LMFDB - Embedded newform 1050.2.bc.h.493.3

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			493.3
Root			$0.277956 + 0.213283i$ of defining polynomial
Character	$\chi$	$=$	1050.493
Dual form			1050.2.bc.h.607.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$			1.00000i			0.408248i
$7$	1.86367	−	1.87796i	0.704402	−	0.709801i
$7$	1.86367	−	1.87796i	0.704402	−	0.709801i
$8$	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	0.0732202	+	0.997316i	$0.476672\pi$
$11$	−2.74315	+	4.75127i	−0.827091	+	1.43256i	−0.900311	+	0.435247i	$0.856661\pi$
$12$	−0.258819	+	0.965926i	−0.0747146	+	0.278839i
$13$	−2.41668	+	2.41668i	−0.670266	+	0.670266i	−0.957777	−	0.287511i	$-0.907172\pi$
$13$	−2.41668	+	2.41668i	−0.670266	+	0.670266i	0.287511	+	0.957777i	$0.407172\pi$
$14$	2.28622	−	1.33161i	0.611018	−	0.355889i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.04607	−	0.548242i	0.496244	−	0.132968i	−0.00201209	−	0.999998i	$-0.500640\pi$
$17$	2.04607	−	0.548242i	0.496244	−	0.132968i	0.498256	+	0.867030i	$0.333974\pi$
$18$	−0.965926	+	0.258819i	−0.227671	+	0.0610042i
$19$	3.49797	+	6.05866i	0.802489	+	1.38995i	0.917974	+	0.396642i	$0.129824\pi$
$19$	3.49797	+	6.05866i	0.802489	+	1.38995i	−0.115485	+	0.993309i	$0.536842\pi$
$20$		0			0
$21$	2.29632	+	1.31412i	0.501098	+	0.286764i
$22$	−3.87940	+	3.87940i	−0.827091	+	0.827091i
$23$	0.454069	−	1.69461i	0.0946800	−	0.353350i	−0.902291	−	0.431128i	$-0.858116\pi$
$23$	0.454069	−	1.69461i	0.0946800	−	0.353350i	0.996971	+	0.0777776i	$0.0247824\pi$
$24$	−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
$28$	2.55297	−	0.694523i	0.482465	−	0.131252i
$29$		−	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	0.866474	−	0.499223i	$-0.166381\pi$
$31$	4.82932	+	2.78821i	0.867371	+	0.500777i	0.000897301		1.00000i	$0.499714\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	−5.29936	−	1.41996i	−0.922500	−	0.247183i
$34$	2.11825			0.363276
$35$		0			0
$36$	−1.00000			−0.166667
$37$	9.46620	+	2.53646i	1.55623	+	0.416992i	0.931469	−	0.363821i	$-0.118528\pi$
$37$	9.46620	+	2.53646i	1.55623	+	0.416992i	0.624765	+	0.780813i	$0.285195\pi$
$38$	1.81068	+	6.75755i	0.293731	+	1.09622i
$39$	−2.95981	−	1.70885i	−0.473950	−	0.273635i
$40$		0			0
$41$		−	2.50597i		−	0.391366i	−0.980667	−	0.195683i	$-0.937308\pi$
$41$		−	2.50597i		−	0.391366i	0.980667	−	0.195683i	$-0.0626924\pi$
$42$	1.87796	+	1.86367i	0.289775	+	0.287571i
$43$	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
$47$	0.912383	−	3.40506i	0.133085	−	0.496679i	−0.866914	−	0.498458i	$-0.833900\pi$
$47$	0.912383	−	3.40506i	0.133085	−	0.496679i	0.999998	+	0.00177938i	$0.000566396\pi$
$48$	−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
$52$	−3.30124	+	0.884566i	−0.457800	+	0.122667i
$53$	−9.08204	+	2.43353i	−1.24751	+	0.334270i	−0.821376	−	0.570388i	$-0.806793\pi$
$53$	−9.08204	+	2.43353i	−1.24751	+	0.334270i	−0.426138	+	0.904658i	$0.640126\pi$
$54$	−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
$58$	0.177190	−	0.661282i	0.0232662	−	0.0868306i
$59$	5.08015	−	8.79907i	0.661379	−	1.14554i	−0.318875	−	0.947797i	$-0.603305\pi$
$59$	5.08015	−	8.79907i	0.661379	−	1.14554i	0.980253	−	0.197745i	$-0.0633618\pi$
$60$		0			0
$61$	1.01469	−	0.585830i	0.129917	−	0.0750079i	−0.433633	−	0.901090i	$-0.642768\pi$
$61$	1.01469	−	0.585830i	0.129917	−	0.0750079i	0.563550	+	0.826082i	$0.309435\pi$
$62$	3.94312	+	3.94312i	0.500777	+	0.500777i
$63$	−0.675009	+	2.55820i	−0.0850431	+	0.322302i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−4.75127	−	2.74315i	−0.584841	−	0.337658i
$67$	−2.57606	−	9.61398i	−0.314716	−	1.17454i	−0.924254	−	0.381778i	$-0.875312\pi$
$67$	−2.57606	−	9.61398i	−0.314716	−	1.17454i	0.609538	−	0.792757i	$-0.291355\pi$
$68$	2.04607	+	0.548242i	0.248122	+	0.0664841i
$69$	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	$0.751478\pi$
$72$	−0.965926	−	0.258819i	−0.113835	−	0.0305021i
$73$	−1.26065	−	4.70482i	−0.147548	−	0.550657i	−0.999629	−	0.0272467i	$-0.991326\pi$
$73$	−1.26065	−	4.70482i	−0.147548	−	0.550657i	0.852081	−	0.523411i	$-0.175341\pi$
$74$	8.48716	+	4.90007i	0.986613	+	0.569621i
$75$		0			0
$76$			6.99593i			0.802489i
$77$	3.81036	+	14.0063i	0.434231	+	1.59617i
$78$	−2.41668	−	2.41668i	−0.273635	−	0.273635i
$79$	−7.21474	+	4.16543i	−0.811722	+	0.468648i	−0.847553	−	0.530710i	$-0.821925\pi$
$79$	−7.21474	+	4.16543i	−0.811722	+	0.468648i	0.0358316	+	0.999358i	$0.488592\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	0.648592	−	2.42058i	0.0716250	−	0.267308i
$83$	−4.05281	+	4.05281i	−0.444854	+	0.444854i	−0.893639	−	0.448786i	$-0.851857\pi$
$83$	−4.05281	+	4.05281i	−0.444854	+	0.444854i	0.448786	+	0.893639i	$0.351857\pi$
$84$	1.33161	+	2.28622i	0.145291	+	0.249447i
$85$		0			0
$86$	1.38101	+	2.39198i	0.148918	+	0.257934i
$87$	0.661282	−	0.177190i	0.0708969	−	0.0189968i
$88$	−5.29936	+	1.41996i	−0.564913	+	0.151368i
$89$	3.59178	+	6.22115i	0.380728	+	0.659440i	0.991166	−	0.132623i	$-0.0423401\pi$
$89$	3.59178	+	6.22115i	0.380728	+	0.659440i	−0.610439	+	0.792064i	$0.709007\pi$
$90$		0			0
$91$	0.0345228	+	9.04232i	0.00361897	+	0.947892i
$92$	1.24054	−	1.24054i	0.129335	−	0.129335i
$93$	−1.44328	+	5.38640i	−0.149661	+	0.558544i
$94$	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	$-0.858898\pi$
$97$	−13.1212	−	13.1212i	−1.33226	−	1.33226i	−0.428909	−	0.903348i	$-0.641102\pi$
$98$	1.76005	−	6.77512i	0.177792	−	0.684390i
$99$		−	5.48630i		−	0.551394i
$100$		0			0
$101$	7.16001	+	4.13383i	0.712447	+	0.411332i	0.811967	−	0.583704i	$-0.198397\pi$
$101$	7.16001	+	4.13383i	0.712447	+	0.411332i	−0.0995192	+	0.995036i	$0.531730\pi$
$102$	0.548242	+	2.04607i	0.0542841	+	0.202591i
$103$	8.98910	+	2.40862i	0.885722	+	0.237329i	0.672874	−	0.739757i	$-0.265059\pi$
$103$	8.98910	+	2.40862i	0.885722	+	0.237329i	0.212848	+	0.977085i	$0.431726\pi$
$104$	−3.41770			−0.335133
$105$		0			0
$106$	−9.40242			−0.913244
$107$	−11.8496	−	3.17510i	−1.14555	−	0.306949i	−0.364369	−	0.931255i	$-0.618715\pi$
$107$	−11.8496	−	3.17510i	−1.14555	−	0.306949i	−0.781180	+	0.624306i	$0.785382\pi$
$108$	−0.258819	−	0.965926i	−0.0249049	−	0.0929463i
