LMFDB - Embedded newform 804.2.bd.a.35.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(23,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 33, 28]))

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

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

chi := DirichletCharacter("804.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.bd (of order $66$, degree $20$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$2640$
Relative dimension:	$132$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			35.6
Character	$\chi$	$=$	804.35
Dual form			804.2.bd.a.23.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39917 - 0.205706i) q^{2} +(-0.594255 - 1.62692i) q^{3} +(1.91537 + 0.575637i) q^{4} +(-1.29680 - 0.592230i) q^{5} +(0.496799 + 2.39858i) q^{6} +(3.42631 - 3.59341i) q^{7} +(-2.56152 - 1.19942i) q^{8} +(-2.29372 + 1.93361i) q^{9} +O(q^{10})$	\(q+(-1.39917 - 0.205706i) q^{2} +(-0.594255 - 1.62692i) q^{3} +(1.91537 + 0.575637i) q^{4} +(-1.29680 - 0.592230i) q^{5} +(0.496799 + 2.39858i) q^{6} +(3.42631 - 3.59341i) q^{7} +(-2.56152 - 1.19942i) q^{8} +(-2.29372 + 1.93361i) q^{9} +(1.69263 + 1.09539i) q^{10} +(3.18208 - 0.303852i) q^{11} +(-0.201704 - 3.45822i) q^{12} +(6.15441 - 1.18617i) q^{13} +(-5.53319 + 4.32299i) q^{14} +(-0.192878 + 2.46173i) q^{15} +(3.33728 + 2.20512i) q^{16} +(0.341061 + 0.661567i) q^{17} +(3.60707 - 2.23362i) q^{18} +(0.192852 + 0.202257i) q^{19} +(-2.14295 - 1.88083i) q^{20} +(-7.88228 - 3.43892i) q^{21} +(-4.51479 - 0.229433i) q^{22} +(6.89104 + 2.75876i) q^{23} +(-0.429160 + 4.88015i) q^{24} +(-1.94334 - 2.24274i) q^{25} +(-8.85509 + 0.393650i) q^{26} +(4.50888 + 2.58264i) q^{27} +(8.63115 - 4.91040i) q^{28} +(5.39619 - 3.11549i) q^{29} +(0.776262 - 3.40470i) q^{30} +(-0.554866 + 2.87892i) q^{31} +(-4.21583 - 3.77184i) q^{32} +(-2.38531 - 4.99642i) q^{33} +(-0.341115 - 0.995805i) q^{34} +(-6.57137 + 2.63078i) q^{35} +(-5.50638 + 2.38322i) q^{36} +(-2.95598 + 5.11991i) q^{37} +(-0.228228 - 0.322664i) q^{38} +(-5.58709 - 9.30784i) q^{39} +(2.61146 + 3.07242i) q^{40} +(2.97048 + 0.141502i) q^{41} +(10.3213 + 6.43308i) q^{42} +(-4.43005 + 6.89330i) q^{43} +(6.26977 + 1.24974i) q^{44} +(4.11964 - 1.14910i) q^{45} +(-9.07427 - 5.27751i) q^{46} +(6.45258 - 5.07437i) q^{47} +(1.60435 - 6.73989i) q^{48} +(-0.839925 - 17.6322i) q^{49} +(2.25773 + 3.53774i) q^{50} +(0.873637 - 0.948018i) q^{51} +(12.4708 + 1.27076i) q^{52} +(0.671456 + 1.04481i) q^{53} +(-5.77743 - 4.54106i) q^{54} +(-4.30648 - 1.49049i) q^{55} +(-13.0866 + 5.09501i) q^{56} +(0.214453 - 0.433947i) q^{57} +(-8.19108 + 3.24908i) q^{58} +(-1.33605 + 1.54189i) q^{59} +(-1.78649 + 4.60409i) q^{60} +(-5.19752 - 0.496303i) q^{61} +(1.36856 - 3.91396i) q^{62} +(-0.910752 + 14.8674i) q^{63} +(5.12278 + 6.14468i) q^{64} +(-8.68354 - 2.10660i) q^{65} +(2.30967 + 7.48153i) q^{66} +(7.16049 + 3.96578i) q^{67} +(0.272436 + 1.46347i) q^{68} +(0.393233 - 12.8506i) q^{69} +(9.73565 - 2.32914i) q^{70} +(-10.0208 - 5.16610i) q^{71} +(8.19463 - 2.20184i) q^{72} +(-16.2714 - 1.55373i) q^{73} +(5.18913 - 6.55557i) q^{74} +(-2.49391 + 4.49442i) q^{75} +(0.252956 + 0.498410i) q^{76} +(9.81093 - 12.4756i) q^{77} +(5.90262 + 14.1726i) q^{78} +(-2.03399 - 0.703971i) q^{79} +(-3.02186 - 4.83604i) q^{80} +(1.52232 - 8.87032i) q^{81} +(-4.12711 - 0.809032i) q^{82} +(-3.86820 - 5.43213i) q^{83} +(-13.1179 - 11.1241i) q^{84} +(-0.0504897 - 1.05991i) q^{85} +(7.61640 - 8.73362i) q^{86} +(-8.27537 - 6.92776i) q^{87} +(-8.51542 - 3.03833i) q^{88} +(-15.2669 - 2.19505i) q^{89} +(-6.00047 + 0.760350i) q^{90} +(16.8245 - 26.1795i) q^{91} +(11.6109 + 9.25078i) q^{92} +(5.01349 - 0.808090i) q^{93} +(-10.0721 + 5.77258i) q^{94} +(-0.130308 - 0.376500i) q^{95} +(-3.63119 + 9.10024i) q^{96} +(2.13540 - 3.69862i) q^{97} +(-2.45185 + 24.8433i) q^{98} +(-6.71128 + 6.84985i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9}+O(q^{10}) $ 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9	$ 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9} - 46 q^{10} - 24 q^{12} - 88 q^{13} - 26 q^{16} - 23 q^{18} - 128 q^{22} - 22 q^{24} + 160 q^{25} + 44 q^{28} - 18 q^{30} - 44 q^{33} - 6 q^{34} - 35 q^{36} - 48 q^{37} - 92 q^{40} - 10 q^{42} + 40 q^{45} + 46 q^{46} - 11 q^{48} - 216 q^{49} - 76 q^{52} + 129 q^{54} - 42 q^{57} - 56 q^{58} - 90 q^{60} - 80 q^{61} - 48 q^{64} - 74 q^{66} - 4 q^{69} + 96 q^{70} - 20 q^{72} - 216 q^{73} + 76 q^{76} - 66 q^{78} - 16 q^{81} + 20 q^{82} - 55 q^{84} - 104 q^{85} - 30 q^{88} - 64 q^{90} - 192 q^{93} - 32 q^{94} - 205 q^{96} - 64 q^{97}+O(q^{100}) $ 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9 - 46 * q^10 - 24 * q^12 - 88 * q^13 - 26 * q^16 - 23 * q^18 - 128 * q^22 - 22 * q^24 + 160 * q^25 + 44 * q^28 - 18 * q^30 - 44 * q^33 - 6 * q^34 - 35 * q^36 - 48 * q^37 - 92 * q^40 - 10 * q^42 + 40 * q^45 + 46 * q^46 - 11 * q^48 - 216 * q^49 - 76 * q^52 + 129 * q^54 - 42 * q^57 - 56 * q^58 - 90 * q^60 - 80 * q^61 - 48 * q^64 - 74 * q^66 - 4 * q^69 + 96 * q^70 - 20 * q^72 - 216 * q^73 + 76 * q^76 - 66 * q^78 - 16 * q^81 + 20 * q^82 - 55 * q^84 - 104 * q^85 - 30 * q^88 - 64 * q^90 - 192 * q^93 - 32 * q^94 - 205 * q^96 - 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{19}{33}\right)$	$-1$

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 $

$2$	−1.39917	−	0.205706i	−0.989365	−	0.145456i
$2$	−1.39917	−	0.205706i	−0.989365	−	0.145456i
$3$	−0.594255	−	1.62692i	−0.343093	−	0.939301i
$3$	−0.594255	−	1.62692i	−0.343093	−	0.939301i
$4$	1.91537	+	0.575637i	0.957685	+	0.287819i
$5$	−1.29680	−	0.592230i	−0.579948	−	0.264853i	0.103768	−	0.994602i	$-0.466910\pi$
$5$	−1.29680	−	0.592230i	−0.579948	−	0.264853i	−0.683716	+	0.729748i	$0.739637\pi$
$6$	0.496799	+	2.39858i	0.202817	+	0.979217i
$7$	3.42631	−	3.59341i	1.29502	−	1.35818i	0.397257	−	0.917707i	$-0.369962\pi$
$7$	3.42631	−	3.59341i	1.29502	−	1.35818i	0.897765	−	0.440474i	$-0.145190\pi$
$8$	−2.56152	−	1.19942i	−0.905635	−	0.424059i
$9$	−2.29372	+	1.93361i	−0.764574	+	0.644536i
$10$	1.69263	+	1.09539i	0.535255	+	0.346393i
$11$	3.18208	−	0.303852i	0.959434	−	0.0916148i	0.396426	−	0.918067i	$-0.370250\pi$
$11$	3.18208	−	0.303852i	0.959434	−	0.0916148i	0.563008	+	0.826452i	$0.309644\pi$
$12$	−0.201704	−	3.45822i	−0.0582269	−	0.998303i
$13$	6.15441	−	1.18617i	1.70693	−	0.328983i	0.759876	−	0.650068i	$-0.225259\pi$
$13$	6.15441	−	1.18617i	1.70693	−	0.328983i	0.947051	+	0.321084i	$0.104047\pi$
$14$	−5.53319	+	4.32299i	−1.47881	+	1.15537i
$15$	−0.192878	+	2.46173i	−0.0498008	+	0.635615i
$16$	3.33728	+	2.20512i	0.834321	+	0.551279i
$17$	0.341061	+	0.661567i	0.0827195	+	0.160454i	0.926567	−	0.376129i	$-0.122745\pi$
$17$	0.341061	+	0.661567i	0.0827195	+	0.160454i	−0.843848	+	0.536583i	$0.819715\pi$
$18$	3.60707	−	2.23362i	0.850194	−	0.526469i
$19$	0.192852	+	0.202257i	0.0442433	+	0.0464010i	0.745484	−	0.666524i	$-0.232219\pi$
$19$	0.192852	+	0.202257i	0.0442433	+	0.0464010i	−0.701240	+	0.712925i	$0.747370\pi$
$20$	−2.14295	−	1.88083i	−0.479177	−	0.420566i
$21$	−7.88228	−	3.43892i	−1.72005	−	0.750434i
$22$	−4.51479	−	0.229433i	−0.962556	−	0.0489153i
$23$	6.89104	+	2.75876i	1.43688	+	0.575241i	0.953829	−	0.300350i	$-0.0971036\pi$
$23$	6.89104	+	2.75876i	1.43688	+	0.575241i	0.483053	+	0.875591i	$0.339528\pi$
$24$	−0.429160	+	4.88015i	−0.0876019	+	0.996156i
$25$	−1.94334	−	2.24274i	−0.388669	−	0.448548i
$26$	−8.85509	+	0.393650i	−1.73663	+	0.0772010i
$27$	4.50888	+	2.58264i	0.867734	+	0.497029i
$28$	8.63115	−	4.91040i	1.63113	−	0.927978i
$29$	5.39619	−	3.11549i	1.00205	−	0.578533i	0.0931942	−	0.995648i	$-0.470292\pi$
$29$	5.39619	−	3.11549i	1.00205	−	0.578533i	0.908854	+	0.417115i	$0.136959\pi$
$30$	0.776262	−	3.40470i	0.141725	−	0.621611i
$31$	−0.554866	+	2.87892i	−0.0996568	+	0.517069i	0.897454	+	0.441108i	$0.145414\pi$
$31$	−0.554866	+	2.87892i	−0.0996568	+	0.517069i	−0.997111	+	0.0759605i	$0.975798\pi$
$32$	−4.21583	−	3.77184i	−0.745260	−	0.666773i
$33$	−2.38531	−	4.99642i	−0.415229	−	0.869765i
$34$	−0.341115	−	0.995805i	−0.0585008	−	0.170779i
$35$	−6.57137	+	2.63078i	−1.11076	+	0.444683i
$36$	−5.50638	+	2.38322i	−0.917730	+	0.397204i
$37$	−2.95598	+	5.11991i	−0.485960	+	0.841708i	−0.999870	−	0.0161365i	$-0.994863\pi$
$37$	−2.95598	+	5.11991i	−0.485960	+	0.841708i	0.513910	+	0.857844i	$0.328197\pi$
$38$	−0.228228	−	0.322664i	−0.0370234	−	0.0523430i
$39$	−5.58709	−	9.30784i	−0.894650	−	1.49045i
$40$	2.61146	+	3.07242i	0.412907	+	0.485792i
$41$	2.97048	+	0.141502i	0.463912	+	0.0220988i	0.278237	−	0.960512i	$-0.410250\pi$
$41$	2.97048	+	0.141502i	0.463912	+	0.0220988i	0.185675	+	0.982611i	$0.440553\pi$
$42$	10.3213	+	6.43308i	1.59261	+	0.992646i
$43$	−4.43005	+	6.89330i	−0.675577	+	1.05122i	0.319055	+	0.947736i	$0.396635\pi$
$43$	−4.43005	+	6.89330i	−0.675577	+	1.05122i	−0.994631	+	0.103482i	$0.967002\pi$
$44$	6.26977	+	1.24974i	0.945204	+	0.188405i
$45$	4.11964	−	1.14910i	0.614120	−	0.171297i
$46$	−9.07427	−	5.27751i	−1.33793	−	0.778126i
$47$	6.45258	−	5.07437i	0.941206	−	0.740172i	−0.0245303	−	0.999699i	$-0.507809\pi$
$47$	6.45258	−	5.07437i	0.941206	−	0.740172i	0.965736	+	0.259527i	$0.0835666\pi$
$48$	1.60435	−	6.73989i	0.231567	−	0.972819i
$49$	−0.839925	−	17.6322i	−0.119989	−	2.51888i
$50$	2.25773	+	3.53774i	0.319291	+	0.500311i
$51$	0.873637	−	0.948018i	0.122334	−	0.132749i
$52$	12.4708	+	1.27076i	1.72939	+	0.176223i
$53$	0.671456	+	1.04481i	0.0922315	+	0.143515i	0.884303	−	0.466913i	$-0.154634\pi$
$53$	0.671456	+	1.04481i	0.0922315	+	0.143515i	−0.792072	+	0.610428i	$0.790997\pi$
$54$	−5.77743	−	4.54106i	−0.786209	−	0.617960i
$55$	−4.30648	−	1.49049i	−0.580686	−	0.200977i
$56$	−13.0866	+	5.09501i	−1.74877	+	0.680850i
$57$	0.214453	−	0.433947i	0.0284050	−	0.0574776i
$58$	−8.19108	+	3.24908i	−1.07554	+	0.426625i
$59$	−1.33605	+	1.54189i	−0.173939	+	0.200736i	−0.836025	−	0.548692i	$-0.815126\pi$
