LMFDB - Embedded newform 38.2.e.a.23.1

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			23.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	38.23
Dual form			38.2.e.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{2} +(-0.326352 - 1.85083i) q^{3} +(0.766044 + 0.642788i) q^{4} +(1.53209 - 1.28558i) q^{5} +(-0.326352 + 1.85083i) q^{6} +(-2.53209 + 4.38571i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.500000 + 0.181985i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.326352 - 1.85083i) q^{3} +(0.766044 + 0.642788i) q^{4} +(1.53209 - 1.28558i) q^{5} +(-0.326352 + 1.85083i) q^{6} +(-2.53209 + 4.38571i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.500000 + 0.181985i) q^{9} +(-1.87939 + 0.684040i) q^{10} +(0.705737 + 1.22237i) q^{11} +(0.939693 - 1.62760i) q^{12} +(-0.226682 + 1.28558i) q^{13} +(3.87939 - 3.25519i) q^{14} +(-2.87939 - 2.41609i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-2.24510 - 0.817150i) q^{17} +0.532089 q^{18} +(2.23396 - 3.74292i) q^{19} +2.00000 q^{20} +(8.94356 + 3.25519i) q^{21} +(-0.245100 - 1.39003i) q^{22} +(-2.34730 - 1.96962i) q^{23} +(-1.43969 + 1.20805i) q^{24} +(-0.173648 + 0.984808i) q^{25} +(0.652704 - 1.13052i) q^{26} +(-2.31908 - 4.01676i) q^{27} +(-4.75877 + 1.73205i) q^{28} +(-7.94356 + 2.89122i) q^{29} +(1.87939 + 3.25519i) q^{30} +(-0.184793 + 0.320070i) q^{31} +(0.173648 - 0.984808i) q^{32} +(2.03209 - 1.70513i) q^{33} +(1.83022 + 1.53574i) q^{34} +(1.75877 + 9.97448i) q^{35} +(-0.500000 - 0.181985i) q^{36} +4.82295 q^{37} +(-3.37939 + 2.75314i) q^{38} +2.45336 q^{39} +(-1.87939 - 0.684040i) q^{40} +(-0.266044 - 1.50881i) q^{41} +(-7.29086 - 6.11776i) q^{42} +(-0.581252 + 0.487728i) q^{43} +(-0.245100 + 1.39003i) q^{44} +(-0.532089 + 0.921605i) q^{45} +(1.53209 + 2.65366i) q^{46} +(9.59627 - 3.49276i) q^{47} +(1.76604 - 0.642788i) q^{48} +(-9.32295 - 16.1478i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-0.779715 + 4.42198i) q^{51} +(-1.00000 + 0.839100i) q^{52} +(1.28312 + 1.07666i) q^{53} +(0.805407 + 4.56769i) q^{54} +(2.65270 + 0.965505i) q^{55} +5.06418 q^{56} +(-7.65657 - 2.91317i) q^{57} +8.45336 q^{58} +(-0.673648 - 0.245188i) q^{59} +(-0.652704 - 3.70167i) q^{60} +(7.47565 + 6.27282i) q^{61} +(0.283119 - 0.237565i) q^{62} +(0.467911 - 2.65366i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(1.30541 + 2.26103i) q^{65} +(-2.49273 + 0.907278i) q^{66} +(1.31908 - 0.480105i) q^{67} +(-1.19459 - 2.06910i) q^{68} +(-2.87939 + 4.98724i) q^{69} +(1.75877 - 9.97448i) q^{70} +(-4.87939 + 4.09429i) q^{71} +(0.407604 + 0.342020i) q^{72} +(-0.791737 - 4.49016i) q^{73} +(-4.53209 - 1.64955i) q^{74} +1.87939 q^{75} +(4.11721 - 1.43128i) q^{76} -7.14796 q^{77} +(-2.30541 - 0.839100i) q^{78} +(-0.389185 - 2.20718i) q^{79} +(1.53209 + 1.28558i) q^{80} +(-7.90033 + 6.62916i) q^{81} +(-0.266044 + 1.50881i) q^{82} +(1.99273 - 3.45150i) q^{83} +(4.75877 + 8.24243i) q^{84} +(-4.49020 + 1.63430i) q^{85} +(0.713011 - 0.259515i) q^{86} +(7.94356 + 13.7587i) q^{87} +(0.705737 - 1.22237i) q^{88} +(-1.84864 + 10.4842i) q^{89} +(0.815207 - 0.684040i) q^{90} +(-5.06418 - 4.24935i) q^{91} +(-0.532089 - 3.01763i) q^{92} +(0.652704 + 0.237565i) q^{93} -10.2121 q^{94} +(-1.38919 - 8.60640i) q^{95} -1.87939 q^{96} +(1.43969 + 0.524005i) q^{97} +(3.23783 + 18.3626i) q^{98} +(-0.575322 - 0.482753i) 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 $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$3$	−0.326352	−	1.85083i	−0.188419	−	1.06858i	−0.921483	−	0.388419i	$-0.873021\pi$
$3$	−0.326352	−	1.85083i	−0.188419	−	1.06858i	0.733064	−	0.680160i	$-0.238090\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	1.53209	−	1.28558i	0.685171	−	0.574927i	−0.232341	−	0.972634i	$-0.574639\pi$
$5$	1.53209	−	1.28558i	0.685171	−	0.574927i	0.917512	+	0.397708i	$0.130194\pi$
$6$	−0.326352	+	1.85083i	−0.133233	+	0.755599i
$7$	−2.53209	+	4.38571i	−0.957040	+	1.65764i	−0.227410	+	0.973799i	$0.573026\pi$
$7$	−2.53209	+	4.38571i	−0.957040	+	1.65764i	−0.729630	+	0.683842i	$0.760308\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−0.500000	+	0.181985i	−0.166667	+	0.0606617i
$10$	−1.87939	+	0.684040i	−0.594314	+	0.216313i
$11$	0.705737	+	1.22237i	0.212788	+	0.368559i	0.952586	−	0.304270i	$-0.0984124\pi$
$11$	0.705737	+	1.22237i	0.212788	+	0.368559i	−0.739798	+	0.672829i	$0.765079\pi$
$12$	0.939693	−	1.62760i	0.271266	−	0.469846i
$13$	−0.226682	+	1.28558i	−0.0628702	+	0.356554i	0.937102	+	0.349056i	$0.113498\pi$
$13$	−0.226682	+	1.28558i	−0.0628702	+	0.356554i	−0.999972	+	0.00749804i	$0.997613\pi$
$14$	3.87939	−	3.25519i	1.03681	−	0.869986i
$15$	−2.87939	−	2.41609i	−0.743454	−	0.623832i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−2.24510	−	0.817150i	−0.544517	−	0.198188i	0.0550919	−	0.998481i	$-0.482455\pi$
$17$	−2.24510	−	0.817150i	−0.544517	−	0.198188i	−0.599609	+	0.800293i	$0.704677\pi$
$18$	0.532089			0.125415
$19$	2.23396	−	3.74292i	0.512505	−	0.858685i
$19$	2.23396	−	3.74292i	0.512505	−	0.858685i
$20$	2.00000			0.447214
$21$	8.94356	+	3.25519i	1.95165	+	0.710341i
$22$	−0.245100	−	1.39003i	−0.0522555	−	0.296356i
$23$	−2.34730	−	1.96962i	−0.489445	−	0.410693i	0.364382	−	0.931249i	$-0.381280\pi$
$23$	−2.34730	−	1.96962i	−0.489445	−	0.410693i	−0.853827	+	0.520556i	$0.825725\pi$
$24$	−1.43969	+	1.20805i	−0.293876	+	0.246591i
$25$	−0.173648	+	0.984808i	−0.0347296	+	0.196962i
$26$	0.652704	−	1.13052i	0.128006	−	0.221712i
$27$	−2.31908	−	4.01676i	−0.446307	−	0.773026i
$28$	−4.75877	+	1.73205i	−0.899323	+	0.327327i
$29$	−7.94356	+	2.89122i	−1.47508	+	0.536886i	−0.949475	−	0.313841i	$-0.898384\pi$
$29$	−7.94356	+	2.89122i	−1.47508	+	0.536886i	−0.525607	+	0.850727i	$0.676162\pi$
$30$	1.87939	+	3.25519i	0.343127	+	0.594314i
$31$	−0.184793	+	0.320070i	−0.0331897	+	0.0574863i	−0.882143	−	0.470981i	$-0.843900\pi$
$31$	−0.184793	+	0.320070i	−0.0331897	+	0.0574863i	0.848953	+	0.528468i	$0.177233\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$	2.03209	−	1.70513i	0.353741	−	0.296824i
$34$	1.83022	+	1.53574i	0.313881	+	0.263377i
$35$	1.75877	+	9.97448i	0.297286	+	1.68600i
$36$	−0.500000	−	0.181985i	−0.0833333	−	0.0303309i
$37$	4.82295			0.792888			0.396444	−	0.918059i	$-0.370244\pi$
$37$	4.82295			0.792888			0.396444	+	0.918059i	$0.370244\pi$
$38$	−3.37939	+	2.75314i	−0.548209	+	0.446618i
$39$	2.45336			0.392853
$40$	−1.87939	−	0.684040i	−0.297157	−	0.108156i
$41$	−0.266044	−	1.50881i	−0.0415492	−	0.235637i	0.956960	−	0.290220i	$-0.0937283\pi$
$41$	−0.266044	−	1.50881i	−0.0415492	−	0.235637i	−0.998509	+	0.0545825i	$0.982617\pi$
$42$	−7.29086	−	6.11776i	−1.12500	−	0.943990i
$43$	−0.581252	+	0.487728i	−0.0886401	+	0.0743779i	−0.686031	−	0.727572i	$-0.740649\pi$
$43$	−0.581252	+	0.487728i	−0.0886401	+	0.0743779i	0.597391	+	0.801950i	$0.296204\pi$
$44$	−0.245100	+	1.39003i	−0.0369502	+	0.209555i
$45$	−0.532089	+	0.921605i	−0.0793191	+	0.137385i
$46$	1.53209	+	2.65366i	0.225894	+	0.391260i
$47$	9.59627	−	3.49276i	1.39976	−	0.509471i	0.471652	−	0.881785i	$-0.343658\pi$
$47$	9.59627	−	3.49276i	1.39976	−	0.509471i	0.928107	+	0.372314i	$0.121435\pi$
$48$	1.76604	−	0.642788i	0.254907	−	0.0927784i
$49$	−9.32295	−	16.1478i	−1.33185	−	2.30683i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−0.779715	+	4.42198i	−0.109182	+	0.619202i
$52$	−1.00000	+	0.839100i	−0.138675	+	0.116362i
$53$	1.28312	+	1.07666i	0.176250	+	0.147891i	0.726645	−	0.687013i	$-0.241078\pi$
$53$	1.28312	+	1.07666i	0.176250	+	0.147891i	−0.550395	+	0.834904i	$0.685523\pi$
$54$	0.805407	+	4.56769i	0.109602	+	0.621584i
$55$	2.65270	+	0.965505i	0.357690	+	0.130189i
$56$	5.06418			0.676729
$57$	−7.65657	−	2.91317i	−1.01414	−	0.385859i
$58$	8.45336			1.10998
$59$	−0.673648	−	0.245188i	−0.0877015	−	0.0319207i	0.297797	−	0.954629i	$-0.403748\pi$
$59$	−0.673648	−	0.245188i	−0.0877015	−	0.0319207i	−0.385498	+	0.922709i	$0.625970\pi$
$60$	−0.652704	−	3.70167i	−0.0842637	−	0.477883i
$61$	7.47565	+	6.27282i	0.957159	+	0.803152i	0.980489	−	0.196576i	$-0.0629822\pi$
$61$	7.47565	+	6.27282i	0.957159	+	0.803152i	−0.0233295	+	0.999728i	$0.507427\pi$
$62$	0.283119	−	0.237565i	0.0359561	−	0.0301707i
$63$	0.467911	−	2.65366i	0.0589513	−	0.334329i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	1.30541	+	2.26103i	0.161916	+	0.280446i
$66$	−2.49273	+	0.907278i	−0.306833	+	0.111678i
$67$	1.31908	−	0.480105i	0.161151	−	0.0586542i	−0.260185	−	0.965559i	$-0.583784\pi$
$67$	1.31908	−	0.480105i	0.161151	−	0.0586542i	0.421336	+	0.906905i	$0.361561\pi$
$68$	−1.19459	−	2.06910i	−0.144866	−	0.250915i
$69$	−2.87939	+	4.98724i	−0.346637	+	0.600393i
$70$	1.75877	−	9.97448i	0.210213	−	1.19218i
$71$	−4.87939	+	4.09429i	−0.579076	+	0.485903i	−0.884644	−	0.466268i	$-0.845598\pi$
$71$	−4.87939	+	4.09429i	−0.579076	+	0.485903i	0.305567	+	0.952171i	$0.401154\pi$
$72$	0.407604	+	0.342020i	0.0480366	+	0.0403075i
$73$	−0.791737	−	4.49016i	−0.0926658	−	0.525534i	−0.995438	−	0.0954141i	$-0.969582\pi$
$73$	−0.791737	−	4.49016i	−0.0926658	−	0.525534i	0.902772	−	0.430120i	$-0.141529\pi$
$74$	−4.53209	−	1.64955i	−0.526845	−	0.191756i
$75$	1.87939			0.217013
$76$	4.11721	−	1.43128i	0.472277	−	0.164179i
$77$	−7.14796			−0.814585
$78$	−2.30541	−	0.839100i	−0.261036	−	0.0950093i
$79$	−0.389185	−	2.20718i	−0.0437868	−	0.248327i	0.955056	−	0.296426i	$-0.0957948\pi$