$109$	0.291523	+	0.168311i	0.0279228	+	0.0161213i	0.513896	−	0.857852i	$-0.328202\pi$
$109$	0.291523	+	0.168311i	0.0279228	+	0.0161213i	−0.485974	+	0.873973i	$0.661535\pi$
$110$		0			0
$111$			9.80013i			0.930188i
$112$	2.55820	+	0.675009i	0.241727	+	0.0637823i
$113$	−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
$117$	0.884566	−	3.30124i	0.0817781	−	0.305200i
$118$	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
$122$	1.13174	−	0.303248i	0.102463	−	0.0274548i
$123$	2.42058	−	0.648592i	0.218256	−	0.0584816i
$124$	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	$0.153237\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	−1.38101	+	2.39198i	−0.121591	+	0.210602i
$130$		0			0
$131$	15.7695	−	9.10455i	1.37779	−	0.795468i	0.385898	−	0.922542i	$-0.373892\pi$
$131$	15.7695	−	9.10455i	1.37779	−	0.795468i	0.991893	+	0.127074i	$0.0405585\pi$
$132$	−3.87940	−	3.87940i	−0.337658	−	0.337658i
$133$	17.8970	+	4.72232i	1.55186	+	0.409477i
$134$		−	9.95313i		−	0.859819i
$135$		0			0
$136$	1.83445	+	1.05912i	0.157303	+	0.0908190i
$137$	−0.565438	−	2.11024i	−0.0483086	−	0.180290i	0.937556	−	0.347835i	$-0.113083\pi$
$137$	−0.565438	−	2.11024i	−0.0483086	−	0.180290i	−0.985865	+	0.167544i	$0.946416\pi$
$138$	1.69461	+	0.454069i	0.144255	+	0.0386529i
$139$	18.1446			1.53900			0.769501	−	0.638645i	$-0.220505\pi$
$139$	18.1446			1.53900			0.769501	+	0.638645i	$0.220505\pi$
$140$		0			0
$141$	3.52518			0.296873
$142$	−11.5637	−	3.09847i	−0.970401	−	0.260018i
$143$	−4.85299	−	18.1116i	−0.405828	−	1.51457i
$144$	−0.866025	−	0.500000i	−0.0721688	−	0.0416667i
$145$		0			0
$146$		−	4.87079i		−	0.403109i
$147$	6.74745	−	1.86331i	0.556520	−	0.153683i
$148$	6.92974	+	6.92974i	0.569621	+	0.569621i
$149$	0.167711	−	0.0968279i	0.0137394	−	0.00793245i	−0.493115	−	0.869964i	$-0.664142\pi$
$149$	0.167711	−	0.0968279i	0.0137394	−	0.00793245i	0.506854	+	0.862032i	$0.330808\pi$
$150$		0			0
$151$	10.6614	−	18.4660i	0.867610	−	1.50274i	0.00317777	−	0.999995i	$-0.498988\pi$
$151$	10.6614	−	18.4660i	0.867610	−	1.50274i	0.864432	−	0.502750i	$-0.167678\pi$
$152$	−1.81068	+	6.75755i	−0.146866	+	0.548110i
$153$	−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
$157$	3.55464	−	0.952462i	0.283691	−	0.0760147i	−0.114168	−	0.993461i	$-0.536420\pi$
$157$	3.55464	−	0.952462i	0.283691	−	0.0760147i	0.397859	+	0.917447i	$0.369753\pi$
$158$	−8.04700	+	2.15619i	−0.640185	+	0.171537i
$159$	−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
$163$	3.64443	−	13.6012i	0.285454	−	1.06533i	−0.663054	−	0.748572i	$-0.730740\pi$
$163$	3.64443	−	13.6012i	0.285454	−	1.06533i	0.948507	−	0.316756i	$-0.102594\pi$
$164$	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	0.901886	−	0.431974i	$-0.142183\pi$
$167$	6.07259	+	6.07259i	0.469911	+	0.469911i	−0.431974	+	0.901886i	$0.642183\pi$
$168$	0.694523	+	2.55297i	0.0535836	+	0.196966i
$169$			1.31933i			0.101487i
$170$		0			0
$171$	−6.05866	−	3.49797i	−0.463317	−	0.267496i
$172$	0.714864	+	2.66791i	0.0545079	+	0.203426i
$173$	3.91108	+	1.04797i	0.297354	+	0.0796757i	0.404412	−	0.914577i	$-0.367476\pi$
$173$	3.91108	+	1.04797i	0.297354	+	0.0796757i	−0.107058	+	0.994253i	$0.534143\pi$
$174$	0.684610			0.0519001
$175$		0			0
$176$	−5.48630			−0.413545
$177$	9.81409	+	2.62968i	0.737672	+	0.197659i
$178$	1.85924	+	6.93879i	0.139356	+	0.520084i
$179$	−3.17428	−	1.83267i	−0.237256	−	0.136980i	0.376659	−	0.926352i	$-0.377073\pi$
$179$	−3.17428	−	1.83267i	−0.237256	−	0.136980i	−0.613915	+	0.789372i	$0.710406\pi$
$180$		0			0
$181$			2.39985i			0.178379i	0.996015	+	0.0891896i	$0.0284277\pi$
$181$			2.39985i			0.178379i	−0.996015	+	0.0891896i	$0.971572\pi$
$182$	−2.30698	+	8.74314i	−0.171005	+	0.648085i
$183$	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
$187$	−3.00782	+	11.2253i	−0.219954	+	0.820878i
$188$	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	0.682164	−	0.731199i	$-0.261039\pi$
$191$	−4.03766	−	6.99344i	−0.292155	−	0.506027i	−0.974319	+	0.225172i	$0.927706\pi$
$192$	−0.965926	+	0.258819i	−0.0697097	+	0.0186787i
$193$	−1.66383	+	0.445821i	−0.119765	+	0.0320909i	−0.318204	−	0.948022i	$-0.603080\pi$
$193$	−1.66383	+	0.445821i	−0.119765	+	0.0320909i	0.198439	+	0.980113i	$0.436413\pi$
$194$	−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	$0.347944\pi$
$198$	1.41996	−	5.29936i	0.100912	−	0.376609i
$199$	−5.50897	+	9.54181i	−0.390520	+	0.676401i	−0.992518	−	0.122097i	$-0.961038\pi$
$199$	−5.50897	+	9.54181i	−0.390520	+	0.676401i	0.601998	+	0.798498i	$0.294372\pi$
$200$		0			0
$201$	8.61966	−	4.97656i	0.607984	−	0.351020i
$202$	5.84612	+	5.84612i	0.411332	+	0.411332i
$203$	−1.28567	−	1.27589i	−0.0902362	−	0.0895498i
$204$			2.11825i			0.148307i
$205$		0			0
$206$	8.05941	+	4.65310i	0.561526	+	0.324197i
$207$	0.454069	+	1.69461i	0.0315600	+	0.117783i
$208$	−3.30124	−	0.884566i	−0.228900	−	0.0613336i
$209$	−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	$0.384259\pi$
$212$	−9.08204	−	2.43353i	−0.623757	−	0.167135i
$213$	−3.09847	−	11.5637i	−0.212304	−	0.792329i
$214$	−10.6241	−	6.13383i	−0.726249	−	0.419300i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	14.2364	−	3.87295i	0.966430	−	0.262913i
$218$	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
$222$	−2.53646	+	9.46620i	−0.170236	+	0.635330i
$223$	3.41183	−	3.41183i	0.228473	−	0.228473i	−0.583582	−	0.812054i	$-0.698349\pi$
$223$	3.41183	−	3.41183i	0.228473	−	0.228473i	0.812054	+	0.583582i	$0.198349\pi$
$224$	2.29632	+	1.31412i	0.153429	+	0.0878032i
$225$		0			0
$226$	−7.20512	−	12.4796i	−0.479277	−	0.830133i
$227$	17.4772	−	4.68301i	1.16000	−	0.310822i	0.373037	−	0.927816i	$-0.378316\pi$
$227$	17.4772	−	4.68301i	1.16000	−	0.310822i	0.786968	+	0.616994i	$0.211650\pi$
$228$	−6.75755	+	1.81068i	−0.447530	+	0.119915i
$229$	−4.82375	−	8.35497i	−0.318762	−	0.552112i	0.661468	−	0.749973i	$-0.269934\pi$
$229$	−4.82375	−	8.35497i	−0.318762	−	0.552112i	−0.980230	+	0.197861i	$0.936600\pi$
$230$		0			0
$231$	−12.5429	+	7.30563i	−0.825262	+	0.480675i
$232$	0.484092	−	0.484092i	0.0317822	−	0.0317822i
