LMFDB - Embedded newform 360.2.bk.a.229.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(229,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2, 3]))

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

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

chi := DirichletCharacter("360.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bk (of order $6$, degree $2$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			229.6
Character	$\chi$	$=$	360.229
Dual form			360.2.bk.a.349.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37959 - 0.311008i) q^{2} +(1.28537 - 1.16096i) q^{3} +(1.80655 + 0.858129i) q^{4} +(2.15709 + 0.589033i) q^{5} +(-2.13435 + 1.20190i) q^{6} +(2.73484 - 1.57896i) q^{7} +(-2.22541 - 1.74572i) q^{8} +(0.304332 - 2.98452i) q^{9} +O(q^{10})$	\(q+(-1.37959 - 0.311008i) q^{2} +(1.28537 - 1.16096i) q^{3} +(1.80655 + 0.858129i) q^{4} +(2.15709 + 0.589033i) q^{5} +(-2.13435 + 1.20190i) q^{6} +(2.73484 - 1.57896i) q^{7} +(-2.22541 - 1.74572i) q^{8} +(0.304332 - 2.98452i) q^{9} +(-2.79271 - 1.48350i) q^{10} +(-1.20586 + 0.696203i) q^{11} +(3.31833 - 0.994324i) q^{12} +(-0.203038 + 0.351673i) q^{13} +(-4.26404 + 1.32777i) q^{14} +(3.45650 - 1.74718i) q^{15} +(2.52723 + 3.10050i) q^{16} +4.89168i q^{17} +(-1.34807 + 4.02278i) q^{18} +2.85078i q^{19} +(3.39142 + 2.91518i) q^{20} +(1.68216 - 5.20460i) q^{21} +(1.88012 - 0.585444i) q^{22} +(-4.12775 - 2.38316i) q^{23} +(-4.88719 + 0.339734i) q^{24} +(4.30608 + 2.54120i) q^{25} +(0.389483 - 0.422018i) q^{26} +(-3.07374 - 4.18952i) q^{27} +(6.29558 - 0.505623i) q^{28} +(-4.93309 + 2.84812i) q^{29} +(-5.31194 + 1.33539i) q^{30} +(5.38957 - 9.33501i) q^{31} +(-2.52226 - 5.06342i) q^{32} +(-0.741705 + 2.29483i) q^{33} +(1.52135 - 6.74852i) q^{34} +(6.82937 - 1.79505i) q^{35} +(3.11090 - 5.13053i) q^{36} -10.3639 q^{37} +(0.886616 - 3.93291i) q^{38} +(0.147300 + 0.687748i) q^{39} +(-3.77213 - 5.07652i) q^{40} +(1.59750 - 2.76695i) q^{41} +(-3.93937 + 6.65705i) q^{42} +(2.73697 + 4.74056i) q^{43} +(-2.77588 + 0.222942i) q^{44} +(2.41446 - 6.25863i) q^{45} +(4.95342 + 4.57155i) q^{46} +(1.75646 - 1.01409i) q^{47} +(6.84798 + 1.05126i) q^{48} +(1.48625 - 2.57426i) q^{49} +(-5.15030 - 4.84504i) q^{50} +(5.67905 + 6.28759i) q^{51} +(-0.668579 + 0.461080i) q^{52} +0.428182 q^{53} +(2.93753 + 6.73579i) q^{54} +(-3.01124 + 0.791482i) q^{55} +(-8.84258 - 1.26042i) q^{56} +(3.30965 + 3.66429i) q^{57} +(7.69144 - 2.39501i) q^{58} +(-6.13487 - 3.54197i) q^{59} +(7.74363 - 0.190241i) q^{60} +(5.91265 - 3.41367i) q^{61} +(-10.3387 + 11.2023i) q^{62} +(-3.88015 - 8.64273i) q^{63} +(1.90493 + 7.76989i) q^{64} +(-0.645119 + 0.638993i) q^{65} +(1.73696 - 2.93526i) q^{66} +(-3.61288 + 6.25768i) q^{67} +(-4.19769 + 8.83705i) q^{68} +(-8.07242 + 1.72893i) q^{69} +(-9.98002 + 0.352449i) q^{70} +11.5407 q^{71} +(-5.88740 + 6.11052i) q^{72} +3.83292i q^{73} +(14.2980 + 3.22327i) q^{74} +(8.48512 - 1.73283i) q^{75} +(-2.44634 + 5.15007i) q^{76} +(-2.19856 + 3.80802i) q^{77} +(0.0106811 - 0.994623i) q^{78} +(-2.02671 - 3.51037i) q^{79} +(3.62516 + 8.17669i) q^{80} +(-8.81476 - 1.81657i) q^{81} +(-3.06444 + 3.32042i) q^{82} +(3.96883 + 6.87422i) q^{83} +(7.50511 - 7.95884i) q^{84} +(-2.88136 + 10.5518i) q^{85} +(-2.30154 - 7.39126i) q^{86} +(-3.03426 + 9.38801i) q^{87} +(3.89891 + 0.555752i) q^{88} -11.6735 q^{89} +(-5.27745 + 7.88344i) q^{90} +1.28236i q^{91} +(-5.41192 - 7.84742i) q^{92} +(-3.91002 - 18.2560i) q^{93} +(-2.73858 + 0.852758i) q^{94} +(-1.67920 + 6.14939i) q^{95} +(-9.12047 - 3.58009i) q^{96} +(-14.9833 + 8.65059i) q^{97} +(-2.85103 + 3.08919i) q^{98} +(1.71085 + 3.81079i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 2 q^{4} - 8 q^{9}+O(q^{10}) $ 136 * q - 2 * q^4 - 8 * q^9	$ 136 q - 2 q^{4} - 8 q^{9} - 10 q^{14} + 2 q^{15} - 2 q^{16} - 2 q^{20} - 38 q^{24} - 2 q^{25} + 16 q^{26} - 12 q^{30} - 4 q^{31} + 8 q^{34} - 24 q^{36} + 4 q^{39} - 6 q^{40} - 4 q^{41} - 56 q^{44} - 28 q^{46} + 40 q^{49} - 12 q^{50} + 10 q^{54} - 28 q^{55} + 26 q^{56} - 58 q^{60} - 20 q^{64} + 18 q^{65} + 16 q^{66} - 6 q^{70} - 128 q^{71} + 36 q^{74} + 12 q^{76} - 4 q^{79} - 36 q^{80} - 16 q^{81} - 110 q^{84} + 44 q^{86} - 32 q^{89} + 32 q^{90} - 34 q^{94} + 8 q^{95} - 2 q^{96}+O(q^{100}) $ 136 * q - 2 * q^4 - 8 * q^9 - 10 * q^14 + 2 * q^15 - 2 * q^16 - 2 * q^20 - 38 * q^24 - 2 * q^25 + 16 * q^26 - 12 * q^30 - 4 * q^31 + 8 * q^34 - 24 * q^36 + 4 * q^39 - 6 * q^40 - 4 * q^41 - 56 * q^44 - 28 * q^46 + 40 * q^49 - 12 * q^50 + 10 * q^54 - 28 * q^55 + 26 * q^56 - 58 * q^60 - 20 * q^64 + 18 * q^65 + 16 * q^66 - 6 * q^70 - 128 * q^71 + 36 * q^74 + 12 * q^76 - 4 * q^79 - 36 * q^80 - 16 * q^81 - 110 * q^84 + 44 * q^86 - 32 * q^89 + 32 * q^90 - 34 * q^94 + 8 * q^95 - 2 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.37959	−	0.311008i	−0.975519	−	0.219916i
$2$	−1.37959	−	0.311008i	−0.975519	−	0.219916i
$3$	1.28537	−	1.16096i	0.742106	−	0.670282i
$3$	1.28537	−	1.16096i	0.742106	−	0.670282i
$4$	1.80655	+	0.858129i	0.903274	+	0.429064i
$5$	2.15709	+	0.589033i	0.964680	+	0.263424i
$5$	2.15709	+	0.589033i	0.964680	+	0.263424i
$6$	−2.13435	+	1.20190i	−0.871345	+	0.490672i
$7$	2.73484	−	1.57896i	1.03367	−	0.596792i	0.115639	−	0.993291i	$-0.463108\pi$
$7$	2.73484	−	1.57896i	1.03367	−	0.596792i	0.918035	+	0.396499i	$0.129775\pi$
$8$	−2.22541	−	1.74572i	−0.786802	−	0.617205i
$9$	0.304332	−	2.98452i	0.101444	−	0.994841i
$10$	−2.79271	−	1.48350i	−0.883133	−	0.469123i
$11$	−1.20586	+	0.696203i	−0.363580	+	0.209913i	−0.670650	−	0.741774i	$-0.733985\pi$
$11$	−1.20586	+	0.696203i	−0.363580	+	0.209913i	0.307070	+	0.951687i	$0.400651\pi$
$12$	3.31833	−	0.994324i	0.957920	−	0.287037i
$13$	−0.203038	+	0.351673i	−0.0563127	+	0.0975364i	−0.892808	−	0.450438i	$-0.851268\pi$
$13$	−0.203038	+	0.351673i	−0.0563127	+	0.0975364i	0.836495	+	0.547975i	$0.184601\pi$
$14$	−4.26404	+	1.32777i	−1.13961	+	0.354860i
$15$	3.45650	−	1.74718i	0.892464	−	0.451119i
$16$	2.52723	+	3.10050i	0.631807	+	0.775125i
$17$			4.89168i			1.18641i	0.805053	+	0.593203i	$0.202137\pi$
$17$			4.89168i			1.18641i	−0.805053	+	0.593203i	$0.797863\pi$
$18$	−1.34807	+	4.02278i	−0.317742	+	0.948177i
$19$			2.85078i			0.654013i	0.945022	+	0.327007i	$0.106040\pi$
$19$			2.85078i			0.654013i	−0.945022	+	0.327007i	$0.893960\pi$
$20$	3.39142	+	2.91518i	0.758345	+	0.651854i
$21$	1.68216	−	5.20460i	0.367077	−	1.13574i
$22$	1.88012	−	0.585444i	0.400843	−	0.124817i
$23$	−4.12775	−	2.38316i	−0.860695	−	0.496922i	0.00355019	−	0.999994i	$-0.498870\pi$
$23$	−4.12775	−	2.38316i	−0.860695	−	0.496922i	−0.864245	+	0.503071i	$0.832203\pi$
$24$	−4.88719	+	0.339734i	−0.997593	+	0.0693478i
$25$	4.30608	+	2.54120i	0.861216	+	0.508239i
$26$	0.389483	−	0.422018i	0.0763839	−	0.0827645i
$27$	−3.07374	−	4.18952i	−0.591542	−	0.806274i
$28$	6.29558	−	0.505623i	1.18975	−	0.0955537i
$29$	−4.93309	+	2.84812i	−0.916052	+	0.528883i	−0.882373	−	0.470550i	$-0.844055\pi$
$29$	−4.93309	+	2.84812i	−0.916052	+	0.528883i	−0.0336783	+	0.999433i	$0.510722\pi$
$30$	−5.31194	+	1.33539i	−0.969823	+	0.243808i
$31$	5.38957	−	9.33501i	0.967995	−	1.67662i	0.266651	−	0.963793i	$-0.414083\pi$
$31$	5.38957	−	9.33501i	0.967995	−	1.67662i	0.701344	−	0.712823i	$-0.252584\pi$
$32$	−2.52226	−	5.06342i	−0.445877	−	0.895094i
$33$	−0.741705	+	2.29483i	−0.129114	+	0.399479i
$34$	1.52135	−	6.74852i	0.260910	−	1.15736i
$35$	6.82937	−	1.79505i	1.15437	−	0.303419i
$36$	3.11090	−	5.13053i	0.518483	−	0.855088i
$37$	−10.3639			−1.70382			−0.851909	−	0.523689i	$-0.824555\pi$
$37$	−10.3639			−1.70382			−0.851909	+	0.523689i	$0.824555\pi$
$38$	0.886616	−	3.93291i	0.143828	−	0.638002i
$39$	0.147300	+	0.687748i	0.0235869	+	0.110128i
$40$	−3.77213	−	5.07652i	−0.596426	−	0.802668i
$41$	1.59750	−	2.76695i	0.249487	−	0.432124i	−0.713896	−	0.700251i	$-0.753071\pi$
$41$	1.59750	−	2.76695i	0.249487	−	0.432124i	0.963384	+	0.268127i	$0.0864046\pi$
$42$	−3.93937	+	6.65705i	−0.607857	+	1.02721i
$43$	2.73697	+	4.74056i	0.417383	+	0.722929i	0.995675	−	0.0929006i	$-0.0296139\pi$
$43$	2.73697	+	4.74056i	0.417383	+	0.722929i	−0.578292	+	0.815830i	$0.696281\pi$
$44$	−2.77588	+	0.222942i	−0.418479	+	0.0336097i
$45$	2.41446	−	6.25863i	0.359926	−	0.932981i
$46$	4.95342	+	4.57155i	0.730343	+	0.674038i
$47$	1.75646	−	1.01409i	0.256205	−	0.147920i	−0.366397	−	0.930459i	$-0.619409\pi$
$47$	1.75646	−	1.01409i	0.256205	−	0.147920i	0.622602	+	0.782538i	$0.286075\pi$
$48$	6.84798	+	1.05126i	0.988421	+	0.151737i
$49$	1.48625	−	2.57426i	0.212321	−	0.367751i
$50$	−5.15030	−	4.84504i	−0.728362	−	0.685192i
$51$	5.67905	+	6.28759i	0.795226	+	0.880439i
$52$	−0.668579	+	0.461080i	−0.0927152	+	0.0639403i
$53$	0.428182			0.0588153			0.0294077	−	0.999568i	$-0.490638\pi$
$53$	0.428182			0.0588153			0.0294077	+	0.999568i	$0.490638\pi$
$54$	2.93753	+	6.73579i	0.399748	+	0.916625i
$55$	−3.01124	+	0.791482i	−0.406035	+	0.106723i
$56$	−8.84258	−	1.26042i	−1.18164	−	0.168431i
$57$	3.30965	+	3.66429i	0.438373	+	0.485348i
$58$	7.69144	−	2.39501i	1.00994	−	0.314480i
$59$	−6.13487	−	3.54197i	−0.798692	−	0.461125i	0.0443216	−	0.999017i	$-0.485887\pi$
$59$	−6.13487	−	3.54197i	−0.798692	−	0.461125i	−0.843014	+	0.537892i	$0.819221\pi$
$60$	7.74363	−	0.190241i	0.999698	−	0.0245600i
$61$	5.91265	−	3.41367i	0.757038	−	0.437076i	−0.0711936	−	0.997463i	$-0.522681\pi$
$61$	5.91265	−	3.41367i	0.757038	−	0.437076i	0.828231	+	0.560387i	$0.189347\pi$
