LMFDB - Embedded newform 912.2.br.a.221.48

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(221,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 6, 10]))

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

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

chi := DirichletCharacter("912.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.br (of order $12$, degree $4$, 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$624$
Relative dimension:	$156$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			221.48
Character	$\chi$	$=$	912.221
Dual form			912.2.br.a.293.48

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.788971 - 1.17368i) q^{2} +(-0.920267 - 1.46735i) q^{3} +(-0.755049 + 1.85200i) q^{4} +(-0.395182 + 1.47484i) q^{5} +(-0.996132 + 2.23779i) q^{6} -2.65158i q^{7} +(2.76937 - 0.574988i) q^{8} +(-1.30622 + 2.70070i) q^{9} +O(q^{10})$	\(q+(-0.788971 - 1.17368i) q^{2} +(-0.920267 - 1.46735i) q^{3} +(-0.755049 + 1.85200i) q^{4} +(-0.395182 + 1.47484i) q^{5} +(-0.996132 + 2.23779i) q^{6} -2.65158i q^{7} +(2.76937 - 0.574988i) q^{8} +(-1.30622 + 2.70070i) q^{9} +(2.04278 - 0.699789i) q^{10} +(-1.98405 - 1.98405i) q^{11} +(3.41237 - 0.596414i) q^{12} +(0.498355 + 1.85989i) q^{13} +(-3.11211 + 2.09202i) q^{14} +(2.52778 - 0.777377i) q^{15} +(-2.85980 - 2.79670i) q^{16} +(-4.07258 + 2.35130i) q^{17} +(4.20033 - 0.597696i) q^{18} +(1.44001 + 4.11417i) q^{19} +(-2.43302 - 1.84545i) q^{20} +(-3.89080 + 2.44017i) q^{21} +(-0.763282 + 3.89400i) q^{22} +(0.221500 - 0.383649i) q^{23} +(-3.39226 - 3.53448i) q^{24} +(2.31114 + 1.33434i) q^{25} +(1.78972 - 2.05231i) q^{26} +(5.16494 - 0.568694i) q^{27} +(4.91073 + 2.00208i) q^{28} +(-3.98513 + 1.06781i) q^{29} +(-2.90673 - 2.35347i) q^{30} +1.03467i q^{31} +(-1.02613 + 5.56301i) q^{32} +(-1.08544 + 4.73715i) q^{33} +(5.97283 + 2.92479i) q^{34} +(3.91066 + 1.04786i) q^{35} +(-4.01544 - 4.45828i) q^{36} +(2.98944 + 2.98944i) q^{37} +(3.69259 - 4.93607i) q^{38} +(2.27048 - 2.44285i) q^{39} +(-0.246389 + 4.31160i) q^{40} +(3.48491 - 2.01201i) q^{41} +(5.93370 + 2.64133i) q^{42} +(6.46906 + 1.73338i) q^{43} +(5.17252 - 2.17641i) q^{44} +(-3.46691 - 2.99373i) q^{45} +(-0.625038 + 0.0427180i) q^{46} +(2.11963 + 1.22377i) q^{47} +(-1.47195 + 6.77003i) q^{48} -0.0309000 q^{49} +(-0.257338 - 3.76530i) q^{50} +(7.19804 + 3.81206i) q^{51} +(-3.82079 - 0.481352i) q^{52} +(2.42058 + 9.03374i) q^{53} +(-4.74245 - 5.61330i) q^{54} +(3.71022 - 2.14210i) q^{55} +(-1.52463 - 7.34321i) q^{56} +(4.71172 - 5.89912i) q^{57} +(4.39742 + 3.83480i) q^{58} +(-6.18435 - 1.65709i) q^{59} +(-0.468893 + 5.26840i) q^{60} +(-2.42499 + 0.649774i) q^{61} +(1.21437 - 0.816324i) q^{62} +(7.16114 + 3.46354i) q^{63} +(7.33878 - 3.18470i) q^{64} -2.93997 q^{65} +(6.41628 - 2.46352i) q^{66} +(1.35855 + 5.07017i) q^{67} +(-1.27962 - 9.31776i) q^{68} +(-0.766785 + 0.0280423i) q^{69} +(-1.85555 - 5.41660i) q^{70} +(9.01111 - 5.20256i) q^{71} +(-2.06452 + 8.23029i) q^{72} +(12.4359 - 7.17988i) q^{73} +(1.15007 - 5.86724i) q^{74} +(-0.168930 - 4.61920i) q^{75} +(-8.70671 - 0.439509i) q^{76} +(-5.26088 + 5.26088i) q^{77} +(-4.65847 - 0.737476i) q^{78} +(-9.36522 + 5.40701i) q^{79} +(5.25483 - 3.11254i) q^{80} +(-5.58759 - 7.05541i) q^{81} +(-5.11095 - 2.50275i) q^{82} +(-2.23882 + 2.23882i) q^{83} +(-1.58144 - 9.04820i) q^{84} +(-1.85839 - 6.93560i) q^{85} +(-3.06947 - 8.96019i) q^{86} +(5.23424 + 4.86490i) q^{87} +(-6.63537 - 4.35376i) q^{88} +(0.103026 + 0.0594823i) q^{89} +(-0.778389 + 6.43101i) q^{90} +(4.93164 - 1.32143i) q^{91} +(0.543274 + 0.699891i) q^{92} +(1.51822 - 0.952172i) q^{93} +(-0.236013 - 3.45328i) q^{94} +(-6.63681 + 0.497932i) q^{95} +(9.10718 - 3.61376i) q^{96} +(-3.17401 + 1.83252i) q^{97} +(0.0243792 + 0.0362667i) q^{98} +(7.94994 - 2.76673i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 624 q - 6 q^{3} - 4 q^{4} - 2 q^{6}+O(q^{10}) $ 624 * q - 6 * q^3 - 4 * q^4 - 2 * q^6	$ 624 q - 6 q^{3} - 4 q^{4} - 2 q^{6} - 24 q^{10} - 12 q^{13} - 12 q^{15} + 12 q^{21} - 12 q^{22} + 14 q^{24} + 12 q^{28} - 56 q^{30} - 12 q^{33} - 12 q^{34} - 18 q^{36} - 12 q^{40} + 30 q^{42} - 4 q^{43} + 12 q^{45} - 6 q^{48} - 560 q^{49} - 6 q^{51} + 36 q^{52} + 20 q^{54} - 16 q^{58} - 48 q^{60} + 28 q^{61} + 24 q^{63} - 64 q^{64} + 2 q^{66} - 12 q^{67} + 144 q^{70} + 126 q^{72} + 4 q^{76} - 18 q^{78} - 24 q^{79} - 4 q^{81} + 20 q^{82} - 60 q^{85} - 114 q^{90} + 72 q^{91} + 4 q^{93} + 24 q^{96} - 24 q^{97} - 52 q^{99}+O(q^{100}) $ 624 * q - 6 * q^3 - 4 * q^4 - 2 * q^6 - 24 * q^10 - 12 * q^13 - 12 * q^15 + 12 * q^21 - 12 * q^22 + 14 * q^24 + 12 * q^28 - 56 * q^30 - 12 * q^33 - 12 * q^34 - 18 * q^36 - 12 * q^40 + 30 * q^42 - 4 * q^43 + 12 * q^45 - 6 * q^48 - 560 * q^49 - 6 * q^51 + 36 * q^52 + 20 * q^54 - 16 * q^58 - 48 * q^60 + 28 * q^61 + 24 * q^63 - 64 * q^64 + 2 * q^66 - 12 * q^67 + 144 * q^70 + 126 * q^72 + 4 * q^76 - 18 * q^78 - 24 * q^79 - 4 * q^81 + 20 * q^82 - 60 * q^85 - 114 * q^90 + 72 * q^91 + 4 * q^93 + 24 * q^96 - 24 * q^97 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−0.788971	−	1.17368i	−0.557887	−	0.829917i
$2$	−0.788971	−	1.17368i	−0.557887	−	0.829917i
$3$	−0.920267	−	1.46735i	−0.531316	−	0.847173i
$3$	−0.920267	−	1.46735i	−0.531316	−	0.847173i
$4$	−0.755049	+	1.85200i	−0.377525	+	0.926000i
$5$	−0.395182	+	1.47484i	−0.176731	+	0.659569i	0.819519	+	0.573051i	$0.194240\pi$
$5$	−0.395182	+	1.47484i	−0.176731	+	0.659569i	−0.996250	+	0.0865173i	$0.972426\pi$
$6$	−0.996132	+	2.23779i	−0.406669	+	0.913575i
$7$		−	2.65158i		−	1.00220i	−0.865388	−	0.501102i	$-0.832928\pi$
$7$		−	2.65158i		−	1.00220i	0.865388	−	0.501102i	$-0.167072\pi$
$8$	2.76937	−	0.574988i	0.979119	−	0.203289i
$9$	−1.30622	+	2.70070i	−0.435406	+	0.900234i
$10$	2.04278	−	0.699789i	0.645983	−	0.221293i
$11$	−1.98405	−	1.98405i	−0.598214	−	0.598214i	0.341623	−	0.939837i	$-0.389023\pi$
$11$	−1.98405	−	1.98405i	−0.598214	−	0.598214i	−0.939837	+	0.341623i	$0.889023\pi$
$12$	3.41237	−	0.596414i	0.985067	−	0.172170i
$13$	0.498355	+	1.85989i	0.138219	+	0.515839i	0.999964	+	0.00849800i	$0.00270503\pi$
$13$	0.498355	+	1.85989i	0.138219	+	0.515839i	−0.861745	+	0.507341i	$0.830628\pi$
$14$	−3.11211	+	2.09202i	−0.831747	+	0.559117i
$15$	2.52778	−	0.777377i	0.652669	−	0.200718i
$16$	−2.85980	−	2.79670i	−0.714950	−	0.699175i
$17$	−4.07258	+	2.35130i	−0.987745	+	0.570275i	−0.904600	−	0.426262i	$-0.859830\pi$
$17$	−4.07258	+	2.35130i	−0.987745	+	0.570275i	−0.0831459	+	0.996537i	$0.526497\pi$
$18$	4.20033	−	0.597696i	0.990027	−	0.140878i
$19$	1.44001	+	4.11417i	0.330360	+	0.943855i
$19$	1.44001	+	4.11417i	0.330360	+	0.943855i
$20$	−2.43302	−	1.84545i	−0.544040	−	0.412656i
$21$	−3.89080	+	2.44017i	−0.849041	+	0.532488i
$22$	−0.763282	+	3.89400i	−0.162732	+	0.830204i
$23$	0.221500	−	0.383649i	0.0461859	−	0.0799963i	−0.842008	−	0.539465i	$-0.818627\pi$
$23$	0.221500	−	0.383649i	0.0461859	−	0.0799963i	0.888194	+	0.459468i	$0.151960\pi$
$24$	−3.39226	−	3.53448i	−0.692443	−	0.721473i
$25$	2.31114	+	1.33434i	0.462228	+	0.266868i
$26$	1.78972	−	2.05231i	0.350994	−	0.402490i
$27$	5.16494	−	0.568694i	0.993993	−	0.109445i
$28$	4.91073	+	2.00208i	0.928041	+	0.378357i
$29$	−3.98513	+	1.06781i	−0.740020	+	0.198288i	−0.609087	−	0.793103i	$-0.708464\pi$
$29$	−3.98513	+	1.06781i	−0.740020	+	0.198288i	−0.130933	+	0.991391i	$0.541797\pi$
$30$	−2.90673	−	2.35347i	−0.530695	−	0.429683i
$31$			1.03467i			0.185832i	0.995674	+	0.0929161i	$0.0296188\pi$
$31$			1.03467i			0.185832i	−0.995674	+	0.0929161i	$0.970381\pi$
$32$	−1.02613	+	5.56301i	−0.181396	+	0.983410i
$33$	−1.08544	+	4.73715i	−0.188950	+	0.824632i
$34$	5.97283	+	2.92479i	1.02433	+	0.501598i
$35$	3.91066	+	1.04786i	0.661023	+	0.177121i
$36$	−4.01544	−	4.45828i	−0.669240	−	0.743046i
$37$	2.98944	+	2.98944i	0.491462	+	0.491462i	0.908767	−	0.417305i	$-0.137025\pi$
$37$	2.98944	+	2.98944i	0.491462	+	0.491462i	−0.417305	+	0.908767i	$0.637025\pi$
$38$	3.69259	−	4.93607i	0.599018	−	0.800736i
$39$	2.27048	−	2.44285i	0.363568	−	0.391169i
$40$	−0.246389	+	4.31160i	−0.0389575	+	0.681723i
$41$	3.48491	−	2.01201i	0.544252	−	0.314224i	−0.202549	−	0.979272i	$-0.564922\pi$
$41$	3.48491	−	2.01201i	0.544252	−	0.314224i	0.746800	+	0.665048i	$0.231589\pi$
$42$	5.93370	+	2.64133i	0.915590	+	0.407566i
$43$	6.46906	+	1.73338i	0.986522	+	0.264338i	0.715789	−	0.698317i	$-0.246067\pi$
$43$	6.46906	+	1.73338i	0.986522	+	0.264338i	0.270733	+	0.962654i	$0.412734\pi$
$44$	5.17252	−	2.17641i	0.779787	−	0.328106i
$45$	−3.46691	−	2.99373i	−0.516817	−	0.446279i
$46$	−0.625038	+	0.0427180i	−0.0921568	+	0.00629843i
$47$	2.11963	+	1.22377i	0.309179	+	0.178505i	0.646559	−	0.762864i	$-0.276207\pi$
$47$	2.11963	+	1.22377i	0.309179	+	0.178505i	−0.337380	+	0.941369i	$0.609541\pi$
$48$	−1.47195	+	6.77003i	−0.212458	+	0.977170i
$49$	−0.0309000			−0.00441429
$50$	−0.257338	−	3.76530i	−0.0363931	−	0.532493i
$51$	7.19804	+	3.81206i	1.00793	+	0.533795i
$52$	−3.82079	−	0.481352i	−0.529848	−	0.0667515i
$53$	2.42058	+	9.03374i	0.332493	+	1.24088i	0.906562	+	0.422073i	$0.138697\pi$
$53$	2.42058	+	9.03374i	0.332493	+	1.24088i	−0.574069	+	0.818807i	$0.694636\pi$
$54$	−4.74245	−	5.61330i	−0.645366	−	0.763874i
$55$	3.71022	−	2.14210i	0.500286	−	0.288840i
$56$	−1.52463	−	7.34321i	−0.203737	−	0.981277i
$57$	4.71172	−	5.89912i	0.624083	−	0.781358i
$58$	4.39742	+	3.83480i	0.577410	+	0.503533i
$59$	−6.18435	−	1.65709i	−0.805133	−	0.215735i	−0.167297	−	0.985907i	$-0.553504\pi$
$59$	−6.18435	−	1.65709i	−0.805133	−	0.215735i	−0.637837	+	0.770172i	$0.720170\pi$
$60$	−0.468893	+	5.26840i	−0.0605339	+	0.680147i
