LMFDB - Embedded newform 153.4.n.a.106.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,4,Mod(4,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9]))

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

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

chi := DirichletCharacter("153.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	153.n (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.02729223088$
Analytic rank:	$0$
Dimension:	$208$
Relative dimension:	$52$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			106.13
Character	$\chi$	$=$	153.106
Dual form			153.4.n.a.13.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.01007 - 1.73786i) q^{2} +(-1.82835 + 4.86386i) q^{3} +(2.04034 + 3.53398i) q^{4} +(2.60647 + 0.698403i) q^{5} +(13.9562 - 11.4631i) q^{6} +(7.74620 - 2.07559i) q^{7} +13.6225i q^{8} +(-20.3143 - 17.7857i) q^{9} +(-6.63194 - 6.63194i) q^{10} +(37.8060 - 10.1301i) q^{11} +(-20.9192 + 3.46260i) q^{12} +(-19.2637 - 33.3657i) q^{13} +(-26.9237 - 7.21418i) q^{14} +(-8.16248 + 11.4006i) q^{15} +(39.9967 - 69.2764i) q^{16} +(-47.6145 + 51.4379i) q^{17} +(30.2383 + 88.8395i) q^{18} +81.9790i q^{19} +(2.84996 + 10.6362i) q^{20} +(-4.06739 + 41.4713i) q^{21} +(-131.403 - 35.2094i) q^{22} +(-41.8183 + 156.068i) q^{23} +(-66.2578 - 24.9066i) q^{24} +(-101.947 - 58.8593i) q^{25} +133.911i q^{26} +(123.649 - 66.2874i) q^{27} +(23.1400 + 23.1400i) q^{28} +(78.9638 + 294.697i) q^{29} +(44.3823 - 20.1313i) q^{30} +(148.968 + 39.9159i) q^{31} +(-146.407 + 84.5279i) q^{32} +(-19.8512 + 202.404i) q^{33} +(232.715 - 72.0841i) q^{34} +21.6399 q^{35} +(21.4061 - 108.079i) q^{36} +(-156.738 + 156.738i) q^{37} +(142.468 - 246.762i) q^{38} +(197.507 - 32.6918i) q^{39} +(-9.51397 + 35.5066i) q^{40} +(10.1270 - 37.7944i) q^{41} +(84.3146 - 117.763i) q^{42} +(-169.705 - 97.9793i) q^{43} +(112.937 + 112.937i) q^{44} +(-40.5271 - 60.5454i) q^{45} +(397.101 - 397.101i) q^{46} +(-218.266 + 378.048i) q^{47} +(263.823 + 321.200i) q^{48} +(-241.351 + 139.344i) q^{49} +(204.579 + 354.341i) q^{50} +(-163.131 - 325.637i) q^{51} +(78.6091 - 136.155i) q^{52} -233.107i q^{53} +(-487.389 - 15.3548i) q^{54} +105.615 q^{55} +(28.2746 + 105.522i) q^{56} +(-398.734 - 149.886i) q^{57} +(274.457 - 1024.29i) q^{58} +(-725.703 + 418.985i) q^{59} +(-56.9437 - 5.58488i) q^{60} +(549.457 - 147.226i) q^{61} +(-379.036 - 379.036i) q^{62} +(-194.274 - 95.6072i) q^{63} -52.3556 q^{64} +(-26.9076 - 100.421i) q^{65} +(411.505 - 574.752i) q^{66} +(-39.7927 - 68.9229i) q^{67} +(-278.930 - 63.3177i) q^{68} +(-682.635 - 488.746i) q^{69} +(-65.1375 - 37.6071i) q^{70} +(217.514 - 217.514i) q^{71} +(242.285 - 276.731i) q^{72} +(-104.528 + 104.528i) q^{73} +(744.179 - 199.402i) q^{74} +(472.678 - 388.242i) q^{75} +(-289.712 + 167.265i) q^{76} +(271.827 - 156.939i) q^{77} +(-651.323 - 244.836i) q^{78} +(491.808 - 131.780i) q^{79} +(152.633 - 152.633i) q^{80} +(96.3399 + 722.606i) q^{81} +(-96.1645 + 96.1645i) q^{82} +(-129.085 - 74.5270i) q^{83} +(-154.858 + 70.2417i) q^{84} +(-160.030 + 100.817i) q^{85} +(340.549 + 589.849i) q^{86} +(-1577.74 - 154.740i) q^{87} +(137.997 + 515.011i) q^{88} +710.308 q^{89} +(16.7696 + 252.677i) q^{90} +(-218.474 - 218.474i) q^{91} +(-636.865 + 170.647i) q^{92} +(-466.511 + 651.579i) q^{93} +(1313.99 - 758.633i) q^{94} +(-57.2543 + 213.676i) q^{95} +(-143.450 - 866.648i) q^{96} +(351.808 + 1312.97i) q^{97} +968.645 q^{98} +(-948.172 - 466.619i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 208 q - 6 q^{3} + 396 q^{4} - 2 q^{5} - 40 q^{6} - 2 q^{7} - 40 q^{10} - 60 q^{11} + 96 q^{12} - 4 q^{13} - 84 q^{14} - 1444 q^{16} - 8 q^{17} - 152 q^{18} + 270 q^{20} - 184 q^{21} - 70 q^{22} + 82 q^{23}+ \cdots - 2658 q^{99}+O(q^{100}) $ 208 * q - 6 * q^3 + 396 * q^4 - 2 * q^5 - 40 * q^6 - 2 * q^7 - 40 * q^10 - 60 * q^11 + 96 * q^12 - 4 * q^13 - 84 * q^14 - 1444 * q^16 - 8 * q^17 - 152 * q^18 + 270 * q^20 - 184 * q^21 - 70 * q^22 + 82 * q^23 - 44 * q^24 - 108 * q^27 + 216 * q^28 - 418 * q^29 + 540 * q^30 - 2 * q^31 - 180 * q^33 - 202 * q^34 + 2176 * q^35 - 8 * q^37 + 516 * q^38 - 242 * q^39 + 268 * q^40 + 152 * q^41 - 1240 * q^44 - 838 * q^45 - 112 * q^46 + 2636 * q^47 - 1300 * q^48 - 228 * q^50 - 2156 * q^51 + 540 * q^52 + 1712 * q^54 - 16 * q^55 + 1356 * q^56 - 1194 * q^57 - 34 * q^58 - 2 * q^61 + 4484 * q^62 - 3878 * q^63 - 9296 * q^64 - 1246 * q^65 - 4 * q^67 + 732 * q^68 + 4776 * q^69 - 4512 * q^71 + 1272 * q^72 + 2476 * q^73 + 2674 * q^74 + 1858 * q^75 + 364 * q^78 - 938 * q^79 + 4932 * q^80 + 3860 * q^81 + 5792 * q^82 + 5028 * q^84 - 1658 * q^85 - 7888 * q^86 + 1726 * q^88 - 5920 * q^89 + 14322 * q^90 + 356 * q^91 - 4844 * q^92 + 1564 * q^95 + 4246 * q^96 + 736 * q^97 - 12008 * q^98 - 2658 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−3.01007	−	1.73786i	−1.06422	−	0.614428i	−0.137623	−	0.990485i	$-0.543946\pi$
$2$	−3.01007	−	1.73786i	−1.06422	−	0.614428i	−0.926597	+	0.376057i	$0.877280\pi$
$3$	−1.82835	+	4.86386i	−0.351866	+	0.936050i
$3$	−1.82835	+	4.86386i	−0.351866	+	0.936050i
$4$	2.04034	+	3.53398i	0.255043	+	0.441747i
$5$	2.60647	+	0.698403i	0.233130	+	0.0624670i	0.373493	−	0.927633i	$-0.378160\pi$
$5$	2.60647	+	0.698403i	0.233130	+	0.0624670i	−0.140362	+	0.990100i	$0.544827\pi$
$6$	13.9562	−	11.4631i	0.949598	−	0.779967i
$7$	7.74620	−	2.07559i	0.418255	−	0.112071i	−0.0435526	−	0.999051i	$-0.513868\pi$
$7$	7.74620	−	2.07559i	0.418255	−	0.112071i	0.461808	+	0.886980i	$0.347201\pi$
$8$			13.6225i			0.602034i
$9$	−20.3143	−	17.7857i	−0.752381	−	0.658729i
$10$	−6.63194	−	6.63194i	−0.209720	−	0.209720i
$11$	37.8060	−	10.1301i	1.03627	−	0.277667i	0.299701	−	0.954033i	$-0.403113\pi$
$11$	37.8060	−	10.1301i	1.03627	−	0.277667i	0.736565	+	0.676366i	$0.236446\pi$
$12$	−20.9192	+	3.46260i	−0.503239	+	0.0832972i
$13$	−19.2637	−	33.3657i	−0.410984	−	0.711845i	0.584014	−	0.811744i	$-0.301481\pi$
$13$	−19.2637	−	33.3657i	−0.410984	−	0.711845i	−0.994998	+	0.0998989i	$0.968148\pi$
$14$	−26.9237	−	7.21418i	−0.513975	−	0.137719i
$15$	−8.16248	+	11.4006i	−0.140503	+	0.196242i
$16$	39.9967	−	69.2764i	0.624949	−	1.08244i
$17$	−47.6145	+	51.4379i	−0.679307	+	0.733854i
$17$	−47.6145	+	51.4379i	−0.679307	+	0.733854i
$18$	30.2383	+	88.8395i	0.395958	+	1.16332i
$19$			81.9790i			0.989856i	0.868934	+	0.494928i	$0.164806\pi$
$19$			81.9790i			0.989856i	−0.868934	+	0.494928i	$0.835194\pi$
$20$	2.84996	+	10.6362i	0.0318636	+	0.118916i
$21$	−4.06739	+	41.4713i	−0.0422655	+	0.430942i
$22$	−131.403	−	35.2094i	−1.27342	−	0.341212i
$23$	−41.8183	+	156.068i	−0.379118	+	1.41489i	0.468115	+	0.883668i	$0.344933\pi$
$23$	−41.8183	+	156.068i	−0.379118	+	1.41489i	−0.847233	+	0.531222i	$0.821733\pi$
$24$	−66.2578	−	24.9066i	−0.563534	−	0.211835i
$25$	−101.947	−	58.8593i	−0.815578	−	0.470874i
$26$			133.911i			1.01008i
$27$	123.649	−	66.2874i	0.881340	−	0.472482i
$28$	23.1400	+	23.1400i	0.156180	+	0.156180i
$29$	78.9638	+	294.697i	0.505628	+	1.88703i	0.459677	+	0.888086i	$0.347965\pi$
$29$	78.9638	+	294.697i	0.505628	+	1.88703i	0.0459509	+	0.998944i	$0.485368\pi$
$30$	44.3823	−	20.1313i	0.270102	−	0.122515i
$31$	148.968	+	39.9159i	0.863079	+	0.231261i	0.663093	−	0.748537i	$-0.269244\pi$
$31$	148.968	+	39.9159i	0.863079	+	0.231261i	0.199986	+	0.979799i	$0.435910\pi$
$32$	−146.407	+	84.5279i	−0.808790	+	0.466955i
