LMFDB - Embedded newform 230.4.j.a.9.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,4,Mod(9,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 10]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("230.9");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	230.j (of order $22$, degree $10$, 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:	$13.5704393013$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$36$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			9.2
Character	$\chi$	$=$	230.9
Dual form			230.4.j.a.179.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.563465 - 1.91899i) q^{2} +(-6.85739 + 5.94196i) q^{3} +(-3.36501 + 2.16256i) q^{4} +(11.1057 - 1.29006i) q^{5} +(15.2664 + 9.81115i) q^{6} +(9.56919 + 4.37010i) q^{7} +(6.04600 + 5.23889i) q^{8} +(7.87438 - 54.7675i) q^{9} +O(q^{10})$	\(q+(-0.563465 - 1.91899i) q^{2} +(-6.85739 + 5.94196i) q^{3} +(-3.36501 + 2.16256i) q^{4} +(11.1057 - 1.29006i) q^{5} +(15.2664 + 9.81115i) q^{6} +(9.56919 + 4.37010i) q^{7} +(6.04600 + 5.23889i) q^{8} +(7.87438 - 54.7675i) q^{9} +(-8.73326 - 20.5847i) q^{10} +(-45.7363 - 13.4294i) q^{11} +(10.2253 - 34.8243i) q^{12} +(62.1402 - 28.3785i) q^{13} +(2.99426 - 20.8255i) q^{14} +(-68.4904 + 74.8359i) q^{15} +(6.64664 - 14.5541i) q^{16} +(-52.7552 + 82.0887i) q^{17} +(-109.535 + 15.7488i) q^{18} +(47.2317 - 30.3540i) q^{19} +(-34.5809 + 28.3578i) q^{20} +(-91.5866 + 26.8923i) q^{21} +95.3342i q^{22} +(108.909 + 17.4906i) q^{23} -72.5890 q^{24} +(121.671 - 28.6539i) q^{25} +(-89.4717 - 103.256i) q^{26} +(138.978 + 216.255i) q^{27} +(-41.6511 + 5.98852i) q^{28} +(142.113 + 91.3304i) q^{29} +(182.201 + 89.2647i) q^{30} +(-134.258 + 154.942i) q^{31} +(-31.6743 - 4.55407i) q^{32} +(393.428 - 179.673i) q^{33} +(187.253 + 54.9824i) q^{34} +(111.910 + 36.1881i) q^{35} +(91.9409 + 201.322i) q^{36} +(255.597 + 36.7493i) q^{37} +(-84.8623 - 73.5336i) q^{38} +(-257.496 + 563.837i) q^{39} +(73.9033 + 50.3816i) q^{40} +(11.4906 + 79.9187i) q^{41} +(103.212 + 160.601i) q^{42} +(-292.421 + 253.384i) q^{43} +(182.945 - 53.7175i) q^{44} +(16.7969 - 618.388i) q^{45} +(-27.8021 - 218.849i) q^{46} +543.063i q^{47} +(40.9014 + 139.297i) q^{48} +(-152.146 - 175.585i) q^{49} +(-123.544 - 217.340i) q^{50} +(-126.005 - 876.384i) q^{51} +(-147.732 + 229.876i) q^{52} +(26.2649 + 11.9948i) q^{53} +(336.680 - 388.550i) q^{54} +(-525.256 - 90.1397i) q^{55} +(34.9608 + 76.5535i) q^{56} +(-143.524 + 488.798i) q^{57} +(95.1861 - 324.174i) q^{58} +(282.264 + 618.071i) q^{59} +(68.6338 - 399.939i) q^{60} +(-77.8902 + 89.8901i) q^{61} +(372.982 + 170.335i) q^{62} +(314.691 - 489.669i) q^{63} +(9.10815 + 63.3486i) q^{64} +(653.498 - 395.326i) q^{65} +(-566.472 - 653.744i) q^{66} +(-31.2669 - 106.485i) q^{67} -390.316i q^{68} +(-850.757 + 527.191i) q^{69} +(6.38708 - 235.144i) q^{70} +(940.078 - 276.032i) q^{71} +(334.529 - 289.871i) q^{72} +(124.904 + 194.354i) q^{73} +(-73.4986 - 511.194i) q^{74} +(-664.088 + 919.459i) q^{75} +(-93.2930 + 204.283i) q^{76} +(-378.971 - 328.380i) q^{77} +(1227.08 + 176.428i) q^{78} +(-418.305 - 915.961i) q^{79} +(55.0397 - 170.208i) q^{80} +(-804.592 - 236.250i) q^{81} +(146.888 - 67.0817i) q^{82} +(-302.544 - 43.4992i) q^{83} +(250.034 - 288.555i) q^{84} +(-479.982 + 979.707i) q^{85} +(651.009 + 418.378i) q^{86} +(-1517.21 + 218.141i) q^{87} +(-206.166 - 320.801i) q^{88} +(50.6205 + 58.4191i) q^{89} +(-1196.14 + 316.207i) q^{90} +718.648 q^{91} +(-404.303 + 176.666i) q^{92} -1860.26i q^{93} +(1042.13 - 305.997i) q^{94} +(485.381 - 398.033i) q^{95} +(244.263 - 156.978i) q^{96} +(706.672 - 101.604i) q^{97} +(-251.217 + 390.902i) q^{98} +(-1095.64 + 2399.11i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q + 144 q^{4} + 32 q^{5} + 8 q^{6} + 224 q^{9}+O(q^{10}) $ 360 * q + 144 * q^4 + 32 * q^5 + 8 * q^6 + 224 * q^9	$ 360 q + 144 q^{4} + 32 q^{5} + 8 q^{6} + 224 q^{9} + 96 q^{11} + 208 q^{14} - 752 q^{15} - 576 q^{16} + 48 q^{19} + 224 q^{20} - 272 q^{21} - 32 q^{24} + 904 q^{25} - 152 q^{26} - 20 q^{29} - 1272 q^{30} + 160 q^{31} + 128 q^{34} - 364 q^{35} - 896 q^{36} - 1476 q^{39} + 216 q^{41} - 384 q^{44} - 820 q^{45} + 416 q^{46} + 3814 q^{49} + 1000 q^{50} + 296 q^{51} - 2772 q^{54} - 4272 q^{55} + 1104 q^{56} - 6250 q^{59} - 72 q^{60} + 96 q^{61} + 2304 q^{64} + 8708 q^{65} - 6144 q^{66} + 14176 q^{69} + 6136 q^{70} - 11144 q^{71} + 4944 q^{74} + 6722 q^{75} - 192 q^{76} - 2680 q^{79} - 896 q^{80} + 4820 q^{81} - 2696 q^{84} - 7290 q^{85} + 2900 q^{86} + 880 q^{89} - 1104 q^{90} + 5272 q^{91} + 864 q^{94} + 7456 q^{95} + 128 q^{96} + 23448 q^{99}+O(q^{100}) $ 360 * q + 144 * q^4 + 32 * q^5 + 8 * q^6 + 224 * q^9 + 96 * q^11 + 208 * q^14 - 752 * q^15 - 576 * q^16 + 48 * q^19 + 224 * q^20 - 272 * q^21 - 32 * q^24 + 904 * q^25 - 152 * q^26 - 20 * q^29 - 1272 * q^30 + 160 * q^31 + 128 * q^34 - 364 * q^35 - 896 * q^36 - 1476 * q^39 + 216 * q^41 - 384 * q^44 - 820 * q^45 + 416 * q^46 + 3814 * q^49 + 1000 * q^50 + 296 * q^51 - 2772 * q^54 - 4272 * q^55 + 1104 * q^56 - 6250 * q^59 - 72 * q^60 + 96 * q^61 + 2304 * q^64 + 8708 * q^65 - 6144 * q^66 + 14176 * q^69 + 6136 * q^70 - 11144 * q^71 + 4944 * q^74 + 6722 * q^75 - 192 * q^76 - 2680 * q^79 - 896 * q^80 + 4820 * q^81 - 2696 * q^84 - 7290 * q^85 + 2900 * q^86 + 880 * q^89 - 1104 * q^90 + 5272 * q^91 + 864 * q^94 + 7456 * q^95 + 128 * q^96 + 23448 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{5}{11}\right)$

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 $

$2$	−0.563465	−	1.91899i	−0.199215	−	0.678464i
$2$	−0.563465	−	1.91899i	−0.199215	−	0.678464i
$3$	−6.85739	+	5.94196i	−1.31971	+	1.14353i	−0.340593	+	0.940211i	$0.610628\pi$
$3$	−6.85739	+	5.94196i	−1.31971	+	1.14353i	−0.979112	+	0.203321i	$0.934827\pi$
$4$	−3.36501	+	2.16256i	−0.420627	+	0.270320i
$5$	11.1057	−	1.29006i	0.993321	−	0.115386i
$5$	11.1057	−	1.29006i	0.993321	−	0.115386i
$6$	15.2664	+	9.81115i	1.03875	+	0.667564i
$7$	9.56919	+	4.37010i	0.516687	+	0.235963i	0.656653	−	0.754193i	$-0.271972\pi$
$7$	9.56919	+	4.37010i	0.516687	+	0.235963i	−0.139965	+	0.990156i	$0.544699\pi$
$8$	6.04600	+	5.23889i	0.267198	+	0.231528i
$9$	7.87438	−	54.7675i	0.291644	−	2.02843i
$10$	−8.73326	−	20.5847i	−0.276170	−	0.650946i
$11$	−45.7363	−	13.4294i	−1.25364	−	0.368101i	−0.413514	−	0.910498i	$-0.635699\pi$
$11$	−45.7363	−	13.4294i	−1.25364	−	0.368101i	−0.840122	+	0.542397i	$0.817517\pi$
$12$	10.2253	−	34.8243i	0.245984	−	0.837743i
$13$	62.1402	−	28.3785i	1.32574	−	0.605444i	0.378388	−	0.925647i	$-0.376478\pi$
$13$	62.1402	−	28.3785i	1.32574	−	0.605444i	0.947349	+	0.320203i	$0.103751\pi$
$14$	2.99426	−	20.8255i	0.0571607	−	0.397561i
$15$	−68.4904	+	74.8359i	−1.17894	+	1.28817i
$16$	6.64664	−	14.5541i	0.103854	−	0.227408i
$17$	−52.7552	+	82.0887i	−0.752648	+	1.17114i	0.227673	+	0.973738i	$0.426888\pi$
$17$	−52.7552	+	82.0887i	−0.752648	+	1.17114i	−0.980322	+	0.197406i	$0.936748\pi$
$18$	−109.535	+	15.7488i	−1.43431	+	0.206223i
$19$	47.2317	−	30.3540i	0.570300	−	0.366509i	−0.223486	−	0.974707i	$-0.571744\pi$
$19$	47.2317	−	30.3540i	0.570300	−	0.366509i	0.793786	+	0.608198i	$0.208107\pi$
$20$	−34.5809	+	28.3578i	−0.386626	+	0.317049i
$21$	−91.5866	+	26.8923i	−0.951707	+	0.279446i
$22$			95.3342i			0.923878i
$23$	108.909	+	17.4906i	0.987348	+	0.158567i
$23$	108.909	+	17.4906i	0.987348	+	0.158567i
$24$	−72.5890			−0.617382
$25$	121.671	−	28.6539i	0.973372	−	0.229231i
$26$	−89.4717	−	103.256i	−0.674879	−	0.778851i
$27$	138.978	+	216.255i	0.990608	+	1.54142i
$28$	−41.6511	+	5.98852i	−0.281118	+	0.0404187i
$29$	142.113	+	91.3304i	0.909990	+	0.584815i	0.909737	−	0.415185i	$-0.136283\pi$
$29$	142.113	+	91.3304i	0.909990	+	0.584815i	0.000252679		1.00000i	$0.499920\pi$
$30$	182.201	+	89.2647i	1.10884	+	0.543248i
$31$	−134.258	+	154.942i	−0.777855	+	0.897693i	−0.996953	−	0.0780100i	$-0.975143\pi$
$31$	−134.258	+	154.942i	−0.777855	+	0.897693i	0.219097	+	0.975703i	$0.429689\pi$
$32$	−31.6743	−	4.55407i	−0.174977	−	0.0251579i
$33$	393.428	−	179.673i	2.07537	−	0.947788i
$34$	187.253	+	54.9824i	0.944518	+	0.277335i
$35$	111.910	+	36.1881i	0.540463	+	0.174768i
$36$	91.9409	+	201.322i	0.425652	+	0.932048i
$37$	255.597	+	36.7493i	1.13567	+	0.163285i	0.684404	−	0.729103i	$-0.260063\pi$
$37$	255.597	+	36.7493i	1.13567	+	0.163285i	0.451268	+	0.892388i	$0.350972\pi$
$38$	−84.8623	−	73.5336i	−0.362276	−	0.313914i
$39$	−257.496	+	563.837i	−1.05724	+	2.31503i
$40$	73.9033	+	50.3816i	0.292128	+	0.199151i
$41$	11.4906	+	79.9187i	0.0437689	+	0.304420i	0.999933	+	0.0115877i	$0.00368856\pi$
$41$	11.4906	+	79.9187i	0.0437689	+	0.304420i	−0.956164	+	0.292832i	$0.905402\pi$
$42$	103.212	+	160.601i	0.379188	+	0.590029i
$43$	−292.421	+	253.384i	−1.03706	+	0.898620i	−0.994938	−	0.100492i	$-0.967958\pi$
$43$	−292.421	+	253.384i	−1.03706	+	0.898620i	−0.0421252	+	0.999112i	$0.513413\pi$
$44$	182.945	−	53.7175i	0.626818	−	0.184050i
$45$	16.7969	−	618.388i	0.0556430	−	2.04853i
$46$	−27.8021	−	218.849i	−0.0891128	−	0.701469i
$47$			543.063i			1.68540i	0.538382	+	0.842701i	$0.319036\pi$
$47$			543.063i			1.68540i	−0.538382	+	0.842701i	$0.680964\pi$
$48$	40.9014	+	139.297i	0.122992	+	0.418872i
$49$	−152.146	−	175.585i	−0.443573	−	0.511911i
$50$	−123.544	−	217.340i	−0.349436	−	0.614732i
$51$	−126.005	−	876.384i	−0.345965	−	2.40624i
$52$	−147.732	+	229.876i	−0.393977	+	0.613040i
$53$	26.2649	+	11.9948i	0.0680709	+	0.0310869i	0.449160	−	0.893452i	$-0.351723\pi$
$53$	26.2649	+	11.9948i	0.0680709	+	0.0310869i	−0.381089	+	0.924538i	$0.624451\pi$
$54$	336.680	−	388.550i	0.848452	−	0.979165i
$55$	−525.256	−	90.1397i	−1.28774	−	0.220990i
