LMFDB - Embedded newform 138.2.f.a.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,2,Mod(5,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 1]))

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

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

chi := DirichletCharacter("138.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	138.f (of order $22$, degree $10$, 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:	$1.10193554789$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.6
Character	$\chi$	$=$	138.11
Dual form			138.2.f.a.113.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.540641 + 0.841254i) q^{2} +(-0.920624 - 1.46712i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(1.43749 - 0.422085i) q^{5} +(0.736496 - 1.56766i) q^{6} +(3.34037 - 2.89445i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(-1.30490 + 2.70134i) q^{9} +O(q^{10})$	\(q+(0.540641 + 0.841254i) q^{2} +(-0.920624 - 1.46712i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(1.43749 - 0.422085i) q^{5} +(0.736496 - 1.56766i) q^{6} +(3.34037 - 2.89445i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(-1.30490 + 2.70134i) q^{9} +(1.13225 + 0.981098i) q^{10} +(1.75207 + 1.12599i) q^{11} +(1.71698 - 0.227963i) q^{12} +(-2.50409 + 2.88987i) q^{13} +(4.24090 + 1.24524i) q^{14} +(-1.94264 - 1.72040i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-1.53425 - 3.35954i) q^{17} +(-2.97799 + 0.362698i) q^{18} +(0.806590 + 0.368357i) q^{19} +(-0.213213 + 1.48293i) q^{20} +(-7.32174 - 2.23604i) q^{21} +2.08269i q^{22} +(-4.39445 - 1.92063i) q^{23} +(1.12005 + 1.32117i) q^{24} +(-2.31804 + 1.48972i) q^{25} +(-3.78493 - 0.544191i) q^{26} +(5.16452 - 0.572458i) q^{27} +(1.24524 + 4.24090i) q^{28} +(-4.85145 + 2.21558i) q^{29} +(0.397019 - 2.56437i) q^{30} +(1.34101 + 9.32693i) q^{31} +(0.281733 - 0.959493i) q^{32} +(0.0389656 - 3.60712i) q^{33} +(1.99675 - 3.10700i) q^{34} +(3.58005 - 5.57066i) q^{35} +(-1.91515 - 2.30916i) q^{36} +(-0.717497 + 2.44357i) q^{37} +(0.126194 + 0.877696i) q^{38} +(6.54513 + 1.01332i) q^{39} +(-1.36279 + 0.622366i) q^{40} +(0.0613750 + 0.209024i) q^{41} +(-2.07735 - 7.36833i) q^{42} +(-3.01815 - 0.433944i) q^{43} +(-1.75207 + 1.12599i) q^{44} +(-0.735594 + 4.43393i) q^{45} +(-0.760086 - 4.73522i) q^{46} -9.62337i q^{47} +(-0.505898 + 1.65652i) q^{48} +(1.78404 - 12.4083i) q^{49} +(-2.50646 - 1.14466i) q^{50} +(-3.51640 + 5.34381i) q^{51} +(-1.58848 - 3.47830i) q^{52} +(8.08324 + 9.32856i) q^{53} +(3.27373 + 4.03518i) q^{54} +(2.99385 + 0.879075i) q^{55} +(-2.89445 + 3.34037i) q^{56} +(-0.202140 - 1.52249i) q^{57} +(-4.48676 - 2.88346i) q^{58} +(6.92648 + 6.00183i) q^{59} +(2.37193 - 1.05241i) q^{60} +(6.28652 - 0.903865i) q^{61} +(-7.12131 + 6.17065i) q^{62} +(3.46001 + 12.8004i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-2.37983 + 5.21111i) q^{65} +(3.05557 - 1.91738i) q^{66} +(-1.67331 - 2.60371i) q^{67} +3.69330 q^{68} +(1.22784 + 8.21538i) q^{69} +6.62186 q^{70} +(-6.11097 - 9.50886i) q^{71} +(0.907182 - 2.85955i) q^{72} +(-1.78840 + 3.91604i) q^{73} +(-2.44357 + 0.717497i) q^{74} +(4.31964 + 2.02939i) q^{75} +(-0.670139 + 0.580679i) q^{76} +(9.11169 - 1.31006i) q^{77} +(2.68610 + 6.05395i) q^{78} +(-9.86473 - 8.54784i) q^{79} +(-1.26035 - 0.809976i) q^{80} +(-5.59445 - 7.04998i) q^{81} +(-0.142660 + 0.164639i) q^{82} +(3.42714 + 1.00630i) q^{83} +(5.07553 - 5.73120i) q^{84} +(-3.62349 - 4.18173i) q^{85} +(-1.26668 - 2.77364i) q^{86} +(7.71689 + 5.07796i) q^{87} +(-1.89449 - 0.865182i) q^{88} +(-1.50592 + 10.4739i) q^{89} +(-4.12775 + 1.77834i) q^{90} +16.9012i q^{91} +(3.57258 - 3.19948i) q^{92} +(12.4492 - 10.5540i) q^{93} +(8.09570 - 5.20279i) q^{94} +(1.31494 + 0.189061i) q^{95} +(-1.66706 + 0.469995i) q^{96} +(-1.95376 - 6.65389i) q^{97} +(11.4031 - 5.20760i) q^{98} +(-5.32797 + 3.26363i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6}+O(q^{10}) $ 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6	$ 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6} - 4 q^{12} + 8 q^{13} - 22 q^{15} - 8 q^{16} - 28 q^{18} - 66 q^{21} - 4 q^{24} - 48 q^{25} - 38 q^{27} - 44 q^{30} - 16 q^{31} - 22 q^{33} - 44 q^{37} - 24 q^{39} - 44 q^{43} - 16 q^{46} + 4 q^{48} - 76 q^{49} - 8 q^{52} - 6 q^{54} + 64 q^{55} + 66 q^{57} + 36 q^{58} + 22 q^{60} + 88 q^{61} + 110 q^{63} + 8 q^{64} + 88 q^{66} + 44 q^{67} + 82 q^{69} + 112 q^{70} + 28 q^{72} + 52 q^{73} + 136 q^{75} + 82 q^{78} + 88 q^{79} + 36 q^{81} + 44 q^{82} + 22 q^{84} + 20 q^{85} - 10 q^{87} + 8 q^{93} - 56 q^{94} + 4 q^{96} - 132 q^{97} - 66 q^{99}+O(q^{100}) $ 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6 - 4 * q^12 + 8 * q^13 - 22 * q^15 - 8 * q^16 - 28 * q^18 - 66 * q^21 - 4 * q^24 - 48 * q^25 - 38 * q^27 - 44 * q^30 - 16 * q^31 - 22 * q^33 - 44 * q^37 - 24 * q^39 - 44 * q^43 - 16 * q^46 + 4 * q^48 - 76 * q^49 - 8 * q^52 - 6 * q^54 + 64 * q^55 + 66 * q^57 + 36 * q^58 + 22 * q^60 + 88 * q^61 + 110 * q^63 + 8 * q^64 + 88 * q^66 + 44 * q^67 + 82 * q^69 + 112 * q^70 + 28 * q^72 + 52 * q^73 + 136 * q^75 + 82 * q^78 + 88 * q^79 + 36 * q^81 + 44 * q^82 + 22 * q^84 + 20 * q^85 - 10 * q^87 + 8 * q^93 - 56 * q^94 + 4 * q^96 - 132 * q^97 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$-1$	$e\left(\frac{9}{22}\right)$

Coefficient data

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

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

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

$2$	0.540641	+	0.841254i	0.382291	+	0.594856i
$2$	0.540641	+	0.841254i	0.382291	+	0.594856i
$3$	−0.920624	−	1.46712i	−0.531522	−	0.847044i
$3$	−0.920624	−	1.46712i	−0.531522	−	0.847044i
$4$	−0.415415	+	0.909632i	−0.207708	+	0.454816i
$5$	1.43749	−	0.422085i	0.642866	−	0.188762i	0.0559796	−	0.998432i	$-0.482172\pi$
$5$	1.43749	−	0.422085i	0.642866	−	0.188762i	0.586886	+	0.809670i	$0.300354\pi$
$6$	0.736496	−	1.56766i	0.300673	−	0.639996i
$7$	3.34037	−	2.89445i	1.26254	−	1.09400i	0.271223	−	0.962517i	$-0.412572\pi$
$7$	3.34037	−	2.89445i	1.26254	−	1.09400i	0.991319	−	0.131481i	$-0.0419734\pi$
$8$	−0.989821	+	0.142315i	−0.349955	+	0.0503159i
$9$	−1.30490	+	2.70134i	−0.434968	+	0.900446i
$10$	1.13225	+	0.981098i	0.358048	+	0.310250i
$11$	1.75207	+	1.12599i	0.528270	+	0.339499i	0.777436	−	0.628962i	$-0.216520\pi$
$11$	1.75207	+	1.12599i	0.528270	+	0.339499i	−0.249166	+	0.968461i	$0.580156\pi$
$12$	1.71698	−	0.227963i	0.495650	−	0.0658074i
$13$	−2.50409	+	2.88987i	−0.694510	+	0.801507i	−0.988000	−	0.154455i	$-0.950638\pi$
$13$	−2.50409	+	2.88987i	−0.694510	+	0.801507i	0.293490	+	0.955962i	$0.405183\pi$
$14$	4.24090	+	1.24524i	1.13343	+	0.332805i
$15$	−1.94264	−	1.72040i	−0.501587	−	0.444204i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	−1.53425	−	3.35954i	−0.372111	−	0.814809i	−0.999352	−	0.0359844i	$-0.988543\pi$
$17$	−1.53425	−	3.35954i	−0.372111	−	0.814809i	0.627241	−	0.778825i	$-0.284184\pi$
$18$	−2.97799	+	0.362698i	−0.701920	+	0.0854887i
$19$	0.806590	+	0.368357i	0.185045	+	0.0845070i	0.505783	−	0.862661i	$-0.331204\pi$
$19$	0.806590	+	0.368357i	0.185045	+	0.0845070i	−0.320738	+	0.947168i	$0.603931\pi$
$20$	−0.213213	+	1.48293i	−0.0476759	+	0.331593i
$21$	−7.32174	−	2.23604i	−1.59773	−	0.487944i
$22$			2.08269i			0.444032i
$23$	−4.39445	−	1.92063i	−0.916306	−	0.400478i
$23$	−4.39445	−	1.92063i	−0.916306	−	0.400478i
$24$	1.12005	+	1.32117i	0.228629	+	0.269683i
$25$	−2.31804	+	1.48972i	−0.463609	+	0.297943i
$26$	−3.78493	−	0.544191i	−0.742286	−	0.106725i
$27$	5.16452	−	0.572458i	0.993913	−	0.110170i
$28$	1.24524	+	4.24090i	0.235329	+	0.801456i
$29$	−4.85145	+	2.21558i	−0.900891	+	0.411423i	−0.811351	−	0.584560i	$-0.801267\pi$
$29$	−4.85145	+	2.21558i	−0.900891	+	0.411423i	−0.0895408	+	0.995983i	$0.528540\pi$
$30$	0.397019	−	2.56437i	0.0724853	−	0.468188i
$31$	1.34101	+	9.32693i	0.240852	+	1.67517i	0.647874	+	0.761747i	$0.275658\pi$
$31$	1.34101	+	9.32693i	0.240852	+	1.67517i	−0.407022	+	0.913418i	$0.633433\pi$
$32$	0.281733	−	0.959493i	0.0498038	−	0.169616i
$33$	0.0389656	−	3.60712i	0.00678304	−	0.627919i
$34$	1.99675	−	3.10700i	0.342440	−	0.532847i
$35$	3.58005	−	5.57066i	0.605139	−	0.941614i
$36$	−1.91515	−	2.30916i	−0.319191	−	0.384860i
$37$	−0.717497	+	2.44357i	−0.117956	+	0.401720i	−0.997211	−	0.0746301i	$-0.976222\pi$
$37$	−0.717497	+	2.44357i	−0.117956	+	0.401720i	0.879256	+	0.476350i	$0.158041\pi$
$38$	0.126194	+	0.877696i	0.0204713	+	0.142381i
$39$	6.54513	+	1.01332i	1.04806	+	0.162262i
$40$	−1.36279	+	0.622366i	−0.215476	+	0.0984046i
$41$	0.0613750	+	0.209024i	0.00958517	+	0.0326441i	0.964147	−	0.265370i	$-0.0854940\pi$
$41$	0.0613750	+	0.209024i	0.00958517	+	0.0326441i	−0.954562	+	0.298014i	$0.903676\pi$
$42$	−2.07735	−	7.36833i	−0.320542	−	1.13696i
$43$	−3.01815	−	0.433944i	−0.460263	−	0.0661759i	−0.0917167	−	0.995785i	$-0.529235\pi$
$43$	−3.01815	−	0.433944i	−0.460263	−	0.0661759i	−0.368547	+	0.929609i	$0.620144\pi$
$44$	−1.75207	+	1.12599i	−0.264135	+	0.169749i
$45$	−0.735594	+	4.43393i	−0.109656	+	0.660971i
$46$	−0.760086	−	4.73522i	−0.112069	−	0.698169i
$47$		−	9.62337i		−	1.40371i	−0.712318	−	0.701856i	$-0.752355\pi$
$47$		−	9.62337i		−	1.40371i	0.712318	−	0.701856i	$-0.247645\pi$
$48$	−0.505898	+	1.65652i	−0.0730201	+	0.239098i
$49$	1.78404	−	12.4083i	0.254863	−	1.77261i
$50$	−2.50646	−	1.14466i	−0.354467	−	0.161879i
$51$	−3.51640	+	5.34381i	−0.492394	+	0.748284i
$52$	−1.58848	−	3.47830i	−0.220283	−	0.482353i
$53$	8.08324	+	9.32856i	1.11032	+	1.28138i	0.956004	+	0.293354i	$0.0947716\pi$
$53$	8.08324	+	9.32856i	1.11032	+	1.28138i	0.154315	+	0.988022i	$0.450683\pi$
$54$	3.27373	+	4.03518i	0.445499	+	0.549118i
$55$	2.99385	+	0.879075i	0.403691	+	0.118534i