$33$	−19.8512	+	202.404i	−0.104717	+	1.06770i
$34$	232.715	−	72.0841i	1.17383	−	0.363598i
$35$	21.6399			0.104509
$36$	21.4061	−	108.079i	0.0991022	−	0.500366i
$37$	−156.738	+	156.738i	−0.696419	+	0.696419i	−0.963636	−	0.267218i	$-0.913896\pi$
$37$	−156.738	+	156.738i	−0.696419	+	0.696419i	0.267218	+	0.963636i	$0.413896\pi$
$38$	142.468	−	246.762i	0.608195	−	1.05342i
$39$	197.507	−	32.6918i	0.810934	−	0.134228i
$40$	−9.51397	+	35.5066i	−0.0376073	+	0.140352i
$41$	10.1270	−	37.7944i	0.0385748	−	0.143963i	−0.943953	−	0.330081i	$-0.892924\pi$
$41$	10.1270	−	37.7944i	0.0385748	−	0.143963i	0.982527	+	0.186118i	$0.0595906\pi$
$42$	84.3146	−	117.763i	0.309763	−	0.432648i
$43$	−169.705	−	97.9793i	−0.601855	−	0.347481i	0.167916	−	0.985801i	$-0.446296\pi$
$43$	−169.705	−	97.9793i	−0.601855	−	0.347481i	−0.769771	+	0.638320i	$0.779630\pi$
$44$	112.937	+	112.937i	0.386951	+	0.386951i
$45$	−40.5271	−	60.5454i	−0.134254	−	0.200568i
$46$	397.101	−	397.101i	1.27281	−	1.27281i
$47$	−218.266	+	378.048i	−0.677391	+	1.17327i	0.298373	+	0.954449i	$0.403556\pi$
$47$	−218.266	+	378.048i	−0.677391	+	1.17327i	−0.975764	+	0.218826i	$0.929777\pi$
$48$	263.823	+	321.200i	0.793324	+	0.965859i
$49$	−241.351	+	139.344i	−0.703648	+	0.406251i
$50$	204.579	+	354.341i	0.578636	+	1.00223i
$51$	−163.131	−	325.637i	−0.447900	−	0.894084i
$52$	78.6091	−	136.155i	0.209637	−	0.363102i
$53$		−	233.107i		−	0.604146i	−0.953285	−	0.302073i	$-0.902321\pi$
$53$		−	233.107i		−	0.604146i	0.953285	−	0.302073i	$-0.0976786\pi$
$54$	−487.389	−	15.3548i	−1.22825	−	0.0386949i
$55$	105.615			0.258930
$56$	28.2746	+	105.522i	0.0674706	+	0.251804i
$57$	−398.734	−	149.886i	−0.926555	−	0.348297i
$58$	274.457	−	1024.29i	0.621344	−	2.31889i
$59$	−725.703	+	418.985i	−1.60133	+	0.924529i	−0.610109	+	0.792317i	$0.708875\pi$
$59$	−725.703	+	418.985i	−1.60133	+	0.924529i	−0.991222	+	0.132212i	$0.957792\pi$
$60$	−56.9437	−	5.58488i	−0.122523	−	0.0120167i
$61$	549.457	−	147.226i	1.15329	−	0.309023i	0.369007	−	0.929426i	$-0.379698\pi$
$61$	549.457	−	147.226i	1.15329	−	0.309023i	0.784283	+	0.620403i	$0.213031\pi$
$62$	−379.036	−	379.036i	−0.776412	−	0.776412i
$63$	−194.274	−	95.6072i	−0.388512	−	0.191197i
$64$	−52.3556			−0.102257
$65$	−26.9076	−	100.421i	−0.0513459	−	0.191625i
$66$	411.505	−	574.752i	0.767466	−	1.07193i
$67$	−39.7927	−	68.9229i	−0.0725589	−	0.125676i	0.827463	−	0.561520i	$-0.189783\pi$
$67$	−39.7927	−	68.9229i	−0.0725589	−	0.125676i	−0.900022	+	0.435844i	$0.856450\pi$
$68$	−278.930	−	63.3177i	−0.497431	−	0.112918i
$69$	−682.635	−	488.746i	−1.19101	−	0.852725i
$70$	−65.1375	−	37.6071i	−0.111220	−	0.0642130i
$71$	217.514	−	217.514i	0.363580	−	0.363580i	−0.501549	−	0.865129i	$-0.667236\pi$
$71$	217.514	−	217.514i	0.363580	−	0.363580i	0.865129	+	0.501549i	$0.167236\pi$
$72$	242.285	−	276.731i	0.396577	−	0.452959i
$73$	−104.528	+	104.528i	−0.167590	+	0.167590i	−0.785919	−	0.618329i	$-0.787810\pi$
$73$	−104.528	+	104.528i	−0.167590	+	0.167590i	0.618329	+	0.785919i	$0.287810\pi$
$74$	744.179	−	199.402i	1.16904	−	0.313244i
$75$	472.678	−	388.242i	0.727736	−	0.597737i
$76$	−289.712	+	167.265i	−0.437266	+	0.252456i
$77$	271.827	−	156.939i	0.402306	−	0.232271i
$78$	−651.323	−	244.836i	−0.945485	−	0.355413i
$79$	491.808	−	131.780i	0.700414	−	0.187675i	0.108998	−	0.994042i	$-0.465236\pi$
$79$	491.808	−	131.780i	0.700414	−	0.187675i	0.591416	+	0.806367i	$0.298569\pi$
$80$	152.633	−	152.633i	0.213312	−	0.213312i
$81$	96.3399	+	722.606i	0.132153	+	0.991229i
$82$	−96.1645	+	96.1645i	−0.129507	+	0.129507i
$83$	−129.085	−	74.5270i	−0.170709	−	0.0985591i	0.412211	−	0.911088i	$-0.364757\pi$
$83$	−129.085	−	74.5270i	−0.170709	−	0.0985591i	−0.582920	+	0.812529i	$0.698090\pi$
$84$	−154.858	+	70.2417i	−0.201147	+	0.0912380i
$85$	−160.030	+	100.817i	−0.204209	+	0.128649i
$86$	340.549	+	589.849i	0.427004	+	0.739593i
$87$	−1577.74	−	154.740i	−1.94427	−	0.190688i
$88$	137.997	+	515.011i	0.167165	+	0.623868i
$89$	710.308			0.845983			0.422992	−	0.906134i	$-0.360980\pi$
$89$	710.308			0.845983			0.422992	+	0.906134i	$0.360980\pi$
$90$	16.7696	+	252.677i	0.0196408	+	0.295938i
$91$	−218.474	−	218.474i	−0.251673	−	0.251673i
$92$	−636.865	+	170.647i	−0.721715	+	0.193383i
$93$	−466.511	+	651.579i	−0.520160	+	0.726512i
$94$	1313.99	−	758.633i	1.44179	−	0.832415i
$95$	−57.2543	+	213.676i	−0.0618334	+	0.230765i
$96$	−143.450	−	866.648i	−0.152508	−	0.921374i
$97$	351.808	+	1312.97i	0.368255	+	1.37435i	0.862954	+	0.505282i	$0.168611\pi$
$97$	351.808	+	1312.97i	0.368255	+	1.37435i	−0.494700	+	0.869064i	$0.664722\pi$
$98$	968.645			0.998448
$99$	−948.172	−	466.619i	−0.962574	−	0.473707i
$100$		−	480.372i		−	0.480372i
$101$	307.489	−	532.586i	0.302933	−	0.524696i	−0.673866	−	0.738854i	$-0.735367\pi$
$101$	307.489	−	532.586i	0.302933	−	0.524696i	0.976799	+	0.214158i	$0.0687008\pi$
$102$	−74.8774	+	1263.69i	−0.0726860	+	1.22670i
$103$	−164.554	−	285.016i	−0.157417	−	0.272655i	0.776519	−	0.630094i	$-0.216983\pi$
$103$	−164.554	−	285.016i	−0.157417	−	0.272655i	−0.933937	+	0.357439i	$0.883650\pi$
$104$	454.523	−	262.419i	0.428555	−	0.247426i
$105$	−39.5652	+	105.253i	−0.0367730	+	0.0978254i
$106$	−405.108	+	701.668i	−0.371204	+	0.642944i
$107$	1159.78	−	1159.78i	1.04785	−	1.04785i	0.0490562	−	0.998796i	$-0.484379\pi$
$107$	1159.78	−	1159.78i	1.04785	−	1.04785i	0.998796	−	0.0490562i	$-0.0156213\pi$
$108$	486.544	+	301.722i	0.433497	+	0.268826i
$109$	672.485	+	672.485i	0.590939	+	0.590939i	0.937885	−	0.346946i	$-0.112781\pi$
$109$	672.485	+	672.485i	0.590939	+	0.590939i	−0.346946	+	0.937885i	$0.612781\pi$
$110$	−317.909	−	183.545i	−0.275559	−	0.159094i
$111$	−475.778	−	1048.92i	−0.406837	−	0.896929i
$112$	166.033	−	619.645i	0.140078	−	0.522777i
$113$	−537.763	+	2006.96i	−0.447686	+	1.67079i	0.261061	+	0.965322i	$0.415927\pi$
$113$	−537.763	+	2006.96i	−0.447686	+	1.67079i	−0.708747	+	0.705463i	$0.750739\pi$
$114$	939.736	+	1144.11i	0.772055	+	0.939965i
$115$	−217.997	+	377.582i	−0.176768	+	0.306171i
$116$	−880.340	+	880.340i	−0.704633	+	0.704633i
$117$	−202.103	+	1020.42i	−0.159696	+	0.806305i
$118$	2912.56			2.27222
$119$	−262.068	+	497.276i	−0.201880	+	0.383069i
$120$	−155.304	−	111.193i	−0.118144	−	0.0845875i
$121$	173.994	−	100.456i	0.130724	−	0.0754738i
$122$	−1909.76	−	511.719i	−1.41723	−	0.379745i
$123$	165.311	+	118.358i	0.121184	+	0.0867638i
$124$	162.884	+	607.892i	0.117963	+	0.440244i
$125$	−463.124	−	463.124i	−0.331385	−	0.331385i
$126$	418.626	+	625.406i	0.295986	+	0.442188i
$127$			960.475i			0.671089i	0.942024	+	0.335545i	$0.108920\pi$
$127$			960.475i			0.671089i	−0.942024	+	0.335545i	$0.891080\pi$
$128$	1328.85	+	767.210i	0.917614	+	0.529785i
$129$	786.837	−	646.281i	0.537032	−	0.441100i
$130$	−93.5236	+	349.035i	−0.0630967	+	0.235480i
$131$	1260.00	+	337.617i	0.840359	+	0.225174i	0.653228	−	0.757161i	$-0.273414\pi$
$131$	1260.00	+	337.617i	0.840359	+	0.225174i	0.187131	+	0.982335i	$0.440081\pi$
$132$	−755.796	+	342.821i	−0.498361	+	0.226051i
$133$	170.154	+	635.025i	0.110934	+	0.414013i
$134$			276.617i			0.178329i
$135$	368.582	−	86.4199i	0.234982	−	0.0550951i
$136$	−700.711	−	648.627i	−0.441805	−	0.408966i
$137$	727.352	−	1259.81i	0.453590	−	0.785641i	−0.545016	−	0.838426i	$-0.683476\pi$
$137$	727.352	−	1259.81i	0.453590	−	0.785641i	0.998606	+	0.0527846i	$0.0168097\pi$
$138$	1205.41	+	2657.48i	0.743557	+	1.63928i
