LMFDB - Embedded newform 775.2.ck.b.299.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(49,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 26]))

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

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

chi := DirichletCharacter("775.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.ck (of order $30$, degree $8$, not 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:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 155)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			299.3
Character	$\chi$	$=$	775.299
Dual form			775.2.ck.b.324.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34623 + 0.437416i) q^{2} +(-2.31753 + 2.08671i) q^{3} +(0.00296283 - 0.00215262i) q^{4} +(2.20716 - 3.82291i) q^{6} +(-0.944642 + 0.0992859i) q^{7} +(1.66098 - 2.28615i) q^{8} +(0.702986 - 6.68846i) q^{9} +O(q^{10})$	\(q+(-1.34623 + 0.437416i) q^{2} +(-2.31753 + 2.08671i) q^{3} +(0.00296283 - 0.00215262i) q^{4} +(2.20716 - 3.82291i) q^{6} +(-0.944642 + 0.0992859i) q^{7} +(1.66098 - 2.28615i) q^{8} +(0.702986 - 6.68846i) q^{9} +(2.64680 + 1.17843i) q^{11} +(-0.00237454 + 0.0111713i) q^{12} +(0.844492 + 3.97302i) q^{13} +(1.22827 - 0.546863i) q^{14} +(-1.23833 + 3.81118i) q^{16} +(2.40356 + 5.39849i) q^{17} +(1.97926 + 9.31169i) q^{18} +(3.85426 + 0.819249i) q^{19} +(1.98205 - 2.20129i) q^{21} +(-4.07866 - 0.428684i) q^{22} +(4.17178 - 5.74196i) q^{23} +(0.921154 + 8.76420i) q^{24} +(-2.87474 - 4.97920i) q^{26} +(6.82861 + 9.39877i) q^{27} +(-0.00258509 + 0.00232762i) q^{28} +(0.690565 + 2.12534i) q^{29} +(4.68304 + 3.01150i) q^{31} -0.0207168i q^{32} +(-8.59307 + 2.79206i) q^{33} +(-5.59713 - 6.21624i) q^{34} +(-0.0123149 - 0.0213300i) q^{36} +(-1.26106 - 0.728076i) q^{37} +(-5.54707 + 0.583021i) q^{38} +(-10.2477 - 7.44538i) q^{39} +(0.928592 - 1.03131i) q^{41} +(-1.70542 + 3.83043i) q^{42} +(2.66625 - 12.5437i) q^{43} +(0.0103787 - 0.00220606i) q^{44} +(-3.10454 + 9.55479i) q^{46} +(1.42464 + 0.462894i) q^{47} +(-5.08297 - 11.4165i) q^{48} +(-5.96454 + 1.26780i) q^{49} +(-16.8354 - 7.49561i) q^{51} +(0.0110545 + 0.00995351i) q^{52} +(-2.69114 - 0.282850i) q^{53} +(-13.3040 - 9.66595i) q^{54} +(-1.34205 + 2.32450i) q^{56} +(-10.6419 + 6.14411i) q^{57} +(-1.85931 - 2.55913i) q^{58} +(2.76666 + 3.07268i) q^{59} +5.75919 q^{61} +(-7.62172 - 2.00573i) q^{62} +6.38800i q^{63} +(-2.46759 - 7.59447i) q^{64} +(10.3469 - 7.51749i) q^{66} +(7.95257 - 4.59142i) q^{67} +(0.0187422 + 0.0108208i) q^{68} +(2.31360 + 22.0125i) q^{69} +(-1.16123 + 11.0483i) q^{71} +(-14.1232 - 12.7165i) q^{72} +(-2.19480 + 4.92960i) q^{73} +(2.01615 + 0.428546i) q^{74} +(0.0131831 - 0.00586947i) q^{76} +(-2.61728 - 0.850405i) q^{77} +(17.0525 + 5.54068i) q^{78} +(-3.76376 + 1.67573i) q^{79} +(-15.7030 - 3.33777i) q^{81} +(-0.798986 + 1.79455i) q^{82} +(12.5706 + 11.3186i) q^{83} +(0.00113393 - 0.0107887i) q^{84} +(1.89744 + 18.0529i) q^{86} +(-6.03537 - 3.48452i) q^{87} +(7.09035 - 4.09361i) q^{88} +(-6.19419 + 4.50034i) q^{89} +(-1.19221 - 3.66924i) q^{91} -0.0259927i q^{92} +(-17.1372 + 2.79291i) q^{93} -2.12037 q^{94} +(0.0432300 + 0.0480118i) q^{96} +(-0.00200089 - 0.00275399i) q^{97} +(7.47508 - 4.31574i) q^{98} +(9.74255 - 16.8746i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{4} - 24 q^{6} - 12 q^{9}+O(q^{10}) $ 80 * q + 4 * q^4 - 24 * q^6 - 12 * q^9	$ 80 q + 4 q^{4} - 24 q^{6} - 12 q^{9} + 32 q^{11} + 20 q^{14} - 32 q^{16} + 18 q^{19} - 48 q^{21} - 220 q^{24} - 8 q^{26} + 44 q^{29} - 12 q^{31} + 32 q^{34} - 2 q^{36} + 110 q^{39} - 48 q^{41} + 104 q^{44} - 100 q^{46} - 186 q^{49} - 84 q^{51} - 204 q^{54} + 10 q^{56} - 62 q^{59} + 136 q^{61} + 46 q^{64} + 96 q^{69} - 60 q^{71} - 100 q^{74} + 28 q^{76} - 98 q^{79} + 50 q^{81} + 36 q^{84} + 326 q^{86} - 8 q^{89} - 74 q^{91} + 188 q^{94} + 44 q^{96} - 34 q^{99}+O(q^{100}) $ 80 * q + 4 * q^4 - 24 * q^6 - 12 * q^9 + 32 * q^11 + 20 * q^14 - 32 * q^16 + 18 * q^19 - 48 * q^21 - 220 * q^24 - 8 * q^26 + 44 * q^29 - 12 * q^31 + 32 * q^34 - 2 * q^36 + 110 * q^39 - 48 * q^41 + 104 * q^44 - 100 * q^46 - 186 * q^49 - 84 * q^51 - 204 * q^54 + 10 * q^56 - 62 * q^59 + 136 * q^61 + 46 * q^64 + 96 * q^69 - 60 * q^71 - 100 * q^74 + 28 * q^76 - 98 * q^79 + 50 * q^81 + 36 * q^84 + 326 * q^86 - 8 * q^89 - 74 * q^91 + 188 * q^94 + 44 * q^96 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{4}{15}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.34623	+	0.437416i	−0.951927	+	0.309300i	−0.743498	−	0.668738i	$-0.766835\pi$
$2$	−1.34623	+	0.437416i	−0.951927	+	0.309300i	−0.208429	+	0.978038i	$0.566835\pi$
$3$	−2.31753	+	2.08671i	−1.33803	+	1.20476i	−0.377685	+	0.925934i	$0.623280\pi$
$3$	−2.31753	+	2.08671i	−1.33803	+	1.20476i	−0.960341	+	0.278830i	$0.910054\pi$
$4$	0.00296283	−	0.00215262i	0.00148141	−	0.00107631i
$5$		0			0
$5$		0			0
$6$	2.20716	−	3.82291i	0.901069	−	1.56070i
$7$	−0.944642	+	0.0992859i	−0.357041	+	0.0375265i	−0.281351	−	0.959605i	$-0.590783\pi$
$7$	−0.944642	+	0.0992859i	−0.357041	+	0.0375265i	−0.0756900	+	0.997131i	$0.524116\pi$
$8$	1.66098	−	2.28615i	0.587246	−	0.808275i
$9$	0.702986	−	6.68846i	0.234329	−	2.22949i
$10$		0			0
$11$	2.64680	+	1.17843i	0.798039	+	0.355310i	0.764907	−	0.644141i	$-0.222785\pi$
$11$	2.64680	+	1.17843i	0.798039	+	0.355310i	0.0331325	+	0.999451i	$0.489452\pi$
$12$	−0.00237454	+	0.0111713i	−0.000685470	+	0.00322488i
$13$	0.844492	+	3.97302i	0.234220	+	1.10192i	0.925328	+	0.379167i	$0.123789\pi$
$13$	0.844492	+	3.97302i	0.234220	+	1.10192i	−0.691108	+	0.722751i	$0.742877\pi$
$14$	1.22827	−	0.546863i	0.328270	−	0.146155i
$15$		0			0
$16$	−1.23833	+	3.81118i	−0.309582	+	0.952795i
$17$	2.40356	+	5.39849i	0.582949	+	1.30933i	0.928642	+	0.370978i	$0.120977\pi$
$17$	2.40356	+	5.39849i	0.582949	+	1.30933i	−0.345692	+	0.938348i	$0.612356\pi$
$18$	1.97926	+	9.31169i	0.466516	+	2.19479i
$19$	3.85426	+	0.819249i	0.884229	+	0.187949i	0.627576	−	0.778555i	$-0.284047\pi$
$19$	3.85426	+	0.819249i	0.884229	+	0.187949i	0.256653	+	0.966504i	$0.417380\pi$
$20$		0			0
$21$	1.98205	−	2.20129i	0.432520	−	0.480362i
$22$	−4.07866	−	0.428684i	−0.869572	−	0.0913957i
$23$	4.17178	−	5.74196i	0.869876	−	1.19728i	−0.109247	−	0.994015i	$-0.534844\pi$
$23$	4.17178	−	5.74196i	0.869876	−	1.19728i	0.979123	−	0.203267i	$-0.0651559\pi$
$24$	0.921154	+	8.76420i	0.188030	+	1.78898i
$25$		0			0
$26$	−2.87474	−	4.97920i	−0.563783	−	0.976501i
$27$	6.82861	+	9.39877i	1.31417	+	1.80879i
$28$	−0.00258509	+	0.00232762i	−0.000488536	+	0.000439879i
$29$	0.690565	+	2.12534i	0.128235	+	0.394666i	0.994477	−	0.104959i	$-0.0334712\pi$
$29$	0.690565	+	2.12534i	0.128235	+	0.394666i	−0.866242	+	0.499625i	$0.833471\pi$
$30$		0			0
$31$	4.68304	+	3.01150i	0.841099	+	0.540882i
$31$	4.68304	+	3.01150i	0.841099	+	0.540882i
$32$		−	0.0207168i		−	0.00366225i
$33$	−8.59307	+	2.79206i	−1.49586	+	0.486035i
$34$	−5.59713	−	6.21624i	−0.959899	−	1.06608i
$35$		0			0
$36$	−0.0123149	−	0.0213300i	−0.00205248	−	0.00355500i
$37$	−1.26106	−	0.728076i	−0.207318	−	0.119695i	0.392746	−	0.919647i	$-0.371525\pi$
$37$	−1.26106	−	0.728076i	−0.207318	−	0.119695i	−0.600064	+	0.799952i	$0.704858\pi$
$38$	−5.54707	+	0.583021i	−0.899854	+	0.0945784i
$39$	−10.2477	−	7.44538i	−1.64094	−	1.19222i
$40$		0			0
$41$	0.928592	−	1.03131i	0.145022	−	0.161063i	−0.666258	−	0.745722i	$-0.732105\pi$
$41$	0.928592	−	1.03131i	0.145022	−	0.161063i	0.811279	+	0.584659i	$0.198772\pi$
$42$	−1.70542	+	3.83043i	−0.263151	+	0.591048i
$43$	2.66625	−	12.5437i	0.406599	−	1.91290i	−0.00158676	−	0.999999i	$-0.500505\pi$
$43$	2.66625	−	12.5437i	0.406599	−	1.91290i	0.408186	−	0.912899i	$-0.366162\pi$
$44$	0.0103787	−	0.00220606i	0.00156465	−	0.000332577i
$45$		0			0
$46$	−3.10454	+	9.55479i	−0.457739	+	1.40878i
$47$	1.42464	+	0.462894i	0.207805	+	0.0675201i	0.411070	−	0.911604i	$-0.365155\pi$
$47$	1.42464	+	0.462894i	0.207805	+	0.0675201i	−0.203265	+	0.979124i	$0.565155\pi$
$48$	−5.08297	−	11.4165i	−0.733664	−	1.64784i
$49$	−5.96454	+	1.26780i	−0.852077	+	0.181115i
$50$		0			0
$51$	−16.8354	−	7.49561i	−2.35743	−	1.04960i
$52$	0.0110545	+	0.00995351i	0.00153298	+	0.00138030i
$53$	−2.69114	−	0.282850i	−0.369657	−	0.0388525i	−0.0821209	−	0.996622i	$-0.526169\pi$
$53$	−2.69114	−	0.282850i	−0.369657	−	0.0388525i	−0.287536	+	0.957770i	$0.592836\pi$
$54$	−13.3040	−	9.66595i	−1.81045	−	1.31537i
$55$		0			0
$56$	−1.34205	+	2.32450i	−0.179339	+	0.310625i
$57$	−10.6419	+	6.14411i	−1.40955	+	0.813807i
$58$	−1.85931	−	2.55913i	−0.244140	−	0.336030i
$59$	2.76666	+	3.07268i	0.360188	+	0.400029i	0.895816	−	0.444425i	$-0.146592\pi$
$59$	2.76666	+	3.07268i	0.360188	+	0.400029i	−0.535628	+	0.844454i	$0.679925\pi$
$60$		0			0
$61$	5.75919			0.737389			0.368695	−	0.929551i	$-0.379805\pi$
