LMFDB - Embedded newform 560.2.cr.a.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(109,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 6, 8]))

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

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

chi := DirichletCharacter("560.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.cr (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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$92$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			109.2
Character	$\chi$	$=$	560.109
Dual form			560.2.cr.a.149.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41398 + 0.0257616i) q^{2} +(-0.111122 - 0.414711i) q^{3} +(1.99867 - 0.0728528i) q^{4} +(0.968683 - 2.01535i) q^{5} +(0.167807 + 0.583530i) q^{6} +(0.251962 + 2.63373i) q^{7} +(-2.82420 + 0.154501i) q^{8} +(2.43844 - 1.40783i) q^{9} +(-1.31778 + 2.87462i) q^{10} +(0.957138 + 3.57209i) q^{11} +(-0.252308 - 0.820776i) q^{12} +(-1.22156 + 1.22156i) q^{13} +(-0.424118 - 3.71754i) q^{14} +(-0.943432 - 0.177775i) q^{15} +(3.98938 - 0.291218i) q^{16} +(6.31141 + 3.64390i) q^{17} +(-3.41163 + 2.05346i) q^{18} +(-0.970329 + 3.62132i) q^{19} +(1.78926 - 4.09860i) q^{20} +(1.06424 - 0.397155i) q^{21} +(-1.44540 - 5.02620i) q^{22} +(-3.08025 - 5.33515i) q^{23} +(0.377903 + 1.15406i) q^{24} +(-3.12330 - 3.90448i) q^{25} +(1.69579 - 1.75872i) q^{26} +(-1.76558 - 1.76558i) q^{27} +(0.695464 + 5.24560i) q^{28} +(3.64853 + 3.64853i) q^{29} +(1.33857 + 0.227065i) q^{30} +(0.114533 - 0.198377i) q^{31} +(-5.63340 + 0.514549i) q^{32} +(1.37503 - 0.793872i) q^{33} +(-9.01808 - 4.98980i) q^{34} +(5.55196 + 2.04345i) q^{35} +(4.77108 - 2.99145i) q^{36} +(-0.661228 + 2.46774i) q^{37} +(1.27873 - 5.14547i) q^{38} +(0.642334 + 0.370852i) q^{39} +(-2.42438 + 5.84143i) q^{40} -12.4045i q^{41} +(-1.49458 + 0.588985i) q^{42} +(7.74469 + 7.74469i) q^{43} +(2.17324 + 7.06971i) q^{44} +(-0.475208 - 6.27806i) q^{45} +(4.49285 + 7.46443i) q^{46} +(6.79722 - 3.92438i) q^{47} +(-0.564078 - 1.62208i) q^{48} +(-6.87303 + 1.32720i) q^{49} +(4.51687 + 5.44039i) q^{50} +(0.809831 - 3.02233i) q^{51} +(-2.35250 + 2.53048i) q^{52} +(6.75661 - 1.81043i) q^{53} +(2.54197 + 2.45100i) q^{54} +(8.12619 + 1.53125i) q^{55} +(-1.11851 - 7.39925i) q^{56} +1.60963 q^{57} +(-5.25294 - 5.06495i) q^{58} +(0.00760944 + 0.0283988i) q^{59} +(-1.89856 - 0.286582i) q^{60} +(1.48861 - 5.55558i) q^{61} +(-0.156837 + 0.283451i) q^{62} +(4.32224 + 6.06746i) q^{63} +(7.95226 - 0.872687i) q^{64} +(1.27857 + 3.64517i) q^{65} +(-1.92381 + 1.15794i) q^{66} +(2.42289 + 9.04236i) q^{67} +(12.8799 + 6.82315i) q^{68} +(-1.87026 + 1.87026i) q^{69} +(-7.90300 - 2.74637i) q^{70} +7.16148i q^{71} +(-6.66914 + 4.35275i) q^{72} +(-4.56415 + 7.90533i) q^{73} +(0.871390 - 3.50636i) q^{74} +(-1.27217 + 1.72914i) q^{75} +(-1.67555 + 7.30852i) q^{76} +(-9.16674 + 3.42087i) q^{77} +(-0.917801 - 0.507829i) q^{78} +(-4.95076 - 8.57496i) q^{79} +(3.27754 - 8.32212i) q^{80} +(3.68749 - 6.38692i) q^{81} +(0.319560 + 17.5397i) q^{82} +(7.20325 - 7.20325i) q^{83} +(2.09813 - 0.871316i) q^{84} +(13.4575 - 9.18995i) q^{85} +(-11.1503 - 10.7513i) q^{86} +(1.10766 - 1.91852i) q^{87} +(-3.25505 - 9.94043i) q^{88} +(1.98369 - 1.14528i) q^{89} +(0.833667 + 8.86481i) q^{90} +(-3.52503 - 2.90946i) q^{91} +(-6.54509 - 10.4388i) q^{92} +(-0.0949962 - 0.0254542i) q^{93} +(-9.51003 + 5.72409i) q^{94} +(6.35830 + 5.46347i) q^{95} +(0.839382 + 2.27906i) q^{96} -7.07495i q^{97} +(9.68413 - 2.05369i) q^{98} +(7.36283 + 7.36283i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 4 q^{4} - 2 q^{5} - 16 q^{6} - 8 q^{10} - 4 q^{11} + 16 q^{14} - 16 q^{15} - 4 q^{16} - 4 q^{19} - 8 q^{20} + 4 q^{21} - 4 q^{24} - 4 q^{26} - 16 q^{29} + 22 q^{30} - 56 q^{31} - 96 q^{34} + 18 q^{35}+ \cdots - 112 q^{99}+O(q^{100}) $ 368 * q - 4 * q^4 - 2 * q^5 - 16 * q^6 - 8 * q^10 - 4 * q^11 + 16 * q^14 - 16 * q^15 - 4 * q^16 - 4 * q^19 - 8 * q^20 + 4 * q^21 - 4 * q^24 - 4 * q^26 - 16 * q^29 + 22 * q^30 - 56 * q^31 - 96 * q^34 + 18 * q^35 + 32 * q^36 - 14 * q^40 - 12 * q^44 - 16 * q^45 + 12 * q^46 - 16 * q^49 - 12 * q^50 - 28 * q^51 - 8 * q^54 - 64 * q^56 + 12 * q^59 - 54 * q^60 - 4 * q^61 - 88 * q^64 - 4 * q^65 - 44 * q^66 + 8 * q^69 + 88 * q^70 - 72 * q^74 + 10 * q^75 + 104 * q^76 - 8 * q^79 + 48 * q^80 + 112 * q^81 + 68 * q^84 - 28 * q^85 + 44 * q^86 - 92 * q^90 - 80 * q^91 - 20 * q^94 + 20 * q^95 - 36 * q^96 - 112 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.41398	+	0.0257616i	−0.999834	+	0.0182162i
$2$	−1.41398	+	0.0257616i	−0.999834	+	0.0182162i
$3$	−0.111122	−	0.414711i	−0.0641560	−	0.239434i	0.926400	−	0.376540i	$-0.122886\pi$
$3$	−0.111122	−	0.414711i	−0.0641560	−	0.239434i	−0.990556	+	0.137107i	$0.956220\pi$
$4$	1.99867	−	0.0728528i	0.999336	−	0.0364264i
$5$	0.968683	−	2.01535i	0.433208	−	0.901294i
$5$	0.968683	−	2.01535i	0.433208	−	0.901294i
$6$	0.167807	+	0.583530i	0.0685070	+	0.238225i
$7$	0.251962	+	2.63373i	0.0952326	+	0.995455i
$7$	0.251962	+	2.63373i	0.0952326	+	0.995455i
$8$	−2.82420	+	0.154501i	−0.998507	+	0.0546245i
$9$	2.43844	−	1.40783i	0.812813	−	0.469278i
$10$	−1.31778	+	2.87462i	−0.416718	+	0.909036i
$11$	0.957138	+	3.57209i	0.288588	+	1.07703i	0.946177	+	0.323649i	$0.104910\pi$
$11$	0.957138	+	3.57209i	0.288588	+	1.07703i	−0.657589	+	0.753377i	$0.728424\pi$
$12$	−0.252308	−	0.820776i	−0.0728352	−	0.236938i
$13$	−1.22156	+	1.22156i	−0.338799	+	0.338799i	−0.855915	−	0.517116i	$-0.827005\pi$
$13$	−1.22156	+	1.22156i	−0.338799	+	0.338799i	0.517116	+	0.855915i	$0.327005\pi$
$14$	−0.424118	−	3.71754i	−0.113350	−	0.993555i
$15$	−0.943432	−	0.177775i	−0.243593	−	0.0459012i
$16$	3.98938	−	0.291218i	0.997346	−	0.0728045i
$17$	6.31141	+	3.64390i	1.53074	+	0.883775i	0.999328	+	0.0366632i	$0.0116729\pi$
$17$	6.31141	+	3.64390i	1.53074	+	0.883775i	0.531415	+	0.847112i	$0.321660\pi$
$18$	−3.41163	+	2.05346i	−0.804130	+	0.484006i
$19$	−0.970329	+	3.62132i	−0.222609	+	0.830788i	0.760740	+	0.649057i	$0.224836\pi$
$19$	−0.970329	+	3.62132i	−0.222609	+	0.830788i	−0.983348	+	0.181730i	$0.941830\pi$
$20$	1.78926	−	4.09860i	0.400090	−	0.916476i
$21$	1.06424	−	0.397155i	0.232236	−	0.0866663i
$22$	−1.44540	−	5.02620i	−0.308160	−	1.07159i
$23$	−3.08025	−	5.33515i	−0.642276	−	1.11246i	−0.984923	−	0.172991i	$-0.944657\pi$
$23$	−3.08025	−	5.33515i	−0.642276	−	1.11246i	0.342647	−	0.939464i	$-0.388676\pi$
$24$	0.377903	+	1.15406i	0.0771392	+	0.235572i
$25$	−3.12330	−	3.90448i	−0.624661	−	0.780896i
$26$	1.69579	−	1.75872i	0.332571	−	0.344914i
$27$	−1.76558	−	1.76558i	−0.339785	−	0.339785i
$28$	0.695464	+	5.24560i	0.131430	+	0.991325i
$29$	3.64853	+	3.64853i	0.677515	+	0.677515i	0.959437	−	0.281922i	$-0.0909720\pi$
$29$	3.64853	+	3.64853i	0.677515	+	0.677515i	−0.281922	+	0.959437i	$0.590972\pi$
$30$	1.33857	+	0.227065i	0.244389	+	0.0414562i
$31$	0.114533	−	0.198377i	0.0205707	−	0.0356296i	−0.855557	−	0.517709i	$-0.826785\pi$
$31$	0.114533	−	0.198377i	0.0205707	−	0.0356296i	0.876128	+	0.482079i	$0.160118\pi$
$32$	−5.63340	+	0.514549i	−0.995855	+	0.0909603i
$33$	1.37503	−	0.793872i	0.239361	−	0.138195i
$34$	−9.01808	−	4.98980i	−1.54659	−	0.855744i
$35$	5.55196	+	2.04345i	0.938453	+	0.345407i
$36$	4.77108	−	2.99145i	0.795179	−	0.498574i
$37$	−0.661228	+	2.46774i	−0.108705	+	0.405694i	−0.998739	−	0.0502008i	$-0.984014\pi$
$37$	−0.661228	+	2.46774i	−0.108705	+	0.405694i	0.890034	+	0.455894i	$0.150681\pi$
$38$	1.27873	−	5.14547i	0.207438	−	0.834705i
$39$	0.642334	+	0.370852i	0.102856	+	0.0593838i
$40$	−2.42438	+	5.84143i	−0.383329	+	0.923612i
$41$		−	12.4045i		−	1.93726i	−0.248513	−	0.968629i	$-0.579942\pi$
$41$		−	12.4045i		−	1.93726i	0.248513	−	0.968629i	$-0.420058\pi$
$42$	−1.49458	+	0.588985i	−0.230618	+	0.0908824i
$43$	7.74469	+	7.74469i	1.18105	+	1.18105i	0.979472	+	0.201582i	$0.0646082\pi$
$43$	7.74469	+	7.74469i	1.18105	+	1.18105i	0.201582	+	0.979472i	$0.435392\pi$
$44$	2.17324	+	7.06971i	0.327629	+	1.06580i
$45$	−0.475208	−	6.27806i	−0.0708398	−	0.935878i
$46$	4.49285	+	7.46443i	0.662434	+	1.10057i
$47$	6.79722	−	3.92438i	0.991477	−	0.572429i	0.0857613	−	0.996316i	$-0.472668\pi$
$47$	6.79722	−	3.92438i	0.991477	−	0.572429i	0.905715	+	0.423886i	$0.139334\pi$
$48$	−0.564078	−	1.62208i	−0.0814176	−	0.234127i
$49$	−6.87303	+	1.32720i	−0.981862	+	0.189600i
$50$	4.51687	+	5.44039i	0.638782	+	0.769388i
$51$	0.809831	−	3.02233i	0.113399	−	0.423211i
$52$	−2.35250	+	2.53048i	−0.326233	+	0.350915i
$53$	6.75661	−	1.81043i	0.928092	−	0.248681i	0.237051	−	0.971497i	$-0.423819\pi$
$53$	6.75661	−	1.81043i	0.928092	−	0.248681i	0.691041	+	0.722816i	$0.257153\pi$
$54$	2.54197	+	2.45100i	0.345919	+	0.333539i
$55$	8.12619	+	1.53125i	1.09573	+	0.206474i
$56$	−1.11851	−	7.39925i	−0.149467	−	0.988767i
$57$	1.60963			0.213200
$58$	−5.25294	−	5.06495i	−0.689745	−	0.665061i
$59$	0.00760944	+	0.0283988i	0.000990664	+	0.00369721i	0.966419	−	0.256970i	$-0.0827241\pi$
$59$	0.00760944	+	0.0283988i	0.000990664	+	0.00369721i	−0.965429	+	0.260667i	$0.916057\pi$
$60$	−1.89856	−	0.286582i	−0.245103	−	0.0369975i
$61$	1.48861	−	5.55558i	0.190597	−	0.711319i	−0.802765	−	0.596295i	$-0.796639\pi$
$61$	1.48861	−	5.55558i	0.190597	−	0.711319i	0.993363	−	0.115024i	$-0.0366944\pi$
$62$	−0.156837	+	0.283451i	−0.0199183	+	0.0359984i
$63$	4.32224	+	6.06746i	0.544551	+	0.764428i
$64$	7.95226	−	0.872687i	0.994032	−	0.109086i
$65$	1.27857	+	3.64517i	0.158587	+	0.452128i
$66$	−1.92381	+	1.15794i	−0.236804	+	0.142533i
