LMFDB - Embedded newform 950.2.q.g.107.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(107,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("950.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.q (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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			107.3
Character	$\chi$	$=$	950.107
Dual form			950.2.q.g.293.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(0.338196 - 1.26216i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.653344 + 1.13162i) q^{6} +(-1.48691 - 1.48691i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.11940 + 0.646284i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(0.338196 - 1.26216i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.653344 + 1.13162i) q^{6} +(-1.48691 - 1.48691i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.11940 + 0.646284i) q^{9} -6.07305 q^{11} +(0.923968 - 0.923968i) q^{12} +(-1.53683 + 0.411793i) q^{13} +(1.05141 + 1.82109i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.689746 + 2.57417i) q^{17} +(-0.913983 - 0.913983i) q^{18} +(-0.396163 + 4.34086i) q^{19} +(-2.37960 + 1.37386i) q^{21} +(5.86611 + 1.57182i) q^{22} +(2.00798 + 7.49390i) q^{23} +(-1.13162 + 0.653344i) q^{24} +1.59105 q^{26} +(3.96619 - 3.96619i) q^{27} +(-0.544248 - 2.03116i) q^{28} +(-1.31744 + 2.28187i) q^{29} -8.53390i q^{31} +(-0.258819 - 0.965926i) q^{32} +(-2.05388 + 7.66518i) q^{33} +(1.33249 - 2.30794i) q^{34} +(0.646284 + 1.11940i) q^{36} +(-5.03508 + 5.03508i) q^{37} +(1.50616 - 4.09041i) q^{38} +2.07900i q^{39} +(-5.76903 + 3.33075i) q^{41} +(2.65410 - 0.711163i) q^{42} +(2.11477 + 0.566652i) q^{43} +(-5.25941 - 3.03652i) q^{44} -7.75825i q^{46} +(0.505817 - 0.135533i) q^{47} +(1.26216 - 0.338196i) q^{48} -2.57817i q^{49} +(3.01575 + 1.74115i) q^{51} +(-1.53683 - 0.411793i) q^{52} +(-2.33496 + 0.625650i) q^{53} +(-4.85758 + 2.80452i) q^{54} +2.10281i q^{56} +(5.34489 + 1.96808i) q^{57} +(1.86314 - 1.86314i) q^{58} +(3.20769 + 5.55588i) q^{59} +(-7.49289 + 12.9781i) q^{61} +(-2.20874 + 8.24311i) q^{62} +(-0.703478 - 2.62541i) q^{63} +1.00000i q^{64} +(3.96779 - 6.87241i) q^{66} +(-2.95335 - 11.0220i) q^{67} +(-1.88442 + 1.88442i) q^{68} +10.1376 q^{69} +(3.66389 - 2.11535i) q^{71} +(-0.334541 - 1.24852i) q^{72} +(3.20699 + 0.859309i) q^{73} +(6.16669 - 3.56034i) q^{74} +(-2.51352 + 3.56121i) q^{76} +(9.03010 + 9.03010i) q^{77} +(0.538085 - 2.00816i) q^{78} +(3.32249 + 5.75472i) q^{79} +(-1.72578 - 2.98915i) q^{81} +(6.43452 - 1.72412i) q^{82} +(-0.732952 + 0.732952i) q^{83} -2.74772 q^{84} +(-1.89605 - 1.09469i) q^{86} +(2.43454 + 2.43454i) q^{87} +(4.29429 + 4.29429i) q^{88} +(-0.347882 + 0.602549i) q^{89} +(2.89744 + 1.67284i) q^{91} +(-2.00798 + 7.49390i) q^{92} +(-10.7712 - 2.88613i) q^{93} -0.523660 q^{94} -1.30669 q^{96} +(1.01518 + 0.272018i) q^{97} +(-0.667280 + 2.49032i) q^{98} +(-6.79814 - 3.92491i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{3} - 24 q^{7}+O(q^{10}) $ 32 * q + 12 * q^3 - 24 * q^7	$ 32 q + 12 q^{3} - 24 q^{7} - 16 q^{11} - 24 q^{13} + 16 q^{16} + 8 q^{17} + 12 q^{22} - 4 q^{23} - 16 q^{26} + 12 q^{28} + 24 q^{33} - 8 q^{36} - 16 q^{38} + 24 q^{41} - 20 q^{42} + 24 q^{43} + 36 q^{47} + 12 q^{48} + 24 q^{51} - 24 q^{52} + 72 q^{53} + 24 q^{57} - 24 q^{58} - 48 q^{61} + 4 q^{62} - 16 q^{63} + 32 q^{66} - 36 q^{67} - 16 q^{68} + 24 q^{71} - 8 q^{73} + 24 q^{77} + 24 q^{78} + 56 q^{81} - 8 q^{82} - 24 q^{83} - 104 q^{87} - 24 q^{91} + 4 q^{92} - 52 q^{93} + 24 q^{97} - 72 q^{98}+O(q^{100}) $ 32 * q + 12 * q^3 - 24 * q^7 - 16 * q^11 - 24 * q^13 + 16 * q^16 + 8 * q^17 + 12 * q^22 - 4 * q^23 - 16 * q^26 + 12 * q^28 + 24 * q^33 - 8 * q^36 - 16 * q^38 + 24 * q^41 - 20 * q^42 + 24 * q^43 + 36 * q^47 + 12 * q^48 + 24 * q^51 - 24 * q^52 + 72 * q^53 + 24 * q^57 - 24 * q^58 - 48 * q^61 + 4 * q^62 - 16 * q^63 + 32 * q^66 - 36 * q^67 - 16 * q^68 + 24 * q^71 - 8 * q^73 + 24 * q^77 + 24 * q^78 + 56 * q^81 - 8 * q^82 - 24 * q^83 - 104 * q^87 - 24 * q^91 + 4 * q^92 - 52 * q^93 + 24 * q^97 - 72 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	0.338196	−	1.26216i	0.195257	−	0.728710i	−0.796943	−	0.604055i	$-0.793551\pi$
$3$	0.338196	−	1.26216i	0.195257	−	0.728710i	0.992200	−	0.124656i	$-0.0397826\pi$
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	−0.653344	+	1.13162i	−0.266727	+	0.461984i
$7$	−1.48691	−	1.48691i	−0.562001	−	0.562001i	0.367875	−	0.929875i	$-0.380086\pi$
$7$	−1.48691	−	1.48691i	−0.562001	−	0.562001i	−0.929875	+	0.367875i	$0.880086\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	1.11940	+	0.646284i	0.373132	+	0.215428i
$10$		0			0
$11$	−6.07305			−1.83109			−0.915546	−	0.402213i	$-0.868241\pi$
$11$	−6.07305			−1.83109			−0.915546	+	0.402213i	$0.868241\pi$
$12$	0.923968	−	0.923968i	0.266727	−	0.266727i
$13$	−1.53683	+	0.411793i	−0.426241	+	0.114211i	−0.465561	−	0.885016i	$-0.654147\pi$
$13$	−1.53683	+	0.411793i	−0.426241	+	0.114211i	0.0393201	+	0.999227i	$0.487481\pi$
$14$	1.05141	+	1.82109i	0.281000	+	0.486707i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.689746	+	2.57417i	−0.167288	+	0.624328i	0.830449	+	0.557094i	$0.188084\pi$
$17$	−0.689746	+	2.57417i	−0.167288	+	0.624328i	−0.997737	+	0.0672332i	$0.978583\pi$
$18$	−0.913983	−	0.913983i	−0.215428	−	0.215428i
$19$	−0.396163	+	4.34086i	−0.0908860	+	0.995861i
$19$	−0.396163	+	4.34086i	−0.0908860	+	0.995861i
$20$		0			0
$21$	−2.37960	+	1.37386i	−0.519271	+	0.299801i
$22$	5.86611	+	1.57182i	1.25066	+	0.335113i
$23$	2.00798	+	7.49390i	0.418693	+	1.56259i	0.777321	+	0.629104i	$0.216578\pi$
$23$	2.00798	+	7.49390i	0.418693	+	1.56259i	−0.358627	+	0.933481i	$0.616755\pi$
$24$	−1.13162	+	0.653344i	−0.230992	+	0.133363i
$25$		0			0
$26$	1.59105			0.312030
$27$	3.96619	−	3.96619i	0.763294	−	0.763294i
$28$	−0.544248	−	2.03116i	−0.102853	−	0.383854i
$29$	−1.31744	+	2.28187i	−0.244642	+	0.423732i	−0.962031	−	0.272941i	$-0.912004\pi$
$29$	−1.31744	+	2.28187i	−0.244642	+	0.423732i	0.717389	+	0.696673i	$0.245337\pi$
$30$		0			0
$31$		−	8.53390i		−	1.53273i	−0.642403	−	0.766367i	$-0.722063\pi$
$31$		−	8.53390i		−	1.53273i	0.642403	−	0.766367i	$-0.277937\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	−2.05388	+	7.66518i	−0.357534	+	1.33434i
$34$	1.33249	−	2.30794i	0.228520	−	0.395808i
$35$		0			0
$36$	0.646284	+	1.11940i	0.107714	+	0.186566i
$37$	−5.03508	+	5.03508i	−0.827763	+	0.827763i	−0.987207	−	0.159444i	$-0.949030\pi$
$37$	−5.03508	+	5.03508i	−0.827763	+	0.827763i	0.159444	+	0.987207i	$0.449030\pi$
$38$	1.50616	−	4.09041i	0.244332	−	0.663553i
$39$			2.07900i			0.332907i
$40$		0			0
$41$	−5.76903	+	3.33075i	−0.900971	+	0.520176i	−0.877515	−	0.479549i	$-0.840800\pi$
$41$	−5.76903	+	3.33075i	−0.900971	+	0.520176i	−0.0234562	+	0.999725i	$0.507467\pi$
$42$	2.65410	−	0.711163i	0.409536	−	0.109735i
$43$	2.11477	+	0.566652i	0.322500	+	0.0864136i	0.416437	−	0.909165i	$-0.363279\pi$
$43$	2.11477	+	0.566652i	0.322500	+	0.0864136i	−0.0939373	+	0.995578i	$0.529945\pi$
$44$	−5.25941	−	3.03652i	−0.792886	−	0.457773i
$45$		0			0
$46$		−	7.75825i		−	1.14389i
$47$	0.505817	−	0.135533i	0.0737810	−	0.0197695i	−0.221740	−	0.975106i	$-0.571174\pi$
$47$	0.505817	−	0.135533i	0.0737810	−	0.0197695i	0.295521	+	0.955336i	$0.404507\pi$
$48$	1.26216	−	0.338196i	0.182178	−	0.0488143i
$49$		−	2.57817i		−	0.368310i
$50$		0			0
$51$	3.01575	+	1.74115i	0.422290	+	0.243809i
$52$	−1.53683	−	0.411793i	−0.213121	−	0.0571055i
$53$	−2.33496	+	0.625650i	−0.320731	+	0.0859397i	−0.415593	−	0.909551i	$-0.636426\pi$
$53$	−2.33496	+	0.625650i	−0.320731	+	0.0859397i	0.0948615	+	0.995490i	$0.469759\pi$
$54$	−4.85758	+	2.80452i	−0.661032	+	0.381647i
$55$		0			0
$56$			2.10281i			0.281000i
$57$	5.34489	+	1.96808i	0.707948	+	0.260679i
$58$	1.86314	−	1.86314i	0.244642	−	0.244642i
$59$	3.20769	+	5.55588i	0.417605	+	0.723313i	0.995698	−	0.0926576i	$-0.0295362\pi$
$59$	3.20769	+	5.55588i	0.417605	+	0.723313i	−0.578093	+	0.815971i	$0.696203\pi$
$60$		0			0
$61$	−7.49289	+	12.9781i	−0.959366	+	1.66167i	−0.235321	+	0.971918i	$0.575614\pi$
$61$	−7.49289	+	12.9781i	−0.959366	+	1.66167i	−0.724045	+	0.689752i	$0.757719\pi$
$62$	−2.20874	+	8.24311i	−0.280510	+	1.04688i
$63$	−0.703478	−	2.62541i	−0.0886299	−	0.330771i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	3.96779	−	6.87241i	0.488401	−	0.845935i