$59$	−1.33605	+	1.54189i	−0.173939	+	0.200736i	0.662086	+	0.749428i	$0.269671\pi$
$60$	−1.78649	+	4.60409i	−0.230635	+	0.594385i
$61$	−5.19752	−	0.496303i	−0.665474	−	0.0635451i	−0.243148	−	0.969989i	$-0.578180\pi$
$61$	−5.19752	−	0.496303i	−0.665474	−	0.0635451i	−0.422326	+	0.906444i	$0.638786\pi$
$62$	1.36856	−	3.91396i	0.173808	−	0.497074i
$63$	−0.910752	+	14.8674i	−0.114744	+	1.87312i
$64$	5.12278	+	6.14468i	0.640348	+	0.768085i
$65$	−8.68354	−	2.10660i	−1.07706	−	0.261292i
$66$	2.30967	+	7.48153i	0.284300	+	0.920913i
$67$	7.16049	+	3.96578i	0.874793	+	0.484497i
$67$	7.16049	+	3.96578i	0.874793	+	0.484497i
$68$	0.272436	+	1.46347i	0.0330377	+	0.177472i
$69$	0.393233	−	12.8506i	0.0473397	−	1.54703i
$70$	9.73565	−	2.32914i	1.16363	−	0.278386i
$71$	−10.0208	−	5.16610i	−1.18926	−	0.613104i	−0.254044	−	0.967193i	$-0.581761\pi$
$71$	−10.0208	−	5.16610i	−1.18926	−	0.613104i	−0.935212	+	0.354089i	$0.884791\pi$
$72$	8.19463	−	2.20184i	0.965746	−	0.259490i
$73$	−16.2714	−	1.55373i	−1.90442	−	0.181850i	−0.924493	−	0.381198i	$-0.875512\pi$
$73$	−16.2714	−	1.55373i	−1.90442	−	0.181850i	−0.979929	+	0.199348i	$0.936118\pi$
$74$	5.18913	−	6.55557i	0.603224	−	0.762070i
$75$	−2.49391	+	4.49442i	−0.287972	+	0.518971i
$76$	0.252956	+	0.498410i	0.0290160	+	0.0571716i
$77$	9.81093	−	12.4756i	1.11806	−	1.42173i
$78$	5.90262	+	14.1726i	0.668340	+	1.60473i
$79$	−2.03399	−	0.703971i	−0.228842	−	0.0792029i	0.210241	−	0.977650i	$-0.432575\pi$
$79$	−2.03399	−	0.703971i	−0.228842	−	0.0792029i	−0.439082	+	0.898447i	$0.644696\pi$
$80$	−3.02186	−	4.83604i	−0.337854	−	0.540686i
$81$	1.52232	−	8.87032i	0.169146	−	0.985591i
$82$	−4.12711	−	0.809032i	−0.455763	−	0.0893427i
$83$	−3.86820	−	5.43213i	−0.424590	−	0.596253i	0.545765	−	0.837939i	$-0.316239\pi$
$83$	−3.86820	−	5.43213i	−0.424590	−	0.596253i	−0.970355	+	0.241685i	$0.922300\pi$
$84$	−13.1179	−	11.1241i	−1.43128	−	1.21374i
$85$	−0.0504897	−	1.05991i	−0.00547637	−	0.114963i
$86$	7.61640	−	8.73362i	0.821298	−	0.941771i
$87$	−8.27537	−	6.92776i	−0.887212	−	0.742734i
$88$	−8.51542	−	3.03833i	−0.907747	−	0.323887i
$89$	−15.2669	−	2.19505i	−1.61829	−	0.232675i	−0.727176	−	0.686451i	$-0.759168\pi$
$89$	−15.2669	−	2.19505i	−1.61829	−	0.232675i	−0.891116	+	0.453776i	$0.850077\pi$
$90$	−6.00047	+	0.760350i	−0.632505	+	0.0801479i
$91$	16.8245	−	26.1795i	1.76369	−	2.74436i
$92$	11.6109	+	9.25078i	1.21052	+	0.964461i
$93$	5.01349	−	0.808090i	0.519875	−	0.0837950i
$94$	−10.0721	+	5.77258i	−1.03886	+	0.595396i
$95$	−0.130308	−	0.376500i	−0.0133693	−	0.0386281i
$96$	−3.63119	+	9.10024i	−0.370607	+	0.928790i
$97$	2.13540	−	3.69862i	0.216817	−	0.375538i	−0.737016	−	0.675875i	$-0.763766\pi$
$97$	2.13540	−	3.69862i	0.216817	−	0.375538i	0.953833	+	0.300337i	$0.0970992\pi$
$98$	−2.45185	+	24.8433i	−0.247674	+	2.50955i
$99$	−6.71128	+	6.84985i	−0.674509	+	0.688436i
$100$	−2.43122	−	5.41433i	−0.243122	−	0.541433i
$101$	−10.5810	+	2.56693i	−1.05285	+	0.255419i	−0.724600	−	0.689170i	$-0.757975\pi$
$101$	−10.5810	+	2.56693i	−1.05285	+	0.255419i	−0.328254	+	0.944590i	$0.606460\pi$
$102$	−1.41738	+	1.14673i	−0.140342	+	0.113543i
$103$	−0.0926553	+	0.480741i	−0.00912960	+	0.0473688i	−0.986208	−	0.165512i	$-0.947072\pi$
$103$	−0.0926553	+	0.480741i	−0.00912960	+	0.0473688i	0.977078	+	0.212881i	$0.0682845\pi$
$104$	−17.1874	−	4.34334i	−1.68536	−	0.425899i
$105$	8.18513	+	9.12772i	0.798787	+	0.890774i
$106$	−0.724559	−	1.59999i	−0.0703754	−	0.155404i
$107$	2.89170	+	6.33194i	0.279551	+	0.612131i	0.996370	−	0.0851279i	$-0.0271299\pi$
$107$	2.89170	+	6.33194i	0.279551	+	0.612131i	−0.716819	+	0.697259i	$0.754403\pi$
$108$	7.14950	+	7.54219i	0.687961	+	0.725747i
$109$	1.11902	+	1.29142i	0.107183	+	0.123696i	0.806806	−	0.590816i	$-0.201194\pi$
$109$	1.11902	+	1.29142i	0.107183	+	0.123696i	−0.699623	+	0.714512i	$0.746649\pi$
$110$	5.71891	+	2.97132i	0.545277	+	0.283304i
$111$	10.0863	+	1.76660i	0.957347	+	0.167679i
$112$	19.3584	−	4.43681i	1.82920	−	0.419239i
$113$	9.43433	+	6.71815i	0.887507	+	0.631991i	0.930182	−	0.367098i	$-0.119649\pi$
$113$	9.43433	+	6.71815i	0.887507	+	0.631991i	−0.0426753	+	0.999089i	$0.513588\pi$
$114$	−0.389322	+	0.563052i	−0.0364633	+	0.0527347i
$115$	−7.30250	−	7.65865i	−0.680962	−	0.714172i
$116$	12.1291	−	2.86107i	1.12616	−	0.265644i
$117$	−11.8229	+	14.6210i	−1.09303	+	1.35171i
$118$	2.18654	−	1.88253i	0.201288	−	0.173301i
$119$	3.54586	+	1.04116i	0.325049	+	0.0954429i
$120$	3.44670	−	6.07442i	0.314640	−	0.554516i
$121$	−0.767892	+	0.147999i	−0.0698083	+	0.0134545i
$122$	7.17014	+	1.76358i	0.649154	+	0.159667i
$123$	−1.53501	−	4.91682i	−0.138408	−	0.443335i
$124$	−2.71998	+	5.19479i	−0.244262	+	0.466506i
$125$	3.20015	+	10.8987i	0.286230	+	0.974811i
$126$	4.33262	−	20.6147i	0.385981	−	1.83651i
$127$	11.7284	−	12.3004i	1.04073	−	1.09148i	0.0450133	−	0.998986i	$-0.485667\pi$
$127$	11.7284	−	12.3004i	1.04073	−	1.09148i	0.995713	−	0.0924960i	$-0.0294845\pi$
$128$	−5.90366	−	9.65126i	−0.521815	−	0.853059i
$129$	13.8474	+	3.11095i	1.21920	+	0.273904i
$130$	11.7164	+	4.73376i	1.02760	+	0.415178i
$131$	1.98674	+	13.8181i	0.173582	+	1.20729i	0.871239	+	0.490859i	$0.163317\pi$
$131$	1.98674	+	13.8181i	0.173582	+	1.20729i	−0.697657	+	0.716432i	$0.745774\pi$
$132$	−1.69263	−	10.9431i	−0.147324	−	0.952472i
$133$	1.38756			0.120317
$134$	−9.20298	−	7.02177i	−0.795016	−	0.606588i
$135$	−4.31761	−	6.01946i	−0.371600	−	0.518073i
$136$	−0.0801397	−	2.10369i	−0.00687192	−	0.180390i
$137$	−3.75621	+	0.540062i	−0.320915	+	0.0461406i	−0.300890	−	0.953659i	$-0.597284\pi$
$137$	−3.75621	+	0.540062i	−0.320915	+	0.0461406i	−0.0200249	+	0.999799i	$0.506375\pi$
$138$	−3.19364	+	17.8993i	−0.271861	+	1.52369i
$139$	3.90056	+	1.78133i	0.330841	+	0.151090i	0.573909	−	0.818919i	$-0.305426\pi$
$139$	3.90056	+	1.78133i	0.330841	+	0.151090i	−0.243067	+	0.970009i	$0.578154\pi$
$140$	−14.1010	+	1.25619i	−1.19175	+	0.106167i
$141$	−12.0901	−	7.48235i	−1.01817	−	0.630127i
$142$	12.9582	+	9.28962i	1.08743	+	0.779568i
$143$	19.2234	−	5.64451i	1.60754	−	0.472018i
$144$	−11.9186	+	1.39507i	−0.993219	+	0.116256i
$145$	−8.84288	+	0.844393i	−0.734361	+	0.0701230i
$146$	22.4469	+	5.52106i	1.85772	+	0.456926i
$147$	−28.1870	+	11.8445i	−2.32482	+	0.976918i
$148$	−8.60901	+	8.10495i	−0.707656	+	0.666222i
$149$	−2.51684	+	8.57156i	−0.206187	+	0.702209i	0.789852	+	0.613297i	$0.210157\pi$
$149$	−2.51684	+	8.57156i	−0.206187	+	0.702209i	−0.996039	+	0.0889121i	$0.971661\pi$
$150$	4.41394	−	5.77546i	0.360397	−	0.471564i
$151$	7.01835	+	13.6137i	0.571145	+	1.10787i	0.980688	+	0.195576i	$0.0626578\pi$
$151$	7.01835	+	13.6137i	0.571145	+	1.10787i	−0.409543	+	0.912291i	$0.634312\pi$
$152$	−0.251403	−	0.749397i	−0.0203915	−	0.0607841i
$153$	−2.06151	−	0.857971i	−0.166663	−	0.0693628i
$154$	−16.2935	+	15.4374i	−1.31297	+	1.24398i
$155$	2.42453	−	3.40478i	0.194743	−	0.273478i
$156$	−5.34340	−	21.0441i	−0.427814	−	1.68488i
$157$	4.45319	+	1.78279i	0.355403	+	0.142282i	0.542492	−	0.840061i	$-0.317481\pi$
$157$	4.45319	+	1.78279i	0.355403	+	0.142282i	−0.187089	+	0.982343i	$0.559905\pi$
$158$	2.70109	+	1.40338i	0.214887	+	0.111647i
$159$	1.30080	−	1.71328i	0.103160	−	0.135872i
$160$	3.23330	+	7.38807i	0.255615	+	0.584078i
$161$	33.5242	−	15.3100i	2.64208	−	1.20660i
$162$	−3.95467	+	12.0980i	−0.310708	+	0.950505i
$163$	−9.67793	+	5.58756i	−0.758034	+	0.437651i	−0.828590	−	0.559857i	$-0.810856\pi$
$163$	−9.67793	+	5.58756i	−0.758034	+	0.437651i	0.0705552	+	0.997508i	$0.477523\pi$
$164$	5.60812	+	1.98095i	0.437921	+	0.154686i
$165$	0.134248	+	7.89202i	0.0104512	+	0.614393i
$166$	4.29486	+	8.39620i	0.333346	+	0.651671i
$167$	−1.72199	−	7.09813i	−0.133252	−	0.549270i	−0.998824	−	0.0484863i	$-0.984560\pi$
$167$	−1.72199	−	7.09813i	−0.133252	−	0.549270i	0.865572	−	0.500784i	$-0.166955\pi$
$168$	16.0659	+	18.2630i	1.23951	+	1.40902i
$169$	24.4010	−	9.76870i	1.87700	−	0.751438i
$170$	−0.147386	+	1.49338i	−0.0113040	+	0.114537i
$171$	−0.833435	−	0.0910218i	−0.0637344	−	0.00696061i
$172$	−12.4532	+	10.6531i	−0.949550	+	0.812292i
$173$	−12.8184	+	4.43650i	−0.974566	+	0.337301i	−0.767516	−	0.641030i	$-0.778508\pi$
$173$	−12.8184	+	4.43650i	−0.974566	+	0.337301i	−0.207050	+	0.978330i	$0.566386\pi$
$174$	10.1536	+	11.3954i	0.769741	+	0.863885i
$175$	−14.7176	−	0.701084i	−1.11254	−	0.0529970i
$176$	11.2895	+	6.00282i	0.850981	+	0.452480i
$177$	3.30248	+	1.25737i	0.248229	+	0.0945098i
$178$	20.9095	+	6.21177i	1.56724	+	0.465591i
$179$	−0.839590	+	5.83948i	−0.0627539	+	0.436463i	0.934087	+	0.357044i	$0.116216\pi$
$179$	−0.839590	+	5.83948i	−0.0627539	+	0.436463i	−0.996841	+	0.0794187i	$0.974694\pi$
$180$	8.55211	+	0.170474i	0.637436	+	0.0127064i
$181$	0.892237	−	0.701663i	0.0663195	−	0.0521542i	−0.584449	−	0.811430i	$-0.698689\pi$
$181$	0.892237	−	0.701663i	0.0663195	−	0.0521542i	0.650768	+	0.759276i	$0.274447\pi$
$182$	−28.9257	+	33.1687i	−2.14412	+	2.45863i
$183$	2.28121	+	8.75087i	0.168632	+	0.646883i
$184$	−14.3426	−	15.3319i	−1.05735	−	1.13028i
$185$	6.86549	−	4.88889i	0.504761	−	0.359438i
$186$	−7.18097	+	0.0993513i	−0.526534	+	0.00728479i
$187$	1.28630	+	2.00153i	0.0940639	+	0.146366i
$188$	15.2801	−	6.00494i	1.11441	−	0.437955i
$189$	24.7293	−	7.35332i	1.79879	−	0.534876i
$190$	0.104875	+	0.553594i	0.00760843	+	0.0401620i
$191$	−8.87627	−	6.98038i	−0.642265	−	0.505082i	0.243087	−	0.970004i	$-0.421840\pi$
$191$	−8.87627	−	6.98038i	−0.642265	−	0.505082i	−0.885352	+	0.464922i	$0.846082\pi$
$192$	6.95265	−	11.9859i	0.501764	−	0.865005i
$193$	−12.3347	+	14.2350i	−0.887872	+	1.02466i	0.111651	+	0.993748i	$0.464386\pi$
$193$	−12.3347	+	14.2350i	−0.887872	+	1.02466i	−0.999522	+	0.0309109i	$0.990159\pi$
$194$	−3.74862	+	4.73575i	−0.269136	+	0.340007i
$195$	1.73297	+	15.3793i	0.124100	+	1.10133i
$196$	8.54098	−	34.2556i	0.610070	−	2.44683i
