LMFDB - Embedded newform 950.2.l.k.251.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			251.2
Character	$\chi$	$=$	950.251
Dual form			950.2.l.k.651.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{2} +(-0.111946 - 0.634880i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.111946 + 0.634880i) q^{6} +(-0.213557 + 0.369892i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.42854 - 0.883915i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.111946 - 0.634880i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.111946 + 0.634880i) q^{6} +(-0.213557 + 0.369892i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.42854 - 0.883915i) q^{9} +(1.50550 + 2.60760i) q^{11} +(0.322337 - 0.558304i) q^{12} +(-0.831564 + 4.71604i) q^{13} +(0.327189 - 0.274544i) q^{14} +(0.173648 + 0.984808i) q^{16} +(-4.46684 - 1.62580i) q^{17} -2.58440 q^{18} +(-2.34299 + 3.67565i) q^{19} +(0.258744 + 0.0941751i) q^{21} +(-0.522855 - 2.96526i) q^{22} +(4.00475 + 3.36038i) q^{23} +(-0.493849 + 0.414388i) q^{24} +(2.39439 - 4.14721i) q^{26} +(-1.80006 - 3.11779i) q^{27} +(-0.401356 + 0.146082i) q^{28} +(0.536257 - 0.195182i) q^{29} +(0.113642 - 0.196834i) q^{31} +(0.173648 - 0.984808i) q^{32} +(1.48698 - 1.24772i) q^{33} +(3.64140 + 3.05550i) q^{34} +(2.42854 + 0.883915i) q^{36} -9.76471 q^{37} +(3.45884 - 2.65263i) q^{38} +3.08721 q^{39} +(1.60935 + 9.12706i) q^{41} +(-0.210930 - 0.176991i) q^{42} +(0.777759 - 0.652617i) q^{43} +(-0.522855 + 2.96526i) q^{44} +(-2.61391 - 4.52743i) q^{46} +(6.78359 - 2.46902i) q^{47} +(0.605795 - 0.220492i) q^{48} +(3.40879 + 5.90419i) q^{49} +(-0.532138 + 3.01791i) q^{51} +(-3.66842 + 3.07817i) q^{52} +(8.29226 + 6.95804i) q^{53} +(0.625153 + 3.54542i) q^{54} +0.427115 q^{56} +(2.59589 + 1.07604i) q^{57} -0.570673 q^{58} +(-0.330827 - 0.120411i) q^{59} +(0.0978266 + 0.0820862i) q^{61} +(-0.174110 + 0.146095i) q^{62} +(-0.191679 + 1.08706i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.82405 + 0.663900i) q^{66} +(-0.246021 + 0.0895442i) q^{67} +(-2.37675 - 4.11666i) q^{68} +(1.68512 - 2.91872i) q^{69} +(0.343144 - 0.287932i) q^{71} +(-1.97976 - 1.66122i) q^{72} +(1.48383 + 8.41521i) q^{73} +(9.17582 + 3.33973i) q^{74} +(-4.15750 + 1.30967i) q^{76} -1.28604 q^{77} +(-2.90103 - 1.05589i) q^{78} +(-2.31546 - 13.1316i) q^{79} +(4.16137 - 3.49181i) q^{81} +(1.60935 - 9.12706i) q^{82} +(0.550970 - 0.954308i) q^{83} +(0.137675 + 0.238460i) q^{84} +(-0.954063 + 0.347250i) q^{86} +(-0.183949 - 0.318609i) q^{87} +(1.50550 - 2.60760i) q^{88} +(-1.75998 + 9.98133i) q^{89} +(-1.56684 - 1.31473i) q^{91} +(0.907803 + 5.14840i) q^{92} +(-0.137688 - 0.0501142i) q^{93} -7.21894 q^{94} -0.644674 q^{96} +(14.5299 + 5.28846i) q^{97} +(-1.18386 - 6.71400i) q^{98} +(5.96106 + 5.00193i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{7} - 12 q^{8}+O(q^{10}) $ 24 * q + 3 * q^7 - 12 * q^8	$ 24 q + 3 q^{7} - 12 q^{8} - 6 q^{11} - 3 q^{12} + 24 q^{13} - 15 q^{14} - 9 q^{17} + 30 q^{18} - 15 q^{19} - 18 q^{21} + 12 q^{23} - 9 q^{26} - 21 q^{27} + 12 q^{28} - 12 q^{29} + 9 q^{31} - 42 q^{33} - 9 q^{34} + 66 q^{37} + 6 q^{38} + 66 q^{39} + 18 q^{41} + 9 q^{42} - 3 q^{43} - 3 q^{46} - 12 q^{47} - 27 q^{49} - 3 q^{51} - 12 q^{52} - 45 q^{53} + 27 q^{54} - 6 q^{56} - 27 q^{57} - 18 q^{58} + 36 q^{59} + 12 q^{61} - 24 q^{62} - 63 q^{63} - 12 q^{64} + 48 q^{66} - 54 q^{67} + 3 q^{68} + 21 q^{69} - 39 q^{71} + 48 q^{73} + 18 q^{74} + 6 q^{76} + 48 q^{77} - 12 q^{78} - 42 q^{79} - 36 q^{81} + 18 q^{82} - 3 q^{83} + 9 q^{84} - 39 q^{86} - 24 q^{87} - 6 q^{88} - 36 q^{89} + 12 q^{91} - 15 q^{92} - 6 q^{93} + 12 q^{94} + 6 q^{96} - 54 q^{97} + 3 q^{98} + 51 q^{99}+O(q^{100}) $ 24 * q + 3 * q^7 - 12 * q^8 - 6 * q^11 - 3 * q^12 + 24 * q^13 - 15 * q^14 - 9 * q^17 + 30 * q^18 - 15 * q^19 - 18 * q^21 + 12 * q^23 - 9 * q^26 - 21 * q^27 + 12 * q^28 - 12 * q^29 + 9 * q^31 - 42 * q^33 - 9 * q^34 + 66 * q^37 + 6 * q^38 + 66 * q^39 + 18 * q^41 + 9 * q^42 - 3 * q^43 - 3 * q^46 - 12 * q^47 - 27 * q^49 - 3 * q^51 - 12 * q^52 - 45 * q^53 + 27 * q^54 - 6 * q^56 - 27 * q^57 - 18 * q^58 + 36 * q^59 + 12 * q^61 - 24 * q^62 - 63 * q^63 - 12 * q^64 + 48 * q^66 - 54 * q^67 + 3 * q^68 + 21 * q^69 - 39 * q^71 + 48 * q^73 + 18 * q^74 + 6 * q^76 + 48 * q^77 - 12 * q^78 - 42 * q^79 - 36 * q^81 + 18 * q^82 - 3 * q^83 + 9 * q^84 - 39 * q^86 - 24 * q^87 - 6 * q^88 - 36 * q^89 + 12 * q^91 - 15 * q^92 - 6 * q^93 + 12 * q^94 + 6 * q^96 - 54 * q^97 + 3 * q^98 + 51 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$

Coefficient data

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

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

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

$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$3$	−0.111946	−	0.634880i	−0.0646323	−	0.366548i	−0.999920	−	0.0126594i	$-0.995970\pi$
$3$	−0.111946	−	0.634880i	−0.0646323	−	0.366548i	0.935288	−	0.353889i	$-0.115141\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$		0			0
$5$		0			0
$6$	−0.111946	+	0.634880i	−0.0457020	+	0.259189i
$7$	−0.213557	+	0.369892i	−0.0807171	+	0.139806i	−0.903558	−	0.428466i	$-0.859054\pi$
$7$	−0.213557	+	0.369892i	−0.0807171	+	0.139806i	0.822841	+	0.568272i	$0.192388\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	2.42854	−	0.883915i	0.809512	−	0.294638i
$10$		0			0
$11$	1.50550	+	2.60760i	0.453925	+	0.786222i	0.998626	−	0.0524090i	$-0.0166900\pi$
$11$	1.50550	+	2.60760i	0.453925	+	0.786222i	−0.544700	+	0.838631i	$0.683357\pi$
$12$	0.322337	−	0.558304i	0.0930507	−	0.161169i
$13$	−0.831564	+	4.71604i	−0.230634	+	1.30799i	0.620981	+	0.783826i	$0.286734\pi$
$13$	−0.831564	+	4.71604i	−0.230634	+	1.30799i	−0.851615	+	0.524167i	$0.824377\pi$
$14$	0.327189	−	0.274544i	0.0874449	−	0.0733750i
$15$		0			0
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−4.46684	−	1.62580i	−1.08337	−	0.394313i	−0.262207	−	0.965012i	$-0.584450\pi$
$17$	−4.46684	−	1.62580i	−1.08337	−	0.394313i	−0.821160	+	0.570698i	$0.806673\pi$
$18$	−2.58440			−0.609148
$19$	−2.34299	+	3.67565i	−0.537519	+	0.843252i
$19$	−2.34299	+	3.67565i	−0.537519	+	0.843252i
$20$		0			0
$21$	0.258744	+	0.0941751i	0.0564626	+	0.0205507i
$22$	−0.522855	−	2.96526i	−0.111473	−	0.632195i
$23$	4.00475	+	3.36038i	0.835048	+	0.700688i	0.956444	−	0.291916i	$-0.0942928\pi$
$23$	4.00475	+	3.36038i	0.835048	+	0.700688i	−0.121396	+	0.992604i	$0.538737\pi$
$24$	−0.493849	+	0.414388i	−0.100807	+	0.0845867i
$25$		0			0
$26$	2.39439	−	4.14721i	0.469579	−	0.813335i
$27$	−1.80006	−	3.11779i	−0.346421	−	0.600019i
$28$	−0.401356	+	0.146082i	−0.0758492	+	0.0276069i
$29$	0.536257	−	0.195182i	0.0995805	−	0.0362443i	−0.291749	−	0.956495i	$-0.594237\pi$
$29$	0.536257	−	0.195182i	0.0995805	−	0.0362443i	0.391330	+	0.920250i	$0.372015\pi$
$30$		0			0
$31$	0.113642	−	0.196834i	0.0204107	−	0.0353524i	−0.855640	−	0.517572i	$-0.826836\pi$
$31$	0.113642	−	0.196834i	0.0204107	−	0.0353524i	0.876050	+	0.482220i	$0.160169\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$	1.48698	−	1.24772i	0.258850	−	0.217201i
$34$	3.64140	+	3.05550i	0.624495	+	0.524013i
$35$		0			0
$36$	2.42854	+	0.883915i	0.404756	+	0.147319i
$37$	−9.76471			−1.60531			−0.802654	−	0.596445i	$-0.796579\pi$
$37$	−9.76471			−1.60531			−0.802654	+	0.596445i	$0.796579\pi$
$38$	3.45884	−	2.65263i	0.561097	−	0.430314i
$39$	3.08721			0.494349
$40$		0			0
$41$	1.60935	+	9.12706i	0.251338	+	1.42541i	0.805301	+	0.592866i	$0.202004\pi$
$41$	1.60935	+	9.12706i	0.251338	+	1.42541i	−0.553963	+	0.832541i	$0.686885\pi$
$42$	−0.210930	−	0.176991i	−0.0325472	−	0.0273104i
$43$	0.777759	−	0.652617i	0.118607	−	0.0995232i	−0.581555	−	0.813507i	$-0.697555\pi$
$43$	0.777759	−	0.652617i	0.118607	−	0.0995232i	0.700162	+	0.713984i	$0.253111\pi$
$44$	−0.522855	+	2.96526i	−0.0788233	+	0.447029i
$45$		0			0
$46$	−2.61391	−	4.52743i	−0.385400	−	0.667533i
$47$	6.78359	−	2.46902i	0.989488	−	0.360144i	0.203966	−	0.978978i	$-0.434617\pi$
$47$	6.78359	−	2.46902i	0.989488	−	0.360144i	0.785522	+	0.618834i	$0.212395\pi$
$48$	0.605795	−	0.220492i	0.0874390	−	0.0318252i
$49$	3.40879	+	5.90419i	0.486970	+	0.843456i
$50$		0			0
$51$	−0.532138	+	3.01791i	−0.0745143	+	0.422592i
$52$	−3.66842	+	3.07817i	−0.508719	+	0.426866i
$53$	8.29226	+	6.95804i	1.13903	+	0.955760i	0.999407	−	0.0344451i	$-0.0109664\pi$
$53$	8.29226	+	6.95804i	1.13903	+	0.955760i	0.139623	+	0.990205i	$0.455411\pi$
$54$	0.625153	+	3.54542i	0.0850726	+	0.482471i
$55$		0			0
$56$	0.427115			0.0570756
$57$	2.59589	+	1.07604i	0.343833	+	0.142525i
$58$	−0.570673			−0.0749330
$59$	−0.330827	−	0.120411i	−0.0430700	−	0.0156762i	0.320395	−	0.947284i	$-0.396184\pi$
