LMFDB - Embedded newform 429.2.m.b.109.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(109,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("429.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.m (of order $4$, degree $2$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.6
Character	$\chi$	$=$	429.109
Dual form			429.2.m.b.307.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.555689 - 0.555689i) q^{2} +1.00000 q^{3} -1.38242i q^{4} +(-2.09993 + 2.09993i) q^{5} +(-0.555689 - 0.555689i) q^{6} +(-1.20106 + 1.20106i) q^{7} +(-1.87957 + 1.87957i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.555689 - 0.555689i) q^{2} +1.00000 q^{3} -1.38242i q^{4} +(-2.09993 + 2.09993i) q^{5} +(-0.555689 - 0.555689i) q^{6} +(-1.20106 + 1.20106i) q^{7} +(-1.87957 + 1.87957i) q^{8} +1.00000 q^{9} +2.33382 q^{10} +(-0.0298401 + 3.31649i) q^{11} -1.38242i q^{12} +(-3.57354 - 0.479383i) q^{13} +1.33483 q^{14} +(-2.09993 + 2.09993i) q^{15} -0.675922 q^{16} -3.86461 q^{17} +(-0.555689 - 0.555689i) q^{18} +(2.60902 + 2.60902i) q^{19} +(2.90299 + 2.90299i) q^{20} +(-1.20106 + 1.20106i) q^{21} +(1.85952 - 1.82636i) q^{22} +5.37795i q^{23} +(-1.87957 + 1.87957i) q^{24} -3.81943i q^{25} +(1.71939 + 2.25217i) q^{26} +1.00000 q^{27} +(1.66037 + 1.66037i) q^{28} -4.16393i q^{29} +2.33382 q^{30} +(0.241306 - 0.241306i) q^{31} +(4.13475 + 4.13475i) q^{32} +(-0.0298401 + 3.31649i) q^{33} +(2.14752 + 2.14752i) q^{34} -5.04429i q^{35} -1.38242i q^{36} +(-6.52671 - 6.52671i) q^{37} -2.89961i q^{38} +(-3.57354 - 0.479383i) q^{39} -7.89395i q^{40} +(5.68971 + 5.68971i) q^{41} +1.33483 q^{42} +3.01228 q^{43} +(4.58478 + 0.0412515i) q^{44} +(-2.09993 + 2.09993i) q^{45} +(2.98847 - 2.98847i) q^{46} +(-4.24006 - 4.24006i) q^{47} -0.675922 q^{48} +4.11491i q^{49} +(-2.12241 + 2.12241i) q^{50} -3.86461 q^{51} +(-0.662709 + 4.94013i) q^{52} -1.36521 q^{53} +(-0.555689 - 0.555689i) q^{54} +(-6.90174 - 7.02707i) q^{55} -4.51496i q^{56} +(2.60902 + 2.60902i) q^{57} +(-2.31385 + 2.31385i) q^{58} +(5.42554 + 5.42554i) q^{59} +(2.90299 + 2.90299i) q^{60} +3.66021i q^{61} -0.268183 q^{62} +(-1.20106 + 1.20106i) q^{63} -3.24343i q^{64} +(8.51086 - 6.49752i) q^{65} +(1.85952 - 1.82636i) q^{66} +(-1.05880 + 1.05880i) q^{67} +5.34251i q^{68} +5.37795i q^{69} +(-2.80305 + 2.80305i) q^{70} +(-8.20263 + 8.20263i) q^{71} +(-1.87957 + 1.87957i) q^{72} +(-1.13276 + 1.13276i) q^{73} +7.25364i q^{74} -3.81943i q^{75} +(3.60677 - 3.60677i) q^{76} +(-3.94746 - 4.01914i) q^{77} +(1.71939 + 2.25217i) q^{78} -12.8821i q^{79} +(1.41939 - 1.41939i) q^{80} +1.00000 q^{81} -6.32342i q^{82} +(-7.95292 - 7.95292i) q^{83} +(1.66037 + 1.66037i) q^{84} +(8.11541 - 8.11541i) q^{85} +(-1.67389 - 1.67389i) q^{86} -4.16393i q^{87} +(-6.17750 - 6.28967i) q^{88} +(-4.96133 - 4.96133i) q^{89} +2.33382 q^{90} +(4.86780 - 3.71627i) q^{91} +7.43458 q^{92} +(0.241306 - 0.241306i) q^{93} +4.71231i q^{94} -10.9575 q^{95} +(4.13475 + 4.13475i) q^{96} +(1.81204 - 1.81204i) q^{97} +(2.28661 - 2.28661i) q^{98} +(-0.0298401 + 3.31649i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 28 q^{3} - 4 q^{5} + 28 q^{9}+O(q^{10}) $ 28 * q + 28 * q^3 - 4 * q^5 + 28 * q^9	$ 28 q + 28 q^{3} - 4 q^{5} + 28 q^{9} - 4 q^{15} - 20 q^{16} - 16 q^{20} - 8 q^{22} + 12 q^{26} + 28 q^{27} + 8 q^{31} - 32 q^{34} - 12 q^{37} + 36 q^{44} - 4 q^{45} - 40 q^{47} - 20 q^{48} + 8 q^{53} - 16 q^{55} + 16 q^{58} - 44 q^{59} - 16 q^{60} - 8 q^{66} - 20 q^{67} - 36 q^{70} - 60 q^{71} + 12 q^{78} - 8 q^{80} + 28 q^{81} + 48 q^{86} + 32 q^{89} + 4 q^{91} + 64 q^{92} + 8 q^{93} + 8 q^{97}+O(q^{100}) $ 28 * q + 28 * q^3 - 4 * q^5 + 28 * q^9 - 4 * q^15 - 20 * q^16 - 16 * q^20 - 8 * q^22 + 12 * q^26 + 28 * q^27 + 8 * q^31 - 32 * q^34 - 12 * q^37 + 36 * q^44 - 4 * q^45 - 40 * q^47 - 20 * q^48 + 8 * q^53 - 16 * q^55 + 16 * q^58 - 44 * q^59 - 16 * q^60 - 8 * q^66 - 20 * q^67 - 36 * q^70 - 60 * q^71 + 12 * q^78 - 8 * q^80 + 28 * q^81 + 48 * q^86 + 32 * q^89 + 4 * q^91 + 64 * q^92 + 8 * q^93 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−0.555689	−	0.555689i	−0.392931	−	0.392931i	0.482799	−	0.875731i	$-0.339620\pi$
$2$	−0.555689	−	0.555689i	−0.392931	−	0.392931i	−0.875731	+	0.482799i	$0.839620\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$		−	1.38242i		−	0.691210i
$5$	−2.09993	+	2.09993i	−0.939118	+	0.939118i	−0.998250	−	0.0591322i	$-0.981167\pi$
$5$	−2.09993	+	2.09993i	−0.939118	+	0.939118i	0.0591322	+	0.998250i	$0.481167\pi$
$6$	−0.555689	−	0.555689i	−0.226859	−	0.226859i
$7$	−1.20106	+	1.20106i	−0.453958	+	0.453958i	−0.896666	−	0.442708i	$-0.854018\pi$
$7$	−1.20106	+	1.20106i	−0.453958	+	0.453958i	0.442708	+	0.896666i	$0.354018\pi$
$8$	−1.87957	+	1.87957i	−0.664530	+	0.664530i
$9$	1.00000			0.333333
$10$	2.33382			0.738018
$11$	−0.0298401	+	3.31649i	−0.00899712	+	0.999960i
$11$	−0.0298401	+	3.31649i	−0.00899712	+	0.999960i
$12$		−	1.38242i		−	0.399070i
$13$	−3.57354	−	0.479383i	−0.991122	−	0.132957i
$13$	−3.57354	−	0.479383i	−0.991122	−	0.132957i
$14$	1.33483			0.356749
$15$	−2.09993	+	2.09993i	−0.542200	+	0.542200i
$16$	−0.675922			−0.168981
$17$	−3.86461			−0.937305			−0.468652	−	0.883383i	$-0.655260\pi$
$17$	−3.86461			−0.937305			−0.468652	+	0.883383i	$0.655260\pi$
$18$	−0.555689	−	0.555689i	−0.130977	−	0.130977i
$19$	2.60902	+	2.60902i	0.598551	+	0.598551i	0.939927	−	0.341376i	$-0.110893\pi$
$19$	2.60902	+	2.60902i	0.598551	+	0.598551i	−0.341376	+	0.939927i	$0.610893\pi$
$20$	2.90299	+	2.90299i	0.649127	+	0.649127i
$21$	−1.20106	+	1.20106i	−0.262093	+	0.262093i
$22$	1.85952	−	1.82636i	0.396451	−	0.389380i
$23$			5.37795i			1.12138i	0.828026	+	0.560690i	$0.189464\pi$
$23$			5.37795i			1.12138i	−0.828026	+	0.560690i	$0.810536\pi$
$24$	−1.87957	+	1.87957i	−0.383666	+	0.383666i
$25$		−	3.81943i		−	0.763885i
$26$	1.71939	+	2.25217i	0.337200	+	0.441686i
$27$	1.00000			0.192450
$28$	1.66037	+	1.66037i	0.313780	+	0.313780i
$29$		−	4.16393i		−	0.773223i	−0.922243	−	0.386611i	$-0.873645\pi$
$29$		−	4.16393i		−	0.773223i	0.922243	−	0.386611i	$-0.126355\pi$
$30$	2.33382			0.426095
$31$	0.241306	−	0.241306i	0.0433399	−	0.0433399i	−0.685105	−	0.728445i	$-0.740244\pi$
$31$	0.241306	−	0.241306i	0.0433399	−	0.0433399i	0.728445	+	0.685105i	$0.240244\pi$
$32$	4.13475	+	4.13475i	0.730927	+	0.730927i
$33$	−0.0298401	+	3.31649i	−0.00519449	+	0.577327i
$34$	2.14752	+	2.14752i	0.368297	+	0.368297i
$35$		−	5.04429i		−	0.852640i
$36$		−	1.38242i		−	0.230403i
$37$	−6.52671	−	6.52671i	−1.07298	−	1.07298i	−0.997118	−	0.0758669i	$-0.975828\pi$
$37$	−6.52671	−	6.52671i	−1.07298	−	1.07298i	−0.0758669	−	0.997118i	$-0.524172\pi$
$38$		−	2.89961i		−	0.470379i
$39$	−3.57354	−	0.479383i	−0.572224	−	0.0767627i
$40$		−	7.89395i		−	1.24814i
$41$	5.68971	+	5.68971i	0.888584	+	0.888584i	0.994387	−	0.105803i	$-0.0337414\pi$
$41$	5.68971	+	5.68971i	0.888584	+	0.888584i	−0.105803	+	0.994387i	$0.533741\pi$
$42$	1.33483			0.205969
$43$	3.01228			0.459368			0.229684	−	0.973265i	$-0.426231\pi$
$43$	3.01228			0.459368			0.229684	+	0.973265i	$0.426231\pi$
$44$	4.58478	+	0.0412515i	0.691182	+	0.00621889i
$45$	−2.09993	+	2.09993i	−0.313039	+	0.313039i
$46$	2.98847	−	2.98847i	0.440625	−	0.440625i
$47$	−4.24006	−	4.24006i	−0.618477	−	0.618477i	0.326664	−	0.945141i	$-0.394075\pi$
$47$	−4.24006	−	4.24006i	−0.618477	−	0.618477i	−0.945141	+	0.326664i	$0.894075\pi$
$48$	−0.675922			−0.0975610
$49$			4.11491i			0.587845i
$50$	−2.12241	+	2.12241i	−0.300155	+	0.300155i
$51$	−3.86461			−0.541153
$52$	−0.662709	+	4.94013i	−0.0919011	+	0.685073i
$53$	−1.36521			−0.187526			−0.0937631	−	0.995595i	$-0.529890\pi$
$53$	−1.36521			−0.187526			−0.0937631	+	0.995595i	$0.529890\pi$
$54$	−0.555689	−	0.555689i	−0.0756197	−	0.0756197i
$55$	−6.90174	−	7.02707i	−0.930631	−	0.947529i
$56$		−	4.51496i		−	0.603337i
$57$	2.60902	+	2.60902i	0.345574	+	0.345574i
$58$	−2.31385	+	2.31385i	−0.303824	+	0.303824i
$59$	5.42554	+	5.42554i	0.706345	+	0.706345i	0.965765	−	0.259420i	$-0.0835314\pi$
$59$	5.42554	+	5.42554i	0.706345	+	0.706345i	−0.259420	+	0.965765i	$0.583531\pi$
$60$	2.90299	+	2.90299i	0.374774	+	0.374774i
$61$			3.66021i			0.468642i	0.972159	+	0.234321i	$0.0752867\pi$
$61$			3.66021i			0.468642i	−0.972159	+	0.234321i	$0.924713\pi$
$62$	−0.268183			−0.0340592
$63$	−1.20106	+	1.20106i	−0.151319	+	0.151319i
