LMFDB - Embedded newform 348.2.t.a.35.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [348,2,Mod(35,348)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(348, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 7, 3]))

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

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

chi := DirichletCharacter("348.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 348 = 2^{2} \cdot 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	348.t (of order $14$, degree $6$, 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:	$2.77879399034$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$56$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			35.19
Character	$\chi$	$=$	348.35
Dual form			348.2.t.a.179.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.801196 - 1.16537i) q^{2} +(0.301364 - 1.70563i) q^{3} +(-0.716169 + 1.86738i) q^{4} +(0.227131 + 0.181131i) q^{5} +(-2.22914 + 1.01535i) q^{6} +(2.72634 + 0.622270i) q^{7} +(2.74998 - 0.661535i) q^{8} +(-2.81836 - 1.02803i) q^{9} +O(q^{10})$	\(q+(-0.801196 - 1.16537i) q^{2} +(0.301364 - 1.70563i) q^{3} +(-0.716169 + 1.86738i) q^{4} +(0.227131 + 0.181131i) q^{5} +(-2.22914 + 1.01535i) q^{6} +(2.72634 + 0.622270i) q^{7} +(2.74998 - 0.661535i) q^{8} +(-2.81836 - 1.02803i) q^{9} +(0.0291078 - 0.409812i) q^{10} +(-2.44077 - 5.06830i) q^{11} +(2.96923 + 1.78428i) q^{12} +(4.69132 - 2.25922i) q^{13} +(-1.45916 - 3.67576i) q^{14} +(0.377391 - 0.332815i) q^{15} +(-2.97420 - 2.67472i) q^{16} -4.28762 q^{17} +(1.06002 + 4.10808i) q^{18} +(-0.385765 - 1.69015i) q^{19} +(-0.500903 + 0.294418i) q^{20} +(1.88299 - 4.46261i) q^{21} +(-3.95091 + 6.90510i) q^{22} +(2.27067 + 2.84733i) q^{23} +(-0.299590 - 4.88981i) q^{24} +(-1.09382 - 4.79236i) q^{25} +(-6.39149 - 3.65704i) q^{26} +(-2.60280 + 4.49727i) q^{27} +(-3.11454 + 4.64546i) q^{28} +(5.37233 - 0.371628i) q^{29} +(-0.690216 - 0.173150i) q^{30} +(-5.36303 + 6.72503i) q^{31} +(-0.734114 + 5.60902i) q^{32} +(-9.38022 + 2.63564i) q^{33} +(3.43522 + 4.99666i) q^{34} +(0.506524 + 0.635161i) q^{35} +(3.93815 - 4.52670i) q^{36} +(-0.0232466 + 0.0482721i) q^{37} +(-1.66057 + 1.80370i) q^{38} +(-2.43960 - 8.68251i) q^{39} +(0.744428 + 0.347850i) q^{40} +7.63789 q^{41} +(-6.70923 + 1.38105i) q^{42} +(-0.385030 - 0.482812i) q^{43} +(11.2124 - 0.928070i) q^{44} +(-0.453927 - 0.743989i) q^{45} +(1.49894 - 4.92744i) q^{46} +(-3.68384 - 7.64958i) q^{47} +(-5.45840 + 4.26683i) q^{48} +(0.738951 + 0.355860i) q^{49} +(-4.70850 + 5.11433i) q^{50} +(-1.29213 + 7.31310i) q^{51} +(0.859039 + 10.3784i) q^{52} +(4.19455 + 3.34505i) q^{53} +(7.32633 - 0.569975i) q^{54} +(0.363652 - 1.59326i) q^{55} +(7.90904 - 0.0923426i) q^{56} +(-2.99903 + 0.148623i) q^{57} +(-4.73737 - 5.96300i) q^{58} +6.71215 q^{59} +(0.351215 + 0.943084i) q^{60} +(-7.16798 - 1.63604i) q^{61} +(12.1340 + 0.861843i) q^{62} +(-7.04410 - 4.55655i) q^{63} +(7.12474 - 3.63841i) q^{64} +(1.47476 + 0.336603i) q^{65} +(10.5869 + 8.81975i) q^{66} +(-0.705540 + 1.46507i) q^{67} +(3.07066 - 8.00660i) q^{68} +(5.54080 - 3.01485i) q^{69} +(0.334372 - 1.09918i) q^{70} +(-3.98478 + 1.91897i) q^{71} +(-8.43050 - 0.962624i) q^{72} +(10.1816 - 8.11959i) q^{73} +(0.0748800 - 0.0115845i) q^{74} +(-8.50364 + 0.421416i) q^{75} +(3.43242 + 0.490063i) q^{76} +(-3.50052 - 15.3368i) q^{77} +(-8.16373 + 9.79943i) q^{78} +(8.78958 + 4.23284i) q^{79} +(-0.191059 - 1.14623i) q^{80} +(6.88630 + 5.79473i) q^{81} +(-6.11945 - 8.90096i) q^{82} +(2.41305 + 10.5723i) q^{83} +(6.98484 + 6.71223i) q^{84} +(-0.973849 - 0.776618i) q^{85} +(-0.254170 + 0.835529i) q^{86} +(0.985167 - 9.27521i) q^{87} +(-10.0649 - 12.3231i) q^{88} +(-2.74726 + 3.44495i) q^{89} +(-0.503336 + 1.12507i) q^{90} +(14.1960 - 3.24014i) q^{91} +(-6.94323 + 2.20103i) q^{92} +(9.85420 + 11.1740i) q^{93} +(-5.96310 + 10.4219i) q^{94} +(0.218518 - 0.453758i) q^{95} +(9.34568 + 2.94248i) q^{96} +(-0.166069 + 0.0379042i) q^{97} +(-0.177336 - 1.14626i) q^{98} +(1.66857 + 16.7935i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9}+O(q^{10}) $ 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9	$ 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9} - 14 q^{10} - 20 q^{13} - 26 q^{16} - 56 q^{18} - 14 q^{21} - 40 q^{22} + 3 q^{24} + 40 q^{25} - 36 q^{28} - 6 q^{30} - 22 q^{33} - 8 q^{34} + 9 q^{36} - 28 q^{37} - 14 q^{40} - 74 q^{42} - 22 q^{45} + 14 q^{48} + 4 q^{49} - 4 q^{52} - 31 q^{54} - 12 q^{57} - 106 q^{58} - 42 q^{60} - 28 q^{61} - 94 q^{64} - 7 q^{66} - 14 q^{69} + 70 q^{72} - 28 q^{73} - 84 q^{76} - 9 q^{78} - 50 q^{81} - 46 q^{82} - 35 q^{84} - 168 q^{85} - 60 q^{88} + 119 q^{90} + 122 q^{93} + 36 q^{94} + 2 q^{96} - 28 q^{97}+O(q^{100}) $ 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9 - 14 * q^10 - 20 * q^13 - 26 * q^16 - 56 * q^18 - 14 * q^21 - 40 * q^22 + 3 * q^24 + 40 * q^25 - 36 * q^28 - 6 * q^30 - 22 * q^33 - 8 * q^34 + 9 * q^36 - 28 * q^37 - 14 * q^40 - 74 * q^42 - 22 * q^45 + 14 * q^48 + 4 * q^49 - 4 * q^52 - 31 * q^54 - 12 * q^57 - 106 * q^58 - 42 * q^60 - 28 * q^61 - 94 * q^64 - 7 * q^66 - 14 * q^69 + 70 * q^72 - 28 * q^73 - 84 * q^76 - 9 * q^78 - 50 * q^81 - 46 * q^82 - 35 * q^84 - 168 * q^85 - 60 * q^88 + 119 * q^90 + 122 * q^93 + 36 * q^94 + 2 * q^96 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/348\mathbb{Z}\right)^\times$.

$n$	$175$	$205$	$233$
$\chi(n)$	$-1$	$e\left(\frac{3}{14}\right)$	$-1$

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 $

$2$	−0.801196	−	1.16537i	−0.566531	−	0.824040i
$2$	−0.801196	−	1.16537i	−0.566531	−	0.824040i
$3$	0.301364	−	1.70563i	0.173993	−	0.984747i
$3$	0.301364	−	1.70563i	0.173993	−	0.984747i
$4$	−0.716169	+	1.86738i	−0.358085	+	0.933689i
$5$	0.227131	+	0.181131i	0.101576	+	0.0810040i	0.672961	−	0.739678i	$-0.265022\pi$
$5$	0.227131	+	0.181131i	0.101576	+	0.0810040i	−0.571385	+	0.820682i	$0.693594\pi$
$6$	−2.22914	+	1.01535i	−0.910043	+	0.414513i
$7$	2.72634	+	0.622270i	1.03046	+	0.235196i	0.704139	−	0.710062i	$-0.251333\pi$
$7$	2.72634	+	0.622270i	1.03046	+	0.235196i	0.326323	+	0.945258i	$0.394190\pi$
$8$	2.74998	−	0.661535i	0.972264	−	0.233888i
$9$	−2.81836	−	1.02803i	−0.939453	−	0.342678i
$10$	0.0291078	−	0.409812i	0.00920470	−	0.129594i
$11$	−2.44077	−	5.06830i	−0.735919	−	1.52815i	−0.845383	−	0.534161i	$-0.820628\pi$
$11$	−2.44077	−	5.06830i	−0.735919	−	1.52815i	0.109464	−	0.993991i	$-0.465086\pi$
$12$	2.96923	+	1.78428i	0.857143	+	0.515078i
$13$	4.69132	−	2.25922i	1.30114	−	0.626595i	0.350402	−	0.936599i	$-0.386045\pi$
$13$	4.69132	−	2.25922i	1.30114	−	0.626595i	0.950735	+	0.310005i	$0.100331\pi$
$14$	−1.45916	−	3.67576i	−0.389977	−	0.982387i
$15$	0.377391	−	0.332815i	0.0974419	−	0.0859324i
$16$	−2.97420	−	2.67472i	−0.743551	−	0.668680i
$17$	−4.28762			−1.03990			−0.519950	−	0.854197i	$-0.674049\pi$
$17$	−4.28762			−1.03990			−0.519950	+	0.854197i	$0.674049\pi$
$18$	1.06002	+	4.10808i	0.249849	+	0.968285i
$19$	−0.385765	−	1.69015i	−0.0885007	−	0.387747i	0.911206	−	0.411950i	$-0.135152\pi$
$19$	−0.385765	−	1.69015i	−0.0885007	−	0.387747i	−0.999707	+	0.0242034i	$0.992295\pi$
$20$	−0.500903	+	0.294418i	−0.112005	+	0.0658340i
$21$	1.88299	−	4.46261i	0.410901	−	0.973821i
$22$	−3.95091	+	6.90510i	−0.842337	+	1.47217i
$23$	2.27067	+	2.84733i	0.473468	+	0.593710i	0.960016	−	0.279944i	$-0.0903158\pi$
$23$	2.27067	+	2.84733i	0.473468	+	0.593710i	−0.486549	+	0.873654i	$0.661744\pi$
$24$	−0.299590	−	4.88981i	−0.0611535	−	0.998128i
$25$	−1.09382	−	4.79236i	−0.218765	−	0.958472i
$26$	−6.39149	−	3.65704i	−1.25347	−	0.717204i
$27$	−2.60280	+	4.49727i	−0.500909	+	0.865500i
$28$	−3.11454	+	4.64546i	−0.588592	+	0.877910i
$29$	5.37233	−	0.371628i	0.997616	−	0.0690096i
$29$	5.37233	−	0.371628i	0.997616	−	0.0690096i
$30$	−0.690216	−	0.173150i	−0.126016	−	0.0316127i
$31$	−5.36303	+	6.72503i	−0.963229	+	1.20785i	0.0149076	+	0.999889i	$0.495255\pi$
$31$	−5.36303	+	6.72503i	−0.963229	+	1.20785i	−0.978137	+	0.207962i	$0.933317\pi$
$32$	−0.734114	+	5.60902i	−0.129774	+	0.991544i
$33$	−9.38022	+	2.63564i	−1.63289	+	0.458807i
$34$	3.43522	+	4.99666i	0.589136	+	0.856919i
$35$	0.506524	+	0.635161i	0.0856182	+	0.107362i
$36$	3.93815	−	4.52670i	0.656358	−	0.754449i
$37$	−0.0232466	+	0.0482721i	−0.00382172	+	0.00793589i	−0.902871	−	0.429912i	$-0.858545\pi$
$37$	−0.0232466	+	0.0482721i	−0.00382172	+	0.00793589i	0.899049	+	0.437847i	$0.144259\pi$
$38$	−1.66057	+	1.80370i	−0.269381	+	0.292599i
$39$	−2.43960	−	8.68251i	−0.390649	−	1.39031i
$40$	0.744428	+	0.347850i	0.117704	+	0.0549999i
$41$	7.63789			1.19284			0.596419	−	0.802673i	$-0.296590\pi$
$41$	7.63789			1.19284			0.596419	+	0.802673i	$0.296590\pi$
$42$	−6.70923	+	1.38105i	−1.03526	+	0.213101i
$43$	−0.385030	−	0.482812i	−0.0587165	−	0.0736281i	0.751606	−	0.659612i	$-0.229280\pi$
$43$	−0.385030	−	0.482812i	−0.0587165	−	0.0736281i	−0.810323	+	0.585984i	$0.800708\pi$
$44$	11.2124	−	0.928070i	1.69034	−	0.139912i
$45$	−0.453927	−	0.743989i	−0.0676675	−	0.110907i
$46$	1.49894	−	4.92744i	0.221007	−	0.726512i
$47$	−3.68384	−	7.64958i	−0.537344	−	1.11581i	−0.976124	−	0.217212i	$-0.930304\pi$
$47$	−3.68384	−	7.64958i	−0.537344	−	1.11581i	0.438781	−	0.898594i	$-0.355411\pi$
$48$	−5.45840	+	4.26683i	−0.787853	+	0.615864i
$49$	0.738951	+	0.355860i	0.105564	+	0.0508371i
$50$	−4.70850	+	5.11433i	−0.665882	+	0.723275i
$51$	−1.29213	+	7.31310i	−0.180935	+	1.02404i
$52$	0.859039	+	10.3784i	0.119127	+	1.43923i
$53$	4.19455	+	3.34505i	0.576166	+	0.459477i	0.867703	−	0.497082i	$-0.165595\pi$
$53$	4.19455	+	3.34505i	0.576166	+	0.459477i	−0.291537	+	0.956560i	$0.594167\pi$
$54$	7.32633	−	0.569975i	0.996987	−	0.0775638i
$55$	0.363652	−	1.59326i	0.0490348	−	0.214836i
$56$	7.90904	−	0.0923426i	1.05689	−	0.0123398i
