LMFDB - Embedded newform 775.2.bs.b.418.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(182,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 2]))

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

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

chi := DirichletCharacter("775.182");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.bs (of order $20$, degree $8$, 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:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 155)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			418.3
Character	$\chi$	$=$	775.418
Dual form			775.2.bs.b.432.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.261704 + 1.65234i) q^{2} +(1.16750 - 0.184914i) q^{3} +(-0.759614 - 0.246814i) q^{4} +1.97750i q^{6} +(0.837296 + 1.64328i) q^{7} +(-0.912378 + 1.79064i) q^{8} +(-1.52430 + 0.495275i) q^{9} +O(q^{10})$	\(q+(-0.261704 + 1.65234i) q^{2} +(1.16750 - 0.184914i) q^{3} +(-0.759614 - 0.246814i) q^{4} +1.97750i q^{6} +(0.837296 + 1.64328i) q^{7} +(-0.912378 + 1.79064i) q^{8} +(-1.52430 + 0.495275i) q^{9} +(-0.476097 - 0.154693i) q^{11} +(-0.932491 - 0.147692i) q^{12} +(-2.21103 + 0.350192i) q^{13} +(-2.93438 + 0.953439i) q^{14} +(-4.01230 - 2.91511i) q^{16} +(-1.38189 + 2.71212i) q^{17} +(-0.419445 - 2.64827i) q^{18} +(3.40553 + 4.68730i) q^{19} +(1.28141 + 1.76371i) q^{21} +(0.380202 - 0.746188i) q^{22} +(-2.62779 - 1.33893i) q^{23} +(-0.734088 + 2.25929i) q^{24} -3.74501i q^{26} +(-4.84770 + 2.47003i) q^{27} +(-0.230436 - 1.45492i) q^{28} +(7.02889 - 5.10678i) q^{29} +(2.18942 + 5.11922i) q^{31} +(3.02466 - 3.02466i) q^{32} +(-0.584449 - 0.0925677i) q^{33} +(-4.11969 - 2.99313i) q^{34} +1.28012 q^{36} +(3.35379 + 3.35379i) q^{37} +(-8.63624 + 4.40039i) q^{38} +(-2.51663 + 0.817701i) q^{39} +(-0.561709 + 0.408105i) q^{41} +(-3.24960 + 1.65575i) q^{42} +(-0.321623 + 2.03065i) q^{43} +(0.323469 + 0.235014i) q^{44} +(2.90006 - 3.99159i) q^{46} +(-2.34062 + 0.370717i) q^{47} +(-5.22342 - 2.66147i) q^{48} +(2.11518 - 2.91129i) q^{49} +(-1.11186 + 3.42194i) q^{51} +(1.76596 + 0.279701i) q^{52} +(2.69217 + 1.37173i) q^{53} +(-2.81265 - 8.65645i) q^{54} -3.70647 q^{56} +(4.84271 + 4.84271i) q^{57} +(6.59864 + 12.9506i) q^{58} +(-3.43500 + 4.72787i) q^{59} +12.5915i q^{61} +(-9.03166 + 2.27794i) q^{62} +(-2.09017 - 2.09017i) q^{63} +(-1.62403 - 2.23529i) q^{64} +(0.305906 - 0.941481i) q^{66} +(11.4144 - 11.4144i) q^{67} +(1.71909 - 1.71909i) q^{68} +(-3.31554 - 1.07728i) q^{69} +(-0.975703 - 3.00291i) q^{71} +(0.503877 - 3.18135i) q^{72} +(-1.01168 - 1.98553i) q^{73} +(-6.41929 + 4.66389i) q^{74} +(-1.43000 - 4.40107i) q^{76} +(-0.144429 - 0.911886i) q^{77} +(-0.692506 - 4.37231i) q^{78} +(-0.204891 - 0.630588i) q^{79} +(-1.31302 + 0.953963i) q^{81} +(-0.527326 - 1.03493i) q^{82} +(1.76911 - 11.1697i) q^{83} +(-0.538070 - 1.65601i) q^{84} +(-3.27114 - 1.06286i) q^{86} +(7.26193 - 7.26193i) q^{87} +(0.711380 - 0.711380i) q^{88} +(4.89763 - 15.0733i) q^{89} +(-2.42675 - 3.34013i) q^{91} +(1.66564 + 1.66564i) q^{92} +(3.50277 + 5.57185i) q^{93} -3.96451i q^{94} +(2.97199 - 4.09060i) q^{96} +(7.08976 + 13.9144i) q^{97} +(4.25688 + 4.25688i) q^{98} +0.802330 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 6 q^{2} + 10 q^{3} + 18 q^{7} + 20 q^{8}+O(q^{10}) $ 112 * q + 6 * q^2 + 10 * q^3 + 18 * q^7 + 20 * q^8	$ 112 q + 6 q^{2} + 10 q^{3} + 18 q^{7} + 20 q^{8} - 20 q^{11} - 10 q^{12} + 10 q^{13} - 12 q^{16} + 10 q^{17} - 4 q^{18} + 20 q^{21} - 60 q^{22} + 40 q^{27} + 48 q^{28} - 4 q^{31} - 44 q^{32} + 26 q^{33} - 64 q^{36} + 32 q^{38} - 16 q^{41} - 70 q^{42} + 10 q^{43} - 60 q^{46} - 46 q^{47} - 150 q^{48} + 12 q^{51} + 80 q^{52} - 10 q^{53} - 24 q^{56} + 10 q^{58} + 54 q^{62} + 200 q^{63} - 52 q^{66} + 68 q^{67} + 8 q^{71} + 18 q^{72} - 30 q^{73} - 128 q^{76} + 30 q^{77} - 36 q^{78} + 64 q^{81} + 44 q^{82} - 160 q^{83} - 20 q^{86} - 60 q^{91} - 10 q^{93} - 92 q^{97} - 144 q^{98}+O(q^{100}) $ 112 * q + 6 * q^2 + 10 * q^3 + 18 * q^7 + 20 * q^8 - 20 * q^11 - 10 * q^12 + 10 * q^13 - 12 * q^16 + 10 * q^17 - 4 * q^18 + 20 * q^21 - 60 * q^22 + 40 * q^27 + 48 * q^28 - 4 * q^31 - 44 * q^32 + 26 * q^33 - 64 * q^36 + 32 * q^38 - 16 * q^41 - 70 * q^42 + 10 * q^43 - 60 * q^46 - 46 * q^47 - 150 * q^48 + 12 * q^51 + 80 * q^52 - 10 * q^53 - 24 * q^56 + 10 * q^58 + 54 * q^62 + 200 * q^63 - 52 * q^66 + 68 * q^67 + 8 * q^71 + 18 * q^72 - 30 * q^73 - 128 * q^76 + 30 * q^77 - 36 * q^78 + 64 * q^81 + 44 * q^82 - 160 * q^83 - 20 * q^86 - 60 * q^91 - 10 * q^93 - 92 * q^97 - 144 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.261704	+	1.65234i	−0.185053	+	1.16838i	0.703872	+	0.710326i	$0.251453\pi$
$2$	−0.261704	+	1.65234i	−0.185053	+	1.16838i	−0.888925	+	0.458052i	$0.848547\pi$
$3$	1.16750	−	0.184914i	0.674058	−	0.106760i	0.189984	−	0.981787i	$-0.439156\pi$
$3$	1.16750	−	0.184914i	0.674058	−	0.106760i	0.484074	+	0.875027i	$0.339156\pi$
$4$	−0.759614	−	0.246814i	−0.379807	−	0.123407i
$5$		0			0
$5$		0			0
$6$			1.97750i			0.807311i
$7$	0.837296	+	1.64328i	0.316468	+	0.621103i	0.993369	−	0.114971i	$-0.0366775\pi$
$7$	0.837296	+	1.64328i	0.316468	+	0.621103i	−0.676901	+	0.736074i	$0.736677\pi$
$8$	−0.912378	+	1.79064i	−0.322574	+	0.633088i
$9$	−1.52430	+	0.495275i	−0.508100	+	0.165092i
$10$		0			0
$11$	−0.476097	−	0.154693i	−0.143549	−	0.0466418i	0.236361	−	0.971665i	$-0.424045\pi$
$11$	−0.476097	−	0.154693i	−0.143549	−	0.0466418i	−0.379910	+	0.925023i	$0.624045\pi$
$12$	−0.932491	−	0.147692i	−0.269187	−	0.0426350i
$13$	−2.21103	+	0.350192i	−0.613229	+	0.0971259i	−0.455320	−	0.890328i	$-0.650475\pi$
$13$	−2.21103	+	0.350192i	−0.613229	+	0.0971259i	−0.157909	+	0.987454i	$0.550475\pi$
$14$	−2.93438	+	0.953439i	−0.784247	+	0.254817i
$15$		0			0
$16$	−4.01230	−	2.91511i	−1.00308	−	0.728777i
$17$	−1.38189	+	2.71212i	−0.335159	+	0.657786i	−0.995663	−	0.0930367i	$-0.970343\pi$
$17$	−1.38189	+	2.71212i	−0.335159	+	0.657786i	0.660504	+	0.750822i	$0.270343\pi$
$18$	−0.419445	−	2.64827i	−0.0988642	−	0.624204i
$19$	3.40553	+	4.68730i	0.781281	+	1.07534i	0.995139	+	0.0984765i	$0.0313969\pi$
$19$	3.40553	+	4.68730i	0.781281	+	1.07534i	−0.213858	+	0.976865i	$0.568603\pi$
$20$		0			0
$21$	1.28141	+	1.76371i	0.279627	+	0.384873i
$22$	0.380202	−	0.746188i	0.0810593	−	0.159088i
$23$	−2.62779	−	1.33893i	−0.547932	−	0.279185i	0.158031	−	0.987434i	$-0.449486\pi$
$23$	−2.62779	−	1.33893i	−0.547932	−	0.279185i	−0.705963	+	0.708249i	$0.749486\pi$
$24$	−0.734088	+	2.25929i	−0.149845	+	0.461176i
$25$		0			0
$26$		−	3.74501i		−	0.734457i
$27$	−4.84770	+	2.47003i	−0.932940	+	0.475357i
$28$	−0.230436	−	1.45492i	−0.0435484	−	0.274954i
$29$	7.02889	−	5.10678i	1.30523	−	0.948306i	0.305239	−	0.952276i	$-0.401264\pi$
$29$	7.02889	−	5.10678i	1.30523	−	0.948306i	0.999992	+	0.00396966i	$0.00126358\pi$
$30$		0			0
$31$	2.18942	+	5.11922i	0.393232	+	0.919439i
$31$	2.18942	+	5.11922i	0.393232	+	0.919439i
$32$	3.02466	−	3.02466i	0.534689	−	0.534689i
$33$	−0.584449	−	0.0925677i	−0.101740	−	0.0161140i
$34$	−4.11969	−	2.99313i	−0.706521	−	0.513317i
$35$		0			0
$36$	1.28012			0.213353
$37$	3.35379	+	3.35379i	0.551360	+	0.551360i	0.926833	−	0.375474i	$-0.122520\pi$
$37$	3.35379	+	3.35379i	0.551360	+	0.551360i	−0.375474	+	0.926833i	$0.622520\pi$
$38$	−8.63624	+	4.40039i	−1.40098	+	0.713837i
$39$	−2.51663	+	0.817701i	−0.402983	+	0.130937i
$40$		0			0
$41$	−0.561709	+	0.408105i	−0.0877242	+	0.0637353i	−0.630783	−	0.775959i	$-0.717266\pi$
$41$	−0.561709	+	0.408105i	−0.0877242	+	0.0637353i	0.543059	+	0.839695i	$0.317266\pi$
$42$	−3.24960	+	1.65575i	−0.501424	+	0.255488i
$43$	−0.321623	+	2.03065i	−0.0490470	+	0.309671i	0.950953	+	0.309336i	$0.100107\pi$
$43$	−0.321623	+	2.03065i	−0.0490470	+	0.309671i	−1.00000		0.000335040i	$0.999893\pi$
$44$	0.323469	+	0.235014i	0.0487649	+	0.0354297i
$45$		0			0
$46$	2.90006	−	3.99159i	0.427591	−	0.588528i
$47$	−2.34062	+	0.370717i	−0.341414	+	0.0540747i	−0.324787	−	0.945787i	$-0.605293\pi$
$47$	−2.34062	+	0.370717i	−0.341414	+	0.0540747i	−0.0166268	+	0.999862i	$0.505293\pi$
$48$	−5.22342	−	2.66147i	−0.753936	−	0.384150i
$49$	2.11518	−	2.91129i	0.302168	−	0.415898i
$50$		0			0
$51$	−1.11186	+	3.42194i	−0.155691	+	0.479167i
$52$	1.76596	+	0.279701i	0.244895	+	0.0387875i
$53$	2.69217	+	1.37173i	0.369798	+	0.188422i	0.629007	−	0.777400i	$-0.283462\pi$
$53$	2.69217	+	1.37173i	0.369798	+	0.188422i	−0.259209	+	0.965821i	$0.583462\pi$
$54$	−2.81265	−	8.65645i	−0.382753	−	1.17799i
$55$		0			0
$56$	−3.70647			−0.495297
$57$	4.84271	+	4.84271i	0.641433	+	0.641433i
$58$	6.59864	+	12.9506i	0.866443	+	1.70049i