$56$	−2.89445	+	3.34037i	−0.386787	+	0.446376i
$57$	−0.202140	−	1.52249i	−0.0267741	−	0.201658i
$58$	−4.48676	−	2.88346i	−0.589140	−	0.378617i
$59$	6.92648	+	6.00183i	0.901751	+	0.781372i	0.976430	−	0.215836i	$-0.0692477\pi$
$59$	6.92648	+	6.00183i	0.901751	+	0.781372i	−0.0746787	+	0.997208i	$0.523793\pi$
$60$	2.37193	−	1.05241i	0.306215	−	0.135865i
$61$	6.28652	−	0.903865i	0.804906	−	0.115728i	0.272433	−	0.962175i	$-0.412172\pi$
$61$	6.28652	−	0.903865i	0.804906	−	0.115728i	0.532473	+	0.846447i	$0.321263\pi$
$62$	−7.12131	+	6.17065i	−0.904407	+	0.783673i
$63$	3.46001	+	12.8004i	0.435921	+	1.61270i
$64$	0.959493	−	0.281733i	0.119937	−	0.0352166i
$65$	−2.37983	+	5.21111i	−0.295182	+	0.646358i
$66$	3.05557	−	1.91738i	0.376115	−	0.236013i
$67$	−1.67331	−	2.60371i	−0.204427	−	0.318094i	0.723869	−	0.689938i	$-0.242362\pi$
$67$	−1.67331	−	2.60371i	−0.204427	−	0.318094i	−0.928295	+	0.371843i	$0.878726\pi$
$68$	3.69330			0.447879
$69$	1.22784	+	8.21538i	0.147814	+	0.989015i
$70$	6.62186			0.791464
$71$	−6.11097	−	9.50886i	−0.725239	−	1.12849i	−0.986585	−	0.163249i	$-0.947803\pi$
$71$	−6.11097	−	9.50886i	−0.725239	−	1.12849i	0.261346	−	0.965245i	$-0.415834\pi$
$72$	0.907182	−	2.85955i	0.106912	−	0.337001i
$73$	−1.78840	+	3.91604i	−0.209316	+	0.458338i	−0.984949	−	0.172846i	$-0.944704\pi$
$73$	−1.78840	+	3.91604i	−0.209316	+	0.458338i	0.775633	+	0.631184i	$0.217431\pi$
$74$	−2.44357	+	0.717497i	−0.284059	+	0.0834073i
$75$	4.31964	+	2.02939i	0.498789	+	0.234334i
$76$	−0.670139	+	0.580679i	−0.0768703	+	0.0666085i
$77$	9.11169	−	1.31006i	1.03837	−	0.149296i
$78$	2.68610	+	6.05395i	0.304141	+	0.685475i
$79$	−9.86473	−	8.54784i	−1.10987	−	0.961707i	−0.110387	−	0.993889i	$-0.535209\pi$
$79$	−9.86473	−	8.54784i	−1.10987	−	0.961707i	−0.999482	+	0.0321821i	$0.989754\pi$
$80$	−1.26035	−	0.809976i	−0.140911	−	0.0905581i
$81$	−5.59445	−	7.04998i	−0.621605	−	0.783331i
$82$	−0.142660	+	0.164639i	−0.0157542	+	0.0181813i
$83$	3.42714	+	1.00630i	0.376177	+	0.110456i	0.464355	−	0.885649i	$-0.346286\pi$
$83$	3.42714	+	1.00630i	0.376177	+	0.110456i	−0.0881777	+	0.996105i	$0.528104\pi$
$84$	5.07553	−	5.73120i	0.553786	−	0.625325i
$85$	−3.62349	−	4.18173i	−0.393023	−	0.453572i
$86$	−1.26668	−	2.77364i	−0.136589	−	0.299089i
$87$	7.71689	+	5.07796i	0.827338	+	0.544414i
$88$	−1.89449	−	0.865182i	−0.201953	−	0.0922287i
$89$	−1.50592	+	10.4739i	−0.159627	+	1.11023i	0.739694	+	0.672943i	$0.234970\pi$
$89$	−1.50592	+	10.4739i	−0.159627	+	1.11023i	−0.899322	+	0.437288i	$0.855939\pi$
$90$	−4.12775	+	1.77834i	−0.435103	+	0.187454i
$91$			16.9012i			1.77173i
$92$	3.57258	−	3.19948i	0.372468	−	0.333568i
$93$	12.4492	−	10.5540i	1.29092	−	1.09440i
$94$	8.09570	−	5.20279i	0.835007	−	0.536627i
$95$	1.31494	+	0.189061i	0.134910	+	0.0193972i
$96$	−1.66706	+	0.469995i	−0.170144	+	0.0479687i
$97$	−1.95376	−	6.65389i	−0.198374	−	0.675600i	−0.997250	−	0.0741047i	$-0.976390\pi$
$97$	−1.95376	−	6.65389i	−0.198374	−	0.675600i	0.798876	−	0.601495i	$-0.205428\pi$
$98$	11.4031	−	5.20760i	1.15188	−	0.526047i
$99$	−5.32797	+	3.26363i	−0.535481	+	0.328007i
$100$	−0.392143	−	2.72742i	−0.0392143	−	0.272742i
$101$	2.92436	−	9.95947i	0.290985	−	0.991004i	−0.676155	−	0.736760i	$-0.736355\pi$
$101$	2.92436	−	9.95947i	0.290985	−	0.991004i	0.967140	−	0.254245i	$-0.0818269\pi$
$102$	−6.39661	−	0.0690988i	−0.633359	−	0.00684180i
$103$	10.4440	−	16.2512i	1.02908	−	1.60127i	0.256299	−	0.966597i	$-0.417497\pi$
$103$	10.4440	−	16.2512i	1.02908	−	1.60127i	0.772777	−	0.634677i	$-0.218867\pi$
$104$	2.06733	−	3.21683i	0.202718	−	0.315436i
$105$	−11.4687	−	0.123890i	−1.11923	−	0.0120904i
$106$	−3.47755	+	11.8435i	−0.337770	+	1.15034i
$107$	−0.778146	−	5.41213i	−0.0752262	−	0.523210i	−0.992238	−	0.124351i	$-0.960315\pi$
$107$	−0.778146	−	5.41213i	−0.0752262	−	0.523210i	0.917012	−	0.398859i	$-0.130594\pi$
$108$	−1.62469	+	4.93562i	−0.156336	+	0.474931i
$109$	−8.78378	+	4.01142i	−0.841334	+	0.384224i	−0.788991	−	0.614405i	$-0.789396\pi$
$109$	−8.78378	+	4.01142i	−0.841334	+	0.384224i	−0.0523429	+	0.998629i	$0.516669\pi$
$110$	0.879075	+	2.99385i	0.0838165	+	0.285453i
$111$	4.24556	−	1.19695i	0.402971	−	0.113610i
$112$	−4.37495	−	0.629023i	−0.413394	−	0.0594371i
$113$	−5.05558	+	3.24902i	−0.475589	+	0.305642i	−0.756387	−	0.654124i	$-0.773037\pi$
$113$	−5.05558	+	3.24902i	−0.475589	+	0.305642i	0.280798	+	0.959767i	$0.409401\pi$
$114$	1.17151	−	0.993169i	0.109722	−	0.0930188i
$115$	−7.12765	−	0.906049i	−0.664657	−	0.0844895i
$116$		−	5.33342i		−	0.495196i
$117$	−4.53893	−	10.5354i	−0.419624	−	0.973998i
$118$	−1.30432	+	9.07176i	−0.120073	+	0.835123i
$119$	−14.8490	−	6.78131i	−1.36121	−	0.621642i
$120$	2.16770	+	1.42642i	0.197883	+	0.130214i
$121$	−2.76766	−	6.06032i	−0.251605	−	0.550938i
$122$	4.15913	+	4.79989i	0.376550	+	0.434561i
$123$	0.250161	−	0.282477i	0.0225563	−	0.0254701i
$124$	−9.04115	−	2.65472i	−0.811919	−	0.238401i
$125$	−7.60887	+	8.78110i	−0.680558	+	0.785406i
$126$	−8.89779	+	9.83119i	−0.792678	+	0.875832i
$127$	11.1438	+	7.16167i	0.988850	+	0.635495i	0.931837	−	0.362878i	$-0.118206\pi$
$127$	11.1438	+	7.16167i	0.988850	+	0.635495i	0.0570134	+	0.998373i	$0.481842\pi$
$128$	0.755750	+	0.654861i	0.0667995	+	0.0578821i
$129$	2.14193	+	4.82750i	0.188586	+	0.425037i
$130$	−5.67050	+	0.815294i	−0.497336	+	0.0715061i
$131$	−5.82456	+	5.04701i	−0.508894	+	0.440959i	−0.871076	−	0.491148i	$-0.836577\pi$
$131$	−5.82456	+	5.04701i	−0.508894	+	0.440959i	0.362182	+	0.932107i	$0.382032\pi$
$132$	3.26497	+	1.53390i	0.284179	+	0.133509i
$133$	3.76050	−	1.10418i	0.326077	−	0.0957448i
$134$	1.28573	−	2.81535i	0.111070	−	0.243209i
$135$	7.18233	−	3.00277i	0.618156	−	0.258438i
$136$	1.99675	+	3.10700i	0.171220	+	0.266423i
$137$	16.0060			1.36748			0.683741	−	0.729725i	$-0.260352\pi$
$137$	16.0060			1.36748			0.683741	+	0.729725i	$0.260352\pi$
$138$	−6.24739	+	5.47449i	−0.531814	+	0.466020i
$139$	0.415789			0.0352668			0.0176334	−	0.999845i	$-0.494387\pi$
$139$	0.415789			0.0352668			0.0176334	+	0.999845i	$0.494387\pi$
$140$	3.58005	+	5.57066i	0.302569	+	0.470807i
$141$	−14.1187	+	8.85950i	−1.18901	+	0.746105i
$142$	4.69552	−	10.2818i	0.394039	−	0.862825i
$143$	−7.64132	+	2.24369i	−0.638999	+	0.187627i
$144$	2.89607	−	0.782819i	0.241339	−	0.0652349i
$145$	−6.03875	+	5.23261i	−0.501491	+	0.434544i
$146$	−4.26126	+	0.612677i	−0.352665	+	0.0507055i
$147$	−19.8469	+	8.80596i	−1.63695	+	0.726303i
$148$	−1.92469	−	1.66775i	−0.158209	−	0.137088i
$149$	−2.64950	−	1.70273i	−0.217055	−	0.139493i	0.427595	−	0.903970i	$-0.359361\pi$
$149$	−2.64950	−	1.70273i	−0.217055	−	0.139493i	−0.644651	+	0.764477i	$0.722997\pi$
$150$	0.628145	+	4.73108i	0.0512878	+	0.386291i
$151$	3.12657	−	3.60826i	0.254437	−	0.293636i	−0.614133	−	0.789203i	$-0.710494\pi$
$151$	3.12657	−	3.60826i	0.254437	−	0.293636i	0.868570	+	0.495567i	$0.165040\pi$
$152$	−0.850803	−	0.249818i	−0.0690092	−	0.0202629i
$153$	11.0773	+	0.239351i	0.895548	+	0.0193504i
$154$	6.02825	+	6.95697i	0.485770	+	0.560608i
$155$	5.86445	+	12.8414i	0.471044	+	1.03144i
$156$	−3.64070	+	5.53271i	−0.291489	+	0.442971i
$157$	−2.06181	−	0.941599i	−0.164551	−	0.0751477i	0.331437	−	0.943477i	$-0.392467\pi$
$157$	−2.06181	−	0.941599i	−0.164551	−	0.0751477i	−0.495988	+	0.868330i	$0.665194\pi$
$158$	1.85762	−	12.9200i	0.147784	−	1.02786i
$159$	6.24453	−	20.4472i	0.495223	−	1.62157i
$160$		−	1.49818i		−	0.118441i
$161$	−20.2382	+	6.30390i	−1.59500	+	0.496817i
$162$	2.90623	−	8.51785i	0.228335	−	0.669226i
$163$	−10.2526	+	6.58893i	−0.803043	+	0.516085i	−0.876608	−	0.481206i	$-0.840199\pi$
$163$	−10.2526	+	6.58893i	−0.803043	+	0.516085i	0.0735643	+	0.997290i	$0.476563\pi$
$164$	−0.215631	−	0.0310031i	−0.0168380	−	0.00242093i
$165$	−1.46650	−	5.20165i	−0.114167	−	0.404948i
$166$	1.00630	+	3.42714i	0.0781039	+	0.265998i
$167$	8.04885	−	3.67579i	0.622839	−	0.284441i	−0.0788919	−	0.996883i	$-0.525138\pi$
$167$	8.04885	−	3.67579i	0.622839	−	0.284441i	0.701731	+	0.712442i	$0.252411\pi$
$168$	7.56543	+	1.17129i	0.583686	+	0.0903669i
$169$	−0.230811	−	1.60533i	−0.0177547	−	0.123487i
$170$	1.55889	−	5.30909i	0.119561	−	0.407188i
$171$	−2.04758	+	1.69820i	−0.156582	+	0.129865i
$172$	1.64851	−	2.56514i	0.125698	−	0.195590i
$173$	9.50005	−	14.7824i	0.722276	−	1.12388i	−0.264905	−	0.964275i	$-0.585341\pi$
$173$	9.50005	−	14.7824i	0.722276	−	1.12388i	0.987180	−	0.159608i	$-0.0510231\pi$
$174$	−0.0997841	+	9.23721i	−0.00756461	+	0.700271i
$175$	−3.43122	+	11.6857i	−0.259376	+	0.883352i
$176$	−0.296398	−	2.06150i	−0.0223419	−	0.155391i
$177$	2.42875	−	15.6874i	0.182556	−	1.17914i
$178$	−9.62536	+	4.39576i	−0.721452	+	0.329476i
$179$	−3.55735	−	12.1152i	−0.265889	−	0.905534i	−0.978893	−	0.204374i	$-0.934484\pi$
$179$	−3.55735	−	12.1152i	−0.265889	−	0.905534i	0.713004	−	0.701160i	$-0.247334\pi$
$180$	−3.72767	−	2.51104i	−0.277844	−	0.187162i
$181$	18.0950	+	2.60167i	1.34499	+	0.193380i	0.776920	−	0.629600i	$-0.216781\pi$
$181$	18.0950	+	2.60167i	1.34499	+	0.193380i	0.568070	+	0.822980i	$0.307690\pi$
$182$	−14.2182	+	9.13748i	−1.05392	+	0.677315i
$183$	−7.11360	−	8.39098i	−0.525852	−	0.620279i
$184$	4.62306	+	1.27568i	0.340816	+	0.0940445i
$185$			3.81545i			0.280518i
$186$	15.6091	+	4.76700i	1.14452	+	0.349533i
$187$	1.09469	−	7.61372i	0.0800515	−	0.556770i
$188$	8.75373	+	3.99769i	0.638431	+	0.291562i
$189$	15.5945	−	16.8607i	1.13433	−	1.22643i
$190$	0.551865	+	1.20842i	0.0400365	+	0.0876677i
$191$	−9.55402	−	11.0259i	−0.691305	−	0.797808i	0.296246	−	0.955112i	$-0.404265\pi$
$191$	−9.55402	−	11.0259i	−0.691305	−	0.797808i	−0.987550	+	0.157304i	$0.949720\pi$
$192$	−1.29667	−	1.14833i	−0.0935790	−	0.0828732i
$193$	0.392170	+	0.115152i	0.0282290	+	0.00828880i	0.295817	−	0.955245i	$-0.404408\pi$
