LMFDB - Embedded newform 429.2.bj.a.112.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(73,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 14, 5]))

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

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

chi := DirichletCharacter("429.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bj (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			112.3
Character	$\chi$	$=$	429.112
Dual form			429.2.bj.a.226.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.753510 - 1.47885i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.443641 + 0.610619i) q^{4} +(1.42413 - 2.79501i) q^{5} +(1.47885 + 0.753510i) q^{6} +(0.104512 + 0.659862i) q^{7} +(-2.04133 - 0.323315i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.753510 - 1.47885i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.443641 + 0.610619i) q^{4} +(1.42413 - 2.79501i) q^{5} +(1.47885 + 0.753510i) q^{6} +(0.104512 + 0.659862i) q^{7} +(-2.04133 - 0.323315i) q^{8} +(0.309017 - 0.951057i) q^{9} -5.20649 q^{10} +(-3.27883 - 0.499275i) q^{11} -0.754767i q^{12} +(3.57199 - 0.490826i) q^{13} +(0.897084 - 0.651770i) q^{14} +(0.490721 + 3.09829i) q^{15} +(1.52650 + 4.69809i) q^{16} +(-1.97560 - 6.08028i) q^{17} +(-1.63931 + 0.259642i) q^{18} +(0.758551 - 4.78930i) q^{19} +(1.07488 + 2.10958i) q^{20} +(-0.472409 - 0.472409i) q^{21} +(1.73228 + 5.22510i) q^{22} +4.04548i q^{23} +(1.84151 - 0.938296i) q^{24} +(-2.84501 - 3.91582i) q^{25} +(-3.41738 - 4.91258i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-0.449290 - 0.228925i) q^{28} +(-0.798298 + 1.09876i) q^{29} +(4.21214 - 3.06030i) q^{30} +(-8.19577 + 4.17595i) q^{31} +(2.87466 - 2.87466i) q^{32} +(2.94610 - 1.52333i) q^{33} +(-7.50317 + 7.50317i) q^{34} +(1.99316 + 0.647617i) q^{35} +(0.443641 + 0.610619i) q^{36} +(-4.35662 + 0.690021i) q^{37} +(-7.65422 + 2.48701i) q^{38} +(-2.60130 + 2.49665i) q^{39} +(-3.81078 + 5.24509i) q^{40} +(0.470994 - 2.97374i) q^{41} +(-0.342656 + 1.05459i) q^{42} -12.5403 q^{43} +(1.75949 - 1.78062i) q^{44} +(-2.21813 - 2.21813i) q^{45} +(5.98264 - 3.04831i) q^{46} +(1.76834 - 11.1649i) q^{47} +(-3.99643 - 2.90358i) q^{48} +(6.23290 - 2.02519i) q^{49} +(-3.64716 + 7.15795i) q^{50} +(5.17220 + 3.75782i) q^{51} +(-1.28497 + 2.39887i) q^{52} +(-2.48752 + 7.65580i) q^{53} +(1.17362 - 1.17362i) q^{54} +(-6.06495 + 8.45333i) q^{55} -1.38079i q^{56} +(2.20140 + 4.32049i) q^{57} +(2.22643 + 0.352632i) q^{58} +(11.4014 - 1.80581i) q^{59} +(-2.10958 - 1.07488i) q^{60} +(8.25870 - 2.68341i) q^{61} +(12.3512 + 8.97366i) q^{62} +(0.659862 + 0.104512i) q^{63} +(2.97891 + 0.967907i) q^{64} +(3.71511 - 10.6827i) q^{65} +(-4.47268 - 3.20898i) q^{66} +(4.19011 + 4.19011i) q^{67} +(4.58920 + 1.49112i) q^{68} +(-2.37787 - 3.27286i) q^{69} +(-0.544140 - 3.43556i) q^{70} +(0.259397 - 0.509094i) q^{71} +(-0.938296 + 1.84151i) q^{72} +(-2.25224 - 14.2201i) q^{73} +(4.30320 + 5.92284i) q^{74} +(4.60333 + 1.49571i) q^{75} +(2.58791 + 2.58791i) q^{76} +(-0.0132243 - 2.21576i) q^{77} +(5.65226 + 1.96567i) q^{78} +(14.0463 + 4.56390i) q^{79} +(15.3051 + 2.42410i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-4.75261 + 1.54422i) q^{82} +(1.21553 + 0.619341i) q^{83} +(0.498042 - 0.0788821i) q^{84} +(-19.8080 - 3.13727i) q^{85} +(9.44922 + 18.5451i) q^{86} -1.35815i q^{87} +(6.53175 + 2.07928i) q^{88} +(2.13107 - 2.13107i) q^{89} +(-1.60889 + 4.95166i) q^{90} +(0.697192 + 2.30572i) q^{91} +(-2.47025 - 1.79474i) q^{92} +(4.17595 - 8.19577i) q^{93} +(-17.8436 + 5.79773i) q^{94} +(-12.3059 - 8.94074i) q^{95} +(-0.635965 + 4.01533i) q^{96} +(4.52560 - 2.30591i) q^{97} +(-7.69150 - 7.69150i) q^{98} +(-1.48805 + 2.96407i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 28 q^{3} - 6 q^{5} - 28 q^{9}+O(q^{10}) $ 112 * q - 28 * q^3 - 6 * q^5 - 28 * q^9	$ 112 q - 28 q^{3} - 6 q^{5} - 28 q^{9} - 10 q^{11} + 10 q^{13} - 60 q^{14} + 4 q^{15} + 80 q^{16} - 74 q^{20} + 8 q^{22} + 30 q^{24} + 38 q^{26} - 28 q^{27} - 20 q^{29} - 8 q^{31} + 20 q^{33} - 48 q^{34} + 20 q^{35} + 12 q^{37} - 10 q^{39} + 40 q^{40} - 110 q^{41} + 20 q^{42} - 36 q^{44} + 4 q^{45} - 20 q^{46} - 30 q^{47} - 20 q^{48} + 90 q^{50} - 10 q^{52} + 52 q^{53} - 64 q^{55} + 30 q^{57} + 24 q^{58} - 36 q^{59} - 74 q^{60} - 60 q^{61} + 48 q^{66} + 60 q^{67} + 60 q^{68} + 116 q^{70} + 20 q^{71} - 30 q^{72} + 70 q^{73} + 120 q^{74} - 52 q^{78} - 120 q^{79} + 8 q^{80} - 28 q^{81} + 30 q^{83} + 30 q^{84} - 40 q^{85} + 62 q^{86} + 48 q^{89} - 4 q^{91} - 144 q^{92} - 8 q^{93} - 20 q^{94} + 82 q^{97} - 10 q^{99}+O(q^{100}) $ 112 * q - 28 * q^3 - 6 * q^5 - 28 * q^9 - 10 * q^11 + 10 * q^13 - 60 * q^14 + 4 * q^15 + 80 * q^16 - 74 * q^20 + 8 * q^22 + 30 * q^24 + 38 * q^26 - 28 * q^27 - 20 * q^29 - 8 * q^31 + 20 * q^33 - 48 * q^34 + 20 * q^35 + 12 * q^37 - 10 * q^39 + 40 * q^40 - 110 * q^41 + 20 * q^42 - 36 * q^44 + 4 * q^45 - 20 * q^46 - 30 * q^47 - 20 * q^48 + 90 * q^50 - 10 * q^52 + 52 * q^53 - 64 * q^55 + 30 * q^57 + 24 * q^58 - 36 * q^59 - 74 * q^60 - 60 * q^61 + 48 * q^66 + 60 * q^67 + 60 * q^68 + 116 * q^70 + 20 * q^71 - 30 * q^72 + 70 * q^73 + 120 * q^74 - 52 * q^78 - 120 * q^79 + 8 * q^80 - 28 * q^81 + 30 * q^83 + 30 * q^84 - 40 * q^85 + 62 * q^86 + 48 * q^89 - 4 * q^91 - 144 * q^92 - 8 * q^93 - 20 * q^94 + 82 * q^97 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.753510	−	1.47885i	−0.532812	−	1.04570i	−0.987876	−	0.155244i	$-0.950384\pi$
$2$	−0.753510	−	1.47885i	−0.532812	−	1.04570i	0.455064	−	0.890459i	$-0.349616\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	−0.443641	+	0.610619i	−0.221820	+	0.305310i
$5$	1.42413	−	2.79501i	0.636890	−	1.24997i	−0.316605	−	0.948557i	$-0.602543\pi$
$5$	1.42413	−	2.79501i	0.636890	−	1.24997i	0.953495	−	0.301409i	$-0.0974570\pi$
$6$	1.47885	+	0.753510i	0.603737	+	0.307619i
$7$	0.104512	+	0.659862i	0.0395018	+	0.249404i	0.999535	−	0.0304804i	$-0.00970373\pi$
$7$	0.104512	+	0.659862i	0.0395018	+	0.249404i	−0.960034	+	0.279885i	$0.909704\pi$
$8$	−2.04133	−	0.323315i	−0.721719	−	0.114309i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−5.20649			−1.64644
$11$	−3.27883	−	0.499275i	−0.988604	−	0.150537i
$11$	−3.27883	−	0.499275i	−0.988604	−	0.150537i
$12$		−	0.754767i		−	0.217882i
$13$	3.57199	−	0.490826i	0.990691	−	0.136131i
$13$	3.57199	−	0.490826i	0.990691	−	0.136131i
$14$	0.897084	−	0.651770i	0.239756	−	0.174193i
$15$	0.490721	+	3.09829i	0.126704	+	0.799976i
$16$	1.52650	+	4.69809i	0.381625	+	1.17452i
$17$	−1.97560	−	6.08028i	−0.479154	−	1.47469i	−0.840272	−	0.542165i	$-0.817605\pi$
$17$	−1.97560	−	6.08028i	−0.479154	−	1.47469i	0.361117	−	0.932520i	$-0.382395\pi$
$18$	−1.63931	+	0.259642i	−0.386390	+	0.0611982i
$19$	0.758551	−	4.78930i	0.174023	−	1.09874i	−0.733793	−	0.679373i	$-0.762252\pi$
$19$	0.758551	−	4.78930i	0.174023	−	1.09874i	0.907816	−	0.419368i	$-0.137748\pi$
$20$	1.07488	+	2.10958i	0.240352	+	0.471717i
$21$	−0.472409	−	0.472409i	−0.103088	−	0.103088i
$22$	1.73228	+	5.22510i	0.369324	+	1.11399i
$23$			4.04548i			0.843541i	0.906703	+	0.421770i	$0.138591\pi$
$23$			4.04548i			0.843541i	−0.906703	+	0.421770i	$0.861409\pi$
$24$	1.84151	−	0.938296i	0.375897	−	0.191529i
$25$	−2.84501	−	3.91582i	−0.569003	−	0.783165i
$26$	−3.41738	−	4.91258i	−0.670204	−	0.963436i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−0.449290	−	0.228925i	−0.0849078	−	0.0432627i
$29$	−0.798298	+	1.09876i	−0.148240	+	0.204035i	−0.876679	−	0.481076i	$-0.840246\pi$
$29$	−0.798298	+	1.09876i	−0.148240	+	0.204035i	0.728439	+	0.685111i	$0.240246\pi$
$30$	4.21214	−	3.06030i	0.769028	−	0.558731i
$31$	−8.19577	+	4.17595i	−1.47200	+	0.750023i	−0.991880	−	0.127178i	$-0.959408\pi$
$31$	−8.19577	+	4.17595i	−1.47200	+	0.750023i	−0.480123	+	0.877201i	$0.659408\pi$
$32$	2.87466	−	2.87466i	0.508172	−	0.508172i
$33$	2.94610	−	1.52333i	0.512849	−	0.265177i
$34$	−7.50317	+	7.50317i	−1.28678	+	1.28678i
$35$	1.99316	+	0.647617i	0.336905	+	0.109467i
$36$	0.443641	+	0.610619i	0.0739401	+	0.101770i
$37$	−4.35662	+	0.690021i	−0.716225	+	0.113439i	−0.503902	−	0.863761i	$-0.668103\pi$
$37$	−4.35662	+	0.690021i	−0.716225	+	0.113439i	−0.212323	+	0.977200i	$0.568103\pi$
$38$	−7.65422	+	2.48701i	−1.24168	+	0.403446i
$39$	−2.60130	+	2.49665i	−0.416541	+	0.399784i
$40$	−3.81078	+	5.24509i	−0.602538	+	0.829322i
$41$	0.470994	−	2.97374i	0.0735570	−	0.464421i	−0.923225	−	0.384260i	$-0.874457\pi$
$41$	0.470994	−	2.97374i	0.0735570	−	0.464421i	0.996782	−	0.0801606i	$-0.0255433\pi$
$42$	−0.342656	+	1.05459i	−0.0528729	+	0.162726i
$43$	−12.5403			−1.91237			−0.956186	−	0.292760i	$-0.905426\pi$
$43$	−12.5403			−1.91237			−0.956186	+	0.292760i	$0.905426\pi$
$44$	1.75949	−	1.78062i	0.265253	−	0.268438i
$45$	−2.21813	−	2.21813i	−0.330660	−	0.330660i
$46$	5.98264	−	3.04831i	0.882093	−	0.449449i
$47$	1.76834	−	11.1649i	0.257939	−	1.62856i	−0.430026	−	0.902817i	$-0.641496\pi$
$47$	1.76834	−	11.1649i	0.257939	−	1.62856i	0.687964	−	0.725744i	$-0.258504\pi$
$48$	−3.99643	−	2.90358i	−0.576835	−	0.419095i
$49$	6.23290	−	2.02519i	0.890414	−	0.289313i
$50$	−3.64716	+	7.15795i	−0.515786	+	1.01229i
$51$	5.17220	+	3.75782i	0.724253	+	0.526200i
$52$	−1.28497	+	2.39887i	−0.178193	+	0.332664i
$53$	−2.48752	+	7.65580i	−0.341687	+	1.05161i	0.621646	+	0.783298i	$0.286464\pi$
$53$	−2.48752	+	7.65580i	−0.341687	+	1.05161i	−0.963333	+	0.268307i	$0.913536\pi$
$54$	1.17362	−	1.17362i	0.159709	−	0.159709i
$55$	−6.06495	+	8.45333i	−0.817798	+	1.13985i
$56$		−	1.38079i		−	0.184515i
$57$	2.20140	+	4.32049i	0.291582	+	0.572263i
$58$	2.22643	+	0.352632i	0.292345	+	0.0463028i
