LMFDB - Embedded newform 805.2.u.d.71.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [805,2,Mod(36,805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(805, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("805.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 805 = 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	805.u (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.42795736271$
Analytic rank:	$0$
Dimension:	$130$
Relative dimension:	$13$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			71.6
Character	$\chi$	$=$	805.71
Dual form			805.2.u.d.771.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366295 - 0.235403i) q^{2} +(0.126863 + 0.882351i) q^{3} +(-0.752073 - 1.64681i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(0.161239 - 0.353064i) q^{6} +(0.654861 - 0.755750i) q^{7} +(-0.236116 + 1.64222i) q^{8} +(2.11603 - 0.621322i) q^{9} +O(q^{10})$	\(q+(-0.366295 - 0.235403i) q^{2} +(0.126863 + 0.882351i) q^{3} +(-0.752073 - 1.64681i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(0.161239 - 0.353064i) q^{6} +(0.654861 - 0.755750i) q^{7} +(-0.236116 + 1.64222i) q^{8} +(2.11603 - 0.621322i) q^{9} +(0.285136 + 0.329065i) q^{10} +(-0.595896 + 0.382959i) q^{11} +(1.35765 - 0.872511i) q^{12} +(-1.66833 - 1.92536i) q^{13} +(-0.417778 + 0.122671i) q^{14} +(0.126863 - 0.882351i) q^{15} +(-1.89806 + 2.19048i) q^{16} +(0.922494 - 2.01998i) q^{17} +(-0.921352 - 0.270533i) q^{18} +(-0.630733 - 1.38111i) q^{19} +(0.257649 + 1.79199i) q^{20} +(0.749914 + 0.481940i) q^{21} +0.308423 q^{22} +(-4.79150 + 0.203864i) q^{23} -1.47897 q^{24} +(0.841254 + 0.540641i) q^{25} +(0.157866 + 1.09798i) q^{26} +(1.92760 + 4.22086i) q^{27} +(-1.73708 - 0.510052i) q^{28} +(2.50813 - 5.49205i) q^{29} +(-0.254177 + 0.293336i) q^{30} +(0.888847 - 6.18207i) q^{31} +(4.39471 - 1.29040i) q^{32} +(-0.413501 - 0.477206i) q^{33} +(-0.813415 + 0.522750i) q^{34} +(-0.841254 + 0.540641i) q^{35} +(-2.61461 - 3.01742i) q^{36} +(-7.40042 + 2.17296i) q^{37} +(-0.0940843 + 0.654371i) q^{38} +(1.48719 - 1.71631i) q^{39} +(0.689220 - 1.50918i) q^{40} +(-10.8432 - 3.18385i) q^{41} +(-0.161239 - 0.353064i) q^{42} +(-1.30495 - 9.07610i) q^{43} +(1.07882 + 0.693314i) q^{44} -2.20536 q^{45} +(1.80309 + 1.05326i) q^{46} -2.90030 q^{47} +(-2.17357 - 1.39687i) q^{48} +(-0.142315 - 0.989821i) q^{49} +(-0.180878 - 0.396068i) q^{50} +(1.89936 + 0.557703i) q^{51} +(-1.91599 + 4.19544i) q^{52} +(-4.63784 + 5.35235i) q^{53} +(0.287534 - 1.99984i) q^{54} +(0.679650 - 0.199563i) q^{55} +(1.08649 + 1.25387i) q^{56} +(1.13861 - 0.731740i) q^{57} +(-2.21156 + 1.42128i) q^{58} +(1.73208 + 1.99893i) q^{59} +(-1.54847 + 0.454673i) q^{60} +(2.05350 - 14.2824i) q^{61} +(-1.78086 + 2.05522i) q^{62} +(0.916141 - 2.00607i) q^{63} +(3.64851 + 1.07130i) q^{64} +(1.05832 + 2.31739i) q^{65} +(0.0391275 + 0.272138i) q^{66} +(1.45193 + 0.933102i) q^{67} -4.02031 q^{68} +(-0.787743 - 4.20192i) q^{69} +0.435415 q^{70} +(10.5174 + 6.75913i) q^{71} +(0.520722 + 3.62170i) q^{72} +(-5.03255 - 11.0197i) q^{73} +(3.22226 + 0.946140i) q^{74} +(-0.370311 + 0.810868i) q^{75} +(-1.80007 + 2.07740i) q^{76} +(-0.100808 + 0.701133i) q^{77} +(-0.948776 + 0.278586i) q^{78} +(-5.60601 - 6.46969i) q^{79} +(2.43831 - 1.56701i) q^{80} +(2.08607 - 1.34063i) q^{81} +(3.22232 + 3.71875i) q^{82} +(6.14573 - 1.80455i) q^{83} +(0.229674 - 1.59742i) q^{84} +(-1.45422 + 1.67826i) q^{85} +(-1.65855 + 3.63171i) q^{86} +(5.16410 + 1.51632i) q^{87} +(-0.488204 - 1.06902i) q^{88} +(-1.64663 - 11.4526i) q^{89} +(0.807812 + 0.519150i) q^{90} -2.54762 q^{91} +(3.93928 + 7.73736i) q^{92} +5.56751 q^{93} +(1.06237 + 0.682741i) q^{94} +(0.216080 + 1.50287i) q^{95} +(1.69611 + 3.71397i) q^{96} +(11.7817 + 3.45943i) q^{97} +(-0.180878 + 0.396068i) q^{98} +(-1.02299 + 1.18060i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9}+O(q^{10}) $ 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9	\( 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9} + 2 q^{10} + 2 q^{11} - 5 q^{12} + 13 q^{13} - 2 q^{14} + 2 q^{15} - 6 q^{16} - 51 q^{17} + q^{18} - 9 q^{19} - 16 q^{20} - 2 q^{21} + 34 q^{22} - 10 q^{23} - 76 q^{24} - 13 q^{25} - 31 q^{26} + 14 q^{27} + 27 q^{28} + 3 q^{29} + 5 q^{30} + 6 q^{31} + 22 q^{32} - 58 q^{33} + q^{34} + 13 q^{35} + 193 q^{36} - 36 q^{37} + 4 q^{38} - 2 q^{39} - 29 q^{40} - 34 q^{41} - 5 q^{42} - 22 q^{43} + 8 q^{44} + 170 q^{45} - 198 q^{46} - 14 q^{47} - 120 q^{48} - 13 q^{49} + 2 q^{50} - 6 q^{51} + 33 q^{52} - 18 q^{53} + 188 q^{54} - 31 q^{55} - 15 q^{56} - 9 q^{57} + 114 q^{58} + 46 q^{59} - 16 q^{60} - 56 q^{61} - 146 q^{62} + 17 q^{63} - 109 q^{64} + 2 q^{65} - 14 q^{66} - 10 q^{67} + 86 q^{68} - 6 q^{69} - 2 q^{70} - 25 q^{72} + 64 q^{73} + 79 q^{74} + 2 q^{75} + 32 q^{76} - 13 q^{77} - 64 q^{78} - 118 q^{79} - 17 q^{80} + 23 q^{81} + 129 q^{82} - 117 q^{83} - 72 q^{84} - 7 q^{85} + 74 q^{86} - 51 q^{87} - 40 q^{88} - 35 q^{89} + 100 q^{90} + 42 q^{91} + 76 q^{92} - 90 q^{93} - 7 q^{94} + 2 q^{95} + 393 q^{96} - 4 q^{97} + 2 q^{98} - 40 q^{99}+O(q^{100}) \) 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9 + 2 * q^10 + 2 * q^11 - 5 * q^12 + 13 * q^13 - 2 * q^14 + 2 * q^15 - 6 * q^16 - 51 * q^17 + q^18 - 9 * q^19 - 16 * q^20 - 2 * q^21 + 34 * q^22 - 10 * q^23 - 76 * q^24 - 13 * q^25 - 31 * q^26 + 14 * q^27 + 27 * q^28 + 3 * q^29 + 5 * q^30 + 6 * q^31 + 22 * q^32 - 58 * q^33 + q^34 + 13 * q^35 + 193 * q^36 - 36 * q^37 + 4 * q^38 - 2 * q^39 - 29 * q^40 - 34 * q^41 - 5 * q^42 - 22 * q^43 + 8 * q^44 + 170 * q^45 - 198 * q^46 - 14 * q^47 - 120 * q^48 - 13 * q^49 + 2 * q^50 - 6 * q^51 + 33 * q^52 - 18 * q^53 + 188 * q^54 - 31 * q^55 - 15 * q^56 - 9 * q^57 + 114 * q^58 + 46 * q^59 - 16 * q^60 - 56 * q^61 - 146 * q^62 + 17 * q^63 - 109 * q^64 + 2 * q^65 - 14 * q^66 - 10 * q^67 + 86 * q^68 - 6 * q^69 - 2 * q^70 - 25 * q^72 + 64 * q^73 + 79 * q^74 + 2 * q^75 + 32 * q^76 - 13 * q^77 - 64 * q^78 - 118 * q^79 - 17 * q^80 + 23 * q^81 + 129 * q^82 - 117 * q^83 - 72 * q^84 - 7 * q^85 + 74 * q^86 - 51 * q^87 - 40 * q^88 - 35 * q^89 + 100 * q^90 + 42 * q^91 + 76 * q^92 - 90 * q^93 - 7 * q^94 + 2 * q^95 + 393 * q^96 - 4 * q^97 + 2 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/805\mathbb{Z}\right)^\times$.

$n$	$162$	$281$	$346$
$\chi(n)$	$1$	$e\left(\frac{1}{11}\right)$	$1$

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 $

$2$	−0.366295	−	0.235403i	−0.259009	−	0.166455i	0.404692	−	0.914453i	$-0.367379\pi$
$2$	−0.366295	−	0.235403i	−0.259009	−	0.166455i	−0.663701	+	0.747998i	$0.731015\pi$
$3$	0.126863	+	0.882351i	0.0732443	+	0.509426i	0.993109	+	0.117191i	$0.0373889\pi$
$3$	0.126863	+	0.882351i	0.0732443	+	0.509426i	−0.919865	+	0.392235i	$0.871702\pi$
$4$	−0.752073	−	1.64681i	−0.376036	−	0.823405i
$5$	−0.959493	−	0.281733i	−0.429098	−	0.125995i
$5$	−0.959493	−	0.281733i	−0.429098	−	0.125995i
$6$	0.161239	−	0.353064i	0.0658256	−	0.144138i
$7$	0.654861	−	0.755750i	0.247514	−	0.285646i
$7$	0.654861	−	0.755750i	0.247514	−	0.285646i
$8$	−0.236116	+	1.64222i	−0.0834797	+	0.580614i
$9$	2.11603	−	0.621322i	0.705343	−	0.207107i
$10$	0.285136	+	0.329065i	0.0901680	+	0.104059i
$11$	−0.595896	+	0.382959i	−0.179669	+	0.115466i	−0.627384	−	0.778710i	$-0.715874\pi$
$11$	−0.595896	+	0.382959i	−0.179669	+	0.115466i	0.447715	+	0.894176i	$0.352238\pi$
$12$	1.35765	−	0.872511i	0.391921	−	0.251872i
$13$	−1.66833	−	1.92536i	−0.462713	−	0.533999i	0.475658	−	0.879630i	$-0.342210\pi$
$13$	−1.66833	−	1.92536i	−0.462713	−	0.533999i	−0.938370	+	0.345632i	$0.887665\pi$
$14$	−0.417778	+	0.122671i	−0.111656	+	0.0327851i
$15$	0.126863	−	0.882351i	0.0327559	−	0.227822i
$16$	−1.89806	+	2.19048i	−0.474516	+	0.547621i
$17$	0.922494	−	2.01998i	0.223738	−	0.489917i	−0.764159	−	0.645027i	$-0.776846\pi$
$17$	0.922494	−	2.01998i	0.223738	−	0.489917i	0.987897	+	0.155110i	$0.0495732\pi$
$18$	−0.921352	−	0.270533i	−0.217165	−	0.0637653i
$19$	−0.630733	−	1.38111i	−0.144700	−	0.316849i	0.823380	−	0.567491i	$-0.192086\pi$
$19$	−0.630733	−	1.38111i	−0.144700	−	0.316849i	−0.968080	+	0.250642i	$0.919358\pi$
$20$	0.257649	+	1.79199i	0.0576120	+	0.400700i
$21$	0.749914	+	0.481940i	0.163645	+	0.105168i
$22$	0.308423			0.0657561
$23$	−4.79150	+	0.203864i	−0.999096	+	0.0425086i
$23$	−4.79150	+	0.203864i	−0.999096	+	0.0425086i
$24$	−1.47897			−0.301894
$25$	0.841254	+	0.540641i	0.168251	+	0.108128i
$26$	0.157866	+	1.09798i	0.0309600	+	0.215332i
$27$	1.92760	+	4.22086i	0.370967	+	0.812305i
$28$	−1.73708	−	0.510052i	−0.328277	−	0.0963909i
$29$	2.50813	−	5.49205i	0.465749	−	1.01985i	−0.520390	−	0.853928i	$-0.674214\pi$
$29$	2.50813	−	5.49205i	0.465749	−	1.01985i	0.986139	−	0.165919i	$-0.0530591\pi$
$30$	−0.254177	+	0.293336i	−0.0464062	+	0.0535557i
$31$	0.888847	−	6.18207i	0.159642	−	1.11033i	−0.739653	−	0.672988i	$-0.765010\pi$
$31$	0.888847	−	6.18207i	0.159642	−	1.11033i	0.899295	−	0.437343i	$-0.144081\pi$
$32$	4.39471	−	1.29040i	0.776882	−	0.228113i
$33$	−0.413501	−	0.477206i	−0.0719813	−	0.0830709i
$34$	−0.813415	+	0.522750i	−0.139499	+	0.0896509i
$35$	−0.841254	+	0.540641i	−0.142198	+	0.0913850i
$36$	−2.61461	−	3.01742i	−0.435768	−	0.502903i
$37$	−7.40042	+	2.17296i	−1.21662	+	0.357232i	−0.826186	−	0.563398i	$-0.809494\pi$
$37$	−7.40042	+	2.17296i	−1.21662	+	0.357232i	−0.390436	+	0.920630i	$0.627676\pi$
$38$	−0.0940843	+	0.654371i	−0.0152625	+	0.106153i
$39$	1.48719	−	1.71631i	0.238142	−	0.274830i
$40$	0.689220	−	1.50918i	0.108975	−	0.238623i
$41$	−10.8432	−	3.18385i	−1.69342	−	0.497234i	−0.714186	−	0.699956i	$-0.753203\pi$
$41$	−10.8432	−	3.18385i	−1.69342	−	0.497234i	−0.979236	+	0.202722i	$0.935021\pi$
$42$	−0.161239	−	0.353064i	−0.0248797	−	0.0544790i
$43$	−1.30495	−	9.07610i	−0.199002	−	1.38409i	−0.807187	−	0.590296i	$-0.799011\pi$
$43$	−1.30495	−	9.07610i	−0.199002	−	1.38409i	0.608184	−	0.793796i	$-0.291898\pi$
$44$	1.07882	+	0.693314i	0.162638	+	0.104521i