$79$	−0.389185	−	2.20718i	−0.0437868	−	0.248327i	−0.998843	+	0.0480989i	$0.984684\pi$
$80$	1.53209	+	1.28558i	0.171293	+	0.143732i
$81$	−7.90033	+	6.62916i	−0.877814	+	0.736574i
$82$	−0.266044	+	1.50881i	−0.0293797	+	0.166621i
$83$	1.99273	−	3.45150i	0.218730	−	0.378852i	−0.735690	−	0.677319i	$-0.763142\pi$
$83$	1.99273	−	3.45150i	0.218730	−	0.378852i	0.954420	+	0.298467i	$0.0964752\pi$
$84$	4.75877	+	8.24243i	0.519224	+	0.899323i
$85$	−4.49020	+	1.63430i	−0.487031	+	0.177265i
$86$	0.713011	−	0.259515i	0.0768860	−	0.0279842i
$87$	7.94356	+	13.7587i	0.851639	+	1.47508i
$88$	0.705737	−	1.22237i	0.0752318	−	0.130305i
$89$	−1.84864	+	10.4842i	−0.195956	+	1.11132i	0.715096	+	0.699026i	$0.246383\pi$
$89$	−1.84864	+	10.4842i	−0.195956	+	1.11132i	−0.911051	+	0.412293i	$0.864728\pi$
$90$	0.815207	−	0.684040i	0.0859304	−	0.0721042i
$91$	−5.06418	−	4.24935i	−0.530870	−	0.445453i
$92$	−0.532089	−	3.01763i	−0.0554741	−	0.314609i
$93$	0.652704	+	0.237565i	0.0676822	+	0.0246343i
$94$	−10.2121			−1.05330
$95$	−1.38919	−	8.60640i	−0.142527	−	0.882998i
$96$	−1.87939			−0.191814
$97$	1.43969	+	0.524005i	0.146179	+	0.0532047i	0.414073	−	0.910244i	$-0.364106\pi$
$97$	1.43969	+	0.524005i	0.146179	+	0.0532047i	−0.267895	+	0.963448i	$0.586328\pi$
$98$	3.23783	+	18.3626i	0.327070	+	1.85491i
$99$	−0.575322	−	0.482753i	−0.0578220	−	0.0485185i
$100$	−0.766044	+	0.642788i	−0.0766044	+	0.0642788i
$101$	1.53209	−	8.68891i	0.152449	−	0.864579i	−0.808633	−	0.588314i	$-0.799792\pi$
$101$	1.53209	−	8.68891i	0.152449	−	0.864579i	0.961081	−	0.276265i	$-0.0890968\pi$
$102$	2.24510	−	3.88863i	0.222298	−	0.385031i
$103$	3.57398	+	6.19031i	0.352155	+	0.609950i	0.986627	−	0.162996i	$-0.0521158\pi$
$103$	3.57398	+	6.19031i	0.352155	+	0.609950i	−0.634472	+	0.772946i	$0.718782\pi$
$104$	1.22668	−	0.446476i	0.120286	−	0.0437805i
$105$	17.8871	−	6.51038i	1.74560	−	0.635348i
$106$	−0.837496	−	1.45059i	−0.0813448	−	0.140893i
$107$	4.68479	−	8.11430i	0.452896	−	0.784439i	−0.545669	−	0.838001i	$-0.683724\pi$
$107$	4.68479	−	8.11430i	0.452896	−	0.784439i	0.998565	+	0.0535622i	$0.0170576\pi$
$108$	0.805407	−	4.56769i	0.0775004	−	0.439526i
$109$	8.47565	−	7.11192i	0.811820	−	0.681198i	−0.139221	−	0.990261i	$-0.544460\pi$
$109$	8.47565	−	7.11192i	0.811820	−	0.681198i	0.951041	+	0.309063i	$0.100015\pi$
$110$	−2.16250	−	1.81456i	−0.206187	−	0.173011i
$111$	−1.57398	−	8.92647i	−0.149395	−	0.847263i
$112$	−4.75877	−	1.73205i	−0.449662	−	0.163663i
$113$	−13.2986			−1.25103			−0.625514	−	0.780213i	$-0.715110\pi$
$113$	−13.2986			−1.25103			−0.625514	+	0.780213i	$0.715110\pi$
$114$	6.19846	+	5.35619i	0.580539	+	0.501653i
$115$	−6.12836			−0.571472
$116$	−7.94356	−	2.89122i	−0.737541	−	0.268443i
$117$	−0.120615	−	0.684040i	−0.0111508	−	0.0632395i
$118$	0.549163	+	0.460802i	0.0505546	+	0.0424203i
$119$	9.26857	−	7.77725i	0.849648	−	0.712940i
$120$	−0.652704	+	3.70167i	−0.0595834	+	0.337914i
$121$	4.50387	−	7.80093i	0.409443	−	0.709176i
$122$	−4.87939	−	8.45134i	−0.441759	−	0.765149i
$123$	−2.70574	+	0.984808i	−0.243968	+	0.0887971i
$124$	−0.347296	+	0.126406i	−0.0311881	+	0.0113516i
$125$	6.00000	+	10.3923i	0.536656	+	0.929516i
$126$	−1.34730	+	2.33359i	−0.120027	+	0.207892i
$127$	−0.992259	+	5.62738i	−0.0880488	+	0.499349i	0.908608	+	0.417650i	$0.137146\pi$
$127$	−0.992259	+	5.62738i	−0.0880488	+	0.499349i	−0.996657	+	0.0816999i	$0.973965\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$	1.09240	+	0.916629i	0.0961801	+	0.0807047i
$130$	−0.453363	−	2.57115i	−0.0397626	−	0.225505i
$131$	9.28359	+	3.37895i	0.811111	+	0.295220i	0.714083	−	0.700062i	$-0.246844\pi$
$131$	9.28359	+	3.37895i	0.811111	+	0.295220i	0.0970281	+	0.995282i	$0.469066\pi$
$132$	2.65270			0.230888
$133$	10.7588	+	19.2749i	0.932904	+	1.67134i
$134$	−1.40373			−0.121264
$135$	−8.71688	−	3.17269i	−0.750230	−	0.273061i
$136$	0.414878	+	2.35289i	0.0355755	+	0.201759i
$137$	4.13429	+	3.46908i	0.353216	+	0.296383i	0.802080	−	0.597217i	$-0.203727\pi$
$137$	4.13429	+	3.46908i	0.353216	+	0.296383i	−0.448864	+	0.893600i	$0.648171\pi$
$138$	4.41147	−	3.70167i	0.375530	−	0.315107i
$139$	−0.406260	+	2.30401i	−0.0344585	+	0.195424i	−0.997178	−	0.0750794i	$-0.976079\pi$
$139$	−0.406260	+	2.30401i	−0.0344585	+	0.195424i	0.962719	+	0.270503i	$0.0871901\pi$
$140$	−5.06418	+	8.77141i	−0.428001	+	0.741320i
$141$	−9.59627	−	16.6212i	−0.808151	−	1.39976i
$142$	5.98545	−	2.17853i	0.502288	−	0.182818i
$143$	−1.73143	+	0.630189i	−0.144789	+	0.0526990i
$144$	−0.266044	−	0.460802i	−0.0221704	−	0.0384002i
$145$	−8.45336	+	14.6417i	−0.702014	+	1.21592i
$146$	−0.791737	+	4.49016i	−0.0655246	+	0.371608i
$147$	−26.8444	+	22.5251i	−2.21409	+	1.85784i
$148$	3.69459	+	3.10013i	0.303694	+	0.254829i
$149$	−2.49525	−	14.1513i	−0.204419	−	1.15932i	−0.898351	−	0.439278i	$-0.855234\pi$
$149$	−2.49525	−	14.1513i	−0.204419	−	1.15932i	0.693932	−	0.720040i	$-0.255877\pi$
$150$	−1.76604	−	0.642788i	−0.144197	−	0.0524834i
$151$	−20.8384			−1.69581			−0.847904	−	0.530150i	$-0.822135\pi$
$151$	−20.8384			−1.69581			−0.847904	+	0.530150i	$0.822135\pi$
$152$	−4.35844	−	0.0632028i	−0.353516	−	0.00512642i
$153$	1.27126			0.102775
$154$	6.71688	+	2.44474i	0.541262	+	0.197003i
$155$	0.128356	+	0.727940i	0.0103098	+	0.0584696i
$156$	1.87939	+	1.57699i	0.150471	+	0.126260i
$157$	4.87939	−	4.09429i	0.389417	−	0.326760i	−0.426969	−	0.904266i	$-0.640419\pi$
$157$	4.87939	−	4.09429i	0.389417	−	0.326760i	0.816386	+	0.577506i	$0.195974\pi$
$158$	−0.389185	+	2.20718i	−0.0309619	+	0.175594i
$159$	1.57398	−	2.72621i	0.124825	−	0.216202i
$160$	−1.00000	−	1.73205i	−0.0790569	−	0.136931i
$161$	14.5817	−	5.30731i	1.14920	−	0.418275i
$162$	9.69119	−	3.52730i	0.761412	−	0.277131i
$163$	−2.36571	−	4.09754i	−0.185297	−	0.320944i	0.758380	−	0.651813i	$-0.225991\pi$
$163$	−2.36571	−	4.09754i	−0.185297	−	0.320944i	−0.943677	+	0.330869i	$0.892658\pi$
$164$	0.766044	−	1.32683i	0.0598180	−	0.103608i
$165$	0.921274	−	5.22481i	0.0717211	−	0.406751i
$166$	−3.05303	+	2.56180i	−0.236961	+	0.198834i
$167$	13.2344	+	11.1050i	1.02411	+	0.859331i	0.990138	−	0.140092i	$-0.0447399\pi$
$167$	13.2344	+	11.1050i	1.02411	+	0.859331i	0.0339719	+	0.999423i	$0.489184\pi$
$168$	−1.65270	−	9.37295i	−0.127509	−	0.723139i
$169$	10.6147	+	3.86343i	0.816514	+	0.297187i
$170$	4.77837			0.366484
$171$	−0.435822	+	2.27801i	−0.0333282	+	0.174203i
$172$	−0.758770			−0.0578557
$173$	−17.6878	−	6.43783i	−1.34478	−	0.489459i	−0.433463	−	0.901171i	$-0.642709\pi$
$173$	−17.6878	−	6.43783i	−1.34478	−	0.489459i	−0.911314	+	0.411712i	$0.864931\pi$
$174$	−2.75877	−	15.6458i	−0.209142	−	1.18610i
$175$	−3.87939	−	3.25519i	−0.293254	−	0.246069i
$176$	−1.08125	+	0.907278i	−0.0815024	+	0.0683887i
$177$	−0.233956	+	1.32683i	−0.0175852	+	0.0997305i
$178$	5.32295	−	9.21962i	0.398972	−	0.691039i
$179$	6.91400	+	11.9754i	0.516777	+	0.895083i	0.999810	+	0.0194816i	$0.00620157\pi$
$179$	6.91400	+	11.9754i	0.516777	+	0.895083i	−0.483034	+	0.875602i	$0.660465\pi$
$180$	−1.00000	+	0.363970i	−0.0745356	+	0.0271287i
$181$	−11.5175	+	4.19204i	−0.856092	+	0.311592i	−0.732522	−	0.680744i	$-0.761657\pi$
$181$	−11.5175	+	4.19204i	−0.856092	+	0.311592i	−0.123570	+	0.992336i	$0.539434\pi$
$182$	3.30541	+	5.72513i	0.245013	+	0.424375i
$183$	9.17024	−	15.8833i	0.677884	−	1.17413i
$184$	−0.532089	+	3.01763i	−0.0392261	+	0.222462i
$185$	7.38919	−	6.20026i	0.543264	−	0.455852i
$186$	−0.532089	−	0.446476i	−0.0390147	−	0.0327372i
$187$	−0.585589	−	3.32104i	−0.0428225	−	0.242859i
$188$	9.59627	+	3.49276i	0.699880	+	0.254735i
$189$	23.4884			1.70853
$190$	−1.63816	+	8.56250i	−0.118844	+	0.621189i
$191$	−20.0993			−1.45433			−0.727166	−	0.686462i	$-0.759163\pi$
$191$	−20.0993			−1.45433			−0.727166	+	0.686462i	$0.759163\pi$
$192$	1.76604	+	0.642788i	0.127453	+	0.0463892i
$193$	2.89734	+	16.4316i	0.208555	+	1.18277i	0.891747	+	0.452535i	$0.149480\pi$
$193$	2.89734	+	16.4316i	0.208555	+	1.18277i	−0.683192	+	0.730239i	$0.739409\pi$
$194$	−1.17365	−	0.984808i	−0.0842630	−	0.0707051i
$195$	3.75877	−	3.15398i	0.269171	−	0.225861i
$196$	3.23783	−	18.3626i	0.231273	−	1.31162i
$197$	−6.49525	+	11.2501i	−0.462768	+	0.801537i	−0.999098	−	0.0424714i	$-0.986477\pi$
$197$	−6.49525	+	11.2501i	−0.462768	+	0.801537i	0.536330	+	0.844008i	$0.319810\pi$
$198$	0.375515	+	0.650411i	0.0266867	+	0.0462227i
$199$	−16.1557	+	5.88019i	−1.14525	+	0.416836i	−0.843806	−	0.536649i	$-0.819690\pi$
$199$	−16.1557	+	5.88019i	−1.14525	+	0.416836i	−0.301441	+	0.953485i	$0.597468\pi$
$200$	0.939693	−	0.342020i	0.0664463	−	0.0241845i
$201$	−1.31908	−	2.28471i	−0.0930406	−	0.161151i
$202$	−4.41147	+	7.64090i	−0.310390	+	0.537612i
$203$	7.43376	−	42.1590i	0.521748	−	2.95898i
$204$	−3.43969	+	2.88624i	−0.240827	+	0.202078i
$205$	−2.34730	−	1.96962i	−0.163942	−	0.137564i
$206$	−1.24123	−	7.03936i	−0.0864806	−	0.490456i
$207$	1.53209	+	0.557635i	0.106488	+	0.0387583i
$208$	−1.30541			−0.0905137
$209$	6.15183	+	0.0892091i	0.425531	+	0.00617072i
$210$	−19.0351			−1.31355
$211$	15.1373	+	5.50952i	1.04209	+	0.379291i	0.805673	−	0.592360i	$-0.201804\pi$
$211$	15.1373	+	5.50952i	1.04209	+	0.379291i	0.236420	+	0.971651i	$0.424026\pi$
$212$	0.290859	+	1.64955i	0.0199763	+	0.113291i
$213$	9.17024	+	7.69475i	0.628335	+	0.527236i
$214$	−7.17752	+	6.02265i	−0.490645	+	0.411700i
$215$	−0.263518	+	1.49449i	−0.0179718	+	0.101923i
$216$	−2.31908	+	4.01676i	−0.157793	+	0.273306i