$64$		−	3.24343i		−	0.405428i
$65$	8.51086	−	6.49752i	1.05564	−	0.805918i
$66$	1.85952	−	1.82636i	0.228891	−	0.224809i
$67$	−1.05880	+	1.05880i	−0.129353	+	0.129353i	−0.768819	−	0.639466i	$-0.779155\pi$
$67$	−1.05880	+	1.05880i	−0.129353	+	0.129353i	0.639466	+	0.768819i	$0.279155\pi$
$68$			5.34251i			0.647874i
$69$			5.37795i			0.647429i
$70$	−2.80305	+	2.80305i	−0.335029	+	0.335029i
$71$	−8.20263	+	8.20263i	−0.973474	+	0.973474i	−0.999657	−	0.0261836i	$-0.991665\pi$
$71$	−8.20263	+	8.20263i	−0.973474	+	0.973474i	0.0261836	+	0.999657i	$0.491665\pi$
$72$	−1.87957	+	1.87957i	−0.221510	+	0.221510i
$73$	−1.13276	+	1.13276i	−0.132579	+	0.132579i	−0.770282	−	0.637703i	$-0.779885\pi$
$73$	−1.13276	+	1.13276i	−0.132579	+	0.132579i	0.637703	+	0.770282i	$0.279885\pi$
$74$			7.25364i			0.843219i
$75$		−	3.81943i		−	0.441029i
$76$	3.60677	−	3.60677i	0.413724	−	0.413724i
$77$	−3.94746	−	4.01914i	−0.449855	−	0.458024i
$78$	1.71939	+	2.25217i	0.194683	+	0.255007i
$79$		−	12.8821i		−	1.44935i	−0.689093	−	0.724673i	$-0.741991\pi$
$79$		−	12.8821i		−	1.44935i	0.689093	−	0.724673i	$-0.258009\pi$
$80$	1.41939	−	1.41939i	0.158693	−	0.158693i
$81$	1.00000			0.111111
$82$		−	6.32342i		−	0.698305i
$83$	−7.95292	−	7.95292i	−0.872946	−	0.872946i	0.119846	−	0.992792i	$-0.461760\pi$
$83$	−7.95292	−	7.95292i	−0.872946	−	0.872946i	−0.992792	+	0.119846i	$0.961760\pi$
$84$	1.66037	+	1.66037i	0.181161	+	0.181161i
$85$	8.11541	−	8.11541i	0.880240	−	0.880240i
$86$	−1.67389	−	1.67389i	−0.180500	−	0.180500i
$87$		−	4.16393i		−	0.446420i
$88$	−6.17750	−	6.28967i	−0.658524	−	0.670481i
$89$	−4.96133	−	4.96133i	−0.525900	−	0.525900i	0.393447	−	0.919347i	$-0.371282\pi$
$89$	−4.96133	−	4.96133i	−0.525900	−	0.525900i	−0.919347	+	0.393447i	$0.871282\pi$
$90$	2.33382			0.246006
$91$	4.86780	−	3.71627i	0.510284	−	0.389571i
$92$	7.43458			0.775108
$93$	0.241306	−	0.241306i	0.0250223	−	0.0250223i
$94$			4.71231i			0.486038i
$95$	−10.9575			−1.12422
$96$	4.13475	+	4.13475i	0.422001	+	0.422001i
$97$	1.81204	−	1.81204i	0.183984	−	0.183984i	−0.609105	−	0.793090i	$-0.708471\pi$
$97$	1.81204	−	1.81204i	0.183984	−	0.183984i	0.793090	+	0.609105i	$0.208471\pi$
$98$	2.28661	−	2.28661i	0.230983	−	0.230983i
$99$	−0.0298401	+	3.31649i	−0.00299904	+	0.333320i
$100$	−5.28005			−0.528005
$101$	8.09372			0.805355			0.402678	−	0.915342i	$-0.368080\pi$
$101$	8.09372			0.805355			0.402678	+	0.915342i	$0.368080\pi$
$102$	2.14752	+	2.14752i	0.212636	+	0.212636i
$103$		−	2.15050i		−	0.211895i	−0.994372	−	0.105948i	$-0.966212\pi$
$103$		−	2.15050i		−	0.211895i	0.994372	−	0.105948i	$-0.0337876\pi$
$104$	7.61777	−	5.81570i	0.746984	−	0.570276i
$105$		−	5.04429i		−	0.492272i
$106$	0.758633	+	0.758633i	0.0736850	+	0.0736850i
$107$		−	2.53571i		−	0.245137i	−0.992460	−	0.122568i	$-0.960887\pi$
$107$		−	2.53571i		−	0.245137i	0.992460	−	0.122568i	$-0.0391131\pi$
$108$		−	1.38242i		−	0.133023i
$109$	9.28576	+	9.28576i	0.889414	+	0.889414i	0.994467	−	0.105052i	$-0.0335010\pi$
$109$	9.28576	+	9.28576i	0.889414	+	0.889414i	−0.105052	+	0.994467i	$0.533501\pi$
$110$	−0.0696413	+	7.74009i	−0.00664003	+	0.737988i
$111$	−6.52671	−	6.52671i	−0.619488	−	0.619488i
$112$	0.811823	−	0.811823i	0.0767101	−	0.0767101i
$113$	−3.87579			−0.364603			−0.182302	−	0.983243i	$-0.558355\pi$
$113$	−3.87579			−0.364603			−0.182302	+	0.983243i	$0.558355\pi$
$114$		−	2.89961i		−	0.271574i
$115$	−11.2933	−	11.2933i	−1.05311	−	1.05311i
$116$	−5.75630			−0.534459
$117$	−3.57354	−	0.479383i	−0.330374	−	0.0443190i
$118$		−	6.02982i		−	0.555090i
$119$	4.64162	−	4.64162i	0.425497	−	0.425497i
$120$		−	7.89395i		−	0.720616i
$121$	−10.9982	−	0.197929i	−0.999838	−	0.0179935i
$122$	2.03394	−	2.03394i	0.184144	−	0.184144i
$123$	5.68971	+	5.68971i	0.513024	+	0.513024i
$124$	−0.333587	−	0.333587i	−0.0299570	−	0.0299570i
$125$	−2.47912	−	2.47912i	−0.221740	−	0.221740i
$126$	1.33483			0.118916
$127$	16.4517			1.45986			0.729928	−	0.683524i	$-0.239554\pi$
$127$	16.4517			1.45986			0.729928	+	0.683524i	$0.239554\pi$
$128$	6.46716	−	6.46716i	0.571622	−	0.571622i
$129$	3.01228			0.265216
$130$	−8.33999	−	1.11879i	−0.731466	−	0.0981246i
$131$			9.76359i			0.853049i	0.904476	+	0.426524i	$0.140262\pi$
$131$			9.76359i			0.853049i	−0.904476	+	0.426524i	$0.859738\pi$
$132$	4.58478	+	0.0412515i	0.399054	+	0.00359048i
$133$	−6.26719			−0.543434
$134$	1.17672			0.101654
$135$	−2.09993	+	2.09993i	−0.180733	+	0.180733i
$136$	7.26381	−	7.26381i	0.622867	−	0.622867i
$137$	0.957427	+	0.957427i	0.0817985	+	0.0817985i	0.746822	−	0.665024i	$-0.231579\pi$
$137$	0.957427	+	0.957427i	0.0817985	+	0.0817985i	−0.665024	+	0.746822i	$0.731579\pi$
$138$	2.98847	−	2.98847i	0.254395	−	0.254395i
$139$			13.9015i			1.17911i	0.807728	+	0.589555i	$0.200697\pi$
$139$			13.9015i			1.17911i	−0.807728	+	0.589555i	$0.799303\pi$
$140$	−6.97332			−0.589353
$141$	−4.24006	−	4.24006i	−0.357078	−	0.357078i
$142$	9.11623			0.765017
$143$	1.69650	−	11.8373i	0.141869	−	0.989885i
$144$	−0.675922			−0.0563269
$145$	8.74397	+	8.74397i	0.726147	+	0.726147i
$146$	1.25892			0.104189
$147$			4.11491i			0.339392i
$148$	−9.02265	+	9.02265i	−0.741658	+	0.741658i
$149$	−11.0375	−	11.0375i	−0.904224	−	0.904224i	0.0915743	−	0.995798i	$-0.470810\pi$
$149$	−11.0375	−	11.0375i	−0.904224	−	0.904224i	−0.995798	+	0.0915743i	$0.970810\pi$
$150$	−2.12241	+	2.12241i	−0.173294	+	0.173294i
$151$	8.95416	−	8.95416i	0.728679	−	0.728679i	−0.241677	−	0.970357i	$-0.577698\pi$
$151$	8.95416	−	8.95416i	0.728679	−	0.728679i	0.970357	+	0.241677i	$0.0776975\pi$
$152$	−9.80770			−0.795510
$153$	−3.86461			−0.312435
$154$	−0.0398314	+	4.42696i	−0.00320971	+	0.356734i
$155$			1.01345i			0.0814026i
$156$	−0.662709	+	4.94013i	−0.0530591	+	0.395527i
$157$	22.0682			1.76124			0.880618	−	0.473827i	$-0.157128\pi$
$157$	22.0682			1.76124			0.880618	+	0.473827i	$0.157128\pi$
$158$	−7.15842	+	7.15842i	−0.569493	+	0.569493i
$159$	−1.36521			−0.108268
$160$	−17.3654			−1.37285
$161$	−6.45924	−	6.45924i	−0.509059	−	0.509059i
$162$	−0.555689	−	0.555689i	−0.0436591	−	0.0436591i
$163$	3.21384	+	3.21384i	0.251728	+	0.251728i	0.821679	−	0.569951i	$-0.193038\pi$
$163$	3.21384	+	3.21384i	0.251728	+	0.251728i	−0.569951	+	0.821679i	$0.693038\pi$
$164$	7.86557	−	7.86557i	0.614198	−	0.614198i
$165$	−6.90174	−	7.02707i	−0.537300	−	0.547056i
$166$			8.83870i			0.686016i
$167$	2.92040	−	2.92040i	0.225987	−	0.225987i	−0.585027	−	0.811014i	$-0.698916\pi$
$167$	2.92040	−	2.92040i	0.225987	−	0.225987i	0.811014	+	0.585027i	$0.198916\pi$
$168$		−	4.51496i		−	0.348337i
$169$	12.5404	+	3.42619i	0.964645	+	0.263553i
$170$	−9.01929			−0.691748
$171$	2.60902	+	2.60902i	0.199517	+	0.199517i
$172$		−	4.16423i		−	0.317520i
$173$	−21.5815			−1.64081			−0.820407	−	0.571780i	$-0.806253\pi$
$173$	−21.5815			−1.64081			−0.820407	+	0.571780i	$0.806253\pi$
$174$	−2.31385	+	2.31385i	−0.175413	+	0.175413i
$175$	4.58736	+	4.58736i	0.346772	+	0.346772i
$176$	0.0201696	−	2.24169i	0.00152034	−	0.168974i
$177$	5.42554	+	5.42554i	0.407808	+	0.407808i
$178$			5.51391i			0.413285i
$179$			14.2798i			1.06732i	0.845698	+	0.533662i	$0.179184\pi$
$179$			14.2798i			1.06732i	−0.845698	+	0.533662i	$0.820816\pi$
$180$	2.90299	+	2.90299i	0.216376	+	0.216376i
$181$			25.2225i			1.87477i	0.348290	+	0.937387i	$0.386762\pi$
$181$			25.2225i			1.87477i	−0.348290	+	0.937387i	$0.613238\pi$
$182$	−4.77007	−	0.639896i	−0.353581	−	0.0474322i
$183$			3.66021i			0.270571i
$184$	−10.1082	−	10.1082i	−0.745190	−	0.745190i
$185$	27.4113			2.01532
$186$	−0.268183			−0.0196641
$187$	0.115320	−	12.8169i	0.00843304	−	0.937267i
$188$	−5.86154	+	5.86154i	−0.427497	+	0.427497i
$189$	−1.20106	+	1.20106i	−0.0873642	+	0.0873642i
$190$	6.08899	+	6.08899i	0.441742	+	0.441742i
$191$	−14.4491			−1.04550			−0.522750	−	0.852486i	$-0.675094\pi$
$191$	−14.4491			−1.04550			−0.522750	+	0.852486i	$0.675094\pi$
$192$		−	3.24343i		−	0.234074i
$193$	−7.90835	+	7.90835i	−0.569255	+	0.569255i	−0.931920	−	0.362665i	$-0.881867\pi$
$193$	−7.90835	+	7.90835i	−0.569255	+	0.569255i	0.362665	+	0.931920i	$0.381867\pi$
$194$	−2.01386			−0.144587
$195$	8.51086	−	6.49752i	0.609476	−	0.465297i
$196$	5.68853			0.406324
$197$	16.1620	+	16.1620i	1.15150	+	1.15150i	0.986252	+	0.165246i	$0.0528417\pi$
$197$	16.1620	+	16.1620i	1.15150	+	1.15150i	0.165246	+	0.986252i	$0.447158\pi$
