LMFDB - Embedded newform 950.2.bb.d.243.4

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			243.4
Character	$\chi$	$=$	950.243
Dual form			950.2.bb.d.907.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.422618 - 0.906308i) q^{2} +(1.68936 + 1.18290i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(0.358120 - 2.03100i) q^{6} +(-0.500613 - 1.86831i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.428624 + 1.17763i) q^{9} +O(q^{10})$	\(q+(-0.422618 - 0.906308i) q^{2} +(1.68936 + 1.18290i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(0.358120 - 2.03100i) q^{6} +(-0.500613 - 1.86831i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.428624 + 1.17763i) q^{9} +(-2.71899 - 4.70944i) q^{11} +(-1.99206 + 0.533771i) q^{12} +(-3.47196 - 4.95847i) q^{13} +(-1.48170 + 1.24329i) q^{14} +(-0.173648 - 0.984808i) q^{16} +(-5.35884 + 2.49887i) q^{17} +(0.886155 - 0.886155i) q^{18} +(-4.11624 + 1.43407i) q^{19} +(1.36432 - 3.74844i) q^{21} +(-3.11910 + 4.45454i) q^{22} +(0.120123 + 1.37302i) q^{23} +(1.32564 + 1.57984i) q^{24} +(-3.02658 + 5.24220i) q^{26} +(0.932384 - 3.47970i) q^{27} +(1.75300 + 0.817436i) q^{28} +(-0.649592 + 0.236432i) q^{29} +(7.23118 + 4.17493i) q^{31} +(-0.819152 + 0.573576i) q^{32} +(0.977446 - 11.1723i) q^{33} +(4.52949 + 3.80069i) q^{34} +(-1.17763 - 0.428624i) q^{36} +(-3.36912 - 3.36912i) q^{37} +(3.03931 + 3.12452i) q^{38} -12.4836i q^{39} +(7.03483 - 1.24043i) q^{41} +(-3.97382 + 0.347664i) q^{42} +(-9.16126 - 0.801506i) q^{43} +(5.35537 + 0.944297i) q^{44} +(1.19361 - 0.689130i) q^{46} +(-0.529071 + 1.13460i) q^{47} +(0.871579 - 1.86911i) q^{48} +(2.82220 - 1.62940i) q^{49} +(-12.0090 - 2.11750i) q^{51} +(6.03014 + 0.527568i) q^{52} +(-2.19748 + 0.192255i) q^{53} +(-3.54773 + 0.625560i) q^{54} -1.93422i q^{56} +(-8.65020 - 2.44645i) q^{57} +(0.488810 + 0.488810i) q^{58} +(4.43437 + 1.61398i) q^{59} +(7.18251 + 6.02684i) q^{61} +(0.727737 - 8.31808i) q^{62} +(1.98561 - 1.39034i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-10.5386 + 3.83573i) q^{66} +(-1.78703 - 0.833307i) q^{67} +(1.53035 - 5.71136i) q^{68} +(-1.42122 + 2.46162i) q^{69} +(2.65771 + 3.16733i) q^{71} +(0.109225 + 1.24844i) q^{72} +(6.39146 - 9.12795i) q^{73} +(-1.62961 + 4.47731i) q^{74} +(1.54730 - 4.07503i) q^{76} +(-7.43753 + 7.43753i) q^{77} +(-11.3140 + 5.27582i) q^{78} +(-1.43747 - 8.15229i) q^{79} +(8.57134 - 7.19221i) q^{81} +(-4.09726 - 5.85149i) q^{82} +(10.3634 - 2.77687i) q^{83} +(1.99450 + 3.45458i) q^{84} +(3.14530 + 8.64165i) q^{86} +(-1.37707 - 0.368986i) q^{87} +(-1.40746 - 5.25269i) q^{88} +(2.19348 - 12.4398i) q^{89} +(-7.52586 + 8.96897i) q^{91} +(-1.12901 - 0.790538i) q^{92} +(7.27755 + 15.6068i) q^{93} +1.25189 q^{94} -2.06233 q^{96} +(1.17445 + 2.51861i) q^{97} +(-2.66945 - 1.86917i) q^{98} +(4.38057 - 5.22056i) 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 $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−0.422618	−	0.906308i	−0.298836	−	0.640856i
$2$	−0.422618	−	0.906308i	−0.298836	−	0.640856i
$3$	1.68936	+	1.18290i	0.975354	+	0.682950i	0.948529	−	0.316690i	$-0.102571\pi$
$3$	1.68936	+	1.18290i	0.975354	+	0.682950i	0.0268252	+	0.999640i	$0.491460\pi$
$4$	−0.642788	+	0.766044i	−0.321394	+	0.383022i
$5$		0			0
$5$		0			0
$6$	0.358120	−	2.03100i	0.146202	−	0.829152i
$7$	−0.500613	−	1.86831i	−0.189214	−	0.706156i	−0.993689	−	0.112169i	$-0.964220\pi$
$7$	−0.500613	−	1.86831i	−0.189214	−	0.706156i	0.804475	−	0.593986i	$-0.202447\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$	0.428624	+	1.17763i	0.142875	+	0.392545i
$10$		0			0
$11$	−2.71899	−	4.70944i	−0.819808	−	1.41995i	−0.905824	−	0.423655i	$-0.860747\pi$
$11$	−2.71899	−	4.70944i	−0.819808	−	1.41995i	0.0860160	−	0.996294i	$-0.472586\pi$
$12$	−1.99206	+	0.533771i	−0.575058	+	0.154086i
$13$	−3.47196	−	4.95847i	−0.962947	−	1.37523i	−0.926665	−	0.375889i	$-0.877337\pi$
$13$	−3.47196	−	4.95847i	−0.962947	−	1.37523i	−0.0362826	−	0.999342i	$-0.511552\pi$
$14$	−1.48170	+	1.24329i	−0.396000	+	0.332284i
$15$		0			0
$16$	−0.173648	−	0.984808i	−0.0434120	−	0.246202i
$17$	−5.35884	+	2.49887i	−1.29971	+	0.606065i	−0.944436	−	0.328697i	$-0.893391\pi$
$17$	−5.35884	+	2.49887i	−1.29971	+	0.606065i	−0.355275	+	0.934762i	$0.615613\pi$
$18$	0.886155	−	0.886155i	0.208869	−	0.208869i
$19$	−4.11624	+	1.43407i	−0.944330	+	0.328999i
$19$	−4.11624	+	1.43407i	−0.944330	+	0.328999i
$20$		0			0
$21$	1.36432	−	3.74844i	0.297719	−	0.817976i
$22$	−3.11910	+	4.45454i	−0.664995	+	0.949711i
$23$	0.120123	+	1.37302i	0.0250474	+	0.286294i	0.998380	+	0.0568955i	$0.0181202\pi$
$23$	0.120123	+	1.37302i	0.0250474	+	0.286294i	−0.973333	+	0.229398i	$0.926324\pi$
$24$	1.32564	+	1.57984i	0.270595	+	0.322483i
$25$		0			0
$26$	−3.02658	+	5.24220i	−0.593562	+	1.02808i
$27$	0.932384	−	3.47970i	0.179437	−	0.669669i
$28$	1.75300	+	0.817436i	0.331285	+	0.154481i
$29$	−0.649592	+	0.236432i	−0.120626	+	0.0439043i	−0.401628	−	0.915803i	$-0.631556\pi$
$29$	−0.649592	+	0.236432i	−0.120626	+	0.0439043i	0.281002	+	0.959707i	$0.409333\pi$
$30$		0			0
$31$	7.23118	+	4.17493i	1.29876	+	0.749839i	0.980190	−	0.198061i	$-0.0634644\pi$
$31$	7.23118	+	4.17493i	1.29876	+	0.749839i	0.318569	+	0.947900i	$0.396798\pi$
$32$	−0.819152	+	0.573576i	−0.144807	+	0.101395i
$33$	0.977446	−	11.1723i	0.170152	−	1.94484i
$34$	4.52949	+	3.80069i	0.776801	+	0.651814i
$35$		0			0
$36$	−1.17763	−	0.428624i	−0.196272	−	0.0714373i
$37$	−3.36912	−	3.36912i	−0.553879	−	0.553879i	0.373679	−	0.927558i	$-0.378096\pi$
$37$	−3.36912	−	3.36912i	−0.553879	−	0.553879i	−0.927558	+	0.373679i	$0.878096\pi$
$38$	3.03931	+	3.12452i	0.493041	+	0.506863i
$39$		−	12.4836i		−	1.99898i
$40$		0			0
$41$	7.03483	−	1.24043i	1.09866	−	0.193723i	0.405204	−	0.914226i	$-0.367200\pi$
$41$	7.03483	−	1.24043i	1.09866	−	0.193723i	0.693451	+	0.720504i	$0.256089\pi$
$42$	−3.97382	+	0.347664i	−0.613174	+	0.0536458i
$43$	−9.16126	−	0.801506i	−1.39708	−	0.122229i	−0.636401	−	0.771358i	$-0.719578\pi$
$43$	−9.16126	−	0.801506i	−1.39708	−	0.122229i	−0.760678	+	0.649130i	$0.775133\pi$
$44$	5.35537	+	0.944297i	0.807353	+	0.142358i
$45$		0			0
$46$	1.19361	−	0.689130i	0.175988	−	0.101607i
$47$	−0.529071	+	1.13460i	−0.0771729	+	0.165498i	−0.941109	−	0.338104i	$-0.890214\pi$
$47$	−0.529071	+	1.13460i	−0.0771729	+	0.165498i	0.863936	+	0.503602i	$0.167992\pi$
$48$	0.871579	−	1.86911i	0.125802	−	0.269782i
$49$	2.82220	−	1.62940i	0.403172	−	0.232771i
$50$		0			0
$51$	−12.0090	−	2.11750i	−1.68159	−	0.296510i
$52$	6.03014	+	0.527568i	0.836229	+	0.0731606i
$53$	−2.19748	+	0.192255i	−0.301848	+	0.0264082i	−0.237073	−	0.971492i	$-0.576188\pi$
$53$	−2.19748	+	0.192255i	−0.301848	+	0.0264082i	−0.0647740	+	0.997900i	$0.520633\pi$
$54$	−3.54773	+	0.625560i	−0.482784	+	0.0851279i
$55$		0			0
$56$		−	1.93422i		−	0.258471i
$57$	−8.65020	−	2.44645i	−1.14575	−	0.324040i
$58$	0.488810	+	0.488810i	0.0641839	+	0.0641839i
$59$	4.43437	+	1.61398i	0.577305	+	0.210122i	0.614137	−	0.789200i	$-0.289504\pi$
$59$	4.43437	+	1.61398i	0.577305	+	0.210122i	−0.0368316	+	0.999321i	$0.511727\pi$
$60$		0			0
$61$	7.18251	+	6.02684i	0.919626	+	0.771658i	0.973926	−	0.226867i	$-0.0728481\pi$
$61$	7.18251	+	6.02684i	0.919626	+	0.771658i	−0.0542995	+	0.998525i	$0.517293\pi$
$62$	0.727737	−	8.31808i	0.0924227	−	1.05640i
$63$	1.98561	−	1.39034i	0.250164	−	0.175167i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$		0			0
$66$	−10.5386	+	3.83573i	−1.29721	+	0.472146i
$67$	−1.78703	−	0.833307i	−0.218321	−	0.101805i	0.310381	−	0.950612i	$-0.399543\pi$
$67$	−1.78703	−	0.833307i	−0.218321	−	0.101805i	−0.528702	+	0.848808i	$0.677321\pi$
$68$	1.53035	−	5.71136i	0.185583	−	0.692604i
$69$	−1.42122	+	2.46162i	−0.171094	+	0.296344i
$70$		0			0
$71$	2.65771	+	3.16733i	0.315412	+	0.375893i	0.900336	−	0.435195i	$-0.143320\pi$
$71$	2.65771	+	3.16733i	0.315412	+	0.375893i	−0.584925	+	0.811088i	$0.698876\pi$
$72$	0.109225	+	1.24844i	0.0128723	+	0.147131i
$73$	6.39146	−	9.12795i	0.748064	−	1.06835i	−0.246991	−	0.969018i	$-0.579442\pi$
$73$	6.39146	−	9.12795i	0.748064	−	1.06835i	0.995055	−	0.0993278i	$-0.0316692\pi$
$74$	−1.62961	+	4.47731i	−0.189438	+	0.520476i
$75$		0			0
$76$	1.54730	−	4.07503i	0.177488	−	0.467438i
$77$	−7.43753	+	7.43753i	−0.847586	+	0.847586i
$78$	−11.3140	+	5.27582i	−1.28106	+	0.597369i
