LMFDB - Embedded newform 1050.2.bc.g.943.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(157,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1050.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.bc (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			943.2
Root			$0.277956 - 0.213283i$ of defining polynomial
Character	$\chi$	$=$	1050.943
Dual form			1050.2.bc.g.157.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(1.87796 - 1.86367i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(1.87796 - 1.86367i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(-2.74315 - 4.75127i) q^{11} +(-0.965926 + 0.258819i) q^{12} +(2.41668 - 2.41668i) q^{13} +(-2.28622 - 1.33161i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.548242 - 2.04607i) q^{17} +(0.258819 - 0.965926i) q^{18} +(-3.49797 + 6.05866i) q^{19} +(2.29632 - 1.31412i) q^{21} +(-3.87940 + 3.87940i) q^{22} +(-1.69461 + 0.454069i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-2.95981 - 1.70885i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.694523 + 2.55297i) q^{28} -0.684610i q^{29} +(4.82932 - 2.78821i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-1.41996 - 5.29936i) q^{33} -2.11825 q^{34} -1.00000 q^{36} +(-2.53646 - 9.46620i) q^{37} +(6.75755 + 1.81068i) q^{38} +(2.95981 - 1.70885i) q^{39} +2.50597i q^{41} +(-1.86367 - 1.87796i) q^{42} +(1.95305 + 1.95305i) q^{43} +(4.75127 + 2.74315i) q^{44} +(0.877194 + 1.51935i) q^{46} +(3.40506 - 0.912383i) q^{47} +(0.707107 - 0.707107i) q^{48} +(0.0534500 - 6.99980i) q^{49} +(1.05912 - 1.83445i) q^{51} +(-0.884566 + 3.30124i) q^{52} +(2.43353 - 9.08204i) q^{53} +(0.500000 - 0.866025i) q^{54} +(2.64573 + 0.0101012i) q^{56} +(-4.94687 + 4.94687i) q^{57} +(-0.661282 + 0.177190i) q^{58} +(-5.08015 - 8.79907i) q^{59} +(1.01469 + 0.585830i) q^{61} +(-3.94312 - 3.94312i) q^{62} +(2.55820 - 0.675009i) q^{63} +1.00000i q^{64} +(-4.75127 + 2.74315i) q^{66} +(9.61398 + 2.57606i) q^{67} +(0.548242 + 2.04607i) q^{68} -1.75439 q^{69} -11.9716 q^{71} +(0.258819 + 0.965926i) q^{72} +(-4.70482 - 1.26065i) q^{73} +(-8.48716 + 4.90007i) q^{74} -6.99593i q^{76} +(-14.0063 - 3.81036i) q^{77} +(-2.41668 - 2.41668i) q^{78} +(7.21474 + 4.16543i) q^{79} +(0.500000 + 0.866025i) q^{81} +(2.42058 - 0.648592i) q^{82} +(4.05281 - 4.05281i) q^{83} +(-1.33161 + 2.28622i) q^{84} +(1.38101 - 2.39198i) q^{86} +(0.177190 - 0.661282i) q^{87} +(1.41996 - 5.29936i) q^{88} +(-3.59178 + 6.22115i) q^{89} +(0.0345228 - 9.04232i) q^{91} +(1.24054 - 1.24054i) q^{92} +(5.38640 - 1.44328i) q^{93} +(-1.76259 - 3.05289i) q^{94} +(-0.866025 - 0.500000i) q^{96} +(13.1212 + 13.1212i) q^{97} +(-6.77512 + 1.76005i) q^{98} -5.48630i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{7}+O(q^{10}) $ 16 * q + 4 * q^7	$ 16 q + 4 q^{7} + 4 q^{11} - 16 q^{13} - 16 q^{14} + 8 q^{16} - 12 q^{17} + 8 q^{19} + 8 q^{21} - 4 q^{22} + 40 q^{23} + 8 q^{24} - 12 q^{26} + 4 q^{28} - 24 q^{31} - 4 q^{33} - 16 q^{34} - 16 q^{36} + 8 q^{37} + 20 q^{38} + 12 q^{39} - 8 q^{42} + 24 q^{43} - 4 q^{46} - 52 q^{49} + 8 q^{51} - 8 q^{52} + 28 q^{53} + 8 q^{54} + 8 q^{56} + 8 q^{57} + 12 q^{58} - 8 q^{59} + 24 q^{61} + 8 q^{62} + 4 q^{63} + 84 q^{67} - 12 q^{68} + 8 q^{69} - 32 q^{71} - 16 q^{73} + 24 q^{74} - 44 q^{77} + 16 q^{78} - 12 q^{79} + 8 q^{81} - 36 q^{82} - 16 q^{83} - 4 q^{84} - 8 q^{86} - 48 q^{87} + 4 q^{88} + 16 q^{89} + 8 q^{91} - 8 q^{92} + 32 q^{93} - 8 q^{94} + 44 q^{97} - 24 q^{98}+O(q^{100}) $ 16 * q + 4 * q^7 + 4 * q^11 - 16 * q^13 - 16 * q^14 + 8 * q^16 - 12 * q^17 + 8 * q^19 + 8 * q^21 - 4 * q^22 + 40 * q^23 + 8 * q^24 - 12 * q^26 + 4 * q^28 - 24 * q^31 - 4 * q^33 - 16 * q^34 - 16 * q^36 + 8 * q^37 + 20 * q^38 + 12 * q^39 - 8 * q^42 + 24 * q^43 - 4 * q^46 - 52 * q^49 + 8 * q^51 - 8 * q^52 + 28 * q^53 + 8 * q^54 + 8 * q^56 + 8 * q^57 + 12 * q^58 - 8 * q^59 + 24 * q^61 + 8 * q^62 + 4 * q^63 + 84 * q^67 - 12 * q^68 + 8 * q^69 - 32 * q^71 - 16 * q^73 + 24 * q^74 - 44 * q^77 + 16 * q^78 - 12 * q^79 + 8 * q^81 - 36 * q^82 - 16 * q^83 - 4 * q^84 - 8 * q^86 - 48 * q^87 + 4 * q^88 + 16 * q^89 + 8 * q^91 - 8 * q^92 + 32 * q^93 - 8 * q^94 + 44 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$		−	1.00000i		−	0.408248i
$7$	1.87796	−	1.86367i	0.709801	−	0.704402i
$7$	1.87796	−	1.86367i	0.709801	−	0.704402i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$		0			0
$11$	−2.74315	−	4.75127i	−0.827091	−	1.43256i	−0.900311	−	0.435247i	$-0.856661\pi$
$11$	−2.74315	−	4.75127i	−0.827091	−	1.43256i	0.0732202	−	0.997316i	$-0.476672\pi$
$12$	−0.965926	+	0.258819i	−0.278839	+	0.0747146i
$13$	2.41668	−	2.41668i	0.670266	−	0.670266i	−0.287511	−	0.957777i	$-0.592828\pi$
$13$	2.41668	−	2.41668i	0.670266	−	0.670266i	0.957777	+	0.287511i	$0.0928279\pi$
$14$	−2.28622	−	1.33161i	−0.611018	−	0.355889i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	0.548242	−	2.04607i	0.132968	−	0.496244i	−0.867030	−	0.498256i	$-0.833974\pi$
$17$	0.548242	−	2.04607i	0.132968	−	0.496244i	0.999998	+	0.00201209i	$0.000640467\pi$
$18$	0.258819	−	0.965926i	0.0610042	−	0.227671i
$19$	−3.49797	+	6.05866i	−0.802489	+	1.38995i	0.115485	+	0.993309i	$0.463158\pi$
$19$	−3.49797	+	6.05866i	−0.802489	+	1.38995i	−0.917974	+	0.396642i	$0.870176\pi$
$20$		0			0
$21$	2.29632	−	1.31412i	0.501098	−	0.286764i
$22$	−3.87940	+	3.87940i	−0.827091	+	0.827091i
$23$	−1.69461	+	0.454069i	−0.353350	+	0.0946800i	−0.431128	−	0.902291i	$-0.641884\pi$
$23$	−1.69461	+	0.454069i	−0.353350	+	0.0946800i	0.0777776	+	0.996971i	$0.475218\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$		0			0
$26$	−2.95981	−	1.70885i	−0.580467	−	0.335133i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−0.694523	+	2.55297i	−0.131252	+	0.482465i
$29$		−	0.684610i		−	0.127129i	−0.997978	−	0.0635644i	$-0.979753\pi$
$29$		−	0.684610i		−	0.127129i	0.997978	−	0.0635644i	$-0.0202468\pi$
$30$		0			0
$31$	4.82932	−	2.78821i	0.867371	−	0.500777i	0.000897301	−	1.00000i	$-0.499714\pi$
$31$	4.82932	−	2.78821i	0.867371	−	0.500777i	0.866474	+	0.499223i	$0.166381\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	−1.41996	−	5.29936i	−0.247183	−	0.922500i
$34$	−2.11825			−0.363276
$35$		0			0
$36$	−1.00000			−0.166667
$37$	−2.53646	−	9.46620i	−0.416992	−	1.55623i	−0.780813	−	0.624765i	$-0.785195\pi$
$37$	−2.53646	−	9.46620i	−0.416992	−	1.55623i	0.363821	−	0.931469i	$-0.381472\pi$
$38$	6.75755	+	1.81068i	1.09622	+	0.293731i
$39$	2.95981	−	1.70885i	0.473950	−	0.273635i
$40$		0			0
$41$			2.50597i			0.391366i	0.980667	+	0.195683i	$0.0626924\pi$
$41$			2.50597i			0.391366i	−0.980667	+	0.195683i	$0.937308\pi$
$42$	−1.86367	−	1.87796i	−0.287571	−	0.289775i
$43$	1.95305	+	1.95305i	0.297837	+	0.297837i	0.840166	−	0.542329i	$-0.182457\pi$
$43$	1.95305	+	1.95305i	0.297837	+	0.297837i	−0.542329	+	0.840166i	$0.682457\pi$
$44$	4.75127	+	2.74315i	0.716282	+	0.413545i
$45$		0			0
$46$	0.877194	+	1.51935i	0.129335	+	0.224015i
$47$	3.40506	−	0.912383i	0.496679	−	0.133085i	−0.00177938	−	0.999998i	$-0.500566\pi$
$47$	3.40506	−	0.912383i	0.496679	−	0.133085i	0.498458	+	0.866914i	$0.333900\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$	0.0534500	−	6.99980i	0.00763571	−	0.999971i
$50$		0			0
$51$	1.05912	−	1.83445i	0.148307	−	0.256875i
$52$	−0.884566	+	3.30124i	−0.122667	+	0.457800i
$53$	2.43353	−	9.08204i	0.334270	−	1.24751i	−0.570388	−	0.821376i	$-0.693207\pi$
$53$	2.43353	−	9.08204i	0.334270	−	1.24751i	0.904658	−	0.426138i	$-0.140126\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$		0			0
$56$	2.64573	+	0.0101012i	0.353551	+	0.00134983i
$57$	−4.94687	+	4.94687i	−0.655229	+	0.655229i
$58$	−0.661282	+	0.177190i	−0.0868306	+	0.0232662i
$59$	−5.08015	−	8.79907i	−0.661379	−	1.14554i	−0.980253	−	0.197745i	$-0.936638\pi$
$59$	−5.08015	−	8.79907i	−0.661379	−	1.14554i	0.318875	−	0.947797i	$-0.396695\pi$
$60$		0			0
$61$	1.01469	+	0.585830i	0.129917	+	0.0750079i	0.563550	−	0.826082i	$-0.309435\pi$
$61$	1.01469	+	0.585830i	0.129917	+	0.0750079i	−0.433633	+	0.901090i	$0.642768\pi$
$62$	−3.94312	−	3.94312i	−0.500777	−	0.500777i
$63$	2.55820	−	0.675009i	0.322302	−	0.0850431i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−4.75127	+	2.74315i	−0.584841	+	0.337658i
$67$	9.61398	+	2.57606i	1.17454	+	0.314716i	0.792757	−	0.609538i	$-0.208645\pi$
$67$	9.61398	+	2.57606i	1.17454	+	0.314716i	0.381778	+	0.924254i	$0.375312\pi$
$68$	0.548242	+	2.04607i	0.0664841	+	0.248122i
$69$	−1.75439			−0.211204