$62$	−10.3387	+	11.2023i	−1.31301	+	1.42269i
$63$	−3.88015	−	8.64273i	−0.488853	−	1.08888i
$64$	1.90493	+	7.76989i	0.238116	+	0.971237i
$65$	−0.645119	+	0.638993i	−0.0800171	+	0.0792574i
$66$	1.73696	−	2.93526i	0.213805	−	0.361305i
$67$	−3.61288	+	6.25768i	−0.441383	+	0.764498i	−0.997792	−	0.0664106i	$-0.978845\pi$
$67$	−3.61288	+	6.25768i	−0.441383	+	0.764498i	0.556409	+	0.830908i	$0.312179\pi$
$68$	−4.19769	+	8.83705i	−0.509045	+	1.07165i
$69$	−8.07242	+	1.72893i	−0.971805	+	0.208139i
$70$	−9.98002	+	0.352449i	−1.19284	+	0.0421257i
$71$	11.5407			1.36963			0.684817	−	0.728715i	$-0.259882\pi$
$71$	11.5407			1.36963			0.684817	+	0.728715i	$0.259882\pi$
$72$	−5.88740	+	6.11052i	−0.693837	+	0.720132i
$73$			3.83292i			0.448610i	0.974519	+	0.224305i	$0.0720111\pi$
$73$			3.83292i			0.448610i	−0.974519	+	0.224305i	$0.927989\pi$
$74$	14.2980	+	3.22327i	1.66211	+	0.374697i
$75$	8.48512	−	1.73283i	0.979778	−	0.200090i
$76$	−2.44634	+	5.15007i	−0.280614	+	0.590753i
$77$	−2.19856	+	3.80802i	−0.250549	+	0.433964i
$78$	0.0106811	−	0.994623i	0.00120939	−	0.112619i
$79$	−2.02671	−	3.51037i	−0.228023	−	0.394948i	0.729199	−	0.684302i	$-0.239893\pi$
$79$	−2.02671	−	3.51037i	−0.228023	−	0.394948i	−0.957222	+	0.289354i	$0.906560\pi$
$80$	3.62516	+	8.17669i	0.405306	+	0.914181i
$81$	−8.81476	−	1.81657i	−0.979418	−	0.201841i
$82$	−3.06444	+	3.32042i	−0.338411	+	0.366679i
$83$	3.96883	+	6.87422i	0.435636	+	0.754544i	0.997347	−	0.0727894i	$-0.0231901\pi$
$83$	3.96883	+	6.87422i	0.435636	+	0.754544i	−0.561711	+	0.827333i	$0.689857\pi$
$84$	7.50511	−	7.95884i	0.818875	−	0.868381i
$85$	−2.88136	+	10.5518i	−0.312527	+	1.14450i
$86$	−2.30154	−	7.39126i	−0.248182	−	0.797020i
$87$	−3.03426	+	9.38801i	−0.325307	+	1.00650i
$88$	3.89891	+	0.555752i	0.415625	+	0.0592434i
$89$	−11.6735			−1.23739			−0.618695	−	0.785631i	$-0.712339\pi$
$89$	−11.6735			−1.23739			−0.618695	+	0.785631i	$0.712339\pi$
$90$	−5.27745	+	7.88344i	−0.556292	+	0.830987i
$91$			1.28236i			0.134428i
$92$	−5.41192	−	7.84742i	−0.564231	−	0.818150i
$93$	−3.91002	−	18.2560i	−0.405451	−	1.89306i
$94$	−2.73858	+	0.852758i	−0.282463	+	0.0879553i
$95$	−1.67920	+	6.14939i	−0.172283	+	0.630914i
$96$	−9.12047	−	3.58009i	−0.930854	−	0.365391i
$97$	−14.9833	+	8.65059i	−1.52132	+	0.878335i	−0.521637	+	0.853167i	$0.674679\pi$
$97$	−14.9833	+	8.65059i	−1.52132	+	0.878335i	−0.999683	+	0.0251675i	$0.991988\pi$
$98$	−2.85103	+	3.08919i	−0.287997	+	0.312055i
$99$	1.71085	+	3.81079i	0.171947	+	0.382999i
$100$	5.59846	+	8.28596i	0.559846	+	0.828596i
$101$	−8.28229	+	4.78178i	−0.824119	+	0.475805i	−0.851835	−	0.523811i	$-0.824510\pi$
$101$	−8.28229	+	4.78178i	−0.824119	+	0.475805i	0.0277161	+	0.999616i	$0.491177\pi$
$102$	−5.87928	−	10.4405i	−0.582136	−	1.03377i
$103$	−6.40007	−	3.69508i	−0.630617	−	0.364087i	0.150374	−	0.988629i	$-0.451952\pi$
$103$	−6.40007	−	3.69508i	−0.630617	−	0.364087i	−0.780991	+	0.624542i	$0.785286\pi$
$104$	1.06577	−	0.428169i	0.104507	−	0.0419854i
$105$	6.69425	−	10.2359i	0.653292	−	0.998925i
$106$	−0.590716	−	0.133168i	−0.0573755	−	0.0129344i
$107$	18.3352			1.77253			0.886263	−	0.463182i	$-0.153292\pi$
$107$	18.3352			1.77253			0.886263	+	0.463182i	$0.153292\pi$
$108$	−1.95771	−	10.2062i	−0.188381	−	0.982096i
$109$			7.70141i			0.737661i	0.929497	+	0.368830i	$0.120242\pi$
$109$			7.70141i			0.737661i	−0.929497	+	0.368830i	$0.879758\pi$
$110$	4.40043	−	0.155404i	0.419565	−	0.0148171i
$111$	−13.3214	+	12.0321i	−1.26441	+	1.14204i
$112$	11.8072	+	4.48899i	1.11567	+	0.424169i
$113$	−1.82287	−	1.05243i	−0.171481	−	0.0990045i	0.411803	−	0.911273i	$-0.364899\pi$
$113$	−1.82287	−	1.05243i	−0.171481	−	0.0990045i	−0.583284	+	0.812268i	$0.698232\pi$
$114$	−3.42634	−	6.08456i	−0.320906	−	0.569871i
$115$	−7.50017	−	7.57206i	−0.699394	−	0.706098i
$116$	−11.3559	+	0.912038i	−1.05437	+	0.0846806i
$117$	0.987784	+	0.712998i	0.0913207	+	0.0659166i
$118$	7.36204	+	6.79447i	0.677730	+	0.625481i
$119$	7.72377	+	13.3780i	0.708037	+	1.22636i
$120$	−10.7422	−	2.14588i	−0.980626	−	0.195891i
$121$	−4.53060	+	7.84723i	−0.411873	+	0.713385i
$122$	−9.21873	+	2.87059i	−0.834624	+	0.259891i
$123$	−1.15895	−	5.41117i	−0.104499	−	0.487909i
$124$	17.7472	−	12.2392i	1.59374	−	1.09911i
$125$	7.79175	+	8.01801i	0.696916	+	0.717153i
$126$	2.66506	+	13.1302i	0.237423	+	1.16973i
$127$		−	6.29662i		−	0.558735i	−0.960184	−	0.279367i	$-0.909875\pi$
$127$		−	6.29662i		−	0.558735i	0.960184	−	0.279367i	$-0.0901247\pi$
$128$	−0.211525	−	11.3117i	−0.0186963	−	0.999825i
$129$	9.02162	+	2.91585i	0.794310	+	0.256726i
$130$	1.08873	−	0.680913i	0.0954882	−	0.0597200i
$131$	4.39564	+	2.53782i	0.384049	+	0.221731i	0.679578	−	0.733603i	$-0.262163\pi$
$131$	4.39564	+	2.53782i	0.384049	+	0.221731i	−0.295530	+	0.955334i	$0.595496\pi$
$132$	−3.30919	+	3.50925i	−0.288028	+	0.305441i
$133$	4.50127	+	7.79643i	0.390310	+	0.676037i
$134$	6.93048	−	7.50942i	0.598703	−	0.648715i
$135$	−4.16257	−	10.8477i	−0.358257	−	0.933623i
$136$	8.53949	−	10.8860i	0.732255	−	0.933467i
$137$	14.5904	−	8.42378i	1.24654	−	0.719692i	0.276125	−	0.961122i	$-0.410950\pi$
$137$	14.5904	−	8.42378i	1.24654	−	0.719692i	0.970418	+	0.241429i	$0.0776162\pi$
$138$	11.6744	+	0.125369i	0.993787	+	0.0106721i
$139$	−17.3282	−	10.0045i	−1.46976	−	0.848567i	−0.470337	−	0.882487i	$-0.655868\pi$
$139$	−17.3282	−	10.0045i	−1.46976	−	0.848567i	−0.999425	+	0.0339193i	$0.989201\pi$
$140$	13.8780	+	2.61763i	1.17290	+	0.221230i
$141$	1.08037	−	3.34266i	0.0909833	−	0.281502i
$142$	−15.9215	−	3.58927i	−1.33610	−	0.301205i
$143$		−	0.565424i		−	0.0472831i
$144$	10.0226	−	6.59899i	0.835220	−	0.549916i
$145$	−12.3188	+	3.23790i	−1.02302	+	0.268893i
$146$	1.19207	−	5.28787i	0.0986564	−	0.437627i
$147$	−1.07824	−	5.03434i	−0.0889319	−	0.415225i
$148$	−18.7229	−	8.89358i	−1.53901	−	0.731048i
$149$	2.89537	+	1.67164i	0.237198	+	0.136946i	0.613888	−	0.789393i	$-0.289605\pi$
$149$	2.89537	+	1.67164i	0.237198	+	0.136946i	−0.376690	+	0.926339i	$0.622938\pi$
$150$	−12.2449	−	0.248345i	−0.999794	−	0.0202773i
$151$	5.86427	+	10.1572i	0.477228	+	0.826583i	0.999659	−	0.0260985i	$-0.00830834\pi$
$151$	5.86427	+	10.1572i	0.477228	+	0.826583i	−0.522432	+	0.852681i	$0.674975\pi$
$152$	4.97666	−	6.34416i	0.403660	−	0.514579i
$153$	14.5993	+	1.48869i	1.18029	+	0.120354i
$154$	4.21744	−	4.56974i	0.339851	−	0.368240i
$155$	17.1244	−	16.9618i	1.37547	−	1.36241i
$156$	−0.324071	+	1.36885i	−0.0259465	+	0.109596i
$157$	1.80350	−	3.12375i	0.143935	−	0.249303i	−0.785040	−	0.619445i	$-0.787358\pi$
$157$	1.80350	−	3.12375i	0.143935	−	0.249303i	0.928975	+	0.370142i	$0.120691\pi$
$158$	1.70428	+	5.47321i	0.135586	+	0.435425i
$159$	0.550371	−	0.497103i	0.0436472	−	0.0394229i
$160$	−2.45823	−	12.4079i	−0.194340	−	0.980934i
$161$	−15.0517			−1.18624
$162$	11.5958	+	5.24759i	0.911053	+	0.412290i
$163$	−8.72123			−0.683099			−0.341550	−	0.939864i	$-0.610952\pi$
$163$	−8.72123			−0.683099			−0.341550	+	0.939864i	$0.610952\pi$
$164$	5.26035	−	3.62776i	0.410765	−	0.283281i
$165$	−2.95166	+	4.51328i	−0.229786	+	0.351358i
$166$	−3.33743	−	10.7180i	−0.259035	−	0.831875i
$167$	9.44749	+	5.45451i	0.731069	+	0.422083i	0.818813	−	0.574060i	$-0.194632\pi$
$167$	9.44749	+	5.45451i	0.731069	+	0.422083i	−0.0877442	+	0.996143i	$0.527966\pi$
$168$	−12.8293	+	8.64580i	−0.989799	+	0.667038i
$169$	6.41755	+	11.1155i	0.493658	+	0.855040i
$170$	7.25679	−	13.6610i	0.556571	−	1.04775i
$171$	8.50822	+	0.867583i	0.650640	+	0.0663457i
$172$	0.876444	+	10.9127i	0.0668282	+	0.832088i
$173$	2.47790	+	4.29185i	0.188391	+	0.326304i	0.944714	−	0.327895i	$-0.106339\pi$
$173$	2.47790	+	4.29185i	0.188391	+	0.326304i	−0.756323	+	0.654199i	$0.773006\pi$
$174$	7.10579	−	12.0079i	0.538689	−	0.910320i
$175$	15.7889	+	0.150635i	1.19353	+	0.0113870i
$176$	−5.20606	−	1.97930i	−0.392422	−	0.149196i
$177$	−11.9976	+	2.56963i	−0.901798	+	0.193145i
$178$	16.1047	+	3.63056i	1.20710	+	0.272122i
$179$			12.4797i			0.932778i	0.884580	+	0.466389i	$0.154445\pi$
$179$			12.4797i			0.932778i	−0.884580	+	0.466389i	$0.845555\pi$
$180$	9.73254	−	9.23459i	0.725420	−	0.688306i
$181$		−	24.0822i		−	1.79001i	−0.446052	−	0.895007i	$-0.647170\pi$
$181$		−	24.0822i		−	1.79001i	0.446052	−	0.895007i	$-0.352830\pi$
$182$	0.398824	−	1.76913i	0.0295628	−	0.131137i
$183$	3.63678	−	11.2522i	0.268838	−	0.831785i
$184$	5.02562	+	12.5094i	0.370494	+	0.922205i
$185$	−22.3559	−	6.10470i	−1.64364	−	0.448826i
$186$	−0.283525	+	26.4019i	−0.0207890	+	1.93588i
$187$	−3.40560	−	5.89868i	−0.249042	−	0.431354i
$188$	4.04334	−	0.324737i	0.294891	−	0.0236839i
$189$	−15.0213	−	6.60437i	−1.09264	−	0.480397i
$190$	4.22913	−	7.96140i	0.306813	−	0.577581i
$191$	−6.15757	−	10.6652i	−0.445546	−	0.771709i	0.552544	−	0.833484i	$-0.313657\pi$
$191$	−6.15757	−	10.6652i	−0.445546	−	0.771709i	−0.998090	+	0.0617752i	$0.980324\pi$
$192$	11.4691	+	7.77561i	0.827710	+	0.561156i
$193$	13.1115	+	7.56994i	0.943788	+	0.544897i	0.891146	−	0.453717i	$-0.149902\pi$
$193$	13.1115	+	7.56994i	0.943788	+	0.544897i	0.0526426	+	0.998613i	$0.483236\pi$
$194$	23.3612	−	7.27437i	1.67724	−	0.522269i
$195$	−0.0873664	+	1.57030i	−0.00625644	+	0.112451i
$196$	4.89402	−	3.37512i	0.349573	−	0.241080i
$197$	−7.79718			−0.555526			−0.277763	−	0.960650i	$-0.589593\pi$
$197$	−7.79718			−0.555526			−0.277763	+	0.960650i	$0.589593\pi$
$198$	−1.17509	−	5.78943i	−0.0835102	−	0.411437i
