LMFDB - Embedded newform 350.2.u.a.79.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(9,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([21, 10]))

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

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

chi := DirichletCharacter("350.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.u (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			79.6
Character	$\chi$	$=$	350.79
Dual form			350.2.u.a.319.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.743145 + 0.669131i) q^{2} +(-0.385644 - 0.0405328i) q^{3} +(0.104528 - 0.994522i) q^{4} +(1.14687 + 1.91955i) q^{5} +(0.313711 - 0.227924i) q^{6} +(-2.20412 + 1.46351i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.78736 - 0.592473i) q^{9} +O(q^{10})$	\(q+(-0.743145 + 0.669131i) q^{2} +(-0.385644 - 0.0405328i) q^{3} +(0.104528 - 0.994522i) q^{4} +(1.14687 + 1.91955i) q^{5} +(0.313711 - 0.227924i) q^{6} +(-2.20412 + 1.46351i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.78736 - 0.592473i) q^{9} +(-2.13672 - 0.659099i) q^{10} +(-1.53049 + 0.325315i) q^{11} +(-0.0806214 + 0.379294i) q^{12} +(2.33897 - 0.759977i) q^{13} +(0.658695 - 2.56244i) q^{14} +(-0.364479 - 0.786749i) q^{15} +(-0.978148 - 0.207912i) q^{16} +(-2.18195 + 4.90074i) q^{17} +(2.46786 - 1.42482i) q^{18} +(-0.0790085 - 0.751716i) q^{19} +(2.02892 - 0.939941i) q^{20} +(0.909323 - 0.475056i) q^{21} +(0.919694 - 1.26585i) q^{22} +(-3.85110 + 3.46754i) q^{23} +(-0.193884 - 0.335817i) q^{24} +(-2.36937 + 4.40296i) q^{25} +(-1.22967 + 2.12985i) q^{26} +(2.15728 + 0.700943i) q^{27} +(1.22510 + 2.34502i) q^{28} +(-1.04137 - 0.756599i) q^{29} +(0.797299 + 0.340785i) q^{30} +(-8.65196 - 3.85210i) q^{31} +(0.866025 - 0.500000i) q^{32} +(0.603408 - 0.0634207i) q^{33} +(-1.65773 - 5.10197i) q^{34} +(-5.33713 - 2.55245i) q^{35} +(-0.880586 + 2.71017i) q^{36} +(-0.687314 + 3.23356i) q^{37} +(0.561711 + 0.505767i) q^{38} +(-0.932813 + 0.198275i) q^{39} +(-0.878837 + 2.05612i) q^{40} +(1.27489 + 3.92370i) q^{41} +(-0.357884 + 0.961491i) q^{42} +0.876481i q^{43} +(0.163553 + 1.55611i) q^{44} +(-2.05947 - 6.02999i) q^{45} +(0.541683 - 5.15377i) q^{46} +(0.777997 + 1.74741i) q^{47} +(0.368789 + 0.119827i) q^{48} +(2.71625 - 6.45151i) q^{49} +(-1.18537 - 4.85746i) q^{50} +(1.04010 - 1.80150i) q^{51} +(-0.511325 - 2.40560i) q^{52} +(12.2132 + 1.28366i) q^{53} +(-2.07220 + 0.922601i) q^{54} +(-2.37973 - 2.56475i) q^{55} +(-2.47955 - 0.922935i) q^{56} +0.293097i q^{57} +(1.28015 - 0.134549i) q^{58} +(4.12143 - 4.57731i) q^{59} +(-0.820538 + 0.280245i) q^{60} +(2.81842 + 3.13017i) q^{61} +(9.00722 - 2.92662i) q^{62} +(7.01077 - 2.77347i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(4.14132 + 3.61818i) q^{65} +(-0.405983 + 0.450889i) q^{66} +(-4.91535 + 11.0400i) q^{67} +(4.64582 + 2.68226i) q^{68} +(1.62570 - 1.18114i) q^{69} +(5.67419 - 1.67440i) q^{70} +(4.95797 + 3.60218i) q^{71} +(-1.15905 - 2.60327i) q^{72} +(-0.845699 - 3.97870i) q^{73} +(-1.65290 - 2.86291i) q^{74} +(1.09220 - 1.60194i) q^{75} -0.755856 q^{76} +(2.89726 - 2.95692i) q^{77} +(0.560543 - 0.771521i) q^{78} +(3.60393 - 1.60457i) q^{79} +(-0.722713 - 2.11605i) q^{80} +(7.00629 + 3.11940i) q^{81} +(-3.57289 - 2.06281i) q^{82} +(-3.08507 - 4.24624i) q^{83} +(-0.377403 - 0.953999i) q^{84} +(-11.9096 + 1.43215i) q^{85} +(-0.586480 - 0.651353i) q^{86} +(0.370930 + 0.333987i) q^{87} +(-1.16278 - 1.04697i) q^{88} +(12.5852 + 13.9773i) q^{89} +(5.56533 + 3.10310i) q^{90} +(-4.04312 + 5.09819i) q^{91} +(3.04600 + 4.19246i) q^{92} +(3.18044 + 1.83623i) q^{93} +(-1.74741 - 0.777997i) q^{94} +(1.35235 - 1.01378i) q^{95} +(-0.354243 + 0.157719i) q^{96} +(-0.781127 + 1.07513i) q^{97} +(2.29833 + 6.61193i) q^{98} +4.45876 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 20 q^{4} - 2 q^{5} + 8 q^{6} - 20 q^{9}+O(q^{10}) $ 160 * q - 20 * q^4 - 2 * q^5 + 8 * q^6 - 20 * q^9	$ 160 q - 20 q^{4} - 2 q^{5} + 8 q^{6} - 20 q^{9} - 2 q^{10} - 6 q^{11} - 16 q^{15} + 20 q^{16} - 20 q^{17} + 4 q^{19} - 4 q^{20} - 12 q^{21} + 40 q^{22} - 30 q^{23} - 16 q^{24} + 48 q^{26} - 120 q^{27} - 10 q^{28} + 24 q^{29} - 26 q^{30} - 6 q^{31} - 50 q^{33} - 16 q^{34} - 36 q^{35} - 40 q^{36} - 32 q^{39} + 2 q^{40} + 68 q^{41} + 10 q^{42} - 4 q^{44} + 16 q^{45} + 12 q^{46} + 24 q^{49} + 32 q^{50} + 12 q^{51} - 20 q^{53} + 16 q^{54} + 24 q^{55} + 24 q^{59} + 2 q^{60} - 8 q^{61} + 40 q^{64} + 2 q^{65} - 116 q^{69} - 118 q^{70} + 68 q^{71} - 40 q^{73} + 16 q^{74} + 196 q^{75} - 32 q^{76} - 80 q^{77} - 8 q^{79} - 2 q^{80} + 64 q^{81} - 160 q^{83} - 18 q^{84} + 12 q^{85} + 12 q^{86} - 10 q^{88} + 54 q^{89} + 44 q^{91} - 40 q^{92} - 16 q^{95} - 4 q^{96} - 20 q^{97} + 40 q^{98} - 24 q^{99}+O(q^{100}) $ 160 * q - 20 * q^4 - 2 * q^5 + 8 * q^6 - 20 * q^9 - 2 * q^10 - 6 * q^11 - 16 * q^15 + 20 * q^16 - 20 * q^17 + 4 * q^19 - 4 * q^20 - 12 * q^21 + 40 * q^22 - 30 * q^23 - 16 * q^24 + 48 * q^26 - 120 * q^27 - 10 * q^28 + 24 * q^29 - 26 * q^30 - 6 * q^31 - 50 * q^33 - 16 * q^34 - 36 * q^35 - 40 * q^36 - 32 * q^39 + 2 * q^40 + 68 * q^41 + 10 * q^42 - 4 * q^44 + 16 * q^45 + 12 * q^46 + 24 * q^49 + 32 * q^50 + 12 * q^51 - 20 * q^53 + 16 * q^54 + 24 * q^55 + 24 * q^59 + 2 * q^60 - 8 * q^61 + 40 * q^64 + 2 * q^65 - 116 * q^69 - 118 * q^70 + 68 * q^71 - 40 * q^73 + 16 * q^74 + 196 * q^75 - 32 * q^76 - 80 * q^77 - 8 * q^79 - 2 * q^80 + 64 * q^81 - 160 * q^83 - 18 * q^84 + 12 * q^85 + 12 * q^86 - 10 * q^88 + 54 * q^89 + 44 * q^91 - 40 * q^92 - 16 * q^95 - 4 * q^96 - 20 * q^97 + 40 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.743145	+	0.669131i	−0.525483	+	0.473147i
$2$	−0.743145	+	0.669131i	−0.525483	+	0.473147i
$3$	−0.385644	−	0.0405328i	−0.222651	−	0.0234016i	−0.00745418	−	0.999972i	$-0.502373\pi$
$3$	−0.385644	−	0.0405328i	−0.222651	−	0.0234016i	−0.215197	+	0.976571i	$0.569039\pi$
$4$	0.104528	−	0.994522i	0.0522642	−	0.497261i
$5$	1.14687	+	1.91955i	0.512897	+	0.858450i
$5$	1.14687	+	1.91955i	0.512897	+	0.858450i
$6$	0.313711	−	0.227924i	0.128072	−	0.0930496i
$7$	−2.20412	+	1.46351i	−0.833077	+	0.553156i
$7$	−2.20412	+	1.46351i	−0.833077	+	0.553156i
$8$	0.587785	+	0.809017i	0.207813	+	0.286031i
$9$	−2.78736	−	0.592473i	−0.929122	−	0.197491i
$10$	−2.13672	−	0.659099i	−0.675691	−	0.208425i
$11$	−1.53049	+	0.325315i	−0.461459	+	0.0980861i	−0.432774	−	0.901502i	$-0.642465\pi$
$11$	−1.53049	+	0.325315i	−0.461459	+	0.0980861i	−0.0286847	+	0.999589i	$0.509132\pi$
$12$	−0.0806214	+	0.379294i	−0.0232734	+	0.109493i
$13$	2.33897	−	0.759977i	0.648714	−	0.210780i	0.0338668	−	0.999426i	$-0.489218\pi$
$13$	2.33897	−	0.759977i	0.648714	−	0.210780i	0.614847	+	0.788647i	$0.289218\pi$
$14$	0.658695	−	2.56244i	0.176044	−	0.684842i
$15$	−0.364479	−	0.786749i	−0.0941081	−	0.203138i
$16$	−0.978148	−	0.207912i	−0.244537	−	0.0519779i
$17$	−2.18195	+	4.90074i	−0.529201	+	1.18860i	0.429208	+	0.903206i	$0.358793\pi$
$17$	−2.18195	+	4.90074i	−0.529201	+	1.18860i	−0.958409	+	0.285398i	$0.907874\pi$
$18$	2.46786	−	1.42482i	0.581680	−	0.335833i
$19$	−0.0790085	−	0.751716i	−0.0181258	−	0.172455i	0.981714	−	0.190363i	$-0.0609663\pi$
$19$	−0.0790085	−	0.751716i	−0.0181258	−	0.172455i	−0.999840	+	0.0179071i	$0.994300\pi$
$20$	2.02892	−	0.939941i	0.453680	−	0.210177i
$21$	0.909323	−	0.475056i	0.198431	−	0.103666i
$22$	0.919694	−	1.26585i	0.196079	−	0.269880i
$23$	−3.85110	+	3.46754i	−0.803009	+	0.723033i	−0.964569	−	0.263830i	$-0.915014\pi$
$23$	−3.85110	+	3.46754i	−0.803009	+	0.723033i	0.161560	+	0.986863i	$0.448348\pi$
$24$	−0.193884	−	0.335817i	−0.0395764	−	0.0685483i
$25$	−2.36937	+	4.40296i	−0.473874	+	0.880593i
$26$	−1.22967	+	2.12985i	−0.241158	+	0.417698i
$27$	2.15728	+	0.700943i	0.415169	+	0.134897i
$28$	1.22510	+	2.34502i	0.231523	+	0.443167i
$29$	−1.04137	−	0.756599i	−0.193377	−	0.140497i	0.486884	−	0.873467i	$-0.338134\pi$
$29$	−1.04137	−	0.756599i	−0.193377	−	0.140497i	−0.680261	+	0.732970i	$0.738134\pi$
$30$	0.797299	+	0.340785i	0.145566	+	0.0622185i
$31$	−8.65196	−	3.85210i	−1.55394	−	0.691858i	−0.563034	−	0.826434i	$-0.690366\pi$
$31$	−8.65196	−	3.85210i	−1.55394	−	0.691858i	−0.990903	+	0.134576i	$0.957033\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	0.603408	−	0.0634207i	0.105040	−	0.0110401i
$34$	−1.65773	−	5.10197i	−0.284298	−	0.874980i
$35$	−5.33713	−	2.55245i	−0.902140	−	0.431443i
$36$	−0.880586	+	2.71017i	−0.146764	+	0.451694i
$37$	−0.687314	+	3.23356i	−0.112994	+	0.531594i	0.884845	+	0.465885i	$0.154264\pi$
$37$	−0.687314	+	3.23356i	−0.112994	+	0.531594i	−0.997839	+	0.0657085i	$0.979069\pi$
$38$	0.561711	+	0.505767i	0.0911215	+	0.0820462i
$39$	−0.932813	+	0.198275i	−0.149370	+	0.0317495i
$40$	−0.878837	+	2.05612i	−0.138956	+	0.325102i
$41$	1.27489	+	3.92370i	0.199104	+	0.612779i	0.999904	+	0.0138473i	$0.00440787\pi$
$41$	1.27489	+	3.92370i	0.199104	+	0.612779i	−0.800800	+	0.598932i	$0.795592\pi$
$42$	−0.357884	+	0.961491i	−0.0552228	+	0.148361i
$43$			0.876481i			0.133662i	0.997764	+	0.0668311i	$0.0212889\pi$
$43$			0.876481i			0.133662i	−0.997764	+	0.0668311i	$0.978711\pi$
$44$	0.163553	+	1.55611i	0.0246566	+	0.234592i
$45$	−2.05947	−	6.02999i	−0.307007	−	0.898897i
$46$	0.541683	−	5.15377i	0.0798669	−	0.759883i
$47$	0.777997	+	1.74741i	0.113482	+	0.254886i	0.961354	−	0.275316i	$-0.0887826\pi$
$47$	0.777997	+	1.74741i	0.113482	+	0.254886i	−0.847871	+	0.530202i	$0.822116\pi$
$48$	0.368789	+	0.119827i	0.0532301	+	0.0172955i
$49$	2.71625	−	6.45151i	0.388036	−	0.921644i
$50$	−1.18537	−	4.85746i	−0.167637	−	0.686948i
$51$	1.04010	−	1.80150i	0.145642	−	0.252260i
$52$	−0.511325	−	2.40560i	−0.0709081	−	0.333596i
$53$	12.2132	+	1.28366i	1.67761	+	0.176324i	0.894963	−	0.446141i	$-0.147202\pi$
$53$	12.2132	+	1.28366i	1.67761	+	0.176324i	0.782648	+	0.622465i	$0.213869\pi$
$54$	−2.07220	+	0.922601i	−0.281990	+	0.125550i
$55$	−2.37973	−	2.56475i	−0.320883	−	0.345831i
