LMFDB - Embedded newform 950.2.bb.d.143.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(143,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([27, 34]))

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

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

chi := DirichletCharacter("950.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.bb (of order $36$, degree $12$, 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:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			143.4
Character	$\chi$	$=$	950.143
Dual form			950.2.bb.d.857.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.573576 + 0.819152i) q^{2} +(0.225912 - 2.58219i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(1.98563 + 1.66614i) q^{6} +(0.690517 + 2.57704i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-3.66223 - 0.645749i) q^{9} +O(q^{10})$	\(q+(-0.573576 + 0.819152i) q^{2} +(0.225912 - 2.58219i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(1.98563 + 1.66614i) q^{6} +(0.690517 + 2.57704i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-3.66223 - 0.645749i) q^{9} +(0.106917 + 0.185185i) q^{11} +(-2.50373 + 0.670872i) q^{12} +(-4.23956 + 0.370913i) q^{13} +(-2.50705 - 0.912493i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(-5.42561 - 3.79906i) q^{17} +(2.62953 - 2.62953i) q^{18} +(1.04529 - 4.23171i) q^{19} +(6.81040 - 1.20086i) q^{21} +(-0.213019 - 0.0186368i) q^{22} +(-6.26930 - 2.92342i) q^{23} +(0.886533 - 2.43573i) q^{24} +(2.12788 - 3.68559i) q^{26} +(-0.482170 + 1.79948i) q^{27} +(2.18546 - 1.53027i) q^{28} +(-0.784560 + 4.44946i) q^{29} +(-0.261450 - 0.150948i) q^{31} +(-0.0871557 - 0.996195i) q^{32} +(0.502336 - 0.234243i) q^{33} +(6.22401 - 2.26535i) q^{34} +(0.645749 + 3.66223i) q^{36} +(-4.30651 - 4.30651i) q^{37} +(2.86686 + 3.28346i) q^{38} +11.0311i q^{39} +(-2.80406 - 3.34175i) q^{41} +(-2.92260 + 6.26754i) q^{42} +(0.787004 + 1.68774i) q^{43} +(0.137449 - 0.163806i) q^{44} +(5.99065 - 3.45870i) q^{46} +(0.732728 + 1.04644i) q^{47} +(1.48674 + 2.12328i) q^{48} +(-0.102164 + 0.0589844i) q^{49} +(-11.0356 + 13.1517i) q^{51} +(1.79856 + 3.85702i) q^{52} +(2.85324 - 6.11879i) q^{53} +(-1.19749 - 1.42711i) q^{54} +2.66795i q^{56} +(-10.6909 - 3.65514i) q^{57} +(-3.19478 - 3.19478i) q^{58} +(0.312500 + 1.77228i) q^{59} +(-11.1219 + 4.04803i) q^{61} +(0.273611 - 0.127587i) q^{62} +(-0.864705 - 9.88362i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-0.0962473 + 0.545846i) q^{66} +(-11.9883 + 8.39433i) q^{67} +(-1.71428 + 6.39776i) q^{68} +(-8.96513 + 15.5281i) q^{69} +(3.60434 - 9.90283i) q^{71} +(-3.37031 - 1.57160i) q^{72} +(6.11393 + 0.534900i) q^{73} +(5.99780 - 1.05757i) q^{74} +(-4.33402 + 0.465075i) q^{76} +(-0.403402 + 0.403402i) q^{77} +(-9.03617 - 6.32719i) q^{78} +(2.97669 - 2.49774i) q^{79} +(-5.94569 - 2.16406i) q^{81} +(4.34575 - 0.380203i) q^{82} +(-14.1353 + 3.78755i) q^{83} +(-3.45773 - 5.98897i) q^{84} +(-1.83392 - 0.323369i) q^{86} +(11.3121 + 3.03107i) q^{87} +(0.0553441 + 0.206547i) q^{88} +(8.21001 + 6.88902i) q^{89} +(-3.88335 - 10.6694i) q^{91} +(-0.602891 + 6.89108i) q^{92} +(-0.448842 + 0.641012i) q^{93} -1.27747 q^{94} -2.59205 q^{96} +(-3.05830 + 4.36771i) q^{97} +(0.0102817 - 0.117520i) q^{98} +(-0.271970 - 0.747230i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{6}+O(q^{10}) $ 96 * q - 12 * q^6	$ 96 q - 12 q^{6} + 12 q^{26} - 72 q^{31} + 12 q^{36} - 24 q^{41} + 12 q^{51} - 72 q^{61} - 36 q^{66} + 168 q^{71} - 12 q^{76} + 12 q^{81} - 48 q^{86} - 72 q^{91}+O(q^{100}) $ 96 * q - 12 * q^6 + 12 * q^26 - 72 * q^31 + 12 * q^36 - 24 * q^41 + 12 * q^51 - 72 * q^61 - 36 * q^66 + 168 * q^71 - 12 * q^76 + 12 * q^81 - 48 * q^86 - 72 * q^91

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−0.573576	+	0.819152i	−0.405580	+	0.579228i
$2$	−0.573576	+	0.819152i	−0.405580	+	0.579228i
$3$	0.225912	−	2.58219i	0.130430	−	1.49083i	−0.595666	−	0.803233i	$-0.703112\pi$
$3$	0.225912	−	2.58219i	0.130430	−	1.49083i	0.726096	−	0.687593i	$-0.241333\pi$
$4$	−0.342020	−	0.939693i	−0.171010	−	0.469846i
$5$		0			0
$5$		0			0
$6$	1.98563	+	1.66614i	0.810628	+	0.680198i
$7$	0.690517	+	2.57704i	0.260991	+	0.974031i	0.964659	+	0.263502i	$0.0848776\pi$
$7$	0.690517	+	2.57704i	0.260991	+	0.974031i	−0.703668	+	0.710529i	$0.748456\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$	−3.66223	−	0.645749i	−1.22074	−	0.215250i
$10$		0			0
$11$	0.106917	+	0.185185i	0.0322366	+	0.0558354i	0.881694	−	0.471822i	$-0.156404\pi$
$11$	0.106917	+	0.185185i	0.0322366	+	0.0558354i	−0.849457	+	0.527658i	$0.823070\pi$
$12$	−2.50373	+	0.670872i	−0.722764	+	0.193664i
$13$	−4.23956	+	0.370913i	−1.17584	+	0.102873i	−0.658280	−	0.752773i	$-0.728716\pi$
$13$	−4.23956	+	0.370913i	−1.17584	+	0.102873i	−0.517562	+	0.855646i	$0.673160\pi$
$14$	−2.50705	−	0.912493i	−0.670039	−	0.243874i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	−5.42561	−	3.79906i	−1.31590	−	0.921406i	−0.316276	−	0.948667i	$-0.602433\pi$
$17$	−5.42561	−	3.79906i	−1.31590	−	0.921406i	−0.999628	+	0.0272610i	$0.991321\pi$
$18$	2.62953	−	2.62953i	0.619787	−	0.619787i
$19$	1.04529	−	4.23171i	0.239807	−	0.970821i
$19$	1.04529	−	4.23171i	0.239807	−	0.970821i
$20$		0			0
$21$	6.81040	−	1.20086i	1.48615	−	0.262049i
$22$	−0.213019	−	0.0186368i	−0.0454159	−	0.00397338i
$23$	−6.26930	−	2.92342i	−1.30724	−	0.609575i	−0.360856	−	0.932622i	$-0.617515\pi$
$23$	−6.26930	−	2.92342i	−1.30724	−	0.609575i	−0.946383	+	0.323046i	$0.895293\pi$
$24$	0.886533	−	2.43573i	0.180963	−	0.497191i
$25$		0			0
$26$	2.12788	−	3.68559i	0.417311	−	0.722804i
$27$	−0.482170	+	1.79948i	−0.0927937	+	0.346311i
$28$	2.18546	−	1.53027i	0.413013	−	0.289195i
$29$	−0.784560	+	4.44946i	−0.145689	+	0.826244i	0.821122	+	0.570753i	$0.193348\pi$
$29$	−0.784560	+	4.44946i	−0.145689	+	0.826244i	−0.966811	+	0.255492i	$0.917763\pi$
$30$		0			0
$31$	−0.261450	−	0.150948i	−0.0469578	−	0.0271111i	0.476337	−	0.879263i	$-0.341964\pi$
$31$	−0.261450	−	0.150948i	−0.0469578	−	0.0271111i	−0.523295	+	0.852152i	$0.675297\pi$
$32$	−0.0871557	−	0.996195i	−0.0154071	−	0.176104i
$33$	0.502336	−	0.234243i	0.0874454	−	0.0407765i
$34$	6.22401	−	2.26535i	1.06741	−	0.388505i
$35$		0			0
$36$	0.645749	+	3.66223i	0.107625	+	0.610371i
$37$	−4.30651	−	4.30651i	−0.707986	−	0.707986i	0.258125	−	0.966111i	$-0.416895\pi$
$37$	−4.30651	−	4.30651i	−0.707986	−	0.707986i	−0.966111	+	0.258125i	$0.916895\pi$
$38$	2.86686	+	3.28346i	0.465066	+	0.532648i
$39$			11.0311i			1.76639i
$40$		0			0
$41$	−2.80406	−	3.34175i	−0.437921	−	0.521894i	0.501269	−	0.865291i	$-0.332867\pi$
$41$	−2.80406	−	3.34175i	−0.437921	−	0.521894i	−0.939190	+	0.343398i	$0.888422\pi$
$42$	−2.92260	+	6.26754i	−0.450967	+	0.967102i
$43$	0.787004	+	1.68774i	0.120017	+	0.257377i	0.957133	−	0.289648i	$-0.0935381\pi$
$43$	0.787004	+	1.68774i	0.120017	+	0.257377i	−0.837116	+	0.547025i	$0.815760\pi$
$44$	0.137449	−	0.163806i	0.0207213	−	0.0246946i
$45$		0			0
$46$	5.99065	−	3.45870i	0.883273	−	0.509958i
$47$	0.732728	+	1.04644i	0.106879	+	0.152640i	0.869029	−	0.494762i	$-0.164745\pi$
$47$	0.732728	+	1.04644i	0.106879	+	0.152640i	−0.762149	+	0.647401i	$0.775856\pi$
$48$	1.48674	+	2.12328i	0.214592	+	0.306469i
$49$	−0.102164	+	0.0589844i	−0.0145948	+	0.00842634i
$50$		0			0
$51$	−11.0356	+	13.1517i	−1.54529	+	1.84161i
$52$	1.79856	+	3.85702i	0.249415	+	0.534873i
$53$	2.85324	−	6.11879i	0.391922	−	0.840480i	−0.607028	−	0.794680i	$-0.707639\pi$
$53$	2.85324	−	6.11879i	0.391922	−	0.840480i	0.998951	−	0.0457997i	$-0.0145836\pi$
$54$	−1.19749	−	1.42711i	−0.162958	−	0.194205i
$55$		0			0
$56$			2.66795i			0.356520i
$57$	−10.6909	−	3.65514i	−1.41605	−	0.484135i
$58$	−3.19478	−	3.19478i	−0.419495	−	0.419495i
$59$	0.312500	+	1.77228i	0.0406841	+	0.230731i	0.998369	−	0.0570871i	$-0.0181813\pi$
$59$	0.312500	+	1.77228i	0.0406841	+	0.230731i	−0.957685	+	0.287818i	$0.907070\pi$
$60$		0			0
$61$	−11.1219	+	4.04803i	−1.42401	+	0.518297i	−0.935208	−	0.354098i	$-0.884788\pi$
$61$	−11.1219	+	4.04803i	−1.42401	+	0.518297i	−0.488801	+	0.872395i	$0.662566\pi$
$62$	0.273611	−	0.127587i	0.0347487	−	0.0162036i
$63$	−0.864705	−	9.88362i	−0.108943	−	1.24522i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$		0			0
$66$	−0.0962473	+	0.545846i	−0.0118472	+	0.0671889i
$67$	−11.9883	+	8.39433i	−1.46461	+	1.02553i	−0.475280	+	0.879834i	$0.657653\pi$
$67$	−11.9883	+	8.39433i	−1.46461	+	1.02553i	−0.989329	+	0.145696i	$0.953458\pi$
$68$	−1.71428	+	6.39776i	−0.207886	+	0.775843i
$69$	−8.96513	+	15.5281i	−1.07927	+	1.86936i
