	−0.953890	+	0.300156i	$0.902961\pi$
$614$	4.41655	−	7.64968i	0.178237	−	0.308716i
$615$	−2.20759	−	3.82365i	−0.0890185	−	0.154185i
$616$	4.85167	−	14.9319i	0.195479	−	0.601624i
$617$	3.54609	−	1.57882i	0.142760	−	0.0635610i	−0.334113	−	0.942533i	$-0.608437\pi$
$617$	3.54609	−	1.57882i	0.142760	−	0.0635610i	0.476873	+	0.878972i	$0.341770\pi$
$618$	1.48835	−	1.08135i	0.0598703	−	0.0434983i
$619$	3.79194			0.152411			0.0762055	−	0.997092i	$-0.475719\pi$
$619$	3.79194			0.152411			0.0762055	+	0.997092i	$0.475719\pi$
$620$	4.68648	−	3.00614i	0.188214	−	0.120729i
$621$	−8.43606			−0.338527
$622$	−18.3009	+	13.2964i	−0.733799	+	0.533136i
$623$	32.6614	−	14.5418i	1.30855	−	0.582604i
$624$	−1.70882	+	5.25921i	−0.0684076	+	0.210537i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	1.23168	−	2.13333i	0.0492278	−	0.0852651i
$627$	1.68130	+	1.86728i	0.0671448	+	0.0745718i
$628$	0.615889	+	1.89551i	0.0245766	+	0.0756391i
$629$	8.57079	−	9.51882i	0.341740	−	0.379540i
$630$	3.70826	+	1.65102i	0.147741	+	0.0657784i
$631$	−27.6303	+	5.87300i	−1.09994	+	0.233800i	−0.721907	−	0.691990i	$-0.756734\pi$
$631$	−27.6303	+	5.87300i	−1.09994	+	0.233800i	−0.378037	+	0.925791i	$0.623401\pi$
$632$	1.81069	+	17.2276i	0.0720253	+	0.685275i
$633$	−2.73344	+	26.0069i	−0.108644	+	1.03368i
$634$	31.6096	+	6.71882i	1.25538	+	0.266839i
$635$	−8.61124	−	6.25643i	−0.341727	−	0.248279i
$636$	9.59097	+	6.96825i	0.380307	+	0.276309i
$637$	−51.2617	−	10.8960i	−2.03106	−	0.431716i
$638$	2.26864	−	21.5847i	0.0898165	−	0.854547i
$639$	1.56194	+	14.8608i	0.0617892	+	0.587885i
$640$	0.978148	−	0.207912i	0.0386647	−	0.00821843i
$641$	−23.7941	−	10.5938i	−0.939810	−	0.418430i	−0.121102	−	0.992640i	$-0.538643\pi$
$641$	−23.7941	−	10.5938i	−0.939810	−	0.418430i	−0.818708	+	0.574210i	$0.805309\pi$
$642$	−10.4906	+	11.6510i	−0.414032	+	0.459830i
$643$	−8.93320	−	27.4936i	−0.352291	−	1.08424i	−0.957564	−	0.288222i	$-0.906936\pi$
$643$	−8.93320	−	27.4936i	−0.352291	−	1.08424i	0.605272	−	0.796018i	$-0.293064\pi$
$644$	−22.9135	−	25.4480i	−0.902917	−	1.00279i
$645$	0.281425	−	0.487442i	0.0110811	−	0.0191930i
$646$	0.709559	+	1.22899i	0.0279172	+	0.0483541i
$647$	6.53641	−	20.1170i	0.256973	−	0.790881i	−0.736462	−	0.676479i	$-0.763505\pi$
$647$	6.53641	−	20.1170i	0.256973	−	0.790881i	0.993435	−	0.114402i	$-0.0364952\pi$
$648$	−0.913545	+	0.406737i	−0.0358875	+	0.0159781i
$649$	14.2326	−	10.3406i	0.558680	−	0.405905i
$650$	−5.52986			−0.216899
$651$	−22.5627	−	1.30961i	−0.884301	−	0.0513278i
$652$	−13.7639			−0.539036
$653$	−3.47326	+	2.52347i	−0.135919	+	0.0987509i	−0.653667	−	0.756782i	$-0.726770\pi$
$653$	−3.47326	+	2.52347i	−0.135919	+	0.0987509i	0.517748	+	0.855533i	$0.326770\pi$
$654$	−5.09916	+	2.27029i	−0.199393	+	0.0887754i
$655$	4.46664	−	13.7469i	0.174526	−	0.537136i
$656$	2.20759	+	3.82365i	0.0861918	+	0.149289i
$657$	−5.10898	+	8.84901i	−0.199320	+	0.345233i
$658$	20.6082	+	22.8878i	0.803392	+	0.892258i
$659$	−8.03309	−	24.7233i	−0.312925	−	0.963084i	−0.976600	−	0.215063i	$-0.931004\pi$
$659$	−8.03309	−	24.7233i	−0.312925	−	0.963084i	0.663675	−	0.748021i	$-0.268996\pi$
$660$	−2.58809	+	2.87437i	−0.100741	+	0.111885i
$661$	−15.7335	−	7.00501i	−0.611962	−	0.272463i	0.0772624	−	0.997011i	$-0.475382\pi$
$661$	−15.7335	−	7.00501i	−0.611962	−	0.272463i	−0.689225	+	0.724548i	$0.742049\pi$
$662$	−21.2752	+	4.52218i	−0.826883	+	0.175759i
$663$	−1.26270	−	12.0138i	−0.0490393	−	0.466578i
$664$	0.381544	−	3.63014i	0.0148068	−	0.140877i
$665$	−2.57935	−	0.548258i	−0.100023	−	0.0212605i
$666$	−4.74367	−	3.44648i	−0.183814	−	0.133548i
$667$	−38.2966	−	27.8241i	−1.48285	−	1.07735i
$668$	0.0704124	+	0.0149666i	0.00272434	+	0.000579075i
$669$	−0.680046	+	6.47020i	−0.0262921	+	0.250153i
$670$	1.41219	+	13.4361i	0.0545578	+	0.519083i
$671$	−5.21433	+	1.10834i	−0.201297	+	0.0427870i