$56$	−2.47955	−	0.922935i	−0.331344	−	0.123332i
$57$			0.293097i			0.0388216i
$58$	1.28015	−	0.134549i	0.168092	−	0.0176672i
$59$	4.12143	−	4.57731i	0.536564	−	0.595915i	−0.412516	−	0.910951i	$-0.635350\pi$
$59$	4.12143	−	4.57731i	0.536564	−	0.595915i	0.949080	+	0.315036i	$0.102016\pi$
$60$	−0.820538	+	0.280245i	−0.105931	+	0.0361794i
$61$	2.81842	+	3.13017i	0.360861	+	0.400777i	0.896048	−	0.443957i	$-0.146426\pi$
$61$	2.81842	+	3.13017i	0.360861	+	0.400777i	−0.535187	+	0.844734i	$0.679759\pi$
$62$	9.00722	−	2.92662i	1.14392	−	0.371681i
$63$	7.01077	−	2.77347i	0.883274	−	0.349424i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	4.14132	+	3.61818i	0.513667	+	0.448780i
$66$	−0.405983	+	0.450889i	−0.0499730	+	0.0555006i
$67$	−4.91535	+	11.0400i	−0.600505	+	1.34876i	0.316010	+	0.948756i	$0.397657\pi$
$67$	−4.91535	+	11.0400i	−0.600505	+	1.34876i	−0.916515	+	0.400001i	$0.869010\pi$
$68$	4.64582	+	2.68226i	0.563388	+	0.325272i
$69$	1.62570	−	1.18114i	0.195711	−	0.142193i
$70$	5.67419	−	1.67440i	0.678195	−	0.200129i
$71$	4.95797	+	3.60218i	0.588403	+	0.427500i	0.841744	−	0.539877i	$-0.181529\pi$
$71$	4.95797	+	3.60218i	0.588403	+	0.427500i	−0.253341	+	0.967377i	$0.581529\pi$
$72$	−1.15905	−	2.60327i	−0.136596	−	0.306799i
$73$	−0.845699	−	3.97870i	−0.0989816	−	0.465672i	−0.999522	−	0.0309005i	$-0.990163\pi$
$73$	−0.845699	−	3.97870i	−0.0989816	−	0.465672i	0.900541	−	0.434771i	$-0.143171\pi$
$74$	−1.65290	−	2.86291i	−0.192146	−	0.332806i
$75$	1.09220	−	1.60194i	0.126116	−	0.184976i
$76$	−0.755856			−0.0867027
$77$	2.89726	−	2.95692i	0.330174	−	0.336972i
$78$	0.560543	−	0.771521i	0.0634690	−	0.0873575i
$79$	3.60393	−	1.60457i	0.405473	−	0.180528i	−0.193858	−	0.981030i	$-0.562100\pi$
$79$	3.60393	−	1.60457i	0.405473	−	0.180528i	0.599331	+	0.800501i	$0.295433\pi$
$80$	−0.722713	−	2.11605i	−0.0808017	−	0.236582i
$81$	7.00629	+	3.11940i	0.778476	+	0.346600i
$82$	−3.57289	−	2.06281i	−0.394560	−	0.227799i
$83$	−3.08507	−	4.24624i	−0.338631	−	0.466085i	0.605410	−	0.795914i	$-0.293009\pi$
$83$	−3.08507	−	4.24624i	−0.338631	−	0.466085i	−0.944041	+	0.329828i	$0.893009\pi$
$84$	−0.377403	−	0.953999i	−0.0411781	−	0.104090i
$85$	−11.9096	+	1.43215i	−1.29178	+	0.155339i
$86$	−0.586480	−	0.651353i	−0.0632418	−	0.0702371i
$87$	0.370930	+	0.333987i	0.0397679	+	0.0358072i
$88$	−1.16278	−	1.04697i	−0.123953	−	0.111608i
$89$	12.5852	+	13.9773i	1.33403	+	1.48159i	0.726087	+	0.687603i	$0.241337\pi$
$89$	12.5852	+	13.9773i	1.33403	+	1.48159i	0.607940	+	0.793983i	$0.291996\pi$
$90$	5.56533	+	3.10310i	0.586637	+	0.327095i
$91$	−4.04312	+	5.09819i	−0.423834	+	0.534436i
$92$	3.04600	+	4.19246i	0.317567	+	0.437094i
$93$	3.18044	+	1.83623i	0.329796	+	0.190408i
$94$	−1.74741	−	0.777997i	−0.180231	−	0.0802442i
$95$	1.35235	−	1.01378i	0.138748	−	0.104012i
$96$	−0.354243	+	0.157719i	−0.0361548	+	0.0160972i
$97$	−0.781127	+	1.07513i	−0.0793114	+	0.109163i	−0.846829	−	0.531865i	$-0.821492\pi$
$97$	−0.781127	+	1.07513i	−0.0793114	+	0.109163i	0.767518	+	0.641027i	$0.221492\pi$
$98$	2.29833	+	6.61193i	0.232167	+	0.667906i
$99$	4.45876			0.448122
$100$	4.13118	+	2.81662i	0.413118	+	0.281662i
$101$	−5.30505	−	9.18862i	−0.527873	−	0.914302i	−0.999472	−	0.0324894i	$-0.989656\pi$
$101$	−5.30505	−	9.18862i	−0.527873	−	0.914302i	0.471599	−	0.881813i	$-0.343677\pi$
$102$	0.432496	+	2.03473i	0.0428235	+	0.201469i
$103$	−4.13274	−	9.28228i	−0.407211	−	0.914610i	−0.994451	−	0.105198i	$-0.966452\pi$
$103$	−4.13274	−	9.28228i	−0.407211	−	0.914610i	0.587241	−	0.809412i	$-0.300214\pi$
$104$	1.98965	+	1.44556i	0.195101	+	0.141749i
$105$	1.95477	+	1.20067i	0.190766	+	0.117173i
$106$	−9.93510	+	7.21827i	−0.964982	+	0.701101i
$107$	14.8612	+	8.58013i	1.43669	+	0.829473i	0.997618	−	0.0689794i	$-0.0219743\pi$
$107$	14.8612	+	8.58013i	1.43669	+	0.829473i	0.439071	+	0.898452i	$0.355308\pi$
$108$	0.922601	−	2.07220i	0.0887773	−	0.199397i
$109$	8.76635	−	9.73602i	0.839664	−	0.932541i	−0.158835	−	0.987305i	$-0.550774\pi$
$109$	8.76635	−	9.73602i	0.839664	−	0.932541i	0.998499	+	0.0547639i	$0.0174406\pi$
$110$	3.48464	+	0.313634i	0.332247	+	0.0299038i
$111$	0.396123	−	1.21914i	0.0375984	−	0.115716i
$112$	2.46023	−	0.973271i	0.232470	−	0.0919655i
$113$	13.7486	−	4.46719i	1.29336	−	0.420238i	0.420093	−	0.907481i	$-0.361997\pi$
$113$	13.7486	−	4.46719i	1.29336	−	0.420238i	0.873266	+	0.487243i	$0.161997\pi$
$114$	−0.196120	−	0.217813i	−0.0183683	−	0.0204001i
$115$	−11.0728	−	3.41556i	−1.03255	−	0.318502i
$116$	−0.861307	+	0.956578i	−0.0799703	+	0.0888161i
$117$	−6.96983	+	0.732559i	−0.644361	+	0.0677251i
$118$			6.15938i			0.567017i
$119$	−2.36303	−	13.9951i	−0.216619	−	1.28293i
$120$	0.422258	−	0.757309i	0.0385467	−	0.0691326i
$121$	−7.81244	+	3.47832i	−0.710222	+	0.316211i
$122$	−4.18898	−	0.440280i	−0.379253	−	0.0398611i
$123$	−0.332614	−	1.56482i	−0.0299908	−	0.141095i
$124$	−4.73537	+	8.20191i	−0.425249	+	0.736553i
$125$	−11.1691	+	0.501506i	−0.998993	+	0.0448560i
$126$	−3.35420	+	6.75221i	−0.298816	+	0.601535i
$127$	−7.09244	−	2.30447i	−0.629352	−	0.204489i	−0.0230640	−	0.999734i	$-0.507342\pi$
$127$	−7.09244	−	2.30447i	−0.629352	−	0.204489i	−0.606288	+	0.795245i	$0.707342\pi$
$128$	−0.406737	−	0.913545i	−0.0359508	−	0.0807468i
$129$	0.0355262	−	0.338009i	0.00312791	−	0.0297601i
$130$	−5.49863	+	0.0822493i	−0.482262	+	0.00721374i
$131$	−1.52294	−	14.4898i	−0.133060	−	1.26598i	−0.833600	−	0.552369i	$-0.813724\pi$
$131$	−1.52294	−	14.4898i	−0.133060	−	1.26598i	0.700539	−	0.713614i	$-0.252943\pi$
$132$		−	0.606731i		−	0.0528092i
$133$	1.27429	+	1.54124i	0.110495	+	0.133642i
$134$	−3.73442	−	11.4934i	−0.322605	−	0.992875i
$135$	1.12863	+	4.94491i	0.0971368	+	0.425590i
$136$	−5.24730	+	1.11535i	−0.449952	+	0.0956403i
$137$	5.10638	+	4.59780i	0.436267	+	0.392817i	0.857789	−	0.514001i	$-0.171837\pi$
$137$	5.10638	+	4.59780i	0.436267	+	0.392817i	−0.421522	+	0.906818i	$0.638504\pi$
$138$	−0.417793	+	1.96556i	−0.0355649	+	0.167320i
$139$	1.10039	−	3.38666i	0.0933341	−	0.287253i	−0.893482	−	0.449099i	$-0.851745\pi$
$139$	1.10039	−	3.38666i	0.0933341	−	0.287253i	0.986816	+	0.161846i	$0.0517449\pi$
$140$	−3.09635	+	5.04109i	−0.261690	+	0.426050i
$141$	−0.229202	−	0.705411i	−0.0193023	−	0.0594064i
$142$	−6.09482	+	0.640591i	−0.511466	+	0.0537572i
$143$	−3.33253	+	1.92404i	−0.278680	+	0.160896i
$144$	2.60327	+	1.15905i	0.216939	+	0.0965876i
$145$	0.258015	−	2.86669i	0.0214270	−	0.238065i
$146$	3.29075	+	2.39087i	0.272344	+	0.197870i
$147$	−1.30900	+	2.37789i	−0.107965	+	0.196125i
$148$	3.14400	+	1.02155i	0.258435	+	0.0839707i
$149$	−7.43102	+	12.8709i	−0.608773	+	1.05443i	0.382670	+	0.923885i	$0.375005\pi$
$149$	−7.43102	+	12.8709i	−0.608773	+	1.05443i	−0.991443	+	0.130541i	$0.958329\pi$
$150$	0.260245	+	1.92129i	0.0212489	+	0.156873i
$151$	5.50125	+	9.52845i	0.447686	+	0.775414i	0.998235	−	0.0593883i	$-0.0189150\pi$
$151$	5.50125	+	9.52845i	0.447686	+	0.775414i	−0.550549	+	0.834803i	$0.685582\pi$
$152$	0.561711	−	0.505767i	0.0455608	−	0.0410231i
$153$	8.98544	−	12.3674i	0.726430	−	0.999845i
$154$	−0.174522	+	4.13607i	−0.0140634	+	0.333294i
$155$	−2.52838	−	21.0258i	−0.203084	−	1.68883i
$156$	0.0996838	+	0.948428i	0.00798109	+	0.0759350i
$157$	−1.69518	+	0.978715i	−0.135290	+	0.0781099i	−0.566118	−	0.824325i	$-0.691555\pi$
$157$	−1.69518	+	0.978715i	−0.135290	+	0.0781099i	0.430827	+	0.902434i	$0.358222\pi$
$158$	−1.60457	+	3.60393i	−0.127653	+	0.286713i
$159$	−4.65791	−	0.990069i	−0.369396	−	0.0785176i
$160$	1.95300	+	1.08895i	0.154398	+	0.0860887i
$161$	3.41346	−	13.2790i	0.269019	−	1.04653i
$162$	−7.29397	+	2.36995i	−0.573068	+	0.186201i
$163$	−0.330534	+	1.55504i	−0.0258894	+	0.121800i	−0.989195	−	0.146608i	$-0.953164\pi$
$163$	−0.330534	+	1.55504i	−0.0258894	+	0.121800i	0.963305	+	0.268408i	$0.0864977\pi$
$164$	4.03547	−	0.857765i	0.315117	−	0.0669802i
$165$	0.813771	+	1.08554i	0.0633520	+	0.0845090i
$166$	5.13395	+	1.09125i	0.398472	+	0.0846977i
$167$	−1.14894	−	1.58137i	−0.0889073	−	0.122370i	0.762246	−	0.647287i	$-0.224096\pi$
$167$	−1.14894	−	1.58137i	−0.0889073	−	0.122370i	−0.851154	+	0.524917i	$0.824096\pi$
$168$	0.918815	+	0.456427i	0.0708881	+	0.0352141i
$169$	−5.62400	+	4.08608i	−0.432616	+	0.314314i
$170$	7.89230	−	9.03341i	0.605312	−	0.692831i
$171$	−0.225146	+	2.14212i	−0.0172173	+	0.163812i
$172$	0.871680	+	0.0916172i	0.0664650	+	0.00698575i
$173$	−15.7775	+	14.2061i	−1.19954	+	1.08007i	−0.204682	+	0.978829i	$0.565616\pi$
$173$	−15.7775	+	14.2061i	−1.19954	+	1.08007i	−0.994862	+	0.101245i	$0.967717\pi$
$174$	−0.499136			−0.0378394
$175$	−1.22144	−	13.1722i	−0.0923319	−	0.995728i
$176$	1.56468			0.117942
$177$	−1.77493	+	1.59816i	−0.133412	+	0.120125i
$178$	−18.7052	−	1.96600i	−1.40202	−	0.147358i
$179$	0.109764	−	1.04434i	0.00820416	−	0.0780574i	−0.989654	−	0.143477i	$-0.954172\pi$
$179$	0.109764	−	1.04434i	0.00820416	−	0.0780574i	0.997858	+	0.0654193i	$0.0208385\pi$
$180$	−6.21223	+	1.41788i	−0.463032	+	0.105683i
$181$	−1.27483	+	0.926220i	−0.0947576	+	0.0688454i	−0.634155	−	0.773206i	$-0.718652\pi$
$181$	−1.27483	+	0.926220i	−0.0947576	+	0.0688454i	0.539398	+	0.842051i	$0.318652\pi$
$182$	−0.406732	−	6.49407i	−0.0301490	−	0.481373i
$183$	−0.960030	−	1.32137i	−0.0709674	−	0.0976783i
$184$	−5.06892	−	1.07743i	−0.373686	−	0.0794294i
$185$	−6.99525	+	2.38914i	−0.514301	+	0.175653i
$186$	−3.59220	+	0.763545i	−0.263393	+	0.0559859i
$187$	1.74516	−	8.21033i	0.127619	−	0.600399i
$188$	1.81916	−	0.591081i	0.132676	−	0.0431090i
$189$	−5.78074	+	1.61225i	−0.420487	+	0.117274i
$190$	−0.326636	+	1.65828i	−0.0236966	+	0.120305i
$191$	−8.84679	−	1.88044i	−0.640131	−	0.136064i	−0.123600	−	0.992332i	$-0.539444\pi$
$191$	−8.84679	−	1.88044i	−0.640131	−	0.136064i	−0.516532	+	0.856268i	$0.672777\pi$
$192$	0.157719	−	0.354243i	0.0113824	−	0.0255653i
$193$	−3.21524	+	1.85632i	−0.231438	+	0.133621i	−0.611235	−	0.791449i	$-0.709327\pi$
