LMFDB - Embedded newform 930.2.bt.a.43.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(13,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([0, 45, 22]))

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

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

chi := DirichletCharacter("930.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bt (of order $60$, degree $16$, 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:	$256$
Relative dimension:	$16$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			43.2
Character	$\chi$	$=$	930.43
Dual form			930.2.bt.a.757.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.987688 + 0.156434i) q^{2} +(0.933580 - 0.358368i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-1.92766 + 1.13319i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.0854612 + 1.63070i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(0.743145 - 0.669131i) q^{9} +O(q^{10})$	\(q+(-0.987688 + 0.156434i) q^{2} +(0.933580 - 0.358368i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-1.92766 + 1.13319i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.0854612 + 1.63070i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(0.743145 - 0.669131i) q^{9} +(1.72666 - 1.42079i) q^{10} +(0.807342 - 3.79825i) q^{11} +(0.777146 - 0.629320i) q^{12} +(1.88665 + 1.52778i) q^{13} +(-0.339506 - 1.59725i) q^{14} +(-1.39353 + 1.74873i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-0.608621 - 0.395243i) q^{17} +(-0.629320 + 0.777146i) q^{18} +(2.72503 + 0.286412i) q^{19} +(-1.48314 + 1.67341i) q^{20} +(0.664174 + 1.49176i) q^{21} +(-0.203226 + 3.87778i) q^{22} +(-0.552207 - 1.08377i) q^{23} +(-0.669131 + 0.743145i) q^{24} +(2.43177 - 4.36881i) q^{25} +(-2.10242 - 1.21383i) q^{26} +(0.453990 - 0.891007i) q^{27} +(0.585192 + 1.52448i) q^{28} +(7.01443 + 5.09628i) q^{29} +(1.10281 - 1.94520i) q^{30} +(2.09002 + 5.16060i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.607451 - 3.83529i) q^{33} +(0.662958 + 0.295168i) q^{34} +(-2.01263 - 3.04659i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-2.96622 + 11.0701i) q^{37} +(-2.73628 + 0.143402i) q^{38} +(2.30885 + 0.750191i) q^{39} +(1.20310 - 1.88482i) q^{40} +(-9.46431 + 4.21378i) q^{41} +(-0.889360 - 1.36949i) q^{42} +(6.32993 + 7.81682i) q^{43} +(-0.405895 - 3.86183i) q^{44} +(-0.674283 + 2.13198i) q^{45} +(0.714948 + 0.984041i) q^{46} +(-1.01179 + 6.38818i) q^{47} +(0.544639 - 0.838671i) q^{48} +(4.30978 - 0.452977i) q^{49} +(-1.71840 + 4.69543i) q^{50} +(-0.709840 - 0.150881i) q^{51} +(2.26642 + 0.869999i) q^{52} +(13.5912 + 0.712285i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(2.74784 + 8.23661i) q^{55} +(-0.816467 - 1.41416i) q^{56} +(2.64667 - 0.709174i) q^{57} +(-7.72530 - 3.93624i) q^{58} +(4.49325 - 10.0920i) q^{59} +(-0.784938 + 2.09377i) q^{60} -0.225951i q^{61} +(-2.87158 - 4.77012i) q^{62} +(1.15466 + 1.15466i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-5.36810 - 0.807118i) q^{65} +(1.19994 + 3.69305i) q^{66} +(-3.44220 - 12.8465i) q^{67} +(-0.700970 - 0.187824i) q^{68} +(-0.903918 - 0.813891i) q^{69} +(2.46444 + 2.69424i) q^{70} +(-4.00586 - 4.44895i) q^{71} +(-0.358368 + 0.933580i) q^{72} +(0.612204 - 0.397570i) q^{73} +(1.19796 - 11.3978i) q^{74} +(0.704615 - 4.95010i) q^{75} +(2.68016 - 0.569686i) q^{76} +(6.26278 + 0.991927i) q^{77} +(-2.39778 - 0.379771i) q^{78} +(-2.92054 + 0.620780i) q^{79} +(-0.893442 + 2.04982i) q^{80} +(0.104528 - 0.994522i) q^{81} +(8.68861 - 5.64245i) q^{82} +(-0.372853 + 0.971315i) q^{83} +(1.09265 + 1.21351i) q^{84} +(1.62110 + 0.0722142i) q^{85} +(-7.47482 - 6.73036i) q^{86} +(8.37488 + 2.24404i) q^{87} +(1.00502 + 3.75079i) q^{88} +(1.38312 + 4.25682i) q^{89} +(0.332466 - 2.21121i) q^{90} +(-2.33011 + 3.20713i) q^{91} +(-0.860083 - 0.860083i) q^{92} +(3.80059 + 4.06884i) q^{93} -6.46781i q^{94} +(-5.57749 + 2.53586i) q^{95} +(-0.406737 + 0.913545i) q^{96} +(14.8275 + 7.55496i) q^{97} +(-4.18586 + 1.12160i) q^{98} +(-1.94155 - 3.36286i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 8 q^{7}+O(q^{10}) $ 256 * q + 8 * q^7	$ 256 q + 8 q^{7} + 4 q^{10} - 24 q^{14} - 8 q^{15} + 64 q^{16} + 36 q^{17} - 40 q^{19} + 12 q^{20} - 16 q^{21} + 8 q^{22} - 32 q^{24} + 20 q^{25} + 4 q^{28} - 16 q^{29} - 8 q^{31} - 4 q^{33} - 24 q^{35} + 128 q^{36} + 4 q^{37} + 4 q^{38} + 48 q^{41} + 32 q^{42} - 24 q^{43} + 4 q^{44} - 12 q^{45} - 20 q^{46} - 168 q^{47} - 40 q^{49} + 48 q^{50} - 64 q^{53} + 64 q^{54} + 64 q^{55} + 28 q^{57} + 68 q^{58} - 24 q^{59} + 4 q^{62} + 4 q^{63} - 60 q^{65} + 12 q^{66} - 76 q^{67} - 4 q^{68} + 12 q^{69} - 16 q^{70} - 48 q^{71} + 52 q^{73} + 68 q^{74} + 48 q^{75} + 48 q^{76} + 84 q^{77} - 56 q^{79} - 32 q^{81} - 32 q^{82} + 136 q^{83} + 68 q^{85} + 24 q^{86} + 20 q^{87} + 56 q^{88} - 224 q^{89} + 40 q^{91} - 48 q^{93} - 4 q^{95} + 8 q^{97} + 64 q^{98} + 4 q^{99}+O(q^{100}) $ 256 * q + 8 * q^7 + 4 * q^10 - 24 * q^14 - 8 * q^15 + 64 * q^16 + 36 * q^17 - 40 * q^19 + 12 * q^20 - 16 * q^21 + 8 * q^22 - 32 * q^24 + 20 * q^25 + 4 * q^28 - 16 * q^29 - 8 * q^31 - 4 * q^33 - 24 * q^35 + 128 * q^36 + 4 * q^37 + 4 * q^38 + 48 * q^41 + 32 * q^42 - 24 * q^43 + 4 * q^44 - 12 * q^45 - 20 * q^46 - 168 * q^47 - 40 * q^49 + 48 * q^50 - 64 * q^53 + 64 * q^54 + 64 * q^55 + 28 * q^57 + 68 * q^58 - 24 * q^59 + 4 * q^62 + 4 * q^63 - 60 * q^65 + 12 * q^66 - 76 * q^67 - 4 * q^68 + 12 * q^69 - 16 * q^70 - 48 * q^71 + 52 * q^73 + 68 * q^74 + 48 * q^75 + 48 * q^76 + 84 * q^77 - 56 * q^79 - 32 * q^81 - 32 * q^82 + 136 * q^83 + 68 * q^85 + 24 * q^86 + 20 * q^87 + 56 * q^88 - 224 * q^89 + 40 * q^91 - 48 * q^93 - 4 * q^95 + 8 * q^97 + 64 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{19}{30}\right)$

Coefficient data

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

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

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

$2$	−0.987688	+	0.156434i	−0.698401	+	0.110616i
$2$	−0.987688	+	0.156434i	−0.698401	+	0.110616i
$3$	0.933580	−	0.358368i	0.539003	−	0.206904i
$3$	0.933580	−	0.358368i	0.539003	−	0.206904i
$4$	0.951057	−	0.309017i	0.475528	−	0.154508i
$5$	−1.92766	+	1.13319i	−0.862077	+	0.506777i
$5$	−1.92766	+	1.13319i	−0.862077	+	0.506777i
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	0.0854612	+	1.63070i	0.0323013	+	0.616346i	0.966040	+	0.258391i	$0.0831923\pi$
$7$	0.0854612	+	1.63070i	0.0323013	+	0.616346i	−0.933739	+	0.357954i	$0.883474\pi$
$8$	−0.891007	+	0.453990i	−0.315018	+	0.160510i
$9$	0.743145	−	0.669131i	0.247715	−	0.223044i
$10$	1.72666	−	1.42079i	0.546018	−	0.449293i
$11$	0.807342	−	3.79825i	0.243423	−	1.14521i	−0.671317	−	0.741170i	$-0.734271\pi$
$11$	0.807342	−	3.79825i	0.243423	−	1.14521i	0.914740	−	0.404044i	$-0.132396\pi$
$12$	0.777146	−	0.629320i	0.224343	−	0.181669i
$13$	1.88665	+	1.52778i	0.523263	+	0.423730i	0.854217	−	0.519917i	$-0.174037\pi$
$13$	1.88665	+	1.52778i	0.523263	+	0.423730i	−0.330954	+	0.943647i	$0.607370\pi$
$14$	−0.339506	−	1.59725i	−0.0907369	−	0.426883i
$15$	−1.39353	+	1.74873i	−0.359808	+	0.451521i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	−0.608621	−	0.395243i	−0.147612	−	0.0958606i	0.468720	−	0.883347i	$-0.344715\pi$
$17$	−0.608621	−	0.395243i	−0.147612	−	0.0958606i	−0.616332	+	0.787486i	$0.711382\pi$
$18$	−0.629320	+	0.777146i	−0.148332	+	0.183175i
$19$	2.72503	+	0.286412i	0.625164	+	0.0657074i	0.411813	−	0.911268i	$-0.364896\pi$
$19$	2.72503	+	0.286412i	0.625164	+	0.0657074i	0.213351	+	0.976976i	$0.431562\pi$
$20$	−1.48314	+	1.67341i	−0.331641	+	0.374185i
$21$	0.664174	+	1.49176i	0.144935	+	0.325529i
$22$	−0.203226	+	3.87778i	−0.0433279	+	0.826745i
$23$	−0.552207	−	1.08377i	−0.115143	−	0.225981i	0.826242	−	0.563316i	$-0.190475\pi$
$23$	−0.552207	−	1.08377i	−0.115143	−	0.225981i	−0.941385	+	0.337335i	$0.890475\pi$
$24$	−0.669131	+	0.743145i	−0.136586	+	0.151694i
$25$	2.43177	−	4.36881i	0.486355	−	0.873761i
$26$	−2.10242	−	1.21383i	−0.412319	−	0.238053i
$27$	0.453990	−	0.891007i	0.0873705	−	0.171474i
$28$	0.585192	+	1.52448i	0.110591	+	0.288099i
$29$	7.01443	+	5.09628i	1.30255	+	0.946356i	0.999977	−	0.00677144i	$-0.00215543\pi$
$29$	7.01443	+	5.09628i	1.30255	+	0.946356i	0.302570	+	0.953127i	$0.402155\pi$
$30$	1.10281	−	1.94520i	0.201345	−	0.355143i
$31$	2.09002	+	5.16060i	0.375378	+	0.926872i
$31$	2.09002	+	5.16060i	0.375378	+	0.926872i
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−0.607451	−	3.83529i	−0.105744	−	0.667639i
$34$	0.662958	+	0.295168i	0.113696	+	0.0506209i
$35$	−2.01263	−	3.04659i	−0.340196	−	0.514968i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−2.96622	+	11.0701i	−0.487644	+	1.81991i	0.0802047	+	0.996778i	$0.474443\pi$
$37$	−2.96622	+	11.0701i	−0.487644	+	1.81991i	−0.567848	+	0.823133i	$0.692224\pi$
$38$	−2.73628	+	0.143402i	−0.443884	+	0.0232630i
$39$	2.30885	+	0.750191i	0.369712	+	0.120127i
$40$	1.20310	−	1.88482i	0.190228	−	0.298016i
$41$	−9.46431	+	4.21378i	−1.47808	+	0.658082i	−0.978134	−	0.207976i	$-0.933312\pi$
$41$	−9.46431	+	4.21378i	−1.47808	+	0.658082i	−0.499943	+	0.866058i	$0.666646\pi$
$42$	−0.889360	−	1.36949i	−0.137231	−	0.211318i
$43$	6.32993	+	7.81682i	0.965306	+	1.19205i	0.981359	+	0.192182i	$0.0615565\pi$
$43$	6.32993	+	7.81682i	0.965306	+	1.19205i	−0.0160533	+	0.999871i	$0.505110\pi$
$44$	−0.405895	−	3.86183i	−0.0611909	−	0.582193i
$45$	−0.674283	+	2.13198i	−0.100516	+	0.317817i
$46$	0.714948	+	0.984041i	0.105413	+	0.145089i
$47$	−1.01179	+	6.38818i	−0.147584	+	0.931812i	0.797104	+	0.603842i	$0.206364\pi$
$47$	−1.01179	+	6.38818i	−0.147584	+	0.931812i	−0.944688	+	0.327969i	$0.893636\pi$
$48$	0.544639	−	0.838671i	0.0786119	−	0.121052i
$49$	4.30978	−	0.452977i	0.615683	−	0.0647109i
$50$	−1.71840	+	4.69543i	−0.243019	+	0.664035i
$51$	−0.709840	−	0.150881i	−0.0993974	−	0.0211276i
$52$	2.26642	+	0.869999i	0.314296	+	0.120647i
$53$	13.5912	+	0.712285i	1.86689	+	0.0978398i	0.952046	−	0.305956i	$-0.0989761\pi$