$45$	−2.20536			−0.328756
$46$	1.80309	+	1.05326i	0.265851	+	0.155295i
$47$	−2.90030			−0.423053			−0.211526	−	0.977372i	$-0.567843\pi$
$47$	−2.90030			−0.423053			−0.211526	+	0.977372i	$0.567843\pi$
$48$	−2.17357	−	1.39687i	−0.313728	−	0.201620i
$49$	−0.142315	−	0.989821i	−0.0203307	−	0.141403i
$50$	−0.180878	−	0.396068i	−0.0255800	−	0.0560124i
$51$	1.89936	+	0.557703i	0.265964	+	0.0780941i
$52$	−1.91599	+	4.19544i	−0.265700	+	0.581803i
$53$	−4.63784	+	5.35235i	−0.637056	+	0.735202i	−0.978851	−	0.204572i	$-0.934420\pi$
$53$	−4.63784	+	5.35235i	−0.637056	+	0.735202i	0.341795	+	0.939774i	$0.388965\pi$
$54$	0.287534	−	1.99984i	0.0391284	−	0.272144i
$55$	0.679650	−	0.199563i	0.0916440	−	0.0269091i
$56$	1.08649	+	1.25387i	0.145188	+	0.167556i
$57$	1.13861	−	0.731740i	0.150813	−	0.0969213i
$58$	−2.21156	+	1.42128i	−0.290392	+	0.186624i
$59$	1.73208	+	1.99893i	0.225498	+	0.260238i	0.857213	−	0.514962i	$-0.172194\pi$
$59$	1.73208	+	1.99893i	0.225498	+	0.260238i	−0.631715	+	0.775201i	$0.717649\pi$
$60$	−1.54847	+	0.454673i	−0.199907	+	0.0586980i
$61$	2.05350	−	14.2824i	0.262923	−	1.82867i	−0.247665	−	0.968846i	$-0.579663\pi$
$61$	2.05350	−	14.2824i	0.262923	−	1.82867i	0.510588	−	0.859826i	$-0.329428\pi$
$62$	−1.78086	+	2.05522i	−0.226169	+	0.261013i
$63$	0.916141	−	2.00607i	0.115423	−	0.252741i
$64$	3.64851	+	1.07130i	0.456064	+	0.133912i
$65$	1.05832	+	2.31739i	0.131268	+	0.287437i
$66$	0.0391275	+	0.272138i	0.00481626	+	0.0334978i
$67$	1.45193	+	0.933102i	0.177382	+	0.113997i	0.626319	−	0.779567i	$-0.284561\pi$
$67$	1.45193	+	0.933102i	0.177382	+	0.113997i	−0.448937	+	0.893564i	$0.648197\pi$
$68$	−4.02031			−0.487534
$69$	−0.787743	−	4.20192i	−0.0948331	−	0.505852i
$70$	0.435415			0.0520421
$71$	10.5174	+	6.75913i	1.24819	+	0.802162i	0.986622	−	0.163024i	$-0.0521248\pi$
$71$	10.5174	+	6.75913i	1.24819	+	0.802162i	0.261566	+	0.965186i	$0.415761\pi$
$72$	0.520722	+	3.62170i	0.0613677	+	0.426822i
$73$	−5.03255	−	11.0197i	−0.589015	−	1.28976i	−0.936035	−	0.351906i	$-0.885534\pi$
$73$	−5.03255	−	11.0197i	−0.589015	−	1.28976i	0.347020	−	0.937858i	$-0.387194\pi$
$74$	3.22226	+	0.946140i	0.374580	+	0.109987i
$75$	−0.370311	+	0.810868i	−0.0427598	+	0.0936310i
$76$	−1.80007	+	2.07740i	−0.206483	+	0.238294i
$77$	−0.100808	+	0.701133i	−0.0114881	+	0.0799015i
$78$	−0.948776	+	0.278586i	−0.107428	+	0.0315436i
$79$	−5.60601	−	6.46969i	−0.630726	−	0.727897i	0.346981	−	0.937872i	$-0.387207\pi$
$79$	−5.60601	−	6.46969i	−0.630726	−	0.727897i	−0.977707	+	0.209976i	$0.932661\pi$
$80$	2.43831	−	1.56701i	0.272611	−	0.175197i
$81$	2.08607	−	1.34063i	0.231785	−	0.148959i
$82$	3.22232	+	3.71875i	0.355845	+	0.410667i
$83$	6.14573	−	1.80455i	0.674582	−	0.198075i	0.0735394	−	0.997292i	$-0.476571\pi$
$83$	6.14573	−	1.80455i	0.674582	−	0.198075i	0.601042	+	0.799217i	$0.294752\pi$
$84$	0.229674	−	1.59742i	0.0250595	−	0.174293i
$85$	−1.45422	+	1.67826i	−0.157732	+	0.182033i
$86$	−1.65855	+	3.63171i	−0.178846	+	0.391618i
$87$	5.16410	+	1.51632i	0.553650	+	0.162566i
$88$	−0.488204	−	1.06902i	−0.0520427	−	0.113958i
$89$	−1.64663	−	11.4526i	−0.174543	−	1.21397i	−0.869137	−	0.494571i	$-0.835325\pi$
$89$	−1.64663	−	11.4526i	−0.174543	−	1.21397i	0.694594	−	0.719402i	$-0.255584\pi$
$90$	0.807812	+	0.519150i	0.0851509	+	0.0547232i
$91$	−2.54762			−0.267063
$92$	3.93928	+	7.73736i	0.410698	+	0.806676i
$93$	5.56751			0.577324
$94$	1.06237	+	0.682741i	0.109575	+	0.0704193i
$95$	0.216080	+	1.50287i	0.0221693	+	0.154191i
$96$	1.69611	+	3.71397i	0.173109	+	0.379056i
$97$	11.7817	+	3.45943i	1.19625	+	0.351252i	0.818419	−	0.574622i	$-0.194851\pi$
$97$	11.7817	+	3.45943i	1.19625	+	0.351252i	0.377834	+	0.925873i	$0.376669\pi$
$98$	−0.180878	+	0.396068i	−0.0182714	+	0.0400089i
$99$	−1.02299	+	1.18060i	−0.102815	+	0.118654i
$100$	0.257649	−	1.79199i	0.0257649	−	0.179199i
$101$	4.05340	−	1.19019i	0.403329	−	0.118428i	−0.0737751	−	0.997275i	$-0.523505\pi$
$101$	4.05340	−	1.19019i	0.403329	−	0.118428i	0.477104	+	0.878847i	$0.341687\pi$
$102$	−0.564441	−	0.651400i	−0.0558880	−	0.0644982i
$103$	−14.9800	+	9.62705i	−1.47602	+	0.948582i	−0.478510	+	0.878082i	$0.658823\pi$
$103$	−14.9800	+	9.62705i	−1.47602	+	0.948582i	−0.997512	+	0.0704993i	$0.977541\pi$
$104$	3.55579	−	2.28517i	0.348674	−	0.224079i
$105$	−0.583759	−	0.673694i	−0.0569690	−	0.0657458i
$106$	2.95878	−	0.868775i	0.287382	−	0.0843829i
$107$	−2.06410	+	14.3562i	−0.199544	+	1.38786i	0.606065	+	0.795415i	$0.292747\pi$
$107$	−2.06410	+	14.3562i	−0.199544	+	1.38786i	−0.805610	+	0.592447i	$0.798162\pi$
$108$	5.50126	−	6.34879i	0.529359	−	0.610913i
$109$	−2.32734	+	5.09616i	−0.222919	+	0.488124i	−0.987738	−	0.156121i	$-0.950101\pi$
$109$	−2.32734	+	5.09616i	−0.222919	+	0.488124i	0.764819	+	0.644245i	$0.222828\pi$
$110$	−0.295930	−	0.0868929i	−0.0282158	−	0.00828491i
$111$	−2.85615	−	6.25410i	−0.271094	−	0.593613i
$112$	0.412489	+	2.86892i	0.0389765	+	0.271088i
$113$	12.5938	+	8.09355i	1.18473	+	0.761377i	0.976249	−	0.216650i	$-0.0695131\pi$
$113$	12.5938	+	8.09355i	1.18473	+	0.761377i	0.208477	+	0.978027i	$0.433150\pi$
$114$	−0.589320			−0.0551949
$115$	4.65484	+	1.15431i	0.434066	+	0.107640i
$116$	−10.9307			−1.01489
$117$	−4.72651	−	3.03755i	−0.436966	−	0.280821i
$118$	−0.163898	−	1.13993i	−0.0150880	−	0.104939i
$119$	−0.922494	−	2.01998i	−0.0845649	−	0.185171i
$120$	1.41906	+	0.416675i	0.129542	+	0.0380370i
$121$	−4.36113	+	9.54954i	−0.396466	+	0.868140i
$122$	−4.11430	+	4.74816i	−0.372492	+	0.429878i
$123$	1.43367	−	9.97141i	0.129270	−	0.899092i
$124$	−10.8492	+	3.18560i	−0.974284	+	0.286076i
$125$	−0.654861	−	0.755750i	−0.0585725	−	0.0675963i
$126$	−0.807812	+	0.519150i	−0.0719657	+	0.0462495i
$127$	8.97153	−	5.76565i	0.796095	−	0.511619i	−0.0782446	−	0.996934i	$-0.524932\pi$
$127$	8.97153	−	5.76565i	0.796095	−	0.511619i	0.874339	+	0.485315i	$0.161295\pi$
$128$	−7.08308	−	8.17432i	−0.626062	−	0.722514i
$129$	7.84275	−	2.30284i	0.690516	−	0.202754i
$130$	0.157866	−	1.09798i	0.0138457	−	0.0962992i
$131$	1.87091	−	2.15915i	0.163462	−	0.188645i	−0.668109	−	0.744063i	$-0.732896\pi$
$131$	1.87091	−	2.15915i	0.163462	−	0.188645i	0.831572	+	0.555418i	$0.187442\pi$
$132$	−0.474884	+	1.03985i	−0.0413334	+	0.0905075i
$133$	−1.45682	−	0.427760i	−0.126322	−	0.0370915i
$134$	−0.312181	−	0.683580i	−0.0269683	−	0.0590524i
$135$	−0.660367	−	4.59296i	−0.0568354	−	0.395299i
$136$	3.09945	+	1.99189i	0.265775	+	0.170803i
$137$	14.1523			1.20911			0.604556	−	0.796562i	$-0.293350\pi$
$137$	14.1523			1.20911			0.604556	+	0.796562i	$0.293350\pi$
$138$	−0.700599	+	1.72458i	−0.0596390	+	0.146806i
$139$	−5.74403			−0.487203			−0.243601	−	0.969875i	$-0.578329\pi$
$139$	−5.74403			−0.487203			−0.243601	+	0.969875i	$0.578329\pi$
$140$	1.52302	+	0.978783i	0.128718	+	0.0827223i
$141$	−0.367941	−	2.55908i	−0.0309862	−	0.215514i
$142$	−2.26135	−	4.95167i	−0.189768	−	0.415535i
$143$	1.73149	+	0.508410i	0.144794	+	0.0425154i
$144$	−2.65536	+	5.81444i	−0.221280	+	0.484536i
$145$	−3.95383	+	4.56296i	−0.328347	+	0.378933i
$146$	−0.750688	+	5.22115i	−0.0621274	+	0.432106i
$147$	0.855315	−	0.251143i	0.0705452	−	0.0207139i
$148$	9.14411	+	10.5529i	0.751641	+	0.867440i
$149$	−14.8723	+	9.55785i	−1.21839	+	0.783009i	−0.982042	−	0.188660i	$-0.939586\pi$
$149$	−14.8723	+	9.55785i	−1.21839	+	0.783009i	−0.236344	+	0.971669i	$0.575949\pi$
$150$	0.326524	−	0.209844i	0.0266606	−	0.0171337i
$151$	−1.54721	−	1.78558i	−0.125910	−	0.145308i	0.689294	−	0.724482i	$-0.257921\pi$
$151$	−1.54721	−	1.78558i	−0.125910	−	0.145308i	−0.815204	+	0.579173i	$0.803375\pi$
$152$	2.41702	−	0.709702i	0.196047	−	0.0575645i
$153$	0.696966	−	4.84751i	0.0563464	−	0.391898i
$154$	0.201974	−	0.233091i	0.0162756	−	0.0187830i
$155$	−2.59453	+	5.68123i	−0.208398	+	0.456327i
$156$	−3.94492	−	1.15833i	−0.315846	−	0.0927408i
$157$	5.85881	+	12.8290i	0.467584	+	1.02387i	0.985693	+	0.168551i	$0.0539088\pi$
$157$	5.85881	+	12.8290i	0.467584	+	1.02387i	−0.518109	+	0.855314i	$0.673364\pi$
$158$	0.530468	+	3.68949i	0.0422018	+	0.293520i
$159$	−5.31102	−	3.41319i	−0.421191	−	0.270683i
$160$	−4.58024			−0.362100
$161$	−2.98369	+	3.75467i	−0.235148	+	0.295910i
$162$	−1.07970			−0.0848296
$163$	6.15599	+	3.95621i	0.482174	+	0.309875i	0.759051	−	0.651031i	$-0.225663\pi$
$163$	6.15599	+	3.95621i	0.482174	+	0.309875i	−0.276877	+	0.960905i	$0.589299\pi$
$164$	2.91168	+	20.2512i	0.227364	+	1.58135i
$165$	0.262307	+	0.574373i	0.0204206	+	0.0447148i
$166$	−2.67595	−	0.785728i	−0.207694	−	0.0609843i
$167$	−2.25591	+	4.93975i	−0.174567	+	0.382249i	−0.976610	−	0.215017i	$-0.931019\pi$
$167$	−2.25591	+	4.93975i	−0.174567	+	0.382249i	0.802043	+	0.597267i	$0.203747\pi$
$168$	−0.968521	+	1.11773i	−0.0747230	+	0.0862350i
$169$	0.926420	−	6.44339i	0.0712631	−	0.495646i
$170$	0.927741	−	0.272409i	0.0711545	−	0.0208929i
$171$	−2.19277	−	2.53059i	−0.167685	−	0.193519i
$172$	−13.9652	+	8.97489i	−1.06484	+	0.684329i
$173$	13.3285	−	8.56572i	1.01335	−	0.651240i	0.0750909	−	0.997177i	$-0.476075\pi$
$173$	13.3285	−	8.56572i	1.01335	−	0.651240i	0.938258	+	0.345937i	$0.112439\pi$
$174$	−1.53464	−	1.77107i	−0.116341	−	0.134264i
$175$	0.959493	−	0.281733i	0.0725309	−	0.0212970i
$176$	0.292183	−	2.03218i	0.0220242	−	0.153181i
$177$	−1.54402	+	1.78189i	−0.116056	+	0.133935i
$178$	−2.09283	+	4.58265i	−0.156864	+	0.343484i
$179$	14.2803	+	4.19309i	1.06736	+	0.313406i	0.767813	−	0.640675i	$-0.221345\pi$
$179$	14.2803	+	4.19309i	1.06736	+	0.313406i	0.299550	+	0.954081i	$0.403163\pi$
$180$	1.65859	+	3.63181i	0.123624	+	0.270699i
$181$	−0.233097	−	1.62123i	−0.0173260	−	0.120505i	0.979323	−	0.202303i	$-0.0648427\pi$
$181$	−0.233097	−	1.62123i	−0.0173260	−	0.120505i	−0.996649	+	0.0817985i	$0.973934\pi$
$182$	0.933178	+	0.599717i	0.0691718	+	0.0444540i
$183$	12.8626			0.950829
$184$	0.796559	−	7.91685i	0.0587231	−	0.583638i
$185$	7.71285			0.567060