$56$	34.9608	+	76.5535i	0.0834256	+	0.182677i
$57$	−143.524	+	488.798i	−0.333513	+	1.13584i
$58$	95.1861	−	324.174i	0.215492	−	0.733899i
$59$	282.264	+	618.071i	0.622841	+	1.36383i	0.913435	+	0.406984i	$0.133420\pi$
$59$	282.264	+	618.071i	0.622841	+	1.36383i	−0.290595	+	0.956846i	$0.593853\pi$
$60$	68.6338	−	399.939i	0.147676	−	0.860531i
$61$	−77.8902	+	89.8901i	−0.163489	+	0.188676i	−0.831583	−	0.555401i	$-0.812565\pi$
$61$	−77.8902	+	89.8901i	−0.163489	+	0.188676i	0.668094	+	0.744077i	$0.267110\pi$
$62$	372.982	+	170.335i	0.764013	+	0.348913i
$63$	314.691	−	489.669i	0.629323	−	0.979246i
$64$	9.10815	+	63.3486i	0.0177894	+	0.123728i
$65$	653.498	−	395.326i	1.24702	−	0.754372i
$66$	−566.472	−	653.744i	−1.05648	−	1.21925i
$67$	−31.2669	−	106.485i	−0.0570128	−	0.194168i	0.926062	−	0.377371i	$-0.123172\pi$
$67$	−31.2669	−	106.485i	−0.0570128	−	0.194168i	−0.983075	+	0.183203i	$0.941353\pi$
$68$		−	390.316i		−	0.696071i
$69$	−850.757	+	527.191i	−1.48433	+	0.919802i
$70$	6.38708	−	235.144i	0.0109057	−	0.401501i
$71$	940.078	−	276.032i	1.57136	−	0.461394i	0.623965	−	0.781453i	$-0.285521\pi$
$71$	940.078	−	276.032i	1.57136	−	0.461394i	0.947398	+	0.320059i	$0.103703\pi$
$72$	334.529	−	289.871i	0.547565	−	0.474468i
$73$	124.904	+	194.354i	0.200259	+	0.311609i	0.926829	−	0.375483i	$-0.122523\pi$
$73$	124.904	+	194.354i	0.200259	+	0.311609i	−0.726570	+	0.687092i	$0.758887\pi$
$74$	−73.4986	−	511.194i	−0.115460	−	0.803041i
$75$	−664.088	+	919.459i	−1.02243	+	1.41560i
$76$	−93.2930	+	204.283i	−0.140808	+	0.308327i
$77$	−378.971	−	328.380i	−0.560880	−	0.486005i
$78$	1227.08	+	176.428i	1.78128	+	0.256110i
$79$	−418.305	−	915.961i	−0.595734	−	1.30448i	−0.931914	−	0.362678i	$-0.881862\pi$
$79$	−418.305	−	915.961i	−0.595734	−	1.30448i	0.336180	−	0.941798i	$-0.390865\pi$
$80$	55.0397	−	170.208i	0.0769203	−	0.237872i
$81$	−804.592	−	236.250i	−1.10369	−	0.324074i
$82$	146.888	−	67.0817i	0.197818	−	0.0903406i
$83$	−302.544	−	43.4992i	−0.400103	−	0.0575261i	−0.0606734	−	0.998158i	$-0.519325\pi$
$83$	−302.544	−	43.4992i	−0.400103	−	0.0575261i	−0.339429	+	0.940632i	$0.610234\pi$
$84$	250.034	−	288.555i	0.324773	−	0.374808i
$85$	−479.982	+	979.707i	−0.612487	+	1.25017i
$86$	651.009	+	418.378i	0.816280	+	0.524591i
$87$	−1517.21	+	218.141i	−1.86967	+	0.268818i
$88$	−206.166	−	320.801i	−0.249743	−	0.388608i
$89$	50.6205	+	58.4191i	0.0602894	+	0.0695777i	0.785093	−	0.619378i	$-0.212615\pi$
$89$	50.6205	+	58.4191i	0.0602894	+	0.0695777i	−0.724804	+	0.688955i	$0.758070\pi$
$90$	−1196.14	+	316.207i	−1.40094	+	0.370346i
$91$	718.648			0.827854
$92$	−404.303	+	176.666i	−0.458169	+	0.200203i
$93$		−	1860.26i		−	2.07419i
$94$	1042.13	−	305.997i	1.14348	−	0.335757i
$95$	485.381	−	398.033i	0.524200	−	0.429866i
$96$	244.263	−	156.978i	0.259687	−	0.166891i
$97$	706.672	−	101.604i	0.739708	−	0.106354i	0.237848	−	0.971302i	$-0.423558\pi$
$97$	706.672	−	101.604i	0.739708	−	0.106354i	0.501861	+	0.864949i	$0.332649\pi$
$98$	−251.217	+	390.902i	−0.258947	+	0.402929i
$99$	−1095.64	+	2399.11i	−1.11228	+	2.43556i
$100$	−347.460	+	359.543i	−0.347460	+	0.359543i
$101$	−112.243	+	780.668i	−0.110580	+	0.769103i	0.856777	+	0.515687i	$0.172463\pi$
$101$	−112.243	+	780.668i	−0.110580	+	0.769103i	−0.967357	+	0.253416i	$0.918446\pi$
$102$	−1610.77	+	735.614i	−1.56363	+	0.714084i
$103$	−204.615	+	696.856i	−0.195741	+	0.666633i	0.801866	+	0.597503i	$0.203841\pi$
$103$	−204.615	+	696.856i	−0.195741	+	0.666633i	−0.997608	+	0.0691301i	$0.977978\pi$
$104$	524.371	+	153.969i	0.494411	+	0.145172i
$105$	−982.438	+	416.808i	−0.913106	+	0.387394i
$106$	8.21845	−	57.1606i	0.00753062	−	0.0523766i
$107$	1239.85	+	1074.34i	1.12020	+	0.970657i	0.999757	−	0.0220635i	$-0.00702359\pi$
$107$	1239.85	+	1074.34i	1.12020	+	0.970657i	0.120441	+	0.992720i	$0.461569\pi$
$108$	−935.329	−	427.150i	−0.833353	−	0.380579i
$109$	−107.969	−	69.3877i	−0.0948770	−	0.0609737i	0.492342	−	0.870402i	$-0.336141\pi$
$109$	−107.969	−	69.3877i	−0.0948770	−	0.0609737i	−0.587219	+	0.809428i	$0.699777\pi$
$110$	122.987	+	1058.75i	0.106603	+	0.917707i
$111$	−1971.09	+	1266.74i	−1.68547	+	1.08319i
$112$	127.206	−	110.225i	0.107320	−	0.0929932i
$113$	−208.959	−	711.649i	−0.173958	−	0.592446i	−0.999601	−	0.0282528i	$-0.991006\pi$
$113$	−208.959	−	711.649i	−0.173958	−	0.592446i	0.825643	−	0.564193i	$-0.190813\pi$
$114$	1018.87			0.837067
$115$	1232.07	+	53.7457i	0.999050	+	0.0435810i
$116$	−675.720			−0.540853
$117$	−1064.90	−	3626.73i	−0.841456	−	2.86574i
$118$	1027.02	−	889.921i	0.801231	−	0.694270i
$119$	−863.561	+	554.977i	−0.665231	+	0.427518i
$120$	−806.149	+	93.6441i	−0.613259	+	0.0712375i
$121$	791.748	+	508.826i	0.594852	+	0.382288i
$122$	216.386	+	98.8203i	0.160579	+	0.0733342i
$123$	−553.669	−	479.757i	−0.405876	−	0.351693i
$124$	116.709	−	811.726i	0.0845221	−	0.587864i
$125$	1314.28	−	475.184i	0.940420	−	0.340014i
$126$	−1116.99	−	327.976i	−0.789754	−	0.231893i
$127$	292.495	−	996.146i	0.204368	−	0.696013i	−0.791974	−	0.610555i	$-0.790946\pi$
$127$	292.495	−	996.146i	0.204368	−	0.696013i	0.996342	−	0.0854581i	$-0.0272354\pi$
$128$	116.433	−	53.1731i	0.0804009	−	0.0367178i
$129$	499.644	−	3475.10i	0.341017	−	2.37183i
$130$	−1126.85	−	1031.30i	−0.760240	−	0.695777i
$131$	−35.8231	+	78.4417i	−0.0238922	+	0.0523167i	−0.921202	−	0.389085i	$-0.872791\pi$
$131$	−35.8231	+	78.4417i	−0.0238922	+	0.0523167i	0.897310	+	0.441402i	$0.145519\pi$
$132$	−935.338	+	1455.41i	−0.616748	+	0.959679i
$133$	584.619	−	84.0555i	0.381149	−	0.0548010i
$134$	−186.726	+	120.001i	−0.120378	+	0.0773622i
$135$	1822.43	+	2222.36i	1.16185	+	1.41682i
$136$	−749.011	+	219.930i	−0.472259	+	0.138668i
$137$		−	799.081i		−	0.498322i	−0.968462	−	0.249161i	$-0.919845\pi$
$137$		−	799.081i		−	0.498322i	0.968462	−	0.249161i	$-0.0801549\pi$
$138$	1491.04	+	1335.54i	0.919755	+	0.823829i
$139$	1951.21			1.19064			0.595321	−	0.803488i	$-0.297025\pi$
$139$	1951.21			1.19064			0.595321	+	0.803488i	$0.297025\pi$
$140$	−454.837	+	120.239i	−0.274577	+	0.0725859i
$141$	−3226.86	−	3724.00i	−1.92731	−	2.22423i
$142$	−1059.40	−	1648.46i	−0.626078	−	0.974196i
$143$	−3223.16	+	463.421i	−1.88486	+	0.271001i
$144$	−744.755	−	478.625i	−0.430992	−	0.276982i
$145$	1696.08	+	830.951i	0.971391	+	0.475908i
$146$	302.584	−	349.200i	0.171521	−	0.197945i
$147$	2086.65	+	300.014i	1.17077	+	0.168332i
$148$	−939.560	+	429.082i	−0.521833	+	0.238313i
$149$	492.763	+	144.688i	0.270931	+	0.0795526i	0.414376	−	0.910106i	$-0.364000\pi$
$149$	492.763	+	144.688i	0.270931	+	0.0795526i	−0.143445	+	0.989658i	$0.545818\pi$
$150$	2138.62	+	756.294i	1.16412	+	0.411674i
$151$	−852.413	−	1866.52i	−0.459393	−	1.00593i	−0.987626	−	0.156831i	$-0.949872\pi$
$151$	−852.413	−	1866.52i	−0.459393	−	1.00593i	0.528232	−	0.849100i	$-0.322855\pi$
$152$	444.584	+	63.9215i	0.237240	+	0.0341100i
$153$	4080.38	+	3535.67i	2.15607	+	1.86825i
$154$	−416.620	+	912.271i	−0.218001	+	0.477356i
$155$	−1291.14	+	1893.94i	−0.669078	+	0.981451i
$156$	−352.856	−	2454.17i	−0.181097	−	1.25956i
$157$	1408.51	+	2191.69i	0.715998	+	1.11411i	0.988391	+	0.151929i	$0.0485484\pi$
$157$	1408.51	+	2191.69i	0.715998	+	1.11411i	−0.272394	+	0.962186i	$0.587815\pi$
$158$	−1522.02	+	1318.83i	−0.766361	+	0.664056i
$159$	−251.381	+	73.8121i	−0.125382	+	0.0368156i
$160$	−357.639	−	9.71433i	−0.176712	−	0.00479991i
$161$	965.731	+	643.312i	0.472735	+	0.314907i
$162$			1677.12i			0.813376i
$163$	−432.662	−	1473.51i	−0.207906	−	0.708064i	−0.995742	−	0.0921791i	$-0.970617\pi$
$163$	−432.662	−	1473.51i	−0.207906	−	0.708064i	0.787836	−	0.615885i	$-0.211201\pi$
$164$	−211.495	−	244.079i	−0.100701	−	0.116215i
$165$	4137.49	−	2502.93i	1.95214	−	1.18093i
$166$	86.9985	+	605.088i	0.0406771	+	0.282915i
$167$	1546.45	−	2406.32i	0.716574	−	1.11501i	−0.271709	−	0.962380i	$-0.587589\pi$
$167$	1546.45	−	2406.32i	0.716574	−	1.11501i	0.988283	−	0.152632i	$-0.0487749\pi$
$168$	−694.618	−	317.221i	−0.318994	−	0.145680i
$169$	1617.33	−	1866.50i	0.736156	−	0.849569i
$170$	2150.50	+	369.049i	0.970210	+	0.166499i
$171$	−1290.49	−	2825.78i	−0.577113	−	1.26370i
$172$	436.041	−	1485.02i	0.193301	−	0.658323i
$173$	−618.421	+	2106.15i	−0.271779	+	0.925593i	0.704614	+	0.709590i	$0.251120\pi$
$173$	−618.421	+	2106.15i	−0.271779	+	0.925593i	−0.976393	+	0.216002i	$0.930698\pi$
$174$	1273.50	+	2788.58i	0.554850	+	1.21495i
$175$	1289.52	+	257.522i	0.557019	+	0.111239i
$176$	−499.445	+	576.390i	−0.213904	+	0.246858i
$177$	−5608.15	−	2561.16i	−2.38155	−	1.08762i
$178$	83.5826	−	130.057i	0.0351954	−	0.0547651i
$179$	487.332	+	3389.47i	0.203491	+	1.41531i	0.793822	+	0.608151i	$0.208088\pi$
$179$	487.332	+	3389.47i	0.203491	+	1.41531i	−0.590330	+	0.807162i	$0.701003\pi$
$180$	1280.78	+	2117.21i	0.530355	+	0.876708i
$181$	−1981.59	−	2286.88i	−0.813759	−	0.939128i	0.185292	−	0.982683i	$-0.440677\pi$
$181$	−1981.59	−	2286.88i	−0.813759	−	0.939128i	−0.999051	+	0.0435557i	$0.986131\pi$
$182$	−404.933	−	1379.07i	−0.164921	−	0.561669i
$183$		−	1079.23i		−	0.435952i
$184$	566.830	+	676.308i	0.227105	+	0.270968i
$185$	2885.98	+	78.3901i	1.14693	+	0.0311533i
$186$	−3569.81	+	1048.19i	−1.40726	+	0.413210i
$187$	3515.23	−	3045.96i	1.37465	−	1.19114i
$188$	−1174.41	−	1827.42i	−0.455599	−	0.708925i
$189$	384.856	+	2676.73i	0.148117	+	1.03018i
$190$	−1037.31	−	707.162i	−0.396077	−	0.270015i
$191$	1628.71	−	3566.37i	0.617010	−	1.35106i	−0.300663	−	0.953730i	$-0.597208\pi$
$191$	1628.71	−	3566.37i	0.617010	−	1.35106i	0.917674	−	0.397334i	$-0.130065\pi$
$192$	−438.873	−	380.286i	−0.164963	−	0.142941i
$193$	2433.62	+	349.902i	0.907648	+	0.130500i	0.580299	−	0.814403i	$-0.302936\pi$