$53$	13.5912	+	0.712285i	1.86689	+	0.0978398i	0.914849	+	0.403796i	$0.132309\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$	2.74784	+	8.23661i	0.370519	+	1.11062i
$56$	−0.816467	−	1.41416i	−0.109105	−	0.188975i
$57$	2.64667	−	0.709174i	0.350560	−	0.0939324i
$58$	−7.72530	−	3.93624i	−1.01438	−	0.516854i
$59$	4.49325	−	10.0920i	0.584971	−	1.31387i	−0.342340	−	0.939576i	$-0.611220\pi$
$59$	4.49325	−	10.0920i	0.584971	−	1.31387i	0.927311	−	0.374291i	$-0.122114\pi$
$60$	−0.784938	+	2.09377i	−0.101335	+	0.270305i
$61$		−	0.225951i		−	0.0289300i	−0.999895	−	0.0144650i	$-0.995395\pi$
$61$		−	0.225951i		−	0.0289300i	0.999895	−	0.0144650i	$-0.00460452\pi$
$62$	−2.87158	−	4.77012i	−0.364691	−	0.605805i
$63$	1.15466	+	1.15466i	0.145473	+	0.145473i
$64$	0.587785	−	0.809017i	0.0734732	−	0.101127i
$65$	−5.36810	−	0.807118i	−0.665830	−	0.100111i
$66$	1.19994	+	3.69305i	0.147703	+	0.454583i
$67$	−3.44220	−	12.8465i	−0.420532	−	1.56945i	−0.773491	−	0.633807i	$-0.781491\pi$
$67$	−3.44220	−	12.8465i	−0.420532	−	1.56945i	0.352960	−	0.935638i	$-0.385175\pi$
$68$	−0.700970	−	0.187824i	−0.0850051	−	0.0227771i
$69$	−0.903918	−	0.813891i	−0.108819	−	0.0979810i
$70$	2.46444	+	2.69424i	0.294557	+	0.322023i
$71$	−4.00586	−	4.44895i	−0.475408	−	0.527994i	0.456969	−	0.889483i	$-0.348935\pi$
$71$	−4.00586	−	4.44895i	−0.475408	−	0.527994i	−0.932376	+	0.361489i	$0.882268\pi$
$72$	−0.358368	+	0.933580i	−0.0422341	+	0.110024i
$73$	0.612204	−	0.397570i	0.0716531	−	0.0465320i	−0.508315	−	0.861171i	$-0.669732\pi$
$73$	0.612204	−	0.397570i	0.0716531	−	0.0465320i	0.579968	+	0.814639i	$0.303065\pi$
$74$	1.19796	−	11.3978i	0.139260	−	1.32497i
$75$	0.704615	−	4.95010i	0.0813620	−	0.571589i
$76$	2.68016	−	0.569686i	0.307436	−	0.0653474i
$77$	6.26278	+	0.991927i	0.713710	+	0.113041i
$78$	−2.39778	−	0.379771i	−0.271495	−	0.0430006i
$79$	−2.92054	+	0.620780i	−0.328587	+	0.0698433i	−0.369251	−	0.929330i	$-0.620386\pi$
$79$	−2.92054	+	0.620780i	−0.328587	+	0.0698433i	0.0406646	+	0.999173i	$0.487052\pi$
$80$	−0.893442	+	2.04982i	−0.0998898	+	0.229177i
$81$	0.104528	−	0.994522i	0.0116143	−	0.110502i
$82$	8.68861	−	5.64245i	0.959496	−	0.623104i
$83$	−0.372853	+	0.971315i	−0.0409259	+	0.106616i	−0.952520	−	0.304475i	$-0.901519\pi$
$83$	−0.372853	+	0.971315i	−0.0409259	+	0.106616i	0.911594	+	0.411091i	$0.134852\pi$
$84$	1.09265	+	1.21351i	0.119218	+	0.132404i
$85$	1.62110	+	0.0722142i	0.175833	+	0.00783273i
$86$	−7.47482	−	6.73036i	−0.806031	−	0.725753i
$87$	8.37488	+	2.24404i	0.897881	+	0.240587i
$88$	1.00502	+	3.75079i	0.107136	+	0.399835i
$89$	1.38312	+	4.25682i	0.146611	+	0.451222i	0.997215	−	0.0745854i	$-0.0237633\pi$
$89$	1.38312	+	4.25682i	0.146611	+	0.451222i	−0.850604	+	0.525807i	$0.823763\pi$
$90$	0.332466	−	2.21121i	0.0350450	−	0.233082i
$91$	−2.33011	+	3.20713i	−0.244262	+	0.336198i
$92$	−0.860083	−	0.860083i	−0.0896699	−	0.0896699i
$93$	3.80059	+	4.06884i	0.394103	+	0.421919i
$94$		−	6.46781i		−	0.667103i
$95$	−5.57749	+	2.53586i	−0.572239	+	0.260174i
$96$	−0.406737	+	0.913545i	−0.0415124	+	0.0932383i
$97$	14.8275	+	7.55496i	1.50550	+	0.767090i	0.995650	−	0.0931730i	$-0.0297010\pi$
$97$	14.8275	+	7.55496i	1.50550	+	0.767090i	0.509850	+	0.860263i	$0.329701\pi$
$98$	−4.18586	+	1.12160i	−0.422836	+	0.113299i
$99$	−1.94155	−	3.36286i	−0.195133	−	0.337981i
$100$	0.962718	−	4.90644i	0.0962718	−	0.490644i
$101$	0.722845	−	2.22469i	0.0719258	−	0.221365i	−0.908631	−	0.417600i	$-0.862871\pi$
$101$	0.722845	−	2.22469i	0.0719258	−	0.221365i	0.980557	+	0.196235i	$0.0628715\pi$
$102$	0.724703	+	0.0379801i	0.0717563	+	0.00376059i
$103$	18.0724	+	6.93733i	1.78072	+	0.683556i	0.998137	+	0.0610145i	$0.0194336\pi$
$103$	18.0724	+	6.93733i	1.78072	+	0.683556i	0.782587	+	0.622541i	$0.213900\pi$
$104$	−2.37462	−	0.504741i	−0.232851	−	0.0494939i
$105$	−2.97075	−	2.12298i	−0.289915	−	0.207181i
$106$	−13.5353	+	1.42262i	−1.31466	+	0.138177i
$107$	−9.46654	+	14.5772i	−0.915165	+	1.40923i	−0.00273543	+	0.999996i	$0.500871\pi$
$107$	−9.46654	+	14.5772i	−0.915165	+	1.40923i	−0.912429	+	0.409234i	$0.865796\pi$
$108$	0.156434	−	0.987688i	0.0150529	−	0.0950404i
$109$	−11.2435	−	15.4753i	−1.07693	−	1.48226i	−0.862858	−	0.505446i	$-0.831328\pi$
$109$	−11.2435	−	15.4753i	−1.07693	−	1.48226i	−0.214070	−	0.976818i	$-0.568672\pi$
$110$	−4.00250	−	7.70535i	−0.381623	−	0.734676i
$111$	1.19796	+	11.3978i	0.113705	+	1.08183i
$112$	1.02764	+	1.26903i	0.0971028	+	0.119912i
$113$	−0.441037	−	0.679137i	−0.0414893	−	0.0638879i	0.817317	−	0.576188i	$-0.195460\pi$
$113$	−0.441037	−	0.679137i	−0.0414893	−	0.0638879i	−0.858807	+	0.512300i	$0.828794\pi$
$114$	−2.50315	+	1.11447i	−0.234441	+	0.104380i
$115$	2.29258	+	1.46339i	0.213784	+	0.136461i
$116$	8.24596	+	2.67927i	0.765618	+	0.248764i
$117$	2.42434	−	0.127054i	0.224130	−	0.0117462i
$118$	−2.85919	+	10.6706i	−0.263210	+	0.982313i
$119$	0.592509	−	1.02625i	0.0543152	−	0.0940766i
$120$	0.447736	−	2.19078i	0.0408726	−	0.199990i
$121$	−3.72587	−	1.65886i	−0.338715	−	0.150806i
$122$	0.0353465	+	0.223169i	0.00320012	+	0.0202048i
$123$	−7.32561	+	7.32561i	−0.660528	+	0.660528i
$124$	3.58244	+	4.26217i	0.321713	+	0.382755i
$125$	0.263036	+	11.1772i	0.0235267	+	0.999723i
$126$	−1.32107	−	0.959815i	−0.117690	−	0.0855071i
$127$	−7.06189	−	18.3969i	−0.626642	−	1.63246i	−0.766469	−	0.642281i	$-0.777988\pi$
$127$	−7.06189	−	18.3969i	−0.626642	−	1.63246i	0.139828	−	0.990176i	$-0.455345\pi$
$128$	−0.453990	+	0.891007i	−0.0401275	+	0.0787546i
$129$	8.71080	+	5.02918i	0.766943	+	0.442795i
$130$	5.42827	−	0.0425745i	0.476090	−	0.00373403i
$131$	−4.57225	+	5.07800i	−0.399480	+	0.443667i	−0.909003	−	0.416790i	$-0.863155\pi$
$131$	−4.57225	+	5.07800i	−0.399480	+	0.443667i	0.509523	+	0.860457i	$0.329822\pi$
$132$	−1.76289	−	3.45987i	−0.153440	−	0.301143i
$133$	−0.234167	+	4.46817i	−0.0203048	+	0.387439i
$134$	5.40945	+	12.1498i	0.467305	+	1.04958i
$135$	0.134536	+	2.23202i	0.0115790	+	0.192101i
$136$	0.721722	+	0.0758561i	0.0618872	+	0.00650460i
$137$	−4.48631	+	5.54013i	−0.383291	+	0.473325i	−0.931880	−	0.362767i	$-0.881832\pi$
$137$	−4.48631	+	5.54013i	−0.383291	+	0.473325i	0.548589	+	0.836092i	$0.315165\pi$
$138$	1.02011	+	0.662467i	0.0868375	+	0.0563929i
$139$	8.32445	−	6.04807i	0.706071	−	0.512991i	−0.175833	−	0.984420i	$-0.556262\pi$
$139$	8.32445	−	6.04807i	0.706071	−	0.512991i	0.881904	+	0.471430i	$0.156262\pi$
$140$	−2.85557	−	2.27555i	−0.241340	−	0.192319i
$141$	1.34473	+	6.32647i	0.113247	+	0.532785i
$142$	4.65251	+	3.76753i	0.390430	+	0.316164i
$143$	7.32606	−	5.93253i	0.612636	−	0.496103i
$144$	0.207912	−	0.978148i	0.0173260	−	0.0815123i
$145$	−19.2965	−	1.87525i	−1.60249	−	0.155731i
$146$	−0.542473	+	0.488445i	−0.0448954	+	0.0404240i
$147$	3.86120	−	1.96738i	0.318466	−	0.162267i
$148$	0.599801	+	11.4449i	0.0493034	+	0.940764i
$149$	8.07476	−	4.66196i	0.661510	−	0.381923i	−0.131342	−	0.991337i	$-0.541929\pi$
$149$	8.07476	−	4.66196i	0.661510	−	0.381923i	0.792852	+	0.609414i	$0.208595\pi$
$150$	0.0784262	+	4.99938i	0.00640348	+	0.408198i
$151$	9.70900	−	3.15464i	0.790107	−	0.256721i	0.113957	−	0.993486i	$-0.463647\pi$
$151$	9.70900	−	3.15464i	0.790107	−	0.256721i	0.676150	+	0.736764i	$0.263647\pi$
$152$	−2.55804	+	0.981941i	−0.207485	+	0.0796460i
$153$	−0.716763	+	0.113524i	−0.0579469	+	0.00917788i
$154$	−6.34085			−0.510960
$155$	−9.87678	−	7.57953i	−0.793322	−	0.608802i
$156$	2.42767			0.194369
$157$	−17.5735	+	2.78337i	−1.40252	+	0.222137i	−0.811421	−	0.584462i	$-0.801306\pi$
$157$	−17.5735	+	2.78337i	−1.40252	+	0.222137i	−0.591099	+	0.806599i	$0.701306\pi$
$158$	2.78747	−	1.07001i	0.221760	−	0.0851255i
$159$	12.9437	−	4.20567i	1.02651	−	0.333532i
$160$	0.561780	−	2.16435i	0.0444126	−	0.171107i
$161$	1.72011	−	0.993103i	0.135563	−	0.0782675i
$162$	0.0523360	+	0.998630i	0.00411190	+	0.0784597i
$163$	−8.67350	+	4.41937i	−0.679361	+	0.346152i	−0.759385	−	0.650641i	$-0.774500\pi$
$163$	−8.67350	+	4.41937i	−0.679361	+	0.346152i	0.0800244	+	0.996793i	$0.474500\pi$
$164$	−7.69896	+	6.93218i	−0.601188	+	0.541312i
$165$	5.51707	+	6.70480i	0.429503	+	0.521968i
$166$	0.216315	−	1.01768i	0.0167893	−	0.0789875i
$167$	2.79720	−	2.26513i	0.216454	−	0.175281i	−0.514961	−	0.857214i	$-0.672194\pi$
$167$	2.79720	−	2.26513i	0.216454	−	0.175281i	0.731415	+	0.681933i	$0.238860\pi$
$168$	−1.26903	−	1.02764i	−0.0979077	−	0.0792841i
$169$	−1.47751	−	6.95113i	−0.113654	−	0.534702i
$170$	−1.61244	+	0.182271i	−0.123669	+	0.0139796i
$171$	2.21674	−	1.61055i	0.169518	−	0.123162i
$172$	8.43565	+	5.47818i	0.643213	+	0.417707i
$173$	−2.67378	+	3.30184i	−0.203283	+	0.251034i	−0.868585	−	0.495541i	$-0.834970\pi$
$173$	−2.67378	+	3.30184i	−0.203283	+	0.251034i	0.665301	+	0.746575i	$0.268303\pi$
$174$	−8.62282	−	0.906294i	−0.653694	−	0.0687060i
$175$	7.33202	+	3.59212i	0.554249	+	0.271539i
$176$	−1.57940	−	3.54739i	−0.119052	−	0.267394i
$177$	0.578159	−	11.0319i	0.0434571	−	0.829211i
$178$	−2.03201	−	3.98804i	−0.152305	−	0.298916i
$179$	−3.07481	+	3.41492i	−0.229822	+	0.255243i	−0.847015	−	0.531568i	$-0.821603\pi$
$179$	−3.07481	+	3.41492i	−0.229822	+	0.255243i	0.617194	+	0.786811i	$0.288270\pi$
$180$	0.0175372	+	2.23600i	0.00130714	+	0.166662i
$181$	−7.91218	−	4.56810i	−0.588108	−	0.339544i	0.176241	−	0.984347i	$-0.443606\pi$
$181$	−7.91218	−	4.56810i	−0.588108	−	0.339544i	−0.764349	+	0.644803i	$0.776940\pi$
$182$	1.79972	−	3.53215i	0.133404	−	0.261820i
$183$	−0.0809736	−	0.210943i	−0.00598574	−	0.0155934i
$184$	0.984041	+	0.714948i	0.0725445	+	0.0527066i
$185$	−6.82661	−	24.7007i	−0.501902	−	1.81603i
$186$	−4.39031	−	3.42420i	−0.321913	−	0.251075i
$187$	−1.99260	+	1.99260i	−0.145713	+	0.145713i
$188$	1.01179	+	6.38818i	0.0737922	+	0.465906i
$189$	1.49176	+	0.664174i	0.108510	+	0.0483116i
$190$	5.11213	−	3.37715i	0.370873	−	0.245004i
$191$	8.46597	−	14.6635i	0.612576	−	1.06101i	−0.378229	−	0.925712i	$-0.623467\pi$
$191$	8.46597	−	14.6635i	0.612576	−	1.06101i	0.990805	−	0.135301i	$-0.0432000\pi$