$61$	5.75919			0.737389			0.368695	+	0.929551i	$0.379805\pi$
$62$	−7.62172	−	2.00573i	−0.967959	−	0.254728i
$63$			6.38800i			0.804813i
$64$	−2.46759	−	7.59447i	−0.308449	−	0.949309i
$65$		0			0
$66$	10.3469	−	7.51749i	1.27362	−	0.925339i
$67$	7.95257	−	4.59142i	0.971561	−	0.560931i	0.0718494	−	0.997415i	$-0.477110\pi$
$67$	7.95257	−	4.59142i	0.971561	−	0.560931i	0.899712	+	0.436484i	$0.143777\pi$
$68$	0.0187422	+	0.0108208i	0.00227283	+	0.00131222i
$69$	2.31360	+	22.0125i	0.278525	+	2.64999i
$70$		0			0
$71$	−1.16123	+	11.0483i	−0.137812	+	1.31119i	0.678935	+	0.734198i	$0.262442\pi$
$71$	−1.16123	+	11.0483i	−0.137812	+	1.31119i	−0.816747	+	0.576996i	$0.804225\pi$
$72$	−14.1232	−	12.7165i	−1.66443	−	1.49866i
$73$	−2.19480	+	4.92960i	−0.256882	+	0.576966i	−0.995241	−	0.0974413i	$-0.968934\pi$
$73$	−2.19480	+	4.92960i	−0.256882	+	0.576966i	0.738359	+	0.674407i	$0.235601\pi$
$74$	2.01615	+	0.428546i	0.234373	+	0.0498175i
$75$		0			0
$76$	0.0131831	−	0.00586947i	0.00151220	−	0.000673275i
$77$	−2.61728	−	0.850405i	−0.298267	−	0.0969127i
$78$	17.0525	+	5.54068i	1.93081	+	0.627358i
$79$	−3.76376	+	1.67573i	−0.423456	+	0.188535i	−0.607390	−	0.794404i	$-0.707783\pi$
$79$	−3.76376	+	1.67573i	−0.423456	+	0.188535i	0.183934	+	0.982939i	$0.441117\pi$
$80$		0			0
$81$	−15.7030	−	3.33777i	−1.74478	−	0.370864i
$82$	−0.798986	+	1.79455i	−0.0882333	+	0.198175i
$83$	12.5706	+	11.3186i	1.37981	+	1.24238i	0.938614	+	0.344970i	$0.112111\pi$
$83$	12.5706	+	11.3186i	1.37981	+	1.24238i	0.441192	+	0.897413i	$0.354556\pi$
$84$	0.00113393	−	0.0107887i	0.000123722	−	0.00117714i
$85$		0			0
$86$	1.89744	+	18.0529i	0.204606	+	1.94670i
$87$	−6.03537	−	3.48452i	−0.647060	−	0.373580i
$88$	7.09035	−	4.09361i	0.755833	−	0.436381i
$89$	−6.19419	+	4.50034i	−0.656583	+	0.477036i	−0.865507	−	0.500896i	$-0.833004\pi$
$89$	−6.19419	+	4.50034i	−0.656583	+	0.477036i	0.208924	+	0.977932i	$0.433004\pi$
$90$		0			0
$91$	−1.19221	−	3.66924i	−0.124977	−	0.384641i
$92$		−	0.0259927i		−	0.00270992i
$93$	−17.1372	+	2.79291i	−1.77705	+	0.289611i
$94$	−2.12037			−0.218700
$95$		0			0
$96$	0.0432300	+	0.0480118i	0.00441215	+	0.00490019i
$97$	−0.00200089	−	0.00275399i	−0.000203160	−	0.000279625i	0.808915	−	0.587925i	$-0.200055\pi$
$97$	−0.00200089	−	0.00275399i	−0.000203160	−	0.000279625i	−0.809119	+	0.587645i	$0.800055\pi$
$98$	7.47508	−	4.31574i	0.755097	−	0.435955i
$99$	9.74255	−	16.8746i	0.979163	−	1.69596i
$100$		0			0
$101$	−3.87721	−	2.81696i	−0.385797	−	0.280298i	0.377934	−	0.925833i	$-0.376635\pi$
$101$	−3.87721	−	2.81696i	−0.385797	−	0.280298i	−0.763731	+	0.645535i	$0.776635\pi$
$102$	25.9430	+	2.72672i	2.56874	+	0.269985i
$103$	−6.14194	−	5.53023i	−0.605183	−	0.544909i	0.308558	−	0.951205i	$-0.400153\pi$
$103$	−6.14194	−	5.53023i	−0.605183	−	0.544909i	−0.913741	+	0.406296i	$0.866820\pi$
$104$	10.4856	+	4.66849i	1.02820	+	0.457783i
$105$		0			0
$106$	3.74661	−	0.796367i	0.363903	−	0.0773500i
$107$	−6.53269	−	14.6727i	−0.631539	−	1.41846i	−0.891580	−	0.452862i	$-0.850403\pi$
$107$	−6.53269	−	14.6727i	−0.631539	−	1.41846i	0.260042	−	0.965597i	$-0.416264\pi$
$108$	0.0404640	+	0.0131475i	0.00389365	+	0.00126512i
$109$	−2.11356	+	6.50487i	−0.202442	+	0.623054i	0.797366	+	0.603496i	$0.206226\pi$
$109$	−2.11356	+	6.50487i	−0.202442	+	0.623054i	−0.999809	+	0.0195581i	$0.993774\pi$
$110$		0			0
$111$	4.44184	−	0.944142i	0.421601	−	0.0896140i
$112$	0.791380	−	3.72315i	0.0747784	−	0.351805i
$113$	−5.79099	+	13.0068i	−0.544770	+	1.22357i	0.406056	+	0.913848i	$0.366904\pi$
$113$	−5.79099	+	13.0068i	−0.544770	+	1.22357i	−0.950826	+	0.309725i	$0.899763\pi$
$114$	11.6389	−	12.9263i	1.09008	−	1.21066i
$115$		0			0
$116$	0.00662107	+	0.00481049i	0.000614751	+	0.000446643i
$117$	27.1671	−	2.85538i	2.51160	−	0.263980i
$118$	−5.06859	−	2.92635i	−0.466602	−	0.269393i
$119$	−2.80650	−	4.86100i	−0.257271	−	0.445607i
$120$		0			0
$121$	−1.74360	−	1.93646i	−0.158509	−	0.176042i
$122$	−7.75319	+	2.51916i	−0.701941	+	0.228074i
$123$			4.32778i			0.390223i
$124$	0.0203577	−	0.00115824i	0.00182817	−	0.000104013i
$125$		0			0
$126$	−2.79421	−	8.59971i	−0.248928	−	0.766123i
$127$	−4.87763	+	4.39184i	−0.432820	+	0.389713i	−0.856540	−	0.516080i	$-0.827391\pi$
$127$	−4.87763	+	4.39184i	−0.432820	+	0.389713i	0.423720	+	0.905793i	$0.360724\pi$
$128$	6.66824	+	9.17804i	0.589395	+	0.811232i
$129$	19.9960	+	34.6341i	1.76055	+	3.04936i
$130$		0			0
$131$	0.929302	+	8.84171i	0.0811935	+	0.772504i	0.957048	+	0.289929i	$0.0936318\pi$
$131$	0.929302	+	8.84171i	0.0811935	+	0.772504i	−0.875855	+	0.482575i	$0.839702\pi$
$132$	−0.0194495	+	0.0267700i	−0.00169287	+	0.00233003i
$133$	−3.72224	−	0.391223i	−0.322759	−	0.0339234i
$134$	−8.69761	+	9.65968i	−0.751359	+	0.834469i
$135$		0			0
$136$	16.3340	+	3.47190i	1.40063	+	0.297713i
$137$	3.66411	+	17.2383i	0.313046	+	1.47277i	0.800350	+	0.599533i	$0.204647\pi$
$137$	3.66411	+	17.2383i	0.313046	+	1.47277i	−0.487304	+	0.873233i	$0.662020\pi$
$138$	−12.7432	−	28.6218i	−1.08478	−	2.43645i
$139$	5.13638	−	15.8081i	0.435662	−	1.34083i	−0.456745	−	0.889598i	$-0.650985\pi$
$139$	5.13638	−	15.8081i	0.435662	−	1.34083i	0.892407	−	0.451232i	$-0.149015\pi$
$140$		0			0
$141$	−4.26758	+	1.90005i	−0.359395	+	0.160013i
$142$	−3.26944	−	15.3815i	−0.274365	−	1.29079i
$143$	−2.44673	+	11.5110i	−0.204606	+	0.962595i
$144$	24.6204	+	10.9617i	2.05170	+	0.913476i
$145$		0			0
$146$	0.798415	−	7.59641i	0.0660773	−	0.628683i
$147$	11.1775	−	15.3844i	0.921901	−	1.26889i
$148$	−0.00530359		0.000557429i	−0.000435952		4.58204e-5i
$149$	2.06741	−	3.58085i	0.169369	−	0.293355i	−0.768829	−	0.639454i	$-0.779161\pi$
$149$	2.06741	−	3.58085i	0.169369	−	0.293355i	0.938198	+	0.346099i	$0.112494\pi$
$150$		0			0
$151$	8.12460	−	5.90287i	0.661171	−	0.480369i	−0.205887	−	0.978576i	$-0.566008\pi$
$151$	8.12460	−	5.90287i	0.661171	−	0.480369i	0.867058	+	0.498207i	$0.166008\pi$
$152$	8.27479	−	7.45065i	0.671174	−	0.604328i
$153$	37.7973	−	12.2811i	3.05573	−	0.992866i
$154$	3.89543			0.313903
$155$		0			0
$156$	−0.0463892			−0.00371411
$157$	−22.2287	+	7.22255i	−1.77404	+	0.576422i	−0.998494	−	0.0548631i	$-0.982528\pi$
$157$	−22.2287	+	7.22255i	−1.77404	+	0.576422i	−0.775551	+	0.631285i	$0.782528\pi$
$158$	4.33388	−	3.90224i	0.344785	−	0.310446i
$159$	6.82702	−	4.96012i	0.541418	−	0.393363i
$160$		0			0
$161$	−3.37074	+	5.83830i	−0.265652	+	0.460122i
$162$	22.5998	−	2.37533i	1.77561	−	0.186624i
$163$	−0.145566	+	0.200354i	−0.0114016	+	0.0156929i	−0.814680	−	0.579911i	$-0.803087\pi$
$163$	−0.145566	+	0.200354i	−0.0114016	+	0.0156929i	0.803278	+	0.595604i	$0.203087\pi$
$164$	0.000531248	−	0.00505448i	4.14835e−5	−	0.000394689i
$165$		0			0
$166$	−21.8739	−	9.73888i	−1.69774	−	0.755884i
$167$	0.0119197	−	0.0560777i	0.000922373	−	0.00433943i	−0.977684	−	0.210081i	$-0.932627\pi$
$167$	0.0119197	−	0.0560777i	0.000922373	−	0.00433943i	0.978606	+	0.205741i	$0.0659606\pi$
$168$	−1.74032	−	8.18758i	−0.134269	−	0.631685i
$169$	−3.19565	+	1.42280i	−0.245819	+	0.109446i
$170$		0			0
$171$	8.18901	−	25.2032i	0.626229	−	1.92734i
$172$	−0.0191022	−	0.0429043i	−0.00145653	−	0.00327142i
$173$	2.79938	+	13.1701i	0.212833	+	1.00130i	0.946727	+	0.322037i	$0.104368\pi$
$173$	2.79938	+	13.1701i	0.212833	+	1.00130i	−0.733894	+	0.679264i	$0.762299\pi$
$174$	9.64918	+	2.05100i	0.731502	+	0.155486i
$175$		0			0
$176$	−7.76881	+	8.62814i	−0.585596	+	0.650370i
$177$	−12.8236	−	1.34782i	−0.963881	−	0.101308i
$178$	6.37027	−	8.76793i	0.477472	−	0.657184i
$179$	−0.316693	−	3.01313i	−0.0236707	−	0.225212i	−0.999962	−	0.00874979i	$-0.997215\pi$
$179$	−0.316693	−	3.01313i	−0.0236707	−	0.225212i	0.976291	−	0.216462i	$-0.0694518\pi$
$180$		0			0
$181$	−3.39081	−	5.87305i	−0.252037	−	0.436540i	0.712050	−	0.702129i	$-0.247767\pi$
$181$	−3.39081	−	5.87305i	−0.252037	−	0.436540i	−0.964086	+	0.265589i	$0.914434\pi$
$182$	3.20997	+	4.41814i	0.237939	+	0.327494i
$183$	−13.3471	+	12.0178i	−0.986646	+	0.888380i
$184$	−6.19771	−	19.0746i	−0.456901	−	1.40620i
$185$		0			0
$186$	21.8489	−	11.2560i	1.60204	−	0.825329i
$187$			17.1211i			1.25202i
$188$	0.00521741	−	0.00169524i	0.000380518	−	0.000123638i
$189$	−7.38376	−	8.20049i	−0.537089	−	0.596498i
$190$		0			0
$191$	5.60468	+	9.70760i	0.405541	+	0.702417i	0.994384	−	0.105830i	$-0.0337499\pi$
$191$	5.60468	+	9.70760i	0.405541	+	0.702417i	−0.588843	+	0.808247i	$0.700417\pi$
$192$	21.5662	+	12.4512i	1.55641	+	0.898591i
$193$	4.64346	−	0.488048i	0.334244	−	0.0351304i	0.0640799	−	0.997945i	$-0.479589\pi$
$193$	4.64346	−	0.488048i	0.334244	−	0.0351304i	0.270164	+	0.962814i	$0.412922\pi$
$194$	0.00389829	+	0.00283228i	0.000279881	+	0.000203346i
$195$		0			0
$196$	−0.0149428	+	0.0165957i	−0.00106734	+	0.00118541i