$198$	1.85952	−	1.82636i	0.132150	−	0.129793i
$199$		−	7.50680i		−	0.532143i	−0.963953	−	0.266072i	$-0.914274\pi$
$199$		−	7.50680i		−	0.532143i	0.963953	−	0.266072i	$-0.0857258\pi$
$200$	7.17889	+	7.17889i	0.507624	+	0.507624i
$201$	−1.05880	+	1.05880i	−0.0746818	+	0.0746818i
$202$	−4.49759	−	4.49759i	−0.316450	−	0.316450i
$203$	5.00113	+	5.00113i	0.351011	+	0.351011i
$204$			5.34251i			0.374050i
$205$	−23.8960			−1.66897
$206$	−1.19501	+	1.19501i	−0.0832604	+	0.0832604i
$207$			5.37795i			0.373793i
$208$	2.41544	+	0.324026i	0.167480	+	0.0224671i
$209$	−8.73066	+	8.57495i	−0.603912	+	0.593142i
$210$	−2.80305	+	2.80305i	−0.193429	+	0.193429i
$211$			17.2372i			1.18666i	0.804960	+	0.593329i	$0.202187\pi$
$211$			17.2372i			1.18666i	−0.804960	+	0.593329i	$0.797813\pi$
$212$			1.88730i			0.129620i
$213$	−8.20263	+	8.20263i	−0.562035	+	0.562035i
$214$	−1.40907	+	1.40907i	−0.0963220	+	0.0963220i
$215$	−6.32557	+	6.32557i	−0.431401	+	0.431401i
$216$	−1.87957	+	1.87957i	−0.127889	+	0.127889i
$217$			0.579647i			0.0393490i
$218$		−	10.3200i		−	0.698958i
$219$	−1.13276	+	1.13276i	−0.0765447	+	0.0765447i
$220$	−9.71435	+	9.54110i	−0.654941	+	0.643261i
$221$	13.8103	+	1.85263i	0.928983	+	0.124621i
$222$			7.25364i			0.486833i
$223$	−6.56283	+	6.56283i	−0.439480	+	0.439480i	−0.891837	−	0.452357i	$-0.850583\pi$
$223$	−6.56283	+	6.56283i	−0.439480	+	0.439480i	0.452357	+	0.891837i	$0.350583\pi$
$224$	−9.93216			−0.663620
$225$		−	3.81943i		−	0.254628i
$226$	2.15373	+	2.15373i	0.143264	+	0.143264i
$227$	18.2796	+	18.2796i	1.21326	+	1.21326i	0.969949	+	0.243310i	$0.0782333\pi$
$227$	18.2796	+	18.2796i	1.21326	+	1.21326i	0.243310	+	0.969949i	$0.421767\pi$
$228$	3.60677	−	3.60677i	0.238864	−	0.238864i
$229$	20.9701	+	20.9701i	1.38575	+	1.38575i	0.834035	+	0.551711i	$0.186025\pi$
$229$	20.9701	+	20.9701i	1.38575	+	1.38575i	0.551711	+	0.834035i	$0.313975\pi$
$230$			12.5512i			0.827598i
$231$	−3.94746	−	4.01914i	−0.259724	−	0.264440i
$232$	7.82642	+	7.82642i	0.513829	+	0.513829i
$233$	23.9759			1.57071			0.785357	−	0.619043i	$-0.212479\pi$
$233$	23.9759			1.57071			0.785357	+	0.619043i	$0.212479\pi$
$234$	1.71939	+	2.25217i	0.112400	+	0.147229i
$235$	17.8077			1.16164
$236$	7.50037	−	7.50037i	0.488232	−	0.488232i
$237$		−	12.8821i		−	0.836780i
$238$	−5.15860			−0.334382
$239$	−8.94929	−	8.94929i	−0.578881	−	0.578881i	0.355714	−	0.934595i	$-0.384238\pi$
$239$	−8.94929	−	8.94929i	−0.578881	−	0.578881i	−0.934595	+	0.355714i	$0.884238\pi$
$240$	1.41939	−	1.41939i	0.0916213	−	0.0916213i
$241$	−18.6089	+	18.6089i	−1.19870	+	1.19870i	−0.224149	+	0.974555i	$0.571960\pi$
$241$	−18.6089	+	18.6089i	−1.19870	+	1.19870i	−0.974555	+	0.224149i	$0.928040\pi$
$242$	6.00160	+	6.22158i	0.385798	+	0.399938i
$243$	1.00000			0.0641500
$244$	5.05995			0.323930
$245$	−8.64103	−	8.64103i	−0.552055	−	0.552055i
$246$		−	6.32342i		−	0.403167i
$247$	−8.07273	−	10.5742i	−0.513656	−	0.672819i
$248$			0.907106i			0.0576013i
$249$	−7.95292	−	7.95292i	−0.503996	−	0.503996i
$250$			2.75524i			0.174257i
$251$		−	8.24119i		−	0.520179i	−0.965584	−	0.260090i	$-0.916248\pi$
$251$		−	8.24119i		−	0.520179i	0.965584	−	0.260090i	$-0.0837521\pi$
$252$	1.66037	+	1.66037i	0.104593	+	0.104593i
$253$	−17.8359	−	0.160478i	−1.12133	−	0.0100892i
$254$	−9.14205	−	9.14205i	−0.573623	−	0.573623i
$255$	8.11541	−	8.11541i	0.508207	−	0.508207i
$256$	−13.6743			−0.854645
$257$			5.22792i			0.326109i	0.986617	+	0.163054i	$0.0521346\pi$
$257$			5.22792i			0.326109i	−0.986617	+	0.163054i	$0.947865\pi$
$258$	−1.67389	−	1.67389i	−0.104212	−	0.104212i
$259$	15.6779			0.974180
$260$	−8.98230	−	11.7656i	−0.557058	−	0.729670i
$261$		−	4.16393i		−	0.257741i
$262$	5.42552	−	5.42552i	0.335190	−	0.335190i
$263$		−	17.5714i		−	1.08350i	−0.840540	−	0.541749i	$-0.817762\pi$
$263$		−	17.5714i		−	1.08350i	0.840540	−	0.541749i	$-0.182238\pi$
$264$	−6.17750	−	6.28967i	−0.380199	−	0.387103i
$265$	2.86685	−	2.86685i	0.176109	−	0.176109i
$266$	3.48261	+	3.48261i	0.213532	+	0.213532i
$267$	−4.96133	−	4.96133i	−0.303628	−	0.303628i
$268$	1.46370	+	1.46370i	0.0894099	+	0.0894099i
$269$	28.7261			1.75146			0.875730	−	0.482801i	$-0.160381\pi$
$269$	28.7261			1.75146			0.875730	+	0.482801i	$0.160381\pi$
$270$	2.33382			0.142032
$271$	−15.1136	+	15.1136i	−0.918087	+	0.918087i	−0.996890	−	0.0788036i	$-0.974890\pi$
$271$	−15.1136	+	15.1136i	−0.918087	+	0.918087i	0.0788036	+	0.996890i	$0.474890\pi$
$272$	2.61217			0.158386
$273$	4.86780	−	3.71627i	0.294613	−	0.224919i
$274$		−	1.06406i		−	0.0642824i
$275$	12.6671	+	0.113972i	0.763854	+	0.00687276i
$276$	7.43458			0.447509
$277$	0.382657			0.0229916			0.0114958	−	0.999934i	$-0.496341\pi$
$277$	0.382657			0.0229916			0.0114958	+	0.999934i	$0.496341\pi$
$278$	7.72492	−	7.72492i	0.463310	−	0.463310i
$279$	0.241306	−	0.241306i	0.0144466	−	0.0144466i
$280$	9.48111	+	9.48111i	0.566604	+	0.566604i
$281$	13.7908	−	13.7908i	0.822690	−	0.822690i	−0.163803	−	0.986493i	$-0.552376\pi$
$281$	13.7908	−	13.7908i	0.822690	−	0.822690i	0.986493	+	0.163803i	$0.0523761\pi$
$282$			4.71231i			0.280614i
$283$	10.0335			0.596431			0.298215	−	0.954499i	$-0.403609\pi$
$283$	10.0335			0.596431			0.298215	+	0.954499i	$0.403609\pi$
$284$	11.3395	+	11.3395i	0.672874	+	0.672874i
$285$	−10.9575			−0.649069
$286$	−7.52059	+	5.63513i	−0.444702	+	0.333212i
$287$	−13.6674			−0.806759
$288$	4.13475	+	4.13475i	0.243642	+	0.243642i
$289$	−2.06481			−0.121460
$290$		−	9.71786i		−	0.570652i
$291$	1.81204	−	1.81204i	0.106223	−	0.106223i
$292$	1.56595	+	1.56595i	0.0916401	+	0.0916401i
$293$	−15.7011	+	15.7011i	−0.917267	+	0.917267i	−0.996830	−	0.0795627i	$-0.974648\pi$
$293$	−15.7011	+	15.7011i	−0.917267	+	0.917267i	0.0795627	+	0.996830i	$0.474648\pi$
$294$	2.28661	−	2.28661i	0.133358	−	0.133358i
$295$	−22.7865			−1.32668
$296$	24.5349			1.42606
$297$	−0.0298401	+	3.31649i	−0.00173150	+	0.192442i
$298$			12.2668i			0.710596i
$299$	2.57810	−	19.2183i	0.149095	−	1.11142i
$300$	−5.28005			−0.304844
$301$	−3.61792	+	3.61792i	−0.208534	+	0.208534i
$302$	−9.95146			−0.572642
$303$	8.09372			0.464972
$304$	−1.76350	−	1.76350i	−0.101144	−	0.101144i
$305$	−7.68619	−	7.68619i	−0.440110	−	0.440110i
$306$	2.14752	+	2.14752i	0.122766	+	0.122766i
$307$	7.24725	−	7.24725i	0.413623	−	0.413623i	−0.469376	−	0.882998i	$-0.655521\pi$
$307$	7.24725	−	7.24725i	0.413623	−	0.413623i	0.882998	+	0.469376i	$0.155521\pi$
$308$	−5.55614	+	5.45705i	−0.316590	+	0.310944i
$309$		−	2.15050i		−	0.122338i
$310$	0.563165	−	0.563165i	0.0319856	−	0.0319856i
$311$		−	14.4358i		−	0.818581i	−0.912404	−	0.409290i	$-0.865776\pi$
$311$		−	14.4358i		−	0.818581i	0.912404	−	0.409290i	$-0.134224\pi$
$312$	7.61777	−	5.81570i	0.431271	−	0.329249i
$313$	−15.2988			−0.864737			−0.432369	−	0.901697i	$-0.642322\pi$
$313$	−15.2988			−0.864737			−0.432369	+	0.901697i	$0.642322\pi$
$314$	−12.2631	−	12.2631i	−0.692045	−	0.692045i
$315$		−	5.04429i		−	0.284213i
$316$	−17.8084			−1.00180
$317$	−16.3083	+	16.3083i	−0.915966	+	0.915966i	−0.996733	−	0.0807675i	$-0.974263\pi$
$317$	−16.3083	+	16.3083i	−0.915966	+	0.915966i	0.0807675	+	0.996733i	$0.474263\pi$
$318$	0.758633	+	0.758633i	0.0425420	+	0.0425420i
$319$	13.8096	+	0.124252i	0.773191	+	0.00695677i
$320$	6.81097	+	6.81097i	0.380745	+	0.380745i
$321$		−	2.53571i		−	0.141530i
$322$			7.17865i			0.400051i
$323$	−10.0829	−	10.0829i	−0.561025	−	0.561025i
$324$		−	1.38242i		−	0.0768011i
$325$	−1.83097	+	13.6489i	−0.101564	+	0.757103i
$326$		−	3.57180i		−	0.197823i
$327$	9.28576	+	9.28576i	0.513504	+	0.513504i
$328$	−21.3885			−1.18098
$329$	10.1851			0.561525
$330$	−0.0696413	+	7.74009i	−0.00383363	+	0.426078i
$331$	23.8825	−	23.8825i	1.31270	−	1.31270i	0.393284	−	0.919417i	$-0.371339\pi$
$331$	23.8825	−	23.8825i	1.31270	−	1.31270i	0.919417	−	0.393284i	$-0.128661\pi$
$332$	−10.9943	+	10.9943i	−0.603389	+	0.603389i
$333$	−6.52671	−	6.52671i	−0.357662	−	0.357662i
$334$	−3.24566			−0.177595
$335$		−	4.44681i		−	0.242955i
$336$	0.811823	−	0.811823i	0.0442886	−	0.0442886i
$337$	−20.5569			−1.11980			−0.559902	−	0.828559i	$-0.689161\pi$
$337$	−20.5569			−1.11980			−0.559902	+	0.828559i	$0.689161\pi$
$338$	−5.06466	−	8.87245i	−0.275481	−	0.482598i
$339$	−3.87579			−0.210504
$340$	−11.2189	−	11.2189i	−0.608430	−	0.608430i
$341$	0.793090	+	0.807491i	0.0429482	+	0.0437281i
$342$		−	2.89961i		−	0.156793i