$70$		0			0
$71$	3.60434	−	9.90283i	0.427756	−	1.17525i	−0.519415	−	0.854522i	$-0.673850\pi$
$71$	3.60434	−	9.90283i	0.427756	−	1.17525i	0.947171	−	0.320728i	$-0.103928\pi$
$72$	−3.37031	−	1.57160i	−0.397194	−	0.185215i
$73$	6.11393	+	0.534900i	0.715581	+	0.0626053i	0.439131	−	0.898423i	$-0.355286\pi$
$73$	6.11393	+	0.534900i	0.715581	+	0.0626053i	0.276450	+	0.961028i	$0.410842\pi$
$74$	5.99780	−	1.05757i	0.697230	−	0.122940i
$75$		0			0
$76$	−4.33402	+	0.465075i	−0.497146	+	0.0533478i
$77$	−0.403402	+	0.403402i	−0.0459719	+	0.0459719i
$78$	−9.03617	−	6.32719i	−1.02314	−	0.716413i
$79$	2.97669	−	2.49774i	0.334904	−	0.281018i	−0.459791	−	0.888027i	$-0.652076\pi$
$79$	2.97669	−	2.49774i	0.334904	−	0.281018i	0.794694	+	0.607010i	$0.207631\pi$
$80$		0			0
$81$	−5.94569	−	2.16406i	−0.660633	−	0.240451i
$82$	4.34575	−	0.380203i	0.479907	−	0.0419864i
$83$	−14.1353	+	3.78755i	−1.55155	+	0.415737i	−0.929977	−	0.367617i	$-0.880174\pi$
$83$	−14.1353	+	3.78755i	−1.55155	+	0.415737i	−0.621575	+	0.783355i	$0.713507\pi$
$84$	−3.45773	−	5.98897i	−0.377270	−	0.653450i
$85$		0			0
$86$	−1.83392	−	0.323369i	−0.197757	−	0.0348698i
$87$	11.3121	+	3.03107i	1.21278	+	0.324965i
$88$	0.0553441	+	0.206547i	0.00589970	+	0.0220180i
$89$	8.21001	+	6.88902i	0.870259	+	0.730234i	0.964153	−	0.265348i	$-0.0854868\pi$
$89$	8.21001	+	6.88902i	0.870259	+	0.730234i	−0.0938933	+	0.995582i	$0.529931\pi$
$90$		0			0
$91$	−3.88335	−	10.6694i	−0.407085	−	1.11846i
$92$	−0.602891	+	6.89108i	−0.0628558	+	0.718445i
$93$	−0.448842	+	0.641012i	−0.0465427	+	0.0664699i
$94$	−1.27747			−0.131761
$95$		0			0
$96$	−2.59205			−0.264550
$97$	−3.05830	+	4.36771i	−0.310524	+	0.443474i	−0.943832	−	0.330426i	$-0.892808\pi$
$97$	−3.05830	+	4.36771i	−0.310524	+	0.443474i	0.633308	+	0.773900i	$0.281697\pi$
$98$	0.0102817	−	0.117520i	0.00103860	−	0.0118713i
$99$	−0.271970	−	0.747230i	−0.0273340	−	0.0750995i
$100$		0			0
$101$	4.91564	+	4.12471i	0.489124	+	0.410424i	0.853712	−	0.520745i	$-0.174346\pi$
$101$	4.91564	+	4.12471i	0.489124	+	0.410424i	−0.364588	+	0.931169i	$0.618790\pi$
$102$	−4.44349	−	16.5833i	−0.439971	−	1.64199i
$103$	13.3868	+	3.58699i	1.31904	+	0.353437i	0.848620	−	0.529003i	$-0.177434\pi$
$103$	13.3868	+	3.58699i	1.31904	+	0.353437i	0.470425	+	0.882440i	$0.344101\pi$
$104$	−4.19110	−	0.739004i	−0.410971	−	0.0724653i
$105$		0			0
$106$	3.37567	+	5.84683i	0.327874	+	0.567894i
$107$	−3.85630	+	1.03329i	−0.372802	+	0.0998921i	−0.440355	−	0.897824i	$-0.645148\pi$
$107$	−3.85630	+	1.03329i	−0.372802	+	0.0998921i	0.0675529	+	0.997716i	$0.478481\pi$
$108$	1.85587	−	0.162368i	0.178581	−	0.0156239i
$109$	11.5547	+	4.20557i	1.10674	+	0.402821i	0.829797	−	0.558066i	$-0.188456\pi$
$109$	11.5547	+	4.20557i	1.10674	+	0.402821i	0.276944	+	0.960886i	$0.410678\pi$
$110$		0			0
$111$	−12.0931	+	10.1473i	−1.14783	+	0.963141i
$112$	−2.18546	−	1.53027i	−0.206506	−	0.144597i
$113$	2.11050	−	2.11050i	0.198539	−	0.198539i	−0.600834	−	0.799374i	$-0.705165\pi$
$113$	2.11050	−	2.11050i	0.198539	−	0.198539i	0.799374	+	0.600834i	$0.205165\pi$
$114$	9.12617	−	6.66099i	0.854744	−	0.623859i
$115$		0			0
$116$	4.44946	−	0.784560i	0.413122	−	0.0728446i
$117$	15.7657	+	1.37932i	1.45754	+	0.127518i
$118$	−1.63101	−	0.760552i	−0.150146	−	0.0700144i
$119$	6.04385	−	16.6054i	0.554039	−	1.52221i
$120$		0			0
$121$	5.47714	−	9.48668i	0.497922	−	0.862426i
$122$	3.06329	−	11.4324i	0.277337	−	1.03504i
$123$	−9.26249	+	6.48567i	−0.835171	+	0.584793i
$124$	−0.0524238	+	0.297310i	−0.00470780	+	0.0266992i
$125$		0			0
$126$	8.59216	+	4.96069i	0.765450	+	0.441933i
$127$	1.12599	+	12.8702i	0.0999158	+	1.14204i	0.866253	+	0.499605i	$0.166521\pi$
$127$	1.12599	+	12.8702i	0.0999158	+	1.14204i	−0.766338	+	0.642438i	$0.777923\pi$
$128$	−0.906308	+	0.422618i	−0.0801070	+	0.0373545i
$129$	4.53584	−	1.65091i	0.399358	−	0.145355i
$130$		0			0
$131$	−3.31820	−	18.8184i	−0.289912	−	1.64417i	−0.687192	−	0.726476i	$-0.741157\pi$
$131$	−3.31820	−	18.8184i	−0.289912	−	1.64417i	0.397280	−	0.917698i	$-0.369954\pi$
$132$	−0.391925	−	0.391925i	−0.0341127	−	0.0341127i
$133$	11.6271	−	0.228300i	1.00820	−	0.0197961i
$134$		−	14.6351i		−	1.26428i
$135$		0			0
$136$	−4.25747	−	5.07386i	−0.365075	−	0.435080i
$137$	7.86555	−	16.8677i	0.672000	−	1.44111i	−0.213724	−	0.976894i	$-0.568559\pi$
$137$	7.86555	−	16.8677i	0.672000	−	1.44111i	0.885723	−	0.464214i	$-0.153663\pi$
$138$	−7.57765	−	16.2503i	−0.645053	−	1.38332i
$139$	−13.4092	+	15.9805i	−1.13736	+	1.35545i	−0.211589	+	0.977359i	$0.567864\pi$
$139$	−13.4092	+	15.9805i	−1.13736	+	1.35545i	−0.925768	+	0.378091i	$0.876581\pi$
$140$		0			0
$141$	2.86765	−	1.65564i	0.241499	−	0.139430i
$142$	6.04456	+	8.63253i	0.507248	+	0.724426i
$143$	−0.521966	−	0.745445i	−0.0436490	−	0.0623373i
$144$	3.22051	−	1.85936i	0.268376	−	0.154947i
$145$		0			0
$146$	−3.94497	+	4.70143i	−0.326488	+	0.389093i
$147$	0.129229	+	0.277131i	0.0106586	+	0.0228574i
$148$	−2.57388	+	5.51971i	−0.211572	+	0.453717i
$149$	−14.7061	−	17.5261i	−1.20477	−	1.43579i	−0.869687	−	0.493603i	$-0.835680\pi$
$149$	−14.7061	−	17.5261i	−1.20477	−	1.43579i	−0.335084	−	0.942188i	$-0.608765\pi$
$150$		0			0
$151$		−	0.621423i		−	0.0505707i	−0.999680	−	0.0252854i	$-0.991951\pi$
$151$		−	0.621423i		−	0.0505707i	0.999680	−	0.0252854i	$-0.00804944\pi$
$152$	2.10492	−	3.81698i	0.170732	−	0.309598i
$153$	17.4166	+	17.4166i	1.40805	+	1.40805i
$154$	−0.0990657	−	0.561829i	−0.00798294	−	0.0452735i
$155$		0			0
$156$	10.3659	−	3.77287i	0.829933	−	0.302071i
$157$	18.6584	−	8.70055i	1.48910	−	0.694380i	0.503584	−	0.863947i	$-0.332015\pi$
$157$	18.6584	−	8.70055i	1.48910	−	0.694380i	0.985519	+	0.169567i	$0.0542368\pi$
$158$	0.338669	+	3.87101i	0.0269431	+	0.307961i
$159$	−15.1553	−	8.74989i	−1.20189	−	0.693912i
$160$		0			0
$161$	3.20473	−	18.1749i	0.252568	−	1.43238i
$162$	5.18300	−	3.62918i	0.407215	−	0.285135i
$163$	3.75723	−	14.0222i	0.294289	−	1.09830i	−0.647492	−	0.762072i	$-0.724182\pi$
$163$	3.75723	−	14.0222i	0.294289	−	1.09830i	0.941781	−	0.336228i	$-0.109151\pi$
$164$	−2.18117	+	3.77790i	−0.170321	+	0.295005i
$165$		0			0
$166$	5.00511	−	13.7514i	0.388472	−	1.06732i
$167$	1.43217	+	0.667830i	0.110824	+	0.0516782i	0.477240	−	0.878773i	$-0.341637\pi$
$167$	1.43217	+	0.667830i	0.110824	+	0.0516782i	−0.366415	+	0.930451i	$0.619415\pi$
$168$	6.88915	+	0.602722i	0.531509	+	0.0465010i
$169$	5.03377	−	0.887590i	0.387213	−	0.0682761i
$170$		0			0
$171$	−6.56072	+	14.8225i	−0.501711	+	1.13350i
$172$	1.31678	−	1.31678i	0.100404	−	0.100404i
$173$	15.4406	+	10.8116i	1.17393	+	0.821993i	0.987054	−	0.160391i	$-0.0512754\pi$
$173$	15.4406	+	10.8116i	1.17393	+	0.821993i	0.186874	+	0.982384i	$0.440164\pi$
$174$	−8.97126	+	7.52778i	−0.680109	+	0.570680i
$175$		0			0
$176$	−0.200937	−	0.0731352i	−0.0151462	−	0.00551278i
$177$	4.64695	−	0.406555i	0.349286	−	0.0305586i
$178$	−10.3522	+	2.77387i	−0.775932	+	0.207910i
$179$	−3.23016	−	5.59480i	−0.241433	−	0.418175i	0.719689	−	0.694296i	$-0.244284\pi$
$179$	−3.23016	−	5.59480i	−0.241433	−	0.418175i	−0.961123	+	0.276121i	$0.910951\pi$
$180$		0			0
$181$	26.3208	+	4.64107i	1.95641	+	0.344968i	0.998279	+	0.0586473i	$0.0186787\pi$
$181$	26.3208	+	4.64107i	1.95641	+	0.344968i	0.958134	+	0.286321i	$0.0924324\pi$
$182$	10.9673	+	2.93867i	0.812947	+	0.217829i
$183$	7.94020	+	29.6332i	0.586957	+	2.19055i
$184$	−5.29904	−	4.44642i	−0.390650	−	0.327795i
$185$		0			0
$186$	−0.267641	−	0.735339i	−0.0196244	−	0.0539177i
$187$	0.123440	−	1.41092i	0.00902681	−	0.103177i
$188$	0.732728	−	1.04644i	0.0534397	−	0.0763198i
$189$	−4.97029			−0.361536
$190$		0			0
$191$	−17.0491			−1.23363			−0.616814	−	0.787109i	$-0.711577\pi$
$191$	−17.0491			−1.23363			−0.616814	+	0.787109i	$0.711577\pi$
$192$	1.48674	−	2.12328i	0.107296	−	0.153235i
$193$	0.0371610	−	0.424752i	0.00267491	−	0.0305743i	−0.994740	−	0.102433i	$-0.967337\pi$
$193$	0.0371610	−	0.424752i	0.00267491	−	0.0305743i	0.997415	+	0.0718583i	$0.0228929\pi$
$194$	−1.82365	−	5.01043i	−0.130930	−	0.359728i
$195$		0			0
$196$	0.0903693	+	0.0758288i	0.00645495	+	0.00541634i
$197$	−0.0910125	−	0.339663i	−0.00648437	−	0.0242000i	0.962608	−	0.270899i	$-0.0873209\pi$
$197$	−0.0910125	−	0.339663i	−0.00648437	−	0.0242000i	−0.969092	+	0.246699i	$0.920654\pi$
$198$	0.768091	+	0.205809i	0.0545858	+	0.0146262i
$199$	5.79408	+	1.02165i	0.410731	+	0.0724230i	0.375196	−	0.926945i	$-0.377575\pi$
$199$	5.79408	+	1.02165i	0.410731	+	0.0724230i	0.0355351	+	0.999368i	$0.488686\pi$
$200$		0			0
