LMFDB - Embedded newform 961.2.g.r.547.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(235,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([26]))

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

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

chi := DirichletCharacter("961.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, not 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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	16.0.26873856000000000000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} + 8x^{10} - 16x^{8} + 32x^{6} - 128x^{2} + 256 $ x^16 - 2x^14 + 8x^10 - 16x^8 + 32x^6 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			547.2
Root			$0.147826 + 1.40647i$ of defining polynomial
Character	$\chi$	$=$	961.547
Dual form			961.2.g.r.448.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.127999 + 0.393941i) q^{2} +(-0.277163 - 0.307821i) q^{3} +(1.47923 - 1.07472i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.0857864 - 0.148586i) q^{6} +(0.0432971 + 0.411944i) q^{7} +(1.28293 + 0.932102i) q^{8} +(0.295651 - 2.81293i) q^{9} +O(q^{10})$	\(q+(0.127999 + 0.393941i) q^{2} +(-0.277163 - 0.307821i) q^{3} +(1.47923 - 1.07472i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.0857864 - 0.148586i) q^{6} +(0.0432971 + 0.411944i) q^{7} +(1.28293 + 0.932102i) q^{8} +(0.295651 - 2.81293i) q^{9} +(0.277163 - 0.307821i) q^{10} +(-2.96230 - 1.31890i) q^{11} +(-0.740809 - 0.157464i) q^{12} +(-3.74477 + 0.795975i) q^{13} +(-0.156740 + 0.0697850i) q^{14} +(-0.127999 + 0.393941i) q^{15} +(0.927051 - 2.85317i) q^{16} +(5.32453 - 2.37063i) q^{17} +(1.14597 - 0.243584i) q^{18} +(-4.31775 - 0.917767i) q^{19} +(-1.67035 - 0.743688i) q^{20} +(0.114805 - 0.127503i) q^{21} +(0.140397 - 1.33579i) q^{22} +(-3.23607 - 2.35114i) q^{23} +(-0.0686600 - 0.653256i) q^{24} +(2.00000 - 3.46410i) q^{25} +(-0.792893 - 1.37333i) q^{26} +(-1.95314 + 1.41904i) q^{27} +(0.506772 + 0.562828i) q^{28} +(2.11010 + 6.49422i) q^{29} -0.171573 q^{30} +4.41421 q^{32} +(0.415055 + 1.27741i) q^{33} +(1.61542 + 1.79411i) q^{34} +(0.335106 - 0.243469i) q^{35} +(-2.58579 - 4.47871i) q^{36} +(0.500000 - 0.866025i) q^{37} +(-0.191123 - 1.81841i) q^{38} +(1.28293 + 0.932102i) q^{39} +(0.165760 - 1.57710i) q^{40} +(-5.00863 + 5.56265i) q^{41} +(0.0649237 + 0.0289059i) q^{42} +(-10.6613 - 2.26613i) q^{43} +(-5.79937 + 1.23269i) q^{44} +(-2.58390 + 1.15042i) q^{45} +(0.511996 - 1.57576i) q^{46} +(2.98413 - 9.18421i) q^{47} +(-1.13521 + 0.505428i) q^{48} +(6.67921 - 1.41971i) q^{49} +(1.62065 + 0.344479i) q^{50} +(-2.20549 - 0.981949i) q^{51} +(-4.68391 + 5.20201i) q^{52} +(0.609237 - 5.79650i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(0.338948 + 3.22488i) q^{55} +(-0.328427 + 0.568852i) q^{56} +(0.914214 + 1.58346i) q^{57} +(-2.28825 + 1.66251i) q^{58} +(2.72408 + 3.02539i) q^{59} +(0.234037 + 0.720292i) q^{60} +2.82843 q^{61} +1.17157 q^{63} +(-1.28909 - 3.96740i) q^{64} +(2.56172 + 2.84508i) q^{65} +(-0.450096 + 0.327014i) q^{66} +(-1.62132 - 2.80821i) q^{67} +(5.32843 - 9.22911i) q^{68} +(0.173188 + 1.64778i) q^{69} +(0.138805 + 0.100848i) q^{70} +(-0.00742861 + 0.0706785i) q^{71} +(3.00124 - 3.33321i) q^{72} +(1.67035 + 0.743688i) q^{73} +(0.405162 + 0.0861198i) q^{74} +(-1.62065 + 0.344479i) q^{75} +(-7.37329 + 3.28280i) q^{76} +(0.415055 - 1.27741i) q^{77} +(-0.202979 + 0.624706i) q^{78} +(6.17315 - 2.74847i) q^{79} +(-2.93444 + 0.623735i) q^{80} +(-7.32171 - 1.55628i) q^{81} +(-2.83245 - 1.26109i) q^{82} +(6.73886 - 7.48426i) q^{83} +(0.0327915 - 0.311990i) q^{84} +(-4.71530 - 3.42586i) q^{85} +(-0.471917 - 4.48999i) q^{86} +(1.41421 - 2.44949i) q^{87} +(-2.57107 - 4.45322i) q^{88} +(3.62867 - 2.63638i) q^{89} +(-0.783935 - 0.870648i) q^{90} +(-0.490035 - 1.50817i) q^{91} -7.31371 q^{92} +4.00000 q^{94} +(1.36407 + 4.19817i) q^{95} +(-1.22346 - 1.35879i) q^{96} +(-4.18389 + 3.03977i) q^{97} +(1.41421 + 2.44949i) q^{98} +(-4.58579 + 7.94282i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 8 q^{5} + 24 q^{6} + 2 q^{7} + 12 q^{8}+O(q^{10}) $ 16 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 8 * q^5 + 24 * q^6 + 2 * q^7 + 12 * q^8	\( 16 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 8 q^{5} + 24 q^{6} + 2 q^{7} + 12 q^{8} - 2 q^{10} + 2 q^{11} + 10 q^{12} + 2 q^{13} - 6 q^{14} - 4 q^{15} - 12 q^{16} + 6 q^{17} - 8 q^{18} + 6 q^{19} + 2 q^{20} + 6 q^{21} - 14 q^{22} - 16 q^{23} - 10 q^{24} + 32 q^{25} - 24 q^{26} - 4 q^{27} + 10 q^{28} - 16 q^{29} - 48 q^{30} + 48 q^{32} - 28 q^{33} + 2 q^{34} - 4 q^{35} - 64 q^{36} + 8 q^{37} - 2 q^{38} + 12 q^{39} - 6 q^{40} + 2 q^{41} - 14 q^{42} + 2 q^{43} + 26 q^{44} + 16 q^{46} - 16 q^{47} + 6 q^{48} - 8 q^{49} + 8 q^{50} - 2 q^{51} - 14 q^{52} - 6 q^{53} - 4 q^{54} + 2 q^{55} + 40 q^{56} - 8 q^{57} - 6 q^{59} - 20 q^{60} + 64 q^{63} + 28 q^{64} + 2 q^{65} + 60 q^{66} + 8 q^{67} + 40 q^{68} + 8 q^{69} + 12 q^{70} - 14 q^{71} - 8 q^{72} - 2 q^{73} + 2 q^{74} - 8 q^{75} - 2 q^{76} - 28 q^{77} - 20 q^{78} + 22 q^{79} + 6 q^{80} - 2 q^{81} - 26 q^{82} + 6 q^{83} + 22 q^{84} - 12 q^{85} + 26 q^{86} + 72 q^{88} - 16 q^{89} - 8 q^{90} + 12 q^{91} + 64 q^{92} + 64 q^{94} - 12 q^{95} + 2 q^{96} - 32 q^{97} - 96 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 8 * q^5 + 24 * q^6 + 2 * q^7 + 12 * q^8 - 2 * q^10 + 2 * q^11 + 10 * q^12 + 2 * q^13 - 6 * q^14 - 4 * q^15 - 12 * q^16 + 6 * q^17 - 8 * q^18 + 6 * q^19 + 2 * q^20 + 6 * q^21 - 14 * q^22 - 16 * q^23 - 10 * q^24 + 32 * q^25 - 24 * q^26 - 4 * q^27 + 10 * q^28 - 16 * q^29 - 48 * q^30 + 48 * q^32 - 28 * q^33 + 2 * q^34 - 4 * q^35 - 64 * q^36 + 8 * q^37 - 2 * q^38 + 12 * q^39 - 6 * q^40 + 2 * q^41 - 14 * q^42 + 2 * q^43 + 26 * q^44 + 16 * q^46 - 16 * q^47 + 6 * q^48 - 8 * q^49 + 8 * q^50 - 2 * q^51 - 14 * q^52 - 6 * q^53 - 4 * q^54 + 2 * q^55 + 40 * q^56 - 8 * q^57 - 6 * q^59 - 20 * q^60 + 64 * q^63 + 28 * q^64 + 2 * q^65 + 60 * q^66 + 8 * q^67 + 40 * q^68 + 8 * q^69 + 12 * q^70 - 14 * q^71 - 8 * q^72 - 2 * q^73 + 2 * q^74 - 8 * q^75 - 2 * q^76 - 28 * q^77 - 20 * q^78 + 22 * q^79 + 6 * q^80 - 2 * q^81 - 26 * q^82 + 6 * q^83 + 22 * q^84 - 12 * q^85 + 26 * q^86 + 72 * q^88 - 16 * q^89 - 8 * q^90 + 12 * q^91 + 64 * q^92 + 64 * q^94 - 12 * q^95 + 2 * q^96 - 32 * q^97 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{15}\right)$

Coefficient data

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

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

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

$2$	0.127999	+	0.393941i	0.0905090	+	0.278558i	0.986057	−	0.166406i	$-0.0532163\pi$
$2$	0.127999	+	0.393941i	0.0905090	+	0.278558i	−0.895548	+	0.444964i	$0.853216\pi$
$3$	−0.277163	−	0.307821i	−0.160020	−	0.177720i	0.657803	−	0.753190i	$-0.271486\pi$
$3$	−0.277163	−	0.307821i	−0.160020	−	0.177720i	−0.817823	+	0.575470i	$0.804819\pi$
$4$	1.47923	−	1.07472i	0.739614	−	0.537361i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$	0.0857864	−	0.148586i	0.0350222	−	0.0606602i
$7$	0.0432971	+	0.411944i	0.0163648	+	0.155700i	0.999653	−	0.0263575i	$-0.00839083\pi$
$7$	0.0432971	+	0.411944i	0.0163648	+	0.155700i	−0.983288	+	0.182058i	$0.941724\pi$
$8$	1.28293	+	0.932102i	0.453584	+	0.329548i
$9$	0.295651	−	2.81293i	0.0985504	−	0.937644i
$10$	0.277163	−	0.307821i	0.0876466	−	0.0973414i
$11$	−2.96230	−	1.31890i	−0.893167	−	0.397664i	−0.0917587	−	0.995781i	$-0.529249\pi$
$11$	−2.96230	−	1.31890i	−0.893167	−	0.397664i	−0.801408	+	0.598118i	$0.795916\pi$
$12$	−0.740809	−	0.157464i	−0.213853	−	0.0454559i
$13$	−3.74477	+	0.795975i	−1.03861	+	0.220764i	−0.695496	−	0.718530i	$-0.744815\pi$
$13$	−3.74477	+	0.795975i	−1.03861	+	0.220764i	−0.343115	+	0.939293i	$0.611482\pi$
$14$	−0.156740	+	0.0697850i	−0.0418904	+	0.0186508i
$15$	−0.127999	+	0.393941i	−0.0330492	+	0.101715i
$16$	0.927051	−	2.85317i	0.231763	−	0.713292i
$17$	5.32453	−	2.37063i	1.29139	−	0.574963i	0.357964	−	0.933735i	$-0.383471\pi$
$17$	5.32453	−	2.37063i	1.29139	−	0.574963i	0.933425	+	0.358772i	$0.116804\pi$
$18$	1.14597	−	0.243584i	0.270108	−	0.0574132i
$19$	−4.31775	−	0.917767i	−0.990560	−	0.210550i	−0.315991	−	0.948762i	$-0.602337\pi$
$19$	−4.31775	−	0.917767i	−0.990560	−	0.210550i	−0.674569	+	0.738212i	$0.735670\pi$
$20$	−1.67035	−	0.743688i	−0.373502	−	0.166294i
$21$	0.114805	−	0.127503i	0.0250524	−	0.0278235i
$22$	0.140397	−	1.33579i	0.0299327	−	0.284791i
$23$	−3.23607	−	2.35114i	−0.674767	−	0.490247i	0.196851	−	0.980433i	$-0.436929\pi$
$23$	−3.23607	−	2.35114i	−0.674767	−	0.490247i	−0.871617	+	0.490187i	$0.836929\pi$
$24$	−0.0686600	−	0.653256i	−0.0140152	−	0.133345i
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	−0.792893	−	1.37333i	−0.155499	−	0.269332i
$27$	−1.95314	+	1.41904i	−0.375882	+	0.273094i
$28$	0.506772	+	0.562828i	0.0957710	+	0.106364i
$29$	2.11010	+	6.49422i	0.391836	+	1.20595i	0.931399	+	0.364001i	$0.118590\pi$
$29$	2.11010	+	6.49422i	0.391836	+	1.20595i	−0.539563	+	0.841945i	$0.681410\pi$
$30$	−0.171573			−0.0313248
$31$		0			0
$31$		0			0
$32$	4.41421			0.780330
$33$	0.415055	+	1.27741i	0.0722518	+	0.222368i
$34$	1.61542	+	1.79411i	0.277043	+	0.307687i
$35$	0.335106	−	0.243469i	0.0566432	−	0.0411537i
$36$	−2.58579	−	4.47871i	−0.430964	−	0.746452i
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$	−0.191123	−	1.81841i	−0.0310042	−	0.294985i
$39$	1.28293	+	0.932102i	0.205433	+	0.149256i
$40$	0.165760	−	1.57710i	0.0262089	−	0.249361i
$41$	−5.00863	+	5.56265i	−0.782217	+	0.868740i	−0.994090	−	0.108557i	$-0.965377\pi$
$41$	−5.00863	+	5.56265i	−0.782217	+	0.868740i	0.211873	+	0.977297i	$0.432044\pi$
$42$	0.0649237	+	0.0289059i	0.0100179	+	0.00446027i
$43$	−10.6613	−	2.26613i	−1.62584	−	0.345582i	−0.697287	−	0.716792i	$-0.745609\pi$
$43$	−10.6613	−	2.26613i	−1.62584	−	0.345582i	−0.928549	+	0.371211i	$0.878943\pi$
$44$	−5.79937	+	1.23269i	−0.874288	+	0.185836i
$45$	−2.58390	+	1.15042i	−0.385185	+	0.171495i
$46$	0.511996	−	1.57576i	0.0754897	−	0.232333i
$47$	2.98413	−	9.18421i	0.435280	−	1.33966i	−0.457519	−	0.889200i	$-0.651262\pi$
$47$	2.98413	−	9.18421i	0.435280	−	1.33966i	0.892799	−	0.450455i	$-0.148738\pi$