$672$	−3.70826	−	1.65102i	−0.143049	−	0.0636896i
$673$	12.2245	−	13.5766i	0.471218	−	0.523341i	−0.459943	−	0.887948i	$-0.652130\pi$
$673$	12.2245	−	13.5766i	0.471218	−	0.523341i	0.931161	+	0.364608i	$0.118797\pi$
$674$	−1.17868	−	3.62761i	−0.0454011	−	0.139730i
$675$	−0.669131	−	0.743145i	−0.0257548	−	0.0286037i
$676$	−8.78968	+	15.2242i	−0.338064	+	0.585545i
$677$	−5.92701	−	10.2659i	−0.227794	−	0.394550i	0.729360	−	0.684130i	$-0.239818\pi$
$677$	−5.92701	−	10.2659i	−0.227794	−	0.394550i	−0.957154	+	0.289580i	$0.906484\pi$
$678$	1.78705	−	5.49998i	0.0686313	−	0.211225i
$679$	−31.7890	+	14.1534i	−1.21995	+	0.543157i
$680$	−1.76730	+	1.28402i	−0.0677729	+	0.0492399i
$681$	7.24420			0.277598
$682$	7.83038	−	20.0612i	0.299841	−	0.768183i
$683$	18.8935			0.722938			0.361469	−	0.932384i	$-0.382275\pi$
$683$	18.8935			0.722938			0.361469	+	0.932384i	$0.382275\pi$
$684$	0.525562	−	0.381843i	0.0200954	−	0.0146001i
$685$	16.2362	−	7.22882i	0.620354	−	0.276199i
$686$	3.10715	−	9.56284i	0.118632	−	0.365111i
$687$	1.52343	+	2.63865i	0.0581224	+	0.100671i
$688$	−0.281425	+	0.487442i	−0.0107292	+	0.0185836i
$689$	43.8662	+	48.7184i	1.67117	+	1.85602i
$690$	2.60689	+	8.02317i	0.0992424	+	0.305437i
$691$	3.63338	−	4.03528i	0.138220	−	0.153509i	−0.670060	−	0.742307i	$-0.733732\pi$
$691$	3.63338	−	4.03528i	0.138220	−	0.153509i	0.808281	+	0.588798i	$0.200398\pi$
$692$	13.1866	+	5.87107i	0.501281	+	0.223185i
$693$	15.3573	−	3.26428i	0.583374	−	0.124000i
$694$	−2.69030	−	25.5965i	−0.102123	−	0.971631i
$695$	−2.40037	+	22.8380i	−0.0910513	+	0.866296i
$696$	−5.48867	−	1.16665i	−0.208047	−	0.0442219i
$697$	−7.80294	−	5.66917i	−0.295557	−	0.214735i
$698$	9.30652	+	6.76159i	0.352257	+	0.255930i
$699$	8.95459	+	1.90336i	0.338694	+	0.0719916i
$700$	0.424302	−	4.03696i	0.0160371	−	0.152583i
$701$	−2.44276	−	23.2413i	−0.0922618	−	0.877813i	−0.938563	−	0.345108i	$-0.887842\pi$
$701$	−2.44276	−	23.2413i	−0.0922618	−	0.877813i	0.846301	−	0.532705i	$-0.178824\pi$
$702$	−5.40902	+	1.14972i	−0.204150	+	0.0433935i
$703$	3.47979	+	1.54930i	0.131243	+	0.0584331i
$704$	2.58809	−	2.87437i	0.0975424	−	0.108332i
$705$	−2.34462	−	7.21599i	−0.0883034	−	0.271770i
$706$	5.27925	+	5.86320i	0.198687	+	0.220664i
$707$	0.134398	−	0.232783i	0.00505454	−	0.00875472i
$708$	−2.27420	−	3.93903i	−0.0854697	−	0.148038i
$709$	−6.86280	+	21.1215i	−0.257738	+	0.793235i	0.735540	+	0.677481i	$0.236928\pi$
$709$	−6.86280	+	21.1215i	−0.257738	+	0.793235i	−0.993278	+	0.115754i	$0.963072\pi$
$710$	13.6508	−	6.07774i	0.512306	−	0.228093i
$711$	−14.0142	+	10.1819i	−0.525572	+	0.381850i
$712$	8.80773			0.330084
$713$	−29.3536	−	36.6680i	−1.09930	−	1.37323i
$714$	8.86733			0.331851
$715$	−17.3038	+	12.5719i	−0.647124	+	0.470163i
$716$	−3.35093	+	1.49193i	−0.125230	+	0.0557561i
$717$	4.83289	−	14.8741i	0.180487	−	0.555483i
$718$	−7.39183	−	12.8030i	−0.275861	−	0.477805i
$719$	−11.2459	+	19.4785i	−0.419402	+	0.726425i	−0.995879	−	0.0906879i	$-0.971093\pi$
$719$	−11.2459	+	19.4785i	−0.419402	+	0.726425i	0.576478	+	0.817113i	$0.304427\pi$
$720$	0.669131	+	0.743145i	0.0249370	+	0.0276954i
$721$	2.30765	+	7.10223i	0.0859415	+	0.264501i
$722$	12.4311	−	13.8061i	0.462637	−	0.513811i
$723$	14.2094	+	6.32643i	0.528453	+	0.235282i
$724$	11.0515	−	2.34908i	0.410727	−	0.0873027i
$725$	−0.586540	−	5.58055i	−0.0217835	−	0.207256i
$726$	−0.413956	+	3.93853i	−0.0153633	+	0.146172i
$727$	−2.73650	−	0.581661i	−0.101491	−	0.0215726i	0.156886	−	0.987617i	$-0.449854\pi$
$727$	−2.73650	−	0.581661i	−0.101491	−	0.0215726i	−0.258377	+	0.966044i	$0.583188\pi$
$728$	−18.1598	−	13.1939i	−0.673048	−	0.488998i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	9.99467	+	2.12443i	0.369919	+	0.0786288i
$731$	0.128523	−	1.22281i	0.00475358	−	0.0452273i
$732$	0.144065	+	1.37069i	0.00532481	+	0.0506622i
