LMFDB - Embedded newform 122.2.i.b.77.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [122,2,Mod(15,122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(122, base_ring=CyclotomicField(30))

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

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

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

chi := DirichletCharacter("122.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 122 = 2 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	122.i (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.974174904660$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			77.2
Character	$\chi$	$=$	122.77
Dual form			122.2.i.b.103.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.978148 - 0.207912i) q^{2} +(0.199917 + 0.615282i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-0.382347 - 3.63779i) q^{5} +(-0.0676242 - 0.643402i) q^{6} +(1.22500 + 1.36050i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(2.08845 - 1.51734i) q^{9} +O(q^{10})$	\(q+(-0.978148 - 0.207912i) q^{2} +(0.199917 + 0.615282i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-0.382347 - 3.63779i) q^{5} +(-0.0676242 - 0.643402i) q^{6} +(1.22500 + 1.36050i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(2.08845 - 1.51734i) q^{9} +(-0.382347 + 3.63779i) q^{10} +3.01277 q^{11} +(-0.0676242 + 0.643402i) q^{12} +(-0.306269 + 0.530473i) q^{13} +(-0.915368 - 1.58546i) q^{14} +(2.16183 - 0.962508i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-2.83078 - 1.26034i) q^{17} +(-2.35828 + 1.04997i) q^{18} +(0.666594 - 0.740328i) q^{19} +(1.13033 - 3.47880i) q^{20} +(-0.592194 + 1.02571i) q^{21} +(-2.94693 - 0.626389i) q^{22} +(-2.91986 + 2.12140i) q^{23} +(0.199917 - 0.615282i) q^{24} +(-8.19659 + 1.74224i) q^{25} +(0.409867 - 0.455204i) q^{26} +(2.92128 + 2.12244i) q^{27} +(0.565729 + 1.74113i) q^{28} +(2.21699 + 3.83994i) q^{29} +(-2.31470 + 0.492005i) q^{30} +(-9.36452 + 1.99049i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.602304 + 1.85370i) q^{33} +(2.50688 + 1.82136i) q^{34} +(4.48085 - 4.97648i) q^{35} +(2.52505 - 0.536716i) q^{36} +(-3.51402 + 10.8150i) q^{37} +(-0.805950 + 0.585557i) q^{38} +(-0.387619 - 0.0823909i) q^{39} +(-1.82891 + 3.16777i) q^{40} +(-0.770956 + 2.37276i) q^{41} +(0.792510 - 0.880171i) q^{42} +(9.47014 - 4.21638i) q^{43} +(2.75230 + 1.22540i) q^{44} +(-6.31829 - 7.01717i) q^{45} +(3.29711 - 1.46797i) q^{46} +(-0.641906 - 1.11181i) q^{47} +(-0.323473 + 0.560271i) q^{48} +(0.381362 - 3.62842i) q^{49} +8.37970 q^{50} +(0.209546 - 1.99369i) q^{51} +(-0.495553 + 0.360040i) q^{52} +(-6.73226 - 4.89127i) q^{53} +(-2.41617 - 2.68342i) q^{54} +(-1.15192 - 10.9598i) q^{55} +(-0.191364 - 1.82071i) q^{56} +(0.588774 + 0.262139i) q^{57} +(-1.37017 - 4.21696i) q^{58} +(4.56554 + 0.970436i) q^{59} +2.36642 q^{60} +(6.40383 - 4.47113i) q^{61} +9.57373 q^{62} +(4.62270 + 0.982586i) q^{63} +(0.309017 + 0.951057i) q^{64} +(2.04685 + 0.911316i) q^{65} +(-0.203736 - 1.93842i) q^{66} +(0.979029 + 9.31484i) q^{67} +(-2.07342 - 2.30276i) q^{68} +(-1.88899 - 1.37243i) q^{69} +(-5.41760 + 3.93612i) q^{70} +(-1.60811 + 15.3001i) q^{71} -2.58146 q^{72} +(-1.17326 + 11.1628i) q^{73} +(5.68580 - 9.84810i) q^{74} +(-2.71061 - 4.69491i) q^{75} +(0.910082 - 0.405195i) q^{76} +(3.69064 + 4.09887i) q^{77} +(0.362018 + 0.161181i) q^{78} +(11.1304 - 4.95556i) q^{79} +(2.44756 - 2.71830i) q^{80} +(1.67126 - 5.14362i) q^{81} +(1.24743 - 2.16062i) q^{82} +(-3.27266 - 0.695625i) q^{83} +(-0.958189 + 0.696165i) q^{84} +(-3.50253 + 10.7797i) q^{85} +(-10.1398 + 2.15529i) q^{86} +(-1.91943 + 2.13174i) q^{87} +(-2.43738 - 1.77086i) q^{88} +(-5.52523 - 17.0049i) q^{89} +(4.72127 + 8.17748i) q^{90} +(-1.09689 + 0.233151i) q^{91} +(-3.53027 + 0.750382i) q^{92} +(-3.09684 - 5.36389i) q^{93} +(0.396720 + 1.22098i) q^{94} +(-2.94803 - 2.14187i) q^{95} +(0.432891 - 0.480774i) q^{96} +(-2.05197 + 0.436160i) q^{97} +(-1.12742 + 3.46984i) q^{98} +(6.29200 - 4.57140i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 12 q^{5} - q^{6} - 4 q^{7} - 6 q^{8} - 19 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 12 * q^5 - q^6 - 4 * q^7 - 6 * q^8 - 19 * q^9	\( 24 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 12 q^{5} - q^{6} - 4 q^{7} - 6 q^{8} - 19 q^{9} - 12 q^{10} + 6 q^{11} - q^{12} + 5 q^{13} - 4 q^{14} - 9 q^{15} + 3 q^{16} + 16 q^{17} + 17 q^{18} - 2 q^{19} - q^{20} + 10 q^{21} + 7 q^{22} + q^{23} - 3 q^{24} + 11 q^{25} - 9 q^{27} - 7 q^{28} + 2 q^{29} - 4 q^{30} + 14 q^{31} - 12 q^{32} + 7 q^{33} - 17 q^{34} + 9 q^{35} + 2 q^{36} - 38 q^{37} + 4 q^{38} - 40 q^{39} - 7 q^{40} - 10 q^{41} + 15 q^{42} - 5 q^{43} + 2 q^{44} - 96 q^{45} - 8 q^{46} + 3 q^{47} - q^{48} + 19 q^{49} + 38 q^{50} + 102 q^{51} + 20 q^{52} - 37 q^{53} + 17 q^{54} + 33 q^{55} + 6 q^{56} - 71 q^{57} + q^{58} - 17 q^{59} - 22 q^{60} + 70 q^{61} + 72 q^{62} + 146 q^{63} - 6 q^{64} + 2 q^{65} - 86 q^{66} - 4 q^{67} + q^{68} - 2 q^{69} - 28 q^{70} - 76 q^{71} + 46 q^{72} + 84 q^{73} + 19 q^{74} + 9 q^{75} - 2 q^{76} - 10 q^{77} - 5 q^{78} - 56 q^{79} - 7 q^{80} + 59 q^{81} - 20 q^{82} - 9 q^{83} + 25 q^{84} - 37 q^{85} - 65 q^{86} - 25 q^{87} - 4 q^{88} - 45 q^{89} - 31 q^{90} + 2 q^{91} + 7 q^{92} - 47 q^{93} + 24 q^{94} - 39 q^{95} + 9 q^{96} + 6 q^{97} + 7 q^{98} - 24 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 12 * q^5 - q^6 - 4 * q^7 - 6 * q^8 - 19 * q^9 - 12 * q^10 + 6 * q^11 - q^12 + 5 * q^13 - 4 * q^14 - 9 * q^15 + 3 * q^16 + 16 * q^17 + 17 * q^18 - 2 * q^19 - q^20 + 10 * q^21 + 7 * q^22 + q^23 - 3 * q^24 + 11 * q^25 - 9 * q^27 - 7 * q^28 + 2 * q^29 - 4 * q^30 + 14 * q^31 - 12 * q^32 + 7 * q^33 - 17 * q^34 + 9 * q^35 + 2 * q^36 - 38 * q^37 + 4 * q^38 - 40 * q^39 - 7 * q^40 - 10 * q^41 + 15 * q^42 - 5 * q^43 + 2 * q^44 - 96 * q^45 - 8 * q^46 + 3 * q^47 - q^48 + 19 * q^49 + 38 * q^50 + 102 * q^51 + 20 * q^52 - 37 * q^53 + 17 * q^54 + 33 * q^55 + 6 * q^56 - 71 * q^57 + q^58 - 17 * q^59 - 22 * q^60 + 70 * q^61 + 72 * q^62 + 146 * q^63 - 6 * q^64 + 2 * q^65 - 86 * q^66 - 4 * q^67 + q^68 - 2 * q^69 - 28 * q^70 - 76 * q^71 + 46 * q^72 + 84 * q^73 + 19 * q^74 + 9 * q^75 - 2 * q^76 - 10 * q^77 - 5 * q^78 - 56 * q^79 - 7 * q^80 + 59 * q^81 - 20 * q^82 - 9 * q^83 + 25 * q^84 - 37 * q^85 - 65 * q^86 - 25 * q^87 - 4 * q^88 - 45 * q^89 - 31 * q^90 + 2 * q^91 + 7 * q^92 - 47 * q^93 + 24 * q^94 - 39 * q^95 + 9 * q^96 + 6 * q^97 + 7 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/122\mathbb{Z}\right)^\times$.

$n$	$63$
$\chi(n)$	$e\left(\frac{1}{15}\right)$

Coefficient data

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

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

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

$2$	−0.978148	−	0.207912i	−0.691655	−	0.147016i
$2$	−0.978148	−	0.207912i	−0.691655	−	0.147016i
$3$	0.199917	+	0.615282i	0.115422	+	0.355233i	0.992035	−	0.125964i	$-0.0402023\pi$
$3$	0.199917	+	0.615282i	0.115422	+	0.355233i	−0.876613	+	0.481197i	$0.840202\pi$
$4$	0.913545	+	0.406737i	0.456773	+	0.203368i
$5$	−0.382347	−	3.63779i	−0.170991	−	1.62687i	−0.657683	−	0.753295i	$-0.728463\pi$
$5$	−0.382347	−	3.63779i	−0.170991	−	1.62687i	0.486692	−	0.873574i	$-0.338203\pi$
$6$	−0.0676242	−	0.643402i	−0.0276075	−	0.262668i
$7$	1.22500	+	1.36050i	0.463007	+	0.514222i	0.928754	−	0.370696i	$-0.120881\pi$
$7$	1.22500	+	1.36050i	0.463007	+	0.514222i	−0.465747	+	0.884918i	$0.654214\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	2.08845	−	1.51734i	0.696149	−	0.505782i
$10$	−0.382347	+	3.63779i	−0.120909	+	1.15037i
$11$	3.01277			0.908383			0.454191	−	0.890904i	$-0.349928\pi$
$11$	3.01277			0.908383			0.454191	+	0.890904i	$0.349928\pi$
$12$	−0.0676242	+	0.643402i	−0.0195214	+	0.185734i
$13$	−0.306269	+	0.530473i	−0.0849436	+	0.147127i	−0.905367	−	0.424630i	$-0.860404\pi$
$13$	−0.306269	+	0.530473i	−0.0849436	+	0.147127i	0.820424	+	0.571756i	$0.193738\pi$
$14$	−0.915368	−	1.58546i	−0.244642	−	0.423733i
$15$	2.16183	−	0.962508i	0.558182	−	0.248518i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	−2.83078	−	1.26034i	−0.686565	−	0.305679i	0.0336455	−	0.999434i	$-0.489288\pi$
$17$	−2.83078	−	1.26034i	−0.686565	−	0.305679i	−0.720211	+	0.693755i	$0.755955\pi$
$18$	−2.35828	+	1.04997i	−0.555852	+	0.247481i
$19$	0.666594	−	0.740328i	0.152927	−	0.169843i	−0.661813	−	0.749669i	$-0.730213\pi$
$19$	0.666594	−	0.740328i	0.152927	−	0.169843i	0.814740	+	0.579826i	$0.196879\pi$
$20$	1.13033	−	3.47880i	0.252750	−	0.777883i
$21$	−0.592194	+	1.02571i	−0.129227	+	0.223828i
$22$	−2.94693	−	0.626389i	−0.628287	−	0.133547i
$23$	−2.91986	+	2.12140i	−0.608832	+	0.442342i	−0.849003	−	0.528388i	$-0.822797\pi$
$23$	−2.91986	+	2.12140i	−0.608832	+	0.442342i	0.240171	+	0.970731i	$0.422797\pi$
$24$	0.199917	−	0.615282i	0.0408079	−	0.125594i
$25$	−8.19659	+	1.74224i	−1.63932	+	0.348448i
$26$	0.409867	−	0.455204i	0.0803816	−	0.0892728i
$27$	2.92128	+	2.12244i	0.562201	+	0.408463i
$28$	0.565729	+	1.74113i	0.106913	+	0.329043i
$29$	2.21699	+	3.83994i	0.411684	+	0.713058i	0.995074	−	0.0991340i	$-0.0316073\pi$
$29$	2.21699	+	3.83994i	0.411684	+	0.713058i	−0.583390	+	0.812192i	$0.698274\pi$
$30$	−2.31470	+	0.492005i	−0.422605	+	0.0898275i
$31$	−9.36452	+	1.99049i	−1.68192	+	0.357503i	−0.947144	−	0.320809i	$-0.896045\pi$
$31$	−9.36452	+	1.99049i	−1.68192	+	0.357503i	−0.734774	+	0.678312i	$0.762712\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	0.602304	+	1.85370i	0.104848	+	0.322688i
$34$	2.50688	+	1.82136i	0.429927	+	0.312360i
$35$	4.48085	−	4.97648i	0.757401	−	0.841179i
$36$	2.52505	−	0.536716i	0.420842	−	0.0894527i
$37$	−3.51402	+	10.8150i	−0.577701	+	1.77798i	0.0490900	+	0.998794i	$0.484368\pi$
$37$	−3.51402	+	10.8150i	−0.577701	+	1.77798i	−0.626791	+	0.779187i	$0.715632\pi$
$38$	−0.805950	+	0.585557i	−0.130742	+	0.0949899i
$39$	−0.387619	−	0.0823909i	−0.0620686	−	0.0131931i
$40$	−1.82891	+	3.16777i	−0.289177	+	0.500869i
$41$	−0.770956	+	2.37276i	−0.120403	+	0.370562i	−0.993036	−	0.117815i	$-0.962411\pi$