$67$	2.42289	+	9.04236i	0.296004	+	1.10470i	0.940417	+	0.340023i	$0.110435\pi$
$67$	2.42289	+	9.04236i	0.296004	+	1.10470i	−0.644413	+	0.764677i	$0.722898\pi$
$68$	12.8799	+	6.82315i	1.56192	+	0.827429i
$69$	−1.87026	+	1.87026i	−0.225153	+	0.225153i
$70$	−7.90300	−	2.74637i	−0.944589	−	0.328255i
$71$			7.16148i			0.849911i	0.905214	+	0.424956i	$0.139710\pi$
$71$			7.16148i			0.849911i	−0.905214	+	0.424956i	$0.860290\pi$
$72$	−6.66914	+	4.35275i	−0.785965	+	0.512977i
$73$	−4.56415	+	7.90533i	−0.534193	+	0.925249i	0.465009	+	0.885306i	$0.346051\pi$
$73$	−4.56415	+	7.90533i	−0.534193	+	0.925249i	−0.999202	+	0.0399433i	$0.987282\pi$
$74$	0.871390	−	3.50636i	0.101297	−	0.407606i
$75$	−1.27217	+	1.72914i	−0.146897	+	0.199664i
$76$	−1.67555	+	7.30852i	−0.192199	+	0.838345i
$77$	−9.16674	+	3.42087i	−1.04465	+	0.389844i
$78$	−0.917801	−	0.507829i	−0.103920	−	0.0575003i
$79$	−4.95076	−	8.57496i	−0.557004	−	0.964758i	−0.997745	−	0.0671241i	$-0.978618\pi$
$79$	−4.95076	−	8.57496i	−0.557004	−	0.964758i	0.440741	−	0.897634i	$-0.354716\pi$
$80$	3.27754	−	8.32212i	0.366441	−	0.930441i
$81$	3.68749	−	6.38692i	0.409721	−	0.709658i
$82$	0.319560	+	17.5397i	0.0352895	+	1.93694i
$83$	7.20325	−	7.20325i	0.790660	−	0.790660i	−0.190942	−	0.981601i	$-0.561154\pi$
$83$	7.20325	−	7.20325i	0.790660	−	0.790660i	0.981601	+	0.190942i	$0.0611541\pi$
$84$	2.09813	−	0.871316i	0.228925	−	0.0950683i
$85$	13.4575	−	9.18995i	1.45967	−	0.996790i
$86$	−11.1503	−	10.7513i	−1.20237	−	1.15934i
$87$	1.10766	−	1.91852i	0.118753	−	0.205687i
$88$	−3.25505	−	9.94043i	−0.346989	−	1.05965i
$89$	1.98369	−	1.14528i	0.210270	−	0.121400i	−0.391167	−	0.920320i	$-0.627928\pi$
$89$	1.98369	−	1.14528i	0.210270	−	0.121400i	0.601437	+	0.798920i	$0.294595\pi$
$90$	0.833667	+	8.86481i	0.0878762	+	0.934433i
$91$	−3.52503	−	2.90946i	−0.369524	−	0.304994i
$92$	−6.54509	−	10.4388i	−0.682373	−	1.08832i
$93$	−0.0949962	−	0.0254542i	−0.00985065	−	0.00263947i
$94$	−9.51003	+	5.72409i	−0.980885	+	0.590395i
$95$	6.35830	+	5.46347i	0.652348	+	0.560540i
$96$	0.839382	+	2.27906i	0.0856690	+	0.232605i
$97$		−	7.07495i		−	0.718352i	−0.933270	−	0.359176i	$-0.883058\pi$
$97$		−	7.07495i		−	0.718352i	0.933270	−	0.359176i	$-0.116942\pi$
$98$	9.68413	−	2.05369i	0.978245	−	0.207454i
$99$	7.36283	+	7.36283i	0.739992	+	0.739992i
$100$	−6.52692	−	7.57624i	−0.652692	−	0.757624i
$101$	1.09613	+	4.09081i	0.109069	+	0.407051i	0.998775	−	0.0494830i	$-0.0157574\pi$
$101$	1.09613	+	4.09081i	0.109069	+	0.407051i	−0.889706	+	0.456534i	$0.849091\pi$
$102$	−1.06722	+	4.29437i	−0.105671	+	0.425206i
$103$	−9.46363	−	16.3915i	−0.932479	−	1.61510i	−0.779069	−	0.626938i	$-0.784308\pi$
$103$	−9.46363	−	16.3915i	−0.932479	−	1.61510i	−0.153410	−	0.988163i	$-0.549026\pi$
$104$	3.26119	−	3.63866i	0.319786	−	0.356800i
$105$	0.230501	−	2.52953i	0.0224946	−	0.246857i
$106$	−9.50706	+	2.73397i	−0.923408	+	0.265546i
$107$	−1.61203	+	6.01618i	−0.155841	+	0.581606i	0.843191	+	0.537614i	$0.180674\pi$
$107$	−1.61203	+	6.01618i	−0.155841	+	0.581606i	−0.999032	+	0.0439920i	$0.985992\pi$
$108$	−3.65744	−	3.40018i	−0.351937	−	0.327183i
$109$	−16.5222	+	4.42712i	−1.58254	+	0.424041i	−0.939712	−	0.341967i	$-0.888907\pi$
$109$	−16.5222	+	4.42712i	−1.58254	+	0.424041i	−0.642831	+	0.766008i	$0.722240\pi$
$110$	−11.5297	−	1.95581i	−1.09931	−	0.186479i
$111$	1.09688			0.104111
$112$	1.77216	+	10.4336i	0.167453	+	0.985880i
$113$		−	9.45041i		−	0.889020i	−0.895774	−	0.444510i	$-0.853378\pi$
$113$		−	9.45041i		−	0.889020i	0.895774	−	0.444510i	$-0.146622\pi$
$114$	−2.27598	+	0.0414666i	−0.213165	+	0.00388370i
$115$	−13.7360	+	1.03972i	−1.28089	+	0.0969547i
$116$	7.55803	+	7.02641i	0.701745	+	0.652386i
$117$	−1.25894	+	4.69844i	−0.116389	+	0.434371i
$118$	−0.0114912	−	0.0399593i	−0.00105785	−	0.00367855i
$119$	−8.00679	+	17.5407i	−0.733981	+	1.60795i
$120$	2.69191	+	0.356310i	0.245737	+	0.0325265i
$121$	−2.31742	+	1.33797i	−0.210675	+	0.121633i
$122$	−1.96175	+	7.89382i	−0.177608	+	0.714673i
$123$	−5.14428	+	1.37841i	−0.463844	+	0.124287i
$124$	0.214462	−	0.404835i	0.0192592	−	0.0363552i
$125$	−10.8944	+	2.51236i	−0.974425	+	0.224712i
$126$	−6.26787	−	8.46791i	−0.558386	−	0.754382i
$127$			1.37453i			0.121970i	0.998139	+	0.0609851i	$0.0194242\pi$
$127$			1.37453i			0.121970i	−0.998139	+	0.0609851i	$0.980576\pi$
$128$	−11.2218	+	1.43882i	−0.991880	+	0.127175i
$129$	2.35121	−	4.07241i	0.207012	−	0.358556i
$130$	−1.90177	−	5.12125i	−0.166796	−	0.449164i
$131$	1.64618	−	6.14363i	0.143827	−	0.536771i	−0.855977	−	0.517013i	$-0.827044\pi$
$131$	1.64618	−	6.14363i	0.143827	−	0.536771i	0.999805	−	0.0197581i	$-0.00628960\pi$
$132$	2.69039	−	1.68686i	0.234169	−	0.146823i
$133$	−9.78205	−	1.64315i	−0.848211	−	0.142479i
$134$	−3.65887	−	12.7233i	−0.316078	−	1.09913i
$135$	−5.26855	+	1.84798i	−0.453444	+	0.159049i
$136$	−18.3877	−	9.31599i	−1.57673	−	0.798839i
$137$	−8.79211	+	15.2284i	−0.751161	+	1.30105i	0.196100	+	0.980584i	$0.437172\pi$
$137$	−8.79211	+	15.2284i	−0.751161	+	1.30105i	−0.947260	+	0.320465i	$0.896161\pi$
$138$	2.59633	−	2.69269i	0.221014	−	0.229217i
$139$	−10.0746	+	10.0746i	−0.854517	+	0.854517i	−0.990686	−	0.136169i	$-0.956521\pi$
$139$	−10.0746	+	10.0746i	−0.854517	+	0.854517i	0.136169	+	0.990686i	$0.456521\pi$
$140$	11.2454	+	3.67972i	0.950412	+	0.310993i
$141$	−2.38280	−	2.38280i	−0.200668	−	0.200668i
$142$	−0.184491	−	10.1262i	−0.0154822	−	0.849770i
$143$	−5.53270	−	3.19431i	−0.462668	−	0.267121i
$144$	9.31788	−	6.32651i	0.776490	−	0.527209i
$145$	10.8874	−	3.81881i	0.904146	−	0.317135i
$146$	6.24995	−	11.2956i	0.517250	−	0.934827i
$147$	1.31415	+	2.70284i	0.108389	+	0.222927i
$148$	−1.14180	+	4.98037i	−0.0938552	+	0.409384i
$149$	−10.5114	−	2.81653i	−0.861130	−	0.230739i	−0.198882	−	0.980024i	$-0.563731\pi$
$149$	−10.5114	−	2.81653i	−0.861130	−	0.230739i	−0.662248	+	0.749284i	$0.730398\pi$
$150$	1.75427	−	2.47774i	0.143235	−	0.202307i
$151$	−9.54480	−	5.51070i	−0.776745	−	0.448454i	0.0585304	−	0.998286i	$-0.481359\pi$
$151$	−9.54480	−	5.51070i	−0.776745	−	0.448454i	−0.835276	+	0.549832i	$0.814692\pi$
$152$	2.18091	−	10.3773i	0.176895	−	0.841707i
$153$	20.5200			1.65894
$154$	12.8735	−	5.07319i	1.03737	−	0.408809i
$155$	−0.288854	−	0.422989i	−0.0232013	−	0.0339753i
$156$	1.31083	+	0.694415i	0.104951	+	0.0555977i
$157$	−1.91421	−	7.14392i	−0.152770	−	0.570146i	−0.999286	−	0.0377827i	$-0.987971\pi$
$157$	−1.91421	−	7.14392i	−0.152770	−	0.570146i	0.846516	−	0.532364i	$-0.178696\pi$
$158$	7.22117	+	11.9973i	0.574485	+	0.954452i
$159$	−1.50161	−	2.60086i	−0.119085	−	0.206262i
$160$	−4.41999	+	11.8517i	−0.349431	+	0.936962i
$161$	13.2752	−	9.45679i	1.04623	−	0.745299i
$162$	−5.04949	+	9.12596i	−0.396726	+	0.717003i
$163$	−8.62475	−	2.31100i	−0.675543	−	0.181011i	−0.0952924	−	0.995449i	$-0.530379\pi$
$163$	−8.62475	−	2.31100i	−0.675543	−	0.181011i	−0.580250	+	0.814438i	$0.697045\pi$
$164$	−0.903703	−	24.7925i	−0.0705673	−	1.93597i
$165$	−0.267968	−	3.54018i	−0.0208613	−	0.275602i
$166$	−9.99968	+	10.3708i	−0.776126	+	0.804932i
$167$	−9.84549			−0.761867			−0.380934	−	0.924602i	$-0.624397\pi$
$167$	−9.84549			−0.761867			−0.380934	+	0.924602i	$0.624397\pi$
$168$	−2.94426	+	1.28607i	−0.227155	+	0.0992227i
$169$			10.0156i			0.770431i
$170$	−18.7919	+	13.3411i	−1.44127	+	1.02321i
$171$	2.73212	+	10.1964i	0.208931	+	0.779740i
$172$	16.0433	+	14.9149i	1.22329	+	1.13725i
$173$	−2.98316	−	0.799334i	−0.226805	−	0.0607723i	0.143627	−	0.989632i	$-0.454124\pi$
$173$	−2.98316	−	0.799334i	−0.226805	−	0.0607723i	−0.370432	+	0.928860i	$0.620790\pi$
$174$	−1.51678	+	2.74128i	−0.114987	+	0.207816i
$175$	9.49638	−	9.20971i	0.717859	−	0.696189i
$176$	4.85865	+	13.9717i	0.366234	+	1.05316i
$177$	0.0109317	−	0.00631144i	0.000821679	−	0.000474397i
$178$	−2.77539	+	1.67051i	−0.208024	+	0.125210i
$179$	1.86083	−	0.498608i	0.139085	−	0.0372677i	−0.188605	−	0.982053i	$-0.560397\pi$
$179$	1.86083	−	0.498608i	0.139085	−	0.0372677i	0.327690	+	0.944785i	$0.393730\pi$
$180$	−1.40716	−	12.5132i	−0.104883	−	0.932677i
$181$	4.23756	−	4.23756i	0.314976	−	0.314976i	−0.531858	−	0.846834i	$-0.678506\pi$
$181$	4.23756	−	4.23756i	0.314976	−	0.314976i	0.846834	+	0.531858i	$0.178506\pi$
$182$	5.05927	+	4.02310i	0.375018	+	0.298212i
$183$	−2.46938			−0.182542
$184$	9.52354	+	14.5916i	0.702085	+	1.07571i
$185$	4.33284	+	3.72307i	0.318557	+	0.273725i
$186$	0.134978	+	0.0335444i	0.00989710	+	0.00245959i
$187$	−6.97543	+	26.0326i	−0.510094	+	1.90370i
$188$	13.2995	−	8.33874i	0.969967	−	0.608165i
$189$	4.20519	−	5.09490i	0.305882	−	0.370600i
$190$	−9.13125	−	7.56143i	−0.662450	−	0.548564i
$191$	5.07277	+	8.78629i	0.367053	+	0.635754i	0.989103	−	0.147223i	$-0.0470335\pi$
$191$	5.07277	+	8.78629i	0.367053	+	0.635754i	−0.622051	+	0.782977i	$0.713700\pi$
$192$	−1.24558	−	3.20092i	−0.0898920	−	0.231006i
$193$	17.4505	+	10.0751i	1.25612	+	0.725220i	0.972318	−	0.233663i	$-0.0750714\pi$
$193$	17.4505	+	10.0751i	1.25612	+	0.725220i	0.283800	+	0.958883i	$0.408405\pi$
$194$	0.182262	+	10.0038i	0.0130857	+	0.718233i
$195$	1.36962	−	0.935293i	0.0980802	−	0.0669777i
$196$	−13.6402	+	3.15335i	−0.974303	+	0.225239i
$197$	−9.90921	−	9.90921i	−0.706002	−	0.706002i	0.259690	−	0.965692i	$-0.416380\pi$
$197$	−9.90921	−	9.90921i	−0.706002	−	0.706002i	−0.965692	+	0.259690i	$0.916380\pi$
$198$	−10.6006	−	10.2212i	−0.753349	−	0.726389i
$199$	13.7036	+	7.91179i	0.971424	+	0.560852i	0.899670	−	0.436570i	$-0.143807\pi$
$199$	13.7036	+	7.91179i	0.971424	+	0.560852i	0.0717540	+	0.997422i	$0.477140\pi$