$197$	5.52524	−	12.4099i	0.393657	−	0.884168i	−0.602626	−	0.798024i	$-0.705879\pi$
$197$	5.52524	−	12.4099i	0.393657	−	0.884168i	0.996283	−	0.0861438i	$-0.0274545\pi$
$198$	−5.73447	+	26.9786i	−0.407531	+	1.91728i
$199$	7.46756	−	1.58728i	0.529361	−	0.112519i	0.0645254	−	0.997916i	$-0.479447\pi$
$199$	7.46756	−	1.58728i	0.529361	−	0.112519i	0.464836	+	0.885397i	$0.346113\pi$
$200$		0			0
$201$	−8.84934	+	27.2355i	−0.624184	+	1.92104i
$202$	6.45180	+	2.09632i	0.453947	+	0.147496i
$203$	−0.863353	−	1.93912i	−0.0605955	−	0.136100i
$204$	−0.0660156	+	0.0140321i	−0.00462202	+	0.000982440i
$205$		0			0
$206$	10.6875	+	4.75836i	0.744630	+	0.331531i
$207$	−35.4722	−	31.9393i	−2.46549	−	2.21993i
$208$	−16.1877	−	1.70139i	−1.12241	−	0.117970i
$209$	9.23603	+	6.71037i	0.638869	+	0.464166i
$210$		0			0
$211$	−9.30466	+	16.1161i	−0.640559	+	1.10948i	0.344749	+	0.938695i	$0.387964\pi$
$211$	−9.30466	+	16.1161i	−0.640559	+	1.10948i	−0.985308	+	0.170786i	$0.945369\pi$
$212$	−0.00858225	+	0.00495497i	−0.000589432	+	0.000340308i
$213$	−20.3635	−	28.0279i	−1.39528	−	1.92044i
$214$	15.2125	+	16.8952i	1.03991	+	1.15494i
$215$		0			0
$216$	32.8292			2.23374
$217$	−4.72280	−	2.37983i	−0.320604	−	0.161554i
$218$		−	9.68155i		−	0.655717i
$219$	−5.20015	−	16.0044i	−0.351393	−	1.08148i
$220$		0			0
$221$	−19.4185	+	14.1084i	−1.30623	+	0.949033i
$222$	−5.56674	+	3.21396i	−0.373615	+	0.215707i
$223$	17.0611	+	9.85023i	1.14250	+	0.659620i	0.947047	−	0.321094i	$-0.104051\pi$
$223$	17.0611	+	9.85023i	1.14250	+	0.659620i	0.195448	+	0.980714i	$0.437384\pi$
$224$	0.00205689	+	0.0195700i	0.000137432	+	0.00130757i
$225$		0			0
$226$	2.10662	−	20.0431i	0.140130	−	1.33325i
$227$	19.1662	+	17.2574i	1.27211	+	1.14541i	0.982094	+	0.188389i	$0.0603266\pi$
$227$	19.1662	+	17.2574i	1.27211	+	1.14541i	0.290014	+	0.957022i	$0.406340\pi$
$228$	−0.0183042	+	0.0411119i	−0.00121222	+	0.00272270i
$229$	0.296092	+	0.0629363i	0.0195663	+	0.00415895i	0.217684	−	0.976019i	$-0.430150\pi$
$229$	0.296092	+	0.0629363i	0.0195663	+	0.00415895i	−0.198118	+	0.980178i	$0.563483\pi$
$230$		0			0
$231$	7.84017	−	3.49067i	0.515845	−	0.229669i
$232$	6.00585	+	1.95142i	0.394303	+	0.128117i
$233$	0.419673	+	0.136360i	0.0274937	+	0.00893324i	0.322732	−	0.946491i	$-0.395399\pi$
$233$	0.419673	+	0.136360i	0.0274937	+	0.00893324i	−0.295238	+	0.955424i	$0.595399\pi$
$234$	−35.3241	+	15.7273i	−2.30921	+	1.02813i
$235$		0			0
$236$	0.0148114	+	0.00314827i	0.000964143	+	0.000204935i
$237$	5.22584	−	11.7374i	0.339455	−	0.762428i
$238$	5.90447	+	5.31641i	0.382730	+	0.344612i
$239$	−1.37323	+	13.0654i	−0.0888270	+	0.845133i	0.855871	+	0.517190i	$0.173022\pi$
$239$	−1.37323	+	13.0654i	−0.0888270	+	0.845133i	−0.944698	+	0.327943i	$0.893645\pi$
$240$		0			0
$241$	−2.71749	−	25.8552i	−0.175049	−	1.66548i	−0.631234	−	0.775593i	$-0.717451\pi$
$241$	−2.71749	−	25.8552i	−0.175049	−	1.66548i	0.456185	−	0.889885i	$-0.349216\pi$
$242$	3.19432	+	1.84424i	0.205339	+	0.118552i
$243$	13.1739	−	7.60596i	0.845106	−	0.487922i
$244$	0.0170635	−	0.0123974i	0.00109238	−	0.000793659i
$245$		0			0
$246$	−1.89304	−	5.82618i	−0.120696	−	0.371464i
$247$			16.0049i			1.01837i
$248$	14.6632	−	5.70406i	0.931113	−	0.362208i
$249$	−52.7515			−3.34299
$250$		0			0
$251$	−11.3115	−	12.5627i	−0.713976	−	0.792951i	0.271559	−	0.962422i	$-0.412461\pi$
$251$	−11.3115	−	12.5627i	−0.713976	−	0.792951i	−0.985535	+	0.169471i	$0.945794\pi$
$252$	0.0137509	+	0.0189265i	0.000866228	+	0.00119226i
$253$	17.8083	−	10.2817i	1.11960	−	0.646402i
$254$	4.64534	−	8.04597i	0.291475	−	0.504849i
$255$		0			0
$256$	−0.0711076	−	0.0516627i	−0.00444423	−	0.00322892i
$257$	4.15731	+	0.436951i	0.259326	+	0.0272562i	0.233299	−	0.972405i	$-0.425048\pi$
$257$	4.15731	+	0.436951i	0.259326	+	0.0272562i	0.0260267	+	0.999661i	$0.491715\pi$
$258$	−42.0687	−	37.8788i	−2.61908	−	2.35823i
$259$	1.26354	+	0.562566i	0.0785127	+	0.0349561i
$260$		0			0
$261$	14.7007	−	3.12473i	0.909951	−	0.193416i
$262$	−5.11856	−	11.4965i	−0.316226	−	0.710254i
$263$	−17.4868	−	5.68182i	−1.07828	−	0.350356i	−0.284575	−	0.958654i	$-0.591853\pi$
$263$	−17.4868	−	5.68182i	−1.07828	−	0.350356i	−0.793709	+	0.608298i	$0.791853\pi$
$264$	−7.88989	+	24.2826i	−0.485589	+	1.49449i
$265$		0			0
$266$	5.18211	−	1.10149i	0.317736	−	0.0675368i
$267$	4.96429	−	23.3552i	0.303810	−	1.42931i
$268$	0.0136785	−	0.0307224i	0.000835548	−	0.00187667i
$269$	−15.0877	+	16.7566i	−0.919911	+	1.02167i	0.0797798	+	0.996813i	$0.474578\pi$
$269$	−15.0877	+	16.7566i	−0.919911	+	1.02167i	−0.999691	+	0.0248525i	$0.992088\pi$
$270$		0			0
$271$	−7.89808	−	5.73829i	−0.479774	−	0.348576i	0.321464	−	0.946922i	$-0.395825\pi$
$271$	−7.89808	−	5.73829i	−0.479774	−	0.348576i	−0.801238	+	0.598345i	$0.795825\pi$
$272$	−23.5510	+	2.47531i	−1.42799	+	0.150088i
$273$	10.4196	+	6.01577i	0.630624	+	0.364091i
$274$	−12.4730	−	21.6039i	−0.753523	−	1.30514i
$275$		0			0
$276$	0.0542392	+	0.0602388i	0.00326482	+	0.00362595i
$277$	24.4535	−	7.94542i	1.46927	−	0.477394i	0.538381	−	0.842702i	$-0.319036\pi$
$277$	24.4535	−	7.94542i	1.46927	−	0.477394i	0.930887	+	0.365308i	$0.119036\pi$
$278$			23.5281i			1.41112i
$279$	23.4344	−	29.2053i	1.40298	−	1.74847i
$280$		0			0
$281$	0.0465029	+	0.143121i	0.00277413	+	0.00853790i	0.952434	−	0.304745i	$-0.0985712\pi$
$281$	0.0465029	+	0.143121i	0.00277413	+	0.00853790i	−0.949660	+	0.313283i	$0.898571\pi$
$282$	4.91402	−	4.42460i	0.292626	−	0.263481i
$283$	−8.86651	−	12.2037i	−0.527059	−	0.725435i	0.459620	−	0.888116i	$-0.347986\pi$
$283$	−8.86651	−	12.2037i	−0.527059	−	0.725435i	−0.986679	+	0.162681i	$0.947986\pi$
$284$	0.0203423	+	0.0352339i	0.00120709	+	0.00209075i
$285$		0			0
$286$	−1.74122	−	16.5666i	−0.102961	−	0.979604i
$287$	−0.774793	+	1.06641i	−0.0457346	+	0.0629482i
$288$	−0.138564	−	0.0145636i	−0.00816494	−	0.000858170i
$289$	−11.9914	+	13.3177i	−0.705374	+	0.783397i
$290$		0			0
$291$	0.0103839	+	0.00220717i	0.000608715	+	0.000129386i
$292$	0.00410875	+	0.0193301i	0.000240446	+	0.00113121i
$293$	−1.68196	−	3.77774i	−0.0982610	−	0.220698i	0.857726	−	0.514107i	$-0.171877\pi$
$293$	−1.68196	−	3.77774i	−0.0982610	−	0.220698i	−0.955987	+	0.293410i	$0.905210\pi$
$294$	−8.31800	+	25.6002i	−0.485116	+	1.49303i
$295$		0			0
$296$	−3.75909	+	1.67366i	−0.218493	+	0.0972793i
$297$	6.99814	+	32.9237i	0.406073	+	1.91043i
$298$	−1.21688	+	5.72496i	−0.0704919	+	0.331638i
$299$	26.3360	+	11.7255i	1.52305	+	0.678105i
$300$		0			0
$301$	−1.27324	+	12.1140i	−0.0733882	+	0.698242i
$302$	−8.35556	+	11.5004i	−0.480808	+	0.661776i
$303$	14.8637	−	1.56224i	0.853899	−	0.0897484i
$304$	−7.89515	+	13.6748i	−0.452818	+	0.784303i
$305$		0			0
$306$	−45.5118	+	33.0662i	−2.60174	+	1.89027i
$307$	−7.72660	+	6.95706i	−0.440980	+	0.397060i	−0.859491	−	0.511152i	$-0.829219\pi$
$307$	−7.72660	+	6.95706i	−0.440980	+	0.397060i	0.418510	+	0.908212i	$0.362552\pi$
$308$	−0.00958514	+	0.00311440i	−0.000546164	+	0.000177459i
$309$	25.7741			1.46624
$310$		0			0
$311$	−21.5627			−1.22271			−0.611353	−	0.791358i	$-0.709375\pi$
$311$	−21.5627			−1.22271			−0.611353	+	0.791358i	$0.709375\pi$
$312$	−34.0425	+	11.0611i	−1.92727	+	0.626209i
$313$	1.53286	−	1.38020i	0.0866426	−	0.0780134i	−0.624671	−	0.780888i	$-0.714767\pi$
$313$	1.53286	−	1.38020i	0.0866426	−	0.0780134i	0.711314	+	0.702874i	$0.248100\pi$
$314$	26.7657	−	19.4464i	1.51047	−	1.09742i
$315$		0			0
$316$	−0.00754414	+	0.0130668i	−0.000424391	+	0.000735067i
$317$	21.6026	−	2.27052i	1.21332	−	0.127525i	0.523833	−	0.851821i	$-0.324501\pi$
$317$	21.6026	−	2.27052i	1.21332	−	0.127525i	0.689490	+	0.724295i	$0.257835\pi$
$318$	−7.02109	+	9.66370i	−0.393723	+	0.541914i
$319$	−0.676779	+	6.43912i	−0.0378924	+	0.360522i
$320$		0			0
$321$	45.7573	+	20.3725i	2.55392	+	1.13708i
$322$	1.98402	−	9.33410i	0.110565	−	0.520169i
$323$	4.84126	+	22.7763i	0.269375	+	1.26731i
$324$	−0.0537102	+	0.0239133i	−0.00298390	+	0.00132852i
$325$		0			0
$326$	0.108327	−	0.333395i	0.00599966	−	0.0184650i
$327$	−8.67556	−	19.4856i	−0.479759	−	1.07756i
$328$	−0.815340	−	3.83588i	−0.0450196	−	0.211801i
$329$	−1.39174	−	0.295823i	−0.0767289	−	0.0163092i
$330$		0			0
$331$	−11.3089	+	12.5598i	−0.621594	+	0.690350i	−0.968914	−	0.247396i	$-0.920425\pi$
$331$	−11.3089	+	12.5598i	−0.621594	+	0.690350i	0.347320	+	0.937747i	$0.387092\pi$
$332$	0.0616093	+	0.00647540i	0.00338125	+	0.000355384i
$333$	−5.75622	+	7.92276i	−0.315439	+	0.434164i
$334$	0.00848268	+	0.0807073i	0.000464151	+	0.00441611i
$335$		0			0
$336$	5.93510	+	10.2799i	0.323786	+	0.560814i
$337$	2.54993	+	3.50967i	0.138903	+	0.191184i	0.872801	−	0.488076i	$-0.162301\pi$
$337$	2.54993	+	3.50967i	0.138903	+	0.191184i	−0.733898	+	0.679260i	$0.762301\pi$
$338$	3.67972	−	3.31324i	0.200150	−	0.180216i
$339$	−13.7206	−	42.2277i	−0.745201	−	2.29349i