$57$	−2.99903	+	0.148623i	−0.397231	+	0.0196856i
$58$	−4.73737	−	5.96300i	−0.622047	−	0.782980i
$59$	6.71215			0.873848			0.436924	−	0.899498i	$-0.356068\pi$
$59$	6.71215			0.873848			0.436924	+	0.899498i	$0.356068\pi$
$60$	0.351215	+	0.943084i	0.0453417	+	0.121752i
$61$	−7.16798	−	1.63604i	−0.917766	−	0.209474i	−0.262552	−	0.964918i	$-0.584564\pi$
$61$	−7.16798	−	1.63604i	−0.917766	−	0.209474i	−0.655214	+	0.755444i	$0.727421\pi$
$62$	12.1340	+	0.861843i	1.54102	+	0.109454i
$63$	−7.04410	−	4.55655i	−0.887474	−	0.574072i
$64$	7.12474	−	3.63841i	0.890593	−	0.454801i
$65$	1.47476	+	0.336603i	0.182921	+	0.0417505i
$66$	10.5869	+	8.81975i	1.30316	+	1.08564i
$67$	−0.705540	+	1.46507i	−0.0861955	+	0.178987i	−0.939611	−	0.342245i	$-0.888813\pi$
$67$	−0.705540	+	1.46507i	−0.0861955	+	0.178987i	0.853415	+	0.521231i	$0.174527\pi$
$68$	3.07066	−	8.00660i	0.372372	−	0.970943i
$69$	5.54080	−	3.01485i	0.667034	−	0.362945i
$70$	0.334372	−	1.09918i	0.0399651	−	0.131377i
$71$	−3.98478	+	1.91897i	−0.472907	+	0.227740i	−0.655128	−	0.755518i	$-0.727385\pi$
$71$	−3.98478	+	1.91897i	−0.472907	+	0.227740i	0.182222	+	0.983257i	$0.441671\pi$
$72$	−8.43050	−	0.962624i	−0.993544	−	0.113446i
$73$	10.1816	−	8.11959i	1.19167	−	0.950327i	0.192154	−	0.981365i	$-0.438453\pi$
$73$	10.1816	−	8.11959i	1.19167	−	0.950327i	0.999518	+	0.0310381i	$0.00988134\pi$
$74$	0.0748800	−	0.0115845i	0.00870462	−	0.00134668i
$75$	−8.50364	+	0.421416i	−0.981916	+	0.0486610i
$76$	3.43242	+	0.490063i	0.393726	+	0.0562141i
$77$	−3.50052	−	15.3368i	−0.398921	−	1.74779i
$78$	−8.16373	+	9.79943i	−0.924360	+	1.10957i
$79$	8.78958	+	4.23284i	0.988905	+	0.476232i	0.857159	−	0.515052i	$-0.172227\pi$
$79$	8.78958	+	4.23284i	0.988905	+	0.476232i	0.131746	+	0.991283i	$0.457942\pi$
$80$	−0.191059	−	1.14623i	−0.0213611	−	0.128152i
$81$	6.88630	+	5.79473i	0.765144	+	0.643859i
$82$	−6.11945	−	8.90096i	−0.675780	−	0.982947i
$83$	2.41305	+	10.5723i	0.264867	+	1.16046i	0.915899	+	0.401408i	$0.131479\pi$
$83$	2.41305	+	10.5723i	0.264867	+	1.16046i	−0.651032	+	0.759050i	$0.725664\pi$
$84$	6.98484	+	6.71223i	0.762109	+	0.732365i
$85$	−0.973849	−	0.776618i	−0.105629	−	0.0842361i
$86$	−0.254170	+	0.835529i	−0.0274078	+	0.0900974i
$87$	0.985167	−	9.27521i	0.105621	−	0.994406i
$88$	−10.0649	−	12.3231i	−1.07292	−	1.31364i
$89$	−2.74726	+	3.44495i	−0.291209	+	0.365164i	−0.905818	−	0.423668i	$-0.860742\pi$
$89$	−2.74726	+	3.44495i	−0.291209	+	0.365164i	0.614609	+	0.788832i	$0.289314\pi$
$90$	−0.503336	+	1.12507i	−0.0530563	+	0.118593i
$91$	14.1960	−	3.24014i	1.48814	−	0.339659i
$92$	−6.94323	+	2.20103i	−0.723882	+	0.229473i
$93$	9.85420	+	11.1740i	1.02183	+	1.15869i
$94$	−5.96310	+	10.4219i	−0.615047	+	1.07493i
$95$	0.218518	−	0.453758i	0.0224195	−	0.0465546i
$96$	9.34568	+	2.94248i	0.953840	+	0.300316i
$97$	−0.166069	+	0.0379042i	−0.0168618	+	0.00384859i	−0.230944	−	0.972967i	$-0.574181\pi$
$97$	−0.166069	+	0.0379042i	−0.0168618	+	0.00384859i	0.214082	+	0.976816i	$0.431324\pi$
$98$	−0.177336	−	1.14626i	−0.0179137	−	0.115790i
$99$	1.66857	+	16.7935i	0.167698	+	1.68781i
$100$	9.73251	+	1.38956i	0.973251	+	0.138956i
$101$	3.38493	+	4.24456i	0.336813	+	0.422350i	0.921178	−	0.389141i	$-0.127228\pi$
$101$	3.38493	+	4.24456i	0.336813	+	0.422350i	−0.584365	+	0.811491i	$0.698657\pi$
$102$	9.55771	−	4.35341i	0.946354	−	0.431052i
$103$	4.99966	+	10.3819i	0.492631	+	1.02296i	0.988025	+	0.154291i	$0.0493094\pi$
$103$	4.99966	+	10.3819i	0.492631	+	1.02296i	−0.495394	+	0.868668i	$0.664976\pi$
$104$	11.4065	−	9.31627i	1.11850	−	0.913535i
$105$	1.23600	−	0.672528i	0.120621	−	0.0656320i
$106$	0.537551	−	7.56824i	0.0522116	−	0.735093i
$107$	17.4998	+	8.42746i	1.69177	+	0.814713i	0.995269	+	0.0971569i	$0.0309749\pi$
$107$	17.4998	+	8.42746i	1.69177	+	0.814713i	0.696500	+	0.717556i	$0.254739\pi$
$108$	−6.53406	−	8.08122i	−0.628740	−	0.777615i
$109$	−1.53997	+	6.74703i	−0.147502	+	0.646248i	0.846072	+	0.533068i	$0.178961\pi$
$109$	−1.53997	+	6.74703i	−0.147502	+	0.646248i	−0.993574	+	0.113180i	$0.963896\pi$
$110$	−2.14810	+	0.852728i	−0.204813	+	0.0813044i
$111$	0.0753288	+	0.0541977i	0.00714989	+	0.00514422i
$112$	−6.44430	−	9.14296i	−0.608929	−	0.863929i
$113$	−3.43811	+	15.0633i	−0.323430	+	1.41704i	0.507975	+	0.861372i	$0.330394\pi$
$113$	−3.43811	+	15.0633i	−0.323430	+	1.41704i	−0.831405	+	0.555667i	$0.812463\pi$
$114$	2.57601	+	3.37590i	0.241265	+	0.316182i
$115$			1.05800i			0.0986594i
$116$	−3.15353	+	10.2983i	−0.292798	+	0.956174i
$117$	−15.5444	+	1.54446i	−1.43708	+	0.142786i
$118$	−5.37775	−	7.82214i	−0.495062	−	0.720086i
$119$	−11.6895	−	2.66806i	−1.07158	−	0.244580i
$120$	0.817648	−	1.16489i	0.0746407	−	0.106339i
$121$	−12.8720	+	16.1410i	−1.17018	+	1.46736i
$122$	3.83636	+	9.66414i	0.347328	+	0.874950i
$123$	2.30179	−	13.0274i	0.207545	−	1.17464i
$124$	−8.71734	−	14.8311i	−0.782840	−	1.33187i
$125$	1.24984	−	2.59532i	0.111789	−	0.232133i
$126$	0.333643	+	11.8597i	0.0297233	+	1.05654i
$127$	15.0978	−	7.27069i	1.33971	−	0.645170i	0.379692	−	0.925113i	$-0.376030\pi$
$127$	15.0978	−	7.27069i	1.33971	−	0.645170i	0.960017	+	0.279943i	$0.0903156\pi$
$128$	−9.94841	−	5.38787i	−0.879323	−	0.476225i
$129$	−0.939534	+	0.511217i	−0.0827213	+	0.0450101i
$130$	−0.789301	−	1.98832i	−0.0692263	−	0.174387i
$131$	−1.66568	+	1.32833i	−0.145531	+	0.116057i	−0.693549	−	0.720409i	$-0.743954\pi$
$131$	−1.66568	+	1.32833i	−0.145531	+	0.116057i	0.548018	+	0.836466i	$0.315382\pi$
$132$	1.79608	−	19.4040i	0.156329	−	1.68890i
$133$		−	4.84798i		−	0.420373i
$134$	2.27262	−	0.351593i	0.196325	−	0.0303730i
$135$	−1.40577	+	0.550021i	−0.120989	+	0.0473383i
$136$	−11.7908	+	2.83641i	−1.01106	+	0.243220i
$137$	−12.7582	−	6.14404i	−1.09001	−	0.524921i	−0.199505	−	0.979897i	$-0.563934\pi$
$137$	−12.7582	−	6.14404i	−1.09001	−	0.524921i	−0.890504	+	0.454976i	$0.849648\pi$
$138$	−7.95268	−	4.04159i	−0.676977	−	0.344043i
$139$	3.94646	−	3.14719i	0.334734	−	0.266942i	−0.441669	−	0.897178i	$-0.645613\pi$
$139$	3.94646	−	3.14719i	0.334734	−	0.266942i	0.776403	+	0.630236i	$0.217042\pi$
$140$	−1.54884	+	0.490989i	−0.130901	+	0.0414961i
$141$	−14.1575	+	3.97797i	−1.19228	+	0.335006i
$142$	5.42890	+	3.10627i	0.455583	+	0.260672i
$143$	−22.9008	−	18.2628i	−1.91506	−	1.52721i
$144$	5.63267	+	10.5959i	0.469389	+	0.882991i
$145$	1.28753	+	0.888684i	0.106924	+	0.0738012i
$146$	−17.6198	−	5.35999i	−1.45823	−	0.443596i
$147$	0.829659	−	1.15313i	0.0684291	−	0.0951089i
$148$	−0.0734938	−	0.0779813i	−0.00604115	−	0.00641002i
$149$	2.27324	−	0.518852i	0.186231	−	0.0425060i	−0.128388	−	0.991724i	$-0.540980\pi$
$149$	2.27324	−	0.518852i	0.186231	−	0.0425060i	0.314619	+	0.949218i	$0.398123\pi$
$150$	7.30419	+	9.57224i	0.596384	+	0.781570i
$151$	−3.41895	+	2.72652i	−0.278231	+	0.221881i	−0.752656	−	0.658414i	$-0.771227\pi$
$151$	−3.41895	+	2.72652i	−0.278231	+	0.221881i	0.474425	+	0.880296i	$0.342656\pi$
$152$	−2.17894	−	4.39267i	−0.176735	−	0.356293i
$153$	12.0840	+	4.40781i	0.976937	+	0.356350i
$154$	−15.0684	+	16.3671i	−1.21424	+	1.31890i
$155$	−2.43622	+	0.556051i	−0.195682	+	0.0446631i
$156$	17.9607	+	1.66249i	1.43801	+	0.133106i
$157$			5.71216i			0.455880i	0.973675	+	0.227940i	$0.0731990\pi$
$157$			5.71216i			0.455880i	−0.973675	+	0.227940i	$0.926801\pi$
$158$	−2.10936	−	13.6344i	−0.167812	−	1.08470i
$159$	6.96950	−	6.14629i	0.552718	−	0.487432i
$160$	−1.18270	+	1.14101i	−0.0935010	+	0.0902047i
$161$	4.41882	+	9.17578i	0.348252	+	0.723153i
$162$	1.23573	−	12.6678i	0.0970878	−	0.995276i
$163$	−9.08769	+	4.37640i	−0.711803	+	0.342786i	−0.754498	−	0.656302i	$-0.772120\pi$
$163$	−9.08769	+	4.37640i	−0.711803	+	0.342786i	0.0426955	+	0.999088i	$0.486405\pi$
$164$	−5.47003	+	14.2628i	−0.427137	+	1.11374i
$165$	−2.60793	−	1.10041i	−0.203027	−	0.0856668i
$166$	10.3873	−	11.2826i	0.806209	−	0.875697i
$167$	−0.937402	+	4.10703i	−0.0725384	+	0.317811i	−0.998160	−	0.0606396i	$-0.980686\pi$
$167$	−0.937402	+	4.10703i	−0.0725384	+	0.317811i	0.925621	+	0.378451i	$0.123543\pi$
$168$	2.22600	−	13.5177i	0.171740	−	1.04292i
$169$	8.79902	−	11.0336i	0.676848	−	0.848740i
$170$	−0.124803	+	1.75712i	−0.00957196	+	0.134765i
$171$	−0.650303	+	5.16003i	−0.0497299	+	0.394597i
$172$	1.17734	−	0.373221i	0.0897713	−	0.0284578i
$173$		−	24.1140i		−	1.83335i	−0.399631	−	0.916676i	$-0.630862\pi$
$173$		−	24.1140i		−	1.83335i	0.399631	−	0.916676i	$-0.369138\pi$
$174$	−11.5983	+	6.28318i	−0.879269	+	0.476326i
$175$		−	13.7463i		−	1.03912i
$176$	−6.29695	+	21.6025i	−0.474651	+	1.62835i
$177$	2.02280	−	11.4485i	0.152043	−	0.860519i
$178$	6.21573	+	0.441486i	0.465889	+	0.0330908i
$179$	9.08167	−	11.3881i	0.678796	−	0.851183i	−0.316447	−	0.948610i	$-0.602490\pi$
$179$	9.08167	−	11.3881i	0.678796	−	0.851183i	0.995243	+	0.0974272i	$0.0310613\pi$
$180$	1.71440	−	0.314832i	0.127784	−	0.0234662i
$181$	−2.27274	+	9.95752i	−0.168931	+	0.740137i	0.817495	+	0.575935i	$0.195362\pi$
$181$	−2.27274	+	9.95752i	−0.168931	+	0.740137i	−0.986427	+	0.164202i	$0.947495\pi$
$182$	−15.1497	−	13.9476i	−1.12297	−	1.03386i
$183$	−4.95066	+	11.7329i	−0.365964	+	0.867320i
$184$	8.12791	+	6.32797i	0.599197	+	0.466504i
$185$	−0.0140236	+	0.00675340i	−0.00103103	+	0.000496520i
$186$	5.12674	−	20.4364i	0.375911	−	1.49847i
$187$	10.4651	+	21.7309i	0.765282	+	1.58912i
$188$	16.9229	−	1.40073i	1.23423	−	0.102159i
$189$	−9.89464	+	10.6415i	−0.719729	+	0.774053i
$190$	−0.703872	+	0.108895i	−0.0510642	+	0.00790006i
$191$			4.60547i			0.333240i	0.986021	+	0.166620i	$0.0532853\pi$
$191$			4.60547i			0.333240i	−0.986021	+	0.166620i	$0.946715\pi$
$192$	−4.05864	−	13.2487i	−0.292907	−	0.956141i
$193$	−9.52013	+	2.17291i	−0.685274	+	0.156409i	−0.550963	−	0.834530i	$-0.685739\pi$
$193$	−9.52013	+	2.17291i	−0.685274	+	0.156409i	−0.134311	+	0.990939i	$0.542882\pi$
