LMFDB - Embedded newform 66.2.h.b.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [66,2,Mod(17,66)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(66, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 9]))

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

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

chi := DirichletCharacter("66.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 66 = 2 \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	66.h (of order $10$, degree $4$, 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:	$0.527012653340$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.185640625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + x^{6} + x^{5} + 4x^{4} + 3x^{3} + 9x^{2} - 81x + 81 $ x^8 - 3x^7 + x^6 + x^5 + 4x^4 + 3x^3 + 9x^2 - 81*x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			17.1
Root			$-0.245684 - 1.71454i$ of defining polynomial
Character	$\chi$	$=$	66.17
Dual form			66.2.h.b.35.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(0.809017 - 1.53150i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.897526 - 0.291624i) q^{5} +(-1.70654 - 0.296161i) q^{6} +(0.897526 + 1.23534i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-1.69098 - 2.47802i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(0.809017 - 1.53150i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.897526 - 0.291624i) q^{5} +(-1.70654 - 0.296161i) q^{6} +(0.897526 + 1.23534i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-1.69098 - 2.47802i) q^{9} +0.943715i q^{10} +(0.151841 + 3.31315i) q^{11} +(0.245684 + 1.71454i) q^{12} +(4.03112 - 1.30979i) q^{13} +(0.897526 - 1.23534i) q^{14} +(-1.17274 + 1.13863i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.906157 + 2.78886i) q^{17} +(-1.83419 + 2.37397i) q^{18} +(-4.16740 + 5.73594i) q^{19} +(0.897526 - 0.291624i) q^{20} +(2.61803 - 0.375151i) q^{21} +(3.10407 - 1.16823i) q^{22} -1.18465i q^{23} +(1.55470 - 0.763481i) q^{24} +(-3.32458 - 2.41545i) q^{25} +(-2.49137 - 3.42908i) q^{26} +(-5.16312 + 0.584981i) q^{27} +(-1.45223 - 0.471857i) q^{28} +(5.17274 - 3.75821i) q^{29} +(1.44530 + 0.763481i) q^{30} +(-2.68830 - 8.27372i) q^{31} -1.00000 q^{32} +(5.19693 + 2.44785i) q^{33} +2.93239 q^{34} +(-0.445299 - 1.37049i) q^{35} +(2.82458 + 1.01082i) q^{36} +(-2.28642 + 1.66118i) q^{37} +(6.74300 + 2.19093i) q^{38} +(1.25530 - 7.23330i) q^{39} +(-0.554701 - 0.763481i) q^{40} +(-5.92001 - 4.30114i) q^{41} +(-1.16581 - 2.37397i) q^{42} +5.34587i q^{43} +(-2.07026 - 2.59114i) q^{44} +(0.795052 + 2.71722i) q^{45} +(-1.12667 + 0.366076i) q^{46} +(-5.58154 + 7.68233i) q^{47} +(-1.20654 - 1.24268i) q^{48} +(1.44261 - 4.43990i) q^{49} +(-1.26988 + 3.90827i) q^{50} +(3.53805 + 3.64402i) q^{51} +(-2.49137 + 3.42908i) q^{52} +(4.62924 - 1.50413i) q^{53} +(2.15184 + 4.72965i) q^{54} +(0.829911 - 3.01792i) q^{55} +1.52696i q^{56} +(5.41309 + 11.0228i) q^{57} +(-5.17274 - 3.75821i) q^{58} +(2.74201 + 3.77405i) q^{59} +(0.279492 - 1.61049i) q^{60} +(-0.685649 - 0.222781i) q^{61} +(-7.03805 + 5.11344i) q^{62} +(1.54349 - 4.31302i) q^{63} +(0.309017 + 0.951057i) q^{64} -4.00000 q^{65} +(0.722103 - 5.69900i) q^{66} +3.89379 q^{67} +(-0.906157 - 2.78886i) q^{68} +(-1.81428 - 0.958399i) q^{69} +(-1.16581 + 0.847008i) q^{70} +(9.47214 + 3.07768i) q^{71} +(0.0885088 - 2.99869i) q^{72} +(1.03051 + 1.41838i) q^{73} +(2.28642 + 1.66118i) q^{74} +(-6.38889 + 3.13745i) q^{75} -7.09001i q^{76} +(-3.95658 + 3.16121i) q^{77} +(-7.26719 + 1.04135i) q^{78} +(-1.56591 + 0.508796i) q^{79} +(-0.554701 + 0.763481i) q^{80} +(-3.28115 + 8.38057i) q^{81} +(-2.26124 + 6.95939i) q^{82} +(1.90347 - 5.85828i) q^{83} +(-1.89753 + 1.84235i) q^{84} +(1.62660 - 2.23882i) q^{85} +(5.08423 - 1.65197i) q^{86} +(-1.57087 - 10.9625i) q^{87} +(-1.82458 + 2.76964i) q^{88} -17.3406i q^{89} +(2.33854 - 1.59581i) q^{90} +(5.23607 + 3.80423i) q^{91} +(0.696317 + 0.958399i) q^{92} +(-14.8461 - 2.57646i) q^{93} +(9.03112 + 2.93439i) q^{94} +(5.41309 - 3.93284i) q^{95} +(-0.809017 + 1.53150i) q^{96} +(3.54074 + 10.8973i) q^{97} -4.66839 q^{98} +(7.95328 - 5.97874i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{6} + 2 q^{8} - 18 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^6 + 2 * q^8 - 18 * q^9	$ 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{6} + 2 q^{8} - 18 q^{9} - q^{11} - 3 q^{12} + 9 q^{15} - 2 q^{16} - 10 q^{17} - 7 q^{18} - 15 q^{19} + 12 q^{21} + 6 q^{22} + 3 q^{24} - 6 q^{25} - 10 q^{26} - 10 q^{27} + 5 q^{28} + 23 q^{29} + 21 q^{30} + 13 q^{31} - 8 q^{32} + 17 q^{33} + 10 q^{34} - 13 q^{35} + 2 q^{36} + 6 q^{37} + 10 q^{38} + 18 q^{39} + 5 q^{40} + 2 q^{41} - 17 q^{42} + 9 q^{44} - 8 q^{45} - 10 q^{46} + 10 q^{47} + 2 q^{48} - 18 q^{49} + q^{50} - 30 q^{51} - 10 q^{52} + 15 q^{53} + 15 q^{54} - 14 q^{55} + 20 q^{57} - 23 q^{58} - 25 q^{59} + 4 q^{60} - 10 q^{61} + 2 q^{62} + 16 q^{63} - 2 q^{64} - 32 q^{65} - 22 q^{66} - 2 q^{67} - 10 q^{68} - 26 q^{69} - 17 q^{70} + 40 q^{71} - 2 q^{72} + 5 q^{73} - 6 q^{74} - 34 q^{75} - 12 q^{77} - 8 q^{78} + 10 q^{79} + 5 q^{80} + 14 q^{81} + 3 q^{82} - 21 q^{83} - 8 q^{84} + 30 q^{85} + 25 q^{86} + 42 q^{87} + 6 q^{88} + 8 q^{90} + 24 q^{91} + 10 q^{92} - 53 q^{93} + 40 q^{94} + 20 q^{95} - 2 q^{96} + 9 q^{97} - 22 q^{98} + 34 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^6 + 2 * q^8 - 18 * q^9 - q^11 - 3 * q^12 + 9 * q^15 - 2 * q^16 - 10 * q^17 - 7 * q^18 - 15 * q^19 + 12 * q^21 + 6 * q^22 + 3 * q^24 - 6 * q^25 - 10 * q^26 - 10 * q^27 + 5 * q^28 + 23 * q^29 + 21 * q^30 + 13 * q^31 - 8 * q^32 + 17 * q^33 + 10 * q^34 - 13 * q^35 + 2 * q^36 + 6 * q^37 + 10 * q^38 + 18 * q^39 + 5 * q^40 + 2 * q^41 - 17 * q^42 + 9 * q^44 - 8 * q^45 - 10 * q^46 + 10 * q^47 + 2 * q^48 - 18 * q^49 + q^50 - 30 * q^51 - 10 * q^52 + 15 * q^53 + 15 * q^54 - 14 * q^55 + 20 * q^57 - 23 * q^58 - 25 * q^59 + 4 * q^60 - 10 * q^61 + 2 * q^62 + 16 * q^63 - 2 * q^64 - 32 * q^65 - 22 * q^66 - 2 * q^67 - 10 * q^68 - 26 * q^69 - 17 * q^70 + 40 * q^71 - 2 * q^72 + 5 * q^73 - 6 * q^74 - 34 * q^75 - 12 * q^77 - 8 * q^78 + 10 * q^79 + 5 * q^80 + 14 * q^81 + 3 * q^82 - 21 * q^83 - 8 * q^84 + 30 * q^85 + 25 * q^86 + 42 * q^87 + 6 * q^88 + 8 * q^90 + 24 * q^91 + 10 * q^92 - 53 * q^93 + 40 * q^94 + 20 * q^95 - 2 * q^96 + 9 * q^97 - 22 * q^98 + 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/66\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	0.809017	−	1.53150i	0.467086	−	0.884212i
$3$	0.809017	−	1.53150i	0.467086	−	0.884212i
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−0.897526	−	0.291624i	−0.401386	−	0.130418i	0.101366	−	0.994849i	$-0.467679\pi$
$5$	−0.897526	−	0.291624i	−0.401386	−	0.130418i	−0.502751	+	0.864431i	$0.667679\pi$
$6$	−1.70654	−	0.296161i	−0.696693	−	0.120907i
$7$	0.897526	+	1.23534i	0.339233	+	0.466914i	0.944217	−	0.329323i	$-0.106821\pi$
$7$	0.897526	+	1.23534i	0.339233	+	0.466914i	−0.604984	+	0.796237i	$0.706821\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	−1.69098	−	2.47802i	−0.563661	−	0.826006i
$10$			0.943715i			0.298429i
$11$	0.151841	+	3.31315i	0.0457819	+	0.998951i
$11$	0.151841	+	3.31315i	0.0457819	+	0.998951i
$12$	0.245684	+	1.71454i	0.0709230	+	0.494944i
$13$	4.03112	−	1.30979i	1.11803	−	0.363270i	0.309015	−	0.951057i	$-0.400001\pi$
$13$	4.03112	−	1.30979i	1.11803	−	0.363270i	0.809016	+	0.587787i	$0.200001\pi$
$14$	0.897526	−	1.23534i	0.239874	−	0.330158i
$15$	−1.17274	+	1.13863i	−0.302799	+	0.293994i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−0.906157	+	2.78886i	−0.219775	+	0.676399i	0.779005	+	0.627018i	$0.215725\pi$
$17$	−0.906157	+	2.78886i	−0.219775	+	0.676399i	−0.998780	+	0.0493808i	$0.984275\pi$
$18$	−1.83419	+	2.37397i	−0.432324	+	0.559550i
$19$	−4.16740	+	5.73594i	−0.956067	+	1.31591i	−0.00728837	+	0.999973i	$0.502320\pi$
$19$	−4.16740	+	5.73594i	−0.956067	+	1.31591i	−0.948779	+	0.315940i	$0.897680\pi$
$20$	0.897526	−	0.291624i	0.200693	−	0.0652091i
$21$	2.61803	−	0.375151i	0.571302	−	0.0818646i
$22$	3.10407	−	1.16823i	0.661790	−	0.249067i
$23$		−	1.18465i		−	0.247016i	−0.992344	−	0.123508i	$-0.960586\pi$
$23$		−	1.18465i		−	0.247016i	0.992344	−	0.123508i	$-0.0394144\pi$
$24$	1.55470	−	0.763481i	0.317352	−	0.155845i
$25$	−3.32458	−	2.41545i	−0.664915	−	0.483089i
$26$	−2.49137	−	3.42908i	−0.488598	−	0.672497i
$27$	−5.16312	+	0.584981i	−0.993643	+	0.112580i
$28$	−1.45223	−	0.471857i	−0.274445	−	0.0891726i
$29$	5.17274	−	3.75821i	0.960553	−	0.697883i	0.00727378	−	0.999974i	$-0.497685\pi$
$29$	5.17274	−	3.75821i	0.960553	−	0.697883i	0.953279	+	0.302091i	$0.0976847\pi$
$30$	1.44530	+	0.763481i	0.263874	+	0.139392i
$31$	−2.68830	−	8.27372i	−0.482832	−	1.48600i	−0.835096	−	0.550104i	$-0.814588\pi$
$31$	−2.68830	−	8.27372i	−0.482832	−	1.48600i	0.352264	−	0.935901i	$-0.385412\pi$
$32$	−1.00000			−0.176777
$33$	5.19693	+	2.44785i	0.904669	+	0.426116i
$34$	2.93239			0.502900
$35$	−0.445299	−	1.37049i	−0.0752692	−	0.231655i
$36$	2.82458	+	1.01082i	0.470763	+	0.168471i
$37$	−2.28642	+	1.66118i	−0.375885	+	0.273097i	−0.759647	−	0.650335i	$-0.774628\pi$
$37$	−2.28642	+	1.66118i	−0.375885	+	0.273097i	0.383762	+	0.923432i	$0.374628\pi$
$38$	6.74300	+	2.19093i	1.09386	+	0.355416i
$39$	1.25530	−	7.23330i	0.201009	−	1.15826i
$40$	−0.554701	−	0.763481i	−0.0877060	−	0.120717i
$41$	−5.92001	−	4.30114i	−0.924551	−	0.671726i	0.0201017	−	0.999798i	$-0.493601\pi$
$41$	−5.92001	−	4.30114i	−0.924551	−	0.671726i	−0.944653	+	0.328072i	$0.893601\pi$
$42$	−1.16581	−	2.37397i	−0.179888	−	0.366312i
$43$			5.34587i			0.815238i	0.913152	+	0.407619i	$0.133641\pi$
$43$			5.34587i			0.815238i	−0.913152	+	0.407619i	$0.866359\pi$
$44$	−2.07026	−	2.59114i	−0.312104	−	0.390629i
$45$	0.795052	+	2.71722i	0.118519	+	0.405059i
$46$	−1.12667	+	0.366076i	−0.166118	+	0.0539749i
$47$	−5.58154	+	7.68233i	−0.814151	+	1.12058i	0.176518	+	0.984297i	$0.443516\pi$