$61$	−2.42499	+	0.649774i	−0.310488	+	0.0831950i	−0.410698	−	0.911771i	$-0.634715\pi$
$61$	−2.42499	+	0.649774i	−0.310488	+	0.0831950i	0.100210	+	0.994966i	$0.468048\pi$
$62$	1.21437	−	0.816324i	0.154225	−	0.103673i
$63$	7.16114	+	3.46354i	0.902219	+	0.436366i
$64$	7.33878	−	3.18470i	0.917347	−	0.398088i
$65$	−2.93997			−0.364659
$66$	6.41628	−	2.46352i	0.789789	−	0.303239i
$67$	1.35855	+	5.07017i	0.165973	+	0.619420i	0.997914	+	0.0645558i	$0.0205631\pi$
$67$	1.35855	+	5.07017i	0.165973	+	0.619420i	−0.831941	+	0.554864i	$0.812770\pi$
$68$	−1.27962	−	9.31776i	−0.155176	−	1.12994i
$69$	−0.766785	+	0.0280423i	−0.0923101	+	0.00337589i
$70$	−1.85555	−	5.41660i	−0.221781	−	0.647407i
$71$	9.01111	−	5.20256i	1.06942	−	0.617431i	0.141398	−	0.989953i	$-0.454840\pi$
$71$	9.01111	−	5.20256i	1.06942	−	0.617431i	0.928023	+	0.372522i	$0.121507\pi$
$72$	−2.06452	+	8.23029i	−0.243306	+	0.969950i
$73$	12.4359	−	7.17988i	1.45551	−	0.840341i	0.456728	−	0.889606i	$-0.349021\pi$
$73$	12.4359	−	7.17988i	1.45551	−	0.840341i	0.998786	+	0.0492647i	$0.0156878\pi$
$74$	1.15007	−	5.86724i	0.133692	−	0.682052i
$75$	−0.168930	−	4.61920i	−0.0195063	−	0.533379i
$76$	−8.70671	−	0.439509i	−0.998728	−	0.0504152i
$77$	−5.26088	+	5.26088i	−0.599533	+	0.599533i
$78$	−4.65847	−	0.737476i	−0.527468	−	0.0835028i
$79$	−9.36522	+	5.40701i	−1.05367	+	0.608336i	−0.923674	−	0.383178i	$-0.874829\pi$
$79$	−9.36522	+	5.40701i	−1.05367	+	0.608336i	−0.129995	+	0.991515i	$0.541496\pi$
$80$	5.25483	−	3.11254i	0.587508	−	0.347993i
$81$	−5.58759	−	7.05541i	−0.620844	−	0.783934i
$82$	−5.11095	−	2.50275i	−0.564410	−	0.276382i
$83$	−2.23882	+	2.23882i	−0.245743	+	0.245743i	−0.819221	−	0.573478i	$-0.805594\pi$
$83$	−2.23882	+	2.23882i	−0.245743	+	0.245743i	0.573478	+	0.819221i	$0.305594\pi$
$84$	−1.58144	−	9.04820i	−0.172550	−	0.987239i
$85$	−1.85839	−	6.93560i	−0.201570	−	0.752271i
$86$	−3.06947	−	8.96019i	−0.330989	−	0.966202i
$87$	5.23424	+	4.86490i	0.561169	+	0.521572i
$88$	−6.63537	−	4.35376i	−0.707333	−	0.464113i
$89$	0.103026	+	0.0594823i	0.0109208	+	0.00630511i	0.505450	−	0.862856i	$-0.331326\pi$
$89$	0.103026	+	0.0594823i	0.0109208	+	0.00630511i	−0.494530	+	0.869161i	$0.664660\pi$
$90$	−0.778389	+	6.43101i	−0.0820494	+	0.677888i
$91$	4.93164	−	1.32143i	0.516977	−	0.138523i
$92$	0.543274	+	0.699891i	0.0566402	+	0.0729687i
$93$	1.51822	−	0.952172i	0.157432	−	0.0987357i
$94$	−0.236013	−	3.45328i	−0.0243429	−	0.356178i
$95$	−6.63681	+	0.497932i	−0.680922	+	0.0510868i
$96$	9.10718	−	3.61376i	0.929498	−	0.368828i
$97$	−3.17401	+	1.83252i	−0.322272	+	0.186064i	−0.652405	−	0.757871i	$-0.726240\pi$
$97$	−3.17401	+	1.83252i	−0.322272	+	0.186064i	0.330133	+	0.943935i	$0.392906\pi$
$98$	0.0243792	+	0.0362667i	0.00246267	+	0.00366349i
$99$	7.94994	−	2.76673i	0.798999	−	0.278067i
$100$	−4.21622	+	3.27274i	−0.421622	+	0.327274i
$101$	12.4407	−	3.33348i	1.23790	−	0.331694i	0.420249	−	0.907409i	$-0.361943\pi$
$101$	12.4407	−	3.33348i	1.23790	−	0.331694i	0.817651	+	0.575715i	$0.195276\pi$
$102$	−1.20491	−	11.4558i	−0.119304	−	1.13429i
$103$	1.81725			0.179059			0.0895293	−	0.995984i	$-0.471464\pi$
$103$	1.81725			0.179059			0.0895293	+	0.995984i	$0.471464\pi$
$104$	2.44954	+	4.86416i	0.240197	+	0.476970i
$105$	−2.06128	−	6.70261i	−0.201160	−	0.654108i
$106$	8.69295	−	9.96835i	0.844334	−	0.968212i
$107$	−6.28341	+	6.28341i	−0.607440	+	0.607440i	−0.942276	−	0.334836i	$-0.891319\pi$
$107$	−6.28341	+	6.28341i	−0.607440	+	0.607440i	0.334836	+	0.942276i	$0.391319\pi$
$108$	−2.84656	+	9.99485i	−0.273911	+	0.961755i
$109$	12.3884	+	3.31945i	1.18659	+	0.317946i	0.797537	−	0.603269i	$-0.206136\pi$
$109$	12.3884	+	3.31945i	1.18659	+	0.317946i	0.389053	+	0.921215i	$0.372802\pi$
$110$	−5.44140	−	2.66456i	−0.518817	−	0.254056i
$111$	1.63547	−	7.13764i	0.155232	−	0.677475i
$112$	−7.41569	+	7.58301i	−0.700717	+	0.716527i
$113$	−15.6281			−1.47017			−0.735084	−	0.677976i	$-0.762857\pi$
$113$	−15.6281			−1.47017			−0.735084	+	0.677976i	$0.762857\pi$
$114$	−10.6411	−	0.875819i	−0.996630	−	0.0820280i
$115$	0.478288	+	0.478288i	0.0446006	+	0.0446006i
$116$	1.03138	−	8.18671i	0.0957614	−	0.760117i
$117$	−5.67396	−	1.08351i	−0.524558	−	0.100170i
$118$	2.93438	+	8.56584i	0.270131	+	0.788549i
$119$	6.23468	+	10.7988i	0.571532	+	0.989923i
$120$	6.55336	−	3.60628i	0.598237	−	0.329207i
$121$		−	3.12707i		−	0.284279i
$122$	2.67587	+	2.33351i	0.242262	+	0.211266i
$123$	−6.15937	−	3.26198i	−0.555372	−	0.294123i
$124$	−1.91621	−	0.781226i	−0.172080	−	0.0701562i
$125$	−8.27955	+	8.27955i	−0.740545	+	0.740545i
$126$	−1.58484	−	11.1375i	−0.141189	−	0.992210i
$127$	11.3070	+	6.52810i	1.00333	+	0.579275i	0.909233	−	0.416288i	$-0.136669\pi$
$127$	11.3070	+	6.52810i	1.00333	+	0.579275i	0.0941005	+	0.995563i	$0.470002\pi$
$128$	−9.52791	−	6.10074i	−0.842156	−	0.539234i
$129$	−3.40979	−	11.0875i	−0.300215	−	0.976202i
$130$	2.31956	+	3.45059i	0.203438	+	0.302637i
$131$	−2.81413	−	0.754043i	−0.245871	−	0.0658810i	0.133779	−	0.991011i	$-0.457289\pi$
$131$	−2.81413	−	0.754043i	−0.245871	−	0.0658810i	−0.379650	+	0.925130i	$0.623956\pi$
$132$	−7.95364	−	5.58701i	−0.692276	−	0.486287i
$133$	10.9091	−	3.81830i	0.945936	−	0.331088i
$134$	4.87890	−	5.59472i	0.421473	−	0.483310i
$135$	−1.20236	+	7.84220i	−0.103483	+	0.674949i
$136$	−9.92649	+	8.85331i	−0.851190	+	0.759165i
$137$	1.25447	−	2.17280i	0.107176	−	0.185635i	−0.807449	−	0.589937i	$-0.799152\pi$
$137$	1.25447	−	2.17280i	0.107176	−	0.185635i	0.914625	+	0.404303i	$0.132486\pi$
$138$	0.637884	+	0.877835i	0.0543003	+	0.0747263i
$139$	1.54353	+	5.76053i	0.130920	+	0.488602i	0.999981	−	0.00610323i	$-0.00194273\pi$
$139$	1.54353	+	5.76053i	0.130920	+	0.488602i	−0.869061	+	0.494705i	$0.835276\pi$
$140$	−4.89338	+	6.45136i	−0.413566	+	0.545239i
$141$	−0.154931	−	4.23642i	−0.0130475	−	0.356771i
$142$	−13.2156	−	6.47148i	−1.10903	−	0.543075i
$143$	2.70135	−	4.67887i	0.225898	−	0.391267i
$144$	11.2886	−	4.07038i	0.940715	−	0.339198i
$145$		−	6.29941i		−	0.523138i
$146$	−18.2385	−	8.93107i	−1.50943	−	0.739141i
$147$	0.0284363	+	0.0453411i	0.00234538	+	0.00373967i
$148$	−7.79363	+	3.27927i	−0.640632	+	0.269554i
$149$	−4.25370	+	15.8750i	−0.348477	+	1.30053i	0.540020	+	0.841652i	$0.318417\pi$
$149$	−4.25370	+	15.8750i	−0.348477	+	1.30053i	−0.888497	+	0.458882i	$0.848250\pi$
$150$	−5.28818	+	3.84268i	−0.431778	+	0.313754i
$151$	−3.56630			−0.290221			−0.145111	−	0.989415i	$-0.546354\pi$
$151$	−3.56630			−0.290221			−0.145111	+	0.989415i	$0.546354\pi$
$152$	6.35350	+	10.5657i	0.515337	+	0.856988i
$153$	−1.03050	−	14.0701i	−0.0833112	−	1.13750i
$154$	10.3253	+	2.02391i	0.832035	+	0.163091i
$155$	−1.52597	−	0.408883i	−0.122569	−	0.0328423i
$156$	2.80984	+	6.04940i	0.224967	+	0.484339i
$157$	−5.08710	+	18.9853i	−0.405995	+	1.51519i	0.396219	+	0.918156i	$0.370322\pi$
$157$	−5.08710	+	18.9853i	−0.405995	+	1.51519i	−0.802214	+	0.597037i	$0.796345\pi$
$158$	13.7350	+	6.72579i	1.09270	+	0.535075i
$159$	11.0281	−	11.8653i	0.874582	−	0.940979i
$160$	−7.79904	−	3.71178i	−0.616568	−	0.293442i
$161$	−1.01728	−	0.587325i	−0.0801727	−	0.0462877i
$162$	−3.87234	+	12.1246i	−0.304240	+	0.952595i
$163$	5.44555	+	5.44555i	0.426528	+	0.426528i	0.887444	−	0.460916i	$-0.152479\pi$
$163$	5.44555	+	5.44555i	0.426528	+	0.426528i	−0.460916	+	0.887444i	$0.652479\pi$
$164$	1.09497	+	7.97322i	0.0855028	+	0.622604i
$165$	−6.55760	−	3.47288i	−0.510508	−	0.270364i
$166$	4.39403	+	0.861295i	0.341043	+	0.0668494i
$167$	14.4701	+	8.35431i	1.11973	+	0.646476i	0.941332	−	0.337482i	$-0.109575\pi$
$167$	14.4701	+	8.35431i	1.11973	+	0.646476i	0.178398	+	0.983958i	$0.442909\pi$
$168$	−9.37197	+	8.99487i	−0.723063	+	0.693969i
$169$	8.04751	−	4.64623i	0.619040	−	0.357403i
$170$	−6.67396	+	7.65314i	−0.511869	+	0.586969i
$171$	−12.9921	−	1.48497i	−0.993531	−	0.113558i
$172$	−8.09467	+	10.6719i	−0.617213	+	0.813725i
$173$	−4.63593	+	17.3015i	−0.352463	+	1.31541i	0.531184	+	0.847256i	$0.321747\pi$
$173$	−4.63593	+	17.3015i	−0.352463	+	1.31541i	−0.883647	+	0.468153i	$0.844920\pi$
$174$	1.58017	−	9.98158i	0.119793	−	0.756702i
$175$	3.53811	−	6.12819i	0.267456	−	0.463248i
$176$	0.125196	+	11.2228i	0.00943697	+	0.845950i
$177$	3.25972	+	10.5995i	0.245016	+	0.796711i
$178$	−0.0114716	−	0.167850i	−0.000859836	−	0.0125809i
$179$	7.04228	+	7.04228i	0.526365	+	0.526365i	0.919487	−	0.393122i	$-0.128605\pi$
$179$	7.04228	+	7.04228i	0.526365	+	0.526365i	−0.393122	+	0.919487i	$0.628605\pi$
$180$	8.16208	−	4.16030i	0.608365	−	0.310091i
$181$	−7.52620	+	2.01664i	−0.559418	+	0.149896i	−0.527439	−	0.849593i	$-0.676848\pi$
$181$	−7.52620	+	2.01664i	−0.559418	+	0.149896i	−0.0319792	+	0.999489i	$0.510181\pi$
$182$	−5.44186	−	4.74560i	−0.403378	−	0.351767i
$183$	3.18508	+	2.96033i	0.235448	+	0.218834i
$184$	0.392820	−	1.18982i	0.0289591	−	0.0877149i
$185$	−5.59033	+	3.22758i	−0.411009	+	0.237296i
$186$	−2.31538	−	1.03067i	−0.169772	−	0.0755722i
$187$	12.7453	+	3.41510i	0.932030	+	0.249737i
$188$	−3.86684	+	3.00154i	−0.282018	+	0.218910i
$189$	−1.50794	−	13.6953i	−0.109686	−	0.996184i
$190$	5.82066	+	7.39663i	0.422275	+	0.536608i
$191$			20.7185i			1.49914i	0.661926	+	0.749569i	$0.269739\pi$
$191$			20.7185i			1.49914i	−0.661926	+	0.749569i	$0.730261\pi$
$192$	−11.4267	−	7.83776i	−0.824651	−	0.565642i
$193$	−22.9021	+	13.2225i	−1.64853	+	0.951777i	−0.670867	+	0.741578i	$0.734078\pi$
$193$	−22.9021	+	13.2225i	−1.64853	+	0.951777i	−0.977659	+	0.210199i	$0.932589\pi$
$194$	4.65499	+	2.27947i	0.334209	+	0.163657i
$195$	2.70556	+	4.31396i	0.193749	+	0.308929i
$196$	0.0233310	−	0.0572268i	0.00166650	−	0.00408763i
$197$	6.92098	+	6.92098i	0.493099	+	0.493099i	0.909281	−	0.416182i	$-0.136632\pi$