$59$	11.4014	−	1.80581i	1.48434	−	0.235096i	0.638950	−	0.769248i	$-0.279369\pi$
$59$	11.4014	−	1.80581i	1.48434	−	0.235096i	0.845388	+	0.534152i	$0.179369\pi$
$60$	−2.10958	−	1.07488i	−0.272346	−	0.138767i
$61$	8.25870	−	2.68341i	1.05742	−	0.343576i	0.271842	−	0.962342i	$-0.412367\pi$
$61$	8.25870	−	2.68341i	1.05742	−	0.343576i	0.785575	+	0.618766i	$0.212367\pi$
$62$	12.3512	+	8.97366i	1.56860	+	1.13966i
$63$	0.659862	+	0.104512i	0.0831348	+	0.0131673i
$64$	2.97891	+	0.967907i	0.372364	+	0.120988i
$65$	3.71511	−	10.6827i	0.460802	−	1.32503i
$66$	−4.47268	−	3.20898i	−0.550549	−	0.394998i
$67$	4.19011	+	4.19011i	0.511904	+	0.511904i	0.915109	−	0.403206i	$-0.132104\pi$
$67$	4.19011	+	4.19011i	0.511904	+	0.511904i	−0.403206	+	0.915109i	$0.632104\pi$
$68$	4.58920	+	1.49112i	0.556522	+	0.180825i
$69$	−2.37787	−	3.27286i	−0.286262	−	0.394006i
$70$	−0.544140	−	3.43556i	−0.0650371	−	0.410628i
$71$	0.259397	−	0.509094i	0.0307847	−	0.0604184i	−0.875102	−	0.483939i	$-0.839206\pi$
$71$	0.259397	−	0.509094i	0.0307847	−	0.0604184i	0.905887	+	0.423520i	$0.139206\pi$
$72$	−0.938296	+	1.84151i	−0.110579	+	0.217024i
$73$	−2.25224	−	14.2201i	−0.263605	−	1.66434i	−0.663801	−	0.747909i	$-0.731058\pi$
$73$	−2.25224	−	14.2201i	−0.263605	−	1.66434i	0.400196	−	0.916430i	$-0.368942\pi$
$74$	4.30320	+	5.92284i	0.500237	+	0.688517i
$75$	4.60333	+	1.49571i	0.531546	+	0.172710i
$76$	2.58791	+	2.58791i	0.296854	+	0.296854i
$77$	−0.0132243	−	2.21576i	−0.00150704	−	0.252509i
$78$	5.65226	+	1.96567i	0.639993	+	0.222569i
$79$	14.0463	+	4.56390i	1.58033	+	0.513479i	0.962141	−	0.272552i	$-0.0878678\pi$
$79$	14.0463	+	4.56390i	1.58033	+	0.513479i	0.618186	+	0.786032i	$0.287868\pi$
$80$	15.3051	+	2.42410i	1.71117	+	0.271022i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−4.75261	+	1.54422i	−0.524838	+	0.170530i
$83$	1.21553	+	0.619341i	0.133421	+	0.0679815i	0.519427	−	0.854515i	$-0.326145\pi$
$83$	1.21553	+	0.619341i	0.133421	+	0.0679815i	−0.386006	+	0.922496i	$0.626145\pi$
$84$	0.498042	−	0.0788821i	0.0543408	−	0.00860674i
$85$	−19.8080	−	3.13727i	−2.14848	−	0.340285i
$86$	9.44922	+	18.5451i	1.01894	+	1.99977i
$87$		−	1.35815i		−	0.145609i
$88$	6.53175	+	2.07928i	0.696287	+	0.221652i
$89$	2.13107	−	2.13107i	0.225893	−	0.225893i	−0.585081	−	0.810975i	$-0.698937\pi$
$89$	2.13107	−	2.13107i	0.225893	−	0.225893i	0.810975	+	0.585081i	$0.198937\pi$
$90$	−1.60889	+	4.95166i	−0.169592	+	0.521951i
$91$	0.697192	+	2.30572i	0.0730856	+	0.241705i
$92$	−2.47025	−	1.79474i	−0.257541	−	0.187114i
$93$	4.17595	−	8.19577i	0.433026	−	0.849862i
$94$	−17.8436	+	5.79773i	−1.84042	+	0.597990i
$95$	−12.3059	−	8.94074i	−1.26256	−	0.917300i
$96$	−0.635965	+	4.01533i	−0.0649079	+	0.409813i
$97$	4.52560	−	2.30591i	0.459505	−	0.234129i	−0.208886	−	0.977940i	$-0.566984\pi$
$97$	4.52560	−	2.30591i	0.459505	−	0.234129i	0.668390	+	0.743811i	$0.266984\pi$
$98$	−7.69150	−	7.69150i	−0.776959	−	0.776959i
$99$	−1.48805	+	2.96407i	−0.149555	+	0.297900i
$100$	3.65324			0.365324
$101$	−2.26752	+	6.97872i	−0.225627	+	0.694409i	0.772600	+	0.634893i	$0.218956\pi$
$101$	−2.26752	+	6.97872i	−0.225627	+	0.694409i	−0.998227	+	0.0595161i	$0.981044\pi$
$102$	1.65994	−	10.4804i	0.164359	−	1.03772i
$103$	0.352875	−	0.485691i	0.0347698	−	0.0478565i	−0.791278	−	0.611456i	$-0.790584\pi$
$103$	0.352875	−	0.485691i	0.0347698	−	0.0478565i	0.826048	+	0.563600i	$0.190584\pi$
$104$	−7.45029	−	0.152939i	−0.730561	−	0.0149969i
$105$	−1.99316	+	0.647617i	−0.194512	+	0.0632009i
$106$	13.1961	−	2.09006i	1.28172	−	0.203005i
$107$	−4.34339	−	5.97816i	−0.419891	−	0.577931i	0.545705	−	0.837978i	$-0.316262\pi$
$107$	−4.34339	−	5.97816i	−0.419891	−	0.577931i	−0.965596	+	0.260047i	$0.916262\pi$
$108$	−0.717826	−	0.233236i	−0.0690728	−	0.0224431i
$109$	10.0191	−	10.0191i	0.959657	−	0.959657i	−0.0395604	−	0.999217i	$-0.512596\pi$
$109$	10.0191	−	10.0191i	0.959657	−	0.959657i	0.999217	+	0.0395604i	$0.0125958\pi$
$110$	17.0712	+	2.59947i	1.62767	+	0.247850i
$111$	3.11900	−	3.11900i	0.296042	−	0.296042i
$112$	−2.94055	+	1.49829i	−0.277856	+	0.141575i
$113$	−0.525079	+	0.381492i	−0.0493952	+	0.0358877i	−0.612209	−	0.790696i	$-0.709719\pi$
$113$	−0.525079	+	0.381492i	−0.0493952	+	0.0358877i	0.562814	+	0.826584i	$0.309719\pi$
$114$	4.73057	−	6.51107i	0.443058	−	0.609817i
$115$	11.3072	+	5.76128i	1.05440	+	0.537242i
$116$	−0.316768	−	0.974912i	−0.0294112	−	0.0905184i
$117$	0.637002	−	3.54883i	0.0588908	−	0.328090i
$118$	−11.2616	−	15.5003i	−1.03671	−	1.42691i
$119$	3.80567	−	1.93909i	0.348866	−	0.177756i
$120$		−	6.48329i		−	0.591841i
$121$	10.5014	+	3.27407i	0.954677	+	0.297643i
$122$	−10.1914	−	10.1914i	−0.922683	−	0.922683i
$123$	1.36688	+	2.68265i	0.123247	+	0.241887i
$124$	1.08606	−	6.85711i	0.0975311	−	0.615787i
$125$	0.495030	−	0.0784050i	0.0442768	−	0.00701276i
$126$	−0.342656	−	1.05459i	−0.0305262	−	0.0939500i
$127$	−0.758630	−	2.33482i	−0.0673176	−	0.207182i	0.911739	−	0.410770i	$-0.134740\pi$
$127$	−0.758630	−	2.33482i	−0.0673176	−	0.207182i	−0.979057	+	0.203587i	$0.934740\pi$
$128$	−2.08518	−	13.1653i	−0.184306	−	1.16366i
$129$	10.1453	−	7.37098i	0.893243	−	0.648979i
$130$	−18.5975	+	2.55548i	−1.63111	+	0.224130i
$131$		−	1.66132i		−	0.145150i	−0.997363	−	0.0725752i	$-0.976878\pi$
$131$		−	1.66132i		−	0.145150i	0.997363	−	0.0725752i	$-0.0231217\pi$
$132$	−0.376836	+	2.47475i	−0.0327994	+	0.215399i
$133$	3.23955			0.280905
$134$	3.03924	−	9.35383i	0.262551	−	0.808048i
$135$	3.09829	+	0.490721i	0.266659	+	0.0422346i
$136$	2.06701	+	13.0506i	0.177245	+	1.11908i
$137$	15.8076	+	8.05436i	1.35053	+	0.688130i	0.971452	−	0.237234i	$-0.0762409\pi$
$137$	15.8076	+	8.05436i	1.35053	+	0.688130i	0.379079	+	0.925364i	$0.376241\pi$
$138$	−3.04831	+	5.98264i	−0.259489	+	0.509277i
$139$	5.23218	−	7.20148i	0.443788	−	0.610822i	−0.527261	−	0.849704i	$-0.676781\pi$
$139$	5.23218	−	7.20148i	0.443788	−	0.610822i	0.971049	+	0.238882i	$0.0767809\pi$
$140$	−1.27969	+	0.929752i	−0.108154	+	0.0785784i
$141$	5.13192	+	10.0720i	0.432186	+	0.848212i
$142$	−0.948331			−0.0795822
$143$	−11.9570	−	0.174069i	−0.999894	−	0.0145564i
$144$	4.93986			0.411655
$145$	1.93418	+	3.79603i	0.160625	+	0.315243i
$146$	−19.3323	+	14.0457i	−1.59995	+	1.16243i
$147$	−3.85214	+	5.30202i	−0.317720	+	0.437303i
$148$	1.51144	−	2.96636i	0.124239	−	0.243833i
$149$	−2.43247	−	1.23940i	−0.199275	−	0.101536i	0.351505	−	0.936186i	$-0.385670\pi$
$149$	−2.43247	−	1.23940i	−0.199275	−	0.101536i	−0.550781	+	0.834650i	$0.685670\pi$
$150$	−1.25673	−	7.93465i	−0.102611	−	0.647862i
$151$	2.09468	+	0.331765i	0.170463	+	0.0269987i	0.241082	−	0.970505i	$-0.422498\pi$
$151$	2.09468	+	0.331765i	0.170463	+	0.0269987i	−0.0706195	+	0.997503i	$0.522498\pi$
$152$	−3.09690	+	9.53129i	−0.251192	+	0.773089i
$153$	−6.39319			−0.516859
$154$	−3.26680	+	1.68915i	−0.263246	+	0.136116i
$155$			28.8543i			2.31764i
$156$	−0.370459	−	2.69602i	−0.0296604	−	0.215854i
$157$	−11.9348	+	8.67114i	−0.952501	+	0.692033i	−0.951397	−	0.307967i	$-0.900351\pi$
$157$	−11.9348	+	8.67114i	−0.952501	+	0.692033i	−0.00110403	+	0.999999i	$0.500351\pi$
$158$	−3.83468	−	24.2112i	−0.305071	−	1.92614i
$159$	−2.48752	−	7.65580i	−0.197273	−	0.607145i
$160$	−3.94081	−	12.1286i	−0.311549	−	0.958848i
$161$	−2.66946	+	0.422801i	−0.210383	+	0.0333213i
$162$	−0.259642	+	1.63931i	−0.0203994	+	0.128797i
$163$	−5.31384	−	10.4290i	−0.416212	−	0.816863i	−0.999988	−	0.00494747i	$-0.998425\pi$
$163$	−5.31384	−	10.4290i	−0.416212	−	0.816863i	0.583775	−	0.811915i	$-0.301575\pi$
$164$	1.60687	+	1.60687i	0.125476	+	0.125476i
$165$	−0.0620928	−	10.4038i	−0.00483391	−	0.809933i
$166$		−	2.26426i		−	0.175740i
$167$	3.09795	−	1.57848i	0.239726	−	0.122147i	−0.330001	−	0.943981i	$-0.607049\pi$
$167$	3.09795	−	1.57848i	0.239726	−	0.122147i	0.569727	+	0.821834i	$0.307049\pi$
$168$	0.811605	+	1.11708i	0.0626167	+	0.0861845i
$169$	12.5182	−	3.50645i	0.962937	−	0.269727i
$170$	10.2860	+	31.6569i	0.788897	+	2.42798i
$171$	−4.32049	−	2.20140i	−0.330396	−	0.168345i
$172$	5.56337	−	7.65732i	0.424203	−	0.583865i
$173$	−3.80605	+	2.76526i	−0.289369	+	0.210239i	−0.722993	−	0.690855i	$-0.757234\pi$
$173$	−3.80605	+	2.76526i	−0.289369	+	0.210239i	0.433625	+	0.901094i	$0.357234\pi$
$174$	−2.00849	+	1.02338i	−0.152263	+	0.0775820i
$175$	2.28657	−	2.28657i	0.172848	−	0.172848i
$176$	−2.65950	−	16.1664i	−0.200467	−	1.21859i
$177$	−8.16251	+	8.16251i	−0.613532	+	0.613532i
$178$	−4.75732	−	1.54575i	−0.356576	−	0.115859i
$179$	2.38682	+	3.28518i	0.178399	+	0.245546i	0.888847	−	0.458205i	$-0.151507\pi$
$179$	2.38682	+	3.28518i	0.178399	+	0.245546i	−0.710447	+	0.703750i	$0.751507\pi$
$180$	2.33849	−	0.370380i	0.174301	−	0.0276065i
$181$	8.72123	−	2.83370i	0.648244	−	0.210627i	0.0336043	−	0.999435i	$-0.489301\pi$
$181$	8.72123	−	2.83370i	0.648244	−	0.210627i	0.614640	+	0.788808i	$0.289301\pi$
$182$	2.88447	−	2.76843i	0.213811	−	0.205209i
$183$	−5.10415	+	7.02527i	−0.377310	+	0.519323i
$184$	1.30796	−	8.25815i	0.0964243	−	0.608799i
$185$	−4.27578	+	13.1595i	−0.314361	+	0.967505i
$186$	−15.2669			−1.11942
$187$	3.44194	+	20.9226i	0.251699	+	1.53001i
$188$	6.03296	+	6.03296i	0.439999	+	0.439999i
$189$	−0.595270	+	0.303305i	−0.0432995	+	0.0220622i
$190$	−3.94938	+	24.9354i	−0.286518	+	1.80901i
$191$	15.3055	+	11.1201i	1.10747	+	0.804622i	0.982263	−	0.187509i	$-0.0600415\pi$
$191$	15.3055	+	11.1201i	1.10747	+	0.804622i	0.125204	+	0.992131i	$0.460041\pi$
$192$	−2.97891	+	0.967907i	−0.214984	+	0.0698527i
$193$	−0.544988	+	1.06960i	−0.0392291	+	0.0769914i	−0.909789	−	0.415071i	$-0.863757\pi$
$193$	−0.544988	+	1.06960i	−0.0392291	+	0.0769914i	0.870560	+	0.492062i	$0.163757\pi$