$193$	2433.62	+	349.902i	0.907648	+	0.130500i	0.327349	+	0.944904i	$0.393845\pi$
$194$	−593.162	−	1298.84i	−0.219518	−	0.480678i
$195$	−2132.28	+	6593.97i	−0.783054	+	2.42156i
$196$	891.687	+	261.823i	0.324959	+	0.0954165i
$197$	−4627.61	+	2113.36i	−1.67362	+	0.764318i	−0.673950	+	0.738777i	$0.735403\pi$
$197$	−4627.61	+	2113.36i	−1.67362	+	0.764318i	−0.999674	+	0.0255408i	$0.991869\pi$
$198$	5221.22	+	750.698i	1.87402	+	0.269443i
$199$	−11.2807	+	13.0186i	−0.00401842	+	0.00463751i	−0.757755	−	0.652539i	$-0.773704\pi$
$199$	−11.2807	+	13.0186i	−0.00401842	+	0.00463751i	0.753737	+	0.657176i	$0.228249\pi$
$200$	885.740	+	464.182i	0.313156	+	0.164113i
$201$	847.140	+	544.424i	0.297277	+	0.191048i
$202$	1561.34	−	224.486i	0.543838	−	0.0781921i
$203$	960.781	+	1495.01i	0.332185	+	0.516891i
$204$	2319.24	+	2676.55i	0.795979	+	0.918608i
$205$	230.710	+	872.727i	0.0786025	+	0.297336i
$206$	1452.55			0.491281
$207$	1815.50	−	5826.93i	0.609595	−	1.95652i
$208$		−	1093.02i		−	0.364361i
$209$	−2567.84	+	753.985i	−0.849861	+	0.249542i
$210$	1353.42	+	1650.43i	0.444737	+	0.542335i
$211$	−1408.69	+	905.309i	−0.459612	+	0.295375i	−0.749884	−	0.661570i	$-0.769891\pi$
$211$	−1408.69	+	905.309i	−0.459612	+	0.295375i	0.290272	+	0.956944i	$0.406254\pi$
$212$	−114.321	+	16.4369i	−0.0370359	+	0.00532495i
$213$	−4806.31	+	7478.76i	−1.54612	+	2.40581i
$214$	1363.03	−	2984.61i	0.435396	−	0.953383i
$215$	−2920.64	+	3191.23i	−0.926448	+	1.01228i
$216$	−292.670	+	2035.57i	−0.0921931	+	0.641217i
$217$	−1961.86	+	895.950i	−0.613731	+	0.280281i
$218$	−72.3171	+	246.289i	−0.0224676	+	0.0765175i
$219$	−2011.36	−	590.588i	−0.620616	−	0.182229i
$220$	1962.43	−	832.578i	0.601395	−	0.255147i
$221$	−948.667	+	6598.12i	−0.288752	+	2.00832i
$222$	3541.50	+	3068.73i	1.07068	+	0.927746i
$223$	2965.13	+	1354.13i	0.890403	+	0.406633i	0.807461	−	0.589921i	$-0.200841\pi$
$223$	2965.13	+	1354.13i	0.890403	+	0.406633i	0.0829419	+	0.996554i	$0.473568\pi$
$224$	−283.195	−	181.999i	−0.0844723	−	0.0542870i
$225$	−611.217	−	6889.28i	−0.181101	−	2.04127i
$226$	−1247.90	+	801.979i	−0.367298	+	0.236048i
$227$	−3127.36	+	2709.87i	−0.914406	+	0.792337i	−0.978637	−	0.205598i	$-0.934086\pi$
$227$	−3127.36	+	2709.87i	−0.914406	+	0.792337i	0.0642306	+	0.997935i	$0.479541\pi$
$228$	−574.096	−	1955.19i	−0.166756	−	0.567920i
$229$	−469.062			−0.135356			−0.0676780	−	0.997707i	$-0.521559\pi$
$229$	−469.062			−0.135356			−0.0676780	+	0.997707i	$0.521559\pi$
$230$	−591.089	−	2394.60i	−0.169458	−	0.686501i
$231$	4549.98			1.29596
$232$	380.744	+	1296.70i	0.107746	+	0.366950i
$233$	2249.11	−	1948.87i	0.632379	−	0.547959i	−0.278603	−	0.960406i	$-0.589871\pi$
$233$	2249.11	−	1948.87i	0.632379	−	0.547959i	0.910982	+	0.412447i	$0.135326\pi$
$234$	−6359.60	+	4087.07i	−1.77667	+	1.14180i
$235$	700.583	+	6031.08i	0.194472	+	1.67414i
$236$	−2286.44	−	1469.41i	−0.630655	−	0.405297i
$237$	8311.09	+	3795.55i	2.27790	+	1.04028i
$238$	1551.58	+	1344.45i	0.422579	+	0.366167i
$239$	106.061	−	737.670i	0.0287051	−	0.199648i	−0.970422	−	0.241413i	$-0.922389\pi$
$239$	106.061	−	737.670i	0.0287051	−	0.199648i	0.999127	+	0.0417652i	$0.0132981\pi$
$240$	633.939	+	1494.22i	0.170502	+	0.401882i
$241$	−3265.90	−	958.955i	−0.872926	−	0.256314i	−0.185567	−	0.982632i	$-0.559412\pi$
$241$	−3265.90	−	958.955i	−0.872926	−	0.256314i	−0.687360	+	0.726317i	$0.741230\pi$
$242$	530.307	−	1806.06i	0.140865	−	0.479743i
$243$	607.719	−	277.536i	0.160433	−	0.0732672i
$244$	67.7087	−	470.924i	0.0177648	−	0.123557i
$245$	−1916.19	−	1753.72i	−0.499678	−	0.457310i
$246$	−608.674	+	1332.81i	−0.157755	+	0.345434i
$247$	2073.59	−	3226.56i	0.534167	−	0.831180i
$248$	−1623.45	+	233.417i	−0.415683	+	0.0597661i
$249$	2333.13	−	1499.41i	0.593800	−	0.381612i
$250$	−1652.42	−	2254.33i	−0.418033	−	0.570305i
$251$	−2492.54	+	731.875i	−0.626803	+	0.184046i	−0.579682	−	0.814843i	$-0.696823\pi$
$251$	−2492.54	+	731.875i	−0.626803	+	0.184046i	−0.0471217	+	0.998889i	$0.515005\pi$
$252$			2328.28i			0.582016i
$253$	−4746.18	−	2262.53i	−1.17941	−	0.562229i
$254$	−2076.40			−0.512933
$255$	−2529.96	−	9570.27i	−0.621302	−	2.35025i
$256$	−167.644	−	193.472i	−0.0409288	−	0.0472343i
$257$	3463.08	+	5388.66i	0.840549	+	1.30792i	0.949466	+	0.313869i	$0.101625\pi$
$257$	3463.08	+	5388.66i	0.840549	+	1.30792i	−0.108917	+	0.994051i	$0.534738\pi$
$258$	−6950.21	+	999.289i	−1.67714	+	0.241136i
$259$	2285.26	+	1468.64i	0.548258	+	0.352344i
$260$	−1344.11	+	2743.51i	−0.320609	+	0.654405i
$261$	6120.99	−	7064.00i	1.45165	−	1.67529i
$262$	170.714	+	24.5449i	0.0402547	+	0.00578775i
$263$	1656.68	−	756.581i	0.388424	−	0.177387i	−0.211625	−	0.977351i	$-0.567875\pi$
$263$	1656.68	−	756.581i	0.388424	−	0.177387i	0.600048	+	0.799964i	$0.295148\pi$
$264$	3319.95	+	974.825i	0.773973	+	0.227259i
$265$	307.163	+	99.3266i	0.0712032	+	0.0230248i
$266$	−490.714	−	1074.51i	−0.113111	−	0.247679i
$267$	−694.249	−	99.8179i	−0.159129	−	0.0228792i
$268$	335.494	+	290.707i	0.0764686	+	0.0662604i
$269$	2746.52	−	6014.05i	0.622522	−	1.36313i	−0.291148	−	0.956678i	$-0.594037\pi$
$269$	2746.52	−	6014.05i	0.622522	−	1.36313i	0.913671	−	0.406456i	$-0.133235\pi$
$270$	3237.81	−	4749.44i	0.729802	−	1.07052i
$271$	−592.432	−	4120.45i	−0.132796	−	0.923615i	−0.941887	−	0.335931i	$-0.890949\pi$
$271$	−592.432	−	4120.45i	−0.132796	−	0.923615i	0.809091	−	0.587684i	$-0.199960\pi$
$272$	844.084	+	1313.42i	0.188162	+	0.292786i
$273$	−4928.05	+	4270.18i	−1.09252	+	0.946677i
$274$	−1533.43	+	450.254i	−0.338094	+	0.0992732i
$275$	−5949.60	−	323.449i	−1.30463	−	0.0709263i
$276$	1722.72	−	3613.82i	0.375710	−	0.788139i
$277$		−	4954.46i		−	1.07467i	−0.843368	−	0.537337i	$-0.819430\pi$
$277$		−	4954.46i		−	1.07467i	0.843368	−	0.537337i	$-0.180570\pi$
$278$	−1099.44	−	3744.34i	−0.237194	−	0.807808i
$279$	7428.61	+	8573.08i	1.59405	+	1.83963i
$280$	487.021	+	805.076i	0.103947	+	0.171830i
$281$	−393.303	−	2735.48i	−0.0834964	−	0.580730i	−0.988022	−	0.154311i	$-0.950684\pi$
$281$	−393.303	−	2735.48i	−0.0834964	−	0.580730i	0.904526	−	0.426419i	$-0.140225\pi$
$282$	−5328.07	+	8290.64i	−1.12511	+	1.75071i
$283$	4063.39	+	1855.69i	0.853510	+	0.389785i	0.793615	−	0.608420i	$-0.208196\pi$
$283$	4063.39	+	1855.69i	0.853510	+	0.389785i	0.0598943	+	0.998205i	$0.480924\pi$
$284$	−2566.44	+	2961.83i	−0.536233	+	0.618846i
$285$	−963.352	+	5613.58i	−0.200225	+	1.16674i
$286$	2705.44	+	5924.08i	0.559356	+	1.22482i
$287$	−239.297	+	814.972i	−0.0492170	+	0.167618i
$288$	−498.831	+	1698.86i	−0.102062	+	0.347592i
$289$	−1914.51	−	4192.20i	−0.389683	−	0.853287i
$290$	638.901	−	3722.96i	0.129371	−	0.753862i
$291$	−4242.20	+	4895.76i	−0.854578	+	0.986235i
$292$	−840.606	−	383.892i	−0.168468	−	0.0769369i
$293$	−2054.35	+	3196.64i	−0.409613	+	0.637370i	−0.983361	−	0.181662i	$-0.941852\pi$
$293$	−2054.35	+	3196.64i	−0.409613	+	0.637370i	0.573748	+	0.819032i	$0.305489\pi$
$294$	−600.029	−	4173.29i	−0.119028	−	0.827861i
$295$	3932.07	+	6499.95i	0.776048	+	1.28285i
$296$	1352.81	+	1561.23i	0.265644	+	0.306569i
$297$	−3452.19	−	11757.1i	−0.674466	−	2.29702i
$298$		−	1027.13i		−	0.199665i
$299$	7263.95	−	2003.79i	1.40497	−	0.387566i
$300$	246.280	−	4530.12i	0.0473965	−	0.871823i
$301$	−3905.54	+	1146.77i	−0.747879	+	0.219597i
$302$	−3101.53	+	2687.49i	−0.590970	+	0.512078i
$303$	−3869.01	−	6020.29i	−0.733560	−	1.14144i
$304$	−127.843	−	889.167i	−0.0241194	−	0.167754i
$305$	−749.059	+	1098.77i	−0.140626	+	0.206280i
$306$	4485.75	−	9822.43i	0.838018	−	1.83500i
$307$	−2800.05	−	2426.26i	−0.520545	−	0.451055i	0.354528	−	0.935045i	$-0.384641\pi$
$307$	−2800.05	−	2426.26i	−0.520545	−	0.451055i	−0.875073	+	0.483991i	$0.839187\pi$
$308$	1985.39	+	285.455i	0.367298	+	0.0528095i
$309$	−2737.56	−	5994.43i	−0.503995	−	1.10360i
$310$	4361.96	+	1410.52i	0.799170	+	0.258426i
$311$	115.145	+	33.8095i	0.0209944	+	0.00616450i	0.292213	−	0.956353i	$-0.405608\pi$
$311$	115.145	+	33.8095i	0.0209944	+	0.00616450i	−0.271219	+	0.962518i	$0.587427\pi$
$312$	−4510.69	+	2059.97i	−0.818487	+	0.373790i
$313$	−1466.37	−	210.832i	−0.264806	−	0.0380733i	0.00863304	−	0.999963i	$-0.497252\pi$
$313$	−1466.37	−	210.832i	−0.264806	−	0.0380733i	−0.273439	+	0.961889i	$0.588161\pi$
$314$	3412.18	−	3937.86i	0.613249	−	0.707727i
$315$	2863.15	−	5844.07i	0.512128	−	1.04532i
$316$	3388.43	+	2177.61i	0.603208	+	0.387658i
$317$	−2467.17	+	354.726i	−0.437130	+	0.0628498i	−0.357367	−	0.933964i	$-0.616325\pi$
$317$	−2467.17	+	354.726i	−0.437130	+	0.0628498i	−0.0797631	+	0.996814i	$0.525416\pi$
$318$	283.289	+	440.806i	0.0499561	+	0.0777332i
$319$	−5273.20	−	6085.60i	−0.925525	−	1.06811i
$320$	182.875	+	691.778i	0.0319470	+	0.120849i
$321$	−14885.8			−2.58831
$322$	690.351	−	2215.71i	0.119477	−	0.383468i
$323$			5478.52i			0.943756i
$324$	3218.37	−	944.999i	0.551847	−	0.162037i
$325$	6747.53	−	5233.41i	1.15165	−	0.893223i
$326$	−2583.86	+	1660.55i	−0.438978	+	0.282114i
$327$	1152.69	−	165.731i	0.194935	−	0.0280274i
$328$	−349.213	+	543.386i	−0.0587868	+	0.0914740i
$329$	−2373.24	+	5196.67i	−0.397693	+	0.870826i
$330$	−7134.42	−	6529.48i	−1.19011	−	1.08920i
$331$	582.749	−	4053.11i	0.0967697	−	0.673048i	−0.882474	−	0.470361i	$-0.844124\pi$
$331$	582.749	−	4053.11i	0.0967697	−	0.673048i	0.979244	−	0.202687i	$-0.0649673\pi$
$332$	1112.13	−	507.895i	0.183844	−	0.0839589i
$333$	4025.34	−	13709.0i	0.662423	−	2.25601i
$334$	−5489.07	−	1611.74i	−0.899247	−	0.264043i
$335$	−484.611	−	1142.25i	−0.0790363	−	0.186292i
$336$	−217.350	+	1511.71i	−0.0352900	+	0.245447i
$337$	6392.14	+	5538.82i	1.03324	+	0.895308i	0.994583	−	0.103944i	$-0.0331464\pi$