$79$	−1.43747	−	8.15229i	−0.161728	−	0.917204i	−0.952374	−	0.304931i	$-0.901366\pi$
$79$	−1.43747	−	8.15229i	−0.161728	−	0.917204i	0.790646	−	0.612273i	$-0.209745\pi$
$80$		0			0
$81$	8.57134	−	7.19221i	0.952372	−	0.799135i
$82$	−4.09726	−	5.85149i	−0.452466	−	0.646189i
$83$	10.3634	−	2.77687i	1.13753	−	0.304802i	0.359575	−	0.933116i	$-0.382922\pi$
$83$	10.3634	−	2.77687i	1.13753	−	0.304802i	0.777959	+	0.628314i	$0.216255\pi$
$84$	1.99450	+	3.45458i	0.217618	+	0.376925i
$85$		0			0
$86$	3.14530	+	8.64165i	0.339167	+	0.931853i
$87$	−1.37707	−	0.368986i	−0.147638	−	0.0395594i
$88$	−1.40746	−	5.25269i	−0.150035	−	0.559939i
$89$	2.19348	−	12.4398i	0.232508	−	1.31862i	−0.615291	−	0.788300i	$-0.710961\pi$
$89$	2.19348	−	12.4398i	0.232508	−	1.31862i	0.847799	−	0.530318i	$-0.177928\pi$
$90$		0			0
$91$	−7.52586	+	8.96897i	−0.788924	+	0.940203i
$92$	−1.12901	−	0.790538i	−0.117707	−	0.0824193i
$93$	7.27755	+	15.6068i	0.754647	+	1.61835i
$94$	1.25189			0.129122
$95$		0			0
$96$	−2.06233			−0.210486
$97$	1.17445	+	2.51861i	0.119247	+	0.255726i	0.956866	−	0.290528i	$-0.0938311\pi$
$97$	1.17445	+	2.51861i	0.119247	+	0.255726i	−0.837619	+	0.546254i	$0.816053\pi$
$98$	−2.66945	−	1.86917i	−0.269655	−	0.188815i
$99$	4.38057	−	5.22056i	0.440264	−	0.524686i
$100$		0			0
$101$	−1.70403	+	9.66402i	−0.169557	+	0.961605i	0.774684	+	0.632349i	$0.217909\pi$
$101$	−1.70403	+	9.66402i	−0.169557	+	0.961605i	−0.944241	+	0.329256i	$0.893202\pi$
$102$	3.15610	+	11.7787i	0.312500	+	1.16627i
$103$	−9.63467	−	2.58160i	−0.949332	−	0.254373i	−0.249253	−	0.968438i	$-0.580185\pi$
$103$	−9.63467	−	2.58160i	−0.949332	−	0.254373i	−0.700079	+	0.714066i	$0.746852\pi$
$104$	−2.07031	−	5.68812i	−0.203010	−	0.557766i
$105$		0			0
$106$	1.10294	+	1.91035i	0.107127	+	0.185549i
$107$	6.40476	−	1.71615i	0.619171	−	0.165906i	0.0644203	−	0.997923i	$-0.479480\pi$
$107$	6.40476	−	1.71615i	0.619171	−	0.165906i	0.554751	+	0.832016i	$0.312813\pi$
$108$	2.06628	+	2.95096i	0.198828	+	0.283956i
$109$	0.389716	−	0.327010i	0.0373280	−	0.0313219i	−0.623933	−	0.781478i	$-0.714466\pi$
$109$	0.389716	−	0.327010i	0.0373280	−	0.0313219i	0.661261	+	0.750156i	$0.270022\pi$
$110$		0			0
$111$	−1.70632	−	9.67701i	−0.161956	−	0.918501i
$112$	−1.75300	+	0.817436i	−0.165643	+	0.0772405i
$113$	−2.58933	+	2.58933i	−0.243584	+	0.243584i	−0.818331	−	0.574747i	$-0.805100\pi$
$113$	−2.58933	+	2.58933i	−0.243584	+	0.243584i	0.574747	+	0.818331i	$0.305100\pi$
$114$	1.43849	+	8.87366i	0.134727	+	0.831094i
$115$		0			0
$116$	0.236432	−	0.649592i	0.0219522	−	0.0603131i
$117$	4.35110	−	6.21401i	0.402259	−	0.574486i
$118$	−0.411284	−	4.70100i	−0.0378617	−	0.432762i
$119$	7.35138	+	8.76103i	0.673900	+	0.803122i
$120$		0			0
$121$	−9.28586	+	16.0836i	−0.844169	+	1.46214i
$122$	2.42671	−	9.05662i	0.219704	−	0.819948i
$123$	13.3517	+	6.22600i	1.20388	+	0.561379i
$124$	−7.84629	+	2.85582i	−0.704618	+	0.256460i
$125$		0			0
$126$	−2.09923	−	1.21199i	−0.187015	−	0.107973i
$127$	4.29581	−	3.00796i	0.381192	−	0.266913i	−0.367239	−	0.930127i	$-0.619697\pi$
$127$	4.29581	−	3.00796i	0.381192	−	0.266913i	0.748430	+	0.663213i	$0.230808\pi$
$128$	0.0871557	−	0.996195i	0.00770355	−	0.0880520i
$129$	−14.5286	−	12.1909i	−1.27917	−	1.07335i
$130$		0			0
$131$	10.9039	+	3.96871i	0.952682	+	0.346748i	0.771162	−	0.636639i	$-0.219676\pi$
$131$	10.9039	+	3.96871i	0.952682	+	0.346748i	0.181520	+	0.983387i	$0.441898\pi$
$132$	7.93016	+	7.93016i	0.690232	+	0.690232i
$133$	4.73994	+	6.97251i	0.411005	+	0.604593i
$134$			1.97177i			0.170335i
$135$		0			0
$136$	−5.82300	+	1.02675i	−0.499318	+	0.0880433i
$137$	4.24901	−	0.371740i	0.363018	−	0.0317599i	0.0958119	−	0.995399i	$-0.469455\pi$
$137$	4.24901	−	0.371740i	0.363018	−	0.0317599i	0.267206	+	0.963640i	$0.413900\pi$
$138$	2.83161	+	0.247734i	0.241043	+	0.0210885i
$139$	−15.8992	−	2.80345i	−1.34855	−	0.237786i	−0.547712	−	0.836667i	$-0.684501\pi$
$139$	−15.8992	−	2.80345i	−1.34855	−	0.237786i	−0.800838	+	0.598881i	$0.795612\pi$
$140$		0			0
$141$	−2.23591	+	1.29091i	−0.188298	+	0.108714i
$142$	1.74738	−	3.74727i	0.146637	−	0.314464i
$143$	−13.9114	+	29.8330i	−1.16333	+	2.49476i
$144$	1.08531	−	0.626606i	0.0904428	−	0.0522172i
$145$		0			0
$146$	−10.9739	−	1.93499i	−0.908205	−	0.160141i
$147$	6.69515	+	0.585749i	0.552206	+	0.0483118i
$148$	4.74652	−	0.415267i	0.390162	−	0.0341347i
$149$	−17.4141	+	3.07057i	−1.42662	+	0.251551i	−0.833035	−	0.553221i	$-0.813399\pi$
$149$	−17.4141	+	3.07057i	−1.42662	+	0.251551i	−0.593584	+	0.804772i	$0.702287\pi$
$150$		0			0
$151$		−	23.2030i		−	1.88823i	−0.329615	−	0.944116i	$-0.606919\pi$
$151$		−	23.2030i		−	1.88823i	0.329615	−	0.944116i	$-0.393081\pi$
$152$	−4.34715	+	0.319847i	−0.352600	+	0.0259430i
$153$	−5.23969	−	5.23969i	−0.423603	−	0.423603i
$154$	9.88393	+	3.59746i	0.796470	+	0.289891i
$155$		0			0
$156$	9.56303	+	8.02433i	0.765655	+	0.642461i
$157$	−1.73615	+	19.8442i	−0.138560	+	1.58374i	0.535157	+	0.844753i	$0.320253\pi$
$157$	−1.73615	+	19.8442i	−0.138560	+	1.58374i	−0.673716	+	0.738990i	$0.735303\pi$
$158$	−6.78098	+	4.74810i	−0.539466	+	0.377738i
$159$	−3.93977	−	2.27463i	−0.312444	−	0.180390i
$160$		0			0
$161$	2.50509	−	0.911777i	0.197429	−	0.0718581i
$162$	−10.1408	−	4.72872i	−0.796734	−	0.371523i
$163$	5.10461	−	19.0507i	0.399824	−	1.49216i	−0.413583	−	0.910466i	$-0.635723\pi$
$163$	5.10461	−	19.0507i	0.399824	−	1.49216i	0.813407	−	0.581696i	$-0.197611\pi$
$164$	−3.57168	+	6.18632i	−0.278901	+	0.483071i
$165$		0			0
$166$	−6.89648	−	8.21891i	−0.535271	−	0.637911i
$167$	0.808994	+	9.24684i	0.0626018	+	0.715542i	0.961034	+	0.276430i	$0.0891514\pi$
$167$	0.808994	+	9.24684i	0.0626018	+	0.715542i	−0.898432	+	0.439112i	$0.855293\pi$
$168$	2.28800	−	3.26760i	0.176523	−	0.252101i
$169$	−8.08565	+	22.2151i	−0.621973	+	1.70886i
$170$		0			0
$171$	−3.45313	−	4.23275i	−0.264068	−	0.323686i
$172$	6.50273	−	6.50273i	0.495829	−	0.495829i
$173$	−6.19991	+	2.89107i	−0.471371	+	0.219804i	−0.643763	−	0.765225i	$-0.722628\pi$
$173$	−6.19991	+	2.89107i	−0.471371	+	0.219804i	0.172393	+	0.985028i	$0.444850\pi$
$174$	0.247562	+	1.40399i	0.0187676	+	0.106436i
$175$		0			0
$176$	−4.16574	+	3.49547i	−0.314005	+	0.263481i
$177$	5.58207	+	7.97203i	0.419574	+	0.599214i
$178$	−12.2013	+	3.26933i	−0.914527	+	0.245047i
$179$	5.45671	+	9.45130i	0.407854	+	0.706423i	0.994649	−	0.103312i	$-0.0329440\pi$
$179$	5.45671	+	9.45130i	0.407854	+	0.706423i	−0.586795	+	0.809735i	$0.699611\pi$
$180$		0			0
$181$	−7.62420	−	20.9473i	−0.566702	−	1.55700i	−0.809620	−	0.586954i	$-0.800327\pi$
$181$	−7.62420	−	20.9473i	−0.566702	−	1.55700i	0.242918	−	0.970047i	$-0.421895\pi$
$182$	11.3092	+	3.03029i	0.838294	+	0.224620i
$183$	5.00469	+	18.6778i	0.369957	+	1.38070i
$184$	−0.239332	+	1.35732i	−0.0176438	+	0.100063i
$185$		0			0
$186$	11.0689	−	13.1914i	0.811612	−	0.967241i
$187$	26.3389	+	18.4427i	1.92609	+	1.34867i
$188$	−0.529071	−	1.13460i	−0.0385865	−	0.0827490i
$189$	−6.96794			−0.506843
$190$		0			0
$191$	1.74054			0.125941			0.0629706	−	0.998015i	$-0.479943\pi$
$191$	1.74054			0.125941			0.0629706	+	0.998015i	$0.479943\pi$
$192$	0.871579	+	1.86911i	0.0629008	+	0.134891i
$193$	−4.26617	−	2.98720i	−0.307086	−	0.215024i	0.409867	−	0.912145i	$-0.365575\pi$
$193$	−4.26617	−	2.98720i	−0.307086	−	0.215024i	−0.716953	+	0.697121i	$0.754464\pi$
$194$	1.78629	−	2.12882i	0.128248	−	0.152840i
$195$		0			0
$196$	−0.565884	+	3.20929i	−0.0404203	+	0.229235i
$197$	−4.43871	−	16.5655i	−0.316245	−	1.18024i	−0.922825	−	0.385220i	$-0.874125\pi$
$197$	−4.43871	−	16.5655i	−0.316245	−	1.18024i	0.606579	−	0.795023i	$-0.292541\pi$
$198$	−6.58274	−	1.76384i	−0.467815	−	0.125351i
$199$	−8.20324	−	22.5382i	−0.581512	−	1.59769i	−0.785597	−	0.618738i	$-0.787644\pi$
$199$	−8.20324	−	22.5382i	−0.581512	−	1.59769i	0.204085	−	0.978953i	$-0.434578\pi$
$200$		0			0
$201$	−2.03322	−	3.52165i	−0.143413	−	0.248398i
$202$	9.47872	−	2.53982i	0.666921	−	0.178701i
$203$	0.766923	+	1.09528i	0.0538274	+	0.0768736i
$204$	9.34131	−	7.83829i	0.654023	−	0.548790i
$205$		0			0
$206$	1.73206	+	9.82301i	0.120678	+	0.684401i
$207$	−1.56542	+	0.729969i	−0.108804	+	0.0507363i
$208$	−4.28024	+	4.28024i	−0.296781	+	0.296781i
$209$	17.9457	+	15.4859i	1.24133	+	1.07118i
$210$		0			0
$211$	4.83350	−	13.2799i	0.332752	−	0.914228i	−0.654641	−	0.755940i	$-0.727180\pi$
