LMFDB - Embedded newform 38.2.e.a.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,2,Mod(5,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	38.e (of order $9$, degree $6$, 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:	$0.303431527681$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	38.25
Dual form			38.2.e.a.35.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(-1.43969 - 0.524005i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.347296 + 1.96962i) q^{5} +(-1.43969 + 0.524005i) q^{6} +(-1.34730 + 2.33359i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.500000 - 0.419550i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(-1.43969 - 0.524005i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.347296 + 1.96962i) q^{5} +(-1.43969 + 0.524005i) q^{6} +(-1.34730 + 2.33359i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.500000 - 0.419550i) q^{9} +(1.53209 + 1.28558i) q^{10} +(-1.59240 - 2.75811i) q^{11} +(-0.766044 + 1.32683i) q^{12} +(5.41147 - 1.96962i) q^{13} +(0.467911 + 2.65366i) q^{14} +(0.532089 - 3.01763i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-4.99273 + 4.18939i) q^{17} -0.652704 q^{18} +(2.82635 - 3.31839i) q^{19} +2.00000 q^{20} +(3.16250 - 2.65366i) q^{21} +(-2.99273 - 1.08926i) q^{22} +(-0.120615 + 0.684040i) q^{23} +(0.266044 + 1.50881i) q^{24} +(0.939693 - 0.342020i) q^{25} +(2.87939 - 4.98724i) q^{26} +(2.79813 + 4.84651i) q^{27} +(2.06418 + 1.73205i) q^{28} +(-2.16250 - 1.81456i) q^{29} +(-1.53209 - 2.65366i) q^{30} +(-1.22668 + 2.12467i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.847296 + 4.80526i) q^{33} +(-1.13176 + 6.41852i) q^{34} +(-5.06418 - 1.84321i) q^{35} +(-0.500000 + 0.419550i) q^{36} -4.36959 q^{37} +(0.0320889 - 4.35878i) q^{38} -8.82295 q^{39} +(1.53209 - 1.28558i) q^{40} +(0.326352 + 0.118782i) q^{41} +(0.716881 - 4.06564i) q^{42} +(1.05303 + 5.97205i) q^{43} +(-2.99273 + 1.08926i) q^{44} +(0.652704 - 1.13052i) q^{45} +(0.347296 + 0.601535i) q^{46} +(6.04189 + 5.06975i) q^{47} +(1.17365 + 0.984808i) q^{48} +(-0.130415 - 0.225885i) q^{49} +(0.500000 - 0.866025i) q^{50} +(9.38326 - 3.41523i) q^{51} +(-1.00000 - 5.67128i) q^{52} +(1.42602 - 8.08737i) q^{53} +(5.25877 + 1.91404i) q^{54} +(4.87939 - 4.09429i) q^{55} +2.69459 q^{56} +(-5.80793 + 3.29644i) q^{57} -2.82295 q^{58} +(0.439693 - 0.368946i) q^{59} +(-2.87939 - 1.04801i) q^{60} +(0.509800 - 2.89122i) q^{61} +(0.426022 + 2.41609i) q^{62} +(1.65270 - 0.601535i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(5.75877 + 9.97448i) q^{65} +(3.73783 + 3.13641i) q^{66} +(-3.79813 - 3.18701i) q^{67} +(3.25877 + 5.64436i) q^{68} +(0.532089 - 0.921605i) q^{69} +(-5.06418 + 1.84321i) q^{70} +(-1.46791 - 8.32494i) q^{71} +(-0.113341 + 0.642788i) q^{72} +(-14.8157 - 5.39246i) q^{73} +(-3.34730 + 2.80872i) q^{74} -1.53209 q^{75} +(-2.77719 - 3.35965i) q^{76} +8.58172 q^{77} +(-6.75877 + 5.67128i) q^{78} +(8.51754 + 3.10013i) q^{79} +(0.347296 - 1.96962i) q^{80} +(-1.14883 - 6.51536i) q^{81} +(0.326352 - 0.118782i) q^{82} +(-4.23783 + 7.34013i) q^{83} +(-2.06418 - 3.57526i) q^{84} +(-9.98545 - 8.37879i) q^{85} +(4.64543 + 3.89798i) q^{86} +(2.16250 + 3.74557i) q^{87} +(-1.59240 + 2.75811i) q^{88} +(-7.27244 + 2.64695i) q^{89} +(-0.226682 - 1.28558i) q^{90} +(-2.69459 + 15.2818i) q^{91} +(0.652704 + 0.237565i) q^{92} +(2.87939 - 2.41609i) q^{93} +7.88713 q^{94} +(7.51754 + 4.41436i) q^{95} +1.53209 q^{96} +(-0.266044 + 0.223238i) q^{97} +(-0.245100 - 0.0892091i) q^{98} +(-0.360967 + 2.04715i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} - 3 q^{6} - 6 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^3 - 3 * q^6 - 6 * q^7 - 3 * q^8 - 3 * q^9	$ 6 q - 3 q^{3} - 3 q^{6} - 6 q^{7} - 3 q^{8} - 3 q^{9} - 6 q^{11} + 12 q^{13} + 12 q^{14} - 6 q^{15} - 12 q^{17} - 6 q^{18} + 18 q^{19} + 12 q^{20} + 24 q^{21} - 12 q^{23} - 3 q^{24} + 6 q^{26} + 3 q^{27} - 6 q^{28} - 18 q^{29} + 6 q^{31} + 3 q^{33} - 12 q^{34} - 12 q^{35} - 3 q^{36} - 12 q^{37} - 9 q^{38} - 12 q^{39} + 3 q^{41} - 12 q^{42} - 6 q^{43} + 6 q^{45} + 30 q^{47} + 6 q^{48} - 15 q^{49} + 3 q^{50} + 21 q^{51} - 6 q^{52} + 24 q^{53} + 9 q^{54} + 18 q^{55} + 12 q^{56} - 24 q^{57} + 24 q^{58} - 3 q^{59} - 6 q^{60} + 6 q^{61} + 18 q^{62} + 12 q^{63} - 3 q^{64} + 12 q^{65} + 3 q^{66} - 9 q^{67} - 3 q^{68} - 6 q^{69} - 12 q^{70} - 18 q^{71} + 6 q^{72} - 30 q^{73} - 18 q^{74} - 6 q^{76} - 12 q^{77} - 18 q^{78} + 6 q^{79} - 33 q^{81} + 3 q^{82} - 6 q^{83} + 6 q^{84} - 24 q^{85} + 12 q^{86} + 18 q^{87} - 6 q^{88} + 12 q^{90} - 12 q^{91} + 6 q^{92} + 6 q^{93} - 12 q^{94} + 3 q^{97} + 21 q^{99}+O(q^{100}) $ 6 * q - 3 * q^3 - 3 * q^6 - 6 * q^7 - 3 * q^8 - 3 * q^9 - 6 * q^11 + 12 * q^13 + 12 * q^14 - 6 * q^15 - 12 * q^17 - 6 * q^18 + 18 * q^19 + 12 * q^20 + 24 * q^21 - 12 * q^23 - 3 * q^24 + 6 * q^26 + 3 * q^27 - 6 * q^28 - 18 * q^29 + 6 * q^31 + 3 * q^33 - 12 * q^34 - 12 * q^35 - 3 * q^36 - 12 * q^37 - 9 * q^38 - 12 * q^39 + 3 * q^41 - 12 * q^42 - 6 * q^43 + 6 * q^45 + 30 * q^47 + 6 * q^48 - 15 * q^49 + 3 * q^50 + 21 * q^51 - 6 * q^52 + 24 * q^53 + 9 * q^54 + 18 * q^55 + 12 * q^56 - 24 * q^57 + 24 * q^58 - 3 * q^59 - 6 * q^60 + 6 * q^61 + 18 * q^62 + 12 * q^63 - 3 * q^64 + 12 * q^65 + 3 * q^66 - 9 * q^67 - 3 * q^68 - 6 * q^69 - 12 * q^70 - 18 * q^71 + 6 * q^72 - 30 * q^73 - 18 * q^74 - 6 * q^76 - 12 * q^77 - 18 * q^78 + 6 * q^79 - 33 * q^81 + 3 * q^82 - 6 * q^83 + 6 * q^84 - 24 * q^85 + 12 * q^86 + 18 * q^87 - 6 * q^88 + 12 * q^90 - 12 * q^91 + 6 * q^92 + 6 * q^93 - 12 * q^94 + 3 * q^97 + 21 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$2$	0.766044	−	0.642788i	0.541675	−	0.454519i
$3$	−1.43969	−	0.524005i	−0.831207	−	0.302535i	−0.108853	−	0.994058i	$-0.534718\pi$
$3$	−1.43969	−	0.524005i	−0.831207	−	0.302535i	−0.722354	+	0.691523i	$0.756940\pi$
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	0.347296	+	1.96962i	0.155316	+	0.880839i	0.958497	+	0.285104i	$0.0920281\pi$
$5$	0.347296	+	1.96962i	0.155316	+	0.880839i	−0.803181	+	0.595735i	$0.796861\pi$
$6$	−1.43969	+	0.524005i	−0.587752	+	0.213924i
$7$	−1.34730	+	2.33359i	−0.509230	+	0.882013i	0.490713	+	0.871321i	$0.336736\pi$
$7$	−1.34730	+	2.33359i	−0.509230	+	0.882013i	−0.999943	+	0.0106911i	$0.996597\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−0.500000	−	0.419550i	−0.166667	−	0.139850i
$10$	1.53209	+	1.28558i	0.484489	+	0.406535i
$11$	−1.59240	−	2.75811i	−0.480126	−	0.831602i	0.519615	−	0.854401i	$-0.326076\pi$
$11$	−1.59240	−	2.75811i	−0.480126	−	0.831602i	−0.999740	+	0.0227990i	$0.992742\pi$
$12$	−0.766044	+	1.32683i	−0.221138	+	0.383022i
$13$	5.41147	−	1.96962i	1.50087	−	0.546273i	0.544586	−	0.838705i	$-0.316687\pi$
$13$	5.41147	−	1.96962i	1.50087	−	0.546273i	0.956286	+	0.292432i	$0.0944644\pi$
$14$	0.467911	+	2.65366i	0.125055	+	0.709219i
$15$	0.532089	−	3.01763i	0.137385	−	0.779148i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−4.99273	+	4.18939i	−1.21091	+	1.01608i	−0.211664	+	0.977342i	$0.567888\pi$
$17$	−4.99273	+	4.18939i	−1.21091	+	1.01608i	−0.999250	+	0.0387350i	$0.987667\pi$
$18$	−0.652704			−0.153844
$19$	2.82635	−	3.31839i	0.648410	−	0.761292i
$19$	2.82635	−	3.31839i	0.648410	−	0.761292i
$20$	2.00000			0.447214
$21$	3.16250	−	2.65366i	0.690115	−	0.579075i
$22$	−2.99273	−	1.08926i	−0.638051	−	0.232232i
$23$	−0.120615	+	0.684040i	−0.0251499	+	0.142632i	−0.994797	−	0.101876i	$-0.967515\pi$
$23$	−0.120615	+	0.684040i	−0.0251499	+	0.142632i	0.969647	+	0.244508i	$0.0786266\pi$
$24$	0.266044	+	1.50881i	0.0543061	+	0.307985i
$25$	0.939693	−	0.342020i	0.187939	−	0.0684040i
$26$	2.87939	−	4.98724i	0.564694	−	0.978079i
$27$	2.79813	+	4.84651i	0.538501	+	0.932711i
$28$	2.06418	+	1.73205i	0.390093	+	0.327327i
$29$	−2.16250	−	1.81456i	−0.401567	−	0.336955i	0.419532	−	0.907741i	$-0.362194\pi$
$29$	−2.16250	−	1.81456i	−0.401567	−	0.336955i	−0.821099	+	0.570786i	$0.806639\pi$
$30$	−1.53209	−	2.65366i	−0.279720	−	0.484489i
$31$	−1.22668	+	2.12467i	−0.220319	+	0.381603i	−0.954905	−	0.296913i	$-0.904043\pi$
$31$	−1.22668	+	2.12467i	−0.220319	+	0.381603i	0.734586	+	0.678515i	$0.237376\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	0.847296	+	4.80526i	0.147495	+	0.836488i
$34$	−1.13176	+	6.41852i	−0.194095	+	1.10077i
$35$	−5.06418	−	1.84321i	−0.856002	−	0.311559i
$36$	−0.500000	+	0.419550i	−0.0833333	+	0.0699250i
$37$	−4.36959			−0.718355			−0.359178	−	0.933269i	$-0.616943\pi$
$37$	−4.36959			−0.718355			−0.359178	+	0.933269i	$0.616943\pi$
$38$	0.0320889	−	4.35878i	0.00520550	−	0.707088i
$39$	−8.82295			−1.41280
$40$	1.53209	−	1.28558i	0.242245	−	0.203267i
$41$	0.326352	+	0.118782i	0.0509676	+	0.0185507i	0.367378	−	0.930072i	$-0.380255\pi$
$41$	0.326352	+	0.118782i	0.0509676	+	0.0185507i	−0.316411	+	0.948622i	$0.602478\pi$
$42$	0.716881	−	4.06564i	0.110617	−	0.627341i
$43$	1.05303	+	5.97205i	0.160586	+	0.910729i	0.953499	+	0.301395i	$0.0974522\pi$
$43$	1.05303	+	5.97205i	0.160586	+	0.910729i	−0.792913	+	0.609334i	$0.791437\pi$
$44$	−2.99273	+	1.08926i	−0.451170	+	0.164213i
$45$	0.652704	−	1.13052i	0.0972993	−	0.168527i
$46$	0.347296	+	0.601535i	0.0512061	+	0.0886915i
$47$	6.04189	+	5.06975i	0.881300	+	0.739499i	0.966446	−	0.256870i	$-0.0826912\pi$
$47$	6.04189	+	5.06975i	0.881300	+	0.739499i	−0.0851459	+	0.996368i	$0.527136\pi$
$48$	1.17365	+	0.984808i	0.169402	+	0.142145i
$49$	−0.130415	−	0.225885i	−0.0186307	−	0.0322693i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	9.38326	−	3.41523i	1.31392	−	0.478227i
$52$	−1.00000	−	5.67128i	−0.138675	−	0.786465i
$53$	1.42602	−	8.08737i	0.195879	−	1.11089i	−0.715282	−	0.698836i	$-0.753702\pi$
$53$	1.42602	−	8.08737i	0.195879	−	1.11089i	0.911161	−	0.412050i	$-0.135187\pi$
$54$	5.25877	+	1.91404i	0.715628	+	0.260467i
$55$	4.87939	−	4.09429i	0.657936	−	0.552074i
$56$	2.69459			0.360080
$57$	−5.80793	+	3.29644i	−0.769280	+	0.436625i