$233$	−3.74597	+	13.9801i	−0.245407	+	0.915870i	0.727772	+	0.685819i	$0.240556\pi$
$233$	−3.74597	+	13.9801i	−0.245407	+	0.915870i	−0.973179	+	0.230051i	$0.926111\pi$
$234$	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
$238$	3.94772	−	3.97798i	0.255892	−	0.257854i
$239$			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	0.885912	−	0.463853i	$-0.153533\pi$
$241$	14.3934	+	8.31003i	0.927161	+	0.535296i	0.0412481	+	0.999149i	$0.486867\pi$
$242$	−4.94331	−	18.4487i	−0.317768	−	1.18593i
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$	1.17166			0.0750079
$245$		0			0
$246$	2.50597			0.159775
$247$	−23.0953	−	6.18836i	−1.46952	−	0.393756i
$248$	1.44328	+	5.38640i	0.0916485	+	0.342037i
$249$	−4.96366	−	2.86577i	−0.314559	−	0.181611i
$250$		0			0
$251$		−	10.7660i		−	0.679546i	−0.940508	−	0.339773i	$-0.889650\pi$
$251$		−	10.7660i		−	0.679546i	0.940508	−	0.339773i	$-0.110350\pi$
$252$	−1.86367	+	1.87796i	−0.117400	+	0.118300i
$253$	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
$257$	3.89328	−	14.5299i	0.242856	−	0.906352i	−0.731593	−	0.681742i	$-0.761223\pi$
$257$	3.89328	−	14.5299i	0.242856	−	0.906352i	0.974449	−	0.224610i	$-0.0721107\pi$
$258$	−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
$262$	17.5886	−	4.71286i	1.08663	−	0.291161i
$263$	21.7637	−	5.83157i	1.34201	−	0.359590i	0.484829	−	0.874609i	$-0.338882\pi$
$263$	21.7637	−	5.83157i	1.34201	−	0.359590i	0.857179	+	0.515019i	$0.172215\pi$
$264$	−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
$268$	2.57606	−	9.61398i	0.157358	−	0.587268i
$269$	−5.52122	+	9.56304i	−0.336635	+	0.583069i	−0.983797	−	0.179283i	$-0.942622\pi$
$269$	−5.52122	+	9.56304i	−0.336635	+	0.583069i	0.647163	+	0.762352i	$0.275955\pi$
$270$		0			0
$271$	4.34433	−	2.50820i	0.263899	−	0.152362i	−0.362213	−	0.932095i	$-0.617979\pi$
$271$	4.34433	−	2.50820i	0.263899	−	0.152362i	0.626112	+	0.779733i	$0.284645\pi$
$272$	1.49783	+	1.49783i	0.0908190	+	0.0908190i
$273$	−8.72527	+	2.37367i	−0.528077	+	0.143661i
$274$		−	2.18468i		−	0.131982i
$275$		0			0
$276$	1.51935	+	0.877194i	0.0914538	+	0.0528009i
$277$	−1.63963	−	6.11920i	−0.0985161	−	0.367667i	0.899013	−	0.437922i	$-0.144285\pi$
$277$	−1.63963	−	6.11920i	−0.0985161	−	0.367667i	−0.997529	+	0.0702549i	$0.977619\pi$
$278$	17.5263	+	4.69616i	1.05116	+	0.281657i
$279$	−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	$0.841846\pi$
$282$	3.40506	+	0.912383i	0.202768	+	0.0543316i
$283$	0.0253192	+	0.0944925i	0.00150507	+	0.00561700i	0.966674	−	0.256009i	$-0.0824078\pi$
$283$	0.0253192	+	0.0944925i	0.00150507	+	0.00561700i	−0.965169	+	0.261626i	$0.915741\pi$
$284$	−10.3677	−	5.98579i	−0.615210	−	0.355191i
$285$		0			0
$286$		−	18.7505i		−	1.10874i
$287$	−4.70610	−	4.67030i	−0.277792	−	0.275679i
$288$	−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
$292$	1.26065	−	4.70482i	0.0737741	−	0.275329i
$293$	−14.0076	+	14.0076i	−0.818330	+	0.818330i	−0.985866	−	0.167536i	$-0.946419\pi$
$293$	−14.0076	+	14.0076i	−0.818330	+	0.818330i	0.167536	+	0.985866i	$0.446419\pi$
$294$	6.99980	−	0.0534500i	0.408236	−	0.00311727i
$295$		0			0
$296$	4.90007	+	8.48716i	0.284811	+	0.493306i
$297$	5.29936	−	1.41996i	0.307500	−	0.0823944i
$298$	0.187057	−	0.0501218i	0.0108359	−	0.00290348i
$299$	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
$303$	−2.13983	+	7.98595i	−0.122930	+	0.458781i
$304$	−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	0.614591	−	0.788846i	$-0.289321\pi$
$307$	−3.05320	−	3.05320i	−0.174255	−	0.174255i	−0.788846	+	0.614591i	$0.789321\pi$
$308$	−3.70330	+	14.0350i	−0.211015	+	0.799720i
$309$			9.30620i			0.529411i
$310$		0			0
$311$	−7.31386	−	4.22266i	−0.414731	−	0.239445i	0.278089	−	0.960555i	$-0.410299\pi$
$311$	−7.31386	−	4.22266i	−0.414731	−	0.239445i	−0.692820	+	0.721110i	$0.743632\pi$
$312$	−0.884566	−	3.30124i	−0.0500787	−	0.186896i
$313$	18.7482	+	5.02358i	1.05971	+	0.283949i	0.746260	−	0.665654i	$-0.231847\pi$
$313$	18.7482	+	5.02358i	1.05971	+	0.283949i	0.313453	+	0.949604i	$0.398514\pi$
$314$	3.68003			0.207676
$315$		0			0
$316$	−8.33087			−0.468648
$317$	−15.0204	−	4.02471i	−0.843632	−	0.226050i	−0.188980	−	0.981981i	$-0.560518\pi$
$317$	−15.0204	−	4.02471i	−0.843632	−	0.226050i	−0.654652	+	0.755931i	$0.727185\pi$
$318$	−2.43353	−	9.08204i	−0.136465	−	0.509296i
$319$	3.25277	+	1.87799i	0.182120	+	0.105147i
$320$		0			0
$321$		−	12.2677i		−	0.684714i
$322$	−1.21846	−	4.47890i	−0.0679023	−	0.249599i
$323$	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
$327$	−0.0871241	+	0.325151i	−0.00481797	+	0.0179809i
$328$	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	0.553211	−	0.833041i	$-0.313402\pi$
$331$	−8.09296	−	14.0174i	−0.444830	−	0.770467i	−0.998040	+	0.0625739i	$0.980069\pi$
$332$	−5.53624	+	1.48343i	−0.303841	+	0.0814139i
$333$	−9.46620	+	2.53646i	−0.518745	+	0.138997i
$334$	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	$0.984936\pi$
$338$	−0.341468	+	1.27438i	−0.0185734	+	0.0693169i
$339$	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
$343$	−13.2449	−	12.9450i	−0.715159	−	0.698962i
$344$			2.76202i			0.148918i
$345$		0			0
$346$	3.50658	+	2.02452i	0.188515	+	0.108839i
$347$	−2.65696	−	9.91592i	−0.142633	−	0.532315i	−0.999849	−	0.0173577i	$-0.994475\pi$
$347$	−2.65696	−	9.91592i	−0.142633	−	0.532315i	0.857216	−	0.514957i	$-0.172192\pi$
$348$	0.661282	+	0.177190i	0.0354484	+	0.00949838i
$349$	−6.61441			−0.354061			−0.177031	−	0.984205i	$-0.556649\pi$
$349$	−6.61441			−0.354061			−0.177031	+	0.984205i	$0.556649\pi$
$350$		0			0
$351$	3.41770			0.182423
$352$	−5.29936	−	1.41996i	−0.282457	−	0.0756841i
$353$	−3.52633	−	13.1604i	−0.187688	−	0.700460i	−0.994039	−	0.109023i	$-0.965228\pi$
$353$	−3.52633	−	13.1604i	−0.187688	−	0.700460i	0.806352	−	0.591436i	$-0.201439\pi$
$354$	8.79907	+	5.08015i	0.467666	+	0.270007i
$355$		0			0
$356$			7.18356i			0.380728i
$357$	5.41889	+	1.42983i	0.286798	+	0.0756749i
$358$	−2.59178	−	2.59178i	−0.136980	−	0.136980i
$359$	14.9791	−	8.64822i	0.790569	−	0.456435i	−0.0495937	−	0.998769i	$-0.515793\pi$
$359$	14.9791	−	8.64822i	0.790569	−	0.456435i	0.840163	+	0.542334i	$0.182459\pi$