$59$	−0.330827	−	0.120411i	−0.0430700	−	0.0156762i	−0.363465	+	0.931608i	$0.618406\pi$
$60$		0			0
$61$	0.0978266	+	0.0820862i	0.0125254	+	0.0105101i	0.649029	−	0.760764i	$-0.275175\pi$
$61$	0.0978266	+	0.0820862i	0.0125254	+	0.0105101i	−0.636503	+	0.771274i	$0.719620\pi$
$62$	−0.174110	+	0.146095i	−0.0221119	+	0.0185541i
$63$	−0.191679	+	1.08706i	−0.0241492	+	0.136957i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	−1.82405	+	0.663900i	−0.224525	+	0.0817204i
$67$	−0.246021	+	0.0895442i	−0.0300562	+	0.0109396i	−0.357005	−	0.934103i	$-0.616202\pi$
$67$	−0.246021	+	0.0895442i	−0.0300562	+	0.0109396i	0.326948	+	0.945042i	$0.393980\pi$
$68$	−2.37675	−	4.11666i	−0.288224	−	0.499218i
$69$	1.68512	−	2.91872i	0.202865	−	0.351372i
$70$		0			0
$71$	0.343144	−	0.287932i	0.0407238	−	0.0341713i	−0.622199	−	0.782859i	$-0.713760\pi$
$71$	0.343144	−	0.287932i	0.0407238	−	0.0341713i	0.662922	+	0.748688i	$0.269316\pi$
$72$	−1.97976	−	1.66122i	−0.233317	−	0.195776i
$73$	1.48383	+	8.41521i	0.173669	+	0.984926i	0.939669	+	0.342085i	$0.111133\pi$
$73$	1.48383	+	8.41521i	0.173669	+	0.984926i	−0.766000	+	0.642841i	$0.777756\pi$
$74$	9.17582	+	3.33973i	1.06667	+	0.388235i
$75$		0			0
$76$	−4.15750	+	1.30967i	−0.476898	+	0.150229i
$77$	−1.28604			−0.146558
$78$	−2.90103	−	1.05589i	−0.328477	−	0.119556i
$79$	−2.31546	−	13.1316i	−0.260510	−	1.47742i	−0.781523	−	0.623876i	$-0.785557\pi$
$79$	−2.31546	−	13.1316i	−0.260510	−	1.47742i	0.521014	−	0.853548i	$-0.325554\pi$
$80$		0			0
$81$	4.16137	−	3.49181i	0.462375	−	0.387978i
$82$	1.60935	−	9.12706i	0.177723	−	1.00791i
$83$	0.550970	−	0.954308i	0.0604768	−	0.104749i	−0.834202	−	0.551459i	$-0.814071\pi$
$83$	0.550970	−	0.954308i	0.0604768	−	0.104749i	0.894679	+	0.446710i	$0.147405\pi$
$84$	0.137675	+	0.238460i	0.0150216	+	0.0260181i
$85$		0			0
$86$	−0.954063	+	0.347250i	−0.102879	+	0.0374450i
$87$	−0.183949	−	0.318609i	−0.0197214	−	0.0341585i
$88$	1.50550	−	2.60760i	0.160487	−	0.277971i
$89$	−1.75998	+	9.98133i	−0.186557	+	1.05802i	0.737381	+	0.675477i	$0.236062\pi$
$89$	−1.75998	+	9.98133i	−0.186557	+	1.05802i	−0.923938	+	0.382542i	$0.875049\pi$
$90$		0			0
$91$	−1.56684	−	1.31473i	−0.164249	−	0.137821i
$92$	0.907803	+	5.14840i	0.0946450	+	0.536758i
$93$	−0.137688	−	0.0501142i	−0.0142775	−	0.00519660i
$94$	−7.21894			−0.744577
$95$		0			0
$96$	−0.644674			−0.0657968
$97$	14.5299	+	5.28846i	1.47529	+	0.536962i	0.949532	−	0.313671i	$-0.101559\pi$
$97$	14.5299	+	5.28846i	1.47529	+	0.536962i	0.525760	+	0.850633i	$0.323781\pi$
$98$	−1.18386	−	6.71400i	−0.119588	−	0.678216i
$99$	5.96106	+	5.00193i	0.599109	+	0.502712i
$100$		0			0
$101$	1.11257	−	6.30968i	0.110705	−	0.627837i	−0.878083	−	0.478508i	$-0.841178\pi$
$101$	1.11257	−	6.30968i	0.110705	−	0.627837i	0.988788	−	0.149329i	$-0.0477113\pi$
$102$	1.53223	−	2.65390i	0.151714	−	0.262776i
$103$	4.63233	+	8.02343i	0.456437	+	0.790572i	0.998770	−	0.0495917i	$-0.0157920\pi$
$103$	4.63233	+	8.02343i	0.456437	+	0.790572i	−0.542332	+	0.840164i	$0.682459\pi$
$104$	4.49999	−	1.63786i	0.441260	−	0.160606i
$105$		0			0
$106$	−5.41239	−	9.37454i	−0.525698	−	0.910535i
$107$	0.0878050	−	0.152083i	0.00848843	−	0.0147024i	−0.861750	−	0.507333i	$-0.830631\pi$
$107$	0.0878050	−	0.152083i	0.00848843	−	0.0147024i	0.870238	+	0.492631i	$0.163965\pi$
$108$	0.625153	−	3.54542i	0.0601554	−	0.341158i
$109$	−3.86393	+	3.24222i	−0.370097	+	0.310548i	−0.808800	−	0.588084i	$-0.799883\pi$
$109$	−3.86393	+	3.24222i	−0.370097	+	0.310548i	0.438703	+	0.898632i	$0.355438\pi$
$110$		0			0
$111$	1.09312	+	6.19942i	0.103755	+	0.588423i
$112$	−0.401356	−	0.146082i	−0.0379246	−	0.0138034i
$113$	6.32672			0.595168			0.297584	−	0.954696i	$-0.403819\pi$
$113$	6.32672			0.595168			0.297584	+	0.954696i	$0.403819\pi$
$114$	−2.07131	−	1.89899i	−0.193996	−	0.177857i
$115$		0			0
$116$	0.536257	+	0.195182i	0.0497902	+	0.0181222i
$117$	2.14909	+	12.1881i	0.198684	+	1.12679i
$118$	0.269692	+	0.226299i	0.0248272	+	0.0208325i
$119$	1.55529	−	1.30505i	0.142574	−	0.119633i
$120$		0			0
$121$	0.966940	−	1.67479i	0.0879036	−	0.152254i
$122$	−0.0638518	−	0.110594i	−0.00578087	−	0.0100128i
$123$	5.61443	−	2.04348i	0.506236	−	0.184255i
$124$	0.213577	−	0.0777357i	0.0191798	−	0.00698087i
$125$		0			0
$126$	0.551916	−	0.955947i	0.0491686	−	0.0851626i
$127$	0.750295	−	4.25513i	0.0665779	−	0.377582i	−0.933253	−	0.359219i	$-0.883043\pi$
$127$	0.750295	−	4.25513i	0.0665779	−	0.377582i	0.999831	−	0.0183635i	$-0.00584561\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$	−0.501401	−	0.420725i	−0.0441459	−	0.0370428i
$130$		0			0
$131$	12.0084	+	4.37069i	1.04918	+	0.381869i	0.808352	−	0.588699i	$-0.200360\pi$
$131$	12.0084	+	4.37069i	1.04918	+	0.381869i	0.240825	+	0.970569i	$0.422582\pi$
$132$	1.94111			0.168952
$133$	−0.859231	−	1.65161i	−0.0745048	−	0.143213i
$134$	0.261810			0.0226169
$135$		0			0
$136$	0.825438	+	4.68129i	0.0707807	+	0.401417i
$137$	12.4137	+	10.4163i	1.06057	+	0.889924i	0.994165	−	0.107868i	$-0.0344025\pi$
$137$	12.4137	+	10.4163i	1.06057	+	0.889924i	0.0664053	+	0.997793i	$0.478847\pi$
$138$	−2.58176	+	2.16635i	−0.219774	+	0.184412i
$139$	2.19570	−	12.4524i	0.186237	−	1.05620i	−0.738120	−	0.674670i	$-0.764286\pi$
$139$	2.19570	−	12.4524i	0.186237	−	1.05620i	0.924356	−	0.381530i	$-0.124603\pi$
$140$		0			0
$141$	−2.32693	−	4.03036i	−0.195963	−	0.339418i
$142$	−0.420929	+	0.153206i	−0.0353236	+	0.0128567i
$143$	−13.5495	+	4.93160i	−1.13306	+	0.412401i
$144$	1.29220	+	2.23815i	0.107683	+	0.186513i
$145$		0			0
$146$	1.48383	−	8.41521i	0.122803	−	0.696448i
$147$	3.36685	−	2.82512i	0.277693	−	0.233012i
$148$	−7.48020	−	6.27663i	−0.614869	−	0.515936i
$149$	−1.16329	−	6.59734i	−0.0953004	−	0.540475i	−0.994655	−	0.103255i	$-0.967074\pi$
$149$	−1.16329	−	6.59734i	−0.0953004	−	0.540475i	0.899355	−	0.437220i	$-0.144037\pi$
$150$		0			0
$151$	−21.6247			−1.75979			−0.879897	−	0.475165i	$-0.842389\pi$
$151$	−21.6247			−1.75979			−0.879897	+	0.475165i	$0.842389\pi$
$152$	4.35470	+	0.191264i	0.353213	+	0.0155136i
$153$	−12.2849			−0.993179
$154$	1.20848	+	0.439852i	0.0973824	+	0.0354443i
$155$		0			0
$156$	2.36494	+	1.98442i	0.189347	+	0.158881i
$157$	−11.2642	+	9.45178i	−0.898981	+	0.754334i	−0.969991	−	0.243141i	$-0.921822\pi$
$157$	−11.2642	+	9.45178i	−0.898981	+	0.754334i	0.0710102	+	0.997476i	$0.477378\pi$
$158$	−2.31546	+	13.1316i	−0.184208	+	1.04470i
$159$	3.48923	−	6.04352i	0.276714	−	0.479282i
$160$		0			0
$161$	−2.09822	+	0.763690i	−0.165363	+	0.0601872i
$162$	−5.10468	+	1.85795i	−0.401061	+	0.145974i
$163$	−5.37685	−	9.31297i	−0.421147	−	0.729448i	0.574905	−	0.818220i	$-0.305039\pi$
$163$	−5.37685	−	9.31297i	−0.421147	−	0.729448i	−0.996052	+	0.0887719i	$0.971706\pi$
$164$	−4.63393	+	8.02620i	−0.361849	+	0.626741i
$165$		0			0
$166$	−0.844135	+	0.708314i	−0.0655176	+	0.0549758i
$167$	0.211984	+	0.177876i	0.0164038	+	0.0137645i	0.650953	−	0.759118i	$-0.274370\pi$
$167$	0.211984	+	0.177876i	0.0164038	+	0.0137645i	−0.634549	+	0.772883i	$0.718814\pi$
$168$	−0.0478140	−	0.271166i	−0.00368893	−	0.0209209i
$169$	−9.33349	−	3.39711i	−0.717961	−	0.261316i
$170$		0			0
$171$	−2.44108	+	10.9975i	−0.186674	+	0.840996i
$172$	1.01529			0.0774153
$173$	−16.7602	−	6.10020i	−1.27425	−	0.463789i	−0.385724	−	0.922614i	$-0.626048\pi$
$173$	−16.7602	−	6.10020i	−1.27425	−	0.463789i	−0.888527	+	0.458825i	$0.848271\pi$
$174$	0.0638848	+	0.362309i	0.00484310	+	0.0274666i
$175$		0			0
$176$	−2.30656	+	1.93543i	−0.173863	+	0.145889i
$177$	−0.0394117	+	0.223515i	−0.00296237	+	0.0168004i
$178$	5.06765	−	8.77743i	0.379837	−	0.657896i
$179$	−9.52909	−	16.5049i	−0.712238	−	1.23363i	−0.964015	−	0.265847i	$-0.914348\pi$
$179$	−9.52909	−	16.5049i	−0.712238	−	1.23363i	0.251777	−	0.967785i	$-0.418985\pi$
$180$		0			0
$181$	−9.29231	+	3.38212i	−0.690692	+	0.251391i	−0.663431	−	0.748237i	$-0.730901\pi$
$181$	−9.29231	+	3.38212i	−0.690692	+	0.251391i	−0.0272604	+	0.999628i	$0.508678\pi$
$182$	1.02268	+	1.77133i	0.0758061	+	0.131300i
$183$	0.0411636	−	0.0712974i	0.00304290	−	0.00527045i
$184$	0.907803	−	5.14840i	0.0669241	−	0.379545i
$185$		0			0
$186$	0.112244	+	0.0941838i	0.00823013	+	0.00690589i
$187$	−2.48539	−	14.0954i	−0.181750	−	1.03076i
$188$	6.78359	+	2.46902i	0.494744	+	0.180072i
$189$	1.53766			0.111848
$190$		0			0
$191$	22.6766			1.64082			0.820409	−	0.571777i	$-0.193746\pi$
$191$	22.6766			1.64082			0.820409	+	0.571777i	$0.193746\pi$
$192$	0.605795	+	0.220492i	0.0437195	+	0.0159126i
$193$	0.502784	+	2.85143i	0.0361912	+	0.205250i	0.997542	−	0.0700776i	$-0.0223247\pi$
$193$	0.502784	+	2.85143i	0.0361912	+	0.205250i	−0.961350	+	0.275328i	$0.911214\pi$
$194$	−11.8449	−	9.93906i	−0.850415	−	0.713583i
$195$		0			0