$201$	18.9674	+	32.8525i	1.33786	+	2.31724i
$202$	−6.19826	+	1.66082i	−0.436108	+	0.116855i
$203$	−12.0082	+	1.05058i	−0.842811	+	0.0737364i
$204$	16.1329	+	5.87191i	1.12953	+	0.411116i
$205$		0			0
$206$	−10.6167	+	8.90844i	−0.739698	+	0.620681i
$207$	21.0718	+	14.7546i	1.46459	+	1.02552i
$208$	3.00927	−	3.00927i	0.208655	−	0.208655i
$209$	0.895408	−	0.258867i	0.0619367	−	0.0179062i
$210$		0			0
$211$	−8.44086	+	1.48835i	−0.581093	+	0.102462i	−0.456465	−	0.889741i	$-0.650885\pi$
$211$	−8.44086	+	1.48835i	−0.581093	+	0.102462i	−0.124628	+	0.992204i	$0.539774\pi$
$212$	−6.72564	−	0.588417i	−0.461919	−	0.0404127i
$213$	−24.7567	−	11.5442i	−1.69630	−	0.790998i
$214$	1.36546	−	3.75157i	0.0933408	−	0.256452i
$215$		0			0
$216$	−0.931481	+	1.61337i	−0.0633793	+	0.109776i
$217$	0.208465	−	0.778001i	0.0141515	−	0.0528142i
$218$	−10.0725	+	7.05285i	−0.682196	+	0.477679i
$219$	2.76242	−	15.6665i	0.186667	−	1.05864i
$220$		0			0
$221$	24.4113	+	14.0939i	1.64208	+	0.948057i
$222$	−1.37588	−	15.7264i	−0.0923429	−	1.05548i
$223$	12.1560	−	5.66844i	0.814027	−	0.379587i	0.0294095	−	0.999567i	$-0.490637\pi$
$223$	12.1560	−	5.66844i	0.814027	−	0.379587i	0.784617	+	0.619981i	$0.212860\pi$
$224$	2.50705	−	0.912493i	0.167510	−	0.0609685i
$225$		0			0
$226$	0.518287	+	2.93935i	0.0344760	+	0.195523i
$227$	−13.2886	−	13.2886i	−0.881993	−	0.881993i	0.111744	−	0.993737i	$-0.464356\pi$
$227$	−13.2886	−	13.2886i	−0.881993	−	0.881993i	−0.993737	+	0.111744i	$0.964356\pi$
$228$	0.221805	+	11.2963i	0.0146894	+	0.748116i
$229$			5.97899i			0.395103i	0.980293	+	0.197552i	$0.0632990\pi$
$229$			5.97899i			0.395103i	−0.980293	+	0.197552i	$0.936701\pi$
$230$		0			0
$231$	0.950526	+	1.13279i	0.0625400	+	0.0745323i
$232$	−1.90943	+	4.09479i	−0.125360	+	0.268836i
$233$	−3.44253	−	7.38253i	−0.225528	−	0.483646i	0.760687	−	0.649119i	$-0.224862\pi$
$233$	−3.44253	−	7.38253i	−0.225528	−	0.483646i	−0.986214	+	0.165474i	$0.947085\pi$
$234$	−10.1727	+	12.1234i	−0.665012	+	0.792531i
$235$		0			0
$236$	1.55852	−	0.899809i	0.101451	−	0.0585726i
$237$	−5.77716	−	8.25064i	−0.375267	−	0.535936i
$238$	10.1357	+	14.4753i	0.657000	+	0.938293i
$239$	−20.0332	+	11.5662i	−1.29584	+	0.748152i	−0.979682	−	0.200555i	$-0.935725\pi$
$239$	−20.0332	+	11.5662i	−1.29584	+	0.748152i	−0.316155	+	0.948707i	$0.602392\pi$
$240$		0			0
$241$	−12.6452	+	15.0700i	−0.814550	+	0.970743i	−0.999929	−	0.0119240i	$-0.996204\pi$
$241$	−12.6452	+	15.0700i	−0.814550	+	0.970743i	0.185379	+	0.982667i	$0.440649\pi$
$242$	4.62948	+	9.92795i	0.297594	+	0.638192i
$243$	−9.29316	+	19.9293i	−0.596157	+	1.27846i
$244$	7.60781	+	9.06663i	0.487040	+	0.580432i
$245$		0			0
$246$		−	11.3074i		−	0.720935i
$247$	−2.86198	+	18.3283i	−0.182104	+	1.16620i
$248$	−0.213473	−	0.213473i	−0.0135556	−	0.0135556i
$249$	6.58681	+	37.3557i	0.417422	+	2.36732i
$250$		0			0
$251$	16.5068	−	6.00797i	1.04190	−	0.379220i	0.236298	−	0.971681i	$-0.424066\pi$
$251$	16.5068	−	6.00797i	1.04190	−	0.379220i	0.805599	+	0.592461i	$0.201844\pi$
$252$	−8.99182	+	4.19295i	−0.566431	+	0.264131i
$253$	−0.128918	−	1.47354i	−0.00810502	−	0.0926407i
$254$	−11.1885	−	6.45967i	−0.702027	−	0.405316i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	2.31830	−	1.62329i	0.144612	−	0.101258i	−0.499032	−	0.866584i	$-0.666311\pi$
$257$	2.31830	−	1.62329i	0.144612	−	0.101258i	0.643644	+	0.765325i	$0.277422\pi$
$258$	−1.24930	+	4.66247i	−0.0777783	+	0.290272i
$259$	8.12435	−	14.0718i	0.504822	−	0.874378i
$260$		0			0
$261$	5.74647	−	15.7883i	0.355698	−	0.977272i
$262$	17.3184	+	8.07570i	1.06993	+	0.498918i
$263$	4.88669	+	0.427530i	0.301326	+	0.0263626i	0.236816	−	0.971554i	$-0.423896\pi$
$263$	4.88669	+	0.427530i	0.301326	+	0.0263626i	0.0645099	+	0.997917i	$0.479452\pi$
$264$	0.545846	−	0.0962473i	0.0335945	−	0.00592361i
$265$		0			0
$266$	−6.48201	+	9.65530i	−0.397438	+	0.592005i
$267$	19.6435	−	19.6435i	1.20216	−	1.20216i
$268$	11.9883	+	8.39433i	0.732305	+	0.512765i
$269$	−0.394469	+	0.330999i	−0.0240512	+	0.0201813i	−0.654734	−	0.755859i	$-0.727219\pi$
$269$	−0.394469	+	0.330999i	−0.0240512	+	0.0201813i	0.630683	+	0.776041i	$0.282775\pi$
$270$		0			0
$271$	−22.1908	−	8.07680i	−1.34800	−	0.490631i	−0.435675	−	0.900104i	$-0.643490\pi$
$271$	−22.1908	−	8.07680i	−1.34800	−	0.490631i	−0.912322	+	0.409473i	$0.865713\pi$
$272$	6.59825	−	0.577272i	0.400077	−	0.0350022i
$273$	−28.4277	+	7.61717i	−1.72052	+	0.461012i
$274$	9.30574	+	16.1180i	0.562180	+	0.973725i
$275$		0			0
$276$	17.6579	+	3.11356i	1.06288	+	0.187414i
$277$	−4.62759	−	1.23996i	−0.278045	−	0.0745019i	0.117102	−	0.993120i	$-0.462640\pi$
$277$	−4.62759	−	1.23996i	−0.278045	−	0.0745019i	−0.395147	+	0.918618i	$0.629306\pi$
$278$	−5.39925	−	20.1503i	−0.323825	−	1.20853i
$279$	0.860015	+	0.721638i	0.0514878	+	0.0432034i
$280$		0			0
$281$	−10.8682	−	29.8600i	−0.648340	−	1.78130i	−0.623777	−	0.781602i	$-0.714403\pi$
$281$	−10.8682	−	29.8600i	−0.648340	−	1.78130i	−0.0245633	−	0.999698i	$-0.507820\pi$
$282$	−0.288597	+	3.29867i	−0.0171857	+	0.196433i
$283$	1.46878	−	2.09764i	0.0873100	−	0.124692i	−0.773121	−	0.634259i	$-0.781305\pi$
$283$	1.46878	−	2.09764i	0.0873100	−	0.124692i	0.860431	+	0.509567i	$0.170194\pi$
$284$	−10.5384			−0.625337
$285$		0			0
$286$	0.910021			0.0538107
$287$	6.67559	−	9.53373i	0.394047	−	0.562758i
$288$	−0.324108	+	3.70457i	−0.0190982	+	0.218294i
$289$	9.19011	+	25.2496i	0.540595	+	1.48527i
$290$		0			0
$291$	10.5873	+	8.88383i	0.620641	+	0.520779i
$292$	−1.58845	−	5.92816i	−0.0929568	−	0.346919i
$293$	−7.43733	−	1.99283i	−0.434493	−	0.116422i	0.0349412	−	0.999389i	$-0.488876\pi$
$293$	−7.43733	−	1.99283i	−0.434493	−	0.116422i	−0.469435	+	0.882967i	$0.655542\pi$
$294$	−0.301135	−	0.0530983i	−0.0175626	−	0.00309675i
$295$		0			0
$296$	−3.04516	−	5.27438i	−0.176996	−	0.306567i
$297$	−0.384789	+	0.103104i	−0.0223277	+	0.00598270i
$298$	22.7916	−	1.99401i	1.32028	−	0.115510i
$299$	27.6634	+	10.0686i	1.59981	+	0.582285i
$300$		0			0
$301$	−3.80593	+	3.19355i	−0.219370	+	0.184073i
$302$	0.509040	+	0.356434i	0.0292920	+	0.0205105i
$303$	11.7613	−	11.7613i	0.675667	−	0.675667i
$304$	1.91935	+	3.91358i	0.110082	+	0.224459i
$305$		0			0
$306$	−24.2566	+	4.27709i	−1.38666	+	0.244505i
$307$	−8.23678	−	0.720625i	−0.470098	−	0.0411283i	−0.150354	−	0.988632i	$-0.548041\pi$
$307$	−8.23678	−	0.720625i	−0.470098	−	0.0411283i	−0.319744	+	0.947504i	$0.603597\pi$
$308$	0.517045	+	0.241102i	0.0294614	+	0.0137381i
$309$	12.2865	−	33.7570i	0.698956	−	1.92037i
$310$		0			0
$311$	−4.22980	+	7.32623i	−0.239850	+	0.415432i	−0.960671	−	0.277689i	$-0.910432\pi$
$311$	−4.22980	+	7.32623i	−0.239850	+	0.415432i	0.720821	+	0.693121i	$0.243765\pi$
$312$	−2.85506	+	10.6552i	−0.161636	+	0.603234i
$313$	27.0345	−	18.9297i	1.52808	−	1.06997i	0.557207	−	0.830373i	$-0.311873\pi$
$313$	27.0345	−	18.9297i	1.52808	−	1.06997i	0.970872	−	0.239599i	$-0.0770160\pi$
$314$	−3.57494	+	20.2745i	−0.201746	+	1.14416i
$315$		0			0
$316$	−3.36520	−	1.94290i	−0.189307	−	0.109296i
$317$	0.791521	+	9.04712i	0.0444562	+	0.508137i	0.985479	+	0.169795i	$0.0543105\pi$
$317$	0.791521	+	9.04712i	0.0444562	+	0.508137i	−0.941023	+	0.338342i	$0.890134\pi$
$318$	15.8602	−	7.39573i	0.889396	−	0.414732i
$319$	−0.907856	+	0.330433i	−0.0508302	+	0.0185007i
$320$		0			0
$321$	1.79697	+	10.1911i	0.100297	+	0.568812i
$322$	13.0499	+	13.0499i	0.727241	+	0.727241i
$323$	−21.7479	+	18.9885i	−1.21008	+	1.05655i
$324$			6.32727i			0.351515i
$325$		0			0
$326$	9.33122	+	11.1205i	0.516809	+	0.615909i
$327$	13.4699	−	28.8863i	0.744888	−	1.59742i
$328$	−1.84361	−	3.95363i	−0.101796	−	0.218303i
$329$	−2.19077	+	2.61086i	−0.120781	+	0.143941i
$330$		0			0
$331$	−11.5245	+	6.65367i	−0.633444	+	0.365719i	−0.782085	−	0.623172i	$-0.785844\pi$
$331$	−11.5245	+	6.65367i	−0.633444	+	0.365719i	0.148641	+	0.988891i	$0.452510\pi$
$332$	8.39369	+	11.9874i	0.460664	+	0.657896i
$333$	12.9905	+	18.5523i	0.711874	+	1.01666i
$334$	−1.36851	+	0.790110i	−0.0748815	+	0.0432329i
$335$		0			0
$336$	−4.44517	+	5.29755i	−0.242504	+	0.289005i
$337$	8.84965	+	18.9781i	0.482071	+	1.03381i	0.985485	+	0.169760i	$0.0542993\pi$
$337$	8.84965	+	18.9781i	0.482071	+	1.03381i	−0.503414	+	0.864045i	$0.667923\pi$
$338$	−2.16018	+	4.63252i	−0.117498	+	0.251976i
$339$	−4.97292	−	5.92649i	−0.270092	−	0.321883i
$340$		0			0
$341$		−	0.0645555i		−	0.00349588i
$342$	−8.37879	−	13.8761i	−0.453073	−	0.750331i
$343$	12.9831	+	12.9831i	0.701024	+	0.701024i
$344$	0.323369	+	1.83392i	0.0174349	+	0.0988783i
$345$		0			0