$197$	−9.64062	+	18.7002i	−0.686866	+	1.33233i	0.244998	+	0.969524i	$0.421213\pi$
$197$	−9.64062	+	18.7002i	−0.686866	+	1.33233i	−0.931863	+	0.362810i	$0.881818\pi$
$198$	10.7993	−	8.20358i	0.767473	−	0.583003i
$199$	6.04987	+	1.46768i	0.428864	+	0.104041i	0.444380	−	0.895838i	$-0.353424\pi$
$199$	6.04987	+	1.46768i	0.428864	+	0.104041i	−0.0155162	+	0.999880i	$0.504939\pi$
$200$	2.28793	+	8.07571i	0.161781	+	0.571039i
$201$	2.19684	−	14.0062i	0.154953	−	0.987922i
$202$	15.3327	−	1.41500i	1.07881	−	0.0995588i
$203$	7.29378	−	30.0654i	0.511923	−	2.11018i
$204$	2.21905	−	1.31291i	0.155365	−	0.0919219i
$205$	−3.76833	−	1.94271i	−0.263192	−	0.135685i
$206$	0.228532	−	0.653580i	0.0159226	−	0.0455371i
$207$	−21.1405	+	6.99676i	−1.46937	+	0.486308i
$208$	23.1547	+	9.61263i	1.60549	+	0.666516i
$209$	0.675127	+	0.585001i	0.0466995	+	0.0404654i
$210$	−9.57479	−	14.4550i	−0.660723	−	0.997489i
$211$	5.13580	−	6.53070i	0.353563	−	0.449592i	−0.576443	−	0.817138i	$-0.695560\pi$
$211$	5.13580	−	6.53070i	0.353563	−	0.449592i	0.930005	+	0.367546i	$0.119802\pi$
$212$	0.684657	+	2.38770i	0.0470224	+	0.163988i
$213$	−2.44989	+	19.3731i	−0.167864	+	1.32742i
$214$	−2.74347	−	9.45432i	−0.187540	−	0.646284i
$215$	9.82732	−	6.31563i	0.670218	−	0.430723i
$216$	−8.45192	−	12.0235i	−0.575080	−	0.818097i
$217$	8.44398	+	11.8579i	0.573215	+	0.804968i
$218$	−1.30005	−	2.03711i	−0.0880508	−	0.137971i
$219$	7.14157	+	27.3955i	0.482582	+	1.85122i
$220$	−7.39053	−	5.33381i	−0.498269	−	0.359605i
$221$	2.88376	+	3.66700i	0.193983	+	0.246669i
$222$	−13.7490	−	4.54660i	−0.922775	−	0.305148i
$223$	−2.26456	−	0.325595i	−0.151646	−	0.0218035i	0.0660735	−	0.997815i	$-0.478953\pi$
$223$	−2.26456	−	0.325595i	−0.151646	−	0.0218035i	−0.217720	+	0.976011i	$0.569862\pi$
$224$	−27.9985	+	2.22571i	−1.87073	+	0.148712i
$225$	8.79406	+	1.38655i	0.586271	+	0.0924367i
$226$	−11.8183	−	11.3406i	−0.786141	−	0.754363i
$227$	0.422346	−	8.86613i	0.0280321	−	0.588466i	−0.940532	−	0.339704i	$-0.889673\pi$
$227$	0.422346	−	8.86613i	0.0280321	−	0.588466i	0.968565	−	0.248762i	$-0.0800238\pi$
$228$	0.660552	−	0.707721i	0.0437461	−	0.0468700i
$229$	2.40322	+	6.94366i	0.158810	+	0.458850i	0.996133	−	0.0878578i	$-0.0280021\pi$
$229$	2.40322	+	6.94366i	0.158810	+	0.458850i	−0.837324	+	0.546708i	$0.815881\pi$
$230$	8.64203	+	12.2179i	0.569839	+	0.805627i
$231$	−26.1270	−	8.54788i	−1.71903	−	0.562409i
$232$	−17.5592	+	1.50810i	−1.15282	+	0.0990117i
$233$	5.78568	+	14.4519i	0.379033	+	0.946778i	0.988121	+	0.153676i	$0.0491111\pi$
$233$	5.78568	+	14.4519i	0.379033	+	0.946778i	−0.609089	+	0.793102i	$0.708465\pi$
$234$	19.5499	−	18.0252i	1.27802	−	1.17834i
$235$	−11.3729	+	2.75904i	−0.741887	+	0.179980i
$236$	−3.44660	+	2.18420i	−0.224354	+	0.142179i
$237$	0.0634066	+	3.72747i	0.00411870	+	0.242125i
$238$	−4.74710	−	2.18617i	−0.307709	−	0.141708i
$239$	9.34980	+	16.1943i	0.604788	+	1.04752i	0.992085	+	0.125569i	$0.0400756\pi$
$239$	9.34980	+	16.1943i	0.604788	+	1.04752i	−0.387297	+	0.921955i	$0.626591\pi$
$240$	−6.07208	+	7.79016i	−0.391951	+	0.502853i
$241$	4.96441	+	10.8706i	0.319786	+	0.700234i	0.999446	−	0.0332939i	$-0.0105997\pi$
$241$	4.96441	+	10.8706i	0.319786	+	0.700234i	−0.679660	+	0.733528i	$0.737872\pi$
$242$	1.10486	−	0.0491160i	0.0710229	−	0.00315730i
$243$	−15.3359	+	2.79455i	−0.983800	+	0.179270i
$244$	−9.66948	−	3.94249i	−0.619025	−	0.252392i
$245$	−9.35309	+	23.3629i	−0.597547	+	1.49260i
$246$	1.13633	+	7.19524i	0.0724497	+	0.458752i
$247$	1.42680	+	1.01602i	0.0907852	+	0.0646478i
$248$	4.87433	−	6.70889i	0.309520	−	0.426015i
$249$	−6.53893	+	9.52131i	−0.414388	+	0.603389i
$250$	−2.23563	−	15.9075i	−0.141394	−	1.00608i
$251$	11.8096	−	6.08825i	0.745413	−	0.384287i	−0.0432891	−	0.999063i	$-0.513784\pi$
$251$	11.8096	−	6.08825i	0.745413	−	0.384287i	0.788702	+	0.614775i	$0.210753\pi$
$252$	−10.3027	+	27.9523i	−0.649007	+	1.76083i
$253$	22.7661	+	6.68474i	1.43129	+	0.420266i
$254$	−18.9403	+	14.7978i	−1.18842	+	0.928494i
$255$	−1.69438	+	0.711999i	−0.106106	+	0.0445871i
$256$	6.27492	+	14.7182i	0.392182	+	0.919887i
$257$	0.236303	+	2.47468i	0.0147402	+	0.154366i	0.999845	−	0.0175868i	$-0.00559834\pi$
$257$	0.236303	+	2.47468i	0.0147402	+	0.154366i	−0.985105	+	0.171953i	$0.944992\pi$
$258$	−18.7350	−	7.20126i	−1.16639	−	0.448331i
$259$	8.26983	+	28.1644i	0.513862	+	1.75005i
$260$	−15.4196	−	9.03350i	−0.956280	−	0.560234i
$261$	−6.35322	+	17.5802i	−0.393254	+	1.08819i
$262$	0.0626733	−	19.7426i	0.00387197	−	1.21970i
$263$	−1.29807	+	2.84238i	−0.0800426	+	0.175269i	−0.945422	−	0.325848i	$-0.894350\pi$
$263$	−1.29807	+	2.84238i	−0.0800426	+	0.175269i	0.865379	+	0.501117i	$0.167077\pi$
$264$	0.117220	+	15.6594i	0.00721439	+	0.963771i
$265$	−0.251980	−	1.75256i	−0.0154790	−	0.107659i
$266$	−1.94144	−	0.285431i	−0.119037	−	0.0175009i
$267$	5.50128	+	26.1425i	0.336673	+	1.59989i
$268$	11.4321	+	11.7178i	0.698329	+	0.715777i
$269$		−	24.2806i		−	1.48041i	−0.672380	−	0.740206i	$-0.734728\pi$
$269$		−	24.2806i		−	1.48041i	0.672380	−	0.740206i	$-0.265272\pi$
$270$	4.80284	+	9.31043i	0.292291	+	0.566615i
$271$	−19.2962	+	2.77437i	−1.17216	+	0.168531i	−0.700765	−	0.713392i	$-0.747158\pi$
$271$	−19.2962	+	2.77437i	−1.17216	+	0.168531i	−0.471394	+	0.881923i	$0.656249\pi$
$272$	−0.320614	+	2.95992i	−0.0194401	+	0.179471i
$273$	−52.5899	−	11.8148i	−3.18289	−	0.715066i
$274$	5.36668	+	0.0170367i	0.324213	+	0.00102922i
$275$	−6.86534	−	6.54609i	−0.413996	−	0.394744i
$276$	8.15045	−	24.3872i	0.490600	−	1.46794i
$277$	−3.57024	+	1.04832i	−0.214515	+	0.0629872i	−0.387224	−	0.921986i	$-0.626566\pi$
$277$	−3.57024	+	1.04832i	−0.214515	+	0.0629872i	0.172709	+	0.984973i	$0.444748\pi$
$278$	−5.09113	−	3.29476i	−0.305346	−	0.197606i
$279$	−4.29399	−	7.67632i	−0.257074	−	0.459569i
$280$	19.9881	+	1.14303i	1.19452	+	0.0683093i
$281$	−4.80575	−	24.9346i	−0.286687	−	1.48747i	−0.784467	−	0.620171i	$-0.787063\pi$
$281$	−4.80575	−	24.9346i	−0.286687	−	1.48747i	0.497780	−	0.867303i	$-0.334149\pi$
$282$	15.3769	+	12.9561i	0.915682	+	0.771525i
$283$	0.327832	−	1.11649i	0.0194876	−	0.0663685i	−0.949175	−	0.314748i	$-0.898080\pi$
$283$	0.327832	−	1.11649i	0.0194876	−	0.0663685i	0.968663	+	0.248380i	$0.0798981\pi$
$284$	−16.2198	−	15.6634i	−0.962469	−	0.929450i
$285$	−0.535099	+	0.435738i	−0.0316965	+	0.0258109i
$286$	−28.0580	+	3.94326i	−1.65911	+	0.233170i
$287$	10.6863	−	10.1893i	0.630790	−	0.601457i
$288$	16.9632	+	0.499787i	0.999566	+	0.0294502i
$289$	9.53962	−	13.3965i	0.561154	−	0.788031i
$290$	12.5464	+	0.637585i	0.736751	+	0.0374403i
$291$	−7.28632	−	1.27619i	−0.427132	−	0.0748119i
$292$	−30.2713	−	12.3424i	−1.77150	−	0.722284i
$293$	−15.0107	+	13.0069i	−0.876935	+	0.759869i	−0.971846	−	0.235617i	$-0.924289\pi$
$293$	−15.0107	+	13.0069i	−0.876935	+	0.759869i	0.0949106	+	0.995486i	$0.469743\pi$
$294$	41.8750	−	10.7743i	2.44220	−	0.628368i
$295$	2.64574	−	1.20827i	0.154041	−	0.0703483i
$296$	13.7127	−	9.56929i	0.797036	−	0.556204i
$297$	15.1324	+	6.84814i	0.878069	+	0.397369i
$298$	5.28471	−	11.4754i	0.306135	−	0.664750i
$299$	45.6827	+	8.80461i	2.64190	+	0.509184i
$300$	−7.36391	+	7.17289i	−0.425156	+	0.414127i
$301$	9.59171	+	39.5376i	0.552857	+	2.27891i
$302$	−7.01946	−	20.4916i	−0.403925	−	1.17916i
$303$	10.4640	+	15.6891i	0.601143	+	0.901314i
$304$	0.197601	+	1.10025i	0.0113332	+	0.0631037i
$305$	6.44623	+	3.72173i	0.369110	+	0.213106i
$306$	2.70792	+	1.62452i	0.154802	+	0.0928674i
$307$	31.3624	−	10.8546i	1.78995	−	0.619507i	0.789967	−	0.613150i	$-0.210098\pi$
$307$	31.3624	−	10.8546i	1.78995	−	0.619507i	0.999980	−	0.00635696i	$-0.00202350\pi$
$308$	25.9730	−	18.2479i	1.47995	−	1.03977i
$309$	0.837187	−	0.134940i	0.0476259	−	0.00767649i
$310$	−4.09272	+	4.26513i	−0.232451	+	0.242243i
$311$	−9.48122	−	6.09321i	−0.537630	−	0.345514i	0.243481	−	0.969906i	$-0.421711\pi$
$311$	−9.48122	−	6.09321i	−0.537630	−	0.345514i	−0.781112	+	0.624392i	$0.785347\pi$
$312$	3.14743	+	30.5435i	0.178188	+	1.72918i
$313$	−2.42856	+	16.8910i	−0.137270	+	0.954736i	0.798467	+	0.602039i	$0.205645\pi$
$313$	−2.42856	+	16.8910i	−0.137270	+	0.954736i	−0.935737	+	0.352698i	$0.885264\pi$
$314$	−5.86405	−	3.41048i	−0.330928	−	0.192464i
$315$	9.98599	−	18.7407i	0.562647	−	1.05592i
$316$	−3.49061	−	2.51920i	−0.196362	−	0.141716i
$317$	−14.1686	+	0.674935i	−0.795789	+	0.0379081i	−0.441538	−	0.897242i	$-0.645567\pi$
$317$	−14.1686	+	0.674935i	−0.795789	+	0.0379081i	−0.354251	+	0.935150i	$0.615264\pi$
$318$	−2.17247	+	2.12960i	−0.121826	+	0.119422i
$319$	16.2245	−	11.5534i	0.908397	−	0.646866i
$320$	−3.00418	−	11.0023i	−0.167939	−	0.615047i
$321$	8.58313	−	8.46734i	0.479064	−	0.472601i
$322$	−50.0555	+	14.5252i	−2.78948	+	0.809457i
$323$	−0.0680324	+	0.196567i	−0.00378542	+	0.0109373i
$324$	8.02189	−	16.1136i	0.445660	−	0.895202i
$325$	−14.6204	−	11.4976i	−0.810994	−	0.637772i
$326$	14.6905	−	5.82715i	0.813632	−	0.322736i
$327$	1.43605	−	2.58799i	0.0794138	−	0.143116i
$328$	−7.43924	−	3.92532i	−0.410763	−	0.216739i
$329$	3.87426	−	40.5731i	0.213595	−	2.23687i
$330$	1.43560	−	11.0699i	0.0790273	−	0.609379i
$331$	1.07170	−	2.07882i	0.0589062	−	0.114262i	−0.857544	−	0.514410i	$-0.828011\pi$
$331$	1.07170	−	2.07882i	0.0589062	−	0.114262i	0.916451	+	0.400148i	$0.131041\pi$
$332$	−4.28210	−	12.6312i	−0.235011	−	0.693228i
$333$	−3.11970	−	17.4594i	−0.170959	−	0.956767i
$334$	0.949229	+	10.2857i	0.0519395	+	0.562811i
$335$	−6.93709	−	9.38349i	−0.379013	−	0.512675i
$336$	−18.7222	−	28.8580i	−1.02138	−	1.57433i
$337$	7.26668	−	29.9537i	0.395841	−	1.63168i	−0.330116	−	0.943940i	$-0.607088\pi$
$337$	7.26668	−	29.9537i	0.395841	−	1.63168i	0.725958	−	0.687739i	$-0.241397\pi$
$338$	−36.1507	+	8.64865i	−1.96634	+	0.470425i
$339$	5.32348	−	19.3412i	0.289132	−	1.05047i
$340$	0.513416	−	2.05918i	0.0278439	−	0.111675i
$341$	−0.890863	+	9.32954i	−0.0482430	+	0.505223i