$67$	−2.95335	−	11.0220i	−0.360809	−	1.34656i	−0.873014	−	0.487694i	$-0.837838\pi$
$67$	−2.95335	−	11.0220i	−0.360809	−	1.34656i	0.512205	−	0.858863i	$-0.328829\pi$
$68$	−1.88442	+	1.88442i	−0.228520	+	0.228520i
$69$	10.1376			1.22043
$70$		0			0
$71$	3.66389	−	2.11535i	0.434824	−	0.251046i	−0.266576	−	0.963814i	$-0.585892\pi$
$71$	3.66389	−	2.11535i	0.434824	−	0.251046i	0.701400	+	0.712768i	$0.252559\pi$
$72$	−0.334541	−	1.24852i	−0.0394260	−	0.147140i
$73$	3.20699	+	0.859309i	0.375349	+	0.100575i	0.441561	−	0.897231i	$-0.354425\pi$
$73$	3.20699	+	0.859309i	0.375349	+	0.100575i	−0.0662122	+	0.997806i	$0.521091\pi$
$74$	6.16669	−	3.56034i	0.716864	−	0.413881i
$75$		0			0
$76$	−2.51352	+	3.56121i	−0.288320	+	0.408499i
$77$	9.03010	+	9.03010i	1.02908	+	1.02908i
$78$	0.538085	−	2.00816i	0.0609262	−	0.227380i
$79$	3.32249	+	5.75472i	0.373809	+	0.647457i	0.990148	−	0.140024i	$-0.0447181\pi$
$79$	3.32249	+	5.75472i	0.373809	+	0.647457i	−0.616339	+	0.787481i	$0.711385\pi$
$80$		0			0
$81$	−1.72578	−	2.98915i	−0.191754	−	0.332127i
$82$	6.43452	−	1.72412i	0.710574	−	0.190398i
$83$	−0.732952	+	0.732952i	−0.0804520	+	0.0804520i	−0.746188	−	0.665736i	$-0.768118\pi$
$83$	−0.732952	+	0.732952i	−0.0804520	+	0.0804520i	0.665736	+	0.746188i	$0.268118\pi$
$84$	−2.74772			−0.299801
$85$		0			0
$86$	−1.89605	−	1.09469i	−0.204457	−	0.118043i
$87$	2.43454	+	2.43454i	0.261010	+	0.261010i
$88$	4.29429	+	4.29429i	0.457773	+	0.457773i
$89$	−0.347882	+	0.602549i	−0.0368754	+	0.0638701i	−0.883874	−	0.467725i	$-0.845074\pi$
$89$	−0.347882	+	0.602549i	−0.0368754	+	0.0638701i	0.846999	+	0.531595i	$0.178407\pi$
$90$		0			0
$91$	2.89744	+	1.67284i	0.303734	+	0.175361i
$92$	−2.00798	+	7.49390i	−0.209347	+	0.781293i
$93$	−10.7712	−	2.88613i	−1.11692	−	0.299277i
$94$	−0.523660			−0.0540114
$95$		0			0
$96$	−1.30669			−0.133363
$97$	1.01518	+	0.272018i	0.103076	+	0.0276192i	0.309989	−	0.950740i	$-0.399675\pi$
$97$	1.01518	+	0.272018i	0.103076	+	0.0276192i	−0.206912	+	0.978360i	$0.566341\pi$
$98$	−0.667280	+	2.49032i	−0.0674054	+	0.251561i
$99$	−6.79814	−	3.92491i	−0.683239	−	0.394468i
$100$		0			0
$101$	−3.32769	+	5.76372i	−0.331117	+	0.573512i	−0.982731	−	0.185039i	$-0.940759\pi$
$101$	−3.32769	+	5.76372i	−0.331117	+	0.573512i	0.651614	+	0.758551i	$0.274092\pi$
$102$	−2.46235	−	2.46235i	−0.243809	−	0.243809i
$103$	−11.7498	−	11.7498i	−1.15774	−	1.15774i	−0.984960	−	0.172780i	$-0.944725\pi$
$103$	−11.7498	−	11.7498i	−1.15774	−	1.15774i	−0.172780	−	0.984960i	$-0.555275\pi$
$104$	1.37789	+	0.795524i	0.135113	+	0.0780075i
$105$		0			0
$106$	2.41733			0.234792
$107$	−9.75847	+	9.75847i	−0.943387	+	0.943387i	−0.998481	−	0.0550939i	$-0.982454\pi$
$107$	−9.75847	+	9.75847i	−0.943387	+	0.943387i	0.0550939	+	0.998481i	$0.482454\pi$
$108$	5.41792	−	1.45173i	0.521340	−	0.139693i
$109$	5.34771	+	9.26251i	0.512218	+	0.887187i	0.999900	+	0.0141659i	$0.00450930\pi$
$109$	5.34771	+	9.26251i	0.512218	+	0.887187i	−0.487682	+	0.873021i	$0.662157\pi$
$110$		0			0
$111$	4.65226	+	8.05794i	0.441573	+	0.764826i
$112$	0.544248	−	2.03116i	0.0514266	−	0.191927i
$113$	6.17733	+	6.17733i	0.581115	+	0.581115i	0.935209	−	0.354095i	$-0.115211\pi$
$113$	6.17733	+	6.17733i	0.581115	+	0.581115i	−0.354095	+	0.935209i	$0.615211\pi$
$114$	−4.65339	−	3.28438i	−0.435830	−	0.307610i
$115$		0			0
$116$	−2.28187	+	1.31744i	−0.211866	+	0.122321i
$117$	−1.98646	−	0.532271i	−0.183648	−	0.0492084i
$118$	−1.66042	−	6.19677i	−0.152854	−	0.570459i
$119$	4.85316	−	2.80197i	0.444889	−	0.256857i
$120$		0			0
$121$	25.8819			2.35290
$122$	10.5965	−	10.5965i	0.959366	−	0.959366i
$123$	2.25289	+	8.40791i	0.203136	+	0.758115i
$124$	4.26695	−	7.39057i	0.383183	−	0.663693i
$125$		0			0
$126$			2.71803i			0.242141i
$127$	1.31390	+	4.90354i	0.116590	+	0.435119i	0.999401	−	0.0346093i	$-0.0110187\pi$
$127$	1.31390	+	4.90354i	0.116590	+	0.435119i	−0.882811	+	0.469728i	$0.844352\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	1.43041	−	2.47755i	0.125941	−	0.218136i
$130$		0			0
$131$	−2.42896	−	4.20709i	−0.212219	−	0.367575i	0.740189	−	0.672398i	$-0.234736\pi$
$131$	−2.42896	−	4.20709i	−0.212219	−	0.367575i	−0.952409	+	0.304824i	$0.901402\pi$
$132$	−5.61130	+	5.61130i	−0.488401	+	0.488401i
$133$	7.04355	−	5.86543i	0.610753	−	0.508597i
$134$			11.4109i			0.985748i
$135$		0			0
$136$	2.30794	−	1.33249i	0.197904	−	0.114260i
$137$	−15.1959	+	4.07173i	−1.29827	+	0.347871i	−0.840797	−	0.541351i	$-0.817913\pi$
$137$	−15.1959	+	4.07173i	−1.29827	+	0.347871i	−0.457476	+	0.889222i	$0.651246\pi$
$138$	−9.79218	−	2.62381i	−0.833566	−	0.223353i
$139$	−8.40472	−	4.85247i	−0.712879	−	0.411581i	0.0992469	−	0.995063i	$-0.468357\pi$
$139$	−8.40472	−	4.85247i	−0.712879	−	0.411581i	−0.812126	+	0.583482i	$0.801690\pi$
$140$		0			0
$141$		−	0.684260i		−	0.0576251i
$142$	−4.08654	+	1.09498i	−0.342935	+	0.0918891i
$143$	9.33326	−	2.50084i	0.780487	−	0.209131i
$144$			1.29257i			0.107714i
$145$		0			0
$146$	−2.87530	−	1.66006i	−0.237962	−	0.137387i
$147$	−3.25407	−	0.871926i	−0.268391	−	0.0719153i
$148$	−6.87805	+	1.84297i	−0.565372	+	0.151491i
$149$	−4.08773	+	2.36005i	−0.334880	+	0.193343i	−0.658005	−	0.753013i	$-0.728600\pi$
$149$	−4.08773	+	2.36005i	−0.334880	+	0.193343i	0.323126	+	0.946356i	$0.395266\pi$
$150$		0			0
$151$		−	5.68462i		−	0.462607i	−0.972882	−	0.231304i	$-0.925701\pi$
$151$		−	5.68462i		−	0.462607i	0.972882	−	0.231304i	$-0.0742991\pi$
$152$	3.34958	−	2.78932i	0.271687	−	0.226244i
$153$	−2.43574	+	2.43574i	−0.196918	+	0.196918i
$154$	−6.38524	−	11.0596i	−0.514538	−	0.891205i
$155$		0			0
$156$	−1.03950	+	1.80047i	−0.0832267	+	0.144153i
$157$	2.42678	−	9.05688i	0.193678	−	0.722818i	−0.798926	−	0.601429i	$-0.794598\pi$
$157$	2.42678	−	9.05688i	0.193678	−	0.722818i	0.992605	−	0.121389i	$-0.0387349\pi$
$158$	−1.71985	−	6.41856i	−0.136824	−	0.510633i
$159$			3.15869i			0.250501i
$160$		0			0
$161$	8.15708	−	14.1285i	0.642868	−	1.11348i
$162$	0.893332	+	3.33396i	0.0701868	+	0.261941i
$163$	−8.77226	+	8.77226i	−0.687096	+	0.687096i	−0.961589	−	0.274493i	$-0.911490\pi$
$163$	−8.77226	+	8.77226i	−0.687096	+	0.687096i	0.274493	+	0.961589i	$0.411490\pi$
$164$	−6.66150			−0.520176
$165$		0			0
$166$	0.897680	−	0.518276i	0.0696735	−	0.0402260i
$167$	−3.88279	−	14.4908i	−0.300460	−	1.12133i	−0.936784	−	0.349909i	$-0.886213\pi$
$167$	−3.88279	−	14.4908i	−0.300460	−	1.12133i	0.636324	−	0.771422i	$-0.280454\pi$
$168$	2.65410	+	0.711163i	0.204768	+	0.0548674i
$169$	−9.06605	+	5.23428i	−0.697388	+	0.402637i
$170$		0			0
$171$	−3.24889	+	4.60311i	−0.248449	+	0.352008i
$172$	1.54812	+	1.54812i	0.118043	+	0.118043i
$173$	−4.00854	+	14.9601i	−0.304763	+	1.13739i	0.628386	+	0.777902i	$0.283716\pi$
$173$	−4.00854	+	14.9601i	−0.304763	+	1.13739i	−0.933149	+	0.359490i	$0.882951\pi$
$174$	−1.72148	−	2.98169i	−0.130505	−	0.226041i
$175$		0			0
$176$	−3.03652	−	5.25941i	−0.228887	−	0.396443i
$177$	8.09725	−	2.16965i	0.608626	−	0.163081i
$178$	0.491980	−	0.491980i	0.0368754	−	0.0368754i
$179$	1.72185			0.128697			0.0643485	−	0.997927i	$-0.479503\pi$
$179$	1.72185			0.128697			0.0643485	+	0.997927i	$0.479503\pi$
$180$		0			0
$181$	−7.79655	−	4.50134i	−0.579513	−	0.334582i	0.181427	−	0.983404i	$-0.441928\pi$
$181$	−7.79655	−	4.50134i	−0.579513	−	0.334582i	−0.760940	+	0.648822i	$0.775262\pi$
$182$	−2.36575	−	2.36575i	−0.175361	−	0.175361i
$183$	13.8464	+	13.8464i	1.02355	+	1.02355i
$184$	3.87913	−	6.71884i	0.285973	−	0.495320i
$185$		0			0
$186$	9.65717	+	5.57557i	0.708098	+	0.408821i
$187$	4.18886	−	15.6330i	0.306320	−	1.14320i
$188$	0.505817	+	0.135533i	0.0368905	+	0.00988477i
$189$	−11.7948			−0.857944
$190$		0			0
$191$	−15.2459			−1.10316			−0.551579	−	0.834123i	$-0.685974\pi$
$191$	−15.2459			−1.10316			−0.551579	+	0.834123i	$0.685974\pi$
$192$	1.26216	+	0.338196i	0.0910888	+	0.0244072i
$193$	2.46449	−	9.19761i	0.177398	−	0.662058i	−0.818733	−	0.574175i	$-0.805323\pi$
$193$	2.46449	−	9.19761i	0.177398	−	0.662058i	0.996131	−	0.0878835i	$-0.0280103\pi$
$194$	−0.910190	−	0.525498i	−0.0653478	−	0.0377286i
$195$		0			0
$196$	1.28909	−	2.23276i	0.0920775	−	0.159483i
$197$	−8.96048	−	8.96048i	−0.638408	−	0.638408i	0.311755	−	0.950163i	$-0.399083\pi$
$197$	−8.96048	−	8.96048i	−0.638408	−	0.638408i	−0.950163	+	0.311755i	$0.899083\pi$
$198$	5.55066	+	5.55066i	0.394468	+	0.394468i