$70$		0			0
$71$	−11.9716			−1.42077			−0.710383	−	0.703816i	$-0.751478\pi$
$71$	−11.9716			−1.42077			−0.710383	+	0.703816i	$0.751478\pi$
$72$	0.258819	+	0.965926i	0.0305021	+	0.113835i
$73$	−4.70482	−	1.26065i	−0.550657	−	0.147548i	−0.0272467	−	0.999629i	$-0.508674\pi$
$73$	−4.70482	−	1.26065i	−0.550657	−	0.147548i	−0.523411	+	0.852081i	$0.675341\pi$
$74$	−8.48716	+	4.90007i	−0.986613	+	0.569621i
$75$		0			0
$76$		−	6.99593i		−	0.802489i
$77$	−14.0063	−	3.81036i	−1.59617	−	0.434231i
$78$	−2.41668	−	2.41668i	−0.273635	−	0.273635i
$79$	7.21474	+	4.16543i	0.811722	+	0.468648i	0.847553	−	0.530710i	$-0.178075\pi$
$79$	7.21474	+	4.16543i	0.811722	+	0.468648i	−0.0358316	+	0.999358i	$0.511408\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	2.42058	−	0.648592i	0.267308	−	0.0716250i
$83$	4.05281	−	4.05281i	0.444854	−	0.444854i	−0.448786	−	0.893639i	$-0.648143\pi$
$83$	4.05281	−	4.05281i	0.444854	−	0.444854i	0.893639	+	0.448786i	$0.148143\pi$
$84$	−1.33161	+	2.28622i	−0.145291	+	0.249447i
$85$		0			0
$86$	1.38101	−	2.39198i	0.148918	−	0.257934i
$87$	0.177190	−	0.661282i	0.0189968	−	0.0708969i
$88$	1.41996	−	5.29936i	0.151368	−	0.564913i
$89$	−3.59178	+	6.22115i	−0.380728	+	0.659440i	−0.991166	−	0.132623i	$-0.957660\pi$
$89$	−3.59178	+	6.22115i	−0.380728	+	0.659440i	0.610439	+	0.792064i	$0.290993\pi$
$90$		0			0
$91$	0.0345228	−	9.04232i	0.00361897	−	0.947892i
$92$	1.24054	−	1.24054i	0.129335	−	0.129335i
$93$	5.38640	−	1.44328i	0.558544	−	0.149661i
$94$	−1.76259	−	3.05289i	−0.181797	−	0.314882i
$95$		0			0
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$	13.1212	+	13.1212i	1.33226	+	1.33226i	0.903348	+	0.428909i	$0.141102\pi$
$97$	13.1212	+	13.1212i	1.33226	+	1.33226i	0.428909	+	0.903348i	$0.358898\pi$
$98$	−6.77512	+	1.76005i	−0.684390	+	0.177792i
$99$		−	5.48630i		−	0.551394i
$100$		0			0
$101$	7.16001	−	4.13383i	0.712447	−	0.411332i	−0.0995192	−	0.995036i	$-0.531730\pi$
$101$	7.16001	−	4.13383i	0.712447	−	0.411332i	0.811967	+	0.583704i	$0.198397\pi$
$102$	−2.04607	−	0.548242i	−0.202591	−	0.0542841i
$103$	2.40862	+	8.98910i	0.237329	+	0.885722i	0.977085	+	0.212848i	$0.0682739\pi$
$103$	2.40862	+	8.98910i	0.237329	+	0.885722i	−0.739757	+	0.672874i	$0.765059\pi$
$104$	3.41770			0.335133
$105$		0			0
$106$	−9.40242			−0.913244
$107$	3.17510	+	11.8496i	0.306949	+	1.14555i	0.931255	+	0.364369i	$0.118715\pi$
$107$	3.17510	+	11.8496i	0.306949	+	1.14555i	−0.624306	+	0.781180i	$0.714618\pi$
$108$	−0.965926	−	0.258819i	−0.0929463	−	0.0249049i
$109$	−0.291523	+	0.168311i	−0.0279228	+	0.0161213i	−0.513896	−	0.857852i	$-0.671798\pi$
$109$	−0.291523	+	0.168311i	−0.0279228	+	0.0161213i	0.485974	+	0.873973i	$0.338465\pi$
$110$		0			0
$111$		−	9.80013i		−	0.930188i
$112$	−0.675009	−	2.55820i	−0.0637823	−	0.241727i
$113$	−10.1896	−	10.1896i	−0.958555	−	0.958555i	0.0406198	−	0.999175i	$-0.487067\pi$
$113$	−10.1896	−	10.1896i	−0.958555	−	0.958555i	−0.999175	+	0.0406198i	$0.987067\pi$
$114$	6.05866	+	3.49797i	0.567445	+	0.327615i
$115$		0			0
$116$	0.342305	+	0.592889i	0.0317822	+	0.0550484i
$117$	3.30124	−	0.884566i	0.305200	−	0.0817781i
$118$	−7.18441	+	7.18441i	−0.661379	+	0.661379i
$119$	−2.78362	−	4.86417i	−0.255174	−	0.445898i
$120$		0			0
$121$	−9.54974	+	16.5406i	−0.868158	+	1.50369i
$122$	0.303248	−	1.13174i	0.0274548	−	0.102463i
$123$	−0.648592	+	2.42058i	−0.0584816	+	0.218256i
$124$	−2.78821	+	4.82932i	−0.250388	+	0.433686i
$125$		0			0
$126$	−1.31412	−	2.29632i	−0.117071	−	0.204573i
$127$	4.77054	−	4.77054i	0.423317	−	0.423317i	−0.463027	−	0.886344i	$-0.653237\pi$
$127$	4.77054	−	4.77054i	0.423317	−	0.423317i	0.886344	+	0.463027i	$0.153237\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	1.38101	+	2.39198i	0.121591	+	0.210602i
$130$		0			0
$131$	15.7695	+	9.10455i	1.37779	+	0.795468i	0.991893	−	0.127074i	$-0.0405585\pi$
$131$	15.7695	+	9.10455i	1.37779	+	0.795468i	0.385898	+	0.922542i	$0.373892\pi$
$132$	3.87940	+	3.87940i	0.337658	+	0.337658i
$133$	4.72232	+	17.8970i	0.409477	+	1.55186i
$134$		−	9.95313i		−	0.859819i
$135$		0			0
$136$	1.83445	−	1.05912i	0.157303	−	0.0908190i
$137$	2.11024	+	0.565438i	0.180290	+	0.0483086i	0.347835	−	0.937556i	$-0.386917\pi$
$137$	2.11024	+	0.565438i	0.180290	+	0.0483086i	−0.167544	+	0.985865i	$0.553584\pi$
$138$	0.454069	+	1.69461i	0.0386529	+	0.144255i
$139$	−18.1446			−1.53900			−0.769501	−	0.638645i	$-0.779495\pi$
$139$	−18.1446			−1.53900			−0.769501	+	0.638645i	$0.779495\pi$
$140$		0			0
$141$	3.52518			0.296873
$142$	3.09847	+	11.5637i	0.260018	+	0.970401i
$143$	−18.1116	−	4.85299i	−1.51457	−	0.405828i
$144$	0.866025	−	0.500000i	0.0721688	−	0.0416667i
$145$		0			0
$146$			4.87079i			0.403109i
$147$	1.86331	−	6.74745i	0.153683	−	0.556520i
$148$	6.92974	+	6.92974i	0.569621	+	0.569621i
$149$	−0.167711	−	0.0968279i	−0.0137394	−	0.00793245i	0.493115	−	0.869964i	$-0.335858\pi$
$149$	−0.167711	−	0.0968279i	−0.0137394	−	0.00793245i	−0.506854	+	0.862032i	$0.669192\pi$
$150$		0			0
$151$	10.6614	+	18.4660i	0.867610	+	1.50274i	0.864432	+	0.502750i	$0.167678\pi$
$151$	10.6614	+	18.4660i	0.867610	+	1.50274i	0.00317777	+	0.999995i	$0.498988\pi$
$152$	−6.75755	+	1.81068i	−0.548110	+	0.146866i
$153$	1.49783	−	1.49783i	0.121092	−	0.121092i
$154$	−0.0554181	+	14.5153i	−0.00446571	+	1.16967i
$155$		0			0
$156$	−1.70885	+	2.95981i	−0.136817	+	0.236975i
$157$	0.952462	−	3.55464i	0.0760147	−	0.283691i	−0.917447	−	0.397859i	$-0.869753\pi$
$157$	0.952462	−	3.55464i	0.0760147	−	0.283691i	0.993461	+	0.114168i	$0.0364201\pi$
$158$	2.15619	−	8.04700i	0.171537	−	0.640185i
$159$	4.70121	−	8.14273i	0.372830	−	0.645761i
$160$		0			0
$161$	−2.33617	+	4.01092i	−0.184116	+	0.316105i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	−13.6012	+	3.64443i	−1.06533	+	0.285454i	−0.748572	−	0.663054i	$-0.769260\pi$
$163$	−13.6012	+	3.64443i	−1.06533	+	0.285454i	−0.316756	+	0.948507i	$0.602594\pi$
$164$	−1.25298	−	2.17023i	−0.0978416	−	0.169467i
$165$		0			0
$166$	−4.96366	−	2.86577i	−0.385255	−	0.222427i
$167$	−6.07259	−	6.07259i	−0.469911	−	0.469911i	0.431974	−	0.901886i	$-0.357817\pi$
$167$	−6.07259	−	6.07259i	−0.469911	−	0.469911i	−0.901886	+	0.431974i	$0.857817\pi$
$168$	2.55297	+	0.694523i	0.196966	+	0.0535836i
$169$			1.31933i			0.101487i
$170$		0			0
$171$	−6.05866	+	3.49797i	−0.463317	+	0.267496i
$172$	−2.66791	−	0.714864i	−0.203426	−	0.0545079i
$173$	1.04797	+	3.91108i	0.0796757	+	0.297354i	0.994253	−	0.107058i	$-0.0341430\pi$
$173$	1.04797	+	3.91108i	0.0796757	+	0.297354i	−0.914577	+	0.404412i	$0.867476\pi$
$174$	−0.684610			−0.0519001
$175$		0			0
$176$	−5.48630			−0.413545
$177$	−2.62968	−	9.81409i	−0.197659	−	0.737672i
$178$	6.93879	+	1.85924i	0.520084	+	0.139356i
$179$	3.17428	−	1.83267i	0.237256	−	0.136980i	−0.376659	−	0.926352i	$-0.622927\pi$
$179$	3.17428	−	1.83267i	0.237256	−	0.136980i	0.613915	+	0.789372i	$0.289594\pi$
$180$		0			0
$181$		−	2.39985i		−	0.178379i	−0.996015	−	0.0891896i	$-0.971572\pi$
$181$		−	2.39985i		−	0.178379i	0.996015	−	0.0891896i	$-0.0284277\pi$
$182$	−8.74314	+	2.30698i	−0.648085	+	0.171005i
$183$	0.828489	+	0.828489i	0.0612437	+	0.0612437i
$184$	−1.51935	−	0.877194i	−0.112008	−	0.0646676i
$185$		0			0
$186$	−2.78821	−	4.82932i	−0.204441	−	0.354103i
$187$	−11.2253	+	3.00782i	−0.820878	+	0.219954i
$188$	−2.49268	+	2.49268i	−0.181797	+	0.181797i
$189$	2.64573	+	0.0101012i	0.192449	+	0.000734752i
$190$		0			0
$191$	−4.03766	+	6.99344i	−0.292155	+	0.506027i	−0.974319	−	0.225172i	$-0.927706\pi$
$191$	−4.03766	+	6.99344i	−0.292155	+	0.506027i	0.682164	+	0.731199i	$0.261039\pi$
$192$	−0.258819	+	0.965926i	−0.0186787	+	0.0697097i
$193$	0.445821	−	1.66383i	0.0320909	−	0.119765i	−0.948022	−	0.318204i	$-0.896920\pi$
$193$	0.445821	−	1.66383i	0.0320909	−	0.119765i	0.980113	+	0.198439i	$0.0635871\pi$
$194$	9.27809	−	16.0701i	0.666128	−	1.15377i
$195$		0			0
$196$	3.45361	+	6.08873i	0.246686	+	0.434909i
$197$	−6.01174	+	6.01174i	−0.428319	+	0.428319i	−0.888055	−	0.459737i	$-0.847944\pi$
$197$	−6.01174	+	6.01174i	−0.428319	+	0.428319i	0.459737	+	0.888055i	$0.347944\pi$
$198$	−5.29936	+	1.41996i	−0.376609	+	0.100912i
$199$	5.50897	+	9.54181i	0.390520	+	0.676401i	0.992518	−	0.122097i	$-0.0389618\pi$
$199$	5.50897	+	9.54181i	0.390520	+	0.676401i	−0.601998	+	0.798498i	$0.705628\pi$
$200$		0			0
$201$	8.61966	+	4.97656i	0.607984	+	0.351020i
$202$	−5.84612	−	5.84612i	−0.411332	−	0.411332i
$203$	−1.27589	−	1.28567i	−0.0895498	−	0.0902362i
