LMFDB - Embedded newform 288.2.bf.a.11.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(11,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 15, 4]))

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

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

chi := DirichletCharacter("288.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bf (of order $24$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			11.17
Character	$\chi$	$=$	288.11
Dual form			288.2.bf.a.131.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.564220 + 1.29679i) q^{2} +(0.888753 - 1.48665i) q^{3} +(-1.36331 - 1.46335i) q^{4} +(0.132037 + 1.00292i) q^{5} +(1.42641 + 1.99132i) q^{6} +(1.09866 + 4.10026i) q^{7} +(2.66685 - 0.942277i) q^{8} +(-1.42024 - 2.64252i) q^{9} +O(q^{10})$	\(q+(-0.564220 + 1.29679i) q^{2} +(0.888753 - 1.48665i) q^{3} +(-1.36331 - 1.46335i) q^{4} +(0.132037 + 1.00292i) q^{5} +(1.42641 + 1.99132i) q^{6} +(1.09866 + 4.10026i) q^{7} +(2.66685 - 0.942277i) q^{8} +(-1.42024 - 2.64252i) q^{9} +(-1.37507 - 0.394642i) q^{10} +(3.30700 - 2.53755i) q^{11} +(-3.38712 + 0.726212i) q^{12} +(-1.16321 + 1.51592i) q^{13} +(-5.93704 - 0.888717i) q^{14} +(1.60833 + 0.695053i) q^{15} +(-0.282759 + 3.98999i) q^{16} +7.82699 q^{17} +(4.22811 - 0.350783i) q^{18} +(-3.14843 + 1.30412i) q^{19} +(1.28761 - 1.56050i) q^{20} +(7.07207 + 2.01079i) q^{21} +(1.42479 + 5.72022i) q^{22} +(4.93477 + 1.32227i) q^{23} +(0.969340 - 4.80212i) q^{24} +(3.84122 - 1.02925i) q^{25} +(-1.30952 - 2.36375i) q^{26} +(-5.19074 - 0.237156i) q^{27} +(4.50227 - 7.19765i) q^{28} +(-2.14969 - 0.283012i) q^{29} +(-1.80879 + 1.69350i) q^{30} +(-7.00638 + 4.04514i) q^{31} +(-5.01463 - 2.61791i) q^{32} +(-0.833338 - 7.17160i) q^{33} +(-4.41614 + 10.1499i) q^{34} +(-3.96715 + 1.64325i) q^{35} +(-1.93069 + 5.68088i) q^{36} +(2.15743 - 5.20851i) q^{37} +(0.0852374 - 4.81866i) q^{38} +(1.21984 + 3.07656i) q^{39} +(1.29715 + 2.55022i) q^{40} +(-0.431132 + 1.60901i) q^{41} +(-6.59777 + 8.03644i) q^{42} +(-1.18374 - 1.54268i) q^{43} +(-8.22180 - 1.37981i) q^{44} +(2.46271 - 1.77329i) q^{45} +(-4.49900 + 5.65330i) q^{46} +(-10.0917 - 5.82647i) q^{47} +(5.68041 + 3.96648i) q^{48} +(-9.54287 + 5.50958i) q^{49} +(-0.832572 + 5.56197i) q^{50} +(6.95626 - 11.6360i) q^{51} +(3.80414 - 0.364501i) q^{52} +(-0.317971 + 0.767651i) q^{53} +(3.23626 - 6.59747i) q^{54} +(2.98160 + 2.98160i) q^{55} +(6.79355 + 9.89954i) q^{56} +(-0.859407 + 5.83965i) q^{57} +(1.57990 - 2.62800i) q^{58} +(-9.53072 + 1.25474i) q^{59} +(-1.17555 - 3.30112i) q^{60} +(1.21590 - 9.23569i) q^{61} +(-1.29254 - 11.3681i) q^{62} +(9.27466 - 8.72657i) q^{63} +(6.22423 - 5.02583i) q^{64} +(-1.67393 - 0.966444i) q^{65} +(9.77023 + 2.96570i) q^{66} +(0.673229 - 0.877369i) q^{67} +(-10.6706 - 11.4536i) q^{68} +(6.35154 - 6.16109i) q^{69} +(0.107403 - 6.07171i) q^{70} +(-0.0648614 - 0.0648614i) q^{71} +(-6.27756 - 5.70896i) q^{72} +(-1.09749 + 1.09749i) q^{73} +(5.53706 + 5.73647i) q^{74} +(1.88376 - 6.62529i) q^{75} +(6.20068 + 2.82932i) q^{76} +(14.0379 + 10.7717i) q^{77} +(-4.67790 - 0.153987i) q^{78} +(-0.495123 + 0.857578i) q^{79} +(-4.03897 + 0.243241i) q^{80} +(-4.96585 + 7.50602i) q^{81} +(-1.84329 - 1.46692i) q^{82} +(-7.26949 - 0.957047i) q^{83} +(-6.69896 - 13.0902i) q^{84} +(1.03345 + 7.84982i) q^{85} +(2.66841 - 0.664647i) q^{86} +(-2.33128 + 2.94430i) q^{87} +(6.42822 - 9.88340i) q^{88} +(6.44315 - 6.44315i) q^{89} +(0.910071 + 4.19413i) q^{90} +(-7.49364 - 3.10397i) q^{91} +(-4.79270 - 9.02394i) q^{92} +(-0.213250 + 14.0111i) q^{93} +(13.2496 - 9.79942i) q^{94} +(-1.72364 - 2.98543i) q^{95} +(-8.34868 + 5.12831i) q^{96} +(-7.74227 + 13.4100i) q^{97} +(-1.76047 - 15.4837i) q^{98} +(-11.4023 - 5.13490i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.564220	+	1.29679i	−0.398964	+	0.916967i
$2$	−0.564220	+	1.29679i	−0.398964	+	0.916967i
$3$	0.888753	−	1.48665i	0.513122	−	0.858316i
$3$	0.888753	−	1.48665i	0.513122	−	0.858316i
$4$	−1.36331	−	1.46335i	−0.681656	−	0.731673i
$5$	0.132037	+	1.00292i	0.0590485	+	0.448518i	0.995273	+	0.0971158i	$0.0309617\pi$
$5$	0.132037	+	1.00292i	0.0590485	+	0.448518i	−0.936225	+	0.351402i	$0.885705\pi$
$6$	1.42641	+	1.99132i	0.582330	+	0.812952i
$7$	1.09866	+	4.10026i	0.415255	+	1.54975i	0.784325	+	0.620350i	$0.213009\pi$
$7$	1.09866	+	4.10026i	0.415255	+	1.54975i	−0.369071	+	0.929401i	$0.620324\pi$
$8$	2.66685	−	0.942277i	0.942875	−	0.333145i
$9$	−1.42024	−	2.64252i	−0.473413	−	0.880841i
$10$	−1.37507	−	0.394642i	−0.434834	−	0.124797i
$11$	3.30700	−	2.53755i	0.997099	−	0.765101i	0.0250038	−	0.999687i	$-0.492040\pi$
$11$	3.30700	−	2.53755i	0.997099	−	0.765101i	0.972095	+	0.234586i	$0.0753735\pi$
$12$	−3.38712	+	0.726212i	−0.977779	+	0.209639i
$13$	−1.16321	+	1.51592i	−0.322616	+	0.420441i	−0.926303	−	0.376780i	$-0.877031\pi$
$13$	−1.16321	+	1.51592i	−0.322616	+	0.420441i	0.603687	+	0.797222i	$0.293698\pi$
$14$	−5.93704	−	0.888717i	−1.58674	−	0.237520i
$15$	1.60833	+	0.695053i	0.415269	+	0.179462i
$16$	−0.282759	+	3.98999i	−0.0706897	+	0.997498i
$17$	7.82699			1.89832			0.949162	−	0.314787i	$-0.101933\pi$
$17$	7.82699			1.89832			0.949162	+	0.314787i	$0.101933\pi$
$18$	4.22811	−	0.350783i	0.996576	−	0.0826803i
$19$	−3.14843	+	1.30412i	−0.722300	+	0.299187i	−0.713384	−	0.700774i	$-0.752838\pi$
$19$	−3.14843	+	1.30412i	−0.722300	+	0.299187i	−0.00891658	+	0.999960i	$0.502838\pi$
$20$	1.28761	−	1.56050i	0.287918	−	0.348939i
$21$	7.07207	+	2.01079i	1.54325	+	0.438791i
$22$	1.42479	+	5.72022i	0.303766	+	1.21955i
$23$	4.93477	+	1.32227i	1.02897	+	0.275712i	0.733536	−	0.679651i	$-0.237869\pi$
$23$	4.93477	+	1.32227i	1.02897	+	0.275712i	0.295435	+	0.955363i	$0.404535\pi$
$24$	0.969340	−	4.80212i	0.197866	−	0.980229i
$25$	3.84122	−	1.02925i	0.768244	−	0.205850i
$26$	−1.30952	−	2.36375i	−0.256819	−	0.463569i
$27$	−5.19074	−	0.237156i	−0.998958	−	0.0456407i
$28$	4.50227	−	7.19765i	0.850850	−	1.36023i
$29$	−2.14969	−	0.283012i	−0.399187	−	0.0525539i	−0.0717395	−	0.997423i	$-0.522855\pi$
$29$	−2.14969	−	0.283012i	−0.399187	−	0.0525539i	−0.327447	+	0.944869i	$0.606188\pi$
$30$	−1.80879	+	1.69350i	−0.330238	+	0.309189i
$31$	−7.00638	+	4.04514i	−1.25838	+	0.726528i	−0.972760	−	0.231814i	$-0.925534\pi$
$31$	−7.00638	+	4.04514i	−1.25838	+	0.726528i	−0.285624	+	0.958342i	$0.592201\pi$
$32$	−5.01463	−	2.61791i	−0.886470	−	0.462786i
$33$	−0.833338	−	7.17160i	−0.145065	−	1.24842i
$34$	−4.41614	+	10.1499i	−0.757362	+	1.74070i
$35$	−3.96715	+	1.64325i	−0.670571	+	0.277760i
$36$	−1.93069	+	5.68088i	−0.321782	+	0.946814i
$37$	2.15743	−	5.20851i	0.354680	−	0.856273i	−0.641349	−	0.767249i	$-0.721625\pi$
$37$	2.15743	−	5.20851i	0.354680	−	0.856273i	0.996029	−	0.0890244i	$-0.0283749\pi$
$38$	0.0852374	−	4.81866i	0.0138273	−	0.781690i
$39$	1.21984	+	3.07656i	0.195330	+	0.492644i
$40$	1.29715	+	2.55022i	0.205097	+	0.403225i
$41$	−0.431132	+	1.60901i	−0.0673315	+	0.251285i	−0.991385	−	0.130978i	$-0.958188\pi$
$41$	−0.431132	+	1.60901i	−0.0673315	+	0.251285i	0.924054	+	0.382263i	$0.124855\pi$
$42$	−6.59777	+	8.03644i	−1.01806	+	1.24005i
$43$	−1.18374	−	1.54268i	−0.180518	−	0.235256i	0.694325	−	0.719661i	$-0.255703\pi$
$43$	−1.18374	−	1.54268i	−0.180518	−	0.235256i	−0.874844	+	0.484405i	$0.839036\pi$
$44$	−8.22180	−	1.37981i	−1.23948	−	0.208014i
$45$	2.46271	−	1.77329i	0.367119	−	0.264346i
$46$	−4.49900	+	5.65330i	−0.663341	+	0.833533i
$47$	−10.0917	−	5.82647i	−1.47203	−	0.849877i	−0.472525	−	0.881317i	$-0.656657\pi$
$47$	−10.0917	−	5.82647i	−1.47203	−	0.849877i	−0.999506	+	0.0314397i	$0.989991\pi$
$48$	5.68041	+	3.96648i	0.819896	+	0.572512i
$49$	−9.54287	+	5.50958i	−1.36327	+	0.787083i
$50$	−0.832572	+	5.56197i	−0.117743	+	0.786581i
$51$	6.95626	−	11.6360i	0.974071	−	1.62936i
$52$	3.80414	−	0.364501i	0.527539	−	0.0505472i
$53$	−0.317971	+	0.767651i	−0.0436767	+	0.105445i	−0.944212	−	0.329337i	$-0.893175\pi$
$53$	−0.317971	+	0.767651i	−0.0436767	+	0.105445i	0.900536	+	0.434782i	$0.143175\pi$
$54$	3.23626	−	6.59747i	0.440399	−	0.897802i
$55$	2.98160	+	2.98160i	0.402039	+	0.402039i
$56$	6.79355	+	9.89954i	0.907826	+	1.32288i
$57$	−0.859407	+	5.83965i	−0.113831	+	0.773481i
$58$	1.57990	−	2.62800i	0.207451	−	0.345074i
$59$	−9.53072	+	1.25474i	−1.24079	+	0.163354i	−0.722211	−	0.691673i	$-0.756874\pi$
$59$	−9.53072	+	1.25474i	−1.24079	+	0.163354i	−0.518584	+	0.855027i	$0.673541\pi$
$60$	−1.17555	−	3.30112i	−0.151763	−	0.426173i
$61$	1.21590	−	9.23569i	0.155680	−	1.18251i	−0.718012	−	0.696031i	$-0.754948\pi$
$61$	1.21590	−	9.23569i	0.155680	−	1.18251i	0.873692	−	0.486479i	$-0.161719\pi$
$62$	−1.29254	−	11.3681i	−0.164153	−	1.44375i
$63$	9.27466	−	8.72657i	1.16850	−	1.09945i
$64$	6.22423	−	5.02583i	0.778028	−	0.628229i
$65$	−1.67393	−	0.966444i	−0.207626	−	0.119873i
$66$	9.77023	+	2.96570i	1.20263	+	0.365052i
$67$	0.673229	−	0.877369i	0.0822480	−	0.107188i	−0.750417	−	0.660965i	$-0.770147\pi$
$67$	0.673229	−	0.877369i	0.0822480	−	0.107188i	0.832665	+	0.553777i	$0.186814\pi$
$68$	−10.6706	−	11.4536i	−1.29400	−	1.38895i
$69$	6.35154	−	6.16109i	0.764635	−	0.741709i
$70$	0.107403	−	6.07171i	0.0128371	−	0.725708i
$71$	−0.0648614	−	0.0648614i	−0.00769763	−	0.00769763i	0.703247	−	0.710945i	$-0.251733\pi$
$71$	−0.0648614	−	0.0648614i	−0.00769763	−	0.00769763i	−0.710945	+	0.703247i	$0.751733\pi$
$72$	−6.27756	−	5.70896i	−0.739817	−	0.672808i
$73$	−1.09749	+	1.09749i	−0.128451	+	0.128451i	−0.768410	−	0.639958i	$-0.778952\pi$