$211$	4.83350	−	13.2799i	0.332752	−	0.914228i	0.987393	−	0.158288i	$-0.0505976\pi$
$212$	1.26524	−	1.80695i	0.0868970	−	0.124102i
$213$	0.743180	+	8.49458i	0.0509218	+	0.582039i
$214$	−4.26213	−	5.07941i	−0.291353	−	0.347221i
$215$		0			0
$216$	1.80123	−	3.11982i	0.122558	−	0.212277i
$217$	4.18004	−	15.6001i	0.283760	−	1.05901i
$218$	−0.461073	−	0.215002i	−0.0312278	−	0.0145618i
$219$	21.5950	−	7.85993i	1.45925	−	0.531125i
$220$		0			0
$221$	30.9962	+	17.8957i	2.08503	+	1.20379i
$222$	−8.04923	+	5.63613i	−0.540229	+	0.378272i
$223$	0.416097	−	4.75601i	0.0278639	−	0.318486i	−0.969453	−	0.245278i	$-0.921121\pi$
$223$	0.416097	−	4.75601i	0.0278639	−	0.318486i	0.997317	−	0.0732079i	$-0.0233237\pi$
$224$	1.48170	+	1.24329i	0.0990001	+	0.0830709i
$225$		0			0
$226$	3.44103	+	1.25243i	0.228894	+	0.0833106i
$227$	−15.6976	−	15.6976i	−1.04189	−	1.04189i	−0.999084	−	0.0428025i	$-0.986371\pi$
$227$	−15.6976	−	15.6976i	−1.04189	−	1.04189i	−0.0428025	−	0.999084i	$-0.513629\pi$
$228$	7.43433	−	5.05389i	0.492351	−	0.334702i
$229$			8.09579i			0.534985i	0.963560	+	0.267492i	$0.0861950\pi$
$229$			8.09579i			0.534985i	−0.963560	+	0.267492i	$0.913805\pi$
$230$		0			0
$231$	−21.3626	+	3.76680i	−1.40556	+	0.247837i
$232$	−0.688651	+	0.0602491i	−0.0452121	+	0.00395555i
$233$	11.5540	+	1.01084i	0.756926	+	0.0662224i	0.459084	−	0.888393i	$-0.348178\pi$
$233$	11.5540	+	1.01084i	0.756926	+	0.0662224i	0.297842	+	0.954615i	$0.403733\pi$
$234$	−7.47066	−	1.31728i	−0.488372	−	0.0861132i
$235$		0			0
$236$	−4.08673	+	2.35948i	−0.266024	+	0.153589i
$237$	7.21498	−	15.4726i	0.468663	−	1.00505i
$238$	4.83336	−	10.3652i	0.313300	−	0.671875i
$239$	18.9765	−	10.9561i	1.22749	−	0.708689i	0.260982	−	0.965344i	$-0.415954\pi$
$239$	18.9765	−	10.9561i	1.22749	−	0.708689i	0.966503	+	0.256655i	$0.0826203\pi$
$240$		0			0
$241$	27.9109	+	4.92145i	1.79790	+	0.317019i	0.969863	−	0.243652i	$-0.0783453\pi$
$241$	27.9109	+	4.92145i	1.79790	+	0.317019i	0.828039	+	0.560670i	$0.189456\pi$
$242$	18.5011	+	1.61863i	1.18929	+	0.104050i
$243$	12.2216	−	1.06925i	0.784015	−	0.0685924i
$244$	−9.23366	+	1.62814i	−0.591124	+	0.104231i
$245$		0			0
$246$		−	14.7320i		−	0.939276i
$247$	21.4022	+	15.4312i	1.36179	+	0.981864i
$248$	5.90424	+	5.90424i	0.374919	+	0.374919i
$249$	20.7924	+	7.56781i	1.31766	+	0.479590i
$250$		0			0
$251$	−13.3714	−	11.2199i	−0.843994	−	0.708195i	0.114465	−	0.993427i	$-0.463485\pi$
$251$	−13.3714	−	11.2199i	−0.843994	−	0.708195i	−0.958458	+	0.285232i	$0.907929\pi$
$252$	−0.211264	+	2.41476i	−0.0133084	+	0.152116i
$253$	6.13952	−	4.29894i	0.385988	−	0.270272i
$254$	−4.54163	−	2.62211i	−0.284967	−	0.164526i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	24.2555	+	11.3105i	1.51302	+	0.705532i	0.989237	−	0.146320i	$-0.0467431\pi$
$257$	24.2555	+	11.3105i	1.51302	+	0.705532i	0.523781	+	0.851853i	$0.324521\pi$
$258$	−4.90869	+	18.3195i	−0.305602	+	1.14052i
$259$	−4.60794	+	7.98118i	−0.286323	+	0.495927i
$260$		0			0
$261$	−0.556861	−	0.663642i	−0.0344689	−	0.0410784i
$262$	−1.01133	−	11.5596i	−0.0624803	−	0.714153i
$263$	2.41954	−	3.45546i	0.149195	−	0.213073i	−0.737597	−	0.675241i	$-0.764040\pi$
$263$	2.41954	−	3.45546i	0.149195	−	0.213073i	0.886792	+	0.462169i	$0.152928\pi$
$264$	3.83573	−	10.5386i	0.236073	−	0.648606i
$265$		0			0
$266$	4.31605	−	7.24255i	0.264634	−	0.444069i
$267$	18.4207	−	18.4207i	1.12733	−	1.12733i
$268$	1.78703	−	0.833307i	0.109160	−	0.0509023i
$269$	3.67765	+	20.8570i	0.224231	+	1.27167i	0.864151	+	0.503233i	$0.167856\pi$
$269$	3.67765	+	20.8570i	0.224231	+	1.27167i	−0.639920	+	0.768442i	$0.721033\pi$
$270$		0			0
$271$	−5.39184	+	4.52429i	−0.327531	+	0.274831i	−0.791693	−	0.610919i	$-0.790800\pi$
$271$	−5.39184	+	4.52429i	−0.327531	+	0.274831i	0.464162	+	0.885750i	$0.346356\pi$
$272$	3.39146	+	4.84351i	0.205637	+	0.293681i
$273$	−23.3233	+	6.24947i	−1.41159	+	0.378235i
$274$	−2.13262	−	3.69381i	−0.128836	−	0.223151i
$275$		0			0
$276$	−0.972169	−	2.67101i	−0.0585177	−	0.160776i
$277$	−5.49430	−	1.47219i	−0.330120	−	0.0884555i	0.0899520	−	0.995946i	$-0.471329\pi$
$277$	−5.49430	−	1.47219i	−0.330120	−	0.0884555i	−0.420072	+	0.907491i	$0.637995\pi$
$278$	4.17849	+	15.5943i	0.250609	+	0.935285i
$279$	−1.81708	+	10.3052i	−0.108786	+	0.616954i
$280$		0			0
$281$	−9.92729	+	11.8309i	−0.592213	+	0.705772i	−0.976030	−	0.217638i	$-0.930165\pi$
$281$	−9.92729	+	11.8309i	−0.592213	+	0.705772i	0.383817	+	0.923409i	$0.374609\pi$
$282$	2.11490	+	1.48087i	0.125940	+	0.0881843i
$283$	−1.53558	−	3.29306i	−0.0912807	−	0.195752i	0.855367	−	0.518023i	$-0.173332\pi$
$283$	−1.53558	−	3.29306i	−0.0912807	−	0.195752i	−0.946648	+	0.322271i	$0.895554\pi$
$284$	−4.13466			−0.245347
$285$		0			0
$286$	32.9171			1.94643
$287$	−5.83923	−	12.5223i	−0.344679	−	0.739167i
$288$	−1.02657	−	0.718813i	−0.0604913	−	0.0423565i
$289$	11.5455	−	13.7594i	0.679146	−	0.809374i
$290$		0			0
$291$	−0.995207	+	5.64410i	−0.0583401	+	0.330863i
$292$	2.88406	+	10.7635i	0.168777	+	0.629885i
$293$	−21.2705	−	5.69941i	−1.24263	−	0.332963i	−0.423147	−	0.906061i	$-0.639075\pi$
$293$	−21.2705	−	5.69941i	−1.24263	−	0.332963i	−0.819487	+	0.573098i	$0.805741\pi$
$294$	−2.29862	−	6.31541i	−0.134058	−	0.368322i
$295$		0			0
$296$	−2.38233	−	4.12631i	−0.138470	−	0.239837i
$297$	−18.9226	+	5.07029i	−1.09800	+	0.294208i
$298$	10.1424	+	14.4848i	0.587534	+	0.839085i
$299$	6.39099	−	5.36268i	0.369600	−	0.310132i
$300$		0			0
$301$	3.08878	+	17.5173i	0.178034	+	1.00968i
$302$	−21.0290	+	9.80600i	−1.21008	+	0.564272i
$303$	−14.3103	+	14.3103i	−0.822107	+	0.822107i
$304$	2.12706	+	3.80468i	0.121995	+	0.218213i
$305$		0			0
$306$	−2.53438	+	6.96315i	−0.144881	+	0.398057i
$307$	−0.336864	+	0.481092i	−0.0192259	+	0.0274574i	−0.828650	−	0.559767i	$-0.810891\pi$
$307$	−0.336864	+	0.481092i	−0.0192259	+	0.0274574i	0.809424	+	0.587225i	$0.199779\pi$
$308$	−0.916727	−	10.4782i	−0.0522354	−	0.597053i
$309$	−13.2227	−	15.7582i	−0.752211	−	0.896450i
$310$		0			0
$311$	−6.26335	+	10.8484i	−0.355162	+	0.615159i	−0.987146	−	0.159823i	$-0.948908\pi$
$311$	−6.26335	+	10.8484i	−0.355162	+	0.615159i	0.631984	+	0.774982i	$0.282241\pi$
$312$	3.23100	−	12.0583i	0.182920	−	0.682665i
$313$	−12.3220	−	5.74584i	−0.696481	−	0.324774i	0.0419347	−	0.999120i	$-0.486648\pi$
$313$	−12.3220	−	5.74584i	−0.696481	−	0.324774i	−0.738416	+	0.674346i	$0.764426\pi$
$314$	18.7187	−	6.81306i	1.05636	−	0.384483i
$315$		0			0
$316$	7.16900	+	4.13903i	0.403288	+	0.232838i
$317$	−17.7337	+	12.4173i	−0.996022	+	0.697422i	−0.953413	−	0.301669i	$-0.902456\pi$
$317$	−17.7337	+	12.4173i	−0.996022	+	0.697422i	−0.0426097	+	0.999092i	$0.513567\pi$
$318$	−0.396493	+	4.53194i	−0.0222342	+	0.254139i
$319$	2.87970	+	2.41635i	0.161232	+	0.135290i
$320$		0			0
$321$	12.8500	+	4.67702i	0.717217	+	0.261046i
$322$	−1.88505	−	1.88505i	−0.105050	−	0.105050i
$323$	18.4747	−	17.9709i	1.02796	−	0.999929i
$324$			11.1891i			0.621616i
$325$		0			0
$326$	−19.4231	+	3.42481i	−1.07574	+	0.189683i
$327$	1.04519	−	0.0914426i	0.0577993	−	0.00505679i
$328$	7.11617	+	0.622584i	0.392925	+	0.0343765i
$329$	2.38464	+	0.420476i	0.131469	+	0.0231816i
$330$		0			0
$331$	−22.1887	+	12.8106i	−1.21960	+	0.704137i	−0.964832	−	0.262866i	$-0.915332\pi$
$331$	−22.1887	+	12.8106i	−1.21960	+	0.704137i	−0.254768	+	0.967002i	$0.581999\pi$
$332$	−4.53428	+	9.72379i	−0.248851	+	0.533662i
$333$	2.52350	−	5.41167i	0.138287	−	0.296558i
$334$	8.03859	−	4.64108i	0.439852	−	0.253949i
$335$		0			0
$336$	−3.92840	−	0.692683i	−0.214312	−	0.0377889i
$337$	−0.163350	−	0.0142913i	−0.00889825	−	0.000778496i	0.0827057	−	0.996574i	$-0.473644\pi$
$337$	−0.163350	−	0.0142913i	−0.00889825	−	0.000778496i	−0.0916040	+	0.995796i	$0.529199\pi$
$338$	23.5509	−	2.06044i	1.28100	−	0.112073i
$339$	−7.43725	+	1.31139i	−0.403936	+	0.0712249i
$340$		0			0
$341$		−	45.4064i		−	2.45889i
$342$	−2.37682	+	4.91844i	−0.128523	+	0.265959i
$343$	−14.0310	−	14.0310i	−0.757600	−	0.757600i
$344$	−8.64165	−	3.14530i	−0.465927	−	0.169583i
$345$		0			0
$346$	5.24039	+	4.39721i	0.281725	+	0.236396i
$347$	−1.86450	+	21.3113i	−0.100092	+	1.14405i	0.765546	+	0.643381i	$0.222469\pi$
$347$	−1.86450	+	21.3113i	−0.100092	+	1.14405i	−0.865637	+	0.500671i	$0.833087\pi$
$348$	1.16783	−	0.817720i	0.0626020	−	0.0438344i
$349$	6.17491	+	3.56509i	0.330535	+	0.190835i	0.656079	−	0.754692i	$-0.272214\pi$