$139$	−2537.42	−	679.900i	−1.54835	−	0.414880i	−0.619400	−	0.785076i	$-0.712624\pi$
$139$	−2537.42	−	679.900i	−1.54835	−	0.414880i	−0.928954	+	0.370196i	$0.879291\pi$
$140$	44.1527	+	76.4748i	0.0266542	+	0.0461664i
$141$	−1439.70	−	1752.82i	−0.859894	−	1.04691i
$142$	−1032.74	+	276.722i	−0.610322	+	0.163535i
$143$	−1066.28	−	1066.28i	−0.623545	−	0.623545i
$144$	−2044.63	+	695.931i	−1.18324	+	0.402738i
$145$			823.269i			0.471509i
$146$	496.291	−	132.981i	0.281324	−	0.0753806i
$147$	−236.476	−	1428.67i	−0.132682	−	0.801596i
$148$	−873.705	−	234.109i	−0.485258	−	0.130024i
$149$	107.678	+	186.504i	0.0592035	+	0.102543i	0.894108	−	0.447851i	$-0.147811\pi$
$149$	107.678	+	186.504i	0.0592035	+	0.102543i	−0.834905	+	0.550395i	$0.814477\pi$
$150$	−2097.51	+	347.184i	−1.14174	+	0.188983i
$151$	−536.528	−	309.765i	−0.289153	−	0.166942i	0.348407	−	0.937343i	$-0.386723\pi$
$151$	−536.528	−	309.765i	−0.289153	−	0.166942i	−0.637560	+	0.770401i	$0.720056\pi$
$152$	−1116.76			−0.595927
$153$	1882.11	−	198.068i	0.994508	−	0.104659i
$154$	−1090.96			−0.570856
$155$	360.404	+	208.079i	0.186763	+	0.107828i
$156$	518.514	+	631.283i	0.266118	+	0.323994i
$157$	631.994	+	1094.65i	0.321265	+	0.556448i	0.980749	−	0.195271i	$-0.0625586\pi$
$157$	631.994	+	1094.65i	0.321265	+	0.556448i	−0.659484	+	0.751718i	$0.729225\pi$
$158$	−1709.39	−	458.030i	−0.860708	−	0.230626i
$159$	1133.80	+	426.201i	0.565511	+	0.212578i
$160$	−440.640	+	118.069i	−0.217723	+	0.0583386i
$161$			1295.73i			0.634273i
$162$	965.802	−	2342.52i	0.468398	−	1.13608i
$163$	1299.93	+	1299.93i	0.624652	+	0.624652i	0.946717	−	0.322065i	$-0.104377\pi$
$163$	1299.93	+	1299.93i	0.624652	+	0.624652i	−0.322065	+	0.946717i	$0.604377\pi$
$164$	154.227	−	41.3250i	0.0734336	−	0.0196765i
$165$	−193.101	+	513.698i	−0.0911087	+	0.242372i
$166$	259.036	+	448.663i	0.121115	+	0.209777i
$167$	−2619.34	−	701.851i	−1.21372	−	0.325215i	−0.405498	−	0.914096i	$-0.632902\pi$
$167$	−2619.34	−	701.851i	−1.21372	−	0.325215i	−0.808220	+	0.588881i	$0.799569\pi$
$168$	−564.942	−	55.4078i	−0.259442	−	0.0254453i
$169$	356.320	−	617.164i	0.162185	−	0.280912i
$170$	656.910	−	25.3565i	0.296369	−	0.0114397i
$171$	1458.05	−	1665.34i	0.652046	−	0.744749i
$172$		−	799.645i		−	0.354491i
$173$	665.479	+	2483.60i	0.292459	+	1.09147i	0.943214	+	0.332185i	$0.107786\pi$
$173$	665.479	+	2483.60i	0.292459	+	1.09147i	−0.650755	+	0.759288i	$0.725548\pi$
$174$	4480.19	+	3207.67i	1.95197	+	1.39755i
$175$	−911.871	−	244.335i	−0.393891	−	0.105543i
$176$	810.341	−	3024.23i	0.347055	−	1.29523i
$177$	−711.046	−	4295.77i	−0.301952	−	1.82424i
$178$	−2138.08	−	1234.42i	−0.900312	−	0.519796i
$179$		−	3533.77i		−	1.47557i	−0.675038	−	0.737783i	$-0.735873\pi$
$179$		−	3533.77i		−	1.47557i	0.675038	−	0.737783i	$-0.264127\pi$
$180$	131.277	−	266.755i	0.0543601	−	0.110460i
$181$	−164.446	−	164.446i	−0.0675315	−	0.0675315i	0.672534	−	0.740066i	$-0.265206\pi$
$181$	−164.446	−	164.446i	−0.0675315	−	0.0675315i	−0.740066	+	0.672534i	$0.765206\pi$
$182$	277.943	+	1037.30i	0.113201	+	0.422471i
$183$	−288.510	+	2941.66i	−0.116542	+	1.18827i
$184$	−2126.03	−	569.669i	−0.851811	−	0.228242i
$185$	−517.998	+	299.066i	−0.205859	+	0.118853i
$186$	2536.59	−	1150.57i	0.999954	−	0.453568i
$187$	−1279.04	+	2427.00i	−0.500176	+	0.949090i
$188$	−1781.35			−0.691055
$189$	820.221	−	770.119i	0.315674	−	0.296391i
$190$	543.679	−	543.679i	0.207593	−	0.207593i
$191$	−654.139	+	1133.00i	−0.247811	+	0.429221i	−0.962918	−	0.269794i	$-0.913044\pi$
$191$	−654.139	+	1133.00i	−0.247811	+	0.429221i	0.715107	+	0.699015i	$0.246378\pi$
$192$	95.7243	−	254.650i	0.0359808	−	0.0957178i
$193$	216.082	−	806.428i	0.0805902	−	0.300767i	−0.913852	−	0.406046i	$-0.866907\pi$
$193$	216.082	−	806.428i	0.0805902	−	0.300767i	0.994443	+	0.105280i	$0.0335738\pi$
$194$	1222.79	−	4563.51i	0.452532	−	1.68887i
$195$	537.629	+	52.7291i	0.197438	+	0.0193641i
$196$	−984.879	−	568.620i	−0.358921	−	0.207223i
$197$	−1290.48	−	1290.48i	−0.466717	−	0.466717i	0.434132	−	0.900849i	$-0.357055\pi$
$197$	−1290.48	−	1290.48i	−0.466717	−	0.466717i	−0.900849	+	0.434132i	$0.857055\pi$
$198$	2043.14	+	3052.35i	0.733332	+	1.09556i
$199$	3829.83	−	3829.83i	1.36427	−	1.36427i	0.495873	−	0.868395i	$-0.334848\pi$
$199$	3829.83	−	3829.83i	1.36427	−	1.36427i	0.868395	−	0.495873i	$-0.165152\pi$
$200$	801.808	−	1388.77i	0.283482	−	0.491005i
$201$	407.986	−	67.5308i	0.143170	−	0.0236978i
$202$	−1851.12	+	1068.75i	−0.644775	+	0.372261i
$203$	1223.34	+	2118.88i	0.422963	+	0.732594i
$204$	817.950	−	1240.91i	0.280725	−	0.425888i
$205$	52.7914	−	91.4374i	0.0179859	−	0.0311525i
$206$			1143.89i			0.386886i
$207$	3625.29	−	2426.64i	1.21727	−	0.814799i
$208$	−3081.94			−1.02738
$209$	830.454	+	3099.30i	0.274850	+	1.02575i
$210$	302.010	−	248.061i	0.0992412	−	0.0815134i
$211$	352.781	−	1316.60i	0.115102	−	0.429565i	−0.884193	−	0.467122i	$-0.845291\pi$
$211$	352.781	−	1316.60i	0.115102	−	0.429565i	0.999294	+	0.0375568i	$0.0119575\pi$
$212$	823.795	−	475.619i	0.266880	−	0.154083i
$213$	660.266	+	1455.65i	0.212398	+	0.468260i
$214$	−5506.56	+	1475.48i	−1.75897	+	0.471316i
$215$	−373.903	−	373.903i	−0.118604	−	0.118604i
$216$	902.998	+	1684.40i	0.284450	+	0.530597i
$217$	1236.78			0.386905
$218$	−855.539	−	3192.91i	−0.265800	−	0.991979i
$219$	−317.296	−	699.522i	−0.0979034	−	0.215842i
$220$	215.491	+	373.242i	0.0660383	+	0.114382i
$221$	2633.49	+	597.808i	0.801575	+	0.181959i
$222$	−390.755	+	3984.16i	−0.118134	+	1.20450i
$223$	1189.37	+	686.685i	0.357158	+	0.206205i	0.667833	−	0.744311i	$-0.267222\pi$
$223$	1189.37	+	686.685i	0.357158	+	0.206205i	−0.310675	+	0.950516i	$0.600555\pi$
$224$	−958.650	+	958.650i	−0.285949	+	0.285949i
$225$	1024.13	+	3008.88i	0.303447	+	0.891521i
$226$	5106.52	−	5106.52i	1.50301	−	1.50301i
$227$	−391.539	+	104.912i	−0.114482	+	0.0306753i	−0.315605	−	0.948891i	$-0.602207\pi$
$227$	−391.539	+	104.912i	−0.114482	+	0.0306753i	0.201123	+	0.979566i	$0.435541\pi$
$228$	−283.860	−	1714.94i	−0.0824522	−	0.498134i
$229$	−1955.34	+	1128.92i	−0.564246	+	0.325768i	−0.754848	−	0.655900i	$-0.772289\pi$
$229$	−1955.34	+	1128.92i	−0.564246	+	0.325768i	0.190602	+	0.981667i	$0.438956\pi$
$230$	1312.37	−	757.698i	0.376240	−	0.217222i
$231$	266.336	+	1609.07i	0.0758600	+	0.458307i
$232$	−4014.50	+	1075.68i	−1.13606	+	0.304405i
$233$	−3190.24	+	3190.24i	−0.896994	+	0.896994i	−0.995169	−	0.0981749i	$-0.968700\pi$
$233$	−3190.24	+	3190.24i	−0.896994	+	0.896994i	0.0981749	+	0.995169i	$0.468700\pi$
$234$	2381.69	−	2720.30i	0.665368	−	0.759964i
$235$	−832.934	+	832.934i	−0.231211	+	0.231211i
$236$	−2961.37	−	1709.75i	−0.816816	−	0.471589i
$237$	−258.239	+	2633.02i	−0.0707783	+	0.721660i
$238$	1653.04	−	1041.40i	0.450213	−	0.283629i
$239$	−898.956	−	1557.04i	−0.243300	−	0.421408i	0.718352	−	0.695679i	$-0.244897\pi$
$239$	−898.956	−	1557.04i	−0.243300	−	0.421408i	−0.961652	+	0.274272i	$0.911563\pi$
$240$	463.320	+	1021.45i	0.124613	+	0.274727i
$241$	−61.5990	−	229.891i	−0.0164645	−	0.0614463i	0.957205	−	0.289411i	$-0.0934595\pi$
$241$	−61.5990	−	229.891i	−0.0164645	−	0.0614463i	−0.973669	+	0.227965i	$0.926793\pi$
$242$	−698.313			−0.185493
$243$	−3690.80	−	852.593i	−0.974341	−	0.225078i
$244$	1641.38	+	1641.38i	0.430649	+	0.430649i
$245$	−726.394	+	194.637i	−0.189419	+	0.0507546i
$246$	−291.908	−	643.553i	−0.0756561	−	0.166794i