$58$	−2.82295			−0.370671
$59$	0.439693	−	0.368946i	0.0572431	−	0.0480327i	−0.613717	−	0.789526i	$-0.710327\pi$
$59$	0.439693	−	0.368946i	0.0572431	−	0.0480327i	0.670960	+	0.741493i	$0.265882\pi$
$60$	−2.87939	−	1.04801i	−0.371727	−	0.135298i
$61$	0.509800	−	2.89122i	0.0652732	−	0.370183i	−0.934621	−	0.355645i	$-0.884261\pi$
$61$	0.509800	−	2.89122i	0.0652732	−	0.370183i	0.999894	−	0.0145378i	$-0.00462769\pi$
$62$	0.426022	+	2.41609i	0.0541049	+	0.306844i
$63$	1.65270	−	0.601535i	0.208221	−	0.0757863i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	5.75877	+	9.97448i	0.714288	+	1.23718i
$66$	3.73783	+	3.13641i	0.460095	+	0.386065i
$67$	−3.79813	−	3.18701i	−0.464016	−	0.389356i	0.380590	−	0.924744i	$-0.375721\pi$
$67$	−3.79813	−	3.18701i	−0.464016	−	0.389356i	−0.844606	+	0.535388i	$0.820165\pi$
$68$	3.25877	+	5.64436i	0.395184	+	0.684479i
$69$	0.532089	−	0.921605i	0.0640560	−	0.110948i
$70$	−5.06418	+	1.84321i	−0.605285	+	0.220306i
$71$	−1.46791	−	8.32494i	−0.174209	−	0.987988i	−0.939053	−	0.343773i	$-0.888295\pi$
$71$	−1.46791	−	8.32494i	−0.174209	−	0.987988i	0.764844	−	0.644216i	$-0.222816\pi$
$72$	−0.113341	+	0.642788i	−0.0133573	+	0.0757532i
$73$	−14.8157	−	5.39246i	−1.73404	−	0.631140i	−0.735138	−	0.677917i	$-0.762883\pi$
$73$	−14.8157	−	5.39246i	−1.73404	−	0.631140i	−0.998905	+	0.0467771i	$0.985105\pi$
$74$	−3.34730	+	2.80872i	−0.389115	+	0.326507i
$75$	−1.53209			−0.176910
$76$	−2.77719	−	3.35965i	−0.318565	−	0.385378i
$77$	8.58172			0.977978
$78$	−6.75877	+	5.67128i	−0.765280	+	0.642146i
$79$	8.51754	+	3.10013i	0.958298	+	0.348792i	0.773366	−	0.633959i	$-0.218571\pi$
$79$	8.51754	+	3.10013i	0.958298	+	0.348792i	0.184932	+	0.982751i	$0.440794\pi$
$80$	0.347296	−	1.96962i	0.0388289	−	0.220210i
$81$	−1.14883	−	6.51536i	−0.127648	−	0.723929i
$82$	0.326352	−	0.118782i	0.0360395	−	0.0131173i
$83$	−4.23783	+	7.34013i	−0.465162	+	0.805684i	−0.999209	−	0.0397709i	$-0.987337\pi$
$83$	−4.23783	+	7.34013i	−0.465162	+	0.805684i	0.534047	+	0.845455i	$0.320671\pi$
$84$	−2.06418	−	3.57526i	−0.225220	−	0.390093i
$85$	−9.98545	−	8.37879i	−1.08307	−	0.908807i
$86$	4.64543	+	3.89798i	0.500930	+	0.420330i
$87$	2.16250	+	3.74557i	0.231845	+	0.401567i
$88$	−1.59240	+	2.75811i	−0.169750	+	0.294016i
$89$	−7.27244	+	2.64695i	−0.770877	+	0.280576i	−0.697363	−	0.716718i	$-0.745644\pi$
$89$	−7.27244	+	2.64695i	−0.770877	+	0.280576i	−0.0735139	+	0.997294i	$0.523421\pi$
$90$	−0.226682	−	1.28558i	−0.0238943	−	0.135512i
$91$	−2.69459	+	15.2818i	−0.282470	+	1.60197i
$92$	0.652704	+	0.237565i	0.0680491	+	0.0247678i
$93$	2.87939	−	2.41609i	0.298578	−	0.250537i
$94$	7.88713			0.813495
$95$	7.51754	+	4.41436i	0.771283	+	0.452904i
$96$	1.53209			0.156368
$97$	−0.266044	+	0.223238i	−0.0270127	+	0.0226664i	−0.656194	−	0.754592i	$-0.727835\pi$
$97$	−0.266044	+	0.223238i	−0.0270127	+	0.0226664i	0.629181	+	0.777259i	$0.283390\pi$
$98$	−0.245100	−	0.0892091i	−0.0247588	−	0.00901148i
$99$	−0.360967	+	2.04715i	−0.0362785	+	0.205746i
$100$	−0.173648	−	0.984808i	−0.0173648	−	0.0984808i
$101$	0.347296	−	0.126406i	0.0345573	−	0.0125778i	−0.324684	−	0.945823i	$-0.605258\pi$
$101$	0.347296	−	0.126406i	0.0345573	−	0.0125778i	0.359241	+	0.933245i	$0.383036\pi$
$102$	4.99273	−	8.64766i	0.494354	−	0.856245i
$103$	−4.29086	−	7.43199i	−0.422791	−	0.732295i	0.573420	−	0.819261i	$-0.305616\pi$
$103$	−4.29086	−	7.43199i	−0.422791	−	0.732295i	−0.996211	+	0.0869659i	$0.972283\pi$
$104$	−4.41147	−	3.70167i	−0.432581	−	0.362978i
$105$	6.32501	+	5.30731i	0.617258	+	0.517941i
$106$	−4.10607	−	7.11192i	−0.398816	−	0.690770i
$107$	5.72668	−	9.91890i	0.553619	−	0.958897i	−0.444390	−	0.895833i	$-0.646580\pi$
$107$	5.72668	−	9.91890i	0.553619	−	0.958897i	0.998010	−	0.0630633i	$-0.0200870\pi$
$108$	5.25877	−	1.91404i	0.506025	−	0.184178i
$109$	1.50980	+	8.56250i	0.144613	+	0.820139i	0.967677	+	0.252191i	$0.0811513\pi$
$109$	1.50980	+	8.56250i	0.144613	+	0.820139i	−0.823065	+	0.567948i	$0.807738\pi$
$110$	1.10607	−	6.27282i	0.105459	−	0.598090i
$111$	6.29086	+	2.28969i	0.597102	+	0.217327i
$112$	2.06418	−	1.73205i	0.195046	−	0.163663i
$113$	2.85978			0.269026			0.134513	−	0.990912i	$-0.457053\pi$
$113$	2.85978			0.269026			0.134513	+	0.990912i	$0.457053\pi$
$114$	−2.33022	+	6.25849i	−0.218245	+	0.586161i
$115$	−1.38919			−0.129542
$116$	−2.16250	+	1.81456i	−0.200783	+	0.168477i
$117$	−3.53209	−	1.28558i	−0.326542	−	0.118851i
$118$	0.0996702	−	0.565258i	0.00917539	−	0.0520362i
$119$	−3.04963	−	17.2953i	−0.279559	−	1.58546i
$120$	−2.87939	+	1.04801i	−0.262851	+	0.0956698i
$121$	0.428548	−	0.742267i	0.0389589	−	0.0674789i
$122$	−1.46791	−	2.54250i	−0.132898	−	0.230187i
$123$	−0.407604	−	0.342020i	−0.0367524	−	0.0308389i
$124$	1.87939	+	1.57699i	0.168774	+	0.141618i
$125$	6.00000	+	10.3923i	0.536656	+	0.929516i
$126$	0.879385	−	1.52314i	0.0783419	−	0.135692i
$127$	−9.14290	+	3.32774i	−0.811301	+	0.295290i	−0.714161	−	0.699981i	$-0.753192\pi$
$127$	−9.14290	+	3.32774i	−0.811301	+	0.295290i	−0.0971401	+	0.995271i	$0.530970\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	1.61334	−	9.14971i	0.142047	−	0.805587i
$130$	10.8229	+	3.93923i	0.949235	+	0.345493i
$131$	−4.95471	+	4.15749i	−0.432895	+	0.363242i	−0.833043	−	0.553209i	$-0.813403\pi$
$131$	−4.95471	+	4.15749i	−0.432895	+	0.363242i	0.400148	+	0.916451i	$0.368959\pi$
$132$	4.87939			0.424696
$133$	3.93582	+	11.0664i	0.341279	+	0.959578i
$134$	−4.95811			−0.428316
$135$	−8.57398	+	7.19442i	−0.737931	+	0.619197i
$136$	6.12449	+	2.22913i	0.525170	+	0.191146i
$137$	−2.02481	+	11.4833i	−0.172992	+	0.981084i	0.767445	+	0.641115i	$0.221528\pi$
$137$	−2.02481	+	11.4833i	−0.172992	+	0.981084i	−0.940437	+	0.339969i	$0.889583\pi$
$138$	−0.184793	−	1.04801i	−0.0157306	−	0.0892126i
$139$	7.76517	−	2.82629i	0.658633	−	0.239723i	0.00898688	−	0.999960i	$-0.497139\pi$
$139$	7.76517	−	2.82629i	0.658633	−	0.239723i	0.649646	+	0.760237i	$0.274917\pi$
$140$	−2.69459	+	4.66717i	−0.227735	+	0.394448i
$141$	−6.04189	−	10.4649i	−0.508819	−	0.881300i
$142$	−6.47565	−	5.43372i	−0.543425	−	0.455987i
$143$	−14.0496	−	11.7890i	−1.17489	−	0.985849i
$144$	0.326352	+	0.565258i	0.0271960	+	0.0471048i
$145$	2.82295	−	4.88949i	0.234433	−	0.406050i
$146$	−14.8157	+	5.39246i	−1.22615	+	0.446284i
$147$	0.0693923	+	0.393544i	0.00572338	+	0.0324589i
$148$	−0.758770	+	4.30320i	−0.0623705	+	0.353721i
$149$	15.4611	+	5.62738i	1.26662	+	0.461013i	0.885986	−	0.463712i	$-0.153483\pi$
$149$	15.4611	+	5.62738i	1.26662	+	0.461013i	0.380637	+	0.924725i	$0.375705\pi$
$150$	−1.17365	+	0.984808i	−0.0958280	+	0.0804092i
$151$	4.65539			0.378850			0.189425	−	0.981895i	$-0.439338\pi$
$151$	4.65539			0.378850			0.189425	+	0.981895i	$0.439338\pi$
$152$	−4.28699	−	0.788496i	−0.347721	−	0.0639554i
$153$	4.25402			0.343917
$154$	6.57398	−	5.51622i	0.529746	−	0.444510i
$155$	−4.61081	−	1.67820i	−0.370350	−	0.134796i
$156$	−1.53209	+	8.68891i	−0.122665	+	0.695669i
$157$	1.46791	+	8.32494i	0.117152	+	0.664402i	0.985662	+	0.168731i	$0.0539669\pi$
$157$	1.46791	+	8.32494i	0.117152	+	0.664402i	−0.868510	+	0.495671i	$0.834922\pi$
$158$	8.51754	−	3.10013i	0.677619	−	0.246633i
$159$	−6.29086	+	10.8961i	−0.498898	+	0.864116i
$160$	−1.00000	−	1.73205i	−0.0790569	−	0.136931i
$161$	−1.43376	−	1.20307i	−0.112996	−	0.0948152i
$162$	−5.06805	−	4.25260i	−0.398183	−	0.334116i
$163$	−8.52481	−	14.7654i	−0.667715	−	1.15652i	−0.978542	−	0.206050i	$-0.933939\pi$
$163$	−8.52481	−	14.7654i	−0.667715	−	1.15652i	0.310826	−	0.950467i	$-0.399394\pi$
$164$	0.173648	−	0.300767i	0.0135596	−	0.0234860i
$165$	−9.17024	+	3.33770i	−0.713903	+	0.259839i
$166$	1.47178	+	8.34689i	0.114232	+	0.647844i
$167$	−0.554378	+	3.14403i	−0.0428990	+	0.243292i	−0.998715	−	0.0506721i	$-0.983864\pi$
$167$	−0.554378	+	3.14403i	−0.0428990	+	0.243292i	0.955816	+	0.293965i	$0.0949748\pi$
$168$	−3.87939	−	1.41198i	−0.299301	−	0.108937i
$169$	15.4461	−	12.9608i	1.18816	−	0.996985i
$170$	−13.0351			−0.999745
$171$	−2.80541	+	0.473401i	−0.214535	+	0.0362019i
$172$	6.06418			0.462389
$173$	7.37733	−	6.19031i	0.560888	−	0.470641i	−0.317720	−	0.948185i	$-0.602917\pi$
$173$	7.37733	−	6.19031i	0.560888	−	0.470641i	0.878608	+	0.477544i	$0.158473\pi$
$174$	4.06418	+	1.47924i	0.308105	+	0.112141i
$175$	−0.467911	+	2.65366i	−0.0353708	+	0.200598i
$176$	0.553033	+	3.13641i	0.0416865	+	0.236416i
$177$	−0.826352	+	0.300767i	−0.0621124	+	0.0226071i
$178$	−3.86959	+	6.70232i	−0.290038	+	0.502360i
$179$	−9.40807	−	16.2953i	−0.703192	−	1.21796i	−0.967340	−	0.253482i	$-0.918424\pi$
$179$	−9.40807	−	16.2953i	−0.703192	−	1.21796i	0.264148	−	0.964482i	$-0.414909\pi$
$180$	−1.00000	−	0.839100i	−0.0745356	−	0.0625428i
$181$	2.12836	+	1.78590i	0.158199	+	0.132745i	0.718451	−	0.695577i	$-0.244851\pi$
$181$	2.12836	+	1.78590i	0.158199	+	0.132745i	−0.560252	+	0.828322i	$0.689296\pi$
$182$	7.75877	+	13.4386i	0.575118	+	0.996134i
$183$	−2.24897	+	3.89533i	−0.166249	+	0.287951i
$184$	0.652704	−	0.237565i	0.0481180	−	0.0175135i
$185$	−1.51754	−	8.60640i	−0.111572	−	0.632755i
$186$	0.652704	−	3.70167i	0.0478586	−	0.271419i
$187$	19.5052	+	7.09932i	1.42636	+	0.519154i
$188$	6.04189	−	5.06975i	0.440650	−	0.369749i
$189$	−15.0797			−1.09688
$190$	8.59627	−	1.45059i	0.623639	−	0.105237i
$191$	9.56212			0.691891			0.345945	−	0.938255i	$-0.387558\pi$
$191$	9.56212			0.691891			0.345945	+	0.938255i	$0.387558\pi$
$192$	1.17365	−	0.984808i	0.0847008	−	0.0710724i
$193$	22.2528	+	8.09937i	1.60179	+	0.583006i	0.979794	−	0.200011i	$-0.0640978\pi$
$193$	22.2528	+	8.09937i	1.60179	+	0.583006i	0.622001	+	0.783017i	$0.286320\pi$
$194$	−0.0603074	+	0.342020i	−0.00432982	+	0.0245556i
$195$	−3.06418	−	17.3778i	−0.219430	−	1.24445i
$196$	−0.245100	+	0.0892091i	−0.0175071	+	0.00637208i
$197$	11.4611	−	19.8512i	0.816570	−	1.41434i	−0.0916253	−	0.995794i	$-0.529206\pi$
$197$	11.4611	−	19.8512i	0.816570	−	1.41434i	0.908195	−	0.418547i	$-0.137460\pi$