$196$	−1.18386	+	6.71400i	−0.0845614	+	0.479571i
$197$	−0.731021	+	1.26617i	−0.0520831	+	0.0902106i	−0.890892	−	0.454216i	$-0.849919\pi$
$197$	−0.731021	+	1.26617i	−0.0520831	+	0.0902106i	0.838808	+	0.544427i	$0.183253\pi$
$198$	−3.89081	−	6.73908i	−0.276508	−	0.478925i
$199$	−16.9886	+	6.18336i	−1.20429	+	0.438327i	−0.864720	−	0.502253i	$-0.832504\pi$
$199$	−16.9886	+	6.18336i	−1.20429	+	0.438327i	−0.339572	+	0.940580i	$0.610282\pi$
$200$		0			0
$201$	0.0843910	+	0.146169i	0.00595248	+	0.0103100i
$202$	−3.20351	+	5.54864i	−0.225398	+	0.390401i
$203$	−0.0423255	+	0.240040i	−0.00297067	+	0.0168475i
$204$	−2.34752	+	1.96980i	−0.164359	+	0.137914i
$205$		0			0
$206$	−1.60879	−	9.12391i	−0.112090	−	0.635693i
$207$	12.6960	+	4.62096i	0.882431	+	0.321179i
$208$	−4.78879			−0.332043
$209$	−13.1120	−	0.575897i	−0.906976	−	0.0398356i
$210$		0			0
$211$	−25.5493	−	9.29918i	−1.75889	−	0.640182i	−0.758945	−	0.651154i	$-0.774285\pi$
$211$	−25.5493	−	9.29918i	−1.75889	−	0.640182i	−0.999940	+	0.0109726i	$0.996507\pi$
$212$	1.87970	+	10.6603i	0.129099	+	0.732154i
$213$	−0.221216	−	0.185623i	−0.0151575	−	0.0127186i
$214$	−0.134525	+	0.112880i	−0.00919594	+	0.00771631i
$215$		0			0
$216$	−1.80006	+	3.11779i	−0.122478	+	0.212139i
$217$	0.0485381	+	0.0840705i	0.00329498	+	0.00570708i
$218$	4.73981	−	1.72515i	0.321020	−	0.116842i
$219$	5.17654	−	1.88411i	0.349798	−	0.127316i
$220$		0			0
$221$	11.3818	−	19.7138i	0.765621	−	1.32609i
$222$	1.09312	−	6.19942i	0.0733657	−	0.416078i
$223$	8.53736	−	7.16369i	0.571704	−	0.479716i	−0.310507	−	0.950571i	$-0.600499\pi$
$223$	8.53736	−	7.16369i	0.571704	−	0.479716i	0.882211	+	0.470855i	$0.156054\pi$
$224$	0.327189	+	0.274544i	0.0218612	+	0.0183437i
$225$		0			0
$226$	−5.94517	−	2.16386i	−0.395467	−	0.143938i
$227$	4.02837			0.267372			0.133686	−	0.991024i	$-0.457319\pi$
$227$	4.02837			0.267372			0.133686	+	0.991024i	$0.457319\pi$
$228$	1.29690	+	2.49290i	0.0858891	+	0.165096i
$229$	−0.482410			−0.0318786			−0.0159393	−	0.999873i	$-0.505074\pi$
$229$	−0.482410			−0.0318786			−0.0159393	+	0.999873i	$0.505074\pi$
$230$		0			0
$231$	0.143968	+	0.816482i	0.00947239	+	0.0537206i
$232$	−0.437161	−	0.366822i	−0.0287010	−	0.0240830i
$233$	12.9946	−	10.9038i	0.851305	−	0.714329i	−0.108772	−	0.994067i	$-0.534692\pi$
$233$	12.9946	−	10.9038i	0.851305	−	0.714329i	0.960077	+	0.279737i	$0.0902474\pi$
$234$	2.14909	−	12.1881i	0.140490	−	0.796761i
$235$		0			0
$236$	−0.176029	−	0.304892i	−0.0114585	−	0.0198468i
$237$	−8.07781	+	2.94008i	−0.524710	+	0.190979i
$238$	−1.90785	+	0.694401i	−0.123668	+	0.0450113i
$239$	−11.2742	−	19.5274i	−0.729265	−	1.26312i	−0.957194	−	0.289446i	$-0.906529\pi$
$239$	−11.2742	−	19.5274i	−0.729265	−	1.26312i	0.227929	−	0.973678i	$-0.426805\pi$
$240$		0			0
$241$	4.14252	−	23.4934i	0.266843	−	1.51334i	−0.496893	−	0.867812i	$-0.665526\pi$
$241$	4.14252	−	23.4934i	0.266843	−	1.51334i	0.763735	−	0.645529i	$-0.223363\pi$
$242$	−1.48144	+	1.24307i	−0.0952304	+	0.0799078i
$243$	−10.9563	−	9.19340i	−0.702845	−	0.589757i
$244$	0.0221755	+	0.125763i	0.00141964	+	0.00805118i
$245$		0			0
$246$	−5.97475			−0.380936
$247$	−15.3861	−	14.1062i	−0.978997	−	0.897554i
$248$	−0.227284			−0.0144325
$249$	−0.667551	−	0.242969i	−0.0423043	−	0.0153975i
$250$		0			0
$251$	18.1707	+	15.2470i	1.14692	+	0.962382i	0.999643	−	0.0267132i	$-0.00850407\pi$
$251$	18.1707	+	15.2470i	1.14692	+	0.962382i	0.147279	+	0.989095i	$0.452949\pi$
$252$	−0.845585	+	0.709530i	−0.0532668	+	0.0446962i
$253$	−2.73339	+	15.5018i	−0.171847	+	0.974593i
$254$	−2.16039	+	3.74190i	−0.135555	+	0.234788i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−12.6846	+	4.61681i	−0.791243	+	0.287989i	−0.705852	−	0.708359i	$-0.749436\pi$
$257$	−12.6846	+	4.61681i	−0.791243	+	0.287989i	−0.0853901	+	0.996348i	$0.527214\pi$
$258$	0.327266	+	0.566842i	0.0203747	+	0.0352900i
$259$	2.08532	−	3.61189i	0.129576	−	0.224432i
$260$		0			0
$261$	1.12980	−	0.948012i	0.0699326	−	0.0586805i
$262$	−9.78932	−	8.21422i	−0.604786	−	0.507476i
$263$	−3.35399	−	19.0214i	−0.206816	−	1.17291i	−0.894557	−	0.446954i	$-0.852509\pi$
$263$	−3.35399	−	19.0214i	−0.206816	−	1.17291i	0.687741	−	0.725956i	$-0.258602\pi$
$264$	−1.82405	−	0.663900i	−0.112263	−	0.0408602i
$265$		0			0
$266$	0.242527	+	1.84588i	0.0148703	+	0.113178i
$267$	6.53397			0.399872
$268$	−0.246021	−	0.0895442i	−0.0150281	−	0.00546978i
$269$	1.06642	+	6.04796i	0.0650207	+	0.368751i	0.999905	+	0.0137976i	$0.00439204\pi$
$269$	1.06642	+	6.04796i	0.0650207	+	0.368751i	−0.934884	+	0.354953i	$0.884497\pi$
$270$		0			0
$271$	−14.5245	+	12.1875i	−0.882299	+	0.740337i	−0.966650	−	0.256099i	$-0.917563\pi$
$271$	−14.5245	+	12.1875i	−0.882299	+	0.740337i	0.0843514	+	0.996436i	$0.473118\pi$
$272$	0.825438	−	4.68129i	0.0500495	−	0.283845i
$273$	−0.659296	+	1.14193i	−0.0399024	+	0.0691130i
$274$	−8.10244	−	14.0338i	−0.489486	−	0.847815i
$275$		0			0
$276$	3.16699	−	1.15269i	0.190631	−	0.0693839i
$277$	−0.0276485	−	0.0478886i	−0.00166124	−	0.00287734i	0.865194	−	0.501438i	$-0.167195\pi$
$277$	−0.0276485	−	0.0478886i	−0.00166124	−	0.00287734i	−0.866855	+	0.498561i	$0.833862\pi$
$278$	−6.32226	+	10.9505i	−0.379184	+	0.656765i
$279$	0.101999	−	0.578468i	0.00610655	−	0.0346320i
$280$		0			0
$281$	2.49918	+	2.09706i	0.149089	+	0.125100i	0.714281	−	0.699859i	$-0.246754\pi$
$281$	2.49918	+	2.09706i	0.149089	+	0.125100i	−0.565193	+	0.824959i	$0.691198\pi$
$282$	0.808135	+	4.58316i	0.0481237	+	0.272923i
$283$	−9.28357	−	3.37894i	−0.551851	−	0.200857i	0.0510177	−	0.998698i	$-0.483754\pi$
$283$	−9.28357	−	3.37894i	−0.551851	−	0.200857i	−0.602869	+	0.797840i	$0.705976\pi$
$284$	0.447943			0.0265805
$285$		0			0
$286$	14.4190			0.852616
$287$	−3.71971	−	1.35387i	−0.219568	−	0.0799161i
$288$	−0.448776	−	2.54513i	−0.0264444	−	0.149973i
$289$	4.28666	+	3.59694i	0.252157	+	0.211584i
$290$		0			0
$291$	1.73097	−	9.81679i	0.101471	−	0.575471i
$292$	−4.27251	+	7.40021i	−0.250030	+	0.433065i
$293$	0.259483	+	0.449437i	0.0151591	+	0.0262564i	0.873505	−	0.486814i	$-0.161841\pi$
$293$	0.259483	+	0.449437i	0.0151591	+	0.0262564i	−0.858346	+	0.513071i	$0.828508\pi$
$294$	−4.13005	+	1.50322i	−0.240870	+	0.0876694i
$295$		0			0
$296$	4.88235	+	8.45648i	0.283781	+	0.491523i
$297$	5.41997	−	9.38767i	0.314499	−	0.544728i
$298$	−1.16329	+	6.59734i	−0.0673875	+	0.382174i
$299$	−19.1779	+	16.0922i	−1.10909	+	0.930634i
$300$		0			0
$301$	0.0753018	+	0.427058i	0.00434033	+	0.0246152i
$302$	20.3206	+	7.39609i	1.16932	+	0.425597i
$303$	−4.13044			−0.237288
$304$	−4.02666	−	1.66912i	−0.230945	−	0.0957309i
$305$		0			0
$306$	11.5441	+	4.20170i	0.659931	+	0.240195i
$307$	3.22456	+	18.2874i	0.184035	+	1.04372i	0.927188	+	0.374595i	$0.122218\pi$
$307$	3.22456	+	18.2874i	0.184035	+	1.04372i	−0.743153	+	0.669121i	$0.766671\pi$
$308$	−0.985165	−	0.826652i	−0.0561350	−	0.0471029i
$309$	4.57534	−	3.83917i	0.260282	−	0.218403i
$310$		0			0
$311$	−14.9978	+	25.9769i	−0.850445	+	1.47301i	0.0303630	+	0.999539i	$0.490334\pi$
$311$	−14.9978	+	25.9769i	−0.850445	+	1.47301i	−0.880808	+	0.473474i	$0.843000\pi$
$312$	−1.54360	−	2.67360i	−0.0873894	−	0.151363i
$313$	26.4314	−	9.62026i	1.49399	−	0.543769i	0.539496	−	0.841988i	$-0.318615\pi$
$313$	26.4314	−	9.62026i	1.49399	−	0.543769i	0.954497	+	0.298219i	$0.0963926\pi$
$314$	13.8176	−	5.02919i	0.779771	−	0.283814i
$315$		0			0
$316$	6.66711	−	11.5478i	0.375054	−	0.649613i
$317$	−0.986015	+	5.59197i	−0.0553801	+	0.314076i	−0.999896	−	0.0143881i	$-0.995420\pi$
$317$	−0.986015	+	5.59197i	−0.0553801	+	0.314076i	0.944516	+	0.328464i	$0.106531\pi$
$318$	−5.34581	+	4.48566i	−0.299778	+	0.251544i
$319$	1.31629	+	1.10450i	0.0736982	+	0.0618401i
$320$		0			0
$321$	−0.106384	−	0.0387205i	−0.00593776	−	0.00216117i
$322$	2.23288			0.124434
$323$	16.4416	−	12.6093i	0.914835	−	0.701600i
$324$	5.43229			0.301794
$325$		0			0
$326$	1.86736	+	10.5903i	0.103423	+	0.586544i
$327$	2.49097	+	2.09018i	0.137751	+	0.115587i
$328$	7.09959	−	5.95726i	0.392009	−	0.328935i
$329$	−0.535412	+	3.03647i	−0.0295182	+	0.167406i
$330$		0			0
$331$	−9.29392	−	16.0975i	−0.510840	−	0.884801i	−0.999921	−	0.0125626i	$-0.996001\pi$
$331$	−9.29392	−	16.0975i	−0.510840	−	0.884801i	0.489081	−	0.872238i	$-0.337332\pi$
$332$	1.03549	−	0.376886i	0.0568296	−	0.0206843i
$333$	−23.7140	+	8.63117i	−1.29952	+	0.472985i
$334$	−0.138363	−	0.239652i	−0.00757089	−	0.0131132i
$335$		0			0
$336$	−0.0478140	+	0.271166i	−0.00260847	+	0.0147933i
$337$	−15.1995	+	12.7539i	−0.827972	+	0.694751i	−0.954824	−	0.297171i	$-0.903957\pi$
$337$	−15.1995	+	12.7539i	−0.827972	+	0.694751i	0.126852	+	0.991922i	$0.459513\pi$
$338$	7.60873	+	6.38449i	0.413861	+	0.347270i