$342$	1.14740	+	0.298798i	0.0620441	+	0.0161572i
$343$	−39.9709	−	34.6350i	−2.15823	−	1.87011i
$344$	19.6156	−	12.3438i	1.05760	−	0.665535i
$345$	−8.12043	+	16.4318i	−0.437190	+	0.884656i
$346$	18.8478	−	3.57060i	1.01326	−	0.191957i
$347$	2.04598	−	5.91147i	0.109834	−	0.317345i	−0.876667	−	0.481097i	$-0.840239\pi$
$347$	2.04598	−	5.91147i	0.109834	−	0.317345i	0.986501	+	0.163752i	$0.0523598\pi$
$348$	−11.8625	−	18.0328i	−0.635897	−	0.966662i
$349$	−15.8868	+	10.2098i	−0.850401	+	0.546520i	−0.891700	−	0.452627i	$-0.850487\pi$
$349$	−15.8868	+	10.2098i	−0.850401	+	0.546520i	0.0412985	+	0.999147i	$0.486851\pi$
$350$	20.4482	+	4.00843i	1.09300	+	0.214260i
$351$	30.8129	+	10.5464i	1.64467	+	0.562923i
$352$	−14.5612	−	10.7213i	−0.776115	−	0.571448i
$353$	12.7927	−	0.609389i	0.680884	−	0.0324345i	0.295709	−	0.955278i	$-0.404444\pi$
$353$	12.7927	−	0.609389i	0.680884	−	0.0324345i	0.385175	+	0.922843i	$0.374141\pi$
$354$	−4.36208	−	2.43862i	−0.231842	−	0.129611i
$355$	9.93553	+	12.6341i	0.527323	+	0.670546i
$356$	−27.9783	−	12.9926i	−1.48285	−	0.688604i
$357$	−0.413267	−	6.38754i	−0.0218724	−	0.338064i
$358$	2.37595	−	7.99773i	0.125573	−	0.422693i
$359$	−11.2549	−	7.23307i	−0.594010	−	0.381747i	0.208821	−	0.977954i	$-0.433037\pi$
$359$	−11.2549	−	7.23307i	−0.594010	−	0.381747i	−0.802831	+	0.596207i	$0.796674\pi$
$360$	−11.9308	−	1.99774i	−0.628809	−	0.105290i
$361$	0.900340	−	18.9005i	0.0473863	−	0.994761i
$362$	−1.39273	+	0.798209i	−0.0732003	+	0.0419529i
$363$	0.697106	+	1.16135i	0.0365886	+	0.0609549i
$364$	47.2951	−	40.4586i	2.47894	−	2.12061i
$365$	20.1806	+	11.6513i	1.05630	+	0.609856i
$366$	−1.39170	−	12.7132i	−0.0727452	−	0.664532i
$367$	−7.88698	−	19.7007i	−0.411697	−	1.02837i	−0.978817	−	0.204735i	$-0.934367\pi$
$367$	−7.88698	−	19.7007i	−0.411697	−	1.02837i	0.567120	−	0.823635i	$-0.308057\pi$
$368$	16.9140	+	24.4023i	0.881702	+	1.27206i
$369$	−7.08707	+	5.41919i	−0.368938	+	0.282112i
$370$	−10.6117	+	5.42813i	−0.551675	+	0.282195i
$371$	6.05503	+	1.16701i	0.314361	+	0.0605882i
$372$	10.0679	+	1.33816i	0.521994	+	0.0693804i
$373$	−6.80062	−	11.7790i	−0.352123	−	0.609895i	0.634498	−	0.772924i	$-0.281207\pi$
$373$	−6.80062	−	11.7790i	−0.352123	−	0.609895i	−0.986621	+	0.163030i	$0.947873\pi$
$374$	−1.38803	−	3.06509i	−0.0717736	−	0.158492i
$375$	15.8296	−	11.6830i	0.817438	−	0.603308i
$376$	−22.6147	+	5.25874i	−1.16627	+	0.271199i
$377$	29.5149	−	25.5748i	1.52009	−	1.31717i
$378$	−36.1132	+	5.20160i	−1.85746	+	0.267541i
$379$	2.70449	−	6.75550i	0.138920	−	0.347007i	−0.842551	−	0.538617i	$-0.818947\pi$
$379$	2.70449	−	6.75550i	0.138920	−	0.347007i	0.981471	+	0.191611i	$0.0613711\pi$
$380$	−0.0328604	−	0.796148i	−0.00168570	−	0.0408415i
$381$	−26.9814	−	11.7716i	−1.38230	−	0.603075i
$382$	10.9835	+	11.5927i	0.561966	+	0.593132i
$383$	−4.51175	+	4.30194i	−0.230540	+	0.219819i	−0.796540	−	0.604586i	$-0.793339\pi$
$383$	−4.51175	+	4.30194i	−0.230540	+	0.219819i	0.566000	+	0.824405i	$0.308490\pi$
$384$	−12.1935	+	15.3401i	−0.622248	+	0.782820i
$385$	−20.1113	+	10.3681i	−1.02497	+	0.528406i
$386$	20.1866	−	17.3799i	1.02747	−	0.884614i
$387$	−3.16763	−	24.3773i	−0.161020	−	1.23917i
$388$	6.21915	−	5.85501i	0.315729	−	0.297243i
$389$	1.17189	+	6.08037i	0.0594174	+	0.308287i	0.999463	−	0.0327614i	$-0.0104301\pi$
$389$	1.17189	+	6.08037i	0.0594174	+	0.308287i	−0.940046	+	0.341048i	$0.889218\pi$
$390$	0.738890	−	21.8747i	0.0374152	−	1.10767i
$391$	0.525166	+	5.49979i	0.0265588	+	0.278136i
$392$	−18.9969	+	46.1726i	−0.959489	+	2.33207i
$393$	21.3002	−	11.4437i	1.07446	−	0.577260i
$394$	17.3356	−	24.1817i	0.873357	−	1.21825i
$395$	2.22077	+	2.11750i	0.111739	+	0.106543i
$396$	−16.7976	+	9.25674i	−0.844112	+	0.465169i
$397$	−6.70871	+	14.6900i	−0.336701	+	0.737272i	−0.999938	−	0.0111376i	$-0.996455\pi$
$397$	−6.70871	+	14.6900i	−0.336701	+	0.737272i	0.663237	+	0.748409i	$0.269182\pi$
$398$	−8.16290	−	3.29804i	−0.409169	−	0.165316i
$399$	−0.824567	−	2.25745i	−0.0412800	−	0.113014i
$400$	−1.53999	−	11.7699i	−0.0769994	−	0.588497i
$401$			12.9954i			0.648960i	0.945892	+	0.324480i	$0.105189\pi$
$401$			12.9954i			0.648960i	−0.945892	+	0.324480i	$0.894811\pi$
$402$	−5.95492	+	19.1452i	−0.297005	+	0.954876i
$403$			18.3762i			0.915384i
$404$	−21.7442	−	1.17422i	−1.08182	−	0.0584195i
$405$	−7.22741	+	10.6015i	−0.359133	+	0.526792i
$406$	−16.3899	+	40.5663i	−0.813417	+	2.01327i
$407$	−7.85048	+	17.1902i	−0.389134	+	0.852084i
$408$	−3.37491	+	1.38051i	−0.167083	+	0.0683455i
$409$	−15.8447	−	15.1079i	−0.783470	−	0.747038i	0.188517	−	0.982070i	$-0.439632\pi$
$409$	−15.8447	−	15.1079i	−0.783470	−	0.747038i	−0.971988	+	0.235032i	$0.924480\pi$
$410$	4.87292	+	3.49335i	0.240656	+	0.172524i
$411$	3.11078	+	5.79011i	0.153444	+	0.285605i
$412$	−0.454202	+	0.867461i	−0.0223769	+	0.0427368i
$413$	0.962901	+	10.0840i	0.0473812	+	0.496199i
$414$	31.0185	−	5.44094i	1.52448	−	0.267408i
$415$	1.79922	+	9.33526i	0.0883204	+	0.458250i
$416$	−30.4200	−	18.2128i	−1.49146	−	0.892955i
$417$	0.580143	−	7.40446i	0.0284097	−	0.362598i
$418$	−0.824281	−	0.957396i	−0.0403169	−	0.0468277i
$419$	4.46176	−	2.30020i	0.217971	−	0.112372i	−0.345783	−	0.938314i	$-0.612387\pi$
$419$	4.46176	−	2.30020i	0.217971	−	0.112372i	0.563754	+	0.825942i	$0.309356\pi$
$420$	10.4233	+	22.1946i	0.508605	+	1.08299i
$421$	−13.3284	+	12.7086i	−0.649587	+	0.619380i	−0.941479	−	0.337072i	$-0.890564\pi$
$421$	−13.3284	+	12.7086i	−0.649587	+	0.619380i	0.291892	+	0.956451i	$0.405715\pi$
$422$	−8.52927	+	8.08111i	−0.415199	+	0.393382i
$423$	−4.98859	+	24.1159i	−0.242553	+	1.17256i
$424$	−0.466788	−	3.48165i	−0.0226692	−	0.169084i
$425$	0.820922	−	2.05056i	0.0398205	−	0.0994669i
$426$	7.41298	−	26.6023i	0.359160	−	1.28889i
$427$	−19.5917	+	16.9763i	−0.948110	+	0.821542i
$428$	1.89377	+	13.7926i	0.0915390	+	0.666689i
$429$	−20.6068	−	27.9207i	−0.994904	−	1.34802i
$430$	−15.0493	+	6.81512i	−0.725741	+	0.328654i
$431$	−2.21554	−	3.83744i	−0.106719	−	0.184843i	0.807720	−	0.589566i	$-0.200701\pi$
$431$	−2.21554	−	3.83744i	−0.106719	−	0.184843i	−0.914439	+	0.404723i	$0.867368\pi$
$432$	9.35238	+	18.5616i	0.449967	+	0.893045i
$433$	17.7424	+	3.41957i	0.852646	+	0.164334i	0.596806	−	0.802385i	$-0.296436\pi$
$433$	17.7424	+	3.41957i	0.852646	+	0.164334i	0.255840	+	0.966719i	$0.417648\pi$
$434$	−9.37534	−	18.3282i	−0.450031	−	0.879784i
$435$	6.62869	+	13.8849i	0.317821	+	0.665728i
$436$	1.39995	+	3.11770i	0.0670456	+	0.149311i
$437$	0.770972	+	1.92580i	0.0368806	+	0.0921233i
$438$	−4.35686	−	39.8001i	−0.208179	−	1.90172i
$439$	−13.9657	−	8.06308i	−0.666545	−	0.384830i	0.128221	−	0.991746i	$-0.459073\pi$
$439$	−13.9657	−	8.06308i	−0.666545	−	0.384830i	−0.794766	+	0.606916i	$0.792407\pi$
$440$	9.24343	+	8.98320i	0.440663	+	0.428257i
$441$	36.0203	+	38.8192i	1.71525	+	1.84854i
$442$	−3.28055	−	5.72397i	−0.156040	−	0.272262i
$443$	−0.330907	+	6.94658i	−0.0157218	+	0.330042i	0.977281	+	0.211949i	$0.0679811\pi$
$443$	−0.330907	+	6.94658i	−0.0157218	+	0.330042i	−0.993003	+	0.118093i	$0.962322\pi$
$444$	18.3020	+	9.18974i	0.868576	+	0.436126i
$445$	18.4982	+	11.8881i	0.876900	+	0.563549i
$446$	3.10154	+	0.921399i	0.146862	+	0.0436295i
$447$	15.4409	−	0.999007i	0.730328	−	0.0472514i
$448$	39.6326	+	2.64531i	1.87246	+	0.124979i
$449$	−20.7888	−	26.4351i	−0.981082	−	1.24755i	−0.968857	−	0.247622i	$-0.920351\pi$
$449$	−20.7888	−	26.4351i	−0.981082	−	1.24755i	−0.0122258	−	0.999925i	$-0.503892\pi$
$450$	−12.0192	−	3.74902i	−0.566590	−	0.176730i
$451$	9.49532	−	0.452318i	0.447117	−	0.0212988i
$452$	14.2030	+	18.2985i	0.668053	+	0.860689i
$453$	17.9777	−	19.5083i	0.844665	−	0.916579i
$454$	−2.41475	+	12.3184i	−0.113330	+	0.578130i
$455$	−37.3224	+	23.9856i	−1.74970	+	1.12446i
$456$	−1.06981	+	0.854345i	−0.0500984	+	0.0400084i
$457$	−4.29406	+	12.4069i	−0.200868	+	0.580369i	−0.999778	−	0.0210813i	$-0.993289\pi$
$457$	−4.29406	+	12.4069i	−0.200868	+	0.580369i	0.798910	+	0.601451i	$0.205410\pi$
$458$	−1.93417	−	10.2097i	−0.0903779	−	0.477070i
$459$	−0.170784	+	3.86376i	−0.00797153	+	0.180345i
$460$	−9.57839	−	18.8727i	−0.446595	−	0.879946i
$461$	−13.4940	−	11.6926i	−0.628479	−	0.544580i	0.281328	−	0.959612i	$-0.409225\pi$
$461$	−13.4940	−	11.6926i	−0.628479	−	0.544580i	−0.909807	+	0.415032i	$0.863771\pi$
$462$	34.7978	+	17.3344i	1.61894	+	0.806472i
$463$	−1.92335	+	20.1422i	−0.0893857	+	0.936090i	0.833885	+	0.551939i	$0.186112\pi$
$463$	−1.92335	+	20.1422i	−0.0893857	+	0.936090i	−0.923270	+	0.384151i	$0.874494\pi$
$464$	24.8786	+	1.50195i	1.15496	+	0.0697264i
$465$	−6.98008	−	1.92121i	−0.323694	−	0.0890938i
$466$	−5.12232	−	21.4109i	−0.237287	−	0.991841i
$467$	4.12747	−	17.0136i	0.190996	−	0.787298i	−0.793017	−	0.609200i	$-0.791491\pi$
$467$	4.12747	−	17.0136i	0.190996	−	0.787298i	0.984013	−	0.178097i	$-0.0569942\pi$
$468$	−31.0617	+	21.1988i	−1.43583	+	0.979916i
$469$	38.7847	−	12.1426i	1.79091	−	0.560692i
$470$	16.4802	−	1.52089i	0.760176	−	0.0701535i
$471$	0.254118	−	8.30440i	0.0117092	−	0.382647i
$472$	5.27169	−	2.34709i	0.242649	−	0.108033i
$473$	−12.0023	+	23.2811i	−0.551864	+	1.07047i
$474$	0.678047	−	5.22842i	0.0311438	−	0.240149i
$475$	0.0788325	−	0.825572i	0.00361709	−	0.0378798i
$476$	6.19231	+	4.03534i	0.283824	+	0.184959i
$477$	−3.56038	−	1.09816i	−0.163018	−	0.0502813i
$478$	−9.75071	−	24.5820i	−0.445987	−	1.12435i
$479$	14.0298	+	11.0332i	0.641038	+	0.504118i	0.884954	−	0.465679i	$-0.154190\pi$
$479$	14.0298	+	11.0332i	0.641038	+	0.504118i	−0.243916	+	0.969796i	$0.578432\pi$
$480$	10.0984	−	9.65072i	0.460926	−	0.440493i
$481$	−12.1193	+	35.0163i	−0.552591	+	1.59661i
$482$	−4.70993	−	16.2310i	−0.214532	−	0.739302i
$483$	−44.8300	−	45.4431i	−2.03984	−	2.06773i
$484$	−1.55599	−	0.158554i	−0.0707268	−	0.00720702i
$485$	−4.95963	+	3.53173i	−0.225205	+	0.160368i