$198$	1.03936	+	1.80023i	0.0738643	+	0.127937i
$199$	7.72462	+	6.48173i	0.547584	+	0.459477i	0.874122	−	0.485707i	$-0.161438\pi$
$199$	7.72462	+	6.48173i	0.547584	+	0.459477i	−0.326538	+	0.945184i	$0.605882\pi$
$200$	−0.766044	−	0.642788i	−0.0541675	−	0.0454519i
$201$	3.79813	+	6.57856i	0.267900	+	0.464016i
$202$	0.184793	−	0.320070i	0.0130020	−	0.0225201i
$203$	7.14796	−	2.60164i	0.501688	−	0.182600i
$204$	−1.73396	−	9.83375i	−0.121401	−	0.688500i
$205$	−0.120615	+	0.684040i	−0.00842410	+	0.0477754i
$206$	−8.06418	−	2.93512i	−0.561858	−	0.204500i
$207$	0.347296	−	0.291416i	0.0241388	−	0.0202548i
$208$	−5.75877			−0.399299
$209$	−13.6532	−	2.51120i	−0.944410	−	0.173703i
$210$	8.25671			0.569767
$211$	−17.1288	+	14.3728i	−1.17920	+	0.989464i	−0.179213	+	0.983810i	$0.557355\pi$
$211$	−17.1288	+	14.3728i	−1.17920	+	0.989464i	−0.999984	+	0.00565322i	$0.998201\pi$
$212$	−7.71688	−	2.80872i	−0.529998	−	0.192903i
$213$	−2.24897	+	12.7545i	−0.154097	+	0.873927i
$214$	−1.98886	−	11.2794i	−0.135955	−	0.771041i
$215$	−11.3969	+	4.14814i	−0.777264	+	0.282901i
$216$	2.79813	−	4.84651i	0.190389	−	0.329763i
$217$	−3.30541	−	5.72513i	−0.224386	−	0.388647i
$218$	6.66044	+	5.58878i	0.451102	+	0.378520i
$219$	18.5043	+	15.5270i	1.25041	+	1.04922i
$220$	−3.18479	−	5.51622i	−0.214719	−	0.371904i
$221$	−18.7665	+	32.5046i	−1.26237	+	2.18649i
$222$	6.29086	−	2.28969i	0.422215	−	0.153674i
$223$	−1.61081	−	9.13538i	−0.107868	−	0.611751i	−0.990036	−	0.140815i	$-0.955028\pi$
$223$	−1.61081	−	9.13538i	−0.107868	−	0.611751i	0.882168	−	0.470935i	$-0.156083\pi$
$224$	0.467911	−	2.65366i	0.0312636	−	0.177305i
$225$	−0.613341	−	0.223238i	−0.0408894	−	0.0148825i
$226$	2.19072	−	1.83823i	0.145725	−	0.122278i
$227$	7.73648			0.513488			0.256744	−	0.966479i	$-0.417350\pi$
$227$	7.73648			0.513488			0.256744	+	0.966479i	$0.417350\pi$
$228$	2.23783	+	6.29212i	0.148204	+	0.416706i
$229$	−23.0351			−1.52220			−0.761101	−	0.648634i	$-0.775341\pi$
$229$	−23.0351			−1.52220			−0.761101	+	0.648634i	$0.775341\pi$
$230$	−1.06418	+	0.892951i	−0.0701698	+	0.0588795i
$231$	−12.3550	−	4.49687i	−0.812902	−	0.295872i
$232$	−0.490200	+	2.78006i	−0.0321832	+	0.182520i
$233$	1.45858	+	8.27201i	0.0955546	+	0.541917i	0.994576	+	0.104012i	$0.0331682\pi$
$233$	1.45858	+	8.27201i	0.0955546	+	0.541917i	−0.899021	+	0.437905i	$0.855721\pi$
$234$	−3.53209	+	1.28558i	−0.230900	+	0.0840407i
$235$	−7.88713	+	13.6609i	−0.514499	+	0.891139i
$236$	−0.286989	−	0.497079i	−0.0186814	−	0.0323571i
$237$	−10.6382	−	8.92647i	−0.691022	−	0.579837i
$238$	−13.4534	−	11.2887i	−0.872052	−	0.731739i
$239$	7.86484	+	13.6223i	0.508734	+	0.881153i	0.999949	+	0.0101147i	$0.00321967\pi$
$239$	7.86484	+	13.6223i	0.508734	+	0.881153i	−0.491215	+	0.871038i	$0.663447\pi$
$240$	−1.53209	+	2.65366i	−0.0988959	+	0.171293i
$241$	−16.4474	+	5.98638i	−1.05947	+	0.385616i	−0.812230	−	0.583337i	$-0.801747\pi$
$241$	−16.4474	+	5.98638i	−1.05947	+	0.385616i	−0.247242	+	0.968954i	$0.579524\pi$
$242$	−0.148833	−	0.844075i	−0.00956736	−	0.0542592i
$243$	1.15523	−	6.55163i	0.0741080	−	0.420288i
$244$	−2.75877	−	1.00411i	−0.176612	−	0.0642816i
$245$	0.399615	−	0.335316i	0.0255304	−	0.0214226i
$246$	−0.532089			−0.0339247
$247$	8.75877	−	23.5242i	0.557307	−	1.49681i
$248$	2.45336			0.155789
$249$	9.94743	−	8.34689i	0.630393	−	0.528963i
$250$	11.2763	+	4.10424i	0.713177	+	0.259575i
$251$	1.48767	−	8.43702i	0.0939011	−	0.532540i	−0.901177	−	0.433450i	$-0.857296\pi$
$251$	1.48767	−	8.43702i	0.0939011	−	0.532540i	0.995079	−	0.0990893i	$-0.0315930\pi$
$252$	−0.305407	−	1.73205i	−0.0192389	−	0.109109i
$253$	2.07873	−	0.756594i	0.130688	−	0.0475667i
$254$	−4.86484	+	8.42615i	−0.305247	+	0.528703i
$255$	9.98545	+	17.2953i	0.625313	+	1.08307i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−6.14724	−	5.15815i	−0.383454	−	0.321756i	0.430602	−	0.902542i	$-0.358301\pi$
$257$	−6.14724	−	5.15815i	−0.383454	−	0.321756i	−0.814057	+	0.580785i	$0.802746\pi$
$258$	−4.64543	−	8.04612i	−0.289212	−	0.500930i
$259$	5.88713	−	10.1968i	0.365808	−	0.633598i
$260$	10.8229	−	3.93923i	0.671211	−	0.244301i
$261$	0.319955	+	1.81456i	0.0198047	+	0.112318i
$262$	−1.12314	+	6.36965i	−0.0693879	+	0.393518i
$263$	5.60132	+	2.03871i	0.345392	+	0.125712i	0.508891	−	0.860831i	$-0.330056\pi$
$263$	5.60132	+	2.03871i	0.345392	+	0.125712i	−0.163499	+	0.986544i	$0.552278\pi$
$264$	3.73783	−	3.13641i	0.230047	−	0.193033i
$265$	16.4243			1.00893
$266$	10.1284	+	5.94745i	0.621009	+	0.364662i
$267$	11.8571			0.725643
$268$	−3.79813	+	3.18701i	−0.232008	+	0.194678i
$269$	1.07873	+	0.392624i	0.0657711	+	0.0239387i	0.374696	−	0.927148i	$-0.377747\pi$
$269$	1.07873	+	0.392624i	0.0657711	+	0.0239387i	−0.308925	+	0.951086i	$0.599969\pi$
$270$	−1.94356	+	11.0225i	−0.118281	+	0.670808i
$271$	3.48246	+	19.7500i	0.211544	+	1.19973i	0.886803	+	0.462147i	$0.152921\pi$
$271$	3.48246	+	19.7500i	0.211544	+	1.19973i	−0.675259	+	0.737581i	$0.735968\pi$
$272$	6.12449	−	2.22913i	0.371351	−	0.135161i
$273$	11.8871	−	20.5891i	0.719442	−	1.24611i
$274$	5.83022	+	10.0982i	0.352217	+	0.610057i
$275$	−2.43969	−	2.04715i	−0.147119	−	0.123447i
$276$	−0.815207	−	0.684040i	−0.0490697	−	0.0411744i
$277$	−8.68004	−	15.0343i	−0.521533	−	0.903322i	−0.999686	−	0.0250457i	$-0.992027\pi$
$277$	−8.68004	−	15.0343i	−0.521533	−	0.903322i	0.478153	−	0.878277i	$-0.341306\pi$
$278$	4.13176	−	7.15642i	0.247806	−	0.429213i
$279$	1.50475	−	0.547683i	0.0900869	−	0.0327889i
$280$	0.935822	+	5.30731i	0.0559261	+	0.317173i
$281$	0.507274	−	2.87689i	0.0302614	−	0.171621i	−0.965931	−	0.258798i	$-0.916674\pi$
$281$	0.507274	−	2.87689i	0.0302614	−	0.171621i	0.996193	+	0.0871772i	$0.0277846\pi$
$282$	−11.3550	−	4.13290i	−0.676183	−	0.246110i
$283$	−7.26264	+	6.09408i	−0.431719	+	0.362255i	−0.832600	−	0.553875i	$-0.813149\pi$
$283$	−7.26264	+	6.09408i	−0.431719	+	0.362255i	0.400881	+	0.916130i	$0.368704\pi$
$284$	−8.45336			−0.501615
$285$	−8.50980	−	10.2946i	−0.504077	−	0.609797i
$286$	−18.3405			−1.08450
$287$	−0.716881	+	0.601535i	−0.0423162	+	0.0355075i
$288$	0.613341	+	0.223238i	0.0361415	+	0.0131544i
$289$	4.42427	−	25.0913i	0.260251	−	1.47596i
$290$	−0.980400	−	5.56012i	−0.0575710	−	0.326502i
$291$	0.500000	−	0.181985i	0.0293105	−	0.0106682i
$292$	−7.88326	+	13.6542i	−0.461333	+	0.799052i
$293$	13.6459	+	23.6354i	0.797202	+	1.38079i	0.921432	+	0.388541i	$0.127021\pi$
$293$	13.6459	+	23.6354i	0.797202	+	1.38079i	−0.124230	+	0.992253i	$0.539646\pi$
$294$	0.306123	+	0.256867i	0.0178534	+	0.0149808i
$295$	0.879385	+	0.737892i	0.0511998	+	0.0429617i
$296$	2.18479	+	3.78417i	0.126988	+	0.219951i
$297$	8.91147	−	15.4351i	0.517096	−	0.895637i
$298$	15.4611	−	5.62738i	0.895638	−	0.325985i
$299$	0.694593	+	3.93923i	0.0401693	+	0.227812i
$300$	−0.266044	+	1.50881i	−0.0153601	+	0.0871114i
$301$	−15.3550	−	5.58878i	−0.885050	−	0.322132i
$302$	3.56624	−	2.99243i	0.205214	−	0.172195i
$303$	−0.566237			−0.0325295
$304$	−3.79086	+	2.15160i	−0.217421	+	0.123403i
$305$	5.87164			0.336209
$306$	3.25877	−	2.73443i	0.186292	−	0.156317i
$307$	−20.0424	−	7.29482i	−1.14388	−	0.416337i	−0.300565	−	0.953761i	$-0.597175\pi$
$307$	−20.0424	−	7.29482i	−1.14388	−	0.416337i	−0.843312	+	0.537424i	$0.819398\pi$
$308$	1.49020	−	8.45134i	0.0849120	−	0.481560i
$309$	2.28312	+	12.9482i	0.129882	+	0.736598i
$310$	−4.61081	+	1.67820i	−0.261877	+	0.0953153i
$311$	14.6459	−	25.3674i	0.830493	−	1.43846i	−0.0671555	−	0.997743i	$-0.521392\pi$
$311$	14.6459	−	25.3674i	0.830493	−	1.43846i	0.897648	−	0.440713i	$-0.145274\pi$
$312$	4.41147	+	7.64090i	0.249751	+	0.432581i
$313$	4.26011	+	3.57466i	0.240796	+	0.202052i	0.755197	−	0.655498i	$-0.227541\pi$
$313$	4.26011	+	3.57466i	0.240796	+	0.202052i	−0.514401	+	0.857550i	$0.671986\pi$
$314$	6.47565	+	5.43372i	0.365442	+	0.306642i
$315$	1.75877	+	3.04628i	0.0990955	+	0.171638i
$316$	4.53209	−	7.84981i	0.254950	−	0.441586i
$317$	−3.57398	+	1.30082i	−0.200735	+	0.0730614i	−0.440431	−	0.897786i	$-0.645174\pi$
$317$	−3.57398	+	1.30082i	−0.200735	+	0.0730614i	0.239696	+	0.970848i	$0.422952\pi$
$318$	2.18479	+	12.3906i	0.122517	+	0.694829i
$319$	−1.56118	+	8.85392i	−0.0874096	+	0.495724i
$320$	−1.87939	−	0.684040i	−0.105061	−	0.0382390i
$321$	−13.4422	+	11.2794i	−0.750271	+	0.629553i
$322$	−1.87164			−0.104303
$323$	−0.209141	+	28.4085i	−0.0116369	+	1.58069i
$324$	−6.61587			−0.367548
$325$	4.41147	−	3.70167i	0.244705	−	0.205332i
$326$	−16.0214	−	5.83132i	−0.887344	−	0.322967i
$327$	2.31315	−	13.1185i	0.127917	−	0.725456i
$328$	−0.0603074	−	0.342020i	−0.00332992	−	0.0188849i
$329$	−19.9709	+	7.26881i	−1.10103	+	0.400743i
$330$	−4.87939	+	8.45134i	−0.268601	+	0.465231i
$331$	−10.2110	−	17.6859i	−0.561245	−	0.972104i	−0.997388	−	0.0722272i	$-0.976989\pi$
$331$	−10.2110	−	17.6859i	−0.561245	−	0.972104i	0.436144	−	0.899877i	$-0.356344\pi$
$332$	6.49273	+	5.44804i	0.356335	+	0.299000i
$333$	2.18479	+	1.83326i	0.119726	+	0.100462i
$334$	1.59627	+	2.76481i	0.0873438	+	0.151284i
$335$	4.95811	−	8.58770i	0.270891	−	0.469196i
$336$	−3.87939	+	1.41198i	−0.211638	+	0.0770299i
$337$	3.52687	+	20.0019i	0.192121	+	1.08957i	0.916459	+	0.400128i	$0.131034\pi$
$337$	3.52687	+	20.0019i	0.192121	+	1.08957i	−0.724338	+	0.689445i	$0.757855\pi$
$338$	3.50134	−	19.8571i	0.190448	−	1.08008i
$339$	−4.11721	−	1.49854i	−0.223616	−	0.0813896i
$340$	−9.98545	+	8.37879i	−0.541537	+	0.454404i
$341$	7.81345			0.423122
$342$	−1.84477	+	2.16593i	−0.0997537	+	0.117120i
$343$	−18.1593			−0.980511
$344$	4.64543	−	3.89798i	0.250465	−	0.210165i
$345$	2.00000	+	0.727940i	0.107676	+	0.0391910i
$346$	1.67230	−	9.48411i	0.0899036	−	0.509869i
$347$	0.905544	+	5.13560i	0.0486122	+	0.275693i	0.999419	−	0.0340920i	$-0.0108539\pi$
$347$	0.905544	+	5.13560i	0.0486122	+	0.275693i	−0.950807	+	0.309785i	$0.899743\pi$
$348$	4.06418	−	1.47924i	0.217863	−	0.0792956i