$247$	2735.29	−	1579.22i	0.704624	−	0.406815i
$248$	−543.752	+	2029.31i	−0.139227	+	0.519603i
$249$	598.501	−	491.588i	0.152323	−	0.125113i
$250$	589.189	+	2198.88i	0.149054	+	0.556278i
$251$	2864.92			0.720446			0.360223	−	0.932866i	$-0.382701\pi$
$251$	2864.92			0.720446			0.360223	+	0.932866i	$0.382701\pi$
$252$	−58.5120	−	881.632i	−0.0146266	−	0.220387i
$253$			6323.93i			1.57147i
$254$	1669.17	−	2891.09i	0.412336	−	0.714187i
$255$	−197.771	−	962.695i	−0.0485682	−	0.236417i
$256$	−2457.19	−	4255.98i	−0.599901	−	1.03906i
$257$	7009.39	−	4046.87i	1.70130	−	0.982245i	0.756848	−	0.653591i	$-0.226738\pi$
$257$	7009.39	−	4046.87i	1.70130	−	0.982245i	0.944450	−	0.328654i	$-0.106595\pi$
$258$	−3491.58	+	577.935i	−0.842545	+	0.139460i
$259$	−888.797	+	1539.44i	−0.213232	+	0.369329i
$260$	299.984	−	299.984i	0.0715546	−	0.0715546i
$261$	3637.29	−	7390.98i	0.862615	−	1.75284i
$262$	−3205.97	−	3205.97i	−0.755974	−	0.755974i
$263$	−2983.68	−	1722.63i	−0.699551	−	0.403886i	0.107629	−	0.994191i	$-0.465674\pi$
$263$	−2983.68	−	1722.63i	−0.699551	−	0.403886i	−0.807180	+	0.590305i	$0.799007\pi$
$264$	−2757.25	−	270.423i	−0.642791	−	0.0630431i
$265$	162.803	−	607.588i	0.0377392	−	0.140845i
$266$	591.411	−	2207.17i	0.136322	−	0.508762i
$267$	−1298.69	+	3454.84i	−0.297673	+	0.791883i
$268$	162.381	−	281.253i	0.0370113	−	0.0641054i
$269$	−3005.02	+	3005.02i	−0.681112	+	0.681112i	−0.960251	−	0.279139i	$-0.909951\pi$
$269$	−3005.02	+	3005.02i	−0.681112	+	0.681112i	0.279139	+	0.960251i	$0.409951\pi$
$270$	−1259.64	−	380.416i	−0.283924	−	0.0857459i
$271$	1633.53			0.366162			0.183081	−	0.983098i	$-0.441393\pi$
$271$	1633.53			0.366162			0.183081	+	0.983098i	$0.441393\pi$
$272$	1659.01	+	5355.91i	0.369824	+	1.19393i
$273$	1462.07	−	663.180i	0.324134	−	0.147024i
$274$	−4378.76	+	2528.08i	−0.965440	+	0.557397i
$275$	−4450.47	−	1192.50i	−0.975902	−	0.261492i
$276$	334.406	−	3409.63i	0.0729307	−	0.743606i
$277$	−866.816	−	3235.00i	−0.188021	−	0.701705i	−0.993964	−	0.109711i	$-0.965007\pi$
$277$	−866.816	−	3235.00i	−0.188021	−	0.701705i	0.805942	−	0.591994i	$-0.201659\pi$
$278$	6456.24	+	6456.24i	1.39288	+	1.39288i
$279$	−2316.25	−	3460.36i	−0.497025	−	0.742531i
$280$			294.788i			0.0629177i
$281$	−6585.49	−	3802.13i	−1.39807	−	0.807175i	−0.403878	−	0.914813i	$-0.632338\pi$
$281$	−6585.49	−	3802.13i	−1.39807	−	0.807175i	−0.994190	+	0.107637i	$0.965671\pi$
$282$	1287.45	+	7778.12i	0.271867	+	1.64248i
$283$	−185.269	+	691.432i	−0.0389155	+	0.145235i	−0.982650	−	0.185469i	$-0.940619\pi$
$283$	−185.269	+	691.432i	−0.0389155	+	0.145235i	0.943735	+	0.330704i	$0.107286\pi$
$284$	1212.49	+	324.886i	0.253339	+	0.0678819i
$285$	−934.610	−	669.152i	−0.194251	−	0.139078i
$286$	1356.53	+	5062.63i	0.280466	+	1.04671i
$287$		−	313.782i		−	0.0645365i
$288$	4477.53	+	886.817i	0.916115	+	0.181445i
$289$	−378.716	−	4898.38i	−0.0770845	−	0.997025i
$290$	1430.73	−	2478.10i	0.289708	−	0.501789i
$291$	−7029.31	−	689.414i	−1.41603	−	0.138880i
$292$	−582.672	−	156.126i	−0.116775	−	0.0312898i
$293$	−971.402	−	1682.52i	−0.193686	−	0.335474i	0.752783	−	0.658269i	$-0.228711\pi$
$293$	−971.402	−	1682.52i	−0.193686	−	0.335474i	−0.946469	+	0.322795i	$0.895378\pi$
$294$	−1771.02	+	4711.35i	−0.351320	+	0.934598i
$295$	−2184.15	+	585.241i	−0.431071	+	0.115505i
$296$	−2135.15	−	2135.15i	−0.419267	−	0.419267i
$297$	4003.16	−	3758.63i	0.782111	−	0.734336i
$298$		−	748.518i		−	0.145505i
$299$	6012.90	−	1611.15i	1.16299	−	0.311623i
$300$	2336.46	+	878.288i	0.449653	+	0.169027i
$301$	−1517.93	−	406.729i	−0.290672	−	0.0778853i
$302$	1076.66	+	1864.83i	0.205148	+	0.355327i
$303$	2028.23	+	2469.33i	0.384550	+	0.468183i
$304$	5679.21	+	3278.89i	1.07146	+	0.618610i
$305$	1534.97			0.288171
$306$	−6009.50	−	2674.66i	−1.12268	−	0.499673i
$307$	−5535.50			−1.02908			−0.514540	−	0.857466i	$-0.672037\pi$
$307$	−5535.50			−1.02908			−0.514540	+	0.857466i	$0.672037\pi$
$308$	1109.24	+	640.420i	0.205210	+	0.118478i
$309$	1687.14	−	279.259i	0.310609	−	0.0514126i
$310$	−723.227	−	1252.67i	−0.132505	−	0.229505i
$311$	1716.95	+	460.054i	0.313052	+	0.0838820i	0.411924	−	0.911218i	$-0.364857\pi$
$311$	1716.95	+	460.054i	0.313052	+	0.0838820i	−0.0988723	+	0.995100i	$0.531524\pi$
$312$	445.343	+	2690.53i	0.0808095	+	0.488210i
$313$	8568.83	−	2296.01i	1.54741	−	0.414627i	0.618758	−	0.785581i	$-0.287636\pi$
$313$	8568.83	−	2296.01i	1.54741	−	0.414627i	0.928651	+	0.370954i	$0.120969\pi$
$314$		−	4393.28i		−	0.789577i
$315$	−439.598	−	384.879i	−0.0786303	−	0.0688428i
$316$	1469.16	+	1469.16i	0.261541	+	0.261541i
$317$	−6669.25	+	1787.02i	−1.18165	+	0.316622i	−0.795580	−	0.605849i	$-0.792834\pi$
$317$	−6669.25	+	1787.02i	−1.18165	+	0.316622i	−0.386068	+	0.922470i	$0.626167\pi$
$318$	−2672.14	−	3253.29i	−0.471214	−	0.573696i
$319$	5970.61	+	10341.4i	1.04793	+	1.81507i
$320$	−136.464	−	36.5653i	−0.0238392	−	0.00638770i
$321$	3520.53	+	7761.49i	0.612139	+	1.34955i
$322$	2251.81	−	3900.24i	0.389715	−	0.675006i
$323$	−4216.83	−	3903.39i	−0.726410	−	0.672416i
$324$	−2357.11	+	1814.83i	−0.404168	+	0.311184i
$325$			4535.39i			0.774086i
$326$	−1653.78	−	6171.97i	−0.280964	−	1.04857i
$327$	−4500.41	+	2041.34i	−0.761080	+	0.345218i
$328$	514.853	+	137.954i	0.0866708	+	0.0232234i
$329$	−906.060	+	3381.46i	−0.151832	+	0.566644i
$330$	1473.99	−	1210.68i	0.245879	−	0.201957i
$331$	−970.480	−	560.307i	−0.161155	−	0.0930431i	0.417253	−	0.908790i	$-0.362993\pi$
$331$	−970.480	−	560.307i	−0.161155	−	0.0930431i	−0.578409	+	0.815747i	$0.696326\pi$
$332$		−	608.243i		−	0.100547i
$333$	5971.69	−	396.328i	0.982723	−	0.0652211i
$334$	6664.68	+	6664.68i	1.09184	+	1.09184i
$335$	−55.5826	−	207.437i	−0.00906508	−	0.0338314i
$336$	2710.30	+	1940.49i	0.440057	+	0.315067i
$337$	5442.19	+	1458.23i	0.879688	+	0.235712i	0.670272	−	0.742115i	$-0.266177\pi$
$337$	5442.19	+	1458.23i	0.879688	+	0.235712i	0.209415	+	0.977827i	$0.432844\pi$
$338$	−2145.09	+	1238.47i	−0.345200	+	0.199302i
$339$	−8778.35	−	6285.02i	−1.40641	−	1.00695i
$340$	−682.804	−	359.842i	−0.108912	−	0.0573975i
$341$	6036.23			0.958593
$342$	−7282.97	+	2478.90i	−1.15152	+	0.391941i
$343$	−3525.35	+	3525.35i	−0.554960	+	0.554960i
$344$	1334.72	−	2311.80i	0.209195	−	0.362337i
$345$	−1437.93	−	1750.66i	−0.224393	−	0.273195i
$346$	2313.02	−	8632.32i	0.359390	−	1.34126i
$347$	−2008.57	+	7496.10i	−0.310737	+	1.15969i	0.617156	+	0.786841i	$0.288285\pi$
$347$	−2008.57	+	7496.10i	−0.310737	+	1.15969i	−0.927893	+	0.372846i	$0.878382\pi$
$348$	−2672.28	−	5891.42i	−0.411636	−	0.907509i
$349$	5230.01	+	3019.55i	0.802166	+	0.463131i	0.844228	−	0.535984i	$-0.180059\pi$
$349$	5230.01	+	3019.55i	0.802166	+	0.463131i	−0.0420617	+	0.999115i	$0.513393\pi$
$350$	2320.17	+	2320.17i	0.354338	+	0.354338i
$351$	−4593.66	−	2848.68i	−0.698551	−	0.433195i
$352$	−4678.77	+	4678.77i	−0.708465	+	0.708465i
$353$	−1786.40	+	3094.14i	−0.269350	+	0.466528i	−0.968694	−	0.248257i	$-0.920142\pi$
$353$	−1786.40	+	3094.14i	−0.269350	+	0.466528i	0.699344	+	0.714785i	$0.253476\pi$
$354$	−5325.17	+	14166.3i	−0.799518	+	2.12692i
$355$	718.857	−	415.032i	0.107473	−	0.0620496i
$356$	1449.27	+	2510.21i	0.215762	+	0.373711i
$357$	−1939.53	−	2183.85i	−0.287537	−	0.323759i
$358$	−6141.21	+	10636.9i	−0.906629	+	1.57033i
$359$			8775.82i			1.29017i	0.764112	+	0.645084i	$0.223178\pi$
$359$			8775.82i			1.29017i	−0.764112	+	0.645084i	$0.776822\pi$