$47$	−5.58154	+	7.68233i	−0.814151	+	1.12058i	−0.990670	+	0.136286i	$0.956484\pi$
$48$	−1.20654	−	1.24268i	−0.174149	−	0.179365i
$49$	1.44261	−	4.43990i	0.206087	−	0.634271i
$50$	−1.26988	+	3.90827i	−0.179587	+	0.552713i
$51$	3.53805	+	3.64402i	0.495426	+	0.510265i
$52$	−2.49137	+	3.42908i	−0.345491	+	0.475527i
$53$	4.62924	−	1.50413i	0.635876	−	0.206609i	0.0266996	−	0.999644i	$-0.491500\pi$
$53$	4.62924	−	1.50413i	0.635876	−	0.206609i	0.609176	+	0.793035i	$0.291500\pi$
$54$	2.15184	+	4.72965i	0.292829	+	0.643624i
$55$	0.829911	−	3.01792i	0.111905	−	0.406936i
$56$			1.52696i			0.204049i
$57$	5.41309	+	11.0228i	0.716981	+	1.46001i
$58$	−5.17274	−	3.75821i	−0.679213	−	0.493477i
$59$	2.74201	+	3.77405i	0.356979	+	0.491340i	0.949304	−	0.314359i	$-0.101790\pi$
$59$	2.74201	+	3.77405i	0.356979	+	0.491340i	−0.592325	+	0.805699i	$0.701790\pi$
$60$	0.279492	−	1.61049i	0.0360822	−	0.207913i
$61$	−0.685649	−	0.222781i	−0.0877883	−	0.0285242i	0.264794	−	0.964305i	$-0.414696\pi$
$61$	−0.685649	−	0.222781i	−0.0877883	−	0.0285242i	−0.352582	+	0.935781i	$0.614696\pi$
$62$	−7.03805	+	5.11344i	−0.893833	+	0.649408i
$63$	1.54349	−	4.31302i	0.194462	−	0.543390i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−4.00000			−0.496139
$66$	0.722103	−	5.69900i	0.0888847	−	0.701498i
$67$	3.89379			0.475702			0.237851	−	0.971302i	$-0.423557\pi$
$67$	3.89379			0.475702			0.237851	+	0.971302i	$0.423557\pi$
$68$	−0.906157	−	2.78886i	−0.109888	−	0.338199i
$69$	−1.81428	−	0.958399i	−0.218414	−	0.115378i
$70$	−1.16581	+	0.847008i	−0.139341	+	0.101237i
$71$	9.47214	+	3.07768i	1.12414	+	0.365254i	0.811345	−	0.584568i	$-0.198736\pi$
$71$	9.47214	+	3.07768i	1.12414	+	0.365254i	0.312791	+	0.949822i	$0.398736\pi$
$72$	0.0885088	−	2.99869i	0.0104309	−	0.353399i
$73$	1.03051	+	1.41838i	0.120612	+	0.166008i	0.865054	−	0.501679i	$-0.167284\pi$
$73$	1.03051	+	1.41838i	0.120612	+	0.166008i	−0.744442	+	0.667688i	$0.767284\pi$
$74$	2.28642	+	1.66118i	0.265791	+	0.193108i
$75$	−6.38889	+	3.13745i	−0.737726	+	0.362282i
$76$		−	7.09001i		−	0.813280i
$77$	−3.95658	+	3.16121i	−0.450894	+	0.360253i
$78$	−7.26719	+	1.04135i	−0.822847	+	0.117910i
$79$	−1.56591	+	0.508796i	−0.176179	+	0.0572440i	−0.395778	−	0.918346i	$-0.629525\pi$
$79$	−1.56591	+	0.508796i	−0.176179	+	0.0572440i	0.219599	+	0.975590i	$0.429525\pi$
$80$	−0.554701	+	0.763481i	−0.0620175	+	0.0853598i
$81$	−3.28115	+	8.38057i	−0.364573	+	0.931175i
$82$	−2.26124	+	6.95939i	−0.249713	+	0.768537i
$83$	1.90347	−	5.85828i	0.208933	−	0.643029i	−0.790596	−	0.612338i	$-0.790229\pi$
$83$	1.90347	−	5.85828i	0.208933	−	0.643029i	0.999529	−	0.0306912i	$-0.00977085\pi$
$84$	−1.89753	+	1.84235i	−0.207037	+	0.201016i
$85$	1.62660	−	2.23882i	0.176429	−	0.242834i
$86$	5.08423	−	1.65197i	0.548246	−	0.178136i
$87$	−1.57087	−	10.9625i	−0.168415	−	1.17530i
$88$	−1.82458	+	2.76964i	−0.194501	+	0.295245i
$89$		−	17.3406i		−	1.83811i	−0.394135	−	0.919053i	$-0.628956\pi$
$89$		−	17.3406i		−	1.83811i	0.394135	−	0.919053i	$-0.371044\pi$
$90$	2.33854	−	1.59581i	0.246504	−	0.168213i
$91$	5.23607	+	3.80423i	0.548889	+	0.398791i
$92$	0.696317	+	0.958399i	0.0725961	+	0.0999200i
$93$	−14.8461	−	2.57646i	−1.53947	−	0.267166i
$94$	9.03112	+	2.93439i	0.931489	+	0.302659i
$95$	5.41309	−	3.93284i	0.555371	−	0.403501i
$96$	−0.809017	+	1.53150i	−0.0825700	+	0.156308i
$97$	3.54074	+	10.8973i	0.359507	+	1.10645i	0.953350	+	0.301868i	$0.0976103\pi$
$97$	3.54074	+	10.8973i	0.359507	+	1.10645i	−0.593842	+	0.804581i	$0.702390\pi$
$98$	−4.66839			−0.471578
$99$	7.95328	−	5.97874i	0.799335	−	0.600886i
$100$	4.10940			0.410940
$101$	−1.44795	−	4.45632i	−0.144076	−	0.443420i	0.852815	−	0.522213i	$-0.174893\pi$
$101$	−1.44795	−	4.45632i	−0.144076	−	0.443420i	−0.996891	+	0.0787929i	$0.974893\pi$
$102$	2.37235	−	4.49095i	0.234898	−	0.444670i
$103$	10.2430	−	7.44197i	1.00927	−	0.733279i	0.0452161	−	0.998977i	$-0.485602\pi$
$103$	10.2430	−	7.44197i	1.00927	−	0.733279i	0.964056	+	0.265698i	$0.0856024\pi$
$104$	4.03112	+	1.30979i	0.395284	+	0.128435i
$105$	−2.45916	−	0.426773i	−0.239989	−	0.0416488i
$106$	−2.86103	−	3.93787i	−0.277888	−	0.382480i
$107$	0.581472	+	0.422464i	0.0562130	+	0.0408412i	0.615537	−	0.788108i	$-0.288939\pi$
$107$	0.581472	+	0.422464i	0.0562130	+	0.0408412i	−0.559324	+	0.828949i	$0.688939\pi$
$108$	3.83321	−	3.50806i	0.368851	−	0.337564i
$109$			9.20929i			0.882090i	0.897485	+	0.441045i	$0.145392\pi$
$109$			9.20929i			0.882090i	−0.897485	+	0.441045i	$0.854608\pi$
$110$	−3.12667	+	0.143295i	−0.298116	+	0.0136626i
$111$	0.694346	+	4.84558i	0.0659044	+	0.459922i
$112$	1.45223	−	0.471857i	0.137223	−	0.0445863i
$113$	2.88295	−	3.96804i	0.271205	−	0.373282i	−0.651591	−	0.758571i	$-0.725898\pi$
$113$	2.88295	−	3.96804i	0.271205	−	0.373282i	0.922796	+	0.385289i	$0.125898\pi$
$114$	8.81061	−	8.55440i	0.825189	−	0.801193i
$115$	−0.345471	+	1.06325i	−0.0322153	+	0.0991486i
$116$	−1.97581	+	6.08092i	−0.183449	+	0.564599i
$117$	−10.0622	−	7.77436i	−0.930254	−	0.718740i
$118$	2.74201	−	3.77405i	0.252423	−	0.347430i
$119$	−4.25849	+	1.38367i	−0.390375	+	0.126841i
$120$	−1.61803	+	0.231856i	−0.147706	+	0.0211655i
$121$	−10.9539	+	1.00615i	−0.995808	+	0.0914678i
$122$			0.720934i			0.0652703i
$123$	−11.3766	+	5.58680i	−1.02579	+	0.503745i
$124$	7.03805	+	5.11344i	0.632035	+	0.459201i
$125$	5.05300	+	6.95486i	0.451954	+	0.622061i
$126$	−4.57889	−	0.135150i	−0.407920	−	0.0120401i
$127$	−5.02793	−	1.63367i	−0.446157	−	0.144965i	0.0773177	−	0.997007i	$-0.475364\pi$
$127$	−5.02793	−	1.63367i	−0.446157	−	0.144965i	−0.523474	+	0.852041i	$0.675364\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	8.18720	+	4.32490i	0.720843	+	0.380786i
$130$	1.23607	+	3.80423i	0.108410	+	0.333653i
$131$	−10.6492			−0.930421			−0.465210	−	0.885200i	$-0.654021\pi$
$131$	−10.6492			−0.930421			−0.465210	+	0.885200i	$0.654021\pi$
$132$	−5.64321	+	1.07433i	−0.491178	+	0.0935081i
$133$	−10.8262			−0.938748
$134$	−1.20325	−	3.70321i	−0.103945	−	0.319909i
$135$	4.80463	+	0.980653i	0.413516	+	0.0844012i
$136$	−2.37235	+	1.72361i	−0.203427	+	0.147799i
$137$	−0.566898	−	0.184196i	−0.0484334	−	0.0157370i	0.284700	−	0.958617i	$-0.408106\pi$
$137$	−0.566898	−	0.184196i	−0.0484334	−	0.0157370i	−0.333133	+	0.942880i	$0.608106\pi$
$138$	−0.350846	+	2.02165i	−0.0298660	+	0.172094i
$139$	−3.01923	−	4.15562i	−0.256088	−	0.352475i	0.661544	−	0.749907i	$-0.269902\pi$
$139$	−3.01923	−	4.15562i	−0.256088	−	0.352475i	−0.917632	+	0.397432i	$0.869902\pi$
$140$	1.16581	+	0.847008i	0.0985286	+	0.0715853i
$141$	7.24993	+	14.7633i	0.610554	+	1.24329i
$142$		−	9.95959i		−	0.835790i
$143$	4.95162	+	13.1568i	0.414075	+	1.10023i
$144$	−2.87928	+	0.842471i	−0.239940	+	0.0702059i
$145$	−5.73865	+	1.86460i	−0.476569	+	0.154847i
$146$	1.03051	−	1.41838i	0.0852857	−	0.117386i
$147$	−5.63261	−	5.80131i	−0.464570	−	0.478484i
$148$	0.873335	−	2.68785i	0.0717877	−	0.220940i
$149$	−5.36735	+	16.5190i	−0.439710	+	1.35329i	0.448471	+	0.893797i	$0.351969\pi$
$149$	−5.36735	+	16.5190i	−0.439710	+	1.35329i	−0.888182	+	0.459492i	$0.848031\pi$
$150$	4.95817	+	5.10667i	0.404833	+	0.416958i
$151$	8.88291	−	12.2263i	0.722881	−	0.994960i	−0.276542	−	0.961002i	$-0.589189\pi$
$151$	8.88291	−	12.2263i	0.722881	−	0.994960i	0.999423	−	0.0339586i	$-0.0108114\pi$
$152$	−6.74300	+	2.19093i	−0.546929	+	0.177708i
$153$	8.44315	−	2.47045i	0.682588	−	0.199724i
$154$	4.22914	+	2.78606i	0.340794	+	0.224507i
$155$			8.20985i			0.659431i
$156$	3.23607	+	6.58971i	0.259093	+	0.527599i
$157$	3.00000	+	2.17963i	0.239426	+	0.173953i	0.701028	−	0.713134i	$-0.252725\pi$
$157$	3.00000	+	2.17963i	0.239426	+	0.173953i	−0.461601	+	0.887087i	$0.652725\pi$
$158$	0.967787	+	1.33204i	0.0769930	+	0.105972i
$159$	1.44156	−	8.30656i	0.114323	−	0.658753i
$160$	0.897526	+	0.291624i	0.0709556	+	0.0230549i
$161$	1.46344	−	1.06325i	0.115335	−	0.0837959i
$162$	8.98433	+	0.530822i	0.705876	+	0.0417053i
$163$	3.32991	+	10.2484i	0.260819	+	0.802718i	0.992627	+	0.121207i	$0.0386766\pi$
$163$	3.32991	+	10.2484i	0.260819	+	0.802718i	−0.731808	+	0.681510i	$0.761323\pi$
$164$	7.31754			0.571404
$165$	−3.95053	−	3.71255i	−0.307548	−	0.289022i
$166$	−6.15976			−0.478090
$167$	−4.10940	−	12.6474i	−0.317995	−	0.978688i	−0.974504	−	0.224370i	$-0.927968\pi$
$167$	−4.10940	−	12.6474i	−0.317995	−	0.978688i	0.656509	−	0.754318i	$-0.272032\pi$
$168$	2.33854	+	1.23534i	0.180422	+	0.0953084i
$169$	4.01715	−	2.91863i	0.309012	−	0.224510i
$170$	−2.63189	−	0.855153i	−0.201857	−	0.0655873i
$171$	21.2608	+	0.627528i	1.62585	+	0.0479883i
$172$	−3.14222	−	4.32490i	−0.239592	−	0.329771i
$173$	−5.75163	−	4.17880i	−0.437288	−	0.317708i	0.347268	−	0.937766i	$-0.387109\pi$
$173$	−5.75163	−	4.17880i	−0.437288	−	0.317708i	−0.784556	+	0.620057i	$0.787109\pi$
$174$	−9.94053	+	4.88159i	−0.753590	+	0.370072i
$175$		−	6.27490i		−	0.474338i
$176$	3.19791	+	0.879409i	0.241052	+	0.0662880i
$177$	7.99830	−	1.14612i	0.601189	−	0.0861473i
$178$	−16.4919	+	5.35856i	−1.23612	+	0.401641i
$179$	−2.47537	+	3.40705i	−0.185018	+	0.254655i	−0.891443	−	0.453132i	$-0.850306\pi$
$179$	−2.47537	+	3.40705i	−0.185018	+	0.254655i	0.706426	+	0.707787i	$0.250306\pi$
$180$	−2.24035	−	1.73095i	−0.166986	−	0.129018i
$181$	2.67906	−	8.24528i	0.199133	−	0.612867i	−0.800771	−	0.598971i	$-0.795577\pi$
$181$	2.67906	−	8.24528i	0.199133	−	0.612867i	0.999903	−	0.0138963i	$-0.00442347\pi$
$182$	2.00000	−	6.15537i	0.148250	−	0.456266i
$183$	−0.895890	+	0.869837i	−0.0662261	+	0.0643002i
$184$	0.696317	−	0.958399i	0.0513332	−	0.0706541i
$185$	2.53656	−	0.824179i	0.186492	−	0.0605948i
$186$	2.13733	+	14.9156i	0.156717	+	1.09367i
$187$	−9.37751	−	2.57877i	−0.685751	−	0.188578i
$188$		−	9.49588i		−	0.692558i
$189$	−5.35668	−	5.85316i	−0.389641	−	0.425755i
$190$	−5.41309	−	3.93284i	−0.392707	−	0.285318i