$59$	−3.43500	+	4.72787i	−0.447199	+	0.615517i	−0.971793	−	0.235836i	$-0.924217\pi$
$59$	−3.43500	+	4.72787i	−0.447199	+	0.615517i	0.524594	+	0.851353i	$0.324217\pi$
$60$		0			0
$61$			12.5915i			1.61217i	0.591797	+	0.806087i	$0.298419\pi$
$61$			12.5915i			1.61217i	−0.591797	+	0.806087i	$0.701581\pi$
$62$	−9.03166	+	2.27794i	−1.14702	+	0.289299i
$63$	−2.09017	−	2.09017i	−0.263336	−	0.263336i
$64$	−1.62403	−	2.23529i	−0.203004	−	0.279412i
$65$		0			0
$66$	0.305906	−	0.941481i	0.0376544	−	0.115888i
$67$	11.4144	−	11.4144i	1.39449	−	1.39449i	0.579570	−	0.814922i	$-0.303221\pi$
$67$	11.4144	−	11.4144i	1.39449	−	1.39449i	0.814922	−	0.579570i	$-0.196779\pi$
$68$	1.71909	−	1.71909i	0.208471	−	0.208471i
$69$	−3.31554	−	1.07728i	−0.399144	−	0.129690i
$70$		0			0
$71$	−0.975703	−	3.00291i	−0.115795	−	0.356379i	0.876317	−	0.481734i	$-0.159993\pi$
$71$	−0.975703	−	3.00291i	−0.115795	−	0.356379i	−0.992112	+	0.125355i	$0.959993\pi$
$72$	0.503877	−	3.18135i	0.0593825	−	0.374926i
$73$	−1.01168	−	1.98553i	−0.118408	−	0.232389i	0.824194	−	0.566308i	$-0.191629\pi$
$73$	−1.01168	−	1.98553i	−0.118408	−	0.232389i	−0.942602	+	0.333919i	$0.891629\pi$
$74$	−6.41929	+	4.66389i	−0.746227	+	0.542166i
$75$		0			0
$76$	−1.43000	−	4.40107i	−0.164032	−	0.504838i
$77$	−0.144429	−	0.911886i	−0.0164592	−	0.103919i
$78$	−0.692506	−	4.37231i	−0.0784108	−	0.495066i
$79$	−0.204891	−	0.630588i	−0.0230520	−	0.0709467i	0.938869	−	0.344275i	$-0.111875\pi$
$79$	−0.204891	−	0.630588i	−0.0230520	−	0.0709467i	−0.961921	+	0.273329i	$0.911875\pi$
$80$		0			0
$81$	−1.31302	+	0.953963i	−0.145891	+	0.105996i
$82$	−0.527326	−	1.03493i	−0.0582334	−	0.114289i
$83$	1.76911	−	11.1697i	0.194185	−	1.22603i	−0.677336	−	0.735674i	$-0.736866\pi$
$83$	1.76911	−	11.1697i	0.194185	−	1.22603i	0.871521	−	0.490359i	$-0.163134\pi$
$84$	−0.538070	−	1.65601i	−0.0587083	−	0.180686i
$85$		0			0
$86$	−3.27114	−	1.06286i	−0.352736	−	0.114611i
$87$	7.26193	−	7.26193i	0.778560	−	0.778560i
$88$	0.711380	−	0.711380i	0.0758334	−	0.0758334i
$89$	4.89763	−	15.0733i	0.519147	−	1.59777i	−0.256459	−	0.966555i	$-0.582556\pi$
$89$	4.89763	−	15.0733i	0.519147	−	1.59777i	0.775607	−	0.631216i	$-0.217444\pi$
$90$		0			0
$91$	−2.42675	−	3.34013i	−0.254392	−	0.350141i
$92$	1.66564	+	1.66564i	0.173655	+	0.173655i
$93$	3.50277	+	5.57185i	0.363221	+	0.577774i
$94$		−	3.96451i		−	0.408908i
$95$		0			0
$96$	2.97199	−	4.09060i	0.303328	−	0.417495i
$97$	7.08976	+	13.9144i	0.719856	+	1.41280i	0.902969	+	0.429705i	$0.141383\pi$
$97$	7.08976	+	13.9144i	0.719856	+	1.41280i	−0.183113	+	0.983092i	$0.558617\pi$
$98$	4.25688	+	4.25688i	0.430010	+	0.430010i
$99$	0.802330			0.0806372
$100$		0			0
$101$	1.09640	+	3.37436i	0.109095	+	0.335761i	0.990670	−	0.136284i	$-0.0435159\pi$
$101$	1.09640	+	3.37436i	0.109095	+	0.335761i	−0.881574	+	0.472045i	$0.843516\pi$
$102$	−5.36322	−	2.73270i	−0.531038	−	0.270577i
$103$	−11.7669	−	1.86370i	−1.15943	−	0.183635i	−0.453060	−	0.891480i	$-0.649668\pi$
$103$	−11.7669	−	1.86370i	−1.15943	−	0.183635i	−0.706368	+	0.707845i	$0.749668\pi$
$104$	1.39022	−	4.27867i	0.136323	−	0.419558i
$105$		0			0
$106$	−2.97111	+	4.08939i	−0.288580	+	0.397196i
$107$	−3.09436	−	1.57666i	−0.299144	−	0.152421i	0.297976	−	0.954573i	$-0.403688\pi$
$107$	−3.09436	−	1.57666i	−0.299144	−	0.152421i	−0.597120	+	0.802152i	$0.703688\pi$
$108$	4.29202	−	0.679789i	0.413000	−	0.0654127i
$109$	7.47847	−	10.2932i	0.716307	−	0.985912i	−0.283331	−	0.959022i	$-0.591440\pi$
$109$	7.47847	−	10.2932i	0.716307	−	0.985912i	0.999638	−	0.0268901i	$-0.00856041\pi$
$110$		0			0
$111$	4.53572	+	3.29539i	0.430512	+	0.312785i
$112$	1.43087	−	9.03417i	0.135205	−	0.853649i
$113$	6.98330	−	3.55817i	0.656933	−	0.334724i	−0.0935492	−	0.995615i	$-0.529821\pi$
$113$	6.98330	−	3.55817i	0.656933	−	0.334724i	0.750482	+	0.660890i	$0.229821\pi$
$114$	−9.26915	+	6.73443i	−0.868135	+	0.630737i
$115$		0			0
$116$	−6.59967	+	2.14436i	−0.612764	+	0.199099i
$117$	3.19683	−	1.62887i	0.295547	−	0.150589i
$118$	−6.91308	−	6.91308i	−0.636401	−	0.636401i
$119$	−5.61384			−0.514620
$120$		0			0
$121$	−8.69645	−	6.31834i	−0.790586	−	0.574395i
$122$	−20.8054	−	3.29525i	−1.88363	−	0.298337i
$123$	−0.580332	+	0.580332i	−0.0523268	+	0.0523268i
$124$	−0.399622	−	4.42901i	−0.0358871	−	0.397737i
$125$		0			0
$126$	4.00067	−	2.90665i	0.356408	−	0.258945i
$127$	1.20416	+	7.60280i	0.106852	+	0.674639i	0.981728	+	0.190291i	$0.0609432\pi$
$127$	1.20416	+	7.60280i	0.106852	+	0.674639i	−0.874875	+	0.484348i	$0.839057\pi$
$128$	11.7411	−	5.98236i	1.03777	−	0.528771i
$129$			2.43026i			0.213972i
$130$		0			0
$131$	2.08088	−	6.40431i	0.181808	−	0.559547i	−0.818071	−	0.575117i	$-0.804956\pi$
$131$	2.08088	−	6.40431i	0.181808	−	0.559547i	0.999879	+	0.0155705i	$0.00495643\pi$
$132$	0.421109	+	0.214566i	0.0366528	+	0.0186755i
$133$	−4.85114	+	9.52091i	−0.420648	+	0.825567i
$134$	15.8733	+	21.8477i	1.37124	+	1.88735i
$135$		0			0
$136$	−3.59563	−	4.94896i	−0.308323	−	0.424370i
$137$	−0.320485	−	2.02346i	−0.0273809	−	0.172876i	0.970208	−	0.242272i	$-0.0778927\pi$
$137$	−0.320485	−	2.02346i	−0.0273809	−	0.172876i	−0.997589	+	0.0693962i	$0.977893\pi$
$138$	2.64773	−	5.19646i	0.225390	−	0.442352i
$139$	18.4604	+	13.4123i	1.56579	+	1.13762i	0.931050	+	0.364892i	$0.118894\pi$
$139$	18.4604	+	13.4123i	1.56579	+	1.13762i	0.634743	+	0.772723i	$0.281106\pi$
$140$		0			0
$141$	−2.66413	+	0.865627i	−0.224360	+	0.0728989i
$142$	5.21716	−	0.826316i	0.437814	−	0.0693429i
$143$	1.10684	+	0.175306i	0.0925582	+	0.0146598i
$144$	7.55974	+	2.45631i	0.629978	+	0.204692i
$145$		0			0
$146$	3.54553	−	1.15201i	0.293430	−	0.0953412i
$147$	1.93113	−	3.79006i	0.159277	−	0.312599i
$148$	−1.71983	−	3.37535i	−0.141369	−	0.277452i
$149$			11.0048i			0.901547i	0.892638	+	0.450773i	$0.148852\pi$
$149$			11.0048i			0.901547i	−0.892638	+	0.450773i	$0.851148\pi$
$150$		0			0
$151$	15.0652	+	4.89497i	1.22598	+	0.398347i	0.849258	−	0.527978i	$-0.177050\pi$
$151$	15.0652	+	4.89497i	1.22598	+	0.398347i	0.376727	+	0.926324i	$0.377050\pi$
$152$	−11.5004	+	1.82149i	−0.932807	+	0.147742i
$153$	0.763176	−	4.81850i	0.0616991	−	0.389553i
$154$	1.54454			0.124463
$155$		0			0
$156$	2.11348			0.169214
$157$	3.09555	−	19.5445i	0.247052	−	1.55982i	−0.482499	−	0.875897i	$-0.660271\pi$
$157$	3.09555	−	19.5445i	0.247052	−	1.55982i	0.729550	−	0.683927i	$-0.239729\pi$
$158$	1.09557	−	0.173520i	0.0871585	−	0.0138045i
$159$	3.39677	+	1.10368i	0.269381	+	0.0875273i
$160$		0			0
$161$		−	5.43929i		−	0.428676i
$162$	−1.23265	−	2.41920i	−0.0968458	−	0.190071i
$163$	−4.43752	+	8.70912i	−0.347573	+	0.682151i	−0.996927	−	0.0783356i	$-0.975039\pi$
$163$	−4.43752	+	8.70912i	−0.347573	+	0.682151i	0.649354	+	0.760486i	$0.275039\pi$
$164$	0.527408	−	0.171365i	0.0411836	−	0.0133814i
$165$		0			0
$166$	17.9931	+	5.84631i	1.39654	+	0.453762i
$167$	10.5815	+	1.67595i	0.818821	+	0.129689i	0.551773	−	0.833994i	$-0.313952\pi$
$167$	10.5815	+	1.67595i	0.818821	+	0.129689i	0.267049	+	0.963683i	$0.413952\pi$
$168$	−4.32731	+	0.685378i	−0.333859	+	0.0528781i
$169$	−7.59773	+	2.46865i	−0.584440	+	0.189896i
$170$		0			0
$171$	−7.51255	−	5.45819i	−0.574499	−	0.417398i
$172$	0.745500	−	1.46313i	0.0568439	−	0.111562i
$173$	−0.846802	−	5.34650i	−0.0643812	−	0.406487i	−0.998741	−	0.0501568i	$-0.984028\pi$
$173$	−0.846802	−	5.34650i	−0.0643812	−	0.406487i	0.934360	−	0.356330i	$-0.115972\pi$
$174$	10.0987	+	13.8996i	0.765578	+	1.05373i
$175$		0			0
$176$	1.45930	+	2.00855i	0.109999	+	0.151400i
$177$	−3.13612	+	6.15498i	−0.235725	+	0.462637i
$178$	23.6245	+	12.0373i	1.77073	+	0.902233i
$179$	−6.34002	+	19.5126i	−0.473875	+	1.45844i	0.373593	+	0.927593i	$0.378126\pi$
$179$	−6.34002	+	19.5126i	−0.473875	+	1.45844i	−0.847468	+	0.530846i	$0.821874\pi$
$180$		0			0
$181$			12.2007i			0.906870i	0.891289	+	0.453435i	$0.149802\pi$
$181$			12.2007i			0.906870i	−0.891289	+	0.453435i	$0.850198\pi$
$182$	6.15412	−	3.13568i	0.456174	−	0.232432i
$183$	2.32834	+	14.7006i	0.172116	+	1.08670i
$184$	4.79508	−	3.48383i	0.353498	−	0.256831i
$185$		0			0
$186$	−10.1233	+	4.32958i	−0.742274	+	0.317460i
$187$	1.07746	−	1.07746i	0.0787918	−	0.0787918i
$188$	1.86946	+	0.296094i	0.136345	+	0.0215949i
$189$	−8.11791	−	5.89801i	−0.590491	−	0.429017i
$190$		0			0
$191$	−8.79161			−0.636138			−0.318069	−	0.948068i	$-0.603034\pi$
$191$	−8.79161			−0.636138			−0.318069	+	0.948068i	$0.603034\pi$
$192$	−2.30940	−	2.30940i	−0.166667	−	0.166667i
$193$	1.27775	−	0.651044i	0.0919742	−	0.0468632i	−0.407398	−	0.913251i	$-0.633564\pi$
$193$	1.27775	−	0.651044i	0.0919742	−	0.0468632i	0.499372	+	0.866387i	$0.333564\pi$