$48$	−1.13521	+	0.505428i	−0.163853	+	0.0729522i
$49$	6.67921	−	1.41971i	0.954173	−	0.202816i
$50$	1.62065	+	0.344479i	0.229194	+	0.0487167i
$51$	−2.20549	−	0.981949i	−0.308831	−	0.137500i
$52$	−4.68391	+	5.20201i	−0.649542	+	0.721390i
$53$	0.609237	−	5.79650i	0.0836851	−	0.796210i	−0.869522	−	0.493893i	$-0.835573\pi$
$53$	0.609237	−	5.79650i	0.0836851	−	0.796210i	0.953207	−	0.302317i	$-0.0977601\pi$
$54$	−0.809017	−	0.587785i	−0.110093	−	0.0799874i
$55$	0.338948	+	3.22488i	0.0457038	+	0.434842i
$56$	−0.328427	+	0.568852i	−0.0438879	+	0.0760161i
$57$	0.914214	+	1.58346i	0.121091	+	0.209735i
$58$	−2.28825	+	1.66251i	−0.300461	+	0.218298i
$59$	2.72408	+	3.02539i	0.354644	+	0.393873i	0.893898	−	0.448271i	$-0.147960\pi$
$59$	2.72408	+	3.02539i	0.354644	+	0.393873i	−0.539253	+	0.842144i	$0.681293\pi$
$60$	0.234037	+	0.720292i	0.0302140	+	0.0929892i
$61$	2.82843			0.362143			0.181071	−	0.983470i	$-0.442043\pi$
$61$	2.82843			0.362143			0.181071	+	0.983470i	$0.442043\pi$
$62$		0			0
$63$	1.17157			0.147604
$64$	−1.28909	−	3.96740i	−0.161136	−	0.495925i
$65$	2.56172	+	2.84508i	0.317742	+	0.352888i
$66$	−0.450096	+	0.327014i	−0.0554030	+	0.0402526i
$67$	−1.62132	−	2.80821i	−0.198076	−	0.343077i	0.749829	−	0.661632i	$-0.230136\pi$
$67$	−1.62132	−	2.80821i	−0.198076	−	0.343077i	−0.947904	+	0.318555i	$0.896803\pi$
$68$	5.32843	−	9.22911i	0.646167	−	1.11919i
$69$	0.173188	+	1.64778i	0.0208494	+	0.198369i
$70$	0.138805	+	0.100848i	0.0165904	+	0.0120536i
$71$	−0.00742861	+	0.0706785i	−0.000881614	+	0.00838799i	−0.994954	−	0.100334i	$-0.968009\pi$
$71$	−0.00742861	+	0.0706785i	−0.000881614	+	0.00838799i	0.994072	+	0.108722i	$0.0346757\pi$
$72$	3.00124	−	3.33321i	0.353699	−	0.392823i
$73$	1.67035	+	0.743688i	0.195500	+	0.0870421i	0.502151	−	0.864780i	$-0.332542\pi$
$73$	1.67035	+	0.743688i	0.195500	+	0.0870421i	−0.306652	+	0.951822i	$0.599209\pi$
$74$	0.405162	+	0.0861198i	0.0470991	+	0.0100112i
$75$	−1.62065	+	0.344479i	−0.187136	+	0.0397771i
$76$	−7.37329	+	3.28280i	−0.845774	+	0.376563i
$77$	0.415055	−	1.27741i	0.0472999	−	0.145574i
$78$	−0.202979	+	0.624706i	−0.0229829	+	0.0707340i
$79$	6.17315	−	2.74847i	0.694534	−	0.309227i	−0.0289369	−	0.999581i	$-0.509212\pi$
$79$	6.17315	−	2.74847i	0.694534	−	0.309227i	0.723471	+	0.690355i	$0.242546\pi$
$80$	−2.93444	+	0.623735i	−0.328081	+	0.0697357i
$81$	−7.32171	−	1.55628i	−0.813523	−	0.172920i
$82$	−2.83245	−	1.26109i	−0.312792	−	0.139264i
$83$	6.73886	−	7.48426i	0.739686	−	0.821504i	−0.249469	−	0.968383i	$-0.580256\pi$
$83$	6.73886	−	7.48426i	0.739686	−	0.821504i	0.989155	+	0.146878i	$0.0469226\pi$
$84$	0.0327915	−	0.311990i	0.00357784	−	0.0340409i
$85$	−4.71530	−	3.42586i	−0.511446	−	0.371587i
$86$	−0.471917	−	4.48999i	−0.0508881	−	0.484168i
$87$	1.41421	−	2.44949i	0.151620	−	0.262613i
$88$	−2.57107	−	4.45322i	−0.274077	−	0.474715i
$89$	3.62867	−	2.63638i	0.384638	−	0.279456i	−0.378617	−	0.925554i	$-0.623600\pi$
$89$	3.62867	−	2.63638i	0.384638	−	0.279456i	0.763255	+	0.646098i	$0.223600\pi$
$90$	−0.783935	−	0.870648i	−0.0826340	−	0.0917744i
$91$	−0.490035	−	1.50817i	−0.0513696	−	0.158099i
$92$	−7.31371			−0.762507
$93$		0			0
$94$	4.00000			0.412568
$95$	1.36407	+	4.19817i	0.139950	+	0.430723i
$96$	−1.22346	−	1.35879i	−0.124869	−	0.138681i
$97$	−4.18389	+	3.03977i	−0.424810	+	0.308642i	−0.779570	−	0.626315i	$-0.784562\pi$
$97$	−4.18389	+	3.03977i	−0.424810	+	0.308642i	0.354760	+	0.934957i	$0.384562\pi$
$98$	1.41421	+	2.44949i	0.142857	+	0.247436i
$99$	−4.58579	+	7.94282i	−0.460889	+	0.798283i
$100$	−0.764491	−	7.27364i	−0.0764491	−	0.727364i
$101$	6.86474	+	4.98752i	0.683067	+	0.496277i	0.874374	−	0.485253i	$-0.161273\pi$
$101$	6.86474	+	4.98752i	0.683067	+	0.496277i	−0.191307	+	0.981530i	$0.561273\pi$
$102$	0.104528	−	0.994522i	0.0103499	−	0.0984723i
$103$	1.38581	−	1.53910i	0.136548	−	0.151652i	−0.670992	−	0.741465i	$-0.734132\pi$
$103$	1.38581	−	1.53910i	0.136548	−	0.151652i	0.807540	+	0.589812i	$0.200798\pi$
$104$	−5.54620	−	2.46933i	−0.543849	−	0.242137i
$105$	−0.167824	−	0.0356720i	−0.0163779	−	0.00348123i
$106$	2.36146	−	0.501943i	0.229365	−	0.0487530i
$107$	11.3409	−	5.04932i	1.09637	−	0.488136i	0.222816	−	0.974861i	$-0.428475\pi$
$107$	11.3409	−	5.04932i	1.09637	−	0.488136i	0.873555	+	0.486725i	$0.161809\pi$
$108$	−1.36407	+	4.19817i	−0.131257	+	0.403969i
$109$	−3.34617	+	10.2984i	−0.320505	+	0.986412i	0.652924	+	0.757423i	$0.273542\pi$
$109$	−3.34617	+	10.2984i	−0.320505	+	0.986412i	−0.973429	+	0.228989i	$0.926458\pi$
$110$	−1.22702	+	0.546307i	−0.116992	+	0.0520883i
$111$	−0.405162	+	0.0861198i	−0.0384563	+	0.00817413i
$112$	1.21549	+	0.258360i	0.114853	+	0.0244127i
$113$	15.2168	+	6.77495i	1.43148	+	0.637334i	0.968495	−	0.249034i	$-0.0801132\pi$
$113$	15.2168	+	6.77495i	1.43148	+	0.637334i	0.462981	+	0.886368i	$0.346780\pi$
$114$	−0.506772	+	0.562828i	−0.0474636	+	0.0527136i
$115$	−0.418114	+	3.97809i	−0.0389893	+	0.370959i
$116$	10.1008	+	7.33866i	0.937836	+	0.681378i
$117$	1.13188	+	10.7691i	0.104642	+	0.995604i
$118$	−0.843146	+	1.46037i	−0.0776179	+	0.134438i
$119$	1.20711	+	2.09077i	0.110655	+	0.191661i
$120$	−0.531406	+	0.386089i	−0.0485105	+	0.0352450i
$121$	−0.324717	−	0.360634i	−0.0295197	−	0.0327849i
$122$	0.362036	+	1.11423i	0.0327772	+	0.100878i
$123$	3.10051			0.279563
$124$		0			0
$125$	−9.00000			−0.804984
$126$	0.149960	+	0.461530i	0.0133595	+	0.0411164i
$127$	−5.95492	−	6.61361i	−0.528414	−	0.586863i	0.418554	−	0.908192i	$-0.362537\pi$
$127$	−5.95492	−	6.61361i	−0.528414	−	0.586863i	−0.946968	+	0.321329i	$0.895871\pi$
$128$	8.54027	−	6.20487i	0.754860	−	0.548438i
$129$	2.25736	+	3.90986i	0.198749	+	0.344244i
$130$	−0.792893	+	1.37333i	−0.0695413	+	0.120449i
$131$	1.38423	+	13.1701i	0.120941	+	1.15068i	0.871679	+	0.490077i	$0.163031\pi$
$131$	1.38423	+	13.1701i	0.120941	+	1.15068i	−0.750738	+	0.660600i	$0.770302\pi$
$132$	1.98682	+	1.44351i	0.172930	+	0.125641i
$133$	0.191123	−	1.81841i	0.0165724	−	0.157676i
$134$	0.898740	−	0.998152i	0.0776393	−	0.0862272i
$135$	2.20549	+	0.981949i	0.189819	+	0.0845127i
$136$	9.04067	+	1.92165i	0.775231	+	0.164780i
$137$	9.27801	−	1.97210i	0.792673	−	0.168488i	0.206257	−	0.978498i	$-0.433872\pi$
$137$	9.27801	−	1.97210i	0.792673	−	0.168488i	0.586416	+	0.810010i	$0.300538\pi$
$138$	−0.626958	+	0.279140i	−0.0533703	+	0.0237620i
$139$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$139$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$140$	0.234037	−	0.720292i	0.0197797	−	0.0608757i
$141$	−3.65418	+	1.62695i	−0.307738	+	0.137014i
$142$	−0.0287940	+	0.00612035i	−0.00241634	+	0.000513608i
$143$	12.1429	+	2.58106i	1.01544	+	0.215839i
$144$	−7.75169	−	3.45127i	−0.645974	−	0.287606i
$145$	4.56911	−	5.07451i	0.379444	−	0.421415i
$146$	−0.0791656	+	0.753210i	−0.00655179	+	0.0623361i
$147$	−2.28825	−	1.66251i	−0.188731	−	0.137121i
$148$	−0.191123	−	1.81841i	−0.0157102	−	0.149472i
$149$	−0.500000	+	0.866025i	−0.0409616	+	0.0709476i	−0.885779	−	0.464107i	$-0.846375\pi$
$149$	−0.500000	+	0.866025i	−0.0409616	+	0.0709476i	0.844818	+	0.535054i	$0.179709\pi$
$150$	−0.343146	−	0.594346i	−0.0280177	−	0.0485281i
$151$	4.29888	−	3.12332i	0.349838	−	0.254172i	−0.398963	−	0.916967i	$-0.630630\pi$
$151$	4.29888	−	3.12332i	0.349838	−	0.254172i	0.748801	+	0.662795i	$0.230630\pi$
$152$	−4.68391	−	5.20201i	−0.379916	−	0.421939i
$153$	−5.09423	−	15.6784i	−0.411844	−	1.26753i
$154$	0.556349			0.0448319
$155$		0			0
$156$	2.89949			0.232145
$157$	2.83417	+	8.72268i	0.226192	+	0.696146i	0.998168	+	0.0604954i	$0.0192681\pi$
$157$	2.83417	+	8.72268i	0.226192	+	0.696146i	−0.771977	+	0.635651i	$0.780732\pi$
$158$	1.87289	+	2.08005i	0.148999	+	0.165480i
$159$	−1.95314	+	1.41904i	−0.154894	+	0.112537i
$160$	−2.20711	−	3.82282i	−0.174487	−	0.302221i
$161$	0.828427	−	1.43488i	0.0652892	−	0.113084i
$162$	−0.324091	−	3.08352i	−0.0254630	−	0.242264i
$163$	−16.9655	−	12.3262i	−1.32884	−	0.965462i	−0.999776	−	0.0211551i	$-0.993266\pi$
$163$	−16.9655	−	12.3262i	−1.32884	−	0.965462i	−0.329068	−	0.944306i	$-0.606734\pi$
$164$	−1.43061	+	13.6113i	−0.111712	+	1.06287i
$165$	0.898740	−	0.998152i	0.0699668	−	0.0777060i
$166$	3.81092	+	1.69673i	0.295785	+	0.131692i
$167$	22.0634	+	4.68973i	1.70732	+	0.362902i	0.955163	−	0.296081i	$-0.0956800\pi$
$167$	22.0634	+	4.68973i	1.70732	+	0.362902i	0.752157	+	0.658983i	$0.229013\pi$
$168$	0.266132	−	0.0565682i	0.0205326	−	0.00436433i
$169$	1.51361	−	0.673903i	0.116432	−	0.0518387i
$170$	0.746033	−	2.29605i	0.0572181	−	0.176099i
$171$	−3.85816	+	11.8742i	−0.295041	+	0.908043i
$172$	−18.2060	+	8.10583i	−1.38819	+	0.618064i
$173$	−8.13203	+	1.72852i	−0.618267	+	0.131417i	−0.506389	−	0.862305i	$-0.669020\pi$
$173$	−8.13203	+	1.72852i	−0.618267	+	0.131417i	−0.111878	+	0.993722i	$0.535687\pi$
$174$	1.14597	+	0.243584i	0.0868759	+	0.0184660i
$175$	1.51361	+	0.673903i	0.114418	+	0.0509423i
$176$	−6.50925	+	7.22925i	−0.490653	+	0.544926i
$177$	0.176265	−	1.67705i	0.0132489	−	0.126055i
$178$	1.50304	+	1.09203i	0.112658	+	0.0818508i
$179$	−1.59329	−	15.1591i	−0.119088	−	1.13305i	−0.876933	−	0.480613i	$-0.840414\pi$
$179$	−1.59329	−	15.1591i	−0.119088	−	1.13305i	0.757845	−	0.652435i	$-0.226252\pi$
$180$	−2.58579	+	4.47871i	−0.192733	+	0.333824i
$181$	6.15685	+	10.6640i	0.457635	+	0.792648i	0.998835	−	0.0482461i	$-0.0153632\pi$
$181$	6.15685	+	10.6640i	0.457635	+	0.792648i	−0.541200	+	0.840894i	$0.682030\pi$
$182$	0.531406	−	0.386089i	0.0393905	−	0.0286188i
$183$	−0.783935	−	0.870648i	−0.0579502	−	0.0643602i
$184$	−1.96014	−	6.03269i	−0.144503	−	0.444736i
$185$	−1.00000			−0.0735215
$186$		0			0
$187$	−18.8995			−1.38207
$188$	−5.45627	−	16.7927i	−0.397939	−	1.22473i
$189$	−0.669131	−	0.743145i	−0.0486721	−	0.0540558i
$190$	−1.47923	+	1.07472i	−0.107315	+	0.0779686i
$191$	10.4497	+	18.0995i	0.756117	+	1.30963i	0.944817	+	0.327599i	$0.106239\pi$
$191$	10.4497	+	18.0995i	0.756117	+	1.30963i	−0.188700	+	0.982035i	$0.560427\pi$
$192$	−0.863961	+	1.49642i	−0.0623510	+	0.107995i
$193$	−0.746556	−	7.10301i	−0.0537383	−	0.511286i	−0.987973	−	0.154627i	$-0.950582\pi$
$193$	−0.746556	−	7.10301i	−0.0537383	−	0.511286i	0.934235	−	0.356659i	$-0.116084\pi$