$192$	0.258819	−	0.965926i	0.0186787	−	0.0697097i
$193$	−9.84343	+	0.515872i	−0.708545	+	0.0371333i	−0.403205	−	0.915110i	$-0.632104\pi$
$193$	−9.84343	+	0.515872i	−0.708545	+	0.0371333i	−0.305341	+	0.952243i	$0.598770\pi$
$194$	−15.8268	−	5.14243i	−1.13630	−	0.369205i
$195$	−5.30079	+	1.17024i	−0.379598	+	0.0838029i
$196$	3.95887	−	1.76260i	0.282776	−	0.125900i
$197$	−4.76120	−	7.33161i	−0.339222	−	0.522356i	0.627355	−	0.778733i	$-0.284138\pi$
$197$	−4.76120	−	7.33161i	−0.339222	−	0.522356i	−0.966577	+	0.256378i	$0.917471\pi$
$198$	2.44371	+	3.01774i	0.173667	+	0.214461i
$199$	−0.515893	−	4.90840i	−0.0365707	−	0.347947i	−0.997472	−	0.0710568i	$-0.977363\pi$
$199$	−0.515893	−	4.90840i	−0.0365707	−	0.347947i	0.960902	−	0.276890i	$-0.0893038\pi$
$200$	−0.183329	+	4.99664i	−0.0129633	+	0.353316i
$201$	−7.81733	−	10.7596i	−0.551392	−	0.758926i
$202$	−0.365928	+	2.31038i	−0.0257466	+	0.162558i
$203$	−7.71103	+	11.8739i	−0.541208	+	0.833388i
$204$	−0.721722	+	0.0758561i	−0.0505307	+	0.00531099i
$205$	13.4690	−	18.8476i	0.940716	−	1.31637i
$206$	−18.9351	−	4.02478i	−1.31927	−	0.280420i
$207$	−1.13555	−	0.435898i	−0.0789264	−	0.0302970i
$208$	2.42434	+	0.127054i	0.168098	+	0.00880964i
$209$	3.28789	−	10.1191i	0.227428	−	0.699952i
$210$	3.26628	+	1.63211i	0.225395	+	0.112626i
$211$	5.68108	+	9.83992i	0.391102	+	0.677408i	0.992595	−	0.121470i	$-0.0387607\pi$
$211$	5.68108	+	9.83992i	0.391102	+	0.677408i	−0.601493	+	0.798878i	$0.705427\pi$
$212$	13.1461	−	3.52249i	0.902878	−	0.241925i
$213$	−5.33415	−	2.71789i	−0.365490	−	0.186226i
$214$	7.06962	−	15.8786i	0.483269	−	1.08544i
$215$	−21.0599	−	7.89519i	−1.43627	−	0.538448i
$216$			1.00000i			0.0680414i
$217$	−8.23676	+	3.84922i	−0.559148	+	0.261302i
$218$	13.5259	+	13.5259i	0.916090	+	0.916090i
$219$	0.429065	−	0.590558i	0.0289935	−	0.0399062i
$220$	5.15860	+	6.98435i	0.347793	+	0.470885i
$221$	−0.544412	−	1.67553i	−0.0366211	−	0.112708i
$222$	−2.96622	−	11.0701i	−0.199080	−	0.742976i
$223$	1.23370	+	0.330568i	0.0826145	+	0.0221365i	0.299890	−	0.953974i	$-0.403050\pi$
$223$	1.23370	+	0.330568i	0.0826145	+	0.0221365i	−0.217275	+	0.976110i	$0.569717\pi$
$224$	−1.21351	−	1.09265i	−0.0810809	−	0.0730055i
$225$	−1.11614	−	4.87383i	−0.0744095	−	0.324922i
$226$	0.541848	+	0.601783i	0.0360432	+	0.0400300i
$227$	3.46573	−	9.02852i	0.230028	−	0.599244i	−0.769180	−	0.639032i	$-0.779335\pi$
$227$	3.46573	−	9.02852i	0.230028	−	0.599244i	0.999208	+	0.0397882i	$0.0126683\pi$
$228$	2.29799	−	1.49233i	0.152188	−	0.0988320i
$229$	−0.267508	+	2.54517i	−0.0176774	+	0.168190i	−0.999799	−	0.0200593i	$-0.993614\pi$
$229$	−0.267508	+	2.54517i	−0.0176774	+	0.168190i	0.982121	+	0.188249i	$0.0602812\pi$
$230$	−2.49328	−	1.08673i	−0.164402	−	0.0716569i
$231$	6.20229	−	1.31834i	0.408081	−	0.0867402i
$232$	−8.56357	−	1.35634i	−0.562226	−	0.0890478i
$233$	−3.37920	−	0.535212i	−0.221379	−	0.0350629i	0.0447597	−	0.998998i	$-0.485748\pi$
$233$	−3.37920	−	0.535212i	−0.221379	−	0.0350629i	−0.266138	+	0.963935i	$0.585748\pi$
$234$	−2.37462	+	0.504741i	−0.155234	+	0.0329959i
$235$	−5.28862	−	13.4608i	−0.344991	−	0.878086i
$236$	1.15473	−	10.9866i	0.0751667	−	0.715164i
$237$	−2.50409	+	1.62618i	−0.162658	+	0.105632i
$238$	−0.424672	+	1.10631i	−0.0275274	+	0.0717113i
$239$	6.36290	+	7.06672i	0.411582	+	0.457108i	0.912917	−	0.408145i	$-0.133824\pi$
$239$	6.36290	+	7.06672i	0.411582	+	0.457108i	−0.501335	+	0.865253i	$0.667158\pi$
$240$	−0.0995100	+	2.23385i	−0.00642334	+	0.144195i
$241$	−12.5888	−	11.3350i	−0.810915	−	0.730151i	0.155306	−	0.987866i	$-0.450364\pi$
$241$	−12.5888	−	11.3350i	−0.810915	−	0.730151i	−0.966221	+	0.257715i	$0.917030\pi$
$242$	3.93950	+	1.05559i	0.253241	+	0.0678556i
$243$	−0.258819	−	0.965926i	−0.0166032	−	0.0619642i
$244$	−0.0698227	−	0.214892i	−0.00446994	−	0.0137571i
$245$	−7.79451	+	5.75698i	−0.497973	+	0.367800i
$246$	6.08944	−	8.38140i	0.388249	−	0.534378i
$247$	4.70361	+	4.70361i	0.299283	+	0.299283i
$248$	−4.20508	−	3.64928i	−0.267023	−	0.231730i
$249$			1.04042i			0.0659339i
$250$	−2.00830	−	10.9985i	−0.127016	−	0.695605i
$251$	0.194007	−	0.435746i	0.0122456	−	0.0275040i	−0.907319	−	0.420443i	$-0.861875\pi$
$251$	0.194007	−	0.435746i	0.0122456	−	0.0275040i	0.919565	+	0.392939i	$0.128541\pi$
$252$	1.45496	+	0.741337i	0.0916536	+	0.0466998i
$253$	−4.56224	+	1.22245i	−0.286825	+	0.0768546i
$254$	9.85285	+	17.0656i	0.618223	+	1.07079i
$255$	1.53931	−	0.513533i	0.0963952	−	0.0321587i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	17.9698	+	0.941759i	1.12093	+	0.0587453i	0.603780	−	0.797151i	$-0.293660\pi$
$257$	17.9698	+	0.941759i	1.12093	+	0.0587453i	0.517148	+	0.855896i	$0.326994\pi$
$258$	−9.39029	−	3.60460i	−0.584614	−	0.224412i
$259$	−18.3055	−	3.89095i	−1.13745	−	0.241772i
$260$	−5.35477	+	0.891218i	−0.332089	+	0.0552710i
$261$	8.62282	−	0.906294i	0.533739	−	0.0560982i
$262$	3.72159	−	5.73074i	0.229920	−	0.354046i
$263$	0.789629	−	4.98552i	0.0486906	−	0.307420i	−0.951309	−	0.308239i	$-0.900260\pi$
$263$	0.789629	−	4.98552i	0.0486906	−	0.307420i	1.00000		0.000818353i	$0.000260490\pi$
$264$	2.28243	+	3.14149i	0.140474	+	0.193346i
$265$	−27.0064	+	14.0283i	−1.65899	+	0.861753i
$266$	−0.467692	−	4.44979i	−0.0286760	−	0.272834i
$267$	2.81676	+	3.47841i	0.172383	+	0.212876i
$268$	−7.24350	−	11.1540i	−0.442467	−	0.681340i
$269$	−24.6896	+	10.9925i	−1.50535	+	0.670226i	−0.983184	−	0.182616i	$-0.941544\pi$
$269$	−24.6896	+	10.9925i	−1.50535	+	0.670226i	−0.522169	+	0.852842i	$0.674877\pi$
$270$	−0.482044	−	2.18349i	−0.0293363	−	0.132883i
$271$	−18.0620	−	5.86871i	−1.09719	−	0.356499i	−0.296170	−	0.955135i	$-0.595709\pi$
$271$	−18.0620	−	5.86871i	−1.09719	−	0.356499i	−0.801021	+	0.598637i	$0.795709\pi$
$272$	−0.724703	+	0.0379801i	−0.0439416	+	0.00230288i
$273$	−1.02602	+	3.82915i	−0.0620974	+	0.231751i
$274$	3.56441	−	6.17374i	0.215334	−	0.372969i
$275$	−14.6305	−	12.7636i	−0.882254	−	0.769674i
$276$	−1.11118	−	0.494731i	−0.0668854	−	0.0297793i
$277$	2.41523	+	15.2492i	0.145117	+	0.916234i	0.947577	+	0.319528i	$0.103524\pi$
$277$	2.41523	+	15.2492i	0.145117	+	0.916234i	−0.802460	+	0.596706i	$0.796476\pi$
$278$	−7.27584	+	7.27584i	−0.436376	+	0.436376i
$279$	5.00630	+	2.43658i	0.299720	+	0.145874i
$280$	3.17639	+	1.80082i	0.189825	+	0.107620i
$281$	−4.88938	−	3.55234i	−0.291676	−	0.211915i	0.432318	−	0.901721i	$-0.357696\pi$
$281$	−4.88938	−	3.55234i	−0.291676	−	0.211915i	−0.723994	+	0.689806i	$0.757696\pi$
$282$	−2.31786	−	6.03822i	−0.138026	−	0.359571i
$283$	−4.75909	+	9.34023i	−0.282898	+	0.555219i	−0.988105	−	0.153783i	$-0.950854\pi$
$283$	−4.75909	+	9.34023i	−0.282898	+	0.555219i	0.705206	+	0.709002i	$0.250854\pi$
$284$	−5.18460	−	2.99333i	−0.307649	−	0.177621i
$285$	−4.29827	+	4.36622i	−0.254607	+	0.258633i
$286$	−6.30782	+	7.00554i	−0.372989	+	0.414246i
$287$	−7.68023	−	15.0733i	−0.453350	−	0.889749i
$288$	−0.0523360	+	0.998630i	−0.00308393	+	0.0588448i
$289$	−6.70032	−	15.0492i	−0.394136	−	0.885245i
$290$	19.3523	−	1.16647i	1.13641	−	0.0684976i
$291$	16.5501	+	1.73948i	0.970183	+	0.101970i
$292$	0.459385	−	0.567293i	0.0268835	−	0.0331983i
$293$	−18.5090	−	12.0199i	−1.08131	−	0.702208i	−0.124290	−	0.992246i	$-0.539665\pi$
$293$	−18.5090	−	12.0199i	−1.08131	−	0.702208i	−0.957015	+	0.290038i	$0.906332\pi$
$294$	−3.50589	+	2.54718i	−0.204468	+	0.148555i
$295$	2.77466	+	24.5457i	0.161547	+	1.42910i
$296$	−2.38279	−	11.2102i	−0.138497	−	0.651577i
$297$	−3.01774	−	2.44371i	−0.175107	−	0.141799i
$298$	−7.24605	+	5.86774i	−0.419752	+	0.339909i
$299$	0.613937	−	2.88835i	0.0355049	−	0.167037i
$300$	−0.859537	−	4.92557i	−0.0496254	−	0.284378i
$301$	−12.2059	+	10.9902i	−0.703536	+	0.633467i
$302$	−9.09597	+	4.63463i	−0.523414	+	0.266693i
$303$	−0.122423	−	2.33597i	−0.00703302	−	0.134198i
$304$	2.37294	−	1.37002i	0.136098	−	0.0785759i
$305$	0.256045	+	0.435557i	0.0146611	+	0.0249399i
$306$	0.690180	−	0.224253i	0.0394549	−	0.0128197i
$307$	19.7914	−	7.59722i	1.12956	−	0.433596i	0.279426	−	0.960167i	$-0.409856\pi$
$307$	19.7914	−	7.59722i	1.12956	−	0.433596i	0.850131	+	0.526571i	$0.176523\pi$
$308$	6.26278	−	0.991927i	0.356855	−	0.0565203i
$309$	19.3581			1.10125
$310$	10.9409	+	5.94114i	0.621400	+	0.337434i
$311$	17.7605			1.00711			0.503554	−	0.863964i	$-0.332026\pi$
$311$	17.7605			1.00711			0.503554	+	0.863964i	$0.332026\pi$
$312$	−2.39778	+	0.379771i	−0.135748	+	0.0215003i
$313$	4.61851	−	1.77288i	0.261054	−	0.100209i	−0.224321	−	0.974515i	$-0.572016\pi$
$313$	4.61851	−	1.77288i	0.261054	−	0.100209i	0.485375	+	0.874306i	$0.338683\pi$
$314$	16.9217	−	5.49821i	0.954949	−	0.310282i
$315$	−3.53424	−	0.917349i	−0.199132	−	0.0516868i
$316$	−2.58577	+	1.49289i	−0.145461	+	0.0839819i
$317$	−0.439248	−	8.38136i	−0.0246706	−	0.470744i	−0.982831	−	0.184511i	$-0.940930\pi$
$317$	−0.439248	−	8.38136i	−0.0246706	−	0.470744i	0.958160	−	0.286234i	$-0.0924033\pi$
$318$	−12.1265	+	6.17874i	−0.680018	+	0.346487i
$319$	25.0200	−	22.5281i	1.40085	−	1.26133i
$320$	−0.216284	+	2.22558i	−0.0120907	+	0.124414i
$321$	−3.61378	+	17.0015i	−0.201701	+	0.948930i
$322$	−1.54357	+	1.24996i	−0.0860199	+	0.0696576i
$323$	−1.54531	−	1.25136i	−0.0859832	−	0.0696278i
$324$	−0.207912	−	0.978148i	−0.0115506	−	0.0543415i
$325$	11.2625	−	4.52721i	0.624731	−	0.251124i
$326$	7.87537	−	5.72179i	0.436176	−	0.316901i
$327$	−16.0425	−	10.4181i	−0.887153	−	0.576124i
$328$	6.51974	−	8.05121i	0.359993	−	0.444554i
$329$	−10.5037	−	1.10398i	−0.579085	−	0.0608643i
$330$	−6.49800	−	5.75919i	−0.357703	−	0.317033i
$331$	−8.28511	−	18.6087i	−0.455391	−	1.02283i	−0.984678	−	0.174382i	$-0.944207\pi$
$331$	−8.28511	−	18.6087i	−0.455391	−	1.02283i	0.529287	−	0.848443i	$-0.322460\pi$
$332$	−0.0544513	+	1.03899i	−0.00298840	+	0.0570221i
$333$	5.20300	+	10.2115i	0.285123	+	0.559585i
$334$	−2.40842	+	2.67482i	−0.131783	+	0.146360i
$335$	21.1929	+	20.8630i	1.15789	+	1.13987i
$336$	1.41416	+	0.816467i	0.0771489	+	0.0445420i