$186$	−2.03935	−	1.31061i	−0.149532	−	0.0960986i
$187$	0.223859	+	1.55698i	0.0163702	+	0.113857i
$188$	2.18124	+	4.77625i	0.159083	+	0.348344i
$189$	4.45223	+	1.30729i	0.323852	+	0.0950915i
$190$	0.274631	−	0.601358i	0.0199238	−	0.0436271i
$191$	7.20401	−	8.31387i	0.521264	−	0.601571i	−0.432683	−	0.901546i	$-0.642433\pi$
$191$	7.20401	−	8.31387i	0.521264	−	0.601571i	0.953947	+	0.299975i	$0.0969785\pi$
$192$	−0.482401	+	3.35518i	−0.0348143	+	0.242139i
$193$	−7.13659	+	2.09549i	−0.513703	+	0.150837i	−0.528302	−	0.849057i	$-0.677171\pi$
$193$	−7.13659	+	2.09549i	−0.513703	+	0.150837i	0.0145987	+	0.999893i	$0.495353\pi$
$194$	−3.50122	−	4.04063i	−0.251373	−	0.290100i
$195$	−1.91049	+	1.22780i	−0.136813	+	0.0879245i
$196$	−1.52302	+	0.978783i	−0.108787	+	0.0699131i
$197$	0.150449	+	0.173627i	0.0107190	+	0.0123704i	0.761084	−	0.648654i	$-0.224668\pi$
$197$	0.150449	+	0.173627i	0.0107190	+	0.0123704i	−0.750365	+	0.661024i	$0.770122\pi$
$198$	0.652633	−	0.191630i	0.0463806	−	0.0136186i
$199$	3.90431	−	27.1551i	0.276769	−	1.92497i	−0.0926276	−	0.995701i	$-0.529527\pi$
$199$	3.90431	−	27.1551i	0.276769	−	1.92497i	0.369397	−	0.929272i	$-0.379564\pi$
$200$	−1.08649	+	1.25387i	−0.0768263	+	0.0886622i
$201$	−0.639127	+	1.39949i	−0.0450805	+	0.0987126i
$202$	−1.76491	−	0.518225i	−0.124179	−	0.0364622i
$203$	−2.50813	−	5.49205i	−0.176037	−	0.385466i
$204$	−0.510028	−	3.54732i	−0.0357091	−	0.248362i
$205$	9.50697	+	6.10976i	0.663996	+	0.426724i
$206$	7.75333			0.540200
$207$	−10.0123	+	3.40845i	−0.695902	+	0.236903i
$208$	7.38407			0.511993
$209$	0.904761	+	0.581455i	0.0625836	+	0.0402200i
$210$	0.0552380	+	0.384189i	0.00381179	+	0.0265116i
$211$	10.1894	+	22.3116i	0.701465	+	1.53599i	0.838186	+	0.545385i	$0.183616\pi$
$211$	10.1894	+	22.3116i	0.701465	+	1.53599i	−0.136721	+	0.990610i	$0.543656\pi$
$212$	12.3023	+	3.61228i	0.844925	+	0.248093i
$213$	−4.62966	+	10.1375i	−0.317219	+	0.694613i
$214$	4.13556	−	4.77269i	0.282701	−	0.326254i
$215$	−1.30495	+	9.07610i	−0.0889966	+	0.618985i
$216$	−7.38674	+	2.16894i	−0.502604	+	0.147578i
$217$	−4.09002	−	4.72014i	−0.277649	−	0.320424i
$218$	2.05215	−	1.31883i	0.138989	−	0.0893227i
$219$	9.08484	−	5.83847i	0.613896	−	0.394527i
$220$	−0.839789	−	0.969168i	−0.0566186	−	0.0653413i
$221$	−5.42822	+	1.59387i	−0.365142	+	0.107215i
$222$	−0.426043	+	2.96319i	−0.0285941	+	0.198876i
$223$	−7.14974	+	8.25124i	−0.478782	+	0.552544i	−0.942833	−	0.333264i	$-0.891850\pi$
$223$	−7.14974	+	8.25124i	−0.478782	+	0.552544i	0.464051	+	0.885808i	$0.346395\pi$
$224$	1.90270	−	4.16634i	0.127130	−	0.278375i
$225$	2.11603	+	0.621322i	0.141069	+	0.0414215i
$226$	−2.70780	−	5.92925i	−0.180120	−	0.394408i
$227$	2.48164	+	17.2602i	0.164712	+	1.14560i	0.889603	+	0.456734i	$0.150981\pi$
$227$	2.48164	+	17.2602i	0.164712	+	1.14560i	−0.724892	+	0.688863i	$0.758110\pi$
$228$	−2.06135	−	1.32475i	−0.136517	−	0.0877338i
$229$	−23.5370			−1.55537			−0.777685	−	0.628655i	$-0.783606\pi$
$229$	−23.5370			−1.55537			−0.777685	+	0.628655i	$0.783606\pi$
$230$	−1.43331	−	1.51858i	−0.0945100	−	0.100132i
$231$	−0.631434			−0.0415453
$232$	8.42697	+	5.41568i	0.553257	+	0.355557i
$233$	−1.44665	−	10.0617i	−0.0947733	−	0.659163i	−0.980726	−	0.195387i	$-0.937404\pi$
$233$	−1.44665	−	10.0617i	−0.0947733	−	0.659163i	0.885953	−	0.463775i	$-0.153505\pi$
$234$	1.01625	+	2.22527i	0.0664342	+	0.145471i
$235$	2.78282	+	0.817110i	0.181531	+	0.0533024i
$236$	1.98920	−	4.35575i	0.129486	−	0.283535i
$237$	4.99734	−	5.76723i	0.324612	−	0.374622i
$238$	−0.137605	+	0.957066i	−0.00891963	+	0.0620374i
$239$	18.3265	−	5.38116i	1.18545	−	0.348078i	0.371175	−	0.928563i	$-0.378955\pi$
$239$	18.3265	−	5.38116i	1.18545	−	0.348078i	0.814271	+	0.580485i	$0.197137\pi$
$240$	1.69198	+	1.95265i	0.109217	+	0.126043i
$241$	10.3885	−	6.67628i	0.669182	−	0.430057i	−0.161448	−	0.986881i	$-0.551617\pi$
$241$	10.3885	−	6.67628i	0.669182	−	0.430057i	0.830631	+	0.556824i	$0.187980\pi$
$242$	3.84545	−	2.47132i	0.247195	−	0.158863i
$243$	10.5636	+	12.1910i	0.677654	+	0.782055i
$244$	−25.0647	+	7.35967i	−1.60461	+	0.471155i
$245$	−0.142315	+	0.989821i	−0.00909216	+	0.0632374i
$246$	−2.87245	+	3.31498i	−0.183141	+	0.211356i
$247$	−1.60687	+	3.51855i	−0.102242	+	0.223880i
$248$	9.94247	+	2.91937i	0.631347	+	0.185380i
$249$	2.37191	+	5.19376i	0.150314	+	0.329141i
$250$	0.0619661	+	0.430983i	0.00391908	+	0.0272578i
$251$	8.36872	+	5.37825i	0.528229	+	0.339472i	0.777420	−	0.628982i	$-0.216528\pi$
$251$	8.36872	+	5.37825i	0.528229	+	0.339472i	−0.249191	+	0.968454i	$0.580165\pi$
$252$	−3.99262			−0.251511
$253$	2.77716	−	1.95643i	0.174599	−	0.123000i
$254$	−4.64348			−0.291358
$255$	−1.66530	−	1.07022i	−0.104285	−	0.0670201i
$256$	−0.412081	−	2.86609i	−0.0257551	−	0.179130i
$257$	−1.35015	−	2.95641i	−0.0842197	−	0.184416i	0.862837	−	0.505483i	$-0.168686\pi$
$257$	−1.35015	−	2.95641i	−0.0842197	−	0.184416i	−0.947056	+	0.321067i	$0.895958\pi$
$258$	−3.41485	−	1.00269i	−0.212600	−	0.0624249i
$259$	−3.20403	+	7.01585i	−0.199089	+	0.435944i
$260$	3.02037	−	3.48570i	0.187316	−	0.216174i
$261$	1.89495	−	13.1797i	0.117295	−	0.815803i
$262$	−1.19357	+	0.350465i	−0.0737393	+	0.0216518i
$263$	−1.00684	−	1.16195i	−0.0620842	−	0.0716489i	0.723858	−	0.689949i	$-0.242367\pi$
$263$	−1.00684	−	1.16195i	−0.0620842	−	0.0716489i	−0.785942	+	0.618300i	$0.787822\pi$
$264$	0.881314	−	0.566386i	0.0542411	−	0.0348586i
$265$	5.95791	−	3.82891i	0.365991	−	0.235208i
$266$	0.432928	+	0.499626i	0.0265445	+	0.0306340i
$267$	9.89631	−	2.90582i	0.605644	−	0.177833i
$268$	0.444681	−	3.09282i	0.0271632	−	0.188924i
$269$	−1.80426	+	2.08223i	−0.110008	+	0.126956i	−0.808083	−	0.589069i	$-0.799495\pi$
$269$	−1.80426	+	2.08223i	−0.110008	+	0.126956i	0.698075	+	0.716024i	$0.254040\pi$
$270$	−0.839308	+	1.83783i	−0.0510786	+	0.111847i
$271$	−0.108643	−	0.0319003i	−0.00659957	−	0.00193781i	0.278431	−	0.960456i	$-0.410186\pi$
$271$	−0.108643	−	0.0319003i	−0.00659957	−	0.00193781i	−0.285031	+	0.958518i	$0.592004\pi$
$272$	2.67378	+	5.85476i	0.162122	+	0.354997i
$273$	−0.323198	−	2.24789i	−0.0195608	−	0.136049i
$274$	−5.18391	−	3.33150i	−0.313172	−	0.201263i
$275$	−0.708343			−0.0427147
$276$	−6.32732	+	4.45741i	−0.380860	+	0.268305i
$277$	27.5200			1.65352			0.826758	−	0.562558i	$-0.190183\pi$
$277$	27.5200			1.65352			0.826758	+	0.562558i	$0.190183\pi$
$278$	2.10401	+	1.35216i	0.126190	+	0.0810974i
$279$	−1.96023	−	13.6337i	−0.117356	−	0.816228i
$280$	−0.689220	−	1.50918i	−0.0411888	−	0.0901908i
$281$	−8.80993	−	2.58683i	−0.525557	−	0.154317i	0.00818257	−	0.999967i	$-0.497395\pi$
$281$	−8.80993	−	2.58683i	−0.525557	−	0.154317i	−0.533739	+	0.845649i	$0.679214\pi$
$282$	−0.467642	+	1.02399i	−0.0278477	+	0.0609779i
$283$	3.41799	−	3.94458i	0.203179	−	0.234481i	−0.645011	−	0.764173i	$-0.723147\pi$
$283$	3.41799	−	3.94458i	0.203179	−	0.234481i	0.848190	+	0.529693i	$0.177693\pi$
$284$	3.22114	−	22.4036i	0.191140	−	1.32941i
$285$	−1.29864	+	0.381316i	−0.0769250	+	0.0225872i
$286$	−0.514553	−	0.593826i	−0.0304262	−	0.0351137i
$287$	−9.50697	+	6.10976i	−0.561179	+	0.360648i
$288$	8.49758	−	5.46106i	0.500725	−	0.321796i
$289$	7.90331	+	9.12090i	0.464900	+	0.536524i
$290$	2.52240	−	0.740644i	0.148120	−	0.0434921i
$291$	−1.55776	+	10.8345i	−0.0913177	+	0.635129i
$292$	−14.3626	+	16.5753i	−0.840507	+	0.969996i
$293$	1.64615	−	3.60456i	0.0961690	−	0.210581i	−0.855433	−	0.517913i	$-0.826709\pi$
$293$	1.64615	−	3.60456i	0.0961690	−	0.210581i	0.951602	+	0.307332i	$0.0994363\pi$
$294$	−0.372417	−	0.109352i	−0.0217198	−	0.00637751i
$295$	−1.09876	−	2.40594i	−0.0639721	−	0.140079i
$296$	−1.82113	−	12.6662i	−0.105851	−	0.736210i
$297$	−2.76507	−	1.77700i	−0.160446	−	0.103112i
$298$	7.69759			0.445910
$299$	8.38633	+	8.88524i	0.484994	+	0.513847i
$300$	1.61385			0.0931755
$301$	−7.71382	−	4.95737i	−0.444617	−	0.285738i
$302$	0.146405	+	1.01827i	0.00842463	+	0.0585946i
$303$	1.56439	+	3.42553i	0.0898718	+	0.196792i
$304$	4.22248	+	1.23983i	0.242176	+	0.0711092i
$305$	−5.99413	+	13.1253i	−0.343223	+	0.751553i
$306$	−1.39641	+	1.61155i	−0.0798277	+	0.0921260i
$307$	2.92409	−	20.3375i	0.166887	−	1.16072i	−0.718384	−	0.695647i	$-0.755118\pi$
$307$	2.92409	−	20.3375i	0.166887	−	1.16072i	0.885271	−	0.465076i	$-0.153973\pi$
$308$	1.23045	−	0.361292i	0.0701112	−	0.0205865i
$309$	−10.3948	−	11.9963i	−0.591342	−	0.682445i
$310$	2.28774	−	1.47024i	0.129935	−	0.0835042i
$311$	16.0798	−	10.3339i	0.911802	−	0.585980i	0.00153385	−	0.999999i	$-0.499512\pi$
$311$	16.0798	−	10.3339i	0.911802	−	0.585980i	0.910268	+	0.414019i	$0.135875\pi$
$312$	2.46742	+	2.84755i	0.139690	+	0.161211i
$313$	−6.57745	+	1.93131i	−0.371780	+	0.109164i	−0.462285	−	0.886732i	$-0.652970\pi$
$313$	−6.57745	+	1.93131i	−0.371780	+	0.109164i	0.0905048	+	0.995896i	$0.471152\pi$
$314$	0.873938	−	6.07838i	0.0493192	−	0.343023i
$315$	−1.44421	+	1.66670i	−0.0813718	+	0.0939080i
$316$	−6.43821	+	14.0977i	−0.362178	+	0.793059i
$317$	−20.1138	−	5.90593i	−1.12970	−	0.331710i	−0.337111	−	0.941465i	$-0.609450\pi$
$317$	−20.1138	−	5.90593i	−1.12970	−	0.331710i	−0.792590	+	0.609754i	$0.791268\pi$
$318$	1.14192	+	2.50046i	0.0640359	+	0.140219i
$319$	0.608643	+	4.23320i	0.0340774	+	0.237014i
$320$	−3.19890	−	2.05581i	−0.178824	−	0.114923i
$321$	−12.9290			−0.721628
$322$	1.97677	−	0.672946i	0.110161	−	0.0375018i
$323$	−3.37167			−0.187605
$324$	−3.77664	−	2.42710i	−0.209814	−	0.134839i
$325$	−0.362564	−	2.52169i	−0.0201114	−	0.139878i
$326$	−1.32360	−	2.89828i	−0.0733074	−	0.160521i
$327$	−4.79186	−	1.40702i	−0.264990	−	0.0778082i
$328$	7.78885	−	17.0552i	0.430067	−	0.941716i
$329$	−1.89929	+	2.19190i	−0.104711	+	0.120843i
$330$	0.0391275	−	0.272138i	0.00215390	−	0.0149807i
$331$	10.2706	−	3.01571i	0.564522	−	0.165759i	0.0129950	−	0.999916i	$-0.495863\pi$
$331$	10.2706	−	3.01571i	0.564522	−	0.165759i	0.551527	+	0.834157i	$0.314045\pi$
$332$	−7.59379	−	8.76370i	−0.416763	−	0.480970i