$73$	−1.09749	+	1.09749i	−0.128451	+	0.128451i	0.639958	+	0.768410i	$0.278952\pi$
$74$	5.53706	+	5.73647i	0.643670	+	0.666852i
$75$	1.88376	−	6.62529i	0.217518	−	0.765022i
$76$	6.20068	+	2.82932i	0.711267	+	0.324545i
$77$	14.0379	+	10.7717i	1.59977	+	1.22754i
$78$	−4.67790	−	0.153987i	−0.529668	−	0.0174356i
$79$	−0.495123	+	0.857578i	−0.0557057	+	0.0964851i	−0.892534	−	0.450981i	$-0.851074\pi$
$79$	−0.495123	+	0.857578i	−0.0557057	+	0.0964851i	0.836828	+	0.547466i	$0.184408\pi$
$80$	−4.03897	+	0.243241i	−0.451570	+	0.0271952i
$81$	−4.96585	+	7.50602i	−0.551761	+	0.834002i
$82$	−1.84329	−	1.46692i	−0.203557	−	0.161994i
$83$	−7.26949	−	0.957047i	−0.797931	−	0.105050i	−0.279474	−	0.960153i	$-0.590160\pi$
$83$	−7.26949	−	0.957047i	−0.797931	−	0.105050i	−0.518457	+	0.855104i	$0.673493\pi$
$84$	−6.69896	−	13.0902i	−0.730916	−	1.42826i
$85$	1.03345	+	7.84982i	0.112093	+	0.851433i
$86$	2.66841	−	0.664647i	0.287742	−	0.0716708i
$87$	−2.33128	+	2.94430i	−0.249939	+	0.315662i
$88$	6.42822	−	9.88340i	0.685250	−	1.05357i
$89$	6.44315	−	6.44315i	0.682973	−	0.682973i	−0.277696	−	0.960669i	$-0.589571\pi$
$89$	6.44315	−	6.44315i	0.682973	−	0.682973i	0.960669	+	0.277696i	$0.0895709\pi$
$90$	0.910071	+	4.19413i	0.0959300	+	0.442100i
$91$	−7.49364	−	3.10397i	−0.785547	−	0.325384i
$92$	−4.79270	−	9.02394i	−0.499674	−	0.940811i
$93$	−0.213250	+	14.0111i	−0.0221130	+	1.45289i
$94$	13.2496	−	9.79942i	1.36660	−	1.01073i
$95$	−1.72364	−	2.98543i	−0.176841	−	0.306298i
$96$	−8.34868	+	5.12831i	−0.852083	+	0.523406i
$97$	−7.74227	+	13.4100i	−0.786109	+	1.36158i	0.142226	+	0.989834i	$0.454574\pi$
$97$	−7.74227	+	13.4100i	−0.786109	+	1.36158i	−0.928335	+	0.371746i	$0.878759\pi$
$98$	−1.76047	−	15.4837i	−0.177835	−	1.56409i
$99$	−11.4023	−	5.13490i	−1.14597	−	0.516077i
$100$	−6.74293	−	4.21784i	−0.674293	−	0.421784i
$101$	7.63399	−	5.85777i	0.759611	−	0.582870i	−0.154663	−	0.987967i	$-0.549429\pi$
$101$	7.63399	−	5.85777i	0.759611	−	0.582870i	0.914273	+	0.405097i	$0.132762\pi$
$102$	11.1645	+	15.5860i	1.10545	+	1.54325i
$103$	−5.45586	−	1.46189i	−0.537582	−	0.144045i	−0.0201946	−	0.999796i	$-0.506429\pi$
$103$	−5.45586	−	1.46189i	−0.537582	−	0.144045i	−0.517387	+	0.855752i	$0.673095\pi$
$104$	−1.67369	+	5.13881i	−0.164119	+	0.503902i
$105$	−1.08289	+	7.35820i	−0.105679	+	0.718087i
$106$	−0.816074	−	0.845465i	−0.0792641	−	0.0821188i
$107$	3.76685	+	1.56028i	0.364155	+	0.150838i	0.557256	−	0.830341i	$-0.311854\pi$
$107$	3.76685	+	1.56028i	0.364155	+	0.150838i	−0.193100	+	0.981179i	$0.561854\pi$
$108$	6.72956	+	7.91916i	0.647552	+	0.762021i
$109$	−3.71905	−	8.97858i	−0.356220	−	0.859992i	−0.995825	−	0.0912874i	$-0.970902\pi$
$109$	−3.71905	−	8.97858i	−0.356220	−	0.859992i	0.639604	−	0.768704i	$-0.279098\pi$
$110$	−5.54878	+	2.18422i	−0.529055	+	0.208257i
$111$	−5.82579	−	7.83642i	−0.552959	−	0.743800i
$112$	−16.6707	+	3.22426i	−1.57523	+	0.304664i
$113$	−5.47869	−	9.48938i	−0.515392	−	0.892685i	−0.999840	−	0.0178655i	$-0.994313\pi$
$113$	−5.47869	−	9.48938i	−0.515392	−	0.892685i	0.484448	−	0.874820i	$-0.339020\pi$
$114$	−7.08789	−	4.40931i	−0.663842	−	0.412970i
$115$	−0.674555	+	5.12375i	−0.0629026	+	0.477792i
$116$	2.51655	+	3.53157i	0.233656	+	0.327898i
$117$	5.65789	+	0.920833i	0.523072	+	0.0851311i
$118$	3.75029	−	13.0673i	0.345242	−	1.20294i
$119$	8.59921	+	32.0927i	0.788288	+	2.94193i
$120$	4.94412	+	0.338112i	0.451334	+	0.0308653i
$121$	1.65009	−	6.15821i	0.150008	−	0.559837i
$122$	11.2907	+	6.78773i	1.02221	+	0.614532i
$123$	2.00886	+	2.07095i	0.181132	+	0.186731i
$124$	15.4713	+	4.73797i	1.38937	+	0.425483i
$125$	3.47499	+	8.38937i	0.310813	+	0.750368i
$126$	6.08356	+	16.9510i	0.541967	+	1.51011i
$127$			2.72724i			0.242003i	0.992652	+	0.121002i	$0.0386107\pi$
$127$			2.72724i			0.242003i	−0.992652	+	0.121002i	$0.961389\pi$
$128$	3.00560	+	10.9072i	0.265660	+	0.964067i
$129$	−3.34547	+	0.388742i	−0.294552	+	0.0342268i
$130$	2.19774	−	1.62544i	0.192754	−	0.142561i
$131$	−1.88148	−	1.44371i	−0.164386	−	0.126138i	0.523293	−	0.852153i	$-0.324703\pi$
$131$	−1.88148	−	1.44371i	−0.164386	−	0.126138i	−0.687679	+	0.726015i	$0.741370\pi$
$132$	−9.35843	+	10.9966i	−0.814547	+	0.957131i
$133$	−8.80630	−	11.4766i	−0.763603	−	0.995147i
$134$	0.757911	+	1.36806i	0.0654736	+	0.118183i
$135$	−0.447519	−	5.23719i	−0.0385163	−	0.450746i
$136$	20.8735	−	7.37520i	1.78988	−	0.632418i
$137$	4.89648	−	1.31201i	0.418334	−	0.112092i	−0.0435108	−	0.999053i	$-0.513854\pi$
$137$	4.89648	−	1.31201i	0.418334	−	0.112092i	0.461845	+	0.886961i	$0.347188\pi$
$138$	4.40596	+	11.7128i	0.375061	+	0.997060i
$139$	14.8882	−	1.96007i	1.26280	−	0.166251i	0.530768	−	0.847517i	$-0.321903\pi$
$139$	14.8882	−	1.96007i	1.26280	−	0.166251i	0.732036	+	0.681266i	$0.238570\pi$
$140$	7.81311	+	3.56505i	0.660328	+	0.301302i
$141$	−17.6310	+	9.82456i	−1.48479	+	0.827377i
$142$	0.120707	−	0.0475153i	0.0101295	−	0.00398740i
$143$			7.96487i			0.666056i
$144$	10.9452	−	4.91954i	0.912103	−	0.409962i
$145$		−	2.19332i		−	0.182146i
$146$	−0.803983	−	2.04243i	−0.0665381	−	0.169033i
$147$	−0.290452	+	19.0835i	−0.0239561	+	1.57398i
$148$	−10.5631	+	3.94375i	−0.868282	+	0.324174i
$149$	3.73629	−	0.491891i	0.306089	−	0.0402973i	0.0240826	−	0.999710i	$-0.492334\pi$
$149$	3.73629	−	0.491891i	0.306089	−	0.0402973i	0.282006	+	0.959413i	$0.409000\pi$
$150$	7.52873	+	6.18095i	0.614718	+	0.504673i
$151$	−4.61351	+	1.23619i	−0.375442	+	0.100599i	−0.441605	−	0.897209i	$-0.645591\pi$
$151$	−4.61351	+	1.23619i	−0.375442	+	0.100599i	0.0661634	+	0.997809i	$0.478924\pi$
$152$	−7.16757	+	6.44461i	−0.581367	+	0.522727i
$153$	−11.1162	−	20.6830i	−0.898691	−	1.67212i
$154$	−21.8890	+	12.1266i	−1.76387	+	0.977187i
$155$	−4.98204	−	6.49271i	−0.400167	−	0.521507i
$156$	2.83905	−	5.97936i	0.227306	−	0.478732i
$157$	−16.0990	−	12.3532i	−1.28484	−	0.985892i	−0.999624	−	0.0274282i	$-0.991268\pi$
$157$	−16.0990	−	12.3532i	−1.28484	−	0.985892i	−0.285215	−	0.958463i	$-0.592065\pi$
$158$	−0.832738	−	1.12593i	−0.0662491	−	0.0895743i
$159$	0.858628	+	1.15496i	0.0680936	+	0.0915945i
$160$	1.96343	−	5.37492i	0.155223	−	0.424925i
$161$			21.6866i			1.70914i
$162$	−6.93188	−	10.6747i	−0.544620	−	0.838683i
$163$	8.62616	+	20.8254i	0.675653	+	1.63117i	0.771847	+	0.635808i	$0.219333\pi$
$163$	8.62616	+	20.8254i	0.675653	+	1.63117i	−0.0961944	+	0.995363i	$0.530667\pi$
$164$	2.94230	−	1.56268i	0.229755	−	0.122025i
$165$	7.08249	−	1.78268i	0.551371	−	0.138782i
$166$	5.34268	−	8.88700i	0.414672	−	0.689765i
$167$	0.494282	−	1.84468i	0.0382487	−	0.142746i	−0.944161	−	0.329485i	$-0.893125\pi$
$167$	0.494282	−	1.84468i	0.0382487	−	0.142746i	0.982410	+	0.186739i	$0.0597917\pi$
$168$	20.7549	−	1.30136i	1.60128	−	0.100402i
$169$	2.41968	+	9.03037i	0.186129	+	0.694644i
$170$	−10.7626	−	3.08886i	−0.825457	−	0.236905i
$171$	7.91770	+	6.46764i	0.605482	+	0.494593i
$172$	−0.643666	+	3.83537i	−0.0490790	+	0.292444i
$173$	1.29330	−	9.82356i	0.0983275	−	0.746872i	−0.869264	−	0.494349i	$-0.835406\pi$
$173$	1.29330	−	9.82356i	0.0983275	−	0.746872i	0.967591	−	0.252523i	$-0.0812602\pi$
$174$	−2.50277	−	4.68440i	−0.189735	−	0.355124i
$175$	8.44039	+	14.6192i	0.638034	+	1.10511i
$176$	9.18974	+	13.9124i	0.692702	+	1.04869i
$177$	−6.60509	+	15.2840i	−0.496469	+	1.14881i
$178$	4.72004	+	11.9907i	0.353782	+	0.898744i
$179$	−3.29857	−	7.96346i	−0.246547	−	0.595217i	0.751359	−	0.659893i	$-0.229399\pi$
$179$	−3.29857	−	7.96346i	−0.246547	−	0.595217i	−0.997906	+	0.0646763i	$0.979399\pi$
$180$	−5.95237	−	1.18624i	−0.443664	−	0.0884173i
$181$	13.4290	+	5.56248i	0.998171	+	0.413456i	0.821126	−	0.570747i	$-0.193346\pi$
$181$	13.4290	+	5.56248i	0.998171	+	0.413456i	0.177045	+	0.984203i	$0.443346\pi$
$182$	8.25325	−	7.96634i	0.611771	−	0.590504i
$183$	−12.6496	−	10.0159i	−0.935084	−	0.740394i
$184$	14.4063	−	1.12363i	1.06204	−	0.0828349i
$185$	5.50856	+	1.47601i	0.404997	+	0.108519i
$186$	−18.0491	−	8.18190i	−1.32343	−	0.599926i
$187$	25.8839	−	19.8614i	1.89282	−	1.45241i
$188$	5.23206	+	22.7110i	0.381587	+	1.65637i
$189$	−4.73046	−	21.5439i	−0.344090	−	1.56709i
$190$	4.84397	−	0.550753i	0.351418	−	0.0399558i
$191$	−4.14354	+	7.17682i	−0.299816	+	0.519297i	−0.976094	−	0.217350i	$-0.930259\pi$
$191$	−4.14354	+	7.17682i	−0.299816	+	0.519297i	0.676278	+	0.736647i	$0.263592\pi$
$192$	−1.93984	−	13.7199i	−0.139996	−	0.990152i
$193$	−2.50096	−	4.33178i	−0.180023	−	0.311809i	0.761865	−	0.647736i	$-0.224284\pi$
$193$	−2.50096	−	4.33178i	−0.180023	−	0.311809i	−0.941888	+	0.335927i	$0.890950\pi$
$194$	−13.0216	−	17.6063i	−0.934895	−	1.26406i
$195$	−2.92447	+	1.62961i	−0.209426	+	0.116699i
$196$	21.0723	+	6.45324i	1.50517	+	0.460946i
$197$	0.250884	+	0.103920i	0.0178748	+	0.00740397i	0.391603	−	0.920134i	$-0.371921\pi$
$197$	0.250884	+	0.103920i	0.0178748	+	0.00740397i	−0.373728	+	0.927538i	$0.621921\pi$
$198$	13.0923	−	11.8891i	0.930426	−	0.844922i
$199$	−6.23316	+	6.23316i	−0.441857	+	0.441857i	−0.892636	−	0.450779i	$-0.851146\pi$
$199$	−6.23316	+	6.23316i	−0.441857	+	0.441857i	0.450779	+	0.892636i	$0.351146\pi$
$200$	9.27414	−	6.36436i	0.655780	−	0.450028i
$201$	−0.706004	−	1.78062i	−0.0497977	−	0.125595i
$202$	3.28903	+	13.2047i	0.231415	+	0.929082i
$203$	−1.20136	−	9.12520i	−0.0843186	−	0.640463i
$204$	−26.5110	+	5.68406i	−1.85614	+	0.397964i
$205$	−1.67063	−	0.219942i	−0.116682	−	0.0153614i