$204$			2.11825i			0.148307i
$205$		0			0
$206$	8.05941	−	4.65310i	0.561526	−	0.324197i
$207$	−1.69461	−	0.454069i	−0.117783	−	0.0315600i
$208$	−0.884566	−	3.30124i	−0.0613336	−	0.228900i
$209$	38.3818			2.65492
$210$		0			0
$211$	10.3323			0.711302			0.355651	−	0.934619i	$-0.384259\pi$
$211$	10.3323			0.711302			0.355651	+	0.934619i	$0.384259\pi$
$212$	2.43353	+	9.08204i	0.167135	+	0.623757i
$213$	−11.5637	−	3.09847i	−0.792329	−	0.212304i
$214$	10.6241	−	6.13383i	0.726249	−	0.419300i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	3.87295	−	14.2364i	0.262913	−	0.966430i
$218$	0.238027	+	0.238027i	0.0161213	+	0.0161213i
$219$	−4.21822	−	2.43539i	−0.285041	−	0.164569i
$220$		0			0
$221$	−3.61976	−	6.26961i	−0.243492	−	0.421740i
$222$	−9.46620	+	2.53646i	−0.635330	+	0.170236i
$223$	−3.41183	+	3.41183i	−0.228473	+	0.228473i	−0.812054	−	0.583582i	$-0.801651\pi$
$223$	−3.41183	+	3.41183i	−0.228473	+	0.228473i	0.583582	+	0.812054i	$0.301651\pi$
$224$	−2.29632	+	1.31412i	−0.153429	+	0.0878032i
$225$		0			0
$226$	−7.20512	+	12.4796i	−0.479277	+	0.830133i
$227$	4.68301	−	17.4772i	0.310822	−	1.16000i	−0.616994	−	0.786968i	$-0.711650\pi$
$227$	4.68301	−	17.4772i	0.310822	−	1.16000i	0.927816	−	0.373037i	$-0.121684\pi$
$228$	1.81068	−	6.75755i	0.119915	−	0.447530i
$229$	4.82375	−	8.35497i	0.318762	−	0.552112i	−0.661468	−	0.749973i	$-0.730066\pi$
$229$	4.82375	−	8.35497i	0.318762	−	0.552112i	0.980230	+	0.197861i	$0.0633996\pi$
$230$		0			0
$231$	−12.5429	−	7.30563i	−0.825262	−	0.480675i
$232$	0.484092	−	0.484092i	0.0317822	−	0.0317822i
$233$	13.9801	−	3.74597i	0.915870	−	0.245407i	0.230051	−	0.973179i	$-0.426111\pi$
$233$	13.9801	−	3.74597i	0.915870	−	0.245407i	0.685819	+	0.727772i	$0.259444\pi$
$234$	−1.70885	−	2.95981i	−0.111711	−	0.193489i
$235$		0			0
$236$	8.79907	+	5.08015i	0.572771	+	0.330689i
$237$	5.89081	+	5.89081i	0.382649	+	0.382649i
$238$	−3.97798	+	3.94772i	−0.257854	+	0.255892i
$239$			29.9736i			1.93883i	0.245427	+	0.969415i	$0.421072\pi$
$239$			29.9736i			1.93883i	−0.245427	+	0.969415i	$0.578928\pi$
$240$		0			0
$241$	14.3934	−	8.31003i	0.927161	−	0.535296i	0.0412481	−	0.999149i	$-0.486867\pi$
$241$	14.3934	−	8.31003i	0.927161	−	0.535296i	0.885912	+	0.463853i	$0.153533\pi$
$242$	18.4487	+	4.94331i	1.18593	+	0.317768i
$243$	0.258819	+	0.965926i	0.0166032	+	0.0619642i
$244$	−1.17166			−0.0750079
$245$		0			0
$246$	2.50597			0.159775
$247$	6.18836	+	23.0953i	0.393756	+	1.46952i
$248$	5.38640	+	1.44328i	0.342037	+	0.0916485i
$249$	4.96366	−	2.86577i	0.314559	−	0.181611i
$250$		0			0
$251$			10.7660i			0.679546i	0.940508	+	0.339773i	$0.110350\pi$
$251$			10.7660i			0.679546i	−0.940508	+	0.339773i	$0.889650\pi$
$252$	−1.87796	+	1.86367i	−0.118300	+	0.117400i
$253$	6.80597	+	6.80597i	0.427888	+	0.427888i
$254$	−5.84270	−	3.37328i	−0.366604	−	0.211659i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	14.5299	−	3.89328i	0.906352	−	0.242856i	0.224610	−	0.974449i	$-0.427889\pi$
$257$	14.5299	−	3.89328i	0.906352	−	0.242856i	0.681742	+	0.731593i	$0.261223\pi$
$258$	1.95305	−	1.95305i	0.121591	−	0.121591i
$259$	−22.4053	−	13.0500i	−1.39220	−	0.810887i
$260$		0			0
$261$	0.342305	−	0.592889i	0.0211881	−	0.0366989i
$262$	4.71286	−	17.5886i	0.291161	−	1.08663i
$263$	−5.83157	+	21.7637i	−0.359590	+	1.34201i	0.515019	+	0.857179i	$0.327785\pi$
$263$	−5.83157	+	21.7637i	−0.359590	+	1.34201i	−0.874609	+	0.484829i	$0.838882\pi$
$264$	2.74315	−	4.75127i	0.168829	−	0.292421i
$265$		0			0
$266$	16.0649	−	9.19348i	0.985003	−	0.563689i
$267$	−5.07954	+	5.07954i	−0.310863	+	0.310863i
$268$	−9.61398	+	2.57606i	−0.587268	+	0.157358i
$269$	5.52122	+	9.56304i	0.336635	+	0.583069i	0.983797	−	0.179283i	$-0.0573779\pi$
$269$	5.52122	+	9.56304i	0.336635	+	0.583069i	−0.647163	+	0.762352i	$0.724045\pi$
$270$		0			0
$271$	4.34433	+	2.50820i	0.263899	+	0.152362i	0.626112	−	0.779733i	$-0.284645\pi$
$271$	4.34433	+	2.50820i	0.263899	+	0.152362i	−0.362213	+	0.932095i	$0.617979\pi$
$272$	−1.49783	−	1.49783i	−0.0908190	−	0.0908190i
$273$	2.37367	−	8.72527i	0.143661	−	0.528077i
$274$		−	2.18468i		−	0.131982i
$275$		0			0
$276$	1.51935	−	0.877194i	0.0914538	−	0.0528009i
$277$	6.11920	+	1.63963i	0.367667	+	0.0985161i	0.437922	−	0.899013i	$-0.355715\pi$
$277$	6.11920	+	1.63963i	0.367667	+	0.0985161i	−0.0702549	+	0.997529i	$0.522381\pi$
$278$	4.69616	+	17.5263i	0.281657	+	1.05116i
$279$	5.57642			0.333851
$280$		0			0
$281$	−29.4723			−1.75817			−0.879085	−	0.476665i	$-0.841846\pi$
$281$	−29.4723			−1.75817			−0.879085	+	0.476665i	$0.841846\pi$
$282$	−0.912383	−	3.40506i	−0.0543316	−	0.202768i
$283$	0.0944925	+	0.0253192i	0.00561700	+	0.00150507i	0.261626	−	0.965169i	$-0.415741\pi$
$283$	0.0944925	+	0.0253192i	0.00561700	+	0.00150507i	−0.256009	+	0.966674i	$0.582408\pi$
$284$	10.3677	−	5.98579i	0.615210	−	0.355191i
$285$		0			0
$286$			18.7505i			1.10874i
$287$	4.67030	+	4.70610i	0.275679	+	0.277792i
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$	10.8366	+	6.25652i	0.637447	+	0.368030i
$290$		0			0
$291$	9.27809	+	16.0701i	0.543891	+	0.942048i
$292$	4.70482	−	1.26065i	0.275329	−	0.0737741i
$293$	14.0076	−	14.0076i	0.818330	−	0.818330i	−0.167536	−	0.985866i	$-0.553581\pi$
$293$	14.0076	−	14.0076i	0.818330	−	0.818330i	0.985866	+	0.167536i	$0.0535810\pi$
$294$	−6.99980	−	0.0534500i	−0.408236	−	0.00311727i
$295$		0			0
$296$	4.90007	−	8.48716i	0.284811	−	0.493306i
$297$	1.41996	−	5.29936i	0.0823944	−	0.307500i
$298$	−0.0501218	+	0.187057i	−0.00290348	+	0.0108359i
$299$	−2.99799	+	5.19266i	−0.173378	+	0.300300i
$300$		0			0
$301$	7.30758	+	0.0278997i	0.421202	+	0.00160811i
$302$	15.0775	−	15.0775i	0.867610	−	0.867610i
$303$	7.98595	−	2.13983i	0.458781	−	0.122930i
$304$	3.49797	+	6.05866i	0.200622	+	0.347488i
$305$		0			0
$306$	−1.83445	−	1.05912i	−0.104869	−	0.0605460i
$307$	3.05320	+	3.05320i	0.174255	+	0.174255i	0.788846	−	0.614591i	$-0.210679\pi$
$307$	3.05320	+	3.05320i	0.174255	+	0.174255i	−0.614591	+	0.788846i	$0.710679\pi$
$308$	14.0350	−	3.70330i	0.799720	−	0.211015i
$309$			9.30620i			0.529411i
$310$		0			0
$311$	−7.31386	+	4.22266i	−0.414731	+	0.239445i	−0.692820	−	0.721110i	$-0.743632\pi$
$311$	−7.31386	+	4.22266i	−0.414731	+	0.239445i	0.278089	+	0.960555i	$0.410299\pi$
$312$	3.30124	+	0.884566i	0.186896	+	0.0500787i
$313$	5.02358	+	18.7482i	0.283949	+	1.05971i	0.949604	+	0.313453i	$0.101486\pi$
$313$	5.02358	+	18.7482i	0.283949	+	1.05971i	−0.665654	+	0.746260i	$0.731847\pi$
$314$	−3.68003			−0.207676
$315$		0			0
$316$	−8.33087			−0.468648
$317$	4.02471	+	15.0204i	0.226050	+	0.843632i	0.981981	+	0.188980i	$0.0605181\pi$
$317$	4.02471	+	15.0204i	0.226050	+	0.843632i	−0.755931	+	0.654652i	$0.772815\pi$
$318$	−9.08204	−	2.43353i	−0.509296	−	0.136465i
$319$	−3.25277	+	1.87799i	−0.182120	+	0.105147i
$320$		0			0
$321$			12.2677i			0.684714i
$322$	4.47890	+	1.21846i	0.249599	+	0.0679023i
$323$	10.4787	+	10.4787i	0.583050	+	0.583050i
$324$	−0.866025	−	0.500000i	−0.0481125	−	0.0277778i
$325$		0			0
$326$	7.04050	+	12.1945i	0.389937	+	0.675391i
$327$	−0.325151	+	0.0871241i	−0.0179809	+	0.00481797i
$328$	−1.77199	+	1.77199i	−0.0978416	+	0.0978416i
$329$	4.69417	−	8.05933i	0.258798	−	0.444325i
$330$		0			0
$331$	−8.09296	+	14.0174i	−0.444830	+	0.770467i	−0.998040	−	0.0625739i	$-0.980069\pi$
$331$	−8.09296	+	14.0174i	−0.444830	+	0.770467i	0.553211	+	0.833041i	$0.313402\pi$
$332$	−1.48343	+	5.53624i	−0.0814139	+	0.303841i
$333$	2.53646	−	9.46620i	0.138997	−	0.518745i
$334$	−4.29397	+	7.43738i	−0.234956	+	0.406955i
$335$		0			0
$336$	0.0101012	−	2.64573i	0.000551064	−	0.144337i
$337$	−19.2055	+	19.2055i	−1.04619	+	1.04619i	−0.0473073	+	0.998880i	$0.515064\pi$
$337$	−19.2055	+	19.2055i	−1.04619	+	1.04619i	−0.998880	+	0.0473073i	$0.984936\pi$
$338$	1.27438	−	0.341468i	0.0693169	−	0.0185734i
$339$	−7.20512	−	12.4796i	−0.391328	−	0.677801i
$340$		0			0
$341$	−26.4951	−	15.2969i	−1.43479	−	0.828376i
$342$	4.94687	+	4.94687i	0.267496	+	0.267496i
$343$	−12.9450	−	13.2449i	−0.698962	−	0.715159i
$344$			2.76202i			0.148918i
$345$		0			0
$346$	3.50658	−	2.02452i	0.188515	−	0.108839i
$347$	9.91592	+	2.65696i	0.532315	+	0.142633i	0.514957	−	0.857216i	$-0.327808\pi$
$347$	9.91592	+	2.65696i	0.532315	+	0.142633i	0.0173577	+	0.999849i	$0.494475\pi$
$348$	0.177190	+	0.661282i	0.00949838	+	0.0354484i
$349$	6.61441			0.354061			0.177031	−	0.984205i	$-0.443351\pi$