$217$	−0.935822	−	1.62089i	−0.0635278	−	0.110033i
$218$	−10.3969	+	3.78417i	−0.704169	+	0.256296i
$219$	−8.05216	+	2.93075i	−0.544114	+	0.198041i
$220$	1.41147	+	2.44474i	0.0951616	+	0.164825i
$221$	1.55943	−	2.70101i	0.104899	−	0.181690i
$222$	−1.57398	+	8.92647i	−0.105638	+	0.599106i
$223$	3.12836	−	2.62500i	0.209490	−	0.175783i	−0.532005	−	0.846741i	$-0.678561\pi$
$223$	3.12836	−	2.62500i	0.209490	−	0.175783i	0.741495	+	0.670958i	$0.234117\pi$
$224$	3.87939	+	3.25519i	0.259202	+	0.217497i
$225$	−0.0923963	−	0.524005i	−0.00615975	−	0.0349337i
$226$	12.4966	+	4.54839i	0.831261	+	0.302554i
$227$	13.6604			0.906676			0.453338	−	0.891339i	$-0.350233\pi$
$227$	13.6604			0.906676			0.453338	+	0.891339i	$0.350233\pi$
$228$	−3.99273	−	7.15317i	−0.264425	−	0.473730i
$229$	−5.22163			−0.345055			−0.172527	−	0.985005i	$-0.555193\pi$
$229$	−5.22163			−0.345055			−0.172527	+	0.985005i	$0.555193\pi$
$230$	5.75877	+	2.09602i	0.379722	+	0.138208i
$231$	2.33275	+	13.2297i	0.153484	+	0.870449i
$232$	6.47565	+	5.43372i	0.425147	+	0.356741i
$233$	−20.7160	+	17.3828i	−1.35715	+	1.13878i	−0.380300	+	0.924863i	$0.624179\pi$
$233$	−20.7160	+	17.3828i	−1.35715	+	1.13878i	−0.976851	+	0.213921i	$0.931376\pi$
$234$	−0.120615	+	0.684040i	−0.00788483	+	0.0447171i
$235$	10.2121	−	17.6879i	0.666166	−	1.15383i
$236$	−0.358441	−	0.620838i	−0.0233325	−	0.0404131i
$237$	−3.95811	+	1.44063i	−0.257107	+	0.0935793i
$238$	−11.3696	+	4.13819i	−0.736981	+	0.268239i
$239$	0.142903	+	0.247516i	0.00924366	+	0.0160105i	0.870610	−	0.491973i	$-0.163724\pi$
$239$	0.142903	+	0.247516i	0.00924366	+	0.0160105i	−0.861367	+	0.507984i	$0.830391\pi$
$240$	1.87939	−	3.25519i	0.121314	−	0.210122i
$241$	0.538485	−	3.05390i	0.0346869	−	0.196719i	−0.962540	−	0.271139i	$-0.912600\pi$
$241$	0.538485	−	3.05390i	0.0346869	−	0.196719i	0.997227	+	0.0744203i	$0.0237106\pi$
$242$	−6.90033	+	5.79006i	−0.443570	+	0.372199i
$243$	4.18866	+	3.51471i	0.268703	+	0.225468i
$244$	1.69459	+	9.61051i	0.108485	+	0.615250i
$245$	−35.0428	−	12.7545i	−2.23880	−	0.814858i
$246$	2.87939			0.183583
$247$	4.30541	+	3.72037i	0.273947	+	0.236721i
$248$	0.369585			0.0234687
$249$	−7.03849	−	2.56180i	−0.446046	−	0.162347i
$250$	−2.08378	−	11.8177i	−0.131790	−	0.747417i
$251$	−9.69640	−	8.13625i	−0.612032	−	0.513555i	0.283256	−	0.959044i	$-0.408585\pi$
$251$	−9.69640	−	8.13625i	−0.612032	−	0.513555i	−0.895287	+	0.445489i	$0.853030\pi$
$252$	2.06418	−	1.73205i	0.130031	−	0.109109i
$253$	0.751030	−	4.25930i	0.0472168	−	0.267780i
$254$	2.85710	−	4.94864i	0.179270	−	0.310505i
$255$	4.49020	+	7.77725i	0.281187	+	0.487031i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	28.5599	−	10.3950i	1.78152	−	0.648419i	0.781828	−	0.623494i	$-0.214287\pi$
$257$	28.5599	−	10.3950i	1.78152	−	0.648419i	0.999689	−	0.0249253i	$-0.00793478\pi$
$258$	−0.713011	−	1.23497i	−0.0443901	−	0.0768860i
$259$	−12.2121	+	21.1520i	−0.758825	+	1.31432i
$260$	−0.453363	+	2.57115i	−0.0281164	+	0.159456i
$261$	3.44562	−	2.89122i	0.213279	−	0.178962i
$262$	−7.56805	−	6.35035i	−0.467556	−	0.392326i
$263$	3.80335	+	21.5699i	0.234524	+	1.33005i	0.843613	+	0.536952i	$0.180424\pi$
$263$	3.80335	+	21.5699i	0.234524	+	1.33005i	−0.609088	+	0.793102i	$0.708465\pi$
$264$	−2.49273	−	0.907278i	−0.153417	−	0.0558391i
$265$	3.34998			0.205788
$266$	−3.51754	−	21.7922i	−0.215674	−	1.33616i
$267$	20.0077			1.22445
$268$	1.31908	+	0.480105i	0.0805755	+	0.0293271i
$269$	−0.248970	−	1.41198i	−0.0151800	−	0.0860900i	0.976277	−	0.216527i	$-0.0694730\pi$
$269$	−0.248970	−	1.41198i	−0.0151800	−	0.0860900i	−0.991457	+	0.130437i	$0.958362\pi$
$270$	7.10607	+	5.96270i	0.432461	+	0.362878i
$271$	12.3892	−	10.3958i	0.752589	−	0.631498i	−0.183597	−	0.983002i	$-0.558774\pi$
$271$	12.3892	−	10.3958i	0.752589	−	0.631498i	0.936186	+	0.351504i	$0.114330\pi$
$272$	0.414878	−	2.35289i	0.0251557	−	0.142665i
$273$	−6.21213	+	10.7597i	−0.375975	+	0.651209i
$274$	−2.69846	−	4.67388i	−0.163020	−	0.282359i
$275$	−1.32635	+	0.482753i	−0.0799820	+	0.0291111i
$276$	−5.41147	+	1.96962i	−0.325732	+	0.118557i
$277$	−5.55438	−	9.62046i	−0.333730	−	0.578038i	0.649510	−	0.760353i	$-0.274974\pi$
$277$	−5.55438	−	9.62046i	−0.333730	−	0.578038i	−0.983240	+	0.182315i	$0.941641\pi$
$278$	1.16978	−	2.02611i	0.0701586	−	0.121518i
$279$	0.0341483	−	0.193665i	0.00204440	−	0.0115944i
$280$	7.75877	−	6.51038i	0.463675	−	0.389070i
$281$	3.25490	+	2.73119i	0.194171	+	0.162929i	0.734690	−	0.678403i	$-0.237328\pi$
$281$	3.25490	+	2.73119i	0.194171	+	0.162929i	−0.540519	+	0.841332i	$0.681772\pi$
$282$	3.33275	+	18.9010i	0.198462	+	1.12554i
$283$	5.12701	+	1.86608i	0.304769	+	0.110927i	0.489878	−	0.871791i	$-0.337041\pi$
$283$	5.12701	+	1.86608i	0.304769	+	0.110927i	−0.185108	+	0.982718i	$0.559264\pi$
$284$	−6.36959			−0.377965
$285$	−15.4757	+	5.37987i	−0.916699	+	0.318676i
$286$	1.84255			0.108952
$287$	7.29086	+	2.65366i	0.430366	+	0.156640i
$288$	0.0923963	+	0.524005i	0.00544450	+	0.0308773i
$289$	−8.65002	−	7.25822i	−0.508824	−	0.426954i
$290$	12.9513	−	10.8674i	0.760527	−	0.638158i
$291$	0.500000	−	2.83564i	0.0293105	−	0.166228i
$292$	2.27972	−	3.94858i	0.133410	−	0.231073i
$293$	−8.90673	−	15.4269i	−0.520337	−	0.901249i	−0.999720	−	0.0236440i	$-0.992473\pi$
$293$	−8.90673	−	15.4269i	−0.520337	−	0.901249i	0.479384	−	0.877605i	$-0.340860\pi$
$294$	32.9295	−	11.9854i	1.92049	−	0.699000i
$295$	−1.34730	+	0.490376i	−0.0784426	+	0.0285508i
$296$	−2.41147	−	4.17680i	−0.140164	−	0.242771i
$297$	3.27332	−	5.66955i	0.189937	−	0.328981i
$298$	−2.49525	+	14.1513i	−0.144546	+	0.819762i
$299$	3.06418	−	2.57115i	0.177206	−	0.148693i
$300$	1.43969	+	1.20805i	0.0831207	+	0.0697465i
$301$	−0.667252	−	3.78417i	−0.0384597	−	0.218116i
$302$	19.5817	+	7.12716i	1.12680	+	0.410122i
$303$	−16.5817			−0.952595
$304$	4.07398	+	1.55007i	0.233659	+	0.0889024i
$305$	19.5175			1.11757
$306$	−1.19459	−	0.434796i	−0.0682903	−	0.0248556i
$307$	−4.97653	−	28.2233i	−0.284026	−	1.61079i	−0.708746	−	0.705464i	$-0.750739\pi$
$307$	−4.97653	−	28.2233i	−0.284026	−	1.61079i	0.424720	−	0.905325i	$-0.360373\pi$
$308$	−5.47565	−	4.59462i	−0.312004	−	0.261803i
$309$	10.2909	−	8.63506i	0.585427	−	0.491231i
$310$	0.128356	−	0.727940i	0.00729011	−	0.0413442i
$311$	−7.90673	+	13.6949i	−0.448349	+	0.776564i	−0.998279	−	0.0586473i	$-0.981321\pi$
$311$	−7.90673	+	13.6949i	−0.448349	+	0.776564i	0.549929	+	0.835211i	$0.314655\pi$
$312$	−1.22668	−	2.12467i	−0.0694472	−	0.120286i
$313$	−12.3478	+	4.49422i	−0.697937	+	0.254028i	−0.666530	−	0.745478i	$-0.732221\pi$
$313$	−12.3478	+	4.49422i	−0.697937	+	0.254028i	−0.0314071	+	0.999507i	$0.509999\pi$
$314$	−5.98545	+	2.17853i	−0.337779	+	0.122941i
$315$	−2.69459	−	4.66717i	−0.151823	−	0.262965i
$316$	1.12061	−	1.94096i	0.0630395	−	0.109188i
$317$	−3.71688	+	21.0795i	−0.208761	+	1.18394i	0.682650	+	0.730746i	$0.260827\pi$
$317$	−3.71688	+	21.0795i	−0.208761	+	1.18394i	−0.891411	+	0.453196i	$0.850284\pi$
$318$	−2.41147	+	2.02347i	−0.135229	+	0.113470i
$319$	−9.14022	−	7.66955i	−0.511754	−	0.429412i
$320$	0.347296	+	1.96962i	0.0194145	+	0.110105i
$321$	−16.5471	−	6.02265i	−0.923569	−	0.336152i
$322$	−15.5175			−0.864759
$323$	−8.07398	+	6.57775i	−0.449248	+	0.365996i
$324$	−10.3131			−0.572953
$325$	−1.22668	−	0.446476i	−0.0680441	−	0.0247660i
$326$	0.821604	+	4.65955i	0.0455044	+	0.258069i
$327$	−15.9290	−	13.3660i	−0.880877	−	0.739143i
$328$	−1.17365	+	0.984808i	−0.0648039	+	0.0543769i
$329$	−8.98040	+	50.9304i	−0.495105	+	2.80788i
$330$	−2.65270	+	4.59462i	−0.146027	+	0.252925i
$331$	12.6989	+	21.9952i	0.697996	+	1.20897i	0.969160	+	0.246432i	$0.0792582\pi$
$331$	12.6989	+	21.9952i	0.697996	+	1.20897i	−0.271164	+	0.962533i	$0.587409\pi$
$332$	3.74510	−	1.36310i	0.205539	−	0.0748101i
$333$	−2.41147	+	0.877705i	−0.132148	+	0.0480979i
$334$	−8.63816	−	14.9617i	−0.472659	−	0.818669i
$335$	1.40373	−	2.43134i	0.0766941	−	0.132838i
$336$	−1.65270	+	9.37295i	−0.0901624	+	0.511336i
$337$	20.2062	−	16.9550i	1.10070	−	0.923599i	0.103230	−	0.994658i	$-0.467082\pi$
$337$	20.2062	−	16.9550i	1.10070	−	0.923599i	0.997472	+	0.0710588i	$0.0226378\pi$
$338$	−8.65317	−	7.26087i	−0.470670	−	0.394939i
$339$	4.34002	+	24.6135i	0.235718	+	1.33682i
$340$	−4.49020	−	1.63430i	−0.243515	−	0.0886323i
$341$	−0.521660			−0.0282495
$342$	1.18866	−	1.99157i	0.0642755	−	0.107692i
$343$	58.9769			3.18445
$344$	0.713011	+	0.259515i	0.0384430	+	0.0139921i
$345$	2.00000	+	11.3426i	0.107676	+	0.610663i
$346$	14.4192	+	12.0992i	0.775182	+	0.650455i
$347$	−19.6348	+	16.4755i	−1.05405	+	0.884452i	−0.993514	−	0.113714i	$-0.963725\pi$
$347$	−19.6348	+	16.4755i	−1.05405	+	0.884452i	−0.0605352	+	0.998166i	$0.519281\pi$
$348$	−2.75877	+	15.6458i	−0.147886	+	0.838701i
$349$	2.92127	−	5.05980i	0.156372	−	0.270845i	−0.777186	−	0.629271i	$-0.783353\pi$
$349$	2.92127	−	5.05980i	0.156372	−	0.270845i	0.933558	+	0.358427i	$0.116687\pi$
$350$	2.53209	+	4.38571i	0.135346	+	0.234426i
$351$	5.68954	−	2.07082i	0.303685	−	0.110532i
$352$	1.32635	−	0.482753i	0.0706948	−	0.0257308i
$353$	11.2049	+	19.4074i	0.596375	+	1.03295i	0.993351	+	0.115122i	$0.0367260\pi$
$353$	11.2049	+	19.4074i	0.596375	+	1.03295i	−0.396977	+	0.917829i	$0.629941\pi$
$354$	0.673648	−	1.16679i	0.0358040	−	0.0620143i
$355$	−2.21213	+	12.5456i	−0.117408	+	0.665853i
$356$	−8.15523	+	6.84305i	−0.432226	+	0.362681i