$191$	−7.90445	−	10.8795i	−0.571946	−	0.787216i	0.420837	−	0.907136i	$-0.361736\pi$
$191$	−7.90445	−	10.8795i	−0.571946	−	0.787216i	−0.992784	+	0.119920i	$0.961736\pi$
$192$	1.70654	+	0.296161i	0.123159	+	0.0213736i
$193$	6.65520	+	2.16241i	0.479052	+	0.155653i	0.538582	−	0.842573i	$-0.318960\pi$
$193$	6.65520	+	2.16241i	0.479052	+	0.155653i	−0.0595300	+	0.998227i	$0.518960\pi$
$194$	9.26977	−	6.73488i	0.665531	−	0.483536i
$195$	−3.23607	+	6.12600i	−0.231740	+	0.438692i
$196$	1.44261	+	4.43990i	0.103044	+	0.317136i
$197$	22.8937			1.63111			0.815554	−	0.578680i	$-0.196432\pi$
$197$	22.8937			1.63111			0.815554	+	0.578680i	$0.196432\pi$
$198$	−8.14382	−	5.71649i	−0.578756	−	0.406253i
$199$	−20.8937			−1.48112			−0.740558	−	0.671993i	$-0.765439\pi$
$199$	−20.8937			−1.48112			−0.740558	+	0.671993i	$0.765439\pi$
$200$	−1.26988	−	3.90827i	−0.0897937	−	0.276357i
$201$	3.15014	−	5.96333i	0.222194	−	0.420621i
$202$	−3.79077	+	2.75416i	−0.266718	+	0.193782i
$203$	9.28533	+	3.01699i	0.651702	+	0.211751i
$204$	−5.00424	−	0.868459i	−0.350367	−	0.0608043i
$205$	4.05905	+	5.58680i	0.283496	+	0.390199i
$206$	−10.2430	−	7.44197i	−0.713663	−	0.518507i
$207$	−2.93557	+	2.00322i	−0.204037	+	0.139233i
$208$		−	4.23857i		−	0.293892i
$209$	−19.6368	−	12.9363i	−1.35830	−	0.894820i
$210$	0.354035	+	2.47068i	0.0244308	+	0.170493i
$211$	3.77185	−	1.22555i	0.259665	−	0.0843701i	−0.176292	−	0.984338i	$-0.556410\pi$
$211$	3.77185	−	1.22555i	0.259665	−	0.0843701i	0.435956	+	0.899968i	$0.356410\pi$
$212$	−2.86103	+	3.93787i	−0.196496	+	0.270454i
$213$	12.3766	−	12.0167i	0.848030	−	0.823369i
$214$	0.222103	−	0.683562i	0.0151826	−	0.0467273i
$215$	1.55898	−	4.79806i	0.106322	−	0.327225i
$216$	−4.52089	−	2.56155i	−0.307608	−	0.174291i
$217$	7.80803	−	10.7468i	0.530044	−	0.729543i
$218$	8.75856	−	2.84583i	0.593204	−	0.192744i
$219$	3.00594	−	0.430736i	0.203123	−	0.0291065i
$220$	1.10247	+	2.92935i	0.0743288	+	0.197497i
$221$			12.4291i			0.836073i
$222$	4.39385	−	2.15773i	0.294896	−	0.144817i
$223$	7.58582	+	5.51142i	0.507984	+	0.369072i	0.812058	−	0.583576i	$-0.198347\pi$
$223$	7.58582	+	5.51142i	0.507984	+	0.369072i	−0.304074	+	0.952648i	$0.598347\pi$
$224$	−0.897526	−	1.23534i	−0.0599685	−	0.0825395i
$225$	−0.363718	+	12.3228i	−0.0242479	+	0.821523i
$226$	−4.66471	−	1.51566i	−0.310292	−	0.100820i
$227$	−1.46877	+	1.06713i	−0.0974859	+	0.0708276i	−0.635460	−	0.772133i	$-0.719190\pi$
$227$	−1.46877	+	1.06713i	−0.0974859	+	0.0708276i	0.537975	+	0.842961i	$0.319190\pi$
$228$	−10.8583	−	5.73594i	−0.719111	−	0.379872i
$229$	−5.74470	−	17.6804i	−0.379620	−	1.16835i	−0.940308	−	0.340324i	$-0.889463\pi$
$229$	−5.74470	−	17.6804i	−0.379620	−	1.16835i	0.560688	−	0.828027i	$-0.310537\pi$
$230$	1.11797			0.0737166
$231$	1.64046	+	8.61697i	0.107934	+	0.566955i
$232$	6.39385			0.419777
$233$	5.58748	+	17.1965i	0.366048	+	1.12658i	0.949322	+	0.314305i	$0.101771\pi$
$233$	5.58748	+	17.1965i	0.366048	+	1.12658i	−0.583274	+	0.812275i	$0.698229\pi$
$234$	−4.28445	+	11.9722i	−0.280083	+	0.782645i
$235$	7.24993	−	5.26738i	0.472933	−	0.343606i
$236$	−4.43667	−	1.44156i	−0.288802	−	0.0938376i
$237$	−0.487629	+	2.80982i	−0.0316749	+	0.182517i
$238$	2.63189	+	3.62249i	0.170600	+	0.234811i
$239$	16.1716	+	11.7494i	1.04606	+	0.760005i	0.971459	−	0.237209i	$-0.0762327\pi$
$239$	16.1716	+	11.7494i	1.04606	+	0.760005i	0.0745980	+	0.997214i	$0.476233\pi$
$240$	0.720508	+	1.46719i	0.0465086	+	0.0947070i
$241$			1.79512i			0.115634i	0.998327	+	0.0578169i	$0.0184140\pi$
$241$			1.79512i			0.115634i	−0.998327	+	0.0578169i	$0.981586\pi$
$242$	4.34184	+	10.1069i	0.279104	+	0.649693i
$243$	10.1803	+	11.8051i	0.653069	+	0.757298i
$244$	0.685649	−	0.222781i	0.0438942	−	0.0142621i
$245$	−2.58956	+	3.56422i	−0.165441	+	0.227710i
$246$	8.82893	+	9.09336i	0.562912	+	0.579772i
$247$	−9.28642	+	28.5807i	−0.590881	+	1.81854i
$248$	2.68830	−	8.27372i	0.170707	−	0.525382i
$249$	−7.43201	−	7.65461i	−0.470984	−	0.485091i
$250$	5.05300	−	6.95486i	0.319580	−	0.439864i
$251$	−12.0779	+	3.92434i	−0.762348	+	0.247702i	−0.664286	−	0.747478i	$-0.731264\pi$
$251$	−12.0779	+	3.92434i	−0.762348	+	0.247702i	−0.0980620	+	0.995180i	$0.531264\pi$
$252$	1.28642	+	4.39655i	0.0810369	+	0.276957i
$253$	3.92491	−	0.179878i	0.246757	−	0.0113088i
$254$			5.28668i			0.331716i
$255$	−2.11281	−	4.30238i	−0.132309	−	0.269425i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−3.11429	−	4.28646i	−0.194264	−	0.267382i	0.700762	−	0.713395i	$-0.252843\pi$
$257$	−3.11429	−	4.28646i	−0.194264	−	0.267382i	−0.895026	+	0.446013i	$0.852843\pi$
$258$	1.58324	−	9.12296i	0.0985683	−	0.567971i
$259$	−4.10424	−	1.33355i	−0.255025	−	0.0828627i
$260$	3.23607	−	2.35114i	0.200692	−	0.145812i
$261$	−18.0599	−	6.46306i	−1.11788	−	0.400053i
$262$	3.29077	+	10.1279i	0.203304	+	0.625707i
$263$	−9.51711			−0.586850			−0.293425	−	0.955982i	$-0.594795\pi$
$263$	−9.51711			−0.586850			−0.293425	+	0.955982i	$0.594795\pi$
$264$	2.76559	+	5.03503i	0.170210	+	0.309884i
$265$	−4.59351			−0.282177
$266$	3.34547	+	10.2963i	0.205124	+	0.631307i
$267$	−26.5572	−	14.0289i	−1.62527	−	0.858553i
$268$	−3.15014	+	2.28871i	−0.192425	+	0.139805i
$269$	0.0695856	+	0.0226097i	0.00424271	+	0.00137854i	0.311138	−	0.950365i	$-0.399290\pi$
$269$	0.0695856	+	0.0226097i	0.00424271	+	0.00137854i	−0.306895	+	0.951743i	$0.599290\pi$
$270$	−0.552055	−	4.87251i	−0.0335970	−	0.296532i
$271$	0.00659354	+	0.00907523i	0.000400529	+	0.000551281i	0.809217	−	0.587510i	$-0.199892\pi$
$271$	0.00659354	+	0.00907523i	0.000400529	+	0.000551281i	−0.808817	+	0.588061i	$0.799892\pi$
$272$	2.37235	+	1.72361i	0.143845	+	0.104509i
$273$	10.0622	−	4.94135i	0.608994	−	0.299064i
$274$			0.596072i			0.0360100i
$275$	7.49792	−	11.3816i	0.452142	−	0.686335i
$276$	2.03112	−	0.291049i	0.122259	−	0.0175191i
$277$	13.2028	−	4.28984i	0.793277	−	0.257751i	0.115778	−	0.993275i	$-0.463064\pi$
$277$	13.2028	−	4.28984i	0.793277	−	0.257751i	0.677499	+	0.735524i	$0.263064\pi$
$278$	−3.01923	+	4.15562i	−0.181082	+	0.249237i
$279$	−15.9566	+	20.6524i	−0.955295	+	1.23643i
$280$	0.445299	−	1.37049i	0.0266117	−	0.0819023i
$281$	−5.25058	+	16.1596i	−0.313223	+	0.964002i	0.663257	+	0.748392i	$0.269174\pi$
$281$	−5.25058	+	16.1596i	−0.313223	+	0.964002i	−0.976480	+	0.215609i	$0.930826\pi$
$282$	11.8003	−	11.4572i	0.702700	−	0.682266i
$283$	−13.6158	+	18.7406i	−0.809378	+	1.11401i	0.182041	+	0.983291i	$0.441730\pi$
$283$	−13.6158	+	18.7406i	−0.809378	+	1.11401i	−0.991419	+	0.130722i	$0.958270\pi$
$284$	−9.47214	+	3.07768i	−0.562068	+	0.182627i
$285$	−1.64386	−	11.4719i	−0.0973739	−	0.679535i
$286$	10.9827	−	8.77495i	0.649423	−	0.518874i
$287$		−	11.1736i		−	0.659557i
$288$	1.69098	+	2.47802i	0.0996421	+	0.146019i
$289$	6.79665	+	4.93805i	0.399803	+	0.290474i
$290$	3.54668	+	4.88159i	0.208268	+	0.286657i
$291$	19.5537	+	3.39344i	1.14626	+	0.198927i
$292$	−1.66740	−	0.541771i	−0.0975773	−	0.0317048i
$293$	−18.9457	+	13.7649i	−1.10682	+	0.804151i	−0.982160	−	0.188048i	$-0.939784\pi$
$293$	−18.9457	+	13.7649i	−1.10682	+	0.804151i	−0.124659	+	0.992200i	$0.539784\pi$
$294$	−3.77680	+	7.14963i	−0.220268	+	0.416975i
$295$	−1.36042	−	4.18695i	−0.0792068	−	0.243774i
$296$	−2.82617			−0.164268
$297$	−2.72210	−	17.0173i	−0.157952	−	0.987447i
$298$	17.3691			1.00617
$299$	−1.55164	−	4.77545i	−0.0897335	−	0.276171i
$300$	3.32458	−	6.29355i	0.191945	−	0.363358i
$301$	−6.60396	+	4.79806i	−0.380646	+	0.276555i
$302$	−14.3729	−	4.67002i	−0.827065	−	0.268730i
$303$	−7.99626	−	1.38771i	−0.459373	−	0.0797218i
$304$	4.16740	+	5.73594i	0.239017	+	0.328978i
$305$	0.550419	+	0.399903i	0.0315169	+	0.0228984i
$306$	−4.95861	−	7.26651i	−0.283465	−	0.415398i
$307$			4.98612i			0.284573i	0.989826	+	0.142286i	$0.0454454\pi$
$307$			4.98612i			0.284573i	−0.989826	+	0.142286i	$0.954555\pi$
$308$	1.34282	−	4.88309i	0.0765145	−	0.278240i
$309$	−3.11062	−	21.7078i	−0.176957	−	1.23492i
$310$	7.80803	−	2.53698i	0.443466	−	0.144091i
$311$	8.22002	−	11.3139i	0.466115	−	0.641552i	−0.509648	−	0.860383i	$-0.670224\pi$
$311$	8.22002	−	11.3139i	0.466115	−	0.641552i	0.975763	+	0.218831i	$0.0702244\pi$
$312$	5.26719	−	5.11402i	0.298196	−	0.289524i
$313$	4.84018	−	14.8965i	0.273583	−	0.842002i	−0.716008	−	0.698092i	$-0.754033\pi$
$313$	4.84018	−	14.8965i	0.273583	−	0.842002i	0.989591	−	0.143910i	$-0.0459675\pi$
$314$	1.14590	−	3.52671i	0.0646668	−	0.199024i
$315$	−2.64310	+	3.42093i	−0.148922	+	0.192748i
$316$	0.967787	−	1.33204i	0.0544423	−	0.0749334i
$317$	30.4366	−	9.88946i	1.70949	−	0.555448i	0.719243	−	0.694758i	$-0.244489\pi$
$317$	30.4366	−	9.88946i	1.70949	−	0.555448i	0.990249	+	0.139310i	$0.0444886\pi$
$318$	−8.34547	+	1.19586i	−0.467991	+	0.0670607i
$319$	13.2369	+	16.5674i	0.741127	+	0.927595i
$320$		−	0.943715i		−	0.0527552i
$321$	1.11742	−	0.548744i	0.0623686	−	0.0306279i
$322$	−1.46344	−	1.06325i	−0.0815542	−	0.0592526i
$323$	−12.2204	−	16.8200i	−0.679963	−	0.935888i
$324$	−2.27147	−	8.70864i	−0.126193	−	0.483813i
$325$	−16.5655	−	5.38246i	−0.918888	−	0.298565i
$326$	8.71782	−	6.33387i	0.482835	−	0.350800i
$327$	14.1040	+	7.45047i	0.779955	+	0.412012i
$328$	−2.26124	−	6.95939i	−0.124856	−	0.384268i
$329$	−14.4999			−0.799403
$330$	−2.31007	+	4.90441i	−0.127165	+	0.269979i
$331$	5.76590			0.316923			0.158461	−	0.987365i	$-0.449347\pi$
$331$	5.76590			0.316923			0.158461	+	0.987365i	$0.449347\pi$
$332$	1.90347	+	5.85828i	0.104466	+	0.321515i
$333$	7.98274	+	2.85676i	0.437451	+	0.156550i
$334$	−10.7586	+	7.81655i	−0.588682	+	0.427703i
$335$	−3.49477	−	1.13552i	−0.190940	−	0.0620401i
$336$	0.452227	−	2.60583i	0.0246710	−	0.142159i
$337$	18.5288	+	25.5028i	1.00933	+	1.38922i	0.919422	+	0.393273i	$0.128657\pi$
$337$	18.5288	+	25.5028i	1.00933	+	1.38922i	0.0899083	+	0.995950i	$0.471343\pi$
$338$	−4.01715	−	2.91863i	−0.218504	−	0.158753i
$339$	−3.74470	−	7.62545i	−0.203384	−	0.414158i