$337$	9.96889	−	19.5650i	0.543040	−	1.06578i	−0.442569	−	0.896734i	$-0.645933\pi$
$337$	9.96889	−	19.5650i	0.543040	−	1.06578i	0.985609	−	0.169041i	$-0.0540671\pi$
$338$	2.54671	+	6.63442i	0.138523	+	0.360865i
$339$	−0.655125	−	0.475976i	−0.0355815	−	0.0258515i
$340$	1.56407	−	0.432268i	0.0848239	−	0.0234430i
$341$	21.2886	−	3.77203i	1.15284	−	0.204267i
$342$	−1.93750	+	1.93750i	−0.104768	+	0.104768i
$343$	2.89512	+	18.2791i	0.156322	+	0.986976i
$344$	−9.18877	−	4.09111i	−0.495425	−	0.220578i
$345$	2.66474	+	0.544600i	0.143465	+	0.0293203i
$346$	2.12434	−	3.67946i	0.114205	−	0.197809i
$347$	−2.30733	+	8.61106i	−0.123864	+	0.462266i	−0.999797	−	0.0201671i	$-0.993580\pi$
$347$	−2.30733	+	8.61106i	−0.123864	+	0.462266i	0.875933	+	0.482433i	$0.160247\pi$
$348$	8.65843	−	0.453769i	0.464141	−	0.0243246i
$349$	−13.4067	−	4.35611i	−0.717646	−	0.233177i	−0.0726436	−	0.997358i	$-0.523144\pi$
$349$	−13.4067	−	4.35611i	−0.717646	−	0.233177i	−0.645002	+	0.764181i	$0.723144\pi$
$350$	−7.80369	−	2.40092i	−0.417125	−	0.128334i
$351$	2.21779	−	0.987422i	0.118377	−	0.0527047i
$352$	2.11489	+	3.25664i	0.112724	+	0.173580i
$353$	2.24762	+	2.77557i	0.119628	+	0.147729i	0.833442	−	0.552607i	$-0.186367\pi$
$353$	2.24762	+	2.77557i	0.119628	+	0.147729i	−0.713814	+	0.700336i	$0.753034\pi$
$354$	1.15473	+	10.9866i	0.0613734	+	0.583929i
$355$	12.7634	+	4.03670i	0.677413	+	0.214246i
$356$	2.63086	+	3.62107i	0.139435	+	0.191916i
$357$	0.185378	−	1.17043i	0.00981122	−	0.0619456i
$358$	2.50274	−	3.85388i	0.132274	−	0.203684i
$359$	7.70523	−	0.809853i	0.406667	−	0.0427424i	0.101013	−	0.994885i	$-0.467792\pi$
$359$	7.70523	−	0.809853i	0.406667	−	0.0427424i	0.305654	+	0.952143i	$0.401125\pi$
$360$	−0.367109	−	2.20573i	−0.0193483	−	0.116252i
$361$	−11.2411	−	2.38936i	−0.591635	−	0.125756i
$362$	8.52938	+	3.27412i	0.448294	+	0.172084i
$363$	−4.07288	−	0.213451i	−0.213771	−	0.0112032i
$364$	−1.22501	+	3.77020i	−0.0642081	+	0.197612i
$365$	−0.729602	+	1.46012i	−0.0381891	+	0.0764263i
$366$	0.112975	+	0.195679i	0.00590532	+	0.0102283i
$367$	12.6420	−	3.38741i	0.659907	−	0.176821i	0.0867027	−	0.996234i	$-0.472367\pi$
$367$	12.6420	−	3.38741i	0.659907	−	0.176821i	0.573204	+	0.819413i	$0.305700\pi$
$368$	−1.08377	−	0.552207i	−0.0564953	−	0.0287858i
$369$	−4.21378	+	9.46431i	−0.219361	+	0.492692i
$370$	10.6066	+	23.3287i	0.551411	+	1.21280i
$371$			22.2240i			1.15381i
$372$	4.87192	+	2.69525i	0.252597	+	0.139742i
$373$	−3.70099	−	3.70099i	−0.191630	−	0.191630i	0.604770	−	0.796400i	$-0.293265\pi$
$373$	−3.70099	−	3.70099i	−0.191630	−	0.191630i	−0.796400	+	0.604770i	$0.793265\pi$
$374$	1.65635	−	2.27978i	0.0856480	−	0.117884i
$375$	4.25113	+	10.3406i	0.219528	+	0.533986i
$376$	−1.99866	−	6.15125i	−0.103073	−	0.317227i
$377$	5.44779	+	20.3314i	0.280576	+	1.04712i
$378$	−1.57729	−	0.422635i	−0.0811272	−	0.0217380i
$379$	7.19076	+	6.47459i	0.369365	+	0.332577i	0.832821	−	0.553542i	$-0.186724\pi$
$379$	7.19076	+	6.47459i	0.369365	+	0.332577i	−0.463456	+	0.886120i	$0.653391\pi$
$380$	−4.52089	+	4.13529i	−0.231917	+	0.212136i
$381$	−13.1857	−	14.6442i	−0.675523	−	0.750245i
$382$	−6.06786	+	15.8073i	−0.310459	+	0.808773i
$383$	8.98153	−	5.83267i	0.458935	−	0.298036i	−0.294389	−	0.955686i	$-0.595116\pi$
$383$	8.98153	−	5.83267i	0.458935	−	0.298036i	0.753324	+	0.657650i	$0.228449\pi$
$384$	−0.104528	+	0.994522i	−0.00533420	+	0.0507515i
$385$	−13.1966	+	5.18480i	−0.672560	+	0.264242i
$386$	9.64154	−	2.04937i	0.490741	−	0.104310i
$387$	9.93453	+	1.57347i	0.505001	+	0.0799842i
$388$	16.4364	+	2.60326i	0.834430	+	0.132161i
$389$	−23.2165	+	4.93482i	−1.17712	+	0.250205i	−0.754624	−	0.656158i	$-0.772181\pi$
$389$	−23.2165	+	4.93482i	−1.17712	+	0.250205i	−0.422500	+	0.906363i	$0.638847\pi$
$390$	5.05247	−	1.98506i	0.255842	−	0.100518i
$391$	−0.0922669	+	0.877861i	−0.00466614	+	0.0443953i
$392$	−3.63440	+	2.36021i	−0.183565	+	0.119208i
$393$	−2.44877	+	6.37927i	−0.123524	+	0.321792i
$394$	5.84950	+	6.49653i	0.294694	+	0.327290i
$395$	4.92636	−	4.50618i	0.247872	−	0.226730i
$396$	−2.88571	−	2.59830i	−0.145012	−	0.130570i
$397$	−37.3633	−	10.0115i	−1.87521	−	0.502461i	−0.999819	−	0.0190465i	$-0.993937\pi$
$397$	−37.3633	−	10.0115i	−1.87521	−	0.502461i	−0.875392	−	0.483415i	$-0.839396\pi$
$398$	1.27738	+	4.76726i	0.0640295	+	0.238961i
$399$	1.38264	+	4.25531i	0.0692183	+	0.213032i
$400$	−0.600575	−	4.96380i	−0.0300287	−	0.248190i
$401$	−2.14928	+	2.95823i	−0.107330	+	0.147727i	−0.859303	−	0.511467i	$-0.829102\pi$
$401$	−2.14928	+	2.95823i	−0.107330	+	0.147727i	0.751973	+	0.659194i	$0.229102\pi$
$402$	9.40426	+	9.40426i	0.469042	+	0.469042i
$403$	−3.94114	+	12.9294i	−0.196322	+	0.644057i
$404$		−	2.33918i		−	0.116378i
$405$	0.925484	+	2.03555i	0.0459877	+	0.101147i
$406$	5.75860	−	12.9340i	0.285795	−	0.641905i
$407$	39.6522	+	20.2038i	1.96548	+	1.00146i
$408$	0.700970	−	0.187824i	0.0347032	−	0.00929869i
$409$	4.12171	+	7.13902i	0.203806	+	0.353002i	0.949752	−	0.313005i	$-0.101336\pi$
$409$	4.12171	+	7.13902i	0.203806	+	0.353002i	−0.745946	+	0.666007i	$0.768002\pi$
$410$	−10.3548	+	20.7226i	−0.511385	+	1.02341i
$411$	−2.20293	+	6.77991i	−0.108662	+	0.334428i
$412$	19.3316	+	1.01313i	0.952400	+	0.0499132i
$413$	16.8410	+	6.46465i	0.828691	+	0.318105i
$414$	1.18976	+	0.252892i	0.0584736	+	0.0124289i
$415$	−0.381947	−	2.29488i	−0.0187490	−	0.112651i
$416$	−2.41437	+	0.253761i	−0.118374	+	0.0124416i
$417$	5.60411	−	8.62958i	0.274435	−	0.422592i
$418$	−1.66444	+	10.5088i	−0.0814103	+	0.514004i
$419$	14.8628	+	20.4569i	0.726094	+	0.999383i	0.999299	+	0.0374271i	$0.0119162\pi$
$419$	14.8628	+	20.4569i	0.726094	+	0.999383i	−0.273205	+	0.961956i	$0.588084\pi$
$420$	−3.48139	−	1.10106i	−0.169874	−	0.0537262i
$421$	0.0346112	+	0.329303i	0.00168685	+	0.0160493i	0.995333	−	0.0965004i	$-0.0307649\pi$
$421$	0.0346112	+	0.329303i	0.00168685	+	0.0160493i	−0.993646	+	0.112550i	$0.964098\pi$
$422$	−7.15044	−	8.83006i	−0.348078	−	0.429840i
$423$	3.52262	+	5.42436i	0.171276	+	0.263741i
$424$	−12.4332	+	5.53562i	−0.603810	+	0.268834i
$425$	−3.20677	+	1.69781i	−0.155551	+	0.0823557i
$426$	5.69365	+	1.84998i	0.275858	+	0.0896318i
$427$	0.368457	−	0.0193100i	0.0178309	−	0.000934478i
$428$	−4.49861	+	16.7891i	−0.217449	+	0.811530i
$429$	4.71344	−	8.16392i	0.227567	−	0.394158i
$430$	22.0357	+	4.50350i	1.06266	+	0.217178i
$431$	19.0163	+	8.46662i	0.915984	+	0.407822i	0.809922	−	0.586537i	$-0.199509\pi$
$431$	19.0163	+	8.46662i	0.915984	+	0.407822i	0.106062	+	0.994360i	$0.466176\pi$
$432$	−0.156434	−	0.987688i	−0.00752646	−	0.0475202i
$433$	−9.74069	+	9.74069i	−0.468108	+	0.468108i	−0.901301	−	0.433193i	$-0.857387\pi$
$433$	−9.74069	+	9.74069i	−0.468108	+	0.468108i	0.433193	+	0.901301i	$0.357387\pi$
$434$	7.53321	−	5.09034i	0.361605	−	0.244344i
$435$	−18.6869	+	5.16455i	−0.895967	+	0.247621i
$436$	−15.4753	−	11.2435i	−0.741132	−	0.538464i
$437$	−1.19438	−	3.11146i	−0.0571348	−	0.148841i
$438$	−0.331399	+	0.650408i	−0.0158349	+	0.0310777i
$439$	11.3716	+	6.56539i	0.542736	+	0.313349i	0.746187	−	0.665736i	$-0.231882\pi$
$439$	11.3716	+	6.56539i	0.542736	+	0.313349i	−0.203451	+	0.979085i	$0.565216\pi$
$440$	−6.18768	−	6.09138i	−0.294986	−	0.290395i
$441$	2.89969	−	3.22044i	0.138081	−	0.153354i
$442$	0.799820	+	1.56973i	0.0380435	+	0.0746646i
$443$	1.89465	−	36.1520i	0.0900174	−	1.71763i	−0.464593	−	0.885524i	$-0.653799\pi$
$443$	1.89465	−	36.1520i	0.0900174	−	1.71763i	0.554611	−	0.832110i	$-0.312867\pi$
$444$	4.66145	+	10.4698i	0.221222	+	0.496874i
$445$	−7.48997	−	6.63837i	−0.355059	−	0.314689i
$446$	−1.27022	−	0.133506i	−0.0601467	−	0.00632167i
$447$	5.86774	−	7.24605i	0.277534	−	0.342726i
$448$	1.36949	+	0.889360i	0.0647025	+	0.0420183i
$449$	19.8556	−	14.4260i	0.937046	−	0.680804i	−0.0106618	−	0.999943i	$-0.503394\pi$
$449$	19.8556	−	14.4260i	0.937046	−	0.680804i	0.947708	+	0.319139i	$0.103394\pi$
$450$	1.86484	+	4.63922i	0.0879092	+	0.218695i
$451$	8.36404	+	39.3497i	0.393847	+	1.85291i
$452$	−0.629316	−	0.509610i	−0.0296005	−	0.0239700i
$453$	7.93361	−	6.42451i	0.372753	−	0.301850i
$454$	−2.01068	+	9.45953i	−0.0943661	+	0.443958i
$455$	0.857400	−	8.82271i	0.0401955	−	0.413615i
$456$	−2.03624	+	1.83344i	−0.0953559	+	0.0858588i
$457$	−13.5485	+	6.90333i	−0.633774	+	0.322924i	−0.741195	−	0.671290i	$-0.765741\pi$
$457$	−13.5485	+	6.90333i	−0.633774	+	0.322924i	0.107421	+	0.994214i	$0.465741\pi$
$458$	−0.133938	−	2.55568i	−0.00625849	−	0.119419i
$459$	−0.628473	+	0.362849i	−0.0293346	+	0.0169363i
$460$	2.63259	+	0.683316i	0.122745	+	0.0318598i
$461$	−1.02382	+	0.332659i	−0.0476841	+	0.0154935i	−0.332762	−	0.943011i	$-0.607981\pi$
$461$	−1.02382	+	0.332659i	−0.0476841	+	0.0154935i	0.285078	+	0.958504i	$0.407981\pi$
$462$	−5.91969	+	2.27236i	−0.275409	+	0.105720i
$463$	24.2105	−	3.83457i	1.12516	−	0.178208i	0.434002	−	0.900912i	$-0.357101\pi$
$463$	24.2105	−	3.83457i	1.12516	−	0.178208i	0.691158	+	0.722704i	$0.257101\pi$
$464$	8.67031			0.402509
$465$	−11.9370	−	3.53657i	−0.553566	−	0.164005i
$466$	3.42132			0.158490
$467$	6.48732	−	1.02749i	0.300197	−	0.0475466i	−0.00451889	−	0.999990i	$-0.501438\pi$
$467$	6.48732	−	1.02749i	0.300197	−	0.0475466i	0.304716	+	0.952443i	$0.401438\pi$
$468$	2.26642	−	0.869999i	0.104765	−	0.0402157i
$469$	20.6545	−	6.71106i	0.953737	−	0.309888i
$470$	7.32924	+	12.4678i	0.338073	+	0.575095i
$471$	−15.4088	+	8.89629i	−0.710001	+	0.409919i
$472$	0.578159	+	11.0319i	0.0266119	+	0.507786i
$473$	34.8006	−	17.7318i	1.60013	−	0.815309i
$474$	2.21887	−	1.99788i	0.101916	−	0.0917658i
$475$	7.87793	−	11.2086i	0.361464	−	0.514287i
$476$	0.246379	−	1.15912i	0.0112928	−	0.0531283i
$477$	10.5768	−	8.56496i	0.484280	−	0.392162i
$478$	−7.39004	−	5.98434i	−0.338013	−	0.273717i
$479$	8.80504	+	41.4244i	0.402312	+	1.89273i	0.448472	+	0.893797i	$0.351968\pi$
$479$	8.80504	+	41.4244i	0.402312	+	1.89273i	−0.0461598	+	0.998934i	$0.514698\pi$
$480$	−0.251167	−	2.22192i	−0.0114641	−	0.101416i
$481$	−22.5089	+	16.3537i	−1.02632	+	0.745664i