$357$	−17.4192	−	14.6165i	−0.921923	−	0.773585i
$358$	−2.40121	−	13.6179i	−0.126908	−	0.719730i
$359$	−9.03684	−	3.28914i	−0.476946	−	0.173594i	0.0923503	−	0.995727i	$-0.470562\pi$
$359$	−9.03684	−	3.28914i	−0.476946	−	0.173594i	−0.569296	+	0.822132i	$0.692784\pi$
$360$	1.06418			0.0560871
$361$	−9.01889	−	16.7230i	−0.474678	−	0.880159i
$362$	12.2567			0.644198
$363$	−15.9081	−	5.79006i	−0.834957	−	0.303900i
$364$	−1.14796	−	6.51038i	−0.0601692	−	0.341237i
$365$	−6.98545	−	5.86149i	−0.365635	−	0.306804i
$366$	−14.0496	+	11.7890i	−0.734386	+	0.616223i
$367$	4.05644	−	23.0052i	0.211744	−	1.20086i	−0.674723	−	0.738071i	$-0.735737\pi$
$367$	4.05644	−	23.0052i	0.211744	−	1.20086i	0.886468	−	0.462791i	$-0.153152\pi$
$368$	1.53209	−	2.65366i	0.0798657	−	0.138331i
$369$	0.407604	+	0.705990i	0.0212190	+	0.0367524i
$370$	−9.06418	+	3.29909i	−0.471224	+	0.171512i
$371$	−7.97090	+	2.90117i	−0.413829	+	0.150621i
$372$	0.347296	+	0.601535i	0.0180065	+	0.0311881i
$373$	12.9709	−	22.4663i	0.671608	−	1.16326i	−0.305840	−	0.952083i	$-0.598937\pi$
$373$	12.9709	−	22.4663i	0.671608	−	1.16326i	0.977448	−	0.211176i	$-0.0677294\pi$
$374$	−0.585589	+	3.32104i	−0.0302801	+	0.171727i
$375$	17.2763	−	14.4965i	0.892145	−	0.748598i
$376$	−7.82295	−	6.56423i	−0.403438	−	0.338524i
$377$	−1.91622	−	10.8674i	−0.0986904	−	0.559701i
$378$	−22.0719	−	8.03352i	−1.13526	−	0.413200i
$379$	9.47834			0.486870			0.243435	−	0.969917i	$-0.421726\pi$
$379$	9.47834			0.486870			0.243435	+	0.969917i	$0.421726\pi$
$380$	4.46791	−	7.48584i	0.229199	−	0.384015i
$381$	10.7392			0.550184
$382$	18.8871	+	6.87435i	0.966349	+	0.351722i
$383$	−2.34224	−	13.2835i	−0.119683	−	0.678756i	−0.984324	−	0.176367i	$-0.943565\pi$
$383$	−2.34224	−	13.2835i	−0.119683	−	0.678756i	0.864641	−	0.502390i	$-0.167546\pi$
$384$	−1.43969	−	1.20805i	−0.0734690	−	0.0616478i
$385$	−10.9513	+	9.18923i	−0.558130	+	0.468327i
$386$	2.89734	−	16.4316i	0.147471	−	0.836347i
$387$	0.201867	−	0.349643i	0.0102615	−	0.0177734i
$388$	0.766044	+	1.32683i	0.0388900	+	0.0673595i
$389$	23.6313	−	8.60111i	1.19816	−	0.436093i	0.335576	−	0.942013i	$-0.391069\pi$
$389$	23.6313	−	8.60111i	1.19816	−	0.436093i	0.862581	+	0.505920i	$0.168847\pi$
$390$	−4.61081	+	1.67820i	−0.233478	+	0.0849789i
$391$	3.66044	+	6.34008i	0.185117	+	0.320631i
$392$	−9.32295	+	16.1478i	−0.470880	+	0.815588i
$393$	3.22416	−	18.2851i	0.162637	−	0.922361i
$394$	9.95130	−	8.35014i	0.501339	−	0.420674i
$395$	−3.43376	−	2.88127i	−0.172771	−	0.144972i
$396$	−0.130415	−	0.739620i	−0.00655360	−	0.0371673i
$397$	−6.17024	−	2.24579i	−0.309676	−	0.112713i	0.182507	−	0.983205i	$-0.441579\pi$
$397$	−6.17024	−	2.24579i	−0.309676	−	0.112713i	−0.492183	+	0.870492i	$0.663801\pi$
$398$	17.1925			0.861784
$399$	32.1634	−	26.2031i	1.61019	−	1.31179i
$400$	−1.00000			−0.0500000
$401$	27.7310	+	10.0933i	1.38482	+	0.504034i	0.923636	−	0.383270i	$-0.125202\pi$
$401$	27.7310	+	10.0933i	1.38482	+	0.504034i	0.461185	+	0.887304i	$0.347425\pi$
$402$	0.458111	+	2.59808i	0.0228485	+	0.129580i
$403$	−0.369585	−	0.310119i	−0.0184103	−	0.0154481i
$404$	6.75877	−	5.67128i	0.336261	−	0.282157i
$405$	−3.58172	+	20.3129i	−0.177977	+	1.00936i
$406$	−21.4047	+	37.0740i	−1.06230	+	1.83995i
$407$	3.40373	+	5.89544i	0.168717	+	0.292226i
$408$	4.21941	−	1.53574i	0.208892	−	0.0760304i
$409$	−19.8567	+	7.22724i	−0.981850	+	0.357364i	−0.782559	−	0.622576i	$-0.786086\pi$
$409$	−19.8567	+	7.22724i	−0.981850	+	0.357364i	−0.199291	+	0.979940i	$0.563864\pi$
$410$	1.53209	+	2.65366i	0.0756645	+	0.131055i
$411$	5.07145	−	8.78401i	0.250156	−	0.433283i
$412$	−1.24123	+	7.03936i	−0.0611510	+	0.346804i
$413$	2.78106	−	2.33359i	0.136847	−	0.114828i
$414$	−1.24897	−	1.04801i	−0.0613835	−	0.0515069i
$415$	−1.38413	−	7.84981i	−0.0679444	−	0.385332i
$416$	1.22668	+	0.446476i	0.0601430	+	0.0218903i
$417$	4.39693			0.215318
$418$	−5.75031	−	2.18788i	−0.281257	−	0.107013i
$419$	−27.8830			−1.36217			−0.681087	−	0.732202i	$-0.738492\pi$
$419$	−27.8830			−1.36217			−0.681087	+	0.732202i	$0.738492\pi$
$420$	17.8871	+	6.51038i	0.872802	+	0.317674i
$421$	−0.00774079	−	0.0439002i	−0.000377263	−	0.00213956i	0.984619	−	0.174718i	$-0.0559013\pi$
$421$	−0.00774079	−	0.0439002i	−0.000377263	−	0.00213956i	−0.984996	+	0.172578i	$0.944790\pi$
$422$	−12.3400	−	10.3545i	−0.600703	−	0.504050i
$423$	−4.16250	+	3.49276i	−0.202388	+	0.169824i
$424$	0.290859	−	1.64955i	0.0141254	−	0.0801090i
$425$	1.19459	−	2.06910i	0.0579463	−	0.100366i
$426$	−5.98545	−	10.3671i	−0.289996	−	0.502288i
$427$	−46.4397	+	16.9027i	−2.24738	+	0.817978i
$428$	8.80453	−	3.20459i	0.425583	−	0.154900i
$429$	1.73143	+	2.99892i	0.0835942	+	0.144789i
$430$	0.758770	−	1.31423i	0.0365912	−	0.0633778i
$431$	−2.04694	+	11.6088i	−0.0985977	+	0.559175i	0.894988	+	0.446091i	$0.147184\pi$
$431$	−2.04694	+	11.6088i	−0.0985977	+	0.559175i	−0.993585	+	0.113084i	$0.963927\pi$
$432$	3.55303	−	2.98135i	0.170945	−	0.143440i
$433$	21.1780	+	17.7704i	1.01775	+	0.853993i	0.989343	−	0.145604i	$-0.0465124\pi$
$433$	21.1780	+	17.7704i	1.01775	+	0.853993i	0.0284060	+	0.999596i	$0.490957\pi$
$434$	0.325008	+	1.84321i	0.0156009	+	0.0884769i
$435$	29.8580	+	10.8674i	1.43158	+	0.521054i
$436$	11.0642			0.529878
$437$	−12.6159	+	4.38571i	−0.603499	+	0.209797i
$438$	8.56893			0.409439
$439$	−35.1908	−	12.8084i	−1.67956	−	0.611311i	−0.686314	−	0.727305i	$-0.740773\pi$
$439$	−35.1908	−	12.8084i	−1.67956	−	0.611311i	−0.993250	+	0.115994i	$0.962995\pi$
$440$	−0.490200	−	2.78006i	−0.0233694	−	0.132534i
$441$	7.60014	+	6.37727i	0.361911	+	0.303680i
$442$	−2.38919	+	2.00476i	−0.113642	+	0.0953569i
$443$	3.64455	−	20.6693i	0.173158	−	0.982027i	−0.767091	−	0.641539i	$-0.778296\pi$
$443$	3.64455	−	20.6693i	0.173158	−	0.982027i	0.940249	−	0.340489i	$-0.110592\pi$
$444$	4.53209	−	7.84981i	0.215083	−	0.372535i
$445$	10.6459	+	18.4392i	0.504664	+	0.874104i
$446$	−3.83750	+	1.39673i	−0.181711	+	0.0661373i
$447$	−25.3773	+	9.23659i	−1.20031	+	0.436876i
$448$	−2.53209	−	4.38571i	−0.119630	−	0.207205i
$449$	10.9474	−	18.9615i	0.516641	−	0.894849i	−0.483172	−	0.875525i	$-0.660515\pi$
$449$	10.9474	−	18.9615i	0.516641	−	0.894849i	0.999813	−	0.0193235i	$-0.00615126\pi$
$450$	−0.0923963	+	0.524005i	−0.00435560	+	0.0247018i
$451$	1.65657	−	1.39003i	0.0780050	−	0.0654540i
$452$	−10.1873	−	8.54818i	−0.479171	−	0.402072i
$453$	6.80066	+	38.5685i	0.319523	+	1.81210i
$454$	−12.8366	−	4.67215i	−0.602452	−	0.219275i
$455$	−13.2216			−0.619840
$456$	1.30541	+	8.08737i	0.0611313	+	0.378726i
$457$	−13.0496			−0.610436			−0.305218	−	0.952283i	$-0.598729\pi$
$457$	−13.0496			−0.610436			−0.305218	+	0.952283i	$0.598729\pi$
$458$	4.90673	+	1.78590i	0.229276	+	0.0834497i
$459$	1.92427	+	10.9131i	0.0898171	+	0.509378i
$460$	−4.69459	−	3.93923i	−0.218887	−	0.183668i
$461$	3.37733	−	2.83391i	0.157298	−	0.131988i	−0.560742	−	0.827991i	$-0.689484\pi$
$461$	3.37733	−	2.83391i	0.157298	−	0.131988i	0.718040	+	0.696002i	$0.245040\pi$
$462$	2.33275	−	13.2297i	0.108529	−	0.615500i
$463$	−13.3327	+	23.0930i	−0.619625	+	1.07322i	0.369929	+	0.929060i	$0.379382\pi$
$463$	−13.3327	+	23.0930i	−0.619625	+	1.07322i	−0.989554	+	0.144162i	$0.953951\pi$
$464$	−4.22668	−	7.32083i	−0.196219	−	0.339861i
$465$	1.30541	−	0.475129i	0.0605368	−	0.0220336i
$466$	25.4119	−	9.24919i	1.17719	−	0.428460i
$467$	−15.0569	−	26.0793i	−0.696750	−	1.20681i	−0.969587	−	0.244747i	$-0.921295\pi$
$467$	−15.0569	−	26.0793i	−0.696750	−	1.20681i	0.272837	−	0.962060i	$-0.412038\pi$
$468$	0.347296	−	0.601535i	0.0160538	−	0.0278060i
$469$	−1.23442	+	7.00076i	−0.0570003	+	0.323265i
$470$	−15.6459	+	13.1285i	−0.721691	+	0.605571i
$471$	−9.17024	−	7.69475i	−0.422543	−	0.354555i
$472$	0.124485	+	0.705990i	0.00572989	+	0.0324958i
$473$	−1.00640	−	0.366298i	−0.0462742	−	0.0168424i
$474$	4.21213			0.193470
$475$	3.29813	+	2.84997i	0.151329	+	0.130765i
$476$	12.0993			0.554569
$477$	−0.837496	−	0.304824i	−0.0383463	−	0.0139569i
$478$	−0.0496299	−	0.281465i	−0.00227002	−	0.0128739i
$479$	6.25671	+	5.25000i	0.285876	+	0.239879i	0.774437	−	0.632651i	$-0.218033\pi$
$479$	6.25671	+	5.25000i	0.285876	+	0.239879i	−0.488560	+	0.872530i	$0.662478\pi$
$480$	−2.87939	+	2.41609i	−0.131425	+	0.110279i
$481$	−1.09327	+	6.20026i	−0.0498490	+	0.282708i
$482$	−1.55051	+	2.68556i	−0.0706237	+	0.122324i
$483$	−14.5817	−	25.2563i	−0.663491	−	1.14920i
$484$	8.46451	−	3.08083i	0.384750	−	0.140038i
$485$	2.87939	−	1.04801i	0.130746	−	0.0475877i
$486$	−2.73396	−	4.73535i	−0.124015	−	0.214800i
$487$	−13.2935	+	23.0251i	−0.602388	+	1.04337i	0.390070	+	0.920785i	$0.372451\pi$
$487$	−13.2935	+	23.0251i	−0.602388	+	1.04337i	−0.992458	+	0.122582i	$0.960883\pi$
$488$	1.69459	−	9.61051i	0.0767106	−	0.435047i
$489$	−6.81180	+	5.71578i	−0.308040	+	0.258477i
$490$	28.5672	+	23.9707i	1.29053	+	1.08289i
$491$	6.74257	+	38.2390i	0.304288	+	1.72570i	0.626837	+	0.779151i	$0.284349\pi$
$491$	6.74257	+	38.2390i	0.304288	+	1.72570i	−0.322549	+	0.946553i	$0.604540\pi$
$492$	−2.70574	−	0.984808i	−0.121984	−	0.0443986i
$493$	20.1967			0.909611
$494$	−2.77332	−	4.96854i	−0.124777	−	0.223545i
$495$	−1.50206			−0.0675125
$496$	−0.347296	−	0.126406i	−0.0155941	−	0.00567578i
$497$	−5.60132	−	31.7667i	−0.251253	−	1.42493i
$498$	5.73783	+	4.81461i	0.257118	+	0.215748i
$499$	15.8255	−	13.2791i	0.708446	−	0.594456i	−0.215717	−	0.976456i	$-0.569209\pi$