$733$	23.7103	−	5.03979i	0.875761	−	0.186149i	0.251966	−	0.967736i	$-0.418923\pi$
$733$	23.7103	−	5.03979i	0.875761	−	0.186149i	0.623796	+	0.781587i	$0.285590\pi$
$734$	33.7159	+	15.0113i	1.24448	+	0.554076i
$735$	−6.34141	+	7.04284i	−0.233906	+	0.259779i
$736$	−2.60689	−	8.02317i	−0.0960911	−	0.295738i
$737$	34.9655	+	38.8331i	1.28797	+	1.43044i
$738$	−2.20759	+	3.82365i	−0.0812624	+	0.140751i
$739$	25.5486	+	44.2514i	0.939820	+	1.62782i	0.765806	+	0.643072i	$0.222340\pi$
$739$	25.5486	+	44.2514i	0.939820	+	1.62782i	0.174014	+	0.984743i	$0.444326\pi$
$740$	−1.81192	+	5.57652i	−0.0666076	+	0.204997i
$741$	3.28179	−	1.46115i	0.120559	−	0.0536765i
$742$	−38.9317	+	28.2855i	−1.42923	+	1.03839i
$743$	31.0967			1.14083			0.570413	−	0.821358i	$-0.306783\pi$
$743$	31.0967			1.14083			0.570413	+	0.821358i	$0.306783\pi$
$744$	−4.94663	−	2.55554i	−0.181352	−	0.0936908i
$745$	−14.4733			−0.530260
$746$	−8.57658	+	6.23125i	−0.314011	+	0.228142i
$747$	3.33457	−	1.48465i	0.122005	−	0.0543203i
$748$	−2.61098	+	8.03578i	−0.0954670	+	0.293817i
$749$	−31.8201	−	55.1140i	−1.16268	−	2.01382i
$750$	−0.500000	+	0.866025i	−0.0182574	+	0.0316228i
$751$	16.0483	+	17.8235i	0.585612	+	0.650388i	0.961022	−	0.276471i	$-0.0891649\pi$
$751$	16.0483	+	17.8235i	0.585612	+	0.650388i	−0.375411	+	0.926859i	$0.622498\pi$
$752$	2.34462	+	7.21599i	0.0854994	+	0.263140i
$753$	15.1954	−	16.8762i	0.553752	−	0.615004i
$754$	−28.3470	−	12.6209i	−1.03234	−	0.459626i
$755$	−11.0197	+	2.34232i	−0.401050	+	0.0852457i
$756$	−0.424302	−	4.03696i	−0.0154317	−	0.146823i
$757$	−2.51038	+	23.8847i	−0.0912414	+	0.868104i	0.849182	+	0.528100i	$0.177095\pi$
$757$	−2.51038	+	23.8847i	−0.0912414	+	0.868104i	−0.940424	+	0.340005i	$0.889571\pi$
$758$	8.09316	+	1.72026i	0.293957	+	0.0624825i
$759$	26.3977	+	19.1791i	0.958176	+	0.696156i
$760$	−0.525562	−	0.381843i	−0.0190641	−	0.0138509i
$761$	14.3506	+	3.05032i	0.520209	+	0.110574i	0.460531	−	0.887644i	$-0.347659\pi$
$761$	14.3506	+	3.05032i	0.520209	+	0.110574i	0.0596784	+	0.998218i	$0.480992\pi$
$762$	−1.11261	+	10.5858i	−0.0403056	+	0.383482i
$763$	−2.36833	−	22.5332i	−0.0857395	−	0.815757i
$764$	−5.77304	+	1.22710i	−0.208861	+	0.0443948i
$765$	−1.99564	−	0.888517i	−0.0721526	−	0.0321244i
$766$	−4.76329	+	5.29017i	−0.172105	+	0.191142i
$767$	−7.77240	−	23.9210i	−0.280645	−	0.863737i
$768$	−0.669131	−	0.743145i	−0.0241452	−	0.0268159i
$769$	−26.5471	+	45.9809i	−0.957313	+	1.65811i	−0.228328	+	0.973584i	$0.573326\pi$
$769$	−26.5471	+	45.9809i	−0.957313	+	1.65811i	−0.728985	+	0.684530i	$0.760008\pi$
$770$	−7.85017	−	13.5969i	−0.282901	−	0.489998i
$771$	−4.23312	+	13.0282i	−0.152452	+	0.469200i
$772$	1.15501	−	0.514244i	0.0415697	−	0.0185080i
$773$	−7.44236	+	5.40719i	−0.267683	+	0.194483i	−0.713527	−	0.700627i	$-0.752904\pi$
$773$	−7.44236	+	5.40719i	−0.267683	+	0.194483i	0.445844	+	0.895111i	$0.352904\pi$
$774$	−0.562850			−0.0202312
$775$	0.901873	−	5.49424i	0.0323962	−	0.197359i
$776$	−8.57249			−0.307734
$777$	19.2555	−	13.9899i	0.690788	−	0.501887i
$778$	14.8915	−	6.63011i	0.533885	−	0.237701i
$779$	0.886332	−	2.72785i	0.0317561	−	0.0977354i
$780$	2.76493	+	4.78900i	0.0990004	+	0.171474i
$781$	28.8980	−	50.0528i	1.03405	−	1.79103i
$782$	12.3311	+	13.6951i	0.440961	+	0.489736i
$783$	−1.73398	−	5.33665i	−0.0619675	−	0.190716i
$784$	6.34141	−	7.04284i	0.226479	−	0.251530i
$785$	1.82075	+	0.810650i	0.0649853	+	0.0289333i
$786$	−14.1385	+	3.00523i	−0.504303	+	0.107193i
$787$	1.87258	+	17.8164i	0.0667504	+	0.635088i	0.975840	+	0.218487i	$0.0701121\pi$
$787$	1.87258	+	17.8164i	0.0667504	+	0.635088i	−0.909090	+	0.416601i	$0.863221\pi$
$788$	−2.47754	+	23.5722i	−0.0882587	+	0.839725i
$789$	−4.82141	−	1.02482i	−0.171647	−	0.0364847i
$790$	14.0142	+	10.1819i	0.498601	+	0.362255i
$791$	18.9912	+	13.7979i	0.675249	+	0.490597i
$792$	3.78332	+	0.804170i	0.134435	+	0.0285749i