$360$		0			0
$361$	−14.9715	+	25.9315i	−0.787976	+	1.36481i
$362$	−0.621126	+	2.31807i	−0.0326457	+	0.121835i
$363$	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
$367$	24.9992	−	6.69852i	1.30495	−	0.349660i	0.461629	−	0.887073i	$-0.347265\pi$
$367$	24.9992	−	6.69852i	1.30495	−	0.349660i	0.843319	+	0.537413i	$0.180598\pi$
$368$	1.69461	−	0.454069i	0.0883376	−	0.0236700i
$369$	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
$373$	−2.37243	+	8.85404i	−0.122840	+	0.458445i	−0.999753	−	0.0222033i	$-0.992932\pi$
$373$	−2.37243	+	8.85404i	−0.122840	+	0.458445i	0.876914	+	0.480648i	$0.159599\pi$
$374$	−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
$378$	−2.55820	−	0.675009i	−0.131579	−	0.0347187i
$379$			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
$382$	−2.09005	−	7.80016i	−0.106936	−	0.399091i
$383$	19.1654	+	5.13534i	0.979304	+	0.262404i	0.712752	−	0.701417i	$-0.247449\pi$
$383$	19.1654	+	5.13534i	0.979304	+	0.262404i	0.266553	+	0.963820i	$0.414115\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−1.72252			−0.0876740
$387$	−2.66791	−	0.714864i	−0.135618	−	0.0363386i
$388$	−4.80269	−	17.9239i	−0.243820	−	0.909948i
$389$	4.44026	+	2.56359i	0.225130	+	0.129979i	0.608323	−	0.793689i	$-0.291842\pi$
$389$	4.44026	+	2.56359i	0.225130	+	0.129979i	−0.383193	+	0.923668i	$0.625176\pi$
$390$		0			0
$391$		−	3.71623i		−	0.187938i
$392$	4.91181	−	4.98740i	0.248084	−	0.251902i
$393$	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
$397$	−6.83113	+	25.4941i	−0.342844	+	1.27951i	0.552266	+	0.833668i	$0.313763\pi$
$397$	−6.83113	+	25.4941i	−0.342844	+	1.27951i	−0.895110	+	0.445845i	$0.852903\pi$
$398$	−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	0.996890	−	0.0788050i	$-0.0251104\pi$
$401$	8.61471	+	14.9211i	0.430198	+	0.745125i	−0.566692	+	0.823930i	$0.691777\pi$
$402$	9.61398	−	2.57606i	0.479502	−	0.128482i
$403$	−18.4091	+	4.93271i	−0.917023	+	0.245716i
$404$	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
$408$	−0.548242	+	2.04607i	−0.0271420	+	0.101295i
$409$	17.8569	−	30.9290i	0.882967	−	1.52934i	0.0349400	−	0.999389i	$-0.488876\pi$
$409$	17.8569	−	30.9290i	0.882967	−	1.52934i	0.848027	−	0.529954i	$-0.177791\pi$
$410$		0			0
$411$	1.89199	−	1.09234i	0.0933251	−	0.0538813i
$412$	6.58048	+	6.58048i	0.324197	+	0.324197i
$413$	−7.05656	−	25.9389i	−0.347230	−	1.27637i
$414$			1.75439i			0.0862235i
$415$		0			0
$416$	−2.95981	−	1.70885i	−0.145117	−	0.0837832i
$417$	4.69616	+	17.5263i	0.229972	+	0.858267i
$418$	−37.0740	−	9.93394i	−1.81335	−	0.485885i
$419$	−14.0414			−0.685966			−0.342983	−	0.939342i	$-0.611437\pi$
$419$	−14.0414			−0.685966			−0.342983	+	0.939342i	$0.611437\pi$
$420$		0			0
$421$	24.4332			1.19080			0.595401	−	0.803429i	$-0.296993\pi$
$421$	24.4332			1.19080			0.595401	+	0.803429i	$0.296993\pi$
$422$	9.98020	+	2.67419i	0.485829	+	0.130177i
$423$	0.912383	+	3.40506i	0.0443616	+	0.165560i
$424$	−8.14273	−	4.70121i	−0.395446	−	0.228311i
$425$		0			0
$426$		−	11.9716i		−	0.580025i
$427$	0.790881	−	2.99734i	0.0382734	−	0.145051i
$428$	−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	0.157354	−	0.987542i	$-0.449704\pi$
$431$	19.3886	−	33.5820i	0.933914	−	1.61759i	0.776559	−	0.630044i	$-0.216963\pi$
$432$	0.258819	−	0.965926i	0.0124524	−	0.0464731i
$433$	−7.85700	+	7.85700i	−0.377583	+	0.377583i	−0.870230	−	0.492646i	$-0.836030\pi$
$433$	−7.85700	+	7.85700i	−0.377583	+	0.377583i	0.492646	+	0.870230i	$0.336030\pi$
$434$	14.7537	−	0.0563283i	0.708200	−	0.00270385i
$435$		0			0
$436$	0.168311	+	0.291523i	0.00806063	+	0.0139614i
$437$	11.8554	−	3.17664i	0.567119	−	0.151959i
$438$	4.70482	−	1.26065i	0.224805	−	0.0602363i
$439$	−10.5640	−	18.2973i	−0.504190	−	0.873283i	−0.999988	−	0.00484487i	$-0.998458\pi$
$439$	−10.5640	−	18.2973i	−0.504190	−	0.873283i	0.495798	−	0.868438i	$-0.334876\pi$
$440$		0			0
$441$	3.54619	+	6.03528i	0.168866	+	0.287394i
$442$	−5.11912	+	5.11912i	−0.243492	+	0.243492i
$443$	−1.73709	+	6.48289i	−0.0825314	+	0.308011i	−0.994835	−	0.101503i	$-0.967635\pi$
$443$	−1.73709	+	6.48289i	−0.0825314	+	0.308011i	0.912304	+	0.409514i	$0.134302\pi$
$444$	−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
$448$	1.87796	+	1.86367i	0.0887252	+	0.0880502i
$449$		−	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
$452$	−3.72964	−	13.9192i	−0.175428	−	0.654705i
$453$	20.5962	+	5.51873i	0.967693	+	0.259293i
$454$	18.0938			0.849182
$455$		0			0
$456$	−6.99593			−0.327615
$457$	21.3296	+	5.71524i	0.997755	+	0.267348i	0.720505	−	0.693450i	$-0.243910\pi$
$457$	21.3296	+	5.71524i	0.997755	+	0.267348i	0.277250	+	0.960798i	$0.410577\pi$
$458$	−2.49695	−	9.31876i	−0.116675	−	0.435437i
$459$	−1.83445	−	1.05912i	−0.0856250	−	0.0494356i
$460$		0			0
$461$			19.0130i			0.885524i	0.896639	+	0.442762i	$0.146001\pi$
$461$			19.0130i			0.885524i	−0.896639	+	0.442762i	$0.853999\pi$
$462$	−14.0063	+	3.81036i	−0.651634	+	0.177274i
$463$	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
$467$	−4.13837	+	15.4446i	−0.191501	+	0.714691i	0.801644	+	0.597802i	$0.203959\pi$
$467$	−4.13837	+	15.4446i	−0.191501	+	0.714691i	−0.993145	+	0.116889i	$0.962708\pi$
$468$	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
$472$	9.81409	−	2.62968i	0.451730	−	0.121041i
$473$	−14.6370	+	3.92196i	−0.673008	+	0.180332i
$474$	−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
$478$	−7.75773	+	28.9523i	−0.354831	+	1.32425i
$479$	−4.50526	+	7.80333i	−0.205850	+	0.356543i	−0.950403	−	0.311020i	$-0.899329\pi$
$479$	−4.50526	+	7.80333i	−0.205850	+	0.356543i	0.744553	+	0.667563i	$0.232663\pi$
$480$		0			0
$481$	−29.0066	+	16.7470i	−1.32259	+	0.763595i
$482$	11.7522	+	11.7522i	0.535296	+	0.535296i
$483$	3.26961	−	3.29467i	0.148772	−	0.149913i
$484$		−	19.0995i		−	0.868158i
$485$		0			0
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	−2.41740	−	9.02186i	−0.109543	−	0.408820i	0.889278	−	0.457367i	$-0.151207\pi$
$487$	−2.41740	−	9.02186i	−0.109543	−	0.408820i	−0.998821	+	0.0485475i	$0.984541\pi$
$488$	1.13174	+	0.303248i	0.0512313	+	0.0137274i
$489$	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	$0.485016\pi$