$499$	15.8255	−	13.2791i	0.708446	−	0.594456i	0.924163	+	0.382000i	$0.124764\pi$
$500$	−2.08378	+	11.8177i	−0.0931894	+	0.528503i
$501$	16.2344	−	28.1188i	0.725301	−	1.25626i
$502$	6.32888	+	10.9619i	0.282472	+	0.489255i
$503$	−0.0692302	+	0.0251977i	−0.00308682	+	0.00112351i	−0.343563	−	0.939130i	$-0.611634\pi$
$503$	−0.0692302	+	0.0251977i	−0.00308682	+	0.00112351i	0.340476	+	0.940253i	$0.389412\pi$
$504$	−2.53209	+	0.921605i	−0.112788	+	0.0410515i
$505$	−8.82295	−	15.2818i	−0.392616	−	0.680031i
$506$	−2.16250	+	3.74557i	−0.0961350	+	0.166511i
$507$	3.68644	−	20.9068i	0.163721	−	0.928506i
$508$	−4.37733	+	3.67301i	−0.194212	+	0.162964i
$509$	11.5057	+	9.65441i	0.509980	+	0.427924i	0.861122	−	0.508398i	$-0.169762\pi$
$509$	11.5057	+	9.65441i	0.509980	+	0.427924i	−0.351142	+	0.936322i	$0.614207\pi$
$510$	−1.55943	−	8.84397i	−0.0690527	−	0.391617i
$511$	21.6973	+	7.89716i	0.959831	+	0.349350i
$512$	1.00000			0.0441942
$513$	−20.2151	−	0.293144i	−0.892520	−	0.0129426i
$514$	−30.3928			−1.34057
$515$	13.4338	+	4.88949i	0.591962	+	0.215457i
$516$	0.247626	+	1.40436i	0.0109011	+	0.0618234i
$517$	11.0419	+	9.26525i	0.485622	+	0.407485i
$518$	18.7101	−	15.6996i	0.822073	−	0.689802i
$519$	−6.14290	+	34.8381i	−0.269644	+	1.52922i
$520$	1.30541	−	2.26103i	0.0572459	−	0.0991528i
$521$	−22.5856	−	39.1194i	−0.989493	−	1.71385i	−0.619959	−	0.784634i	$-0.712851\pi$
$521$	−22.5856	−	39.1194i	−0.989493	−	1.71385i	−0.369533	−	0.929217i	$-0.620482\pi$
$522$	−4.22668	+	1.53839i	−0.184997	+	0.0673333i
$523$	−0.157451	+	0.0573076i	−0.00688487	+	0.00250589i	−0.345460	−	0.938433i	$-0.612277\pi$
$523$	−0.157451	+	0.0573076i	−0.00688487	+	0.00250589i	0.338575	+	0.940939i	$0.390055\pi$
$524$	4.93969	+	8.55580i	0.215791	+	0.373762i
$525$	−4.75877	+	8.24243i	−0.207690	+	0.359729i
$526$	3.80335	−	21.5699i	0.165834	−	0.940490i
$527$	0.676423	−	0.567586i	0.0294654	−	0.0247244i
$528$	2.03209	+	1.70513i	0.0884353	+	0.0742060i
$529$	−2.36349	−	13.4040i	−0.102761	−	0.582784i
$530$	−3.14796	−	1.14576i	−0.136738	−	0.0497687i
$531$	0.381445			0.0165533
$532$	−4.14796	+	21.6810i	−0.179837	+	0.939991i
$533$	2.00000			0.0866296
$534$	−18.8011	−	6.84305i	−0.813604	−	0.296128i
$535$	−3.25402	−	18.4545i	−0.140684	−	0.797857i
$536$	−1.07532	−	0.902302i	−0.0464468	−	0.0389735i
$537$	19.9081	−	16.7049i	0.859097	−	0.720868i
$538$	−0.248970	+	1.41198i	−0.0107339	+	0.0608748i
$539$	13.1591	−	22.7922i	0.566803	−	0.981731i
$540$	−4.63816	−	8.03352i	−0.199594	−	0.345708i
$541$	0.921274	−	0.335316i	0.0396087	−	0.0144164i	−0.322140	−	0.946692i	$-0.604402\pi$
$541$	0.921274	−	0.335316i	0.0396087	−	0.0144164i	0.361749	+	0.932276i	$0.382180\pi$
$542$	−15.1976	+	5.53147i	−0.652792	+	0.237597i
$543$	11.5175	+	19.9490i	0.494265	+	0.856092i
$544$	−1.19459	+	2.06910i	−0.0512177	+	0.0887117i
$545$	3.84255	−	21.7922i	0.164597	−	0.933474i
$546$	9.51754	−	7.98617i	0.407313	−	0.341776i
$547$	21.7592	+	18.2582i	0.930358	+	0.780663i	0.975882	−	0.218300i	$-0.0700512\pi$
$547$	21.7592	+	18.2582i	0.930358	+	0.780663i	−0.0455238	+	0.998963i	$0.514496\pi$
$548$	0.937166	+	5.31493i	0.0400338	+	0.227043i
$549$	−4.87939	−	1.77595i	−0.208247	−	0.0757957i
$550$	1.41147			0.0601855
$551$	−6.92396	+	36.1910i	−0.294971	+	1.54179i
$552$	5.75877			0.245110
$553$	10.6655	+	3.88192i	0.453543	+	0.165076i
$554$	1.92902	+	10.9400i	0.0819560	+	0.464796i
$555$	−13.8871	−	11.6527i	−0.589476	−	0.494629i
$556$	−1.79220	+	1.50384i	−0.0760064	+	0.0637769i
$557$	6.18748	−	35.0909i	0.262172	−	1.48685i	−0.514797	−	0.857312i	$-0.672133\pi$
$557$	6.18748	−	35.0909i	0.262172	−	1.48685i	0.776969	−	0.629539i	$-0.216756\pi$
$558$	−0.0983261	+	0.170306i	−0.00416247	+	0.00720962i
$559$	−0.495252	−	0.857802i	−0.0209469	−	0.0362812i
$560$	−9.51754	+	3.46410i	−0.402190	+	0.146385i
$561$	−5.95558	+	2.16766i	−0.251445	+	0.0915185i
$562$	−2.12449	−	3.67972i	−0.0896160	−	0.155219i
$563$	−4.31386	+	7.47183i	−0.181808	+	0.314900i	−0.942496	−	0.334217i	$-0.891528\pi$
$563$	−4.31386	+	7.47183i	−0.181808	+	0.314900i	0.760688	+	0.649117i	$0.224861\pi$
$564$	3.33275	−	18.9010i	0.140334	−	0.795874i
$565$	−20.3746	+	17.0964i	−0.857167	+	0.719249i
$566$	−4.17958	−	3.50708i	−0.175681	−	0.147414i
$567$	−9.06923	−	51.4342i	−0.380872	−	2.16003i
$568$	5.98545	+	2.17853i	0.251144	+	0.0914089i
$569$	22.3310			0.936164			0.468082	−	0.883685i	$-0.344945\pi$
$569$	22.3310			0.936164			0.468082	+	0.883685i	$0.344945\pi$
$570$	16.3824	+	0.237565i	0.686182	+	0.00995049i
$571$	−9.56448			−0.400261			−0.200131	−	0.979769i	$-0.564137\pi$
$571$	−9.56448			−0.400261			−0.200131	+	0.979769i	$0.564137\pi$
$572$	−1.73143	−	0.630189i	−0.0723947	−	0.0263495i
$573$	6.55943	+	37.2004i	0.274024	+	1.55407i
$574$	−5.94356	−	4.98724i	−0.248080	−	0.208163i
$575$	2.34730	−	1.96962i	0.0978890	−	0.0821386i
$576$	0.0923963	−	0.524005i	0.00384984	−	0.0218336i
$577$	−11.2378	+	19.4645i	−0.467837	+	0.810317i	−0.999325	−	0.0367489i	$-0.988300\pi$
$577$	−11.2378	+	19.4645i	−0.467837	+	0.810317i	0.531488	+	0.847066i	$0.321633\pi$
$578$	5.64590	+	9.77898i	0.234838	+	0.406752i
$579$	29.4666	−	10.7250i	1.22459	−	0.445715i
$580$	−15.8871	+	5.78244i	−0.659677	+	0.240103i
$581$	10.0915	+	17.4790i	0.418667	+	0.725152i
$582$	−1.43969	+	2.49362i	−0.0596772	+	0.103364i
$583$	−0.410540	+	2.32829i	−0.0170028	+	0.0964279i
$584$	−3.49273	+	2.93075i	−0.144530	+	0.121275i
$585$	−1.06418	−	0.892951i	−0.0439983	−	0.0369190i
$586$	3.09327	+	17.5428i	0.127782	+	0.724687i
$587$	−3.89780	−	1.41868i	−0.160880	−	0.0585554i	0.260325	−	0.965521i	$-0.416170\pi$
$587$	−3.89780	−	1.41868i	−0.160880	−	0.0585554i	−0.421205	+	0.906966i	$0.638393\pi$
$588$	−35.0428			−1.44514
$589$	0.785178	+	1.40669i	0.0323527	+	0.0579615i
$590$	1.43376			0.0590271
$591$	22.9418	+	8.35014i	0.943700	+	0.343479i
$592$	0.837496	+	4.74968i	0.0344209	+	0.195211i
$593$	7.98024	+	6.69621i	0.327709	+	0.274981i	0.791766	−	0.610825i	$-0.209162\pi$
$593$	7.98024	+	6.69621i	0.327709	+	0.274981i	−0.464057	+	0.885806i	$0.653607\pi$
$594$	−5.01501	+	4.20810i	−0.205769	+	0.172660i
$595$	4.20203	−	23.8309i	0.172266	−	0.976971i
$596$	7.18479	−	12.4444i	0.294301	−	0.509744i
$597$	16.1557	+	27.9825i	0.661209	+	1.14525i
$598$	−3.75877	+	1.36808i	−0.153708	+	0.0559450i
$599$	37.2645	−	13.5632i	1.52258	−	0.554175i	0.560792	−	0.827957i	$-0.310497\pi$
$599$	37.2645	−	13.5632i	1.52258	−	0.554175i	0.961792	+	0.273781i	$0.0882744\pi$
$600$	−0.939693	−	1.62760i	−0.0383628	−	0.0664463i
$601$	−11.9324	+	20.6676i	−0.486734	+	0.843047i	−0.999884	−	0.0152517i	$-0.995145\pi$
$601$	−11.9324	+	20.6676i	−0.486734	+	0.843047i	0.513150	+	0.858299i	$0.328478\pi$
$602$	−0.667252	+	3.78417i	−0.0271951	+	0.154231i
$603$	−0.572167	+	0.480105i	−0.0233004	+	0.0195514i
$604$	−15.9632	−	13.3947i	−0.649532	−	0.545022i
$605$	−3.12836	−	17.7418i	−0.127186	−	0.721306i
$606$	15.5817	+	5.67128i	0.632964	+	0.230380i
$607$	−29.9317			−1.21489			−0.607445	−	0.794362i	$-0.707806\pi$
$607$	−29.9317			−1.21489			−0.607445	+	0.794362i	$0.707806\pi$
$608$	−3.29813	−	2.84997i	−0.133757	−	0.115581i
$609$	−80.4552			−3.26021
$610$	−18.3405	−	6.67539i	−0.742585	−	0.270279i
$611$	2.31490	+	13.1285i	0.0936509	+	0.531121i
$612$	0.973841	+	0.817150i	0.0393652	+	0.0330313i
$613$	−27.2540	+	22.8688i	−1.10078	+	0.923664i	−0.997477	−	0.0709862i	$-0.977385\pi$
$613$	−27.2540	+	22.8688i	−1.10078	+	0.923664i	−0.103302	+	0.994650i	$0.532941\pi$
$614$	−4.97653	+	28.2233i	−0.200836	+	1.13900i
$615$	−2.87939	+	4.98724i	−0.116108	+	0.201105i
$616$	3.57398	+	6.19031i	0.144000	+	0.249415i
$617$	−11.3068	+	4.11532i	−0.455193	+	0.165677i	−0.559433	−	0.828876i	$-0.688981\pi$
$617$	−11.3068	+	4.11532i	−0.455193	+	0.165677i	0.104240	+	0.994552i	$0.466759\pi$
$618$	−12.6236	+	4.59462i	−0.507796	+	0.184823i
$619$	8.55644	+	14.8202i	0.343912	+	0.595673i	0.985156	−	0.171664i	$-0.0549144\pi$
$619$	8.55644	+	14.8202i	0.343912	+	0.595673i	−0.641243	+	0.767338i	$0.721581\pi$
$620$	−0.369585	+	0.640140i	−0.0148429	+	0.0257086i
$621$	−2.46791	+	13.9962i	−0.0990339	+	0.561649i
$622$	12.1138	−	10.1647i	0.485719	−	0.407567i
$623$	−41.2995	−	34.6544i	−1.65463	−	1.38840i
$624$	0.426022	+	2.41609i	0.0170545	+	0.0967211i
$625$	17.8542	+	6.49838i	0.714166	+	0.259935i
$626$	13.1402			0.525189
$627$	−1.84255	−	11.4151i	−0.0735843	−	0.455876i
$628$	6.36959			0.254174
$629$	−10.8280	−	3.94107i	−0.431741	−	0.157141i
$630$	0.935822	+	5.30731i	0.0372840	+	0.211448i
$631$	14.0496	+	11.7890i	0.559307	+	0.469314i	0.878078	−	0.478517i	$-0.158826\pi$
$631$	14.0496	+	11.7890i	0.559307	+	0.469314i	−0.318771	+	0.947832i	$0.603270\pi$
$632$	−1.71688	+	1.44063i	−0.0682939	+	0.0573054i
$633$	5.25712	−	29.8146i	0.208952	−	1.18502i
$634$	10.7023	−	18.5370i	0.425044	−	0.736198i
$635$	5.71419	+	9.89727i	0.226761	+	0.392761i
$636$	2.95811	−	1.07666i	0.117297	−	0.0426925i
$637$	22.8726	−	8.32494i	0.906245	−	0.329846i
$638$	5.96585	+	10.3332i	0.236190	+	0.409094i
$639$	1.69459	−	2.93512i	0.0670371	−	0.116112i
$640$	0.347296	−	1.96962i	0.0137281	−	0.0778559i
$641$	−23.8837	+	20.0408i	−0.943350	+	0.791565i	−0.978165	−	0.207829i	$-0.933360\pi$
$641$	−23.8837	+	20.0408i	−0.943350	+	0.791565i	0.0348149	+	0.999394i	$0.488916\pi$
$642$	13.4893	+	11.3189i	0.532381	+	0.446721i
$643$	−5.54798	−	31.4642i	−0.218791	−	1.24083i	−0.874206	−	0.485556i	$-0.838617\pi$
$643$	−5.54798	−	31.4642i	−0.218791	−	1.24083i	0.655414	−	0.755269i	$-0.272494\pi$