$343$	−13.3497	−	13.3497i	−0.720815	−	0.720815i
$344$	−5.66179	+	5.66179i	−0.305263	+	0.305263i
$345$	−11.2933	−	11.2933i	−0.608012	−	0.608012i
$346$	11.9926	+	11.9926i	0.644728	+	0.644728i
$347$			6.29678i			0.338029i	0.985614	+	0.169014i	$0.0540584\pi$
$347$			6.29678i			0.338029i	−0.985614	+	0.169014i	$0.945942\pi$
$348$	−5.75630			−0.308570
$349$	−12.7457	+	12.7457i	−0.682260	+	0.682260i	−0.960509	−	0.278249i	$-0.910246\pi$
$349$	−12.7457	+	12.7457i	−0.682260	+	0.682260i	0.278249	+	0.960509i	$0.410246\pi$
$350$		−	5.09829i		−	0.272515i
$351$	−3.57354	−	0.479383i	−0.190741	−	0.0255876i
$352$	−13.8362	+	13.5895i	−0.737474	+	0.724321i
$353$	−10.1990	+	10.1990i	−0.542838	+	0.542838i	−0.924360	−	0.381521i	$-0.875400\pi$
$353$	−10.1990	+	10.1990i	−0.542838	+	0.542838i	0.381521	+	0.924360i	$0.375400\pi$
$354$		−	6.02982i		−	0.320481i
$355$		−	34.4499i		−	1.82841i
$356$	−6.85864	+	6.85864i	−0.363507	+	0.363507i
$357$	4.64162	−	4.64162i	0.245661	−	0.245661i
$358$	7.93514	−	7.93514i	0.419385	−	0.419385i
$359$	10.0729	−	10.0729i	0.531628	−	0.531628i	−0.389429	−	0.921057i	$-0.627328\pi$
$359$	10.0729	−	10.0729i	0.531628	−	0.531628i	0.921057	+	0.389429i	$0.127328\pi$
$360$		−	7.89395i		−	0.416048i
$361$		−	5.38599i		−	0.283473i
$362$	14.0159	−	14.0159i	0.736658	−	0.736658i
$363$	−10.9982	−	0.197929i	−0.577257	−	0.0103886i
$364$	−5.13744	−	6.72935i	−0.269275	−	0.352714i
$365$		−	4.75743i		−	0.249015i
$366$	2.03394	−	2.03394i	0.106316	−	0.106316i
$367$	24.3006			1.26848			0.634241	−	0.773135i	$-0.281313\pi$
$367$	24.3006			1.26848			0.634241	+	0.773135i	$0.281313\pi$
$368$		−	3.63507i		−	0.189491i
$369$	5.68971	+	5.68971i	0.296195	+	0.296195i
$370$	−15.2322	−	15.2322i	−0.791882	−	0.791882i
$371$	1.63970	−	1.63970i	0.0851290	−	0.0851290i
$372$	−0.333587	−	0.333587i	−0.0172957	−	0.0172957i
$373$		−	3.96469i		−	0.205284i	−0.994718	−	0.102642i	$-0.967270\pi$
$373$		−	3.96469i		−	0.205284i	0.994718	−	0.102642i	$-0.0327296\pi$
$374$	−7.18631	+	7.05815i	−0.371595	+	0.364968i
$375$	−2.47912	−	2.47912i	−0.128021	−	0.128021i
$376$	15.9390			0.821992
$377$	−1.99612	+	14.8800i	−0.102805	+	0.766358i
$378$	1.33483			0.0686563
$379$	12.2012	−	12.2012i	0.626734	−	0.626734i	−0.320511	−	0.947245i	$-0.603855\pi$
$379$	12.2012	−	12.2012i	0.626734	−	0.626734i	0.947245	+	0.320511i	$0.103855\pi$
$380$			15.1479i			0.777072i
$381$	16.4517			0.842848
$382$	8.02920	+	8.02920i	0.410810	+	0.410810i
$383$	−25.6588	+	25.6588i	−1.31110	+	1.31110i	−0.390497	+	0.920604i	$0.627697\pi$
$383$	−25.6588	+	25.6588i	−1.31110	+	1.31110i	−0.920604	+	0.390497i	$0.872303\pi$
$384$	6.46716	−	6.46716i	0.330026	−	0.330026i
$385$	16.7293	+	0.150522i	0.852606	+	0.00767130i
$386$	8.78916			0.447357
$387$	3.01228			0.153123
$388$	−2.50499	−	2.50499i	−0.127172	−	0.127172i
$389$		−	19.2616i		−	0.976603i	−0.872675	−	0.488301i	$-0.837617\pi$
$389$		−	19.2616i		−	0.976603i	0.872675	−	0.488301i	$-0.162383\pi$
$390$	−8.33999	−	1.11879i	−0.422312	−	0.0566523i
$391$		−	20.7837i		−	1.05107i
$392$	−7.73428	−	7.73428i	−0.390640	−	0.390640i
$393$			9.76359i			0.492508i
$394$		−	17.9621i		−	0.904920i
$395$	27.0515	+	27.0515i	1.36111	+	1.36111i
$396$	4.58478	+	0.0412515i	0.230394	+	0.00207296i
$397$	0.0401347	+	0.0401347i	0.00201430	+	0.00201430i	0.708113	−	0.706099i	$-0.249547\pi$
$397$	0.0401347	+	0.0401347i	0.00201430	+	0.00201430i	−0.706099	+	0.708113i	$0.749547\pi$
$398$	−4.17145	+	4.17145i	−0.209096	+	0.209096i
$399$	−6.26719			−0.313752
$400$			2.58164i			0.129082i
$401$	2.09790	+	2.09790i	0.104764	+	0.104764i	0.757546	−	0.652782i	$-0.226398\pi$
$401$	2.09790	+	2.09790i	0.104764	+	0.104764i	−0.652782	+	0.757546i	$0.726398\pi$
$402$	1.17672			0.0586897
$403$	−0.977996	+	0.746640i	−0.0487175	+	0.0371928i
$404$		−	11.1889i		−	0.556669i
$405$	−2.09993	+	2.09993i	−0.104346	+	0.104346i
$406$		−	5.55815i		−	0.275846i
$407$	21.8405	−	21.4510i	1.08260	−	1.06329i
$408$	7.26381	−	7.26381i	0.359612	−	0.359612i
$409$	26.6371	+	26.6371i	1.31712	+	1.31712i	0.916046	+	0.401074i	$0.131363\pi$
$409$	26.6371	+	26.6371i	1.31712	+	1.31712i	0.401074	+	0.916046i	$0.368637\pi$
$410$	13.2788	+	13.2788i	0.655791	+	0.655791i
$411$	0.957427	+	0.957427i	0.0472264	+	0.0472264i
$412$	−2.97290			−0.146464
$413$	−13.0328			−0.641301
$414$	2.98847	−	2.98847i	0.146875	−	0.146875i
$415$	33.4012			1.63960
$416$	−12.7936	−	16.7578i	−0.627256	−	0.821620i
$417$			13.9015i			0.680760i
$418$	9.61654	+	0.0865246i	0.470360	+	0.00423206i
$419$	9.37291			0.457896			0.228948	−	0.973439i	$-0.426471\pi$
$419$	9.37291			0.457896			0.228948	+	0.973439i	$0.426471\pi$
$420$	−6.97332			−0.340263
$421$	15.7274	−	15.7274i	0.766507	−	0.766507i	−0.210983	−	0.977490i	$-0.567666\pi$
$421$	15.7274	−	15.7274i	0.766507	−	0.766507i	0.977490	+	0.210983i	$0.0676664\pi$
$422$	9.57852	−	9.57852i	0.466275	−	0.466275i
$423$	−4.24006	−	4.24006i	−0.206159	−	0.206159i
$424$	2.56602	−	2.56602i	0.124617	−	0.124617i
$425$			14.7606i			0.715993i
$426$	9.11623			0.441683
$427$	−4.39613	−	4.39613i	−0.212744	−	0.212744i
$428$	−3.50542			−0.169441
$429$	1.69650	−	11.8373i	0.0819080	−	0.571511i
$430$	7.03010			0.339022
$431$	−15.6511	−	15.6511i	−0.753888	−	0.753888i	0.221315	−	0.975202i	$-0.428965\pi$
$431$	−15.6511	−	15.6511i	−0.753888	−	0.753888i	−0.975202	+	0.221315i	$0.928965\pi$
$432$	−0.675922			−0.0325203
$433$			39.7367i			1.90963i	0.297209	+	0.954813i	$0.403944\pi$
$433$			39.7367i			1.90963i	−0.297209	+	0.954813i	$0.596056\pi$
$434$	0.322103	−	0.322103i	0.0154615	−	0.0154615i
$435$	8.74397	+	8.74397i	0.419241	+	0.419241i
$436$	12.8368	−	12.8368i	0.614772	−	0.614772i
$437$	−14.0312	+	14.0312i	−0.671203	+	0.671203i
$438$	1.25892			0.0601537
$439$	23.9618			1.14364			0.571818	−	0.820381i	$-0.306239\pi$
$439$	23.9618			1.14364			0.571818	+	0.820381i	$0.306239\pi$
$440$	26.1802	+	0.235556i	1.24809	+	0.0112297i
$441$			4.11491i			0.195948i
$442$	−6.64476	−	8.70373i	−0.316059	−	0.413994i
$443$	2.97355			0.141278			0.0706388	−	0.997502i	$-0.477496\pi$
$443$	2.97355			0.141278			0.0706388	+	0.997502i	$0.477496\pi$
$444$	−9.02265	+	9.02265i	−0.428196	+	0.428196i
$445$	20.8369			0.987764
$446$	7.29379			0.345371
$447$	−11.0375	−	11.0375i	−0.522054	−	0.522054i
$448$	3.89555	+	3.89555i	0.184047	+	0.184047i
$449$	−19.8661	−	19.8661i	−0.937539	−	0.937539i	0.0606217	−	0.998161i	$-0.480692\pi$
$449$	−19.8661	−	19.8661i	−0.937539	−	0.937539i	−0.998161	+	0.0606217i	$0.980692\pi$
$450$	−2.12241	+	2.12241i	−0.100052	+	0.100052i
$451$	−19.0397	+	18.7001i	−0.896543	+	0.880553i
$452$			5.35796i			0.252017i
$453$	8.95416	−	8.95416i	0.420703	−	0.420703i
$454$		−	20.3155i		−	0.953455i
$455$	−2.41815	+	18.0260i	−0.113364	+	0.845070i
$456$	−9.80770			−0.459288
$457$	−15.7597	−	15.7597i	−0.737208	−	0.737208i	0.234829	−	0.972037i	$-0.424547\pi$
$457$	−15.7597	−	15.7597i	−0.737208	−	0.737208i	−0.972037	+	0.234829i	$0.924547\pi$
$458$		−	23.3058i		−	1.08901i
$459$	−3.86461			−0.180384
$460$	−15.6121	+	15.6121i	−0.727918	+	0.727918i
$461$	12.5640	+	12.5640i	0.585163	+	0.585163i	0.936318	−	0.351154i	$-0.114211\pi$
$461$	12.5640	+	12.5640i	0.585163	+	0.585163i	−0.351154	+	0.936318i	$0.614211\pi$
$462$	−0.0398314	+	4.42696i	−0.00185313	+	0.205961i
$463$	−19.9151	−	19.9151i	−0.925534	−	0.925534i	0.0718792	−	0.997413i	$-0.477100\pi$
$463$	−19.9151	−	19.9151i	−0.925534	−	0.925534i	−0.997413	+	0.0718792i	$0.977100\pi$
$464$			2.81449i			0.130660i
$465$			1.01345i			0.0469978i
$466$	−13.3232	−	13.3232i	−0.617183	−	0.617183i
$467$		−	17.2912i		−	0.800142i	−0.916484	−	0.400071i	$-0.868985\pi$
$467$		−	17.2912i		−	0.800142i	0.916484	−	0.400071i	$-0.131015\pi$
$468$	−0.662709	+	4.94013i	−0.0306337	+	0.228358i
$469$		−	2.54336i		−	0.117441i
$470$	−9.89553	−	9.89553i	−0.456447	−	0.456447i
$471$	22.0682			1.01685
$472$	−20.3954			−0.938774
$473$	−0.0898865	+	9.99019i	−0.00413299	+	0.459349i
$474$	−7.15842	+	7.15842i	−0.328797	+	0.328797i
$475$	9.96498	−	9.96498i	0.457224	−	0.457224i
$476$	−6.41667	−	6.41667i	−0.294108	−	0.294108i
$477$	−1.36521			−0.0625087
$478$			9.94605i			0.454922i
$479$	−2.36036	+	2.36036i	−0.107847	+	0.107847i	−0.758971	−	0.651124i	$-0.774298\pi$
$479$	−2.36036	+	2.36036i	−0.107847	+	0.107847i	0.651124	+	0.758971i	$0.274298\pi$
$480$	−17.3654			−0.792618
$481$	20.1947	+	26.4523i	0.920798	+	1.20612i