$194$	0.177226	+	0.163163i	0.0127241	+	0.0117144i
$195$	1.01856	−	2.41395i	0.0729406	−	0.172866i
$196$	−1.19374	+	1.12504i	−0.0852671	+	0.0803603i
$197$	−3.69639	+	2.94777i	−0.263357	+	0.210020i	−0.746262	−	0.665653i	$-0.768153\pi$
$197$	−3.69639	+	2.94777i	−0.263357	+	0.210020i	0.482905	+	0.875673i	$0.339582\pi$
$198$	18.2338	−	15.3994i	1.29582	−	1.09439i
$199$	−11.2171	+	2.56023i	−0.795160	+	0.181490i	−0.600757	−	0.799432i	$-0.705134\pi$
$199$	−11.2171	+	2.56023i	−0.795160	+	0.181490i	−0.194403	+	0.980922i	$0.562277\pi$
$200$	−6.17830	−	12.4553i	−0.436872	−	0.880721i
$201$	2.28624	+	1.64491i	0.161259	+	0.116023i
$202$	2.23449	−	7.34542i	0.157218	−	0.516822i
$203$	14.8781	+	2.32985i	1.04424	+	0.163524i
$204$	−12.7309	−	7.65032i	−0.891343	−	0.535630i
$205$	1.73480	+	1.38346i	0.121164	+	0.0966247i
$206$	8.09304	−	14.1444i	0.563869	−	0.985487i
$207$	−3.47242	−	10.3591i	−0.241350	−	0.720010i
$208$	−19.9957	−	5.82858i	−1.38645	−	0.404139i
$209$	−7.62463	+	6.08044i	−0.527406	+	0.420593i
$210$	−1.77402	−	0.901567i	−0.122419	−	0.0622140i
$211$	−5.98198	−	2.88077i	−0.411816	−	0.198320i	0.216493	−	0.976284i	$-0.430538\pi$
$211$	−5.98198	−	2.88077i	−0.411816	−	0.198320i	−0.628309	+	0.777964i	$0.716253\pi$
$212$	−9.25048	+	5.43720i	−0.635325	+	0.373428i
$213$	2.07219	+	7.37488i	0.141984	+	0.505319i
$214$	−4.19967	−	27.1458i	−0.287084	−	1.85565i
$215$		−	0.179402i		−	0.0122351i
$216$	−4.18253	+	14.0892i	−0.284585	+	0.958651i
$217$	−18.8063	+	14.9975i	−1.27665	+	1.01810i
$218$	9.09659	−	3.61107i	0.616099	−	0.244572i
$219$	−10.7807	−	19.8131i	−0.728489	−	1.33885i
$220$	2.71479	+	1.82012i	0.183031	+	0.122713i
$221$	−20.1146	+	9.68667i	−1.35305	+	0.651596i
$222$	0.00280718	−	0.131209i	0.000188406	−	0.00880616i
$223$	−0.0566980	+	0.117735i	−0.00379678	+	0.00788409i	−0.902859	−	0.429938i	$-0.858536\pi$
$223$	−0.0566980	+	0.117735i	−0.00379678	+	0.00788409i	0.899062	+	0.437822i	$0.144250\pi$
$224$	−5.49177	+	14.8353i	−0.366934	+	0.991225i
$225$	−1.84391	+	14.6311i	−0.122927	+	0.975405i
$226$	20.3089	−	8.06202i	1.35093	−	0.536278i
$227$	−7.69206	+	9.64554i	−0.510540	+	0.640197i	−0.968570	−	0.248740i	$-0.919984\pi$
$227$	−7.69206	+	9.64554i	−0.510540	+	0.640197i	0.458030	+	0.888937i	$0.348555\pi$
$228$	1.87028	−	5.70676i	0.123862	−	0.377939i
$229$	19.6728	+	4.49020i	1.30002	+	0.296721i	0.815855	−	0.578257i	$-0.196267\pi$
$229$	19.6728	+	4.49020i	1.30002	+	0.296721i	0.484164	+	0.874978i	$0.339124\pi$
$230$	1.23297	−	0.847669i	0.0812993	−	0.0558936i
$231$	−27.2138	+	1.34864i	−1.79054	+	0.0887339i
$232$	14.5279	−	4.57595i	0.953805	−	0.300426i
$233$		−	10.3827i		−	0.680196i	−0.940390	−	0.340098i	$-0.889540\pi$
$233$		−	10.3827i		−	0.680196i	0.940390	−	0.340098i	$-0.110460\pi$
$234$	14.2540	+	16.8775i	0.931810	+	1.10332i
$235$	0.548859	−	2.40471i	0.0358036	−	0.156866i
$236$	−4.80704	+	12.5341i	−0.312912	+	0.815902i
$237$	9.86853	−	13.7162i	0.641030	−	0.890960i
$238$	6.25633	+	15.7602i	0.405538	+	1.02158i
$239$	3.11810	−	13.6613i	0.201693	−	0.883676i	−0.768212	−	0.640195i	$-0.778853\pi$
$239$	3.11810	−	13.6613i	0.201693	−	0.883676i	0.969906	−	0.243481i	$-0.0782894\pi$
$240$	−2.01262	−	0.0195561i	−0.129914	−	0.00126234i
$241$	10.1826	+	4.90369i	0.655920	+	0.315874i	0.732077	−	0.681221i	$-0.238551\pi$
$241$	10.1826	+	4.90369i	0.655920	+	0.315874i	−0.0761576	+	0.997096i	$0.524265\pi$
$242$	29.1231	+	2.06854i	1.87211	+	0.132971i
$243$	11.9590	−	9.99916i	0.767168	−	0.641446i
$244$	8.18860	−	12.2136i	0.524222	−	0.781899i
$245$	0.103381	+	0.214673i	0.00660478	+	0.0137150i
$246$	−17.0260	+	7.75510i	−1.08553	+	0.494447i
$247$	−5.62817	−	7.05750i	−0.358112	−	0.449058i
$248$	−10.2994	+	22.0415i	−0.654011	+	1.39964i
$249$	18.7596	−	0.929673i	1.18884	−	0.0589156i
$250$	−4.02588	+	0.622836i	−0.254619	+	0.0393916i
$251$	6.11811	−	1.39642i	0.386172	−	0.0881412i	−0.0250273	−	0.999687i	$-0.507967\pi$
$251$	6.11811	−	1.39642i	0.386172	−	0.0881412i	0.411199	+	0.911546i	$0.365110\pi$
$252$	13.5536	−	9.89074i	0.853795	−	0.623058i
$253$	8.88897	−	18.4581i	0.558845	−	1.16045i
$254$	−20.5693	−	11.7692i	−1.29063	−	0.738465i
$255$	−1.61811	+	1.42698i	−0.101330	+	0.0893611i
$256$	1.69176	+	15.9103i	0.105735	+	0.994394i
$257$	−12.6654	+	2.89080i	−0.790047	+	0.180323i	−0.598460	−	0.801152i	$-0.704221\pi$
$257$	−12.6654	+	2.89080i	−0.790047	+	0.180323i	−0.191587	+	0.981476i	$0.561363\pi$
$258$	1.34851	+	0.685319i	0.0839544	+	0.0426661i
$259$	−0.0934167	+	0.117141i	−0.00580463	+	0.00727877i
$260$	−1.68474	+	2.51286i	−0.104483	+	0.155841i
$261$	−15.5232	−	4.47555i	−0.960861	−	0.277029i
$262$	2.88253	+	0.876873i	0.178083	+	0.0541734i
$263$	9.61927	+	7.67111i	0.593150	+	0.473021i	0.873465	−	0.486887i	$-0.161868\pi$
$263$	9.61927	+	7.67111i	0.593150	+	0.473021i	−0.280315	+	0.959908i	$0.590439\pi$
$264$	−24.0518	+	13.4533i	−1.48029	+	0.827993i
$265$	0.346821	+	1.51952i	0.0213051	+	0.0933436i
$266$	−5.64968	+	3.88418i	−0.346404	+	0.238154i
$267$	5.04789	+	5.72399i	0.308926	+	0.350303i
$268$	−2.23055	−	2.36675i	−0.136253	−	0.144572i
$269$	17.9062	+	8.62319i	1.09176	+	0.525765i	0.891059	−	0.453887i	$-0.149963\pi$
$269$	17.9062	+	8.62319i	1.09176	+	0.525765i	0.200704	+	0.979652i	$0.435677\pi$
$270$	1.76727	+	1.19756i	0.107553	+	0.0728814i
$271$	3.57449	+	15.6609i	0.217135	+	0.951330i	0.959583	+	0.281426i	$0.0908074\pi$
$271$	3.57449	+	15.6609i	0.217135	+	0.951330i	−0.742448	+	0.669904i	$0.766335\pi$
$272$	12.7522	+	11.4682i	0.773218	+	0.695360i
$273$	−1.24832	−	25.1896i	−0.0755521	−	1.52454i
$274$	3.06177	+	19.7906i	0.184968	+	1.19560i
$275$	−21.6194	+	17.2409i	−1.30370	+	1.03966i
$276$	1.66171	+	12.5059i	0.100023	+	0.752767i
$277$	−2.42652	+	1.16855i	−0.145795	+	0.0702113i	−0.505359	−	0.862909i	$-0.668640\pi$
$277$	−2.42652	+	1.16855i	−0.145795	+	0.0702113i	0.359564	+	0.933121i	$0.382926\pi$
$278$	−6.82953	−	2.07756i	−0.409608	−	0.124604i
$279$	22.0285	−	13.4402i	1.31881	−	0.804642i
$280$	1.81311	+	1.41159i	0.108354	+	0.0843589i
$281$	−7.12552	+	14.7963i	−0.425073	+	0.882672i	0.572936	+	0.819600i	$0.305804\pi$
$281$	−7.12552	+	14.7963i	−0.425073	+	0.882672i	−0.998009	+	0.0630726i	$0.979910\pi$
$282$	15.9788	+	13.3116i	0.951522	+	0.792696i
$283$	−25.2535	−	5.76394i	−1.50116	−	0.342631i	−0.608573	−	0.793498i	$-0.708258\pi$
$283$	−25.2535	−	5.76394i	−1.50116	−	0.342631i	−0.892591	+	0.450867i	$0.851115\pi$
$284$	−0.729664	−	8.81541i	−0.0432976	−	0.523098i
$285$	−0.708091	−	0.509459i	−0.0419437	−	0.0301777i
$286$	−2.93484	+	41.3200i	−0.173541	+	2.44330i
$287$	20.8235	+	4.75283i	1.22917	+	0.280551i
$288$	7.83525	−	15.0535i	0.461697	−	0.887038i
$289$	1.38366			0.0813919
$290$	0.00407911	−	2.21246i	0.000239533	−	0.129920i
$291$	0.0146033	+	0.294676i	0.000856061	+	0.0172742i
$292$	7.87057	+	24.8280i	0.460590	+	1.45295i
$293$	−0.366891	+	1.60745i	−0.0214340	+	0.0939084i	−0.984514	−	0.175309i	$-0.943908\pi$
$293$	−0.366891	+	1.60745i	−0.0214340	+	0.0939084i	0.963080	+	0.269217i	$0.0867649\pi$
$294$	−2.00855	−	0.0429724i	−0.117141	−	0.00250620i
$295$	1.52454	+	1.21578i	0.0887619	+	0.0707852i
$296$	−0.0319940	+	0.148126i	−0.00185961	+	0.00860963i
$297$	29.1464	+	2.21499i	1.69124	+	0.128527i
$298$	−2.42596	−	2.23346i	−0.140532	−	0.129381i
$299$	17.0852	+	8.22780i	0.988062	+	0.475826i
$300$	5.30310	−	16.1813i	0.306175	−	0.934229i
$301$	−0.749284	−	1.55590i	−0.0431880	−	0.0896808i
$302$	5.91666	+	1.79986i	0.340466	+	0.103570i
$303$	8.25976	−	4.49428i	0.474511	−	0.258190i
$304$	−3.37333	+	6.05866i	−0.193474	+	0.347488i
$305$	−1.33173	−	1.66994i	−0.0762546	−	0.0956203i
$306$	−4.54496	−	17.6139i	−0.259818	−	1.00692i
$307$	3.71065			0.211778			0.105889	−	0.994378i	$-0.466231\pi$
$307$	3.71065			0.211778			0.105889	+	0.994378i	$0.466231\pi$
$308$	31.1465	+	4.44693i	1.77474	+	0.253387i
$309$	19.2144	−	5.39885i	1.09307	−	0.307130i
$310$	2.59989	+	2.39359i	0.147664	+	0.135947i
$311$	−7.75590	+	16.1053i	−0.439797	+	0.913247i	0.556787	+	0.830655i	$0.312034\pi$
$311$	−7.75590	+	16.1053i	−0.439797	+	0.913247i	−0.996583	+	0.0825918i	$0.973680\pi$
$312$	−12.4526	−	22.2628i	−0.704991	−	1.26038i
$313$	1.57908	+	1.98010i	0.0892547	+	0.111922i	0.824454	−	0.565930i	$-0.191483\pi$
$313$	1.57908	+	1.98010i	0.0892547	+	0.111922i	−0.735199	+	0.677852i	$0.762911\pi$
$314$	6.65677	−	4.57656i	0.375663	−	0.258270i
$315$	−0.774600	−	2.31083i	−0.0436438	−	0.130201i
$316$	−14.1991	+	13.3820i	−0.798764	+	0.752799i
$317$	−1.19091	+	1.49335i	−0.0668881	+	0.0838751i	−0.814150	−	0.580655i	$-0.802797\pi$
$317$	−1.19091	+	1.49335i	−0.0668881	+	0.0838751i	0.747262	+	0.664530i	$0.231368\pi$
$318$	−12.7466	−	3.19766i	−0.714796	−	0.179316i
$319$	−14.9961	−	26.3215i	−0.839621	−	1.47372i
$320$	2.27727	+	0.464115i	0.127303	+	0.0259448i
$321$	19.6480	−	27.3085i	1.09664	−	1.52421i
$322$	7.15283	−	12.5012i	0.398611	−	0.696662i
$323$	1.65401	+	7.24671i	0.0920318	+	0.403218i
$324$	−15.7527	+	8.70931i	−0.875151	+	0.483851i
$325$	−15.9585	−	20.0113i	−0.885217	−	1.11003i
$326$	12.3811	+	7.08416i	0.685728	+	0.392355i
$327$	11.0439	+	4.65993i	0.610727	+	0.257695i
$328$	21.0040	−	5.05273i	1.15975	−	0.278990i
$329$	−5.28332	−	23.1477i	−0.291279	−	1.27618i
$330$	0.807080	+	3.92084i	0.0444283	+	0.215835i
$331$	15.8514			0.871269			0.435635	−	0.900124i	$-0.356524\pi$
$331$	15.8514			0.871269			0.435635	+	0.900124i	$0.356524\pi$
$332$	−21.4706	−	3.06546i	−1.17835	−	0.168239i
$333$	0.115143	−	0.112150i	0.00630978	−	0.00614578i
$334$	5.53724	−	2.19812i	0.302985	−	0.120276i
$335$	−0.425619	+	0.204967i	−0.0232540	+	0.0111985i
$336$	−17.5366	+	8.23625i	−0.956700	+	0.449324i
$337$	−14.0166	−	29.1058i	−0.763534	−	1.58550i	−0.809898	−	0.586570i	$-0.800478\pi$
$337$	−14.0166	−	29.1058i	−0.763534	−	1.58550i	0.0463641	−	0.998925i	$-0.485237\pi$