$349$	6.17491	+	3.56509i	0.330535	+	0.190835i	−0.325543	+	0.945527i	$0.605547\pi$
$350$		0			0
$351$	−20.4912	+	7.45818i	−1.09374	+	0.398088i
$352$	4.92849	+	2.29819i	0.262689	+	0.122494i
$353$	−3.08271	+	11.5048i	−0.164076	+	0.612340i	0.834080	+	0.551643i	$0.185999\pi$
$353$	−3.08271	+	11.5048i	−0.164076	+	0.612340i	−0.998156	+	0.0606967i	$0.980668\pi$
$354$	4.86602	−	8.42820i	0.258626	−	0.447954i
$355$		0			0
$356$	8.11952	+	9.67647i	0.430334	+	0.512852i
$357$	2.05568	+	23.4965i	0.108798	+	1.24357i
$358$	6.25968	−	8.93975i	0.330834	−	0.472481i
$359$	0.609873	−	1.67561i	0.0321878	−	0.0884354i	−0.922558	−	0.385859i	$-0.873905\pi$
$359$	0.609873	−	1.67561i	0.0321878	−	0.0884354i	0.954746	+	0.297424i	$0.0961274\pi$
$360$		0			0
$361$	14.8869	−	11.8060i	0.783519	−	0.621367i
$362$	−15.7626	+	15.7626i	−0.828463	+	0.828463i
$363$	−34.7125	+	16.1867i	−1.82194	+	0.849583i
$364$	−2.03310	−	11.5303i	−0.106563	−	0.604351i
$365$		0			0
$366$	14.8127	−	12.4293i	0.774273	−	0.649692i
$367$	−13.3951	−	19.1301i	−0.699217	−	0.998585i	−0.999006	−	0.0445794i	$-0.985805\pi$
$367$	−13.3951	−	19.1301i	−0.699217	−	0.998585i	0.299789	−	0.954005i	$-0.403084\pi$
$368$	1.33130	−	0.356720i	0.0693987	−	0.0185953i
$369$	4.47607	+	7.75278i	0.233015	+	0.403594i
$370$		0			0
$371$	1.45928	+	4.00934i	0.0757621	+	0.208155i
$372$	−16.6334	−	4.45691i	−0.862402	−	0.231080i
$373$	−2.59778	−	9.69503i	−0.134508	−	0.501990i	−0.999999	−	0.00106642i	$-0.999661\pi$
$373$	−2.59778	−	9.69503i	−0.134508	−	0.501990i	0.865492	−	0.500923i	$-0.167006\pi$
$374$	5.58347	−	31.6654i	0.288714	−	1.63738i
$375$		0			0
$376$	−0.804699	+	0.959002i	−0.0414992	+	0.0494568i
$377$	3.42769	+	2.40010i	0.176535	+	0.123611i
$378$	2.94478	+	6.31510i	0.151463	+	0.324813i
$379$	0.566143			0.0290808			0.0145404	−	0.999894i	$-0.495371\pi$
$379$	0.566143			0.0290808			0.0145404	+	0.999894i	$0.495371\pi$
$380$		0			0
$381$	10.8153			0.554086
$382$	−0.735585	−	1.57747i	−0.0376358	−	0.0807103i
$383$	30.9106	+	21.6438i	1.57946	+	1.10595i	0.942075	+	0.335401i	$0.108872\pi$
$383$	30.9106	+	21.6438i	1.57946	+	1.10595i	0.637383	+	0.770547i	$0.280017\pi$
$384$	1.32564	−	1.57984i	0.0676489	−	0.0806208i
$385$		0			0
$386$	−0.904365	+	5.12891i	−0.0460310	+	0.261055i
$387$	−2.98285	−	11.1322i	−0.151627	−	0.565880i
$388$	−2.68428	−	0.719252i	−0.136274	−	0.0365145i
$389$	5.89341	+	16.1920i	0.298808	+	0.820968i	0.994700	+	0.102822i	$0.0327871\pi$
$389$	5.89341	+	16.1920i	0.298808	+	0.820968i	−0.695892	+	0.718147i	$0.744991\pi$
$390$		0			0
$391$	−4.07471	−	7.05761i	−0.206067	−	0.356919i
$392$	3.14776	−	0.843439i	0.158986	−	0.0426001i
$393$	13.7261	+	19.6029i	0.692391	+	0.988837i
$394$	−13.1376	+	11.0237i	−0.661861	+	0.555367i
$395$		0			0
$396$	1.18340	+	6.71142i	0.0594683	+	0.337262i
$397$	20.4986	−	9.55867i	1.02880	−	0.479736i	0.166448	−	0.986050i	$-0.446770\pi$
$397$	20.4986	−	9.55867i	1.02880	−	0.479736i	0.862349	+	0.506314i	$0.168992\pi$
$398$	−16.9597	+	16.9597i	−0.850114	+	0.850114i
$399$	−0.240334	+	17.3860i	−0.0120317	+	0.870388i
$400$		0			0
$401$	−6.53098	+	17.9437i	−0.326141	+	0.896066i	0.662937	+	0.748675i	$0.269310\pi$
$401$	−6.53098	+	17.9437i	−0.326141	+	0.896066i	−0.989078	+	0.147391i	$0.952912\pi$
$402$	−2.33242	+	3.33104i	−0.116330	+	0.166137i
$403$	−4.40512	−	50.3507i	−0.219435	−	2.50815i
$404$	−6.30774	−	7.51727i	−0.313822	−	0.373998i
$405$		0			0
$406$	0.668545	−	1.15795i	0.0331793	−	0.0574683i
$407$	−6.70603	+	25.0273i	−0.332406	+	1.24055i
$408$	−11.0517	−	5.15350i	−0.547141	−	0.255136i
$409$	5.35396	−	1.94868i	0.264736	−	0.0963561i	−0.206242	−	0.978501i	$-0.566123\pi$
$409$	5.35396	−	1.94868i	0.264736	−	0.0963561i	0.470978	+	0.882145i	$0.343901\pi$
$410$		0			0
$411$	7.61786	+	4.39817i	0.375761	+	0.216946i
$412$	8.17067	−	5.72116i	0.402540	−	0.281861i
$413$	0.795513	−	9.09276i	0.0391446	−	0.447425i
$414$	1.32315	+	1.11026i	0.0650294	+	0.0545662i
$415$		0			0
$416$	5.68812	+	2.07031i	0.278883	+	0.101505i
$417$	−23.5432	−	23.5432i	−1.15292	−	1.15292i
$418$	6.45084	−	22.8090i	0.315521	−	1.11562i
$419$		−	25.4320i		−	1.24244i	−0.783638	−	0.621218i	$-0.786638\pi$
$419$		−	25.4320i		−	1.24244i	0.783638	−	0.621218i	$-0.213362\pi$
$420$		0			0
$421$	−16.0747	+	2.83440i	−0.783431	+	0.138140i	−0.551036	−	0.834481i	$-0.685767\pi$
$421$	−16.0747	+	2.83440i	−0.783431	+	0.138140i	−0.232395	+	0.972621i	$0.574656\pi$
$422$	−14.0784	+	1.23170i	−0.685327	+	0.0599584i
$423$	−1.56291	−	0.136737i	−0.0759914	−	0.00664839i
$424$	−2.17236	−	0.383047i	−0.105499	−	0.0186024i
$425$		0			0
$426$	7.38463	−	4.26352i	0.357786	−	0.206568i
$427$	7.66437	−	16.4363i	0.370905	−	0.795408i
$428$	−2.80225	+	6.00945i	−0.135452	+	0.290478i
$429$	−58.7909	+	33.9430i	−2.83845	+	1.63878i
$430$		0			0
$431$	−7.96091	−	1.40372i	−0.383464	−	0.0676150i	−0.0214065	−	0.999771i	$-0.506814\pi$
$431$	−7.96091	−	1.40372i	−0.383464	−	0.0676150i	−0.362057	+	0.932156i	$0.617926\pi$
$432$	−3.58875	−	0.313975i	−0.172664	−	0.0151061i
$433$	27.6292	−	2.41724i	1.32777	−	0.116165i	0.598906	−	0.800820i	$-0.295602\pi$
$433$	27.6292	−	2.41724i	1.32777	−	0.116165i	0.728868	+	0.684654i	$0.240047\pi$
$434$	−15.9051	+	2.80449i	−0.763468	+	0.134620i
$435$		0			0
$436$			0.508738i			0.0243641i
$437$	−2.46346	−	5.47940i	−0.117843	−	0.262115i
$438$	−16.2500	−	16.2500i	−0.776453	−	0.776453i
$439$	−15.8946	−	5.78516i	−0.758607	−	0.276111i	−0.0663844	−	0.997794i	$-0.521146\pi$
$439$	−15.8946	−	5.78516i	−0.758607	−	0.276111i	−0.692223	+	0.721684i	$0.743369\pi$
$440$		0			0
$441$	3.12850	+	2.62512i	0.148976	+	0.125006i
$442$	3.11942	−	35.6552i	0.148376	−	1.69594i
$443$	18.2132	−	12.7530i	0.865334	−	0.605913i	−0.0543722	−	0.998521i	$-0.517316\pi$
$443$	18.2132	−	12.7530i	0.865334	−	0.605913i	0.919706	+	0.392607i	$0.128427\pi$
$444$	8.50982	+	4.91315i	0.403858	+	0.233168i
$445$		0			0
$446$	−4.48626	+	1.63286i	−0.212430	+	0.0773183i
$447$	−33.0509	−	15.4119i	−1.56326	−	0.728958i
$448$	0.500613	−	1.86831i	0.0236517	−	0.0882695i
$449$	−18.2730	+	31.6497i	−0.862355	+	1.49364i	0.00729403	+	0.999973i	$0.497678\pi$
$449$	−18.2730	+	31.6497i	−0.862355	+	1.49364i	−0.869649	+	0.493670i	$0.835655\pi$
$450$		0			0
$451$	−24.9694	−	29.7574i	−1.17576	−	1.40122i
$452$	−0.319153	−	3.64793i	−0.0150117	−	0.171584i
$453$	27.4469	−	39.1983i	1.28957	−	1.84169i
$454$	−7.59276	+	20.8609i	−0.356346	+	0.979053i
$455$		0			0
$456$	−7.72226	−	4.60193i	−0.361628	−	0.215505i
$457$	15.7713	−	15.7713i	0.737752	−	0.737752i	−0.234391	−	0.972143i	$-0.575309\pi$
$457$	15.7713	−	15.7713i	0.737752	−	0.737752i	0.972143	+	0.234391i	$0.0753094\pi$
$458$	7.33728	−	3.42143i	0.342848	−	0.159873i
$459$	3.69883	+	20.9771i	0.172647	+	0.979127i
$460$		0			0
$461$	9.36537	−	7.85847i	0.436189	−	0.366006i	−0.398092	−	0.917345i	$-0.630328\pi$
$461$	9.36537	−	7.85847i	0.436189	−	0.366006i	0.834281	+	0.551340i	$0.185883\pi$
$462$	12.4421	+	17.7692i	0.578859	+	0.826696i
$463$	−27.3909	+	7.33938i	−1.27296	+	0.341090i	−0.831166	−	0.556025i	$-0.812326\pi$
$463$	−27.3909	+	7.33938i	−1.27296	+	0.341090i	−0.441798	+	0.897114i	$0.645659\pi$
$464$	0.345641	+	0.598667i	0.0160460	+	0.0277924i
$465$		0			0
$466$	−3.96679	−	10.8987i	−0.183758	−	0.504870i
$467$	−5.06288	−	1.35660i	−0.234282	−	0.0627757i	0.139768	−	0.990184i	$-0.455364\pi$
$467$	−5.06288	−	1.35660i	−0.234282	−	0.0627757i	−0.374050	+	0.927409i	$0.622031\pi$
$468$	1.96338	+	7.32742i	0.0907572	+	0.338710i
$469$	−0.662266	+	3.75590i	−0.0305806	+	0.173431i
$470$		0			0
$471$	−26.4068	+	31.4704i	−1.21676	+	1.45008i
$472$	3.86554	+	2.70668i	0.177926	+	0.124585i
$473$	21.1348	+	45.3237i	0.971778	+	2.08398i
$474$	−17.0721			−0.784147
$475$		0			0
$476$	−11.4367			−0.524201
$477$	−1.16830	−	2.50543i	−0.0534928	−	0.114716i
$478$	−17.9494	−	12.5683i	−0.820985	−	0.574860i
$479$	4.06967	−	4.85004i	0.185948	−	0.221604i	−0.665015	−	0.746830i	$-0.731575\pi$
$479$	4.06967	−	4.85004i	0.185948	−	0.221604i	0.850963	+	0.525226i	$0.176019\pi$
$480$		0			0
$481$	−5.00823	+	28.4031i	−0.228356	+	1.29507i
$482$	−7.33532	−	27.3758i	−0.334115	−	1.24693i
$483$	5.31055	+	1.42296i	0.241638	+	0.0647468i
$484$	−6.35190	−	17.4517i	−0.288723	−	0.793260i
$485$		0			0
$486$	−6.13413	−	10.6246i	−0.278250	−	0.481943i
$487$	−17.9726	+	4.81574i	−0.814415	+	0.218222i	−0.641903	−	0.766786i	$-0.721855\pi$