$337$	6392.14	+	5538.82i	1.03324	+	0.895308i	0.0386574	+	0.999253i	$0.487692\pi$
$338$	−4493.11	−	2051.93i	−0.723056	−	0.330208i
$339$	5661.51	+	3638.43i	0.907053	+	0.582928i
$340$	−503.531	−	4334.72i	−0.0803171	−	0.691421i
$341$	8221.26	−	5283.48i	1.30559	−	0.839051i
$342$	−4695.49	+	4068.67i	−0.742407	+	0.643299i
$343$	−1705.16	−	5807.25i	−0.268426	−	0.914174i
$344$	−3095.42			−0.485157
$345$	−8768.11	+	6952.33i	−1.36829	+	1.08493i
$346$	4390.13			0.682124
$347$	2238.19	+	7622.56i	0.346260	+	1.17925i	0.930076	+	0.367366i	$0.119740\pi$
$347$	2238.19	+	7622.56i	0.346260	+	1.17925i	−0.583817	+	0.811885i	$0.698441\pi$
$348$	4633.67	−	4015.10i	0.713767	−	0.618483i
$349$	−410.624	+	263.892i	−0.0629806	+	0.0404752i	−0.571752	−	0.820426i	$-0.693736\pi$
$349$	−410.624	+	263.892i	−0.0629806	+	0.0404752i	0.508772	+	0.860902i	$0.330100\pi$
$350$	−232.417	−	2619.67i	−0.0354949	−	0.400078i
$351$	14773.1	+	9494.11i	2.24653	+	1.44376i
$352$	1387.50	+	633.652i	0.210097	+	0.0959482i
$353$	−3753.88	−	3252.76i	−0.566003	−	0.490444i	0.324212	−	0.945984i	$-0.394901\pi$
$353$	−3753.88	−	3252.76i	−0.566003	−	0.490444i	−0.890215	+	0.455540i	$0.849446\pi$
$354$	−1754.83	+	12205.1i	−0.263469	+	1.83246i
$355$	10084.1	−	4278.27i	1.50763	−	0.639626i
$356$	−296.674	−	87.1112i	−0.0441676	−	0.0129688i
$357$	2624.12	−	8936.94i	0.389029	−	1.32491i
$358$	6229.75	−	2845.03i	0.919700	−	0.420013i
$359$	−1095.82	+	7621.61i	−0.161101	+	1.12048i	0.735462	+	0.677566i	$0.236965\pi$
$359$	−1095.82	+	7621.61i	−0.161101	+	1.12048i	−0.896563	+	0.442916i	$0.853944\pi$
$360$	3341.22	−	3650.78i	0.489160	−	0.534480i
$361$	−1539.86	+	3371.83i	−0.224502	+	0.491592i
$362$	−3271.93	+	5091.22i	−0.475051	+	0.739194i
$363$	−8452.75	+	1215.32i	−1.22219	+	0.175724i
$364$	−2418.26	+	1554.12i	−0.348218	+	0.223786i
$365$	1637.87	+	1997.30i	0.234876	+	0.286420i
$366$	−2071.03	+	608.110i	−0.295778	+	0.0868481i
$367$		−	9309.15i		−	1.32407i	−0.749473	−	0.662035i	$-0.769693\pi$
$367$		−	9309.15i		−	1.32407i	0.749473	−	0.662035i	$-0.230307\pi$
$368$	978.436	−	1468.81i	0.138599	−	0.208063i
$369$	4467.43			0.630258
$370$	−1475.72	−	5582.33i	−0.207349	−	0.784355i
$371$	198.915	+	229.560i	0.0278360	+	0.0321245i
$372$	4022.93	+	6259.80i	0.560697	+	0.872461i
$373$	−10128.1	+	1456.20i	−1.40593	+	0.202142i	−0.803156	−	0.595769i	$-0.796847\pi$
$373$	−10128.1	+	1456.20i	−1.40593	+	0.202142i	−0.602775	+	0.797912i	$0.705938\pi$
$374$	−7825.87	−	5029.38i	−1.08199	−	0.695356i
$375$	−6188.99	+	11067.9i	−0.852261	+	1.52412i
$376$	−2845.05	+	3283.36i	−0.390218	+	0.450336i
$377$	11422.7	+	1642.34i	1.56048	+	0.224363i
$378$	4919.76	−	2246.78i	0.669431	−	0.305719i
$379$	−3545.23	−	1040.97i	−0.480492	−	0.141085i	0.0325122	−	0.999471i	$-0.489649\pi$
$379$	−3545.23	−	1040.97i	−0.480492	−	0.141085i	−0.513004	+	0.858386i	$0.671467\pi$
$380$	−772.543	+	2389.05i	−0.104291	+	0.322515i
$381$	3913.31	+	8568.96i	0.526207	+	1.15223i
$382$	−7761.53	−	1115.94i	−1.03957	−	0.149467i
$383$	−8543.90	−	7403.33i	−1.13988	−	0.987709i	−0.139880	−	0.990169i	$-0.544672\pi$
$383$	−8543.90	−	7403.33i	−1.13988	−	0.987709i	−0.999997	+	0.00245984i	$0.999217\pi$
$384$	−482.473	+	1056.47i	−0.0641175	+	0.140398i
$385$	−4632.35	−	3157.99i	−0.613212	−	0.418041i
$386$	−699.805	−	4867.25i	−0.0922775	−	0.641804i
$387$	11574.6	+	18010.4i	1.52033	+	2.36568i
$388$	−2158.24	+	1870.12i	−0.282391	+	0.244694i
$389$	1333.49	−	391.548i	0.173806	−	0.0510341i	−0.193672	−	0.981066i	$-0.562040\pi$
$389$	1333.49	−	391.548i	0.173806	−	0.0510341i	0.367478	+	0.930032i	$0.380221\pi$
$390$	13855.2	+	376.340i	1.79894	+	0.0488634i
$391$	−7181.28	+	8017.45i	−0.928830	+	1.03698i
$392$		−	1858.66i		−	0.239481i
$393$	−220.445	−	750.765i	−0.0282951	−	0.0963641i
$394$	6663.01	+	7689.52i	0.851973	+	0.983230i
$395$	−5827.20	−	9632.71i	−0.742274	−	1.22702i
$396$	−1501.40	−	10442.4i	−0.190525	−	1.32513i
$397$	−3030.45	+	4715.48i	−0.383108	+	0.596128i	−0.978234	−	0.207504i	$-0.933466\pi$
$397$	−3030.45	+	4715.48i	−0.383108	+	0.596128i	0.595126	+	0.803633i	$0.297102\pi$
$398$	31.3388	+	14.3119i	0.00394691	+	0.00180249i
$399$	−3509.51	+	4050.18i	−0.440338	+	0.508178i
$400$	391.674	−	1961.27i	0.0489593	−	0.245159i
$401$	−365.166	−	799.602i	−0.0454751	−	0.0995765i	0.885531	−	0.464581i	$-0.153795\pi$
$401$	−365.166	−	799.602i	−0.0454751	−	0.0995765i	−0.931006	+	0.365004i	$0.881068\pi$
$402$	567.408	−	1932.41i	0.0703973	−	0.239751i
$403$	−3945.81	+	13438.2i	−0.487729	+	1.66105i
$404$	−1310.54	−	2869.69i	−0.161391	−	0.353397i
$405$	−9240.31	−	1585.74i	−1.13371	−	0.194558i
$406$	2327.53	−	2686.11i	0.284515	−	0.328348i
$407$	−11196.5	−	5113.28i	−1.36361	−	0.622742i
$408$	3829.45	−	5958.74i	0.464672	−	0.723043i
$409$	949.560	+	6604.34i	0.114799	+	0.798444i	0.963141	+	0.268996i	$0.0866918\pi$
$409$	949.560	+	6604.34i	0.114799	+	0.798444i	−0.848342	+	0.529448i	$0.822399\pi$
$410$	1544.75	−	934.481i	0.186073	−	0.112563i
$411$	4748.11	+	5479.61i	0.569847	+	0.657638i
$412$	−818.461	−	2787.42i	−0.0978706	−	0.333317i
$413$			7147.96i			0.851642i
$414$	−12204.8	−	200.654i	−1.44887	−	0.0238203i
$415$	−3416.07	−	92.7885i	−0.404068	−	0.0109754i
$416$	−2097.48	+	615.877i	−0.247206	+	0.0725862i
$417$	−13380.2	+	11594.0i	−1.57130	+	1.36154i
$418$	2893.77	+	4502.80i	0.338610	+	0.526888i
$419$	−368.471	−	2562.77i	−0.0429617	−	0.298805i	−0.999962	−	0.00871837i	$-0.997225\pi$
$419$	−368.471	−	2562.77i	−0.0429617	−	0.298805i	0.957000	−	0.290087i	$-0.0936843\pi$
$420$	2404.54	−	3527.15i	0.279356	−	0.409779i
$421$	−3206.22	+	7020.65i	−0.371168	+	0.812745i	0.628229	+	0.778028i	$0.283780\pi$
$421$	−3206.22	+	7020.65i	−0.371168	+	0.812745i	−0.999397	+	0.0347162i	$0.988947\pi$
$422$	2531.02	+	2193.14i	0.291963	+	0.252987i
$423$	29742.2	+	4276.29i	3.41872	+	0.491537i
$424$	95.9581	+	210.119i	0.0109909	+	0.0240667i
$425$	−4066.64	+	11499.5i	−0.464144	+	1.31249i
$426$	17059.8	+	5009.22i	1.94026	+	0.569712i
$427$	−1138.18	+	519.787i	−0.128993	+	0.0589093i
$428$	−6495.45	−	933.905i	−0.733574	−	0.105472i
$429$	19348.9	−	22329.8i	2.17756	−	2.51303i
$430$	7769.62	+	3806.52i	0.871358	+	0.426900i
$431$	5607.73	+	3603.87i	0.626717	+	0.402766i	0.815093	−	0.579331i	$-0.196686\pi$
$431$	5607.73	+	3603.87i	0.626717	+	0.402766i	−0.188376	+	0.982097i	$0.560322\pi$
$432$	4071.14	−	585.341i	0.453409	−	0.0651903i
$433$	−4885.75	−	7602.38i	−0.542250	−	0.843758i	0.456698	−	0.889622i	$-0.349032\pi$
$433$	−4885.75	−	7602.38i	−0.542250	−	0.843758i	−0.998948	+	0.0458643i	$0.985396\pi$
$434$	2824.75	+	3259.94i	0.312425	+	0.360558i
$435$	−16568.2	+	4379.89i	−1.82617	+	0.482757i
$436$	513.374			0.0563902
$437$	5674.85	−	2479.70i	0.621201	−	0.271442i
$438$			4192.54i			0.457369i
$439$	−5227.52	+	1534.94i	−0.568328	+	0.166876i	−0.553257	−	0.833010i	$-0.686615\pi$
$439$	−5227.52	+	1534.94i	−0.568328	+	0.166876i	−0.0150703	+	0.999886i	$0.504797\pi$
$440$	−2703.47	−	3296.74i	−0.292915	−	0.357195i
$441$	−10814.4	+	6950.02i	−1.16774	+	0.750461i
$442$	13196.2	−	1897.33i	1.42009	−	0.204179i
$443$	−370.958	+	577.222i	−0.0397850	+	0.0619066i	−0.860576	−	0.509321i	$-0.829896\pi$
$443$	−370.958	+	577.222i	−0.0397850	+	0.0619066i	0.820791	+	0.571228i	$0.193533\pi$
$444$	3893.33	−	8525.21i	0.416148	−	0.911236i
$445$	637.538	+	583.480i	0.0679150	+	0.0621564i
$446$	927.808	−	6453.05i	0.0985045	−	0.685114i
$447$	−4238.80	+	1935.80i	−0.448520	+	0.204832i
$448$	−189.682	+	645.998i	−0.0200036	+	0.0681262i
$449$	−12261.8	−	3600.38i	−1.28880	−	0.378424i	−0.435659	−	0.900112i	$-0.643485\pi$
$449$	−12261.8	−	3600.38i	−1.28880	−	0.378424i	−0.853137	+	0.521687i	$0.825303\pi$
$450$	−12876.0	+	5054.79i	−1.34885	+	0.529522i
$451$	547.723	−	3809.49i	0.0571868	−	0.397743i
$452$	2242.14	+	1942.82i	0.233321	+	0.202174i
$453$	16936.1	+	7734.47i	1.75658	+	0.802202i
$454$	6962.37	+	4474.44i	0.719736	+	0.462546i
$455$	7981.06	−	927.098i	0.822325	−	0.0955231i
$456$	−3428.50	+	2203.37i	−0.352093	+	0.226276i
$457$	11861.8	−	10278.3i	1.21416	−	1.05208i	0.217048	−	0.976161i	$-0.430357\pi$
$457$	11861.8	−	10278.3i	1.21416	−	1.05208i	0.997114	−	0.0759167i	$-0.0241883\pi$
$458$	264.300	+	900.124i	0.0269649	+	0.0918341i
$459$	−25083.9			−2.55080
$460$	−4262.15	+	2483.57i	−0.432008	+	0.251732i
$461$	795.463			0.0803653			0.0401826	−	0.999192i	$-0.487206\pi$
$461$	795.463			0.0803653			0.0401826	+	0.999192i	$0.487206\pi$
$462$	−2563.75	−	8731.34i	−0.258174	−	0.879261i
$463$	8473.81	−	7342.59i	0.850564	−	0.737018i	−0.116053	−	0.993243i	$-0.537024\pi$
$463$	8473.81	−	7342.59i	0.850564	−	0.737018i	0.966617	+	0.256225i	$0.0824788\pi$
$464$	2273.81	−	1461.29i	0.227497	−	0.146204i
$465$	−2399.84	−	20659.4i	−0.239334	−	2.06034i
$466$	−5007.15	−	3217.90i	−0.497750	−	0.319885i
$467$	−14694.8	−	6710.90i	−1.45609	−	0.664975i	−0.479005	−	0.877812i	$-0.659002\pi$
$467$	−14694.8	−	6710.90i	−1.45609	−	0.664975i	−0.977088	+	0.212837i	$0.931730\pi$
$468$	11426.4	+	9901.07i	1.12861	+	0.977942i
$469$	166.152	−	1155.62i	0.0163586	−	0.113777i
$470$	11178.8	−	4742.71i	1.09711	−	0.465457i
$471$	−22681.7	−	6659.94i	−2.21893	−	0.651537i
$472$	−1531.44	+	5215.60i	−0.149344	+	0.508618i
$473$	16777.0	−	7661.80i	1.63088	−	0.744799i
$474$	2600.59	−	18087.5i	0.252002	−	1.75272i
$475$	4876.99	−	5046.59i	0.471098	−	0.487481i
$476$	1705.72	−	3735.01i	0.164247	−	0.359651i
$477$	863.743	−	1344.01i	0.0829101	−	0.129011i
$478$	−1475.34	+	212.122i	−0.141173	+	0.0202976i
$479$	10529.0	−	6766.58i	1.00435	−	0.645455i	0.0684233	−	0.997656i	$-0.478203\pi$
$479$	10529.0	−	6766.58i	1.00435	−	0.645455i	0.935924	+	0.352201i	$0.114567\pi$
$480$	2510.19	−	2058.46i	0.238696	−	0.195741i
$481$	16925.7	−	4969.84i	1.60446	−	0.471113i