$41$	−0.770956	+	2.37276i	−0.120403	+	0.370562i	0.872633	+	0.488377i	$0.162411\pi$
$42$	0.792510	−	0.880171i	0.122287	−	0.135813i
$43$	9.47014	−	4.21638i	1.44418	−	0.642992i	0.472943	−	0.881093i	$-0.343192\pi$
$43$	9.47014	−	4.21638i	1.44418	−	0.642992i	0.971240	+	0.238101i	$0.0765251\pi$
$44$	2.75230	+	1.22540i	0.414925	+	0.184736i
$45$	−6.31829	−	7.01717i	−0.941875	−	1.04606i
$46$	3.29711	−	1.46797i	0.486133	−	0.216440i
$47$	−0.641906	−	1.11181i	−0.0936316	−	0.162175i	0.815405	−	0.578891i	$-0.196514\pi$
$47$	−0.641906	−	1.11181i	−0.0936316	−	0.162175i	−0.909037	+	0.416716i	$0.863181\pi$
$48$	−0.323473	+	0.560271i	−0.0466893	+	0.0808682i
$49$	0.381362	−	3.62842i	0.0544803	−	0.518345i
$50$	8.37970			1.18507
$51$	0.209546	−	1.99369i	0.0293423	−	0.279173i
$52$	−0.495553	+	0.360040i	−0.0687208	+	0.0499286i
$53$	−6.73226	−	4.89127i	−0.924747	−	0.671868i	0.0199539	−	0.999801i	$-0.493648\pi$
$53$	−6.73226	−	4.89127i	−0.924747	−	0.671868i	−0.944701	+	0.327933i	$0.893648\pi$
$54$	−2.41617	−	2.68342i	−0.328798	−	0.365168i
$55$	−1.15192	−	10.9598i	−0.155325	−	1.47782i
$56$	−0.191364	−	1.82071i	−0.0255721	−	0.243302i
$57$	0.588774	+	0.262139i	0.0779850	+	0.0347212i
$58$	−1.37017	−	4.21696i	−0.179913	−	0.553714i
$59$	4.56554	+	0.970436i	0.594383	+	0.126340i	0.495274	−	0.868737i	$-0.335068\pi$
$59$	4.56554	+	0.970436i	0.594383	+	0.126340i	0.0991085	+	0.995077i	$0.468401\pi$
$60$	2.36642			0.305503
$61$	6.40383	−	4.47113i	0.819926	−	0.572469i
$61$	6.40383	−	4.47113i	0.819926	−	0.572469i
$62$	9.57373			1.21587
$63$	4.62270	+	0.982586i	0.582406	+	0.123794i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	2.04685	+	0.911316i	0.253880	+	0.113035i
$66$	−0.203736	−	1.93842i	−0.0250782	−	0.238603i
$67$	0.979029	+	9.31484i	0.119607	+	1.13799i	0.875475	+	0.483264i	$0.160549\pi$
$67$	0.979029	+	9.31484i	0.119607	+	1.13799i	−0.755867	+	0.654725i	$0.772785\pi$
$68$	−2.07342	−	2.30276i	−0.251439	−	0.279251i
$69$	−1.88899	−	1.37243i	−0.227407	−	0.165221i
$70$	−5.41760	+	3.93612i	−0.647527	+	0.470456i
$71$	−1.60811	+	15.3001i	−0.190847	+	1.81579i	0.310530	+	0.950564i	$0.399494\pi$
$71$	−1.60811	+	15.3001i	−0.190847	+	1.81579i	−0.501377	+	0.865229i	$0.667173\pi$
$72$	−2.58146			−0.304228
$73$	−1.17326	+	11.1628i	−0.137320	+	1.30651i	0.681228	+	0.732071i	$0.261446\pi$
$73$	−1.17326	+	11.1628i	−0.137320	+	1.30651i	−0.818548	+	0.574438i	$0.805221\pi$
$74$	5.68580	−	9.84810i	0.660961	−	1.14482i
$75$	−2.71061	−	4.69491i	−0.312994	−	0.542121i
$76$	0.910082	−	0.405195i	0.104394	−	0.0464790i
$77$	3.69064	+	4.09887i	0.420588	+	0.467110i
$78$	0.362018	+	0.161181i	0.0409905	+	0.0182501i
$79$	11.1304	−	4.95556i	1.25227	−	0.557544i	0.329956	−	0.943996i	$-0.392966\pi$
$79$	11.1304	−	4.95556i	1.25227	−	0.557544i	0.922310	+	0.386452i	$0.126299\pi$
$80$	2.44756	−	2.71830i	0.273646	−	0.303915i
$81$	1.67126	−	5.14362i	0.185696	−	0.571514i
$82$	1.24743	−	2.16062i	0.137756	−	0.238600i
$83$	−3.27266	−	0.695625i	−0.359221	−	0.0763548i	0.0247661	−	0.999693i	$-0.492116\pi$
$83$	−3.27266	−	0.695625i	−0.359221	−	0.0763548i	−0.383987	+	0.923339i	$0.625449\pi$
$84$	−0.958189	+	0.696165i	−0.104547	+	0.0759579i
$85$	−3.50253	+	10.7797i	−0.379903	+	1.16922i
$86$	−10.1398	+	2.15529i	−1.09341	+	0.232411i
$87$	−1.91943	+	2.13174i	−0.205784	+	0.228547i
$88$	−2.43738	−	1.77086i	−0.259825	−	0.188774i
$89$	−5.52523	−	17.0049i	−0.585673	−	1.80252i	−0.596551	−	0.802575i	$-0.703463\pi$
$89$	−5.52523	−	17.0049i	−0.585673	−	1.80252i	0.0108782	−	0.999941i	$-0.496537\pi$
$90$	4.72127	+	8.17748i	0.497666	+	0.861982i
$91$	−1.09689	+	0.233151i	−0.114985	+	0.0244409i
$92$	−3.53027	+	0.750382i	−0.368056	+	0.0782328i
$93$	−3.09684	−	5.36389i	−0.321128	−	0.556209i
$94$	0.396720	+	1.22098i	0.0409185	+	0.125934i
$95$	−2.94803	−	2.14187i	−0.302461	−	0.219751i
$96$	0.432891	−	0.480774i	0.0441818	−	0.0490688i
$97$	−2.05197	+	0.436160i	−0.208346	+	0.0442853i	−0.310902	−	0.950442i	$-0.600631\pi$
$97$	−2.05197	+	0.436160i	−0.208346	+	0.0442853i	0.102556	+	0.994727i	$0.467298\pi$
$98$	−1.12742	+	3.46984i	−0.113886	+	0.350507i
$99$	6.29200	−	4.57140i	0.632370	−	0.459443i
$100$	−8.19659	−	1.74224i	−0.819659	−	0.174224i
$101$	−3.32008	+	5.75054i	−0.330360	+	0.572200i	−0.982582	−	0.185827i	$-0.940503\pi$
$101$	−3.32008	+	5.75054i	−0.330360	+	0.572200i	0.652222	+	0.758028i	$0.273837\pi$
$102$	−0.619479	+	1.90656i	−0.0613375	+	0.188777i
$103$	−9.87973	+	10.9726i	−0.973479	+	1.08116i	0.0232004	+	0.999731i	$0.492614\pi$
$103$	−9.87973	+	10.9726i	−0.973479	+	1.08116i	−0.996679	+	0.0814270i	$0.974052\pi$
$104$	0.559580	−	0.249141i	0.0548714	−	0.0244303i
$105$	3.95774	+	1.76210i	0.386236	+	0.171963i
$106$	5.56819	+	6.18410i	0.540831	+	0.600653i
$107$	−8.68727	+	3.86782i	−0.839831	+	0.373917i	−0.781137	−	0.624359i	$-0.785360\pi$
$107$	−8.68727	+	3.86782i	−0.839831	+	0.373917i	−0.0586933	+	0.998276i	$0.518693\pi$
$108$	1.80545	+	3.12713i	0.173730	+	0.300909i
$109$	6.62010	−	11.4664i	0.634091	−	1.09828i	−0.352616	−	0.935768i	$-0.614708\pi$
$109$	6.62010	−	11.4664i	0.634091	−	1.09828i	0.986707	−	0.162510i	$-0.0519589\pi$
$110$	−1.15192	+	10.9598i	−0.109831	+	1.04498i
$111$	−7.35681			−0.698278
$112$	−0.191364	+	1.82071i	−0.0180822	+	0.172041i
$113$	8.73172	−	6.34397i	0.821411	−	0.596790i	−0.0957051	−	0.995410i	$-0.530511\pi$
$113$	8.73172	−	6.34397i	0.821411	−	0.596790i	0.917116	+	0.398619i	$0.130511\pi$
$114$	−0.521406	−	0.378824i	−0.0488341	−	0.0354801i
$115$	8.83360	+	9.81071i	0.823738	+	0.914853i
$116$	0.463477	+	4.40969i	0.0430327	+	0.409429i
$117$	0.165285	+	1.57258i	0.0152806	+	0.145385i
$118$	−4.26401	−	1.89846i	−0.392534	−	0.174767i
$119$	−1.75301	−	5.39521i	−0.160698	−	0.494578i
$120$	−2.31470	−	0.492005i	−0.211303	−	0.0449138i
$121$	−1.92325			−0.174841
$122$	−7.19349	+	3.04199i	−0.651268	+	0.275409i
$123$	−1.61404			−0.145533
$124$	−9.36452	−	1.99049i	−0.840959	−	0.178751i
$125$	3.82018	+	11.7573i	0.341687	+	1.05161i
$126$	−4.31739	−	1.92223i	−0.384624	−	0.171246i
$127$	−1.53125	−	14.5689i	−0.135877	−	1.29278i	−0.823751	−	0.566952i	$-0.808122\pi$
$127$	−1.53125	−	14.5689i	−0.135877	−	1.29278i	0.687874	−	0.725830i	$-0.258544\pi$
$128$	−0.104528	−	0.994522i	−0.00923910	−	0.0879041i
$129$	4.48751	+	4.98388i	0.395103	+	0.438806i
$130$	−1.81265	−	1.31697i	−0.158980	−	0.115505i
$131$	−5.56780	+	4.04525i	−0.486461	+	0.353435i	−0.803822	−	0.594870i	$-0.797203\pi$
$131$	−5.56780	+	4.04525i	−0.486461	+	0.353435i	0.317361	+	0.948305i	$0.397203\pi$
$132$	−0.203736	+	1.93842i	−0.0177329	+	0.168718i
$133$	1.82380			0.158143
$134$	0.979029	−	9.31484i	0.0845752	−	0.804679i
$135$	6.60403	−	11.4385i	0.568384	−	0.984470i
$136$	1.54934	+	2.68353i	0.132855	+	0.230111i
$137$	−8.82305	+	3.92828i	−0.753804	+	0.335615i	−0.747409	−	0.664364i	$-0.768702\pi$
$137$	−8.82305	+	3.92828i	−0.753804	+	0.335615i	−0.00639531	+	0.999980i	$0.502036\pi$
$138$	1.56236	+	1.73518i	0.132997	+	0.147708i
$139$	8.21336	+	3.65682i	0.696648	+	0.310168i	0.724334	−	0.689449i	$-0.242147\pi$
$139$	8.21336	+	3.65682i	0.696648	+	0.310168i	−0.0276861	+	0.999617i	$0.508814\pi$
$140$	6.11757	−	2.72372i	0.517029	−	0.230196i
$141$	0.555751	−	0.617224i	0.0468027	−	0.0519796i
$142$	4.75405	−	14.6314i	0.398951	−	1.22784i
$143$	−0.922715	+	1.59819i	−0.0771613	+	0.133647i
$144$	2.52505	+	0.536716i	0.210421	+	0.0447263i
$145$	13.1212	−	9.53313i	1.08966	−	0.791683i
$146$	3.46850	−	10.6749i	0.287055	−	0.883465i
$147$	2.30874	−	0.490738i	0.190422	−	0.0404754i
$148$	−7.60909	+	8.45075i	−0.625463	+	0.694647i
$149$	−2.76581	−	2.00948i	−0.226584	−	0.164623i	0.468701	−	0.883357i	$-0.344722\pi$
$149$	−2.76581	−	2.00948i	−0.226584	−	0.164623i	−0.695286	+	0.718734i	$0.744722\pi$
$150$	1.67525	+	5.15588i	0.136783	+	0.420976i
$151$	−3.29187	−	5.70169i	−0.267889	−	0.463997i	0.700428	−	0.713723i	$-0.252993\pi$
$151$	−3.29187	−	5.70169i	−0.267889	−	0.463997i	−0.968316	+	0.249726i	$0.919659\pi$
$152$	−0.974439	+	0.207123i	−0.0790375	+	0.0167999i
$153$	−7.82431	+	1.66311i	−0.632558	+	0.134454i
$154$	−2.75779	−	4.77663i	−0.222229	−	0.384912i
$155$	10.8215	+	33.3051i	0.869202	+	2.67513i
$156$	−0.320596	−	0.232926i	−0.0256682	−	0.0186490i
$157$	9.14592	−	10.1576i	0.729924	−	0.810663i	−0.257911	−	0.966169i	$-0.583034\pi$
$157$	9.14592	−	10.1576i	0.729924	−	0.810663i	0.987835	+	0.155506i	$0.0497007\pi$
$158$	−11.9175	+	2.53314i	−0.948103	+	0.201526i
$159$	1.66362	−	5.12009i	0.131933	−	0.406049i
$160$	−2.95924	+	2.15002i	−0.233949	+	0.169974i
$161$	−6.46300	−	1.37375i	−0.509356	−	0.108267i
$162$	−2.70416	+	4.68375i	−0.212459	+	0.367990i
$163$	3.12283	−	9.61108i	0.244599	−	0.752798i	−0.751103	−	0.660185i	$-0.770478\pi$
$163$	3.12283	−	9.61108i	0.244599	−	0.752798i	0.995702	−	0.0926133i	$-0.0295220\pi$
$164$	−1.66939	+	1.85405i	−0.130357	+	0.144777i
$165$	6.51308	−	2.89981i	0.507043	−	0.225750i
$166$	3.05651	+	1.36085i	0.237232	+	0.105622i
$167$	−5.65266	−	6.27792i	−0.437416	−	0.485800i	0.483619	−	0.875278i	$-0.339322\pi$
$167$	−5.65266	−	6.27792i	−0.437416	−	0.485800i	−0.921035	+	0.389479i	$0.872655\pi$
$168$	1.08199	−	0.481734i	0.0834775	−	0.0371666i
$169$	6.31240	+	10.9334i	0.485569	+	0.841030i
$170$	5.66721	−	9.81590i	0.434655	−	0.752845i
$171$	0.268813	−	2.55759i	0.0205567	−	0.195584i
$172$	10.3664			0.790428
$173$	−0.466090	+	4.43455i	−0.0354362	+	0.337153i	0.962412	+	0.271592i	$0.0875502\pi$
$173$	−0.466090	+	4.43455i	−0.0354362	+	0.337153i	−0.997849	+	0.0655605i	$0.979116\pi$
$174$	2.32070	−	1.68609i	0.175932	−	0.127822i
$175$	−12.4112	−	9.01723i	−0.938195	−	0.681639i
$176$	2.01593	+	2.23892i	0.151957	+	0.168765i
$177$	0.315639	+	3.00310i	0.0237249	+	0.225727i
$178$	1.86897	+	17.7821i	0.140085	+	1.33282i
$179$	−8.66326	−	3.85713i	−0.647523	−	0.288296i	0.0565755	−	0.998398i	$-0.481982\pi$
$179$	−8.66326	−	3.85713i	−0.647523	−	0.288296i	−0.704098	+	0.710103i	$0.748649\pi$
$180$	−2.91791	−	8.98039i	−0.217488	−	0.669359i
$181$	−12.0903	−	2.56987i	−0.898666	−	0.191017i	−0.264656	−	0.964343i	$-0.585259\pi$