$349$	6.61441			0.354061			0.177031	+	0.984205i	$0.443351\pi$
$350$		0			0
$351$	3.41770			0.182423
$352$	1.41996	+	5.29936i	0.0756841	+	0.282457i
$353$	−13.1604	−	3.52633i	−0.700460	−	0.187688i	−0.109023	−	0.994039i	$-0.534772\pi$
$353$	−13.1604	−	3.52633i	−0.700460	−	0.187688i	−0.591436	+	0.806352i	$0.701439\pi$
$354$	−8.79907	+	5.08015i	−0.467666	+	0.270007i
$355$		0			0
$356$		−	7.18356i		−	0.380728i
$357$	−1.42983	−	5.41889i	−0.0756749	−	0.286798i
$358$	−2.59178	−	2.59178i	−0.136980	−	0.136980i
$359$	−14.9791	−	8.64822i	−0.790569	−	0.456435i	0.0495937	−	0.998769i	$-0.484207\pi$
$359$	−14.9791	−	8.64822i	−0.790569	−	0.456435i	−0.840163	+	0.542334i	$0.817541\pi$
$360$		0			0
$361$	−14.9715	−	25.9315i	−0.787976	−	1.36481i
$362$	−2.31807	+	0.621126i	−0.121835	+	0.0326457i
$363$	−13.5054	+	13.5054i	−0.708848	+	0.708848i
$364$	4.49126	+	7.84814i	0.235406	+	0.411354i
$365$		0			0
$366$	0.585830	−	1.01469i	0.0306218	−	0.0530386i
$367$	6.69852	−	24.9992i	0.349660	−	1.30495i	−0.537413	−	0.843319i	$-0.680598\pi$
$367$	6.69852	−	24.9992i	0.349660	−	1.30495i	0.887073	−	0.461629i	$-0.152735\pi$
$368$	−0.454069	+	1.69461i	−0.0236700	+	0.0883376i
$369$	−1.25298	+	2.17023i	−0.0652277	+	0.112978i
$370$		0			0
$371$	−12.3559	−	21.5910i	−0.641486	−	1.12095i
$372$	−3.94312	+	3.94312i	−0.204441	+	0.204441i
$373$	8.85404	−	2.37243i	0.458445	−	0.122840i	−0.0222033	−	0.999753i	$-0.507068\pi$
$373$	8.85404	−	2.37243i	0.458445	−	0.122840i	0.480648	+	0.876914i	$0.340401\pi$
$374$	5.81066	+	10.0644i	0.300462	+	0.520416i
$375$		0			0
$376$	3.05289	+	1.76259i	0.157441	+	0.0908985i
$377$	−1.65448	−	1.65448i	−0.0852101	−	0.0852101i
$378$	−0.675009	−	2.55820i	−0.0347187	−	0.131579i
$379$			18.6871i			0.959891i	0.877298	+	0.479946i	$0.159344\pi$
$379$			18.6871i			0.959891i	−0.877298	+	0.479946i	$0.840656\pi$
$380$		0			0
$381$	5.84270	−	3.37328i	0.299331	−	0.172819i
$382$	7.80016	+	2.09005i	0.399091	+	0.106936i
$383$	5.13534	+	19.1654i	0.262404	+	0.979304i	0.963820	+	0.266553i	$0.0858846\pi$
$383$	5.13534	+	19.1654i	0.262404	+	0.979304i	−0.701417	+	0.712752i	$0.747449\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−1.72252			−0.0876740
$387$	0.714864	+	2.66791i	0.0363386	+	0.135618i
$388$	−17.9239	−	4.80269i	−0.909948	−	0.243820i
$389$	−4.44026	+	2.56359i	−0.225130	+	0.129979i	−0.608323	−	0.793689i	$-0.708158\pi$
$389$	−4.44026	+	2.56359i	−0.225130	+	0.129979i	0.383193	+	0.923668i	$0.374824\pi$
$390$		0			0
$391$			3.71623i			0.187938i
$392$	4.98740	−	4.91181i	0.251902	−	0.248084i
$393$	12.8758	+	12.8758i	0.649497	+	0.649497i
$394$	7.36285	+	4.25094i	0.370935	+	0.214159i
$395$		0			0
$396$	2.74315	+	4.75127i	0.137848	+	0.238761i
$397$	−25.4941	+	6.83113i	−1.27951	+	0.342844i	−0.833668	−	0.552266i	$-0.813763\pi$
$397$	−25.4941	+	6.83113i	−1.27951	+	0.342844i	−0.445845	+	0.895110i	$0.647097\pi$
$398$	7.79086	−	7.79086i	0.390520	−	0.390520i
$399$	−0.0706671	+	18.5094i	−0.00353778	+	0.926627i
$400$		0			0
$401$	8.61471	−	14.9211i	0.430198	−	0.745125i	−0.566692	−	0.823930i	$-0.691777\pi$
$401$	8.61471	−	14.9211i	0.430198	−	0.745125i	0.996890	+	0.0788050i	$0.0251104\pi$
$402$	2.57606	−	9.61398i	0.128482	−	0.479502i
$403$	4.93271	−	18.4091i	0.245716	−	0.917023i
$404$	−4.13383	+	7.16001i	−0.205666	+	0.356224i
$405$		0			0
$406$	−0.911636	+	1.56517i	−0.0452437	+	0.0776780i
$407$	−38.0186	+	38.0186i	−1.88451	+	1.88451i
$408$	2.04607	−	0.548242i	0.101295	−	0.0271420i
$409$	−17.8569	−	30.9290i	−0.882967	−	1.52934i	−0.848027	−	0.529954i	$-0.822209\pi$
$409$	−17.8569	−	30.9290i	−0.882967	−	1.52934i	−0.0349400	−	0.999389i	$-0.511124\pi$
$410$		0			0
$411$	1.89199	+	1.09234i	0.0933251	+	0.0538813i
$412$	−6.58048	−	6.58048i	−0.324197	−	0.324197i
$413$	−25.9389	−	7.05656i	−1.27637	−	0.347230i
$414$			1.75439i			0.0862235i
$415$		0			0
$416$	−2.95981	+	1.70885i	−0.145117	+	0.0837832i
$417$	−17.5263	−	4.69616i	−0.858267	−	0.229972i
$418$	−9.93394	−	37.0740i	−0.485885	−	1.81335i
$419$	14.0414			0.685966			0.342983	−	0.939342i	$-0.388563\pi$
$419$	14.0414			0.685966			0.342983	+	0.939342i	$0.388563\pi$
$420$		0			0
$421$	24.4332			1.19080			0.595401	−	0.803429i	$-0.296993\pi$
$421$	24.4332			1.19080			0.595401	+	0.803429i	$0.296993\pi$
$422$	−2.67419	−	9.98020i	−0.130177	−	0.485829i
$423$	3.40506	+	0.912383i	0.165560	+	0.0443616i
$424$	8.14273	−	4.70121i	0.395446	−	0.228311i
$425$		0			0
$426$			11.9716i			0.580025i
$427$	2.99734	−	0.790881i	0.145051	−	0.0382734i
$428$	−8.67454	−	8.67454i	−0.419300	−	0.419300i
$429$	−16.2384	−	9.37526i	−0.783999	−	0.452642i
$430$		0			0
$431$	19.3886	+	33.5820i	0.933914	+	1.61759i	0.776559	+	0.630044i	$0.216963\pi$
$431$	19.3886	+	33.5820i	0.933914	+	1.61759i	0.157354	+	0.987542i	$0.449704\pi$
$432$	0.965926	−	0.258819i	0.0464731	−	0.0124524i
$433$	7.85700	−	7.85700i	0.377583	−	0.377583i	−0.492646	−	0.870230i	$-0.663970\pi$
$433$	7.85700	−	7.85700i	0.377583	−	0.377583i	0.870230	+	0.492646i	$0.163970\pi$
$434$	−14.7537	−	0.0563283i	−0.708200	−	0.00270385i
$435$		0			0
$436$	0.168311	−	0.291523i	0.00806063	−	0.0139614i
$437$	3.17664	−	11.8554i	0.151959	−	0.567119i
$438$	−1.26065	+	4.70482i	−0.0602363	+	0.224805i
$439$	10.5640	−	18.2973i	0.504190	−	0.873283i	−0.495798	−	0.868438i	$-0.665124\pi$
$439$	10.5640	−	18.2973i	0.504190	−	0.873283i	0.999988	−	0.00484487i	$-0.00154217\pi$
$440$		0			0
$441$	3.54619	−	6.03528i	0.168866	−	0.287394i
$442$	−5.11912	+	5.11912i	−0.243492	+	0.243492i
$443$	6.48289	−	1.73709i	0.308011	−	0.0825314i	−0.101503	−	0.994835i	$-0.532365\pi$
$443$	6.48289	−	1.73709i	0.308011	−	0.0825314i	0.409514	+	0.912304i	$0.365698\pi$
$444$	4.90007	+	8.48716i	0.232547	+	0.402783i
$445$		0			0
$446$	4.17862	+	2.41253i	0.197863	+	0.114236i
$447$	−0.136935	−	0.136935i	−0.00647682	−	0.00647682i
$448$	1.86367	+	1.87796i	0.0880502	+	0.0887252i
$449$		−	8.28979i		−	0.391219i	−0.980682	−	0.195610i	$-0.937331\pi$
$449$		−	8.28979i		−	0.391219i	0.980682	−	0.195610i	$-0.0626685\pi$
$450$		0			0
$451$	11.9065	−	6.87424i	0.560657	−	0.323695i
$452$	13.9192	+	3.72964i	0.654705	+	0.175428i
$453$	5.51873	+	20.5962i	0.259293	+	0.967693i
$454$	−18.0938			−0.849182
$455$		0			0
$456$	−6.99593			−0.327615
$457$	−5.71524	−	21.3296i	−0.267348	−	0.997755i	−0.960798	−	0.277250i	$-0.910577\pi$
$457$	−5.71524	−	21.3296i	−0.267348	−	0.997755i	0.693450	−	0.720505i	$-0.256090\pi$
$458$	−9.31876	−	2.49695i	−0.435437	−	0.116675i
$459$	1.83445	−	1.05912i	0.0856250	−	0.0494356i
$460$		0			0
$461$		−	19.0130i		−	0.885524i	−0.896639	−	0.442762i	$-0.853999\pi$
$461$		−	19.0130i		−	0.885524i	0.896639	−	0.442762i	$-0.146001\pi$
$462$	−3.81036	+	14.0063i	−0.177274	+	0.651634i
$463$	16.6091	+	16.6091i	0.771891	+	0.771891i	0.978437	−	0.206546i	$-0.0662222\pi$
$463$	16.6091	+	16.6091i	0.771891	+	0.771891i	−0.206546	+	0.978437i	$0.566222\pi$
$464$	−0.592889	−	0.342305i	−0.0275242	−	0.0158911i
$465$		0			0
$466$	−7.23665	−	12.5343i	−0.335232	−	0.580638i
$467$	−15.4446	+	4.13837i	−0.714691	+	0.191501i	−0.597802	−	0.801644i	$-0.703959\pi$
$467$	−15.4446	+	4.13837i	−0.714691	+	0.191501i	−0.116889	+	0.993145i	$0.537292\pi$
$468$	−2.41668	+	2.41668i	−0.111711	+	0.111711i
$469$	22.8556	−	13.0796i	1.05537	−	0.603959i
$470$		0			0
$471$	1.84001	−	3.18700i	0.0847834	−	0.146849i
$472$	2.62968	−	9.81409i	0.121041	−	0.451730i
$473$	3.92196	−	14.6370i	0.180332	−	0.673008i
$474$	4.16543	−	7.21474i	0.191325	−	0.331384i
$475$		0			0
$476$	4.84278	+	2.82069i	0.221968	+	0.129286i
$477$	6.64852	−	6.64852i	0.304415	−	0.304415i
$478$	28.9523	−	7.75773i	1.32425	−	0.354831i
$479$	4.50526	+	7.80333i	0.205850	+	0.356543i	0.950403	−	0.311020i	$-0.100671\pi$
$479$	4.50526	+	7.80333i	0.205850	+	0.356543i	−0.744553	+	0.667563i	$0.767337\pi$
$480$		0			0
$481$	−29.0066	−	16.7470i	−1.32259	−	0.763595i
$482$	−11.7522	−	11.7522i	−0.535296	−	0.535296i
$483$	−3.29467	+	3.26961i	−0.149913	+	0.148772i
$484$		−	19.0995i		−	0.868158i
$485$		0			0
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$	9.02186	+	2.41740i	0.408820	+	0.109543i	0.457367	−	0.889278i	$-0.348793\pi$
$487$	9.02186	+	2.41740i	0.408820	+	0.109543i	−0.0485475	+	0.998821i	$0.515459\pi$
$488$	0.303248	+	1.13174i	0.0137274	+	0.0512313i
$489$	−14.0810			−0.636764
$490$		0			0
$491$	2.08535			0.0941107			0.0470554	−	0.998892i	$-0.485016\pi$
$491$	2.08535			0.0941107			0.0470554	+	0.998892i	$0.485016\pi$
$492$	−0.648592	−	2.42058i	−0.0292408	−	0.109128i
$493$	−1.40076	−	0.375332i	−0.0630870	−	0.0169041i