$340$		0			0
$341$	8.84621	+	13.4895i	0.479049	+	0.730496i
$342$			37.5112i			2.02837i
$343$	11.8320	−	3.84444i	0.638867	−	0.207580i
$344$	−24.2482	−	26.9303i	−1.30737	−	1.45198i
$345$		0			0
$346$	−9.52940	−	16.5054i	−0.512304	−	0.887336i
$347$	9.08535	+	5.24543i	0.487727	+	0.281589i	0.723631	−	0.690187i	$-0.242472\pi$
$347$	9.08535	+	5.24543i	0.487727	+	0.281589i	−0.235904	+	0.971776i	$0.575805\pi$
$348$	−0.0253826	+	0.00266782i	−0.00136065	+	0.000143010i
$349$	4.52158	+	3.28512i	0.242035	+	0.175849i	0.702189	−	0.711990i	$-0.252206\pi$
$349$	4.52158	+	3.28512i	0.242035	+	0.175849i	−0.460155	+	0.887839i	$0.652206\pi$
$350$		0			0
$351$	−31.5748	+	35.0674i	−1.68534	+	1.87176i
$352$	0.0244133	−	0.0548332i	0.00130123	−	0.00292262i
$353$	−6.21600	+	29.2440i	−0.330844	+	1.55650i	0.427115	+	0.904197i	$0.359530\pi$
$353$	−6.21600	+	29.2440i	−0.330844	+	1.55650i	−0.757959	+	0.652302i	$0.773803\pi$
$354$	17.8531	−	3.79478i	0.948879	−	0.201691i
$355$		0			0
$356$	−0.00866479	+	0.0266675i	−0.000459233	+	0.00141337i
$357$	16.6477	+	5.40915i	0.881087	+	0.286283i
$358$	1.74433	+	3.91784i	0.0921909	+	0.207064i
$359$	4.53424	−	0.963782i	0.239308	−	0.0508665i	−0.0866962	−	0.996235i	$-0.527631\pi$
$359$	4.53424	−	0.963782i	0.239308	−	0.0508665i	0.326004	+	0.945368i	$0.394298\pi$
$360$		0			0
$361$	−3.17318	−	1.41279i	−0.167009	−	0.0743574i
$362$	7.13377	+	6.42327i	0.374942	+	0.337600i
$363$	8.08168	+	0.849419i	0.424178	+	0.0445829i
$364$	−0.0114308	−	0.00830495i	−0.000599136	−	0.000435298i
$365$		0			0
$366$	12.7115	−	22.0169i	0.664439	−	1.15084i
$367$	−22.9593	+	13.2555i	−1.19846	+	0.691934i	−0.960213	−	0.279270i	$-0.909908\pi$
$367$	−22.9593	+	13.2555i	−1.19846	+	0.691934i	−0.238252	+	0.971203i	$0.576574\pi$
$368$	16.7176	+	23.0098i	0.871466	+	1.19947i
$369$	−6.24506	−	6.93584i	−0.325105	−	0.361066i
$370$		0			0
$371$	2.57025			0.133441
$372$	−0.0447625	+	0.0451648i	−0.00232083	+	0.00234169i
$373$		−	1.86550i		−	0.0965919i	−0.998833	−	0.0482959i	$-0.984621\pi$
$373$		−	1.86550i		−	0.0965919i	0.998833	−	0.0482959i	$-0.0153791\pi$
$374$	−7.48906	−	23.0489i	−0.387250	−	1.19183i
$375$		0			0
$376$	3.42455	−	2.48808i	0.176608	−	0.128313i
$377$	−7.86085	+	4.53846i	−0.404854	+	0.233743i
$378$	13.5272	+	7.80996i	0.695766	+	0.401701i
$379$	0.152228	+	1.44835i	0.00781942	+	0.0743968i	0.997736	−	0.0672569i	$-0.0214247\pi$
$379$	0.152228	+	1.44835i	0.00781942	+	0.0743968i	−0.989916	+	0.141654i	$0.954758\pi$
$380$		0			0
$381$	2.13955	−	20.3564i	0.109612	−	1.04289i
$382$	−11.7914	−	10.6171i	−0.603303	−	0.543216i
$383$	5.60769	−	12.5951i	0.286539	−	0.643578i	−0.711726	−	0.702458i	$-0.752086\pi$
$383$	5.60769	−	12.5951i	0.286539	−	0.643578i	0.998265	+	0.0588794i	$0.0187527\pi$
$384$	−34.6058	−	7.35568i	−1.76597	−	0.375368i
$385$		0			0
$386$	−6.03768	+	2.68815i	−0.307310	+	0.136823i
$387$	−82.0238	−	26.6511i	−4.16950	−	1.35475i
$388$	−1.18566e−5	0	3.85244e-6i	−6.01927e−7	0	1.95578e-7i
$389$	14.7869	−	6.58357i	0.749727	−	0.333800i	0.00394702	−	0.999992i	$-0.498744\pi$
$389$	14.7869	−	6.58357i	0.749727	−	0.333800i	0.745780	+	0.666192i	$0.232077\pi$
$390$		0			0
$391$	41.0250	+	8.72014i	2.07473	+	0.440996i
$392$	−7.00862	+	15.7416i	−0.353989	+	0.795071i
$393$	−20.6038	−	18.5517i	−1.03932	−	0.935812i
$394$	−2.00995	+	19.1234i	−0.101260	+	0.963421i
$395$		0			0
$396$	−0.00745909	−	0.0709685i	−0.000374833	−	0.00356630i
$397$	−21.1560	−	12.2144i	−1.06179	−	0.613023i	−0.135861	−	0.990728i	$-0.543380\pi$
$397$	−21.1560	−	12.2144i	−1.06179	−	0.613023i	−0.925926	+	0.377705i	$0.876713\pi$
$398$	−9.35874	+	5.40327i	−0.469111	+	0.270841i
$399$	9.44277	−	6.86057i	0.472730	−	0.343458i
$400$		0			0
$401$	−2.02856	−	6.24326i	−0.101301	−	0.311774i	0.887543	−	0.460725i	$-0.152410\pi$
$401$	−2.02856	−	6.24326i	−0.101301	−	0.311774i	−0.988845	+	0.148951i	$0.952410\pi$
$402$		−	40.5360i		−	2.02175i
$403$	−8.00998	+	21.1490i	−0.399006	+	1.05351i
$404$	−0.0175514			−0.000873213
$405$		0			0
$406$	2.01047	+	2.23286i	0.0997781	+	0.110815i
$407$	−2.47980	−	3.41315i	−0.122919	−	0.169183i
$408$	−45.0994	+	26.0381i	−2.23275	+	1.28908i
$409$	13.9181	−	24.1069i	0.688208	−	1.19201i	−0.284210	−	0.958762i	$-0.591731\pi$
$409$	13.9181	−	24.1069i	0.688208	−	1.19201i	0.972417	−	0.233248i	$-0.0749355\pi$
$410$		0			0
$411$	−44.4630	−	32.3043i	−2.19320	−	1.59345i
$412$	−0.0301020	−	0.00316384i	−0.00148302	−	0.000155871i
$413$	−2.91857	−	2.62790i	−0.143614	−	0.129310i
$414$	61.7244	+	27.4815i	3.03359	+	1.35064i
$415$		0			0
$416$	0.0823084	−	0.0174952i	0.00403550	−	0.000857772i
$417$	21.0833	+	47.3540i	1.03246	+	2.31893i
$418$	−15.3690	−	4.99370i	−0.751723	−	0.244250i
$419$	6.28700	−	19.3494i	0.307140	−	0.945279i	−0.671730	−	0.740796i	$-0.734449\pi$
$419$	6.28700	−	19.3494i	0.307140	−	0.945279i	0.978870	−	0.204483i	$-0.0655514\pi$
$420$		0			0
$421$	13.0345	−	2.77056i	0.635262	−	0.135029i	0.120986	−	0.992654i	$-0.461394\pi$
$421$	13.0345	−	2.77056i	0.635262	−	0.135029i	0.514275	+	0.857625i	$0.328061\pi$
$422$	5.47673	−	25.7660i	0.266603	−	1.25427i
$423$	4.09756	−	9.20326i	0.199230	−	0.447478i
$424$	−5.11657	+	5.68253i	−0.248483	+	0.275968i
$425$		0			0
$426$	39.6738	+	28.8247i	1.92220	+	1.39656i
$427$	−5.44038	+	0.571807i	−0.263278	+	0.0276717i
$428$	−0.0509399	−	0.0294102i	−0.00246227	−	0.00142159i
$429$	−18.3497	−	31.7826i	−0.885931	−	1.53448i
$430$		0			0
$431$	−15.3433	−	17.0405i	−0.739062	−	0.820812i	0.250010	−	0.968243i	$-0.419566\pi$
$431$	−15.3433	−	17.0405i	−0.739062	−	0.820812i	−0.989072	+	0.147431i	$0.952899\pi$
$432$	−44.2764	+	14.3863i	−2.13025	+	0.692161i
$433$			6.35044i			0.305183i	0.988289	+	0.152591i	$0.0487618\pi$
$433$			6.35044i			0.305183i	−0.988289	+	0.152591i	$0.951238\pi$
$434$	7.39894	+	1.13797i	0.355160	+	0.0546244i
$435$		0			0
$436$	0.00774040	+	0.0238225i	0.000370698	+	0.00114089i
$437$	20.7832	−	18.7133i	0.994197	−	0.895179i
$438$	14.0012	+	19.2710i	0.669002	+	0.920802i
$439$	5.60915	+	9.71534i	0.267710	+	0.463688i	0.968270	−	0.249906i	$-0.0803997\pi$
$439$	5.60915	+	9.71534i	0.267710	+	0.463688i	−0.700560	+	0.713594i	$0.747066\pi$
$440$		0			0
$441$	4.28666	+	40.7849i	0.204127	+	1.94214i
$442$	19.9705	−	27.4871i	0.949901	−	1.30743i
$443$	−1.92826	−	0.202669i	−0.0916146	−	0.00962908i	0.0586102	−	0.998281i	$-0.481333\pi$
$443$	−1.92826	−	0.202669i	−0.0916146	−	0.00962908i	−0.150225	+	0.988652i	$0.548000\pi$
$444$	0.0111280	−	0.0123589i	0.000528112	−	0.000586528i
$445$		0			0
$446$	−27.2768	−	5.79786i	−1.29159	−	0.274536i
$447$	2.68094	+	12.6128i	0.126804	+	0.596566i
$448$	3.08502	+	6.92906i	0.145753	+	0.327367i
$449$	−3.70576	+	11.4052i	−0.174886	+	0.538243i	−0.999628	−	0.0272656i	$-0.991320\pi$
$449$	−3.70576	+	11.4052i	−0.174886	+	0.538243i	0.824743	+	0.565508i	$0.191320\pi$
$450$		0			0
$451$	3.67311	−	1.63538i	0.172960	−	0.0770068i
$452$	0.0108409	+	0.0510026i	0.000509915	+	0.00239896i
$453$	−6.51141	+	30.6338i	−0.305933	+	1.43930i
$454$	−33.3508	−	14.8487i	−1.56523	−	0.696885i
$455$		0			0
$456$	−3.62969	+	34.5342i	−0.169976	+	1.61721i
$457$	−13.7224	+	18.8873i	−0.641908	+	0.883510i	−0.998716	−	0.0506677i	$-0.983865\pi$
$457$	−13.7224	+	18.8873i	−0.641908	+	0.883510i	0.356808	+	0.934178i	$0.383865\pi$
$458$	−0.426137	+	0.0447888i	−0.0199121	+	0.00209284i
$459$	−34.3262	+	59.4547i	−1.60221	+	2.77511i
$460$		0			0
$461$	27.2238	−	19.7792i	1.26794	−	0.921210i	0.268818	−	0.963191i	$-0.413367\pi$
$461$	27.2238	−	19.7792i	1.26794	−	0.921210i	0.999118	+	0.0419810i	$0.0133669\pi$
$462$	−9.02778	+	8.12865i	−0.420010	+	0.378179i
$463$	−26.2572	+	8.53149i	−1.22028	+	0.396492i	−0.847183	−	0.531301i	$-0.821703\pi$
$463$	−26.2572	+	8.53149i	−1.22028	+	0.396492i	−0.373094	+	0.927793i	$0.621703\pi$
$464$	−8.95519			−0.415734
$465$		0			0
$466$	−0.624622			−0.0289350
$467$	32.6305	−	10.6023i	1.50996	−	0.490615i	0.567055	−	0.823680i	$-0.308083\pi$
$467$	32.6305	−	10.6023i	1.50996	−	0.490615i	0.942904	+	0.333065i	$0.108083\pi$
$468$	0.0743448	−	0.0669404i	0.00343659	−	0.00309432i
$469$	−7.05647	+	5.12683i	−0.325838	+	0.236735i
$470$		0			0
$471$	36.4443	−	63.1234i	1.67926	−	2.90857i
$472$	11.6200	−	1.22131i	0.534852	−	0.0562153i
$473$	21.8389	−	30.0587i	1.00415	−	1.38210i
$474$	−1.90103	+	18.0871i	−0.0873173	+	0.830769i
$475$		0			0
$476$	−0.0187791	−	0.00836098i	−0.000860737	−	0.000383225i
$477$	−3.78367	+	17.8008i	−0.173242	+	0.815041i
$478$	−3.86635	−	18.1897i	−0.176843	−	0.831979i
$479$	−22.0079	+	9.79853i	−1.00556	+	0.447706i	−0.842377	−	0.538889i	$-0.818844\pi$
$479$	−22.0079	+	9.79853i	−1.00556	+	0.447706i	−0.163188	+	0.986595i	$0.552178\pi$
$480$		0			0
$481$	1.82770	−	5.62509i	0.0833361	−	0.256482i
$482$	14.9678	+	33.6183i	0.681766	+	1.53127i
$483$	−4.37105	−	20.5642i	−0.198890	−	0.935703i