$349$	−7.17024	+	12.4192i	−0.383814	+	0.664786i	−0.991604	−	0.129312i	$-0.958723\pi$
$349$	−7.17024	+	12.4192i	−0.383814	+	0.664786i	0.607790	+	0.794098i	$0.292056\pi$
$350$	1.34730	+	2.33359i	0.0720160	+	0.124735i
$351$	24.6878	+	20.7155i	1.31774	+	1.10571i
$352$	2.43969	+	2.04715i	0.130036	+	0.109113i
$353$	−13.1250	−	22.7331i	−0.698571	−	1.20996i	−0.968962	−	0.247209i	$-0.920486\pi$
$353$	−13.1250	−	22.7331i	−0.698571	−	1.20996i	0.270391	−	0.962750i	$-0.412847\pi$
$354$	−0.439693	+	0.761570i	−0.0233694	+	0.0404770i
$355$	15.8871	−	5.78244i	0.843201	−	0.306900i
$356$	1.34389	+	7.62159i	0.0712262	+	0.403944i
$357$	−4.67230	+	26.4980i	−0.247285	+	1.40242i
$358$	−17.6814	−	6.43550i	−0.934490	−	0.340127i
$359$	−25.8084	+	21.6558i	−1.36212	+	1.14295i	−0.386792	+	0.922167i	$0.626417\pi$
$359$	−25.8084	+	21.6558i	−1.36212	+	1.14295i	−0.975323	+	0.220784i	$0.929139\pi$
$360$	−1.30541			−0.0688010
$361$	−3.02347	−	18.7579i	−0.159130	−	0.987258i
$362$	2.77837			0.146028
$363$	−1.00593	+	0.844075i	−0.0527976	+	0.0443025i
$364$	14.5817	+	5.30731i	0.764290	+	0.278179i
$365$	5.47565	−	31.0540i	0.286609	−	1.62544i
$366$	0.781059	+	4.42961i	0.0408266	+	0.231539i
$367$	9.83750	−	3.58056i	0.513513	−	0.186903i	−0.0722488	−	0.997387i	$-0.523018\pi$
$367$	9.83750	−	3.58056i	0.513513	−	0.186903i	0.585762	+	0.810483i	$0.300795\pi$
$368$	0.347296	−	0.601535i	0.0181041	−	0.0313572i
$369$	−0.113341	−	0.196312i	−0.00590029	−	0.0102196i
$370$	−6.69459	−	5.61743i	−0.348035	−	0.292036i
$371$	16.9513	+	14.2238i	0.880068	+	0.738465i
$372$	−1.87939	−	3.25519i	−0.0974416	−	0.168774i
$373$	−11.9513	+	20.7003i	−0.618815	+	1.07182i	0.370887	+	0.928678i	$0.379054\pi$
$373$	−11.9513	+	20.7003i	−0.618815	+	1.07182i	−0.989702	+	0.143141i	$0.954280\pi$
$374$	19.5052	−	7.09932i	1.00859	−	0.367097i
$375$	−3.19253	−	18.1058i	−0.164862	−	0.934977i
$376$	1.36959	−	7.76730i	0.0706310	−	0.400568i
$377$	−15.2763	−	5.56012i	−0.786770	−	0.286361i
$378$	−11.5517	+	9.69302i	−0.594155	+	0.498555i
$379$	17.8135			0.915016			0.457508	−	0.889206i	$-0.348742\pi$
$379$	17.8135			0.915016			0.457508	+	0.889206i	$0.348742\pi$
$380$	5.65270	−	6.63679i	0.289978	−	0.340460i
$381$	14.9067			0.763695
$382$	7.32501	−	6.14641i	0.374780	−	0.314478i
$383$	−23.5672	−	8.57775i	−1.20423	−	0.438302i	−0.339529	−	0.940596i	$-0.610268\pi$
$383$	−23.5672	−	8.57775i	−1.20423	−	0.438302i	−0.864697	+	0.502293i	$0.832490\pi$
$384$	0.266044	−	1.50881i	0.0135765	−	0.0769963i
$385$	2.98040	+	16.9027i	0.151895	+	0.861441i
$386$	22.2528	−	8.09937i	1.13264	−	0.412247i
$387$	1.97906	−	3.42782i	0.100601	−	0.174246i
$388$	0.173648	+	0.300767i	0.00881565	+	0.0152692i
$389$	−7.21482	−	6.05395i	−0.365806	−	0.306948i	0.441294	−	0.897363i	$-0.354520\pi$
$389$	−7.21482	−	6.05395i	−0.365806	−	0.306948i	−0.807100	+	0.590415i	$0.798964\pi$
$390$	−13.5175	−	11.3426i	−0.684487	−	0.574353i
$391$	−2.26352	−	3.92053i	−0.114471	−	0.198270i
$392$	−0.130415	+	0.225885i	−0.00658695	+	0.0114089i
$393$	9.31180	−	3.38922i	0.469718	−	0.170964i
$394$	−3.98040	−	22.5740i	−0.200530	−	1.13726i
$395$	−3.14796	+	17.8529i	−0.158391	+	0.898279i
$396$	1.95336	+	0.710966i	0.0981602	+	0.0357274i
$397$	5.24897	−	4.40441i	0.263438	−	0.221051i	−0.501495	−	0.865161i	$-0.667216\pi$
$397$	5.24897	−	4.40441i	0.263438	−	0.221051i	0.764933	+	0.644110i	$0.222772\pi$
$398$	10.0838			0.505454
$399$	0.132474	−	17.9946i	0.00663201	−	0.900857i
$400$	−1.00000			−0.0500000
$401$	3.63634	−	3.05126i	0.181590	−	0.152372i	−0.547461	−	0.836831i	$-0.684406\pi$
$401$	3.63634	−	3.05126i	0.181590	−	0.152372i	0.729052	+	0.684458i	$0.239961\pi$
$402$	7.13816	+	2.59808i	0.356019	+	0.129580i
$403$	−2.45336	+	13.9137i	−0.122211	+	0.693091i
$404$	−0.0641778	−	0.363970i	−0.00319296	−	0.0181082i
$405$	12.4338	−	4.52552i	0.617839	−	0.224875i
$406$	3.80335	−	6.58759i	0.188757	−	0.326937i
$407$	6.95811	+	12.0518i	0.344901	+	0.597386i
$408$	−7.64930	−	6.41852i	−0.378697	−	0.317764i
$409$	24.2781	+	20.3718i	1.20048	+	1.00732i	0.999616	+	0.0276988i	$0.00881794\pi$
$409$	24.2781	+	20.3718i	1.20048	+	1.00732i	0.200860	+	0.979620i	$0.435627\pi$
$410$	0.347296	+	0.601535i	0.0171517	+	0.0297077i
$411$	8.93242	−	15.4714i	0.440604	−	0.763148i
$412$	−8.06418	+	2.93512i	−0.397294	+	0.144603i
$413$	0.268571	+	1.52314i	0.0132155	+	0.0749488i
$414$	0.0787257	−	0.446476i	0.00386916	−	0.0219431i
$415$	−15.9290	−	5.79769i	−0.781925	−	0.284597i
$416$	−4.41147	+	3.70167i	−0.216290	+	0.181489i
$417$	−12.6604			−0.619985
$418$	−12.0731	+	6.85240i	−0.590515	+	0.335162i
$419$	−11.0101			−0.537879			−0.268939	−	0.963157i	$-0.586673\pi$
$419$	−11.0101			−0.537879			−0.268939	+	0.963157i	$0.586673\pi$
$420$	6.32501	−	5.30731i	0.308629	−	0.258970i
$421$	8.14290	+	2.96377i	0.396861	+	0.144446i	0.532738	−	0.846280i	$-0.321163\pi$
$421$	8.14290	+	2.96377i	0.396861	+	0.144446i	−0.135877	+	0.990726i	$0.543385\pi$
$422$	−3.88279	+	22.0204i	−0.189011	+	1.07194i
$423$	−0.893933	−	5.06975i	−0.0434645	−	0.246500i
$424$	−7.71688	+	2.80872i	−0.374765	+	0.136403i
$425$	−3.25877	+	5.64436i	−0.158074	+	0.273791i
$426$	6.47565	+	11.2162i	0.313746	+	0.543425i
$427$	6.06006	+	5.08499i	0.293267	+	0.246080i
$428$	−8.77379	−	7.36208i	−0.424097	−	0.355860i
$429$	14.0496	+	24.3347i	0.678323	+	1.17489i
$430$	−6.06418	+	10.5035i	−0.292441	+	0.506522i
$431$	28.0847	−	10.2220i	1.35279	−	0.492376i	0.438975	−	0.898499i	$-0.355342\pi$
$431$	28.0847	−	10.2220i	1.35279	−	0.492376i	0.913818	+	0.406123i	$0.133120\pi$
$432$	−0.971782	−	5.51125i	−0.0467549	−	0.265160i
$433$	1.60813	−	9.12014i	0.0772816	−	0.438286i	−0.921475	−	0.388437i	$-0.873015\pi$
$433$	1.60813	−	9.12014i	0.0772816	−	0.438286i	0.998757	−	0.0498486i	$-0.0158739\pi$
$434$	−6.21213	−	2.26103i	−0.298192	−	0.108533i
$435$	−6.62630	+	5.56012i	−0.317707	+	0.266587i
$436$	8.69459			0.416395
$437$	1.92902	+	2.33359i	0.0922773	+	0.111631i
$438$	24.1557			1.15420
$439$	15.9813	−	13.4099i	0.762747	−	0.640021i	−0.176093	−	0.984374i	$-0.556346\pi$
$439$	15.9813	−	13.4099i	0.762747	−	0.640021i	0.938840	+	0.344352i	$0.111902\pi$
$440$	−5.98545	−	2.17853i	−0.285345	−	0.103857i
$441$	−0.0295627	+	0.167658i	−0.00140775	+	0.00798372i
$442$	6.51754	+	36.9628i	0.310008	+	1.75814i
$443$	−22.3910	+	8.14966i	−1.06383	+	0.387202i	−0.813865	−	0.581054i	$-0.802641\pi$
$443$	−22.3910	+	8.14966i	−1.06383	+	0.387202i	−0.249963	+	0.968255i	$0.580418\pi$
$444$	3.34730	−	5.79769i	0.158856	−	0.275146i
$445$	−7.73917	−	13.4046i	−0.366872	−	0.635441i
$446$	−7.10607	−	5.96270i	−0.336482	−	0.282342i
$447$	−19.3105	−	16.2034i	−0.913353	−	0.766395i
$448$	−1.34730	−	2.33359i	−0.0636538	−	0.110252i
$449$	1.09105	−	1.88976i	0.0514899	−	0.0891832i	−0.839132	−	0.543928i	$-0.816936\pi$
$449$	1.09105	−	1.88976i	0.0514899	−	0.0891832i	0.890622	+	0.454745i	$0.150270\pi$
$450$	−0.613341	+	0.223238i	−0.0289132	+	0.0105235i
$451$	−0.192066	−	1.08926i	−0.00904406	−	0.0512914i
$452$	0.496596	−	2.81634i	0.0233579	−	0.132469i
$453$	−6.70233	−	2.43945i	−0.314903	−	0.114615i
$454$	5.92649	−	4.97291i	0.278144	−	0.233390i
$455$	−31.0351			−1.45495
$456$	5.75877	+	3.38160i	0.269679	+	0.158358i
$457$	1.78106			0.0833144			0.0416572	−	0.999132i	$-0.486736\pi$
$457$	1.78106			0.0833144			0.0416572	+	0.999132i	$0.486736\pi$
$458$	−17.6459	+	14.8067i	−0.824539	+	0.691870i
$459$	−34.2743	−	12.4748i	−1.59979	−	0.582274i
$460$	−0.241230	+	1.36808i	−0.0112474	+	0.0637871i
$461$	−2.68954	−	15.2531i	−0.125264	−	0.710410i	−0.981150	−	0.193245i	$-0.938099\pi$
$461$	−2.68954	−	15.2531i	−0.125264	−	0.710410i	0.855886	−	0.517164i	$-0.173012\pi$
$462$	−12.3550	+	4.49687i	−0.574808	+	0.209213i
$463$	1.35504	−	2.34699i	0.0629739	−	0.109074i	−0.832820	−	0.553545i	$-0.813275\pi$
$463$	1.35504	−	2.34699i	0.0629739	−	0.109074i	0.895793	+	0.444471i	$0.146608\pi$
$464$	1.41147	+	2.44474i	0.0655260	+	0.113494i
$465$	5.75877	+	4.83218i	0.267057	+	0.224087i
$466$	6.43448	+	5.39917i	0.298071	+	0.250112i
$467$	−6.45677	−	11.1834i	−0.298784	−	0.517508i	0.677074	−	0.735915i	$-0.263248\pi$
$467$	−6.45677	−	11.1834i	−0.298784	−	0.517508i	−0.975858	+	0.218406i	$0.929914\pi$
$468$	−1.87939	+	3.25519i	−0.0868746	+	0.150471i
$469$	12.5544	−	4.56942i	0.579707	−	0.210996i
$470$	2.73917	+	15.5346i	0.126348	+	0.716558i
$471$	2.24897	−	12.7545i	0.103627	−	0.587698i
$472$	−0.539363	−	0.196312i	−0.0248262	−	0.00903599i
$473$	14.7947	−	12.4143i	0.680262	−	0.570808i
$474$	−13.8871			−0.637857
$475$	1.52094	−	4.08494i	0.0697857	−	0.187430i
$476$	−17.5621			−0.804958
$477$	−4.10607	+	3.44540i	−0.188004	+	0.157754i
$478$	14.7811	+	5.37987i	0.676070	+	0.246069i
$479$	−3.22163	+	18.2708i	−0.147200	+	0.834813i	0.818374	+	0.574685i	$0.194876\pi$
$479$	−3.22163	+	18.2708i	−0.147200	+	0.834813i	−0.965574	+	0.260127i	$0.916236\pi$
$480$	0.532089	+	3.01763i	0.0242864	+	0.137735i
$481$	−23.6459	+	8.60640i	−1.07816	+	0.392418i
$482$	−8.75150	+	15.1580i	−0.398620	+	0.690430i
$483$	1.43376	+	2.48335i	0.0652385	+	0.112996i
$484$	−0.656574	−	0.550931i	−0.0298443	−	0.0250423i
$485$	−0.532089	−	0.446476i	−0.0241609	−	0.0202734i
$486$	−3.32635	−	5.76141i	−0.150886	−	0.261343i
$487$	−20.5868	+	35.6573i	−0.932876	+	1.61579i	−0.154497	+	0.987993i	$0.549376\pi$
$487$	−20.5868	+	35.6573i	−0.932876	+	1.61579i	−0.778379	+	0.627795i	$0.783958\pi$
$488$	−2.75877	+	1.00411i	−0.124884	+	0.0454539i
$489$	4.53596	+	25.7247i	0.205123	+	1.16331i
$490$	0.0905853	−	0.513735i	0.00409223	−	0.0232082i
$491$	21.2160	+	7.72199i	0.957465	+	0.348489i	0.773040	−	0.634358i	$-0.218735\pi$
$491$	21.2160	+	7.72199i	0.957465	+	0.348489i	0.184425	+	0.982847i	$0.440958\pi$
$492$	−0.407604	+	0.342020i	−0.0183762	+	0.0154195i
$493$	18.3987			0.828635
$494$	−8.41147	−	23.6506i	−0.378450	−	1.06409i
$495$	−4.15745			−0.186864
$496$	1.87939	−	1.57699i	0.0843869	−	0.0708090i
$497$	21.4047	+	7.79066i	0.960131	+	0.349459i
$498$	2.25490	−	12.7882i	0.101044	−	0.573052i