$199$	−6.88042	−	3.97241i	−0.487740	−	0.281597i	0.235896	−	0.971778i	$-0.424197\pi$
$199$	−6.88042	−	3.97241i	−0.487740	−	0.281597i	−0.723636	+	0.690181i	$0.757531\pi$
$200$		0			0
$201$	−14.9104			−1.05170
$202$	4.70606	−	4.70606i	0.331117	−	0.331117i
$203$	5.35186	−	1.43403i	0.375627	−	0.100649i
$204$	1.74115	+	3.01575i	0.121905	+	0.211145i
$205$		0			0
$206$	8.30835	+	14.3905i	0.578870	+	1.00263i
$207$	−2.59545	+	9.68636i	−0.180396	+	0.673249i
$208$	−1.12504	−	1.12504i	−0.0780075	−	0.0780075i
$209$	2.40591	−	26.3622i	0.166421	−	1.82351i
$210$		0			0
$211$	14.1070	−	8.14469i	0.971167	−	0.560704i	0.0715754	−	0.997435i	$-0.477197\pi$
$211$	14.1070	−	8.14469i	0.971167	−	0.560704i	0.899592	+	0.436731i	$0.143864\pi$
$212$	−2.33496	−	0.625650i	−0.160366	−	0.0429698i
$213$	−1.43080	−	5.33983i	−0.0980370	−	0.365879i
$214$	11.9516	−	6.90028i	0.816997	−	0.471694i
$215$		0			0
$216$	−5.60904			−0.381647
$217$	−12.6892	+	12.6892i	−0.861397	+	0.861397i
$218$	−2.76818	−	10.3310i	−0.187485	−	0.699703i
$219$	2.16918	−	3.75712i	0.146579	−	0.253883i
$220$		0			0
$221$		−	4.24010i		−	0.285220i
$222$	−2.40818	−	8.98747i	−0.161627	−	0.603199i
$223$	2.69204	−	10.0468i	0.180272	−	0.672785i	−0.815321	−	0.579009i	$-0.803440\pi$
$223$	2.69204	−	10.0468i	0.180272	−	0.672785i	0.995593	−	0.0937760i	$-0.0298938\pi$
$224$	−1.05141	+	1.82109i	−0.0702501	+	0.121677i
$225$		0			0
$226$	−4.36803	−	7.56566i	−0.290557	−	0.503260i
$227$	−1.98492	+	1.98492i	−0.131744	+	0.131744i	−0.769904	−	0.638160i	$-0.779696\pi$
$227$	−1.98492	+	1.98492i	−0.131744	+	0.131744i	0.638160	+	0.769904i	$0.279696\pi$
$228$	3.64477	+	4.37686i	0.241381	+	0.289864i
$229$		−	26.8346i		−	1.77328i	−0.462458	−	0.886641i	$-0.653032\pi$
$229$		−	26.8346i		−	1.77328i	0.462458	−	0.886641i	$-0.346968\pi$
$230$		0			0
$231$	14.4514	−	8.34352i	0.950832	−	0.548963i
$232$	2.54509	−	0.681956i	0.167094	−	0.0447726i
$233$	4.03425	+	1.08097i	0.264293	+	0.0708170i	0.388532	−	0.921435i	$-0.372982\pi$
$233$	4.03425	+	1.08097i	0.264293	+	0.0708170i	−0.124239	+	0.992252i	$0.539649\pi$
$234$	1.78101	+	1.02827i	0.116428	+	0.0672200i
$235$		0			0
$236$			6.41537i			0.417605i
$237$	8.38705	−	2.24730i	0.544798	−	0.145978i
$238$	−5.41300	+	1.45041i	−0.350873	+	0.0940160i
$239$		−	12.9002i		−	0.834442i	−0.908805	−	0.417221i	$-0.863004\pi$
$239$		−	12.9002i		−	0.834442i	0.908805	−	0.417221i	$-0.136996\pi$
$240$		0			0
$241$	7.82897	+	4.52006i	0.504308	+	0.291163i	0.730491	−	0.682922i	$-0.239291\pi$
$241$	7.82897	+	4.52006i	0.504308	+	0.291163i	−0.226183	+	0.974085i	$0.572625\pi$
$242$	−25.0000	−	6.69872i	−1.60706	−	0.430610i
$243$	11.8973	−	3.18788i	0.763213	−	0.204502i
$244$	−12.9781	+	7.49289i	−0.830835	+	0.479683i
$245$		0			0
$246$		−	8.70451i		−	0.554979i
$247$	−1.17870	−	6.83432i	−0.0749989	−	0.434857i
$248$	−6.03438	+	6.03438i	−0.383183	+	0.383183i
$249$	0.677224	+	1.17299i	0.0429174	+	0.0743350i
$250$		0			0
$251$	−5.34569	+	9.25901i	−0.337417	+	0.584424i	−0.983946	−	0.178466i	$-0.942887\pi$
$251$	−5.34569	+	9.25901i	−0.337417	+	0.584424i	0.646529	+	0.762889i	$0.276220\pi$
$252$	0.703478	−	2.62541i	0.0443149	−	0.165386i
$253$	−12.1946	−	45.5108i	−0.766666	−	2.86124i
$254$		−	5.07652i		−	0.318529i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.06410	−	26.3636i	−0.440647	−	1.64452i	−0.727181	−	0.686445i	$-0.759170\pi$
$257$	−7.06410	−	26.3636i	−0.440647	−	1.64452i	0.286535	−	0.958070i	$-0.407497\pi$
$258$	−2.02291	+	2.02291i	−0.125941	+	0.125941i
$259$	14.9735			0.930407
$260$		0			0
$261$	−2.94947	+	1.70288i	−0.182568	+	0.105405i
$262$	1.25732	+	4.69239i	0.0776777	+	0.289897i
$263$	−0.921033	−	0.246790i	−0.0567933	−	0.0152177i	0.230311	−	0.973117i	$-0.426026\pi$
$263$	−0.921033	−	0.246790i	−0.0567933	−	0.0152177i	−0.287104	+	0.957899i	$0.592692\pi$
$264$	6.87241	−	3.96779i	0.422968	−	0.244200i
$265$		0			0
$266$	−8.32163	+	3.84256i	−0.510232	+	0.235603i
$267$	0.642864	+	0.642864i	0.0393426	+	0.0393426i
$268$	2.95335	−	11.0220i	0.180404	−	0.673279i
$269$	12.2285	+	21.1805i	0.745587	+	1.29140i	0.949920	+	0.312494i	$0.101164\pi$
$269$	12.2285	+	21.1805i	0.745587	+	1.29140i	−0.204333	+	0.978902i	$0.565502\pi$
$270$		0			0
$271$	−7.66991	−	13.2847i	−0.465914	−	0.806987i	0.533328	−	0.845908i	$-0.320941\pi$
$271$	−7.66991	−	13.2847i	−0.465914	−	0.806987i	−0.999242	+	0.0389217i	$0.987608\pi$
$272$	−2.57417	+	0.689746i	−0.156082	+	0.0418220i
$273$	3.09130	−	3.09130i	0.187094	−	0.187094i
$274$	15.7319			0.950401
$275$		0			0
$276$	8.77943	+	5.06881i	0.528460	+	0.305106i
$277$	−7.81021	−	7.81021i	−0.469270	−	0.469270i	0.432408	−	0.901678i	$-0.357664\pi$
$277$	−7.81021	−	7.81021i	−0.469270	−	0.469270i	−0.901678	+	0.432408i	$0.857664\pi$
$278$	6.86243	+	6.86243i	0.411581	+	0.411581i
$279$	5.51532	−	9.55281i	0.330193	−	0.571912i
$280$		0			0
$281$	19.1158	+	11.0365i	1.14035	+	0.658382i	0.946517	−	0.322653i	$-0.104575\pi$
$281$	19.1158	+	11.0365i	1.14035	+	0.658382i	0.193833	+	0.981034i	$0.437908\pi$
$282$	−0.177100	+	0.660945i	−0.0105461	+	0.0393587i
$283$	10.2597	+	2.74908i	0.609877	+	0.163416i	0.550522	−	0.834821i	$-0.314429\pi$
$283$	10.2597	+	2.74908i	0.609877	+	0.163416i	0.0593554	+	0.998237i	$0.481095\pi$
$284$	4.23070			0.251046
$285$		0			0
$286$	−9.66250			−0.571356
$287$	13.5306	+	3.62551i	0.798686	+	0.214007i
$288$	0.334541	−	1.24852i	0.0197130	−	0.0735700i
$289$	8.57184	+	4.94895i	0.504226	+	0.291115i
$290$		0			0
$291$	0.686662	−	1.18933i	0.0402528	−	0.0697200i
$292$	2.34768	+	2.34768i	0.137387	+	0.137387i
$293$	6.23887	+	6.23887i	0.364479	+	0.364479i	0.865459	−	0.500980i	$-0.167027\pi$
$293$	6.23887	+	6.23887i	0.364479	+	0.364479i	−0.500980	+	0.865459i	$0.667027\pi$
$294$	2.91752	+	1.68443i	0.170153	+	0.0982381i
$295$		0			0
$296$	7.12068			0.413881
$297$	−24.0869	+	24.0869i	−1.39766	+	1.39766i
$298$	4.55927	−	1.22165i	0.264111	−	0.0707684i
$299$	−6.17187	−	10.6900i	−0.356929	−	0.618219i
$300$		0			0
$301$	−2.30192	−	3.98705i	−0.132681	−	0.229810i
$302$	−1.47129	+	5.49092i	−0.0846630	+	0.315967i
$303$	6.14935	+	6.14935i	0.353271	+	0.353271i
$304$	−3.95738	+	1.82734i	−0.226971	+	0.104805i
$305$		0			0
$306$	2.98316	−	1.72233i	0.170536	−	0.0984590i
$307$	8.85997	+	2.37402i	0.505665	+	0.135493i	0.502628	−	0.864503i	$-0.332367\pi$
$307$	8.85997	+	2.37402i	0.505665	+	0.135493i	0.00303736	+	0.999995i	$0.499033\pi$
$308$	3.30525	+	12.3353i	0.188334	+	0.702871i
$309$	−18.8039	+	10.8564i	−1.06971	+	0.617600i
$310$		0			0
$311$	−6.82400			−0.386954			−0.193477	−	0.981105i	$-0.561976\pi$
$311$	−6.82400			−0.386954			−0.193477	+	0.981105i	$0.561976\pi$
$312$	1.47008	−	1.47008i	0.0832267	−	0.0832267i
$313$	−3.64997	−	13.6219i	−0.206308	−	0.769953i	−0.989047	−	0.147602i	$-0.952844\pi$
$313$	−3.64997	−	13.6219i	−0.206308	−	0.769953i	0.782739	−	0.622351i	$-0.213822\pi$
$314$	−4.68819	+	8.12018i	−0.264570	+	0.458248i
$315$		0			0
$316$			6.64498i			0.373809i
$317$	4.39999	+	16.4210i	0.247128	+	0.922294i	0.972302	+	0.233728i	$0.0750926\pi$
$317$	4.39999	+	16.4210i	0.247128	+	0.922294i	−0.725174	+	0.688566i	$0.758241\pi$
$318$	0.817530	−	3.05106i	0.0458448	−	0.171095i
$319$	8.00086	−	13.8579i	0.447962	−	0.775893i
$320$		0			0
$321$	9.01651	+	15.6171i	0.503253	+	0.871659i
$322$	−11.5359	+	11.5359i	−0.642868	+	0.642868i
$323$	−10.9009	−	4.01388i	−0.606540	−	0.223338i
$324$		−	3.45157i		−	0.191754i
$325$		0			0
$326$	10.7438	−	6.20292i	0.595043	−	0.343548i
$327$	13.4994	−	3.61715i	0.746517	−	0.200029i
$328$	6.43452	+	1.72412i	0.355287	+	0.0951988i
$329$	−0.953633	−	0.550580i	−0.0525755	−	0.0303545i
$330$		0			0
$331$		−	34.3118i		−	1.88595i	−0.332866	−	0.942974i	$-0.608016\pi$
$331$		−	34.3118i		−	1.88595i	0.332866	−	0.942974i	$-0.391984\pi$
$332$	−1.00123	+	0.268279i	−0.0549497	+	0.0147237i
$333$	−8.89035	+	2.38216i	−0.487188	+	0.130542i
$334$			15.0020i			0.820871i
$335$		0			0
$336$	−2.37960	−	1.37386i	−0.129818	−	0.0749503i
$337$	31.2455	+	8.37221i	1.70205	+	0.456063i	0.973455	−	0.228879i	$-0.0735060\pi$
$337$	31.2455	+	8.37221i	1.70205	+	0.456063i	0.728597	+	0.684943i	$0.240173\pi$
$338$	10.1119	−	2.70946i	0.550013	−	0.147375i
$339$	9.88595	−	5.70766i	0.536931	−	0.309997i
$340$		0			0
$341$			51.8267i			2.80658i
$342$	4.32956	−	3.60539i	0.234116	−	0.194957i
$343$	−14.2419	+	14.2419i	−0.768991	+	0.768991i
$344$	−1.09469	−	1.89605i	−0.0590216	−	0.102228i