$793$	−0.796661	+	7.57973i	−0.0282903	+	0.269164i
$794$	2.95377	+	28.1033i	0.104825	+	0.997348i
$795$	11.5960	−	2.46481i	0.411269	−	0.0874179i
$796$	5.76286	+	2.56579i	0.204259	+	0.0909420i
$797$	−11.6402	+	12.9278i	−0.412317	+	0.457925i	−0.913153	−	0.407618i	$-0.866360\pi$
$797$	−11.6402	+	12.9278i	−0.412317	+	0.457925i	0.500835	+	0.865543i	$0.333026\pi$
$798$	0.814871	+	2.50791i	0.0288461	+	0.0887792i
$799$	−11.0906	−	12.3173i	−0.392356	−	0.435755i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	4.40387	+	7.62772i	0.155603	+	0.269512i
$802$	−2.55399	+	7.86037i	−0.0901845	+	0.277559i
$803$	36.1047	−	16.0748i	1.27411	−	0.567268i
$804$	10.9299	−	7.94106i	0.385469	−	0.280060i
$805$	−34.2436			−1.20693
$806$	−23.8183	−	19.5102i	−0.838963	−	0.687219i
$807$	−27.0519			−0.952272
$808$	0.0535721	−	0.0389224i	0.00188466	−	0.00136929i
$809$	−33.3306	+	14.8397i	−1.17184	+	0.521738i	−0.897982	−	0.440032i	$-0.854967\pi$
$809$	−33.3306	+	14.8397i	−1.17184	+	0.521738i	−0.273860	+	0.961770i	$0.588300\pi$
$810$	−0.309017	+	0.951057i	−0.0108578	+	0.0334167i
$811$	25.8057	+	44.6968i	0.906161	+	1.56952i	0.819351	+	0.573292i	$0.194334\pi$
$811$	25.8057	+	44.6968i	0.906161	+	1.56952i	0.0868103	+	0.996225i	$0.472333\pi$
$812$	11.3887	−	19.7257i	0.399664	−	0.692238i
$813$	−19.2062	−	21.3306i	−0.673591	−	0.748098i
$814$	7.00823	+	21.5691i	0.245638	+	0.755997i
$815$	−9.20986	+	10.2286i	−0.322607	+	0.358292i
$816$	1.99564	+	0.888517i	0.0698615	+	0.0311043i
$817$	0.357654	−	0.0760217i	0.0125127	−	0.00265966i
$818$	−2.12544	−	20.2222i	−0.0743144	−	0.707054i
$819$	2.34633	−	22.3238i	0.0819874	−	0.780058i
$820$	4.31869	+	0.917967i	0.150815	+	0.0320568i
$821$	0.268908	+	0.195373i	0.00938496	+	0.00681858i	0.592468	−	0.805594i	$-0.298154\pi$
$821$	0.268908	+	0.195373i	0.00938496	+	0.00681858i	−0.583083	+	0.812413i	$0.698154\pi$
$822$	−14.3784	−	10.4466i	−0.501506	−	0.364365i
$823$	31.5977	+	6.71631i	1.10143	+	0.234116i	0.722542	−	0.691327i	$-0.242974\pi$
$823$	31.5977	+	6.71631i	1.10143	+	0.234116i	0.378887	+	0.925443i	$0.376307\pi$
$824$	−0.192301	+	1.82963i	−0.00669914	+	0.0637381i
$825$	0.404300	+	3.84666i	0.0140759	+	0.133923i
$826$	18.0594	−	3.83864i	0.628367	−	0.133564i
$827$	−22.7593	−	10.1331i	−0.791420	−	0.352363i	−0.0291111	−	0.999576i	$-0.509268\pi$
$827$	−22.7593	−	10.1331i	−0.791420	−	0.352363i	−0.762309	+	0.647213i	$0.775934\pi$
$828$	5.64483	−	6.26921i	0.196171	−	0.217870i
$829$	−5.77893	−	17.7857i	−0.200711	−	0.617724i	−0.999862	−	0.0165942i	$-0.994718\pi$
$829$	−5.77893	−	17.7857i	−0.200711	−	0.617724i	0.799152	−	0.601129i	$-0.205282\pi$
$830$	−2.44242	−	2.71258i	−0.0847776	−	0.0941551i
$831$	0.728601	−	1.26197i	0.0252749	−	0.0437774i
$832$	−2.76493	−	4.78900i	−0.0958567	−	0.166029i
$833$	−6.39749	+	19.6894i	−0.221660	+	0.682199i
$834$	20.9785	−	9.34023i	0.726426	−	0.323426i
$835$	0.0582374	−	0.0423120i	0.00201539	−	0.00146427i
$836$	−2.51267			−0.0869024
$837$	−0.260151	−	5.56168i	−0.00899212	−	0.192240i
$838$	17.1881			0.593755
$839$	−0.392527	+	0.285187i	−0.0135515	+	0.00984576i	−0.594540	−	0.804066i	$-0.702666\pi$
$839$	−0.392527	+	0.285187i	−0.0135515	+	0.00984576i	0.580989	+	0.813911i	$0.302666\pi$
$840$	−3.70826	+	1.65102i	−0.127947	+	0.0569657i
$841$	0.768394	−	2.36487i	0.0264964	−	0.0815474i
$842$	−8.46942	−	14.6695i	−0.291876	−	0.505543i
$843$	1.65390	−	2.86464i	0.0569633	−	0.0986634i
$844$	−17.4979	−	19.4333i	−0.602301	−	0.668923i
$845$	5.43232	+	16.7190i	0.186877	+	0.575150i
$846$	−5.07692	+	5.63849i	−0.174548	+	0.193855i
$847$	−14.6855	−	6.53842i	−0.504601	−	0.224663i
$848$	−11.5960	+	2.46481i	−0.398209	+	0.0846420i
$849$	0.506461	+	4.81866i	0.0173817	+	0.165376i
$850$	−0.228343	+	2.17254i	−0.00783209	+	0.0745174i
$851$	48.3839	+	10.2843i	1.65858	+	0.352542i
$852$	−12.0889	−	8.78309i	−0.414158	−	0.300904i