$494$	20.7067	−	11.9550i	0.931637	−	0.537881i
$495$		0			0
$496$		−	5.57642i		−	0.250388i
$497$	−22.4821	+	22.3111i	−1.00846	+	1.00079i
$498$	−4.05281	−	4.05281i	−0.181611	−	0.181611i
$499$	−11.6260	−	6.71229i	−0.520452	−	0.300483i	0.216668	−	0.976245i	$-0.430481\pi$
$499$	−11.6260	−	6.71229i	−0.520452	−	0.300483i	−0.737120	+	0.675762i	$0.763815\pi$
$500$		0			0
$501$	−4.29397	−	7.43738i	−0.191841	−	0.332278i
$502$	10.3992	−	2.78645i	0.464138	−	0.124366i
$503$	7.19669	−	7.19669i	0.320885	−	0.320885i	−0.528222	−	0.849106i	$-0.677141\pi$
$503$	7.19669	−	7.19669i	0.320885	−	0.320885i	0.849106	+	0.528222i	$0.177141\pi$
$504$	2.28622	+	1.33161i	0.101836	+	0.0593148i
$505$		0			0
$506$	4.81255	−	8.33558i	0.213944	−	0.370562i
$507$	−0.341468	+	1.27438i	−0.0151651	+	0.0565970i
$508$	−1.74614	+	6.51668i	−0.0774724	+	0.289131i
$509$	2.14078	−	3.70794i	0.0948884	−	0.164352i	−0.814674	−	0.579920i	$-0.803084\pi$
$509$	2.14078	−	3.70794i	0.0948884	−	0.164352i	0.909562	+	0.415568i	$0.136417\pi$
$510$		0			0
$511$	−11.1849	+	6.40079i	−0.494791	+	0.283154i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−6.75755	+	1.81068i	−0.298353	+	0.0799435i
$514$	−7.52124	−	13.0272i	−0.331748	−	0.574604i
$515$		0			0
$516$	−2.39198	−	1.38101i	−0.105301	−	0.0607957i
$517$	−13.6756	−	13.6756i	−0.601451	−	0.601451i
$518$	−6.80642	+	25.0194i	−0.299057	+	1.09929i
$519$			4.04905i			0.177733i
$520$		0			0
$521$	−12.6226	+	7.28768i	−0.553007	+	0.319279i	−0.750334	−	0.661059i	$-0.770107\pi$
$521$	−12.6226	+	7.28768i	−0.553007	+	0.319279i	0.197327	+	0.980338i	$0.436774\pi$
$522$	−0.661282	−	0.177190i	−0.0289435	−	0.00775540i
$523$	−9.85794	−	36.7904i	−0.431058	−	1.60873i	−0.750328	−	0.661066i	$-0.770104\pi$
$523$	−9.85794	−	36.7904i	−0.431058	−	1.60873i	0.319270	−	0.947664i	$-0.396562\pi$
$524$	−18.2091			−0.795468
$525$		0			0
$526$	22.5315			0.982418
$527$	−3.05723	−	11.4097i	−0.133175	−	0.497015i
$528$	−5.29936	−	1.41996i	−0.230625	−	0.0617958i
$529$	−17.2531	+	9.96106i	−0.750133	+	0.433090i
$530$		0			0
$531$		−	10.1603i		−	0.440919i
$532$	−13.0381	−	13.1381i	−0.565275	−	0.569607i
$533$	6.05612	+	6.05612i	0.262319	+	0.262319i
$534$	6.22115	+	3.59178i	0.269215	+	0.155432i
$535$		0			0
$536$	4.97656	+	8.61966i	0.214955	+	0.372313i
$537$	3.54044	−	0.948659i	0.152781	−	0.0409377i
$538$	7.80819	−	7.80819i	0.336635	−	0.336635i
$539$	−33.4046	+	18.9475i	−1.43884	+	0.816128i
$540$		0			0
$541$	−8.43016	+	14.6015i	−0.362441	+	0.627766i	−0.988362	−	0.152121i	$-0.951390\pi$
$541$	−8.43016	+	14.6015i	−0.362441	+	0.627766i	0.625921	+	0.779886i	$0.284723\pi$
$542$	1.29834	−	4.84547i	0.0557684	−	0.208131i
$543$	0.621126	−	2.31807i	0.0266551	−	0.0994781i
$544$	−1.05912	+	1.83445i	−0.0454095	+	0.0786516i
$545$		0			0
$546$	−9.04232	−	0.0345228i	−0.386975	−	0.00147744i
$547$	2.04444	−	2.04444i	0.0874141	−	0.0874141i	−0.662048	−	0.749462i	$-0.730312\pi$
$547$	2.04444	−	2.04444i	0.0874141	−	0.0874141i	0.749462	+	0.662048i	$0.230312\pi$
$548$	−2.11024	+	0.565438i	−0.0901451	+	0.0241543i
$549$	0.585830	+	1.01469i	0.0250026	+	0.0433058i
$550$		0			0
$551$	4.14781	+	2.39474i	0.176703	+	0.102019i
$552$	−1.24054	−	1.24054i	−0.0528009	−	0.0528009i
$553$	21.3120	−	5.62341i	0.906278	−	0.239132i
$554$		−	6.33506i		−	0.269151i
$555$		0			0
$556$	15.7137	−	9.07229i	0.666408	−	0.384751i
$557$	4.04187	+	1.08302i	0.171260	+	0.0458889i	0.343430	−	0.939178i	$-0.388411\pi$
$557$	4.04187	+	1.08302i	0.171260	+	0.0458889i	−0.172170	+	0.985067i	$0.555078\pi$
$558$	−1.44328	−	5.38640i	−0.0610990	−	0.228025i
$559$	9.43977			0.399260
$560$		0			0
$561$	−11.6213			−0.490653
$562$	7.62799	+	28.4681i	0.321767	+	1.20085i
$563$	−24.1918	−	6.48217i	−1.01956	−	0.273191i	−0.289943	−	0.957044i	$-0.593636\pi$
$563$	−24.1918	−	6.48217i	−1.01956	−	0.273191i	−0.729620	+	0.683853i	$0.760303\pi$
$564$	−3.05289	+	1.76259i	−0.128550	+	0.0742183i
$565$		0			0
$566$		−	0.0978259i		−	0.00411193i
$567$	2.55297	+	0.694523i	0.107215	+	0.0291672i
$568$	−8.46519	−	8.46519i	−0.355191	−	0.355191i
$569$	−1.99827	−	1.15370i	−0.0837720	−	0.0483658i	0.457529	−	0.889195i	$-0.348735\pi$
$569$	−1.99827	−	1.15370i	−0.0837720	−	0.0483658i	−0.541301	+	0.840829i	$0.682068\pi$
$570$		0			0
$571$	−7.94325	−	13.7581i	−0.332415	−	0.575759i	0.650570	−	0.759446i	$-0.274530\pi$
$571$	−7.94325	−	13.7581i	−0.332415	−	0.575759i	−0.982985	+	0.183687i	$0.941197\pi$
$572$	18.1116	−	4.85299i	0.757285	−	0.202914i
$573$	−5.71012	+	5.71012i	−0.238544	+	0.238544i
$574$	3.33698	−	5.72919i	0.139283	−	0.239132i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−1.03550	+	3.86453i	−0.0431084	+	0.160883i	−0.984125	−	0.177479i	$-0.943206\pi$
$577$	−1.03550	+	3.86453i	−0.0431084	+	0.160883i	0.941016	+	0.338361i	$0.109873\pi$
$578$	3.23861	−	12.0867i	0.134709	−	0.502739i
$579$	0.861260	−	1.49175i	0.0357928	−	0.0619949i
$580$		0			0
$581$	0.0578953	−	15.1641i	0.00240190	−	0.629114i
$582$	13.1212	−	13.1212i	0.543891	−	0.543891i
$583$	−49.8268	+	13.3510i	−2.06361	+	0.552944i
$584$	−2.43539	−	4.21822i	−0.100777	−	0.174551i
$585$		0			0
$586$	−17.1557	−	9.90484i	−0.708695	−	0.409165i
$587$	5.31785	+	5.31785i	0.219491	+	0.219491i	0.808284	−	0.588793i	$-0.200397\pi$
$587$	5.31785	+	5.31785i	0.219491	+	0.219491i	−0.588793	+	0.808284i	$0.700397\pi$
$588$	1.76005	+	6.77512i	0.0725833	+	0.279401i
$589$			39.0122i			1.60747i
$590$		0			0
$591$	−7.36285	+	4.25094i	−0.302867	+	0.174860i
$592$	−9.46620	−	2.53646i	−0.389059	−	0.104248i
$593$	−4.58156	−	17.0986i	−0.188142	−	0.702156i	−0.993936	−	0.109960i	$-0.964928\pi$
$593$	−4.58156	−	17.0986i	−0.188142	−	0.702156i	0.805794	−	0.592196i	$-0.201739\pi$
$594$	−5.48630			−0.225106
$595$		0			0
$596$	0.193656			0.00793245
$597$	2.85165	+	10.6425i	0.116710	+	0.435569i
$598$	5.79167	+	1.55187i	0.236839	+	0.0634608i
$599$	−27.0972	+	15.6446i	−1.10716	+	0.639220i	−0.938093	−	0.346384i	$-0.887409\pi$
$599$	−27.0972	+	15.6446i	−1.10716	+	0.639220i	−0.169069	+	0.985604i	$0.554076\pi$
$600$		0			0
$601$		−	47.5637i		−	1.94016i	−0.242776	−	0.970082i	$-0.578058\pi$
$601$		−	47.5637i		−	1.94016i	0.242776	−	0.970082i	$-0.421942\pi$
$602$	−1.86439	−	7.06580i	−0.0759869	−	0.287980i
$603$	7.03792	+	7.03792i	0.286606	+	0.286606i
$604$	−18.4660	−	10.6614i	−0.751372	−	0.433805i
$605$		0			0
$606$	−4.13383	−	7.16001i	−0.167925	−	0.290855i
$607$	−23.7082	+	6.35260i	−0.962287	+	0.257844i	−0.705568	−	0.708642i	$-0.749308\pi$
$607$	−23.7082	+	6.35260i	−0.962287	+	0.257844i	−0.256719	+	0.966486i	$0.582641\pi$
$608$	4.94687	−	4.94687i	0.200622	−	0.200622i
$609$	−0.899658	−	1.57208i	−0.0364560	−	0.0637041i
$610$		0			0
$611$	6.02400	−	10.4339i	0.243705	−	0.422109i
$612$	−0.548242	+	2.04607i	−0.0221614	+	0.0827074i
$613$	7.20472	−	26.8884i	0.290996	−	1.08601i	−0.653349	−	0.757056i	$-0.726637\pi$
$613$	7.20472	−	26.8884i	0.290996	−	1.08601i	0.944345	−	0.328955i	$-0.106697\pi$
$614$	2.15894	−	3.73939i	0.0871277	−	0.150910i
$615$		0			0
$616$	−7.20965	−	12.5983i	−0.290485	−	0.507600i
$617$	24.4884	−	24.4884i	0.985865	−	0.985865i	−0.0140365	−	0.999901i	$-0.504468\pi$
$617$	24.4884	−	24.4884i	0.985865	−	0.985865i	0.999901	+	0.0140365i	$0.00446811\pi$
$618$	8.98910	−	2.40862i	0.361595	−	0.0968890i
$619$	−15.9137	−	27.5634i	−0.639627	−	1.10787i	−0.985515	−	0.169590i	$-0.945756\pi$
$619$	−15.9137	−	27.5634i	−0.639627	−	1.10787i	0.345888	−	0.938276i	$-0.387578\pi$
$620$		0			0
$621$	−1.51935	−	0.877194i	−0.0609692	−	0.0352006i
$622$	5.97174	+	5.97174i	0.239445	+	0.239445i
$623$	4.84897	+	18.3770i	0.194270	+	0.736257i
$624$		−	3.41770i		−	0.136817i
$625$		0			0
$626$	16.8092	−	9.70480i	0.671831	−	0.387882i
$627$	37.0740	+	9.93394i	1.48059	+	0.396723i
$628$	0.952462	+	3.55464i	0.0380074	+	0.141845i
$629$	−20.7591			−0.827719
$630$		0			0
$631$	−34.9471			−1.39122			−0.695610	−	0.718419i	$-0.744866\pi$
$631$	−34.9471			−1.39122			−0.695610	+	0.718419i	$0.744866\pi$
$632$	2.15619	+	8.04700i	0.0857685	+	0.320092i
$633$	9.98020	+	2.67419i	0.396677	+	0.106289i
$634$	13.4670	−	7.77515i	0.534841	−	0.308791i
$635$		0			0
$636$			9.40242i			0.372830i
$637$	−16.7871	−	17.0454i	−0.665128	−	0.675364i
$638$	2.65587	+	2.65587i	0.105147	+	0.105147i
$639$	−10.3677	−	5.98579i	−0.410140	−	0.236794i
$640$		0			0
$641$	5.61488	+	9.72526i	0.221774	+	0.384125i	0.955347	−	0.295487i	$-0.0954818\pi$
$641$	5.61488	+	9.72526i	0.221774	+	0.384125i	−0.733572	+	0.679611i	$0.762148\pi$