$482$			6807.56i			0.643311i
$483$	−10444.9	+	1326.90i	−0.983977	+	0.125002i
$484$	−3764.61			−0.353551
$485$	7716.99	−	2040.03i	0.722496	−	0.190996i
$486$	−875.016	−	1009.82i	−0.0816698	−	0.0942520i
$487$	−674.574	−	1049.66i	−0.0627677	−	0.0976684i	0.808451	−	0.588563i	$-0.200306\pi$
$487$	−674.574	−	1049.66i	−0.0627677	−	0.0976684i	−0.871219	+	0.490895i	$0.836670\pi$
$488$	−941.848	+	135.417i	−0.0873678	+	0.0125616i
$489$	11722.5	+	7533.59i	1.08407	+	0.696689i
$490$	−2285.65	+	4665.31i	−0.210725	+	0.430117i
$491$	7681.40	−	8864.81i	0.706022	−	0.814793i	−0.283531	−	0.958963i	$-0.591506\pi$
$491$	7681.40	−	8864.81i	0.706022	−	0.814793i	0.989553	+	0.144170i	$0.0460513\pi$
$492$	2900.61	+	417.045i	0.265792	+	0.0382151i
$493$	−14994.4	+	6847.71i	−1.36980	+	0.625569i
$494$	−7360.13	−	2161.13i	−0.670339	−	0.196829i
$495$	−9072.80	+	28057.2i	−0.823822	+	2.54763i
$496$	1362.68	+	2983.86i	0.123359	+	0.270119i
$497$	10202.1	+	1466.84i	0.920775	+	0.132387i
$498$	−4191.99	−	3632.38i	−0.377204	−	0.326849i
$499$	−272.111	+	595.840i	−0.0244115	+	0.0534538i	−0.921445	−	0.388509i	$-0.872990\pi$
$499$	−272.111	+	595.840i	−0.0244115	+	0.0534538i	0.897033	+	0.441963i	$0.145718\pi$
$500$	−3394.95	+	4441.21i	−0.303653	+	0.397234i
$501$	3693.67	+	25690.0i	0.329383	+	2.29091i
$502$	2808.92	+	4370.76i	0.249737	+	0.388599i
$503$	−14638.9	+	12684.7i	−1.29765	+	1.12442i	−0.313022	+	0.949746i	$0.601341\pi$
$503$	−14638.9	+	12684.7i	−1.29765	+	1.12442i	−0.984626	+	0.174673i	$0.944113\pi$
$504$	4467.94	−	1311.91i	0.394877	−	0.115946i
$505$	−239.427	+	8814.64i	−0.0210977	+	0.776725i
$506$	−1667.45	+	10382.7i	−0.146496	+	0.912190i
$507$			22409.5i			1.96300i
$508$	1169.98	+	3984.58i	0.102184	+	0.348007i
$509$	−12438.7	−	14355.1i	−1.08318	−	1.25005i	−0.966440	−	0.256891i	$-0.917302\pi$
$509$	−12438.7	−	14355.1i	−1.08318	−	1.25005i	−0.116738	−	0.993163i	$-0.537244\pi$
$510$	−16939.7	+	10247.5i	−1.47079	+	0.889736i
$511$	345.881	+	2405.65i	0.0299430	+	0.208258i
$512$	−276.808	+	430.722i	−0.0238932	+	0.0371785i
$513$	13128.4	+	5995.53i	1.12989	+	0.516002i
$514$	8389.44	−	9681.93i	0.719927	−	0.830840i
$515$	−1373.40	+	8003.01i	−0.117513	+	0.684767i
$516$	5833.82	+	12774.3i	0.497712	+	1.08984i
$517$	7293.00	−	24837.7i	0.620398	−	2.11288i
$518$	1530.65	−	5212.90i	0.129832	−	0.442166i
$519$	−8273.90	−	18117.3i	−0.699777	−	1.53230i
$520$	6022.12	+	1033.46i	0.507860	+	0.0871543i
$521$	−3294.47	+	3802.03i	−0.277032	+	0.319712i	−0.877166	−	0.480188i	$-0.840568\pi$
$521$	−3294.47	+	3802.03i	−0.277032	+	0.319712i	0.600134	+	0.799900i	$0.295114\pi$
$522$	−17004.7	−	7765.78i	−1.42581	−	0.651147i
$523$	5097.87	−	7932.44i	0.426222	−	0.663215i	−0.560028	−	0.828474i	$-0.689210\pi$
$523$	5097.87	−	7932.44i	0.426222	−	0.663215i	0.986250	+	0.165259i	$0.0528460\pi$
$524$	−49.0898	−	341.427i	−0.00409256	−	0.0284644i
$525$	−10372.9	+	5896.34i	−0.862307	+	0.490166i
$526$	−2385.35	−	2752.84i	−0.197731	−	0.228193i
$527$	−5636.20	−	19195.1i	−0.465876	−	1.58663i
$528$		−	6920.22i		−	0.570386i
$529$	11555.2	+	3809.74i	0.949713	+	0.313121i
$530$	17.5308	−	645.408i	0.00143677	−	0.0528957i
$531$	36072.9	−	10592.0i	2.94808	−	0.865634i
$532$	−1785.48	+	1547.12i	−0.145508	+	0.126083i
$533$	2982.00	+	4640.08i	0.242335	+	0.377081i
$534$	199.636	+	1388.50i	0.0161781	+	0.112521i
$535$	15155.4	+	10331.8i	1.22472	+	0.834918i
$536$	368.824	−	807.612i	0.0297216	−	0.0650812i
$537$	−23481.9	−	20347.2i	−1.88700	−	1.63510i
$538$	−13088.4	−	1881.83i	−1.04885	−	0.150802i
$539$	4600.57	+	10073.8i	0.367645	+	0.805030i
$540$	−10938.5	−	3537.16i	−0.871700	−	0.281880i
$541$	−4101.77	−	1204.39i	−0.325968	−	0.0957128i	0.114654	−	0.993405i	$-0.463424\pi$
$541$	−4101.77	−	1204.39i	−0.325968	−	0.0957128i	−0.440622	+	0.897693i	$0.645242\pi$
$542$	−7573.28	+	3458.60i	−0.600185	+	0.274095i
$543$	27177.1	+	3907.47i	2.14784	+	0.308813i
$544$	2044.82	−	2359.85i	0.161160	−	0.185989i
$545$	−1288.59	−	631.310i	−0.101279	−	0.0496190i
$546$	10971.2	+	7050.76i	0.859934	+	0.552646i
$547$	257.429	−	37.0127i	0.0201223	−	0.00289315i	−0.132246	−	0.991217i	$-0.542219\pi$
$547$	257.429	−	37.0127i	0.0201223	−	0.00289315i	0.152369	+	0.988324i	$0.451310\pi$
$548$	1728.06	+	2688.92i	0.134707	+	0.209608i
$549$	4309.72	+	4973.69i	0.335036	+	0.386652i
$550$	2731.70	+	11599.5i	0.211782	+	0.899277i
$551$	9484.47			0.733307
$552$	−7905.57	−	1269.62i	−0.609571	−	0.0978962i
$553$		−	10593.0i		−	0.814578i
$554$	−9507.54	+	2791.67i	−0.729127	+	0.214091i
$555$	−20256.1	+	16610.8i	−1.54923	+	1.27043i
$556$	−6565.84	+	4219.61i	−0.500816	+	0.321855i
$557$	23235.5	−	3340.76i	1.76754	−	0.254134i	0.819681	−	0.572820i	$-0.194151\pi$
$557$	23235.5	−	3340.76i	1.76754	−	0.254134i	0.947860	+	0.318686i	$0.103241\pi$
$558$	12265.9	−	19086.0i	0.930564	−	1.44799i
$559$	−10980.4	+	24043.8i	−0.830809	+	1.81922i
$560$	1270.51	−	1388.22i	0.0958729	−	0.104755i
$561$	−6006.29	+	41774.7i	−0.452025	+	3.14390i
$562$	−5027.74	+	2296.09i	−0.377371	+	0.172339i
$563$	2566.47	−	8740.60i	0.192120	−	0.654302i	−0.805937	−	0.592001i	$-0.798338\pi$
$563$	2566.47	−	8740.60i	0.192120	−	0.654302i	0.998057	−	0.0623009i	$-0.0198438\pi$
$564$	18911.8	+	5553.01i	1.41193	+	0.414581i
$565$	−3238.70	−	7633.77i	−0.241156	−	0.568416i
$566$	1271.46	−	8843.19i	0.0944230	−	0.656726i
$567$	−6666.86	−	5776.87i	−0.493795	−	0.427876i
$568$	7129.81	+	3256.07i	0.526690	+	0.240531i
$569$	9670.52	+	6214.86i	0.712494	+	0.457892i	0.846019	−	0.533153i	$-0.178993\pi$
$569$	9670.52	+	6214.86i	0.712494	+	0.457892i	−0.133525	+	0.991046i	$0.542630\pi$
$570$	11315.2	−	1314.40i	0.831476	−	0.0965862i
$571$	16335.8	−	10498.4i	1.19725	−	0.769426i	0.218772	−	0.975776i	$-0.429795\pi$
$571$	16335.8	−	10498.4i	1.19725	−	0.769426i	0.978478	+	0.206350i	$0.0661584\pi$
$572$	9843.82	−	8529.71i	0.719564	−	0.623506i
$573$	10022.6	+	34133.7i	0.730712	+	2.48858i
$574$	1698.76			0.123527
$575$	13752.2	−	992.555i	0.997406	−	0.0719868i
$576$	3541.17			0.256161
$577$	1706.54	+	5811.94i	0.123127	+	0.419331i	0.997868	−	0.0652584i	$-0.0207872\pi$
$577$	1706.54	+	5811.94i	0.123127	+	0.419331i	−0.874742	+	0.484590i	$0.838969\pi$
$578$	−6966.01	+	6036.08i	−0.501294	+	0.434373i
$579$	−18767.4	+	12061.1i	−1.34706	+	0.865702i
$580$	−7504.31	+	871.718i	−0.537241	+	0.0624071i
$581$	−2705.00	−	1738.40i	−0.193154	−	0.124132i
$582$	11785.2	+	5382.13i	0.839370	+	0.383327i
$583$	−1040.17	−	901.316i	−0.0738930	−	0.0640287i
$584$	−263.031	+	1829.42i	−0.0186375	+	0.129627i
$585$	−16505.1	−	38903.4i	−1.16650	−	2.74950i
$586$	7291.86	+	2141.08i	0.514034	+	0.150934i
$587$	427.395	−	1455.57i	0.0300519	−	0.102347i	−0.943101	−	0.332505i	$-0.892106\pi$
$587$	427.395	−	1455.57i	0.0300519	−	0.102347i	0.973153	+	0.230158i	$0.0739243\pi$
$588$	−7670.39	+	3502.95i	−0.537962	+	0.245679i
$589$	−1638.13	+	11393.5i	−0.114598	+	0.797045i
$590$	10257.7	−	11208.1i	0.715770	−	0.782084i
$591$	19175.8	−	41989.2i	1.33467	−	2.92252i
$592$	2233.71	−	3475.73i	0.155076	−	0.241303i
$593$	5781.68	−	831.280i	0.400380	−	0.0575659i	0.0608161	−	0.998149i	$-0.480630\pi$
$593$	5781.68	−	831.280i	0.400380	−	0.0575659i	0.339564	+	0.940583i	$0.389721\pi$
$594$	−20616.5	+	13249.4i	−1.42408	+	0.915201i
$595$	−8874.46	+	7277.43i	−0.611458	+	0.501421i
$596$	−1971.05	+	578.754i	−0.135466	+	0.0397763i
$597$		−	156.303i		−	0.0107153i
$598$	−7938.23	−	12810.4i	−0.542840	−	0.876011i
$599$	4600.69			0.313821			0.156911	−	0.987613i	$-0.449847\pi$
$599$	4600.69			0.313821			0.156911	+	0.987613i	$0.449847\pi$
$600$	−8832.02	+	2079.96i	−0.600943	+	0.141523i
$601$	−7080.32	−	8171.13i	−0.480553	−	0.554588i	0.462764	−	0.886482i	$-0.346858\pi$
$601$	−7080.32	−	8171.13i	−0.480553	−	0.554588i	−0.943317	+	0.331894i	$0.892312\pi$
$602$	4401.27	+	6848.51i	0.297977	+	0.463662i
$603$	−6078.14	+	873.904i	−0.410482	+	0.0590185i
$604$	6904.85	+	4437.48i	0.465157	+	0.298938i
$605$	9449.31	+	4629.45i	0.634990	+	0.311097i
$606$	−9372.80	+	10816.8i	−0.628290	+	0.725086i
$607$	−9823.67	−	1412.43i	−0.656887	−	0.0944461i	−0.194192	−	0.980964i	$-0.562209\pi$
$607$	−9823.67	−	1412.43i	−0.656887	−	0.0944461i	−0.462695	+	0.886517i	$0.653118\pi$
$608$	−1634.26	+	746.344i	−0.109010	+	0.0497833i
$609$	−15471.7	−	4542.91i	−1.02947	−	0.302279i
$610$	2530.60	+	818.314i	0.167969	+	0.0543157i
$611$	15411.3	+	33746.0i	1.02042	+	2.23440i
$612$	−21376.7	−	3073.50i	−1.41193	−	0.203005i
$613$	5646.82	+	4893.00i	0.372060	+	0.322392i	0.820742	−	0.571300i	$-0.193561\pi$
$613$	5646.82	+	4893.00i	0.372060	+	0.322392i	−0.448681	+	0.893692i	$0.648106\pi$
$614$	−3078.22	+	6740.37i	−0.202324	+	0.443028i
$615$	−6767.78	−	4613.76i	−0.443745	−	0.302512i
$616$	−570.911	−	3970.77i	−0.0373420	−	0.259719i
$617$	−4663.97	−	7257.28i	−0.304318	−	0.473528i	0.655089	−	0.755551i	$-0.272631\pi$
$617$	−4663.97	−	7257.28i	−0.304318	−	0.473528i	−0.959408	+	0.282023i	$0.908995\pi$
$618$	−9960.70	+	8631.00i	−0.648347	+	0.561796i
$619$	12907.6	−	3790.02i	0.838128	−	0.246097i	0.165623	−	0.986189i	$-0.447037\pi$
$619$	12907.6	−	3790.02i	0.838128	−	0.246097i	0.672505	+	0.740093i	$0.265218\pi$
$620$	248.952	−	9165.31i	0.0161260	−	0.593690i
$621$	11353.5	+	25982.8i	0.733658	+	1.67899i
$622$		−	240.011i		−	0.0154720i
$623$	229.099	+	780.240i	0.0147330	+	0.0501760i
$624$	6494.66	+	7495.24i	0.416658	+	0.480849i
$625$	13982.9	−	6972.73i	0.894906	−	0.446255i
$626$	421.665	+	2932.74i	0.0269219	+	0.187246i
$627$	13128.5	−	20428.4i	0.836207	−	1.30116i
$628$	−9479.34	−	4329.07i	−0.602336	−	0.275078i
$629$	−16500.8	+	19042.9i	−1.04599	+	1.20714i
$630$	−12828.0	−	2201.42i	−0.811236	−	0.139217i
$631$	−10132.6	−	22187.3i	−0.639260	−	1.39978i	−0.900648	−	0.434550i	$-0.856907\pi$
