LMFDB - Embedded newform 230.2.l.a.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(7,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("230.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			17.2
Character	$\chi$	$=$	230.17
Dual form			230.2.l.a.203.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.936950 + 0.349464i) q^{2} +(-1.69758 + 0.926949i) q^{3} +(0.755750 - 0.654861i) q^{4} +(-1.50435 + 1.65436i) q^{5} +(1.26661 - 1.46175i) q^{6} +(-0.735871 - 0.983009i) q^{7} +(-0.479249 + 0.877679i) q^{8} +(0.400622 - 0.623380i) q^{9} +(0.831363 - 2.07577i) q^{10} +(3.08362 - 1.40824i) q^{11} +(-0.675923 + 1.81222i) q^{12} +(-5.47285 - 4.09692i) q^{13} +(1.03300 + 0.663869i) q^{14} +(1.02025 - 4.20287i) q^{15} +(0.142315 - 0.989821i) q^{16} +(-0.214766 - 3.00282i) q^{17} +(-0.157514 + 0.724078i) q^{18} +(-1.88225 - 2.17223i) q^{19} +(-0.0535372 + 2.23543i) q^{20} +(2.16040 + 0.986621i) q^{21} +(-2.39707 + 2.39707i) q^{22} +(3.93443 + 2.74231i) q^{23} -1.93417i q^{24} +(-0.473838 - 4.97750i) q^{25} +(6.55951 + 1.92605i) q^{26} +(0.311700 - 4.35813i) q^{27} +(-1.19987 - 0.261015i) q^{28} +(-3.99884 - 3.46501i) q^{29} +(0.512830 + 4.29442i) q^{30} +(-5.92845 + 1.74075i) q^{31} +(0.212565 + 0.977147i) q^{32} +(-3.92933 + 5.24896i) q^{33} +(1.25060 + 2.73844i) q^{34} +(2.73326 + 0.261395i) q^{35} +(-0.105457 - 0.733470i) q^{36} +(-6.54487 + 1.42375i) q^{37} +(2.52269 + 1.37749i) q^{38} +(13.0882 + 1.88180i) q^{39} +(-0.731040 - 2.11319i) q^{40} +(-2.34072 + 1.50429i) q^{41} +(-2.36897 - 0.169432i) q^{42} +(4.04137 + 7.40121i) q^{43} +(1.40824 - 3.08362i) q^{44} +(0.428620 + 1.60056i) q^{45} +(-4.64470 - 1.19446i) q^{46} +(5.79351 + 5.79351i) q^{47} +(0.675923 + 1.81222i) q^{48} +(1.54733 - 5.26972i) q^{49} +(2.18342 + 4.49808i) q^{50} +(3.14805 + 4.89846i) q^{51} +(-6.81902 + 0.487706i) q^{52} +(-8.41893 + 6.30233i) q^{53} +(1.23096 + 4.19228i) q^{54} +(-2.30911 + 7.21993i) q^{55} +(1.21543 - 0.174753i) q^{56} +(5.20882 + 1.94279i) q^{57} +(4.95761 + 1.84909i) q^{58} +(-7.66795 + 1.10249i) q^{59} +(-1.98124 - 3.84444i) q^{60} +(0.704279 + 2.39855i) q^{61} +(4.94633 - 3.70278i) q^{62} +(-0.907593 + 0.0649124i) q^{63} +(-0.540641 - 0.841254i) q^{64} +(15.0109 - 2.89086i) q^{65} +(1.84726 - 6.29117i) q^{66} +(-3.20331 - 8.58840i) q^{67} +(-2.12874 - 2.12874i) q^{68} +(-9.22099 - 1.00827i) q^{69} +(-2.65228 + 0.710264i) q^{70} +(-1.74986 + 3.83166i) q^{71} +(0.355130 + 0.650371i) q^{72} +(0.769439 + 0.0550313i) q^{73} +(5.63467 - 3.62118i) q^{74} +(5.41826 + 8.01048i) q^{75} +(-2.84502 - 0.409052i) q^{76} +(-3.65346 - 1.99494i) q^{77} +(-12.9206 + 2.81071i) q^{78} +(-0.551491 - 3.83570i) q^{79} +(1.42343 + 1.72448i) q^{80} +(4.43411 + 9.70936i) q^{81} +(1.66744 - 2.22744i) q^{82} +(-2.57122 - 11.8197i) q^{83} +(2.27882 - 0.669122i) q^{84} +(5.29085 + 4.16201i) q^{85} +(-6.37301 - 5.52225i) q^{86} +(10.0002 + 2.17542i) q^{87} +(-0.241837 + 3.38133i) q^{88} +(-10.7709 - 3.16262i) q^{89} +(-0.960932 - 1.34985i) q^{90} +8.39466i q^{91} +(4.76927 - 0.504008i) q^{92} +(8.45044 - 8.45044i) q^{93} +(-7.45285 - 3.40360i) q^{94} +(6.42523 + 0.153881i) q^{95} +(-1.26661 - 1.46175i) q^{96} +(1.36894 - 6.29292i) q^{97} +(0.391808 + 5.47819i) q^{98} +(0.357496 - 2.48644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{22}\right)$

Coefficient data

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

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

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

$2$	−0.936950	+	0.349464i	−0.662524	+	0.247108i
$2$	−0.936950	+	0.349464i	−0.662524	+	0.247108i
$3$	−1.69758	+	0.926949i	−0.980098	+	0.535174i	−0.887638	−	0.460542i	$-0.847655\pi$
$3$	−1.69758	+	0.926949i	−0.980098	+	0.535174i	−0.0924605	+	0.995716i	$0.529473\pi$
$4$	0.755750	−	0.654861i	0.377875	−	0.327430i
$5$	−1.50435	+	1.65436i	−0.672768	+	0.739854i
$5$	−1.50435	+	1.65436i	−0.672768	+	0.739854i
$6$	1.26661	−	1.46175i	0.517092	−	0.596756i
$7$	−0.735871	−	0.983009i	−0.278133	−	0.371542i	0.639622	−	0.768690i	$-0.279091\pi$
$7$	−0.735871	−	0.983009i	−0.278133	−	0.371542i	−0.917755	+	0.397148i	$0.870000\pi$
$8$	−0.479249	+	0.877679i	−0.169440	+	0.310306i
$9$	0.400622	−	0.623380i	0.133541	−	0.207793i
$10$	0.831363	−	2.07577i	0.262900	−	0.656417i
$11$	3.08362	−	1.40824i	0.929747	−	0.424601i	0.107805	−	0.994172i	$-0.465618\pi$
$11$	3.08362	−	1.40824i	0.929747	−	0.424601i	0.821942	+	0.569571i	$0.192891\pi$
$12$	−0.675923	+	1.81222i	−0.195122	+	0.523143i
$13$	−5.47285	−	4.09692i	−1.51790	−	1.13628i	−0.949603	−	0.313455i	$-0.898513\pi$
$13$	−5.47285	−	4.09692i	−1.51790	−	1.13628i	−0.568292	−	0.822827i	$-0.692396\pi$
$14$	1.03300	+	0.663869i	0.276081	+	0.177426i
$15$	1.02025	−	4.20287i	0.263428	−	1.08518i
$16$	0.142315	−	0.989821i	0.0355787	−	0.247455i
$17$	−0.214766	−	3.00282i	−0.0520885	−	0.728292i	−0.954650	−	0.297731i	$-0.903770\pi$
$17$	−0.214766	−	3.00282i	−0.0520885	−	0.728292i	0.902561	−	0.430561i	$-0.141684\pi$
$18$	−0.157514	+	0.724078i	−0.0371263	+	0.170667i
$19$	−1.88225	−	2.17223i	−0.431818	−	0.498344i	0.497583	−	0.867416i	$-0.334221\pi$
$19$	−1.88225	−	2.17223i	−0.431818	−	0.498344i	−0.929401	+	0.369072i	$0.879675\pi$
$20$	−0.0535372	+	2.23543i	−0.0119713	+	0.499857i
$21$	2.16040	+	0.986621i	0.471438	+	0.215298i
$22$	−2.39707	+	2.39707i	−0.511057	+	0.511057i
$23$	3.93443	+	2.74231i	0.820386	+	0.571810i
$23$	3.93443	+	2.74231i	0.820386	+	0.571810i
$24$		−	1.93417i		−	0.394811i
$25$	−0.473838	−	4.97750i	−0.0947675	−	0.995499i
$26$	6.55951	+	1.92605i	1.28643	+	0.377729i
$27$	0.311700	−	4.35813i	0.0599867	−	0.838723i
$28$	−1.19987	−	0.261015i	−0.226754	−	0.0493273i
$29$	−3.99884	−	3.46501i	−0.742565	−	0.643436i	0.199103	−	0.979979i	$-0.436197\pi$
$29$	−3.99884	−	3.46501i	−0.742565	−	0.643436i	−0.941668	+	0.336542i	$0.890743\pi$
$30$	0.512830	+	4.29442i	0.0936295	+	0.784051i
$31$	−5.92845	+	1.74075i	−1.06478	+	0.312648i	−0.766775	−	0.641916i	$-0.778140\pi$
$31$	−5.92845	+	1.74075i	−1.06478	+	0.312648i	−0.298007	+	0.954564i	$0.596322\pi$
$32$	0.212565	+	0.977147i	0.0375766	+	0.172737i
$33$	−3.92933	+	5.24896i	−0.684008	+	0.913727i
$34$	1.25060	+	2.73844i	0.214477	+	0.469639i
$35$	2.73326	+	0.261395i	0.462006	+	0.0441838i
$36$	−0.105457	−	0.733470i	−0.0175762	−	0.122245i
$37$	−6.54487	+	1.42375i	−1.07597	+	0.234063i	−0.715433	−	0.698682i	$-0.753770\pi$
$37$	−6.54487	+	1.42375i	−1.07597	+	0.234063i	−0.360538	+	0.932745i	$0.617407\pi$
$38$	2.52269	+	1.37749i	0.409234	+	0.223459i
$39$	13.0882	+	1.88180i	2.09580	+	0.301330i
$40$	−0.731040	−	2.11319i	−0.115588	−	0.334125i
$41$	−2.34072	+	1.50429i	−0.365559	+	0.234930i	−0.710505	−	0.703692i	$-0.751533\pi$
$41$	−2.34072	+	1.50429i	−0.365559	+	0.234930i	0.344946	+	0.938622i	$0.387897\pi$
$42$	−2.36897	−	0.169432i	−0.365541	−	0.0261440i
$43$	4.04137	+	7.40121i	0.616302	+	1.12867i	0.980345	+	0.197291i	$0.0632145\pi$
$43$	4.04137	+	7.40121i	0.616302	+	1.12867i	−0.364042	+	0.931382i	$0.618604\pi$
$44$	1.40824	−	3.08362i	0.212301	−	0.464873i
$45$	0.428620	+	1.60056i	0.0638948	+	0.238597i
$46$	−4.64470	−	1.19446i	−0.684824	−	0.176114i
$47$	5.79351	+	5.79351i	0.845070	+	0.845070i	0.989513	−	0.144443i	$-0.0461389\pi$
$47$	5.79351	+	5.79351i	0.845070	+	0.845070i	−0.144443	+	0.989513i	$0.546139\pi$
$48$	0.675923	+	1.81222i	0.0975611	+	0.261571i
$49$	1.54733	−	5.26972i	0.221047	−	0.752817i
$50$	2.18342	+	4.49808i	0.308782	+	0.636124i
$51$	3.14805	+	4.89846i	0.440815	+	0.685921i
$52$	−6.81902	+	0.487706i	−0.945628	+	0.0676326i
$53$	−8.41893	+	6.30233i	−1.15643	+	0.865692i	−0.992676	−	0.120809i	$-0.961451\pi$
$53$	−8.41893	+	6.30233i	−1.15643	+	0.865692i	−0.163754	+	0.986501i	$0.552360\pi$
$54$	1.23096	+	4.19228i	0.167513	+	0.570497i
$55$	−2.30911	+	7.21993i	−0.311361	+	0.973535i
$56$	1.21543	−	0.174753i	0.162419	−	0.0233523i
$57$	5.20882	+	1.94279i	0.689925	+	0.257329i
$58$	4.95761	+	1.84909i	0.650966	+	0.242798i
$59$	−7.66795	+	1.10249i	−0.998282	+	0.143531i	−0.622036	−	0.782988i	$-0.713694\pi$
$59$	−7.66795	+	1.10249i	−0.998282	+	0.143531i	−0.376246	+	0.926520i	$0.622785\pi$
$60$	−1.98124	−	3.84444i	−0.255777	−	0.496315i
$61$	0.704279	+	2.39855i	0.0901737	+	0.307103i	0.992213	−	0.124550i	$-0.0397486\pi$
$61$	0.704279	+	2.39855i	0.0901737	+	0.307103i	−0.902040	+	0.431653i	$0.857930\pi$
$62$	4.94633	−	3.70278i	0.628185	−	0.470253i
$63$	−0.907593	+	0.0649124i	−0.114346	+	0.00817819i
$64$	−0.540641	−	0.841254i	−0.0675801	−	0.105157i
$65$	15.0109	−	2.89086i	1.86187	−	0.358567i
$66$	1.84726	−	6.29117i	0.227381	−	0.774390i
$67$	−3.20331	−	8.58840i	−0.391346	−	1.04924i	−0.971978	−	0.235073i	$-0.924467\pi$
$67$	−3.20331	−	8.58840i	−0.391346	−	1.04924i	0.580631	−	0.814167i	$-0.302806\pi$
$68$	−2.12874	−	2.12874i	−0.258148	−	0.258148i
$69$	−9.22099	−	1.00827i	−1.11008	−	0.121381i
$70$	−2.65228	+	0.710264i	−0.317008	+	0.0848928i
$71$	−1.74986	+	3.83166i	−0.207670	+	0.454734i	−0.984593	−	0.174862i	$-0.944052\pi$
$71$	−1.74986	+	3.83166i	−0.207670	+	0.454734i	0.776923	+	0.629596i	$0.216779\pi$
$72$	0.355130	+	0.650371i	0.0418524	+	0.0766470i
$73$	0.769439	+	0.0550313i	0.0900560	+	0.00644093i	0.116294	−	0.993215i	$-0.462898\pi$
$73$	0.769439	+	0.0550313i	0.0900560	+	0.00644093i	−0.0262385	+	0.999656i	$0.508353\pi$
$74$	5.63467	−	3.62118i	0.655017	−	0.420954i