$486$	22.0325	−	0.755361i	0.999413	−	0.0342639i
$487$	20.4160	−	0.972535i	0.925138	−	0.0440697i	0.420397	−	0.907340i	$-0.361891\pi$
$487$	20.4160	−	0.972535i	0.925138	−	0.0440697i	0.504741	+	0.863271i	$0.331588\pi$
$488$	12.7183	+	7.50530i	0.575730	+	0.339749i
$489$	14.8417	+	12.4248i	0.671163	+	0.561867i
$490$	17.8925	−	30.7647i	0.808300	−	1.38981i
$491$	−4.88031	+	33.9433i	−0.220245	+	1.53184i	0.516865	+	0.856067i	$0.327099\pi$
$491$	−4.88031	+	33.9433i	−0.220245	+	1.53184i	−0.737110	+	0.675773i	$0.763810\pi$
$492$	−0.109814	−	10.3011i	−0.00495079	−	0.464411i
$493$	3.90154	+	2.50737i	0.175717	+	0.112926i
$494$	−1.78734	−	1.71509i	−0.0804162	−	0.0771656i
$495$	12.7599	−	4.90829i	0.573515	−	0.220611i
$496$	−8.20009	+	8.38421i	−0.368195	+	0.376462i
$497$	−52.8984	+	18.3083i	−2.37282	+	0.821241i
$498$	11.1077	−	11.9769i	0.497747	−	0.536696i
$499$	2.58319	+	1.49141i	0.115640	+	0.0667645i	0.556704	−	0.830711i	$-0.312066\pi$
$499$	2.58319	+	1.49141i	0.115640	+	0.0667645i	−0.441065	+	0.897475i	$0.645399\pi$
$500$	−0.144234	+	22.7172i	−0.00645036	+	1.01594i
$501$	−10.5248	+	7.01964i	−0.470212	+	0.313614i
$502$	−17.7760	+	6.08922i	−0.793382	+	0.271775i
$503$	−5.43162	−	22.3895i	−0.242184	−	0.998296i	−0.954920	−	0.296864i	$-0.904059\pi$
$503$	−5.43162	−	22.3895i	−0.242184	−	0.998296i	0.712736	−	0.701433i	$-0.247456\pi$
$504$	20.1652	−	36.9908i	0.898229	−	1.64770i
$505$	15.2417	+	2.93761i	0.678249	+	0.130722i
$506$	−30.4787	−	14.0362i	−1.35494	−	0.623987i
$507$	−30.3933	−	33.8934i	−1.34981	−	1.50526i
$508$	29.5448	−	16.8085i	1.31084	−	0.745756i
$509$	12.5793	−	5.74475i	0.557566	−	0.254632i	−0.116641	−	0.993174i	$-0.537213\pi$
$509$	12.5793	−	5.74475i	0.557566	−	0.254632i	0.674207	+	0.738542i	$0.264486\pi$
$510$	2.51719	−	0.647664i	0.111463	−	0.0286791i
$511$	−61.3340	+	53.1462i	−2.71326	+	2.35105i
$512$	−5.75207	−	21.8841i	−0.254208	−	0.967150i
$513$	0.347188	+	1.41002i	0.0153287	+	0.0622539i
$514$	0.178428	−	3.51111i	0.00787012	−	0.154869i
$515$	0.404865	−	0.568553i	0.0178405	−	0.0250534i
$516$	24.7321	+	13.9297i	1.08877	+	0.613221i
$517$	18.9908	−	18.1077i	0.835214	−	0.796375i
$518$	−5.77731	−	41.1081i	−0.253841	−	1.80619i
$519$	14.8352	+	18.2181i	0.651194	+	0.799686i
$520$	19.7164	+	15.8113i	0.864620	+	0.693372i
$521$	4.55114	−	15.4998i	0.199389	−	0.679057i	−0.797717	−	0.603032i	$-0.793959\pi$
$521$	4.55114	−	15.4998i	0.199389	−	0.679057i	0.997106	−	0.0760249i	$-0.0242228\pi$
$522$	12.5056	−	23.2908i	0.547356	−	1.01941i
$523$	0.889745	+	4.61643i	0.0389058	+	0.201863i	0.996181	−	0.0873175i	$-0.0278295\pi$
$523$	0.889745	+	4.61643i	0.0389058	+	0.201863i	−0.957275	+	0.289180i	$0.906617\pi$
$524$	−4.14886	+	27.6104i	−0.181244	+	1.20616i
$525$	7.60538	+	24.3609i	0.331926	+	1.06320i
$526$	2.40093	−	3.70996i	0.104685	−	0.161762i
$527$	−2.09384	+	0.614806i	−0.0912090	+	0.0267814i
$528$	3.05723	−	21.9344i	0.133049	−	0.954571i
$529$	23.2299	+	22.1496i	1.00999	+	0.963027i
$530$	−0.00794893	+	2.50397i	−0.000345279	+	0.108766i
$531$	0.0831271	−	6.12005i	0.00360741	−	0.265588i
$532$	2.65770	+	0.798734i	0.115226	+	0.0346295i
$533$	18.4494	−	2.65263i	0.799133	−	0.114898i
$534$	−2.31958	−	37.7095i	−0.100378	−	1.63185i
$535$		−	9.92382i		−	0.429044i
$536$	−13.5851	−	18.7469i	−0.586787	−	0.809741i
$537$	9.99928	−	2.10420i	0.431501	−	0.0908028i
$538$	−4.99466	+	33.9727i	−0.215335	+	1.46467i
$539$	−8.03029	−	55.8519i	−0.345889	−	2.40571i
$540$	−4.80479	−	14.0149i	−0.206765	−	0.603104i
$541$	−11.7539	+	25.7374i	−0.505339	+	1.10654i	0.469359	+	0.883008i	$0.344485\pi$
$541$	−11.7539	+	25.7374i	−0.505339	+	1.10654i	−0.974697	+	0.223529i	$0.928242\pi$
$542$	27.5694	+	0.0875198i	1.18421	+	0.00375930i
$543$	−1.67176	−	1.03463i	−0.0717423	−	0.0444002i
$544$	1.05747	−	4.07548i	0.0453385	−	0.174735i
$545$	−0.686334	−	2.33744i	−0.0293993	−	0.100125i
$546$	71.1520	+	27.3491i	3.04503	+	1.17043i
$547$	2.88892	+	30.2541i	0.123521	+	1.29357i	0.818485	+	0.574527i	$0.194814\pi$
$547$	2.88892	+	30.2541i	0.123521	+	1.29357i	−0.694964	+	0.719044i	$0.744580\pi$
$548$	−7.50541	−	1.12780i	−0.320615	−	0.0481771i
$549$	12.8813	−	8.91159i	0.549761	−	0.380337i
$550$	8.25923	+	10.5714i	0.352175	+	0.450764i
$551$	1.67080	+	0.490590i	0.0711784	+	0.0208999i
$552$	−16.4205	+	32.4454i	−0.698903	+	1.38097i
$553$	−9.49873	+	4.89694i	−0.403927	+	0.208239i
$554$	5.21103	−	0.732356i	0.221395	−	0.0311148i
$555$	−12.0337	−	8.26433i	−0.510801	−	0.350801i
$556$	6.44562	+	5.65721i	0.273355	+	0.239919i
$557$	19.1637	+	13.6464i	0.811993	+	0.578218i	0.908870	−	0.417079i	$-0.136946\pi$
$557$	19.1637	+	13.6464i	0.811993	+	0.578218i	−0.0968773	+	0.995296i	$0.530885\pi$
$558$	4.42896	+	11.6238i	0.187493	+	0.492075i
$559$	−19.0878	+	47.6790i	−0.807327	+	2.01661i
$560$	−27.7317	−	5.71098i	−1.17188	−	0.241333i
$561$	2.49193	−	3.28213i	0.105209	−	0.138572i
$562$	1.59487	+	35.8764i	0.0672756	+	1.51335i
$563$	14.3922	+	31.5146i	0.606561	+	1.32818i	0.924901	+	0.380207i	$0.124147\pi$
$563$	14.3922	+	31.5146i	0.606561	+	1.32818i	−0.318341	+	0.947976i	$0.603126\pi$
$564$	−18.8498	−	21.2910i	−0.793720	−	0.896511i
$565$	−8.25577	−	14.2994i	−0.347323	−	0.601581i
$566$	−0.688362	+	1.49473i	−0.0289340	+	0.0628281i
$567$	−26.6588	−	35.8628i	−1.11956	−	1.50609i
$568$	19.4723	+	25.2523i	0.817039	+	1.05956i
$569$	−18.0303	+	4.37411i	−0.755870	+	0.183372i	−0.595135	−	0.803625i	$-0.702902\pi$
$569$	−18.0303	+	4.37411i	−0.755870	+	0.183372i	−0.160735	+	0.986998i	$0.551386\pi$
$570$	0.838330	−	0.499599i	0.0351138	−	0.0209259i
$571$	−6.93140	−	17.3138i	−0.290070	−	0.724560i	−0.999798	−	0.0200845i	$-0.993606\pi$
$571$	−6.93140	−	17.3138i	−0.290070	−	0.724560i	0.709728	−	0.704476i	$-0.248818\pi$
$572$	40.0692	+	0.254404i	1.67538	+	0.0106372i
$573$	−6.08173	+	18.5891i	−0.254068	+	0.776570i
$574$	−17.0479	+	12.0584i	−0.711568	+	0.503308i
$575$	−7.20449	−	20.8160i	−0.300448	−	0.868088i
$576$	−23.6316	−	4.18873i	−0.984652	−	0.174530i
$577$	1.35549	−	28.4553i	0.0564300	−	1.18461i	−0.776092	−	0.630619i	$-0.782801\pi$
$577$	1.35549	−	28.4553i	0.0564300	−	1.18461i	0.832522	−	0.553991i	$-0.186896\pi$
$578$	−16.1033	+	16.7817i	−0.669810	+	0.698026i
$579$	30.4892	+	11.6083i	1.26709	+	0.482425i
$580$	−17.4235	−	3.47297i	−0.723470	−	0.144207i
$581$	−32.7735	−	4.71212i	−1.35967	−	0.195492i
$582$	9.93231	+	3.28446i	0.411707	+	0.136145i
$583$	2.45409	+	3.12063i	0.101638	+	0.129243i
$584$	39.8159	+	23.4961i	1.64760	+	0.972277i
$585$	23.9910	−	11.9586i	0.991905	−	0.494427i
$586$	23.6782	−	15.1110i	0.978137	−	0.624232i
$587$	11.6165	+	16.3131i	0.479466	+	0.673316i	0.981485	−	0.191541i	$-0.0613486\pi$
$587$	11.6165	+	16.3131i	0.479466	+	0.673316i	−0.502019	+	0.864857i	$0.667409\pi$
$588$	−60.8066	+	6.46113i	−2.50762	+	0.266452i
$589$	−0.689289	+	0.442979i	−0.0284016	+	0.0182526i
$590$	−3.95040	+	1.14633i	−0.162636	+	0.0471938i
$591$	36.1527	+	4.57181i	1.48712	+	0.188059i
$592$	−21.1549	+	10.5683i	−0.869463	+	0.434355i
$593$	14.4885	−	18.4237i	0.594972	−	0.756569i	−0.391557	−	0.920154i	$-0.628063\pi$
$593$	14.4885	−	18.4237i	0.594972	−	0.756569i	0.986529	+	0.163585i	$0.0523059\pi$
$594$	−19.7641	−	12.6946i	−0.810930	−	0.520864i
$595$	−3.98168	−	3.45014i	−0.163233	−	0.141442i
$596$	−9.75478	+	14.9689i	−0.399571	+	0.613151i
$597$	−1.20737	−	10.7148i	−0.0494143	−	0.438528i
$598$	−62.1068	−	21.7164i	−2.53974	−	0.888049i
$599$	−1.66823	−	0.860032i	−0.0681620	−	0.0351400i	0.423809	−	0.905752i	$-0.360693\pi$
$599$	−1.66823	−	0.860032i	−0.0681620	−	0.0351400i	−0.491971	+	0.870612i	$0.663723\pi$
$600$	11.7789	−	8.52130i	0.480871	−	0.347881i
$601$	2.15446	−	8.88080i	0.0878822	−	0.362255i	−0.910842	−	0.412756i	$-0.864566\pi$
$601$	2.15446	−	8.88080i	0.0878822	−	0.362255i	0.998724	+	0.0505001i	$0.0160815\pi$
$602$	−5.28733	−	57.2929i	−0.215496	−	2.33509i
$603$	−24.0924	+	4.74919i	−0.981120	+	0.193402i
$604$	5.60618	+	30.1153i	0.228112	+	1.22537i
$605$	1.08345	+	0.262843i	0.0440486	+	0.0106861i
$606$	−11.4136	−	24.1042i	−0.463648	−	0.979168i
$607$	12.6178	−	24.4750i	0.512139	−	0.993411i	−0.481027	−	0.876706i	$-0.659736\pi$
$607$	12.6178	−	24.4750i	0.512139	−	0.993411i	0.993167	−	0.116706i	$-0.0372335\pi$
$608$	−0.0501488	−	1.58009i	−0.00203380	−	0.0640811i
$609$	−53.2482	+	6.00012i	−2.15773	+	0.243137i
$610$	−8.25381	−	6.53338i	−0.334187	−	0.264529i
$611$	33.6928	−	38.8836i	1.36306	−	1.57306i
$612$	−3.45468	−	2.83001i	−0.139647	−	0.114397i
$613$	−23.2256	−	18.2648i	−0.938074	−	0.737709i	0.0270145	−	0.999635i	$-0.491400\pi$
$613$	−23.2256	−	18.2648i	−0.938074	−	0.737709i	−0.965088	+	0.261926i	$0.915642\pi$
$614$	−46.1143	+	8.73606i	−1.86102	+	0.352559i
$615$	−0.921278	+	7.28523i	−0.0371495	+	0.293769i
$616$	−40.0944	+	20.1891i	−1.61545	+	0.813443i
$617$	−10.5756	−	16.4560i	−0.425759	−	0.662494i	0.560414	−	0.828213i	$-0.310642\pi$
$617$	−10.5756	−	16.4560i	−0.425759	−	0.662494i	−0.986173	+	0.165718i	$0.947006\pi$
$618$	−1.19913	+	0.0165904i	−0.0482360	+	0.000667362i
$619$	−13.5959	+	9.68163i	−0.546467	+	0.389137i	−0.819685	−	0.572815i	$-0.805851\pi$
$619$	−13.5959	+	9.68163i	−0.546467	+	0.389137i	0.273218	+	0.961952i	$0.411912\pi$
$620$	6.60379	−	5.12576i	0.265215	−	0.205855i
$621$	23.9460	+	30.2360i	0.960920	+	1.21333i
$622$	12.0124	+	10.4758i	0.481655	+	0.420041i
$623$	−60.1970	+	47.3394i	−2.41174	+	1.89661i
$624$	1.87918	−	43.3831i	0.0752275	−	1.73671i
$625$	0.192937	−	1.34191i	0.00771750	−	0.0536764i
$626$	6.87256	−	23.1339i	0.274683	−	0.924616i
$627$	0.550551	−	1.44602i	0.0219869	−	0.0577483i
$628$	7.50326	+	5.97812i	0.299413	+	0.238553i
$629$	−4.39533	−	0.209376i	−0.175253	−	0.00834835i
$630$	−17.8272	+	24.1673i	−0.710253	+	0.962850i
$631$	−23.4647	+	8.12120i	−0.934114	+	0.323300i	−0.751386	−	0.659863i	$-0.770614\pi$
$631$	−23.4647	+	8.12120i	−0.934114	+	0.323300i	−0.182728	+	0.983163i	$0.558493\pi$
$632$	4.36575	+	4.24284i	0.173660	+	0.168771i