$346$	−17.7127	+	6.44691i	−0.952243	+	0.346588i
$347$	−6.29334	+	2.93463i	−0.337844	+	0.157539i	−0.584135	−	0.811657i	$-0.698566\pi$
$347$	−6.29334	+	2.93463i	−0.337844	+	0.157539i	0.246291	+	0.969196i	$0.420788\pi$
$348$	−1.02069	−	11.6666i	−0.0547149	−	0.625394i
$349$	−12.8839	−	7.43850i	−0.689657	−	0.398174i	0.113826	−	0.993501i	$-0.463689\pi$
$349$	−12.8839	−	7.43850i	−0.689657	−	0.398174i	−0.803484	+	0.595327i	$0.797023\pi$
$350$		0			0
$351$	1.37674	−	7.80786i	0.0734847	−	0.416753i
$352$	0.175162	−	0.122650i	0.00933616	−	0.00653725i
$353$	6.28498	−	23.4559i	0.334516	−	1.24843i	−0.569878	−	0.821730i	$-0.693009\pi$
$353$	6.28498	−	23.4559i	0.334516	−	1.24843i	0.904393	−	0.426700i	$-0.140324\pi$
$354$	−2.33235	+	4.03975i	−0.123963	+	0.214710i
$355$		0			0
$356$	3.66557	−	10.0711i	0.194275	−	0.533766i
$357$	−41.5127	−	19.3577i	−2.19709	−	1.02452i
$358$	6.43573	+	0.563054i	0.340139	+	0.0297583i
$359$	23.7538	−	4.18844i	1.25368	−	0.221058i	0.492911	−	0.870080i	$-0.335933\pi$
$359$	23.7538	−	4.18844i	1.25368	−	0.221058i	0.760769	+	0.649022i	$0.224822\pi$
$360$		0			0
$361$	−16.8147	−	8.84675i	−0.884985	−	0.465619i
$362$	−18.8988	+	18.8988i	−0.993297	+	0.993297i
$363$	−23.2590	−	16.2861i	−1.22078	−	0.854801i
$364$	−8.69778	+	7.29830i	−0.455887	+	0.382535i
$365$		0			0
$366$	−28.8284	−	10.4927i	−1.50689	−	0.548462i
$367$	18.1746	−	1.59007i	0.948708	−	0.0830012i	0.397713	−	0.917510i	$-0.369804\pi$
$367$	18.1746	−	1.59007i	0.948708	−	0.0830012i	0.550995	+	0.834509i	$0.314248\pi$
$368$	6.68170	−	1.79036i	0.348308	−	0.0933287i
$369$	8.11117	+	14.0490i	0.422251	+	0.731360i
$370$		0			0
$371$	17.7386	+	3.12779i	0.920941	+	0.162387i
$372$	0.755867	+	0.202534i	0.0391899	+	0.0105009i
$373$	−6.62975	−	24.7426i	−0.343276	−	1.28112i	−0.894614	−	0.446840i	$-0.852549\pi$
$373$	−6.62975	−	24.7426i	−0.343276	−	1.28112i	0.551338	−	0.834282i	$-0.314117\pi$
$374$	1.08496	+	0.910389i	0.0561019	+	0.0470751i
$375$		0			0
$376$	0.436922	+	1.20043i	0.0225325	+	0.0619076i
$377$	1.67582	−	19.1548i	0.0863093	−	0.986520i
$378$	2.85084	−	4.07143i	0.146632	−	0.209412i
$379$	−17.8932			−0.919110			−0.459555	−	0.888149i	$-0.651991\pi$
$379$	−17.8932			−0.919110			−0.459555	+	0.888149i	$0.651991\pi$
$380$		0			0
$381$	33.4876			1.71562
$382$	9.77895	−	13.9658i	0.500335	−	0.714552i
$383$	0.728445	−	8.32617i	0.0372218	−	0.425447i	−0.954607	−	0.297869i	$-0.903724\pi$
$383$	0.728445	−	8.32617i	0.0372218	−	0.425447i	0.991829	−	0.127578i	$-0.0407203\pi$
$384$	0.886533	+	2.43573i	0.0452407	+	0.124298i
$385$		0			0
$386$	0.326622	+	0.274068i	0.0166246	+	0.0139497i
$387$	−1.79233	−	6.68907i	−0.0911094	−	0.340025i
$388$	5.15031	+	1.38002i	0.261467	+	0.0700599i
$389$	−7.27709	−	1.28315i	−0.368963	−	0.0650582i	−0.0139075	−	0.999903i	$-0.504427\pi$
$389$	−7.27709	−	1.28315i	−0.368963	−	0.0650582i	−0.355056	+	0.934845i	$0.615538\pi$
$390$		0			0
$391$	22.9085	+	39.6788i	1.15853	+	2.00664i
$392$	−0.113949	+	0.0305325i	−0.00575529	+	0.00154213i
$393$	−49.3423	+	4.31689i	−2.48899	+	0.217758i
$394$	0.330438	+	0.120270i	0.0166472	+	0.00605910i
$395$		0			0
$396$	−0.609148	+	0.511136i	−0.0306108	+	0.0256855i
$397$	12.3711	+	8.66232i	0.620887	+	0.434750i	0.841233	−	0.540672i	$-0.181830\pi$
$397$	12.3711	+	8.66232i	0.620887	+	0.434750i	−0.220347	+	0.975422i	$0.570719\pi$
$398$	−4.16024	+	4.16024i	−0.208534	+	0.208534i
$399$	2.03719	−	30.0749i	0.101987	−	1.50563i
$400$		0			0
$401$	21.9628	−	3.87263i	1.09677	−	0.193390i	0.404149	−	0.914693i	$-0.367568\pi$
$401$	21.9628	−	3.87263i	1.09677	−	0.193390i	0.692619	+	0.721303i	$0.256457\pi$
$402$	−37.7905	−	3.30624i	−1.88482	−	0.164900i
$403$	1.16442	+	0.542979i	0.0580040	+	0.0270477i
$404$	2.19471	−	6.02992i	0.109191	−	0.300000i
$405$		0			0
$406$	6.02704	−	10.4391i	0.299117	−	0.518086i
$407$	0.337064	−	1.25794i	0.0167076	−	0.0623537i
$408$	−14.0635	+	9.84734i	−0.696245	+	0.487516i
$409$	3.11112	−	17.6440i	0.153835	−	0.872440i	−0.806009	−	0.591904i	$-0.798376\pi$
$409$	3.11112	−	17.6440i	0.153835	−	0.872440i	0.959843	−	0.280537i	$-0.0905124\pi$
$410$		0			0
$411$	−41.7787	−	24.1209i	−2.06079	−	1.18980i
$412$	−1.20790	−	13.8063i	−0.0595089	−	0.680189i
$413$	−4.35145	+	2.02912i	−0.214121	+	0.0998462i
$414$	−24.1726	+	8.79809i	−1.18802	+	0.432403i
$415$		0			0
$416$	0.739004	+	4.19110i	0.0362326	+	0.205485i
$417$	38.2354	+	38.2354i	1.87239	+	1.87239i
$418$	−0.301533	+	0.881955i	−0.0147485	+	0.0431378i
$419$		−	28.9255i		−	1.41310i	−0.707661	−	0.706552i	$-0.750249\pi$
$419$		−	28.9255i		−	1.41310i	0.707661	−	0.706552i	$-0.249751\pi$
$420$		0			0
$421$	−8.42190	−	10.0368i	−0.410458	−	0.489165i	0.520721	−	0.853727i	$-0.325663\pi$
$421$	−8.42190	−	10.0368i	−0.410458	−	0.489165i	−0.931179	+	0.364562i	$0.881219\pi$
$422$	3.62229	−	7.76803i	0.176330	−	0.378142i
$423$	−2.00768	−	4.30548i	−0.0976166	−	0.209339i
$424$	4.33967	−	5.17182i	0.210753	−	0.251166i
$425$		0			0
$426$	23.6563	−	13.6580i	1.14615	−	0.661732i
$427$	−18.1118	−	25.8663i	−0.876491	−	1.25176i
$428$	2.28991	+	3.27033i	0.110687	+	0.158077i
$429$	−2.04280	+	1.17941i	−0.0986272	+	0.0569424i
$430$		0			0
$431$	−3.00403	+	3.58006i	−0.144699	+	0.172446i	−0.833526	−	0.552480i	$-0.813682\pi$
$431$	−3.00403	+	3.58006i	−0.144699	+	0.172446i	0.688827	+	0.724926i	$0.258126\pi$
$432$	−0.787322	−	1.68842i	−0.0378800	−	0.0812340i
$433$	−11.2509	+	24.1276i	−0.540682	+	1.15950i	0.426284	+	0.904590i	$0.359823\pi$
$433$	−11.2509	+	24.1276i	−0.540682	+	1.15950i	−0.966966	+	0.254907i	$0.917955\pi$
$434$	0.517731	+	0.617007i	0.0248519	+	0.0296173i
$435$		0			0
$436$		−	12.2963i		−	0.588884i
$437$	−18.9243	+	23.4740i	−0.905273	+	1.12291i
$438$	11.2488	+	11.2488i	0.537486	+	0.537486i
$439$	−1.63792	−	9.28909i	−0.0781735	−	0.443344i	−0.998622	−	0.0524801i	$-0.983287\pi$
$439$	−1.63792	−	9.28909i	−0.0781735	−	0.443344i	0.920448	−	0.390864i	$-0.127824\pi$
$440$		0			0
$441$	0.412236	−	0.150042i	0.0196303	−	0.00714485i
$442$	−25.5468	+	11.9127i	−1.21514	+	0.566628i
$443$	−1.41494	−	16.1728i	−0.0672258	−	0.768395i	−0.952741	−	0.303784i	$-0.901750\pi$
$443$	−1.41494	−	16.1728i	−0.0672258	−	0.768395i	0.885515	−	0.464611i	$-0.153806\pi$
$444$	13.6714	+	7.89321i	0.648818	+	0.374595i
$445$		0			0
$446$	−2.32909	+	13.2089i	−0.110285	+	0.625460i
$447$	−48.5778	+	34.0146i	−2.29765	+	1.60883i
$448$	−0.690517	+	2.57704i	−0.0326239	+	0.121754i
$449$	0.493609	−	0.854956i	0.0232949	−	0.0403479i	−0.854143	−	0.520038i	$-0.825918\pi$
$449$	0.493609	−	0.854956i	0.0232949	−	0.0403479i	0.877438	+	0.479690i	$0.159251\pi$
$450$		0			0
$451$	0.319041	−	0.876558i	0.0150231	−	0.0412755i
$452$	−2.70506	−	1.26139i	−0.127235	−	0.0593307i
$453$	−1.60463	−	0.140387i	−0.0753921	−	0.00659596i
$454$	18.5074	−	3.26335i	0.868594	−	0.153157i
$455$		0			0
$456$	−9.38061	−	6.29760i	−0.439287	−	0.294912i
$457$	−21.6192	+	21.6192i	−1.01131	+	1.01131i	−0.0113702	+	0.999935i	$0.503619\pi$
$457$	−21.6192	+	21.6192i	−1.01131	+	1.01131i	−0.999935	+	0.0113702i	$0.996381\pi$
$458$	−4.89771	−	3.42941i	−0.228855	−	0.160246i
$459$	9.45241	−	7.93151i	0.441201	−	0.370211i
$460$		0			0
$461$	25.2287	+	9.18248i	1.17502	+	0.427671i	0.854439	−	0.519552i	$-0.173901\pi$
$461$	25.2287	+	9.18248i	1.17502	+	0.427671i	0.320577	+	0.947222i	$0.396123\pi$
$462$	−1.47313	+	0.128882i	−0.0685361	+	0.00599613i
$463$	36.7114	−	9.83679i	1.70612	−	0.457154i	0.731654	−	0.681676i	$-0.238749\pi$
$463$	36.7114	−	9.83679i	1.70612	−	0.457154i	0.974469	+	0.224522i	$0.0720820\pi$
$464$	−2.25905	−	3.91279i	−0.104874	−	0.181647i
$465$		0			0
$466$	8.02197	+	1.41449i	0.371611	+	0.0655250i
$467$	−21.9339	−	5.87718i	−1.01498	−	0.271963i	−0.287272	−	0.957849i	$-0.592748\pi$
$467$	−21.9339	−	5.87718i	−1.01498	−	0.271963i	−0.727709	+	0.685886i	$0.759415\pi$
$468$	−4.09606	−	15.2867i	−0.189340	−	0.706628i
$469$	−29.9107	−	25.0981i	−1.38115	−	1.15892i
$470$		0			0
$471$	−18.2513	−	50.1450i	−0.840975	−	2.31056i
$472$	−0.156847	+	1.79277i	−0.00721947	+	0.0825189i
$473$	−0.228399	+	0.326188i	−0.0105018	+	0.0149981i
$474$	10.0722			0.462630
$475$		0			0
$476$	−17.6710			−0.809951
$477$	−14.4004	+	20.5659i	−0.659349	+	0.941648i
$478$	2.01611	−	23.0443i	0.0922149	−	1.05402i
$479$	−1.82511	−	5.01446i	−0.0833915	−	0.229116i	0.890988	−	0.454027i	$-0.150013\pi$
$479$	−1.82511	−	5.01446i	−0.0833915	−	0.229116i	−0.974379	+	0.224911i	$0.927791\pi$
$480$		0			0
$481$	19.8550	+	16.6604i	0.905312	+	0.759647i
$482$	−5.09161	−	19.0021i	−0.231916	−	0.865524i
$483$	−46.2070	−	12.3811i	−2.10249	−	0.563361i
$484$	−10.7879	−	1.90219i	−0.490357	−	0.0864632i