$197$	6.92098	+	6.92098i	0.493099	+	0.493099i	−0.416182	+	0.909281i	$0.636632\pi$
$198$	−9.51953	−	7.14781i	−0.676524	−	0.507973i
$199$	−21.8980	−	12.6428i	−1.55231	−	0.896225i	−0.997953	−	0.0639444i	$-0.979632\pi$
$199$	−21.8980	−	12.6428i	−1.55231	−	0.896225i	−0.554354	−	0.832281i	$-0.687035\pi$
$200$	7.16763	+	2.36639i	0.506828	+	0.167329i
$201$	6.18947	−	6.65937i	0.436572	−	0.469716i
$202$	−13.7278	−	11.9714i	−0.965886	−	0.842306i
$203$	2.83140	+	10.5669i	0.198725	+	0.741652i
$204$	−12.4948	+	10.4525i	−0.874811	+	0.731819i
$205$	1.59022	+	5.93480i	0.111066	+	0.414504i
$206$	−1.43376	−	2.13287i	−0.0998945	−	0.148604i
$207$	0.746795	+	1.09933i	0.0519058	+	0.0764090i
$208$	3.77635	−	6.71265i	0.261843	−	0.465439i
$209$	5.30568	−	11.0198i	0.367001	−	0.762254i
$210$	−6.24043	+	7.70745i	−0.430631	+	0.531865i
$211$	−5.49600	−	1.47265i	−0.378360	−	0.101381i	0.0646264	−	0.997910i	$-0.479414\pi$
$211$	−5.49600	−	1.47265i	−0.378360	−	0.101381i	−0.442987	+	0.896528i	$0.646081\pi$
$212$	−18.5581	−	2.33800i	−1.27458	−	0.160574i
$213$	−15.9266	−	8.43467i	−1.09127	−	0.577934i
$214$	12.3321	+	2.41728i	0.843008	+	0.165242i
$215$	−5.11291	+	8.85583i	−0.348698	+	0.603962i
$216$	13.9766	−	4.54470i	0.950988	−	0.309228i
$217$	2.74351			0.186242
$218$	−5.87809	−	17.1589i	−0.398114	−	1.16215i
$219$	−21.9797	−	11.6404i	−1.48525	−	0.786586i
$220$	1.16576	+	8.48872i	0.0785957	+	0.572309i
$221$	−6.40275	−	6.40275i	−0.430695	−	0.430695i
$222$	−9.66764	+	3.71188i	−0.648850	+	0.249125i
$223$	7.79325	−	4.49944i	0.521875	−	0.301305i	−0.215827	−	0.976432i	$-0.569245\pi$
$223$	7.79325	−	4.49944i	0.521875	−	0.301305i	0.737701	+	0.675127i	$0.235911\pi$
$224$	14.7508	+	2.72087i	0.985578	+	0.181796i
$225$	−6.62251	+	4.49877i	−0.441500	+	0.299918i
$226$	12.3301	+	18.3424i	0.820187	+	1.22012i
$227$	−4.13064	−	4.13064i	−0.274160	−	0.274160i	0.556612	−	0.830772i	$-0.312101\pi$
$227$	−4.13064	−	4.13064i	−0.274160	−	0.274160i	−0.830772	+	0.556612i	$0.812101\pi$
$228$	7.36759	+	13.1802i	0.487930	+	0.872883i
$229$	−5.00621	+	5.00621i	−0.330819	+	0.330819i	−0.852898	−	0.522078i	$-0.825157\pi$
$229$	−5.00621	+	5.00621i	−0.330819	+	0.330819i	0.522078	+	0.852898i	$0.325157\pi$
$230$	0.184002	−	0.938712i	0.0121327	−	0.0618968i
$231$	12.5610	+	2.87813i	0.826451	+	0.189367i
$232$	−10.4223	+	5.24857i	−0.684258	+	0.344585i
$233$	8.22598	+	14.2478i	0.538902	+	0.933406i	0.998963	+	0.0455186i	$0.0144940\pi$
$233$	8.22598	+	14.2478i	0.538902	+	0.933406i	−0.460061	+	0.887887i	$0.652173\pi$
$234$	3.20490	+	7.51427i	0.209511	+	0.491223i
$235$	−2.64250	+	2.64250i	−0.172378	+	0.172378i
$236$	7.73841	−	10.2022i	0.503728	−	0.664108i
$237$	16.5525	+	8.76613i	1.07520	+	0.569422i
$238$	7.75533	−	15.8375i	0.502704	−	1.02659i
$239$		−	10.5509i		−	0.682483i	−0.939976	−	0.341241i	$-0.889153\pi$
$239$		−	10.5509i		−	0.682483i	0.939976	−	0.341241i	$-0.110847\pi$
$240$	−9.40303	−	4.84629i	−0.606963	−	0.312827i
$241$	−23.6247	−	13.6397i	−1.52180	−	0.878612i	−0.999668	−	0.0257484i	$-0.991803\pi$
$241$	−23.6247	−	13.6397i	−1.52180	−	0.878612i	−0.522133	−	0.852864i	$-0.674864\pi$
$242$	−3.67018	+	2.46717i	−0.235928	+	0.158596i
$243$	−5.21066	+	14.6918i	−0.334264	+	0.942480i
$244$	0.627605	−	4.98169i	0.0401783	−	0.318920i
$245$	0.0122111	−	0.0455726i	0.000780141	−	0.00291153i
$246$	1.03104	+	9.80274i	0.0657368	+	0.625000i
$247$	−6.93425	+	4.72856i	−0.441216	+	0.300871i
$248$	0.594922	+	2.86538i	0.0377776	+	0.181952i
$249$	5.34544	+	1.22482i	0.338754	+	0.0776195i
$250$	16.2499	+	3.18522i	1.02773	+	0.201451i
$251$	11.8023	−	3.16241i	0.744952	−	0.199609i	0.133674	−	0.991025i	$-0.457322\pi$
$251$	11.8023	−	3.16241i	0.744952	−	0.199609i	0.611278	+	0.791416i	$0.290656\pi$
$252$	−11.8215	+	10.6473i	−0.744684	+	0.670716i
$253$	−1.20065	+	0.321712i	−0.0754840	+	0.0202259i
$254$	−1.25900	−	18.4213i	−0.0789965	−	1.15585i
$255$	−8.46672	+	9.10950i	−0.530206	+	0.570459i
$256$	0.356930	+	15.9960i	0.0223081	+	0.999751i
$257$	13.9586	−	24.1769i	0.870711	−	1.50812i	0.00944917	−	0.999955i	$-0.496992\pi$
$257$	13.9586	−	24.1769i	0.870711	−	1.50812i	0.861262	−	0.508161i	$-0.169674\pi$
$258$	−10.3230	+	12.7497i	−0.642681	+	0.793764i
$259$	7.92677	−	7.92677i	0.492545	−	0.492545i
$260$	2.21983	−	5.44483i	0.137668	−	0.337674i
$261$	2.32160	−	12.1575i	0.143704	−	0.752527i
$262$	1.33526	+	3.89780i	0.0824926	+	0.240807i
$263$	−5.44501	−	9.43103i	−0.335754	−	0.581542i	0.647876	−	0.761746i	$-0.275658\pi$
$263$	−5.44501	−	9.43103i	−0.335754	−	0.581542i	−0.983629	+	0.180204i	$0.942324\pi$
$264$	−0.282165	+	13.7430i	−0.0173661	+	0.845825i
$265$	−14.2799			−0.877207
$266$	−13.0884	−	9.79122i	−0.802501	−	0.600338i
$267$	−0.00753057	−	0.205915i	−0.000460863	−	0.0126018i
$268$	−10.4157	−	1.31220i	−0.636241	−	0.0801552i
$269$	2.98646	−	11.1456i	0.182088	−	0.679561i	−0.813147	−	0.582058i	$-0.802248\pi$
$269$	2.98646	−	11.1456i	0.182088	−	0.679561i	0.995235	−	0.0975030i	$-0.0310856\pi$
$270$	10.1529	−	4.77608i	0.617883	−	0.290663i
$271$	−4.53553	−	7.85576i	−0.275514	−	0.477203i	0.694751	−	0.719250i	$-0.255515\pi$
$271$	−4.53553	−	7.85576i	−0.275514	−	0.477203i	−0.970265	+	0.242047i	$0.922181\pi$
$272$	18.2227	+	4.66552i	1.10491	+	0.282889i
$273$	−6.47743	−	6.02037i	−0.392032	−	0.364369i
$274$	−3.53991	+	0.241934i	−0.213854	+	0.0146158i
$275$	−1.93803	−	7.23283i	−0.116868	−	0.436156i
$276$	0.527026	−	1.44126i	0.0317232	−	0.0867536i
$277$	−11.0421	+	11.0421i	−0.663456	+	0.663456i	−0.956193	−	0.292737i	$-0.905434\pi$
$277$	−11.0421	+	11.0421i	−0.663456	+	0.663456i	0.292737	+	0.956193i	$0.405434\pi$
$278$	5.54322	−	6.35650i	0.332460	−	0.381238i
$279$	−2.79434	−	1.35150i	−0.167292	−	0.0809124i
$280$	11.4326	+	0.653322i	0.683226	+	0.0390434i
$281$	−5.04984	−	2.91553i	−0.301248	−	0.173926i	0.341755	−	0.939789i	$-0.388979\pi$
$281$	−5.04984	−	2.91553i	−0.301248	−	0.173926i	−0.643004	+	0.765863i	$0.722312\pi$
$282$	−4.84996	+	3.52425i	−0.288811	+	0.209866i
$283$	−14.2277	−	3.81229i	−0.845747	−	0.226617i	−0.190175	−	0.981750i	$-0.560906\pi$
$283$	−14.2277	−	3.81229i	−0.845747	−	0.226617i	−0.655572	+	0.755133i	$0.727572\pi$
$284$	2.83132	+	20.6168i	0.168008	+	1.22338i
$285$	6.83827	+	9.28027i	0.405064	+	0.549716i
$286$	−7.62279	+	0.520977i	−0.450745	+	0.0308060i
$287$	−5.33502	−	9.24053i	−0.314917	−	0.545451i
$288$	−13.6837	−	10.0378i	−0.806319	−	0.591481i
$289$	2.55727	−	4.42931i	0.150427	−	0.260548i
$290$	−7.39349	+	4.97005i	−0.434161	+	0.291852i
$291$	5.60988	+	2.97097i	0.328857	+	0.174162i
$292$	3.90740	+	28.4525i	0.228663	+	1.66506i
$293$	11.2023	−	11.2023i	0.654446	−	0.654446i	−0.299615	−	0.954060i	$-0.596858\pi$
$293$	11.2023	−	11.2023i	0.654446	−	0.654446i	0.954060	+	0.299615i	$0.0968581\pi$
$294$	0.0307805	−	0.0691479i	0.00179516	−	0.00403279i
$295$	4.88789	−	8.46607i	0.284584	−	0.492914i
$296$	9.99776	+	6.55997i	0.581108	+	0.381291i
$297$	−11.3758	−	9.11919i	−0.660092	−	0.529149i
$298$	21.9883	−	7.53246i	1.27375	−	0.436344i
$299$	0.823928	+	0.220771i	0.0476490	+	0.0127675i
$300$	8.68230	+	3.17486i	0.501273	+	0.183301i
$301$	4.59620	−	17.1533i	0.264921	−	0.988697i
$302$	2.81371	+	4.18569i	0.161911	+	0.240860i
$303$	−16.3402	−	15.1872i	−0.938719	−	0.872481i
$304$	7.38797	−	15.7930i	0.423729	−	0.905789i
$305$		−	3.83325i		−	0.219491i
$306$	−15.7008	+	12.3104i	−0.897555	+	0.703740i
$307$	−20.4259	−	5.47309i	−1.16577	−	0.312366i	−0.376499	−	0.926417i	$-0.622872\pi$
$307$	−20.4259	−	5.47309i	−1.16577	−	0.312366i	−0.789266	+	0.614051i	$0.789539\pi$
$308$	−5.77093	−	13.7154i	−0.328829	−	0.781506i
$309$	−1.67235	−	2.66653i	−0.0951368	−	0.151694i
$310$	0.724050	+	2.11360i	0.0411233	+	0.120044i
$311$	−11.0671			−0.627556			−0.313778	−	0.949496i	$-0.601595\pi$
$311$	−11.0671			−0.627556			−0.313778	+	0.949496i	$0.601595\pi$
$312$	4.88318	−	8.07065i	0.276455	−	0.456910i
$313$	−10.7000	−	6.17767i	−0.604802	−	0.349183i	0.166126	−	0.986105i	$-0.446874\pi$
$313$	−10.7000	−	6.17767i	−0.604802	−	0.349183i	−0.770928	+	0.636922i	$0.780207\pi$
$314$	26.2963	−	9.00824i	1.48398	−	0.508364i
$315$	−7.93813	+	9.19281i	−0.447263	+	0.517956i
$316$	−2.94258	−	21.4269i	−0.165533	−	1.20536i
$317$	−31.4282	+	8.42117i	−1.76519	+	0.472980i	−0.987758	−	0.155992i	$-0.950143\pi$
$317$	−31.4282	+	8.42117i	−1.76519	+	0.472980i	−0.777428	+	0.628972i	$0.783476\pi$
$318$	−22.6269	−	3.58203i	−1.26885	−	0.200870i
$319$	10.0253	+	5.78811i	0.561309	+	0.324072i
$320$	1.79677	+	12.0821i	0.100443	+	0.675408i
$321$	15.0024	+	3.43753i	0.837350	+	0.191864i
$322$	0.113270	+	1.65734i	0.00631231	+	0.0923600i
$323$	−15.5382	−	13.3694i	−0.864569	−	0.743892i
$324$	17.2855	−	5.02104i	0.960307	−	0.278947i
$325$	−1.32995	+	4.96343i	−0.0737723	+	0.275322i
$326$	2.09495	−	10.6877i	0.116029	−	0.591937i
$327$	−6.52982	−	21.2328i	−0.361100	−	1.17418i
$328$	8.49411	−	7.57578i	0.469009	−	0.418303i
$329$	3.24492	−	5.62037i	0.178898	−	0.309861i
$330$	1.09770	+	10.4365i	0.0604265	+	0.574512i
$331$	11.4248	+	11.4248i	0.627962	+	0.627962i	0.947555	−	0.319593i	$-0.103546\pi$
$331$	11.4248	+	11.4248i	0.627962	+	0.627962i	−0.319593	+	0.947555i	$0.603546\pi$
$332$	−2.45588	−	5.83672i	−0.134784	−	0.320331i
$333$	−11.9785	+	4.16874i	−0.656416	+	0.228445i
$334$	−1.61120	−	23.5746i	−0.0881608	−	1.28994i
$335$	−8.01456			−0.437882
$336$	17.9513	+	3.90300i	0.979325	+	0.212926i
$337$	21.3268	−	12.3130i	1.16175	−	0.670734i	0.210024	−	0.977696i	$-0.432646\pi$
$337$	21.3268	−	12.3130i	1.16175	−	0.670734i	0.951722	+	0.306962i	$0.0993124\pi$
$338$	−11.8024	−	5.77946i	−0.641969	−	0.314361i
$339$	14.3820	+	22.9318i	0.781124	+	1.24549i
$340$	14.2479	+	1.79498i	0.772701	+	0.0973467i
$341$	2.05284	−	2.05284i	0.111167	−	0.111167i