$487$	−17.9726	+	4.81574i	−0.814415	+	0.218222i	−0.172512	+	0.985007i	$0.555188\pi$
$488$	5.37791	+	7.68045i	0.243447	+	0.347678i
$489$	31.1586	−	26.1452i	1.40904	−	1.18233i
$490$		0			0
$491$	−2.85790	−	16.2079i	−0.128975	−	0.731454i	−0.978867	−	0.204497i	$-0.934444\pi$
$491$	−2.85790	−	16.2079i	−0.128975	−	0.731454i	0.849892	−	0.526957i	$-0.176667\pi$
$492$	−13.3517	+	6.22600i	−0.601941	+	0.280690i
$493$	2.89025	−	2.89025i	0.130170	−	0.130170i
$494$	4.94045	−	25.9185i	0.222282	−	1.16613i
$495$		0			0
$496$	2.85582	−	7.84629i	0.128230	−	0.352309i
$497$	4.58708	−	6.55103i	0.205759	−	0.293854i
$498$	−1.92848	−	22.0426i	−0.0864171	−	0.987752i
$499$	−1.87717	−	2.23713i	−0.0840339	−	0.100148i	0.722389	−	0.691487i	$-0.243044\pi$
$499$	−1.87717	−	2.23713i	−0.0840339	−	0.100148i	−0.806423	+	0.591339i	$0.798600\pi$
$500$		0			0
$501$	−9.57145	+	16.5782i	−0.427621	+	0.740661i
$502$	−4.51771	+	16.8603i	−0.201635	+	0.752513i
$503$	−30.9167	−	14.4167i	−1.37851	−	0.642808i	−0.414835	−	0.909897i	$-0.636161\pi$
$503$	−30.9167	−	14.4167i	−1.37851	−	0.642808i	−0.963672	+	0.267089i	$0.913938\pi$
$504$	2.27780	−	0.829053i	0.101461	−	0.0369289i
$505$		0			0
$506$	−6.49083	−	3.74748i	−0.288553	−	0.166596i
$507$	−39.9380	+	27.9649i	−1.77371	+	1.24196i
$508$	−0.457064	+	5.22426i	−0.0202789	+	0.231789i
$509$	1.24397	+	1.04382i	0.0551381	+	0.0462663i	0.669940	−	0.742415i	$-0.266320\pi$
$509$	1.24397	+	1.04382i	0.0551381	+	0.0462663i	−0.614802	+	0.788681i	$0.710764\pi$
$510$		0			0
$511$	−20.2535	−	7.37167i	−0.895962	−	0.326104i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	1.15223	+	15.6604i	0.0508724	+	0.691424i
$514$		−	26.7630i		−	1.18047i
$515$		0			0
$516$	18.6776	−	3.29336i	0.822235	−	0.144982i
$517$	6.78185	−	0.593335i	0.298266	−	0.0260949i
$518$	9.18081	+	0.803217i	0.403382	+	0.0352913i
$519$	−13.8938	−	2.44984i	−0.609868	−	0.107536i
$520$		0			0
$521$	17.4382	−	10.0680i	0.763983	−	0.441086i	−0.0667410	−	0.997770i	$-0.521260\pi$
$521$	17.4382	−	10.0680i	0.763983	−	0.441086i	0.830724	+	0.556685i	$0.187927\pi$
$522$	−0.366124	+	0.785155i	−0.0160248	+	0.0343653i
$523$	−0.602430	+	1.29191i	−0.0263424	+	0.0564915i	−0.919039	−	0.394167i	$-0.871033\pi$
$523$	−0.602430	+	1.29191i	−0.0263424	+	0.0564915i	0.892696	+	0.450659i	$0.148811\pi$
$524$	−10.0491	+	5.80187i	−0.438998	+	0.253456i
$525$		0			0
$526$	−4.15425	−	0.732506i	−0.181134	−	0.0319388i
$527$	−49.1834	−	4.30299i	−2.14246	−	0.187441i
$528$	−11.1723	+	0.977446i	−0.486210	+	0.0425379i
$529$	20.7798	−	3.66405i	0.903471	−	0.159306i
$530$		0			0
$531$			5.91385i			0.256639i
$532$	−8.38802	−	0.850837i	−0.363667	−	0.0368885i
$533$	−30.5752	−	30.5752i	−1.32436	−	1.32436i
$534$	−24.4798	−	8.90990i	−1.05934	−	0.385569i
$535$		0			0
$536$	−1.51046	−	1.26743i	−0.0652421	−	0.0547447i
$537$	−1.96162	+	22.4214i	−0.0846503	+	0.967557i
$538$	17.3486	−	12.1476i	0.747953	−	0.523722i
$539$	−15.3471	−	8.86065i	−0.661046	−	0.381655i
$540$		0			0
$541$	−6.01799	+	2.19037i	−0.258734	+	0.0941714i	−0.468130	−	0.883659i	$-0.655072\pi$
$541$	−6.01799	+	2.19037i	−0.258734	+	0.0941714i	0.209397	+	0.977831i	$0.432850\pi$
$542$	6.37909	+	2.97462i	0.274005	+	0.127771i
$543$	11.8986	−	44.4063i	0.510619	−	1.90566i
$544$	2.95642	−	5.12066i	0.126755	−	0.219547i
$545$		0			0
$546$	15.5208	+	18.4970i	0.664230	+	0.791598i
$547$	0.678395	+	7.75409i	0.0290061	+	0.331541i	0.996808	+	0.0798300i	$0.0254377\pi$
$547$	0.678395	+	7.75409i	0.0290061	+	0.331541i	−0.967802	+	0.251711i	$0.919007\pi$
$548$	−2.44644	+	3.49388i	−0.104507	+	0.149251i
$549$	−4.01882	+	11.0416i	−0.171519	+	0.471245i
$550$		0			0
$551$	2.33482	−	1.90477i	0.0994665	−	0.0811461i
$552$	−2.00990	+	2.00990i	−0.0855471	+	0.0855471i
$553$	−14.5114	+	6.76678i	−0.617088	+	0.287753i
$554$	0.987731	+	5.60170i	0.0419647	+	0.237993i
$555$		0			0
$556$	12.3674	−	10.3774i	0.524493	−	0.440102i
$557$	19.3015	+	27.5653i	0.817829	+	1.16798i	0.983340	+	0.181773i	$0.0581837\pi$
$557$	19.3015	+	27.5653i	0.817829	+	1.16798i	−0.165511	+	0.986208i	$0.552927\pi$
$558$	10.1076	−	2.70832i	0.427888	−	0.114652i
$559$	27.8332	+	48.2086i	1.17722	+	2.03901i
$560$		0			0
$561$	22.6801	+	62.3129i	0.957552	+	2.63085i
$562$	14.9179	+	3.99723i	0.629273	+	0.168613i
$563$	−4.93280	−	18.4095i	−0.207893	−	0.775866i	−0.988548	−	0.150905i	$-0.951781\pi$
$563$	−4.93280	−	18.4095i	−0.207893	−	0.775866i	0.780656	−	0.624962i	$-0.214885\pi$
$564$	0.448327	−	2.54259i	0.0188780	−	0.107062i
$565$		0			0
$566$	−2.33556	+	2.78342i	−0.0981710	+	0.116996i
$567$	−17.7282	−	12.4134i	−0.744515	−	0.521315i
$568$	1.74738	+	3.74727i	0.0733185	+	0.157232i
$569$	−5.28060			−0.221374			−0.110687	−	0.993855i	$-0.535305\pi$
$569$	−5.28060			−0.221374			−0.110687	+	0.993855i	$0.535305\pi$
$570$		0			0
$571$	2.38346			0.0997448			0.0498724	−	0.998756i	$-0.484119\pi$
$571$	2.38346			0.0997448			0.0498724	+	0.998756i	$0.484119\pi$
$572$	−13.9114	−	29.8330i	−0.581663	−	1.24738i
$573$	2.94041	+	2.05890i	0.122837	+	0.0860117i
$574$	−8.88127	+	10.5843i	−0.370697	+	0.441780i
$575$		0			0
$576$	−0.217618	+	1.23417i	−0.00906742	+	0.0514239i
$577$	3.32621	+	12.4136i	0.138472	+	0.516784i	0.999959	+	0.00900560i	$0.00286661\pi$
$577$	3.32621	+	12.4136i	0.138472	+	0.516784i	−0.861487	+	0.507779i	$0.830467\pi$
$578$	−17.3495	−	4.64880i	−0.721646	−	0.193364i
$579$	−3.67353	−	10.0929i	−0.152667	−	0.419448i
$580$		0			0
$581$	−10.3761	−	17.9720i	−0.430475	−	0.745604i
$582$	5.53588	−	1.48334i	0.229470	−	0.0614863i
$583$	6.88036	+	9.82617i	0.284955	+	0.406958i
$584$	8.53616	−	7.16269i	0.353229	−	0.296394i
$585$		0			0
$586$	3.82387	+	21.6863i	0.157963	+	0.895852i
$587$	−32.8562	+	15.3211i	−1.35612	+	0.632370i	−0.958477	−	0.285169i	$-0.907950\pi$
$587$	−32.8562	+	15.3211i	−1.35612	+	0.632370i	−0.397645	+	0.917539i	$0.630172\pi$
$588$	−4.75227	+	4.75227i	−0.195980	+	0.195980i
$589$	−35.7524	−	6.81495i	−1.47315	−	0.280805i
$590$		0			0
$591$	12.0968	−	33.2357i	0.497596	−	1.36714i
$592$	−2.73289	+	3.90297i	−0.112321	+	0.160411i
$593$	2.80399	+	32.0497i	0.115146	+	1.31612i	0.805475	+	0.592629i	$0.201910\pi$
$593$	2.80399	+	32.0497i	0.115146	+	1.31612i	−0.690329	+	0.723495i	$0.742534\pi$
$594$	12.5923	+	15.0069i	0.516668	+	0.615740i
$595$		0			0
$596$	8.84137	−	15.3137i	0.362157	−	0.627274i
$597$	12.8023	−	47.7789i	0.523964	−	1.95546i
$598$	−7.56119	−	3.52584i	−0.309200	−	0.144182i
$599$	−2.44672	+	0.890532i	−0.0999701	+	0.0363861i	−0.391521	−	0.920169i	$-0.628051\pi$
$599$	−2.44672	+	0.890532i	−0.0999701	+	0.0363861i	0.291551	+	0.956555i	$0.405829\pi$
$600$		0			0
$601$	−21.5436	−	12.4382i	−0.878782	−	0.507365i	−0.00852540	−	0.999964i	$-0.502714\pi$
$601$	−21.5436	−	12.4382i	−0.878782	−	0.507365i	−0.870257	+	0.492599i	$0.836047\pi$
$602$	14.5707	−	10.2025i	0.593858	−	0.415824i
$603$	0.215366	−	2.46165i	0.00877039	−	0.100246i
$604$	17.7745	+	14.9146i	0.723234	+	0.606866i
$605$		0			0
$606$	19.0174	+	6.92176i	0.772528	+	0.281177i
$607$	−2.18161	−	2.18161i	−0.0885487	−	0.0885487i	0.661445	−	0.749994i	$-0.269943\pi$
$607$	−2.18161	−	2.18161i	−0.0885487	−	0.0885487i	−0.749994	+	0.661445i	$0.769943\pi$
$608$	2.54928	−	3.53570i	0.103387	−	0.143392i
$609$			2.75752i			0.111740i
$610$		0			0
$611$	7.46277	−	1.31589i	0.301911	−	0.0532351i
$612$	7.38184	−	0.645827i	0.298393	−	0.0261060i
$613$	15.9276	+	1.39348i	0.643310	+	0.0562823i	0.404143	−	0.914696i	$-0.367570\pi$
$613$	15.9276	+	1.39348i	0.643310	+	0.0562823i	0.239167	+	0.970978i	$0.423126\pi$
$614$	0.578383	+	0.101985i	0.0233416	+	0.00411576i
$615$		0			0
$616$	−9.10908	+	5.25913i	−0.367015	+	0.211896i
$617$	11.4556	−	24.5667i	0.461186	−	0.989016i	−0.528917	−	0.848673i	$-0.677402\pi$
$617$	11.4556	−	24.5667i	0.461186	−	0.989016i	0.990103	−	0.140343i	$-0.0448204\pi$
$618$	−8.69360	+	18.6435i	−0.349708	+	0.749951i
$619$	29.5462	−	17.0585i	1.18756	−	0.685639i	0.229810	−	0.973235i	$-0.426189\pi$
$619$	29.5462	−	17.0585i	1.18756	−	0.685639i	0.957752	+	0.287596i	$0.0928561\pi$
$620$		0			0
$621$	4.88969	+	0.862184i	0.196217	+	0.0345983i
$622$	12.4790	+	1.09177i	0.500364	+	0.0437762i
$623$	−24.3396	+	2.12944i	−0.975144	+	0.0853140i
$624$	−12.2940	+	2.16776i	−0.492153	+	0.0867799i
$625$		0			0
$626$			13.5958i			0.543399i
$627$	11.9984	+	47.3894i	0.479171	+	1.89255i
$628$	−14.0856	−	14.0856i	−0.562077	−	0.562077i