$333$	−14.3094	+	9.19610i	−0.784151	+	0.503943i
$334$	1.98916	−	1.27836i	0.108842	−	0.0699485i
$335$	−1.13024	−	1.30436i	−0.0617514	−	0.0712649i
$336$	−2.47907	+	0.727920i	−0.135244	+	0.0397113i
$337$	1.78908	−	12.4433i	0.0974573	−	0.677830i	−0.881262	−	0.472628i	$-0.843306\pi$
$337$	1.78908	−	12.4433i	0.0974573	−	0.677830i	0.978719	−	0.205203i	$-0.0657854\pi$
$338$	−1.85614	+	2.14210i	−0.100961	+	0.116515i
$339$	−5.54366	+	12.1389i	−0.301090	+	0.659296i
$340$	3.85746	+	1.13265i	0.209200	+	0.0614267i
$341$	1.83782	+	4.02426i	0.0995234	+	0.217926i
$342$	0.207490	+	1.44313i	0.0112198	+	0.0780353i
$343$	−0.841254	−	0.540641i	−0.0454234	−	0.0291919i
$344$	15.2131			0.820236
$345$	−0.427983	+	4.25364i	−0.0230418	+	0.229008i
$346$	−6.89856			−0.370869
$347$	19.5707	+	12.5773i	1.05061	+	0.675186i	0.947589	−	0.319493i	$-0.103512\pi$
$347$	19.5707	+	12.5773i	1.05061	+	0.675186i	0.103022	+	0.994679i	$0.467149\pi$
$348$	−1.38670	−	9.64468i	−0.0743347	−	0.517009i
$349$	0.390831	+	0.855801i	0.0209207	+	0.0458100i	0.919804	−	0.392378i	$-0.128348\pi$
$349$	0.390831	+	0.855801i	0.0209207	+	0.0458100i	−0.898883	+	0.438188i	$0.855620\pi$
$350$	−0.417778	−	0.122671i	−0.0223312	−	0.00655702i
$351$	4.91079	−	10.7531i	0.262119	−	0.573960i
$352$	−2.12462	+	2.45194i	−0.113243	+	0.130689i
$353$	2.49040	−	17.3211i	0.132550	−	0.921908i	−0.809663	−	0.586895i	$-0.800350\pi$
$353$	2.49040	−	17.3211i	0.132550	−	0.921908i	0.942213	−	0.335013i	$-0.108741\pi$
$354$	0.985030	−	0.289231i	0.0523537	−	0.0153724i
$355$	−8.18712	−	9.44844i	−0.434527	−	0.501471i
$356$	−17.6219	+	11.3249i	−0.933957	+	0.600218i
$357$	1.66530	−	1.07022i	0.0881371	−	0.0566423i
$358$	−4.24375	−	4.89754i	−0.224289	−	0.258843i
$359$	29.9328	−	8.78907i	1.57979	−	0.463869i	0.629961	−	0.776627i	$-0.283071\pi$
$359$	29.9328	−	8.78907i	1.57979	−	0.463869i	0.949833	+	0.312758i	$0.101253\pi$
$360$	0.520722	−	3.62170i	0.0274445	−	0.190880i
$361$	10.9327	−	12.6170i	0.575406	−	0.664053i
$362$	−0.296260	+	0.648718i	−0.0155711	+	0.0340959i
$363$	−8.97931	−	2.63656i	−0.471292	−	0.138384i
$364$	1.91599	+	4.19544i	0.100425	+	0.219901i
$365$	1.72407	+	11.9912i	0.0902422	+	0.627648i
$366$	−4.71149	−	3.02789i	−0.246274	−	0.158271i
$367$	−3.65477			−0.190777			−0.0953887	−	0.995440i	$-0.530409\pi$
$367$	−3.65477			−0.190777			−0.0953887	+	0.995440i	$0.530409\pi$
$368$	8.64801	−	10.8826i	0.450809	−	0.567297i
$369$	−24.9227			−1.29743
$370$	−2.82517	−	1.81563i	−0.146874	−	0.0943901i
$371$	1.00790	+	7.01009i	0.0523275	+	0.363946i
$372$	−4.18718	−	9.16864i	−0.217095	−	0.475372i
$373$	−29.7603	−	8.73842i	−1.54093	−	0.452458i	−0.602557	−	0.798076i	$-0.705851\pi$
$373$	−29.7603	−	8.73842i	−1.54093	−	0.452458i	−0.938375	+	0.345618i	$0.887669\pi$
$374$	0.284519	−	0.623009i	0.0147121	−	0.0322150i
$375$	0.583759	−	0.673694i	0.0301452	−	0.0347894i
$376$	0.684809	−	4.76295i	0.0353163	−	0.245630i
$377$	−14.7586	+	4.33351i	−0.760105	+	0.223187i
$378$	−1.32309	−	1.52692i	−0.0680522	−	0.0785364i
$379$	−6.55555	+	4.21299i	−0.336736	+	0.216407i	−0.698070	−	0.716029i	$-0.745958\pi$
$379$	−6.55555	+	4.21299i	−0.336736	+	0.216407i	0.361334	+	0.932436i	$0.382321\pi$
$380$	2.31243	−	1.48611i	0.118625	−	0.0762357i
$381$	6.22548	+	7.18459i	0.318941	+	0.368078i
$382$	−4.59590	+	1.34948i	−0.235147	+	0.0690454i
$383$	−2.34308	+	16.2965i	−0.119726	+	0.832713i	0.838131	+	0.545469i	$0.183648\pi$
$383$	−2.34308	+	16.2965i	−0.119726	+	0.832713i	−0.957857	+	0.287244i	$0.907261\pi$
$384$	6.31403	−	7.28678i	0.322212	−	0.371852i
$385$	0.294256	−	0.644331i	0.0149967	−	0.0328382i
$386$	3.10738	+	0.912410i	0.158162	+	0.0464404i
$387$	−8.40049	−	18.3945i	−0.427021	−	0.935045i
$388$	−3.16370	−	22.0040i	−0.160612	−	1.11708i
$389$	−17.7808	−	11.4271i	−0.901525	−	0.579375i	0.00571723	−	0.999984i	$-0.498180\pi$
$389$	−17.7808	−	11.4271i	−0.901525	−	0.579375i	−0.907242	+	0.420609i	$0.861817\pi$
$390$	0.988831			0.0500714
$391$	−4.00833	+	9.86680i	−0.202710	+	0.498985i
$392$	1.65911			0.0837978
$393$	2.14247	+	1.37688i	0.108074	+	0.0694546i
$394$	−0.0142362	−	0.0990147i	−0.000717207	−	0.00498829i
$395$	3.55621	+	7.78701i	0.178932	+	0.391807i
$396$	2.71358	+	0.796780i	0.136363	+	0.0400397i
$397$	−9.63124	+	21.0895i	−0.483378	+	1.05845i	0.498143	+	0.867095i	$0.334016\pi$
$397$	−9.63124	+	21.0895i	−0.483378	+	1.05845i	−0.981521	+	0.191355i	$0.938712\pi$
$398$	−7.82252	+	9.02767i	−0.392108	+	0.452516i
$399$	0.192619	−	1.33969i	0.00964299	−	0.0670685i
$400$	−2.78102	+	0.816581i	−0.139051	+	0.0408290i
$401$	−0.888952	−	1.02591i	−0.0443922	−	0.0512313i	0.733119	−	0.680100i	$-0.238064\pi$
$401$	−0.888952	−	1.02591i	−0.0443922	−	0.0512313i	−0.777511	+	0.628869i	$0.783518\pi$
$402$	0.563554	−	0.362174i	0.0281075	−	0.0180636i
$403$	−13.3856	+	8.60240i	−0.666784	+	0.428516i
$404$	−5.00847	−	5.78008i	−0.249181	−	0.287570i
$405$	−2.37927	+	0.698616i	−0.118227	+	0.0347145i
$406$	−0.374130	+	2.60213i	−0.0185678	+	0.129142i
$407$	3.57773	−	4.12892i	0.177341	−	0.204663i
$408$	−1.36434	+	2.98750i	−0.0675451	+	0.147903i
$409$	−36.1838	−	10.6245i	−1.78917	−	0.525348i	−0.792725	−	0.609579i	$-0.791338\pi$
$409$	−36.1838	−	10.6245i	−1.78917	−	0.525348i	−0.996446	+	0.0842309i	$0.973157\pi$
$410$	−2.04410	−	4.47595i	−0.100951	−	0.221051i
$411$	1.79540	+	12.4873i	0.0885607	+	0.615953i
$412$	27.1200	+	17.4289i	1.33610	+	0.858662i
$413$	2.64496			0.130150
$414$	4.46981	+	1.10843i	0.219679	+	0.0544763i
$415$	−6.40519			−0.314418
$416$	−9.81633	−	6.30858i	−0.481285	−	0.309303i
$417$	−0.728705	−	5.06825i	−0.0356848	−	0.248193i
$418$	−0.194533	−	0.425967i	−0.00951491	−	0.0208347i
$419$	−25.6259	−	7.52444i	−1.25191	−	0.367593i	−0.412430	−	0.910989i	$-0.635320\pi$
$419$	−25.6259	−	7.52444i	−1.25191	−	0.367593i	−0.839476	+	0.543396i	$0.817138\pi$
$420$	−0.670416	+	1.46801i	−0.0327130	+	0.0716314i
$421$	−2.52708	+	2.91640i	−0.123162	+	0.142137i	−0.813982	−	0.580890i	$-0.802704\pi$
$421$	−2.52708	+	2.91640i	−0.123162	+	0.142137i	0.690820	+	0.723027i	$0.257250\pi$
$422$	1.51991	−	10.5712i	0.0739882	−	0.514600i
$423$	−6.13713	+	1.80202i	−0.298397	+	0.0876174i
$424$	−7.69470	−	8.88015i	−0.373687	−	0.431258i
$425$	1.86814	−	1.20058i	0.0906179	−	0.0582366i
$426$	4.08223	−	2.62349i	0.197785	−	0.127108i
$427$	−9.44915	−	10.9049i	−0.457276	−	0.527725i
$428$	25.1942	−	7.39769i	1.21781	−	0.357581i
$429$	−0.228935	+	1.59228i	−0.0110531	+	0.0768759i
$430$	2.61454	−	3.01734i	0.126084	−	0.145509i
$431$	3.85027	−	8.43091i	0.185461	−	0.406103i	−0.793949	−	0.607984i	$-0.791978\pi$
$431$	3.85027	−	8.43091i	0.185461	−	0.406103i	0.979410	+	0.201882i	$0.0647056\pi$
$432$	−12.9044	−	3.78909i	−0.620865	−	0.182302i
$433$	−7.84245	−	17.1726i	−0.376884	−	0.825261i	−0.999100	−	0.0424156i	$-0.986495\pi$
$433$	−7.84245	−	17.1726i	−0.376884	−	0.825261i	0.622216	−	0.782846i	$-0.286233\pi$
$434$	0.387017	+	2.69177i	0.0185774	+	0.129209i
$435$	−4.52772	−	2.90979i	−0.217088	−	0.139514i
$436$	10.1427			0.485749
$437$	3.30372	+	6.48901i	0.158038	+	0.310412i
$438$	−4.70212			−0.224676
$439$	−19.0748	−	12.2586i	−0.910389	−	0.585071i	−0.000534771	−	1.00000i	$-0.500170\pi$
$439$	−19.0748	−	12.2586i	−0.910389	−	0.585071i	−0.909854	+	0.414929i	$0.863807\pi$
$440$	0.167251	+	1.16326i	0.00797339	+	0.0554562i
$441$	−0.916141	−	2.00607i	−0.0436258	−	0.0955271i
$442$	2.36353	+	0.693995i	0.112422	+	0.0330100i
$443$	−7.93068	+	17.3658i	−0.376798	+	0.825073i	0.622307	+	0.782773i	$0.286196\pi$
$443$	−7.93068	+	17.3658i	−0.376798	+	0.825073i	−0.999105	+	0.0422995i	$0.986532\pi$
$444$	−8.15128	+	9.40708i	−0.386843	+	0.446440i
$445$	−1.64663	+	11.4526i	−0.0780580	+	0.542905i
$446$	4.56128	−	1.33931i	0.215983	−	0.0634183i
$447$	−10.3201	−	11.9101i	−0.488125	−	0.563326i
$448$	3.19890	−	2.05581i	0.151134	−	0.0971279i
$449$	−24.1708	+	15.5336i	−1.14069	+	0.733077i	−0.967764	−	0.251858i	$-0.918958\pi$
$449$	−24.1708	+	15.5336i	−1.14069	+	0.733077i	−0.172926	+	0.984935i	$0.555322\pi$
$450$	−0.628829	−	0.725707i	−0.0296433	−	0.0342102i
$451$	7.68070	−	2.25526i	0.361670	−	0.106196i
$452$	3.85708	−	26.8266i	0.181422	−	1.26181i
$453$	1.37922	−	1.59171i	0.0648015	−	0.0747849i
$454$	3.15409	−	6.90649i	0.148029	−	0.324138i
$455$	2.44442	+	0.717746i	0.114596	+	0.0336485i
$456$	0.932837	+	2.04263i	0.0436841	+	0.0956548i
$457$	0.568418	+	3.95343i	0.0265894	+	0.184934i	0.998788	−	0.0492257i	$-0.0156753\pi$
$457$	0.568418	+	3.95343i	0.0265894	+	0.184934i	−0.972198	+	0.234159i	$0.924766\pi$
$458$	8.62148	+	5.54069i	0.402855	+	0.258899i
$459$	10.3043			0.480962
$460$	−1.59984	−	8.53377i	−0.0745932	−	0.397889i
$461$	27.6366			1.28717			0.643583	−	0.765376i	$-0.277447\pi$
$461$	27.6366			1.28717			0.643583	+	0.765376i	$0.277447\pi$
$462$	0.231291	+	0.148642i	0.0107606	+	0.00691543i
$463$	−5.39756	−	37.5409i	−0.250846	−	1.74467i	−0.593158	−	0.805086i	$-0.702119\pi$
$463$	−5.39756	−	37.5409i	−0.250846	−	1.74467i	0.342312	−	0.939587i	$-0.388790\pi$
$464$	7.26964	+	15.9183i	0.337484	+	0.738988i
$465$	−5.34199	−	1.56855i	−0.247729	−	0.0727397i
$466$	−1.83865	+	4.02609i	−0.0851739	+	0.186505i
$467$	7.76633	−	8.96282i	0.359383	−	0.414750i	−0.547050	−	0.837100i	$-0.684249\pi$
$467$	7.76633	−	8.96282i	0.359383	−	0.414750i	0.906433	+	0.422350i	$0.138795\pi$
$468$	−1.44758	+	10.0681i	−0.0669143	+	0.465399i
$469$	1.65601	−	0.486247i	0.0764673	−	0.0224528i
$470$	−0.826982	−	0.954388i	−0.0381458	−	0.0440226i
$471$	−10.5764	+	6.79705i	−0.487335	+	0.313191i
$472$	−3.69166	+	2.37249i	−0.169923	+	0.109203i
$473$	4.25339	+	4.90867i	0.195571	+	0.225701i
$474$	−3.18812	+	0.936118i	−0.146435	+	0.0429973i
$475$	0.216080	−	1.50287i	0.00991441	−	0.0689562i
$476$	−2.63274	+	3.03835i	−0.120672	+	0.139262i
$477$	−6.48827	+	14.2073i	−0.297078	+	0.650509i
$478$	−7.97966	−	2.34304i	−0.364981	−	0.107168i
$479$	15.0540	+	32.9636i	0.687833	+	1.50614i	0.854125	+	0.520068i	$0.174093\pi$