$194$	−24.8468	+	8.07320i	−1.78389	+	0.579622i
$195$		0			0
$196$	−2.32526	+	1.68940i	−0.166090	+	0.120672i
$197$	−17.8958	+	9.11837i	−1.27502	+	0.649657i	−0.954677	−	0.297643i	$-0.903799\pi$
$197$	−17.8958	+	9.11837i	−1.27502	+	0.649657i	−0.320347	+	0.947300i	$0.603799\pi$
$198$	−0.209973	+	1.32572i	−0.0149222	+	0.0942148i
$199$	10.4630	+	7.60182i	0.741703	+	0.538879i	0.893244	−	0.449572i	$-0.148424\pi$
$199$	10.4630	+	7.60182i	0.741703	+	0.538879i	−0.151541	+	0.988451i	$0.548424\pi$
$200$		0			0
$201$	11.2157	−	15.4370i	0.791092	−	1.08885i
$202$	−5.86251	+	0.928530i	−0.412485	+	0.0653311i
$203$	14.2772	+	7.27457i	1.00206	+	0.510575i
$204$	1.68916	−	2.32493i	0.118265	−	0.162778i
$205$		0			0
$206$	6.15891	−	18.9552i	0.429111	−	1.32067i
$207$	4.66868	+	0.739446i	0.324496	+	0.0513951i
$208$	9.89217	+	5.04031i	0.685898	+	0.349483i
$209$	−0.896265	−	2.75842i	−0.0619960	−	0.190804i
$210$		0			0
$211$	6.77300			0.466272			0.233136	−	0.972444i	$-0.425101\pi$
$211$	6.77300			0.466272			0.233136	+	0.972444i	$0.425101\pi$
$212$	−1.70645	−	1.70645i	−0.117199	−	0.117199i
$213$	−1.69442	−	3.32548i	−0.116099	−	0.227858i
$214$	3.41498	−	4.70031i	0.233443	−	0.321307i
$215$		0			0
$216$		−	10.9341i		−	0.743971i
$217$	−6.57915	+	7.88415i	−0.446622	+	0.535211i
$218$	15.0507	+	15.0507i	1.01936	+	1.01936i
$219$	−1.54829	−	2.13104i	−0.104624	−	0.144002i
$220$		0			0
$221$	2.10564	−	6.48050i	0.141641	−	0.435926i
$222$	−6.63212	+	6.63212i	−0.445119	+	0.445119i
$223$	13.4715	−	13.4715i	0.902121	−	0.902121i	−0.0934987	−	0.995619i	$-0.529805\pi$
$223$	13.4715	−	13.4715i	0.902121	−	0.902121i	0.995619	+	0.0934987i	$0.0298051\pi$
$224$	7.50290	+	2.43784i	0.501309	+	0.162885i
$225$		0			0
$226$	4.05173	+	12.4699i	0.269517	+	0.829488i
$227$	−2.38358	+	15.0493i	−0.158204	+	0.998860i	0.773012	+	0.634392i	$0.218749\pi$
$227$	−2.38358	+	15.0493i	−0.158204	+	0.998860i	−0.931216	+	0.364468i	$0.881251\pi$
$228$	−2.48334	−	4.87384i	−0.164464	−	0.322778i
$229$	6.08627	−	4.42193i	0.402192	−	0.292209i	−0.368241	−	0.929730i	$-0.620040\pi$
$229$	6.08627	−	4.42193i	0.402192	−	0.292209i	0.770433	+	0.637521i	$0.220040\pi$
$230$		0			0
$231$	−0.337242	−	1.03792i	−0.0221889	−	0.0682903i
$232$	2.73143	+	17.2455i	0.179327	+	1.13223i
$233$	−0.631250	−	3.98555i	−0.0413545	−	0.261102i	0.958345	−	0.285613i	$-0.0921972\pi$
$233$	−0.631250	−	3.98555i	−0.0413545	−	0.261102i	−0.999700	+	0.0245107i	$0.992197\pi$
$234$	1.85481	+	5.70852i	0.121253	+	0.373178i
$235$		0			0
$236$	3.77618	−	2.74355i	0.245808	−	0.178590i
$237$	−0.355815	−	0.698327i	−0.0231127	−	0.0453612i
$238$	1.46917	−	9.27595i	0.0952319	−	0.601271i
$239$	−6.68217	−	20.5656i	−0.432233	−	1.33028i	−0.895895	−	0.444265i	$-0.853465\pi$
$239$	−6.68217	−	20.5656i	−0.432233	−	1.33028i	0.463662	−	0.886012i	$-0.346535\pi$
$240$		0			0
$241$	20.6827	+	6.72022i	1.33229	+	0.432888i	0.886698	−	0.462348i	$-0.152993\pi$
$241$	20.6827	+	6.72022i	1.33229	+	0.432888i	0.445593	+	0.895236i	$0.352993\pi$
$242$	12.7159	−	12.7159i	0.817411	−	0.817411i
$243$	10.1849	−	10.1849i	0.653363	−	0.653363i
$244$	3.10775	−	9.56467i	0.198953	−	0.612315i
$245$		0			0
$246$	−0.807028	−	1.11078i	−0.0514542	−	0.0708207i
$247$	−9.17117	−	9.17117i	−0.583548	−	0.583548i
$248$	−11.1643	−	0.750193i	−0.708932	−	0.0476373i
$249$		−	13.3678i		−	0.847148i
$250$		0			0
$251$	−1.08226	+	1.48960i	−0.0683115	+	0.0940227i	−0.841806	−	0.539781i	$-0.818507\pi$
$251$	−1.08226	+	1.48960i	−0.0683115	+	0.0940227i	0.773494	+	0.633803i	$0.218507\pi$
$252$	1.07184	+	2.10360i	0.0675195	+	0.132515i
$253$	1.04396	+	1.04396i	0.0656332	+	0.0656332i
$254$	−12.8775			−0.808007
$255$		0			0
$256$	5.10458	+	15.7103i	0.319036	+	0.981893i
$257$	6.06834	+	3.09197i	0.378532	+	0.192872i	0.632896	−	0.774237i	$-0.281866\pi$
$257$	6.06834	+	3.09197i	0.378532	+	0.192872i	−0.254364	+	0.967109i	$0.581866\pi$
$258$	−4.01560	−	0.636009i	−0.250001	−	0.0395962i
$259$	−2.70312	+	8.31934i	−0.167964	+	0.516939i
$260$		0			0
$261$	−8.18487	+	11.2655i	−0.506631	+	0.697317i
$262$	10.0375	+	5.11436i	0.620118	+	0.315966i
$263$	8.99697	−	1.42498i	0.554777	−	0.0878680i	0.127250	−	0.991871i	$-0.459385\pi$
$263$	8.99697	−	1.42498i	0.554777	−	0.0878680i	0.427527	+	0.904003i	$0.359385\pi$
$264$	0.698994	−	0.962083i	0.0430201	−	0.0592121i
$265$		0			0
$266$	−14.4622	−	10.5074i	−0.886733	−	0.644249i
$267$	2.93072	−	18.5038i	0.179357	−	1.13241i
$268$	−11.4878	+	5.85332i	−0.701728	+	0.357548i
$269$	0.0907440	−	0.0659294i	0.00553276	−	0.00401979i	−0.585015	−	0.811022i	$-0.698912\pi$
$269$	0.0907440	−	0.0659294i	0.00553276	−	0.00401979i	0.590548	+	0.807002i	$0.298912\pi$
$270$		0			0
$271$	11.3145	−	3.67632i	0.687310	−	0.223320i	0.0555169	−	0.998458i	$-0.482319\pi$
$271$	11.3145	−	3.67632i	0.687310	−	0.223320i	0.631793	+	0.775137i	$0.282319\pi$
$272$	13.4507	−	6.85348i	0.815569	−	0.415553i
$273$	−3.45088	−	3.45088i	−0.208856	−	0.208856i
$274$	3.42731			0.207052
$275$		0			0
$276$	2.25264	+	1.63664i	0.135593	+	0.0985142i
$277$	9.70790	+	1.53758i	0.583291	+	0.0923842i	0.441105	−	0.897456i	$-0.354587\pi$
$277$	9.70790	+	1.53758i	0.583291	+	0.0923842i	0.142186	+	0.989840i	$0.454587\pi$
$278$	−26.9928	+	26.9928i	−1.61892	+	1.61892i
$279$	−5.87276	−	6.71886i	−0.351593	−	0.402248i
$280$		0			0
$281$	−2.70181	+	1.96298i	−0.161176	+	0.117101i	−0.665450	−	0.746442i	$-0.731760\pi$
$281$	−2.70181	+	1.96298i	−0.161176	+	0.117101i	0.504274	+	0.863544i	$0.331760\pi$
$282$	−0.733094	−	4.62857i	−0.0436551	−	0.275627i
$283$	17.8486	−	9.09434i	1.06099	−	0.540602i	0.165743	−	0.986169i	$-0.446998\pi$
$283$	17.8486	−	9.09434i	1.06099	−	0.540602i	0.895249	+	0.445567i	$0.146998\pi$
$284$			2.52187i			0.149645i
$285$		0			0
$286$	−0.579327	+	1.78299i	−0.0342563	+	0.105430i
$287$	−1.14095	−	0.581343i	−0.0673481	−	0.0343156i
$288$	−3.11245	+	6.10852i	−0.183403	+	0.359948i
$289$	4.54639	+	6.25756i	0.267434	+	0.368092i
$290$		0			0
$291$	10.8503	+	14.9341i	0.636055	+	0.875455i
$292$	0.278429	+	1.75793i	0.0162938	+	0.102875i
$293$	13.3716	−	26.2432i	0.781175	−	1.53314i	−0.0635735	−	0.997977i	$-0.520250\pi$
$293$	13.3716	−	26.2432i	0.781175	−	1.53314i	0.844748	−	0.535164i	$-0.179750\pi$
$294$	5.75707	+	4.18276i	0.335759	+	0.243943i
$295$		0			0
$296$	−9.06536	+	2.94551i	−0.526913	+	0.171205i
$297$	2.69007	−	0.426065i	0.156094	−	0.0247228i
$298$	−18.1836	−	2.88000i	−1.05335	−	0.166834i
$299$	6.27900	+	2.04017i	0.363124	+	0.117986i
$300$		0			0
$301$	−3.60622	+	1.17173i	−0.207859	+	0.0675376i
$302$	−12.0307	+	23.6117i	−0.692292	+	1.35870i
$303$	1.90401	+	3.73683i	0.109383	+	0.214675i
$304$		−	28.7344i		−	1.64803i
$305$		0			0
$306$	7.76206	+	2.52205i	0.443728	+	0.144176i
$307$	−9.92765	+	1.57239i	−0.566601	+	0.0897408i	−0.433162	−	0.901316i	$-0.642602\pi$
$307$	−9.92765	+	1.57239i	−0.566601	+	0.0897408i	−0.133439	+	0.991057i	$0.542602\pi$
$308$	−0.115356	+	0.728329i	−0.00657302	+	0.0415004i
$309$	−14.0825			−0.801127
$310$		0			0
$311$	−29.3296			−1.66313			−0.831565	−	0.555427i	$-0.812555\pi$
$311$	−29.3296			−1.66313			−0.831565	+	0.555427i	$0.812555\pi$
$312$	0.831903	−	5.25243i	0.0470972	−	0.297360i
$313$	−27.7061	+	4.38821i	−1.56604	+	0.248036i	−0.878368	−	0.477985i	$-0.841367\pi$
$313$	−27.7061	+	4.38821i	−1.56604	+	0.248036i	−0.687672	+	0.726021i	$0.741367\pi$
$314$	31.4840	+	10.2298i	1.77675	+	0.577300i
$315$		0			0
$316$			0.529574i			0.0297909i
$317$	−14.1528	−	27.7765i	−0.794903	−	1.56008i	−0.828063	−	0.560634i	$-0.810557\pi$
$317$	−14.1528	−	27.7765i	−0.794903	−	1.56008i	0.0331608	−	0.999450i	$-0.489443\pi$
$318$	−2.71260	+	5.32377i	−0.152115	+	0.298542i
$319$	−4.13641	+	1.34400i	−0.231595	+	0.0752497i
$320$		0			0
$321$	−3.90423	−	1.26856i	−0.217913	−	0.0708041i
$322$	8.98753	+	1.42349i	0.500856	+	0.0793277i
$323$	−17.4186	+	2.75884i	−0.969197	+	0.153506i
$324$	1.23284	−	0.400573i	0.0684910	−	0.0222541i
$325$		0			0
$326$	−13.2291	−	9.61149i	−0.732691	−	0.532331i
$327$	6.82777	−	13.4002i	0.377576	−	0.741035i
$328$	−0.218280	−	1.37817i	−0.0120525	−	0.0760965i
$329$	−2.56898	−	3.53590i	−0.141633	−	0.194941i
$330$		0			0
$331$	−5.49461	−	7.56268i	−0.302011	−	0.415683i	0.630858	−	0.775898i	$-0.282703\pi$
$331$	−5.49461	−	7.56268i	−0.302011	−	0.415683i	−0.932869	+	0.360216i	$0.882703\pi$
$332$	−4.10067	+	8.04802i	−0.225053	+	0.441692i
$333$	−6.77323	−	3.45113i	−0.371171	−	0.189121i
$334$	−5.53845	+	17.0456i	−0.303051	+	0.932694i
$335$		0			0
$336$		−	10.8120i		−	0.589843i
$337$	8.19410	−	4.17510i	0.446361	−	0.227432i	−0.216337	−	0.976319i	$-0.569411\pi$
$337$	8.19410	−	4.17510i	0.446361	−	0.227432i	0.662699	+	0.748886i	$0.269411\pi$