$340$			2.76733i			0.150080i
$341$	27.0039	−	10.1630i	1.46234	−	0.550358i
$342$	−5.97312	−	20.4141i	−0.322989	−	1.10387i
$343$	16.9451	−	5.50581i	0.914952	−	0.297286i
$344$	−3.14222	+	4.32490i	−0.169417	+	0.233183i
$345$	1.34888	+	1.38928i	0.0726210	+	0.0747961i
$346$	−2.19693	+	6.76144i	−0.118107	+	0.363497i
$347$	9.33453	−	28.7287i	0.501104	−	1.54224i	−0.306120	−	0.951993i	$-0.599031\pi$
$347$	9.33453	−	28.7287i	0.501104	−	1.54224i	0.807224	−	0.590246i	$-0.200969\pi$
$348$	7.71446	+	7.94551i	0.413538	+	0.425924i
$349$	−5.67246	+	7.80747i	−0.303640	+	0.417924i	−0.933385	−	0.358878i	$-0.883160\pi$
$349$	−5.67246	+	7.80747i	−0.303640	+	0.417924i	0.629745	+	0.776802i	$0.283160\pi$
$350$	−5.96779	+	1.93905i	−0.318992	+	0.103647i
$351$	−20.0469	+	9.12073i	−1.07003	+	0.486829i
$352$	−0.151841	−	3.31315i	−0.00809317	−	0.176591i
$353$			13.7385i			0.731224i	0.930767	+	0.365612i	$0.119140\pi$
$353$			13.7385i			0.731224i	−0.930767	+	0.365612i	$0.880860\pi$
$354$	−3.56163	−	7.25266i	−0.189299	−	0.385475i
$355$	−7.60396	−	5.52460i	−0.403576	−	0.293215i
$356$	10.1926	+	14.0289i	0.540206	+	0.743529i
$357$	−1.32610	+	7.64129i	−0.0701849	+	0.404420i
$358$	4.00523	+	1.30138i	0.211683	+	0.0687799i
$359$	−23.6610	+	17.1908i	−1.24878	+	0.907293i	−0.998151	−	0.0607894i	$-0.980638\pi$
$359$	−23.6610	+	17.1908i	−1.24878	+	0.907293i	−0.250631	+	0.968083i	$0.580638\pi$
$360$	−0.953930	+	2.66559i	−0.0502765	+	0.140489i
$361$	−9.66240	−	29.7378i	−0.508547	−	1.56515i
$362$	−8.66960			−0.455664
$363$	−7.32097	+	17.5899i	−0.384251	+	0.923229i
$364$	−6.47214			−0.339232
$365$	−0.511278	−	1.57355i	−0.0267615	−	0.0823634i
$366$	1.10411	+	0.583248i	0.0577127	+	0.0304868i
$367$	−9.12557	+	6.63012i	−0.476351	+	0.346089i	−0.799911	−	0.600118i	$-0.795120\pi$
$367$	−9.12557	+	6.63012i	−0.476351	+	0.346089i	0.323560	+	0.946208i	$0.395120\pi$
$368$	−1.12667	−	0.366076i	−0.0587315	−	0.0190830i
$369$	−0.647667	+	21.9431i	−0.0337162	+	1.14231i
$370$	−1.56768	−	2.15773i	−0.0814999	−	0.112175i
$371$	6.01298	+	4.36869i	0.312178	+	0.226811i
$372$	13.5251	−	6.64191i	0.701246	−	0.344367i
$373$			5.73545i			0.296971i	0.988915	+	0.148485i	$0.0474398\pi$
$373$			5.73545i			0.296971i	−0.988915	+	0.148485i	$0.952560\pi$
$374$	0.445257	+	9.71542i	0.0230237	+	0.502373i
$375$	14.7393	−	2.11207i	0.761135	−	0.109067i
$376$	−9.03112	+	2.93439i	−0.465744	+	0.151330i
$377$	15.9294	−	21.9250i	0.820408	−	1.12920i
$378$	−3.91138	+	6.90323i	−0.201180	+	0.355064i
$379$	8.34075	−	25.6702i	0.428435	−	1.31859i	−0.471231	−	0.882010i	$-0.656190\pi$
$379$	8.34075	−	25.6702i	0.428435	−	1.31859i	0.899666	−	0.436578i	$-0.143810\pi$
$380$	−2.06761	+	6.36346i	−0.106066	+	0.326439i
$381$	−6.56965	+	6.37860i	−0.336573	+	0.326786i
$382$	−7.90445	+	10.8795i	−0.404427	+	0.556646i
$383$	−0.600988	+	0.195273i	−0.0307090	+	0.00997797i	−0.324331	−	0.945944i	$-0.605139\pi$
$383$	−0.600988	+	0.195273i	−0.0307090	+	0.00997797i	0.293622	+	0.955922i	$0.405139\pi$
$384$	−0.245684	−	1.71454i	−0.0125375	−	0.0874946i
$385$	4.47301	−	1.68344i	0.227966	−	0.0857959i
$386$		−	6.99770i		−	0.356173i
$387$	13.2472	−	9.03978i	0.673392	−	0.459518i
$388$	−9.26977	−	6.73488i	−0.470601	−	0.341912i
$389$	15.7180	+	21.6340i	0.796934	+	1.09688i	0.993210	+	0.116336i	$0.0371150\pi$
$389$	15.7180	+	21.6340i	0.796934	+	1.09688i	−0.196276	+	0.980549i	$0.562885\pi$
$390$	6.82617	+	1.18465i	0.345657	+	0.0599869i
$391$	3.30382	+	1.07347i	0.167081	+	0.0542880i
$392$	3.77680	−	2.74401i	0.190757	−	0.138593i
$393$	−8.61535	+	16.3092i	−0.434587	+	0.822689i
$394$	−7.07454	−	21.7732i	−0.356410	−	1.09692i
$395$	1.55382			0.0781814
$396$	−2.92012	+	9.51172i	−0.146742	+	0.477982i
$397$	36.0170			1.80764			0.903820	−	0.427913i	$-0.140751\pi$
$397$	36.0170			1.80764			0.903820	+	0.427913i	$0.140751\pi$
$398$	6.45651	+	19.8711i	0.323636	+	0.996048i
$399$	−8.75856	+	16.5803i	−0.438476	+	0.830052i
$400$	−3.32458	+	2.41545i	−0.166229	+	0.120772i
$401$	−19.7141	−	6.40551i	−0.984478	−	0.319876i	−0.227831	−	0.973701i	$-0.573163\pi$
$401$	−19.7141	−	6.40551i	−0.984478	−	0.319876i	−0.756646	+	0.653824i	$0.773163\pi$
$402$	−6.64491	−	1.15319i	−0.331418	−	0.0575159i
$403$	−21.6737	−	29.8313i	−1.07964	−	1.48600i
$404$	3.79077	+	2.75416i	0.188598	+	0.137024i
$405$	5.38889	−	6.56492i	0.267776	−	0.326214i
$406$		−	9.76317i		−	0.484538i
$407$	−5.85091	−	7.32301i	−0.290019	−	0.362988i
$408$	0.720442	+	5.02768i	0.0356672	+	0.248907i
$409$	−15.7096	+	5.10437i	−0.776791	+	0.252395i	−0.670469	−	0.741937i	$-0.733907\pi$
$409$	−15.7096	+	5.10437i	−0.776791	+	0.252395i	−0.106321	+	0.994332i	$0.533907\pi$
$410$	4.05905	−	5.58680i	0.200462	−	0.275913i
$411$	−0.740727	+	0.719186i	−0.0365373	+	0.0354748i
$412$	−3.91248	+	12.0414i	−0.192754	+	0.593235i
$413$	−2.20121	+	6.77462i	−0.108314	+	0.333357i
$414$	2.81231	+	2.17287i	0.138218	+	0.106791i
$415$	−3.41683	+	4.70286i	−0.167725	+	0.230854i
$416$	−4.03112	+	1.30979i	−0.197642	+	0.0642177i
$417$	−8.80694	+	1.26199i	−0.431278	+	0.0617999i
$418$	−6.23502	+	22.6732i	−0.304965	+	1.10898i
$419$			16.0213i			0.782693i	0.920243	+	0.391347i	$0.127991\pi$
$419$			16.0213i			0.782693i	−0.920243	+	0.391347i	$0.872009\pi$
$420$	2.24035	−	1.10019i	0.109318	−	0.0536837i
$421$	−10.5988	−	7.70048i	−0.516554	−	0.375298i	0.298750	−	0.954331i	$-0.403430\pi$
$421$	−10.5988	−	7.70048i	−0.516554	−	0.375298i	−0.815304	+	0.579033i	$0.803430\pi$
$422$	−2.33113	−	3.20852i	−0.113478	−	0.156189i
$423$	28.4752	+	0.840469i	1.38451	+	0.0408650i
$424$	4.62924	+	1.50413i	0.224816	+	0.0730471i
$425$	9.74894	−	7.08302i	0.472893	−	0.343577i
$426$	−15.2531	−	8.05748i	−0.739016	−	0.390386i
$427$	−0.340178	−	1.04696i	−0.0164624	−	0.0506659i
$428$	−0.718739			−0.0347416
$429$	24.1556	+	3.06068i	1.16624	+	0.147771i
$430$	−5.04498			−0.243290
$431$	3.65126	+	11.2374i	0.175875	+	0.541287i	0.999672	−	0.0255970i	$-0.00814866\pi$
$431$	3.65126	+	11.2374i	0.175875	+	0.541287i	−0.823797	+	0.566884i	$0.808149\pi$
$432$	−1.03914	+	5.09119i	−0.0499957	+	0.244950i
$433$	−9.23019	+	6.70613i	−0.443575	+	0.322276i	−0.787054	−	0.616884i	$-0.788395\pi$
$433$	−9.23019	+	6.70613i	−0.443575	+	0.322276i	0.343479	+	0.939160i	$0.388395\pi$
$434$	−12.6337	−	4.10493i	−0.606435	−	0.197043i
$435$	−1.78703	+	10.2972i	−0.0856815	+	0.493714i
$436$	−5.41309	−	7.45047i	−0.259240	−	0.356813i
$437$	6.79505	+	4.93689i	0.325051	+	0.236164i
$438$	−1.33854	−	2.72572i	−0.0639580	−	0.130240i
$439$			16.0229i			0.764733i	0.924011	+	0.382366i	$0.124891\pi$
$439$			16.0229i			0.764733i	−0.924011	+	0.382366i	$0.875109\pi$
$440$	2.44530	−	1.95374i	0.116575	−	0.0931407i
$441$	−13.4416	+	3.93298i	−0.640075	+	0.187285i
$442$	11.8208	−	3.84081i	0.562258	−	0.182689i
$443$	2.78323	−	3.83079i	0.132235	−	0.182006i	−0.737765	−	0.675058i	$-0.764119\pi$
$443$	2.78323	−	3.83079i	0.132235	−	0.182006i	0.870000	+	0.493052i	$0.164119\pi$
$444$	−3.40990	−	3.51203i	−0.161827	−	0.166673i
$445$	−5.05695	+	15.5637i	−0.239722	+	0.737789i
$446$	2.89753	−	8.91767i	0.137202	−	0.422264i
$447$	20.9566	+	21.5843i	0.991212	+	1.02090i
$448$	−0.897526	+	1.23534i	−0.0424041	+	0.0583642i
$449$	−24.5951	+	7.99144i	−1.16072	+	0.377139i	−0.825170	−	0.564884i	$-0.808921\pi$
$449$	−24.5951	+	7.99144i	−1.16072	+	0.377139i	−0.335546	+	0.942024i	$0.608921\pi$
$450$	11.8321	−	3.46205i	0.557771	−	0.163203i
$451$	13.3514	−	20.2670i	0.628694	−	0.954334i
$452$			4.90477i			0.230701i
$453$	−11.5381	−	23.4954i	−0.542108	−	1.10391i
$454$	1.46877	+	1.06713i	0.0689329	+	0.0500827i
$455$	−3.59010	−	4.94135i	−0.168307	−	0.231654i
$456$	−2.09979	+	12.0994i	−0.0983315	+	0.566606i
$457$	−21.7712	−	7.07390i	−1.01841	−	0.330903i	−0.248214	−	0.968705i	$-0.579844\pi$
$457$	−21.7712	−	7.07390i	−1.01841	−	0.330903i	−0.770200	+	0.637802i	$0.779844\pi$
$458$	−15.0398	+	10.9271i	−0.702765	+	0.510588i
$459$	3.04716	−	14.9293i	0.142229	−	0.696841i
$460$	−0.345471	−	1.06325i	−0.0161077	−	0.0495743i
$461$	21.2809			0.991151			0.495575	−	0.868565i	$-0.334957\pi$
$461$	21.2809			0.991151			0.495575	+	0.868565i	$0.334957\pi$
$462$	7.68830	−	4.22296i	0.357692	−	0.196470i
$463$	−20.7617			−0.964880			−0.482440	−	0.875929i	$-0.660249\pi$
$463$	−20.7617			−0.964880			−0.482440	+	0.875929i	$0.660249\pi$
$464$	−1.97581	−	6.08092i	−0.0917246	−	0.282299i
$465$	12.5734	+	6.64191i	0.583077	+	0.308011i
$466$	14.6282	−	10.6280i	0.677639	−	0.492334i
$467$	3.70774	+	1.20472i	0.171574	+	0.0557477i	0.393544	−	0.919306i	$-0.371249\pi$
$467$	3.70774	+	1.20472i	0.171574	+	0.0557477i	−0.221970	+	0.975053i	$0.571249\pi$
$468$	12.7102	+	0.375151i	0.587528	+	0.0173414i
$469$	3.49477	+	4.81014i	0.161374	+	0.222112i
$470$	−7.24993	−	5.26738i	−0.334414	−	0.242966i
$471$	5.76515	−	2.83114i	0.265644	−	0.130452i
$472$			4.66499i			0.214723i
$473$	−17.7117	+	0.811724i	−0.814383	+	0.0373231i
$474$	2.82298	−	0.404519i	0.129664	−	0.0185802i
$475$	27.7097	−	9.00342i	1.27141	−	0.413105i
$476$	2.63189	−	3.62249i	0.120633	−	0.166036i
$477$	−11.5552	−	8.92789i	−0.529078	−	0.408780i
$478$	6.17702	−	19.0109i	0.282530	−	0.869539i
$479$	10.7639	−	33.1280i	0.491817	−	1.51366i	−0.330043	−	0.943966i	$-0.607063\pi$
$479$	10.7639	−	33.1280i	0.491817	−	1.51366i	0.821860	−	0.569690i	$-0.192937\pi$
$480$	1.17274	−	1.13863i	0.0535278	−	0.0519712i
$481$	−7.04104	+	9.69115i	−0.321044	+	0.441879i
$482$	1.70726	−	0.554722i	0.0777635	−	0.0252669i
$483$	−0.444421	−	3.10144i	−0.0202219	−	0.141121i
$484$	8.27048	−	7.25252i	0.375931	−	0.329660i
$485$		−	10.8131i		−	0.490999i
$486$	8.08143	−	13.3301i	0.366581	−	0.604664i
$487$	−4.07454	−	2.96033i	−0.184635	−	0.134145i	0.491628	−	0.870805i	$-0.336402\pi$
$487$	−4.07454	−	2.96033i	−0.184635	−	0.134145i	−0.676263	+	0.736660i	$0.736402\pi$
$488$	−0.423754	−	0.583248i	−0.0191825	−	0.0264024i
$489$	18.3894	+	3.19138i	0.831597	+	0.144319i
$490$	4.19000	+	1.36141i	0.189285	+	0.0615024i