$482$	20.6815			0.942017
$483$	−6.45924	−	6.45924i	−0.293905	−	0.293905i
$484$	−0.273620	+	15.2042i	−0.0124373	+	0.691098i
$485$			7.61031i			0.345566i
$486$	−0.555689	−	0.555689i	−0.0252066	−	0.0252066i
$487$	−18.6152	+	18.6152i	−0.843536	+	0.843536i	−0.989317	−	0.145781i	$-0.953431\pi$
$487$	−18.6152	+	18.6152i	−0.843536	+	0.843536i	0.145781	+	0.989317i	$0.453431\pi$
$488$	−6.87963	−	6.87963i	−0.311426	−	0.311426i
$489$	3.21384	+	3.21384i	0.145335	+	0.145335i
$490$			9.60345i			0.433840i
$491$	5.21788			0.235479			0.117740	−	0.993044i	$-0.462435\pi$
$491$	5.21788			0.235479			0.117740	+	0.993044i	$0.462435\pi$
$492$	7.86557	−	7.86557i	0.354607	−	0.354607i
$493$			16.0920i			0.724745i
$494$	−1.39003	+	10.3619i	−0.0625402	+	0.466203i
$495$	−6.90174	−	7.02707i	−0.310210	−	0.315843i
$496$	−0.163104	+	0.163104i	−0.00732360	+	0.00732360i
$497$		−	19.7037i		−	0.883832i
$498$			8.83870i			0.396072i
$499$	20.6937	−	20.6937i	0.926379	−	0.926379i	−0.0710908	−	0.997470i	$-0.522648\pi$
$499$	20.6937	−	20.6937i	0.926379	−	0.926379i	0.997470	+	0.0710908i	$0.0226480\pi$
$500$	−3.42719	+	3.42719i	−0.153269	+	0.153269i
$501$	2.92040	−	2.92040i	0.130474	−	0.130474i
$502$	−4.57954	+	4.57954i	−0.204395	+	0.204395i
$503$			17.2599i			0.769581i	0.923004	+	0.384791i	$0.125726\pi$
$503$			17.2599i			0.769581i	−0.923004	+	0.384791i	$0.874274\pi$
$504$		−	4.51496i		−	0.201112i
$505$	−16.9963	+	16.9963i	−0.756324	+	0.756324i
$506$	9.82204	+	10.0004i	0.436643	+	0.444572i
$507$	12.5404	+	3.42619i	0.556938	+	0.152162i
$508$		−	22.7432i		−	1.00907i
$509$	−20.2872	+	20.2872i	−0.899213	+	0.899213i	−0.995367	−	0.0961536i	$-0.969346\pi$
$509$	−20.2872	+	20.2872i	−0.899213	+	0.899213i	0.0961536	+	0.995367i	$0.469346\pi$
$510$	−9.01929			−0.399381
$511$		−	2.72102i		−	0.120371i
$512$	−5.33566	−	5.33566i	−0.235805	−	0.235805i
$513$	2.60902	+	2.60902i	0.115191	+	0.115191i
$514$	2.90510	−	2.90510i	0.128138	−	0.128138i
$515$	4.51591	+	4.51591i	0.198995	+	0.198995i
$516$		−	4.16423i		−	0.183320i
$517$	14.1886	−	13.9356i	0.624016	−	0.612887i
$518$	−8.71206	−	8.71206i	−0.382786	−	0.382786i
$519$	−21.5815			−0.947325
$520$	−3.78423	+	28.2094i	−0.165949	+	1.23706i
$521$	28.2027			1.23558			0.617792	−	0.786342i	$-0.288027\pi$
$521$	28.2027			1.23558			0.617792	+	0.786342i	$0.288027\pi$
$522$	−2.31385	+	2.31385i	−0.101275	+	0.101275i
$523$		−	16.1781i		−	0.707417i	−0.935356	−	0.353708i	$-0.884921\pi$
$523$		−	16.1781i		−	0.707417i	0.935356	−	0.353708i	$-0.115079\pi$
$524$	13.4974			0.589636
$525$	4.58736	+	4.58736i	0.200209	+	0.200209i
$526$	−9.76422	+	9.76422i	−0.425740	+	0.425740i
$527$	−0.932554	+	0.932554i	−0.0406227	+	0.0406227i
$528$	0.0201696	−	2.24169i	0.000877767	−	0.0975570i
$529$	−5.92232			−0.257492
$530$	−3.18616			−0.138398
$531$	5.42554	+	5.42554i	0.235448	+	0.235448i
$532$			8.66388i			0.375627i
$533$	−17.6049	−	23.0600i	−0.762551	−	0.998838i
$534$			5.51391i			0.238610i
$535$	5.32483	+	5.32483i	0.230212	+	0.230212i
$536$		−	3.98018i		−	0.171917i
$537$			14.2798i			0.616219i
$538$	−15.9628	−	15.9628i	−0.688204	−	0.688204i
$539$	−13.6471	−	0.122789i	−0.587821	−	0.00528891i
$540$	2.90299	+	2.90299i	0.124925	+	0.124925i
$541$	−8.12042	+	8.12042i	−0.349124	+	0.349124i	−0.859783	−	0.510659i	$-0.829401\pi$
$541$	−8.12042	+	8.12042i	−0.349124	+	0.349124i	0.510659	+	0.859783i	$0.329401\pi$
$542$	16.7969			0.721490
$543$			25.2225i			1.08240i
$544$	−15.9792	−	15.9792i	−0.685102	−	0.685102i
$545$	−38.9989			−1.67053
$546$	−4.77007	−	0.639896i	−0.204140	−	0.0273850i
$547$			11.1556i			0.476981i	0.971145	+	0.238490i	$0.0766525\pi$
$547$			11.1556i			0.476981i	−0.971145	+	0.238490i	$0.923347\pi$
$548$	1.32357	−	1.32357i	0.0565399	−	0.0565399i
$549$			3.66021i			0.156214i
$550$	−6.97563	−	7.10230i	−0.297442	−	0.302843i
$551$	10.8638	−	10.8638i	0.462813	−	0.462813i
$552$	−10.1082	−	10.1082i	−0.430236	−	0.430236i
$553$	15.4721	+	15.4721i	0.657942	+	0.657942i
$554$	−0.212638	−	0.212638i	−0.00903413	−	0.00903413i
$555$	27.4113			1.16354
$556$	19.2177			0.815013
$557$	−5.50900	+	5.50900i	−0.233424	+	0.233424i	−0.814120	−	0.580696i	$-0.802780\pi$
$557$	−5.50900	+	5.50900i	−0.233424	+	0.233424i	0.580696	+	0.814120i	$0.302780\pi$
$558$	−0.268183			−0.0113531
$559$	−10.7645	−	1.44403i	−0.455289	−	0.0610761i
$560$			3.40955i			0.144080i
$561$	0.115320	−	12.8169i	0.00486882	−	0.541131i
$562$	−15.3268			−0.646522
$563$	−18.1264			−0.763935			−0.381967	−	0.924176i	$-0.624753\pi$
$563$	−18.1264			−0.763935			−0.381967	+	0.924176i	$0.624753\pi$
$564$	−5.86154	+	5.86154i	−0.246816	+	0.246816i
$565$	8.13889	−	8.13889i	0.342405	−	0.342405i
$566$	−5.57551	−	5.57551i	−0.234356	−	0.234356i
$567$	−1.20106	+	1.20106i	−0.0504398	+	0.0504398i
$568$		−	30.8349i		−	1.29380i
$569$	−31.3682			−1.31502			−0.657512	−	0.753444i	$-0.728391\pi$
$569$	−31.3682			−1.31502			−0.657512	+	0.753444i	$0.728391\pi$
$570$	6.08899	+	6.08899i	0.255040	+	0.255040i
$571$	−11.7107			−0.490076			−0.245038	−	0.969513i	$-0.578800\pi$
$571$	−11.7107			−0.490076			−0.245038	+	0.969513i	$0.578800\pi$
$572$	−16.3641	−	2.34528i	−0.684218	−	0.0980611i
$573$	−14.4491			−0.603619
$574$	7.59481	+	7.59481i	0.317001	+	0.317001i
$575$	20.5407			0.856605
$576$		−	3.24343i		−	0.135143i
$577$	19.4184	−	19.4184i	0.808399	−	0.808399i	−0.175993	−	0.984391i	$-0.556313\pi$
$577$	19.4184	−	19.4184i	0.808399	−	0.808399i	0.984391	+	0.175993i	$0.0563135\pi$
$578$	1.14739	+	1.14739i	0.0477253	+	0.0477253i
$579$	−7.90835	+	7.90835i	−0.328660	+	0.328660i
$580$	12.0878	−	12.0878i	0.501920	−	0.501920i
$581$	19.1039			0.792562
$582$	−2.01386			−0.0834771
$583$	0.0407380	−	4.52771i	0.00168720	−	0.187519i
$584$		−	4.25821i		−	0.176206i
$585$	8.51086	−	6.49752i	0.351881	−	0.268639i
$586$	17.4498			0.720846
$587$	−8.36249	+	8.36249i	−0.345157	+	0.345157i	−0.858302	−	0.513145i	$-0.828480\pi$
$587$	−8.36249	+	8.36249i	−0.345157	+	0.345157i	0.513145	+	0.858302i	$0.328480\pi$
$588$	5.68853			0.234591
$589$	1.25915			0.0518823
$590$	12.6622	+	12.6622i	0.521295	+	0.521295i
$591$	16.1620	+	16.1620i	0.664818	+	0.664818i
$592$	4.41155	+	4.41155i	0.181314	+	0.181314i
$593$	16.4025	−	16.4025i	0.673571	−	0.673571i	−0.284966	−	0.958538i	$-0.591982\pi$
$593$	16.4025	−	16.4025i	0.673571	−	0.673571i	0.958538	+	0.284966i	$0.0919824\pi$
$594$	1.85952	−	1.82636i	0.0762970	−	0.0749363i
$595$			19.4942i			0.799184i
$596$	−15.2584	+	15.2584i	−0.625008	+	0.625008i
$597$		−	7.50680i		−	0.307233i
$598$	−12.1120	+	9.24679i	−0.495298	+	0.378129i
$599$	−13.3902			−0.547108			−0.273554	−	0.961857i	$-0.588199\pi$
$599$	−13.3902			−0.547108			−0.273554	+	0.961857i	$0.588199\pi$
$600$	7.17889	+	7.17889i	0.293077	+	0.293077i
$601$			6.54965i			0.267166i	0.991038	+	0.133583i	$0.0426483\pi$
$601$			6.54965i			0.267166i	−0.991038	+	0.133583i	$0.957352\pi$
$602$	4.02088			0.163879
$603$	−1.05880	+	1.05880i	−0.0431176	+	0.0431176i
$604$	−12.3784	−	12.3784i	−0.503670	−	0.503670i
$605$	23.5111	−	22.6799i	0.955864	−	0.922068i
$606$	−4.49759	−	4.49759i	−0.182702	−	0.182702i
$607$		−	14.1544i		−	0.574508i	−0.957854	−	0.287254i	$-0.907258\pi$
$607$		−	14.1544i		−	0.574508i	0.957854	−	0.287254i	$-0.0927424\pi$
$608$			21.5753i			0.874995i
$609$	5.00113	+	5.00113i	0.202656	+	0.202656i
$610$			8.54226i			0.345866i
$611$	13.1194	+	17.1846i	0.530755	+	0.695216i
$612$			5.34251i			0.215958i
$613$	7.38248	+	7.38248i	0.298176	+	0.298176i	0.840299	−	0.542123i	$-0.182379\pi$
$613$	7.38248	+	7.38248i	0.298176	+	0.298176i	−0.542123	+	0.840299i	$0.682379\pi$
$614$	−8.05444			−0.325051
$615$	−23.8960			−0.963580
$616$	14.9738	+	0.134727i	0.603312	+	0.00542829i
$617$	9.94361	−	9.94361i	0.400315	−	0.400315i	−0.478029	−	0.878344i	$-0.658649\pi$
$617$	9.94361	−	9.94361i	0.400315	−	0.400315i	0.878344	+	0.478029i	$0.158649\pi$
$618$	−1.19501	+	1.19501i	−0.0480704	+	0.0480704i
$619$	−30.6084	−	30.6084i	−1.23026	−	1.23026i	−0.963865	−	0.266392i	$-0.914169\pi$
$619$	−30.6084	−	30.6084i	−1.23026	−	1.23026i	−0.266392	−	0.963865i	$-0.585831\pi$
$620$	1.40102			0.0562662
$621$			5.37795i			0.215810i
$622$	−8.02183	+	8.02183i	−0.321646	+	0.321646i
$623$	11.9177			0.477473
$624$	2.41544	+	0.324026i	0.0966948	+	0.0129714i
$625$	29.5091			1.18036
$626$	8.50136	+	8.50136i	0.339783	+	0.339783i
$627$	−8.73066	+	8.57495i	−0.348669	+	0.342451i
$628$		−	30.5075i		−	1.21738i