$206$	4.97407	−	6.25026i	0.346560	−	0.435476i
$207$	−3.51443	−	14.9182i	−0.244270	−	1.03689i
$208$	−5.71961	−	5.06983i	−0.396584	−	0.351530i
$209$	−7.10260	+	12.3021i	−0.491297	+	0.850951i
$210$	−8.93103	−	5.55591i	−0.616299	−	0.383394i
$211$	−15.9397	−	12.2310i	−1.09733	−	0.842014i	−0.108959	−	0.994046i	$-0.534752\pi$
$211$	−15.9397	−	12.2310i	−1.09733	−	0.842014i	−0.988376	+	0.152032i	$0.951418\pi$
$212$	1.55683	−	0.581246i	0.106924	−	0.0399201i
$213$	−0.154072	+	0.0387803i	−0.0105568	+	0.00265718i
$214$	−4.14869	+	4.00446i	−0.283598	+	0.273740i
$215$	1.39088	−	1.39088i	0.0948573	−	0.0948573i
$216$	−14.0664	+	4.25865i	−0.957098	+	0.289765i
$217$	−24.2837	−	24.2837i	−1.64849	−	1.64849i
$218$	13.7417	+	0.243077i	0.930703	+	0.0164632i
$219$	0.656181	+	2.60697i	0.0443406	+	0.176163i
$220$	0.298258	−	8.42796i	0.0201086	−	0.568213i
$221$	−9.10443	+	11.8651i	−0.612430	+	0.798134i
$222$	13.4492	−	3.13334i	0.902650	−	0.210296i
$223$	7.37362	+	4.25716i	0.493774	+	0.285081i	0.726139	−	0.687548i	$-0.241313\pi$
$223$	7.37362	+	4.25716i	0.493774	+	0.285081i	−0.232365	+	0.972629i	$0.574646\pi$
$224$	5.22473	−	23.4375i	0.349092	−	1.56598i
$225$	−8.17527	−	8.68873i	−0.545018	−	0.579249i
$226$	15.3969	−	1.75061i	1.02419	−	0.116449i
$227$	1.93758	−	14.7174i	0.128602	−	0.976826i	−0.798495	−	0.602002i	$-0.794370\pi$
$227$	1.93758	−	14.7174i	0.128602	−	0.976826i	0.927096	−	0.374824i	$-0.122297\pi$
$228$	9.71707	−	6.70366i	0.643529	−	0.443961i
$229$	−2.28312	+	0.300578i	−0.150873	+	0.0198627i	−0.205584	−	0.978639i	$-0.565909\pi$
$229$	−2.28312	+	0.300578i	−0.150873	+	0.0198627i	0.0547116	+	0.998502i	$0.482576\pi$
$230$	−6.26382	−	3.76568i	−0.413024	−	0.248301i
$231$	28.4899	−	11.2961i	1.87450	−	0.743226i
$232$	−5.99958	+	1.27085i	−0.393892	+	0.0834354i
$233$	1.12094	+	1.12094i	0.0734350	+	0.0734350i	0.742870	−	0.669435i	$-0.233464\pi$
$233$	1.12094	+	1.12094i	0.0734350	+	0.0734350i	−0.669435	+	0.742870i	$0.733464\pi$
$234$	−4.38642	+	6.81753i	−0.286749	+	0.445676i
$235$	4.51098	−	10.8905i	0.294264	−	0.710416i
$236$	14.8295	+	12.2361i	0.965317	+	0.796504i
$237$	0.834874	+	1.49825i	0.0542309	+	0.0973216i
$238$	−46.4692	−	6.95598i	−3.01215	−	0.450889i
$239$	13.9672	−	8.06399i	0.903465	−	0.521616i	0.0251425	−	0.999684i	$-0.491996\pi$
$239$	13.9672	−	8.06399i	0.903465	−	0.521616i	0.878323	+	0.478068i	$0.158663\pi$
$240$	−3.22803	+	6.22070i	−0.208368	+	0.401544i
$241$	2.34561	+	1.35424i	0.151094	+	0.0872341i	0.573641	−	0.819107i	$-0.305531\pi$
$241$	2.34561	+	1.35424i	0.151094	+	0.0872341i	−0.422547	+	0.906341i	$0.638864\pi$
$242$	7.05488	+	5.61440i	0.453505	+	0.360907i
$243$	6.74539	+	14.0535i	0.432717	+	0.901530i
$244$	−15.1727	+	10.8119i	−0.971330	+	0.692158i
$245$	−6.78566	−	8.84324i	−0.433520	−	0.564974i
$246$	−3.81902	+	1.43659i	−0.243492	+	0.0915934i
$247$	1.68533	−	6.28975i	0.107235	−	0.400207i
$248$	−14.8734	+	17.3898i	−0.944460	+	1.10425i
$249$	−7.88357	+	9.95659i	−0.499601	+	0.630973i
$250$	−12.8399	−	0.227125i	−0.812066	−	0.0143647i
$251$	−3.22989	+	7.79764i	−0.203869	+	0.492183i	−0.992436	−	0.122766i	$-0.960823\pi$
$251$	−3.22989	+	7.79764i	−0.203869	+	0.492183i	0.788567	+	0.614949i	$0.210823\pi$
$252$	−25.4143	−	1.67498i	−1.60095	−	0.105514i
$253$	19.6746	−	8.14950i	1.23693	−	0.512355i
$254$	−3.53665	−	1.53876i	−0.221909	−	0.0965506i
$255$	12.5884	+	5.44018i	0.788316	+	0.340677i
$256$	−15.8401	−	2.25641i	−0.990006	−	0.141026i
$257$	8.27354	−	4.77673i	0.516090	−	0.297964i	−0.219244	−	0.975670i	$-0.570359\pi$
$257$	8.27354	−	4.77673i	0.516090	−	0.297964i	0.735333	+	0.677706i	$0.237026\pi$
$258$	1.38346	−	4.55770i	0.0861307	−	0.283750i
$259$	23.7265	+	3.12365i	1.47429	+	0.194094i
$260$	0.867849	+	3.76710i	0.0538217	+	0.233626i
$261$	2.30520	+	6.08254i	0.142688	+	0.376500i
$262$	2.93376	−	1.62531i	0.181248	−	0.100412i
$263$	1.92401	−	0.515536i	0.118639	−	0.0317893i	−0.199011	−	0.979997i	$-0.563773\pi$
$263$	1.92401	−	0.515536i	0.118639	−	0.0317893i	0.317650	+	0.948208i	$0.397106\pi$
$264$	−8.98003	−	18.3404i	−0.552683	−	1.12877i
$265$	−0.811874	−	0.217541i	−0.0498730	−	0.0133634i
$266$	19.8514	−	4.94458i	1.21717	−	0.303171i
$267$	−3.85232	−	15.3051i	−0.235758	−	0.936654i
$268$	−2.20171	+	0.210962i	−0.134491	+	0.0128865i
$269$	5.62252	−	2.32892i	0.342811	−	0.141997i	−0.204634	−	0.978839i	$-0.565601\pi$
$269$	5.62252	−	2.32892i	0.342811	−	0.141997i	0.547445	+	0.836842i	$0.315601\pi$
$270$	7.04402	+	2.37459i	0.428685	+	0.144513i
$271$	−26.4527			−1.60689			−0.803444	−	0.595381i	$-0.797001\pi$
$271$	−26.4527			−1.60689			−0.803444	+	0.595381i	$0.797001\pi$
$272$	−2.21315	+	31.2297i	−0.134192	+	1.89358i
$273$	−11.2745	+	8.38174i	−0.682364	+	0.507286i
$274$	−1.06129	+	7.08995i	−0.0641152	+	0.428319i
$275$	10.0911	−	13.1510i	0.608519	−	0.793038i
$276$	−17.6749	−	0.894996i	−1.06391	−	0.0538724i
$277$	−3.71550	+	2.85101i	−0.223243	+	0.171300i	−0.714327	−	0.699812i	$-0.753267\pi$
$277$	−3.71550	+	2.85101i	−0.223243	+	0.171300i	0.491085	+	0.871112i	$0.336601\pi$
$278$	−5.85844	+	20.4128i	−0.351366	+	1.22428i
$279$	20.6401	+	12.7695i	1.23569	+	0.764488i
$280$	−9.03142	+	8.12046i	−0.539731	+	0.485291i
$281$	−2.28217	−	8.51716i	−0.136143	−	0.508091i	−0.999991	−	0.00433862i	$-0.998619\pi$
$281$	−2.28217	−	8.51716i	−0.136143	−	0.508091i	0.863848	−	0.503753i	$-0.168048\pi$
$282$	−2.79263	−	28.4068i	−0.166299	−	1.69160i
$283$	3.12166	+	23.7114i	0.185563	+	1.40949i	0.790130	+	0.612940i	$0.210013\pi$
$283$	3.12166	+	23.7114i	0.185563	+	1.40949i	−0.604566	+	0.796555i	$0.706653\pi$
$284$	−0.00648827	+	0.183341i	−0.000385008	+	0.0108793i
$285$	−5.97016	−	0.0908660i	−0.353642	−	0.00538244i
$286$	−10.3287	−	4.49393i	−0.610751	−	0.265732i
$287$	−7.07101			−0.417388
$288$	0.204085	+	16.9693i	0.0120258	+	0.999928i
$289$	44.2618			2.60364
$290$	2.84427	+	1.23752i	0.167022	+	0.0726695i
$291$	13.0550	+	23.4282i	0.765297	+	1.37339i
$292$	3.10222	+	0.109785i	0.181544	+	0.00642467i
$293$	0.737720	+	5.60354i	0.0430981	+	0.327362i	0.999389	+	0.0349460i	$0.0111259\pi$
$293$	0.737720	+	5.60354i	0.0430981	+	0.327362i	−0.956291	+	0.292416i	$0.905541\pi$
$294$	−24.5834	−	11.1440i	−1.43373	−	0.649929i
$295$	−2.51681	−	9.39285i	−0.146534	−	0.546873i
$296$	0.845705	−	15.9232i	0.0491556	−	0.925519i
$297$	−17.7676	+	12.3875i	−1.03098	+	0.718795i
$298$	−1.47021	+	5.12270i	−0.0851669	+	0.296750i
$299$	−7.74463	+	5.94266i	−0.447883	+	0.343673i
$300$	−12.2632	+	6.27575i	−0.708018	+	0.362330i
$301$	5.02485	−	6.54851i	0.289628	−	0.377450i
$302$	0.999962	−	6.68022i	0.0575414	−	0.384403i
$303$	−1.92370	−	16.5552i	−0.110514	−	0.951069i
$304$	−4.31320	−	12.9310i	−0.247379	−	0.741643i
$305$	9.42318			0.539570
$306$	33.0934	−	2.74557i	1.89183	−	0.156954i
$307$	−10.0384	+	4.15804i	−0.572921	+	0.237312i	−0.650284	−	0.759691i	$-0.725350\pi$
$307$	−10.0384	+	4.15804i	−0.572921	+	0.237312i	0.0773627	+	0.997003i	$0.475350\pi$
$308$	−3.37538	−	35.2274i	−0.192330	−	2.00727i
$309$	−7.02223	+	6.81167i	−0.399480	+	0.387503i
$310$	11.2306	−	2.79732i	0.637857	−	0.158877i
$311$	25.0313	+	6.70712i	1.41940	+	0.380326i	0.885270	−	0.465078i	$-0.153974\pi$
$311$	25.0313	+	6.70712i	1.41940	+	0.380326i	0.534127	+	0.845404i	$0.320641\pi$
$312$	6.15210	+	7.05531i	0.348294	+	0.399429i
$313$	−13.1450	+	3.52220i	−0.743001	+	0.199087i	−0.610412	−	0.792084i	$-0.708996\pi$
$313$	−13.1450	+	3.52220i	−0.743001	+	0.199087i	−0.132590	+	0.991171i	$0.542329\pi$
$314$	25.1028	−	13.9070i	1.41663	−	0.784820i
$315$	9.97662	+	8.14949i	0.562119	+	0.459172i
$316$	1.92994	−	0.444611i	0.108568	−	0.0250113i
$317$	−22.1136	−	2.91131i	−1.24202	−	0.163516i	−0.519264	−	0.854614i	$-0.673794\pi$
$317$	−22.1136	−	2.91131i	−1.24202	−	0.163516i	−0.722761	+	0.691098i	$0.757127\pi$
$318$	−1.98220	+	0.461805i	−0.111156	+	0.0258967i
$319$	−7.82718	+	4.51902i	−0.438238	+	0.253017i
$320$	5.86232	+	5.57879i	0.327714	+	0.311864i
$321$	5.66739	−	4.21328i	0.316323	−	0.235162i
$322$	−28.1228	−	12.2360i	−1.56722	−	0.681884i
$323$	−24.6428	+	10.2074i	−1.37116	+	0.567953i
$324$	17.7539	−	2.96630i	0.986328	−	0.164794i
$325$	−2.90787	+	7.02023i	−0.161300	+	0.389412i
$326$	−31.8731	−	0.563805i	−1.76529	−	0.0312263i
$327$	−16.6533	−	2.45082i	−0.920929	−	0.135531i
$328$	0.366364	+	4.69723i	0.0202291	+	0.259361i
$329$	12.8026	−	47.7800i	0.705831	−	2.63420i
$330$	−1.68432	+	10.1903i	−0.0927189	+	0.560958i
$331$	6.98413	+	9.10189i	0.383882	+	0.500285i	0.944828	−	0.327567i	$-0.106229\pi$
$331$	6.98413	+	9.10189i	0.383882	+	0.500285i	−0.560945	+	0.827853i	$0.689562\pi$
$332$	8.51010	+	11.9425i	0.467052	+	0.655432i
$333$	−16.8277	+	1.69625i	−0.922150	+	0.0929540i
$334$	2.11328	+	1.68179i	0.115634	+	0.0920232i
$335$	0.968819	+	0.559348i	0.0529322	+	0.0305604i
$336$	−10.0227	+	27.6489i	−0.546785	+	1.50837i
$337$	28.3201	−	16.3506i	1.54269	−	0.890674i	0.544024	−	0.839069i	$-0.316900\pi$
$337$	28.3201	−	16.3506i	1.54269	−	0.890674i	0.998668	−	0.0516043i	$-0.0164335\pi$
$338$	−13.0757	−	1.95730i	−0.711224	−	0.106463i
$339$	−18.9766	−	0.288824i	−1.03066	−	0.0156868i
$340$	10.0781	−	12.2141i	0.546561	−	0.662400i
$341$	−12.9054	+	31.1564i	−0.698866	+	1.68721i
$342$	−12.8545	+	6.61840i	−0.695090	+	0.357882i
$343$	−12.0639	−	12.0639i	−0.651389	−	0.651389i
$344$	−4.61049	−	2.99869i	−0.248581	−	0.161678i
$345$	7.01770	+	5.55657i	0.377820	+	0.299156i
$346$	12.0094	+	7.21978i	0.645627	+	0.388138i
$347$	20.3101	−	2.67387i	1.09030	−	0.143541i	0.436128	−	0.899885i	$-0.356350\pi$