$491$	11.3418	−	8.24030i	0.511848	−	0.371879i	−0.301676	−	0.953410i	$-0.597546\pi$
$491$	11.3418	−	8.24030i	0.511848	−	0.371879i	0.813524	+	0.581531i	$0.197546\pi$
$492$	5.92001	−	11.2068i	0.266895	−	0.505242i
$493$	5.79383	+	17.8316i	0.260941	+	0.803094i
$494$	30.0515			1.35208
$495$	−8.88182	+	3.04671i	−0.399208	+	0.136939i
$496$	−8.69951			−0.390619
$497$	4.69951	+	14.4636i	0.210802	+	0.648781i
$498$	−4.98335	+	9.43366i	−0.223309	+	0.422733i
$499$	11.2013	−	8.13820i	0.501438	−	0.364316i	−0.308128	−	0.951345i	$-0.599703\pi$
$499$	11.2013	−	8.13820i	0.501438	−	0.364316i	0.809566	+	0.587029i	$0.199703\pi$
$500$	−8.17592	−	2.65652i	−0.365638	−	0.118803i
$501$	−22.6941	−	3.93845i	−1.01390	−	0.175957i
$502$	7.46453	+	10.2740i	0.333158	+	0.458553i
$503$	−18.2723	−	13.2756i	−0.814724	−	0.591931i	0.100473	−	0.994940i	$-0.467965\pi$
$503$	−18.2723	−	13.2756i	−0.814724	−	0.591931i	−0.915196	+	0.403008i	$0.867965\pi$
$504$	3.78384	−	2.58207i	0.168546	−	0.115014i
$505$			4.42191i			0.196773i
$506$	−1.38394	−	3.67722i	−0.0615235	−	0.163472i
$507$	−1.21994	−	8.51349i	−0.0541795	−	0.378098i
$508$	5.02793	−	1.63367i	0.223078	−	0.0724825i
$509$	−15.1884	+	20.9050i	−0.673212	+	0.926597i	−0.999828	−	0.0185605i	$-0.994092\pi$
$509$	−15.1884	+	20.9050i	−0.673212	+	0.926597i	0.326616	+	0.945157i	$0.394092\pi$
$510$	−3.43891	+	3.33891i	−0.152278	+	0.147849i
$511$	−0.827265	+	2.54606i	−0.0365960	+	0.112631i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	18.1614	−	32.0532i	0.801844	−	1.41518i
$514$	−3.11429	+	4.28646i	−0.137366	+	0.189068i
$515$	−11.3636	+	3.69226i	−0.500741	+	0.162700i
$516$	−9.16570	+	1.31340i	−0.403497	+	0.0578191i
$517$	−26.3002	−	17.3260i	−1.15668	−	0.761995i
$518$			4.31546i			0.189610i
$519$	−11.0530	+	5.42789i	−0.485173	+	0.238258i
$520$	−3.23607	−	2.35114i	−0.141911	−	0.103104i
$521$	−16.8875	−	23.2436i	−0.739854	−	1.01832i	−0.998627	−	0.0523840i	$-0.983318\pi$
$521$	−16.8875	−	23.2436i	−0.739854	−	1.01832i	0.258773	−	0.965938i	$-0.416682\pi$
$522$	−0.565912	+	19.1732i	−0.0247693	+	0.839189i
$523$	−3.45339	−	1.12207i	−0.151006	−	0.0490648i	0.232539	−	0.972587i	$-0.425297\pi$
$523$	−3.45339	−	1.12207i	−0.151006	−	0.0490648i	−0.383545	+	0.923522i	$0.625297\pi$
$524$	8.61535	−	6.25942i	0.376363	−	0.273444i
$525$	−9.61001	−	5.07650i	−0.419415	−	0.221557i
$526$	2.94095	+	9.05131i	0.128232	+	0.394656i
$527$	25.5103			1.11125
$528$	3.93398	−	4.18614i	0.171204	−	0.182179i
$529$	21.5966			0.938983
$530$	1.41947	+	4.36869i	0.0616579	+	0.189764i
$531$	4.71548	−	13.1766i	0.204635	−	0.571817i
$532$	8.75856	−	6.36346i	0.379732	−	0.275891i
$533$	−29.4979	−	9.58444i	−1.27770	−	0.415148i
$534$	−5.13563	+	29.5926i	−0.222241	+	1.28060i
$535$	−0.398686	−	0.548744i	−0.0172367	−	0.0237243i
$536$	3.15014	+	2.28871i	0.136065	+	0.0988572i
$537$	3.21528	+	6.54738i	0.138750	+	0.282540i
$538$		−	0.0731666i		−	0.00315444i
$539$	14.9291	+	4.10542i	0.643041	+	0.176833i
$540$	−4.46344	+	2.03072i	−0.192076	+	0.0873884i
$541$	−38.8402	+	12.6199i	−1.66987	+	0.542573i	−0.982904	−	0.184117i	$-0.941057\pi$
$541$	−38.8402	+	12.6199i	−1.66987	+	0.542573i	−0.686965	+	0.726691i	$0.741057\pi$
$542$	0.00659354	−	0.00907523i	0.000283217	−	0.000389814i
$543$	−10.4602	−	10.7735i	−0.448892	−	0.462337i
$544$	0.906157	−	2.78886i	0.0388512	−	0.119572i
$545$	2.68565	−	8.26558i	0.115041	−	0.354058i
$546$	−7.80891	−	8.04280i	−0.334190	−	0.344200i
$547$	4.23174	−	5.82450i	0.180936	−	0.249037i	−0.708909	−	0.705300i	$-0.750812\pi$
$547$	4.23174	−	5.82450i	0.180936	−	0.249037i	0.889845	+	0.456263i	$0.150812\pi$
$548$	0.566898	−	0.184196i	0.0242167	−	0.00786848i
$549$	0.607365	+	2.07577i	0.0259217	+	0.0885917i
$550$	−13.1415	−	3.61385i	−0.560356	−	0.154095i
$551$			45.3325i			1.93123i
$552$	−0.904455	−	1.84177i	−0.0384961	−	0.0783910i
$553$	−2.03398	−	1.47777i	−0.0864937	−	0.0628414i
$554$	−8.15976	−	11.2309i	−0.346675	−	0.477157i
$555$	0.789892	−	4.55152i	0.0335290	−	0.193201i
$556$	4.88522	+	1.58730i	0.207180	+	0.0673167i
$557$	−27.2935	+	19.8299i	−1.15646	+	0.840219i	−0.989327	−	0.145715i	$-0.953452\pi$
$557$	−27.2935	+	19.8299i	−1.15646	+	0.840219i	−0.167135	+	0.985934i	$0.553452\pi$
$558$	24.5724	+	8.79367i	1.04023	+	0.372266i
$559$	7.00197	+	21.5499i	0.296152	+	0.911462i
$560$	−1.44102			−0.0608941
$561$	−11.5359	+	12.2754i	−0.487048	+	0.518267i
$562$	16.9912			0.716731
$563$	1.47279	+	4.53277i	0.0620705	+	0.191033i	0.977283	−	0.211938i	$-0.0679774\pi$
$563$	1.47279	+	4.53277i	0.0620705	+	0.191033i	−0.915213	+	0.402971i	$0.867977\pi$
$564$	−14.5429	−	7.68233i	−0.612368	−	0.323484i
$565$	−3.74470	+	2.72068i	−0.157541	+	0.114460i
$566$	22.0309	+	7.15827i	0.926028	+	0.300885i
$567$	−13.2978	+	3.46845i	−0.558454	+	0.145661i
$568$	5.85410	+	8.05748i	0.245633	+	0.338084i
$569$	12.0407	+	8.74811i	0.504774	+	0.366740i	0.810837	−	0.585271i	$-0.199012\pi$
$569$	12.0407	+	8.74811i	0.504774	+	0.366740i	−0.306064	+	0.952011i	$0.599012\pi$
$570$	−10.4024	+	5.10841i	−0.435709	+	0.213968i
$571$		−	8.91378i		−	0.373030i	−0.982452	−	0.186515i	$-0.940281\pi$
$571$		−	8.91378i		−	0.373030i	0.982452	−	0.186515i	$-0.0597193\pi$
$572$	−11.7393	−	7.73360i	−0.490846	−	0.323358i
$573$	−23.0569	+	3.30393i	−0.963214	+	0.138024i
$574$	−10.6267	+	3.45283i	−0.443551	+	0.144119i
$575$	−2.86145	+	3.93845i	−0.119331	+	0.164245i
$576$	1.83419	−	2.37397i	0.0764247	−	0.0989154i
$577$	−3.30341	+	10.1668i	−0.137523	+	0.423251i	−0.995974	−	0.0896439i	$-0.971427\pi$
$577$	−3.30341	+	10.1668i	−0.137523	+	0.423251i	0.858451	+	0.512895i	$0.171427\pi$
$578$	2.59609	−	7.98994i	0.107983	−	0.332338i
$579$	8.69590	−	8.44302i	0.361389	−	0.350880i
$580$	3.54668	−	4.88159i	0.147268	−	0.202697i
$581$	8.94537	−	2.90653i	0.371116	−	0.120583i
$582$	−2.81507	−	19.6453i	−0.116688	−	0.814323i
$583$	5.68632	+	15.1090i	0.235503	+	0.625750i
$584$			1.75321i			0.0725483i
$585$	6.76393	+	9.91207i	0.279654	+	0.409814i
$586$	18.9457	+	13.7649i	0.782639	+	0.568621i
$587$	16.6724	+	22.9476i	0.688144	+	0.947150i	0.999996	−	0.00298142i	$-0.000949016\pi$
$587$	16.6724	+	22.9476i	0.688144	+	0.947150i	−0.311851	+	0.950131i	$0.600949\pi$
$588$	7.96680	+	1.38260i	0.328545	+	0.0570173i
$589$	58.6607	+	19.0600i	2.41707	+	0.785355i
$590$	−3.56163	+	2.58768i	−0.146630	+	0.106533i
$591$	18.5214	−	35.0617i	0.761868	−	1.44225i
$592$	0.873335	+	2.68785i	0.0358938	+	0.110470i
$593$	26.8555			1.10282			0.551411	−	0.834234i	$-0.314090\pi$
$593$	26.8555			1.10282			0.551411	+	0.834234i	$0.314090\pi$
$594$	−15.3433	+	7.84752i	−0.629543	+	0.321988i
$595$	4.22562			0.173233
$596$	−5.36735	−	16.5190i	−0.219855	−	0.676645i
$597$	−16.9034	+	31.9987i	−0.691809	+	1.30962i
$598$	−4.06224	+	2.95139i	−0.166117	+	0.120691i
$599$	−15.8754	−	5.15824i	−0.648653	−	0.210760i	−0.0338328	−	0.999428i	$-0.510771\pi$
$599$	−15.8754	−	5.15824i	−0.648653	−	0.210760i	−0.614820	+	0.788667i	$0.710771\pi$
$600$	−7.01287	−	1.21705i	−0.286299	−	0.0496857i
$601$	4.76046	+	6.55221i	0.194183	+	0.267270i	0.894995	−	0.446076i	$-0.147179\pi$
$601$	4.76046	+	6.55221i	0.194183	+	0.267270i	−0.700812	+	0.713346i	$0.747179\pi$
$602$	6.60396	+	4.79806i	0.269157	+	0.195554i
$603$	−6.58433	−	9.64887i	−0.268134	−	0.392933i
$604$			15.1125i			0.614919i
$605$	10.1248	+	2.29137i	0.411632	+	0.0931576i
$606$	1.15119	+	8.03372i	0.0467639	+	0.326348i
$607$	4.80362	−	1.56079i	0.194973	−	0.0633505i	−0.209903	−	0.977722i	$-0.567315\pi$
$607$	4.80362	−	1.56079i	0.194973	−	0.0633505i	0.404876	+	0.914372i	$0.367315\pi$
$608$	4.16740	−	5.73594i	0.169010	−	0.232623i
$609$	12.1325	−	11.7797i	0.491634	−	0.477337i
$610$	0.210241	−	0.647057i	0.00851243	−	0.0261986i
$611$	−12.4376	+	38.2790i	−0.503172	+	1.54860i
$612$	−5.37856	+	6.96140i	−0.217415	+	0.281398i
$613$	17.6683	−	24.3183i	0.713616	−	0.982208i	−0.286096	−	0.958201i	$-0.592358\pi$
$613$	17.6683	−	24.3183i	0.713616	−	0.982208i	0.999712	−	0.0240072i	$-0.00764247\pi$
$614$	4.74208	−	1.54079i	0.191375	−	0.0621814i
$615$	11.8400	−	1.69662i	0.477436	−	0.0684141i
$616$	−5.05905	+	0.231856i	−0.203835	+	0.00934174i
$617$		−	1.33268i		−	0.0536518i	−0.999640	−	0.0268259i	$-0.991460\pi$
$617$		−	1.33268i		−	0.0536518i	0.999640	−	0.0268259i	$-0.00853997\pi$
$618$	−19.6841	+	9.66646i	−0.791812	+	0.388842i
$619$	1.11705	+	0.811583i	0.0448980	+	0.0326203i	0.610008	−	0.792395i	$-0.291166\pi$
$619$	1.11705	+	0.811583i	0.0448980	+	0.0326203i	−0.565110	+	0.825016i	$0.691166\pi$
$620$	−4.82563	−	6.64191i	−0.193802	−	0.266745i
$621$	0.692995	+	6.11647i	0.0278089	+	0.245445i
$622$	−13.3003	−	4.32152i	−0.533293	−	0.173277i
$623$	21.4216	−	15.5637i	0.858237	−	0.623546i
$624$	−6.49137	−	3.42908i	−0.259863	−	0.137273i
$625$	3.84238	+	11.8256i	0.153695	+	0.473025i
$626$	−15.6631			−0.626025
$627$	−35.6984	+	19.6081i	−1.42566	+	0.783071i
$628$	−3.70820			−0.147973
$629$	−2.56095	−	7.88181i	−0.102112	−	0.314268i
$630$	4.07026	+	1.45661i	0.162163	+	0.0580329i
$631$	14.7715	−	10.7321i	0.588046	−	0.427240i	−0.253570	−	0.967317i	$-0.581605\pi$
$631$	14.7715	−	10.7321i	0.588046	−	0.427240i	0.841616	+	0.540077i	$0.181605\pi$
$632$	−1.56591	−	0.508796i	−0.0622887	−	0.0202388i
$633$	1.17456	−	6.76807i	0.0466847	−	0.269007i
$634$	−18.8109	−	25.8910i	−0.747075	−	1.02826i
$635$	4.03628	+	2.93253i	0.160175	+	0.116374i
$636$	3.71623	+	7.56747i	0.147358	+	0.300070i
$637$		−	19.7873i		−	0.784001i
$638$	11.6661	−	17.7087i	0.461864	−	0.701094i
$639$	−8.39066	−	28.6764i	−0.331930	−	1.13442i
$640$	−0.897526	+	0.291624i	−0.0354778	+	0.0115274i
$641$	12.4155	−	17.0884i	0.490381	−	0.674952i	−0.490077	−	0.871679i	$-0.663031\pi$
$641$	12.4155	−	17.0884i	0.490381	−	0.674952i	0.980458	+	0.196727i	$0.0630314\pi$
$642$	−0.867190	−	0.893163i	−0.0342252	−	0.0352503i
$643$	−0.228154	+	0.702185i	−0.00899751	+	0.0276915i	−0.955454	−	0.295139i	$-0.904634\pi$