$345$		0			0
$346$	7.74390	−	13.4128i	0.416314	−	0.721078i
$347$	1.30783	−	4.88089i	0.0702080	−	0.262020i	−0.921896	−	0.387437i	$-0.873360\pi$
$347$	1.30783	−	4.88089i	0.0702080	−	0.262020i	0.992104	+	0.125418i	$0.0400270\pi$
$348$	0.891103	+	3.32564i	0.0477681	+	0.178273i
$349$			29.0150i			1.55314i	0.630033	+	0.776568i	$0.283041\pi$
$349$			29.0150i			1.55314i	−0.630033	+	0.776568i	$0.716959\pi$
$350$		0			0
$351$	−4.46213	+	7.72863i	−0.238171	+	0.412524i
$352$	1.57182	+	5.86611i	0.0837783	+	0.312665i
$353$	−18.7215	+	18.7215i	−0.996447	+	0.996447i	−0.999994	−	0.00354655i	$-0.998871\pi$
$353$	−18.7215	+	18.7215i	−0.996447	+	0.996447i	0.00354655	+	0.999994i	$0.498871\pi$
$354$	−8.38289			−0.445545
$355$		0			0
$356$	−0.602549	+	0.347882i	−0.0319351	+	0.0184377i
$357$	−1.89523	−	7.07310i	−0.100306	−	0.374348i
$358$	−1.66318	−	0.445647i	−0.0879017	−	0.0235532i
$359$	−12.5921	+	7.27006i	−0.664586	+	0.383699i	−0.794022	−	0.607889i	$-0.792017\pi$
$359$	−12.5921	+	7.27006i	−0.664586	+	0.383699i	0.129436	+	0.991588i	$0.458683\pi$
$360$		0			0
$361$	−18.6861	−	3.43937i	−0.983479	−	0.181020i
$362$	6.36586	+	6.36586i	0.334582	+	0.334582i
$363$	8.75314	−	32.6672i	0.459421	−	1.71458i
$364$	1.67284	+	2.89744i	0.0876806	+	0.151867i
$365$		0			0
$366$	−9.79086	−	16.9583i	−0.511777	−	0.886423i
$367$	−12.5757	+	3.36966i	−0.656449	+	0.175895i	−0.571643	−	0.820503i	$-0.693694\pi$
$367$	−12.5757	+	3.36966i	−0.656449	+	0.175895i	−0.0848059	+	0.996397i	$0.527027\pi$
$368$	−5.48591	+	5.48591i	−0.285973	+	0.285973i
$369$	−8.61044			−0.448242
$370$		0			0
$371$	4.40217	+	2.54160i	0.228549	+	0.131953i
$372$	−7.88505	−	7.88505i	−0.408821	−	0.408821i
$373$	2.70629	+	2.70629i	0.140126	+	0.140126i	0.773690	−	0.633564i	$-0.218409\pi$
$373$	2.70629	+	2.70629i	0.140126	+	0.140126i	−0.633564	+	0.773690i	$0.718409\pi$
$374$	−8.09226	+	14.0162i	−0.418441	+	0.724761i
$375$		0			0
$376$	−0.453503	−	0.261830i	−0.0233876	−	0.0135029i
$377$	1.08502	−	4.04936i	0.0558816	−	0.208553i
$378$	11.3929	+	3.05271i	0.585987	+	0.157015i
$379$	−12.5541			−0.644862			−0.322431	−	0.946593i	$-0.604500\pi$
$379$	−12.5541			−0.644862			−0.322431	+	0.946593i	$0.604500\pi$
$380$		0			0
$381$	6.63342			0.339840
$382$	14.7264	+	3.94594i	0.753470	+	0.201892i
$383$	1.06696	−	3.98193i	0.0545189	−	0.203467i	−0.933294	−	0.359113i	$-0.883079\pi$
$383$	1.06696	−	3.98193i	0.0545189	−	0.203467i	0.987813	+	0.155646i	$0.0497459\pi$
$384$	−1.13162	−	0.653344i	−0.0577480	−	0.0333408i
$385$		0			0
$386$	−4.76103	+	8.24635i	−0.242330	+	0.419728i
$387$	2.00105	+	2.00105i	0.101719	+	0.101719i
$388$	0.743167	+	0.743167i	0.0377286	+	0.0377286i
$389$	−18.8624	−	10.8902i	−0.956363	−	0.552157i	−0.0613113	−	0.998119i	$-0.519528\pi$
$389$	−18.8624	−	10.8902i	−0.956363	−	0.552157i	−0.895052	+	0.445962i	$0.852862\pi$
$390$		0			0
$391$	−20.6755			−1.04561
$392$	−1.82304	+	1.82304i	−0.0920775	+	0.0920775i
$393$	−6.13149	+	1.64293i	−0.309293	+	0.0828748i
$394$	6.33602	+	10.9743i	0.319204	+	0.552878i
$395$		0			0
$396$	−3.92491	−	6.79814i	−0.197234	−	0.341620i
$397$	−5.41412	+	20.2058i	−0.271727	+	1.01410i	0.686276	+	0.727341i	$0.259244\pi$
$397$	−5.41412	+	20.2058i	−0.271727	+	1.01410i	−0.958003	+	0.286757i	$0.907423\pi$
$398$	5.61784	+	5.61784i	0.281597	+	0.281597i
$399$	−5.02103	−	10.8738i	−0.251366	−	0.544369i
$400$		0			0
$401$	15.9070	−	9.18393i	0.794359	−	0.458623i	−0.0471358	−	0.998888i	$-0.515009\pi$
$401$	15.9070	−	9.18393i	0.794359	−	0.458623i	0.841495	+	0.540265i	$0.181676\pi$
$402$	14.4024	+	3.85910i	0.718325	+	0.192475i
$403$	3.51420	+	13.1152i	0.175055	+	0.653314i
$404$	−5.76372	+	3.32769i	−0.286756	+	0.165559i
$405$		0			0
$406$	−5.54065			−0.274978
$407$	30.5783	−	30.5783i	1.51571	−	1.51571i
$408$	−0.901283	−	3.36363i	−0.0446202	−	0.166525i
$409$	6.60824	−	11.4458i	0.326757	−	0.565959i	−0.655110	−	0.755534i	$-0.727378\pi$
$409$	6.60824	−	11.4458i	0.326757	−	0.565959i	0.981866	+	0.189575i	$0.0607110\pi$
$410$		0			0
$411$			20.5567i			1.01399i
$412$	−4.30072	−	16.0505i	−0.211881	−	0.790751i
$413$	3.49156	−	13.0307i	0.171808	−	0.641197i
$414$	5.01403	−	8.68456i	0.246426	−	0.426823i
$415$		0			0
$416$	0.795524	+	1.37789i	0.0390038	+	0.0675565i
$417$	−8.96705	+	8.96705i	−0.439118	+	0.439118i
$418$	−9.14698	+	24.8413i	−0.447394	+	1.21503i
$419$			5.90391i			0.288425i	0.989547	+	0.144212i	$0.0460648\pi$
$419$			5.90391i			0.288425i	−0.989547	+	0.144212i	$0.953935\pi$
$420$		0			0
$421$	5.65898	−	3.26722i	0.275802	−	0.159234i	−0.355719	−	0.934593i	$-0.615764\pi$
$421$	5.65898	−	3.26722i	0.275802	−	0.159234i	0.631521	+	0.775358i	$0.282431\pi$
$422$	−15.7343	+	4.21600i	−0.765936	+	0.205232i
$423$	0.653802	+	0.175186i	0.0317890	+	0.00851782i
$424$	2.09347	+	1.20866i	0.101668	+	0.0586979i
$425$		0			0
$426$			5.52820i			0.267842i
$427$	30.4385	−	8.15598i	1.47302	−	0.394696i
$428$	−13.3303	+	3.57185i	−0.644345	+	0.172652i
$429$		−	12.6259i		−	0.609583i
$430$		0			0
$431$	−18.3796	−	10.6115i	−0.885314	−	0.511136i	−0.0129070	−	0.999917i	$-0.504109\pi$
$431$	−18.3796	−	10.6115i	−0.885314	−	0.511136i	−0.872407	+	0.488781i	$0.837442\pi$
$432$	5.41792	+	1.45173i	0.260670	+	0.0698463i
$433$	12.6336	−	3.38515i	0.607130	−	0.162680i	0.0578599	−	0.998325i	$-0.481572\pi$
$433$	12.6336	−	3.38515i	0.607130	−	0.162680i	0.549271	+	0.835645i	$0.314906\pi$
$434$	15.5410	−	8.97260i	0.745992	−	0.430699i
$435$		0			0
$436$			10.6954i			0.512218i
$437$	−33.3254	+	5.74757i	−1.59417	+	0.274944i
$438$	−3.06768	+	3.06768i	−0.146579	+	0.146579i
$439$	9.74980	+	16.8872i	0.465333	+	0.805980i	0.999216	−	0.0395779i	$-0.0126013\pi$
$439$	9.74980	+	16.8872i	0.465333	+	0.805980i	−0.533884	+	0.845558i	$0.679268\pi$
$440$		0			0
$441$	1.66623	−	2.88599i	0.0793443	−	0.137428i
$442$	−1.09742	+	4.09562i	−0.0521989	+	0.194809i
$443$	7.68917	+	28.6964i	0.365324	+	1.36341i	0.866981	+	0.498340i	$0.166057\pi$
$443$	7.68917	+	28.6964i	0.365324	+	1.36341i	−0.501658	+	0.865066i	$0.667276\pi$
$444$			9.30451i			0.441573i
$445$		0			0
$446$	−5.20062	+	9.00774i	−0.246256	+	0.426529i
$447$	1.59632	+	5.95754i	0.0755033	+	0.281782i
$448$	1.48691	−	1.48691i	0.0702501	−	0.0702501i
$449$	−28.3109			−1.33607			−0.668037	−	0.744128i	$-0.732865\pi$
$449$	−28.3109			−1.33607			−0.668037	+	0.744128i	$0.732865\pi$
$450$		0			0
$451$	35.0356	−	20.2278i	1.64976	−	0.952490i
$452$	2.26106	+	8.43839i	0.106351	+	0.396909i
$453$	−7.17491	−	1.92251i	−0.337107	−	0.0903275i
$454$	2.43102	−	1.40355i	0.114093	−	0.0658719i
$455$		0			0
$456$	−2.38777	−	5.17105i	−0.111817	−	0.242157i
$457$	5.64227	+	5.64227i	0.263934	+	0.263934i	0.826650	−	0.562716i	$-0.190244\pi$
$457$	5.64227	+	5.64227i	0.263934	+	0.263934i	−0.562716	+	0.826650i	$0.690244\pi$
$458$	−6.94531	+	25.9203i	−0.324533	+	1.21117i
$459$	7.47398	+	12.9453i	0.348856	+	0.604236i
$460$		0			0
$461$	−7.84975	−	13.5962i	−0.365599	−	0.633236i	0.623273	−	0.782004i	$-0.285803\pi$
$461$	−7.84975	−	13.5962i	−0.365599	−	0.633236i	−0.988872	+	0.148768i	$0.952469\pi$
$462$	−16.1184	+	4.31892i	−0.749898	+	0.200935i
$463$	−21.4745	+	21.4745i	−0.998003	+	0.998003i	−0.999998	−	0.00199541i	$-0.999365\pi$
$463$	−21.4745	+	21.4745i	−0.998003	+	0.998003i	0.00199541	+	0.999998i	$0.499365\pi$
$464$	−2.63487			−0.122321
$465$		0			0
$466$	−3.61701	−	2.08828i	−0.167555	−	0.0967378i
$467$	10.5990	+	10.5990i	0.490462	+	0.490462i	0.908452	−	0.417990i	$-0.137265\pi$
$467$	10.5990	+	10.5990i	0.490462	+	0.490462i	−0.417990	+	0.908452i	$0.637265\pi$
$468$	−1.45419	−	1.45419i	−0.0672200	−	0.0672200i
$469$	−11.9975	+	20.7802i	−0.553991	+	0.959541i
$470$		0			0
$471$	−10.6105	−	6.12600i	−0.488908	−	0.282271i
$472$	1.66042	−	6.19677i	0.0764270	−	0.285230i
$473$	−12.8431	−	3.44130i	−0.590527	−	0.158231i
$474$	−8.68291			−0.398819
$475$		0			0
$476$	5.60395			0.256857
$477$	−3.01809	−	0.808695i	−0.138189	−	0.0370276i
$478$	−3.33881	+	12.4606i	−0.152713	+	0.569934i
$479$	23.3434	+	13.4773i	1.06659	+	0.615793i	0.927247	−	0.374451i	$-0.122169\pi$
$479$	23.3434	+	13.4773i	1.06659	+	0.615793i	0.139339	+	0.990245i	$0.455502\pi$
$480$		0			0
$481$	5.66467	−	9.81150i	0.258287	−	0.447366i
$482$	−6.39233	−	6.39233i	−0.291163	−	0.291163i
$483$	−15.0738	−	15.0738i	−0.685880	−	0.685880i
$484$	22.4144	+	12.9409i	1.01883	+	0.588225i
$485$		0			0
$486$	−12.3170			−0.558711