$342$	8.50752	+	16.4202i	0.460034	+	0.887901i
$343$		−	18.4792i		−	0.997781i
$344$	18.9119	+	1.08073i	1.01966	+	0.0582691i
$345$	0.261662	−	1.14197i	0.0140874	−	0.0614814i
$346$	23.9640	−	8.20930i	1.28832	−	0.441335i
$347$	2.16510	−	8.08028i	0.116229	−	0.433772i	−0.883147	−	0.469096i	$-0.844580\pi$
$347$	2.16510	−	8.08028i	0.116229	−	0.433772i	0.999376	+	0.0353242i	$0.0112464\pi$
$348$	−12.9619	+	6.02056i	−0.694831	+	0.322736i
$349$	20.4818	+	20.4818i	1.09636	+	1.09636i	0.994832	+	0.101532i	$0.0323743\pi$
$349$	20.4818	+	20.4818i	1.09636	+	1.09636i	0.101532	+	0.994832i	$0.467626\pi$
$350$	−9.98400	+	0.682354i	−0.533667	+	0.0364733i
$351$	3.63168	+	9.32278i	0.193845	+	0.497613i
$352$	13.0732	−	9.00140i	0.696804	−	0.479776i
$353$			26.7053i			1.42138i	0.703506	+	0.710689i	$0.251617\pi$
$353$			26.7053i			1.42138i	−0.703506	+	0.710689i	$0.748383\pi$
$354$	9.86865	−	12.1886i	0.524513	−	0.647817i
$355$	4.11192	+	15.3459i	0.218238	+	0.814476i
$356$	−0.187951	+	0.145893i	−0.00996139	+	0.00773230i
$357$	10.1080	−	19.0862i	0.534972	−	1.01015i
$358$	2.70923	−	13.8215i	0.143187	−	0.730491i
$359$	3.90458	+	6.76294i	0.206076	+	0.356934i	0.950475	−	0.310801i	$-0.100597\pi$
$359$	3.90458	+	6.76294i	0.206076	+	0.356934i	−0.744399	+	0.667735i	$0.767264\pi$
$360$	−11.3225	−	6.29731i	−0.596748	−	0.331897i
$361$	−14.8528	+	11.8489i	−0.781724	+	0.623624i
$362$	8.30485	+	7.24228i	0.436493	+	0.380646i
$363$	−4.58850	+	2.87774i	−0.240834	+	0.151042i
$364$	−1.27635	+	10.1311i	−0.0668987	+	0.531016i
$365$	5.67472	+	21.1784i	0.297029	+	1.10853i
$366$	0.961549	−	6.07388i	0.0502610	−	0.317487i
$367$	−2.81245	+	4.87131i	−0.146809	+	0.254280i	−0.930046	−	0.367442i	$-0.880234\pi$
$367$	−2.81245	+	4.87131i	−0.146809	+	0.254280i	0.783238	+	0.621723i	$0.213567\pi$
$368$	−1.70640	+	0.477691i	−0.0889520	+	0.0249014i
$369$	0.881803	+	12.0398i	0.0459048	+	0.626769i
$370$	8.19875	+	4.01479i	0.426233	+	0.208719i
$371$	23.9537	−	6.41838i	1.24362	−	0.333226i
$372$	0.617092	+	3.53068i	0.0319947	+	0.183057i
$373$	2.77708	+	2.77708i	0.143791	+	0.143791i	0.775338	−	0.631547i	$-0.217580\pi$
$373$	2.77708	+	2.77708i	0.143791	+	0.143791i	−0.631547	+	0.775338i	$0.717580\pi$
$374$	−6.04746	−	17.6533i	−0.312707	−	0.912833i
$375$	19.7684	+	4.52958i	1.02083	+	0.233906i
$376$	6.57367	+	2.17030i	0.339011	+	0.111925i
$377$	−3.97202	−	6.87974i	−0.204569	−	0.354325i
$378$	−14.8841	+	12.5750i	−0.765558	+	0.646789i
$379$	−22.9921	−	22.9921i	−1.18103	−	1.18103i	−0.979479	−	0.201547i	$-0.935403\pi$
$379$	−22.9921	−	22.9921i	−1.18103	−	1.18103i	−0.201547	−	0.979479i	$-0.564597\pi$
$380$	4.08894	−	12.6673i	0.209758	−	0.649820i
$381$	−0.826469	−	22.5989i	−0.0423413	−	1.15778i
$382$	24.3169	−	16.3463i	1.24416	−	0.836349i
$383$	16.9148	+	29.2973i	0.864305	+	1.49702i	0.867735	+	0.497026i	$0.165575\pi$
$383$	16.9148	+	29.2973i	0.864305	+	1.49702i	−0.00343013	+	0.999994i	$0.501092\pi$
$384$	−0.183683	+	19.5951i	−0.00937352	+	0.999956i
$385$	−5.67995	−	9.83797i	−0.289477	−	0.501389i
$386$	33.5880	+	16.4475i	1.70959	+	0.837156i
$387$	−13.1313	+	15.2068i	−0.667503	+	0.773007i
$388$	−0.997285	−	7.26191i	−0.0506295	−	0.368668i
$389$	34.6414	−	9.28215i	1.75639	−	0.470623i	0.770419	−	0.637538i	$-0.220047\pi$
$389$	34.6414	−	9.28215i	1.75639	−	0.470623i	0.985971	+	0.166914i	$0.0533802\pi$
$390$	2.92860	−	6.57906i	0.148296	−	0.333144i
$391$			2.08325i			0.105355i
$392$	−0.0855735	+	0.0177671i	−0.00432211	+	0.000897376i
$393$	1.48330	+	4.82322i	0.0748228	+	0.243299i
$394$	2.66256	−	13.5835i	0.134138	−	0.684325i
$395$	−4.27351	−	15.9490i	−0.215024	−	0.802479i
$396$	−0.878608	+	16.8123i	−0.0441517	+	0.844850i
$397$	−1.78283	+	6.65363i	−0.0894779	+	0.333936i	−0.996124	−	0.0879549i	$-0.971967\pi$
$397$	−1.78283	+	6.65363i	−0.0894779	+	0.333936i	0.906647	+	0.421891i	$0.138634\pi$
$398$	2.43827	+	35.6761i	0.122219	+	1.78828i
$399$	−15.6420	−	12.4935i	−0.783081	−	0.625459i
$400$	−2.87766	−	10.2795i	−0.143883	−	0.513976i
$401$	−18.3041	−	31.7037i	−0.914064	−	1.58321i	−0.808265	−	0.588819i	$-0.799593\pi$
$401$	−18.3041	−	31.7037i	−0.914064	−	1.58321i	−0.105799	−	0.994388i	$-0.533740\pi$
$402$	−12.6993	−	2.01041i	−0.633383	−	0.100270i
$403$	−1.92437	+	0.515633i	−0.0958596	+	0.0256855i
$404$	−3.21975	+	25.5572i	−0.160189	+	1.27152i
$405$	12.6137	−	5.45264i	0.626781	−	0.270944i
$406$	10.1683	−	11.6601i	0.504643	−	0.578683i
$407$		−	11.8624i		−	0.587999i
$408$	22.1259	+	6.41820i	1.09540	+	0.317748i
$409$	−13.8093	+	23.9185i	−0.682828	+	1.18269i	0.291287	+	0.956636i	$0.405917\pi$
$409$	−13.8093	+	23.9185i	−0.682828	+	1.18269i	−0.974114	+	0.226056i	$0.927417\pi$
$410$	5.71091	−	6.54880i	0.282042	−	0.323422i
$411$	−4.34270	+	0.158818i	−0.214209	+	0.00783390i
$412$	−1.37211	+	3.36554i	−0.0675991	+	0.165808i
$413$	−4.39392	+	16.3983i	−0.216210	+	0.806908i
$414$	0.701066	−	1.74384i	0.0344555	−	0.0857051i
$415$	−2.41716	−	4.18665i	−0.118654	−	0.205514i
$416$	−10.8579	+	0.863866i	−0.532354	+	0.0423545i
$417$	7.03224	−	7.56612i	0.344370	−	0.370515i
$418$	−17.1197	+	2.46711i	−0.837353	+	0.120671i
$419$	−12.8795	+	12.8795i	−0.629207	+	0.629207i	−0.947869	−	0.318662i	$-0.896767\pi$
$419$	−12.8795	+	12.8795i	−0.629207	+	0.629207i	0.318662	+	0.947869i	$0.396767\pi$
$420$	13.9696	+	1.24331i	0.681647	+	0.0606673i
$421$	−4.69029	+	17.5044i	−0.228591	+	0.853113i	0.752343	+	0.658772i	$0.228924\pi$
$421$	−4.69029	+	17.5044i	−0.228591	+	0.853113i	−0.980934	+	0.194341i	$0.937743\pi$
$422$	2.60777	+	7.61242i	0.126944	+	0.370567i
$423$	−6.07372	+	4.12597i	−0.295314	+	0.200612i
$424$	11.8978	+	23.6259i	0.577807	+	1.14738i
$425$	−12.5497			−0.608752
$426$	2.66601	+	25.3474i	0.129169	+	1.22809i
$427$	1.72293	+	6.43006i	0.0833784	+	0.311172i
$428$	−6.89259	−	16.3812i	−0.333166	−	0.791813i
$429$	−9.35149	+	0.341996i	−0.451494	+	0.0165117i
$430$	14.4278	−	0.986067i	0.695773	−	0.0475524i
$431$	−11.2523	+	19.4895i	−0.542002	+	0.938775i	0.456787	+	0.889576i	$0.349000\pi$
$431$	−11.2523	+	19.4895i	−0.542002	+	0.938775i	−0.998789	+	0.0491989i	$0.984333\pi$
$432$	−16.3612	−	12.8184i	−0.787177	−	0.616727i
$433$	−13.6406	−	7.87540i	−0.655525	−	0.378467i	0.135045	−	0.990839i	$-0.456882\pi$
$433$	−13.6406	−	7.87540i	−0.655525	−	0.378467i	−0.790570	+	0.612372i	$0.790215\pi$
$434$	−2.16455	−	3.22001i	−0.103902	−	0.154565i
$435$	−9.24343	+	5.79714i	−0.443188	+	0.277952i
$436$	−15.5014	+	20.4369i	−0.742385	+	0.978750i
$437$	1.89736	+	0.358831i	0.0907629	+	0.0171652i
$438$	3.67927	+	34.9811i	0.175803	+	1.67146i
$439$	−17.9299	−	31.0556i	−0.855749	−	1.48220i	−0.875948	−	0.482406i	$-0.839763\pi$
$439$	−17.9299	−	31.0556i	−0.855749	−	1.48220i	0.0201986	−	0.999796i	$-0.493570\pi$
$440$	9.04329	−	8.06559i	0.431122	−	0.384512i
$441$	0.0403621	−	0.0834518i	0.00192201	−	0.00397389i
$442$	−2.46319	+	12.5664i	−0.117162	+	0.597721i
$443$	2.02767	−	0.543312i	0.0963375	−	0.0258136i	−0.210328	−	0.977631i	$-0.567453\pi$
$443$	2.02767	−	0.543312i	0.0963375	−	0.0258136i	0.306666	+	0.951817i	$0.400787\pi$
$444$	11.9840	+	8.41815i	0.568738	+	0.399508i
$445$	−0.128441	+	0.128441i	−0.00608869	+	0.00608869i
$446$	−11.4295	−	5.59686i	−0.541205	−	0.265019i
$447$	27.2087	−	8.36762i	1.28693	−	0.395775i
$448$	−8.44451	−	19.4594i	−0.398966	−	0.919370i
$449$	11.2391			0.530406			0.265203	−	0.964193i	$-0.414561\pi$
$449$	11.2391			0.530406			0.265203	+	0.964193i	$0.414561\pi$
$450$	10.5051	+	4.22330i	0.495215	+	0.199088i
$451$	−10.9062	−	2.92230i	−0.513552	−	0.137606i
$452$	11.8000	−	28.9432i	0.555024	−	1.36137i
$453$	3.28195	+	5.23300i	0.154199	+	0.245868i
$454$	−1.58909	+	8.10700i	−0.0745798	+	0.380481i
$455$			7.79559i			0.365463i
$456$	9.65657	−	19.0460i	0.452210	−	0.891911i
$457$		−	7.78414i		−	0.364127i	−0.983287	−	0.182063i	$-0.941722\pi$
$457$		−	7.78414i		−	0.364127i	0.983287	−	0.182063i	$-0.0582776\pi$
$458$	9.82544	+	1.92593i	0.459113	+	0.0899929i
$459$	−19.6974	+	14.4604i	−0.919398	+	0.674953i
$460$	−1.24692	+	0.524658i	−0.0581379	+	0.0244623i
$461$	−13.5658	−	3.63493i	−0.631820	−	0.169296i	−0.0713246	−	0.997453i	$-0.522723\pi$
$461$	−13.5658	−	3.63493i	−0.631820	−	0.169296i	−0.560496	+	0.828157i	$0.689389\pi$
$462$	−6.53224	−	17.0133i	−0.303907	−	0.791531i
$463$	39.6643			1.84336			0.921678	−	0.387956i	$-0.126819\pi$
$463$	39.6643			1.84336			0.921678	+	0.387956i	$0.126819\pi$
$464$	14.3830	+	8.09149i	0.667716	+	0.375638i
$465$	0.804329	+	2.61541i	0.0372998	+	0.121287i
$466$	10.2323	−	20.8958i	0.474003	−	0.967979i
$467$	8.95182	−	8.95182i	0.414241	−	0.414241i	−0.468972	−	0.883213i	$-0.655376\pi$
$467$	8.95182	−	8.95182i	0.414241	−	0.414241i	0.883213	+	0.468972i	$0.155376\pi$
$468$	6.29077	−	9.69007i	0.290791	−	0.447923i
$469$	13.4440	−	3.60230i	0.620785	−	0.166339i
$470$	5.18630	+	1.01659i	0.239226	+	0.0468919i
$471$	32.5395	−	10.0070i	1.49934	−	0.461099i
$472$	−18.0795	−	1.03317i	−0.832178	−	0.0475554i
$473$	−9.39584	−	16.2741i	−0.432021	−	0.748282i
$474$	−2.77078	−	26.3435i	−0.127266	−	1.21000i
$475$	−2.16164	+	11.4299i	−0.0991826	+	0.524439i
$476$	−24.7068	+	3.39301i	−1.13244	+	0.155518i
$477$	−27.5593	−	5.26275i	−1.26185	−	0.240965i
$478$	−12.3834	+	8.32438i	−0.566404	+	0.380748i
$479$	27.3485	+	15.7897i	1.24959	+	0.721449i	0.971027	−	0.238971i	$-0.0768099\pi$
$479$	27.3485	+	15.7897i	1.24959	+	0.721449i	0.278559	+	0.960419i	$0.410143\pi$
$480$	1.73073	+	14.8597i	0.0789965	+	0.678251i
$481$	−4.07022	+	7.04983i	−0.185586	+	0.321445i
$482$	2.63053	+	38.4892i	0.119818	+	1.75314i
$483$	0.0743564	+	2.03319i	0.00338334	+	0.0925136i
$484$	5.79133	+	2.36109i	0.263242	+	0.107322i
$485$	−1.44836	−	5.40534i	−0.0657665	−	0.245444i
$486$	21.3545	−	5.47576i	0.968661	−	0.248386i