$194$	−1.73302	−	1.25912i	−0.124424	−	0.0903992i
$195$	0.165760	−	1.57710i	0.0118703	−	0.112938i
$196$	8.35428	−	9.27837i	0.596735	−	0.662741i
$197$	12.3194	+	5.48496i	0.877722	+	0.390787i	0.795591	−	0.605834i	$-0.207161\pi$
$197$	12.3194	+	5.48496i	0.877722	+	0.390787i	0.0821314	+	0.996622i	$0.473827\pi$
$198$	−3.71597	−	0.789854i	−0.264083	−	0.0561325i
$199$	18.0118	−	3.82853i	1.27682	−	0.271397i	0.480890	−	0.876781i	$-0.340314\pi$
$199$	18.0118	−	3.82853i	1.27682	−	0.271397i	0.795934	+	0.605384i	$0.206980\pi$
$200$	5.79475	−	2.57999i	0.409751	−	0.182433i
$201$	−0.415055	+	1.27741i	−0.0292757	+	0.0901014i
$202$	−1.08611	+	3.34270i	−0.0764183	+	0.235191i
$203$	−2.58390	+	1.15042i	−0.181354	+	0.0807440i
$204$	−4.31775	+	0.917767i	−0.302303	+	0.0642565i
$205$	7.32171	+	1.55628i	0.511370	+	0.108695i
$206$	0.783698	+	0.348925i	0.0546028	+	0.0243107i
$207$	−7.57035	+	8.40772i	−0.526176	+	0.584377i
$208$	−1.20054	+	11.4224i	−0.0832424	+	0.791998i
$209$	11.5800	+	8.41339i	0.801008	+	0.581966i
$210$	−0.00742861	−	0.0706785i	−0.000512623	−	0.00487728i
$211$	−5.20711	+	9.01897i	−0.358472	+	0.620892i	−0.987706	−	0.156324i	$-0.950035\pi$
$211$	−5.20711	+	9.01897i	−0.358472	+	0.620892i	0.629234	+	0.777216i	$0.283369\pi$
$212$	−5.32843	−	9.22911i	−0.365958	−	0.633858i
$213$	0.0238152	−	0.0173028i	0.00163179	−	0.00118557i
$214$	3.44076	+	3.82135i	0.235206	+	0.261222i
$215$	3.36813	+	10.3660i	0.229705	+	0.706958i
$216$	−3.82843			−0.260491
$217$		0			0
$218$	−4.48528			−0.303782
$219$	−0.234037	−	0.720292i	−0.0158147	−	0.0486728i
$220$	3.96723	+	4.40606i	0.267471	+	0.297056i
$221$	−18.0522	+	13.1157i	−1.21432	+	0.882255i
$222$	−0.0857864	−	0.148586i	−0.00575761	−	0.00997247i
$223$	−11.8640	+	20.5490i	−0.794470	+	1.37606i	0.128706	+	0.991683i	$0.458918\pi$
$223$	−11.8640	+	20.5490i	−0.794470	+	1.37606i	−0.923175	+	0.384379i	$0.874416\pi$
$224$	0.191123	+	1.81841i	0.0127699	+	0.121498i
$225$	−9.15298	−	6.65003i	−0.610199	−	0.443335i
$226$	−0.721194	+	6.86170i	−0.0479731	+	0.456433i
$227$	−12.3215	+	13.6844i	−0.817808	+	0.908267i	−0.997144	−	0.0755204i	$-0.975938\pi$
$227$	−12.3215	+	13.6844i	−0.817808	+	0.908267i	0.179337	+	0.983788i	$0.442605\pi$
$228$	3.05412	+	1.35978i	0.202264	+	0.0900536i
$229$	−5.36541	−	1.14045i	−0.354557	−	0.0753633i	0.0271902	−	0.999630i	$-0.491344\pi$
$229$	−5.36541	−	1.14045i	−0.354557	−	0.0753633i	−0.381747	+	0.924267i	$0.624677\pi$
$230$	−1.62065	+	0.344479i	−0.106862	+	0.0227143i
$231$	−0.508250	+	0.226288i	−0.0334404	+	0.0148886i
$232$	−3.34617	+	10.2984i	−0.219687	+	0.676126i
$233$	−2.83417	+	8.72268i	−0.185673	+	0.571442i	−0.999959	−	0.00902109i	$-0.997128\pi$
$233$	−2.83417	+	8.72268i	−0.185673	+	0.571442i	0.814287	+	0.580463i	$0.197128\pi$
$234$	−4.09751	+	1.82433i	−0.267863	+	0.119260i
$235$	−9.44583	+	2.00777i	−0.616178	+	0.130973i
$236$	7.28099	+	1.54762i	0.473952	+	0.100742i
$237$	−2.55700	−	1.13845i	−0.166095	−	0.0739504i
$238$	−0.669131	+	0.743145i	−0.0433733	+	0.0481709i
$239$	−2.22046	+	21.1263i	−0.143630	+	1.36654i	0.650828	+	0.759225i	$0.274422\pi$
$239$	−2.22046	+	21.1263i	−0.143630	+	1.36654i	−0.794458	+	0.607320i	$0.792245\pi$
$240$	1.00532	+	0.730406i	0.0648930	+	0.0471475i
$241$	1.39474	+	13.2701i	0.0898430	+	0.854799i	0.942921	+	0.333016i	$0.108066\pi$
$241$	1.39474	+	13.2701i	0.0898430	+	0.854799i	−0.853078	+	0.521783i	$0.825267\pi$
$242$	0.100505	−	0.174080i	0.00646071	−	0.0111903i
$243$	5.17157	+	8.95743i	0.331757	+	0.574619i
$244$	4.18389	−	3.03977i	0.267846	−	0.194602i
$245$	−4.56911	−	5.07451i	−0.291910	−	0.324199i
$246$	0.396862	+	1.22141i	0.0253030	+	0.0778745i
$247$	16.8995			1.07529
$248$		0			0
$249$	−4.17157			−0.264363
$250$	−1.15199	−	3.54546i	−0.0728583	−	0.224235i
$251$	−4.29195	−	4.76669i	−0.270905	−	0.300871i	0.592307	−	0.805713i	$-0.298217\pi$
$251$	−4.29195	−	4.76669i	−0.270905	−	0.300871i	−0.863212	+	0.504842i	$0.831551\pi$
$252$	1.73302	−	1.25912i	0.109170	−	0.0793168i
$253$	6.48528	+	11.2328i	0.407726	+	0.706202i
$254$	1.84315	−	3.19242i	0.115649	−	0.200310i
$255$	0.252354	+	2.40099i	0.0158030	+	0.150356i
$256$	−3.21225	−	2.33384i	−0.200766	−	0.145865i
$257$	−2.33242	+	22.1915i	−0.145492	+	1.38427i	0.641415	+	0.767194i	$0.278348\pi$
$257$	−2.33242	+	22.1915i	−0.145492	+	1.38427i	−0.786907	+	0.617072i	$0.788319\pi$
$258$	−1.25131	+	1.38972i	−0.0779033	+	0.0865204i
$259$	0.378403	+	0.168476i	0.0235128	+	0.0104686i
$260$	6.84703	+	1.45538i	0.424635	+	0.0902589i
$261$	18.8917	−	4.01555i	1.16936	−	0.248556i
$262$	−5.01105	+	2.23106i	−0.309584	+	0.137836i
$263$	7.20433	−	22.1727i	0.444238	−	1.36722i	−0.439079	−	0.898448i	$-0.644695\pi$
$263$	7.20433	−	22.1727i	0.444238	−	1.36722i	0.883317	−	0.468776i	$-0.155305\pi$
$264$	−0.658188	+	2.02570i	−0.0405087	+	0.124673i
$265$	−5.32453	+	2.37063i	−0.327083	+	0.145627i
$266$	0.740809	−	0.157464i	0.0454219	−	0.00965473i
$267$	−1.81727	−	0.386272i	−0.111215	−	0.0236394i
$268$	−5.41635	−	2.41151i	−0.330856	−	0.147307i
$269$	17.5122	−	19.4493i	1.06774	−	1.18584i	0.0858639	−	0.996307i	$-0.472635\pi$
$269$	17.5122	−	19.4493i	1.06774	−	1.18584i	0.981874	−	0.189536i	$-0.0606984\pi$
$270$	−0.104528	+	0.994522i	−0.00636140	+	0.0605247i
$271$	−0.555221	−	0.403392i	−0.0337273	−	0.0245043i	0.570794	−	0.821093i	$-0.306636\pi$
$271$	−0.555221	−	0.403392i	−0.0337273	−	0.0245043i	−0.604521	+	0.796589i	$0.706636\pi$
$272$	−1.82771	−	17.3895i	−0.110821	−	1.05439i
$273$	−0.328427	+	0.568852i	−0.0198773	+	0.0344285i
$274$	1.96447	+	3.40256i	0.118678	+	0.205556i
$275$	−10.4934	+	7.62391i	−0.632776	+	0.459739i
$276$	2.02709	+	2.25131i	0.122016	+	0.135513i
$277$	−4.37016	−	13.4500i	−0.262577	−	0.808130i	−0.992242	−	0.124325i	$-0.960324\pi$
$277$	−4.37016	−	13.4500i	−0.262577	−	0.808130i	0.729664	−	0.683806i	$-0.239676\pi$
$278$		0			0
$279$		0			0
$280$	0.656854			0.0392545
$281$	0.618034	+	1.90211i	0.0368688	+	0.113471i	0.967797	−	0.251731i	$-0.0809999\pi$
$281$	0.618034	+	1.90211i	0.0368688	+	0.113471i	−0.930928	+	0.365202i	$0.881000\pi$
$282$	−1.10865	−	1.23128i	−0.0660193	−	0.0733218i
$283$	11.0486	−	8.02730i	0.656773	−	0.477173i	−0.208799	−	0.977959i	$-0.566955\pi$
$283$	11.0486	−	8.02730i	0.656773	−	0.477173i	0.865572	+	0.500785i	$0.166955\pi$
$284$	0.0649712	+	0.112533i	0.00385533	+	0.00667763i
$285$	0.914214	−	1.58346i	0.0541533	−	0.0937963i
$286$	0.537500	+	5.11397i	0.0317830	+	0.302395i
$287$	−2.50836	−	1.82243i	−0.148064	−	0.107575i
$288$	1.30507	−	12.4169i	0.0769018	−	0.731672i
$289$	11.3555	−	12.6116i	0.667972	−	0.741858i
$290$	2.58390	+	1.15042i	0.151732	+	0.0675553i
$291$	2.09532	+	0.445375i	0.122830	+	0.0261083i
$292$	3.27009	−	0.695079i	0.191368	−	0.0406764i
$293$	13.5195	−	6.01929i	0.789821	−	0.351651i	0.0281404	−	0.999604i	$-0.491041\pi$
$293$	13.5195	−	6.01929i	0.789821	−	0.351651i	0.761680	+	0.647953i	$0.224375\pi$
$294$	0.362036	−	1.11423i	0.0211144	−	0.0649833i
$295$	1.25803	−	3.87182i	0.0732453	−	0.225426i
$296$	1.44869	−	0.644997i	0.0842033	−	0.0374897i
$297$	7.65736	−	1.62762i	0.444325	−	0.0944442i
$298$	−0.405162	−	0.0861198i	−0.0234704	−	0.00498879i
$299$	13.9898	+	6.22865i	0.809049	+	0.360212i
$300$	−2.02709	+	2.25131i	−0.117034	+	0.129979i
$301$	0.471917	−	4.48999i	0.0272008	−	0.258799i
$302$	1.78065	+	1.29372i	0.102465	+	0.0744453i
$303$	−0.367388	−	3.49546i	−0.0211059	−	0.200809i
$304$	−6.62132	+	11.4685i	−0.379759	+	0.657761i
$305$	−1.41421	−	2.44949i	−0.0809776	−	0.140257i
$306$	5.52431	−	4.01365i	0.315804	−	0.229445i
$307$	−7.52279	−	8.35491i	−0.429349	−	0.476840i	0.489187	−	0.872179i	$-0.337294\pi$
$307$	−7.52279	−	8.35491i	−0.429349	−	0.476840i	−0.918535	+	0.395339i	$0.870627\pi$
$308$	−0.758898	−	2.33565i	−0.0432422	−	0.133086i
$309$	−0.857864			−0.0488022
$310$		0			0
$311$	11.3137			0.641542			0.320771	−	0.947157i	$-0.396058\pi$
$311$	11.3137			0.641542			0.320771	+	0.947157i	$0.396058\pi$
$312$	0.777091	+	2.39164i	0.0439941	+	0.135400i
$313$	1.22346	+	1.35879i	0.0691539	+	0.0768031i	0.776729	−	0.629835i	$-0.216878\pi$
$313$	1.22346	+	1.35879i	0.0691539	+	0.0768031i	−0.707575	+	0.706638i	$0.750211\pi$
$314$	−3.07345	+	2.23299i	−0.173445	+	0.126015i
$315$	−0.585786	−	1.01461i	−0.0330053	−	0.0571669i
$316$	6.17767	−	10.7000i	0.347521	−	0.601924i
$317$	0.818293	+	7.78554i	0.0459599	+	0.437280i	0.993171	+	0.116669i	$0.0372215\pi$
$317$	0.818293	+	7.78554i	0.0459599	+	0.437280i	−0.947211	+	0.320611i	$0.896112\pi$
$318$	−0.809017	−	0.587785i	−0.0453674	−	0.0329614i
$319$	2.31448	−	22.0208i	0.129586	−	1.23293i
$320$	−2.79133	+	3.10008i	−0.156040	+	0.173300i
$321$	−4.69757	−	2.09149i	−0.262193	−	0.116736i
$322$	0.671294	+	0.142688i	0.0374098	+	0.00795169i
$323$	−25.1657	+	5.34914i	−1.40026	+	0.297634i
$324$	−12.5030	+	5.56672i	−0.694614	+	0.309262i
$325$	−4.73220	+	14.5642i	−0.262495	+	0.807877i
$326$	2.68421	−	8.26115i	0.148665	−	0.457543i
$327$	4.09751	−	1.82433i	0.226593	−	0.100886i
$328$	−11.6107	+	2.46792i	−0.641092	+	0.136268i
$329$	3.91259	+	0.831647i	0.215708	+	0.0458502i
$330$	0.508250	+	0.226288i	0.0279783	+	0.0124567i
$331$	−6.18453	+	6.86862i	−0.339933	+	0.377534i	−0.888737	−	0.458417i	$-0.848417\pi$
$331$	−6.18453	+	6.86862i	−0.339933	+	0.377534i	0.548804	+	0.835951i	$0.315083\pi$
$332$	1.92481	−	18.3133i	0.105638	−	1.00508i
$333$	−2.28825	−	1.66251i	−0.125395	−	0.0911049i
$334$	0.976625	+	9.29196i	0.0534385	+	0.508434i
$335$	−1.62132	+	2.80821i	−0.0885822	+	0.153429i
$336$	−0.257359	−	0.445759i	−0.0140401	−	0.0243182i
$337$	7.53495	−	5.47446i	0.410455	−	0.298213i	−0.363331	−	0.931660i	$-0.618361\pi$
$337$	7.53495	−	5.47446i	0.410455	−	0.298213i	0.773786	+	0.633447i	$0.218361\pi$
$338$	0.459219	+	0.510014i	0.0249782	+	0.0277411i
$339$	−2.13206	−	6.56181i	−0.115798	−	0.356389i
$340$	−10.6569			−0.577949
$341$		0			0
$342$	−5.17157			−0.279647
$343$	1.77003	+	5.44758i	0.0955724	+	0.294142i
$344$	−11.5654	−	12.8447i	−0.623566	−	0.692541i
$345$	1.34042	−	0.973874i	0.0721660	−	0.0524316i
$346$	−1.72183	−	2.98229i	−0.0925659	−	0.160329i
$347$	−4.27817	+	7.41002i	−0.229664	+	0.397790i	−0.957709	−	0.287740i	$-0.907096\pi$