$485$		0			0
$486$	−10.9947	−	19.0435i	−0.498732	−	0.863829i
$487$	−12.5530	+	3.36357i	−0.568831	+	0.152418i	−0.531761	−	0.846895i	$-0.678469\pi$
$487$	−12.5530	+	3.36357i	−0.568831	+	0.152418i	−0.0370707	+	0.999313i	$0.511803\pi$
$488$	−11.7906	+	1.03154i	−0.533736	+	0.0466958i
$489$	−35.3590	−	12.8696i	−1.59899	−	0.581985i
$490$		0			0
$491$	−28.4761	+	23.8943i	−1.28511	+	1.07834i	−0.292592	+	0.956238i	$0.594518\pi$
$491$	−28.4761	+	23.8943i	−1.28511	+	1.07834i	−0.992518	+	0.122098i	$0.961038\pi$
$492$	9.26249	+	6.48567i	0.417585	+	0.292396i
$493$	21.1605	−	21.1605i	0.953020	−	0.953020i
$494$	−13.3721	−	12.8571i	−0.601639	−	0.578467i
$495$		0			0
$496$	0.297310	−	0.0524238i	0.0133496	−	0.00235390i
$497$	28.0089	+	2.45046i	1.25637	+	0.109918i
$498$	−34.3780	−	16.0307i	−1.54052	−	0.718354i
$499$	4.99335	−	13.7191i	0.223533	−	0.614151i	−0.776336	−	0.630319i	$-0.782924\pi$
$499$	4.99335	−	13.7191i	0.223533	−	0.614151i	0.999869	+	0.0161673i	$0.00514644\pi$
$500$		0			0
$501$	2.04800	−	3.54725i	0.0914980	−	0.158479i
$502$	−4.54645	+	16.9676i	−0.202918	+	0.757300i
$503$	13.3699	−	9.36172i	0.596135	−	0.417418i	−0.236189	−	0.971707i	$-0.575899\pi$
$503$	13.3699	−	9.36172i	0.596135	−	0.417418i	0.832324	+	0.554289i	$0.187010\pi$
$504$	1.72283	−	9.77064i	0.0767409	−	0.435219i
$505$		0			0
$506$	1.28100	+	0.739585i	0.0569473	+	0.0328786i
$507$	−1.15473	−	13.1987i	−0.0512835	−	0.586173i
$508$	11.7089	−	5.45995i	0.519498	−	0.242246i
$509$	6.72863	−	2.44902i	0.298241	−	0.108551i	−0.188566	−	0.982061i	$-0.560384\pi$
$509$	6.72863	−	2.44902i	0.298241	−	0.108551i	0.486807	+	0.873510i	$0.338162\pi$
$510$		0			0
$511$	2.84331	+	16.1252i	0.125781	+	0.713338i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	7.11088	+	3.92139i	0.313953	+	0.173134i
$514$			2.83013i			0.124832i
$515$		0			0
$516$	−3.10270	−	3.69765i	−0.136589	−	0.162780i
$517$	−0.115445	+	0.247573i	−0.00507726	+	0.0108882i
$518$	6.86700	+	14.7263i	0.301719	+	0.647037i
$519$	31.4059	−	37.4281i	1.37856	−	1.64291i
$520$		0			0
$521$	6.63730	−	3.83204i	0.290785	−	0.167885i	−0.347511	−	0.937676i	$-0.612973\pi$
$521$	6.63730	−	3.83204i	0.290785	−	0.167885i	0.638296	+	0.769791i	$0.279640\pi$
$522$	9.63698	+	13.7630i	0.421799	+	0.602392i
$523$	17.2190	+	24.5912i	0.752933	+	1.07530i	0.994482	+	0.104911i	$0.0334557\pi$
$523$	17.2190	+	24.5912i	0.752933	+	1.07530i	−0.241549	+	0.970389i	$0.577655\pi$
$524$	−16.5486	+	9.55437i	−0.722931	+	0.417384i
$525$		0			0
$526$	−3.15310	+	3.75772i	−0.137482	+	0.163844i
$527$	0.845067	+	1.81225i	0.0368117	+	0.0789429i
$528$	−0.234243	+	0.502336i	−0.0101941	+	0.0218614i
$529$	15.9736	+	19.0366i	0.694503	+	0.827677i
$530$		0			0
$531$		−	6.69228i		−	0.290420i
$532$	−4.19123	−	10.8478i	−0.181713	−	0.470312i
$533$	13.1275	+	13.1275i	0.568614	+	0.568614i
$534$	4.82396	+	27.3580i	0.208753	+	1.18390i
$535$		0			0
$536$	−13.7525	+	5.00549i	−0.594016	+	0.216204i
$537$	−15.1765	+	7.07694i	−0.654916	+	0.305392i
$538$	−0.0448802	−	0.512983i	−0.00193492	−	0.0221163i
$539$	−0.0218460	−	0.0126128i	−0.000940975	−	0.000543272i
$540$		0			0
$541$	5.59063	−	31.7061i	0.240360	−	1.36315i	−0.590666	−	0.806916i	$-0.701135\pi$
$541$	5.59063	−	31.7061i	0.240360	−	1.36315i	0.831026	−	0.556234i	$-0.187754\pi$
$542$	19.3443	−	13.5450i	0.830908	−	0.581808i
$543$	17.9303	−	66.9168i	0.769463	−	2.87168i
$544$	−3.31173	+	5.73608i	−0.141989	+	0.245932i
$545$		0			0
$546$	10.0658	−	27.6556i	0.430778	−	1.18355i
$547$	−26.5448	−	12.3780i	−1.13497	−	0.529247i	−0.237971	−	0.971272i	$-0.576482\pi$
$547$	−26.5448	−	12.3780i	−1.13497	−	0.529247i	−0.897003	+	0.442025i	$0.854260\pi$
$548$	−18.5407	−	1.62210i	−0.792018	−	0.0692926i
$549$	43.3448	−	7.64286i	1.84991	−	0.326189i
$550$		0			0
$551$	18.0087	+	7.97102i	0.767198	+	0.339577i
$552$	−12.6786	+	12.6786i	−0.539637	+	0.539637i
$553$	8.49224	+	5.94633i	0.361127	+	0.252864i
$554$	3.66999	−	3.07949i	0.155923	−	0.130835i
$555$		0			0
$556$	19.6030	+	7.13491i	0.831353	+	0.302588i
$557$	−40.9159	+	3.57967i	−1.73366	+	0.151676i	−0.909781	−	0.415089i	$-0.863750\pi$
$557$	−40.9159	+	3.57967i	−1.73366	+	0.151676i	−0.823880	+	0.566765i	$0.808195\pi$
$558$	−1.08442	+	0.290568i	−0.0459070	+	0.0123007i
$559$	−3.96255	−	6.86334i	−0.167598	−	0.290288i
$560$		0			0
$561$	−3.61538	−	0.637489i	−0.152642	−	0.0269148i
$562$	30.6936	+	8.22433i	1.29473	+	0.346923i
$563$	7.14811	+	26.6771i	0.301257	+	1.12431i	0.936120	+	0.351681i	$0.114390\pi$
$563$	7.14811	+	26.6771i	0.301257	+	1.12431i	−0.634863	+	0.772625i	$0.718943\pi$
$564$	−2.53658	−	2.12845i	−0.106809	−	0.0896237i
$565$		0			0
$566$	0.875825	+	2.40631i	0.0368137	+	0.101145i
$567$	1.47126	−	16.8166i	0.0617873	−	0.706232i
$568$	6.04456	−	8.63253i	0.253624	−	0.362213i
$569$	−5.87661			−0.246360			−0.123180	−	0.992384i	$-0.539309\pi$
$569$	−5.87661			−0.246360			−0.123180	+	0.992384i	$0.539309\pi$
$570$		0			0
$571$	25.8071			1.07999			0.539997	−	0.841667i	$-0.318425\pi$
$571$	25.8071			1.07999			0.539997	+	0.841667i	$0.318425\pi$
$572$	−0.521966	+	0.745445i	−0.0218245	+	0.0311686i
$573$	−3.85159	+	44.0239i	−0.160903	+	1.83913i
$574$	3.98061	+	10.9366i	0.166148	+	0.456487i
$575$		0			0
$576$	−2.84871	−	2.39035i	−0.118696	−	0.0995978i
$577$	4.14031	+	15.4518i	0.172363	+	0.643269i	0.996986	+	0.0775851i	$0.0247209\pi$
$577$	4.14031	+	15.4518i	0.172363	+	0.643269i	−0.824622	+	0.565684i	$0.808612\pi$
$578$	−25.9545	−	6.95449i	−1.07957	−	0.289269i
$579$	−1.08839	−	0.191913i	−0.0452321	−	0.00797564i
$580$		0			0
$581$	−19.5213	−	33.8120i	−0.809882	−	1.40276i
$582$	−13.3499	+	3.57708i	−0.553369	+	0.148275i
$583$	1.43817	−	0.125823i	0.0595627	−	0.00521106i
$584$	5.76716	+	2.09907i	0.238647	+	0.0868603i
$585$		0			0
$586$	5.89831	−	4.94927i	0.243657	−	0.204452i
$587$	16.9343	+	11.8575i	0.698952	+	0.489412i	0.868233	−	0.496156i	$-0.165256\pi$
$587$	16.9343	+	11.8575i	0.698952	+	0.489412i	−0.169281	+	0.985568i	$0.554145\pi$
$588$	0.216220	−	0.216220i	0.00891675	−	0.00891675i
$589$	−0.912062	+	0.948596i	−0.0375808	+	0.0390862i
$590$		0			0
$591$	−0.897634	+	0.158277i	−0.0369237	+	0.00651065i
$592$	6.06715	+	0.530807i	0.249358	+	0.0218160i
$593$	−25.1334	−	11.7199i	−1.03211	−	0.481279i	−0.168635	−	0.985678i	$-0.553936\pi$
$593$	−25.1334	−	11.7199i	−1.03211	−	0.481279i	−0.863470	+	0.504400i	$0.831714\pi$
$594$	0.136248	−	0.374339i	0.00559033	−	0.0153593i
$595$		0			0
$596$	−11.4393	+	19.8135i	−0.468573	+	0.811592i
$597$	3.94705	−	14.7306i	0.161542	−	0.602883i
$598$	−24.1148	+	16.8854i	−0.986128	+	0.690494i
$599$	−2.63405	+	14.9385i	−0.107624	+	0.610369i	0.882515	+	0.470284i	$0.155849\pi$
$599$	−2.63405	+	14.9385i	−0.107624	+	0.610369i	−0.990140	+	0.140085i	$0.955263\pi$
$600$		0			0
$601$	25.9669	+	14.9920i	1.05921	+	0.611537i	0.925214	−	0.379445i	$-0.123885\pi$
$601$	25.9669	+	14.9920i	1.05921	+	0.611537i	0.133998	+	0.990982i	$0.457218\pi$
$602$	−0.433015	−	4.94938i	−0.0176484	−	0.201722i
$603$	49.3247	−	23.0005i	2.00866	−	0.936652i
$604$	−0.583947	+	0.212539i	−0.0237605	+	0.00864810i
$605$		0			0
$606$	2.88828	+	16.3803i	0.117328	+	0.665403i
$607$	0.102589	+	0.102589i	0.00416395	+	0.00416395i	0.709186	−	0.705022i	$-0.249063\pi$
$607$	0.102589	+	0.102589i	0.00416395	+	0.00416395i	−0.705022	+	0.709186i	$0.749063\pi$
$608$	−4.30671	−	0.672498i	−0.174660	−	0.0272734i
$609$			31.2448i			1.26610i
$610$		0			0
$611$	−3.49458	−	4.16468i	−0.141376	−	0.168485i
$612$	10.4094	−	22.3231i	0.420776	−	0.902356i
$613$	−4.05745	−	8.70122i	−0.163879	−	0.351439i	0.807171	−	0.590318i	$-0.200998\pi$
$613$	−4.05745	−	8.70122i	−0.163879	−	0.351439i	−0.971049	+	0.238879i	$0.923220\pi$
$614$	5.31473	−	6.33385i	0.214485	−	0.255613i
$615$		0			0
$616$	−0.494065	+	0.285248i	−0.0199064	+	0.0114930i
$617$	−12.9551	−	18.5019i	−0.521554	−	0.744857i	0.468817	−	0.883295i	$-0.344680\pi$
$617$	−12.9551	−	18.5019i	−0.521554	−	0.744857i	−0.990371	+	0.138439i	$0.955792\pi$
$618$	20.6048	+	29.4267i	0.828848	+	1.18372i
$619$	−27.4671	+	15.8582i	−1.10400	+	0.637393i	−0.937268	−	0.348610i	$-0.886654\pi$
$619$	−27.4671	+	15.8582i	−1.10400	+	0.637393i	−0.166729	+	0.986003i	$0.553321\pi$
$620$		0			0
$621$	8.28352	−	9.87191i	0.332406	−	0.396146i
$622$	−3.57518	−	7.66700i	−0.143352	−	0.307419i
$623$	−12.0841	+	25.9145i	−0.484141	+	1.03824i
$624$	−7.09067	−	8.45033i	−0.283854	−	0.338284i
$625$		0			0
$626$			33.0030i			1.31907i
$627$	−0.466160	−	2.37059i	−0.0186166	−	0.0946723i
$628$	−14.5574	−	14.5574i	−0.580903	−	0.580903i
$629$	7.00479	+	39.7261i	0.279299	+	1.58398i
$630$		0			0