$853$	−23.3058	−	16.9327i	−0.797975	−	0.579763i	0.112344	−	0.993669i	$-0.464164\pi$
$853$	−23.3058	−	16.9327i	−0.797975	−	0.579763i	−0.910319	+	0.413906i	$0.864164\pi$
$854$	−5.47230	−	1.16317i	−0.187258	−	0.0398029i
$855$	0.0679048	−	0.646071i	0.00232230	−	0.0220952i
$856$	−1.63880	−	15.5921i	−0.0560130	−	0.532928i
$857$	−36.1203	+	7.67761i	−1.23385	+	0.262262i	−0.778267	−	0.627933i	$-0.783901\pi$
$857$	−36.1203	+	7.67761i	−1.23385	+	0.262262i	−0.455579	+	0.890195i	$0.650568\pi$
$858$	19.5395	+	8.69954i	0.667067	+	0.296997i
$859$	32.4140	−	35.9994i	1.10595	−	1.22828i	0.134533	−	0.990909i	$-0.457047\pi$
$859$	32.4140	−	35.9994i	1.10595	−	1.22828i	0.971418	−	0.237374i	$-0.0762867\pi$
$860$	0.173930	+	0.535302i	0.00593097	+	0.0182536i
$861$	−11.9922	−	13.3187i	−0.408693	−	0.453900i
$862$	6.47378	−	11.2129i	0.220498	−	0.381913i
$863$	6.70056	+	11.6057i	0.228090	+	0.395063i	0.957242	−	0.289289i	$-0.0934187\pi$
$863$	6.70056	+	11.6057i	0.228090	+	0.395063i	−0.729152	+	0.684352i	$0.760085\pi$
$864$	0.309017	−	0.951057i	0.0105130	−	0.0323556i
$865$	13.1866	−	5.87107i	0.448360	−	0.199623i
$866$	16.5168	−	12.0001i	0.561263	−	0.407782i
$867$	12.2279			0.415283
$868$	16.0706	−	15.8910i	0.545472	−	0.539377i
$869$	67.0005			2.27284
$870$	−4.53963	+	3.29823i	−0.153908	+	0.111821i
$871$	68.2503	−	30.3870i	2.31257	−	1.02962i
$872$	1.72485	−	5.30854i	0.0584107	−	0.179770i
$873$	−4.28625	−	7.42399i	−0.145067	−	0.251264i
$874$	−2.74016	+	4.74609i	−0.0926873	+	0.160539i
$875$	−2.71613	−	3.01657i	−0.0918221	−	0.101979i
$876$	−3.15752	−	9.71785i	−0.106683	−	0.328336i
$877$	13.0502	−	14.4937i	0.440673	−	0.489417i	−0.481363	−	0.876521i	$-0.659858\pi$
$877$	13.0502	−	14.4937i	0.440673	−	0.489417i	0.922036	+	0.387104i	$0.126525\pi$
$878$	26.6701	+	11.8743i	0.900072	+	0.400738i
$879$	−21.0538	+	4.47512i	−0.710127	+	0.150942i
$880$	−0.404300	−	3.84666i	−0.0136289	−	0.129671i
$881$	2.50348	−	23.8190i	0.0843444	−	0.802483i	−0.867816	−	0.496885i	$-0.834477\pi$
$881$	2.50348	−	23.8190i	0.0843444	−	0.802483i	0.952161	−	0.305598i	$-0.0988563\pi$
$882$	9.26998	+	1.97040i	0.312137	+	0.0663467i
$883$	13.4565	+	9.77669i	0.452846	+	0.329012i	0.790718	−	0.612180i	$-0.209707\pi$
$883$	13.4565	+	9.77669i	0.452846	+	0.329012i	−0.337872	+	0.941192i	$0.609707\pi$
$884$	9.77292	+	7.10044i	0.328699	+	0.238814i
$885$	−4.44901	−	0.945666i	−0.149552	−	0.0317882i
$886$	−0.876253	+	8.33699i	−0.0294383	+	0.280087i
$887$	−4.51717	−	42.9780i	−0.151672	−	1.44306i	−0.760284	−	0.649591i	$-0.774940\pi$
$887$	−4.51717	−	42.9780i	−0.151672	−	1.44306i	0.608612	−	0.793468i	$-0.291727\pi$
$888$	5.73537	−	1.21909i	0.192466	−	0.0409100i
$889$	−39.4710	−	17.5736i	−1.32382	−	0.589400i
$890$	5.89352	−	6.54542i	0.197551	−	0.219403i
$891$	1.19523	+	3.67854i	0.0400417	+	0.123236i
$892$	−4.35326	−	4.83478i	−0.145758	−	0.161881i
$893$	2.46448	−	4.26861i	0.0824708	−	0.142844i
$894$	7.23664	+	12.5342i	0.242030	+	0.419208i
$895$	−1.13349	+	3.48853i	−0.0378884	+	0.116609i
$896$	3.70826	−	1.65102i	0.123884	−	0.0551568i
$897$	37.7408	−	27.4203i	1.26013	−	0.915538i
$898$	−30.3444			−1.01260
$899$	17.1627	−	26.1060i	0.572410	−	0.870684i
$900$	1.00000			0.0333333
$901$	20.9515	−	15.2222i	0.697996	−	0.507124i
$902$	15.6008	−	6.94593i	0.519450	−	0.231274i
$903$	0.706017	−	2.17290i	0.0234948	−	0.0723094i
$904$	2.89151	+	5.00824i	0.0961702	+	0.166572i
$905$	5.64922	−	9.78473i	0.187786	−	0.325255i
$906$	7.53838	+	8.37222i	0.250446	+	0.278148i
$907$	10.8426	+	33.3700i	0.360022	+	1.10803i	0.953040	+	0.302845i	$0.0979363\pi$
$907$	10.8426	+	33.3700i	0.360022	+	1.10803i	−0.593018	+	0.805189i	$0.702064\pi$
$908$	−4.84731	+	5.38349i	−0.160864	+	0.178657i
$909$	0.0604939	+	0.0269336i	0.00200646	+	0.000893332i
$910$	−21.9563	+	4.66695i	−0.727843	+	0.154708i
$911$	3.26445	+	31.0591i	0.108156	+	1.02903i	0.905163	+	0.425065i	$0.139749\pi$