$193$	−3.21524	+	1.85632i	−0.231438	+	0.133621i	0.379797	+	0.925070i	$0.375994\pi$
$194$	−0.138911	−	1.32165i	−0.00997325	−	0.0948891i
$195$	−1.45042	−	1.56319i	−0.103867	−	0.111942i
$196$	−6.13224	−	3.37574i	−0.438017	−	0.241124i
$197$	−11.2708	+	15.5129i	−0.803008	+	1.10525i	0.189356	+	0.981908i	$0.439360\pi$
$197$	−11.2708	+	15.5129i	−0.803008	+	1.10525i	−0.992365	+	0.123338i	$0.960640\pi$
$198$	−3.31351	+	2.98349i	−0.235481	+	0.212028i
$199$	11.4009	+	19.7469i	0.808186	+	1.39982i	0.914119	+	0.405446i	$0.132884\pi$
$199$	11.4009	+	19.7469i	0.808186	+	1.39982i	−0.105933	+	0.994373i	$0.533783\pi$
$200$	−4.95475	+	0.671137i	−0.350354	+	0.0474566i
$201$	2.34306	−	4.05829i	0.165266	−	0.286250i
$202$	10.0908	+	3.27870i	0.709987	+	0.230689i
$203$	3.40259	+	0.143573i	0.238815	+	0.0100769i
$204$	−1.68291	−	1.22271i	−0.117827	−	0.0856065i
$205$	−6.06962	+	6.94719i	−0.423920	+	0.485213i
$206$	9.28228	+	4.13274i	0.646727	+	0.287942i
$207$	12.7888	−	7.38364i	0.888886	−	0.513198i
$208$	−2.44587	+	0.257071i	−0.169590	+	0.0178247i
$209$	0.365466	+	1.12479i	0.0252798	+	0.0778032i
$210$	−2.25608	+	0.415729i	−0.155684	+	0.0286880i
$211$	−7.50049	+	23.0841i	−0.516355	+	1.58918i	0.264448	+	0.964400i	$0.414810\pi$
$211$	−7.50049	+	23.0841i	−0.516355	+	1.58918i	−0.780803	+	0.624777i	$0.785190\pi$
$212$	2.55325	−	12.0121i	0.175358	−	0.824995i
$213$	−1.76600	−	1.59012i	−0.121005	−	0.108953i
$214$	−16.7853	+	3.56782i	−1.14742	+	0.243891i
$215$	−1.68245	+	1.00521i	−0.114742	+	0.0685549i
$216$	0.700943	+	2.15728i	0.0476932	+	0.146784i
$217$	24.7075	−	4.17179i	1.67726	−	0.283200i
$218$			13.1011i			0.887319i
$219$	0.164871	+	1.56864i	0.0111409	+	0.105999i
$220$	−2.79945	+	2.09860i	−0.188739	+	0.141488i
$221$	−1.37906	+	13.1209i	−0.0927659	+	0.882608i
$222$	0.521388	+	1.17106i	0.0349933	+	0.0785962i
$223$	−27.9722	−	9.08873i	−1.87316	−	0.608626i	−0.990292	−	0.139004i	$-0.955610\pi$
$223$	−27.9722	−	9.08873i	−1.87316	−	0.608626i	−0.882867	−	0.469622i	$-0.844390\pi$
$224$	−1.17706	+	2.36950i	−0.0786458	+	0.158319i
$225$	9.21293	−	10.8689i	0.614195	−	0.724592i
$226$	−7.22807	+	12.5194i	−0.480804	+	0.832777i
$227$	2.69795	+	12.6929i	0.179070	+	0.842456i	0.972337	+	0.233583i	$0.0750449\pi$
$227$	2.69795	+	12.6929i	0.179070	+	0.842456i	−0.793267	+	0.608873i	$0.791622\pi$
$228$	0.291491	+	0.0306370i	0.0193045	+	0.00202898i
$229$	17.1828	−	7.65027i	1.13547	−	0.505544i	0.249080	−	0.968483i	$-0.419872\pi$
$229$	17.1828	−	7.65027i	1.13547	−	0.505544i	0.886390	+	0.462939i	$0.153205\pi$
$230$	10.5142	−	4.87093i	0.693285	−	0.321180i
$231$	−1.23716	+	1.02288i	−0.0813994	+	0.0673007i
$232$		−	1.28720i		−	0.0845090i
$233$	−9.84850	+	1.03512i	−0.645196	+	0.0678129i	−0.421475	−	0.906840i	$-0.638487\pi$
$233$	−9.84850	+	1.03512i	−0.645196	+	0.0678129i	−0.223722	+	0.974653i	$0.571821\pi$
$234$	4.68942	−	5.20812i	0.306557	−	0.340466i
$235$	−2.46198	+	3.49746i	−0.160602	+	0.228149i
$236$	−4.12143	−	4.57731i	−0.268282	−	0.297957i
$237$	−1.45487	+	0.472715i	−0.0945039	+	0.0307062i
$238$	11.1206	+	8.81922i	0.720844	+	0.571665i
$239$	−7.63061	+	23.4846i	−0.493583	+	1.51909i	0.325571	+	0.945518i	$0.394444\pi$
$239$	−7.63061	+	23.4846i	−0.493583	+	1.51909i	−0.819153	+	0.573574i	$0.805556\pi$
$240$	0.192940	+	0.845336i	0.0124542	+	0.0545662i
$241$	14.4511	−	16.0496i	0.930880	−	1.03385i	−0.0684648	−	0.997654i	$-0.521810\pi$
$241$	14.4511	−	16.0496i	0.930880	−	1.03385i	0.999345	−	0.0361935i	$-0.0115233\pi$
$242$	3.47832	−	7.81244i	0.223595	−	0.502203i
$243$	−8.46871	−	4.88941i	−0.543268	−	0.313656i
$244$	3.40763	−	2.47579i	0.218151	−	0.158496i
$245$	15.4992	−	2.18506i	0.990208	−	0.139599i
$246$	1.29425	+	0.940329i	0.0825185	+	0.0599532i
$247$	−0.756086	−	1.69820i	−0.0481086	−	0.108054i
$248$	−1.96908	−	9.26379i	−0.125037	−	0.588251i
$249$	1.01763	+	1.76258i	0.0644895	+	0.111699i
$250$	7.96468	−	7.84627i	0.503730	−	0.496242i
$251$	1.59995			0.100988			0.0504941	−	0.998724i	$-0.483920\pi$
$251$	1.59995			0.100988			0.0504941	+	0.998724i	$0.483920\pi$
$252$	−2.02545	−	7.26227i	−0.127591	−	0.457480i
$253$	4.76601	−	6.55984i	0.299636	−	0.412414i
$254$	6.81270	−	3.03321i	0.427467	−	0.190321i
$255$	4.65093	−	0.0695692i	0.291252	−	0.00435659i
$256$	0.913545	+	0.406737i	0.0570966	+	0.0254210i
$257$	−12.7362	−	7.35327i	−0.794465	−	0.458685i	0.0470671	−	0.998892i	$-0.485013\pi$
$257$	−12.7362	−	7.35327i	−0.794465	−	0.458685i	−0.841532	+	0.540207i	$0.818346\pi$
$258$	0.199771	+	0.274962i	0.0124372	+	0.0171184i
$259$	−3.21744	−	8.13303i	−0.199922	−	0.505362i
$260$	4.03125	−	3.74043i	0.250007	−	0.231971i
$261$	2.45441	+	2.72590i	0.151924	+	0.168729i
$262$	10.8274	+	9.74900i	0.668917	+	0.602295i
$263$	−20.7993	−	18.7278i	−1.28254	−	1.15480i	−0.979416	−	0.201853i	$-0.935304\pi$
$263$	−20.7993	−	18.7278i	−1.28254	−	1.15480i	−0.303124	−	0.952951i	$-0.598030\pi$
$264$	0.405983	+	0.450889i	0.0249865	+	0.0277503i
$265$	11.5429	+	24.9161i	0.709076	+	1.53058i
$266$	−1.97827	−	0.292697i	−0.121296	−	0.0179464i
$267$	−4.28686	−	5.90035i	−0.262351	−	0.361096i
$268$	10.4658	+	6.04242i	0.639299	+	0.369100i
$269$	1.95894	+	0.872176i	0.119439	+	0.0531775i	0.465586	−	0.885003i	$-0.345844\pi$
$269$	1.95894	+	0.872176i	0.119439	+	0.0531775i	−0.346147	+	0.938180i	$0.612510\pi$
$270$	−4.14752	−	2.91958i	−0.252410	−	0.177680i
$271$	13.1722	−	5.86464i	0.800154	−	0.356251i	0.0344188	−	0.999407i	$-0.489042\pi$
$271$	13.1722	−	5.86464i	0.800154	−	0.356251i	0.765735	+	0.643156i	$0.222375\pi$
$272$	3.15319	−	4.33999i	0.191190	−	0.263151i
$273$	1.76585	−	1.80221i	0.106874	−	0.109075i
$274$	−6.87131			−0.415111
$275$	2.19394	−	7.50946i	0.132299	−	0.452838i
$276$	−1.00474	−	1.74026i	−0.0604781	−	0.104751i
$277$	−3.03512	−	14.2791i	−0.182363	−	0.857948i	−0.970246	−	0.242123i	$-0.922156\pi$
$277$	−3.03512	−	14.2791i	−0.182363	−	0.857948i	0.787883	−	0.615825i	$-0.211177\pi$
$278$	1.44837	+	3.25309i	0.0868673	+	0.195107i
$279$	21.8339	+	15.8633i	1.30716	+	0.949708i
$280$	−1.07211	−	5.81813i	−0.0640708	−	0.347699i
$281$	16.0431	−	11.6560i	0.957050	−	0.695337i	0.00458612	−	0.999989i	$-0.498540\pi$
$281$	16.0431	−	11.6560i	0.957050	−	0.695337i	0.952464	+	0.304652i	$0.0985402\pi$
$282$	0.642343	+	0.370857i	0.0382509	+	0.0220842i
$283$	−1.79519	+	4.03206i	−0.106713	+	0.239681i	−0.959007	−	0.283381i	$-0.908544\pi$
$283$	−1.79519	+	4.03206i	−0.106713	+	0.239681i	0.852294	+	0.523062i	$0.175210\pi$
$284$	4.10069	−	4.55428i	0.243331	−	0.270247i
$285$	−0.562615	+	0.336144i	−0.0333264	+	0.0199115i
$286$	1.18912	−	3.65973i	0.0703141	−	0.216405i
$287$	−8.55239	−	6.78247i	−0.504832	−	0.400357i
$288$	−2.71017	+	0.880586i	−0.159698	+	0.0518890i
$289$	−7.88112	−	8.75288i	−0.463596	−	0.514875i
$290$	1.72644	+	2.30301i	0.101380	+	0.135237i
$291$	0.344814	−	0.382955i	0.0202134	−	0.0224492i
$292$	−4.04531	+	0.425179i	−0.236734	+	0.0248817i
$293$			33.5604i			1.96062i	0.197462	+	0.980311i	$0.436730\pi$
$293$			33.5604i			1.96062i	−0.197462	+	0.980311i	$0.563270\pi$
$294$	−0.618337	−	2.64301i	−0.0360622	−	0.154143i
$295$	13.5131	+	2.66171i	0.786765	+	0.154971i
$296$	−3.02000	+	1.34459i	−0.175534	+	0.0781527i
$297$	−3.52972	−	0.370988i	−0.204815	−	0.0215269i
$298$	−3.08999	−	14.5373i	−0.178998	−	0.842121i
$299$	−6.37235	+	11.0372i	−0.368522	+	0.638299i
$300$	−1.47900	−	1.25366i	−0.0853899	−	0.0723802i
$301$	−1.28274	−	1.93187i	−0.0739361	−	0.111351i
$302$	−10.4640	−	3.39996i	−0.602136	−	0.195646i
$303$	1.67342	+	3.75856i	0.0961354	+	0.215924i
$304$	−0.0790085	+	0.751716i	−0.00453145	+	0.0431139i
$305$	−2.77616	+	9.00000i	−0.158963	+	0.515339i
$306$	1.59792	+	15.2032i	0.0913471	+	0.869110i
$307$		−	18.5532i		−	1.05889i	−0.848345	−	0.529444i	$-0.822401\pi$
$307$		−	18.5532i		−	1.05889i	0.848345	−	0.529444i	$-0.177599\pi$
$308$	−2.63787	−	3.19047i	−0.150307	−	0.181794i
$309$	1.21753	+	3.74716i	0.0692627	+	0.213169i
$310$	15.9479	+	13.9334i	0.905782	+	0.791362i
$311$	20.6833	−	4.39636i	1.17284	−	0.249295i	0.420016	−	0.907517i	$-0.362024\pi$
$311$	20.6833	−	4.39636i	1.17284	−	0.249295i	0.752824	+	0.658222i	$0.228691\pi$
$312$	−0.708702	−	0.638118i	−0.0401223	−	0.0361263i
$313$	6.30609	−	29.6678i	0.356441	−	1.67692i	−0.325519	−	0.945536i	$-0.605539\pi$
$313$	6.30609	−	29.6678i	0.356441	−	1.67692i	0.681960	−	0.731389i	$-0.261128\pi$
$314$	0.604879	−	1.86163i	0.0341353	−	0.105058i
$315$	13.3643	+	10.2767i	0.752992	+	0.579028i
$316$	−1.21907	−	3.75191i	−0.0685780	−	0.211061i
$317$	20.1121	−	2.11386i	1.12961	−	0.118726i	0.478767	−	0.877942i	$-0.341084\pi$
$317$	20.1121	−	2.11386i	1.12961	−	0.118726i	0.650839	+	0.759215i	$0.274417\pi$
$318$	4.12398	−	2.38098i	0.231262	−	0.133519i
$319$	1.83993	+	0.819191i	0.103016	+	0.0458659i
$320$	−2.18001	+	0.497566i	−0.121866	+	0.0278148i
$321$	−5.38336	−	3.91124i	−0.300470	−	0.218304i
$322$	6.34869	+	12.1523i	0.353799	+	0.677220i
$323$	3.85636	+	1.25301i	0.214573	+	0.0697191i
$324$	3.83467	−	6.64184i	0.213037	−	0.368991i
$325$	−2.19573	+	12.0991i	−0.121797	+	0.671136i
$326$	−0.794891	−	1.37679i	−0.0440249	−	0.0762534i
$327$	−3.77531	+	3.39931i	−0.208775	+	0.187982i
$328$	−2.42498	+	3.33770i	−0.133897	+	0.184294i
$329$	−4.27215	−	2.71288i	−0.235531	−	0.149566i
$330$	−1.33112	−	0.262193i	−0.0732755	−	0.0144332i
$331$	−0.694378	−	6.60656i	−0.0381664	−	0.363129i	−0.996891	−	0.0787930i	$-0.974893\pi$
$331$	−0.694378	−	6.60656i	−0.0381664	−	0.363129i	0.958725	−	0.284336i	$-0.0917733\pi$
$332$	−4.54546	+	2.62432i	−0.249464	+	0.144028i
$333$	3.83159	−	8.60589i	0.209970	−	0.471600i
$334$	1.91197	+	0.406402i	0.104618	+	0.0222373i
$335$	−26.8292	+	3.22625i	−1.46584	+	0.176269i
$336$	−0.988222	+	0.275616i	−0.0539119	+	0.0150361i
$337$	−17.4884	+	5.68231i	−0.952651	+	0.309535i	−0.743793	−	0.668411i	$-0.766975\pi$
$337$	−17.4884	+	5.68231i	−0.952651	+	0.309535i	−0.208859	+	0.977946i	$0.566975\pi$
$338$	1.44533	−	6.79974i	0.0786156	−	0.369857i