$181$	−12.0903	−	2.56987i	−0.898666	−	0.191017i	−0.634009	+	0.773325i	$0.718592\pi$
$182$	1.12139			0.0831233
$183$	4.03124	+	3.04630i	0.297998	+	0.225189i
$184$	3.60914			0.266069
$185$	40.6864	+	8.64816i	2.99132	+	0.635826i
$186$	1.91395	+	5.89054i	0.140338	+	0.431916i
$187$	−8.52848	−	3.79712i	−0.623664	−	0.277673i
$188$	−0.134195	−	1.27678i	−0.00978717	−	0.0931187i
$189$	0.690997	+	6.57440i	0.0502626	+	0.478217i
$190$	2.43829	+	2.70799i	0.176892	+	0.196458i
$191$	5.92732	+	4.30645i	0.428886	+	0.311604i	0.781203	−	0.624277i	$-0.214606\pi$
$191$	5.92732	+	4.30645i	0.428886	+	0.311604i	−0.352317	+	0.935881i	$0.614606\pi$
$192$	−0.523390	+	0.380265i	−0.0377724	+	0.0274433i
$193$	0.955802	−	9.09385i	0.0688001	−	0.654589i	−0.904723	−	0.426001i	$-0.859922\pi$
$193$	0.955802	−	9.09385i	0.0688001	−	0.654589i	0.973523	−	0.228589i	$-0.0734112\pi$
$194$	2.09781			0.150614
$195$	−0.151516	+	1.44158i	−0.0108503	+	0.103233i
$196$	1.82420	−	3.15961i	0.130300	−	0.225686i
$197$	−2.56377	−	4.44058i	−0.182661	−	0.316378i	0.760125	−	0.649777i	$-0.225138\pi$
$197$	−2.56377	−	4.44058i	−0.182661	−	0.316378i	−0.942786	+	0.333399i	$0.891804\pi$
$198$	−7.10495	+	3.16333i	−0.504927	+	0.224808i
$199$	−11.0936	−	12.3207i	−0.786407	−	0.873393i	0.208095	−	0.978109i	$-0.433274\pi$
$199$	−11.0936	−	12.3207i	−0.786407	−	0.873393i	−0.994502	+	0.104715i	$0.966607\pi$
$200$	7.65524	+	3.40833i	0.541307	+	0.241005i
$201$	−5.53552	+	2.46457i	−0.390446	+	0.173838i
$202$	4.44313	−	4.93459i	0.312617	−	0.347197i
$203$	−2.50843	+	7.72015i	−0.176057	+	0.541848i
$204$	1.00234	−	1.73610i	0.0701777	−	0.121551i
$205$	8.92636	+	1.89736i	0.623444	+	0.132517i
$206$	11.9452	−	8.67867i	0.832259	−	0.604671i
$207$	−2.87907	+	8.86086i	−0.200109	+	0.615872i
$208$	−0.599152	+	0.127354i	−0.0415437	+	0.00883038i
$209$	2.00829	−	2.23043i	0.138916	−	0.154282i
$210$	−3.50489	−	2.54645i	−0.241860	−	0.175722i
$211$	3.03556	+	9.34249i	0.208976	+	0.643163i	0.999527	+	0.0307660i	$0.00979467\pi$
$211$	3.03556	+	9.34249i	0.208976	+	0.643163i	−0.790550	+	0.612397i	$0.790205\pi$
$212$	−4.16077	−	7.20666i	−0.285763	−	0.494955i
$213$	−9.73539	+	2.06932i	−0.667058	+	0.141787i
$214$	9.30160	−	1.97712i	0.635844	−	0.135153i
$215$	−18.9592	−	32.8383i	−1.29301	−	2.23955i
$216$	−1.11583	−	3.43417i	−0.0759226	−	0.233666i
$217$	−14.1796	−	10.3021i	−0.962576	−	0.699352i
$218$	−8.85943	+	9.83939i	−0.600036	+	0.666408i
$219$	−7.10283	+	1.50975i	−0.479965	+	0.102020i
$220$	3.40542	−	10.4808i	0.229593	−	0.706616i
$221$	1.53556	−	1.11565i	0.103293	−	0.0750466i
$222$	7.19605	+	1.52957i	0.482967	+	0.102658i
$223$	4.43105	−	7.67481i	0.296725	−	0.513943i	−0.678659	−	0.734453i	$-0.737439\pi$
$223$	4.43105	−	7.67481i	0.296725	−	0.513943i	0.975385	+	0.220510i	$0.0707721\pi$
$224$	0.565729	−	1.74113i	0.0377993	−	0.116334i
$225$	−14.4746	+	16.0756i	−0.964970	+	1.07171i
$226$	−9.85990	+	4.38991i	−0.655871	+	0.292012i
$227$	4.63951	+	2.06564i	0.307935	+	0.137102i	0.554886	−	0.831926i	$-0.312762\pi$
$227$	4.63951	+	2.06564i	0.307935	+	0.137102i	−0.246951	+	0.969028i	$0.579429\pi$
$228$	0.431250	+	0.478952i	0.0285602	+	0.0317194i
$229$	15.6975	−	6.98897i	1.03732	−	0.461844i	0.183832	−	0.982958i	$-0.441150\pi$
$229$	15.6975	−	6.98897i	1.03732	−	0.461844i	0.853488	+	0.521113i	$0.174483\pi$
$230$	−6.60081	−	11.4329i	−0.435244	−	0.753865i
$231$	−1.78414	+	3.09022i	−0.117388	+	0.203322i
$232$	0.463477	−	4.40969i	0.0304287	−	0.289510i
$233$	21.7009			1.42168			0.710838	−	0.703356i	$-0.248316\pi$
$233$	21.7009			1.42168			0.710838	+	0.703356i	$0.248316\pi$
$234$	0.165285	−	1.57258i	0.0108050	−	0.102803i
$235$	−3.79911	+	2.76022i	−0.247827	+	0.180057i
$236$	3.77612	+	2.74351i	0.245804	+	0.178587i
$237$	5.27422	+	5.85762i	0.342598	+	0.380493i
$238$	0.592975	+	5.64178i	0.0384369	+	0.365702i
$239$	2.60579	+	24.7924i	0.168554	+	1.60369i	0.672597	+	0.740009i	$0.265179\pi$
$239$	2.60579	+	24.7924i	0.168554	+	1.60369i	−0.504042	+	0.863679i	$0.668154\pi$
$240$	2.16183	+	0.962508i	0.139545	+	0.0621296i
$241$	−1.79301	−	5.51832i	−0.115498	−	0.355466i	0.876553	−	0.481306i	$-0.159837\pi$
$241$	−1.79301	−	5.51832i	−0.115498	−	0.355466i	−0.992051	+	0.125840i	$0.959837\pi$
$242$	1.88122	+	0.399865i	0.120929	+	0.0257043i
$243$	14.3316			0.919373
$244$	7.66876	−	1.47991i	0.490942	−	0.0947414i
$245$	−13.3452			−0.852595
$246$	1.57877	+	0.335578i	0.100659	+	0.0213957i
$247$	0.188567	+	0.580349i	0.0119982	+	0.0369267i
$248$	8.74604	+	3.89399i	0.555374	+	0.247268i
$249$	−0.226255	−	2.15267i	−0.0143383	−	0.136420i
$250$	−1.29222	−	12.2946i	−0.0817271	−	0.777582i
$251$	−3.60928	−	4.00851i	−0.227815	−	0.253015i	0.618390	−	0.785871i	$-0.287785\pi$
$251$	−3.60928	−	4.00851i	−0.227815	−	0.253015i	−0.846206	+	0.532857i	$0.821119\pi$
$252$	3.82339	+	2.77786i	0.240851	+	0.174989i
$253$	−8.79684	+	6.39128i	−0.553053	+	0.401816i
$254$	−1.53125	+	14.5689i	−0.0960795	+	0.914135i
$255$	−7.33275			−0.459195
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	−1.03613	+	1.79462i	−0.0646318	+	0.111946i	−0.896531	−	0.442982i	$-0.853921\pi$
$257$	−1.03613	+	1.79462i	−0.0646318	+	0.111946i	0.831899	+	0.554927i	$0.187254\pi$
$258$	−3.35324	−	5.80797i	−0.208763	−	0.361589i
$259$	−19.0186	+	8.46761i	−1.18176	+	0.526152i
$260$	1.49922	+	1.66506i	0.0929779	+	0.103262i
$261$	10.4566	+	4.65557i	0.647245	+	0.288172i
$262$	6.28719	−	2.79924i	0.388424	−	0.172937i
$263$	−15.2415	+	16.9274i	−0.939833	+	1.04379i	0.0591298	+	0.998250i	$0.481167\pi$
$263$	−15.2415	+	16.9274i	−0.939833	+	1.04379i	−0.998963	+	0.0455397i	$0.985499\pi$
$264$	0.602304	−	1.85370i	0.0370692	−	0.114087i
$265$	−15.2194	+	26.3607i	−0.934918	+	1.61933i
$266$	−1.78394	−	0.379189i	−0.109381	−	0.0232495i
$267$	9.35822	−	6.79914i	0.572714	−	0.416101i
$268$	−2.89430	+	8.90773i	−0.176797	+	0.544126i
$269$	21.7985	−	4.63342i	1.32908	−	0.282504i	0.511977	−	0.858999i	$-0.328913\pi$
$269$	21.7985	−	4.63342i	1.32908	−	0.282504i	0.817101	+	0.576495i	$0.195580\pi$
$270$	−8.83792	+	9.81550i	−0.537858	+	0.597352i
$271$	−15.6249	−	11.3522i	−0.949145	−	0.689594i	0.00145923	−	0.999999i	$-0.499536\pi$
$271$	−15.6249	−	11.3522i	−0.949145	−	0.689594i	−0.950605	+	0.310404i	$0.899536\pi$
$272$	−0.957543	−	2.94702i	−0.0580596	−	0.178689i
$273$	−0.362741	−	0.628285i	−0.0219541	−	0.0380255i
$274$	9.44698	−	2.00802i	0.570713	−	0.121309i
$275$	−24.6944	+	5.24895i	−1.48913	+	0.316524i
$276$	−1.16746	−	2.02210i	−0.0702728	−	0.121716i
$277$	−4.66586	−	14.3600i	−0.280344	−	0.862811i	−0.987756	−	0.156009i	$-0.950137\pi$
$277$	−4.66586	−	14.3600i	−0.280344	−	0.862811i	0.707412	−	0.706802i	$-0.249863\pi$
$278$	−7.27358	−	5.28457i	−0.436241	−	0.316947i
$279$	−16.5370	+	18.3662i	−0.990047	+	1.09956i
$280$	−6.55018	+	1.39228i	−0.391448	+	0.0832049i
$281$	−3.45512	+	10.6338i	−0.206115	+	0.634357i	0.793551	+	0.608504i	$0.208230\pi$
$281$	−3.45512	+	10.6338i	−0.206115	+	0.634357i	−0.999666	+	0.0258526i	$0.991770\pi$
$282$	−0.671935	+	0.488189i	−0.0400131	+	0.0290712i
$283$	20.2713	+	4.30880i	1.20500	+	0.256131i	0.766290	−	0.642495i	$-0.222101\pi$
$283$	20.2713	+	4.30880i	1.20500	+	0.256131i	0.438714	+	0.898627i	$0.355434\pi$
$284$	−7.69221	+	13.3233i	−0.456449	+	0.790592i
$285$	0.728490	−	2.24206i	0.0431520	−	0.132808i
$286$	1.23483	−	1.37142i	0.0730173	−	0.0810939i
$287$	−4.17256	+	1.85775i	−0.246299	+	0.109659i
$288$	−2.35828	−	1.04997i	−0.138963	−	0.0618704i
$289$	−4.95037	−	5.49794i	−0.291198	−	0.323408i
$290$	−14.8165	+	6.59675i	−0.870057	+	0.387374i
$291$	−0.678586	−	1.17534i	−0.0397794	−	0.0688999i
$292$	−5.61215	+	9.72053i	−0.328426	+	0.568851i
$293$	2.89724	−	27.5654i	0.169259	−	1.61039i	−0.499097	−	0.866546i	$-0.666335\pi$
$293$	2.89724	−	27.5654i	0.169259	−	1.61039i	0.668356	−	0.743842i	$-0.266998\pi$
$294$	−2.36032			−0.137657
$295$	1.78462	−	16.9795i	0.103905	−	0.988586i
$296$	9.19982	−	6.68406i	0.534729	−	0.388503i
$297$	8.80113	+	6.39440i	0.510694	+	0.371041i
$298$	2.28758	+	2.54061i	0.132516	+	0.147174i
$299$	−0.231084	−	2.19862i	−0.0133640	−	0.127150i
$300$	−0.566671	−	5.39151i	−0.0327168	−	0.311279i
$301$	17.3373	+	7.71908i	0.999307	+	0.444920i
$302$	2.03449	+	6.26151i	0.117072	+	0.360310i
$303$	−4.20194	−	0.893151i	−0.241395	−	0.0513102i
$304$	0.996209			0.0571365
$305$	−18.7135	−	21.5863i	−1.07153	−	1.23603i
$306$	7.99911			0.457279
$307$	23.7411	+	5.04632i	1.35497	+	0.288009i	0.827454	−	0.561534i	$-0.189788\pi$
$307$	23.7411	+	5.04632i	1.35497	+	0.288009i	0.527520	+	0.849542i	$0.323122\pi$
$308$	1.70441	+	5.24563i	0.0971176	+	0.298897i
$309$	−8.72634	−	3.88522i	−0.496424	−	0.221022i
$310$	−3.66049	−	34.8272i	−0.207902	−	1.97805i
$311$	0.213328	+	2.02968i	0.0120967	+	0.115093i	0.998904	−	0.0468071i	$-0.0149046\pi$
$311$	0.213328	+	2.02968i	0.0120967	+	0.115093i	−0.986807	+	0.161900i	$0.948238\pi$
$312$	0.265162	+	0.294492i	0.0150118	+	0.0166723i
$313$	−2.45236	−	1.78175i	−0.138616	−	0.100710i	0.516316	−	0.856398i	$-0.327303\pi$
$313$	−2.45236	−	1.78175i	−0.138616	−	0.100710i	−0.654932	+	0.755688i	$0.727303\pi$
$314$	−11.0579	+	8.03407i	−0.624036	+	0.453389i
$315$	1.80696	−	17.1921i	0.101811	−	0.968665i
$316$	12.1837			0.685388
$317$	−0.126490	+	1.20347i	−0.00710438	+	0.0675936i	−0.997500	−	0.0706713i	$-0.977486\pi$
$317$	−0.126490	+	1.20347i	−0.00710438	+	0.0675936i	0.990395	+	0.138265i	$0.0441525\pi$
$318$	−2.69179	+	4.66232i	−0.150948	+	0.261450i
$319$	6.67927	+	11.5688i	0.373967	+	0.647730i
$320$	3.34159	−	1.48777i	0.186801	−	0.0831690i
$321$	−4.11654	−	4.57188i	−0.229763	−	0.255177i
$322$	6.03615	+	2.68747i	0.336381	+	0.149767i
$323$	−2.82005	+	1.25557i	−0.156912	+	0.0698616i
$324$	3.61888	−	4.01917i	0.201049	−	0.223287i
$325$	1.58615	−	4.88166i	0.0879836	−	0.270786i
$326$	−5.05285	+	8.75179i	−0.279851	+	0.484717i
$327$	8.37851	+	1.78091i	0.463333	+	0.0984844i
$328$	2.01839	−	1.46644i	0.111447	−	0.0809709i
$329$	0.726289	−	2.23529i	0.0400416	−	0.123235i
$330$	−6.97366	+	1.48230i	−0.383887	+	0.0815978i
$331$	−19.0967	+	21.2090i	−1.04965	+	1.16575i	−0.0638269	+	0.997961i	$0.520331\pi$