$338$	−2.09068	−	13.2001i	−0.113718	−	0.717988i
$339$	7.49506	−	5.44548i	0.407076	−	0.295758i
$340$		0			0
$341$	−0.250468	−	2.77593i	−0.0135636	−	0.150325i
$342$	10.9848	−	10.9848i	0.593991	−	0.593991i
$343$	19.3063	+	3.05781i	1.04244	+	0.165106i
$344$	−3.34272	−	2.42863i	−0.180227	−	0.130943i
$345$		0			0
$346$	9.05583			0.486844
$347$	19.7278	+	19.7278i	1.05905	+	1.05905i	0.998144	+	0.0609019i	$0.0193977\pi$
$347$	19.7278	+	19.7278i	1.05905	+	1.05905i	0.0609019	+	0.998144i	$0.480602\pi$
$348$	−7.30861	+	3.72392i	−0.391782	+	0.199623i
$349$	−24.9595	+	8.10985i	−1.33605	+	0.434110i	−0.887978	−	0.459886i	$-0.847890\pi$
$349$	−24.9595	+	8.10985i	−1.33605	+	0.434110i	−0.448075	+	0.893996i	$0.647890\pi$
$350$		0			0
$351$	9.85341	−	7.15892i	0.525936	−	0.382115i
$352$	−1.90792	+	0.972135i	−0.101693	+	0.0518150i
$353$	−5.27336	+	33.2947i	−0.280672	+	1.77210i	0.296066	+	0.955168i	$0.404325\pi$
$353$	−5.27336	+	33.2947i	−0.280672	+	1.77210i	−0.576738	+	0.816929i	$0.695675\pi$
$354$	−9.34937	−	6.79271i	−0.496913	−	0.361029i
$355$		0			0
$356$	−7.44061	+	10.2411i	−0.394352	+	0.542779i
$357$	−6.55417	+	1.03808i	−0.346884	+	0.0549410i
$358$	−30.5821	−	15.5824i	−1.61632	−	0.823554i
$359$	−1.75444	+	2.41478i	−0.0925959	+	0.127447i	−0.852801	−	0.522235i	$-0.825098\pi$
$359$	−1.75444	+	2.41478i	−0.0925959	+	0.127447i	0.760205	+	0.649683i	$0.225098\pi$
$360$		0			0
$361$	−4.50189	+	13.8554i	−0.236942	+	0.729231i
$362$	−20.1596	−	3.19297i	−1.05957	−	0.167819i
$363$	−11.3215	−	5.76858i	−0.594224	−	0.302772i
$364$	1.01900	+	3.13617i	0.0534103	+	0.164380i
$365$		0			0
$366$	−24.8997			−1.30153
$367$	−10.0768	−	10.0768i	−0.526004	−	0.526004i	0.393374	−	0.919378i	$-0.371308\pi$
$367$	−10.0768	−	10.0768i	−0.526004	−	0.526004i	−0.919378	+	0.393374i	$0.871308\pi$
$368$	6.64038	+	13.0325i	0.346154	+	0.679365i
$369$	0.654088	−	0.900275i	0.0340505	−	0.0468665i
$370$		0			0
$371$			5.57255i			0.289312i
$372$	−1.28555	−	5.09699i	−0.0666526	−	0.264267i
$373$	−26.6787	−	26.6787i	−1.38137	−	1.38137i	−0.842191	−	0.539179i	$-0.818735\pi$
$373$	−26.6787	−	26.6787i	−1.38137	−	1.38137i	−0.539179	−	0.842191i	$-0.681265\pi$
$374$	1.49835	+	2.06231i	0.0774780	+	0.106639i
$375$		0			0
$376$	1.47171	−	4.52944i	0.0758974	−	0.233588i
$377$	−13.7527	+	13.7527i	−0.708300	+	0.708300i
$378$	11.8700	−	11.8700i	0.610527	−	0.610527i
$379$	−20.1306	−	6.54083i	−1.03404	−	0.335980i	−0.257654	−	0.966237i	$-0.582949\pi$
$379$	−20.1306	−	6.54083i	−1.03404	−	0.335980i	−0.776386	+	0.630258i	$0.782949\pi$
$380$		0			0
$381$	2.81173	+	8.65362i	0.144049	+	0.443338i
$382$	2.30080	−	14.5267i	0.117719	−	0.743250i
$383$	8.03508	+	15.7697i	0.410574	+	0.805796i	0.999998	−	0.00202751i	$-0.000645378\pi$
$383$	8.03508	+	15.7697i	0.410574	+	0.805796i	−0.589424	+	0.807824i	$0.700645\pi$
$384$	12.6015	−	9.15551i	0.643067	−	0.467215i
$385$		0			0
$386$	0.741352	+	2.28165i	0.0377338	+	0.116133i
$387$	−0.515479	−	3.25461i	−0.0262033	−	0.165441i
$388$	−1.95121	−	12.3195i	−0.0990577	−	0.625426i
$389$	−8.64664	−	26.6116i	−0.438402	−	1.34926i	−0.889560	−	0.456818i	$-0.848989\pi$
$389$	−8.64664	−	26.6116i	−0.438402	−	1.34926i	0.451158	−	0.892444i	$-0.351011\pi$
$390$		0			0
$391$	7.26266	−	5.27663i	0.367288	−	0.266851i
$392$	3.28324	+	6.44372i	0.165829	+	0.325457i
$393$	1.24519	−	7.86183i	0.0628116	−	0.396577i
$394$	−10.3832	−	31.9562i	−0.523098	−	1.60993i
$395$		0			0
$396$	−0.609461	−	0.198026i	−0.0306266	−	0.00995118i
$397$	−21.9537	+	21.9537i	−1.10182	+	1.10182i	−0.107634	+	0.994191i	$0.534327\pi$
$397$	−21.9537	+	21.9537i	−1.10182	+	1.10182i	−0.994191	+	0.107634i	$0.965673\pi$
$398$	−15.2990	+	15.2990i	−0.766869	+	0.766869i
$399$	−3.90317	+	12.0127i	−0.195403	+	0.601389i
$400$		0			0
$401$	−10.2941	−	14.1686i	−0.514063	−	0.707547i	0.470535	−	0.882381i	$-0.344061\pi$
$401$	−10.2941	−	14.1686i	−0.514063	−	0.707547i	−0.984598	+	0.174834i	$0.944061\pi$
$402$	22.5720	+	22.5720i	1.12579	+	1.12579i
$403$	−6.63359	−	10.5520i	−0.330442	−	0.525634i
$404$		−	2.83382i		−	0.140988i
$405$		0			0
$406$	−15.7564	+	21.6869i	−0.781979	+	1.07630i
$407$	−1.07792	−	2.11554i	−0.0534305	−	0.104863i
$408$	−5.11304	−	5.11304i	−0.253133	−	0.253133i
$409$	8.72402			0.431375			0.215688	−	0.976462i	$-0.430801\pi$
$409$	8.72402			0.431375			0.215688	+	0.976462i	$0.430801\pi$
$410$		0			0
$411$	−0.748334	−	2.30314i	−0.0369126	−	0.113605i
$412$	8.47833	+	4.31992i	0.417697	+	0.212827i
$413$	−10.6454	−	1.68606i	−0.523824	−	0.0829655i
$414$	−2.44363	+	7.52071i	−0.120098	+	0.369623i
$415$		0			0
$416$	−5.62839	+	7.74681i	−0.275954	+	0.379819i
$417$	24.0327	+	12.2453i	1.17689	+	0.599654i
$418$	4.79240	−	0.759041i	0.234404	−	0.0371259i
$419$	1.93897	−	2.66876i	0.0947249	−	0.130378i	−0.759024	−	0.651063i	$-0.774323\pi$
$419$	1.93897	−	2.66876i	0.0947249	−	0.130378i	0.853749	+	0.520685i	$0.174323\pi$
$420$		0			0
$421$	7.72076	+	5.60946i	0.376287	+	0.273388i	0.759813	−	0.650142i	$-0.225290\pi$
$421$	7.72076	+	5.60946i	0.376287	+	0.273388i	−0.383526	+	0.923530i	$0.625290\pi$
$422$	−1.77252	+	11.1913i	−0.0862851	+	0.544782i
$423$	3.38420	−	1.72433i	0.164545	−	0.0838400i
$424$	−4.91256	+	3.56918i	−0.238575	+	0.173335i
$425$		0			0
$426$	5.93825	−	1.92945i	0.287709	−	0.0934823i
$427$	−20.6914	+	10.5428i	−1.00133	+	0.510201i
$428$	1.96138	+	1.96138i	0.0948070	+	0.0948070i
$429$	1.32465			0.0639547
$430$		0			0
$431$	−23.1013	−	16.7841i	−1.11275	−	0.808460i	−0.129655	−	0.991559i	$-0.541387\pi$
$431$	−23.1013	−	16.7841i	−1.11275	−	0.808460i	−0.983094	+	0.183099i	$0.941387\pi$
$432$	26.6508	+	4.22108i	1.28224	+	0.203087i
$433$	−7.88154	+	7.88154i	−0.378763	+	0.378763i	−0.870656	−	0.491893i	$-0.836305\pi$
$433$	−7.88154	+	7.88154i	−0.378763	+	0.378763i	0.491893	+	0.870656i	$0.336305\pi$
$434$	−11.3055	−	12.9343i	−0.542680	−	0.620865i
$435$		0			0
$436$	−8.22126	+	5.97309i	−0.393727	+	0.286059i
$437$	−2.67305	−	16.8770i	−0.127870	−	0.807337i
$438$	3.92639	−	2.00060i	0.187610	−	0.0955921i
$439$		−	16.7419i		−	0.799046i	−0.916723	−	0.399523i	$-0.869176\pi$
$439$		−	16.7419i		−	0.799046i	0.916723	−	0.399523i	$-0.130824\pi$
$440$		0			0
$441$	−1.78227	+	5.48527i	−0.0848701	+	0.261203i
$442$	10.1569	+	5.17521i	0.483115	+	0.246159i
$443$	−11.5467	+	22.6616i	−0.548598	+	1.07668i	0.435687	+	0.900098i	$0.356505\pi$
$443$	−11.5467	+	22.6616i	−0.548598	+	1.07668i	−0.984285	+	0.176586i	$0.943495\pi$
$444$	−2.63205	−	3.62271i	−0.124912	−	0.171926i
$445$		0			0
$446$	18.7340	+	25.7851i	0.887078	+	1.22096i
$447$	2.03494	+	12.8481i	0.0962494	+	0.607695i
$448$	2.31342	−	4.54035i	0.109299	−	0.214511i
$449$	9.82815	+	7.14057i	0.463819	+	0.336984i	0.795028	−	0.606573i	$-0.207456\pi$
$449$	9.82815	+	7.14057i	0.463819	+	0.336984i	−0.331208	+	0.943558i	$0.607456\pi$
$450$		0			0
$451$	0.330559	−	0.107405i	0.0155654	−	0.00505751i
$452$	−6.18281	+	0.979262i	−0.290815	+	0.0460606i
$453$	18.4938	+	2.92912i	0.868913	+	0.137622i
$454$	−24.2428	−	7.87696i	−1.13777	−	0.369684i
$455$		0			0
$456$	−13.0899	+	4.25318i	−0.612993	+	0.199173i
$457$	6.83293	−	13.4104i	0.319631	−	0.627311i	−0.674159	−	0.738587i	$-0.735494\pi$
$457$	6.83293	−	13.4104i	0.319631	−	0.627311i	0.993790	+	0.111276i	$0.0354936\pi$
$458$	5.71372	+	11.2138i	0.266984	+	0.523987i
$459$		−	16.5609i		−	0.772995i
$460$		0			0
$461$	−25.1540	−	8.17304i	−1.17154	−	0.380656i	−0.342323	−	0.939582i	$-0.611214\pi$
$461$	−25.1540	−	8.17304i	−1.17154	−	0.380656i	−0.829218	+	0.558926i	$0.811214\pi$
$462$	1.80326	−	0.285608i	0.0838951	−	0.0132877i
$463$	1.12161	−	7.08159i	0.0521258	−	0.329109i	−0.947821	−	0.318803i	$-0.896719\pi$
$463$	1.12161	−	7.08159i	0.0521258	−	0.329109i	0.999947	−	0.0103066i	$-0.00328076\pi$
$464$	−43.0889			−2.00035
$465$		0			0
$466$	6.75068			0.312719
$467$	3.48772	−	22.0206i	0.161392	−	1.01899i	−0.765438	−	0.643510i	$-0.777478\pi$
$467$	3.48772	−	22.0206i	0.161392	−	1.01899i	0.926830	−	0.375481i	$-0.122522\pi$
$468$	−2.83038	+	0.448289i	−0.130834	+	0.0207221i
$469$	28.3144	+	9.19990i	1.30744	+	0.424812i
$470$		0			0
$471$		−	23.3907i		−	1.07779i
$472$	−5.33191	−	10.4645i	−0.245421	−	0.481666i
$473$	0.467251	−	0.917031i	0.0214842	−	0.0421651i
$474$	1.24699	−	0.405171i	0.0572761	−	0.0186101i
$475$		0			0
$476$	4.26435	+	1.38557i	0.195456	+	0.0635076i
$477$	−4.78306	−	0.757563i	−0.219001	−	0.0346864i
$478$	35.7300	−	5.65908i	1.63425	−	0.258840i
$479$	−12.1314	+	3.94174i	−0.554299	+	0.180103i	−0.572754	−	0.819727i	$-0.694125\pi$
$479$	−12.1314	+	3.94174i	−0.554299	+	0.180103i	0.0184557	+	0.999830i	$0.494125\pi$
$480$		0			0
$481$	−8.58979	−	6.24085i	−0.391661	−	0.284558i
$482$	−16.5168	+	32.4161i	−0.752321	+	1.47651i