$339$	−5.48312	+	1.16547i	−0.297802	+	0.0632999i
$340$	0.179410	+	11.9941i	0.00972985	+	0.650472i
$341$	14.4948	+	3.08097i	0.784940	+	0.166844i
$342$	−1.26604	−	1.74255i	−0.0684596	−	0.0942266i
$343$	3.45494	+	18.1951i	0.186549	+	0.982446i
$344$	−0.709088	+	0.515183i	−0.0382315	+	0.0277768i
$345$	4.13173	+	1.76600i	0.222445	+	0.0950783i
$346$	2.21922	−	21.1145i	0.119306	−	1.13512i
$347$	4.32896	+	0.454992i	0.232391	+	0.0244252i	0.220008	−	0.975498i	$-0.429392\pi$
$347$	4.32896	+	0.454992i	0.232391	+	0.0244252i	0.0123827	+	0.999923i	$0.496058\pi$
$348$	0.370930	−	0.333987i	0.0198839	−	0.0179036i
$349$	−10.6121			−0.568052			−0.284026	−	0.958817i	$-0.591670\pi$
$349$	−10.6121			−0.568052			−0.284026	+	0.958817i	$0.591670\pi$
$350$	9.72166	+	8.97159i	0.519644	+	0.479551i
$351$	5.57852			0.297759
$352$	−1.16278	+	1.04697i	−0.0619765	+	0.0558039i
$353$	0.541816	+	0.0569472i	0.0288380	+	0.00303099i	0.118936	−	0.992902i	$-0.462052\pi$
$353$	0.541816	+	0.0569472i	0.0288380	+	0.00303099i	−0.0900985	+	0.995933i	$0.528718\pi$
$354$	0.249657	−	2.37532i	0.0132691	−	0.126247i
$355$	−1.22841	+	13.6483i	−0.0651974	+	0.724378i
$356$	15.2162	−	11.0552i	0.806457	−	0.585925i
$357$	0.344027	+	5.49290i	0.0182079	+	0.290715i
$358$	0.617227	+	0.849540i	0.0326214	+	0.0448996i
$359$	−15.0884	−	3.20715i	−0.796337	−	0.169267i	−0.208262	−	0.978073i	$-0.566781\pi$
$359$	−15.0884	−	3.20715i	−0.796337	−	0.169267i	−0.588075	+	0.808806i	$0.700114\pi$
$360$	3.66784	−	5.21048i	0.193312	−	0.274616i
$361$	18.0260	−	3.83154i	0.948735	−	0.201660i
$362$	0.327623	−	1.54135i	0.0172195	−	0.0810113i
$363$	3.15380	−	1.02473i	0.165532	−	0.0537845i
$364$	4.64764	+	4.55388i	0.243603	+	0.238688i
$365$	6.66742	−	6.18643i	0.348989	−	0.323812i
$366$	1.59761	+	0.339582i	0.0835083	+	0.0177502i
$367$	1.87173	−	4.20399i	0.0977038	−	0.219446i	−0.858080	−	0.513515i	$-0.828343\pi$
$367$	1.87173	−	4.20399i	0.0977038	−	0.219446i	0.955784	+	0.294069i	$0.0950096\pi$
$368$	4.48788	−	2.59108i	0.233947	−	0.135069i
$369$	−1.22889	−	11.6921i	−0.0639735	−	0.608667i
$370$	3.59984	−	6.45621i	0.187147	−	0.335643i
$371$	−28.7979	+	15.0448i	−1.49511	+	0.781089i
$372$	2.15861	−	2.97107i	0.111919	−	0.154043i
$373$	−27.4768	+	24.7402i	−1.42270	+	1.28100i	−0.517713	+	0.855555i	$0.673216\pi$
$373$	−27.4768	+	24.7402i	−1.42270	+	1.28100i	−0.904984	+	0.425447i	$0.860117\pi$
$374$	4.19688	+	7.26921i	0.217015	+	0.375882i
$375$	4.32761	+	0.259312i	0.223477	+	0.0133908i
$376$	−0.956389	+	1.65651i	−0.0493220	+	0.0854282i
$377$	−3.01073	−	0.978245i	−0.155060	−	0.0503822i
$378$	3.21712	−	5.06621i	0.165471	−	0.260578i
$379$	20.8942	+	15.1805i	1.07326	+	0.779770i	0.976496	−	0.215537i	$-0.0691502\pi$
$379$	20.8942	+	15.1805i	1.07326	+	0.779770i	0.0967659	+	0.995307i	$0.469150\pi$
$380$	−0.866871	−	1.45091i	−0.0444695	−	0.0744299i
$381$	2.64175	+	1.17618i	0.135341	+	0.0602576i
$382$	7.83271	−	4.52222i	0.400756	−	0.231377i
$383$	37.3310	−	3.92365i	1.90752	−	0.200489i	0.924144	−	0.382045i	$-0.124780\pi$
$383$	37.3310	−	3.92365i	1.90752	−	0.200489i	0.983381	+	0.181556i	$0.0581133\pi$
$384$	0.119827	+	0.368789i	0.00611489	+	0.0188197i
$385$	8.99875	+	2.17025i	0.458619	+	0.110606i
$386$	1.14727	−	3.53093i	0.0583944	−	0.179719i
$387$	0.519291	−	2.44307i	0.0263971	−	0.124188i
$388$	0.987589	+	0.889229i	0.0501372	+	0.0451438i
$389$	−27.4939	+	5.84401i	−1.39400	+	0.296303i	−0.842869	−	0.538119i	$-0.819135\pi$
$389$	−27.4939	+	5.84401i	−1.39400	+	0.296303i	−0.551127	+	0.834422i	$0.685802\pi$
$390$	2.12385	+	0.191156i	0.107545	+	0.00967956i
$391$	−8.59063	−	26.4392i	−0.434447	−	1.33709i
$392$	6.81595	−	1.59461i	0.344258	−	0.0805399i
$393$			5.64964i			0.284987i
$394$	−2.00433	−	19.0699i	−0.100977	−	0.960729i
$395$	7.21330	+	5.07769i	0.362941	+	0.255486i
$396$	0.466067	−	4.43434i	0.0234208	−	0.222834i
$397$	−1.18665	−	2.66527i	−0.0595565	−	0.133766i	0.881316	−	0.472528i	$-0.156658\pi$
$397$	−1.18665	−	2.66527i	−0.0595565	−	0.133766i	−0.940872	+	0.338762i	$0.889992\pi$
$398$	−21.6857	−	7.04612i	−1.08701	−	0.353190i
$399$	−0.428951	−	0.646019i	−0.0214744	−	0.0323414i
$400$	3.23302	−	3.81413i	0.161651	−	0.190706i
$401$	15.0624	−	26.0889i	0.752181	−	1.30282i	−0.194583	−	0.980886i	$-0.562335\pi$
$401$	15.0624	−	26.0889i	0.752181	−	1.30282i	0.946764	−	0.321929i	$-0.104331\pi$
$402$	0.974297	+	4.58371i	0.0485935	+	0.228615i
$403$	−23.1642	−	2.43465i	−1.15389	−	0.121279i
$404$	−9.69282	+	4.31552i	−0.482236	+	0.214705i
$405$	2.04746	+	17.0265i	0.101739	+	0.846053i
$406$	−2.62469	+	2.17008i	−0.130261	+	0.107699i
$407$		−	5.17251i		−	0.256392i
$408$	2.06880	−	0.217439i	0.102421	−	0.0107648i
$409$	11.5234	−	12.7980i	0.569795	−	0.632822i	−0.387522	−	0.921860i	$-0.626669\pi$
$409$	11.5234	−	12.7980i	0.569795	−	0.632822i	0.957317	+	0.289039i	$0.0933356\pi$
$410$	−0.137976	−	9.22414i	−0.00681415	−	0.455548i
$411$	−1.78288	−	1.98009i	−0.0879430	−	0.0976706i
$412$	−9.66342	+	3.13984i	−0.476083	+	0.154689i
$413$	−2.38515	+	16.1207i	−0.117365	+	0.793247i
$414$	−4.56334	+	14.0445i	−0.224276	+	0.690250i
$415$	4.61270	−	10.7919i	0.226428	−	0.529751i
$416$	1.64562	−	1.82764i	0.0806831	−	0.0896077i
$417$	−0.561630	+	1.26144i	−0.0275031	+	0.0617731i
$418$	−1.02422	−	0.591336i	−0.0500964	−	0.0289232i
$419$	−10.0164	+	7.27736i	−0.489335	+	0.355523i	−0.804928	−	0.593372i	$-0.797796\pi$
$419$	−10.0164	+	7.27736i	−0.489335	+	0.355523i	0.315594	+	0.948894i	$0.397796\pi$
$420$	1.39842	−	1.81856i	0.0682358	−	0.0887366i
$421$	−6.70767	−	4.87341i	−0.326912	−	0.237515i	0.412207	−	0.911090i	$-0.364758\pi$
$421$	−6.70767	−	4.87341i	−0.326912	−	0.237515i	−0.739119	+	0.673575i	$0.764758\pi$
$422$	−9.87235	−	22.1737i	−0.480578	−	1.07940i
$423$	−1.13327	−	5.33161i	−0.0551014	−	0.259232i
$424$	6.14023	+	10.6352i	0.298196	+	0.516491i
$425$	−16.4079	−	21.2187i	−0.795902	−	1.02926i
$426$	2.37639			0.115137
$427$	−10.7932	−	2.77446i	−0.522318	−	0.134266i
$428$	10.0866	−	13.8829i	0.487552	−	0.671058i
$429$	1.36315	−	0.606915i	0.0658137	−	0.0293022i
$430$	0.577688	−	1.87280i	0.0278586	−	0.0903144i
$431$	1.44154	+	0.641815i	0.0694366	+	0.0309152i	0.441161	−	0.897428i	$-0.354567\pi$
$431$	1.44154	+	0.641815i	0.0694366	+	0.0309152i	−0.371725	+	0.928343i	$0.621233\pi$
$432$	−1.96441	−	1.13415i	−0.0945125	−	0.0545668i
$433$	−13.7818	−	18.9690i	−0.662311	−	0.911593i	0.337244	−	0.941417i	$-0.390505\pi$
$433$	−13.7818	−	18.9690i	−0.662311	−	0.911593i	−0.999555	+	0.0298240i	$0.990505\pi$
$434$	−15.5698	+	19.6328i	−0.747374	+	0.942405i
$435$	−0.215696	+	1.09506i	−0.0103419	+	0.0525041i
$436$	−8.76635	−	9.73602i	−0.419832	−	0.466271i
$437$	2.91088	+	2.62096i	0.139246	+	0.125378i
$438$	−1.17215	−	1.05541i	−0.0560074	−	0.0504293i
$439$	14.0854	+	15.6434i	0.672258	+	0.746618i	0.978706	−	0.205269i	$-0.0658070\pi$
$439$	14.0854	+	15.6434i	0.672258	+	0.746618i	−0.306447	+	0.951888i	$0.599140\pi$
$440$	0.676159	−	3.43277i	0.0322346	−	0.163651i
$441$	−11.3935	+	16.3734i	−0.542549	+	0.779686i
$442$	−7.75476	−	10.6735i	−0.368856	−	0.507687i
$443$	29.5881	+	17.0827i	1.40578	+	0.811625i	0.994977	−	0.100102i	$-0.0319168\pi$
$443$	29.5881	+	17.0827i	1.40578	+	0.811625i	0.410798	+	0.911726i	$0.365250\pi$
$444$	−1.17106	−	0.521388i	−0.0555759	−	0.0247440i
$445$	−12.3965	+	40.1880i	−0.587650	+	1.90510i
$446$	26.8690	−	11.9628i	1.27228	−	0.566457i
$447$	3.38742	−	4.66238i	0.160219	−	0.220523i
$448$	−0.710776	−	2.54849i	−0.0335810	−	0.120405i
$449$	−20.0298			−0.945264			−0.472632	−	0.881260i	$-0.656696\pi$
$449$	−20.0298			−0.945264			−0.472632	+	0.881260i	$0.656696\pi$
$450$	0.426157	+	14.2418i	0.0200892	+	0.671365i
$451$	−3.22763	−	5.59043i	−0.151983	−	0.263243i
$452$	−3.00560	−	14.1402i	−0.141371	−	0.665100i
$453$	−1.73531	−	3.89757i	−0.0815319	−	0.183124i
$454$	−10.4982	−	7.62736i	−0.492703	−	0.357970i
$455$	−14.4232	−	1.91401i	−0.676170	−	0.0897303i
$456$	−0.237120	+	0.172278i	−0.0111042	+	0.00806765i
$457$	−11.0912	−	6.40349i	−0.518823	−	0.299542i	0.217630	−	0.976031i	$-0.430167\pi$
$457$	−11.0912	−	6.40349i	−0.518823	−	0.299542i	−0.736453	+	0.676489i	$0.763501\pi$
$458$	−7.65027	+	17.1828i	−0.357473	+	0.802899i
$459$	−8.14222	+	9.04285i	−0.380046	+	0.422084i
$460$	−4.55427	+	10.6552i	−0.212344	+	0.496800i
$461$	1.99000	−	6.12457i	0.0926833	−	0.285250i	−0.893960	−	0.448147i	$-0.852084\pi$
$461$	1.99000	−	6.12457i	0.0926833	−	0.285250i	0.986643	+	0.162897i	$0.0520840\pi$
$462$	0.234950	−	1.58797i	0.0109308	−	0.0738792i
$463$	29.3948	−	9.55095i	1.36609	−	0.443870i	0.468020	−	0.883718i	$-0.344968\pi$
$463$	29.3948	−	9.55095i	1.36609	−	0.443870i	0.898072	+	0.439848i	$0.144968\pi$
$464$	0.861307	+	0.956578i	0.0399852	+	0.0444080i
$465$	0.122820	+	8.21093i	0.00569565	+	0.380773i
$466$	6.62623	−	7.35917i	0.306954	−	0.340907i
$467$	−20.1713	+	2.12009i	−0.933416	+	0.0981059i	−0.559012	−	0.829160i	$-0.688819\pi$
$467$	−20.1713	+	2.12009i	−0.933416	+	0.0981059i	−0.374404	+	0.927266i	$0.622153\pi$
$468$			7.00822i			0.323955i
$469$	−5.32328	−	31.5272i	−0.245806	−	1.45579i
$470$	−0.510649	−	4.24651i	−0.0235545	−	0.195877i
$471$	0.693406	−	0.308724i	0.0319505	−	0.0142253i
$472$	6.12564	+	0.643830i	0.281955	+	0.0296347i
$473$	−0.285132	−	1.34144i	−0.0131104	−	0.0616796i
$474$	0.764870	−	1.32479i	0.0351316	−	0.0608498i
$475$	3.49698	+	1.43322i	0.160452	+	0.0657607i
$476$	−14.1654	+	0.887200i	−0.649272	+	0.0406647i
$477$	−33.2821	−	10.8140i	−1.52388	−	0.495139i
$478$	−10.0436	−	22.5583i	−0.459384	−	1.03179i
$479$	−4.08951	+	38.9091i	−0.186855	+	1.77780i	0.352586	+	0.935779i	$0.385302\pi$
$479$	−4.08951	+	38.9091i	−0.186855	+	1.77780i	−0.539441	+	0.842024i	$0.681364\pi$
$480$	−0.709023	−	0.499105i	−0.0323623	−	0.0227809i
$481$	0.849825	+	8.08554i	0.0387487	+	0.368669i
$482$			21.5969i			0.983712i
$483$	−1.85462	+	4.98260i	−0.0843879	+	0.226716i
$484$	2.64265	+	8.13323i	0.120120	+	0.369692i