$339$	−0.708254	−	4.01671i	−0.0384671	−	0.218158i
$340$		0			0
$341$	0.684352			0.0370597
$342$	6.05521	−	9.49933i	0.327428	−	0.513665i
$343$	−5.90169			−0.318661
$344$	−0.954063	−	0.347250i	−0.0514396	−	0.0187225i
$345$		0			0
$346$	13.6630	+	11.4646i	0.734528	+	0.616342i
$347$	23.2960	−	19.5477i	1.25060	−	1.04938i	0.253978	−	0.967210i	$-0.418261\pi$
$347$	23.2960	−	19.5477i	1.25060	−	1.04938i	0.996619	−	0.0821654i	$-0.0261836\pi$
$348$	0.0638848	−	0.362309i	0.00342459	−	0.0194218i
$349$	−15.9349	+	27.6000i	−0.852974	+	1.47739i	0.0255384	+	0.999674i	$0.491870\pi$
$349$	−15.9349	+	27.6000i	−0.852974	+	1.47739i	−0.878512	+	0.477720i	$0.841463\pi$
$350$		0			0
$351$	16.2005	−	5.89649i	0.864718	−	0.314731i
$352$	2.82941	−	1.02982i	0.150808	−	0.0548897i
$353$	−14.7849	−	25.6083i	−0.786923	−	1.36299i	−0.927844	−	0.372970i	$-0.878340\pi$
$353$	−14.7849	−	25.6083i	−0.786923	−	1.36299i	0.140921	−	0.990021i	$-0.454994\pi$
$354$	0.113481	−	0.196556i	0.00603147	−	0.0104468i
$355$		0			0
$356$	−7.76409	+	6.51485i	−0.411496	+	0.345286i
$357$	−1.00266	−	0.841330i	−0.0530663	−	0.0445279i
$358$	3.30942	+	18.7686i	0.174908	+	0.991954i
$359$	13.7525	+	5.00550i	0.725829	+	0.264180i	0.678398	−	0.734695i	$-0.262675\pi$
$359$	13.7525	+	5.00550i	0.725829	+	0.264180i	0.0474305	+	0.998875i	$0.484897\pi$
$360$		0			0
$361$	−8.02080	−	17.2240i	−0.422147	−	0.906527i
$362$	9.88867			0.519737
$363$	−1.17154	−	0.426404i	−0.0614897	−	0.0223804i
$364$	−0.355173	−	2.01429i	−0.0186161	−	0.105577i
$365$		0			0
$366$	−0.0630662	+	0.0529189i	−0.00329653	+	0.00276611i
$367$	2.36744	−	13.4264i	0.123580	−	0.700855i	−0.858562	−	0.512710i	$-0.828642\pi$
$367$	2.36744	−	13.4264i	0.123580	−	0.700855i	0.982141	−	0.188145i	$-0.0602474\pi$
$368$	−2.61391	+	4.52743i	−0.136260	+	0.236009i
$369$	11.9759	+	20.7429i	0.623441	+	1.07983i
$370$		0			0
$371$	−4.34459	+	1.58130i	−0.225560	+	0.0820972i
$372$	−0.0732620	−	0.126894i	−0.00379846	−	0.00657912i
$373$	−7.84492	+	13.5878i	−0.406195	+	0.703550i	−0.994460	−	0.105118i	$-0.966478\pi$
$373$	−7.84492	+	13.5878i	−0.406195	+	0.703550i	0.588265	+	0.808668i	$0.299811\pi$
$374$	−2.48539	+	14.0954i	−0.128517	+	0.728854i
$375$		0			0
$376$	−5.53003	−	4.64025i	−0.285190	−	0.239302i
$377$	0.474551	+	2.69131i	0.0244406	+	0.138610i
$378$	−1.44493	−	0.525911i	−0.0743191	−	0.0270500i
$379$	16.7588			0.860841			0.430421	−	0.902628i	$-0.358365\pi$
$379$	16.7588			0.860841			0.430421	+	0.902628i	$0.358365\pi$
$380$		0			0
$381$	−2.78549			−0.142705
$382$	−21.3090	−	7.75584i	−1.09026	−	0.396823i
$383$	1.68331	+	9.54653i	0.0860131	+	0.487805i	0.997133	+	0.0756641i	$0.0241077\pi$
$383$	1.68331	+	9.54653i	0.0860131	+	0.487805i	−0.911120	+	0.412141i	$0.864781\pi$
$384$	−0.493849	−	0.414388i	−0.0252016	−	0.0211467i
$385$		0			0
$386$	0.502784	−	2.85143i	0.0255910	−	0.145134i
$387$	1.31196	−	2.27238i	0.0666906	−	0.115511i
$388$	7.73122	+	13.3909i	0.392493	+	0.679818i
$389$	5.85303	−	2.13033i	0.296760	−	0.108012i	−0.189349	−	0.981910i	$-0.560638\pi$
$389$	5.85303	−	2.13033i	0.296760	−	0.108012i	0.486110	+	0.873898i	$0.338416\pi$
$390$		0			0
$391$	−12.4253	−	21.5212i	−0.628372	−	1.08837i
$392$	3.40879	−	5.90419i	0.172170	−	0.298207i
$393$	1.43057	−	8.11316i	0.0721627	−	0.409255i
$394$	1.11999	−	0.939783i	0.0564242	−	0.0473456i
$395$		0			0
$396$	1.35126	+	7.66339i	0.0679035	+	0.385100i
$397$	5.51531	+	2.00741i	0.276806	+	0.100749i	0.476693	−	0.879070i	$-0.341835\pi$
$397$	5.51531	+	2.00741i	0.276806	+	0.100749i	−0.199887	+	0.979819i	$0.564058\pi$
$398$	18.0789			0.906215
$399$	−0.952389	+	0.730401i	−0.0476791	+	0.0365658i
$400$		0			0
$401$	11.2098	+	4.08004i	0.559792	+	0.203747i	0.606392	−	0.795166i	$-0.292616\pi$
$401$	11.2098	+	4.08004i	0.559792	+	0.203747i	−0.0466000	+	0.998914i	$0.514839\pi$
$402$	−0.0293087	−	0.166218i	−0.00146178	−	0.00829019i
$403$	0.833774	+	0.699620i	0.0415332	+	0.0348505i
$404$	4.90806	−	4.11835i	0.244185	−	0.204896i
$405$		0			0
$406$	0.121871	−	0.211087i	0.00604837	−	0.0104761i
$407$	−14.7008	−	25.4625i	−0.728690	−	1.26213i
$408$	2.87965	−	1.04811i	0.142564	−	0.0518891i
$409$	12.5375	−	4.56328i	0.619940	−	0.225640i	−0.0129067	−	0.999917i	$-0.504108\pi$
$409$	12.5375	−	4.56328i	0.619940	−	0.225640i	0.632847	+	0.774277i	$0.281886\pi$
$410$		0			0
$411$	5.22343	−	9.04725i	0.257653	−	0.446268i
$412$	−1.60879	+	9.12391i	−0.0792595	+	0.449503i
$413$	0.115190	−	0.0966555i	0.00566811	−	0.00475611i
$414$	−10.3499	−	8.68456i	−0.508667	−	0.426823i
$415$		0			0
$416$	4.49999	+	1.63786i	0.220630	+	0.0803028i
$417$	−8.15159			−0.399185
$418$	12.1243	+	5.02573i	0.593018	+	0.245817i
$419$	35.9961			1.75852			0.879262	−	0.476339i	$-0.158037\pi$
$419$	35.9961			1.75852			0.879262	+	0.476339i	$0.158037\pi$
$420$		0			0
$421$	5.84335	+	33.1393i	0.284787	+	1.61511i	0.706044	+	0.708168i	$0.250478\pi$
$421$	5.84335	+	33.1393i	0.284787	+	1.61511i	−0.421257	+	0.906941i	$0.638411\pi$
$422$	20.8280	+	17.4767i	1.01389	+	0.850754i
$423$	14.2918	−	11.9922i	0.694890	−	0.583082i
$424$	1.87970	−	10.6603i	0.0912865	−	0.517711i
$425$		0			0
$426$	0.144389	+	0.250089i	0.00699566	+	0.0121168i
$427$	−0.0512546	+	0.0186552i	−0.00248038	+	0.000902786i
$428$	0.165019	−	0.0600621i	0.00797651	−	0.00290321i
$429$	4.64779	+	8.05021i	0.224397	+	0.388668i
$430$		0			0
$431$	5.40572	−	30.6574i	0.260384	−	1.47671i	−0.521479	−	0.853264i	$-0.674620\pi$
$431$	5.40572	−	30.6574i	0.260384	−	1.47671i	0.781864	−	0.623449i	$-0.214269\pi$
$432$	2.75785	−	2.31411i	0.132687	−	0.111338i
$433$	12.4419	+	10.4400i	0.597922	+	0.501716i	0.890777	−	0.454441i	$-0.150161\pi$
$433$	12.4419	+	10.4400i	0.597922	+	0.501716i	−0.292855	+	0.956157i	$0.594605\pi$
$434$	−0.0168571	−	0.0956015i	−0.000809168	−	0.00458902i
$435$		0			0
$436$	−5.04400			−0.241564
$437$	−21.7347	+	6.84671i	−1.03971	+	0.327522i
$438$	−5.50876			−0.263219
$439$	24.2875	+	8.83994i	1.15918	+	0.421907i	0.848805	−	0.528706i	$-0.177323\pi$
$439$	24.2875	+	8.83994i	1.15918	+	0.421907i	0.310376	+	0.950614i	$0.399545\pi$
$440$		0			0
$441$	13.4972	+	11.3255i	0.642722	+	0.539308i
$442$	−17.4379	+	14.6321i	−0.829436	+	0.695979i
$443$	−6.64594	+	37.6910i	−0.315758	+	1.79075i	0.252177	+	0.967681i	$0.418854\pi$
$443$	−6.64594	+	37.6910i	−0.315758	+	1.79075i	−0.567935	+	0.823073i	$0.692258\pi$
$444$	−3.14753	+	5.45168i	−0.149375	+	0.258725i
$445$		0			0
$446$	−10.4726	+	3.81172i	−0.495893	+	0.180490i
$447$	−4.05829	+	1.47710i	−0.191951	+	0.0698643i
$448$	−0.213557	−	0.369892i	−0.0100896	−	0.0174758i
$449$	1.65413	−	2.86504i	0.0780632	−	0.135209i	−0.824351	−	0.566079i	$-0.808460\pi$
$449$	1.65413	−	2.86504i	0.0780632	−	0.135209i	0.902414	+	0.430869i	$0.141793\pi$
$450$		0			0
$451$	−21.3769	+	17.9373i	−1.00660	+	0.844635i
$452$	4.84655	+	4.06674i	0.227962	+	0.191283i
$453$	2.42081	+	13.7291i	0.113740	+	0.645049i
$454$	−3.78543	−	1.37778i	−0.177659	−	0.0646626i
$455$		0			0
$456$	−0.366064	−	2.78612i	−0.0171425	−	0.130472i
$457$	−4.88090			−0.228319			−0.114159	−	0.993462i	$-0.536417\pi$
$457$	−4.88090			−0.228319			−0.114159	+	0.993462i	$0.536417\pi$
$458$	0.453317	+	0.164994i	0.0211821	+	0.00770966i
$459$	2.97167	+	16.8532i	0.138706	+	0.786639i
$460$		0			0
$461$	−18.5055	+	15.5280i	−0.861888	+	0.723210i	−0.962374	−	0.271729i	$-0.912405\pi$
$461$	−18.5055	+	15.5280i	−0.861888	+	0.723210i	0.100486	+	0.994938i	$0.467960\pi$
$462$	0.143968	−	0.816482i	0.00669799	−	0.0379862i
$463$	17.9383	−	31.0701i	0.833665	−	1.44395i	−0.0614485	−	0.998110i	$-0.519572\pi$
$463$	17.9383	−	31.0701i	0.833665	−	1.44395i	0.895113	−	0.445839i	$-0.147095\pi$
$464$	0.285336	+	0.494217i	0.0132464	+	0.0229435i
$465$		0			0
$466$	−15.9402	+	5.80177i	−0.738417	+	0.268762i
$467$	−12.2857	−	21.2794i	−0.568514	−	0.984694i	−0.996713	−	0.0810103i	$-0.974185\pi$
$467$	−12.2857	−	21.2794i	−0.568514	−	0.984694i	0.428200	−	0.903684i	$-0.359148\pi$
$468$	−6.18806	+	10.7180i	−0.286043	+	0.495441i
$469$	0.0194178	−	0.110124i	0.000896632	−	0.00508505i
$470$		0			0
$471$	7.26174	+	6.09332i	0.334603	+	0.280765i
$472$	0.0611343	+	0.346710i	0.00281394	+	0.0159586i
$473$	2.87268	+	1.04557i	0.132086	+	0.0480754i
$474$	8.59622			0.394838
$475$		0			0
$476$	2.03029			0.0930583
$477$	26.2884	+	9.56819i	1.20366	+	0.438097i
$478$	3.91548	+	22.2058i	0.179090	+	1.01567i
$479$	4.24307	+	3.56036i	0.193871	+	0.162677i	0.734556	−	0.678548i	$-0.237391\pi$
$479$	4.24307	+	3.56036i	0.193871	+	0.162677i	−0.540685	+	0.841225i	$0.681835\pi$
$480$		0			0
$481$	8.11998	−	46.0507i	0.370239	−	2.09973i
$482$	−11.9279	+	20.6597i	−0.543301	+	0.941025i
$483$	0.719740	+	1.24663i	0.0327493	+	0.0567235i
$484$	1.81725	−	0.661426i	0.0826024	−	0.0300648i
$485$		0			0