$499$	−5.09286	−	28.8831i	−0.227988	−	1.29298i	−0.856890	−	0.515499i	$-0.827607\pi$
$499$	−5.09286	−	28.8831i	−0.227988	−	1.29298i	0.628902	−	0.777484i	$-0.283505\pi$
$500$	11.2763	−	4.10424i	0.504292	−	0.183547i
$501$	2.44562	−	4.23594i	0.109262	−	0.189248i
$502$	−4.28359	−	7.41939i	−0.191186	−	0.331143i
$503$	25.7520	+	21.6085i	1.14822	+	0.963474i	0.999677	−	0.0254316i	$-0.00809602\pi$
$503$	25.7520	+	21.6085i	1.14822	+	0.963474i	0.148547	+	0.988905i	$0.452540\pi$
$504$	−1.34730	−	1.13052i	−0.0600133	−	0.0503572i
$505$	0.369585	+	0.640140i	0.0164463	+	0.0284859i
$506$	1.10607	−	1.91576i	0.0491707	−	0.0851661i
$507$	−29.0292	+	10.5657i	−1.28923	+	0.469241i
$508$	1.68954	+	9.58186i	0.0749612	+	0.425126i
$509$	0.699645	−	3.96788i	0.0310112	−	0.175873i	−0.965368	−	0.260891i	$-0.915984\pi$
$509$	0.699645	−	3.96788i	0.0310112	−	0.175873i	0.996379	+	0.0850178i	$0.0270947\pi$
$510$	18.7665	+	6.83045i	0.830995	+	0.302457i
$511$	32.5449	−	27.3084i	1.43970	−	1.20805i
$512$	1.00000			0.0441942
$513$	23.9911	+	4.41263i	1.05923	+	0.194822i
$514$	−8.02465			−0.353952
$515$	13.1480	−	11.0324i	0.579368	−	0.486148i
$516$	−8.73055	−	3.17766i	−0.384341	−	0.139889i
$517$	4.36184	−	24.7372i	0.191834	−	1.08794i
$518$	−2.04458	−	11.5954i	−0.0898336	−	0.509472i
$519$	−13.8648	+	5.04639i	−0.608599	+	0.221512i
$520$	5.75877	−	9.97448i	0.252539	−	0.437410i
$521$	−2.49479	−	4.32110i	−0.109299	−	0.189311i	0.806188	−	0.591660i	$-0.201527\pi$
$521$	−2.49479	−	4.32110i	−0.109299	−	0.189311i	−0.915486	+	0.402349i	$0.868194\pi$
$522$	1.41147	+	1.18437i	0.0617785	+	0.0518384i
$523$	−20.3405	−	17.0677i	−0.889427	−	0.746318i	0.0786677	−	0.996901i	$-0.474933\pi$
$523$	−20.3405	−	17.0677i	−0.889427	−	0.746318i	−0.968095	+	0.250583i	$0.919378\pi$
$524$	3.23396	+	5.60138i	0.141276	+	0.244697i
$525$	2.06418	−	3.57526i	0.0900881	−	0.156037i
$526$	5.60132	−	2.03871i	0.244229	−	0.0888921i
$527$	−2.77662	−	15.7470i	−0.120951	−	0.685949i
$528$	0.847296	−	4.80526i	0.0368738	−	0.209122i
$529$	21.1596	+	7.70145i	0.919981	+	0.334846i
$530$	12.5817	−	10.5573i	0.546515	−	0.458580i
$531$	−0.374638			−0.0162579
$532$	11.5817	−	1.95437i	0.502131	−	0.0847326i
$533$	2.00000			0.0866296
$534$	9.08306	−	7.62159i	0.393063	−	0.329819i
$535$	21.5253	+	7.83456i	0.930619	+	0.338718i
$536$	−0.860967	+	4.88279i	−0.0371881	+	0.210904i
$537$	5.00593	+	28.3900i	0.216022	+	1.22512i
$538$	1.07873	−	0.392624i	0.0465072	−	0.0169272i
$539$	−0.415345	+	0.719398i	−0.0178902	+	0.0309867i
$540$	5.59627	+	9.69302i	0.240825	+	0.417121i
$541$	−9.17024	−	7.69475i	−0.394260	−	0.330823i	0.424010	−	0.905657i	$-0.360622\pi$
$541$	−9.17024	−	7.69475i	−0.394260	−	0.330823i	−0.818270	+	0.574834i	$0.805067\pi$
$542$	15.3628	+	12.8909i	0.659888	+	0.553712i
$543$	−2.12836	−	3.68642i	−0.0913365	−	0.158199i
$544$	3.25877	−	5.64436i	0.139719	−	0.242000i
$545$	−16.3405	+	5.94745i	−0.699950	+	0.254761i
$546$	−4.12836	−	23.4131i	−0.176677	−	1.00199i
$547$	0.555093	−	3.14809i	0.0237341	−	0.134603i	−0.970638	−	0.240543i	$-0.922674\pi$
$547$	0.555093	−	3.14809i	0.0237341	−	0.134603i	0.994372	+	0.105941i	$0.0337855\pi$
$548$	10.9572	+	3.98811i	0.468070	+	0.170363i
$549$	−1.46791	+	1.23172i	−0.0626489	+	0.0525687i
$550$	−3.18479			−0.135800
$551$	−12.1334	+	2.04746i	−0.516901	+	0.0872249i
$552$	−1.06418			−0.0452944
$553$	−18.7101	+	15.6996i	−0.795633	+	0.667616i
$554$	−16.3131	−	5.93750i	−0.693079	−	0.252260i
$555$	−2.32501	+	13.1858i	−0.0986911	+	0.559705i
$556$	−1.43494	−	8.13798i	−0.0608552	−	0.345127i
$557$	22.5303	−	8.20037i	0.954641	−	0.347461i	0.182710	−	0.983167i	$-0.441513\pi$
$557$	22.5303	−	8.20037i	0.954641	−	0.347461i	0.771931	+	0.635706i	$0.219291\pi$
$558$	0.800660	−	1.38678i	0.0338946	−	0.0587072i
$559$	17.4611	+	30.2435i	0.738526	+	1.27916i
$560$	4.12836	+	3.46410i	0.174455	+	0.146385i
$561$	−24.3614	−	20.4417i	−1.02854	−	0.863048i
$562$	−1.46064	−	2.52990i	−0.0616133	−	0.106717i
$563$	4.37851	−	7.58380i	0.184532	−	0.319619i	−0.758887	−	0.651223i	$-0.774256\pi$
$563$	4.37851	−	7.58380i	0.184532	−	0.319619i	0.943419	+	0.331604i	$0.107590\pi$
$564$	−11.3550	+	4.13290i	−0.478133	+	0.174026i
$565$	0.993193	+	5.63268i	0.0417839	+	0.236968i
$566$	−1.64631	+	9.33667i	−0.0691994	+	0.392450i
$567$	16.7520	+	6.09722i	0.703516	+	0.256059i
$568$	−6.47565	+	5.43372i	−0.271712	+	0.227994i
$569$	−36.4201			−1.52681			−0.763406	−	0.645919i	$-0.776474\pi$
$569$	−36.4201			−1.52681			−0.763406	+	0.645919i	$0.776474\pi$
$570$	−13.1361	−	2.41609i	−0.550211	−	0.101199i
$571$	34.2131			1.43177			0.715886	−	0.698217i	$-0.246023\pi$
$571$	34.2131			1.43177			0.715886	+	0.698217i	$0.246023\pi$
$572$	−14.0496	+	11.7890i	−0.587445	+	0.492924i
$573$	−13.7665	−	5.01060i	−0.575104	−	0.209321i
$574$	−0.162504	+	0.921605i	−0.00678278	+	0.0384670i
$575$	0.120615	+	0.684040i	0.00502998	+	0.0285265i
$576$	0.613341	−	0.223238i	0.0255559	−	0.00930157i
$577$	−7.75490	+	13.4319i	−0.322841	+	0.559177i	−0.981073	−	0.193638i	$-0.937971\pi$
$577$	−7.75490	+	13.4319i	−0.322841	+	0.559177i	0.658232	+	0.752815i	$0.271304\pi$
$578$	−12.7392	−	22.0649i	−0.529880	−	0.917778i
$579$	−27.7931	−	23.3212i	−1.15504	−	0.969196i
$580$	−4.32501	−	3.62911i	−0.179586	−	0.150691i
$581$	−11.4192	−	19.7787i	−0.473749	−	0.820557i
$582$	0.266044	−	0.460802i	0.0110279	−	0.0191009i
$583$	−24.5767	+	8.94517i	−1.01786	+	0.370471i
$584$	2.73783	+	15.5270i	0.113292	+	0.642511i
$585$	1.30541	−	7.40333i	0.0539719	−	0.306090i
$586$	25.6459	+	9.33434i	1.05942	+	0.385598i
$587$	−8.87211	+	7.44459i	−0.366191	+	0.307271i	−0.807253	−	0.590206i	$-0.799047\pi$
$587$	−8.87211	+	7.44459i	−0.366191	+	0.307271i	0.441061	+	0.897477i	$0.354602\pi$
$588$	0.399615			0.0164798
$589$	3.58347	+	10.0757i	0.147654	+	0.415162i
$590$	1.14796			0.0472606
$591$	−26.9026	+	22.5740i	−1.10663	+	0.928569i
$592$	4.10607	+	1.49449i	0.168758	+	0.0614230i
$593$	−8.05603	+	45.6880i	−0.330821	+	1.87618i	0.134310	+	0.990939i	$0.457118\pi$
$593$	−8.05603	+	45.6880i	−0.330821	+	1.87618i	−0.465131	+	0.885242i	$0.653993\pi$
$594$	−3.09492	−	17.5522i	−0.126986	−	0.720175i
$595$	33.0060	−	12.0132i	1.35311	−	0.492493i
$596$	8.22668	−	14.2490i	0.336978	−	0.583663i
$597$	−7.72462	−	13.3794i	−0.316148	−	0.547584i
$598$	3.06418	+	2.57115i	0.125304	+	0.105142i
$599$	19.6355	+	16.4761i	0.802283	+	0.673196i	0.948753	−	0.316019i	$-0.102346\pi$
$599$	19.6355	+	16.4761i	0.802283	+	0.673196i	−0.146469	+	0.989215i	$0.546791\pi$
$600$	0.766044	+	1.32683i	0.0312736	+	0.0541675i
$601$	−3.99613	+	6.92150i	−0.163006	+	0.282334i	−0.935945	−	0.352146i	$-0.885452\pi$
$601$	−3.99613	+	6.92150i	−0.163006	+	0.282334i	0.772940	+	0.634480i	$0.218786\pi$
$602$	−15.3550	+	5.58878i	−0.625825	+	0.227782i
$603$	0.561956	+	3.18701i	0.0228846	+	0.129785i
$604$	0.808400	−	4.58467i	0.0328933	−	0.186547i
$605$	1.61081	+	0.586289i	0.0654889	+	0.0238360i
$606$	−0.433763	+	0.363970i	−0.0176204	+	0.0147853i
$607$	−26.9905			−1.09551			−0.547755	−	0.836639i	$-0.684518\pi$
$607$	−26.9905			−1.09551			−0.547755	+	0.836639i	$0.684518\pi$
$608$	−1.52094	+	4.08494i	−0.0616824	+	0.165666i
$609$	−11.6541			−0.472249
$610$	4.49794	−	3.77422i	0.182116	−	0.152814i
$611$	42.6810	+	15.5346i	1.72669	+	0.628463i
$612$	0.738703	−	4.18939i	0.0298603	−	0.169346i
$613$	−2.47472	−	14.0348i	−0.0999529	−	0.566861i	−0.993117	−	0.117130i	$-0.962631\pi$
$613$	−2.47472	−	14.0348i	−0.0999529	−	0.566861i	0.893164	−	0.449732i	$-0.148480\pi$
$614$	−20.0424	+	7.29482i	−0.808844	+	0.294395i
$615$	0.532089	−	0.921605i	0.0214559	−	0.0371627i
$616$	−4.29086	−	7.43199i	−0.172884	−	0.299443i
$617$	−23.4106	−	19.6438i	−0.942475	−	0.790831i	0.0355392	−	0.999368i	$-0.488685\pi$
$617$	−23.4106	−	19.6438i	−0.942475	−	0.790831i	−0.978014	+	0.208538i	$0.933130\pi$
$618$	10.0719	+	8.45134i	0.405152	+	0.339963i
$619$	14.3375	+	24.8333i	0.576273	+	0.998133i	0.995902	+	0.0904380i	$0.0288267\pi$
$619$	14.3375	+	24.8333i	0.576273	+	0.998133i	−0.419629	+	0.907695i	$0.637840\pi$
$620$	−2.45336	+	4.24935i	−0.0985294	+	0.170658i
$621$	−3.65270	+	1.32948i	−0.146578	+	0.0533500i
$622$	−5.08647	−	28.8468i	−0.203949	−	1.15665i
$623$	3.62124	−	20.5371i	0.145082	−	0.822801i
$624$	8.29086	+	3.01763i	0.331900	+	0.120802i
$625$	−14.5548	+	12.2130i	−0.582194	+	0.488519i
$626$	5.56118			0.222270
$627$	18.3405	+	10.7697i	0.732449	+	0.430100i
$628$	8.45336			0.337326
$629$	21.8161	−	18.3059i	0.869867	−	0.729905i
$630$	3.30541	+	1.20307i	0.131691	+	0.0479315i
$631$	−0.781059	+	4.42961i	−0.0310935	+	0.176340i	−0.996400	−	0.0847809i	$-0.972981\pi$
$631$	−0.781059	+	4.42961i	−0.0310935	+	0.176340i	0.965306	+	0.261121i	$0.0840921\pi$
$632$	−1.57398	−	8.92647i	−0.0626095	−	0.355076i
$633$	32.1917	−	11.7168i	1.27950	−	0.465701i
$634$	−1.90167	+	3.29380i	−0.0755251	+	0.130813i
$635$	−9.72967	−	16.8523i	−0.386110	−	0.668763i
$636$	9.63816	+	8.08737i	0.382178	+	0.320685i
$637$	−1.15064	−	0.965505i	−0.0455902	−	0.0382547i
$638$	4.49525	+	7.78601i	0.177969	+	0.308251i
$639$	−2.75877	+	4.77833i	−0.109135	+	0.189028i
$640$	−1.87939	+	0.684040i	−0.0742892	+	0.0270391i
$641$	−2.01573	−	11.4318i	−0.0796165	−	0.451528i	−0.998389	−	0.0567403i	$-0.981929\pi$
$641$	−2.01573	−	11.4318i	−0.0796165	−	0.451528i	0.918772	−	0.394788i	$-0.129182\pi$
$642$	−3.04710	+	17.2810i	−0.120260	+	0.682026i
$643$	−24.4748	−	8.90809i	−0.965191	−	0.351301i	−0.189125	−	0.981953i	$-0.560565\pi$
$643$	−24.4748	−	8.90809i	−0.965191	−	0.351301i	−0.776066	+	0.630652i	$0.782787\pi$
$644$	−1.43376	+	1.20307i	−0.0564982	+	0.0474076i
$645$	18.5817			0.731654
$646$	18.1004	+	21.8966i	0.712152	+	0.861511i
$647$	−2.31490			−0.0910082			−0.0455041	−	0.998964i	$-0.514489\pi$
$647$	−2.31490			−0.0910082			−0.0455041	+	0.998964i	$0.514489\pi$
$648$	−5.06805	+	4.25260i	−0.199092	+	0.167058i
$649$	−1.71776	−	0.625213i	−0.0674279	−	0.0245418i
$650$	1.00000	−	5.67128i	0.0392232	−	0.222446i