$644$	14.5817	+	5.30731i	0.574600	+	0.209137i
$645$	2.85204			0.112299
$646$	9.83678	−	3.41960i	0.387023	−	0.134542i
$647$	2.99588			0.117780			0.0588901	−	0.998264i	$-0.481244\pi$
$647$	2.99588			0.117780			0.0588901	+	0.998264i	$0.481244\pi$
$648$	9.69119	+	3.52730i	0.380706	+	0.138566i
$649$	−0.175708	−	0.996487i	−0.00689713	−	0.0391155i
$650$	1.00000	+	0.839100i	0.0392232	+	0.0329122i
$651$	−2.69459	+	2.26103i	−0.105609	+	0.0886168i
$652$	0.821604	−	4.65955i	0.0321765	−	0.182482i
$653$	−0.467911	+	0.810446i	−0.0183108	+	0.0317152i	−0.875036	−	0.484059i	$-0.839162\pi$
$653$	−0.467911	+	0.810446i	−0.0183108	+	0.0317152i	0.856725	+	0.515774i	$0.172495\pi$
$654$	10.3969	+	18.0080i	0.406552	+	0.704169i
$655$	18.5672	−	6.75790i	0.725479	−	0.264053i
$656$	1.43969	−	0.524005i	0.0562106	−	0.0204590i
$657$	1.21301	+	2.10100i	0.0473241	+	0.0819677i
$658$	25.8580	−	44.7874i	1.00805	−	1.74600i
$659$	−2.12495	+	12.0512i	−0.0827764	+	0.469448i	0.915038	+	0.403368i	$0.132160\pi$
$659$	−2.12495	+	12.0512i	−0.0827764	+	0.469448i	−0.997814	+	0.0660804i	$0.978951\pi$
$660$	4.06418	−	3.41025i	0.158198	−	0.132744i
$661$	−9.15839	−	7.68480i	−0.356220	−	0.298904i	0.447062	−	0.894503i	$-0.352470\pi$
$661$	−9.15839	−	7.68480i	−0.356220	−	0.298904i	−0.803282	+	0.595599i	$0.796915\pi$
$662$	−4.41029	−	25.0120i	−0.171411	−	0.972119i
$663$	−5.50805	−	2.00476i	−0.213915	−	0.0778586i
$664$	−3.98545			−0.154666
$665$	41.2627	+	15.6996i	1.60010	+	0.608805i
$666$	2.56624			0.0994397
$667$	24.3405	+	8.85921i	0.942468	+	0.343030i
$668$	3.00000	+	17.0138i	0.116073	+	0.658285i
$669$	−5.87939	−	4.93339i	−0.227310	−	0.190736i
$670$	−2.15064	+	1.80460i	−0.0830866	+	0.0697180i
$671$	−2.39187	+	13.5650i	−0.0923373	+	0.523671i
$672$	4.75877	−	8.24243i	0.183574	−	0.317959i
$673$	−22.4317	−	38.8529i	−0.864679	−	1.49767i	−0.867366	−	0.497671i	$-0.834189\pi$
$673$	−22.4317	−	38.8529i	−0.864679	−	1.49767i	0.00268731	−	0.999996i	$-0.499145\pi$
$674$	−24.7866	+	9.02158i	−0.954743	+	0.347498i
$675$	4.35844	−	1.58634i	0.167756	−	0.0610584i
$676$	5.64796	+	9.78255i	0.217229	+	0.376252i
$677$	−0.472964	+	0.819197i	−0.0181775	+	0.0314843i	−0.874971	−	0.484175i	$-0.839120\pi$
$677$	−0.472964	+	0.819197i	−0.0181775	+	0.0314843i	0.856794	+	0.515660i	$0.172453\pi$
$678$	4.34002	−	24.6135i	0.166678	−	0.945275i
$679$	−5.94356	+	4.98724i	−0.228093	+	0.191393i
$680$	3.66044	+	3.07148i	0.140372	+	0.117786i
$681$	−4.45811	−	25.2832i	−0.170835	−	0.968854i
$682$	0.490200	+	0.178418i	0.0187707	+	0.00683198i
$683$	−5.92221			−0.226607			−0.113303	−	0.993560i	$-0.536143\pi$
$683$	−5.92221			−0.226607			−0.113303	+	0.993560i	$0.536143\pi$
$684$	−1.79813	+	1.46491i	−0.0687533	+	0.0560123i
$685$	10.7939			0.412412
$686$	−55.4201	−	20.1713i	−2.11595	−	0.770143i
$687$	1.70409	+	9.66436i	0.0650150	+	0.368718i
$688$	−0.581252	−	0.487728i	−0.0221600	−	0.0185945i
$689$	−1.67499	+	1.40549i	−0.0638121	+	0.0535447i
$690$	2.00000	−	11.3426i	0.0761387	−	0.431804i
$691$	−0.103074	+	0.178529i	−0.00392111	+	0.00679156i	−0.867979	−	0.496600i	$-0.834581\pi$
$691$	−0.103074	+	0.178529i	−0.00392111	+	0.00679156i	0.864058	+	0.503392i	$0.167915\pi$
$692$	−9.41147	−	16.3012i	−0.357771	−	0.619677i
$693$	3.57398	−	1.30082i	0.135764	−	0.0494141i
$694$	24.0856	−	8.76644i	0.914276	−	0.332769i
$695$	2.33956	+	4.05223i	0.0887444	+	0.153710i
$696$	7.94356	−	13.7587i	0.301100	−	0.521520i
$697$	−0.635630	+	3.60483i	−0.0240762	+	0.136543i
$698$	−4.47565	+	3.75552i	−0.169406	+	0.142148i
$699$	38.9334	+	32.6690i	1.47259	+	1.23565i
$700$	−0.879385	−	4.98724i	−0.0332376	−	0.188500i
$701$	−4.10607	−	1.49449i	−0.155084	−	0.0564460i	0.263312	−	0.964711i	$-0.415185\pi$
$701$	−4.10607	−	1.49449i	−0.155084	−	0.0564460i	−0.418396	+	0.908265i	$0.637407\pi$
$702$	−6.05468			−0.228519
$703$	10.7743	−	18.0519i	0.406359	−	0.680840i
$704$	−1.41147			−0.0531969
$705$	−36.0702	−	13.1285i	−1.35848	−	0.494447i
$706$	−3.89141	−	22.0693i	−0.146455	−	0.830588i
$707$	34.2276	+	28.7204i	1.28726	+	1.08014i
$708$	−1.03209	+	0.866025i	−0.0387883	+	0.0325472i
$709$	1.52023	−	8.62165i	0.0570934	−	0.323793i	−0.942863	−	0.333182i	$-0.891878\pi$
$709$	1.52023	−	8.62165i	0.0570934	−	0.323793i	0.999956	+	0.00938924i	$0.00298873\pi$
$710$	6.36959	−	11.0324i	0.239046	−	0.414040i
$711$	0.596267	+	1.03276i	0.0223617	+	0.0387317i
$712$	10.0039	−	3.64111i	0.374911	−	0.136456i
$713$	1.06418	−	0.387329i	0.0398538	−	0.0145056i
$714$	11.3696	+	19.6927i	0.425496	+	0.736981i
$715$	−1.84255	+	3.19139i	−0.0689074	+	0.119351i
$716$	−2.40121	+	13.6179i	−0.0897373	+	0.508926i
$717$	0.411474	−	0.345268i	0.0153668	−	0.0128943i
$718$	7.36690	+	6.18156i	0.274930	+	0.230694i
$719$	−4.79385	−	27.1873i	−0.178781	−	1.01391i	−0.933689	−	0.358085i	$-0.883430\pi$
$719$	−4.79385	−	27.1873i	−0.178781	−	1.01391i	0.754909	−	0.655830i	$-0.227681\pi$
$720$	−1.00000	−	0.363970i	−0.0372678	−	0.0135644i
$721$	−36.1985			−1.34810
$722$	2.75537	+	18.7991i	0.102544	+	0.699632i
$723$	−5.82800			−0.216746
$724$	−11.5175	−	4.19204i	−0.428046	−	0.155796i
$725$	−1.46791	−	8.32494i	−0.0545169	−	0.309180i
$726$	12.9684	+	10.8818i	0.481302	+	0.403860i
$727$	21.9368	−	18.4071i	0.813589	−	0.682682i	−0.137872	−	0.990450i	$-0.544026\pi$
$727$	21.9368	−	18.4071i	0.813589	−	0.682682i	0.951462	+	0.307768i	$0.0995819\pi$
$728$	−1.14796	+	6.51038i	−0.0425461	+	0.241291i
$729$	−10.3316	+	17.8948i	−0.382651	+	0.662770i
$730$	4.55943	+	7.89716i	0.168752	+	0.292287i
$731$	1.70352	−	0.620029i	0.0630068	−	0.0229326i
$732$	17.2344	−	6.27282i	0.637003	−	0.231850i
$733$	−18.4807	−	32.0095i	−0.682600	−	1.18230i	−0.974184	−	0.225753i	$-0.927516\pi$
$733$	−18.4807	−	32.0095i	−0.682600	−	1.18230i	0.291584	−	0.956545i	$-0.405818\pi$
$734$	−11.6800	+	20.2304i	−0.431118	+	0.746719i
$735$	−12.1702	+	69.0209i	−0.448906	+	2.54587i
$736$	−2.34730	+	1.96962i	−0.0865225	+	0.0726010i
$737$	1.51779	+	1.27358i	0.0559085	+	0.0469128i
$738$	−0.141559	−	0.802823i	−0.00521087	−	0.0295523i
$739$	−43.2508	−	15.7420i	−1.59101	−	0.579079i	−0.613446	−	0.789737i	$-0.710217\pi$
$739$	−43.2508	−	15.7420i	−1.59101	−	0.579079i	−0.977560	+	0.210658i	$0.932439\pi$
$740$	9.64590			0.354590
$741$	5.48070	−	9.18274i	0.201339	−	0.337336i
$742$	8.48246			0.311401
$743$	−24.8179	−	9.03298i	−0.910480	−	0.331388i	−0.156036	−	0.987751i	$-0.549871\pi$
$743$	−24.8179	−	9.03298i	−0.910480	−	0.331388i	−0.754445	+	0.656364i	$0.772094\pi$
$744$	−0.120615	−	0.684040i	−0.00442195	−	0.0250781i
$745$	−22.0155	−	18.4732i	−0.806585	−	0.676805i
$746$	−19.8726	+	16.6751i	−0.727587	+	0.610518i
$747$	−0.368241	+	2.08840i	−0.0134732	+	0.0764105i
$748$	1.68614	−	2.92047i	0.0616513	−	0.106783i
$749$	23.7246	+	41.0923i	0.866879	+	1.50148i
$750$	−21.1925	+	7.71345i	−0.773842	+	0.281655i
$751$	25.5381	−	9.29510i	0.931898	−	0.339183i	0.168936	−	0.985627i	$-0.445967\pi$
$751$	25.5381	−	9.29510i	0.931898	−	0.339183i	0.762961	+	0.646444i	$0.223745\pi$
$752$	5.10607	+	8.84397i	0.186199	+	0.322506i
$753$	−11.8944	+	20.6017i	−0.433456	+	0.750768i
$754$	−1.91622	+	10.8674i	−0.0697847	+	0.395769i
$755$	−31.9263	+	26.7894i	−1.16192	+	0.974965i
$756$	17.9932	+	15.0981i	0.654406	+	0.549112i
$757$	3.36959	+	19.1099i	0.122470	+	0.694560i	0.982779	+	0.184787i	$0.0591595\pi$
$757$	3.36959	+	19.1099i	0.122470	+	0.694560i	−0.860309	+	0.509773i	$0.829729\pi$
$758$	−8.90673	−	3.24178i	−0.323507	−	0.117747i
$759$	−8.12836			−0.295041
$760$	−6.75877	+	5.50627i	−0.245166	+	0.199733i
$761$	40.2645			1.45959			0.729793	−	0.683669i	$-0.239617\pi$
$761$	40.2645			1.45959			0.729793	+	0.683669i	$0.239617\pi$
$762$	−10.0915	−	3.67301i	−0.365577	−	0.133059i
$763$	9.72967	+	55.1797i	0.352238	+	1.99764i
$764$	−15.3969	−	12.9196i	−0.557041	−	0.467413i
$765$	1.94768	−	1.63430i	0.0704186	−	0.0590882i
$766$	−2.34224	+	13.2835i	−0.0846287	+	0.479953i
$767$	0.467911	−	0.810446i	0.0168953	−	0.0292635i
$768$	0.939693	+	1.62760i	0.0339082	+	0.0587308i
$769$	36.5933	−	13.3189i	1.31959	−	0.480291i	0.416263	−	0.909244i	$-0.363340\pi$
$769$	36.5933	−	13.3189i	1.31959	−	0.480291i	0.903327	+	0.428953i	$0.141117\pi$
$770$	13.4338	−	4.88949i	0.484119	−	0.176205i
$771$	−28.5599	−	49.4672i	−1.02856	−	1.78152i
$772$	−8.34255	+	14.4497i	−0.300255	+	0.520057i
$773$	−1.17436	+	6.66015i	−0.0422389	+	0.239549i	−0.998616	−	0.0525847i	$-0.983254\pi$
$773$	−1.17436	+	6.66015i	−0.0422389	+	0.239549i	0.956378	+	0.292133i	$0.0943652\pi$
$774$	−0.309278	+	0.259515i	−0.0111168	+	0.00932807i
$775$	−0.283119	−	0.237565i	−0.0101699	−	0.00853358i
$776$	−0.266044	−	1.50881i	−0.00955044	−	0.0541632i
$777$	43.1343	+	15.6996i	1.54744	+	0.563221i
$778$	−25.1480			−0.901598
$779$	−6.24170	−	2.37484i	−0.223632	−	0.0850874i
$780$	4.90673			0.175689
$781$	−8.44831	−	3.07493i	−0.302304	−	0.110030i
$782$	−1.27126	−	7.20967i	−0.0454601	−	0.257817i
$783$	30.0351	+	25.2024i	1.07337	+	0.900661i
$784$	14.2836	−	11.9854i	0.510128	−	0.428048i
$785$	2.21213	−	12.5456i	0.0789544	−	0.447773i
$786$	−9.28359	+	16.0796i	−0.331135	+	0.573542i
$787$	−2.90239	−	5.02709i	−0.103459	−	0.179196i	0.809649	−	0.586915i	$-0.199658\pi$
$787$	−2.90239	−	5.02709i	−0.103459	−	0.179196i	−0.913108	+	0.407719i	$0.866324\pi$
$788$	−12.2071	+	4.44301i	−0.434859	+	0.158276i
$789$	38.6810	−	14.0787i	1.37708	−	0.501216i
$790$	2.24123	+	3.88192i	0.0797394	+	0.138113i
$791$	33.6732	−	58.3238i	1.19728	−	2.07375i