$360$	824.778	−	552.079i	0.120749	−	0.0808253i
$361$	138.449			0.0201850
$362$	209.210	+	780.781i	0.0303752	+	0.113362i
$363$	170.480	+	1029.95i	0.0246498	+	0.148921i
$364$	326.320	−	1217.84i	0.0469885	−	0.175364i
$365$	−345.452	+	199.447i	−0.0495391	+	0.0286014i
$366$	5980.64	−	8353.21i	0.854134	−	1.19298i
$367$	7164.30	−	1919.67i	1.01900	−	0.273041i	0.289616	−	0.957143i	$-0.406473\pi$
$367$	7164.30	−	1919.67i	1.01900	−	0.273041i	0.729386	+	0.684102i	$0.239806\pi$
$368$	9139.24	+	9139.24i	1.29461	+	1.29461i
$369$	−877.921	+	587.651i	−0.123856	+	0.0829048i
$370$	2078.95			0.292106
$371$	−483.834	−	1805.69i	−0.0677073	−	0.252687i
$372$	−3254.51	−	319.193i	−0.453598	−	0.0444876i
$373$	2883.45	+	4994.28i	0.400266	+	0.693282i	0.993758	−	0.111559i	$-0.0355843\pi$
$373$	2883.45	+	4994.28i	0.400266	+	0.693282i	−0.593492	+	0.804840i	$0.702251\pi$
$374$	8067.80	−	5082.63i	1.11544	−	0.702718i
$375$	3099.33	−	1405.82i	0.426796	−	0.193590i
$376$	−5149.94	−	2973.32i	−0.706351	−	0.407812i
$377$	8311.64	−	8311.64i	1.13547	−	1.13547i
$378$	−3807.28	+	892.678i	−0.518057	+	0.121467i
$379$	8987.17	−	8987.17i	1.21805	−	1.21805i	0.249733	−	0.968315i	$-0.419657\pi$
$379$	8987.17	−	8987.17i	1.21805	−	1.21805i	0.968315	−	0.249733i	$-0.0803429\pi$
$380$	−871.945	+	233.637i	−0.117710	+	0.0315403i
$381$	−4671.61	−	1756.08i	−0.628173	−	0.236133i
$382$	3938.01	−	2273.61i	0.527450	−	0.304523i
$383$	2077.49	−	1199.44i	0.277167	−	0.160022i	−0.354973	−	0.934876i	$-0.615510\pi$
$383$	2077.49	−	1199.44i	0.277167	−	0.160022i	0.632140	+	0.774854i	$0.282177\pi$
$384$	−6161.20	+	5060.60i	−0.818783	+	0.672520i
$385$	818.116	−	219.214i	0.108299	−	0.0290186i
$386$	−2051.88	+	2051.88i	−0.270565	+	0.270565i
$387$	1704.81	+	5008.70i	0.223928	+	0.657897i
$388$	−3922.18	+	3922.18i	−0.513193	+	0.513193i
$389$	−619.848	−	357.869i	−0.0807906	−	0.0466445i	0.459060	−	0.888405i	$-0.348186\pi$
$389$	−619.848	−	357.869i	−0.0807906	−	0.0466445i	−0.539851	+	0.841761i	$0.681519\pi$
$390$	−1526.66	−	1093.04i	−0.198220	−	0.141919i
$391$	−6036.66	−	9582.16i	−0.780785	−	1.23936i
$392$	−1898.21	−	3287.80i	−0.244577	−	0.423620i
$393$	−3945.85	+	5511.20i	−0.506468	+	0.707388i
$394$	1641.76	+	6127.13i	0.209926	+	0.783453i
$395$	1373.92			0.175011
$396$	−285.573	−	4302.88i	−0.0362388	−	0.546030i
$397$	3975.17	+	3975.17i	0.502540	+	0.502540i	0.912226	−	0.409687i	$-0.134362\pi$
$397$	3975.17	+	3975.17i	0.502540	+	0.502540i	−0.409687	+	0.912226i	$0.634362\pi$
$398$	−18183.8	+	4872.33i	−2.29013	+	0.613637i
$399$	−3399.78	−	333.440i	−0.426571	−	0.0418368i
$400$	−8155.11	+	4708.36i	−1.01939	+	0.588545i
$401$	−734.694	+	2741.91i	−0.0914934	+	0.341458i	−0.996464	−	0.0840150i	$-0.973226\pi$
$401$	−734.694	+	2741.91i	−0.0914934	+	0.341458i	0.904971	+	0.425473i	$0.139892\pi$
$402$	−1345.43	−	505.752i	−0.166925	−	0.0627479i
$403$	−1537.85	−	5739.35i	−0.190089	−	0.709423i
$404$	2509.53			0.309044
$405$	−253.563	+	1950.74i	−0.0311102	+	0.239341i
$406$		−	8503.99i		−	1.03952i
$407$	−4337.85	+	7513.38i	−0.528303	+	0.915048i
$408$	4435.98	−	2222.24i	0.538269	−	0.269651i
$409$	−511.059	−	885.180i	−0.0617854	−	0.107015i	0.833478	−	0.552552i	$-0.186346\pi$
$409$	−511.059	−	885.180i	−0.0617854	−	0.107015i	−0.895264	+	0.445537i	$0.853013\pi$
$410$	−317.812	+	183.489i	−0.0382820	+	0.0221021i
$411$	4797.69	+	5841.11i	0.575797	+	0.701024i
$412$	671.493	−	1163.06i	0.0802964	−	0.139077i
$413$	−4751.80	+	4751.80i	−0.566152	+	0.566152i
$414$	−15129.5	+	1004.11i	−1.79608	+	0.119202i
$415$	−284.406	−	284.406i	−0.0336408	−	0.0336408i
$416$	5640.67	+	3256.64i	0.664799	+	0.383822i
$417$	7946.23	−	11098.6i	0.933162	−	1.30335i
$418$	2886.43	−	10772.3i	0.337751	−	1.26050i
$419$	−2733.92	+	10203.1i	−0.318760	+	1.18963i	0.601677	+	0.798739i	$0.294499\pi$
$419$	−2733.92	+	10203.1i	−0.318760	+	1.18963i	−0.920437	+	0.390890i	$0.872167\pi$
$420$	−452.689	+	74.9302i	−0.0525928	+	0.00870528i
$421$	4190.52	−	7258.20i	0.485115	−	0.840244i	−0.514738	−	0.857347i	$-0.672111\pi$
$421$	4190.52	−	7258.20i	0.485115	−	0.840244i	0.999854	+	0.0171029i	$0.00544429\pi$
$422$	−3349.96	+	3349.96i	−0.386430	+	0.386430i
$423$	11157.7	−	3797.76i	1.28253	−	0.436533i
$424$	3175.49			0.363716
$425$	7881.77	−	2441.40i	0.899581	−	0.278647i
$426$	542.274	−	5529.06i	0.0616743	−	0.628835i
$427$	3950.62	−	2280.89i	0.447737	−	0.258501i
$428$	6464.99	+	1732.29i	0.730133	+	0.195639i
$429$	7135.77	−	3236.71i	0.803073	−	0.364265i
$430$	475.681	+	1775.27i	0.0533474	+	0.199095i
$431$	−3398.58	−	3398.58i	−0.379823	−	0.379823i	0.491215	−	0.871038i	$-0.336553\pi$
$431$	−3398.58	−	3398.58i	−0.379823	−	0.379823i	−0.871038	+	0.491215i	$0.836553\pi$
$432$	353.389	−	11217.2i	0.0393575	−	1.24928i
$433$		−	4305.85i		−	0.477889i	−0.971033	−	0.238944i	$-0.923199\pi$
$433$		−	4305.85i		−	0.477889i	0.971033	−	0.238944i	$-0.0768014\pi$
$434$	−3722.81	−	2149.36i	−0.411752	−	0.237725i
$435$	−4004.26	−	1505.22i	−0.441356	−	0.165908i
$436$	−1004.45	+	3748.65i	−0.110331	+	0.411761i
$437$	−12794.3	−	3428.22i	−1.40054	−	0.375273i
$438$	−260.593	+	2657.03i	−0.0284284	+	0.289858i
$439$	−3908.71	−	14587.5i	−0.424948	−	1.58593i	−0.764035	−	0.645174i	$-0.776785\pi$
$439$	−3908.71	−	14587.5i	−0.424948	−	1.58593i	0.339087	−	0.940755i	$-0.389882\pi$
$440$			1438.74i			0.155885i
$441$	7381.21	+	1461.92i	0.797020	+	0.157857i
$442$	−6888.09	−	6376.10i	−0.741251	−	0.686154i
$443$	4990.07	−	8643.06i	0.535181	−	0.926962i	−0.463973	−	0.885849i	$-0.653577\pi$
$443$	4990.07	−	8643.06i	0.535181	−	0.926962i	0.999155	−	0.0411122i	$-0.0130901\pi$
$444$	2736.11	−	3821.55i	0.292455	−	0.408474i
$445$	1851.40	+	496.081i	0.197224	+	0.0528461i
$446$	−2386.73	−	4133.94i	−0.253397	−	0.438896i
$447$	−1104.00	+	182.737i	−0.116817	+	0.0193359i
$448$	−405.557	+	108.669i	−0.0427696	+	0.0114601i
$449$	−3353.92	−	3353.92i	−0.352520	−	0.352520i	0.508526	−	0.861046i	$-0.330190\pi$
$449$	−3353.92	−	3353.92i	−0.352520	−	0.352520i	−0.861046	+	0.508526i	$0.830190\pi$
$450$	2146.32	−	10836.8i	0.224841	−	1.13522i
$451$		−	1531.44i		−	0.159895i
$452$	−8189.77	+	2194.44i	−0.852244	+	0.228358i
$453$	2487.61	−	2043.24i	0.258009	−	0.211920i
$454$	1360.88	+	364.647i	0.140681	+	0.0376955i
$455$	−416.864	−	722.029i	−0.0429514	−	0.0743940i
$456$	2041.82	−	5431.74i	0.209686	−	0.557817i
$457$	8223.01	+	4747.55i	0.841698	+	0.485955i	0.857841	−	0.513915i	$-0.171805\pi$
$457$	8223.01	+	4747.55i	0.841698	+	0.485955i	−0.0161430	+	0.999870i	$0.505139\pi$
$458$	7847.61			0.800643
$459$	−2477.78	+	9516.47i	−0.251967	+	0.967736i
$460$	−1779.15			−0.180334
$461$	13779.4	+	7955.54i	1.39213	+	0.803745i	0.993551	−	0.113390i	$-0.0361709\pi$
$461$	13779.4	+	7955.54i	1.39213	+	0.803745i	0.398577	+	0.917135i	$0.369504\pi$
$462$	1994.65	−	5306.26i	0.200865	−	0.534350i
$463$	−9199.18	−	15933.4i	−0.923374	−	1.59933i	−0.794156	−	0.607714i	$-0.792087\pi$
$463$	−9199.18	−	15933.4i	−0.923374	−	1.59933i	−0.129217	−	0.991616i	$-0.541246\pi$
$464$	23573.8	+	6316.59i	2.35860	+	0.631984i
$465$	−1671.01	+	1372.51i	−0.166648	+	0.136879i
$466$	15147.1	−	4058.64i	1.50574	−	0.403461i
$467$		−	605.093i		−	0.0599579i	−0.999551	−	0.0299790i	$-0.990456\pi$
$467$		−	605.093i		−	0.0599579i	0.999551	−	0.0299790i	$-0.00954403\pi$
$468$	−4018.50	+	1367.77i	−0.396912	+	0.135097i
$469$	−451.297	−	451.297i	−0.0444328	−	0.0444328i