$331$	−19.0967	+	21.2090i	−1.04965	+	1.16575i	−0.985822	+	0.167793i	$0.946336\pi$
$332$	−2.70679	−	1.96660i	−0.148554	−	0.107931i
$333$	9.07131	+	27.9186i	0.497104	+	1.52993i
$334$	4.22388	+	7.31598i	0.231121	+	0.400313i
$335$	33.5111	−	7.12300i	1.83091	−	0.389171i
$336$	−1.15851	+	0.246248i	−0.0632017	+	0.0134339i
$337$	−6.15783	−	10.6657i	−0.335438	−	0.580996i	0.648130	−	0.761529i	$-0.275551\pi$
$337$	−6.15783	−	10.6657i	−0.335438	−	0.580996i	−0.983569	+	0.180533i	$0.942218\pi$
$338$	−3.90128	−	12.0069i	−0.212202	−	0.653089i
$339$	5.64895	+	4.10420i	0.306809	+	0.222910i
$340$	−7.58421	+	8.42312i	−0.411311	+	0.456808i
$341$	−28.2131	+	5.99688i	−1.52783	+	0.324749i
$342$	−0.794691	+	2.44581i	−0.0429720	+	0.132254i
$343$	15.7713	−	11.4585i	0.851571	−	0.618703i
$344$	−10.1398	−	2.15529i	−0.546703	−	0.116205i
$345$	−4.27036	+	7.39648i	−0.229909	+	0.398213i
$346$	1.37790	−	4.24074i	0.0740764	−	0.227984i
$347$	11.7497	−	13.0494i	0.630758	−	0.700527i	−0.340044	−	0.940409i	$-0.610442\pi$
$347$	11.7497	−	13.0494i	0.630758	−	0.700527i	0.970802	+	0.239882i	$0.0771088\pi$
$348$	−2.62054	+	1.16674i	−0.140476	+	0.0625439i
$349$	−4.30679	−	1.91751i	−0.230537	−	0.102642i	0.288217	−	0.957565i	$-0.406937\pi$
$349$	−4.30679	−	1.91751i	−0.230537	−	0.102642i	−0.518754	+	0.854923i	$0.673604\pi$
$350$	10.2652	+	11.4006i	0.548695	+	0.609388i
$351$	−2.02059	+	0.899625i	−0.107851	+	0.0480184i
$352$	−1.50638	−	2.60913i	−0.0802905	−	0.139067i
$353$	8.75966	−	15.1722i	0.466230	−	0.807533i	−0.533027	−	0.846099i	$-0.678945\pi$
$353$	8.75966	−	15.1722i	0.466230	−	0.807533i	0.999256	+	0.0385652i	$0.0122787\pi$
$354$	0.315639	−	3.00310i	0.0167760	−	0.159613i
$355$	56.2735			2.98669
$356$	1.86897	−	17.7821i	0.0990552	−	0.942447i
$357$	2.96912	−	2.15719i	0.157142	−	0.114171i
$358$	7.67201	+	5.57404i	0.405478	+	0.294597i
$359$	5.12432	+	5.69114i	0.270452	+	0.300367i	0.863037	−	0.505141i	$-0.168559\pi$
$359$	5.12432	+	5.69114i	0.270452	+	0.300367i	−0.592585	+	0.805508i	$0.701893\pi$
$360$	0.987014	+	9.39081i	0.0520202	+	0.494939i
$361$	1.88230	+	17.9089i	0.0990686	+	0.942575i
$362$	11.2918	+	5.02743i	0.593484	+	0.264236i
$363$	−0.384490	−	1.18334i	−0.0201805	−	0.0621092i
$364$	−1.09689	−	0.233151i	−0.0574926	−	0.0122204i
$365$	41.0566			2.14900
$366$	−3.30979	−	3.81788i	−0.173005	−	0.199564i
$367$	1.21577			0.0634625			0.0317313	−	0.999496i	$-0.489898\pi$
$367$	1.21577			0.0634625			0.0317313	+	0.999496i	$0.489898\pi$
$368$	−3.53027	−	0.750382i	−0.184028	−	0.0391164i
$369$	1.99019	+	6.12518i	0.103605	+	0.318864i
$370$	−37.9993	−	16.9184i	−1.97549	−	0.879544i
$371$	−1.59244	−	15.1511i	−0.0826755	−	0.786605i
$372$	−0.647416	−	6.15975i	−0.0335670	−	0.319368i
$373$	5.01194	+	5.56633i	0.259509	+	0.288214i	0.858793	−	0.512323i	$-0.171215\pi$
$373$	5.01194	+	5.56633i	0.259509	+	0.288214i	−0.599284	+	0.800536i	$0.704548\pi$
$374$	7.55264	+	5.48732i	0.390538	+	0.283742i
$375$	−6.47034	+	4.70098i	−0.334127	+	0.242757i
$376$	−0.134195	+	1.27678i	−0.00692057	+	0.0658449i
$377$	−2.71598			−0.139880
$378$	0.690997	−	6.57440i	0.0355411	−	0.338151i
$379$	1.00843	−	1.74665i	0.0517996	−	0.0897195i	−0.838963	−	0.544189i	$-0.816838\pi$
$379$	1.00843	−	1.74665i	0.0517996	−	0.0897195i	0.890763	+	0.454469i	$0.150171\pi$
$380$	−1.82198	−	3.15576i	−0.0934656	−	0.161887i
$381$	8.65787	−	3.85473i	0.443556	−	0.197484i
$382$	−4.90244	−	5.44471i	−0.250830	−	0.278575i
$383$	−28.7476	−	12.7993i	−1.46894	−	0.654012i	−0.492597	−	0.870258i	$-0.663952\pi$
$383$	−28.7476	−	12.7993i	−1.46894	−	0.654012i	−0.976339	+	0.216245i	$0.930619\pi$
$384$	0.591014	−	0.263137i	0.0301601	−	0.0134281i
$385$	13.4997	−	14.9930i	0.688010	−	0.764113i
$386$	−2.82563	+	8.69640i	−0.143821	+	0.442635i
$387$	13.3802	−	23.1751i	0.680153	−	1.17806i
$388$	−2.05197	−	0.436160i	−0.104173	−	0.0221427i
$389$	26.0014	−	18.8911i	1.31832	−	0.957819i	0.318373	−	0.947965i	$-0.396864\pi$
$389$	26.0014	−	18.8911i	1.31832	−	0.957819i	0.999951	−	0.00985341i	$-0.00313649\pi$
$390$	0.447925	−	1.37857i	0.0226816	−	0.0698068i
$391$	10.9392	−	2.32519i	0.553217	−	0.117590i
$392$	−2.44126	+	2.71129i	−0.123302	+	0.136941i
$393$	−3.60207	−	2.61705i	−0.181700	−	0.132013i
$394$	1.58450	+	4.87658i	0.0798258	+	0.245678i
$395$	−22.2830	−	38.5952i	−1.12118	−	1.94194i
$396$	7.60738	−	1.61700i	0.382285	−	0.0812573i
$397$	−19.8362	+	4.21632i	−0.995552	+	0.211611i	−0.676752	−	0.736211i	$-0.736613\pi$
$397$	−19.8362	+	4.21632i	−0.995552	+	0.211611i	−0.318800	+	0.947822i	$0.603280\pi$
$398$	8.28959	+	14.3580i	0.415520	+	0.719701i
$399$	0.364608	+	1.12215i	0.0182532	+	0.0561777i
$400$	−6.77932	−	4.92547i	−0.338966	−	0.246273i
$401$	1.92308	−	2.13580i	0.0960341	−	0.106657i	−0.693212	−	0.720734i	$-0.743805\pi$
$401$	1.92308	−	2.13580i	0.0960341	−	0.106657i	0.789246	+	0.614077i	$0.210472\pi$
$402$	5.92697	−	1.25982i	0.295611	−	0.0628340i
$403$	1.81216	−	5.57725i	0.0902700	−	0.277822i
$404$	−5.37200	+	3.90298i	−0.267267	+	0.194181i
$405$	−19.3504	−	4.11306i	−0.961530	−	0.204380i
$406$	4.05872	−	7.02991i	0.201431	−	0.348889i
$407$	−10.5869	+	32.5832i	−0.524774	+	1.61509i
$408$	−1.34139	+	1.48976i	−0.0664087	+	0.0737543i
$409$	−9.24136	+	4.11452i	−0.456956	+	0.203450i	−0.622288	−	0.782788i	$-0.713797\pi$
$409$	−9.24136	+	4.11452i	−0.456956	+	0.203450i	0.165333	+	0.986238i	$0.447130\pi$
$410$	−8.33682	−	3.71179i	−0.411726	−	0.183312i
$411$	−4.18088	−	4.64333i	−0.206227	−	0.229039i
$412$	−13.4885	+	6.00548i	−0.664532	+	0.295869i
$413$	4.27252	+	7.40022i	0.210237	+	0.364141i
$414$	4.65843	−	8.06863i	0.228949	−	0.396552i
$415$	−1.27925	+	12.1712i	−0.0627957	+	0.597461i
$416$	0.612537			0.0300321
$417$	−0.607985	+	5.78459i	−0.0297732	+	0.283273i
$418$	−2.42814	+	1.76415i	−0.118764	+	0.0862872i
$419$	−21.4887	−	15.6124i	−1.04979	−	0.762718i	−0.0776181	−	0.996983i	$-0.524731\pi$
$419$	−21.4887	−	15.6124i	−1.04979	−	0.762718i	−0.972173	+	0.234266i	$0.924731\pi$
$420$	2.89886	+	3.21951i	0.141450	+	0.157096i
$421$	−0.655745	−	6.23900i	−0.0319591	−	0.304070i	−0.998812	−	0.0487353i	$-0.984481\pi$
$421$	−0.655745	−	6.23900i	−0.0319591	−	0.304070i	0.966853	−	0.255335i	$-0.0821857\pi$
$422$	−1.02681	−	9.76946i	−0.0499844	−	0.475570i
$423$	−3.02759	−	1.34797i	−0.147207	−	0.0655406i
$424$	2.57150	+	7.91425i	0.124883	+	0.384350i
$425$	25.3986	+	5.39863i	1.23201	+	0.261872i
$426$	9.95288			0.482219
$427$	13.9277	+	3.23528i	0.674008	+	0.156566i
$428$	−9.50941			−0.459654
$429$	−1.16780	−	0.248224i	−0.0563821	−	0.0119844i
$430$	11.7174	+	36.0625i	0.565064	+	1.73909i
$431$	34.2569	+	15.2521i	1.65010	+	0.734670i	0.999690	−	0.0249173i	$-0.00793225\pi$
$431$	34.2569	+	15.2521i	1.65010	+	0.734670i	0.650406	+	0.759587i	$0.274599\pi$
$432$	0.377442	+	3.59112i	0.0181597	+	0.172778i
$433$	0.574000	+	5.46124i	0.0275847	+	0.262451i	0.999619	+	0.0276107i	$0.00878989\pi$
$433$	0.574000	+	5.46124i	0.0275847	+	0.262451i	−0.972034	+	0.234840i	$0.924543\pi$
$434$	11.7278	+	13.0251i	0.562954	+	0.625224i
$435$	8.48872	+	6.16742i	0.407003	+	0.295705i
$436$	10.7116	−	7.78240i	0.512990	−	0.372709i
$437$	−0.375828	+	3.57576i	−0.0179783	+	0.171052i
$438$	7.26152			0.346969
$439$	−0.546690	+	5.20141i	−0.0260921	+	0.248250i	0.973700	+	0.227836i	$0.0731650\pi$
$439$	−0.546690	+	5.20141i	−0.0260921	+	0.248250i	−0.999792	+	0.0204137i	$0.993502\pi$
$440$	−5.51009	+	9.54375i	−0.262683	+	0.454981i
$441$	−4.70911	−	8.15641i	−0.224243	−	0.388401i
$442$	−1.73396	+	0.772008i	−0.0824760	+	0.0367207i
$443$	−1.98876	−	2.20874i	−0.0944887	−	0.104940i	0.694046	−	0.719931i	$-0.255827\pi$
$443$	−1.98876	−	2.20874i	−0.0944887	−	0.104940i	−0.788535	+	0.614990i	$0.789160\pi$
$444$	−6.72078	−	2.99228i	−0.318954	−	0.142008i
$445$	−59.7477	+	26.6014i	−2.83231	+	1.26103i
$446$	−5.92991	+	6.58583i	−0.280789	+	0.311848i
$447$	0.683464	−	2.10348i	0.0323267	−	0.0994914i
$448$	−0.915368	+	1.58546i	−0.0432471	+	0.0749062i
$449$	−17.3533	−	3.68855i	−0.818952	−	0.174074i	−0.220659	−	0.975351i	$-0.570821\pi$
$449$	−17.3533	−	3.68855i	−0.818952	−	0.174074i	−0.598293	+	0.801278i	$0.704154\pi$
$450$	17.5006	−	12.7149i	0.824984	−	0.599386i
$451$	−2.32271	+	7.14856i	−0.109372	+	0.336613i
$452$	10.5571	−	2.24399i	0.496567	−	0.105548i
$453$	2.85004	−	3.16530i	0.133907	−	0.148719i
$454$	−4.10866	−	2.98511i	−0.192829	−	0.140098i
$455$	1.26755	+	3.90111i	0.0594235	+	0.182887i
$456$	−0.322247	−	0.558147i	−0.0150906	−	0.0261376i
$457$	−22.3749	+	4.75593i	−1.04665	+	0.222473i	−0.698979	−	0.715142i	$-0.746362\pi$
$457$	−22.3749	+	4.75593i	−1.04665	+	0.222473i	−0.347674	+	0.937615i	$0.613029\pi$
$458$	−16.8076	+	3.57256i	−0.785366	+	0.166935i
$459$	−5.59451	−	9.68997i	−0.261129	−	0.452289i
$460$	4.07952	+	12.5555i	0.190209	+	0.585402i
$461$	8.43645	+	6.12944i	0.392925	+	0.285477i	0.766653	−	0.642062i	$-0.221921\pi$
$461$	8.43645	+	6.12944i	0.392925	+	0.285477i	−0.373728	+	0.927538i	$0.621921\pi$
$462$	2.38765	−	2.65175i	0.111083	−	0.123371i
$463$	−12.0808	+	2.56785i	−0.561442	+	0.119338i	−0.479886	−	0.877331i	$-0.659322\pi$
$463$	−12.0808	+	2.56785i	−0.561442	+	0.119338i	−0.0815554	+	0.996669i	$0.525989\pi$
$464$	−1.37017	+	4.21696i	−0.0636087	+	0.195768i
$465$	−18.3286	+	13.3165i	−0.849970	+	0.617539i
$466$	−21.2267	−	4.51188i	−0.983308	−	0.209009i
$467$	−5.32712	+	9.22684i	−0.246510	+	0.426967i	−0.962555	−	0.271087i	$-0.912617\pi$
$467$	−5.32712	+	9.22684i	−0.246510	+	0.426967i	0.716045	+	0.698054i	$0.245950\pi$
$468$	−0.488630	+	1.50385i	−0.0225869	+	0.0695155i
$469$	−11.4735	+	12.7427i	−0.529799	+	0.588401i
$470$	4.28998	−	1.91002i	0.197882	−	0.0881027i
$471$	8.07820	+	3.59665i	0.372224	+	0.165725i
$472$	−3.12319	−	3.46866i	−0.143757	−	0.159658i
$473$	28.5313	−	12.7030i	1.31187	−	0.584083i
$474$	−3.94110	−	6.82619i	−0.181021	−	0.313537i
$475$	−4.17397	+	7.22952i	−0.191515	+	0.331713i
$476$	0.592975	−	5.64178i	0.0271790	−	0.258591i
$477$	−21.4817			−0.983580
$478$	2.60579	−	24.7924i	0.119186	−	1.13398i
$479$	−24.5978	+	17.8714i	−1.12390	+	0.816564i	−0.984796	−	0.173714i	$-0.944423\pi$