$485$	−2.95962	−	0.266379i	−0.134389	−	0.0120957i
$486$	9.56513	−	2.03313i	0.433883	−	0.0922247i
$487$	28.3330	+	25.5111i	1.28389	+	1.15602i	0.979051	+	0.203614i	$0.0652689\pi$
$487$	28.3330	+	25.5111i	1.28389	+	1.15602i	0.304838	+	0.952404i	$0.401398\pi$
$488$	−0.875736	+	4.12001i	−0.0396427	+	0.186504i
$489$	0.190498	−	0.586294i	0.00861464	−	0.0265131i
$490$	−10.0561	+	11.9948i	−0.454287	+	0.541871i
$491$	7.90099	+	24.3168i	0.356567	+	1.09740i	0.955095	+	0.296298i	$0.0957522\pi$
$491$	7.90099	+	24.3168i	0.356567	+	1.09740i	−0.598529	+	0.801101i	$0.704248\pi$
$492$	−1.59102	+	0.167223i	−0.0717287	+	0.00753899i
$493$	5.98011	−	3.45262i	0.269331	−	0.155498i
$494$	1.69820	+	0.756086i	0.0764055	+	0.0340179i
$495$	5.11363	+	8.55883i	0.229841	+	0.384691i
$496$	7.66200	+	5.56677i	0.344034	+	0.249955i
$497$	−16.1998	−	0.683554i	−0.726660	−	0.0306616i
$498$	−1.93564	−	0.628928i	−0.0867382	−	0.0281829i
$499$	10.7811	−	18.6735i	0.482630	−	0.835940i	−0.517171	−	0.855882i	$-0.673015\pi$
$499$	10.7811	−	18.6735i	0.482630	−	0.835940i	0.999801	+	0.0199421i	$0.00634820\pi$
$500$	−0.668729	+	11.1603i	−0.0299065	+	0.499105i
$501$	0.378982	+	0.656416i	0.0169317	+	0.0293265i
$502$	−1.18900	+	1.07058i	−0.0530676	+	0.0477823i
$503$	−17.2349	+	23.7218i	−0.768466	+	1.05770i	0.227996	+	0.973662i	$0.426783\pi$
$503$	−17.2349	+	23.7218i	−0.768466	+	1.05770i	−0.996462	+	0.0840411i	$0.973217\pi$
$504$	6.36461	+	4.04162i	0.283502	+	0.180028i
$505$	11.5538	−	20.7215i	0.514139	−	0.922095i
$506$	0.847560	+	8.06399i	0.0376786	+	0.358488i
$507$	2.33448	−	1.34781i	0.103678	−	0.0598585i
$508$	−3.03321	+	6.81270i	−0.134577	+	0.302265i
$509$	−22.0313	−	4.68290i	−0.976521	−	0.207566i	−0.308104	−	0.951353i	$-0.599695\pi$
$509$	−22.0313	−	4.68290i	−0.976521	−	0.207566i	−0.668417	+	0.743787i	$0.733028\pi$
$510$	−3.40976	+	3.16378i	−0.150987	+	0.140094i
$511$	7.68691	+	7.53183i	0.340049	+	0.333188i
$512$	−0.951057	+	0.309017i	−0.0420312	+	0.0136568i
$513$	0.356467	−	1.67704i	0.0157384	−	0.0740433i
$514$	14.3852	−	3.05766i	0.634503	−	0.134868i
$515$	13.0781	−	18.5786i	0.576290	−	0.818671i
$516$	−0.332444	−	0.0706632i	−0.0146350	−	0.00311077i
$517$	−1.75917	−	2.42129i	−0.0773682	−	0.106488i
$518$	7.83308	+	3.89113i	0.344166	+	0.170967i
$519$	6.66031	−	4.83900i	0.292355	−	0.212409i
$520$	−0.492965	+	5.47711i	−0.0216179	+	0.240187i
$521$	0.994710	−	9.46403i	0.0435790	−	0.414627i	−0.950885	−	0.309545i	$-0.899823\pi$
$521$	0.994710	−	9.46403i	0.0435790	−	0.414627i	0.994464	−	0.105081i	$-0.0335102\pi$
$522$	−3.64797	−	0.383417i	−0.159667	−	0.0167817i
$523$	−7.09503	+	6.38839i	−0.310244	+	0.279345i	−0.809513	−	0.587102i	$-0.800269\pi$
$523$	−7.09503	+	6.38839i	−0.310244	+	0.279345i	0.499269	+	0.866447i	$0.333602\pi$
$524$	−14.5696			−0.636478
$525$	−0.0628687	+	5.12930i	−0.00274381	+	0.223861i
$526$	27.9882			1.22034
$527$	37.7563	−	33.9959i	1.64469	−	1.48088i
$528$	−0.603408	−	0.0634207i	−0.0262599	−	0.00276003i
$529$	0.402937	−	3.83369i	0.0175190	−	0.166682i
$530$	−25.2502	−	10.7925i	−1.09680	−	0.468797i
$531$	−14.1999	+	10.3168i	−0.616221	+	0.447711i
$532$	1.66600	−	1.10621i	0.0722300	−	0.0479601i
$533$	5.96385	+	8.20853i	0.258323	+	0.355551i
$534$	7.13386	+	1.51635i	0.308712	+	0.0656188i
$535$	0.573903	+	38.3672i	0.0248120	+	1.65876i
$536$	−11.8208	+	2.51258i	−0.510579	+	0.108527i
$537$	−0.0846597	+	0.398292i	−0.00365333	+	0.0171876i
$538$	−2.03938	+	0.662633i	−0.0879237	+	0.0285681i
$539$	−2.05841	+	10.7576i	−0.0886621	+	0.463362i
$540$	5.03579	−	0.605561i	0.216706	−	0.0260592i
$541$	−22.8447	−	4.85579i	−0.982171	−	0.208767i	−0.311276	−	0.950319i	$-0.600756\pi$
$541$	−22.8447	−	4.85579i	−0.982171	−	0.208767i	−0.670895	+	0.741553i	$0.734090\pi$
$542$	−5.86464	+	13.1722i	−0.251908	+	0.565794i
$543$	0.529173	−	0.305518i	0.0227090	−	0.0131110i
$544$	0.560746	+	5.33514i	0.0240418	+	0.228742i
$545$	28.7427	+	5.66151i	1.23120	+	0.242512i
$546$	−0.106369	+	2.52088i	−0.00455218	+	0.107884i
$547$	17.3982	−	23.9465i	0.743892	−	1.02388i	−0.254493	−	0.967075i	$-0.581909\pi$
$547$	17.3982	−	23.9465i	0.743892	−	1.02388i	0.998385	−	0.0568055i	$-0.0180915\pi$
$548$	5.10638	−	4.59780i	0.218134	−	0.196408i
$549$	−6.00142	−	10.3948i	−0.256134	−	0.443637i
$550$	3.39440	+	7.04865i	0.144738	+	0.300555i
$551$	−0.486470	+	0.842591i	−0.0207243	+	0.0358956i
$552$	1.91112	+	0.620962i	0.0813429	+	0.0264299i
$553$	−5.59516	+	8.81106i	−0.237930	+	0.374684i
$554$	11.8101	+	8.58055i	0.501764	+	0.364553i
$555$	2.79451	−	0.637820i	0.118620	−	0.0270740i
$556$	−3.25309	−	1.44837i	−0.137962	−	0.0614245i
$557$	−18.9544	+	10.9434i	−0.803125	+	0.463685i	−0.844563	−	0.535456i	$-0.820140\pi$
$557$	−18.9544	+	10.9434i	−0.803125	+	0.463685i	0.0414374	+	0.999141i	$0.486806\pi$
$558$	−26.8403	+	2.82103i	−1.13624	+	0.119424i
$559$	0.666106	+	2.05006i	0.0281733	+	0.0867084i
$560$	4.68982	+	3.60633i	0.198181	+	0.152395i
$561$	−1.00580	+	3.09552i	−0.0424648	+	0.130693i
$562$	−4.12296	+	19.3970i	−0.173917	+	0.818213i
$563$	−20.1047	−	18.1024i	−0.847314	−	0.762925i	0.126090	−	0.992019i	$-0.459757\pi$
$563$	−20.1047	−	18.1024i	−0.847314	−	0.762925i	−0.973404	+	0.229094i	$0.926424\pi$
$564$	−0.725505	+	0.154211i	−0.0305493	+	0.00649345i
$565$	24.3429	+	21.2679i	1.02411	+	0.894746i
$566$	−1.36389	−	4.19762i	−0.0573285	−	0.176439i
$567$	−20.0080	+	3.37828i	−0.840255	+	0.141874i
$568$			6.12839i			0.257142i
$569$	−0.458314	−	4.36056i	−0.0192135	−	0.182804i	0.980706	−	0.195488i	$-0.0626291\pi$
$569$	−0.458314	−	4.36056i	−0.0192135	−	0.182804i	−0.999920	+	0.0126839i	$0.995962\pi$
$570$	0.193180	−	0.626267i	0.00809141	−	0.0262314i
$571$	−0.935749	+	8.90306i	−0.0391599	+	0.372581i	0.957338	+	0.288969i	$0.0933124\pi$
$571$	−0.935749	+	8.90306i	−0.0391599	+	0.372581i	−0.996498	+	0.0836124i	$0.973354\pi$
$572$	1.56515	+	3.51539i	0.0654423	+	0.146986i
$573$	3.33549	+	1.08377i	0.139342	+	0.0452750i
$574$	10.8940	−	0.682306i	0.454708	−	0.0284789i
$575$	−6.14280	−	25.1721i	−0.256172	−	1.04975i
$576$	1.42482	−	2.46786i	0.0593674	−	0.102827i
$577$	6.27794	+	29.5354i	0.261354	+	1.22957i	0.891472	+	0.453075i	$0.149673\pi$
$577$	6.27794	+	29.5354i	0.261354	+	1.22957i	−0.630118	+	0.776499i	$0.716994\pi$
$578$	11.7136	+	1.23115i	0.487223	+	0.0512092i
$579$	1.31518	−	0.585555i	0.0546569	−	0.0243348i
$580$	−2.82401	−	0.556252i	−0.117261	−	0.0230971i
$581$	13.0143	+	4.84416i	0.539924	+	0.200969i
$582$			0.515317i			0.0213606i
$583$	−19.1097	+	2.00851i	−0.791443	+	0.0831840i
$584$	2.72175	−	3.02281i	0.112627	−	0.125085i
$585$	−9.39969	−	12.5388i	−0.388629	−	0.518416i
$586$	−22.4563	−	24.9403i	−0.927662	−	1.03027i
$587$	−0.950898	+	0.308965i	−0.0392478	+	0.0127524i	−0.328575	−	0.944478i	$-0.606568\pi$
$587$	−0.950898	+	0.308965i	−0.0392478	+	0.0127524i	0.289327	+	0.957230i	$0.406568\pi$
$588$	2.22803	+	1.55039i	0.0918825	+	0.0639369i
$589$	−2.21211	+	6.80816i	−0.0911482	+	0.280525i
$590$	−11.8233	+	7.06402i	−0.486756	+	0.290821i
$591$	4.97528	−	5.52560i	0.204655	−	0.227293i
$592$	1.34459	−	3.02000i	0.0552623	−	0.124121i
$593$	−14.1289	−	8.15730i	−0.580203	−	0.334980i	0.181011	−	0.983481i	$-0.442063\pi$
$593$	−14.1289	−	8.15730i	−0.580203	−	0.334980i	−0.761214	+	0.648501i	$0.775396\pi$
$594$	2.87133	−	2.08614i	0.117812	−	0.0855955i
$595$	24.1543	−	20.5866i	0.990228	−	0.843967i
$596$	12.0236	+	8.73569i	0.492508	+	0.357828i
$597$	−3.59627	−	8.07736i	−0.147186	−	0.330584i
$598$	−2.64977	−	12.4662i	−0.108357	−	0.509780i
$599$	−12.9242	−	22.3854i	−0.528068	−	0.914641i	−0.999465	−	0.0327197i	$-0.989583\pi$
$599$	−12.9242	−	22.3854i	−0.528068	−	0.914641i	0.471396	−	0.881922i	$-0.343750\pi$
$600$	1.93797	−	0.0579899i	0.0791173	−	0.00236743i
$601$	−19.7116			−0.804054			−0.402027	−	0.915628i	$-0.631694\pi$
$601$	−19.7116			−0.804054			−0.402027	+	0.915628i	$0.631694\pi$
$602$	2.24593	+	0.577334i	0.0915375	+	0.0235304i
$603$	20.2418	−	27.8604i	0.824309	−	1.13456i
$604$	10.0513	−	4.47512i	0.408981	−	0.182090i
$605$	−15.6367	−	11.0072i	−0.635722	−	0.447507i
$606$	−3.75856	−	1.67342i	−0.152681	−	0.0679780i
$607$	7.30751	+	4.21899i	0.296603	+	0.171244i	0.640916	−	0.767611i	$-0.278555\pi$
$607$	7.30751	+	4.21899i	0.296603	+	0.171244i	−0.344313	+	0.938855i	$0.611888\pi$
$608$	−0.444281	−	0.611501i	−0.0180180	−	0.0247996i
$609$	−1.30637	−	0.193284i	−0.0529367	−	0.00783228i
$610$	−3.95909	−	8.54592i	−0.160299	−	0.346014i
$611$	3.14770	+	3.49588i	0.127342	+	0.141428i
$612$	−11.3604	−	10.2290i	−0.459218	−	0.413481i
$613$	−0.740305	−	0.666573i	−0.0299006	−	0.0269226i	0.654045	−	0.756456i	$-0.273071\pi$
$613$	−0.740305	−	0.666573i	−0.0299006	−	0.0269226i	−0.683946	+	0.729533i	$0.739737\pi$
$614$	12.4145	+	13.7877i	0.501010	+	0.556428i
$615$	2.62230	−	2.43312i	0.105741	−	0.0981130i
$616$	4.09517	+	0.605903i	0.164999	+	0.0244125i
$617$	1.67959	+	2.31175i	0.0676176	+	0.0930676i	0.841486	−	0.540278i	$-0.181681\pi$
$617$	1.67959	+	2.31175i	0.0676176	+	0.0930676i	−0.773869	+	0.633346i	$0.781681\pi$
$618$	−3.41214	−	1.97000i	−0.137256	−	0.0792450i
$619$	31.5875	+	14.0637i	1.26961	+	0.565267i	0.927300	−	0.374320i	$-0.122124\pi$
$619$	31.5875	+	14.0637i	1.26961	+	0.565267i	0.342311	+	0.939587i	$0.388790\pi$
$620$	−21.1749	+	0.316737i	−0.850403	+	0.0127205i
$621$	−10.7385	+	4.78107i	−0.430919	+	0.191858i
$622$	−12.4289	+	17.1069i	−0.498354	+	0.685926i
$623$	−48.1951	−	12.3889i	−1.93090	−	0.496351i
$624$	0.953652			0.0381766
$625$	−13.7722	−	20.8645i	−0.550887	−	0.834580i
$626$	15.1653	+	26.2671i	0.606128	+	1.04984i
$627$	−0.0953487	−	0.448580i	−0.00380786	−	0.0179146i
$628$	0.796158	+	1.78820i	0.0317702	+	0.0713570i
$629$	−14.3471	−	10.4238i	−0.572058	−	0.415625i
$630$	−16.8081	+	1.30535i	−0.669649	+	0.0520064i
$631$	−23.9605	+	17.4083i	−0.953851	+	0.693013i	−0.951715	−	0.306984i	$-0.900680\pi$
$631$	−23.9605	+	17.4083i	−0.953851	+	0.693013i	−0.00213649	+	0.999998i	$0.500680\pi$