$199$	−20.9906			−1.48799			−0.743993	−	0.668187i	$-0.767071\pi$
$199$	−20.9906			−1.48799			−0.743993	+	0.668187i	$0.767071\pi$
$200$	−5.14659	−	13.1724i	−0.363919	−	0.931431i
$201$	2.62107	+	12.2378i	0.184876	+	0.863190i
$202$	12.9134	−	4.02105i	0.908580	−	0.282920i
$203$	−8.99415	+	15.5783i	−0.631266	+	1.09338i
$204$	4.86391	+	16.2322i	0.340542	+	1.13648i
$205$	5.07577	−	5.02758i	0.354507	−	0.351141i
$206$	7.68028	+	7.08818i	0.535111	+	0.493857i
$207$	−8.36879	+	11.5941i	−0.581671	+	0.805845i
$208$	−1.60349	+	0.259237i	−0.111182	+	0.0179748i
$209$	−1.98472	−	3.43764i	−0.137286	−	0.237786i
$210$	−12.4188	+	12.0395i	−0.856978	+	0.830801i
$211$	−7.48058	−	4.31892i	−0.514985	−	0.297326i	0.219896	−	0.975523i	$-0.429428\pi$
$211$	−7.48058	−	4.31892i	−0.514985	−	0.297326i	−0.734880	+	0.678197i	$0.762762\pi$
$212$	0.773531	+	0.367435i	0.0531263	+	0.0252356i
$213$	14.8341	−	13.3984i	1.01641	−	0.918041i
$214$	−25.2950	−	5.70238i	−1.72913	−	0.389807i
$215$	3.11153	+	11.8380i	0.212205	+	0.807344i
$216$	−0.473383	+	14.6893i	−0.0322096	+	0.999481i
$217$		−	34.0397i		−	2.31077i
$218$	2.39520	−	10.6248i	0.162223	−	0.719602i
$219$	4.44988	+	4.92671i	0.300695	+	0.332916i
$220$	−6.11914	−	1.15418i	−0.412552	−	0.0778147i
$221$	−1.72027	−	0.993197i	−0.115718	−	0.0668097i
$222$	22.1202	−	12.4563i	1.48461	−	0.836015i
$223$	1.70183	−	0.982552i	0.113963	−	0.0657966i	−0.441935	−	0.897047i	$-0.645708\pi$
$223$	1.70183	−	0.982552i	0.113963	−	0.0657966i	0.555898	+	0.831250i	$0.312374\pi$
$224$	−14.8929	−	9.86509i	−0.995077	−	0.659139i
$225$	8.89474	−	12.0782i	0.592983	−	0.805215i
$226$	2.18750	+	2.01885i	0.145510	+	0.134292i
$227$	−7.50979	−	13.0073i	−0.498443	−	0.863328i	0.501556	−	0.865125i	$-0.332761\pi$
$227$	−7.50979	−	13.0073i	−0.498443	−	0.863328i	−0.999998	+	0.00179748i	$0.999428\pi$
$228$	2.83460	+	9.45983i	0.187726	+	0.626492i
$229$	8.86952	+	5.12082i	0.586114	+	0.338393i	0.763560	−	0.645737i	$-0.223450\pi$
$229$	8.86952	+	5.12082i	0.586114	+	0.338393i	−0.177445	+	0.984131i	$0.556783\pi$
$230$	7.99219	+	12.7790i	0.526990	+	0.842620i
$231$	1.59501	+	7.44714i	0.104944	+	0.489986i
$232$	15.9502	+	2.27354i	1.04718	+	0.149265i
$233$			11.1699i			0.731767i	0.930661	+	0.365884i	$0.119233\pi$
$233$			11.1699i			0.731767i	−0.930661	+	0.365884i	$0.880767\pi$
$234$	−1.14099	−	1.29085i	−0.0745889	−	0.0843858i
$235$	4.38617	−	1.15287i	0.286122	−	0.0752051i
$236$	−8.04347	−	11.6632i	−0.523585	−	0.759213i
$237$	−6.68048	−	2.15917i	−0.433944	−	0.140253i
$238$	−6.49500	−	20.8583i	−0.421008	−	1.35204i
$239$	8.11757	−	14.0601i	0.525082	−	0.909469i	−0.474491	−	0.880260i	$-0.657368\pi$
$239$	8.11757	−	14.0601i	0.525082	−	0.909469i	0.999573	−	0.0292088i	$-0.00929878\pi$
$240$	14.1525	+	6.30135i	0.913539	+	0.406751i
$241$	10.5043	+	18.1941i	0.676644	+	1.17198i	0.975985	+	0.217836i	$0.0698998\pi$
$241$	10.5043	+	18.1941i	0.676644	+	1.17198i	−0.299341	+	0.954146i	$0.596767\pi$
$242$	8.69094	−	9.41692i	0.558674	−	0.605343i
$243$	−13.4392	+	7.89865i	−0.862123	+	0.506699i
$244$	13.6109	−	1.09314i	0.871346	−	0.0699812i
$245$	4.72229	−	4.67745i	0.301696	−	0.298831i
$246$	−0.0840383	+	7.82566i	−0.00535809	+	0.498946i
$247$	−1.00254	−	0.578817i	−0.0637901	−	0.0368292i
$248$	−28.2903	+	11.3656i	−1.79644	+	0.721715i
$249$	13.0821	+	4.22822i	0.829046	+	0.267953i
$250$	−8.25577	−	13.4849i	−0.522141	−	0.852859i
$251$		−	24.5568i		−	1.55001i	−0.631955	−	0.775005i	$-0.717747\pi$
$251$		−	24.5568i		−	1.55001i	0.631955	−	0.775005i	$-0.282253\pi$
$252$	0.406902	−	18.9432i	0.0256324	−	1.19331i
$253$	6.63665			0.417242
$254$	−1.95830	+	8.68677i	−0.122875	+	0.545056i
$255$	8.54663	+	16.9081i	0.535211	+	1.05882i
$256$	−3.22622	+	15.6714i	−0.201639	+	0.979460i
$257$	3.61501	+	2.08712i	0.225498	+	0.130191i	0.608493	−	0.793559i	$-0.291774\pi$
$257$	3.61501	+	2.08712i	0.225498	+	0.130191i	−0.382996	+	0.923750i	$0.625108\pi$
$258$	−11.5393	−	6.82848i	−0.718406	−	0.425122i
$259$	−28.3437	+	16.3642i	−1.76119	+	1.01682i
$260$	−1.71378	+	0.600777i	−0.106284	+	0.0372586i
$261$	6.99899	+	15.5897i	0.433226	+	0.964978i
$262$	−5.27491	−	4.86824i	−0.325885	−	0.300761i
$263$	−15.6333	+	9.02586i	−0.963988	+	0.556559i	−0.897398	−	0.441222i	$-0.854545\pi$
$263$	−15.6333	+	9.02586i	−0.963988	+	0.556559i	−0.0665897	+	0.997780i	$0.521212\pi$
$264$	5.65674	−	3.81215i	0.348148	−	0.234621i
$265$	0.923627	+	0.252213i	0.0567380	+	0.0154933i
$266$	−3.78516	−	12.1558i	−0.232083	−	0.745322i
$267$	−15.0048	+	13.5525i	−0.918276	+	0.829401i
$268$	−11.8967	+	8.20449i	−0.726709	+	0.501169i
$269$			2.49635i			0.152205i	0.997100	+	0.0761026i	$0.0242477\pi$
$269$			2.49635i			0.152205i	−0.997100	+	0.0761026i	$0.975752\pi$
$270$	2.36892	+	16.2600i	0.144168	+	0.989553i
$271$	−3.84924			−0.233825			−0.116912	−	0.993142i	$-0.537300\pi$
$271$	−3.84924			−0.233825			−0.116912	+	0.993142i	$0.537300\pi$
$272$	−15.1667	+	12.3624i	−0.919613	+	0.749580i
$273$	1.48877	+	1.64830i	0.0901045	+	0.0997597i
$274$	−22.7487	+	7.08364i	−1.37430	+	0.427938i
$275$	−6.96172	−	0.0664188i	−0.419807	−	0.00400520i
$276$	−16.0669	−	3.80378i	−0.967111	−	0.228961i
$277$	3.25382	+	5.63578i	0.195503	+	0.338621i	0.947065	−	0.321041i	$-0.104033\pi$
$277$	3.25382	+	5.63578i	0.195503	+	0.338621i	−0.751562	+	0.659662i	$0.770699\pi$
$278$	20.7944	+	19.1913i	1.24717	+	1.15102i
$279$	−26.2203	−	18.9262i	−1.56977	−	1.13308i
$280$	−18.3318	−	7.92742i	−1.09554	−	0.473754i
$281$	−9.88879	−	17.1279i	−0.589916	−	1.02176i	−0.994243	−	0.107150i	$-0.965828\pi$
$281$	−9.88879	−	17.1279i	−0.589916	−	1.02176i	0.404327	−	0.914615i	$-0.367506\pi$
$282$	−2.53006	+	4.27550i	−0.150663	+	0.254602i
$283$	−0.991494	+	1.71732i	−0.0589382	+	0.102084i	−0.893989	−	0.448089i	$-0.852105\pi$
$283$	−0.991494	+	1.71732i	−0.0589382	+	0.102084i	0.835051	+	0.550173i	$0.185438\pi$
$284$	20.8489	+	9.90345i	1.23715	+	0.587661i
$285$	4.98082	+	9.85371i	0.295038	+	0.583683i
$286$	−0.175851	+	0.780054i	−0.0103983	+	0.0461256i
$287$		−	10.0896i		−	0.595568i
$288$	−15.8795	+	5.98680i	−0.935708	+	0.352775i
$289$	−6.92850			−0.407559
$290$	18.0019	−	0.635745i	1.05711	−	0.0373322i
$291$	−9.21597	+	28.5142i	−0.540250	+	1.67153i
$292$	−3.28914	+	6.92436i	−0.192482	+	0.405217i
$293$	15.3016	−	26.5032i	0.893930	−	1.54833i	0.0588064	−	0.998269i	$-0.481271\pi$
$293$	15.3016	−	26.5032i	0.893930	−	1.54833i	0.835123	−	0.550063i	$-0.185396\pi$
$294$	−0.0781858	+	7.28067i	−0.00455989	+	0.424617i
$295$	−11.1471	−	11.2540i	−0.649011	−	0.655233i
$296$	23.0640	+	18.0925i	1.34057	+	1.05161i
$297$	6.62326	+	2.91203i	0.384321	+	0.168973i
$298$	−3.47454	−	3.20667i	−0.201275	−	0.185758i
$299$	1.67618	−	0.967743i	0.0969360	−	0.0559660i
$300$	16.8158	+	4.15089i	0.970859	+	0.239652i
$301$	14.9704	+	8.64314i	0.862877	+	0.498182i
$302$	−4.93132	−	15.8367i	−0.283766	−	0.911297i
$303$	−5.09430	+	15.7618i	−0.292660	+	0.905490i
$304$	−8.83884	+	7.20457i	−0.506942	+	0.413210i
$305$	14.7649	−	3.88085i	0.845435	−	0.222217i
$306$	−19.6781	−	6.59430i	−1.12492	−	0.376971i
$307$	10.3129			0.588590			0.294295	−	0.955715i	$-0.404915\pi$
$307$	10.3129			0.588590			0.294295	+	0.955715i	$0.404915\pi$
$308$	−7.23957	+	4.99271i	−0.412513	+	0.284486i
$309$	−12.5163	+	2.68071i	−0.712026	+	0.152500i
$310$	−28.9000	+	18.0746i	−1.64141	+	1.02657i
$311$	0.495424	−	0.858100i	0.0280929	−	0.0486584i	−0.851637	−	0.524132i	$-0.824390\pi$
$311$	0.495424	−	0.858100i	0.0280929	−	0.0486584i	0.879730	+	0.475473i	$0.157723\pi$
$312$	0.872810	−	1.78767i	0.0494132	−	0.101207i
$313$	13.1187	−	7.57408i	0.741512	−	0.428112i	−0.0811068	−	0.996705i	$-0.525845\pi$
$313$	13.1187	−	7.57408i	0.741512	−	0.428112i	0.822619	+	0.568593i	$0.192512\pi$
$314$	−3.45961	+	3.74860i	−0.195237	+	0.211546i
$315$	−3.27898	−	20.9287i	−0.184750	−	1.17920i
$316$	−0.649004	−	8.08084i	−0.0365093	−	0.454583i
$317$	8.11260	+	14.0514i	0.455649	+	0.789207i	0.998725	−	0.0504760i	$-0.0160739\pi$
$317$	8.11260	+	14.0514i	0.455649	+	0.789207i	−0.543076	+	0.839683i	$0.682741\pi$
$318$	−0.913890	+	0.514630i	−0.0512484	+	0.0288590i
$319$	3.96574	−	6.86887i	0.222039	−	0.384583i
$320$	−0.467620	+	17.8824i	−0.0261407	+	0.999658i
$321$	23.5674	−	21.2864i	1.31540	−	1.18809i
$322$	20.7651	+	4.68119i	1.15720	+	0.260872i
$323$	−13.9451			−0.775925
$324$	−14.3654	−	10.8459i	−0.798080	−	0.602552i
$325$	−1.76797	+	0.998370i	−0.0980692	+	0.0553796i
$326$	12.0317	+	2.71237i	0.666376	+	0.150224i
$327$	8.94104	+	9.89912i	0.494441	+	0.547423i
$328$	−8.38540	+	3.36882i	−0.463006	+	0.186012i
$329$	3.20242	−	5.54675i	0.176555	−	0.305802i
$330$	5.47575	−	5.30849i	0.301430	−	0.292223i
$331$	14.1823	−	8.18815i	0.779530	−	0.450062i	−0.0567340	−	0.998389i	$-0.518069\pi$
$331$	14.1823	−	8.18815i	0.779530	−	0.450062i	0.836264	+	0.548328i	$0.184735\pi$
$332$	1.27092	+	15.8244i	0.0697507	+	0.868476i
$333$	−3.15407	+	30.9314i	−0.172842	+	1.69503i
$334$	−11.3373	−	10.4632i	−0.620349	−	0.572524i
$335$	−11.4793	+	11.3703i	−0.627180	+	0.621225i
$336$	20.3881	−	7.93767i	1.11226	−	0.433036i
$337$	−22.0551	−	12.7335i	−1.20142	−	0.693640i	−0.240549	−	0.970637i	$-0.577328\pi$
$337$	−22.0551	−	12.7335i	−1.20142	−	0.693640i	−0.960871	+	0.276997i	$0.910661\pi$
$338$	−5.39658	−	17.3308i	−0.293535	−	0.942671i
$339$	−3.56488	+	0.763518i	−0.193618	+	0.0414686i
$340$	−14.2601	+	16.5897i	−0.773363	+	0.899705i
$341$			15.0089i			0.812780i
$342$	−11.4680	−	3.84304i	−0.620121	−	0.207808i