$492$	2.42058	+	0.648592i	0.109128	+	0.0292408i
$493$	−0.375332	−	1.40076i	−0.0169041	−	0.0630870i
$494$	−20.7067	−	11.9550i	−0.931637	−	0.537881i
$495$		0			0
$496$			5.57642i			0.250388i
$497$	−22.3111	+	22.4821i	−1.00079	+	1.00846i
$498$	−4.05281	−	4.05281i	−0.181611	−	0.181611i
$499$	11.6260	−	6.71229i	0.520452	−	0.300483i	−0.216668	−	0.976245i	$-0.569519\pi$
$499$	11.6260	−	6.71229i	0.520452	−	0.300483i	0.737120	+	0.675762i	$0.236185\pi$
$500$		0			0
$501$	−4.29397	+	7.43738i	−0.191841	+	0.332278i
$502$	2.78645	−	10.3992i	0.124366	−	0.464138i
$503$	−7.19669	+	7.19669i	−0.320885	+	0.320885i	−0.849106	−	0.528222i	$-0.822859\pi$
$503$	−7.19669	+	7.19669i	−0.320885	+	0.320885i	0.528222	+	0.849106i	$0.322859\pi$
$504$	−2.28622	+	1.33161i	−0.101836	+	0.0593148i
$505$		0			0
$506$	4.81255	+	8.33558i	0.213944	+	0.370562i
$507$	−1.27438	+	0.341468i	−0.0565970	+	0.0151651i
$508$	6.51668	−	1.74614i	0.289131	−	0.0774724i
$509$	−2.14078	−	3.70794i	−0.0948884	−	0.164352i	0.814674	−	0.579920i	$-0.196916\pi$
$509$	−2.14078	−	3.70794i	−0.0948884	−	0.164352i	−0.909562	+	0.415568i	$0.863583\pi$
$510$		0			0
$511$	−11.1849	−	6.40079i	−0.494791	−	0.283154i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	1.81068	−	6.75755i	0.0799435	−	0.298353i
$514$	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
$518$	25.0194	−	6.80642i	1.09929	−	0.299057i
$519$			4.04905i			0.177733i
$520$		0			0
$521$	−12.6226	−	7.28768i	−0.553007	−	0.319279i	0.197327	−	0.980338i	$-0.436774\pi$
$521$	−12.6226	−	7.28768i	−0.553007	−	0.319279i	−0.750334	+	0.661059i	$0.770107\pi$
$522$	0.177190	+	0.661282i	0.00775540	+	0.0289435i
$523$	−36.7904	−	9.85794i	−1.60873	−	0.431058i	−0.661066	−	0.750328i	$-0.729896\pi$
$523$	−36.7904	−	9.85794i	−1.60873	−	0.431058i	−0.947664	+	0.319270i	$0.896562\pi$
$524$	18.2091			0.795468
$525$		0			0
$526$	22.5315			0.982418
$527$	11.4097	+	3.05723i	0.497015	+	0.133175i
$528$	−1.41996	−	5.29936i	−0.0617958	−	0.230625i
$529$	17.2531	+	9.96106i	0.750133	+	0.433090i
$530$		0			0
$531$			10.1603i			0.440919i
$532$	13.1381	+	13.0381i	0.569607	+	0.565275i
$533$	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
$537$	0.948659	−	3.54044i	0.0409377	−	0.152781i
$538$	−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	0.625921	−	0.779886i	$-0.284723\pi$
$541$	−8.43016	−	14.6015i	−0.362441	−	0.627766i	−0.988362	+	0.152121i	$0.951390\pi$
$542$	4.84547	−	1.29834i	0.208131	−	0.0557684i
$543$	−2.31807	+	0.621126i	−0.0994781	+	0.0266551i
$544$	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	$0.230312\pi$
$548$	0.565438	−	2.11024i	0.0241543	−	0.0901451i
$549$	−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
$553$	−5.62341	+	21.3120i	−0.239132	+	0.906278i
$554$		−	6.33506i		−	0.269151i
$555$		0			0
$556$	15.7137	+	9.07229i	0.666408	+	0.384751i
$557$	−1.08302	−	4.04187i	−0.0458889	−	0.171260i	0.939178	−	0.343430i	$-0.111589\pi$
$557$	−1.08302	−	4.04187i	−0.0458889	−	0.171260i	−0.985067	+	0.172170i	$0.944922\pi$
$558$	−5.38640	−	1.44328i	−0.228025	−	0.0610990i
$559$	−9.43977			−0.399260
$560$		0			0
$561$	−11.6213			−0.490653
$562$	−28.4681	−	7.62799i	−1.20085	−	0.321767i
$563$	−6.48217	−	24.1918i	−0.273191	−	1.01956i	−0.957044	−	0.289943i	$-0.906364\pi$
$563$	−6.48217	−	24.1918i	−0.273191	−	1.01956i	0.683853	−	0.729620i	$-0.260303\pi$
$564$	3.05289	+	1.76259i	0.128550	+	0.0742183i
$565$		0			0
$566$			0.0978259i			0.00411193i
$567$	−0.694523	−	2.55297i	−0.0291672	−	0.107215i
$568$	−8.46519	−	8.46519i	−0.355191	−	0.355191i
$569$	1.99827	−	1.15370i	0.0837720	−	0.0483658i	−0.457529	−	0.889195i	$-0.651265\pi$
$569$	1.99827	−	1.15370i	0.0837720	−	0.0483658i	0.541301	+	0.840829i	$0.317932\pi$
$570$		0			0
$571$	−7.94325	+	13.7581i	−0.332415	+	0.575759i	−0.982985	−	0.183687i	$-0.941197\pi$
$571$	−7.94325	+	13.7581i	−0.332415	+	0.575759i	0.650570	+	0.759446i	$0.274530\pi$
$572$	4.85299	−	18.1116i	0.202914	−	0.757285i
$573$	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
$577$	−3.86453	+	1.03550i	−0.160883	+	0.0431084i	−0.338361	−	0.941016i	$-0.609873\pi$
$577$	−3.86453	+	1.03550i	−0.160883	+	0.0431084i	0.177479	+	0.984125i	$0.443206\pi$
$578$	−12.0867	+	3.23861i	−0.502739	+	0.134709i
$579$	−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
$583$	13.3510	−	49.8268i	0.552944	−	2.06361i
$584$	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	0.588793	−	0.808284i	$-0.299603\pi$
$587$	−5.31785	−	5.31785i	−0.219491	−	0.219491i	−0.808284	+	0.588793i	$0.799603\pi$
$588$	6.77512	+	1.76005i	0.279401	+	0.0725833i
$589$			39.0122i			1.60747i
$590$		0			0
$591$	−7.36285	−	4.25094i	−0.302867	−	0.174860i
$592$	2.53646	+	9.46620i	0.104248	+	0.389059i
$593$	−17.0986	−	4.58156i	−0.702156	−	0.188142i	−0.109960	−	0.993936i	$-0.535072\pi$
$593$	−17.0986	−	4.58156i	−0.702156	−	0.188142i	−0.592196	+	0.805794i	$0.701739\pi$
$594$	5.48630			0.225106
$595$		0			0
$596$	0.193656			0.00793245
$597$	−10.6425	−	2.85165i	−0.435569	−	0.116710i
$598$	1.55187	+	5.79167i	0.0634608	+	0.236839i
$599$	27.0972	+	15.6446i	1.10716	+	0.639220i	0.938093	−	0.346384i	$-0.112591\pi$
$599$	27.0972	+	15.6446i	1.10716	+	0.639220i	0.169069	+	0.985604i	$0.445924\pi$
$600$		0			0
$601$			47.5637i			1.94016i	0.242776	+	0.970082i	$0.421942\pi$
$601$			47.5637i			1.94016i	−0.242776	+	0.970082i	$0.578058\pi$
$602$	7.06580	+	1.86439i	0.287980	+	0.0759869i
$603$	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
$607$	−6.35260	+	23.7082i	−0.257844	+	0.962287i	0.708642	+	0.705568i	$0.249308\pi$
$607$	−6.35260	+	23.7082i	−0.257844	+	0.962287i	−0.966486	+	0.256719i	$0.917359\pi$
$608$	−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
$612$	−2.04607	+	0.548242i	−0.0827074	+	0.0221614i
$613$	−26.8884	+	7.20472i	−1.08601	+	0.290996i	−0.757056	−	0.653349i	$-0.773363\pi$
$613$	−26.8884	+	7.20472i	−1.08601	+	0.290996i	−0.328955	+	0.944345i	$0.606697\pi$
$614$	−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	$0.00446811\pi$
$618$	−2.40862	+	8.98910i	−0.0968890	+	0.361595i
$619$	15.9137	−	27.5634i	0.639627	−	1.10787i	−0.345888	−	0.938276i	$-0.612422\pi$