$75$	5.41826	+	8.01048i	0.625647	+	0.924970i
$76$	−2.84502	−	0.409052i	−0.326346	−	0.0469215i
$77$	−3.65346	−	1.99494i	−0.416351	−	0.227345i
$78$	−12.9206	+	2.81071i	−1.46297	+	0.318251i
$79$	−0.551491	−	3.83570i	−0.0620476	−	0.431550i	−0.997040	−	0.0768830i	$-0.975503\pi$
$79$	−0.551491	−	3.83570i	−0.0620476	−	0.431550i	0.934993	−	0.354667i	$-0.115406\pi$
$80$	1.42343	+	1.72448i	0.159145	+	0.192803i
$81$	4.43411	+	9.70936i	0.492679	+	1.07882i
$82$	1.66744	−	2.22744i	0.184138	−	0.245979i
$83$	−2.57122	−	11.8197i	−0.282228	−	1.29738i	−0.871879	−	0.489722i	$-0.837098\pi$
$83$	−2.57122	−	11.8197i	−0.282228	−	1.29738i	0.589651	−	0.807658i	$-0.299265\pi$
$84$	2.27882	−	0.669122i	0.248640	−	0.0730072i
$85$	5.29085	+	4.16201i	0.573873	+	0.451433i
$86$	−6.37301	−	5.52225i	−0.687220	−	0.595479i
$87$	10.0002	+	2.17542i	1.07214	+	0.233229i
$88$	−0.241837	+	3.38133i	−0.0257800	+	0.360451i
$89$	−10.7709	−	3.16262i	−1.14171	−	0.335237i	−0.344412	−	0.938819i	$-0.611922\pi$
$89$	−10.7709	−	3.16262i	−1.14171	−	0.335237i	−0.797302	+	0.603581i	$0.793740\pi$
$90$	−0.960932	−	1.34985i	−0.101291	−	0.142287i
$91$			8.39466i			0.880000i
$92$	4.76927	−	0.504008i	0.497231	−	0.0525465i
$93$	8.45044	−	8.45044i	0.876270	−	0.876270i
$94$	−7.45285	−	3.40360i	−0.768703	−	0.351055i
$95$	6.42523	+	0.153881i	0.659215	+	0.0157878i
$96$	−1.26661	−	1.46175i	−0.129273	−	0.149189i
$97$	1.36894	−	6.29292i	0.138995	−	0.638949i	−0.853948	−	0.520358i	$-0.825799\pi$
$97$	1.36894	−	6.29292i	0.138995	−	0.638949i	0.992943	−	0.118591i	$-0.0378378\pi$
$98$	0.391808	+	5.47819i	0.0395786	+	0.553381i
$99$	0.357496	−	2.48644i	0.0359297	−	0.249897i
$100$	−3.61767	−	3.45144i	−0.361767	−	0.345144i
$101$	−7.95674	−	5.11349i	−0.791725	−	0.508811i	0.0811808	−	0.996699i	$-0.474131\pi$
$101$	−7.95674	−	5.11349i	−0.791725	−	0.508811i	−0.872906	+	0.487889i	$0.837767\pi$
$102$	−4.66140	−	3.48948i	−0.461547	−	0.345510i
$103$	0.807867	−	2.16597i	0.0796015	−	0.213420i	−0.891053	−	0.453900i	$-0.850032\pi$
$103$	0.807867	−	2.16597i	0.0796015	−	0.213420i	0.970654	+	0.240480i	$0.0773050\pi$
$104$	6.21864	−	2.83996i	0.609788	−	0.278481i
$105$	−4.88223	+	2.08986i	−0.476457	+	0.203949i
$106$	5.68568	−	8.84709i	0.552242	−	0.859305i
$107$	−0.459167	+	0.840901i	−0.0443893	+	0.0812930i	−0.898932	−	0.438088i	$-0.855656\pi$
$107$	−0.459167	+	0.840901i	−0.0443893	+	0.0812930i	0.854543	+	0.519381i	$0.173838\pi$
$108$	−2.61840	−	3.49778i	−0.251956	−	0.336574i
$109$	2.27494	−	2.62542i	0.217900	−	0.251470i	−0.636267	−	0.771469i	$-0.719522\pi$
$109$	2.27494	−	2.62542i	0.217900	−	0.251470i	0.854167	+	0.519999i	$0.174068\pi$
$110$	−0.359583	−	7.57166i	−0.0342849	−	0.721929i
$111$	9.79070	−	8.48369i	0.929293	−	0.805237i
$112$	−1.07773	+	0.588484i	−0.101836	+	0.0556065i
$113$	7.31563	−	2.72859i	0.688197	−	0.256684i	0.0190545	−	0.999818i	$-0.493934\pi$
$113$	7.31563	−	2.72859i	0.688197	−	0.256684i	0.669142	+	0.743134i	$0.266662\pi$
$114$	−5.55933			−0.520679
$115$	−10.4556	+	2.38358i	−0.974985	+	0.222270i
$116$	−5.29122			−0.491277
$117$	−4.74648	+	1.77035i	−0.438812	+	0.163669i
$118$	6.79921	−	3.71265i	0.625918	−	0.341777i
$119$	−2.79376	+	2.42081i	−0.256104	+	0.221915i
$120$	3.19982	+	2.90968i	0.292102	+	0.265616i
$121$	0.322105	−	0.371729i	0.0292823	−	0.0337936i
$122$	−1.49808	−	2.00120i	−0.135630	−	0.181181i
$123$	2.57916	−	4.72337i	0.232555	−	0.425892i
$124$	−3.34048	+	5.19788i	−0.299984	+	0.466784i
$125$	8.94741	+	6.70402i	0.800281	+	0.599626i
$126$	0.827685	−	0.377991i	0.0737360	−	0.0336741i
$127$	2.12418	−	5.69516i	0.188491	−	0.505363i	−0.807989	−	0.589198i	$-0.799444\pi$
$127$	2.12418	−	5.69516i	0.188491	−	0.505363i	0.996480	+	0.0838343i	$0.0267167\pi$
$128$	0.800541	+	0.599278i	0.0707585	+	0.0529692i
$129$	−13.7211	−	8.81801i	−1.20807	−	0.776382i
$130$	−13.0542	+	7.95436i	−1.14493	+	0.697644i
$131$	−0.343618	+	2.38992i	−0.0300220	+	0.208808i	−0.999311	−	0.0371170i	$-0.988183\pi$
$131$	−0.343618	+	2.38992i	−0.0300220	+	0.208808i	0.969289	+	0.245925i	$0.0790917\pi$
$132$	0.467755	+	6.54006i	0.0407128	+	0.569239i
$133$	−0.750229	+	3.44875i	−0.0650531	+	0.299044i
$134$	6.00268	+	6.92746i	0.518552	+	0.598441i
$135$	6.74103	+	7.07184i	0.580175	+	0.608647i
$136$	2.73844	+	1.25060i	0.234820	+	0.107238i
$137$	−11.5177	+	11.5177i	−0.984027	+	0.984027i	−0.999874	−	0.0158474i	$-0.994955\pi$
$137$	−11.5177	+	11.5177i	−0.984027	+	0.984027i	0.0158474	+	0.999874i	$0.494955\pi$
$138$	8.99196	−	2.27771i	0.765446	−	0.193892i
$139$			2.36411i			0.200522i	0.994961	+	0.100261i	$0.0319677\pi$
$139$			2.36411i			0.200522i	−0.994961	+	0.100261i	$0.968032\pi$
$140$	2.23684	−	1.59236i	0.189048	−	0.134579i
$141$	−15.2052	−	4.46466i	−1.28051	−	0.375992i
$142$	0.300503	−	4.20158i	0.0252177	−	0.352589i
$143$	−22.6457	−	4.92626i	−1.89372	−	0.411955i
$144$	−0.560020	−	0.485260i	−0.0466683	−	0.0404383i
$145$	11.7481	−	1.40293i	0.975623	−	0.116507i
$146$	−0.740157	+	0.217330i	−0.0612558	+	0.0179863i
$147$	2.25804	+	10.3801i	0.186240	+	0.856133i
$148$	−4.01393	+	5.36198i	−0.329943	+	0.440752i
$149$	7.08181	+	15.5070i	0.580164	+	1.27038i	0.941206	+	0.337833i	$0.109694\pi$
$149$	7.08181	+	15.5070i	0.580164	+	1.27038i	−0.361042	+	0.932550i	$0.617579\pi$
$150$	−7.87601	−	5.61193i	−0.643074	−	0.458212i
$151$	−1.51690	−	10.5503i	−0.123443	−	0.858568i	−0.953608	−	0.301050i	$-0.902663\pi$
$151$	−1.51690	−	10.5503i	−0.123443	−	0.858568i	0.830165	−	0.557518i	$-0.188246\pi$
$152$	2.80859	−	0.610971i	0.227807	−	0.0495563i
$153$	−1.95794	−	1.06912i	−0.158290	−	0.0864329i
$154$	4.12027	+	0.592406i	0.332021	+	0.0477374i
$155$	6.03866	−	12.4265i	0.485037	−	0.998122i
$156$	11.1237	−	7.14880i	0.890613	−	0.572362i
$157$	−19.7227	−	1.41059i	−1.57404	−	0.112578i	−0.743193	−	0.669077i	$-0.766689\pi$
$157$	−19.7227	−	1.41059i	−1.57404	−	0.112578i	−0.830848	+	0.556500i	$0.812144\pi$
$158$	1.85716	+	3.40114i	0.147748	+	0.270580i
$159$	8.44987	−	18.5026i	0.670118	−	1.46735i
$160$	−1.93633	−	1.11831i	−0.153080	−	0.0884105i
$161$	−0.199523	−	5.88556i	−0.0157247	−	0.463847i
$162$	−7.54761	−	7.54761i	−0.592997	−	0.592997i
$163$	−4.29560	−	11.5169i	−0.336457	−	0.902077i	−0.989471	−	0.144731i	$-0.953768\pi$
$163$	−4.29560	−	11.5169i	−0.336457	−	0.902077i	0.653014	−	0.757346i	$-0.273504\pi$
$164$	−0.783897	+	2.66971i	−0.0612121	+	0.208469i
$165$	−2.77260	−	14.3968i	−0.215847	−	1.12079i
$166$	6.53966	+	10.1759i	0.507576	+	0.789804i
$167$	25.1992	−	1.80228i	1.94997	−	0.139465i	0.959932	−	0.280233i	$-0.0904118\pi$
$167$	25.1992	−	1.80228i	1.94997	−	0.139465i	0.990043	+	0.140768i	$0.0449572\pi$
$168$	−1.90131	+	1.42330i	−0.146689	+	0.109810i
$169$	9.50477	+	32.3703i	0.731136	+	2.49002i
$170$	−6.41173	−	2.05063i	−0.491757	−	0.157276i
$171$	−2.10819	+	0.303113i	−0.161218	+	0.0231796i
$172$	7.90102	+	2.94693i	0.602447	+	0.224701i
$173$	14.2724	+	5.32333i	1.08511	+	0.404725i	0.827467	−	0.561515i	$-0.189781\pi$
$173$	14.2724	+	5.32333i	1.08511	+	0.404725i	0.257644	+	0.966240i	$0.417054\pi$
$174$	−10.1299	+	1.45647i	−0.767949	+	0.110414i
$175$	−4.54424	+	4.12858i	−0.343512	+	0.312091i
$176$	−0.955064	−	3.25265i	−0.0719906	−	0.245178i
$177$	11.9950	−	8.97936i	0.901601	−	0.674930i
$178$	11.1970	−	0.800827i	0.839252	−	0.0600245i
$179$	8.47074	+	13.1807i	0.633133	+	0.985174i	0.998524	+	0.0543197i	$0.0172990\pi$
$179$	8.47074	+	13.1807i	0.633133	+	0.985174i	−0.365391	+	0.930854i	$0.619065\pi$
$180$	1.37207	+	0.928935i	0.102268	+	0.0692387i
$181$	0.978450	−	3.33229i	0.0727276	−	0.247687i	−0.915103	−	0.403220i	$-0.867891\pi$
$181$	0.978450	−	3.33229i	0.0727276	−	0.247687i	0.987831	+	0.155532i	$0.0497092\pi$
$182$	−2.93363	−	7.86538i	−0.217455	−	0.583021i
$183$	−3.41891	−	3.41891i	−0.252733	−	0.252733i
$184$	−4.29244	+	2.13892i	−0.316443	+	0.157683i
$185$	7.49041	−	12.9694i	0.550706	−	0.953531i
$186$	−4.96451	+	10.8708i	−0.364016	+	0.797083i
$187$	−4.89096	−	8.95713i	−0.357663	−	0.655010i
$188$	8.17239	+	0.584501i	0.596033	+	0.0426291i
$189$	−4.51345	+	2.90062i	−0.328305	+	0.210989i
$190$	−6.07389	+	2.10121i	−0.440646	+	0.152438i
$191$	5.15843	+	0.741671i	0.373251	+	0.0536654i	0.326388	−	0.945236i	$-0.394168\pi$
$191$	5.15843	+	0.741671i	0.373251	+	0.0536654i	0.0468632	+	0.998901i	$0.485078\pi$
$192$	1.69758	+	0.926949i	0.122512	+	0.0668968i
$193$	9.98077	−	2.17118i	0.718431	−	0.156285i	0.161535	−	0.986867i	$-0.448356\pi$
$193$	9.98077	−	2.17118i	0.718431	−	0.156285i	0.556897	+	0.830582i	$0.311992\pi$
$194$	0.916521	+	6.37454i	0.0658023	+	0.457665i
$195$	−22.8025	+	18.8218i	−1.63292	+	1.34786i
$196$	−2.28154	−	4.99587i	−0.162967	−	0.356848i
$197$	−7.65502	+	10.2259i	−0.545398	+	0.728566i	−0.985555	−	0.169355i	$-0.945832\pi$
$197$	−7.65502	+	10.2259i	−0.545398	+	0.728566i	0.440158	+	0.897921i	$0.354923\pi$
$198$	0.533966	+	2.45460i	0.0379473	+	0.174441i
$199$	−12.5975	+	3.69896i	−0.893013	+	0.262212i	−0.695874	−	0.718164i	$-0.744983\pi$
$199$	−12.5975	+	3.69896i	−0.893013	+	0.262212i	−0.197138	+	0.980376i	$0.563165\pi$
$200$	4.59573	+	1.96958i	0.324967	+	0.139271i
$201$	13.3989	+	11.6102i	0.945084	+	0.818920i
$202$	9.24205	+	2.01048i	0.650268	+	0.141457i
$203$	−0.463508	+	6.48069i	−0.0325319	+	0.454855i
$204$	5.58694	+	1.64047i	0.391164	+	0.114856i
$205$	1.03263	−	6.13538i	0.0721219	−	0.428513i
$206$			2.31173i			0.161066i
$207$	3.28572	−	1.35402i	0.228373	−	0.0941107i