$792$	−0.130415	+	0.739620i	−0.00463409	+	0.0262812i
$793$	−9.75877	+	8.18858i	−0.346544	+	0.290785i
$794$	5.03003	+	4.22070i	0.178509	+	0.149787i
$795$	−1.09327	−	6.20026i	−0.0387744	−	0.219901i
$796$	−16.1557	−	5.88019i	−0.572623	−	0.208418i
$797$	−39.2181			−1.38918			−0.694589	−	0.719407i	$-0.744414\pi$
$797$	−39.2181			−1.38918			−0.694589	+	0.719407i	$0.744414\pi$
$798$	−39.1857	+	13.6223i	−1.38716	+	0.482224i
$799$	−24.3987			−0.863163
$800$	0.939693	+	0.342020i	0.0332232	+	0.0120922i
$801$	−0.983641	−	5.57851i	−0.0347552	−	0.197107i
$802$	−22.6065	−	18.9691i	−0.798264	−	0.669823i
$803$	4.92989	−	4.13667i	0.173972	−	0.145980i
$804$	0.458111	−	2.59808i	0.0161563	−	0.0916271i
$805$	15.5175	−	26.8772i	0.546921	−	0.947296i
$806$	0.241230	+	0.417822i	0.00849695	+	0.0147171i
$807$	−2.53209	+	0.921605i	−0.0891338	+	0.0324420i
$808$	−8.29086	+	3.01763i	−0.291671	+	0.106160i
$809$	−3.50134	−	6.06451i	−0.123101	−	0.213217i	0.797888	−	0.602805i	$-0.205950\pi$
$809$	−3.50134	−	6.06451i	−0.123101	−	0.213217i	−0.920989	+	0.389589i	$0.872617\pi$
$810$	10.3131	−	17.8629i	0.362367	−	0.627638i
$811$	7.58584	−	43.0214i	0.266375	−	1.51069i	−0.498717	−	0.866765i	$-0.666195\pi$
$811$	7.58584	−	43.0214i	0.266375	−	1.51069i	0.765092	−	0.643921i	$-0.222694\pi$
$812$	32.7939	−	27.5173i	1.15084	−	0.965668i
$813$	−23.2841	−	19.5376i	−0.816607	−	0.685215i
$814$	−1.18210	−	6.70405i	−0.0414327	−	0.234977i
$815$	−8.89218	−	3.23649i	−0.311479	−	0.113369i
$816$	−4.49020			−0.157188
$817$	0.527036	+	3.26514i	0.0184387	+	0.114233i
$818$	21.1310			0.738830
$819$	3.30541	+	1.20307i	0.115500	+	0.0420387i
$820$	−0.532089	−	3.01763i	−0.0185813	−	0.105380i
$821$	9.48751	+	7.96097i	0.331116	+	0.277840i	0.793155	−	0.609020i	$-0.208437\pi$
$821$	9.48751	+	7.96097i	0.331116	+	0.277840i	−0.462038	+	0.886860i	$0.652882\pi$
$822$	−7.76991	+	6.51973i	−0.271007	+	0.227402i
$823$	−2.22762	+	12.6334i	−0.0776498	+	0.440374i	0.921052	+	0.389439i	$0.127331\pi$
$823$	−2.22762	+	12.6334i	−0.0776498	+	0.440374i	−0.998702	+	0.0509347i	$0.983780\pi$
$824$	3.57398	−	6.19031i	0.124505	−	0.215650i
$825$	1.32635	+	2.29731i	0.0461776	+	0.0799820i
$826$	−3.41147	+	1.24168i	−0.118700	+	0.0432034i
$827$	−23.5831	+	8.58353i	−0.820063	+	0.298479i	−0.717774	−	0.696276i	$-0.754839\pi$
$827$	−23.5831	+	8.58353i	−0.820063	+	0.298479i	−0.102289	+	0.994755i	$0.532617\pi$
$828$	0.815207	+	1.41198i	0.0283304	+	0.0490697i
$829$	−14.1634	+	24.5318i	−0.491917	+	0.852024i	−0.999957	−	0.00930899i	$-0.997037\pi$
$829$	−14.1634	+	24.5318i	−0.491917	+	0.852024i	0.508040	+	0.861333i	$0.330370\pi$
$830$	−1.38413	+	7.84981i	−0.0480440	+	0.272471i
$831$	−15.9932	+	13.4199i	−0.554798	+	0.465531i
$832$	−1.00000	−	0.839100i	−0.0346688	−	0.0290905i
$833$	7.73577	+	43.8717i	0.268028	+	1.52006i
$834$	−4.13176	−	1.50384i	−0.143071	−	0.0520736i
$835$	34.5526			1.19574
$836$	4.65523	+	4.02266i	0.161004	+	0.139126i
$837$	1.71419			0.0592512
$838$	26.2015	+	9.53655i	0.905114	+	0.329435i
$839$	−5.26682	−	29.8696i	−0.181831	−	1.03121i	−0.929960	−	0.367660i	$-0.880159\pi$
$839$	−5.26682	−	29.8696i	−0.181831	−	1.03121i	0.748129	−	0.663553i	$-0.230952\pi$
$840$	−14.5817	−	12.2355i	−0.503117	−	0.422165i
$841$	32.5257	−	27.2923i	1.12158	−	0.941115i
$842$	−0.00774079	+	0.0439002i	−0.000266765	+	0.00151290i
$843$	3.99273	−	6.91560i	0.137517	−	0.238186i
$844$	8.05438	+	13.9506i	0.277243	+	0.480199i
$845$	21.2294	−	7.72686i	0.730313	−	0.265812i
$846$	5.10607	−	1.85846i	0.175550	−	0.0638950i
$847$	22.8084	+	39.5053i	0.783706	+	1.35742i
$848$	−0.837496	+	1.45059i	−0.0287597	+	0.0498133i
$849$	1.78059	−	10.0982i	0.0611098	−	0.346571i
$850$	−1.83022	+	1.53574i	−0.0627761	+	0.0526754i
$851$	−11.3209	−	9.49935i	−0.388075	−	0.325634i
$852$	2.07873	+	11.7890i	0.0712160	+	0.403886i
$853$	41.0009	+	14.9231i	1.40385	+	0.510958i	0.929317	−	0.369283i	$-0.120397\pi$
$853$	41.0009	+	14.9231i	1.40385	+	0.510958i	0.474528	+	0.880240i	$0.342619\pi$
$854$	49.4201			1.69112
$855$	2.26083	+	4.05039i	0.0773188	+	0.138520i
$856$	−9.36959			−0.320246
$857$	29.6095	+	10.7770i	1.01144	+	0.368135i	0.793987	−	0.607935i	$-0.208002\pi$
$857$	29.6095	+	10.7770i	1.01144	+	0.368135i	0.217456	+	0.976070i	$0.430224\pi$
$858$	−0.601319	−	3.41025i	−0.0205287	−	0.116424i
$859$	−14.3234	−	12.0188i	−0.488709	−	0.410075i	0.364855	−	0.931065i	$-0.381119\pi$
$859$	−14.3234	−	12.0188i	−0.488709	−	0.410075i	−0.853563	+	0.520989i	$0.825563\pi$
$860$	−1.16250	+	0.975457i	−0.0396411	+	0.0332628i
$861$	2.53209	−	14.3602i	0.0862934	−	0.489394i
$862$	5.89393	−	10.2086i	0.200748	−	0.347706i
$863$	−5.31315	−	9.20264i	−0.180862	−	0.313262i	0.761313	−	0.648385i	$-0.224555\pi$
$863$	−5.31315	−	9.20264i	−0.180862	−	0.313262i	−0.942174	+	0.335123i	$0.891222\pi$
$864$	−4.35844	+	1.58634i	−0.148277	+	0.0539685i
$865$	−35.3756	+	12.8757i	−1.20281	+	0.437785i
$866$	−13.8229	−	23.9420i	−0.469723	−	0.813584i
$867$	−10.6108	+	18.3785i	−0.360362	+	0.624166i
$868$	0.325008	−	1.84321i	0.0110315	−	0.0625626i
$869$	2.42333	−	2.03342i	0.0822060	−	0.0689790i
$870$	−24.3405	−	20.4241i	−0.825220	−	0.692442i
$871$	0.318201	+	1.80460i	0.0107818	+	0.0611467i
$872$	−10.3969	−	3.78417i	−0.352084	−	0.128148i
$873$	−0.815207			−0.0275906
$874$	13.3550	+	0.193665i	0.451741	+	0.00655080i
$875$	−60.7701			−2.05441
$876$	−8.05216	−	2.93075i	−0.272057	−	0.0990207i
$877$	7.79654	+	44.2164i	0.263270	+	1.49308i	0.773915	+	0.633289i	$0.218296\pi$
$877$	7.79654	+	44.2164i	0.263270	+	1.49308i	−0.510645	+	0.859792i	$0.670593\pi$
$878$	28.6878	+	24.0719i	0.968166	+	0.812388i
$879$	−25.6459	+	21.5195i	−0.865015	+	0.725833i
$880$	−0.490200	+	2.78006i	−0.0165246	+	0.0937158i
$881$	9.00821	−	15.6027i	0.303494	−	0.525667i	−0.673431	−	0.739250i	$-0.735180\pi$
$881$	9.00821	−	15.6027i	0.303494	−	0.525667i	0.976925	+	0.213583i	$0.0685134\pi$
$882$	−4.96064	−	8.59208i	−0.167033	−	0.289310i
$883$	43.7879	−	15.9375i	1.47358	−	0.536340i	0.524511	−	0.851404i	$-0.324248\pi$
$883$	43.7879	−	15.9375i	1.47358	−	0.536340i	0.949070	+	0.315064i	$0.102026\pi$
$884$	2.93077	−	1.06671i	0.0985725	−	0.0358774i
$885$	1.34730	+	2.33359i	0.0452889	+	0.0784426i
$886$	−10.4941	+	18.1763i	−0.352555	+	0.610643i
$887$	1.22937	−	6.97210i	0.0412782	−	0.234100i	−0.957188	−	0.289467i	$-0.906522\pi$
$887$	1.22937	−	6.97210i	0.0412782	−	0.234100i	0.998466	+	0.0553671i	$0.0176329\pi$
$888$	−6.94356	+	5.82634i	−0.233011	+	0.195519i
$889$	−22.1676	−	18.6008i	−0.743476	−	0.623850i
$890$	−3.69728	−	20.9683i	−0.123933	−	0.702860i
$891$	−13.6789	−	4.97870i	−0.458259	−	0.166793i
$892$	4.08378			0.136735
$893$	8.36453	−	43.7207i	0.279908	−	1.46306i
$894$	27.0060			0.903215
$895$	25.9881	+	9.45891i	0.868688	+	0.316176i
$896$	0.879385	+	4.98724i	0.0293782	+	0.166612i
$897$	−5.75877	−	4.83218i	−0.192280	−	0.161342i
$898$	−16.7724	+	14.0737i	−0.559704	+	0.469647i
$899$	0.542518	−	3.07677i	0.0180940	−	0.102616i
$900$	0.266044	−	0.460802i	0.00886815	−	0.0153601i
$901$	−2.00093	−	3.46572i	−0.0666608	−	0.115460i
$902$	−2.03209	+	0.739620i	−0.0676612	+	0.0246266i
$903$	−6.78611	+	2.46994i	−0.225828	+	0.0821945i
$904$	6.64930	+	11.5169i	0.221152	+	0.383047i
$905$	−12.2567	+	21.2292i	−0.407427	+	0.705684i
$906$	6.80066	−	38.5685i	0.225937	−	1.28135i
$907$	11.5792	−	9.71610i	0.384481	−	0.322618i	−0.429978	−	0.902840i	$-0.641479\pi$
$907$	11.5792	−	9.71610i	0.384481	−	0.322618i	0.814458	+	0.580222i	$0.197034\pi$
$908$	10.4645	+	8.78076i	0.347277	+	0.291400i
$909$	0.815207	+	4.62327i	0.0270387	+	0.153344i
$910$	12.4243	+	4.52206i	0.411860	+	0.149905i
$911$	−12.8366			−0.425294			−0.212647	−	0.977129i	$-0.568208\pi$
$911$	−12.8366			−0.425294			−0.212647	+	0.977129i	$0.568208\pi$
$912$	1.53936	−	8.04612i	0.0509734	−	0.266434i
$913$	5.62536			0.186172
$914$	12.2626	+	4.46324i	0.405612	+	0.147631i
$915$	−6.36959	−	36.1237i	−0.210572	−	1.19421i
$916$	−4.00000	−	3.35640i	−0.132164	−	0.110899i
$917$	−38.3259	+	32.1593i	−1.26563	+	1.06199i
$918$	1.92427	−	10.9131i	0.0635103	−	0.360185i
$919$	10.3396	−	17.9086i	0.341070	−	0.590751i	−0.643561	−	0.765395i	$-0.722544\pi$
$919$	10.3396	−	17.9086i	0.341070	−	0.590751i	0.984632	+	0.174643i	$0.0558772\pi$
$920$	3.06418	+	5.30731i	0.101023	+	0.174977i
$921$	−50.6125	+	18.4215i	−1.66774	+	0.607007i
$922$	−4.14290	+	1.50789i	−0.136439	+	0.0496598i
$923$	−4.15745	−	7.20092i	−0.136844	−	0.237021i
$924$	−6.71688	+	11.6340i	−0.220969	+	0.382730i
$925$	−0.837496	+	4.74968i	−0.0275367	+	0.156168i
$926$	20.4270	−	17.1403i	0.671271	−	0.563264i
$927$	−2.91353	−	2.44474i	−0.0956930	−	0.0802960i
$928$	1.46791	+	8.32494i	0.0481865	+	0.273279i
$929$	17.1493	+	6.24183i	0.562650	+	0.204788i	0.607658	−	0.794199i	$-0.292109\pi$
$929$	17.1493	+	6.24183i	0.562650	+	0.204788i	−0.0450079	+	0.998987i	$0.514331\pi$
$930$	−1.38919			−0.0455532
$931$	−81.2670	−	1.17847i	−2.66342	−	0.0386229i
$932$	−27.0428			−0.885817
$933$	27.9273	+	10.1647i	0.914297	+	0.332777i
$934$	5.22921	+	29.6563i	0.171105	+	0.970384i
$935$	−5.16662	−	4.33531i	−0.168967	−	0.141780i
$936$	−0.532089	+	0.446476i	−0.0173919	+	0.0145935i
$937$	−0.824292	+	4.67479i	−0.0269285	+	0.152719i	−0.995307	−	0.0967660i	$-0.969150\pi$
$937$	−0.824292	+	4.67479i	−0.0269285	+	0.152719i	0.968379	+	0.249485i	$0.0802613\pi$
$938$	3.55438	−	6.15636i	0.116055	−	0.201012i
$939$	12.3478	+	21.3870i	0.402954	+	0.697937i
$940$	19.1925	−	6.98551i	0.625991	−	0.227842i