$200$	9.42410	+	10.5445i	0.666384	+	0.745608i
$201$	3.48073	−	2.00960i	0.245512	−	0.141746i
$202$	−1.65529	−	5.75608i	−0.116466	−	0.404997i
$203$	−8.68994	+	10.5285i	−0.609914	+	0.738958i
$204$	1.39840	−	6.09965i	0.0979077	−	0.427061i
$205$	−24.9995	−	12.0160i	−1.74604	−	0.839236i
$206$	13.8036	+	22.9334i	0.961745	+	1.59785i
$207$	−15.0220	−	8.67295i	−1.04410	−	0.602812i
$208$	−4.51752	+	5.22900i	−0.313234	+	0.362566i
$209$	−13.8644			−0.959021
$210$	−0.260759	+	3.58264i	−0.0179941	+	0.247226i
$211$	2.35491	+	2.35491i	0.162119	+	0.162119i	0.783505	−	0.621386i	$-0.213430\pi$
$211$	2.35491	+	2.35491i	0.162119	+	0.162119i	−0.621386	+	0.783505i	$0.713430\pi$
$212$	13.3724	−	4.11069i	0.918417	−	0.282323i
$213$	2.96995	−	0.795795i	0.203497	−	0.0545270i
$214$	2.12439	−	8.54828i	0.145220	−	0.584348i
$215$	23.1104	−	8.10614i	1.57612	−	0.552834i
$216$	5.25913	+	4.71356i	0.357839	+	0.320717i
$217$	0.551329	+	0.251665i	0.0374266	+	0.0170841i
$218$	23.2480	−	6.68549i	1.57456	−	0.452799i
$219$	3.78561	+	1.01435i	0.255807	+	0.0685434i
$220$	16.3531	+	2.46845i	1.10253	+	0.166423i
$221$	−12.1610	+	3.25852i	−0.818035	+	0.219192i
$222$	−1.55096	+	0.0282573i	−0.104093	+	0.00189651i
$223$		−	12.7596i		−	0.854448i	−0.904146	−	0.427224i	$-0.859492\pi$
$223$		−	12.7596i		−	0.854448i	0.904146	−	0.427224i	$-0.140508\pi$
$224$	−2.77458	−	14.7072i	−0.185385	−	0.982666i
$225$	−13.1128	−	5.12374i	−0.874190	−	0.341583i
$226$	0.243458	+	13.3627i	0.0161946	+	0.888872i
$227$	−2.27239	−	8.48068i	−0.150824	−	0.562883i	−0.999427	−	0.0338524i	$-0.989222\pi$
$227$	−2.27239	−	8.48068i	−0.150824	−	0.562883i	0.848603	−	0.529030i	$-0.177444\pi$
$228$	3.21712	−	0.117266i	0.213059	−	0.00776612i
$229$	8.80005	+	2.35797i	0.581523	+	0.155819i	0.537576	−	0.843215i	$-0.319340\pi$
$229$	8.80005	+	2.35797i	0.581523	+	0.155819i	0.0439471	+	0.999034i	$0.486007\pi$
$230$	19.3956	−	1.82401i	1.27891	−	0.120272i
$231$	2.43730	+	3.42142i	0.160362	+	0.225113i
$232$	−10.8679	−	9.74049i	−0.713513	−	0.639495i
$233$	2.79443	+	4.84010i	0.183069	+	0.317085i	0.942924	−	0.333007i	$-0.108063\pi$
$233$	2.79443	+	4.84010i	0.183069	+	0.317085i	−0.759855	+	0.650093i	$0.774730\pi$
$234$	1.65908	−	6.67592i	0.108457	−	0.436419i
$235$	−1.32466	−	17.5003i	−0.0864110	−	1.14159i
$236$	0.0172777	+	0.0562055i	0.00112468	+	0.00365867i
$237$	−3.00600	+	3.00600i	−0.195260	+	0.195260i
$238$	10.8696	−	25.0084i	0.704569	−	1.62105i
$239$	−2.27521			−0.147171			−0.0735857	−	0.997289i	$-0.523444\pi$
$239$	−2.27521			−0.147171			−0.0735857	+	0.997289i	$0.523444\pi$
$240$	−3.81548	−	0.434467i	−0.246288	−	0.0280447i
$241$	−1.69647	+	2.93837i	−0.109279	+	0.189277i	−0.915478	−	0.402367i	$-0.868188\pi$
$241$	−1.69647	+	2.93837i	−0.109279	+	0.189277i	0.806199	+	0.591644i	$0.201521\pi$
$242$	3.24232	−	1.95156i	0.208424	−	0.125451i
$243$	−10.2940	−	2.75826i	−0.660357	−	0.176942i
$244$	2.57051	−	11.2122i	0.164560	−	0.717789i
$245$	−3.98302	+	15.1372i	−0.254466	+	0.967082i
$246$	7.23840	−	2.08156i	0.461503	−	0.132716i
$247$	−3.23833	−	5.60896i	−0.206050	−	0.356889i
$248$	−0.292815	+	0.577953i	−0.0185938	+	0.0367000i
$249$	−3.78771	−	2.18683i	−0.240036	−	0.138585i
$250$	15.3397	−	3.83308i	0.970170	−	0.242425i
$251$	−4.50204	+	4.50204i	−0.284166	+	0.284166i	−0.834768	−	0.550602i	$-0.814398\pi$
$251$	−4.50204	+	4.50204i	−0.284166	+	0.284166i	0.550602	+	0.834768i	$0.314398\pi$
$252$	9.08078	+	11.8120i	0.572035	+	0.744085i
$253$	16.1094	−	16.1094i	1.01279	−	1.01279i
$254$	−0.0354103	−	1.94356i	−0.00222184	−	0.121950i
$255$	−5.30659	−	4.55978i	−0.332312	−	0.285544i
$256$	15.8304	−	2.32356i	0.989399	−	0.145223i
$257$	−1.76163	+	1.01708i	−0.109888	+	0.0634437i	−0.553937	−	0.832559i	$-0.686875\pi$
$257$	−1.76163	+	1.01708i	−0.109888	+	0.0634437i	0.444049	+	0.896003i	$0.353542\pi$
$258$	−3.21964	+	5.81887i	−0.200446	+	0.362267i
$259$	−6.66595	−	1.11972i	−0.414202	−	0.0695759i
$260$	2.82100	+	7.19235i	0.174951	+	0.446051i
$261$	14.0332	+	3.76020i	0.868636	+	0.232750i
$262$	−2.16939	+	8.72937i	−0.134026	+	0.539302i
$263$	0.199613	−	0.345740i	0.0123087	−	0.0213192i	−0.859805	−	0.510622i	$-0.829415\pi$
$263$	0.199613	−	0.345740i	0.0123087	−	0.0213192i	0.872114	+	0.489303i	$0.162749\pi$
$264$	−3.76070	+	2.45450i	−0.231455	+	0.151064i
$265$	2.89636	−	15.3707i	0.177922	−	0.944214i
$266$	13.8739	+	2.07138i	0.850666	+	0.127004i
$267$	−0.695392	−	0.695392i	−0.0425573	−	0.0425573i
$268$	5.50133	+	17.8962i	0.336047	+	1.09319i
$269$	20.7282	−	5.55411i	1.26382	−	0.338640i	0.436161	−	0.899869i	$-0.356338\pi$
$269$	20.7282	−	5.55411i	1.26382	−	0.338640i	0.827661	+	0.561228i	$0.189671\pi$
$270$	7.40201	−	2.74873i	0.450472	−	0.167282i
$271$	−3.45409	−	5.98266i	−0.209821	−	0.363421i	0.741837	−	0.670580i	$-0.233955\pi$
$271$	−3.45409	−	5.98266i	−0.209821	−	0.363421i	−0.951658	+	0.307159i	$0.900621\pi$
$272$	26.2398	+	12.6989i	1.59102	+	0.769985i
$273$	−0.814878	+	1.78517i	−0.0493187	+	0.108044i
$274$	12.0396	−	21.7591i	0.727336	−	1.31452i
$275$	10.9577	−	14.8938i	0.660775	−	0.898133i
$276$	−3.60179	+	3.87430i	−0.216802	+	0.233205i
$277$	−9.82783	+	2.63336i	−0.590497	+	0.158223i	−0.541680	−	0.840585i	$-0.682212\pi$
$277$	−9.82783	+	2.63336i	−0.590497	+	0.158223i	−0.0488168	+	0.998808i	$0.515545\pi$
$278$	13.9857	−	14.5048i	0.838809	−	0.869941i
$279$		−	0.644973i		−	0.0386136i
$280$	−15.9956	−	4.91335i	−0.955920	−	0.293629i
$281$			4.76958i			0.284529i	0.989829	+	0.142265i	$0.0454384\pi$
$281$			4.76958i			0.284529i	−0.989829	+	0.142265i	$0.954562\pi$
$282$	3.43062	+	3.30785i	0.204290	+	0.196979i
$283$	−13.9862	+	3.74759i	−0.831394	+	0.222771i	−0.649322	−	0.760514i	$-0.724947\pi$
$283$	−13.9862	+	3.74759i	−0.831394	+	0.222771i	−0.182072	+	0.983285i	$0.558280\pi$
$284$	0.521734	+	14.3135i	0.0309592	+	0.849347i
$285$	1.55922	−	3.24397i	0.0923601	−	0.192156i
$286$	7.90542	+	4.37415i	0.467457	+	0.258649i
$287$	32.6701	−	3.12546i	1.92845	−	0.184490i
$288$	−13.0123	+	9.18559i	−0.766758	+	0.541266i
$289$	18.0560	+	31.2739i	1.06212	+	1.83964i
$290$	−15.2961	+	5.68019i	−0.898219	+	0.333553i
$291$	−2.93406	+	0.786179i	−0.171998	+	0.0460866i
$292$	−8.54631	+	16.1327i	−0.500135	+	0.944094i
$293$	−8.77215	−	8.77215i	−0.512474	−	0.512474i	0.402809	−	0.915284i	$-0.368034\pi$
$293$	−8.77215	−	8.77215i	−0.512474	−	0.512474i	−0.915284	+	0.402809i	$0.868034\pi$
$294$	−1.92780	−	3.78791i	−0.112432	−	0.220915i
$295$	0.0646048	+	0.0121737i	0.00376144	+	0.000708782i
$296$	1.48617	−	7.07156i	0.0863821	−	0.411026i
$297$	4.61689	−	7.99670i	0.267899	−	0.464015i
$298$	14.9355	+	3.71172i	0.865190	+	0.215014i
$299$	10.2799	+	2.75448i	0.594501	+	0.159296i
$300$	−2.41667	+	3.54867i	−0.139526	+	0.204882i
$301$	−18.4460	+	22.3487i	−1.06321	+	1.28816i
$302$	13.6381	+	7.54612i	0.784785	+	0.434230i
$303$	1.57470	−	0.909155i	0.0904643	−	0.0522296i
$304$	−2.81642	+	14.7294i	−0.161533	+	0.844790i
$305$	−9.75446	−	8.38168i	−0.558539	−	0.479933i
$306$	−29.0148	+	0.528629i	−1.65867	+	0.0302197i
$307$	7.23548	−	7.23548i	0.412951	−	0.412951i	−0.469814	−	0.882765i	$-0.655679\pi$
$307$	7.23548	−	7.23548i	0.412951	−	0.412951i	0.882765	+	0.469814i	$0.155679\pi$
$308$	−18.0721	+	7.50502i	−1.02975	+	0.427638i
$309$	−5.74612	+	5.74612i	−0.326885	+	0.326885i
$310$	0.419330	+	0.590656i	0.0238163	+	0.0335470i
$311$	−28.0027	−	16.1673i	−1.58788	−	0.916766i	−0.993655	−	0.112470i	$-0.964124\pi$
$311$	−28.0027	−	16.1673i	−1.58788	−	0.916766i	−0.594230	−	0.804295i	$-0.702543\pi$
$312$	−1.87138	−	0.948120i	−0.105946	−	0.0536767i
$313$	10.4849	+	18.1603i	0.592640	+	1.02648i	0.993875	+	0.110508i	$0.0352477\pi$
$313$	10.4849	+	18.1603i	0.592640	+	1.02648i	−0.401235	+	0.915975i	$0.631419\pi$
$314$	2.89069	+	10.0520i	0.163131	+	0.567269i
$315$	16.4150	−	2.83340i	0.924879	−	0.159644i
$316$	−10.5196	−	16.7779i	−0.591777	−	0.943828i
$317$	−30.9219	−	8.28549i	−1.73675	−	0.465360i	−0.755026	−	0.655695i	$-0.772376\pi$
$317$	−30.9219	−	8.28549i	−1.73675	−	0.465360i	−0.981719	+	0.190335i	$0.939043\pi$
$318$	2.19025	+	3.63888i	0.122823	+	0.204058i
$319$	−9.54073	+	16.5250i	−0.534178	+	0.925224i
$320$	5.94445	−	16.8720i	0.332305	−	0.943172i
$321$	2.67411			0.149254
$322$	−18.5272	+	13.7137i	−1.03248	+	0.764234i
$323$	−19.3199	+	19.3199i	−1.07499	+	1.07499i
$324$	6.90478	−	13.0340i	0.383599	−	0.724111i
$325$	8.58483	+	0.954249i	0.476201	+	0.0529322i
$326$	12.2548	+	3.04551i	0.678728	+	0.168675i
$327$	3.67195	+	6.36001i	0.203059	+	0.351709i
$328$	1.91651	+	35.0328i	0.105822	+	1.93436i
$329$	12.0484	+	16.9132i	0.664249	+	0.932457i
$330$	0.470102	+	4.99883i	0.0258782	+	0.275177i
$331$	18.9540	+	5.07871i	1.04181	+	0.279151i	0.738861	−	0.673857i	$-0.235364\pi$
$331$	18.9540	+	5.07871i	1.04181	+	0.279151i	0.302944	+	0.953008i	$0.402030\pi$
$332$	13.8722	−	14.9217i	0.761334	−	0.818936i
$333$	1.86180	+	6.94833i	0.102026	+	0.380766i
$334$	13.9213	−	0.253636i	0.761741	−	0.0138783i
$335$	20.5706	+	3.87620i	1.12389	+	0.211779i
$336$	4.12999	−	1.89433i	0.225310	−	0.103344i
$337$		−	14.5042i		−	0.790096i	−0.918660	−	0.395048i	$-0.870728\pi$
$337$		−	14.5042i		−	0.790096i	0.918660	−	0.395048i	$-0.129272\pi$
$338$	−0.258018	−	14.1619i	−0.0140343	−	0.770303i
$339$	−3.91919	+	1.05014i	−0.212861	+	0.0570360i
$340$	26.2276	−	19.3481i	1.42239	−	1.04930i
$341$	0.818244	+	0.219248i	0.0443104	+	0.0118729i
$342$	−4.12584	−	14.3471i	−0.223100	−	0.775805i
$343$	−5.22721	−	17.7673i	−0.282243	−	0.959343i
$344$	−23.0691	−	20.6760i	−1.24380	−	1.11478i
$345$	1.95755	+	5.58094i	0.105391	+	0.300467i