$194$	−6.82017	−	4.95514i	−0.489660	−	0.355759i
$195$	3.27357	+	10.8262i	0.234425	+	0.775280i
$196$	−1.52855	+	4.70439i	−0.109182	+	0.336028i
$197$	−16.4466	+	16.4466i	−1.17177	+	1.17177i	−0.189985	+	0.981787i	$0.560844\pi$
$197$	−16.4466	+	16.4466i	−1.17177	+	1.17177i	−0.981787	+	0.189985i	$0.939156\pi$
$198$	5.50467	−	0.0328534i	0.391200	−	0.00233479i
$199$		−	23.7615i		−	1.68441i	−0.539161	−	0.842203i	$-0.681258\pi$
$199$		−	23.7615i		−	1.68441i	0.539161	−	0.842203i	$-0.318742\pi$
$200$	4.54156	+	8.91332i	0.321137	+	0.630267i
$201$	−5.85276	−	0.926986i	−0.412822	−	0.0653846i
$202$	12.0291	−	1.90522i	0.846362	−	0.134051i
$203$	−0.808464	−	0.411933i	−0.0567430	−	0.0289120i
$204$	−4.58920	+	1.49112i	−0.321308	+	0.104399i
$205$	−7.64088	−	5.55143i	−0.533662	−	0.387728i
$206$	−0.984157	−	0.155875i	−0.0685695	−	0.0108603i
$207$	3.84748	+	1.25012i	0.267418	+	0.0868895i
$208$	7.75858	+	16.0323i	0.537961	+	1.11164i
$209$	−4.87833	+	15.3246i	−0.337441	+	1.06002i
$210$	2.45959	+	2.45959i	0.169728	+	0.169728i
$211$	−0.577638	−	0.187686i	−0.0397662	−	0.0129208i	0.289066	−	0.957309i	$-0.406655\pi$
$211$	−0.577638	−	0.187686i	−0.0397662	−	0.0129208i	−0.328833	+	0.944388i	$0.606655\pi$
$212$	−3.57121	−	4.91535i	−0.245272	−	0.337588i
$213$	0.0893820	+	0.564335i	0.00612435	+	0.0386676i
$214$	−5.56800	+	10.9278i	−0.380621	+	0.747010i
$215$	−17.8590	+	35.0502i	−1.21797	+	2.39040i
$216$	−0.323315	−	2.04133i	−0.0219988	−	0.138895i
$217$	−3.61211	−	4.97164i	−0.245206	−	0.337497i
$218$	−22.3662	−	7.26723i	−1.51483	−	0.492199i
$219$	10.1805	+	10.1805i	0.687933	+	0.687933i
$220$	−2.47110	−	7.45362i	−0.166602	−	0.502523i
$221$	−10.0412	−	20.7490i	−0.675444	−	1.39573i
$222$	−6.96272	−	2.26232i	−0.467307	−	0.151837i
$223$	13.3391	+	2.11270i	0.893251	+	0.141477i	0.586153	−	0.810201i	$-0.300642\pi$
$223$	13.3391	+	2.11270i	0.893251	+	0.141477i	0.307098	+	0.951678i	$0.400642\pi$
$224$	2.19731	+	1.59644i	0.146814	+	0.106667i
$225$	−4.60333	+	1.49571i	−0.306889	+	0.0997141i
$226$	0.959820	+	0.489053i	0.0638463	+	0.0325313i
$227$	14.9764	−	2.37203i	0.994018	−	0.157437i	0.361824	−	0.932247i	$-0.382154\pi$
$227$	14.9764	−	2.37203i	0.994018	−	0.157437i	0.632195	+	0.774810i	$0.282154\pi$
$228$	−3.61480	−	0.572529i	−0.239396	−	0.0379166i
$229$	7.17651	+	14.0847i	0.474237	+	0.930743i	0.996936	+	0.0782256i	$0.0249254\pi$
$229$	7.17651	+	14.0847i	0.474237	+	0.930743i	−0.522698	+	0.852518i	$0.675075\pi$
$230$		−	21.0627i		−	1.38884i
$231$	1.31309	+	1.78481i	0.0863948	+	0.117432i
$232$	1.98484	−	1.98484i	0.130311	−	0.130311i
$233$	3.09754	−	9.53326i	0.202927	−	0.624545i	−0.796865	−	0.604157i	$-0.793510\pi$
$233$	3.09754	−	9.53326i	0.202927	−	0.624545i	0.999792	−	0.0203877i	$-0.00649005\pi$
$234$	−5.72817	+	1.73206i	−0.374462	+	0.113228i
$235$	−28.6875	−	20.8427i	−1.87137	−	1.35963i
$236$	−3.95547	+	7.76305i	−0.257479	+	0.505332i
$237$	−14.0463	+	4.56390i	−0.912402	+	0.296457i
$238$	−5.73523	−	4.16689i	−0.371760	−	0.270099i
$239$	1.18229	−	7.46472i	0.0764763	−	0.482852i	−0.919489	−	0.393115i	$-0.871397\pi$
$239$	1.18229	−	7.46472i	0.0764763	−	0.482852i	0.995965	−	0.0897370i	$-0.0286027\pi$
$240$	−13.8070	+	7.03500i	−0.891235	+	0.454107i
$241$	−9.35202	−	9.35202i	−0.602416	−	0.602416i	0.338537	−	0.940953i	$-0.390068\pi$
$241$	−9.35202	−	9.35202i	−0.602416	−	0.602416i	−0.940953	+	0.338537i	$0.890068\pi$
$242$	−3.07110	−	17.9971i	−0.197418	−	1.15690i
$243$	1.00000			0.0641500
$244$	−2.02535	+	6.23339i	−0.129660	+	0.399052i
$245$	3.21602	−	20.3052i	0.205464	−	1.29725i
$246$	2.93727	−	4.04281i	0.187274	−	0.257760i
$247$	0.358821	−	17.4796i	0.0228313	−	1.11220i
$248$	18.0804	−	5.87468i	1.14811	−	0.373043i
$249$	−1.34742	+	0.213410i	−0.0853893	+	0.0135243i
$250$	−0.488959	−	0.672994i	−0.0309245	−	0.0425639i
$251$	−14.3022	−	4.64706i	−0.902746	−	0.293320i	−0.179376	−	0.983781i	$-0.557408\pi$
$251$	−14.3022	−	4.64706i	−0.902746	−	0.293320i	−0.723370	+	0.690460i	$0.757408\pi$
$252$	−0.356559	+	0.356559i	−0.0224611	+	0.0224611i
$253$	2.01981	−	13.2644i	0.126984	−	0.833928i
$254$	−2.88121	+	2.88121i	−0.180783	+	0.180783i
$255$	17.8690	−	9.10473i	1.11900	−	0.570160i
$256$	−12.8303	+	9.32175i	−0.801893	+	0.582609i
$257$	−7.17454	+	9.87491i	−0.447536	+	0.615980i	−0.971866	−	0.235535i	$-0.924316\pi$
$257$	−7.17454	+	9.87491i	−0.447536	+	0.615980i	0.524330	+	0.851515i	$0.324316\pi$
$258$	−18.5451	−	9.44922i	−1.15457	−	0.588283i
$259$	−0.910638	−	2.80266i	−0.0565843	−	0.174149i
$260$	4.87491	+	7.00781i	0.302329	+	0.434606i
$261$	0.798298	+	1.09876i	0.0494134	+	0.0680118i
$262$	−2.45684	+	1.25182i	−0.151784	+	0.0773379i
$263$			7.12773i			0.439515i	0.975555	+	0.219757i	$0.0705266\pi$
$263$			7.12773i			0.439515i	−0.975555	+	0.219757i	$0.929473\pi$
$264$	−6.50646	+	2.15709i	−0.400445	+	0.132760i
$265$	17.8555	+	17.8555i	1.09685	+	1.09685i
$266$	−2.44104	−	4.79081i	−0.149670	−	0.293743i
$267$	−0.471461	+	2.97669i	−0.0288529	+	0.182170i
$268$	−4.41747	+	0.699658i	−0.269840	+	0.0427384i
$269$	−2.12988	−	6.55509i	−0.129861	−	0.399671i	0.864894	−	0.501954i	$-0.167385\pi$
$269$	−2.12988	−	6.55509i	−0.129861	−	0.399671i	−0.994755	+	0.102283i	$0.967385\pi$
$270$	−1.60889	−	4.95166i	−0.0979141	−	0.301349i
$271$	4.50119	+	28.4194i	0.273428	+	1.72636i	0.616767	+	0.787146i	$0.288442\pi$
$271$	4.50119	+	28.4194i	0.273428	+	1.72636i	−0.343339	+	0.939211i	$0.611558\pi$
$272$	25.5499	−	18.5631i	1.54919	−	1.12555i
$273$	−1.91931	−	1.45557i	−0.116162	−	0.0880950i
$274$		−	29.4460i		−	1.77890i
$275$	7.37324	+	14.2598i	0.444623	+	0.859896i
$276$	3.05339			0.183793
$277$	4.31908	−	13.2928i	0.259508	−	0.798685i	−0.733399	−	0.679798i	$-0.762067\pi$
$277$	4.31908	−	13.2928i	0.259508	−	0.798685i	0.992908	−	0.118887i	$-0.0379325\pi$
$278$	−14.5924	−	2.31121i	−0.875194	−	0.138617i
$279$	1.43894	+	9.08508i	0.0861468	+	0.543909i
$280$	−3.85931	−	1.96642i	−0.230638	−	0.117516i
$281$	−10.4431	+	20.4957i	−0.622982	+	1.22267i	0.336708	+	0.941609i	$0.390687\pi$
$281$	−10.4431	+	20.4957i	−0.622982	+	1.22267i	−0.959690	+	0.281062i	$0.909313\pi$
$282$	11.0279	−	15.1786i	0.656704	−	0.903875i
$283$	−21.0718	+	15.3095i	−1.25259	+	0.910058i	−0.998369	−	0.0570891i	$-0.981818\pi$
$283$	−21.0718	+	15.3095i	−1.25259	+	0.910058i	−0.254218	+	0.967147i	$0.581818\pi$
$284$	0.195784	+	0.384247i	0.0116176	+	0.0228009i
$285$	15.2109			0.901015
$286$	8.75230	+	17.8137i	0.517534	+	1.05335i
$287$	2.01148			0.118734
$288$	−1.84564	−	3.62228i	−0.108756	−	0.213445i
$289$	−19.3136	+	14.0321i	−1.13609	+	0.825419i
$290$	4.15633	−	5.72070i	0.244068	−	0.335931i
$291$	−2.30591	+	4.52560i	−0.135175	+	0.265295i
$292$	9.68226	+	4.93336i	0.566611	+	0.288703i
$293$	−2.47470	−	15.6247i	−0.144574	−	0.912802i	−0.948201	−	0.317670i	$-0.897100\pi$
$293$	−2.47470	−	15.6247i	−0.144574	−	0.912802i	0.803628	−	0.595132i	$-0.202900\pi$
$294$	10.7435	+	1.70160i	0.626574	+	0.0992396i
$295$	11.1898	−	34.4388i	0.651498	−	2.00510i
$296$	9.11640			0.529880
$297$	−0.538376	−	3.27264i	−0.0312397	−	0.189898i
$298$			4.53115i			0.262482i
$299$	1.98562	+	14.4504i	0.114832	+	0.835688i
$300$	−2.95553	+	2.14732i	−0.170638	+	0.123976i
$301$	−1.31061	−	8.27484i	−0.0755421	−	0.476954i
$302$	−1.08773	−	3.34770i	−0.0625921	−	0.192639i
$303$	−2.26752	−	6.97872i	−0.130266	−	0.400917i
$304$	23.6585	−	3.74713i	1.35691	−	0.214913i
$305$	4.26128	−	26.9047i	0.244000	−	1.54056i
$306$	4.81733	+	9.45455i	0.275389	+	0.540481i
$307$	10.7982	+	10.7982i	0.616288	+	0.616288i	0.944577	−	0.328289i	$-0.106472\pi$
$307$	10.7982	+	10.7982i	0.616288	+	0.616288i	−0.328289	+	0.944577i	$0.606472\pi$
$308$	1.35885	+	0.974924i	0.0774276	+	0.0555515i
$309$			0.600347i			0.0341525i
$310$	42.6712	−	21.7420i	2.42356	−	1.23487i
$311$	−4.89333	−	6.73509i	−0.277475	−	0.381912i	0.647420	−	0.762133i	$-0.275848\pi$
$311$	−4.89333	−	6.73509i	−0.277475	−	0.381912i	−0.924896	+	0.380221i	$0.875848\pi$
$312$	6.11731	−	4.25544i	0.346324	−	0.240917i
$313$	−3.41167	−	10.5000i	−0.192839	−	0.593497i	−0.999995	−	0.00315917i	$-0.998994\pi$
$313$	−3.41167	−	10.5000i	−0.192839	−	0.593497i	0.807156	−	0.590338i	$-0.201006\pi$
$314$	21.8163	+	11.1160i	1.23116	+	0.627310i
$315$	1.23184	−	1.69548i	0.0694063	−	0.0955296i
$316$	−9.01830	+	6.55218i	−0.507319	+	0.368589i
$317$	−17.8914	+	9.11615i	−1.00488	+	0.512014i	−0.877366	−	0.479823i	$-0.840701\pi$
$317$	−17.8914	+	9.11615i	−1.00488	+	0.512014i	−0.127518	+	0.991836i	$0.540701\pi$
$318$	−9.44739	+	9.44739i	−0.529783	+	0.529783i
$319$	3.16607	−	3.20409i	0.177266	−	0.179395i
$320$	6.94766	−	6.94766i	0.388386	−	0.388386i
$321$	7.02775	+	2.28346i	0.392251	+	0.127450i
$322$	2.63672	+	3.62914i	0.146939	+	0.202244i
$323$	−30.6189	+	4.84956i	−1.70368	+	0.269837i
$324$	0.717826	−	0.233236i	0.0398792	−	0.0129575i
$325$	−12.0843	−	12.5909i	−0.670318	−	0.698416i
$326$	−11.4189	+	15.7167i	−0.632433	+	0.870469i
$327$	−2.21655	+	13.9947i	−0.122575	+	0.773910i
$328$	−1.92291	+	5.91811i	−0.106175	+	0.326773i
$329$	7.55207			0.416359
$330$	−15.3388	+	7.93118i	−0.844374	+	0.436597i
$331$	1.60983	+	1.60983i	0.0884845	+	0.0884845i	0.749964	−	0.661479i	$-0.230071\pi$
$331$	1.60983	+	1.60983i	0.0884845	+	0.0884845i	−0.661479	+	0.749964i	$0.730071\pi$
$332$	−0.917438	+	0.467458i	−0.0503510	+	0.0256551i
$333$	−0.690021	+	4.35662i	−0.0378129	+	0.238742i
$334$	−4.66867	−	3.39199i	−0.255458	−	0.185601i
$335$	17.6787	−	5.74415i	0.965889	−	0.313836i
$336$	1.49829	−	2.94055i	0.0817382	−	0.160420i
$337$	−4.86438	−	3.53418i	−0.264980	−	0.192519i	0.447360	−	0.894354i	$-0.352364\pi$
$337$	−4.86438	−	3.53418i	−0.264980	−	0.192519i	−0.712340	+	0.701835i	$0.752364\pi$
$338$	−14.6181	−	15.8703i	−0.795118	−	0.863232i