$483$	−1.00580	−	6.35038i	−0.0457656	−	0.288952i
$484$	5.04649	+	6.94590i	0.229386	+	0.315723i
$485$		0			0
$486$	14.1635	+	19.4944i	0.642468	+	0.884282i
$487$	3.53302	−	6.93394i	0.160096	−	0.314207i	−0.796999	−	0.603981i	$-0.793580\pi$
$487$	3.53302	−	6.93394i	0.160096	−	0.314207i	0.957095	+	0.289774i	$0.0935803\pi$
$488$	−22.5468	−	11.4882i	−1.02065	−	0.520046i
$489$	−3.57037	+	10.9885i	−0.161458	+	0.496916i
$490$		0			0
$491$			12.4740i			0.562943i	0.959570	+	0.281472i	$0.0908225\pi$
$491$			12.4740i			0.562943i	−0.959570	+	0.281472i	$0.909177\pi$
$492$	0.584062	−	0.297595i	0.0263316	−	0.0134166i
$493$	4.13704	+	26.1202i	0.186323	+	1.17640i
$494$	17.5540	−	12.7537i	0.789792	−	0.573817i
$495$		0			0
$496$	6.13847	−	26.9223i	0.275625	−	1.20885i
$497$	4.11768	−	4.11768i	0.184703	−	0.184703i
$498$	22.0881	+	3.49841i	0.989790	+	0.156767i
$499$	26.3216	+	19.1238i	1.17832	+	0.856097i	0.991981	−	0.126389i	$-0.0403389\pi$
$499$	26.3216	+	19.1238i	1.17832	+	0.856097i	0.186336	+	0.982486i	$0.440339\pi$
$500$		0			0
$501$	12.6638			0.565779
$502$	−2.17809	−	2.17809i	−0.0972128	−	0.0972128i
$503$	7.94255	−	4.04693i	0.354141	−	0.180444i	−0.267865	−	0.963456i	$-0.586318\pi$
$503$	7.94255	−	4.04693i	0.354141	−	0.180444i	0.622006	+	0.783013i	$0.286318\pi$
$504$	5.64977	−	1.83572i	0.251661	−	0.0817695i
$505$		0			0
$506$	−1.99818	+	1.45176i	−0.0888300	+	0.0645388i
$507$	−8.41388	+	4.28708i	−0.373673	+	0.190396i
$508$	0.961773	−	6.07240i	0.0426718	−	0.269419i
$509$	5.50192	+	3.99738i	0.243868	+	0.177181i	0.703005	−	0.711185i	$-0.251841\pi$
$509$	5.50192	+	3.99738i	0.243868	+	0.177181i	−0.459137	+	0.888366i	$0.651841\pi$
$510$		0			0
$511$	2.41572	−	3.32495i	0.106865	−	0.147087i
$512$	−1.26448	+	0.200273i	−0.0558824	+	0.00885091i
$513$	−28.0867	−	14.3109i	−1.24006	−	0.631842i
$514$	−6.69709	+	9.21775i	−0.295396	+	0.406578i
$515$		0			0
$516$	0.599821	−	1.84606i	0.0264056	−	0.0812682i
$517$	1.17171	+	0.185580i	0.0515316	+	0.00816181i
$518$	−13.0389	−	6.64367i	−0.572898	−	0.291906i
$519$	−1.97729	−	6.08547i	−0.0867933	−	0.267122i
$520$		0			0
$521$	8.22121			0.360178			0.180089	−	0.983650i	$-0.442361\pi$
$521$	8.22121			0.360178			0.180089	+	0.983650i	$0.442361\pi$
$522$	−16.4724	−	16.4724i	−0.720977	−	0.720977i
$523$	−0.155123	−	0.304446i	−0.00678305	−	0.0133125i	0.887590	−	0.460634i	$-0.152378\pi$
$523$	−0.155123	−	0.304446i	−0.00678305	−	0.0133125i	−0.894373	+	0.447322i	$0.852378\pi$
$524$	−3.16134	+	4.35121i	−0.138104	+	0.190084i
$525$		0			0
$526$			15.2389i			0.664449i
$527$	−16.9095	−	1.13625i	−0.736589	−	0.0494957i
$528$	2.07514	+	2.07514i	0.0903090	+	0.0903090i
$529$	−8.40650	−	11.5706i	−0.365500	−	0.503068i
$530$		0			0
$531$	2.89437	−	8.90797i	0.125605	−	0.386573i
$532$	6.03489	−	6.03489i	0.261646	−	0.261646i
$533$	1.09904	−	1.09904i	0.0476046	−	0.0476046i
$534$	29.8075	+	9.68506i	1.28990	+	0.419114i
$535$		0			0
$536$	10.0249	+	30.8534i	0.433009	+	1.33266i
$537$	−3.79384	+	23.9533i	−0.163716	+	1.03366i
$538$	0.0851895	+	0.167194i	0.00367278	+	0.00720823i
$539$	−1.45738	+	1.05885i	−0.0627740	+	0.0456080i
$540$		0			0
$541$	−13.0472	−	40.1553i	−0.560945	−	1.72641i	−0.679704	−	0.733487i	$-0.737892\pi$
$541$	−13.0472	−	40.1553i	−0.560945	−	1.72641i	0.118759	−	0.992923i	$-0.462108\pi$
$542$	3.11345	+	19.6575i	0.133734	+	0.844364i
$543$	2.25608	+	14.2443i	0.0968177	+	0.611283i
$544$	4.02348	+	12.3830i	0.172505	+	0.530916i
$545$		0			0
$546$	6.60512	−	4.79890i	0.282673	−	0.205374i
$547$	16.5934	+	32.5664i	0.709483	+	1.39244i	0.910773	+	0.412907i	$0.135487\pi$
$547$	16.5934	+	32.5664i	0.709483	+	1.39244i	−0.201290	+	0.979532i	$0.564513\pi$
$548$	−0.255973	+	1.61615i	−0.0109346	+	0.0690385i
$549$	−6.23625	−	19.1932i	−0.266156	−	0.819145i
$550$		0			0
$551$	47.8741	+	15.5552i	2.03951	+	0.662675i
$552$	4.95406	−	4.95406i	0.210859	−	0.210859i
$553$	0.864682	−	0.864682i	0.0367700	−	0.0367700i
$554$	−5.08120	+	15.6383i	−0.215879	+	0.664409i
$555$		0			0
$556$	−10.7125	−	14.7444i	−0.454310	−	0.625304i
$557$	−17.7435	−	17.7435i	−0.751816	−	0.751816i	0.223002	−	0.974818i	$-0.428414\pi$
$557$	−17.7435	−	17.7435i	−0.751816	−	0.751816i	−0.974818	+	0.223002i	$0.928414\pi$
$558$	12.6388	−	7.94542i	0.535041	−	0.336356i
$559$		−	4.60245i		−	0.194663i
$560$		0			0
$561$	1.05870	−	1.45718i	0.0446984	−	0.0615221i
$562$	−2.53643	−	4.97802i	−0.106993	−	0.209985i
$563$	8.17684	+	8.17684i	0.344613	+	0.344613i	0.858098	−	0.513485i	$-0.171646\pi$
$563$	8.17684	+	8.17684i	0.344613	+	0.344613i	−0.513485	+	0.858098i	$0.671646\pi$
$564$	2.23736			0.0942097
$565$		0			0
$566$	10.3558	+	31.8720i	0.435288	+	1.33968i
$567$	−2.66702	−	1.35891i	−0.112004	−	0.0570690i
$568$	6.26734	+	0.992649i	0.262972	+	0.0416506i
$569$	−11.7255	+	36.0873i	−0.491557	+	1.51286i	0.330696	+	0.943737i	$0.392716\pi$
$569$	−11.7255	+	36.0873i	−0.491557	+	1.51286i	−0.822254	+	0.569121i	$0.807284\pi$
$570$		0			0
$571$	15.1529	−	20.8562i	0.634131	−	0.872806i	−0.364155	−	0.931339i	$-0.618642\pi$
$571$	15.1529	−	20.8562i	0.634131	−	0.872806i	0.998286	+	0.0585322i	$0.0186420\pi$
$572$	−0.797500	−	0.406347i	−0.0333452	−	0.0169902i
$573$	−10.2642	+	1.62569i	−0.428794	+	0.0679143i
$574$	1.25917	−	1.73309i	0.0525566	−	0.0723379i
$575$		0			0
$576$	3.58260	+	2.60291i	0.149275	+	0.108455i
$577$	−2.37812	+	15.0148i	−0.0990022	+	0.625076i	0.887435	+	0.460934i	$0.152485\pi$
$577$	−2.37812	+	15.0148i	−0.0990022	+	0.625076i	−0.986437	+	0.164142i	$0.947515\pi$
$578$	−11.5294	+	5.87453i	−0.479560	+	0.244348i
$579$	1.37138	−	0.996369i	0.0569928	−	0.0414077i
$580$		0			0
$581$	19.8362	−	6.44519i	0.822946	−	0.267391i
$582$	−27.5158	+	14.0200i	−1.14057	+	0.581148i
$583$	−1.06954	−	1.06954i	−0.0442957	−	0.0442957i
$584$	4.47841			0.185318
$585$		0			0
$586$	39.8631	+	28.9623i	1.64673	+	1.19642i
$587$	13.9423	+	2.20824i	0.575460	+	0.0911440i	0.437380	−	0.899277i	$-0.355907\pi$
$587$	13.9423	+	2.20824i	0.575460	+	0.0911440i	0.138081	+	0.990421i	$0.455907\pi$
$588$	−2.40236	+	2.40236i	−0.0990715	+	0.0990715i
$589$	−16.5392	+	27.6961i	−0.681486	+	1.14120i
$590$		0			0
$591$	−19.2073	+	13.9549i	−0.790083	+	0.574029i
$592$	−3.67976	−	23.2331i	−0.151237	−	0.954874i
$593$	11.0391	−	5.62470i	0.453321	−	0.230979i	−0.212395	−	0.977184i	$-0.568126\pi$
$593$	11.0391	−	5.62470i	0.453321	−	0.230979i	0.665716	+	0.746205i	$0.268126\pi$
$594$			4.55640i			0.186952i
$595$		0			0
$596$	2.71613	−	8.35939i	0.111257	−	0.342414i
$597$	13.6213	+	6.94039i	0.557482	+	0.284051i
$598$	−5.01429	+	9.84110i	−0.205050	+	0.402433i
$599$	15.2759	+	21.0255i	0.624158	+	0.859080i	0.997647	−	0.0685549i	$-0.0218388\pi$
$599$	15.2759	+	21.0255i	0.624158	+	0.859080i	−0.373490	+	0.927634i	$0.621839\pi$
$600$		0			0
$601$	−25.7569	−	35.4514i	−1.05065	−	1.44609i	−0.888247	−	0.459366i	$-0.848077\pi$
$601$	−25.7569	−	35.4514i	−1.05065	−	1.44609i	−0.162400	−	0.986725i	$-0.551923\pi$
$602$	−0.992333	−	6.26534i	−0.0404445	−	0.255356i
$603$	−11.7457	+	23.0523i	−0.478323	+	0.938761i
$604$	−10.2356	−	7.43657i	−0.416479	−	0.302590i
$605$		0			0
$606$	−6.67280	+	2.16812i	−0.271064	+	0.0880740i
$607$	−4.16862	+	0.660245i	−0.169199	+	0.0267985i	−0.240459	−	0.970659i	$-0.577298\pi$
$607$	−4.16862	+	0.660245i	−0.169199	+	0.0267985i	0.0712599	+	0.997458i	$0.477298\pi$
$608$	24.4780	+	3.87694i	0.992715	+	0.157231i
$609$	18.0138	+	5.85304i	0.729956	+	0.237177i
$610$		0			0
$611$	5.04535	−	1.63933i	0.204113	−	0.0663203i
$612$	−1.76899	+	3.47184i	−0.0715072	+	0.140341i
$613$	6.76038	+	13.2680i	0.273049	+	0.535889i	0.986288	−	0.165032i	$-0.0527726\pi$
$613$	6.76038	+	13.2680i	0.273049	+	0.535889i	−0.713239	+	0.700921i	$0.752773\pi$
$614$		−	16.8153i		−	0.678611i
$615$		0			0
$616$	1.76464	+	0.573365i	0.0710992	+	0.0231015i
$617$	8.69476	−	1.37712i	0.350038	−	0.0554406i	0.0210601	−	0.999778i	$-0.493296\pi$
$617$	8.69476	−	1.37712i	0.350038	−	0.0554406i	0.328978	+	0.944338i	$0.393296\pi$
$618$	3.68546	−	23.2691i	0.148251	−	0.936020i
$619$	0.759234			0.0305162			0.0152581	−	0.999884i	$-0.495143\pi$
$619$	0.759234			0.0305162			0.0152581	+	0.999884i	$0.495143\pi$
$620$		0			0
$621$	16.0459			0.643901
$622$	7.67569	−	48.4624i	0.307767	−	1.94317i
$623$	28.8706	−	4.57265i	1.15667	−	0.183199i
$624$	12.4812	+	4.05537i	0.499646	+	0.162345i
$625$		0			0
$626$		−	46.9282i		−	1.87563i
$627$	−1.55646	−	3.05473i	−0.0621592	−	0.121994i
$628$	−7.17528	+	14.0823i	−0.286325	+	0.561944i
$629$	−13.7305	+	4.46130i	−0.547469	+	0.177884i
$630$		0			0
$631$	−1.49143	−	0.484594i	−0.0593728	−	0.0192914i	0.279180	−	0.960239i	$-0.409937\pi$