$482$	14.2070	+	9.22612i	0.647110	+	0.420238i
$483$	1.24996	−	1.54357i	0.0568752	−	0.0702350i
$484$	−4.05613	−	0.426316i	−0.184369	−	0.0193780i
$485$	−37.1435	+	2.23885i	−1.68660	+	0.101661i
$486$	0.406737	+	0.913545i	0.0184499	+	0.0414393i
$487$	−1.54449	+	29.4707i	−0.0699877	+	1.33544i	0.707575	+	0.706638i	$0.249789\pi$
$487$	−1.54449	+	29.4707i	−0.0699877	+	1.33544i	−0.777562	+	0.628806i	$0.783544\pi$
$488$	0.102580	+	0.201324i	0.00464356	+	0.00911350i
$489$	−6.51365	+	7.23414i	−0.294557	+	0.327139i
$490$	6.79795	−	6.90543i	0.307100	−	0.311956i
$491$	36.5586	+	21.1071i	1.64987	+	0.952551i	0.977123	+	0.212674i	$0.0682174\pi$
$491$	36.5586	+	21.1071i	1.64987	+	0.952551i	0.672743	+	0.739876i	$0.265116\pi$
$492$	−4.70333	+	9.23080i	−0.212042	+	0.416157i
$493$	−2.25486	−	5.87411i	−0.101554	−	0.264557i
$494$	−5.38150	−	3.90989i	−0.242125	−	0.175914i
$495$	7.55341	+	4.28233i	0.339501	+	0.192476i
$496$	4.72419	+	2.94653i	0.212122	+	0.132303i
$497$	6.91255	−	6.91255i	0.310070	−	0.310070i
$498$	−0.162757	−	1.02761i	−0.00729333	−	0.0460483i
$499$	−39.8122	−	17.7255i	−1.78224	−	0.793504i	−0.980688	−	0.195579i	$-0.937341\pi$
$499$	−39.8122	−	17.7255i	−1.78224	−	0.793504i	−0.801552	−	0.597925i	$-0.795992\pi$
$500$	3.70412	+	10.5489i	0.165653	+	0.471762i
$501$	1.79966	−	3.11711i	0.0804029	−	0.139262i
$502$	−0.123452	+	0.460731i	−0.00550995	+	0.0205634i
$503$	−39.1341	+	2.05093i	−1.74490	+	0.0914465i	−0.897916	−	0.440166i	$-0.854920\pi$
$503$	−39.1341	+	2.05093i	−1.74490	+	0.0914465i	−0.846988	+	0.531613i	$0.821586\pi$
$504$	−1.55301	−	0.504605i	−0.0691767	−	0.0224769i
$505$	1.12759	+	5.10757i	0.0501769	+	0.227284i
$506$	4.31484	−	1.92109i	0.191818	−	0.0854028i
$507$	−3.87044	−	5.95995i	−0.171892	−	0.264691i
$508$	−12.4012	−	15.3142i	−0.550214	−	0.679458i
$509$	−1.22512	−	11.6563i	−0.0543026	−	0.516655i	−0.987537	−	0.157387i	$-0.949693\pi$
$509$	−1.22512	−	11.6563i	−0.0543026	−	0.516655i	0.933234	−	0.359268i	$-0.116974\pi$
$510$	−1.44002	+	0.748012i	−0.0637653	+	0.0331225i
$511$	0.700636	+	0.964342i	0.0309943	+	0.0426600i
$512$	−0.156434	+	0.987688i	−0.00691349	+	0.0436501i
$513$	1.49233	−	2.29799i	0.0658880	−	0.101459i
$514$	−17.8959	+	1.88094i	−0.789355	+	0.0829646i
$515$	−42.6988	+	7.10654i	−1.88153	+	0.313151i
$516$	9.83857	+	2.09125i	0.433119	+	0.0920622i
$517$	23.4470	+	9.00046i	1.03120	+	0.395840i
$518$	18.6888	+	0.979437i	0.821137	+	0.0430340i
$519$	−1.31291	+	4.04073i	−0.0576304	+	0.177368i
$520$	5.14943	−	1.71792i	0.225818	−	0.0753357i
$521$	12.0482	+	20.8681i	0.527843	+	0.914250i	0.999473	+	0.0324539i	$0.0103322\pi$
$521$	12.0482	+	20.8681i	0.527843	+	0.914250i	−0.471631	+	0.881796i	$0.656334\pi$
$522$	−8.37488	+	2.24404i	−0.366558	+	0.0982190i
$523$	−16.7122	−	8.51527i	−0.730772	−	0.372347i	0.0486755	−	0.998815i	$-0.484500\pi$
$523$	−16.7122	−	8.51527i	−0.730772	−	0.372347i	−0.779447	+	0.626468i	$0.784500\pi$
$524$	−2.77928	+	6.24237i	−0.121414	+	0.272699i
$525$	8.13234	+	0.725973i	0.354924	+	0.0316840i
$526$			5.04766i			0.220089i
$527$	0.767664	−	3.96692i	0.0334400	−	0.172802i
$528$	−2.74577	−	2.74577i	−0.119494	−	0.119494i
$529$	12.6494	−	17.4105i	0.549976	−	0.756977i
$530$	24.4794	−	18.0803i	1.06332	−	0.785360i
$531$	−3.41373	−	10.5064i	−0.148143	−	0.455938i
$532$	1.15803	+	4.32184i	0.0502072	+	0.187376i
$533$	−24.2936	−	6.50945i	−1.05227	−	0.281956i
$534$	−3.32623	−	2.99495i	−0.143940	−	0.129604i
$535$	1.72961	−	38.8273i	0.0747777	−	1.67865i
$536$	8.89919	+	9.88356i	0.384387	+	0.426905i
$537$	−1.64678	+	4.29001i	−0.0710639	+	0.185128i
$538$	22.6660	−	14.7195i	0.977203	−	0.634603i
$539$	1.75895	−	16.7353i	0.0757635	−	0.720841i
$540$	0.817683	+	2.08120i	0.0351875	+	0.0895606i
$541$	−17.0847	+	3.63147i	−0.734530	+	0.156129i	−0.559965	−	0.828517i	$-0.689185\pi$
$541$	−17.0847	+	3.63147i	−0.734530	+	0.156129i	−0.174565	+	0.984646i	$0.555852\pi$
$542$	18.7577	+	2.97093i	0.805713	+	0.127612i
$543$	−9.02372	−	1.42922i	−0.387245	−	0.0613336i
$544$	0.709840	−	0.150881i	0.0304341	−	0.00646897i
$545$	39.2100	+	17.0902i	1.67957	+	0.732064i
$546$	0.414374	−	3.94251i	0.0177336	−	0.168724i
$547$	−15.5845	+	10.1207i	−0.666347	+	0.432731i	−0.832991	−	0.553286i	$-0.813374\pi$
$547$	−15.5845	+	10.1207i	−0.666347	+	0.432731i	0.166644	+	0.986017i	$0.446707\pi$
$548$	−2.55474	+	6.65532i	−0.109133	+	0.284301i
$549$	−0.151191	−	0.167914i	−0.00645266	−	0.00716640i
$550$	16.4471	+	10.3177i	0.701305	+	0.439950i
$551$	17.6549	+	15.8965i	0.752123	+	0.677215i
$552$	1.17490	+	0.314812i	0.0500069	+	0.0133993i
$553$	−1.26190	−	4.70947i	−0.0536614	−	0.200267i
$554$	−4.77099	−	14.6836i	−0.202700	−	0.623847i
$555$	−15.2251	−	20.6136i	−0.646270	−	0.875001i
$556$	6.04807	−	8.32445i	0.256495	−	0.353035i
$557$	11.4599	+	11.4599i	0.485570	+	0.485570i	0.906905	−	0.421335i	$-0.138438\pi$
$557$	11.4599	+	11.4599i	0.485570	+	0.485570i	−0.421335	+	0.906905i	$0.638438\pi$
$558$	−5.32583	−	1.62342i	−0.225460	−	0.0687250i
$559$			24.4184i			1.03279i
$560$	−3.41899	−	1.28175i	−0.144479	−	0.0541639i
$561$	−1.14617	+	2.57433i	−0.0483912	+	0.108688i
$562$	5.38489	+	2.74374i	0.227148	+	0.115738i
$563$	−2.83377	+	0.759306i	−0.119429	+	0.0320009i	−0.318039	−	0.948078i	$-0.603024\pi$
$563$	−2.83377	+	0.759306i	−0.119429	+	0.0320009i	0.198609	+	0.980079i	$0.436357\pi$
$564$	3.23390	+	5.60129i	0.136172	+	0.235857i
$565$	1.61976	+	0.809371i	0.0681439	+	0.0340505i
$566$	3.23936	−	9.96972i	0.136160	−	0.419059i
$567$	1.63070	+	0.0854612i	0.0684828	+	0.00358903i
$568$	5.58903	+	2.14543i	0.234510	+	0.0900201i
$569$	25.2952	+	5.37666i	1.06043	+	0.225401i	0.704931	−	0.709276i	$-0.250978\pi$
$569$	25.2952	+	5.37666i	1.06043	+	0.225401i	0.355498	+	0.934677i	$0.384311\pi$
$570$	3.56232	−	4.98487i	0.149209	−	0.208793i
$571$	0.858939	−	0.0902781i	0.0359455	−	0.00377802i	−0.0865387	−	0.996248i	$-0.527581\pi$
$571$	0.858939	−	0.0902781i	0.0359455	−	0.00377802i	0.122484	+	0.992470i	$0.460914\pi$
$572$	5.13425	−	7.90605i	0.214674	−	0.330569i
$573$	2.64874	−	16.7235i	0.110653	−	0.698633i
$574$	9.94366	+	13.6863i	0.415040	+	0.571254i
$575$	−6.07762	−	0.222990i	−0.253454	−	0.00929934i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	−25.4918	−	31.4798i	−1.06124	−	1.31052i	−0.948459	−	0.316901i	$-0.897358\pi$
$577$	−25.4918	−	31.4798i	−1.06124	−	1.31052i	−0.112780	−	0.993620i	$-0.535976\pi$
$578$	8.97204	+	13.8157i	0.373188	+	0.574658i
$579$	−9.00476	+	4.00918i	−0.374225	+	0.166616i
$580$	−18.9315	+	4.17947i	−0.786090	+	0.173543i
$581$	−1.61578	−	0.525000i	−0.0670340	−	0.0217807i
$582$	−16.6184	+	0.870935i	−0.688856	+	0.0361014i
$583$	13.6782	−	51.0476i	0.566492	−	2.11418i
$584$	−0.364985	+	0.632172i	−0.0151032	+	0.0261595i
$585$	−4.52934	+	2.99215i	−0.187265	+	0.123710i
$586$	20.1614	+	8.97644i	0.832860	+	0.370813i
$587$	−3.50496	−	22.1295i	−0.144665	−	0.913381i	−0.948096	−	0.317983i	$-0.896994\pi$
$587$	−3.50496	−	22.1295i	−0.144665	−	0.913381i	0.803431	−	0.595398i	$-0.203006\pi$
$588$	3.06426	−	3.06426i	0.126368	−	0.126368i
$589$	4.21730	+	14.6614i	0.173771	+	0.604112i
$590$	−6.58028	−	23.8094i	−0.270906	−	0.980218i
$591$	−7.07238	−	5.13838i	−0.290919	−	0.211365i
$592$	4.10711	+	10.6994i	0.168801	+	0.439742i
$593$	−4.72879	+	9.28077i	−0.194188	+	0.381116i	−0.967485	−	0.252928i	$-0.918606\pi$
$593$	−4.72879	+	9.28077i	−0.194188	+	0.381116i	0.773297	+	0.634044i	$0.218606\pi$
$594$	3.36286	+	1.94155i	0.137980	+	0.0796628i
$595$	0.0207819	+	2.64970i	0.000851973	+	0.108627i
$596$	6.23892	−	6.92903i	0.255556	−	0.283824i
$597$	−2.24064	−	4.39750i	−0.0917033	−	0.179978i
$598$	−0.154541	+	2.94883i	−0.00631967	+	0.120587i
$599$	5.07703	+	11.4032i	0.207442	+	0.465922i	0.987064	−	0.160329i	$-0.0512554\pi$
$599$	5.07703	+	11.4032i	0.207442	+	0.465922i	−0.779622	+	0.626250i	$0.784589\pi$
$600$	1.61948	+	4.73046i	0.0661151	+	0.193120i
$601$	−20.1380	−	2.11659i	−0.821446	−	0.0863374i	−0.315525	−	0.948917i	$-0.602181\pi$
$601$	−20.1380	−	2.11659i	−0.821446	−	0.0863374i	−0.505921	+	0.862580i	$0.668847\pi$
$602$	10.3364	−	12.7644i	0.421279	−	0.520236i
$603$	−11.1540	−	7.24350i	−0.454227	−	0.294978i
$604$	8.25897	−	6.00049i	0.336053	−	0.244156i
$605$	9.06202	−	1.02438i	0.368423	−	0.0416468i
$606$	0.486342	+	2.28806i	0.0197563	+	0.0929461i
$607$	0.126071	+	0.102090i	0.00511707	+	0.00414372i	0.631876	−	0.775070i	$-0.282285\pi$
$607$	0.126071	+	0.102090i	0.00511707	+	0.00414372i	−0.626758	+	0.779214i	$0.715619\pi$
$608$	−2.12941	+	1.72436i	−0.0863589	+	0.0699321i
$609$	−2.94363	+	13.8487i	−0.119282	+	0.561176i
$610$	−0.321028	−	0.390141i	−0.0129981	−	0.0157963i
$611$	−11.6686	+	10.5065i	−0.472062	+	0.425047i
$612$	−0.646601	+	0.329460i	−0.0261373	+	0.0133176i
$613$	0.460973	+	8.79589i	0.0186185	+	0.355263i	0.992014	+	0.126130i	$0.0402557\pi$
$613$	0.460973	+	8.79589i	0.0186185	+	0.355263i	−0.973395	+	0.229133i	$0.926411\pi$
$614$	−18.3593	+	10.5997i	−0.740921	+	0.427771i
$615$	5.82002	−	22.4226i	0.234686	−	0.904166i
$616$	−6.03051	+	1.95943i	−0.242976	+	0.0789477i
$617$	−34.0235	+	13.0604i	−1.36974	+	0.525792i	−0.928411	−	0.371555i	$-0.878825\pi$
$617$	−34.0235	+	13.0604i	−1.36974	+	0.525792i	−0.441325	+	0.897347i	$0.645491\pi$
$618$	−19.1198	+	3.02828i	−0.769111	+	0.121815i
$619$	22.1559			0.890520			0.445260	−	0.895401i	$-0.353111\pi$
$619$	22.1559			0.890520			0.445260	+	0.895401i	$0.353111\pi$
$620$	−11.7356	−	4.15646i	−0.471312	−	0.166928i
$621$	−1.21634			−0.0488101
$622$	−17.5419	+	2.77836i	−0.703365	+	0.111402i
$623$	−6.82338	+	2.61925i	−0.273373	+	0.104938i
$624$	2.30885	−	0.750191i	0.0924280	−	0.0300317i
$625$	−13.1730	−	21.2479i	−0.526918	−	0.849916i
$626$	−4.28431	+	2.47355i	−0.171235	+	0.0988628i
$627$	−0.556846	−	10.6253i	−0.0222383	−	0.424332i
$628$	−15.8533	+	8.07766i	−0.632616	+	0.322334i
$629$	6.18068	−	5.56511i	0.246440	−	0.221896i
$630$	3.63423	+	0.353178i	0.144791	+	0.0140710i
$631$	0.669172	−	3.14821i	0.0266393	−	0.125328i	−0.962819	−	0.270149i	$-0.912927\pi$