$487$	33.2341			1.50598			0.752991	−	0.658031i	$-0.228610\pi$
$487$	33.2341			1.50598			0.752991	+	0.658031i	$0.228610\pi$
$488$	−6.34207	+	3.19380i	−0.287092	+	0.144577i
$489$	2.97915	−	13.0019i	0.134722	−	0.587965i
$490$	−0.0631219	+	0.0216235i	−0.00285156	+	0.000976850i
$491$	10.3688	−	38.6970i	0.467938	−	1.74637i	−0.179021	−	0.983845i	$-0.557293\pi$
$491$	10.3688	−	38.6970i	0.467938	−	1.74637i	0.646959	−	0.762525i	$-0.276040\pi$
$492$	10.6918	−	8.94419i	0.482024	−	0.403235i
$493$	13.7190	−	13.7190i	0.617873	−	0.617873i
$494$	11.0207	+	4.40789i	0.495847	+	0.198320i
$495$	0.938814	+	12.8183i	0.0421966	+	0.576138i
$496$	2.89366	−	2.95895i	0.129929	−	0.132861i
$497$	−13.7950	−	23.8937i	−0.618792	−	1.07178i
$498$	−2.77986	−	7.24018i	−0.124568	−	0.324440i
$499$	9.28166	−	34.6396i	0.415504	−	1.55068i	−0.368320	−	0.929699i	$-0.620067\pi$
$499$	9.28166	−	34.6396i	0.415504	−	1.55068i	0.783824	−	0.620983i	$-0.213266\pi$
$500$	−9.08225	−	21.5852i	−0.406171	−	0.965319i
$501$	−1.05767	−	28.9209i	−0.0472533	−	1.29209i
$502$	−13.0233	−	11.3570i	−0.581258	−	0.506889i
$503$	5.56401	−	9.63715i	0.248087	−	0.429699i	−0.714908	−	0.699218i	$-0.753531\pi$
$503$	5.56401	−	9.63715i	0.248087	−	0.429699i	0.962995	+	0.269519i	$0.0868648\pi$
$504$	21.8233	+	5.47425i	0.972088	+	0.243843i
$505$			19.6654i			0.875100i
$506$	1.32486	+	1.15535i	0.0588973	+	0.0513617i
$507$	−14.2235	−	7.53272i	−0.631688	−	0.334540i
$508$	−20.6274	+	16.0115i	−0.915191	+	0.710396i
$509$	24.7152	−	6.62243i	1.09548	−	0.293534i	0.334559	−	0.942375i	$-0.391413\pi$
$509$	24.7152	−	6.62243i	1.09548	−	0.293534i	0.760924	+	0.648841i	$0.224746\pi$
$510$	17.3716	+	2.75008i	0.769229	+	0.121776i
$511$	−19.0381	−	32.9749i	−0.842194	−	1.45872i
$512$	18.4926	−	13.0393i	0.817265	−	0.576262i
$513$	9.77724	+	20.4305i	0.431676	+	0.902029i
$514$	−39.3889	+	2.69202i	−1.73737	+	0.118740i
$515$	−0.718144	+	2.68015i	−0.0316452	+	0.118101i
$516$	23.1087	+	2.05670i	1.01730	+	0.0905410i
$517$	−1.77743	−	6.63346i	−0.0781713	−	0.291739i
$518$	−15.5575	−	3.04950i	−0.683556	−	0.133987i
$519$	29.6536	−	9.11950i	1.30165	−	0.400301i
$520$	−8.14187	+	1.69045i	−0.357044	+	0.0741311i
$521$			24.6461i			1.07976i	0.841741	+	0.539882i	$0.181531\pi$
$521$			24.6461i			1.07976i	−0.841741	+	0.539882i	$0.818469\pi$
$522$	−16.1006	+	6.86706i	−0.704706	+	0.300563i
$523$	−39.1954	+	10.5024i	−1.71389	+	0.459237i	−0.976374	−	0.216088i	$-0.930670\pi$
$523$	−39.1954	+	10.5024i	−1.71389	+	0.459237i	−0.737521	+	0.675324i	$0.764004\pi$
$524$	3.52129	−	4.64242i	0.153828	−	0.202805i
$525$	−12.2482	+	0.447931i	−0.534555	+	0.0195493i
$526$	−6.77306	+	13.8315i	−0.295319	+	0.603082i
$527$	−2.43282	−	4.21377i	−0.105975	−	0.183555i
$528$	16.3525	−	10.5117i	0.711653	−	0.457462i
$529$	11.4019	+	19.7486i	0.495734	+	0.858636i
$530$	11.2664	+	16.7600i	0.489382	+	0.728009i
$531$	12.5534	−	14.5376i	0.544771	−	0.630876i
$532$	−1.16540	+	23.0866i	−0.0505263	+	1.00093i
$533$	5.47884	+	5.47884i	0.237315	+	0.237315i
$534$	−0.235737	+	0.171300i	−0.0102013	+	0.00741286i
$535$	−6.78394	−	11.7501i	−0.293295	−	0.508002i
$536$	6.67760	+	13.2600i	0.288429	+	0.572745i
$537$	3.85269	−	16.8143i	0.166256	−	0.725589i
$538$	−15.4376	+	5.28843i	−0.665563	+	0.228000i
$539$	0.0613073	+	0.0613073i	0.00264069	+	0.00264069i
$540$	−13.6159	−	8.14801i	−0.585935	−	0.350635i
$541$	26.8111	−	7.18400i	1.15270	−	0.308864i	0.368652	−	0.929567i	$-0.379819\pi$
$541$	26.8111	−	7.18400i	1.15270	−	0.308864i	0.784046	+	0.620703i	$0.213153\pi$
$542$	−5.64175	+	11.5212i	−0.242334	+	0.494879i
$543$	9.88523	+	9.18771i	0.424216	+	0.394282i
$544$	−8.90133	−	25.0685i	−0.381641	−	1.07480i
$545$	−9.79133	+	16.9591i	−0.419414	+	0.726447i
$546$	−1.95548	+	12.3523i	−0.0836869	+	0.528630i
$547$	2.32677	+	8.68361i	0.0994854	+	0.371284i	0.997661	−	0.0683518i	$-0.0217740\pi$
$547$	2.32677	+	8.68361i	0.0994854	+	0.371284i	−0.898176	+	0.439636i	$0.855107\pi$
$548$	3.07684	+	3.96384i	0.131436	+	0.169327i
$549$	1.41272	−	7.39792i	0.0602932	−	0.315735i
$550$	−6.95997	+	7.98112i	−0.296774	+	0.340316i
$551$	−10.1318	−	14.8578i	−0.431628	−	0.632965i
$552$	−2.10738	+	0.518551i	−0.0896962	+	0.0220710i
$553$	14.3371	+	24.8327i	0.609677	+	1.05599i
$554$	21.6718	+	4.24800i	0.920747	+	0.180480i
$555$	9.88057	+	5.23272i	0.419407	+	0.222117i
$556$	−11.8339	−	1.49087i	−0.501871	−	0.0632269i
$557$	−0.766051	−	2.85894i	−0.0324586	−	0.121137i	0.947796	−	0.318878i	$-0.103306\pi$
$557$	−0.766051	−	2.85894i	−0.0324586	−	0.121137i	−0.980254	+	0.197741i	$0.936639\pi$
$558$	0.618418	+	4.34595i	0.0261797	+	0.183979i
$559$			12.8955i			0.545424i
$560$	−8.25317	−	13.9336i	−0.348760	−	0.588803i
$561$	−6.71796	−	21.8446i	−0.283633	−	0.922281i
$562$	0.562283	+	8.22717i	0.0237185	+	0.347042i
$563$	−15.3488	−	15.3488i	−0.646874	−	0.646874i	0.305362	−	0.952236i	$-0.401222\pi$
$563$	−15.3488	−	15.3488i	−0.646874	−	0.646874i	−0.952236	+	0.305362i	$0.901222\pi$
$564$	7.96282	+	2.91177i	0.335295	+	0.122608i
$565$	6.17594	−	23.0489i	0.259824	−	0.969676i
$566$	6.75081	+	19.7065i	0.283758	+	0.828326i
$567$	−18.7080	+	14.8160i	−0.785663	+	0.622213i
$568$	21.9636	−	19.5891i	0.921574	−	0.821940i
$569$			31.8573i			1.33553i	0.744373	+	0.667764i	$0.232749\pi$
$569$			31.8573i			1.33553i	−0.744373	+	0.667764i	$0.767251\pi$
$570$	5.49687	−	15.3478i	0.230238	−	0.642849i
$571$	−29.2966	+	29.2966i	−1.22602	+	1.22602i	−0.260567	+	0.965456i	$0.583909\pi$
$571$	−29.2966	+	29.2966i	−1.22602	+	1.22602i	−0.965456	+	0.260567i	$0.916091\pi$
$572$	6.62562	+	8.53567i	0.277031	+	0.356894i
$573$	30.4012	−	19.0666i	1.27003	−	0.796517i
$574$	−6.63625	+	13.5521i	−0.276992	+	0.565655i
$575$	1.02383	−	0.591111i	0.0426969	−	0.0246510i
$576$	−0.985099	+	23.9798i	−0.0410458	+	0.999157i
$577$	36.1214			1.50375			0.751876	−	0.659304i	$-0.229149\pi$
$577$	36.1214			1.50375			0.751876	+	0.659304i	$0.229149\pi$
$578$	−7.21621	+	0.493190i	−0.300155	+	0.0205140i
$579$	40.4780	+	21.4370i	1.68221	+	0.890893i
$580$	11.6665	+	4.75637i	0.484425	+	0.197497i
$581$	5.93643	+	5.93643i	0.246284	+	0.246284i
$582$	−0.939059	−	8.92822i	−0.0389253	−	0.370086i
$583$	13.1209	−	22.7260i	0.543410	−	0.941214i
$584$	30.3113	−	27.0342i	1.25429	−	1.11868i
$585$	3.84025	−	7.94000i	0.158775	−	0.328279i
$586$	−21.9862	−	4.30963i	−0.908242	−	0.178029i
$587$	0.948089	−	3.53832i	0.0391318	−	0.146042i	−0.943596	−	0.331099i	$-0.892580\pi$
$587$	0.948089	−	3.53832i	0.0391318	−	0.146042i	0.982728	+	0.185057i	$0.0592471\pi$
$588$	−0.105442	+	0.0184292i	−0.00434837	+	0.000760008i
$589$	−4.25681	+	1.48993i	−0.175399	+	0.0613915i
$590$	−13.7929	+	0.942669i	−0.567843	+	0.0388091i
$591$	3.78633	−	16.5246i	0.155749	−	0.679732i
$592$	−0.188637	−	16.9098i	−0.00775292	−	0.694989i
$593$	4.23855	+	2.44713i	0.174056	+	0.100491i	0.584497	−	0.811396i	$-0.301292\pi$
$593$	4.23855	+	2.44713i	0.174056	+	0.100491i	−0.410441	+	0.911887i	$0.634625\pi$
$594$	−1.72781	+	20.5464i	−0.0708930	+	0.843027i
$595$	−18.3903	+	4.92767i	−0.753930	+	0.202015i
$596$	−26.1888	−	19.8643i	−1.07274	−	0.813673i
$597$	1.60060	+	43.7667i	0.0655083	+	1.79125i
$598$	−0.390941	−	1.14121i	−0.0159868	−	0.0466675i
$599$	7.36862	+	4.25427i	0.301073	+	0.173825i	0.642925	−	0.765929i	$-0.277721\pi$
$599$	7.36862	+	4.25427i	0.301073	+	0.173825i	−0.341852	+	0.939754i	$0.611054\pi$
$600$	−3.12381	−	12.6951i	−0.127529	−	0.518276i
$601$	20.1634			0.822482			0.411241	−	0.911527i	$-0.365095\pi$
$601$	20.1634			0.822482			0.411241	+	0.911527i	$0.365095\pi$
$602$	−23.7587	+	8.13895i	−0.968332	+	0.331719i
$603$	−15.4676	−	2.95371i	−0.629889	−	0.120284i
$604$	2.69273	−	6.60478i	0.109566	−	0.268745i
$605$	4.61193	+	1.23576i	0.187502	+	0.0502409i
$606$	−4.93296	+	31.1604i	−0.200388	+	1.26580i
$607$			7.95360i			0.322826i	0.986887	+	0.161413i	$0.0516052\pi$
$607$			7.95360i			0.322826i	−0.986887	+	0.161413i	$0.948395\pi$
$608$	−24.3648	+	3.78909i	−0.988123	+	0.153668i
$609$	12.8997	−	13.8790i	0.522722	−	0.562406i
$610$	−4.49901	+	3.02432i	−0.182159	+	0.122451i
$611$	−1.21974	+	4.55213i	−0.0493454	+	0.184159i
$612$	26.8360	+	8.71516i	1.08478	+	0.352289i
$613$	−15.7634	−	4.22380i	−0.636679	−	0.170598i	−0.0739805	−	0.997260i	$-0.523570\pi$
$613$	−15.7634	−	4.22380i	−0.636679	−	0.170598i	−0.562699	+	0.826662i	$0.690237\pi$
$614$	9.69176	+	28.2915i	0.391128	+	1.14175i
$615$	7.24498	−	7.79501i	0.292146	−	0.314325i
$616$	−11.5444	+	17.5943i	−0.465136	+	0.708893i
$617$	23.2674	−	40.3003i	0.936710	−	1.62243i	0.165154	−	0.986268i	$-0.447188\pi$
$617$	23.2674	−	40.3003i	0.936710	−	1.62243i	0.771556	−	0.636162i	$-0.219479\pi$
$618$	−1.81022	+	4.06662i	−0.0728177	+	0.163584i
$619$	10.6969	−	10.6969i	0.429943	−	0.429943i	−0.458666	−	0.888609i	$-0.651672\pi$
$619$	10.6969	−	10.6969i	0.429943	−	0.429943i	0.888609	+	0.458666i	$0.151672\pi$
$620$	1.90944	−	2.51737i	0.0766848	−	0.101100i
$621$	0.925854	−	2.10749i	0.0371532	−	0.0845706i
$622$	8.73160	+	12.9892i	0.350105	+	0.520820i
$623$	0.157722	−	0.273183i	0.00631901	−	0.0109449i
$624$	−13.3250	+	0.636220i	−0.533429	+	0.0254692i
$625$	−2.26739	−	3.92723i	−0.0906955	−	0.157089i
$626$	1.19141	+	17.4324i	0.0476185	+	0.696740i
$627$	−21.0525	+	2.35586i	−0.840755	+	0.0940840i
$628$	−31.3198	−	23.7561i	−1.24980	−	0.947974i
$629$	−19.2038	−	5.14565i	−0.765707	−	0.205171i
$630$	17.0524	+	2.06396i	0.679383	+	0.0822303i
$631$	4.97810	+	2.87411i	0.198175	+	0.114417i	0.595804	−	0.803130i	$-0.296833\pi$
$631$	4.97810	+	2.87411i	0.198175	+	0.114417i	−0.397629	+	0.917546i	$0.630167\pi$
$632$	−22.8268	+	20.3589i	−0.907999	+	0.809833i
$633$	2.89690	+	9.41977i	0.115141	+	0.374402i
$634$	34.6797	+	30.2426i	1.37731	+	1.20109i