$911$	3.26445	+	31.0591i	0.108156	+	1.02903i	−0.797007	+	0.603970i	$0.793585\pi$
$912$	−0.0679048	+	0.646071i	−0.00224855	+	0.0213936i
$913$	−13.8097	−	2.93533i	−0.457033	−	0.0971454i
$914$	−26.2231	−	19.0522i	−0.867382	−	0.630190i
$915$	1.11502	+	0.810110i	0.0368614	+	0.0267814i
$916$	−2.98027	−	0.633477i	−0.0984711	−	0.0209307i
$917$	6.13301	−	58.3517i	0.202530	−	1.92694i
$918$	0.228343	+	2.17254i	0.00753643	+	0.0717044i
$919$	−8.01505	+	1.70365i	−0.264392	+	0.0561983i	−0.338200	−	0.941074i	$-0.609818\pi$
$919$	−8.01505	+	1.70365i	−0.264392	+	0.0561983i	0.0738082	+	0.997272i	$0.476485\pi$
$920$	−7.70672	−	3.43125i	−0.254083	−	0.113125i
$921$	−5.91049	+	6.56427i	−0.194757	+	0.216300i
$922$	−1.11670	−	3.43684i	−0.0367765	−	0.113186i
$923$	−55.2909	−	61.4068i	−1.81992	−	2.02123i
$924$	−7.85017	+	13.5969i	−0.258252	+	0.447305i
$925$	2.93175	+	5.07794i	0.0963954	+	0.166962i
$926$	−0.289307	+	0.890396i	−0.00950723	+	0.0292602i
$927$	−1.68065	+	0.748275i	−0.0551999	+	0.0245766i
$928$	4.53963	−	3.29823i	0.149021	−	0.108270i
$929$	54.2530			1.77998			0.889992	−	0.455975i	$-0.150710\pi$
$929$	54.2530			1.77998			0.889992	+	0.455975i	$0.150710\pi$
$930$	−5.20908	+	1.96607i	−0.170813	+	0.0644701i
$931$	−6.15660			−0.201774
$932$	−7.40626	+	5.38096i	−0.242600	+	0.176259i
$933$	20.6654	−	9.20085i	0.676556	−	0.301222i
$934$	7.33112	−	22.5629i	0.239881	−	0.738279i
$935$	4.22466	+	7.31732i	0.138161	+	0.239302i
$936$	2.76493	−	4.78900i	0.0903746	−	0.156533i
$937$	−5.91061	−	6.56440i	−0.193091	−	0.214450i	0.638823	−	0.769354i	$-0.279422\pi$
$937$	−5.91061	−	6.56440i	−0.193091	−	0.214450i	−0.831914	+	0.554904i	$0.812755\pi$
$938$	16.9466	+	52.1563i	0.553326	+	1.70296i
$939$	−1.64831	+	1.83063i	−0.0537905	+	0.0597404i
$940$	6.93138	+	3.08605i	0.226077	+	0.100656i
$941$	−52.7946	+	11.2218i	−1.72106	+	0.365822i	−0.959376	−	0.282132i	$-0.908958\pi$
$941$	−52.7946	+	11.2218i	−1.72106	+	0.365822i	−0.761680	+	0.647953i	$0.775625\pi$
$942$	−0.208331	−	1.98214i	−0.00678780	−	0.0645816i
$943$	3.89334	−	37.0426i	0.126785	−	1.20627i
$944$	4.44901	+	0.945666i	0.144803	+	0.0307788i
$945$	−3.28396	−	2.38594i	−0.106827	−	0.0776145i
$946$	1.76124	+	1.27962i	0.0572629	+	0.0416039i
$947$	−3.65348	−	0.776572i	−0.118722	−	0.0252352i	0.148167	−	0.988962i	$-0.452663\pi$
$947$	−3.65348	−	0.776572i	−0.118722	−	0.0252352i	−0.266890	+	0.963727i	$0.585996\pi$
$948$	1.81069	−	17.2276i	0.0588084	−	0.559525i
$949$	−5.90626	−	56.1943i	−0.191725	−	1.82415i
$950$	−0.635434	+	0.135066i	−0.0206162	+	0.00438211i
$951$	−29.5219	−	13.1440i	−0.957314	−	0.426223i
$952$	−5.93340	+	6.58971i	−0.192303	+	0.213574i
$953$	−9.22360	−	28.3873i	−0.298782	−	0.919556i	−0.981925	−	0.189271i	$-0.939387\pi$
$953$	−9.22360	−	28.3873i	−0.298782	−	0.919556i	0.683143	−	0.730285i	$-0.260613\pi$
$954$	−7.93261	−	8.81005i	−0.256828	−	0.285236i
$955$	−2.95101	+	5.11129i	−0.0954924	+	0.165398i
$956$	7.81977	+	13.5442i	0.252910	+	0.438052i
$957$	−6.70678	+	20.6413i	−0.216799	+	0.667240i
$958$	−3.71184	+	1.65262i	−0.119924	+	0.0533936i
$959$	58.3650	−	42.4046i	1.88470	−	1.36932i
$960$	−1.00000			−0.0322749
$961$	23.2691	−	20.4829i	0.750617	−	0.660738i
$962$	32.4244			1.04540
$963$	12.6838	−	9.21530i	0.408729	−	0.296959i
$964$	−14.2094	+	6.32643i	−0.457654	+	0.203761i
$965$	0.390695	−	1.20244i	0.0125769	−	0.0387078i
$966$	17.1218	+	29.6559i	0.550885	+	0.954161i
$967$	6.55738	−	11.3577i	0.210871	−	0.365239i	−0.741116	−	0.671377i	$-0.765703\pi$
$967$	6.55738	−	11.3577i	0.210871	−	0.365239i	0.951987	+	0.306137i	$0.0990367\pi$
$968$	−2.64990	−	2.94302i	−0.0851711	−	0.0945921i
$969$	−0.438532	−	1.34966i	−0.0140877	−	0.0433574i
$970$	−5.73612	+	6.37060i	−0.184176	+	0.204548i
$971$	11.7814	+	5.24544i	0.378084	+	0.168334i	0.586975	−	0.809605i	$-0.300319\pi$
$971$	11.7814	+	5.24544i	0.378084	+	0.168334i	−0.208891	+	0.977939i	$0.566985\pi$