$208$	−4.83409	+	4.83409i	−0.335184	+	0.335184i
$209$	−8.86317	−	4.04768i	−0.613078	−	0.279984i
$210$	3.84408	−	3.66426i	0.265267	−	0.252858i
$211$	−7.81515	−	9.01916i	−0.538017	−	0.620905i	0.420032	−	0.907509i	$-0.362019\pi$
$211$	−7.81515	−	9.01916i	−0.538017	−	0.620905i	−0.958049	+	0.286605i	$0.907473\pi$
$212$	−2.23545	+	10.2762i	−0.153532	+	0.705773i
$213$	−0.581224	−	8.12658i	−0.0398248	−	0.556824i
$214$	0.136351	−	0.948344i	0.00932078	−	0.0648275i
$215$	−18.3239	−	4.44815i	−1.24968	−	0.303361i
$216$	3.67566	+	2.36220i	0.250097	+	0.160728i
$217$	6.07375	+	4.54675i	0.412313	+	0.308654i
$218$	−1.21402	+	3.25490i	−0.0822235	+	0.220450i
$219$	−1.35720	+	0.619810i	−0.0917108	+	0.0418829i
$220$	2.98294	+	6.96860i	0.201109	+	0.469823i
$221$	−11.1270	+	17.3139i	−0.748480	+	1.16466i
$222$	−6.20865	+	11.3703i	−0.416697	+	0.763124i
$223$	15.4764	+	20.6740i	1.03637	+	1.38443i	0.920309	+	0.391191i	$0.127937\pi$
$223$	15.4764	+	20.6740i	1.03637	+	1.38443i	0.116064	+	0.993242i	$0.462972\pi$
$224$	0.804123	−	0.928008i	0.0537277	−	0.0620051i
$225$	−3.29270	−	1.69871i	−0.219513	−	0.113248i
$226$	−5.90083	+	5.11310i	−0.392518	+	0.340119i
$227$	−16.5910	+	9.05939i	−1.10119	+	0.601293i	−0.923810	−	0.382851i	$-0.874942\pi$
$227$	−16.5910	+	9.05939i	−1.10119	+	0.601293i	−0.177375	+	0.984143i	$0.556761\pi$
$228$	5.20882	−	1.94279i	0.344962	−	0.128664i
$229$	16.1141			1.06485			0.532425	−	0.846477i	$-0.321281\pi$
$229$	16.1141			1.06485			0.532425	+	0.846477i	$0.321281\pi$
$230$	8.96335	−	5.88714i	0.591026	−	0.388186i
$231$	8.05125			0.529734
$232$	4.95761	−	1.84909i	0.325483	−	0.121399i
$233$	−18.5433	+	10.1254i	−1.21481	+	0.663338i	−0.953348	−	0.301875i	$-0.902388\pi$
$233$	−18.5433	+	10.1254i	−1.21481	+	0.663338i	−0.261466	+	0.965213i	$0.584206\pi$
$234$	3.82854	−	3.31745i	0.250280	−	0.216868i
$235$	−18.3001	+	0.869082i	−1.19376	+	0.0566926i
$236$	−5.07308	+	5.85464i	−0.330229	+	0.381105i
$237$	4.49170	+	6.00021i	0.291767	+	0.389756i
$238$	1.77163	−	3.24450i	0.114838	−	0.210309i
$239$	6.52812	−	10.1580i	0.422269	−	0.657064i	−0.563316	−	0.826241i	$-0.690475\pi$
$239$	6.52812	−	10.1580i	0.422269	−	0.657064i	0.985586	+	0.169178i	$0.0541111\pi$
$240$	−4.01490	−	1.60800i	−0.259161	−	0.103796i
$241$	10.8647	−	4.96172i	0.699854	−	0.319613i	−0.0335197	−	0.999438i	$-0.510672\pi$
$241$	10.8647	−	4.96172i	0.699854	−	0.319613i	0.733374	+	0.679825i	$0.237944\pi$
$242$	−0.171890	+	0.460856i	−0.0110495	+	0.0296249i
$243$	−6.03401	−	4.51700i	−0.387082	−	0.289766i
$244$	2.10298	+	1.35150i	0.134629	+	0.0865210i
$245$	6.39030	+	10.4874i	0.408261	+	0.670013i
$246$	−0.765891	+	5.32689i	−0.0488314	+	0.339630i
$247$	1.40180	+	19.5997i	0.0891944	+	1.24710i
$248$	1.31338	−	6.03753i	0.0834000	−	0.383384i
$249$	15.3211	+	17.6815i	0.970935	+	1.12052i
$250$	−10.7261	−	3.15453i	−0.678377	−	0.199510i
$251$	−0.919601	−	0.419968i	−0.0580447	−	0.0265081i	0.386181	−	0.922423i	$-0.373794\pi$
$251$	−0.919601	−	0.419968i	−0.0580447	−	0.0265081i	−0.444226	+	0.895915i	$0.646521\pi$
$252$	−0.643405	+	0.643405i	−0.0405307	+	0.0405307i
$253$	15.9941	+	2.91560i	1.00554	+	0.183302i
$254$			6.07840i			0.381393i
$255$	−12.8396	−	2.16100i	−0.804048	−	0.135327i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	0.655430	−	9.16410i	0.0408846	−	0.571641i	−0.935182	−	0.354168i	$-0.884764\pi$
$257$	0.655430	−	9.16410i	0.0408846	−	0.571641i	0.976066	−	0.217473i	$-0.0697814\pi$
$258$	15.9375	+	3.46700i	0.992228	+	0.215846i
$259$	6.21574	+	5.38597i	0.386227	+	0.334668i
$260$	9.45137	−	12.0148i	0.586149	−	0.745127i
$261$	−3.76204	+	1.10463i	−0.232864	+	0.0683751i
$262$	−0.513237	−	2.35931i	−0.0317079	−	0.145759i
$263$	4.30463	−	5.75031i	0.265435	−	0.354579i	−0.647946	−	0.761687i	$-0.724372\pi$
$263$	4.30463	−	5.75031i	0.265435	−	0.354579i	0.913380	+	0.407107i	$0.133463\pi$
$264$	−2.72378	−	5.96425i	−0.167637	−	0.367074i
$265$	2.23870	−	23.4089i	0.137522	−	1.43800i
$266$	−0.502287	−	3.49348i	−0.0307972	−	0.214199i
$267$	21.2161	−	4.61527i	1.29840	−	0.282450i
$268$	−8.04510	−	4.39296i	−0.491433	−	0.268343i
$269$	7.47323	+	1.07449i	0.455651	+	0.0655127i	0.366319	−	0.930489i	$-0.380618\pi$
$269$	7.47323	+	1.07449i	0.455651	+	0.0655127i	0.0893315	+	0.996002i	$0.471527\pi$
$270$	−8.78736	−	4.27021i	−0.534782	−	0.259877i
$271$	−17.8817	+	11.4919i	−1.08624	+	0.698083i	−0.955990	−	0.293399i	$-0.905214\pi$
$271$	−17.8817	+	11.4919i	−1.08624	+	0.698083i	−0.130248	+	0.991481i	$0.541577\pi$
$272$	−3.00282	−	0.214766i	−0.182073	−	0.0130221i
$273$	−7.78142	−	14.2506i	−0.470953	−	0.862487i
$274$	6.76651	−	14.8166i	0.408780	−	0.895102i
$275$	−8.47066	−	14.6814i	−0.510800	−	0.885324i
$276$	−7.62904	+	5.27647i	−0.459214	+	0.317606i
$277$	−18.4280	−	18.4280i	−1.10723	−	1.10723i	−0.993513	−	0.113720i	$-0.963723\pi$
$277$	−18.4280	−	18.4280i	−1.10723	−	1.10723i	−0.113720	−	0.993513i	$-0.536277\pi$
$278$	−0.826173	−	2.21506i	−0.0495506	−	0.132850i
$279$	−1.28992	+	4.39306i	−0.0772254	+	0.263006i
$280$	−1.53933	+	2.27366i	−0.0919929	+	0.135877i
$281$	−14.0624	−	21.8815i	−0.838890	−	1.30534i	−0.950228	−	0.311556i	$-0.899150\pi$
$281$	−14.0624	−	21.8815i	−0.838890	−	1.30534i	0.111338	−	0.993783i	$-0.464486\pi$
$282$	15.8068	−	1.13052i	0.941280	−	0.0673217i
$283$	22.1937	−	16.6140i	1.31928	−	0.987601i	0.320089	−	0.947388i	$-0.396287\pi$
$283$	22.1937	−	16.6140i	1.31928	−	0.987601i	0.999191	−	0.0402131i	$-0.0128037\pi$
$284$	1.18675	+	4.04169i	0.0704205	+	0.239830i
$285$	−11.0500	+	5.69463i	−0.654544	+	0.337321i
$286$	22.9394	−	3.29819i	1.35643	−	0.195026i
$287$	3.20119	+	1.19398i	0.188961	+	0.0704786i
$288$	0.694292	+	0.258957i	0.0409115	+	0.0152592i
$289$	7.85613	−	1.12954i	0.462125	−	0.0664436i
$290$	−10.5171	+	5.41999i	−0.617583	+	0.318273i
$291$	3.50933	+	11.9517i	0.205720	+	0.700619i
$292$	0.617541	−	0.462285i	0.0361388	−	0.0270532i
$293$	−28.1843	+	2.01578i	−1.64654	+	0.117763i	−0.863549	−	0.504266i	$-0.831763\pi$
$293$	−28.1843	+	2.01578i	−1.64654	+	0.117763i	−0.782995	+	0.622029i	$0.786309\pi$
$294$	−5.74313	−	8.93649i	−0.334946	−	0.521187i
$295$	9.71140	−	14.3441i	0.565420	−	0.835146i
$296$	1.88703	−	6.42663i	0.109681	−	0.373540i
$297$	−5.17614	−	13.8778i	−0.300350	−	0.805270i
$298$	−12.0544	−	12.0544i	−0.698295	−	0.698295i
$299$	−10.2975	−	31.1273i	−0.595522	−	1.80014i
$300$	9.34060	+	2.50571i	0.539280	+	0.144667i
$301$	4.30153	−	9.41903i	0.247936	−	0.542904i
$302$	5.10820	+	9.35496i	0.293944	+	0.538318i
$303$	18.2471	+	1.30506i	1.04827	+	0.0749738i
$304$	−2.41799	+	1.55395i	−0.138681	+	0.0891251i
$305$	−5.02757	−	2.44314i	−0.287878	−	0.139894i
$306$	2.20811	+	0.317478i	0.126229	+	0.0181490i
$307$	17.9666	+	9.81051i	1.02541	+	0.559916i	0.901682	−	0.432401i	$-0.142333\pi$
$307$	17.9666	+	9.81051i	1.02541	+	0.559916i	0.123727	+	0.992316i	$0.460515\pi$
$308$	−4.06751	+	0.884833i	−0.231768	+	0.0504180i
$309$	0.636329	+	4.42577i	0.0361995	+	0.251773i
$310$	−1.31529	+	13.7533i	−0.0747037	+	0.781136i
$311$	−5.98405	−	13.1032i	−0.339324	−	0.743017i	0.660646	−	0.750698i	$-0.270282\pi$
$311$	−5.98405	−	13.1032i	−0.339324	−	0.743017i	−0.999971	+	0.00768068i	$0.997555\pi$
$312$	−7.92414	+	10.5854i	−0.448616	+	0.599281i
$313$	−5.25270	−	24.1463i	−0.296900	−	1.36483i	−0.847826	−	0.530274i	$-0.822089\pi$
$313$	−5.25270	−	24.1463i	−0.296900	−	1.36483i	0.550926	−	0.834554i	$-0.314275\pi$
$314$	18.9721	−	5.57071i	1.07066	−	0.314373i
$315$	1.25795	−	1.59914i	0.0708776	−	0.0901014i
$316$	−2.92864	−	2.53768i	−0.164749	−	0.142756i
$317$	14.5685	+	3.16918i	0.818248	+	0.177999i	0.602161	−	0.798375i	$-0.294307\pi$
$317$	14.5685	+	3.16918i	0.818248	+	0.177999i	0.216088	+	0.976374i	$0.430670\pi$
$318$	−1.45110	+	20.2890i	−0.0813734	+	1.13775i
$319$	−17.2105	−	5.05345i	−0.963602	−	0.282939i
$320$	2.20505	+	0.371127i	0.123266	+	0.0207466i
$321$		−	1.85312i		−	0.103431i
$322$	2.24374	+	5.44475i	0.125039	+	0.303424i
$323$	−6.11859	+	6.11859i	−0.340447	+	0.340447i
$324$	9.70936	+	4.43411i	0.539409	+	0.246340i
$325$	−17.7992	+	29.1824i	−0.987321	+	1.61875i
$326$	8.04952	+	9.28964i	0.445822	+	0.514506i
$327$	−1.42826	+	6.56562i	−0.0789832	+	0.363080i
$328$	−0.198495	−	2.77533i	−0.0109601	−	0.153242i
$329$	1.43179	−	9.95835i	0.0789374	−	0.549022i
$330$	7.62896	+	12.5202i	0.419961	+	0.689214i
$331$	17.3472	+	11.1484i	0.953487	+	0.612769i	0.922188	−	0.386741i	$-0.126399\pi$
$331$	17.3472	+	11.1484i	0.953487	+	0.612769i	0.0312988	+	0.999510i	$0.490036\pi$
$332$	−9.68345	−	7.24894i	−0.531448	−	0.397837i
$333$	−1.73448	+	4.65033i	−0.0950490	+	0.254836i
$334$	−22.9806	+	10.4949i	−1.25744	+	0.574254i
$335$	19.0272	+	7.62056i	1.03957	+	0.416356i
$336$	1.28404	−	1.99800i	0.0700499	−	0.109000i
$337$	3.18001	−	5.82375i	0.173226	−	0.317240i	−0.776614	−	0.629977i	$-0.783064\pi$
$337$	3.18001	−	5.82375i	0.173226	−	0.317240i	0.949840	+	0.312738i	$0.101246\pi$
$338$	−20.2177	−	27.0077i	−1.09970	−	1.46903i
$339$	−9.88961	+	11.4132i	−0.537130	+	0.619881i
$340$	6.72409	−	0.319331i	0.364665	−	0.0173182i
$341$	−15.8297	+	13.7165i	−0.857227	+	0.742791i
$342$	1.86935	−	1.02074i	0.101083	−	0.0551953i
$343$	−14.3724	+	5.36062i	−0.776035	+	0.289446i
$344$	−8.43271			−0.454661
$345$	15.5397	−	13.7381i	0.836628	−	0.739633i
$346$	−15.2328			−0.818922
$347$	9.31595	−	3.47467i	0.500106	−	0.186530i	−0.0867358	−	0.996231i	$-0.527644\pi$