$338$	−19.9080	−	1.41401i	−1.08285	−	0.0769119i
$339$	24.6564	+	10.4037i	1.33915	+	0.565051i
$340$	2.14768	−	1.26235i	0.116474	−	0.0684607i
$341$	47.1744	+	10.7673i	2.55464	+	0.583079i
$342$	6.53435	−	3.37635i	0.353337	−	0.182572i
$343$	−13.5113	−	10.7749i	−0.729542	−	0.581791i
$344$	−1.37822	−	1.07301i	−0.0743086	−	0.0578529i
$345$	1.80457	+	0.318845i	0.0971546	+	0.0171660i
$346$	−28.1017	+	19.3200i	−1.51076	+	1.03865i
$347$	−27.8089			−1.49286			−0.746429	−	0.665465i	$-0.768233\pi$
$347$	−27.8089			−1.49286			−0.746429	+	0.665465i	$0.768233\pi$
$348$	16.6148	+	8.48230i	0.890645	+	0.454699i
$349$	6.25044			0.334578			0.167289	−	0.985908i	$-0.446499\pi$
$349$	6.25044			0.334578			0.167289	+	0.985908i	$0.446499\pi$
$350$	−16.0195	+	11.0135i	−0.856277	+	0.588694i
$351$	−2.05023	+	26.9784i	−0.109433	+	1.44000i
$352$	30.2200	−	9.96959i	1.61073	−	0.531381i
$353$	−26.2348	−	20.9216i	−1.39634	−	1.11354i	−0.978785	−	0.204891i	$-0.934316\pi$
$353$	−26.2348	−	20.9216i	−1.39634	−	1.11354i	−0.417554	−	0.908652i	$-0.637112\pi$
$354$	−14.9623	+	6.81515i	−0.795240	+	0.362221i
$355$	−1.25265	−	0.285909i	−0.0664838	−	0.0151745i
$356$	−4.46553	−	7.59734i	−0.236672	−	0.402658i
$357$	−8.07353	+	19.1340i	−0.427296	+	1.01268i
$358$	−20.5475	−	1.45943i	−1.08597	−	0.0771333i
$359$	−10.9577	−	22.7539i	−0.578324	−	1.20090i	−0.960879	−	0.276970i	$-0.910670\pi$
$359$	−10.9577	−	22.7539i	−0.578324	−	1.20090i	0.382554	−	0.923933i	$-0.375044\pi$
$360$	−1.74046	−	1.74566i	−0.0917305	−	0.0920045i
$361$	14.4106	−	6.93979i	0.758454	−	0.365252i
$362$	13.4251	−	5.32935i	0.705608	−	0.280104i
$363$	23.6514	+	26.8192i	1.24137	+	1.40764i
$364$	−4.11616	+	28.8298i	−0.215746	+	1.51109i
$365$	3.78327			0.198025
$366$	17.6396	−	3.63100i	0.922037	−	0.189795i
$367$	1.58827	+	6.95867i	0.0829070	+	0.363239i	0.999315	−	0.0370059i	$-0.0117820\pi$
$367$	1.58827	+	6.95867i	0.0829070	+	0.363239i	−0.916408	+	0.400245i	$0.868925\pi$
$368$	0.862374	−	14.5420i	0.0449543	−	0.758052i
$369$	−21.5263	−	7.85201i	−1.12062	−	0.408759i
$370$	0.0191058	+	0.0109318i	0.000993265	+	0.000568320i
$371$	9.35428	+	11.7299i	0.485650	+	0.608986i
$372$	−27.9234	+	10.3990i	−1.44776	+	0.539164i
$373$	3.18505	+	13.9546i	0.164916	+	0.722543i	0.987978	+	0.154593i	$0.0494065\pi$
$373$	3.18505	+	13.9546i	0.164916	+	0.722543i	−0.823062	+	0.567951i	$0.807736\pi$
$374$	16.9400	−	29.6064i	0.875946	−	1.53091i
$375$	−4.05001	−	2.91391i	−0.209141	−	0.150473i
$376$	−15.1909	−	18.5992i	−0.783413	−	0.959179i
$377$	24.3637	−	13.8807i	1.25479	−	0.714892i
$378$	20.3288	+	3.00501i	1.04560	+	0.154561i
$379$	5.92732	−	7.43263i	0.304466	−	0.381789i	−0.605936	−	0.795514i	$-0.707201\pi$
$379$	5.92732	−	7.43263i	0.304466	−	0.381789i	0.910402	+	0.413725i	$0.135773\pi$
$380$	0.690842	+	0.733024i	0.0354395	+	0.0376034i
$381$	−7.85120	−	27.9423i	−0.402229	−	1.43153i
$382$	5.36707	−	3.68989i	0.274603	−	0.188791i
$383$	−13.4453	−	16.8598i	−0.687021	−	0.861498i	0.308958	−	0.951076i	$-0.400020\pi$
$383$	−13.4453	−	16.8598i	−0.687021	−	0.861498i	−0.995980	+	0.0895780i	$0.971448\pi$
$384$	−12.1878	+	15.3446i	−0.621957	+	0.783051i
$385$	1.98288	−	4.11750i	0.101057	−	0.209847i
$386$	10.1597	+	9.35354i	0.517117	+	0.476083i
$387$	0.588805	+	1.75656i	0.0299307	+	0.0892910i
$388$	0.0481522	−	0.337260i	0.00244456	−	0.0171218i
$389$	−17.6671			−0.895757			−0.447879	−	0.894094i	$-0.647820\pi$
$389$	−17.6671			−0.895757			−0.447879	+	0.894094i	$0.647820\pi$
$390$	−3.62921	+	0.747049i	−0.183772	+	0.0378283i
$391$	−9.73577	−	12.2083i	−0.492359	−	0.617399i
$392$	2.26751	+	0.489765i	0.114527	+	0.0247369i
$393$	1.76367	+	3.24134i	0.0889655	+	0.163504i
$394$	6.39677	+	1.94591i	0.322265	+	0.0980337i
$395$	1.22969	+	2.55347i	0.0618722	+	0.128479i
$396$	−32.5548	−	8.91113i	−1.63594	−	0.447801i
$397$	−15.9125	−	7.66306i	−0.798626	−	0.384598i	−0.0103706	−	0.999946i	$-0.503301\pi$
$397$	−15.9125	−	7.66306i	−0.798626	−	0.384598i	−0.788255	+	0.615348i	$0.789015\pi$
$398$	11.9707	+	11.0208i	0.600038	+	0.552424i
$399$	−8.26887	−	1.46101i	−0.413961	−	0.0731419i
$400$	−9.56495	+	17.1791i	−0.478248	+	0.858956i
$401$	10.3154	+	8.22623i	0.515125	+	0.410798i	0.846248	−	0.532789i	$-0.178856\pi$
$401$	10.3154	+	8.22623i	0.515125	+	0.410798i	−0.331123	+	0.943588i	$0.607428\pi$
$402$	0.0851985	−	3.98222i	0.00424932	−	0.198615i
$403$	−9.96637	+	43.6655i	−0.496460	+	2.17513i
$404$	−10.3504	+	3.28111i	−0.514951	+	0.163241i
$405$	0.514485	+	2.56348i	0.0255650	+	0.127380i
$406$	−9.20511	−	19.2051i	−0.456842	−	0.953133i
$407$	0.301398			0.0149397
$408$	1.28453	+	20.9656i	0.0635935	+	1.03795i
$409$	25.3261	+	5.78051i	1.25229	+	0.285828i	0.796708	−	0.604364i	$-0.206573\pi$
$409$	25.3261	+	5.78051i	1.25229	+	0.285828i	0.455586	+	0.890192i	$0.349430\pi$
$410$	0.222322	−	3.13010i	0.0109797	−	0.154585i
$411$	−14.3243	+	19.9092i	−0.706568	+	0.982051i
$412$	−22.9676	+	1.90106i	−1.13153	+	0.0936584i
$413$	18.2996	+	4.17677i	0.900467	+	0.205526i
$414$	−9.29012	+	12.3463i	−0.456585	+	0.606790i
$415$	−1.36688	+	2.83836i	−0.0670977	+	0.139330i
$416$	9.22804	+	27.9722i	0.452442	+	1.37145i
$417$	−4.17863	−	7.67965i	−0.204629	−	0.376074i
$418$	13.1948	+	4.01388i	0.645377	+	0.196325i
$419$	7.04633	−	3.39333i	0.344236	−	0.165775i	−0.253775	−	0.967263i	$-0.581672\pi$
$419$	7.04633	−	3.39333i	0.344236	−	0.165775i	0.598011	+	0.801488i	$0.295958\pi$
$420$	0.370680	+	2.78972i	0.0180874	+	0.136124i
$421$	11.6027	−	9.25281i	0.565479	−	0.450954i	−0.298552	−	0.954393i	$-0.596504\pi$
$421$	11.6027	−	9.25281i	0.565479	−	0.450954i	0.864031	+	0.503439i	$0.167932\pi$
$422$	1.43558	+	9.27927i	0.0698829	+	0.451708i
$423$	2.51837	+	25.3464i	0.122448	+	1.23238i
$424$	13.7478	+	6.42395i	0.667652	+	0.311975i
$425$	4.68990	+	20.5478i	0.227494	+	0.996715i
$426$	6.93423	−	8.32359i	0.335965	−	0.403279i
$427$	−18.5243	−	8.92084i	−0.896455	−	0.431710i
$428$	−28.2701	+	26.6433i	−1.36649	+	1.28785i
$429$	−38.0511	+	33.5566i	−1.83712	+	1.62013i
$430$	−0.209070	+	0.143736i	−0.0100822	+	0.00693157i
$431$	−5.03642	−	22.0660i	−0.242596	−	1.06288i	−0.938644	−	0.344886i	$-0.887917\pi$
$431$	−5.03642	−	22.0660i	−0.242596	−	1.06288i	0.696049	−	0.717995i	$-0.254940\pi$
$432$	19.7702	−	6.41404i	0.951193	−	0.308596i
$433$	1.06219	+	0.847065i	0.0510454	+	0.0407073i	0.648680	−	0.761061i	$-0.275321\pi$
$433$	1.06219	+	0.847065i	0.0510454	+	0.0407073i	−0.597635	+	0.801768i	$0.703893\pi$
$434$	32.5451	+	9.90030i	1.56222	+	0.475230i
$435$	1.90378	−	1.92824i	0.0912795	−	0.0924520i
$436$	−11.4964	−	7.70772i	−0.550577	−	0.369133i
$437$	3.93647	−	4.93618i	0.188307	−	0.236129i
$438$	−14.4522	+	28.4376i	−0.690551	+	1.35880i
$439$	9.75887	−	2.22740i	0.465765	−	0.106308i	0.0168034	−	0.999859i	$-0.494651\pi$
$439$	9.75887	−	2.22740i	0.465765	−	0.106308i	0.448962	+	0.893551i	$0.351794\pi$
$440$	−0.0539646	−	4.62201i	−0.00257266	−	0.220346i
$441$	−1.71679	−	1.76261i	−0.0817520	−	0.0839337i
$442$	27.4043	+	15.6800i	1.30349	+	0.745821i
$443$	3.17957	−	6.60244i	0.151066	−	0.313692i	−0.811679	−	0.584104i	$-0.801446\pi$
$443$	3.17957	−	6.60244i	0.151066	−	0.313692i	0.962744	+	0.270413i	$0.0871602\pi$
$444$	−0.155156	+	0.101853i	−0.00736337	+	0.00483371i
$445$	−1.24797	+	0.284841i	−0.0591595	+	0.0135028i
$446$	0.182630	−	0.0282544i	0.00864780	−	0.00133789i
$447$	−0.199897	−	4.03367i	−0.00945481	−	0.190786i
$448$	21.6886	−	5.48604i	1.02469	−	0.259191i
$449$	−11.9970	−	15.0437i	−0.566172	−	0.709957i	0.413514	−	0.910498i	$-0.364301\pi$
$449$	−11.9970	−	15.0437i	−0.566172	−	0.709957i	−0.979685	+	0.200541i	$0.935730\pi$
$450$	18.5279	−	9.57352i	0.873415	−	0.451300i
$451$	−18.6423	−	38.7112i	−0.877832	−	1.82284i
$452$	−25.6667	−	17.2081i	−1.20726	−	0.809403i
$453$	3.62010	+	6.65315i	0.170087	+	0.312592i
$454$	17.4035	+	1.23612i	0.816785	+	0.0580140i
$455$	3.81123	+	1.83539i	0.178673	+	0.0860445i
$456$	−8.14894	+	2.39267i	−0.381609	+	0.112047i
$457$	2.46198	−	10.7867i	0.115167	−	0.504579i	−0.884136	−	0.467230i	$-0.845252\pi$
$457$	2.46198	−	10.7867i	0.115167	−	0.504579i	0.999302	−	0.0373481i	$-0.0118910\pi$
$458$	−10.5291	−	26.5237i	−0.491991	−	1.23937i
$459$	11.1598	−	19.2826i	0.520895	−	0.900033i
$460$	−1.97569	−	0.757710i	−0.0921172	−	0.0353284i
$461$	−4.12711	+	18.0821i	−0.192219	+	0.842165i	0.783194	+	0.621778i	$0.213589\pi$
$461$	−4.12711	+	18.0821i	−0.192219	+	0.842165i	−0.975412	+	0.220387i	$0.929268\pi$
$462$	23.3752	+	30.6336i	1.08751	+	1.42520i
$463$		−	14.8614i		−	0.690669i	−0.938480	−	0.345335i	$-0.887765\pi$
$463$		−	14.8614i		−	0.690669i	0.938480	−	0.345335i	$-0.112235\pi$
$464$	−16.9724	−	13.2642i	−0.787923	−	0.615773i
$465$	0.214229	+	4.32286i	0.00993462	+	0.200468i
$466$	−12.0997	+	8.31862i	−0.560509	+	0.385352i
$467$	16.1272	+	3.68093i	0.746278	+	0.170333i	0.578717	−	0.815529i	$-0.303554\pi$
$467$	16.1272	+	3.68093i	0.746278	+	0.170333i	0.167561	+	0.985862i	$0.446411\pi$
$468$	8.24831	−	30.1333i	0.381278	−	1.39291i
$469$	−2.83522	+	3.55525i	−0.130918	+	0.164166i
$470$	−3.24212	+	1.28702i	−0.149548	+	0.0593658i
$471$	9.74284	+	1.72144i	0.448926	+	0.0793198i
$472$	18.4583	−	4.44032i	0.849611	−	0.204382i
$473$	−1.50727	+	3.12988i	−0.0693044	+	0.143912i
$474$	−23.8910	−	0.511142i	−1.09735	−	0.0234775i
$475$	−7.67784	+	3.69745i	−0.352283	+	0.169651i
$476$	13.3539	−	19.9180i	0.612077	−	0.912939i
$477$	−8.38294	−	13.7397i	−0.383829	−	0.629097i
$478$	−18.4187	+	7.31164i	−0.842450	+	0.334427i
$479$	−2.83844	+	2.26358i	−0.129691	+	0.103425i	−0.686187	−	0.727425i	$-0.740717\pi$
$479$	−2.83844	+	2.26358i	−0.129691	+	0.103425i	0.556496	+	0.830850i	$0.312146\pi$
$480$	1.58972	+	2.36112i	0.0725603	+	0.107770i
$481$			0.278979i			0.0127204i
$482$	−2.44367	−	15.7953i	−0.111306	−	0.719457i
$483$	16.9822	−	4.77163i	0.772716	−	0.217117i
$484$	−20.9227	−	35.5965i	−0.951034	−	1.61802i