$633$	−13.6769	−	4.47462i	−0.543607	−	0.177850i
$634$	19.9632	+	1.97022i	0.792840	+	0.0782476i
$635$	−22.4941	+	9.00526i	−0.892649	+	0.357363i
$636$	3.47774	−	2.53279i	0.137901	−	0.100431i
$637$	−26.0839	−	107.519i	−1.03348	−	4.26008i
$638$	−25.0775	+	12.8277i	−0.992826	+	0.507855i
$639$	32.9742	−	7.52678i	1.30444	−	0.297755i
$640$	1.94012	+	16.0121i	0.0766899	+	0.632934i
$641$	−21.6475	+	12.4982i	−0.855023	+	0.493648i	−0.862343	−	0.506325i	$-0.831004\pi$
$641$	−21.6475	+	12.4982i	−0.855023	+	0.493648i	0.00731916	+	0.999973i	$0.497670\pi$
$642$	−13.7511	+	10.0817i	−0.542712	+	0.397892i
$643$	22.0114	−	10.0523i	0.868045	−	0.396423i	0.0689446	−	0.997620i	$-0.478037\pi$
$643$	22.0114	−	10.0523i	0.868045	−	0.396423i	0.799100	+	0.601198i	$0.205310\pi$
$644$	73.0242	−	10.0265i	2.87756	−	0.395100i
$645$	−16.1150	−	12.2351i	−0.634526	−	0.481758i
$646$	0.135624	−	0.261036i	0.00533606	−	0.0102703i
$647$	34.6642	+	13.8775i	1.36279	+	0.545580i	0.933822	−	0.357739i	$-0.116452\pi$
$647$	34.6642	+	13.8775i	1.36279	+	0.545580i	0.428970	+	0.903319i	$0.358876\pi$
$648$	−14.5387	+	20.8956i	−0.571133	+	0.820857i
$649$	−3.78292	+	5.31237i	−0.148493	+	0.208529i
$650$	18.0913	+	19.0946i	0.709600	+	0.748954i
$651$	14.2740	−	20.7843i	0.559441	−	0.814600i
$652$	−21.7532	+	5.13126i	−0.851922	+	0.200956i
$653$	7.26711	+	14.0962i	0.284384	+	0.551628i	0.987151	−	0.159792i	$-0.0510825\pi$
$653$	7.26711	+	14.0962i	0.284384	+	0.551628i	−0.702767	+	0.711421i	$0.748052\pi$
$654$	−2.54165	+	3.32565i	−0.0993864	+	0.130043i
$655$	5.60707	−	19.0959i	0.219086	−	0.746139i
$656$	9.60132	+	7.02250i	0.374869	+	0.274182i
$657$	40.3263	−	27.8987i	1.57328	−	1.08843i
$658$	−13.7669	+	55.9718i	−0.536690	+	2.18201i
$659$	−14.3009	+	1.36557i	−0.557083	+	0.0531950i	−0.369801	−	0.929111i	$-0.620574\pi$
$659$	−14.3009	+	1.36557i	−0.557083	+	0.0531950i	−0.187283	+	0.982306i	$0.559968\pi$
$660$	−4.28581	+	15.1934i	−0.166825	+	0.591403i
$661$	23.2151	−	6.81658i	0.902964	−	0.265134i	0.202888	−	0.979202i	$-0.434967\pi$
$661$	23.2151	−	6.81658i	0.902964	−	0.265134i	0.700077	+	0.714068i	$0.253149\pi$
$662$	−1.92712	+	2.68817i	−0.0748998	+	0.104479i
$663$	4.25222	−	6.87077i	0.165142	−	0.266839i
$664$	3.39308	+	18.5541i	0.131677	+	0.720039i
$665$	−1.79940	−	0.821757i	−0.0697776	−	0.0318664i
$666$	0.773503	+	25.0704i	0.0299726	+	0.971458i
$667$	45.7803	−	6.58221i	1.77262	−	0.254864i
$668$	0.787706	−	14.5868i	0.0304773	−	0.564380i
$669$	0.816012	+	3.87775i	0.0315489	+	0.149922i
$670$	7.77594	+	14.5561i	0.300411	+	0.562352i
$671$	−16.6897			−0.644300
$672$	20.2593	+	44.2286i	0.781520	+	1.70616i
$673$	5.07200	+	35.2765i	0.195511	+	1.35981i	0.817113	+	0.576477i	$0.195573\pi$
$673$	5.07200	+	35.2765i	0.195511	+	1.35981i	−0.621602	+	0.783333i	$0.713518\pi$
$674$	−16.3290	+	40.4155i	−0.628969	+	1.55675i
$675$	−2.97011	−	15.1312i	−0.114320	−	0.582400i
$676$	52.3602	−	4.66452i	2.01385	−	0.179405i
$677$	30.3802	−	31.8618i	1.16761	−	1.22455i	0.197914	−	0.980219i	$-0.436583\pi$
$677$	30.3802	−	31.8618i	1.16761	−	1.22455i	0.969692	−	0.244331i	$-0.0785682\pi$
$678$	−11.4271	+	25.9666i	−0.438854	+	0.997240i
$679$	−5.97412	−	20.3460i	−0.229266	−	0.780807i
$680$	−1.14194	+	2.77554i	−0.0437916	+	0.106437i
$681$	−14.6754	+	4.58162i	−0.562364	+	0.175568i
$682$	3.16562	−	12.8704i	0.121218	−	0.492833i
$683$	−0.310505	+	0.0598449i	−0.0118811	+	0.00228990i	−0.195188	−	0.980766i	$-0.562532\pi$
$683$	−0.310505	+	0.0598449i	−0.0118811	+	0.00228990i	0.183307	+	0.983056i	$0.441320\pi$
$684$	−1.54394	−	0.654097i	−0.0590341	−	0.0250100i
$685$	5.19090	+	1.52419i	0.198334	+	0.0582362i
$686$	48.8016	+	56.6826i	1.86325	+	2.16415i
$687$	9.86863	−	8.03615i	0.376512	−	0.306598i
$688$	−29.9849	+	13.2361i	−1.14316	+	0.504622i
$689$	5.37173	+	5.63371i	0.204646	+	0.214627i
$690$	14.7420	−	21.3205i	0.561219	−	0.811656i
$691$	−6.66297	−	4.74468i	−0.253471	−	0.180496i	0.446258	−	0.894905i	$-0.352757\pi$
$691$	−6.66297	−	4.74468i	−0.253471	−	0.180496i	−0.699729	+	0.714408i	$0.746696\pi$
$692$	−27.1058	+	1.11877i	−1.03041	+	0.0425294i
$693$	1.61941	+	47.5861i	0.0615162	+	1.80765i
$694$	−4.07871	+	7.85030i	−0.154826	+	0.297993i
$695$	−4.00330	−	4.62006i	−0.151854	−	0.175249i
$696$	12.8882	+	27.6712i	0.488527	+	1.04888i
$697$	0.919505	+	2.01343i	0.0348287	+	0.0762643i
$698$	24.3286	−	11.0173i	0.920852	−	0.417011i
$699$	20.0739	−	18.0010i	0.759266	−	0.680859i
$700$	−27.7860	−	9.81482i	−1.05021	−	0.370965i
$701$	−3.84616	+	19.9558i	−0.145267	+	0.753719i	0.834097	+	0.551618i	$0.185989\pi$
$701$	−3.84616	+	19.9558i	−0.145267	+	0.753719i	−0.979365	+	0.202102i	$0.935223\pi$
$702$	−40.9432	−	21.0946i	−1.54530	−	0.796164i
$703$	−1.60561	+	0.389516i	−0.0605566	+	0.0146909i
$704$	18.1682	+	17.9963i	0.684740	+	0.678261i
$705$	11.2471	+	16.8632i	0.423592	+	0.635106i
$706$	−18.0245	−	1.77889i	−0.678361	−	0.0669494i
$707$	−27.0299	+	46.8171i	−1.01656	+	1.76074i
$708$	5.60167	+	4.30936i	0.210524	+	0.161956i
$709$	4.14651	+	11.9805i	0.155725	+	0.449939i	0.995695	−	0.0926953i	$-0.0295482\pi$
$709$	4.14651	+	11.9805i	0.155725	+	0.449939i	−0.839969	+	0.542634i	$0.817427\pi$
$710$	−11.3026	−	19.7210i	−0.424180	−	0.740117i
$711$	6.02661	−	2.31823i	0.226015	−	0.0869403i
$712$	36.4738	+	23.9341i	1.36691	+	0.896970i
$713$	−11.7658	+	18.3080i	−0.440634	+	0.685640i
$714$	−0.735725	+	9.02228i	−0.0275338	+	0.337650i
$715$	−28.2718	−	4.06488i	−1.05731	−	0.152018i
$716$	−4.96955	+	10.7015i	−0.185721	+	0.399932i
$717$	20.7907	−	24.8349i	0.776442	−	0.927477i
$718$	14.2596	+	12.4355i	0.532165	+	0.464089i
$719$	1.59587	+	33.5015i	0.0595160	+	1.24939i	0.809174	+	0.587569i	$0.199915\pi$
$719$	1.59587	+	33.5015i	0.0595160	+	1.24939i	−0.749658	+	0.661825i	$0.769782\pi$
$720$	16.2823	+	5.24943i	0.606806	+	0.195635i
$721$	1.41003	+	1.98012i	0.0525124	+	0.0737434i
$722$	−5.14768	+	26.2598i	−0.191577	+	0.977289i
$723$	14.7354	−	14.5366i	0.548014	−	0.540621i
$724$	2.11287	−	0.830339i	0.0785241	−	0.0308593i
$725$	−17.4739	−	6.04777i	−0.648964	−	0.224609i
$726$	−0.736475	−	1.76832i	−0.0273332	−	0.0656287i
$727$	−13.0952	+	16.6518i	−0.485672	+	0.617583i	−0.965697	−	0.259672i	$-0.916385\pi$
$727$	−13.0952	+	16.6518i	−0.485672	+	0.617583i	0.480024	+	0.877255i	$0.340628\pi$
$728$	−74.4966	+	46.8796i	−2.76103	+	1.73748i
$729$	13.6600	+	23.2896i	0.505924	+	0.862578i
$730$	−25.8394	−	20.4534i	−0.956360	−	0.757016i
$731$	−6.07130	−	0.579739i	−0.224555	−	0.0214424i
$732$	−0.667967	+	18.0743i	−0.0246888	+	0.668045i
$733$	−11.5543	−	5.95664i	−0.426767	−	0.220014i	0.231442	−	0.972849i	$-0.425655\pi$
$733$	−11.5543	−	5.95664i	−0.426767	−	0.220014i	−0.658209	+	0.752835i	$0.728686\pi$
$734$	6.98269	+	29.1871i	0.257736	+	1.07732i
$735$	43.5676	+	1.33319i	1.60702	+	0.0491754i
$736$	−18.6459	−	37.6224i	−0.687296	−	1.38678i
$737$	23.9903	+	10.4437i	0.883693	+	0.384699i
$738$	11.0308	−	6.12453i	0.406049	−	0.225447i
$739$	5.68305	+	1.37869i	0.209054	+	0.0507161i	0.338918	−	0.940816i	$-0.389939\pi$
$739$	5.68305	+	1.37869i	0.209054	+	0.0507161i	−0.129864	+	0.991532i	$0.541454\pi$
$740$	15.9642	−	5.41200i	0.586855	−	0.198949i
$741$	0.805098	−	2.92506i	0.0295760	−	0.107455i
$742$	−8.23197	−	2.87841i	−0.302205	−	0.105670i
$743$	21.9211	+	2.09321i	0.804208	+	0.0767925i	0.489060	−	0.872250i	$-0.337340\pi$
$743$	21.9211	+	2.09321i	0.804208	+	0.0767925i	0.315148	+	0.949043i	$0.397946\pi$
$744$	−13.8114	−	3.94334i	−0.506351	−	0.144570i
$745$	8.34017	−	9.62507i	0.305560	−	0.352635i
$746$	7.09223	+	17.8798i	0.259665	+	0.654627i
$747$	19.3762	+	4.98020i	0.708937	+	0.182216i
$748$	1.31159	+	4.57411i	0.0479566	+	0.167246i
$749$	32.6611	+	11.3041i	1.19341	+	0.413043i
$750$	−24.5516	+	13.0903i	−0.896499	+	0.477990i
$751$	−5.74579	−	8.94062i	−0.209667	−	0.326248i	0.720453	−	0.693503i	$-0.243934\pi$
$751$	−5.74579	−	8.94062i	−0.209667	−	0.326248i	−0.930120	+	0.367256i	$0.880297\pi$
$752$	32.7237	−	2.70590i	1.19331	−	0.0986740i
$753$	−16.9230	−	15.5952i	−0.616708	−	0.568321i
$754$	−46.5574	+	29.7122i	−1.69552	+	1.08205i
$755$	−1.03897	−	21.8108i	−0.0378121	−	0.793775i
$756$	51.5986	+	0.150769i	1.87662	+	0.00548340i
$757$	0.360420	−	0.283437i	0.0130997	−	0.0103017i	−0.611588	−	0.791177i	$-0.709469\pi$
$757$	0.360420	−	0.283437i	0.0130997	−	0.0103017i	0.624687	+	0.780875i	$0.285226\pi$
$758$	−5.17370	+	8.89578i	−0.187917	+	0.323109i
$759$	−2.65337	−	41.0111i	−0.0963113	−	1.48861i
$760$	−0.117795	+	1.12071i	−0.00427288	+	0.0406524i
$761$	26.6334	−	41.4424i	0.965460	−	1.50228i	0.103925	−	0.994585i	$-0.466860\pi$
$761$	26.6334	−	41.4424i	0.965460	−	1.50228i	0.861534	−	0.507699i	$-0.169504\pi$
$762$	35.3301	+	22.0207i	1.27987	+	0.797725i
$763$	8.47473	+	0.403701i	0.306806	+	0.0146150i
$764$	−12.9832	−	18.4795i	−0.469715	−	0.668566i
$765$	2.16526	+	2.33351i	0.0782850	+	0.0843681i
$766$	7.19765	−	5.09107i	0.260062	−	0.183948i
$767$	−6.39368	+	11.0742i	−0.230862	+	0.399865i
$768$	20.2164	−	18.9551i	0.729496	−	0.683985i
$769$	−20.9230	+	8.37632i	−0.754504	+	0.302058i	−0.716845	−	0.697233i	$-0.754414\pi$
$769$	−20.9230	+	8.37632i	−0.754504	+	0.302058i	−0.0376590	+	0.999291i	$0.511990\pi$
$770$	30.2719	−	10.3697i	1.09092	−	0.373699i
$771$	3.88567	−	1.85504i	0.139939	−	0.0668075i
$772$	−31.8197	+	20.1650i	−1.14522	+	0.725754i
$773$	−3.52217	+	18.2747i	−0.126684	+	0.657297i	0.861955	+	0.506985i	$0.169240\pi$
$773$	−3.52217	+	18.2747i	−0.126684	+	0.657297i	−0.988639	+	0.150312i	$0.951972\pi$
$774$	−0.582502	+	34.7596i	−0.0209376	+	1.24941i
$775$	7.53495	−	4.35030i	0.270663	−	0.156268i
$776$	−9.90607	+	6.91286i	−0.355607	+	0.248157i
$777$	40.9068	−	30.1912i	1.46752	−	1.08310i
$778$	−0.388914	−	8.74855i	−0.0139432	−	0.313651i
$779$	0.544244	+	0.628091i	0.0194996	+	0.0225037i
$780$	−5.53361	+	30.4545i	−0.198135	+	1.09045i
$781$	−33.4569	−	13.3941i	−1.19718	−	0.479279i
$782$	0.396543	−	7.80319i	0.0141804	−	0.279042i