$193$	0.392170	+	0.115152i	0.0282290	+	0.00828880i	−0.267588	+	0.963534i	$0.586226\pi$
$194$	4.54132	−	5.24097i	0.326048	−	0.376280i
$195$	9.83627	−	1.30596i	0.704390	−	0.0935216i
$196$	10.5459	+	6.77742i	0.753276	+	0.484101i
$197$	13.2726	+	11.5008i	0.945637	+	0.819399i	0.983689	−	0.179877i	$-0.0575699\pi$
$197$	13.2726	+	11.5008i	0.945637	+	0.819399i	−0.0380522	+	0.999276i	$0.512115\pi$
$198$	−5.62606	−	2.71772i	−0.399827	−	0.193140i
$199$	8.87881	−	1.27658i	0.629403	−	0.0904944i	0.179771	−	0.983709i	$-0.442464\pi$
$199$	8.87881	−	1.27658i	0.629403	−	0.0904944i	0.449632	+	0.893214i	$0.351555\pi$
$200$	2.08244	−	1.80444i	0.147251	−	0.127593i
$201$	−2.27949	+	4.85199i	−0.160783	+	0.342233i
$202$	9.95947	−	2.92436i	0.700746	−	0.205758i
$203$	−9.79275	+	21.4431i	−0.687316	+	1.50501i
$204$	−3.40014	−	5.41853i	−0.238057	−	0.379373i
$205$	0.176452	+	0.274565i	0.0123239	+	0.0191764i
$206$	19.3178			1.34593
$207$	10.9226	−	9.36466i	0.759173	−	0.650889i
$208$	3.82385			0.265136
$209$	0.998439	+	1.55360i	0.0690635	+	0.107465i
$210$	−6.09624	−	9.71509i	−0.420681	−	0.670405i
$211$	5.24063	−	11.4754i	0.360780	−	0.789998i	−0.639004	−	0.769204i	$-0.720653\pi$
$211$	5.24063	−	11.4754i	0.360780	−	0.789998i	0.999784	−	0.0207943i	$-0.00661951\pi$
$212$	−11.8435	+	3.47755i	−0.813412	+	0.238839i
$213$	−8.32477	+	17.7196i	−0.570404	+	1.21413i
$214$	4.13227	−	3.58063i	0.282476	−	0.244767i
$215$	−4.52172	+	0.650126i	−0.308379	+	0.0443382i
$216$	−5.03049	+	1.30162i	−0.342281	+	0.0885640i
$217$	31.4758	+	27.2739i	2.13671	+	1.85147i
$218$	−8.12349	−	5.22065i	−0.550192	−	0.353587i
$219$	7.39176	−	0.981401i	0.499489	−	0.0663170i
$220$	−2.04333	+	2.35812i	−0.137761	+	0.158985i
$221$	13.5506	+	3.97880i	0.911510	+	0.267643i
$222$	3.30226	+	2.92447i	0.221633	+	0.196278i
$223$	−9.65557	−	11.1431i	−0.646585	−	0.746198i	0.333940	−	0.942594i	$-0.391622\pi$
$223$	−9.65557	−	11.1431i	−0.646585	−	0.746198i	−0.980525	+	0.196396i	$0.937076\pi$
$224$	−1.83611	−	4.02052i	−0.122680	−	0.268632i
$225$	−0.999400	−	8.20575i	−0.0666267	−	0.547050i
$226$	−5.46651	−	2.49647i	−0.363627	−	0.166063i
$227$	−1.98541	+	13.8089i	−0.131777	+	0.916526i	0.811461	+	0.584407i	$0.198673\pi$
$227$	−1.98541	+	13.8089i	−0.131777	+	0.916526i	−0.943237	+	0.332119i	$0.892236\pi$
$228$	1.46887	+	0.448591i	0.0972786	+	0.0297086i
$229$			4.45353i			0.294298i	0.989114	+	0.147149i	$0.0470096\pi$
$229$			4.45353i			0.294298i	−0.989114	+	0.147149i	$0.952990\pi$
$230$	−3.09128	−	6.48601i	−0.203833	−	0.427675i
$231$	−10.3105	−	12.1619i	−0.678379	−	0.800194i
$232$	4.48676	−	2.88346i	0.294570	−	0.189309i
$233$	8.57581	+	1.23301i	0.561820	+	0.0807775i	0.417373	−	0.908735i	$-0.362951\pi$
$233$	8.57581	+	1.23301i	0.561820	+	0.0807775i	0.144446	+	0.989513i	$0.453860\pi$
$234$	6.40901	−	9.51425i	0.418970	−	0.621966i
$235$	−4.06189	−	13.8335i	−0.264968	−	0.902399i
$236$	−8.33682	+	3.80730i	−0.542681	+	0.247834i
$237$	−3.45903	+	22.3421i	−0.224688	+	1.45128i
$238$	−2.32317	−	16.1580i	−0.150589	−	1.04737i
$239$	−6.42524	+	21.8824i	−0.415614	+	1.41545i	0.440075	+	0.897961i	$0.354952\pi$
$239$	−6.42524	+	21.8824i	−0.415614	+	1.41545i	−0.855689	+	0.517491i	$0.826866\pi$
$240$	−0.0280297	+	2.59477i	−0.00180931	+	0.167492i
$241$	−10.5755	+	16.4557i	−0.681225	+	1.06001i	0.312689	+	0.949855i	$0.398770\pi$
$241$	−10.5755	+	16.4557i	−0.681225	+	1.06001i	−0.993915	+	0.110152i	$0.964866\pi$
$242$	3.60196	−	5.60476i	0.231543	−	0.360287i
$243$	−5.19281	+	14.6981i	−0.333119	+	0.942885i
$244$	−1.78933	+	6.09390i	−0.114550	+	0.390122i
$245$	−2.67282	−	18.5898i	−0.170760	−	1.18766i
$246$	0.372882	+	0.0577301i	0.0237741	+	0.00368073i
$247$	−3.08428	+	1.40854i	−0.196248	+	0.0896235i
$248$	−2.65472	−	9.04115i	−0.168575	−	0.574113i
$249$	−1.67874	−	5.95446i	−0.106386	−	0.377349i
$250$	−11.5008	−	1.65357i	−0.727374	−	0.104581i
$251$	−11.8661	+	7.62590i	−0.748983	+	0.481342i	−0.858609	−	0.512631i	$-0.828671\pi$
$251$	−11.8661	+	7.62590i	−0.748983	+	0.481342i	0.109626	+	0.993973i	$0.465035\pi$
$252$	−13.0810	−	2.17016i	−0.824028	−	0.136707i
$253$	−5.53680	−	8.31318i	−0.348095	−	0.522645i
$254$			13.2466i			0.831167i
$255$	−2.79925	+	9.16591i	−0.175296	+	0.573991i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	7.29558	+	3.33178i	0.455086	+	0.207831i	0.629751	−	0.776797i	$-0.283157\pi$
$257$	7.29558	+	3.33178i	0.455086	+	0.207831i	−0.174665	+	0.984628i	$0.555884\pi$
$258$	−2.90313	+	4.41185i	−0.180741	+	0.274670i
$259$	4.67608	+	10.2392i	0.290557	+	0.636232i
$260$	−3.75157	−	4.32954i	−0.232663	−	0.268507i
$261$	0.345642	−	15.9965i	0.0213947	−	0.990160i
$262$	−7.39481	−	2.17131i	−0.456853	−	0.134144i
$263$	12.4722	−	14.3937i	0.769069	−	0.887553i	−0.227201	−	0.973848i	$-0.572957\pi$
$263$	12.4722	−	14.3937i	0.769069	−	0.887553i	0.996270	+	0.0862953i	$0.0275029\pi$
$264$	0.474778	+	3.57595i	0.0292206	+	0.220085i
$265$	15.5570	+	9.99790i	0.955661	+	0.614166i
$266$	2.96198	+	2.56657i	0.181611	+	0.157366i
$267$	16.7529	−	7.43315i	1.02526	−	0.454901i
$268$	3.06354	−	0.440470i	0.187135	−	0.0269060i
$269$	1.95976	−	1.69814i	0.119489	−	0.103537i	−0.593067	−	0.805153i	$-0.702083\pi$
$269$	1.95976	−	1.69814i	0.119489	−	0.103537i	0.712556	+	0.701616i	$0.247538\pi$
$270$	6.40915	+	4.41874i	0.390049	+	0.268916i
$271$	−1.61521	+	0.474268i	−0.0981170	+	0.0288098i	−0.330423	−	0.943833i	$-0.607191\pi$
$271$	−1.61521	+	0.474268i	−0.0981170	+	0.0288098i	0.232306	+	0.972643i	$0.425373\pi$
$272$	−1.53425	+	3.35954i	−0.0930277	+	0.203702i
$273$	24.7962	−	15.5596i	1.50073	−	0.941712i
$274$	8.65347	+	13.4651i	0.522775	+	0.813454i
$275$	−5.73879			−0.346062
$276$	−7.98303	−	2.29591i	−0.480522	−	0.138198i
$277$	−12.1413			−0.729498			−0.364749	−	0.931106i	$-0.618845\pi$
$277$	−12.1413			−0.729498			−0.364749	+	0.931106i	$0.618845\pi$
$278$	0.224793	+	0.349784i	0.0134822	+	0.0209787i
$279$	−26.9451	−	8.54823i	−1.61316	−	0.511769i
$280$	−2.75082	+	6.02346i	−0.164393	+	0.359970i
$281$	14.4675	−	4.24804i	0.863059	−	0.253417i	0.179899	−	0.983685i	$-0.442423\pi$
$281$	14.4675	−	4.24804i	0.863059	−	0.253417i	0.683161	+	0.730268i	$0.260605\pi$
$282$	−15.0862	−	7.08758i	−0.898371	−	0.422059i
$283$	−18.9926	+	16.4572i	−1.12899	+	0.978278i	−0.999911	−	0.0133560i	$-0.995749\pi$
$283$	−18.9926	+	16.4572i	−1.12899	+	0.978278i	−0.129082	+	0.991634i	$0.541203\pi$
$284$	11.1881	−	1.60861i	0.663895	−	0.0954536i
$285$	−0.933194	−	2.10324i	−0.0552776	−	0.124585i
$286$	−6.01872	−	5.21525i	−0.355894	−	0.308384i
$287$	0.810025	+	0.520571i	0.0478142	+	0.0307283i
$288$	2.22428	+	2.01310i	0.131067	+	0.118623i
$289$	2.20002	−	2.53896i	0.129413	−	0.149351i
$290$	−7.66674	−	2.25116i	−0.450207	−	0.132193i
$291$	−7.96340	+	8.99213i	−0.466823	+	0.527128i
$292$	−2.81923	−	3.25357i	−0.164983	−	0.190401i
$293$	−10.0554	−	22.0182i	−0.587443	−	1.28632i	−0.936975	−	0.349396i	$-0.886387\pi$
$293$	−10.0554	−	22.0182i	−0.587443	−	1.28632i	0.349533	−	0.936924i	$-0.386340\pi$
$294$	−18.1381	−	11.9354i	−1.05784	−	0.696090i
$295$	12.4900	+	5.70401i	0.727198	+	0.332100i
$296$	0.362437	−	2.52081i	0.0210662	−	0.146519i
$297$	9.69321	+	4.81221i	0.562457	+	0.279233i
$298$		−	3.14946i		−	0.182443i
$299$	16.5545	−	7.88999i	0.957369	−	0.456290i
$300$	−3.64044	+	3.08625i	−0.210181	+	0.178185i
$301$	−11.3378	+	7.28634i	−0.653498	+	0.419977i
$302$	4.72581	+	0.679469i	0.271940	+	0.0390990i
$303$	−17.3040	+	4.87852i	−0.994090	+	0.280264i
$304$	−0.249818	−	0.850803i	−0.0143281	−	0.0487969i
$305$	8.65530	−	3.95274i	0.495601	−	0.226334i
$306$	5.78749	+	9.44824i	0.330849	+	0.540120i
$307$	1.99118	+	13.8489i	0.113642	+	0.790401i	0.964325	+	0.264721i	$0.0852799\pi$
$307$	1.99118	+	13.8489i	0.113642	+	0.790401i	−0.850683	+	0.525680i	$0.823811\pi$
$308$	−2.59346	+	8.83251i	−0.147776	+	0.503279i
$309$	−33.4574	−	0.361421i	−1.90333	−	0.0205605i
$310$	−7.63227	+	11.8761i	−0.433484	+	0.674514i
$311$	−4.32275	+	6.72633i	−0.245121	+	0.381415i	−0.941913	−	0.335858i	$-0.890974\pi$
$311$	−4.32275	+	6.72633i	−0.245121	+	0.381415i	0.696792	+	0.717273i	$0.254610\pi$
$312$	−6.62272	−	0.0715413i	−0.374938	−	0.00405023i
$313$	2.64169	−	8.99677i	0.149317	−	0.508527i	−0.850532	−	0.525924i	$-0.823720\pi$
$313$	2.64169	−	8.99677i	0.149317	−	0.508527i	0.999849	+	0.0173966i	$0.00553780\pi$
$314$	−0.322577	−	2.24357i	−0.0182041	−	0.126612i
$315$	10.3766	+	16.9401i	0.584656	+	0.954467i
$316$	11.8733	−	5.42237i	0.667928	−	0.305032i
$317$	5.80350	+	19.7649i	0.325957	+	1.11011i	0.945629	+	0.325246i	$0.105447\pi$
$317$	5.80350	+	19.7649i	0.325957	+	1.11011i	−0.619673	+	0.784860i	$0.712735\pi$
$318$	20.5773	−	5.80136i	1.15392	−	0.325324i
$319$	−10.9948	−	1.58082i	−0.615592	−	0.0885087i
$320$	1.26035	−	0.809976i	0.0704556	−	0.0452790i
$321$	−7.22388	+	6.12417i	−0.403198	+	0.341818i
$322$	−16.2448	−	13.6173i	−0.905287	−	0.758865i
$323$		−	3.27493i		−	0.182222i
$324$	8.73690	−	2.16022i	0.485383	−	0.120012i
$325$	1.49950	−	10.4292i	0.0831771	−	0.578510i
$326$	−11.0859	−	5.06277i	−0.613992	−	0.280401i
$327$	13.9718	+	9.19389i	0.772643	+	0.508423i
$328$	−0.0904975	−	0.198162i	−0.00499689	−	0.0109417i
$329$	−27.8543	−	32.1456i	−1.53566	−	1.77225i
$330$	3.58306	−	4.04592i	0.197241	−	0.222721i
$331$	12.4601	+	3.65863i	0.684871	+	0.201096i	0.605615	−	0.795758i	$-0.292927\pi$
$331$	12.4601	+	3.65863i	0.684871	+	0.201096i	0.0792563	+	0.996854i	$0.474745\pi$
$332$	−2.33905	+	2.69940i	−0.128372	+	0.148149i
$333$	−5.66464	−	5.12682i	−0.310420	−	0.280948i
$334$	7.44381	+	4.78384i	0.407307	+	0.261760i
$335$	−3.50435	−	3.03654i	−0.191463	−	0.165904i
$336$	3.10483	+	6.99769i	0.169382	+	0.381755i
$337$	3.56137	−	0.512047i	0.194000	−	0.0278930i	−0.0446298	−	0.999004i	$-0.514211\pi$