$643$	−0.228154	+	0.702185i	−0.00899751	+	0.0276915i	0.946457	+	0.322830i	$0.104634\pi$
$644$	−0.558984	+	1.72037i	−0.0220270	+	0.0677923i
$645$	−6.08698	−	6.26929i	−0.239675	−	0.246853i
$646$	−12.2204	+	16.8200i	−0.480806	+	0.661773i
$647$	−34.1070	+	11.0820i	−1.34088	+	0.435680i	−0.889616	−	0.456709i	$-0.849028\pi$
$647$	−34.1070	+	11.0820i	−1.34088	+	0.435680i	−0.451268	+	0.892388i	$0.649028\pi$
$648$	−7.58049	+	4.85141i	−0.297790	+	0.190582i
$649$	−12.0876	+	9.65774i	−0.474482	+	0.379100i
$650$			17.4180i			0.683190i
$651$	−10.1419	−	20.6524i	−0.397494	−	0.809430i
$652$	−8.71782	−	6.33387i	−0.341416	−	0.248053i
$653$	9.84112	+	13.5451i	0.385113	+	0.530062i	0.956930	−	0.290319i	$-0.0937613\pi$
$653$	9.84112	+	13.5451i	0.385113	+	0.530062i	−0.571817	+	0.820381i	$0.693761\pi$
$654$	2.72744	−	15.7161i	0.106651	−	0.614546i
$655$	9.55789	+	3.10555i	0.373458	+	0.121344i
$656$	−5.92001	+	4.30114i	−0.231138	+	0.167931i
$657$	1.77219	−	4.95207i	0.0691396	−	0.193199i
$658$	4.48070	+	13.7902i	0.174676	+	0.537597i
$659$	−36.3989			−1.41790			−0.708951	−	0.705258i	$-0.750831\pi$
$659$	−36.3989			−1.41790			−0.708951	+	0.705258i	$0.750831\pi$
$660$	5.37823	+	0.681459i	0.209347	+	0.0265257i
$661$	−16.8578			−0.655694			−0.327847	−	0.944731i	$-0.606323\pi$
$661$	−16.8578			−0.655694			−0.327847	+	0.944731i	$0.606323\pi$
$662$	−1.78176	−	5.48370i	−0.0692501	−	0.213130i
$663$	19.0352	+	10.0554i	0.739266	+	0.390518i
$664$	4.98335	−	3.62061i	0.193391	−	0.140507i
$665$	9.71677	+	3.15717i	0.376800	+	0.122430i
$666$	0.250141	−	8.47482i	0.00969277	−	0.328393i
$667$	−4.45215	−	6.12786i	−0.172388	−	0.237272i
$668$	10.7586	+	7.81655i	0.416261	+	0.302431i
$669$	14.5778	−	7.15885i	0.563610	−	0.276777i
$670$			3.67462i			0.141963i
$671$	0.633996	−	2.30548i	0.0244751	−	0.0890022i
$672$	−2.61803	+	0.375151i	−0.100993	+	0.0144718i
$673$	−9.70460	+	3.15322i	−0.374085	+	0.121548i	−0.490024	−	0.871709i	$-0.663012\pi$
$673$	−9.70460	+	3.15322i	−0.374085	+	0.121548i	0.115940	+	0.993256i	$0.463012\pi$
$674$	18.5288	−	25.5028i	0.713704	−	0.982329i
$675$	18.5782	+	10.5264i	0.715074	+	0.405162i
$676$	−1.53442	+	4.72245i	−0.0590160	+	0.181633i
$677$	9.68951	−	29.8213i	0.372398	−	1.14612i	−0.572819	−	0.819682i	$-0.694150\pi$
$677$	9.68951	−	29.8213i	0.372398	−	1.14612i	0.945217	−	0.326442i	$-0.105850\pi$
$678$	−6.09506	+	5.91782i	−0.234079	+	0.227272i
$679$	−10.2839	+	14.1546i	−0.394660	+	0.543203i
$680$	2.63189	−	0.855153i	0.100928	−	0.0327936i
$681$	0.446041	+	3.11275i	0.0170923	+	0.119281i
$682$	−18.0103	−	22.5417i	−0.689648	−	0.863165i
$683$		−	46.5132i		−	1.77978i	−0.456178	−	0.889889i	$-0.650782\pi$
$683$		−	46.5132i		−	1.77978i	0.456178	−	0.889889i	$-0.349218\pi$
$684$	−17.5692	+	11.9891i	−0.671774	+	0.458414i
$685$	0.455089	+	0.330642i	0.0173881	+	0.0126332i
$686$	−10.4727	−	14.4144i	−0.399849	−	0.550345i
$687$	−31.7250	−	5.50571i	−1.21039	−	0.210056i
$688$	5.08423	+	1.65197i	0.193834	+	0.0629806i
$689$	16.6909	−	12.1267i	0.635874	−	0.461990i
$690$	0.904455	−	1.71217i	0.0344320	−	0.0651811i
$691$	9.08650	+	27.9654i	0.345667	+	1.06385i	0.961226	+	0.275762i	$0.0889301\pi$
$691$	9.08650	+	27.9654i	0.345667	+	1.06385i	−0.615559	+	0.788091i	$0.711070\pi$
$692$	7.10940			0.270259
$693$	14.5240	+	4.45892i	0.551723	+	0.169380i
$694$	−30.2072			−1.14665
$695$	1.49796	+	4.61025i	0.0568210	+	0.174877i
$696$	5.17274	−	9.79218i	0.196072	−	0.371172i
$697$	17.3598	−	12.6126i	0.657548	−	0.477737i
$698$	9.17824	+	2.98219i	0.347401	+	0.112878i
$699$	30.8568	+	5.35503i	1.16711	+	0.202546i
$700$	3.68830	+	5.07650i	0.139404	+	0.191874i
$701$	−22.1405	−	16.0860i	−0.836236	−	0.607561i	0.0850807	−	0.996374i	$-0.472885\pi$
$701$	−22.1405	−	16.0860i	−0.836236	−	0.607561i	−0.921317	+	0.388813i	$0.872885\pi$
$702$	14.8692	+	16.2473i	0.561201	+	0.613216i
$703$		−	20.0376i		−	0.755731i
$704$	−3.10407	+	1.16823i	−0.116989	+	0.0440293i
$705$	−2.20168	−	15.3647i	−0.0829200	−	0.578667i
$706$	13.0660	−	4.24542i	0.491747	−	0.159778i
$707$	4.20549	−	5.78836i	0.158164	−	0.217694i
$708$	−5.79709	+	5.62851i	−0.217868	+	0.211532i
$709$	13.1638	−	40.5141i	0.494378	−	1.52154i	−0.323546	−	0.946213i	$-0.604875\pi$
$709$	13.1638	−	40.5141i	0.494378	−	1.52154i	0.817924	−	0.575327i	$-0.195125\pi$
$710$	−2.90445	+	8.93899i	−0.109002	+	0.335474i
$711$	3.90874	+	3.02000i	0.146589	+	0.113259i
$712$	10.1926	−	14.0289i	0.381983	−	0.525754i
$713$	−9.80143	+	3.18468i	−0.367066	+	0.119267i
$714$	7.67708	−	1.10009i	0.287308	−	0.0411697i
$715$	−0.607365	−	13.2526i	−0.0227142	−	0.495619i
$716$		−	4.21134i		−	0.157385i
$717$	31.0773	−	15.2614i	1.16060	−	0.569948i
$718$	23.6610	+	17.1908i	0.883022	+	0.641553i
$719$	9.60723	+	13.2232i	0.358289	+	0.493143i	0.949671	−	0.313249i	$-0.101417\pi$
$719$	9.60723	+	13.2232i	0.358289	+	0.493143i	−0.591382	+	0.806392i	$0.701417\pi$
$720$	2.82991	+	0.0835271i	0.105465	+	0.00311287i
$721$	18.3867	+	5.97420i	0.684757	+	0.222491i
$722$	−25.2965	+	18.3790i	−0.941438	+	0.683995i
$723$	2.74922	+	1.45228i	0.102245	+	0.0540109i
$724$	2.67906	+	8.24528i	0.0995663	+	0.306434i
$725$	−26.2749			−0.975826
$726$	18.9913	+	1.52709i	0.704832	+	0.0566756i
$727$	−21.6566			−0.803197			−0.401599	−	0.915816i	$-0.631545\pi$
$727$	−21.6566			−0.803197			−0.401599	+	0.915816i	$0.631545\pi$
$728$	2.00000	+	6.15537i	0.0741249	+	0.228133i
$729$	26.3156	−	6.04065i	0.974652	−	0.223728i
$730$	−1.33854	+	0.972508i	−0.0495417	+	0.0359941i
$731$	−14.9089	−	4.84420i	−0.551426	−	0.179169i
$732$	0.213513	−	1.23030i	0.00789166	−	0.0454734i
$733$	−16.0834	−	22.1368i	−0.594052	−	0.817643i	0.401095	−	0.916036i	$-0.368630\pi$
$733$	−16.0834	−	22.1368i	−0.594052	−	0.817643i	−0.995148	+	0.0983933i	$0.968630\pi$
$734$	9.12557	+	6.63012i	0.336831	+	0.244722i
$735$	3.36361	+	6.84943i	0.124069	+	0.252645i
$736$			1.18465i			0.0436666i
$737$	0.591238	+	12.9007i	0.0217785	+	0.475203i
$738$	21.0692	−	6.16481i	0.775569	−	0.226930i
$739$	−47.3897	+	15.3979i	−1.74326	+	0.566420i	−0.995257	−	0.0972762i	$-0.968987\pi$
$739$	−47.3897	+	15.3979i	−1.74326	+	0.566420i	−0.748003	+	0.663696i	$0.768987\pi$
$740$	−1.56768	+	2.15773i	−0.0576291	+	0.0793197i
$741$	36.2584	+	37.3444i	1.33199	+	1.37188i
$742$	2.29675	−	7.06868i	0.0843165	−	0.259499i
$743$	−6.29906	+	19.3865i	−0.231090	+	0.711222i	0.766526	+	0.642213i	$0.221984\pi$
$743$	−6.29906	+	19.3865i	−0.231090	+	0.711222i	−0.997616	+	0.0690089i	$0.978016\pi$
$744$	−10.4963	−	10.8107i	−0.384814	−	0.396340i
$745$	9.63467	−	13.2610i	0.352987	−	0.485845i
$746$	5.45474	−	1.77235i	0.199712	−	0.0648904i
$747$	−17.7357	+	5.18941i	−0.648914	+	0.189871i
$748$	9.10233	−	3.42570i	0.332814	−	0.125256i
$749$			1.09749i			0.0401013i
$750$	−6.56340	−	13.3653i	−0.239661	−	0.488030i
$751$	15.4668	+	11.2373i	0.564390	+	0.410053i	0.833063	−	0.553178i	$-0.186585\pi$
$751$	15.4668	+	11.2373i	0.564390	+	0.410053i	−0.268673	+	0.963231i	$0.586585\pi$
$752$	5.58154	+	7.68233i	0.203538	+	0.280146i
$753$	−3.76108	+	21.6721i	−0.137061	+	0.789775i
$754$	−25.7744	−	8.37461i	−0.938648	−	0.304985i
$755$	−11.5381	+	8.38293i	−0.419915	+	0.305086i
$756$	7.77405	+	1.58673i	0.282739	+	0.0577088i
$757$	5.81223	+	17.8882i	0.211249	+	0.650158i	0.999399	+	0.0346742i	$0.0110394\pi$
$757$	5.81223	+	17.8882i	0.211249	+	0.650158i	−0.788150	+	0.615484i	$0.788961\pi$
$758$	−26.9912			−0.980365
$759$	2.89983	−	6.15652i	0.105257	−	0.223467i
$760$	6.69094			0.242706
$761$	7.25897	+	22.3408i	0.263138	+	0.809854i	0.992117	+	0.125318i	$0.0399952\pi$
$761$	7.25897	+	22.3408i	0.263138	+	0.809854i	−0.728979	+	0.684536i	$0.760005\pi$
$762$	8.09655	+	4.27701i	0.293307	+	0.154940i
$763$	−11.3766	+	8.26558i	−0.411860	+	0.299234i
$764$	12.7897	+	4.15562i	0.462714	+	0.150345i
$765$	−8.29839	−	0.244934i	−0.300029	−	0.00885559i
$766$	0.371431	+	0.511231i	0.0134203	+	0.0184715i
$767$	15.9966	+	11.6222i	0.577604	+	0.419654i
$768$	−1.55470	+	0.763481i	−0.0561005	+	0.0275498i
$769$		−	38.7115i		−	1.39597i	−0.716111	−	0.697987i	$-0.754080\pi$
$769$		−	38.7115i		−	1.39597i	0.716111	−	0.697987i	$-0.245920\pi$
$770$	−2.98328	−	3.73388i	−0.107510	−	0.134560i
$771$	−9.08423	+	1.30172i	−0.327160	+	0.0468804i
$772$	−6.65520	+	2.16241i	−0.239526	+	0.0778267i
$773$	−13.5353	+	18.6298i	−0.486832	+	0.670067i	−0.979800	−	0.199981i	$-0.935912\pi$
$773$	−13.5353	+	18.6298i	−0.486832	+	0.670067i	0.492968	+	0.870048i	$0.335912\pi$
$774$	−12.6909	−	9.80536i	−0.456166	−	0.352446i
$775$	−11.0473	+	34.0001i	−0.396830	+	1.22132i
$776$	−3.54074	+	10.8973i	−0.127105	+	0.391189i
$777$	−5.36273	+	5.20678i	−0.192387	+	0.186792i
$778$	15.7180	−	21.6340i	0.563517	−	0.775615i
$779$	49.3421	−	16.0322i	1.76787	−	0.574414i
$780$	−0.982738	−	6.85815i	−0.0351877	−	0.245561i
$781$	−8.75856	+	31.8499i	−0.313406	+	1.13968i
$782$		−	3.47384i		−	0.124224i
$783$	−24.5090	+	22.4300i	−0.875879	+	0.801585i
$784$	−3.77680	−	2.74401i	−0.134886	−	0.0980003i
$785$	−2.05695	−	2.83114i	−0.0734156	−	0.101048i
$786$	18.1732	+	3.15387i	0.648218	+	0.112495i
$787$	−19.1541	−	6.22355i	−0.682770	−	0.221846i	−0.0529625	−	0.998597i	$-0.516866\pi$
$787$	−19.1541	−	6.22355i	−0.682770	−	0.221846i	−0.629808	+	0.776751i	$0.716866\pi$
$788$	−18.5214	+	13.4566i	−0.659797	+	0.479371i
$789$	−7.69951	+	14.5755i	−0.274110	+	0.518900i
$790$	−0.480158	−	1.47777i	−0.0170833	−	0.0525768i
$791$	7.48940			0.266292
$792$	9.94855	−	0.162083i	0.353506	−	0.00575937i
$793$	−3.05573			−0.108512
$794$	−11.1299	−	34.2542i	−0.394984	−	1.21563i
$795$	−3.71623	+	7.03496i	−0.131801	+	0.249504i
$796$	16.9034	−	12.2810i	0.599124	−	0.435289i
$797$	−8.13556	−	2.64340i	−0.288176	−	0.0936341i	0.161362	−	0.986895i	$-0.448411\pi$
$797$	−8.13556	−	2.64340i	−0.288176	−	0.0936341i	−0.449538	+	0.893261i	$0.648411\pi$
$798$	18.4753	+	3.20629i	0.654019	+	0.113502i
$799$	−16.3672	−	22.5275i	−0.579031	−	0.796967i
$800$	3.32458	+	2.41545i	0.117542	+	0.0853989i
$801$	−42.9705	+	29.3227i	−1.51829	+	1.03607i