$343$			12.7186i			0.686738i
$344$	2.18481	−	15.3277i	0.117797	−	0.826414i
$345$	−18.4313	−	1.02546i	−0.992310	−	0.0552090i
$346$	−2.08369	−	6.69166i	−0.112020	−	0.359746i
$347$	−4.54095	+	7.86516i	−0.243771	+	0.422224i	−0.961785	−	0.273805i	$-0.911718\pi$
$347$	−4.54095	+	7.86516i	−0.243771	+	0.422224i	0.718014	+	0.696028i	$0.245051\pi$
$348$	−13.5377	+	14.3561i	−0.725695	+	0.769567i
$349$	−0.810958	+	0.468207i	−0.0434096	+	0.0250625i	−0.521548	−	0.853222i	$-0.674645\pi$
$349$	−0.810958	+	0.468207i	−0.0434096	+	0.0250625i	0.478138	+	0.878285i	$0.341312\pi$
$350$	−21.7354	−	5.11830i	−1.16181	−	0.273584i
$351$	2.09743	−	0.230317i	0.111952	−	0.0122934i
$352$	6.56666	+	4.34976i	0.350004	+	0.231843i
$353$	20.9110	−	12.0730i	1.11298	−	0.642580i	0.173381	−	0.984855i	$-0.444531\pi$
$353$	20.9110	−	12.0730i	1.11298	−	0.642580i	0.939600	+	0.342275i	$0.111197\pi$
$354$	17.3510	+	0.186330i	0.922197	+	0.00990331i
$355$	24.8944	+	6.79788i	1.32126	+	0.360794i
$356$	−21.0888	−	10.0174i	−1.11770	−	0.530921i
$357$	25.4592	+	8.22858i	1.34744	+	0.435502i
$358$	3.88130	−	17.2169i	0.205133	−	0.909942i
$359$	17.8566			0.942434			0.471217	−	0.882017i	$-0.343815\pi$
$359$	17.8566			0.942434			0.471217	+	0.882017i	$0.343815\pi$
$360$	−16.2990	+	9.71307i	−0.859031	+	0.511924i
$361$	10.8731			0.572266
$362$	−7.48976	+	33.2236i	−0.393653	+	1.74619i
$363$	3.28686	+	15.3464i	0.172515	+	0.805478i
$364$	−1.10043	+	2.31664i	−0.0576782	+	0.121425i
$365$	−2.25772	+	8.26796i	−0.118174	+	0.432765i
$366$	−8.51679	+	14.3924i	−0.445180	+	0.752300i
$367$	−7.17043	+	4.13985i	−0.374293	+	0.216098i	−0.675333	−	0.737513i	$-0.736000\pi$
$367$	−7.17043	+	4.13985i	−0.374293	+	0.216098i	0.301039	+	0.953612i	$0.402667\pi$
$368$	−3.04278	−	18.8209i	−0.158616	−	0.981106i
$369$	−7.77185	−	5.60984i	−0.404586	−	0.292037i
$370$	28.9434	+	15.3749i	1.50470	+	0.799301i
$371$	1.17101	−	0.676083i	0.0607959	−	0.0351005i
$372$	8.60235	−	36.3356i	0.446011	−	1.88391i
$373$	13.4732	−	23.3362i	0.697614	−	1.20830i	−0.271677	−	0.962389i	$-0.587578\pi$
$373$	13.4732	−	23.3362i	0.697614	−	1.20830i	0.969291	−	0.245915i	$-0.0790884\pi$
$374$	2.86380	+	9.19694i	0.148084	+	0.475562i
$375$	19.3239	+	1.26015i	0.997880	+	0.0650738i
$376$	−5.67915	−	0.809508i	−0.292880	−	0.0417472i
$377$		−	2.31311i		−	0.119131i
$378$	18.6693	+	13.7831i	0.960243	+	0.708925i
$379$		−	25.7659i		−	1.32350i	−0.749723	−	0.661752i	$-0.769813\pi$
$379$		−	25.7659i		−	1.32350i	0.749723	−	0.661752i	$-0.230187\pi$
$380$	−8.31053	+	9.66819i	−0.426321	+	0.495968i
$381$	−7.31014	−	8.09346i	−0.374510	−	0.414641i
$382$	5.17796	+	16.6287i	0.264928	+	0.850799i
$383$	−3.85283	−	2.22443i	−0.196870	−	0.113663i	0.398324	−	0.917245i	$-0.369592\pi$
$383$	−3.85283	−	2.22443i	−0.196870	−	0.113663i	−0.595195	+	0.803581i	$0.702925\pi$
$384$	−13.4044	−	14.2941i	−0.684040	−	0.729445i
$385$	−6.98554	+	6.91921i	−0.356016	+	0.352636i
$386$	−15.7342	−	14.5212i	−0.800852	−	0.739111i
$387$	14.9813	−	6.72584i	0.761541	−	0.341893i
$388$	−34.4913	+	2.77013i	−1.75103	+	0.140632i
$389$	13.3751	−	7.72211i	0.678144	−	0.391527i	−0.121011	−	0.992651i	$-0.538614\pi$
$389$	13.3751	−	7.72211i	0.678144	−	0.391527i	0.799155	+	0.601125i	$0.205280\pi$
$390$	0.608906	−	2.13920i	0.0308332	−	0.108323i
$391$	11.6576	−	20.1916i	0.589551	−	1.02113i
$392$	−7.80144	+	3.13421i	−0.394032	+	0.158302i
$393$	8.59633	−	1.84114i	0.433627	−	0.0928733i
$394$	10.7569	+	2.42499i	0.541926	+	0.122169i
$395$	−2.30408	−	8.76599i	−0.115931	−	0.441065i
$396$	−0.179413	+	8.35252i	−0.00901584	+	0.419730i
$397$	31.6978			1.59087			0.795433	−	0.606041i	$-0.207243\pi$
$397$	31.6978			1.59087			0.795433	+	0.606041i	$0.207243\pi$
$398$	28.9585	+	6.52826i	1.45156	+	0.327232i
$399$	14.8372	+	4.79546i	0.742787	+	0.240073i
$400$	3.00347	+	19.7732i	0.150173	+	0.988660i
$401$	6.23557	−	10.8003i	0.311389	−	0.539342i	−0.667274	−	0.744812i	$-0.732539\pi$
$401$	6.23557	−	10.8003i	0.311389	−	0.539342i	0.978663	+	0.205470i	$0.0658723\pi$
$402$	0.190060	−	17.6984i	0.00947932	−	0.882715i
$403$	2.18858	+	3.79073i	0.109021	+	0.188830i
$404$	−19.0657	+	1.53124i	−0.948556	+	0.0761823i
$405$	−17.9442	−	9.11070i	−0.891656	−	0.452714i
$406$	17.2532	−	18.6945i	0.856264	−	0.927791i
$407$	12.4974	−	7.21540i	0.619475	−	0.357654i
$408$	−1.66187	−	23.9065i	−0.0822747	−	1.18355i
$409$	12.5896	−	21.8058i	0.622516	−	1.07823i	−0.366499	−	0.930418i	$-0.619444\pi$
$409$	12.5896	−	21.8058i	0.622516	−	1.07823i	0.989016	−	0.147811i	$-0.0472228\pi$
$410$	−8.56611	+	5.35740i	−0.423050	+	0.264583i
$411$	8.97433	−	27.7666i	0.442671	−	1.36962i
$412$	−8.39117	−	12.1674i	−0.413403	−	0.599446i
$413$	−22.3705			−1.10078
$414$	15.1514	−	13.3923i	0.744649	−	0.658198i
$415$	4.51199	+	17.1661i	0.221485	+	0.842651i
$416$	2.29278	+	0.141056i	0.112413	+	0.00691586i
$417$	−33.8879	+	7.25804i	−1.65950	+	0.355428i
$418$	1.66897	+	5.35980i	0.0816321	+	0.262157i
$419$	9.01497	+	5.20480i	0.440410	+	0.254271i	0.703772	−	0.710426i	$-0.251498\pi$
$419$	9.01497	+	5.20480i	0.440410	+	0.254271i	−0.263361	+	0.964697i	$0.584831\pi$
$420$	20.8772	−	12.7472i	1.01870	−	0.621999i
$421$	−10.2483	+	5.91687i	−0.499472	+	0.288370i	−0.728496	−	0.685051i	$-0.759780\pi$
$421$	−10.2483	+	5.91687i	−0.499472	+	0.288370i	0.229023	+	0.973421i	$0.426447\pi$
$422$	8.97693	+	8.28486i	0.436990	+	0.403301i
$423$	−2.49203	−	5.55080i	−0.121167	−	0.269889i
$424$	−0.952882	−	0.747486i	−0.0462760	−	0.0363011i
$425$	−12.4307	+	21.0639i	−0.602978	+	1.02175i
$426$	−24.6320	+	13.8708i	−1.19342	+	0.672041i
$427$	10.7801	−	18.6717i	0.521687	−	0.903588i
$428$	33.1233	+	15.7339i	1.60108	+	0.760528i
$429$	−0.656436	−	0.726776i	−0.0316930	−	0.0350891i
$430$	−0.610934	−	17.2993i	−0.0294618	−	0.834247i
$431$	−19.7932			−0.953403			−0.476702	−	0.879065i	$-0.658168\pi$
$431$	−19.7932			−0.953403			−0.476702	+	0.879065i	$0.658168\pi$
$432$	5.22157	−	20.1180i	0.251223	−	0.967929i
$433$			31.7661i			1.52658i	0.646055	+	0.763291i	$0.276418\pi$
$433$			31.7661i			1.52658i	−0.646055	+	0.763291i	$0.723582\pi$
$434$	−10.5866	+	46.9609i	−0.508175	+	2.25420i
$435$	−12.0750	+	18.4635i	−0.578953	+	0.885257i
$436$	−6.60880	+	13.9130i	−0.316504	+	0.666310i
$437$	6.79385	−	11.7673i	0.324994	−	0.562906i
$438$	−4.60677	−	8.18079i	−0.220120	−	0.390893i
$439$	3.57698	+	6.19552i	0.170720	+	0.295696i	0.938672	−	0.344812i	$-0.112057\pi$
$439$	3.57698	+	6.19552i	0.170720	+	0.295696i	−0.767952	+	0.640508i	$0.778724\pi$
$440$	8.08295	+	3.49540i	0.385340	+	0.166636i
$441$	−7.23061	−	5.21917i	−0.344315	−	0.248532i
$442$	2.06438	+	1.90522i	0.0981923	+	0.0906223i
$443$	−12.3140	−	21.3285i	−0.585056	−	1.01335i	−0.994868	−	0.101177i	$-0.967739\pi$
$443$	−12.3140	−	21.3285i	−0.585056	−	1.01335i	0.409812	−	0.912170i	$-0.365594\pi$
$444$	−34.3909	+	10.3051i	−1.63212	+	0.489058i
$445$	−25.1808	−	6.87609i	−1.19369	−	0.325958i
$446$	−2.65341	+	0.826238i	−0.125643	+	0.0391235i
$447$	5.66233	−	1.21274i	0.267819	−	0.0573609i
$448$	17.4781	+	18.2416i	0.825761	+	0.861836i
$449$	−25.5999			−1.20813			−0.604067	−	0.796934i	$-0.706454\pi$
$449$	−25.5999			−1.20813			−0.604067	+	0.796934i	$0.706454\pi$
$450$	−16.0275	+	13.8967i	−0.755545	+	0.655096i
$451$			4.44873i			0.209483i
$452$	−2.38997	−	3.46552i	−0.112415	−	0.163004i
$453$	19.3299	+	6.24754i	0.908197	+	0.293535i
$454$	6.31506	+	20.2804i	0.296380	+	0.951808i
$455$	−0.755352	+	2.76616i	−0.0354115	+	0.129680i
$456$	−0.968505	−	13.9323i	−0.0453544	−	0.652439i
$457$	7.58332	−	4.37823i	0.354733	−	0.204805i	−0.312035	−	0.950071i	$-0.601011\pi$
$457$	7.58332	−	4.37823i	0.354733	−	0.204805i	0.666768	+	0.745266i	$0.267677\pi$
$458$	−10.6437	−	9.82314i	−0.497348	−	0.459005i
$459$	20.4938	−	15.0358i	0.956568	−	0.701809i
$460$	−7.05160	−	20.1154i	−0.328783	−	0.937885i
$461$	−17.2716	+	9.97176i	−0.804419	+	0.464431i	−0.845014	−	0.534744i	$-0.820408\pi$
$461$	−17.2716	+	9.97176i	−0.804419	+	0.464431i	0.0405952	+	0.999176i	$0.487075\pi$
$462$	0.115658	−	10.7701i	0.00538089	−	0.501069i
$463$	4.28597	+	2.47450i	0.199186	+	0.115000i	0.596276	−	0.802780i	$-0.296647\pi$
$463$	4.28597	+	2.47450i	0.199186	+	0.115000i	−0.397090	+	0.917780i	$0.629980\pi$
$464$	−21.2976	−	8.09720i	−0.988718	−	0.375903i
$465$	2.31911	−	41.6829i	0.107546	−	1.93300i
$466$	3.47394	−	15.4100i	0.160927	−	0.713853i
$467$	−4.34750			−0.201179			−0.100589	−	0.994928i	$-0.532073\pi$
$467$	−4.34750			−0.201179			−0.100589	+	0.994928i	$0.532073\pi$
$468$	1.17264	+	2.13571i	0.0542051	+	0.0987232i
$469$			22.8184i			1.05365i
$470$	−6.40967	+	0.226361i	−0.295656	+	0.0104412i
$471$	−1.30840	−	6.10896i	−0.0602881	−	0.281486i
$472$	7.46934	+	18.5921i	0.343804	+	0.855771i
$473$	−6.60080	−	3.81097i	−0.303505	−	0.175229i
$474$	8.54482	+	5.05646i	0.392476	+	0.232251i
$475$	−7.24439	+	12.2757i	−0.332395	+	0.563247i
$476$	2.47334	+	30.7959i	0.113366	+	1.41153i
$477$	0.130309	−	1.27792i	0.00596646	−	0.0585119i
$478$	−15.5717	+	16.8725i	−0.712234	+	0.771730i
$479$	16.3137	+	28.2562i	0.745394	+	1.29106i	0.950011	+	0.312218i	$0.101072\pi$
$479$	16.3137	+	28.2562i	0.745394	+	1.29106i	−0.204617	+	0.978842i	$0.565595\pi$
$480$	−17.5649	−	13.0948i	−0.801724	−	0.597695i
$481$	2.10427	−	3.64471i	0.0959466	−	0.166184i
$482$	−8.83321	−	28.3673i	−0.402342	−	1.29210i
$483$	−19.3469	+	17.4744i	−0.880314	+	0.795113i
$484$	−14.9187	+	10.2886i	−0.678122	+	0.467662i
$485$	−37.4158	+	9.83447i	−1.69896	+	0.446560i