$651$	1.75877	+	9.97448i	0.0689316	+	0.390931i
$652$	−16.0214	+	5.83132i	−0.627447	+	0.228372i
$653$	−1.65270	+	2.86257i	−0.0646753	+	0.112021i	−0.896550	−	0.442943i	$-0.853934\pi$
$653$	−1.65270	+	2.86257i	−0.0646753	+	0.112021i	0.831875	+	0.554964i	$0.187268\pi$
$654$	−6.66044	−	11.5362i	−0.260444	−	0.451102i
$655$	−9.90941	−	8.31499i	−0.387193	−	0.324893i
$656$	−0.266044	−	0.223238i	−0.0103873	−	0.00871597i
$657$	5.14543	+	8.91215i	0.200742	+	0.347696i
$658$	−10.6263	+	18.4053i	−0.414256	+	0.717513i
$659$	12.9201	−	4.70253i	0.503295	−	0.183185i	−0.0778802	−	0.996963i	$-0.524815\pi$
$659$	12.9201	−	4.70253i	0.503295	−	0.183185i	0.581176	+	0.813778i	$0.302593\pi$
$660$	1.69459	+	9.61051i	0.0659619	+	0.374089i
$661$	−0.579030	+	3.28384i	−0.0225217	+	0.127727i	−0.993996	−	0.109419i	$-0.965101\pi$
$661$	−0.579030	+	3.28384i	−0.0225217	+	0.127727i	0.971474	+	0.237146i	$0.0762120\pi$
$662$	−19.1903	−	6.98470i	−0.745853	−	0.271468i
$663$	44.0506	−	36.9628i	1.71078	−	1.43552i
$664$	8.47565			0.328919
$665$	−20.4296	+	11.5954i	−0.792228	+	0.449649i
$666$	2.85204			0.110514
$667$	1.50206	−	1.26038i	0.0581600	−	0.0488020i
$668$	3.00000	+	1.09191i	0.116073	+	0.0422473i
$669$	−2.46791	+	13.9962i	−0.0954150	+	0.541125i
$670$	−1.72193	−	9.76557i	−0.0665241	−	0.377277i
$671$	−8.78611	+	3.19788i	−0.339184	+	0.123453i
$672$	−2.06418	+	3.57526i	−0.0796274	+	0.137919i
$673$	−19.4905	−	33.7585i	−0.751304	−	1.30130i	−0.947191	−	0.320670i	$-0.896092\pi$
$673$	−19.4905	−	33.7585i	−0.751304	−	1.30130i	0.195887	−	0.980626i	$-0.437241\pi$
$674$	15.5587	+	13.0553i	0.599299	+	0.502872i
$675$	4.28699	+	3.59721i	0.165006	+	0.138457i
$676$	−10.0817	−	17.4620i	−0.387758	−	0.671617i
$677$	21.7939	−	37.7481i	0.837606	−	1.45078i	−0.0542853	−	0.998525i	$-0.517288\pi$
$677$	21.7939	−	37.7481i	0.837606	−	1.45078i	0.891891	−	0.452250i	$-0.149379\pi$
$678$	−4.11721	+	1.49854i	−0.158121	+	0.0575512i
$679$	−0.162504	−	0.921605i	−0.00623632	−	0.0353680i
$680$	−2.26352	+	12.8370i	−0.0868020	+	0.492278i
$681$	−11.1382	−	4.05396i	−0.426815	−	0.155348i
$682$	5.98545	−	5.02239i	0.229195	−	0.192317i
$683$	32.9317			1.26010			0.630048	−	0.776556i	$-0.283035\pi$
$683$	32.9317			1.26010			0.630048	+	0.776556i	$0.283035\pi$
$684$	−0.0209445	+	2.84499i	−0.000800834	+	0.108781i
$685$	−23.3209			−0.891045
$686$	−13.9108	+	11.6726i	−0.531119	+	0.445661i
$687$	33.1634	+	12.0705i	1.26526	+	0.460518i
$688$	1.05303	−	5.97205i	0.0401465	−	0.227682i
$689$	−8.21213	−	46.5733i	−0.312857	−	1.77430i
$690$	2.00000	−	0.727940i	0.0761387	−	0.0277122i
$691$	−17.1604	+	29.7228i	−0.652814	+	1.13071i	0.329623	+	0.944113i	$0.393078\pi$
$691$	−17.1604	+	29.7228i	−0.652814	+	1.13071i	−0.982437	+	0.186594i	$0.940255\pi$
$692$	−4.81521	−	8.34018i	−0.183047	−	0.317046i
$693$	−4.29086	−	3.60046i	−0.162996	−	0.136770i
$694$	3.99479	+	3.35202i	0.151640	+	0.127241i
$695$	8.26352	+	14.3128i	0.313453	+	0.542917i
$696$	2.16250	−	3.74557i	0.0819695	−	0.141975i
$697$	−2.12701	+	0.774169i	−0.0805663	+	0.0293237i
$698$	2.49020	+	14.1226i	0.0942555	+	0.534549i
$699$	2.23467	−	12.6734i	0.0845230	−	0.479354i
$700$	2.53209	+	0.921605i	0.0957040	+	0.0348334i
$701$	4.94356	−	4.14814i	0.186716	−	0.156673i	−0.544638	−	0.838671i	$-0.683333\pi$
$701$	4.94356	−	4.14814i	0.186716	−	0.156673i	0.731354	+	0.681998i	$0.238889\pi$
$702$	32.2276			1.21635
$703$	−12.3500	+	14.5000i	−0.465788	+	0.546878i
$704$	3.18479			0.120031
$705$	18.5134	−	15.5346i	0.697256	−	0.585067i
$706$	−24.6668	−	8.97800i	−0.928349	−	0.337891i
$707$	−0.172933	+	0.980752i	−0.00650381	+	0.0368850i
$708$	0.152704	+	0.866025i	0.00573895	+	0.0325472i
$709$	3.17530	−	1.15571i	0.119251	−	0.0434037i	−0.281706	−	0.959501i	$-0.590900\pi$
$709$	3.17530	−	1.15571i	0.119251	−	0.0434037i	0.400956	+	0.916097i	$0.368678\pi$
$710$	8.45336	−	14.6417i	0.317249	−	0.549492i
$711$	−2.95811	−	5.12360i	−0.110938	−	0.192150i
$712$	5.92855	+	4.97464i	0.222182	+	0.186433i
$713$	−1.30541	−	1.09537i	−0.0488879	−	0.0410218i
$714$	13.4534	+	23.3019i	0.503479	+	0.872052i
$715$	18.3405	−	31.7667i	0.685895	−	1.18801i
$716$	−17.6814	+	6.43550i	−0.660785	+	0.240506i
$717$	−4.18479	−	23.7331i	−0.156284	−	0.886330i
$718$	−5.85029	+	33.1786i	−0.218331	+	1.23822i
$719$	29.3209	+	10.6719i	1.09348	+	0.397996i	0.824911	−	0.565263i	$-0.191225\pi$
$719$	29.3209	+	10.6719i	1.09348	+	0.397996i	0.268574	+	0.963259i	$0.413448\pi$
$720$	−1.00000	+	0.839100i	−0.0372678	+	0.0312714i
$721$	23.1242			0.861192
$722$	−14.3735	−	12.4259i	−0.534925	−	0.462445i
$723$	26.8161			0.997303
$724$	2.12836	−	1.78590i	0.0790997	−	0.0663725i
$725$	−2.65270	−	0.965505i	−0.0985189	−	0.0358580i
$726$	−0.228026	+	1.29320i	−0.00846283	+	0.0479951i
$727$	−4.45605	−	25.2715i	−0.165266	−	0.937269i	−0.948790	−	0.315908i	$-0.897691\pi$
$727$	−4.45605	−	25.2715i	−0.165266	−	0.937269i	0.783524	−	0.621361i	$-0.213420\pi$
$728$	14.5817	−	5.30731i	0.540434	−	0.196702i
$729$	−15.0201	+	26.0155i	−0.556299	+	0.963538i
$730$	−15.7665	−	27.3084i	−0.583545	−	1.01073i
$731$	−30.2768	−	25.4052i	−1.11983	−	0.939647i
$732$	3.44562	+	2.89122i	0.127354	+	0.106863i
$733$	11.9368	+	20.6751i	0.440894	+	0.763651i	0.997756	−	0.0669540i	$-0.0213281\pi$
$733$	11.9368	+	20.6751i	0.440894	+	0.763651i	−0.556862	+	0.830605i	$0.687995\pi$
$734$	5.23442	−	9.06629i	0.193206	−	0.334643i
$735$	−0.751030	+	0.273352i	−0.0277021	+	0.0100828i
$736$	−0.120615	−	0.684040i	−0.00444592	−	0.0252141i
$737$	−2.74200	+	15.5507i	−0.101003	+	0.572816i
$738$	−0.213011	−	0.0775297i	−0.00784104	−	0.00285391i
$739$	−35.1924	+	29.5299i	−1.29457	+	1.08628i	−0.303517	+	0.952826i	$0.598161\pi$
$739$	−35.1924	+	29.5299i	−1.29457	+	1.08628i	−0.991056	+	0.133449i	$0.957395\pi$
$740$	−8.73917			−0.321258
$741$	−24.9368	+	29.2780i	−0.916075	+	1.07555i
$742$	22.1284			0.812357
$743$	−39.0770	+	32.7895i	−1.43360	+	1.20293i	−0.490046	+	0.871697i	$0.663020\pi$
$743$	−39.0770	+	32.7895i	−1.43360	+	1.20293i	−0.943549	+	0.331232i	$0.892536\pi$
$744$	−3.53209	−	1.28558i	−0.129493	−	0.0471315i
$745$	−5.71419	+	32.4068i	−0.209352	+	1.18729i
$746$	4.15064	+	23.5395i	0.151966	+	0.861841i
$747$	5.19846	−	1.89209i	0.190202	−	0.0692278i
$748$	10.3785	−	17.9761i	0.379476	−	0.657271i
$749$	15.4311	+	26.7274i	0.563839	+	0.976598i
$750$	−14.0838	−	11.8177i	−0.514267	−	0.431521i
$751$	−27.8607	−	23.3779i	−1.01665	−	0.853072i	−0.0274489	−	0.999623i	$-0.508738\pi$
$751$	−27.8607	−	23.3779i	−1.01665	−	0.853072i	−0.989203	+	0.146551i	$0.953183\pi$
$752$	−3.94356	−	6.83045i	−0.143807	−	0.249081i
$753$	−6.56283	+	11.3672i	−0.239163	+	0.414242i
$754$	−15.2763	+	5.56012i	−0.556330	+	0.202488i
$755$	1.61680	+	9.16933i	0.0588414	+	0.333706i
$756$	−2.61856	+	14.8506i	−0.0952359	+	0.540110i
$757$	5.45336	+	1.98486i	0.198206	+	0.0721410i	0.439216	−	0.898382i	$-0.355256\pi$
$757$	5.45336	+	1.98486i	0.198206	+	0.0721410i	−0.241010	+	0.970523i	$0.577479\pi$
$758$	13.6459	−	11.4503i	0.495641	−	0.415892i
$759$	−3.38919			−0.123020
$760$	0.0641778	−	8.71756i	0.00232797	−	0.316219i
$761$	22.6355			0.820535			0.410268	−	0.911965i	$-0.365435\pi$
$761$	22.6355			0.820535			0.410268	+	0.911965i	$0.365435\pi$
$762$	11.4192	−	9.58186i	0.413675	−	0.347114i
$763$	−22.0155	−	8.01298i	−0.797014	−	0.290089i
$764$	1.66044	−	9.41685i	0.0600728	−	0.340690i
$765$	1.47741	+	8.37879i	0.0534157	+	0.302936i
$766$	−23.5672	+	8.57775i	−0.851516	+	0.309927i
$767$	1.65270	−	2.86257i	0.0596757	−	0.103361i
$768$	−0.766044	−	1.32683i	−0.0276422	−	0.0478778i
$769$	8.35188	+	7.00806i	0.301177	+	0.252717i	0.780834	−	0.624739i	$-0.214795\pi$
$769$	8.35188	+	7.00806i	0.301177	+	0.252717i	−0.479657	+	0.877456i	$0.659239\pi$
$770$	13.1480	+	11.0324i	0.473819	+	0.397582i
$771$	6.14724	+	10.6473i	0.221387	+	0.383454i
$772$	11.8405	−	20.5083i	0.426149	−	0.738111i
$773$	4.93407	−	1.79585i	0.177466	−	0.0645924i	−0.251759	−	0.967790i	$-0.581009\pi$
$773$	4.93407	−	1.79585i	0.177466	−	0.0645924i	0.429225	+	0.903198i	$0.358787\pi$
$774$	−0.687319	−	3.89798i	−0.0247052	−	0.140110i
$775$	−0.426022	+	2.41609i	−0.0153032	+	0.0867886i
$776$	0.326352	+	0.118782i	0.0117153	+	0.00426404i
$777$	−13.8188	+	11.5954i	−0.495748	+	0.415982i
$778$	−9.41828			−0.337662
$779$	1.31655	−	0.747243i	0.0471704	−	0.0267728i
$780$	−17.6459			−0.631824
$781$	−20.6236	+	17.3053i	−0.737971	+	0.619231i
$782$	−4.25402	−	1.54834i	−0.152124	−	0.0553684i
$783$	2.74329	−	15.5580i	0.0980371	−	0.555996i
$784$	0.0452926	+	0.256867i	0.00161759	+	0.00917383i
$785$	−15.8871	+	5.78244i	−0.567036	+	0.206384i
$786$	4.95471	−	8.58180i	0.176729	−	0.306103i
$787$	1.19372	+	2.06758i	0.0425514	+	0.0737011i	0.886517	−	0.462697i	$-0.153118\pi$
$787$	1.19372	+	2.06758i	0.0425514	+	0.0737011i	−0.843965	+	0.536398i	$0.819785\pi$
$788$	−17.5594	−	14.7341i	−0.625529	−	0.524881i
$789$	−6.99588	−	5.87024i	−0.249060	−	0.208986i
$790$	9.06418	+	15.6996i	0.322489	+	0.558567i
$791$	−3.85298	+	6.67355i	−0.136996	+	0.237284i
$792$	1.95336	−	0.710966i	0.0694097	−	0.0252631i
$793$	−2.93582	−	16.6499i	−0.104254	−	0.591254i
$794$	1.18984	−	6.74795i	0.0422260	−	0.239476i
$795$	−23.6459	−	8.60640i	−0.838634	−	0.305238i
$796$	7.72462	−	6.48173i	0.273792	−	0.229739i
$797$	31.0951			1.10145			0.550723	−	0.834688i	$-0.314352\pi$
$797$	31.0951			1.10145			0.550723	+	0.834688i	$0.314352\pi$
$798$	−11.4652	−	13.8698i	−0.405864	−	0.490986i
$799$	−51.4047			−1.81857
$800$	−0.766044	+	0.642788i	−0.0270838	+	0.0227260i
$801$	4.74675	+	1.72768i	0.167718	+	0.0610444i
$802$	0.824292	−	4.67479i	0.0291068	−	0.165073i
$803$	8.71941	+	49.4502i	0.307701	+	1.74506i
$804$	7.13816	−	2.59808i	0.251743	−	0.0916271i
$805$	1.87164	−	3.24178i	0.0659668	−	0.114258i
$806$	7.06418	+	12.2355i	0.248825	+	0.430978i
$807$	−1.34730	−	1.13052i	−0.0474271	−	0.0397960i
$808$	−0.283119	−	0.237565i	−0.00996008	−	0.00835750i
$809$	−11.1518	−	19.3155i	−0.392077	−	0.679098i	0.600646	−	0.799515i	$-0.294910\pi$