$337$	3.56137	−	0.512047i	0.194000	−	0.0278930i	0.238630	+	0.971111i	$0.423302\pi$
$338$	1.22570	−	1.06208i	0.0666693	−	0.0577693i
$339$	9.42101	+	4.42603i	0.511679	+	0.240389i
$340$	5.30909	−	1.55889i	0.287926	−	0.0845426i
$341$	−8.15247	+	17.8514i	−0.441481	+	0.966709i
$342$	−2.53562	−	0.804418i	−0.137111	−	0.0434979i
$343$	−13.2286	−	20.5841i	−0.714276	−	1.11144i
$344$	3.04918			0.164401
$345$	5.23260	+	11.2913i	0.281714	+	0.607902i
$346$	17.5718			0.944668
$347$	−10.3610	−	16.1220i	−0.556207	−	0.865475i	0.443316	−	0.896366i	$-0.353802\pi$
$347$	−10.3610	−	16.1220i	−0.556207	−	0.865475i	−0.999523	+	0.0308903i	$0.990166\pi$
$348$	−7.82479	+	4.91007i	−0.419453	+	0.263207i
$349$	3.67410	−	8.04515i	0.196670	−	0.430647i	−0.785444	−	0.618932i	$-0.787566\pi$
$349$	3.67410	−	8.04515i	0.196670	−	0.430647i	0.982114	+	0.188285i	$0.0602929\pi$
$350$	−11.6857	+	3.43122i	−0.624624	+	0.183406i
$351$	−11.2781	+	16.3583i	−0.601980	+	0.873142i
$352$	1.57400	−	1.36387i	0.0838942	−	0.0726948i
$353$	−17.0199	+	2.44709i	−0.905878	+	0.130246i	−0.579480	−	0.814987i	$-0.696744\pi$
$353$	−17.0199	+	2.44709i	−0.905878	+	0.130246i	−0.326399	+	0.945232i	$0.605835\pi$
$354$	14.5102	−	6.43807i	0.771208	−	0.342180i
$355$	−12.7980	−	11.0895i	−0.679248	−	0.588572i
$356$	−8.90181	−	5.72085i	−0.471795	−	0.303204i
$357$	3.72131	+	28.0283i	0.196953	+	1.48342i
$358$	8.26872	−	9.54262i	0.437016	−	0.504343i
$359$	25.0701	+	7.36126i	1.32315	+	0.388512i	0.865629	−	0.500686i	$-0.166919\pi$
$359$	25.0701	+	7.36126i	1.32315	+	0.388512i	0.457522	+	0.889198i	$0.348737\pi$
$360$	0.0970922	−	4.49348i	0.00511721	−	0.236827i
$361$	−11.9275	−	13.7650i	−0.627761	−	0.724474i
$362$	7.59423	+	16.6290i	0.399144	+	0.874003i
$363$	−6.34327	+	9.63977i	−0.332935	+	0.505956i
$364$	−15.3739	−	7.02101i	−0.805810	−	0.368001i
$365$	−0.917900	+	6.38413i	−0.0480451	+	0.334161i
$366$	3.21304	−	10.5208i	0.167948	−	0.549933i
$367$		−	10.8935i		−	0.568637i	−0.958730	−	0.284318i	$-0.908233\pi$
$367$		−	10.8935i		−	0.568637i	0.958730	−	0.284318i	$-0.0917673\pi$
$368$	1.42624	+	4.57885i	0.0743479	+	0.238689i
$369$	−0.644733	−	0.106962i	−0.0335635	−	0.00556821i
$370$	−3.20976	+	2.06279i	−0.166868	+	0.107239i
$371$	54.0020	+	7.76432i	2.80365	+	0.403103i
$372$	4.42869	+	15.7085i	0.229617	+	0.814447i
$373$	−4.61692	−	15.7238i	−0.239055	−	0.814147i	−0.988388	−	0.151953i	$-0.951444\pi$
$373$	−4.61692	−	15.7238i	−0.239055	−	0.814147i	0.749333	−	0.662194i	$-0.230374\pi$
$374$	6.99690	−	3.19538i	0.361801	−	0.165229i
$375$	19.8879	+	3.07906i	1.02701	+	0.159002i
$376$	1.36955	+	9.52542i	0.0706291	+	0.491236i
$377$	5.74571	−	19.5681i	0.295919	−	1.00781i
$378$	22.6151	+	4.00334i	1.16319	+	0.205910i
$379$	−4.54460	+	7.07153i	−0.233440	+	0.363240i	−0.938135	−	0.346271i	$-0.887448\pi$
$379$	−4.54460	+	7.07153i	−0.233440	+	0.363240i	0.704694	+	0.709511i	$0.251084\pi$
$380$	−0.718223	+	1.11758i	−0.0368441	+	0.0573305i
$381$	0.247834	−	22.9425i	0.0126969	−	1.17538i
$382$	4.11031	−	13.9984i	0.210302	−	0.716222i
$383$	−2.07801	−	14.4529i	−0.106181	−	0.738506i	−0.971458	−	0.237212i	$-0.923766\pi$
$383$	−2.07801	−	14.4529i	−0.106181	−	0.738506i	0.865277	−	0.501294i	$-0.167143\pi$
$384$	0.265001	−	1.71166i	0.0135233	−	0.0873477i
$385$	12.5450	−	5.72912i	0.639353	−	0.291983i
$386$	0.115152	+	0.392170i	0.00586106	+	0.0199610i
$387$	5.11062	−	7.58678i	0.259788	−	0.385658i
$388$	6.86421	+	0.986924i	0.348477	+	0.0501035i
$389$	−1.39589	+	0.897083i	−0.0707743	+	0.0454839i	−0.575549	−	0.817767i	$-0.695212\pi$
$389$	−1.39589	+	0.897083i	−0.0707743	+	0.0454839i	0.504775	+	0.863251i	$0.331575\pi$
$390$	6.41653	+	7.56874i	0.324914	+	0.383258i
$391$	0.289769	+	17.7101i	0.0146542	+	0.895637i
$392$			12.5359i			0.633158i
$393$	12.7668	+	3.89896i	0.644001	+	0.196676i
$394$	−2.49937	+	17.3835i	−0.125916	+	0.875767i
$395$	−17.7884	−	8.12368i	−0.895030	−	0.408747i
$396$	−0.755388	−	6.20225i	−0.0379597	−	0.311675i
$397$	−0.289503	−	0.633922i	−0.0145297	−	0.0318156i	0.902228	−	0.431259i	$-0.141931\pi$
$397$	−0.289503	−	0.633922i	−0.0145297	−	0.0318156i	−0.916758	+	0.399444i	$0.869203\pi$
$398$	5.87418	+	6.77916i	0.294446	+	0.339809i
$399$	−5.08198	−	4.50058i	−0.254417	−	0.225311i
$400$	2.64385	+	0.776304i	0.132192	+	0.0388152i
$401$	−6.66635	+	7.69338i	−0.332902	+	0.384189i	−0.897380	−	0.441259i	$-0.854532\pi$
$401$	−6.66635	+	7.69338i	−0.332902	+	0.384189i	0.564478	+	0.825448i	$0.309077\pi$
$402$	−5.31414	+	0.705556i	−0.265045	+	0.0351899i
$403$	−30.3116	−	19.4801i	−1.50993	−	0.970374i
$404$	7.84463	+	6.79741i	0.390285	+	0.338184i
$405$	−11.0177	−	7.77294i	−0.547472	−	0.386241i
$406$	−23.3335	+	3.35485i	−1.15802	+	0.166498i
$407$	−4.00854	+	3.47342i	−0.198696	+	0.172171i
$408$	2.72010	−	5.78986i	0.134665	−	0.286641i
$409$	6.83524	−	2.00701i	0.337981	−	0.0992402i	−0.108338	−	0.994114i	$-0.534553\pi$
$409$	6.83524	−	2.00701i	0.337981	−	0.0992402i	0.446319	+	0.894874i	$0.352735\pi$
$410$	−0.135581	+	0.296882i	−0.00669589	+	0.0146620i
$411$	−14.7355	−	23.4827i	−0.726847	−	1.15832i
$412$	10.4440	+	16.2512i	0.514538	+	0.800637i
$413$	40.5090			1.99332
$414$	13.7833	+	4.12576i	0.677410	+	0.202770i
$415$	5.35123			0.262681
$416$	2.06733	+	3.21683i	0.101359	+	0.157718i
$417$	−0.382785	−	0.610014i	−0.0187451	−	0.0298725i
$418$	−0.767176	+	1.67988i	−0.0375238	+	0.0821657i
$419$	−28.9174	+	8.49091i	−1.41271	+	0.414808i	−0.897028	−	0.441974i	$-0.854278\pi$
$419$	−28.9174	+	8.49091i	−1.41271	+	0.414808i	−0.515678	+	0.856782i	$0.672460\pi$
$420$	4.87698	−	10.3809i	0.237972	−	0.506534i
$421$	1.45761	−	1.26303i	0.0710398	−	0.0615563i	−0.618617	−	0.785693i	$-0.712307\pi$
$421$	1.45761	−	1.26303i	0.0710398	−	0.0615563i	0.689657	+	0.724136i	$0.257761\pi$
$422$	12.4870	−	1.79536i	0.607858	−	0.0873968i
$423$	25.9960	+	12.5576i	1.26397	+	0.610571i
$424$	−9.32856	−	8.08324i	−0.453035	−	0.392557i
$425$	8.56123	+	5.50197i	0.415281	+	0.266885i
$426$	−19.4074	+	2.57672i	−0.940292	+	0.124842i
$427$	18.3831	−	21.2152i	0.889621	−	1.02668i
$428$	5.24630	+	1.54045i	0.253589	+	0.0744605i
$429$	10.3266	+	9.14516i	0.498571	+	0.441533i
$430$	−2.99155	−	3.45243i	−0.144265	−	0.166491i
$431$	−7.36638	−	16.1301i	−0.354826	−	0.776960i	−0.999917	−	0.0128549i	$-0.995908\pi$
$431$	−7.36638	−	16.1301i	−0.354826	−	0.776960i	0.645092	−	0.764105i	$-0.276819\pi$
$432$	−3.81468	−	3.52821i	−0.183534	−	0.169751i
$433$	11.7875	+	5.38317i	0.566471	+	0.258699i	0.677999	−	0.735063i	$-0.262847\pi$
$433$	11.7875	+	5.38317i	0.566471	+	0.258699i	−0.111528	+	0.993761i	$0.535575\pi$
$434$	−5.92719	+	41.2245i	−0.284514	+	1.97884i
$435$	13.2363	+	4.04233i	0.634632	+	0.193815i
$436$		−	9.65641i		−	0.462458i
$437$	−2.83704	−	3.16789i	−0.135714	−	0.151541i
$438$	4.82189	+	5.68776i	0.230399	+	0.271772i
$439$	30.1165	−	19.3547i	1.43738	−	0.923748i	0.437683	−	0.899129i	$-0.355799\pi$
$439$	30.1165	−	19.3547i	1.43738	−	0.923748i	0.999697	−	0.0246192i	$-0.00783731\pi$
$440$	−3.08849	−	0.444057i	−0.147238	−	0.0211696i
$441$	31.1910	+	21.0109i	1.48529	+	1.00052i
$442$	3.97880	+	13.5506i	0.189252	+	0.644535i
$443$	−27.0628	+	12.3591i	−1.28579	+	0.587201i	−0.936780	−	0.349918i	$-0.886209\pi$
$443$	−27.0628	+	12.3591i	−1.28579	+	0.587201i	−0.349010	+	0.937119i	$0.613482\pi$
$444$	−0.674886	+	4.35913i	−0.0320287	+	0.206875i
$445$	2.25613	+	15.6918i	0.106951	+	0.743861i
$446$	4.15399	−	14.1472i	0.196697	−	0.669890i
$447$	−0.0589240	+	5.45471i	−0.00278701	+	0.257999i
$448$	2.38960	−	3.71829i	0.112898	−	0.175673i
$449$	−19.2115	+	29.8936i	−0.906645	+	1.41077i	0.00509021	+	0.999987i	$0.498380\pi$
$449$	−19.2115	+	29.8936i	−0.906645	+	1.41077i	−0.911735	+	0.410779i	$0.865257\pi$
$450$	6.36280	−	5.27711i	0.299945	−	0.248766i
$451$	−0.127825	+	0.435333i	−0.00601906	+	0.0204990i
$452$	−0.855252	−	5.94841i	−0.0402277	−	0.279790i
$453$	−8.17215	−	1.26522i	−0.383961	−	0.0594453i
$454$	−12.6902	+	5.79540i	−0.595578	+	0.271991i
$455$	7.13375	+	24.2953i	0.334435	+	1.13898i
$456$	0.416755	+	1.47822i	0.0195163	+	0.0692241i
$457$	−31.1612	−	4.48030i	−1.45766	−	0.209580i	−0.632535	−	0.774532i	$-0.717986\pi$
$457$	−31.1612	−	4.48030i	−1.45766	−	0.209580i	−0.825124	+	0.564952i	$0.808895\pi$
$458$	−3.74655	+	2.40776i	−0.175065	+	0.112507i
$459$	−9.84688	−	16.4721i	−0.459613	−	0.768854i
$460$	3.78510	−	6.10715i	0.176481	−	0.284748i
$461$		−	12.6427i		−	0.588831i	−0.955678	−	0.294415i	$-0.904875\pi$
$461$		−	12.6427i		−	0.588831i	0.955678	−	0.294415i	$-0.0951249\pi$
$462$	4.65699	−	15.2489i	0.216663	−	0.709445i
$463$	0.769592	−	5.35263i	0.0357660	−	0.248758i	−0.964093	−	0.265566i	$-0.914441\pi$
$463$	0.769592	−	5.35263i	0.0357660	−	0.248758i	0.999859	+	0.0168079i	$0.00535039\pi$
$464$	4.85145	+	2.21558i	0.225223	+	0.102856i
$465$	13.4409	−	20.4259i	0.623307	−	0.947230i
$466$	3.59915	+	7.88105i	0.166728	+	0.365082i
$467$	−8.57841	−	9.90001i	−0.396961	−	0.458118i	0.521720	−	0.853117i	$-0.325290\pi$
$467$	−8.57841	−	9.90001i	−0.396961	−	0.458118i	−0.918682	+	0.394999i	$0.870745\pi$
$468$	11.4689	+	0.247812i	0.530149	+	0.0114551i
$469$	−13.1258	−	3.85408i	−0.606092	−	0.177965i
$470$	9.44147	−	10.8960i	0.435503	−	0.502597i
$471$	0.516712	+	3.89179i	0.0238088	+	0.179324i
$472$	−7.71013	−	4.95500i	−0.354887	−	0.228072i
$473$	−4.79940	−	4.15870i	−0.220677	−	0.191217i
$474$	−20.6655	+	9.16914i	−0.949197	+	0.421152i
$475$	−2.41846	+	0.347722i	−0.110967	+	0.0159546i
$476$	12.3370	−	10.6901i	0.565465	−	0.489978i
$477$	−35.7474	+	9.66269i	−1.63676	+	0.442424i
$478$	−21.8824	+	6.42524i	−1.00088	+	0.293884i
$479$	8.56405	−	18.7527i	0.391302	−	0.856831i	−0.606777	−	0.794872i	$-0.707538\pi$
$479$	8.56405	−	18.7527i	0.391302	−	0.856831i	0.998079	−	0.0619589i	$-0.0197348\pi$
$480$	−2.19801	+	1.37926i	−0.100325	+	0.0629542i