$619$	15.9137	−	27.5634i	0.639627	−	1.10787i	0.985515	−	0.169590i	$-0.0542445\pi$
$620$		0			0
$621$	−1.51935	+	0.877194i	−0.0609692	+	0.0352006i
$622$	−5.97174	−	5.97174i	−0.239445	−	0.239445i
$623$	18.3770	+	4.84897i	0.736257	+	0.194270i
$624$		−	3.41770i		−	0.136817i
$625$		0			0
$626$	16.8092	+	9.70480i	0.671831	+	0.387882i
$627$	−9.93394	−	37.0740i	−0.396723	−	1.48059i
$628$	3.55464	+	0.952462i	0.141845	+	0.0380074i
$629$	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	$0.744866\pi$
$632$	−8.04700	−	2.15619i	−0.320092	−	0.0857685i
$633$	2.67419	+	9.98020i	0.106289	+	0.396677i
$634$	−13.4670	−	7.77515i	−0.534841	−	0.308791i
$635$		0			0
$636$		−	9.40242i		−	0.372830i
$637$	17.0454	+	16.7871i	0.675364	+	0.665128i
$638$	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	−0.733572	−	0.679611i	$-0.762148\pi$
$641$	5.61488	−	9.72526i	0.221774	−	0.384125i	0.955347	+	0.295487i	$0.0954818\pi$
$642$	3.17510	−	11.8496i	0.125311	−	0.467668i
$643$	9.89036	−	9.89036i	0.390038	−	0.390038i	−0.484663	−	0.874701i	$-0.661058\pi$
$643$	9.89036	−	9.89036i	0.390038	−	0.390038i	0.874701	+	0.484663i	$0.161058\pi$
$644$	−0.0177214	−	4.64164i	−0.000698320	−	0.182906i
$645$		0			0
$646$	7.40955	+	12.8337i	0.291525	+	0.504936i
$647$	−15.1576	+	4.06147i	−0.595908	+	0.159673i	−0.544152	−	0.838987i	$-0.683148\pi$
$647$	−15.1576	+	4.06147i	−0.595908	+	0.159673i	−0.0517559	+	0.998660i	$0.516482\pi$
$648$	0.965926	−	0.258819i	0.0379452	−	0.0101674i
$649$	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
$653$	−4.12761	+	15.4045i	−0.161526	+	0.602823i	0.836932	+	0.547307i	$0.184347\pi$
$653$	−4.12761	+	15.4045i	−0.161526	+	0.602823i	−0.998458	+	0.0555160i	$0.982320\pi$
$654$	−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
$658$	−2.44832	−	8.99966i	−0.0954453	−	0.350843i
$659$			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	0.0331084	−	0.999452i	$-0.489459\pi$
$661$	−20.9764	−	12.1107i	−0.815888	−	0.471053i	−0.848996	+	0.528399i	$0.822793\pi$
$662$	−4.18923	−	15.6344i	−0.162819	−	0.607648i
$663$	−6.99285	−	1.87373i	−0.271580	−	0.0727695i
$664$	−5.73154			−0.222427
$665$		0			0
$666$	−9.80013			−0.379747
$667$	−1.16015	−	0.310860i	−0.0449210	−	0.0120366i
$668$	2.22272	+	8.29532i	0.0859998	+	0.320955i
$669$	4.17862	+	2.41253i	0.161555	+	0.0932736i
$670$		0			0
$671$			6.42808i			0.248153i
$672$	−0.675009	+	2.55820i	−0.0260390	+	0.0986845i
$673$	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
$677$	3.32260	−	12.4001i	0.127698	−	0.476575i	−0.872223	−	0.489108i	$-0.837323\pi$
$677$	3.32260	−	12.4001i	0.127698	−	0.476575i	0.999921	+	0.0125322i	$0.00398922\pi$
$678$	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
$682$	−29.5514	+	7.91828i	−1.13158	+	0.303207i
$683$	20.6373	−	5.52974i	0.789663	−	0.211589i	0.158622	−	0.987339i	$-0.449295\pi$
$683$	20.6373	−	5.52974i	0.789663	−	0.211589i	0.631040	+	0.775750i	$0.282628\pi$
$684$	−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
$688$	−0.714864	+	2.66791i	−0.0272540	+	0.101713i
$689$	16.0673	−	27.8294i	0.612116	−	1.06022i
$690$		0			0
$691$	−37.0127	+	21.3693i	−1.40803	+	0.812927i	−0.995198	−	0.0978797i	$-0.968794\pi$
$691$	−37.0127	+	21.3693i	−1.40803	+	0.812927i	−0.412833	+	0.910807i	$0.635461\pi$
$692$	2.86311	+	2.86311i	0.108839	+	0.108839i
$693$	−10.3030	−	10.2247i	−0.391380	−	0.388403i
$694$		−	10.2657i		−	0.389681i
$695$		0			0
$696$	0.592889	+	0.342305i	0.0224734	+	0.0129750i
$697$	−1.37388	−	5.12738i	−0.0520393	−	0.194213i
$698$	−6.38903	−	1.71194i	−0.241828	−	0.0647977i
$699$	−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	$0.181271\pi$
$702$	3.30124	+	0.884566i	0.124597	+	0.0333858i
$703$	17.7449	+	66.2249i	0.669262	+	2.49772i
$704$	−4.75127	−	2.74315i	−0.179070	−	0.103386i
$705$		0			0
$706$		−	13.6247i		−	0.512772i
$707$	21.1071	−	5.74208i	0.793813	−	0.215953i
$708$	7.18441	+	7.18441i	0.270007	+	0.270007i
$709$	−35.8750	+	20.7125i	−1.34732	+	0.777873i	−0.987869	−	0.155293i	$-0.950368\pi$
$709$	−35.8750	+	20.7125i	−1.34732	+	0.777873i	−0.359447	+	0.933166i	$0.617035\pi$
$710$		0			0
$711$	4.16543	−	7.21474i	0.156216	−	0.270574i
$712$	−1.85924	+	6.93879i	−0.0696781	+	0.260042i
$713$	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
$717$	−28.9523	+	7.75773i	−1.08124	+	0.289718i
$718$	16.7071	−	4.47665i	0.623502	−	0.167067i
$719$	11.7839	+	20.4103i	0.439464	+	0.761174i	0.997648	−	0.0685431i	$-0.0218351\pi$
$719$	11.7839	+	20.4103i	0.439464	+	0.761174i	−0.558184	+	0.829717i	$0.688502\pi$
$720$		0			0
$721$	21.2760	−	12.3923i	0.792361	−	0.461512i
$722$	−21.1730	+	21.1730i	−0.787976	+	0.787976i
$723$	−4.30159	+	16.0538i	−0.159978	+	0.597046i
$724$	−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	0.767096	−	0.641532i	$-0.221701\pi$
$727$	3.38556	+	3.38556i	0.125563	+	0.125563i	−0.641532	+	0.767096i	$0.721701\pi$
$728$	−6.36947	+	6.41829i	−0.236068	+	0.237878i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	5.06681	+	2.92532i	0.187403	+	0.108197i
$732$	0.303248	+	1.13174i	0.0112084	+	0.0418302i
$733$	−37.9373	−	10.1653i	−1.40125	−	0.375463i	−0.522454	−	0.852667i	$-0.674983\pi$
$733$	−37.9373	−	10.1653i	−1.40125	−	0.375463i	−0.878792	+	0.477204i	$0.841650\pi$
$734$	25.8811			0.955288
$735$		0			0
$736$	1.75439			0.0646676
$737$	52.7452	+	14.1330i	1.94289	+	0.520597i
$738$	0.648592	+	2.42058i	0.0238750	+	0.0891027i
$739$	−38.6211	−	22.2979i	−1.42070	−	0.820242i	−0.424343	−	0.905502i	$-0.639495\pi$
$739$	−38.6211	−	22.2979i	−1.42070	−	0.820242i	−0.996359	+	0.0852593i	$0.972828\pi$
$740$		0			0
$741$		−	23.9100i		−	0.878356i
$742$	−17.5230	+	17.6573i	−0.643291	+	0.648222i
$743$	−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
$747$	1.48343	−	5.53624i	0.0542759	−	0.202561i
$748$	−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	0.815800	−	0.578335i	$-0.196297\pi$
$751$	−2.54731	−	4.41207i	−0.0929526	−	0.160999i	−0.908752	+	0.417336i	$0.862964\pi$
$752$	3.40506	−	0.912383i	0.124170	−	0.0332712i
$753$	10.3992	−	2.78645i	0.378967	−	0.101544i
$754$	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	$0.405510\pi$
$758$	−4.83657	+	18.0503i	−0.175672	+	0.655618i