$347$	9.31595	−	3.47467i	0.500106	−	0.186530i	0.586842	+	0.809701i	$0.300371\pi$
$348$	8.98227	−	4.90469i	0.481500	−	0.262919i
$349$	−5.68455	+	4.92569i	−0.304287	+	0.263666i	−0.793597	−	0.608444i	$-0.791794\pi$
$349$	−5.68455	+	4.92569i	−0.304287	+	0.263666i	0.489310	+	0.872110i	$0.337249\pi$
$350$	2.81493	−	5.45632i	0.150464	−	0.291653i
$351$	−19.5608	+	22.5744i	−1.04408	+	1.20493i
$352$	2.03153	+	2.71381i	0.108281	+	0.144646i
$353$	11.6693	−	21.3708i	0.621097	−	1.13745i	−0.357935	−	0.933746i	$-0.616519\pi$
$353$	11.6693	−	21.3708i	0.621097	−	1.13745i	0.979032	−	0.203707i	$-0.0652990\pi$
$354$	−8.10076	+	12.6050i	−0.430551	+	0.669950i
$355$	−3.70655	−	8.65908i	−0.196723	−	0.459576i
$356$	−10.2112	+	4.66329i	−0.541192	+	0.247154i
$357$	2.49867	−	6.69919i	0.132244	−	0.354559i
$358$	−12.5429	−	9.38946i	−0.662910	−	0.496248i
$359$	−13.4835	−	8.66533i	−0.711633	−	0.457339i	0.134084	−	0.990970i	$-0.457191\pi$
$359$	−13.4835	−	8.66533i	−0.711633	−	0.457339i	−0.845717	+	0.533631i	$0.820827\pi$
$360$	−1.61019	−	0.390875i	−0.0848645	−	0.0206009i
$361$	1.52826	−	10.6292i	0.0804345	−	0.559434i
$362$	0.247759	+	3.46413i	0.0130219	+	0.182070i
$363$	−0.202225	+	0.929615i	−0.0106141	+	0.0487921i
$364$	5.49734	+	6.34426i	0.288139	+	0.332530i
$365$	−1.24855	+	1.19014i	−0.0653521	+	0.0622950i
$366$	4.39813	+	2.00856i	0.229894	+	0.104989i
$367$	−13.8234	+	13.8234i	−0.721574	+	0.721574i	−0.968926	−	0.247352i	$-0.920440\pi$
$367$	−13.8234	+	13.8234i	−0.721574	+	0.721574i	0.247352	+	0.968926i	$0.420440\pi$
$368$	3.27432	−	3.50411i	0.170686	−	0.182665i
$369$			2.06181i			0.107333i
$370$	−2.48579	+	14.7693i	−0.129230	+	0.767821i
$371$	12.3905	+	3.63818i	0.643283	+	0.188885i
$372$	0.852555	−	11.9203i	0.0442029	−	0.618038i
$373$	28.6578	+	6.23412i	1.48384	+	0.322791i	0.880254	−	0.474504i	$-0.157372\pi$
$373$	28.6578	+	6.23412i	1.48384	+	0.322791i	0.603591	+	0.797294i	$0.293736\pi$
$374$	7.71278	+	6.68317i	0.398819	+	0.345578i
$375$	−21.4032	−	3.08682i	−1.10526	−	0.159403i
$376$	−7.86138	+	2.30831i	−0.405420	+	0.119042i
$377$	7.68914	+	35.3464i	0.396011	+	1.82043i
$378$	3.21522	−	4.29503i	0.165373	−	0.220912i
$379$	−1.51456	−	3.31643i	−0.0777979	−	0.170354i	0.866736	−	0.498767i	$-0.166214\pi$
$379$	−1.51456	−	3.31643i	−0.0777979	−	0.170354i	−0.944534	+	0.328413i	$0.893486\pi$
$380$	4.95663	−	4.09134i	0.254270	−	0.209881i
$381$	1.67315	+	11.6370i	0.0857179	+	0.596181i
$382$	−5.09238	+	1.10778i	−0.260549	+	0.0566789i
$383$	−22.4606	−	12.2644i	−1.14768	−	0.626682i	−0.211216	−	0.977440i	$-0.567742\pi$
$383$	−22.4606	−	12.2644i	−1.14768	−	0.626682i	−0.936466	+	0.350758i	$0.885924\pi$
$384$	−1.91448	−	0.275261i	−0.0976980	−	0.0140469i
$385$	8.79646	−	3.04306i	0.448309	−	0.155089i
$386$	−8.59273	+	5.52221i	−0.437358	+	0.281073i
$387$	6.23282	+	0.445780i	0.316832	+	0.0226603i
$388$	−3.08641	−	5.65233i	−0.156689	−	0.286954i
$389$	8.13773	−	17.8191i	0.412599	−	0.903466i	−0.583237	−	0.812302i	$-0.698214\pi$
$389$	8.13773	−	17.8191i	0.412599	−	0.903466i	0.995836	−	0.0911640i	$-0.0290587\pi$
$390$	14.7873	−	25.6038i	0.748783	−	1.29650i
$391$	7.38968	−	12.4034i	0.373712	−	0.627265i
$392$	3.88356	+	3.88356i	0.196150	+	0.196150i
$393$	−1.63201	−	4.37559i	−0.0823241	−	0.220719i
$394$	3.59878	−	12.2563i	0.181304	−	0.617464i
$395$	7.17529	+	4.85789i	0.361028	+	0.244427i
$396$	−1.35809	−	2.11324i	−0.0682468	−	0.106194i
$397$	−10.1587	+	0.726566i	−0.509851	+	0.0364653i	−0.323896	−	0.946093i	$-0.604993\pi$
$397$	−10.1587	+	0.726566i	−0.509851	+	0.0364653i	−0.185956	+	0.982558i	$0.559538\pi$
$398$	10.5106	−	7.86811i	0.526847	−	0.394393i
$399$	−1.92324	−	6.54995i	−0.0962824	−	0.327908i
$400$	−4.99427	−	0.239357i	−0.249713	−	0.0119679i
$401$	4.96565	−	0.713952i	0.247973	−	0.0356531i	−0.0172077	−	0.999852i	$-0.505478\pi$
$401$	4.96565	−	0.713952i	0.247973	−	0.0356531i	0.265180	+	0.964199i	$0.414569\pi$
$402$	−16.6114	−	6.19574i	−0.828502	−	0.309015i
$403$	39.5773	+	14.7616i	1.97148	+	0.735325i
$404$	−9.36192	+	1.34604i	−0.465773	+	0.0669681i
$405$	−22.7333	−	7.27067i	−1.12963	−	0.361283i
$406$	−1.83049	−	6.23406i	−0.0908455	−	0.309391i
$407$	−18.1769	+	13.6071i	−0.900997	+	0.674478i
$408$	−5.80797	+	0.415394i	−0.287538	+	0.0205651i
$409$	15.0034	+	23.3458i	0.741872	+	1.15437i	0.982951	+	0.183869i	$0.0588623\pi$
$409$	15.0034	+	23.3458i	0.741872	+	1.15437i	−0.241079	+	0.970505i	$0.577501\pi$
$410$	1.17657	+	6.10941i	0.0581068	+	0.301722i
$411$	8.87593	−	30.2286i	0.437817	−	1.49107i
$412$	−0.807867	−	2.16597i	−0.0398007	−	0.106710i
$413$	6.72638	+	6.72638i	0.330983	+	0.330983i
$414$	−2.60537	+	2.41689i	−0.128047	+	0.118783i
$415$	23.4221	+	13.5273i	1.14975	+	0.664028i
$416$	2.83996	−	6.21864i	0.139240	−	0.304894i
$417$	−2.19141	−	4.01327i	−0.107314	−	0.196531i
$418$	9.71886	+	0.695107i	0.475365	+	0.0339988i
$419$	−9.79338	+	6.29382i	−0.478438	+	0.307473i	−0.757541	−	0.652788i	$-0.773599\pi$
$419$	−9.79338	+	6.29382i	−0.478438	+	0.307473i	0.279103	+	0.960261i	$0.409963\pi$
$420$	−2.32118	+	4.77659i	−0.113262	+	0.233074i
$421$	−15.7117	−	2.25899i	−0.765739	−	0.110097i	−0.251632	−	0.967823i	$-0.580967\pi$
$421$	−15.7117	−	2.25899i	−0.765739	−	0.110097i	−0.514107	+	0.857726i	$0.671876\pi$
$422$	10.4743	+	5.71938i	0.509880	+	0.278415i
$423$	5.93256	−	1.29055i	0.288451	−	0.0627487i
$424$	−1.49666	−	10.4095i	−0.0726843	−	0.505530i
$425$	−14.8448	+	2.49185i	−0.720078	+	0.120872i
$426$	3.38453	+	7.41108i	0.163981	+	0.359068i
$427$	1.83954	−	2.45734i	0.0890216	−	0.118919i
$428$	0.203658	+	0.936201i	0.00984418	+	0.0452530i
$429$	43.0092	−	12.6286i	2.07650	−	0.609717i
$430$	18.7231	−	2.23587i	0.902907	−	0.107823i
$431$	−11.3614	−	9.84467i	−0.547257	−	0.474201i	0.336802	−	0.941575i	$-0.390655\pi$
$431$	−11.3614	−	9.84467i	−0.547257	−	0.474201i	−0.884060	+	0.467374i	$0.845200\pi$
$432$	−4.26941	−	0.928754i	−0.205412	−	0.0446847i
$433$	0.139823	−	1.95499i	0.00671949	−	0.0939507i	−0.992986	−	0.118235i	$-0.962276\pi$
$433$	0.139823	−	1.95499i	0.00671949	−	0.0939507i	0.999705	+	0.0242847i	$0.00773081\pi$
$434$	−7.27973	−	2.13752i	−0.349438	−	0.102604i
$435$	−18.6428	+	13.2714i	−0.893855	+	0.636316i
$436$		−	3.47393i		−	0.166371i
$437$	−1.44866	−	13.7082i	−0.0692987	−	0.655752i
$438$	1.05502	−	1.05502i	0.0504109	−	0.0504109i
$439$	20.0871	+	9.17346i	0.958704	+	0.437825i	0.832406	−	0.554167i	$-0.186963\pi$
$439$	20.0871	+	9.17346i	0.958704	+	0.437825i	0.126298	+	0.991992i	$0.459690\pi$
$440$	−5.23014	−	5.48680i	−0.249337	−	0.261573i
$441$	−2.66514	−	3.07574i	−0.126911	−	0.146464i
$442$	4.37482	−	20.1107i	0.208089	−	0.956569i
$443$	0.872890	+	12.2046i	0.0414722	+	0.579858i	0.975122	+	0.221670i	$0.0711507\pi$
$443$	0.872890	+	12.2046i	0.0414722	+	0.579858i	−0.933650	+	0.358188i	$0.883395\pi$
$444$	1.84368	−	12.8231i	0.0874973	−	0.608557i
$445$	21.4354	−	13.0613i	1.01613	−	0.619165i
$446$	−21.7254	−	13.9621i	−1.02873	−	0.661123i
$447$	−26.3961	−	19.7599i	−1.24849	−	0.934611i
$448$	−0.429118	+	1.15051i	−0.0202739	+	0.0543564i
$449$	−29.4535	+	13.4510i	−1.39000	+	0.634790i	−0.963009	−	0.269468i	$-0.913152\pi$
$449$	−29.4535	+	13.4510i	−1.39000	+	0.634790i	−0.426987	+	0.904258i	$0.640425\pi$
$450$	3.67873	+	0.440928i	0.173417	+	0.0207855i
$451$	−5.09948	+	7.93495i	−0.240125	+	0.373642i
$452$	3.74194	−	6.85285i	0.176006	−	0.322331i
$453$	12.3546	+	16.5038i	0.580470	+	0.775417i
$454$	12.3790	−	14.2862i	0.580977	−	0.670483i
$455$	−13.8878	−	12.6285i	−0.651071	−	0.592035i
$456$	−4.20146	+	3.64059i	−0.196752	+	0.170486i
$457$	16.8155	−	9.18193i	0.786594	−	0.429513i	−0.0351413	−	0.999382i	$-0.511188\pi$
$457$	16.8155	−	9.18193i	0.786594	−	0.429513i	0.821735	+	0.569870i	$0.193006\pi$
$458$	−15.0981	+	5.63130i	−0.705488	+	0.263133i
$459$	−13.1537			−0.613960
$460$	−6.34086	+	8.64832i	−0.295644	+	0.403230i
$461$	3.60200			0.167762			0.0838809	−	0.996476i	$-0.473268\pi$
$461$	3.60200			0.167762			0.0838809	+	0.996476i	$0.473268\pi$
$462$	−7.54362	+	2.81362i	−0.350961	+	0.130902i
$463$	−32.5481	+	17.7726i	−1.51264	+	0.825963i	−0.999477	−	0.0323300i	$-0.989707\pi$
$463$	−32.5481	+	17.7726i	−1.51264	+	0.825963i	−0.513160	+	0.858293i	$0.671525\pi$
$464$	−3.99884	+	3.46501i	−0.185641	+	0.160859i
$465$	1.26765	+	26.6925i	0.0587857	+	1.23784i
$466$	13.8357	−	15.9672i	0.640926	−	0.739668i
$467$	9.73712	+	13.0073i	0.450580	+	0.601905i	0.967108	−	0.254366i	$-0.0818667\pi$
$467$	9.73712	+	13.0073i	0.450580	+	0.601905i	−0.516528	+	0.856270i	$0.672776\pi$
$468$	−2.42782	+	4.44622i	−0.112226	+	0.205527i
$469$	−6.08525	+	9.46883i	−0.280991	+	0.437230i
$470$	16.8425	−	7.20950i	0.776888	−	0.332550i
$471$	34.7884	−	15.8873i	1.60296	−	0.732049i
$472$	2.70723	−	7.25837i	0.124610	−	0.334093i
$473$	22.8847	+	17.1313i	1.05224	+	0.787698i
$474$	−6.30536	−	4.05221i	−0.289615	−	0.186124i
$475$	−9.92039	+	10.3982i	−0.455179	+	0.477101i
$476$	−0.526092	+	3.65905i	−0.0241134	+	0.167712i
$477$	0.555939	+	7.77304i	0.0254547	+	0.355903i
$478$	−2.56668	+	11.7988i	−0.117397	+	0.539667i
$479$	−7.69236	−	8.87745i	−0.351473	−	0.405621i	0.552292	−	0.833651i	$-0.313753\pi$
$479$	−7.69236	−	8.87745i	−0.351473	−	0.405621i	−0.903765	+	0.428030i	$0.859208\pi$
$480$	4.32370	+	0.103550i	0.197349	+	0.00472639i
$481$	41.6521	+	19.0219i	1.89917	+	0.867323i
$482$	−8.44570	+	8.44570i	−0.384691	+	0.384691i