$631$	−24.3974	+	8.87993i	−0.971245	+	0.353504i	−0.778430	−	0.627731i	$-0.783984\pi$
$631$	−24.3974	+	8.87993i	−0.971245	+	0.353504i	−0.192815	+	0.981235i	$0.561762\pi$
$632$	3.52172	−	1.64221i	0.140087	−	0.0653235i
$633$	1.93631	+	22.1321i	0.0769614	+	0.879673i
$634$	−7.86497	−	4.54084i	−0.312358	−	0.180340i
$635$		0			0
$636$	−3.03881	+	17.2339i	−0.120497	+	0.683370i
$637$	0.411252	−	0.287962i	0.0162944	−	0.0114095i
$638$	0.250050	−	0.933200i	0.00989959	−	0.0369458i
$639$	−19.5946	+	33.9389i	−0.775152	+	1.34260i
$640$		0			0
$641$	−11.1820	+	30.7222i	−0.441661	+	1.21345i	0.496738	+	0.867901i	$0.334531\pi$
$641$	−11.1820	+	30.7222i	−0.441661	+	1.21345i	−0.938399	+	0.345553i	$0.887691\pi$
$642$	−9.37877	−	4.37339i	−0.370151	−	0.172604i
$643$	0.743211	+	0.0650225i	0.0293094	+	0.00256424i	0.101801	−	0.994805i	$-0.467540\pi$
$643$	0.743211	+	0.0650225i	0.0293094	+	0.00256424i	−0.0724916	+	0.997369i	$0.523095\pi$
$644$	−18.1749	+	3.20473i	−0.716192	+	0.126284i
$645$		0			0
$646$	−3.08040	−	28.7061i	−0.121197	−	1.12943i
$647$	−15.8239	+	15.8239i	−0.622101	+	0.622101i	−0.946068	−	0.323967i	$-0.894983\pi$
$647$	−15.8239	+	15.8239i	−0.622101	+	0.622101i	0.323967	+	0.946068i	$0.394983\pi$
$648$	−5.18300	−	3.62918i	−0.203607	−	0.142567i
$649$	−0.294788	+	0.247356i	−0.0115714	+	0.00970958i
$650$		0			0
$651$	−1.96185	−	0.714055i	−0.0768909	−	0.0279860i
$652$	−14.4616	+	1.26522i	−0.566359	+	0.0495500i
$653$	−43.2444	+	11.5873i	−1.69228	+	0.453446i	−0.970978	−	0.239171i	$-0.923124\pi$
$653$	−43.2444	+	11.5873i	−1.69228	+	0.453446i	−0.721306	+	0.692617i	$0.756458\pi$
$654$	15.9363	+	27.6024i	0.623157	+	1.07934i
$655$		0			0
$656$	4.29607	+	0.757513i	0.167733	+	0.0295759i
$657$	−22.0452	−	5.90699i	−0.860064	−	0.230454i
$658$	−0.882117	−	3.29210i	−0.0343885	−	0.128340i
$659$	31.9917	+	26.8443i	1.24622	+	1.04570i	0.997011	+	0.0772545i	$0.0246154\pi$
$659$	31.9917	+	26.8443i	1.24622	+	1.04570i	0.249210	+	0.968449i	$0.419829\pi$
$660$		0			0
$661$	9.40771	+	25.8475i	0.365918	+	1.00535i	0.976898	+	0.213705i	$0.0685530\pi$
$661$	9.40771	+	25.8475i	0.365918	+	1.00535i	−0.610981	+	0.791645i	$0.709225\pi$
$662$	1.15981	−	13.2567i	0.0450774	−	0.515237i
$663$	41.9078	−	59.8506i	1.62757	−	2.32440i
$664$	−14.6340			−0.567908
$665$		0			0
$666$	−22.6482			−0.877601
$667$	17.9263	−	25.6014i	0.694109	−	0.991290i
$668$	0.137725	−	1.57421i	0.00532875	−	0.0609079i
$669$	−11.8908	−	32.6697i	−0.459724	−	1.26308i
$670$		0			0
$671$	−1.93875	−	1.62680i	−0.0748445	−	0.0628020i
$672$	−1.78985	−	6.67983i	−0.0690451	−	0.257680i
$673$	−11.5770	−	3.10205i	−0.446261	−	0.119575i	0.0286886	−	0.999588i	$-0.490867\pi$
$673$	−11.5770	−	3.10205i	−0.446261	−	0.119575i	−0.474949	+	0.880013i	$0.657534\pi$
$674$	−20.6219	−	3.63620i	−0.794327	−	0.140061i
$675$		0			0
$676$	−2.55571	−	4.42662i	−0.0982966	−	0.170255i
$677$	43.5140	−	11.6595i	1.67238	−	0.448112i	0.706627	−	0.707586i	$-0.250216\pi$
$677$	43.5140	−	11.6595i	1.67238	−	0.448112i	0.965750	+	0.259474i	$0.0835490\pi$
$678$	7.70705	−	0.674279i	0.295987	−	0.0258955i
$679$	−13.3676	−	4.86541i	−0.513001	−	0.186717i
$680$		0			0
$681$	−37.3156	+	31.3115i	−1.42994	+	1.19986i
$682$	0.0528808	+	0.0370275i	0.00202491	+	0.00141786i
$683$	13.9730	−	13.9730i	0.534662	−	0.534662i	−0.387294	−	0.921956i	$-0.626590\pi$
$683$	13.9730	−	13.9730i	0.534662	−	0.534662i	0.921956	+	0.387294i	$0.126590\pi$
$684$	16.1725	+	1.09548i	0.618370	+	0.0418866i
$685$		0			0
$686$	−18.0820	+	3.18834i	−0.690373	+	0.121731i
$687$	15.4389	+	1.35073i	0.589030	+	0.0515334i
$688$	−1.68774	−	0.787004i	−0.0643443	−	0.0300042i
$689$	−9.82692	+	26.9992i	−0.374376	+	1.02859i
$690$		0			0
$691$	−6.01252	+	10.4140i	−0.228727	+	0.396167i	−0.957431	−	0.288662i	$-0.906790\pi$
$691$	−6.01252	+	10.4140i	−0.228727	+	0.396167i	0.728704	+	0.684829i	$0.240123\pi$
$692$	4.87861	−	18.2072i	0.185457	−	0.692135i
$693$	1.73785	−	1.21685i	0.0660153	−	0.0462244i
$694$	1.20580	−	6.83844i	0.0457716	−	0.259583i
$695$		0			0
$696$	10.1422	+	5.85557i	0.384437	+	0.221955i
$697$	2.51826	+	28.7838i	0.0953859	+	1.09027i
$698$	13.4831	−	6.28729i	0.510344	−	0.237978i
$699$	−19.8408	+	7.22145i	−0.750447	+	0.273140i
$700$		0			0
$701$	−4.73336	−	26.8442i	−0.178777	−	1.01389i	−0.933694	−	0.358073i	$-0.883434\pi$
$701$	−4.73336	−	26.8442i	−0.178777	−	1.01389i	0.754917	−	0.655820i	$-0.227677\pi$
$702$	5.60616	+	5.60616i	0.211591	+	0.211591i
$703$	−22.7255	+	13.7223i	−0.857107	+	0.517548i
$704$			0.213833i			0.00805914i
$705$		0			0
$706$	15.6090	+	18.6021i	0.587453	+	0.700099i
$707$	−7.23523	+	15.5160i	−0.272109	+	0.583539i
$708$	−1.97139	−	4.22765i	−0.0740893	−	0.158885i
$709$	−6.99335	+	8.33436i	−0.262641	+	0.313003i	−0.881208	−	0.472729i	$-0.843269\pi$
$709$	−6.99335	+	8.33436i	−0.262641	+	0.313003i	0.618567	+	0.785732i	$0.287714\pi$
$710$		0			0
$711$	−12.5142	+	7.22509i	−0.469320	+	0.270962i
$712$	6.14725	+	8.77919i	0.230378	+	0.329014i
$713$	1.19782	+	1.71067i	0.0448588	+	0.0640651i
$714$	39.6676	−	22.9021i	1.48452	−	0.857090i
$715$		0			0
$716$	−4.15261	+	4.94889i	−0.155190	+	0.184949i
$717$	25.3402	+	54.3423i	0.946348	+	2.02945i
$718$	−10.1937	+	21.8604i	−0.380424	+	0.815823i
$719$	15.8334	+	18.8695i	0.590485	+	0.703712i	0.975699	−	0.219115i	$-0.0703170\pi$
$719$	15.8334	+	18.8695i	0.590485	+	0.703712i	−0.385214	+	0.922827i	$0.625873\pi$
$720$		0			0
$721$			36.9753i			1.37703i
$722$	16.8914	−	8.69953i	0.628632	−	0.323763i
$723$	36.0568	+	36.0568i	1.34097	+	1.34097i
$724$	−4.64107	−	26.3208i	−0.172484	−	0.978206i
$725$		0			0
$726$	26.6817	−	9.71133i	0.990249	−	0.360421i
$727$	24.6473	−	11.4932i	0.914119	−	0.426261i	0.0921190	−	0.995748i	$-0.470636\pi$
$727$	24.6473	−	11.4932i	0.914119	−	0.426261i	0.822000	+	0.569487i	$0.192858\pi$
$728$	−0.989579	−	11.3109i	−0.0366762	−	0.419211i
$729$	32.9229	+	19.0080i	1.21937	+	0.704001i
$730$		0			0
$731$	2.14182	−	12.1469i	0.0792181	−	0.449268i
$732$	25.1304	−	17.5965i	0.928847	−	0.650386i
$733$	−0.847289	+	3.16213i	−0.0312953	+	0.116796i	−0.979807	−	0.199948i	$-0.935923\pi$
$733$	−0.847289	+	3.16213i	−0.0312953	+	0.116796i	0.948511	+	0.316743i	$0.102589\pi$
$734$	−9.12202	+	15.7998i	−0.336700	+	0.583182i
$735$		0			0
$736$	−2.36589	+	6.50023i	−0.0872079	+	0.239602i
$737$	−2.83626	−	1.32257i	−0.104475	−	0.0487174i
$738$	−16.1606	−	1.41387i	−0.594881	−	0.0520453i
$739$	12.2064	−	2.15231i	0.449019	−	0.0791741i	0.0554337	−	0.998462i	$-0.482346\pi$
$739$	12.2064	−	2.15231i	0.449019	−	0.0791741i	0.393585	+	0.919288i	$0.371235\pi$
$740$		0			0
$741$	46.6805	+	11.5308i	1.71485	+	0.423593i
$742$	−12.7366	+	12.7366i	−0.467574	+	0.467574i
$743$	−1.37216	−	0.960799i	−0.0503398	−	0.0352483i	0.548136	−	0.836389i	$-0.315338\pi$
$743$	−1.37216	−	0.960799i	−0.0503398	−	0.0352483i	−0.598476	+	0.801141i	$0.704227\pi$
$744$	−0.599454	+	0.503001i	−0.0219770	+	0.0184409i
$745$		0			0
$746$	24.0706	+	8.76098i	0.881287	+	0.320762i
$747$	54.2125	−	4.74298i	1.98353	−	0.173537i
$748$	−1.36805	+	0.366569i	−0.0500210	+	0.0134031i
$749$	−5.32568	−	9.22434i	−0.194596	−	0.337050i
$750$		0			0
$751$	−17.9765	−	3.16974i	−0.655971	−	0.115665i	−0.164251	−	0.986419i	$-0.552521\pi$
$751$	−17.9765	−	3.16974i	−0.655971	−	0.115665i	−0.491720	+	0.870753i	$0.663632\pi$
$752$	−1.23394	−	0.330634i	−0.0449973	−	0.0120570i
$753$	−11.7846	−	43.9808i	−0.429455	−	1.60275i
$754$	14.7294	+	12.3595i	0.536415	+	0.450105i
$755$		0			0
$756$	1.69994	+	4.67055i	0.0618263	+	0.169866i
$757$	−1.46072	+	16.6961i	−0.0530908	+	0.606831i	0.922319	+	0.386430i	$0.126292\pi$
$757$	−1.46072	+	16.6961i	−0.0530908	+	0.606831i	−0.975409	+	0.220401i	$0.929263\pi$
$758$	10.2631	−	14.6572i	0.372772	−	0.532374i
$759$	−3.83408			−0.139168
$760$		0			0
$761$	1.25083			0.0453424			0.0226712	−	0.999743i	$-0.492783\pi$
$761$	1.25083			0.0453424			0.0226712	+	0.999743i	$0.492783\pi$
$762$	−19.2077	+	27.4314i	−0.695821	+	0.993735i
$763$	−2.85922	+	32.6810i	−0.103511	+	1.18313i
$764$	5.83113	+	16.0209i	0.210963	+	0.579616i
$765$		0			0
$766$	6.40258	+	5.37240i	0.231335	+	0.194113i
$767$	−1.98222	−	7.39776i	−0.0715740	−	0.267118i
$768$	−2.50373	−	0.670872i	−0.0903455	−	0.0242080i
$769$	17.2121	+	3.03496i	0.620684	+	0.109443i	0.475143	−	0.879909i	$-0.342396\pi$
$769$	17.2121	+	3.03496i	0.620684	+	0.109443i	0.145542	+	0.989352i	$0.453508\pi$
$770$		0			0
$771$	−3.66792	−	6.35302i	−0.132097	−	0.228798i
$772$	−0.411846	+	0.110354i	−0.0148227	+	0.00397172i
$773$	9.04174	−	0.791050i	0.325209	−	0.0284521i	0.0766176	−	0.997061i	$-0.475588\pi$