$809$	−11.1518	−	19.3155i	−0.392077	−	0.679098i	−0.992723	+	0.120417i	$0.961577\pi$
$810$	6.61587	−	11.4590i	0.232458	−	0.402629i
$811$	−3.11886	+	1.13517i	−0.109518	+	0.0398613i	−0.396198	−	0.918165i	$-0.629671\pi$
$811$	−3.11886	+	1.13517i	−0.109518	+	0.0398613i	0.286680	+	0.958026i	$0.407448\pi$
$812$	−1.32089	−	7.49113i	−0.0463541	−	0.262887i
$813$	5.33544	−	30.2588i	0.187122	−	1.06122i
$814$	13.0770	+	4.75963i	0.458348	+	0.166825i
$815$	26.1215	−	21.9186i	0.914998	−	0.767774i
$816$	−9.98545			−0.349561
$817$	22.7939	+	13.3847i	0.797456	+	0.468273i
$818$	31.6928			1.10811
$819$	7.75877	−	6.51038i	0.271113	−	0.227491i
$820$	0.652704	+	0.237565i	0.0227934	+	0.00829612i
$821$	−0.318201	+	1.80460i	−0.0111053	+	0.0629811i	−0.989857	−	0.142069i	$-0.954625\pi$
$821$	−0.318201	+	1.80460i	−0.0111053	+	0.0629811i	0.978752	+	0.205050i	$0.0657357\pi$
$822$	−3.10220	−	17.5934i	−0.108202	−	0.613641i
$823$	32.1729	−	11.7100i	1.12148	−	0.408185i	0.286287	−	0.958144i	$-0.407579\pi$
$823$	32.1729	−	11.7100i	1.12148	−	0.408185i	0.835191	+	0.549959i	$0.185357\pi$
$824$	−4.29086	+	7.43199i	−0.149479	+	0.258906i
$825$	2.43969	+	4.22567i	0.0849392	+	0.147119i
$826$	1.18479	+	0.994159i	0.0412242	+	0.0345912i
$827$	−15.2181	−	12.7695i	−0.529184	−	0.444038i	0.338636	−	0.940918i	$-0.390035\pi$
$827$	−15.2181	−	12.7695i	−0.529184	−	0.444038i	−0.867820	+	0.496880i	$0.834479\pi$
$828$	−0.226682	−	0.392624i	−0.00787773	−	0.0136446i
$829$	17.8675	−	30.9475i	0.620565	−	1.07485i	−0.368816	−	0.929502i	$-0.620237\pi$
$829$	17.8675	−	30.9475i	0.620565	−	1.07485i	0.989381	−	0.145347i	$-0.0464300\pi$
$830$	−15.9290	+	5.79769i	−0.552904	+	0.201241i
$831$	4.61856	+	26.1931i	0.160216	+	0.908630i
$832$	−1.00000	+	5.67128i	−0.0346688	+	0.196616i
$833$	1.59745	+	0.581424i	0.0553483	+	0.0201451i
$834$	−9.69846	+	8.13798i	−0.335830	+	0.281795i
$835$	−6.38507			−0.220964
$836$	−4.84389	+	13.0097i	−0.167530	+	0.449949i
$837$	−13.7297			−0.474567
$838$	−8.43423	+	7.07716i	−0.291356	+	0.244476i
$839$	51.1147	+	18.6042i	1.76468	+	0.642290i	0.999998	−	0.00212143i	$-0.000675272\pi$
$839$	51.1147	+	18.6042i	1.76468	+	0.642290i	0.764679	+	0.644411i	$0.222897\pi$
$840$	1.43376	−	8.13127i	0.0494695	−	0.280556i
$841$	−3.65199	−	20.7115i	−0.125931	−	0.714188i
$842$	8.14290	−	2.96377i	0.280623	−	0.102138i
$843$	−2.23783	+	3.87603i	−0.0770748	+	0.133498i
$844$	11.1800	+	19.3644i	0.384833	+	0.666550i
$845$	30.8922	+	25.9216i	1.06272	+	0.891731i
$846$	−3.94356	−	3.30904i	−0.135582	−	0.113767i
$847$	1.15476	+	2.00011i	0.0396781	+	0.0687245i
$848$	−4.10607	+	7.11192i	−0.141003	+	0.244224i
$849$	13.6493	−	4.96794i	0.468443	−	0.170499i
$850$	1.13176	+	6.41852i	0.0388190	+	0.220154i
$851$	0.527036	−	2.98897i	0.0180666	−	0.102461i
$852$	12.1702	+	4.42961i	0.416946	+	0.151756i
$853$	12.2385	−	10.2694i	0.419040	−	0.351616i	−0.408758	−	0.912643i	$-0.634038\pi$
$853$	12.2385	−	10.2694i	0.419040	−	0.351616i	0.827798	+	0.561027i	$0.189594\pi$
$854$	7.91085			0.270704
$855$	−1.90673	−	5.36116i	−0.0652087	−	0.183348i
$856$	−11.4534			−0.391468
$857$	−19.9283	+	16.7218i	−0.680738	+	0.571207i	−0.916222	−	0.400671i	$-0.868777\pi$
$857$	−19.9283	+	16.7218i	−0.680738	+	0.571207i	0.235484	+	0.971878i	$0.424332\pi$
$858$	26.4047	+	9.61051i	0.901440	+	0.328097i
$859$	9.25031	−	52.4611i	0.315617	−	1.78995i	−0.253124	−	0.967434i	$-0.581458\pi$
$859$	9.25031	−	52.4611i	0.315617	−	1.78995i	0.568740	−	0.822517i	$-0.307431\pi$
$860$	2.10607	+	11.9441i	0.0718163	+	0.407290i
$861$	1.34730	−	0.490376i	0.0459157	−	0.0167120i
$862$	14.9436	−	25.8830i	0.508980	−	0.881579i
$863$	−1.61587	−	2.79876i	−0.0550048	−	0.0952710i	0.837212	−	0.546879i	$-0.184184\pi$
$863$	−1.61587	−	2.79876i	−0.0550048	−	0.0952710i	−0.892217	+	0.451608i	$0.850851\pi$
$864$	−4.28699	−	3.59721i	−0.145846	−	0.122380i
$865$	14.7547	+	12.3806i	0.501673	+	0.420954i
$866$	−4.63041	−	8.02011i	−0.157348	−	0.272535i
$867$	−19.5175	+	33.8054i	−0.662850	+	1.14809i
$868$	−6.21213	+	2.26103i	−0.210854	+	0.0767444i
$869$	−5.01279	−	28.4290i	−0.170047	−	0.964387i
$870$	−1.50206	+	8.51860i	−0.0509246	+	0.288808i
$871$	−26.8307	−	9.76557i	−0.909123	−	0.330894i
$872$	6.66044	−	5.58878i	0.225551	−	0.189260i
$873$	0.226682			0.00767201
$874$	2.97771	+	0.547683i	0.100723	+	0.0185257i
$875$	−32.3351			−1.09313
$876$	18.5043	−	15.5270i	0.625204	−	0.524608i
$877$	−11.0172	−	4.00995i	−0.372026	−	0.135406i	0.149239	−	0.988801i	$-0.452317\pi$
$877$	−11.0172	−	4.00995i	−0.372026	−	0.135406i	−0.521265	+	0.853395i	$0.674540\pi$
$878$	3.62267	−	20.5452i	0.122259	−	0.693367i
$879$	−7.26083	−	41.1782i	−0.244902	−	1.38891i
$880$	−5.98545	+	2.17853i	−0.201770	+	0.0734381i
$881$	−13.5236	+	23.4236i	−0.455623	+	0.789162i	−0.998724	−	0.0505056i	$-0.983917\pi$
$881$	−13.5236	+	23.4236i	−0.455623	+	0.789162i	0.543101	+	0.839667i	$0.317250\pi$
$882$	0.0851223	+	0.147436i	0.00286622	+	0.00496443i
$883$	11.0931	+	9.30823i	0.373313	+	0.313247i	0.810070	−	0.586333i	$-0.199429\pi$
$883$	11.0931	+	9.30823i	0.373313	+	0.313247i	−0.436758	+	0.899579i	$0.643873\pi$
$884$	28.7520	+	24.1258i	0.967033	+	0.811437i
$885$	−0.879385	−	1.52314i	−0.0295602	−	0.0511998i
$886$	−11.9140	+	20.6357i	−0.400259	+	0.693268i
$887$	10.8922	−	3.96443i	0.365724	−	0.133112i	−0.152620	−	0.988285i	$-0.548771\pi$
$887$	10.8922	−	3.96443i	0.365724	−	0.133112i	0.518344	+	0.855172i	$0.326549\pi$
$888$	−1.16250	−	6.59289i	−0.0390111	−	0.221243i
$889$	4.55262	−	25.8192i	0.152690	−	0.865948i
$890$	−14.5449	−	5.29390i	−0.487546	−	0.177452i
$891$	−16.1407	+	13.5436i	−0.540733	+	0.453729i
$892$	−9.27631			−0.310594
$893$	33.8999	−	5.72048i	1.13442	−	0.191428i
$894$	−25.2080			−0.843082
$895$	28.8280	−	24.1896i	0.963614	−	0.808568i
$896$	−2.53209	−	0.921605i	−0.0845912	−	0.0307887i
$897$	1.06418	−	6.03525i	0.0355319	−	0.201511i
$898$	−0.378918	−	2.14895i	−0.0126447	−	0.0717115i
$899$	6.50805	−	2.36873i	0.217055	−	0.0790017i
$900$	−0.326352	+	0.565258i	−0.0108784	+	0.0188419i
$901$	26.7615	+	46.3522i	0.891553	+	1.54422i
$902$	−0.847296	−	0.710966i	−0.0282119	−	0.0236726i
$903$	19.1780	+	16.0922i	0.638203	+	0.535516i
$904$	−1.42989	−	2.47665i	−0.0475575	−	0.0823720i
$905$	−2.77837	+	4.81228i	−0.0923562	+	0.159966i
$906$	−6.70233	+	2.43945i	−0.222670	+	0.0810453i
$907$	7.28952	+	41.3409i	0.242044	+	1.37270i	0.827258	+	0.561823i	$0.189900\pi$
$907$	7.28952	+	41.3409i	0.242044	+	1.37270i	−0.585213	+	0.810879i	$0.698989\pi$
$908$	1.34343	−	7.61895i	0.0445832	−	0.252844i
$909$	−0.226682	−	0.0825054i	−0.00751855	−	0.00273653i
$910$	−23.7743	+	19.9490i	−0.788109	+	0.661302i
$911$	−44.8675			−1.48653			−0.743264	−	0.668999i	$-0.766723\pi$
$911$	−44.8675			−1.48653			−0.743264	+	0.668999i	$0.766723\pi$
$912$	6.58512	−	1.11121i	0.218055	−	0.0367959i
$913$	26.9932			0.893344
$914$	1.36437	−	1.14484i	0.0451294	−	0.0378680i
$915$	−8.45336	−	3.07677i	−0.279460	−	0.101715i
$916$	−4.00000	+	22.6851i	−0.132164	+	0.749538i
$917$	−3.02641	−	17.1636i	−0.0999408	−	0.566792i
$918$	−34.2743	+	12.4748i	−1.13122	+	0.411730i
$919$	16.2635	−	28.1692i	0.536484	−	0.929217i	−0.462606	−	0.886564i	$-0.653086\pi$
$919$	16.2635	−	28.1692i	0.536484	−	0.929217i	0.999090	−	0.0426535i	$-0.0135811\pi$
$920$	0.694593	+	1.20307i	0.0229000	+	0.0396640i
$921$	25.0323	+	21.0046i	0.824843	+	0.692125i
$922$	−11.8648	−	9.95578i	−0.390748	−	0.327876i
$923$	−24.3405	−	42.1590i	−0.801177	−	1.38768i
$924$	−6.57398	+	11.3865i	−0.216268	+	0.374587i
$925$	−4.10607	+	1.49449i	−0.135007	+	0.0491384i
$926$	−0.470599	−	2.66890i	−0.0154649	−	0.0877056i
$927$	−0.972659	+	5.51622i	−0.0319463	+	0.181177i
$928$	2.65270	+	0.965505i	0.0870793	+	0.0316943i
$929$	9.07011	−	7.61072i	0.297581	−	0.249700i	−0.481756	−	0.876305i	$-0.660001\pi$
$929$	9.07011	−	7.61072i	0.297581	−	0.249700i	0.779336	+	0.626606i	$0.215556\pi$
$930$	7.51754			0.246510
$931$	−1.11817	−	0.205663i	−0.0366467	−	0.00674034i
$932$	8.39961			0.275139
$933$	−34.3783	+	28.8468i	−1.12549	+	0.944401i
$934$	−12.1348	−	4.41669i	−0.397061	−	0.144518i
$935$	−7.20884	+	40.8833i	−0.235754	+	1.33703i
$936$	0.652704	+	3.70167i	0.0213343	+	0.120993i
$937$	0.717759	−	0.261243i	0.0234482	−	0.00853443i	−0.330269	−	0.943887i	$-0.607140\pi$
$937$	0.717759	−	0.261243i	0.0234482	−	0.00853443i	0.353718	+	0.935352i	$0.384917\pi$
$938$	6.68004	−	11.5702i	0.218111	−	0.377780i
$939$	−4.26011	−	7.37874i	−0.139024	−	0.240796i
$940$	12.0838	+	10.1395i	0.394129	+	0.330714i
$941$	−16.4652	−	13.8160i	−0.536751	−	0.450388i	0.333674	−	0.942688i	$-0.391711\pi$
$941$	−16.4652	−	13.8160i	−0.536751	−	0.450388i	−0.870425	+	0.492301i	$0.836156\pi$
$942$	−6.47565	−	11.2162i	−0.210988	−	0.365442i
$943$	−0.120615	+	0.208911i	−0.00392776	+	0.00680307i
$944$	−0.539363	+	0.196312i	−0.0175548	+	0.00638941i
$945$	−5.23711	−	29.7011i	−0.170363	−	0.966178i
$946$	3.35369	−	19.0197i	0.109038	−	0.618385i
$947$	−29.7743	−	10.8369i	−0.967533	−	0.352153i	−0.190552	−	0.981677i	$-0.561028\pi$
$947$	−29.7743	−	10.8369i	−0.967533	−	0.352153i	−0.776981	+	0.629524i	$0.783250\pi$
$948$	−10.6382	+	8.92647i	−0.345511	+	0.289918i
$949$	−90.7957			−2.94735
$950$	−1.46064	−	4.10689i	−0.0473893	−	0.133245i
$951$	5.82707			0.188956
$952$	−13.4534	+	11.2887i	−0.436026	+	0.365869i
$953$	−52.5017	−	19.1091i	−1.70070	−	0.619003i	−0.704792	−	0.709414i	$-0.748960\pi$
$953$	−52.5017	−	19.1091i	−1.70070	−	0.619003i	−0.995905	+	0.0904104i	$0.971182\pi$
$954$	−0.930770	+	5.27866i	−0.0301348	+	0.170903i
$955$	3.32089	+	18.8337i	0.107461	+	0.609444i
$956$	14.7811	−	5.37987i	0.478054	−	0.173997i
$957$	6.88713	−	11.9289i	0.222629	−	0.385605i
$958$	9.27631	+	16.0670i	0.299704	+	0.519103i
$959$	−24.0692	−	20.1965i	−0.777236	−	0.652178i
$960$	2.34730	+	1.96962i	0.0757587	+	0.0635691i
$961$	12.4905	+	21.6342i	0.402920	+	0.697877i
$962$	−12.5817	+	21.7922i	−0.405651	+	0.702608i
$963$	−7.02481	+	2.55682i	−0.226371	+	0.0823925i