$479$	15.0540	+	32.9636i	0.687833	+	1.50614i	−0.166292	+	0.986077i	$0.553179\pi$
$480$	−0.581063	−	4.04138i	−0.0265218	−	0.184463i
$481$	16.5301	+	10.6233i	0.753708	+	0.484379i
$482$	−5.37687			−0.244910
$483$	−3.69146	−	2.15633i	−0.167967	−	0.0981166i
$484$	19.0062			0.863917
$485$	−10.3298	−	6.63859i	−0.469054	−	0.301443i
$486$	−0.999577	−	6.95221i	−0.0453417	−	0.315359i
$487$	−13.0345	−	28.5417i	−0.590652	−	1.29335i	−0.935048	−	0.354522i	$-0.884644\pi$
$487$	−13.0345	−	28.5417i	−0.590652	−	1.29335i	0.344396	−	0.938824i	$-0.388084\pi$
$488$	22.9700	+	6.74460i	1.03980	+	0.305314i
$489$	−2.70980	+	5.93364i	−0.122541	+	0.268328i
$490$	0.285136	−	0.329065i	0.0128811	−	0.0148656i
$491$	2.69149	−	18.7197i	0.121465	−	0.844809i	−0.834433	−	0.551110i	$-0.814204\pi$
$491$	2.69149	−	18.7197i	0.121465	−	0.844809i	0.955898	−	0.293699i	$-0.0948864\pi$
$492$	−17.4993	+	5.13824i	−0.788927	+	0.231650i
$493$	−8.78009	−	10.1328i	−0.395436	−	0.456357i
$494$	1.41686	−	0.910563i	0.0637477	−	0.0409682i
$495$	1.31417	−	0.844564i	0.0590674	−	0.0379603i
$496$	11.8546	+	13.6810i	0.532288	+	0.614293i
$497$	11.9957	−	3.52224i	0.538079	−	0.157994i
$498$	0.353810	−	2.46080i	0.0158546	−	0.110271i
$499$	5.18490	−	5.98370i	0.232108	−	0.267867i	−0.627733	−	0.778429i	$-0.716017\pi$
$499$	5.18490	−	5.98370i	0.232108	−	0.267867i	0.859841	+	0.510562i	$0.170562\pi$
$500$	−0.752073	+	1.64681i	−0.0336337	+	0.0736476i
$501$	−4.64478	−	1.36383i	−0.207514	−	0.0609315i
$502$	−1.79936	−	3.94005i	−0.0803094	−	0.175853i
$503$	2.43234	+	16.9173i	0.108453	+	0.754306i	0.969378	+	0.245574i	$0.0789765\pi$
$503$	2.43234	+	16.9173i	0.108453	+	0.754306i	−0.860925	+	0.508732i	$0.830114\pi$
$504$	3.07810	+	1.97817i	0.137109	+	0.0881149i
$505$	−4.22453			−0.187989
$506$	−1.47781	+	0.0628765i	−0.0656966	+	0.00279520i
$507$	5.80286			0.257714
$508$	−16.2422	−	10.4382i	−0.720630	−	0.463121i
$509$	1.61795	+	11.2531i	0.0717145	+	0.498785i	0.993745	+	0.111669i	$0.0356196\pi$
$509$	1.61795	+	11.2531i	0.0717145	+	0.498785i	−0.922031	+	0.387116i	$0.873471\pi$
$510$	0.358057	+	0.784035i	0.0158550	+	0.0347176i
$511$	−11.6238	−	3.41305i	−0.514206	−	0.150985i
$512$	−9.51014	+	20.8243i	−0.420293	+	0.920313i
$513$	4.61368	−	5.32448i	0.203699	−	0.235081i
$514$	−0.201397	+	1.40074i	−0.00888322	+	0.0617842i
$515$	17.0854	−	5.01674i	0.752875	−	0.221064i
$516$	−9.69067	−	11.1836i	−0.426608	−	0.492332i
$517$	1.72828	−	1.11070i	0.0760096	−	0.0488484i
$518$	2.82517	−	1.81563i	0.124131	−	0.0797742i
$519$	9.24887	+	10.6738i	0.405980	+	0.468526i
$520$	−4.05557	+	1.19082i	−0.177848	+	0.0522210i
$521$	−0.257278	+	1.78940i	−0.0112715	+	0.0783952i	−0.994681	−	0.103006i	$-0.967154\pi$
$521$	−0.257278	+	1.78940i	−0.0112715	+	0.0783952i	0.983409	+	0.181401i	$0.0580631\pi$
$522$	−3.79666	+	4.38157i	−0.166175	+	0.191776i
$523$	−8.64497	+	18.9299i	−0.378018	+	0.827745i	0.621016	+	0.783798i	$0.286720\pi$
$523$	−8.64497	+	18.9299i	−0.378018	+	0.827745i	−0.999034	+	0.0439464i	$0.986007\pi$
$524$	−4.96277	−	1.45720i	−0.216799	−	0.0636581i
$525$	0.370311	+	0.810868i	0.0161617	+	0.0353892i
$526$	0.0952716	+	0.662629i	0.00415404	+	0.0288920i
$527$	−11.6677	−	7.49837i	−0.508253	−	0.326634i
$528$	1.83016			0.0796476
$529$	22.9169	−	1.95363i	0.996386	−	0.0849404i
$530$	−3.08369			−0.133947
$531$	4.90712	+	3.15361i	0.212951	+	0.136855i
$532$	0.391193	+	2.72081i	0.0169604	+	0.117962i
$533$	11.9600	+	26.1888i	0.518046	+	1.13436i
$534$	−4.30901	−	1.26524i	−0.186469	−	0.0547522i
$535$	6.02509	−	13.1931i	0.260487	−	0.570388i
$536$	−1.87519	+	2.16408i	−0.0809958	+	0.0934741i
$537$	−1.88813	+	13.1322i	−0.0814787	+	0.566697i
$538$	1.15105	−	0.337980i	0.0496255	−	0.0145713i
$539$	0.463866	+	0.535330i	0.0199801	+	0.0230583i
$540$	−7.06708	+	4.54174i	−0.304119	+	0.195445i
$541$	20.4423	−	13.1375i	0.878885	−	0.564825i	−0.0215733	−	0.999767i	$-0.506868\pi$
$541$	20.4423	−	13.1375i	0.878885	−	0.564825i	0.900458	+	0.434942i	$0.143231\pi$
$542$	0.0322857	+	0.0372597i	0.00138679	+	0.00160044i
$543$	1.40092	−	0.411347i	0.0601192	−	0.0176526i
$544$	1.44751	−	10.0676i	0.0620613	−	0.431646i
$545$	3.66882	−	4.23405i	0.157155	−	0.181367i
$546$	−0.410775	+	0.899472i	−0.0175796	+	0.0384939i
$547$	27.8410	+	8.17484i	1.19039	+	0.349531i	0.816172	−	0.577808i	$-0.196092\pi$
$547$	27.8410	+	8.17484i	1.19039	+	0.349531i	0.374221	+	0.927339i	$0.377910\pi$
$548$	−10.6436	−	23.3062i	−0.454671	−	0.995590i
$549$	−4.52870	−	31.4978i	−0.193280	−	1.34429i
$550$	0.259462	+	0.166746i	0.0110635	+	0.00711008i
$551$	−9.16710			−0.390532
$552$	7.08649	−	0.301510i	0.301621	−	0.0128331i
$553$	−8.56062			−0.364035
$554$	−10.0804	−	6.47830i	−0.428276	−	0.275236i
$555$	0.978474	+	6.80544i	0.0415339	+	0.288875i
$556$	4.31993	+	9.45933i	0.183206	+	0.401165i
$557$	1.97148	+	0.578880i	0.0835345	+	0.0245279i	0.323233	−	0.946320i	$-0.395230\pi$
$557$	1.97148	+	0.578880i	0.0835345	+	0.0245279i	−0.239698	+	0.970847i	$0.577049\pi$
$558$	−2.49139	+	5.45539i	−0.105469	+	0.230945i
$559$	−15.2977	+	17.6545i	−0.647023	+	0.746704i
$560$	0.412489	−	2.86892i	0.0174308	−	0.121234i
$561$	−1.34540	+	0.395045i	−0.0568028	+	0.0166788i
$562$	2.61808	+	3.02143i	0.110437	+	0.127451i
$563$	−14.2152	+	9.13553i	−0.599098	+	0.385017i	−0.804755	−	0.593607i	$-0.797703\pi$
$563$	−14.2152	+	9.13553i	−0.599098	+	0.385017i	0.205657	+	0.978624i	$0.434067\pi$
$564$	−3.93761	+	2.53055i	−0.165803	+	0.106555i
$565$	−9.80345	−	11.3138i	−0.412434	−	0.475975i
$566$	−2.18056	+	0.640270i	−0.0916557	+	0.0269125i
$567$	0.352900	−	2.45447i	0.0148204	−	0.103078i
$568$	−13.5834	+	15.6760i	−0.569945	+	0.657751i
$569$	5.71763	−	12.5199i	0.239695	−	0.524860i	−0.751106	−	0.660181i	$-0.770479\pi$
$569$	5.71763	−	12.5199i	0.239695	−	0.524860i	0.990802	+	0.135322i	$0.0432067\pi$
$570$	0.565449	+	0.166031i	0.0236840	+	0.00695426i
$571$	11.9519	+	26.1711i	0.500173	+	1.09523i	0.976413	+	0.215912i	$0.0692723\pi$
$571$	11.9519	+	26.1711i	0.500173	+	1.09523i	−0.476239	+	0.879316i	$0.658000\pi$
$572$	−0.464949	−	3.23379i	−0.0194405	−	0.135212i
$573$	8.24968	+	5.30175i	0.344635	+	0.221484i
$574$	4.92061			0.205382
$575$	−4.14108	−	2.41898i	−0.172695	−	0.100878i
$576$	8.38598			0.349416
$577$	−23.6853	−	15.2216i	−0.986033	−	0.633685i	−0.0549489	−	0.998489i	$-0.517500\pi$
$577$	−23.6853	−	15.2216i	−0.986033	−	0.633685i	−0.931084	+	0.364804i	$0.881136\pi$
$578$	−0.747849	−	5.20140i	−0.0311064	−	0.216350i
$579$	−2.75433	−	6.03114i	−0.114466	−	0.250646i
$580$	10.4879	+	3.07952i	0.435486	+	0.127870i
$581$	2.66081	−	5.82636i	0.110389	−	0.241718i
$582$	3.12107	−	3.60191i	0.129373	−	0.149304i
$583$	0.713938	−	4.96555i	0.0295683	−	0.205652i
$584$	19.2852	−	5.66264i	0.798026	−	0.234322i
$585$	3.67928	+	4.24612i	0.152120	+	0.175555i
$586$	−1.45150	+	0.932823i	−0.0599609	+	0.0385346i
$587$	6.28917	−	4.04181i	0.259582	−	0.166823i	−0.404377	−	0.914593i	$-0.632511\pi$
$587$	6.28917	−	4.04181i	0.259582	−	0.166823i	0.663959	+	0.747769i	$0.268875\pi$
$588$	−1.05684	−	1.21966i	−0.0435835	−	0.0502981i
$589$	−9.09875	+	2.67164i	−0.374908	+	0.110083i
$590$	−0.163898	+	1.13993i	−0.00674757	+	0.0469304i
$591$	−0.134113	+	0.154775i	−0.00551669	+	0.00636660i
$592$	9.28665	−	20.3349i	0.381679	−	0.835760i
$593$	21.9416	+	6.44263i	0.901033	+	0.264567i	0.699262	−	0.714866i	$-0.253512\pi$
$593$	21.9416	+	6.44263i	0.901033	+	0.264567i	0.201771	+	0.979433i	$0.435330\pi$
$594$	0.594518	+	1.30181i	0.0243934	+	0.0534140i
$595$	0.316032	+	2.19805i	0.0129561	+	0.0901114i
$596$	26.9250	+	17.3037i	1.10289	+	0.708785i
$597$	24.4556			1.00090
$598$	−0.980252	−	5.22878i	−0.0400855	−	0.213821i
$599$	42.7015			1.74474			0.872369	−	0.488848i	$-0.162583\pi$
$599$	42.7015			1.74474			0.872369	+	0.488848i	$0.162583\pi$
$600$	−1.24419	−	0.799593i	−0.0507939	−	0.0326433i
$601$	−4.07113	−	28.3154i	−0.166065	−	1.15501i	−0.886920	−	0.461922i	$-0.847160\pi$
$601$	−4.07113	−	28.3154i	−0.166065	−	1.15501i	0.720855	−	0.693086i	$-0.243749\pi$
$602$	1.65855	+	3.63171i	0.0675974	+	0.148018i
$603$	3.65210	+	1.07235i	0.148725	+	0.0436695i
$604$	−1.77689	+	3.89085i	−0.0723007	+	0.158316i
$605$	6.87489	−	7.93405i	0.279504	−	0.322565i
$606$	0.233355	−	1.62302i	0.00947938	−	0.0659306i
$607$	36.7649	−	10.7951i	1.49224	−	0.438161i	0.568985	−	0.822348i	$-0.307336\pi$
$607$	36.7649	−	10.7951i	1.49224	−	0.438161i	0.923255	+	0.384187i	$0.125518\pi$
$608$	−4.55408	−	5.25569i	−0.184692	−	0.213146i
$609$	4.52772	−	2.90979i	0.183473	−	0.117911i
$610$	5.28536	−	3.39669i	0.213998	−	0.137528i
$611$	4.83867	+	5.58413i	0.195752	+	0.225910i
$612$	−8.50709	+	2.49791i	−0.343879	+	0.100972i
$613$	−0.919979	+	6.39859i	−0.0371576	+	0.258437i	−0.999929	−	0.0118786i	$-0.996219\pi$
$613$	−0.919979	+	6.39859i	−0.0371576	+	0.258437i	0.962772	+	0.270315i	$0.0871279\pi$
$614$	−5.85860	+	6.76118i	−0.236434	+	0.272859i
$615$	−4.18487	+	9.16359i	−0.168750	+	0.369512i
$616$	−1.12762	−	0.331098i	−0.0454329	−	0.0133403i
$617$	7.60391	+	16.6502i	0.306122	+	0.670314i	0.998697	−	0.0510322i	$-0.0162511\pi$
$617$	7.60391	+	16.6502i	0.306122	+	0.670314i	−0.692575	+	0.721346i	$0.743524\pi$
$618$	0.983610	+	6.84115i	0.0395666	+	0.275192i
$619$	36.4456	+	23.4222i	1.46487	+	0.941418i	0.998380	+	0.0568931i	$0.0181194\pi$
$619$	36.4456	+	23.4222i	1.46487	+	0.941418i	0.466494	+	0.884524i	$0.345517\pi$
$620$	11.3072			0.454107
$621$	−10.0966	−	19.8313i	−0.405162	−	0.795802i
$622$	−8.32257			−0.333705
$623$	−9.73361	−	6.25541i	−0.389969	−	0.250618i
$624$	0.936765	+	6.51534i	0.0375006	+	0.260822i
$625$	0.415415	+	0.909632i	0.0166166	+	0.0363853i
$626$	2.86392	+	0.840924i	0.114465	+	0.0336101i
$627$	−0.398266	+	0.872082i	−0.0159052	+	0.0348276i
$628$	16.7207	−	19.2967i	0.667228	−	0.770022i
$629$	−2.43751	+	16.9533i	−0.0971899	+	0.675971i
$630$	0.921352	−	0.270533i	0.0367075	−	0.0107783i
$631$	1.69740	+	1.95890i	0.0675722	+	0.0779825i	0.788529	−	0.614997i	$-0.210843\pi$