$479$	−24.5978	+	17.8714i	−1.12390	+	0.816564i	−0.139107	+	0.990277i	$0.544423\pi$
$480$	−1.91447	−	1.39094i	−0.0873832	−	0.0634876i
$481$	−4.66085	−	5.17640i	−0.212516	−	0.236023i
$482$	0.606506	+	5.77052i	0.0276256	+	0.262840i
$483$	−0.446819	−	4.25120i	−0.0203310	−	0.193436i
$484$	−1.75697	−	0.782255i	−0.0798624	−	0.0355570i
$485$	2.37122	+	7.29788i	0.107672	+	0.331379i
$486$	−14.0184	−	2.97971i	−0.635888	−	0.135162i
$487$	30.7454			1.39321			0.696603	−	0.717457i	$-0.254694\pi$
$487$	30.7454			1.39321			0.696603	+	0.717457i	$0.254694\pi$
$488$	−7.80887	−	0.146856i	−0.353491	−	0.00664785i
$489$	6.53783			0.295651
$490$	13.0536	+	2.77463i	0.589702	+	0.125345i
$491$	−5.43340	−	16.7223i	−0.245206	−	0.754666i	−0.995603	−	0.0936781i	$-0.970138\pi$
$491$	−5.43340	−	16.7223i	−0.245206	−	0.754666i	0.750397	−	0.660988i	$-0.229862\pi$
$492$	−1.47450	−	0.656490i	−0.0664756	−	0.0295969i
$493$	−1.43616	−	13.6642i	−0.0646816	−	0.615404i
$494$	−0.0637848	−	0.606872i	−0.00286982	−	0.0273045i
$495$	−19.0355	−	21.1411i	−0.855584	−	0.950222i
$496$	−7.74531	−	5.62730i	−0.347775	−	0.252673i
$497$	−22.7858	+	16.5549i	−1.02208	+	0.742587i
$498$	−0.226255	+	2.15267i	−0.0101387	+	0.0964637i
$499$	−26.4774			−1.18529			−0.592647	−	0.805463i	$-0.701917\pi$
$499$	−26.4774			−1.18529			−0.592647	+	0.805463i	$0.701917\pi$
$500$	−1.29222	+	12.2946i	−0.0577898	+	0.549833i
$501$	2.73262	−	4.73304i	0.122085	−	0.211457i
$502$	2.69699	+	4.67132i	0.120373	+	0.208491i
$503$	12.6458	−	5.63026i	0.563847	−	0.251041i	−0.104961	−	0.994476i	$-0.533472\pi$
$503$	12.6458	−	5.63026i	0.563847	−	0.251041i	0.668808	+	0.743436i	$0.266805\pi$
$504$	−3.16230	−	3.51208i	−0.140860	−	0.156441i
$505$	22.1887	+	9.87904i	0.987383	+	0.439611i
$506$	9.93343	−	4.42265i	0.441595	−	0.196611i
$507$	−5.46516	+	6.06968i	−0.242716	+	0.269564i
$508$	4.52684	−	13.9322i	0.200846	−	0.618141i
$509$	−18.3366	+	31.7600i	−0.812757	+	1.40774i	0.0981705	+	0.995170i	$0.468701\pi$
$509$	−18.3366	+	31.7600i	−0.812757	+	1.40774i	−0.910927	+	0.412567i	$0.864632\pi$
$510$	7.17252	+	1.52457i	0.317604	+	0.0675089i
$511$	−16.6243	+	12.0783i	−0.735415	+	0.534310i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	3.51861	−	0.747903i	0.155350	−	0.0330207i
$514$	1.38661	−	1.53998i	0.0611607	−	0.0679258i
$515$	43.6933	+	31.7451i	1.92536	+	1.39885i
$516$	2.07241	+	6.37823i	0.0912329	+	0.280786i
$517$	−1.93391	−	3.34963i	−0.0850534	−	0.147317i
$518$	20.3635	−	4.32839i	0.894720	−	0.190179i
$519$	−2.82168	+	0.599766i	−0.123858	+	0.0263268i
$520$	−1.12028	−	1.94038i	−0.0491274	−	0.0850912i
$521$	−3.64810	−	11.2277i	−0.159826	−	0.491895i	0.838792	−	0.544453i	$-0.183263\pi$
$521$	−3.64810	−	11.2277i	−0.159826	−	0.491895i	−0.998618	+	0.0525580i	$0.983263\pi$
$522$	−9.26012	−	6.72787i	−0.405305	−	0.294471i
$523$	−8.91952	+	9.90613i	−0.390023	+	0.433165i	−0.905896	−	0.423501i	$-0.860801\pi$
$523$	−8.91952	+	9.90613i	−0.390023	+	0.433165i	0.515872	+	0.856665i	$0.327468\pi$
$524$	−6.73179	+	1.43089i	−0.294080	+	0.0625086i
$525$	3.06694	−	9.43906i	0.133852	−	0.411954i
$526$	18.4279	−	13.3886i	0.803493	−	0.583772i
$527$	29.0176	+	6.16788i	1.26403	+	0.268677i
$528$	−0.974548	+	1.68797i	−0.0424117	+	0.0734593i
$529$	−3.08217	+	9.48594i	−0.134007	+	0.412432i
$530$	20.3675	−	22.6204i	0.884707	−	0.982567i
$531$	11.0074	−	4.90080i	0.477679	−	0.212677i
$532$	1.66612	+	0.741805i	0.0722355	+	0.0321613i
$533$	−1.02256	−	1.13567i	−0.0442921	−	0.0491914i
$534$	−10.5673	+	4.70488i	−0.457294	+	0.203600i
$535$	17.3919	+	30.1236i	0.751917	+	1.30236i
$536$	4.68307	−	8.11132i	0.202278	−	0.350356i
$537$	0.641289	−	6.10146i	0.0276737	−	0.263297i
$538$	−22.2855			−0.960796
$539$	1.14895	−	10.9316i	0.0494890	−	0.470856i
$540$	10.6855	−	7.76350i	0.459833	−	0.334088i
$541$	−5.07120	−	3.68445i	−0.218028	−	0.158407i	0.473410	−	0.880842i	$-0.343023\pi$
$541$	−5.07120	−	3.68445i	−0.218028	−	0.158407i	−0.691439	+	0.722435i	$0.743023\pi$
$542$	12.9232	+	14.3527i	0.555100	+	0.616501i
$543$	−0.835864	−	7.95271i	−0.0358703	−	0.341283i
$544$	0.323900	+	3.08170i	0.0138871	+	0.132127i
$545$	−44.2434	−	19.6984i	−1.89518	−	0.843787i
$546$	0.224186	+	0.689973i	0.00959427	+	0.0295281i
$547$	5.48959	+	1.16685i	0.234718	+	0.0498908i	0.323769	−	0.946136i	$-0.395050\pi$
$547$	5.48959	+	1.16685i	0.234718	+	0.0498908i	−0.0890509	+	0.996027i	$0.528383\pi$
$548$	−9.65803			−0.412571
$549$	6.58980	−	19.0545i	0.281246	−	0.813227i
$550$	25.2461			1.07650
$551$	4.32064	+	0.918381i	0.184066	+	0.0391243i
$552$	0.721529	+	2.22064i	0.0307103	+	0.0945166i
$553$	20.3768	+	9.07233i	0.866509	+	0.385795i
$554$	1.57828	+	15.0163i	0.0670546	+	0.637982i
$555$	2.81286	+	26.7625i	0.119399	+	1.13601i
$556$	6.01591	+	6.68135i	0.255132	+	0.283352i
$557$	−25.7106	−	18.6798i	−1.08939	−	0.791490i	−0.110096	−	0.993921i	$-0.535116\pi$
$557$	−25.7106	−	18.6798i	−1.08939	−	0.791490i	−0.979297	+	0.202431i	$0.935116\pi$
$558$	19.9942	−	14.5267i	0.846423	−	0.614962i
$559$	−0.663733	+	6.31499i	−0.0280729	+	0.267096i
$560$	6.69652			0.282980
$561$	0.631312	−	6.00653i	0.0266540	−	0.253596i
$562$	5.59049	−	9.68302i	0.235821	−	0.408454i
$563$	−11.8404	−	20.5083i	−0.499015	−	0.864320i	0.500984	−	0.865456i	$-0.332971\pi$
$563$	−11.8404	−	20.5083i	−0.499015	−	0.864320i	−0.999999	+	0.00113674i	$0.999638\pi$
$564$	0.758751	−	0.337818i	0.0319492	−	0.0142247i
$565$	−26.4166	−	29.3386i	−1.11135	−	1.23428i
$566$	−18.9325	−	8.42928i	−0.795791	−	0.354309i
$567$	9.04522	−	4.02719i	0.379863	−	0.169126i
$568$	10.2942	−	11.4328i	0.431934	−	0.479712i
$569$	−1.77415	+	5.46028i	−0.0743764	+	0.228907i	−0.981333	−	0.192318i	$-0.938400\pi$
$569$	−1.77415	+	5.46028i	−0.0743764	+	0.228907i	0.906956	+	0.421225i	$0.138400\pi$
$570$	−1.17872	+	2.04161i	−0.0493712	+	0.0855135i
$571$	32.7394	+	6.95897i	1.37010	+	0.291224i	0.833457	−	0.552585i	$-0.186358\pi$
$571$	32.7394	+	6.95897i	1.37010	+	0.291224i	0.536644	+	0.843809i	$0.319692\pi$
$572$	−1.49298	+	1.08472i	−0.0624248	+	0.0453543i
$573$	−1.46471	+	4.50791i	−0.0611891	+	0.188321i
$574$	4.46763	−	0.949624i	0.186475	−	0.0396365i
$575$	20.2369	−	22.4753i	0.843936	−	0.937285i
$576$	2.08845	+	1.51734i	0.0870186	+	0.0632227i
$577$	−5.59318	−	17.2140i	−0.232847	−	0.716629i	−0.997400	−	0.0720681i	$-0.977040\pi$
$577$	−5.59318	−	17.2140i	−0.232847	−	0.716629i	0.764553	−	0.644561i	$-0.222960\pi$
$578$	3.69910	+	6.40704i	0.153862	+	0.266498i
$579$	5.78636	−	1.22993i	0.240473	−	0.0511141i
$580$	15.8643	−	3.37206i	0.658729	−	0.140017i
$581$	−3.06261	−	5.30460i	−0.127059	−	0.220072i
$582$	0.419389	+	1.29075i	0.0173842	+	0.0535032i
$583$	−20.2827	−	14.7363i	−0.840025	−	0.610314i
$584$	7.51053	−	8.34128i	0.310788	−	0.345165i
$585$	5.65751	−	1.20254i	0.233909	−	0.0497190i
$586$	−8.56510	+	26.3607i	−0.353821	+	1.08895i
$587$	5.79529	−	4.21053i	0.239197	−	0.173787i	−0.461728	−	0.887021i	$-0.652770\pi$
$587$	5.79529	−	4.21053i	0.239197	−	0.173787i	0.700926	+	0.713234i	$0.252770\pi$
$588$	2.30874	+	0.490738i	0.0952108	+	0.0202377i
$589$	−4.76872	+	8.25966i	−0.196492	+	0.340333i
$590$	−5.27586	+	16.2374i	−0.217204	+	0.668485i
$591$	2.21967	−	2.46519i	0.0913048	−	0.101404i
$592$	−10.3885	+	4.62525i	−0.426964	+	0.190097i
$593$	21.6397	+	9.63460i	0.888635	+	0.395646i	0.799706	−	0.600392i	$-0.204989\pi$
$593$	21.6397	+	9.63460i	0.888635	+	0.395646i	0.0889291	+	0.996038i	$0.471656\pi$
$594$	−7.27934	−	8.08452i	−0.298675	−	0.331712i
$595$	−18.9564	+	8.43992i	−0.777136	+	0.346003i
$596$	−1.70937	−	2.96071i	−0.0700184	−	0.121275i
$597$	5.36291	−	9.28884i	0.219489	−	0.380167i
$598$	−0.231084	+	2.19862i	−0.00944974	+	0.0899083i
$599$	10.4326			0.426265			0.213132	−	0.977023i	$-0.431633\pi$
$599$	10.4326			0.426265			0.213132	+	0.977023i	$0.431633\pi$
$600$	−0.566671	+	5.39151i	−0.0231342	+	0.220108i
$601$	22.5857	−	16.4095i	0.921291	−	0.669357i	−0.0225540	−	0.999746i	$-0.507180\pi$
$601$	22.5857	−	16.4095i	0.921291	−	0.669357i	0.943845	+	0.330389i	$0.107180\pi$
$602$	−15.3536	−	11.1550i	−0.625765	−	0.454645i
$603$	16.1785	+	17.9680i	0.658838	+	0.731714i
$604$	−0.688189	−	6.54768i	−0.0280020	−	0.266421i
$605$	0.735347	+	6.99636i	0.0298961	+	0.284443i
$606$	3.92442	+	1.74727i	0.159419	+	0.0709778i
$607$	−14.3731	−	44.2360i	−0.583387	−	1.79548i	−0.605652	−	0.795730i	$-0.707088\pi$
$607$	−14.3731	−	44.2360i	−0.583387	−	1.79548i	0.0222645	−	0.999752i	$-0.492912\pi$
$608$	−0.974439	−	0.207123i	−0.0395187	−	0.00839997i
$609$	−5.25155			−0.212803
$610$	13.8165	+	25.0053i	0.559415	+	1.01243i
$611$	0.786383			0.0318136
$612$	−7.82431	−	1.66311i	−0.316279	−	0.0672272i
$613$	0.540466	+	1.66338i	0.0218292	+	0.0671835i	0.961378	−	0.275232i	$-0.0887548\pi$
$613$	0.540466	+	1.66338i	0.0218292	+	0.0671835i	−0.939548	+	0.342416i	$0.888755\pi$
$614$	−22.1731	−	9.87209i	−0.894833	−	0.398405i
$615$	0.617124	+	5.87154i	0.0248848	+	0.236764i
$616$	−0.576535	−	5.48536i	−0.0232293	−	0.221012i
$617$	−2.88875	−	3.20828i	−0.116297	−	0.129161i	0.682185	−	0.731180i	$-0.261030\pi$
$617$	−2.88875	−	3.20828i	−0.116297	−	0.129161i	−0.798482	+	0.602019i	$0.794363\pi$
$618$	7.72787	+	5.61462i	0.310860	+	0.225853i
$619$	−6.20834	+	4.51062i	−0.249534	+	0.181297i	−0.705520	−	0.708690i	$-0.749287\pi$
$619$	−6.20834	+	4.51062i	−0.249534	+	0.181297i	0.455986	+	0.889987i	$0.349287\pi$
$620$	−3.66049	+	34.8272i	−0.147009	+	1.39869i
$621$	−13.0323			−0.522966
$622$	0.213328	−	2.02968i	0.00855367	−	0.0813827i
$623$	16.3668	−	28.3481i	0.655722	−	1.13574i
$624$	−0.198139	−	0.343187i	−0.00793191	−	0.0137385i
$625$	3.03379	−	1.35073i	0.121352	−	0.0540293i
$626$	2.02833	+	2.25269i	0.0810683	+	0.0900355i
$627$	1.77384	+	0.789763i	0.0708402	+	0.0315401i
$628$	12.4867	−	5.55943i	0.498273	−	0.221845i
$629$	23.5781	−	26.1861i	0.940120	−	1.04411i
$630$	−5.34192	+	16.4407i	−0.212827	+	0.655014i
$631$	−16.6902	+	28.9082i	−0.664425	+	1.15082i	0.315016	+	0.949086i	$0.397990\pi$
$631$	−16.6902	+	28.9082i	−0.664425	+	1.15082i	−0.979441	+	0.201731i	$0.935343\pi$
$632$	−11.9175	−	2.53314i	−0.474052	−	0.100763i
$633$	−5.14140	+	3.73545i	−0.204352	+	0.148471i