$642$	11.8496	−	3.17510i	0.467668	−	0.125311i
$643$	−9.89036	+	9.89036i	−0.390038	+	0.390038i	−0.874701	−	0.484663i	$-0.838942\pi$
$643$	−9.89036	+	9.89036i	−0.390038	+	0.390038i	0.484663	+	0.874701i	$0.338942\pi$
$644$	0.0177214	−	4.64164i	0.000698320	−	0.182906i
$645$		0			0
$646$	7.40955	−	12.8337i	0.291525	−	0.504936i
$647$	−4.06147	+	15.1576i	−0.159673	+	0.595908i	0.838987	+	0.544152i	$0.183148\pi$
$647$	−4.06147	+	15.1576i	−0.159673	+	0.595908i	−0.998660	+	0.0517559i	$0.983518\pi$
$648$	−0.258819	+	0.965926i	−0.0101674	+	0.0379452i
$649$	−27.8712	+	48.2744i	−1.09404	+	1.89493i
$650$		0			0
$651$	7.42563	−	12.7489i	0.291033	−	0.499669i
$652$	9.95676	−	9.95676i	0.389937	−	0.389937i
$653$	15.4045	−	4.12761i	0.602823	−	0.161526i	0.0555160	−	0.998458i	$-0.482320\pi$
$653$	15.4045	−	4.12761i	0.602823	−	0.161526i	0.547307	+	0.836932i	$0.315653\pi$
$654$	0.168311	+	0.291523i	0.00658147	+	0.0113994i
$655$		0			0
$656$	2.17023	+	1.25298i	0.0847333	+	0.0489208i
$657$	−3.44417	−	3.44417i	−0.134370	−	0.134370i
$658$	−8.99966	−	2.44832i	−0.350843	−	0.0954453i
$659$			10.4778i			0.408157i	0.978955	+	0.204078i	$0.0654198\pi$
$659$			10.4778i			0.408157i	−0.978955	+	0.204078i	$0.934580\pi$
$660$		0			0
$661$	−20.9764	+	12.1107i	−0.815888	+	0.471053i	−0.848996	−	0.528399i	$-0.822793\pi$
$661$	−20.9764	+	12.1107i	−0.815888	+	0.471053i	0.0331084	+	0.999452i	$0.489459\pi$
$662$	15.6344	+	4.18923i	0.607648	+	0.162819i
$663$	−1.87373	−	6.99285i	−0.0727695	−	0.271580i
$664$	5.73154			0.222427
$665$		0			0
$666$	−9.80013			−0.379747
$667$	0.310860	+	1.16015i	0.0120366	+	0.0449210i
$668$	8.29532	+	2.22272i	0.320955	+	0.0859998i
$669$	−4.17862	+	2.41253i	−0.161555	+	0.0932736i
$670$		0			0
$671$		−	6.42808i		−	0.248153i
$672$	−2.55820	+	0.675009i	−0.0986845	+	0.0260390i
$673$	1.16725	+	1.16725i	0.0449943	+	0.0449943i	0.729246	−	0.684252i	$-0.239871\pi$
$673$	1.16725	+	1.16725i	0.0449943	+	0.0449943i	−0.684252	+	0.729246i	$0.739871\pi$
$674$	23.5218	+	13.5803i	0.906025	+	0.523094i
$675$		0			0
$676$	−0.659666	−	1.14257i	−0.0253718	−	0.0439452i
$677$	12.4001	−	3.32260i	0.476575	−	0.127698i	−0.0125322	−	0.999921i	$-0.503989\pi$
$677$	12.4001	−	3.32260i	0.476575	−	0.127698i	0.489108	+	0.872223i	$0.337323\pi$
$678$	−10.1896	+	10.1896i	−0.391328	+	0.391328i
$679$	49.0947	+	0.187439i	1.88408	+	0.00719326i
$680$		0			0
$681$	9.04688	−	15.6697i	0.346677	−	0.600463i
$682$	−7.91828	+	29.5514i	−0.303207	+	1.13158i
$683$	−5.52974	+	20.6373i	−0.211589	+	0.789663i	0.775750	+	0.631040i	$0.217372\pi$
$683$	−5.52974	+	20.6373i	−0.211589	+	0.789663i	−0.987339	+	0.158622i	$0.949295\pi$
$684$	3.49797	−	6.05866i	0.133748	−	0.231658i
$685$		0			0
$686$	−9.44322	+	15.9319i	−0.360544	+	0.608283i
$687$	6.82181	−	6.82181i	0.260268	−	0.260268i
$688$	2.66791	−	0.714864i	0.101713	−	0.0272540i
$689$	−16.0673	−	27.8294i	−0.612116	−	1.06022i
$690$		0			0
$691$	−37.0127	−	21.3693i	−1.40803	−	0.812927i	−0.412833	−	0.910807i	$-0.635461\pi$
$691$	−37.0127	−	21.3693i	−1.40803	−	0.812927i	−0.995198	+	0.0978797i	$0.968794\pi$
$692$	−2.86311	−	2.86311i	−0.108839	−	0.108839i
$693$	−10.2247	−	10.3030i	−0.388403	−	0.391380i
$694$		−	10.2657i		−	0.389681i
$695$		0			0
$696$	0.592889	−	0.342305i	0.0224734	−	0.0129750i
$697$	5.12738	+	1.37388i	0.194213	+	0.0520393i
$698$	−1.71194	−	6.38903i	−0.0647977	−	0.241828i
$699$	14.4733			0.547431
$700$		0			0
$701$	44.5959			1.68436			0.842182	−	0.539194i	$-0.181271\pi$
$701$	44.5959			1.68436			0.842182	+	0.539194i	$0.181271\pi$
$702$	−0.884566	−	3.30124i	−0.0333858	−	0.124597i
$703$	66.2249	+	17.7449i	2.49772	+	0.669262i
$704$	4.75127	−	2.74315i	0.179070	−	0.103386i
$705$		0			0
$706$			13.6247i			0.512772i
$707$	5.74208	−	21.1071i	0.215953	−	0.793813i
$708$	7.18441	+	7.18441i	0.270007	+	0.270007i
$709$	35.8750	+	20.7125i	1.34732	+	0.777873i	0.987869	−	0.155293i	$-0.0496320\pi$
$709$	35.8750	+	20.7125i	1.34732	+	0.777873i	0.359447	+	0.933166i	$0.382965\pi$
$710$		0			0
$711$	4.16543	+	7.21474i	0.156216	+	0.270574i
$712$	−6.93879	+	1.85924i	−0.260042	+	0.0696781i
$713$	−6.91777	+	6.91777i	−0.259072	+	0.259072i
$714$	−4.86417	+	2.78362i	−0.182037	+	0.104175i
$715$		0			0
$716$	−1.83267	+	3.17428i	−0.0684900	+	0.118628i
$717$	−7.75773	+	28.9523i	−0.289718	+	1.08124i
$718$	−4.47665	+	16.7071i	−0.167067	+	0.623502i
$719$	−11.7839	+	20.4103i	−0.439464	+	0.761174i	−0.997648	−	0.0685431i	$-0.978165\pi$
$719$	−11.7839	+	20.4103i	−0.439464	+	0.761174i	0.558184	+	0.829717i	$0.311498\pi$
$720$		0			0
$721$	21.2760	+	12.3923i	0.792361	+	0.461512i
$722$	−21.1730	+	21.1730i	−0.787976	+	0.787976i
$723$	16.0538	−	4.30159i	0.597046	−	0.159978i
$724$	1.19992	+	2.07833i	0.0445948	+	0.0772405i
$725$		0			0
$726$	16.5406	+	9.54974i	0.613881	+	0.354424i
$727$	−3.38556	−	3.38556i	−0.125563	−	0.125563i	0.641532	−	0.767096i	$-0.278299\pi$
$727$	−3.38556	−	3.38556i	−0.125563	−	0.125563i	−0.767096	+	0.641532i	$0.778299\pi$
$728$	6.41829	−	6.36947i	0.237878	−	0.236068i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	5.06681	−	2.92532i	0.187403	−	0.108197i
$732$	−1.13174	−	0.303248i	−0.0418302	−	0.0112084i
$733$	−10.1653	−	37.9373i	−0.375463	−	1.40125i	−0.852667	−	0.522454i	$-0.825017\pi$
$733$	−10.1653	−	37.9373i	−0.375463	−	1.40125i	0.477204	−	0.878792i	$-0.341650\pi$
$734$	−25.8811			−0.955288
$735$		0			0
$736$	1.75439			0.0646676
$737$	−14.1330	−	52.7452i	−0.520597	−	1.94289i
$738$	2.42058	+	0.648592i	0.0891027	+	0.0238750i
$739$	38.6211	−	22.2979i	1.42070	−	0.820242i	0.424343	−	0.905502i	$-0.360505\pi$
$739$	38.6211	−	22.2979i	1.42070	−	0.820242i	0.996359	+	0.0852593i	$0.0271719\pi$
$740$		0			0
$741$			23.9100i			0.878356i
$742$	−17.6573	+	17.5230i	−0.648222	+	0.643291i
$743$	−24.7787	−	24.7787i	−0.909041	−	0.909041i	0.0871537	−	0.996195i	$-0.472223\pi$
$743$	−24.7787	−	24.7787i	−0.909041	−	0.909041i	−0.996195	+	0.0871537i	$0.972223\pi$
$744$	4.82932	+	2.78821i	0.177051	+	0.102221i
$745$		0			0
$746$	−4.58319	−	7.93832i	−0.167802	−	0.290642i
$747$	5.53624	−	1.48343i	0.202561	−	0.0542759i
$748$	8.21752	−	8.21752i	0.300462	−	0.300462i
$749$	28.0466	+	16.3358i	1.02480	+	0.596897i
$750$		0			0
$751$	−2.54731	+	4.41207i	−0.0929526	+	0.160999i	−0.908752	−	0.417336i	$-0.862964\pi$
$751$	−2.54731	+	4.41207i	−0.0929526	+	0.160999i	0.815800	+	0.578335i	$0.196297\pi$
$752$	0.912383	−	3.40506i	0.0332712	−	0.124170i
$753$	−2.78645	+	10.3992i	−0.101544	+	0.378967i
$754$	−1.16989	+	2.02632i	−0.0426051	+	0.0737941i
$755$		0			0
$756$	−2.29632	+	1.31412i	−0.0835164	+	0.0477940i
$757$	−18.2623	+	18.2623i	−0.663754	+	0.663754i	−0.956263	−	0.292509i	$-0.905510\pi$
$757$	−18.2623	+	18.2623i	−0.663754	+	0.663754i	0.292509	+	0.956263i	$0.405510\pi$
$758$	18.0503	−	4.83657i	0.655618	−	0.175672i
$759$	4.81255	+	8.33558i	0.174685	+	0.302562i
$760$		0			0
$761$	24.3626	+	14.0657i	0.883142	+	0.509882i	0.871693	−	0.490052i	$-0.163022\pi$
$761$	24.3626	+	14.0657i	0.883142	+	0.509882i	0.0114488	+	0.999934i	$0.496356\pi$
$762$	−4.77054	−	4.77054i	−0.172819	−	0.172819i
$763$	−0.233791	+	0.859384i	−0.00846382	+	0.0311118i
$764$		−	8.07532i		−	0.292155i
$765$		0			0
$766$	17.1832	−	9.92072i	0.620854	−	0.358450i
$767$	−33.5416	−	8.98745i	−1.21112	−	0.324518i
$768$	−0.258819	−	0.965926i	−0.00933933	−	0.0348548i
$769$	−3.03517			−0.109451			−0.0547256	−	0.998501i	$-0.517428\pi$
$769$	−3.03517			−0.109451			−0.0547256	+	0.998501i	$0.517428\pi$
$770$		0			0
$771$	15.0425			0.541742
$772$	0.445821	+	1.66383i	0.0160455	+	0.0598825i
$773$	46.8575	+	12.5554i	1.68535	+	0.451588i	0.969183	−	0.246342i	$-0.0792288\pi$
$773$	46.8575	+	12.5554i	1.68535	+	0.451588i	0.716166	+	0.697930i	$0.245895\pi$
$774$	2.39198	−	1.38101i	0.0859781	−	0.0496395i
$775$		0			0
$776$			18.5562i			0.666128i
$777$	−18.2642	−	18.4042i	−0.655226	−	0.660248i
$778$	3.62546	+	3.62546i	0.129979	+	0.129979i
$779$	−15.1828	−	8.76579i	−0.543980	−	0.314067i
$780$		0			0
$781$	32.8398	+	56.8803i	1.17510	+	2.03534i
$782$	3.58960	−	0.961830i	0.128364	−	0.0343950i
$783$	0.484092	−	0.484092i	0.0173000	−	0.0173000i
$784$	−6.03528	−	3.54619i	−0.215546	−	0.126650i
$785$		0			0
$786$	9.10455	−	15.7695i	0.324748	−	0.562481i
$787$	9.83063	−	36.6884i	0.350424	−	1.30780i	−0.535722	−	0.844394i	$-0.679961\pi$
$787$	9.83063	−	36.6884i	0.350424	−	1.30780i	0.886146	−	0.463406i	$-0.153373\pi$
$788$	2.20045	−	8.21219i	0.0783878	−	0.292547i
$789$	−11.2657	+	19.5128i	−0.401070	+	0.694674i
$790$		0			0