$631$	1.69740	+	1.95890i	0.0675722	+	0.0779825i	−0.720957	+	0.692980i	$0.756297\pi$
$632$	11.9483	−	7.67874i	0.475280	−	0.305444i
$633$	−18.3940	+	11.8211i	−0.731096	+	0.469847i
$634$	5.97729	+	6.89816i	0.237388	+	0.273961i
$635$	−10.2325	+	3.00453i	−0.406064	+	0.119231i
$636$	−1.62659	+	11.3132i	−0.0644987	+	0.448598i
$637$	−1.66833	+	1.92536i	−0.0661018	+	0.0762855i
$638$	0.773567	−	1.69388i	0.0306258	−	0.0670612i
$639$	26.4548	+	7.76782i	1.04653	+	0.307290i
$640$	4.49320	+	9.83873i	0.177609	+	0.388910i
$641$	−4.45205	−	30.9647i	−0.175845	−	1.22303i	−0.866251	−	0.499608i	$-0.833477\pi$
$641$	−4.45205	−	30.9647i	−0.175845	−	1.22303i	0.690406	−	0.723422i	$-0.257432\pi$
$642$	4.73583	+	3.04353i	0.186908	+	0.120119i
$643$	24.1715			0.953230			0.476615	−	0.879112i	$-0.341864\pi$
$643$	24.1715			0.953230			0.476615	+	0.879112i	$0.341864\pi$
$644$	8.42719	+	2.08979i	0.332078	+	0.0823491i
$645$	−8.17385			−0.321845
$646$	1.23502	+	0.793702i	0.0485914	+	0.0312278i
$647$	−2.20569	−	15.3409i	−0.0867147	−	0.603114i	−0.986125	−	0.166007i	$-0.946912\pi$
$647$	−2.20569	−	15.3409i	−0.0867147	−	0.603114i	0.899410	−	0.437106i	$-0.143997\pi$
$648$	1.70907	+	3.74234i	0.0671385	+	0.147013i
$649$	−1.79765	−	0.527837i	−0.0705639	−	0.0207194i
$650$	−0.460808	+	1.00903i	−0.0180744	+	0.0395773i
$651$	3.64595	−	4.20764i	0.142896	−	0.164911i
$652$	1.88538	−	13.1131i	0.0738372	−	0.513549i
$653$	−43.8402	+	12.8726i	−1.71560	+	0.503746i	−0.984027	−	0.178018i	$-0.943031\pi$
$653$	−43.8402	+	12.8726i	−1.71560	+	0.503746i	−0.731573	+	0.681764i	$0.761213\pi$
$654$	1.42402	+	1.64340i	0.0556834	+	0.0642621i
$655$	−2.40343	+	1.54459i	−0.0939097	+	0.0603521i
$656$	27.5552	−	17.7087i	1.07585	−	0.691408i
$657$	−17.4958	−	20.1913i	−0.682578	−	0.787737i
$658$	1.21168	−	0.355782i	0.0472363	−	0.0138698i
$659$	2.75489	−	19.1607i	0.107315	−	0.746395i	−0.863114	−	0.505009i	$-0.831489\pi$
$659$	2.75489	−	19.1607i	0.107315	−	0.746395i	0.970429	−	0.241386i	$-0.0776019\pi$
$660$	0.748608	−	0.863940i	0.0291395	−	0.0336288i
$661$	−10.6366	+	23.2910i	−0.413717	+	0.905913i	0.581977	+	0.813206i	$0.302280\pi$
$661$	−10.6366	+	23.2910i	−0.413717	+	0.905913i	−0.995693	+	0.0927079i	$0.970448\pi$
$662$	−4.47197	−	1.31309i	−0.173808	−	0.0510346i
$663$	−2.09499	−	4.58739i	−0.0813627	−	0.178159i
$664$	1.51237	+	10.5188i	0.0586913	+	0.408207i
$665$	1.27729	+	0.820866i	0.0495313	+	0.0318318i
$666$	7.40625			0.286986
$667$	−10.8981	+	26.8265i	−0.421976	+	1.03872i
$668$	9.83144			0.380390
$669$	−8.18753	−	5.26181i	−0.316548	−	0.203433i
$670$	0.106948	+	0.743842i	0.00413178	+	0.0287371i
$671$	4.24590	+	9.29722i	0.163911	+	0.358915i
$672$	3.91755	+	1.15030i	0.151123	+	0.0443737i
$673$	−2.42090	+	5.30103i	−0.0933189	+	0.204340i	−0.950535	−	0.310616i	$-0.899465\pi$
$673$	−2.42090	+	5.30103i	−0.0933189	+	0.204340i	0.857216	+	0.514956i	$0.172192\pi$
$674$	−3.58453	+	4.13676i	−0.138071	+	0.159342i
$675$	−0.660367	+	4.59296i	−0.0254176	+	0.176783i
$676$	−11.3078	+	3.32026i	−0.434915	+	0.127702i
$677$	−31.8568	−	36.7647i	−1.22435	−	1.41298i	−0.880559	−	0.473936i	$-0.842833\pi$
$677$	−31.8568	−	36.7647i	−1.22435	−	1.41298i	−0.343796	−	0.939044i	$-0.611713\pi$
$678$	4.88816	−	3.14143i	0.187729	−	0.120646i
$679$	10.3298	−	6.63859i	0.396423	−	0.254766i
$680$	−2.41272	−	2.78442i	−0.0925234	−	0.106778i
$681$	−14.9147	+	4.37935i	−0.571532	+	0.167817i
$682$	0.274141	−	1.90669i	0.0104974	−	0.0730110i
$683$	−19.3663	+	22.3499i	−0.741032	+	0.855196i	−0.993667	−	0.112365i	$-0.964157\pi$
$683$	−19.3663	+	22.3499i	−0.741032	+	0.855196i	0.252635	+	0.967562i	$0.418703\pi$
$684$	−2.51828	+	5.51426i	−0.0962887	+	0.210843i
$685$	−13.5790	−	3.98716i	−0.518828	−	0.152342i
$686$	0.180878	+	0.396068i	0.00690596	+	0.0151219i
$687$	−2.98597	−	20.7679i	−0.113922	−	0.792345i
$688$	22.3579	+	14.3686i	0.852387	+	0.547796i
$689$	18.0427			0.687371
$690$	1.15809	−	1.45734i	0.0440877	−	0.0554799i
$691$	29.1274			1.10806			0.554029	−	0.832497i	$-0.313090\pi$
$691$	29.1274			1.10806			0.554029	+	0.832497i	$0.313090\pi$
$692$	−24.1301	−	15.5075i	−0.917290	−	0.589507i
$693$	0.222318	+	1.54625i	0.00844514	+	0.0587373i
$694$	−4.20790	−	9.21402i	−0.159730	−	0.349759i
$695$	5.51136	+	1.61828i	0.209058	+	0.0613849i
$696$	−3.70946	+	8.12259i	−0.140607	+	0.307886i
$697$	−16.4341	+	18.9660i	−0.622486	+	0.718387i
$698$	0.0582990	−	0.405478i	0.00220665	−	0.0153476i
$699$	8.69441	−	2.55291i	0.328853	−	0.0965599i
$700$	−1.18557	−	1.36822i	−0.0448103	−	0.0517138i
$701$	−12.5232	+	8.04816i	−0.472994	+	0.303975i	−0.755334	−	0.655339i	$-0.772526\pi$
$701$	−12.5232	+	8.04816i	−0.472994	+	0.303975i	0.282340	+	0.959314i	$0.408889\pi$
$702$	−4.33012	+	2.78280i	−0.163430	+	0.105030i
$703$	7.66880	+	8.85026i	0.289234	+	0.333794i
$704$	−2.58440	+	0.758847i	−0.0974031	+	0.0286001i
$705$	−0.367941	+	2.55908i	−0.0138575	+	0.0963807i
$706$	−4.98966	+	5.75837i	−0.187788	+	0.216719i
$707$	1.75493	−	3.84277i	0.0660010	−	0.144522i
$708$	4.09566	+	1.20259i	0.153924	+	0.0451962i
$709$	9.39893	+	20.5808i	0.352984	+	0.772928i	0.999946	+	0.0104052i	$0.00331215\pi$
$709$	9.39893	+	20.5808i	0.352984	+	0.772928i	−0.646962	+	0.762523i	$0.723961\pi$
$710$	0.774704	+	5.38819i	0.0290741	+	0.202215i
$711$	−15.8823	−	10.2069i	−0.595631	−	0.382789i
$712$	19.1965			0.719421
$713$	−2.99860	+	29.8025i	−0.112299	+	1.11611i
$714$	−0.861925			−0.0322567
$715$	−1.51811	−	0.975633i	−0.0567742	−	0.0364866i
$716$	−3.83464	−	26.6705i	−0.143307	−	0.996724i
$717$	7.07303	+	15.4878i	0.264147	+	0.578401i
$718$	−13.0332	−	3.82689i	−0.486395	−	0.142818i
$719$	−9.45274	+	20.6986i	−0.352528	+	0.771928i	0.647424	+	0.762130i	$0.275846\pi$
$719$	−9.45274	+	20.6986i	−0.352528	+	0.771928i	−0.999952	+	0.00979843i	$0.996881\pi$
$720$	4.18592	−	4.83081i	0.156000	−	0.180034i
$721$	−2.53416	+	17.6255i	−0.0943772	+	0.656408i
$722$	−6.97468	+	2.04795i	−0.259571	+	0.0762168i
$723$	7.20874	+	8.31933i	0.268096	+	0.309399i
$724$	−2.49454	+	1.60315i	−0.0927090	+	0.0595805i
$725$	5.07920	−	3.26421i	0.188637	−	0.121230i
$726$	2.66842	+	3.07952i	0.0990343	+	0.114292i
$727$	18.4017	−	5.40321i	0.682480	−	0.200394i	0.0779268	−	0.996959i	$-0.475170\pi$
$727$	18.4017	−	5.40321i	0.682480	−	0.200394i	0.604553	+	0.796565i	$0.293352\pi$
$728$	0.601534	−	4.18376i	0.0222943	−	0.155060i
$729$	−4.54503	+	5.24525i	−0.168335	+	0.194268i
$730$	2.19125	−	4.79816i	0.0811017	−	0.177588i
$731$	−19.5374	−	5.73668i	−0.722615	−	0.212179i
$732$	−9.67360	−	21.1822i	−0.357547	−	0.782918i
$733$	−0.547986	−	3.81133i	−0.0202403	−	0.140775i	0.977195	−	0.212342i	$-0.0681090\pi$
$733$	−0.547986	−	3.81133i	−0.0202403	−	0.140775i	−0.997436	+	0.0715672i	$0.977200\pi$
$734$	1.33872	+	0.860344i	0.0494131	+	0.0317559i
$735$	−0.891424			−0.0328807
$736$	−20.7942	+	7.07889i	−0.766483	+	0.260931i
$737$	−1.22254			−0.0450329
$738$	9.12906	+	5.86689i	0.336045	+	0.215963i
$739$	7.13562	+	49.6293i	0.262488	+	1.82564i	0.514000	+	0.857790i	$0.328163\pi$
$739$	7.13562	+	49.6293i	0.262488	+	1.82564i	−0.251513	+	0.967854i	$0.580928\pi$
$740$	−5.80062	−	12.7016i	−0.213235	−	0.466920i
$741$	−3.30844	−	0.971447i	−0.121539	−	0.0356870i
$742$	1.28101	−	2.80502i	0.0470274	−	0.102976i
$743$	−24.3335	+	28.0824i	−0.892711	+	1.03024i	0.106643	+	0.994297i	$0.465990\pi$
$743$	−24.3335	+	28.0824i	−0.892711	+	1.03024i	−0.999354	+	0.0359458i	$0.988556\pi$
$744$	−1.31458	+	9.14311i	−0.0481949	+	0.335203i
$745$	16.9626	−	4.98068i	0.621463	−	0.182478i
$746$	8.84400	+	10.2065i	0.323802	+	0.373687i
$747$	11.8833	−	7.63696i	0.434789	−	0.279422i
$748$	2.39568	−	1.53961i	0.0875949	−	0.0562938i
$749$	9.49796	+	10.9612i	0.347048	+	0.400515i
$750$	−0.372417	+	0.109352i	−0.0135988	+	0.00399296i
$751$	−1.61027	+	11.1997i	−0.0587597	+	0.408683i	0.939120	+	0.343590i	$0.111643\pi$
$751$	−1.61027	+	11.1997i	−0.0587597	+	0.408683i	−0.997879	+	0.0650921i	$0.979266\pi$
$752$	5.50496	−	6.35306i	0.200745	−	0.231672i
$753$	−3.68382	+	8.06645i	−0.134246	+	0.293958i
$754$	6.42611	+	1.88688i	0.234025	+	0.0687160i
$755$	0.981483	+	2.14915i	0.0357198	+	0.0782155i
$756$	−1.19554	−	8.31515i	−0.0434813	−	0.302419i
$757$	10.1803	+	6.54246i	0.370008	+	0.237790i	0.712410	−	0.701764i	$-0.247604\pi$
$757$	10.1803	+	6.54246i	0.370008	+	0.237790i	−0.342401	+	0.939554i	$0.611240\pi$
$758$	3.39301			0.123240
$759$	2.07858	+	2.20223i	0.0754475	+	0.0799360i
$760$	−2.51906			−0.0913761
$761$	38.0395	+	24.4465i	1.37893	+	0.886185i	0.999242	−	0.0389298i	$-0.0123949\pi$
$761$	38.0395	+	24.4465i	1.37893	+	0.886185i	0.379688	+	0.925114i	$0.376031\pi$
$762$	−0.589085	−	4.09718i	−0.0213403	−	0.148425i
$763$	2.32734	+	5.09616i	0.0842554	+	0.184494i
$764$	−19.1093	−	5.61100i	−0.691351	−	0.202999i
$765$	−2.03443	+	4.45479i	−0.0735551	+	0.161063i
$766$	4.69451	−	5.41775i	0.169620	−	0.195751i
$767$	0.958967	−	6.66976i	0.0346263	−	0.240831i
$768$	2.47661	−	0.727200i	0.0893671	−	0.0262406i
$769$	8.90184	+	10.2733i	0.321009	+	0.370464i	0.893202	−	0.449655i	$-0.148453\pi$
$769$	8.90184	+	10.2733i	0.321009	+	0.370464i	−0.572194	+	0.820118i	$0.693908\pi$
$770$	−0.259462	+	0.166746i	−0.00935037	+	0.00600912i
$771$	2.43730	−	1.56636i	0.0877774	−	0.0564111i
$772$	8.81812	+	10.1767i	0.317371	+	0.366266i
$773$	−33.3739	+	9.79947i	−1.20038	+	0.352462i	−0.819997	−	0.572368i	$-0.806025\pi$
$773$	−33.3739	+	9.79947i	−1.20038	+	0.352462i	−0.380380	+	0.924830i	$0.624207\pi$
$774$	−1.25307	+	8.71531i	−0.0450408	+	0.313265i
$775$	4.09002	−	4.72014i	0.146918	−	0.169552i
$776$	−8.46301	+	18.5314i	−0.303804	+	0.665239i
$777$	−6.59692	−	1.93703i	−0.236663	−	0.0694906i
$778$	3.82306	+	8.37134i	0.137063	+	0.300127i
$779$	2.44191	+	16.9838i	0.0874904	+	0.608509i
$780$	3.45878	+	2.22282i	0.123844	+	0.0795899i
$781$	−8.85576			−0.316884
$782$	3.79090	−	2.67058i	0.135562	−	0.0954998i
$783$	28.0159			1.00121
$784$	2.43831	+	1.56701i	0.0870825	+	0.0559645i
$785$	−2.00714	−	13.9600i	−0.0716378	−	0.498252i