$634$	0.373941	−	1.15087i	0.0148511	−	0.0457070i
$635$	−52.4132	+	11.1408i	−2.07995	+	0.442108i
$636$	3.60232	−	4.00078i	0.142841	−	0.158641i
$637$	1.80798	+	1.31357i	0.0716347	+	0.0520456i
$638$	−4.12801	−	12.7047i	−0.163430	−	0.502985i
$639$	19.8571	+	34.3936i	0.785536	+	1.36059i
$640$	−3.57790	+	0.760505i	−0.141429	+	0.0300616i
$641$	21.7971	−	4.63312i	0.860935	−	0.182997i	0.243772	−	0.969833i	$-0.421615\pi$
$641$	21.7971	−	4.63312i	0.860935	−	0.182997i	0.617163	+	0.786835i	$0.288282\pi$
$642$	3.07603	+	5.32785i	0.121401	+	0.210273i
$643$	−5.44372	−	16.7540i	−0.214679	−	0.660715i	−0.999176	−	0.0405823i	$-0.987079\pi$
$643$	−5.44372	−	16.7540i	−0.214679	−	0.660715i	0.784497	−	0.620133i	$-0.212921\pi$
$644$	−5.34549	−	3.88372i	−0.210642	−	0.153040i
$645$	16.4145	−	18.2302i	0.646321	−	0.717812i
$646$	3.01947	−	0.641809i	0.118800	−	0.0252516i
$647$	2.53676	−	7.80733i	0.0997302	−	0.306938i	−0.888727	−	0.458436i	$-0.848410\pi$
$647$	2.53676	−	7.80733i	0.0997302	−	0.306938i	0.988458	+	0.151498i	$0.0484098\pi$
$648$	−4.37543	+	3.17893i	−0.171883	+	0.124880i
$649$	13.7549	+	2.92369i	0.539927	+	0.114765i
$650$	−2.56644	+	4.44520i	−0.100664	+	0.174355i
$651$	3.50394	−	10.7840i	0.137330	−	0.422660i
$652$	6.76203	−	7.50999i	0.264821	−	0.294114i
$653$	−6.57275	+	2.92637i	−0.257211	+	0.114518i	−0.531292	−	0.847189i	$-0.678293\pi$
$653$	−6.57275	+	2.92637i	−0.257211	+	0.114518i	0.274080	+	0.961707i	$0.411627\pi$
$654$	−7.82515	−	3.48398i	−0.305988	−	0.136234i
$655$	16.8446	+	18.7078i	0.658172	+	0.730974i
$656$	−2.27917	+	1.01475i	−0.0889867	+	0.0396194i
$657$	14.4876	+	25.0932i	0.565213	+	0.978978i
$658$	−1.17516	+	2.03544i	−0.0458125	+	0.0793497i
$659$	−4.33462	+	41.2412i	−0.168853	+	1.60653i	0.501953	+	0.864895i	$0.332615\pi$
$659$	−4.33462	+	41.2412i	−0.168853	+	1.60653i	−0.670806	+	0.741633i	$0.734052\pi$
$660$	7.12945			0.277514
$661$	−4.77495	+	45.4306i	−0.185724	+	1.76705i	0.363713	+	0.931511i	$0.381509\pi$
$661$	−4.77495	+	45.4306i	−0.185724	+	1.76705i	−0.549437	+	0.835535i	$0.685158\pi$
$662$	23.0890	−	16.7751i	0.897379	−	0.651984i
$663$	0.993422	+	0.721764i	0.0385813	+	0.0280310i
$664$	2.23876	+	2.48639i	0.0868807	+	0.0964908i
$665$	−0.697323	−	6.63459i	−0.0270410	−	0.257278i
$666$	−3.06847	−	29.1945i	−0.118901	−	1.13127i
$667$	−14.6193	−	6.50894i	−0.566063	−	0.252027i
$668$	−2.61050	−	8.03431i	−0.101003	−	0.310857i
$669$	5.60802	+	1.19202i	0.216818	+	0.0460862i
$670$	−34.2597			−1.32357
$671$	19.2932	−	13.4705i	0.744807	−	0.520021i
$672$	1.18439			0.0456887
$673$	−26.8962	−	5.71696i	−1.03677	−	0.220373i	−0.342073	−	0.939673i	$-0.611129\pi$
$673$	−26.8962	−	5.71696i	−1.03677	−	0.220373i	−0.694699	+	0.719301i	$0.744462\pi$
$674$	3.80575	+	11.7129i	0.146592	+	0.451164i
$675$	−27.6423	−	12.3072i	−1.06395	−	0.473703i
$676$	1.31965	+	12.5556i	0.0507558	+	0.482909i
$677$	3.77449	+	35.9118i	0.145065	+	1.38020i	0.788656	+	0.614835i	$0.210777\pi$
$677$	3.77449	+	35.9118i	0.145065	+	1.38020i	−0.643591	+	0.765370i	$0.722556\pi$
$678$	−4.67219	−	5.18900i	−0.179435	−	0.199282i
$679$	−3.10707	−	2.25742i	−0.119238	−	0.0866316i
$680$	9.16974	−	6.66221i	0.351643	−	0.255484i
$681$	−0.343435	+	3.26757i	−0.0131605	+	0.125213i
$682$	28.8434			1.10447
$683$	2.42153	−	23.0394i	0.0926574	−	0.881576i	−0.845175	−	0.534489i	$-0.820504\pi$
$683$	2.42153	−	23.0394i	0.0926574	−	0.881576i	0.937833	−	0.347087i	$-0.112829\pi$
$684$	1.28584	−	2.22714i	0.0491652	−	0.0851567i
$685$	17.6637	+	30.5944i	0.674896	+	1.16895i
$686$	−17.8090	+	7.92910i	−0.679952	+	0.302734i
$687$	7.43839	+	8.26117i	0.283792	+	0.315183i
$688$	9.47014	+	4.21638i	0.361046	+	0.160748i
$689$	4.65657	−	2.07324i	0.177401	−	0.0789840i
$690$	5.71486	−	6.34700i	0.217561	−	0.241626i
$691$	−0.598456	+	1.84186i	−0.0227663	+	0.0700676i	−0.961794	−	0.273773i	$-0.911728\pi$
$691$	−0.598456	+	1.84186i	−0.0227663	+	0.0700676i	0.939028	+	0.343841i	$0.111728\pi$
$692$	−2.22949	+	3.86159i	−0.0847525	+	0.146796i
$693$	13.9271	+	2.96030i	0.529047	+	0.112452i
$694$	−14.2061	+	10.3213i	−0.539255	+	0.391792i
$695$	10.1624	−	31.2767i	0.385482	−	1.18639i
$696$	2.80586	−	0.596404i	0.106356	−	0.0226066i
$697$	5.17290	−	5.74509i	0.195938	−	0.217611i
$698$	3.81400	+	2.77104i	0.144362	+	0.104885i
$699$	4.33839	+	13.3522i	0.164093	+	0.505026i
$700$	−7.67051	−	13.2857i	−0.289918	−	0.502153i
$701$	7.40531	−	1.57405i	0.279695	−	0.0594509i	−0.0659284	−	0.997824i	$-0.521001\pi$
$701$	7.40531	−	1.57405i	0.279695	−	0.0594509i	0.345623	+	0.938373i	$0.387668\pi$
$702$	2.16348	−	0.459861i	0.0816552	−	0.0173564i
$703$	5.66425	+	9.81077i	0.213631	+	0.370020i
$704$	0.930996	+	2.86531i	0.0350882	+	0.107990i
$705$	−2.45782	−	1.78571i	−0.0925669	−	0.0672538i
$706$	−11.7227	+	13.0194i	−0.441190	+	0.489991i
$707$	−11.8907	+	2.52745i	−0.447197	+	0.0950546i
$708$	−0.933121	+	2.87185i	−0.0350688	+	0.107931i
$709$	−0.167174	+	0.121459i	−0.00627836	+	0.00456150i	−0.590920	−	0.806730i	$-0.701235\pi$
$709$	−0.167174	+	0.121459i	−0.00627836	+	0.00456150i	0.584642	+	0.811292i	$0.301235\pi$
$710$	−55.0438	−	11.6999i	−2.06576	−	0.439090i
$711$	15.7259	−	27.2381i	0.589767	−	1.02151i
$712$	−5.52523	+	17.0049i	−0.207067	+	0.637286i
$713$	23.1204	−	25.6778i	0.865867	−	0.961642i
$714$	−3.35274	+	1.49274i	−0.125473	+	0.0558643i
$715$	6.16667	+	2.74558i	0.230621	+	0.102679i
$716$	−6.34545	−	7.04733i	−0.237140	−	0.263371i
$717$	−14.7334	+	6.55972i	−0.550228	+	0.244977i
$718$	−3.82909	−	6.63218i	−0.142900	−	0.247511i
$719$	−8.02834	+	13.9055i	−0.299407	+	0.518588i	−0.976000	−	0.217769i	$-0.930122\pi$
$719$	−8.02834	+	13.9055i	−0.299407	+	0.518588i	0.676594	+	0.736357i	$0.263455\pi$
$720$	0.987014	−	9.39081i	0.0367838	−	0.349975i
$721$	−27.0309			−1.00668
$722$	1.88230	−	17.9089i	0.0700521	−	0.666501i
$723$	3.03687	−	2.20641i	0.112942	−	0.0820574i
$724$	−9.99979	−	7.26527i	−0.371639	−	0.270012i
$725$	−24.8618	−	27.6119i	−0.923345	−	1.02548i
$726$	0.130058	+	1.23742i	0.00482691	+	0.0459249i
$727$	−1.28723	−	12.2472i	−0.0477407	−	0.454223i	−0.992113	−	0.125345i	$-0.959996\pi$
$727$	−1.28723	−	12.2472i	−0.0477407	−	0.454223i	0.944373	−	0.328878i	$-0.106670\pi$
$728$	1.02444	+	0.456112i	0.0379684	+	0.0169046i
$729$	−2.14866	−	6.61290i	−0.0795800	−	0.244922i
$730$	−40.1594	−	8.53614i	−1.48637	−	0.315937i
$731$	−32.1220			−1.18807
$732$	2.44368	+	4.42259i	0.0903209	+	0.163464i
$733$	39.9860			1.47692			0.738459	−	0.674299i	$-0.235554\pi$
$733$	39.9860			1.47692			0.738459	+	0.674299i	$0.235554\pi$
$734$	−1.18920	−	0.252772i	−0.0438942	−	0.00932999i
$735$	−2.66794	−	8.21108i	−0.0984085	−	0.302870i
$736$	3.29711	+	1.46797i	0.121533	+	0.0541101i
$737$	2.94958	+	28.0634i	0.108649	+	1.03373i
$738$	−0.673205	−	6.40511i	−0.0247810	−	0.235776i
$739$	−33.1088	−	36.7710i	−1.21793	−	1.35264i	−0.916944	−	0.399015i	$-0.869352\pi$
$739$	−33.1088	−	36.7710i	−1.21793	−	1.35264i	−0.300982	−	0.953630i	$-0.597315\pi$
$740$	33.6514	+	24.4491i	1.23705	+	0.898769i
$741$	−0.319380	+	0.232043i	−0.0117327	+	0.00852433i
$742$	−1.59244	+	15.1511i	−0.0584604	+	0.556214i
$743$	8.72775			0.320190			0.160095	−	0.987102i	$-0.448820\pi$
$743$	8.72775			0.320190			0.160095	+	0.987102i	$0.448820\pi$
$744$	−0.647416	+	6.15975i	−0.0237354	+	0.225828i
$745$	−6.25257	+	10.8298i	−0.229076	+	0.396772i
$746$	−3.74512	−	6.48673i	−0.137118	−	0.237496i
$747$	−7.89027	+	3.51298i	−0.288690	+	0.128533i
$748$	−6.24672	−	6.93769i	−0.228403	−	0.253667i
$749$	−15.9041	−	7.08097i	−0.581124	−	0.258733i
$750$	7.30634	−	3.25299i	0.266790	−	0.118782i
$751$	6.32419	−	7.02372i	0.230773	−	0.256299i	−0.616626	−	0.787256i	$-0.711501\pi$
$751$	6.32419	−	7.02372i	0.230773	−	0.256299i	0.847399	+	0.530957i	$0.178167\pi$
$752$	0.396720	−	1.22098i	0.0144669	−	0.0445245i
$753$	1.74481	−	3.02209i	0.0635842	−	0.110131i
$754$	2.65662	+	0.564683i	0.0967486	+	0.0205645i
$755$	−19.4829	+	14.1552i	−0.709056	+	0.515159i
$756$	−2.04279	+	6.28706i	−0.0742956	+	0.228658i
$757$	5.72499	−	1.21688i	0.208078	−	0.0442284i	−0.102693	−	0.994713i	$-0.532746\pi$
$757$	5.72499	−	1.21688i	0.208078	−	0.0442284i	0.310771	+	0.950485i	$0.399413\pi$
$758$	−1.34954	+	1.49882i	−0.0490176	+	0.0544396i
$759$	−5.69108	−	4.13481i	−0.206573	−	0.150084i
$760$	1.12605	+	3.46561i	0.0408460	+	0.125711i
$761$	2.83103	+	4.90348i	0.102625	+	0.177751i	0.912765	−	0.408484i	$-0.133943\pi$
$761$	2.83103	+	4.90348i	0.102625	+	0.177751i	−0.810141	+	0.586236i	$0.800609\pi$
$762$	−9.27011	+	1.97042i	−0.335821	+	0.0713809i
$763$	23.7096	−	5.03964i	0.858347	−	0.182447i
$764$	3.66329	+	6.34500i	0.132533	+	0.229554i
$765$	9.04164	+	27.8273i	0.326901	+	1.00610i
$766$	25.4583	+	18.4966i	0.919847	+	0.668308i
$767$	−1.91307	+	2.12468i	−0.0690770	+	0.0767178i
$768$	−0.632808	+	0.134508i	−0.0228345	+	0.00485362i
$769$	−7.54211	+	23.2122i	−0.271976	+	0.837055i	0.718028	+	0.696014i	$0.245045\pi$
$769$	−7.54211	+	23.2122i	−0.271976	+	0.837055i	−0.990004	+	0.141041i	$0.954955\pi$
$770$	−16.3219	+	11.8586i	−0.588202	+	0.427354i
$771$	−1.31134	−	0.278734i	−0.0472267	−	0.0100384i
$772$	4.57197	−	7.91888i	0.164549	−	0.285007i
$773$	6.98655	−	21.5024i	0.251289	−	0.773387i	−0.743250	−	0.669014i	$-0.766717\pi$
$773$	6.98655	−	21.5024i	0.251289	−	0.773387i	0.994538	−	0.104373i	$-0.0332835\pi$
$774$	−17.9062	+	19.8868i	−0.643624	+	0.714817i
$775$	73.2892	−	32.6305i	2.63263	−	1.17212i
$776$	1.91645	+	0.853258i	0.0687965	+	0.0306302i
$777$	−9.01211	−	10.0090i	−0.323308	−	0.359069i
$778$	−29.3609	+	13.0723i	−1.05264	+	0.468666i
$779$	1.24270	+	2.15243i	0.0445245	+	0.0771186i
$780$	−0.724759	+	1.25532i	−0.0259505	+	0.0449476i
$781$	−4.84486	+	46.0957i	−0.173363	+	1.64943i
$782$	−11.1836			−0.399923
$783$	−1.67357	+	15.9230i	−0.0598085	+	0.569040i
$784$	2.95162	−	2.14448i	0.105415	−	0.0765885i
$785$	−40.4480	−	29.3872i	−1.44365	−	1.04888i
$786$	2.97924	+	3.30878i	0.106266	+	0.118020i
$787$	−3.23251	−	30.7553i	−0.115227	−	1.09631i	−0.887433	−	0.460936i	$-0.847514\pi$
$787$	−3.23251	−	30.7553i	−0.115227	−	1.09631i	0.772207	−	0.635371i	$-0.219153\pi$