$631$	0.669172	−	3.14821i	0.0266393	−	0.125328i	0.989458	+	0.144821i	$0.0462605\pi$
$632$	2.32039	−	1.87902i	0.0923003	−	0.0747433i
$633$	8.83006	+	7.15044i	0.350963	+	0.284204i
$634$	1.74497	+	8.20946i	0.0693018	+	0.326039i
$635$	34.4600	+	27.4605i	1.36750	+	1.08974i
$636$	11.0106	−	7.99967i	0.436599	−	0.317208i
$637$	8.82312	+	5.72980i	0.349585	+	0.227023i
$638$	−21.1878	+	26.1647i	−0.838832	+	1.03587i
$639$	−5.95386	−	0.625776i	−0.235531	−	0.0247553i
$640$	−0.134536	−	2.23202i	−0.00531801	−	0.0882282i
$641$	−12.2207	−	27.4482i	−0.482689	−	1.08414i	−0.976686	−	0.214673i	$-0.931131\pi$
$641$	−12.2207	−	27.4482i	−0.482689	−	1.08414i	0.493997	−	0.869464i	$-0.335535\pi$
$642$	0.909667	−	17.3575i	0.0359017	−	0.685045i
$643$	−18.8784	−	37.0510i	−0.744493	−	1.46115i	−0.882299	−	0.470690i	$-0.844005\pi$
$643$	−18.8784	−	37.0510i	−0.744493	−	1.46115i	0.137806	−	0.990459i	$-0.455995\pi$
$644$	1.32903	−	1.47604i	0.0523712	−	0.0581641i
$645$	−22.4905	+	0.176395i	−0.885562	+	0.00694556i
$646$	1.72204	+	0.994219i	0.0677527	+	0.0391170i
$647$	−6.69109	+	13.1320i	−0.263054	+	0.516273i	−0.984321	−	0.176384i	$-0.943560\pi$
$647$	−6.69109	+	13.1320i	−0.263054	+	0.516273i	0.721267	+	0.692657i	$0.243560\pi$
$648$	0.358368	+	0.933580i	0.0140780	+	0.0366745i
$649$	−34.7043	−	25.2142i	−1.36226	−	0.989742i
$650$	−10.4156	+	6.23331i	−0.408534	+	0.244491i
$651$	−6.31025	+	6.54535i	−0.247318	+	0.256532i
$652$	−6.88333	+	6.88333i	−0.269572	+	0.269572i
$653$	1.01303	+	6.39605i	0.0396431	+	0.250297i	0.999549	−	0.0300253i	$-0.00955879\pi$
$653$	1.01303	+	6.39605i	0.0396431	+	0.250297i	−0.959906	+	0.280322i	$0.909559\pi$
$654$	17.4748	+	7.78027i	0.683317	+	0.304233i
$655$	3.05944	−	14.9699i	0.119542	−	0.584922i
$656$	−5.17999	+	8.97200i	−0.202245	+	0.350298i
$657$	0.188930	−	0.705096i	0.00737086	−	0.0275084i
$658$	10.5470	−	0.552747i	0.411166	−	0.0215483i
$659$	16.7134	+	5.43050i	0.651060	+	0.211542i	0.615882	−	0.787839i	$-0.288800\pi$
$659$	16.7134	+	5.43050i	0.651060	+	0.211542i	0.0351787	+	0.999381i	$0.488800\pi$
$660$	7.31894	+	4.67178i	0.284889	+	0.181849i
$661$	21.1319	−	9.40854i	0.821937	−	0.365950i	0.0477124	−	0.998861i	$-0.484807\pi$
$661$	21.1319	−	9.40854i	0.821937	−	0.365950i	0.774224	+	0.632911i	$0.218140\pi$
$662$	11.0941	+	17.0835i	0.431186	+	0.663969i
$663$	−1.10871	−	1.36914i	−0.0430586	−	0.0531730i
$664$	−0.108753	−	1.03472i	−0.00422045	−	0.0401549i
$665$	−4.61188	−	8.87848i	−0.178841	−	0.344293i
$666$	−6.73637	−	9.27182i	−0.261029	−	0.359276i
$667$	1.64977	−	10.4162i	0.0638792	−	0.403318i
$668$	1.96033	−	3.01865i	0.0758475	−	0.116795i
$669$	1.27022	−	0.133506i	0.0491096	−	0.00516162i
$670$	−24.1956	−	17.2909i	−0.934758	−	0.668004i
$671$	−0.858217	−	0.182420i	−0.0331311	−	0.00704223i
$672$	−1.52448	−	0.585192i	−0.0588079	−	0.0225743i
$673$	50.4273	+	2.64278i	1.94383	+	0.101872i	0.983939	−	0.178506i	$-0.0571265\pi$
$673$	50.4273	+	2.64278i	1.94383	+	0.101872i	0.959890	+	0.280378i	$0.0904599\pi$
$674$	−6.78551	+	20.8836i	−0.261368	+	0.804408i
$675$	−2.78863	−	4.15012i	−0.107335	−	0.159738i
$676$	−3.55321	−	6.15434i	−0.136662	−	0.236706i
$677$	20.3105	−	5.44218i	0.780596	−	0.209160i	0.153548	−	0.988141i	$-0.450930\pi$
$677$	20.3105	−	5.44218i	0.780596	−	0.209160i	0.627047	+	0.778981i	$0.284263\pi$
$678$	0.721518	+	0.367632i	0.0277097	+	0.0141188i
$679$	−11.0527	+	24.8247i	−0.424163	+	0.952686i
$680$	−1.47720	+	0.671622i	−0.0566479	+	0.0257555i
$681$		−	9.67086i		−	0.370588i
$682$	−20.4364	+	7.05586i	−0.782551	+	0.270183i
$683$	10.9276	+	10.9276i	0.418134	+	0.418134i	0.884560	−	0.466426i	$-0.154459\pi$
$683$	10.9276	+	10.9276i	0.418134	+	0.418134i	−0.466426	+	0.884560i	$0.654459\pi$
$684$	1.61055	−	2.21674i	0.0615810	−	0.0847590i
$685$	2.37009	−	15.7633i	0.0905565	−	0.602286i
$686$	−5.71895	−	17.6011i	−0.218350	−	0.672014i
$687$	0.662367	+	2.47199i	0.0252709	+	0.0943122i
$688$	9.71563	+	2.60330i	0.370405	+	0.0992497i
$689$	24.5537	+	22.1082i	0.935420	+	0.842256i
$690$	−2.71713	−	0.121038i	−0.103439	−	0.00460784i
$691$	27.9560	+	31.0483i	1.06350	+	1.18113i	0.982853	+	0.184391i	$0.0590312\pi$
$691$	27.9560	+	31.0483i	1.06350	+	1.18113i	0.0806444	+	0.996743i	$0.474302\pi$
$692$	−1.52259	+	3.96648i	−0.0578801	+	0.150783i
$693$	5.31788	−	3.45347i	0.202010	−	0.131187i
$694$	0.931853	−	8.86599i	0.0353727	−	0.336548i
$695$	−9.19315	+	21.0918i	−0.348716	+	0.800058i
$696$	−8.48085	+	1.80266i	−0.321466	+	0.0683296i
$697$	7.42565	+	1.17611i	0.281266	+	0.0445482i
$698$	13.9231	+	2.20520i	0.526998	+	0.0834682i
$699$	−3.34656	+	0.711332i	−0.126578	+	0.0269051i
$700$	8.08320	+	1.15059i	0.305516	+	0.0434883i
$701$	3.60637	−	34.3124i	0.136211	−	1.29596i	−0.686345	−	0.727276i	$-0.740786\pi$
$701$	3.60637	−	34.3124i	0.136211	−	1.29596i	0.822556	−	0.568684i	$-0.192547\pi$
$702$	−2.03601	+	1.32220i	−0.0768444	+	0.0499033i
$703$	−11.2536	+	29.3167i	−0.424439	+	1.10570i
$704$	−2.59830	−	2.88571i	−0.0979272	−	0.108759i
$705$	−9.76127	−	10.6715i	−0.367631	−	0.401911i
$706$	−2.65414	−	2.38980i	−0.0998898	−	0.0899412i
$707$	3.68957	+	0.988617i	0.138760	+	0.0371808i
$708$	−2.85919	−	10.6706i	−0.107455	−	0.401028i
$709$	−13.3527	−	41.0953i	−0.501470	−	1.54337i	−0.806625	−	0.591063i	$-0.798708\pi$
$709$	−13.3527	−	41.0953i	−0.501470	−	1.54337i	0.305156	−	0.952303i	$-0.401292\pi$
$710$	−13.2378	−	1.99036i	−0.496805	−	0.0746969i
$711$	−1.75500	+	2.41555i	−0.0658177	+	0.0905904i
$712$	−3.16493	−	3.16493i	−0.118611	−	0.118611i
$713$	4.43877	−	5.11482i	0.166233	−	0.191551i
$714$			1.18502i			0.0443482i
$715$	−7.39952	+	19.7377i	−0.276726	+	0.738149i
$716$	−1.86905	+	4.19795i	−0.0698496	+	0.156885i
$717$	8.47276	+	4.31709i	0.316421	+	0.161225i
$718$	−7.48368	+	2.00525i	−0.279288	+	0.0748351i
$719$	−0.856269	−	1.48310i	−0.0319335	−	0.0553104i	0.849617	−	0.527400i	$-0.176833\pi$
$719$	−0.856269	−	1.48310i	−0.0319335	−	0.0553104i	−0.881550	+	0.472090i	$0.843500\pi$
$720$	0.707641	+	2.12114i	0.0263722	+	0.0790503i
$721$	−9.76820	+	30.0634i	−0.363787	+	1.11962i
$722$	11.4764	+	0.601455i	0.427109	+	0.0223838i
$723$	−15.8147	−	6.07071i	−0.588157	−	0.225772i
$724$	−8.93656	−	1.89952i	−0.332124	−	0.0705952i
$725$	39.3222	−	18.2517i	1.46039	−	0.677851i
$726$	4.05613	−	0.426316i	0.150537	−	0.0158221i
$727$	20.8902	−	32.1681i	0.774775	−	1.19305i	−0.202127	−	0.979359i	$-0.564785\pi$
$727$	20.8902	−	32.1681i	0.774775	−	1.19305i	0.976902	−	0.213689i	$-0.0685480\pi$
$728$	0.620141	−	3.91542i	0.0229840	−	0.145115i
$729$	−0.587785	−	0.809017i	−0.0217698	−	0.0299636i
$730$	0.492206	−	1.55628i	0.0182174	−	0.0576006i
$731$	−0.762988	−	7.25935i	−0.0282201	−	0.268497i
$732$	−0.142195	−	0.175597i	−0.00525570	−	0.00649024i
$733$	11.9591	+	18.4155i	0.441721	+	0.680191i	0.987479	−	0.157752i	$-0.0504248\pi$
$733$	11.9591	+	18.4155i	0.441721	+	0.680191i	−0.545758	+	0.837943i	$0.683758\pi$
$734$	−11.9564	+	5.32335i	−0.441320	+	0.196488i
$735$	−5.21368	+	8.16790i	−0.192310	+	0.301278i
$736$	1.15681	+	0.375870i	0.0426406	+	0.0138548i
$737$	−51.5730	+	2.70283i	−1.89972	+	0.0995600i
$738$	2.68136	−	10.0070i	0.0987022	−	0.368362i
$739$	−20.2869	+	35.1379i	−0.746265	+	1.29257i	0.203336	+	0.979109i	$0.434822\pi$
$739$	−20.2869	+	35.1379i	−0.746265	+	1.29257i	−0.949601	+	0.313461i	$0.898512\pi$
$740$	−14.1254	−	21.3822i	−0.519261	−	0.786026i
$741$	6.07682	+	2.70557i	0.223237	+	0.0993917i
$742$	−3.47660	−	21.9504i	−0.127630	−	0.805824i
$743$	17.4108	−	17.4108i	0.638742	−	0.638742i	−0.311503	−	0.950245i	$-0.600833\pi$
$743$	17.4108	−	17.4108i	0.638742	−	0.638742i	0.950245	+	0.311503i	$0.100833\pi$
$744$	−5.23357	−	1.89993i	−0.191872	−	0.0696549i
$745$	−10.2825	+	18.1369i	−0.376723	+	0.664485i
$746$	4.23438	+	3.07646i	0.155032	+	0.112637i
$747$	0.372853	+	0.971315i	0.0136420	+	0.0355385i
$748$	−1.27933	+	2.51082i	−0.0467768	+	0.0918046i
$749$	−24.5800	−	14.1913i	−0.898134	−	0.518538i
$750$	−5.81642	−	9.54826i	−0.212386	−	0.348653i
$751$	18.2820	−	20.3043i	0.667121	−	0.740913i	−0.310665	−	0.950520i	$-0.600552\pi$
$751$	18.2820	−	20.3043i	0.667121	−	0.740913i	0.977786	+	0.209607i	$0.0672183\pi$
$752$	2.93632	+	5.76286i	0.107077	+	0.210150i
$753$	0.0249634	−	0.476330i	0.000909716	−	0.0173584i
$754$	−8.56126	−	19.2289i	−0.311783	−	0.700275i
$755$	−15.1409	+	17.0832i	−0.551033	+	0.621721i
$756$	1.62399	+	0.170688i	0.0590639	+	0.00620787i
$757$	−28.9142	+	35.7060i	−1.05090	+	1.29776i	−0.0977687	+	0.995209i	$0.531171\pi$
$757$	−28.9142	+	35.7060i	−1.05090	+	1.29776i	−0.953134	+	0.302548i	$0.902163\pi$
$758$	−8.11508	−	5.27000i	−0.294753	−	0.191415i
$759$	−3.82113	+	2.77621i	−0.138698	+	0.100770i
$760$	3.81833	−	4.79160i	0.138505	−	0.173809i
$761$	−0.176376	−	0.829785i	−0.00639364	−	0.0300797i	0.974835	−	0.222927i	$-0.0715611\pi$
$761$	−0.176376	−	0.829785i	−0.00639364	−	0.0300797i	−0.981229	+	0.192847i	$0.938228\pi$
$762$	15.3142	+	12.4012i	0.554775	+	0.449248i
$763$	24.2746	−	19.6572i	0.878801	−	0.711639i
$764$	3.52035	−	16.5619i	0.127362	−	0.599190i
$765$	1.25303	−	1.03106i	0.0453035	−	0.0372782i
$766$	−7.95852	+	7.16588i	−0.287553	+	0.258914i
$767$	23.8956	−	12.1754i	0.862819	−	0.439628i
$768$	−0.0523360	−	0.998630i	−0.00188851	−	0.0360349i
$769$	−8.59609	+	4.96295i	−0.309983	+	0.178969i	−0.646919	−	0.762559i	$-0.723943\pi$
$769$	−8.59609	+	4.96295i	−0.309983	+	0.178969i	0.336936	+	0.941528i	$0.390609\pi$
$770$	12.2230	−	7.18537i	0.440487	−	0.258943i
$771$	17.1138	−	5.56061i	0.616338	−	0.200260i
$772$	−9.20224	+	3.53241i	−0.331196	+	0.127134i
$773$	−5.90060	+	0.934563i	−0.212230	+	0.0336139i	−0.261644	−	0.965164i	$-0.584265\pi$
$773$	−5.90060	+	0.934563i	−0.212230	+	0.0336139i	0.0494141	+	0.998778i	$0.484265\pi$
$774$	−10.0584			−0.361540
$775$	27.6281	+	3.41853i	0.992432	+	0.122797i
$776$	−16.6412			−0.597386
$777$	−18.4840	+	2.92758i	−0.663110	+	0.105026i
$778$	22.1587	−	8.50593i	0.794428	−	0.304952i
$779$	−26.9974	+	8.77198i	−0.967281	+	0.314289i
$780$	−4.67973	+	2.75100i	−0.167561	+	0.0985017i