$481$	−5.26493	−	8.19239i	−0.240060	−	0.373541i
$482$	−19.5610			−0.890978
$483$	27.8804	+	23.8885i	1.26860	+	1.08696i
$484$	6.66239			0.302836
$485$	−5.61702	−	8.74025i	−0.255056	−	0.396874i
$486$	−15.1723	+	3.57794i	−0.688229	+	0.162299i
$487$	−14.7470	+	32.2913i	−0.668249	+	1.46326i	0.206382	+	0.978471i	$0.433831\pi$
$487$	−14.7470	+	32.2913i	−0.668249	+	1.46326i	−0.874631	+	0.484789i	$0.838896\pi$
$488$	−6.09390	+	1.78933i	−0.275858	+	0.0809991i
$489$	19.1055	+	8.97587i	0.863982	+	0.405903i
$490$	14.1937	−	12.2989i	0.641208	−	0.555609i
$491$	4.90904	−	0.705814i	0.221542	−	0.0318529i	−0.0306499	−	0.999530i	$-0.509758\pi$
$491$	4.90904	−	0.705814i	0.221542	−	0.0318529i	0.252192	+	0.967677i	$0.418849\pi$
$492$	0.153030	+	0.344900i	0.00689911	+	0.0155493i
$493$	14.8867	+	12.8994i	0.670463	+	0.580960i
$494$	−2.85243	−	1.83315i	−0.128337	−	0.0824771i
$495$	−6.28137	+	6.94030i	−0.282327	+	0.311943i
$496$	6.17065	−	7.12131i	0.277070	−	0.319756i
$497$	−47.9358	−	14.0752i	−2.15021	−	0.631360i
$498$	4.10161	−	4.63147i	0.183798	−	0.207541i
$499$	15.2358	+	17.5831i	0.682050	+	0.787128i	0.986211	−	0.165493i	$-0.0529215\pi$
$499$	15.2358	+	17.5831i	0.682050	+	0.787128i	−0.304161	+	0.952621i	$0.598376\pi$
$500$	−4.82673	−	10.5691i	−0.215858	−	0.472663i
$501$	−12.8028	−	8.42465i	−0.571987	−	0.376385i
$502$	−12.8306	−	5.85955i	−0.572659	−	0.261525i
$503$	1.77720	−	12.3607i	0.0792414	−	0.551136i	−0.911068	−	0.412256i	$-0.864741\pi$
$503$	1.77720	−	12.3607i	0.0792414	−	0.551136i	0.990309	−	0.138880i	$-0.0443501\pi$
$504$	−5.24649	−	12.1777i	−0.233697	−	0.542440i
$505$		−	15.5510i		−	0.692010i
$506$	4.00008	−	9.15230i	0.177825	−	0.406869i
$507$	−2.14272	+	1.81653i	−0.0951616	+	0.0806749i
$508$	−11.1438	+	7.16167i	−0.494425	+	0.317748i
$509$	6.78322	+	0.975280i	0.300661	+	0.0432285i	0.290994	−	0.956725i	$-0.406014\pi$
$509$	6.78322	+	0.975280i	0.300661	+	0.0432285i	0.00966659	+	0.999953i	$0.496923\pi$
$510$	−9.22424	+	2.60059i	−0.408456	+	0.115156i
$511$	5.36087	+	18.2574i	0.237151	+	0.807662i
$512$	−0.909632	+	0.415415i	−0.0402004	+	0.0183589i
$513$	4.37652	+	1.44065i	0.193228	+	0.0636063i
$514$	1.14142	+	7.93872i	0.0503457	+	0.350162i
$515$	8.15376	−	27.7692i	0.359298	−	1.22366i
$516$	−5.28103	−	0.0570479i	−0.232485	−	0.00251139i
$517$	10.8358	−	16.8609i	0.476559	−	0.741540i
$518$	−6.08567	+	9.46949i	−0.267389	+	0.416065i
$519$	−30.4335	−	0.328755i	−1.33588	−	0.0144308i
$520$	1.61399	−	5.49675i	0.0707782	−	0.241049i
$521$	6.08273	+	42.3063i	0.266489	+	1.85347i	0.480961	+	0.876742i	$0.340288\pi$
$521$	6.08273	+	42.3063i	0.266489	+	1.85347i	−0.214472	+	0.976730i	$0.568803\pi$
$522$	13.6440	−	8.35760i	0.597182	−	0.365802i
$523$	23.6188	−	10.7863i	1.03278	−	0.471654i	0.174402	−	0.984675i	$-0.444201\pi$
$523$	23.6188	−	10.7863i	1.03278	−	0.471654i	0.858376	+	0.513021i	$0.171474\pi$
$524$	−2.17131	−	7.39481i	−0.0948542	−	0.323044i
$525$	20.3032	−	5.72407i	0.886103	−	0.249819i
$526$	18.8517	+	2.71047i	0.821974	+	0.118182i
$527$	29.2768	−	18.8150i	1.27532	−	0.819596i
$528$	−2.75160	+	2.33271i	−0.119748	+	0.101518i
$529$	15.6224	+	16.8802i	0.679234	+	0.733921i
$530$			18.4927i			0.803271i
$531$	−25.2514	+	10.8789i	−1.09582	+	0.472106i
$532$	−0.557769	+	3.87937i	−0.0241823	+	0.168192i
$533$	−0.757742	−	0.346049i	−0.0328214	−	0.0149891i
$534$	15.3105	+	10.0748i	0.662548	+	0.435978i
$535$	−3.40296	−	7.45144i	−0.147123	−	0.322154i
$536$	2.02682	+	2.33908i	0.0875453	+	0.101033i
$537$	−14.4995	+	16.3726i	−0.625702	+	0.706531i
$538$	2.48809	+	0.730570i	0.107269	+	0.0314971i
$539$	17.0974	−	19.7314i	0.736437	−	0.849893i
$540$	−0.252228	+	7.78067i	−0.0108542	+	0.334827i
$541$	−9.67306	−	6.21650i	−0.415877	−	0.267268i	0.315926	−	0.948784i	$-0.397685\pi$
$541$	−9.67306	−	6.21650i	−0.415877	−	0.267268i	−0.731803	+	0.681516i	$0.761321\pi$
$542$	−1.27223	−	1.10239i	−0.0546469	−	0.0473518i
$543$	−12.8417	−	28.9428i	−0.551090	−	1.24205i
$544$	−3.65571	+	0.525612i	−0.156737	+	0.0225354i
$545$	−10.9334	+	9.47389i	−0.468337	+	0.405817i
$546$	26.4954	+	12.4477i	1.13390	+	0.532711i
$547$	−13.8188	+	4.05757i	−0.590849	+	0.173489i	−0.563471	−	0.826136i	$-0.690534\pi$
$547$	−13.8188	+	4.05757i	−0.590849	+	0.173489i	−0.0273786	+	0.999625i	$0.508716\pi$
$548$	−6.64911	+	14.5595i	−0.284036	+	0.621952i
$549$	−5.76166	+	18.1615i	−0.245902	+	0.775112i
$550$	−3.10262	−	4.82777i	−0.132296	−	0.205857i
$551$	−4.72926			−0.201473
$552$	−2.38451	−	7.95702i	−0.101492	−	0.338673i
$553$	−57.6931			−2.45336
$554$	−6.56406	−	10.2139i	−0.278880	−	0.433946i
$555$	5.59774	−	3.51260i	0.237611	−	0.149101i
$556$	−0.172725	+	0.378215i	−0.00732518	+	0.0160399i
$557$	10.8451	−	3.18441i	0.459522	−	0.134928i	−0.0437750	−	0.999041i	$-0.513938\pi$
$557$	10.8451	−	3.18441i	0.459522	−	0.134928i	0.503297	+	0.864114i	$0.332120\pi$
$558$	−7.37637	−	27.2892i	−0.312267	−	1.15524i
$559$	8.81176	−	7.63543i	0.372698	−	0.322944i
$560$	−6.55446	+	0.942389i	−0.276976	+	0.0398232i
$561$	−12.1781	+	5.40333i	−0.514158	+	0.228129i
$562$	11.3954	+	9.87418i	0.480686	+	0.416517i
$563$	−7.28347	−	4.68080i	−0.306962	−	0.197272i	0.378086	−	0.925770i	$-0.376582\pi$
$563$	−7.28347	−	4.68080i	−0.306962	−	0.197272i	−0.685048	+	0.728498i	$0.740219\pi$
$564$	−2.19378	−	16.5232i	−0.0923746	−	0.695751i
$565$	−5.89599	+	6.80433i	−0.248046	+	0.286260i
$566$	−24.1128	−	7.08017i	−1.01354	−	0.297602i
$567$	−39.0933	−	7.35669i	−1.64176	−	0.308952i
$568$	7.40202	+	8.54239i	0.310582	+	0.358431i
$569$	−4.99059	−	10.9279i	−0.209216	−	0.458120i	0.775711	−	0.631088i	$-0.217391\pi$
$569$	−4.99059	−	10.9279i	−0.209216	−	0.458120i	−0.984927	+	0.172968i	$0.944664\pi$
$570$	1.26484	−	1.92215i	0.0529781	−	0.0805100i
$571$	25.9567	+	11.8540i	1.08626	+	0.496076i	0.876364	−	0.481649i	$-0.159962\pi$
$571$	25.9567	+	11.8540i	1.08626	+	0.496076i	0.209891	+	0.977725i	$0.432689\pi$
$572$	1.13338	−	7.88285i	0.0473891	−	0.329598i
$573$	−7.38075	+	24.1677i	−0.308335	+	1.00962i
$574$			0.962878i			0.0401898i
$575$	13.0477	−	2.09439i	0.544127	−	0.0873421i
$576$	−0.490992	+	2.95955i	−0.0204580	+	0.123315i
$577$	−11.5536	+	7.42507i	−0.480984	+	0.309110i	−0.758570	−	0.651591i	$-0.774102\pi$
$577$	−11.5536	+	7.42507i	−0.480984	+	0.309110i	0.277587	+	0.960701i	$0.410465\pi$
$578$	3.32533	+	0.478111i	0.138316	+	0.0198868i
$579$	−0.192100	−	0.681374i	−0.00798339	−	0.0283169i
$580$	−2.25116	−	7.66674i	−0.0934743	−	0.318344i
$581$	14.3606	−	6.55826i	0.595778	−	0.272083i
$582$	−11.8700	−	1.83773i	−0.492027	−	0.0761762i
$583$	3.65858	+	25.4460i	0.151523	+	1.05386i
$584$	1.21288	−	4.13070i	0.0501894	−	0.170930i
$585$	−10.9715	−	13.2287i	−0.453616	−	0.546941i
$586$	13.0866	−	20.3631i	0.540601	−	0.841192i
$587$	19.5497	−	30.4200i	0.806904	−	1.25557i	−0.156544	−	0.987671i	$-0.550035\pi$
$587$	19.5497	−	30.4200i	0.806904	−	1.25557i	0.963448	−	0.267896i	$-0.0863284\pi$
$588$	0.234537	−	21.7115i	0.00967213	−	0.895369i
$589$	−2.35400	+	8.01698i	−0.0969948	+	0.330334i
$590$	1.95411	+	13.5911i	0.0804493	+	0.559537i
$591$	4.65401	−	30.0605i	0.191440	−	1.23653i
$592$	2.31659	−	1.05795i	0.0952111	−	0.0434815i
$593$	−4.24596	−	14.4604i	−0.174361	−	0.593818i	−0.999579	−	0.0290042i	$-0.990766\pi$
$593$	−4.24596	−	14.4604i	−0.174361	−	0.593818i	0.825219	−	0.564813i	$-0.191052\pi$
$594$	1.19226	+	10.7561i	0.0489188	+	0.441329i
$595$	−24.2076	−	3.48053i	−0.992415	−	0.142688i
$596$	2.64950	−	1.70273i	0.108528	−	0.0697465i
$597$	−10.0469	−	11.8511i	−0.411194	−	0.485032i
$598$	15.5875	+	9.66085i	0.637420	+	0.395062i
$599$			42.6957i			1.74450i	0.489062	+	0.872249i	$0.337339\pi$
$599$			42.6957i			1.74450i	−0.489062	+	0.872249i	$0.662661\pi$
$600$	−4.56449	−	1.39398i	−0.186344	−	0.0569091i
$601$	−4.00534	+	27.8577i	−0.163381	+	1.13634i	0.728821	+	0.684704i	$0.240069\pi$
$601$	−4.00534	+	27.8577i	−0.163381	+	1.13634i	−0.892202	+	0.451636i	$0.850840\pi$
$602$	−12.2593	−	5.59864i	−0.499652	−	0.228184i
$603$	9.21702	−	1.12256i	0.375346	−	0.0457144i
$604$	1.98336	+	4.34295i	0.0807018	+	0.176712i
$605$	−6.53645	−	7.54347i	−0.265745	−	0.306686i
$606$	−13.4593	−	11.9195i	−0.546748	−	0.484198i
$607$	20.6007	+	6.04891i	0.836156	+	0.245518i	0.671660	−	0.740860i	$-0.265582\pi$
$607$	20.6007	+	6.04891i	0.836156	+	0.245518i	0.164497	+	0.986378i	$0.447400\pi$
$608$	0.580679	−	0.670139i	0.0235496	−	0.0271777i
$609$	40.4752	−	5.37387i	1.64014	−	0.217760i
$610$	8.00467	+	5.14429i	0.324100	+	0.208286i
$611$	27.8103	+	24.0978i	1.12509	+	0.974892i
$612$	−4.81941	+	9.97685i	−0.194813	+	0.403290i
$613$	−28.8038	+	4.14136i	−1.16337	+	0.167268i	−0.696834	−	0.717232i	$-0.745409\pi$
$613$	−28.8038	+	4.14136i	−1.16337	+	0.167268i	−0.466540	+	0.884500i	$0.654500\pi$
$614$	−10.5740	+	9.16239i	−0.426730	+	0.369764i
$615$	0.240375	−	0.511648i	0.00969284	−	0.0206316i
$616$	−8.83251	+	2.59346i	−0.355872	+	0.104493i
$617$	−9.61666	+	21.0575i	−0.387152	+	0.847745i	0.611261	+	0.791429i	$0.290663\pi$
$617$	−9.61666	+	21.0575i	−0.387152	+	0.847745i	−0.998413	+	0.0563157i	$0.982065\pi$
$618$	−17.7844	−	28.3416i	−0.715394	−	1.14007i
$619$	−0.784765	−	1.22112i	−0.0315424	−	0.0490809i	0.825124	−	0.564951i	$-0.191105\pi$
$619$	−0.784765	−	1.22112i	−0.0315424	−	0.0490809i	−0.856667	+	0.515870i	$0.827469\pi$
$620$	−14.1171			−0.566956
$621$	−23.7947	−	7.40348i	−0.954849	−	0.297091i
$622$	−7.99561			−0.320595
$623$	25.2858	+	39.3455i	1.01305	+	1.57634i
$624$	−3.52033	−	5.61006i	−0.140926	−	0.224582i
$625$	−1.50800	+	3.30206i	−0.0603201	+	0.132083i
$626$	8.99677	−	2.64169i	0.359583	−	0.105583i
$627$	1.36014	−	2.89512i	0.0543187	−	0.115620i
$628$	1.71302	−	1.48434i	0.0683568	−	0.0592315i
$629$	9.31010	−	1.33859i	0.371218	−	0.0533731i
$630$	−8.64090	+	17.8879i	−0.344262	+	0.712670i