$347$	−4.27817	+	7.41002i	−0.229664	+	0.397790i	0.728044	+	0.685530i	$0.240430\pi$
$348$	−0.540577	−	5.14324i	−0.0289779	−	0.275707i
$349$	21.9346	+	15.9364i	1.17413	+	0.853058i	0.991498	−	0.130122i	$-0.0415370\pi$
$349$	21.9346	+	15.9364i	1.17413	+	0.853058i	0.182636	+	0.983181i	$0.441537\pi$
$350$	−0.0717370	+	0.682532i	−0.00383450	+	0.0364829i
$351$	6.18453	−	6.86862i	0.330106	−	0.366620i
$352$	−13.0762	−	5.82191i	−0.696965	−	0.310309i
$353$	2.93444	+	0.623735i	0.156185	+	0.0331981i	0.285340	−	0.958426i	$-0.407893\pi$
$353$	2.93444	+	0.623735i	0.156185	+	0.0331981i	−0.129156	+	0.991624i	$0.541227\pi$
$354$	0.683221	−	0.145223i	0.0363128	−	0.00771852i
$355$	0.0649237	−	0.0289059i	0.00344579	−	0.00153416i
$356$	2.53425	−	7.79962i	0.134315	−	0.413379i
$357$	0.309017	−	0.951057i	0.0163549	−	0.0503352i
$358$	5.76786	−	2.56802i	0.304841	−	0.135724i
$359$	−6.94534	+	1.47628i	−0.366561	+	0.0779150i	−0.387510	−	0.921866i	$-0.626665\pi$
$359$	−6.94534	+	1.47628i	−0.366561	+	0.0779150i	0.0209487	+	0.999781i	$0.493331\pi$
$360$	−4.38727	−	0.932542i	−0.231229	−	0.0491493i
$361$	0.443327	+	0.197382i	0.0233330	+	0.0103885i
$362$	−3.41290	+	3.79041i	−0.179378	+	0.199220i
$363$	−0.0210113	+	0.199909i	−0.00110281	+	0.0104925i
$364$	−2.34574	−	1.70428i	−0.122950	−	0.0893286i
$365$	−0.191123	−	1.81841i	−0.0100038	−	0.0951800i
$366$	0.242641	−	0.420266i	0.0126830	−	0.0219677i
$367$	−12.1066	−	20.9692i	−0.631959	−	1.09459i	−0.987151	−	0.159792i	$-0.948918\pi$
$367$	−12.1066	−	20.9692i	−0.631959	−	1.09459i	0.355191	−	0.934794i	$-0.384416\pi$
$368$	−9.70820	+	7.05342i	−0.506075	+	0.367685i
$369$	14.1665	+	15.7335i	0.737481	+	0.819056i
$370$	−0.127999	−	0.393941i	−0.00665435	−	0.0204800i
$371$	2.41421			0.125340
$372$		0			0
$373$	10.0000			0.517780			0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000			0.517780			0.258890	+	0.965907i	$0.416643\pi$
$374$	−2.41912	−	7.44528i	−0.125090	−	0.384986i
$375$	2.49447	+	2.77039i	0.128814	+	0.143062i
$376$	12.3891	−	9.00117i	0.638916	−	0.464200i
$377$	−13.0711	−	22.6398i	−0.673194	−	1.16601i
$378$	0.207107	−	0.358719i	0.0106524	−	0.0184505i
$379$	−0.771919	−	7.34432i	−0.0396508	−	0.377252i	−0.996296	−	0.0859951i	$-0.972593\pi$
$379$	−0.771919	−	7.34432i	−0.0396508	−	0.377252i	0.956645	−	0.291257i	$-0.0940736\pi$
$380$	6.52963	+	4.74405i	0.334963	+	0.243365i
$381$	−0.385322	+	3.66610i	−0.0197407	+	0.187820i
$382$	−5.79257	+	6.43330i	−0.296373	+	0.329156i
$383$	−4.65954	−	2.07456i	−0.238092	−	0.106005i	0.284223	−	0.958758i	$-0.408265\pi$
$383$	−4.65954	−	2.07456i	−0.238092	−	0.106005i	−0.522314	+	0.852753i	$0.674931\pi$
$384$	−4.27703	−	0.909111i	−0.218261	−	0.0463929i
$385$	−1.31379	+	0.279256i	−0.0669572	+	0.0142322i
$386$	2.70260	−	1.20328i	0.137559	−	0.0612452i
$387$	−9.52651	+	29.3196i	−0.484260	+	1.49040i
$388$	−2.92202	+	8.99304i	−0.148343	+	0.456553i
$389$	10.1788	−	4.53191i	0.516088	−	0.229777i	−0.132129	−	0.991232i	$-0.542181\pi$
$389$	10.1788	−	4.53191i	0.516088	−	0.229777i	0.648217	+	0.761455i	$0.275515\pi$
$390$	0.642500	−	0.136568i	0.0325343	−	0.00691537i
$391$	−22.8042	−	4.84719i	−1.15326	−	0.245133i
$392$	9.89226	+	4.40432i	0.499635	+	0.222452i
$393$	3.67037	−	4.07636i	0.185146	−	0.205625i
$394$	−0.583874	+	5.55519i	−0.0294151	+	0.279866i
$395$	−5.46682	−	3.97188i	−0.275065	−	0.199847i
$396$	1.75290	+	16.6777i	0.0880863	+	0.838085i
$397$	16.7426	−	28.9991i	0.840289	−	1.45542i	−0.0493613	−	0.998781i	$-0.515719\pi$
$397$	16.7426	−	28.9991i	0.840289	−	1.45542i	0.889650	−	0.456642i	$-0.150948\pi$
$398$	3.81371	+	6.60554i	0.191164	+	0.331106i
$399$	−0.612717	+	0.445165i	−0.0306742	+	0.0222861i
$400$	−8.02957	−	8.91774i	−0.401478	−	0.445887i
$401$	8.29044	+	25.5154i	0.414005	+	1.27418i	0.913138	+	0.407651i	$0.133652\pi$
$401$	8.29044	+	25.5154i	0.414005	+	1.27418i	−0.499133	+	0.866525i	$0.666348\pi$
$402$	−0.556349			−0.0277482
$403$		0			0
$404$	15.5147			0.771886
$405$	2.31308	+	7.11893i	0.114938	+	0.353742i
$406$	−0.783935	−	0.870648i	−0.0389061	−	0.0432096i
$407$	−2.62335	+	1.90598i	−0.130035	+	0.0944757i
$408$	−1.91421	−	3.31552i	−0.0947677	−	0.164142i
$409$	10.3284	−	17.8894i	0.510708	−	0.884572i	−0.489215	−	0.872163i	$-0.662717\pi$
$409$	10.3284	−	17.8894i	0.510708	−	0.884572i	0.999923	−	0.0124088i	$-0.00394995\pi$
$410$	0.324091	+	3.08352i	0.0160057	+	0.152284i
$411$	−3.17857	−	2.30937i	−0.156787	−	0.113913i
$412$	0.395828	−	3.76605i	0.0195010	−	0.185540i
$413$	−1.12835	+	1.25316i	−0.0555224	+	0.0616639i
$414$	−4.28114	−	1.90609i	−0.210407	−	0.0936790i
$415$	−9.85099	−	2.09389i	−0.483566	−	0.102785i
$416$	−16.5302	+	3.51360i	−0.810460	+	0.172269i
$417$		0			0
$418$	−1.83214	+	5.63875i	−0.0896129	+	0.275800i
$419$	8.65248	−	26.6296i	0.422701	−	1.30094i	−0.482477	−	0.875908i	$-0.660263\pi$
$419$	8.65248	−	26.6296i	0.422701	−	1.30094i	0.905178	−	0.425032i	$-0.139737\pi$
$420$	−0.286587	+	0.127597i	−0.0139840	+	0.00622608i
$421$	30.4616	−	6.47481i	1.48461	−	0.315563i	0.606907	−	0.794773i	$-0.292410\pi$
$421$	30.4616	−	6.47481i	1.48461	−	0.315563i	0.877701	+	0.479210i	$0.159077\pi$
$422$	−4.21944	−	0.896870i	−0.205399	−	0.0436590i
$423$	−24.9523	−	11.1095i	−1.21322	−	0.540162i
$424$	6.18453	−	6.86862i	0.300348	−	0.333570i
$425$	2.43695	−	23.1860i	0.118209	−	1.12469i
$426$	0.00986459	+	0.00716705i	0.000477941	+	0.000347245i
$427$	0.122463	+	1.16515i	0.00592639	+	0.0563858i
$428$	11.3492	−	19.6575i	0.548586	−	0.950179i
$429$	−2.57107	−	4.45322i	−0.124132	−	0.215003i
$430$	−3.65248	+	2.65369i	−0.176138	+	0.127972i
$431$	−11.2129	−	12.4531i	−0.540105	−	0.599847i	0.409882	−	0.912139i	$-0.365570\pi$
$431$	−11.2129	−	12.4531i	−0.540105	−	0.599847i	−0.949986	+	0.312292i	$0.898903\pi$
$432$	2.23810	+	6.88816i	0.107681	+	0.331407i
$433$	−27.1127			−1.30295			−0.651477	−	0.758669i	$-0.725850\pi$
$433$	−27.1127			−1.30295			−0.651477	+	0.758669i	$0.725850\pi$
$434$		0			0
$435$	−2.82843			−0.135613
$436$	6.11822	+	18.8300i	0.293010	+	0.901791i
$437$	11.8147	+	13.1216i	0.565176	+	0.627691i
$438$	0.253796	−	0.184393i	0.0121268	−	0.00881065i
$439$	−1.03553	−	1.79360i	−0.0494233	−	0.0856037i	0.840255	−	0.542191i	$-0.182405\pi$
$439$	−1.03553	−	1.79360i	−0.0494233	−	0.0856037i	−0.889679	+	0.456587i	$0.849072\pi$
$440$	−2.57107	+	4.45322i	−0.122571	+	0.212299i
$441$	−2.01883	−	19.2079i	−0.0961349	−	0.914662i
$442$	−7.47745	−	5.43269i	−0.355666	−	0.258407i
$443$	0.497279	−	4.73130i	0.0236265	−	0.224791i	−0.976337	−	0.216254i	$-0.930616\pi$
$443$	0.497279	−	4.73130i	0.0236265	−	0.224791i	0.999964	−	0.00853659i	$-0.00271731\pi$
$444$	−0.506772	+	0.562828i	−0.0240503	+	0.0267106i
$445$	−4.09751	−	1.82433i	−0.194241	−	0.0864815i
$446$	−9.61365	−	2.04344i	−0.455220	−	0.0967599i
$447$	0.405162	−	0.0861198i	0.0191635	−	0.00407333i
$448$	1.57854	−	0.702809i	0.0745788	−	0.0332046i
$449$	12.5546	−	38.6390i	0.592486	−	1.82349i	0.0256264	−	0.999672i	$-0.491842\pi$
$449$	12.5546	−	38.6390i	0.592486	−	1.82349i	0.566860	−	0.823814i	$-0.308158\pi$
$450$	1.44814	−	4.45693i	0.0682661	−	0.210102i
$451$	22.1736	−	9.87234i	1.04412	−	0.464870i
$452$	29.7903	−	6.33213i	1.40122	−	0.297838i
$453$	−2.15291	−	0.457616i	−0.101153	−	0.0215007i
$454$	−6.96799	−	3.10235i	−0.327024	−	0.145600i
$455$	−1.06110	+	1.17847i	−0.0497451	+	0.0552475i
$456$	−0.303080	+	2.88361i	−0.0141930	+	0.135037i
$457$	−25.1707	−	18.2876i	−1.17744	−	0.855457i	−0.185556	−	0.982634i	$-0.559409\pi$
$457$	−25.1707	−	18.2876i	−1.17744	−	0.855457i	−0.991880	+	0.127177i	$0.959409\pi$
$458$	−0.237497	−	2.25963i	−0.0110975	−	0.105586i
$459$	−7.03553	+	12.1859i	−0.328391	+	0.568789i
$460$	3.65685	+	6.33386i	0.170502	+	0.295318i
$461$	−1.73302	+	1.25912i	−0.0807150	+	0.0586429i	−0.627411	−	0.778688i	$-0.715885\pi$
$461$	−1.73302	+	1.25912i	−0.0807150	+	0.0586429i	0.546696	+	0.837331i	$0.315885\pi$
$462$	−0.154199	−	0.171256i	−0.00717401	−	0.00796754i
$463$	2.77206	+	8.53151i	0.128828	+	0.396493i	0.994579	−	0.103982i	$-0.0331586\pi$
$463$	2.77206	+	8.53151i	0.128828	+	0.396493i	−0.865751	+	0.500475i	$0.833159\pi$
$464$	20.4853			0.951005
$465$		0			0
$466$	−3.79899			−0.175985
$467$	−2.47214	−	7.60845i	−0.114397	−	0.352077i	0.877424	−	0.479716i	$-0.159260\pi$
$467$	−2.47214	−	7.60845i	−0.114397	−	0.352077i	−0.991821	+	0.127639i	$0.959260\pi$
$468$	13.2481	+	14.7135i	0.612394	+	0.680133i
$469$	1.08663	−	0.789481i	0.0501758	−	0.0364549i
$470$	−2.00000	−	3.46410i	−0.0922531	−	0.159787i
$471$	1.89949	−	3.29002i	0.0875241	−	0.151596i
$472$	0.674819	+	6.42048i	0.0310611	+	0.295526i
$473$	28.5932	+	20.7742i	1.31472	+	0.955198i
$474$	0.121188	−	1.15303i	0.00556636	−	0.0529603i
$475$	−11.8147	+	13.1216i	−0.542098	+	0.602060i
$476$	4.03258	+	1.79542i	0.184833	+	0.0822931i
$477$	−16.1250	−	3.42748i	−0.738315	−	0.156934i
$478$	−8.60671	+	1.82941i	−0.393662	+	0.0836754i
$479$	−14.3682	+	6.39712i	−0.656499	+	0.292292i	−0.707823	−	0.706390i	$-0.750322\pi$
$479$	−14.3682	+	6.39712i	−0.656499	+	0.292292i	0.0513242	+	0.998682i	$0.483656\pi$
$480$	−0.565015	+	1.73894i	−0.0257893	+	0.0793713i
$481$	−1.18305	+	3.64105i	−0.0539424	+	0.166018i
$482$	−5.04909	+	2.24800i	−0.229980	+	0.102393i
$483$	−0.671294	+	0.142688i	−0.0305450	+	0.00649253i
$484$	−0.867912	−	0.184480i	−0.0394505	−	0.00838547i
$485$	4.72447	+	2.10347i	0.214527	+	0.0955136i
$486$	−2.86674	+	3.18383i	−0.130038	+	0.144422i
$487$	2.02626	−	19.2786i	0.0918186	−	0.873596i	−0.847557	−	0.530705i	$-0.821927\pi$
$487$	2.02626	−	19.2786i	0.0918186	−	0.873596i	0.939375	−	0.342891i	$-0.111406\pi$
$488$	3.62867	+	2.63638i	0.164262	+	0.119343i
$489$	0.907965	+	8.63871i	0.0410596	+	0.390656i
$490$	1.41421	−	2.44949i	0.0638877	−	0.110657i
$491$	0.792893	+	1.37333i	0.0357828	+	0.0619776i	0.883362	−	0.468691i	$-0.155274\pi$
$491$	0.792893	+	1.37333i	0.0357828	+	0.0619776i	−0.847579	+	0.530669i	$0.821941\pi$
$492$	4.58636	−	3.33218i	0.206769	−	0.150226i
$493$	26.6307	+	29.5764i	1.19939	+	1.33205i
$494$	2.16312	+	6.65740i	0.0973233	+	0.299530i
$495$	9.17157			0.412232
$496$		0			0
$497$	−0.0294373			−0.00132044
$498$	−0.533957	−	1.64335i	−0.0239272	−	0.0736403i
$499$	1.48092	+	1.64473i	0.0662952	+	0.0736283i	0.775380	−	0.631495i	$-0.217558\pi$