$347$	20.3101	−	2.67387i	1.09030	−	0.143541i	0.654174	+	0.756344i	$0.273016\pi$
$348$	7.48678	−	0.602533i	0.401334	−	0.0322992i
$349$	−2.87085	+	21.8063i	−0.153673	+	1.16726i	0.724622	+	0.689146i	$0.242014\pi$
$349$	−2.87085	+	21.8063i	−0.153673	+	1.16726i	−0.878296	+	0.478118i	$0.841319\pi$
$350$	−23.7202	+	2.69696i	−1.26790	+	0.144158i
$351$	6.39742	−	7.59290i	0.341469	−	0.405279i
$352$	−23.2265	+	4.06746i	−1.23798	+	0.216796i
$353$	−12.9853	−	7.49706i	−0.691137	−	0.399028i	0.112901	−	0.993606i	$-0.463986\pi$
$353$	−12.9853	−	7.49706i	−0.691137	−	0.399028i	−0.804038	+	0.594578i	$0.797319\pi$
$354$	−16.0933	−	17.1889i	−0.855351	−	0.913581i
$355$	0.0564865	−	0.0736146i	0.00299799	−	0.00390706i
$356$	−18.2126	−	0.644527i	−0.965265	−	0.0341599i
$357$	55.3531	+	15.7385i	2.92959	+	0.832968i
$358$	12.1880	+	0.215594i	0.644157	+	0.0113945i
$359$	−3.20910	−	3.20910i	−0.169370	−	0.169370i	0.617332	−	0.786702i	$-0.288213\pi$
$359$	−3.20910	−	3.20910i	−0.169370	−	0.169370i	−0.786702	+	0.617332i	$0.788213\pi$
$360$	4.89675	−	7.04966i	0.258081	−	0.371550i
$361$	−5.22313	+	5.22313i	−0.274902	+	0.274902i
$362$	−14.7903	+	14.2761i	−0.777359	+	0.750336i
$363$	−7.68857	−	7.92622i	−0.403545	−	0.416019i
$364$	5.67400	+	15.1975i	0.297398	+	0.796564i
$365$	−1.24560	−	0.955780i	−0.0651975	−	0.0500278i
$366$	20.1256	−	10.7527i	1.05198	−	0.562051i
$367$	13.0863	−	22.6661i	0.683100	−	1.18316i	−0.290930	−	0.956744i	$-0.593965\pi$
$367$	13.0863	−	22.6661i	0.683100	−	1.18316i	0.974030	−	0.226419i	$-0.0727019\pi$
$368$	−6.67119	+	19.3158i	−0.347760	+	1.00691i
$369$	4.86415	−	1.14590i	0.253217	−	0.0596530i
$370$	−5.02211	+	6.31063i	−0.261087	+	0.328074i
$371$	−3.49691	−	0.460377i	−0.181550	−	0.0239016i
$372$	20.7939	−	18.7895i	1.07811	−	0.974191i
$373$	−2.79106	−	21.2002i	−0.144516	−	1.09770i	−0.897924	−	0.440151i	$-0.854925\pi$
$373$	−2.79106	−	21.2002i	−0.144516	−	1.09770i	0.753408	−	0.657553i	$-0.228409\pi$
$374$	11.1518	+	44.7721i	0.576647	+	2.31511i
$375$	15.5604	+	2.28999i	0.803538	+	0.118255i
$376$	−32.4033	−	6.02912i	−1.67107	−	0.310928i
$377$	2.92956	−	2.92956i	0.150880	−	0.150880i
$378$	30.6069	+	6.02110i	1.57425	+	0.309692i
$379$	9.05526	+	3.75081i	0.465137	+	0.192666i	0.602929	−	0.797795i	$-0.294000\pi$
$379$	9.05526	+	3.75081i	0.465137	+	0.192666i	−0.137791	+	0.990461i	$0.544000\pi$
$380$	−2.01885	+	6.59234i	−0.103565	+	0.338180i
$381$	4.05444	+	2.42384i	0.207715	+	0.124177i
$382$	−6.96894	−	9.42259i	−0.356562	−	0.482102i
$383$	−3.15833	−	5.47038i	−0.161383	−	0.279524i	0.773982	−	0.633208i	$-0.218262\pi$
$383$	−3.15833	−	5.47038i	−0.161383	−	0.279524i	−0.935365	+	0.353684i	$0.884929\pi$
$384$	18.8863	+	5.22550i	0.963790	+	0.266663i
$385$	−8.94956	+	15.5011i	−0.456112	+	0.790009i
$386$	7.02849	−	0.799130i	0.357741	−	0.0406746i
$387$	−2.39537	+	5.31903i	−0.121764	+	0.270381i
$388$	30.1786	−	6.95241i	1.53209	−	0.352955i
$389$	−7.40216	+	5.67988i	−0.375305	+	0.287981i	−0.779140	−	0.626850i	$-0.784344\pi$
$389$	−7.40216	+	5.67988i	−0.375305	+	0.287981i	0.403835	+	0.914832i	$0.367677\pi$
$390$	−0.463218	−	4.71188i	−0.0234559	−	0.238595i
$391$	38.6244	+	10.3494i	1.95332	+	0.523391i
$392$	−20.2579	+	23.6853i	−1.02318	+	1.19629i
$393$	−3.81847	+	1.51400i	−0.192616	+	0.0763711i
$394$	−0.276315	+	0.266710i	−0.0139206	+	0.0134366i
$395$	−0.925454	−	0.383336i	−0.0465646	−	0.0192877i
$396$	8.03073	+	23.6859i	0.403559	+	1.19026i
$397$	−7.81517	−	18.8675i	−0.392232	−	0.946933i	−0.989453	−	0.144855i	$-0.953728\pi$
$397$	−7.81517	−	18.8675i	−0.392232	−	0.946933i	0.597221	−	0.802077i	$-0.296272\pi$
$398$	−4.56621	−	11.6000i	−0.228883	−	0.581453i
$399$	−24.8883	+	2.89201i	−1.24597	+	0.144781i
$400$	3.02057	+	15.6175i	0.151028	+	0.780874i
$401$	−0.620953	−	1.07552i	−0.0310089	−	0.0537090i	0.850104	−	0.526614i	$-0.176539\pi$
$401$	−0.620953	−	1.07552i	−0.0310089	−	0.0537090i	−0.881113	+	0.472905i	$0.843205\pi$
$402$	2.70742	+	0.0891227i	0.135034	+	0.00444504i
$403$	2.01777	−	15.3265i	0.100512	−	0.763466i
$404$	−18.9795	−	3.18520i	−0.944263	−	0.158470i
$405$	−8.18359	−	3.98926i	−0.406646	−	0.198228i
$406$	12.5113	+	3.59072i	0.620924	+	0.178204i
$407$	−6.08222	−	22.6992i	−0.301484	−	1.12516i
$408$	7.58702	−	37.5862i	0.375613	−	1.86079i
$409$	0.181901	−	0.678865i	0.00899444	−	0.0335677i	−0.961283	−	0.275564i	$-0.911135\pi$
$409$	0.181901	−	0.678865i	0.00899444	−	0.0335677i	0.970277	+	0.241996i	$0.0778021\pi$
$410$	1.22782	−	2.04235i	0.0606376	−	0.100864i
$411$	2.40127	−	8.44538i	0.118446	−	0.416580i
$412$	5.29878	+	9.97682i	0.261052	+	0.491523i
$413$	−15.6158	−	37.6999i	−0.768403	−	1.85509i
$414$	21.3286	+	3.85967i	1.04824	+	0.189692i
$415$		−	7.41706i		−	0.364089i
$416$	9.80161	−	4.55662i	0.480564	−	0.223407i
$417$	10.3180	−	23.8756i	0.505276	−	1.16919i
$418$	−11.9457	−	16.1516i	−0.584285	−	0.790002i
$419$	−23.5855	−	18.0978i	−1.15223	−	0.884133i	−0.157582	−	0.987506i	$-0.550370\pi$
$419$	−23.5855	−	18.0978i	−1.15223	−	0.884133i	−0.994643	+	0.103372i	$0.967037\pi$
$420$	12.2439	−	8.44688i	0.597441	−	0.412166i
$421$	0.573374	+	0.747235i	0.0279445	+	0.0364180i	0.807117	−	0.590392i	$-0.201027\pi$
$421$	0.573374	+	0.747235i	0.0279445	+	0.0364180i	−0.779172	+	0.626810i	$0.784360\pi$
$422$	24.8544	−	13.7694i	1.20990	−	0.670286i
$423$	−1.06390	+	34.9426i	−0.0517287	+	1.69897i
$424$	−0.124643	+	2.34683i	−0.00605322	+	0.113972i
$425$	30.0652	−	8.05595i	1.45838	−	0.390771i
$426$	0.0366405	−	0.221679i	0.00177524	−	0.0107404i
$427$	39.2046	−	5.16138i	1.89724	−	0.249777i
$428$	−2.85217	−	7.63936i	−0.137865	−	0.369262i
$429$	11.8409	+	7.07879i	0.571686	+	0.341767i
$430$	1.01891	+	2.58844i	0.0491364	+	0.124826i
$431$		−	4.18512i		−	0.201590i	−0.994907	−	0.100795i	$-0.967861\pi$
$431$		−	4.18512i		−	0.201590i	0.994907	−	0.100795i	$-0.0321386\pi$
$432$	2.41398	−	20.6440i	0.116143	−	0.993233i
$433$			34.4965i			1.65780i	0.559399	+	0.828899i	$0.311032\pi$
$433$			34.4965i			1.65780i	−0.559399	+	0.828899i	$0.688968\pi$
$434$	45.1922	−	17.7895i	2.16929	−	0.853922i
$435$	−3.26070	−	1.94932i	−0.156339	−	0.0934629i
$436$	−8.06853	+	17.6829i	−0.386413	+	0.846855i
$437$	−17.2612	+	2.27248i	−0.825715	+	0.108707i
$438$	−3.75092	−	0.619977i	−0.179226	−	0.0296236i
$439$	−38.7430	+	10.3811i	−1.84910	+	0.495465i	−0.999490	−	0.0319448i	$-0.989830\pi$
$439$	−38.7430	+	10.3811i	−1.84910	+	0.495465i	−0.849611	+	0.527410i	$0.823163\pi$
$440$	10.7610	+	5.14200i	0.513010	+	0.245135i
$441$	28.1123	+	17.3923i	1.33868	+	0.828206i
$442$	−10.2496	−	18.5010i	−0.487525	−	0.880004i
$443$	−24.3018	−	31.6708i	−1.15461	−	1.50472i	−0.829025	−	0.559212i	$-0.811104\pi$
$443$	−24.3018	−	31.6708i	−1.15461	−	1.50472i	−0.325590	−	0.945511i	$-0.605563\pi$
$444$	−3.52502	+	19.2086i	−0.167290	+	0.911601i
$445$	7.31267	+	5.61121i	0.346654	+	0.265997i
$446$	−9.68098	+	7.16004i	−0.458407	+	0.339038i
$447$	2.58937	−	5.99171i	0.122473	−	0.283398i
$448$	27.4455	+	19.9992i	1.29668	+	0.944875i
$449$			4.67579i			0.220664i	0.993895	+	0.110332i	$0.0351914\pi$
$449$			4.67579i			0.220664i	−0.993895	+	0.110332i	$0.964809\pi$
$450$	15.8801	−	5.69923i	0.748594	−	0.268664i
$451$	2.65719	+	6.41501i	0.125122	+	0.302071i
$452$	−6.41706	+	20.9542i	−0.301833	+	0.985603i
$453$	−2.26249	+	7.95732i	−0.106301	+	0.373867i
$454$	17.9921	+	10.8165i	0.844409	+	0.507641i
$455$	2.12359	−	7.92534i	0.0995553	−	0.371546i
$456$	3.21066	+	16.3833i	0.150353	+	0.767218i
$457$	1.28695	+	4.80296i	0.0602009	+	0.224673i	0.989472	−	0.144726i	$-0.0462302\pi$
$457$	1.28695	+	4.80296i	0.0602009	+	0.224673i	−0.929271	+	0.369399i	$0.879564\pi$
$458$	0.898393	−	3.13031i	0.0419792	−	0.146270i
$459$	−40.6279	−	1.85622i	−1.89635	−	0.0866409i
$460$	8.41745	−	5.99817i	0.392466	−	0.279666i
$461$	−3.58069	+	27.1980i	−0.166769	+	1.26674i	0.679378	+	0.733788i	$0.262250\pi$
$461$	−3.58069	+	27.1980i	−0.166769	+	1.26674i	−0.846147	+	0.532949i	$0.821084\pi$
$462$	−1.42596	+	43.3187i	−0.0663418	+	2.01537i
$463$	17.1819	+	29.7600i	0.798513	+	1.38306i	0.920585	+	0.390543i	$0.127713\pi$
$463$	17.1819	+	29.7600i	0.798513	+	1.38306i	−0.122072	+	0.992521i	$0.538954\pi$
$464$	1.73706	−	8.49721i	0.0806409	−	0.394473i
$465$	−14.0802	+	1.63611i	−0.652952	+	0.0758728i
$466$	−2.08607	+	0.821162i	−0.0966354	+	0.0380396i
$467$	3.80888	+	9.19546i	0.176254	+	0.425515i	0.987175	−	0.159640i	$-0.0510335\pi$
$467$	3.80888	+	9.19546i	0.176254	+	0.425515i	−0.810921	+	0.585156i	$0.801033\pi$
$468$	−6.36598	−	9.53483i	−0.294267	−	0.440748i
$469$	4.33709	+	1.79648i	0.200268	+	0.0829538i
$470$	11.5774	+	11.9944i	0.534028	+	0.553261i
$471$	−32.6728	+	12.9546i	−1.50549	+	0.596916i
$472$	−24.2347	+	12.3268i	−1.11549	+	0.567387i
$473$	−7.82926	−	2.09784i	−0.359990	−	0.0964589i
$474$	−2.41396	+	0.237313i	−0.110877	+	0.0109001i
$475$	−10.7516	+	8.24996i	−0.493315	+	0.378534i
$476$	35.2393	−	56.3360i	1.61519	−	2.58215i
$477$	2.48013	−	0.250000i	0.113557	−	0.0114467i
$478$	2.57668	+	22.6624i	0.117855	+	1.03655i
$479$	−5.35925	+	9.28249i	−0.244870	+	0.424128i	−0.962095	−	0.272714i	$-0.912079\pi$
$479$	−5.35925	+	9.28249i	−0.244870	+	0.424128i	0.717225	+	0.696842i	$0.245412\pi$
$480$	−6.24560	−	7.69590i	−0.285071	−	0.351268i
$481$	5.38615	+	9.32908i	0.245587	+	0.425370i
$482$	−3.07960	+	2.27767i	−0.140272	+	0.103745i
$483$	32.2402	+	19.2740i	1.46698	+	0.876996i
$484$	−11.2612	+	5.98092i	−0.511872	+	0.271860i
$485$	−14.4714	−	5.99424i	−0.657112	−	0.272185i