$631$	8.63569	+	7.48287i	0.343781	+	0.297888i	0.809588	−	0.586998i	$-0.199690\pi$
$631$	8.63569	+	7.48287i	0.343781	+	0.297888i	−0.465807	+	0.884886i	$0.654236\pi$
$632$	10.9808	+	7.05693i	0.436793	+	0.280710i
$633$	−21.6605	+	2.87585i	−0.860926	+	0.114305i
$634$	−13.4897	+	15.5679i	−0.535744	+	0.618281i
$635$	19.0419	+	5.59121i	0.755655	+	0.221880i
$636$	16.0054	+	14.1743i	0.634654	+	0.562048i
$637$	31.3910	+	36.2272i	1.24376	+	1.43537i
$638$	−4.61438	−	10.1041i	−0.182685	−	0.400024i
$639$	33.6609	−	4.09964i	1.33160	−	0.162179i
$640$	1.36279	+	0.622366i	0.0538690	+	0.0246012i
$641$	−3.86823	+	26.9041i	−0.152786	+	1.06265i	0.758736	+	0.651398i	$0.225817\pi$
$641$	−3.86823	+	26.9041i	−0.152786	+	1.06265i	−0.911522	+	0.411251i	$0.865092\pi$
$642$	−9.05750	−	2.76614i	−0.357471	−	0.109171i
$643$			26.1567i			1.03152i	0.856733	+	0.515760i	$0.172490\pi$
$643$			26.1567i			1.03152i	−0.856733	+	0.515760i	$0.827510\pi$
$644$	2.67304	−	21.0281i	0.105332	−	0.828623i
$645$	5.11662	+	6.03541i	0.201467	+	0.237644i
$646$	2.75505	−	1.77056i	0.108396	−	0.0696618i
$647$	−3.72851	−	0.536079i	−0.146583	−	0.0210755i	0.0686327	−	0.997642i	$-0.478136\pi$
$647$	−3.72851	−	0.536079i	−0.146583	−	0.0210755i	−0.215216	+	0.976567i	$0.569045\pi$
$648$	6.54082	+	6.18204i	0.256948	+	0.242854i
$649$	5.37771	+	18.3148i	0.211093	+	0.718918i
$650$	9.58432	−	4.37701i	0.375928	−	0.171681i
$651$	11.0369	−	71.2878i	0.432569	−	2.79399i
$652$	−1.73443	−	12.0632i	−0.0679254	−	0.472432i
$653$	2.06178	−	7.02179i	0.0806839	−	0.274784i	−0.909263	−	0.416221i	$-0.863354\pi$
$653$	2.06178	−	7.02179i	0.0806839	−	0.274784i	0.989947	+	0.141437i	$0.0451723\pi$
$654$	−0.180664	+	16.7244i	−0.00706452	+	0.653977i
$655$	−6.24248	+	9.71350i	−0.243914	+	0.379538i
$656$	0.117778	−	0.183266i	0.00459845	−	0.00715533i
$657$	−8.24486	−	9.94112i	−0.321663	−	0.387840i
$658$	11.9834	−	40.8118i	0.467163	−	1.59101i
$659$	5.49519	+	38.2199i	0.214062	+	1.48884i	0.759403	+	0.650621i	$0.225491\pi$
$659$	5.49519	+	38.2199i	0.214062	+	1.48884i	−0.545340	+	0.838215i	$0.683600\pi$
$660$	5.34080	+	0.826868i	0.207890	+	0.0321858i
$661$	44.4075	−	20.2802i	1.72725	−	0.788810i	0.733187	−	0.680027i	$-0.238032\pi$
$661$	44.4075	−	20.2802i	1.72725	−	0.788810i	0.994066	−	0.108782i	$-0.0346951\pi$
$662$	3.65863	+	12.4601i	0.142197	+	0.484277i
$663$	−6.63757	−	23.5433i	−0.257782	−	0.914348i
$664$	−3.53547	−	0.508323i	−0.137203	−	0.0197268i
$665$	4.93963	−	3.17451i	0.191551	−	0.123102i
$666$	1.25042	−	7.53717i	0.0484529	−	0.292059i
$667$	25.5748	−	0.418449i	0.990258	−	0.0162024i
$668$			8.84847i			0.342358i
$669$	−7.45919	+	24.4245i	−0.288389	+	0.944307i
$670$	0.659903	−	4.58973i	0.0254943	−	0.177317i
$671$	12.0322	+	5.49491i	0.464497	+	0.212129i
$672$	−4.20824	+	6.39519i	−0.162336	+	0.246700i
$673$	−13.5600	−	29.6923i	−0.522701	−	1.14455i	−0.968407	−	0.249376i	$-0.919775\pi$
$673$	−13.5600	−	29.6923i	−0.522701	−	1.14455i	0.445706	−	0.895179i	$-0.352953\pi$
$674$	2.35618	+	2.71918i	0.0907567	+	0.104739i
$675$	−11.1188	+	9.02065i	−0.427962	+	0.347205i
$676$	1.55614	+	0.456923i	0.0598515	+	0.0175740i
$677$	4.82277	−	5.56578i	0.185354	−	0.213910i	−0.655466	−	0.755225i	$-0.727528\pi$
$677$	4.82277	−	5.56578i	0.185354	−	0.213910i	0.840820	+	0.541315i	$0.182073\pi$
$678$	1.36996	+	10.3183i	0.0526132	+	0.396274i
$679$	−25.7856	−	16.5714i	−0.989560	−	0.635952i
$680$	4.18173	+	3.62349i	0.160362	+	0.138954i
$681$	22.0871	−	9.79991i	0.846381	−	0.375534i
$682$	−19.4251	+	2.79291i	−0.743827	+	0.106946i
$683$	−25.0432	+	21.7001i	−0.958252	+	0.830330i	−0.985565	−	0.169297i	$-0.945850\pi$
$683$	−25.0432	+	21.7001i	−0.958252	+	0.830330i	0.0273133	+	0.999627i	$0.491305\pi$
$684$	−0.694142	−	2.56800i	−0.0265412	−	0.0981901i
$685$	23.0084	−	6.75588i	0.879106	−	0.258129i
$686$	10.1645	−	22.2572i	0.388083	−	0.849783i
$687$	6.53388	−	4.10003i	0.249283	−	0.156426i
$688$	1.64851	+	2.56514i	0.0628490	+	0.0977949i
$689$	−47.1995			−1.79816
$690$	−6.66987	+	10.5065i	−0.253918	+	0.399974i
$691$	51.7368			1.96816			0.984080	−	0.177724i	$-0.0568734\pi$
$691$	51.7368			1.96816			0.984080	+	0.177724i	$0.0568734\pi$
$692$	9.50005	+	14.7824i	0.361138	+	0.561941i
$693$	−8.35096	+	26.3233i	−0.317227	+	0.999938i
$694$	7.96113	−	17.4324i	0.302200	−	0.661726i
$695$	0.597693	−	0.175499i	0.0226718	−	0.00665704i
$696$	−8.36101	−	3.92804i	−0.316923	−	0.148892i
$697$	0.608061	−	0.526888i	0.0230320	−	0.0199573i
$698$	8.75438	−	1.25869i	0.331358	−	0.0476421i
$699$	−6.08610	−	13.7169i	−0.230198	−	0.518821i
$700$	−9.20427	−	7.97554i	−0.347889	−	0.301447i
$701$	−7.67794	−	4.93431i	−0.289992	−	0.186366i	0.387554	−	0.921847i	$-0.373320\pi$
$701$	−7.67794	−	4.93431i	−0.289992	−	0.186366i	−0.677546	+	0.735481i	$0.736956\pi$
$702$	−19.8589	−	0.643771i	−0.749525	−	0.0242976i
$703$	−1.47883	+	1.70666i	−0.0557752	+	0.0643680i
$704$	1.99833	+	0.586763i	0.0753149	+	0.0221145i
$705$	−16.5560	+	18.6947i	−0.623535	+	0.704085i
$706$	−11.2603	−	12.9951i	−0.423786	−	0.489076i
$707$	−19.0587	−	41.7327i	−0.716776	−	1.56952i
$708$	13.2609	+	8.72606i	0.498373	+	0.327945i
$709$	−11.9108	−	5.43948i	−0.447320	−	0.204284i	0.179002	−	0.983849i	$-0.442713\pi$
$709$	−11.9108	−	5.43948i	−0.447320	−	0.204284i	−0.626322	+	0.779565i	$0.715440\pi$
$710$	2.40999	−	16.7618i	0.0904453	−	0.629061i
$711$	35.9631	−	15.4938i	1.34872	−	0.581065i
$712$		−	10.5816i		−	0.396562i
$713$	12.0205	−	43.5623i	0.450173	−	1.63142i
$714$	−21.5671	+	18.2838i	−0.807127	+	0.684255i
$715$	−10.0373	+	6.45058i	−0.375374	+	0.241238i
$716$	12.4982	+	1.79697i	0.467079	+	0.0671558i
$717$	38.0193	−	10.7188i	1.41986	−	0.400300i
$718$	7.36126	+	25.0701i	0.274720	+	0.935609i
$719$	−10.3331	+	4.71899i	−0.385361	+	0.175988i	−0.598669	−	0.800997i	$-0.704304\pi$
$719$	−10.3331	+	4.71899i	−0.385361	+	0.175988i	0.213308	+	0.976985i	$0.431576\pi$
$720$	3.83265	−	2.34768i	0.142835	−	0.0874929i
$721$	−12.1513	−	84.5145i	−0.452540	−	3.14748i
$722$	5.13140	−	17.4759i	0.190971	−	0.650387i
$723$	33.8786	+	0.365971i	1.25996	+	0.0136106i
$724$	−9.88349	+	15.3790i	−0.367317	+	0.571557i
$725$	7.94528	−	12.3631i	0.295080	−	0.459154i
$726$	−11.5389	−	0.124648i	−0.428249	−	0.00462612i
$727$	−0.576048	+	1.96184i	−0.0213644	+	0.0727606i	−0.969485	−	0.245150i	$-0.921163\pi$
$727$	−0.576048	+	1.96184i	−0.0213644	+	0.0727606i	0.948121	+	0.317910i	$0.102981\pi$
$728$	−2.40529	−	16.7292i	−0.0891460	−	0.620024i
$729$	26.3446	−	5.91295i	0.975725	−	0.218998i
$730$	−5.86693	+	2.67934i	−0.217145	+	0.0991667i
$731$	3.17275	+	10.8054i	0.117348	+	0.399652i
$732$	10.5878	−	2.98502i	0.391336	−	0.110329i
$733$	45.4669	+	6.53715i	1.67936	+	0.241455i	0.915033	−	0.403378i	$-0.132164\pi$
$733$	45.4669	+	6.53715i	1.67936	+	0.241455i	0.764323	+	0.644833i	$0.223073\pi$
$734$	9.16421	−	5.88948i	0.338257	−	0.217385i
$735$	−24.8129	+	21.0356i	−0.915239	+	0.775910i
$736$	−3.08089	+	3.67534i	−0.113563	+	0.135475i
$737$		−	6.44602i		−	0.237442i
$738$	−0.258587	−	0.600212i	−0.00951872	−	0.0220941i
$739$	5.99347	−	41.6855i	0.220473	−	1.53343i	−0.515781	−	0.856720i	$-0.672498\pi$
$739$	5.99347	−	41.6855i	0.220473	−	1.53343i	0.736254	−	0.676705i	$-0.236593\pi$
$740$	−3.47066	−	1.58500i	−0.127584	−	0.0582656i
$741$	4.90597	+	3.22828i	0.180225	+	0.118594i
$742$	22.6639	+	49.6271i	0.832020	+	1.82187i
$743$	23.1670	+	26.7362i	0.849915	+	0.980854i	0.999969	−	0.00782329i	$-0.00249025\pi$
$743$	23.1670	+	26.7362i	0.849915	+	0.980854i	−0.150054	+	0.988678i	$0.547945\pi$
$744$	−10.8205	+	12.2183i	−0.396698	+	0.447944i
$745$	−4.52733	−	1.32934i	−0.165868	−	0.0487033i
$746$	10.7316	−	12.3849i	0.392912	−	0.453444i
$747$	−7.19044	+	7.94473i	−0.263084	+	0.290683i
$748$	6.47094	+	4.15862i	0.236601	+	0.152054i
$749$	−18.2644	−	15.8262i	−0.667367	−	0.578277i
$750$	8.16192	+	18.3954i	0.298031	+	0.671705i
$751$	−1.69293	+	0.243406i	−0.0617758	+	0.00888202i	−0.173133	−	0.984898i	$-0.555389\pi$
$751$	−1.69293	+	0.243406i	−0.0617758	+	0.00888202i	0.111358	+	0.993780i	$0.464480\pi$
$752$	−7.27286	+	6.30197i	−0.265214	+	0.229809i
$753$	22.1124	+	10.3885i	0.805820	+	0.378578i
$754$	19.5681	−	5.74571i	0.712628	−	0.209246i
$755$	2.97143	−	6.50652i	0.108141	−	0.236796i
$756$	8.85882	+	21.1894i	0.322192	+	0.770651i
$757$	7.66632	+	11.9290i	0.278637	+	0.433568i	0.952161	−	0.305598i	$-0.0988563\pi$
$757$	7.66632	+	11.9290i	0.278637	+	0.433568i	−0.673523	+	0.739166i	$0.735220\pi$
$758$	−8.40595			−0.305318
$759$	−7.09916	+	15.7765i	−0.257683	+	0.572650i
$760$	−1.32847			−0.0481886
$761$	5.36055	+	8.34118i	0.194320	+	0.302367i	0.924717	−	0.380655i	$-0.124301\pi$
$761$	5.36055	+	8.34118i	0.194320	+	0.302367i	−0.730397	+	0.683022i	$0.760665\pi$
$762$	19.4344	−	12.1952i	0.704036	−	0.441784i
$763$	−17.7302	+	38.8238i	−0.641878	+	1.40552i
$764$	13.9984	−	4.11031i	0.506445	−	0.148706i
$765$	16.0246	−	4.33151i	0.579370	−	0.156606i
$766$	11.0351	−	9.56193i	0.398713	−	0.345487i
$767$	−34.6891	+	4.98753i	−1.25255	+	0.180089i
$768$	1.58321	−	0.702459i	0.0571291	−	0.0253478i
$769$	6.27029	+	5.43323i	0.226112	+	0.195927i	0.760548	−	0.649282i	$-0.224930\pi$
$769$	6.27029	+	5.43323i	0.226112	+	0.195927i	−0.534436	+	0.845209i	$0.679476\pi$
$770$	11.6020	+	7.45614i	0.418107	+	0.268701i
$771$	−1.82835	−	13.7708i	−0.0658464	−	0.495944i
$772$	−0.267659	+	0.308895i	−0.00963326	+	0.0111174i
$773$	−13.9220	−	4.08786i	−0.500739	−	0.147030i	0.0216027	−	0.999767i	$-0.493123\pi$
$773$	−13.9220	−	4.08786i	−0.500739	−	0.147030i	−0.522341	+	0.852737i	$0.674941\pi$
$774$	9.14542	+	0.197608i	0.328725	+	0.00710287i
$775$	−17.0030	−	19.6225i	−0.610765	−	0.704861i
$776$	2.88082	+	6.30811i	0.103415	+	0.226448i
$777$	10.7172	−	16.2868i	0.384479	−	0.584286i
$778$	−1.50935	−	0.689296i	−0.0541128	−	0.0247125i