$631$	−1.49143	−	0.484594i	−0.0593728	−	0.0192914i	−0.338553	+	0.940947i	$0.609937\pi$
$632$	1.31610	+	0.208449i	0.0523515	+	0.00829166i
$633$	7.90749	−	1.25242i	0.314295	−	0.0497794i
$634$	49.6000	−	16.1160i	1.96987	−	0.640049i
$635$		0			0
$636$	−2.30783	−	1.67674i	−0.0915115	−	0.0664870i
$637$	−3.65720	+	7.17766i	−0.144904	+	0.284389i
$638$	−1.13823	−	7.18648i	−0.0450628	−	0.284515i
$639$	2.97453	+	4.09409i	0.117671	+	0.161960i
$640$		0			0
$641$	20.9627	+	28.8527i	0.827977	+	1.13961i	0.988296	+	0.152547i	$0.0487476\pi$
$641$	20.9627	+	28.8527i	0.827977	+	1.13961i	−0.160319	+	0.987065i	$0.551252\pi$
$642$	3.11784	−	6.11911i	0.123051	−	0.241502i
$643$	43.5456	+	22.1876i	1.71727	+	0.874992i	0.979897	+	0.199506i	$0.0639336\pi$
$643$	43.5456	+	22.1876i	1.71727	+	0.874992i	0.737372	+	0.675487i	$0.236066\pi$
$644$	−1.34249	+	4.13176i	−0.0529015	+	0.162814i
$645$		0			0
$646$		−	29.5034i		−	1.16080i
$647$	38.2923	−	19.5109i	1.50542	−	0.767052i	0.509782	−	0.860304i	$-0.329726\pi$
$647$	38.2923	−	19.5109i	1.50542	−	0.767052i	0.995643	+	0.0932514i	$0.0297260\pi$
$648$	−0.510239	−	3.22152i	−0.0200441	−	0.126553i
$649$	2.36676	−	1.71955i	0.0929035	−	0.0674984i
$650$		0			0
$651$	−6.22328	+	10.4213i	−0.243910	+	0.408445i
$652$	5.52033	−	5.52033i	0.216193	−	0.216193i
$653$	−29.6123	−	4.69013i	−1.15882	−	0.183539i	−0.452721	−	0.891652i	$-0.649547\pi$
$653$	−29.6123	−	4.69013i	−1.15882	−	0.183539i	−0.706099	+	0.708113i	$0.749547\pi$
$654$	20.3549	+	14.7887i	0.795938	+	0.578283i
$655$		0			0
$656$	3.44342			0.134443
$657$	2.52549	+	2.52549i	0.0985286	+	0.0985286i
$658$	6.51481	−	3.31946i	0.253974	−	0.129406i
$659$	−4.87005	+	1.58238i	−0.189710	+	0.0616406i	−0.402331	−	0.915494i	$-0.631800\pi$
$659$	−4.87005	+	1.58238i	−0.189710	+	0.0616406i	0.212621	+	0.977135i	$0.431800\pi$
$660$		0			0
$661$	−18.5962	+	13.5109i	−0.723307	+	0.525513i	−0.887439	−	0.460925i	$-0.847518\pi$
$661$	−18.5962	+	13.5109i	−0.723307	+	0.525513i	0.164132	+	0.986438i	$0.447518\pi$
$662$	13.9341	−	7.09976i	0.541563	−	0.275940i
$663$	1.26001	−	7.95537i	0.0489346	−	0.308961i
$664$	18.3868	+	13.3588i	0.713547	+	0.518423i
$665$		0			0
$666$	7.47502	−	10.2885i	0.289651	−	0.398671i
$667$	−25.3081	+	4.00840i	−0.979932	+	0.155206i
$668$	−7.62422	−	3.88473i	−0.294990	−	0.150305i
$669$	13.2370	−	18.2191i	0.511771	−	0.704392i
$670$		0			0
$671$	1.94782	−	5.99476i	0.0751946	−	0.231425i
$672$	9.21045	+	1.45879i	0.355301	+	0.0562741i
$673$	−36.0723	−	18.3797i	−1.39048	−	0.708487i	−0.411307	−	0.911497i	$-0.634928\pi$
$673$	−36.0723	−	18.3797i	−1.39048	−	0.708487i	−0.979177	+	0.203010i	$0.934928\pi$
$674$	4.75424	+	14.6321i	0.183127	+	0.563606i
$675$		0			0
$676$	6.38064			0.245409
$677$	−18.4970	−	18.4970i	−0.710897	−	0.710897i	0.255826	−	0.966723i	$-0.417653\pi$
$677$	−18.4970	−	18.4970i	−0.710897	−	0.710897i	−0.966723	+	0.255826i	$0.917653\pi$
$678$	7.03628	+	13.8095i	0.270227	+	0.530350i
$679$	−16.9292	+	23.3010i	−0.649682	+	0.894210i
$680$		0			0
$681$			18.0109i			0.690179i
$682$	4.65232	+	0.312617i	0.178147	+	0.0119707i
$683$	23.1576	+	23.1576i	0.886099	+	0.886099i	0.994146	−	0.108047i	$-0.0344596\pi$
$683$	23.1576	+	23.1576i	0.886099	+	0.886099i	−0.108047	+	0.994146i	$0.534460\pi$
$684$	4.35948	+	6.00031i	0.166689	+	0.229428i
$685$		0			0
$686$	−10.1051	+	31.1002i	−0.385813	+	1.18741i
$687$	6.28806	−	6.28806i	0.239904	−	0.239904i
$688$	7.21000	−	7.21000i	0.274879	−	0.274879i
$689$	−6.43284	−	2.09016i	−0.245072	−	0.0796286i
$690$		0			0
$691$	−1.10454	−	3.39941i	−0.0420185	−	0.129320i	0.927847	−	0.372962i	$-0.121658\pi$
$691$	−1.10454	−	3.39941i	−0.0420185	−	0.129320i	−0.969865	+	0.243642i	$0.921658\pi$
$692$	−0.676346	+	4.27028i	−0.0257108	+	0.162332i
$693$	0.671787	+	1.31846i	0.0255191	+	0.0500840i
$694$	−37.7599	+	27.4342i	−1.43335	+	1.04139i
$695$		0			0
$696$	6.37789	+	19.6291i	0.241753	+	0.744040i
$697$	−0.330608	−	2.08738i	−0.0125227	−	0.0790651i
$698$	−6.86817	−	43.3639i	−0.259964	−	1.64135i
$699$	−1.47397	−	4.53642i	−0.0557507	−	0.171583i
$700$		0			0
$701$	−8.93559	+	6.49209i	−0.337493	+	0.245203i	−0.743603	−	0.668621i	$-0.766885\pi$
$701$	−8.93559	+	6.49209i	−0.337493	+	0.245203i	0.406111	+	0.913824i	$0.366885\pi$
$702$	9.25027	+	18.1547i	0.349129	+	0.685204i
$703$	−4.29881	+	27.1416i	−0.162133	+	1.02367i
$704$	0.427413	+	1.31544i	0.0161087	+	0.0495776i
$705$		0			0
$706$	−53.6339	−	17.4267i	−2.01854	−	0.655863i
$707$	−4.62703	+	4.62703i	−0.174017	+	0.174017i
$708$	3.90138	−	3.90138i	0.146623	−	0.146623i
$709$	−12.1279	+	37.3258i	−0.455473	+	1.40180i	0.415107	+	0.909773i	$0.363744\pi$
$709$	−12.1279	+	37.3258i	−0.455473	+	1.40180i	−0.870579	+	0.492028i	$0.836256\pi$
$710$		0			0
$711$	0.624630	+	0.859729i	0.0234254	+	0.0322423i
$712$	22.5225	+	22.5225i	0.844066	+	0.844066i
$713$	1.10092	−	16.3837i	0.0412297	−	0.613575i
$714$		−	11.1014i		−	0.415458i
$715$		0			0
$716$	9.63194	−	13.2572i	0.359963	−	0.495446i
$717$	−11.6043	−	22.7748i	−0.433371	−	0.850539i
$718$	−3.53089	−	3.53089i	−0.131772	−	0.131772i
$719$	48.9840			1.82680			0.913398	−	0.407068i	$-0.133449\pi$
$719$	48.9840			1.82680			0.913398	+	0.407068i	$0.133449\pi$
$720$		0			0
$721$	−6.78980	−	20.8969i	−0.252865	−	0.778240i
$722$	−21.7156	−	11.0647i	−0.808171	−	0.411784i
$723$	25.3898	+	4.02135i	0.944257	+	0.149556i
$724$	3.01130	−	9.26782i	0.111914	−	0.344436i
$725$		0			0
$726$	12.4945	−	17.1972i	0.463715	−	0.638249i
$727$	−25.3185	−	12.9004i	−0.939011	−	0.478450i	−0.0836572	−	0.996495i	$-0.526660\pi$
$727$	−25.3185	−	12.9004i	−0.939011	−	0.478450i	−0.855354	+	0.518045i	$0.826660\pi$
$728$	8.19510	−	1.29798i	0.303731	−	0.0481062i
$729$	12.8695	−	17.7133i	0.476647	−	0.656049i
$730$		0			0
$731$	−5.06291	−	3.67842i	−0.187258	−	0.136051i
$732$	1.85966	−	11.7414i	0.0687351	−	0.433976i
$733$	14.4725	−	7.37412i	0.534555	−	0.272369i	−0.165806	−	0.986158i	$-0.553023\pi$
$733$	14.4725	−	7.37412i	0.534555	−	0.272369i	0.700361	+	0.713789i	$0.253023\pi$
$734$	19.2874	−	14.0131i	0.711911	−	0.517234i
$735$		0			0
$736$	−11.9980	+	3.89837i	−0.442251	+	0.143696i
$737$	−7.20010	+	3.66863i	−0.265219	+	0.135136i
$738$	1.31638	+	1.31638i	0.0484566	+	0.0484566i
$739$	−47.9986			−1.76566			−0.882829	−	0.469694i	$-0.844364\pi$
$739$	−47.9986			−1.76566			−0.882829	+	0.469694i	$0.844364\pi$
$740$		0			0
$741$	−12.4032	−	9.01149i	−0.455645	−	0.331045i
$742$	−9.20773	−	1.45836i	−0.338026	−	0.0535381i
$743$	−9.20464	+	9.20464i	−0.337686	+	0.337686i	−0.855496	−	0.517810i	$-0.826747\pi$
$743$	−9.20464	+	9.20464i	−0.337686	+	0.337686i	0.517810	+	0.855496i	$0.326747\pi$
$744$	−13.1730	+	1.18858i	−0.482947	+	0.0435755i
$745$		0			0
$746$	51.0641	−	37.1002i	1.86959	−	1.35834i
$747$	2.83542	+	17.9022i	0.103743	+	0.655006i
$748$	−1.08439	+	0.552523i	−0.0396491	+	0.0202022i
$749$		−	6.40505i		−	0.234035i
$750$		0			0
$751$	−6.24117	+	19.2083i	−0.227744	+	0.700923i	0.770258	+	0.637732i	$0.220127\pi$
$751$	−6.24117	+	19.2083i	−0.227744	+	0.700923i	−0.998002	+	0.0631902i	$0.979873\pi$
$752$	10.4719	+	5.33572i	0.381873	+	0.194574i
$753$	−0.988090	+	1.93924i	−0.0360080	+	0.0706697i
$754$	−19.1250	−	26.3232i	−0.696490	−	0.958636i
$755$		0			0
$756$	4.71077	+	6.48382i	0.171329	+	0.235814i
$757$	−2.09287	−	13.2139i	−0.0760667	−	0.480266i	−0.996086	−	0.0883924i	$-0.971827\pi$
$757$	−2.09287	−	13.2139i	−0.0760667	−	0.480266i	0.920019	−	0.391874i	$-0.128173\pi$
$758$	16.0759	−	31.5508i	0.583904	−	1.14598i
$759$	1.41187	+	1.02578i	0.0512476	+	0.0372336i
$760$		0			0
$761$	−40.0234	+	13.0044i	−1.45085	+	0.471409i	−0.925261	−	0.379331i	$-0.876154\pi$
$761$	−40.0234	+	13.0044i	−1.45085	+	0.471409i	−0.525587	+	0.850740i	$0.676154\pi$
$762$	−15.0345	+	2.38124i	−0.544644	+	0.0862631i
$763$	23.1764	+	3.67078i	0.839042	+	0.132891i
$764$	6.67823	+	2.16989i	0.241610	+	0.0785038i
$765$		0			0
$766$	−28.1597	+	9.14965i	−1.01745	+	0.330590i
$767$	5.93922	−	11.6564i	0.214453	−	0.420887i
$768$	8.86467	+	17.3979i	0.319876	+	0.627793i
$769$		−	43.3460i		−	1.56310i	−0.623845	−	0.781548i	$-0.714430\pi$
$769$		−	43.3460i		−	1.56310i	0.623845	−	0.781548i	$-0.285570\pi$
$770$		0			0
$771$	7.65655	+	2.48776i	0.275744	+	0.0895946i
$772$	−1.13128	+	0.179177i	−0.0407157	+	0.00644873i
$773$	1.98021	−	12.5025i	0.0712232	−	0.449685i	−0.926144	−	0.377170i	$-0.876897\pi$
$773$	1.98021	−	12.5025i	0.0712232	−	0.449685i	0.997367	−	0.0725155i	$-0.0231027\pi$
$774$	5.51261			0.198147
$775$		0			0
$776$	−31.3843			−1.12663
$777$	−1.61753	+	10.2127i	−0.0580287	+	0.366379i
$778$	46.2342	−	7.32278i	1.65758	−	0.262534i
$779$	−3.82583	−	1.24309i	−0.137074	−	0.0445382i
$780$		0			0
$781$			1.58061i			0.0565586i