$486$	−22.0302	+	0.818098i	−0.999311	+	0.0371097i
$487$	19.8590	−	19.8590i	0.899897	−	0.899897i	−0.0955294	−	0.995427i	$-0.530454\pi$
$487$	19.8590	−	19.8590i	0.899897	−	0.899897i	0.995427	+	0.0955294i	$0.0304544\pi$
$488$	−5.45995	−	25.7760i	−0.247160	−	1.16682i
$489$	38.6265	+	5.68457i	1.74675	+	0.257065i
$490$	15.2964	−	3.81002i	0.691021	−	0.172119i
$491$	5.50833	+	41.8399i	0.248588	+	1.88821i	0.426996	+	0.904253i	$0.359572\pi$
$491$	5.50833	+	41.8399i	0.248588	+	1.88821i	−0.178409	+	0.983956i	$0.557095\pi$
$492$	0.291818	−	5.76300i	0.0131562	−	0.259816i
$493$	−16.8256	−	2.21513i	−0.757786	−	0.0997644i
$494$	7.20557	+	5.73432i	0.324194	+	0.257999i
$495$	3.64436	−	12.1135i	0.163802	−	0.544463i
$496$	−14.1590	−	29.0992i	−0.635756	−	1.30659i
$497$	0.194688	−	0.337209i	0.00873293	−	0.0151259i
$498$	−8.46351	−	15.8410i	−0.379259	−	0.709853i
$499$	−12.2064	−	9.36631i	−0.546434	−	0.419294i	0.298306	−	0.954470i	$-0.403578\pi$
$499$	−12.2064	−	9.36631i	−0.546434	−	0.419294i	−0.844740	+	0.535177i	$0.820245\pi$
$500$	7.53905	−	16.5225i	0.337157	−	0.738907i
$501$	−2.30310	−	2.37429i	−0.102895	−	0.106075i
$502$	−8.28951	−	8.58806i	−0.369979	−	0.383304i
$503$	13.7130	−	13.7130i	0.611435	−	0.611435i	−0.331885	−	0.943320i	$-0.607685\pi$
$503$	13.7130	−	13.7130i	0.611435	−	0.611435i	0.943320	+	0.331885i	$0.107685\pi$
$504$	16.5113	−	32.0118i	0.735472	−	1.42592i
$505$	6.88282	+	6.88282i	0.306282	+	0.306282i
$506$	−0.532650	+	30.1119i	−0.0236792	+	1.33864i
$507$	15.5755	+	4.42855i	0.691731	+	0.196679i
$508$	3.99089	−	3.71808i	0.177067	−	0.164963i
$509$	−24.8470	+	32.3813i	−1.10133	+	1.43528i	−0.212425	+	0.977177i	$0.568136\pi$
$509$	−24.8470	+	32.3813i	−1.10133	+	1.43528i	−0.888901	+	0.458099i	$0.848531\pi$
$510$	−14.1574	+	13.2550i	−0.626899	+	0.586942i
$511$	−5.70574	−	3.29421i	−0.252407	−	0.145727i
$512$	11.8634	−	19.2681i	0.524292	−	0.851538i
$513$	16.6520	−	6.02269i	0.735203	−	0.265908i
$514$	1.52631	+	13.4241i	0.0673226	+	0.592114i
$515$	0.745784	−	5.66480i	0.0328632	−	0.249621i
$516$	5.12978	+	4.36560i	0.225826	+	0.192185i
$517$	−48.1584	+	6.34017i	−2.11800	+	0.278840i
$518$	−17.4377	+	29.0058i	−0.766167	+	1.27444i
$519$	−13.4547	−	10.6534i	−0.590598	−	0.467632i
$520$	−5.37479	−	1.00006i	−0.235700	−	0.0438555i
$521$	−1.80374	−	1.80374i	−0.0790233	−	0.0790233i	0.666490	−	0.745514i	$-0.267796\pi$
$521$	−1.80374	−	1.80374i	−0.0790233	−	0.0790233i	−0.745514	+	0.666490i	$0.767796\pi$
$522$	−9.18840	−	0.442532i	−0.402165	−	0.0193691i
$523$	−0.318064	+	0.767873i	−0.0139079	+	0.0335768i	−0.930681	−	0.365832i	$-0.880785\pi$
$523$	−0.318064	+	0.767873i	−0.0139079	+	0.0335768i	0.916773	+	0.399409i	$0.130785\pi$
$524$	0.452399	+	4.72149i	0.0197631	+	0.206259i
$525$	29.2350	+	0.444958i	1.27592	+	0.0194195i
$526$	−0.417022	+	2.78590i	−0.0181830	+	0.121471i
$527$	−54.8389	+	31.6613i	−2.38882	+	1.37919i
$528$	28.8503	−	1.29718i	1.25555	−	0.0564524i
$529$	2.68500	+	1.55018i	0.116739	+	0.0673993i
$530$	0.740179	−	0.930087i	0.0321513	−	0.0404004i
$531$	16.8516	+	23.4031i	0.731296	+	1.01561i
$532$	−4.78848	+	28.5328i	−0.207607	+	1.23706i
$533$	−1.93763	−	2.52517i	−0.0839282	−	0.109377i
$534$	22.0210	+	3.63977i	0.952940	+	0.157508i
$535$	−1.06747	+	3.98385i	−0.0461508	+	0.172237i
$536$	0.968678	−	2.97418i	0.0418405	−	0.128465i
$537$	−14.7705	−	2.17373i	−0.637393	−	0.0938034i
$538$	−0.152218	+	8.60523i	−0.00656259	+	0.370998i
$539$	−17.5775	+	42.4357i	−0.757115	+	1.82784i
$540$	−7.05371	+	7.79480i	−0.303543	+	0.335435i
$541$	1.25482	−	0.519761i	0.0539487	−	0.0223463i	−0.355546	−	0.934659i	$-0.615705\pi$
$541$	1.25482	−	0.519761i	0.0539487	−	0.0223463i	0.409495	+	0.912313i	$0.365705\pi$
$542$	14.9251	−	34.3035i	0.641089	−	1.47346i
$543$	20.2045	−	15.0205i	0.867059	−	0.644593i
$544$	−39.2495	−	20.4904i	−1.68281	−	0.878517i
$545$	8.51372	−	4.91540i	0.364688	−	0.210552i
$546$	−4.50804	−	19.3498i	−0.192926	−	0.828094i
$547$	−43.3007	−	5.70064i	−1.85140	−	0.243742i	−0.878963	−	0.476890i	$-0.841764\pi$
$547$	−43.3007	−	5.70064i	−1.85140	−	0.243742i	−0.972441	+	0.233148i	$0.925097\pi$
$548$	−8.59535	−	5.37656i	−0.367175	−	0.229675i
$549$	−26.1324	+	9.90383i	−1.11530	+	0.422685i
$550$	11.3605	+	20.5061i	0.484412	+	0.874385i
$551$	7.13723	−	1.91241i	0.304056	−	0.0814716i
$552$	11.1332	−	22.4157i	0.473859	−	0.954073i
$553$	−4.06026	−	1.08794i	−0.172660	−	0.0462641i
$554$	−1.60079	−	6.42681i	−0.0680109	−	0.273049i
$555$	7.09006	−	6.87747i	0.300956	−	0.291932i
$556$	−23.1656	−	19.1145i	−0.982440	−	0.810633i
$557$	−3.10590	+	1.28650i	−0.131601	+	0.0545109i	−0.447512	−	0.894278i	$-0.647690\pi$
$557$	−3.10590	+	1.28650i	−0.131601	+	0.0545109i	0.315911	+	0.948789i	$0.397690\pi$
$558$	−28.2048	+	19.5610i	−1.19401	+	0.828084i
$559$	3.71552			0.157150
$560$	−5.43480	−	16.2936i	−0.229662	−	0.688528i
$561$	−6.52253	−	56.1321i	−0.275381	−	2.36990i
$562$	12.3326	+	1.84607i	0.520219	+	0.0778716i
$563$	10.0113	−	13.0470i	0.421926	−	0.549865i	−0.533229	−	0.845971i	$-0.679022\pi$
$563$	10.0113	−	13.0470i	0.421926	−	0.549865i	0.955155	+	0.296106i	$0.0956883\pi$
$564$	38.4132	+	12.4062i	1.61749	+	0.522396i
$565$	8.79367	−	6.74762i	0.369952	−	0.283874i
$566$	−32.5099	−	9.33029i	−1.36649	−	0.392181i
$567$	−36.2324	−	12.1147i	−1.52162	−	0.508769i
$568$	−0.234093	−	0.111858i	−0.00982234	−	0.00469348i
$569$	4.02452	+	15.0197i	0.168717	+	0.629659i	0.997537	+	0.0701440i	$0.0223459\pi$
$569$	4.02452	+	15.0197i	0.168717	+	0.629659i	−0.828820	+	0.559515i	$0.810987\pi$
$570$	3.48631	−	7.69076i	0.146026	−	0.322130i
$571$	−1.73675	−	13.1920i	−0.0726809	−	0.552066i	−0.988584	−	0.150668i	$-0.951858\pi$
$571$	−1.73675	−	13.1920i	−0.0726809	−	0.552066i	0.915904	−	0.401399i	$-0.131476\pi$
$572$	11.6553	−	10.8586i	0.487335	−	0.454021i
$573$	6.98682	+	12.5384i	0.291878	+	0.523799i
$574$	3.98960	−	9.16959i	0.166523	−	0.382731i
$575$	20.3165			0.847256
$576$	−22.1208	−	9.30978i	−0.921698	−	0.387907i
$577$	26.8898			1.11944			0.559719	−	0.828682i	$-0.310909\pi$
$577$	26.8898			1.11944			0.559719	+	0.828682i	$0.310909\pi$
$578$	−24.9734	+	57.3982i	−1.03876	+	2.38745i
$579$	−8.66256	−	0.131845i	−0.360004	−	0.00547927i
$580$	−3.20959	+	2.99019i	−0.133271	+	0.124161i
$581$	−4.06257	−	30.8583i	−0.168544	−	1.28022i
$582$	−37.7473	+	3.71088i	−1.56467	+	0.153821i
$583$	0.896422	+	3.34549i	0.0371260	+	0.138556i
$584$	−1.89270	+	3.96098i	−0.0783205	+	0.163906i
$585$	−0.176471	+	5.79598i	−0.00729617	+	0.239634i
$586$	−7.68283	−	2.20496i	−0.317375	−	0.0910861i
$587$	2.06759	−	1.58652i	0.0853387	−	0.0654827i	−0.565211	−	0.824946i	$-0.691205\pi$
$587$	2.06759	−	1.58652i	0.0853387	−	0.0654827i	0.650550	+	0.759464i	$0.274539\pi$
$588$	28.3218	−	25.5918i	1.16797	−	1.05539i
$589$	16.7838	−	21.8730i	0.691563	−	0.901263i
$590$	13.6006	+	2.03587i	0.559926	+	0.0838154i
$591$	0.377466	−	0.280617i	0.0155269	−	0.0115431i
$592$	20.1719	+	10.0809i	0.829059	+	0.414322i
$593$	−35.1862			−1.44492			−0.722462	−	0.691410i	$-0.756990\pi$
$593$	−35.1862			−1.44492			−0.722462	+	0.691410i	$0.756990\pi$
$594$	−6.03912	−	30.0300i	−0.247788	−	1.23215i
$595$	−31.0509	+	12.8617i	−1.27296	+	0.527278i
$596$	−5.81353	−	4.79688i	−0.238132	−	0.196488i
$597$	3.72677	+	14.8063i	0.152527	+	0.605980i
$598$	−3.33669	−	13.3961i	−0.136448	−	0.547807i
$599$	−13.9700	−	3.74325i	−0.570799	−	0.152945i	−0.0381361	−	0.999273i	$-0.512142\pi$
$599$	−13.9700	−	3.74325i	−0.570799	−	0.152945i	−0.532663	+	0.846327i	$0.678809\pi$
$600$	−1.21915	−	19.4437i	−0.0497714	−	0.793786i
$601$	42.3244	−	11.3408i	1.72645	−	0.462601i	0.747089	−	0.664724i	$-0.231451\pi$
$601$	42.3244	−	11.3408i	1.72645	−	0.462601i	0.979360	+	0.202123i	$0.0647841\pi$
$602$	5.65691	+	10.2110i	0.230558	+	0.416168i
$603$	−3.27461	−	0.532950i	−0.133352	−	0.0217034i
$604$	8.09862	+	5.06585i	0.329528	+	0.206126i
$605$	6.39405	+	0.841792i	0.259955	+	0.0342237i
$606$	22.5539	+	6.84611i	0.916190	+	0.278104i
$607$	10.3379	−	5.96857i	0.419601	−	0.242257i	−0.275306	−	0.961357i	$-0.588779\pi$
$607$	10.3379	−	5.96857i	0.419601	−	0.242257i	0.694907	+	0.719100i	$0.255446\pi$
$608$	19.2023	+	1.70261i	0.778757	+	0.0690502i
$609$	−14.6337	−	6.32405i	−0.592986	−	0.256264i
$610$	−5.31674	+	12.2199i	−0.215269	+	0.494767i
$611$	20.5713	−	8.52090i	0.832224	−	0.344719i
$612$	−15.1115	+	44.4642i	−0.610848	+	1.79736i
$613$	−2.98637	+	7.20975i	−0.120619	+	0.291199i	−0.972644	−	0.232302i	$-0.925374\pi$
$613$	−2.98637	+	7.20975i	−0.120619	+	0.291199i	0.852025	+	0.523501i	$0.175374\pi$
$614$	0.271769	−	15.3637i	0.0109677	−	0.620028i
$615$	−1.81175	+	2.28816i	−0.0730568	+	0.0922674i
$616$	47.5869	+	15.4988i	1.91733	+	0.624466i
$617$	6.84218	−	25.5354i	0.275456	−	1.02802i	−0.680079	−	0.733138i	$-0.738055\pi$
$617$	6.84218	−	25.5354i	0.275456	−	1.02802i	0.955535	−	0.294877i	$-0.0952786\pi$
$618$	−4.87121	−	12.9496i	−0.195949	−	0.520910i
$619$	−9.21115	−	12.0042i	−0.370227	−	0.482490i	0.570671	−	0.821179i	$-0.306683\pi$
$619$	−9.21115	−	12.0042i	−0.370227	−	0.482490i	−0.940898	+	0.338689i	$0.890016\pi$
$620$	−2.70901	+	16.1420i	−0.108797	+	0.648280i
$621$	−25.3015	−	8.03386i	−1.01532	−	0.322388i
$622$	−22.8209	+	28.6760i	−0.915034	+	1.14980i
$623$	33.4974	+	19.3397i	1.34205	+	0.774830i
$624$	−12.6204	+	3.99722i	−0.505219	+	0.160017i
$625$	9.26470	−	5.34898i	0.370588	−	0.213959i
$626$	2.84914	−	19.0336i	0.113875	−	0.760736i
$627$	11.9764	+	21.4925i	0.478290	+	0.858329i
$628$	3.87097	+	40.3996i	0.154469	+	1.61212i