$781$	−20.1323	+	11.6234i	−0.720391	+	0.415918i
$782$	−0.0461967	−	0.881486i	−0.00165199	−	0.0315219i
$783$	7.72530	−	3.93624i	0.276080	−	0.140670i
$784$	3.22044	−	2.89969i	0.115016	−	0.103560i
$785$	30.7218	−	25.2795i	1.09651	−	0.902264i
$786$	1.42069	−	6.68381i	0.0506742	−	0.238403i
$787$	−0.988649	+	0.800592i	−0.0352415	+	0.0285380i	−0.646779	−	0.762677i	$-0.723885\pi$
$787$	−0.988649	+	0.800592i	−0.0352415	+	0.0285380i	0.611538	+	0.791215i	$0.290551\pi$
$788$	−6.79377	−	5.50148i	−0.242018	−	0.195982i
$789$	−1.04947	−	4.93736i	−0.0373621	−	0.175775i
$790$	−4.16079	+	5.22135i	−0.148034	+	0.185767i
$791$	1.06978	−	0.777238i	0.0380369	−	0.0276354i
$792$	3.25664	+	2.11489i	0.115720	+	0.0751493i
$793$	0.345204	−	0.426291i	0.0122585	−	0.0151380i
$794$	38.4694	+	4.04330i	1.36523	+	0.143491i
$795$	−20.1854	+	22.7748i	−0.715901	+	0.807739i
$796$	−2.00742	−	4.50874i	−0.0711512	−	0.159808i
$797$	2.19030	−	41.7935i	0.0775845	−	1.48040i	−0.631554	−	0.775331i	$-0.717583\pi$
$797$	2.19030	−	41.7935i	0.0775845	−	1.48040i	0.709139	−	0.705069i	$-0.249084\pi$
$798$	−2.03129	−	3.98663i	−0.0719069	−	0.141125i
$799$	3.14068	−	3.48808i	0.111109	−	0.123399i
$800$	1.36969	+	4.80874i	0.0484259	+	0.170015i
$801$	3.87623	+	2.23794i	0.136960	+	0.0790738i
$802$	1.66005	−	3.25803i	0.0586184	−	0.115045i
$803$	−1.01581	−	2.64628i	−0.0358472	−	0.0933850i
$804$	−10.7596	−	7.81733i	−0.379463	−	0.275696i
$805$	−2.19041	+	3.86357i	−0.0772019	+	0.136173i
$806$	1.87002	−	13.3867i	0.0658685	−	0.471527i
$807$	−19.1104	+	19.1104i	−0.672717	+	0.672717i
$808$	0.365928	+	2.31038i	0.0128733	+	0.0812788i
$809$	−32.7928	−	14.6003i	−1.15293	−	0.513319i	−0.260934	−	0.965357i	$-0.584030\pi$
$809$	−32.7928	−	14.6003i	−1.15293	−	0.513319i	−0.891999	+	0.452038i	$0.850697\pi$
$810$	−1.23252	−	1.86572i	−0.0433064	−	0.0655546i
$811$	8.85844	−	15.3433i	0.311062	−	0.538775i	−0.667531	−	0.744582i	$-0.732649\pi$
$811$	8.85844	−	15.3433i	0.311062	−	0.538775i	0.978593	+	0.205807i	$0.0659820\pi$
$812$	−3.66437	+	13.6756i	−0.128594	+	0.479921i
$813$	−18.9655	+	0.993941i	−0.665150	+	0.0348590i
$814$	−42.3245	−	13.7521i	−1.48347	−	0.482010i
$815$	11.7116	−	18.3478i	0.410240	−	0.642694i
$816$	−0.662958	+	0.295168i	−0.0232082	+	0.0103329i
$817$	15.0104	+	23.1140i	0.525148	+	0.808657i
$818$	−5.18776	−	6.40635i	−0.181386	−	0.223993i
$819$	0.414374	+	3.94251i	0.0144794	+	0.137762i
$820$	6.98555	−	22.0873i	0.243946	−	0.771321i
$821$	23.5602	+	32.4278i	0.822256	+	1.13174i	0.989315	+	0.145792i	$0.0465729\pi$
$821$	23.5602	+	32.4278i	0.822256	+	1.13174i	−0.167059	+	0.985947i	$0.553427\pi$
$822$	1.11519	−	7.04105i	0.0388968	−	0.245585i
$823$	3.80281	−	5.85582i	0.132558	−	0.204121i	−0.766159	−	0.642652i	$-0.777834\pi$
$823$	3.80281	−	5.85582i	0.132558	−	0.204121i	0.898716	+	0.438531i	$0.144501\pi$
$824$	−19.2521	+	2.02348i	−0.670678	+	0.0704911i
$825$	−18.2328	−	6.67273i	−0.634786	−	0.232315i
$826$	−17.6449	−	3.75055i	−0.613946	−	0.130498i
$827$	−37.9693	−	14.5751i	−1.32032	−	0.506824i	−0.406765	−	0.913533i	$-0.633343\pi$
$827$	−37.9693	−	14.5751i	−1.32032	−	0.506824i	−0.913558	+	0.406709i	$0.866676\pi$
$828$	−1.21467	−	0.0636584i	−0.0422129	−	0.00221228i
$829$	−1.38551	+	4.26417i	−0.0481208	+	0.148101i	−0.972230	−	0.234029i	$-0.924809\pi$
$829$	−1.38551	+	4.26417i	−0.0481208	+	0.148101i	0.924109	+	0.382129i	$0.124809\pi$
$830$	0.736243	+	2.20688i	0.0255554	+	0.0766018i
$831$	7.71963	+	13.3708i	0.267791	+	0.463828i
$832$	2.34495	−	0.628327i	0.0812965	−	0.0217833i
$833$	−2.80206	−	1.42772i	−0.0970857	−	0.0494676i
$834$	−4.18515	+	9.40001i	−0.144920	+	0.325496i
$835$	−2.82525	+	7.53615i	−0.0977717	+	0.260799i
$836$		−	10.6398i		−	0.367987i
$837$	5.54698	+	0.480645i	0.191732	+	0.0166135i
$838$	−17.8799	−	17.8799i	−0.617653	−	0.617653i
$839$	2.60422	−	3.58440i	0.0899075	−	0.123747i	−0.761694	−	0.647937i	$-0.775632\pi$
$839$	2.60422	−	3.58440i	0.0899075	−	0.123747i	0.851601	+	0.524190i	$0.175632\pi$
$840$	3.61077	+	0.542895i	0.124583	+	0.0187317i
$841$	14.2686	+	43.9144i	0.492022	+	1.51429i
$842$	−0.0856994	−	0.319835i	−0.00295340	−	0.0110222i
$843$	−5.83768	−	1.56420i	−0.201060	−	0.0538739i
$844$	8.44373	+	7.60277i	0.290645	+	0.261698i
$845$	10.7251	+	11.7251i	0.368954	+	0.403357i
$846$	−4.32781	−	4.80652i	−0.148793	−	0.165251i
$847$	2.38669	−	6.21753i	0.0820075	−	0.213637i
$848$	11.4142	−	7.41246i	0.391965	−	0.254545i
$849$	−1.09575	+	10.4254i	−0.0376060	+	0.357797i
$850$	2.90169	−	2.17855i	0.0995273	−	0.0747238i
$851$	13.6354	−	2.89829i	0.467415	−	0.0993521i
$852$	−5.91295	−	0.936520i	−0.202574	−	0.0320846i
$853$	11.7835	+	1.86633i	0.403461	+	0.0639019i	0.354867	−	0.934917i	$-0.384526\pi$
$853$	11.7835	+	1.86633i	0.403461	+	0.0639019i	0.0485937	+	0.998819i	$0.484526\pi$
$854$	−0.360900	+	0.0767117i	−0.0123498	+	0.00262502i
$855$	−2.44806	+	5.61658i	−0.0837220	+	0.192083i
$856$	1.81684	−	17.2861i	0.0620984	−	0.590826i
$857$	−24.3661	+	15.8235i	−0.832330	+	0.540521i	−0.889019	−	0.457871i	$-0.848612\pi$
$857$	−24.3661	+	15.8235i	−0.832330	+	0.540521i	0.0566892	+	0.998392i	$0.481946\pi$
$858$	−3.37829	+	8.80075i	−0.115333	+	0.300453i
$859$	−0.405824	−	0.450714i	−0.0138465	−	0.0153781i	0.736182	−	0.676784i	$-0.236627\pi$
$859$	−0.405824	−	0.450714i	−0.0138465	−	0.0153781i	−0.750028	+	0.661406i	$0.769960\pi$
$860$	−22.4689	−	1.00091i	−0.766183	−	0.0341307i
$861$	−12.5719	−	11.3198i	−0.428449	−	0.385777i
$862$	−20.1067	−	5.38757i	−0.684836	−	0.183501i
$863$	−7.65760	−	28.5785i	−0.260668	−	0.972825i	−0.964849	−	0.262805i	$-0.915353\pi$
$863$	−7.65760	−	28.5785i	−0.260668	−	0.972825i	0.704181	−	0.710020i	$-0.251314\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	1.41254	−	9.39472i	0.0480278	−	0.319430i
$866$	8.09699	−	11.1445i	0.275147	−	0.378707i
$867$	−11.6484	−	11.6484i	−0.395601	−	0.395601i
$868$	−6.64416	+	6.20612i	−0.225517	+	0.210650i
$869$			11.5941i			0.393304i
$870$	17.6489	−	8.02423i	0.598353	−	0.272047i
$871$	13.1324	−	29.4957i	0.444973	−	0.999425i
$872$	17.0436	+	8.68416i	0.577170	+	0.294083i
$873$	16.0742	−	4.30707i	0.544029	−	0.145772i
$874$	1.66641	+	2.88631i	0.0563672	+	0.0976308i
$875$	−18.2042	+	1.38415i	−0.615415	+	0.0467929i
$876$	0.225573	−	0.694242i	0.00762141	−	0.0234563i
$877$	−22.2293	−	1.16499i	−0.750629	−	0.0393388i	−0.326816	−	0.945088i	$-0.605976\pi$
$877$	−22.2293	−	1.16499i	−0.750629	−	0.0393388i	−0.423814	+	0.905749i	$0.639309\pi$
$878$	−12.2586	−	4.70565i	−0.413709	−	0.158808i
$879$	−21.5871	−	4.58849i	−0.728116	−	0.154766i
$880$	7.06441	+	5.04842i	0.238141	+	0.170182i
$881$	24.1333	−	2.53651i	0.813072	−	0.0854573i	0.311140	−	0.950364i	$-0.399289\pi$
$881$	24.1333	−	2.53651i	0.813072	−	0.0854573i	0.501932	+	0.864907i	$0.332623\pi$
$882$	−2.36021	+	3.63440i	−0.0794723	+	0.122377i
$883$	4.09472	−	25.8530i	0.137798	−	0.870023i	−0.817833	−	0.575456i	$-0.804825\pi$
$883$	4.09472	−	25.8530i	0.137798	−	0.870023i	0.955631	−	0.294567i	$-0.0951754\pi$
$884$	−1.03553	−	1.42529i	−0.0348287	−	0.0479377i
$885$	11.3867	+	21.9210i	0.382761	+	0.736867i
$886$	3.78410	+	36.0033i	0.127129	+	1.20956i
$887$	−25.9553	−	32.0521i	−0.871494	−	1.07621i	−0.996462	−	0.0840444i	$-0.973216\pi$
$887$	−25.9553	−	32.0521i	−0.871494	−	1.07621i	0.124968	−	0.992161i	$-0.460117\pi$
$888$	−6.24189	−	9.61167i	−0.209464	−	0.322546i
$889$	29.3962	−	13.0880i	0.985916	−	0.438958i
$890$	8.43623	+	5.38496i	0.282783	+	0.180504i
$891$	−3.69305	−	1.19994i	−0.123722	−	0.0401996i
$892$	1.27547	−	0.0668444i	0.0427058	−	0.00223812i
$893$	−4.58680	+	17.1182i	−0.153491	+	0.572838i
$894$	−4.66196	+	8.07476i	−0.155919	+	0.270060i
$895$	2.05745	−	10.0671i	0.0687730	−	0.336508i
$896$	−1.49176	−	0.664174i	−0.0498362	−	0.0221885i
$897$	−0.461931	−	2.91652i	−0.0154234	−	0.0973797i
$898$	−17.3545	+	17.3545i	−0.579126	+	0.579126i
$899$	−11.6396	+	46.8500i	−0.388203	+	1.56254i
$900$	−2.56761	−	4.29038i	−0.0855871	−	0.143013i
$901$	−7.99037	−	5.80534i	−0.266198	−	0.193404i
$902$	−14.4167	−	37.5568i	−0.480024	−	1.25051i
$903$	−7.45664	+	14.6345i	−0.248141	+	0.487005i
$904$	0.701289	+	0.404889i	0.0233245	+	0.0134664i
$905$	20.4285	−	0.160223i	0.679068	−	0.00532600i
$906$	−6.83092	+	7.58650i	−0.226942	+	0.252045i
$907$	−15.3216	−	30.0703i	−0.508745	−	0.998469i	−0.992382	−	0.123200i	$-0.960684\pi$
$907$	−15.3216	−	30.0703i	−0.508745	−	0.998469i	0.483637	−	0.875269i	$-0.339316\pi$
$908$	0.506134	−	9.65760i	0.0167966	−	0.320499i
$909$	−0.951429	−	2.13694i	−0.0315569	−	0.0708779i
$910$	0.533332	+	8.84822i	0.0176798	+	0.293316i
$911$	−45.4620	−	4.77825i	−1.50622	−	0.158311i	−0.684843	−	0.728691i	$-0.740129\pi$
$911$	−45.4620	−	4.77825i	−1.50622	−	0.158311i	−0.821381	+	0.570380i	$0.806796\pi$
$912$	1.72436	−	2.12941i	0.0570993	−	0.0705118i
$913$	3.38827	+	2.20037i	0.112135	+	0.0728216i
$914$	12.3018	−	8.93780i	0.406908	−	0.295636i
$915$	0.395128	+	0.314870i	0.0130625	+	0.0104093i
$916$	0.532085	+	2.50327i	0.0175806	+	0.0827102i
$917$	−8.67143	−	7.02199i	−0.286356	−	0.231886i
$918$	0.563973	−	0.456696i	0.0186139	−	0.0150732i
$919$	3.32119	−	15.6250i	0.109556	−	0.515420i	−0.888810	−	0.458276i	$-0.848467\pi$
$919$	3.32119	−	15.6250i	0.109556	−	0.515420i	0.998366	−	0.0571442i	$-0.0181995\pi$
$920$	−2.70707	−	0.263076i	−0.0892494	−	0.00867335i
$921$	15.7543	−	14.1852i	0.519122	−	0.467419i
$922$	0.959176	−	0.488725i	0.0315888	−	0.0160953i
$923$	−0.760631	−	14.5137i	−0.0250365	−	0.477724i
$924$	5.49134	−	3.17043i	0.180652	−	0.104299i
$925$	41.1499	+	39.8788i	1.35300	+	1.31121i
$926$	−23.3126	+	7.57473i	−0.766100	+	0.248921i
$927$	18.0724	−	6.93733i	0.593575	−	0.227852i
$928$	−8.56357	+	1.35634i	−0.281113	+	0.0445239i
$929$	36.0896			1.18406			0.592031	−	0.805915i	$-0.298326\pi$
$929$	36.0896			1.18406			0.592031	+	0.805915i	$0.298326\pi$
$930$	12.3433	+	1.62567i	0.404753	+	0.0533078i
$931$	11.8740			0.389155
$932$	−3.37920	+	0.535212i	−0.110689	+	0.0175315i
$933$	16.5809	−	6.36481i	0.542834	−	0.208374i
$934$	−6.24671	+	2.02968i	−0.204399	+	0.0664132i