$786$	−0.460654	−	1.00869i	−0.0164310	−	0.0359788i
$787$	−10.0412	−	2.94836i	−0.357930	−	0.105098i	0.0978234	−	0.995204i	$-0.468812\pi$
$787$	−10.0412	−	2.94836i	−0.357930	−	0.105098i	−0.455754	+	0.890106i	$0.650630\pi$
$788$	0.172782	−	0.378340i	0.00615511	−	0.0134778i
$789$	0.897518	−	1.03579i	0.0319525	−	0.0368751i
$790$	0.530468	−	3.68949i	0.0188732	−	0.131266i
$791$	14.3639	−	4.21762i	0.510721	−	0.149961i
$792$	−1.69726	−	1.95874i	−0.0603095	−	0.0696009i
$793$	−30.9246	+	19.8741i	−1.09817	+	0.705748i
$794$	8.49240	−	5.45774i	0.301384	−	0.193688i
$795$	4.13428	+	4.77122i	0.146628	+	0.169218i
$796$	−47.6556	+	13.9929i	−1.68911	+	0.495967i
$797$	−4.38898	+	30.5261i	−0.155466	+	1.08129i	0.751393	+	0.659855i	$0.229382\pi$
$797$	−4.38898	+	30.5261i	−0.155466	+	1.08129i	−0.906859	+	0.421434i	$0.861527\pi$
$798$	−0.385923	+	0.445379i	−0.0136615	+	0.0157662i
$799$	−2.67551	+	5.85856i	−0.0946528	+	0.207261i
$800$	4.39471	+	1.29040i	0.155376	+	0.0456227i
$801$	−10.6001	−	23.2109i	−0.374536	−	0.820119i
$802$	0.0841169	+	0.585046i	0.00297027	+	0.0206587i
$803$	7.21899	+	4.63936i	0.254752	+	0.163719i
$804$	2.78537			0.0982323
$805$	3.92065	−	2.76198i	0.138185	−	0.0973470i
$806$	6.92810			0.244032
$807$	−2.06615	−	1.32783i	−0.0727319	−	0.0467419i
$808$	0.997480	+	6.93762i	0.0350912	+	0.244065i
$809$	19.9058	+	43.5877i	0.699852	+	1.53246i	0.840151	+	0.542353i	$0.182466\pi$
$809$	19.9058	+	43.5877i	0.699852	+	1.53246i	−0.140299	+	0.990109i	$0.544806\pi$
$810$	1.03597	+	0.304188i	0.0364002	+	0.0106881i
$811$	7.92976	−	17.3637i	0.278451	−	0.609724i	−0.717798	−	0.696251i	$-0.754850\pi$
$811$	7.92976	−	17.3637i	0.278451	−	0.609724i	0.996249	+	0.0865278i	$0.0275771\pi$
$812$	−7.15806	+	8.26084i	−0.251199	+	0.289899i
$813$	0.0143646	−	0.0999078i	0.000503788	−	0.00350392i
$814$	−2.28246	+	0.670192i	−0.0800003	+	0.0234902i
$815$	−4.79203	−	5.53030i	−0.167858	−	0.193718i
$816$	−4.82675	+	3.10196i	−0.168970	+	0.108590i
$817$	−11.7120	+	7.52687i	−0.409753	+	0.263332i
$818$	10.7529	+	12.4095i	0.375965	+	0.433887i
$819$	−5.39083	+	1.58289i	−0.188371	+	0.0553107i
$820$	2.91168	−	20.2512i	0.101680	−	0.707201i
$821$	−23.9146	+	27.5989i	−0.834625	+	0.963209i	−0.999734	−	0.0230666i	$-0.992657\pi$
$821$	−23.9146	+	27.5989i	−0.834625	+	0.963209i	0.165109	+	0.986275i	$0.447202\pi$
$822$	2.28190	−	4.99667i	0.0795905	−	0.174279i
$823$	−13.5261	−	3.97162i	−0.471490	−	0.138442i	0.0373515	−	0.999302i	$-0.488108\pi$
$823$	−13.5261	−	3.97162i	−0.471490	−	0.138442i	−0.508841	+	0.860860i	$0.669926\pi$
$824$	−12.2728	−	26.8736i	−0.427542	−	0.936186i
$825$	−0.0898624	−	0.625007i	−0.00312861	−	0.0217599i
$826$	−0.968835	−	0.622633i	−0.0337101	−	0.0216642i
$827$	−50.1406			−1.74356			−0.871781	−	0.489897i	$-0.837034\pi$
$827$	−50.1406			−1.74356			−0.871781	+	0.489897i	$0.837034\pi$
$828$	13.1430	+	13.9249i	0.456752	+	0.483925i
$829$	−32.3269			−1.12276			−0.561379	−	0.827559i	$-0.689729\pi$
$829$	−32.3269			−1.12276			−0.561379	+	0.827559i	$0.689729\pi$
$830$	2.34619	+	1.50780i	0.0814373	+	0.0523366i
$831$	3.49127	+	24.2823i	0.121111	+	0.842343i
$832$	−4.02430	−	8.81198i	−0.139517	−	0.305501i
$833$	−2.13071	−	0.625631i	−0.0738246	−	0.0216768i
$834$	−0.926163	+	2.02801i	−0.0320704	+	0.0702243i
$835$	3.55622	−	4.10409i	0.123068	−	0.142028i
$836$	0.277099	−	1.92727i	0.00958367	−	0.0666559i
$837$	27.8070	−	8.16487i	0.961150	−	0.282219i
$838$	7.61535	+	8.78858i	0.263068	+	0.303596i
$839$	−3.46529	+	2.22701i	−0.119635	+	0.0768849i	−0.599090	−	0.800682i	$-0.704471\pi$
$839$	−3.46529	+	2.22701i	−0.119635	+	0.0768849i	0.479455	+	0.877567i	$0.340834\pi$
$840$	1.24419	−	0.799593i	0.0429287	−	0.0275886i
$841$	−4.88090	−	5.63285i	−0.168307	−	0.194236i
$842$	1.61219	−	0.473380i	0.0555596	−	0.0163138i
$843$	1.16484	−	8.10162i	0.0401191	−	0.279035i
$844$	29.0798	−	33.5599i	1.00097	−	1.15518i
$845$	−2.70421	+	5.92139i	−0.0930276	+	0.203702i
$846$	2.67220	+	0.784628i	0.0918721	+	0.0269761i
$847$	4.36113	+	9.54954i	0.149850	+	0.328126i
$848$	−2.92132	−	20.3182i	−0.100318	−	0.697730i
$849$	3.91412	+	2.51545i	0.134332	+	0.0863300i
$850$	−0.966908			−0.0331647
$851$	35.0161	−	11.9204i	1.20034	−	0.408627i
$852$	20.1764			0.691233
$853$	−28.7116	−	18.4518i	−0.983067	−	0.631779i	−0.0527780	−	0.998606i	$-0.516808\pi$
$853$	−28.7116	−	18.4518i	−0.983067	−	0.631779i	−0.930289	+	0.366827i	$0.880444\pi$
$854$	0.894124	+	6.21877i	0.0305963	+	0.212802i
$855$	1.39100	+	3.04585i	0.0475710	+	0.104166i
$856$	−23.0887	−	6.77944i	−0.789154	−	0.231717i
$857$	4.98169	−	10.9084i	0.170171	−	0.372623i	−0.805262	−	0.592919i	$-0.797975\pi$
$857$	4.98169	−	10.9084i	0.170171	−	0.372623i	0.975433	+	0.220297i	$0.0707025\pi$
$858$	0.458685	−	0.529351i	0.0156592	−	0.0180717i
$859$	4.02389	−	27.9868i	0.137293	−	0.954897i	−0.798411	−	0.602113i	$-0.794326\pi$
$859$	4.02389	−	27.9868i	0.137293	−	0.954897i	0.935705	−	0.352784i	$-0.114765\pi$
$860$	15.9280	−	4.67689i	0.543141	−	0.159481i
$861$	−6.59704	−	7.61339i	−0.224826	−	0.259463i
$862$	−3.39500	+	2.18183i	−0.115634	+	0.0743135i
$863$	18.5330	−	11.9105i	0.630871	−	0.405436i	−0.185761	−	0.982595i	$-0.559475\pi$
$863$	18.5330	−	11.9105i	0.630871	−	0.405436i	0.816632	+	0.577159i	$0.195839\pi$
$864$	13.9179	+	16.0621i	0.473496	+	0.546443i
$865$	−15.2019	+	4.46367i	−0.516879	+	0.151769i
$866$	−1.16983	+	8.13636i	−0.0397525	+	0.276485i
$867$	−7.04520	+	8.13059i	−0.239267	+	0.276129i
$868$	−4.69717	+	10.2854i	−0.159432	+	0.349108i
$869$	5.81823	+	1.70839i	0.197370	+	0.0579530i
$870$	0.973507	+	2.13168i	0.0330050	+	0.0722708i
$871$	−0.625755	−	4.35222i	−0.0212029	−	0.147469i
$872$	−7.81952	−	5.02530i	−0.264802	−	0.170178i
$873$	27.0799			0.916516
$874$	0.317402	−	3.15460i	0.0107363	−	0.106706i
$875$	−1.00000			−0.0338062
$876$	−16.4473	−	10.5700i	−0.555703	−	0.357129i
$877$	−2.06621	−	14.3708i	−0.0697709	−	0.485267i	−0.994508	−	0.104661i	$-0.966624\pi$
$877$	−2.06621	−	14.3708i	−0.0697709	−	0.485267i	0.924737	−	0.380606i	$-0.124285\pi$
$878$	4.10127	+	8.98052i	0.138411	+	0.303078i
$879$	3.38932	+	0.995195i	0.114319	+	0.0335671i
$880$	−0.852879	+	1.86755i	−0.0287506	+	0.0629549i
$881$	−24.6879	+	28.4913i	−0.831755	+	0.959897i	−0.999664	−	0.0259057i	$-0.991753\pi$
$881$	−24.6879	+	28.4913i	−0.831755	+	0.959897i	0.167909	+	0.985802i	$0.446299\pi$
$882$	−0.136658	+	0.950475i	−0.00460150	+	0.0320041i
$883$	41.1832	−	12.0925i	1.38593	−	0.406944i	0.498098	−	0.867121i	$-0.334032\pi$
$883$	41.1832	−	12.0925i	1.38593	−	0.406944i	0.887828	+	0.460176i	$0.152214\pi$
$884$	6.70722	+	7.74054i	0.225588	+	0.260343i
$885$	1.98349	−	1.27471i	0.0666744	−	0.0428490i
$886$	6.99293	−	4.49408i	0.234932	−	0.150982i
$887$	11.8062	+	13.6251i	0.396413	+	0.457485i	0.918508	−	0.395402i	$-0.129395\pi$
$887$	11.8062	+	13.6251i	0.396413	+	0.457485i	−0.522095	+	0.852887i	$0.674849\pi$
$888$	10.9450	−	3.21375i	0.367291	−	0.107846i
$889$	1.51771	−	10.5559i	0.0509025	−	0.354035i
$890$	3.29913	−	3.80740i	0.110587	−	0.127624i
$891$	−0.729671	+	1.59776i	−0.0244449	+	0.0535269i
$892$	18.9654	+	5.56873i	0.635007	+	0.186455i
$893$	1.82932	+	4.00564i	0.0612157	+	0.134044i
$894$	0.976539	+	6.79198i	0.0326603	+	0.227158i
$895$	−12.5206	−	8.04647i	−0.418516	−	0.268964i
$896$	−10.8162			−0.361343
$897$	−6.77599	+	8.52689i	−0.226244	+	0.284705i
$898$	12.5103			0.417474
$899$	−31.7229	−	20.3870i	−1.05802	−	0.679946i
$900$	−0.568209	−	3.95198i	−0.0189403	−	0.131733i
$901$	6.53327	+	14.3059i	0.217655	+	0.476597i
$902$	−3.34429	−	0.981973i	−0.111353	−	0.0326961i
$903$	3.39554	−	7.43520i	0.112997	−	0.247428i
$904$	−16.2650	+	18.7708i	−0.540967	+	0.624309i
$905$	−0.233097	+	1.62123i	−0.00774841	+	0.0538914i
$906$	−0.879895	+	0.258360i	−0.0292325	+	0.00858345i
$907$	−12.7950	−	14.7662i	−0.424850	−	0.490303i	0.502458	−	0.864602i	$-0.332429\pi$
$907$	−12.7950	−	14.7662i	−0.424850	−	0.490303i	−0.927308	+	0.374298i	$0.877884\pi$
$908$	26.5578	−	17.0677i	0.881352	−	0.566411i
$909$	7.83763	−	5.03694i	0.259958	−	0.167065i
$910$	−0.726418	−	0.838331i	−0.0240805	−	0.0277904i
$911$	−26.4387	+	7.76312i	−0.875955	+	0.257203i	−0.688646	−	0.725098i	$-0.741795\pi$
$911$	−26.4387	+	7.76312i	−0.875955	+	0.257203i	−0.187309	+	0.982301i	$0.559976\pi$
$912$	−0.558290	+	3.88299i	−0.0184868	+	0.128579i
$913$	−2.97115	+	3.42889i	−0.0983306	+	0.113480i
$914$	0.722442	−	1.58193i	0.0238963	−	0.0523255i
$915$	−12.3416	−	3.62381i	−0.407999	−	0.119799i
$916$	17.7015	+	38.7610i	0.584876	+	1.28070i
$917$	−0.406588	−	2.82788i	−0.0134267	−	0.0933848i
$918$	−3.77440	−	2.42566i	−0.124574	−	0.0800586i
$919$	31.0999			1.02589			0.512945	−	0.858421i	$-0.328554\pi$
$919$	31.0999			1.02589			0.512945	+	0.858421i	$0.328554\pi$
$920$	−2.99473	+	7.37175i	−0.0987332	+	0.243039i
$921$	18.3158			0.603526
$922$	−10.1231	−	6.50575i	−0.333388	−	0.214256i
$923$	−4.53280	−	31.5263i	−0.149199	−	1.03770i
$924$	0.474884	+	1.03985i	0.0156226	+	0.0342086i
$925$	−7.40042	−	2.17296i	−0.243324	−	0.0714465i
$926$	−6.86015	+	15.0216i	−0.225438	+	0.493641i
$927$	−25.7166	+	29.6785i	−0.844644	+	0.974771i
$928$	3.93557	−	27.3725i	0.129191	−	0.898545i
$929$	18.0621	−	5.30351i	0.592599	−	0.174003i	0.0283366	−	0.999598i	$-0.490979\pi$
$929$	18.0621	−	5.30351i	0.592599	−	0.174003i	0.564262	+	0.825596i	$0.309161\pi$
$930$	1.58750	+	1.83207i	0.0520562	+	0.0600760i
$931$	−1.27729	+	0.820866i	−0.0418616	+	0.0269028i
$932$	−15.4817	+	9.94948i	−0.507120	+	0.325906i
$933$	11.1580	+	12.8770i	0.365297	+	0.421576i
$934$	−4.95464	+	1.45481i	−0.162121	+	0.0476030i
$935$	0.223859	−	1.55698i	0.00732098	−	0.0509186i
$936$	6.10434	−	7.04478i	0.199527	−	0.230266i
$937$	19.6833	−	43.1003i	0.643024	−	1.40803i	−0.254506	−	0.967071i	$-0.581913\pi$
$937$	19.6833	−	43.1003i	0.643024	−	1.40803i	0.897529	−	0.440954i	$-0.145360\pi$
$938$	−0.721051	−	0.211720i	−0.0235431	−	0.00691289i
$939$	−2.53853	−	5.55861i	−0.0828419	−	0.181398i
$940$	−0.747259	−	5.19730i	−0.0243729	−	0.169517i