$782$	6.81810	+	13.3813i	0.243815	+	0.478513i
$783$	−21.4600	+	42.1177i	−0.766919	+	1.50516i
$784$	−16.9735	+	5.51501i	−0.606195	+	0.196965i
$785$		0			0
$786$	12.6645	+	4.11495i	0.451728	+	0.146775i
$787$	17.9835	+	2.84830i	0.641042	+	0.101531i	0.468489	−	0.883469i	$-0.344798\pi$
$787$	17.9835	+	2.84830i	0.641042	+	0.101531i	0.172553	+	0.985000i	$0.444798\pi$
$788$	15.8445	−	2.50952i	0.564435	−	0.0893978i
$789$	10.2405	−	3.32733i	0.364571	−	0.118456i
$790$		0			0
$791$	11.6942	+	8.49631i	0.415797	+	0.302094i
$792$	−0.732028	+	1.43669i	−0.0260115	+	0.0510504i
$793$	−4.40944	−	27.8401i	−0.156584	−	0.988631i
$794$	−30.5295	−	42.0203i	−1.08345	−	1.49124i
$795$		0			0
$796$	−6.07162	−	8.35686i	−0.215203	−	0.296201i
$797$	−13.2635	+	26.0310i	−0.469816	+	0.922065i	0.527550	+	0.849524i	$0.323111\pi$
$797$	−13.2635	+	26.0310i	−0.469816	+	0.922065i	−0.997365	+	0.0725409i	$0.976889\pi$
$798$	−18.8276	−	9.59314i	−0.666490	−	0.339593i
$799$	2.22906	−	6.86033i	0.0788583	−	0.242701i
$800$		0			0
$801$			25.4020i			0.897535i
$802$	26.1053	−	13.3013i	0.921811	−	0.469686i
$803$	0.174509	+	1.10180i	0.00615828	+	0.0388818i
$804$	−12.3297	+	8.95802i	−0.434833	+	0.315925i
$805$		0			0
$806$	19.1715	−	8.19941i	0.675288	−	0.288812i
$807$	0.0937526	−	0.0937526i	0.00330025	−	0.00330025i
$808$	−7.04260	−	1.11544i	−0.247758	−	0.0392410i
$809$	16.3525	+	11.8808i	0.574924	+	0.417707i	0.836891	−	0.547370i	$-0.184371\pi$
$809$	16.3525	+	11.8808i	0.574924	+	0.417707i	−0.261967	+	0.965077i	$0.584371\pi$
$810$		0			0
$811$	−18.3841			−0.645553			−0.322776	−	0.946475i	$-0.604616\pi$
$811$	−18.3841			−0.645553			−0.322776	+	0.946475i	$0.604616\pi$
$812$	−9.04967	−	9.04967i	−0.317581	−	0.317581i
$813$	12.5300	−	6.38433i	0.439445	−	0.223908i
$814$	3.77767	−	1.22744i	0.132407	−	0.0430218i
$815$		0			0
$816$	14.4364	−	10.4887i	0.505376	−	0.367177i
$817$	−10.6136	+	5.40787i	−0.371321	+	0.189198i
$818$	−2.28311	+	14.4150i	−0.0798272	+	0.504009i
$819$	5.35338	+	3.88946i	0.187062	+	0.135909i
$820$		0			0
$821$	−6.98478	+	9.61372i	−0.243770	+	0.335521i	−0.913317	−	0.407249i	$-0.866488\pi$
$821$	−6.98478	+	9.61372i	−0.243770	+	0.335521i	0.669547	+	0.742770i	$0.266488\pi$
$822$	4.00140	−	0.633759i	0.139565	−	0.0221049i
$823$	−8.19412	−	4.17511i	−0.285629	−	0.145535i	0.305306	−	0.952254i	$-0.401241\pi$
$823$	−8.19412	−	4.17511i	−0.285629	−	0.145535i	−0.590935	+	0.806719i	$0.701241\pi$
$824$	14.0731	−	19.3699i	0.490259	−	0.674784i
$825$		0			0
$826$	5.57187	−	17.1485i	0.193870	−	0.596671i
$827$	−41.7473	−	6.61212i	−1.45170	−	0.229926i	−0.619757	−	0.784794i	$-0.712769\pi$
$827$	−41.7473	−	6.61212i	−1.45170	−	0.229926i	−0.831939	+	0.554868i	$0.812769\pi$
$828$	−3.36389	−	1.71399i	−0.116903	−	0.0595652i
$829$	2.23278	+	6.87179i	0.0775477	+	0.238667i	0.982314	−	0.187241i	$-0.0599546\pi$
$829$	2.23278	+	6.87179i	0.0775477	+	0.238667i	−0.904766	+	0.425908i	$0.859955\pi$
$830$		0			0
$831$	11.6183			0.403035
$832$	4.37357	+	4.37357i	0.151626	+	0.151626i
$833$	4.97282	+	9.75970i	0.172298	+	0.338154i
$834$	−26.5228	+	36.5055i	−0.918410	+	1.26408i
$835$		0			0
$836$			2.31655i			0.0801194i
$837$	−23.2583	−	19.4085i	−0.803923	−	0.670857i
$838$	3.90226	+	3.90226i	0.134801	+	0.134801i
$839$	−0.972405	−	1.33840i	−0.0335711	−	0.0462067i	0.791901	−	0.610649i	$-0.209091\pi$
$839$	−0.972405	−	1.33840i	−0.0335711	−	0.0462067i	−0.825473	+	0.564442i	$0.809091\pi$
$840$		0			0
$841$	14.3645	−	44.2094i	0.495327	−	1.52446i
$842$	−11.2893	+	11.2893i	−0.389054	+	0.389054i
$843$	−2.79139	+	2.79139i	−0.0961404	+	0.0961404i
$844$	−5.14486	−	1.67167i	−0.177094	−	0.0575412i
$845$		0			0
$846$	1.96352	+	6.04310i	0.0675072	+	0.207766i
$847$	3.10134	−	19.5811i	0.106563	−	0.672813i
$848$	−6.80307	−	13.3518i	−0.233618	−	0.458502i
$849$	19.1567	−	13.9181i	0.657455	−	0.477669i
$850$		0			0
$851$	−4.32258	−	13.3035i	−0.148176	−	0.456039i
$852$	0.466329	+	2.94429i	0.0159762	+	0.100870i
$853$	−3.25791	−	20.5697i	−0.111549	−	0.704292i	−0.978554	−	0.205992i	$-0.933958\pi$
$853$	−3.25791	−	20.5697i	−0.111549	−	0.704292i	0.867005	−	0.498300i	$-0.166042\pi$
$854$	−12.0052	−	36.9482i	−0.410810	−	1.26434i
$855$		0			0
$856$	5.64646	−	4.10239i	0.192992	−	0.140217i
$857$	8.37269	+	16.4323i	0.286006	+	0.561318i	0.988652	−	0.150221i	$-0.0479986\pi$
$857$	8.37269	+	16.4323i	0.286006	+	0.561318i	−0.702647	+	0.711539i	$0.747999\pi$
$858$	−0.346667	+	2.18877i	−0.0118350	+	0.0747233i
$859$	−2.97147	−	9.14523i	−0.101385	−	0.312031i	0.887480	−	0.460846i	$-0.152454\pi$
$859$	−2.97147	−	9.14523i	−0.101385	−	0.312031i	−0.988865	+	0.148815i	$0.952454\pi$
$860$		0			0
$861$	−1.43956	−	0.467741i	−0.0490601	−	0.0159406i
$862$	33.7786	−	33.7786i	1.15050	−	1.15050i
$863$	7.80973	−	7.80973i	0.265846	−	0.265846i	−0.561578	−	0.827424i	$-0.689805\pi$
$863$	7.80973	−	7.80973i	0.265846	−	0.265846i	0.827424	+	0.561578i	$0.189805\pi$
$864$	−7.19164	+	22.1336i	−0.244665	+	0.753001i
$865$		0			0
$866$	−10.9603	−	15.0856i	−0.372447	−	0.512630i
$867$	6.46503	+	6.46503i	0.219564	+	0.219564i
$868$	6.94353	−	4.36509i	0.235679	−	0.148161i
$869$			0.331916i			0.0112595i
$870$		0			0
$871$	−21.2403	+	29.2348i	−0.719702	+	0.990584i
$872$	11.6083	+	22.7826i	0.393107	+	0.771515i
$873$	−17.6984	−	17.6984i	−0.599000	−	0.599000i
$874$	28.5860			0.966937
$875$		0			0
$876$	0.650134	+	2.00091i	0.0219660	+	0.0676044i
$877$	2.51245	+	1.28016i	0.0848394	+	0.0432278i	0.495895	−	0.868382i	$-0.334840\pi$
$877$	2.51245	+	1.28016i	0.0848394	+	0.0432278i	−0.411056	+	0.911610i	$0.634840\pi$
$878$	27.6632	+	4.38142i	0.933588	+	0.147866i
$879$	10.7586	−	33.1115i	0.362878	−	1.11682i
$880$		0			0
$881$	−3.36729	+	4.63467i	−0.113447	+	0.156146i	−0.861964	−	0.506969i	$-0.830766\pi$
$881$	−3.36729	+	4.63467i	−0.113447	+	0.156146i	0.748518	+	0.663115i	$0.230766\pi$
$882$	−8.59709	−	4.38043i	−0.289479	−	0.147497i
$883$	−36.2404	+	5.73991i	−1.21958	+	0.193163i	−0.732852	−	0.680388i	$-0.761811\pi$
$883$	−36.2404	+	5.73991i	−1.21958	+	0.193163i	−0.486733	+	0.873551i	$0.661811\pi$
$884$	−3.19895	+	4.40298i	−0.107592	+	0.148088i
$885$		0			0
$886$	−34.4227	−	25.0096i	−1.15645	−	0.840214i
$887$	7.01679	−	44.3022i	0.235601	−	1.48752i	−0.532082	−	0.846693i	$-0.678590\pi$
$887$	7.01679	−	44.3022i	0.235601	−	1.48752i	0.767682	−	0.640831i	$-0.221410\pi$
$888$	−10.0392	+	5.11521i	−0.336892	+	0.171655i
$889$	−11.4853	+	8.34458i	−0.385205	+	0.279868i
$890$		0			0
$891$	0.772695	−	0.251064i	0.0258863	−	0.00841096i
$892$	−13.5581	+	6.90821i	−0.453960	+	0.231304i
$893$	−9.70870	−	9.70870i	−0.324889	−	0.324889i
$894$	−21.7620			−0.727829
$895$		0			0
$896$	19.6615	+	14.2849i	0.656843	+	0.477225i
$897$	7.70801	+	1.22083i	0.257363	+	0.0407623i
$898$	−14.3707	+	14.3707i	−0.479556	+	0.479556i
$899$	41.5320	+	24.8015i	1.38517	+	0.827177i
$900$		0			0
$901$	−7.44059	+	5.40591i	−0.247882	+	0.180097i
$902$	0.0909606	+	0.574303i	0.00302866	+	0.0191222i
$903$	−3.99361	+	2.03484i	−0.132899	+	0.0677154i
$904$			15.7510i			0.523870i
$905$		0			0
$906$	−9.67980	+	29.7914i	−0.321590	+	0.989751i
$907$	−28.9448	−	14.7481i	−0.961098	−	0.489704i	−0.0982466	−	0.995162i	$-0.531323\pi$
$907$	−28.9448	−	14.7481i	−0.961098	−	0.489704i	−0.862851	+	0.505458i	$0.831323\pi$
$908$	5.52499	−	10.8434i	0.183353	−	0.359851i
$909$	−3.34247	−	4.60052i	−0.110863	−	0.152590i
$910$		0			0
$911$	4.63874	+	6.38468i	0.153688	+	0.211534i	0.878918	−	0.476974i	$-0.158266\pi$
$911$	4.63874	+	6.38468i	0.153688	+	0.211534i	−0.725229	+	0.688507i	$0.758266\pi$
$912$	−5.31339	−	33.5475i	−0.175944	−	1.11087i
$913$	−2.57014	+	5.04418i	−0.0850592	+	0.166938i
$914$	20.3703	+	14.7999i	0.673788	+	0.489536i
$915$		0			0
$916$	−5.71461	+	1.85679i	−0.188816	+	0.0613500i
$917$	12.2664	−	1.94281i	0.405073	−	0.0641572i
$918$	27.3641	+	4.33405i	0.903150	+	0.143045i
$919$	14.1257	+	4.58971i	0.465963	+	0.151401i	0.532583	−	0.846378i	$-0.321221\pi$
$919$	14.1257	+	4.58971i	0.465963	+	0.151401i	−0.0666197	+	0.997778i	$0.521221\pi$
$920$		0			0
$921$	−11.2998	+	3.67153i	−0.372341	+	0.120981i
$922$	20.0875	−	39.4240i	0.661548	−	1.29836i
$923$	3.20890	+	6.29782i	0.105622	+	0.207295i
$924$			0.871657i			0.0286754i
$925$		0			0
$926$	11.4076	+	3.70657i	0.374878	+	0.121805i
$927$	18.8594	−	2.98703i	0.619422	−	0.0981069i
$928$	5.81370	−	36.7062i	0.190844	−	1.20494i
$929$	−31.7419			−1.04142			−0.520709	−	0.853734i	$-0.674333\pi$
$929$	−31.7419			−1.04142			−0.520709	+	0.853734i	$0.674333\pi$
$930$		0			0
$931$	20.8494			0.683311
$932$	−0.504183	+	3.18328i	−0.0165151	+	0.104272i
$933$	−34.2424	+	5.42347i	−1.12105	+	0.177556i
$934$	35.4727	+	11.5258i	1.16070	+	0.377135i