$339$	0.200562	−	0.617267i	0.0108930	−	0.0335253i
$340$	10.7033	−	10.7033i	0.580468	−	0.580468i
$341$	28.9575	−	9.60030i	1.56814	−	0.519885i
$342$			8.04812i			0.435193i
$343$	4.11090	+	8.06809i	0.221968	+	0.435636i
$344$	25.5988	+	4.05445i	1.38020	+	0.218601i
$345$	−12.5341	+	1.98520i	−0.674812	+	0.106880i
$346$	6.95729	+	3.54492i	0.374026	+	0.190576i
$347$	9.51586	−	3.09189i	0.510838	−	0.165981i	−0.0422453	−	0.999107i	$-0.513451\pi$
$347$	9.51586	−	3.09189i	0.510838	−	0.165981i	0.553083	+	0.833126i	$0.313451\pi$
$348$	0.829310	+	0.602529i	0.0444557	+	0.0322989i
$349$	−11.7161	−	1.85564i	−0.627147	−	0.0993303i	−0.165232	−	0.986255i	$-0.552837\pi$
$349$	−11.7161	−	1.85564i	−0.627147	−	0.0993303i	−0.461915	+	0.886924i	$0.652837\pi$
$350$	−5.10443	−	1.65853i	−0.272843	−	0.0886522i
$351$	1.57061	+	3.24549i	0.0838328	+	0.173231i
$352$	−10.8608	+	7.99027i	−0.578880	+	0.425883i
$353$	−7.77760	−	7.77760i	−0.413960	−	0.413960i	0.469156	−	0.883115i	$-0.344558\pi$
$353$	−7.77760	−	7.77760i	−0.413960	−	0.413960i	−0.883115	+	0.469156i	$0.844558\pi$
$354$	18.2216	+	5.92057i	0.968470	+	0.314675i
$355$	−1.05351	−	1.45003i	−0.0559145	−	0.0769597i
$356$	0.355843	+	2.24670i	0.0188596	+	0.119075i
$357$	−1.93909	+	3.80567i	−0.102627	+	0.201418i
$358$	3.05978	−	6.00515i	0.161714	−	0.317382i
$359$	−1.61845	−	10.2185i	−0.0854188	−	0.539313i	−0.992874	−	0.119165i	$-0.961978\pi$
$359$	−1.61845	−	10.2185i	−0.0854188	−	0.539313i	0.907456	−	0.420148i	$-0.138022\pi$
$360$	3.81078	+	5.24509i	0.200846	+	0.276441i
$361$	−4.29192	−	1.39453i	−0.225890	−	0.0733963i
$362$	−10.7621	−	10.7621i	−0.565646	−	0.565646i
$363$	−10.4203	+	3.52382i	−0.546924	+	0.184952i
$364$	−1.71722	−	0.597193i	−0.0900068	−	0.0313014i
$365$	−42.9529	−	13.9562i	−2.24826	−	0.730502i
$366$	14.2353	+	2.25465i	0.744093	+	0.117853i
$367$	24.3594	+	17.6981i	1.27155	+	0.923834i	0.999263	−	0.0383825i	$-0.0122205\pi$
$367$	24.3594	+	17.6981i	1.27155	+	0.923834i	0.272285	+	0.962217i	$0.412221\pi$
$368$	−19.0060	+	6.17543i	−0.990757	+	0.321916i
$369$	−2.68265	−	1.36688i	−0.139653	−	0.0711569i
$370$	22.6827	−	3.59259i	1.17922	−	0.186770i
$371$	−5.31175	−	0.841298i	−0.275772	−	0.0436780i
$372$	3.15187	+	6.18589i	0.163417	+	0.320724i
$373$			6.88870i			0.356683i	0.983969	+	0.178342i	$0.0570732\pi$
$373$			6.88870i			0.356683i	−0.983969	+	0.178342i	$0.942927\pi$
$374$	28.3478	−	20.8555i	1.46583	−	1.07841i
$375$	−0.354402	+	0.354402i	−0.0183012	+	0.0183012i
$376$	−7.21952	+	22.2194i	−0.372318	+	1.14588i
$377$	−2.31221	+	4.31659i	−0.119085	+	0.222316i
$378$	0.897084	+	0.651770i	0.0461410	+	0.0335234i
$379$	1.99996	−	3.92515i	0.102731	−	0.201621i	−0.833920	−	0.551886i	$-0.813908\pi$
$379$	1.99996	−	3.92515i	0.102731	−	0.201621i	0.936651	+	0.350265i	$0.113908\pi$
$380$	10.9188	−	3.54772i	0.560121	−	0.181994i
$381$	1.98612	+	1.44300i	0.101752	+	0.0739272i
$382$	4.91207	−	31.0136i	0.251323	−	1.58679i
$383$	0.650213	−	0.331300i	0.0332243	−	0.0169286i	−0.437299	−	0.899316i	$-0.644065\pi$
$383$	0.650213	−	0.331300i	0.0332243	−	0.0169286i	0.470524	+	0.882387i	$0.344065\pi$
$384$	9.42534	+	9.42534i	0.480985	+	0.480985i
$385$	−6.21189	−	3.11856i	−0.316587	−	0.158936i
$386$	1.99243			0.101412
$387$	−3.87515	+	11.9265i	−0.196985	+	0.606258i
$388$	−0.599709	+	3.78641i	−0.0304456	+	0.192226i
$389$	−10.5531	+	14.5251i	−0.535064	+	0.736452i	−0.987892	−	0.155146i	$-0.950415\pi$
$389$	−10.5531	+	14.5251i	−0.535064	+	0.736452i	0.452828	+	0.891598i	$0.350415\pi$
$390$	13.5436	−	12.9988i	0.685808	−	0.658218i
$391$	24.5977	−	7.99227i	1.24396	−	0.404186i
$392$	−13.3782	+	2.11890i	−0.675700	+	0.107020i
$393$	0.976501	+	1.34404i	0.0492580	+	0.0677978i
$394$	36.7147	+	11.9293i	1.84966	+	0.600991i
$395$	32.7598	−	32.7598i	1.64833	−	1.64833i
$396$	−1.14976	−	2.22361i	−0.0577774	−	0.111741i
$397$	11.9258	−	11.9258i	0.598540	−	0.598540i	−0.341384	−	0.939924i	$-0.610896\pi$
$397$	11.9258	−	11.9258i	0.598540	−	0.598540i	0.939924	+	0.341384i	$0.110896\pi$
$398$	−35.1396	+	17.9045i	−1.76139	+	0.897472i
$399$	−2.62085	+	1.90416i	−0.131207	+	0.0953273i
$400$	14.0540	−	19.3436i	0.702698	−	0.967181i
$401$	−11.8009	−	6.01285i	−0.589308	−	0.300267i	0.133794	−	0.991009i	$-0.457284\pi$
$401$	−11.8009	−	6.01285i	−0.589308	−	0.300267i	−0.723101	+	0.690742i	$0.757284\pi$
$402$	3.03924	+	9.35383i	0.151584	+	0.466527i
$403$	−27.2255	+	18.9391i	−1.35620	+	0.943426i
$404$	−3.25538	−	4.48064i	−0.161961	−	0.222920i
$405$	−2.79501	+	1.42413i	−0.138885	+	0.0707655i
$406$			1.50599i			0.0747410i
$407$	14.6291	−	0.0873109i	0.725140	−	0.00432784i
$408$	−9.34320	−	9.34320i	−0.462557	−	0.462557i
$409$	8.88918	+	17.4460i	0.439542	+	0.862649i	0.999419	+	0.0340738i	$0.0108481\pi$
$409$	8.88918	+	17.4460i	0.439542	+	0.862649i	−0.559878	+	0.828575i	$0.689152\pi$
$410$	−2.45223	+	15.4828i	−0.121107	+	0.764639i
$411$	−17.5228	+	2.77534i	−0.864337	+	0.136898i
$412$	0.140022	+	0.430944i	0.00689840	+	0.0212311i
$413$	2.38317	+	7.33463i	0.117268	+	0.360914i
$414$	−1.05038	−	6.63181i	−0.0516232	−	0.325936i
$415$	3.46213	−	2.51539i	0.169949	−	0.123475i
$416$	8.85728	−	11.6792i	0.434264	−	0.572620i
$417$			8.90152i			0.435909i
$418$	26.3386	−	4.33291i	1.28826	−	0.211930i
$419$	−28.7040			−1.40228			−0.701142	−	0.713022i	$-0.747326\pi$
$419$	−28.7040			−1.40228			−0.701142	+	0.713022i	$0.747326\pi$
$420$	0.488799	−	1.50437i	0.0238510	−	0.0734057i
$421$	13.7183	+	2.17277i	0.668590	+	0.105894i	0.481497	−	0.876448i	$-0.340093\pi$
$421$	13.7183	+	2.17277i	0.668590	+	0.105894i	0.187094	+	0.982342i	$0.440093\pi$
$422$	0.157697	+	0.995661i	0.00767658	+	0.0484680i
$423$	−10.0720	−	5.13192i	−0.489715	−	0.249522i
$424$	7.55308	−	14.8238i	0.366810	−	0.719906i
$425$	−18.1887	+	25.0346i	−0.882282	+	1.21436i
$426$	0.767216	−	0.557415i	0.0371717	−	0.0270068i
$427$	2.63381	+	5.16915i	0.127459	+	0.250153i
$428$	5.57729			0.269588
$429$	9.77573	−	6.88732i	0.471977	−	0.332523i
$430$	65.2907			3.14860
$431$	−3.59099	−	7.04772i	−0.172972	−	0.339477i	0.788203	−	0.615415i	$-0.211011\pi$
$431$	−3.59099	−	7.04772i	−0.172972	−	0.339477i	−0.961175	+	0.275938i	$0.911011\pi$
$432$	−3.99643	+	2.90358i	−0.192278	+	0.139698i
$433$	−5.67766	+	7.81462i	−0.272851	+	0.375547i	−0.923350	−	0.383960i	$-0.874560\pi$
$433$	−5.67766	+	7.81462i	−0.272851	+	0.375547i	0.650499	+	0.759507i	$0.274560\pi$
$434$	−4.63053	+	9.08793i	−0.222273	+	0.436235i
$435$	−3.79603	−	1.93418i	−0.182006	−	0.0927366i
$436$	1.67297	+	10.5627i	0.0801209	+	0.505864i
$437$	19.3750	+	3.06870i	0.926832	+	0.146796i
$438$	7.38428	−	22.7265i	0.352834	−	1.08591i
$439$	−2.23429			−0.106637			−0.0533185	−	0.998578i	$-0.516980\pi$
$439$	−2.23429			−0.106637			−0.0533185	+	0.998578i	$0.516980\pi$
$440$	15.1137	−	15.2951i	0.720515	−	0.729167i
$441$		−	6.55366i		−	0.312079i
$442$	−23.1185	+	30.4840i	−1.09963	+	1.44998i
$443$	16.9274	−	12.2985i	0.804244	−	0.584318i	−0.107912	−	0.994160i	$-0.534416\pi$
$443$	16.9274	−	12.2985i	0.804244	−	0.584318i	0.912156	+	0.409843i	$0.134416\pi$
$444$	0.520805	+	3.28823i	0.0247163	+	0.156053i
$445$	−2.92145	−	8.99129i	−0.138490	−	0.426228i
$446$	−6.92677	−	21.3184i	−0.327992	−	1.00946i
$447$	2.69641	−	0.427069i	0.127536	−	0.0201997i
$448$	−0.327353	+	2.06683i	−0.0154660	+	0.0976484i
$449$	17.6729	+	34.6850i	0.834035	+	1.63689i	0.769216	+	0.638989i	$0.220647\pi$
$449$	17.6729	+	34.6850i	0.834035	+	1.63689i	0.0648193	+	0.997897i	$0.479353\pi$
$450$	5.68058	+	5.68058i	0.267785	+	0.267785i
$451$	−3.02902	+	9.51524i	−0.142631	+	0.448055i
$452$		−	0.489868i		−	0.0230415i
$453$	−1.88964	+	0.962820i	−0.0887830	+	0.0452372i
$454$	−14.7927	−	20.3605i	−0.694257	−	0.955563i
$455$	7.43741	+	1.33498i	0.348671	+	0.0625850i
$456$	−3.09690	−	9.53129i	−0.145026	−	0.446343i
$457$	−13.0460	−	6.64727i	−0.610267	−	0.310946i	0.121406	−	0.992603i	$-0.461260\pi$
$457$	−13.0460	−	6.64727i	−0.610267	−	0.310946i	−0.731672	+	0.681657i	$0.761260\pi$
$458$	15.4215	−	21.2259i	0.720601	−	0.991823i
$459$	5.17220	−	3.75782i	0.241418	−	0.175400i
$460$	−8.53426	+	4.34842i	−0.397912	+	0.202746i
$461$	0.489039	−	0.489039i	0.0227768	−	0.0227768i	−0.695627	−	0.718403i	$-0.744873\pi$
$461$	0.489039	−	0.489039i	0.0227768	−	0.0227768i	0.718403	+	0.695627i	$0.244873\pi$
$462$	1.65004	−	3.28673i	0.0767667	−	0.152912i
$463$	−1.66975	+	1.66975i	−0.0775999	+	0.0775999i	−0.744841	−	0.667242i	$-0.767475\pi$
$463$	−1.66975	+	1.66975i	−0.0775999	+	0.0775999i	0.667242	+	0.744841i	$0.267475\pi$
$464$	−6.38069	−	2.07321i	−0.296216	−	0.0962464i
$465$	−16.9602	−	23.3437i	−0.786509	−	1.08254i
$466$	−16.4323	+	2.60262i	−0.761210	+	0.120564i
$467$	−8.89760	+	2.89100i	−0.411732	+	0.133780i	−0.507556	−	0.861618i	$-0.669451\pi$
$467$	−8.89760	+	2.89100i	−0.411732	+	0.133780i	0.0958248	+	0.995398i	$0.469451\pi$
$468$	1.88439	+	1.96337i	0.0871058	+	0.0907570i
$469$	−2.32698	+	3.20281i	−0.107450	+	0.147892i
$470$	−9.20684	+	58.1297i	−0.424680	+	2.68132i
$471$	4.55869	−	14.0302i	0.210053	−	0.646478i
$472$	−23.8579			−1.09815
$473$	41.1174	+	6.26104i	1.89058	+	0.287883i
$474$	17.3333	+	17.3333i	0.796145	+	0.796145i
$475$	−20.9121	+	10.6553i	−0.959515	+	0.488897i
$476$	−0.504308	+	3.18408i	−0.0231149	+	0.145942i
$477$	6.51242	+	4.73155i	0.298183	+	0.216643i
$478$	−11.9300	+	3.87631i	−0.545668	+	0.177298i
$479$	12.1398	−	23.8257i	0.554682	−	1.08863i	−0.428078	−	0.903742i	$-0.640809\pi$
$479$	12.1398	−	23.8257i	0.554682	−	1.08863i	0.982760	−	0.184884i	$-0.0591909\pi$
$480$	10.3172	+	7.49587i	0.470913	+	0.342138i
$481$	−15.2231	+	4.60309i	−0.694115	+	0.209883i
$482$	−6.78336	+	20.8770i	−0.308974	+	0.950924i
$483$	1.91112	−	1.91112i	0.0869590	−	0.0869590i