$783$	32.3770	−	0.110959i	1.15706	−	0.00396536i
$784$	36.0780	−	60.6957i	1.28850	−	2.16770i
$785$	−4.71909	−	4.94923i	−0.168431	−	0.176646i
$786$	−32.1568	+	11.6302i	−1.14699	+	0.414834i
$787$	−13.3321	−	25.8607i	−0.475239	−	0.921835i	−0.997609	−	0.0691155i	$-0.977982\pi$
$787$	−13.3321	−	25.8607i	−0.475239	−	0.921835i	0.522370	−	0.852719i	$-0.325048\pi$
$788$	−29.2299	+	30.2683i	−1.04127	+	1.07826i
$789$	5.39571	+	0.422757i	0.192092	+	0.0150505i
$790$	−2.67166	−	3.41958i	−0.0950533	−	0.121663i
$791$	56.4660	−	10.8829i	2.00770	−	0.386952i
$792$	25.4069	−	9.49640i	0.902796	−	0.337440i
$793$	−32.5764	+	3.11067i	−1.15682	+	0.110463i
$794$	12.4085	−	19.1739i	0.440360	−	0.680455i
$795$	−2.70153	+	1.45142i	−0.0958135	+	0.0514766i
$796$	10.7429	+	6.29369i	0.380771	+	0.223074i
$797$	−0.0666538	+	0.0699045i	−0.00236100	+	0.00247614i	−0.724913	−	0.688840i	$-0.758120\pi$
$797$	−0.0666538	+	0.0699045i	−0.00236100	+	0.00247614i	0.722552	+	0.691316i	$0.242969\pi$
$798$	0.689340	+	3.32818i	0.0244024	+	0.117816i
$799$	5.55776	+	2.53814i	0.196619	+	0.0897931i
$800$	−0.266443	+	16.7850i	−0.00942020	+	0.593439i
$801$	39.2625	−	24.4854i	1.38727	−	0.865150i
$802$	2.67324	−	18.1828i	0.0943954	−	0.642059i
$803$	−52.2490			−1.84383
$804$	12.2703	−	25.5625i	0.432739	−	0.901519i
$805$	−52.5413			−1.85184
$806$	3.78010	−	25.7115i	0.133148	−	0.905648i
$807$	−39.5025	+	14.4288i	−1.39055	+	0.507919i
$808$	30.1824	+	6.11586i	1.06181	+	0.215155i
$809$	−1.08974	−	0.497665i	−0.0383130	−	0.0174970i	0.396166	−	0.918179i	$-0.370340\pi$
$809$	−1.08974	−	0.497665i	−0.0383130	−	0.0174970i	−0.434479	+	0.900682i	$0.643068\pi$
$810$	12.2932	−	13.3466i	0.431939	−	0.468951i
$811$	32.9269	−	34.5327i	1.15622	−	1.21261i	0.182905	−	0.983131i	$-0.441450\pi$
$811$	32.9269	−	34.5327i	1.15622	−	1.21261i	0.973314	−	0.229477i	$-0.0737017\pi$
$812$	31.2770	−	53.3877i	1.09761	−	1.87354i
$813$	15.9805	+	29.7446i	0.560462	+	1.04319i
$814$	14.5203	−	22.4371i	0.508936	−	0.786420i
$815$	15.8595	−	1.51440i	0.555534	−	0.0530470i
$816$	5.00607	−	1.23733i	0.175247	−	0.0433153i
$817$	−2.24856	+	0.433375i	−0.0786673	+	0.0151619i
$818$	19.0617	+	24.3979i	0.666477	+	0.853053i
$819$	12.0301	+	92.5805i	0.420365	+	3.23503i
$820$	−6.09945	−	5.89020i	−0.213002	−	0.205695i
$821$	5.35598	+	10.3892i	0.186925	+	0.362584i	0.963613	−	0.267302i	$-0.0861320\pi$
$821$	5.35598	+	10.3892i	0.186925	+	0.362584i	−0.776688	+	0.629886i	$0.783102\pi$
$822$	−3.16146	−	8.74127i	−0.110269	−	0.304887i
$823$	36.1334	+	37.8956i	1.25953	+	1.32096i	0.925669	+	0.378335i	$0.123503\pi$
$823$	36.1334	+	37.8956i	1.25953	+	1.32096i	0.333862	+	0.942622i	$0.391648\pi$
$824$	0.813949	−	1.12030i	0.0283553	−	0.0390274i
$825$	−6.57018	+	15.0594i	−0.228744	+	0.524301i
$826$	0.727068	−	14.3073i	0.0252979	−	0.497814i
$827$	−41.8924	−	16.7712i	−1.45674	−	0.583191i	−0.497926	−	0.867220i	$-0.665905\pi$
$827$	−41.8924	−	16.7712i	−1.45674	−	0.583191i	−0.958816	+	0.284028i	$0.908329\pi$
$828$	−44.5195	+	1.23212i	−1.54716	+	0.0428192i
$829$	24.9285	+	28.7691i	0.865804	+	0.999191i	0.999966	+	0.00823191i	$0.00262033\pi$
$829$	24.9285	+	28.7691i	0.865804	+	0.999191i	−0.134162	+	0.990959i	$0.542834\pi$
$830$	−0.597104	−	13.4318i	−0.0207258	−	0.466223i
$831$	3.82716	+	5.18552i	0.132763	+	0.179884i
$832$	38.8163	+	31.7404i	1.34571	+	1.10040i
$833$	11.3784	−	6.56932i	0.394238	−	0.227614i
$834$	−2.33486	+	10.2408i	−0.0808497	+	0.354609i
$835$	−1.97065	+	10.2247i	−0.0681971	+	0.353840i
$836$	0.956370	+	1.50912i	0.0330767	+	0.0521941i
$837$	−9.93702	+	11.5477i	−0.343474	+	0.399146i
$838$	−6.71594	+	2.30056i	−0.231998	+	0.0794716i
$839$	9.87215	−	3.95221i	0.340825	−	0.136446i	−0.194935	−	0.980816i	$-0.562450\pi$
$839$	9.87215	−	3.95221i	0.340825	−	0.136446i	0.535760	+	0.844371i	$0.320025\pi$
$840$	−10.0184	−	33.1983i	−0.345668	−	1.14545i
$841$	4.91259	−	8.50886i	0.169400	−	0.293409i
$842$	21.2630	−	15.0398i	0.732771	−	0.518306i
$843$	−37.7107	+	22.6361i	−1.29883	+	0.779628i
$844$	13.5963	−	9.55234i	0.468003	−	0.328805i
$845$	−37.4286	−	1.78294i	−1.28758	−	0.0613352i
$846$	11.9407	−	32.7162i	0.410530	−	1.12481i
$847$	−2.09921	+	3.26644i	−0.0721298	+	0.112236i
$848$	−0.0630804	+	4.96745i	−0.00216619	+	0.170583i
$849$	−2.01126	+	0.130126i	−0.0690261	+	0.00446592i
$850$	−1.57042	+	2.70022i	−0.0538651	+	0.0926169i
$851$	−34.4944	+	27.1267i	−1.18245	+	0.929891i
$852$	−15.8443	+	35.6964i	−0.542817	+	1.22294i
$853$	0.0364310	+	0.764781i	0.00124737	+	0.0261856i	0.999405	−	0.0344850i	$-0.0109791\pi$
$853$	0.0364310	+	0.764781i	0.00124737	+	0.0261856i	−0.998158	+	0.0606706i	$0.980676\pi$
$854$	30.9044	−	19.7227i	1.05753	−	0.674896i
$855$	1.02689	+	0.611622i	0.0351191	+	0.0209170i
$856$	0.187503	−	19.6878i	0.00640872	−	0.672914i
$857$	7.24373	+	11.2715i	0.247441	+	0.385026i	0.942651	−	0.333781i	$-0.108325\pi$
$857$	7.24373	+	11.2715i	0.247441	+	0.385026i	−0.695209	+	0.718807i	$0.744688\pi$
$858$	23.0890	+	43.3048i	0.788245	+	1.47840i
$859$	−22.5906	−	7.81870i	−0.770783	−	0.266770i	−0.0867581	−	0.996229i	$-0.527651\pi$
$859$	−22.5906	−	7.81870i	−0.770783	−	0.266770i	−0.684025	+	0.729459i	$0.739772\pi$
$860$	22.4585	−	6.43980i	0.765827	−	0.219595i
$861$	−22.9276	−	11.3306i	−0.781370	−	0.386146i
$862$	2.31054	+	5.82499i	0.0786975	+	0.198400i
$863$	23.4729	−	27.0892i	0.799028	−	0.922128i	−0.199299	−	0.979939i	$-0.563867\pi$
$863$	23.4729	−	27.0892i	0.799028	−	0.922128i	0.998328	+	0.0578110i	$0.0184121\pi$
$864$	−9.26736	−	27.8947i	−0.315282	−	0.948998i
$865$	19.2504	+	1.83819i	0.654533	+	0.0625003i
$866$	−24.1213	−	8.43430i	−0.819674	−	0.286609i
$867$	−27.4640	−	7.55922i	−0.932726	−	0.256725i
$868$	9.34749	+	27.5730i	0.317274	+	0.935887i
$869$	−6.68623	−	1.62206i	−0.226815	−	0.0550246i
$870$	−6.41848	−	20.7909i	−0.217607	−	0.704877i
$871$	48.7727	+	15.9135i	1.65260	+	0.539209i
$872$	−1.31745	−	4.65018i	−0.0446143	−	0.157475i
$873$	2.25367	+	12.6126i	0.0762753	+	0.426873i
$874$	−0.682575	−	2.85312i	−0.0230885	−	0.0965081i
$875$	50.1283	+	25.8429i	1.69465	+	0.873650i
$876$	−2.09114	+	56.5835i	−0.0706532	+	1.91178i
$877$	14.4864	+	1.38329i	0.489173	+	0.0467103i	0.336729	−	0.941602i	$-0.390680\pi$
$877$	14.4864	+	1.38329i	0.489173	+	0.0467103i	0.152444	+	0.988312i	$0.451286\pi$
$878$	17.8818	+	14.1545i	0.603480	+	0.477690i
$879$	30.0813	+	16.6918i	1.01462	+	0.563001i
$880$	−11.0853	−	14.4705i	−0.373684	−	0.487800i
$881$	−29.9820	+	38.1252i	−1.01012	+	1.28447i	−0.0518329	+	0.998656i	$0.516506\pi$
$881$	−29.9820	+	38.1252i	−1.01012	+	1.28447i	−0.958285	+	0.285814i	$0.907736\pi$
$882$	−42.4133	−	61.7244i	−1.42813	−	2.07837i
$883$	32.5958	+	11.2815i	1.09694	+	0.379653i	0.814812	−	0.579725i	$-0.196840\pi$
$883$	32.5958	+	11.2815i	1.09694	+	0.379653i	0.282124	+	0.959378i	$0.408961\pi$
$884$	3.41261	+	8.68366i	0.114778	+	0.292063i
$885$	−3.53801	−	3.58639i	−0.118929	−	0.120555i
$886$	1.89195	−	9.65140i	0.0635614	−	0.324245i
$887$	19.9482	+	28.0133i	0.669793	+	0.940593i	0.999994	−	0.00331732i	$-0.00105594\pi$
$887$	19.9482	+	28.0133i	0.669793	+	0.940593i	−0.330201	+	0.943911i	$0.607117\pi$
$888$	−23.7173	−	16.6229i	−0.795901	−	0.557827i
$889$	−4.01522	−	84.2898i	−0.134666	−	2.82699i
$890$	−23.4368	−	20.4387i	−0.785602	−	0.685106i
$891$	2.14887	−	28.6886i	0.0719900	−	0.961106i
$892$	−4.15005	−	1.92720i	−0.138954	−	0.0645275i
$893$	2.27072	+	0.326480i	0.0759868	+	0.0109252i
$894$	−21.8099	−	1.77850i	−0.729433	−	0.0594819i
$895$	4.54710	−	7.07542i	0.151993	−	0.236505i
$896$	−54.9087	−	11.8539i	−1.83437	−	0.396012i
$897$	−12.8228	−	79.5541i	−0.428140	−	2.65624i
$898$	23.6492	+	41.2636i	0.789185	+	1.37698i
$899$	5.97508	+	17.2639i	0.199280	+	0.575782i
$900$	16.0457	+	7.71795i	0.534858	+	0.257265i
$901$	−0.462201	+	0.800556i	−0.0153981	+	0.0266704i
$902$	−13.3786	−	1.32038i	−0.445460	−	0.0439637i
$903$	58.6244	−	39.1003i	1.95090	−	1.30118i
$904$	−16.1083	−	28.5244i	−0.535756	−	0.948708i
$905$	−1.57260	+	0.381509i	−0.0522750	+	0.0126818i
$906$	−29.1669	+	23.5973i	−0.969004	+	0.783969i
$907$	1.18112	−	6.12825i	0.0392185	−	0.203485i	−0.957034	−	0.289975i	$-0.906353\pi$
$907$	1.18112	−	6.12825i	0.0392185	−	0.203485i	0.996253	+	0.0864901i	$0.0275651\pi$
$908$	5.91263	−	16.7388i	0.196217	−	0.555497i
$909$	19.3065	−	26.3474i	0.640357	−	0.873889i
$910$	57.1545	−	25.8826i	1.89465	−	0.858000i
$911$	−16.6496	−	36.4574i	−0.551624	−	1.20789i	−0.956019	−	0.293304i	$-0.905245\pi$
$911$	−16.6496	−	36.4574i	−0.551624	−	1.20789i	0.404395	−	0.914584i	$-0.367482\pi$
$912$	1.67259	−	0.975310i	0.0553851	−	0.0322957i
$913$	−13.9595	−	16.1101i	−0.461992	−	0.533167i
$914$	8.56031	−	16.4761i	0.283150	−	0.544979i
$915$	2.22425	−	12.6991i	0.0735314	−	0.419821i
$916$	0.606033	+	14.6831i	0.0200239	+	0.485142i
$917$	56.4612	+	40.2058i	1.86451	+	1.32771i
$918$	1.03376	−	5.37094i	0.0341191	−	0.177267i
$919$	−38.0833	−	39.9406i	−1.25625	−	1.31752i	−0.927838	−	0.372984i	$-0.878335\pi$
$919$	−38.0833	−	39.9406i	−1.25625	−	1.31752i	−0.328414	−	0.944534i	$-0.606514\pi$
$920$	9.51959	+	28.3766i	0.313852	+	0.935547i
$921$	−36.2969	−	44.5736i	−1.19602	−	1.46875i
$922$	16.4752	+	19.1358i	0.542582	+	0.630204i
$923$	−67.8003	−	19.9080i	−2.23167	−	0.655278i
$924$	−45.1224	−	31.4120i	−1.48442	−	1.03338i
$925$	17.2271	−	3.32025i	0.566424	−	0.109169i
$926$	6.83449	−	27.7868i	0.224595	−	0.913132i
$927$	−0.717040	−	1.28185i	−0.0235507	−	0.0421013i
$928$	−34.5006	−	7.21919i	−1.13254	−	0.236981i
$929$	−3.94492	−	13.4352i	−0.129429	−	0.440793i	0.869123	−	0.494596i	$-0.164684\pi$
$929$	−3.94492	−	13.4352i	−0.129429	−	0.440793i	−0.998552	+	0.0538026i	$0.982866\pi$
$930$	9.37114	+	4.12395i	0.307292	+	0.135229i
$931$	3.40426	−	3.57028i	0.111570	−	0.117011i
$932$	2.76265	+	31.0113i	0.0904935	+	1.01581i
$933$	−4.27888	+	19.0461i	−0.140084	+	0.623541i
$934$	−9.27485	+	22.9560i	−0.303482	+	0.751143i
$935$	−0.482718	−	3.35737i	−0.0157866	−	0.109798i