$788$	−0.535974	−	5.09945i	−0.0190933	−	0.181660i
$789$	−13.4622	−	5.99375i	−0.479266	−	0.213383i
$790$	13.7716	+	42.3847i	0.489973	+	1.50798i
$791$	19.3274	+	4.10816i	0.687202	+	0.146069i
$792$	−7.77734			−0.276356
$793$	0.410521	+	4.76642i	0.0145780	+	0.169261i
$794$	20.2794			0.719689
$795$	−19.2619	−	4.09424i	−0.683149	−	0.145208i
$796$	−5.12325	−	15.7677i	−0.181589	−	0.558873i
$797$	37.1774	+	16.5524i	1.31689	+	0.586318i	0.940390	−	0.340098i	$-0.110460\pi$
$797$	37.1774	+	16.5524i	1.31689	+	0.586318i	0.376501	+	0.926416i	$0.377127\pi$
$798$	−0.123333	−	1.17343i	−0.00436593	−	0.0415391i
$799$	0.415827	+	3.95633i	0.0147109	+	0.139965i
$800$	5.60712	+	6.22733i	0.198241	+	0.220169i
$801$	−37.3414	−	27.1301i	−1.31939	−	0.958596i
$802$	−2.32511	+	1.68929i	−0.0821026	+	0.0596510i
$803$	−3.53476	+	33.6309i	−0.124739	+	1.18681i
$804$	−6.05939			−0.213698
$805$	−2.52631	+	24.0363i	−0.0890409	+	0.847167i
$806$	−2.93213	+	5.07860i	−0.103280	+	0.178886i
$807$	7.20875	+	12.4859i	0.253760	+	0.439525i
$808$	6.06608	−	2.70079i	0.213404	−	0.0950136i
$809$	25.0466	+	27.8171i	0.880593	+	0.977997i	0.999890	−	0.0148615i	$-0.00473073\pi$
$809$	25.0466	+	27.8171i	0.880593	+	0.977997i	−0.119297	+	0.992859i	$0.538064\pi$
$810$	18.0724	+	8.04636i	0.635000	+	0.282720i
$811$	−23.7808	+	10.5879i	−0.835056	+	0.371791i	−0.779298	−	0.626653i	$-0.784424\pi$
$811$	−23.7808	+	10.5879i	−0.835056	+	0.371791i	−0.0557582	+	0.998444i	$0.517758\pi$
$812$	−5.43163	+	6.03244i	−0.190613	+	0.211697i
$813$	3.86109	−	11.8832i	0.135414	−	0.416762i
$814$	17.1300	−	29.6700i	0.600406	−	1.03993i
$815$	−36.1571	−	7.68543i	−1.26653	−	0.269209i
$816$	1.62182	−	1.17832i	0.0567749	−	0.0412494i
$817$	3.19124	−	9.82162i	0.111647	−	0.343615i
$818$	9.89487	−	2.10322i	0.345966	−	0.0735374i
$819$	−1.93702	+	2.15128i	−0.0676851	+	0.0751719i
$820$	7.38291	+	5.36400i	0.257823	+	0.187319i
$821$	1.47450	+	4.53805i	0.0514604	+	0.158379i	0.973484	−	0.228754i	$-0.0734653\pi$
$821$	1.47450	+	4.53805i	0.0514604	+	0.158379i	−0.922024	+	0.387133i	$0.873465\pi$
$822$	3.12411	+	5.41112i	0.108966	+	0.188734i
$823$	−12.5673	+	2.67126i	−0.438068	+	0.0931142i	−0.421666	−	0.906751i	$-0.638554\pi$
$823$	−12.5673	+	2.67126i	−0.438068	+	0.0931142i	−0.0164019	+	0.999865i	$0.505221\pi$
$824$	14.4424	−	3.06982i	0.503124	−	0.106942i
$825$	−8.16642	−	14.1447i	−0.284318	−	0.492454i
$826$	−2.64056	−	8.12681i	−0.0918768	−	0.282768i
$827$	35.1330	+	25.5256i	1.22169	+	0.887612i	0.996239	−	0.0866422i	$-0.0276137\pi$
$827$	35.1330	+	25.5256i	1.22169	+	0.887612i	0.225453	+	0.974254i	$0.427614\pi$
$828$	−6.23419	+	6.92377i	−0.216653	+	0.240618i
$829$	39.9411	−	8.48974i	1.38721	−	0.294861i	0.547006	−	0.837129i	$-0.315768\pi$
$829$	39.9411	−	8.48974i	1.38721	−	0.294861i	0.840206	+	0.542268i	$0.182434\pi$
$830$	3.78183	−	11.6393i	0.131269	−	0.404005i
$831$	7.90268	−	5.74163i	0.274141	−	0.199175i
$832$	−0.599152	−	0.127354i	−0.0207718	−	0.00441519i
$833$	−5.65261	+	9.79061i	−0.195851	+	0.339224i
$834$	1.79738	−	5.53178i	0.0622383	−	0.191550i
$835$	−20.6765	+	22.9635i	−0.715538	+	0.794686i
$836$	2.74186	−	1.22076i	0.0948293	−	0.0422207i
$837$	−31.5811	−	14.0608i	−1.09160	−	0.486013i
$838$	17.7731	+	19.7390i	0.613961	+	0.681873i
$839$	3.79624	−	1.69019i	0.131061	−	0.0583520i	−0.340159	−	0.940368i	$-0.610481\pi$
$839$	3.79624	−	1.69019i	0.131061	−	0.0583520i	0.471219	+	0.882016i	$0.343814\pi$
$840$	−2.16614	−	3.75187i	−0.0747390	−	0.129452i
$841$	4.66992	−	8.08854i	0.161032	−	0.278915i
$842$	−0.655745	+	6.23900i	−0.0225985	+	0.215010i
$843$	−7.23349			−0.249135
$844$	−1.02681	+	9.76946i	−0.0353443	+	0.336279i
$845$	37.3599	−	27.1435i	1.28522	−	0.933766i
$846$	2.68117	+	1.94799i	0.0921806	+	0.0669731i
$847$	−2.35598	−	2.61658i	−0.0809524	−	0.0899068i
$848$	−0.869837	−	8.27595i	−0.0298703	−	0.284197i
$849$	1.40146	+	13.3340i	0.0480979	+	0.457621i
$850$	−23.7211	−	10.5613i	−0.813627	−	0.362250i
$851$	−12.6826	−	39.0330i	−0.434754	−	1.33803i
$852$	−9.73539	−	2.06932i	−0.333529	−	0.0708937i
$853$	−17.9927			−0.616059			−0.308030	−	0.951377i	$-0.599670\pi$
$853$	−17.9927			−0.616059			−0.308030	+	0.951377i	$0.599670\pi$
$854$	−12.9507	−	6.06031i	−0.443163	−	0.207380i
$855$	−9.40674			−0.321704
$856$	9.30160	+	1.97712i	0.317922	+	0.0675765i
$857$	5.59460	+	17.2184i	0.191108	+	0.588170i	1.00000		0.000212595i	$6.76712e-5\pi$
$857$	5.59460	+	17.2184i	0.191108	+	0.588170i	−0.808892	+	0.587957i	$0.799932\pi$
$858$	1.09068	+	0.485600i	0.0372351	+	0.0165781i
$859$	1.34337	+	12.7813i	0.0458351	+	0.436092i	0.993242	+	0.116061i	$0.0370268\pi$
$859$	1.34337	+	12.7813i	0.0458351	+	0.436092i	−0.947407	+	0.320031i	$0.896307\pi$
$860$	−3.96355	−	37.7106i	−0.135156	−	1.28592i
$861$	−1.97720	−	2.19591i	−0.0673829	−	0.0748363i
$862$	−30.3372	−	22.0412i	−1.03329	−	0.750728i
$863$	1.26315	−	0.917729i	0.0429980	−	0.0312399i	−0.566079	−	0.824351i	$-0.691540\pi$
$863$	1.26315	−	0.917729i	0.0429980	−	0.0312399i	0.609077	+	0.793111i	$0.291540\pi$
$864$	0.377442	−	3.59112i	0.0128408	−	0.122172i
$865$	16.3102			0.554563
$866$	0.574000	−	5.46124i	0.0195053	−	0.185581i
$867$	2.39312	−	4.14500i	0.0812746	−	0.140772i
$868$	−8.76349	−	15.1788i	−0.297452	−	0.515202i
$869$	33.5332	−	14.9299i	1.13754	−	0.506464i
$870$	−7.02094	−	7.79755i	−0.238032	−	0.264362i
$871$	−5.24111	−	2.33349i	−0.177588	−	0.0790674i
$872$	−12.0955	+	5.38528i	−0.409606	+	0.182369i
$873$	−3.62363	+	4.02444i	−0.122641	+	0.136207i
$874$	1.11106	−	3.41948i	0.0375821	−	0.115666i
$875$	−11.3161	+	19.6001i	−0.382555	+	0.662604i
$876$	−7.10283	−	1.50975i	−0.239983	−	0.0510099i
$877$	−16.1687	+	11.7473i	−0.545979	+	0.396677i	−0.826301	−	0.563229i	$-0.809559\pi$
$877$	−16.1687	+	11.7473i	−0.545979	+	0.396677i	0.280322	+	0.959906i	$0.409559\pi$
$878$	1.61618	−	4.97408i	0.0545433	−	0.167867i
$879$	17.5397	−	3.72818i	0.591599	−	0.125748i
$880$	7.37394	−	8.18959i	0.248575	−	0.276071i
$881$	21.9506	+	15.9481i	0.739535	+	0.537304i	0.892566	−	0.450918i	$-0.148903\pi$
$881$	21.9506	+	15.9481i	0.739535	+	0.537304i	−0.153030	+	0.988222i	$0.548903\pi$
$882$	2.91039	+	8.95725i	0.0979978	+	0.301606i
$883$	−21.7732	−	37.7124i	−0.732728	−	1.26912i	−0.955713	−	0.294300i	$-0.904913\pi$
$883$	−21.7732	−	37.7124i	−0.732728	−	1.26912i	0.222985	−	0.974822i	$-0.428420\pi$
$884$	1.85658	−	0.394628i	0.0624434	−	0.0132728i
$885$	10.8040	−	2.29645i	0.363171	−	0.0771945i
$886$	1.48608	+	2.57396i	0.0499257	+	0.0864739i
$887$	−3.42715	−	10.5477i	−0.115072	−	0.354156i	0.876890	−	0.480692i	$-0.159614\pi$
$887$	−3.42715	−	10.5477i	−0.115072	−	0.354156i	−0.991962	+	0.126535i	$0.959614\pi$
$888$	5.95179	+	4.32423i	0.199729	+	0.145111i
$889$	17.9453	−	19.9302i	0.601865	−	0.668438i
$890$	63.9728	−	13.5978i	2.14437	−	0.455801i
$891$	5.03513	−	15.4965i	0.168683	−	0.519153i
$892$	7.16960	−	5.20902i	0.240056	−	0.174411i
$893$	−1.25100	−	0.265908i	−0.0418630	−	0.00889826i
$894$	−1.10587	+	1.91542i	−0.0369857	+	0.0640612i
$895$	−10.7191	+	32.9899i	−0.358299	+	1.10273i
$896$	1.22500	−	1.36050i	0.0409244	−	0.0454512i
$897$	1.30657	−	0.581724i	0.0436252	−	0.0194232i
$898$	16.2072	+	7.21590i	0.540840	+	0.240798i
$899$	−28.4044	−	31.5463i	−0.947340	−	1.05213i
$900$	−19.7617	+	8.79848i	−0.658723	+	0.293283i
$901$	12.8929	+	22.3311i	0.429524	+	0.743957i
$902$	3.75822	−	6.50943i	0.125135	−	0.216740i
$903$	−1.28338	+	12.2105i	−0.0427081	+	0.406341i
$904$	−10.7930			−0.358970
$905$	−4.72597	+	44.9646i	−0.157097	+	1.49467i
$906$	−3.44587	+	2.50357i	−0.114481	+	0.0831755i
$907$	−3.12664	−	2.27163i	−0.103818	−	0.0754284i	0.534665	−	0.845064i	$-0.320438\pi$
$907$	−3.12664	−	2.27163i	−0.103818	−	0.0754284i	−0.638483	+	0.769636i	$0.720438\pi$
$908$	3.39823	+	3.77412i	0.112774	+	0.125249i
$909$	1.79175	+	17.0474i	0.0594287	+	0.565426i
$910$	−0.428762	−	4.07940i	−0.0142133	−	0.135231i
$911$	−0.538432	−	0.239725i	−0.0178390	−	0.00794246i	0.397798	−	0.917473i	$-0.369775\pi$
$911$	−0.538432	−	0.239725i	−0.0178390	−	0.00794246i	−0.415637	+	0.909531i	$0.636441\pi$
$912$	0.199159	+	0.612949i	0.00659482	+	0.0202968i
$913$	−9.85975	−	2.09575i	−0.326310	−	0.0693594i
$914$	22.8748			0.756630
$915$	9.54048	−	15.8295i	0.315398	−	0.523309i
$916$	17.1830			0.567744
$917$	−12.3241	−	2.61958i	−0.406979	−	0.0865060i
$918$	3.45760	+	10.6414i	0.114118	+	0.351218i
$919$	0.674723	+	0.300406i	0.0222570	+	0.00990948i	0.417835	−	0.908523i	$-0.362789\pi$
$919$	0.674723	+	0.300406i	0.0222570	+	0.00990948i	−0.395578	+	0.918432i	$0.629456\pi$
$920$	−1.37994	−	13.1293i	−0.0454954	−	0.432860i
$921$	1.64134	+	15.6163i	0.0540840	+	0.514574i
$922$	−6.97771	−	7.74954i	−0.229799	−	0.255217i
$923$	−7.62379	−	5.53901i	−0.250940	−	0.182319i
$924$	−2.88680	+	2.09738i	−0.0949687	+	0.0689988i
$925$	9.96059	−	94.7687i	0.327502	−	3.11597i
$926$	12.3507			0.405868
$927$	−3.98414	+	37.9065i	−0.130856	+	1.24501i
$928$	2.21699	−	3.83994i	0.0727762	−	0.126052i
$929$	−15.8975	−	27.5354i	−0.521582	−	0.903406i	−0.999685	−	0.0251022i	$-0.992009\pi$
$929$	−15.8975	−	27.5354i	−0.521582	−	0.903406i	0.478103	−	0.878304i	$-0.341324\pi$
$930$	20.6968	−	9.21479i	0.678674	−	0.302165i
$931$	−2.43200	−	2.70101i	−0.0797057	−	0.0885221i
$932$	19.8248	+	8.82656i	0.649382	+	0.289124i
$933$	−1.20618	+	0.537024i	−0.0394885	+	0.0175814i
$934$	7.12907	−	7.91764i	0.233270	−	0.259073i
$935$	−10.5523	+	32.4766i	−0.345097	+	1.06210i
$936$	0.790620	−	1.36939i	0.0258422	−	0.0447601i
$937$	35.3109	+	7.50556i	1.15356	+	0.245196i	0.744698	−	0.667402i	$-0.232594\pi$
$937$	35.3109	+	7.50556i	1.15356	+	0.245196i	0.408859	+	0.912598i	$0.365927\pi$
$938$	13.8722	−	10.0787i	0.452942	−	0.329082i
$939$	0.606007	−	1.86510i	0.0197763	−	0.0608651i
$940$	−4.59335	+	0.976346i	−0.149818	+	0.0318449i
$941$	19.1819	−	21.3037i	0.625313	−	0.694481i	−0.344373	−	0.938833i	$-0.611909\pi$
$941$	19.1819	−	21.3037i	0.625313	−	0.694481i	0.969687	+	0.244352i	$0.0785752\pi$
$942$	−7.15389	−	5.19760i	−0.233086	−	0.169347i
$943$	−2.78249	−	8.56361i	−0.0906102	−	0.278870i
$944$	2.33377	+	4.04221i	0.0759577	+	0.131563i