$972$	0.978148	−	0.207912i	0.0313741	−	0.00666877i
$973$	9.74359	+	92.7040i	0.312365	+	2.97196i
$974$	−3.87198	+	36.8394i	−0.124066	+	1.18041i
$975$	5.40902	+	1.14972i	0.173227	+	0.0368206i
$976$	−1.11502	−	0.810110i	−0.0356909	−	0.0259310i
$977$	−22.6228	−	16.4365i	−0.723769	−	0.525849i	0.163817	−	0.986491i	$-0.447619\pi$
$977$	−22.6228	−	16.4365i	−0.723769	−	0.525849i	−0.887586	+	0.460642i	$0.847619\pi$
$978$	13.4631	+	2.86168i	0.430504	+	0.0915064i
$979$	3.56097	−	33.8803i	0.113809	−	1.08282i
$980$	−0.990625	−	9.42517i	−0.0316443	−	0.301076i
$981$	5.45975	−	1.16051i	0.174316	−	0.0370521i
$982$	10.8191	+	4.81695i	0.345250	+	0.153715i
$983$	29.5731	−	32.8442i	0.943234	−	1.04757i	−0.0555588	−	0.998455i	$-0.517694\pi$
$983$	29.5731	−	32.8442i	0.943234	−	1.04757i	0.998793	−	0.0491126i	$-0.0156393\pi$
$984$	−1.36436	−	4.19908i	−0.0434943	−	0.133862i
$985$	15.8598	+	17.6141i	0.505334	+	0.561231i
$986$	−6.12894	+	10.6156i	−0.195185	+	0.338071i
$987$	−15.3993	−	26.6723i	−0.490164	−	0.848989i
$988$	−1.11010	+	3.41654i	−0.0353170	+	0.108695i
$989$	4.33773	−	1.93128i	0.137932	−	0.0614111i
$990$	3.12915	−	2.27346i	0.0994510	−	0.0722554i
$991$	−3.16395			−0.100506			−0.0502530	−	0.998737i	$-0.516003\pi$
$991$	−3.16395			−0.100506			−0.0502530	+	0.998737i	$0.516003\pi$
$992$	5.20908	−	1.96607i	0.165389	−	0.0624229i
$993$	21.7505			0.690231
$994$	49.0712	−	35.6523i	1.55644	−	1.13082i
$995$	5.76286	−	2.56579i	0.182695	−	0.0813410i
$996$	−1.12796	+	3.47149i	−0.0357406	+	0.109998i
$997$	13.8794	+	24.0398i	0.439564	+	0.761347i	0.997656	−	0.0684321i	$-0.0217997\pi$
$997$	13.8794	+	24.0398i	0.439564	+	0.761347i	−0.558092	+	0.829779i	$0.688466\pi$
$998$	12.0902	−	20.9408i	0.382708	−	0.662870i
$999$	3.92345	+	4.35743i	0.124132	+	0.137863i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.h.421.1	yes	24
31.19	even	15	inner	930.2.bg.h.391.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.h.391.1	✓	24	31.19	even	15	inner
930.2.bg.h.421.1	yes	24	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)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.913545 + 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-2.71613 - 3.01657i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +O(q^{10})\)	\(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} +(-2.71613 - 3.01657i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +(-0.913545 - 0.406737i) q^{10} +(-3.78332 + 0.804170i) q^{11} +(0.104528 + 0.994522i) q^{12} +(-0.578028 + 5.49957i) q^{13} +(-3.97049 - 0.843955i) q^{14} +(0.809017 + 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(2.13677 + 0.454184i) q^{17} +(0.104528 - 0.994522i) q^{18} +(0.0679048 + 0.646071i) q^{19} +(-0.978148 + 0.207912i) q^{20} +(3.70826 + 1.65102i) q^{21} +(-2.58809 + 2.87437i) q^{22} +(2.60689 + 8.02317i) q^{23} +(0.669131 + 0.743145i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.76493 + 4.78900i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-3.70826 + 1.65102i) q^{28} +(-4.53963 + 3.29823i) q^{29} +1.00000 q^{30} +(-5.20908 + 1.96607i) q^{31} -1.00000 q^{32} +(3.12915 - 2.27346i) q^{33} +(1.99564 - 0.888517i) q^{34} +(-1.25436 + 3.86053i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(2.93175 - 5.07794i) q^{37} +(0.434687 + 0.482769i) q^{38} +(-1.70882 - 5.25921i) q^{39} +(-0.669131 + 0.743145i) q^{40} +(-4.03346 - 1.79581i) q^{41} +(3.97049 - 0.843955i) q^{42} +(-0.0588338 - 0.559766i) q^{43} +(-0.404300 + 3.84666i) q^{44} +(-0.978148 - 0.207912i) q^{45} +(6.82492 + 4.95859i) q^{46} +(-6.13829 - 4.45973i) q^{47} +(0.978148 + 0.207912i) q^{48} +(-0.990625 + 9.42517i) q^{49} +(0.104528 + 0.994522i) q^{50} +(-2.13677 + 0.454184i) q^{51} +(5.05178 + 2.24920i) q^{52} +(7.93261 - 8.81005i) q^{53} +(0.309017 + 0.951057i) q^{54} +(2.58809 + 2.87437i) q^{55} +(-2.02960 + 