$470$	3954.72	−	1059.66i	0.388122	−	0.103997i
$471$	−6479.71	+	1072.54i	−0.633905	+	0.104925i
$472$	−5707.61	−	9885.87i	−0.556598	−	0.964055i
$473$	−7408.40	−	1985.08i	−0.720167	−	0.192968i
$474$	5353.16	−	7476.80i	0.518731	−	0.724516i
$475$	4825.22	−	8357.53i	0.466098	−	0.807305i
$476$	−2292.07	+	88.4732i	−0.220708	+	0.00851924i
$477$	−4145.97	+	4735.40i	−0.397968	+	0.454548i
$478$			6249.05i			0.597960i
$479$	408.867	+	1525.91i	0.0390012	+	0.145555i	0.982681	−	0.185306i	$-0.0593277\pi$
$479$	408.867	+	1525.91i	0.0390012	+	0.145555i	−0.943680	+	0.330861i	$0.892661\pi$
$480$	231.372	−	2359.08i	0.0220013	−	0.224327i
$481$	8249.00	+	2210.31i	0.781959	+	0.209525i
$482$	−214.101	+	799.037i	−0.0202325	+	0.0755086i
$483$	−6302.26	−	2369.05i	−0.593712	−	0.223179i
$484$	710.016	+	409.928i	0.0666807	+	0.0384981i
$485$			3667.92i			0.343405i
$486$	9627.87	+	8980.47i	0.898619	+	0.838194i
$487$	−3196.34	−	3196.34i	−0.297413	−	0.297413i	0.542587	−	0.840000i	$-0.317445\pi$
$487$	−3196.34	−	3196.34i	−0.297413	−	0.297413i	−0.840000	+	0.542587i	$0.817445\pi$
$488$	2005.59	+	7484.95i	0.186042	+	0.694320i
$489$	−8699.39	+	3945.95i	−0.804499	+	0.364912i
$490$	2524.75	+	676.504i	0.232768	+	0.0623701i
$491$	−18210.8	+	10514.0i	−1.67381	+	0.966377i	−0.708343	+	0.705868i	$0.750557\pi$
$491$	−18210.8	+	10514.0i	−1.67381	+	0.966377i	−0.965471	+	0.260509i	$0.916110\pi$
$492$	−80.9818	+	825.696i	−0.00742062	+	0.0756611i
$493$	−18918.4	−	9970.12i	−1.72828	−	0.910815i
$494$	−10977.9			−0.999833
$495$	−2145.50	−	1878.44i	−0.194814	−	0.170565i
$496$	8723.46	−	8723.46i	0.789708	−	0.789708i
$497$	1233.44	−	2136.37i	0.111322	−	0.192816i
$498$	−2655.84	+	439.601i	−0.238978	+	0.0395562i
$499$	−4219.33	+	15746.8i	−0.378524	+	1.41267i	0.469604	+	0.882877i	$0.344397\pi$
$499$	−4219.33	+	15746.8i	−0.378524	+	1.41267i	−0.848128	+	0.529792i	$0.822270\pi$
$500$	691.739	−	2581.60i	0.0618710	−	0.230906i
$501$	8202.78	−	11456.9i	0.731483	−	1.02167i
$502$	−8623.60	−	4978.84i	−0.766713	−	0.442662i
$503$	−226.442	−	226.442i	−0.0200726	−	0.0200726i	0.696999	−	0.717072i	$-0.254518\pi$
$503$	−226.442	−	226.442i	−0.0200726	−	0.0200726i	−0.717072	+	0.696999i	$0.754518\pi$
$504$	1302.41	−	2646.49i	0.115107	−	0.233897i
$505$	1173.42	−	1173.42i	0.103399	−	0.103399i
$506$	10990.1	−	19035.5i	0.965556	−	1.67239i
$507$	2350.32	+	2861.48i	0.205881	+	0.250656i
$508$	−3394.30	+	1959.70i	−0.296452	+	0.171157i
$509$	−2018.95	−	3496.92i	−0.175812	−	0.304515i	0.764630	−	0.644469i	$-0.222922\pi$
$509$	−2018.95	−	3496.92i	−0.175812	−	0.304515i	−0.940442	+	0.339954i	$0.889588\pi$
$510$	−1077.73	+	3241.48i	−0.0935739	+	0.281441i
$511$	−592.737	+	1026.65i	−0.0513134	+	0.0888774i
$512$			4805.70i			0.414812i
$513$	5434.17	+	10136.6i	0.467689	+	0.872400i
$514$	−28131.7			−2.41407
$515$	−229.850	−	857.812i	−0.0196668	−	0.0733975i
$516$	3889.36	+	1462.03i	0.331821	+	0.124733i
$517$	−4422.10	+	16503.5i	−0.376178	+	1.40391i
$518$	5350.68	−	3089.22i	0.453852	−	0.262032i
$519$	−13296.6	−	1304.09i	−1.12458	−	0.110295i
$520$	1367.98	−	366.548i	0.115365	−	0.0309120i
$521$	−4774.73	−	4774.73i	−0.401506	−	0.401506i	0.477257	−	0.878764i	$-0.341631\pi$
$521$	−4774.73	−	4774.73i	−0.401506	−	0.401506i	−0.878764	+	0.477257i	$0.841631\pi$
$522$	−23793.0	+	15926.2i	−1.99500	+	1.33539i
$523$	−944.136			−0.0789372			−0.0394686	−	0.999221i	$-0.512567\pi$
$523$	−944.136			−0.0789372			−0.0394686	+	0.999221i	$0.512567\pi$
$524$	1377.71	+	5141.68i	0.114858	+	0.428655i
$525$	2855.63	−	3988.48i	0.237390	−	0.331565i
$526$	5987.40	+	10370.5i	0.496317	+	0.859647i
$527$	−9146.23	+	5762.03i	−0.756007	+	0.476277i
$528$	13227.9	+	9470.74i	1.09028	+	0.780608i
$529$	−12071.6	−	6969.52i	−0.992156	−	0.572821i
$530$	−1545.95	+	1545.95i	−0.126702	+	0.126702i
$531$	22194.1	+	4395.74i	1.81382	+	0.359245i
$532$	−1896.99	+	1896.99i	−0.154596	+	0.154596i
$533$	−1456.12	+	390.166i	−0.118333	+	0.0317073i
$534$	9913.19	−	8142.36i	0.803344	−	0.659839i
$535$	3832.93	−	2212.94i	0.309742	−	0.178830i
$536$	938.900	−	542.074i	0.0756610	−	0.0436829i
$537$	17187.8	+	6460.96i	1.38120	+	0.519201i
$538$	14267.6	−	3823.00i	1.14335	−	0.306359i
$539$	−7712.95	+	7712.95i	−0.616364	+	0.616364i
$540$	1057.44	+	1126.24i	0.0842685	+	0.0897508i
$541$	−10784.6	+	10784.6i	−0.857056	+	0.857056i	−0.990990	−	0.133934i	$-0.957239\pi$
$541$	−10784.6	+	10784.6i	−0.857056	+	0.857056i	0.133934	+	0.990990i	$0.457239\pi$
$542$	−4917.03	−	2838.85i	−0.389677	−	0.224980i
$543$	1100.51	−	499.179i	0.0869750	−	0.0394509i
$544$	2623.14	−	11555.6i	0.206740	−	0.910740i
$545$	1283.15	+	2222.48i	0.100852	+	0.174680i
$546$	−5553.46	−	544.667i	−0.435286	−	0.0426915i
$547$	4096.76	+	15289.3i	0.320228	+	1.19511i	0.919022	+	0.394206i	$0.128980\pi$
$547$	4096.76	+	15289.3i	0.320228	+	1.19511i	−0.598794	+	0.800903i	$0.704353\pi$
$548$	5936.19			0.462740
$549$	−13780.3	−	6781.65i	−1.07128	−	0.527202i
$550$	11323.8	+	11323.8i	0.877907	+	0.877907i
$551$	−24159.0	+	6473.37i	−1.86789	+	0.500499i
$552$	6657.92	−	9299.18i	0.513369	−	0.717027i
$553$	3536.12	−	2041.58i	0.271919	−	0.156992i
$554$	−3012.82	+	11244.0i	−0.231051	+	0.862295i
$555$	−507.536	−	3066.27i	−0.0388175	−	0.234515i
$556$	−2774.46	−	10354.4i	−0.211624	−	0.789793i
$557$	−20494.9			−1.55906			−0.779531	−	0.626363i	$-0.784543\pi$
$557$	−20494.9			−1.55906			−0.779531	+	0.626363i	$0.784543\pi$
$558$	958.433	+	14441.2i	0.0727127	+	1.09560i
$559$			7549.77i			0.571237i
$560$	865.524	−	1499.13i	0.0653126	−	0.113125i
$561$	−9466.05	−	10658.5i	−0.712401	−	0.802142i
$562$	13215.2	+	22889.4i	0.991902	+	1.71802i
$563$	10160.7	−	5866.26i	0.760605	−	0.439136i	−0.0689077	−	0.997623i	$-0.521951\pi$
$563$	10160.7	−	5866.26i	0.760605	−	0.439136i	0.829513	+	0.558487i	$0.188618\pi$
$564$	3256.93	−	8664.24i	0.243159	−	0.646862i
$565$	−2803.33	+	4855.51i	−0.208738	+	0.361545i
$566$	1759.29	−	1759.29i	0.130651	−	0.130651i
$567$	2246.10	+	5397.49i	0.166362	+	0.399776i
$568$	2963.08	+	2963.08i	0.218887	+	0.218887i
$569$	16481.7	+	9515.70i	1.21432	+	0.701087i	0.963697	−	0.266998i	$-0.0860316\pi$
$569$	16481.7	+	9515.70i	1.21432	+	0.701087i	0.250622	+	0.968085i	$0.419365\pi$
$570$	1650.35	+	3638.42i	0.121273	+	0.267362i
$571$	−928.717	+	3466.02i	−0.0680658	+	0.254025i	−0.991572	−	0.129559i	$-0.958644\pi$
$571$	−928.717	+	3466.02i	−0.0680658	+	0.254025i	0.923506	+	0.383584i	$0.125310\pi$
$572$	1592.63	−	5943.79i	0.116418	−	0.434480i
$573$	−4314.77	−	5253.16i	−0.314576	−	0.382991i
$574$	−545.311	+	944.506i	−0.0396530	+	0.0686811i
$575$	13449.3	−	13449.3i	0.975435	−	0.975435i
$576$	1063.57	+	931.180i	0.0769362	+	0.0673596i
$577$	25278.3			1.82383			0.911913	−	0.410383i	$-0.134605\pi$
$577$	25278.3			1.82383			0.911913	+	0.410383i	$0.134605\pi$
$578$	−7372.76	+	15402.6i	−0.530565	+	1.10842i
$579$	3527.28	+	2525.42i	0.253176	+	0.181266i
$580$	−2909.41	+	1679.75i	−0.208288	+	0.120255i
$581$	−1154.60	−	309.375i	−0.0824457	−	0.0220913i
$582$	19960.6	+	14291.2i	1.42164	+	1.01785i
$583$	−2361.39	−	8812.84i	−0.167751	−	0.626056i
$584$	−1423.93	−	1423.93i	−0.100895	−	0.100895i
$585$	−1239.44	+	2518.54i	−0.0875975	+	0.177998i
$586$			6752.66i			0.476024i
$587$	17953.4	+	10365.4i	1.26238	+	0.728837i	0.973535	−	0.228539i	$-0.0733948\pi$
$587$	17953.4	+	10365.4i	1.26238	+	0.728837i	0.288847	+	0.957375i	$0.406728\pi$
$588$	4566.39	−	3750.68i	0.320263	−	0.263053i