$346$	4.23871	+	1.05339i	0.227875	+	0.0566306i
$347$	2.87849	−	0.771288i	0.154525	−	0.0414049i	−0.180727	−	0.983533i	$-0.557845\pi$
$347$	2.87849	−	0.771288i	0.154525	−	0.0414049i	0.335252	+	0.942128i	$0.391178\pi$
$348$	2.07407	−	3.91518i	0.111182	−	0.209876i
$349$	11.9063	+	11.9063i	0.637331	+	0.637331i	0.949896	−	0.312566i	$-0.101188\pi$
$349$	11.9063	+	11.9063i	0.637331	+	0.637331i	−0.312566	+	0.949896i	$0.601188\pi$
$350$	−13.1904	+	13.2670i	−0.705058	+	0.709150i
$351$	4.31350			0.230238
$352$	−7.22996	−	19.6305i	−0.385358	−	1.04631i
$353$	1.64693	+	0.950854i	0.0876571	+	0.0506089i	0.543188	−	0.839611i	$-0.317217\pi$
$353$	1.64693	+	0.950854i	0.0876571	+	0.0506089i	−0.455531	+	0.890220i	$0.650550\pi$
$354$	−0.0152946	+	0.00920586i	−0.000812901	+	0.000489286i
$355$	14.4329	+	6.93721i	0.766020	+	0.368189i
$356$	3.88130	−	2.43356i	0.205709	−	0.128978i
$357$	8.16404	+	1.37136i	0.432087	+	0.0725801i
$358$	−2.61833	+	0.752960i	−0.138383	+	0.0397952i
$359$	−9.28373	+	5.35996i	−0.489976	+	0.282888i	−0.724565	−	0.689207i	$-0.757959\pi$
$359$	−9.28373	+	5.35996i	−0.489976	+	0.282888i	0.234588	+	0.972095i	$0.424626\pi$
$360$	2.31205	+	17.6571i	0.121856	+	0.930611i
$361$	4.28207	+	2.47225i	0.225372	+	0.130119i
$362$	−5.88266	+	6.10099i	−0.309186	+	0.320661i
$363$	0.812385	+	0.812385i	0.0426392	+	0.0426392i
$364$	−7.25734	−	5.55825i	−0.380388	−	0.291331i
$365$	11.5108	+	16.8561i	0.602505	+	0.882290i
$366$	3.49165	−	0.0636152i	0.182511	−	0.00332522i
$367$	0.966905	+	0.558243i	0.0504720	+	0.0291400i	0.525024	−	0.851088i	$-0.324056\pi$
$367$	0.966905	+	0.558243i	0.0504720	+	0.0291400i	−0.474552	+	0.880228i	$0.657390\pi$
$368$	−13.8420	−	20.3869i	−0.721563	−	1.06274i
$369$	−17.4635	−	30.2476i	−0.909112	−	1.57463i
$370$	−6.22246	−	5.15271i	−0.323490	−	0.267877i
$371$	6.47058	+	17.3389i	0.335936	+	0.900191i
$372$	−0.191721	−	0.0439538i	−0.00994026	−	0.00227890i
$373$	−3.61422	+	13.4884i	−0.187137	+	0.698405i	0.807026	+	0.590516i	$0.201076\pi$
$373$	−3.61422	+	13.4884i	−0.187137	+	0.698405i	−0.994163	+	0.107889i	$0.965591\pi$
$374$	9.19246	−	36.9893i	0.475331	−	1.91267i
$375$	2.25251	+	4.23885i	0.116319	+	0.218893i
$376$	−18.5904	+	12.1334i	−0.958728	+	0.625734i
$377$	−8.91377			−0.459083
$378$	−5.81479	+	7.31242i	−0.299081	+	0.376110i
$379$	−16.6704	+	16.6704i	−0.856299	+	0.856299i	−0.990900	−	0.134601i	$-0.957025\pi$
$379$	−16.6704	+	16.6704i	−0.856299	+	0.856299i	0.134601	+	0.990900i	$0.457025\pi$
$380$	13.1062	+	10.4565i	0.672333	+	0.536405i
$381$	0.570035	−	0.152740i	0.0292038	−	0.00782513i
$382$	−7.39914	−	12.2930i	−0.378573	−	0.628962i
$383$	−15.3198	+	8.84486i	−0.782803	+	0.451951i	−0.837423	−	0.546556i	$-0.815939\pi$
$383$	−15.3198	+	8.84486i	−0.782803	+	0.451951i	0.0546199	+	0.998507i	$0.482605\pi$
$384$	1.84369	+	4.49394i	0.0940852	+	0.229330i
$385$	−1.98541	+	21.7880i	−0.101186	+	1.11042i
$386$	−24.9343	−	13.7964i	−1.26912	−	0.702218i
$387$	29.7882	+	7.98172i	1.51422	+	0.405733i
$388$	−0.515430	−	14.1405i	−0.0261670	−	0.717875i
$389$	−1.82514	−	6.81150i	−0.0925381	−	0.345357i	0.904097	−	0.427328i	$-0.140545\pi$
$389$	−1.82514	−	6.81150i	−0.0925381	−	0.345357i	−0.996635	+	0.0819713i	$0.973878\pi$
$390$	−1.91251	+	1.35777i	−0.0968439	+	0.0687532i
$391$		−	44.8964i		−	2.27051i
$392$	19.2058	−	4.81017i	0.970039	−	0.242950i
$393$	−2.73076			−0.137749
$394$	14.2667	+	13.7561i	0.718746	+	0.693024i
$395$	−22.0773	+	1.67110i	−1.11083	+	0.0840824i
$396$	15.2523	+	14.1795i	0.766456	+	0.712546i
$397$	11.4176	+	3.05934i	0.573033	+	0.153544i	0.533687	−	0.845682i	$-0.320806\pi$
$397$	11.4176	+	3.05934i	0.573033	+	0.153544i	0.0393457	+	0.999226i	$0.487473\pi$
$398$	−19.5805	−	10.8341i	−0.981480	−	0.543063i
$399$	0.405564	+	4.23931i	0.0203036	+	0.212231i
$400$	−13.5971	−	14.6669i	−0.679856	−	0.733346i
$401$	−14.1657	−	24.5356i	−0.707399	−	1.22525i	−0.965819	−	0.259218i	$-0.916535\pi$
$401$	−14.1657	−	24.5356i	−0.707399	−	1.22525i	0.258420	−	0.966033i	$-0.416798\pi$
$402$	−4.86991	+	2.93121i	−0.242889	+	0.146195i
$403$	0.102420	+	0.382237i	0.00510191	+	0.0190406i
$404$	2.48883	+	8.09634i	0.123824	+	0.402808i
$405$	−9.29989	−	13.6185i	−0.462115	−	0.676709i
$406$	12.0162	−	15.1110i	0.596352	−	0.749945i
$407$	−9.44786			−0.468313
$408$	−1.82017	+	8.66080i	−0.0901120	+	0.428773i
$409$	−3.26738	−	1.88643i	−0.161562	−	0.0932777i	0.417039	−	0.908889i	$-0.363068\pi$
$409$	−3.26738	−	1.88643i	−0.161562	−	0.0932777i	−0.578601	+	0.815611i	$0.696401\pi$
$410$	35.6583	+	16.3464i	1.76104	+	0.807291i
$411$	7.29237	+	1.95399i	0.359706	+	0.0963830i
$412$	−20.1089	−	32.0718i	−0.990692	−	1.58006i
$413$	−0.0728774	+	0.0271966i	−0.00358606	+	0.00133826i
$414$	21.4642	+	11.8764i	1.05491	+	0.583692i
$415$	−7.53944	−	21.4948i	−0.370096	−	1.05514i
$416$	6.25297	−	7.51007i	0.306577	−	0.368211i
$417$	5.29756	+	3.05855i	0.259422	+	0.149778i
$418$	19.6040	−	0.357170i	0.958862	−	0.0174698i
$419$	−17.2752	−	17.2752i	−0.843947	−	0.843947i	0.145423	−	0.989370i	$-0.453546\pi$
$419$	−17.2752	−	17.2752i	−0.843947	−	0.843947i	−0.989370	+	0.145423i	$0.953546\pi$
$420$	0.276412	−	5.07250i	0.0134875	−	0.247513i
$421$	−25.9624	+	25.9624i	−1.26533	+	1.26533i	−0.316854	+	0.948474i	$0.602627\pi$
$421$	−25.9624	+	25.9624i	−1.26533	+	1.26533i	−0.948474	+	0.316854i	$0.897373\pi$
$422$	−3.39046	−	3.26913i	−0.165045	−	0.159139i
$423$	11.0497	−	19.1387i	0.537257	−	0.930556i
$424$	−18.8023	+	6.15692i	−0.913122	+	0.299007i
$425$	−5.48495	−	36.0238i	−0.266059	−	1.74741i
$426$	−4.17894	+	1.20175i	−0.202470	+	0.0582249i
$427$	15.0069	+	2.52080i	0.726237	+	0.121990i
$428$	−2.78363	+	12.1418i	−0.134552	+	0.586897i
$429$	−0.709913	+	2.64943i	−0.0342749	+	0.127916i
$430$	−32.4688	+	12.0573i	−1.56579	+	0.581453i
$431$	−7.29809	+	12.6407i	−0.351536	+	0.608879i	−0.986519	−	0.163648i	$-0.947674\pi$
$431$	−7.29809	+	12.6407i	−0.351536	+	0.608879i	0.634982	+	0.772527i	$0.281007\pi$
$432$	−7.55773	−	6.52940i	−0.363622	−	0.314146i
$433$		−	8.93115i		−	0.429203i	−0.976702	−	0.214602i	$-0.931155\pi$
$433$		−	8.93115i		−	0.429203i	0.976702	−	0.214602i	$-0.0688454\pi$
$434$	−0.786050	−	0.341646i	−0.0377316	−	0.0163995i
$435$	−2.79352	−	4.09076i	−0.133939	−	0.196137i
$436$	−32.7000	+	10.0521i	−1.56605	+	0.481406i
$437$	22.3091	−	5.97771i	1.06719	−	0.285953i
$438$	−5.37890	−	1.33675i	−0.257014	−	0.0638722i
$439$	13.7297	−	7.92685i	0.655283	−	0.378328i	−0.135194	−	0.990819i	$-0.543166\pi$
$439$	13.7297	−	7.92685i	0.655283	−	0.378328i	0.790477	+	0.612491i	$0.209833\pi$
$440$	−23.1866	−	3.06906i	−1.10538	−	0.146312i
$441$	−14.8910	+	12.9124i	−0.709095	+	0.614875i
$442$	17.1114	−	4.92077i	0.813907	−	0.234057i
$443$	7.79868	−	29.1051i	0.370526	−	1.38282i	−0.489246	−	0.872146i	$-0.662728\pi$
$443$	7.79868	−	29.1051i	0.370526	−	1.38282i	0.859772	−	0.510678i	$-0.170605\pi$
$444$	2.19229	−	0.0799104i	0.104042	−	0.00379238i
$445$	−0.386585	−	5.10725i	−0.0183259	−	0.242107i
$446$	0.328709	+	18.0418i	0.0155648	+	0.854306i
$447$			4.67219i			0.220987i
$448$	4.30208	+	20.7242i	0.203254	+	0.979126i
$449$	4.44796			0.209912			0.104956	−	0.994477i	$-0.466530\pi$
$449$	4.44796			0.209912			0.104956	+	0.994477i	$0.466530\pi$
$450$	18.6733	+	6.90706i	0.880267	+	0.325602i
$451$	44.3100	−	11.8728i	2.08647	−	0.559069i
$452$	−0.688489	−	18.8883i	−0.0323838	−	0.888430i
$453$	−1.22471	+	4.57069i	−0.0575421	+	0.214750i
$454$	3.43159	+	11.9330i	0.161053	+	0.560042i
$455$	−9.27823	+	4.28584i	−0.434970	+	0.200923i
$456$	−4.54591	+	0.248690i	−0.212882	+	0.0116460i
$457$	−3.48457	−	6.03545i	−0.163001	−	0.282327i	0.772942	−	0.634476i	$-0.218784\pi$
$457$	−3.48457	−	6.03545i	−0.163001	−	0.282327i	−0.935944	+	0.352150i	$0.885451\pi$
$458$	−12.5038	−	3.10741i	−0.584265	−	0.145200i
$459$	−4.70971	−	17.5769i	−0.219830	−	0.820418i
$460$	−27.3780	+	3.07877i	−1.27651	+	0.143549i
$461$	11.3888	+	11.3888i	0.530429	+	0.530429i	0.920700	−	0.390271i	$-0.127619\pi$
$461$	11.3888	+	11.3888i	0.530429	+	0.530429i	−0.390271	+	0.920700i	$0.627619\pi$
$462$	−3.53443	−	4.77502i	−0.164436	−	0.222154i
$463$			24.8754i			1.15606i	0.816016	+	0.578029i	$0.196178\pi$
$463$			24.8754i			1.15606i	−0.816016	+	0.578029i	$0.803822\pi$
$464$	15.6179	+	13.4929i	0.725043	+	0.626391i
$465$	−0.143320	+	0.166794i	−0.00664633	+	0.00773489i
$466$	−4.07596	−	6.77181i	−0.188815	−	0.313698i
$467$	−24.9354	−	6.68143i	−1.15387	−	0.309180i	−0.369357	−	0.929287i	$-0.620422\pi$
$467$	−24.9354	−	6.68143i	−1.15387	−	0.309180i	−0.784516	+	0.620108i	$0.787089\pi$
$468$	−2.17392	+	9.48235i	−0.100489	+	0.438322i
$469$	−23.2046	+	8.65957i	−1.07149	+	0.399862i
$470$	2.32387	+	24.7109i	0.107192	+	1.13983i
$471$	−2.74995	+	1.58769i	−0.126711	+	0.0731567i
$472$	−0.0258783	−	0.0790283i	−0.00119114	−	0.00363757i
$473$	−20.2520	+	35.0774i	−0.931187	+	1.61286i
$474$	4.17298	−	4.32785i	0.191671	−	0.198785i
$475$	17.1700	−	7.52185i	0.787814	−	0.345126i
$476$	−14.7251	+	35.6414i	−0.674922	+	1.63362i
$477$	13.9268	−	13.9268i	0.637664	−	0.637664i
$478$	3.21710	−	0.0586132i	0.147147	−	0.00268091i
$479$	13.2375	−	22.9280i	0.604835	−	1.04761i	−0.387242	−	0.921978i	$-0.626572\pi$
$479$	13.2375	−	22.9280i	0.604835	−	1.04761i	0.992078	−	0.125627i	$-0.0400944\pi$
$480$	5.40620	+	0.516034i	0.246758	+	0.0235536i
$481$	−2.20675	−	3.82221i	−0.100619	−	0.174278i
$482$	2.32308	−	4.19850i	0.105813	−	0.191236i
$483$	−5.39700	−	4.45453i	−0.245572	−	0.202688i
$484$	−4.53430	+	2.84299i	−0.206104	+	0.129227i
$485$	−14.2585	−	6.85338i	−0.647446	−	0.311196i
$486$	14.6265	+	3.63493i	0.663471	+	0.164884i