$779$	−0.0274911	+	0.191205i	−0.000984971	+	0.00685062i
$780$	−2.89819	+	9.48990i	−0.103772	+	0.339793i
$781$		−	23.5411i		−	0.842367i
$782$	−14.7420	+	9.81856i	−0.527173	+	0.351111i
$783$	−23.7871	+	14.2197i	−0.850081	+	0.508170i
$784$	−10.5459	+	6.77742i	−0.376638	+	0.242051i
$785$	−3.36127	−	0.483278i	−0.119969	−	0.0172489i
$786$	3.62225	+	12.8481i	0.129201	+	0.458275i
$787$	0.396259	+	1.34953i	0.0141251	+	0.0481057i	0.966254	−	0.257591i	$-0.0829288\pi$
$787$	0.396259	+	1.34953i	0.0141251	+	0.0481057i	−0.952129	+	0.305697i	$0.901111\pi$
$788$	−15.9752	+	7.29561i	−0.569092	+	0.259895i
$789$	−32.5995	−	5.04709i	−1.16057	−	0.179681i
$790$	−2.78305	−	19.3565i	−0.0990164	−	0.688674i
$791$	−7.48338	+	25.4861i	−0.266078	+	0.906180i
$792$	4.80927	−	3.98866i	0.170890	−	0.141731i
$793$	−13.1299	+	20.4306i	−0.466258	+	0.725512i
$794$	0.376772	−	0.586269i	0.0133712	−	0.0208059i
$795$	0.345984	−	32.0284i	0.0122708	−	1.13593i
$796$	−2.52717	+	8.60676i	−0.0895733	+	0.305059i
$797$	3.94092	+	27.4097i	0.139595	+	0.970902i	0.932400	+	0.361428i	$0.117711\pi$
$797$	3.94092	+	27.4097i	0.139595	+	0.970902i	−0.792805	+	0.609475i	$0.791380\pi$
$798$	1.03861	−	6.70843i	0.0367663	−	0.237476i
$799$	−32.3301	+	14.7647i	−1.14376	+	0.522337i
$800$	0.776304	+	2.64385i	0.0274465	+	0.0934741i
$801$	−26.3284	−	17.7354i	−0.930270	−	0.626651i
$802$	−10.0762	−	1.44874i	−0.355802	−	0.0511566i
$803$	−7.54282	+	4.84748i	−0.266180	+	0.171064i
$804$	−3.46659	−	4.08908i	−0.122257	−	0.144211i
$805$	−26.4315	+	17.6041i	−0.931588	+	0.620462i
$806$		−	36.0315i		−	1.26916i
$807$	−4.29558	−	1.31186i	−0.151212	−	0.0461797i
$808$	−1.47722	+	10.2743i	−0.0519683	+	0.361448i
$809$	−10.2155	−	4.66526i	−0.359157	−	0.164022i	0.227661	−	0.973741i	$-0.426892\pi$
$809$	−10.2155	−	4.66526i	−0.359157	−	0.164022i	−0.586818	+	0.809719i	$0.699620\pi$
$810$	0.582417	−	13.4710i	0.0204641	−	0.473323i
$811$	−12.5767	−	27.5392i	−0.441628	−	0.967031i	−0.991297	−	0.131648i	$-0.957973\pi$
$811$	−12.5767	−	27.5392i	−0.441628	−	0.967031i	0.549668	−	0.835383i	$-0.314754\pi$
$812$	−15.4373	−	17.8156i	−0.541743	−	0.625205i
$813$	2.18281	+	1.93309i	0.0765545	+	0.0677964i
$814$	−5.08921	−	1.49433i	−0.178377	−	0.0523761i
$815$	−11.9569	+	13.7990i	−0.418832	+	0.483357i
$816$	6.34134	−	0.841937i	0.221991	−	0.0294737i
$817$	−2.27456	−	1.46177i	−0.0795769	−	0.0511409i
$818$	5.38381	+	4.66510i	0.188241	+	0.163111i
$819$	−45.6558	−	22.0545i	−1.59534	−	0.770645i
$820$	−0.323054	+	0.0464481i	−0.0112815	+	0.00162204i
$821$	0.364119	−	0.315511i	0.0127078	−	0.0110114i	−0.648484	−	0.761229i	$-0.724597\pi$
$821$	0.364119	−	0.315511i	0.0127078	−	0.0110114i	0.661192	+	0.750217i	$0.270051\pi$
$822$	11.7883	−	25.0920i	0.411165	−	0.875183i
$823$	−16.1435	+	4.74017i	−0.562728	+	0.165232i	−0.550711	−	0.834696i	$-0.685643\pi$
$823$	−16.1435	+	4.74017i	−0.562728	+	0.165232i	−0.0120171	+	0.999928i	$0.503825\pi$
$824$	−8.02490	+	17.5721i	−0.279561	+	0.612153i
$825$	5.28326	+	8.41951i	0.183940	+	0.293130i
$826$	21.9008	+	34.0783i	0.762027	+	1.18574i
$827$	−16.4983			−0.573702			−0.286851	−	0.957975i	$-0.592608\pi$
$827$	−16.4983			−0.573702			−0.286851	+	0.957975i	$0.592608\pi$
$828$	3.98098	+	13.8258i	0.138349	+	0.480479i
$829$	−54.1508			−1.88074			−0.940368	−	0.340160i	$-0.889519\pi$
$829$	−54.1508			−1.88074			−0.940368	+	0.340160i	$0.889519\pi$
$830$	2.89309	+	4.50174i	0.100421	+	0.156258i
$831$	11.1775	+	17.8127i	0.387744	+	0.617917i
$832$	−1.58848	+	3.47830i	−0.0550708	+	0.120588i
$833$	−44.4234	+	13.0439i	−1.53918	+	0.451944i
$834$	0.306227	−	0.651818i	0.0106038	−	0.0225706i
$835$	10.0187	−	8.68122i	0.346710	−	0.300426i
$836$	−1.82797	+	0.262823i	−0.0632217	+	0.00908991i
$837$	12.2650	+	47.4015i	0.423939	+	1.63843i
$838$	−22.7769	−	19.7363i	−0.786816	−	0.681780i
$839$	8.19416	+	5.26607i	0.282894	+	0.181805i	0.674391	−	0.738375i	$-0.264406\pi$
$839$	8.19416	+	5.26607i	0.282894	+	0.181805i	−0.391497	+	0.920179i	$0.628043\pi$
$840$	11.3696	−	1.50954i	0.392289	−	0.0520841i
$841$	−0.363213	+	0.419171i	−0.0125246	+	0.0144542i
$842$	1.85058	+	0.543378i	0.0637750	+	0.0187260i
$843$	−19.5515	−	17.3148i	−0.673391	−	0.596353i
$844$	8.26134	+	9.53409i	0.284367	+	0.328177i
$845$	−1.00937	−	2.21022i	−0.0347235	−	0.0760339i
$846$	3.49037	+	28.6583i	0.120002	+	0.985294i
$847$	−26.7863	−	12.2329i	−0.920387	−	0.420327i
$848$	1.75666	−	12.2178i	0.0603238	−	0.419561i
$849$	41.6298	+	12.7136i	1.42873	+	0.436331i
$850$			10.1768i			0.349060i
$851$	7.84619	−	9.36010i	0.268964	−	0.320860i
$852$	−12.6601	−	14.9335i	−0.433728	−	0.511612i
$853$	11.5277	−	7.40841i	0.394701	−	0.253659i	−0.328203	−	0.944607i	$-0.606443\pi$
$853$	11.5277	−	7.40841i	0.394701	−	0.253659i	0.722904	+	0.690948i	$0.242807\pi$
$854$	27.7860	+	3.99503i	0.950819	+	0.136707i
$855$	−2.22659	+	3.30540i	−0.0761479	+	0.113042i
$856$	1.54045	+	5.24630i	0.0526515	+	0.179315i
$857$	4.00899	−	1.83084i	0.136944	−	0.0625404i	−0.345764	−	0.938321i	$-0.612380\pi$
$857$	4.00899	−	1.83084i	0.136944	−	0.0625404i	0.482709	+	0.875781i	$0.339653\pi$
$858$	−2.11044	+	13.6315i	−0.0720494	+	0.465372i
$859$	2.73096	+	18.9942i	0.0931791	+	0.648075i	0.981868	+	0.189565i	$0.0607076\pi$
$859$	2.73096	+	18.9942i	0.0931791	+	0.648075i	−0.888689	+	0.458510i	$0.848383\pi$
$860$	1.28702	−	4.38318i	0.0438869	−	0.149465i
$861$	0.0180147	−	1.66766i	0.000613939	−	0.0568336i
$862$	9.58695	−	14.9176i	0.326533	−	0.508095i
$863$	0.532218	−	0.828147i	0.0181169	−	0.0281904i	−0.832077	−	0.554660i	$-0.812848\pi$
$863$	0.532218	−	0.828147i	0.0181169	−	0.0281904i	0.850194	+	0.526470i	$0.176485\pi$
$864$	0.905744	−	5.11660i	0.0308141	−	0.174070i
$865$	7.41682	−	25.2594i	0.252179	−	0.858844i
$866$	1.84419	+	12.8266i	0.0626682	+	0.435867i
$867$	−5.75036	−	0.890278i	−0.195293	−	0.0302354i
$868$	−37.8847	+	17.3014i	−1.28589	+	0.587247i
$869$	−7.65896	−	26.0840i	−0.259812	−	0.884840i
$870$	3.75546	+	13.3205i	0.127322	+	0.451608i
$871$	11.7145	+	1.68429i	0.396931	+	0.0570701i
$872$	8.12349	−	5.22065i	0.275096	−	0.176794i
$873$	20.5239	+	3.40493i	0.694627	+	0.115239i
$874$	1.13117	−	4.09936i	0.0382625	−	0.138663i
$875$			51.3556i			1.73614i
$876$	−2.17793	+	7.13147i	−0.0735856	+	0.240950i
$877$	−7.53147	+	52.3825i	−0.254320	+	1.76883i	0.317311	+	0.948322i	$0.397220\pi$
$877$	−7.53147	+	52.3825i	−0.254320	+	1.76883i	−0.571631	+	0.820511i	$0.693689\pi$
$878$	32.5644	+	14.8717i	1.09899	+	0.501894i
$879$	−23.0463	+	35.0230i	−0.777331	+	1.18130i
$880$	−1.29620	−	2.83828i	−0.0436948	−	0.0956783i
$881$	3.01122	+	3.47513i	0.101450	+	0.117080i	0.804204	−	0.594353i	$-0.202592\pi$
$881$	3.01122	+	3.47513i	0.101450	+	0.117080i	−0.702754	+	0.711433i	$0.748046\pi$
$882$	−0.812412	+	37.5989i	−0.0273553	+	1.26602i
$883$	6.84681	+	2.01040i	0.230413	+	0.0676555i	0.394901	−	0.918724i	$-0.370779\pi$
$883$	6.84681	+	2.01040i	0.230413	+	0.0676555i	−0.164488	+	0.986379i	$0.552597\pi$
$884$	−9.24836	+	10.6732i	−0.311056	+	0.358978i
$885$	−3.13014	−	23.5757i	−0.105218	−	0.792488i
$886$	−25.0284	−	16.0848i	−0.840846	−	0.540379i
$887$	−13.2873	−	11.5135i	−0.446142	−	0.386584i	0.402613	−	0.915370i	$-0.368102\pi$
$887$	−13.2873	−	11.5135i	−0.446142	−	0.386584i	−0.848755	+	0.528786i	$0.822647\pi$
$888$	−4.03201	+	1.78897i	−0.135305	+	0.0600340i
$889$	57.9534	−	8.33244i	1.94369	−	0.279461i
$890$	−11.9810	+	10.3816i	−0.401604	+	0.347992i
$891$	−1.86369	−	18.6514i	−0.0624359	−	0.624844i
$892$	14.1472	−	4.15399i	0.473683	−	0.139086i
$893$	3.54484	−	7.76212i	0.118624	−	0.259749i
$894$	−4.62065	+	2.89947i	−0.154538	+	0.0969728i
$895$	−10.2273	−	15.9140i	−0.341862	−	0.531947i
$896$	4.41994			0.147660
$897$	−26.8160	−	17.0237i	−0.895361	−	0.568406i
$898$	−35.5346			−1.18580
$899$	−27.1704	−	42.2780i	−0.906184	−	1.41005i
$900$	7.87938	+	2.49971i	0.262646	+	0.0833236i
$901$	18.9380	−	41.4684i	0.630915	−	1.38151i
$902$	−0.435333	+	0.127825i	−0.0144950	+	0.00425612i
$903$	21.1278	+	9.92592i	0.703088	+	0.330314i
$904$	4.54174	−	3.93544i	0.151056	−	0.130891i
$905$	27.1095	−	3.89776i	0.901151	−	0.129566i
$906$	−3.35383	−	7.55888i	−0.111423	−	0.251127i
$907$	−12.0689	−	10.4577i	−0.400740	−	0.347243i	0.431055	−	0.902325i	$-0.358141\pi$
$907$	−12.0689	−	10.4577i	−0.400740	−	0.347243i	−0.831796	+	0.555082i	$0.812687\pi$
$908$	−11.7362	−	7.54241i	−0.389480	−	0.250304i
$909$	23.0879	+	20.8959i	0.765776	+	0.693072i
$910$	−16.5817	+	19.1363i	−0.549679	+	0.634363i
$911$	−28.1729	−	8.27230i	−0.933409	−	0.274074i	−0.220546	−	0.975377i	$-0.570784\pi$
$911$	−28.1729	−	8.27230i	−0.933409	−	0.274074i	−0.712863	+	0.701303i	$0.752602\pi$
$912$	−1.01824	+	1.14978i	−0.0337175	+	0.0380731i
$913$	4.87152	+	5.62203i	0.161224	+	0.186062i
$914$	−13.0779	−	28.6367i	−0.432580	−	0.947217i
$915$	−13.7674	−	9.05941i	−0.455138	−	0.299495i
$916$	−4.05107	−	1.85006i	−0.133851	−	0.0611278i
$917$	−4.84788	+	33.7178i	−0.160091	+	1.11346i
$918$	8.53363	−	17.1892i	0.281652	−	0.567329i
$919$		−	11.5173i		−	0.379922i	−0.981792	−	0.189961i	$-0.939164\pi$
$919$		−	11.5173i		−	0.379922i	0.981792	−	0.189961i	$-0.0608361\pi$
$920$	7.18405	−	0.117544i	0.236851	−	0.00387531i
$921$	18.4850	−	15.6710i	0.609101	−	0.516376i
$922$	10.6357	−	6.83518i	0.350270	−	0.225105i
$923$	42.7818	+	6.15110i	1.40818	+	0.202466i
$924$	15.3460	−	4.32649i	0.504846	−	0.142331i
$925$	−1.97704	−	6.73316i	−0.0650045	−	0.221385i
$926$	4.91899	−	2.24643i	0.161648	−	0.0738222i
$927$	30.2715	+	49.4190i	0.994245	+	1.62313i
$928$	0.759025	+	5.27913i	0.0249162	+	0.173296i
$929$	16.7706	−	57.1156i	0.550227	−	1.87390i	0.0683518	−	0.997661i	$-0.478226\pi$
$929$	16.7706	−	57.1156i	0.550227	−	1.87390i	0.481875	−	0.876240i	$-0.339956\pi$
$930$	24.4501	+	0.264120i	0.801750	+	0.00866083i