$759$	−4.81255	+	8.33558i	−0.174685	+	0.302562i
$760$		0			0
$761$	24.3626	−	14.0657i	0.883142	−	0.509882i	0.0114488	−	0.999934i	$-0.496356\pi$
$761$	24.3626	−	14.0657i	0.883142	−	0.509882i	0.871693	+	0.490052i	$0.163022\pi$
$762$	4.77054	+	4.77054i	0.172819	+	0.172819i
$763$	0.859384	−	0.233791i	0.0311118	−	0.00846382i
$764$		−	8.07532i		−	0.292155i
$765$		0			0
$766$	17.1832	+	9.92072i	0.620854	+	0.358450i
$767$	8.98745	+	33.5416i	0.324518	+	1.21112i
$768$	−0.965926	−	0.258819i	−0.0348548	−	0.00933933i
$769$	3.03517			0.109451			0.0547256	−	0.998501i	$-0.482572\pi$
$769$	3.03517			0.109451			0.0547256	+	0.998501i	$0.482572\pi$
$770$		0			0
$771$	15.0425			0.541742
$772$	−1.66383	−	0.445821i	−0.0598825	−	0.0160455i
$773$	12.5554	+	46.8575i	0.451588	+	1.68535i	0.697930	+	0.716166i	$0.254105\pi$
$773$	12.5554	+	46.8575i	0.451588	+	1.68535i	−0.246342	+	0.969183i	$0.579229\pi$
$774$	−2.39198	−	1.38101i	−0.0859781	−	0.0496395i
$775$		0			0
$776$		−	18.5562i		−	0.666128i
$777$	18.4042	+	18.2642i	0.660248	+	0.655226i
$778$	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
$782$	0.961830	−	3.58960i	0.0343950	−	0.128364i
$783$	−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
$787$	36.6884	−	9.83063i	1.30780	−	0.350424i	0.463406	−	0.886146i	$-0.346627\pi$
$787$	36.6884	−	9.83063i	1.30780	−	0.350424i	0.844394	+	0.535722i	$0.179961\pi$
$788$	−8.21219	+	2.20045i	−0.292547	+	0.0783878i
$789$	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
$793$	−1.03641	+	3.86794i	−0.0368040	+	0.137354i
$794$	−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	$-0.919362\pi$
$797$	−34.4058	−	34.4058i	−1.21871	−	1.21871i	−0.250632	−	0.968082i	$-0.580638\pi$
$798$	−4.72232	+	17.8970i	−0.167168	+	0.633546i
$799$		−	7.46719i		−	0.264170i
$800$		0			0
$801$	−6.22115	−	3.59178i	−0.219813	−	0.126909i
$802$	4.45930	+	16.6423i	0.157463	+	0.587661i
$803$	25.8120	+	6.91632i	0.910887	+	0.244071i
$804$	9.95313			0.351020
$805$		0			0
$806$	−19.0585			−0.671307
$807$	−10.6662	−	2.85799i	−0.375467	−	0.100606i
$808$	2.13983	+	7.98595i	0.0752789	+	0.280945i
$809$	−33.6569	−	19.4318i	−1.18331	−	0.683186i	−0.226534	−	0.974003i	$-0.572740\pi$
$809$	−33.6569	−	19.4318i	−1.18331	−	0.683186i	−0.956779	+	0.290817i	$0.906073\pi$
$810$		0			0
$811$			15.3545i			0.539168i	0.962977	+	0.269584i	$0.0868862\pi$
$811$			15.3545i			0.539168i	−0.962977	+	0.269584i	$0.913114\pi$
$812$	−0.475477	−	1.74779i	−0.0166860	−	0.0613352i
$813$	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
$817$	−5.00114	+	18.6645i	−0.174968	+	0.652989i
$818$	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	0.578393	−	0.815758i	$-0.303680\pi$
$821$	−11.9561	−	20.7086i	−0.417271	−	0.722735i	−0.995664	+	0.0930235i	$0.970347\pi$
$822$	2.11024	−	0.565438i	0.0736032	−	0.0197219i
$823$	−27.3473	+	7.32768i	−0.953267	+	0.255427i	−0.701748	−	0.712425i	$-0.747597\pi$
$823$	−27.3473	+	7.32768i	−0.953267	+	0.255427i	−0.251519	+	0.967852i	$0.580930\pi$
$824$	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	$0.420524\pi$
$828$	−0.454069	+	1.69461i	−0.0157800	+	0.0588917i
$829$	4.14106	−	7.17253i	0.143825	−	0.249112i	−0.785109	−	0.619358i	$-0.787393\pi$
$829$	4.14106	−	7.17253i	0.143825	−	0.249112i	0.928934	+	0.370246i	$0.120726\pi$
$830$		0			0
$831$	5.48632	−	3.16753i	0.190318	−	0.109880i
$832$	−2.41668	−	2.41668i	−0.0837832	−	0.0837832i
$833$	−3.94695	−	14.2928i	−0.136754	−	0.495215i
$834$			18.1446i			0.628295i
$835$		0			0
$836$	−33.2396	−	19.1909i	−1.14962	−	0.663731i
$837$	−1.44328	−	5.38640i	−0.0498871	−	0.186181i
$838$	−13.5629	−	3.63417i	−0.468523	−	0.125540i
$839$	8.03334			0.277342			0.138671	−	0.990339i	$-0.455717\pi$
$839$	8.03334			0.277342			0.138671	+	0.990339i	$0.455717\pi$
$840$		0			0
$841$	28.5313			0.983838
$842$	23.6007	+	6.32378i	0.813333	+	0.217932i
$843$	−7.62799	−	28.4681i	−0.262722	−	0.980492i
$844$	8.94800	+	5.16613i	0.308003	+	0.177826i
$845$		0			0
$846$			3.52518i			0.121198i
$847$	−48.8602	−	12.8923i	−1.67886	−	0.442985i
$848$	−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
$852$	3.09847	−	11.5637i	0.106152	−	0.396165i
$853$	−23.8654	+	23.8654i	−0.817136	+	0.817136i	−0.985692	−	0.168556i	$-0.946089\pi$
$853$	−23.8654	+	23.8654i	−0.817136	+	0.817136i	0.168556	+	0.985692i	$0.446089\pi$
$854$	1.53970	−	2.69051i	0.0526875	−	0.0920673i
$855$		0			0
$856$	−6.13383	−	10.6241i	−0.209650	−	0.363124i
$857$	−23.1984	+	6.21598i	−0.792441	+	0.212334i	−0.632263	−	0.774754i	$-0.717874\pi$
$857$	−23.1984	+	6.21598i	−0.792441	+	0.212334i	−0.160178	+	0.987088i	$0.551207\pi$
$858$	18.1116	−	4.85299i	0.618320	−	0.165678i
$859$	−3.26421	−	5.65377i	−0.111373	−	0.192904i	0.804951	−	0.593341i	$-0.202192\pi$
$859$	−3.26421	−	5.65377i	−0.111373	−	0.192904i	−0.916324	+	0.400437i	$0.868858\pi$
$860$		0			0
$861$	3.29314	−	5.75451i	0.112230	−	0.196113i
$862$	27.4196	−	27.4196i	0.933914	−	0.933914i
$863$	4.28582	−	15.9949i	0.145891	−	0.544473i	−0.853823	−	0.520563i	$-0.825722\pi$
$863$	4.28582	−	15.9949i	0.145891	−	0.544473i	0.999714	−	0.0239095i	$-0.00761137\pi$
$864$	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
$868$	14.2656	+	3.76413i	0.484205	+	0.127763i
$869$		−	45.7056i		−	1.55046i
$870$		0			0
$871$	29.4594	+	17.0084i	0.998194	+	0.576308i
$872$	0.0871241	+	0.325151i	0.00295039	+	0.0110110i
$873$	17.9239	+	4.80269i	0.606632	+	0.162547i
$874$	12.2736			0.415160
$875$		0			0
$876$	4.87079			0.164569
$877$	35.7050	+	9.56712i	1.20567	+	0.323059i	0.805062	−	0.593190i	$-0.202132\pi$
$877$	35.7050	+	9.56712i	1.20567	+	0.323059i	0.400609	+	0.916249i	$0.368798\pi$
$878$	−5.46830	−	20.4080i	−0.184546	−	0.688736i
$879$	−17.1557	−	9.90484i	−0.578647	−	0.334082i
$880$		0			0
$881$		−	17.4940i		−	0.589386i	−0.955592	−	0.294693i	$-0.904783\pi$
$881$		−	17.4940i		−	0.589386i	0.955592	−	0.294693i	$-0.0952174\pi$
$882$	1.86331	+	6.74745i	0.0627409	+	0.227198i
$883$	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
$887$	10.6152	−	39.6163i	0.356422	−	1.33018i	−0.522264	−	0.852784i	$-0.674912\pi$
$887$	10.6152	−	39.6163i	0.356422	−	1.33018i	0.878686	−	0.477401i	$-0.158421\pi$