$487$	3.08470	−	5.34285i	0.139781	−	0.242108i	−0.787633	−	0.616145i	$-0.788693\pi$
$487$	3.08470	−	5.34285i	0.139781	−	0.242108i	0.927414	+	0.374037i	$0.122027\pi$
$488$	−3.34580	+	15.9201i	−0.151457	+	0.720668i
$489$			3.83358i			0.173361i
$490$	5.24194	−	21.5063i	0.236807	−	0.971557i
$491$	17.1827	−	17.1827i	0.775446	−	0.775446i	−0.203607	−	0.979053i	$-0.565266\pi$
$491$	17.1827	−	17.1827i	0.775446	−	0.775446i	0.979053	+	0.203607i	$0.0652663\pi$
$492$	−10.1813	+	3.12976i	−0.459009	+	0.141100i
$493$	9.73252	+	36.3223i	0.438331	+	1.63587i
$494$	4.72343	+	7.84752i	0.212517	+	0.353077i
$495$	21.9710	−	7.70646i	0.987521	−	0.346380i
$496$	0.399145	−	0.824756i	0.0179222	−	0.0370326i
$497$	−18.8614	+	1.80442i	−0.846049	+	0.0809393i
$498$	5.41207	+	2.99456i	0.242521	+	0.134189i
$499$	0.312461	−	1.16612i	0.0139877	−	0.0522027i	−0.958579	−	0.284826i	$-0.908064\pi$
$499$	0.312461	−	1.16612i	0.0139877	−	0.0522027i	0.972567	+	0.232623i	$0.0747309\pi$
$500$	−21.5913	+	5.81507i	−0.965593	+	0.260058i
$501$	1.09405	+	4.08304i	0.0488784	+	0.182417i
$502$	6.24981	−	6.48177i	0.278942	−	0.289295i
$503$	−17.3083			−0.771739			−0.385869	−	0.922553i	$-0.626098\pi$
$503$	−17.3083			−0.771739			−0.385869	+	0.922553i	$0.626098\pi$
$504$	−13.1443	−	16.4680i	−0.585495	−	0.733541i
$505$	9.30624	+	1.75361i	0.414122	+	0.0780347i
$506$	−22.3633	+	23.1933i	−0.994172	+	1.03107i
$507$	4.15358	−	1.11295i	0.184467	−	0.0494278i
$508$	0.100139	+	2.74725i	0.00444294	+	0.121889i
$509$	1.53053	−	5.71201i	0.0678395	−	0.253181i	−0.923675	−	0.383177i	$-0.874830\pi$
$509$	1.53053	−	5.71201i	0.0678395	−	0.253181i	0.991514	+	0.129996i	$0.0414966\pi$
$510$	7.62088	+	6.31072i	0.337458	+	0.279443i
$511$	−21.9705	−	10.0289i	−0.971917	−	0.443651i
$512$	−22.3240	+	3.69328i	−0.986589	+	0.163222i
$513$	8.10691	−	4.68052i	0.357929	−	0.206650i
$514$	2.46471	−	1.48351i	0.108714	−	0.0654349i
$515$	−42.2019	+	3.19440i	−1.85964	+	0.140762i
$516$	4.40261	−	8.31071i	0.193814	−	0.365858i
$517$	20.5241	+	20.5241i	0.902649	+	0.902649i
$518$	9.45436	+	1.41153i	0.415401	+	0.0620192i
$519$			1.32597i			0.0582037i
$520$	−4.17412	−	10.0972i	−0.183047	−	0.442790i
$521$	1.77039	+	1.02213i	0.0775621	+	0.0447805i	0.538279	−	0.842766i	$-0.319074\pi$
$521$	1.77039	+	1.02213i	0.0775621	+	0.0447805i	−0.460717	+	0.887547i	$0.652408\pi$
$522$	−19.9396	−	4.95532i	−0.872732	−	0.216888i
$523$	1.63758	−	6.11153i	0.0716063	−	0.267238i	−0.920836	−	0.389950i	$-0.872492\pi$
$523$	1.63758	−	6.11153i	0.0716063	−	0.267238i	0.992442	+	0.122712i	$0.0391590\pi$
$524$	2.84260	−	12.3990i	0.124179	−	0.541654i
$525$	−4.87462	−	2.91486i	−0.212746	−	0.127215i
$526$	−0.273342	+	0.494011i	−0.0119183	+	0.0215399i
$527$	1.44573	−	0.834693i	0.0629770	−	0.0363598i
$528$	5.25432	−	3.56749i	0.228665	−	0.155255i
$529$	−7.47586	+	12.9486i	−0.325037	+	0.562981i
$530$	−3.69942	+	21.8085i	−0.160693	+	0.947299i
$531$	0.0585359	+	0.0585359i	0.00254024	+	0.00254024i
$532$	−19.6708	−	2.57147i	−0.852838	−	0.111487i
$533$	15.1528	+	15.1528i	0.656340	+	0.656340i
$534$	1.00118	+	0.965355i	0.0433254	+	0.0417750i
$535$	10.5632	+	9.07659i	0.456686	+	0.392415i
$536$	−8.23981	−	25.1631i	−0.355905	−	1.08688i
$537$	−0.413557	−	0.716302i	−0.0178463	−	0.0309107i
$538$	−29.1662	+	8.38739i	−1.25744	+	0.361606i
$539$	−11.3193	−	23.2808i	−0.487557	−	1.00277i
$540$	−10.3955	+	4.07733i	−0.447350	+	0.175460i
$541$	5.87223	−	21.9155i	0.252467	−	0.942219i	−0.717015	−	0.697057i	$-0.754492\pi$
$541$	5.87223	−	21.9155i	0.252467	−	0.942219i	0.969482	−	0.245162i	$-0.0788410\pi$
$542$	5.03814	+	8.37037i	0.216406	+	0.359538i
$543$	−2.22825	−	1.28648i	−0.0956234	−	0.0552082i
$544$	−37.4297	−	17.2800i	−1.60479	−	0.740874i
$545$	−7.08260	+	37.5866i	−0.303385	+	1.61003i
$546$	1.10623	−	2.54519i	0.0473424	−	0.108924i
$547$	0.414111	−	0.414111i	0.0177061	−	0.0177061i	−0.698198	−	0.715904i	$-0.746015\pi$
$547$	0.414111	−	0.414111i	0.0177061	−	0.0177061i	0.715904	+	0.698198i	$0.246015\pi$
$548$	−16.4631	+	31.0771i	−0.703270	+	1.32755i
$549$	−4.19144	−	15.6427i	−0.178886	−	0.667612i
$550$	−15.1103	+	21.3419i	−0.644305	+	0.910021i
$551$	−16.7528	+	9.67222i	−0.713692	+	0.412050i
$552$	4.99305	−	5.57096i	0.212518	−	0.237116i
$553$	21.3367	−	15.1995i	0.907329	−	0.646348i
$554$	13.8285	−	3.97670i	0.587517	−	0.168954i
$555$	1.06252	−	2.21059i	0.0451017	−	0.0938344i
$556$	−19.4019	+	20.8698i	−0.822823	+	0.885077i
$557$	−3.02334	−	11.2833i	−0.128103	−	0.478087i	0.871828	−	0.489812i	$-0.162934\pi$
$557$	−3.02334	−	11.2833i	−0.128103	−	0.478087i	−0.999931	+	0.0117248i	$0.996268\pi$
$558$	0.0166156	+	0.911979i	0.000703393	+	0.0386071i
$559$	−18.9211			−0.800279
$560$	22.7440	+	6.53530i	0.961110	+	0.276167i
$561$	11.5711			0.488534
$562$	−0.122872	−	6.74408i	−0.00518305	−	0.284482i
$563$	−8.09640	−	30.2162i	−0.341223	−	1.27346i	−0.896963	−	0.442105i	$-0.854232\pi$
$563$	−8.09640	−	30.2162i	−0.341223	−	1.27346i	0.555741	−	0.831356i	$-0.312435\pi$
$564$	−4.93603	−	4.58885i	−0.207844	−	0.193225i
$565$	−19.0459	−	9.15445i	−0.801268	−	0.385131i
$566$	19.6797	−	5.65933i	0.827198	−	0.237879i
$567$	17.7505	+	8.10258i	0.745451	+	0.340276i
$568$	−1.10646	−	20.2255i	−0.0464260	−	0.848642i
$569$	−30.8623	+	17.8184i	−1.29381	+	0.746984i	−0.979328	−	0.202278i	$-0.935166\pi$
$569$	−30.8623	+	17.8184i	−1.29381	+	0.746984i	−0.314486	+	0.949262i	$0.601832\pi$
$570$	−2.12113	+	4.62707i	−0.0888444	+	0.193807i
$571$	−7.46148	−	27.8466i	−0.312253	−	1.16535i	−0.926520	−	0.376246i	$-0.877215\pi$
$571$	−7.46148	−	27.8466i	−0.312253	−	1.16535i	0.614266	−	0.789099i	$-0.289452\pi$
$572$	−11.2908	−	5.98130i	−0.472091	−	0.250091i
$573$	3.08008	−	3.08008i	0.128672	−	0.128672i
$574$	−46.1143	+	5.26097i	−1.92477	+	0.219589i
$575$	−11.2104	+	28.6901i	−0.467507	+	1.19646i
$576$	18.1625	−	13.3234i	0.756771	−	0.555144i
$577$	31.8312	+	18.3777i	1.32515	+	0.765075i	0.984545	−	0.175131i	$-0.0560350\pi$
$577$	31.8312	+	18.3777i	1.32515	+	0.765075i	0.340604	+	0.940207i	$0.389368\pi$
$578$	−26.3364	−	43.7554i	−1.09545	−	1.81999i
$579$	2.23912	−	8.35650i	0.0930545	−	0.347284i
$580$	21.4820	−	8.42573i	0.891993	−	0.349859i
$581$	20.7863	+	17.1565i	0.862363	+	0.711770i
$582$	4.12845	−	1.18723i	0.171130	−	0.0492121i
$583$	12.9340	+	22.4024i	0.535672	+	0.927812i
$584$	11.6687	−	23.0314i	0.482854	−	0.953048i
$585$	8.24950	+	7.08851i	0.341075	+	0.293074i
$586$	12.6296	+	12.1776i	0.521725	+	0.503054i
$587$	−8.59652	−	8.59652i	−0.354816	−	0.354816i	0.507082	−	0.861898i	$-0.330724\pi$
$587$	−8.59652	−	8.59652i	−0.354816	−	0.354816i	−0.861898	+	0.507082i	$0.830724\pi$
$588$	2.82346	+	5.30636i	0.116437	+	0.218831i
$589$	0.607252	+	0.607252i	0.0250214	+	0.0250214i
$590$	−0.0916634	−	0.0155491i	−0.00377372	−	0.000640146i
$591$	−3.00833	+	5.21059i	−0.123746	+	0.214335i
$592$	−1.91924	+	10.0373i	−0.0788805	+	0.412531i
$593$	34.5679	−	19.9578i	1.41953	−	0.819568i	0.423276	−	0.906001i	$-0.360880\pi$
$593$	34.5679	−	19.9578i	1.41953	−	0.819568i	0.996258	+	0.0864328i	$0.0275468\pi$
$594$	−6.32218	+	11.4261i	−0.259402	+	0.468818i
$595$	27.5946	+	33.1279i	1.13127	+	1.35811i
$596$	−21.2141	−	4.86353i	−0.868963	−	0.199218i
$597$	1.75834	−	6.56222i	0.0719641	−	0.268574i
$598$	−14.6065	−	3.62996i	−0.597304	−	0.148440i
$599$	16.8639	+	9.73639i	0.689041	+	0.397818i	0.803253	−	0.595638i	$-0.203101\pi$
$599$	16.8639	+	9.73639i	0.689041	+	0.397818i	−0.114211	+	0.993456i	$0.536434\pi$
$600$	3.32570	−	5.08000i	0.135771	−	0.207390i
$601$			8.55859i			0.349112i	0.984647	+	0.174556i	$0.0558491\pi$
$601$			8.55859i			0.349112i	−0.984647	+	0.174556i	$0.944151\pi$
$602$	25.5065	−	32.0759i	1.03957	−	1.30731i
$603$	18.6382	+	18.6382i	0.759007	+	0.759007i
$604$	−19.4784	−	10.3187i	−0.792565	−	0.419862i
$605$	0.451624	+	5.96650i	0.0183611	+	0.242573i
$606$	−2.20317	+	1.32609i	−0.0894978	+	0.0538688i
$607$	−6.96334	+	4.02028i	−0.282633	+	0.163178i	−0.634615	−	0.772829i	$-0.718841\pi$
$607$	−6.96334	+	4.02028i	−0.282633	+	0.163178i	0.351982	+	0.936007i	$0.385508\pi$
$608$	3.60291	−	20.8996i	0.146117	−	0.847592i
$609$	5.33194	+	2.43387i	0.216061	+	0.0986254i
$610$	14.0085	+	11.6002i	0.567189	+	0.469679i
$611$	−3.50934	+	13.0970i	−0.141973	+	0.529849i
$612$	41.0128	−	1.49494i	1.65784	−	0.0604294i
$613$	10.4738	−	2.80644i	0.423032	−	0.113351i	−0.0410217	−	0.999158i	$-0.513061\pi$
$613$	10.4738	−	2.80644i	0.423032	−	0.113351i	0.464053	+	0.885807i	$0.346395\pi$
$614$	−10.0444	+	10.4172i	−0.405360	+	0.420405i
$615$	−2.20520	+	11.7028i	−0.0889224	+	0.471902i
$616$	25.3602	−	11.0775i	1.02179	−	0.446326i
$617$	1.38836			0.0558931			0.0279466	−	0.999609i	$-0.491103\pi$
$617$	1.38836			0.0558931			0.0279466	+	0.999609i	$0.491103\pi$
$618$	7.97686	−	8.27292i	0.320876	−	0.332786i
$619$	−6.28116	−	23.4416i	−0.252461	−	0.942197i	−0.969485	−	0.245149i	$-0.921163\pi$
$619$	−6.28116	−	23.4416i	−0.252461	−	0.942197i	0.717024	−	0.697048i	$-0.245504\pi$
$620$	−0.608140	−	0.824373i	−0.0244235	−	0.0331076i
$621$	−3.98120	+	14.8580i	−0.159760	+	0.596232i
$622$	40.0117	+	22.1389i	1.60432	+	0.887688i
$623$	3.51617	+	4.93592i	0.140872	+	0.197754i
$624$	2.67052	+	1.29241i	0.106906	+	0.0517379i
$625$	−5.48993	+	24.3898i	−0.219597	+	0.975591i
$626$	−15.2932	−	25.4082i	−0.611240	−	1.01552i
$627$	1.54063	+	5.74973i	0.0615270	+	0.229622i
$628$	−4.34633	−	14.1389i	−0.173437	−	0.564203i
$629$	−13.1655	+	13.1655i	−0.524941	+	0.524941i
$630$	−23.1374	+	4.42924i	−0.921817	+	0.176465i
$631$		−	14.7668i		−	0.587856i	−0.955828	−	0.293928i	$-0.905037\pi$