$935$	1.58307	−	6.09904i	0.0517719	−	0.199460i
$936$	−2.10242	+	1.21383i	−0.0687198	+	0.0396754i
$937$	2.55708	+	48.7921i	0.0835363	+	1.59397i	0.643497	+	0.765448i	$0.277483\pi$
$937$	2.55708	+	48.7921i	0.0835363	+	1.59397i	−0.559961	+	0.828519i	$0.689184\pi$
$938$	−19.3504	+	9.85951i	−0.631812	+	0.321924i
$939$	3.67641	−	3.31025i	0.119975	−	0.108026i
$940$	−9.18939	−	11.1677i	−0.299725	−	0.364251i
$941$	−6.47007	+	30.4393i	−0.210918	+	0.992292i	0.737519	+	0.675326i	$0.235997\pi$
$941$	−6.47007	+	30.4393i	−0.210918	+	0.992292i	−0.948437	+	0.316965i	$0.897336\pi$
$942$	13.8274	−	11.1972i	0.450522	−	0.364825i
$943$	9.79302	+	7.93023i	0.318905	+	0.258244i
$944$	−2.29681	−	10.8057i	−0.0747550	−	0.351694i
$945$	−3.62825	+	0.410139i	−0.118027	+	0.0133418i
$946$	−31.5983	+	22.9575i	−1.02735	+	0.746413i
$947$	−24.5564	−	15.9471i	−0.797977	−	0.518212i	0.0800688	−	0.996789i	$-0.474486\pi$
$947$	−24.5564	−	15.9471i	−0.797977	−	0.518212i	−0.878045	+	0.478577i	$0.841153\pi$
$948$	−1.87902	+	2.32039i	−0.0610277	+	0.0753629i
$949$	1.76242	+	0.185237i	0.0572105	+	0.00601306i
$950$	−6.02752	+	12.3030i	−0.195559	+	0.399162i
$951$	−3.41368	−	7.66726i	−0.110696	−	0.248628i
$952$	−0.0620190	+	1.18339i	−0.00201005	+	0.0383540i
$953$	−11.8090	−	23.1765i	−0.382531	−	0.750760i	0.616808	−	0.787114i	$-0.288426\pi$
$953$	−11.8090	−	23.1765i	−0.382531	−	0.750760i	−0.999339	+	0.0363539i	$0.988426\pi$
$954$	−9.10677	+	10.1141i	−0.294842	+	0.327456i
$955$	0.296938	+	37.8598i	0.00960870	+	1.22511i
$956$	8.23521	+	4.75460i	0.266346	+	0.153775i
$957$	15.2848	−	29.9981i	0.494088	−	0.969702i
$958$	−15.1768	−	39.5370i	−0.490341	−	1.27738i
$959$	−9.41768	−	6.84235i	−0.304113	−	0.220951i
$960$	0.595659	+	2.15527i	0.0192248	+	0.0695611i
$961$	−22.2637	+	21.5715i	−0.718182	+	0.695855i
$962$	19.6735	−	19.6735i	0.634299	−	0.634299i
$963$	2.71904	+	17.1673i	0.0876197	+	0.553209i
$964$	−15.4754	−	6.89007i	−0.498428	−	0.221914i
$965$	18.3902	−	12.1489i	0.592003	−	0.391086i
$966$	−0.993103	+	1.72011i	−0.0319526	+	0.0553435i
$967$	−8.64275	+	32.2552i	−0.277932	+	1.03726i	0.675919	+	0.736976i	$0.263747\pi$
$967$	−8.64275	+	32.2552i	−0.277932	+	1.03726i	−0.953851	+	0.300281i	$0.902920\pi$
$968$	4.07288	−	0.213451i	0.130907	−	0.00686056i
$969$	−1.89112	−	0.614461i	−0.0607514	−	0.0197393i
$970$	36.3360	−	8.02181i	1.16668	−	0.257565i
$971$	3.91564	−	1.74336i	0.125659	−	0.0559469i	−0.342944	−	0.939356i	$-0.611424\pi$
$971$	3.91564	−	1.74336i	0.125659	−	0.0559469i	0.468603	+	0.883409i	$0.344757\pi$
$972$	−0.544639	−	0.838671i	−0.0174693	−	0.0269004i
$973$	10.5740	+	13.0578i	0.338986	+	0.418613i
$974$	−3.08475	−	29.3495i	−0.0988419	−	0.940417i
$975$	8.89204	−	8.26263i	0.284773	−	0.264616i
$976$	−0.132811	−	0.182798i	−0.00425116	−	0.00585122i
$977$	2.34978	−	14.8359i	0.0751760	−	0.474643i	−0.921165	−	0.389173i	$-0.872761\pi$
$977$	2.34978	−	14.8359i	0.0751760	−	0.474643i	0.996341	−	0.0854698i	$-0.0272391\pi$
$978$	5.30179	−	8.16403i	0.169532	−	0.261057i
$979$	17.2851	−	1.81674i	0.552434	−	0.0580631i
$980$	−5.63401	+	7.88385i	−0.179972	+	0.251840i
$981$	−18.7105	−	3.97704i	−0.597381	−	0.126977i
$982$	−39.4104	−	15.1282i	−1.25764	−	0.482761i
$983$	−6.03801	−	0.316439i	−0.192583	−	0.0100928i	−0.0441992	−	0.999023i	$-0.514074\pi$
$983$	−6.03801	−	0.316439i	−0.192583	−	0.0100928i	−0.148383	+	0.988930i	$0.547407\pi$
$984$	3.20141	−	9.85292i	0.102057	−	0.314100i
$985$	17.4861	+	8.73754i	0.557153	+	0.278401i
$986$	3.14601	+	5.44905i	0.100189	+	0.173533i
$987$	−10.2016	+	2.73352i	−0.324722	+	0.0870089i
$988$	5.92689	+	3.01990i	0.188559	+	0.0960758i
$989$	4.97618	−	11.1767i	0.158233	−	0.355398i
$990$	−8.13032	−	3.04799i	−0.258398	−	0.0968716i
$991$		−	23.8665i		−	0.758145i	−0.925367	−	0.379073i	$-0.876243\pi$
$991$		−	23.8665i		−	0.758145i	0.925367	−	0.379073i	$-0.123757\pi$
$992$	−5.12696	−	2.17123i	−0.162781	−	0.0689367i
$993$	−14.4036	−	14.4036i	−0.457084	−	0.457084i
$994$	−5.74608	+	7.90881i	−0.182255	+	0.250852i
$995$	6.55660	+	8.87713i	0.207858	+	0.281424i
$996$	0.321507	+	0.989497i	0.0101873	+	0.0313534i
$997$	−4.02958	−	15.0386i	−0.127618	−	0.476277i	0.872301	−	0.488969i	$-0.162627\pi$
$997$	−4.02958	−	15.0386i	−0.127618	−	0.476277i	−0.999919	+	0.0126913i	$0.995960\pi$
$998$	42.0950	+	11.2793i	1.33249	+	0.357040i
$999$	8.51689	+	7.66864i	0.269462	+	0.242625i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bt.a.43.2	✓	256
5.2	odd	4		930.2.bt.b.787.4	yes	256
31.13	odd	30		930.2.bt.b.13.4	yes	256
155.137	even	60	inner	930.2.bt.a.757.2	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bt.a.43.2	✓	256	1.1	even	1	trivial
930.2.bt.a.757.2	yes	256	155.137	even	60	inner
930.2.bt.b.13.4	yes	256	31.13	odd	30
930.2.bt.b.787.4	yes	256	5.2	odd	4

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.bt (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.987688 + 0.156434i) q^{2} +(0.933580 - 0.358368i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-1.92766 + 1.13319i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.0854612 + 1.63070i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(0.743145 - 0.669131i) q^{9} +O(q^{10})\)	\(q+(-0.987688 + 0.156434i) q^{2} +(0.933580 - 0.358368i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-1.92766 + 1.13319i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.0854612 + 1.63070i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(0.743145 - 0.669131i) q^{9} +(1.72666 - 1.42079i) q^{10} +(0.807342 - 3.79825i) q^{11} +(0.777146 - 0.629320i) q^{12} +(1.88665 + 1.52778i) q^{13} +(-0.339506 - 1.59725i) q^{14} +(-1.39353 + 1.74873i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-0.608621 - 0.395243i) q^{17} +(-0.629320 + 0.777146i) q^{18} +(2.72503 + 0.286412i) q^{19} +(-1.48314 + 1.67341i) q^{20} +(0.664174 + 1.49176i) q^{21} +(-0.203226 + 3.87778i) q^{22} +(-0.552207 - 1.08377i) q^{23} +(-0.669131 + 0.743145i) q^{24} +(2.43177 - 4.36881i) q^{25} +(-2.10242 - 1.21383i) q^{26} +(0.453990 - 0.891007i) q^{27} +(0.585192 + 1.52448i) q^{28} +(7.01443 + 5.09628i) q^{29} +(1.10281 - 1.94520i) q^{30} +(2.09002 + 5.16060i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.607451 - 3.83529i) q^{33} +(0.662958 + 0.295168i) q^{34} +(-2.01263 - 3.04659i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-2.96622 + 11.0701i) q^{37} +(-2.73628 + 0.143402i) q^{38} +(2.30885 + 0.750191i) q^{39} +(1.20310 - 1.88482i) q^{40} +(-9.46431 + 4.21378i) q^{41} +(-0.889360 - 1.36949i) q^{42} +(6.32993 + 7.81682i) q^{43} +(-0.405895 - 3.86183i) q^{44} +(-0.674283 + 2.13198i) q^{45} +(0.714948 + 0.984041i) q^{46} +(-1.01179 + 6.38818i) q^{47} +(0.544639 - 0.838671i) q^{48} +(4.30978 - 0.452977i) q^{49} +(-1.71840 + 4.69543i) q^{50} +(-0.709840 - 0.150881i) q^{51} +(2.26642 + 0.869999i) q^{52} +(13.5912 + 0.712285i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(2.74784 + 8.23661i) q^{55} +(-0.816467 - 1.41416i) q^{56} +(2.64667 - 0.709174i) q^{57} +(-7.72530 - 3.93624i) q^{58} +(4.49325 - 10.0920i) q^{59} +(-0.784938 + 2.09377i) q^{60} -0.225951i q^{61} +(-2.87158 - 4.77012i) q^{62} +(1.15466 + 1.15466i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-5.36810 - 0.807118i) q^{65} +(1.19994 + 3.69305i) q^{66} +(-3.44220 - 12.8465i) q^{67} +(-0.700970 - 0.187824i) q^{68} +(-0.903918 - 0.813891i) q^{69} +(2.46444 + 2.69424i) q^{70} +(-4.00586 - 4.44895i) q^{71} +(-0.358368 + 0.933580i) q^{72} +(0.612204 - 0.397570i) q^{73} +(1.19796 - 11.3978i) q^{74} +(0.704615 - 4.95010i) q^{75} +(2.68016 - 0.569686i) q^{76} +(6.26278 + 0.991927i) q^{77} +(-2.39778 - 0.379771i) q^{78} +(-2.92054 + 0.620780i) q^{79} +(-0.893442 + 2.04982i) q^{80} +(0.104528 - 0.994522i) q^{81} +(8.68861 - 5.64245i) q^{82} +(-0.372853 + 0.971315i) q^{83} +(1.09265 + 1.21351i) q^{84} +(1.62110 + 0.0722142i) q^{85} +(-7.47482 - 6.73036i) q^{86} +(8.37488 + 2.24404i) q^{87} +(1.00502 + 3.75079i) q^{88} +(1.38312 + 4.25682i) q^{89} +(0.332466 - 2.21121i) q^{90} +(-2.33011 + 3.20713i) q^{91} +(-0.860083 - 0.860083i) q^{92} +(3.80059 + 4.06884i) q^{93} -6.46781i q^{94} +(-5.57749 + 2.53586i) q^{95} +(-0.406737 + 0.913545i) q^{96} +(14.8275 + 7.55496i) q^{97} +(-4.18586 + 1.12160i) q^{98} +(-1.94155 - 3.36286i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 8 q^{7}+O(q^{10}) \) 256 * q + 8 * q^7	\( 256 q + 8 q^{7} + 4 q^{10} - 24 q^{14} - 8 q^{15} + 64 q^{16} + 36 q^{17} - 40 q^{19} + 12 q^{20} - 16 q^{21} + 8 q^{22} - 32 q^{24} + 20 q^{25} + 4 q^{28} - 16 q^{29} - 8 q^{31} - 4 q^{33} - 24 q^{35} + 128 q^{36} + 4 q^{37} + 4 q^{38} + 48 q^{41} + 32 q^{42} - 24 q^{43} + 4 q^{44} - 12 q^{45} - 20 q^{46} - 168 q^{47} - 40 q^{49} + 48 q^{50} - 64 q^{53} + 64 q^{54} + 64 q^{55} + 28 q^{57} + 68 q^{58} - 24 q^{59} + 4 q^{62} + 4 q^{63} - 60 q^{65} + 12 q^{66} - 76 q^{67} - 4 q^{68} + 12 q^{69} - 16 q^{70} - 48 q^{71} + 52 q^{73} + 68 q^{74} + 48 q^{75} + 48 q^{76} + 84 q^{77} - 56 q^{79} - 32 q^{81} - 32 q^{82} + 136 q^{83} + 68 q^{85} + 24 q^{86} + 20 q^{87} + 56 q^{88} - 224 q^{89} + 40 q^{91} - 48 q^{93} - 4 q^{95} + 8 q^{97} + 64 q^{98} + 4 q^{99}+O(q^{100}) \) 256 * q + 8 * q^7 + 4 * q^10 - 24 * q^14 - 8 * q^15 + 64 * q^16 + 36 * q^17 - 40 * q^19 + 12 * q^20 - 16 * q^21 + 8 * q^22 - 32 * q^24 + 20 * q^25 + 4 * q^28 - 16 * q^29 - 8 * q^31 - 4 * q^33 - 24 * q^35 + 128 * q^36 + 4 * q^37 + 4 * q^38 + 48 * q^41 + 32 * q^42 - 24 * q^43 + 4 * q^44 - 12 * q^45 - 20 * q^46 - 168 * q^47 - 40 * q^49 + 48 * q^50 - 64 * q^53 + 64 * q^54 + 64 * q^55 + 28 * q^57 + 68 * q^58 - 24 * q^59 + 4 * q^62 + 4 * q^63 - 60 * q^65 + 12 * q^66 - 76 * q^67 - 4 * q^68 + 12 * q^69 - 16 * q^70 - 48 * q^71 + 52 * q^73 + 68 * q^74 + 48 * q^75 + 48 * q^76 + 84 * q^77 - 56 * q^79 - 32 * q^81 - 32 * q^82 + 136 * q^83 + 68 * q^85 + 24 * q^86 + 20 * q^87 + 56 * q^88 - 224 * q^89 + 40 * q^91 - 48 * q^93 - 4 * q^95 + 8 * q^97 + 64 * q^98 + 4 * q^99

Introduction

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