$629$	26.4736	+	9.63559i	1.05557	+	0.384196i
$630$		0			0
$631$	10.5988	+	8.89349i	0.421933	+	0.354044i	0.828898	−	0.559400i	$-0.188968\pi$
$631$	10.5988	+	8.89349i	0.421933	+	0.354044i	−0.406965	+	0.913444i	$0.633413\pi$
$632$	0.721480	−	8.24655i	0.0286989	−	0.328030i
$633$	23.8744	−	16.7171i	0.948924	−	0.664443i
$634$	18.7484	+	10.8244i	0.744595	+	0.429892i
$635$		0			0
$636$	4.27490	−	1.55594i	0.169511	−	0.0616969i
$637$	−17.8779	−	8.33659i	−0.708347	−	0.330308i
$638$	0.972947	−	3.63109i	0.0385194	−	0.143756i
$639$	−2.59080	+	4.48740i	−0.102491	+	0.177519i
$640$		0			0
$641$	10.7706	+	12.8359i	0.425415	+	0.506989i	0.935594	−	0.353079i	$-0.114865\pi$
$641$	10.7706	+	12.8359i	0.425415	+	0.506989i	−0.510179	+	0.860068i	$0.670421\pi$
$642$	−1.19183	−	13.6227i	−0.0470377	−	0.537643i
$643$	5.31771	−	7.59447i	0.209710	−	0.299497i	−0.700493	−	0.713659i	$-0.747037\pi$
$643$	5.31771	−	7.59447i	0.209710	−	0.299497i	0.910203	+	0.414162i	$0.135925\pi$
$644$	−0.911777	+	2.50509i	−0.0359291	+	0.0987143i
$645$		0			0
$646$	−24.0949	−	9.14895i	−0.948003	−	0.359961i
$647$	17.3871	−	17.3871i	0.683557	−	0.683557i	−0.277243	−	0.960800i	$-0.589421\pi$
$647$	17.3871	−	17.3871i	0.683557	−	0.683557i	0.960800	+	0.277243i	$0.0894206\pi$
$648$	10.1408	−	4.72872i	0.398367	−	0.185762i
$649$	−4.45609	−	25.2718i	−0.174917	−	0.992003i
$650$		0			0
$651$	25.5151	−	21.4097i	1.00001	−	0.839112i
$652$	11.3125	+	16.1559i	0.443030	+	0.632713i
$653$	16.9196	−	4.53360i	0.662117	−	0.177414i	0.0879156	−	0.996128i	$-0.471979\pi$
$653$	16.9196	−	4.53360i	0.662117	−	0.177414i	0.574201	+	0.818714i	$0.305313\pi$
$654$	−0.524593	−	0.908621i	−0.0205132	−	0.0355299i
$655$		0			0
$656$	−2.44317	−	6.71255i	−0.0953898	−	0.262081i
$657$	13.4889	+	3.61435i	0.526253	+	0.141009i
$658$	−0.626711	−	2.33892i	−0.0244318	−	0.0911806i
$659$	3.83616	−	21.7559i	0.149435	−	0.847490i	−0.814263	−	0.580496i	$-0.802859\pi$
$659$	3.83616	−	21.7559i	0.149435	−	0.847490i	0.963698	−	0.266994i	$-0.0860304\pi$
$660$		0			0
$661$	11.8035	−	14.0669i	0.459104	−	0.547139i	−0.485979	−	0.873971i	$-0.661537\pi$
$661$	11.8035	−	14.0669i	0.459104	−	0.547139i	0.945082	+	0.326832i	$0.105981\pi$
$662$	20.9877	+	14.6958i	0.815711	+	0.571167i
$663$	31.1950	+	66.8979i	1.21151	+	2.59810i
$664$	10.7290			0.416367
$665$		0			0
$666$	−5.97112			−0.231376
$667$	−0.402656	−	0.863499i	−0.0155909	−	0.0334348i
$668$	−7.60350	−	5.32403i	−0.294188	−	0.205993i
$669$	6.32884	−	7.54242i	0.244687	−	0.291607i
$670$		0			0
$671$	8.85382	−	50.2125i	0.341798	−	1.93843i
$672$	1.03243	+	3.85308i	0.0398268	+	0.148636i
$673$	−25.8667	−	6.93096i	−0.997088	−	0.267169i	−0.276863	−	0.960909i	$-0.589295\pi$
$673$	−25.8667	−	6.93096i	−0.997088	−	0.267169i	−0.720225	+	0.693741i	$0.755961\pi$
$674$	0.0560825	+	0.154085i	0.00216022	+	0.00593515i
$675$		0			0
$676$	−11.8204	−	20.4736i	−0.454632	−	0.787446i
$677$	−14.2530	+	3.81909i	−0.547788	+	0.146779i	−0.522090	−	0.852890i	$-0.674848\pi$
$677$	−14.2530	+	3.81909i	−0.547788	+	0.146779i	−0.0256982	+	0.999670i	$0.508181\pi$
$678$	4.33164	+	6.18622i	0.166356	+	0.237581i
$679$	4.11760	−	3.45508i	0.158019	−	0.132594i
$680$		0			0
$681$	−7.95018	−	45.0877i	−0.304652	−	1.72776i
$682$	−41.1522	+	19.1896i	−1.57580	+	0.734807i
$683$	21.7958	−	21.7958i	0.833994	−	0.833994i	−0.154067	−	0.988060i	$-0.549237\pi$
$683$	21.7958	−	21.7958i	0.833994	−	0.833994i	0.988060	+	0.154067i	$0.0492371\pi$
$684$	5.46211	+	0.0755050i	0.208849	+	0.00288701i
$685$		0			0
$686$	−6.78662	+	18.6461i	−0.259114	+	0.711911i
$687$	−9.57655	+	13.6767i	−0.365368	+	0.521800i
$688$	0.801506	+	9.16126i	0.0305571	+	0.349270i
$689$	8.58285	+	10.2286i	0.326981	+	0.389680i
$690$		0			0
$691$	−25.6716	+	44.4646i	−0.976595	+	1.69151i	−0.302028	+	0.953299i	$0.597664\pi$
$691$	−25.6716	+	44.4646i	−0.976595	+	1.69151i	−0.674567	+	0.738214i	$0.735670\pi$
$692$	1.77054	−	6.60775i	0.0673059	−	0.251189i
$693$	−11.9466	−	5.57079i	−0.453814	−	0.211617i
$694$	20.1026	−	7.31675i	0.763085	−	0.277740i
$695$		0			0
$696$	−1.23465	−	0.712826i	−0.0467993	−	0.0270196i
$697$	−34.5989	+	24.2264i	−1.31053	+	0.917640i
$698$	0.621435	−	7.10304i	0.0235217	−	0.268854i
$699$	18.3231	+	15.3749i	0.693044	+	0.581533i
$700$		0			0
$701$	−34.2702	−	12.4733i	−1.29437	−	0.471112i	−0.399210	−	0.916860i	$-0.630716\pi$
$701$	−34.2702	−	12.4733i	−1.29437	−	0.471112i	−0.895159	+	0.445748i	$0.852938\pi$
$702$	15.4194	+	15.4194i	0.581966	+	0.581966i
$703$	18.6997	+	9.03653i	0.705271	+	0.340819i
$704$		−	5.43799i		−	0.204952i
$705$		0			0
$706$	11.7297	−	2.06826i	0.441454	−	0.0778402i
$707$	18.9085	−	1.65428i	0.711126	−	0.0622154i
$708$	−9.69501	−	0.848204i	−0.364361	−	0.0318775i
$709$	31.6128	+	5.57419i	1.18724	+	0.209343i	0.732177	−	0.681115i	$-0.238505\pi$
$709$	31.6128	+	5.57419i	1.18724	+	0.209343i	0.455066	+	0.890458i	$0.349616\pi$
$710$		0			0
$711$	8.98429	−	5.18708i	0.336937	−	0.194531i
$712$	5.33840	−	11.4482i	0.200065	−	0.429041i
$713$	−4.86360	+	10.4300i	−0.182143	+	0.390608i
$714$	20.4263	−	11.7931i	0.764436	−	0.441347i
$715$		0			0
$716$	−10.7476	−	1.89510i	−0.401657	−	0.0708231i
$717$	45.0181	+	3.93858i	1.68123	+	0.147089i
$718$	−1.77636	+	0.155412i	−0.0662933	+	0.00579991i
$719$	13.2135	−	2.32990i	0.492781	−	0.0868907i	0.0782652	−	0.996933i	$-0.475062\pi$
$719$	13.2135	−	2.32990i	0.492781	−	0.0868907i	0.414516	+	0.910042i	$0.363951\pi$
$720$		0			0
$721$			19.2930i			0.718507i
$722$	−16.9913	−	8.50266i	−0.632351	−	0.316436i
$723$	41.3301	+	41.3301i	1.53708	+	1.53708i
$724$	20.9473	+	7.62420i	0.778501	+	0.283351i
$725$		0			0
$726$	29.3403	+	24.6194i	1.08892	+	0.913713i
$727$	1.62646	−	18.5905i	0.0603221	−	0.689485i	−0.904481	−	0.426513i	$-0.859742\pi$
$727$	1.62646	−	18.5905i	0.0603221	−	0.689485i	0.964803	−	0.262972i	$-0.0847027\pi$
$728$	−9.59076	+	6.71552i	−0.355457	+	0.248894i
$729$	−7.15862	−	4.13303i	−0.265134	−	0.153075i
$730$		0			0
$731$	51.0966	−	18.5977i	1.88988	−	0.687859i
$732$	−17.5249	−	8.17201i	−0.647741	−	0.302046i
$733$	−10.5956	+	39.5433i	−0.391357	+	1.46057i	0.436539	+	0.899685i	$0.356204\pi$
$733$	−10.5956	+	39.5433i	−0.391357	+	1.46057i	−0.827897	+	0.560881i	$0.810463\pi$
$734$	−11.6768	+	20.2248i	−0.430998	+	0.746511i
$735$		0			0
$736$	−0.885929	−	1.05581i	−0.0326558	−	0.0389176i
$737$	0.934525	+	10.6817i	0.0344237	+	0.393464i
$738$	5.13474	−	7.33316i	0.189012	−	0.269937i
$739$	11.1308	−	30.5816i	0.409453	−	1.12496i	−0.548027	−	0.836461i	$-0.684621\pi$
$739$	11.1308	−	30.5816i	0.409453	−	1.12496i	0.957479	−	0.288502i	$-0.0931571\pi$
$740$		0			0
$741$	17.9025	+	51.3857i	0.657663	+	1.88770i
$742$	3.01698	−	3.01698i	0.110757	−	0.110757i
$743$	−24.1693	+	11.2703i	−0.886686	+	0.413469i	−0.811945	−	0.583734i	$-0.801591\pi$
$743$	−24.1693	+	11.2703i	−0.886686	+	0.413469i	−0.0747416	+	0.997203i	$0.523813\pi$
$744$	2.99025	+	16.9585i	0.109628	+	0.621731i
$745$		0			0
$746$	−7.68881	+	6.45168i	−0.281508	+	0.236213i
$747$	7.71216	+	11.0141i	0.282173	+	0.402985i
$748$	−31.0583	+	8.32204i	−1.13560	+	0.304284i
$749$	−6.41261	−	11.1070i	−0.234312	−	0.405840i
$750$		0			0
$751$	4.27189	+	11.7369i	0.155884	+	0.428287i	0.992909	−	0.118877i	$-0.0379296\pi$
$751$	4.27189	+	11.7369i	0.155884	+	0.428287i	−0.837025	+	0.547164i	$0.815707\pi$
$752$	1.20923	+	0.324013i	0.0440961	+	0.0118155i
$753$	−9.31702	−	34.7716i	−0.339531	−	1.26715i
$754$	0.726621	−	4.12087i	0.0264620	−	0.150073i
$755$		0			0
$756$	4.47890	−	5.33775i	0.162896	−	0.194132i
$757$	12.6755	+	8.87549i	0.460699	+	0.322585i	0.780781	−	0.624805i	$-0.214821\pi$
$757$	12.6755	+	8.87549i	0.460699	+	0.322585i	−0.320082	+	0.947390i	$0.603710\pi$
$758$	−0.239262	−	0.513100i	−0.00869040	−	0.0186366i
$759$	15.4571			0.561057
$760$		0			0
$761$	0.945561			0.0342766			0.0171383	−	0.999853i	$-0.494544\pi$
$761$	0.945561			0.0342766			0.0171383	+	0.999853i	$0.494544\pi$
$762$	−4.57075	−	9.80201i	−0.165581	−	0.355089i
$763$	−0.806054	−	0.564405i	−0.0291811	−	0.0204328i
$764$	−1.11880	+	1.33333i	−0.0404767	+	0.0482383i
$765$		0			0
$766$	6.55259	−	37.1616i	0.236755	−	1.34270i
$767$	−7.39307	−	27.5913i	−0.266948	−	0.996264i
$768$	−1.99206	−	0.533771i	−0.0718823	−	0.0192608i
$769$	−11.9299	−	32.7771i	−0.430202	−	1.18197i	−0.945689	−	0.325074i	$-0.894611\pi$
$769$	−11.9299	−	32.7771i	−0.430202	−	1.18197i	0.515486	−	0.856898i	$-0.327611\pi$