$791$	−38.1256	−	0.145560i	−1.35559	−	0.00517553i
$792$	3.87940	−	3.87940i	0.137848	−	0.137848i
$793$	3.86794	−	1.03641i	0.137354	−	0.0368040i
$794$	13.1967	+	22.8574i	0.468334	+	0.811179i
$795$		0			0
$796$	−9.54181	−	5.50897i	−0.338200	−	0.195260i
$797$	34.4058	+	34.4058i	1.21871	+	1.21871i	0.968082	+	0.250632i	$0.0806384\pi$
$797$	34.4058	+	34.4058i	1.21871	+	1.21871i	0.250632	+	0.968082i	$0.419362\pi$
$798$	17.8970	−	4.72232i	0.633546	−	0.167168i
$799$		−	7.46719i		−	0.264170i
$800$		0			0
$801$	−6.22115	+	3.59178i	−0.219813	+	0.126909i
$802$	−16.6423	−	4.45930i	−0.587661	−	0.157463i
$803$	6.91632	+	25.8120i	0.244071	+	0.910887i
$804$	−9.95313			−0.351020
$805$		0			0
$806$	−19.0585			−0.671307
$807$	2.85799	+	10.6662i	0.100606	+	0.375467i
$808$	7.98595	+	2.13983i	0.280945	+	0.0752789i
$809$	33.6569	−	19.4318i	1.18331	−	0.683186i	0.226534	−	0.974003i	$-0.427260\pi$
$809$	33.6569	−	19.4318i	1.18331	−	0.683186i	0.956779	+	0.290817i	$0.0939271\pi$
$810$		0			0
$811$		−	15.3545i		−	0.539168i	−0.962977	−	0.269584i	$-0.913114\pi$
$811$		−	15.3545i		−	0.539168i	0.962977	−	0.269584i	$-0.0868862\pi$
$812$	1.74779	+	0.475477i	0.0613352	+	0.0166860i
$813$	3.54713	+	3.54713i	0.124403	+	0.124403i
$814$	46.5631	+	26.8832i	1.63204	+	0.942257i
$815$		0			0
$816$	−1.05912	−	1.83445i	−0.0370767	−	0.0642187i
$817$	−18.6645	+	5.00114i	−0.652989	+	0.174968i
$818$	−25.2535	+	25.2535i	−0.882967	+	0.882967i
$819$	4.55106	−	7.81361i	0.159027	−	0.273030i
$820$		0			0
$821$	−11.9561	+	20.7086i	−0.417271	+	0.722735i	−0.995664	−	0.0930235i	$-0.970347\pi$
$821$	−11.9561	+	20.7086i	−0.417271	+	0.722735i	0.578393	+	0.815758i	$0.303680\pi$
$822$	0.565438	−	2.11024i	0.0197219	−	0.0736032i
$823$	7.32768	−	27.3473i	0.255427	−	0.953267i	−0.712425	−	0.701748i	$-0.752403\pi$
$823$	7.32768	−	27.3473i	0.255427	−	0.953267i	0.967852	−	0.251519i	$-0.0809300\pi$
$824$	−4.65310	+	8.05941i	−0.162098	+	0.280763i
$825$		0			0
$826$	−0.102631	+	26.8814i	−0.00357099	+	0.935324i
$827$	−20.7600	+	20.7600i	−0.721898	+	0.721898i	−0.968992	−	0.247094i	$-0.920524\pi$
$827$	−20.7600	+	20.7600i	−0.721898	+	0.721898i	0.247094	+	0.968992i	$0.420524\pi$
$828$	1.69461	−	0.454069i	0.0588917	−	0.0157800i
$829$	−4.14106	−	7.17253i	−0.143825	−	0.249112i	0.785109	−	0.619358i	$-0.212607\pi$
$829$	−4.14106	−	7.17253i	−0.143825	−	0.249112i	−0.928934	+	0.370246i	$0.879274\pi$
$830$		0			0
$831$	5.48632	+	3.16753i	0.190318	+	0.109880i
$832$	2.41668	+	2.41668i	0.0837832	+	0.0837832i
$833$	−14.2928	−	3.94695i	−0.495215	−	0.136754i
$834$			18.1446i			0.628295i
$835$		0			0
$836$	−33.2396	+	19.1909i	−1.14962	+	0.663731i
$837$	5.38640	+	1.44328i	0.186181	+	0.0498871i
$838$	−3.63417	−	13.5629i	−0.125540	−	0.468523i
$839$	−8.03334			−0.277342			−0.138671	−	0.990339i	$-0.544283\pi$
$839$	−8.03334			−0.277342			−0.138671	+	0.990339i	$0.544283\pi$
$840$		0			0
$841$	28.5313			0.983838
$842$	−6.32378	−	23.6007i	−0.217932	−	0.813333i
$843$	−28.4681	−	7.62799i	−0.980492	−	0.262722i
$844$	−8.94800	+	5.16613i	−0.308003	+	0.177826i
$845$		0			0
$846$		−	3.52518i		−	0.121198i
$847$	12.8923	+	48.8602i	0.442985	+	1.67886i
$848$	−6.64852	−	6.64852i	−0.228311	−	0.228311i
$849$	0.0847197	+	0.0489129i	0.00290757	+	0.00167869i
$850$		0			0
$851$	8.59662	+	14.8898i	0.294688	+	0.510415i
$852$	11.5637	−	3.09847i	0.396165	−	0.106152i
$853$	23.8654	−	23.8654i	0.817136	−	0.817136i	−0.168556	−	0.985692i	$-0.553911\pi$
$853$	23.8654	−	23.8654i	0.817136	−	0.817136i	0.985692	+	0.168556i	$0.0539105\pi$
$854$	−1.53970	−	2.69051i	−0.0526875	−	0.0920673i
$855$		0			0
$856$	−6.13383	+	10.6241i	−0.209650	+	0.363124i
$857$	−6.21598	+	23.1984i	−0.212334	+	0.792441i	0.774754	+	0.632263i	$0.217874\pi$
$857$	−6.21598	+	23.1984i	−0.212334	+	0.792441i	−0.987088	+	0.160178i	$0.948793\pi$
$858$	−4.85299	+	18.1116i	−0.165678	+	0.618320i
$859$	3.26421	−	5.65377i	0.111373	−	0.192904i	−0.804951	−	0.593341i	$-0.797808\pi$
$859$	3.26421	−	5.65377i	0.111373	−	0.192904i	0.916324	+	0.400437i	$0.131142\pi$
$860$		0			0
$861$	3.29314	+	5.75451i	0.112230	+	0.196113i
$862$	27.4196	−	27.4196i	0.933914	−	0.933914i
$863$	−15.9949	+	4.28582i	−0.544473	+	0.145891i	−0.520563	−	0.853823i	$-0.674278\pi$
$863$	−15.9949	+	4.28582i	−0.544473	+	0.145891i	−0.0239095	+	0.999714i	$0.507611\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$		0			0
$866$	−9.62282	−	5.55574i	−0.326997	−	0.188792i
$867$	8.84805	+	8.84805i	0.300496	+	0.300496i
$868$	3.76413	+	14.2656i	0.127763	+	0.484205i
$869$		−	45.7056i		−	1.55046i
$870$		0			0
$871$	29.4594	−	17.0084i	0.998194	−	0.576308i
$872$	−0.325151	−	0.0871241i	−0.0110110	−	0.00295039i
$873$	4.80269	+	17.9239i	0.162547	+	0.606632i
$874$	−12.2736			−0.415160
$875$		0			0
$876$	4.87079			0.164569
$877$	−9.56712	−	35.7050i	−0.323059	−	1.20567i	−0.916249	−	0.400609i	$-0.868798\pi$
$877$	−9.56712	−	35.7050i	−0.323059	−	1.20567i	0.593190	−	0.805062i	$-0.297868\pi$
$878$	−20.4080	−	5.46830i	−0.688736	−	0.184546i
$879$	17.1557	−	9.90484i	0.578647	−	0.334082i
$880$		0			0
$881$			17.4940i			0.589386i	0.955592	+	0.294693i	$0.0952174\pi$
$881$			17.4940i			0.589386i	−0.955592	+	0.294693i	$0.904783\pi$
$882$	−6.74745	−	1.86331i	−0.227198	−	0.0627409i
$883$	14.0857	+	14.0857i	0.474022	+	0.474022i	0.903214	−	0.429191i	$-0.141201\pi$
$883$	14.0857	+	14.0857i	0.474022	+	0.474022i	−0.429191	+	0.903214i	$0.641201\pi$
$884$	6.26961	+	3.61976i	0.210870	+	0.121746i
$885$		0			0
$886$	−3.35579	−	5.81240i	−0.112740	−	0.195271i
$887$	39.6163	−	10.6152i	1.33018	−	0.356422i	0.477401	−	0.878686i	$-0.341579\pi$
$887$	39.6163	−	10.6152i	1.33018	−	0.356422i	0.852784	+	0.522264i	$0.174912\pi$
$888$	6.92974	−	6.92974i	0.232547	−	0.232547i
$889$	0.0681482	−	17.8496i	0.00228562	−	0.598657i
$890$		0			0
$891$	2.74315	−	4.75127i	0.0918990	−	0.159174i
$892$	1.24882	−	4.66064i	0.0418134	−	0.156050i
$893$	−6.38297	+	23.8216i	−0.213598	+	0.797158i
$894$	−0.0968279	+	0.167711i	−0.00323841	+	0.00560909i
$895$		0			0
$896$	1.33161	−	2.28622i	0.0444861	−	0.0763773i
$897$	−4.23979	+	4.23979i	−0.141563	+	0.141563i
$898$	−8.00732	+	2.14555i	−0.267208	+	0.0715981i
$899$	−1.90883	−	3.30620i	−0.0636632	−	0.110268i
$900$		0			0
$901$	−17.2483	−	9.95832i	−0.574625	−	0.331760i
$902$	−9.72165	−	9.72165i	−0.323695	−	0.323695i
$903$	7.05136	+	1.91829i	0.234654	+	0.0638367i
$904$		−	14.4102i		−	0.479277i
$905$		0			0
$906$	18.4660	−	10.6614i	0.613493	−	0.354200i
$907$	19.3010	+	5.17169i	0.640879	+	0.171723i	0.564602	−	0.825364i	$-0.309030\pi$
$907$	19.3010	+	5.17169i	0.640879	+	0.171723i	0.0762776	+	0.997087i	$0.475696\pi$
$908$	4.68301	+	17.4772i	0.155411	+	0.580002i
$909$	8.26766			0.274221
$910$		0			0
$911$	−21.3131			−0.706136			−0.353068	−	0.935598i	$-0.614862\pi$
$911$	−21.3131			−0.706136			−0.353068	+	0.935598i	$0.614862\pi$
$912$	1.81068	+	6.75755i	0.0599576	+	0.223765i
$913$	−30.3735	−	8.13855i	−1.00522	−	0.269347i
$914$	−19.1236	+	11.0410i	−0.632551	+	0.365204i
$915$		0			0
$916$			9.64749i			0.318762i
$917$	46.5824	−	12.2913i	1.53829	−	0.405894i
$918$	−1.49783	−	1.49783i	−0.0494356	−	0.0494356i
$919$	−11.4010	−	6.58238i	−0.376085	−	0.217133i	0.300029	−	0.953930i	$-0.403004\pi$
$919$	−11.4010	−	6.58238i	−0.376085	−	0.217133i	−0.676114	+	0.736797i	$0.736337\pi$
$920$		0			0
$921$	2.15894	+	3.73939i	0.0711394	+	0.123217i
$922$	−18.3652	+	4.92093i	−0.604824	+	0.162062i
$923$	−28.9315	+	28.9315i	−0.952291	+	0.952291i
$924$	14.5153	+	0.0554181i	0.477518	+	0.00182312i
$925$		0			0
$926$	11.7444	−	20.3419i	0.385946	−	0.668478i
$927$	−2.40862	+	8.98910i	−0.0791095	+	0.295241i
$928$	−0.177190	+	0.661282i	−0.00581655	+	0.0217076i
$929$	2.59922	−	4.50199i	0.0852777	−	0.147705i	−0.820232	−	0.572031i	$-0.806156\pi$
$929$	2.59922	−	4.50199i	0.0852777	−	0.147705i	0.905510	+	0.424326i	$0.139489\pi$
$930$		0			0
$931$	42.2224	+	24.8089i	1.38378	+	0.813078i
$932$	−10.2342	+	10.2342i	−0.335232	+	0.335232i
$933$	−8.15755	+	2.18581i	−0.267066	+	0.0715602i
$934$	7.99472	+	13.8473i	0.261595	+	0.453096i
$935$		0			0
$936$	2.95981	+	1.70885i	0.0967446	+	0.0558555i
$937$	3.54515	+	3.54515i	0.115815	+	0.115815i	0.762639	−	0.646824i	$-0.223903\pi$
$937$	3.54515	+	3.54515i	0.115815	+	0.115815i	−0.646824	+	0.762639i	$0.723903\pi$
$938$	−18.5494	−	18.6916i	−0.605658	−	0.610301i
$939$			19.4096i			0.633409i
$940$		0			0
$941$	8.88464	−	5.12955i	0.289631	−	0.167219i	−0.348144	−	0.937441i	$-0.613188\pi$