$941$	−44.1857	+	16.0823i	−1.44041	+	0.524268i	−0.939897	−	0.341459i	$-0.889079\pi$
$941$	−44.1857	+	16.0823i	−1.44041	+	0.524268i	−0.500517	+	0.865727i	$0.666857\pi$
$942$	5.98545	+	10.3671i	0.195017	+	0.337779i
$943$	−2.34730	+	4.06564i	−0.0764385	+	0.132395i
$944$	0.124485	−	0.705990i	0.00405165	−	0.0229780i
$945$	35.9864	−	30.1962i	1.17064	−	0.982281i
$946$	0.820422	+	0.688416i	0.0266742	+	0.0223823i
$947$	6.42427	+	36.4338i	0.208761	+	1.18394i	0.891411	+	0.453195i	$0.149716\pi$
$947$	6.42427	+	36.4338i	0.208761	+	1.18394i	−0.682651	+	0.730745i	$0.739173\pi$
$948$	−3.95811	−	1.44063i	−0.128553	−	0.0467896i
$949$	5.95191			0.193207
$950$	−2.12449	−	3.80612i	−0.0689274	−	0.123487i
$951$	40.2276			1.30447
$952$	−11.3696	−	4.13819i	−0.368490	−	0.134120i
$953$	−6.54814	−	37.1364i	−0.212115	−	1.20296i	−0.885843	−	0.463985i	$-0.846419\pi$
$953$	−6.54814	−	37.1364i	−0.212115	−	1.20296i	0.673728	−	0.738980i	$-0.264692\pi$
$954$	0.682733	+	0.572881i	0.0221043	+	0.0185477i
$955$	−30.7939	+	25.8391i	−0.996466	+	0.836134i
$956$	−0.0496299	+	0.281465i	−0.00160514	+	0.00910322i
$957$	−11.2121	+	19.4200i	−0.362437	+	0.627759i
$958$	−4.08378	−	7.07331i	−0.131941	−	0.228528i
$959$	−25.6827	+	9.34775i	−0.829339	+	0.301855i
$960$	3.53209	−	1.28558i	0.113998	−	0.0414918i
$961$	15.4317	+	26.7285i	0.497797	+	0.862209i
$962$	3.14796	−	5.45242i	0.101494	−	0.175793i
$963$	−0.865715	+	4.90971i	−0.0278973	+	0.158213i
$964$	2.37551	−	1.99329i	0.0765102	−	0.0641997i
$965$	25.5631	+	21.4499i	0.822904	+	0.690498i
$966$	5.06418	+	28.7204i	0.162937	+	0.924063i
$967$	−38.0702	−	13.8564i	−1.22425	−	0.445592i	−0.352628	−	0.935764i	$-0.614712\pi$
$967$	−38.0702	−	13.8564i	−1.22425	−	0.445592i	−0.871626	+	0.490172i	$0.836934\pi$
$968$	−9.00774			−0.289520
$969$	14.8093	+	12.7969i	0.475743	+	0.411096i
$970$	−3.06418			−0.0983848
$971$	13.2289	+	4.81493i	0.424536	+	0.154518i	0.545448	−	0.838145i	$-0.316360\pi$
$971$	13.2289	+	4.81493i	0.424536	+	0.154518i	−0.120912	+	0.992663i	$0.538582\pi$
$972$	0.949493	+	5.38484i	0.0304550	+	0.172719i
$973$	−9.07604	−	7.61570i	−0.290964	−	0.244148i
$974$	20.3669	−	17.0899i	0.652597	−	0.547594i
$975$	−0.426022	+	2.41609i	−0.0136436	+	0.0773768i
$976$	−4.87939	+	8.45134i	−0.156185	+	0.270521i
$977$	17.6028	+	30.4890i	0.563164	+	0.975429i	0.997218	+	0.0745421i	$0.0237495\pi$
$977$	17.6028	+	30.4890i	0.563164	+	0.975429i	−0.434054	+	0.900887i	$0.642917\pi$
$978$	8.35591	−	3.04130i	0.267193	−	0.0972502i
$979$	−14.1202	+	5.13933i	−0.451284	+	0.164254i
$980$	−18.6459	−	32.2956i	−0.595621	−	1.03165i
$981$	−2.94356	+	5.09840i	−0.0939807	+	0.162779i
$982$	6.74257	−	38.2390i	0.215164	−	1.22026i
$983$	17.1898	−	14.4240i	0.548271	−	0.460054i	−0.326084	−	0.945341i	$-0.605729\pi$
$983$	17.1898	−	14.4240i	0.548271	−	0.460054i	0.874355	+	0.485287i	$0.161285\pi$
$984$	2.20574	+	1.85083i	0.0703163	+	0.0590024i
$985$	4.51155	+	25.5863i	0.143750	+	0.815247i
$986$	−18.9786	−	6.90766i	−0.604403	−	0.219985i
$987$	97.1944			3.09373
$988$	0.906726	+	5.61743i	0.0288468	+	0.178714i
$989$	2.32501			0.0739309
$990$	1.41147	+	0.513735i	0.0448596	+	0.0163276i
$991$	4.70645	+	26.6916i	0.149505	+	0.847887i	0.963639	+	0.267209i	$0.0861014\pi$
$991$	4.70645	+	26.6916i	0.149505	+	0.847887i	−0.814133	+	0.580678i	$0.802787\pi$
$992$	0.283119	+	0.237565i	0.00898902	+	0.00754269i
$993$	36.5651	−	30.6818i	1.16036	−	0.973657i
$994$	−5.60132	+	31.7667i	−0.177663	+	1.00758i
$995$	−17.1925	+	29.7783i	−0.545040	+	0.944037i
$996$	−3.74510	−	6.48670i	−0.118668	−	0.205539i
$997$	−26.2618	+	9.55850i	−0.831718	+	0.302721i	−0.722564	−	0.691304i	$-0.757037\pi$
$997$	−26.2618	+	9.55850i	−0.831718	+	0.302721i	−0.109154	+	0.994025i	$0.534814\pi$
$998$	−19.4128	+	7.06569i	−0.614502	+	0.223660i
$999$	−11.1848	−	19.3726i	−0.353871	−	0.612923i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.2.e.a.23.1	yes	6
3.2	odd	2		342.2.u.c.289.1		6
4.3	odd	2		304.2.u.c.289.1		6
5.2	odd	4		950.2.u.b.99.2		12
5.3	odd	4		950.2.u.b.99.1		12
5.4	even	2		950.2.l.d.251.1		6
19.2	odd	18		722.2.e.a.415.1		6
19.3	odd	18		722.2.e.l.245.1		6
19.4	even	9		722.2.c.k.653.3		6
19.5	even	9	inner	38.2.e.a.5.1	✓	6
19.6	even	9		722.2.c.k.429.3		6
19.7	even	3		722.2.e.m.595.1		6
19.8	odd	6		722.2.e.l.389.1		6
19.9	even	9		722.2.a.l.1.1		3
19.10	odd	18		722.2.a.k.1.3		3
19.11	even	3		722.2.e.b.389.1		6
19.12	odd	6		722.2.e.a.595.1		6
19.13	odd	18		722.2.c.l.429.1		6
19.14	odd	18		722.2.e.k.423.1		6
19.15	odd	18		722.2.c.l.653.1		6
19.16	even	9		722.2.e.b.245.1		6
19.17	even	9		722.2.e.m.415.1		6
19.18	odd	2		722.2.e.k.99.1		6
57.5	odd	18		342.2.u.c.271.1		6
57.29	even	18		6498.2.a.bq.1.3		3
57.47	odd	18		6498.2.a.bl.1.3		3
76.43	odd	18		304.2.u.c.81.1		6
76.47	odd	18		5776.2.a.bn.1.3		3
76.67	even	18		5776.2.a.bo.1.1		3
95.24	even	18		950.2.l.d.651.1		6
95.43	odd	36		950.2.u.b.499.2		12
95.62	odd	36		950.2.u.b.499.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.e.a.5.1	✓	6	19.5	even	9	inner
38.2.e.a.23.1	yes	6	1.1	even	1	trivial
304.2.u.c.81.1		6	76.43	odd	18
304.2.u.c.289.1		6	4.3	odd	2
342.2.u.c.271.1		6	57.5	odd	18
342.2.u.c.289.1		6	3.2	odd	2
722.2.a.k.1.3		3	19.10	odd	18
722.2.a.l.1.1		3	19.9	even	9
722.2.c.k.429.3		6	19.6	even	9
722.2.c.k.653.3		6	19.4	even	9
722.2.c.l.429.1		6	19.13	odd	18
722.2.c.l.653.1		6	19.15	odd	18
722.2.e.a.415.1		6	19.2	odd	18
722.2.e.a.595.1		6	19.12	odd	6
722.2.e.b.245.1		6	19.16	even	9
722.2.e.b.389.1		6	19.11	even	3
722.2.e.k.99.1		6	19.18	odd	2
722.2.e.k.423.1		6	19.14	odd	18
722.2.e.l.245.1		6	19.3	odd	18
722.2.e.l.389.1		6	19.8	odd	6
722.2.e.m.415.1		6	19.17	even	9
722.2.e.m.595.1		6	19.7	even	3
950.2.l.d.251.1		6	5.4	even	2
950.2.l.d.651.1		6	95.24	even	18
950.2.u.b.99.1		12	5.3	odd	4
950.2.u.b.99.2		12	5.2	odd	4
950.2.u.b.499.1		12	95.62	odd	36
950.2.u.b.499.2		12	95.43	odd	36
5776.2.a.bn.1.3		3	76.47	odd	18
5776.2.a.bo.1.1		3	76.67	even	18
6498.2.a.bl.1.3		3	57.47	odd	18
6498.2.a.bq.1.3		3	57.29	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)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.326352 - 1.85083i) q^{3} +(0.766044 + 0.642788i) q^{4} +(1.53209 - 1.28558i) q^{5} +(-0.326352 + 1.85083i) q^{6} +(-2.53209 + 4.38571i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.500000 + 0.181985i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.326352 - 1.85083i) q^{3} +(0.766044 + 0.642788i) q^{4} +(1.53209 - 1.28558i) q^{5} +(-0.326352 + 1.85083i) q^{6} +(-2.53209 + 4.38571i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.500000 + 0.181985i) q^{9} +(-1.87939 + 0.684040i) q^{10} +(0.705737 + 1.22237i) q^{11} +(0.939693 - 1.62760i) q^{12} +(-0.226682 + 1.28558i) q^{13} +(3.87939 - 3.25519i) q^{14} +(-2.87939 - 2.41609i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-2.24510 - 0.817150i) q^{17} +0.532089 q^{18} +(2.23396 - 3.74292i) q^{19} +2.00000 q^{20} +(8.94356 + 3.25519i) q^{21} +(-0.245100 - 1.39003i) q^{22} +(-2.34730 - 1.96962i) q^{23} +(-1.43969 + 1.20805i) q^{24} +(-0.173648 + 0.984808i) q^{25} +(0.652704 - 1.13052i) q^{26} +(-2.31908 - 4.01676i) q^{27} +(-4.75877 + 1.73205i) q^{28} +(-7.94356 + 2.89122i) q^{29} +(1.87939 + 3.25519i) q^{30} +(-0.184793 + 0.320070i) q^{31} +(0.173648 - 0.984808i) q^{32} +(2.03209 - 1.70513i) q^{33} +(1.83022 + 1.53574i) q^{34} +(1.75877 + 9.97448i) q^{35} +(-0.500000 - 0.181985i) q^{36} +4.82295 q^{37} +(-3.37939 + 2.75314i) q^{38} +2.45336 q^{39} +(-1.87939 - 0.684040i) q^{40} +(-0.266044 - 1.50881i) q^{41} +(-7.29086 - 6.11776i) q^{42} +(-0.581252 + 0.487728i) q^{43} +(-0.245100 + 1.39003i) q^{44} +(-0.532089 + 0.921605i) q^{45} +(1.53209 + 2.65366i) q^{46} +(9.59627 - 3.49276i) q^{47} +(1.76604 - 0.642788i) q^{48} +(-9.32295 - 16.1478i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-0.779715 + 4.42198i) q^{51} +(-1.00000 + 0.839100i) q^{52} +(1.28312 + 1.07666i) q^{53} +(0.805407 + 4.56769i) q^{54} +(2.65270 + 0.965505i) q^{55} +5.06418 q^{56} +(-7.65657 - 2.91317i) q^{57} +8.45336 q^{58} +(-0.673648 - 0.245188i) q^{59} +(-0.652704 - 3.70167i) q^{60} +(7.47565 + 6.27282i) q^{61} +(0.283119 - 0.237565i) q^{62} +(0.467911 - 2.65366i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(1.30541 + 2.26103i) q^{65} +(-2.49273 + 0.907278i) q^{66} +(1.31908 - 0.480105i) q^{67} +(-1.19459 - 2.06910i) q^{68} +(-2.87939 + 4.98724i) q^{69} +(1.75877 - 9.97448i) q^{70} +(-4.87939 + 4.09429i) q^{71} +(0.407604 + 0.342020i) q^{72} +(-0.791737 - 4.49016i) q^{73} +(-4.53209 - 1.64955i) q^{74} +1.87939 q^{75} +(4.11721 - 1.43128i) q^{76} -7.14796 q^{77} +(-2.30541 - 0.839100i) q^{78} +(-0.389185 - 2.20718i) q^{79} +(1.53209 + 1.28558i) q^{80} +(-7.90033 + 6.62916i) q^{81} +(-0.266044 + 1.50881i) q^{82} +(1.99273 - 3.45150i) q^{83} +(4.75877 + 8.24243i) q^{84} +(-4.49020 + 1.63430i) q^{85} +(0.713011 - 0.259515i) q^{86} +(7.94356 + 13.7587i) q^{87} +(0.705737 - 1.22237i) q^{88} +(-1.84864 + 10.4842i) q^{89} +(0.815207 - 0.684040i) q^{90} +(-5.06418 - 4.24935i) q^{91} +(-0.532089 - 3.01763i) q^{92} +(0.652704 + 0.237565i) q^{93} -10.2121 q^{94} +(-1.38919 - 8.60640i) q^{95} -1.87939 q^{96} +(1.43969 + 0.524005i) q^{97} +(3.23783 + 18.3626i) q^{98} +(-0.575322 - 0.482753i) 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

Fields

Representations

Groups

Database

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