$635$	−14.0962	+	14.0962i	−0.559391	+	0.559391i
$636$	13.6478	+	29.3828i	0.541170	+	1.16510i
$637$	−0.0153992	−	0.0574705i	−0.000610138	−	0.00227706i
$638$	−1.11628	−	16.3332i	−0.0441941	−	0.646636i
$639$	2.28012	+	31.1320i	0.0902002	+	1.23156i
$640$	12.7629	−	11.6412i	0.504497	−	0.460160i
$641$	−4.62675	−	8.01376i	−0.182746	−	0.316525i	0.760069	−	0.649842i	$-0.225165\pi$
$641$	−4.62675	−	8.01376i	−0.182746	−	0.316525i	−0.942815	+	0.333318i	$0.891832\pi$
$642$	−7.80187	−	20.3201i	−0.307915	−	0.801970i
$643$	10.4703	−	39.0756i	0.412907	−	1.54099i	−0.376083	−	0.926586i	$-0.622729\pi$
$643$	10.4703	−	39.0756i	0.412907	−	1.54099i	0.788990	−	0.614405i	$-0.210604\pi$
$644$	1.85582	−	1.44054i	0.0731295	−	0.0567651i
$645$	17.6998	−	0.647304i	0.696930	−	0.0254876i
$646$	−3.43218	+	28.7849i	−0.135037	+	1.13253i
$647$	−18.1399			−0.713152			−0.356576	−	0.934266i	$-0.616056\pi$
$647$	−18.1399			−0.713152			−0.356576	+	0.934266i	$0.616056\pi$
$648$	−19.5309	−	16.3262i	−0.767245	−	0.641354i
$649$	8.98231	+	15.5578i	0.352587	+	0.610698i
$650$	6.87477	−	2.35507i	0.269651	−	0.0923736i
$651$	−2.52477	−	4.02569i	−0.0989534	−	0.157779i
$652$	−14.1968	+	5.97349i	−0.555990	+	0.233940i
$653$	18.4355	−	18.4355i	0.721435	−	0.721435i	−0.247462	−	0.968898i	$-0.579597\pi$
$653$	18.4355	−	18.4355i	0.721435	−	0.721435i	0.968898	+	0.247462i	$0.0795966\pi$
$654$	−19.7687	+	24.4160i	−0.773017	+	0.954741i
$655$	2.22419	−	3.85240i	0.0869061	−	0.150526i
$656$	−15.5932	−	3.99229i	−0.608810	−	0.155873i
$657$	3.14672	+	42.9642i	0.122765	+	1.67619i
$658$	−9.15666	+	0.625809i	−0.356964	+	0.0243966i
$659$	8.70366	−	2.33214i	0.339047	−	0.0908472i	−0.0852786	−	0.996357i	$-0.527178\pi$
$659$	8.70366	−	2.33214i	0.339047	−	0.0908472i	0.424325	+	0.905510i	$0.360511\pi$
$660$	11.3831	−	9.52247i	0.443086	−	0.370662i
$661$	9.07146	−	2.43069i	0.352839	−	0.0945429i	−0.0780461	−	0.996950i	$-0.524868\pi$
$661$	9.07146	−	2.43069i	0.352839	−	0.0945429i	0.430885	+	0.902407i	$0.358201\pi$
$662$	4.39521	−	22.4228i	0.170825	−	0.871488i
$663$	−3.50282	+	15.2873i	−0.136038	+	0.593709i
$664$	−4.91282	+	7.48741i	−0.190654	+	0.290568i
$665$	1.32031	+	17.5981i	0.0511994	+	0.682423i
$666$	14.3434	+	10.7699i	0.555797	+	0.417324i
$667$	−0.473040	+	1.76541i	−0.0183162	+	0.0683570i
$668$	−26.3978	+	20.4907i	−1.02136	+	0.792809i
$669$	−13.7741	−	7.29473i	−0.532538	−	0.282030i
$670$	6.32326	+	9.40653i	0.244289	+	0.363406i
$671$	6.10049	+	3.52212i	0.235507	+	0.135970i
$672$	−9.58220	−	24.1485i	−0.369641	−	0.931547i
$673$			29.7122i			1.14532i	0.819792	+	0.572661i	$0.194089\pi$
$673$			29.7122i			1.14532i	−0.819792	+	0.572661i	$0.805911\pi$
$674$	−31.2778	−	15.3162i	−1.20478	−	0.589959i
$675$	12.6957	+	5.57745i	0.488659	+	0.214676i
$676$	2.52855	+	18.4121i	0.0972521	+	0.708159i
$677$	−30.7508	+	30.7508i	−1.18185	+	1.18185i	−0.202582	+	0.979265i	$0.564933\pi$
$677$	−30.7508	+	30.7508i	−1.18185	+	1.18185i	−0.979265	+	0.202582i	$0.935067\pi$
$678$	15.5676	−	34.9724i	0.597872	−	1.34311i
$679$	4.85907	+	8.41616i	0.186474	+	0.322983i
$680$	−9.13444	−	18.1387i	−0.350290	−	0.695586i
$681$	−2.25979	+	9.86237i	−0.0865954	+	0.377927i
$682$	−4.02901	−	0.789745i	−0.154279	−	0.0302409i
$683$	4.30855	−	4.30855i	0.164862	−	0.164862i	−0.619855	−	0.784717i	$-0.712808\pi$
$683$	4.30855	−	4.30855i	0.164862	−	0.164862i	0.784717	+	0.619855i	$0.212808\pi$
$684$	12.5598	−	22.9401i	0.480238	−	0.877138i
$685$	2.70879	+	2.70879i	0.103498	+	0.103498i
$686$	−21.6886	+	14.5795i	−0.828075	+	0.556649i
$687$	11.9529	+	2.73880i	0.456031	+	0.104492i
$688$	−13.6525	−	23.0491i	−0.520496	−	0.878740i
$689$	−15.5954	+	9.00402i	−0.594138	+	0.343026i
$690$	−1.54675	+	0.593872i	−0.0588837	+	0.0226083i
$691$	−32.8618	−	32.8618i	−1.25012	−	1.25012i	−0.955664	−	0.294458i	$-0.904861\pi$
$691$	−32.8618	−	32.8618i	−1.25012	−	1.25012i	−0.294458	−	0.955664i	$-0.595139\pi$
$692$	−28.5420	−	21.6492i	−1.08501	−	0.822980i
$693$	−7.33623	−	21.0799i	−0.278680	−	0.800761i
$694$	−11.1919	+	3.83397i	−0.424837	+	0.145535i
$695$	−9.10584			−0.345404
$696$	17.2928	+	10.4631i	0.655481	+	0.396601i
$697$	−9.46172	+	16.3882i	−0.358388	+	0.620746i
$698$	7.87952	−	40.1986i	0.298244	−	1.52154i
$699$	13.3364	−	25.1822i	0.504429	−	0.952477i
$700$	8.67795	+	11.1797i	0.327996	+	0.422552i
$701$	−4.25610	−	1.14042i	−0.160751	−	0.0430731i	0.177546	−	0.984112i	$-0.443184\pi$
$701$	−4.25610	−	1.14042i	−0.160751	−	0.0430731i	−0.338297	+	0.941039i	$0.609851\pi$
$702$	8.07667	−	11.6178i	0.304834	−	0.438487i
$703$	−7.99426	+	16.6039i	−0.301509	+	0.626228i
$704$	−20.8791	−	8.24190i	−0.786912	−	0.310628i
$705$	6.30927	+	1.44566i	0.237621	+	0.0544467i
$706$	31.3434	−	21.0697i	1.17963	−	0.792968i
$707$	−8.83902	−	32.9877i	−0.332425	−	1.24063i
$708$	−22.0916	−	1.96618i	−0.830253	−	0.0738935i
$709$	2.20594	+	8.23267i	0.0828458	+	0.309185i	0.994898	−	0.100890i	$-0.0321692\pi$
$709$	2.20594	+	8.23267i	0.0828458	+	0.309185i	−0.912052	+	0.410075i	$0.865502\pi$
$710$	14.7670	−	16.9336i	0.554195	−	0.635505i
$711$	−2.36972	−	32.3554i	−0.0888716	−	1.21342i
$712$	0.319519	+	0.105489i	0.0119745	+	0.00395338i
$713$	0.396950	+	0.229179i	0.0148659	+	0.00858282i
$714$	−30.3760	+	3.19491i	−1.13679	+	0.119567i
$715$	5.83306	+	5.83306i	0.218144	+	0.218144i
$716$	−18.3596	+	7.72503i	−0.686129	+	0.288698i
$717$	−15.4819	+	9.70967i	−0.578181	+	0.362614i
$718$	4.85692	−	9.91849i	0.181259	−	0.370155i
$719$	4.85087	−	2.80065i	0.180907	−	0.104447i	−0.406812	−	0.913512i	$-0.633359\pi$
$719$	4.85087	−	2.80065i	0.180907	−	0.104447i	0.587719	+	0.809065i	$0.300026\pi$
$720$	1.54211	+	18.2574i	0.0574710	+	0.680413i
$721$		−	4.81858i		−	0.179453i
$722$	25.6252	+	8.08399i	0.953670	+	0.300855i
$723$	1.72682	+	47.2179i	0.0642210	+	1.75605i
$724$	1.94784	−	15.4612i	0.0723908	−	0.574610i
$725$	−10.6350	−	2.84965i	−0.394975	−	0.105833i
$726$	6.99774	+	3.11498i	0.259710	+	0.115608i
$727$	2.38661	−	1.37791i	0.0885145	−	0.0511039i	−0.455089	−	0.890446i	$-0.650393\pi$
$727$	2.38661	−	1.37791i	0.0885145	−	0.0511039i	0.543604	+	0.839342i	$0.317059\pi$
$728$	12.8977	−	6.49516i	0.478021	−	0.240727i
$729$	26.3532	−	5.87454i	0.976044	−	0.217575i
$730$	20.3794	−	23.3694i	0.754276	−	0.864941i
$731$	−30.4215	+	8.15140i	−1.12518	+	0.301491i
$732$	−7.88743	+	3.66357i	−0.291528	+	0.135409i
$733$	5.48759	+	5.48759i	0.202689	+	0.202689i	0.801151	−	0.598462i	$-0.204221\pi$
$733$	5.48759	+	5.48759i	0.202689	+	0.202689i	−0.598462	+	0.801151i	$0.704221\pi$
$734$	7.93630	−	0.542404i	0.292934	−	0.0200205i
$735$	−0.0781083	+	0.0240210i	−0.00288107	+	0.000886027i
$736$	1.90695	+	1.62588i	0.0702912	+	0.0599307i
$737$	7.36405	−	12.7549i	0.271258	−	0.469833i
$738$	13.4352	−	10.5340i	0.494556	−	0.387763i
$739$	−2.87423	+	10.7268i	−0.105730	+	0.394591i	−0.998427	−	0.0560670i	$-0.982144\pi$
$739$	−2.87423	+	10.7268i	−0.105730	+	0.394591i	0.892697	+	0.450658i	$0.148811\pi$
$740$	−1.75650	−	12.7903i	−0.0645702	−	0.470179i
$741$	13.3198	+	5.82341i	0.489315	+	0.213928i
$742$	−26.4319	−	23.0501i	−0.970347	−	0.846196i
$743$	−2.45838	+	1.41935i	−0.0901892	+	0.0520708i	−0.544416	−	0.838815i	$-0.683249\pi$
$743$	−2.45838	+	1.41935i	−0.0901892	+	0.0520708i	0.454227	+	0.890886i	$0.349915\pi$
$744$	3.65702	−	3.50987i	0.134073	−	0.128678i
$745$	−21.7322	−	12.5471i	−0.796205	−	0.459689i
$746$	1.06837	−	5.45043i	0.0391156	−	0.199554i
$747$	−3.12201	−	8.97078i	−0.114228	−	0.328224i
$748$	−15.9481	+	21.0258i	−0.583120	+	0.768778i
$749$	16.6610	+	16.6610i	0.608780	+	0.608780i
$750$	−10.2804	−	26.7754i	−0.375387	−	0.977701i
$751$	−20.9919	−	12.1197i	−0.766004	−	0.442253i	0.0654431	−	0.997856i	$-0.479154\pi$
$751$	−20.9919	−	12.1197i	−0.766004	−	0.442253i	−0.831447	+	0.555603i	$0.812487\pi$
$752$	−2.63920	−	9.42769i	−0.0962417	−	0.343792i
$753$	−15.5016	−	14.4078i	−0.564909	−	0.525048i
$754$	−4.94080	+	10.0898i	−0.179933	+	0.367449i
$755$	1.40934	−	5.25972i	0.0512910	−	0.191421i
$756$	26.5022	+	7.54790i	0.963876	+	0.274514i
$757$	−6.87222	−	1.84141i	−0.249775	−	0.0669271i	0.131759	−	0.991282i	$-0.457937\pi$
$757$	−6.87222	−	1.84141i	−0.249775	−	0.0669271i	−0.381534	+	0.924355i	$0.624604\pi$
$758$	−8.84527	+	45.1255i	−0.321275	+	1.63903i
$759$	1.57698	+	1.46570i	0.0572407	+	0.0532017i
$760$	−18.0934	+	5.19504i	−0.656318	+	0.188444i
$761$	13.8433			0.501820			0.250910	−	0.968010i	$-0.419270\pi$
$761$	13.8433			0.501820			0.250910	+	0.968010i	$0.419270\pi$
$762$	−25.8718	+	18.7999i	−0.937236	+	0.681048i
$763$	8.80181	−	32.8488i	0.318647	−	1.18921i
$764$	−38.3706	−	15.6435i	−1.38820	−	0.565961i
$765$	21.1584	+	4.04044i	0.764985	+	0.146082i
$766$	21.0403	−	42.9672i	0.760218	−	1.55247i
$767$		−	12.3280i		−	0.445138i
$768$	23.1432	−	15.2443i	0.835110	−	0.550083i
$769$	−2.05593	+	3.56098i	−0.0741388	+	0.128412i	−0.900711	−	0.434418i	$-0.856954\pi$
$769$	−2.05593	+	3.56098i	−0.0741388	+	0.128412i	0.826573	+	0.562830i	$0.190287\pi$
$770$	−7.06531	+	14.4283i	−0.254616	+	0.519961i
$771$	−48.3216	+	1.76718i	−1.74026	+	0.0636434i
$772$	−7.19589	−	52.3982i	−0.258986	−	1.88585i
$773$	9.00639	+	33.6123i	0.323937	+	1.20895i	0.915376	+	0.402600i	$0.131894\pi$
$773$	9.00639	+	33.6123i	0.323937	+	1.20895i	−0.591439	+	0.806350i	$0.701440\pi$
$774$	28.2082	+	3.41423i	1.01392	+	0.122722i
$775$	−1.38060	+	2.39127i	−0.0495926	+	0.0858969i
$776$	−7.73633	+	6.89993i	−0.277718	+	0.247693i
$777$	−18.9261	−	4.33658i	−0.678969	−	0.155574i
$778$	−38.2254	−	33.3346i	−1.37045	−	1.19510i
$779$	13.2961	+	11.4402i	0.476381	+	0.409888i
$780$	−10.0323	+	1.75344i	−0.359214	+	0.0627833i
$781$	−28.2007	−	7.55635i	−1.00910	−	0.270387i
$782$	2.44507	−	1.64363i	0.0874356	−	0.0587760i