$631$		−	14.7668i		−	0.587856i	0.955828	−	0.293928i	$-0.0949626\pi$
$632$	15.3068	+	23.4525i	0.608871	+	0.932892i
$633$	0.714927	−	1.23829i	0.0284158	−	0.0492176i
$634$	43.9363	+	10.9189i	1.74493	+	0.433645i
$635$	2.77017	+	1.33149i	0.109931	+	0.0528385i
$636$	−3.19071	−	5.08888i	−0.126520	−	0.201787i
$637$	6.77455	−	10.0170i	0.268417	−	0.396889i
$638$	13.0647	−	23.6118i	0.517236	−	0.934801i
$639$	10.0822	+	17.4628i	0.398845	+	0.690819i
$640$	−7.97067	+	24.0098i	−0.315069	+	0.949069i
$641$	10.8358	−	18.7682i	0.427988	−	0.741298i	−0.568706	−	0.822541i	$-0.692556\pi$
$641$	10.8358	−	18.7682i	0.427988	−	0.741298i	0.996694	+	0.0812432i	$0.0258891\pi$
$642$	−3.78113	+	0.0688894i	−0.149229	+	0.00271885i
$643$	−6.20686	+	6.20686i	−0.244775	+	0.244775i	−0.818822	−	0.574047i	$-0.805372\pi$
$643$	−6.20686	+	6.20686i	−0.244775	+	0.244775i	0.574047	+	0.818822i	$0.305372\pi$
$644$	25.8439	−	19.8682i	1.01839	−	0.782915i
$645$	−5.92977	−	8.68339i	−0.233485	−	0.341908i
$646$	26.8202	−	27.8156i	1.05523	−	1.09439i
$647$	−1.68954	+	2.92638i	−0.0664229	+	0.115048i	−0.897324	−	0.441372i	$-0.854492\pi$
$647$	−1.68954	+	2.92638i	−0.0664229	+	0.115048i	0.830901	+	0.556420i	$0.187825\pi$
$648$	−9.42743	+	18.6077i	−0.370345	+	0.730979i
$649$	−0.0941598	+	0.0543632i	−0.00369609	+	0.00213394i
$650$	−12.1634	−	1.12813i	−0.477086	−	0.0442489i
$651$	0.0431039	−	0.256608i	0.00168937	−	0.0100572i
$652$	−17.4064	−	3.99059i	−0.681688	−	0.156283i
$653$	33.5519	+	8.99019i	1.31299	+	0.351813i	0.846346	−	0.532634i	$-0.178798\pi$
$653$	33.5519	+	8.99019i	1.31299	+	0.351813i	0.466640	+	0.884447i	$0.345464\pi$
$654$	−5.35591	−	8.89832i	−0.209432	−	0.347952i
$655$	−10.7870	−	9.26887i	−0.421482	−	0.362165i
$656$	−3.61241	−	49.4863i	−0.141041	−	1.93212i
$657$			25.7022i			1.00274i
$658$	−17.4719	−	23.6046i	−0.681124	−	0.920202i
$659$	9.82441	+	9.82441i	0.382705	+	0.382705i	0.872076	−	0.489371i	$-0.162774\pi$
$659$	9.82441	+	9.82441i	0.382705	+	0.382705i	−0.489371	+	0.872076i	$0.662774\pi$
$660$	−0.793492	−	7.05613i	−0.0308866	−	0.274660i
$661$	1.02651	+	3.83098i	0.0399266	+	0.149008i	0.983011	−	0.183544i	$-0.0587570\pi$
$661$	1.02651	+	3.83098i	0.0399266	+	0.149008i	−0.943085	+	0.332552i	$0.892090\pi$
$662$	−26.9314	−	6.69290i	−1.04672	−	0.260127i
$663$	2.70269	+	4.68120i	0.104964	+	0.181803i
$664$	−19.2305	+	21.4564i	−0.746290	+	0.832669i
$665$	−12.7872	+	18.1226i	−0.495868	+	0.702764i
$666$	−2.81154	−	9.77682i	−0.108945	−	0.378844i
$667$	8.22707	−	30.7038i	0.318553	−	1.18886i
$668$	−19.6779	+	0.717272i	−0.761361	+	0.0277521i
$669$	−5.29156	+	1.41787i	−0.204583	+	0.0548180i
$670$	−29.1862	−	4.95093i	−1.12756	−	0.191271i
$671$	21.2698			0.821112
$672$	−5.79092	+	2.78494i	−0.223390	+	0.107431i
$673$		−	21.4030i		−	0.825024i	−0.910952	−	0.412512i	$-0.864651\pi$
$673$		−	21.4030i		−	0.825024i	0.910952	−	0.412512i	$-0.135349\pi$
$674$	0.373653	+	20.5087i	0.0143926	+	0.789965i
$675$	−1.37922	+	12.4081i	−0.0530864	+	0.477588i
$676$	0.729665	+	20.0179i	0.0280640	+	0.769920i
$677$	3.80301	−	14.1930i	0.146161	−	0.545482i	−0.853540	−	0.521028i	$-0.825549\pi$
$677$	3.80301	−	14.1930i	0.146161	−	0.545482i	0.999701	−	0.0244537i	$-0.00778462\pi$
$678$	5.51460	−	1.58585i	0.211787	−	0.0609041i
$679$	18.6335	−	1.78262i	0.715087	−	0.0684105i
$680$	−36.5869	+	28.0335i	−1.40304	+	1.07504i
$681$	−3.26452	+	1.88477i	−0.125097	+	0.0722247i
$682$	−1.16263	−	0.288933i	−0.0445193	−	0.0110638i
$683$	18.1658	−	4.86751i	0.695095	−	0.186250i	0.106063	−	0.994359i	$-0.466176\pi$
$683$	18.1658	−	4.86751i	0.695095	−	0.186250i	0.589033	+	0.808109i	$0.299509\pi$
$684$	6.20346	+	20.1803i	0.237195	+	0.771612i
$685$	22.1738	+	32.4707i	0.847218	+	1.24064i
$686$	7.84889	+	24.9879i	0.299672	+	0.954042i
$687$		−	3.91150i		−	0.149233i
$688$	33.1519	+	28.6411i	1.26391	+	1.09193i
$689$	−6.04204	+	10.4651i	−0.230183	+	0.398689i
$690$	−2.91171	−	7.84090i	−0.110847	−	0.298498i
$691$	10.6536	−	39.7596i	0.405280	−	1.51253i	−0.398258	−	0.917274i	$-0.630385\pi$
$691$	10.6536	−	39.7596i	0.405280	−	1.51253i	0.803538	−	0.595253i	$-0.202948\pi$
$692$	−6.02059	−	1.38028i	−0.228868	−	0.0524702i
$693$	−17.5365	+	21.2468i	−0.666158	+	0.807100i
$694$	−4.05025	+	1.16474i	−0.153745	+	0.0442129i
$695$	10.5448	+	30.0630i	0.399987	+	1.14035i
$696$	−2.83183	+	5.58942i	−0.107340	+	0.211866i
$697$	45.2007	−	78.2899i	1.71210	−	2.96544i
$698$	−17.1420	−	16.5286i	−0.648835	−	0.625615i
$699$	1.69672	−	1.69672i	0.0641759	−	0.0641759i
$700$	18.3092	−	19.0990i	0.692023	−	0.721876i
$701$	−18.5137	−	18.5137i	−0.699253	−	0.699253i	0.264996	−	0.964249i	$-0.414629\pi$
$701$	−18.5137	−	18.5137i	−0.699253	−	0.699253i	−0.964249	+	0.264996i	$0.914629\pi$
$702$	−6.09920	+	0.111123i	−0.230199	+	0.00419406i
$703$	−8.29486	−	4.78904i	−0.312846	−	0.180622i
$704$	10.7287	+	27.5709i	0.404354	+	1.03912i
$705$	−7.11037	+	2.49401i	−0.267792	+	0.0939298i
$706$	−2.35322	−	1.30206i	−0.0885645	−	0.0490037i
$707$	−10.4979	+	3.91763i	−0.394814	+	0.147338i
$708$	0.0213891	−	0.0134109i	0.000803853	−	0.000504013i
$709$	42.1261	+	11.2876i	1.58208	+	0.423916i	0.939568	−	0.342361i	$-0.111227\pi$
$709$	42.1261	+	11.2876i	1.58208	+	0.423916i	0.642509	+	0.766278i	$0.277893\pi$
$710$	−20.5866	−	9.43725i	−0.772600	−	0.354174i
$711$	−24.1442	−	13.9397i	−0.905479	−	0.522779i
$712$	−5.42539	+	3.54099i	−0.203325	+	0.132704i
$713$	−1.41116			−0.0528484
$714$	−11.5791	−	1.72876i	−0.433337	−	0.0646971i
$715$	−11.7971	+	8.05608i	−0.441187	+	0.301280i
$716$	3.68287	−	1.13212i	0.137635	−	0.0423094i
$717$	0.252825	+	0.943557i	0.00944193	+	0.0352378i
$718$	12.9889	−	7.81804i	0.484742	−	0.291767i
$719$	16.3417	+	28.3047i	0.609443	+	1.05559i	0.991332	+	0.131379i	$0.0419403\pi$
$719$	16.3417	+	28.3047i	0.609443	+	1.05559i	−0.381889	+	0.924208i	$0.624726\pi$
$720$	−3.72407	−	24.9072i	−0.138788	−	0.928237i
$721$	40.7862	−	29.0546i	1.51896	−	1.08205i
$722$	−6.11845	−	3.38540i	−0.227705	−	0.125992i
$723$	1.40709	+	0.377029i	0.0523303	+	0.0140219i
$724$	8.16079	−	8.77822i	0.303293	−	0.326240i
$725$	2.85014	−	25.6411i	0.105852	−	0.952286i
$726$	−1.16962	−	1.12777i	−0.0434088	−	0.0418554i
$727$	12.9439			0.480063			0.240032	−	0.970765i	$-0.422842\pi$
$727$	12.9439			0.480063			0.240032	+	0.970765i	$0.422842\pi$
$728$	10.4049	+	7.67228i	0.385632	+	0.284354i
$729$		−	17.5494i		−	0.649978i
$730$	−16.7103	−	23.5377i	−0.618477	−	0.871169i
$731$	20.6591	+	77.1008i	0.764104	+	2.85167i
$732$	−4.93548	+	0.179901i	−0.182420	+	0.00664934i
$733$	9.10882	+	2.44070i	0.336442	+	0.0901493i	0.423085	−	0.906090i	$-0.360947\pi$
$733$	9.10882	+	2.44070i	0.336442	+	0.0901493i	−0.0866429	+	0.996239i	$0.527614\pi$
$734$	−1.38156	−	0.764435i	−0.0509945	−	0.0282158i
$735$	6.72018	−	0.0302690i	0.247877	−	0.00111649i
$736$	20.0975	+	28.4701i	0.740803	+	1.04942i
$737$	−29.9811	+	17.3096i	−1.10437	+	0.637607i
$738$	25.4722	+	42.3196i	0.937645	+	1.55781i
$739$	−17.0410	+	4.56611i	−0.626862	+	0.167967i	−0.558245	−	0.829676i	$-0.688525\pi$
$739$	−17.0410	+	4.56611i	−0.626862	+	0.167967i	−0.0686168	+	0.997643i	$0.521859\pi$
$740$	8.93117	+	7.12553i	0.328316	+	0.261940i
$741$	−1.96625	+	1.96625i	−0.0722319	+	0.0722319i
$742$	−9.59594	−	24.3501i	−0.352278	−	0.893922i
$743$	−18.1390			−0.665455			−0.332727	−	0.943023i	$-0.607969\pi$
$743$	−18.1390			−0.665455			−0.332727	+	0.943023i	$0.607969\pi$
$744$	0.272221	+	0.0572107i	0.00998012	+	0.00209745i
$745$	−15.8586	+	18.4559i	−0.581012	+	0.676173i
$746$	4.76294	−	19.1655i	0.174384	−	0.701698i
$747$	7.42371	−	27.7057i	0.271619	−	1.01370i
$748$	−12.0450	+	52.5389i	−0.440410	+	1.92101i
$749$	−16.2511	−	2.72980i	−0.593804	−	0.0997447i
$750$	−3.29420	−	5.93562i	−0.120287	−	0.216738i
$751$	−21.9848	−	38.0788i	−0.802236	−	1.38951i	−0.918141	−	0.396254i	$-0.870310\pi$
$751$	−21.9848	−	38.0788i	−0.802236	−	1.38951i	0.115905	−	0.993260i	$-0.463023\pi$
$752$	25.9739	−	17.6353i	0.947170	−	0.643094i
$753$	2.36732	+	1.36677i	0.0862699	+	0.0498079i
$754$	12.6039	−	0.229633i	0.459006	−	0.00836275i
$755$	−20.3519	+	13.8980i	−0.740681	+	0.505802i
$756$	8.03362	−	10.4894i	0.292180	−	0.381496i
$757$	−25.0554	−	25.0554i	−0.910656	−	0.910656i	0.0856682	−	0.996324i	$-0.472697\pi$
$757$	−25.0554	−	25.0554i	−0.910656	−	0.910656i	−0.996324	+	0.0856682i	$0.972697\pi$
$758$	23.1421	−	24.0010i	0.840559	−	0.871756i
$759$	−8.47085	−	4.89065i	−0.307472	−	0.177519i
$760$	−18.8012	−	14.4476i	−0.681993	−	0.524069i
$761$	22.4815	−	12.9797i	0.814954	−	0.470514i	−0.0337194	−	0.999431i	$-0.510735\pi$
$761$	22.4815	−	12.9797i	0.814954	−	0.470514i	0.848673	+	0.528918i	$0.177402\pi$
$762$	−0.802083	+	0.230657i	−0.0290564	+	0.00835581i
$763$	−15.8228	−	42.3996i	−0.572823	−	1.53497i
$764$	10.7789	+	17.1914i	0.389967	+	0.621962i
$765$	19.8774	−	41.3551i	0.718668	−	1.49520i
$766$	21.4339	−	12.9011i	0.774440	−	0.466136i
$767$	−0.0439861	−	0.0253954i	−0.00158825	−	0.000916974i
$768$	−2.72270	−	6.30684i	−0.0982471	−	0.227578i
$769$	−17.5611			−0.633268			−0.316634	−	0.948548i	$-0.602553\pi$
$769$	−17.5611			−0.633268			−0.316634	+	0.948548i	$0.602553\pi$
$770$	2.24603	−	30.8589i	0.0809412	−	1.11208i
$771$	0.617549	+	0.617549i	0.0222405	+	0.0222405i
$772$	35.6119	+	18.8655i	1.28170	+	0.678983i
$773$	11.0494	−	2.96069i	0.397421	−	0.106489i	−0.0545728	−	0.998510i	$-0.517380\pi$
$773$	11.0494	−	2.96069i	0.397421	−	0.106489i	0.451993	+	0.892021i	$0.350713\pi$
$774$	−42.3255	−	10.5186i	−1.52136	−	0.378083i
$775$	−1.13228	+	0.172400i	−0.0406727	+	0.00619279i
$776$	1.09309	+	19.9811i	0.0392396	+	0.717279i