$631$	−10132.6	−	22187.3i	−0.639260	−	1.39978i	0.261388	−	0.965234i	$-0.415820\pi$
$632$	2269.54	−	7729.35i	0.142844	−	0.486483i
$633$	4280.61	−	14578.4i	0.268782	−	0.915388i
$634$	2070.88	+	4534.59i	0.129724	+	0.284056i
$635$	1963.26	−	11440.2i	0.122692	−	0.714945i
$636$	686.277	−	792.006i	0.0427872	−	0.0493791i
$637$	−14437.2	−	6593.25i	−0.897995	−	0.410101i
$638$	−8706.91	+	13548.2i	−0.540298	+	0.840720i
$639$	−7715.05	−	53659.3i	−0.477625	−	3.32196i
$640$	1224.47	−	740.728i	0.0756271	−	0.0457498i
$641$	−12721.2	−	14681.0i	−0.783864	−	0.904627i	0.213518	−	0.976939i	$-0.431508\pi$
$641$	−12721.2	−	14681.0i	−0.783864	−	0.904627i	−0.997382	+	0.0723117i	$0.976962\pi$
$642$	8387.65	+	28565.7i	0.515630	+	1.75607i
$643$			512.250i			0.0314171i	0.999877	+	0.0157085i	$0.00500038\pi$
$643$			512.250i			0.0314171i	−0.999877	+	0.0157085i	$0.995000\pi$
$644$	−4640.90	−	76.2992i	−0.283971	−	0.00466865i
$645$	1065.79	−	39237.9i	0.0650630	−	2.39533i
$646$	10513.2	−	3086.96i	0.640304	−	0.188010i
$647$	−12948.0	+	11219.5i	−0.786770	+	0.681740i	−0.952536	−	0.304425i	$-0.901536\pi$
$647$	−12948.0	+	11219.5i	−0.786770	+	0.681740i	0.165767	+	0.986165i	$0.446990\pi$
$648$	−3626.88	−	5643.53i	−0.219872	−	0.342128i
$649$	−4609.37	−	32058.9i	−0.278788	−	1.93902i
$650$	−13844.8	−	9999.58i	−0.835445	−	0.603409i
$651$	8129.52	−	17801.2i	0.489433	−	1.07171i
$652$	4642.48	+	4022.73i	0.278855	+	0.241629i
$653$	−15747.0	−	2264.08i	−0.943688	−	0.135682i	−0.346739	−	0.937962i	$-0.612711\pi$
$653$	−15747.0	−	2264.08i	−0.943688	−	0.135682i	−0.596948	+	0.802280i	$0.703620\pi$
$654$	−967.536	−	2118.61i	−0.0578496	−	0.126673i
$655$	−296.645	+	917.361i	−0.0176960	+	0.0547241i
$656$	1239.52	+	363.956i	0.0737730	+	0.0216617i
$657$	11627.8	−	5310.25i	0.690479	−	0.315331i
$658$	11309.6	+	1626.07i	0.670051	+	0.0963387i
$659$	−12935.0	+	14927.8i	−0.764607	+	0.882404i	−0.995898	−	0.0904807i	$-0.971160\pi$
$659$	−12935.0	+	14927.8i	−0.764607	+	0.882404i	0.231291	+	0.972885i	$0.425705\pi$
$660$	−8509.98	+	17370.0i	−0.501895	+	1.02443i
$661$	24792.3	+	15933.1i	1.45887	+	0.937556i	0.998765	+	0.0496893i	$0.0158231\pi$
$661$	24792.3	+	15933.1i	1.45887	+	0.937556i	0.460101	+	0.887867i	$0.347813\pi$
$662$	−8106.21	+	1165.50i	−0.475917	+	0.0684265i
$663$	−32700.4	−	50882.8i	−1.91550	−	2.98058i
$664$	−1601.29	−	1847.99i	−0.0935876	−	0.108006i
$665$	6384.14	−	1687.68i	0.372280	−	0.0984144i
$666$	−28575.6			−1.66258
$667$	13879.9	+	12432.3i	0.805745	+	0.721710i
$668$			11441.6i			0.662708i
$669$	−28379.2	+	8332.90i	−1.64007	+	0.481567i
$670$	−1918.90	+	1573.58i	−0.110647	+	0.0907355i
$671$	4769.58	−	3065.22i	0.274408	−	0.176351i
$672$	3023.41	−	434.701i	0.173557	−	0.0249538i
$673$	−5332.22	+	8297.10i	−0.305412	+	0.475230i	−0.959704	−	0.281012i	$-0.909330\pi$
$673$	−5332.22	+	8297.10i	−0.305412	+	0.475230i	0.654293	+	0.756241i	$0.272966\pi$
$674$	7027.17	−	15387.4i	0.401597	−	0.879375i
$675$	23106.3	+	22329.8i	1.31757	+	1.27329i
$676$	−1405.92	+	9778.40i	−0.0799910	+	0.556350i
$677$	−1325.03	+	605.123i	−0.0752219	+	0.0343527i	−0.452671	−	0.891678i	$-0.649529\pi$
$677$	−1325.03	+	605.123i	−0.0752219	+	0.0343527i	0.377449	+	0.926030i	$0.376801\pi$
$678$	3792.03	−	12914.5i	0.214797	−	0.731531i
$679$	7206.30	+	2115.96i	0.407294	+	0.119592i
$680$	−8034.55	+	3408.73i	−0.453104	+	0.192234i
$681$	5343.56	−	37165.3i	0.300684	−	2.09130i
$682$	−14771.3	−	12799.4i	−0.829359	−	0.718644i
$683$	−29855.0	−	13634.3i	−1.67258	−	0.763840i	−0.999710	−	0.0240753i	$-0.992336\pi$
$683$	−29855.0	−	13634.3i	−1.67258	−	0.763840i	−0.672866	−	0.739765i	$-0.734937\pi$
$684$	10453.5	+	6718.03i	0.584354	+	0.375541i
$685$	−1030.86	−	8874.33i	−0.0574996	−	0.494994i
$686$	−10183.2	+	6544.36i	−0.566760	+	0.364235i
$687$	3216.54	−	2787.15i	0.178630	−	0.154784i
$688$	1744.16	+	5940.07i	0.0966505	+	0.329162i
$689$	1972.50			0.109066
$690$	18282.0	+	12908.5i	1.00867	+	0.712200i
$691$	21913.7			1.20642			0.603211	−	0.797582i	$-0.293888\pi$
$691$	21913.7			1.20642			0.603211	+	0.797582i	$0.293888\pi$
$692$	−2473.68	−	8424.60i	−0.135889	−	0.462796i
$693$	−20968.7	+	18169.5i	−1.14940	+	0.995964i
$694$	13366.4	−	8590.09i	0.731100	−	0.469849i
$695$	21669.5	−	2517.17i	1.18269	−	0.137384i
$696$	−10315.8	−	6629.58i	−0.561811	−	0.361054i
$697$	−7166.61	−	3272.88i	−0.389462	−	0.177861i
$698$	737.778	+	639.288i	0.0400076	+	0.0346668i
$699$	−3842.95	+	26728.3i	−0.207945	+	1.44629i
$700$	−4896.15	+	1922.10i	−0.264367	+	0.103784i
$701$	6200.56	+	1820.65i	0.334083	+	0.0980956i	0.444472	−	0.895793i	$-0.353391\pi$
$701$	6200.56	+	1820.65i	0.334083	+	0.0980956i	−0.110389	+	0.993888i	$0.535210\pi$
$702$	9894.93	−	33699.0i	0.531994	−	1.81181i
$703$	13187.8	−	6022.65i	0.707519	−	0.323113i
$704$	434.159	−	3019.64i	0.0232429	−	0.161658i
$705$	−40640.6	−	37194.6i	−2.17108	−	1.98699i
$706$	−4126.81	+	9036.46i	−0.219992	+	0.481716i
$707$	−4485.67	+	6979.84i	−0.238615	+	0.371293i
$708$	24410.2	−	3509.65i	1.29575	−	0.186300i
$709$	9203.81	−	5914.93i	0.487526	−	0.313314i	−0.273683	−	0.961820i	$-0.588242\pi$
$709$	9203.81	−	5914.93i	0.487526	−	0.313314i	0.761210	+	0.648506i	$0.224606\pi$
$710$	−13892.0	−	16940.6i	−0.734305	−	0.895448i
$711$	−53458.8	+	15696.9i	−2.81978	+	0.827961i
$712$			618.397i			0.0325497i
$713$	−17331.9	+	14526.3i	−0.910358	+	0.762994i
$714$	−18628.5			−0.976404
$715$	−35197.5	+	9304.67i	−1.84100	+	0.486678i
$716$	−8969.82	−	10351.7i	−0.468182	−	0.540310i
$717$	3655.91	+	5688.70i	0.190422	+	0.296302i
$718$	15243.2	−	2191.64i	0.792300	−	0.113916i
$719$	19283.9	+	12393.0i	1.00023	+	0.642811i	0.934848	−	0.355049i	$-0.115536\pi$
$719$	19283.9	+	12393.0i	1.00023	+	0.642811i	0.0653857	+	0.997860i	$0.479172\pi$
$720$	−8888.45	−	4354.67i	−0.460074	−	0.225401i
$721$	−5003.33	+	5774.15i	−0.258438	+	0.298253i
$722$	7338.15	+	1055.07i	0.378251	+	0.0543843i
$723$	28093.6	−	12829.9i	1.44511	−	0.659959i
$724$	11613.6	+	3410.06i	0.596154	+	0.175047i
$725$	19908.1	+	7040.22i	1.01982	+	0.360644i
$726$	7095.02	+	15535.9i	0.362701	+	0.794204i
$727$	−22862.7	−	3287.17i	−1.16634	−	0.167695i	−0.468180	−	0.883633i	$-0.655090\pi$
$727$	−22862.7	−	3287.17i	−1.16634	−	0.167695i	−0.698164	+	0.715938i	$0.745999\pi$
$728$	4344.94	+	3764.91i	0.221201	+	0.191672i
$729$	6887.20	−	15080.9i	0.349906	−	0.766188i
$730$	2909.90	−	4268.45i	0.147535	−	0.216414i
$731$	−5373.25	−	37371.8i	−0.271870	−	1.89089i
$732$	2333.91	+	3631.63i	0.117847	+	0.183373i
$733$	−1015.84	+	880.227i	−0.0511880	+	0.0443546i	−0.680079	−	0.733139i	$-0.738055\pi$
$733$	−1015.84	+	880.227i	−0.0511880	+	0.0443546i	0.628891	+	0.777493i	$0.283509\pi$
$734$	−17864.1	+	5245.38i	−0.898334	+	0.263775i
$735$	23560.6	+	639.962i	1.18238	+	0.0321162i
$736$	−3369.95	−	1049.98i	−0.168774	−	0.0525852i
$737$			5290.13i			0.264402i
$738$	−2517.24	−	8572.94i	−0.125557	−	0.427607i
$739$	−3515.91	−	4057.57i	−0.175013	−	0.201976i	0.661465	−	0.749976i	$-0.269935\pi$
$739$	−3515.91	−	4057.57i	−0.175013	−	0.201976i	−0.836478	+	0.548000i	$0.815389\pi$
$740$	−9880.89	+	5977.33i	−0.490850	+	0.296934i
$741$	4952.73	+	34447.0i	0.245537	+	1.70775i
$742$	328.441	−	511.064i	0.0162499	−	0.0252854i
$743$	−29068.0	−	13274.9i	−1.43526	−	0.655463i	−0.462363	−	0.886691i	$-0.652998\pi$
$743$	−29068.0	−	13274.9i	−1.43526	−	0.655463i	−0.972900	+	0.231228i	$0.925726\pi$
$744$	9745.69	−	11247.1i	0.480234	−	0.554220i
$745$	5659.12	+	971.167i	0.278301	+	0.0477595i
$746$	8501.24	+	18615.1i	0.417229	+	0.913603i
$747$	−4764.69	+	16227.1i	−0.233375	+	0.794802i
$748$	−5241.70	+	17851.6i	−0.256224	+	0.872619i
$749$	7169.42	+	15698.8i	0.349753	+	0.765852i
$750$	24726.4	+	5640.20i	1.20384	+	0.274601i
$751$	−11516.6	+	13290.9i	−0.559584	+	0.645795i	−0.963089	−	0.269183i	$-0.913246\pi$
$751$	−11516.6	+	13290.9i	−0.559584	+	0.645795i	0.403505	+	0.914977i	$0.367792\pi$
$752$	7903.80	+	3609.55i	0.383274	+	0.175035i
$753$	12743.5	−	19829.3i	0.616733	−	0.959656i
$754$	−3284.68	−	22845.5i	−0.158649	−	1.10343i
$755$	−11874.5	−	19629.3i	−0.572395	−	0.946204i
$756$	−7083.65	−	8174.96i	−0.340780	−	0.393281i
$757$	8042.96	+	27391.8i	0.386164	+	1.31516i	0.891808	+	0.452413i	$0.149437\pi$
$757$	8042.96	+	27391.8i	0.386164	+	1.31516i	−0.505644	+	0.862742i	$0.668745\pi$
$758$			7389.81i			0.354103i
$759$	45990.3	−	12686.6i	2.19940	−	0.606713i
$760$	5019.86	+	136.351i	0.239591	+	0.00650787i
$761$	13893.0	−	4079.37i	0.661790	−	0.194319i	0.0664463	−	0.997790i	$-0.478834\pi$
$761$	13893.0	−	4079.37i	0.661790	−	0.194319i	0.595344	+	0.803471i	$0.297016\pi$
$762$	14238.7	−	12337.9i	0.676920	−	0.586555i
$763$	−729.948	−	1135.82i	−0.0346342	−	0.0538918i
$764$	2231.88	+	15523.1i	0.105689	+	0.735084i
$765$	49876.6	+	34002.1i	2.35724	+	1.60699i
$766$	−9392.70	+	20567.1i	−0.443044	+	0.970132i
$767$	35079.8	+	30396.8i	1.65145	+	1.43099i
$768$	2299.21	+	330.576i	0.108028	+	0.0155321i
$769$	2747.50	+	6016.18i	0.128839	+	0.282118i	0.963048	−	0.269331i	$-0.0868024\pi$
$769$	2747.50	+	6016.18i	0.128839	+	0.282118i	−0.834209	+	0.551449i	$0.814075\pi$
$770$	−3449.96	+	10668.8i	−0.161465	+	0.499322i
$771$	−55766.9	−	16374.6i	−2.60492	−	0.764875i
$772$	−8945.86	+	4085.44i	−0.417058	+	0.190464i
$773$	−20777.9	−	2987.41i	−0.966790	−	0.139003i	−0.359205	−	0.933259i	$-0.616952\pi$
$773$	−20777.9	−	2987.41i	−0.966790	−	0.139003i	−0.607584	+	0.794255i	$0.707861\pi$
$774$	28039.8	−	32359.7i	1.30216	−	1.50277i
$775$	−11895.7	+	22699.1i	−0.551363	+	1.05210i
$776$	4804.83	+	3087.88i	0.222272	+	0.142846i
$777$	−24397.5	+	3507.83i	−1.12646	+	0.161960i
$778$	−1502.75	−	2338.32i	−0.0692496	−	0.107754i
$779$	2968.57	+	3425.91i	0.136534	+	0.157569i