$483$	5.79432	+	9.80627i	0.263651	+	0.446201i
$484$		−	0.491868i		−	0.0223576i
$485$	8.35140	+	11.7315i	0.379218	+	0.532700i
$486$	7.23210	+	2.12353i	0.328055	+	0.0963255i
$487$	−1.16504	+	16.2893i	−0.0527929	+	0.738141i	0.900263	+	0.435346i	$0.143374\pi$
$487$	−1.16504	+	16.2893i	−0.0527929	+	0.738141i	−0.953056	+	0.302794i	$0.902080\pi$
$488$	−2.44269	−	0.531374i	−0.110575	−	0.0240542i
$489$	17.9677	+	15.5691i	0.812530	+	0.704061i
$490$	−9.65234	−	7.59295i	−0.436048	−	0.343015i
$491$	37.4107	−	10.9848i	1.68832	−	0.495736i	0.710241	−	0.703959i	$-0.248586\pi$
$491$	37.4107	−	10.9848i	1.68832	−	0.495736i	0.978081	+	0.208223i	$0.0667679\pi$
$492$	−1.14396	−	5.25868i	−0.0515735	−	0.237079i
$493$	−9.54601	+	12.7520i	−0.429931	+	0.574320i
$494$	−8.16282	−	17.8741i	−0.367262	−	0.804193i
$495$	3.57567	+	4.33191i	0.160715	+	0.194705i
$496$	0.879326	+	6.11585i	0.0394829	+	0.274610i
$497$	5.05422	−	1.09948i	0.226713	−	0.0493184i
$498$	−20.5342	−	11.2125i	−0.920157	−	0.502444i
$499$	17.6253	+	2.53413i	0.789016	+	0.113443i	0.525031	−	0.851083i	$-0.324054\pi$
$499$	17.6253	+	2.53413i	0.789016	+	0.113443i	0.263985	+	0.964527i	$0.414963\pi$
$500$	11.1522	−	0.792748i	0.498742	−	0.0354528i
$501$	−41.1071	+	26.4179i	−1.83653	+	1.18027i
$502$	1.00838	+	0.0721210i	0.0450063	+	0.00321892i
$503$	3.40276	+	6.23170i	0.151722	+	0.277858i	0.942475	−	0.334278i	$-0.108492\pi$
$503$	3.40276	+	6.23170i	0.151722	+	0.277858i	−0.790753	+	0.612136i	$0.790311\pi$
$504$	0.377991	−	0.827685i	0.0168371	−	0.0368680i
$505$	20.4293	−	5.47085i	0.909093	−	0.243449i
$506$	−16.0046	+	2.85761i	−0.711491	+	0.127036i
$507$	−46.1407	−	46.1407i	−2.04918	−	2.04918i
$508$	−2.12418	−	5.69516i	−0.0942454	−	0.252682i
$509$	3.19265	−	10.8732i	0.141512	−	0.481944i	−0.857985	−	0.513675i	$-0.828284\pi$
$509$	3.19265	−	10.8732i	0.141512	−	0.481944i	0.999496	+	0.0317306i	$0.0101019\pi$
$510$	12.7853	−	2.46224i	0.566141	−	0.109030i
$511$	−0.512111	−	0.796861i	−0.0226545	−	0.0352511i
$512$	0.997452	−	0.0713392i	0.0440816	−	0.00315278i
$513$	−10.0536	+	7.52601i	−0.443876	+	0.332281i
$514$	2.58842	+	8.81535i	0.114170	+	0.388829i
$515$	2.36799	+	4.59490i	0.104346	+	0.202475i
$516$	−16.1443	+	2.32120i	−0.710712	+	0.102185i
$517$	26.0237	+	9.70632i	1.14452	+	0.426884i
$518$	−7.70604	−	2.87420i	−0.338584	−	0.126285i
$519$	−29.1630	+	4.19301i	−1.28011	+	0.184053i
$520$	−4.65671	+	14.5602i	−0.204210	+	0.638507i
$521$	2.48744	+	8.47144i	0.108977	+	0.371141i	0.995865	−	0.0908429i	$-0.0289561\pi$
$521$	2.48744	+	8.47144i	0.108977	+	0.371141i	−0.886889	+	0.461984i	$0.847138\pi$
$522$	3.13881	−	2.34968i	0.137382	−	0.102843i
$523$	−23.7469	+	1.69841i	−1.03838	+	0.0742664i	−0.580103	−	0.814543i	$-0.696988\pi$
$523$	−23.7469	+	1.69841i	−1.03838	+	0.0742664i	−0.458277	+	0.888809i	$0.651533\pi$
$524$	1.30537	+	2.03120i	0.0570255	+	0.0887334i
$525$	3.88723	−	11.2209i	0.169652	−	0.489719i
$526$	−2.02369	+	6.89206i	−0.0882372	+	0.300508i
$527$	6.50040	+	17.4283i	0.283162	+	0.759187i
$528$	4.63634	+	4.63634i	0.201771	+	0.201771i
$529$	7.95951	+	21.5788i	0.346066	+	0.938210i
$530$	6.08303	+	22.7153i	0.264230	+	0.986691i
$531$	−2.38468	+	5.22172i	−0.103486	+	0.226604i
$532$	1.69146	+	3.09769i	0.0733343	+	0.134302i
$533$	18.9733	+	1.35700i	0.821827	+	0.0587782i
$534$	−18.2655	+	11.7385i	−0.790426	+	0.507976i
$535$	−0.700407	−	2.02464i	−0.0302812	−	0.0875329i
$536$	9.07304	+	1.30451i	0.391896	+	0.0563461i
$537$	−26.5976	−	14.5234i	−1.14777	−	0.626731i
$538$	−7.37753	+	1.60488i	−0.318068	+	0.0691915i
$539$	−2.64966	−	18.4288i	−0.114129	−	0.793786i
$540$	9.72560	+	0.930104i	0.418523	+	0.0400253i
$541$	−10.9010	−	23.8698i	−0.468669	−	1.02624i	−0.985425	−	0.170109i	$-0.945588\pi$
$541$	−10.9010	−	23.8698i	−0.468669	−	1.02624i	0.516756	−	0.856133i	$-0.327139\pi$
$542$	12.7383	−	17.0164i	0.547156	−	0.730915i
$543$	1.42787	+	6.56381i	0.0612757	+	0.281680i
$544$	2.88855	−	0.848154i	0.123846	−	0.0363643i
$545$	0.921086	+	7.71315i	0.0394550	+	0.330395i
$546$	12.2709	+	10.6328i	0.525145	+	0.455041i
$547$	−11.5243	−	2.50695i	−0.492743	−	0.107190i	−0.0406736	−	0.999172i	$-0.512950\pi$
$547$	−11.5243	−	2.50695i	−0.492743	−	0.107190i	−0.452069	+	0.891983i	$0.649314\pi$
$548$	−1.16201	+	16.2470i	−0.0496387	+	0.694039i
$549$	1.77736	+	0.521880i	0.0758558	+	0.0222733i
$550$	13.0672	+	10.7956i	0.557188	+	0.460325i
$551$			15.2084i			0.647900i
$552$	5.30409	−	7.60986i	0.225757	−	0.323897i
$553$	−3.36470	+	3.36470i	−0.143082	+	0.143082i
$554$	23.7061	+	10.8262i	1.00717	+	0.459961i
$555$	−0.693572	+	28.9599i	−0.0294405	+	1.22928i
$556$	1.54817	+	1.78668i	0.0656569	+	0.0757721i
$557$	6.63181	−	30.4859i	0.280999	−	1.29173i	−0.592764	−	0.805376i	$-0.701963\pi$
$557$	6.63181	−	30.4859i	0.280999	−	1.29173i	0.873762	−	0.486353i	$-0.161673\pi$
$558$	−0.326628	−	4.56686i	−0.0138273	−	0.193330i
$559$	8.20440	−	57.0629i	0.347009	−	2.41350i
$560$	0.647718	−	2.66824i	0.0273711	−	0.112754i
$561$	16.6056	+	10.6718i	0.701089	+	0.450563i
$562$	20.8225	+	15.5875i	0.878344	+	0.657520i
$563$	−5.69451	+	15.2676i	−0.239995	+	0.643451i	−0.999979	−	0.00649040i	$-0.997934\pi$
$563$	−5.69451	+	15.2676i	−0.239995	+	0.643451i	0.759984	+	0.649942i	$0.225207\pi$
$564$	−14.4151	+	6.58315i	−0.606985	+	0.277201i
$565$	−6.49122	+	16.2075i	−0.273088	+	0.681854i
$566$	−14.9884	+	23.3224i	−0.630010	+	0.980314i
$567$	6.28144	−	11.5036i	0.263796	−	0.483106i
$568$	−2.52435	−	3.37213i	−0.105919	−	0.141492i
$569$	11.4435	−	13.2065i	0.479736	−	0.553645i	−0.463358	−	0.886171i	$-0.653356\pi$
$569$	11.4435	−	13.2065i	0.479736	−	0.553645i	0.943094	+	0.332526i	$0.107901\pi$
$570$	8.36321	−	9.19716i	0.350296	−	0.385227i
$571$	17.9309	−	15.5372i	0.750384	−	0.650211i	−0.193270	−	0.981146i	$-0.561909\pi$
$571$	17.9309	−	15.5372i	0.750384	−	0.650211i	0.943654	+	0.330935i	$0.107364\pi$
$572$	−20.3405	+	11.1067i	−0.850477	+	0.464396i
$573$	−9.44435	+	3.52256i	−0.394543	+	0.147157i
$574$	−3.41661			−0.142607
$575$	11.7855	−	20.8830i	0.491491	−	0.870883i
$576$	−0.741013			−0.0308755
$577$	−11.6423	+	4.34235i	−0.484674	+	0.180774i	−0.579910	−	0.814681i	$-0.696912\pi$
$577$	−11.6423	+	4.34235i	−0.484674	+	0.180774i	0.0952356	+	0.995455i	$0.469640\pi$
$578$	−6.96607	+	3.80376i	−0.289750	+	0.158216i
$579$	−14.9306	+	12.9374i	−0.620494	+	0.537661i
$580$	7.95987	−	8.75360i	0.330515	−	0.363473i
$581$	−9.72678	+	11.2253i	−0.403535	+	0.465704i
$582$	−7.46474	−	9.97173i	−0.309423	−	0.413341i
$583$	−17.0856	+	31.2899i	−0.707613	+	1.29590i
$584$	−0.417053	+	0.648947i	−0.0172578	+	0.0268536i
$585$	4.21159	−	10.5156i	0.174128	−	0.434768i
$586$	25.7028	−	11.7381i	1.06177	−	0.484896i
$587$	−1.93614	+	5.19098i	−0.0799129	+	0.214255i	−0.970762	−	0.240045i	$-0.922838\pi$
$587$	−1.93614	+	5.19098i	−0.0799129	+	0.214255i	0.890849	+	0.454300i	$0.150110\pi$
$588$	8.50401	+	6.36602i	0.350699	+	0.262530i
$589$	14.9401	+	9.60145i	0.615598	+	0.395621i
$590$	−4.08635	+	16.8335i	−0.168232	+	0.693024i
$591$	3.51611	−	24.4551i	0.144634	−	1.00595i
$592$	0.477826	+	6.68088i	0.0196385	+	0.274582i
$593$	−6.50107	+	29.8849i	−0.266967	+	1.22723i	0.626973	+	0.779041i	$0.284294\pi$
$593$	−6.50107	+	29.8849i	−0.266967	+	1.22723i	−0.893940	+	0.448186i	$0.852070\pi$
$594$	9.69957	+	11.1939i	0.397978	+	0.459291i
$595$	0.197910	−	8.26365i	0.00811351	−	0.338777i
$596$	15.5070	+	7.08181i	0.635191	+	0.290082i
$597$	17.9565	−	17.9565i	0.734911	−	0.734911i
$598$	20.5261	+	25.5661i	0.839376	+	1.04548i
$599$			7.13312i			0.291451i	0.989325	+	0.145726i	$0.0465517\pi$
$599$			7.13312i			0.291451i	−0.989325	+	0.145726i	$0.953448\pi$
$600$	−9.62732	+	0.916482i	−0.393034	+	0.0374152i
$601$	17.7450	+	5.21042i	0.723836	+	0.212537i	0.622840	−	0.782350i	$-0.285979\pi$
$601$	17.7450	+	5.21042i	0.723836	+	0.212537i	0.100996	+	0.994887i	$0.467797\pi$
$602$	−0.738701	+	10.3284i	−0.0301072	+	0.420954i
$603$	−6.63715	−	1.44382i	−0.270286	−	0.0587970i
$604$	−8.05535	−	6.98000i	−0.327767	−	0.284012i
$605$	0.130415	+	1.09209i	0.00530212	+	0.0443998i
$606$	−17.5527	+	5.15395i	−0.713031	+	0.209365i
$607$	−8.21220	−	37.7509i	−0.333323	−	1.53226i	−0.773177	−	0.634191i	$-0.781333\pi$
$607$	−8.21220	−	37.7509i	−0.333323	−	1.53226i	0.439854	−	0.898069i	$-0.355030\pi$
$608$	1.72249	−	2.30097i	0.0698561	−	0.0933168i
$609$	−5.22043	−	11.4311i	−0.211542	−	0.463213i
$610$	5.56437	+	0.532146i	0.225295	+	0.0215460i
$611$	−7.97144	−	55.4426i	−0.322490	−	2.24297i
$612$	−2.17983	+	0.474194i	−0.0881146	+	0.0191682i
$613$	−30.4571	−	16.6308i	−1.23015	−	0.671713i	−0.273198	−	0.961958i	$-0.588082\pi$
$613$	−30.4571	−	16.6308i	−1.23015	−	0.671713i	−0.956953	+	0.290245i	$0.906263\pi$
$614$	−20.2622	−	2.91327i	−0.817717	−	0.117570i
$615$	3.93421	+	11.3725i	0.158643	+	0.458583i
$616$	3.50184	−	2.25049i	0.141093	−	0.0906750i
$617$	−34.6946	−	2.48141i	−1.39675	−	0.0998978i	−0.647442	−	0.762115i	$-0.724161\pi$
$617$	−34.6946	−	2.48141i	−1.39675	−	0.0998978i	−0.749312	+	0.662217i	$0.769616\pi$
$618$	−2.14286	−	3.92435i	−0.0861983	−	0.157860i
$619$	−7.95624	+	17.4217i	−0.319788	+	0.700238i	−0.999446	−	0.0332912i	$-0.989401\pi$
$619$	−7.95624	+	17.4217i	−0.319788	+	0.700238i	0.679658	+	0.733530i	$0.262128\pi$
$620$	−3.57393	−	13.3458i	−0.143532	−	0.535981i
$621$	13.1777	−	16.2920i	0.528803	−	0.653775i
$622$	10.1859	+	10.1859i	0.408416	+	0.408416i