$777$	0.276371	+	2.88887i	0.00991474	+	0.103638i
$778$	2.75618	+	9.58430i	0.0988138	+	0.343614i
$779$	44.9206	+	12.0365i	1.60945	+	0.431251i
$780$	2.66928	−	1.96912i	0.0955754	−	0.0705060i
$781$	−25.5814	+	6.85453i	−0.915376	+	0.245274i
$782$	1.15661	+	63.4826i	0.0413601	+	2.27013i
$783$		−	12.8835i		−	0.460419i
$784$	−27.0327	+	7.29625i	−0.965452	+	0.260580i
$785$	−16.2518	−	3.06239i	−0.580051	−	0.109301i
$786$	3.86123	−	0.0703488i	0.137726	−	0.00250926i
$787$	−3.55601	−	13.2712i	−0.126758	−	0.473068i	0.873138	−	0.487473i	$-0.162081\pi$
$787$	−3.55601	−	13.2712i	−0.126758	−	0.473068i	−0.999896	+	0.0144050i	$0.995415\pi$
$788$	−20.5272	−	19.0834i	−0.731251	−	0.679816i
$789$	−0.165564	−	0.0443626i	−0.00589422	−	0.00157935i
$790$	31.1738	−	2.93165i	1.10911	−	0.104304i
$791$	24.8898	−	2.38114i	0.884979	−	0.0846637i
$792$	−21.9317	−	19.6566i	−0.779309	−	0.698466i
$793$	4.96802	+	8.60487i	0.176420	+	0.305568i
$794$	−16.2231	−	4.03170i	−0.575735	−	0.143080i
$795$	−6.69625	+	0.506861i	−0.237491	+	0.0179765i
$796$	27.9655	+	14.8147i	0.991209	+	0.525094i
$797$	−19.7870	+	19.7870i	−0.700891	+	0.700891i	−0.964602	−	0.263711i	$-0.915053\pi$
$797$	−19.7870	+	19.7870i	−0.700891	+	0.700891i	0.263711	+	0.964602i	$0.415053\pi$
$798$	−0.682671	−	5.98385i	−0.0241663	−	0.211826i
$799$	57.2001			2.02359
$800$	19.6039	+	20.3884i	0.693102	+	0.720840i
$801$	3.22473	−	5.58540i	0.113940	−	0.197350i
$802$	20.6620	+	34.3279i	0.729601	+	1.21216i
$803$	−32.6071	−	8.73704i	−1.15068	−	0.308323i
$804$	6.81044	−	4.27012i	0.240186	−	0.150595i
$805$	−6.19929	−	35.9149i	−0.218496	−	1.26583i
$806$	−0.154667	−	0.537837i	−0.00544791	−	0.0189445i
$807$	−4.60670	−	7.97905i	−0.162164	−	0.280876i
$808$	−3.72773	−	11.3839i	−0.131141	−	0.400485i
$809$	9.78635	+	5.65015i	0.344070	+	0.198649i	0.662070	−	0.749442i	$-0.269678\pi$
$809$	9.78635	+	5.65015i	0.344070	+	0.198649i	−0.318001	+	0.948091i	$0.603011\pi$
$810$	13.5007	+	19.0167i	0.474366	+	0.668178i
$811$	−36.9777	+	36.9777i	−1.29846	+	1.29846i	−0.369055	+	0.929408i	$0.620318\pi$
$811$	−36.9777	+	36.9777i	−1.29846	+	1.29846i	−0.929408	+	0.369055i	$0.879682\pi$
$812$	−16.6013	+	21.6762i	−0.582592	+	0.760684i
$813$	−2.09725	+	2.09725i	−0.0735539	+	0.0735539i
$814$	13.3591	−	0.243392i	0.468236	−	0.00853090i
$815$	−13.0121	+	15.1433i	−0.455795	+	0.530447i
$816$	2.35057	−	12.2931i	0.0822864	−	0.430344i
$817$	−35.5609	+	20.5311i	−1.24412	+	0.718292i
$818$	4.66861	+	2.58319i	0.163234	+	0.0903192i
$819$	−12.6916	−	2.13188i	−0.443480	−	0.0744940i
$820$	−50.8411	−	22.1948i	−1.77545	−	0.775077i
$821$	−17.4141	−	4.66608i	−0.607755	−	0.162847i	−0.0581999	−	0.998305i	$-0.518536\pi$
$821$	−17.4141	−	4.66608i	−0.607755	−	0.162847i	−0.549555	+	0.835458i	$0.685203\pi$
$822$	−10.3616	−	2.57503i	−0.361402	−	0.0898145i
$823$	0.0693104	−	0.120049i	0.00241601	−	0.00418465i	−0.864815	−	0.502091i	$-0.832564\pi$
$823$	0.0693104	−	0.120049i	0.00241601	−	0.00418465i	0.867231	+	0.497906i	$0.165898\pi$
$824$	29.2597	+	44.8308i	1.01931	+	1.56175i
$825$	−7.39428	−	2.88926i	−0.257436	−	0.100591i
$826$	0.102346	−	0.0403328i	0.00356109	−	0.00140336i
$827$	24.8996	+	24.8996i	0.865844	+	0.865844i	0.992009	−	0.126165i	$-0.0402670\pi$
$827$	24.8996	+	24.8996i	0.865844	+	0.865844i	−0.126165	+	0.992009i	$0.540267\pi$
$828$	−30.6559	−	16.2400i	−1.06537	−	0.564379i
$829$	25.9040	−	6.94095i	0.899683	−	0.241069i	0.220803	−	0.975319i	$-0.429132\pi$
$829$	25.9040	−	6.94095i	0.899683	−	0.241069i	0.678880	+	0.734249i	$0.262466\pi$
$830$	11.2143	+	30.1989i	0.389256	+	1.04822i
$831$	2.18417	+	3.78309i	0.0757679	+	0.131234i
$832$	−8.64809	+	10.7802i	−0.299819	+	0.373735i
$833$	−48.2147	−	16.6681i	−1.67054	−	0.577516i
$834$	−7.56943	−	4.18824i	−0.262108	−	0.145027i
$835$	−9.53716	+	19.8422i	−0.330047	+	0.686666i
$836$	−27.7104	+	1.01006i	−0.958385	+	0.0349337i
$837$	−0.552466	+	0.148033i	−0.0190960	+	0.00511677i
$838$	24.8717	+	23.9817i	0.859180	+	0.828433i
$839$		−	48.9962i		−	1.69154i	−0.533550	−	0.845768i	$-0.679142\pi$
$839$		−	48.9962i		−	1.69154i	0.533550	−	0.845768i	$-0.320858\pi$
$840$	−0.260165	+	7.17953i	−0.00897656	+	0.247717i
$841$		−	2.37644i		−	0.0819461i
$842$	36.0414	−	37.3791i	1.24207	−	1.28817i
$843$	1.97800	−	0.530002i	0.0681258	−	0.0182543i
$844$	4.87826	+	4.53514i	0.167917	+	0.156106i
$845$	20.1850	+	9.70195i	0.694385	+	0.333757i
$846$	−15.1311	+	27.3464i	−0.520216	+	0.940188i
$847$	−4.10774	−	5.76635i	−0.141144	−	0.198134i
$848$	26.4275	−	9.19014i	0.907524	−	0.315591i
$849$	3.10834	+	5.38380i	0.106678	+	0.184772i
$850$	8.68363	+	50.7956i	0.297846	+	1.74227i
$851$	15.2025	−	4.07349i	0.521135	−	0.139638i
$852$	5.87797	−	1.80690i	0.201376	−	0.0619034i
$853$	3.92256	+	3.92256i	0.134306	+	0.134306i	0.771064	−	0.636758i	$-0.219725\pi$
$853$	3.92256	+	3.92256i	0.134306	+	0.134306i	−0.636758	+	0.771064i	$0.719725\pi$
$854$	−21.2844	−	3.17776i	−0.728339	−	0.108741i
$855$	23.1960	+	4.37091i	0.793286	+	0.149482i
$856$	3.62320	−	17.2400i	0.123838	−	0.589250i
$857$	−20.1949	+	34.9786i	−0.689846	+	1.19485i	0.282042	+	0.959402i	$0.408988\pi$
$857$	−20.1949	+	34.9786i	−0.689846	+	1.19485i	−0.971888	+	0.235446i	$0.924345\pi$
$858$	0.935548	−	3.76453i	0.0319391	−	0.128519i
$859$	−30.5565	−	8.18760i	−1.04258	−	0.279357i	−0.303395	−	0.952865i	$-0.598120\pi$
$859$	−30.5565	−	8.18760i	−1.04258	−	0.279357i	−0.739180	+	0.673508i	$0.764787\pi$
$860$	45.5996	−	17.8852i	1.55493	−	0.609879i
$861$	−4.92651	−	13.2013i	−0.167895	−	0.449900i
$862$	9.99369	−	18.0616i	0.340387	−	0.615182i
$863$	10.9272	−	6.30881i	0.371966	−	0.214755i	−0.302351	−	0.953197i	$-0.597772\pi$
$863$	10.9272	−	6.30881i	0.371966	−	0.214755i	0.674317	+	0.738442i	$0.264438\pi$
$864$	10.8547	+	9.03773i	0.369284	+	0.307470i
$865$	−4.50068	+	5.23781i	−0.153028	+	0.178091i
$866$	0.230081	+	12.6285i	0.00781847	+	0.429132i
$867$	10.9632	−	10.9632i	0.372330	−	0.372330i
$868$	1.12026	+	0.462830i	0.0380241	+	0.0157095i
$869$	25.8920	−	25.8920i	0.878325	−	0.878325i
$870$	4.05537	+	5.71228i	0.137490	+	0.193664i
$871$	−14.0055	−	8.08605i	−0.474557	−	0.273985i
$872$	45.9782	−	15.0558i	1.55702	−	0.509854i
$873$	−9.96035	−	17.2518i	−0.337107	−	0.583886i
$874$	−31.3906	+	9.02708i	−1.06180	+	0.305345i
$875$	−9.36184	−	28.0599i	−0.316488	−	0.948596i
$876$	7.64008	+	1.75156i	0.258135	+	0.0591798i
$877$	41.0489	+	10.9990i	1.38612	+	0.371411i	0.873342	−	0.487108i	$-0.161948\pi$
$877$	41.0489	+	10.9990i	1.38612	+	0.371411i	0.512782	+	0.858519i	$0.328615\pi$
$878$	−19.2093	+	11.5621i	−0.648282	+	0.390202i
$879$	−2.66313	+	4.61268i	−0.0898253	+	0.155582i
$880$	32.8644	+	3.74226i	1.10786	+	0.126151i
$881$	−27.3275			−0.920686			−0.460343	−	0.887741i	$-0.652274\pi$
$881$	−27.3275			−0.920686			−0.460343	+	0.887741i	$0.652274\pi$
$882$	20.7229	−	18.6414i	0.697777	−	0.627690i
$883$	−23.7842	+	23.7842i	−0.800400	+	0.800400i	−0.983158	−	0.182758i	$-0.941498\pi$
$883$	−23.7842	+	23.7842i	−0.800400	+	0.800400i	0.182758	+	0.983158i	$0.441498\pi$
$884$	−24.0684	+	7.39868i	−0.809508	+	0.248845i
$885$	−0.00213040	−	0.0281451i	−7.16125e−5	−	0.000946087i
$886$	−10.2774	+	41.3549i	−0.345275	+	1.38934i
$887$	−3.14288	−	5.44363i	−0.105528	−	0.182779i	0.808426	−	0.588598i	$-0.200320\pi$
$887$	−3.14288	−	5.44363i	−0.105528	−	0.182779i	−0.913954	+	0.405819i	$0.866986\pi$
$888$	−3.09780	+	0.169469i	−0.103955	+	0.00568700i
$889$	−3.62015	+	0.346330i	−0.121416	+	0.0116155i
$890$	0.678194	+	7.21158i	0.0227331	+	0.241733i
$891$	26.3441	+	7.05887i	0.882560	+	0.236481i
$892$	−0.929575	−	25.5023i	−0.0311245	−	0.853881i
$893$	7.61588	+	28.4228i	0.254856	+	0.951134i
$894$	−0.120363	−	6.60637i	−0.00402555	−	0.220950i
$895$	0.797684	−	4.23323i	0.0266636	−	0.141501i
$896$	−6.61695	−	29.1927i	−0.221057	−	0.975261i
$897$		−	4.56926i		−	0.152563i
$898$	−6.28933	+	0.114587i	−0.209877	+	0.00382381i
$899$	1.14166	−	0.305907i	0.0380766	−	0.0102026i
$900$	−26.5816	−	9.28538i	−0.886052	−	0.309513i
$901$	49.2408	+	13.1940i	1.64045	+	0.439557i
$902$	−62.3475	+	17.9294i	−2.07594	+	0.596984i
$903$	11.3180	+	5.16634i	0.376640	+	0.171925i
$904$	1.46010	+	26.6899i	0.0485623	+	0.887692i
$905$	−4.43533	−	12.6451i	−0.147436	−	0.420336i
$906$	1.61397	−	6.49442i	0.0536206	−	0.215763i
$907$	−44.7374	+	11.9874i	−1.48548	+	0.398033i	−0.908209	−	0.418518i	$-0.862550\pi$
$907$	−44.7374	+	11.9874i	−1.48548	+	0.398033i	−0.577273	+	0.816551i	$0.695883\pi$
$908$	−5.15961	−	16.7846i	−0.171228	−	0.557015i
$909$	8.43203	+	8.43203i	0.279673	+	0.279673i
$910$	13.0088	−	6.29911i	0.431238	−	0.208813i
$911$	42.6199			1.41206			0.706031	−	0.708181i	$-0.250484\pi$
$911$	42.6199			1.41206			0.706031	+	0.708181i	$0.250484\pi$
$912$	6.42142	−	0.468752i	0.212634	−	0.0155219i
$913$	32.6252	+	18.8362i	1.07974	+	0.623386i
$914$	5.08259	+	8.44423i	0.168117	+	0.279310i
$915$	−2.39204	+	4.97667i	−0.0790786	+	0.164524i
$916$	17.7602	+	4.07169i	0.586813	+	0.134533i
$917$	16.5954	+	2.78763i	0.548029	+	0.0920556i
$918$	7.11223	+	24.7320i	0.234739	+	0.816277i
$919$	−16.0881	+	9.28845i	−0.530696	+	0.306398i	−0.741300	−	0.671174i	$-0.765790\pi$
$919$	−16.0881	+	9.28845i	−0.530696	+	0.306398i	0.210604	+	0.977572i	$0.432457\pi$
$920$	38.6326	−	5.05862i	1.27368	−	0.166778i
$921$	−3.80465	−	2.19662i	−0.125368	−	0.0723810i
$922$	−16.3969	−	15.8101i	−0.540003	−	0.520678i
$923$	−8.74815	−	8.74815i	−0.287949	−	0.287949i
$924$	5.12062	+	6.66073i	0.168456	+	0.219122i
$925$	11.7004	−	5.12574i	0.384708	−	0.168533i
$926$	−0.640832	−	35.1733i	−0.0210590	−	1.15587i