3.51537i) q^{56} +(-0.324815 - 0.562596i) q^{57} +(-1.73398 + 5.33665i) q^{58} +(-4.15517 + 1.85000i) q^{59} +(0.809017 - 0.587785i) q^{60} +1.37824 q^{61} +(-3.05861 + 4.65241i) q^{62} -4.05920 q^{63} +(-0.809017 + 0.587785i) q^{64} +(5.05178 - 2.24920i) q^{65} +(1.19523 - 3.67854i) q^{66} +(-6.75507 - 11.7001i) q^{67} +(1.09225 - 1.89183i) q^{68} +(-5.64483 - 6.26921i) q^{69} +(1.25436 + 3.86053i) q^{70} +(-9.99861 + 11.1046i) q^{71} +(-0.913545 - 0.406737i) q^{72} +(-9.99467 + 2.12443i) q^{73} +(-0.612903 - 5.83138i) q^{74} +(0.104528 - 0.994522i) q^{75} +(0.635434 + 0.135066i) q^{76} +(12.7018 + 9.22843i) q^{77} +(-4.47375 - 3.25037i) q^{78} +(-16.9439 - 3.60154i) q^{79} +(-0.104528 + 0.994522i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(-4.31869 + 0.917967i) q^{82} +(3.33457 + 1.48465i) q^{83} +(2.71613 - 3.01657i) q^{84} +(-0.675048 - 2.07759i) q^{85} +(-0.376620 - 0.418279i) q^{86} +(2.80565 - 4.85952i) q^{87} +(1.93392 + 3.34965i) q^{88} +(-2.72174 + 8.37665i) q^{89} +(-0.913545 + 0.406737i) q^{90} +(18.1598 - 13.1939i) q^{91} +8.43606 q^{92} +(3.95906 - 3.91482i) q^{93} -7.58734 q^{94} +(0.525562 - 0.381843i) q^{95} +(0.913545 - 0.406737i) q^{96} +(2.64905 - 8.15292i) q^{97} +(4.73854 + 8.20739i) q^{98} +(-1.93392 + 3.34965i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} - 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 11 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 - 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 - 11 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q + 6 q^{2} - 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 11 q^{7} + 6 q^{8} + 3 q^{9} - 3 q^{10} - 5 q^{11} - 3 q^{12} - 13 q^{13} - 4 q^{14} + 6 q^{15} - 6 q^{16} + 31 q^{17} - 3 q^{18} - 3 q^{19} + 3 q^{20} - 4 q^{21} + 5 q^{22} - 9 q^{23} + 3 q^{24} - 12 q^{25} + 3 q^{26} + 6 q^{27} + 4 q^{28} + 11 q^{29} + 24 q^{30} + 17 q^{31} - 24 q^{32} + 10 q^{33} + 9 q^{34} + 7 q^{35} - 12 q^{36} + 8 q^{37} - 2 q^{38} - q^{39} - 3 q^{40} + 12 q^{41} + 4 q^{42} - 7 q^{43} - 10 q^{44} + 3 q^{45} - 6 q^{46} - 46 q^{47} - 3 q^{48} + 20 q^{49} - 3 q^{50} - 31 q^{51} + 17 q^{52} + 48 q^{53} - 6 q^{54} - 5 q^{55} + q^{56} - 2 q^{57} + 14 q^{58} + 12 q^{59} + 6 q^{60} - 4 q^{61} + 13 q^{62} + 2 q^{63} - 6 q^{64} + 17 q^{65} + 10 q^{66} - 33 q^{67} + q^{68} - 12 q^{69} - 7 q^{70} - 35 q^{71} - 3 q^{72} + 19 q^{73} + 7 q^{74} - 3 q^{75} + 2 q^{76} + 26 q^{77} - 4 q^{78} - 12 q^{79} + 3 q^{80} + 3 q^{81} - 12 q^{82} + 11 q^{84} - 2 q^{85} - 48 q^{86} + 3 q^{87} + 21 q^{89} - 3 q^{90} + 72 q^{91} + 6 q^{92} + 19 q^{93} - 14 q^{94} + 6 q^{95} + 3 q^{96} - 35 q^{97} - 5 q^{98}+O(q^{100}) \) 24 * q + 6 * q^2 - 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 - 11 * q^7 + 6 * q^8 + 3 * q^9 - 3 * q^10 - 5 * q^11 - 3 * q^12 - 13 * q^13 - 4 * q^14 + 6 * q^15 - 6 * q^16 + 31 * q^17 - 3 * q^18 - 3 * q^19 + 3 * q^20 - 4 * q^21 + 5 * q^22 - 9 * q^23 + 3 * q^24 - 12 * q^25 + 3 * q^26 + 6 * q^27 + 4 * q^28 + 11 * q^29 + 24 * q^30 + 17 * q^31 - 24 * q^32 + 10 * q^33 + 9 * q^34 + 7 * q^35 - 12 * q^36 + 8 * q^37 - 2 * q^38 - q^39 - 3 * q^40 + 12 * q^41 + 4 * q^42 - 7 * q^43 - 10 * q^44 + 3 * q^45 - 6 * q^46 - 46 * q^47 - 3 * q^48 + 20 * q^49 - 3 * q^50 - 31 * q^51 + 17 * q^52 + 48 * q^53 - 6 * q^54 - 5 * q^55 + q^56 - 2 * q^57 + 14 * q^58 + 12 * q^59 + 6 * q^60 - 4 * q^61 + 13 * q^62 + 2 * q^63 - 6 * q^64 + 17 * q^65 + 10 * q^66 - 33 * q^67 + q^68 - 12 * q^69 - 7 * q^70 - 35 * q^71 - 3 * q^72 + 19 * q^73 + 7 * q^74 - 3 * q^75 + 2 * q^76 + 26 * q^77 - 4 * q^78 - 12 * q^79 + 3 * q^80 + 3 * q^81 - 12 * q^82 + 11 * q^84 - 2 * q^85 - 48 * q^86 + 3 * q^87 + 21 * q^89 - 3 * q^90 + 72 * q^91 + 6 * q^92 + 19 * q^93 - 14 * q^94 + 6 * q^95 + 3 * q^96 - 35 * q^97 - 5 * q^98

Introduction

L-functions

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