$773$	9.04174	−	0.791050i	0.325209	−	0.0284521i	0.248591	+	0.968608i	$0.420032\pi$
$774$	6.50741	+	2.36850i	0.233904	+	0.0851341i
$775$		0			0
$776$	−4.08454	+	3.42734i	−0.146626	+	0.123034i
$777$	−34.5006	−	24.1576i	−1.23770	−	0.866648i
$778$	5.22506	−	5.22506i	0.187328	−	0.187328i
$779$	−17.0724	+	8.37286i	−0.611682	+	0.299989i
$780$		0			0
$781$	2.21922	−	0.391308i	0.0794099	−	0.0140021i
$782$	−45.6427	−	3.99322i	−1.63218	−	0.142797i
$783$	−7.62844	−	3.55720i	−0.272618	−	0.127124i
$784$	0.0403477	−	0.110854i	0.00144099	−	0.00395908i
$785$		0			0
$786$	24.7654	−	42.8949i	0.883352	−	1.53001i
$787$	5.94684	−	22.1939i	0.211982	−	0.791128i	−0.775225	−	0.631685i	$-0.782364\pi$
$787$	5.94684	−	22.1939i	0.211982	−	0.791128i	0.987207	−	0.159443i	$-0.0509698\pi$
$788$	−0.288051	+	0.201695i	−0.0102614	+	0.00718510i
$789$	2.20792	−	12.5218i	0.0786042	−	0.445786i
$790$		0			0
$791$	6.89619	+	3.98152i	0.245200	+	0.141566i
$792$	−0.0693050	−	0.792160i	−0.00246265	−	0.0281482i
$793$	45.6504	−	21.2871i	1.62109	−	0.755927i
$794$	−14.1915	+	5.16529i	−0.503638	+	0.183309i
$795$		0			0
$796$	−1.02165	−	5.79408i	−0.0362115	−	0.205366i
$797$	9.04794	+	9.04794i	0.320494	+	0.320494i	0.848957	−	0.528462i	$-0.177231\pi$
$797$	9.04794	+	9.04794i	0.320494	+	0.320494i	−0.528462	+	0.848957i	$0.677231\pi$
$798$	23.4674	+	18.9190i	0.830738	+	0.669726i
$799$		−	8.46128i		−	0.299339i
$800$		0			0
$801$	−25.6183	−	30.5307i	−0.905179	−	1.07875i
$802$	−9.42505	+	20.2121i	−0.332810	+	0.713714i
$803$	0.554625	+	1.18940i	0.0195723	+	0.0419729i
$804$	24.3840	−	29.0598i	0.859959	−	1.02486i
$805$		0			0
$806$	−1.11267	+	0.642399i	−0.0391920	+	0.0226275i
$807$	0.765585	+	1.09337i	0.0269499	+	0.0384884i
$808$	3.68059	+	5.25643i	0.129483	+	0.184920i
$809$	6.83580	−	3.94665i	0.240334	−	0.138757i	−0.374996	−	0.927026i	$-0.622356\pi$
$809$	6.83580	−	3.94665i	0.240334	−	0.138757i	0.615330	+	0.788269i	$0.289023\pi$
$810$		0			0
$811$	9.03082	−	10.7625i	0.317115	−	0.377923i	−0.583815	−	0.811886i	$-0.698441\pi$
$811$	9.03082	−	10.7625i	0.317115	−	0.377923i	0.900931	+	0.433963i	$0.142885\pi$
$812$	5.09428	+	10.9247i	0.178774	+	0.383382i
$813$	−25.8690	+	55.4762i	−0.907265	+	1.94564i
$814$	0.837111	+	0.997630i	0.0293407	+	0.0349669i
$815$		0			0
$816$		−	17.1683i		−	0.601011i
$817$	7.96465	−	1.56619i	0.278648	−	0.0547942i
$818$	12.6687	+	12.6687i	0.442950	+	0.442950i
$819$	7.33193	+	41.5814i	0.256198	+	1.45297i
$820$		0			0
$821$	−4.90043	+	1.78361i	−0.171026	+	0.0622484i	−0.426114	−	0.904669i	$-0.640118\pi$
$821$	−4.90043	+	1.78361i	−0.171026	+	0.0622484i	0.255088	+	0.966918i	$0.417896\pi$
$822$	43.7220	−	20.3879i	1.52498	−	0.711110i
$823$	−0.256082	−	2.92703i	−0.00892645	−	0.102030i	0.990424	−	0.138056i	$-0.0440855\pi$
$823$	−0.256082	−	2.92703i	−0.00892645	−	0.102030i	−0.999351	+	0.0360265i	$0.988530\pi$
$824$	12.0023	+	6.92954i	0.418120	+	0.241402i
$825$		0			0
$826$	0.833736	−	4.72835i	0.0290094	−	0.164520i
$827$	−33.0925	+	23.1716i	−1.15074	+	0.805756i	−0.983633	−	0.180184i	$-0.942331\pi$
$827$	−33.0925	+	23.1716i	−1.15074	+	0.805756i	−0.167105	+	0.985939i	$0.553442\pi$
$828$	6.65783	−	24.8474i	0.231376	−	0.863506i
$829$	16.2474	−	28.1413i	0.564294	−	0.977386i	−0.432821	−	0.901480i	$-0.642482\pi$
$829$	16.2474	−	28.1413i	0.564294	−	0.977386i	0.997115	−	0.0759063i	$-0.0241850\pi$
$830$		0			0
$831$	−4.24723	+	11.6692i	−0.147335	+	0.404799i
$832$	−3.85702	−	1.79856i	−0.133718	−	0.0623538i
$833$	0.778387	+	0.0681000i	0.0269695	+	0.00235953i
$834$	−53.2515	+	9.38967i	−1.84395	+	0.325138i
$835$		0			0
$836$	−0.549503	−	0.752870i	−0.0190050	−	0.0260386i
$837$	0.397693	−	0.397693i	0.0137463	−	0.0137463i
$838$	23.6944	+	16.5910i	0.818510	+	0.573127i
$839$	−37.6271	+	31.5728i	−1.29903	+	1.09002i	−0.308718	+	0.951153i	$0.599900\pi$
$839$	−37.6271	+	31.5728i	−1.29903	+	1.09002i	−0.990312	+	0.138862i	$0.955655\pi$
$840$		0			0
$841$	8.06890	+	2.93684i	0.278238	+	0.101270i
$842$	13.0523	−	1.14193i	0.449812	−	0.0393534i
$843$	−79.5594	+	21.3179i	−2.74017	+	0.734227i
$844$	4.28554	+	7.42277i	0.147514	+	0.255502i
$845$		0			0
$846$	4.67840	+	0.824927i	0.160847	+	0.0283616i
$847$	28.2296	+	7.56411i	0.969982	+	0.259906i
$848$	1.74737	+	6.52129i	0.0600051	+	0.223942i
$849$	−5.08467	−	4.26655i	−0.174506	−	0.146428i
$850$		0			0
$851$	14.4090	+	39.5885i	0.493936	+	1.35708i
$852$	−2.38075	+	27.2120i	−0.0815630	+	0.932269i
$853$	8.97043	−	12.8111i	0.307142	−	0.438644i	−0.635674	−	0.771957i	$-0.719278\pi$
$853$	8.97043	−	12.8111i	0.307142	−	0.438644i	0.942816	+	0.333314i	$0.108167\pi$
$854$	31.5769			1.08054
$855$		0			0
$856$	−3.99233			−0.136455
$857$	5.37831	−	7.68102i	0.183720	−	0.262379i	−0.716719	−	0.697362i	$-0.754357\pi$
$857$	5.37831	−	7.68102i	0.183720	−	0.262379i	0.900438	+	0.434984i	$0.143246\pi$
$858$	0.205585	−	2.34984i	0.00701854	−	0.0802223i
$859$	−6.92844	−	19.0357i	−0.236395	−	0.649491i	−0.999993	−	0.00379844i	$-0.998791\pi$
$859$	−6.92844	−	19.0357i	−0.236395	−	0.649491i	0.763597	−	0.645693i	$-0.223431\pi$
$860$		0			0
$861$	−23.1098	−	19.3914i	−0.787578	−	0.660857i
$862$	−1.20958	−	4.51420i	−0.0411983	−	0.153754i
$863$	2.31521	+	0.620358i	0.0788106	+	0.0211172i	0.298009	−	0.954563i	$-0.403677\pi$
$863$	2.31521	+	0.620358i	0.0788106	+	0.0211172i	−0.219198	+	0.975680i	$0.570344\pi$
$864$	1.83466	+	0.323500i	0.0624164	+	0.0110057i
$865$		0			0
$866$	−13.3109	−	23.0552i	−0.452323	−	0.783446i
$867$	67.2754	−	18.0264i	2.28479	−	0.612208i
$868$	−0.802381	+	0.0701992i	−0.0272346	+	0.00238272i
$869$	0.780801	+	0.284188i	0.0264869	+	0.00964043i
$870$		0			0
$871$	47.7117	−	40.0349i	1.61665	−	1.35653i
$872$	10.0725	+	7.05285i	0.341098	+	0.238840i
$873$	14.0206	−	14.0206i	0.474527	−	0.474527i
$874$	−8.37424	−	28.9660i	−0.283263	−	0.979791i
$875$		0			0
$876$	−15.6665	+	2.76242i	−0.529321	+	0.0933335i
$877$	14.3930	+	1.25922i	0.486016	+	0.0425209i	0.327531	−	0.944841i	$-0.393784\pi$
$877$	14.3930	+	1.25922i	0.486016	+	0.0425209i	0.158485	+	0.987361i	$0.449339\pi$
$878$	8.54865	+	3.98630i	0.288503	+	0.134531i
$879$	−6.82603	+	18.7544i	−0.230236	+	0.632569i
$880$		0			0
$881$	11.2307	−	19.4522i	0.378372	−	0.655360i	−0.612453	−	0.790507i	$-0.709817\pi$
$881$	11.2307	−	19.4522i	0.378372	−	0.655360i	0.990826	+	0.135147i	$0.0431506\pi$
$882$	−0.113542	+	0.423745i	−0.00382316	+	0.0142682i
$883$	−36.7197	+	25.7114i	−1.23572	+	0.865258i	−0.994451	−	0.105201i	$-0.966451\pi$
$883$	−36.7197	+	25.7114i	−1.23572	+	0.865258i	−0.241266	+	0.970459i	$0.577563\pi$
$884$	4.89475	−	27.7595i	0.164628	−	0.933654i
$885$		0			0
$886$	14.0596	+	8.11731i	0.472341	+	0.272706i
$887$	−1.71671	−	19.6221i	−0.0576415	−	0.658846i	−0.968972	−	0.247170i	$-0.920499\pi$
$887$	−1.71671	−	19.6221i	−0.0576415	−	0.658846i	0.911331	−	0.411675i	$-0.135056\pi$
$888$	−14.3074	+	6.67163i	−0.480124	+	0.223885i
$889$	−32.3895	+	11.7888i	−1.08631	+	0.395384i
$890$		0			0
$891$	−0.234943	−	1.33243i	−0.00787087	−	0.0446379i
$892$	−9.48419	−	9.48419i	−0.317554	−	0.317554i
$893$	5.19417	−	2.00685i	0.173816	−	0.0671567i
$894$		−	59.3026i		−	1.98338i
$895$		0			0
$896$	−1.71493	−	2.04377i	−0.0572917	−	0.0682776i
$897$	32.2486	−	69.1574i	1.07675	−	2.30910i
$898$	0.417217	+	0.894724i	0.0139227	+	0.0298573i
$899$	0.876763	−	1.04488i	0.0292417	−	0.0348489i
$900$		0			0
$901$	−38.7262	+	22.3586i	−1.29016	+	0.744872i
$902$	0.535040	+	0.764117i	0.0178149	+	0.0254423i
$903$	7.38654	+	10.5491i	0.245809	+	0.351051i
$904$	2.58482	−	1.49235i	0.0859700	−	0.0496348i
$905$		0			0
$906$	1.03538	−	1.23391i	0.0343981	−	0.0409940i
$907$	−9.54524	−	20.4698i	−0.316945	−	0.679690i	0.681706	−	0.731626i	$-0.261238\pi$
$907$	−9.54524	−	20.4698i	−0.316945	−	0.679690i	−0.998650	+	0.0519366i	$0.983461\pi$
$908$	−7.94221	+	17.0321i	−0.263572	+	0.565231i
$909$	−15.3387	−	18.2799i	−0.508751	−	0.606306i
$910$		0			0
$911$		−	40.5589i		−	1.34378i	−0.740652	−	0.671889i	$-0.765483\pi$
$911$		−	40.5589i		−	1.34378i	0.740652	−	0.671889i	$-0.234517\pi$
$912$	10.5392	−	4.07199i	0.348988	−	0.134837i
$913$	−2.21270	−	2.21270i	−0.0732295	−	0.0732295i
$914$	−5.30916	−	30.1097i	−0.175611	−	0.995942i
$915$		0			0
$916$	5.61842	−	2.04494i	0.185638	−	0.0675666i
$917$	46.2046	−	21.5456i	1.52581	−	0.711498i
$918$	1.07544	+	12.2923i	0.0354947	+	0.405706i
$919$	−40.3138	−	23.2752i	−1.32983	−	0.767777i	−0.344556	−	0.938766i	$-0.611970\pi$
$919$	−40.3138	−	23.2752i	−1.32983	−	0.767777i	−0.985273	+	0.170989i	$0.945304\pi$
$920$		0			0
$921$	−3.72158	+	21.1061i	−0.122630	+	0.695470i
$922$	−21.9924	+	15.3993i	−0.724282	+	0.507148i