$486$	7.15120	+	12.3862i	0.324385	+	0.561851i
$487$	17.4892	−	30.2922i	0.792511	−	1.37267i	−0.131897	−	0.991263i	$-0.542107\pi$
$487$	17.4892	−	30.2922i	0.792511	−	1.37267i	0.924408	−	0.381406i	$-0.124560\pi$
$488$	0.0221755	−	0.125763i	0.00100384	−	0.00569304i
$489$	−5.31070	+	4.45621i	−0.240158	+	0.201517i
$490$		0			0
$491$	5.83077	+	33.0680i	0.263139	+	1.49234i	0.774282	+	0.632840i	$0.218111\pi$
$491$	5.83077	+	33.0680i	0.263139	+	1.49234i	−0.511143	+	0.859496i	$0.670778\pi$
$492$	5.61443	+	2.04348i	0.253118	+	0.0921274i
$493$	−2.71270			−0.122174
$494$	9.63366	+	18.5178i	0.433439	+	0.833157i
$495$		0			0
$496$	0.213577	+	0.0777357i	0.00958989	+	0.00349044i
$497$	0.0332229	+	0.188416i	0.00149025	+	0.00845163i
$498$	0.544192	+	0.456631i	0.0243858	+	0.0204621i
$499$	8.64628	−	7.25509i	0.387061	−	0.324783i	−0.428406	−	0.903586i	$-0.640925\pi$
$499$	8.64628	−	7.25509i	0.387061	−	0.324783i	0.815467	+	0.578804i	$0.196480\pi$
$500$		0			0
$501$	0.0891990	−	0.154497i	0.00398512	−	0.00690243i
$502$	−11.8601	−	20.5422i	−0.529340	−	0.916844i
$503$	−4.72559	+	1.71998i	−0.210704	+	0.0766899i	−0.445216	−	0.895423i	$-0.646873\pi$
$503$	−4.72559	+	1.71998i	−0.210704	+	0.0766899i	0.234512	+	0.972113i	$0.424651\pi$
$504$	1.03726	−	0.377533i	0.0462034	−	0.0168167i
$505$		0			0
$506$	7.87049	−	13.6321i	0.349886	−	0.606020i
$507$	−1.11191	+	6.30594i	−0.0493816	+	0.280057i
$508$	3.30991	−	2.77734i	0.146853	−	0.123225i
$509$	16.3493	+	13.7187i	0.724672	+	0.608072i	0.928673	−	0.370899i	$-0.120950\pi$
$509$	16.3493	+	13.7187i	0.724672	+	0.608072i	−0.204002	+	0.978971i	$0.565395\pi$
$510$		0			0
$511$	−3.42960	−	1.24827i	−0.151717	−	0.0552203i
$512$	1.00000			0.0441942
$513$	15.6774	+	0.688573i	0.692175	+	0.0304012i
$514$	13.4987			0.595400
$515$		0			0
$516$	−0.113658	−	0.644589i	−0.00500353	−	0.0283764i
$517$	16.6509	+	13.9718i	0.732307	+	0.614478i
$518$	−3.19490	+	2.68084i	−0.140376	+	0.117789i
$519$	−1.99665	+	11.3236i	−0.0876434	+	0.497050i
$520$		0			0
$521$	−14.6860	−	25.4370i	−0.643407	−	1.11441i	−0.984667	−	0.174444i	$-0.944187\pi$
$521$	−14.6860	−	25.4370i	−0.643407	−	1.11441i	0.341260	−	0.939969i	$-0.389146\pi$
$522$	−1.38590	+	0.504427i	−0.0606592	+	0.0220782i
$523$	26.2338	−	9.54833i	1.14712	−	0.417519i	0.302643	−	0.953104i	$-0.402131\pi$
$523$	26.2338	−	9.54833i	1.14712	−	0.417519i	0.844482	+	0.535585i	$0.179909\pi$
$524$	6.38953	+	11.0670i	0.279128	+	0.483463i
$525$		0			0
$526$	−3.35399	+	19.0214i	−0.146241	+	0.829373i
$527$	−0.827631	+	0.694465i	−0.0360522	+	0.0302514i
$528$	1.48698	+	1.24772i	0.0647125	+	0.0543002i
$529$	0.751926	+	4.26439i	0.0326924	+	0.185408i
$530$		0			0
$531$	−0.909858			−0.0394845
$532$	0.403429	−	1.81751i	0.0174908	−	0.0787992i
$533$	−44.3818			−1.92239
$534$	−6.13992	−	2.23475i	−0.265700	−	0.0967070i
$535$		0			0
$536$	0.200558	+	0.168288i	0.00866278	+	0.00726894i
$537$	−9.41187	+	7.89749i	−0.406152	+	0.340802i
$538$	1.06642	−	6.04796i	0.0459766	−	0.260746i
$539$	−10.2639	+	17.7775i	−0.442096	+	0.765732i
$540$		0			0
$541$	−32.2336	+	11.7321i	−1.38583	+	0.504401i	−0.923940	−	0.382537i	$-0.875050\pi$
$541$	−32.2336	+	11.7321i	−1.38583	+	0.504401i	−0.461889	+	0.886938i	$0.652828\pi$
$542$	17.8169	−	6.48482i	0.765302	−	0.278547i
$543$	3.18748	+	5.52088i	0.136788	+	0.236924i
$544$	−2.37675	+	4.11666i	−0.101902	+	0.176500i
$545$		0			0
$546$	1.01010	−	0.847574i	0.0432283	−	0.0362728i
$547$	−14.7680	−	12.3918i	−0.631433	−	0.529835i	0.269941	−	0.962877i	$-0.412996\pi$
$547$	−14.7680	−	12.3918i	−0.631433	−	0.529835i	−0.901374	+	0.433042i	$0.857440\pi$
$548$	2.81395	+	15.9587i	0.120206	+	0.681722i
$549$	0.310133	+	0.112879i	0.0132361	+	0.00481756i
$550$		0			0
$551$	−0.539026	+	2.42840i	−0.0229633	+	0.103453i
$552$	−3.37024			−0.143447
$553$	5.35177	+	1.94789i	0.227580	+	0.0828325i
$554$	0.00960221	+	0.0544569i	0.000407959	+	0.00231365i
$555$		0			0
$556$	9.68626	−	8.12774i	0.410789	−	0.344693i
$557$	1.43325	−	8.12837i	0.0607288	−	0.344410i	−0.939270	−	0.343178i	$-0.888497\pi$
$557$	1.43325	−	8.12837i	0.0607288	−	0.344410i	0.999999	−	0.00123221i	$-0.000392224\pi$
$558$	−0.293696	+	0.508696i	−0.0124331	+	0.0215348i
$559$	2.43101	+	4.21063i	0.102821	+	0.178091i
$560$		0			0
$561$	−8.67064	+	3.15585i	−0.366075	+	0.133240i
$562$	−1.63123	−	2.82537i	−0.0688091	−	0.119181i
$563$	14.7581	−	25.5618i	0.621980	−	1.07730i	−0.367136	−	0.930167i	$-0.619662\pi$
$563$	14.7581	−	25.5618i	0.621980	−	1.07730i	0.989117	−	0.147134i	$-0.0470049\pi$
$564$	0.808135	−	4.58316i	0.0340286	−	0.192986i
$565$		0			0
$566$	7.56804	+	6.35034i	0.318108	+	0.266925i
$567$	0.402900	+	2.28496i	0.0169202	+	0.0959593i
$568$	−0.420929	−	0.153206i	−0.0176618	−	0.00642837i
$569$	−41.1441			−1.72485			−0.862426	−	0.506184i	$-0.831056\pi$
$569$	−41.1441			−1.72485			−0.862426	+	0.506184i	$0.831056\pi$
$570$		0			0
$571$	46.8278			1.95968			0.979842	−	0.199774i	$-0.0640209\pi$
$571$	46.8278			1.95968			0.979842	+	0.199774i	$0.0640209\pi$
$572$	−13.5495	−	4.93160i	−0.566532	−	0.206201i
$573$	−2.53856	−	14.3969i	−0.106050	−	0.601439i
$574$	3.03234	+	2.54443i	0.126567	+	0.106203i
$575$		0			0
$576$	−0.448776	+	2.54513i	−0.0186990	+	0.106047i
$577$	7.02145	−	12.1615i	0.292307	−	0.506290i	−0.682048	−	0.731307i	$-0.738911\pi$
$577$	7.02145	−	12.1615i	0.292307	−	0.506290i	0.974355	+	0.225017i	$0.0722439\pi$
$578$	−2.79792	−	4.84614i	−0.116378	−	0.201573i
$579$	1.75403	−	0.638415i	0.0728950	−	0.0265316i
$580$		0			0
$581$	0.235327	+	0.407599i	0.00976303	+	0.0169101i
$582$	−4.98412	+	8.63274i	−0.206598	+	0.357839i
$583$	−5.65979	+	32.0982i	−0.234404	+	1.32937i
$584$	6.54587	−	5.49264i	0.270870	−	0.227287i
$585$		0			0
$586$	−0.0901174	−	0.511081i	−0.00372272	−	0.0211126i
$587$	−16.7973	−	6.11370i	−0.693297	−	0.252340i	−0.0287509	−	0.999587i	$-0.509153\pi$
$587$	−16.7973	−	6.11370i	−0.693297	−	0.252340i	−0.664546	+	0.747247i	$0.731375\pi$
$588$	4.39511			0.181251
$589$	0.457230	+	0.878887i	0.0188398	+	0.0362139i
$590$		0			0
$591$	0.885698	+	0.322368i	0.0364328	+	0.0132604i
$592$	−1.69562	−	9.61636i	−0.0696897	−	0.395230i
$593$	−2.80331	−	2.35225i	−0.115118	−	0.0965955i	0.583412	−	0.812177i	$-0.301718\pi$
$593$	−2.80331	−	2.35225i	−0.115118	−	0.0965955i	−0.698530	+	0.715581i	$0.746162\pi$
$594$	−8.30388	+	6.96778i	−0.340712	+	0.285892i
$595$		0			0
$596$	3.34956	−	5.80160i	0.137203	−	0.237643i
$597$	5.82751	+	10.0935i	0.238504	+	0.413101i
$598$	23.5252	−	8.56246i	0.962015	−	0.350145i
$599$	8.71824	−	3.17318i	0.356217	−	0.129653i	−0.157712	−	0.987485i	$-0.550412\pi$
$599$	8.71824	−	3.17318i	0.356217	−	0.129653i	0.513929	+	0.857833i	$0.328189\pi$
$600$		0			0
$601$	3.17787	−	5.50423i	0.129628	−	0.224522i	−0.793905	−	0.608042i	$-0.791955\pi$
$601$	3.17787	−	5.50423i	0.129628	−	0.224522i	0.923532	+	0.383520i	$0.125288\pi$
$602$	0.0753018	−	0.427058i	0.00306907	−	0.0174056i
$603$	−0.518321	+	0.434923i	−0.0211077	+	0.0177114i
$604$	−16.5655	−	13.9001i	−0.674040	−	0.565587i
$605$		0			0
$606$	3.88134	+	1.41269i	0.157669	+	0.0573868i
$607$	−45.6489			−1.85283			−0.926415	−	0.376503i	$-0.877126\pi$
$607$	−45.6489			−1.85283			−0.926415	+	0.376503i	$0.877126\pi$
$608$	3.21295	+	2.94566i	0.130302	+	0.119462i
$609$	0.157135			0.00636742
$610$		0			0
$611$	6.00301	+	34.0448i	0.242856	+	1.37730i
$612$	−9.41081	−	7.89661i	−0.380410	−	0.319202i
$613$	2.47372	−	2.07570i	0.0999127	−	0.0838367i	−0.591463	−	0.806332i	$-0.701449\pi$
$613$	2.47372	−	2.07570i	0.0999127	−	0.0838367i	0.691376	+	0.722495i	$0.257005\pi$
$614$	3.22456	−	18.2874i	0.130133	−	0.738019i
$615$		0			0
$616$	0.643021	+	1.11374i	0.0259081	+	0.0448741i
$617$	−15.9908	+	5.82019i	−0.643767	+	0.234312i	−0.643212	−	0.765688i	$-0.722399\pi$
$617$	−15.9908	+	5.82019i	−0.643767	+	0.234312i	−0.000554682		1.00000i	$0.500177\pi$
$618$	−5.61249	+	2.04278i	−0.225767	+	0.0821726i
$619$	8.09643	+	14.0234i	0.325423	+	0.563649i	0.981598	−	0.190960i	$-0.0611599\pi$
$619$	8.09643	+	14.0234i	0.325423	+	0.563649i	−0.656175	+	0.754609i	$0.727827\pi$
$620$		0			0
$621$	3.26819	−	18.5348i	0.131148	−	0.743778i
$622$	22.9779	−	19.2807i	0.921330	−	0.773087i
$623$	−3.31616	−	2.78259i	−0.132859	−	0.111482i
$624$	0.536088	+	3.04031i	0.0214607	+	0.121710i
$625$		0			0
$626$	−28.1278			−1.12421
$627$	1.10222	+	8.38902i	0.0440183	+	0.335025i
$628$	−14.7044			−0.586768
$629$	43.6173	+	15.8754i	1.73914	+	0.632994i
$630$		0			0
$631$	14.8437	+	12.4554i	0.590920	+	0.495841i	0.888513	−	0.458852i	$-0.151739\pi$
$631$	14.8437	+	12.4554i	0.590920	+	0.495841i	−0.297593	+	0.954693i	$0.596184\pi$
$632$	−10.2146	+	8.57107i	−0.406315	+	0.340939i
$633$	−3.04371	+	17.2617i	−0.120977	+	0.686092i
$634$	2.83912	−	4.91750i	0.112756	−	0.195299i