$486$	20.9971	−	6.71722i	0.952449	−	0.304699i
$487$		−	28.4322i		−	1.28839i	−0.764863	−	0.644193i	$-0.777193\pi$
$487$		−	28.4322i		−	1.28839i	0.764863	−	0.644193i	$-0.222807\pi$
$488$	−19.1174	−	2.72500i	−0.865404	−	0.123355i
$489$	−11.2100	+	10.1250i	−0.506932	+	0.457869i
$490$	−7.96956	+	4.98430i	−0.360028	+	0.225168i
$491$	−15.5229	−	8.96217i	−0.700540	−	0.404457i	0.107008	−	0.994258i	$-0.465873\pi$
$491$	−15.5229	−	8.96217i	−0.700540	−	0.404457i	−0.807549	+	0.589801i	$0.799206\pi$
$492$	2.54978	−	10.7701i	0.114953	−	0.485553i
$493$	−13.9321	−	24.1311i	−0.627469	−	1.08681i
$494$	1.20308	+	1.11033i	0.0541291	+	0.0499561i
$495$	1.44578	+	9.22798i	0.0649831	+	0.414767i
$496$	42.5639	−	6.88133i	1.91117	−	0.308981i
$497$	31.5621	−	18.2224i	1.41575	−	0.817387i
$498$	−16.7330	−	9.90187i	−0.749823	−	0.443714i
$499$	20.1219	+	11.6174i	0.900778	+	0.520065i	0.877453	−	0.479663i	$-0.159241\pi$
$499$	20.1219	+	11.6174i	0.900778	+	0.520065i	0.0233257	+	0.999728i	$0.492575\pi$
$500$	7.19569	+	21.1713i	0.321801	+	0.946807i
$501$	18.4760	−	3.95714i	0.825446	−	0.176792i
$502$	−7.63737	+	33.8784i	−0.340872	+	1.51206i
$503$		−	23.0944i		−	1.02973i	−0.857271	−	0.514865i	$-0.827842\pi$
$503$		−	23.0944i		−	1.02973i	0.857271	−	0.514865i	$-0.172158\pi$
$504$	−6.45285	+	26.0073i	−0.287433	+	1.15846i
$505$	−20.6823	+	5.43619i	−0.920349	+	0.241907i
$506$	−9.15586	−	2.06405i	−0.407028	−	0.0917583i
$507$	21.1536	+	6.83698i	0.939465	+	0.303641i
$508$	5.40331	−	11.3751i	0.239733	−	0.504691i
$509$	−14.0983	−	8.13966i	−0.624896	−	0.360784i	0.153877	−	0.988090i	$-0.450824\pi$
$509$	−14.0983	−	8.13966i	−0.624896	−	0.360784i	−0.778773	+	0.627306i	$0.784158\pi$
$510$	−6.53231	−	25.9843i	−0.289256	−	1.15060i
$511$	6.05204	+	10.4824i	0.267726	+	0.463716i
$512$	9.32479	−	20.6167i	0.412102	−	0.911138i
$513$	11.9434	−	8.76256i	0.527314	−	0.386876i
$514$	−4.33812	−	4.00368i	−0.191346	−	0.176595i
$515$	−11.6290	−	11.7405i	−0.512435	−	0.517347i
$516$	13.7958	+	13.0093i	0.607327	+	0.572704i
$517$	−1.41203	+	2.44570i	−0.0621008	+	0.107562i
$518$	44.1922	−	13.7609i	1.94169	−	0.604617i
$519$	8.16769	+	2.63985i	0.358522	+	0.115877i
$520$	2.55116	−	0.295828i	0.111876	−	0.0129729i
$521$	39.2433			1.71928			0.859639	−	0.510901i	$-0.170688\pi$
$521$	39.2433			1.71928			0.859639	+	0.510901i	$0.170688\pi$
$522$	−4.80722	−	23.6842i	−0.210406	−	1.03663i
$523$	−18.2721			−0.798984			−0.399492	−	0.916737i	$-0.630813\pi$
$523$	−18.2721			−0.798984			−0.399492	+	0.916737i	$0.630813\pi$
$524$	5.76315	+	8.35673i	0.251765	+	0.365065i
$525$	20.4694	−	18.1367i	0.893358	−	0.791551i
$526$	24.3746	−	7.58994i	1.06278	−	0.330937i
$527$	45.6638	+	26.3640i	1.98915	+	1.14843i
$528$	−8.98960	+	3.49991i	−0.391222	+	0.152314i
$529$	−0.141139	−	0.244460i	−0.00613647	−	0.0106287i
$530$	−1.19579	−	0.635207i	−0.0519417	−	0.0275916i
$531$	−12.4381	+	17.2317i	−0.539769	+	0.747793i
$532$	1.44142	+	17.9473i	0.0624934	+	0.778114i
$533$	0.648706	+	1.12359i	0.0280986	+	0.0486682i
$534$	24.9154	−	14.0303i	1.07819	−	0.607153i
$535$	39.5506	+	10.8000i	1.70992	+	0.466925i
$536$	18.9643	−	7.61887i	0.819133	−	0.329085i
$537$	14.4885	+	16.0410i	0.625224	+	0.692221i
$538$	0.776386	−	3.44395i	0.0334724	−	0.148479i
$539$			4.13892i			0.178276i
$540$	1.78886	−	23.1689i	0.0769801	−	0.997033i
$541$			11.4573i			0.492587i	0.969195	+	0.246294i	$0.0792127\pi$
$541$			11.4573i			0.492587i	−0.969195	+	0.246294i	$0.920787\pi$
$542$	5.31039	+	1.19715i	0.228101	+	0.0514219i
$543$	−27.9585	−	30.9544i	−1.19981	−	1.32838i
$544$	24.7686	−	12.3381i	1.06194	−	0.528992i
$545$	−4.53638	+	16.6126i	−0.194317	+	0.711607i
$546$	−1.54126	−	2.73700i	−0.0659599	−	0.117133i
$547$	−3.34689	−	5.79698i	−0.143103	−	0.247861i	0.785561	−	0.618784i	$-0.212375\pi$
$547$	−3.34689	−	5.79698i	−0.143103	−	0.247861i	−0.928663	+	0.370923i	$0.879041\pi$
$548$	33.5870	−	2.69750i	1.43476	−	0.115232i
$549$	−8.38877	−	18.6853i	−0.358024	−	0.797471i
$550$	9.58367	+	2.25678i	0.408649	+	0.0962295i
$551$	−8.11936	−	14.0631i	−0.345896	−	0.599110i
$552$	20.9827	+	10.2446i	0.893083	+	0.436039i
$553$	−11.0855	−	6.40021i	−0.471403	−	0.272165i
$554$	−2.73617	−	8.78705i	−0.116249	−	0.373326i
$555$	−35.8229	+	18.1076i	−1.52060	+	0.768626i
$556$	−22.7192	−	32.9434i	−0.963507	−	1.39711i
$557$	−23.0003			−0.974555			−0.487278	−	0.873247i	$-0.662010\pi$
$557$	−23.0003			−0.974555			−0.487278	+	0.873247i	$0.662010\pi$
$558$	30.2871	+	34.2652i	1.28216	+	1.45056i
$559$	−2.22284			−0.0940159
$560$	22.8249	+	16.6380i	0.964530	+	0.703082i
$561$	−11.2256	−	3.62818i	−0.473945	−	0.153182i
$562$	8.31558	+	26.7050i	0.350772	+	1.12648i
$563$	1.99175	−	3.44982i	0.0839425	−	0.145393i	−0.820998	−	0.570932i	$-0.806582\pi$
$563$	1.99175	−	3.44982i	0.0839425	−	0.145393i	0.904940	+	0.425539i	$0.139915\pi$
$564$	4.82016	−	5.11157i	0.202966	−	0.215236i
$565$	−3.31217	−	3.34392i	−0.139344	−	0.140680i
$566$	1.90196	−	2.06084i	0.0799452	−	0.0866234i
$567$	−26.9753	+	8.95015i	−1.13286	+	0.375871i
$568$	−25.6829	−	20.1469i	−1.07763	−	0.845345i
$569$	−2.39943	−	4.15594i	−0.100589	−	0.174226i	0.811338	−	0.584577i	$-0.198740\pi$
$569$	−2.39943	−	4.15594i	−0.100589	−	0.174226i	−0.911928	+	0.410351i	$0.865406\pi$
$570$	−3.80691	−	15.1432i	−0.159454	−	0.634278i
$571$	6.80723	+	3.93016i	0.284874	+	0.164472i	0.635628	−	0.771996i	$-0.280741\pi$
$571$	6.80723	+	3.93016i	0.284874	+	0.164472i	−0.350754	+	0.936468i	$0.614075\pi$
$572$	0.485206	−	1.02146i	0.0202875	−	0.0427096i
$573$	−20.2967	−	6.56001i	−0.847905	−	0.274048i
$574$	−3.13794	+	13.9195i	−0.130975	+	0.580987i
$575$	−11.7183	−	20.7515i	−0.488689	−	0.865396i
$576$	23.7692	−	3.32068i	0.990382	−	0.138362i
$577$			6.67354i			0.277823i	0.990305	+	0.138912i	$0.0443604\pi$
$577$			6.67354i			0.277823i	−0.990305	+	0.138912i	$0.955640\pi$
$578$	9.55850	+	2.15482i	0.397581	+	0.0896287i
$579$	25.6415	−	5.49184i	1.06563	−	0.228233i
$580$	−25.0330	−	4.72166i	−1.03944	−	0.196056i
$581$	21.7083	+	12.5333i	0.900611	+	0.519968i
$582$	21.5824	−	36.4717i	0.894620	−	1.51180i
$583$	−0.516327	+	0.298102i	−0.0213841	+	0.0123461i
$584$	6.69120	−	8.52983i	0.276884	−	0.352967i
$585$	1.71076	+	2.11984i	0.0707312	+	0.0876445i
$586$	−29.3527	+	31.8046i	−1.21255	+	1.31384i
$587$	−1.98124	−	3.43161i	−0.0817746	−	0.141638i	0.822238	−	0.569144i	$-0.192725\pi$
$587$	−1.98124	−	3.43161i	−0.0817746	−	0.141638i	−0.904012	+	0.427507i	$0.859392\pi$
$588$	2.37221	−	10.0200i	0.0978285	−	0.413220i
$589$	26.6120	+	15.3645i	1.09653	+	0.633082i
$590$	11.8784	+	18.9928i	0.489026	+	0.781920i
$591$	−10.0222	+	9.05223i	−0.412259	+	0.372359i
$592$	−26.1920	−	32.1334i	−1.07648	−	1.32067i
$593$			21.4151i			0.879412i	0.898142	+	0.439706i	$0.144917\pi$
$593$			21.4151i			0.879412i	−0.898142	+	0.439706i	$0.855083\pi$
$594$	−8.23174	−	6.07730i	−0.337752	−	0.249355i
$595$	8.78081	+	33.4071i	0.359978	+	1.36956i
$596$	3.79614	+	5.50451i	0.155496	+	0.225473i
$597$	−26.9806	+	24.3693i	−1.10424	+	0.997371i
$598$	−2.61342	+	0.813785i	−0.106871	+	0.0332781i
$599$	−15.7764	+	27.3255i	−0.644605	+	1.11649i	0.339787	+	0.940502i	$0.389645\pi$
$599$	−15.7764	+	27.3255i	−0.644605	+	1.11649i	−0.984393	+	0.175987i	$0.943688\pi$
$600$	−21.9079	−	10.9564i	−0.894388	−	0.447292i
$601$	−3.22187	−	5.58045i	−0.131423	−	0.227631i	0.792802	−	0.609479i	$-0.208621\pi$
$601$	−3.22187	−	5.58045i	−0.131423	−	0.227631i	−0.924225	+	0.381848i	$0.875288\pi$
$602$	−17.9649	−	16.5799i	−0.732194	−	0.675746i
$603$	17.5767	+	12.6871i	0.715778	+	0.516660i
$604$	1.87789	+	23.3818i	0.0764101	+	0.951392i
$605$	−14.3952	+	14.2585i	−0.585248	+	0.579691i
$606$	11.9301	−	20.1604i	0.484627	−	0.818962i
$607$	−31.7495	−	18.3306i	−1.28867	−	0.744016i	−0.310256	−	0.950653i	$-0.600415\pi$
$607$	−31.7495	−	18.3306i	−1.28867	−	0.744016i	−0.978418	+	0.206637i	$0.933748\pi$
$608$	14.4347	−	7.19041i	0.585404	−	0.291610i
$609$	6.52508	+	30.4657i	0.264409	+	1.23453i
$610$	−21.5765	+	0.761985i	−0.873607	+	0.0308519i
$611$			0.823596i			0.0333191i
$612$	25.0969	+	15.2175i	1.01448	+	0.615131i
$613$	−6.95892			−0.281068			−0.140534	−	0.990076i	$-0.544882\pi$
$613$	−6.95892			−0.281068			−0.140534	+	0.990076i	$0.544882\pi$
$614$	−14.2276	−	3.20740i	−0.574180	−	0.129440i
$615$	0.687396	−	12.3551i	0.0277185	−	0.498204i
$616$	11.5404	−	4.63634i	0.464977	−	0.186804i
$617$	−16.5832	−	9.57431i	−0.667614	−	0.385447i	0.127558	−	0.991831i	$-0.459286\pi$
$617$	−16.5832	−	9.57431i	−0.667614	−	0.385447i	−0.795172	+	0.606384i	$0.792620\pi$
$618$	18.1011	+	0.194384i	0.728132	+	0.00781928i
$619$	35.8753	−	20.7126i	1.44195	−	0.832509i	0.443969	−	0.896042i	$-0.353570\pi$
$619$	35.8753	−	20.7126i	1.44195	−	0.832509i	0.997980	+	0.0635327i	$0.0202367\pi$
$620$	45.4915	−	15.9474i	1.82698	−	0.640462i
$621$	2.70334	+	24.6185i	0.108481	+	0.987906i
$622$	−0.950360	+	1.02975i	−0.0381060	+	0.0412891i
$623$	−31.9253	+	18.4321i	−1.27906	+	0.738465i
$624$	−1.76010	+	2.19480i	−0.0704605	+	0.0878623i
$625$	12.0846	+	21.8852i	0.483386	+	0.875407i
$626$	−20.4540	+	6.36912i	−0.817508	+	0.254561i
$627$	−6.54206	−	2.11444i	−0.261265	−	0.0844425i
$628$	5.93869	−	4.09558i	0.236980	−	0.163431i
$629$		−	50.6970i		−	2.02142i
$630$	−1.98534	+	29.8929i	−0.0790980	+	1.19096i
$631$	−6.68622			−0.266174			−0.133087	−	0.991104i	$-0.542489\pi$
$631$	−6.68622			−0.266174			−0.133087	+	0.991104i	$0.542489\pi$
$632$	−1.61785	+	11.3501i	−0.0643545	+	0.451483i