$923$	−11.6077	+	43.3205i	−0.382072	+	1.42591i
$924$	0.739378	−	1.28064i	0.0243237	−	0.0421300i
$925$		0			0
$926$	−12.9990	+	35.7144i	−0.427172	+	1.17365i
$927$	−46.7093	−	21.7809i	−1.53414	−	0.715379i
$928$	4.50091	+	0.393779i	0.147750	+	0.0129264i
$929$	−4.31795	+	0.761371i	−0.141667	+	0.0249798i	−0.244032	−	0.969767i	$-0.578470\pi$
$929$	−4.31795	+	0.761371i	−0.141667	+	0.0249798i	0.102365	+	0.994747i	$0.467359\pi$
$930$		0			0
$931$	0.142813	+	0.493984i	0.00468052	+	0.0161897i
$932$	−5.75989	+	5.75989i	−0.188672	+	0.188672i
$933$	17.9621	+	12.5772i	0.588053	+	0.411759i
$934$	17.3951	−	14.5962i	0.569185	−	0.477603i
$935$		0			0
$936$	14.8715	+	5.41280i	0.486091	+	0.176923i
$937$	−8.54029	+	0.747179i	−0.278999	+	0.0244093i	−0.225797	−	0.974174i	$-0.572498\pi$
$937$	−8.54029	+	0.747179i	−0.278999	+	0.0244093i	−0.0532026	+	0.998584i	$0.516943\pi$
$938$	37.7152	−	10.1058i	1.23145	−	0.329965i
$939$	−42.7727	−	74.0845i	−1.39583	−	2.41766i
$940$		0			0
$941$	−18.5453	−	3.27004i	−0.604561	−	0.106600i	−0.137015	−	0.990569i	$-0.543751\pi$
$941$	−18.5453	−	3.27004i	−0.604561	−	0.106600i	−0.467546	+	0.883969i	$0.654862\pi$
$942$	51.5449	+	13.8114i	1.67942	+	0.450000i
$943$	7.81015	+	29.1479i	0.254333	+	0.949186i
$944$	−1.37859	−	1.15677i	−0.0448692	−	0.0376497i
$945$		0			0
$946$	−0.136193	−	0.374188i	−0.00442802	−	0.0121659i
$947$	−0.584960	+	6.68612i	−0.0190086	+	0.217270i	0.980749	+	0.195271i	$0.0625586\pi$
$947$	−0.584960	+	6.68612i	−0.0190086	+	0.217270i	−0.999758	+	0.0219989i	$0.992997\pi$
$948$	−5.77716	+	8.25064i	−0.187633	+	0.267968i
$949$	−26.1188			−0.847851
$950$		0			0
$951$	23.5402			0.763342
$952$	10.1357	−	14.4753i	0.328500	−	0.469146i
$953$	−3.10238	+	35.4604i	−0.100496	+	1.14868i	0.763717	+	0.645551i	$0.223372\pi$
$953$	−3.10238	+	35.4604i	−0.100496	+	1.14868i	−0.864214	+	0.503125i	$0.832183\pi$
$954$	−8.58687	−	23.5922i	−0.278010	−	0.763827i
$955$		0			0
$956$	17.7204	+	14.8692i	0.573118	+	0.480903i
$957$	0.648143	+	2.41890i	0.0209515	+	0.0781920i
$958$	5.15444	+	1.38113i	0.166533	+	0.0446223i
$959$	48.9002	+	8.62242i	1.57907	+	0.278433i
$960$		0			0
$961$	−15.4544	−	26.7679i	−0.498530	−	0.863479i
$962$	−25.0358	+	6.70831i	−0.807185	+	0.216285i
$963$	14.7899	−	1.29395i	0.476597	−	0.0416969i
$964$	18.4861	+	6.72838i	0.595396	+	0.216707i
$965$		0			0
$966$	36.6453	−	30.7491i	1.17904	−	0.989335i
$967$	42.3777	+	29.6732i	1.36278	+	0.954226i	0.999748	+	0.0224480i	$0.00714601\pi$
$967$	42.3777	+	29.6732i	1.36278	+	0.954226i	0.363028	+	0.931778i	$0.381743\pi$
$968$	7.74584	−	7.74584i	0.248961	−	0.248961i
$969$	44.1187	+	60.4467i	1.41730	+	1.94183i
$970$		0			0
$971$	−10.7005	+	1.88679i	−0.343397	+	0.0605501i	−0.342687	−	0.939450i	$-0.611337\pi$
$971$	−10.7005	+	1.88679i	−0.343397	+	0.0605501i	−0.000709705		1.00000i	$0.500226\pi$
$972$	21.9058	+	1.91651i	0.702629	+	0.0614721i
$973$	−50.4418	−	23.5214i	−1.61709	−	0.754062i
$974$	4.44484	−	12.2121i	0.142422	−	0.391301i
$975$		0			0
$976$	5.91782	−	10.2500i	0.189425	−	0.328094i
$977$	2.54277	−	9.48976i	0.0813506	−	0.303604i	−0.913248	−	0.407405i	$-0.866434\pi$
$977$	2.54277	−	9.48976i	0.0813506	−	0.303604i	0.994598	+	0.103801i	$0.0331004\pi$
$978$	30.8233	−	21.5827i	0.985620	−	0.690138i
$979$	−0.397956	+	2.25692i	−0.0127187	+	0.0721315i
$980$		0			0
$981$	−39.6002	−	22.8632i	−1.26434	−	0.729966i
$982$	−3.23984	−	37.0315i	−0.103387	−	1.18172i
$983$	−44.2160	+	20.6182i	−1.41027	+	0.657620i	−0.970635	−	0.240557i	$-0.922670\pi$
$983$	−44.2160	+	20.6182i	−1.41027	+	0.657620i	−0.439635	+	0.898177i	$0.644892\pi$
$984$	−10.6255	+	3.86736i	−0.338728	+	0.123287i
$985$		0			0
$986$	5.19650	+	29.4708i	0.165490	+	0.938541i
$987$	6.24681	+	6.24681i	0.198838	+	0.198838i
$988$	18.2018	−	3.57926i	0.579077	−	0.113871i
$989$		−	12.8817i		−	0.409613i
$990$		0			0
$991$	−25.3834	−	30.2508i	−0.806331	−	0.960947i	0.193466	−	0.981107i	$-0.438027\pi$
$991$	−25.3834	−	30.2508i	−0.806331	−	0.960947i	−0.999797	+	0.0201596i	$0.993583\pi$
$992$	−0.127587	+	0.273611i	−0.00405089	+	0.00868717i
$993$	14.5775	+	31.2616i	0.462603	+	0.992055i
$994$	−18.0725	+	21.5380i	−0.573226	+	0.683144i
$995$		0			0
$996$	32.8500	−	18.9660i	1.04089	−	0.600960i
$997$	−30.2751	−	43.2374i	−0.958823	−	1.36934i	−0.929118	−	0.369782i	$-0.879432\pi$
$997$	−30.2751	−	43.2374i	−0.958823	−	1.36934i	−0.0297047	−	0.999559i	$-0.509457\pi$
$998$	8.37397	+	11.9593i	0.265073	+	0.378564i
$999$	9.82597	−	5.67302i	0.310880	−	0.179487i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.d.143.4	✓	96
5.2	odd	4	inner	950.2.bb.d.257.1	yes	96
5.3	odd	4	inner	950.2.bb.d.257.8	yes	96
5.4	even	2	inner	950.2.bb.d.143.5	yes	96
19.2	odd	18	inner	950.2.bb.d.743.1	yes	96
95.2	even	36	inner	950.2.bb.d.857.4	yes	96
95.59	odd	18	inner	950.2.bb.d.743.8	yes	96
95.78	even	36	inner	950.2.bb.d.857.5	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.bb.d.143.4	✓	96	1.1	even	1	trivial
950.2.bb.d.143.5	yes	96	5.4	even	2	inner
950.2.bb.d.257.1	yes	96	5.2	odd	4	inner
950.2.bb.d.257.8	yes	96	5.3	odd	4	inner
950.2.bb.d.743.1	yes	96	19.2	odd	18	inner
950.2.bb.d.743.8	yes	96	95.59	odd	18	inner
950.2.bb.d.857.4	yes	96	95.2	even	36	inner
950.2.bb.d.857.5	yes	96	95.78	even	36	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.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.573576 + 0.819152i) q^{2} +(0.225912 - 2.58219i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(1.98563 + 1.66614i) q^{6} +(0.690517 + 2.57704i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-3.66223 - 0.645749i) q^{9} +O(q^{10})\)	\(q+(-0.573576 + 0.819152i) q^{2} +(0.225912 - 2.58219i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(1.98563 + 1.66614i) q^{6} +(0.690517 + 2.57704i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-3.66223 - 0.645749i) q^{9} +(0.106917 + 0.185185i) q^{11} +(-2.50373 + 0.670872i) q^{12} +(-4.23956 + 0.370913i) q^{13} +(-2.50705 - 0.912493i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(-5.42561 - 3.79906i) q^{17} +(2.62953 - 2.62953i) q^{18} +(1.04529 - 4.23171i) q^{19} +(6.81040 - 1.20086i) q^{21} +(-0.213019 - 0.0186368i) q^{22} +(-6.26930 - 2.92342i) q^{23} +(0.886533 - 2.43573i) q^{24} +(2.12788 - 3.68559i) q^{26} +(-0.482170 + 1.79948i) q^{27} +(2.18546 - 1.53027i) q^{28} +(-0.784560 + 4.44946i) q^{29} +(-0.261450 - 0.150948i) q^{31} +(-0.0871557 - 0.996195i) q^{32} +(0.502336 - 0.234243i) q^{33} +(6.22401 - 2.26535i) q^{34} +(0.645749 + 3.66223i) q^{36} +(-4.30651 - 4.30651i) q^{37} +(2.86686 + 3.28346i) q^{38} +11.0311i q^{39} +(-2.80406 - 3.34175i) q^{41} +(-2.92260 + 6.26754i) q^{42} +(0.787004 + 1.68774i) q^{43} +(0.137449 - 0.163806i) q^{44} +(5.99065 - 3.45870i) q^{46} +(0.732728 + 1.04644i) q^{47} +(1.48674 + 2.12328i) q^{48} +(-0.102164 + 0.0589844i) q^{49} +(-11.0356 + 13.1517i) q^{51} +(1.79856 + 3.85702i) q^{52} +(2.85324 - 6.11879i) q^{53} +(-1.19749 - 1.42711i) q^{54} +2.66795i q^{56} +(-10.6909 - 3.65514i) q^{57} +(-3.19478 - 3.19478i) q^{58} +(0.312500 + 1.77228i) q^{59} +(-11.1219 + 4.04803i) q^{61} +(0.273611 - 0.127587i) q^{62} +(-0.864705 - 9.88362i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-0.0962473 + 0.545846i) q^{66} +(-11.9883 + 8.39433i) q^{67} +(-1.71428 + 6.39776i) q^{68} +(-8.96513 + 15.5281i) q^{69} +(3.60434 - 9.90283i) q^{71} +(-3.37031 - 1.57160i) q^{72} +(6.11393 + 0.534900i) q^{73} +(5.99780 - 1.05757i) q^{74} +(-4.33402 + 0.465075i) q^{76} +(-0.403402 + 0.403402i) q^{77} +(-9.03617 - 6.32719i) q^{78} +(2.97669 - 2.49774i) q^{79} +(-5.94569 - 2.16406i) q^{81} +(4.34575 - 0.380203i) q^{82} +(-14.1353 + 3.78755i) q^{83} +(-3.45773 - 5.98897i) q^{84} +(-1.83392 - 0.323369i) q^{86} +(11.3121 + 3.03107i) q^{87} +(0.0553441 + 0.206547i) q^{88} +(8.21001 + 6.88902i) q^{89} +(-3.88335 - 10.6694i) q^{91} +(-0.602891 + 6.89108i) q^{92} +(-0.448842 + 0.641012i) q^{93} -1.27747 q^{94} -2.59205 q^{96} +(-3.05830 + 4.36771i) q^{97} +(0.0102817 - 0.117520i) q^{98} +(-0.271970 - 0.747230i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{6}+O(q^{10}) \) 96 * q - 12 * q^6	\( 96 q - 12 q^{6} + 12 q^{26} - 72 q^{31} + 12 q^{36} - 24 q^{41} + 12 q^{51} - 72 q^{61} - 36 q^{66} + 168 q^{71} - 12 q^{76} + 12 q^{81} - 48 q^{86} - 72 q^{91}+O(q^{100}) \) 96 * q - 12 * q^6 + 12 * q^26 - 72 * q^31 + 12 * q^36 - 24 * q^41 + 12 * q^51 - 72 * q^61 - 36 * q^66 + 168 * q^71 - 12 * q^76 + 12 * q^81 - 48 * q^86 - 72 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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