$629$	16.8862	−	40.7670i	0.673298	−	1.62548i
$630$	−16.1972	+	8.33945i	−0.645310	+	0.332252i
$631$	−25.3516	−	25.3516i	−1.00923	−	1.00923i	−0.999957	−	0.00927583i	$-0.997047\pi$
$631$	−25.3516	−	25.3516i	−1.00923	−	1.00923i	−0.00927583	−	0.999957i	$-0.502953\pi$
$632$	−0.512344	+	2.75358i	−0.0203800	+	0.109531i
$633$	−32.3496	+	12.8264i	−1.28578	+	0.509804i
$634$	16.2523	−	27.0340i	0.645461	−	1.07366i
$635$	−2.73520	+	0.360095i	−0.108543	+	0.0142899i
$636$	0.519531	−	2.83104i	0.0206008	−	0.112258i
$637$	2.74825	−	20.8750i	0.108890	−	0.827099i
$638$	−1.44396	−	12.6999i	−0.0571670	−	0.502794i
$639$	−0.0792791	+	0.263516i	−0.00313623	+	0.0104245i
$640$	−10.5421	+	4.45452i	−0.416714	+	0.176080i
$641$	19.3163	+	11.1523i	0.762947	+	0.440487i	0.830353	−	0.557238i	$-0.188139\pi$
$641$	19.3163	+	11.1523i	0.762947	+	0.440487i	−0.0674061	+	0.997726i	$0.521472\pi$
$642$	2.26607	+	9.72661i	0.0894346	+	0.383879i
$643$	−2.40762	+	3.13767i	−0.0949472	+	0.123738i	−0.838411	−	0.545039i	$-0.816515\pi$
$643$	−2.40762	+	3.13767i	−0.0949472	+	0.123738i	0.743464	+	0.668776i	$0.233182\pi$
$644$	31.7349	−	29.5655i	1.25053	−	1.16505i
$645$	−0.831600	−	3.30390i	−0.0327442	−	0.130091i
$646$	0.667152	−	37.7156i	0.0262488	−	1.48390i
$647$	−15.9793	−	15.9793i	−0.628209	−	0.628209i	0.319408	−	0.947617i	$-0.396516\pi$
$647$	−15.9793	−	15.9793i	−0.628209	−	0.628209i	−0.947617	+	0.319408i	$0.896516\pi$
$648$	−6.17044	+	24.6967i	−0.242398	+	0.970177i
$649$	−28.3342	+	28.3342i	−1.11221	+	1.11221i
$650$	−7.46306	−	7.73184i	−0.292725	−	0.303268i
$651$	−57.6836	+	14.5191i	−2.26080	+	0.569049i
$652$	18.7146	−	41.0146i	0.732920	−	1.60625i
$653$	33.3029	+	25.5542i	1.30324	+	1.00001i	0.998873	+	0.0474597i	$0.0151126\pi$
$653$	33.3029	+	25.5542i	1.30324	+	1.00001i	0.304370	+	0.952554i	$0.401554\pi$
$654$	12.5743	−	20.2130i	0.491694	−	0.790389i
$655$	1.19950	−	2.07759i	0.0468683	−	0.0811783i
$656$	−6.29802	−	2.17518i	−0.245896	−	0.0849263i
$657$	4.45883	+	1.34144i	0.173955	+	0.0523346i
$658$	54.7370	+	43.5607i	2.13387	+	1.69817i
$659$	24.7875	+	3.26333i	0.965583	+	0.127121i	0.596797	−	0.802393i	$-0.296440\pi$
$659$	24.7875	+	3.26333i	0.965583	+	0.127121i	0.368787	+	0.929514i	$0.379773\pi$
$660$	−12.2643	−	7.93378i	−0.477388	−	0.308822i
$661$	2.37840	+	18.0658i	0.0925091	+	0.702677i	0.973360	+	0.229283i	$0.0736380\pi$
$661$	2.37840	+	18.0658i	0.0925091	+	0.702677i	−0.880851	+	0.473394i	$0.843029\pi$
$662$	−15.7438	+	3.92146i	−0.611900	+	0.152412i
$663$	9.54766	+	24.0802i	0.370800	+	0.935198i
$664$	−20.2885	+	4.29757i	−0.787346	+	0.166778i
$665$	10.3473	−	10.3473i	0.401252	−	0.401252i
$666$	7.29482	−	22.7790i	0.282669	−	0.882667i
$667$	−10.2340	−	4.23906i	−0.396262	−	0.164137i
$668$	−3.37327	+	1.79158i	−0.130516	+	0.0693182i
$669$	12.8822	−	7.17841i	0.498056	−	0.277533i
$670$	−1.27198	+	0.940756i	−0.0491409	+	0.0363446i
$671$	−19.4151	−	33.6279i	−0.749511	−	1.29819i
$672$	−30.1998	−	28.5974i	−1.16498	−	1.10317i
$673$	−15.9906	+	27.6966i	−0.616394	+	1.06762i	0.373745	+	0.927532i	$0.378074\pi$
$673$	−15.9906	+	27.6966i	−0.616394	+	1.06762i	−0.990138	+	0.140093i	$0.955260\pi$
$674$	5.22450	+	45.9504i	0.201240	+	1.76994i
$675$	−20.1829	+	4.43161i	−0.776839	+	0.170573i
$676$	9.91577	−	15.8520i	0.381376	−	0.609694i
$677$	11.7275	−	8.99883i	0.450724	−	0.345853i	−0.358322	−	0.933598i	$-0.616651\pi$
$677$	11.7275	−	8.99883i	0.450724	−	0.345853i	0.809046	+	0.587745i	$0.199984\pi$
$678$	11.0815	−	24.4456i	0.425582	−	0.938827i
$679$	−63.4906	−	17.0123i	−2.43655	−	0.652870i
$680$	10.1528	+	19.9605i	0.389341	+	0.765452i
$681$	−20.1575	−	15.9606i	−0.772437	−	0.611611i
$682$	−33.1217	−	34.3146i	−1.26829	−	1.31397i
$683$	41.8397	+	17.3306i	1.60095	+	0.663136i	0.991550	−	0.129726i	$-0.0414099\pi$
$683$	41.8397	+	17.3306i	1.60095	+	0.663136i	0.609401	+	0.792862i	$0.291410\pi$
$684$	−1.32991	−	20.4037i	−0.0508504	−	0.780157i
$685$	1.96235	+	4.73753i	0.0749775	+	0.181012i
$686$	22.4510	−	8.83761i	0.857182	−	0.337422i
$687$	−1.58227	+	3.66133i	−0.0603674	+	0.139688i
$688$	6.48999	−	4.28690i	0.247429	−	0.163437i
$689$	−0.793833	−	1.37496i	−0.0302426	−	0.0523817i
$690$	−11.1652	+	5.96533i	−0.425053	+	0.227096i
$691$	0.0102402	−	0.0777817i	0.000389554	−	0.00295896i	−0.991249	−	0.132006i	$-0.957858\pi$
$691$	0.0102402	−	0.0777817i	0.000389554	−	0.00295896i	0.991639	+	0.129047i	$0.0411917\pi$
$692$	−16.1384	+	11.5000i	−0.613491	+	0.437166i
$693$	8.52719	−	52.3938i	0.323921	−	1.99027i
$694$	−7.99190	+	27.8465i	−0.303368	+	1.05704i
$695$	3.93158	+	14.6729i	0.149133	+	0.556574i
$696$	−3.44283	+	10.0487i	−0.130500	+	0.380896i
$697$	−3.37447	+	12.5937i	−0.127817	+	0.477020i
$698$	−26.6583	−	16.0264i	−1.00903	−	0.606609i
$699$	2.66267	−	0.670202i	0.100712	−	0.0253494i
$700$	9.88603	−	32.2817i	0.373657	−	1.22013i
$701$	11.8882	+	28.7008i	0.449013	+	1.08401i	0.972693	+	0.232097i	$0.0745588\pi$
$701$	11.8882	+	28.7008i	0.449013	+	1.08401i	−0.523680	+	0.851915i	$0.675441\pi$
$702$	6.23682	+	12.5802i	0.235393	+	0.474807i
$703$			19.2122i			0.724602i
$704$	7.83022	−	32.4148i	0.295113	−	1.22168i
$705$	−12.1811	−	16.3852i	−0.458769	−	0.617102i
$706$	17.0486	−	12.6092i	0.641634	−	0.474552i
$707$	32.4055	+	24.8656i	1.21874	+	0.935168i
$708$	31.3705	−	11.1713i	1.17898	−	0.419843i
$709$	28.8802	+	37.6373i	1.08462	+	1.41350i	0.902744	+	0.430178i	$0.141549\pi$
$709$	28.8802	+	37.6373i	1.08462	+	1.41350i	0.181873	+	0.983322i	$0.441784\pi$
$710$	0.0635917	+	0.114786i	0.00238655	+	0.00430783i
$711$	2.96936	+	0.0904085i	0.111360	+	0.00339058i
$712$	11.1117	−	23.2542i	0.416429	−	0.871487i
$713$	−39.9237	+	10.6975i	−1.49515	+	0.400625i
$714$	−51.6407	+	62.9012i	−1.93261	+	2.35402i
$715$	−7.98810	+	1.05165i	−0.298738	+	0.0393296i
$716$	−7.15631	+	15.6836i	−0.267444	+	0.586125i
$717$	0.425114	−	27.9312i	0.0158762	−	1.04311i
$718$	5.97216	−	2.35088i	0.222879	−	0.0877342i
$719$		−	20.7556i		−	0.774054i	−0.922068	−	0.387027i	$-0.873502\pi$
$719$		−	20.7556i		−	0.774054i	0.922068	−	0.387027i	$-0.126498\pi$
$720$	6.37906	+	10.3276i	0.237734	+	0.384887i
$721$		−	23.9765i		−	0.892933i
$722$	−3.82630	−	9.72029i	−0.142400	−	0.361752i
$723$	4.09794	−	2.28351i	0.152404	−	0.0849246i
$724$	−10.1681	−	27.2347i	−0.377895	−	1.01217i
$725$	−8.54871	+	1.12546i	−0.317491	+	0.0417985i
$726$	14.6167	−	5.49830i	0.542475	−	0.204061i
$727$	23.9644	−	6.42125i	0.888791	−	0.238151i	0.214595	−	0.976703i	$-0.431157\pi$
$727$	23.9644	−	6.42125i	0.888791	−	0.238151i	0.674196	+	0.738552i	$0.264490\pi$
$728$	−22.9093	−	1.21674i	−0.849074	−	0.0450955i
$729$	26.8875	+	2.46203i	0.995834	+	0.0911863i
$730$	1.94223	−	1.07600i	0.0718853	−	0.0398247i
$731$	−9.26512	−	12.0745i	−0.342683	−	0.446593i
$732$	2.58866	+	32.1655i	0.0956797	+	1.18887i
$733$	18.8461	+	14.4611i	0.696095	+	0.534132i	0.895100	−	0.445866i	$-0.147104\pi$
$733$	18.8461	+	14.4611i	0.696095	+	0.534132i	−0.199005	+	0.979999i	$0.563771\pi$
$734$	22.0096	+	29.7588i	0.812390	+	1.09842i
$735$	−19.1775	+	2.22842i	−0.707374	+	0.0821966i
$736$	−21.2845	−	19.5495i	−0.784557	−	0.720603i
$737$		−	4.60982i		−	0.169805i
$738$	−1.25846	+	6.95430i	−0.0463247	+	0.255991i
$739$	1.90483	+	4.59865i	0.0700701	+	0.169164i	0.955035	−	0.296494i	$-0.0958175\pi$
$739$	1.90483	+	4.59865i	0.0700701	+	0.169164i	−0.884965	+	0.465658i	$0.845818\pi$
$740$	−5.34997	−	10.0732i	−0.196669	−	0.370298i
$741$	−7.85279	−	8.09553i	−0.288480	−	0.297397i
$742$	2.57003	−	4.27499i	0.0943490	−	0.156940i
$743$	−10.4510	+	39.0038i	−0.383411	+	1.43091i	0.457245	+	0.889341i	$0.348836\pi$
$743$	−10.4510	+	39.0038i	−0.383411	+	1.43091i	−0.840656	+	0.541569i	$0.817830\pi$
$744$	12.6337	+	37.5666i	0.463173	+	1.37726i
$745$	0.986652	+	3.68224i	0.0361481	+	0.134907i
$746$	29.0669	+	8.34216i	1.06422	+	0.305428i
$747$	7.79539	+	20.5690i	0.285218	+	0.752582i
$748$	−64.3519	−	10.7998i	−2.35294	−	0.394879i
$749$	−2.25906	+	17.1593i	−0.0825444	+	0.626987i
$750$	−11.7491	+	18.8865i	−0.429018	+	0.689638i
$751$	−2.80921	−	4.86570i	−0.102510	−	0.177552i	0.810208	−	0.586142i	$-0.199354\pi$
$751$	−2.80921	−	4.86570i	−0.102510	−	0.177552i	−0.912718	+	0.408590i	$0.866021\pi$
$752$	26.1011	−	38.6185i	0.951809	−	1.40827i
$753$	8.72177	+	11.7319i	0.317839	+	0.427533i
$754$	2.14610	+	5.45193i	0.0781563	+	0.198547i
$755$	−1.84894	−	4.46374i	−0.0672899	−	0.162452i
$756$	−25.0771	+	36.2934i	−0.912045	+	1.31998i
$757$	16.0230	+	6.63695i	0.582367	+	0.241224i	0.654363	−	0.756181i	$-0.272937\pi$
$757$	16.0230	+	6.63695i	0.582367	+	0.241224i	−0.0719961	+	0.997405i	$0.522937\pi$
$758$	−9.97316	+	9.62646i	−0.362241	+	0.349649i
$759$	5.37045	−	36.4921i	0.194935	−	1.32458i
$760$	−7.40979	−	6.33755i	−0.268781	−	0.229887i
$761$	26.8985	+	7.20744i	0.975072	+	0.261270i	0.710968	−	0.703225i	$-0.248257\pi$
$761$	26.8985	+	7.20744i	0.975072	+	0.261270i	0.264104	+	0.964494i	$0.414924\pi$
$762$	−5.43080	+	3.89017i	−0.196737	+	0.140926i
$763$	32.7285	−	25.1135i	1.18485	−	0.909168i
$764$	16.1511	−	3.72082i	0.584326	−	0.134615i
$765$	19.2756	−	13.8795i	0.696911	−	0.501815i
$766$	8.87591	−	1.00918i	0.320700	−	0.0364631i
$767$	9.18412	−	15.9074i	0.331619	−	0.574382i
$768$	−17.4324	+	21.5432i	−0.629038	+	0.777375i
$769$	−2.49302	−	4.31804i	−0.0899008	−	0.155713i	0.817568	−	0.575832i	$-0.195322\pi$
$769$	−2.49302	−	4.31804i	−0.0899008	−	0.155713i	−0.907469	+	0.420119i	$0.861988\pi$
$770$	−15.0521	−	20.3517i	−0.542440	−	0.733424i