$487$	11.3158	−	11.3158i	0.512770	−	0.512770i	−0.402604	−	0.915374i	$-0.631895\pi$
$487$	11.3158	−	11.3158i	0.512770	−	0.512770i	0.915374	+	0.402604i	$0.131895\pi$
$488$	14.4751	−	3.87860i	0.655259	−	0.175576i
$489$	8.10528	+	14.0388i	0.366534	+	0.634855i
$490$		0			0
$491$	12.2626	+	21.2394i	0.553403	+	0.958522i	0.998026	+	0.0628045i	$0.0200044\pi$
$491$	12.2626	+	21.2394i	0.553403	+	0.958522i	−0.444623	+	0.895718i	$0.646662\pi$
$492$	−2.25289	+	8.40791i	−0.101568	+	0.379058i
$493$	−4.96522	−	4.96522i	−0.223622	−	0.223622i
$494$	−0.630314	+	6.90651i	−0.0283592	+	0.310739i
$495$		0			0
$496$	7.39057	−	4.26695i	0.331846	−	0.191592i
$497$	−8.59323	−	2.30255i	−0.385459	−	0.103283i
$498$	−0.350557	−	1.30830i	−0.0157088	−	0.0586262i
$499$	27.9143	−	16.1164i	1.24962	−	0.721467i	0.278584	−	0.960412i	$-0.410135\pi$
$499$	27.9143	−	16.1164i	1.24962	−	0.721467i	0.971033	+	0.238945i	$0.0768015\pi$
$500$		0			0
$501$	−19.6029			−0.875792
$502$	7.55995	−	7.55995i	0.337417	−	0.337417i
$503$	−6.66010	−	24.8558i	−0.296959	−	1.10827i	−0.939649	−	0.342140i	$-0.888848\pi$
$503$	−6.66010	−	24.8558i	−0.296959	−	1.10827i	0.642690	−	0.766127i	$-0.277819\pi$
$504$	−1.35901	+	2.35388i	−0.0605353	+	0.104850i
$505$		0			0
$506$			47.1162i			2.09457i
$507$	3.54042	+	13.2130i	0.157236	+	0.586812i
$508$	−1.31390	+	4.90354i	−0.0582948	+	0.217559i
$509$	−5.79313	+	10.0340i	−0.256776	+	0.444749i	−0.965376	−	0.260861i	$-0.915994\pi$
$509$	−5.79313	+	10.0340i	−0.256776	+	0.444749i	0.708601	+	0.705610i	$0.249327\pi$
$510$		0			0
$511$	−3.49079	−	6.04623i	−0.154424	−	0.267470i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	15.6454	+	18.7879i	0.690763	+	0.829508i
$514$			27.2936i			1.20387i
$515$		0			0
$516$	2.47755	−	1.43041i	0.109068	−	0.0629705i
$517$	−3.07185	+	0.823099i	−0.135100	+	0.0361999i
$518$	−14.4633	−	3.87542i	−0.635480	−	0.170276i
$519$	17.5264	+	10.1189i	0.769322	+	0.444168i
$520$		0			0
$521$		−	2.72440i		−	0.119358i	−0.998218	−	0.0596790i	$-0.980992\pi$
$521$		−	2.72440i		−	0.119358i	0.998218	−	0.0596790i	$-0.0190077\pi$
$522$	3.28970	−	0.881474i	0.143986	−	0.0385811i
$523$	4.28722	−	1.14876i	0.187467	−	0.0502317i	−0.163864	−	0.986483i	$-0.552396\pi$
$523$	4.28722	−	1.14876i	0.187467	−	0.0502317i	0.351331	+	0.936251i	$0.385729\pi$
$524$		−	4.85792i		−	0.212219i
$525$		0			0
$526$	0.825776	+	0.476762i	0.0360055	+	0.0207878i
$527$	21.9677	+	5.88622i	0.956928	+	0.256408i
$528$	−7.66518	+	2.05388i	−0.333584	+	0.0893836i
$529$	−32.2079	+	18.5952i	−1.40034	+	0.808488i
$530$		0			0
$531$			8.29230i			0.359855i
$532$	9.03260	−	1.55783i	0.391613	−	0.0675407i
$533$	7.49446	−	7.49446i	0.324621	−	0.324621i
$534$	−0.454573	−	0.787344i	−0.0196713	−	0.0340717i
$535$		0			0
$536$	−5.70543	+	9.88210i	−0.246437	+	0.426842i
$537$	0.582322	−	2.17326i	0.0251291	−	0.0937829i
$538$	−6.32996	−	23.6237i	−0.272904	−	1.01849i
$539$			15.6574i			0.674410i
$540$		0			0
$541$	4.15815	−	7.20213i	0.178773	−	0.309644i	−0.762688	−	0.646767i	$-0.776121\pi$
$541$	4.15815	−	7.20213i	0.178773	−	0.309644i	0.941461	+	0.337123i	$0.109454\pi$
$542$	3.97024	+	14.8171i	0.170536	+	0.636450i
$543$	−8.31819	+	8.31819i	−0.356968	+	0.356968i
$544$	2.66498			0.114260
$545$		0			0
$546$	−3.78605	+	2.18588i	−0.162028	+	0.0935469i
$547$	9.65134	+	36.0193i	0.412662	+	1.54007i	0.789474	+	0.613784i	$0.210354\pi$
$547$	9.65134	+	36.0193i	0.412662	+	1.54007i	−0.376812	+	0.926290i	$0.622980\pi$
$548$	−15.1959	−	4.07173i	−0.649136	−	0.173936i
$549$	−16.7750	+	9.68506i	−0.715940	+	0.413348i
$550$		0			0
$551$	−9.38335	−	6.62280i	−0.399744	−	0.282141i
$552$	−7.16837	−	7.16837i	−0.305106	−	0.305106i
$553$	3.61652	−	13.4970i	0.153790	−	0.573952i
$554$	5.52265	+	9.56551i	0.234635	+	0.406400i
$555$		0			0
$556$	−4.85247	−	8.40472i	−0.205791	−	0.356440i
$557$	36.3906	−	9.75082i	1.54192	−	0.413156i	0.615033	−	0.788502i	$-0.289143\pi$
$557$	36.3906	−	9.75082i	1.54192	−	0.413156i	0.926885	+	0.375346i	$0.122476\pi$
$558$	−7.79984	+	7.79984i	−0.330193	+	0.330193i
$559$	−3.48340			−0.147332
$560$		0			0
$561$	−18.3148	−	10.5741i	−0.773251	−	0.446437i
$562$	−15.6080	−	15.6080i	−0.658382	−	0.658382i
$563$	−2.54061	−	2.54061i	−0.107074	−	0.107074i	0.651540	−	0.758614i	$-0.274123\pi$
$563$	−2.54061	−	2.54061i	−0.107074	−	0.107074i	−0.758614	+	0.651540i	$0.774123\pi$
$564$	0.342130	−	0.592587i	0.0144063	−	0.0249524i
$565$		0			0
$566$	−9.19862	−	5.31082i	−0.386647	−	0.223231i
$567$	−1.87851	+	7.01070i	−0.0788900	+	0.294422i
$568$	−4.08654	−	1.09498i	−0.171467	−	0.0459445i
$569$	25.5831			1.07250			0.536249	−	0.844060i	$-0.319841\pi$
$569$	25.5831			1.07250			0.536249	+	0.844060i	$0.319841\pi$
$570$		0			0
$571$	−7.83552			−0.327906			−0.163953	−	0.986468i	$-0.552425\pi$
$571$	−7.83552			−0.327906			−0.163953	+	0.986468i	$0.552425\pi$
$572$	9.33326	+	2.50084i	0.390243	+	0.104565i
$573$	−5.15611	+	19.2429i	−0.215400	+	0.803882i
$574$	−12.1312	−	7.00395i	−0.506347	−	0.292339i
$575$		0			0
$576$	−0.646284	+	1.11940i	−0.0269285	+	0.0466415i
$577$	24.7899	+	24.7899i	1.03202	+	1.03202i	0.999470	+	0.0325455i	$0.0103614\pi$
$577$	24.7899	+	24.7899i	1.03202	+	1.03202i	0.0325455	+	0.999470i	$0.489639\pi$
$578$	−6.99888	−	6.99888i	−0.291115	−	0.291115i
$579$	−10.7754	−	6.22118i	−0.447810	−	0.258543i
$580$		0			0
$581$	2.17968			0.0904282
$582$	−0.971087	+	0.971087i	−0.0402528	+	0.0402528i
$583$	14.1803	−	3.79960i	0.587288	−	0.157363i
$584$	−1.66006	−	2.87530i	−0.0686937	−	0.118981i
$585$		0			0
$586$	−4.41155	−	7.64103i	−0.182239	−	0.315648i
$587$	6.61358	−	24.6822i	0.272972	−	1.01874i	−0.684217	−	0.729279i	$-0.739856\pi$
$587$	6.61358	−	24.6822i	0.272972	−	1.01874i	0.957188	−	0.289466i	$-0.0934776\pi$
$588$	−2.38215	−	2.38215i	−0.0982381	−	0.0982381i
$589$	37.0444	+	3.38081i	1.52639	+	0.139304i
$590$		0			0
$591$	−14.3400	+	8.27920i	−0.589868	+	0.340561i
$592$	−6.87805	−	1.84297i	−0.282686	−	0.0757456i
$593$	0.680798	+	2.54077i	0.0279570	+	0.104337i	0.978495	−	0.206273i	$-0.0661334\pi$
$593$	0.680798	+	2.54077i	0.0279570	+	0.104337i	−0.950538	+	0.310610i	$0.899467\pi$
$594$	29.5003	−	17.0320i	1.21041	−	0.698831i
$595$		0			0
$596$	−4.72010			−0.193343
$597$	−7.34076	+	7.34076i	−0.300437	+	0.300437i
$598$	3.19480	+	11.9231i	0.130645	+	0.487574i
$599$	4.79808	−	8.31052i	0.196044	−	0.339559i	−0.751198	−	0.660077i	$-0.770524\pi$
$599$	4.79808	−	8.31052i	0.196044	−	0.339559i	0.947242	+	0.320518i	$0.103857\pi$
$600$		0			0
$601$			6.09928i			0.248795i	0.992232	+	0.124397i	$0.0396998\pi$
$601$			6.09928i			0.248795i	−0.992232	+	0.124397i	$0.960300\pi$
$602$	1.19156	+	4.44697i	0.0485645	+	0.181245i
$603$	3.81740	−	14.2467i	0.155457	−	0.580172i
$604$	2.84231	−	4.92302i	0.115652	−	0.200315i
$605$		0			0
$606$	−4.34825	−	7.53138i	−0.176635	−	0.305942i
$607$	−13.0321	+	13.0321i	−0.528956	+	0.528956i	−0.920261	−	0.391305i	$-0.872024\pi$
$607$	−13.0321	+	13.0321i	−0.528956	+	0.528956i	0.391305	+	0.920261i	$0.372024\pi$
$608$	4.29548	−	0.740833i	0.174205	−	0.0300448i
$609$		−	7.23990i		−	0.293376i
$610$		0			0
$611$	−0.721545	+	0.416584i	−0.0291906	+	0.0168532i
$612$	−3.32729	+	0.891544i	−0.134498	+	0.0360385i
$613$	−33.8183	−	9.06158i	−1.36591	−	0.365994i	−0.499925	−	0.866069i	$-0.666639\pi$
$613$	−33.8183	−	9.06158i	−1.36591	−	0.365994i	−0.865982	+	0.500075i	$0.833306\pi$
$614$	−7.94364	−	4.58626i	−0.320579	−	0.185086i
$615$		0			0
$616$		−	12.7705i		−	0.514538i
$617$	−13.4909	+	3.61488i	−0.543123	+	0.145529i	−0.519942	−	0.854202i	$-0.674046\pi$
$617$	−13.4909	+	3.61488i	−0.543123	+	0.145529i	−0.0231816	+	0.999731i	$0.507380\pi$
$618$	20.9730	−	5.61970i	0.843657	−	0.226057i
$619$			9.51669i			0.382508i	0.981541	+	0.191254i	$0.0612554\pi$
$619$			9.51669i			0.382508i	−0.981541	+	0.191254i	$0.938745\pi$
$620$		0			0
$621$	37.6863	+	21.7582i	1.51230	+	0.873126i
$622$	6.59148	+	1.76618i	0.264294	+	0.0708174i
$623$	1.41321	−	0.378669i	0.0566191	−	0.0151710i
$624$	−1.80047	+	1.03950i	−0.0720764	+	0.0416133i
$625$		0			0
$626$			14.1024i			0.563645i
$627$	−32.4598	−	11.9523i	−1.29632	−	0.477327i
$628$	6.63010	−	6.63010i	0.264570	−	0.264570i
$629$	−9.48822	−	16.4341i	−0.378320	−	0.655270i
$630$		0			0
$631$	−11.1141	+	19.2502i	−0.442445	+	0.766338i	−0.997870	−	0.0652289i	$-0.979222\pi$
$631$	−11.1141	+	19.2502i	−0.442445	+	0.766338i	0.555425	+	0.831567i	$0.312556\pi$