$783$	−19.9757	+	7.78151i	−0.713873	+	0.278088i
$784$	0.0883679	+	0.0864181i	0.00315600	+	0.00308636i
$785$	−25.9900	−	15.0053i	−0.927622	−	0.535563i
$786$	4.49063	−	5.54631i	0.160176	−	0.197830i
$787$	14.1891	−	14.1891i	0.505786	−	0.505786i	−0.407444	−	0.913230i	$-0.633580\pi$
$787$	14.1891	−	14.1891i	0.505786	−	0.505786i	0.913230	+	0.407444i	$0.133580\pi$
$788$	−18.0433	+	7.59197i	−0.642767	+	0.270453i
$789$	−8.82774	+	16.6688i	−0.314276	+	0.593424i
$790$	−15.3473	+	17.5990i	−0.546032	+	0.626144i
$791$			41.4392i			1.47341i
$792$	20.4255	−	12.2332i	0.725787	−	0.434688i
$793$	−2.41701	−	4.18638i	−0.0858305	−	0.148663i
$794$	9.21584	−	3.15704i	0.327058	−	0.112039i
$795$	13.1413	+	20.9536i	0.466075	+	0.743147i
$796$	39.9485	−	31.0091i	1.41594	−	1.09909i
$797$	−0.0164964	−	0.0164964i	−0.000584332	−	0.000584332i	0.706815	−	0.707399i	$-0.250132\pi$
$797$	−0.0164964	−	0.0164964i	−0.000584332	−	0.000584332i	−0.707399	+	0.706815i	$0.750132\pi$
$798$	−2.32231	+	28.2158i	−0.0822088	+	0.998827i
$799$	−11.5098			−0.407187
$800$	−9.79447	+	11.4877i	−0.346287	+	0.406151i
$801$	−0.295219	+	0.200547i	−0.0104310	+	0.00708598i
$802$	−22.7685	+	46.4965i	−0.803985	+	1.64185i
$803$	−38.9188	−	10.4283i	−1.37341	−	0.368005i
$804$	7.65979	+	16.4911i	0.270140	+	0.581595i
$805$	1.26822	−	1.26822i	0.0446989	−	0.0446989i
$806$	2.12346	+	1.85177i	0.0747956	+	0.0652259i
$807$	−19.1028	+	5.87478i	−0.672452	+	0.206802i
$808$	32.5362	−	16.3849i	1.14462	−	0.576419i
$809$	30.0265			1.05568			0.527839	−	0.849345i	$-0.323003\pi$
$809$	30.0265			1.05568			0.527839	+	0.849345i	$0.323003\pi$
$810$	−16.3515	−	10.5025i	−0.574533	−	0.369020i
$811$	−0.146036	+	0.0391303i	−0.00512802	+	0.00137405i	−0.261382	−	0.965235i	$-0.584178\pi$
$811$	−0.146036	+	0.0391303i	−0.00512802	+	0.00137405i	0.256254	+	0.966609i	$0.417512\pi$
$812$	−21.7078	−	2.73480i	−0.761793	−	0.0959725i
$813$	−7.35324	+	13.8846i	−0.257889	+	0.486954i
$814$	−13.9227	+	9.35912i	−0.487990	+	0.328037i
$815$	−10.1833	+	5.87933i	−0.356705	+	0.205944i
$816$	−9.92378	−	31.0325i	−0.347402	−	1.08635i
$817$	2.18407	+	29.1109i	0.0764109	+	1.01846i
$818$	38.9678	−	2.66324i	1.36248	−	0.0931181i
$819$	−2.87301	+	15.0450i	−0.100391	+	0.525714i
$820$	−12.1919	−	1.53597i	−0.425761	−	0.0536384i
$821$	−15.1634	+	4.06302i	−0.529206	+	0.141800i	−0.513521	−	0.858077i	$-0.671659\pi$
$821$	−15.1634	+	4.06302i	−0.529206	+	0.141800i	−0.0156842	+	0.999877i	$0.504993\pi$
$822$	3.61266	+	4.97163i	0.126006	+	0.173406i
$823$	32.5276	+	18.7798i	1.13384	+	0.654623i	0.944898	−	0.327365i	$-0.106161\pi$
$823$	32.5276	+	18.7798i	1.13384	+	0.654623i	0.188942	+	0.981988i	$0.439494\pi$
$824$	5.03262	−	1.04489i	0.175320	−	0.0364006i
$825$	−8.82956	+	9.49989i	−0.307406	+	0.330744i
$826$	22.7130	−	7.78075i	0.790288	−	0.270727i
$827$	5.01846	+	18.7292i	0.174509	+	0.651277i	0.996635	+	0.0819706i	$0.0261214\pi$
$827$	5.01846	+	18.7292i	0.174509	+	0.651277i	−0.822126	+	0.569306i	$0.807212\pi$
$828$	−2.59983	+	0.553012i	−0.0903504	+	0.0192185i
$829$	−26.0171	+	26.0171i	−0.903612	+	0.903612i	−0.995747	−	0.0921350i	$-0.970631\pi$
$829$	−26.0171	+	26.0171i	−0.903612	+	0.903612i	0.0921350	+	0.995747i	$0.470631\pi$
$830$	−3.00671	+	6.14012i	−0.104365	+	0.213127i
$831$	26.3643	+	6.04092i	0.914567	+	0.209557i
$832$	9.58050	+	12.0622i	0.332144	+	0.418181i
$833$	0.125843	−	0.0726554i	0.00436019	−	0.00251736i
$834$	−14.4284	−	2.28415i	−0.499616	−	0.0790936i
$835$	−18.0396	+	18.0396i	−0.624286	+	0.624286i
$836$	16.4026	+	18.1466i	0.567295	+	0.627613i
$837$	0.588410	+	5.34400i	0.0203384	+	0.184716i
$838$	25.2780	+	4.95487i	0.873216	+	0.171163i
$839$	−41.3467	+	23.8715i	−1.42745	+	0.824136i	−0.996919	−	0.0784419i	$-0.975006\pi$
$839$	−41.3467	+	23.8715i	−1.42745	+	0.824136i	−0.430527	+	0.902578i	$0.641672\pi$
$840$	−9.56236	−	17.3768i	−0.329933	−	0.599556i
$841$	−10.3737	+	5.98925i	−0.357713	+	0.206526i
$842$	24.2451	−	8.30557i	0.835541	−	0.286229i
$843$	0.369111	+	10.0929i	0.0127129	+	0.347619i
$844$	6.87710	−	9.06667i	0.236719	−	0.312088i
$845$	3.67222	+	13.7049i	0.126328	+	0.471463i
$846$	9.63456	+	3.87333i	0.331243	+	0.133168i
$847$	−8.29169			−0.284906
$848$	18.3423	−	32.6044i	0.629877	−	1.11964i
$849$	7.49929	+	24.3852i	0.257375	+	0.836900i
$850$	9.90139	+	14.7294i	0.339615	+	0.505214i
$851$	1.80906	−	0.484736i	0.0620137	−	0.0166165i
$852$	27.6464	−	23.1274i	0.947149	−	0.792333i
$853$	−26.0587	−	6.98242i	−0.892234	−	0.239073i	−0.216556	−	0.976270i	$-0.569482\pi$
$853$	−26.0587	−	6.98242i	−0.892234	−	0.239073i	−0.675678	+	0.737197i	$0.736149\pi$
$854$	6.18749	−	7.09530i	0.211732	−	0.242796i
$855$	7.32434	−	18.5744i	0.250487	−	0.635233i
$856$	−13.7882	+	21.0140i	−0.471270	+	0.718242i
$857$	4.36326	−	2.51913i	0.149046	−	0.0860517i	−0.423622	−	0.905839i	$-0.639242\pi$
$857$	4.36326	−	2.51913i	0.149046	−	0.0860517i	0.572668	+	0.819787i	$0.305908\pi$
$858$	7.77945	+	10.7058i	0.265586	+	0.365491i
$859$	−5.26029	−	19.6317i	−0.179479	−	0.669824i	−0.995745	−	0.0921487i	$-0.970627\pi$
$859$	−5.26029	−	19.6317i	−0.179479	−	0.669824i	0.816266	−	0.577676i	$-0.196040\pi$
$860$	−12.5405	−	16.1557i	−0.427627	−	0.550905i
$861$	−8.64943	+	16.3321i	−0.294772	+	0.556596i
$862$	31.7521	−	2.17009i	1.08148	−	0.0739135i
$863$	−35.1101			−1.19516			−0.597581	−	0.801808i	$-0.703871\pi$
$863$	−35.1101			−1.19516			−0.597581	+	0.801808i	$0.703871\pi$
$864$	−2.13625	+	29.3161i	−0.0726768	+	0.997356i
$865$	−23.6849	−	13.6745i	−0.805312	−	0.464947i
$866$	1.51883	+	22.2231i	0.0516121	+	0.755173i
$867$	−8.85271	+	0.323755i	−0.300654	+	0.0109953i
$868$	−2.07149	+	5.08099i	−0.0703109	+	0.172460i
$869$	29.3089	+	7.85329i	0.994236	+	0.266405i
$870$	14.0968	+	6.27505i	0.477926	+	0.212744i
$871$	−8.75290	+	5.05349i	−0.296581	+	0.171231i
$872$	36.2166	+	2.06962i	1.22645	+	0.0700862i
$873$	−0.803135	−	10.9657i	−0.0271820	−	0.371134i
$874$	−1.07581	−	2.51000i	−0.0363897	−	0.0849019i
$875$	21.9539	+	21.9539i	0.742178	+	0.742178i
$876$	38.1538	−	31.9174i	1.28910	−	1.07839i
$877$	35.5078	+	9.51428i	1.19901	+	0.321274i	0.802442	−	0.596730i	$-0.203534\pi$
$877$	35.5078	+	9.51428i	1.19901	+	0.321274i	0.396570	+	0.918004i	$0.370200\pi$
$878$	−22.3031	+	45.5460i	−0.752693	+	1.53710i
$879$	−26.7468	−	6.12856i	−0.902147	−	0.206711i
$880$	−16.6013	−	4.25041i	−0.559630	−	0.143281i
$881$		−	45.8533i		−	1.54484i	−0.635114	−	0.772418i	$-0.719047\pi$
$881$		−	45.8533i		−	1.54484i	0.635114	−	0.772418i	$-0.280953\pi$
$882$	−0.129790	+	0.0184688i	−0.00437026	+	0.000621877i
$883$	21.5978	−	5.78713i	0.726825	−	0.194752i	0.123610	−	0.992331i	$-0.460553\pi$
$883$	21.5978	−	5.78713i	0.726825	−	0.194752i	0.603215	+	0.797579i	$0.293886\pi$
$884$	16.6923	−	7.02349i	0.561422	−	0.236226i
$885$	−16.9208	+	0.618815i	−0.568787	+	0.0208013i
$886$	−2.23745	−	1.95118i	−0.0751685	−	0.0655511i
$887$	3.69225	+	2.13172i	0.123973	+	0.0715761i	0.560704	−	0.828016i	$-0.310530\pi$
$887$	3.69225	+	2.13172i	0.123973	+	0.0715761i	−0.436731	+	0.899592i	$0.643864\pi$
$888$	0.425149	−	20.7071i	0.0142671	−	0.694885i
$889$	17.3098	−	29.9814i	0.580552	−	1.00555i
$890$	0.252085	+	0.0494124i	0.00844991	+	0.00165631i
$891$	−2.91222	+	25.0844i	−0.0975631	+	0.840358i
$892$	2.44866	+	17.8304i	0.0819873	+	0.597006i
$893$	−1.98251	+	10.4827i	−0.0663421	+	0.350791i
$894$	−31.2878	−	25.3326i	−1.04642	−	0.847247i
$895$	−13.1692	+	7.60326i	−0.440199	+	0.254149i
$896$	−16.1766	+	25.2640i	−0.540423	+	0.844013i
$897$	−0.434286	−	1.41216i	−0.0145004	−	0.0471506i
$898$	−8.86732	−	13.1911i	−0.295906	−	0.440193i
$899$	−1.10483	−	4.12329i	−0.0368483	−	0.137520i
$900$	−3.33141	−	15.6617i	−0.111047	−	0.522056i
$901$	−31.0991	−	31.0991i	−1.03606	−	1.03606i
$902$	5.17482	+	15.1060i	0.172303	+	0.502974i
$903$	−29.3995	+	9.04135i	−0.978355	+	0.300877i
$904$	−43.2799	+	8.98596i	−1.43947	+	0.298869i
$905$		−	11.8969i		−	0.395466i
$906$	3.55250	−	7.98064i	0.118024	−	0.265139i
$907$	10.3574	−	38.6543i	0.343911	−	1.28349i	−0.549968	−	0.835186i	$-0.685360\pi$
$907$	10.3574	−	38.6543i	0.343911	−	1.28349i	0.893879	−	0.448308i	$-0.147973\pi$
$908$	10.7688	−	4.53110i	0.357374	−	0.150370i
$909$	−7.24755	+	37.9530i	−0.240386	+	1.25882i
$910$	9.14953	−	6.15050i	0.303304	−	0.203887i
$911$	48.2068			1.59716			0.798581	−	0.601887i	$-0.205584\pi$
$911$	48.2068			1.59716			0.798581	+	0.601887i	$0.205584\pi$
$912$	−29.9727	+	3.69304i	−0.992495	+	0.122289i
$913$	8.88388			0.294014
$914$	−9.13609	+	6.14146i	−0.302195	+	0.203142i
$915$	−5.62471	+	3.52761i	−0.185947	+	0.116619i
$916$	−5.49156	−	13.0514i	−0.181446	−	0.431231i
$917$	−1.99941	+	7.46189i	−0.0660263	+	0.246413i
$918$	32.5126	+	11.7097i	1.07308	+	0.386477i
$919$		−	24.8558i		−	0.819918i	−0.912104	−	0.409959i	$-0.865543\pi$
$919$		−	24.8558i		−	0.819918i	0.912104	−	0.409959i	$-0.134457\pi$
$920$	1.59956	+	1.04954i	0.0527361	+	0.0346025i
$921$	10.7663	+	35.0086i	0.354762	+	1.15357i
$922$	6.43674	+	18.7897i	0.211983	+	0.618806i
$923$	14.1669	+	14.1669i	0.466309	+	0.466309i
$924$	−14.8144	+	21.0898i	−0.487359	+	0.693802i
$925$	2.92010	+	10.8980i	0.0960123	+	0.358323i
$926$	−31.2940	−	46.5532i	−1.02838	−	1.52983i
$927$	−2.37372	+	4.90784i	−0.0779632	+	0.161195i
$928$	−1.85099	−	23.2650i	−0.0607616	−	0.763712i
$929$	17.2550	−	9.96219i	0.566119	−	0.326849i	−0.189479	−	0.981885i	$-0.560680\pi$
$929$	17.2550	−	9.96219i	0.566119	−	0.326849i	0.755598	+	0.655036i	$0.227347\pi$
$930$	2.43507	−	3.00751i	0.0798490	−	0.0986201i
$931$	−0.0444962	−	0.127128i	−0.00145830	−	0.00416645i
$932$	−32.5980	+	4.47671i	−1.06778	+	0.146639i
$933$	10.1847	+	16.2392i	0.333431	+	0.531649i
$934$	−17.5693	−	3.44384i	−0.574885	−	0.112686i