$633$	−14.6294	+	3.13329i	−0.581466	+	0.124537i
$634$	−6.82197	−	21.9083i	−0.270935	−	0.870091i
$635$	3.70892	−	13.5824i	0.147184	−	0.539000i
$636$	1.42085	−	0.425752i	0.0563403	−	0.0168822i
$637$	0.603530	+	1.04534i	0.0239127	+	0.0414181i
$638$	−7.60738	+	8.24286i	−0.301179	+	0.326338i
$639$	3.51222	−	34.4436i	0.138941	−	1.36257i
$640$	6.20671	−	24.5250i	0.245342	−	0.969437i
$641$	19.3748	+	33.5582i	0.765259	+	1.32547i	0.940110	+	0.340873i	$0.110722\pi$
$641$	19.3748	+	33.5582i	0.765259	+	1.32547i	−0.174850	+	0.984595i	$0.555944\pi$
$642$	−39.1336	+	22.0369i	−1.54448	+	0.869728i
$643$	4.75281	−	8.23211i	0.187433	−	0.324643i	−0.756961	−	0.653460i	$-0.773317\pi$
$643$	4.75281	−	8.23211i	0.187433	−	0.324643i	0.944394	+	0.328817i	$0.106650\pi$
$644$	−27.1915	−	12.9163i	−1.07150	−	0.508972i
$645$	17.7429	+	11.6038i	0.698627	+	0.456898i
$646$	19.2385	+	4.33704i	0.756930	+	0.170638i
$647$		−	11.0968i		−	0.436260i	−0.975920	−	0.218130i	$-0.930004\pi$
$647$		−	11.0968i		−	0.436260i	0.975920	−	0.218130i	$-0.0699957\pi$
$648$	16.4453	+	19.4307i	0.646031	+	0.763311i
$649$	9.86372			0.387185
$650$	2.74958	−	0.827490i	0.107847	−	0.0324568i
$651$	−39.5188	−	43.7535i	−1.54886	−	1.71483i
$652$	−15.7553	−	7.48394i	−0.617026	−	0.293094i
$653$	6.22466	−	10.7814i	0.243590	−	0.421910i	−0.718145	−	0.695894i	$-0.755008\pi$
$653$	6.22466	−	10.7814i	0.243590	−	0.421910i	0.961734	+	0.273984i	$0.0883417\pi$
$654$	−9.25628	−	16.4375i	−0.361949	−	0.642757i
$655$	7.98693	+	8.06350i	0.312075	+	0.315067i
$656$	12.6162	−	2.03967i	0.492579	−	0.0796355i
$657$	11.4394	+	1.16648i	0.446295	+	0.0455087i
$658$	−6.14312	+	6.65628i	−0.239484	+	0.259489i
$659$	−26.6530	+	15.3881i	−1.03825	+	0.599437i	−0.919338	−	0.393468i	$-0.871275\pi$
$659$	−26.6530	+	15.3881i	−1.03825	+	0.599437i	−0.118916	+	0.992904i	$0.537942\pi$
$660$	−9.20529	+	5.62055i	−0.358315	+	0.218779i
$661$	−16.2026	−	9.35460i	−0.630210	−	0.363852i	0.150623	−	0.988591i	$-0.451872\pi$
$661$	−16.2026	−	9.35460i	−0.630210	−	0.363852i	−0.780833	+	0.624739i	$0.785205\pi$
$662$	−22.1124	+	6.88550i	−0.859422	+	0.267612i
$663$	−3.36424	+	0.720545i	−0.130656	+	0.0279836i
$664$	3.16816	−	22.2265i	0.122949	−	0.862554i
$665$	5.11729	+	19.4690i	0.198440	+	0.754976i
$666$	13.9712	−	41.6917i	0.541375	−	1.61552i
$667$	27.1501			1.05125
$668$	12.3867	+	17.9610i	0.479255	+	0.694932i
$669$	1.04677	−	3.23870i	0.0404704	−	0.125215i
$670$	19.3730	−	12.1162i	0.748443	−	0.468090i
$671$	−4.75322	+	8.23282i	−0.183496	+	0.317824i
$672$	−30.5959	+	4.60989i	−1.18026	+	0.177830i
$673$	4.08225	−	2.35689i	0.157359	−	0.0908514i	−0.419253	−	0.907870i	$-0.637708\pi$
$673$	4.08225	−	2.35689i	0.157359	−	0.0908514i	0.576612	+	0.817018i	$0.304374\pi$
$674$	26.4669	+	24.4264i	1.01947	+	0.940871i
$675$	−2.58938	−	25.8514i	−0.0996652	−	0.995021i
$676$	2.05506	+	25.5878i	0.0790407	+	0.984147i
$677$	−1.80982	−	3.13470i	−0.0695570	−	0.120476i	0.829149	−	0.559027i	$-0.188825\pi$
$677$	−1.80982	−	3.13470i	−0.0695570	−	0.120476i	−0.898706	+	0.438551i	$0.855492\pi$
$678$	5.15555	+	0.0553645i	0.197998	+	0.00212626i
$679$	−27.3179	+	47.3160i	−1.04837	+	1.81582i
$680$	24.8327	−	18.4520i	0.952290	−	0.707604i
$681$	−24.7539	−	8.00061i	−0.948571	−	0.306584i
$682$	4.66791	−	20.7062i	0.178743	−	0.792882i
$683$	46.7402			1.78846			0.894232	−	0.447603i	$-0.147722\pi$
$683$	46.7402			1.78846			0.894232	+	0.447603i	$0.147722\pi$
$684$	14.6260	+	8.86848i	0.559239	+	0.339095i
$685$	36.4347	−	9.57662i	1.39210	−	0.365904i
$686$	3.95558	−	17.5464i	0.151025	−	0.669926i
$687$	17.3457	−	3.71505i	0.661778	−	0.141738i
$688$	−7.78119	+	20.4665i	−0.296655	+	0.780277i
$689$	−0.0869373	+	0.150580i	−0.00331205	+	0.00573664i
$690$	25.1088	+	7.14702i	0.955876	+	0.272082i
$691$	−6.26524	+	3.61724i	−0.238341	+	0.137606i	−0.614414	−	0.788984i	$-0.710608\pi$
$691$	−6.26524	+	3.61724i	−0.238341	+	0.137606i	0.376073	+	0.926590i	$0.377274\pi$
$692$	0.793486	+	9.87980i	0.0301638	+	0.375574i
$693$	10.6960	+	7.72055i	0.406308	+	0.293279i
$694$	8.71079	−	9.43843i	0.330657	−	0.358278i
$695$	−31.4856	−	31.7874i	−1.19432	−	1.20577i
$696$	23.1413	−	15.5952i	0.877169	−	0.591136i
$697$	13.5350	+	7.81444i	0.512675	+	0.295993i
$698$	1.26441	−	0.393720i	0.0478585	−	0.0149025i
$699$	12.9679	+	14.3575i	0.490490	+	0.543049i
$700$	28.3942	+	13.8211i	1.07320	+	0.522387i
$701$		−	46.3121i		−	1.74918i	−0.484859	−	0.874592i	$-0.661129\pi$
$701$		−	46.3121i		−	1.74918i	0.484859	−	0.874592i	$-0.338871\pi$
$702$	−2.96522	−	0.334573i	−0.111915	−	0.0126277i
$703$		−	29.5452i		−	1.11432i
$704$	−7.70651	−	8.04318i	−0.290450	−	0.303139i
$705$	4.29939	−	6.57404i	0.161924	−	0.247593i
$706$	−32.6035	+	10.1523i	−1.22705	+	0.382086i
$707$	−15.1005	+	26.1549i	−0.567913	+	0.983655i
$708$	−23.8794	−	5.65337i	−0.897443	−	0.212467i
$709$	21.2728	−	12.2818i	0.798916	−	0.461254i	−0.0441761	−	0.999024i	$-0.514066\pi$
$709$	21.2728	−	12.2818i	0.798916	−	0.461254i	0.843092	+	0.537770i	$0.180733\pi$
$710$	−32.2300	−	17.1207i	−1.20957	−	0.642527i
$711$	−11.0936	+	4.98046i	−0.416042	+	0.186782i
$712$	25.9784	+	20.3787i	0.973582	+	0.763724i
$713$	−44.4935	+	25.6884i	−1.66630	+	0.962037i
$714$	−32.5642	−	19.2701i	−1.21868	−	0.721165i
$715$	0.333053	−	1.21967i	0.0124555	−	0.0456131i
$716$	−10.7092	+	22.5452i	−0.400222	+	0.842554i
$717$	−5.88914	−	27.4965i	−0.219934	−	1.02688i
$718$	−24.6348	−	5.55354i	−0.919362	−	0.207256i
$719$	13.1804			0.491546			0.245773	−	0.969327i	$-0.420958\pi$
$719$	13.1804			0.491546			0.245773	+	0.969327i	$0.420958\pi$
$720$	25.5068	−	8.33096i	0.950581	−	0.310477i
$721$	−23.3376			−0.869137
$722$	−15.0004	−	3.38161i	−0.558257	−	0.125851i
$723$	34.6245	+	11.1909i	1.28770	+	0.416193i
$724$	20.6656	−	43.5056i	0.768032	−	1.61687i
$725$	−28.4799	−	0.271715i	−1.05772	−	0.0100912i
$726$	0.238338	−	22.1940i	0.00884555	−	0.823698i
$727$	−2.21221	+	1.27722i	−0.0820465	+	0.0473696i	−0.540462	−	0.841368i	$-0.681751\pi$
$727$	−2.21221	+	1.27722i	−0.0820465	+	0.0473696i	0.458415	+	0.888738i	$0.348417\pi$
$728$	2.23864	−	2.85378i	0.0829695	−	0.105768i
$729$	−8.10421	+	25.7550i	−0.300156	+	0.953890i
$730$	5.68613	−	10.7042i	0.210453	−	0.396182i
$731$	−23.1893	+	13.3884i	−0.857688	+	0.495186i
$732$	16.2258	−	17.2068i	0.599724	−	0.635981i
$733$	−2.97612	+	5.15480i	−0.109926	+	0.190397i	−0.915740	−	0.401771i	$-0.868395\pi$
$733$	−2.97612	+	5.15480i	−0.109926	+	0.190397i	0.805814	+	0.592168i	$0.201728\pi$
$734$	11.1798	−	3.48124i	0.412654	−	0.128495i
$735$	0.639525	−	11.4946i	0.0235892	−	0.423986i
$736$	−1.65565	+	26.9114i	−0.0610279	+	0.991969i
$737$		−	10.0612i		−	0.370609i
$738$	8.97727	+	10.1564i	0.330458	+	0.373862i
$739$		−	18.2750i		−	0.672256i	−0.941816	−	0.336128i	$-0.890883\pi$
$739$		−	18.2750i		−	0.672256i	0.941816	−	0.336128i	$-0.109117\pi$
$740$	−35.1484	−	30.2127i	−1.29208	−	1.11064i
$741$	−1.96062	+	0.419920i	−0.0720250	+	0.0154262i
$742$	−1.82578	+	0.568525i	−0.0670267	+	0.0208712i
$743$	−0.518610	−	0.299419i	−0.0190259	−	0.0109846i	0.490457	−	0.871465i	$-0.336830\pi$
$743$	−0.518610	−	0.299419i	−0.0190259	−	0.0109846i	−0.509483	+	0.860481i	$0.670163\pi$
$744$	−23.1684	+	47.4529i	−0.849395	+	1.73971i
$745$	5.26093	+	5.31136i	0.192745	+	0.194593i
$746$	−25.8452	+	28.0042i	−0.946261	+	1.02531i
$747$	21.7241	−	9.75304i	0.794844	−	0.356845i
$748$	−1.09056	−	13.5787i	−0.0398747	−	0.496486i
$749$	50.1438	−	28.9505i	1.83221	−	1.05783i
$750$	−26.2671	−	7.74837i	−0.959140	−	0.282931i
$751$	−7.80534	+	13.5193i	−0.284821	+	0.493325i	−0.972566	−	0.232628i	$-0.925268\pi$
$751$	−7.80534	+	13.5193i	−0.284821	+	0.493325i	0.687745	+	0.725953i	$0.258601\pi$
$752$	7.58315	+	2.88305i	0.276529	+	0.105134i
$753$	−28.5095	−	31.5645i	−1.03894	−	1.15027i
$754$	−0.719396	+	3.19115i	−0.0261989	+	0.116215i
$755$	6.66683	+	25.3643i	0.242631	+	0.923101i
$756$	−21.4693	−	24.8213i	−0.780831	−	0.902743i
$757$	−41.6214			−1.51275			−0.756377	−	0.654136i	$-0.773032\pi$
$757$	−41.6214			−1.51275			−0.756377	+	0.654136i	$0.773032\pi$
$758$	−8.01340	+	35.5464i	−0.291060	+	1.29110i
$759$	8.53052	−	7.70490i	0.309638	−	0.279670i
$760$	14.4720	−	10.7535i	0.524956	−	0.390071i
$761$	−18.6453	+	32.2947i	−0.675893	+	1.17068i	0.300314	+	0.953840i	$0.402908\pi$
$761$	−18.6453	+	32.2947i	−0.675893	+	1.17068i	−0.976207	+	0.216840i	$0.930425\pi$
$762$	7.56788	+	13.4392i	0.274155	+	0.486851i
$763$	12.1602	+	21.0621i	0.440230	+	0.762501i
$764$	−1.97181	−	24.5512i	−0.0713374	−	0.888232i
$765$	30.6152	+	11.8107i	1.10689	+	0.427018i
$766$	4.62352	+	4.26707i	0.167054	+	0.154176i
$767$	2.49123	−	1.43831i	0.0899530	−	0.0519344i
$768$	14.0470	+	23.8890i	0.506877	+	0.862019i
$769$	19.5634	−	33.8848i	0.705474	−	1.22192i	−0.261046	−	0.965326i	$-0.584067\pi$
$769$	19.5634	−	33.8848i	0.705474	−	1.22192i	0.966520	−	0.256591i	$-0.0825994\pi$
$770$	11.7891	−	7.37313i	0.424851	−	0.265709i
$771$	7.06968	−	1.51417i	0.254608	−	0.0545314i
$772$	17.1906	+	24.9268i	0.618704	+	0.897137i
$773$	12.2276			0.439795			0.219897	−	0.975523i	$-0.429428\pi$
$773$	12.2276			0.439795			0.219897	+	0.975523i	$0.429428\pi$
$774$	−22.7598	+	4.61961i	−0.818085	+	0.166048i
$775$	46.9300	−	26.5013i	1.68577	−	0.951956i
$776$	48.4455	+	6.90543i	1.73909	+	0.247890i
$777$	−17.4338	+	53.9400i	−0.625433	+	1.93509i
$778$	−20.8538	+	6.49360i	−0.747645	+	0.232807i
$779$	7.88795	+	4.55411i	0.282615	+	0.163168i
$780$	−1.50535	+	2.76185i	−0.0539002	+	0.0988900i