$632$	1.71985	−	6.41856i	0.0684119	−	0.255317i
$633$	−5.50900	−	20.5599i	−0.218963	−	0.817181i
$634$		−	17.0002i		−	0.675166i
$635$		0			0
$636$	−1.57935	+	2.73551i	−0.0626251	+	0.108470i
$637$	1.06167	+	3.96222i	0.0420650	+	0.156989i
$638$	−11.3149	+	11.3149i	−0.447962	+	0.447962i
$639$	5.46846			0.216329
$640$		0			0
$641$	−7.67289	+	4.42994i	−0.303061	+	0.174972i	−0.643817	−	0.765179i	$-0.722650\pi$
$641$	−7.67289	+	4.42994i	−0.303061	+	0.174972i	0.340756	+	0.940152i	$0.389317\pi$
$642$	−4.66729	−	17.4186i	−0.184203	−	0.687456i
$643$	37.8519	+	10.1424i	1.49273	+	0.399977i	0.910659	−	0.413159i	$-0.135575\pi$
$643$	37.8519	+	10.1424i	1.49273	+	0.399977i	0.582075	+	0.813135i	$0.302241\pi$
$644$	14.1285	−	8.15708i	0.556740	−	0.321434i
$645$		0			0
$646$	9.49054	+	6.69846i	0.373400	+	0.263547i
$647$	−21.5139	−	21.5139i	−0.845797	−	0.845797i	0.143809	−	0.989606i	$-0.454065\pi$
$647$	−21.5139	−	21.5139i	−0.845797	−	0.845797i	−0.989606	+	0.143809i	$0.954065\pi$
$648$	−0.893332	+	3.33396i	−0.0350934	+	0.130970i
$649$	−19.4804	−	33.7411i	−0.764674	−	1.32445i
$650$		0			0
$651$	11.7244	+	20.3072i	0.459515	+	0.795903i
$652$	−11.9831	+	3.21087i	−0.469296	+	0.125747i
$653$	12.8479	−	12.8479i	0.502776	−	0.502776i	−0.409523	−	0.912300i	$-0.634305\pi$
$653$	12.8479	−	12.8479i	0.502776	−	0.502776i	0.912300	+	0.409523i	$0.134305\pi$
$654$	−13.9756			−0.546488
$655$		0			0
$656$	−5.76903	−	3.33075i	−0.225243	−	0.130044i
$657$	3.03453	+	3.03453i	0.118388	+	0.118388i
$658$	0.778638	+	0.778638i	0.0303545	+	0.0303545i
$659$	−23.5321	+	40.7588i	−0.916681	+	1.58774i	−0.112260	+	0.993679i	$0.535809\pi$
$659$	−23.5321	+	40.7588i	−0.916681	+	1.58774i	−0.804421	+	0.594060i	$0.797524\pi$
$660$		0			0
$661$	−23.4662	−	13.5482i	−0.912730	−	0.526965i	−0.0314216	−	0.999506i	$-0.510003\pi$
$661$	−23.4662	−	13.5482i	−0.912730	−	0.526965i	−0.881309	+	0.472541i	$0.843337\pi$
$662$	−8.88055	+	33.1427i	−0.345152	+	1.28813i
$663$	−5.35170	−	1.43398i	−0.207843	−	0.0556913i
$664$	1.03655			0.0402260
$665$		0			0
$666$	9.20396			0.356646
$667$	−19.7455	−	5.29078i	−0.764548	−	0.204860i
$668$	3.88279	−	14.4908i	0.150230	−	0.560665i
$669$	−11.7703	−	6.79558i	−0.455066	−	0.262732i
$670$		0			0
$671$	45.5046	−	78.8164i	1.75669	−	3.04267i
$672$	1.94293	+	1.94293i	0.0749503	+	0.0749503i
$673$	13.9554	+	13.9554i	0.537941	+	0.537941i	0.922924	−	0.384983i	$-0.125793\pi$
$673$	13.9554	+	13.9554i	0.537941	+	0.537941i	−0.384983	+	0.922924i	$0.625793\pi$
$674$	−28.0140	−	16.1739i	−1.07906	−	0.622994i
$675$		0			0
$676$	−10.4686			−0.402637
$677$	25.0198	−	25.0198i	0.961590	−	0.961590i	−0.0376990	−	0.999289i	$-0.512003\pi$
$677$	25.0198	−	25.0198i	0.961590	−	0.961590i	0.999289	+	0.0376990i	$0.0120028\pi$
$678$	−11.0263	+	2.95450i	−0.423464	+	0.113467i
$679$	−1.10503	−	1.91396i	−0.0424070	−	0.0734510i
$680$		0			0
$681$	1.83400	+	3.17659i	0.0702791	+	0.121727i
$682$	13.4137	−	50.0608i	0.513639	−	1.91693i
$683$	36.2789	+	36.2789i	1.38817	+	1.38817i	0.829155	+	0.559019i	$0.188822\pi$
$683$	36.2789	+	36.2789i	1.38817	+	1.38817i	0.559019	+	0.829155i	$0.311178\pi$
$684$	−5.11517	+	2.36196i	−0.195584	+	0.0903119i
$685$		0			0
$686$	17.4427	−	10.0706i	0.665966	−	0.384496i
$687$	−33.8697	−	9.07536i	−1.29221	−	0.346246i
$688$	0.566652	+	2.11477i	0.0216034	+	0.0806249i
$689$	3.33080	−	1.92304i	0.126894	−	0.0732620i
$690$		0			0
$691$	−10.5724			−0.402194			−0.201097	−	0.979571i	$-0.564451\pi$
$691$	−10.5724			−0.402194			−0.201097	+	0.979571i	$0.564451\pi$
$692$	−10.9515	+	10.9515i	−0.416314	+	0.416314i
$693$	4.27225	+	15.9443i	0.162289	+	0.605672i
$694$	−2.52653	+	4.37608i	−0.0959059	+	0.166114i
$695$		0			0
$696$		−	3.44296i		−	0.130505i
$697$	−4.59475	−	17.1478i	−0.174039	−	0.649521i
$698$	7.50963	−	28.0263i	0.284244	−	1.06081i
$699$	2.72873	−	4.72630i	0.103210	−	0.178765i
$700$		0			0
$701$	−17.3425	−	30.0381i	−0.655018	−	1.13453i	−0.981889	−	0.189456i	$-0.939328\pi$
$701$	−17.3425	−	30.0381i	−0.655018	−	1.13453i	0.326871	−	0.945069i	$-0.394006\pi$
$702$	6.31040	−	6.31040i	0.238171	−	0.238171i
$703$	−19.8619	−	23.8513i	−0.749105	−	0.899569i
$704$		−	6.07305i		−	0.228887i
$705$		0			0
$706$	22.9291	−	13.2381i	0.862949	−	0.498224i
$707$	13.5181	−	3.62218i	0.508402	−	0.136226i
$708$	8.09725	+	2.16965i	0.304313	+	0.0815405i
$709$	26.0474	+	15.0385i	0.978232	+	0.564783i	0.901736	−	0.432287i	$-0.142293\pi$
$709$	26.0474	+	15.0385i	0.978232	+	0.564783i	0.0764963	+	0.997070i	$0.475627\pi$
$710$		0			0
$711$			8.58908i			0.322116i
$712$	0.672057	−	0.180077i	0.0251864	−	0.00674867i
$713$	63.9521	−	17.1359i	2.39503	−	0.641745i
$714$			7.32261i			0.274042i
$715$		0			0
$716$	1.49117	+	0.860925i	0.0557275	+	0.0321743i
$717$	−16.2821	−	4.36278i	−0.608066	−	0.162931i
$718$	14.0447	−	3.76326i	0.524143	−	0.140444i
$719$	7.91608	−	4.57035i	0.295220	−	0.170445i	−0.345074	−	0.938576i	$-0.612146\pi$
$719$	7.91608	−	4.57035i	0.295220	−	0.170445i	0.640294	+	0.768130i	$0.278813\pi$
$720$		0			0
$721$			34.9418i			1.30130i
$722$	17.1592	+	8.15850i	0.638600	+	0.303628i
$723$	8.35278	−	8.35278i	0.310643	−	0.310643i
$724$	−4.50134	−	7.79655i	−0.167291	−	0.289757i
$725$		0			0
$726$	−16.9098	+	29.2886i	−0.627580	+	1.08700i
$727$	5.23921	−	19.5530i	0.194312	−	0.725181i	−0.798132	−	0.602482i	$-0.794178\pi$
$727$	5.23921	−	19.5530i	0.194312	−	0.725181i	0.992444	−	0.122699i	$-0.0391549\pi$
$728$	−0.865925	−	3.23168i	−0.0320933	−	0.119774i
$729$		−	26.4492i		−	0.979600i
$730$		0			0
$731$	−2.91731	+	5.05293i	−0.107901	+	0.186890i
$732$	5.06812	+	18.9145i	0.187323	+	0.699100i
$733$	−34.1007	+	34.1007i	−1.25954	+	1.25954i	−0.308223	+	0.951314i	$0.599734\pi$
$733$	−34.1007	+	34.1007i	−1.25954	+	1.25954i	−0.951314	+	0.308223i	$0.900266\pi$
$734$	13.0194			0.480554
$735$		0			0
$736$	6.71884	−	3.87913i	0.247660	−	0.142986i
$737$	17.9358	+	66.9374i	0.660674	+	2.46567i
$738$	8.31705	+	2.22855i	0.306155	+	0.0820339i
$739$	18.8096	−	10.8597i	0.691923	−	0.399482i	−0.112409	−	0.993662i	$-0.535857\pi$
$739$	18.8096	−	10.8597i	0.691923	−	0.399482i	0.804332	+	0.594180i	$0.202523\pi$
$740$		0			0
$741$	−9.02466	−	0.823623i	−0.331529	−	0.0302566i
$742$	−3.59436	−	3.59436i	−0.131953	−	0.131953i
$743$	−2.62745	+	9.80579i	−0.0963920	+	0.359740i	−0.997227	−	0.0744222i	$-0.976289\pi$
$743$	−2.62745	+	9.80579i	−0.0963920	+	0.359740i	0.900835	+	0.434162i	$0.142955\pi$
$744$	5.57557	+	9.65717i	0.204410	+	0.354049i
$745$		0			0
$746$	−1.91363	−	3.31451i	−0.0700631	−	0.121353i
$747$	−1.29416	+	0.346769i	−0.0473508	+	0.0126876i
$748$	11.4442	−	11.4442i	0.418441	−	0.418441i
$749$	29.0200			1.06037
$750$		0			0
$751$	37.0699	+	21.4023i	1.35270	+	0.780981i	0.988627	−	0.150389i	$-0.0480527\pi$
$751$	37.0699	+	21.4023i	1.35270	+	0.780981i	0.364073	+	0.931371i	$0.381386\pi$
$752$	0.370284	+	0.370284i	0.0135029	+	0.0135029i
$753$	9.87850	+	9.87850i	0.359992	+	0.359992i
$754$	−2.09611	+	3.63056i	−0.0763357	+	0.132217i
$755$		0			0
$756$	−10.2146	−	5.89739i	−0.371501	−	0.214486i
$757$	−3.11932	+	11.6415i	−0.113374	+	0.423116i	−0.999160	−	0.0409770i	$-0.986953\pi$
$757$	−3.11932	+	11.6415i	−0.113374	+	0.423116i	0.885787	+	0.464093i	$0.153620\pi$
$758$	12.1263	+	3.24924i	0.440449	+	0.118018i
$759$	−61.5662			−2.23471
$760$		0			0
$761$	32.0124			1.16045			0.580225	−	0.814456i	$-0.302965\pi$
$761$	32.0124			1.16045			0.580225	+	0.814456i	$0.302965\pi$
$762$	−6.40739	−	1.71686i	−0.232115	−	0.0621951i
$763$	5.82097	−	21.7241i	0.210733	−	0.786467i
$764$	−13.2034	−	7.62297i	−0.477681	−	0.275789i
$765$		0			0
$766$	−2.06120	+	3.57010i	−0.0744742	+	0.128993i
$767$	−7.21755	−	7.21755i	−0.260611	−	0.260611i
$768$	0.923968	+	0.923968i	0.0333408	+	0.0333408i
$769$	7.17526	+	4.14264i	0.258746	+	0.149387i	0.623763	−	0.781614i	$-0.285603\pi$
$769$	7.17526	+	4.14264i	0.258746	+	0.149387i	−0.365016	+	0.931001i	$0.618937\pi$
$770$		0			0
$771$	−35.6642			−1.28441
$772$	6.73312	−	6.73312i	0.242330	−	0.242330i
$773$	−18.2832	+	4.89897i	−0.657601	+	0.176204i	−0.572163	−	0.820140i	$-0.693896\pi$
$773$	−18.2832	+	4.89897i	−0.657601	+	0.176204i	−0.0854376	+	0.996344i	$0.527229\pi$
$774$	−1.41496	−	2.45078i	−0.0508595	−	0.0880913i
$775$		0			0
$776$	−0.525498	−	0.910190i	−0.0188643	−	0.0326739i
$777$	5.06397	−	18.8990i	0.181669	−	0.677997i
$778$	15.4011	+	15.4011i	0.552157	+	0.552157i
$779$	−12.1728	−	26.3621i	−0.436138	−	0.944519i