$780$	−7084.73	−	26800.0i	−0.325223	−	1.23025i
$781$	−46702.6			−2.13976
$782$	19431.8	+	9263.21i	0.888592	+	0.423596i
$783$			43425.5i			1.98200i
$784$	−3566.75	+	1047.29i	−0.162479	+	0.0477083i
$785$	18469.9	+	22523.1i	0.839769	+	1.02406i
$786$	−1316.50	+	846.060i	−0.0597428	+	0.0383944i
$787$	9449.69	−	1358.66i	0.428012	−	0.0615388i	0.0750571	−	0.997179i	$-0.476086\pi$
$787$	9449.69	−	1358.66i	0.428012	−	0.0615388i	0.352955	+	0.935640i	$0.385177\pi$
$788$	11001.7	−	17119.0i	0.497360	−	0.773907i
$789$	−6864.94	+	15032.1i	−0.309757	+	0.678273i
$790$	−15201.6	+	16610.0i	−0.684619	+	0.748048i
$791$	1110.41	−	7723.08i	0.0499136	−	0.347157i
$792$	−19192.9	+	8765.11i	−0.861099	+	0.393251i
$793$	−2289.17	+	7796.19i	−0.102510	+	0.349119i
$794$	10756.5	+	3158.39i	0.480772	+	0.141168i
$795$	−2696.53	+	1144.03i	−0.120297	+	0.0510371i
$796$	9.80610	−	68.2030i	0.000436643	−	0.00303692i
$797$	14766.5	+	12795.3i	0.656282	+	0.568671i	0.918053	−	0.396459i	$-0.129761\pi$
$797$	14766.5	+	12795.3i	0.656282	+	0.568671i	−0.261771	+	0.965130i	$0.584306\pi$
$798$	9749.73	+	4452.55i	0.432502	+	0.197517i
$799$	−44579.4	−	28649.4i	−1.97385	−	1.26852i
$800$	−3984.35	+	353.491i	−0.176085	+	0.0156223i
$801$	3598.08	−	2312.34i	0.158716	−	0.102001i
$802$	−1328.67	+	1151.30i	−0.0584998	+	0.0506904i
$803$	−3102.58	−	10566.4i	−0.136348	−	0.464359i
$804$	−4027.99			−0.176687
$805$	11555.0	+	5898.56i	0.505913	+	0.258257i
$806$	28011.0			1.22413
$807$	16901.3	+	57560.4i	0.737240	+	2.51081i
$808$	−4768.45	+	4131.89i	−0.207616	+	0.179900i
$809$	−19941.3	+	12815.5i	−0.866625	+	0.556946i	−0.896719	−	0.442601i	$-0.854056\pi$
$809$	−19941.3	+	12815.5i	−0.866625	+	0.556946i	0.0300933	+	0.999547i	$0.490420\pi$
$810$	2163.58	+	18625.5i	0.0938525	+	0.807944i
$811$	−18730.3	−	12037.2i	−0.810985	−	0.521188i	0.0681988	−	0.997672i	$-0.478275\pi$
$811$	−18730.3	−	12037.2i	−0.810985	−	0.521188i	−0.879183	+	0.476484i	$0.841911\pi$
$812$	−6466.09	−	2952.96i	−0.279452	−	0.127622i
$813$	28546.1	+	24735.3i	1.23143	+	1.06704i
$814$	−3503.46	+	24367.1i	−0.150855	+	1.04922i
$815$	−6705.92	−	15806.2i	−0.288219	−	0.679345i
$816$	−13592.5	−	3991.12i	−0.583128	−	0.171222i
$817$	−6120.31	+	20843.9i	−0.262084	+	0.892576i
$818$	12138.6	−	5543.51i	0.518846	−	0.236949i
$819$	5658.91	−	39358.6i	0.241439	−	1.67924i
$820$	−2663.67	−	2437.81i	−0.113438	−	0.103820i
$821$	−501.557	+	1098.26i	−0.0213209	+	0.0466863i	−0.919993	−	0.391935i	$-0.871806\pi$
$821$	−501.557	+	1098.26i	−0.0213209	+	0.0466863i	0.898672	+	0.438621i	$0.144533\pi$
$822$	7839.91	−	12199.1i	0.332662	−	0.517632i
$823$	−36531.7	+	5252.47i	−1.54729	+	0.222466i	−0.862416	−	0.506200i	$-0.831050\pi$
$823$	−36531.7	+	5252.47i	−1.54729	+	0.222466i	−0.684869	+	0.728666i	$0.740141\pi$
$824$	−4887.85	+	3141.23i	−0.206646	+	0.132803i
$825$	42720.7	−	33134.3i	1.80284	−	1.39829i
$826$	13716.8	−	4027.62i	0.577808	−	0.169660i
$827$		−	38964.1i		−	1.63835i	−0.573543	−	0.819175i	$-0.694432\pi$
$827$		−	38964.1i		−	1.63835i	0.573543	−	0.819175i	$-0.305568\pi$
$828$	6491.91	+	23533.8i	0.272475	+	0.987750i
$829$	36974.6			1.54907			0.774536	−	0.632529i	$-0.217983\pi$
$829$	36974.6			1.54907			0.774536	+	0.632529i	$0.217983\pi$
$830$	1746.77	+	6607.67i	0.0730499	+	0.276332i
$831$	29439.2	+	33974.7i	1.22892	+	1.41825i
$832$	2363.72	+	3678.02i	0.0984942	+	0.153260i
$833$	22440.1	−	3226.40i	0.933376	−	0.134199i
$834$	29788.0	+	19143.6i	1.23678	+	0.794830i
$835$	14070.1	−	28718.8i	0.583131	−	1.19025i
$836$	7010.27	−	8090.28i	0.290018	−	0.334699i
$837$	−52166.1	−	7500.35i	−2.15427	−	0.309737i
$838$	−4710.30	+	2151.12i	−0.194170	+	0.0886745i
$839$	13078.0	+	3840.04i	0.538142	+	0.158013i	0.539499	−	0.841986i	$-0.318614\pi$
$839$	13078.0	+	3840.04i	0.538142	+	0.158013i	−0.00135663	+	0.999999i	$0.500432\pi$
$840$	−8123.43	−	2626.86i	−0.333672	−	0.107899i
$841$	1723.27	+	3773.44i	0.0706577	+	0.154719i
$842$	15279.1	+	2196.81i	0.625360	+	0.0899132i
$843$	18951.2	+	16421.3i	0.774274	+	0.670912i
$844$	2782.47	−	6092.76i	0.113479	−	0.248485i
$845$	15553.7	−	22815.2i	0.633210	−	0.928837i
$846$	−8552.58	−	59484.5i	−0.347569	−	2.41740i
$847$	5352.77	+	8329.07i	0.217147	+	0.337887i
$848$	349.146	−	302.537i	0.0141388	−	0.0122514i
$849$	−38890.6	+	11419.3i	−1.57211	+	0.461614i
$850$	24358.8	+	1324.26i	0.982941	+	0.0534375i
$851$	27193.9	+	8472.84i	1.09541	+	0.341299i
$852$		−	35560.1i		−	1.42989i
$853$	4395.19	+	14968.6i	0.176423	+	0.600840i	0.999460	+	0.0328533i	$0.0104594\pi$
$853$	4395.19	+	14968.6i	0.176423	+	0.600840i	−0.823038	+	0.567987i	$0.807722\pi$
$854$	1638.79	+	1891.26i	0.0656652	+	0.0757817i
$855$	−17977.2	−	29717.4i	−0.719073	−	1.18867i
$856$	1867.81	+	12990.9i	0.0745799	+	0.518715i
$857$	14883.7	−	23159.5i	0.593254	−	0.923122i	−0.406700	−	0.913562i	$-0.633321\pi$
$857$	14883.7	−	23159.5i	0.593254	−	0.923122i	0.999954	−	0.00955981i	$-0.00304303\pi$
$858$	−53752.9	−	24548.1i	−2.13881	−	0.976760i
$859$	6621.75	−	7641.91i	0.263017	−	0.303537i	−0.608845	−	0.793289i	$-0.708367\pi$
$859$	6621.75	−	7641.91i	0.263017	−	0.303537i	0.871862	+	0.489751i	$0.162912\pi$
$860$	2926.76	−	17054.6i	0.116048	−	0.676230i
$861$	−3201.58	−	7010.48i	−0.126724	−	0.277487i
$862$	3756.02	−	12791.8i	0.148411	−	0.505442i
$863$	−1729.07	+	5888.66i	−0.0682018	+	0.232274i	−0.986539	−	0.163524i	$-0.947714\pi$
$863$	−1729.07	+	5888.66i	−0.0682018	+	0.232274i	0.918338	+	0.395798i	$0.129532\pi$
$864$	−3417.20	−	7482.63i	−0.134555	−	0.294635i
$865$	−4150.92	+	24188.0i	−0.163162	+	0.950770i
$866$	−11835.9	+	13659.4i	−0.464435	+	0.535986i
$867$	38038.4	+	17371.6i	1.49003	+	0.680473i
$868$	4664.13	−	7257.53i	0.182386	−	0.283798i
$869$	6830.93	+	47510.2i	0.266655	+	1.85463i
$870$	17740.5	+	29326.1i	0.691333	+	1.14282i
$871$	−4964.81	−	5729.70i	−0.193142	−	0.222897i
$872$	−289.268	−	985.157i	−0.0112338	−	0.0382588i
$873$		−	39502.8i		−	1.53146i
$874$	−7956.09	−	9492.73i	−0.307916	−	0.367387i
$875$	14653.2	+	1196.40i	0.566134	+	0.0462236i
$876$	8045.43	−	2362.35i	0.310308	−	0.0911147i
$877$	−32183.4	+	27887.1i	−1.23917	+	1.07375i	−0.244611	+	0.969621i	$0.578660\pi$
$877$	−32183.4	+	27887.1i	−1.23917	+	1.07375i	−0.994564	+	0.104129i	$0.966794\pi$
$878$	5891.05	+	9166.65i	0.226439	+	0.352346i
$879$	−4906.79	−	34127.5i	−0.188284	−	1.30955i
$880$	−4803.09	+	7045.51i	−0.183991	+	0.269891i
$881$	19816.0	−	43391.0i	0.757796	−	1.65934i	0.00596839	−	0.999982i	$-0.498100\pi$
$881$	19816.0	−	43391.0i	0.757796	−	1.65934i	0.751828	−	0.659360i	$-0.229173\pi$
$882$	19430.5	+	16836.7i	0.741792	+	0.642766i
$883$	−43117.3	−	6199.33i	−1.64328	−	0.236267i	−0.742279	−	0.670091i	$-0.766255\pi$
$883$	−43117.3	−	6199.33i	−1.64328	−	0.236267i	−0.900998	+	0.433824i	$0.857164\pi$
$884$	−11076.6	−	24254.3i	−0.421432	−	0.922807i
$885$	−65586.2	−	21208.5i	−2.49114	−	0.805554i
$886$	1316.70	+	386.619i	0.0499272	+	0.0146599i
$887$	13247.8	−	6050.08i	0.501486	−	0.229021i	−0.148577	−	0.988901i	$-0.547469\pi$
$887$	13247.8	−	6050.08i	0.501486	−	0.229021i	0.650064	+	0.759880i	$0.274742\pi$
$888$	−18553.5	−	2667.59i	−0.701144	−	0.100809i
$889$	7152.20	−	8254.07i	0.269828	−	0.311398i
$890$	760.459	−	1552.20i	0.0286412	−	0.0584604i
$891$	33626.4	+	21610.3i	1.26434	+	0.812541i
$892$	−12906.1	+	1855.62i	−0.484449	+	0.0696532i
$893$	16484.1	+	25649.8i	0.617716	+	0.961184i
$894$	6103.19	+	7043.45i	0.228323	+	0.263499i
$895$	9784.76	+	37013.6i	0.365440	+	1.38238i
$896$	1346.54			0.0502062
$897$	−37905.3	+	56902.9i	−1.41095	+	2.11810i
$898$			25558.9i			0.949789i
$899$	−33230.8	+	9757.44i	−1.23282	+	0.361990i
$900$	16955.3	+	21860.7i	0.627973	+	0.809657i
$901$	−2370.24	+	1523.26i	−0.0876407	+	0.0563233i
$902$	−7618.99	+	1095.45i	−0.281247	+	0.0404372i
$903$	19967.7	−	31070.4i	0.735864	−	1.14503i
$904$	2464.88	−	5397.34i	0.0906867	−	0.198576i
$905$	−24957.1	−	22840.9i	−0.916686	−	0.838958i
$906$	5299.43	−	36858.3i	0.194329	−	1.35158i
$907$	21273.1	−	9715.11i	0.778790	−	0.355662i	0.0139676	−	0.999902i	$-0.495554\pi$
$907$	21273.1	−	9715.11i	0.778790	−	0.355662i	0.764823	+	0.644241i	$0.222827\pi$
$908$	4663.34	−	15881.9i	0.170439	−	0.580461i
$909$	41871.4	+	12294.6i	1.52782	+	0.448608i
$910$	−6276.14	−	14793.2i	−0.228628	−	0.538888i
$911$	−1873.97	+	13033.7i	−0.0681528	+	0.474013i	0.926951	+	0.375182i	$0.122420\pi$
$911$	−1873.97	+	13033.7i	−0.0681528	+	0.474013i	−0.995104	+	0.0988318i	$0.968489\pi$
$912$	6160.07	+	5337.73i	0.223663	+	0.193805i
$913$	13253.1	+	6052.47i	0.480408	+	0.219395i
$914$	−26407.7	−	16971.2i	−0.955676	−	0.614176i
$915$	−1392.27	−	11985.6i	−0.0503029	−	0.433040i
$916$	1578.40	−	1014.38i	0.0569343	−	0.0365895i
$917$	−685.597	+	594.073i	−0.0246896	+	0.0213937i
$918$	14133.9	+	48135.7i	0.508158	+	1.73063i
$919$	−28409.9			−1.01976			−0.509879	−	0.860246i	$-0.670310\pi$
$919$	−28409.9			−1.01976			−0.509879	+	0.860246i	$0.670310\pi$
$920$	7167.50	+	6779.60i	0.256854	+	0.242953i
$921$	33617.8			1.20276
$922$	−448.215	−	1526.48i	−0.0160100	−	0.0545249i
$923$	50583.2	−	43830.6i	1.80387	−	1.56306i
$924$	−15310.7	+	9839.61i	−0.545115	+	0.350324i
$925$	32151.9	−	2852.51i	1.14286	−	0.101395i
$926$	−18865.0	−	12123.8i	−0.669485	−	0.430252i
$927$	36553.9	+	16693.6i	1.29513	+	0.591466i
$928$	−4085.40	−	3540.02i	−0.144515	−	0.125223i
$929$	−5161.43	+	35898.5i	−0.182283	+	1.26781i	0.669064	+	0.743204i	$0.266695\pi$
$929$	−5161.43	+	35898.5i	−0.182283	+	1.26781i	−0.851347	+	0.524602i	$0.824214\pi$
$930$	−38292.9	+	16246.1i	−1.35019	+	0.572829i
$931$	−12515.8	−	3674.98i	−0.440590	−	0.129369i
$932$	−3353.75	+	11421.8i	−0.117871	+	0.401431i
$933$	−990.486	+	452.340i	−0.0347557	+	0.0158724i