$936$	47.8214	−	23.2712i	1.56309	−	0.760644i
$937$	−36.3475			−1.18742			−0.593710	−	0.804679i	$-0.702337\pi$
$937$	−36.3475			−1.18742			−0.593710	+	0.804679i	$0.702337\pi$
$938$	−56.7643	+	9.01131i	−1.85342	+	0.294230i
$939$	28.9235	−	6.08650i	0.943882	−	0.198626i
$940$	−23.3715	−	1.26209i	−0.762296	−	0.0411650i
$941$	1.66682	−	0.239652i	0.0543368	−	0.00781245i	−0.115093	−	0.993355i	$-0.536717\pi$
$941$	1.66682	−	0.239652i	0.0543368	−	0.00781245i	0.169430	+	0.985542i	$0.445807\pi$
$942$	−2.06382	+	11.5670i	−0.0672430	+	0.376874i
$943$	20.0794	+	9.16994i	0.653874	+	0.298614i
$944$	−7.85882	+	2.19956i	−0.255783	+	0.0715895i
$945$	−36.4239	−	5.10961i	−1.18487	−	0.166216i
$946$	21.5823	−	30.1054i	0.701701	−	0.978810i
$947$	−28.9855	+	8.51091i	−0.941902	+	0.276567i	−0.716412	−	0.697678i	$-0.754217\pi$
$947$	−28.9855	+	8.51091i	−0.941902	+	0.276567i	−0.225491	+	0.974245i	$0.572398\pi$
$948$	−2.02422	+	7.17599i	−0.0657438	+	0.233065i
$949$	−101.984	+	9.73828i	−3.31054	+	0.316118i
$950$	−0.280126	+	1.13890i	−0.00908848	+	0.0369508i
$951$	9.51784	+	22.6501i	0.308637	+	0.734480i
$952$	−7.83401	−	6.91993i	−0.253902	−	0.224276i
$953$	−1.31182	+	4.46765i	−0.0424940	+	0.144721i	−0.978008	−	0.208570i	$-0.933119\pi$
$953$	−1.31182	+	4.46765i	−0.0424940	+	0.144721i	0.935514	+	0.353291i	$0.114937\pi$
$954$	4.75568	+	2.26891i	0.153971	+	0.0734586i
$955$	7.37678	+	14.3090i	0.238707	+	0.463027i
$956$	8.58626	+	36.4002i	0.277700	+	1.17727i
$957$	−28.4379	−	19.5302i	−0.919267	−	0.631323i
$958$	−17.3605	−	18.3233i	−0.560893	−	0.591999i
$959$	−10.9293	+	15.3480i	−0.352925	+	0.495613i
$960$	−16.1146	+	11.4257i	−0.520096	+	0.368764i
$961$	20.7991	+	8.32671i	0.670940	+	0.268604i
$962$	24.1600	−	46.5009i	0.778950	−	1.49925i
$963$	−18.8762	−	8.93229i	−0.608278	−	0.287839i
$964$	3.25119	+	23.6788i	0.104714	+	0.762644i
$965$	24.4261	−	11.1550i	0.786303	−	0.359093i
$966$	53.3770	+	72.8045i	1.71738	+	2.34245i
$967$	21.8618	−	12.6219i	0.703029	−	0.405894i	−0.105446	−	0.994425i	$-0.533627\pi$
$967$	21.8618	−	12.6219i	0.703029	−	0.405894i	0.808475	+	0.588531i	$0.200294\pi$
$968$	2.14448	+	0.541922i	0.0689263	+	0.0174180i
$969$	0.360226	−	0.00612768i	0.0115721	−	0.000196849i
$970$	7.66587	−	3.92128i	0.246136	−	0.125905i
$971$	0.656667	+	2.70682i	0.0210734	+	0.0868659i	0.981377	−	0.192090i	$-0.0615267\pi$
$971$	0.656667	+	2.70682i	0.0210734	+	0.0868659i	−0.960304	+	0.278956i	$0.910012\pi$
$972$	−30.9826	−	3.47534i	−0.993768	−	0.111471i
$973$	19.7656	−	7.91294i	0.633655	−	0.253677i
$974$	−28.7656	−	2.83896i	−0.921709	−	0.0909661i
$975$	−10.0174	+	30.6187i	−0.320814	+	0.980583i
$976$	−16.2512	−	13.1174i	−0.520188	−	0.419879i
$977$	25.9822	−	8.99253i	0.831245	−	0.287697i	0.121886	−	0.992544i	$-0.461106\pi$
$977$	25.9822	−	8.99253i	0.831245	−	0.287697i	0.709359	+	0.704848i	$0.248985\pi$
$978$	−18.2102	−	20.4374i	−0.582298	−	0.653517i
$979$	−49.2476	−	2.34595i	−1.57396	−	0.0749770i
$980$	−31.3632	+	39.3646i	−1.00186	+	1.25746i
$981$	−5.06383	−	0.798409i	−0.161676	−	0.0254912i
$982$	13.8108	−	46.4886i	0.440719	−	1.48351i
$983$	−4.67773	+	32.5343i	−0.149197	+	1.03768i	0.768343	+	0.640039i	$0.221082\pi$
$983$	−4.67773	+	32.5343i	−0.149197	+	1.03768i	−0.917539	+	0.397646i	$0.869827\pi$
$984$	−1.96536	+	14.4357i	−0.0626534	+	0.460192i
$985$	23.5768	−	18.5410i	0.751219	−	0.590765i
$986$	−4.94315	−	4.31081i	−0.157422	−	0.137284i
$987$	−68.3114	+	17.8077i	−2.17438	+	0.566824i
$988$	2.14799	+	2.76738i	0.0683367	+	0.0880419i
$989$	−49.5446	+	35.2806i	−1.57543	+	1.12186i
$990$	−18.8630	+	4.24275i	−0.599504	+	0.134843i
$991$	−16.1384	−	25.1118i	−0.512653	−	0.797703i	0.484366	−	0.874866i	$-0.339050\pi$
$991$	−16.1384	−	25.1118i	−0.512653	−	0.797703i	−0.997019	+	0.0771622i	$0.975414\pi$
$992$	13.1980	−	10.0442i	0.419038	−	0.318902i
$993$	−4.01893	−	0.508227i	−0.127537	−	0.0161281i
$994$	77.7802	−	14.7350i	2.46704	−	0.467365i
$995$	−6.97628	−	5.48621i	−0.221163	−	0.173924i
$996$	−18.0053	+	14.4728i	−0.570519	+	0.458588i
$997$	7.11281	−	8.20862i	0.225265	−	0.259969i	−0.631855	−	0.775087i	$-0.717706\pi$
$997$	7.11281	−	8.20862i	0.225265	−	0.259969i	0.857120	+	0.515117i	$0.172252\pi$
$998$	−3.30754	−	2.61811i	−0.104698	−	0.0828750i
$999$	−26.5510	+	15.4508i	−0.840038	+	0.488842i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.bd.a.35.6	yes	2640
3.2	odd	2	inner	804.2.bd.a.35.127	yes	2640
4.3	odd	2	inner	804.2.bd.a.35.12	yes	2640
12.11	even	2	inner	804.2.bd.a.35.121	yes	2640
67.23	even	33	inner	804.2.bd.a.23.121	yes	2640
201.23	odd	66	inner	804.2.bd.a.23.12	yes	2640
268.23	odd	66	inner	804.2.bd.a.23.127	yes	2640
804.23	even	66	inner	804.2.bd.a.23.6	✓	2640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.bd.a.23.6	✓	2640	804.23	even	66	inner
804.2.bd.a.23.12	yes	2640	201.23	odd	66	inner
804.2.bd.a.23.121	yes	2640	67.23	even	33	inner
804.2.bd.a.23.127	yes	2640	268.23	odd	66	inner
804.2.bd.a.35.6	yes	2640	1.1	even	1	trivial
804.2.bd.a.35.12	yes	2640	4.3	odd	2	inner
804.2.bd.a.35.121	yes	2640	12.11	even	2	inner
804.2.bd.a.35.127	yes	2640	3.2	odd	2	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.bd (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39917 - 0.205706i) q^{2} +(-0.594255 - 1.62692i) q^{3} +(1.91537 + 0.575637i) q^{4} +(-1.29680 - 0.592230i) q^{5} +(0.496799 + 2.39858i) q^{6} +(3.42631 - 3.59341i) q^{7} +(-2.56152 - 1.19942i) q^{8} +(-2.29372 + 1.93361i) q^{9} +O(q^{10})\)	\(q+(-1.39917 - 0.205706i) q^{2} +(-0.594255 - 1.62692i) q^{3} +(1.91537 + 0.575637i) q^{4} +(-1.29680 - 0.592230i) q^{5} +(0.496799 + 2.39858i) q^{6} +(3.42631 - 3.59341i) q^{7} +(-2.56152 - 1.19942i) q^{8} +(-2.29372 + 1.93361i) q^{9} +(1.69263 + 1.09539i) q^{10} +(3.18208 - 0.303852i) q^{11} +(-0.201704 - 3.45822i) q^{12} +(6.15441 - 1.18617i) q^{13} +(-5.53319 + 4.32299i) q^{14} +(-0.192878 + 2.46173i) q^{15} +(3.33728 + 2.20512i) q^{16} +(0.341061 + 0.661567i) q^{17} +(3.60707 - 2.23362i) q^{18} +(0.192852 + 0.202257i) q^{19} +(-2.14295 - 1.88083i) q^{20} +(-7.88228 - 3.43892i) q^{21} +(-4.51479 - 0.229433i) q^{22} +(6.89104 + 2.75876i) q^{23} +(-0.429160 + 4.88015i) q^{24} +(-1.94334 - 2.24274i) q^{25} +(-8.85509 + 0.393650i) q^{26} +(4.50888 + 2.58264i) q^{27} +(8.63115 - 4.91040i) q^{28} +(5.39619 - 3.11549i) q^{29} +(0.776262 - 3.40470i) q^{30} +(-0.554866 + 2.87892i) q^{31} +(-4.21583 - 3.77184i) q^{32} +(-2.38531 - 4.99642i) q^{33} +(-0.341115 - 0.995805i) q^{34} +(-6.57137 + 2.63078i) q^{35} +(-5.50638 + 2.38322i) q^{36} +(-2.95598 + 5.11991i) q^{37} +(-0.228228 - 0.322664i) q^{38} +(-5.58709 - 9.30784i) q^{39} +(2.61146 + 3.07242i) q^{40} +(2.97048 + 0.141502i) q^{41} +(10.3213 + 6.43308i) q^{42} +(-4.43005 + 6.89330i) q^{43} +(6.26977 + 1.24974i) q^{44} +(4.11964 - 1.14910i) q^{45} +(-9.07427 - 5.27751i) q^{46} +(6.45258 - 5.07437i) q^{47} +(1.60435 - 6.73989i) q^{48} +(-0.839925 - 17.6322i) q^{49} +(2.25773 + 3.53774i) q^{50} +(0.873637 - 0.948018i) q^{51} +(12.4708 + 1.27076i) q^{52} +(0.671456 + 1.04481i) q^{53} +(-5.77743 - 4.54106i) q^{54} +(-4.30648 - 1.49049i) q^{55} +(-13.0866 + 5.09501i) q^{56} +(0.214453 - 0.433947i) q^{57} +(-8.19108 + 3.24908i) q^{58} +(-1.33605 + 1.54189i) q^{59} +(-1.78649 + 4.60409i) q^{60} +(-5.19752 - 0.496303i) q^{61} +(1.36856 - 3.91396i) q^{62} +(-0.910752 + 14.8674i) q^{63} +(5.12278 + 6.14468i) q^{64} +(-8.68354 - 2.10660i) q^{65} +(2.30967 + 7.48153i) q^{66} +(7.16049 + 3.96578i) q^{67} +(0.272436 + 1.46347i) q^{68} +(0.393233 - 12.8506i) q^{69} +(9.73565 - 2.32914i) q^{70} +(-10.0208 - 5.16610i) q^{71} +(8.19463 - 2.20184i) q^{72} +(-16.2714 - 1.55373i) q^{73} +(5.18913 - 6.55557i) q^{74} +(-2.49391 + 4.49442i) q^{75} +(0.252956 + 0.498410i) q^{76} +(9.81093 - 12.4756i) q^{77} +(5.90262 + 14.1726i) q^{78} +(-2.03399 - 0.703971i) q^{79} +(-3.02186 - 4.83604i) q^{80} +(1.52232 - 8.87032i) q^{81} +(-4.12711 - 0.809032i) q^{82} +(-3.86820 - 5.43213i) q^{83} +(-13.1179 - 11.1241i) q^{84} +(-0.0504897 - 1.05991i) q^{85} +(7.61640 - 8.73362i) q^{86} +(-8.27537 - 6.92776i) q^{87} +(-8.51542 - 3.03833i) q^{88} +(-15.2669 - 2.19505i) q^{89} +(-6.00047 + 0.760350i) q^{90} +(16.8245 - 26.1795i) q^{91} +(11.6109 + 9.25078i) q^{92} +(5.01349 - 0.808090i) q^{93} +(-10.0721 + 5.77258i) q^{94} +(-0.130308 - 0.376500i) q^{95} +(-3.63119 + 9.10024i) q^{96} +(2.13540 - 3.69862i) q^{97} +(-2.45185 + 24.8433i) q^{98} +(-6.71128 + 6.84985i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9}+O(q^{10}) \) 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9	\( 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9} - 46 q^{10} - 24 q^{12} - 88 q^{13} - 26 q^{16} - 23 q^{18} - 128 q^{22} - 22 q^{24} + 160 q^{25} + 44 q^{28} - 18 q^{30} - 44 q^{33} - 6 q^{34} - 35 q^{36} - 48 q^{37} - 92 q^{40} - 10 q^{42} + 40 q^{45} + 46 q^{46} - 11 q^{48} - 216 q^{49} - 76 q^{52} + 129 q^{54} - 42 q^{57} - 56 q^{58} - 90 q^{60} - 80 q^{61} - 48 q^{64} - 74 q^{66} - 4 q^{69} + 96 q^{70} - 20 q^{72} - 216 q^{73} + 76 q^{76} - 66 q^{78} - 16 q^{81} + 20 q^{82} - 55 q^{84} - 104 q^{85} - 30 q^{88} - 64 q^{90} - 192 q^{93} - 32 q^{94} - 205 q^{96} - 64 q^{97}+O(q^{100}) \) 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9 - 46 * q^10 - 24 * q^12 - 88 * q^13 - 26 * q^16 - 23 * q^18 - 128 * q^22 - 22 * q^24 + 160 * q^25 + 44 * q^28 - 18 * q^30 - 44 * q^33 - 6 * q^34 - 35 * q^36 - 48 * q^37 - 92 * q^40 - 10 * q^42 + 40 * q^45 + 46 * q^46 - 11 * q^48 - 216 * q^49 - 76 * q^52 + 129 * q^54 - 42 * q^57 - 56 * q^58 - 90 * q^60 - 80 * q^61 - 48 * q^64 - 74 * q^66 - 4 * q^69 + 96 * q^70 - 20 * q^72 - 216 * q^73 + 76 * q^76 - 66 * q^78 - 16 * q^81 + 20 * q^82 - 55 * q^84 - 104 * q^85 - 30 * q^88 - 64 * q^90 - 192 * q^93 - 32 * q^94 - 205 * q^96 - 64 * q^97

Introduction

L-functions

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