$635$		0			0
$636$	6.55760	−	2.38677i	0.260026	−	0.0946417i
$637$	−30.6790	+	11.1662i	−1.21555	+	0.442423i
$638$	−0.859148	−	1.48809i	−0.0340140	−	0.0589140i
$639$	0.578831	−	1.00257i	0.0228982	−	0.0396609i
$640$		0			0
$641$	19.0062	−	15.9481i	0.750698	−	0.629911i	−0.184989	−	0.982741i	$-0.559225\pi$
$641$	19.0062	−	15.9481i	0.750698	−	0.629911i	0.935687	+	0.352830i	$0.114781\pi$
$642$	0.0867248	+	0.0727707i	0.00342275	+	0.00287203i
$643$	1.29930	+	7.36870i	0.0512394	+	0.290593i	0.999650	−	0.0264512i	$-0.00842066\pi$
$643$	1.29930	+	7.36870i	0.0512394	+	0.290593i	−0.948411	+	0.317044i	$0.897310\pi$
$644$	−2.09822	−	0.763690i	−0.0826815	−	0.0300936i
$645$		0			0
$646$	−19.7627	+	6.22551i	−0.777553	+	0.244939i
$647$	35.7785			1.40660			0.703299	−	0.710894i	$-0.251709\pi$
$647$	35.7785			1.40660			0.703299	+	0.710894i	$0.251709\pi$
$648$	−5.10468	−	1.85795i	−0.200531	−	0.0729872i
$649$	−0.184075	−	1.04394i	−0.00722559	−	0.0409784i
$650$		0			0
$651$	0.0479410	−	0.0402273i	0.00187896	−	0.00157663i
$652$	1.86736	−	10.5903i	0.0731315	−	0.414749i
$653$	−9.82618	+	17.0195i	−0.384528	+	0.666023i	−0.991704	−	0.128545i	$-0.958969\pi$
$653$	−9.82618	+	17.0195i	−0.384528	+	0.666023i	0.607175	+	0.794568i	$0.292303\pi$
$654$	−1.62587	−	2.81609i	−0.0635765	−	0.110118i
$655$		0			0
$656$	−8.70894	+	3.16979i	−0.340027	+	0.123760i
$657$	11.0419	+	19.1251i	0.430784	+	0.746140i
$658$	1.54166	−	2.67023i	0.0601001	−	0.104096i
$659$	6.38321	−	36.2010i	0.248654	−	1.41019i	−0.563196	−	0.826324i	$-0.690428\pi$
$659$	6.38321	−	36.2010i	0.248654	−	1.41019i	0.811850	−	0.583866i	$-0.198461\pi$
$660$		0			0
$661$	−18.8107	−	15.7840i	−0.731651	−	0.613928i	0.198930	−	0.980014i	$-0.436253\pi$
$661$	−18.8107	−	15.7840i	−0.731651	−	0.613928i	−0.930581	+	0.366085i	$0.880698\pi$
$662$	3.22774	+	18.3055i	0.125450	+	0.711462i
$663$	−13.7901	−	5.01917i	−0.535561	−	0.194928i
$664$	−1.10194			−0.0427636
$665$		0			0
$666$	25.2359			0.977870
$667$	2.80346	+	1.02038i	0.108550	+	0.0395091i
$668$	0.0480530	+	0.272522i	0.00185923	+	0.0105442i
$669$	−5.50381	−	4.61825i	−0.212790	−	0.178552i
$670$		0			0
$671$	−0.0667704	+	0.378674i	−0.00257764	+	0.0146185i
$672$	0.137675	−	0.238460i	0.00531092	−	0.00919879i
$673$	14.2427	+	24.6692i	0.549017	+	0.950926i	0.998342	+	0.0575576i	$0.0183313\pi$
$673$	14.2427	+	24.6692i	0.549017	+	0.950926i	−0.449325	+	0.893369i	$0.648335\pi$
$674$	18.6450	−	6.78623i	0.718179	−	0.261396i
$675$		0			0
$676$	−4.96625	−	8.60179i	−0.191010	−	0.330838i
$677$	23.6418	−	40.9488i	0.908627	−	1.57379i	0.0926549	−	0.995698i	$-0.470465\pi$
$677$	23.6418	−	40.9488i	0.908627	−	1.57379i	0.815973	−	0.578091i	$-0.196202\pi$
$678$	−0.708254	+	4.01671i	−0.0272003	+	0.154261i
$679$	−5.05913	+	4.24512i	−0.194152	+	0.162913i
$680$		0			0
$681$	−0.450962	−	2.55753i	−0.0172809	−	0.0980049i
$682$	−0.643080	−	0.234062i	−0.0246248	−	0.00896270i
$683$	−13.3196			−0.509660			−0.254830	−	0.966986i	$-0.582020\pi$
$683$	−13.3196			−0.509660			−0.254830	+	0.966986i	$0.582020\pi$
$684$	−8.93900	+	6.85545i	−0.341791	+	0.262125i
$685$		0			0
$686$	5.54577	+	2.01850i	0.211739	+	0.0770665i
$687$	0.0540041	+	0.306273i	0.00206039	+	0.0116850i
$688$	0.777759	+	0.652617i	0.0296518	+	0.0248808i
$689$	−39.7099	+	33.3206i	−1.51283	+	1.26941i
$690$		0			0
$691$	−2.37228	+	4.10890i	−0.0902456	+	0.156310i	−0.907614	−	0.419805i	$-0.862099\pi$
$691$	−2.37228	+	4.10890i	−0.0902456	+	0.156310i	0.817369	+	0.576115i	$0.195432\pi$
$692$	−8.91789	−	15.4462i	−0.339007	−	0.587178i
$693$	−3.12320	+	1.13675i	−0.118641	+	0.0431816i
$694$	−28.5768	+	10.4011i	−1.08476	+	0.394821i
$695$		0			0
$696$	−0.183949	+	0.318609i	−0.00697257	+	0.0120768i
$697$	7.65004	−	43.3855i	0.289766	−	1.64334i
$698$	24.4136	−	20.4855i	0.924069	−	0.775386i
$699$	−8.37728	−	7.02937i	−0.316858	−	0.265875i
$700$		0			0
$701$	41.0097	+	14.9263i	1.54892	+	0.563759i	0.968163	−	0.250321i	$-0.0805363\pi$
$701$	41.0097	+	14.9263i	1.54892	+	0.563759i	0.580752	+	0.814080i	$0.302758\pi$
$702$	−17.2402			−0.650689
$703$	22.8786	−	35.8916i	0.862883	−	1.35368i
$704$	−3.01100			−0.113481
$705$		0			0
$706$	5.13476	+	29.1206i	0.193249	+	1.09597i
$707$	2.09631	+	1.75901i	0.0788397	+	0.0661543i
$708$	−0.173864	+	0.145889i	−0.00653420	+	0.00548284i
$709$	7.87634	−	44.6689i	0.295802	−	1.67758i	−0.368123	−	0.929777i	$-0.619999\pi$
$709$	7.87634	−	44.6689i	0.295802	−	1.67758i	0.663925	−	0.747799i	$-0.268890\pi$
$710$		0			0
$711$	−17.2304	−	29.8440i	−0.646192	−	1.11924i
$712$	9.52407	−	3.46648i	0.356930	−	0.129912i
$713$	1.11654	−	0.406389i	0.0418149	−	0.0152194i
$714$	0.654438	+	1.13352i	0.0244917	+	0.0424209i
$715$		0			0
$716$	3.30942	−	18.7686i	0.123679	−	0.701417i
$717$	−11.1355	+	9.34377i	−0.415862	+	0.348949i
$718$	−11.2111	−	9.40726i	−0.418396	−	0.351076i
$719$	−5.11321	−	28.9985i	−0.190691	−	1.08146i	−0.918423	−	0.395599i	$-0.870537\pi$
$719$	−5.11321	−	28.9985i	−0.190691	−	1.08146i	0.727732	−	0.685861i	$-0.240574\pi$
$720$		0			0
$721$	−3.95707			−0.147369
$722$	1.64612	+	18.9286i	0.0612623	+	0.704448i
$723$	−15.3792			−0.571959
$724$	−9.29231	−	3.38212i	−0.345346	−	0.125696i
$725$		0			0
$726$	0.955045	+	0.801378i	0.0354450	+	0.0297419i
$727$	4.14617	−	3.47905i	0.153773	−	0.129031i	−0.562655	−	0.826692i	$-0.690220\pi$
$727$	4.14617	−	3.47905i	0.153773	−	0.129031i	0.716428	+	0.697661i	$0.245776\pi$
$728$	−0.355173	+	2.01429i	−0.0131636	+	0.0746545i
$729$	3.53824	−	6.12840i	0.131046	−	0.226978i
$730$		0			0
$731$	−4.53514	+	1.65066i	−0.167738	+	0.0610518i
$732$	0.0773622	−	0.0281575i	0.00285939	−	0.00104073i
$733$	−1.24308	−	2.15308i	−0.0459143	−	0.0795259i	0.842155	−	0.539236i	$-0.181287\pi$
$733$	−1.24308	−	2.15308i	−0.0459143	−	0.0795259i	−0.888069	+	0.459710i	$0.847953\pi$
$734$	−6.81679	+	11.8070i	−0.251612	+	0.435805i
$735$		0			0
$736$	4.00475	−	3.36038i	0.147617	−	0.123865i
$737$	−0.603880	−	0.506715i	−0.0222442	−	0.0186651i
$738$	−4.15919	−	23.5879i	−0.153102	−	0.868284i
$739$	−2.92161	−	1.06338i	−0.107473	−	0.0391170i	0.287724	−	0.957713i	$-0.407101\pi$
$739$	−2.92161	−	1.06338i	−0.107473	−	0.0391170i	−0.395197	+	0.918596i	$0.629324\pi$
$740$		0			0
$741$	−7.23330	+	11.3475i	−0.265722	+	0.416861i
$742$	4.62342			0.169731
$743$	−25.4895	−	9.27744i	−0.935121	−	0.340356i	−0.170883	−	0.985291i	$-0.554662\pi$
$743$	−25.4895	−	9.27744i	−0.935121	−	0.340356i	−0.764237	+	0.644935i	$0.776884\pi$
$744$	0.0254436	+	0.144298i	0.000932809	+	0.00529022i
$745$		0			0
$746$	12.0191	−	10.0852i	0.440051	−	0.369247i
$747$	0.494524	−	2.80458i	0.0180937	−	0.102614i
$748$	7.15641	−	12.3953i	0.261664	−	0.453216i
$749$	0.0375028	+	0.0649567i	0.00137032	+	0.00237347i
$750$		0			0
$751$	18.2513	−	6.64292i	0.665999	−	0.242404i	0.0131746	−	0.999913i	$-0.495806\pi$
$751$	18.2513	−	6.64292i	0.665999	−	0.242404i	0.652824	+	0.757509i	$0.273584\pi$
$752$	3.60947	+	6.25179i	0.131624	+	0.227979i
$753$	7.64587	−	13.2430i	0.278631	−	0.482603i
$754$	0.474551	−	2.69131i	0.0172821	−	0.0980119i
$755$		0			0
$756$	1.17792	+	0.988390i	0.0428404	+	0.0359474i
$757$	4.54236	+	25.7610i	0.165095	+	0.936300i	0.948967	+	0.315377i	$0.102131\pi$
$757$	4.54236	+	25.7610i	0.165095	+	0.936300i	−0.783872	+	0.620923i	$0.786758\pi$
$758$	−15.7481	−	5.73184i	−0.571997	−	0.208190i
$759$	10.1478			0.368342
$760$		0			0
$761$	44.7386			1.62177			0.810887	−	0.585203i	$-0.198985\pi$
$761$	44.7386			1.62177			0.810887	+	0.585203i	$0.198985\pi$
$762$	2.61751	+	0.952694i	0.0948222	+	0.0345125i
$763$	−0.374102	−	2.12164i	−0.0135434	−	0.0768084i
$764$	17.3712	+	14.5762i	0.628470	+	0.527349i
$765$		0			0
$766$	1.68331	−	9.54653i	0.0608205	−	0.344930i
$767$	0.842967	−	1.46006i	0.0304378	−	0.0527198i
$768$	0.322337	+	0.558304i	0.0116313	+	0.0201461i
$769$	−47.0535	+	17.1261i	−1.69679	+	0.617582i	−0.995454	−	0.0952452i	$-0.969636\pi$
$769$	−47.0535	+	17.1261i	−1.69679	+	0.617582i	−0.701339	+	0.712827i	$0.747414\pi$
$770$		0			0
$771$	4.35112	+	7.53635i	0.156702	+	0.271415i
$772$	−1.44771	+	2.50750i	−0.0521041	+	0.0902470i
$773$	6.56489	−	37.2313i	0.236123	−	1.33912i	−0.604114	−	0.796898i	$-0.706473\pi$
$773$	6.56489	−	37.2313i	0.236123	−	1.33912i	0.840237	−	0.542220i	$-0.182416\pi$
$774$	−2.01004	+	1.68662i	−0.0722493	+	0.0606243i
$775$		0			0
$776$	−2.68502	−	15.2275i	−0.0963867	−	0.546636i
$777$	−2.52656	−	0.919592i	−0.0906398	−	0.0329902i
$778$	−6.22866			−0.223308
$779$	−37.3185	−	15.4692i	−1.33708	−	0.554242i
$780$		0			0
$781$	1.26742	+	0.461302i	0.0453518	+	0.0165067i
$782$	4.31525	+	24.4730i	0.154313	+	0.875152i
$783$	−1.57383	−	1.32060i	−0.0562441	−	0.0471944i
$784$	−5.22256	+	4.38225i	−0.186520	+	0.156509i
$785$		0			0
$786$	−4.11916	+	7.13460i	−0.146926	+	0.254483i