$781$	−13.9165	+	8.03471i	−0.497972	+	0.287504i
$782$	−22.3625	+	24.2306i	−0.799682	+	0.866483i
$783$	27.0953	+	11.9129i	0.968307	+	0.425732i
$784$	11.7376	−	1.89762i	0.419199	−	0.0677722i
$785$	5.73031	−	5.67590i	0.204524	−	0.202582i
$786$	−12.4320	−	0.133505i	−0.443436	−	0.00476198i
$787$	−3.35657	+	5.81375i	−0.119649	+	0.207238i	−0.919629	−	0.392789i	$-0.871510\pi$
$787$	−3.35657	+	5.81375i	−0.119649	+	0.207238i	0.799980	+	0.600027i	$0.204844\pi$
$788$	−14.0860	−	6.69099i	−0.501792	−	0.238357i
$789$	−9.61576	+	29.7512i	−0.342330	+	1.05917i
$790$	0.452394	+	12.8101i	0.0160955	+	0.455762i
$791$	−6.64700			−0.236340
$792$	2.84522	−	11.4673i	0.101100	−	0.407471i
$793$			2.77242i			0.0984516i
$794$	−43.7300	−	9.85828i	−1.55192	−	0.349857i
$795$	1.48001	−	0.748110i	0.0524905	−	0.0265327i
$796$	−37.9206	−	18.0127i	−1.34406	−	0.638442i
$797$	10.7678	−	18.6504i	0.381416	−	0.660631i	−0.609849	−	0.792518i	$-0.708770\pi$
$797$	10.7678	−	18.6504i	0.381416	−	0.660631i	0.991265	+	0.131886i	$0.0421033\pi$
$798$	−18.9778	−	11.2303i	−0.671806	−	0.397547i
$799$	4.96060	+	8.59201i	0.175493	+	0.303963i
$800$	2.00607	−	28.2130i	0.0709252	−	0.997482i
$801$	−3.55262	+	34.8399i	−0.125526	+	1.23101i
$802$	−11.9615	+	12.9607i	−0.422376	+	0.457659i
$803$	−2.66849	−	4.62197i	−0.0941691	−	0.163106i
$804$	−5.76655	+	24.3574i	−0.203370	+	0.859020i
$805$	−32.4678	−	8.86593i	−1.14434	−	0.312483i
$806$	−1.84040	−	5.91032i	−0.0648252	−	0.208182i
$807$	2.89817	+	3.20873i	0.102020	+	0.112953i
$808$	26.7792	+	3.81711i	0.942088	+	0.134285i
$809$	−35.7462			−1.25677			−0.628384	−	0.777903i	$-0.716283\pi$
$809$	−35.7462			−1.25677			−0.628384	+	0.777903i	$0.716283\pi$
$810$	21.9222	+	18.1498i	0.770268	+	0.637721i
$811$			31.6301i			1.11068i	0.831623	+	0.555341i	$0.187412\pi$
$811$			31.6301i			1.11068i	−0.831623	+	0.555341i	$0.812588\pi$
$812$	−29.6166	+	20.4248i	−1.03934	+	0.716772i
$813$	−4.94769	+	4.46883i	−0.173523	+	0.156729i
$814$	−19.4854	+	6.06750i	−0.682963	+	0.212666i
$815$	−18.8125	−	5.13709i	−0.658972	−	0.179944i
$816$	−5.14243	+	33.4981i	−0.180021	+	1.17267i
$817$	−13.5143	+	7.80248i	−0.472805	+	0.272974i
$818$	−24.1503	+	26.1677i	−0.844396	+	0.914932i
$819$	3.82723	+	0.390263i	0.133734	+	0.0136369i
$820$	13.4839	−	4.72689i	0.470879	−	0.165070i
$821$	−33.0358	+	19.0732i	−1.15296	+	0.665660i	−0.949606	−	0.313446i	$-0.898517\pi$
$821$	−33.0358	+	19.0732i	−1.15296	+	0.665660i	−0.203351	+	0.979106i	$0.565183\pi$
$822$	−21.0166	+	35.5154i	−0.733036	+	1.23874i
$823$	−4.67019	−	2.69633i	−0.162792	−	0.0939883i	0.416390	−	0.909186i	$-0.363295\pi$
$823$	−4.67019	−	2.69633i	−0.162792	−	0.0939883i	−0.579183	+	0.815198i	$0.696628\pi$
$824$	7.79222	+	19.3958i	0.271455	+	0.675685i
$825$	−9.02547	+	7.99692i	−0.314226	+	0.278417i
$826$	30.8622	+	6.95743i	1.07383	+	0.242080i
$827$	−28.7367			−0.999274			−0.499637	−	0.866235i	$-0.666533\pi$
$827$	−28.7367			−0.999274			−0.499637	+	0.866235i	$0.666533\pi$
$828$	−25.0678	+	13.7638i	−0.871168	+	0.478324i
$829$		−	4.67845i		−	0.162489i	−0.996694	−	0.0812446i	$-0.974111\pi$
$829$		−	4.67845i		−	0.162489i	0.996694	−	0.0812446i	$-0.0258895\pi$
$830$	−0.885906	−	25.0855i	−0.0307502	−	0.870730i
$831$	10.7253	+	3.46648i	0.372056	+	0.120251i
$832$	−3.11923	−	0.907674i	−0.108140	−	0.0314679i
$833$	12.5924	+	7.27024i	0.436302	+	0.251899i
$834$	49.0088	+	0.526297i	1.69704	+	0.0182242i
$835$	17.1662	+	17.3308i	0.594061	+	0.599756i
$836$	−0.635557	−	7.91341i	−0.0219812	−	0.273691i
$837$	−55.6754	+	6.11368i	−1.92442	+	0.211320i
$838$	−10.8183	−	9.98423i	−0.373710	−	0.344899i
$839$	−20.7724	−	35.9789i	−0.717143	−	1.24213i	−0.962127	−	0.272601i	$-0.912116\pi$
$839$	−20.7724	−	35.9789i	−0.717143	−	1.24213i	0.244984	−	0.969527i	$-0.421217\pi$
$840$	−32.7665	+	11.0929i	−1.13055	+	0.382742i
$841$	1.72358	−	2.98532i	0.0594337	−	0.102942i
$842$	15.9787	−	4.97555i	0.550662	−	0.171469i
$843$	−32.5956	−	10.5351i	−1.12265	−	0.362848i
$844$	−9.80784	−	14.2216i	−0.337600	−	0.489529i
$845$	7.29583	+	27.7573i	0.250984	+	0.954882i
$846$	1.71164	+	8.43288i	0.0588474	+	0.289928i
$847$			28.6146i			0.983209i
$848$	1.08211	+	1.32758i	0.0371600	+	0.0455893i
$849$	0.719309	+	3.35847i	0.0246866	+	0.115262i
$850$	23.7004	−	25.1936i	0.812916	−	0.864133i
$851$	42.7796	+	24.6988i	1.46647	+	0.846665i
$852$	38.2960	−	11.4752i	1.31200	−	0.393135i
$853$	14.9584	+	25.9086i	0.512164	+	0.887094i	0.999901	+	0.0141034i	$0.00448941\pi$
$853$	14.9584	+	25.9086i	0.512164	+	0.887094i	−0.487736	+	0.872991i	$0.662177\pi$
$854$	−20.6792	+	22.4066i	−0.707628	+	0.766739i
$855$	17.8420	+	6.88308i	0.610182	+	0.235396i
$856$	−40.8033	−	32.0080i	−1.39463	−	1.09401i
$857$	−24.5716	+	14.1864i	−0.839349	+	0.484598i	−0.857043	−	0.515245i	$-0.827701\pi$
$857$	−24.5716	+	14.1864i	−0.839349	+	0.484598i	0.0176940	+	0.999843i	$0.494368\pi$
$858$	0.679580	+	1.20681i	0.0232005	+	0.0411999i
$859$	−38.3319	−	22.1309i	−1.30787	−	0.755097i	−0.326126	−	0.945326i	$-0.605743\pi$
$859$	−38.3319	−	22.1309i	−1.30787	−	0.755097i	−0.981740	+	0.190229i	$0.939077\pi$
$860$	−4.53739	+	24.0560i	−0.154724	+	0.820303i
$861$	−11.7136	−	12.9688i	−0.399198	−	0.441975i
$862$	27.3065	+	6.15584i	0.930063	+	0.209669i
$863$		−	37.1118i		−	1.26330i	−0.775254	−	0.631650i	$-0.782378\pi$
$863$		−	37.1118i		−	1.26330i	0.775254	−	0.631650i	$-0.217622\pi$
$864$	−13.4605	+	26.1307i	−0.457936	+	0.888985i
$865$	2.81702	+	10.7175i	0.0957814	+	0.364405i
$866$	9.87953	−	43.8243i	0.335720	−	1.48921i
$867$	−8.90566	+	8.04373i	−0.302452	+	0.273179i
$868$	29.2105	−	61.4944i	0.991468	−	2.08725i
$869$	4.88787	+	2.82201i	0.165810	+	0.0957302i
$870$	22.4009	−	21.7167i	0.759462	−	0.736264i
$871$	−1.46710	−	2.54110i	−0.0497109	−	0.0861018i
$872$	13.4445	−	17.1388i	0.455288	−	0.580393i
$873$	21.2580	+	47.3506i	0.719475	+	1.60257i
$874$	−13.0325	+	14.1211i	−0.440830	+	0.477654i
$875$	33.9694	+	9.62513i	1.14837	+	0.325389i
$876$	3.81117	+	12.7189i	0.128767	+	0.429732i
$877$	−7.25335	+	12.5632i	−0.244928	+	0.424228i	−0.962111	−	0.272656i	$-0.912098\pi$
$877$	−7.25335	+	12.5632i	−0.244928	+	0.424228i	0.717183	+	0.696885i	$0.245431\pi$
$878$	−3.00792	−	9.65976i	−0.101512	−	0.326001i
$879$	−11.1010	−	51.8309i	−0.374428	−	1.74821i
$880$	−10.0641	−	7.33609i	−0.339260	−	0.247299i
$881$	27.6383			0.931159			0.465580	−	0.885006i	$-0.345846\pi$
$881$	27.6383			0.931159			0.465580	+	0.885006i	$0.345846\pi$
$882$	8.35209	+	9.44910i	0.281230	+	0.318168i
$883$	−22.0323			−0.741447			−0.370724	−	0.928743i	$-0.620890\pi$
$883$	−22.0323			−0.741447			−0.370724	+	0.928743i	$0.620890\pi$
$884$	−2.25546	−	3.27047i	−0.0758592	−	0.109998i
$885$	−27.3936	−	1.52409i	−0.920826	−	0.0512318i
$886$	10.3550	+	33.2544i	0.347882	+	1.11720i
$887$	4.98660	+	2.87901i	0.167433	+	0.0966678i	0.581375	−	0.813636i	$-0.302515\pi$
$887$	4.98660	+	2.87901i	0.167433	+	0.0966678i	−0.413942	+	0.910303i	$0.635848\pi$
$888$	50.6504	−	3.52097i	1.69972	−	0.118156i
$889$	−9.94213	−	17.2203i	−0.333448	−	0.577550i
$890$	32.6008	+	17.3177i	1.09278	+	0.580489i
$891$	11.8941	−	3.94634i	0.398466	−	0.132207i
$892$	3.91760	−	0.314638i	0.131171	−	0.0105348i
$893$	2.89095	+	5.00726i	0.0967418	+	0.167562i
$894$	−8.18888	−	0.0879389i	−0.273877	−	0.00294112i
$895$	−7.35097	+	26.9199i	−0.245716	+	0.899833i
$896$	−18.4393	−	30.6018i	−0.616013	−	1.02234i
$897$	1.03099	−	3.18989i	0.0344238	−	0.106507i
$898$	35.3174	+	7.96178i	1.17856	+	0.265688i
$899$			61.4005i			2.04782i
$900$	26.4334	−	14.1871i	0.881115	−	0.472902i
$901$			2.09453i			0.0697788i
$902$	1.38359	−	6.13744i	0.0460686	−	0.204354i
$903$	29.2767	−	6.27042i	0.974269	−	0.208667i
$904$	2.21938	+	5.52431i	0.0738155	+	0.183736i
$905$	14.1852	−	51.9474i	0.471532	−	1.72679i
$906$	−24.7243	−	14.6308i	−0.821410	−	0.486076i
$907$	−8.05363	−	13.9493i	−0.267416	−	0.463179i	0.700777	−	0.713380i	$-0.252837\pi$
$907$	−8.05363	−	13.9493i	−0.267416	−	0.463179i	−0.968194	+	0.250201i	$0.919503\pi$
$908$	−2.40482	−	29.9428i	−0.0798068	−	0.993685i
$909$	11.7508	+	26.1739i	0.389749	+	0.868135i
$910$	1.90238	−	3.58126i	0.0630632	−	0.118718i
$911$	10.0789	+	17.4572i	0.333929	+	0.578382i	0.983278	−	0.182108i	$-0.0582922\pi$
$911$	10.0789	+	17.4572i	0.333929	+	0.578382i	−0.649350	+	0.760490i	$0.724959\pi$
$912$	−2.99691	+	19.5221i	−0.0992377	+	0.646441i
$913$	−9.57172	−	5.52623i	−0.316778	−	0.182892i
$914$	−11.8236	+	3.68170i	−0.391088	+	0.121780i
$915$	14.4728	−	22.1298i	0.478455	−	0.731589i
$916$	11.6289	+	16.8622i	0.384229	+	0.557143i
$917$	16.0285			0.529308
$918$	−32.9493	+	14.3695i	−1.08749	+	0.474263i
$919$	−1.68072			−0.0554417			−0.0277209	−	0.999616i	$-0.508825\pi$
$919$	−1.68072			−0.0554417			−0.0277209	+	0.999616i	$0.508825\pi$
$920$	3.47227	+	29.9442i	0.114477	+	0.987229i
$921$	13.2559	−	11.9729i	0.436796	−	0.394521i
$922$	26.9291	−	8.38535i	0.886862	−	0.276157i
$923$	−2.34321	+	4.05856i	−0.0771278	+	0.133589i
$924$	−3.50914	+	14.8223i	−0.115442	+	0.487619i
$925$	−44.6279	−	26.3368i	−1.46736	−	0.865947i
$926$	−5.14329	−	4.74678i	−0.169019	−	0.155989i
$927$	−12.9758	+	17.9766i	−0.426181	+	0.590430i
$928$	26.8638	+	17.7946i	0.881846	+	0.584136i
$929$	8.61458	+	14.9209i	0.282635	+	0.489538i	0.972033	−	0.234845i	$-0.0754581\pi$
$929$	8.61458	+	14.9209i	0.282635	+	0.489538i	−0.689398	+	0.724383i	$0.742125\pi$
$930$	−16.1632	+	56.7842i	−0.530011	+	1.86203i
$931$	7.33863	+	4.23696i	0.240514	+	0.138861i