$589$	−3272.26	+	12212.2i	−0.228915	+	0.854324i
$590$	7591.50	+	2034.14i	0.529724	+	0.141939i
$591$	8636.19	−	3917.28i	0.601092	−	0.272649i
$592$	4589.22	+	17127.2i	0.318608	+	1.18906i
$593$		−	13764.8i		−	0.953208i	−0.879118	−	0.476604i	$-0.841868\pi$
$593$		−	13764.8i		−	0.953208i	0.879118	−	0.476604i	$-0.158132\pi$
$594$	−18581.8	+	4356.79i	−1.28353	+	0.300945i
$595$	−1030.37	+	1113.11i	−0.0709935	+	0.0766941i
$596$	−439.400	+	761.063i	−0.0301989	+	0.0523059i
$597$	11625.5	+	25630.0i	0.796984	+	1.75706i
$598$	−20899.2	−	5599.92i	−1.42915	−	0.382940i
$599$	−5695.78	−	9865.37i	−0.388519	−	0.672935i	0.603731	−	0.797188i	$-0.293680\pi$
$599$	−5695.78	−	9865.37i	−0.388519	−	0.672935i	−0.992251	+	0.124253i	$0.960347\pi$
$600$	5288.81	+	6439.05i	0.359858	+	0.438122i
$601$	6873.65	−	1841.79i	0.466526	−	0.125005i	−0.0178957	−	0.999840i	$-0.505697\pi$
$601$	6873.65	−	1841.79i	0.466526	−	0.125005i	0.484422	+	0.874835i	$0.339030\pi$
$602$	3862.24	+	3862.24i	0.261484	+	0.261484i
$603$	−417.481	+	2107.86i	−0.0281943	+	0.142353i
$604$		−	2528.11i		−	0.170310i
$605$	523.670	−	140.317i	0.0351904	−	0.00942925i
$606$	−1813.73	−	10957.6i	−0.121581	−	0.734528i
$607$	−14221.8	−	3810.71i	−0.950978	−	0.254814i	−0.250201	−	0.968194i	$-0.580497\pi$
$607$	−14221.8	−	3810.71i	−0.950978	−	0.254814i	−0.700777	+	0.713380i	$0.747163\pi$
$608$	−6929.51	−	12002.3i	−0.462219	−	0.800586i
$609$	−12542.6	+	2076.09i	−0.834571	+	0.138140i
$610$	−4620.36	−	2667.57i	−0.306677	−	0.177060i
$611$	16818.4			1.11359
$612$	4540.12	+	6247.22i	0.299875	+	0.412629i
$613$	−19148.8			−1.26169			−0.630843	−	0.775910i	$-0.717291\pi$
$613$	−19148.8			−1.26169			−0.630843	+	0.775910i	$0.717291\pi$
$614$	16662.2	+	9619.94i	1.09517	+	0.632295i
$615$	348.218	+	423.950i	0.0228317	+	0.0277972i
$616$	2137.90	+	3702.95i	0.139835	+	0.242202i
$617$	−1319.77	−	353.630i	−0.0861131	−	0.0230739i	0.215505	−	0.976503i	$-0.430860\pi$
$617$	−1319.77	−	353.630i	−0.0861131	−	0.0230739i	−0.301618	+	0.953429i	$0.597527\pi$
$618$	−5563.72	−	2091.43i	−0.362145	−	0.136132i
$619$	−14986.8	+	4015.69i	−0.973133	+	0.260750i	−0.710150	−	0.704051i	$-0.751373\pi$
$619$	−14986.8	+	4015.69i	−0.973133	+	0.260750i	−0.262983	+	0.964801i	$0.584706\pi$
$620$			1698.21i			0.110003i
$621$	5174.57	+	22069.6i	0.334378	+	1.42613i
$622$	−4368.62	−	4368.62i	−0.281617	−	0.281617i
$623$	5502.19	−	1474.31i	0.353837	−	0.0948103i
$624$	5634.86	−	14990.1i	0.361499	−	0.961676i
$625$	6473.73	+	11212.8i	0.414319	+	0.717621i
$626$	−29782.9	−	7980.31i	−1.90154	−	0.509517i
$627$	−16592.9	−	1627.38i	−1.05687	−	0.103655i
$628$	−2578.97	+	4466.91i	−0.163873	+	0.283836i
$629$	−599.269	−	15525.2i	−0.0379879	−	0.984152i
$630$	654.353	+	1922.48i	0.0413810	+	0.121577i
$631$		−	31433.1i		−	1.98309i	−0.129748	−	0.991547i	$-0.541417\pi$
$631$		−	31433.1i		−	1.98309i	0.129748	−	0.991547i	$-0.458583\pi$
$632$	1795.16	+	6699.64i	0.112987	+	0.421673i
$633$	5758.74	+	4123.08i	0.361594	+	0.258890i
$634$	23180.5	+	6211.19i	1.45207	+	0.389082i
$635$	−670.798	+	2503.45i	−0.0419210	+	0.156451i
$636$	807.157	+	4876.42i	0.0503236	+	0.304029i
$637$	9298.64	+	5368.57i	0.578376	+	0.333925i
$638$		−	41504.4i		−	2.57551i
$639$	−8287.27	+	550.008i	−0.513051	+	0.0340500i
$640$	2927.79	+	2927.79i	0.180829	+	0.180829i
$641$	678.424	+	2531.91i	0.0418036	+	0.156013i	0.983673	−	0.179967i	$-0.0575991\pi$
$641$	678.424	+	2531.91i	0.0418036	+	0.156013i	−0.941869	+	0.335980i	$0.890932\pi$
$642$	2891.39	−	29480.8i	0.177748	−	1.81233i
$643$	10178.8	+	2727.39i	0.624278	+	0.167275i	0.557072	−	0.830464i	$-0.311925\pi$
$643$	10178.8	+	2727.39i	0.624278	+	0.167275i	0.0672063	+	0.997739i	$0.478591\pi$
$644$	−4579.09	+	2643.74i	−0.280188	+	0.161767i
$645$	2502.24	−	1134.99i	0.152753	−	0.0692869i
$646$	5909.38	+	19077.7i	0.359909	+	1.16193i
$647$	12348.1			0.750315			0.375158	−	0.926961i	$-0.377589\pi$
$647$	12348.1			0.750315			0.375158	+	0.926961i	$0.377589\pi$
$648$	−9843.68	+	1312.39i	−0.596753	+	0.0795608i
$649$	−23191.6	+	23191.6i	−1.40269	+	1.40269i
$650$	7881.89	−	13651.8i	0.475620	−	0.823798i
$651$	−2261.27	+	6015.55i	−0.136139	+	0.362163i
$652$	−1941.62	+	7246.22i	−0.116625	+	0.435251i
$653$	−7016.62	+	26186.4i	−0.420492	+	1.56930i	0.353082	+	0.935593i	$0.385134\pi$
$653$	−7016.62	+	26186.4i	−0.420492	+	1.56930i	−0.773574	+	0.633706i	$0.781533\pi$
$654$	17094.1	+	1676.54i	1.02207	+	0.100241i
$655$	3048.38	+	1759.98i	0.181847	+	0.104990i
$656$	−2213.21	−	2213.21i	−0.131725	−	0.131725i
$657$	3982.51	−	264.310i	0.236488	−	0.0156952i
$658$	8603.82	−	8603.82i	0.509745	−	0.509745i
$659$	13556.7	−	23480.9i	0.801358	−	1.38799i	−0.117364	−	0.993089i	$-0.537444\pi$
$659$	13556.7	−	23480.9i	0.801358	−	1.38799i	0.918722	−	0.394904i	$-0.129222\pi$
$660$	−2209.39	+	365.703i	−0.130304	+	0.0215681i
$661$	9879.96	−	5704.20i	0.581371	−	0.335655i	−0.180307	−	0.983610i	$-0.557709\pi$
$661$	9879.96	−	5704.20i	0.581371	−	0.335655i	0.761678	+	0.647956i	$0.224376\pi$
$662$	1947.47	+	3373.13i	0.114336	+	0.198037i
$663$	−7722.60	+	11715.9i	−0.452369	+	0.686289i
$664$	1015.24	−	1758.45i	0.0593359	−	0.102773i
$665$			1774.01i			0.103449i
$666$	−18664.0	−	9185.01i	−1.08591	−	0.534402i
$667$	−49294.9			−2.86163
$668$	−2864.03	−	10688.7i	−0.165887	−	0.619100i
$669$	−5514.53	+	4529.44i	−0.318690	+	0.261761i
$670$	−193.190	+	720.995i	−0.0111397	+	0.0415738i
$671$	19281.3	−	11132.1i	1.10931	−	0.640461i
$672$	−2909.99	−	6415.49i	−0.167047	−	0.368278i
$673$	−15666.7	+	4197.88i	−0.897336	+	0.240440i	−0.677872	−	0.735180i	$-0.737098\pi$
$673$	−15666.7	+	4197.88i	−0.897336	+	0.240440i	−0.219464	+	0.975621i	$0.570431\pi$
$674$	−13847.2	−	13847.2i	−0.791354	−	0.791354i
$675$	−16507.3	−	520.048i	−0.941281	−	0.0296543i
$676$	2908.06			0.165456
$677$	−8711.43	−	32511.5i	−0.494545	−	1.84567i	−0.532561	−	0.846392i	$-0.678770\pi$
$677$	−8711.43	−	32511.5i	−0.494545	−	1.84567i	0.0380155	−	0.999277i	$-0.487896\pi$
$678$	15500.9	+	34173.9i	0.878037	+	1.93575i
$679$	5450.35	+	9440.29i	0.308049	+	0.533557i
$680$	−1373.38	−	2180.01i	−0.0774512	−	0.122940i
$681$	205.590	−	2096.21i	0.0115686	−	0.117954i
$682$	−18169.5	−	10490.2i	−1.02015	−	0.588986i
$683$	−1892.44	+	1892.44i	−0.106021	+	0.106021i	−0.758127	−	0.652107i	$-0.773885\pi$
$683$	−1892.44	+	1892.44i	−0.106021	+	0.106021i	0.652107	+	0.758127i	$0.273885\pi$
$684$	8860.21	+	1754.85i	0.495290	+	0.0980969i
$685$	2775.68	−	2775.68i	0.154822	−	0.154822i
$686$	16738.1	−	4484.97i	0.931582	−	0.249617i
$687$	−1915.85	−	11574.5i	−0.106396	−	0.642790i
$688$	−13575.3	+	7837.70i	−0.752258	+	0.434316i
$689$	−7777.78	+	4490.51i	−0.430058	+	0.248294i
$690$	1285.86	+	7768.52i	0.0709449	+	0.428613i
$691$	28773.5	−	7709.83i	1.58407	−	0.424451i	0.643890	−	0.765118i	$-0.277320\pi$
$691$	28773.5	−	7709.83i	1.58407	−	0.424451i	0.940184	+	0.340667i	$0.110653\pi$
$692$	−7419.19	+	7419.19i	−0.407565	+	0.407565i
$693$	−8313.23	−	1646.51i	−0.455691	−	0.0902538i
$694$	19073.1	−	19073.1i	1.04324	−	1.04324i
$695$	−6138.88	−	3544.28i	−0.335052	−	0.193442i
$696$	2107.94	−	21492.7i	0.114801	−	1.17052i
$697$	1461.87	+	2320.47i	0.0794439	+	0.126104i
$698$	−10495.1	−	18178.1i	−0.569121	−	0.985747i
$699$	−9684.01	−	21349.8i	−0.524010	−	1.15525i
$700$	−997.055	−	3721.06i	−0.0538359	−	0.200918i
$701$	−17957.3			−0.967532			−0.483766	−	0.875198i	$-0.660731\pi$
$701$	−17957.3			−0.967532			−0.483766	+	0.875198i	$0.660731\pi$