$623$	4.81711	+	12.9152i	0.192994	+	0.517436i
$624$	3.72530	−	12.6872i	0.149131	−	0.507895i
$625$	−24.5510	+	4.71705i	−0.982038	+	0.188682i
$626$	13.3598	+	20.7882i	0.533964	+	0.830864i
$627$	18.7979	−	1.34445i	0.750717	−	0.0536923i
$628$	−15.8291	+	11.8495i	−0.631652	+	0.472848i
$629$	5.68089	+	19.3473i	0.226512	+	0.771429i
$630$	−0.619796	+	1.93792i	−0.0246933	+	0.0772087i
$631$	−28.4882	+	4.09599i	−1.13410	+	0.163059i	−0.683696	−	0.729767i	$-0.739629\pi$
$631$	−28.4882	+	4.09599i	−1.13410	+	0.163059i	−0.450403	+	0.892825i	$0.648720\pi$
$632$	3.63082	+	1.35423i	0.144426	+	0.0538682i
$633$	21.6271	+	8.06650i	0.859601	+	0.320615i
$634$	−14.7575	+	2.12180i	−0.586094	+	0.0842676i
$635$	6.22633	+	12.0817i	0.247085	+	0.479448i
$636$	−5.73066	−	19.5169i	−0.227236	−	0.773893i
$637$	−30.0579	+	22.5011i	−1.19094	+	0.891525i
$638$	17.8913	−	1.27961i	0.708325	−	0.0506604i
$639$	1.68755	+	2.62587i	0.0667583	+	0.103878i
$640$	−2.19572	+	0.422860i	−0.0867935	+	0.0167150i
$641$	7.58857	−	25.8443i	0.299731	−	1.02079i	−0.662615	−	0.748960i	$-0.730554\pi$
$641$	7.58857	−	25.8443i	0.299731	−	1.02079i	0.962346	−	0.271828i	$-0.0876283\pi$
$642$	0.647599	+	1.73628i	0.0255587	+	0.0685255i
$643$	−8.89632	−	8.89632i	−0.350837	−	0.350837i	0.509584	−	0.860421i	$-0.329799\pi$
$643$	−8.89632	−	8.89632i	−0.350837	−	0.350837i	−0.860421	+	0.509584i	$0.829799\pi$
$644$	−4.00501	−	4.31735i	−0.157820	−	0.170128i
$645$	35.2296	−	9.43426i	1.38716	−	0.371474i
$646$	3.59458	−	7.87103i	0.141427	−	0.309682i
$647$	10.3165	+	18.8933i	0.405585	+	0.742774i	0.998024	−	0.0628418i	$-0.0200163\pi$
$647$	10.3165	+	18.8933i	0.405585	+	0.742774i	−0.592438	+	0.805616i	$0.701835\pi$
$648$	−10.6467	−	0.761470i	−0.418244	−	0.0299134i
$649$	−22.0925	+	14.1980i	−0.867206	+	0.557320i
$650$	6.47875	−	33.5626i	0.254117	−	1.31643i
$651$	−14.5253	−	2.08842i	−0.569291	−	0.0818517i
$652$	−10.7884	−	5.89091i	−0.422506	−	0.230706i
$653$	6.31659	−	1.37409i	0.247187	−	0.0537723i	−0.0872645	−	0.996185i	$-0.527813\pi$
$653$	6.31659	−	1.37409i	0.247187	−	0.0537723i	0.334452	+	0.942413i	$0.391449\pi$
$654$	−0.956239	−	6.65079i	−0.0373919	−	0.260066i
$655$	−3.43687	−	4.16375i	−0.134289	−	0.162691i
$656$	1.15586	+	2.53097i	0.0451287	+	0.0988180i
$657$	0.342559	−	0.457606i	0.0133645	−	0.0178529i
$658$	2.13857	+	9.83083i	0.0833700	+	0.383246i
$659$	11.2516	−	3.30376i	0.438298	−	0.128696i	−0.0551364	−	0.998479i	$-0.517559\pi$
$659$	11.2516	−	3.30376i	0.438298	−	0.128696i	0.493435	+	0.869783i	$0.335741\pi$
$660$	−11.5233	−	9.06474i	−0.448544	−	0.352844i
$661$	−18.8706	−	16.3515i	−0.733982	−	0.635999i	0.205476	−	0.978662i	$-0.434126\pi$
$661$	−18.8706	−	16.3515i	−0.733982	−	0.635999i	−0.939458	+	0.342663i	$0.888671\pi$
$662$	−20.1494	−	4.38323i	−0.783128	−	0.170359i
$663$	2.83982	−	39.7058i	0.110289	−	1.54205i
$664$	11.6062	+	3.40787i	0.450406	+	0.132251i
$665$	−4.57687	−	6.42929i	−0.177484	−	0.249317i
$666$		−	4.96326i		−	0.192322i
$667$	−6.23103	−	24.5989i	−0.241266	−	0.952473i
$668$	17.8641	−	17.8641i	0.691181	−	0.691181i
$669$	−45.4361	−	20.7500i	−1.75666	−	0.802240i
$670$	−20.4907	−	0.490740i	−0.791624	−	0.0189589i
$671$	5.54948	+	6.40444i	0.214235	+	0.247241i
$672$	−0.504848	+	2.32075i	−0.0194749	+	0.0895248i
$673$	−3.42165	−	47.8409i	−0.131895	−	1.84413i	−0.446350	−	0.894859i	$-0.647276\pi$
$673$	−3.42165	−	47.8409i	−0.131895	−	1.84413i	0.314455	−	0.949272i	$-0.398178\pi$
$674$	−0.944315	+	6.56786i	−0.0363737	+	0.252984i
$675$	−21.8403	+	0.513562i	−0.840633	+	0.0197670i
$676$	28.3812	+	18.2395i	1.09159	+	0.701520i
$677$	20.2806	+	15.1819i	0.779448	+	0.583487i	0.913193	−	0.407528i	$-0.133609\pi$
$677$	20.2806	+	15.1819i	0.779448	+	0.583487i	−0.133745	+	0.991016i	$0.542700\pi$
$678$	5.27756	−	14.1497i	0.202683	−	0.543415i
$679$	−7.19335	+	3.28509i	−0.276056	+	0.126070i
$680$	−6.18854	+	2.64903i	−0.237320	+	0.101586i
$681$	19.7670	−	30.7581i	0.757474	−	1.17865i
$682$	10.0382	−	18.3836i	0.384383	−	0.703945i
$683$	−17.5202	−	23.4042i	−0.670392	−	0.895538i	0.328407	−	0.944536i	$-0.393488\pi$
$683$	−17.5202	−	23.4042i	−0.670392	−	0.895538i	−0.998799	+	0.0489979i	$0.984397\pi$
$684$	−1.39477	+	1.60965i	−0.0533304	+	0.0615465i
$685$	−1.72777	−	36.3813i	−0.0660147	−	1.39006i
$686$	11.5928	−	10.0453i	0.442617	−	0.383530i
$687$	−27.3550	+	14.9369i	−1.04366	+	0.569880i
$688$	7.90102	−	2.94693i	0.301224	−	0.112351i
$689$	71.8957			2.73901
$690$	−9.75893	+	18.3025i	−0.371516	+	0.696762i
$691$	24.3592			0.926668			0.463334	−	0.886184i	$-0.346653\pi$
$691$	24.3592			0.926668			0.463334	+	0.886184i	$0.346653\pi$
$692$	14.2724	−	5.32333i	0.542555	−	0.202363i
$693$	−2.70726	+	1.47828i	−0.102840	+	0.0561551i
$694$	−7.51430	+	6.51118i	−0.285239	+	0.247161i
$695$	−3.91111	−	3.55647i	−0.148357	−	0.134904i
$696$	−6.70192	+	7.73443i	−0.254036	+	0.293173i
$697$	5.01982	+	6.70569i	0.190139	+	0.253996i
$698$	3.60479	−	6.60167i	0.136443	−	0.249877i
$699$	22.0930	−	34.3774i	0.835635	−	1.30027i
$700$	−0.730660	+	6.09602i	−0.0276164	+	0.230408i
$701$	−25.1061	+	11.4656i	−0.948244	+	0.433049i	−0.828646	−	0.559774i	$-0.810888\pi$
$701$	−25.1061	+	11.4656i	−0.948244	+	0.433049i	−0.119599	+	0.992822i	$0.538161\pi$
$702$	10.4386	−	27.9869i	0.393978	−	1.05630i
$703$	15.4118	+	11.5371i	0.581267	+	0.435131i
$704$	−2.85182	−	1.83275i	−0.107482	−	0.0690745i
$705$	30.2602	−	18.4386i	1.13967	−	0.694436i
$706$	−3.46526	+	24.1014i	−0.130417	+	0.907068i
$707$	0.828533	+	11.5844i	0.0311602	+	0.435677i
$708$	3.18500	−	14.6412i	0.119700	−	0.550250i
$709$	−25.9265	−	29.9208i	−0.973691	−	1.12370i	−0.992298	−	0.123872i	$-0.960469\pi$
$709$	−25.9265	−	29.9208i	−0.973691	−	1.12370i	0.0186073	−	0.999827i	$-0.494077\pi$
$710$	6.49889	+	6.81781i	0.243899	+	0.255868i
$711$	−2.61204	−	1.19288i	−0.0979591	−	0.0447364i
$712$	7.93771	−	7.93771i	0.297478	−	0.297478i
$713$	−28.0988	−	9.40877i	−1.05231	−	0.352361i
$714$			7.15000i			0.267582i
$715$	42.2169	−	30.0533i	1.57882	−	1.12393i
$716$	15.0333	+	4.41418i	0.561821	+	0.164965i
$717$	−1.66610	+	23.2952i	−0.0622218	+	0.869975i
$718$	15.6616	+	3.40697i	0.584486	+	0.127147i
$719$	−3.42425	−	2.96713i	−0.127703	−	0.110655i	0.588668	−	0.808375i	$-0.299653\pi$
$719$	−3.42425	−	2.96713i	−0.127703	−	0.110655i	−0.716371	+	0.697720i	$0.754198\pi$
$720$	1.64527	−	0.196474i	0.0613154	−	0.00732214i
$721$	−2.72366	+	0.799738i	−0.101434	+	0.0297838i
$722$	2.28264	+	10.4931i	0.0849512	+	0.390514i
$723$	−13.8444	+	18.4939i	−0.514878	+	0.687796i
$724$	−1.44273	−	3.15913i	−0.0536185	−	0.117408i
$725$	−15.3523	+	21.5460i	−0.570170	+	0.800200i
$726$	−0.135392	−	0.941673i	−0.00502487	−	0.0349488i
$727$	26.3207	−	5.72571i	0.976180	−	0.212355i	0.303942	−	0.952690i	$-0.401697\pi$
$727$	26.3207	−	5.72571i	0.976180	−	0.212355i	0.672238	+	0.740336i	$0.265333\pi$
$728$	−7.36782	−	4.02313i	−0.273070	−	0.149107i
$729$	−17.2656	−	2.48242i	−0.639468	−	0.0919416i
$730$	0.753916	−	1.55143i	0.0279037	−	0.0574210i
$731$	21.3566	−	13.7250i	0.789902	−	0.507639i
$732$	−4.82275	−	0.344930i	−0.178254	−	0.0127490i
$733$	16.8430	+	30.8456i	0.622110	+	1.13931i	0.978748	+	0.205067i	$0.0657411\pi$
$733$	16.8430	+	30.8456i	0.622110	+	1.13931i	−0.356638	+	0.934243i	$0.616077\pi$
$734$	8.12103	−	17.7826i	0.299753	−	0.656367i
$735$	−20.5693	−	11.8797i	−0.758710	−	0.438188i
$736$	−1.84331	+	4.42744i	−0.0679454	+	0.163197i
$737$	−21.9723	−	21.9723i	−0.809361	−	0.809361i
$738$	−0.720527	−	1.93181i	−0.0265230	−	0.0711108i
$739$	8.09710	−	27.5762i	0.297857	−	1.01441i	−0.665548	−	0.746355i	$-0.731802\pi$
$739$	8.09710	−	27.5762i	0.297857	−	1.01441i	0.963405	−	0.268052i	$-0.0863798\pi$
$740$	−2.83230	−	14.7068i	−0.104117	−	0.540633i
$741$	−20.5476	−	31.9727i	−0.754835	−	1.17455i
$742$	−12.8807	+	0.921245i	−0.472865	+	0.0338200i
$743$	−29.1376	+	21.8121i	−1.06895	+	0.800210i	−0.980627	−	0.195882i	$-0.937243\pi$
$743$	−29.1376	+	21.8121i	−1.06895	+	0.800210i	−0.0883274	+	0.996091i	$0.528152\pi$
$744$	3.36691	+	11.4666i	0.123437	+	0.420387i
$745$	−36.3078	−	11.6121i	−1.33021	−	0.425435i
$746$	−29.0295	+	4.17381i	−1.06285	+	0.152814i
$747$	−8.39824	−	3.13238i	−0.307276	−	0.114608i
$748$	−9.56202	−	3.56645i	−0.349622	−	0.130402i
$749$	1.16450	−	0.167430i	0.0425499	−	0.00611775i
$750$	21.1325	−	4.58747i	0.771649	−	0.167511i
$751$	2.27644	+	7.75284i	0.0830685	+	0.282905i	0.990543	−	0.137202i	$-0.0438108\pi$
$751$	2.27644	+	7.75284i	0.0830685	+	0.282905i	−0.907475	+	0.420107i	$0.861993\pi$
$752$	6.55904	−	4.91004i	0.239184	−	0.179051i
$753$	1.95038	−	0.139494i	0.0710759	−	0.00508345i
$754$	−19.5566	−	30.4307i	−0.712211	−	1.10822i
$755$	19.7359	+	13.3618i	0.718264	+	0.486287i
$756$	−1.51154	+	5.14783i	−0.0549741	+	0.187225i
$757$	−8.33650	−	22.3510i	−0.302995	−	0.812362i	−0.995827	−	0.0912623i	$-0.970910\pi$
$757$	−8.33650	−	22.3510i	−0.302995	−	0.812362i	0.692832	−	0.721099i	$-0.256363\pi$
$758$	2.57805	+	2.57805i	0.0936388	+	0.0936388i
$759$	−29.8539	+	9.87628i	−1.08363	+	0.358486i
$760$	−3.21434	+	5.56554i	−0.116596	+	0.201883i
$761$	−16.4549	+	36.0311i	−0.596489	+	1.30613i	0.334952	+	0.942235i	$0.391280\pi$
$761$	−16.4549	+	36.0311i	−0.596489	+	1.30613i	−0.931441	+	0.363893i	$0.881447\pi$
$762$	−5.63437	−	10.3186i	−0.204112	−	0.373802i
$763$	−4.25488	−	0.304315i	−0.154037	−	0.0110169i
$764$	4.38418	−	2.81754i	0.158614	−	0.101935i