$934$	−4598.10	+	31980.5i	−0.161086	+	1.12038i
$935$	35109.5	−	38362.3i	1.22802	−	1.34180i
$936$	12561.6	−	27506.1i	0.438664	−	0.960539i
$937$	−9036.65	+	14061.3i	−0.315063	+	0.490248i	−0.962281	−	0.272057i	$-0.912296\pi$
$937$	−9036.65	+	14061.3i	−0.315063	+	0.490248i	0.647218	+	0.762305i	$0.275932\pi$
$938$	−2311.23	+	332.305i	−0.0804524	+	0.0115673i
$939$	11308.2	−	7267.36i	0.393004	−	0.252568i
$940$	−15400.1	−	18779.6i	−0.534356	−	0.651620i
$941$	−36162.4	+	10618.2i	−1.25277	+	0.367847i	−0.839800	−	0.542896i	$-0.817328\pi$
$941$	−36162.4	+	10618.2i	−1.25277	+	0.367847i	−0.412973	+	0.910743i	$0.635510\pi$
$942$			47278.5i			1.63526i
$943$	−146.400	+	8904.81i	−0.00505562	+	0.307509i
$944$	10871.6			0.374830
$945$	7727.22	+	29230.4i	0.265996	+	1.00621i
$946$	−24156.1	−	27877.7i	−0.830216	−	0.958120i
$947$	30722.5	+	47805.1i	1.05422	+	1.64040i	0.714143	+	0.699999i	$0.246816\pi$
$947$	30722.5	+	47805.1i	1.05422	+	1.64040i	0.340076	+	0.940398i	$0.389547\pi$
$948$	−36175.0	+	5201.18i	−1.23936	+	0.178193i
$949$	13277.0	+	8532.62i	0.454152	+	0.291866i
$950$	−12432.3	−	6515.30i	−0.424588	−	0.222510i
$951$	14810.6	−	17092.3i	0.505012	−	0.582815i
$952$	−8128.54	−	1168.71i	−0.276731	−	0.0397879i
$953$	−41685.1	+	19036.9i	−1.41691	+	0.647080i	−0.969014	−	0.247007i	$-0.920553\pi$
$953$	−41685.1	+	19036.9i	−1.41691	+	0.647080i	−0.447894	+	0.894087i	$0.647826\pi$
$954$	−3065.83	−	900.208i	−0.104046	−	0.0305506i
$955$	13487.0	−	41708.0i	0.456995	−	1.41323i
$956$	1238.36	+	2711.63i	0.0418949	+	0.0917369i
$957$	72320.8	+	10398.2i	2.44284	+	0.351228i
$958$	−18917.7	−	16392.3i	−0.637999	−	0.552829i
$959$	3492.07	−	7646.56i	0.117586	−	0.257477i
$960$	−5364.57	−	3657.15i	−0.180355	−	0.122952i
$961$	−1742.14	−	12116.9i	−0.0584789	−	0.406729i
$962$	−19074.1	−	29679.9i	−0.639266	−	0.994717i
$963$	68602.0	−	59444.0i	2.29561	−	1.98915i
$964$	13063.6	−	3835.82i	0.436463	−	0.128157i
$965$	27478.4	+	746.379i	0.916643	+	0.0248982i
$966$	8431.65	+	19296.0i	0.280832	+	0.642691i
$967$		−	49236.2i		−	1.63736i	−0.574249	−	0.818681i	$-0.694706\pi$
$967$		−	49236.2i		−	1.63736i	0.574249	−	0.818681i	$-0.305294\pi$
$968$	2121.23	+	7224.24i	0.0704327	+	0.239872i
$969$	−32553.2	−	37568.4i	−1.07921	−	1.24548i
$970$	−8263.04	−	13659.3i	−0.273516	−	0.452138i
$971$	−2235.78	−	15550.2i	−0.0738924	−	0.513933i	−0.992830	−	0.119531i	$-0.961861\pi$
$971$	−2235.78	−	15550.2i	−0.0738924	−	0.513933i	0.918938	−	0.394402i	$-0.129048\pi$
$972$	−1444.79	+	2248.14i	−0.0476767	+	0.0741865i
$973$	18671.5	+	8526.97i	0.615190	+	0.280948i
$974$	−1634.18	+	1885.94i	−0.0537603	+	0.0620426i
$975$	−15173.7	+	75981.1i	−0.498409	+	2.49574i
$976$	790.563	+	1731.09i	0.0259276	+	0.0567734i
$977$	−4846.14	+	16504.4i	−0.158692	+	0.540454i	−1.00000		0.000101515i	$-0.999968\pi$
$977$	−4846.14	+	16504.4i	−0.158692	+	0.540454i	0.841308	+	0.540555i	$0.181786\pi$
$978$	7851.64	−	26740.2i	0.256715	−	0.874292i
$979$	−1530.66	−	3351.67i	−0.0499694	−	0.109418i
$980$	10240.5	+	1757.39i	0.333798	+	0.0572834i
$981$	−4650.39	+	5366.83i	−0.151351	+	0.174668i
$982$	−21339.6	−	9745.49i	−0.693458	−	0.316692i
$983$	16026.2	−	24937.3i	0.519997	−	0.809132i	−0.477588	−	0.878584i	$-0.658489\pi$
$983$	16026.2	−	24937.3i	0.519997	−	0.809132i	0.997585	+	0.0694524i	$0.0221252\pi$
$984$	−834.090	−	5801.22i	−0.0270222	−	0.187943i
$985$	−48666.4	+	29440.2i	−1.57425	+	0.952326i
$986$	21589.5	+	24915.6i	0.697311	+	0.804740i
$987$	−14604.2	−	49737.3i	−0.470979	−	1.60401i
$988$			15341.7i			0.494013i
$989$	−36278.9	+	22481.1i	−1.16643	+	0.722807i
$990$	58953.6	+	1601.32i	1.89259	+	0.0514073i
$991$	−16483.7	+	4840.06i	−0.528378	+	0.155146i	−0.535031	−	0.844832i	$-0.679700\pi$
$991$	−16483.7	+	4840.06i	−0.528378	+	0.155146i	0.00665363	+	0.999978i	$0.497882\pi$
$992$	4958.16	−	4296.27i	0.158691	−	0.137507i
$993$	20087.3	+	31256.4i	0.641944	+	0.998884i
$994$	−2933.67	−	20404.1i	−0.0936121	−	0.651086i
$995$	−108.485	+	159.133i	−0.00345648	+	0.00507020i
$996$	−4608.45	+	10091.1i	−0.146611	+	0.321033i
$997$	−32366.7	−	28045.9i	−1.02815	−	0.890895i	−0.0340541	−	0.999420i	$-0.510842\pi$
$997$	−32366.7	−	28045.9i	−1.02815	−	0.890895i	−0.994094	+	0.108525i	$0.965387\pi$
$998$	1296.73	+	186.442i	0.0411296	+	0.00591355i
$999$	27575.3	+	60381.4i	0.873316	+	1.91229i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.j.a.9.2	✓	360
5.4	even	2	inner	230.4.j.a.9.35	yes	360
23.18	even	11	inner	230.4.j.a.179.35	yes	360
115.64	even	22	inner	230.4.j.a.179.2	yes	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.j.a.9.2	✓	360	1.1	even	1	trivial
230.4.j.a.9.35	yes	360	5.4	even	2	inner
230.4.j.a.179.2	yes	360	115.64	even	22	inner
230.4.j.a.179.35	yes	360	23.18	even	11	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.563465 - 1.91899i) q^{2} +(-6.85739 + 5.94196i) q^{3} +(-3.36501 + 2.16256i) q^{4} +(11.1057 - 1.29006i) q^{5} +(15.2664 + 9.81115i) q^{6} +(9.56919 + 4.37010i) q^{7} +(6.04600 + 5.23889i) q^{8} +(7.87438 - 54.7675i) q^{9} +O(q^{10})\)	\(q+(-0.563465 - 1.91899i) q^{2} +(-6.85739 + 5.94196i) q^{3} +(-3.36501 + 2.16256i) q^{4} +(11.1057 - 1.29006i) q^{5} +(15.2664 + 9.81115i) q^{6} +(9.56919 + 4.37010i) q^{7} +(6.04600 + 5.23889i) q^{8} +(7.87438 - 54.7675i) q^{9} +(-8.73326 - 20.5847i) q^{10} +(-45.7363 - 13.4294i) q^{11} +(10.2253 - 34.8243i) q^{12} +(62.1402 - 28.3785i) q^{13} +(2.99426 - 20.8255i) q^{14} +(-68.4904 + 74.8359i) q^{15} +(6.64664 - 14.5541i) q^{16} +(-52.7552 + 82.0887i) q^{17} +(-109.535 + 15.7488i) q^{18} +(47.2317 - 30.3540i) q^{19} +(-34.5809 + 28.3578i) q^{20} +(-91.5866 + 26.8923i) q^{21} +95.3342i q^{22} +(108.909 + 17.4906i) q^{23} -72.5890 q^{24} +(121.671 - 28.6539i) q^{25} +(-89.4717 - 103.256i) q^{26} +(138.978 + 216.255i) q^{27} +(-41.6511 + 5.98852i) q^{28} +(142.113 + 91.3304i) q^{29} +(182.201 + 89.2647i) q^{30} +(-134.258 + 154.942i) q^{31} +(-31.6743 - 4.55407i) q^{32} +(393.428 - 179.673i) q^{33} +(187.253 + 54.9824i) q^{34} +(111.910 + 36.1881i) q^{35} +(91.9409 + 201.322i) q^{36} +(255.597 + 36.7493i) q^{37} +(-84.8623 - 73.5336i) q^{38} +(-257.496 + 563.837i) q^{39} +(73.9033 + 50.3816i) q^{40} +(11.4906 + 79.9187i) q^{41} +(103.212 + 160.601i) q^{42} +(-292.421 + 253.384i) q^{43} +(182.945 - 53.7175i) q^{44} +(16.7969 - 618.388i) q^{45} +(-27.8021 - 218.849i) q^{46} +543.063i q^{47} +(40.9014 + 139.297i) q^{48} +(-152.146 - 175.585i) q^{49} +(-123.544 - 217.340i) q^{50} +(-126.005 - 876.384i) q^{51} +(-147.732 + 229.876i) q^{52} +(26.2649 + 11.9948i) q^{53} +(336.680 - 388.550i) q^{54} +(-525.256 - 90.1397i) q^{55} +(34.9608 + 76.5535i) q^{56} +(-143.524 + 488.798i) q^{57} +(95.1861 - 324.174i) q^{58} +(282.264 + 618.071i) q^{59} +(68.6338 - 399.939i) q^{60} +(-77.8902 + 89.8901i) q^{61} +(372.982 + 170.335i) q^{62} +(314.691 - 489.669i) q^{63} +(9.10815 + 63.3486i) q^{64} +(653.498 - 395.326i) q^{65} +(-566.472 - 653.744i) q^{66} +(-31.2669 - 106.485i) q^{67} -390.316i q^{68} +(-850.757 + 527.191i) q^{69} +(6.38708 - 235.144i) q^{70} +(940.078 - 276.032i) q^{71} +(334.529 - 289.871i) q^{72} +(124.904 + 194.354i) q^{73} +(-73.4986 - 511.194i) q^{74} +(-664.088 + 919.459i) q^{75} +(-93.2930 + 204.283i) q^{76} +(-378.971 - 328.380i) q^{77} +(1227.08 + 176.428i) q^{78} +(-418.305 - 915.961i) q^{79} +(55.0397 - 170.208i) q^{80} +(-804.592 - 236.250i) q^{81} +(146.888 - 67.0817i) q^{82} +(-302.544 - 43.4992i) q^{83} +(250.034 - 288.555i) q^{84} +(-479.982 + 979.707i) q^{85} +(651.009 + 418.378i) q^{86} +(-1517.21 + 218.141i) q^{87} +(-206.166 - 320.801i) q^{88} +(50.6205 + 58.4191i) q^{89} +(-1196.14 + 316.207i) q^{90} +718.648 q^{91} +(-404.303 + 176.666i) q^{92} -1860.26i q^{93} +(1042.13 - 305.997i) q^{94} +(485.381 - 398.033i) q^{95} +(244.263 - 156.978i) q^{96} +(706.672 - 101.604i) q^{97} +(-251.217 + 390.902i) q^{98} +(-1095.64 + 2399.11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q + 144 q^{4} + 32 q^{5} + 8 q^{6} + 224 q^{9}+O(q^{10}) \) 360 * q + 144 * q^4 + 32 * q^5 + 8 * q^6 + 224 * q^9	\( 360 q + 144 q^{4} + 32 q^{5} + 8 q^{6} + 224 q^{9} + 96 q^{11} + 208 q^{14} - 752 q^{15} - 576 q^{16} + 48 q^{19} + 224 q^{20} - 272 q^{21} - 32 q^{24} + 904 q^{25} - 152 q^{26} - 20 q^{29} - 1272 q^{30} + 160 q^{31} + 128 q^{34} - 364 q^{35} - 896 q^{36} - 1476 q^{39} + 216 q^{41} - 384 q^{44} - 820 q^{45} + 416 q^{46} + 3814 q^{49} + 1000 q^{50} + 296 q^{51} - 2772 q^{54} - 4272 q^{55} + 1104 q^{56} - 6250 q^{59} - 72 q^{60} + 96 q^{61} + 2304 q^{64} + 8708 q^{65} - 6144 q^{66} + 14176 q^{69} + 6136 q^{70} - 11144 q^{71} + 4944 q^{74} + 6722 q^{75} - 192 q^{76} - 2680 q^{79} - 896 q^{80} + 4820 q^{81} - 2696 q^{84} - 7290 q^{85} + 2900 q^{86} + 880 q^{89} - 1104 q^{90} + 5272 q^{91} + 864 q^{94} + 7456 q^{95} + 128 q^{96} + 23448 q^{99}+O(q^{100}) \) 360 * q + 144 * q^4 + 32 * q^5 + 8 * q^6 + 224 * q^9 + 96 * q^11 + 208 * q^14 - 752 * q^15 - 576 * q^16 + 48 * q^19 + 224 * q^20 - 272 * q^21 - 32 * q^24 + 904 * q^25 - 152 * q^26 - 20 * q^29 - 1272 * q^30 + 160 * q^31 + 128 * q^34 - 364 * q^35 - 896 * q^36 - 1476 * q^39 + 216 * q^41 - 384 * q^44 - 820 * q^45 + 416 * q^46 + 3814 * q^49 + 1000 * q^50 + 296 * q^51 - 2772 * q^54 - 4272 * q^55 + 1104 * q^56 - 6250 * q^59 - 72 * q^60 + 96 * q^61 + 2304 * q^64 + 8708 * q^65 - 6144 * q^66 + 14176 * q^69 + 6136 * q^70 - 11144 * q^71 + 4944 * q^74 + 6722 * q^75 - 192 * q^76 - 2680 * q^79 - 896 * q^80 + 4820 * q^81 - 2696 * q^84 - 7290 * q^85 + 2900 * q^86 + 880 * q^89 - 1104 * q^90 + 5272 * q^91 + 864 * q^94 + 7456 * q^95 + 128 * q^96 + 23448 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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