$935$		0			0
$936$			7.21052i			0.235683i
$937$	16.1026	+	31.6031i	0.526048	+	1.03243i	0.989258	+	0.146180i	$0.0466977\pi$
$937$	16.1026	+	31.6031i	0.526048	+	1.03243i	−0.463210	+	0.886249i	$0.653302\pi$
$938$	−22.6113	+	44.3772i	−0.738286	+	1.44897i
$939$	−31.5355	+	10.2465i	−1.02912	+	0.334382i
$940$		0			0
$941$	16.1896	+	5.26032i	0.527766	+	0.171482i	0.560767	−	0.827974i	$-0.310506\pi$
$941$	16.1896	+	5.26032i	0.527766	+	0.171482i	−0.0330008	+	0.999455i	$0.510506\pi$
$942$	38.6493	+	6.12145i	1.25926	+	0.199448i
$943$	2.02248	−	0.320329i	0.0658609	−	0.0104313i
$944$	27.5645	−	8.95626i	0.897149	−	0.291501i
$945$		0			0
$946$	1.39296	+	1.01205i	0.0452891	+	0.0329045i
$947$	11.8265	−	23.2108i	0.384310	−	0.754250i	−0.615106	−	0.788445i	$-0.710887\pi$
$947$	11.8265	−	23.2108i	0.384310	−	0.754250i	0.999415	+	0.0341947i	$0.0108866\pi$
$948$	0.0979257	+	0.618279i	0.00318048	+	0.0200808i
$949$	2.93217	+	4.03578i	0.0951822	+	0.131007i
$950$		0			0
$951$	−21.6598	−	29.8121i	−0.702366	−	0.966723i
$952$	5.12194	−	10.0524i	0.166003	−	0.325800i
$953$	−1.52298	−	0.775995i	−0.0493340	−	0.0251369i	0.429149	−	0.903233i	$-0.358813\pi$
$953$	−1.52298	−	0.775995i	−0.0493340	−	0.0251369i	−0.478484	+	0.878097i	$0.658813\pi$
$954$	2.50350	−	7.70497i	0.0810537	−	0.249458i
$955$		0			0
$956$			17.2712i			0.558590i
$957$	−4.58075	+	2.33401i	−0.148075	+	0.0754478i
$958$	−3.33823	−	21.0768i	−0.107853	−	0.680959i
$959$	3.05678	−	2.22088i	0.0987087	−	0.0717161i
$960$		0			0
$961$	−21.4129	+	22.4163i	−0.690738	+	0.723106i
$962$	12.5600	−	12.5600i	0.404950	−	0.404950i
$963$	5.49762	+	0.870738i	0.177158	+	0.0280591i
$964$	−14.0522	−	10.2096i	−0.452592	−	0.328828i
$965$		0			0
$966$	10.7562			0.346075
$967$	8.87448	+	8.87448i	0.285384	+	0.285384i	0.835252	−	0.549868i	$-0.185322\pi$
$967$	8.87448	+	8.87448i	0.285384	+	0.285384i	−0.549868	+	0.835252i	$0.685322\pi$
$968$	19.2483	−	9.80752i	0.618665	−	0.315226i
$969$	−19.8261	+	6.44190i	−0.636907	+	0.206944i
$970$		0			0
$971$	26.1646	−	19.0097i	0.839662	−	0.610050i	−0.0826142	−	0.996582i	$-0.526327\pi$
$971$	26.1646	−	19.0097i	0.839662	−	0.610050i	0.922276	+	0.386531i	$0.126327\pi$
$972$	−10.2504	+	5.22283i	−0.328781	+	0.167522i
$973$	−6.58337	+	41.5658i	−0.211053	+	1.33254i
$974$	10.5326	+	7.65238i	0.337486	+	0.245198i
$975$		0			0
$976$	36.7055	−	50.5208i	1.17492	−	1.61713i
$977$	47.0894	−	7.45823i	1.50652	−	0.238610i	0.652078	−	0.758152i	$-0.273897\pi$
$977$	47.0894	−	7.45823i	1.50652	−	0.238610i	0.854445	+	0.519542i	$0.173897\pi$
$978$	−17.2223	−	8.77519i	−0.550708	−	0.280600i
$979$	−4.66349	+	6.41874i	−0.149046	+	0.205144i
$980$		0			0
$981$	−6.30145	+	19.3939i	−0.201190	+	0.619198i
$982$	−20.6112	−	3.26450i	−0.657731	−	0.104174i
$983$	−43.3522	−	22.0891i	−1.38272	−	0.704532i	−0.404976	−	0.914327i	$-0.632720\pi$
$983$	−43.3522	−	22.0891i	−1.38272	−	0.704532i	−0.977745	+	0.209796i	$0.932720\pi$
$984$	−0.509685	−	1.56865i	−0.0162482	−	0.0500067i
$985$		0			0
$986$	−44.2421			−1.40895
$987$	−3.65313	−	3.65313i	−0.116280	−	0.116280i
$988$	4.70298	+	9.23012i	0.149622	+	0.293649i
$989$	3.56404	−	4.90548i	0.113330	−	0.155985i
$990$		0			0
$991$			39.5538i			1.25647i	0.778025	+	0.628234i	$0.216222\pi$
$991$			39.5538i			1.25647i	−0.778025	+	0.628234i	$0.783778\pi$
$992$	22.1061	+	8.86164i	0.701870	+	0.281357i
$993$	−7.81342	−	7.81342i	−0.247951	−	0.247951i
$994$	5.72618	+	7.88140i	0.181623	+	0.249983i
$995$		0			0
$996$	−3.29935	+	10.1544i	−0.104544	+	0.321753i
$997$	−1.09262	+	1.09262i	−0.0346036	+	0.0346036i	−0.724197	−	0.689593i	$-0.757789\pi$
$997$	−1.09262	+	1.09262i	−0.0346036	+	0.0346036i	0.689593	+	0.724197i	$0.257789\pi$
$998$	−38.4874	+	38.4874i	−1.21830	+	1.21830i
$999$	−24.5421	−	7.97422i	−0.776478	−	0.252293i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.bs.b.418.3		112
5.2	odd	4	inner	775.2.bs.b.232.3		112
5.3	odd	4		155.2.r.a.77.12	✓	112
5.4	even	2		155.2.r.a.108.12	yes	112
31.29	odd	10	inner	775.2.bs.b.618.3		112
155.29	odd	10		155.2.r.a.153.12	yes	112
155.122	even	20	inner	775.2.bs.b.432.3		112
155.153	even	20		155.2.r.a.122.12	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.r.a.77.12	✓	112	5.3	odd	4
155.2.r.a.108.12	yes	112	5.4	even	2
155.2.r.a.122.12	yes	112	155.153	even	20
155.2.r.a.153.12	yes	112	155.29	odd	10
775.2.bs.b.232.3		112	5.2	odd	4	inner
775.2.bs.b.418.3		112	1.1	even	1	trivial
775.2.bs.b.432.3		112	155.122	even	20	inner
775.2.bs.b.618.3		112	31.29	odd	10	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:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.bs (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.261704 + 1.65234i) q^{2} +(1.16750 - 0.184914i) q^{3} +(-0.759614 - 0.246814i) q^{4} +1.97750i q^{6} +(0.837296 + 1.64328i) q^{7} +(-0.912378 + 1.79064i) q^{8} +(-1.52430 + 0.495275i) q^{9} +O(q^{10})\)	\(q+(-0.261704 + 1.65234i) q^{2} +(1.16750 - 0.184914i) q^{3} +(-0.759614 - 0.246814i) q^{4} +1.97750i q^{6} +(0.837296 + 1.64328i) q^{7} +(-0.912378 + 1.79064i) q^{8} +(-1.52430 + 0.495275i) q^{9} +(-0.476097 - 0.154693i) q^{11} +(-0.932491 - 0.147692i) q^{12} +(-2.21103 + 0.350192i) q^{13} +(-2.93438 + 0.953439i) q^{14} +(-4.01230 - 2.91511i) q^{16} +(-1.38189 + 2.71212i) q^{17} +(-0.419445 - 2.64827i) q^{18} +(3.40553 + 4.68730i) q^{19} +(1.28141 + 1.76371i) q^{21} +(0.380202 - 0.746188i) q^{22} +(-2.62779 - 1.33893i) q^{23} +(-0.734088 + 2.25929i) q^{24} -3.74501i q^{26} +(-4.84770 + 2.47003i) q^{27} +(-0.230436 - 1.45492i) q^{28} +(7.02889 - 5.10678i) q^{29} +(2.18942 + 5.11922i) q^{31} +(3.02466 - 3.02466i) q^{32} +(-0.584449 - 0.0925677i) q^{33} +(-4.11969 - 2.99313i) q^{34} +1.28012 q^{36} +(3.35379 + 3.35379i) q^{37} +(-8.63624 + 4.40039i) q^{38} +(-2.51663 + 0.817701i) q^{39} +(-0.561709 + 0.408105i) q^{41} +(-3.24960 + 1.65575i) q^{42} +(-0.321623 + 2.03065i) q^{43} +(0.323469 + 0.235014i) q^{44} +(2.90006 - 3.99159i) q^{46} +(-2.34062 + 0.370717i) q^{47} +(-5.22342 - 2.66147i) q^{48} +(2.11518 - 2.91129i) q^{49} +(-1.11186 + 3.42194i) q^{51} +(1.76596 + 0.279701i) q^{52} +(2.69217 + 1.37173i) q^{53} +(-2.81265 - 8.65645i) q^{54} -3.70647 q^{56} +(4.84271 + 4.84271i) q^{57} +(6.59864 + 12.9506i) q^{58} +(-3.43500 + 4.72787i) q^{59} +12.5915i q^{61} +(-9.03166 + 2.27794i) q^{62} +(-2.09017 - 2.09017i) q^{63} +(-1.62403 - 2.23529i) q^{64} +(0.305906 - 0.941481i) q^{66} +(11.4144 - 11.4144i) q^{67} +(1.71909 - 1.71909i) q^{68} +(-3.31554 - 1.07728i) q^{69} +(-0.975703 - 3.00291i) q^{71} +(0.503877 - 3.18135i) q^{72} +(-1.01168 - 1.98553i) q^{73} +(-6.41929 + 4.66389i) q^{74} +(-1.43000 - 4.40107i) q^{76} +(-0.144429 - 0.911886i) q^{77} +(-0.692506 - 4.37231i) q^{78} +(-0.204891 - 0.630588i) q^{79} +(-1.31302 + 0.953963i) q^{81} +(-0.527326 - 1.03493i) q^{82} +(1.76911 - 11.1697i) q^{83} +(-0.538070 - 1.65601i) q^{84} +(-3.27114 - 1.06286i) q^{86} +(7.26193 - 7.26193i) q^{87} +(0.711380 - 0.711380i) q^{88} +(4.89763 - 15.0733i) q^{89} +(-2.42675 - 3.34013i) q^{91} +(1.66564 + 1.66564i) q^{92} +(3.50277 + 5.57185i) q^{93} -3.96451i q^{94} +(2.97199 - 4.09060i) q^{96} +(7.08976 + 13.9144i) q^{97} +(4.25688 + 4.25688i) q^{98} +0.802330 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 6 q^{2} + 10 q^{3} + 18 q^{7} + 20 q^{8}+O(q^{10}) \) 112 * q + 6 * q^2 + 10 * q^3 + 18 * q^7 + 20 * q^8	\( 112 q + 6 q^{2} + 10 q^{3} + 18 q^{7} + 20 q^{8} - 20 q^{11} - 10 q^{12} + 10 q^{13} - 12 q^{16} + 10 q^{17} - 4 q^{18} + 20 q^{21} - 60 q^{22} + 40 q^{27} + 48 q^{28} - 4 q^{31} - 44 q^{32} + 26 q^{33} - 64 q^{36} + 32 q^{38} - 16 q^{41} - 70 q^{42} + 10 q^{43} - 60 q^{46} - 46 q^{47} - 150 q^{48} + 12 q^{51} + 80 q^{52} - 10 q^{53} - 24 q^{56} + 10 q^{58} + 54 q^{62} + 200 q^{63} - 52 q^{66} + 68 q^{67} + 8 q^{71} + 18 q^{72} - 30 q^{73} - 128 q^{76} + 30 q^{77} - 36 q^{78} + 64 q^{81} + 44 q^{82} - 160 q^{83} - 20 q^{86} - 60 q^{91} - 10 q^{93} - 92 q^{97} - 144 q^{98}+O(q^{100}) \) 112 * q + 6 * q^2 + 10 * q^3 + 18 * q^7 + 20 * q^8 - 20 * q^11 - 10 * q^12 + 10 * q^13 - 12 * q^16 + 10 * q^17 - 4 * q^18 + 20 * q^21 - 60 * q^22 + 40 * q^27 + 48 * q^28 - 4 * q^31 - 44 * q^32 + 26 * q^33 - 64 * q^36 + 32 * q^38 - 16 * q^41 - 70 * q^42 + 10 * q^43 - 60 * q^46 - 46 * q^47 - 150 * q^48 + 12 * q^51 + 80 * q^52 - 10 * q^53 - 24 * q^56 + 10 * q^58 + 54 * q^62 + 200 * q^63 - 52 * q^66 + 68 * q^67 + 8 * q^71 + 18 * q^72 - 30 * q^73 - 128 * q^76 + 30 * q^77 - 36 * q^78 + 64 * q^81 + 44 * q^82 - 160 * q^83 - 20 * q^86 - 60 * q^91 - 10 * q^93 - 92 * q^97 - 144 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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