$484$	−0.00933445	−	0.00198410i	−0.000424293	−	9.01863e-5i
$485$		0			0
$486$	−14.4081	+	16.0018i	−0.653565	+	0.725858i
$487$	3.79482	+	0.398851i	0.171960	+	0.0180737i	0.190117	−	0.981761i	$-0.439113\pi$
$487$	3.79482	+	0.398851i	0.171960	+	0.0180737i	−0.0181573	+	0.999835i	$0.505780\pi$
$488$	9.56592	−	13.1664i	0.433029	−	0.596013i
$489$	−0.0807285	−	0.768080i	−0.00365067	−	0.0347338i
$490$		0			0
$491$	−1.42799	−	2.47336i	−0.0644445	−	0.111621i	0.832003	−	0.554771i	$-0.187194\pi$
$491$	−1.42799	−	2.47336i	−0.0644445	−	0.111621i	−0.896447	+	0.443150i	$0.853861\pi$
$492$	0.00931607	+	0.0128225i	0.000420001	+	0.000578082i
$493$	−9.81381	+	8.83639i	−0.441992	+	0.397971i
$494$	−7.00081	−	21.5463i	−0.314981	−	0.969413i
$495$		0			0
$496$	−17.2765	+	14.1187i	−0.775738	+	0.633947i
$497$		−	10.5520i		−	0.473322i
$498$	71.0156	−	23.0744i	3.18229	−	1.03399i
$499$	11.4047	+	12.6662i	0.510545	+	0.567018i	0.942213	−	0.335015i	$-0.108741\pi$
$499$	11.4047	+	12.6662i	0.510545	+	0.567018i	−0.431667	+	0.902033i	$0.642075\pi$
$500$		0			0
$501$	0.0893939	+	0.154835i	0.00399382	+	0.00691750i
$502$	20.7230	+	11.9644i	0.924912	+	0.533998i
$503$	19.8213	−	2.08330i	0.883786	−	0.0928897i	0.348250	−	0.937402i	$-0.386776\pi$
$503$	19.8213	−	2.08330i	0.883786	−	0.0928897i	0.535536	+	0.844512i	$0.320109\pi$
$504$	14.6039	+	10.6104i	0.650510	+	0.472623i
$505$		0			0
$506$	−19.4767	+	21.6311i	−0.865846	+	0.961620i
$507$	4.43705	−	9.96577i	0.197056	−	0.442596i
$508$	−0.00499762	+	0.0235120i	−0.000221734	+	0.00104317i
$509$	−22.1274	+	4.70332i	−0.980780	+	0.208471i	−0.670285	−	0.742104i	$-0.733828\pi$
$509$	−22.1274	+	4.70332i	−0.980780	+	0.208471i	−0.310495	+	0.950575i	$0.600495\pi$
$510$		0			0
$511$	1.58386	−	4.87462i	0.0700659	−	0.215641i
$512$	−21.4605	−	6.97295i	−0.948431	−	0.308164i
$513$	18.6193	+	41.8197i	0.822063	+	1.84638i
$514$	−5.78782	+	1.23024i	−0.255290	+	0.0542635i
$515$		0			0
$516$	0.133799	+	0.0595710i	0.00589016	+	0.00262247i
$517$	3.22525	+	2.90403i	0.141846	+	0.127719i
$518$	−1.94709	−	0.204648i	−0.0855503	−	0.00899170i
$519$	−33.9698	−	24.6805i	−1.49111	−	1.08335i
$520$		0			0
$521$	−1.76098	+	3.05010i	−0.0771499	+	0.133628i	−0.902019	−	0.431696i	$-0.857915\pi$
$521$	−1.76098	+	3.05010i	−0.0771499	+	0.133628i	0.824869	+	0.565324i	$0.191249\pi$
$522$	−18.4237	+	10.6369i	−0.806383	+	0.465566i
$523$	−23.1228	−	31.8259i	−1.01109	−	1.39165i	−0.918265	−	0.395966i	$-0.870410\pi$
$523$	−23.1228	−	31.8259i	−1.01109	−	1.39165i	−0.0928261	−	0.995682i	$-0.529590\pi$
$524$	0.0217862	+	0.0241960i	0.000951735	+	0.00105701i
$525$		0			0
$526$	26.0266			1.13481
$527$	−5.00159	+	32.5197i	−0.217873	+	1.41658i
$528$		−	36.2072i		−	1.57572i
$529$	−8.45898	−	26.0341i	−0.367782	−	1.13192i
$530$		0			0
$531$	22.4964	−	16.3446i	0.976263	−	0.709296i
$532$	−0.0118705	+	0.00685344i	−0.000514652	+	0.000297134i
$533$	4.88159	+	2.81839i	0.211445	+	0.122078i
$534$	3.53285	+	33.6128i	0.152881	+	1.45457i
$535$		0			0
$536$	2.71243	−	25.8070i	0.117159	−	1.11469i
$537$	7.02148	+	6.32217i	0.302999	+	0.272822i
$538$	12.9819	−	29.1577i	0.559688	−	1.25708i
$539$	−17.2809	−	3.67318i	−0.744343	−	0.158215i
$540$		0			0
$541$	1.04711	−	0.466202i	0.0450186	−	0.0200436i	−0.384104	−	0.923290i	$-0.625490\pi$
$541$	1.04711	−	0.466202i	0.0450186	−	0.0200436i	0.429122	+	0.903246i	$0.358823\pi$
$542$	13.1426	+	4.27030i	0.564525	+	0.183425i
$543$	20.1137	+	6.53532i	0.863160	+	0.280458i
$544$	0.111840	−	0.0497942i	0.00479508	−	0.00213491i
$545$		0			0
$546$	−16.6586	−	3.54089i	−0.712921	−	0.151536i
$547$	10.9514	−	24.5971i	0.468246	−	1.05170i	−0.512903	−	0.858446i	$-0.671430\pi$
$547$	10.9514	−	24.5971i	0.468246	−	1.05170i	0.981149	−	0.193251i	$-0.0619033\pi$
$548$	0.0479636	+	0.0431866i	0.00204890	+	0.00184484i
$549$	4.04863	−	38.5202i	0.172791	−	1.64400i
$550$		0			0
$551$	0.920436	+	8.75736i	0.0392119	+	0.373076i
$552$	54.1665	+	31.2731i	2.30548	+	1.33107i
$553$	3.38903	−	1.95666i	0.144116	−	0.0832054i
$554$	−29.4445	+	21.3927i	−1.25098	+	0.908888i
$555$		0			0
$556$	−0.0188107	−	0.0578935i	−0.000797753	−	0.00245523i
$557$		−	5.09359i		−	0.215822i	−0.994161	−	0.107911i	$-0.965584\pi$
$557$		−	5.09359i		−	0.215822i	0.994161	−	0.107911i	$-0.0344162\pi$
$558$	−18.7732	+	49.5676i	−0.794734	+	2.09836i
$559$	52.0881			2.20309
$560$		0			0
$561$	−35.7269	−	39.6787i	−1.50839	−	1.67524i
$562$	−0.125207	−	0.172333i	−0.00528154	−	0.00726942i
$563$	−25.8636	+	14.9324i	−1.09002	+	0.629325i	−0.933582	−	0.358363i	$-0.883335\pi$
$563$	−25.8636	+	14.9324i	−1.09002	+	0.629325i	−0.156440	+	0.987688i	$0.550002\pi$
$564$	−0.00855401	+	0.0148160i	−0.000360189	+	0.000623866i
$565$		0			0
$566$	17.2744	+	12.5506i	0.726098	+	0.527541i
$567$	15.1651	+	1.59392i	0.636875	+	0.0669382i
$568$	23.3293	+	21.0058i	0.978876	+	0.881384i
$569$	12.6321	+	5.62416i	0.529564	+	0.235777i	0.654059	−	0.756443i	$-0.273065\pi$
$569$	12.6321	+	5.62416i	0.529564	+	0.235777i	−0.124496	+	0.992220i	$0.539731\pi$
$570$		0			0
$571$	10.9925	−	2.33652i	0.460020	−	0.0977803i	0.0279284	−	0.999610i	$-0.491109\pi$
$571$	10.9925	−	2.33652i	0.460020	−	0.0977803i	0.432092	+	0.901830i	$0.357776\pi$
$572$	0.0175295	+	0.0393719i	0.000732944	+	0.00164622i
$573$	−33.2460	−	10.8023i	−1.38887	−	0.451271i
$574$	0.576583	−	1.77454i	0.0240661	−	0.0740678i
$575$		0			0
$576$	−52.5300	+	11.1656i	−2.18875	+	0.465233i
$577$	4.85267	−	22.8300i	0.202020	−	0.950427i	−0.753943	−	0.656939i	$-0.771851\pi$
$577$	4.85267	−	22.8300i	0.202020	−	0.950427i	0.955963	−	0.293488i	$-0.0948159\pi$
$578$	10.3177	−	23.1739i	0.429160	−	0.963908i
$579$	−9.74295	+	10.8206i	−0.404903	+	0.449690i
$580$		0			0
$581$	−12.9985	−	9.44399i	−0.539270	−	0.391803i
$582$	−0.0149446	+	0.00157074i	−0.000619472	+	6.51091e-5i
$583$	−6.78958	−	3.91997i	−0.281196	−	0.162348i
$584$	7.62426	+	13.2056i	0.315494	+	0.546452i
$585$		0			0
$586$	3.91674	+	4.34998i	0.161799	+	0.179696i
$587$	0.0287292	−	0.00933469i	0.00118578	−	0.000385284i	−0.308424	−	0.951249i	$-0.599802\pi$
$587$	0.0287292	−	0.00933469i	0.00118578	−	0.000385284i	0.309610	+	0.950864i	$0.399802\pi$
$588$		−	0.0696423i		−	0.00287200i
$589$	15.5825	+	15.4437i	0.642066	+	0.636347i
$590$		0			0
$591$	13.0910	+	40.2898i	0.538490	+	1.65730i
$592$	4.33644	−	3.90455i	0.178227	−	0.160476i
$593$	4.48509	+	6.17320i	0.184181	+	0.253503i	0.891116	−	0.453775i	$-0.149923\pi$
$593$	4.48509	+	6.17320i	0.184181	+	0.253503i	−0.706936	+	0.707278i	$0.749923\pi$
$594$	−23.8224	−	41.2617i	−0.977446	−	1.69299i
$595$		0			0
$596$	−0.00158285	−	0.0150598i	−6.48360e−5	−	0.000616873i
$597$	−13.9941	+	19.2612i	−0.572740	+	0.788309i
$598$	−40.5832	−	4.26546i	−1.65957	−	0.174428i
$599$	5.47027	−	6.07535i	0.223509	−	0.248232i	−0.620952	−	0.783848i	$-0.713254\pi$
$599$	5.47027	−	6.07535i	0.223509	−	0.248232i	0.844462	+	0.535616i	$0.179921\pi$
$600$		0			0
$601$	−0.823421	−	0.175024i	−0.0335880	−	0.00713936i	0.191087	−	0.981573i	$-0.438799\pi$
$601$	−0.823421	−	0.175024i	−0.0335880	−	0.00713936i	−0.224675	+	0.974434i	$0.572132\pi$
$602$	−3.58481	−	16.8652i	−0.146106	−	0.687374i
$603$	−25.1190	−	56.4182i	−1.02292	−	2.29753i
$604$	0.0113652	−	0.0349784i	0.000462442	−	0.00142325i
$605$		0			0
$606$	−19.3266	+	8.60477i	−0.785091	+	0.349545i
$607$	9.36525	+	44.0600i	0.380124	+	1.78834i	0.586586	+	0.809887i	$0.300472\pi$
$607$	9.36525	+	44.0600i	0.380124	+	1.78834i	−0.206462	+	0.978455i	$0.566195\pi$
$608$	0.0169722	−	0.0798481i	0.000688315	−	0.00323827i
$609$	6.04723	+	2.69240i	0.245046	+	0.109102i
$610$		0			0
$611$	−0.635991	+	6.05105i	−0.0257294	+	0.244799i
$612$	0.0855503	−	0.117750i	0.00345816	−	0.00475975i
$613$	−39.3673	+	4.13767i	−1.59003	+	0.167119i	−0.857816	−	0.513956i	$-0.828179\pi$
$613$	−39.3673	+	4.13767i	−1.59003	+	0.167119i	−0.732213	+	0.681075i	$0.761513\pi$
$614$	7.35863	−	12.7455i	0.296970	−	0.514368i
$615$		0			0
$616$	−6.29140	+	4.57097i	−0.253488	+	0.184170i
$617$	22.0382	−	19.8433i	0.887226	−	0.798862i	−0.0932207	−	0.995645i	$-0.529716\pi$
$617$	22.0382	−	19.8433i	0.887226	−	0.798862i	0.980447	+	0.196783i	$0.0630496\pi$
$618$	−34.6978	+	11.2740i	−1.39575	+	0.453507i
$619$	19.6256			0.788820			0.394410	−	0.918934i	$-0.370949\pi$
$619$	19.6256			0.788820			0.394410	+	0.918934i	$0.370949\pi$
$620$		0			0
$621$	82.4548			3.30880
$622$	29.0283	−	9.43185i	1.16393	−	0.378183i
$623$	5.40448	−	4.86621i	0.216526	−	0.194961i
$624$	41.0657	−	29.8360i	1.64394	−	1.19439i
$625$		0			0
$626$	−1.45986	+	2.52856i	−0.0583479	+	0.101062i
$627$	−35.4074	+	3.72146i	−1.41403	+	0.148621i
$628$	−0.0503124	+	0.0692491i	−0.00200769	+	0.00276334i
$629$	0.899463	−	8.55782i	0.0358639	−	0.341223i
$630$		0			0
$631$	18.0599	+	8.04080i	0.718955	+	0.320099i	0.733401	−	0.679796i	$-0.237932\pi$