$765$	4.71414	−	1.63082i	0.170440	−	0.0589622i
$766$	25.3304	+	3.64196i	0.915225	+	0.131589i
$767$	46.4823	+	25.3813i	1.67838	+	0.916465i
$768$	1.88997	−	0.411137i	0.0681983	−	0.0148356i
$769$	2.52310	+	17.5486i	0.0909855	+	0.632818i	0.983380	+	0.181561i	$0.0581150\pi$
$769$	2.52310	+	17.5486i	0.0909855	+	0.632818i	−0.892394	+	0.451257i	$0.850976\pi$
$770$	−7.17840	+	5.92524i	−0.258692	+	0.213531i
$771$	7.38201	+	16.1643i	0.265857	+	0.582145i
$772$	6.12114	−	8.17688i	0.220305	−	0.294292i
$773$	−2.80311	−	12.8857i	−0.100821	−	0.463466i	−0.999682	−	0.0252315i	$-0.991968\pi$
$773$	−2.80311	−	12.8857i	−0.100821	−	0.463466i	0.898861	−	0.438234i	$-0.144396\pi$
$774$	−5.99562	+	1.76047i	−0.215508	+	0.0632789i
$775$	11.4737	+	28.6840i	0.412148	+	1.03036i
$776$	4.86710	+	4.21736i	0.174719	+	0.151395i
$777$	−15.5442	−	3.38144i	−0.557646	−	0.121309i
$778$	−1.39749	+	19.5395i	−0.0501025	+	0.700524i
$779$	7.67347	+	2.25314i	0.274931	+	0.0807269i
$780$	−4.90734	+	29.1571i	−0.175711	+	1.04399i
$781$			14.2796i			0.510965i
$782$	−2.58923	+	14.2038i	−0.0925907	+	0.507925i
$783$	−16.3474	+	16.3474i	−0.584209	+	0.584209i
$784$	−4.99587	−	2.28154i	−0.178424	−	0.0814835i
$785$	32.0035	−	30.5064i	1.14225	−	1.08882i
$786$	3.05822	+	3.52938i	0.109083	+	0.125889i
$787$	−3.10021	+	14.2514i	−0.110511	+	0.508009i	0.888301	+	0.459263i	$0.151886\pi$
$787$	−3.10021	+	14.2514i	−0.110511	+	0.508009i	−0.998811	+	0.0487465i	$0.984477\pi$
$788$	0.911268	+	12.7412i	0.0324626	+	0.453886i
$789$	−1.97721	+	13.7518i	−0.0703905	+	0.489576i
$790$	−8.42054	−	2.04409i	−0.299589	−	0.0727256i
$791$	−8.06559	−	5.18344i	−0.286779	−	0.184302i
$792$	2.01097	+	1.50539i	0.0714566	+	0.0534917i
$793$	5.97228	−	16.0123i	0.212082	−	0.568614i
$794$	9.26430	−	4.23086i	0.328778	−	0.150148i
$795$	17.8985	+	41.8137i	0.634794	+	1.48298i
$796$	−7.09825	+	11.0451i	−0.251591	+	0.391483i
$797$	−26.5996	+	48.7136i	−0.942207	+	1.72552i	−0.309972	+	0.950746i	$0.600320\pi$
$797$	−26.5996	+	48.7136i	−0.942207	+	1.72552i	−0.632234	+	0.774777i	$0.717862\pi$
$798$	4.09095	+	5.46487i	0.144818	+	0.193454i
$799$	16.1526	−	18.6411i	0.571440	−	0.659476i
$800$	4.76302	−	1.52105i	0.168398	−	0.0537773i
$801$	−6.28657	+	5.44735i	−0.222125	+	0.192473i
$802$	−4.40306	+	2.40425i	−0.155477	+	0.0848971i
$803$	2.45016	−	0.913861i	0.0864641	−	0.0322494i
$804$	17.7293			0.625263
$805$	10.0370	+	8.52389i	0.353758	+	0.300428i
$806$	−42.2405			−1.48786
$807$	−13.6824	+	5.10327i	−0.481643	+	0.179644i
$808$	8.30126	−	4.53283i	0.292037	−	0.159464i
$809$	6.31919	−	5.47561i	0.222171	−	0.192512i	−0.536662	−	0.843797i	$-0.680315\pi$
$809$	6.31919	−	5.47561i	0.222171	−	0.192512i	0.758833	+	0.651285i	$0.225770\pi$
$810$	23.8408	−	1.13221i	0.837680	−	0.0397819i
$811$	−14.6408	+	16.8963i	−0.514107	+	0.593311i	−0.952145	−	0.305645i	$-0.901128\pi$
$811$	−14.6408	+	16.8963i	−0.514107	+	0.593311i	0.438039	+	0.898956i	$0.355673\pi$
$812$	3.89365	+	5.20131i	0.136640	+	0.182530i
$813$	19.7033	−	36.0839i	0.691024	−	1.26552i
$814$	12.2757	−	19.1013i	0.430262	−	0.669501i
$815$	25.5153	+	10.2191i	0.893763	+	0.357959i
$816$	5.29661	−	2.41888i	0.185419	−	0.0846778i
$817$	8.47028	−	22.7097i	0.296338	−	0.794512i
$818$	−22.2160	−	16.6307i	−0.776763	−	0.581478i
$819$	5.23306	+	3.36308i	0.182858	+	0.117516i
$820$	−3.23741	−	5.31304i	−0.113055	−	0.185539i
$821$	1.51923	−	10.5665i	0.0530215	−	0.368773i	−0.945985	−	0.324210i	$-0.894901\pi$
$821$	1.51923	−	10.5665i	0.0530215	−	0.368773i	0.999007	−	0.0445626i	$-0.0141894\pi$
$822$	2.24753	+	31.4245i	0.0783915	+	1.09606i
$823$	2.91588	−	13.4041i	0.101641	−	0.467236i	−0.897988	−	0.440019i	$-0.854972\pi$
$823$	2.91588	−	13.4041i	0.101641	−	0.467236i	0.999630	−	0.0272174i	$-0.00866464\pi$
$824$	1.51386	+	1.74709i	0.0527379	+	0.0608627i
$825$	27.9886	+	17.0710i	0.974437	+	0.594338i
$826$	−8.65290	−	3.95165i	−0.301073	−	0.137495i
$827$	−4.87874	+	4.87874i	−0.169650	+	0.169650i	−0.786826	−	0.617175i	$-0.788277\pi$
$827$	−4.87874	+	4.87874i	−0.169650	+	0.169650i	0.617175	+	0.786826i	$0.288277\pi$
$828$	1.59649	−	3.17498i	0.0554817	−	0.110338i
$829$			38.5688i			1.33955i	0.742565	+	0.669774i	$0.233609\pi$
$829$			38.5688i			1.33955i	−0.742565	+	0.669774i	$0.766391\pi$
$830$	−26.6726	−	4.48920i	−0.925820	−	0.155822i
$831$	48.3649	+	14.2012i	1.67776	+	0.492635i
$832$	−0.487706	+	6.81902i	−0.0169082	+	0.236407i
$833$	−16.1563	−	3.51460i	−0.559784	−	0.121774i
$834$	3.45574	+	2.99442i	0.119662	+	0.103688i
$835$	−34.9269	+	44.4000i	−1.20870	+	1.53652i
$836$	−9.34900	+	2.74511i	−0.323342	+	0.0949418i
$837$	5.73853	+	26.3796i	0.198352	+	0.911812i
$838$	6.97644	−	9.31943i	0.240997	−	0.321934i
$839$	−7.93709	−	17.3798i	−0.274019	−	0.600018i	0.721725	−	0.692180i	$-0.243349\pi$
$839$	−7.93709	−	17.3798i	−0.274019	−	0.600018i	−0.995744	+	0.0921621i	$0.970622\pi$
$840$	0.505582	−	5.28660i	0.0174442	−	0.182405i
$841$	−0.142743	−	0.992796i	−0.00492216	−	0.0342343i
$842$	15.5105	−	3.37410i	0.534526	−	0.116279i
$843$	44.1550	+	24.1104i	1.52078	+	0.830408i
$844$	−11.8126	−	1.69839i	−0.406606	−	0.0584611i
$845$	−67.8507	−	32.9720i	−2.33414	−	1.13427i
$846$	−5.10751	+	3.28240i	−0.175600	+	0.112851i
$847$	−0.602441	−	0.0430874i	−0.0207001	−	0.00148050i
$848$	5.04005	+	9.23016i	0.173076	+	0.316965i
$849$	−22.2753	+	48.7761i	−0.764486	+	1.67399i
$850$	13.0380	−	7.52246i	0.447200	−	0.258018i
$851$	−29.6547	−	12.3464i	−1.01655	−	0.423229i
$852$	−5.76104	−	5.76104i	−0.197370	−	0.197370i
$853$	−8.90970	−	23.8878i	−0.305062	−	0.817904i	−0.995522	−	0.0945326i	$-0.969864\pi$
$853$	−8.90970	−	23.8878i	−0.305062	−	0.817904i	0.690459	−	0.723371i	$-0.257408\pi$
$854$	−0.864805	+	2.94526i	−0.0295930	+	0.100785i
$855$	2.67001	−	3.94371i	0.0913125	−	0.134872i
$856$	−0.517986	−	0.806002i	−0.0177044	−	0.0275486i
$857$	8.17093	−	0.584396i	0.279114	−	0.0199626i	0.0689193	−	0.997622i	$-0.478045\pi$
$857$	8.17093	−	0.584396i	0.279114	−	0.0199626i	0.210194	+	0.977660i	$0.432590\pi$
$858$	−35.8842	+	26.8626i	−1.22507	+	0.917073i
$859$	−6.68434	−	22.7648i	−0.228067	−	0.776724i	−0.991417	−	0.130739i	$-0.958265\pi$
$859$	−6.68434	−	22.7648i	−0.228067	−	0.776724i	0.763350	−	0.645985i	$-0.223553\pi$
$860$	−16.7612	+	8.63794i	−0.571553	+	0.294551i
$861$	−6.54105	+	0.940460i	−0.222918	+	0.0320508i
$862$	14.0854	+	5.25358i	0.479750	+	0.178937i
$863$	40.3341	+	15.0438i	1.37299	+	0.512098i	0.924326	−	0.381604i	$-0.124628\pi$
$863$	40.3341	+	15.0438i	1.37299	+	0.512098i	0.448662	+	0.893702i	$0.351901\pi$
$864$	4.32479	−	0.621811i	0.147132	−	0.0211544i
$865$	−30.2775	+	15.6036i	−1.02946	+	0.530537i
$866$	0.552191	+	1.88059i	0.0187642	+	0.0639050i
$867$	−12.2894	+	9.19972i	−0.417369	+	0.312439i
$868$	7.56772	−	0.541254i	0.256865	−	0.0183714i
$869$	−7.10219	−	11.0512i	−0.240925	−	0.374887i
$870$	12.8295	−	18.9497i	0.434961	−	0.642454i
$871$	−17.6548	+	60.1267i	−0.598210	+	2.03732i
$872$	1.21402	+	3.25490i	0.0411118	+	0.110225i
$873$	−3.37445	−	3.37445i	−0.114208	−	0.114208i
$874$	6.14784	+	12.3376i	0.207954	+	0.417327i
$875$	0.00596829	−	13.7287i	0.000201765	−	0.464114i
$876$	−0.619810	+	1.35720i	−0.0209415	+	0.0458554i
$877$	−13.6185	−	24.9403i	−0.459862	−	0.842175i	−1.00000		0.000598267i	$-0.999810\pi$
$877$	−13.6185	−	24.9403i	−0.459862	−	0.842175i	0.540137	−	0.841577i	$-0.318372\pi$
$878$	−22.0264	−	1.57536i	−0.743354	−	0.0531657i
$879$	45.9765	−	29.5473i	1.55075	−	0.996607i
$880$	6.81782	+	3.31311i	0.229829	+	0.111685i
$881$	−3.07893	−	0.442684i	−0.103732	−	0.0149144i	0.0902534	−	0.995919i	$-0.471232\pi$
$881$	−3.07893	−	0.442684i	−0.103732	−	0.0149144i	−0.193985	+	0.981004i	$0.562141\pi$
$882$	3.57196	+	1.95044i	0.120274	+	0.0656747i
$883$	14.0083	−	3.04732i	0.471418	−	0.102551i	0.0294206	−	0.999567i	$-0.490634\pi$
$883$	14.0083	−	3.04732i	0.471418	−	0.102551i	0.441997	+	0.897016i	$0.354270\pi$
$884$	2.92899	+	20.3716i	0.0985126	+	0.685170i
$885$	−3.18963	+	33.3523i	−0.107218	+	1.12112i
$886$	−5.08292	−	11.1300i	−0.170764	−	0.373921i
$887$	28.4059	−	37.9458i	0.953777	−	1.27410i	−0.00791616	−	0.999969i	$-0.502520\pi$
$887$	28.4059	−	37.9458i	0.953777	−	1.27410i	0.961693	−	0.274128i	$-0.0883893\pi$
$888$	2.75377	+	12.6589i	0.0924106	+	0.424805i
$889$	−7.16151	+	2.10281i	−0.240189	+	0.0705260i
$890$	−15.5194	+	19.7287i	−0.520212	+	0.661307i
$891$	27.3463	+	23.6957i	0.916134	+	0.793835i
$892$	25.2348	+	5.48950i	0.844925	+	0.183802i
$893$	1.68001	−	23.4897i	0.0562196	−	0.786052i
$894$	31.6372	+	9.28953i	1.05811	+	0.310688i
$895$	−34.5487	−	5.81480i	−1.15484	−	0.194367i
$896$		−	1.22793i		−	0.0410223i
$897$	46.3343	+	43.2958i	1.54706	+	1.44560i
$898$	22.8958	−	22.8958i	0.764043	−	0.764043i
$899$	29.7386	+	13.5812i	0.991839	+	0.452958i
$900$	−3.60088	+	0.872458i	−0.120029	+	0.0290819i
$901$	20.7329	+	23.9271i	0.690713	+	0.797126i
$902$	2.00498	−	9.21674i	0.0667585	−	0.306884i
$903$	1.42877	+	19.9769i	0.0475466	+	0.664788i
$904$	−1.11118	+	7.72845i	−0.0369574	+	0.257044i
$905$	4.04089	+	6.63166i	0.134324	+	0.220444i
$906$	−17.3431	−	11.1458i	−0.576187	−	0.370293i
$907$	−18.7164	−	14.0109i	−0.621467	−	0.465224i	0.241558	−	0.970386i	$-0.422342\pi$
$907$	−18.7164	−	14.0109i	−0.621467	−	0.465224i	−0.863024	+	0.505162i	$0.831433\pi$
$908$	−6.60603	+	17.7114i	−0.219229	+	0.587775i
$909$	−6.37529	+	2.91150i	−0.211455	+	0.0965682i
$910$	17.4254	+	6.97902i	0.577647	+	0.231352i