$770$		0			0
$771$	27.5971	+	47.7996i	0.993886	+	1.72146i
$772$	5.03057	−	1.34794i	0.181054	−	0.0485133i
$773$	30.0468	+	42.9113i	1.08071	+	1.54341i	0.815090	+	0.579334i	$0.196687\pi$
$773$	30.0468	+	42.9113i	1.08071	+	1.54341i	0.265619	+	0.964078i	$0.414424\pi$
$774$	−8.82856	+	7.40804i	−0.317336	+	0.266276i
$775$		0			0
$776$	0.482564	+	2.73676i	0.0173230	+	0.0982438i
$777$	−17.2255	+	8.03237i	−0.617960	+	0.288160i
$778$	12.1843	−	12.1843i	0.436828	−	0.436828i
$779$	−27.1782	+	15.1944i	−0.973759	+	0.544395i
$780$		0			0
$781$	7.69005	−	21.1282i	0.275172	−	0.756028i
$782$	−4.67432	+	6.67562i	−0.167153	+	0.238720i
$783$	0.217045	+	2.48083i	0.00775655	+	0.0886578i
$784$	−2.09471	−	2.49638i	−0.0748112	−	0.0891565i
$785$		0			0
$786$	11.9654	−	20.7246i	0.426791	−	0.739224i
$787$	11.8637	−	44.2758i	0.422894	−	1.57826i	−0.345586	−	0.938387i	$-0.612320\pi$
$787$	11.8637	−	44.2758i	0.422894	−	1.57826i	0.768480	−	0.639874i	$-0.221013\pi$
$788$	15.5431	+	7.24785i	0.553699	+	0.258194i
$789$	8.17495	−	2.97544i	0.291036	−	0.105928i
$790$		0			0
$791$	6.13393	+	3.54143i	0.218097	+	0.125919i
$792$	5.58249	−	3.90890i	0.198365	−	0.138897i
$793$	4.94654	−	56.5392i	0.175657	−	2.00776i
$794$	−17.3262	−	14.5384i	−0.614884	−	0.515949i
$795$		0			0
$796$	22.5382	+	8.20324i	0.798846	+	0.290756i
$797$	23.8634	+	23.8634i	0.845286	+	0.845286i	0.989541	−	0.144255i	$-0.0460785\pi$
$797$	23.8634	+	23.8634i	0.845286	+	0.845286i	−0.144255	+	0.989541i	$0.546078\pi$
$798$	15.8586	−	7.12982i	0.561389	−	0.252393i
$799$		−	7.40221i		−	0.261871i
$800$		0			0
$801$	15.5897	−	2.74889i	0.550837	−	0.0971273i
$802$	19.0226	−	1.66427i	0.671713	−	0.0587672i
$803$	−60.3658	−	5.28133i	−2.13026	−	0.186374i
$804$	4.00467	+	0.706131i	0.141234	+	0.0249033i
$805$		0			0
$806$	−43.7716	+	25.2715i	−1.54179	+	0.890152i
$807$	−18.4590	+	39.5854i	−0.649787	+	1.39347i
$808$	−4.14719	+	8.89369i	−0.145898	+	0.312879i
$809$	1.15512	−	0.666909i	0.0406119	−	0.0234473i	−0.479557	−	0.877511i	$-0.659202\pi$
$809$	1.15512	−	0.666909i	0.0406119	−	0.0234473i	0.520168	+	0.854064i	$0.325869\pi$
$810$		0			0
$811$	6.05406	+	1.06749i	0.212587	+	0.0374848i	0.278927	−	0.960312i	$-0.410021\pi$
$811$	6.05406	+	1.06749i	0.212587	+	0.0374848i	−0.0663403	+	0.997797i	$0.521132\pi$
$812$	−1.33200	−	0.116535i	−0.0467441	−	0.00408958i
$813$	−14.4606	+	1.26514i	−0.507155	+	0.0443703i
$814$	25.5165	−	4.49924i	0.894352	−	0.157698i
$815$		0			0
$816$			12.1942i			0.426883i
$817$	38.8594	−	9.83872i	1.35952	−	0.344213i
$818$	−4.02879	−	4.02879i	−0.140863	−	0.140863i
$819$	−13.7879	−	5.01840i	−0.481789	−	0.175357i
$820$		0			0
$821$	−25.2415	−	21.1801i	−0.880935	−	0.739192i	0.0854364	−	0.996344i	$-0.472772\pi$
$821$	−25.2415	−	21.1801i	−0.880935	−	0.739192i	−0.966371	+	0.257152i	$0.917216\pi$
$822$	0.766652	−	8.76287i	0.0267401	−	0.305640i
$823$	37.2660	−	26.0939i	1.29901	−	0.909577i	0.299995	−	0.953941i	$-0.403015\pi$
$823$	37.2660	−	26.0939i	1.29901	−	0.909577i	0.999015	+	0.0443640i	$0.0141261\pi$
$824$	−8.63821	−	4.98727i	−0.300926	−	0.173740i
$825$		0			0
$826$	−8.57703	+	3.12179i	−0.298433	+	0.108621i
$827$	14.8727	+	6.93526i	0.517175	+	0.241163i	0.663639	−	0.748053i	$-0.269011\pi$
$827$	14.8727	+	6.93526i	0.517175	+	0.241163i	−0.146463	+	0.989216i	$0.546789\pi$
$828$	0.447046	−	1.66840i	0.0155359	−	0.0579809i
$829$	−10.8189	+	18.7389i	−0.375757	+	0.650830i	−0.990440	−	0.137944i	$-0.955951\pi$
$829$	−10.8189	+	18.7389i	−0.375757	+	0.650830i	0.614683	+	0.788774i	$0.289284\pi$
$830$		0			0
$831$	−7.54040	−	8.98630i	−0.261574	−	0.311731i
$832$	−0.527568	−	6.03014i	−0.0182901	−	0.209057i
$833$	−11.0521	+	15.7840i	−0.382932	+	0.546883i
$834$	−11.3876	+	31.2872i	−0.394321	+	1.08339i
$835$		0			0
$836$	−23.3982	+	3.79304i	−0.809244	+	0.131185i
$837$	21.2697	−	21.2697i	0.735190	−	0.735190i
$838$	−23.0493	+	10.7480i	−0.796223	+	0.371285i
$839$	7.00820	+	39.7455i	0.241950	+	1.37217i	0.827470	+	0.561509i	$0.189779\pi$
$839$	7.00820	+	39.7455i	0.241950	+	1.37217i	−0.585520	+	0.810658i	$0.699110\pi$
$840$		0			0
$841$	−21.8492	+	18.3337i	−0.753421	+	0.632196i
$842$	9.36228	+	13.3707i	0.322646	+	0.460786i
$843$	−30.7656	+	8.24362i	−1.05962	+	0.283925i
$844$	7.06610	+	12.2389i	0.243225	+	0.421279i
$845$		0			0
$846$	0.536590	+	1.47427i	0.0184483	+	0.0506864i
$847$	34.6978	+	9.29724i	1.19223	+	0.319457i
$848$	0.570923	+	2.13071i	0.0196056	+	0.0731690i
$849$	1.30123	−	7.37962i	0.0446580	−	0.253268i
$850$		0			0
$851$	4.22114	−	5.03056i	0.144699	−	0.172445i
$852$	−6.98494	−	4.89090i	−0.239300	−	0.167560i
$853$	23.0000	+	49.3237i	0.787506	+	1.68881i	0.722952	+	0.690898i	$0.242785\pi$
$853$	23.0000	+	49.3237i	0.787506	+	1.68881i	0.0645545	+	0.997914i	$0.479437\pi$
$854$	−18.1354			−0.620582
$855$		0			0
$856$	6.63069			0.226632
$857$	−17.8256	−	38.2271i	−0.608911	−	1.30581i	−0.933031	−	0.359797i	$-0.882846\pi$
$857$	−17.8256	−	38.2271i	−0.608911	−	1.30581i	0.324120	−	0.946016i	$-0.394932\pi$
$858$	55.6089	+	38.9378i	1.89846	+	1.32931i
$859$	7.04550	−	8.39650i	0.240389	−	0.286485i	−0.632338	−	0.774692i	$-0.717905\pi$
$859$	7.04550	−	8.39650i	0.240389	−	0.286485i	0.872728	+	0.488208i	$0.162349\pi$
$860$		0			0
$861$	4.94808	−	28.0619i	0.168630	−	0.956348i
$862$	2.09222	+	7.80828i	0.0712614	+	0.265951i
$863$	−36.0415	−	9.65728i	−1.22687	−	0.328738i	−0.413508	−	0.910501i	$-0.635697\pi$
$863$	−36.0415	−	9.65728i	−1.22687	−	0.328738i	−0.813358	+	0.581763i	$0.802363\pi$
$864$	1.23211	+	3.38520i	0.0419173	+	0.115167i
$865$		0			0
$866$	−13.8674	−	24.0190i	−0.471232	−	0.816198i
$867$	35.7805	−	9.58736i	1.21517	−	0.325604i
$868$	9.26351	+	13.2297i	0.314424	+	0.449044i
$869$	−34.4842	+	28.9357i	−1.16980	+	0.981576i
$870$		0			0
$871$	2.07257	+	11.7541i	0.0702264	+	0.398274i
$872$	0.461073	−	0.215002i	0.0156139	−	0.00728088i
$873$	−2.46260	+	2.46260i	−0.0833465	+	0.0833465i
$874$	−3.92492	+	4.54835i	−0.132762	+	0.153850i
$875$		0			0
$876$	−7.85993	+	21.5950i	−0.265563	+	0.729627i
$877$	−15.1352	+	21.6153i	−0.511080	+	0.729897i	−0.988904	−	0.148558i	$-0.952537\pi$
$877$	−15.1352	+	21.6153i	−0.511080	+	0.729897i	0.477824	+	0.878456i	$0.341426\pi$
$878$	1.47421	+	16.8503i	0.0497522	+	0.568670i
$879$	−29.1917	−	34.7893i	−0.984612	−	1.17341i
$880$		0			0
$881$	26.2397	−	45.4484i	0.884037	−	1.53120i	0.0372235	−	0.999307i	$-0.488149\pi$
$881$	26.2397	−	45.4484i	0.884037	−	1.53120i	0.846813	−	0.531890i	$-0.178518\pi$
$882$	1.05701	−	3.94481i	0.0355913	−	0.132829i
$883$	4.12314	+	1.92265i	0.138755	+	0.0647024i	0.490756	−	0.871297i	$-0.336721\pi$
$883$	4.12314	+	1.92265i	0.138755	+	0.0647024i	−0.352001	+	0.936000i	$0.614499\pi$
$884$	−33.6329	+	12.2414i	−1.13120	+	0.411722i
$885$		0			0
$886$	−19.2554	−	11.1171i	−0.646897	−	0.373486i
$887$	45.4533	−	31.8268i	1.52617	−	1.06864i	0.554537	−	0.832159i	$-0.312895\pi$
$887$	45.4533	−	31.8268i	1.52617	−	1.06864i	0.971636	−	0.236480i	$-0.0759936\pi$
$888$	0.856418	−	9.78890i	0.0287395	−	0.328494i
$889$	−7.77035	−	6.52010i	−0.260609	−	0.218677i
$890$		0			0
$891$	−57.1767	−	20.8106i	−1.91549	−	0.697182i
$892$	3.37585	+	3.37585i	0.113032	+	0.113032i
$893$	0.550689	−	5.42900i	0.0184281	−	0.181675i
$894$			36.4677i			1.21966i
$895$		0			0
$896$	−1.90483	+	0.335874i	−0.0636360	+	0.0112207i
$897$	17.1402	−	1.49958i	0.572296	−	0.0500694i
$898$	36.4069	+	3.18519i	1.21491	+	0.106291i
$899$	−5.68440	−	1.00231i	−0.189586	−	0.0334290i
$900$		0			0
$901$	11.2956	−	6.52149i	0.376309	−	0.217262i
$902$	−16.4168	+	35.2059i	−0.546620	+	1.17223i
$903$	−15.5033	+	33.2469i	−0.515917	+	1.10639i
$904$	−3.17127	+	1.83093i	−0.105475	+	0.0608960i
$905$		0			0
$906$	−47.1252	−	8.30945i	−1.56563	−	0.276063i
$907$	13.8328	+	1.21021i	0.459310	+	0.0401844i	0.314463	−	0.949270i	$-0.398176\pi$
$907$	13.8328	+	1.21021i	0.459310	+	0.0401844i	0.144847	+	0.989454i	$0.453731\pi$
$908$	22.1153	−	1.93484i	0.733921	−	0.0642098i
$909$	−12.1111	+	2.13551i	−0.401699	+	0.0708303i
$910$		0			0
$911$			20.9077i			0.692704i	0.938105	+	0.346352i	$0.112580\pi$
$911$			20.9077i			0.692704i	−0.938105	+	0.346352i	$0.887420\pi$
$912$	−0.907192	+	8.94360i	−0.0300401	+	0.296152i
$913$	−41.2556	−	41.2556i	−1.36536	−	1.36536i
$914$	−20.9589	−	7.62843i	−0.693260	−	0.252326i
$915$		0			0
$916$	−6.20174	−	5.20387i	−0.204911	−	0.171941i
$917$	1.95614	−	22.3588i	0.0645974	−	0.738351i