$631$	18.0599	+	8.04080i	0.718955	+	0.320099i	−0.0144462	+	0.999896i	$0.504599\pi$
$632$	−2.42056	+	11.3879i	−0.0962848	+	0.452985i
$633$	−12.0659	−	56.7658i	−0.479578	−	2.25624i
$634$	−28.0889	+	12.5060i	−1.11555	+	0.496675i
$635$		0			0
$636$	0.00955003	−	0.0293920i	0.000378683	−	0.00116547i
$637$	−10.0740	−	22.6266i	−0.399147	−	0.896499i
$638$	−1.90548	−	8.96456i	−0.0754385	−	0.354910i
$639$	73.0800	+	15.5336i	2.89100	+	0.614501i
$640$		0			0
$641$	27.0021	−	29.9889i	1.06652	−	1.18449i	0.0843623	−	0.996435i	$-0.473115\pi$
$641$	27.0021	−	29.9889i	1.06652	−	1.18449i	0.982158	−	0.188056i	$-0.0602187\pi$
$642$	−70.5110	−	7.41101i	−2.78285	−	0.292489i
$643$	16.8980	−	23.2581i	0.666391	−	0.917208i	−0.333281	−	0.942828i	$-0.608156\pi$
$643$	16.8980	−	23.2581i	0.666391	−	0.917208i	0.999672	+	0.0256194i	$0.00815579\pi$
$644$	0.00258071	+	0.0245538i	0.000101694	+	0.000967555i
$645$		0			0
$646$	−16.4802	−	28.5445i	−0.648403	−	1.12307i
$647$	−22.8229	−	31.4131i	−0.897262	−	1.23498i	−0.971333	−	0.237723i	$-0.923599\pi$
$647$	−22.8229	−	31.4131i	−0.897262	−	1.23498i	0.0740708	−	0.997253i	$-0.476401\pi$
$648$	−33.7130	+	30.3553i	−1.32437	+	1.19247i
$649$	3.70184	+	11.3931i	0.145310	+	0.447217i
$650$		0			0
$651$	15.9112	−	4.33978i	0.623611	−	0.170090i
$652$		0	0.000906962i		0	3.55194e-5i
$653$	41.4492	−	13.4677i	1.62203	−	0.527030i	0.649612	−	0.760266i	$-0.274931\pi$
$653$	41.4492	−	13.4677i	1.62203	−	0.527030i	0.972420	+	0.233235i	$0.0749312\pi$
$654$	20.2026	+	22.4373i	0.789984	+	0.877366i
$655$		0			0
$656$	2.78059	+	4.81612i	0.108564	+	0.188038i
$657$	31.4285	+	18.1453i	1.22614	+	0.707915i
$658$	2.00299	−	0.210523i	0.0780848	−	0.00820704i
$659$	−1.37480	−	0.998853i	−0.0535548	−	0.0389098i	0.560686	−	0.828029i	$-0.310538\pi$
$659$	−1.37480	−	0.998853i	−0.0535548	−	0.0389098i	−0.614241	+	0.789119i	$0.710538\pi$
$660$		0			0
$661$	2.18741	−	2.42937i	0.0850804	−	0.0944914i	−0.699101	−	0.715023i	$-0.746416\pi$
$661$	2.18741	−	2.42937i	0.0850804	−	0.0944914i	0.784182	+	0.620531i	$0.213083\pi$
$662$	9.73051	−	21.8551i	0.378187	−	0.849422i
$663$	15.5629	−	73.2175i	0.604411	−	2.84353i
$664$	46.7557	−	9.93822i	1.81447	−	0.385678i
$665$		0			0
$666$	4.28364	−	13.1837i	0.165988	−	0.510858i
$667$	15.0845	+	4.90125i	0.584074	+	0.189777i
$668$	−8.53981e−5	0	0.000191807i	−3.30415e−6	0	7.42124e-6i
$669$	−60.0942	+	12.7734i	−2.32337	+	0.493849i
$670$		0			0
$671$	15.2434	+	6.78681i	0.588466	+	0.262002i
$672$	−0.0456038	−	0.0410619i	−0.00175921	−	0.00158400i
$673$	−18.4625	−	1.94049i	−0.711678	−	0.0748004i	−0.258231	−	0.966083i	$-0.583139\pi$
$673$	−18.4625	−	1.94049i	−0.711678	−	0.0748004i	−0.453448	+	0.891283i	$0.649806\pi$
$674$	−4.96797	−	3.60944i	−0.191359	−	0.139031i
$675$		0			0
$676$	−0.00640542	+	0.0110945i	−0.000246362	+	0.000426712i
$677$	−21.9558	+	12.6762i	−0.843831	+	0.487186i	−0.858565	−	0.512705i	$-0.828643\pi$
$677$	−21.9558	+	12.6762i	−0.843831	+	0.487186i	0.0147335	+	0.999891i	$0.495310\pi$
$678$	36.9421	+	50.8465i	1.41875	+	1.95275i
$679$	0.00216356	+	0.00240288i	8.30298e−5	+	9.22139e-5i
$680$		0			0
$681$	−80.4295			−3.08206
$682$	−17.8095	−	14.2904i	−0.681962	−	0.547209i
$683$			19.8387i			0.759106i	0.925170	+	0.379553i	$0.123922\pi$
$683$			19.8387i			0.759106i	−0.925170	+	0.379553i	$0.876078\pi$
$684$	−0.0299902	−	0.0923005i	−0.00114671	−	0.00352920i
$685$		0			0
$686$	−14.2469	+	10.3510i	−0.543950	+	0.395203i
$687$	−0.817532	+	0.472002i	−0.0311908	+	0.0180080i
$688$	44.5046	+	25.6948i	1.69672	+	0.979604i
$689$	−1.14888	−	10.9308i	−0.0437687	−	0.416431i
$690$		0			0
$691$	2.77024	−	26.3571i	0.105385	−	1.00267i	−0.806223	−	0.591612i	$-0.798492\pi$
$691$	2.77024	−	26.3571i	0.105385	−	1.00267i	0.911608	−	0.411060i	$-0.134841\pi$
$692$	0.0366442	+	0.0329946i	0.00139300	+	0.00125427i
$693$	−7.52781	+	16.9077i	−0.285958	+	0.642272i
$694$	−14.5254	−	3.08747i	−0.551376	−	0.117199i
$695$		0			0
$696$	−17.9908	+	8.01001i	−0.681939	+	0.303619i
$697$	7.79942	+	2.53418i	0.295424	+	0.0959891i
$698$	−7.52404	−	2.44471i	−0.284789	−	0.0925336i
$699$	−1.25715	+	0.559718i	−0.0475497	+	0.0211705i
$700$		0			0
$701$	−10.2362	−	2.17576i	−0.386615	−	0.0821775i	0.0105038	−	0.999945i	$-0.496656\pi$
$701$	−10.2362	−	2.17576i	−0.386615	−	0.0821775i	−0.397119	+	0.917767i	$0.629990\pi$
$702$	27.1679	−	61.0200i	1.02539	−	2.30305i
$703$	−4.26400	−	3.83932i	−0.160820	−	0.144803i
$704$	2.41833	−	23.0089i	0.0911444	−	0.867181i
$705$		0			0
$706$	−4.42363	−	42.0880i	−0.166486	−	1.58400i
$707$	3.94226	+	2.27607i	0.148264	+	0.0856003i
$708$	−0.0408955	+	0.0236110i	−0.00153695	+	0.000887356i
$709$	−0.951875	+	0.691578i	−0.0357484	+	0.0259728i	−0.605516	−	0.795833i	$-0.707033\pi$
$709$	−0.951875	+	0.691578i	−0.0357484	+	0.0259728i	0.569768	+	0.821806i	$0.307033\pi$
$710$		0			0
$711$	8.56220	+	26.3518i	0.321108	+	0.988268i
$712$			21.6358i			0.810837i
$713$	36.8285	−	14.3265i	1.37924	−	0.536532i
$714$	−24.7776			−0.927278
$715$		0			0
$716$	−0.00742444	−	0.00824567i	−0.000277464	−	0.000308155i
$717$	−24.0813	−	33.1451i	−0.899333	−	1.23783i
$718$	−5.68255	+	3.28082i	−0.212071	+	0.122439i
$719$	−19.4477	+	33.6843i	−0.725276	+	1.25621i	0.233585	+	0.972336i	$0.424954\pi$
$719$	−19.4477	+	33.6843i	−0.725276	+	1.25621i	−0.958860	+	0.283878i	$0.908379\pi$
$720$		0			0
$721$	6.35101	+	4.61428i	0.236524	+	0.171845i
$722$	4.88980	+	0.513939i	0.181980	+	0.0191268i
$723$	60.2501	+	54.2495i	2.24073	+	2.01756i
$724$	−0.0226888	−	0.0101017i	−0.000843223	−	0.000375427i
$725$		0			0
$726$	−11.2513	+	2.39155i	−0.417576	+	0.0887586i
$727$	3.41823	+	7.67746i	0.126775	+	0.284741i	0.965771	−	0.259396i	$-0.0835236\pi$
$727$	3.41823	+	7.67746i	0.126775	+	0.284741i	−0.838996	+	0.544138i	$0.816857\pi$
$728$	−10.3687	−	3.36898i	−0.384288	−	0.124863i
$729$	0.223240	−	0.687063i	0.00826816	−	0.0254468i
$730$		0			0
$731$	74.1256	−	15.7559i	2.74163	−	0.582752i
$732$	−0.0136754	+	0.0643378i	−0.000505458	+	0.00237799i
$733$	−16.3468	+	36.7154i	−0.603781	+	1.35611i	0.310321	+	0.950632i	$0.399563\pi$
$733$	−16.3468	+	36.7154i	−0.603781	+	1.35611i	−0.914102	+	0.405483i	$0.867103\pi$
$734$	25.1102	−	27.8877i	0.926835	−	1.02935i
$735$		0			0
$736$	−0.118955	−	0.0864260i	−0.00438475	−	0.00318570i
$737$	26.4595	−	2.78101i	0.974649	−	0.102440i
$738$	11.4411	+	6.60554i	0.421154	+	0.243153i
$739$	4.55735	+	7.89357i	0.167645	+	0.290370i	0.937591	−	0.347739i	$-0.113050\pi$
$739$	4.55735	+	7.89357i	0.167645	+	0.290370i	−0.769946	+	0.638109i	$0.779717\pi$
$740$		0			0
$741$	−33.3977	−	37.0919i	−1.22689	−	1.36260i
$742$	−3.46014	+	1.12427i	−0.127026	+	0.0412732i
$743$		−	6.65317i		−	0.244081i	−0.992525	−	0.122041i	$-0.961056\pi$
$743$		−	6.65317i		−	0.244081i	0.992525	−	0.122041i	$-0.0389438\pi$
$744$	−22.0796	+	43.8171i	−0.809478	+	1.60641i
$745$		0			0
$746$	0.815999	+	2.51139i	0.0298759	+	0.0919484i
$747$	84.5413	−	76.1213i	3.09321	−	2.78513i
$748$	0.0368553	+	0.0507270i	0.00134756	+	0.00185476i
$749$	7.62784	+	13.2118i	0.278715	+	0.482749i
$750$		0			0
$751$	4.14886	+	39.4738i	0.151394	+	1.44042i	0.761534	+	0.648125i	$0.224447\pi$
$751$	4.14886	+	39.4738i	0.151394	+	1.44042i	−0.610139	+	0.792294i	$0.708887\pi$
$752$	−3.52835	+	4.85635i	−0.128666	+	0.177093i
$753$	52.4295	+	5.51056i	1.91064	+	0.200816i
$754$	8.59729	−	9.54826i	0.313095	−	0.347727i
$755$		0			0
$756$	−0.0395293	−	0.00840222i	−0.00143767	−	0.000305586i
$757$	2.91405	+	13.7095i	0.105913	+	0.498281i	0.998843	+	0.0480862i	$0.0153122\pi$
$757$	2.91405	+	13.7095i	0.105913	+	0.498281i	−0.892930	+	0.450195i	$0.851354\pi$
$758$	−0.838465	−	1.88322i	−0.0304544	−	0.0684017i
$759$	−19.8165	+	60.9889i	−0.719293	+	2.21376i
$760$		0			0
$761$	−31.5132	+	14.0306i	−1.14235	+	0.508609i	−0.888610	−	0.458663i	$-0.848328\pi$
$761$	−31.5132	+	14.0306i	−1.14235	+	0.508609i	−0.253743	+	0.967272i	$0.581662\pi$
$762$	6.02391	+	28.3403i	0.218223	+	1.02666i
$763$	1.35072	−	6.35463i	0.0488993	−	0.230053i
$764$	0.0375025	+	0.0166972i	0.00135679	+	0.000604083i
$765$		0			0
$766$	−2.03994	+	19.4087i	−0.0737060	+	0.701266i
$767$	−9.87142	+	13.5868i	−0.356436	+	0.490593i
$768$	0.272599	−	0.0286513i	0.00983657	−	0.00103387i
$769$	−13.5658	+	23.4966i	−0.489195	+	0.847310i	−0.999923	−	0.0124321i	$-0.996043\pi$
$769$	−13.5658	+	23.4966i	−0.489195	+	0.847310i	0.510728	+	0.859742i	$0.329376\pi$
$770$		0			0
$771$	−10.5465	+	7.66246i	−0.379822	+	0.275957i
$772$	0.0127072	−	0.0114416i	0.000457342	−	0.000411793i
$773$	26.8373	−	8.71995i	0.965269	−	0.313635i	0.216364	−	0.976313i	$-0.430580\pi$
$773$	26.8373	−	8.71995i	0.965269	−	0.313635i	0.748905	+	0.662678i	$0.230580\pi$
$774$	122.080			4.38809
$775$		0			0
$776$	−0.00961947			−0.000345319
$777$	−4.10221	+	1.33289i	−0.147166	+	0.0478171i
$778$	−17.0268	+	15.3310i	−0.610441	+	0.549644i