$931$	6.00968	−	9.35125i	0.196959	−	0.306475i
$932$	−4.68411	+	7.28862i	−0.153433	+	0.238747i
$933$	13.8480	+	0.149592i	0.453363	+	0.00489741i
$934$	3.69058	−	12.5690i	0.120760	−	0.411269i
$935$	−1.64004	−	11.4067i	−0.0536350	−	0.373039i
$936$	5.99207	+	9.78221i	0.195857	+	0.319741i
$937$	−7.04122	+	3.21562i	−0.230027	+	0.105050i	−0.527094	−	0.849807i	$-0.676719\pi$
$937$	−7.04122	+	3.21562i	−0.230027	+	0.105050i	0.297068	+	0.954856i	$0.403991\pi$
$938$	−3.85408	−	13.1258i	−0.125840	−	0.428572i
$939$	−15.6314	+	4.40695i	−0.510111	+	0.143815i
$940$	14.2708	+	2.05183i	0.465461	+	0.0669232i
$941$	3.36880	−	2.16500i	0.109820	−	0.0705769i	−0.484578	−	0.874748i	$-0.661027\pi$
$941$	3.36880	−	2.16500i	0.109820	−	0.0705769i	0.594398	+	0.804171i	$0.297390\pi$
$942$	−2.99463	+	2.53875i	−0.0975703	+	0.0827169i
$943$	0.131748	−	1.03642i	0.00429029	−	0.0337506i
$944$		−	9.16505i		−	0.298297i
$945$	15.3003	−	30.8192i	0.497718	−	1.00255i
$946$	0.903773	−	6.28588i	0.0293842	−	0.204372i
$947$	−11.0994	−	5.06894i	−0.360683	−	0.164718i	0.226827	−	0.973935i	$-0.427165\pi$
$947$	−11.0994	−	5.06894i	−0.360683	−	0.164718i	−0.587511	+	0.809217i	$0.699892\pi$
$948$	−18.8862	−	12.4277i	−0.613394	−	0.403633i
$949$	−6.83856	−	14.9744i	−0.221989	−	0.486088i
$950$	−1.60004	−	1.84654i	−0.0519121	−	0.0599098i
$951$	23.6547	−	26.7105i	0.767056	−	0.866146i
$952$	15.6629	+	4.59905i	0.507639	+	0.149056i
$953$	−1.21111	+	1.39770i	−0.0392318	+	0.0452760i	−0.775026	−	0.631929i	$-0.782263\pi$
$953$	−1.21111	+	1.39770i	−0.0392318	+	0.0452760i	0.735795	+	0.677205i	$0.236809\pi$
$954$	−27.4553	−	24.8486i	−0.888898	−	0.804504i
$955$	−18.3877	−	11.8171i	−0.595012	−	0.382391i
$956$	−17.2357	−	14.9349i	−0.557444	−	0.483028i
$957$	7.80283	+	17.5861i	0.252230	+	0.568478i
$958$	20.4058	−	2.93391i	0.659282	−	0.0947905i
$959$	53.4658	−	46.3284i	1.72650	−	1.49602i
$960$	−2.34864	−	1.10340i	−0.0758021	−	0.0356122i
$961$	−55.4490	+	16.2813i	−1.78868	+	0.525203i
$962$	4.04544	−	8.85828i	0.130430	−	0.285602i
$963$	15.6354	+	4.96027i	0.503843	+	0.159843i
$964$	−10.5755	−	16.4557i	−0.340613	−	0.530004i
$965$	0.612345			0.0197121
$966$	−5.02298	+	36.3696i	−0.161612	+	1.17017i
$967$	−1.73918			−0.0559283			−0.0279642	−	0.999609i	$-0.508902\pi$
$967$	−1.73918			−0.0559283			−0.0279642	+	0.999609i	$0.508902\pi$
$968$	3.60196	+	5.60476i	0.115771	+	0.180144i
$969$	−4.80473	+	3.01498i	−0.154350	+	0.0968550i
$970$	4.31598	−	9.45067i	0.138578	−	0.303443i
$971$	−7.51465	+	2.20650i	−0.241157	+	0.0708100i	−0.400077	−	0.916481i	$-0.631017\pi$
$971$	−7.51465	+	2.20650i	−0.241157	+	0.0708100i	0.158921	+	0.987291i	$0.449199\pi$
$972$	−11.2127	−	10.8294i	−0.359648	−	0.347352i
$973$	1.38889	−	1.20348i	0.0445258	−	0.0385818i
$974$	−35.1380	+	5.05208i	−1.12589	+	0.161879i
$975$	−16.6814	+	7.40145i	−0.534234	+	0.237036i
$976$	−4.79989	−	4.15913i	−0.153641	−	0.133130i
$977$	21.1684	+	13.6041i	0.677237	+	0.435234i	0.833528	−	0.552477i	$-0.186317\pi$
$977$	21.1684	+	13.6041i	0.677237	+	0.435234i	−0.156291	+	0.987711i	$0.549954\pi$
$978$	2.77825	+	20.9253i	0.0888386	+	0.669118i
$979$	−14.4320	+	16.6554i	−0.461248	+	0.532309i
$980$	18.0202	+	5.29122i	0.575635	+	0.169022i
$981$	0.625802	−	28.9625i	0.0199803	−	0.924701i
$982$	3.24780	+	3.74816i	0.103641	+	0.119608i
$983$	16.2116	+	35.4985i	0.517071	+	1.13223i	0.970537	+	0.240954i	$0.0774602\pi$
$983$	16.2116	+	35.4985i	0.517071	+	1.13223i	−0.453466	+	0.891274i	$0.649812\pi$
$984$	−0.207414	+	0.315204i	−0.00661212	+	0.0100483i
$985$	23.9336	+	10.9301i	0.762589	+	0.348263i
$986$	−2.80331	+	19.4974i	−0.0892755	+	0.620924i
$987$	−21.5182	+	70.4598i	−0.684933	+	2.24276i
$988$		−	3.39069i		−	0.107872i
$989$	12.4297	+	7.70368i	0.395240	+	0.244963i
$990$	−9.23452	−	1.53202i	−0.293492	−	0.0486907i
$991$	10.6501	−	6.84440i	0.338311	−	0.217419i	−0.360443	−	0.932781i	$-0.617374\pi$
$991$	10.6501	−	6.84440i	0.338311	−	0.217419i	0.698754	+	0.715362i	$0.253738\pi$
$992$	9.32693	+	1.34101i	0.296130	+	0.0425771i
$993$	−6.10344	−	21.6488i	−0.193687	−	0.687003i
$994$	−14.0752	−	47.9358i	−0.446439	−	1.52043i
$995$	12.2244	−	5.58269i	0.387539	−	0.176983i
$996$	6.11374	+	0.946536i	0.193721	+	0.0299922i
$997$	−3.92973	−	27.3318i	−0.124456	−	0.865608i	−0.952412	−	0.304815i	$-0.901405\pi$
$997$	−3.92973	−	27.3318i	−0.124456	−	0.865608i	0.827956	−	0.560793i	$-0.189504\pi$
$998$	−6.55473	+	22.3234i	−0.207486	+	0.706633i
$999$	−2.30669	+	13.0306i	−0.0729803	+	0.412270i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.f.a.11.6	yes	80
3.2	odd	2	inner	138.2.f.a.11.3	✓	80
23.21	odd	22	inner	138.2.f.a.113.3	yes	80
69.44	even	22	inner	138.2.f.a.113.6	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.f.a.11.3	✓	80	3.2	odd	2	inner
138.2.f.a.11.6	yes	80	1.1	even	1	trivial
138.2.f.a.113.3	yes	80	23.21	odd	22	inner
138.2.f.a.113.6	yes	80	69.44	even	22	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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	138.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.540641 + 0.841254i) q^{2} +(-0.920624 - 1.46712i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(1.43749 - 0.422085i) q^{5} +(0.736496 - 1.56766i) q^{6} +(3.34037 - 2.89445i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(-1.30490 + 2.70134i) q^{9} +O(q^{10})\)	\(q+(0.540641 + 0.841254i) q^{2} +(-0.920624 - 1.46712i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(1.43749 - 0.422085i) q^{5} +(0.736496 - 1.56766i) q^{6} +(3.34037 - 2.89445i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(-1.30490 + 2.70134i) q^{9} +(1.13225 + 0.981098i) q^{10} +(1.75207 + 1.12599i) q^{11} +(1.71698 - 0.227963i) q^{12} +(-2.50409 + 2.88987i) q^{13} +(4.24090 + 1.24524i) q^{14} +(-1.94264 - 1.72040i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-1.53425 - 3.35954i) q^{17} +(-2.97799 + 0.362698i) q^{18} +(0.806590 + 0.368357i) q^{19} +(-0.213213 + 1.48293i) q^{20} +(-7.32174 - 2.23604i) q^{21} +2.08269i q^{22} +(-4.39445 - 1.92063i) q^{23} +(1.12005 + 1.32117i) q^{24} +(-2.31804 + 1.48972i) q^{25} +(-3.78493 - 0.544191i) q^{26} +(5.16452 - 0.572458i) q^{27} +(1.24524 + 4.24090i) q^{28} +(-4.85145 + 2.21558i) q^{29} +(0.397019 - 2.56437i) q^{30} +(1.34101 + 9.32693i) q^{31} +(0.281733 - 0.959493i) q^{32} +(0.0389656 - 3.60712i) q^{33} +(1.99675 - 3.10700i) q^{34} +(3.58005 - 5.57066i) q^{35} +(-1.91515 - 2.30916i) q^{36} +(-0.717497 + 2.44357i) q^{37} +(0.126194 + 0.877696i) q^{38} +(6.54513 + 1.01332i) q^{39} +(-1.36279 + 0.622366i) q^{40} +(0.0613750 + 0.209024i) q^{41} +(-2.07735 - 7.36833i) q^{42} +(-3.01815 - 0.433944i) q^{43} +(-1.75207 + 1.12599i) q^{44} +(-0.735594 + 4.43393i) q^{45} +(-0.760086 - 4.73522i) q^{46} -9.62337i q^{47} +(-0.505898 + 1.65652i) q^{48} +(1.78404 - 12.4083i) q^{49} +(-2.50646 - 1.14466i) q^{50} +(-3.51640 + 5.34381i) q^{51} +(-1.58848 - 3.47830i) q^{52} +(8.08324 + 9.32856i) q^{53} +(3.27373 + 4.03518i) q^{54} +(2.99385 + 0.879075i) q^{55} +(-2.89445 + 3.34037i) q^{56} +(-0.202140 - 1.52249i) q^{57} +(-4.48676 - 2.88346i) q^{58} +(6.92648 + 6.00183i) q^{59} +(2.37193 - 1.05241i) q^{60} +(6.28652 - 0.903865i) q^{61} +(-7.12131 + 6.17065i) q^{62} +(3.46001 + 12.8004i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-2.37983 + 5.21111i) q^{65} +(3.05557 - 1.91738i) q^{66} +(-1.67331 - 2.60371i) q^{67} +3.69330 q^{68} +(1.22784 + 8.21538i) q^{69} +6.62186 q^{70} +(-6.11097 - 9.50886i) q^{71} +(0.907182 - 2.85955i) q^{72} +(-1.78840 + 3.91604i) q^{73} +(-2.44357 + 0.717497i) q^{74} +(4.31964 + 2.02939i) q^{75} +(-0.670139 + 0.580679i) q^{76} +(9.11169 - 1.31006i) q^{77} +(2.68610 + 6.05395i) q^{78} +(-9.86473 - 8.54784i) q^{79} +(-1.26035 - 0.809976i) q^{80} +(-5.59445 - 7.04998i) q^{81} +(-0.142660 + 0.164639i) q^{82} +(3.42714 + 1.00630i) q^{83} +(5.07553 - 5.73120i) q^{84} +(-3.62349 - 4.18173i) q^{85} +(-1.26668 - 2.77364i) q^{86} +(7.71689 + 5.07796i) q^{87} +(-1.89449 - 0.865182i) q^{88} +(-1.50592 + 10.4739i) q^{89} +(-4.12775 + 1.77834i) q^{90} +16.9012i q^{91} +(3.57258 - 3.19948i) q^{92} +(12.4492 - 10.5540i) q^{93} +(8.09570 - 5.20279i) q^{94} +(1.31494 + 0.189061i) q^{95} +(-1.66706 + 0.469995i) q^{96} +(-1.95376 - 6.65389i) q^{97} +(11.4031 - 5.20760i) q^{98} +(-5.32797 + 3.26363i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6}+O(q^{10}) \) 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6	\( 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6} - 4 q^{12} + 8 q^{13} - 22 q^{15} - 8 q^{16} - 28 q^{18} - 66 q^{21} - 4 q^{24} - 48 q^{25} - 38 q^{27} - 44 q^{30} - 16 q^{31} - 22 q^{33} - 44 q^{37} - 24 q^{39} - 44 q^{43} - 16 q^{46} + 4 q^{48} - 76 q^{49} - 8 q^{52} - 6 q^{54} + 64 q^{55} + 66 q^{57} + 36 q^{58} + 22 q^{60} + 88 q^{61} + 110 q^{63} + 8 q^{64} + 88 q^{66} + 44 q^{67} + 82 q^{69} + 112 q^{70} + 28 q^{72} + 52 q^{73} + 136 q^{75} + 82 q^{78} + 88 q^{79} + 36 q^{81} + 44 q^{82} + 22 q^{84} + 20 q^{85} - 10 q^{87} + 8 q^{93} - 56 q^{94} + 4 q^{96} - 132 q^{97} - 66 q^{99}+O(q^{100}) \) 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6 - 4 * q^12 + 8 * q^13 - 22 * q^15 - 8 * q^16 - 28 * q^18 - 66 * q^21 - 4 * q^24 - 48 * q^25 - 38 * q^27 - 44 * q^30 - 16 * q^31 - 22 * q^33 - 44 * q^37 - 24 * q^39 - 44 * q^43 - 16 * q^46 + 4 * q^48 - 76 * q^49 - 8 * q^52 - 6 * q^54 + 64 * q^55 + 66 * q^57 + 36 * q^58 + 22 * q^60 + 88 * q^61 + 110 * q^63 + 8 * q^64 + 88 * q^66 + 44 * q^67 + 82 * q^69 + 112 * q^70 + 28 * q^72 + 52 * q^73 + 136 * q^75 + 82 * q^78 + 88 * q^79 + 36 * q^81 + 44 * q^82 + 22 * q^84 + 20 * q^85 - 10 * q^87 + 8 * q^93 - 56 * q^94 + 4 * q^96 - 132 * q^97 - 66 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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