$771$	0.251818	−	16.5452i	0.00906901	−	0.595860i
$772$	−2.92931	+	9.56534i	−0.105428	+	0.344264i
$773$	−27.2038	−	11.2682i	−0.978452	−	0.405288i	−0.164600	−	0.986360i	$-0.552633\pi$
$773$	−27.2038	−	11.2682i	−0.978452	−	0.405288i	−0.813852	+	0.581072i	$0.802633\pi$
$774$	−5.54613	−	6.10739i	−0.199351	−	0.219525i
$775$	−22.7496	+	22.7496i	−0.817190	+	0.817190i
$776$	−8.01157	+	43.0579i	−0.287598	+	1.54569i
$777$	25.7308	−	32.4968i	0.923086	−	1.16582i
$778$	−3.18915	−	12.8037i	−0.114336	−	0.459036i
$779$	−0.740954	−	5.62810i	−0.0265474	−	0.201648i
$780$	6.37166	+	2.05784i	0.228142	+	0.0736824i
$781$	−0.379086	−	0.0499076i	−0.0135648	−	0.00178584i
$782$	−35.2136	+	44.2483i	−1.25924	+	1.58232i
$783$	11.0913	+	1.97885i	0.396372	+	0.0707183i
$784$	−19.2849	−	39.6339i	−0.688745	−	1.41550i
$785$	10.2636	−	17.7770i	0.366322	−	0.634489i
$786$	0.191120	−	5.80596i	0.00681703	−	0.207092i
$787$	25.0409	+	19.2146i	0.892613	+	0.684926i	0.949605	−	0.313448i	$-0.101484\pi$
$787$	25.0409	+	19.2146i	0.892613	+	0.684926i	−0.0569920	+	0.998375i	$0.518151\pi$
$788$	−0.189963	−	0.508805i	−0.00676716	−	0.0181254i
$789$	0.943546	−	3.31850i	0.0335911	−	0.118142i
$790$	1.01926	−	0.983831i	0.0362638	−	0.0350031i
$791$	32.8897	−	32.8897i	1.16942	−	1.16942i
$792$	−35.2467	−	2.94993i	−1.25244	−	0.104821i
$793$	12.5863	+	12.5863i	0.446951	+	0.446951i
$794$	28.8766	+	0.510799i	1.02479	+	0.0181276i
$795$	−1.04496	+	1.01363i	−0.0370610	+	0.0359497i
$796$	17.6190	+	0.623521i	0.624490	+	0.0221001i
$797$	5.98294	−	7.79712i	0.211927	−	0.276188i	−0.675279	−	0.737562i	$-0.735977\pi$
$797$	5.98294	−	7.79712i	0.211927	−	0.276188i	0.887206	+	0.461374i	$0.152643\pi$
$798$	10.2921	−	33.9065i	0.364338	−	1.20028i
$799$	−78.9880	−	45.6037i	−2.79439	−	1.61334i
$800$	−21.9568	−	4.89465i	−0.776290	−	0.173052i
$801$	−26.1770	−	7.87536i	−0.924918	−	0.278262i
$802$	1.74508	−	0.198413i	0.0616208	−	0.00700621i
$803$	−0.844462	+	6.41433i	−0.0298004	+	0.226357i
$804$	−1.64315	+	3.46066i	−0.0579496	+	0.122048i
$805$	−21.7498	+	2.86342i	−0.766580	+	0.100922i
$806$	18.7367	+	11.2641i	0.659972	+	0.396762i
$807$	1.53474	−	10.4285i	0.0540254	−	0.367102i
$808$	14.8391	−	22.8152i	0.522038	−	0.802634i
$809$	17.9777	+	17.9777i	0.632064	+	0.632064i	0.948585	−	0.316522i	$-0.102515\pi$
$809$	17.9777	+	17.9777i	0.632064	+	0.632064i	−0.316522	+	0.948585i	$0.602515\pi$
$810$	9.79057	−	8.36155i	0.344005	−	0.293795i
$811$	−0.735125	+	1.77475i	−0.0258137	+	0.0623198i	−0.936261	−	0.351306i	$-0.885738\pi$
$811$	−0.735125	+	1.77475i	−0.0258137	+	0.0623198i	0.910447	+	0.413626i	$0.135738\pi$
$812$	−11.7155	+	14.1985i	−0.411133	+	0.498270i
$813$	−23.5099	+	39.3258i	−0.824528	+	1.37922i
$814$	32.8677	+	4.91997i	1.15201	+	0.172445i
$815$	−19.7472	+	11.4010i	−0.691713	+	0.399361i
$816$	44.4605	+	31.0456i	1.55643	+	1.08681i
$817$	5.73877	+	3.31328i	0.200774	+	0.115917i
$818$	0.777710	+	0.618916i	0.0271920	+	0.0216399i
$819$	2.44045	+	24.2105i	0.0852762	+	0.845983i
$820$	1.95573	+	2.74455i	0.0682972	+	0.0958439i
$821$	15.3964	+	20.0650i	0.537338	+	0.700273i	0.980578	−	0.196130i	$-0.0628376\pi$
$821$	15.3964	+	20.0650i	0.537338	+	0.700273i	−0.443240	+	0.896403i	$0.646171\pi$
$822$	9.59702	+	7.87898i	0.334734	+	0.274811i
$823$	12.3335	−	46.0291i	0.429917	−	1.60447i	−0.323027	−	0.946390i	$-0.604700\pi$
$823$	12.3335	−	46.0291i	0.429917	−	1.60447i	0.752944	−	0.658084i	$-0.228633\pi$
$824$	−15.9275	+	1.24228i	−0.554860	+	0.0432767i
$825$	−10.5824	−	26.6900i	−0.368433	−	0.929226i
$826$	57.6994	+	1.02065i	2.00762	+	0.0355128i
$827$	7.06339	−	17.0525i	0.245618	−	0.592975i	−0.752204	−	0.658930i	$-0.771009\pi$
$827$	7.06339	−	17.0525i	0.245618	−	0.592975i	0.997823	+	0.0659550i	$0.0210094\pi$
$828$	−17.0392	+	25.4810i	−0.592153	+	0.885525i
$829$	−41.9688	+	17.3840i	−1.45764	+	0.603773i	−0.964002	−	0.265896i	$-0.914332\pi$
$829$	−41.9688	+	17.3840i	−1.45764	+	0.603773i	−0.493635	+	0.869669i	$0.664332\pi$
$830$	9.61835	+	4.18485i	0.333858	+	0.145258i
$831$	0.936276	+	8.05748i	0.0324791	+	0.279511i
$832$	0.378703	+	15.2815i	0.0131292	+	0.529792i
$833$	−74.6920	+	43.1234i	−2.58792	+	1.49414i
$834$	25.1399	+	26.8514i	0.870524	+	0.929786i
$835$	1.91533	+	0.252158i	0.0662827	+	0.00872628i
$836$	27.6852	−	6.37800i	0.957513	−	0.220588i
$837$	37.3276	−	19.3356i	1.29023	−	0.668338i
$838$	36.7763	−	20.3742i	1.27042	−	0.703815i
$839$	44.2150	−	11.8474i	1.52647	−	0.409017i	0.604605	−	0.796525i	$-0.293331\pi$
$839$	44.2150	−	11.8474i	1.52647	−	0.409017i	0.921866	+	0.387509i	$0.126664\pi$
$840$	4.04556	+	20.6436i	0.139585	+	0.712273i
$841$	−23.4708	−	6.28898i	−0.809338	−	0.216861i
$842$	−1.29251	+	0.321939i	−0.0445429	+	0.0110947i
$843$	−14.6903	−	4.17687i	−0.505961	−	0.143859i
$844$	3.83267	+	39.9999i	0.131926	+	1.37685i
$845$	−8.73722	+	3.61908i	−0.300570	+	0.124500i
$846$	−44.7128	−	21.0950i	−1.53726	−	0.725260i
$847$	27.0631			0.929900
$848$	−2.97301	−	1.48576i	−0.102094	−	0.0510213i
$849$	38.0248	+	16.4327i	1.30501	+	0.563970i
$850$	−6.51653	+	43.5335i	−0.223515	+	1.49319i
$851$	17.5335	−	22.8501i	0.601040	−	0.783291i
$852$	0.266797	+	0.172590i	0.00914031	+	0.00591285i
$853$	14.3688	−	11.0256i	0.491978	−	0.377508i	−0.332770	−	0.943008i	$-0.607983\pi$
$853$	14.3688	−	11.0256i	0.491978	−	0.377508i	0.824748	+	0.565500i	$0.191317\pi$
$854$	−15.4268	+	53.7521i	−0.527894	+	1.83936i
$855$	−5.44108	+	8.79476i	−0.186081	+	0.300774i
$856$	11.5159	+	0.611624i	0.393604	+	0.0209049i
$857$	14.7229	+	54.9466i	0.502925	+	1.87694i	0.480123	+	0.877201i	$0.340592\pi$
$857$	14.7229	+	54.9466i	0.502925	+	1.87694i	0.0228014	+	0.999740i	$0.492741\pi$
$858$	−15.8606	+	11.3612i	−0.541471	+	0.387864i
$859$	3.42607	+	26.0236i	0.116896	+	0.887913i	0.944939	+	0.327248i	$0.106121\pi$
$859$	3.42607	+	26.0236i	0.116896	+	0.887913i	−0.828043	+	0.560665i	$0.810546\pi$
$860$	−3.93155	−	0.139134i	−0.134065	−	0.00474443i
$861$	−6.28438	+	10.5121i	−0.214171	+	0.358251i
$862$	5.42721	+	2.36133i	0.184851	+	0.0804271i
$863$	−15.1328			−0.515127			−0.257563	−	0.966261i	$-0.582920\pi$
$863$	−15.1328			−0.515127			−0.257563	+	0.966261i	$0.582920\pi$
$864$	25.4088	+	14.7781i	0.864425	+	0.502762i
$865$	10.0230			0.340791
$866$	−44.7347	−	19.4636i	−1.52015	−	0.661401i
$867$	39.3378	−	65.8017i	1.33598	−	2.23474i
$868$	−2.42917	+	68.6418i	−0.0824515	+	2.32986i
$869$	0.538777	+	4.09241i	0.0182767	+	0.138826i
$870$	4.36761	−	3.12859i	0.148076	−	0.106069i
$871$	0.546918	+	2.04113i	0.0185316	+	0.0691609i
$872$	−18.3785	−	20.4402i	−0.622374	−	0.692192i
$873$	46.4321	+	1.41372i	1.57149	+	0.0478473i
$874$	6.79219	−	23.6663i	0.229749	−	0.800524i
$875$	−30.5808	+	23.4654i	−1.03382	+	0.793277i
$876$	2.92032	−	4.51433i	0.0986684	−	0.152525i
$877$	26.0934	−	34.0056i	0.881112	−	1.14829i	−0.106955	−	0.994264i	$-0.534110\pi$
$877$	26.0934	−	34.0056i	0.881112	−	1.14829i	0.988067	−	0.154024i	$-0.0492233\pi$
$878$	8.39741	−	56.0986i	0.283399	−	1.89324i
$879$	8.98613	+	3.88343i	0.303095	+	0.130985i
$880$	−12.7396	+	11.0535i	−0.429453	+	0.372613i
$881$	27.9352			0.941161			0.470581	−	0.882357i	$-0.344044\pi$
$881$	27.9352			0.941161			0.470581	+	0.882357i	$0.344044\pi$
$882$	−38.4157	+	26.6426i	−1.29352	+	0.897103i
$883$	43.8533	−	18.1646i	1.47578	−	0.611288i	0.507611	−	0.861586i	$-0.330529\pi$
$883$	43.8533	−	18.1646i	1.47578	−	0.611288i	0.968169	+	0.250298i	$0.0805286\pi$
$884$	29.7749	−	2.85294i	1.00144	−	0.0959549i
$885$	−16.2007	−	4.60632i	−0.544580	−	0.154840i
$886$	54.7818	−	13.6450i	1.84043	−	0.458414i
$887$	38.1927	+	10.2337i	1.28239	+	0.343615i	0.834764	−	0.550608i	$-0.185604\pi$
$887$	38.1927	+	10.2337i	1.28239	+	0.343615i	0.447623	+	0.894222i	$0.352271\pi$
$888$	−22.9206	−	15.4091i	−0.769165	−	0.517095i
$889$	−11.1824	+	2.99631i	−0.375045	+	0.100493i
$890$	−11.4025	+	6.31702i	−0.382213	+	0.211747i
$891$	2.62485	+	37.4235i	0.0879357	+	1.25374i
$892$	−3.82285	−	16.5940i	−0.127999	−	0.555608i
$893$	39.3716	+	5.18337i	1.31752	+	0.173455i
$894$	6.30900	+	6.73849i	0.211004	+	0.225369i
$895$	7.55116	−	4.35966i	0.252407	−	0.145727i
$896$	−41.4201	+	24.3070i	−1.38375	+	0.812041i
$897$	1.95158	+	16.7951i	0.0651614	+	0.560771i
$898$	−6.06350	−	2.63817i	−0.202342	−	0.0880369i
$899$	16.2064	−	6.71289i	0.540512	−	0.223887i
$900$	−1.56917	+	23.8087i	−0.0523055	+	0.793623i
$901$	−2.48876	+	6.00840i	−0.0829126	+	0.200169i
$902$	−9.81814	−	0.173673i	−0.326908	−	0.00578269i
$903$	−5.26948	−	13.2902i	−0.175357	−	0.442270i
$904$	−23.5525	−	20.1443i	−0.783345	−	0.669991i
$905$	−3.80559	+	14.2026i	−0.126502	+	0.472112i
$906$	−9.04240	−	7.42365i	−0.300414	−	0.246634i
$907$	−2.79171	−	3.63823i	−0.0926973	−	0.120805i	0.744702	−	0.667397i	$-0.232592\pi$
$907$	−2.79171	−	3.63823i	−0.0926973	−	0.120805i	−0.837399	+	0.546592i	$0.815925\pi$
$908$	−24.1781	+	17.2290i	−0.802379	+	0.571765i
$909$	−26.3214	−	11.8536i	−0.873025	−	0.393158i
$910$	9.07931	+	7.22547i	0.300976	+	0.239522i
$911$	31.8098	+	18.3654i	1.05391	+	0.608473i	0.923740	−	0.383019i	$-0.125116\pi$
$911$	31.8098	+	18.3654i	1.05391	+	0.608473i	0.130166	+	0.991492i	$0.458449\pi$
$912$	−23.0572	−	5.08024i	−0.763499	−	0.168224i
$913$	−26.4688	+	15.2818i	−0.875989	+	0.505753i
$914$	−6.95453	−	1.04103i	−0.230036	−	0.0344340i
$915$	8.37487	−	14.0089i	0.276865	−	0.463121i
$916$	3.55245	+	2.93120i	0.117376	+	0.0968497i
$917$	3.85248	−	9.30072i	0.127220	−	0.307137i
$918$	25.3302	−	51.6384i	0.836020	−	1.70432i