$629$	25.2232	+	25.2232i	1.00571	+	1.00571i
$630$	−2.80305	+	2.80305i	−0.111676	+	0.111676i
$631$	−15.1418	−	15.1418i	−0.602787	−	0.602787i	0.338264	−	0.941051i	$-0.390160\pi$
$631$	−15.1418	−	15.1418i	−0.602787	−	0.602787i	−0.941051	+	0.338264i	$0.890160\pi$
$632$	24.2128	+	24.2128i	0.963133	+	0.963133i
$633$			17.2372i			0.685117i
$634$	18.1247			0.719823
$635$	−34.5475	+	34.5475i	−1.37098	+	1.37098i
$636$			1.88730i			0.0748361i
$637$	1.97262	−	14.7048i	0.0781580	−	0.582626i
$638$	−7.60482	−	7.74291i	−0.301078	−	0.306545i
$639$	−8.20263	+	8.20263i	−0.324491	+	0.324491i
$640$			27.1612i			1.07364i
$641$		−	12.0230i		−	0.474879i	−0.971402	−	0.237440i	$-0.923692\pi$
$641$		−	12.0230i		−	0.474879i	0.971402	−	0.237440i	$-0.0763082\pi$
$642$	−1.40907	+	1.40907i	−0.0556115	+	0.0556115i
$643$	−26.6519	+	26.6519i	−1.05105	+	1.05105i	−0.0524238	+	0.998625i	$0.516695\pi$
$643$	−26.6519	+	26.6519i	−1.05105	+	1.05105i	−0.998625	+	0.0524238i	$0.983305\pi$
$644$	−8.92937	+	8.92937i	−0.351867	+	0.351867i
$645$	−6.32557	+	6.32557i	−0.249069	+	0.249069i
$646$			11.2059i			0.440889i
$647$		−	36.9555i		−	1.45287i	−0.687236	−	0.726435i	$-0.741176\pi$
$647$		−	36.9555i		−	1.45287i	0.687236	−	0.726435i	$-0.258824\pi$
$648$	−1.87957	+	1.87957i	−0.0738366	+	0.0738366i
$649$	−18.1556	+	17.8318i	−0.712671	+	0.699961i
$650$	8.60198	−	6.56708i	0.337397	−	0.257582i
$651$			0.579647i			0.0227181i
$652$	4.44288	−	4.44288i	0.173997	−	0.173997i
$653$	32.2621			1.26251			0.631256	−	0.775574i	$-0.282540\pi$
$653$	32.2621			1.26251			0.631256	+	0.775574i	$0.282540\pi$
$654$		−	10.3200i		−	0.403543i
$655$	−20.5029	−	20.5029i	−0.801113	−	0.801113i
$656$	−3.84580	−	3.84580i	−0.150153	−	0.150153i
$657$	−1.13276	+	1.13276i	−0.0441931	+	0.0441931i
$658$	−5.65977	−	5.65977i	−0.220641	−	0.220641i
$659$		−	50.4228i		−	1.96419i	−0.188380	−	0.982096i	$-0.560324\pi$
$659$		−	50.4228i		−	1.96419i	0.188380	−	0.982096i	$-0.439676\pi$
$660$	−9.71435	+	9.54110i	−0.378131	+	0.371387i
$661$	5.71549	+	5.71549i	0.222307	+	0.222307i	0.809469	−	0.587162i	$-0.199755\pi$
$661$	5.71549	+	5.71549i	0.222307	+	0.222307i	−0.587162	+	0.809469i	$0.699755\pi$
$662$	−26.5425			−1.03160
$663$	13.8103	+	1.85263i	0.536349	+	0.0719501i
$664$	29.8962			1.16020
$665$	13.1607	−	13.1607i	0.510349	−	0.510349i
$666$			7.25364i			0.281073i
$667$	22.3934			0.867076
$668$	−4.03721	−	4.03721i	−0.156204	−	0.156204i
$669$	−6.56283	+	6.56283i	−0.253734	+	0.253734i
$670$	−2.47104	+	2.47104i	−0.0954647	+	0.0954647i
$671$	−12.1391	−	0.109221i	−0.468623	−	0.00421643i
$672$	−9.93216			−0.383141
$673$	−34.6702			−1.33644			−0.668220	−	0.743964i	$-0.732943\pi$
$673$	−34.6702			−1.33644			−0.668220	+	0.743964i	$0.732943\pi$
$674$	11.4232	+	11.4232i	0.440006	+	0.440006i
$675$		−	3.81943i		−	0.147010i
$676$	4.73643	−	17.3361i	0.182170	−	0.666772i
$677$			5.73000i			0.220222i	0.993919	+	0.110111i	$0.0351206\pi$
$677$			5.73000i			0.220222i	−0.993919	+	0.110111i	$0.964879\pi$
$678$	2.15373	+	2.15373i	0.0827136	+	0.0827136i
$679$			4.35273i			0.167042i
$680$			30.5070i			1.16989i
$681$	18.2796	+	18.2796i	0.700475	+	0.700475i
$682$	0.00800258	−	0.889425i	0.000306435	−	0.0340578i
$683$	20.1652	+	20.1652i	0.771600	+	0.771600i	0.978386	−	0.206786i	$-0.0663004\pi$
$683$	20.1652	+	20.1652i	0.771600	+	0.771600i	−0.206786	+	0.978386i	$0.566300\pi$
$684$	3.60677	−	3.60677i	0.137908	−	0.137908i
$685$	−4.02106			−0.153637
$686$			14.8365i			0.566461i
$687$	20.9701	+	20.9701i	0.800061	+	0.800061i
$688$	−2.03606			−0.0776242
$689$	4.87864	+	0.654459i	0.185861	+	0.0249329i
$690$			12.5512i			0.477814i
$691$	5.21220	−	5.21220i	0.198282	−	0.198282i	−0.600981	−	0.799263i	$-0.705223\pi$
$691$	5.21220	−	5.21220i	0.198282	−	0.198282i	0.799263	+	0.600981i	$0.205223\pi$
$692$			29.8347i			1.13415i
$693$	−3.94746	−	4.01914i	−0.149952	−	0.152675i
$694$	3.49905	−	3.49905i	0.132822	−	0.132822i
$695$	−29.1922	−	29.1922i	−1.10732	−	1.10732i
$696$	7.82642	+	7.82642i	0.296660	+	0.296660i
$697$	−21.9885	−	21.9885i	−0.832874	−	0.832874i
$698$	14.1653			0.536163
$699$	23.9759			0.906852
$700$	6.34165	−	6.34165i	0.239692	−	0.239692i
$701$	−31.1840			−1.17780			−0.588901	−	0.808205i	$-0.700439\pi$
$701$	−31.1840			−1.17780			−0.588901	+	0.808205i	$0.700439\pi$
$702$	1.71939	+	2.25217i	0.0648942	+	0.0850025i
$703$		−	34.0567i		−	1.28447i
$704$	10.7568	+	0.0967840i	0.405412	+	0.00364768i
$705$	17.8077			0.670676
$706$	11.3350			0.426597
$707$	−9.72104	+	9.72104i	−0.365597	+	0.365597i
$708$	7.50037	−	7.50037i	0.281881	−	0.281881i
$709$	−2.76609	−	2.76609i	−0.103883	−	0.103883i	0.653255	−	0.757138i	$-0.273403\pi$
$709$	−2.76609	−	2.76609i	−0.103883	−	0.103883i	−0.757138	+	0.653255i	$0.773403\pi$
$710$	−19.1435	+	19.1435i	−0.718441	+	0.718441i
$711$		−	12.8821i		−	0.483115i
$712$	18.6504			0.698952
$713$	1.29773	+	1.29773i	0.0486005	+	0.0486005i
$714$	−5.15860			−0.193056
$715$	21.2950	+	28.4201i	0.796388	+	1.06285i
$716$	19.7407			0.737744
$717$	−8.94929	−	8.94929i	−0.334217	−	0.334217i
$718$	−11.1948			−0.417786
$719$			16.5549i			0.617392i	0.951161	+	0.308696i	$0.0998925\pi$
$719$			16.5549i			0.617392i	−0.951161	+	0.308696i	$0.900107\pi$
$720$	1.41939	−	1.41939i	0.0528976	−	0.0528976i
$721$	2.58288	+	2.58288i	0.0961916	+	0.0961916i
$722$	−2.99293	+	2.99293i	−0.111385	+	0.111385i
$723$	−18.6089	+	18.6089i	−0.692072	+	0.692072i
$724$	34.8681			1.29586
$725$	−15.9038			−0.590653
$726$	6.00160	+	6.22158i	0.222740	+	0.230904i
$727$			30.4580i			1.12962i	0.825220	+	0.564812i	$0.191051\pi$
$727$			30.4580i			1.12962i	−0.825220	+	0.564812i	$0.808949\pi$
$728$	−2.16440	+	16.1344i	−0.0802178	+	0.597980i
$729$	1.00000			0.0370370
$730$	−2.64365	+	2.64365i	−0.0978459	+	0.0978459i
$731$	−11.6413			−0.430568
$732$	5.05995			0.187021
$733$	−18.9219	−	18.9219i	−0.698898	−	0.698898i	0.265275	−	0.964173i	$-0.414537\pi$
$733$	−18.9219	−	18.9219i	−0.698898	−	0.698898i	−0.964173	+	0.265275i	$0.914537\pi$
$734$	−13.5036	−	13.5036i	−0.498426	−	0.498426i
$735$	−8.64103	−	8.64103i	−0.318729	−	0.318729i
$736$	−22.2365	+	22.2365i	−0.819647	+	0.819647i
$737$	−3.47990	−	3.54309i	−0.128184	−	0.130511i
$738$		−	6.32342i		−	0.232768i
$739$	−15.2211	+	15.2211i	−0.559918	+	0.559918i	−0.929284	−	0.369366i	$-0.879575\pi$
$739$	−15.2211	+	15.2211i	−0.559918	+	0.559918i	0.369366	+	0.929284i	$0.379575\pi$
$740$		−	37.8939i		−	1.39301i
$741$	−8.07273	−	10.5742i	−0.296559	−	0.388452i
$742$	−1.82233			−0.0668997
$743$	8.54965	+	8.54965i	0.313656	+	0.313656i	0.846324	−	0.532668i	$-0.178811\pi$
$743$	8.54965	+	8.54965i	0.313656	+	0.313656i	−0.532668	+	0.846324i	$0.678811\pi$
$744$			0.907106i			0.0332561i
$745$	46.3558			1.69835
$746$	−2.20314	+	2.20314i	−0.0806625	+	0.0806625i
$747$	−7.95292	−	7.95292i	−0.290982	−	0.290982i
$748$	−17.7184	−	0.159421i	−0.647848	−	0.00582900i
$749$	3.04554	+	3.04554i	0.111282	+	0.111282i
$750$			2.75524i			0.100607i
$751$			46.3464i			1.69121i	0.533813	+	0.845603i	$0.320759\pi$
$751$			46.3464i			1.69121i	−0.533813	+	0.845603i	$0.679241\pi$
$752$	2.86595	+	2.86595i	0.104511	+	0.104511i
$753$		−	8.24119i		−	0.300326i
$754$	9.37786	−	7.15942i	0.341522	−	0.260731i
$755$			37.6063i			1.36863i
$756$	1.66037	+	1.66037i	0.0603870	+	0.0603870i
$757$	−29.8417			−1.08462			−0.542308	−	0.840179i	$-0.682450\pi$
$757$	−29.8417			−1.08462			−0.542308	+	0.840179i	$0.682450\pi$
$758$	−13.5602			−0.492527
$759$	−17.8359	−	0.160478i	−0.647403	−	0.00582499i
$760$	20.5955	−	20.5955i	0.747078	−	0.747078i
$761$	−13.1416	+	13.1416i	−0.476383	+	0.476383i	−0.903973	−	0.427590i	$-0.859363\pi$
$761$	−13.1416	+	13.1416i	−0.476383	+	0.476383i	0.427590	+	0.903973i	$0.359363\pi$
$762$	−9.14205	−	9.14205i	−0.331181	−	0.331181i
$763$	−22.3055			−0.807513
$764$			19.9747i			0.722659i
$765$	8.11541	−	8.11541i	0.293413	−	0.293413i
$766$	28.5166			1.03035
$767$	−16.7875	−	21.9893i	−0.606160	−	0.793987i
$768$	−13.6743			−0.493429
$769$	−33.2430	−	33.2430i	−1.19877	−	1.19877i	−0.974534	−	0.224238i	$-0.928011\pi$
$769$	−33.2430	−	33.2430i	−1.19877	−	1.19877i	−0.224238	−	0.974534i	$-0.571989\pi$
$770$	−9.21266	−	9.37995i	−0.332001	−	0.338030i
$771$			5.22792i			0.188279i
$772$	10.9327	+	10.9327i	0.393475	+	0.393475i
$773$	−5.48192	+	5.48192i	−0.197171	+	0.197171i	−0.798786	−	0.601615i	$-0.794524\pi$