$484$	−6.65808	+	4.95987i	−0.302640	+	0.225449i
$485$		−	15.9330i		−	0.723480i
$486$	−0.753510	−	1.47885i	−0.0341799	−	0.0670819i
$487$	−31.9079	−	5.05371i	−1.44588	−	0.229005i	−0.616354	−	0.787469i	$-0.711391\pi$
$487$	−31.9079	−	5.05371i	−1.44588	−	0.229005i	−0.829529	+	0.558463i	$0.811391\pi$
$488$	−17.7263	+	2.80757i	−0.802432	+	0.127093i
$489$	10.4290	+	5.31384i	0.471616	+	0.240300i
$490$	−32.4515	+	10.5441i	−1.46601	+	0.476336i
$491$	34.5150	+	25.0766i	1.55764	+	1.13169i	0.937910	+	0.346878i	$0.112758\pi$
$491$	34.5150	+	25.0766i	1.55764	+	1.13169i	0.619731	+	0.784814i	$0.287242\pi$
$492$	−2.24448	−	0.355491i	−0.101189	−	0.0160268i
$493$	8.25792	+	2.68316i	0.371918	+	0.120843i
$494$	−26.1201	+	12.6404i	−1.17520	+	0.568720i
$495$	6.16542	+	8.38034i	0.277115	+	0.376668i
$496$	−32.1298	−	32.1298i	−1.44267	−	1.44267i
$497$	0.363042	+	0.117960i	0.0162847	+	0.00529121i
$498$	1.33090	+	1.83182i	0.0596389	+	0.0820859i
$499$	−3.18958	−	20.1382i	−0.142785	−	0.901511i	−0.950226	−	0.311562i	$-0.899148\pi$
$499$	−3.18958	−	20.1382i	−0.142785	−	0.901511i	0.807441	−	0.589949i	$-0.200852\pi$
$500$	−0.171740	+	0.337058i	−0.00768043	+	0.0150737i
$501$	−1.57848	+	3.09795i	−0.0705214	+	0.138406i
$502$	3.90455	+	24.6524i	0.174269	+	1.10029i
$503$	22.7500	+	31.3127i	1.01437	+	1.39616i	0.916075	+	0.401007i	$0.131340\pi$
$503$	22.7500	+	31.3127i	1.01437	+	1.39616i	0.0982972	+	0.995157i	$0.468660\pi$
$504$	−1.31321	−	0.426686i	−0.0584948	−	0.0190061i
$505$	16.2764	+	16.2764i	0.724288	+	0.724288i
$506$	−21.1380	+	7.00791i	−0.939700	+	0.311539i
$507$	−8.06638	+	10.1948i	−0.358241	+	0.452766i
$508$	1.76225	+	0.572589i	0.0781871	+	0.0254045i
$509$	−16.7951	−	2.66008i	−0.744428	−	0.117906i	−0.227313	−	0.973822i	$-0.572994\pi$
$509$	−16.7951	−	2.66008i	−0.744428	−	0.117906i	−0.517115	+	0.855916i	$0.672994\pi$
$510$	−26.9290	−	19.5651i	−1.19244	−	0.866355i
$511$	9.14793	−	2.97234i	0.404680	−	0.131489i
$512$	−0.300048	−	0.152882i	−0.0132604	−	0.00675650i
$513$	4.78930	−	0.758551i	0.211453	−	0.0334908i
$514$	20.0096	+	3.16921i	0.882585	+	0.139788i
$515$	−0.854971	−	1.67797i	−0.0376745	−	0.0739404i
$516$			9.46497i			0.416672i
$517$	−11.3724	+	35.7248i	−0.500158	+	1.57117i
$518$	−3.45852	+	3.45852i	−0.151959	+	0.151959i
$519$	1.45378	−	4.47428i	0.0638140	−	0.196399i
$520$	−11.0376	+	20.6058i	−0.484033	+	0.903626i
$521$	−0.210759	−	0.153125i	−0.00923351	−	0.00670853i	0.583159	−	0.812358i	$-0.301816\pi$
$521$	−0.210759	−	0.153125i	−0.00923351	−	0.00670853i	−0.592392	+	0.805650i	$0.701816\pi$
$522$	1.02338	−	2.00849i	0.0447920	−	0.0879093i
$523$	18.6709	−	6.06654i	0.816421	−	0.265271i	0.129106	−	0.991631i	$-0.458789\pi$
$523$	18.6709	−	6.06654i	0.816421	−	0.265271i	0.687315	+	0.726360i	$0.258789\pi$
$524$	1.01444	+	0.737031i	0.0443158	+	0.0321973i
$525$	−0.505861	+	3.19388i	−0.0220776	+	0.139392i
$526$	10.5408	−	5.37082i	0.459602	−	0.234179i
$527$	41.5826	+	41.5826i	1.81137	+	1.81137i
$528$	11.6539	+	11.5157i	0.507172	+	0.501154i
$529$	6.63410			0.288439
$530$	12.9513	−	39.8599i	0.562566	−	1.73140i
$531$	1.80581	−	11.4014i	0.0783654	−	0.494779i
$532$	−1.43720	+	1.97813i	−0.0623104	+	0.0857630i
$533$	0.222797	−	10.8533i	0.00965042	−	0.470111i
$534$	4.75732	−	1.54575i	0.205869	−	0.0668910i
$535$	−22.8946	+	3.62615i	−0.989819	+	0.156772i
$536$	−7.19868	−	9.90813i	−0.310935	−	0.427966i
$537$	−3.86196	−	1.25483i	−0.166656	−	0.0541497i
$538$	−8.08909	+	8.08909i	−0.348745	+	0.348745i
$539$	−21.4477	+	3.52833i	−0.923820	+	0.151976i
$540$	−1.67417	+	1.67417i	−0.0720449	+	0.0720449i
$541$	26.9433	−	13.7283i	1.15838	−	0.590225i	0.234203	−	0.972188i	$-0.424752\pi$
$541$	26.9433	−	13.7283i	1.15838	−	0.590225i	0.924178	+	0.381963i	$0.124752\pi$
$542$	38.6363	−	28.0709i	1.65957	−	1.20575i
$543$	−5.39002	+	7.41872i	−0.231308	+	0.318368i
$544$	−23.1579	−	11.7995i	−0.992888	−	0.505901i
$545$	−13.7350	−	42.2720i	−0.588343	−	1.81073i
$546$	−0.706344	+	3.93515i	−0.0302287	+	0.168409i
$547$	−7.30294	−	10.0516i	−0.312251	−	0.429777i	0.623830	−	0.781560i	$-0.285576\pi$
$547$	−7.30294	−	10.0516i	−0.312251	−	0.429777i	−0.936082	+	0.351783i	$0.885576\pi$
$548$	−11.9310	+	6.07916i	−0.509668	+	0.259689i
$549$		−	8.68371i		−	0.370612i
$550$	15.5322	−	21.6488i	0.662295	−	0.923107i
$551$	4.65676	+	4.65676i	0.198385	+	0.198385i
$552$	3.79586	+	7.44979i	0.161562	+	0.317084i
$553$	−1.54355	+	9.74557i	−0.0656383	+	0.414424i
$554$	−22.9124	+	3.62897i	−0.973456	+	0.154180i
$555$	−4.27578	−	13.1595i	−0.181497	−	0.558589i
$556$	2.07615	+	6.38974i	0.0880485	+	0.270985i
$557$	1.73439	+	10.9505i	0.0734883	+	0.463987i	0.996800	+	0.0799355i	$0.0254714\pi$
$557$	1.73439	+	10.9505i	0.0734883	+	0.463987i	−0.923312	+	0.384051i	$0.874529\pi$
$558$	12.3512	−	8.97366i	0.522868	−	0.379886i
$559$	−44.7937	+	6.15508i	−1.89457	+	0.260332i
$560$			10.3526i			0.437478i
$561$	−15.0826	−	14.9036i	−0.636787	−	0.629231i
$562$	38.1790			1.61048
$563$	−3.57929	+	11.0159i	−0.150849	+	0.464266i	−0.997717	−	0.0675381i	$-0.978486\pi$
$563$	−3.57929	+	11.0159i	−0.150849	+	0.464266i	0.846868	+	0.531804i	$0.178486\pi$
$564$	−8.42686	−	1.33468i	−0.354835	−	0.0562003i
$565$	0.318494	+	2.01089i	0.0133992	+	0.0845989i
$566$	38.5183	+	19.6260i	1.61904	+	0.824944i
$567$	0.303305	−	0.595270i	0.0127376	−	0.0249990i
$568$	−0.694112	+	0.955363i	−0.0291243	+	0.0400861i
$569$	10.3235	−	7.50049i	0.432785	−	0.314437i	−0.349976	−	0.936759i	$-0.613810\pi$
$569$	10.3235	−	7.50049i	0.432785	−	0.314437i	0.782762	+	0.622322i	$0.213810\pi$
$570$	−11.4616	−	22.4946i	−0.480072	−	0.942194i
$571$	−37.2513			−1.55892			−0.779459	−	0.626454i	$-0.784506\pi$
$571$	−37.2513			−1.55892			−0.779459	+	0.626454i	$0.784506\pi$
$572$	5.41090	−	7.22394i	0.226241	−	0.302048i
$573$	−18.9186			−0.790337
$574$	−1.51567	−	2.97468i	−0.0632630	−	0.124161i
$575$	15.8414	−	11.5094i	0.660631	−	0.479977i
$576$	1.84107	−	2.53401i	0.0767112	−	0.105584i
$577$	12.2304	−	24.0034i	0.509156	−	0.999276i	−0.483158	−	0.875533i	$-0.660510\pi$
$577$	12.2304	−	24.0034i	0.509156	−	0.999276i	0.992314	−	0.123743i	$-0.0394897\pi$
$578$	35.3043	+	17.9885i	1.46847	+	0.748221i
$579$	−0.187790	−	1.18566i	−0.00780429	−	0.0492743i
$580$	−3.17601	−	0.503030i	−0.131877	−	0.0208872i
$581$	−0.281643	+	0.866808i	−0.0116845	+	0.0359612i
$582$	8.43019			0.349443
$583$	11.9785	−	23.8601i	0.496099	−	0.988185i
$584$			29.7561i			1.23132i
$585$	−9.01186	−	6.83442i	−0.372594	−	0.282569i
$586$	−21.2418	+	15.4330i	−0.877489	+	0.637533i
$587$	−1.29261	−	8.16120i	−0.0533516	−	0.336849i	−0.999898	−	0.0142812i	$-0.995454\pi$
$587$	−1.29261	−	8.16120i	−0.0533516	−	0.336849i	0.946546	−	0.322568i	$-0.104546\pi$
$588$	−1.52855	−	4.70439i	−0.0630362	−	0.194006i
$589$	13.7830	+	42.4197i	0.567918	+	1.74787i
$590$	−59.3614	+	9.40192i	−2.44387	+	0.387071i
$591$	3.63851	−	22.9727i	0.149668	−	0.944969i
$592$	−9.89217	−	19.4145i	−0.406566	−	0.797930i
$593$	−1.49824	−	1.49824i	−0.0615253	−	0.0615253i	0.675675	−	0.737200i	$-0.263852\pi$
$593$	−1.49824	−	1.49824i	−0.0615253	−	0.0615253i	−0.737200	+	0.675675i	$0.763852\pi$
$594$	−4.43406	+	3.26214i	−0.181932	+	0.133847i
$595$		−	13.3984i		−	0.549281i
$596$	1.83594	−	0.935460i	0.0752032	−	0.0383180i
$597$	13.9666	+	19.2234i	0.571617	+	0.786763i
$598$	19.8737	−	13.8250i	0.812698	−	0.565345i
$599$	7.89406	+	24.2954i	0.322543	+	0.992684i	0.972538	+	0.232745i	$0.0747709\pi$
$599$	7.89406	+	24.2954i	0.322543	+	0.992684i	−0.649995	+	0.759938i	$0.725229\pi$
$600$	−8.91332	−	4.54156i	−0.363885	−	0.185409i
$601$	1.36230	−	1.87504i	0.0555693	−	0.0764846i	−0.780328	−	0.625370i	$-0.784948\pi$
$601$	1.36230	−	1.87504i	0.0555693	−	0.0764846i	0.835897	+	0.548886i	$0.184948\pi$
$602$	−11.2497	+	8.17337i	−0.458502	+	0.333121i
$603$	5.27985	−	2.69022i	0.215012	−	0.109554i
$604$	−1.13187	+	1.13187i	−0.0460551	+	0.0460551i
$605$	24.1065	−	24.6890i	0.980068	−	1.00375i
$606$	−8.61186	+	8.61186i	−0.349833	+	0.349833i
$607$	−18.3290	−	5.95544i	−0.743950	−	0.241724i	−0.0875741	−	0.996158i	$-0.527911\pi$
$607$	−18.3290	−	5.95544i	−0.743950	−	0.241724i	−0.656376	+	0.754434i	$0.727911\pi$
$608$	−11.5870	−	15.9482i	−0.469916	−	0.646784i
$609$	0.896189	−	0.141942i	0.0363154	−	0.00575180i
$610$	−42.9988	+	13.9712i	−1.74097	+	0.565676i
$611$	0.836487	−	40.7486i	0.0338407	−	1.64851i
$612$	2.83628	−	3.90380i	0.114650	−	0.157802i
$613$	−5.22355	+	32.9802i	−0.210977	+	1.33206i	0.623850	+	0.781544i	$0.285568\pi$
$613$	−5.22355	+	32.9802i	−0.210977	+	1.33206i	−0.834827	+	0.550513i	$0.814432\pi$
$614$	7.83236	−	24.1055i	0.316088	−	0.972819i
$615$	9.44465			0.380845
$616$	−0.689391	+	4.52736i	−0.0277764	+	0.182413i
$617$	−14.7627	−	14.7627i	−0.594323	−	0.594323i	0.344473	−	0.938796i	$-0.388058\pi$
$617$	−14.7627	−	14.7627i	−0.594323	−	0.594323i	−0.938796	+	0.344473i	$0.888058\pi$
$618$	0.887821	−	0.452367i	0.0357134	−	0.0181969i
$619$	3.70284	−	23.3788i	0.148830	−	0.939673i	−0.794367	−	0.607438i	$-0.792197\pi$
$619$	3.70284	−	23.3788i	0.148830	−	0.939673i	0.943197	−	0.332235i	$-0.107803\pi$
$620$	−17.6190	−	12.8010i	−0.707597	−	0.514099i
$621$	−3.84748	+	1.25012i	−0.154394	+	0.0501657i
$622$	−6.27300	+	12.3115i	−0.251524	+	0.493644i
$623$	1.62894	+	1.18349i	0.0652620	+	0.0474156i
$624$	−15.7003	−	8.40999i	−0.628517	−	0.336669i
$625$	7.96440	−	24.5119i	0.318576	−	0.980476i
$626$	−12.9572	+	12.9572i	−0.517875	+	0.517875i
$627$	−5.06090	−	15.2653i	−0.202113	−	0.609635i
$628$		−	11.1345i		−	0.444315i
$629$	12.8025	+	25.1263i	0.510469	+	1.00185i
$630$	−3.43556	−	0.544140i	−0.136876	−	0.0216790i
$631$	−28.4140	+	4.50034i	−1.13114	+	0.179156i	−0.693820	−	0.720148i	$-0.744074\pi$