$932$	−9.58525	+	20.1790i	−0.313975	+	0.660986i
$933$	−0.359420	−	1.67814i	−0.0117669	−	0.0549399i
$934$	5.99778	+	1.35211i	0.196253	+	0.0442424i
$935$	−3.87168	−	14.7300i	−0.126617	−	0.481722i
$936$	−0.953534	−	3.31111i	−0.0311672	−	0.108227i
$937$		−	50.2907i		−	1.64292i	−0.570263	−	0.821462i	$-0.693159\pi$
$937$		−	50.2907i		−	1.64292i	0.570263	−	0.821462i	$-0.306841\pi$
$938$	7.09671	−	31.4801i	0.231716	−	1.02786i
$939$	8.06910	−	24.9658i	0.263325	−	0.814727i
$940$	8.91313	+	1.68118i	0.290714	+	0.0548339i
$941$	48.3696	+	27.9262i	1.57680	+	0.910368i	0.995302	+	0.0968235i	$0.0308682\pi$
$941$	48.3696	+	27.9262i	1.57680	+	0.910368i	0.581502	+	0.813545i	$0.302465\pi$
$942$	−0.0948753	+	8.83480i	−0.00309121	+	0.287853i
$943$	−13.1881	+	7.61417i	−0.429465	+	0.247951i
$944$	−4.52234	−	27.9725i	−0.147190	−	0.910429i
$945$	−28.5121	−	23.0943i	−0.927500	−	0.751257i
$946$	7.92116	+	7.31049i	0.257539	+	0.237684i
$947$	5.93505	+	10.2798i	0.192863	+	0.334049i	0.946198	−	0.323588i	$-0.104889\pi$
$947$	5.93505	+	10.2798i	0.192863	+	0.334049i	−0.753335	+	0.657637i	$0.771556\pi$
$948$	−10.2158	−	9.63336i	−0.331792	−	0.312877i
$949$	−1.34793	−	0.778230i	−0.0437558	−	0.0252624i
$950$	13.8121	−	14.6824i	0.448125	−	0.476359i
$951$	26.7409	+	8.64282i	0.867132	+	0.280262i
$952$	6.16559	−	43.2551i	0.199828	−	1.40190i
$953$		−	9.40964i		−	0.304808i	−0.988318	−	0.152404i	$-0.951298\pi$
$953$		−	9.40964i		−	0.304808i	0.988318	−	0.152404i	$-0.0487015\pi$
$954$	−0.577217	+	1.72248i	−0.0186881	+	0.0557673i
$955$	−7.00026	−	26.6329i	−0.226523	−	0.861819i
$956$	26.7301	−	18.4342i	0.864514	−	0.596206i
$957$	−2.87707	−	13.4331i	−0.0930024	−	0.434230i
$958$	−13.7184	−	44.0558i	−0.443221	−	1.42338i
$959$	26.6017	−	46.0755i	0.859013	−	1.48785i
$960$	20.1598	+	23.5284i	0.650654	+	0.759375i
$961$	−42.5949	−	73.7765i	−1.37403	−	2.37989i
$962$	−4.03657	+	4.37376i	−0.130144	+	0.141016i
$963$	5.57997	−	54.7217i	0.179812	−	1.76338i
$964$	3.36375	+	41.8825i	0.108339	+	1.34895i
$965$	23.8238	+	24.0522i	0.766915	+	0.774267i
$966$	32.1255	−	18.0905i	1.03362	−	0.582053i
$967$	−33.3008	−	19.2262i	−1.07088	−	0.618274i	−0.142460	−	0.989801i	$-0.545501\pi$
$967$	−33.3008	−	19.2262i	−1.07088	−	0.618274i	−0.928422	+	0.371526i	$0.878835\pi$
$968$	23.7815	−	9.55418i	0.764367	−	0.307083i
$969$	−17.9245	+	16.1897i	−0.575819	+	0.520089i
$970$	54.6771	−	1.93095i	1.75558	−	0.0619990i
$971$		−	3.37445i		−	0.108291i	−0.998533	−	0.0541456i	$-0.982756\pi$
$971$		−	3.37445i		−	0.108291i	0.998533	−	0.0541456i	$-0.0172435\pi$
$972$	−31.0566	+	2.73675i	−0.996140	+	0.0877813i
$973$	−63.1867			−2.02567
$974$	−8.84265	+	39.2248i	−0.283337	+	1.25684i
$975$	−1.11342	+	3.33582i	−0.0356578	+	0.106832i
$976$	25.5267	+	9.70506i	0.817090	+	0.310651i
$977$	44.4984	+	25.6912i	1.42363	+	0.821934i	0.996607	−	0.0823068i	$-0.0262288\pi$
$977$	44.4984	+	25.6912i	1.42363	+	0.821934i	0.427024	+	0.904240i	$0.359562\pi$
$978$	18.6141	−	10.4820i	0.595215	−	0.335177i
$979$	14.0766	−	8.12715i	0.449891	−	0.259745i
$980$	12.5449	−	4.39771i	0.400732	−	0.140480i
$981$	22.9850	+	2.34378i	0.733855	+	0.0748312i
$982$	18.6280	+	17.1919i	0.594444	+	0.548616i
$983$	28.5852	−	16.5037i	0.911725	−	0.526385i	0.0307394	−	0.999527i	$-0.490214\pi$
$983$	28.5852	−	16.5037i	0.911725	−	0.526385i	0.880986	+	0.473143i	$0.156880\pi$
$984$	−6.86724	+	14.0653i	−0.218920	+	0.448386i
$985$	−16.8192	−	4.59280i	−0.535905	−	0.146339i
$986$	11.7156	+	37.6240i	0.373101	+	1.19819i
$987$	−2.32329	−	10.8475i	−0.0739512	−	0.345280i
$988$	−1.31444	−	1.90597i	−0.0418178	−	0.0606370i
$989$		−	26.0905i		−	0.829629i
$990$	0.875387	−	13.1805i	0.0278216	−	0.418904i
$991$	−6.52604			−0.207306			−0.103653	−	0.994614i	$-0.533053\pi$
$991$	−6.52604			−0.207306			−0.103653	+	0.994614i	$0.533053\pi$
$992$	−60.8609	−	3.74429i	−1.93234	−	0.118881i
$993$	8.72330	−	26.9899i	0.276826	−	0.856498i
$994$	−49.2102	+	15.3234i	−1.56085	+	0.486029i
$995$	−45.2787	−	12.3642i	−1.43543	−	0.391971i
$996$	20.0051	+	18.8646i	0.633886	+	0.597749i
$997$	1.98168	+	3.43237i	0.0627605	+	0.108704i	0.895698	−	0.444662i	$-0.146676\pi$
$997$	1.98168	+	3.43237i	0.0627605	+	0.108704i	−0.832938	+	0.553366i	$0.813343\pi$
$998$	−24.1469	−	22.2853i	−0.764356	−	0.705428i
$999$	31.8560	+	43.4199i	1.00788	+	1.37374i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bk.a.229.6	✓	136
5.4	even	2	inner	360.2.bk.a.229.63	yes	136
8.5	even	2	inner	360.2.bk.a.229.27	yes	136
9.7	even	3	inner	360.2.bk.a.349.42	yes	136
40.29	even	2	inner	360.2.bk.a.229.42	yes	136
45.34	even	6	inner	360.2.bk.a.349.27	yes	136
72.61	even	6	inner	360.2.bk.a.349.63	yes	136
360.349	even	6	inner	360.2.bk.a.349.6	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bk.a.229.6	✓	136	1.1	even	1	trivial
360.2.bk.a.229.27	yes	136	8.5	even	2	inner
360.2.bk.a.229.42	yes	136	40.29	even	2	inner
360.2.bk.a.229.63	yes	136	5.4	even	2	inner
360.2.bk.a.349.6	yes	136	360.349	even	6	inner
360.2.bk.a.349.27	yes	136	45.34	even	6	inner
360.2.bk.a.349.42	yes	136	9.7	even	3	inner
360.2.bk.a.349.63	yes	136	72.61	even	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37959 - 0.311008i) q^{2} +(1.28537 - 1.16096i) q^{3} +(1.80655 + 0.858129i) q^{4} +(2.15709 + 0.589033i) q^{5} +(-2.13435 + 1.20190i) q^{6} +(2.73484 - 1.57896i) q^{7} +(-2.22541 - 1.74572i) q^{8} +(0.304332 - 2.98452i) q^{9} +O(q^{10})\)	\(q+(-1.37959 - 0.311008i) q^{2} +(1.28537 - 1.16096i) q^{3} +(1.80655 + 0.858129i) q^{4} +(2.15709 + 0.589033i) q^{5} +(-2.13435 + 1.20190i) q^{6} +(2.73484 - 1.57896i) q^{7} +(-2.22541 - 1.74572i) q^{8} +(0.304332 - 2.98452i) q^{9} +(-2.79271 - 1.48350i) q^{10} +(-1.20586 + 0.696203i) q^{11} +(3.31833 - 0.994324i) q^{12} +(-0.203038 + 0.351673i) q^{13} +(-4.26404 + 1.32777i) q^{14} +(3.45650 - 1.74718i) q^{15} +(2.52723 + 3.10050i) q^{16} +4.89168i q^{17} +(-1.34807 + 4.02278i) q^{18} +2.85078i q^{19} +(3.39142 + 2.91518i) q^{20} +(1.68216 - 5.20460i) q^{21} +(1.88012 - 0.585444i) q^{22} +(-4.12775 - 2.38316i) q^{23} +(-4.88719 + 0.339734i) q^{24} +(4.30608 + 2.54120i) q^{25} +(0.389483 - 0.422018i) q^{26} +(-3.07374 - 4.18952i) q^{27} +(6.29558 - 0.505623i) q^{28} +(-4.93309 + 2.84812i) q^{29} +(-5.31194 + 1.33539i) q^{30} +(5.38957 - 9.33501i) q^{31} +(-2.52226 - 5.06342i) q^{32} +(-0.741705 + 2.29483i) q^{33} +(1.52135 - 6.74852i) q^{34} +(6.82937 - 1.79505i) q^{35} +(3.11090 - 5.13053i) q^{36} -10.3639 q^{37} +(0.886616 - 3.93291i) q^{38} +(0.147300 + 0.687748i) q^{39} +(-3.77213 - 5.07652i) q^{40} +(1.59750 - 2.76695i) q^{41} +(-3.93937 + 6.65705i) q^{42} +(2.73697 + 4.74056i) q^{43} +(-2.77588 + 0.222942i) q^{44} +(2.41446 - 6.25863i) q^{45} +(4.95342 + 4.57155i) q^{46} +(1.75646 - 1.01409i) q^{47} +(6.84798 + 1.05126i) q^{48} +(1.48625 - 2.57426i) q^{49} +(-5.15030 - 4.84504i) q^{50} +(5.67905 + 6.28759i) q^{51} +(-0.668579 + 0.461080i) q^{52} +0.428182 q^{53} +(2.93753 + 6.73579i) q^{54} +(-3.01124 + 0.791482i) q^{55} +(-8.84258 - 1.26042i) q^{56} +(3.30965 + 3.66429i) q^{57} +(7.69144 - 2.39501i) q^{58} +(-6.13487 - 3.54197i) q^{59} +(7.74363 - 0.190241i) q^{60} +(5.91265 - 3.41367i) q^{61} +(-10.3387 + 11.2023i) q^{62} +(-3.88015 - 8.64273i) q^{63} +(1.90493 + 7.76989i) q^{64} +(-0.645119 + 0.638993i) q^{65} +(1.73696 - 2.93526i) q^{66} +(-3.61288 + 6.25768i) q^{67} +(-4.19769 + 8.83705i) q^{68} +(-8.07242 + 1.72893i) q^{69} +(-9.98002 + 0.352449i) q^{70} +11.5407 q^{71} +(-5.88740 + 6.11052i) q^{72} +3.83292i q^{73} +(14.2980 + 3.22327i) q^{74} +(8.48512 - 1.73283i) q^{75} +(-2.44634 + 5.15007i) q^{76} +(-2.19856 + 3.80802i) q^{77} +(0.0106811 - 0.994623i) q^{78} +(-2.02671 - 3.51037i) q^{79} +(3.62516 + 8.17669i) q^{80} +(-8.81476 - 1.81657i) q^{81} +(-3.06444 + 3.32042i) q^{82} +(3.96883 + 6.87422i) q^{83} +(7.50511 - 7.95884i) q^{84} +(-2.88136 + 10.5518i) q^{85} +(-2.30154 - 7.39126i) q^{86} +(-3.03426 + 9.38801i) q^{87} +(3.89891 + 0.555752i) q^{88} -11.6735 q^{89} +(-5.27745 + 7.88344i) q^{90} +1.28236i q^{91} +(-5.41192 - 7.84742i) q^{92} +(-3.91002 - 18.2560i) q^{93} +(-2.73858 + 0.852758i) q^{94} +(-1.67920 + 6.14939i) q^{95} +(-9.12047 - 3.58009i) q^{96} +(-14.9833 + 8.65059i) q^{97} +(-2.85103 + 3.08919i) q^{98} +(1.71085 + 3.81079i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 2 q^{4} - 8 q^{9}+O(q^{10}) \) 136 * q - 2 * q^4 - 8 * q^9	\( 136 q - 2 q^{4} - 8 q^{9} - 10 q^{14} + 2 q^{15} - 2 q^{16} - 2 q^{20} - 38 q^{24} - 2 q^{25} + 16 q^{26} - 12 q^{30} - 4 q^{31} + 8 q^{34} - 24 q^{36} + 4 q^{39} - 6 q^{40} - 4 q^{41} - 56 q^{44} - 28 q^{46} + 40 q^{49} - 12 q^{50} + 10 q^{54} - 28 q^{55} + 26 q^{56} - 58 q^{60} - 20 q^{64} + 18 q^{65} + 16 q^{66} - 6 q^{70} - 128 q^{71} + 36 q^{74} + 12 q^{76} - 4 q^{79} - 36 q^{80} - 16 q^{81} - 110 q^{84} + 44 q^{86} - 32 q^{89} + 32 q^{90} - 34 q^{94} + 8 q^{95} - 2 q^{96}+O(q^{100}) \) 136 * q - 2 * q^4 - 8 * q^9 - 10 * q^14 + 2 * q^15 - 2 * q^16 - 2 * q^20 - 38 * q^24 - 2 * q^25 + 16 * q^26 - 12 * q^30 - 4 * q^31 + 8 * q^34 - 24 * q^36 + 4 * q^39 - 6 * q^40 - 4 * q^41 - 56 * q^44 - 28 * q^46 + 40 * q^49 - 12 * q^50 + 10 * q^54 - 28 * q^55 + 26 * q^56 - 58 * q^60 - 20 * q^64 + 18 * q^65 + 16 * q^66 - 6 * q^70 - 128 * q^71 + 36 * q^74 + 12 * q^76 - 4 * q^79 - 36 * q^80 - 16 * q^81 - 110 * q^84 + 44 * q^86 - 32 * q^89 + 32 * q^90 - 34 * q^94 + 8 * q^95 - 2 * q^96

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