$499$	1.48092	+	1.64473i	0.0662952	+	0.0736283i	−0.709085	+	0.705123i	$0.750892\pi$
$500$	−13.3131	+	9.67250i	−0.595378	+	0.432567i
$501$	−4.67157	−	8.09140i	−0.208710	−	0.361497i
$502$	1.32843	−	2.30090i	0.0592906	−	0.102694i
$503$	1.39909	+	13.3115i	0.0623823	+	0.593528i	0.980404	+	0.196998i	$0.0631192\pi$
$503$	1.39909	+	13.3115i	0.0623823	+	0.593528i	−0.918022	+	0.396530i	$0.870214\pi$
$504$	1.50304	+	1.09203i	0.0669509	+	0.0486427i
$505$	0.886953	−	8.43880i	0.0394689	−	0.375522i
$506$	−3.59496	+	3.99261i	−0.159815	+	0.177493i
$507$	−0.626958	−	0.279140i	−0.0278442	−	0.0123970i
$508$	−15.9165	−	3.38316i	−0.706180	−	0.150103i
$509$	−32.0823	+	6.81929i	−1.42202	+	0.302260i	−0.853794	−	0.520612i	$-0.825704\pi$
$509$	−32.0823	+	6.81929i	−1.42202	+	0.302260i	−0.568227	+	0.822872i	$0.692371\pi$
$510$	−0.913545	+	0.406737i	−0.0404525	+	0.0180106i
$511$	−0.234037	+	0.720292i	−0.0103532	+	0.0318638i
$512$	7.03241	−	21.6435i	0.310792	−	0.956518i
$513$	9.73552	−	4.33453i	0.429834	−	0.191374i
$514$	−9.04067	+	1.92165i	−0.398767	+	0.0847605i
$515$	−2.02581	−	0.430599i	−0.0892679	−	0.0189745i
$516$	7.54117	+	3.35754i	0.331981	+	0.147808i
$517$	−20.9530	+	23.2706i	−0.921510	+	1.02344i
$518$	−0.0179342	+	0.170633i	−0.000787986	+	0.00749718i
$519$	2.78597	+	2.02413i	0.122291	+	0.0888493i
$520$	0.634599	+	6.03781i	0.0278290	+	0.264775i
$521$	10.2279	−	17.7153i	0.448093	−	0.776121i	−0.550169	−	0.835054i	$-0.685437\pi$
$521$	10.2279	−	17.7153i	0.448093	−	0.776121i	0.998262	+	0.0589331i	$0.0187699\pi$
$522$	4.00000	+	6.92820i	0.175075	+	0.303239i
$523$	−6.47214	+	4.70228i	−0.283007	+	0.205616i	−0.720228	−	0.693738i	$-0.755963\pi$
$523$	−6.47214	+	4.70228i	−0.283007	+	0.205616i	0.437221	+	0.899354i	$0.355963\pi$
$524$	16.2018	+	17.9939i	0.707779	+	0.786068i
$525$	−0.212076	−	0.652702i	−0.00925574	−	0.0284863i
$526$	9.65685			0.421059
$527$		0			0
$528$	4.02944			0.175359
$529$	−2.16312	−	6.65740i	−0.0940487	−	0.289452i
$530$	−1.61542	−	1.79411i	−0.0701695	−	0.0779312i
$531$	9.31560	−	6.76818i	0.404263	−	0.293714i
$532$	−1.67157	−	2.89525i	−0.0724719	−	0.125525i
$533$	14.3284	−	24.8176i	0.620633	−	1.07497i
$534$	−0.0804402	−	0.765337i	−0.00348099	−	0.0331194i
$535$	−10.0433	−	7.29689i	−0.434210	−	0.315472i
$536$	0.537500	−	5.11397i	0.0232164	−	0.220890i
$537$	−4.22470	+	4.69200i	−0.182309	+	0.202475i
$538$	9.90340	+	4.40928i	0.426966	+	0.190097i
$539$	−21.6583	−	4.60361i	−0.932888	−	0.198291i
$540$	4.31775	−	0.917767i	0.185806	−	0.0394944i
$541$	−28.5796	+	12.7245i	−1.22873	+	0.547067i	−0.915388	−	0.402572i	$-0.868116\pi$
$541$	−28.5796	+	12.7245i	−1.22873	+	0.547067i	−0.313345	+	0.949639i	$0.601450\pi$
$542$	0.0878446	−	0.270358i	0.00377325	−	0.0116129i
$543$	1.57614	−	4.85087i	0.0676388	−	0.208171i
$544$	23.5036	−	10.4645i	1.00771	−	0.448661i
$545$	10.5918	−	2.25136i	0.453703	−	0.0964375i
$546$	−0.266132	−	0.0565682i	−0.0113894	−	0.00242089i
$547$	−18.0224	−	8.02407i	−0.770580	−	0.343084i	−0.0164975	−	0.999864i	$-0.505252\pi$
$547$	−18.0224	−	8.02407i	−0.770580	−	0.343084i	−0.754083	+	0.656779i	$0.771918\pi$
$548$	11.6048	−	12.8885i	0.495734	−	0.550568i
$549$	0.836228	−	7.95618i	0.0356893	−	0.339561i
$550$	−4.34651	−	3.15793i	−0.185336	−	0.134654i
$551$	−3.15071	−	29.9770i	−0.134225	−	1.27706i
$552$	−1.31371	+	2.27541i	−0.0559151	+	0.0968479i
$553$	1.39949	+	2.42400i	0.0595126	+	0.103079i
$554$	4.73911	−	3.44317i	0.201346	−	0.146286i
$555$	0.277163	+	0.307821i	0.0117649	+	0.0130663i
$556$		0			0
$557$	−27.5147			−1.16584			−0.582918	−	0.812531i	$-0.698089\pi$
$557$	−27.5147			−1.16584			−0.582918	+	0.812531i	$0.698089\pi$
$558$		0			0
$559$	41.7279			1.76490
$560$	−0.383997	−	1.18182i	−0.0162268	−	0.0499411i
$561$	5.23824	+	5.81766i	0.221159	+	0.245622i
$562$	−0.670212	+	0.486937i	−0.0282712	+	0.0205402i
$563$	−6.62132	−	11.4685i	−0.279055	−	0.483338i	0.692095	−	0.721807i	$-0.256688\pi$
$563$	−6.62132	−	11.4685i	−0.279055	−	0.483338i	−0.971150	+	0.238468i	$0.923355\pi$
$564$	−3.65685	+	6.33386i	−0.153981	+	0.266704i
$565$	−1.74112	−	16.5656i	−0.0732493	−	0.696920i
$566$	4.57649	+	3.32502i	0.192364	+	0.139761i
$567$	0.324091	−	3.08352i	0.0136105	−	0.129496i
$568$	−0.0754099	+	0.0837512i	−0.00316413	+	0.00351412i
$569$	12.0059	+	5.34539i	0.503315	+	0.224090i	0.642657	−	0.766154i	$-0.277832\pi$
$569$	12.0059	+	5.34539i	0.503315	+	0.224090i	−0.139342	+	0.990244i	$0.544499\pi$
$570$	0.740809	+	0.157464i	0.0310291	+	0.00659544i
$571$	−20.6394	+	4.38704i	−0.863732	+	0.183592i	−0.618416	−	0.785851i	$-0.712225\pi$
$571$	−20.6394	+	4.38704i	−0.863732	+	0.183592i	−0.245317	+	0.969443i	$0.578892\pi$
$572$	20.7361	−	9.23231i	0.867020	−	0.386022i
$573$	2.67512	−	8.23316i	0.111755	−	0.343945i
$574$	0.396862	−	1.22141i	0.0165647	−	0.0509809i
$575$	−14.6167	+	6.50779i	−0.609560	+	0.271393i
$576$	−11.5412	+	2.45315i	−0.480881	+	0.102214i
$577$	0.0287940	+	0.00612035i	0.00119871	+	0.000254793i	0.208511	−	0.978020i	$-0.433138\pi$
$577$	0.0287940	+	0.00612035i	0.00119871	+	0.000254793i	−0.207312	+	0.978275i	$0.566472\pi$
$578$	6.42171	+	2.85913i	0.267108	+	0.118924i
$579$	−1.97954	+	2.19850i	−0.0822667	+	0.0913664i
$580$	1.30507	−	12.4169i	0.0541900	−	0.515583i
$581$	3.37487	+	2.45199i	0.140013	+	0.101726i
$582$	0.0927483	+	0.882441i	0.00384454	+	0.0365784i
$583$	−9.44975	+	16.3674i	−0.391369	+	0.677870i
$584$	1.44975	+	2.51104i	0.0599910	+	0.103907i
$585$	8.76038	−	6.36479i	0.362197	−	0.263152i
$586$	4.10173	+	4.55543i	0.169441	+	0.188183i
$587$	9.78251	+	30.1075i	0.403767	+	1.24267i	0.921920	+	0.387380i	$0.126620\pi$
$587$	9.78251	+	30.1075i	0.403767	+	1.24267i	−0.518153	+	0.855288i	$0.673380\pi$
$588$	−5.17157			−0.213272
$589$		0			0
$590$	1.68629			0.0694235
$591$	−1.72610	−	5.31240i	−0.0710024	−	0.218523i
$592$	−2.00739	−	2.22943i	−0.0825033	−	0.0916292i
$593$	1.06281	−	0.772178i	0.0436445	−	0.0317096i	−0.565749	−	0.824577i	$-0.691413\pi$
$593$	1.06281	−	0.772178i	0.0436445	−	0.0317096i	0.609394	+	0.792868i	$0.291413\pi$
$594$	1.62132	+	2.80821i	0.0665236	+	0.115222i
$595$	1.20711	−	2.09077i	0.0494866	−	0.0857132i
$596$	0.191123	+	1.81841i	0.00782869	+	0.0744850i
$597$	−6.17071	−	4.48328i	−0.252550	−	0.183489i
$598$	−0.663039	+	6.30840i	−0.0271137	+	0.257970i
$599$	10.1042	−	11.2219i	0.412847	−	0.458513i	−0.500475	−	0.865751i	$-0.666841\pi$
$599$	10.1042	−	11.2219i	0.412847	−	0.458513i	0.913322	+	0.407238i	$0.133508\pi$
$600$	−2.40026	−	1.06867i	−0.0979904	−	0.0436281i
$601$	−6.37236	−	1.35449i	−0.259934	−	0.0552506i	0.0761013	−	0.997100i	$-0.475753\pi$
$601$	−6.37236	−	1.35449i	−0.259934	−	0.0552506i	−0.336035	+	0.941849i	$0.609086\pi$
$602$	1.82919	−	0.388807i	0.0745523	−	0.0158466i
$603$	−8.37865	+	3.73041i	−0.341205	+	0.151914i
$604$	3.00233	−	9.24021i	0.122163	−	0.375979i
$605$	−0.149960	+	0.461530i	−0.00609675	+	0.0187639i
$606$	1.32998	−	0.592145i	0.0540267	−	0.0240543i
$607$	1.55113	−	0.329704i	0.0629586	−	0.0133823i	−0.176325	−	0.984332i	$-0.556421\pi$
$607$	1.55113	−	0.329704i	0.0629586	−	0.0133823i	0.239283	+	0.970950i	$0.423088\pi$
$608$	−19.0595	−	4.05122i	−0.772964	−	0.164299i
$609$	1.07029	+	0.476522i	0.0433701	+	0.0193096i
$610$	0.783935	−	0.870648i	0.0317406	−	0.0352515i
$611$	−3.86448	+	36.7680i	−0.156340	+	1.48748i
$612$	−24.3855	−	17.7171i	−0.985725	−	0.716171i
$613$	1.28713	+	12.2463i	0.0519868	+	0.494621i	0.989275	+	0.146066i	$0.0466611\pi$
$613$	1.28713	+	12.2463i	0.0519868	+	0.494621i	−0.937288	+	0.348556i	$0.886672\pi$
$614$	2.32843	−	4.03295i	0.0939677	−	0.162757i
$615$	−1.55025	−	2.68512i	−0.0625122	−	0.108274i
$616$	1.72316	−	1.25195i	0.0694281	−	0.0504424i
$617$	−22.2715	−	24.7350i	−0.896618	−	0.995795i	−0.999999	−	0.00115320i	$-0.999633\pi$
$617$	−22.2715	−	24.7350i	−0.896618	−	0.995795i	0.103382	−	0.994642i	$-0.467034\pi$
$618$	−0.109806	−	0.337948i	−0.00441704	−	0.0135942i
$619$	20.3431			0.817660			0.408830	−	0.912611i	$-0.365937\pi$
$619$	20.3431			0.817660			0.408830	+	0.912611i	$0.365937\pi$
$620$		0			0
$621$	9.65685			0.387516
$622$	1.44814	+	4.45693i	0.0580653	+	0.178707i
$623$	1.24315	+	1.38066i	0.0498059	+	0.0553151i
$624$	3.84878	−	2.79631i	0.154075	−	0.111942i
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	−0.378680	+	0.655892i	−0.0151351	+	0.0262147i
$627$	−0.619742	−	5.89645i	−0.0247501	−	0.235482i
$628$	13.5669	+	9.85690i	0.541376	+	0.393333i
$629$	0.609237	−	5.79650i	0.0242919	−	0.231122i
$630$	0.324717	−	0.360634i	0.0129370	−	0.0143680i
$631$	−45.6884	−	20.3418i	−1.81883	−	0.809794i	−0.948055	−	0.318107i	$-0.896953\pi$
$631$	−45.6884	−	20.3418i	−1.81883	−	0.809794i	−0.870772	−	0.491686i	$-0.836381\pi$
$632$	10.4816	+	2.22793i	0.416934	+	0.0886221i
$633$	4.21944	−	0.896870i	0.167708	−	0.0356474i
$634$	−2.96230	+	1.31890i	−0.117648	+	0.0523802i
$635$	−2.75010	+	8.46392i	−0.109134	+	0.335881i
$636$	−1.36407	+	4.19817i	−0.0540888	+	0.166468i
$637$	−23.8820	+	10.6330i	−0.946240	+	0.421293i
$638$	8.97115	−	1.90688i	0.355171	−	0.0754940i
$639$	0.196618	+	0.0417924i	0.00777807	+	0.00165328i
$640$	−9.64370	−	4.29365i	−0.381201	−	0.169722i
$641$	9.34813	−	10.3822i	0.369229	−	0.410070i	−0.529686	−	0.848194i	$-0.677690\pi$
$641$	9.34813	−	10.3822i	0.369229	−	0.410070i	0.898915	+	0.438124i	$0.144357\pi$
$642$	0.222640	−	2.11827i	0.00878688	−	0.0836016i
$643$	28.5694	+	20.7569i	1.12667	+	0.818571i	0.985206	−	0.171373i	$-0.0548202\pi$
$643$	28.5694	+	20.7569i	1.12667	+	0.818571i	0.141460	+	0.989944i	$0.454820\pi$
$644$	−0.316662	−	3.01284i	−0.0124782	−	0.118723i
$645$	2.25736	−	3.90986i	0.0888834	−	0.153951i
$646$	−5.32843	−	9.22911i	−0.209644	−	0.363114i
$647$	−36.6596	+	26.6347i	−1.44124	+	1.04712i	−0.453454	+	0.891280i	$0.649808\pi$
$647$	−36.6596	+	26.6347i	−1.44124	+	1.04712i	−0.987782	+	0.155839i	$0.950192\pi$
$648$	−7.94262	−	8.82117i	−0.312016	−	0.346528i
$649$	−4.07934	−	12.5549i	−0.160128	−	0.492823i
$650$	−6.34315			−0.248799
$651$		0			0
$652$	−38.3431			−1.50163
$653$	−1.89802	−	5.84152i	−0.0742754	−	0.228596i	0.907026	−	0.421075i	$-0.138347\pi$
$653$	−1.89802	−	5.84152i	−0.0742754	−	0.228596i	−0.981301	+	0.192479i	$0.938347\pi$
$654$	1.24315	+	1.38066i	0.0486112	+	0.0539882i