$941$	8.88464	−	5.12955i	0.289631	−	0.167219i	0.637775	+	0.770222i	$0.279855\pi$
$942$	−3.55464	−	0.952462i	−0.115816	−	0.0310329i
$943$	−1.13788	−	4.24663i	−0.0370545	−	0.138289i
$944$	−10.1603			−0.330689
$945$		0			0
$946$	−15.1533			−0.492676
$947$	−7.26545	−	27.1150i	−0.236096	−	0.881120i	−0.977652	−	0.210230i	$-0.932579\pi$
$947$	−7.26545	−	27.1150i	−0.236096	−	0.881120i	0.741556	−	0.670890i	$-0.234088\pi$
$948$	−8.04700	−	2.15619i	−0.261354	−	0.0700297i
$949$	−14.4166	+	8.32344i	−0.467983	+	0.270190i
$950$		0			0
$951$			15.5503i			0.504253i
$952$	1.47117	−	5.40781i	0.0476809	−	0.175268i
$953$	29.6648	+	29.6648i	0.960937	+	0.960937i	0.999265	−	0.0383279i	$-0.0122031\pi$
$953$	29.6648	+	29.6648i	0.960937	+	0.960937i	−0.0383279	+	0.999265i	$0.512203\pi$
$954$	−8.14273	−	4.70121i	−0.263631	−	0.152207i
$955$		0			0
$956$	−14.9868	−	25.9579i	−0.484708	−	0.839538i
$957$	−3.62799	+	0.972117i	−0.117276	+	0.0314241i
$958$	6.37140	−	6.37140i	0.205850	−	0.205850i
$959$	5.01674	−	2.87093i	0.161999	−	0.0927073i
$960$		0			0
$961$	0.0482042	−	0.0834922i	0.00155498	−	0.00269330i
$962$	−8.66886	+	32.3526i	−0.279495	+	1.04309i
$963$	−3.17510	+	11.8496i	−0.102316	+	0.381850i
$964$	−8.31003	+	14.3934i	−0.267648	+	0.463580i
$965$		0			0
$966$	4.01092	+	2.33617i	0.129049	+	0.0751650i
$967$	3.20889	−	3.20889i	0.103191	−	0.103191i	−0.653626	−	0.756817i	$-0.726753\pi$
$967$	3.20889	−	3.20889i	0.103191	−	0.103191i	0.756817	+	0.653626i	$0.226753\pi$
$968$	−18.4487	+	4.94331i	−0.592963	+	0.158884i
$969$	7.40955	+	12.8337i	0.238029	+	0.412278i
$970$		0			0
$971$	51.1699	+	29.5430i	1.64212	+	0.948079i	0.980078	+	0.198612i	$0.0636433\pi$
$971$	51.1699	+	29.5430i	1.64212	+	0.948079i	0.662042	+	0.749467i	$0.269690\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	−34.0747	+	33.8155i	−1.09239	+	1.08408i
$974$		−	9.34012i		−	0.299277i
$975$		0			0
$976$	1.01469	−	0.585830i	0.0324794	−	0.0187520i
$977$	−11.4234	−	3.06089i	−0.365467	−	0.0979266i	0.0714120	−	0.997447i	$-0.477249\pi$
$977$	−11.4234	−	3.06089i	−0.365467	−	0.0979266i	−0.436879	+	0.899520i	$0.643916\pi$
$978$	3.64443	+	13.6012i	0.116536	+	0.434918i
$979$	39.4112			1.25959
$980$		0			0
$981$	−0.336622			−0.0107475
$982$	−0.539730	−	2.01430i	−0.0172235	−	0.0642788i
$983$	36.7070	+	9.83561i	1.17077	+	0.313707i	0.791260	−	0.611480i	$-0.209425\pi$
$983$	36.7070	+	9.83561i	1.17077	+	0.313707i	0.379511	+	0.925187i	$0.376092\pi$
$984$	−2.17023	+	1.25298i	−0.0691844	+	0.0399437i
$985$		0			0
$986$			1.45017i			0.0461829i
$987$	6.62013	−	6.56977i	0.210721	−	0.209118i
$988$	−16.9069	−	16.9069i	−0.537881	−	0.537881i
$989$	−4.19647	−	2.42283i	−0.133440	−	0.0770416i
$990$		0			0
$991$	−4.00630	−	6.93911i	−0.127264	−	0.220428i	0.795352	−	0.606148i	$-0.207286\pi$
$991$	−4.00630	−	6.93911i	−0.127264	−	0.220428i	−0.922616	+	0.385720i	$0.873953\pi$
$992$	−5.38640	+	1.44328i	−0.171018	+	0.0458243i
$993$	−11.4452	+	11.4452i	−0.363202	+	0.363202i
$994$	27.3697	+	15.9415i	0.868114	+	0.505635i
$995$		0			0
$996$	−2.86577	+	4.96366i	−0.0908054	+	0.157280i
$997$	−11.0150	+	41.1086i	−0.348849	+	1.30192i	0.539202	+	0.842176i	$0.318726\pi$
$997$	−11.0150	+	41.1086i	−0.348849	+	1.30192i	−0.888051	+	0.459745i	$0.847941\pi$
$998$	−3.47453	+	12.9671i	−0.109984	+	0.410468i
$999$	4.90007	−	8.48716i	0.155031	−	0.268522i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.bc.g.943.2		16
5.2	odd	4		1050.2.bc.h.607.3		16
5.3	odd	4		210.2.u.a.187.1	yes	16
5.4	even	2		210.2.u.b.103.3	yes	16
7.3	odd	6		1050.2.bc.h.493.3		16
15.8	even	4		630.2.bv.a.397.4		16
15.14	odd	2		630.2.bv.b.523.2		16
35.3	even	12		210.2.u.b.157.3	yes	16
35.9	even	6		1470.2.m.e.1273.7		16
35.17	even	12	inner	1050.2.bc.g.157.2		16
35.19	odd	6		1470.2.m.d.1273.6		16
35.23	odd	12		1470.2.m.d.97.6		16
35.24	odd	6		210.2.u.a.73.1	✓	16
35.33	even	12		1470.2.m.e.97.7		16
105.38	odd	12		630.2.bv.b.577.2		16
105.59	even	6		630.2.bv.a.73.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.73.1	✓	16	35.24	odd	6
210.2.u.a.187.1	yes	16	5.3	odd	4
210.2.u.b.103.3	yes	16	5.4	even	2
210.2.u.b.157.3	yes	16	35.3	even	12
630.2.bv.a.73.4		16	105.59	even	6
630.2.bv.a.397.4		16	15.8	even	4
630.2.bv.b.523.2		16	15.14	odd	2
630.2.bv.b.577.2		16	105.38	odd	12
1050.2.bc.g.157.2		16	35.17	even	12	inner
1050.2.bc.g.943.2		16	1.1	even	1	trivial
1050.2.bc.h.493.3		16	7.3	odd	6
1050.2.bc.h.607.3		16	5.2	odd	4
1470.2.m.d.97.6		16	35.23	odd	12
1470.2.m.d.1273.6		16	35.19	odd	6
1470.2.m.e.97.7		16	35.33	even	12
1470.2.m.e.1273.7		16	35.9	even	6

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(1.87796 - 1.86367i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(1.87796 - 1.86367i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(-2.74315 - 4.75127i) q^{11} +(-0.965926 + 0.258819i) q^{12} +(2.41668 - 2.41668i) q^{13} +(-2.28622 - 1.33161i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.548242 - 2.04607i) q^{17} +(0.258819 - 0.965926i) q^{18} +(-3.49797 + 6.05866i) q^{19} +(2.29632 - 1.31412i) q^{21} +(-3.87940 + 3.87940i) q^{22} +(-1.69461 + 0.454069i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-2.95981 - 1.70885i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.694523 + 2.55297i) q^{28} -0.684610i q^{29} +(4.82932 - 2.78821i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-1.41996 - 5.29936i) q^{33} -2.11825 q^{34} -1.00000 q^{36} +(-2.53646 - 9.46620i) q^{37} +(6.75755 + 1.81068i) q^{38} +(2.95981 - 1.70885i) q^{39} +2.50597i q^{41} +(-1.86367 - 1.87796i) q^{42} +(1.95305 + 1.95305i) q^{43} +(4.75127 + 2.74315i) q^{44} +(0.877194 + 1.51935i) q^{46} +(3.40506 - 0.912383i) q^{47} +(0.707107 - 0.707107i) q^{48} +(0.0534500 - 6.99980i) q^{49} +(1.05912 - 1.83445i) q^{51} +(-0.884566 + 3.30124i) q^{52} +(2.43353 - 9.08204i) q^{53} +(0.500000 - 0.866025i) q^{54} +(2.64573 + 0.0101012i) q^{56} +(-4.94687 + 4.94687i) q^{57} +(-0.661282 + 0.177190i) q^{58} +(-5.08015 - 8.79907i) q^{59} +(1.01469 + 0.585830i) q^{61} +(-3.94312 - 3.94312i) q^{62} +(2.55820 - 0.675009i) q^{63} +1.00000i q^{64} +(-4.75127 + 2.74315i) q^{66} +(9.61398 + 2.57606i) q^{67} +(0.548242 + 2.04607i) q^{68} -1.75439 q^{69} -11.9716 q^{71} +(0.258819 + 0.965926i) q^{72} +(-4.70482 - 1.26065i) q^{73} +(-8.48716 + 4.90007i) q^{74} -6.99593i q^{76} +(-14.0063 - 3.81036i) q^{77} +(-2.41668 - 2.41668i) q^{78} +(7.21474 + 4.16543i) q^{79} +(0.500000 + 0.866025i) q^{81} +(2.42058 - 0.648592i) q^{82} +(4.05281 - 4.05281i) q^{83} +(-1.33161 + 2.28622i) q^{84} +(1.38101 - 2.39198i) q^{86} +(0.177190 - 0.661282i) q^{87} +(1.41996 - 5.29936i) q^{88} +(-3.59178 + 6.22115i) q^{89} +(0.0345228 - 9.04232i) q^{91} +(1.24054 - 1.24054i) q^{92} +(5.38640 - 1.44328i) q^{93} +(-1.76259 - 3.05289i) q^{94} +(-0.866025 - 0.500000i) q^{96} +(13.1212 + 13.1212i) q^{97} +(-6.77512 + 1.76005i) q^{98} -5.48630i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{7}+O(q^{10}) \) 16 * q + 4 * q^7	\( 16 q + 4 q^{7} + 4 q^{11} - 16 q^{13} - 16 q^{14} + 8 q^{16} - 12 q^{17} + 8 q^{19} + 8 q^{21} - 4 q^{22} + 40 q^{23} + 8 q^{24} - 12 q^{26} + 4 q^{28} - 24 q^{31} - 4 q^{33} - 16 q^{34} - 16 q^{36} + 8 q^{37} + 20 q^{38} + 12 q^{39} - 8 q^{42} + 24 q^{43} - 4 q^{46} - 52 q^{49} + 8 q^{51} - 8 q^{52} + 28 q^{53} + 8 q^{54} + 8 q^{56} + 8 q^{57} + 12 q^{58} - 8 q^{59} + 24 q^{61} + 8 q^{62} + 4 q^{63} + 84 q^{67} - 12 q^{68} + 8 q^{69} - 32 q^{71} - 16 q^{73} + 24 q^{74} - 44 q^{77} + 16 q^{78} - 12 q^{79} + 8 q^{81} - 36 q^{82} - 16 q^{83} - 4 q^{84} - 8 q^{86} - 48 q^{87} + 4 q^{88} + 16 q^{89} + 8 q^{91} - 8 q^{92} + 32 q^{93} - 8 q^{94} + 44 q^{97} - 24 q^{98}+O(q^{100}) \) 16 * q + 4 * q^7 + 4 * q^11 - 16 * q^13 - 16 * q^14 + 8 * q^16 - 12 * q^17 + 8 * q^19 + 8 * q^21 - 4 * q^22 + 40 * q^23 + 8 * q^24 - 12 * q^26 + 4 * q^28 - 24 * q^31 - 4 * q^33 - 16 * q^34 - 16 * q^36 + 8 * q^37 + 20 * q^38 + 12 * q^39 - 8 * q^42 + 24 * q^43 - 4 * q^46 - 52 * q^49 + 8 * q^51 - 8 * q^52 + 28 * q^53 + 8 * q^54 + 8 * q^56 + 8 * q^57 + 12 * q^58 - 8 * q^59 + 24 * q^61 + 8 * q^62 + 4 * q^63 + 84 * q^67 - 12 * q^68 + 8 * q^69 - 32 * q^71 - 16 * q^73 + 24 * q^74 - 44 * q^77 + 16 * q^78 - 12 * q^79 + 8 * q^81 - 36 * q^82 - 16 * q^83 - 4 * q^84 - 8 * q^86 - 48 * q^87 + 4 * q^88 + 16 * q^89 + 8 * q^91 - 8 * q^92 + 32 * q^93 - 8 * q^94 + 44 * q^97 - 24 * q^98

Introduction

L-functions

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Database

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