$935$	−10.0734	+	17.4477i	−0.329437	+	0.570602i
$936$	−16.3363	+	0.261832i	−0.533968	+	0.00855825i
$937$	6.85308	+	3.95663i	0.223880	+	0.129257i	0.607746	−	0.794132i	$-0.292074\pi$
$937$	6.85308	+	3.95663i	0.223880	+	0.129257i	−0.383865	+	0.923389i	$0.625407\pi$
$938$	−14.8349	−	12.9368i	−0.484376	−	0.422402i
$939$	0.782105	+	21.3858i	0.0255230	+	0.697899i
$940$	−2.89869	−	6.88912i	−0.0945448	−	0.224698i
$941$	9.55658	−	2.56068i	0.311536	−	0.0834757i	−0.0996637	−	0.995021i	$-0.531777\pi$
$941$	9.55658	−	2.56068i	0.311536	−	0.0834757i	0.411199	+	0.911545i	$0.365110\pi$
$942$	−37.4178	−	30.2958i	−1.21914	−	0.987089i
$943$		−	1.78264i		−	0.0580508i
$944$	13.0516	+	22.0347i	0.424794	+	0.717169i
$945$	20.7942	+	3.18816i	0.676437	+	0.103711i
$946$	−11.6875	+	23.8675i	−0.379993	+	0.775999i
$947$	42.9330	+	11.5039i	1.39513	+	0.373825i	0.876595	−	0.481228i	$-0.159809\pi$
$947$	42.9330	+	11.5039i	1.39513	+	0.373825i	0.518540	+	0.855054i	$0.326476\pi$
$948$	−28.7328	+	24.0363i	−0.933198	+	0.780662i
$949$	19.5513	+	19.5513i	0.634661	+	0.634661i
$950$	15.1205	−	6.48078i	0.490574	−	0.210264i
$951$	41.2792	+	38.3664i	1.33857	+	1.24412i
$952$	23.4753	+	26.3209i	0.760839	+	0.853066i
$953$	0.254397	−	0.146876i	0.00824071	−	0.00475778i	−0.495874	−	0.868394i	$-0.665152\pi$
$953$	0.254397	−	0.146876i	0.00824071	−	0.00475778i	0.504115	+	0.863637i	$0.331819\pi$
$954$	15.5667	+	36.4979i	0.503990	+	1.18166i
$955$	−30.5565	−	8.18758i	−0.988784	−	0.264944i
$956$	19.5403	+	7.96647i	0.631979	+	0.257654i
$957$	−0.732786	−	20.0372i	−0.0236876	−	0.647711i
$958$	−3.04517	−	44.5560i	−0.0983849	−	1.43954i
$959$	−5.76136	−	3.32632i	−0.186044	−	0.107413i
$960$	16.0751	−	13.7552i	0.518821	−	0.443948i
$961$	29.9295			0.965466
$962$	11.4855	−	0.784975i	0.370308	−	0.0253086i
$963$	−8.76213	−	25.1771i	−0.282356	−	0.811322i
$964$	43.0986	−	33.4543i	1.38811	−	1.07749i
$965$	−10.4506	−	39.0022i	−0.336417	−	1.25552i
$966$	2.32765	−	1.69140i	0.0748911	−	0.0544200i
$967$	17.0648	−	9.85238i	0.548768	−	0.316831i	−0.199857	−	0.979825i	$-0.564048\pi$
$967$	17.0648	−	9.85238i	0.548768	−	0.316831i	0.748625	+	0.662994i	$0.230714\pi$
$968$	−1.79803	−	8.66000i	−0.0577908	−	0.278343i
$969$	−5.31824	+	35.1033i	−0.170846	+	1.12768i
$970$	−5.20143	+	5.96456i	−0.167008	+	0.191511i
$971$	21.2082	+	5.68271i	0.680603	+	0.182367i	0.582526	−	0.812812i	$-0.302064\pi$
$971$	21.2082	+	5.68271i	0.680603	+	0.182367i	0.0980766	+	0.995179i	$0.468731\pi$
$972$	−23.2749	−	20.7432i	−0.746543	−	0.665337i
$973$	15.2745	−	4.09280i	0.489679	−	0.131209i
$974$	−26.2208	−	39.0062i	−0.840168	−	1.24984i
$975$	8.50699	−	2.61619i	0.272442	−	0.0837851i
$976$	8.75221	+	4.92374i	0.280151	+	0.157605i
$977$	35.1669			1.12509			0.562545	−	0.826767i	$-0.309822\pi$
$977$	35.1669			1.12509			0.562545	+	0.826767i	$0.309822\pi$
$978$	−17.6105	+	6.76153i	−0.563121	+	0.216210i
$979$	−0.0863937	−	0.322426i	−0.00276116	−	0.0103048i
$980$	0.0751804	+	0.0570246i	0.00240155	+	0.00182158i
$981$	−25.1468	+	29.1214i	−0.802874	+	0.929774i
$982$	−53.5986	+	18.3611i	−1.71040	+	0.585927i
$983$	−33.3398	+	19.2487i	−1.06337	+	0.613939i	−0.926363	−	0.376631i	$-0.877082\pi$
$983$	−33.3398	+	19.2487i	−1.06337	+	0.613939i	−0.137010	+	0.990570i	$0.543749\pi$
$984$	−18.9332	−	5.49207i	−0.603567	−	0.175081i
$985$	−12.9424	+	7.47229i	−0.412379	+	0.238087i
$986$	−26.9256	−	5.27782i	−0.857487	−	0.168080i
$987$	−11.2332	+	0.410813i	−0.357557	+	0.0130763i
$988$	−3.52159	−	16.4125i	−0.112037	−	0.522152i
$989$	2.09790	−	2.09790i	0.0667094	−	0.0667094i
$990$	14.3038	−	11.2151i	0.454606	−	0.356439i
$991$	−49.9944	+	28.8643i	−1.58812	+	0.916904i	−0.594508	+	0.804090i	$0.702653\pi$
$991$	−49.9944	+	28.8643i	−1.58812	+	0.916904i	−0.993616	+	0.112814i	$0.964014\pi$
$992$	−5.75588	−	1.06171i	−0.182749	−	0.0337092i
$993$	6.25026	−	27.2779i	0.198346	−	0.865639i
$994$	−17.1597	+	35.0424i	−0.544272	+	1.11148i
$995$	27.2998	−	27.2998i	0.865463	−	0.865463i
$996$	−6.30443	+	8.97496i	−0.199764	+	0.284383i
$997$	−3.04008	−	11.3457i	−0.0962802	−	0.359322i	0.900930	−	0.433964i	$-0.142885\pi$
$997$	−3.04008	−	11.3457i	−0.0962802	−	0.359322i	−0.997210	+	0.0746414i	$0.976219\pi$
$998$	−47.9788	+	16.4360i	−1.51874	+	0.520271i
$999$	17.1404	+	13.7402i	0.542297	+	0.434721i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.br.a.221.48	✓	624
3.2	odd	2	inner	912.2.br.a.221.109	yes	624
16.5	even	4	inner	912.2.br.a.677.57	yes	624
19.8	odd	6	inner	912.2.br.a.749.100	yes	624
48.5	odd	4	inner	912.2.br.a.677.100	yes	624
57.8	even	6	inner	912.2.br.a.749.57	yes	624
304.293	odd	12	inner	912.2.br.a.293.109	yes	624
912.293	even	12	inner	912.2.br.a.293.48	yes	624

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.br.a.221.48	✓	624	1.1	even	1	trivial
912.2.br.a.221.109	yes	624	3.2	odd	2	inner
912.2.br.a.293.48	yes	624	912.293	even	12	inner
912.2.br.a.293.109	yes	624	304.293	odd	12	inner
912.2.br.a.677.57	yes	624	16.5	even	4	inner
912.2.br.a.677.100	yes	624	48.5	odd	4	inner
912.2.br.a.749.57	yes	624	57.8	even	6	inner
912.2.br.a.749.100	yes	624	19.8	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.br (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.788971 - 1.17368i) q^{2} +(-0.920267 - 1.46735i) q^{3} +(-0.755049 + 1.85200i) q^{4} +(-0.395182 + 1.47484i) q^{5} +(-0.996132 + 2.23779i) q^{6} -2.65158i q^{7} +(2.76937 - 0.574988i) q^{8} +(-1.30622 + 2.70070i) q^{9} +O(q^{10})\)	\(q+(-0.788971 - 1.17368i) q^{2} +(-0.920267 - 1.46735i) q^{3} +(-0.755049 + 1.85200i) q^{4} +(-0.395182 + 1.47484i) q^{5} +(-0.996132 + 2.23779i) q^{6} -2.65158i q^{7} +(2.76937 - 0.574988i) q^{8} +(-1.30622 + 2.70070i) q^{9} +(2.04278 - 0.699789i) q^{10} +(-1.98405 - 1.98405i) q^{11} +(3.41237 - 0.596414i) q^{12} +(0.498355 + 1.85989i) q^{13} +(-3.11211 + 2.09202i) q^{14} +(2.52778 - 0.777377i) q^{15} +(-2.85980 - 2.79670i) q^{16} +(-4.07258 + 2.35130i) q^{17} +(4.20033 - 0.597696i) q^{18} +(1.44001 + 4.11417i) q^{19} +(-2.43302 - 1.84545i) q^{20} +(-3.89080 + 2.44017i) q^{21} +(-0.763282 + 3.89400i) q^{22} +(0.221500 - 0.383649i) q^{23} +(-3.39226 - 3.53448i) q^{24} +(2.31114 + 1.33434i) q^{25} +(1.78972 - 2.05231i) q^{26} +(5.16494 - 0.568694i) q^{27} +(4.91073 + 2.00208i) q^{28} +(-3.98513 + 1.06781i) q^{29} +(-2.90673 - 2.35347i) q^{30} +1.03467i q^{31} +(-1.02613 + 5.56301i) q^{32} +(-1.08544 + 4.73715i) q^{33} +(5.97283 + 2.92479i) q^{34} +(3.91066 + 1.04786i) q^{35} +(-4.01544 - 4.45828i) q^{36} +(2.98944 + 2.98944i) q^{37} +(3.69259 - 4.93607i) q^{38} +(2.27048 - 2.44285i) q^{39} +(-0.246389 + 4.31160i) q^{40} +(3.48491 - 2.01201i) q^{41} +(5.93370 + 2.64133i) q^{42} +(6.46906 + 1.73338i) q^{43} +(5.17252 - 2.17641i) q^{44} +(-3.46691 - 2.99373i) q^{45} +(-0.625038 + 0.0427180i) q^{46} +(2.11963 + 1.22377i) q^{47} +(-1.47195 + 6.77003i) q^{48} -0.0309000 q^{49} +(-0.257338 - 3.76530i) q^{50} +(7.19804 + 3.81206i) q^{51} +(-3.82079 - 0.481352i) q^{52} +(2.42058 + 9.03374i) q^{53} +(-4.74245 - 5.61330i) q^{54} +(3.71022 - 2.14210i) q^{55} +(-1.52463 - 7.34321i) q^{56} +(4.71172 - 5.89912i) q^{57} +(4.39742 + 3.83480i) q^{58} +(-6.18435 - 1.65709i) q^{59} +(-0.468893 + 5.26840i) q^{60} +(-2.42499 + 0.649774i) q^{61} +(1.21437 - 0.816324i) q^{62} +(7.16114 + 3.46354i) q^{63} +(7.33878 - 3.18470i) q^{64} -2.93997 q^{65} +(6.41628 - 2.46352i) q^{66} +(1.35855 + 5.07017i) q^{67} +(-1.27962 - 9.31776i) q^{68} +(-0.766785 + 0.0280423i) q^{69} +(-1.85555 - 5.41660i) q^{70} +(9.01111 - 5.20256i) q^{71} +(-2.06452 + 8.23029i) q^{72} +(12.4359 - 7.17988i) q^{73} +(1.15007 - 5.86724i) q^{74} +(-0.168930 - 4.61920i) q^{75} +(-8.70671 - 0.439509i) q^{76} +(-5.26088 + 5.26088i) q^{77} +(-4.65847 - 0.737476i) q^{78} +(-9.36522 + 5.40701i) q^{79} +(5.25483 - 3.11254i) q^{80} +(-5.58759 - 7.05541i) q^{81} +(-5.11095 - 2.50275i) q^{82} +(-2.23882 + 2.23882i) q^{83} +(-1.58144 - 9.04820i) q^{84} +(-1.85839 - 6.93560i) q^{85} +(-3.06947 - 8.96019i) q^{86} +(5.23424 + 4.86490i) q^{87} +(-6.63537 - 4.35376i) q^{88} +(0.103026 + 0.0594823i) q^{89} +(-0.778389 + 6.43101i) q^{90} +(4.93164 - 1.32143i) q^{91} +(0.543274 + 0.699891i) q^{92} +(1.51822 - 0.952172i) q^{93} +(-0.236013 - 3.45328i) q^{94} +(-6.63681 + 0.497932i) q^{95} +(9.10718 - 3.61376i) q^{96} +(-3.17401 + 1.83252i) q^{97} +(0.0243792 + 0.0362667i) q^{98} +(7.94994 - 2.76673i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 624 q - 6 q^{3} - 4 q^{4} - 2 q^{6}+O(q^{10}) \) 624 * q - 6 * q^3 - 4 * q^4 - 2 * q^6	\( 624 q - 6 q^{3} - 4 q^{4} - 2 q^{6} - 24 q^{10} - 12 q^{13} - 12 q^{15} + 12 q^{21} - 12 q^{22} + 14 q^{24} + 12 q^{28} - 56 q^{30} - 12 q^{33} - 12 q^{34} - 18 q^{36} - 12 q^{40} + 30 q^{42} - 4 q^{43} + 12 q^{45} - 6 q^{48} - 560 q^{49} - 6 q^{51} + 36 q^{52} + 20 q^{54} - 16 q^{58} - 48 q^{60} + 28 q^{61} + 24 q^{63} - 64 q^{64} + 2 q^{66} - 12 q^{67} + 144 q^{70} + 126 q^{72} + 4 q^{76} - 18 q^{78} - 24 q^{79} - 4 q^{81} + 20 q^{82} - 60 q^{85} - 114 q^{90} + 72 q^{91} + 4 q^{93} + 24 q^{96} - 24 q^{97} - 52 q^{99}+O(q^{100}) \) 624 * q - 6 * q^3 - 4 * q^4 - 2 * q^6 - 24 * q^10 - 12 * q^13 - 12 * q^15 + 12 * q^21 - 12 * q^22 + 14 * q^24 + 12 * q^28 - 56 * q^30 - 12 * q^33 - 12 * q^34 - 18 * q^36 - 12 * q^40 + 30 * q^42 - 4 * q^43 + 12 * q^45 - 6 * q^48 - 560 * q^49 - 6 * q^51 + 36 * q^52 + 20 * q^54 - 16 * q^58 - 48 * q^60 + 28 * q^61 + 24 * q^63 - 64 * q^64 + 2 * q^66 - 12 * q^67 + 144 * q^70 + 126 * q^72 + 4 * q^76 - 18 * q^78 - 24 * q^79 - 4 * q^81 + 20 * q^82 - 60 * q^85 - 114 * q^90 + 72 * q^91 + 4 * q^93 + 24 * q^96 - 24 * q^97 - 52 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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