$655$	10.7135	−	7.78383i	0.418612	−	0.304139i
$656$	11.2279	+	19.4473i	0.438377	+	0.759291i
$657$	2.58579	−	4.47871i	0.100881	−	0.174731i
$658$	0.173188	+	1.64778i	0.00675159	+	0.0642371i
$659$	1.34042	+	0.973874i	0.0522155	+	0.0379368i	0.613587	−	0.789627i	$-0.289726\pi$
$659$	1.34042	+	0.973874i	0.0522155	+	0.0379368i	−0.561371	+	0.827564i	$0.689726\pi$
$660$	0.256706	−	2.44239i	0.00999225	−	0.0950699i
$661$	3.25055	−	3.61010i	0.126432	−	0.140416i	−0.676605	−	0.736346i	$-0.736550\pi$
$661$	3.25055	−	3.61010i	0.126432	−	0.140416i	0.803037	+	0.595930i	$0.203216\pi$
$662$	−3.49744	−	1.55716i	−0.135932	−	0.0605208i
$663$	9.04067	+	1.92165i	0.351110	+	0.0746308i
$664$	15.6216	−	3.32047i	0.606234	−	0.128859i
$665$	−1.67035	+	0.743688i	−0.0647734	+	0.0288390i
$666$	0.362036	−	1.11423i	0.0140286	−	0.0431756i
$667$	8.44040	−	25.9769i	0.326814	−	1.00583i
$668$	37.6770	−	16.7749i	1.45777	−	0.649040i
$669$	9.61365	−	2.04344i	0.371685	−	0.0790041i
$670$	−1.31379	−	0.279256i	−0.0507563	−	0.0107886i
$671$	−8.37865	−	3.73041i	−0.323454	−	0.144011i
$672$	0.506772	−	0.562828i	0.0195492	−	0.0217115i
$673$	0.976625	−	9.29196i	0.0376461	−	0.358179i	−0.959441	−	0.281909i	$-0.909032\pi$
$673$	0.976625	−	9.29196i	0.0376461	−	0.358179i	0.997087	−	0.0762697i	$-0.0243010\pi$
$674$	3.12108	+	2.26760i	0.120219	+	0.0873445i
$675$	1.00942	+	9.60395i	0.0388524	+	0.369656i
$676$	1.51472	−	2.62357i	0.0582584	−	0.100907i
$677$	−19.2990	−	33.4268i	−0.741720	−	1.28470i	−0.951711	−	0.306994i	$-0.900677\pi$
$677$	−19.2990	−	33.4268i	−0.741720	−	1.28470i	0.209991	−	0.977703i	$-0.432657\pi$
$678$	2.31206	−	1.67981i	0.0887942	−	0.0645127i
$679$	−1.43337	−	1.59192i	−0.0550076	−	0.0610922i
$680$	−2.85613	−	8.79027i	−0.109528	−	0.337092i
$681$	7.62742			0.292283
$682$		0			0
$683$	−1.37258			−0.0525204			−0.0262602	−	0.999655i	$-0.508360\pi$
$683$	−1.37258			−0.0525204			−0.0262602	+	0.999655i	$0.508360\pi$
$684$	7.05437	+	21.7111i	0.269731	+	0.830146i
$685$	−6.34689	−	7.04894i	−0.242502	−	0.269326i
$686$	−1.91946	+	1.39457i	−0.0732853	+	0.0532449i
$687$	1.13604	+	1.96768i	0.0433426	+	0.0750716i
$688$	−16.3492	+	28.3177i	−0.623309	+	1.07960i
$689$	2.33242	+	22.1915i	0.0888580	+	0.845428i
$690$	0.555221	+	0.403392i	0.0211369	+	0.0153569i
$691$	0.00742861	−	0.0706785i	0.000282598	−	0.00268874i	−0.994380	−	0.105873i	$-0.966236\pi$
$691$	0.00742861	−	0.0706785i	0.000282598	−	0.00268874i	0.994662	+	0.103184i	$0.0329031\pi$
$692$	−10.1715	+	11.2966i	−0.386661	+	0.429430i
$693$	−3.47055	−	1.54519i	−0.131835	−	0.0586969i
$694$	−3.46671	−	0.736871i	−0.131594	−	0.0279713i
$695$		0			0
$696$	4.09751	−	1.82433i	0.155316	−	0.0691510i
$697$	−13.4816	+	41.4921i	−0.510653	+	1.57163i
$698$	−3.47040	+	10.6808i	−0.131357	+	0.404274i
$699$	3.47055	−	1.54519i	0.131268	−	0.0584444i
$700$	2.96324	−	0.629855i	0.112000	−	0.0238063i
$701$	13.1906	+	2.80375i	0.498202	+	0.105896i	0.450158	−	0.892949i	$-0.351368\pi$
$701$	13.1906	+	2.80375i	0.498202	+	0.105896i	0.0480443	+	0.998845i	$0.484701\pi$
$702$	3.49744	+	1.55716i	0.132002	+	0.0587713i
$703$	−2.95369	+	3.28040i	−0.111400	+	0.123723i
$704$	−1.41395	+	13.4528i	−0.0532901	+	0.507022i
$705$	3.23607	+	2.35114i	0.121877	+	0.0885491i
$706$	0.129891	+	1.23583i	0.00488852	+	0.0465112i
$707$	−1.75736	+	3.04384i	−0.0660923	+	0.114475i
$708$	−1.54163	−	2.67018i	−0.0579380	−	0.100352i
$709$	14.0071	−	10.1767i	0.526047	−	0.382196i	−0.292830	−	0.956165i	$-0.594597\pi$
$709$	14.0071	−	10.1767i	0.526047	−	0.382196i	0.818877	+	0.573969i	$0.194597\pi$
$710$	0.0196974	+	0.0218761i	0.000739229	+	0.000820997i
$711$	−5.90615	−	18.1773i	−0.221498	−	0.681700i
$712$	7.11270			0.266560
$713$		0			0
$714$	0.414214			0.0155016
$715$	−3.83620	−	11.8066i	−0.143466	−	0.441543i
$716$	−18.6487	−	20.7115i	−0.696935	−	0.774025i
$717$	7.11853	−	5.17192i	0.265846	−	0.193149i
$718$	−1.47056	−	2.54709i	−0.0548809	−	0.0950565i
$719$	−4.03553	+	6.98975i	−0.150500	+	0.260674i	−0.931411	−	0.363968i	$-0.881422\pi$
$719$	−4.03553	+	6.98975i	−0.150500	+	0.260674i	0.780911	+	0.624642i	$0.214755\pi$
$720$	0.886953	+	8.43880i	0.0330548	+	0.314495i
$721$	0.694027	+	0.504240i	0.0258469	+	0.0187789i
$722$	−0.0210113	+	0.199909i	−0.000781959	+	0.00743984i
$723$	3.69823	−	4.10730i	0.137539	−	0.152752i
$724$	20.5682	+	9.15756i	0.764412	+	0.340338i
$725$	26.7168	+	5.67884i	0.992238	+	0.210907i
$726$	−0.0814417	+	0.0173110i	−0.00302258	+	0.000642470i
$727$	37.3098	−	16.6114i	1.38374	−	0.616082i	0.426267	−	0.904597i	$-0.359828\pi$
$727$	37.3098	−	16.6114i	1.38374	−	0.616082i	0.957475	+	0.288515i	$0.0931616\pi$
$728$	0.777091	−	2.39164i	0.0288009	−	0.0886401i
$729$	−5.61532	+	17.2822i	−0.207975	+	0.640081i
$730$	0.691882	−	0.308046i	0.0256077	−	0.0114013i
$731$	−62.1387	+	13.2080i	−2.29828	+	0.488515i
$732$	−2.09532	−	0.445375i	−0.0774454	−	0.0164615i
$733$	14.2764	+	6.35624i	0.527309	+	0.234773i	0.653084	−	0.757286i	$-0.273475\pi$
$733$	14.2764	+	6.35624i	0.527309	+	0.234773i	−0.125775	+	0.992059i	$0.540142\pi$
$734$	6.71100	−	7.45332i	0.247708	−	0.275107i
$735$	−0.295651	+	2.81293i	−0.0109053	+	0.103757i
$736$	−14.2847	−	10.3784i	−0.526541	−	0.382554i
$737$	1.09909	+	10.4571i	0.0404854	+	0.385193i
$738$	−4.38478	+	7.59466i	−0.161406	+	0.279563i
$739$	22.9350	+	39.7246i	0.843679	+	1.46129i	0.886764	+	0.462223i	$0.152948\pi$
$739$	22.9350	+	39.7246i	0.843679	+	1.46129i	−0.0430851	+	0.999071i	$0.513719\pi$
$740$	−1.47923	+	1.07472i	−0.0543775	+	0.0395076i
$741$	−4.68391	−	5.20201i	−0.172068	−	0.191101i
$742$	0.309017	+	0.951057i	0.0113444	+	0.0349144i
$743$	−5.65685			−0.207530			−0.103765	−	0.994602i	$-0.533089\pi$
$743$	−5.65685			−0.207530			−0.103765	+	0.994602i	$0.533089\pi$
$744$		0			0
$745$	1.00000			0.0366372
$746$	1.27999	+	3.93941i	0.0468638	+	0.144232i
$747$	−19.0604	−	21.1687i	−0.697383	−	0.774522i
$748$	−27.9567	+	20.3117i	−1.02220	+	0.742670i
$749$	2.57107	+	4.45322i	0.0939448	+	0.162717i
$750$	−0.772078	+	1.33728i	−0.0281923	+	0.0488305i
$751$	−0.757062	−	7.20296i	−0.0276256	−	0.262840i	−0.999613	−	0.0278082i	$-0.991147\pi$
$751$	−0.757062	−	7.20296i	−0.0276256	−	0.262840i	0.971988	−	0.235032i	$-0.0755194\pi$
$752$	−23.4377	−	17.0285i	−0.854684	−	0.620964i
$753$	−0.277717	+	2.64230i	−0.0101206	+	0.0962908i
$754$	7.24563	−	8.04709i	0.263870	−	0.293058i
$755$	−4.85431	−	2.16128i	−0.176667	−	0.0786570i
$756$	−1.78847	−	0.380151i	−0.0650461	−	0.0138260i
$757$	22.8330	−	4.85331i	0.829881	−	0.176397i	0.226663	−	0.973973i	$-0.427218\pi$
$757$	22.8330	−	4.85331i	0.829881	−	0.176397i	0.603218	+	0.797577i	$0.293885\pi$
$758$	2.79442	−	1.24416i	0.101498	−	0.0451898i
$759$	1.66022	−	5.10963i	0.0602621	−	0.185468i
$760$	−2.16312	+	6.65740i	−0.0784646	+	0.241489i
$761$	−27.8228	+	12.3875i	−1.00858	+	0.449047i	−0.843440	−	0.537224i	$-0.819473\pi$
$761$	−27.8228	+	12.3875i	−1.00858	+	0.449047i	−0.165136	+	0.986271i	$0.552806\pi$
$762$	−1.49355	+	0.317463i	−0.0541054	+	0.0115005i
$763$	−4.38727	−	0.932542i	−0.158830	−	0.0337603i
$764$	34.9095	+	15.5427i	1.26298	+	0.562316i
$765$	−11.0308	+	12.2510i	−0.398820	+	0.442934i
$766$	0.220837	−	2.10112i	0.00797917	−	0.0759167i
$767$	−12.6092	−	9.16110i	−0.455291	−	0.330788i
$768$	0.171914	+	1.63565i	0.00620341	+	0.0590215i
$769$	−18.0563	+	31.2745i	−0.651129	+	1.12779i	0.331721	+	0.943378i	$0.392371\pi$
$769$	−18.0563	+	31.2745i	−0.651129	+	1.12779i	−0.982849	+	0.184410i	$0.940963\pi$
$770$	−0.278175	−	0.481813i	−0.0100247	−	0.0173633i
$771$	7.47745	−	5.43269i	0.269294	−	0.195653i
$772$	−8.73809	−	9.70464i	−0.314491	−	0.349277i
$773$	−5.56231	−	17.1190i	−0.200062	−	0.615728i	−0.999880	−	0.0154855i	$-0.995071\pi$
$773$	−5.56231	−	17.1190i	−0.200062	−	0.615728i	0.799818	−	0.600243i	$-0.204929\pi$
$774$	−12.7696			−0.458992
$775$		0			0
$776$	−8.20101			−0.294399
$777$	−0.0530189	−	0.163176i	−0.00190204	−	0.00585389i
$778$	3.08819	+	3.42978i	0.110717	+	0.122964i
$779$	26.7312	−	19.4214i	0.957746	−	0.695843i
$780$	−1.44975	−	2.51104i	−0.0519093	−	0.0899095i
$781$	0.115224	−	0.199573i	0.00412303	−	0.00714129i
$782$	−1.00942	−	9.60395i	−0.0360966	−	0.343437i
$783$	−13.3369	−	9.68981i	−0.476621	−	0.346285i
$784$	2.14129	−	20.3731i	0.0764748	−	0.727609i
$785$	6.13698	−	6.81581i	0.219038	−	0.243267i
$786$	2.07565	+	0.924137i	0.0740359	+	0.0329629i
$787$	41.4874	+	8.81841i	1.47886	+	0.314342i	0.875537	−	0.483151i	$-0.160508\pi$
$787$	41.4874	+	8.81841i	1.47886	+	0.314342i	0.603328	+	0.797493i	$0.293841\pi$
$788$	24.1180	−	5.12645i	0.859170	−	0.182622i
$789$	−8.82198	+	3.92780i	−0.314071	+	0.139833i
$790$	0.864935	−	2.66200i	0.0307730	−	0.0947096i
$791$	−2.13206	+	6.56181i	−0.0758074	+	0.233311i
$792$	−13.2867	+	5.91564i	−0.472124	+	0.210203i
$793$	−10.5918	+	2.25136i	−0.376126	+	0.0799480i
$794$	13.5670	+	2.88375i	0.481474	+	0.102340i
$795$	2.20549	+	0.981949i	0.0782208	+	0.0348261i
$796$	22.5290	−	25.0210i	0.798519	−	0.886845i
$797$	2.97445	−	28.3000i	0.105360	−	1.00244i	−0.806304	−	0.591501i	$-0.798536\pi$
$797$	2.97445	−	28.3000i	0.105360	−	1.00244i	0.911665	−	0.410935i	$-0.134798\pi$
$798$	−0.253796	−	0.184393i	−0.00898426	−	0.00652745i
$799$	−5.88331	−	55.9759i	−0.208136	−	1.98029i
$800$	8.82843	−	15.2913i	0.312132	−	0.540629i
$801$	−6.34315	−	10.9867i	−0.224124	−	0.388194i
$802$	−8.99036	+	6.53188i	−0.317461	+	0.230649i
$803$	−3.96723	−	4.40606i	−0.140001	−	0.155486i
$804$	0.758898	+	2.33565i	0.0267643	+	0.0823719i
$805$	−1.65685			−0.0583964
$806$		0			0
$807$	−10.8406			−0.381608
$808$	4.15808	+	12.7973i	0.146281	+	0.450206i
$809$	8.04926	+	8.93961i	0.282997	+	0.314300i	0.867837	−	0.496848i	$-0.165509\pi$
$809$	8.04926	+	8.93961i	0.282997	+	0.314300i	−0.584840	+	0.811148i	$0.698843\pi$
$810$	−2.50836	+	1.82243i	−0.0881348	+	0.0640337i
$811$	6.86396	+	11.8887i	0.241026	+	0.417470i	0.961007	−	0.276524i	$-0.0891827\pi$
$811$	6.86396	+	11.8887i	0.241026	+	0.417470i	−0.719981	+	0.693994i	$0.755849\pi$
$812$	−2.58579	+	4.47871i	−0.0907433	+	0.157172i
$813$	0.0297144	+	0.282714i	0.00104213	+	0.00991521i
$814$	−1.08663	−	0.789481i	−0.0380863	−	0.0276713i
$815$	−2.19202	+	20.8557i	−0.0767831	+	0.730543i
$816$	−4.84627	+	5.38233i	−0.169653	+	0.188419i