$632$	3.41646	+	1.97249i	0.135899	+	0.0784616i
$633$	3.82818	−	8.59823i	0.152156	−	0.341749i
$634$	−13.5317	+	15.0285i	−0.537414	+	0.596858i
$635$	−3.71056	−	16.2572i	−0.147249	−	0.645149i
$636$	−1.47153	+	4.52890i	−0.0583499	+	0.179583i
$637$	1.45023	−	17.1542i	0.0574603	−	0.679673i
$638$	−1.91548	+	0.622378i	−0.0758347	+	0.0246402i
$639$	−11.6855	−	12.9780i	−0.462271	−	0.513404i
$640$	1.28712	−	1.82847i	0.0508781	−	0.0722767i
$641$	13.5822	−	15.0846i	0.536465	−	0.595805i	−0.412589	−	0.910917i	$-0.635376\pi$
$641$	13.5822	−	15.0846i	0.536465	−	0.595805i	0.949054	+	0.315112i	$0.102042\pi$
$642$	6.61775	−	0.695553i	0.261182	−	0.0274513i
$643$			3.54036i			0.139618i	0.997560	+	0.0698091i	$0.0222390\pi$
$643$			3.54036i			0.139618i	−0.997560	+	0.0698091i	$0.977761\pi$
$644$	−12.8495	−	4.78280i	−0.506339	−	0.188469i
$645$	0.689571	−	0.319459i	0.0271518	−	0.0125787i
$646$	−3.70426	+	1.64924i	−0.145742	+	0.0648885i
$647$	28.5281	+	2.99842i	1.12155	+	0.117880i	0.647103	−	0.762402i	$-0.275980\pi$
$647$	28.5281	+	2.99842i	1.12155	+	0.117880i	0.474450	+	0.880282i	$0.342647\pi$
$648$	1.59454	+	7.50174i	0.0626396	+	0.294696i
$649$	−4.81872	+	8.34627i	−0.189151	+	0.327620i
$650$	−6.46411	−	10.4606i	−0.253543	−	0.410298i
$651$	−9.69739	+	0.607360i	−0.380071	+	0.0238043i
$652$	1.51197	+	0.491269i	0.0592134	+	0.0192396i
$653$	10.6359	+	23.8886i	0.416214	+	0.934833i	0.993019	+	0.117951i	$0.0376326\pi$
$653$	10.6359	+	23.8886i	0.416214	+	0.934833i	−0.576805	+	0.816882i	$0.695701\pi$
$654$	0.531024	−	5.05235i	0.0207647	−	0.197563i
$655$	26.0674	−	19.5414i	1.01854	−	0.763544i
$656$	−0.431245	−	4.10302i	−0.0168373	−	0.160196i
$657$			11.5911i			0.452214i
$658$	4.99010	−	0.842563i	0.194534	−	0.0328465i
$659$	−10.2187	−	31.4499i	−0.398064	−	1.22511i	−0.926550	−	0.376173i	$-0.877240\pi$
$659$	−10.2187	−	31.4499i	−0.398064	−	1.22511i	0.528486	−	0.848942i	$-0.322760\pi$
$660$	1.16465	−	0.695843i	0.0453341	−	0.0270857i
$661$	29.2600	−	6.21941i	1.13808	−	0.241907i	0.399933	−	0.916544i	$-0.369033\pi$
$661$	29.2600	−	6.21941i	1.13808	−	0.241907i	0.738149	+	0.674638i	$0.235700\pi$
$662$	4.93668	+	4.44500i	0.191869	+	0.172760i
$663$	1.06365	−	5.00410i	0.0413089	−	0.194343i
$664$	1.62192	−	4.99175i	0.0629427	−	0.193718i
$665$	−1.49704	+	4.21367i	−0.0580528	+	0.163399i
$666$	2.91104	+	8.95926i	0.112801	+	0.347164i
$667$	6.63395	−	0.697257i	0.256868	−	0.0269979i
$668$	−1.69281	+	0.977343i	−0.0654967	+	0.0378145i
$669$	10.4189	+	4.63880i	0.402819	+	0.179346i
$670$	17.7792	−	20.3498i	0.686871	−	0.786183i
$671$	−5.33184	−	3.87381i	−0.205833	−	0.149547i
$672$	0.549969	−	0.866072i	0.0212155	−	0.0334095i
$673$	37.4323	+	12.1625i	1.44291	+	0.468830i	0.922803	−	0.385272i	$-0.125892\pi$
$673$	37.4323	+	12.1625i	1.44291	+	0.468830i	0.520106	+	0.854101i	$0.325892\pi$
$674$	9.19417	−	15.9248i	0.354146	−	0.613399i
$675$	−8.19762	+	7.83764i	−0.315527	+	0.301671i
$676$	3.47583	+	6.02031i	0.133686	+	0.231550i
$677$	−10.0269	+	9.02827i	−0.385365	+	0.346984i	−0.838930	−	0.544239i	$-0.816819\pi$
$677$	−10.0269	+	9.02827i	−0.385365	+	0.346984i	0.453565	+	0.891223i	$0.350152\pi$
$678$	3.29490	−	4.53504i	0.126540	−	0.174167i
$679$	0.148228	−	3.51290i	0.00568845	−	0.134813i
$680$	−8.15895	−	8.79331i	−0.312881	−	0.337208i
$681$	−0.525971	−	5.00428i	−0.0201553	−	0.191764i
$682$	−12.8333	+	7.40933i	−0.491414	+	0.283718i
$683$	10.9908	−	24.6857i	0.420550	−	0.944570i	−0.571717	−	0.820451i	$-0.693723\pi$
$683$	10.9908	−	24.6857i	0.420550	−	0.944570i	0.992267	−	0.124120i	$-0.0396107\pi$
$684$	2.10685	+	0.447824i	0.0805573	+	0.0171230i
$685$	−2.96937	+	15.0751i	−0.113454	+	0.575988i
$686$	−14.7425	−	11.2098i	−0.562869	−	0.427993i
$687$	−6.93651	+	2.25381i	−0.264645	+	0.0859882i
$688$	0.182231	−	0.857328i	0.00694748	−	0.0326853i
$689$	29.5418	−	6.27931i	1.12545	−	0.239223i
$690$	−4.25216	+	1.45227i	−0.161877	+	0.0552871i
$691$	21.0418	+	4.47258i	0.800469	+	0.170145i	0.589945	−	0.807444i	$-0.299150\pi$
$691$	21.0418	+	4.47258i	0.800469	+	0.170145i	0.210524	+	0.977589i	$0.432483\pi$
$692$	12.4791	+	17.1760i	0.474385	+	0.652935i
$693$	−9.82763	+	6.52546i	−0.373321	+	0.247882i
$694$	−3.52149	+	2.55851i	−0.133674	+	0.0971198i
$695$	7.76289	−	1.77180i	0.294463	−	0.0672084i
$696$	−0.0521739	+	0.496401i	−0.00197765	+	0.0188160i
$697$	−22.0108	−	2.31343i	−0.833717	−	0.0876272i
$698$	7.88632	−	7.10088i	0.298502	−	0.268772i
$699$	3.83996			0.145241
$700$	−13.2278	−	0.162130i	−0.499962	−	0.00612793i
$701$	18.2535			0.689425			0.344712	−	0.938708i	$-0.387976\pi$
$701$	18.2535			0.689425			0.344712	+	0.938708i	$0.387976\pi$
$702$	−4.14565	+	3.73276i	−0.156467	+	0.140884i
$703$	2.48502	+	0.261186i	0.0937243	+	0.00985083i
$704$	0.163553	−	1.55611i	0.00616415	−	0.0586479i
$705$	1.09121	−	1.24898i	0.0410973	−	0.0470394i
$706$	−0.440753	+	0.320226i	−0.0165880	+	0.0120519i
$707$	25.1406	+	12.4888i	0.945511	+	0.469688i
$708$	1.40387	+	1.93226i	0.0527607	+	0.0726189i
$709$	−26.7141	−	5.67826i	−1.00327	−	0.213252i	−0.323146	−	0.946349i	$-0.604741\pi$
$709$	−26.7141	−	5.67826i	−1.00327	−	0.213252i	−0.680124	+	0.733097i	$0.738074\pi$
$710$	−8.21963	−	10.9647i	−0.308477	−	0.411496i
$711$	−10.9961	+	2.33730i	−0.412387	+	0.0876555i
$712$	−3.91046	+	18.3973i	−0.146551	+	0.689466i
$713$	46.6769	−	15.1662i	1.74806	−	0.567980i
$714$	−3.93113	−	3.85182i	−0.147119	−	0.144151i
$715$	−7.51527	−	4.19034i	−0.281055	−	0.156710i
$716$	−1.02714	−	0.218326i	−0.0383861	−	0.00815922i
$717$	3.89459	−	8.74739i	0.145446	−	0.326677i
$718$	13.3589	−	7.71276i	0.498550	−	0.287838i
$719$	3.61223	+	34.3680i	0.134713	+	1.28171i	0.827868	+	0.560923i	$0.189554\pi$
$719$	3.61223	+	34.3680i	0.134713	+	1.28171i	−0.693155	+	0.720789i	$0.743780\pi$
$720$	0.760759	+	6.32640i	0.0283518	+	0.235771i
$721$	22.6938	+	14.4109i	0.845161	+	0.536690i
$722$	−10.8321	+	14.9091i	−0.403129	+	0.554860i
$723$	−6.22353	+	5.60369i	−0.231455	+	0.208403i
$724$	0.787890	+	1.36467i	0.0292817	+	0.0507174i
$725$	5.79866	−	2.79245i	0.215357	−	0.103709i
$726$	−1.65805	+	2.87183i	−0.0615361	+	0.106584i
$727$	−4.03252	−	1.31025i	−0.149558	−	0.0485944i	0.233281	−	0.972409i	$-0.425054\pi$
$727$	−4.03252	−	1.31025i	−0.149558	−	0.0485944i	−0.382839	+	0.923815i	$0.625054\pi$
$728$	−6.50101	−	0.274312i	−0.240944	−	0.0101667i
$729$	−15.5461	−	11.2949i	−0.575783	−	0.418331i
$730$	−0.815332	+	9.05879i	−0.0301768	+	0.335281i
$731$	−4.29541	−	1.91244i	−0.158871	−	0.0707341i
$732$	−1.41448	+	0.816650i	−0.0522807	+	0.0301843i
$733$	18.7596	−	1.97171i	0.692900	−	0.0728268i	0.248469	−	0.968640i	$-0.420073\pi$
$733$	18.7596	−	1.97171i	0.692900	−	0.0728268i	0.444431	+	0.895813i	$0.353406\pi$
$734$	1.42205	+	4.37660i	0.0524886	+	0.161543i
$735$	−6.06574	+	0.214430i	−0.223738	+	0.00790938i
$736$	−1.60138	+	4.92853i	−0.0590275	+	0.181668i
$737$	3.93138	−	18.4957i	0.144814	−	0.681297i
$738$	8.73680	+	7.86665i	0.321606	+	0.289575i
$739$	40.7945	−	8.67113i	1.50065	−	0.318973i	0.616940	−	0.787010i	$-0.288372\pi$
$739$	40.7945	−	8.67113i	1.50065	−	0.318973i	0.883709	+	0.468037i	$0.155039\pi$
$740$	1.64485	+	7.20666i	0.0604659	+	0.264922i
$741$	0.222747	+	0.685545i	0.00818281	+	0.0251841i
$742$	11.3341	−	30.4501i	0.416087	−	1.11786i
$743$			19.2859i			0.707532i	0.935334	+	0.353766i	$0.115099\pi$
$743$			19.2859i			0.707532i	−0.935334	+	0.353766i	$0.884901\pi$
$744$	0.383876	+	3.65233i	0.0140736	+	0.133901i
$745$	−33.2288	+	0.497041i	−1.21741	+	0.0182102i
$746$	3.86481	−	36.7712i	0.141501	−	1.34629i
$747$	6.08345	+	13.6636i	0.222582	+	0.499927i
$748$	−7.98294	−	2.59381i	−0.291885	−	0.0948392i
$749$	−45.3130	+	2.83801i	−1.65570	+	0.103699i
$750$	−3.38956	+	2.70303i	−0.123769	+	0.0987008i
$751$	1.51540	−	2.62476i	0.0552979	−	0.0957788i	−0.837051	−	0.547124i	$-0.815722\pi$
$751$	1.51540	−	2.62476i	0.0552979	−	0.0957788i	0.892349	+	0.451346i	$0.149056\pi$
$752$	−0.397689	−	1.87098i	−0.0145022	−	0.0682276i
$753$	−0.617012	−	0.0648506i	−0.0224852	−	0.00236329i
$754$	2.89198	−	1.28759i	0.105320	−	0.0468914i
$755$	−11.9811	+	21.4879i	−0.436038	+	0.782023i
$756$	0.999168	+	5.91760i	0.0363394	+	0.215221i
$757$		−	20.8627i		−	0.758269i	−0.925342	−	0.379134i	$-0.876222\pi$
$757$		−	20.8627i		−	0.758269i	0.925342	−	0.379134i	$-0.123778\pi$
$758$	−25.6851	+	2.69962i	−0.932926	+	0.0980545i
$759$	−2.10387	+	2.33658i	−0.0763656	+	0.0848125i
$760$	1.61506	+	0.498184i	0.0585843	+	0.0180710i
$761$	−7.87632	−	8.74754i	−0.285516	−	0.317098i	0.583277	−	0.812274i	$-0.301770\pi$
$761$	−7.87632	−	8.74754i	−0.285516	−	0.317098i	−0.868793	+	0.495176i	$0.835104\pi$
$762$	−2.75022	+	0.893600i	−0.0996299	+	0.0323717i
$763$	−5.07325	+	34.2890i	−0.183664	+	1.24134i
$764$	−2.79488	+	8.60177i	−0.101115	+	0.311201i
$765$	34.0450	+	3.06421i	1.23090	+	0.110787i
$766$	−25.1169	+	27.8951i	−0.907510	+	1.00789i
$767$	6.16125	−	13.8384i	0.222470	−	0.499675i
$768$	−0.335817	−	0.193884i	−0.0121177	−	0.00699618i
$769$	25.6142	−	18.6098i	0.923672	−	0.671087i	−0.0207636	−	0.999784i	$-0.506610\pi$
$769$	25.6142	−	18.6098i	0.923672	−	0.671087i	0.944435	+	0.328698i	$0.106610\pi$
$770$	−8.13956	+	4.40853i	−0.293329	+	0.158873i
$771$	4.61360	+	3.35198i	0.166155	+	0.120719i
$772$	1.51007	+	3.39166i	0.0543484	+	0.122069i
$773$	−0.0853617	−	0.401595i	−0.00307025	−	0.0144444i	0.976586	−	0.215128i	$-0.0690169\pi$
$773$	−0.0853617	−	0.401595i	−0.00307025	−	0.0144444i	−0.979656	+	0.200684i	$0.935684\pi$
$774$	1.24883	+	2.16303i	0.0448881	+	0.0777485i
$775$	37.4603	−	28.9672i	1.34562	−	1.04053i
$776$	−1.32893			−0.0477059
$777$	0.911130	+	3.26686i	0.0326866	+	0.117198i
$778$	16.5215	−	22.7399i	0.592326	−	0.815267i
$779$	2.84878	−	1.26836i	0.102068	−	0.0454437i
$780$	−1.70623	+	1.27907i	−0.0610930	+	0.0457982i
$781$	−8.75995	−	3.90018i	−0.313456	−	0.139559i
$782$	24.0754	+	13.8999i	0.860934	+	0.497060i
$783$	−1.71619	−	2.36214i	−0.0613317	−	0.0844159i
$784$	−3.99824	+	5.74579i	−0.142794	+	0.205207i