$941$	−43.9022	−	28.2142i	−1.43117	−	0.919758i	−0.999846	−	0.0175617i	$-0.994410\pi$
$941$	−43.9022	−	28.2142i	−1.43117	−	0.919758i	−0.431326	−	0.902196i	$-0.641954\pi$
$942$	5.47413			0.178357
$943$	52.6042	+	13.0449i	1.71303	+	0.424799i
$944$	−7.66622			−0.249514
$945$	−3.90357	−	2.50867i	−0.126983	−	0.0816072i
$946$	−0.402476	−	2.79928i	−0.0130856	−	0.0910124i
$947$	−15.2637	−	33.4229i	−0.496005	−	1.08610i	−0.977747	−	0.209786i	$-0.932723\pi$
$947$	−15.2637	−	33.4229i	−0.496005	−	1.08610i	0.481743	−	0.876313i	$-0.340004\pi$
$948$	−13.2559	−	3.89228i	−0.430532	−	0.126416i
$949$	−12.8210	+	28.0741i	−0.416187	+	0.911323i
$950$	−0.432928	+	0.499626i	−0.0140461	+	0.0162100i
$951$	2.65942	−	18.4966i	0.0862375	−	0.599795i
$952$	3.53508	−	1.03799i	0.114573	−	0.0336415i
$953$	−1.48622	−	1.71518i	−0.0481432	−	0.0555603i	0.731167	−	0.682198i	$-0.238976\pi$
$953$	−1.48622	−	1.71518i	−0.0481432	−	0.0555603i	−0.779310	+	0.626638i	$0.784430\pi$
$954$	5.72107	−	3.67671i	0.185226	−	0.119038i
$955$	−9.25449	+	5.94750i	−0.299468	+	0.192457i
$956$	−22.6446	−	26.1333i	−0.732380	−	0.845212i
$957$	−3.65796	+	1.07407i	−0.118245	+	0.0347198i
$958$	2.24555	−	15.6181i	0.0725504	−	0.504599i
$959$	9.26779	−	10.6956i	0.299272	−	0.345379i
$960$	1.40812	−	3.08336i	0.0454470	−	0.0995150i
$961$	−7.68360	−	2.25611i	−0.247858	−	0.0727777i
$962$	−3.55414	−	7.78248i	−0.114590	−	0.250917i
$963$	4.55210	+	31.6605i	0.146689	+	1.02025i
$964$	−18.8075	−	12.0868i	−0.605748	−	0.389291i
$965$	7.43788			0.239434
$966$	0.844554	+	1.65884i	0.0271731	+	0.0533722i
$967$	−9.65457			−0.310470			−0.155235	−	0.987878i	$-0.549613\pi$
$967$	−9.65457			−0.310470			−0.155235	+	0.987878i	$0.549613\pi$
$968$	−14.6528	−	9.41676i	−0.470958	−	0.302666i
$969$	−0.427740	−	2.97500i	−0.0137410	−	0.0955706i
$970$	2.22102	+	4.86336i	0.0713127	+	0.156153i
$971$	25.2271	+	7.40735i	0.809577	+	0.237713i	0.660222	−	0.751071i	$-0.270462\pi$
$971$	25.2271	+	7.40735i	0.809577	+	0.237713i	0.149355	+	0.988784i	$0.452280\pi$
$972$	12.1317	−	26.5648i	0.389125	−	0.852065i
$973$	−3.76154	+	4.34105i	−0.120589	+	0.139168i
$974$	−1.94432	+	13.5230i	−0.0623000	+	0.433306i
$975$	2.17902	−	0.639817i	0.0697843	−	0.0204905i
$976$	27.3876	+	31.6070i	0.876657	+	1.01172i
$977$	−7.53139	+	4.84013i	−0.240950	+	0.154849i	−0.655543	−	0.755158i	$-0.727560\pi$
$977$	−7.53139	+	4.84013i	−0.240950	+	0.154849i	0.414593	+	0.910007i	$0.363924\pi$
$978$	2.38938	−	1.53556i	0.0764041	−	0.0491019i
$979$	5.36710	+	6.19396i	0.171533	+	0.197960i
$980$	1.73708	−	0.510052i	0.0554890	−	0.0162930i
$981$	−1.75836	+	12.2297i	−0.0561401	+	0.390463i
$982$	−5.39256	+	6.22335i	−0.172084	+	0.198595i
$983$	6.85145	−	15.0026i	0.218527	−	0.478508i	−0.768340	−	0.640042i	$-0.778917\pi$
$983$	6.85145	−	15.0026i	0.218527	−	0.478508i	0.986867	+	0.161534i	$0.0516442\pi$
$984$	16.0368	+	4.70883i	0.511234	+	0.150112i
$985$	−0.0954380	−	0.208980i	−0.00304091	−	0.00665866i
$986$	0.830814	+	5.77844i	0.0264585	+	0.184023i
$987$	−2.17498	−	1.39777i	−0.0692303	−	0.0444916i
$988$	7.00286			0.222791
$989$	8.10294	+	43.2221i	0.257658	+	1.37438i
$990$	−0.680185			−0.0216177
$991$	0.597455	+	0.383961i	0.0189788	+	0.0121969i	0.550096	−	0.835102i	$-0.314591\pi$
$991$	0.597455	+	0.383961i	0.0189788	+	0.0121969i	−0.531117	+	0.847298i	$0.678228\pi$
$992$	−4.07113	−	28.3154i	−0.129259	−	0.899013i
$993$	3.96387	+	8.67967i	0.125790	+	0.275441i
$994$	−5.22309	−	1.53364i	−0.165666	−	0.0486441i
$995$	−11.3966	+	24.9551i	−0.361297	+	0.791131i
$996$	6.76929	−	7.81217i	0.214493	−	0.247538i
$997$	7.77347	−	54.0657i	0.246188	−	1.71228i	−0.373668	−	0.927562i	$-0.621900\pi$
$997$	7.77347	−	54.0657i	0.246188	−	1.71228i	0.619857	−	0.784715i	$-0.287191\pi$
$998$	−3.30779	+	0.971253i	−0.104706	+	0.0307445i
$999$	−23.4368	−	27.0476i	−0.741509	−	0.855747i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	805.2.u.d.71.6	✓	130
23.12	even	11	inner	805.2.u.d.771.6	yes	130

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.u.d.71.6	✓	130	1.1	even	1	trivial
805.2.u.d.771.6	yes	130	23.12	even	11	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:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.u (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366295 - 0.235403i) q^{2} +(0.126863 + 0.882351i) q^{3} +(-0.752073 - 1.64681i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(0.161239 - 0.353064i) q^{6} +(0.654861 - 0.755750i) q^{7} +(-0.236116 + 1.64222i) q^{8} +(2.11603 - 0.621322i) q^{9} +O(q^{10})\)	\(q+(-0.366295 - 0.235403i) q^{2} +(0.126863 + 0.882351i) q^{3} +(-0.752073 - 1.64681i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(0.161239 - 0.353064i) q^{6} +(0.654861 - 0.755750i) q^{7} +(-0.236116 + 1.64222i) q^{8} +(2.11603 - 0.621322i) q^{9} +(0.285136 + 0.329065i) q^{10} +(-0.595896 + 0.382959i) q^{11} +(1.35765 - 0.872511i) q^{12} +(-1.66833 - 1.92536i) q^{13} +(-0.417778 + 0.122671i) q^{14} +(0.126863 - 0.882351i) q^{15} +(-1.89806 + 2.19048i) q^{16} +(0.922494 - 2.01998i) q^{17} +(-0.921352 - 0.270533i) q^{18} +(-0.630733 - 1.38111i) q^{19} +(0.257649 + 1.79199i) q^{20} +(0.749914 + 0.481940i) q^{21} +0.308423 q^{22} +(-4.79150 + 0.203864i) q^{23} -1.47897 q^{24} +(0.841254 + 0.540641i) q^{25} +(0.157866 + 1.09798i) q^{26} +(1.92760 + 4.22086i) q^{27} +(-1.73708 - 0.510052i) q^{28} +(2.50813 - 5.49205i) q^{29} +(-0.254177 + 0.293336i) q^{30} +(0.888847 - 6.18207i) q^{31} +(4.39471 - 1.29040i) q^{32} +(-0.413501 - 0.477206i) q^{33} +(-0.813415 + 0.522750i) q^{34} +(-0.841254 + 0.540641i) q^{35} +(-2.61461 - 3.01742i) q^{36} +(-7.40042 + 2.17296i) q^{37} +(-0.0940843 + 0.654371i) q^{38} +(1.48719 - 1.71631i) q^{39} +(0.689220 - 1.50918i) q^{40} +(-10.8432 - 3.18385i) q^{41} +(-0.161239 - 0.353064i) q^{42} +(-1.30495 - 9.07610i) q^{43} +(1.07882 + 0.693314i) q^{44} -2.20536 q^{45} +(1.80309 + 1.05326i) q^{46} -2.90030 q^{47} +(-2.17357 - 1.39687i) q^{48} +(-0.142315 - 0.989821i) q^{49} +(-0.180878 - 0.396068i) q^{50} +(1.89936 + 0.557703i) q^{51} +(-1.91599 + 4.19544i) q^{52} +(-4.63784 + 5.35235i) q^{53} +(0.287534 - 1.99984i) q^{54} +(0.679650 - 0.199563i) q^{55} +(1.08649 + 1.25387i) q^{56} +(1.13861 - 0.731740i) q^{57} +(-2.21156 + 1.42128i) q^{58} +(1.73208 + 1.99893i) q^{59} +(-1.54847 + 0.454673i) q^{60} +(2.05350 - 14.2824i) q^{61} +(-1.78086 + 2.05522i) q^{62} +(0.916141 - 2.00607i) q^{63} +(3.64851 + 1.07130i) q^{64} +(1.05832 + 2.31739i) q^{65} +(0.0391275 + 0.272138i) q^{66} +(1.45193 + 0.933102i) q^{67} -4.02031 q^{68} +(-0.787743 - 4.20192i) q^{69} +0.435415 q^{70} +(10.5174 + 6.75913i) q^{71} +(0.520722 + 3.62170i) q^{72} +(-5.03255 - 11.0197i) q^{73} +(3.22226 + 0.946140i) q^{74} +(-0.370311 + 0.810868i) q^{75} +(-1.80007 + 2.07740i) q^{76} +(-0.100808 + 0.701133i) q^{77} +(-0.948776 + 0.278586i) q^{78} +(-5.60601 - 6.46969i) q^{79} +(2.43831 - 1.56701i) q^{80} +(2.08607 - 1.34063i) q^{81} +(3.22232 + 3.71875i) q^{82} +(6.14573 - 1.80455i) q^{83} +(0.229674 - 1.59742i) q^{84} +(-1.45422 + 1.67826i) q^{85} +(-1.65855 + 3.63171i) q^{86} +(5.16410 + 1.51632i) q^{87} +(-0.488204 - 1.06902i) q^{88} +(-1.64663 - 11.4526i) q^{89} +(0.807812 + 0.519150i) q^{90} -2.54762 q^{91} +(3.93928 + 7.73736i) q^{92} +5.56751 q^{93} +(1.06237 + 0.682741i) q^{94} +(0.216080 + 1.50287i) q^{95} +(1.69611 + 3.71397i) q^{96} +(11.7817 + 3.45943i) q^{97} +(-0.180878 + 0.396068i) q^{98} +(-1.02299 + 1.18060i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9}+O(q^{10}) \) 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9	\( 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9} + 2 q^{10} + 2 q^{11} - 5 q^{12} + 13 q^{13} - 2 q^{14} + 2 q^{15} - 6 q^{16} - 51 q^{17} + q^{18} - 9 q^{19} - 16 q^{20} - 2 q^{21} + 34 q^{22} - 10 q^{23} - 76 q^{24} - 13 q^{25} - 31 q^{26} + 14 q^{27} + 27 q^{28} + 3 q^{29} + 5 q^{30} + 6 q^{31} + 22 q^{32} - 58 q^{33} + q^{34} + 13 q^{35} + 193 q^{36} - 36 q^{37} + 4 q^{38} - 2 q^{39} - 29 q^{40} - 34 q^{41} - 5 q^{42} - 22 q^{43} + 8 q^{44} + 170 q^{45} - 198 q^{46} - 14 q^{47} - 120 q^{48} - 13 q^{49} + 2 q^{50} - 6 q^{51} + 33 q^{52} - 18 q^{53} + 188 q^{54} - 31 q^{55} - 15 q^{56} - 9 q^{57} + 114 q^{58} + 46 q^{59} - 16 q^{60} - 56 q^{61} - 146 q^{62} + 17 q^{63} - 109 q^{64} + 2 q^{65} - 14 q^{66} - 10 q^{67} + 86 q^{68} - 6 q^{69} - 2 q^{70} - 25 q^{72} + 64 q^{73} + 79 q^{74} + 2 q^{75} + 32 q^{76} - 13 q^{77} - 64 q^{78} - 118 q^{79} - 17 q^{80} + 23 q^{81} + 129 q^{82} - 117 q^{83} - 72 q^{84} - 7 q^{85} + 74 q^{86} - 51 q^{87} - 40 q^{88} - 35 q^{89} + 100 q^{90} + 42 q^{91} + 76 q^{92} - 90 q^{93} - 7 q^{94} + 2 q^{95} + 393 q^{96} - 4 q^{97} + 2 q^{98} - 40 q^{99}+O(q^{100}) \) 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9 + 2 * q^10 + 2 * q^11 - 5 * q^12 + 13 * q^13 - 2 * q^14 + 2 * q^15 - 6 * q^16 - 51 * q^17 + q^18 - 9 * q^19 - 16 * q^20 - 2 * q^21 + 34 * q^22 - 10 * q^23 - 76 * q^24 - 13 * q^25 - 31 * q^26 + 14 * q^27 + 27 * q^28 + 3 * q^29 + 5 * q^30 + 6 * q^31 + 22 * q^32 - 58 * q^33 + q^34 + 13 * q^35 + 193 * q^36 - 36 * q^37 + 4 * q^38 - 2 * q^39 - 29 * q^40 - 34 * q^41 - 5 * q^42 - 22 * q^43 + 8 * q^44 + 170 * q^45 - 198 * q^46 - 14 * q^47 - 120 * q^48 - 13 * q^49 + 2 * q^50 - 6 * q^51 + 33 * q^52 - 18 * q^53 + 188 * q^54 - 31 * q^55 - 15 * q^56 - 9 * q^57 + 114 * q^58 + 46 * q^59 - 16 * q^60 - 56 * q^61 - 146 * q^62 + 17 * q^63 - 109 * q^64 + 2 * q^65 - 14 * q^66 - 10 * q^67 + 86 * q^68 - 6 * q^69 - 2 * q^70 - 25 * q^72 + 64 * q^73 + 79 * q^74 + 2 * q^75 + 32 * q^76 - 13 * q^77 - 64 * q^78 - 118 * q^79 - 17 * q^80 + 23 * q^81 + 129 * q^82 - 117 * q^83 - 72 * q^84 - 7 * q^85 + 74 * q^86 - 51 * q^87 - 40 * q^88 - 35 * q^89 + 100 * q^90 + 42 * q^91 + 76 * q^92 - 90 * q^93 - 7 * q^94 + 2 * q^95 + 393 * q^96 - 4 * q^97 + 2 * q^98 - 40 * q^99

Introduction

L-functions

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