$485$	−0.0445850	−	0.0214710i	−0.00202450	−	0.000974948i
$486$	−21.2342	−	5.92531i	−0.963202	−	0.268778i
$487$	−24.6637	+	19.6687i	−1.11762	+	0.891272i	−0.994870	−	0.101166i	$-0.967743\pi$
$487$	−24.6637	+	19.6687i	−1.11762	+	0.891272i	−0.122750	+	0.992438i	$0.539171\pi$
$488$	−20.7941	+	0.242783i	−0.941304	+	0.0109903i
$489$	4.72582	+	16.8191i	0.213709	+	0.760588i
$490$	0.167345	−	0.292473i	0.00755987	−	0.0132126i
$491$	3.05910	+	2.43955i	0.138055	+	0.110095i	0.690083	−	0.723731i	$-0.257574\pi$
$491$	3.05910	+	2.43955i	0.138055	+	0.110095i	−0.552027	+	0.833826i	$0.686146\pi$
$492$	22.6787	+	13.6282i	1.02243	+	0.614405i
$493$	−23.0345	+	1.59340i	−1.03742	+	0.0717630i
$494$	−3.71532	+	12.2133i	−0.167160	+	0.549504i
$495$	−2.66283	+	4.11654i	−0.119685	+	0.185025i
$496$	33.9383	−	5.65700i	1.52388	−	0.254007i
$497$	−12.0580	+	2.75216i	−0.540876	+	0.123451i
$498$	−16.1135	−	21.1170i	−0.722065	−	0.946276i
$499$	13.2741	−	10.5858i	0.594232	−	0.473884i	−0.279597	−	0.960117i	$-0.590201\pi$
$499$	13.2741	−	10.5858i	0.594232	−	0.473884i	0.873829	+	0.486233i	$0.161629\pi$
$500$	3.95135	+	4.19262i	0.176710	+	0.187500i
$501$	6.72258	+	2.83657i	0.300343	+	0.126729i
$502$	−6.52915	−	6.01105i	−0.291410	−	0.268286i
$503$	−23.9600	+	5.46872i	−1.06832	+	0.243838i	−0.720311	−	0.693651i	$-0.756001\pi$
$503$	−23.9600	+	5.46872i	−1.06832	+	0.243838i	−0.348014	+	0.937489i	$0.613144\pi$
$504$	−22.3854	−	7.87050i	−0.997127	−	0.350580i
$505$			1.57718i			0.0701838i
$506$	−28.6323	+	4.42966i	−1.27286	+	0.196922i
$507$	−16.1676	−	18.3330i	−0.718028	−	0.814198i
$508$	2.76459	+	33.4003i	0.122659	+	1.48190i
$509$	−14.4265	−	29.9570i	−0.639445	−	1.32782i	−0.928794	−	0.370598i	$-0.879153\pi$
$509$	−14.4265	−	29.9570i	−0.639445	−	1.32782i	0.289348	−	0.957224i	$-0.406561\pi$
$510$	2.95938	+	0.742400i	0.131044	+	0.0328740i
$511$	32.8113	−	15.8011i	1.45148	−	0.698998i
$512$	17.1859	−	14.7188i	0.759519	−	0.650486i
$513$	8.60513	+	2.66423i	0.379926	+	0.117628i
$514$	13.5163	+	12.4438i	0.596180	+	0.548872i
$515$	−0.744904	+	3.26364i	−0.0328244	+	0.143813i
$516$	−0.281770	−	2.12058i	−0.0124042	−	0.0933534i
$517$	−29.7790	+	37.3417i	−1.30968	+	1.64229i
$518$	0.211357	+	0.0150121i	0.00928651	+	0.000659595i
$519$	−41.1296	−	7.26709i	−1.80539	−	0.318990i
$520$	4.27822	−	0.0499507i	0.187612	−	0.00219048i
$521$		−	4.44026i		−	0.194531i	−0.995258	−	0.0972656i	$-0.968990\pi$
$521$		−	4.44026i		−	0.194531i	0.995258	−	0.0972656i	$-0.0310096\pi$
$522$	7.22146	+	21.6760i	0.316075	+	0.948734i
$523$		−	26.8481i		−	1.17399i	−0.809592	−	0.586993i	$-0.800312\pi$
$523$		−	26.8481i		−	1.17399i	0.809592	−	0.586993i	$-0.199688\pi$
$524$	−1.28759	−	4.06176i	−0.0562488	−	0.177439i
$525$	−23.4461	−	4.14264i	−1.02327	−	0.180799i
$526$	1.23275	−	17.3561i	0.0537506	−	0.756760i
$527$	22.9946	−	28.8344i	1.00166	−	1.25604i
$528$	34.9483	+	17.2505i	1.52093	+	0.750732i
$529$	2.16663	−	9.49262i	0.0942013	−	0.412723i
$530$	1.49293	−	1.62161i	0.0648489	−	0.0704383i
$531$	−18.9173	−	6.90032i	−0.820939	−	0.299448i
$532$	9.05301	+	3.47197i	0.392498	+	0.150529i
$533$	35.8318	−	17.2557i	1.55205	−	0.747426i
$534$	2.62621	−	10.4687i	0.113647	−	0.453025i
$535$	2.44827	+	5.08388i	0.105848	+	0.219795i
$536$	−0.971025	+	4.49565i	−0.0419419	+	0.194182i
$537$	−16.6869	−	18.9219i	−0.720094	−	0.816542i
$538$	−4.29721	−	27.7762i	−0.185266	−	1.19752i
$539$		−	4.61380i		−	0.198730i
$540$	−0.0203293	−	3.01901i	−0.000874835	−	0.129917i
$541$	8.58334	−	1.95909i	0.369027	−	0.0842280i	−0.0339860	−	0.999422i	$-0.510820\pi$
$541$	8.58334	−	1.95909i	0.369027	−	0.0842280i	0.403013	+	0.915194i	$0.367963\pi$
$542$	15.3868	−	16.7130i	0.660920	−	0.717886i
$543$	16.2989	+	6.87730i	0.699455	+	0.295133i
$544$	3.14760	−	24.0493i	0.134952	−	1.03111i
$545$	−1.57187	+	1.25352i	−0.0673314	+	0.0536950i
$546$	−28.3550	+	21.6366i	−1.21348	+	0.925960i
$547$	−14.2220	+	3.24608i	−0.608090	+	0.138792i	−0.515468	−	0.856909i	$-0.672382\pi$
$547$	−14.2220	+	3.24608i	−0.608090	+	0.138792i	−0.0926217	+	0.995701i	$0.529525\pi$
$548$	20.6103	−	19.4243i	0.880428	−	0.829764i
$549$	18.5200	+	11.9799i	0.790416	+	0.511289i
$550$	37.4133	+	11.3812i	1.59531	+	0.485297i
$551$	−2.70056	−	8.93667i	−0.115048	−	0.380715i
$552$	13.2426	−	11.9562i	0.563645	−	0.508889i
$553$	21.3295	+	17.0097i	0.907021	+	0.723325i
$554$	3.30591	+	1.89155i	0.140455	+	0.0803643i
$555$	0.00729261	+	0.0259543i	0.000309554	+	0.00110170i
$556$	3.05067	+	9.62345i	0.129377	+	0.408125i
$557$	−14.3218	+	11.4213i	−0.606834	+	0.483934i	−0.878040	−	0.478587i	$-0.841149\pi$
$557$	−14.3218	+	11.4213i	−0.606834	+	0.483934i	0.271206	+	0.962521i	$0.412578\pi$
$558$	−33.3119	−	14.9031i	−1.41021	−	0.630899i
$559$	−2.89708	−	1.39516i	−0.122533	−	0.0590089i
$560$	0.192372	−	3.24391i	0.00812918	−	0.137080i
$561$	40.2188	−	11.3006i	1.69804	−	0.477113i
$562$	22.9521	−	3.55087i	0.968175	−	0.149785i
$563$		−	3.59603i		−	0.151554i	−0.997125	−	0.0757772i	$-0.975856\pi$
$563$		−	3.59603i		−	0.151554i	0.997125	−	0.0757772i	$-0.0241438\pi$
$564$	2.71083	−	29.2864i	0.114146	−	1.23318i
$565$	−3.50933	+	2.79860i	−0.147639	+	0.117738i
$566$	13.5159	+	34.0477i	0.568115	+	1.43113i
$567$	15.1685	+	20.0836i	0.637018	+	0.843431i
$568$	−9.68860	+	7.91320i	−0.406524	+	0.332030i
$569$	−28.1294	+	13.5464i	−1.17925	+	0.567896i	−0.917692	−	0.397293i	$-0.869950\pi$
$569$	−28.1294	+	13.5464i	−1.17925	+	0.567896i	−0.261556	+	0.965188i	$0.584235\pi$
$570$	−0.0263875	+	1.23336i	−0.00110525	+	0.0516599i
$571$	1.23182	−	2.55791i	0.0515503	−	0.107045i	−0.873603	−	0.486640i	$-0.838222\pi$
$571$	1.23182	−	2.55791i	0.0515503	−	0.107045i	0.925153	+	0.379595i	$0.123937\pi$
$572$	50.5044	−	29.6852i	2.11170	−	1.24120i
$573$	7.85524	+	1.38792i	0.328157	+	0.0579814i
$574$	−11.1449	−	28.0750i	−0.465180	−	1.17183i
$575$	11.1617	−	13.9964i	0.465476	−	0.583689i
$576$	−23.8205	+	2.92988i	−0.992520	+	0.122078i
$577$	−15.6547	−	3.57309i	−0.651714	−	0.148750i	−0.116134	−	0.993234i	$-0.537050\pi$
$577$	−15.6547	−	3.57309i	−0.651714	−	0.148750i	−0.535581	+	0.844484i	$0.679907\pi$
$578$	−1.10858	−	1.61248i	−0.0461110	−	0.0670702i
$579$	0.837153	+	16.8927i	0.0347909	+	0.702036i
$580$	−2.58160	+	1.76786i	−0.107195	+	0.0734065i
$581$			30.3252i			1.25810i
$582$	0.331706	−	0.253112i	0.0137497	−	0.0104918i
$583$	6.71578	−	29.4238i	0.278139	−	1.21861i
$584$	22.6279	−	29.0642i	0.936349	−	1.20269i
$585$	−3.81035	−	2.46477i	−0.157539	−	0.101906i
$586$	2.16723	−	0.860322i	0.0895273	−	0.0355396i
$587$	2.90943	−	12.7470i	0.120085	−	0.526126i	−0.878724	−	0.477330i	$-0.841605\pi$
$587$	2.90943	−	12.7470i	0.120085	−	0.526126i	0.998809	−	0.0487958i	$-0.0155384\pi$
$588$	1.55916	+	2.37513i	0.0642987	+	0.0979486i
$589$	13.4352	+	6.47004i	0.553587	+	0.266593i
$590$	0.195376	−	2.75072i	0.00804351	−	0.113245i
$591$	3.91385	+	7.19303i	0.160994	+	0.295882i
$592$	0.198255	−	0.0813929i	0.00814821	−	0.00334523i
$593$	17.7934	+	36.9484i	0.730689	+	1.51729i	0.851351	+	0.524597i	$0.175784\pi$
$593$	17.7934	+	36.9484i	0.730689	+	1.51729i	−0.120662	+	0.992694i	$0.538502\pi$
$594$	−20.7707	−	35.7409i	−0.852231	−	1.46647i
$595$	−2.17178	−	2.72333i	−0.0890343	−	0.111645i
$596$	−0.659131	+	4.61658i	−0.0269991	+	0.189103i
$597$	0.986377	+	19.9038i	0.0403697	+	0.814609i
$598$	−4.10017	−	26.5026i	−0.167669	−	1.08377i
$599$	1.30236	−	0.297255i	0.0532130	−	0.0121455i	−0.195832	−	0.980638i	$-0.562741\pi$
$599$	1.30236	−	0.297255i	0.0532130	−	0.0121455i	0.249045	+	0.968492i	$0.419883\pi$
$600$	−23.1060	+	6.78434i	−0.943300	+	0.276969i
$601$	−20.5880	+	42.7515i	−0.839803	+	1.74387i	−0.193018	+	0.981195i	$0.561828\pi$
$601$	−20.5880	+	42.7515i	−0.839803	+	1.74387i	−0.646784	+	0.762673i	$0.723887\pi$
$602$	−1.21288	+	2.11978i	−0.0494333	+	0.0863957i
$603$	3.49461	−	3.40377i	0.142311	−	0.138612i
$604$	−2.64290	−	8.33713i	−0.107538	−	0.339233i
$605$	−5.84724	+	1.33459i	−0.237724	+	0.0542590i
$606$	−11.8552	−	6.02487i	−0.481584	−	0.244744i
$607$	−26.0382	+	32.6509i	−1.05686	+	1.32526i	−0.113480	+	0.993540i	$0.536200\pi$
$607$	−26.0382	+	32.6509i	−1.05686	+	1.32526i	−0.943378	+	0.331719i	$0.892372\pi$
$608$	9.76327	−	0.923004i	0.395953	−	0.0374328i
$609$	8.45759	−	24.6744i	0.342719	−	0.999856i
$610$	−0.879115	+	2.88990i	−0.0355943	+	0.117009i
$611$	−34.5642	−	27.5640i	−1.39832	−	1.11512i
$612$	−16.8853	+	19.4087i	−0.682547	+	0.784552i
$613$	3.92936	+	17.2156i	0.158705	+	0.695333i	0.990183	+	0.139775i	$0.0446381\pi$
$613$	3.92936	+	17.2156i	0.158705	+	0.695333i	−0.831478	+	0.555558i	$0.812505\pi$
$614$	−2.97296	−	4.32428i	−0.119979	−	0.174514i
$615$	2.88247	−	2.54200i	0.116233	−	0.102503i
$616$	−19.7721	−	39.8600i	−0.796642	−	1.60601i
$617$	38.0513	+	18.3246i	1.53189	+	0.737719i	0.994413	−	0.105561i	$-0.0336637\pi$
$617$	38.0513	+	18.3246i	1.53189	+	0.737719i	0.537476	+	0.843279i	$0.319378\pi$
$618$	−21.6862	−	18.0664i	−0.872346	−	0.726736i
$619$	5.40266	+	23.6706i	0.217151	+	0.951402i	0.959571	+	0.281467i	$0.0908210\pi$
$619$	5.40266	+	23.6706i	0.217151	+	0.951402i	−0.742420	+	0.669935i	$0.766322\pi$
$620$	0.706387	−	4.94757i	0.0283692	−	0.198699i
$621$	−18.7153	+	2.80079i	−0.751020	+	0.112392i
$622$	24.9826	−	3.86501i	1.00171	−	0.154973i
$623$	−9.63366	+	7.68259i	−0.385964	+	0.307796i
$624$	−15.9674	+	32.3488i	−0.639207	+	1.29499i
$625$	−21.3901	+	10.3009i	−0.855602	+	0.412036i
$626$	1.04240	−	3.42665i	0.0416625	−	0.136957i
$627$	8.07319	+	14.8372i	0.322412	+	0.592542i
$628$	−10.6668	−	4.09087i	−0.425650	−	0.163244i
$629$	0.0996727	−	0.206972i	0.00397421	−	0.00825253i
$630$	−2.07237	+	2.75413i	−0.0825651	+	0.109727i
$631$	3.26807	+	0.745915i	0.130100	+	0.0296944i	0.287075	−	0.957908i	$-0.407317\pi$
$631$	3.26807	+	0.745915i	0.130100	+	0.0296944i	−0.156975	+	0.987603i	$0.550174\pi$