$631$	−28.4140	+	4.50034i	−1.13114	+	0.179156i	−0.437324	+	0.899304i	$0.644074\pi$
$632$	−27.1975	−	13.8578i	−1.08186	−	0.551233i
$633$	0.577638	−	0.187686i	0.0229590	−	0.00745984i
$634$	26.9628	+	19.5896i	1.07083	+	0.778002i
$635$	−7.60625	−	1.20471i	−0.301845	−	0.0478075i
$636$	5.77835	+	1.87750i	0.229126	+	0.0744476i
$637$	21.2698	−	10.2932i	0.842741	−	0.407833i
$638$	−7.12402	−	2.26782i	−0.282043	−	0.0897838i
$639$	−0.404020	−	0.404020i	−0.0159828	−	0.0159828i
$640$	−39.7668	−	12.9210i	−1.57192	−	0.510748i
$641$	25.8550	+	35.5864i	1.02121	+	1.40558i	0.911351	+	0.411629i	$0.135040\pi$
$641$	25.8550	+	35.5864i	1.02121	+	1.40558i	0.109860	+	0.993947i	$0.464960\pi$
$642$	−1.91860	−	12.1136i	−0.0757212	−	0.478085i
$643$	7.28113	−	14.2900i	0.287140	−	0.563543i	−0.701710	−	0.712463i	$-0.747580\pi$
$643$	7.28113	−	14.2900i	0.287140	−	0.563543i	0.988849	+	0.148920i	$0.0475796\pi$
$644$	0.926110	−	1.81759i	0.0364938	−	0.0716232i
$645$	−6.15377	−	38.8534i	−0.242305	−	1.52985i
$646$	30.2434	+	41.6265i	1.18991	+	1.63777i
$647$	2.04344	+	0.663954i	0.0803359	+	0.0261027i	0.348909	−	0.937157i	$-0.386552\pi$
$647$	2.04344	+	0.663954i	0.0803359	+	0.0261027i	−0.268573	+	0.963259i	$0.586552\pi$
$648$	1.46143	+	1.46143i	0.0574104	+	0.0574104i
$649$	−38.2849	+	0.228495i	−1.50281	+	0.00896923i
$650$	−9.51430	+	27.3582i	−0.373181	+	1.07308i
$651$	5.84451	+	1.89900i	0.229064	+	0.0744276i
$652$	8.72559	+	1.38200i	0.341720	+	0.0541232i
$653$	−19.9480	−	14.4931i	−0.780626	−	0.567158i	0.124541	−	0.992214i	$-0.460254\pi$
$653$	−19.9480	−	14.4931i	−0.780626	−	0.567158i	−0.905167	+	0.425057i	$0.860254\pi$
$654$	22.3662	−	7.26723i	0.874589	−	0.284171i
$655$	−4.64342	−	2.36594i	−0.181433	−	0.0924449i
$656$	14.6899	−	2.32665i	0.573543	−	0.0908403i
$657$	−14.2201	−	2.25224i	−0.554780	−	0.0878684i
$658$	−5.69056	−	11.1684i	−0.221841	−	0.435388i
$659$			2.02584i			0.0789157i	0.999221	+	0.0394578i	$0.0125631\pi$
$659$			2.02584i			0.0789157i	−0.999221	+	0.0394578i	$0.987437\pi$
$660$	6.38029	+	4.57763i	0.248353	+	0.178184i
$661$	22.2684	−	22.2684i	0.866142	−	0.866142i	−0.125901	−	0.992043i	$-0.540182\pi$
$661$	22.2684	−	22.2684i	0.866142	−	0.866142i	0.992043	+	0.125901i	$0.0401822\pi$
$662$	1.16767	−	3.59373i	0.0453829	−	0.139674i
$663$	20.3195	+	10.8842i	0.789143	+	0.422709i
$664$	−2.28105	−	1.65728i	−0.0885218	−	0.0643148i
$665$	4.61354	−	9.05459i	0.178906	−	0.351122i
$666$	6.96272	−	2.26232i	0.269800	−	0.0876633i
$667$	−4.44502	−	3.22950i	−0.172112	−	0.125047i
$668$	−0.410524	+	2.59195i	−0.0158836	+	0.100285i
$669$	−12.0334	+	6.13130i	−0.465237	+	0.237050i
$670$	−21.8158	−	21.8158i	−0.842817	−	0.842817i
$671$	−28.4186	+	4.67510i	−1.09709	+	0.180480i
$672$	−2.71603			−0.104773
$673$	14.1495	−	43.5478i	0.545425	−	1.67865i	−0.174553	−	0.984648i	$-0.555848\pi$
$673$	14.1495	−	43.5478i	0.545425	−	1.67865i	0.719978	−	0.693997i	$-0.244152\pi$
$674$	−1.56115	+	9.85672i	−0.0601333	+	0.379667i
$675$	2.84501	−	3.91582i	0.109505	−	0.150720i
$676$	−3.41247	+	9.19944i	−0.131249	+	0.353825i
$677$	7.32165	−	2.37895i	0.281394	−	0.0914304i	−0.164920	−	0.986307i	$-0.552737\pi$
$677$	7.32165	−	2.37895i	0.281394	−	0.0914304i	0.446314	+	0.894877i	$0.352737\pi$
$678$	−1.06397	+	0.168516i	−0.0408615	+	0.00647182i
$679$	1.99456	+	2.74528i	0.0765442	+	0.105354i
$680$	39.4203	+	12.8084i	1.51170	+	0.491181i
$681$	−10.7219	+	10.7219i	−0.410865	+	0.410865i
$682$	−36.0171	−	35.5898i	−1.37917	−	1.36280i
$683$	−0.0927289	+	0.0927289i	−0.00354817	+	0.00354817i	−0.708879	−	0.705330i	$-0.750799\pi$
$683$	−0.0927289	+	0.0927289i	−0.00354817	+	0.00354817i	0.705330	+	0.708879i	$0.250799\pi$
$684$	3.26096	−	1.66154i	0.124686	−	0.0635307i
$685$	45.0240	−	32.7119i	1.72028	−	1.24986i
$686$	8.83387	−	12.1588i	0.337279	−	0.464224i
$687$	−14.0847	−	7.17651i	−0.537365	−	0.273801i
$688$	−19.1427	−	58.9152i	−0.729809	−	2.24612i
$689$	−5.12773	+	28.5674i	−0.195351	+	1.08833i
$690$	12.3804	+	17.0401i	0.471313	+	0.648706i
$691$	14.8280	−	7.55525i	0.564085	−	0.287415i	−0.148603	−	0.988897i	$-0.547478\pi$
$691$	14.8280	−	7.55525i	0.564085	−	0.287415i	0.712688	+	0.701481i	$0.247478\pi$
$692$		−	3.55083i		−	0.134982i
$693$	−2.11139	−	0.672129i	−0.0802053	−	0.0255321i
$694$	−11.7427	−	11.7427i	−0.445748	−	0.445748i
$695$	−12.6769	−	24.8798i	−0.480863	−	0.943746i
$696$	−0.439109	+	2.77242i	−0.0166444	+	0.105088i
$697$	−19.0117	+	3.01116i	−0.720119	+	0.114056i
$698$	6.08396	+	18.7245i	0.230281	+	0.708733i
$699$	3.09754	+	9.53326i	0.117160	+	0.360581i
$700$	0.381807	+	2.41063i	0.0144309	+	0.0911134i
$701$	−30.0235	+	21.8134i	−1.13397	+	0.823879i	−0.986268	−	0.165153i	$-0.947188\pi$
$701$	−30.0235	+	21.8134i	−1.13397	+	0.823879i	−0.147704	+	0.989032i	$0.547188\pi$
$702$	3.61611	−	4.76820i	0.136481	−	0.179964i
$703$			21.3886i			0.806686i
$704$	−9.28409	−	4.66090i	−0.349907	−	0.175664i
$705$	35.4597			1.33549
$706$	−5.64138	+	17.3624i	−0.212316	+	0.653442i
$707$	−4.84198	−	0.766894i	−0.182101	−	0.0288420i
$708$	−1.36296	−	8.60541i	−0.0512233	−	0.323411i
$709$	−17.0383	−	8.68142i	−0.639885	−	0.326038i	0.103770	−	0.994601i	$-0.466909\pi$
$709$	−17.0383	−	8.68142i	−0.639885	−	0.326038i	−0.743655	+	0.668564i	$0.766909\pi$
$710$	−1.35055	+	2.65059i	−0.0506851	+	0.0994750i
$711$	8.68106	−	11.9485i	0.325565	−	0.448102i
$712$	−5.03923	+	3.66121i	−0.188853	+	0.137210i
$713$	−16.8937	−	33.1558i	−0.632675	−	1.24169i
$714$	7.08913			0.265304
$715$	−17.5148	+	33.1720i	−0.655017	+	1.24056i
$716$	−3.06488			−0.114540
$717$	3.43115	+	6.73402i	0.128139	+	0.251486i
$718$	−13.8921	+	10.0932i	−0.518449	+	0.376675i
$719$	−23.0614	+	31.7413i	−0.860044	+	1.18375i	0.121515	+	0.992590i	$0.461225\pi$
$719$	−23.0614	+	31.7413i	−0.860044	+	1.18375i	−0.981559	+	0.191159i	$0.938775\pi$
$720$	7.03500	−	13.8070i	0.262179	−	0.514555i
$721$	0.357368	+	0.182088i	0.0133091	+	0.00678132i
$722$	1.17171	+	7.39788i	0.0436065	+	0.275321i
$723$	13.0629	+	2.06896i	0.485815	+	0.0769456i
$724$	−2.13878	+	6.58250i	−0.0794872	+	0.244637i
$725$	6.57373			0.244142
$726$	13.0630	+	12.7548i	0.484813	+	0.473375i
$727$			9.08039i			0.336773i	0.985721	+	0.168387i	$0.0538557\pi$
$727$			9.08039i			0.336773i	−0.985721	+	0.168387i	$0.946144\pi$
$728$	−0.677725	−	4.93215i	−0.0251182	−	0.182798i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	11.7263	+	74.0369i	0.434009	+	2.74023i
$731$	24.7746	+	76.2484i	0.916322	+	2.82015i
$732$	−2.02535	−	6.23339i	−0.0748591	−	0.230393i
$733$	1.02424	−	0.162224i	0.0378314	−	0.00599190i	−0.137490	−	0.990503i	$-0.543904\pi$
$733$	1.02424	−	0.162224i	0.0378314	−	0.00599190i	0.175321	+	0.984511i	$0.443904\pi$
$734$	7.81778	−	49.3595i	0.288559	−	1.82189i
$735$	9.33326	+	18.3175i	0.344262	+	0.675653i
$736$	11.6294	+	11.6294i	0.428664	+	0.428664i
$737$	−11.6467	−	15.8307i	−0.429010	−	0.583131i
$738$			4.99719i			0.183949i
$739$	−38.2729	+	19.5010i	−1.40789	+	0.717356i	−0.982257	−	0.187540i	$-0.939949\pi$
$739$	−38.2729	+	19.5010i	−1.40789	+	0.717356i	−0.425634	+	0.904896i	$0.639949\pi$
$740$	−6.13853	−	8.44896i	−0.225657	−	0.310590i
$741$	9.98398	+	14.3522i	0.366771	+	0.527242i
$742$	2.75831	+	8.48919i	0.101261	+	0.311648i
$743$	−0.880149	−	0.448458i	−0.0322895	−	0.0164523i	0.437771	−	0.899086i	$-0.355768\pi$
$743$	−0.880149	−	0.448458i	−0.0322895	−	0.0164523i	−0.470061	+	0.882634i	$0.655768\pi$
$744$	−11.1743	+	15.3801i	−0.409670	+	0.563862i
$745$	−6.92829	+	5.03370i	−0.253833	+	0.184420i
$746$	10.1873	−	5.19071i	0.372985	−	0.190045i
$747$	0.964647	−	0.964647i	0.0352946	−	0.0352946i
$748$	−14.3027	−	7.18040i	−0.522959	−	0.262541i
$749$	3.49083	−	3.49083i	0.127552	−	0.127552i
$750$	0.791152	+	0.257061i	0.0288888	+	0.00938654i
$751$	−0.0978289	−	0.134650i	−0.00356983	−	0.00491344i	0.807228	−	0.590239i	$-0.200967\pi$
$751$	−0.0978289	−	0.134650i	−0.00356983	−	0.00491344i	−0.810798	+	0.585326i	$0.800967\pi$
$752$	55.1528	−	8.73535i	2.01122	−	0.318545i
$753$	14.3022	−	4.64706i	0.521201	−	0.169348i
$754$	8.12586	+	0.166807i	0.295926	+	0.00607477i
$755$	3.91038	−	5.38218i	0.142313	−	0.195878i
$756$	0.0788821	−	0.498042i	0.00286891	−	0.0181136i
$757$	−5.55328	+	17.0913i	−0.201838	+	0.621192i	0.797991	+	0.602669i	$0.205896\pi$
$757$	−5.55328	+	17.0913i	−0.201838	+	0.621192i	−0.999828	+	0.0185226i	$0.994104\pi$
$758$	−7.31169			−0.265572
$759$	6.16258	+	11.9184i	0.223688	+	0.432609i
$760$	22.2297	+	22.2297i	0.806354	+	0.806354i
$761$	31.5211	−	16.0608i	1.14264	−	0.582203i	0.222940	−	0.974832i	$-0.428434\pi$
$761$	31.5211	−	16.0608i	1.14264	−	0.582203i	0.919697	+	0.392629i	$0.128434\pi$
$762$	0.637416	−	4.02448i	0.0230911	−	0.145792i
$763$	7.65835	+	5.56411i	0.277251	+	0.201434i
$764$	−13.5803	+	4.41250i	−0.491317	+	0.159639i
$765$	−9.10473	+	17.8690i	−0.329182	+	0.646056i
$766$	−0.979884	−	0.711927i	−0.0354046	−	0.0257230i
$767$	39.8394	−	12.0464i	1.43852	−	0.434971i
$768$	4.90073	−	15.0829i	0.176840	−	0.544258i
$769$	−16.5813	+	16.5813i	−0.597936	+	0.597936i	−0.939763	−	0.341827i	$-0.888954\pi$
$769$	−16.5813	+	16.5813i	−0.597936	+	0.597936i	0.341827	+	0.939763i	$0.388954\pi$
$770$	0.0688520	+	11.5363i	0.00248125	+	0.415740i
$771$		−	12.2061i		−	0.439591i
$772$	−0.411339	−	0.807298i	−0.0148044	−	0.0290553i
$773$	−15.4833	−	2.45231i	−0.556895	−	0.0882035i	−0.128358	−	0.991728i	$-0.540971\pi$
$773$	−15.4833	−	2.45231i	−0.556895	−	0.0882035i	−0.428537	+	0.903524i	$0.640971\pi$
$774$	20.5574	−	3.25598i	0.738922	−	0.117034i
$775$	39.6694	+	20.2125i	1.42497	+	0.726056i
$776$	−9.98377	+	3.24392i	−0.358396	+	0.116450i
$777$	2.38408	+	1.73214i	0.0855284	+	0.0621400i
$778$	29.4323	+	4.66161i	1.05520	+	0.167127i
$779$	−13.8849	−	4.51147i	−0.497477	−	0.161640i