$802$			20.7287i			0.731955i
$803$	−4.54281	+	3.62960i	−0.160312	+	0.128086i
$804$	0.956643	+	6.67604i	0.0337382	+	0.235446i
$805$	−1.62354	+	0.527521i	−0.0572224	+	0.0185927i
$806$	−21.6737	+	29.8313i	−0.763423	+	1.05076i
$807$	0.0909228	−	0.0882787i	0.00320063	−	0.00310756i
$808$	1.44795	−	4.45632i	0.0509385	−	0.156773i
$809$	8.21303	−	25.2771i	0.288755	−	0.888696i	−0.696493	−	0.717563i	$-0.745257\pi$
$809$	8.21303	−	25.2771i	0.288755	−	0.888696i	0.985248	−	0.171132i	$-0.0547426\pi$
$810$	−7.90887	−	3.09647i	−0.277889	−	0.108799i
$811$	−10.4155	+	14.3358i	−0.365739	+	0.503397i	−0.951737	−	0.306916i	$-0.900703\pi$
$811$	−10.4155	+	14.3358i	−0.365739	+	0.503397i	0.585997	+	0.810313i	$0.300703\pi$
$812$	−9.28533	+	3.01699i	−0.325851	+	0.105875i
$813$	0.0192330	−	0.00275599i	0.000674530	−	9.66568e-5i
$814$	−5.15657	+	7.82748i	−0.180738	+	0.274353i
$815$		−	10.1693i		−	0.356215i
$816$	4.55898	−	2.23882i	0.159596	−	0.0783744i
$817$	−30.6636	−	22.2784i	−1.07278	−	0.779422i
$818$	9.70908	+	13.3634i	0.339470	+	0.467240i
$819$	0.572841	−	19.4080i	0.0200167	−	0.678169i
$820$	−6.56768	−	2.13397i	−0.229353	−	0.0745214i
$821$	31.3364	−	22.7672i	1.09365	−	0.794581i	0.113635	−	0.993523i	$-0.463751\pi$
$821$	31.3364	−	22.7672i	1.09365	−	0.794581i	0.980011	+	0.198942i	$0.0637505\pi$
$822$	0.912884	+	0.482232i	0.0318405	+	0.0168198i
$823$	−10.3524	−	31.8614i	−0.360862	−	1.11062i	−0.952532	−	0.304439i	$-0.901531\pi$
$823$	−10.3524	−	31.8614i	−0.360862	−	1.11062i	0.591670	−	0.806180i	$-0.298469\pi$
$824$	12.6610			0.441068
$825$	−11.3649	−	20.6910i	−0.395676	−	0.720367i
$826$	7.12326			0.247850
$827$	10.6771	+	32.8609i	0.371281	+	1.14268i	0.945954	+	0.324301i	$0.105129\pi$
$827$	10.6771	+	32.8609i	0.371281	+	1.14268i	−0.574673	+	0.818383i	$0.694871\pi$
$828$	1.19747	−	3.34612i	0.0416149	−	0.116286i
$829$	−24.3518	+	17.6927i	−0.845775	+	0.614491i	−0.923978	−	0.382446i	$-0.875082\pi$
$829$	−24.3518	+	17.6927i	−0.845775	+	0.614491i	0.0782031	+	0.996937i	$0.475082\pi$
$830$	5.52854	+	1.79633i	0.191898	+	0.0623516i
$831$	4.11137	−	23.6906i	0.142622	−	0.821817i
$832$	2.49137	+	3.42908i	0.0863727	+	0.118882i
$833$	11.0750	+	8.04649i	0.383728	+	0.278794i
$834$	3.92172	+	7.98592i	0.135798	+	0.276530i
$835$			12.5498i			0.434304i
$836$	23.4902	−	1.07656i	0.812427	−	0.0372335i
$837$	18.7200	+	41.1456i	0.647056	+	1.42220i
$838$	15.2372	−	4.95086i	0.526360	−	0.171025i
$839$	−6.48932	+	8.93178i	−0.224036	+	0.308359i	−0.906208	−	0.422833i	$-0.861036\pi$
$839$	−6.48932	+	8.93178i	−0.224036	+	0.308359i	0.682172	+	0.731192i	$0.261036\pi$
$840$	−1.73865	−	1.79072i	−0.0599891	−	0.0617858i
$841$	3.67154	−	11.2998i	0.126605	−	0.389650i
$842$	−4.04838	+	12.4596i	−0.139516	+	0.429387i
$843$	20.5006	+	21.1147i	0.706079	+	0.727227i
$844$	−2.33113	+	3.20852i	−0.0802408	+	0.110442i
$845$	−4.45664	+	1.44805i	−0.153313	+	0.0498145i
$846$	−8.00000	−	27.3413i	−0.275046	−	0.940013i
$847$	−11.0743	−	12.6287i	−0.380518	−	0.433928i
$848$		−	4.86748i		−	0.167150i
$849$	17.6858	+	36.0141i	0.606974	+	1.23600i
$850$	−9.74894	−	7.08302i	−0.334386	−	0.242946i
$851$	1.96791	+	2.70860i	0.0674592	+	0.0928496i
$852$	−2.94965	+	16.9965i	−0.101053	+	0.582290i
$853$	15.0696	+	4.89641i	0.515973	+	0.167650i	0.555417	−	0.831572i	$-0.312559\pi$
$853$	15.0696	+	4.89641i	0.515973	+	0.167650i	−0.0394441	+	0.999222i	$0.512559\pi$
$854$	−0.890597	+	0.647057i	−0.0304756	+	0.0221418i
$855$	−18.8991	−	6.76337i	−0.646335	−	0.231302i
$856$	0.222103	+	0.683562i	0.00759131	+	0.0233637i
$857$	−37.7235			−1.28861			−0.644305	−	0.764769i	$-0.722853\pi$
$857$	−37.7235			−1.28861			−0.644305	+	0.764769i	$0.722853\pi$
$858$	−4.55361	−	23.9191i	−0.155458	−	0.816586i
$859$	22.4943			0.767497			0.383749	−	0.923438i	$-0.374633\pi$
$859$	22.4943			0.767497			0.383749	+	0.923438i	$0.374633\pi$
$860$	1.55898	+	4.79806i	0.0531609	+	0.163612i
$861$	−17.1124	−	9.03964i	−0.583188	−	0.308070i
$862$	9.55912	−	6.94510i	0.325585	−	0.236551i
$863$	−4.45269	−	1.44677i	−0.151571	−	0.0492485i	0.232249	−	0.972656i	$-0.425392\pi$
$863$	−4.45269	−	1.44677i	−0.151571	−	0.0492485i	−0.383820	+	0.923408i	$0.625392\pi$
$864$	5.16312	−	0.584981i	0.175653	−	0.0199015i
$865$	3.94360	+	5.42789i	0.134086	+	0.184554i
$866$	9.23019	+	6.70613i	0.313655	+	0.227883i
$867$	13.0612	−	6.41409i	0.443583	−	0.217834i
$868$			13.2838i			0.450882i
$869$	−1.92349	−	5.11084i	−0.0652498	−	0.173373i
$870$	10.3455	−	1.48245i	0.350744	−	0.0502599i
$871$	15.6963	−	5.10004i	0.531849	−	0.172808i
$872$	−5.41309	+	7.45047i	−0.183310	+	0.252305i
$873$	21.0163	−	27.2011i	0.711294	−	0.920618i
$874$	2.59548	−	7.98806i	0.0877934	−	0.270200i
$875$	−4.05640	+	12.4843i	−0.137131	+	0.422047i
$876$	−2.17868	+	2.11532i	−0.0736107	+	0.0714701i
$877$	24.0621	−	33.1186i	0.812520	−	1.11834i	−0.178410	−	0.983956i	$-0.557095\pi$
$877$	24.0621	−	33.1186i	0.812520	−	1.11834i	0.990930	−	0.134381i	$-0.0429046\pi$
$878$	15.2387	−	4.95136i	0.514282	−	0.167100i
$879$	5.75348	+	40.1513i	0.194060	+	1.35427i
$880$	−2.61375	−	1.72188i	−0.0881096	−	0.0580445i
$881$		−	53.8892i		−	1.81557i	−0.419431	−	0.907787i	$-0.637770\pi$
$881$		−	53.8892i		−	1.81557i	0.419431	−	0.907787i	$-0.362230\pi$
$882$	7.89416	+	11.5683i	0.265810	+	0.389527i
$883$	8.88868	+	6.45800i	0.299128	+	0.217329i	0.727217	−	0.686407i	$-0.240813\pi$
$883$	8.88868	+	6.45800i	0.299128	+	0.217329i	−0.428090	+	0.903736i	$0.640813\pi$
$884$	−7.30565	−	10.0554i	−0.245716	−	0.338199i
$885$	−7.51291	−	1.30383i	−0.252544	−	0.0438276i
$886$	−4.50336	−	1.46323i	−0.151293	−	0.0491582i
$887$	22.3015	−	16.2030i	0.748811	−	0.544043i	−0.146647	−	0.989189i	$-0.546848\pi$
$887$	22.3015	−	16.2030i	0.748811	−	0.544043i	0.895458	+	0.445146i	$0.146848\pi$
$888$	−2.28642	+	4.32828i	−0.0767273	+	0.145248i
$889$	−2.49456	−	7.67746i	−0.0836648	−	0.257494i
$890$	16.3646			0.548543
$891$	−28.2643	−	9.59842i	−0.946889	−	0.321559i
$892$	−9.37659			−0.313951
$893$	−20.8048	−	64.0307i	−0.696207	−	2.14271i
$894$	14.0519	−	26.6008i	0.469966	−	0.889663i
$895$	3.21528	−	2.33604i	0.107475	−	0.0780852i
$896$	1.45223	+	0.471857i	0.0485155	+	0.0157636i
$897$	−8.56890	−	1.48709i	−0.286107	−	0.0496524i
$898$	15.2006	+	20.9219i	0.507251	+	0.698172i
$899$	−45.0002	−	32.6946i	−1.50084	−	1.09043i
$900$	−6.94893	−	10.1832i	−0.231631	−	0.339439i
$901$			14.2733i			0.475513i
$902$	−23.4008	−	6.43511i	−0.779163	−	0.214266i
$903$	2.00551	+	13.9957i	0.0667392	+	0.465747i
$904$	4.66471	−	1.51566i	0.155146	−	0.0504100i
$905$	−4.80904	+	6.61908i	−0.159858	+	0.220026i
$906$	−18.7800	+	18.2339i	−0.623924	+	0.605780i
$907$	−16.0446	+	49.3803i	−0.532753	+	1.63965i	0.215702	+	0.976459i	$0.430796\pi$
$907$	−16.0446	+	49.3803i	−0.532753	+	1.63965i	−0.748455	+	0.663186i	$0.769204\pi$
$908$	0.561021	−	1.72665i	0.0186181	−	0.0573007i
$909$	−8.59439	+	11.1236i	−0.285058	+	0.368946i
$910$	−3.59010	+	4.94135i	−0.119011	+	0.163804i
$911$	32.9754	−	10.7144i	1.09252	−	0.354982i	0.293302	−	0.956020i	$-0.405246\pi$
$911$	32.9754	−	10.7144i	1.09252	−	0.354982i	0.799221	+	0.601037i	$0.205246\pi$
$912$	12.1561	−	1.74190i	0.402528	−	0.0576802i
$913$	19.6984	+	5.41694i	0.651920	+	0.179275i
$914$			22.8916i			0.757187i
$915$	1.05775	−	0.519439i	0.0349681	−	0.0171721i
$916$	15.0398	+	10.9271i	0.496930	+	0.361040i
$917$	−9.55789	−	13.1553i	−0.315629	−	0.434427i
$918$	−15.1403	+	1.71539i	−0.499703	+	0.0566163i
$919$	2.83223	+	0.920248i	0.0934267	+	0.0303562i	0.355357	−	0.934731i	$-0.384359\pi$
$919$	2.83223	+	0.920248i	0.0934267	+	0.0303562i	−0.261931	+	0.965087i	$0.584359\pi$
$920$	−0.904455	+	0.657125i	−0.0298190	+	0.0216648i
$921$	7.63624	+	4.03385i	0.251623	+	0.132920i
$922$	−6.57616	−	20.2393i	−0.216574	−	0.666547i
$923$	42.2144			1.38950
$924$	−6.39208	−	6.00704i	−0.210284	−	0.197617i
$925$	11.6139			0.381862
$926$	6.41573	+	19.7456i	0.210834	+	0.648880i
$927$	−35.7621	−	12.7981i	−1.17458	−	0.420344i
$928$	−5.17274	+	3.75821i	−0.169803	+	0.123369i
$929$	43.8878	+	14.2600i	1.43991	+	0.467856i	0.921870	−	0.387498i	$-0.126661\pi$
$929$	43.8878	+	14.2600i	1.43991	+	0.467856i	0.518043	+	0.855355i	$0.326661\pi$
$930$	2.43144	−	14.0105i	0.0797301	−	0.459421i
$931$	19.4550	+	26.7776i	0.637613	+	0.877599i
$932$	−14.6282	−	10.6280i	−0.479163	−	0.348132i
$933$	−10.6771	−	21.7421i	−0.349552	−	0.711804i
$934$		−	3.89855i		−	0.127565i
$935$	7.66453	+	5.04921i	0.250657	+	0.165127i
$936$	−3.57087	−	12.2040i	−0.116718	−	0.398901i
$937$	34.1863	−	11.1078i	1.11682	−	0.362876i	0.308266	−	0.951300i	$-0.400251\pi$
$937$	34.1863	−	11.1078i	1.11682	−	0.362876i	0.808552	+	0.588424i	$0.200251\pi$
$938$	3.49477	−	4.81014i	0.114108	−	0.157057i
$939$	−18.8983	−	19.4643i	−0.616721	−	0.635193i
$940$	−2.76923	+	8.52280i	−0.0903222	+	0.277983i
$941$	4.43429	−	13.6473i	0.144554	−	0.444891i	−0.852400	−	0.522891i	$-0.824854\pi$
$941$	4.43429	−	13.6473i	0.144554	−	0.444891i	0.996953	+	0.0780003i	$0.0248535\pi$
$942$	−4.47411	−	4.60811i	−0.145774	−	0.150140i
$943$	−5.09533	+	7.01312i	−0.165927	+	0.228379i
$944$	4.43667	−	1.44156i	0.144401	−	0.0469188i
$945$	3.10084	+	6.81550i	0.100870	+	0.221708i
$946$	6.24520	+	16.5940i	0.203049	+	0.539516i
$947$			12.3625i			0.401726i	0.979619	+	0.200863i	$0.0643746\pi$
$947$			12.3625i			0.401726i	−0.979619	+	0.200863i	$0.935625\pi$
$948$	−1.25707	−	2.55981i	−0.0408277	−	0.0831388i
$949$	6.01189	+	4.36789i	0.195154	+	0.141788i
$950$	−17.1255	−	23.5713i	−0.555626	−	0.764753i
$951$	9.47805	−	54.6145i	0.307347	−	1.77100i
$952$	−4.25849	−	1.38367i	−0.138018	−	0.0448449i
$953$	18.6023	−	13.5153i	0.602586	−	0.437805i	−0.244210	−	0.969722i	$-0.578529\pi$
$953$	18.6023	−	13.5153i	0.602586	−	0.437805i	0.846796	+	0.531918i	$0.178529\pi$
$954$	−4.92016	+	13.7486i	−0.159296	+	0.445126i
$955$	3.92172	+	12.0698i	0.126904	+	0.390570i
$956$	−19.9892			−0.646499
$957$	36.0819	−	6.86909i	1.16636	−	0.222046i