$632$	26.9713	+	5.82560i	1.07286	+	0.231730i
$633$	−6.71628	+	9.33489i	−0.266948	+	0.371029i
$634$	2.69446	+	0.191380i	0.107011	+	0.00760067i
$635$	4.74610	+	1.08327i	0.188343	+	0.0429882i
$636$	6.48610	+	17.4165i	0.257191	+	0.690609i
$637$	4.27062			0.169208
$638$	−18.6595	+	38.5647i	−0.738735	+	1.52679i
$639$	13.2033	−	1.31186i	0.522315	−	0.0518964i
$640$	−1.28368	−	3.02571i	−0.0507418	−	0.119602i
$641$	9.56849	−	41.9223i	0.377933	−	1.65583i	−0.325854	−	0.945420i	$-0.605652\pi$
$641$	9.56849	−	41.9223i	0.377933	−	1.65583i	0.703787	−	0.710411i	$-0.251491\pi$
$642$	−47.5663	−	1.01767i	−1.87729	−	0.0401642i
$643$	10.2505	+	8.17450i	0.404240	+	0.322371i	0.804415	−	0.594068i	$-0.202479\pi$
$643$	10.2505	+	8.17450i	0.404240	+	0.322371i	−0.400175	+	0.916439i	$0.631051\pi$
$644$	−20.2993	+	1.68020i	−0.799904	+	0.0662092i
$645$	−0.305994	−	0.0540654i	−0.0120485	−	0.00212882i
$646$	7.11990	−	7.73357i	0.280129	−	0.304273i
$647$	1.53179	+	0.737671i	0.0602208	+	0.0290008i	0.463752	−	0.885965i	$-0.346503\pi$
$647$	1.53179	+	0.737671i	0.0602208	+	0.0290008i	−0.403531	+	0.914966i	$0.632217\pi$
$648$	22.7706	+	11.3799i	0.894513	+	0.447043i
$649$	−16.3828	−	34.0192i	−0.643081	−	1.33537i
$650$	−10.5347	+	34.6305i	−0.413204	+	1.35832i
$651$	19.9127	+	36.5963i	0.780439	+	1.43432i
$652$	−1.66407	−	20.1044i	−0.0651700	−	0.787349i
$653$	−21.6258	−	27.1180i	−0.846285	−	1.06121i	−0.997355	−	0.0726845i	$-0.976843\pi$
$653$	−21.6258	−	27.1180i	−0.846285	−	1.06121i	0.151070	−	0.988523i	$-0.451728\pi$
$654$	−3.41776	−	16.6037i	−0.133645	−	0.649256i
$655$	−0.618928			−0.0241835
$656$	−22.7166	−	20.4292i	−0.886936	−	0.797627i
$657$	−37.0428	+	12.4169i	−1.44518	+	0.484428i
$658$	−22.7427	+	24.7029i	−0.886602	+	0.963019i
$659$	−19.5031	+	40.4985i	−0.759731	+	1.57760i	0.0554979	+	0.998459i	$0.482325\pi$
$659$	−19.5031	+	40.4985i	−0.759731	+	1.57760i	−0.815229	+	0.579139i	$0.803389\pi$
$660$	3.92260	−	4.08191i	0.152687	−	0.158888i
$661$	−29.2717	−	36.7055i	−1.13854	−	1.42768i	−0.888162	−	0.459531i	$-0.848018\pi$
$661$	−29.2717	−	36.7055i	−1.13854	−	1.42768i	−0.250375	−	0.968149i	$-0.580554\pi$
$662$	−12.7000	−	18.4727i	−0.493601	−	0.717961i
$663$	10.4601	+	37.2273i	0.406236	+	1.44579i
$664$	13.6298	+	27.4772i	0.528937	+	1.06632i
$665$	0.878117	−	1.10112i	0.0340519	−	0.0426997i
$666$	−0.222948	−	0.0443297i	−0.00863906	−	0.00171774i
$667$	13.2569	+	14.4530i	0.513311	+	0.559621i
$668$	−6.99803	−	4.69181i	−0.270762	−	0.181532i
$669$	0.183725	+	0.132187i	0.00710322	+	0.00511064i
$670$	0.579866	+	0.331784i	0.0224022	+	0.0128179i
$671$	9.20340	+	40.3227i	0.355293	+	1.55664i
$672$	23.6485	+	13.8378i	0.912262	+	0.533803i
$673$	19.4076	+	24.3364i	0.748109	+	0.938099i	0.999557	−	0.0297718i	$-0.00947804\pi$
$673$	19.4076	+	24.3364i	0.748109	+	0.938099i	−0.251448	+	0.967871i	$0.580907\pi$
$674$	−22.6890	+	39.6540i	−0.873946	+	1.52742i
$675$	24.3995	+	7.55432i	0.939139	+	0.290766i
$676$	14.3024	+	24.3330i	0.550091	+	0.935886i
$677$	−6.60700	−	28.9472i	−0.253928	−	1.11253i	−0.927622	−	0.373520i	$-0.878151\pi$
$677$	−6.60700	−	28.9472i	−0.253928	−	1.11253i	0.673694	−	0.739010i	$-0.264706\pi$
$678$	−7.63045	−	37.0692i	−0.293046	−	1.42363i
$679$	−0.476349			−0.0182806
$680$	−3.19182	−	1.49145i	−0.122401	−	0.0571944i
$681$	14.1336	+	16.0266i	0.541602	+	0.614142i
$682$	−25.2481	−	63.6023i	−0.966801	−	2.43546i
$683$	29.1471	−	14.0365i	1.11528	−	0.537091i	0.216850	−	0.976205i	$-0.430422\pi$
$683$	29.1471	−	14.0365i	1.11528	−	0.537091i	0.898431	+	0.439114i	$0.144708\pi$
$684$	−9.16999	−	4.90981i	−0.350623	−	0.187731i
$685$	−1.78491	−	3.70640i	−0.0681979	−	0.141614i
$686$	−1.73154	+	24.3785i	−0.0661104	+	0.930775i
$687$	13.5873	−	32.2014i	0.518389	−	1.22856i
$688$	−0.146230	+	2.46583i	−0.00557495	+	0.0940088i
$689$	27.2352	+	6.21625i	1.03758	+	0.236820i
$690$	−1.07424	−	2.35844i	−0.0408956	−	0.0897844i
$691$	18.1927	+	14.5082i	0.692082	+	0.551917i	0.905135	−	0.425124i	$-0.139769\pi$
$691$	18.1927	+	14.5082i	0.692082	+	0.551917i	−0.213053	+	0.977041i	$0.568341\pi$
$692$	45.0299	+	17.2697i	1.71178	+	0.656495i
$693$	−5.90098	+	46.8231i	−0.224160	+	1.77866i
$694$	22.2803	+	32.4076i	0.845750	+	1.23017i
$695$	1.46641			0.0556242
$696$	−3.42668	−	26.1583i	−0.129888	−	0.991529i
$697$	−32.7484			−1.24043
$698$	−5.00783	−	7.28407i	−0.189549	−	0.275706i
$699$	−17.7091	−	3.12899i	−0.669821	−	0.118349i
$700$	25.6695	+	9.84466i	0.970216	+	0.372093i
$701$	21.8797	+	17.4485i	0.826386	+	0.659021i	0.942497	−	0.334216i	$-0.108471\pi$
$701$	21.8797	+	17.4485i	0.826386	+	0.659021i	−0.116111	+	0.993236i	$0.537043\pi$
$702$	33.0824	−	19.2257i	1.24862	−	0.725628i
$703$	0.0905549	+	0.0206686i	0.00341534	+	0.000779529i
$704$	−35.8304	−	27.2299i	−1.35041	−	1.02626i
$705$	−3.93614	−	1.66085i	−0.148244	−	0.0625511i
$706$	−3.36211	+	47.3355i	−0.126535	+	1.78150i
$707$	6.58721	+	13.6785i	0.247738	+	0.514432i
$708$	19.9299	+	11.9764i	0.749013	+	0.450100i
$709$	25.0455	−	12.0613i	0.940602	−	0.452970i	0.100221	−	0.994965i	$-0.468045\pi$
$709$	25.0455	−	12.0613i	0.940602	−	0.452970i	0.840382	+	0.541995i	$0.182331\pi$
$710$	0.670429	+	1.68887i	0.0251607	+	0.0633821i
$711$	−20.4207	−	20.9656i	−0.765836	−	0.786273i
$712$	−5.27594	+	11.2909i	−0.197724	+	0.423146i
$713$	−31.3261			−1.17317
$714$	28.7666	−	5.92142i	1.07656	−	0.221604i
$715$	−1.89353	−	8.29608i	−0.0708138	−	0.310256i
$716$	14.7618	+	25.1147i	0.551674	+	0.938580i
$717$	−22.3615	−	9.43536i	−0.835104	−	0.352370i
$718$	−17.7374	+	31.0000i	−0.661953	+	1.15691i
$719$	7.40678	+	9.28781i	0.276226	+	0.346377i	0.900521	−	0.434812i	$-0.143185\pi$
$719$	7.40678	+	9.28781i	0.276226	+	0.346377i	−0.624295	+	0.781189i	$0.714614\pi$
$720$	−0.639888	+	3.42690i	−0.0238472	+	0.127713i
$721$	7.17045	+	31.4158i	0.267042	+	1.16999i
$722$	−19.6331	−	11.2336i	−0.730670	−	0.418070i
$723$	11.4326	−	15.8900i	0.425182	−	0.590955i
$724$	−16.9668	−	11.3753i	−0.630566	−	0.422761i
$725$	−7.65736	−	25.3396i	−0.284387	−	0.941090i
$726$	12.3048	−	49.0500i	0.456675	−	1.82042i
$727$	−17.3518	+	21.7585i	−0.643544	+	0.806978i	−0.991441	−	0.130554i	$-0.958324\pi$
$727$	−17.3518	+	21.7585i	−0.643544	+	0.806978i	0.347898	+	0.937533i	$0.386896\pi$
$728$	36.8952	−	18.3015i	1.36743	−	0.678297i
$729$	−13.4509	−	23.4110i	−0.498181	−	0.867073i
$730$	−3.03114	−	4.40891i	−0.112188	−	0.163181i
$731$	1.65086	+	2.07011i	0.0610593	+	0.0765659i
$732$	−18.3642	−	17.6475i	−0.678761	−	0.652270i
$733$	3.27593	−	6.80255i	0.120999	−	0.251258i	−0.831667	−	0.555274i	$-0.812613\pi$
$733$	3.27593	−	6.80255i	0.120999	−	0.251258i	0.952667	+	0.304016i	$0.0983277\pi$
$734$	6.83690	−	7.42618i	0.252355	−	0.274105i
$735$	0.397309	−	0.111635i	0.0146550	−	0.00411773i
$736$	−17.6377	+	10.6460i	−0.650133	+	0.392416i
$737$	9.14748			0.336952
$738$	8.09633	+	31.3771i	0.298030	+	1.15501i
$739$	−19.5646	−	24.5332i	−0.719694	−	0.902468i	0.278627	−	0.960400i	$-0.410121\pi$
$739$	−19.5646	−	24.5332i	−0.719694	−	0.902468i	−0.998321	+	0.0579319i	$0.981549\pi$
$740$	−0.00256789	−	0.0310239i	−9.43977e−5	−	0.00114046i
$741$	−13.7336	+	7.47270i	−0.504517	+	0.274517i
$742$	6.17504	−	20.2991i	0.226693	−	0.745204i
$743$	4.75266	+	9.86900i	0.174358	+	0.362058i	0.969774	−	0.244006i	$-0.0784617\pi$
$743$	4.75266	+	9.86900i	0.174358	+	0.362058i	−0.795416	+	0.606064i	$0.792747\pi$
$744$	34.4908	+	24.2095i	1.26450	+	0.887562i
$745$	0.610302	+	0.293906i	0.0223597	+	0.0107679i
$746$	13.7104	−	14.8922i	0.501975	−	0.545241i
$747$	4.06780	−	32.2772i	0.148833	−	1.18096i
$748$	−48.0747	+	3.97921i	−1.75778	+	0.145494i
$749$	42.4663	+	33.8658i	1.55169	+	1.23743i
$750$	−0.150926	+	7.05436i	−0.00551105	+	0.257589i
$751$	5.59760	−	24.5247i	0.204259	−	0.894919i	−0.764048	−	0.645159i	$-0.776791\pi$
$751$	5.59760	−	24.5247i	0.204259	−	0.894919i	0.968308	−	0.249760i	$-0.0803518\pi$
$752$	−9.50397	+	32.6046i	−0.346574	+	1.18897i
$753$	−0.537996	−	10.8561i	−0.0196057	−	0.395617i
$754$	−35.6962	−	17.2715i	−1.29998	−	0.628993i
$755$	−1.27041			−0.0462348
$756$	−12.7854	−	26.0981i	−0.465000	−	0.949180i
$757$	35.2435	+	8.04410i	1.28095	+	0.292368i	0.808240	−	0.588853i	$-0.200420\pi$
$757$	35.2435	+	8.04410i	1.28095	+	0.292368i	0.472706	+	0.881220i	$0.343277\pi$
$758$	−13.4107	−	0.952525i	−0.487099	−	0.0345973i
$759$	−28.8040	−	20.7239i	−1.04552	−	0.752231i
$760$	0.300744	−	1.39238i	0.0109091	−	0.0505070i
$761$	−19.2272	−	4.38849i	−0.696987	−	0.159083i	−0.140674	−	0.990056i	$-0.544927\pi$
$761$	−19.2272	−	4.38849i	−0.696987	−	0.159083i	−0.556312	+	0.830973i	$0.687784\pi$
$762$	−26.2728	+	31.5368i	−0.951762	+	1.14246i
$763$	−8.39695	+	17.4365i	−0.303990	+	0.631242i
$764$	−8.60016	−	3.29830i	−0.311143	−	0.119328i
$765$	1.94627	+	3.18994i	0.0703674	+	0.115332i
$766$	−8.87563	+	29.1767i	−0.320690	+	1.05420i
$767$	31.4888	−	15.1642i	1.13700	−	0.547549i
$768$	27.6470	+	1.90927i	0.997624	+	0.0688949i
$769$	−8.97562	+	7.15782i	−0.323669	+	0.258118i	−0.771821	−	0.635840i	$-0.780654\pi$
$769$	−8.97562	+	7.15782i	−0.323669	+	0.258118i	0.448152	+	0.893957i	$0.352082\pi$
$770$	−6.38708	+	0.988134i	−0.230174	+	0.0356099i
$771$	1.11373	+	22.4737i	0.0401102	+	0.809372i
$772$	2.76039	−	19.3339i	0.0993484	−	0.695841i
$773$	−10.7306	−	47.0140i	−0.385955	−	1.69098i	−0.678398	−	0.734695i	$-0.737325\pi$
$773$	−10.7306	−	47.0140i	−0.385955	−	1.69098i	0.292443	−	0.956283i	$-0.405532\pi$
$774$	1.57529	−	2.09353i	0.0566227	−	0.0752502i
$775$	38.0950	+	18.3456i	1.36841	+	0.658993i
$776$	−0.431612	+	0.214096i	−0.0154940	+	0.00768561i
$777$	0.171647	+	0.194636i	0.00615779	+	0.00698254i
$778$	14.1548	+	20.5887i	0.507474	+	0.738140i
$779$	−2.94644	−	12.9092i	−0.105567	−	0.462519i
$780$	3.77829	+	3.63083i	0.135285	+	0.130005i
$781$	19.4519	+	15.5123i	0.696042	+	0.555075i
$782$	−6.42688	+	21.1270i	−0.229825	+	0.755500i