$964$	3.03936	+	17.2371i	0.0978913	+	0.555169i
$965$	−8.22432	+	46.6424i	−0.264750	+	1.50147i
$966$	2.69459	+	0.980752i	0.0866971	+	0.0315552i
$967$	16.5134	−	13.8564i	0.531036	−	0.445592i	−0.337423	−	0.941353i	$-0.609555\pi$
$967$	16.5134	−	13.8564i	0.531036	−	0.445592i	0.868459	+	0.495761i	$0.165111\pi$
$968$	−0.857097			−0.0275481
$969$	15.1873	−	40.7900i	0.487887	−	1.31036i
$970$	−0.694593			−0.0223020
$971$	37.2729	−	31.2757i	1.19614	−	1.00368i	0.196413	−	0.980521i	$-0.437071\pi$
$971$	37.2729	−	31.2757i	1.19614	−	1.00368i	0.999732	−	0.0231632i	$-0.00737372\pi$
$972$	−6.25150	−	2.27536i	−0.200517	−	0.0729822i
$973$	−3.86659	+	21.9285i	−0.123957	+	0.702996i
$974$	7.14971	+	40.5480i	0.229092	+	1.29924i
$975$	−8.29086	+	3.01763i	−0.265520	+	0.0966414i
$976$	−1.46791	+	2.54250i	−0.0469867	+	0.0813833i
$977$	25.2741	+	43.7760i	0.808590	+	1.40052i	0.913841	+	0.406073i	$0.133102\pi$
$977$	25.2741	+	43.7760i	0.808590	+	1.40052i	−0.105251	+	0.994446i	$0.533565\pi$
$978$	20.0103	+	16.7906i	0.639858	+	0.536904i
$979$	18.8812	+	15.8432i	0.603446	+	0.506351i
$980$	−0.260830	−	0.451771i	−0.00833190	−	0.0144313i
$981$	2.83750	−	4.91469i	0.0905943	−	0.156914i
$982$	21.2160	−	7.72199i	0.677030	−	0.246419i
$983$	−5.21987	−	29.6034i	−0.166488	−	0.944201i	−0.947517	−	0.319706i	$-0.896416\pi$
$983$	−5.21987	−	29.6034i	−0.166488	−	0.944201i	0.781029	−	0.624495i	$-0.214695\pi$
$984$	−0.0923963	+	0.524005i	−0.00294549	+	0.0167047i
$985$	43.0797	+	15.6797i	1.37263	+	0.499597i
$986$	14.0942	−	11.8264i	0.448851	−	0.376631i
$987$	32.5609			1.03642
$988$	−21.6459	−	12.7106i	−0.688648	−	0.404379i
$989$	−4.21213			−0.133938
$990$	−3.18479	+	2.67236i	−0.101219	+	0.0849331i
$991$	−2.58677	−	0.941508i	−0.0821715	−	0.0299080i	0.300607	−	0.953748i	$-0.402811\pi$
$991$	−2.58677	−	0.941508i	−0.0821715	−	0.0299080i	−0.382779	+	0.923840i	$0.625033\pi$
$992$	0.426022	−	2.41609i	0.0135262	−	0.0767110i
$993$	5.43313	+	30.8128i	0.172415	+	0.977816i
$994$	21.4047	−	7.79066i	0.678915	−	0.247105i
$995$	−10.0838	+	17.4656i	−0.319677	+	0.553697i
$996$	−6.49273	−	11.2457i	−0.205730	−	0.356335i
$997$	6.66819	+	5.59527i	0.211184	+	0.177204i	0.742244	−	0.670130i	$-0.233762\pi$
$997$	6.66819	+	5.59527i	0.211184	+	0.177204i	−0.531060	+	0.847334i	$0.678206\pi$
$998$	−22.4670	−	18.8521i	−0.711182	−	0.596752i
$999$	−12.2267	−	21.1772i	−0.386835	−	0.670018i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.2.e.a.25.1	✓	6
3.2	odd	2		342.2.u.c.253.1		6
4.3	odd	2		304.2.u.c.177.1		6
5.2	odd	4		950.2.u.b.899.2		12
5.3	odd	4		950.2.u.b.899.1		12
5.4	even	2		950.2.l.d.101.1		6
19.2	odd	18		722.2.e.l.423.1		6
19.3	odd	18		722.2.e.k.415.1		6
19.4	even	9		722.2.a.l.1.3		3
19.5	even	9		722.2.e.m.245.1		6
19.6	even	9		722.2.c.k.653.1		6
19.7	even	3		722.2.e.m.389.1		6
19.8	odd	6		722.2.e.l.99.1		6
19.9	even	9		722.2.c.k.429.1		6
19.10	odd	18		722.2.c.l.429.3		6
19.11	even	3		722.2.e.b.99.1		6
19.12	odd	6		722.2.e.a.389.1		6
19.13	odd	18		722.2.c.l.653.3		6
19.14	odd	18		722.2.e.a.245.1		6
19.15	odd	18		722.2.a.k.1.1		3
19.16	even	9	inner	38.2.e.a.35.1	yes	6
19.17	even	9		722.2.e.b.423.1		6
19.18	odd	2		722.2.e.k.595.1		6
57.23	odd	18		6498.2.a.bl.1.2		3
57.35	odd	18		342.2.u.c.73.1		6
57.53	even	18		6498.2.a.bq.1.2		3
76.15	even	18		5776.2.a.bo.1.3		3
76.23	odd	18		5776.2.a.bn.1.1		3
76.35	odd	18		304.2.u.c.225.1		6
95.54	even	18		950.2.l.d.301.1		6
95.73	odd	36		950.2.u.b.149.2		12
95.92	odd	36		950.2.u.b.149.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.e.a.25.1	✓	6	1.1	even	1	trivial
38.2.e.a.35.1	yes	6	19.16	even	9	inner
304.2.u.c.177.1		6	4.3	odd	2
304.2.u.c.225.1		6	76.35	odd	18
342.2.u.c.73.1		6	57.35	odd	18
342.2.u.c.253.1		6	3.2	odd	2
722.2.a.k.1.1		3	19.15	odd	18
722.2.a.l.1.3		3	19.4	even	9
722.2.c.k.429.1		6	19.9	even	9
722.2.c.k.653.1		6	19.6	even	9
722.2.c.l.429.3		6	19.10	odd	18
722.2.c.l.653.3		6	19.13	odd	18
722.2.e.a.245.1		6	19.14	odd	18
722.2.e.a.389.1		6	19.12	odd	6
722.2.e.b.99.1		6	19.11	even	3
722.2.e.b.423.1		6	19.17	even	9
722.2.e.k.415.1		6	19.3	odd	18
722.2.e.k.595.1		6	19.18	odd	2
722.2.e.l.99.1		6	19.8	odd	6
722.2.e.l.423.1		6	19.2	odd	18
722.2.e.m.245.1		6	19.5	even	9
722.2.e.m.389.1		6	19.7	even	3
950.2.l.d.101.1		6	5.4	even	2
950.2.l.d.301.1		6	95.54	even	18
950.2.u.b.149.1		12	95.92	odd	36
950.2.u.b.149.2		12	95.73	odd	36
950.2.u.b.899.1		12	5.3	odd	4
950.2.u.b.899.2		12	5.2	odd	4
5776.2.a.bn.1.1		3	76.23	odd	18
5776.2.a.bo.1.3		3	76.15	even	18
6498.2.a.bl.1.2		3	57.23	odd	18
6498.2.a.bq.1.2		3	57.53	even	18

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(-1.43969 - 0.524005i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.347296 + 1.96962i) q^{5} +(-1.43969 + 0.524005i) q^{6} +(-1.34730 + 2.33359i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.500000 - 0.419550i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(-1.43969 - 0.524005i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.347296 + 1.96962i) q^{5} +(-1.43969 + 0.524005i) q^{6} +(-1.34730 + 2.33359i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.500000 - 0.419550i) q^{9} +(1.53209 + 1.28558i) q^{10} +(-1.59240 - 2.75811i) q^{11} +(-0.766044 + 1.32683i) q^{12} +(5.41147 - 1.96962i) q^{13} +(0.467911 + 2.65366i) q^{14} +(0.532089 - 3.01763i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-4.99273 + 4.18939i) q^{17} -0.652704 q^{18} +(2.82635 - 3.31839i) q^{19} +2.00000 q^{20} +(3.16250 - 2.65366i) q^{21} +(-2.99273 - 1.08926i) q^{22} +(-0.120615 + 0.684040i) q^{23} +(0.266044 + 1.50881i) q^{24} +(0.939693 - 0.342020i) q^{25} +(2.87939 - 4.98724i) q^{26} +(2.79813 + 4.84651i) q^{27} +(2.06418 + 1.73205i) q^{28} +(-2.16250 - 1.81456i) q^{29} +(-1.53209 - 2.65366i) q^{30} +(-1.22668 + 2.12467i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(0.847296 + 4.80526i) q^{33} +(-1.13176 + 6.41852i) q^{34} +(-5.06418 - 1.84321i) q^{35} +(-0.500000 + 0.419550i) q^{36} -4.36959 q^{37} +(0.0320889 - 4.35878i) q^{38} -8.82295 q^{39} +(1.53209 - 1.28558i) q^{40} +(0.326352 + 0.118782i) q^{41} +(0.716881 - 4.06564i) q^{42} +(1.05303 + 5.97205i) q^{43} +(-2.99273 + 1.08926i) q^{44} +(0.652704 - 1.13052i) q^{45} +(0.347296 + 0.601535i) q^{46} +(6.04189 + 5.06975i) q^{47} +(1.17365 + 0.984808i) q^{48} +(-0.130415 - 0.225885i) q^{49} +(0.500000 - 0.866025i) q^{50} +(9.38326 - 3.41523i) q^{51} +(-1.00000 - 5.67128i) q^{52} +(1.42602 - 8.08737i) q^{53} +(5.25877 + 1.91404i) q^{54} +(4.87939 - 4.09429i) q^{55} +2.69459 q^{56} +(-5.80793 + 3.29644i) q^{57} -2.82295 q^{58} +(0.439693 - 0.368946i) q^{59} +(-2.87939 - 1.04801i) q^{60} +(0.509800 - 2.89122i) q^{61} +(0.426022 + 2.41609i) q^{62} +(1.65270 - 0.601535i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(5.75877 + 9.97448i) q^{65} +(3.73783 + 3.13641i) q^{66} +(-3.79813 - 3.18701i) q^{67} +(3.25877 + 5.64436i) q^{68} +(0.532089 - 0.921605i) q^{69} +(-5.06418 + 1.84321i) q^{70} +(-1.46791 - 8.32494i) q^{71} +(-0.113341 + 0.642788i) q^{72} +(-14.8157 - 5.39246i) q^{73} +(-3.34730 + 2.80872i) q^{74} -1.53209 q^{75} +(-2.77719 - 3.35965i) q^{76} +8.58172 q^{77} +(-6.75877 + 5.67128i) q^{78} +(8.51754 + 3.10013i) q^{79} +(0.347296 - 1.96962i) q^{80} +(-1.14883 - 6.51536i) q^{81} +(0.326352 - 0.118782i) q^{82} +(-4.23783 + 7.34013i) q^{83} +(-2.06418 - 3.57526i) q^{84} +(-9.98545 - 8.37879i) q^{85} +(4.64543 + 3.89798i) q^{86} +(2.16250 + 3.74557i) q^{87} +(-1.59240 + 2.75811i) q^{88} +(-7.27244 + 2.64695i) q^{89} +(-0.226682 - 1.28558i) q^{90} +(-2.69459 + 15.2818i) q^{91} +(0.652704 + 0.237565i) q^{92} +(2.87939 - 2.41609i) q^{93} +7.88713 q^{94} +(7.51754 + 4.41436i) q^{95} +1.53209 q^{96} +(-0.266044 + 0.223238i) q^{97} +(-0.245100 - 0.0892091i) q^{98} +(-0.360967 + 2.04715i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} - 3 q^{6} - 6 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^3 - 3 * q^6 - 6 * q^7 - 3 * q^8 - 3 * q^9	\( 6 q - 3 q^{3} - 3 q^{6} - 6 q^{7} - 3 q^{8} - 3 q^{9} - 6 q^{11} + 12 q^{13} + 12 q^{14} - 6 q^{15} - 12 q^{17} - 6 q^{18} + 18 q^{19} + 12 q^{20} + 24 q^{21} - 12 q^{23} - 3 q^{24} + 6 q^{26} + 3 q^{27} - 6 q^{28} - 18 q^{29} + 6 q^{31} + 3 q^{33} - 12 q^{34} - 12 q^{35} - 3 q^{36} - 12 q^{37} - 9 q^{38} - 12 q^{39} + 3 q^{41} - 12 q^{42} - 6 q^{43} + 6 q^{45} + 30 q^{47} + 6 q^{48} - 15 q^{49} + 3 q^{50} + 21 q^{51} - 6 q^{52} + 24 q^{53} + 9 q^{54} + 18 q^{55} + 12 q^{56} - 24 q^{57} + 24 q^{58} - 3 q^{59} - 6 q^{60} + 6 q^{61} + 18 q^{62} + 12 q^{63} - 3 q^{64} + 12 q^{65} + 3 q^{66} - 9 q^{67} - 3 q^{68} - 6 q^{69} - 12 q^{70} - 18 q^{71} + 6 q^{72} - 30 q^{73} - 18 q^{74} - 6 q^{76} - 12 q^{77} - 18 q^{78} + 6 q^{79} - 33 q^{81} + 3 q^{82} - 6 q^{83} + 6 q^{84} - 24 q^{85} + 12 q^{86} + 18 q^{87} - 6 q^{88} + 12 q^{90} - 12 q^{91} + 6 q^{92} + 6 q^{93} - 12 q^{94} + 3 q^{97} + 21 q^{99}+O(q^{100}) \) 6 * q - 3 * q^3 - 3 * q^6 - 6 * q^7 - 3 * q^8 - 3 * q^9 - 6 * q^11 + 12 * q^13 + 12 * q^14 - 6 * q^15 - 12 * q^17 - 6 * q^18 + 18 * q^19 + 12 * q^20 + 24 * q^21 - 12 * q^23 - 3 * q^24 + 6 * q^26 + 3 * q^27 - 6 * q^28 - 18 * q^29 + 6 * q^31 + 3 * q^33 - 12 * q^34 - 12 * q^35 - 3 * q^36 - 12 * q^37 - 9 * q^38 - 12 * q^39 + 3 * q^41 - 12 * q^42 - 6 * q^43 + 6 * q^45 + 30 * q^47 + 6 * q^48 - 15 * q^49 + 3 * q^50 + 21 * q^51 - 6 * q^52 + 24 * q^53 + 9 * q^54 + 18 * q^55 + 12 * q^56 - 24 * q^57 + 24 * q^58 - 3 * q^59 - 6 * q^60 + 6 * q^61 + 18 * q^62 + 12 * q^63 - 3 * q^64 + 12 * q^65 + 3 * q^66 - 9 * q^67 - 3 * q^68 - 6 * q^69 - 12 * q^70 - 18 * q^71 + 6 * q^72 - 30 * q^73 - 18 * q^74 - 6 * q^76 - 12 * q^77 - 18 * q^78 + 6 * q^79 - 33 * q^81 + 3 * q^82 - 6 * q^83 + 6 * q^84 - 24 * q^85 + 12 * q^86 + 18 * q^87 - 6 * q^88 + 12 * q^90 - 12 * q^91 + 6 * q^92 + 6 * q^93 - 12 * q^94 + 3 * q^97 + 21 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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