$919$	3.75554	+	3.75554i	0.123884	+	0.123884i	0.766330	−	0.642447i	$-0.222081\pi$
$919$	3.75554	+	3.75554i	0.123884	+	0.123884i	−0.642447	+	0.766330i	$0.722081\pi$
$920$	3.02906	+	14.2999i	0.0998651	+	0.471455i
$921$	−2.74011	+	18.6190i	−0.0902897	+	0.613517i
$922$	−33.2497	−	19.9890i	−1.09502	−	0.658304i
$923$	0.173772	−	0.0228775i	0.00571978	−	0.000753023i
$924$	−55.3706	−	26.2904i	−1.82156	−	0.864892i
$925$	2.92631	−	22.2276i	0.0962166	−	0.730838i
$926$	−48.2868	+	5.49014i	−1.58680	+	0.180417i
$927$	3.88553	+	16.4935i	0.127618	+	0.541716i
$928$	10.0390	+	7.04689i	0.329546	+	0.231325i
$929$	−42.0905	−	24.3010i	−1.38094	−	0.797288i	−0.388673	−	0.921376i	$-0.627066\pi$
$929$	−42.0905	−	24.3010i	−1.38094	−	0.797288i	−0.992271	+	0.124087i	$0.960400\pi$
$930$	5.82262	−	19.1821i	0.190931	−	0.629006i
$931$	22.8599	−	29.7916i	0.749204	−	0.976381i
$932$	0.112131	−	3.16851i	0.00367296	−	0.103788i
$933$	32.2178	−	31.2518i	1.05476	−	1.02314i
$934$	−14.0736	−	0.248948i	−0.460502	−	0.00814583i
$935$	23.3370	+	23.3370i	0.763200	+	0.763200i
$936$	15.9565	−	2.87558i	0.521553	−	0.0939911i
$937$	5.70289	−	5.70289i	0.186305	−	0.186305i	−0.607791	−	0.794097i	$-0.707944\pi$
$937$	5.70289	−	5.70289i	0.186305	−	0.186305i	0.794097	+	0.607791i	$0.207944\pi$
$938$	−4.77672	+	4.61067i	−0.155965	+	0.150544i
$939$	−6.44641	+	22.6724i	−0.210371	+	0.739886i
$940$	−22.0864	+	8.24600i	−0.720379	+	0.268955i
$941$	31.4181	+	24.1080i	1.02420	+	0.785897i	0.977054	−	0.212991i	$-0.0683206\pi$
$941$	31.4181	+	24.1080i	1.02420	+	0.785897i	0.0471465	+	0.998888i	$0.484987\pi$
$942$	1.63533	−	49.6789i	0.0532818	−	1.61863i
$943$	−4.25508	+	7.37001i	−0.138564	+	0.240001i
$944$	−2.31152	−	38.3823i	−0.0752337	−	1.24924i
$945$	20.9822	−	7.58884i	0.682550	−	0.246865i
$946$	7.13788	−	8.96923i	0.232072	−	0.291615i
$947$	−24.5086	−	3.22662i	−0.796424	−	0.104851i	−0.278677	−	0.960385i	$-0.589896\pi$
$947$	−24.5086	−	3.22662i	−0.796424	−	0.104851i	−0.517747	+	0.855534i	$0.673229\pi$
$948$	1.05426	−	3.26429i	0.0342408	−	0.106019i
$949$	−0.387099	−	2.94031i	−0.0125658	−	0.0954466i
$950$	−4.63220	−	18.5973i	−0.150288	−	0.603375i
$951$	−23.9816	+	30.2877i	−0.777658	+	0.982146i
$952$	53.1730	+	77.4837i	1.72335	+	2.51126i
$953$	−15.9824	+	15.9824i	−0.517721	+	0.517721i	−0.916881	−	0.399160i	$-0.869302\pi$
$953$	−15.9824	+	15.9824i	−0.517721	+	0.517721i	0.399160	+	0.916881i	$0.369302\pi$
$954$	−1.07514	+	3.35725i	−0.0348090	+	0.108695i
$955$	−7.74485	−	3.20802i	−0.250618	−	0.103809i
$956$	−30.8421	−	9.44515i	−0.997505	−	0.305478i
$957$	−0.238232	+	15.6525i	−0.00770096	+	0.505975i
$958$	−9.01362	−	12.1872i	−0.291217	−	0.393749i
$959$	10.7591	+	18.6354i	0.347430	+	0.601767i
$960$	13.5038	−	3.75704i	0.435835	−	0.121258i
$961$	17.2263	−	29.8368i	0.555686	−	0.962477i
$962$	−15.1368	+	1.72103i	−0.488030	+	0.0554884i
$963$	−1.22675	−	12.1700i	−0.0395314	−	0.392172i
$964$	−1.21608	−	5.27868i	−0.0391673	−	0.170015i
$965$	4.01420	−	3.08020i	0.129222	−	0.0991553i
$966$	−43.1848	+	30.9340i	−1.38945	+	0.995284i
$967$	−2.99445	−	0.802360i	−0.0962949	−	0.0258022i	0.210350	−	0.977626i	$-0.432540\pi$
$967$	−2.99445	−	0.802360i	−0.0962949	−	0.0258022i	−0.306645	+	0.951824i	$0.599206\pi$
$968$	−1.40220	−	17.9779i	−0.0450684	−	0.577831i
$969$	−6.72657	+	45.7069i	−0.216089	+	1.46832i
$970$	15.9383	−	15.3842i	0.511748	−	0.493958i
$971$	−4.31202	−	1.78610i	−0.138379	−	0.0573186i	0.312419	−	0.949944i	$-0.398861\pi$
$971$	−4.31202	−	1.78610i	−0.138379	−	0.0573186i	−0.450798	+	0.892626i	$0.648861\pi$
$972$	11.3690	−	29.0301i	0.364660	−	0.931141i
$973$	24.3939	+	58.8922i	0.782034	+	1.88800i
$974$	14.5481	+	36.9577i	0.466150	+	1.18420i
$975$	7.85222	+	10.5622i	0.251472	+	0.338262i
$976$	36.5066	+	7.46292i	1.16855	+	0.238882i
$977$	−9.78381	−	16.9461i	−0.313012	−	0.542152i	0.666001	−	0.745951i	$-0.268005\pi$
$977$	−9.78381	−	16.9461i	−0.313012	−	0.542152i	−0.979013	+	0.203798i	$0.934671\pi$
$978$	−29.1655	+	46.8830i	−0.932610	+	1.49915i
$979$	4.95768	−	37.6574i	0.158448	−	1.20353i
$980$	−3.68974	+	21.9859i	−0.117865	+	0.702312i
$981$	−18.4442	+	22.5794i	−0.588877	+	0.720904i
$982$	−57.3654	−	16.4638i	−1.83060	−	0.525380i
$983$	11.9408	+	44.5635i	0.380851	+	1.42136i	0.844604	+	0.535392i	$0.179836\pi$
$983$	11.9408	+	44.5635i	0.380851	+	1.42136i	−0.463753	+	0.885965i	$0.653497\pi$
$984$	7.30874	+	3.63002i	0.232994	+	0.115721i
$985$	−0.0710969	+	0.265337i	−0.00226533	+	0.00845435i
$986$	12.3659	−	20.5694i	0.393810	−	0.655062i
$987$	−59.6536	−	61.4976i	−1.89880	−	1.95749i
$988$	−11.5017	+	6.10867i	−0.365918	+	0.194343i
$989$	−3.80165	−	9.17799i	−0.120885	−	0.291843i
$990$	13.6524	+	11.5607i	0.433903	+	0.367422i
$991$			48.5211i			1.54132i	0.637245	+	0.770662i	$0.280074\pi$
$991$			48.5211i			1.54132i	−0.637245	+	0.770662i	$0.719926\pi$
$992$	45.7243	−	1.94279i	1.45175	−	0.0616838i
$993$	19.7385	−	2.29360i	0.626381	−	0.0727853i
$994$	0.327441	+	0.442728i	0.0103858	+	0.0140425i
$995$	−7.07435	−	5.42834i	−0.224272	−	0.172090i
$996$	25.3177	−	2.03756i	0.802222	−	0.0645625i
$997$	23.5498	+	30.6908i	0.745831	+	0.971986i	0.999988	+	0.00482300i	$0.00153522\pi$
$997$	23.5498	+	30.6908i	0.745831	+	0.971986i	−0.254157	+	0.967163i	$0.581798\pi$
$998$	19.0332	−	10.5445i	0.602486	−	0.333779i
$999$	−12.4339	+	26.5243i	−0.393391	+	0.839193i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.11.17	✓	368
3.2	odd	2		864.2.bn.a.683.30		368
9.4	even	3		864.2.bn.a.395.15		368
9.5	odd	6	inner	288.2.bf.a.203.32	yes	368
32.3	odd	8	inner	288.2.bf.a.227.32	yes	368
96.35	even	8		864.2.bn.a.35.15		368
288.67	odd	24		864.2.bn.a.611.30		368
288.131	even	24	inner	288.2.bf.a.131.17	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.17	✓	368	1.1	even	1	trivial
288.2.bf.a.131.17	yes	368	288.131	even	24	inner
288.2.bf.a.203.32	yes	368	9.5	odd	6	inner
288.2.bf.a.227.32	yes	368	32.3	odd	8	inner
864.2.bn.a.35.15		368	96.35	even	8
864.2.bn.a.395.15		368	9.4	even	3
864.2.bn.a.611.30		368	288.67	odd	24
864.2.bn.a.683.30		368	3.2	odd	2

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bf (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.564220 + 1.29679i) q^{2} +(0.888753 - 1.48665i) q^{3} +(-1.36331 - 1.46335i) q^{4} +(0.132037 + 1.00292i) q^{5} +(1.42641 + 1.99132i) q^{6} +(1.09866 + 4.10026i) q^{7} +(2.66685 - 0.942277i) q^{8} +(-1.42024 - 2.64252i) q^{9} +O(q^{10})\)	\(q+(-0.564220 + 1.29679i) q^{2} +(0.888753 - 1.48665i) q^{3} +(-1.36331 - 1.46335i) q^{4} +(0.132037 + 1.00292i) q^{5} +(1.42641 + 1.99132i) q^{6} +(1.09866 + 4.10026i) q^{7} +(2.66685 - 0.942277i) q^{8} +(-1.42024 - 2.64252i) q^{9} +(-1.37507 - 0.394642i) q^{10} +(3.30700 - 2.53755i) q^{11} +(-3.38712 + 0.726212i) q^{12} +(-1.16321 + 1.51592i) q^{13} +(-5.93704 - 0.888717i) q^{14} +(1.60833 + 0.695053i) q^{15} +(-0.282759 + 3.98999i) q^{16} +7.82699 q^{17} +(4.22811 - 0.350783i) q^{18} +(-3.14843 + 1.30412i) q^{19} +(1.28761 - 1.56050i) q^{20} +(7.07207 + 2.01079i) q^{21} +(1.42479 + 5.72022i) q^{22} +(4.93477 + 1.32227i) q^{23} +(0.969340 - 4.80212i) q^{24} +(3.84122 - 1.02925i) q^{25} +(-1.30952 - 2.36375i) q^{26} +(-5.19074 - 0.237156i) q^{27} +(4.50227 - 7.19765i) q^{28} +(-2.14969 - 0.283012i) q^{29} +(-1.80879 + 1.69350i) q^{30} +(-7.00638 + 4.04514i) q^{31} +(-5.01463 - 2.61791i) q^{32} +(-0.833338 - 7.17160i) q^{33} +(-4.41614 + 10.1499i) q^{34} +(-3.96715 + 1.64325i) q^{35} +(-1.93069 + 5.68088i) q^{36} +(2.15743 - 5.20851i) q^{37} +(0.0852374 - 4.81866i) q^{38} +(1.21984 + 3.07656i) q^{39} +(1.29715 + 2.55022i) q^{40} +(-0.431132 + 1.60901i) q^{41} +(-6.59777 + 8.03644i) q^{42} +(-1.18374 - 1.54268i) q^{43} +(-8.22180 - 1.37981i) q^{44} +(2.46271 - 1.77329i) q^{45} +(-4.49900 + 5.65330i) q^{46} +(-10.0917 - 5.82647i) q^{47} +(5.68041 + 3.96648i) q^{48} +(-9.54287 + 5.50958i) q^{49} +(-0.832572 + 5.56197i) q^{50} +(6.95626 - 11.6360i) q^{51} +(3.80414 - 0.364501i) q^{52} +(-0.317971 + 0.767651i) q^{53} +(3.23626 - 6.59747i) q^{54} +(2.98160 + 2.98160i) q^{55} +(6.79355 + 9.89954i) q^{56} +(-0.859407 + 5.83965i) q^{57} +(1.57990 - 2.62800i) q^{58} +(-9.53072 + 1.25474i) q^{59} +(-1.17555 - 3.30112i) q^{60} +(1.21590 - 9.23569i) q^{61} +(-1.29254 - 11.3681i) q^{62} +(9.27466 - 8.72657i) q^{63} +(6.22423 - 5.02583i) q^{64} +(-1.67393 - 0.966444i) q^{65} +(9.77023 + 2.96570i) q^{66} +(0.673229 - 0.877369i) q^{67} +(-10.6706 - 11.4536i) q^{68} +(6.35154 - 6.16109i) q^{69} +(0.107403 - 6.07171i) q^{70} +(-0.0648614 - 0.0648614i) q^{71} +(-6.27756 - 5.70896i) q^{72} +(-1.09749 + 1.09749i) q^{73} +(5.53706 + 5.73647i) q^{74} +(1.88376 - 6.62529i) q^{75} +(6.20068 + 2.82932i) q^{76} +(14.0379 + 10.7717i) q^{77} +(-4.67790 - 0.153987i) q^{78} +(-0.495123 + 0.857578i) q^{79} +(-4.03897 + 0.243241i) q^{80} +(-4.96585 + 7.50602i) q^{81} +(-1.84329 - 1.46692i) q^{82} +(-7.26949 - 0.957047i) q^{83} +(-6.69896 - 13.0902i) q^{84} +(1.03345 + 7.84982i) q^{85} +(2.66841 - 0.664647i) q^{86} +(-2.33128 + 2.94430i) q^{87} +(6.42822 - 9.88340i) q^{88} +(6.44315 - 6.44315i) q^{89} +(0.910071 + 4.19413i) q^{90} +(-7.49364 - 3.10397i) q^{91} +(-4.79270 - 9.02394i) q^{92} +(-0.213250 + 14.0111i) q^{93} +(13.2496 - 9.79942i) q^{94} +(-1.72364 - 2.98543i) q^{95} +(-8.34868 + 5.12831i) q^{96} +(-7.74227 + 13.4100i) q^{97} +(-1.76047 - 15.4837i) q^{98} +(-11.4023 - 5.13490i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

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