$787$	21.0637	+	36.4835i	0.750841	+	1.30049i	0.947416	+	0.320006i	$0.103685\pi$
$787$	21.0637	+	36.4835i	0.750841	+	1.30049i	−0.196574	+	0.980489i	$0.562982\pi$
$788$	−1.37387	+	0.500048i	−0.0489421	+	0.0178135i
$789$	−11.7008	+	4.25876i	−0.416561	+	0.151616i
$790$		0			0
$791$	−1.35112	+	2.34020i	−0.0480402	+	0.0832080i
$792$	1.35126	−	7.66339i	0.0480150	−	0.272307i
$793$	−0.468471	+	0.393094i	−0.0166359	+	0.0139592i
$794$	−4.49613	−	3.77270i	−0.159562	−	0.133888i
$795$		0			0
$796$	−16.9886	−	6.18336i	−0.602146	−	0.219163i
$797$	−17.9260			−0.634973			−0.317486	−	0.948263i	$-0.602839\pi$
$797$	−17.9260			−0.634973			−0.317486	+	0.948263i	$0.602839\pi$
$798$	1.14477	−	0.360616i	0.0405242	−	0.0127657i
$799$	−34.3153			−1.21399
$800$		0			0
$801$	4.54848	+	25.7957i	0.160713	+	0.911446i
$802$	−9.13833	−	7.66797i	−0.322686	−	0.270765i
$803$	−19.7096	+	16.5383i	−0.695537	+	0.583625i
$804$	−0.0293087	+	0.166218i	−0.00103364	+	0.00586205i
$805$		0			0
$806$	−0.544207	−	0.942595i	−0.0191689	−	0.0332015i
$807$	3.72035	−	1.35410i	0.130962	−	0.0476664i
$808$	−6.02063	+	2.19133i	−0.211805	+	0.0770907i
$809$	−5.36376	−	9.29031i	−0.188580	−	0.326630i	0.756197	−	0.654344i	$-0.227055\pi$
$809$	−5.36376	−	9.29031i	−0.188580	−	0.326630i	−0.944777	+	0.327714i	$0.893722\pi$
$810$		0			0
$811$	−5.09993	+	28.9231i	−0.179083	+	1.01563i	0.754242	+	0.656596i	$0.228004\pi$
$811$	−5.09993	+	28.9231i	−0.179083	+	1.01563i	−0.933325	+	0.359033i	$0.883107\pi$
$812$	−0.186718	+	0.156675i	−0.00655251	+	0.00549821i
$813$	9.36355	+	7.85695i	0.328394	+	0.275555i
$814$	5.10552	+	28.9549i	0.178948	+	1.01487i
$815$		0			0
$816$	−3.06446			−0.107278
$817$	0.576511	+	4.38784i	0.0201696	+	0.153511i
$818$	−13.3421			−0.466497
$819$	−4.96724	−	1.80793i	−0.173569	−	0.0631740i
$820$		0			0
$821$	−1.65248	−	1.38659i	−0.0576718	−	0.0483924i	0.613496	−	0.789698i	$-0.289763\pi$
$821$	−1.65248	−	1.38659i	−0.0576718	−	0.0483924i	−0.671168	+	0.741305i	$0.734207\pi$
$822$	−8.00276	+	6.71512i	−0.279128	+	0.234217i
$823$	−3.16374	+	17.9425i	−0.110281	+	0.625435i	0.878698	+	0.477378i	$0.158413\pi$
$823$	−3.16374	+	17.9425i	−0.110281	+	0.625435i	−0.988979	+	0.148056i	$0.952698\pi$
$824$	4.63233	−	8.02343i	0.161375	−	0.279510i
$825$		0			0
$826$	−0.141301	+	0.0514293i	−0.00491649	+	0.00178946i
$827$	−10.8882	+	3.96299i	−0.378621	+	0.137807i	−0.524318	−	0.851523i	$-0.675680\pi$
$827$	−10.8882	+	3.96299i	−0.378621	+	0.137807i	0.145697	+	0.989329i	$0.453457\pi$
$828$	6.75539	+	11.7007i	0.234766	+	0.406626i
$829$	27.4900	−	47.6141i	0.954768	−	1.65371i	0.219869	−	0.975529i	$-0.429437\pi$
$829$	27.4900	−	47.6141i	0.954768	−	1.65371i	0.734899	−	0.678177i	$-0.237230\pi$
$830$		0			0
$831$	−0.0273083	+	0.0229144i	−0.000947316	+	0.000794892i
$832$	−3.66842	−	3.07817i	−0.127180	−	0.106716i
$833$	−5.62748	−	31.9150i	−0.194981	−	1.10579i
$834$	7.65999	+	2.78801i	0.265244	+	0.0965408i
$835$		0			0
$836$	−9.67420	−	8.86940i	−0.334589	−	0.306754i
$837$	−0.818248			−0.0282828
$838$	−33.8252	−	12.3114i	−1.16847	−	0.425290i
$839$	−4.83147	−	27.4006i	−0.166801	−	0.945974i	−0.947188	−	0.320678i	$-0.896089\pi$
$839$	−4.83147	−	27.4006i	−0.166801	−	0.945974i	0.780387	−	0.625296i	$-0.215022\pi$
$840$		0			0
$841$	−21.9658	+	18.4315i	−0.757442	+	0.635569i
$842$	5.84335	−	33.1393i	0.201375	−	1.14205i
$843$	1.05161	−	1.82144i	0.0362194	−	0.0627338i
$844$	−13.5945	−	23.5463i	−0.467942	−	0.810499i
$845$		0			0
$846$	−17.5315	+	6.38093i	−0.602744	+	0.219381i
$847$	0.412994	+	0.715327i	0.0141906	+	0.0245789i
$848$	−5.41239	+	9.37454i	−0.185862	+	0.321923i
$849$	−1.10596	+	6.27221i	−0.0379565	+	0.215262i
$850$		0			0
$851$	−39.1052	−	32.8131i	−1.34051	−	1.12482i
$852$	−0.0501457	−	0.284390i	−0.00171796	−	0.00974305i
$853$	−11.9377	−	4.34497i	−0.408739	−	0.148769i	0.129464	−	0.991584i	$-0.458674\pi$
$853$	−11.9377	−	4.34497i	−0.408739	−	0.148769i	−0.538203	+	0.842815i	$0.680897\pi$
$854$	0.0545440			0.00186646
$855$		0			0
$856$	−0.175610			−0.00600222
$857$	39.3151	+	14.3095i	1.34298	+	0.488804i	0.910749	−	0.412961i	$-0.135505\pi$
$857$	39.3151	+	14.3095i	1.34298	+	0.488804i	0.432228	+	0.901764i	$0.357728\pi$
$858$	−1.61416	−	9.15436i	−0.0551065	−	0.312525i
$859$	−9.91170	−	8.31690i	−0.338183	−	0.283769i	0.457841	−	0.889034i	$-0.348623\pi$
$859$	−9.91170	−	8.31690i	−0.338183	−	0.283769i	−0.796024	+	0.605265i	$0.793067\pi$
$860$		0			0
$861$	−0.443133	+	2.51313i	−0.0151019	+	0.0856473i
$862$	−15.5651	+	26.9596i	−0.530151	+	0.918249i
$863$	20.9131	+	36.2225i	0.711890	+	1.23303i	0.964147	+	0.265369i	$0.0854939\pi$
$863$	20.9131	+	36.2225i	0.711890	+	1.23303i	−0.252257	+	0.967660i	$0.581173\pi$
$864$	−3.38300	+	1.23131i	−0.115092	+	0.0418901i
$865$		0			0
$866$	−8.12090	−	14.0658i	−0.275960	−	0.477976i
$867$	1.80375	−	3.12418i	0.0612584	−	0.106103i
$868$	−0.0168571	+	0.0956015i	−0.000572168	+	0.00324493i
$869$	30.7562	−	25.8075i	1.04333	−	0.875459i
$870$		0			0
$871$	−0.217712	−	1.23470i	−0.00737688	−	0.0418364i
$872$	4.73981	+	1.72515i	0.160510	+	0.0584209i
$873$	39.9610			1.35248
$874$	22.7656	+	0.999896i	0.770059	+	0.0338220i
$875$		0			0
$876$	5.17654	+	1.88411i	0.174899	+	0.0636580i
$877$	3.73324	+	21.1722i	0.126062	+	0.714935i	0.980671	+	0.195663i	$0.0626859\pi$
$877$	3.73324	+	21.1722i	0.126062	+	0.714935i	−0.854609	+	0.519272i	$0.826203\pi$
$878$	−19.7994	−	16.6137i	−0.668197	−	0.560684i
$879$	0.256291	−	0.215053i	0.00864447	−	0.00725357i
$880$		0			0
$881$	−2.38477	+	4.13054i	−0.0803449	+	0.139161i	−0.903398	−	0.428803i	$-0.858936\pi$
$881$	−2.38477	+	4.13054i	−0.0803449	+	0.139161i	0.823053	+	0.567964i	$0.192269\pi$
$882$	−8.80965	−	15.2588i	−0.296636	−	0.513789i
$883$	−13.2527	+	4.82360i	−0.445990	+	0.162327i	−0.555245	−	0.831687i	$-0.687376\pi$
$883$	−13.2527	+	4.82360i	−0.445990	+	0.162327i	0.109256	+	0.994014i	$0.465153\pi$
$884$	21.3907	−	7.78559i	0.719448	−	0.261858i
$885$		0			0
$886$	19.1362	−	33.1449i	0.642894	−	1.11353i
$887$	−1.39576	+	7.91577i	−0.0468651	+	0.265785i	−0.999233	−	0.0391672i	$-0.987530\pi$
$887$	−1.39576	+	7.91577i	−0.0468651	+	0.265785i	0.952368	+	0.304953i	$0.0986406\pi$
$888$	4.82229	−	4.04638i	0.161825	−	0.135788i
$889$	1.41371	+	1.18624i	0.0474143	+	0.0397853i
$890$		0			0
$891$	15.3702	+	5.59429i	0.514921	+	0.187416i
$892$	11.1447			0.373153
$893$	−6.81861	+	30.7190i	−0.228176	+	1.02797i
$894$	4.31875			0.144440
$895$		0			0
$896$	0.0741677	+	0.420626i	0.00247777	+	0.0140521i
$897$	12.3635	+	10.3742i	0.412805	+	0.346384i
$898$	−2.53427	+	2.12651i	−0.0845698	+	0.0709625i
$899$	0.0225230	−	0.127734i	0.000751184	−	0.00426018i
$900$		0			0
$901$	−25.7278	−	44.5619i	−0.857119	−	1.48457i
$902$	26.2226	−	9.54425i	0.873117	−	0.317789i
$903$	0.262701	−	0.0956153i	0.00874213	−	0.00318188i
$904$	−3.16336	−	5.47910i	−0.105212	−	0.182232i
$905$		0			0
$906$	2.42081	−	13.7291i	0.0804260	−	0.456119i
$907$	−29.6981	+	24.9196i	−0.986108	+	0.827443i	−0.985000	−	0.172556i	$-0.944797\pi$
$907$	−29.6981	+	24.9196i	−0.986108	+	0.827443i	−0.00110859	+	0.999999i	$0.500353\pi$
$908$	3.08591	+	2.58939i	0.102410	+	0.0859318i
$909$	−2.87531	−	16.3067i	−0.0953682	−	0.540860i
$910$		0			0
$911$	−45.9152			−1.52124			−0.760620	−	0.649198i	$-0.775105\pi$
$911$	−45.9152			−1.52124			−0.760620	+	0.649198i	$0.775105\pi$
$912$	−0.608923	+	2.74330i	−0.0201635	+	0.0908398i
$913$	3.31794			0.109808
$914$	4.58655	+	1.66937i	0.151710	+	0.0552178i
$915$		0			0
$916$	−0.369548	−	0.310087i	−0.0122102	−	0.0102456i
$917$	−4.18116	+	3.50841i	−0.138074	+	0.115858i
$918$	2.97167	−	16.8532i	0.0980798	−	0.556238i
$919$	7.66328	−	13.2732i	0.252788	−	0.437842i	−0.711504	−	0.702682i	$-0.751986\pi$
$919$	7.66328	−	13.2732i	0.252788	−	0.437842i	0.964292	+	0.264840i	$0.0853191\pi$
$920$		0			0
$921$	11.2493	−	4.09442i	0.370678	−	0.134916i
$922$	22.7004	−	8.26226i	0.747597	−	0.272103i
$923$	1.07255	+	1.85772i	0.0353035	+	0.0611475i
$924$	−0.414539	+	0.718002i	−0.0136373	+	0.0236205i
$925$		0			0
$926$	−27.4831	+	23.0611i	−0.903151	+	0.757834i
$927$	18.3418	+	15.3906i	0.602425	+	0.505494i
$928$	−0.0990963	−	0.562003i	−0.00325300	−	0.0184487i
$929$	−14.3277	−	5.21484i	−0.470075	−	0.171093i	0.0961113	−	0.995371i	$-0.469360\pi$
$929$	−14.3277	−	5.21484i	−0.470075	−	0.171093i	−0.566186	+	0.824277i	$0.691582\pi$
$930$		0			0
$931$	−29.6885	−	1.30396i	−0.973001	−	0.0427355i
$932$	16.9632			0.555650
$933$	18.1711	+	6.61376i	0.594896	+	0.216525i
$934$	4.26677	+	24.1981i	0.139613	+	0.791785i
$935$		0			0
$936$	9.48066	−	7.95522i	0.309885	−	0.260024i
$937$	−3.93212	+	22.3002i	−0.128457	+	0.728515i	0.850738	+	0.525591i	$0.176156\pi$
$937$	−3.93212	+	22.3002i	−0.128457	+	0.728515i	−0.979194	+	0.202924i	$0.934955\pi$