$780$		0			0
$781$	−22.2510	+	12.8466i	−0.796202	+	0.459688i
$782$	19.9710	+	5.35123i	0.714163	+	0.191359i
$783$	3.82512	+	14.2755i	0.136699	+	0.510166i
$784$	2.23276	−	1.28909i	0.0797415	−	0.0460388i
$785$		0			0
$786$	6.34779			0.226418
$787$	−2.47487	+	2.47487i	−0.0882195	+	0.0882195i	−0.749839	−	0.661620i	$-0.769869\pi$
$787$	−2.47487	+	2.47487i	−0.0882195	+	0.0882195i	0.661620	+	0.749839i	$0.269869\pi$
$788$	−3.27977	−	12.2402i	−0.116837	−	0.436041i
$789$	−0.622979	+	1.07903i	−0.0221786	+	0.0384145i
$790$		0			0
$791$		−	18.3703i		−	0.653174i
$792$	2.03168	+	7.58234i	0.0721927	+	0.269427i
$793$	6.17104	−	23.0306i	0.219140	−	0.817842i
$794$	10.4593	−	18.1160i	0.371186	−	0.642912i
$795$		0			0
$796$	−3.97241	−	6.88042i	−0.140798	−	0.243870i
$797$	6.23173	−	6.23173i	0.220739	−	0.220739i	−0.588070	−	0.808810i	$-0.700112\pi$
$797$	6.23173	−	6.23173i	0.220739	−	0.220739i	0.808810	+	0.588070i	$0.200112\pi$
$798$	2.03560	+	11.8028i	0.0720596	+	0.417814i
$799$			1.39554i			0.0493707i
$800$		0			0
$801$	−0.778836	+	0.449661i	−0.0275188	+	0.0158880i
$802$	−17.7420	+	4.75395i	−0.626491	+	0.167868i
$803$	−19.4762	−	5.21862i	−0.687299	−	0.184161i
$804$	−12.9128	−	7.45522i	−0.455400	−	0.262925i
$805$		0			0
$806$		−	13.5778i		−	0.478259i
$807$	30.8688	−	8.27128i	1.08663	−	0.291163i
$808$	6.42860	−	1.72254i	0.226157	−	0.0605986i
$809$		−	44.2611i		−	1.55614i	−0.628180	−	0.778068i	$-0.716200\pi$
$809$		−	44.2611i		−	1.55614i	0.628180	−	0.778068i	$-0.283800\pi$
$810$		0			0
$811$	45.6623	+	26.3631i	1.60342	+	0.925735i	0.990797	+	0.135359i	$0.0432189\pi$
$811$	45.6623	+	26.3631i	1.60342	+	0.925735i	0.612623	+	0.790375i	$0.290114\pi$
$812$	5.35186	+	1.43403i	0.187813	+	0.0503245i
$813$	−19.3614	+	5.18786i	−0.679033	+	0.181946i
$814$	−37.4506	+	21.6221i	−1.31264	+	0.757855i
$815$		0			0
$816$			3.48229i			0.121905i
$817$	−3.29755	+	8.95544i	−0.115367	+	0.313311i
$818$	−9.34546	+	9.34546i	−0.326757	+	0.326757i
$819$	2.16226	+	3.74514i	0.0755554	+	0.130866i
$820$		0			0
$821$	10.0032	−	17.3260i	0.349113	−	0.604682i	−0.636979	−	0.770881i	$-0.719816\pi$
$821$	10.0032	−	17.3260i	0.349113	−	0.604682i	0.986092	+	0.166199i	$0.0531495\pi$
$822$	5.32047	−	19.8563i	0.185573	−	0.692567i
$823$	10.1795	+	37.9903i	0.354834	+	1.32426i	0.880693	+	0.473687i	$0.157077\pi$
$823$	10.1795	+	37.9903i	0.354834	+	1.32426i	−0.525859	+	0.850572i	$0.676256\pi$
$824$			16.6167i			0.578870i
$825$		0			0
$826$	−6.74517	+	11.6830i	−0.234694	+	0.406503i
$827$	−0.812556	−	3.03250i	−0.0282553	−	0.105450i	0.950358	−	0.311158i	$-0.100717\pi$
$827$	−0.812556	−	3.03250i	−0.0282553	−	0.105450i	−0.978613	+	0.205708i	$0.934050\pi$
$828$	−7.09091	+	7.09091i	−0.246426	+	0.246426i
$829$	−2.77840			−0.0964977			−0.0482488	−	0.998835i	$-0.515364\pi$
$829$	−2.77840			−0.0964977			−0.0482488	+	0.998835i	$0.515364\pi$
$830$		0			0
$831$	−12.4991	+	7.21638i	−0.433590	+	0.250333i
$832$	−0.411793	−	1.53683i	−0.0142764	−	0.0532801i
$833$	6.63665	+	1.77828i	0.229946	+	0.0616139i
$834$	10.9823	−	6.34066i	0.380288	−	0.219559i
$835$		0			0
$836$	15.2647	−	21.6274i	0.527941	−	0.748000i
$837$	−33.8471	−	33.8471i	−1.16993	−	1.16993i
$838$	1.52804	−	5.70274i	0.0527854	−	0.196998i
$839$	13.5941	+	23.5457i	0.469321	+	0.812887i	0.999385	−	0.0350703i	$-0.0111655\pi$
$839$	13.5941	+	23.5457i	0.469321	+	0.812887i	−0.530064	+	0.847958i	$0.677832\pi$
$840$		0			0
$841$	11.0287	+	19.1023i	0.380301	+	0.658700i
$842$	−6.31178	+	1.69124i	−0.217518	+	0.0582838i
$843$	20.3947	−	20.3947i	0.702431	−	0.702431i
$844$	16.2894			0.560704
$845$		0			0
$846$	−0.586183	−	0.338433i	−0.0201534	−	0.0116356i
$847$	−38.4841	−	38.4841i	−1.32233	−	1.32233i
$848$	−1.70931	−	1.70931i	−0.0586979	−	0.0586979i
$849$	6.93959	−	12.0197i	0.238166	−	0.412516i
$850$		0			0
$851$	−47.8428	−	27.6220i	−1.64003	−	0.946871i
$852$	1.43080	−	5.33983i	0.0490185	−	0.182940i
$853$	−38.1515	−	10.2227i	−1.30628	−	0.350017i	−0.462460	−	0.886640i	$-0.653033\pi$
$853$	−38.1515	−	10.2227i	−1.30628	−	0.350017i	−0.843822	+	0.536622i	$0.819700\pi$
$854$	−31.5123			−1.07833
$855$		0			0
$856$	13.8006			0.471694
$857$	−19.8056	−	5.30690i	−0.676547	−	0.181280i	−0.0958450	−	0.995396i	$-0.530555\pi$
$857$	−19.8056	−	5.30690i	−0.676547	−	0.181280i	−0.580702	+	0.814116i	$0.697222\pi$
$858$	−3.26782	+	12.1957i	−0.111561	+	0.416353i
$859$	−19.9019	−	11.4904i	−0.679043	−	0.392046i	0.120451	−	0.992719i	$-0.461566\pi$
$859$	−19.9019	−	11.4904i	−0.679043	−	0.392046i	−0.799494	+	0.600673i	$0.794899\pi$
$860$		0			0
$861$	9.15198	−	15.8517i	0.311899	−	0.540224i
$862$	15.0069	+	15.0069i	0.511136	+	0.511136i
$863$	−34.0671	−	34.0671i	−1.15966	−	1.15966i	−0.984549	−	0.175108i	$-0.943973\pi$
$863$	−34.0671	−	34.0671i	−1.15966	−	1.15966i	−0.175108	−	0.984549i	$-0.556027\pi$
$864$	−4.85758	−	2.80452i	−0.165258	−	0.0954118i
$865$		0			0
$866$	−13.0792			−0.444450
$867$	9.14535	−	9.14535i	0.310592	−	0.310592i
$868$	−17.3337	+	4.64456i	−0.588345	+	0.157647i
$869$	−20.1776	−	34.9487i	−0.684479	−	1.18555i
$870$		0			0
$871$	9.07761	+	15.7229i	0.307583	+	0.532750i
$872$	2.76818	−	10.3310i	0.0937424	−	0.349851i
$873$	0.960593	+	0.960593i	0.0325111	+	0.0325111i
$874$	33.6775	+	3.07353i	1.13916	+	0.103964i
$875$		0			0
$876$	3.75712	−	2.16918i	0.126941	−	0.0732897i
$877$	9.18427	+	2.46092i	0.310131	+	0.0830993i	0.410528	−	0.911848i	$-0.365345\pi$
$877$	9.18427	+	2.46092i	0.310131	+	0.0830993i	−0.100397	+	0.994947i	$0.532011\pi$
$878$	−5.04687	−	18.8352i	−0.170324	−	0.635656i
$879$	9.98444	−	5.76452i	0.336767	−	0.194432i
$880$		0			0
$881$	42.3187			1.42575			0.712876	−	0.701290i	$-0.247392\pi$
$881$	42.3187			1.42575			0.712876	+	0.701290i	$0.247392\pi$
$882$	−2.35640	+	2.35640i	−0.0793443	+	0.0793443i
$883$	4.86403	+	18.1528i	0.163688	+	0.610891i	0.998204	+	0.0599076i	$0.0190806\pi$
$883$	4.86403	+	18.1528i	0.163688	+	0.610891i	−0.834516	+	0.550983i	$0.814253\pi$
$884$	2.12005	−	3.67204i	0.0713050	−	0.123504i
$885$		0			0
$886$		−	29.7087i		−	0.998083i
$887$	0.344987	+	1.28751i	0.0115835	+	0.0432303i	0.971476	−	0.237139i	$-0.0762097\pi$
$887$	0.344987	+	1.28751i	0.0115835	+	0.0432303i	−0.959892	+	0.280369i	$0.909543\pi$
$888$	2.40818	−	8.98747i	0.0808134	−	0.301600i
$889$	5.33749	−	9.24480i	0.179014	−	0.310061i
$890$		0			0
$891$	10.4808	+	18.1532i	0.351119	+	0.608156i
$892$	7.35479	−	7.35479i	0.246256	−	0.246256i
$893$	0.387945	+	2.24937i	0.0129821	+	0.0752724i
$894$		−	6.16770i		−	0.206279i
$895$		0			0
$896$	−1.82109	+	1.05141i	−0.0608384	+	0.0351251i
$897$	−15.5798	+	4.17460i	−0.520195	+	0.139386i
$898$	27.3462	+	7.32740i	0.912556	+	0.244519i
$899$	19.4732	+	11.2429i	0.649469	+	0.374971i
$900$		0			0
$901$		−	6.44212i		−	0.214618i
$902$	−39.0771	+	10.4707i	−1.30113	+	0.348636i
$903$	−5.81081	+	1.55700i	−0.193372	+	0.0518137i
$904$		−	8.73607i		−	0.290557i
$905$		0			0
$906$	6.43285	+	3.71401i	0.213717	+	0.123390i
$907$	−17.3973	−	4.66158i	−0.577666	−	0.154785i	−0.0418560	−	0.999124i	$-0.513327\pi$
$907$	−17.3973	−	4.66158i	−0.577666	−	0.154785i	−0.535810	+	0.844338i	$0.679994\pi$
$908$	−2.71145	+	0.726531i	−0.0899827	+	0.0241108i
$909$	−7.45000	+	4.30126i	−0.247101	+	0.142664i
$910$		0			0
$911$			29.0987i			0.964083i	0.876148	+	0.482042i	$0.160105\pi$
$911$			29.0987i			0.964083i	−0.876148	+	0.482042i	$0.839895\pi$
$912$	0.968038	+	5.61285i	0.0320549	+	0.185860i
$913$	4.45125	−	4.45125i	0.147315	−	0.147315i
$914$	−3.98969	−	6.91034i	−0.131967	−	0.228574i
$915$		0			0
$916$	13.4173	−	23.2395i	0.443321	−	0.767854i
$917$	−2.64392	+	9.86723i	−0.0873099	+	0.325845i
$918$	−3.86882	−	14.4386i	−0.127690	−	0.476546i
$919$			2.40207i			0.0792369i	0.999215	+	0.0396185i	$0.0126142\pi$
$919$			2.40207i			0.0792369i	−0.999215	+	0.0396185i	$0.987386\pi$
$920$		0			0
$921$	5.99281	−	10.3799i	0.197470	−	0.342028i
$922$	4.06333	+	15.1645i	0.133819	+	0.499418i
$923$	−4.75970	+	4.75970i	−0.156668	+	0.156668i
$924$	16.6870			0.548963
$925$		0			0
$926$	26.3007	−	15.1847i	0.864296	−	0.499001i
$927$	−5.55897	−	20.7463i	−0.182580	−	0.681399i
$928$	2.54509	+	0.681956i	0.0835468	+	0.0223863i
$929$	42.0317	−	24.2670i	1.37901	−	0.796175i	0.386974	−	0.922091i	$-0.373520\pi$
$929$	42.0317	−	24.2670i	1.37901	−	0.796175i	0.992041	+	0.125916i	$0.0401870\pi$
$930$		0			0
$931$	11.1915	+	1.02138i	0.366786	+	0.0334742i