$779$	4.42393	−	3.21418i	0.158504	−	0.115160i
$780$		0			0
$781$	−16.0932	+	27.8742i	−0.575860	+	0.997419i
$782$	−59.0434	+	6.20571i	−2.11139	+	0.221916i
$783$	−15.2600	+	21.0036i	−0.545347	+	0.750606i
$784$	2.55423	−	24.3019i	0.0912226	−	0.867925i
$785$		0			0
$786$	35.8522	+	15.9624i	1.27881	+	0.569361i
$787$	−0.164770	+	0.775181i	−0.00587341	+	0.0276322i	−0.980987	−	0.194075i	$-0.937830\pi$
$787$	−0.164770	+	0.775181i	−0.00587341	+	0.0276322i	0.975113	+	0.221707i	$0.0711629\pi$
$788$	−0.0103434	−	0.0486621i	−0.000368470	−	0.00173351i
$789$	52.3825	−	23.3222i	1.86487	−	0.830293i
$790$		0			0
$791$	4.17902	−	12.8617i	0.148589	−	0.457310i
$792$	−22.3956	−	50.3013i	−0.795792	−	1.78738i
$793$	4.86359	+	22.8814i	0.172711	+	0.812543i
$794$	33.8235	+	7.18941i	1.20035	+	0.255143i
$795$		0			0
$796$	0.0187083	−	0.0207777i	0.000663097	−	0.000736444i
$797$	26.5598	+	2.79155i	0.940796	+	0.0988817i	0.562495	−	0.826801i	$-0.309842\pi$
$797$	26.5598	+	2.79155i	0.940796	+	0.0988817i	0.378301	+	0.925682i	$0.376508\pi$
$798$	−9.71120	+	13.3663i	−0.343773	+	0.473162i
$799$	0.925287	+	8.80351i	0.0327343	+	0.311446i
$800$		0			0
$801$	25.7460	+	44.5933i	0.909689	+	1.57563i
$802$	5.46181	+	7.51753i	0.192863	+	0.265453i
$803$	−11.6184	+	10.4612i	−0.410004	+	0.369169i
$804$	0.0324086	+	0.0997433i	0.00114296	+	0.00351767i
$805$		0			0
$806$	1.53235	−	31.9751i	0.0539746	−	1.12627i
$807$		−	70.3174i		−	2.47529i
$808$	−12.8800	+	4.18495i	−0.453116	+	0.147226i
$809$	22.5806	+	25.0783i	0.793890	+	0.881705i	0.995204	−	0.0978222i	$-0.0311876\pi$
$809$	22.5806	+	25.0783i	0.793890	+	0.881705i	−0.201313	+	0.979527i	$0.564521\pi$
$810$		0			0
$811$	4.46711	+	7.73726i	0.156861	+	0.271692i	0.933735	−	0.357964i	$-0.116529\pi$
$811$	4.46711	+	7.73726i	0.156861	+	0.271692i	−0.776874	+	0.629656i	$0.783196\pi$
$812$	−0.00673216	−	0.00388681i	−0.000236252	−	0.000136400i
$813$	30.2782	−	3.18237i	1.06190	−	0.111610i
$814$	4.83133	+	3.51017i	0.169338	+	0.123031i
$815$		0			0
$816$	49.4149	−	54.8808i	1.72987	−	1.92121i
$817$	20.5528	−	46.1624i	0.719053	−	1.61502i
$818$	−8.19223	+	38.5414i	−0.286435	+	1.34757i
$819$	−25.3797	+	5.39462i	−0.886838	+	0.188503i
$820$		0			0
$821$	−5.15729	+	15.8725i	−0.179991	+	0.553955i	−0.999826	−	0.0186447i	$-0.994065\pi$
$821$	−5.15729	+	15.8725i	−0.179991	+	0.553955i	0.819835	+	0.572599i	$0.194065\pi$
$822$	73.9878	+	24.0401i	2.58062	+	0.838494i
$823$	−19.0195	−	42.7184i	−0.662977	−	1.48907i	−0.860858	−	0.508845i	$-0.830073\pi$
$823$	−19.0195	−	42.7184i	−0.662977	−	1.48907i	0.197881	−	0.980226i	$-0.436594\pi$
$824$	−22.8446	+	4.85576i	−0.795828	+	0.169158i
$825$		0			0
$826$	5.07855	+	2.26112i	0.176705	+	0.0786743i
$827$	−17.0531	−	15.3547i	−0.592994	−	0.533935i	0.317070	−	0.948402i	$-0.397301\pi$
$827$	−17.0531	−	15.3547i	−0.592994	−	0.533935i	−0.910064	+	0.414468i	$0.863968\pi$
$828$	−0.173851	−	0.0182725i	−0.00604174	−	0.000635013i
$829$	−10.9766	−	7.97494i	−0.381232	−	0.276981i	0.380621	−	0.924731i	$-0.375710\pi$
$829$	−10.9766	−	7.97494i	−0.381232	−	0.276981i	−0.761853	+	0.647750i	$0.775710\pi$
$830$		0			0
$831$	−40.0918	+	69.4411i	−1.39077	+	2.40889i
$832$	28.0891	−	16.2173i	0.973816	−	0.562233i
$833$	−21.1804	−	29.1523i	−0.733856	−	1.01007i
$834$	−49.0964	−	54.5270i	−1.70007	−	1.88812i
$835$		0			0
$836$	0.0418096			0.00144602
$837$	3.67420	+	64.5792i	0.126999	+	2.23218i
$838$			28.7987i			0.994835i
$839$	5.03944	+	15.5098i	0.173981	+	0.535458i	0.999585	−	0.0287910i	$-0.00916571\pi$
$839$	5.03944	+	15.5098i	0.173981	+	0.535458i	−0.825605	+	0.564249i	$0.809166\pi$
$840$		0			0
$841$	19.4213	−	14.1104i	0.669700	−	0.486566i
$842$	−16.3355	+	9.43130i	−0.562958	+	0.325024i
$843$	−0.406425	−	0.234649i	−0.0139980	−	0.00808176i
$844$	0.00712383	+	0.0677787i	0.000245212	+	0.00233304i
$845$		0			0
$846$	−1.49059	+	14.1820i	−0.0512476	+	0.487588i
$847$	1.83934	+	1.65615i	0.0632005	+	0.0569060i
$848$	4.41051	−	9.90616i	0.151457	−	0.340179i
$849$	46.0140	+	9.78057i	1.57920	+	0.335668i
$850$		0			0
$851$	−9.44147	+	4.20361i	−0.323649	+	0.144098i
$852$	−0.120667	−	0.0392071i	−0.00413398	−	0.00134321i
$853$	−41.3684	−	13.4414i	−1.41643	−	0.460225i	−0.501961	−	0.864890i	$-0.667388\pi$
$853$	−41.3684	−	13.4414i	−1.41643	−	0.460225i	−0.914465	+	0.404665i	$0.867388\pi$
$854$	7.07387	−	3.14949i	0.242063	−	0.107773i
$855$		0			0
$856$	−44.3945	−	9.43635i	−1.51737	−	0.322528i
$857$	1.21881	−	2.73749i	0.0416338	−	0.0935110i	−0.891531	−	0.452959i	$-0.850368\pi$
$857$	1.21881	−	2.73749i	0.0416338	−	0.0935110i	0.933165	+	0.359448i	$0.117035\pi$
$858$	38.6051	+	34.7602i	1.31796	+	1.18669i
$859$	3.97319	−	37.8023i	0.135563	−	1.28980i	−0.689304	−	0.724472i	$-0.742083\pi$
$859$	3.97319	−	37.8023i	0.135563	−	1.28980i	0.824867	−	0.565327i	$-0.191250\pi$
$860$		0			0
$861$	−0.429688	−	4.08821i	−0.0146437	−	0.139326i
$862$	28.1094	+	16.2290i	0.957410	+	0.552761i
$863$	3.72036	−	2.14795i	0.126642	−	0.0731170i	−0.435340	−	0.900266i	$-0.643372\pi$
$863$	3.72036	−	2.14795i	0.126642	−	0.0731170i	0.561983	+	0.827149i	$0.310039\pi$
$864$	0.194713	−	0.141467i	0.00662426	−	0.00481281i
$865$		0			0
$866$	−2.77778	−	8.54914i	−0.0943929	−	0.290512i
$867$		−	55.8867i		−	1.89801i
$868$	−0.0191157	+	0.00311535i	−0.000648829	+	0.000105742i
$869$	−11.9366			−0.404922
$870$		0			0
$871$	24.9577	+	27.7183i	0.845659	+	0.939200i
$872$	11.3605	+	15.6364i	0.384715	+	0.529515i
$873$	−0.0198266	+	0.0114469i	−0.000671027	+	0.000387418i
$874$	−19.7935	+	34.2833i	−0.669524	+	1.15965i
$875$		0			0
$876$	−0.0498585	−	0.0362243i	−0.00168456	−	0.00122391i
$877$	−8.29006	−	0.871320i	−0.279935	−	0.0294224i	−0.0364796	−	0.999334i	$-0.511614\pi$
$877$	−8.29006	−	0.871320i	−0.279935	−	0.0294224i	−0.243456	+	0.969912i	$0.578281\pi$
$878$	−11.8008	−	10.6255i	−0.398259	−	0.358594i
$879$	11.7810	+	5.24525i	0.397364	+	0.176918i
$880$		0			0
$881$	−13.6695	+	2.90554i	−0.460537	+	0.0978903i	−0.432337	−	0.901712i	$-0.642311\pi$
$881$	−13.6695	+	2.90554i	−0.460537	+	0.0978903i	−0.0282003	+	0.999602i	$0.508978\pi$
$882$	−23.6108	−	53.0307i	−0.795016	−	1.78564i
$883$	5.07760	+	1.64981i	0.170875	+	0.0555206i	0.393205	−	0.919451i	$-0.371366\pi$
$883$	5.07760	+	1.64981i	0.170875	+	0.0555206i	−0.222330	+	0.974971i	$0.571366\pi$
$884$	−0.0271637	+	0.0836014i	−0.000913616	+	0.00281182i
$885$		0			0
$886$	2.68453	−	0.570615i	0.0901887	−	0.0191702i
$887$	1.46021	−	6.86974i	0.0490290	−	0.230663i	−0.946810	−	0.321793i	$-0.895714\pi$
$887$	1.46021	−	6.86974i	0.0490290	−	0.230663i	0.995839	+	0.0911297i	$0.0290478\pi$
$888$	5.21937	−	11.7229i	0.175151	−	0.393395i
$889$	4.17157	−	4.63300i	0.139910	−	0.155386i
$890$		0			0
$891$	−37.6293	−	27.3393i	−1.26063	−	0.915901i
$892$	0.0717529	−	0.00754153i	0.00240246	−	0.000252509i
$893$	5.11172	+	2.95125i	0.171057	+	0.0987600i
$894$	−9.12620	−	15.8070i	−0.305226	−	0.528666i
$895$		0			0
$896$	−7.21035	−	8.00791i	−0.240881	−	0.267525i
$897$	−85.5022	+	27.7813i	−2.85483	+	0.927592i
$898$		−	16.9749i		−	0.566460i
$899$	−3.16653	+	12.0327i	−0.105610	+	0.401312i
$900$		0			0
$901$	−4.94136	−	15.2079i	−0.164621	−	0.506650i
$902$	−4.22951	+	3.80827i	−0.140827	+	0.126801i
$903$	−22.3277	−	30.7315i	−0.743021	−	1.02268i
$904$	20.1166	+	34.8430i	0.669069	+	1.15886i
$905$		0			0
$906$	−4.63386	−	44.0882i	−0.153950	−	1.46473i
$907$	16.3662	−	22.5261i	0.543429	−	0.747966i	−0.445673	−	0.895196i	$-0.647036\pi$
$907$	16.3662	−	22.5261i	0.543429	−	0.747966i	0.989102	+	0.147230i	$0.0470356\pi$
$908$	0.0939348	+	0.00987295i	0.00311734	+	0.000327645i
$909$	−21.5668	+	23.9523i	−0.715324	+	0.794448i
$910$		0			0
$911$	−20.1754	−	4.28841i	−0.668440	−	0.142081i	−0.138822	−	0.990317i	$-0.544331\pi$
$911$	−20.1754	−	4.28841i	−0.668440	−	0.142081i	−0.529618	+	0.848236i	$0.677665\pi$
$912$	−10.2381	−	48.1666i	−0.339018	−	1.59496i
$913$	19.9337	+	44.7718i	0.659708	+	1.48173i
$914$	10.2119	−	31.4290i	0.337780	−	1.03958i
$915$		0			0
$916$	0.00101275		0.000450904i	3.34621e−5		1.48983e-5i
$917$	−1.75572	−	8.25999i	−0.0579788	−	0.272769i
$918$	20.2044	−	95.0544i	0.666846	−	3.13726i
$919$	−3.16738	−	1.41021i	−0.104482	−	0.0465185i	0.353830	−	0.935310i	$-0.384879\pi$
$919$	−3.16738	−	1.41021i	−0.104482	−	0.0465185i	−0.458312	+	0.888791i	$0.651546\pi$
$920$		0			0
$921$	3.38923	−	32.2464i	0.111679	−	1.06255i
$922$	−27.9976	+	38.5354i	−0.922053	+	1.26910i
$923$	−44.8759	+	4.71664i	−1.47711	+	0.155250i
$924$	0.0157150	−	0.0272191i	0.000516985	−	0.000895444i
$925$		0			0
$926$	31.6164	−	22.9707i	1.03898	−	0.754863i
$927$	−41.3064	+	37.1925i	−1.35668	+	1.22156i
$928$	0.0440303	−	0.0143063i	0.00144536	−	0.000469627i
$929$	16.0952			0.528066			0.264033	−	0.964514i	$-0.414947\pi$
$929$	16.0952			0.528066			0.264033	+	0.964514i	$0.414947\pi$
$930$		0			0
$931$	−24.0276			−0.787472