$780$	−8.06298	−	2.80404i	−0.288701	−	0.100401i
$781$	−1.10470	+	1.53972i	−0.0395291	+	0.0550956i
$782$	−30.3539	−	30.3539i	−1.08545	−	1.08545i
$783$	−1.29167	−	0.419690i	−0.0461607	−	0.0149985i
$784$	19.0291	+	26.1912i	0.679609	+	0.935402i
$785$	7.23923	+	45.7067i	0.258379	+	1.63134i
$786$	1.25182	−	2.45684i	0.0446511	−	0.0876327i
$787$	−9.97245	+	19.5720i	−0.355479	+	0.697668i	−0.997622	−	0.0689172i	$-0.978046\pi$
$787$	−9.97245	+	19.5720i	−0.355479	+	0.697668i	0.642143	+	0.766585i	$0.278046\pi$
$788$	−2.74623	−	17.3390i	−0.0978303	−	0.617676i
$789$	−4.18958	−	5.76646i	−0.149153	−	0.205291i
$790$	−73.1317	−	23.7619i	−2.60191	−	0.845411i
$791$	−0.306609	−	0.306609i	−0.0109018	−	0.0109018i
$792$	3.99593	−	5.56953i	0.141989	−	0.197905i
$793$	28.1829	−	13.6387i	1.00080	−	0.484324i
$794$	−26.6227	−	8.65024i	−0.944804	−	0.306986i
$795$	−24.9406	−	3.95020i	−0.884552	−	0.140099i
$796$	14.5092	+	10.5416i	0.514265	+	0.373635i
$797$	31.8855	−	10.3602i	1.12944	−	0.366979i	0.316079	−	0.948733i	$-0.397633\pi$
$797$	31.8855	−	10.3602i	1.12944	−	0.366979i	0.813365	+	0.581754i	$0.197633\pi$
$798$	4.79081	+	2.44104i	0.169593	+	0.0864118i
$799$	−71.3790	+	11.3053i	−2.52521	+	0.399954i
$800$	−19.4351	−	3.07822i	−0.687134	−	0.108831i
$801$	−1.36823	−	2.68531i	−0.0483441	−	0.0948807i
$802$			21.9824i			0.776227i
$803$	0.284985	+	47.7498i	0.0100569	+	1.68505i
$804$	3.16256	−	3.16256i	0.111535	−	0.111535i
$805$	−2.61992	+	8.06328i	−0.0923400	+	0.284193i
$806$	48.5228	+	25.9915i	1.70914	+	0.915513i
$807$	5.57609	+	4.05127i	0.196288	+	0.142611i
$808$	6.88509	−	13.5127i	0.242217	−	0.475377i
$809$	25.4966	−	8.28434i	0.896412	−	0.291262i	0.175657	−	0.984451i	$-0.443795\pi$
$809$	25.4966	−	8.28434i	0.896412	−	0.291262i	0.720755	+	0.693189i	$0.243795\pi$
$810$	4.21214	+	3.06030i	0.147999	+	0.107528i
$811$	6.79623	−	42.9097i	0.238648	−	1.50676i	−0.519381	−	0.854543i	$-0.673837\pi$
$811$	6.79623	−	42.9097i	0.238648	−	1.50676i	0.758029	−	0.652221i	$-0.226163\pi$
$812$	0.610202	−	0.310913i	0.0214139	−	0.0109109i
$813$	−20.3461	−	20.3461i	−0.713567	−	0.713567i
$814$	−11.1523	−	21.5685i	−0.390889	−	0.755975i
$815$	−36.7168			−1.28613
$816$	−9.75921	+	30.0358i	−0.341641	+	1.05146i
$817$	−9.51242	+	60.0591i	−0.332798	+	2.10120i
$818$	19.1019	−	26.2915i	0.667881	−	0.919260i
$819$	2.40832	+	0.0494378i	0.0841533	+	0.00172750i
$820$	6.77961	−	2.20283i	0.236754	−	0.0769262i
$821$	9.84886	−	1.55991i	0.343728	−	0.0544411i	0.0178158	−	0.999841i	$-0.494329\pi$
$821$	9.84886	−	1.55991i	0.343728	−	0.0544411i	0.325912	+	0.945400i	$0.394329\pi$
$822$	17.3079	+	23.8223i	0.603683	+	0.830899i
$823$	27.6221	+	8.97497i	0.962847	+	0.312848i	0.747925	−	0.663783i	$-0.231050\pi$
$823$	27.6221	+	8.97497i	0.962847	+	0.312848i	0.214922	+	0.976631i	$0.431050\pi$
$824$	−0.877365	+	0.877365i	−0.0305645	+	0.0305645i
$825$	−14.3468	−	7.20251i	−0.499490	−	0.250759i
$826$	9.05106	−	9.05106i	0.314927	−	0.314927i
$827$	5.56213	−	2.83405i	0.193414	−	0.0985494i	−0.354601	−	0.935018i	$-0.615383\pi$
$827$	5.56213	−	2.83405i	0.193414	−	0.0985494i	0.548016	+	0.836468i	$0.315383\pi$
$828$	−2.47025	+	1.79474i	−0.0858470	+	0.0623715i
$829$	0.950104	−	1.30771i	0.0329985	−	0.0454185i	−0.792199	−	0.610263i	$-0.791064\pi$
$829$	0.950104	−	1.30771i	0.0329985	−	0.0454185i	0.825197	+	0.564844i	$0.191064\pi$
$830$	−6.32862	−	3.22459i	−0.219670	−	0.111927i
$831$	4.31908	+	13.2928i	0.149827	+	0.461121i
$832$	11.1157	+	1.99522i	0.385368	+	0.0691720i
$833$	−24.6275	−	33.8968i	−0.853292	−	1.17446i
$834$	13.1640	−	6.70739i	0.455832	−	0.232258i
$835$		−	10.9068i		−	0.377444i
$836$	−7.19325	−	9.77741i	−0.248784	−	0.338159i
$837$	−6.50420	−	6.50420i	−0.224818	−	0.224818i
$838$	21.6288	+	42.4489i	0.747154	+	1.46637i
$839$	0.605330	−	3.82191i	0.0208983	−	0.131947i	−0.975033	−	0.222059i	$-0.928722\pi$
$839$	0.605330	−	3.82191i	0.0208983	−	0.131947i	0.995932	+	0.0901117i	$0.0287224\pi$
$840$	4.27808	−	0.677581i	0.147608	−	0.0233788i
$841$	8.39149	+	25.8264i	0.289362	+	0.890564i
$842$	−7.12371	−	21.9245i	−0.245499	−	0.755569i
$843$	−3.59844	−	22.7197i	−0.123937	−	0.782507i
$844$	0.370868	−	0.269452i	0.0127658	−	0.00927490i
$845$	8.02695	−	39.9821i	0.276135	−	1.37543i
$846$			18.7618i			0.645045i
$847$	−1.06291	+	7.27169i	−0.0365220	+	0.249858i
$848$	−39.7648			−1.36553
$849$	8.04870	−	24.7714i	0.276231	−	0.850151i
$850$	50.7277	+	8.03448i	1.73995	+	0.275581i
$851$	−2.79147	−	17.6246i	−0.0956903	−	0.604165i
$852$	−0.384247	−	0.195784i	−0.0131641	−	0.00670745i
$853$	−12.1134	+	23.7740i	−0.414757	+	0.814006i	0.585239	+	0.810861i	$0.301001\pi$
$853$	−12.1134	+	23.7740i	−0.414757	+	0.814006i	−0.999995	+	0.00314435i	$0.998999\pi$
$854$	5.65978	−	7.79002i	0.193674	−	0.266569i
$855$	−12.3059	+	8.94074i	−0.420852	+	0.305767i
$856$	6.93346	+	13.6077i	0.236981	+	0.465101i
$857$	47.1791			1.61161			0.805803	−	0.592184i	$-0.201734\pi$
$857$	47.1791			1.61161			0.805803	+	0.592184i	$0.201734\pi$
$858$	−17.5514	−	9.26714i	−0.599195	−	0.316375i
$859$	−29.7621			−1.01547			−0.507735	−	0.861513i	$-0.669517\pi$
$859$	−29.7621			−1.01547			−0.507735	+	0.861513i	$0.669517\pi$
$860$	−13.4793	−	26.4547i	−0.459642	−	0.902098i
$861$	−1.62732	+	1.18232i	−0.0554591	+	0.0402934i
$862$	−7.71665	+	10.6211i	−0.262830	+	0.361755i
$863$	−13.4344	+	26.3666i	−0.457314	+	0.897529i	0.541085	+	0.840968i	$0.318014\pi$
$863$	−13.4344	+	26.3666i	−0.457314	+	0.897529i	−0.998399	+	0.0565612i	$0.981986\pi$
$864$	3.62228	+	1.84564i	0.123232	+	0.0627901i
$865$	2.30862	+	14.5760i	0.0784954	+	0.495600i
$866$	15.8348	+	2.50799i	0.538089	+	0.0852249i
$867$	7.37712	−	22.7045i	0.250540	−	0.771084i
$868$	4.63826			0.157433
$869$	−43.7766	−	21.9772i	−1.48502	−	0.745526i
$870$			7.07117i			0.239735i
$871$	17.0236	+	12.9104i	0.576824	+	0.437453i
$872$	−23.6916	+	17.2130i	−0.802300	+	0.582905i
$873$	−0.794562	−	5.01666i	−0.0268918	−	0.169788i
$874$	−10.0611	−	30.9650i	−0.340323	−	1.04741i
$875$	0.103473	+	0.318457i	0.00349802	+	0.0107658i
$876$	−10.7329	+	1.69992i	−0.362630	+	0.0574350i
$877$	−1.73437	+	10.9504i	−0.0585657	+	0.369769i	0.940947	+	0.338554i	$0.109938\pi$
$877$	−1.73437	+	10.9504i	−0.0585657	+	0.369769i	−0.999513	+	0.0312152i	$0.990062\pi$
$878$	1.68356	+	3.30418i	0.0568175	+	0.111511i
$879$	11.1860	+	11.1860i	0.377295	+	0.377295i
$880$	−48.9726	−	15.5897i	−1.65087	−	0.525527i
$881$			23.8564i			0.803744i	0.915696	+	0.401872i	$0.131640\pi$
$881$			23.8564i			0.803744i	−0.915696	+	0.401872i	$0.868360\pi$
$882$	−9.69186	+	4.93825i	−0.326342	+	0.166280i
$883$	−13.4211	−	18.4725i	−0.451656	−	0.621651i	0.521097	−	0.853498i	$-0.325523\pi$
$883$	−13.4211	−	18.4725i	−0.451656	−	0.621651i	−0.972752	+	0.231847i	$0.925523\pi$
$884$	17.1244	+	3.07377i	0.575957	+	0.103382i
$885$	11.1898	+	34.4388i	0.376142	+	1.15765i
$886$	−30.9425	−	15.7660i	−1.03953	−	0.529669i
$887$	19.9185	−	27.4154i	0.668797	−	0.920521i	−0.330935	−	0.943654i	$-0.607364\pi$
$887$	19.9185	−	27.4154i	0.668797	−	0.920521i	0.999732	+	0.0231329i	$0.00736410\pi$
$888$	−7.37532	+	5.35848i	−0.247500	+	0.179819i
$889$	1.46138	−	0.744608i	0.0490130	−	0.0249734i
$890$	−11.0954	+	11.0954i	−0.371919	+	0.371919i
$891$	2.35916	+	2.33117i	0.0790349	+	0.0780971i
$892$	−7.20782	+	7.20782i	−0.241336	+	0.241336i
$893$	−52.1304	−	16.9382i	−1.74448	−	0.566816i
$894$	−2.66334	−	3.66578i	−0.0890755	−	0.122602i
$895$	12.5812	−	1.99267i	0.420544	−	0.0666077i
$896$	8.46938	−	2.75187i	0.282942	−	0.0919335i
$897$	−10.1001	−	10.5235i	−0.337234	−	0.351369i
$898$	37.9771	−	52.2710i	1.26731	−	1.74431i
$899$	1.95428	−	12.3389i	0.0651790	−	0.411524i
$900$	1.12891	−	3.47444i	0.0376304	−	0.115815i
$901$	51.4638			1.71451
$902$	16.3540	−	2.69037i	0.544528	−	0.0895794i
$903$	5.92413	+	5.92413i	0.197143	+	0.197143i
$904$	1.19520	−	0.608985i	0.0397518	−	0.0202545i
$905$	4.49994	−	28.4115i	0.149583	−	0.944430i
$906$	2.84773	+	2.06899i	0.0946094	+	0.0687377i
$907$	2.10092	−	0.682631i	0.0697600	−	0.0226664i	−0.273929	−	0.961750i	$-0.588323\pi$
$907$	2.10092	−	0.682631i	0.0697600	−	0.0226664i	0.343689	+	0.939083i	$0.388323\pi$
$908$	−5.19573	+	10.1972i	−0.172426	+	0.338406i
$909$	5.93646	+	4.31309i	0.196900	+	0.143056i
$910$	−3.62992	−	12.0047i	−0.120331	−	0.397952i
$911$	13.7629	−	42.3578i	0.455984	−	1.40338i	−0.413991	−	0.910281i	$-0.635866\pi$
$911$	13.7629	−	42.3578i	0.455984	−	1.40338i	0.869976	−	0.493095i	$-0.164134\pi$
$912$	−16.9376	+	16.9376i	−0.560860	+	0.560860i
$913$	−3.67628	−	2.63760i	−0.121667	−	0.0872917i
$914$			24.3018i			0.803833i
$915$	12.3667	+	24.2710i	0.408831	+	0.802376i
$916$	−11.7842	−	1.86643i	−0.389360	−	0.0616686i
$917$	1.09624	−	0.173628i	0.0362012	−	0.00573370i
$918$	−9.45455	−	4.81733i	−0.312047	−	0.158996i
$919$	28.5702	−	9.28302i	0.942444	−	0.306218i	0.202802	−	0.979220i	$-0.434995\pi$
$919$	28.5702	−	9.28302i	0.942444	−	0.306218i	0.739641	+	0.673001i	$0.234995\pi$
$920$	−21.2189	−	15.4164i	−0.699567	−	0.508265i
$921$	−15.0830	−	2.38891i	−0.497002	−	0.0787173i
$922$	−1.09171	−	0.354718i	−0.0359536	−	0.0116820i
$923$	0.676684	−	1.94580i	0.0222733	−	0.0640467i
$924$	−1.67238	+	0.00998124i	−0.0550172	+	0.000328359i
$925$	15.0967	+	15.0967i	0.496375	+	0.496375i
$926$	3.72748	+	1.21113i	0.122493	+	0.0398003i
$927$	−0.352875	−	0.485691i	−0.0115899	−	0.0159522i
$928$	0.863734	+	5.45340i	0.0283535	+	0.179017i
$929$	−24.8923	+	48.8539i	−0.816690	+	1.60284i	−0.0189660	+	0.999820i	$0.506037\pi$
$929$	−24.8923	+	48.8539i	−0.816690	+	1.60284i	−0.797724	+	0.603023i	$0.793963\pi$
$930$	−21.7420	+	42.6712i	−0.712950	+	1.39924i
$931$	−4.97128	−	31.3874i	−0.162927	−	1.02868i
$932$	4.44699	+	6.12076i	0.145666	+	0.200492i