$888$	−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
$892$	4.66064	−	1.24882i	0.156050	−	0.0418134i
$893$	23.8216	−	6.38297i	0.797158	−	0.213598i
$894$	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
$898$	2.14555	−	8.00732i	0.0715981	−	0.267208i
$899$	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
$903$	1.91829	+	7.05136i	0.0638367	+	0.234654i
$904$		−	14.4102i		−	0.479277i
$905$		0			0
$906$	18.4660	+	10.6614i	0.613493	+	0.354200i
$907$	−5.17169	−	19.3010i	−0.171723	−	0.640879i	−0.997087	−	0.0762776i	$-0.975696\pi$
$907$	−5.17169	−	19.3010i	−0.171723	−	0.640879i	0.825364	−	0.564602i	$-0.190970\pi$
$908$	17.4772	+	4.68301i	0.580002	+	0.155411i
$909$	−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	$0.614862\pi$
$912$	−6.75755	−	1.81068i	−0.223765	−	0.0599576i
$913$	−8.13855	−	30.3735i	−0.269347	−	1.00522i
$914$	19.1236	+	11.0410i	0.632551	+	0.365204i
$915$		0			0
$916$		−	9.64749i		−	0.318762i
$917$	12.2913	−	46.5824i	0.405894	−	1.53829i
$918$	−1.49783	−	1.49783i	−0.0494356	−	0.0494356i
$919$	11.4010	−	6.58238i	0.376085	−	0.217133i	−0.300029	−	0.953930i	$-0.596996\pi$
$919$	11.4010	−	6.58238i	0.376085	−	0.217133i	0.676114	+	0.736797i	$0.263663\pi$
$920$		0			0
$921$	2.15894	−	3.73939i	0.0711394	−	0.123217i
$922$	−4.92093	+	18.3652i	−0.162062	+	0.604824i
$923$	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
$927$	−8.98910	+	2.40862i	−0.295241	+	0.0791095i
$928$	0.661282	−	0.177190i	0.0217076	−	0.00581655i
$929$	−2.59922	−	4.50199i	−0.0852777	−	0.147705i	0.820232	−	0.572031i	$-0.193844\pi$
$929$	−2.59922	−	4.50199i	−0.0852777	−	0.147705i	−0.905510	+	0.424326i	$0.860511\pi$
$930$		0			0
$931$	42.2224	−	24.8089i	1.38378	−	0.813078i
$932$	−10.2342	+	10.2342i	−0.335232	+	0.335232i
$933$	2.18581	−	8.15755i	0.0715602	−	0.267066i
$934$	−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	0.646824	−	0.762639i	$-0.276097\pi$
$937$	−3.54515	−	3.54515i	−0.115815	−	0.115815i	−0.762639	+	0.646824i	$0.776097\pi$
$938$	−18.6916	−	18.5494i	−0.610301	−	0.605658i
$939$			19.4096i			0.633409i
$940$		0			0
$941$	8.88464	+	5.12955i	0.289631	+	0.167219i	0.637775	−	0.770222i	$-0.279855\pi$
$941$	8.88464	+	5.12955i	0.289631	+	0.167219i	−0.348144	+	0.937441i	$0.613188\pi$
$942$	0.952462	+	3.55464i	0.0310329	+	0.115816i
$943$	−4.24663	−	1.13788i	−0.138289	−	0.0370545i
$944$	10.1603			0.330689
$945$		0			0
$946$	−15.1533			−0.492676
$947$	27.1150	+	7.26545i	0.881120	+	0.236096i	0.670890	−	0.741556i	$-0.265912\pi$
$947$	27.1150	+	7.26545i	0.881120	+	0.236096i	0.210230	+	0.977652i	$0.432579\pi$
$948$	−2.15619	−	8.04700i	−0.0700297	−	0.261354i
$949$	14.4166	+	8.32344i	0.467983	+	0.270190i
$950$		0			0
$951$		−	15.5503i		−	0.504253i
$952$	5.40781	−	1.47117i	0.175268	−	0.0476809i
$953$	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
$957$	−0.972117	+	3.62799i	−0.0314241	+	0.117276i
$958$	−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
$962$	−32.3526	+	8.66886i	−1.04309	+	0.279495i
$963$	11.8496	−	3.17510i	0.381850	−	0.102316i
$964$	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	$0.226753\pi$
$968$	4.94331	−	18.4487i	0.158884	−	0.592963i
$969$	−7.40955	+	12.8337i	−0.238029	+	0.412278i
$970$		0			0
$971$	51.1699	−	29.5430i	1.64212	−	0.948079i	0.662042	−	0.749467i	$-0.269690\pi$
$971$	51.1699	−	29.5430i	1.64212	−	0.948079i	0.980078	−	0.198612i	$-0.0636433\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	33.8155	−	34.0747i	1.08408	−	1.09239i
$974$		−	9.34012i		−	0.299277i
$975$		0			0
$976$	1.01469	+	0.585830i	0.0324794	+	0.0187520i
$977$	3.06089	+	11.4234i	0.0979266	+	0.365467i	0.997447	−	0.0714120i	$-0.0227505\pi$
$977$	3.06089	+	11.4234i	0.0979266	+	0.365467i	−0.899520	+	0.436879i	$0.856084\pi$
$978$	13.6012	+	3.64443i	0.434918	+	0.116536i
$979$	−39.4112			−1.25959
$980$		0			0
$981$	−0.336622			−0.0107475
$982$	2.01430	+	0.539730i	0.0642788	+	0.0172235i
$983$	9.83561	+	36.7070i	0.313707	+	1.17077i	0.925187	+	0.379511i	$0.123908\pi$
$983$	9.83561	+	36.7070i	0.313707	+	1.17077i	−0.611480	+	0.791260i	$0.709425\pi$
$984$	2.17023	+	1.25298i	0.0691844	+	0.0399437i
$985$		0			0
$986$		−	1.45017i		−	0.0461829i
$987$	6.56977	−	6.62013i	0.209118	−	0.210721i
$988$	−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	−0.922616	−	0.385720i	$-0.873953\pi$
$991$	−4.00630	+	6.93911i	−0.127264	+	0.220428i	0.795352	+	0.606148i	$0.207286\pi$
$992$	−1.44328	+	5.38640i	−0.0458243	+	0.171018i
$993$	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
$997$	−41.1086	+	11.0150i	−1.30192	+	0.348849i	−0.842176	−	0.539202i	$-0.818726\pi$
$997$	−41.1086	+	11.0150i	−1.30192	+	0.348849i	−0.459745	+	0.888051i	$0.652059\pi$
$998$	12.9671	−	3.47453i	0.410468	−	0.109984i
$999$	−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.h.493.3		16
5.2	odd	4		1050.2.bc.g.157.2		16
5.3	odd	4		210.2.u.b.157.3	yes	16
5.4	even	2		210.2.u.a.73.1	✓	16
7.5	odd	6		1050.2.bc.g.943.2		16
15.8	even	4		630.2.bv.b.577.2		16
15.14	odd	2		630.2.bv.a.73.4		16
35.3	even	12		1470.2.m.d.97.6		16
35.4	even	6		1470.2.m.d.1273.6		16
35.12	even	12	inner	1050.2.bc.h.607.3		16
35.18	odd	12		1470.2.m.e.97.7		16
35.19	odd	6		210.2.u.b.103.3	yes	16
35.24	odd	6		1470.2.m.e.1273.7		16
35.33	even	12		210.2.u.a.187.1	yes	16
105.68	odd	12		630.2.bv.a.397.4		16
105.89	even	6		630.2.bv.b.523.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.73.1	✓	16	5.4	even	2
210.2.u.a.187.1	yes	16	35.33	even	12
210.2.u.b.103.3	yes	16	35.19	odd	6
210.2.u.b.157.3	yes	16	5.3	odd	4
630.2.bv.a.73.4		16	15.14	odd	2
630.2.bv.a.397.4		16	105.68	odd	12
630.2.bv.b.523.2		16	105.89	even	6
630.2.bv.b.577.2		16	15.8	even	4
1050.2.bc.g.157.2		16	5.2	odd	4
1050.2.bc.g.943.2		16	7.5	odd	6
1050.2.bc.h.493.3		16	1.1	even	1	trivial
1050.2.bc.h.607.3		16	35.12	even	12	inner
1470.2.m.d.97.6		16	35.3	even	12
1470.2.m.d.1273.6		16	35.4	even	6
1470.2.m.e.97.7		16	35.18	odd	12
1470.2.m.e.1273.7		16	35.24	odd	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)

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

Introduction

L-functions

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