$773$	−5.48192	+	5.48192i	−0.197171	+	0.197171i	0.601615	+	0.798786i	$0.294524\pi$
$774$	−1.67389	−	1.67389i	−0.0601667	−	0.0601667i
$775$	−0.921652	−	0.921652i	−0.0331067	−	0.0331067i
$776$			6.81171i			0.244526i
$777$	15.6779			0.562443
$778$	−10.7035	+	10.7035i	−0.383738	+	0.383738i
$779$			29.6892i			1.06373i
$780$	−8.98230	−	11.7656i	−0.321618	−	0.421275i
$781$	−26.9592	−	27.4487i	−0.964676	−	0.982193i
$782$	−11.5492	+	11.5492i	−0.413000	+	0.413000i
$783$		−	4.16393i		−	0.148807i
$784$		−	2.78136i		−	0.0993343i
$785$	−46.3418	+	46.3418i	−1.65401	+	1.65401i
$786$	5.42552	−	5.42552i	0.193522	−	0.193522i
$787$	29.8081	−	29.8081i	1.06254	−	1.06254i	0.0646331	−	0.997909i	$-0.479412\pi$
$787$	29.8081	−	29.8081i	1.06254	−	1.06254i	0.997909	−	0.0646331i	$-0.0205877\pi$
$788$	22.3427	−	22.3427i	0.795927	−	0.795927i
$789$		−	17.5714i		−	0.625558i
$790$		−	30.0644i		−	1.06964i
$791$	4.65505	−	4.65505i	0.165515	−	0.165515i
$792$	−6.17750	−	6.28967i	−0.219508	−	0.223494i
$793$	1.75464	−	13.0799i	0.0623092	−	0.464481i
$794$		−	0.0446048i		−	0.00158297i
$795$	2.86685	−	2.86685i	0.101677	−	0.101677i
$796$	−10.3776			−0.367823
$797$			49.5814i			1.75626i	0.478418	+	0.878132i	$0.341210\pi$
$797$			49.5814i			1.75626i	−0.478418	+	0.878132i	$0.658790\pi$
$798$	3.48261	+	3.48261i	0.123283	+	0.123283i
$799$	16.3862	+	16.3862i	0.579701	+	0.579701i
$800$	15.7924	−	15.7924i	0.558345	−	0.558345i
$801$	−4.96133	−	4.96133i	−0.175300	−	0.175300i
$802$		−	2.33156i		−	0.0823303i
$803$	−3.72298	−	3.79058i	−0.131381	−	0.133767i
$804$	1.46370	+	1.46370i	0.0516208	+	0.0516208i
$805$	27.1279			0.956133
$806$	0.958361	+	0.128562i	0.0337568	+	0.00452841i
$807$	28.7261			1.01121
$808$	−15.2127	+	15.2127i	−0.535182	+	0.535182i
$809$		−	15.6394i		−	0.549852i	−0.961465	−	0.274926i	$-0.911347\pi$
$809$		−	15.6394i		−	0.549852i	0.961465	−	0.274926i	$-0.0886534\pi$
$810$	2.33382			0.0820020
$811$	−38.3800	−	38.3800i	−1.34770	−	1.34770i	−0.888149	−	0.459556i	$-0.848009\pi$
$811$	−38.3800	−	38.3800i	−1.34770	−	1.34770i	−0.459556	−	0.888149i	$-0.651991\pi$
$812$	6.91366	−	6.91366i	0.242622	−	0.242622i
$813$	−15.1136	+	15.1136i	−0.530058	+	0.530058i
$814$	−24.0566	−	0.216449i	−0.843185	−	0.00758654i
$815$	−13.4977			−0.472804
$816$	2.61217			0.0914444
$817$	7.85910	+	7.85910i	0.274955	+	0.274955i
$818$		−	29.6039i		−	1.03508i
$819$	4.86780	−	3.71627i	0.170095	−	0.129857i
$820$			33.0343i			1.15361i
$821$	38.6771	+	38.6771i	1.34984	+	1.34984i	0.885828	+	0.464013i	$0.153591\pi$
$821$	38.6771	+	38.6771i	1.34984	+	1.34984i	0.464013	+	0.885828i	$0.346409\pi$
$822$		−	1.06406i		−	0.0371135i
$823$			8.81111i			0.307136i	0.988138	+	0.153568i	$0.0490764\pi$
$823$			8.81111i			0.307136i	−0.988138	+	0.153568i	$0.950924\pi$
$824$	4.04203	+	4.04203i	0.140811	+	0.140811i
$825$	12.6671	+	0.113972i	0.441012	+	0.00396799i
$826$	7.24217	+	7.24217i	0.251987	+	0.251987i
$827$	−18.8157	+	18.8157i	−0.654284	+	0.654284i	−0.954022	−	0.299737i	$-0.903101\pi$
$827$	−18.8157	+	18.8157i	−0.654284	+	0.654284i	0.299737	+	0.954022i	$0.403101\pi$
$828$	7.43458			0.258369
$829$		−	46.8681i		−	1.62780i	−0.581007	−	0.813898i	$-0.697341\pi$
$829$		−	46.8681i		−	1.62780i	0.581007	−	0.813898i	$-0.302659\pi$
$830$	−18.5607	−	18.5607i	−0.644250	−	0.644250i
$831$	0.382657			0.0132742
$832$	−1.55484	+	11.5905i	−0.0539045	+	0.401829i
$833$		−	15.9025i		−	0.550990i
$834$	7.72492	−	7.72492i	0.267492	−	0.267492i
$835$			12.2653i			0.424457i
$836$	11.8542	+	12.0694i	0.409985	+	0.417430i
$837$	0.241306	−	0.241306i	0.00834077	−	0.00834077i
$838$	−5.20842	−	5.20842i	−0.179922	−	0.179922i
$839$	3.10149	+	3.10149i	0.107075	+	0.107075i	0.758615	−	0.651539i	$-0.225877\pi$
$839$	3.10149	+	3.10149i	0.107075	+	0.107075i	−0.651539	+	0.758615i	$0.725877\pi$
$840$	9.48111	+	9.48111i	0.327129	+	0.327129i
$841$	11.6617			0.402127
$842$	−17.4791			−0.602370
$843$	13.7908	−	13.7908i	0.474980	−	0.474980i
$844$	23.8290			0.820229
$845$	−33.5287	+	19.1392i	−1.15342	+	0.658408i
$846$			4.71231i			0.162013i
$847$	13.4472	−	12.9718i	0.462053	−	0.445716i
$848$	0.922777			0.0316883
$849$	10.0335			0.344349
$850$	8.20229	−	8.20229i	0.281336	−	0.281336i
$851$	35.1003	−	35.1003i	1.20322	−	1.20322i
$852$	11.3395	+	11.3395i	0.388484	+	0.388484i
$853$	14.7203	−	14.7203i	0.504012	−	0.504012i	−0.408670	−	0.912682i	$-0.634007\pi$
$853$	14.7203	−	14.7203i	0.504012	−	0.504012i	0.912682	+	0.408670i	$0.134007\pi$
$854$			4.88576i			0.167187i
$855$	−10.9575			−0.374740
$856$	4.76606	+	4.76606i	0.162901	+	0.162901i
$857$	1.19547			0.0408365			0.0204182	−	0.999792i	$-0.493500\pi$
$857$	1.19547			0.0408365			0.0204182	+	0.999792i	$0.493500\pi$
$858$	−7.52059	+	5.63513i	−0.256749	+	0.192380i
$859$	−11.7469			−0.400800			−0.200400	−	0.979714i	$-0.564224\pi$
$859$	−11.7469			−0.400800			−0.200400	+	0.979714i	$0.564224\pi$
$860$	8.74460	+	8.74460i	0.298188	+	0.298188i
$861$	−13.6674			−0.465783
$862$			17.3943i			0.592453i
$863$	8.00957	−	8.00957i	0.272649	−	0.272649i	−0.557517	−	0.830166i	$-0.688246\pi$
$863$	8.00957	−	8.00957i	0.272649	−	0.272649i	0.830166	+	0.557517i	$0.188246\pi$
$864$	4.13475	+	4.13475i	0.140667	+	0.140667i
$865$	45.3198	−	45.3198i	1.54092	−	1.54092i
$866$	22.0813	−	22.0813i	0.750352	−	0.750352i
$867$	−2.06481			−0.0701247
$868$	0.801315			0.0271984
$869$	42.7232	+	0.384401i	1.44929	+	0.0130399i
$870$		−	9.71786i		−	0.329466i
$871$	4.29123	−	3.27609i	0.145403	−	0.111006i
$872$	−34.9065			−1.18208
$873$	1.81204	−	1.81204i	0.0613281	−	0.0613281i
$874$	15.5940			0.527474
$875$	5.95515			0.201321
$876$	1.56595	+	1.56595i	0.0529085	+	0.0529085i
$877$	4.04042	+	4.04042i	0.136435	+	0.136435i	0.772026	−	0.635591i	$-0.219243\pi$
$877$	4.04042	+	4.04042i	0.136435	+	0.136435i	−0.635591	+	0.772026i	$0.719243\pi$
$878$	−13.3153	−	13.3153i	−0.449370	−	0.449370i
$879$	−15.7011	+	15.7011i	−0.529584	+	0.529584i
$880$	4.66504	+	4.74975i	0.157258	+	0.160114i
$881$		−	50.3839i		−	1.69748i	−0.528814	−	0.848738i	$-0.677363\pi$
$881$		−	50.3839i		−	1.69748i	0.528814	−	0.848738i	$-0.322637\pi$
$882$	2.28661	−	2.28661i	0.0769942	−	0.0769942i
$883$			5.00125i			0.168305i	0.996453	+	0.0841527i	$0.0268184\pi$
$883$			5.00125i			0.168305i	−0.996453	+	0.0841527i	$0.973182\pi$
$884$	2.56111	−	19.0917i	0.0861394	−	0.642122i
$885$	−22.7865			−0.765960
$886$	−1.65237	−	1.65237i	−0.0555124	−	0.0555124i
$887$			37.8985i			1.27251i	0.771480	+	0.636254i	$0.219517\pi$
$887$			37.8985i			1.27251i	−0.771480	+	0.636254i	$0.780483\pi$
$888$	24.5349			0.823336
$889$	−19.7595	+	19.7595i	−0.662713	+	0.662713i
$890$	−11.5788	−	11.5788i	−0.388123	−	0.388123i
$891$	−0.0298401	+	3.31649i	−0.000999680	+	0.111107i
$892$	9.07259	+	9.07259i	0.303773	+	0.303773i
$893$		−	22.1248i		−	0.740380i
$894$			12.2668i			0.410263i
$895$	−29.9866	−	29.9866i	−1.00234	−	1.00234i
$896$			15.5349i			0.518984i
$897$	2.57810	−	19.2183i	0.0860802	−	0.641681i
$898$			22.0787i			0.736777i
$899$	−1.00478	−	1.00478i	−0.0335114	−	0.0335114i
$900$	−5.28005			−0.176002
$901$	5.27601			0.175769
$902$	20.9716	+	0.188691i	0.698277	+	0.00628273i
$903$	−3.61792	+	3.61792i	−0.120397	+	0.120397i
$904$	7.28482	−	7.28482i	0.242290	−	0.242290i
$905$	−52.9655	−	52.9655i	−1.76063	−	1.76063i
$906$	−9.95146			−0.330615
$907$		−	38.6871i		−	1.28459i	−0.766459	−	0.642293i	$-0.777983\pi$
$907$		−	38.6871i		−	1.28459i	0.766459	−	0.642293i	$-0.222017\pi$
$908$	25.2701	−	25.2701i	0.838616	−	0.838616i
$909$	8.09372			0.268452
$910$	11.3606	−	8.67309i	0.376599	−	0.287510i
$911$	32.3534			1.07192			0.535958	−	0.844245i	$-0.319951\pi$
$911$	32.3534			1.07192			0.535958	+	0.844245i	$0.319951\pi$
$912$	−1.76350	−	1.76350i	−0.0583952	−	0.0583952i
$913$	26.6131	−	26.1385i	0.880765	−	0.865057i
$914$			17.5150i			0.579344i
$915$	−7.68619	−	7.68619i	−0.254098	−	0.254098i
$916$	28.9895	−	28.9895i	0.957841	−	0.957841i
$917$	−11.7267	−	11.7267i	−0.387248	−	0.387248i
$918$	2.14752	+	2.14752i	0.0708787	+	0.0708787i
$919$			24.6934i			0.814560i	0.913303	+	0.407280i	$0.133523\pi$
$919$			24.6934i			0.814560i	−0.913303	+	0.407280i	$0.866477\pi$
$920$	42.4533			1.39964
$921$	7.24725	−	7.24725i	0.238805	−	0.238805i
$922$		−	13.9633i		−	0.459858i
$923$	33.2447	−	25.3802i	1.09426	−	0.835401i
$924$	−5.55614	+	5.45705i	−0.182784	+	0.179524i
$925$	−24.9283	+	24.9283i	−0.819637	+	0.819637i
$926$			22.1332i			0.727343i