$911$	25.2316	−	39.2611i	0.835959	−	1.30078i	−0.115595	−	0.993296i	$-0.536877\pi$
$911$	25.2316	−	39.2611i	0.835959	−	1.30078i	0.951554	−	0.307481i	$-0.0994862\pi$
$912$	2.66430	−	4.87931i	0.0882240	−	0.161570i
$913$	−24.5737	−	32.8266i	−0.813270	−	1.08640i
$914$	−12.5465	+	14.4794i	−0.415001	+	0.478936i
$915$	10.7994	−	0.512869i	0.357016	−	0.0169549i
$916$	12.1782	−	10.5525i	0.402380	−	0.348664i
$917$	2.60217	−	1.42089i	0.0859311	−	0.0469219i
$918$	12.3243	−	4.59673i	0.406763	−	0.151715i
$919$	24.2999			0.801580			0.400790	−	0.916170i	$-0.368736\pi$
$919$	24.2999			0.801580			0.400790	+	0.916170i	$0.368736\pi$
$920$	2.91879	−	10.3189i	0.0962298	−	0.340206i
$921$	−39.5936			−1.30465
$922$	−3.37489	+	1.25877i	−0.111146	+	0.0414554i
$923$	25.2747	−	13.8010i	0.831928	−	0.454267i
$924$	6.08473	−	5.27245i	0.200173	−	0.173451i
$925$	10.1879	+	31.9025i	0.334977	+	1.04895i
$926$	24.2850	−	28.0264i	0.798056	−	0.921005i
$927$	−1.02658	−	1.37134i	−0.0337172	−	0.0450409i
$928$	2.53581	−	4.64399i	0.0832421	−	0.152446i
$929$	20.0501	−	31.1986i	0.657824	−	1.02359i	−0.338749	−	0.940877i	$-0.610004\pi$
$929$	20.0501	−	31.1986i	0.657824	−	1.02359i	0.996573	−	0.0827170i	$-0.0263598\pi$
$930$	−10.5158	−	24.5666i	−0.344827	−	0.805570i
$931$	−14.3595	+	6.55776i	−0.470614	+	0.214922i
$932$	−7.38337	+	19.7956i	−0.241850	+	0.648426i
$933$	22.3044	+	16.6969i	0.730215	+	0.546632i
$934$	−13.6688	−	8.78438i	−0.447256	−	0.287434i
$935$	22.1761	+	5.38326i	0.725236	+	0.176052i
$936$	0.720951	−	5.01432i	0.0235650	−	0.163898i
$937$	1.16943	+	16.3507i	0.0382035	+	0.534155i	0.980133	+	0.198343i	$0.0635560\pi$
$937$	1.16943	+	16.3507i	0.0382035	+	0.534155i	−0.941929	+	0.335812i	$0.890989\pi$
$938$	2.39255	−	10.9984i	0.0781197	−	0.359110i
$939$	31.2993	+	36.1213i	1.02141	+	1.17877i
$940$	−13.2611	+	12.6408i	−0.432531	+	0.412298i
$941$	−32.4604	−	14.8242i	−1.05818	−	0.483254i	−0.191176	−	0.981556i	$-0.561230\pi$
$941$	−32.4604	−	14.8242i	−1.05818	−	0.483254i	−0.867004	+	0.498302i	$0.833957\pi$
$942$	−27.0429	+	27.0429i	−0.881105	+	0.881105i
$943$	−13.3346	−	0.500447i	−0.434235	−	0.0162968i
$944$			7.74680i			0.252137i
$945$	1.99115	−	11.8305i	0.0647721	−	0.384845i
$946$	−27.4286	−	8.05377i	−0.891782	−	0.261851i
$947$	1.02820	−	14.3762i	0.0334122	−	0.467163i	−0.953011	−	0.302937i	$-0.902033\pi$
$947$	1.02820	−	14.3762i	0.0334122	−	0.467163i	0.986423	−	0.164226i	$-0.0525126\pi$
$948$	7.32390	+	1.59322i	0.237869	+	0.0517453i
$949$	−3.98556	−	3.45351i	−0.129377	−	0.112106i
$950$	5.66112	−	13.2094i	0.183671	−	0.428569i
$951$	−27.6689	+	8.12431i	−0.897224	+	0.263449i
$952$	−0.785785	−	3.61220i	−0.0254674	−	0.117072i
$953$	−13.8333	+	18.4791i	−0.448105	+	0.598598i	−0.966539	−	0.256519i	$-0.917424\pi$
$953$	−13.8333	+	18.4791i	−0.448105	+	0.598598i	0.518434	+	0.855118i	$0.326515\pi$
$954$	−3.23729	−	7.08867i	−0.104811	−	0.229504i
$955$	−8.98710	+	7.41819i	−0.290816	+	0.240047i
$956$	−1.71842	−	11.9519i	−0.0555777	−	0.386552i
$957$	33.9004	−	7.37459i	1.09585	−	0.238387i
$958$	10.3097	+	5.62952i	0.333091	+	0.181882i
$959$	19.7976	+	2.84647i	0.639298	+	0.0919172i
$960$	−4.08727	+	1.41396i	−0.131916	+	0.0456352i
$961$	6.03749	−	3.88006i	0.194758	−	0.125163i
$962$	−45.6734	−	3.26662i	−1.47257	−	0.105320i
$963$	0.340248	+	0.623118i	0.0109643	+	0.0200797i
$964$	4.96172	−	10.8647i	0.159806	−	0.349927i
$965$	−11.4227	+	19.7780i	−0.367709	+	0.636678i
$966$	−8.85593	−	7.16307i	−0.284935	−	0.230468i
$967$	29.8120	+	29.8120i	0.958690	+	0.958690i	0.999180	−	0.0404896i	$-0.0128918\pi$
$967$	29.8120	+	29.8120i	0.958690	+	0.958690i	−0.0404896	+	0.999180i	$0.512892\pi$
$968$	0.171890	+	0.460856i	0.00552476	+	0.0148125i
$969$	4.71517	−	16.0584i	0.151473	−	0.515870i
$970$	−11.9246	−	8.07331i	−0.382875	−	0.259218i
$971$	5.82284	+	9.06052i	0.186864	+	0.290766i	0.922028	−	0.387123i	$-0.126531\pi$
$971$	5.82284	+	9.06052i	0.186864	+	0.290766i	−0.735164	+	0.677889i	$0.762895\pi$
$972$	−7.51821	+	0.537713i	−0.241147	+	0.0172472i
$973$	2.32395	−	1.73968i	0.0745023	−	0.0557717i
$974$	−4.60096	−	15.6694i	−0.147424	−	0.502081i
$975$	3.16498	−	66.0383i	0.101360	−	2.11492i
$976$	2.47437	−	0.355761i	0.0792026	−	0.0113876i
$977$	−31.5678	−	11.7742i	−1.00994	−	0.376690i	−0.210606	−	0.977571i	$-0.567544\pi$
$977$	−31.5678	−	11.7742i	−1.00994	−	0.376690i	−0.799338	+	0.600881i	$0.794817\pi$
$978$	−22.2757	−	8.30842i	−0.712299	−	0.265674i
$979$	−37.6671	+	5.41572i	−1.20385	+	0.173087i
$980$	11.6972	+	3.74106i	0.373654	+	0.119504i
$981$	−0.725244	−	2.46996i	−0.0231553	−	0.0788596i
$982$	−31.2132	+	23.3659i	−0.996053	+	0.745636i
$983$	−6.26344	+	0.447970i	−0.199773	+	0.0142880i	−0.170867	−	0.985294i	$-0.554657\pi$
$983$	−6.26344	+	0.447970i	−0.199773	+	0.0142880i	−0.0289058	+	0.999582i	$0.509202\pi$
$984$	2.90955	+	4.52734i	0.0927530	+	0.144326i
$985$	−5.40151	−	28.0476i	−0.172106	−	0.893670i
$986$	4.48777	−	15.2839i	0.142920	−	0.486740i
$987$	6.80029	+	18.2323i	0.216456	+	0.580340i
$988$	13.8945	+	13.8945i	0.442043	+	0.442043i
$989$	−4.39591	+	40.2022i	−0.139782	+	1.27836i
$990$	−4.86407	−	2.80921i	−0.154590	−	0.0892827i
$991$	4.08645	−	8.94808i	0.129810	−	0.284245i	−0.833555	−	0.552436i	$-0.813698\pi$
$991$	4.08645	−	8.94808i	0.129810	−	0.284245i	0.963366	+	0.268191i	$0.0864257\pi$
$992$	−2.96115	−	5.42295i	−0.0940167	−	0.172179i
$993$	−39.7822	−	2.84528i	−1.26245	−	0.0902922i
$994$	−4.35133	+	2.79643i	−0.138016	+	0.0886973i
$995$	12.8317	−	26.4054i	0.406791	−	0.837107i
$996$	23.1578	+	3.32959i	0.733784	+	0.105502i
$997$	−29.5968	−	16.1611i	−0.937340	−	0.511826i	−0.0634688	−	0.997984i	$-0.520216\pi$
$997$	−29.5968	−	16.1611i	−0.937340	−	0.511826i	−0.873871	+	0.486157i	$0.838398\pi$
$998$	−17.3996	+	3.78505i	−0.550774	+	0.119814i
$999$	4.16486	+	28.9672i	0.131770	+	0.916482i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.17.2	✓	240
5.3	odd	4	inner	230.2.l.a.63.8	yes	240
23.19	odd	22	inner	230.2.l.a.157.8	yes	240
115.88	even	44	inner	230.2.l.a.203.2	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.17.2	✓	240	1.1	even	1	trivial
230.2.l.a.63.8	yes	240	5.3	odd	4	inner
230.2.l.a.157.8	yes	240	23.19	odd	22	inner
230.2.l.a.203.2	yes	240	115.88	even	44	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.936950 + 0.349464i) q^{2} +(-1.69758 + 0.926949i) q^{3} +(0.755750 - 0.654861i) q^{4} +(-1.50435 + 1.65436i) q^{5} +(1.26661 - 1.46175i) q^{6} +(-0.735871 - 0.983009i) q^{7} +(-0.479249 + 0.877679i) q^{8} +(0.400622 - 0.623380i) q^{9} +(0.831363 - 2.07577i) q^{10} +(3.08362 - 1.40824i) q^{11} +(-0.675923 + 1.81222i) q^{12} +(-5.47285 - 4.09692i) q^{13} +(1.03300 + 0.663869i) q^{14} +(1.02025 - 4.20287i) q^{15} +(0.142315 - 0.989821i) q^{16} +(-0.214766 - 3.00282i) q^{17} +(-0.157514 + 0.724078i) q^{18} +(-1.88225 - 2.17223i) q^{19} +(-0.0535372 + 2.23543i) q^{20} +(2.16040 + 0.986621i) q^{21} +(-2.39707 + 2.39707i) q^{22} +(3.93443 + 2.74231i) q^{23} -1.93417i q^{24} +(-0.473838 - 4.97750i) q^{25} +(6.55951 + 1.92605i) q^{26} +(0.311700 - 4.35813i) q^{27} +(-1.19987 - 0.261015i) q^{28} +(-3.99884 - 3.46501i) q^{29} +(0.512830 + 4.29442i) q^{30} +(-5.92845 + 1.74075i) q^{31} +(0.212565 + 0.977147i) q^{32} +(-3.92933 + 5.24896i) q^{33} +(1.25060 + 2.73844i) q^{34} +(2.73326 + 0.261395i) q^{35} +(-0.105457 - 0.733470i) q^{36} +(-6.54487 + 1.42375i) q^{37} +(2.52269 + 1.37749i) q^{38} +(13.0882 + 1.88180i) q^{39} +(-0.731040 - 2.11319i) q^{40} +(-2.34072 + 1.50429i) q^{41} +(-2.36897 - 0.169432i) q^{42} +(4.04137 + 7.40121i) q^{43} +(1.40824 - 3.08362i) q^{44} +(0.428620 + 1.60056i) q^{45} +(-4.64470 - 1.19446i) q^{46} +(5.79351 + 5.79351i) q^{47} +(0.675923 + 1.81222i) q^{48} +(1.54733 - 5.26972i) q^{49} +(2.18342 + 4.49808i) q^{50} +(3.14805 + 4.89846i) q^{51} +(-6.81902 + 0.487706i) q^{52} +(-8.41893 + 6.30233i) q^{53} +(1.23096 + 4.19228i) q^{54} +(-2.30911 + 7.21993i) q^{55} +(1.21543 - 0.174753i) q^{56} +(5.20882 + 1.94279i) q^{57} +(4.95761 + 1.84909i) q^{58} +(-7.66795 + 1.10249i) q^{59} +(-1.98124 - 3.84444i) q^{60} +(0.704279 + 2.39855i) q^{61} +(4.94633 - 3.70278i) q^{62} +(-0.907593 + 0.0649124i) q^{63} +(-0.540641 - 0.841254i) q^{64} +(15.0109 - 2.89086i) q^{65} +(1.84726 - 6.29117i) q^{66} +(-3.20331 - 8.58840i) q^{67} +(-2.12874 - 2.12874i) q^{68} +(-9.22099 - 1.00827i) q^{69} +(-2.65228 + 0.710264i) q^{70} +(-1.74986 + 3.83166i) q^{71} +(0.355130 + 0.650371i) q^{72} +(0.769439 + 0.0550313i) q^{73} +(5.63467 - 3.62118i) q^{74} +(5.41826 + 8.01048i) q^{75} +(-2.84502 - 0.409052i) q^{76} +(-3.65346 - 1.99494i) q^{77} +(-12.9206 + 2.81071i) q^{78} +(-0.551491 - 3.83570i) q^{79} +(1.42343 + 1.72448i) q^{80} +(4.43411 + 9.70936i) q^{81} +(1.66744 - 2.22744i) q^{82} +(-2.57122 - 11.8197i) q^{83} +(2.27882 - 0.669122i) q^{84} +(5.29085 + 4.16201i) q^{85} +(-6.37301 - 5.52225i) q^{86} +(10.0002 + 2.17542i) q^{87} +(-0.241837 + 3.38133i) q^{88} +(-10.7709 - 3.16262i) q^{89} +(-0.960932 - 1.34985i) q^{90} +8.39466i q^{91} +(4.76927 - 0.504008i) q^{92} +(8.45044 - 8.45044i) q^{93} +(-7.45285 - 3.40360i) q^{94} +(6.42523 + 0.153881i) q^{95} +(-1.26661 - 1.46175i) q^{96} +(1.36894 - 6.29292i) q^{97} +(0.391808 + 5.47819i) q^{98} +(0.357496 - 2.48644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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