$785$	−3.82285	−	2.13153i	−0.136443	−	0.0760777i
$786$	−3.78035	−	4.19850i	−0.134841	−	0.149756i
$787$	6.96515	+	6.27145i	0.248281	+	0.223553i	0.783869	−	0.620926i	$-0.213243\pi$
$787$	6.96515	+	6.27145i	0.248281	+	0.223553i	−0.535588	+	0.844479i	$0.679910\pi$
$788$	14.2498	+	12.8306i	0.507627	+	0.457070i
$789$	7.26203	+	8.06530i	0.258535	+	0.287132i
$790$	−8.75817	+	1.05318i	−0.311602	+	0.0374705i
$791$	−23.7657	+	29.9675i	−0.845011	+	1.06552i
$792$	2.62079	+	3.60721i	0.0931259	+	0.128177i
$793$	8.97105	+	5.17944i	0.318571	+	0.183927i
$794$	2.66527	+	1.18665i	0.0945868	+	0.0421128i
$795$	−3.44153	−	10.0766i	−0.122059	−	0.357380i
$796$	20.8304	−	9.27430i	0.738314	−	0.328719i
$797$	9.09888	−	12.5235i	0.322299	−	0.443607i	−0.616868	−	0.787066i	$-0.711599\pi$
$797$	9.09888	−	12.5235i	0.322299	−	0.443607i	0.939167	+	0.343460i	$0.111599\pi$
$798$	0.751044	+	0.193061i	0.0265867	+	0.00683430i
$799$	−10.2611			−0.363013
$800$	0.149548	+	4.99776i	0.00528732	+	0.176698i
$801$	−26.7983	−	46.4161i	−0.946873	−	1.64003i
$802$	6.26330	+	29.4665i	0.221165	+	1.04050i
$803$	2.58866	+	5.81423i	0.0913519	+	0.205180i
$804$	−3.79114	−	2.75443i	−0.133703	−	0.0971411i
$805$	29.4046	−	8.67699i	1.03637	−	0.305824i
$806$	18.8434	−	13.6906i	0.663732	−	0.482230i
$807$	−0.720100	−	0.415750i	−0.0253487	−	0.0146351i
$808$	4.31552	−	9.69282i	0.151819	−	0.340992i
$809$	10.7559	−	11.9456i	0.378158	−	0.419987i	−0.523780	−	0.851854i	$-0.675478\pi$
$809$	10.7559	−	11.9456i	0.378158	−	0.419987i	0.901937	+	0.431867i	$0.142145\pi$
$810$	−12.9145	−	11.2831i	−0.453769	−	0.396449i
$811$	−6.61280	+	20.3521i	−0.232207	+	0.714659i	0.765273	+	0.643706i	$0.222604\pi$
$811$	−6.61280	+	20.3521i	−0.232207	+	0.714659i	−0.997480	+	0.0709530i	$0.977396\pi$
$812$	0.498454	−	3.36894i	0.0174923	−	0.118227i
$813$	−5.31748	+	1.72775i	−0.186492	+	0.0605950i
$814$	3.46108	+	3.84392i	0.121311	+	0.134729i
$815$	−3.36406	+	1.14895i	−0.117838	+	0.0402461i
$816$	−1.39192	+	1.54588i	−0.0487269	+	0.0541167i
$817$	0.658865	−	0.0692495i	0.0230508	−	0.00242273i
$818$			17.2214i			0.602134i
$819$	14.2902	−	11.8151i	0.499340	−	0.412853i
$820$	6.27469	+	6.76255i	0.219122	+	0.236158i
$821$	−32.4232	+	14.4357i	−1.13158	+	0.503810i	−0.885129	−	0.465346i	$-0.845930\pi$
$821$	−32.4232	+	14.4357i	−1.13158	+	0.503810i	−0.246447	+	0.969156i	$0.579263\pi$
$822$	2.64988	+	0.278513i	0.0924250	+	0.00971426i
$823$	8.79791	+	41.3909i	0.306676	+	1.44280i	0.813911	+	0.580989i	$0.197334\pi$
$823$	8.79791	+	41.3909i	0.306676	+	1.44280i	−0.507235	+	0.861808i	$0.669333\pi$
$824$	5.08036	−	8.79944i	0.176983	−	0.306543i
$825$	−1.15046	+	2.80705i	−0.0400538	+	0.0977289i
$826$	−9.01434	−	13.5760i	−0.313649	−	0.472369i
$827$	45.0530	+	14.6386i	1.56664	+	0.509034i	0.958573	−	0.284848i	$-0.0919431\pi$
$827$	45.0530	+	14.6386i	1.56664	+	0.509034i	0.608072	+	0.793882i	$0.291943\pi$
$828$	−6.00639	−	13.4906i	−0.208737	−	0.468830i
$829$	4.09418	−	38.9535i	0.142197	−	1.35291i	−0.657929	−	0.753080i	$-0.728567\pi$
$829$	4.09418	−	38.9535i	0.142197	−	1.35291i	0.800126	−	0.599832i	$-0.204766\pi$
$830$	3.79326	+	11.1064i	0.131666	+	0.385509i
$831$	0.591702	+	5.62967i	0.0205259	+	0.195291i
$832$			2.45934i			0.0852622i
$833$	25.6904	+	27.3885i	0.890121	+	0.948956i
$834$	−0.426697	−	1.31324i	−0.0147753	−	0.0454737i
$835$	1.71785	−	4.01908i	0.0594486	−	0.139086i
$836$	1.15683	−	0.245891i	0.0400097	−	0.00850433i
$837$	−15.9646	−	14.3746i	−0.551818	−	0.496859i
$838$	2.57415	−	12.1104i	0.0889226	−	0.418348i
$839$	8.44567	−	25.9931i	0.291577	−	0.897381i	−0.692773	−	0.721156i	$-0.743611\pi$
$839$	8.44567	−	25.9931i	0.291577	−	0.897381i	0.984350	−	0.176225i	$-0.0563888\pi$
$840$	0.177627	+	2.28718i	0.00612872	+	0.0789151i
$841$	−8.44949	−	26.0048i	−0.291362	−	0.896719i
$842$	8.24571	−	0.866659i	0.284166	−	0.0298671i
$843$	−6.65936	+	3.84478i	−0.229360	+	0.132421i
$844$	22.1737	+	9.87235i	0.763249	+	0.339820i
$845$	−14.2935	−	6.10937i	−0.491710	−	0.210169i
$846$	4.40972	+	3.20385i	0.151609	+	0.110151i
$847$	12.1290	−	19.1003i	0.416756	−	0.656292i
$848$	−11.6794	−	3.79487i	−0.401073	−	0.130316i
$849$	0.855733	−	1.48217i	0.0293687	−	0.0508681i
$850$	26.3916	+	4.78952i	0.905223	+	0.164279i
$851$	−8.56559	−	14.8360i	−0.293625	−	0.508573i
$852$	−1.76600	+	1.59012i	−0.0605023	+	0.0544765i
$853$	21.7299	−	29.9087i	0.744019	−	1.02405i	−0.254359	−	0.967110i	$-0.581864\pi$
$853$	21.7299	−	29.9087i	0.744019	−	1.02405i	0.998377	−	0.0569441i	$-0.0181357\pi$
$854$	9.87736	−	5.16021i	0.337996	−	0.176579i
$855$	−4.37012	+	2.02455i	−0.149455	+	0.0692383i
$856$	1.79374	+	17.0663i	0.0613087	+	0.583313i
$857$	−0.00363221	+	0.00209706i	−0.000124074	+	7.16342e-5i	−0.500062	−	0.865990i	$-0.666689\pi$
$857$	−0.00363221	+	0.00209706i	−0.000124074	+	7.16342e-5i	0.499938	+	0.866061i	$0.333356\pi$
$858$	−0.606915	+	1.36315i	−0.0207197	+	0.0465373i
$859$	7.79178	+	1.65619i	0.265852	+	0.0565086i	0.338909	−	0.940819i	$-0.389942\pi$
$859$	7.79178	+	1.65619i	0.265852	+	0.0565086i	−0.0730568	+	0.997328i	$0.523275\pi$
$860$	0.823841	+	1.77831i	0.0280927	+	0.0606398i
$861$	3.02326	+	2.96227i	0.103032	+	0.100954i
$862$	−1.50073	+	0.487617i	−0.0511151	+	0.0166083i
$863$	−0.0974622	+	0.458524i	−0.00331765	+	0.0156083i	−0.979775	−	0.200101i	$-0.935873\pi$
$863$	−0.0974622	+	0.458524i	−0.00331765	+	0.0156083i	0.976458	+	0.215709i	$0.0692063\pi$
$864$	2.21873	−	0.471606i	0.0754828	−	0.0160444i
$865$	−45.3643	−	13.9932i	−1.54243	−	0.475782i
$866$	22.9346	+	4.87491i	0.779351	+	0.165656i
$867$	2.68453	+	3.69493i	0.0911713	+	0.125487i
$868$	−1.56630	−	25.0082i	−0.0531636	−	0.848835i
$869$	−4.99377	+	3.62818i	−0.169402	+	0.123078i
$870$	−0.572445	−	0.958118i	−0.0194077	−	0.0324832i
$871$	−3.10666	+	29.5579i	−0.105265	+	1.00153i
$872$	13.0293	+	1.36944i	0.441229	+	0.0463750i
$873$	2.81427	−	2.53398i	0.0952486	−	0.0857622i
$874$	−3.91697			−0.132494
$875$	23.8840	−	17.4515i	0.807427	−	0.589968i
$876$	1.57728			0.0532913
$877$	28.6091	−	25.7597i	0.966060	−	0.869844i	−0.0254765	−	0.999675i	$-0.508110\pi$
$877$	28.6091	−	25.7597i	0.966060	−	0.869844i	0.991536	+	0.129831i	$0.0414436\pi$
$878$	−20.9349	−	2.20035i	−0.706520	−	0.0742583i
$879$	1.36030	−	12.9424i	0.0458817	−	0.436535i
$880$	1.79448	+	3.00348i	0.0604921	+	0.101247i
$881$	7.82788	−	5.68729i	0.263728	−	0.191610i	−0.448061	−	0.894003i	$-0.647885\pi$
$881$	7.82788	−	5.68729i	0.263728	−	0.191610i	0.711789	+	0.702393i	$0.247885\pi$
$882$	−2.48890	−	19.7916i	−0.0838058	−	0.666417i
$883$	1.25718	+	1.73036i	0.0423076	+	0.0582313i	0.829647	−	0.558289i	$-0.188542\pi$
$883$	1.25718	+	1.73036i	0.0423076	+	0.0582313i	−0.787339	+	0.616520i	$0.788542\pi$
$884$	12.9049	+	2.74302i	0.434038	+	0.0922577i
$885$	−5.10337	−	1.57420i	−0.171548	−	0.0529161i
$886$	−33.4189	+	7.10340i	−1.12273	+	0.238643i
$887$	1.46543	−	6.89429i	0.0492042	−	0.231488i	−0.946673	−	0.322195i	$-0.895579\pi$
$887$	1.46543	−	6.89429i	0.0492042	−	0.231488i	0.995878	+	0.0907072i	$0.0289127\pi$
$888$	1.21914	−	0.396123i	0.0409117	−	0.0132930i
$889$	19.0052	−	5.30056i	0.637413	−	0.177775i
$890$	−17.6787	−	38.1604i	−0.592590	−	1.27914i
$891$	−11.7378	−	2.49495i	−0.393231	−	0.0835839i
$892$	−11.9628	+	26.8690i	−0.400545	+	0.899640i
$893$	1.25209	−	0.722893i	0.0418995	−	0.0241907i
$894$	0.602400	+	5.73145i	0.0201473	+	0.191688i
$895$	2.13054	−	0.987022i	0.0712163	−	0.0329925i
$896$	2.23348	+	1.41830i	0.0746154	+	0.0473819i
$897$	2.90482	−	3.99815i	0.0969892	−	0.133494i
$898$	14.8850	−	13.4025i	0.496720	−	0.447249i
$899$	6.09539	+	10.5575i	0.203293	+	0.352113i
$900$	−9.84633	−	10.2986i	−0.328211	−	0.343286i
$901$	−32.9394	+	57.0528i	−1.09737	+	1.90070i
$902$	6.13932	+	1.99479i	0.204417	+	0.0664192i
$903$	0.416378	+	0.797005i	0.0138562	+	0.0265227i
$904$	11.6953	+	8.49710i	0.388978	+	0.282609i
$905$	−3.24000	−	1.38485i	−0.107701	−	0.0460341i
$906$	3.89757	+	1.73531i	0.129488	+	0.0576518i
$907$	−35.7635	+	20.6481i	−1.18751	+	0.685608i	−0.957739	−	0.287638i	$-0.907130\pi$
$907$	−35.7635	+	20.6481i	−1.18751	+	0.685608i	−0.229768	+	0.973245i	$0.573797\pi$
$908$	12.9054	−	1.35641i	0.428279	−	0.0450140i
$909$	9.34311	+	28.7551i	0.309892	+	0.953748i
$910$	11.9993	−	8.22862i	0.397771	−	0.272776i
$911$	−13.9255	+	42.8583i	−0.461372	+	1.41996i	0.402116	+	0.915589i	$0.368275\pi$
$911$	−13.9255	+	42.8583i	−0.461372	+	1.41996i	−0.863488	+	0.504369i	$0.831725\pi$
$912$	0.0609382	−	0.286692i	0.00201787	−	0.00949332i
$913$	6.10303	+	5.49519i	0.201981	+	0.181864i
$914$	12.5271	−	2.66272i	0.414360	−	0.0880749i
$915$	1.43540	−	3.35827i	0.0474530	−	0.111021i
$916$	−5.81227	−	17.8883i	−0.192043	−	0.591047i
$917$	24.5628	+	29.7084i	0.811136	+	0.981059i
$918$		−	12.1684i		−	0.401616i
$919$	0.310059	+	2.95002i	0.0102279	+	0.0973121i	0.998445	−	0.0557472i	$-0.0177541\pi$
$919$	0.310059	+	2.95002i	0.0102279	+	0.0973121i	−0.988217	+	0.153059i	$0.951087\pi$
$920$	−3.74521	−	10.9657i	−0.123476	−	0.361530i
$921$	−0.752013	+	7.15493i	−0.0247797	+	0.235763i
$922$	2.61929	+	5.88301i	0.0862616	+	0.193747i
$923$	14.3341	+	4.65744i	0.471813	+	0.153301i
$924$	0.887960	+	1.33731i	0.0292117	+	0.0439941i
$925$	−12.6087	−	10.6877i	−0.414573	−	0.351410i
$926$	−15.4538	+	26.7667i	−0.507842	+	0.879608i
$927$	6.01995	+	28.3216i	0.197721	+	0.930205i
$928$	−1.28015	−	0.134549i	−0.0420230	−	0.00441680i
$929$	−12.4518	+	5.54390i	−0.408531	+	0.181890i	−0.600704	−	0.799471i	$-0.705113\pi$
$929$	−12.4518	+	5.54390i	−0.408531	+	0.181890i	0.192173	+	0.981361i	$0.438446\pi$
$930$	−5.58546	−	6.01973i	−0.183154	−	0.197395i
$931$	−5.06431	−	1.53213i	−0.165976	−	0.0502134i
$932$			9.90274i			0.324375i
$933$	−8.15456	+	0.857079i	−0.266968	+	0.0280595i
$934$	13.5716	−	15.0728i	0.444075	−	0.493196i
$935$	17.7616	−	6.06627i	0.580868	−	0.198388i
$936$	−4.68942	−	5.20812i	−0.153278	−	0.170233i
$937$	27.9306	−	9.07520i	0.912453	−	0.296474i	0.185086	−	0.982722i	$-0.440744\pi$