$945$	23.6521	−	5.02740i	0.769402	−	0.163541i
$946$	−30.5489	+	6.49338i	−0.993231	+	0.211118i
$947$	29.1208	+	50.4387i	0.946298	+	1.63904i	0.753131	+	0.657870i	$0.228542\pi$
$947$	29.1208	+	50.4387i	0.946298	+	1.63904i	0.193167	+	0.981166i	$0.438124\pi$
$948$	2.43573	+	7.49642i	0.0791090	+	0.243472i
$949$	−5.56224	−	4.04120i	−0.180558	−	0.131183i
$950$	5.58586	−	6.20372i	0.181229	−	0.201275i
$951$	−0.765761	+	0.162768i	−0.0248315	+	0.00527810i
$952$	−1.75301	+	5.39521i	−0.0568154	+	0.174860i
$953$	33.8079	−	24.5629i	1.09515	−	0.795671i	0.114886	−	0.993379i	$-0.463350\pi$
$953$	33.8079	−	24.5629i	1.09515	−	0.795671i	0.980261	+	0.197708i	$0.0633498\pi$
$954$	21.0123	+	4.46630i	0.680298	+	0.144602i
$955$	13.3997	−	23.2089i	0.433603	−	0.751023i
$956$	−7.70348	+	23.7089i	−0.249148	+	0.766800i
$957$	−5.78279	+	6.42244i	−0.186931	+	0.207608i
$958$	27.7760	−	12.3667i	0.897401	−	0.399549i
$959$	−16.1527	−	7.19164i	−0.521597	−	0.232230i
$960$	1.58344	+	1.75859i	0.0511053	+	0.0567582i
$961$	55.4123	−	24.6711i	1.78749	−	0.795844i
$962$	3.48277	+	6.03233i	0.112289	+	0.194490i
$963$	−12.2741	+	21.2593i	−0.395527	+	0.685072i
$964$	0.606506	−	5.77052i	0.0195342	−	0.185856i
$965$	−33.4469			−1.07670
$966$	−0.446819	+	4.25120i	−0.0143762	+	0.136780i
$967$	−35.8052	+	26.0140i	−1.15142	+	0.836553i	−0.988669	−	0.150115i	$-0.952036\pi$
$967$	−35.8052	+	26.0140i	−1.15142	+	0.836553i	−0.162748	+	0.986668i	$0.552036\pi$
$968$	1.55594	+	1.13046i	0.0500098	+	0.0363342i
$969$	−1.33630	−	1.48412i	−0.0429283	−	0.0476767i
$970$	−0.802093	−	7.63140i	−0.0257537	−	0.245030i
$971$	−1.57985	−	15.0312i	−0.0506997	−	0.482375i	−0.990183	−	0.139780i	$-0.955361\pi$
$971$	−1.57985	−	15.0312i	−0.0506997	−	0.482375i	0.939483	−	0.342596i	$-0.111306\pi$
$972$	13.0926	+	5.82919i	0.419944	+	0.186971i
$973$	5.08627	+	15.6539i	0.163058	+	0.501841i
$974$	−30.0735	−	6.39233i	−0.963618	−	0.204823i
$975$	3.32069			0.106347
$976$	7.60769	+	1.76720i	0.243516	+	0.0565667i
$977$	−23.8235			−0.762183			−0.381091	−	0.924537i	$-0.624452\pi$
$977$	−23.8235			−0.762183			−0.381091	+	0.924537i	$0.624452\pi$
$978$	−6.39497	−	1.35929i	−0.204488	−	0.0434654i
$979$	−16.6462	−	51.2318i	−0.532015	−	1.63737i
$980$	−12.1915	−	5.42799i	−0.389442	−	0.173391i
$981$	−3.57269	−	33.9918i	−0.114067	−	1.08528i
$982$	1.83791	+	17.4865i	0.0586500	+	0.558017i
$983$	28.3741	+	31.5127i	0.904994	+	1.00510i	0.999954	+	0.00961682i	$0.00306118\pi$
$983$	28.3741	+	31.5127i	0.904994	+	1.00510i	−0.0949595	+	0.995481i	$0.530272\pi$
$984$	1.30579	+	0.948710i	0.0416270	+	0.0302438i
$985$	−15.1736	+	11.0243i	−0.483472	+	0.351263i
$986$	−1.43616	+	13.6642i	−0.0457368	+	0.435157i
$987$	1.52053			0.0483990
$988$	−0.0637848	+	0.606872i	−0.00202927	+	0.0193072i
$989$	−18.7068	+	32.4012i	−0.594842	+	1.03030i
$990$	14.2241	+	24.6368i	0.452071	+	0.783010i
$991$	13.1078	−	5.83596i	0.416382	−	0.185385i	−0.187843	−	0.982199i	$-0.560149\pi$
$991$	13.1078	−	5.83596i	0.416382	−	0.185385i	0.604225	+	0.796814i	$0.293483\pi$
$992$	6.40608	+	7.11467i	0.203393	+	0.225891i
$993$	−16.8673	−	7.50980i	−0.535267	−	0.238316i
$994$	25.7298	−	11.4557i	0.816101	−	0.363352i
$995$	−40.5786	+	45.0671i	−1.28643	+	1.42872i
$996$	0.668877	−	2.05859i	0.0211942	−	0.0652290i
$997$	26.1423	−	45.2799i	0.827936	−	1.43403i	−0.0717178	−	0.997425i	$-0.522848\pi$
$997$	26.1423	−	45.2799i	0.827936	−	1.43403i	0.899654	−	0.436603i	$-0.143819\pi$
$998$	25.8988	+	5.50497i	0.819814	+	0.174257i
$999$	−33.2197	+	24.1355i	−1.05102	+	0.763613i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	122.2.i.b.77.2	✓	24
4.3	odd	2		976.2.bw.b.321.2		24
61.15	even	15		7442.2.a.w.1.7		12
61.42	even	15	inner	122.2.i.b.103.2	yes	24
61.46	even	30		7442.2.a.u.1.7		12
244.103	odd	30		976.2.bw.b.225.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
122.2.i.b.77.2	✓	24	1.1	even	1	trivial
122.2.i.b.103.2	yes	24	61.42	even	15	inner
976.2.bw.b.225.2		24	244.103	odd	30
976.2.bw.b.321.2		24	4.3	odd	2
7442.2.a.u.1.7		12	61.46	even	30
7442.2.a.w.1.7		12	61.15	even	15

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:	\( N \)	\(=\)	\( 122 = 2 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	122.i (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.978148 - 0.207912i) q^{2} +(0.199917 + 0.615282i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-0.382347 - 3.63779i) q^{5} +(-0.0676242 - 0.643402i) q^{6} +(1.22500 + 1.36050i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(2.08845 - 1.51734i) q^{9} +O(q^{10})\)	\(q+(-0.978148 - 0.207912i) q^{2} +(0.199917 + 0.615282i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-0.382347 - 3.63779i) q^{5} +(-0.0676242 - 0.643402i) q^{6} +(1.22500 + 1.36050i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(2.08845 - 1.51734i) q^{9} +(-0.382347 + 3.63779i) q^{10} +3.01277 q^{11} +(-0.0676242 + 0.643402i) q^{12} +(-0.306269 + 0.530473i) q^{13} +(-0.915368 - 1.58546i) q^{14} +(2.16183 - 0.962508i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-2.83078 - 1.26034i) q^{17} +(-2.35828 + 1.04997i) q^{18} +(0.666594 - 0.740328i) q^{19} +(1.13033 - 3.47880i) q^{20} +(-0.592194 + 1.02571i) q^{21} +(-2.94693 - 0.626389i) q^{22} +(-2.91986 + 2.12140i) q^{23} +(0.199917 - 0.615282i) q^{24} +(-8.19659 + 1.74224i) q^{25} +(0.409867 - 0.455204i) q^{26} +(2.92128 + 2.12244i) q^{27} +(0.565729 + 1.74113i) q^{28} +(2.21699 + 3.83994i) q^{29} +(-2.31470 + 0.492005i) q^{30} +(-9.36452 + 1.99049i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.602304 + 1.85370i) q^{33} +(2.50688 + 1.82136i) q^{34} +(4.48085 - 4.97648i) q^{35} +(2.52505 - 0.536716i) q^{36} +(-3.51402 + 10.8150i) q^{37} +(-0.805950 + 0.585557i) q^{38} +(-0.387619 - 0.0823909i) q^{39} +(-1.82891 + 3.16777i) q^{40} +(-0.770956 + 2.37276i) q^{41} +(0.792510 - 0.880171i) q^{42} +(9.47014 - 4.21638i) q^{43} +(2.75230 + 1.22540i) q^{44} +(-6.31829 - 7.01717i) q^{45} +(3.29711 - 1.46797i) q^{46} +(-0.641906 - 1.11181i) q^{47} +(-0.323473 + 0.560271i) q^{48} +(0.381362 - 3.62842i) q^{49} +8.37970 q^{50} +(0.209546 - 1.99369i) q^{51} +(-0.495553 + 0.360040i) q^{52} +(-6.73226 - 4.89127i) q^{53} +(-2.41617 - 2.68342i) q^{54} +(-1.15192 - 10.9598i) q^{55} +(-0.191364 - 1.82071i) q^{56} +(0.588774 + 0.262139i) q^{57} +(-1.37017 - 4.21696i) q^{58} +(4.56554 + 0.970436i) q^{59} +2.36642 q^{60} +(6.40383 - 4.47113i) q^{61} +9.57373 q^{62} +(4.62270 + 0.982586i) q^{63} +(0.309017 + 0.951057i) q^{64} +(2.04685 + 0.911316i) q^{65} +(-0.203736 - 1.93842i) q^{66} +(0.979029 + 9.31484i) q^{67} +(-2.07342 - 2.30276i) q^{68} +(-1.88899 - 1.37243i) q^{69} +(-5.41760 + 3.93612i) q^{70} +(-1.60811 + 15.3001i) q^{71} -2.58146 q^{72} +(-1.17326 + 11.1628i) q^{73} +(5.68580 - 9.84810i) q^{74} +(-2.71061 - 4.69491i) q^{75} +(0.910082 - 0.405195i) q^{76} +(3.69064 + 4.09887i) q^{77} +(0.362018 + 0.161181i) q^{78} +(11.1304 - 4.95556i) q^{79} +(2.44756 - 2.71830i) q^{80} +(1.67126 - 5.14362i) q^{81} +(1.24743 - 2.16062i) q^{82} +(-3.27266 - 0.695625i) q^{83} +(-0.958189 + 0.696165i) q^{84} +(-3.50253 + 10.7797i) q^{85} +(-10.1398 + 2.15529i) q^{86} +(-1.91943 + 2.13174i) q^{87} +(-2.43738 - 1.77086i) q^{88} +(-5.52523 - 17.0049i) q^{89} +(4.72127 + 8.17748i) q^{90} +(-1.09689 + 0.233151i) q^{91} +(-3.53027 + 0.750382i) q^{92} +(-3.09684 - 5.36389i) q^{93} +(0.396720 + 1.22098i) q^{94} +(-2.94803 - 2.14187i) q^{95} +(0.432891 - 0.480774i) q^{96} +(-2.05197 + 0.436160i) q^{97} +(-1.12742 + 3.46984i) q^{98} +(6.29200 - 4.57140i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 12 q^{5} - q^{6} - 4 q^{7} - 6 q^{8} - 19 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 12 * q^5 - q^6 - 4 * q^7 - 6 * q^8 - 19 * q^9	\( 24 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 12 q^{5} - q^{6} - 4 q^{7} - 6 q^{8} - 19 q^{9} - 12 q^{10} + 6 q^{11} - q^{12} + 5 q^{13} - 4 q^{14} - 9 q^{15} + 3 q^{16} + 16 q^{17} + 17 q^{18} - 2 q^{19} - q^{20} + 10 q^{21} + 7 q^{22} + q^{23} - 3 q^{24} + 11 q^{25} - 9 q^{27} - 7 q^{28} + 2 q^{29} - 4 q^{30} + 14 q^{31} - 12 q^{32} + 7 q^{33} - 17 q^{34} + 9 q^{35} + 2 q^{36} - 38 q^{37} + 4 q^{38} - 40 q^{39} - 7 q^{40} - 10 q^{41} + 15 q^{42} - 5 q^{43} + 2 q^{44} - 96 q^{45} - 8 q^{46} + 3 q^{47} - q^{48} + 19 q^{49} + 38 q^{50} + 102 q^{51} + 20 q^{52} - 37 q^{53} + 17 q^{54} + 33 q^{55} + 6 q^{56} - 71 q^{57} + q^{58} - 17 q^{59} - 22 q^{60} + 70 q^{61} + 72 q^{62} + 146 q^{63} - 6 q^{64} + 2 q^{65} - 86 q^{66} - 4 q^{67} + q^{68} - 2 q^{69} - 28 q^{70} - 76 q^{71} + 46 q^{72} + 84 q^{73} + 19 q^{74} + 9 q^{75} - 2 q^{76} - 10 q^{77} - 5 q^{78} - 56 q^{79} - 7 q^{80} + 59 q^{81} - 20 q^{82} - 9 q^{83} + 25 q^{84} - 37 q^{85} - 65 q^{86} - 25 q^{87} - 4 q^{88} - 45 q^{89} - 31 q^{90} + 2 q^{91} + 7 q^{92} - 47 q^{93} + 24 q^{94} - 39 q^{95} + 9 q^{96} + 6 q^{97} + 7 q^{98} - 24 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 12 * q^5 - q^6 - 4 * q^7 - 6 * q^8 - 19 * q^9 - 12 * q^10 + 6 * q^11 - q^12 + 5 * q^13 - 4 * q^14 - 9 * q^15 + 3 * q^16 + 16 * q^17 + 17 * q^18 - 2 * q^19 - q^20 + 10 * q^21 + 7 * q^22 + q^23 - 3 * q^24 + 11 * q^25 - 9 * q^27 - 7 * q^28 + 2 * q^29 - 4 * q^30 + 14 * q^31 - 12 * q^32 + 7 * q^33 - 17 * q^34 + 9 * q^35 + 2 * q^36 - 38 * q^37 + 4 * q^38 - 40 * q^39 - 7 * q^40 - 10 * q^41 + 15 * q^42 - 5 * q^43 + 2 * q^44 - 96 * q^45 - 8 * q^46 + 3 * q^47 - q^48 + 19 * q^49 + 38 * q^50 + 102 * q^51 + 20 * q^52 - 37 * q^53 + 17 * q^54 + 33 * q^55 + 6 * q^56 - 71 * q^57 + q^58 - 17 * q^59 - 22 * q^60 + 70 * q^61 + 72 * q^62 + 146 * q^63 - 6 * q^64 + 2 * q^65 - 86 * q^66 - 4 * q^67 + q^68 - 2 * q^69 - 28 * q^70 - 76 * q^71 + 46 * q^72 + 84 * q^73 + 19 * q^74 + 9 * q^75 - 2 * q^76 - 10 * q^77 - 5 * q^78 - 56 * q^79 - 7 * q^80 + 59 * q^81 - 20 * q^82 - 9 * q^83 + 25 * q^84 - 37 * q^85 - 65 * q^86 - 25 * q^87 - 4 * q^88 - 45 * q^89 - 31 * q^90 + 2 * q^91 + 7 * q^92 - 47 * q^93 + 24 * q^94 - 39 * q^95 + 9 * q^96 + 6 * q^97 + 7 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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