$927$		−	2.15050i		−	0.0706318i
$928$	17.2168	−	17.2168i	0.565170	−	0.565170i
$929$	1.53789	−	1.53789i	0.0504565	−	0.0504565i	−0.681428	−	0.731885i	$-0.738641\pi$
$929$	1.53789	−	1.53789i	0.0504565	−	0.0504565i	0.731885	+	0.681428i	$0.238641\pi$
$930$	0.563165	−	0.563165i	0.0184669	−	0.0184669i
$931$	−10.7359	+	10.7359i	−0.351855	+	0.351855i
$932$		−	33.1448i		−	1.08569i
$933$		−	14.4358i		−	0.472608i
$934$	−9.60854	+	9.60854i	−0.314401	+	0.314401i
$935$	26.6725	+	27.1568i	0.872285	+	0.888124i
$936$	7.61777	−	5.81570i	0.248995	−	0.190092i
$937$			11.5909i			0.378660i	0.981914	+	0.189330i	$0.0606315\pi$
$937$			11.5909i			0.378660i	−0.981914	+	0.189330i	$0.939368\pi$
$938$	−1.41332	+	1.41332i	−0.0461464	+	0.0461464i
$939$	−15.2988			−0.499256
$940$		−	24.6177i		−	0.802940i
$941$	−18.0136	−	18.0136i	−0.587227	−	0.587227i	0.349653	−	0.936879i	$-0.386300\pi$
$941$	−18.0136	−	18.0136i	−0.587227	−	0.587227i	−0.936879	+	0.349653i	$0.886300\pi$
$942$	−12.2631	−	12.2631i	−0.399552	−	0.399552i
$943$	−30.5990	+	30.5990i	−0.996440	+	0.996440i
$944$	−3.66724	−	3.66724i	−0.119358	−	0.119358i
$945$		−	5.04429i		−	0.164091i
$946$	5.60139	−	5.50149i	0.182117	−	0.178869i
$947$	−12.1742	−	12.1742i	−0.395608	−	0.395608i	0.481073	−	0.876681i	$-0.340247\pi$
$947$	−12.1742	−	12.1742i	−0.395608	−	0.395608i	−0.876681	+	0.481073i	$0.840247\pi$
$948$	−17.8084			−0.578390
$949$	4.59098	−	3.50493i	0.149030	−	0.113775i
$950$	−11.0749			−0.359316
$951$	−16.3083	+	16.3083i	−0.528833	+	0.528833i
$952$			17.4485i			0.565511i
$953$	48.5047			1.57122			0.785611	−	0.618721i	$-0.212349\pi$
$953$	48.5047			1.57122			0.785611	+	0.618721i	$0.212349\pi$
$954$	0.758633	+	0.758633i	0.0245617	+	0.0245617i
$955$	30.3421	−	30.3421i	0.981847	−	0.981847i
$956$	−12.3717	+	12.3717i	−0.400128	+	0.400128i
$957$	13.8096	+	0.124252i	0.446402	+	0.00401650i
$958$	2.62325			0.0847533
$959$	−2.29985			−0.0742661
$960$	6.81097	+	6.81097i	0.219823	+	0.219823i
$961$			30.8835i			0.996243i
$962$	3.47727	−	25.9212i	0.112112	−	0.835733i
$963$		−	2.53571i		−	0.0817123i
$964$	25.7253	+	25.7253i	0.828556	+	0.828556i
$965$		−	33.2140i		−	1.06920i
$966$			7.17865i			0.230969i
$967$	−21.4874	−	21.4874i	−0.690988	−	0.690988i	0.271461	−	0.962449i	$-0.412493\pi$
$967$	−21.4874	−	21.4874i	−0.690988	−	0.690988i	−0.962449	+	0.271461i	$0.912493\pi$
$968$	21.0440	−	20.2999i	0.676379	−	0.652465i
$969$	−10.0829	−	10.0829i	−0.323908	−	0.323908i
$970$	4.22896	−	4.22896i	0.135784	−	0.135784i
$971$	6.06986			0.194791			0.0973955	−	0.995246i	$-0.468949\pi$
$971$	6.06986			0.194791			0.0973955	+	0.995246i	$0.468949\pi$
$972$		−	1.38242i		−	0.0443411i
$973$	−16.6965	−	16.6965i	−0.535267	−	0.535267i
$974$	20.6885			0.662904
$975$	−1.83097	+	13.6489i	−0.0586379	+	0.437114i
$976$		−	2.47402i		−	0.0791914i
$977$	0.247338	−	0.247338i	0.00791305	−	0.00791305i	−0.703139	−	0.711052i	$-0.748219\pi$
$977$	0.247338	−	0.247338i	0.00791305	−	0.00791305i	0.711052	+	0.703139i	$0.248219\pi$
$978$		−	3.57180i		−	0.114213i
$979$	16.6022	−	16.3062i	0.530610	−	0.521147i
$980$	−11.9455	+	11.9455i	−0.381586	+	0.381586i
$981$	9.28576	+	9.28576i	0.296471	+	0.296471i
$982$	−2.89952	−	2.89952i	−0.0925273	−	0.0925273i
$983$	13.1994	+	13.1994i	0.420996	+	0.420996i	0.885546	−	0.464551i	$-0.153784\pi$
$983$	13.1994	+	13.1994i	0.420996	+	0.420996i	−0.464551	+	0.885546i	$0.653784\pi$
$984$	−21.3885			−0.681839
$985$	−67.8784			−2.16279
$986$	8.94213	−	8.94213i	0.284775	−	0.284775i
$987$	10.1851			0.324196
$988$	−14.6179	+	11.1599i	−0.465059	+	0.355044i
$989$			16.1999i			0.515126i
$990$	−0.0696413	+	7.74009i	−0.00221334	+	0.245996i
$991$	−46.3956			−1.47380			−0.736902	−	0.676000i	$-0.763712\pi$
$991$	−46.3956			−1.47380			−0.736902	+	0.676000i	$0.763712\pi$
$992$	1.99548			0.0633566
$993$	23.8825	−	23.8825i	0.757888	−	0.757888i
$994$	−10.9491	+	10.9491i	−0.347285	+	0.347285i
$995$	15.7638	+	15.7638i	0.499745	+	0.499745i
$996$	−10.9943	+	10.9943i	−0.348367	+	0.348367i
$997$			36.0228i			1.14085i	0.821348	+	0.570427i	$0.193222\pi$
$997$			36.0228i			1.14085i	−0.821348	+	0.570427i	$0.806778\pi$
$998$	−22.9986			−0.728007
$999$	−6.52671	−	6.52671i	−0.206496	−	0.206496i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.m.b.109.6	✓	28
11.10	odd	2	inner	429.2.m.b.109.9	yes	28
13.8	odd	4	inner	429.2.m.b.307.9	yes	28
143.21	even	4	inner	429.2.m.b.307.6	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.m.b.109.6	✓	28	1.1	even	1	trivial
429.2.m.b.109.9	yes	28	11.10	odd	2	inner
429.2.m.b.307.6	yes	28	143.21	even	4	inner
429.2.m.b.307.9	yes	28	13.8	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.555689 - 0.555689i) q^{2} +1.00000 q^{3} -1.38242i q^{4} +(-2.09993 + 2.09993i) q^{5} +(-0.555689 - 0.555689i) q^{6} +(-1.20106 + 1.20106i) q^{7} +(-1.87957 + 1.87957i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.555689 - 0.555689i) q^{2} +1.00000 q^{3} -1.38242i q^{4} +(-2.09993 + 2.09993i) q^{5} +(-0.555689 - 0.555689i) q^{6} +(-1.20106 + 1.20106i) q^{7} +(-1.87957 + 1.87957i) q^{8} +1.00000 q^{9} +2.33382 q^{10} +(-0.0298401 + 3.31649i) q^{11} -1.38242i q^{12} +(-3.57354 - 0.479383i) q^{13} +1.33483 q^{14} +(-2.09993 + 2.09993i) q^{15} -0.675922 q^{16} -3.86461 q^{17} +(-0.555689 - 0.555689i) q^{18} +(2.60902 + 2.60902i) q^{19} +(2.90299 + 2.90299i) q^{20} +(-1.20106 + 1.20106i) q^{21} +(1.85952 - 1.82636i) q^{22} +5.37795i q^{23} +(-1.87957 + 1.87957i) q^{24} -3.81943i q^{25} +(1.71939 + 2.25217i) q^{26} +1.00000 q^{27} +(1.66037 + 1.66037i) q^{28} -4.16393i q^{29} +2.33382 q^{30} +(0.241306 - 0.241306i) q^{31} +(4.13475 + 4.13475i) q^{32} +(-0.0298401 + 3.31649i) q^{33} +(2.14752 + 2.14752i) q^{34} -5.04429i q^{35} -1.38242i q^{36} +(-6.52671 - 6.52671i) q^{37} -2.89961i q^{38} +(-3.57354 - 0.479383i) q^{39} -7.89395i q^{40} +(5.68971 + 5.68971i) q^{41} +1.33483 q^{42} +3.01228 q^{43} +(4.58478 + 0.0412515i) q^{44} +(-2.09993 + 2.09993i) q^{45} +(2.98847 - 2.98847i) q^{46} +(-4.24006 - 4.24006i) q^{47} -0.675922 q^{48} +4.11491i q^{49} +(-2.12241 + 2.12241i) q^{50} -3.86461 q^{51} +(-0.662709 + 4.94013i) q^{52} -1.36521 q^{53} +(-0.555689 - 0.555689i) q^{54} +(-6.90174 - 7.02707i) q^{55} -4.51496i q^{56} +(2.60902 + 2.60902i) q^{57} +(-2.31385 + 2.31385i) q^{58} +(5.42554 + 5.42554i) q^{59} +(2.90299 + 2.90299i) q^{60} +3.66021i q^{61} -0.268183 q^{62} +(-1.20106 + 1.20106i) q^{63} -3.24343i q^{64} +(8.51086 - 6.49752i) q^{65} +(1.85952 - 1.82636i) q^{66} +(-1.05880 + 1.05880i) q^{67} +5.34251i q^{68} +5.37795i q^{69} +(-2.80305 + 2.80305i) q^{70} +(-8.20263 + 8.20263i) q^{71} +(-1.87957 + 1.87957i) q^{72} +(-1.13276 + 1.13276i) q^{73} +7.25364i q^{74} -3.81943i q^{75} +(3.60677 - 3.60677i) q^{76} +(-3.94746 - 4.01914i) q^{77} +(1.71939 + 2.25217i) q^{78} -12.8821i q^{79} +(1.41939 - 1.41939i) q^{80} +1.00000 q^{81} -6.32342i q^{82} +(-7.95292 - 7.95292i) q^{83} +(1.66037 + 1.66037i) q^{84} +(8.11541 - 8.11541i) q^{85} +(-1.67389 - 1.67389i) q^{86} -4.16393i q^{87} +(-6.17750 - 6.28967i) q^{88} +(-4.96133 - 4.96133i) q^{89} +2.33382 q^{90} +(4.86780 - 3.71627i) q^{91} +7.43458 q^{92} +(0.241306 - 0.241306i) q^{93} +4.71231i q^{94} -10.9575 q^{95} +(4.13475 + 4.13475i) q^{96} +(1.81204 - 1.81204i) q^{97} +(2.28661 - 2.28661i) q^{98} +(-0.0298401 + 3.31649i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{3} - 4 q^{5} + 28 q^{9}+O(q^{10}) \) 28 * q + 28 * q^3 - 4 * q^5 + 28 * q^9	\( 28 q + 28 q^{3} - 4 q^{5} + 28 q^{9} - 4 q^{15} - 20 q^{16} - 16 q^{20} - 8 q^{22} + 12 q^{26} + 28 q^{27} + 8 q^{31} - 32 q^{34} - 12 q^{37} + 36 q^{44} - 4 q^{45} - 40 q^{47} - 20 q^{48} + 8 q^{53} - 16 q^{55} + 16 q^{58} - 44 q^{59} - 16 q^{60} - 8 q^{66} - 20 q^{67} - 36 q^{70} - 60 q^{71} + 12 q^{78} - 8 q^{80} + 28 q^{81} + 48 q^{86} + 32 q^{89} + 4 q^{91} + 64 q^{92} + 8 q^{93} + 8 q^{97}+O(q^{100}) \) 28 * q + 28 * q^3 - 4 * q^5 + 28 * q^9 - 4 * q^15 - 20 * q^16 - 16 * q^20 - 8 * q^22 + 12 * q^26 + 28 * q^27 + 8 * q^31 - 32 * q^34 - 12 * q^37 + 36 * q^44 - 4 * q^45 - 40 * q^47 - 20 * q^48 + 8 * q^53 - 16 * q^55 + 16 * q^58 - 44 * q^59 - 16 * q^60 - 8 * q^66 - 20 * q^67 - 36 * q^70 - 60 * q^71 + 12 * q^78 - 8 * q^80 + 28 * q^81 + 48 * q^86 + 32 * q^89 + 4 * q^91 + 64 * q^92 + 8 * q^93 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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