$783$	−12.3118	+	25.1281i	−0.439987	+	0.898004i
$784$	−1.24596	−	3.03488i	−0.0444987	−	0.108389i
$785$	−1.03465	+	1.29741i	−0.0369281	+	0.0463064i
$786$	2.36431	−	4.65228i	0.0843323	−	0.165941i
$787$	32.2697	−	7.36535i	1.15029	−	0.262546i	0.395471	−	0.918479i	$-0.370581\pi$
$787$	32.2697	−	7.36535i	1.15029	−	0.262546i	0.754820	+	0.655932i	$0.227724\pi$
$788$	−2.85736	−	9.01366i	−0.101789	−	0.321098i
$789$	15.9830	−	14.0951i	0.569010	−	0.501800i
$790$	1.99051	−	3.47887i	0.0708193	−	0.123773i
$791$	−18.7469	+	38.9284i	−0.666564	+	1.38413i
$792$	15.6980	+	45.0779i	0.557805	+	1.60177i
$793$	−37.3235	+	8.51884i	−1.32539	+	0.302513i
$794$	3.81875	+	24.6836i	0.135522	+	0.875987i
$795$	2.69627	−	0.133619i	0.0956268	−	0.00473899i
$796$	3.25243	−	22.7801i	0.115279	−	0.807421i
$797$	5.26380	+	6.60060i	0.186454	+	0.233805i	0.866269	−	0.499578i	$-0.166512\pi$
$797$	5.26380	+	6.60060i	0.186454	+	0.233805i	−0.679815	+	0.733383i	$0.737940\pi$
$798$	4.92237	+	10.8068i	0.174250	+	0.382558i
$799$	15.7949	+	32.7985i	0.558784	+	1.16033i
$800$	27.6834	−	2.61715i	0.978757	−	0.0925301i
$801$	11.2843	−	6.88484i	0.398711	−	0.243264i
$802$	1.32196	−	18.6120i	0.0466800	−	0.657213i
$803$	−66.0036	−	31.7857i	−2.32922	−	1.12169i
$804$	−4.70901	+	3.09125i	−0.166074	+	0.109020i
$805$	−0.658365	+	2.88448i	−0.0232043	+	0.101665i
$806$	58.8715	−	23.3702i	2.07366	−	0.823179i
$807$	20.1043	−	27.9427i	0.707705	−	0.983631i
$808$	12.1164	+	9.43321i	0.426253	+	0.331859i
$809$	−5.48900	+	24.0489i	−0.192983	+	0.845514i	0.782008	+	0.623269i	$0.214196\pi$
$809$	−5.48900	+	24.0489i	−0.192983	+	0.845514i	−0.974991	+	0.222245i	$0.928661\pi$
$810$	2.57520	−	2.65341i	0.0904831	−	0.0932315i
$811$		−	13.2080i		−	0.463795i	−0.972740	−	0.231898i	$-0.925507\pi$
$811$		−	13.2080i		−	0.463795i	0.972740	−	0.231898i	$-0.0744935\pi$
$812$	−15.0059	+	26.1144i	−0.526605	+	0.916436i
$813$	27.7889	−	1.37714i	0.974599	−	0.0482984i
$814$	−0.241479	−	0.351239i	−0.00846382	−	0.0123109i
$815$	−2.85679	−	0.652044i	−0.100069	−	0.0228401i
$816$	23.4035	−	18.2945i	0.819288	−	0.640437i
$817$	−0.667493	+	0.837010i	−0.0233526	+	0.0292833i
$818$	−13.5547	−	34.1456i	−0.473930	−	1.19387i
$819$	−43.3404	−	5.46206i	−1.51444	−	0.190860i
$820$	−3.82585	+	2.24874i	−0.133604	+	0.0785293i
$821$	16.0005	−	33.2253i	0.558420	−	1.15957i	−0.410422	−	0.911896i	$-0.634619\pi$
$821$	16.0005	−	33.2253i	0.558420	−	1.15957i	0.968843	−	0.247676i	$-0.0796670\pi$
$822$	34.6782	+	0.741932i	1.20954	+	0.0258779i
$823$	28.3036	−	13.6303i	0.986601	−	0.475122i	0.130230	−	0.991484i	$-0.458428\pi$
$823$	28.3036	−	13.6303i	0.986601	−	0.475122i	0.856370	+	0.516362i	$0.172714\pi$
$824$	20.6169	+	25.2426i	0.718225	+	0.879366i
$825$	22.8913	+	42.0705i	0.796972	+	1.46471i
$826$	−9.79412	−	24.6723i	−0.340781	−	0.858457i
$827$	12.6336	−	10.0750i	0.439314	−	0.350341i	−0.378720	−	0.925511i	$-0.623636\pi$
$827$	12.6336	−	10.0750i	0.439314	−	0.350341i	0.818034	+	0.575170i	$0.195064\pi$
$828$	21.8313	+	0.934577i	0.758689	+	0.0324788i
$829$			43.4071i			1.50759i	0.657109	+	0.753796i	$0.271779\pi$
$829$			43.4071i			1.50759i	−0.657109	+	0.753796i	$0.728221\pi$
$830$	4.40288	−	0.681162i	0.152826	−	0.0236435i
$831$	1.26185	+	4.49090i	0.0437731	+	0.155788i
$832$	25.2045	−	33.1653i	0.873808	−	1.14980i
$833$	−3.16834	−	1.52579i	−0.109776	−	0.0528655i
$834$	−5.60172	+	11.0226i	−0.193972	+	0.381680i
$835$	−0.956821	+	0.763039i	−0.0331121	+	0.0264061i
$836$	−5.89395	−	18.5927i	−0.203847	−	0.643041i
$837$	−16.2854	−	41.6229i	−0.562905	−	1.43870i
$838$	−9.59998	−	5.49285i	−0.331626	−	0.189747i
$839$	35.6940	+	28.4650i	1.23229	+	0.982722i	0.999949	+	0.0100882i	$0.00321123\pi$
$839$	35.6940	+	28.4650i	1.23229	+	0.982722i	0.232345	+	0.972633i	$0.425360\pi$
$840$	2.95407	−	2.66709i	0.101925	−	0.0920235i
$841$	28.7238	−	3.99301i	0.990475	−	0.137690i
$842$	−20.0789	−	6.10806i	−0.691966	−	0.210498i
$843$	23.0896	+	16.6126i	0.795249	+	0.572168i
$844$	9.66359	−	9.10749i	0.332635	−	0.313493i
$845$	3.99705	−	0.912301i	0.137503	−	0.0313841i
$846$	27.5202	−	23.2423i	0.946163	−	0.799085i
$847$	−45.1375	+	35.9959i	−1.55094	+	1.23684i
$848$	−3.52840	−	21.1681i	−0.121166	−	0.726915i
$849$	−17.4417	+	41.3361i	−0.598596	+	1.41865i
$850$	20.1882	−	21.9283i	0.692451	−	0.752134i
$851$	−0.190232	+	0.0434193i	−0.00652108	+	0.00148839i
$852$	−15.2557	−	1.41211i	−0.522653	−	0.0483781i
$853$			14.9124i			0.510591i	0.966863	+	0.255295i	$0.0821727\pi$
$853$			14.9124i			0.510591i	−0.966863	+	0.255295i	$0.917827\pi$
$854$	4.44554	+	28.7350i	0.152123	+	0.983292i
$855$	−1.08234	+	1.05421i	−0.0370153	+	0.0360532i
$856$	53.6991	+	11.5986i	1.83540	+	0.396432i
$857$	19.5171	+	40.5277i	0.666692	+	1.38440i	0.910065	+	0.414466i	$0.136032\pi$
$857$	19.5171	+	40.5277i	0.666692	+	1.38440i	−0.243373	+	0.969933i	$0.578254\pi$
$858$	69.5922	+	17.4581i	2.37584	+	0.596011i
$859$	−6.25626	+	3.01286i	−0.213461	+	0.102797i	−0.537559	−	0.843226i	$-0.680653\pi$
$859$	−6.25626	+	3.01286i	−0.213461	+	0.102797i	0.324098	+	0.946023i	$0.394939\pi$
$860$	0.335011	+	0.128482i	0.0114238	+	0.00438121i
$861$	14.3821	−	34.0849i	0.490139	−	1.16161i
$862$	−21.6799	+	23.5485i	−0.738419	+	0.802064i
$863$	−1.80222	+	7.89603i	−0.0613482	+	0.268784i	−0.996295	−	0.0860046i	$-0.972590\pi$
$863$	−1.80222	+	7.89603i	−0.0613482	+	0.268784i	0.934947	+	0.354789i	$0.115447\pi$
$864$	−23.3145	−	17.9006i	−0.793176	−	0.608992i
$865$	4.36778	−	5.47702i	0.148509	−	0.186224i
$866$	0.136124	−	1.91650i	0.00462568	−	0.0651254i
$867$	0.416986	−	2.36002i	0.0141616	−	0.0801504i
$868$	−14.5375	−	45.8592i	−0.493436	−	1.55656i
$869$		−	54.8796i		−	1.86166i
$870$	−3.77241	−	0.673714i	−0.127897	−	0.0228410i
$871$			8.46708i			0.286896i
$872$	0.228525	+	19.5729i	0.00773884	+	0.662823i
$873$	0.507010	+	0.0638970i	0.0171597	+	0.00216258i
$874$	−8.90635	−	0.632593i	−0.301262	−	0.0213978i
$875$	5.02249	−	6.29800i	0.169791	−	0.212911i
$876$	44.7193	−	5.94202i	1.51093	−	0.200762i
$877$	−1.62927	+	7.13829i	−0.0550165	+	0.241043i	−0.994958	−	0.100293i	$-0.968022\pi$
$877$	−1.62927	+	7.13829i	−0.0550165	+	0.241043i	0.939941	+	0.341336i	$0.110879\pi$
$878$	−10.4145	−	9.58810i	−0.351473	−	0.323583i
$879$	2.63115	+	1.11021i	0.0887467	+	0.0374464i
$880$	−5.34311	+	3.76602i	−0.180116	+	0.126953i
$881$	−42.9878	+	20.7018i	−1.44829	+	0.697462i	−0.982298	−	0.187324i	$-0.940018\pi$
$881$	−42.9878	+	20.7018i	−1.44829	+	0.697462i	−0.465997	+	0.884786i	$0.654304\pi$
$882$	−0.678599	+	3.41289i	−0.0228496	+	0.114918i
$883$	−15.3550	−	31.8851i	−0.516739	−	1.07302i	−0.982180	−	0.187940i	$-0.939819\pi$
$883$	−15.3550	−	31.8851i	−0.516739	−	1.07302i	0.465442	−	0.885078i	$-0.345895\pi$
$884$	−3.68323	−	44.4988i	−0.123880	−	1.49666i
$885$	2.53311	−	2.23390i	0.0851495	−	0.0750919i
$886$	−10.2417	+	1.58448i	−0.344078	+	0.0532317i
$887$		−	22.9648i		−	0.771082i	−0.922691	−	0.385541i	$-0.874015\pi$
$887$		−	22.9648i		−	0.771082i	0.922691	−	0.385541i	$-0.125985\pi$
$888$	0.243006	+	0.0992098i	0.00815475	+	0.00332926i
$889$	45.6860	−	10.4275i	1.53226	−	0.349728i
$890$	1.33182	+	1.22613i	0.0446426	+	0.0411001i
$891$	12.5616	−	49.0454i	0.420830	−	1.64308i
$892$	−0.179250	−	0.190194i	−0.00600172	−	0.00636818i
$893$	−11.5078	+	9.17719i	−0.385095	+	0.307103i
$894$	−4.54056	+	3.46472i	−0.151859	+	0.115877i
$895$	4.12545	−	0.941607i	0.137899	−	0.0314744i
$896$	−23.7701	−	20.8798i	−0.794102	−	0.697545i
$897$	19.1825	−	26.6615i	0.640484	−	0.890201i
$898$	−7.91956	+	26.0339i	−0.264279	+	0.868761i
$899$	−26.3128	+	38.1221i	−0.877580	+	1.27144i
$900$	−26.0012	−	13.9216i	−0.866707	−	0.464054i
$901$	−17.9846	−	14.3423i	−0.599155	−	0.477810i
$902$	−30.1766	+	52.7404i	−1.00477	+	1.75606i
$903$	−2.87961	+	0.809109i	−0.0958273	+	0.0269254i
$904$	0.510203	+	43.6982i	0.0169691	+	1.45338i
$905$	−2.31982	+	1.85000i	−0.0771134	+	0.0614959i
$906$	4.85297	−	9.54923i	0.161229	−	0.317252i
$907$	−24.9411	−	12.0110i	−0.828154	−	0.398818i	−0.0287317	−	0.999587i	$-0.509147\pi$
$907$	−24.9411	−	12.0110i	−0.828154	−	0.398818i	−0.799423	+	0.600769i	$0.794861\pi$
$908$	−12.5030	−	21.2718i	−0.414928	−	0.705930i
$909$	−5.17639	−	15.4425i	−0.171690	−	0.512196i
$910$	−0.914635	−	5.91200i	−0.0303199	−	0.195981i
$911$			0.736204i			0.0243915i	0.999926	+	0.0121958i	$0.00388213\pi$
$911$			0.736204i			0.0243915i	−0.999926	+	0.0121958i	$0.996118\pi$
$912$	9.31724	+	7.57952i	0.308525	+	0.250983i
$913$	47.6938	−	38.0345i	1.57843	−	1.25876i
$914$	−14.5430	+	5.77311i	−0.481039	+	0.190957i
$915$	−3.24963	+	1.76818i	−0.107430	+	0.0584543i
$916$	−22.4740	+	33.5209i	−0.742562	+	1.10756i
$917$	−5.36779	+	2.58499i	−0.177260	+	0.0853640i
$918$	−31.4125	+	2.44384i	−1.03677	+	0.0806586i
$919$	−4.32881	+	8.98888i	−0.142794	+	0.296516i	−0.960084	−	0.279711i	$-0.909761\pi$
$919$	−4.32881	+	8.98888i	−0.142794	+	0.296516i	0.817290	+	0.576227i	$0.195476\pi$
$920$	0.699907	+	2.90949i	0.0230752	+	0.0959230i
$921$	1.11826	−	6.32901i	0.0368479	−	0.208548i
$922$	24.3789	−	9.67766i	0.802876	−	0.318717i
$923$	−14.3585	+	18.0050i	−0.472616	+	0.592642i
$924$	16.9713	−	51.7843i	0.558314	−	1.70358i
$925$	0.256765	+	0.0586050i	0.00844239	+	0.00192692i
$926$	−17.3191	+	11.9069i	−0.569139	+	0.391286i
$927$	−3.41790	−	34.3998i	−0.112259	−	1.12984i
$928$	−1.85943	+	30.4063i	−0.0610388	+	0.998135i
$929$			39.4347i			1.29381i	0.762570	+	0.646905i	$0.223937\pi$
$929$			39.4347i			1.29381i	−0.762570	+	0.646905i	$0.776063\pi$
$930$	4.86609	−	3.71312i	0.159565	−	0.121758i
$931$	0.316395	−	1.38622i	0.0103694	−	0.0454314i
$932$	19.3885	+	7.43581i	0.635092	+	0.243568i
$933$	25.1323	+	18.0823i	0.822796	+	0.591987i
$934$	−8.63141	−	21.7433i	−0.282428	−	0.711462i
$935$	−1.55920	+	6.83131i	−0.0509913	+	0.223408i
$936$	−41.7249	+	14.5304i	−1.36382	+	0.474940i