$937$	27.9306	−	9.07520i	0.912453	−	0.296474i	0.727367	+	0.686248i	$0.240744\pi$
$938$	25.0518	+	19.8673i	0.817970	+	0.648691i
$939$	−3.63442	+	11.1856i	−0.118605	+	0.365028i
$940$	3.22095	+	2.81408i	0.105056	+	0.0917851i
$941$	−18.6666	+	20.7314i	−0.608514	+	0.675824i	−0.966133	−	0.258044i	$-0.916922\pi$
$941$	−18.6666	+	20.7314i	−0.608514	+	0.675824i	0.357619	+	0.933868i	$0.383589\pi$
$942$	−0.308724	+	0.693406i	−0.0100588	+	0.0225924i
$943$	−18.5153	−	10.6898i	−0.602942	−	0.348108i
$944$	−4.98304	+	3.62039i	−0.162184	+	0.117834i
$945$	−9.72457	−	9.24739i	−0.316340	−	0.300818i
$946$	1.10949	+	0.806095i	0.0360728	+	0.0262084i
$947$	7.94901	+	17.8538i	0.258308	+	0.580169i	0.995420	−	0.0956016i	$-0.0304775\pi$
$947$	7.94901	+	17.8538i	0.258308	+	0.580169i	−0.737112	+	0.675771i	$0.763811\pi$
$948$	0.318051	+	1.49631i	0.0103298	+	0.0485979i
$949$	−5.00179	−	8.66335i	−0.162365	−	0.281224i
$950$	−3.55777	+	1.27484i	−0.115429	+	0.0413614i
$951$	−7.84177			−0.254287
$952$	9.93333	−	10.1379i	0.321941	−	0.328570i
$953$	−2.44685	+	3.36780i	−0.0792611	+	0.109094i	−0.846807	−	0.531901i	$-0.821478\pi$
$953$	−2.44685	+	3.36780i	−0.0792611	+	0.109094i	0.767545	+	0.640995i	$0.221478\pi$
$954$	31.9694	−	14.2337i	1.03505	−	0.460833i
$955$	−6.53653	−	19.1385i	−0.211517	−	0.619308i
$956$	22.5583	+	10.0436i	0.729588	+	0.324834i
$957$	−0.676354	−	0.390493i	−0.0218634	−	0.0126229i
$958$	−22.9962	−	31.6515i	−0.742973	−	1.02261i
$959$	−17.9840	−	2.66083i	−0.580734	−	0.0859228i
$960$	0.860873	−	0.103521i	0.0277846	−	0.00334113i
$961$	39.2747	+	43.6189i	1.26692	+	1.40706i
$962$	−6.04183	−	5.44008i	−0.194796	−	0.175395i
$963$	−36.3402	−	32.7208i	−1.17105	−	1.05441i
$964$	−14.4511	−	16.0496i	−0.465440	−	0.516924i
$965$	−7.25077	−	4.04286i	−0.233410	−	0.130144i
$966$	−1.95577	−	4.94378i	−0.0629257	−	0.159063i
$967$	−18.4768	−	25.4311i	−0.594174	−	0.817810i	0.400985	−	0.916084i	$-0.368668\pi$
$967$	−18.4768	−	25.4311i	−0.594174	−	0.817810i	−0.995159	+	0.0982741i	$0.968668\pi$
$968$	−7.40606	−	4.27589i	−0.238040	−	0.137432i
$969$	−1.43639	−	0.639522i	−0.0461435	−	0.0205444i
$970$	2.37767	−	1.78241i	0.0763423	−	0.0572299i
$971$	−20.5620	+	9.15479i	−0.659866	+	0.293791i	−0.709217	−	0.704990i	$-0.750951\pi$
$971$	−20.5620	+	9.15479i	−0.659866	+	0.293791i	0.0493509	+	0.998782i	$0.484285\pi$
$972$	−5.74785	+	7.91123i	−0.184362	+	0.253753i
$973$	2.53103	+	9.07503i	0.0811412	+	0.290932i
$974$	−38.1258			−1.22163
$975$	1.33718	−	4.57693i	0.0428240	−	0.146579i
$976$	−2.10603	−	3.64775i	−0.0674123	−	0.116762i
$977$	9.77739	+	45.9990i	0.312807	+	1.47164i	0.800874	+	0.598833i	$0.204369\pi$
$977$	9.77739	+	45.9990i	0.312807	+	1.47164i	−0.488067	+	0.872806i	$0.662298\pi$
$978$	0.250739	+	0.563170i	0.00801776	+	0.0180082i
$979$	−23.8084	−	17.2978i	−0.760921	−	0.552842i
$980$	−0.552986	−	15.6427i	−0.0176645	−	0.499688i
$981$	−30.2033	+	21.9440i	−0.964318	+	0.700618i
$982$	−22.1427	−	12.7841i	−0.706601	−	0.407956i
$983$	−10.3852	+	23.3256i	−0.331237	+	0.743970i	0.668763	+	0.743475i	$0.266824\pi$
$983$	−10.3852	+	23.3256i	−0.331237	+	0.743970i	−1.00000		0.000494145i	$0.999843\pi$
$984$	1.07046	−	1.18887i	0.0341251	−	0.0378998i
$985$	−42.7039	−	3.84355i	−1.36066	−	0.122466i
$986$	−2.13384	+	6.56727i	−0.0679552	+	0.209144i
$987$	1.53757	+	1.21937i	0.0489413	+	0.0388129i
$988$	−1.76793	+	0.574434i	−0.0562452	+	0.0182752i
$989$	−3.03924	−	3.37541i	−0.0966421	−	0.107332i
$990$	−9.52714	−	2.93876i	−0.302792	−	0.0934001i
$991$	−16.5881	+	18.4229i	−0.526937	+	0.585223i	−0.946581	−	0.322466i	$-0.895488\pi$
$991$	−16.5881	+	18.4229i	−0.526937	+	0.585223i	0.419644	+	0.907689i	$0.362155\pi$
$992$	−9.41887	+	0.989963i	−0.299049	+	0.0314313i
$993$			2.57592i			0.0817444i
$994$	12.4962	−	10.3318i	0.396355	−	0.327705i
$995$	−24.8298	+	44.5317i	−0.787159	+	1.41175i
$996$	1.85930	−	0.827812i	0.0589141	−	0.0262302i
$997$	−33.8812	−	3.56106i	−1.07303	−	0.112780i	−0.448501	−	0.893782i	$-0.648042\pi$
$997$	−33.8812	−	3.56106i	−1.07303	−	0.112780i	−0.624528	+	0.781002i	$0.714709\pi$
$998$	4.48305	+	21.0911i	0.141908	+	0.667627i
$999$	−3.74927	+	6.49393i	−0.118622	+	0.205459i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.u.a.79.6	✓	160
7.4	even	3	inner	350.2.u.a.179.5	yes	160
25.19	even	10	inner	350.2.u.a.219.5	yes	160
175.144	even	30	inner	350.2.u.a.319.6	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.u.a.79.6	✓	160	1.1	even	1	trivial
350.2.u.a.179.5	yes	160	7.4	even	3	inner
350.2.u.a.219.5	yes	160	25.19	even	10	inner
350.2.u.a.319.6	yes	160	175.144	even	30	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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.u (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.743145 + 0.669131i) q^{2} +(-0.385644 - 0.0405328i) q^{3} +(0.104528 - 0.994522i) q^{4} +(1.14687 + 1.91955i) q^{5} +(0.313711 - 0.227924i) q^{6} +(-2.20412 + 1.46351i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.78736 - 0.592473i) q^{9} +O(q^{10})\)	\(q+(-0.743145 + 0.669131i) q^{2} +(-0.385644 - 0.0405328i) q^{3} +(0.104528 - 0.994522i) q^{4} +(1.14687 + 1.91955i) q^{5} +(0.313711 - 0.227924i) q^{6} +(-2.20412 + 1.46351i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-2.78736 - 0.592473i) q^{9} +(-2.13672 - 0.659099i) q^{10} +(-1.53049 + 0.325315i) q^{11} +(-0.0806214 + 0.379294i) q^{12} +(2.33897 - 0.759977i) q^{13} +(0.658695 - 2.56244i) q^{14} +(-0.364479 - 0.786749i) q^{15} +(-0.978148 - 0.207912i) q^{16} +(-2.18195 + 4.90074i) q^{17} +(2.46786 - 1.42482i) q^{18} +(-0.0790085 - 0.751716i) q^{19} +(2.02892 - 0.939941i) q^{20} +(0.909323 - 0.475056i) q^{21} +(0.919694 - 1.26585i) q^{22} +(-3.85110 + 3.46754i) q^{23} +(-0.193884 - 0.335817i) q^{24} +(-2.36937 + 4.40296i) q^{25} +(-1.22967 + 2.12985i) q^{26} +(2.15728 + 0.700943i) q^{27} +(1.22510 + 2.34502i) q^{28} +(-1.04137 - 0.756599i) q^{29} +(0.797299 + 0.340785i) q^{30} +(-8.65196 - 3.85210i) q^{31} +(0.866025 - 0.500000i) q^{32} +(0.603408 - 0.0634207i) q^{33} +(-1.65773 - 5.10197i) q^{34} +(-5.33713 - 2.55245i) q^{35} +(-0.880586 + 2.71017i) q^{36} +(-0.687314 + 3.23356i) q^{37} +(0.561711 + 0.505767i) q^{38} +(-0.932813 + 0.198275i) q^{39} +(-0.878837 + 2.05612i) q^{40} +(1.27489 + 3.92370i) q^{41} +(-0.357884 + 0.961491i) q^{42} +0.876481i q^{43} +(0.163553 + 1.55611i) q^{44} +(-2.05947 - 6.02999i) q^{45} +(0.541683 - 5.15377i) q^{46} +(0.777997 + 1.74741i) q^{47} +(0.368789 + 0.119827i) q^{48} +(2.71625 - 6.45151i) q^{49} +(-1.18537 - 4.85746i) q^{50} +(1.04010 - 1.80150i) q^{51} +(-0.511325 - 2.40560i) q^{52} +(12.2132 + 1.28366i) q^{53} +(-2.07220 + 0.922601i) q^{54} +(-2.37973 - 2.56475i) q^{55} +(-2.47955 - 0.922935i) q^{56} +0.293097i q^{57} +(1.28015 - 0.134549i) q^{58} +(4.12143 - 4.57731i) q^{59} +(-0.820538 + 0.280245i) q^{60} +(2.81842 + 3.13017i) q^{61} +(9.00722 - 2.92662i) q^{62} +(7.01077 - 2.77347i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(4.14132 + 3.61818i) q^{65} +(-0.405983 + 0.450889i) q^{66} +(-4.91535 + 11.0400i) q^{67} +(4.64582 + 2.68226i) q^{68} +(1.62570 - 1.18114i) q^{69} +(5.67419 - 1.67440i) q^{70} +(4.95797 + 3.60218i) q^{71} +(-1.15905 - 2.60327i) q^{72} +(-0.845699 - 3.97870i) q^{73} +(-1.65290 - 2.86291i) q^{74} +(1.09220 - 1.60194i) q^{75} -0.755856 q^{76} +(2.89726 - 2.95692i) q^{77} +(0.560543 - 0.771521i) q^{78} +(3.60393 - 1.60457i) q^{79} +(-0.722713 - 2.11605i) q^{80} +(7.00629 + 3.11940i) q^{81} +(-3.57289 - 2.06281i) q^{82} +(-3.08507 - 4.24624i) q^{83} +(-0.377403 - 0.953999i) q^{84} +(-11.9096 + 1.43215i) q^{85} +(-0.586480 - 0.651353i) q^{86} +(0.370930 + 0.333987i) q^{87} +(-1.16278 - 1.04697i) q^{88} +(12.5852 + 13.9773i) q^{89} +(5.56533 + 3.10310i) q^{90} +(-4.04312 + 5.09819i) q^{91} +(3.04600 + 4.19246i) q^{92} +(3.18044 + 1.83623i) q^{93} +(-1.74741 - 0.777997i) q^{94} +(1.35235 - 1.01378i) q^{95} +(-0.354243 + 0.157719i) q^{96} +(-0.781127 + 1.07513i) q^{97} +(2.29833 + 6.61193i) q^{98} +4.45876 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 20 q^{4} - 2 q^{5} + 8 q^{6} - 20 q^{9}+O(q^{10}) \) 160 * q - 20 * q^4 - 2 * q^5 + 8 * q^6 - 20 * q^9	\( 160 q - 20 q^{4} - 2 q^{5} + 8 q^{6} - 20 q^{9} - 2 q^{10} - 6 q^{11} - 16 q^{15} + 20 q^{16} - 20 q^{17} + 4 q^{19} - 4 q^{20} - 12 q^{21} + 40 q^{22} - 30 q^{23} - 16 q^{24} + 48 q^{26} - 120 q^{27} - 10 q^{28} + 24 q^{29} - 26 q^{30} - 6 q^{31} - 50 q^{33} - 16 q^{34} - 36 q^{35} - 40 q^{36} - 32 q^{39} + 2 q^{40} + 68 q^{41} + 10 q^{42} - 4 q^{44} + 16 q^{45} + 12 q^{46} + 24 q^{49} + 32 q^{50} + 12 q^{51} - 20 q^{53} + 16 q^{54} + 24 q^{55} + 24 q^{59} + 2 q^{60} - 8 q^{61} + 40 q^{64} + 2 q^{65} - 116 q^{69} - 118 q^{70} + 68 q^{71} - 40 q^{73} + 16 q^{74} + 196 q^{75} - 32 q^{76} - 80 q^{77} - 8 q^{79} - 2 q^{80} + 64 q^{81} - 160 q^{83} - 18 q^{84} + 12 q^{85} + 12 q^{86} - 10 q^{88} + 54 q^{89} + 44 q^{91} - 40 q^{92} - 16 q^{95} - 4 q^{96} - 20 q^{97} + 40 q^{98} - 24 q^{99}+O(q^{100}) \) 160 * q - 20 * q^4 - 2 * q^5 + 8 * q^6 - 20 * q^9 - 2 * q^10 - 6 * q^11 - 16 * q^15 + 20 * q^16 - 20 * q^17 + 4 * q^19 - 4 * q^20 - 12 * q^21 + 40 * q^22 - 30 * q^23 - 16 * q^24 + 48 * q^26 - 120 * q^27 - 10 * q^28 + 24 * q^29 - 26 * q^30 - 6 * q^31 - 50 * q^33 - 16 * q^34 - 36 * q^35 - 40 * q^36 - 32 * q^39 + 2 * q^40 + 68 * q^41 + 10 * q^42 - 4 * q^44 + 16 * q^45 + 12 * q^46 + 24 * q^49 + 32 * q^50 + 12 * q^51 - 20 * q^53 + 16 * q^54 + 24 * q^55 + 24 * q^59 + 2 * q^60 - 8 * q^61 + 40 * q^64 + 2 * q^65 - 116 * q^69 - 118 * q^70 + 68 * q^71 - 40 * q^73 + 16 * q^74 + 196 * q^75 - 32 * q^76 - 80 * q^77 - 8 * q^79 - 2 * q^80 + 64 * q^81 - 160 * q^83 - 18 * q^84 + 12 * q^85 + 12 * q^86 - 10 * q^88 + 54 * q^89 + 44 * q^91 - 40 * q^92 - 16 * q^95 - 4 * q^96 - 20 * q^97 + 40 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

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