$958$	−34.8328			−1.12540
$959$	−0.281261	−	0.865632i	−0.00908238	−	0.0279527i
$960$	−1.44530	−	0.763481i	−0.0466468	−	0.0246412i
$961$	−36.1480	+	26.2631i	−1.16607	+	0.847196i
$962$	11.3926	+	3.70169i	0.367313	+	0.119347i
$963$	0.0636148	−	2.15528i	0.00204996	−	0.0694529i
$964$	−1.05514	−	1.45228i	−0.0339839	−	0.0467748i
$965$	−5.34261	−	3.88163i	−0.171985	−	0.124954i
$966$	−2.81231	+	1.38107i	−0.0904847	+	0.0444351i
$967$		−	58.6116i		−	1.88482i	−0.334455	−	0.942412i	$-0.608552\pi$
$967$		−	58.6116i		−	1.88482i	0.334455	−	0.942412i	$-0.391448\pi$
$968$	−9.45328	−	5.62455i	−0.303840	−	0.180780i
$969$	−35.6463	+	5.10794i	−1.14512	+	0.164091i
$970$	−10.2839	+	3.34144i	−0.330196	+	0.107287i
$971$	−20.5172	+	28.2395i	−0.658428	+	0.906249i	−0.999428	−	0.0338147i	$-0.989234\pi$
$971$	−20.5172	+	28.2395i	−0.658428	+	0.906249i	0.341000	+	0.940063i	$0.389234\pi$
$972$	−15.1749	−	3.56668i	−0.486736	−	0.114401i
$973$	2.42375	−	7.45955i	0.0777020	−	0.239142i
$974$	−1.55634	+	4.78991i	−0.0498683	+	0.153479i
$975$	−21.6450	+	21.0156i	−0.693195	+	0.673036i
$976$	−0.423754	+	0.583248i	−0.0135640	+	0.0186693i
$977$	−45.7412	+	14.8622i	−1.46339	+	0.475485i	−0.929104	−	0.369819i	$-0.879420\pi$
$977$	−45.7412	+	14.8622i	−1.46339	+	0.475485i	−0.534287	+	0.845303i	$0.679420\pi$
$978$	−2.64745	−	18.4755i	−0.0846562	−	0.590783i
$979$	57.4521	−	2.63303i	1.83618	−	0.0841519i
$980$		−	4.40562i		−	0.140733i
$981$	22.8208	−	15.5728i	0.728612	−	0.497200i
$982$	−11.3418	−	8.24030i	−0.361931	−	0.262958i
$983$	3.53254	+	4.86212i	0.112670	+	0.155078i	0.861628	−	0.507541i	$-0.169445\pi$
$983$	3.53254	+	4.86212i	0.112670	+	0.155078i	−0.748957	+	0.662618i	$0.769445\pi$
$984$	−12.4877	−	2.16717i	−0.398093	−	0.0690870i
$985$	−20.5477	−	6.67635i	−0.654704	−	0.212726i
$986$	15.1685	−	11.0205i	0.483062	−	0.350965i
$987$	−11.7306	+	22.2065i	−0.373390	+	0.706841i
$988$	−9.28642	−	28.5807i	−0.295440	−	0.909272i
$989$	6.33296			0.201377
$990$	5.64222	+	7.50563i	0.179322	+	0.238544i
$991$	51.4597			1.63467			0.817336	−	0.576161i	$-0.195450\pi$
$991$	51.4597			1.63467			0.817336	+	0.576161i	$0.195450\pi$
$992$	2.68830	+	8.27372i	0.0853535	+	0.262691i
$993$	4.66471	−	8.83048i	0.148030	−	0.280227i
$994$	12.3035	−	8.93899i	0.390242	−	0.283528i
$995$	18.7526	+	6.09310i	0.594499	+	0.193164i
$996$	10.5119	+	1.82428i	0.333082	+	0.0578046i
$997$	21.7299	+	29.9086i	0.688192	+	0.947215i	0.999996	−	0.00293153i	$-0.000933137\pi$
$997$	21.7299	+	29.9086i	0.688192	+	0.947215i	−0.311804	+	0.950147i	$0.600933\pi$
$998$	−11.2013	−	8.13820i	−0.354570	−	0.257610i
$999$	10.8333	−	9.91439i	0.342751	−	0.313677i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	66.2.h.b.17.1	yes	8
3.2	odd	2		66.2.h.a.17.1	✓	8
4.3	odd	2		528.2.bn.a.17.2		8
11.2	odd	10		66.2.h.a.35.1	yes	8
11.3	even	5		726.2.b.c.725.6		8
11.4	even	5		726.2.h.f.239.1		8
11.5	even	5		726.2.h.h.161.2		8
11.6	odd	10		726.2.h.c.161.2		8
11.7	odd	10		726.2.h.a.239.1		8
11.8	odd	10		726.2.b.e.725.6		8
11.9	even	5		726.2.h.j.233.1		8
11.10	odd	2		726.2.h.d.215.1		8
12.11	even	2		528.2.bn.b.17.2		8
33.2	even	10	inner	66.2.h.b.35.2	yes	8
33.5	odd	10		726.2.h.a.161.1		8
33.8	even	10		726.2.b.c.725.5		8
33.14	odd	10		726.2.b.e.725.5		8
33.17	even	10		726.2.h.f.161.1		8
33.20	odd	10		726.2.h.d.233.2		8
33.26	odd	10		726.2.h.c.239.2		8
33.29	even	10		726.2.h.h.239.2		8
33.32	even	2		726.2.h.j.215.1		8
44.35	even	10		528.2.bn.b.497.2		8
132.35	odd	10		528.2.bn.a.497.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.h.a.17.1	✓	8	3.2	odd	2
66.2.h.a.35.1	yes	8	11.2	odd	10
66.2.h.b.17.1	yes	8	1.1	even	1	trivial
66.2.h.b.35.2	yes	8	33.2	even	10	inner
528.2.bn.a.17.2		8	4.3	odd	2
528.2.bn.a.497.1		8	132.35	odd	10
528.2.bn.b.17.2		8	12.11	even	2
528.2.bn.b.497.2		8	44.35	even	10
726.2.b.c.725.5		8	33.8	even	10
726.2.b.c.725.6		8	11.3	even	5
726.2.b.e.725.5		8	33.14	odd	10
726.2.b.e.725.6		8	11.8	odd	10
726.2.h.a.161.1		8	33.5	odd	10
726.2.h.a.239.1		8	11.7	odd	10
726.2.h.c.161.2		8	11.6	odd	10
726.2.h.c.239.2		8	33.26	odd	10
726.2.h.d.215.1		8	11.10	odd	2
726.2.h.d.233.2		8	33.20	odd	10
726.2.h.f.161.1		8	33.17	even	10
726.2.h.f.239.1		8	11.4	even	5
726.2.h.h.161.2		8	11.5	even	5
726.2.h.h.239.2		8	33.29	even	10
726.2.h.j.215.1		8	33.32	even	2
726.2.h.j.233.1		8	11.9	even	5

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:	\( N \)	\(=\)	\( 66 = 2 \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	66.h (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.809017 - 1.53150i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.897526 - 0.291624i) q^{5} +(-1.70654 - 0.296161i) q^{6} +(0.897526 + 1.23534i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-1.69098 - 2.47802i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.809017 - 1.53150i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.897526 - 0.291624i) q^{5} +(-1.70654 - 0.296161i) q^{6} +(0.897526 + 1.23534i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-1.69098 - 2.47802i) q^{9} +0.943715i q^{10} +(0.151841 + 3.31315i) q^{11} +(0.245684 + 1.71454i) q^{12} +(4.03112 - 1.30979i) q^{13} +(0.897526 - 1.23534i) q^{14} +(-1.17274 + 1.13863i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.906157 + 2.78886i) q^{17} +(-1.83419 + 2.37397i) q^{18} +(-4.16740 + 5.73594i) q^{19} +(0.897526 - 0.291624i) q^{20} +(2.61803 - 0.375151i) q^{21} +(3.10407 - 1.16823i) q^{22} -1.18465i q^{23} +(1.55470 - 0.763481i) q^{24} +(-3.32458 - 2.41545i) q^{25} +(-2.49137 - 3.42908i) q^{26} +(-5.16312 + 0.584981i) q^{27} +(-1.45223 - 0.471857i) q^{28} +(5.17274 - 3.75821i) q^{29} +(1.44530 + 0.763481i) q^{30} +(-2.68830 - 8.27372i) q^{31} -1.00000 q^{32} +(5.19693 + 2.44785i) q^{33} +2.93239 q^{34} +(-0.445299 - 1.37049i) q^{35} +(2.82458 + 1.01082i) q^{36} +(-2.28642 + 1.66118i) q^{37} +(6.74300 + 2.19093i) q^{38} +(1.25530 - 7.23330i) q^{39} +(-0.554701 - 0.763481i) q^{40} +(-5.92001 - 4.30114i) q^{41} +(-1.16581 - 2.37397i) q^{42} +5.34587i q^{43} +(-2.07026 - 2.59114i) q^{44} +(0.795052 + 2.71722i) q^{45} +(-1.12667 + 0.366076i) q^{46} +(-5.58154 + 7.68233i) q^{47} +(-1.20654 - 1.24268i) q^{48} +(1.44261 - 4.43990i) q^{49} +(-1.26988 + 3.90827i) q^{50} +(3.53805 + 3.64402i) q^{51} +(-2.49137 + 3.42908i) q^{52} +(4.62924 - 1.50413i) q^{53} +(2.15184 + 4.72965i) q^{54} +(0.829911 - 3.01792i) q^{55} +1.52696i q^{56} +(5.41309 + 11.0228i) q^{57} +(-5.17274 - 3.75821i) q^{58} +(2.74201 + 3.77405i) q^{59} +(0.279492 - 1.61049i) q^{60} +(-0.685649 - 0.222781i) q^{61} +(-7.03805 + 5.11344i) q^{62} +(1.54349 - 4.31302i) q^{63} +(0.309017 + 0.951057i) q^{64} -4.00000 q^{65} +(0.722103 - 5.69900i) q^{66} +3.89379 q^{67} +(-0.906157 - 2.78886i) q^{68} +(-1.81428 - 0.958399i) q^{69} +(-1.16581 + 0.847008i) q^{70} +(9.47214 + 3.07768i) q^{71} +(0.0885088 - 2.99869i) q^{72} +(1.03051 + 1.41838i) q^{73} +(2.28642 + 1.66118i) q^{74} +(-6.38889 + 3.13745i) q^{75} -7.09001i q^{76} +(-3.95658 + 3.16121i) q^{77} +(-7.26719 + 1.04135i) q^{78} +(-1.56591 + 0.508796i) q^{79} +(-0.554701 + 0.763481i) q^{80} +(-3.28115 + 8.38057i) q^{81} +(-2.26124 + 6.95939i) q^{82} +(1.90347 - 5.85828i) q^{83} +(-1.89753 + 1.84235i) q^{84} +(1.62660 - 2.23882i) q^{85} +(5.08423 - 1.65197i) q^{86} +(-1.57087 - 10.9625i) q^{87} +(-1.82458 + 2.76964i) q^{88} -17.3406i q^{89} +(2.33854 - 1.59581i) q^{90} +(5.23607 + 3.80423i) q^{91} +(0.696317 + 0.958399i) q^{92} +(-14.8461 - 2.57646i) q^{93} +(9.03112 + 2.93439i) q^{94} +(5.41309 - 3.93284i) q^{95} +(-0.809017 + 1.53150i) q^{96} +(3.54074 + 10.8973i) q^{97} -4.66839 q^{98} +(7.95328 - 5.97874i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{6} + 2 q^{8} - 18 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^6 + 2 * q^8 - 18 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{6} + 2 q^{8} - 18 q^{9} - q^{11} - 3 q^{12} + 9 q^{15} - 2 q^{16} - 10 q^{17} - 7 q^{18} - 15 q^{19} + 12 q^{21} + 6 q^{22} + 3 q^{24} - 6 q^{25} - 10 q^{26} - 10 q^{27} + 5 q^{28} + 23 q^{29} + 21 q^{30} + 13 q^{31} - 8 q^{32} + 17 q^{33} + 10 q^{34} - 13 q^{35} + 2 q^{36} + 6 q^{37} + 10 q^{38} + 18 q^{39} + 5 q^{40} + 2 q^{41} - 17 q^{42} + 9 q^{44} - 8 q^{45} - 10 q^{46} + 10 q^{47} + 2 q^{48} - 18 q^{49} + q^{50} - 30 q^{51} - 10 q^{52} + 15 q^{53} + 15 q^{54} - 14 q^{55} + 20 q^{57} - 23 q^{58} - 25 q^{59} + 4 q^{60} - 10 q^{61} + 2 q^{62} + 16 q^{63} - 2 q^{64} - 32 q^{65} - 22 q^{66} - 2 q^{67} - 10 q^{68} - 26 q^{69} - 17 q^{70} + 40 q^{71} - 2 q^{72} + 5 q^{73} - 6 q^{74} - 34 q^{75} - 12 q^{77} - 8 q^{78} + 10 q^{79} + 5 q^{80} + 14 q^{81} + 3 q^{82} - 21 q^{83} - 8 q^{84} + 30 q^{85} + 25 q^{86} + 42 q^{87} + 6 q^{88} + 8 q^{90} + 24 q^{91} + 10 q^{92} - 53 q^{93} + 40 q^{94} + 20 q^{95} - 2 q^{96} + 9 q^{97} - 22 q^{98} + 34 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^6 + 2 * q^8 - 18 * q^9 - q^11 - 3 * q^12 + 9 * q^15 - 2 * q^16 - 10 * q^17 - 7 * q^18 - 15 * q^19 + 12 * q^21 + 6 * q^22 + 3 * q^24 - 6 * q^25 - 10 * q^26 - 10 * q^27 + 5 * q^28 + 23 * q^29 + 21 * q^30 + 13 * q^31 - 8 * q^32 + 17 * q^33 + 10 * q^34 - 13 * q^35 + 2 * q^36 + 6 * q^37 + 10 * q^38 + 18 * q^39 + 5 * q^40 + 2 * q^41 - 17 * q^42 + 9 * q^44 - 8 * q^45 - 10 * q^46 + 10 * q^47 + 2 * q^48 - 18 * q^49 + q^50 - 30 * q^51 - 10 * q^52 + 15 * q^53 + 15 * q^54 - 14 * q^55 + 20 * q^57 - 23 * q^58 - 25 * q^59 + 4 * q^60 - 10 * q^61 + 2 * q^62 + 16 * q^63 - 2 * q^64 - 32 * q^65 - 22 * q^66 - 2 * q^67 - 10 * q^68 - 26 * q^69 - 17 * q^70 + 40 * q^71 - 2 * q^72 + 5 * q^73 - 6 * q^74 - 34 * q^75 - 12 * q^77 - 8 * q^78 + 10 * q^79 + 5 * q^80 + 14 * q^81 + 3 * q^82 - 21 * q^83 - 8 * q^84 + 30 * q^85 + 25 * q^86 + 42 * q^87 + 6 * q^88 + 8 * q^90 + 24 * q^91 + 10 * q^92 - 53 * q^93 + 40 * q^94 + 20 * q^95 - 2 * q^96 + 9 * q^97 - 22 * q^98 + 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more