$932$	0.00153695		0.000499385i	5.03445e−5		1.63579e-5i
$933$	49.9721	−	44.9951i	1.63601	−	1.47307i
$934$	−39.2905	+	28.5462i	−1.28562	+	0.934060i
$935$		0			0
$936$	38.5962	−	66.8506i	1.26156	−	2.18508i
$937$	2.90279	−	0.305096i	0.0948300	−	0.00996704i	−0.0569946	−	0.998374i	$-0.518152\pi$
$937$	2.90279	−	0.305096i	0.0948300	−	0.00996704i	0.151825	+	0.988407i	$0.451485\pi$
$938$	7.25707	−	9.98849i	0.236952	−	0.326136i
$939$	−0.672383	+	6.39729i	−0.0219424	+	0.208768i
$940$		0			0
$941$	−43.6925	−	19.4531i	−1.42433	−	0.634154i	−0.457418	−	0.889252i	$-0.651226\pi$
$941$	−43.6925	−	19.4531i	−1.42433	−	0.634154i	−0.966915	+	0.255097i	$0.917892\pi$
$942$	−21.4512	+	100.920i	−0.698917	+	3.28814i
$943$	−2.04784	−	9.63431i	−0.0666867	−	0.313736i
$944$	−15.1366	+	6.73924i	−0.492653	+	0.219343i
$945$		0			0
$946$	−16.2520	+	50.0185i	−0.528398	+	1.62624i
$947$	14.4237	+	32.3961i	0.468706	+	1.05273i	0.981015	+	0.193931i	$0.0621236\pi$
$947$	14.4237	+	32.3961i	0.468706	+	1.05273i	−0.512309	+	0.858801i	$0.671210\pi$
$948$	−0.00978296	−	0.0460252i	−0.000317736	−	0.00149483i
$949$	−21.4389	−	4.55698i	−0.695936	−	0.147926i
$950$		0			0
$951$	−45.3267	+	50.3404i	−1.46982	+	1.63240i
$952$	−15.7745	−	1.65797i	−0.511255	−	0.0537350i
$953$	−16.5362	+	22.7601i	−0.535660	+	0.737273i	−0.987980	−	0.154583i	$-0.950597\pi$
$953$	−16.5362	+	22.7601i	−0.535660	+	0.737273i	0.452319	+	0.891856i	$0.350597\pi$
$954$	−2.69266	−	25.6189i	−0.0871780	−	0.829443i
$955$		0			0
$956$	0.0240563	+	0.0416667i	0.000778035	+	0.00134760i
$957$	−11.8681	−	16.3351i	−0.383643	−	0.528039i
$958$	25.3416	−	22.8176i	0.818749	−	0.737204i
$959$	−5.17279	−	15.9202i	−0.167038	−	0.514091i
$960$		0			0
$961$	12.8617	+	28.2060i	0.414894	+	0.909870i
$962$			8.37212i			0.269928i
$963$	−102.730	+	33.3790i	−3.31043	+	1.07562i
$964$	−0.0637078	−	0.0707547i	−0.00205189	−	0.00227885i
$965$		0			0
$966$	14.8795	+	25.7721i	0.478741	+	0.829204i
$967$	−45.2698	−	26.1365i	−1.45578	−	0.840494i	−0.456978	−	0.889478i	$-0.651068\pi$
$967$	−45.2698	−	26.1365i	−1.45578	−	0.840494i	−0.998800	+	0.0489843i	$0.984402\pi$
$968$	−7.32313	+	0.769691i	−0.235374	+	0.0247388i
$969$	−58.7474	−	42.6825i	−1.88724	−	1.37116i
$970$		0			0
$971$	−21.2859	+	23.6404i	−0.683097	+	0.758656i	−0.980590	−	0.196068i	$-0.937183\pi$
$971$	−21.2859	+	23.6404i	−0.683097	+	0.758656i	0.297493	+	0.954724i	$0.403849\pi$
$972$	0.0226593	−	0.0508935i	0.000726796	−	0.00163241i
$973$	−3.28251	+	15.4430i	−0.105233	+	0.495080i
$974$	−5.28315	+	1.12297i	−0.169283	+	0.0359822i
$975$		0			0
$976$	−7.13177	+	21.9493i	−0.228282	+	0.702581i
$977$	−37.6768	−	12.2419i	−1.20539	−	0.391654i	−0.363648	−	0.931537i	$-0.618469\pi$
$977$	−37.6768	−	12.2419i	−1.20539	−	0.391654i	−0.841741	+	0.539882i	$0.818469\pi$
$978$	0.444649	+	0.998699i	0.0142183	+	0.0319349i
$979$	−21.6981	+	4.61208i	−0.693475	+	0.147403i
$980$		0			0
$981$	42.0218	+	18.7093i	1.34165	+	0.597342i
$982$	3.00429	+	2.70508i	0.0958708	+	0.0863225i
$983$	−13.6615	−	1.43588i	−0.435734	−	0.0457975i	−0.115878	−	0.993264i	$-0.536968\pi$
$983$	−13.6615	−	1.43588i	−0.435734	−	0.0457975i	−0.319856	+	0.947466i	$0.603635\pi$
$984$	9.89394	+	7.18837i	0.315407	+	0.229157i
$985$		0			0
$986$	9.34644	−	16.1885i	0.297651	−	0.515547i
$987$	3.84269	−	2.21858i	0.122314	−	0.0706181i
$988$	0.0344525	+	0.0474198i	0.00109608	+	0.00150863i
$989$	−60.9025	−	67.6391i	−1.93659	−	2.15080i
$990$		0			0
$991$	2.43802			0.0774461			0.0387231	−	0.999250i	$-0.487671\pi$
$991$	2.43802			0.0774461			0.0387231	+	0.999250i	$0.487671\pi$
$992$	0.0623888	−	0.0970177i	0.00198085	−	0.00308031i
$993$		−	52.7062i		−	1.67258i
$994$	4.61562	+	14.2054i	0.146398	+	0.450568i
$995$		0			0
$996$	−0.156294	+	0.113554i	−0.00495236	+	0.00359810i
$997$	−25.1800	+	14.5377i	−0.797458	+	0.460413i	−0.842582	−	0.538569i	$-0.818965\pi$
$997$	−25.1800	+	14.5377i	−0.797458	+	0.460413i	0.0451235	+	0.998981i	$0.485632\pi$
$998$	−20.8938	−	12.0630i	−0.661381	−	0.381848i
$999$	−1.76829	−	16.8242i	−0.0559464	−	0.532294i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.ck.b.299.3		80
5.2	odd	4		155.2.q.b.51.2	✓	40
5.3	odd	4		775.2.bl.b.51.4		40
5.4	even	2	inner	775.2.ck.b.299.8		80
31.14	even	15	inner	775.2.ck.b.324.8		80
155.14	even	30	inner	775.2.ck.b.324.3		80
155.107	odd	60		155.2.q.b.76.2	yes	40
155.137	even	60		4805.2.a.z.1.6		20
155.138	odd	60		775.2.bl.b.76.4		40
155.142	odd	60		4805.2.a.ba.1.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
155.2.q.b.51.2	✓	40	5.2	odd	4
155.2.q.b.76.2	yes	40	155.107	odd	60
775.2.bl.b.51.4		40	5.3	odd	4
775.2.bl.b.76.4		40	155.138	odd	60
775.2.ck.b.299.3		80	1.1	even	1	trivial
775.2.ck.b.299.8		80	5.4	even	2	inner
775.2.ck.b.324.3		80	155.14	even	30	inner
775.2.ck.b.324.8		80	31.14	even	15	inner
4805.2.a.z.1.6		20	155.137	even	60
4805.2.a.ba.1.6		20	155.142	odd	60

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.ck (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.34623 + 0.437416i) q^{2} +(-2.31753 + 2.08671i) q^{3} +(0.00296283 - 0.00215262i) q^{4} +(2.20716 - 3.82291i) q^{6} +(-0.944642 + 0.0992859i) q^{7} +(1.66098 - 2.28615i) q^{8} +(0.702986 - 6.68846i) q^{9} +O(q^{10})\)	\(q+(-1.34623 + 0.437416i) q^{2} +(-2.31753 + 2.08671i) q^{3} +(0.00296283 - 0.00215262i) q^{4} +(2.20716 - 3.82291i) q^{6} +(-0.944642 + 0.0992859i) q^{7} +(1.66098 - 2.28615i) q^{8} +(0.702986 - 6.68846i) q^{9} +(2.64680 + 1.17843i) q^{11} +(-0.00237454 + 0.0111713i) q^{12} +(0.844492 + 3.97302i) q^{13} +(1.22827 - 0.546863i) q^{14} +(-1.23833 + 3.81118i) q^{16} +(2.40356 + 5.39849i) q^{17} +(1.97926 + 9.31169i) q^{18} +(3.85426 + 0.819249i) q^{19} +(1.98205 - 2.20129i) q^{21} +(-4.07866 - 0.428684i) q^{22} +(4.17178 - 5.74196i) q^{23} +(0.921154 + 8.76420i) q^{24} +(-2.87474 - 4.97920i) q^{26} +(6.82861 + 9.39877i) q^{27} +(-0.00258509 + 0.00232762i) q^{28} +(0.690565 + 2.12534i) q^{29} +(4.68304 + 3.01150i) q^{31} -0.0207168i q^{32} +(-8.59307 + 2.79206i) q^{33} +(-5.59713 - 6.21624i) q^{34} +(-0.0123149 - 0.0213300i) q^{36} +(-1.26106 - 0.728076i) q^{37} +(-5.54707 + 0.583021i) q^{38} +(-10.2477 - 7.44538i) q^{39} +(0.928592 - 1.03131i) q^{41} +(-1.70542 + 3.83043i) q^{42} +(2.66625 - 12.5437i) q^{43} +(0.0103787 - 0.00220606i) q^{44} +(-3.10454 + 9.55479i) q^{46} +(1.42464 + 0.462894i) q^{47} +(-5.08297 - 11.4165i) q^{48} +(-5.96454 + 1.26780i) q^{49} +(-16.8354 - 7.49561i) q^{51} +(0.0110545 + 0.00995351i) q^{52} +(-2.69114 - 0.282850i) q^{53} +(-13.3040 - 9.66595i) q^{54} +(-1.34205 + 2.32450i) q^{56} +(-10.6419 + 6.14411i) q^{57} +(-1.85931 - 2.55913i) q^{58} +(2.76666 + 3.07268i) q^{59} +5.75919 q^{61} +(-7.62172 - 2.00573i) q^{62} +6.38800i q^{63} +(-2.46759 - 7.59447i) q^{64} +(10.3469 - 7.51749i) q^{66} +(7.95257 - 4.59142i) q^{67} +(0.0187422 + 0.0108208i) q^{68} +(2.31360 + 22.0125i) q^{69} +(-1.16123 + 11.0483i) q^{71} +(-14.1232 - 12.7165i) q^{72} +(-2.19480 + 4.92960i) q^{73} +(2.01615 + 0.428546i) q^{74} +(0.0131831 - 0.00586947i) q^{76} +(-2.61728 - 0.850405i) q^{77} +(17.0525 + 5.54068i) q^{78} +(-3.76376 + 1.67573i) q^{79} +(-15.7030 - 3.33777i) q^{81} +(-0.798986 + 1.79455i) q^{82} +(12.5706 + 11.3186i) q^{83} +(0.00113393 - 0.0107887i) q^{84} +(1.89744 + 18.0529i) q^{86} +(-6.03537 - 3.48452i) q^{87} +(7.09035 - 4.09361i) q^{88} +(-6.19419 + 4.50034i) q^{89} +(-1.19221 - 3.66924i) q^{91} -0.0259927i q^{92} +(-17.1372 + 2.79291i) q^{93} -2.12037 q^{94} +(0.0432300 + 0.0480118i) q^{96} +(-0.00200089 - 0.00275399i) q^{97} +(7.47508 - 4.31574i) q^{98} +(9.74255 - 16.8746i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{4} - 24 q^{6} - 12 q^{9}+O(q^{10}) \) 80 * q + 4 * q^4 - 24 * q^6 - 12 * q^9	\( 80 q + 4 q^{4} - 24 q^{6} - 12 q^{9} + 32 q^{11} + 20 q^{14} - 32 q^{16} + 18 q^{19} - 48 q^{21} - 220 q^{24} - 8 q^{26} + 44 q^{29} - 12 q^{31} + 32 q^{34} - 2 q^{36} + 110 q^{39} - 48 q^{41} + 104 q^{44} - 100 q^{46} - 186 q^{49} - 84 q^{51} - 204 q^{54} + 10 q^{56} - 62 q^{59} + 136 q^{61} + 46 q^{64} + 96 q^{69} - 60 q^{71} - 100 q^{74} + 28 q^{76} - 98 q^{79} + 50 q^{81} + 36 q^{84} + 326 q^{86} - 8 q^{89} - 74 q^{91} + 188 q^{94} + 44 q^{96} - 34 q^{99}+O(q^{100}) \) 80 * q + 4 * q^4 - 24 * q^6 - 12 * q^9 + 32 * q^11 + 20 * q^14 - 32 * q^16 + 18 * q^19 - 48 * q^21 - 220 * q^24 - 8 * q^26 + 44 * q^29 - 12 * q^31 + 32 * q^34 - 2 * q^36 + 110 * q^39 - 48 * q^41 + 104 * q^44 - 100 * q^46 - 186 * q^49 - 84 * q^51 - 204 * q^54 + 10 * q^56 - 62 * q^59 + 136 * q^61 + 46 * q^64 + 96 * q^69 - 60 * q^71 - 100 * q^74 + 28 * q^76 - 98 * q^79 + 50 * q^81 + 36 * q^84 + 326 * q^86 - 8 * q^89 - 74 * q^91 + 188 * q^94 + 44 * q^96 - 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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