$927$	−46.1530	−	26.6464i	−1.51586	−	0.875183i
$928$	−22.4310	−	18.6763i	−0.736334	−	0.613080i
$929$	17.4381	+	30.2036i	0.572124	+	0.990948i	0.996348	+	0.0853907i	$0.0272138\pi$
$929$	17.4381	+	30.2036i	0.572124	+	0.990948i	−0.424223	+	0.905558i	$0.639453\pi$
$930$	0.198355	−	0.239535i	0.00650432	−	0.00785468i
$931$	1.86290	−	26.1773i	0.0610541	−	0.857925i
$932$	5.93777	+	9.47019i	0.194498	+	0.310206i
$933$	−3.59308	+	13.4096i	−0.117632	+	0.439009i
$934$	35.4303	+	8.80502i	1.15931	+	0.288109i
$935$	45.7080	+	39.2753i	1.49481	+	1.28444i
$936$	2.82959	−	13.4639i	0.0924882	−	0.440080i
$937$	−27.7844			−0.907677			−0.453839	−	0.891084i	$-0.649946\pi$
$937$	−27.7844			−0.907677			−0.453839	+	0.891084i	$0.649946\pi$
$938$	32.5878	−	12.8422i	1.06403	−	0.419314i
$939$	6.36620	−	6.36620i	0.207753	−	0.207753i
$940$	−3.92250	−	34.8808i	−0.127938	−	1.13769i
$941$	−25.2910	+	6.77670i	−0.824462	+	0.220914i	−0.646296	−	0.763086i	$-0.723683\pi$
$941$	−25.2910	+	6.77670i	−0.824462	+	0.220914i	−0.178166	+	0.984000i	$0.557016\pi$
$942$	3.84747	−	2.31580i	0.125357	−	0.0754527i
$943$	−66.1798	+	38.2089i	−2.15511	+	1.24425i
$944$	0.0386272	+	0.111078i	0.00125721	+	0.00361527i
$945$	−6.19454	−	13.4103i	−0.201508	−	0.436237i
$946$	27.7322	−	50.1205i	0.901652	−	1.62956i
$947$	36.8306	+	9.86873i	1.19683	+	0.320691i	0.801583	−	0.597883i	$-0.203991\pi$
$947$	36.8306	+	9.86873i	1.19683	+	0.320691i	0.395250	+	0.918574i	$0.370658\pi$
$948$	−5.78901	+	6.22700i	−0.188018	+	0.202243i
$949$	−4.08145	−	15.2322i	−0.132489	−	0.494457i
$950$	−24.0842	+	11.0781i	−0.781396	+	0.359420i
$951$			13.7443i			0.445691i
$952$	19.9028	−	50.7755i	0.645052	−	1.64564i
$953$	−19.8672			−0.643562			−0.321781	−	0.946814i	$-0.604281\pi$
$953$	−19.8672			−0.643562			−0.321781	+	0.946814i	$0.604281\pi$
$954$	−19.3334	+	20.0510i	−0.625943	+	0.649174i
$955$	22.6214	−	1.71229i	0.732011	−	0.0554084i
$956$	−4.54741	+	0.165756i	−0.147074	+	0.00536092i
$957$	7.91329	+	2.12036i	0.255800	+	0.0685415i
$958$	−18.1268	+	32.7607i	−0.585651	+	1.05845i
$959$	−42.3227	−	19.3190i	−1.36667	−	0.623845i
$960$	−7.65755	−	0.590389i	−0.247146	−	0.0190547i
$961$	15.4738	+	26.8013i	0.499154	+	0.864560i
$962$	3.21877	+	5.34767i	0.103777	+	0.172416i
$963$	4.53894	+	16.9396i	0.146265	+	0.545870i
$964$	−3.17662	+	5.99644i	−0.102312	+	0.193132i
$965$	37.2089	−	25.4095i	1.19780	−	0.817960i
$966$	7.74600	+	6.15957i	0.249223	+	0.198181i
$967$	14.9646			0.481229			0.240614	−	0.970621i	$-0.422651\pi$
$967$	14.9646			0.481229			0.240614	+	0.970621i	$0.422651\pi$
$968$	6.33816	−	4.13673i	0.203716	−	0.132960i
$969$	10.1590	+	5.86531i	0.326355	+	0.188421i
$970$	20.3378	+	9.32322i	0.653008	+	0.299350i
$971$	−47.5682	−	12.7459i	−1.52654	−	0.409034i	−0.604649	−	0.796492i	$-0.706687\pi$
$971$	−47.5682	−	12.7459i	−1.52654	−	0.409034i	−0.921887	+	0.387458i	$0.873353\pi$
$972$	−20.7752	−	4.76291i	−0.666364	−	0.152770i
$973$	−29.0722	−	23.9953i	−0.932011	−	0.769255i
$974$	−4.22406	+	7.63415i	−0.135347	+	0.244614i
$975$	−0.558222	−	3.66626i	−0.0178774	−	0.117414i
$976$	4.32076	−	22.5968i	0.138304	−	0.723307i
$977$	−42.6096	−	24.6007i	−1.36320	−	0.787045i	−0.373153	−	0.927770i	$-0.621723\pi$
$977$	−42.6096	−	24.6007i	−1.36320	−	0.787045i	−0.990049	+	0.140725i	$0.955057\pi$
$978$	−0.0987594	−	5.42060i	−0.00315798	−	0.173332i
$979$	5.98971	+	5.98971i	0.191432	+	0.191432i
$980$	−6.85796	+	30.5445i	−0.219070	+	0.975709i
$981$	−34.0558	+	34.0558i	−1.08732	+	1.08732i
$982$	−23.8534	+	24.7387i	−0.761192	+	0.789443i
$983$	−22.6703	+	39.2661i	−0.723071	+	1.25239i	0.236693	+	0.971585i	$0.423937\pi$
$983$	−22.6703	+	39.2661i	−0.723071	+	1.25239i	−0.959763	+	0.280810i	$0.909397\pi$
$984$	14.3155	−	4.68770i	0.456363	−	0.149438i
$985$	−29.5695	+	10.3717i	−0.942161	+	0.330469i
$986$	−14.6973	−	51.1082i	−0.468057	−	1.62762i
$987$	5.67527	−	6.87602i	0.180646	−	0.218866i
$988$	−6.88099	−	10.9745i	−0.218914	−	0.349147i
$989$	17.4635	−	65.1746i	0.555306	−	2.07243i
$990$	−30.8679	+	11.4628i	−0.981047	+	0.364311i
$991$	6.61251	−	11.4532i	0.210053	−	0.363823i	−0.741678	−	0.670756i	$-0.765970\pi$
$991$	6.61251	−	11.4532i	0.210053	−	0.363823i	0.951731	+	0.306934i	$0.0993030\pi$
$992$	−0.543136	+	1.17647i	−0.0172446	+	0.0373530i
$993$		−	8.42478i		−	0.267352i
$994$	26.6231	−	3.03731i	0.844434	−	0.0963377i
$995$	29.2195	−	19.9536i	0.926321	−	0.632573i
$996$	−7.72970	−	4.09482i	−0.244925	−	0.129749i
$997$	−46.1972	+	12.3785i	−1.46308	+	0.392031i	−0.900552	−	0.434747i	$-0.856838\pi$
$997$	−46.1972	+	12.3785i	−1.46308	+	0.392031i	−0.562528	+	0.826779i	$0.690171\pi$
$998$	−0.411772	+	1.65692i	−0.0130344	+	0.0524488i
$999$	5.52443	−	3.18953i	0.174785	−	0.100912i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.cr.a.109.2	✓	368
5.4	even	2	inner	560.2.cr.a.109.91	yes	368
7.2	even	3	inner	560.2.cr.a.429.63	yes	368
16.5	even	4	inner	560.2.cr.a.389.30	yes	368
35.9	even	6	inner	560.2.cr.a.429.30	yes	368
80.69	even	4	inner	560.2.cr.a.389.63	yes	368
112.37	even	12	inner	560.2.cr.a.149.91	yes	368
560.149	even	12	inner	560.2.cr.a.149.2	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.cr.a.109.2	✓	368	1.1	even	1	trivial
560.2.cr.a.109.91	yes	368	5.4	even	2	inner
560.2.cr.a.149.2	yes	368	560.149	even	12	inner
560.2.cr.a.149.91	yes	368	112.37	even	12	inner
560.2.cr.a.389.30	yes	368	16.5	even	4	inner
560.2.cr.a.389.63	yes	368	80.69	even	4	inner
560.2.cr.a.429.30	yes	368	35.9	even	6	inner
560.2.cr.a.429.63	yes	368	7.2	even	3	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.cr (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41398 + 0.0257616i) q^{2} +(-0.111122 - 0.414711i) q^{3} +(1.99867 - 0.0728528i) q^{4} +(0.968683 - 2.01535i) q^{5} +(0.167807 + 0.583530i) q^{6} +(0.251962 + 2.63373i) q^{7} +(-2.82420 + 0.154501i) q^{8} +(2.43844 - 1.40783i) q^{9} +(-1.31778 + 2.87462i) q^{10} +(0.957138 + 3.57209i) q^{11} +(-0.252308 - 0.820776i) q^{12} +(-1.22156 + 1.22156i) q^{13} +(-0.424118 - 3.71754i) q^{14} +(-0.943432 - 0.177775i) q^{15} +(3.98938 - 0.291218i) q^{16} +(6.31141 + 3.64390i) q^{17} +(-3.41163 + 2.05346i) q^{18} +(-0.970329 + 3.62132i) q^{19} +(1.78926 - 4.09860i) q^{20} +(1.06424 - 0.397155i) q^{21} +(-1.44540 - 5.02620i) q^{22} +(-3.08025 - 5.33515i) q^{23} +(0.377903 + 1.15406i) q^{24} +(-3.12330 - 3.90448i) q^{25} +(1.69579 - 1.75872i) q^{26} +(-1.76558 - 1.76558i) q^{27} +(0.695464 + 5.24560i) q^{28} +(3.64853 + 3.64853i) q^{29} +(1.33857 + 0.227065i) q^{30} +(0.114533 - 0.198377i) q^{31} +(-5.63340 + 0.514549i) q^{32} +(1.37503 - 0.793872i) q^{33} +(-9.01808 - 4.98980i) q^{34} +(5.55196 + 2.04345i) q^{35} +(4.77108 - 2.99145i) q^{36} +(-0.661228 + 2.46774i) q^{37} +(1.27873 - 5.14547i) q^{38} +(0.642334 + 0.370852i) q^{39} +(-2.42438 + 5.84143i) q^{40} -12.4045i q^{41} +(-1.49458 + 0.588985i) q^{42} +(7.74469 + 7.74469i) q^{43} +(2.17324 + 7.06971i) q^{44} +(-0.475208 - 6.27806i) q^{45} +(4.49285 + 7.46443i) q^{46} +(6.79722 - 3.92438i) q^{47} +(-0.564078 - 1.62208i) q^{48} +(-6.87303 + 1.32720i) q^{49} +(4.51687 + 5.44039i) q^{50} +(0.809831 - 3.02233i) q^{51} +(-2.35250 + 2.53048i) q^{52} +(6.75661 - 1.81043i) q^{53} +(2.54197 + 2.45100i) q^{54} +(8.12619 + 1.53125i) q^{55} +(-1.11851 - 7.39925i) q^{56} +1.60963 q^{57} +(-5.25294 - 5.06495i) q^{58} +(0.00760944 + 0.0283988i) q^{59} +(-1.89856 - 0.286582i) q^{60} +(1.48861 - 5.55558i) q^{61} +(-0.156837 + 0.283451i) q^{62} +(4.32224 + 6.06746i) q^{63} +(7.95226 - 0.872687i) q^{64} +(1.27857 + 3.64517i) q^{65} +(-1.92381 + 1.15794i) q^{66} +(2.42289 + 9.04236i) q^{67} +(12.8799 + 6.82315i) q^{68} +(-1.87026 + 1.87026i) q^{69} +(-7.90300 - 2.74637i) q^{70} +7.16148i q^{71} +(-6.66914 + 4.35275i) q^{72} +(-4.56415 + 7.90533i) q^{73} +(0.871390 - 3.50636i) q^{74} +(-1.27217 + 1.72914i) q^{75} +(-1.67555 + 7.30852i) q^{76} +(-9.16674 + 3.42087i) q^{77} +(-0.917801 - 0.507829i) q^{78} +(-4.95076 - 8.57496i) q^{79} +(3.27754 - 8.32212i) q^{80} +(3.68749 - 6.38692i) q^{81} +(0.319560 + 17.5397i) q^{82} +(7.20325 - 7.20325i) q^{83} +(2.09813 - 0.871316i) q^{84} +(13.4575 - 9.18995i) q^{85} +(-11.1503 - 10.7513i) q^{86} +(1.10766 - 1.91852i) q^{87} +(-3.25505 - 9.94043i) q^{88} +(1.98369 - 1.14528i) q^{89} +(0.833667 + 8.86481i) q^{90} +(-3.52503 - 2.90946i) q^{91} +(-6.54509 - 10.4388i) q^{92} +(-0.0949962 - 0.0254542i) q^{93} +(-9.51003 + 5.72409i) q^{94} +(6.35830 + 5.46347i) q^{95} +(0.839382 + 2.27906i) q^{96} -7.07495i q^{97} +(9.68413 - 2.05369i) q^{98} +(7.36283 + 7.36283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 4 q^{4} - 2 q^{5} - 16 q^{6} - 8 q^{10} - 4 q^{11} + 16 q^{14} - 16 q^{15} - 4 q^{16} - 4 q^{19} - 8 q^{20} + 4 q^{21} - 4 q^{24} - 4 q^{26} - 16 q^{29} + 22 q^{30} - 56 q^{31} - 96 q^{34} + 18 q^{35}+ \cdots - 112 q^{99}+O(q^{100}) \) 368 * q - 4 * q^4 - 2 * q^5 - 16 * q^6 - 8 * q^10 - 4 * q^11 + 16 * q^14 - 16 * q^15 - 4 * q^16 - 4 * q^19 - 8 * q^20 + 4 * q^21 - 4 * q^24 - 4 * q^26 - 16 * q^29 + 22 * q^30 - 56 * q^31 - 96 * q^34 + 18 * q^35 + 32 * q^36 - 14 * q^40 - 12 * q^44 - 16 * q^45 + 12 * q^46 - 16 * q^49 - 12 * q^50 - 28 * q^51 - 8 * q^54 - 64 * q^56 + 12 * q^59 - 54 * q^60 - 4 * q^61 - 88 * q^64 - 4 * q^65 - 44 * q^66 + 8 * q^69 + 88 * q^70 - 72 * q^74 + 10 * q^75 + 104 * q^76 - 8 * q^79 + 48 * q^80 + 112 * q^81 + 68 * q^84 - 28 * q^85 + 44 * q^86 - 92 * q^90 - 80 * q^91 - 20 * q^94 + 20 * q^95 - 36 * q^96 - 112 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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