$932$	2.95328	+	2.95328i	0.0967378	+	0.0967378i
$933$	−2.30785	+	8.61300i	−0.0755555	+	0.281977i
$934$	−7.49460	−	12.9810i	−0.245231	−	0.424752i
$935$		0			0
$936$	1.02827	+	1.78101i	0.0336100	+	0.0582142i
$937$	−9.40919	+	2.52118i	−0.307385	+	0.0823635i	−0.409214	−	0.912438i	$-0.634197\pi$
$937$	−9.40919	+	2.52118i	−0.307385	+	0.0823635i	0.101829	+	0.994802i	$0.467530\pi$
$938$	16.9670	−	16.9670i	0.553991	−	0.553991i
$939$	−18.4274			−0.601356
$940$		0			0
$941$	−36.7450	−	21.2147i	−1.19785	−	0.691580i	−0.237776	−	0.971320i	$-0.576418\pi$
$941$	−36.7450	−	21.2147i	−1.19785	−	0.691580i	−0.960076	+	0.279740i	$0.909752\pi$
$942$	8.66347	+	8.66347i	0.282271	+	0.282271i
$943$	−36.5444	−	36.5444i	−1.19005	−	1.19005i
$944$	−3.20769	+	5.55588i	−0.104401	+	0.180828i
$945$		0			0
$946$	11.5148	+	6.64808i	0.374379	+	0.216148i
$947$	−4.95615	+	18.4966i	−0.161053	+	0.601058i	0.837458	+	0.546502i	$0.184041\pi$
$947$	−4.95615	+	18.4966i	−0.161053	+	0.601058i	−0.998511	+	0.0545561i	$0.982626\pi$
$948$	8.38705	+	2.24730i	0.272399	+	0.0729890i
$949$	−5.28246			−0.171476
$950$		0			0
$951$	22.2140			0.720339
$952$	−5.41300	−	1.45041i	−0.175436	−	0.0470080i
$953$	15.7273	−	58.6949i	0.509456	−	1.90131i	0.0836613	−	0.996494i	$-0.473339\pi$
$953$	15.7273	−	58.6949i	0.509456	−	1.90131i	0.425794	−	0.904820i	$-0.359995\pi$
$954$	2.70595	+	1.56228i	0.0876082	+	0.0505806i
$955$		0			0
$956$	6.45008	−	11.1719i	0.208610	−	0.361324i
$957$	−14.7851	−	14.7851i	−0.477933	−	0.477933i
$958$	−19.0598	−	19.0598i	−0.615793	−	0.615793i
$959$	28.6493	+	16.5407i	0.925134	+	0.534126i
$960$		0			0
$961$	−41.8274			−1.34927
$962$	−8.01106	+	8.01106i	−0.258287	+	0.258287i
$963$	−17.2303	+	4.61686i	−0.555240	+	0.148776i
$964$	4.52006	+	7.82897i	0.145581	+	0.252154i
$965$		0			0
$966$	10.6588	+	18.4615i	0.342940	+	0.593989i
$967$	−11.9185	+	44.4804i	−0.383273	+	1.43039i	0.457598	+	0.889159i	$0.348710\pi$
$967$	−11.9185	+	44.4804i	−0.383273	+	1.43039i	−0.840871	+	0.541236i	$0.817957\pi$
$968$	−18.3013	−	18.3013i	−0.588225	−	0.588225i
$969$	−8.75279	+	12.4012i	−0.281180	+	0.398383i
$970$		0			0
$971$	−48.8463	+	28.2014i	−1.56755	+	0.905027i	−0.571100	+	0.820880i	$0.693483\pi$
$971$	−48.8463	+	28.2014i	−1.56755	+	0.905027i	−0.996453	+	0.0841471i	$0.973183\pi$
$972$	11.8973	+	3.18788i	0.381607	+	0.102251i
$973$	5.28190	+	19.7123i	0.169330	+	0.631948i
$974$	−13.8590	+	8.00151i	−0.444072	+	0.256385i
$975$		0			0
$976$	−14.9858			−0.479683
$977$	−1.83920	+	1.83920i	−0.0588413	+	0.0588413i	−0.735915	−	0.677074i	$-0.763248\pi$
$977$	−1.83920	+	1.83920i	−0.0588413	+	0.0588413i	0.677074	+	0.735915i	$0.263248\pi$
$978$	−4.19560	−	15.6582i	−0.134161	−	0.500694i
$979$	2.11270	−	3.65931i	0.0675223	−	0.116952i
$980$		0			0
$981$			13.8246i			0.441384i
$982$	−6.34759	−	23.6895i	−0.202560	−	0.755963i
$983$	−8.76918	+	32.7270i	−0.279694	+	1.04383i	0.672937	+	0.739700i	$0.265033\pi$
$983$	−8.76918	+	32.7270i	−0.279694	+	1.04383i	−0.952630	+	0.304131i	$0.901634\pi$
$984$	4.35225	−	7.53832i	0.138745	−	0.240313i
$985$		0			0
$986$	3.51094	+	6.08112i	0.111811	+	0.193662i
$987$	−1.01744	+	1.01744i	−0.0323854	+	0.0323854i
$988$	2.39637	−	6.50804i	0.0762388	−	0.207048i
$989$			16.9857i			0.540114i
$990$		0			0
$991$	−21.2885	+	12.2909i	−0.676251	+	0.390434i	−0.798441	−	0.602073i	$-0.794342\pi$
$991$	−21.2885	+	12.2909i	−0.676251	+	0.390434i	0.122190	+	0.992507i	$0.461008\pi$
$992$	−8.24311	+	2.20874i	−0.261719	+	0.0701274i
$993$	−43.3071	−	11.6041i	−1.37431	−	0.368245i
$994$	7.70448	+	4.44818i	0.244371	+	0.141088i
$995$		0			0
$996$			1.35445i			0.0429174i
$997$	8.56348	−	2.29458i	0.271208	−	0.0726700i	−0.120652	−	0.992695i	$-0.538498\pi$
$997$	8.56348	−	2.29458i	0.271208	−	0.0726700i	0.391860	+	0.920025i	$0.371832\pi$
$998$	−31.1344	+	8.34244i	−0.985542	+	0.264075i
$999$			39.9402i			1.26365i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.q.g.107.3		32
5.2	odd	4		190.2.m.b.183.6	yes	32
5.3	odd	4	inner	950.2.q.g.943.3		32
5.4	even	2		190.2.m.b.107.6	yes	32
19.8	odd	6	inner	950.2.q.g.407.3		32
95.8	even	12	inner	950.2.q.g.293.3		32
95.27	even	12		190.2.m.b.103.6	yes	32
95.84	odd	6		190.2.m.b.27.6	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.m.b.27.6	✓	32	95.84	odd	6
190.2.m.b.103.6	yes	32	95.27	even	12
190.2.m.b.107.6	yes	32	5.4	even	2
190.2.m.b.183.6	yes	32	5.2	odd	4
950.2.q.g.107.3		32	1.1	even	1	trivial
950.2.q.g.293.3		32	95.8	even	12	inner
950.2.q.g.407.3		32	19.8	odd	6	inner
950.2.q.g.943.3		32	5.3	odd	4	inner

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.q (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.338196 - 1.26216i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.653344 + 1.13162i) q^{6} +(-1.48691 - 1.48691i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.11940 + 0.646284i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.338196 - 1.26216i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.653344 + 1.13162i) q^{6} +(-1.48691 - 1.48691i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.11940 + 0.646284i) q^{9} -6.07305 q^{11} +(0.923968 - 0.923968i) q^{12} +(-1.53683 + 0.411793i) q^{13} +(1.05141 + 1.82109i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.689746 + 2.57417i) q^{17} +(-0.913983 - 0.913983i) q^{18} +(-0.396163 + 4.34086i) q^{19} +(-2.37960 + 1.37386i) q^{21} +(5.86611 + 1.57182i) q^{22} +(2.00798 + 7.49390i) q^{23} +(-1.13162 + 0.653344i) q^{24} +1.59105 q^{26} +(3.96619 - 3.96619i) q^{27} +(-0.544248 - 2.03116i) q^{28} +(-1.31744 + 2.28187i) q^{29} -8.53390i q^{31} +(-0.258819 - 0.965926i) q^{32} +(-2.05388 + 7.66518i) q^{33} +(1.33249 - 2.30794i) q^{34} +(0.646284 + 1.11940i) q^{36} +(-5.03508 + 5.03508i) q^{37} +(1.50616 - 4.09041i) q^{38} +2.07900i q^{39} +(-5.76903 + 3.33075i) q^{41} +(2.65410 - 0.711163i) q^{42} +(2.11477 + 0.566652i) q^{43} +(-5.25941 - 3.03652i) q^{44} -7.75825i q^{46} +(0.505817 - 0.135533i) q^{47} +(1.26216 - 0.338196i) q^{48} -2.57817i q^{49} +(3.01575 + 1.74115i) q^{51} +(-1.53683 - 0.411793i) q^{52} +(-2.33496 + 0.625650i) q^{53} +(-4.85758 + 2.80452i) q^{54} +2.10281i q^{56} +(5.34489 + 1.96808i) q^{57} +(1.86314 - 1.86314i) q^{58} +(3.20769 + 5.55588i) q^{59} +(-7.49289 + 12.9781i) q^{61} +(-2.20874 + 8.24311i) q^{62} +(-0.703478 - 2.62541i) q^{63} +1.00000i q^{64} +(3.96779 - 6.87241i) q^{66} +(-2.95335 - 11.0220i) q^{67} +(-1.88442 + 1.88442i) q^{68} +10.1376 q^{69} +(3.66389 - 2.11535i) q^{71} +(-0.334541 - 1.24852i) q^{72} +(3.20699 + 0.859309i) q^{73} +(6.16669 - 3.56034i) q^{74} +(-2.51352 + 3.56121i) q^{76} +(9.03010 + 9.03010i) q^{77} +(0.538085 - 2.00816i) q^{78} +(3.32249 + 5.75472i) q^{79} +(-1.72578 - 2.98915i) q^{81} +(6.43452 - 1.72412i) q^{82} +(-0.732952 + 0.732952i) q^{83} -2.74772 q^{84} +(-1.89605 - 1.09469i) q^{86} +(2.43454 + 2.43454i) q^{87} +(4.29429 + 4.29429i) q^{88} +(-0.347882 + 0.602549i) q^{89} +(2.89744 + 1.67284i) q^{91} +(-2.00798 + 7.49390i) q^{92} +(-10.7712 - 2.88613i) q^{93} -0.523660 q^{94} -1.30669 q^{96} +(1.01518 + 0.272018i) q^{97} +(-0.667280 + 2.49032i) q^{98} +(-6.79814 - 3.92491i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{3} - 24 q^{7}+O(q^{10}) \) 32 * q + 12 * q^3 - 24 * q^7	\( 32 q + 12 q^{3} - 24 q^{7} - 16 q^{11} - 24 q^{13} + 16 q^{16} + 8 q^{17} + 12 q^{22} - 4 q^{23} - 16 q^{26} + 12 q^{28} + 24 q^{33} - 8 q^{36} - 16 q^{38} + 24 q^{41} - 20 q^{42} + 24 q^{43} + 36 q^{47} + 12 q^{48} + 24 q^{51} - 24 q^{52} + 72 q^{53} + 24 q^{57} - 24 q^{58} - 48 q^{61} + 4 q^{62} - 16 q^{63} + 32 q^{66} - 36 q^{67} - 16 q^{68} + 24 q^{71} - 8 q^{73} + 24 q^{77} + 24 q^{78} + 56 q^{81} - 8 q^{82} - 24 q^{83} - 104 q^{87} - 24 q^{91} + 4 q^{92} - 52 q^{93} + 24 q^{97} - 72 q^{98}+O(q^{100}) \) 32 * q + 12 * q^3 - 24 * q^7 - 16 * q^11 - 24 * q^13 + 16 * q^16 + 8 * q^17 + 12 * q^22 - 4 * q^23 - 16 * q^26 + 12 * q^28 + 24 * q^33 - 8 * q^36 - 16 * q^38 + 24 * q^41 - 20 * q^42 + 24 * q^43 + 36 * q^47 + 12 * q^48 + 24 * q^51 - 24 * q^52 + 72 * q^53 + 24 * q^57 - 24 * q^58 - 48 * q^61 + 4 * q^62 - 16 * q^63 + 32 * q^66 - 36 * q^67 - 16 * q^68 + 24 * q^71 - 8 * q^73 + 24 * q^77 + 24 * q^78 + 56 * q^81 - 8 * q^82 - 24 * q^83 - 104 * q^87 - 24 * q^91 + 4 * q^92 - 52 * q^93 + 24 * q^97 - 72 * q^98

Introduction

L-functions

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