$817$	43.9531	+	19.5692i	1.53773	+	0.684640i
$818$	8.36937	+	1.77897i	0.292628	+	0.0622001i
$819$	−4.38727	+	0.932542i	−0.153304	+	0.0325857i
$820$	12.5030	−	5.56672i	0.436625	−	0.194398i
$821$	−2.62210	+	8.06998i	−0.0915118	+	0.281644i	−0.986329	−	0.164789i	$-0.947306\pi$
$821$	−2.62210	+	8.06998i	−0.0915118	+	0.281644i	0.894817	+	0.446433i	$0.147306\pi$
$822$	0.502900	−	1.54777i	0.0175406	−	0.0539845i
$823$	−33.0824	+	14.7292i	−1.15318	+	0.513429i	−0.892078	−	0.451882i	$-0.850753\pi$
$823$	−33.0824	+	14.7292i	−1.15318	+	0.513429i	−0.261103	+	0.965311i	$0.584086\pi$
$824$	3.21250	−	0.682838i	0.111913	−	0.0237878i
$825$	5.25518	+	1.11702i	0.182962	+	0.0388897i
$826$	−0.638098	−	0.284099i	−0.0222023	−	0.00988508i
$827$	−24.6906	+	27.4217i	−0.858576	+	0.953545i	−0.999334	−	0.0364992i	$-0.988379\pi$
$827$	−24.6906	+	27.4217i	−0.858576	+	0.953545i	0.140758	+	0.990044i	$0.455046\pi$
$828$	−2.16231	+	20.5730i	−0.0751453	+	0.714960i
$829$	31.0876	+	22.5865i	1.07972	+	0.784461i	0.977634	−	0.210315i	$-0.0674490\pi$
$829$	31.0876	+	22.5865i	1.07972	+	0.784461i	0.102084	+	0.994776i	$0.467449\pi$
$830$	−0.436048	−	4.14872i	−0.0151355	−	0.144004i
$831$	−2.92893	+	5.07306i	−0.101604	+	0.175982i
$832$	7.98528	+	13.8309i	0.276840	+	0.479501i
$833$	32.1981	−	23.3933i	1.11560	−	0.810528i
$834$		0			0
$835$	−6.97030	−	21.4524i	−0.241217	−	0.742390i
$836$	26.1716			0.905163
$837$		0			0
$838$	11.5980			0.400646
$839$	−4.52012	−	13.9115i	−0.156052	−	0.480278i	0.842214	−	0.539143i	$-0.181252\pi$
$839$	−4.52012	−	13.9115i	−0.156052	−	0.480278i	−0.998266	+	0.0588649i	$0.981252\pi$
$840$	−0.182056	−	0.202193i	−0.00628152	−	0.00697633i
$841$	−14.2609	+	10.3611i	−0.491754	+	0.357281i
$842$	6.44975	+	11.1713i	0.222273	+	0.384988i
$843$	0.414214	−	0.717439i	0.0142663	−	0.0247099i
$844$	1.99039	+	18.9373i	0.0685121	+	0.651849i
$845$	−1.34042	−	0.973874i	−0.0461120	−	0.0335023i
$846$	1.18260	−	11.2517i	0.0406588	−	0.386842i
$847$	0.134502	−	0.149380i	0.00462154	−	0.00513275i
$848$	−15.9736	−	7.11190i	−0.548536	−	0.244224i
$849$	−5.53324	−	1.17613i	−0.189900	−	0.0403645i
$850$	9.44583	−	2.00777i	0.323989	−	0.0688660i
$851$	−3.65418	+	1.62695i	−0.125264	+	0.0557710i
$852$	0.0166325	−	0.0511895i	0.000569820	−	0.00175372i
$853$	−4.79431	+	14.7554i	−0.164154	+	0.505214i	−0.998973	−	0.0453103i	$-0.985572\pi$
$853$	−4.79431	+	14.7554i	−0.164154	+	0.505214i	0.834819	+	0.550525i	$0.185572\pi$
$854$	−0.443327	+	0.197382i	−0.0151703	+	0.00675426i
$855$	12.2124	−	2.59584i	0.417657	−	0.0887757i
$856$	19.2561	+	4.09301i	0.658160	+	0.139896i
$857$	−17.8007	−	7.92538i	−0.608060	−	0.270726i	0.0795213	−	0.996833i	$-0.474661\pi$
$857$	−17.8007	−	7.92538i	−0.608060	−	0.270726i	−0.687581	+	0.726107i	$0.741328\pi$
$858$	1.42521	−	1.58286i	0.0486559	−	0.0540378i
$859$	−5.16211	+	49.1142i	−0.176129	+	1.67576i	0.447691	+	0.894188i	$0.352246\pi$
$859$	−5.16211	+	49.1142i	−0.176129	+	1.67576i	−0.623820	+	0.781568i	$0.714420\pi$
$860$	16.1228	+	11.7139i	0.549784	+	0.399442i
$861$	0.134243	+	1.27724i	0.00457499	+	0.0435281i
$862$	3.47056	−	6.01119i	0.118208	−	0.204742i
$863$	−1.30761	−	2.26485i	−0.0445116	−	0.0770964i	0.842911	−	0.538053i	$-0.180840\pi$
$863$	−1.30761	−	2.26485i	−0.0445116	−	0.0770964i	−0.887423	+	0.460956i	$0.847507\pi$
$864$	−8.62158	+	6.26394i	−0.293312	+	0.213104i
$865$	5.56296	+	6.17829i	0.189146	+	0.210068i
$866$	−3.47040	−	10.6808i	−0.117929	−	0.362948i
$867$	−7.02944			−0.238732
$868$		0			0
$869$	−21.9117			−0.743303
$870$	−0.362036	−	1.11423i	−0.0122742	−	0.0377760i
$871$	8.30673	+	9.22556i	0.281463	+	0.312596i
$872$	−13.8921	+	10.0932i	−0.470446	+	0.341799i
$873$	7.31371	+	12.6677i	0.247532	+	0.428737i
$874$	−3.65685	+	6.33386i	−0.123695	+	0.214246i
$875$	−0.389674	−	3.70750i	−0.0131734	−	0.125336i
$876$	−1.12031	−	0.813951i	−0.0378517	−	0.0275009i
$877$	−5.62660	+	53.5335i	−0.189997	+	1.80770i	0.319886	+	0.947456i	$0.396355\pi$
$877$	−5.62660	+	53.5335i	−0.189997	+	1.80770i	−0.509883	+	0.860244i	$0.670311\pi$
$878$	0.574023	−	0.637517i	0.0193723	−	0.0215152i
$879$	−5.59998	−	2.49327i	−0.188883	−	0.0840960i
$880$	9.51534	+	2.02255i	0.320762	+	0.0681801i
$881$	11.4309	−	2.42972i	0.385117	−	0.0818592i	−0.0112845	−	0.999936i	$-0.503592\pi$
$881$	11.4309	−	2.42972i	0.385117	−	0.0818592i	0.396402	+	0.918077i	$0.370259\pi$
$882$	7.30836	−	3.25389i	0.246085	−	0.109564i
$883$	9.35835	−	28.8021i	0.314934	−	0.969266i	−0.660848	−	0.750520i	$-0.729803\pi$
$883$	9.35835	−	28.8021i	0.314934	−	0.969266i	0.975782	−	0.218747i	$-0.0701968\pi$
$884$	−12.6076	+	38.8021i	−0.424039	+	1.30506i
$885$	−1.54050	+	0.685877i	−0.0517835	+	0.0230555i
$886$	1.92750	−	0.409703i	0.0647557	−	0.0137642i
$887$	50.2043	+	10.6713i	1.68570	+	0.358306i	0.948354	−	0.317214i	$-0.102747\pi$
$887$	50.2043	+	10.6713i	1.68570	+	0.358306i	0.737342	+	0.675520i	$0.236081\pi$
$888$	−0.600066	−	0.267167i	−0.0201369	−	0.00896553i
$889$	2.46661	−	2.73945i	0.0827275	−	0.0918782i
$890$	0.194200	−	1.84769i	0.00650959	−	0.0619346i
$891$	19.6365	+	14.2668i	0.657848	+	0.477955i
$892$	4.53494	+	43.1471i	0.151841	+	1.44467i
$893$	−21.3137	+	36.9164i	−0.713236	+	1.23536i
$894$	0.0857864	+	0.148586i	0.00286913	+	0.00496947i
$895$	−12.3316	+	8.95940i	−0.412198	+	0.299480i
$896$	2.92583	+	3.24946i	0.0977451	+	0.108557i
$897$	−1.96014	−	6.03269i	−0.0654472	−	0.201426i
$898$	16.8284			0.561572
$899$		0			0
$900$	−20.6863			−0.689543
$901$	−10.4975	−	32.3079i	−0.349722	−	1.07633i
$902$	6.72732	+	7.47145i	0.223995	+	0.248772i
$903$	−1.51291	+	1.09919i	−0.0503464	+	0.0365788i
$904$	13.2071	+	22.8754i	0.439262	+	0.760824i
$905$	6.15685	−	10.6640i	0.204661	−	0.354483i
$906$	−0.0952974	−	0.906694i	−0.00316604	−	0.0301229i
$907$	−26.4438	−	19.2125i	−0.878051	−	0.637941i	0.0546843	−	0.998504i	$-0.482585\pi$
$907$	−26.4438	−	19.2125i	−0.878051	−	0.637941i	−0.932735	+	0.360562i	$0.882585\pi$
$908$	−3.51937	+	33.4846i	−0.116795	+	1.11123i
$909$	16.0591	−	17.8355i	0.532648	−	0.591565i
$910$	−0.600066	−	0.267167i	−0.0198920	−	0.00885649i
$911$	0.937427	+	0.199256i	0.0310583	+	0.00660165i	0.223415	−	0.974723i	$-0.428280\pi$
$911$	0.937427	+	0.199256i	0.0310583	+	0.00660165i	−0.192356	+	0.981325i	$0.561613\pi$
$912$	5.36541	−	1.14045i	0.177667	−	0.0377642i
$913$	−29.8335	+	13.2827i	−0.987345	+	0.439595i
$914$	3.98240	−	12.2566i	0.131726	−	0.405411i
$915$	−0.362036	+	1.11423i	−0.0119685	+	0.0368354i
$916$	−9.16235	+	4.07934i	−0.302732	+	0.134785i
$917$	−5.36541	+	1.14045i	−0.177182	+	0.0376611i
$918$	−5.70106	−	1.21180i	−0.188163	−	0.0399953i
$919$	−31.8823	−	14.1949i	−1.05170	−	0.468247i	−0.193252	−	0.981149i	$-0.561904\pi$
$919$	−31.8823	−	14.1949i	−1.05170	−	0.468247i	−0.858447	+	0.512902i	$0.828570\pi$
$920$	−4.24439	+	4.71388i	−0.139933	+	0.155412i
$921$	−0.486774	+	4.63134i	−0.0160397	+	0.152608i
$922$	−0.717842	−	0.521543i	−0.0236409	−	0.0171761i
$923$	−0.0284399	−	0.270587i	−0.000936110	−	0.00890649i
$924$	−0.508622	+	0.880959i	−0.0167324	+	0.0289814i
$925$	−2.00000	−	3.46410i	−0.0657596	−	0.113899i
$926$	−3.00609	+	2.18405i	−0.0987862	+	0.0717724i
$927$	−3.91968	−	4.35324i	−0.128739	−	0.142979i
$928$	9.31443	+	28.6669i	0.305761	+	0.941036i
$929$	−7.51472			−0.246550			−0.123275	−	0.992373i	$-0.539340\pi$
$929$	−7.51472			−0.246550			−0.123275	+	0.992373i	$0.539340\pi$
$930$		0			0
$931$	−30.1421			−0.987869
$932$	5.18208	+	15.9488i	0.169745	+	0.522420i
$933$	−3.13574	−	3.48259i	−0.102660	−	0.114015i
$934$	2.68085	−	1.94775i	0.0877200	−	0.0637323i
$935$	9.44975	+	16.3674i	0.309040	+	0.535273i
$936$	−8.58579	+	14.8710i	−0.280635	+	0.486074i
$937$	−1.63966	−	15.6004i	−0.0535655	−	0.509642i	−0.988105	−	0.153782i	$-0.950855\pi$
$937$	−1.63966	−	15.6004i	−0.0535655	−	0.509642i	0.934539	−	0.355860i	$-0.115812\pi$
$938$	0.450096	+	0.327014i	0.0146962	+	0.0106774i
$939$	0.0791656	−	0.753210i	0.00258347	−	0.0245801i
$940$	−11.8147	+	13.1216i	−0.385354	+	0.427979i
$941$	31.9741	+	14.2358i	1.04233	+	0.464073i	0.855219	−	0.518266i	$-0.173422\pi$
$941$	31.9741	+	14.2358i	1.04233	+	0.464073i	0.187106	+	0.982340i	$0.440089\pi$
$942$	1.53921	+	0.327168i	0.0501501	+	0.0106597i
$943$	29.2868	−	6.22511i	0.953711	−	0.202717i
$944$	11.1573	−	4.96756i	0.363140	−	0.161680i
$945$	−0.309017	+	0.951057i	−0.0100523	+	0.0309379i
$946$	−4.52389	+	13.9231i	−0.147084	+	0.452679i
$947$	−17.4492	+	7.76888i	−0.567022	+	0.252455i	−0.670165	−	0.742212i	$-0.733777\pi$
$947$	−17.4492	+	7.76888i	−0.567022	+	0.252455i	0.103143	+	0.994667i	$0.467110\pi$
$948$	−5.00591	+	1.06404i	−0.162585	+	0.0345584i
$949$	−6.84703	−	1.45538i	−0.222264	−	0.0472437i
$950$	−6.68141	−	2.97475i	−0.216773	−	0.0965137i
$951$	2.16975	−	2.40975i	0.0703590	−	0.0781416i
$952$	−0.400180	+	3.80745i	−0.0129699	+	0.123400i
$953$	2.84347	+	2.06590i	0.0921089	+	0.0669211i	0.632887	−	0.774245i	$-0.281870\pi$
$953$	2.84347	+	2.06590i	0.0921089	+	0.0669211i	−0.540778	+	0.841166i	$0.681870\pi$
$954$	−0.713765	−	6.79102i	−0.0231090	−	0.219867i
$955$	10.4497	−	18.0995i	0.338146	−	0.585686i
$956$	19.4203	+	33.6370i	0.628098	+	1.08790i
$957$	−7.41996	+	5.39092i	−0.239853	+	0.174264i
$958$	−4.35920	−	4.84138i	−0.140839	−	0.156418i
$959$	1.21411	+	3.73664i	0.0392056	+	0.120662i
$960$	1.72792			0.0557684
$961$		0			0
$962$	−1.58579			−0.0511278
$963$	−10.8504	−	33.3942i	−0.349650	−	1.07611i
$964$	16.3248	+	18.1305i	0.525785	+	0.583943i
$965$	−5.77811	+	4.19804i	−0.186004	+	0.135140i
$966$	−0.142136	−	0.246186i	−0.00457314	−	0.00792091i
$967$	−7.72183	+	13.3746i	−0.248317	+	0.430098i	−0.963059	−	0.269290i	$-0.913211\pi$
$967$	−7.72183	+	13.3746i	−0.248317	+	0.430098i	0.714742	+	0.699388i	$0.246544\pi$
$968$	−0.0804402	−	0.765337i	−0.00258544	−	0.0245989i
$969$	8.62158	+	6.26394i	0.276965	+	0.201227i
$970$	−0.223914	+	2.13040i	−0.00718945	+	0.0684030i
$971$	−0.467378	+	0.519075i	−0.0149989	+	0.0166579i	−0.750598	−	0.660760i	$-0.770234\pi$
$971$	−0.467378	+	0.519075i	−0.0149989	+	0.0166579i	0.735599	+	0.677418i	$0.236901\pi$
$972$	17.2767	+	7.69208i	0.554150	+	0.246723i
$973$		0			0
$974$	7.85397	−	1.66941i	0.251658	−	0.0534915i
$975$	5.79475	−	2.57999i	0.185581	−	0.0826258i