$933$	7.91758	+	2.57258i	0.259210	+	0.0842224i
$934$	10.9798	+	10.9798i	0.359269	+	0.359269i
$935$	63.3806	+	20.1762i	2.07277	+	0.659833i
$936$	−2.44772	+	7.03839i	−0.0800063	+	0.230057i
$937$	32.9279	+	10.6989i	1.07571	+	0.349518i	0.792708	−	0.609602i	$-0.208671\pi$
$937$	32.9279	+	10.6989i	1.07571	+	0.349518i	0.282999	+	0.959120i	$0.408671\pi$
$938$	6.48987	+	1.02790i	0.211902	+	0.0335620i
$939$	8.93187	+	6.48938i	0.291480	+	0.211773i
$940$	25.4539	−	8.27048i	0.830215	−	0.269753i
$941$	−3.65174	−	1.86065i	−0.119043	−	0.0606555i	0.393455	−	0.919344i	$-0.371280\pi$
$941$	−3.65174	−	1.86065i	−0.119043	−	0.0606555i	−0.512498	+	0.858688i	$0.671280\pi$
$942$	−24.1835	+	3.83030i	−0.787943	+	0.124798i
$943$	12.0302	+	1.90540i	0.391758	+	0.0620483i
$944$	25.8881	+	50.8083i	0.842586	+	1.65367i
$945$			2.09573i			0.0681742i
$946$	−21.7233	−	65.5241i	−0.706284	−	2.13037i
$947$	7.50834	−	7.50834i	0.243988	−	0.243988i	−0.574510	−	0.818498i	$-0.694807\pi$
$947$	7.50834	−	7.50834i	0.243988	−	0.243988i	0.818498	+	0.574510i	$0.194807\pi$
$948$	3.44468	−	10.6016i	0.111878	−	0.344325i
$949$	−15.0246	−	49.6886i	−0.487719	−	1.61296i
$950$	31.5150	+	22.8970i	1.02248	+	0.742877i
$951$	9.11615	−	17.8914i	0.295611	−	0.580170i
$952$	−8.39557	+	2.72789i	−0.272102	+	0.0884113i
$953$	−3.56513	−	2.59022i	−0.115486	−	0.0839055i	0.528543	−	0.848906i	$-0.322738\pi$
$953$	−3.56513	−	2.59022i	−0.115486	−	0.0839055i	−0.644029	+	0.765001i	$0.722738\pi$
$954$	2.09006	−	13.1961i	0.0676683	−	0.427241i
$955$	52.8778	−	26.9426i	1.71108	−	0.871841i
$956$	4.03358	+	4.03358i	0.130455	+	0.130455i
$957$	−0.678088	+	4.45313i	−0.0219195	+	0.143949i
$958$	−44.3821			−1.43392
$959$	−3.66268	+	11.2726i	−0.118274	+	0.364011i
$960$	−1.53704	+	9.70451i	−0.0496079	+	0.313212i
$961$	31.5107	−	43.3707i	1.01647	−	1.39906i
$962$	18.2780	+	19.0442i	0.589308	+	0.614010i
$963$	−7.02775	+	2.28346i	−0.226466	+	0.0735833i
$964$	9.85946	−	1.56158i	0.317552	−	0.0502953i
$965$	2.21341	+	3.04649i	0.0712521	+	0.0980701i
$966$	−4.26630	−	1.38621i	−0.137266	−	0.0446005i
$967$	−12.1944	+	12.1944i	−0.392144	+	0.392144i	−0.875451	−	0.483307i	$-0.839436\pi$
$967$	−12.1944	+	12.1944i	−0.392144	+	0.392144i	0.483307	+	0.875451i	$0.339436\pi$
$968$	−20.3784	−	10.0787i	−0.654985	−	0.323943i
$969$	21.9207	−	21.9207i	0.704195	−	0.704195i
$970$	−23.5625	+	12.0057i	−0.756545	+	0.385479i
$971$	12.2947	−	8.93262i	0.394555	−	0.286661i	−0.372764	−	0.927926i	$-0.621590\pi$
$971$	12.2947	−	8.93262i	0.394555	−	0.286661i	0.767320	+	0.641265i	$0.221590\pi$
$972$	−0.443641	+	0.610619i	−0.0142298	+	0.0195856i
$973$	5.29881	+	2.69988i	0.169872	+	0.0865541i
$974$	16.5692	+	50.9949i	0.530913	+	1.63398i
$975$	17.1772	+	3.08323i	0.550109	+	0.0987424i
$976$	25.2138	+	34.7038i	0.807074	+	1.11084i
$977$	47.2250	−	24.0624i	1.51086	−	0.769823i	0.514702	−	0.857369i	$-0.327902\pi$
$977$	47.2250	−	24.0624i	1.51086	−	0.769823i	0.996161	+	0.0875457i	$0.0279024\pi$
$978$		−	19.4269i		−	0.621205i
$979$	−8.05142	+	5.92343i	−0.257324	+	0.189314i
$980$	10.9720	+	10.9720i	0.350486	+	0.350486i
$981$	−6.43266	−	12.6248i	−0.205379	−	0.403079i
$982$	11.0771	−	69.9379i	0.353484	−	2.23181i
$983$	8.61211	−	1.36402i	0.274684	−	0.0435056i	−0.0175728	−	0.999846i	$-0.505594\pi$
$983$	8.61211	−	1.36402i	0.274684	−	0.0435056i	0.292257	+	0.956340i	$0.405594\pi$
$984$	−1.92291	−	5.91811i	−0.0613001	−	0.188662i
$985$	22.5463	+	69.3905i	0.718386	+	2.21097i
$986$	−2.25444	−	14.2340i	−0.0717961	−	0.453302i
$987$	−6.10976	+	4.43900i	−0.194476	+	0.141295i
$988$	10.5142	+	7.97378i	0.334502	+	0.253680i
$989$		−	50.7314i		−	1.61316i
$990$	7.74753	−	15.4324i	0.246233	−	0.490473i
$991$	4.53819			0.144161			0.0720803	−	0.997399i	$-0.477036\pi$
$991$	4.53819			0.144161			0.0720803	+	0.997399i	$0.477036\pi$
$992$	−11.5556	+	35.5645i	−0.366890	+	1.12917i
$993$	−2.24862	−	0.356146i	−0.0713578	−	0.0113020i
$994$	−0.0991118	−	0.625767i	−0.00314364	−	0.0198481i
$995$	−66.4135	−	33.8394i	−2.10545	−	1.07278i
$996$	0.467458	−	0.917438i	0.0148120	−	0.0290701i
$997$	−5.00235	+	6.88514i	−0.158426	+	0.218055i	−0.880850	−	0.473396i	$-0.843028\pi$
$997$	−5.00235	+	6.88514i	−0.158426	+	0.218055i	0.722424	+	0.691451i	$0.243028\pi$
$998$	−27.3780	+	19.8913i	−0.866634	+	0.629647i
$999$	−2.00252	−	3.93017i	−0.0633569	−	0.124345i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bj.a.112.3	✓	112
11.6	odd	10	inner	429.2.bj.a.424.3	yes	112
13.5	odd	4	inner	429.2.bj.a.343.3	yes	112
143.83	even	20	inner	429.2.bj.a.226.3	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bj.a.112.3	✓	112	1.1	even	1	trivial
429.2.bj.a.226.3	yes	112	143.83	even	20	inner
429.2.bj.a.343.3	yes	112	13.5	odd	4	inner
429.2.bj.a.424.3	yes	112	11.6	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.753510 - 1.47885i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.443641 + 0.610619i) q^{4} +(1.42413 - 2.79501i) q^{5} +(1.47885 + 0.753510i) q^{6} +(0.104512 + 0.659862i) q^{7} +(-2.04133 - 0.323315i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.753510 - 1.47885i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.443641 + 0.610619i) q^{4} +(1.42413 - 2.79501i) q^{5} +(1.47885 + 0.753510i) q^{6} +(0.104512 + 0.659862i) q^{7} +(-2.04133 - 0.323315i) q^{8} +(0.309017 - 0.951057i) q^{9} -5.20649 q^{10} +(-3.27883 - 0.499275i) q^{11} -0.754767i q^{12} +(3.57199 - 0.490826i) q^{13} +(0.897084 - 0.651770i) q^{14} +(0.490721 + 3.09829i) q^{15} +(1.52650 + 4.69809i) q^{16} +(-1.97560 - 6.08028i) q^{17} +(-1.63931 + 0.259642i) q^{18} +(0.758551 - 4.78930i) q^{19} +(1.07488 + 2.10958i) q^{20} +(-0.472409 - 0.472409i) q^{21} +(1.73228 + 5.22510i) q^{22} +4.04548i q^{23} +(1.84151 - 0.938296i) q^{24} +(-2.84501 - 3.91582i) q^{25} +(-3.41738 - 4.91258i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-0.449290 - 0.228925i) q^{28} +(-0.798298 + 1.09876i) q^{29} +(4.21214 - 3.06030i) q^{30} +(-8.19577 + 4.17595i) q^{31} +(2.87466 - 2.87466i) q^{32} +(2.94610 - 1.52333i) q^{33} +(-7.50317 + 7.50317i) q^{34} +(1.99316 + 0.647617i) q^{35} +(0.443641 + 0.610619i) q^{36} +(-4.35662 + 0.690021i) q^{37} +(-7.65422 + 2.48701i) q^{38} +(-2.60130 + 2.49665i) q^{39} +(-3.81078 + 5.24509i) q^{40} +(0.470994 - 2.97374i) q^{41} +(-0.342656 + 1.05459i) q^{42} -12.5403 q^{43} +(1.75949 - 1.78062i) q^{44} +(-2.21813 - 2.21813i) q^{45} +(5.98264 - 3.04831i) q^{46} +(1.76834 - 11.1649i) q^{47} +(-3.99643 - 2.90358i) q^{48} +(6.23290 - 2.02519i) q^{49} +(-3.64716 + 7.15795i) q^{50} +(5.17220 + 3.75782i) q^{51} +(-1.28497 + 2.39887i) q^{52} +(-2.48752 + 7.65580i) q^{53} +(1.17362 - 1.17362i) q^{54} +(-6.06495 + 8.45333i) q^{55} -1.38079i q^{56} +(2.20140 + 4.32049i) q^{57} +(2.22643 + 0.352632i) q^{58} +(11.4014 - 1.80581i) q^{59} +(-2.10958 - 1.07488i) q^{60} +(8.25870 - 2.68341i) q^{61} +(12.3512 + 8.97366i) q^{62} +(0.659862 + 0.104512i) q^{63} +(2.97891 + 0.967907i) q^{64} +(3.71511 - 10.6827i) q^{65} +(-4.47268 - 3.20898i) q^{66} +(4.19011 + 4.19011i) q^{67} +(4.58920 + 1.49112i) q^{68} +(-2.37787 - 3.27286i) q^{69} +(-0.544140 - 3.43556i) q^{70} +(0.259397 - 0.509094i) q^{71} +(-0.938296 + 1.84151i) q^{72} +(-2.25224 - 14.2201i) q^{73} +(4.30320 + 5.92284i) q^{74} +(4.60333 + 1.49571i) q^{75} +(2.58791 + 2.58791i) q^{76} +(-0.0132243 - 2.21576i) q^{77} +(5.65226 + 1.96567i) q^{78} +(14.0463 + 4.56390i) q^{79} +(15.3051 + 2.42410i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-4.75261 + 1.54422i) q^{82} +(1.21553 + 0.619341i) q^{83} +(0.498042 - 0.0788821i) q^{84} +(-19.8080 - 3.13727i) q^{85} +(9.44922 + 18.5451i) q^{86} -1.35815i q^{87} +(6.53175 + 2.07928i) q^{88} +(2.13107 - 2.13107i) q^{89} +(-1.60889 + 4.95166i) q^{90} +(0.697192 + 2.30572i) q^{91} +(-2.47025 - 1.79474i) q^{92} +(4.17595 - 8.19577i) q^{93} +(-17.8436 + 5.79773i) q^{94} +(-12.3059 - 8.94074i) q^{95} +(-0.635965 + 4.01533i) q^{96} +(4.52560 - 2.30591i) q^{97} +(-7.69150 - 7.69150i) q^{98} +(-1.48805 + 2.96407i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 28 q^{3} - 6 q^{5} - 28 q^{9}+O(q^{10}) \) 112 * q - 28 * q^3 - 6 * q^5 - 28 * q^9	\( 112 q - 28 q^{3} - 6 q^{5} - 28 q^{9} - 10 q^{11} + 10 q^{13} - 60 q^{14} + 4 q^{15} + 80 q^{16} - 74 q^{20} + 8 q^{22} + 30 q^{24} + 38 q^{26} - 28 q^{27} - 20 q^{29} - 8 q^{31} + 20 q^{33} - 48 q^{34} + 20 q^{35} + 12 q^{37} - 10 q^{39} + 40 q^{40} - 110 q^{41} + 20 q^{42} - 36 q^{44} + 4 q^{45} - 20 q^{46} - 30 q^{47} - 20 q^{48} + 90 q^{50} - 10 q^{52} + 52 q^{53} - 64 q^{55} + 30 q^{57} + 24 q^{58} - 36 q^{59} - 74 q^{60} - 60 q^{61} + 48 q^{66} + 60 q^{67} + 60 q^{68} + 116 q^{70} + 20 q^{71} - 30 q^{72} + 70 q^{73} + 120 q^{74} - 52 q^{78} - 120 q^{79} + 8 q^{80} - 28 q^{81} + 30 q^{83} + 30 q^{84} - 40 q^{85} + 62 q^{86} + 48 q^{89} - 4 q^{91} - 144 q^{92} - 8 q^{93} - 20 q^{94} + 82 q^{97} - 10 q^{99}+O(q^{100}) \) 112 * q - 28 * q^3 - 6 * q^5 - 28 * q^9 - 10 * q^11 + 10 * q^13 - 60 * q^14 + 4 * q^15 + 80 * q^16 - 74 * q^20 + 8 * q^22 + 30 * q^24 + 38 * q^26 - 28 * q^27 - 20 * q^29 - 8 * q^31 + 20 * q^33 - 48 * q^34 + 20 * q^35 + 12 * q^37 - 10 * q^39 + 40 * q^40 - 110 * q^41 + 20 * q^42 - 36 * q^44 + 4 * q^45 - 20 * q^46 - 30 * q^47 - 20 * q^48 + 90 * q^50 - 10 * q^52 + 52 * q^53 - 64 * q^55 + 30 * q^57 + 24 * q^58 - 36 * q^59 - 74 * q^60 - 60 * q^61 + 48 * q^66 + 60 * q^67 + 60 * q^68 + 116 * q^70 + 20 * q^71 - 30 * q^72 + 70 * q^73 + 120 * q^74 - 52 * q^78 - 120 * q^79 + 8 * q^80 - 28 * q^81 + 30 * q^83 + 30 * q^84 - 40 * q^85 + 62 * q^86 + 48 * q^89 - 4 * q^91 - 144 * q^92 - 8 * q^93 - 20 * q^94 + 82 * q^97 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more