$938$	−0.0559114	+	0.0968414i	−0.00182557	+	0.00316198i
$939$	−9.06662	−	15.7038i	−0.295878	−	0.512475i
$940$		0			0
$941$	−21.5784	+	7.85391i	−0.703437	+	0.256030i	−0.668878	−	0.743373i	$-0.733225\pi$
$941$	−21.5784	+	7.85391i	−0.703437	+	0.256030i	−0.0345594	+	0.999403i	$0.511003\pi$
$942$	−4.73976	−	8.20951i	−0.154430	−	0.267480i
$943$	−24.2254	+	41.9596i	−0.788887	+	1.36639i
$944$	0.0611343	−	0.346710i	0.00198975	−	0.0112844i
$945$		0			0
$946$	−2.34183	−	1.96503i	−0.0761395	−	0.0638886i
$947$	−2.57686	−	14.6141i	−0.0837368	−	0.474895i	−0.997622	−	0.0689223i	$-0.978044\pi$
$947$	−2.57686	−	14.6141i	−0.0837368	−	0.474895i	0.913885	−	0.405973i	$-0.133067\pi$
$948$	−8.07781	−	2.94008i	−0.262355	−	0.0954894i
$949$	−40.9203			−1.32833
$950$		0			0
$951$	3.66061			0.118703
$952$	−1.90785	−	0.694401i	−0.0618338	−	0.0225057i
$953$	−8.35120	−	47.3620i	−0.270522	−	1.53421i	−0.752837	−	0.658208i	$-0.771315\pi$
$953$	−8.35120	−	47.3620i	−0.270522	−	1.53421i	0.482315	−	0.875998i	$-0.339796\pi$
$954$	−21.4305	−	17.9823i	−0.693838	−	0.582199i
$955$		0			0
$956$	3.91548	−	22.2058i	0.126636	−	0.718186i
$957$	0.553871	−	0.959332i	0.0179041	−	0.0310108i
$958$	−2.76946	−	4.79685i	−0.0894773	−	0.154979i
$959$	−6.50393	+	2.36724i	−0.210023	+	0.0764421i
$960$		0			0
$961$	15.4742	+	26.8021i	0.499167	+	0.864582i
$962$	−23.3806	+	40.4963i	−0.753819	+	1.30565i
$963$	0.0788095	−	0.446951i	0.00253960	−	0.0144028i
$964$	18.2746	−	15.3342i	0.588585	−	0.493882i
$965$		0			0
$966$	−0.249963	−	1.41761i	−0.00804243	−	0.0456109i
$967$	23.8954	+	8.69723i	0.768426	+	0.279684i	0.696338	−	0.717714i	$-0.254812\pi$
$967$	23.8954	+	8.69723i	0.768426	+	0.279684i	0.0720879	+	0.997398i	$0.477034\pi$
$968$	−1.93388			−0.0621573
$969$	−9.84597	−	9.02688i	−0.316298	−	0.289985i
$970$		0			0
$971$	6.33215	+	2.30471i	0.203208	+	0.0739618i	0.441619	−	0.897203i	$-0.354404\pi$
$971$	6.33215	+	2.30471i	0.203208	+	0.0739618i	−0.238411	+	0.971164i	$0.576626\pi$
$972$	−2.48359	−	14.0851i	−0.0796610	−	0.451780i
$973$	4.13714	+	3.47147i	0.132631	+	0.111290i
$974$	−26.7950	+	22.4837i	−0.858567	+	0.720423i
$975$		0			0
$976$	−0.0638518	+	0.110594i	−0.00204384	+	0.00354004i
$977$	−23.7149	−	41.0755i	−0.758708	−	1.31412i	−0.943509	−	0.331346i	$-0.892497\pi$
$977$	−23.7149	−	41.0755i	−0.758708	−	1.31412i	0.184801	−	0.982776i	$-0.440836\pi$
$978$	6.51454	−	2.37110i	0.208312	−	0.0758194i
$979$	−28.6770	+	10.4376i	−0.916520	+	0.333586i
$980$		0			0
$981$	−6.51784	+	11.2892i	−0.208099	+	0.360438i
$982$	5.83077	−	33.0680i	0.186067	−	1.05524i
$983$	2.73043	−	2.29110i	0.0870873	−	0.0730749i	−0.598205	−	0.801343i	$-0.704119\pi$
$983$	2.73043	−	2.29110i	0.0870873	−	0.0730749i	0.685292	+	0.728268i	$0.259675\pi$
$984$	−4.57692	−	3.84049i	−0.145907	−	0.122430i
$985$		0			0
$986$	2.54910	+	0.927798i	0.0811800	+	0.0295471i
$987$	1.98773			0.0632702
$988$	−2.71921	−	20.6960i	−0.0865094	−	0.658427i
$989$	5.30777			0.168777
$990$		0			0
$991$	−3.18511	−	18.0636i	−0.101178	−	0.573810i	−0.992678	−	0.120789i	$-0.961457\pi$
$991$	−3.18511	−	18.0636i	−0.101178	−	0.573810i	0.891500	−	0.453021i	$-0.149654\pi$
$992$	−0.174110	−	0.146095i	−0.00552799	−	0.00463853i
$993$	−9.17959	+	7.70259i	−0.291305	+	0.244434i
$994$	0.0332229	−	0.188416i	0.00105377	−	0.00597621i
$995$		0			0
$996$	−0.355196	−	0.615218i	−0.0112548	−	0.0194939i
$997$	15.9000	−	5.78714i	0.503560	−	0.183281i	−0.0777347	−	0.996974i	$-0.524769\pi$
$997$	15.9000	−	5.78714i	0.503560	−	0.183281i	0.581294	+	0.813693i	$0.302547\pi$
$998$	−10.6062	+	3.86035i	−0.335735	+	0.122197i
$999$	17.5770	+	30.4443i	0.556113	+	0.963215i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.k.251.2	yes	24
5.2	odd	4		950.2.u.h.99.6		48
5.3	odd	4		950.2.u.h.99.3		48
5.4	even	2		950.2.l.j.251.3	✓	24
19.5	even	9	inner	950.2.l.k.651.2	yes	24
95.24	even	18		950.2.l.j.651.3	yes	24
95.43	odd	36		950.2.u.h.499.6		48
95.62	odd	36		950.2.u.h.499.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.l.j.251.3	✓	24	5.4	even	2
950.2.l.j.651.3	yes	24	95.24	even	18
950.2.l.k.251.2	yes	24	1.1	even	1	trivial
950.2.l.k.651.2	yes	24	19.5	even	9	inner
950.2.u.h.99.3		48	5.3	odd	4
950.2.u.h.99.6		48	5.2	odd	4
950.2.u.h.499.3		48	95.62	odd	36
950.2.u.h.499.6		48	95.43	odd	36

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.111946 - 0.634880i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.111946 + 0.634880i) q^{6} +(-0.213557 + 0.369892i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.42854 - 0.883915i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.111946 - 0.634880i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.111946 + 0.634880i) q^{6} +(-0.213557 + 0.369892i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.42854 - 0.883915i) q^{9} +(1.50550 + 2.60760i) q^{11} +(0.322337 - 0.558304i) q^{12} +(-0.831564 + 4.71604i) q^{13} +(0.327189 - 0.274544i) q^{14} +(0.173648 + 0.984808i) q^{16} +(-4.46684 - 1.62580i) q^{17} -2.58440 q^{18} +(-2.34299 + 3.67565i) q^{19} +(0.258744 + 0.0941751i) q^{21} +(-0.522855 - 2.96526i) q^{22} +(4.00475 + 3.36038i) q^{23} +(-0.493849 + 0.414388i) q^{24} +(2.39439 - 4.14721i) q^{26} +(-1.80006 - 3.11779i) q^{27} +(-0.401356 + 0.146082i) q^{28} +(0.536257 - 0.195182i) q^{29} +(0.113642 - 0.196834i) q^{31} +(0.173648 - 0.984808i) q^{32} +(1.48698 - 1.24772i) q^{33} +(3.64140 + 3.05550i) q^{34} +(2.42854 + 0.883915i) q^{36} -9.76471 q^{37} +(3.45884 - 2.65263i) q^{38} +3.08721 q^{39} +(1.60935 + 9.12706i) q^{41} +(-0.210930 - 0.176991i) q^{42} +(0.777759 - 0.652617i) q^{43} +(-0.522855 + 2.96526i) q^{44} +(-2.61391 - 4.52743i) q^{46} +(6.78359 - 2.46902i) q^{47} +(0.605795 - 0.220492i) q^{48} +(3.40879 + 5.90419i) q^{49} +(-0.532138 + 3.01791i) q^{51} +(-3.66842 + 3.07817i) q^{52} +(8.29226 + 6.95804i) q^{53} +(0.625153 + 3.54542i) q^{54} +0.427115 q^{56} +(2.59589 + 1.07604i) q^{57} -0.570673 q^{58} +(-0.330827 - 0.120411i) q^{59} +(0.0978266 + 0.0820862i) q^{61} +(-0.174110 + 0.146095i) q^{62} +(-0.191679 + 1.08706i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.82405 + 0.663900i) q^{66} +(-0.246021 + 0.0895442i) q^{67} +(-2.37675 - 4.11666i) q^{68} +(1.68512 - 2.91872i) q^{69} +(0.343144 - 0.287932i) q^{71} +(-1.97976 - 1.66122i) q^{72} +(1.48383 + 8.41521i) q^{73} +(9.17582 + 3.33973i) q^{74} +(-4.15750 + 1.30967i) q^{76} -1.28604 q^{77} +(-2.90103 - 1.05589i) q^{78} +(-2.31546 - 13.1316i) q^{79} +(4.16137 - 3.49181i) q^{81} +(1.60935 - 9.12706i) q^{82} +(0.550970 - 0.954308i) q^{83} +(0.137675 + 0.238460i) q^{84} +(-0.954063 + 0.347250i) q^{86} +(-0.183949 - 0.318609i) q^{87} +(1.50550 - 2.60760i) q^{88} +(-1.75998 + 9.98133i) q^{89} +(-1.56684 - 1.31473i) q^{91} +(0.907803 + 5.14840i) q^{92} +(-0.137688 - 0.0501142i) q^{93} -7.21894 q^{94} -0.644674 q^{96} +(14.5299 + 5.28846i) q^{97} +(-1.18386 - 6.71400i) q^{98} +(5.96106 + 5.00193i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{7} - 12 q^{8}+O(q^{10}) \) 24 * q + 3 * q^7 - 12 * q^8	\( 24 q + 3 q^{7} - 12 q^{8} - 6 q^{11} - 3 q^{12} + 24 q^{13} - 15 q^{14} - 9 q^{17} + 30 q^{18} - 15 q^{19} - 18 q^{21} + 12 q^{23} - 9 q^{26} - 21 q^{27} + 12 q^{28} - 12 q^{29} + 9 q^{31} - 42 q^{33} - 9 q^{34} + 66 q^{37} + 6 q^{38} + 66 q^{39} + 18 q^{41} + 9 q^{42} - 3 q^{43} - 3 q^{46} - 12 q^{47} - 27 q^{49} - 3 q^{51} - 12 q^{52} - 45 q^{53} + 27 q^{54} - 6 q^{56} - 27 q^{57} - 18 q^{58} + 36 q^{59} + 12 q^{61} - 24 q^{62} - 63 q^{63} - 12 q^{64} + 48 q^{66} - 54 q^{67} + 3 q^{68} + 21 q^{69} - 39 q^{71} + 48 q^{73} + 18 q^{74} + 6 q^{76} + 48 q^{77} - 12 q^{78} - 42 q^{79} - 36 q^{81} + 18 q^{82} - 3 q^{83} + 9 q^{84} - 39 q^{86} - 24 q^{87} - 6 q^{88} - 36 q^{89} + 12 q^{91} - 15 q^{92} - 6 q^{93} + 12 q^{94} + 6 q^{96} - 54 q^{97} + 3 q^{98} + 51 q^{99}+O(q^{100}) \) 24 * q + 3 * q^7 - 12 * q^8 - 6 * q^11 - 3 * q^12 + 24 * q^13 - 15 * q^14 - 9 * q^17 + 30 * q^18 - 15 * q^19 - 18 * q^21 + 12 * q^23 - 9 * q^26 - 21 * q^27 + 12 * q^28 - 12 * q^29 + 9 * q^31 - 42 * q^33 - 9 * q^34 + 66 * q^37 + 6 * q^38 + 66 * q^39 + 18 * q^41 + 9 * q^42 - 3 * q^43 - 3 * q^46 - 12 * q^47 - 27 * q^49 - 3 * q^51 - 12 * q^52 - 45 * q^53 + 27 * q^54 - 6 * q^56 - 27 * q^57 - 18 * q^58 + 36 * q^59 + 12 * q^61 - 24 * q^62 - 63 * q^63 - 12 * q^64 + 48 * q^66 - 54 * q^67 + 3 * q^68 + 21 * q^69 - 39 * q^71 + 48 * q^73 + 18 * q^74 + 6 * q^76 + 48 * q^77 - 12 * q^78 - 42 * q^79 - 36 * q^81 + 18 * q^82 - 3 * q^83 + 9 * q^84 - 39 * q^86 - 24 * q^87 - 6 * q^88 - 36 * q^89 + 12 * q^91 - 15 * q^92 - 6 * q^93 + 12 * q^94 + 6 * q^96 - 54 * q^97 + 3 * q^98 + 51 * q^99

Introduction

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