$976$	2.62210	−	8.06998i	0.0839313	−	0.258314i
$977$	−0.149960	+	0.461530i	−0.00479765	+	0.0147657i	−0.953427	−	0.301625i	$-0.902471\pi$
$977$	−0.149960	+	0.461530i	−0.00479765	+	0.0147657i	0.948629	+	0.316391i	$0.102471\pi$
$978$	−3.28692	+	1.46343i	−0.105104	+	0.0467953i
$979$	−14.2263	+	3.02390i	−0.454676	+	0.0966443i
$980$	−12.2124	−	2.59584i	−0.390112	−	0.0829209i
$981$	27.9795	+	12.4573i	0.893318	+	0.397731i
$982$	−0.439521	+	0.488138i	−0.0140257	+	0.0155771i
$983$	−4.05995	+	38.6278i	−0.129492	+	1.23204i	0.716020	+	0.698080i	$0.245962\pi$
$983$	−4.05995	+	38.6278i	−0.129492	+	1.23204i	−0.845512	+	0.533957i	$0.820705\pi$
$984$	3.97773	+	2.88999i	0.126805	+	0.0921294i
$985$	−1.40960	−	13.4114i	−0.0449135	−	0.427323i
$986$	−8.24264	+	14.2767i	−0.262499	+	0.454662i
$987$	−0.828427	−	1.43488i	−0.0263691	−	0.0456727i
$988$	24.9982	−	18.1623i	0.795299	−	0.577819i
$989$	29.1727	+	32.3996i	0.927639	+	1.03025i
$990$	1.17395	+	3.61305i	0.0373107	+	0.114830i
$991$	−47.9411			−1.52290			−0.761450	−	0.648224i	$-0.775512\pi$
$991$	−47.9411			−1.52290			−0.761450	+	0.648224i	$0.775512\pi$
$992$		0			0
$993$	3.82843			0.121491
$994$	−0.00376794	−	0.0115965i	−0.000119512	−	0.000367819i
$995$	−12.3215	−	13.6844i	−0.390618	−	0.433826i
$996$	−6.17071	+	4.48328i	−0.195526	+	0.142058i
$997$	−16.2990	−	28.2307i	−0.516194	−	0.894075i	−0.999823	−	0.0188015i	$-0.994015\pi$
$997$	−16.2990	−	28.2307i	−0.516194	−	0.894075i	0.483629	−	0.875273i	$-0.339318\pi$
$998$	−0.458369	+	0.793919i	−0.0145094	+	0.0251311i
$999$	0.252354	+	2.40099i	0.00798413	+	0.0759639i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.r.547.2		16
31.2	even	5	inner	961.2.g.r.235.1		16
31.3	odd	30		31.2.c.a.25.2	yes	4
31.4	even	5	inner	961.2.g.r.816.1		16
31.5	even	3		961.2.d.i.531.2		8
31.6	odd	6		961.2.g.o.844.2		16
31.7	even	15	inner	961.2.g.r.732.1		16
31.8	even	5	inner	961.2.g.r.846.2		16
31.9	even	15		961.2.d.i.628.2		8
31.10	even	15		961.2.d.i.388.1		8
31.11	odd	30		961.2.d.l.374.1		8
31.12	odd	30		961.2.g.o.338.1		16
31.13	odd	30		961.2.a.a.1.2		2
31.14	even	15	inner	961.2.g.r.448.2		16
31.15	odd	10		31.2.c.a.5.2	✓	4
31.16	even	5		961.2.c.a.439.2		4
31.17	odd	30		961.2.g.o.448.2		16
31.18	even	15		961.2.a.c.1.2		2
31.19	even	15	inner	961.2.g.r.338.1		16
31.20	even	15		961.2.d.i.374.1		8
31.21	odd	30		961.2.d.l.388.1		8
31.22	odd	30		961.2.d.l.628.2		8
31.23	odd	10		961.2.g.o.846.2		16
31.24	odd	30		961.2.g.o.732.1		16
31.25	even	3	inner	961.2.g.r.844.2		16
31.26	odd	6		961.2.d.l.531.2		8
31.27	odd	10		961.2.g.o.816.1		16
31.28	even	15		961.2.c.a.521.2		4
31.29	odd	10		961.2.g.o.235.1		16
31.30	odd	2		961.2.g.o.547.2		16
93.44	even	30		8649.2.a.l.1.1		2
93.65	even	30		279.2.h.c.118.1		4
93.77	even	10		279.2.h.c.253.1		4
93.80	odd	30		8649.2.a.k.1.1		2
124.3	even	30		496.2.i.h.273.2		4
124.15	even	10		496.2.i.h.129.2		4
155.3	even	60		775.2.o.d.149.2		8
155.34	odd	30		775.2.e.e.676.1		4
155.77	even	20		775.2.o.d.749.3		8
155.108	even	20		775.2.o.d.749.2		8
155.127	even	60		775.2.o.d.149.3		8
155.139	odd	10		775.2.e.e.501.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.c.a.5.2	✓	4	31.15	odd	10
31.2.c.a.25.2	yes	4	31.3	odd	30
279.2.h.c.118.1		4	93.65	even	30
279.2.h.c.253.1		4	93.77	even	10
496.2.i.h.129.2		4	124.15	even	10
496.2.i.h.273.2		4	124.3	even	30
775.2.e.e.501.1		4	155.139	odd	10
775.2.e.e.676.1		4	155.34	odd	30
775.2.o.d.149.2		8	155.3	even	60
775.2.o.d.149.3		8	155.127	even	60
775.2.o.d.749.2		8	155.108	even	20
775.2.o.d.749.3		8	155.77	even	20
961.2.a.a.1.2		2	31.13	odd	30
961.2.a.c.1.2		2	31.18	even	15
961.2.c.a.439.2		4	31.16	even	5
961.2.c.a.521.2		4	31.28	even	15
961.2.d.i.374.1		8	31.20	even	15
961.2.d.i.388.1		8	31.10	even	15
961.2.d.i.531.2		8	31.5	even	3
961.2.d.i.628.2		8	31.9	even	15
961.2.d.l.374.1		8	31.11	odd	30
961.2.d.l.388.1		8	31.21	odd	30
961.2.d.l.531.2		8	31.26	odd	6
961.2.d.l.628.2		8	31.22	odd	30
961.2.g.o.235.1		16	31.29	odd	10
961.2.g.o.338.1		16	31.12	odd	30
961.2.g.o.448.2		16	31.17	odd	30
961.2.g.o.547.2		16	31.30	odd	2
961.2.g.o.732.1		16	31.24	odd	30
961.2.g.o.816.1		16	31.27	odd	10
961.2.g.o.844.2		16	31.6	odd	6
961.2.g.o.846.2		16	31.23	odd	10
961.2.g.r.235.1		16	31.2	even	5	inner
961.2.g.r.338.1		16	31.19	even	15	inner
961.2.g.r.448.2		16	31.14	even	15	inner
961.2.g.r.547.2		16	1.1	even	1	trivial
961.2.g.r.732.1		16	31.7	even	15	inner
961.2.g.r.816.1		16	31.4	even	5	inner
961.2.g.r.844.2		16	31.25	even	3	inner
961.2.g.r.846.2		16	31.8	even	5	inner
8649.2.a.k.1.1		2	93.80	odd	30
8649.2.a.l.1.1		2	93.44	even	30

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.127999 + 0.393941i) q^{2} +(-0.277163 - 0.307821i) q^{3} +(1.47923 - 1.07472i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.0857864 - 0.148586i) q^{6} +(0.0432971 + 0.411944i) q^{7} +(1.28293 + 0.932102i) q^{8} +(0.295651 - 2.81293i) q^{9} +O(q^{10})\)	\(q+(0.127999 + 0.393941i) q^{2} +(-0.277163 - 0.307821i) q^{3} +(1.47923 - 1.07472i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.0857864 - 0.148586i) q^{6} +(0.0432971 + 0.411944i) q^{7} +(1.28293 + 0.932102i) q^{8} +(0.295651 - 2.81293i) q^{9} +(0.277163 - 0.307821i) q^{10} +(-2.96230 - 1.31890i) q^{11} +(-0.740809 - 0.157464i) q^{12} +(-3.74477 + 0.795975i) q^{13} +(-0.156740 + 0.0697850i) q^{14} +(-0.127999 + 0.393941i) q^{15} +(0.927051 - 2.85317i) q^{16} +(5.32453 - 2.37063i) q^{17} +(1.14597 - 0.243584i) q^{18} +(-4.31775 - 0.917767i) q^{19} +(-1.67035 - 0.743688i) q^{20} +(0.114805 - 0.127503i) q^{21} +(0.140397 - 1.33579i) q^{22} +(-3.23607 - 2.35114i) q^{23} +(-0.0686600 - 0.653256i) q^{24} +(2.00000 - 3.46410i) q^{25} +(-0.792893 - 1.37333i) q^{26} +(-1.95314 + 1.41904i) q^{27} +(0.506772 + 0.562828i) q^{28} +(2.11010 + 6.49422i) q^{29} -0.171573 q^{30} +4.41421 q^{32} +(0.415055 + 1.27741i) q^{33} +(1.61542 + 1.79411i) q^{34} +(0.335106 - 0.243469i) q^{35} +(-2.58579 - 4.47871i) q^{36} +(0.500000 - 0.866025i) q^{37} +(-0.191123 - 1.81841i) q^{38} +(1.28293 + 0.932102i) q^{39} +(0.165760 - 1.57710i) q^{40} +(-5.00863 + 5.56265i) q^{41} +(0.0649237 + 0.0289059i) q^{42} +(-10.6613 - 2.26613i) q^{43} +(-5.79937 + 1.23269i) q^{44} +(-2.58390 + 1.15042i) q^{45} +(0.511996 - 1.57576i) q^{46} +(2.98413 - 9.18421i) q^{47} +(-1.13521 + 0.505428i) q^{48} +(6.67921 - 1.41971i) q^{49} +(1.62065 + 0.344479i) q^{50} +(-2.20549 - 0.981949i) q^{51} +(-4.68391 + 5.20201i) q^{52} +(0.609237 - 5.79650i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(0.338948 + 3.22488i) q^{55} +(-0.328427 + 0.568852i) q^{56} +(0.914214 + 1.58346i) q^{57} +(-2.28825 + 1.66251i) q^{58} +(2.72408 + 3.02539i) q^{59} +(0.234037 + 0.720292i) q^{60} +2.82843 q^{61} +1.17157 q^{63} +(-1.28909 - 3.96740i) q^{64} +(2.56172 + 2.84508i) q^{65} +(-0.450096 + 0.327014i) q^{66} +(-1.62132 - 2.80821i) q^{67} +(5.32843 - 9.22911i) q^{68} +(0.173188 + 1.64778i) q^{69} +(0.138805 + 0.100848i) q^{70} +(-0.00742861 + 0.0706785i) q^{71} +(3.00124 - 3.33321i) q^{72} +(1.67035 + 0.743688i) q^{73} +(0.405162 + 0.0861198i) q^{74} +(-1.62065 + 0.344479i) q^{75} +(-7.37329 + 3.28280i) q^{76} +(0.415055 - 1.27741i) q^{77} +(-0.202979 + 0.624706i) q^{78} +(6.17315 - 2.74847i) q^{79} +(-2.93444 + 0.623735i) q^{80} +(-7.32171 - 1.55628i) q^{81} +(-2.83245 - 1.26109i) q^{82} +(6.73886 - 7.48426i) q^{83} +(0.0327915 - 0.311990i) q^{84} +(-4.71530 - 3.42586i) q^{85} +(-0.471917 - 4.48999i) q^{86} +(1.41421 - 2.44949i) q^{87} +(-2.57107 - 4.45322i) q^{88} +(3.62867 - 2.63638i) q^{89} +(-0.783935 - 0.870648i) q^{90} +(-0.490035 - 1.50817i) q^{91} -7.31371 q^{92} +4.00000 q^{94} +(1.36407 + 4.19817i) q^{95} +(-1.22346 - 1.35879i) q^{96} +(-4.18389 + 3.03977i) q^{97} +(1.41421 + 2.44949i) q^{98} +(-4.58579 + 7.94282i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 8 q^{5} + 24 q^{6} + 2 q^{7} + 12 q^{8}+O(q^{10}) \) 16 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 8 * q^5 + 24 * q^6 + 2 * q^7 + 12 * q^8	\( 16 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 8 q^{5} + 24 q^{6} + 2 q^{7} + 12 q^{8} - 2 q^{10} + 2 q^{11} + 10 q^{12} + 2 q^{13} - 6 q^{14} - 4 q^{15} - 12 q^{16} + 6 q^{17} - 8 q^{18} + 6 q^{19} + 2 q^{20} + 6 q^{21} - 14 q^{22} - 16 q^{23} - 10 q^{24} + 32 q^{25} - 24 q^{26} - 4 q^{27} + 10 q^{28} - 16 q^{29} - 48 q^{30} + 48 q^{32} - 28 q^{33} + 2 q^{34} - 4 q^{35} - 64 q^{36} + 8 q^{37} - 2 q^{38} + 12 q^{39} - 6 q^{40} + 2 q^{41} - 14 q^{42} + 2 q^{43} + 26 q^{44} + 16 q^{46} - 16 q^{47} + 6 q^{48} - 8 q^{49} + 8 q^{50} - 2 q^{51} - 14 q^{52} - 6 q^{53} - 4 q^{54} + 2 q^{55} + 40 q^{56} - 8 q^{57} - 6 q^{59} - 20 q^{60} + 64 q^{63} + 28 q^{64} + 2 q^{65} + 60 q^{66} + 8 q^{67} + 40 q^{68} + 8 q^{69} + 12 q^{70} - 14 q^{71} - 8 q^{72} - 2 q^{73} + 2 q^{74} - 8 q^{75} - 2 q^{76} - 28 q^{77} - 20 q^{78} + 22 q^{79} + 6 q^{80} - 2 q^{81} - 26 q^{82} + 6 q^{83} + 22 q^{84} - 12 q^{85} + 26 q^{86} + 72 q^{88} - 16 q^{89} - 8 q^{90} + 12 q^{91} + 64 q^{92} + 64 q^{94} - 12 q^{95} + 2 q^{96} - 32 q^{97} - 96 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 8 * q^5 + 24 * q^6 + 2 * q^7 + 12 * q^8 - 2 * q^10 + 2 * q^11 + 10 * q^12 + 2 * q^13 - 6 * q^14 - 4 * q^15 - 12 * q^16 + 6 * q^17 - 8 * q^18 + 6 * q^19 + 2 * q^20 + 6 * q^21 - 14 * q^22 - 16 * q^23 - 10 * q^24 + 32 * q^25 - 24 * q^26 - 4 * q^27 + 10 * q^28 - 16 * q^29 - 48 * q^30 + 48 * q^32 - 28 * q^33 + 2 * q^34 - 4 * q^35 - 64 * q^36 + 8 * q^37 - 2 * q^38 + 12 * q^39 - 6 * q^40 + 2 * q^41 - 14 * q^42 + 2 * q^43 + 26 * q^44 + 16 * q^46 - 16 * q^47 + 6 * q^48 - 8 * q^49 + 8 * q^50 - 2 * q^51 - 14 * q^52 - 6 * q^53 - 4 * q^54 + 2 * q^55 + 40 * q^56 - 8 * q^57 - 6 * q^59 - 20 * q^60 + 64 * q^63 + 28 * q^64 + 2 * q^65 + 60 * q^66 + 8 * q^67 + 40 * q^68 + 8 * q^69 + 12 * q^70 - 14 * q^71 - 8 * q^72 - 2 * q^73 + 2 * q^74 - 8 * q^75 - 2 * q^76 - 28 * q^77 - 20 * q^78 + 22 * q^79 + 6 * q^80 - 2 * q^81 - 26 * q^82 + 6 * q^83 + 22 * q^84 - 12 * q^85 + 26 * q^86 + 72 * q^88 - 16 * q^89 - 8 * q^90 + 12 * q^91 + 64 * q^92 + 64 * q^94 - 12 * q^95 + 2 * q^96 - 32 * q^97 - 96 * q^99

Introduction

L-functions

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