$918$	17.4485	−	12.2176i	0.575887	−	0.403240i
$919$	15.0990	+	8.71740i	0.498070	+	0.287561i	0.727916	−	0.685666i	$-0.240489\pi$
$919$	15.0990	+	8.71740i	0.498070	+	0.287561i	−0.229846	+	0.973227i	$0.573822\pi$
$920$		0			0
$921$	−1.13817	+	0.414261i	−0.0375041	+	0.0136504i
$922$	−11.0802	−	5.16677i	−0.364906	−	0.170158i
$923$	6.47766	−	24.1750i	0.213215	−	0.795729i
$924$	10.8461	−	18.7860i	0.356810	−	0.618012i
$925$		0			0
$926$	18.2276	+	21.7229i	0.598997	+	0.713857i
$927$	−1.08947	−	12.4527i	−0.0357828	−	0.408999i
$928$	0.396503	−	0.566265i	0.0130158	−	0.0185885i
$929$	8.68224	−	23.8543i	0.284855	−	0.782633i	−0.711911	−	0.702270i	$-0.752170\pi$
$929$	8.68224	−	23.8543i	0.284855	−	0.782633i	0.996766	−	0.0803626i	$-0.0256078\pi$
$930$		0			0
$931$	−9.28018	+	10.7542i	−0.304146	+	0.352456i
$932$	−8.20110	+	8.20110i	−0.268636	+	0.268636i
$933$	−23.4138	+	10.9180i	−0.766532	+	0.357440i
$934$	0.910174	+	5.16185i	0.0297818	+	0.168901i
$935$		0			0
$936$	5.81114	−	4.87613i	0.189943	−	0.159381i
$937$	3.67567	+	5.24940i	0.120079	+	0.171491i	0.874691	−	0.484680i	$-0.161064\pi$
$937$	3.67567	+	5.24940i	0.120079	+	0.171491i	−0.754612	+	0.656171i	$0.772175\pi$
$938$	3.68389	−	0.987094i	0.120283	−	0.0322298i
$939$	−14.0196	−	24.2826i	−0.457511	−	0.792432i
$940$		0			0
$941$	−7.30833	−	20.0795i	−0.238245	−	0.654572i	−0.999978	−	0.00668078i	$-0.997873\pi$
$941$	−7.30833	−	20.0795i	−0.238245	−	0.654572i	0.761733	−	0.647891i	$-0.224349\pi$
$942$	39.6819	+	10.6327i	1.29291	+	0.346433i
$943$	2.54818	+	9.50993i	0.0829801	+	0.309686i
$944$	0.819438	−	4.64726i	0.0266704	−	0.151255i
$945$		0			0
$946$	32.1452	−	38.3092i	1.04513	−	1.24554i
$947$	41.3288	+	28.9387i	1.34300	+	0.940382i	0.999999	+	0.00104850i	$0.000333747\pi$
$947$	41.3288	+	28.9387i	1.34300	+	0.940382i	0.343005	+	0.939333i	$0.388555\pi$
$948$	7.21498	+	15.4726i	0.234332	+	0.502526i
$949$	−67.4515			−2.18957
$950$		0			0
$951$	−44.6470			−1.44778
$952$	4.83336	+	10.3652i	0.156650	+	0.335937i
$953$	12.4736	+	8.73414i	0.404061	+	0.282927i	0.757888	−	0.652384i	$-0.226231\pi$
$953$	12.4736	+	8.73414i	0.404061	+	0.282927i	−0.353827	+	0.935311i	$0.615120\pi$
$954$	−1.77694	+	2.11768i	−0.0575307	+	0.0685624i
$955$		0			0
$956$	−3.80500	+	21.5792i	−0.123063	+	0.697922i
$957$	2.00654	+	7.48851i	0.0648622	+	0.242069i
$958$	−6.11555	−	1.63866i	−0.197584	−	0.0529426i
$959$	−2.82164	−	7.75238i	−0.0911154	−	0.250337i
$960$		0			0
$961$	19.3600	+	33.5325i	0.624516	+	1.08169i
$962$	27.8585	−	7.46466i	0.898194	−	0.240670i
$963$	4.76623	+	6.80688i	0.153590	+	0.219349i
$964$	−21.7109	+	18.2176i	−0.699260	+	0.586749i
$965$		0			0
$966$	−0.954697	−	5.41436i	−0.0307169	−	0.174204i
$967$	39.6889	−	18.5073i	1.27631	−	0.595153i	0.338065	−	0.941123i	$-0.390228\pi$
$967$	39.6889	−	18.5073i	1.27631	−	0.595153i	0.938246	+	0.345969i	$0.112450\pi$
$968$	−13.1322	+	13.1322i	−0.422085	+	0.422085i
$969$	52.4684	−	8.50557i	1.68553	−	0.273238i
$970$		0			0
$971$	1.59506	−	4.38240i	0.0511880	−	0.140638i	−0.911464	−	0.411380i	$-0.865047\pi$
$971$	1.59506	−	4.38240i	0.0511880	−	0.140638i	0.962652	+	0.270742i	$0.0872691\pi$
$972$	−7.03679	+	10.0496i	−0.225705	+	0.322340i
$973$	2.72160	+	31.1080i	0.0872505	+	0.997278i
$974$	11.9601	+	14.2535i	0.383225	+	0.456710i
$975$		0			0
$976$	4.68805	−	8.11994i	0.150061	−	0.259913i
$977$	−8.12751	+	30.3323i	−0.260022	+	0.970415i	0.705205	+	0.709003i	$0.250855\pi$
$977$	−8.12751	+	30.3323i	−0.260022	+	0.970415i	−0.965227	+	0.261412i	$0.915812\pi$
$978$	−36.8638	−	17.1899i	−1.17877	−	0.549672i
$979$	−64.5486	+	23.4938i	−2.06298	+	0.750864i
$980$		0			0
$981$	0.552140	+	0.318778i	0.0176285	+	0.0101778i
$982$	−13.4816	+	9.43991i	−0.430215	+	0.301240i
$983$	1.50479	−	17.1998i	0.0479953	−	0.548589i	−0.933690	−	0.358081i	$-0.883431\pi$
$983$	1.50479	−	17.1998i	0.0479953	−	0.548589i	0.981686	−	0.190508i	$-0.0610134\pi$
$984$	11.2853	+	9.46952i	0.359763	+	0.301877i
$985$		0			0
$986$	−3.84093	−	1.39798i	−0.122320	−	0.0445209i
$987$	3.53114	+	3.53114i	0.112397	+	0.112397i
$988$	−25.5781	+	6.47606i	−0.813746	+	0.206031i
$989$		−	12.6748i		−	0.403036i
$990$		0			0
$991$	29.0906	−	5.12946i	0.924094	−	0.162943i	0.308697	−	0.951160i	$-0.400107\pi$
$991$	29.0906	−	5.12946i	0.924094	−	0.162943i	0.615396	+	0.788218i	$0.288996\pi$
$992$	−8.31808	+	0.727737i	−0.264099	+	0.0231057i
$993$	−52.6385	−	4.60527i	−1.67043	−	0.146144i
$994$	−7.87583	−	1.38872i	−0.249806	−	0.0440476i
$995$		0			0
$996$	−19.1624	+	11.0634i	−0.607183	+	0.350557i
$997$	3.58935	−	7.69739i	0.113676	−	0.243779i	−0.841236	−	0.540668i	$-0.818171\pi$
$997$	3.58935	−	7.69739i	0.113676	−	0.243779i	0.954912	+	0.296889i	$0.0959492\pi$
$998$	−1.23420	+	2.64675i	−0.0390679	+	0.0837814i
$999$	−14.8648	+	8.58222i	−0.470303	+	0.271529i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.d.243.4	✓	96
5.2	odd	4	inner	950.2.bb.d.357.8	yes	96
5.3	odd	4	inner	950.2.bb.d.357.1	yes	96
5.4	even	2	inner	950.2.bb.d.243.5	yes	96
19.14	odd	18	inner	950.2.bb.d.793.8	yes	96
95.14	odd	18	inner	950.2.bb.d.793.1	yes	96
95.33	even	36	inner	950.2.bb.d.907.5	yes	96
95.52	even	36	inner	950.2.bb.d.907.4	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.bb.d.243.4	✓	96	1.1	even	1	trivial
950.2.bb.d.243.5	yes	96	5.4	even	2	inner
950.2.bb.d.357.1	yes	96	5.3	odd	4	inner
950.2.bb.d.357.8	yes	96	5.2	odd	4	inner
950.2.bb.d.793.1	yes	96	95.14	odd	18	inner
950.2.bb.d.793.8	yes	96	19.14	odd	18	inner
950.2.bb.d.907.4	yes	96	95.52	even	36	inner
950.2.bb.d.907.5	yes	96	95.33	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)

\(f(q)\)	\(=\)	\(q+(-0.422618 - 0.906308i) q^{2} +(1.68936 + 1.18290i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(0.358120 - 2.03100i) q^{6} +(-0.500613 - 1.86831i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.428624 + 1.17763i) q^{9} +O(q^{10})\)	\(q+(-0.422618 - 0.906308i) q^{2} +(1.68936 + 1.18290i) q^{3} +(-0.642788 + 0.766044i) q^{4} +(0.358120 - 2.03100i) q^{6} +(-0.500613 - 1.86831i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.428624 + 1.17763i) q^{9} +(-2.71899 - 4.70944i) q^{11} +(-1.99206 + 0.533771i) q^{12} +(-3.47196 - 4.95847i) q^{13} +(-1.48170 + 1.24329i) q^{14} +(-0.173648 - 0.984808i) q^{16} +(-5.35884 + 2.49887i) q^{17} +(0.886155 - 0.886155i) q^{18} +(-4.11624 + 1.43407i) q^{19} +(1.36432 - 3.74844i) q^{21} +(-3.11910 + 4.45454i) q^{22} +(0.120123 + 1.37302i) q^{23} +(1.32564 + 1.57984i) q^{24} +(-3.02658 + 5.24220i) q^{26} +(0.932384 - 3.47970i) q^{27} +(1.75300 + 0.817436i) q^{28} +(-0.649592 + 0.236432i) q^{29} +(7.23118 + 4.17493i) q^{31} +(-0.819152 + 0.573576i) q^{32} +(0.977446 - 11.1723i) q^{33} +(4.52949 + 3.80069i) q^{34} +(-1.17763 - 0.428624i) q^{36} +(-3.36912 - 3.36912i) q^{37} +(3.03931 + 3.12452i) q^{38} -12.4836i q^{39} +(7.03483 - 1.24043i) q^{41} +(-3.97382 + 0.347664i) q^{42} +(-9.16126 - 0.801506i) q^{43} +(5.35537 + 0.944297i) q^{44} +(1.19361 - 0.689130i) q^{46} +(-0.529071 + 1.13460i) q^{47} +(0.871579 - 1.86911i) q^{48} +(2.82220 - 1.62940i) q^{49} +(-12.0090 - 2.11750i) q^{51} +(6.03014 + 0.527568i) q^{52} +(-2.19748 + 0.192255i) q^{53} +(-3.54773 + 0.625560i) q^{54} -1.93422i q^{56} +(-8.65020 - 2.44645i) q^{57} +(0.488810 + 0.488810i) q^{58} +(4.43437 + 1.61398i) q^{59} +(7.18251 + 6.02684i) q^{61} +(0.727737 - 8.31808i) q^{62} +(1.98561 - 1.39034i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-10.5386 + 3.83573i) q^{66} +(-1.78703 - 0.833307i) q^{67} +(1.53035 - 5.71136i) q^{68} +(-1.42122 + 2.46162i) q^{69} +(2.65771 + 3.16733i) q^{71} +(0.109225 + 1.24844i) q^{72} +(6.39146 - 9.12795i) q^{73} +(-1.62961 + 4.47731i) q^{74} +(1.54730 - 4.07503i) q^{76} +(-7.43753 + 7.43753i) q^{77} +(-11.3140 + 5.27582i) q^{78} +(-1.43747 - 8.15229i) q^{79} +(8.57134 - 7.19221i) q^{81} +(-4.09726 - 5.85149i) q^{82} +(10.3634 - 2.77687i) q^{83} +(1.99450 + 3.45458i) q^{84} +(3.14530 + 8.64165i) q^{86} +(-1.37707 - 0.368986i) q^{87} +(-1.40746 - 5.25269i) q^{88} +(2.19348 - 12.4398i) q^{89} +(-7.52586 + 8.96897i) q^{91} +(-1.12901 - 0.790538i) q^{92} +(7.27755 + 15.6068i) q^{93} +1.25189 q^{94} -2.06233 q^{96} +(1.17445 + 2.51861i) q^{97} +(-2.66945 - 1.86917i) q^{98} +(4.38057 - 5.22056i) 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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