$937$	−21.0921	−	10.1574i	−0.689049	−	0.331829i	0.0563838	−	0.998409i	$-0.482043\pi$
$937$	−21.0921	−	10.1574i	−0.689049	−	0.331829i	−0.745433	+	0.666581i	$0.767757\pi$
$938$	6.41474	+	0.455621i	0.209449	+	0.0148766i
$939$	3.85320	−	2.09659i	0.125744	−	0.0684197i
$940$	4.09743	+	2.74711i	0.133643	+	0.0896008i
$941$	15.9804	+	33.1836i	0.520945	+	1.08175i	0.981026	+	0.193877i	$0.0621061\pi$
$941$	15.9804	+	33.1836i	0.520945	+	1.08175i	−0.460081	+	0.887877i	$0.652180\pi$
$942$	−5.79981	−	12.7332i	−0.188968	−	0.414870i
$943$	17.3432	+	21.7476i	0.564771	+	0.708200i
$944$	−19.9633	−	17.9531i	−0.649750	−	0.584324i
$945$	−4.17487	+	0.624779i	−0.135809	+	0.0203241i
$946$	4.85508	−	0.751121i	0.157852	−	0.0244211i
$947$	−21.3095	+	4.86375i	−0.692466	+	0.158051i	−0.554249	−	0.832351i	$-0.686994\pi$
$947$	−21.3095	+	4.86375i	−0.692466	+	0.158051i	−0.138217	+	0.990402i	$0.544137\pi$
$948$	18.5457	+	28.2514i	0.602337	+	0.917562i
$949$	29.4214	−	61.0942i	0.955059	−	1.98320i
$950$	10.4604	+	5.98513i	0.339379	+	0.194183i
$951$	2.18821	+	2.48130i	0.0709577	+	0.0804615i
$952$	−33.9109	+	0.395930i	−1.09906	+	0.0128322i
$953$	−50.5987	+	11.5488i	−1.63905	+	0.374103i	−0.940055	−	0.341022i	$-0.889227\pi$
$953$	−50.5987	+	11.5488i	−1.63905	+	0.374103i	−0.698997	+	0.715125i	$0.746370\pi$
$954$	−9.29541	+	20.7774i	−0.300950	+	0.672693i
$955$	−0.834192	+	1.04604i	−0.0269938	+	0.0338492i
$956$	23.2777	+	15.6065i	0.752856	+	0.504750i
$957$	−49.4141	+	17.6455i	−1.59733	+	0.570398i
$958$	4.91205	+	1.49426i	0.158701	+	0.0482772i
$959$	−30.9601	−	24.6898i	−0.999753	−	0.797276i
$960$	1.47790	−	3.74432i	0.0476989	−	0.120848i
$961$	−9.56577	−	41.9104i	−0.308573	−	1.35195i
$962$	0.325114	−	0.223517i	0.0104821	−	0.00720648i
$963$	−40.6570	−	41.7420i	−1.31015	−	1.34512i
$964$	−16.4495	+	15.5029i	−0.529803	+	0.499315i
$965$	−2.55589	−	1.23085i	−0.0822771	−	0.0396226i
$966$	−19.1668	−	15.9675i	−0.616681	−	0.513746i
$967$	−6.59879	−	28.9112i	−0.212203	−	0.929721i	−0.963066	−	0.269264i	$-0.913220\pi$
$967$	−6.59879	−	28.9112i	−0.212203	−	0.929721i	0.750864	−	0.660457i	$-0.229637\pi$
$968$	−24.7198	+	52.9025i	−0.794526	+	1.70035i
$969$	12.8587	−	0.637240i	0.413080	−	0.0204711i
$970$	0.0106997	+	0.0691605i	0.000343546	+	0.00222061i
$971$	43.2436	−	34.4856i	1.38775	−	1.10670i	0.406570	−	0.913620i	$-0.366725\pi$
$971$	43.2436	−	34.4856i	1.38775	−	1.10670i	0.981184	−	0.193077i	$-0.0618467\pi$
$972$	10.1076	+	29.4930i	0.324200	+	0.945988i
$973$	12.7178	−	6.12457i	0.407714	−	0.196345i
$974$	42.6817	+	12.9839i	1.36761	+	0.416030i
$975$	−38.9412	+	21.1886i	−1.24712	+	0.678578i
$976$	16.9431	+	24.0383i	0.542334	+	0.769446i
$977$	−17.3523	+	36.0325i	−0.555151	+	1.15278i	0.414897	+	0.909868i	$0.363818\pi$
$977$	−17.3523	+	36.0325i	−0.555151	+	1.15278i	−0.970048	+	0.242914i	$0.921897\pi$
$978$	15.8142	−	18.9828i	0.505682	−	0.607002i
$979$	24.1655	+	5.51561i	0.772332	+	0.176280i
$980$	−0.474914	+	0.0393094i	−0.0151706	+	0.00125569i
$981$	11.2763	−	17.4324i	0.360026	−	0.556574i
$982$	0.392038	−	5.51954i	0.0125104	−	0.176136i
$983$	48.1263	+	10.9845i	1.53499	+	0.350351i	0.904714	−	0.426020i	$-0.140085\pi$
$983$	48.1263	+	10.9845i	1.53499	+	0.350351i	0.630276	+	0.776371i	$0.282942\pi$
$984$	−2.28824	−	37.3479i	−0.0729463	−	1.19061i
$985$	−1.37349			−0.0437632
$986$	20.3120	+	25.5670i	0.646867	+	0.814221i
$987$	−41.0737	+	2.03550i	−1.30739	+	0.0647906i
$988$	17.2097	−	5.45555i	0.547515	−	0.173564i
$989$	0.500450	−	2.19262i	0.0159134	−	0.0697211i
$990$	6.93074	−	0.194980i	0.220273	−	0.00619686i
$991$	−48.8365	−	38.9458i	−1.55134	−	1.23715i	−0.853785	−	0.520626i	$-0.825699\pi$
$991$	−48.8365	−	38.9458i	−1.55134	−	1.23715i	−0.697558	−	0.716529i	$-0.745730\pi$
$992$	−33.7837	−	35.0183i	−1.07263	−	1.11183i
$993$	4.77703	−	27.0366i	0.151595	−	0.857980i
$994$	12.8681	+	11.8470i	0.408152	+	0.375764i
$995$	−3.01148	−	1.45025i	−0.0954705	−	0.0459762i
$996$	−11.6990	+	35.6971i	−0.370697	+	1.13111i
$997$	−4.66349	−	9.68384i	−0.147694	−	0.306690i	0.813976	−	0.580898i	$-0.197299\pi$
$997$	−4.66349	−	9.68384i	−0.147694	−	0.306690i	−0.961670	+	0.274208i	$0.911584\pi$
$998$	−22.9715	−	6.98799i	−0.727151	−	0.221201i
$999$	−0.156587	−	0.230189i	−0.00495418	−	0.00728286i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	348.2.t.a.35.19	yes	336
3.2	odd	2	inner	348.2.t.a.35.38	yes	336
4.3	odd	2	inner	348.2.t.a.35.51	yes	336
12.11	even	2	inner	348.2.t.a.35.6	✓	336
29.5	even	14	inner	348.2.t.a.179.6	yes	336
87.5	odd	14	inner	348.2.t.a.179.51	yes	336
116.63	odd	14	inner	348.2.t.a.179.38	yes	336
348.179	even	14	inner	348.2.t.a.179.19	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
348.2.t.a.35.6	✓	336	12.11	even	2	inner
348.2.t.a.35.19	yes	336	1.1	even	1	trivial
348.2.t.a.35.38	yes	336	3.2	odd	2	inner
348.2.t.a.35.51	yes	336	4.3	odd	2	inner
348.2.t.a.179.6	yes	336	29.5	even	14	inner
348.2.t.a.179.19	yes	336	348.179	even	14	inner
348.2.t.a.179.38	yes	336	116.63	odd	14	inner
348.2.t.a.179.51	yes	336	87.5	odd	14	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:	\( N \)	\(=\)	\( 348 = 2^{2} \cdot 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	348.t (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.801196 - 1.16537i) q^{2} +(0.301364 - 1.70563i) q^{3} +(-0.716169 + 1.86738i) q^{4} +(0.227131 + 0.181131i) q^{5} +(-2.22914 + 1.01535i) q^{6} +(2.72634 + 0.622270i) q^{7} +(2.74998 - 0.661535i) q^{8} +(-2.81836 - 1.02803i) q^{9} +O(q^{10})\)	\(q+(-0.801196 - 1.16537i) q^{2} +(0.301364 - 1.70563i) q^{3} +(-0.716169 + 1.86738i) q^{4} +(0.227131 + 0.181131i) q^{5} +(-2.22914 + 1.01535i) q^{6} +(2.72634 + 0.622270i) q^{7} +(2.74998 - 0.661535i) q^{8} +(-2.81836 - 1.02803i) q^{9} +(0.0291078 - 0.409812i) q^{10} +(-2.44077 - 5.06830i) q^{11} +(2.96923 + 1.78428i) q^{12} +(4.69132 - 2.25922i) q^{13} +(-1.45916 - 3.67576i) q^{14} +(0.377391 - 0.332815i) q^{15} +(-2.97420 - 2.67472i) q^{16} -4.28762 q^{17} +(1.06002 + 4.10808i) q^{18} +(-0.385765 - 1.69015i) q^{19} +(-0.500903 + 0.294418i) q^{20} +(1.88299 - 4.46261i) q^{21} +(-3.95091 + 6.90510i) q^{22} +(2.27067 + 2.84733i) q^{23} +(-0.299590 - 4.88981i) q^{24} +(-1.09382 - 4.79236i) q^{25} +(-6.39149 - 3.65704i) q^{26} +(-2.60280 + 4.49727i) q^{27} +(-3.11454 + 4.64546i) q^{28} +(5.37233 - 0.371628i) q^{29} +(-0.690216 - 0.173150i) q^{30} +(-5.36303 + 6.72503i) q^{31} +(-0.734114 + 5.60902i) q^{32} +(-9.38022 + 2.63564i) q^{33} +(3.43522 + 4.99666i) q^{34} +(0.506524 + 0.635161i) q^{35} +(3.93815 - 4.52670i) q^{36} +(-0.0232466 + 0.0482721i) q^{37} +(-1.66057 + 1.80370i) q^{38} +(-2.43960 - 8.68251i) q^{39} +(0.744428 + 0.347850i) q^{40} +7.63789 q^{41} +(-6.70923 + 1.38105i) q^{42} +(-0.385030 - 0.482812i) q^{43} +(11.2124 - 0.928070i) q^{44} +(-0.453927 - 0.743989i) q^{45} +(1.49894 - 4.92744i) q^{46} +(-3.68384 - 7.64958i) q^{47} +(-5.45840 + 4.26683i) q^{48} +(0.738951 + 0.355860i) q^{49} +(-4.70850 + 5.11433i) q^{50} +(-1.29213 + 7.31310i) q^{51} +(0.859039 + 10.3784i) q^{52} +(4.19455 + 3.34505i) q^{53} +(7.32633 - 0.569975i) q^{54} +(0.363652 - 1.59326i) q^{55} +(7.90904 - 0.0923426i) q^{56} +(-2.99903 + 0.148623i) q^{57} +(-4.73737 - 5.96300i) q^{58} +6.71215 q^{59} +(0.351215 + 0.943084i) q^{60} +(-7.16798 - 1.63604i) q^{61} +(12.1340 + 0.861843i) q^{62} +(-7.04410 - 4.55655i) q^{63} +(7.12474 - 3.63841i) q^{64} +(1.47476 + 0.336603i) q^{65} +(10.5869 + 8.81975i) q^{66} +(-0.705540 + 1.46507i) q^{67} +(3.07066 - 8.00660i) q^{68} +(5.54080 - 3.01485i) q^{69} +(0.334372 - 1.09918i) q^{70} +(-3.98478 + 1.91897i) q^{71} +(-8.43050 - 0.962624i) q^{72} +(10.1816 - 8.11959i) q^{73} +(0.0748800 - 0.0115845i) q^{74} +(-8.50364 + 0.421416i) q^{75} +(3.43242 + 0.490063i) q^{76} +(-3.50052 - 15.3368i) q^{77} +(-8.16373 + 9.79943i) q^{78} +(8.78958 + 4.23284i) q^{79} +(-0.191059 - 1.14623i) q^{80} +(6.88630 + 5.79473i) q^{81} +(-6.11945 - 8.90096i) q^{82} +(2.41305 + 10.5723i) q^{83} +(6.98484 + 6.71223i) q^{84} +(-0.973849 - 0.776618i) q^{85} +(-0.254170 + 0.835529i) q^{86} +(0.985167 - 9.27521i) q^{87} +(-10.0649 - 12.3231i) q^{88} +(-2.74726 + 3.44495i) q^{89} +(-0.503336 + 1.12507i) q^{90} +(14.1960 - 3.24014i) q^{91} +(-6.94323 + 2.20103i) q^{92} +(9.85420 + 11.1740i) q^{93} +(-5.96310 + 10.4219i) q^{94} +(0.218518 - 0.453758i) q^{95} +(9.34568 + 2.94248i) q^{96} +(-0.166069 + 0.0379042i) q^{97} +(-0.177336 - 1.14626i) q^{98} +(1.66857 + 16.7935i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9}+O(q^{10}) \) 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9	\( 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9} - 14 q^{10} - 20 q^{13} - 26 q^{16} - 56 q^{18} - 14 q^{21} - 40 q^{22} + 3 q^{24} + 40 q^{25} - 36 q^{28} - 6 q^{30} - 22 q^{33} - 8 q^{34} + 9 q^{36} - 28 q^{37} - 14 q^{40} - 74 q^{42} - 22 q^{45} + 14 q^{48} + 4 q^{49} - 4 q^{52} - 31 q^{54} - 12 q^{57} - 106 q^{58} - 42 q^{60} - 28 q^{61} - 94 q^{64} - 7 q^{66} - 14 q^{69} + 70 q^{72} - 28 q^{73} - 84 q^{76} - 9 q^{78} - 50 q^{81} - 46 q^{82} - 35 q^{84} - 168 q^{85} - 60 q^{88} + 119 q^{90} + 122 q^{93} + 36 q^{94} + 2 q^{96} - 28 q^{97}+O(q^{100}) \) 336 * q - 10 * q^4 - 3 * q^6 - 10 * q^9 - 14 * q^10 - 20 * q^13 - 26 * q^16 - 56 * q^18 - 14 * q^21 - 40 * q^22 + 3 * q^24 + 40 * q^25 - 36 * q^28 - 6 * q^30 - 22 * q^33 - 8 * q^34 + 9 * q^36 - 28 * q^37 - 14 * q^40 - 74 * q^42 - 22 * q^45 + 14 * q^48 + 4 * q^49 - 4 * q^52 - 31 * q^54 - 12 * q^57 - 106 * q^58 - 42 * q^60 - 28 * q^61 - 94 * q^64 - 7 * q^66 - 14 * q^69 + 70 * q^72 - 28 * q^73 - 84 * q^76 - 9 * q^78 - 50 * q^81 - 46 * q^82 - 35 * q^84 - 168 * q^85 - 60 * q^88 + 119 * q^90 + 122 * q^93 + 36 * q^94 + 2 * q^96 - 28 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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