$702$	8876.60	+	16557.9i	0.477244	+	0.890224i
$703$	−12849.2	−	12849.2i	−0.689354	−	0.689354i
$704$	−1979.36	+	530.367i	−0.105966	+	0.0283934i
$705$	−2528.38	−	5574.17i	−0.135070	−	0.297781i
$706$	10754.4	−	6209.05i	0.573296	−	0.330992i
$707$	1276.44	−	4763.73i	0.0679002	−	0.253407i
$708$	13730.4	−	11277.7i	0.728841	−	0.598645i
$709$	2394.32	+	8935.74i	0.126828	+	0.473327i	0.999898	−	0.0142669i	$-0.00454145\pi$
$709$	2394.32	+	8935.74i	0.126828	+	0.473327i	−0.873071	+	0.487594i	$0.837875\pi$
$710$	−2885.08			−0.152500
$711$	−12334.5	−	6070.13i	−0.650605	−	0.320179i
$712$			9676.15i			0.509310i
$713$	−12459.2	+	21579.9i	−0.654418	+	1.13349i
$714$	2042.88	+	9944.19i	0.107077	+	0.521221i
$715$	−2034.54	−	3523.93i	−0.106416	−	0.184318i
$716$	12488.3	−	7210.10i	0.651827	−	0.376333i
$717$	9216.82	−	1525.59i	0.480068	−	0.0794619i
$718$	15251.2	−	26415.8i	0.792715	−	1.37302i
$719$	5515.39	−	5515.39i	0.286077	−	0.286077i	−0.549450	−	0.835527i	$-0.685163\pi$
$719$	5515.39	−	5515.39i	0.286077	−	0.286077i	0.835527	+	0.549450i	$0.185163\pi$
$720$	−5815.32	+	385.950i	−0.301006	+	0.0199771i
$721$	−1866.24	−	1866.24i	−0.0963974	−	0.0963974i
$722$	−416.740	−	240.605i	−0.0214813	−	0.0124022i
$723$	1230.78	+	120.711i	0.0633101	+	0.00620927i
$724$	245.623	−	916.677i	0.0126084	−	0.0470553i
$725$	9295.51	−	34691.3i	0.476174	−	1.77711i
$726$	1276.76	−	3396.50i	0.0652686	−	0.173631i
$727$	−11212.8	+	19421.1i	−0.572021	+	0.990770i	0.424337	+	0.905504i	$0.360507\pi$
$727$	−11212.8	+	19421.1i	−0.572021	+	0.990770i	−0.996358	+	0.0852653i	$0.972826\pi$
$728$	2976.15	−	2976.15i	0.151516	−	0.151516i
$729$	10895.0	−	16392.7i	0.553521	−	0.832835i
$730$	1386.44			0.0702940
$731$	13120.3	−	4064.04i	0.663845	−	0.205628i
$732$	−10984.4	+	4982.41i	−0.554639	+	0.251578i
$733$	7982.86	−	4608.91i	0.402256	−	0.232243i	−0.285201	−	0.958468i	$-0.592060\pi$
$733$	7982.86	−	4608.91i	0.402256	−	0.232243i	0.687457	+	0.726225i	$0.258727\pi$
$734$	−24901.2	−	6672.25i	−1.25221	−	0.335528i
$735$	381.416	−	3888.94i	0.0191412	−	0.195164i
$736$	−7069.63	−	26384.2i	−0.354063	−	1.32138i
$737$	−2202.60	−	2202.60i	−0.110086	−	0.110086i
$738$	3663.86	−	243.162i	0.182749	−	0.0121286i
$739$			27741.3i			1.38089i	0.723383	+	0.690447i	$0.242586\pi$
$739$			27741.3i			1.38089i	−0.723383	+	0.690447i	$0.757414\pi$
$740$	−2113.79	−	1220.40i	−0.105006	−	0.0606252i
$741$	2680.04	+	16191.4i	0.132866	+	0.802708i
$742$	−1681.68	+	6276.10i	−0.0832025	+	0.310516i
$743$	29425.1	+	7884.45i	1.45290	+	0.389303i	0.897031	−	0.441967i	$-0.145719\pi$
$743$	29425.1	+	7884.45i	1.45290	+	0.389303i	0.555868	+	0.831271i	$0.312386\pi$
$744$	−8876.12	−	6355.03i	−0.437385	−	0.313154i
$745$	150.405	+	561.319i	0.00739653	+	0.0276042i
$746$		−	20044.2i		−	0.983739i
$747$	1296.75	+	3809.82i	0.0635147	+	0.186605i
$748$	−11186.7	+	431.801i	−0.546824	+	0.0211072i
$749$	6576.66	−	11391.1i	0.320836	−	0.555704i
$750$	−11772.3	−	1154.59i	−0.573152	−	0.0562130i
$751$	19407.1	+	5200.12i	0.942977	+	0.252670i	0.697379	−	0.716702i	$-0.254349\pi$
$751$	19407.1	+	5200.12i	0.942977	+	0.252670i	0.245597	+	0.969372i	$0.421016\pi$
$752$	17459.9	+	30241.4i	0.846669	+	1.46647i
$753$	−5238.07	+	13934.6i	−0.253500	+	0.674374i
$754$	−39463.1	+	10574.1i	−1.90605	+	0.510725i
$755$	−1182.11	−	1182.11i	−0.0569818	−	0.0569818i
$756$	4395.12	+	1327.34i	0.211440	+	0.0638555i
$757$			6310.70i			0.302994i	0.988458	+	0.151497i	$0.0484093\pi$
$757$			6310.70i			0.302994i	−0.988458	+	0.151497i	$0.951591\pi$
$758$	−42670.5	+	11433.5i	−2.04467	+	0.547869i
$759$	−30758.7	−	11562.4i	−1.47098	−	0.552947i
$760$	−2910.80	−	779.945i	−0.138928	−	0.0372258i
$761$	9237.56	+	15999.9i	0.440028	+	0.762151i	0.997691	−	0.0679168i	$-0.0216352\pi$
$761$	9237.56	+	15999.9i	0.440028	+	0.762151i	−0.557663	+	0.830067i	$0.688302\pi$
$762$	11010.0	+	13404.6i	0.523428	+	0.637265i
$763$	6605.00	+	3813.40i	0.313391	+	0.180936i
$764$	−5338.67			−0.252809
$765$	5044.01	+	798.213i	0.238388	+	0.0377248i
$766$	−8337.86			−0.393289
$767$	27959.5	+	16142.4i	1.31624	+	0.759933i
$768$	25193.1	−	4170.02i	1.18370	−	0.195928i
$769$	13768.9	+	23848.5i	0.645670	+	1.11833i	0.984146	+	0.177358i	$0.0567551\pi$
$769$	13768.9	+	23848.5i	0.645670	+	1.11833i	−0.338477	+	0.940975i	$0.609912\pi$
$770$	−2843.55	−	761.927i	−0.133084	−	0.0356597i
$771$	6867.81	+	41491.8i	0.320802	+	1.93812i
$772$	3290.78	−	881.762i	0.153417	−	0.0411079i
$773$		−	22052.1i		−	1.02608i	−0.858366	−	0.513038i	$-0.828520\pi$
$773$		−	22052.1i		−	1.02608i	0.858366	−	0.513038i	$-0.171480\pi$
$774$	3572.84	−	18039.2i	0.165921	−	0.837736i
$775$	−12837.5	−	12837.5i	−0.595013	−	0.595013i
$776$	−17885.8	+	4792.50i	−0.827402	+	0.221702i
$777$	−5862.60	−	7137.62i	−0.270682	−	0.329551i
$778$	1243.86	+	2154.42i	0.0573193	+	0.0992799i
$779$	3098.35	+	830.199i	0.142503	+	0.0381835i
$780$	910.604	+	2007.55i	0.0418011	+	0.0921564i
$781$	6019.89	−	10426.8i	0.275811	−	0.477719i
$782$	1518.27	+	39333.8i	0.0694288	+	1.79869i
$783$	29298.5	+	31204.6i	1.33722	+	1.42422i
$784$			22293.3i			1.01555i
$785$	882.773	+	3294.55i	0.0401370	+	0.149793i
$786$	21455.0	−	9731.75i	0.973632	−	0.441628i
$787$	6408.60	+	1717.18i	0.290269	+	0.0777774i	0.401015	−	0.916071i	$-0.368657\pi$
$787$	6408.60	+	1717.18i	0.290269	+	0.0777774i	−0.110746	+	0.993849i	$0.535324\pi$
$788$	1927.51	−	7193.57i	0.0871380	−	0.325204i
$789$	13833.9	−	11362.7i	0.624206	−	0.512701i
$790$	−4135.59	−	2387.69i	−0.186250	−	0.107532i
$791$			16662.5i			0.748987i
$792$	6356.51	−	12916.4i	0.285188	−	0.579502i
$793$	−15496.9	−	15496.9i	−0.693960	−	0.693960i
$794$	−5057.23	−	18873.9i	−0.226038	−	0.843587i
$795$	2657.56	+	1902.73i	0.118559	+	0.0848842i
$796$	21348.7	+	5720.37i	0.950609	+	0.254715i
$797$	23791.2	−	13735.8i	1.05737	−	0.610475i	0.132668	−	0.991160i	$-0.457645\pi$
$797$	23791.2	−	13735.8i	1.05737	−	0.610475i	0.924704	+	0.380686i	$0.124312\pi$
$798$	9654.09	+	6912.03i	0.428259	+	0.306620i
$799$	−9053.35	−	29227.7i	−0.400857	−	1.29412i
$800$	19901.0			0.879509
$801$	−14429.4	−	12633.3i	−0.636501	−	0.557273i
$802$	6976.55	−	6976.55i	0.307170	−	0.307170i
$803$	−2892.90	+	5010.66i	−0.127134	+	0.220202i
$804$	1071.08	+	1304.03i	0.0469829	+	0.0572009i
$805$	−904.943	+	3377.29i	−0.0396212	+	0.147868i
$806$	−5345.16	+	19948.4i	−0.233592	+	0.871778i
$807$	−9121.76	−	20110.2i	−0.397895	−	0.877215i
$808$	7255.13	+	4188.75i	0.315884	+	0.182376i
$809$	8763.55	+	8763.55i	0.380853	+	0.380853i	0.871409	−	0.490556i	$-0.163206\pi$
$809$	8763.55	+	8763.55i	0.380853	+	0.380853i	−0.490556	+	0.871409i	$0.663206\pi$
$810$	4153.36	−	5431.20i	0.180166	−	0.235596i
$811$	12541.7	−	12541.7i	0.543031	−	0.543031i	−0.381385	−	0.924416i	$-0.624553\pi$
$811$	12541.7	−	12541.7i	0.543031	−	0.543031i	0.924416	+	0.381385i	$0.124553\pi$
$812$	−4992.06	+	8646.50i	−0.215748	+	0.373686i
$813$	−2986.66	+	7945.26i	−0.128840	+	0.342746i
$814$	26114.5	−	15077.2i	1.12446	−	0.649208i
$815$	2480.36	+	4296.10i	0.106605	+	0.184645i
$816$	−29083.6	−	1723.30i	−1.24771	−	0.0739307i
$817$	8032.24	−	13912.2i	0.343956	−	0.595750i
$818$			3552.60i			0.151851i
$819$	552.435	+	8323.84i	0.0235698	+	0.355139i
$820$	430.851			0.0183487
$821$	7392.11	+	27587.7i	0.314235	+	1.17274i	0.924700	+	0.380696i	$0.124316\pi$
$821$	7392.11	+	27587.7i	0.314235	+	1.17274i	−0.610465	+	0.792043i	$0.709018\pi$
$822$	−4290.32	−	25919.9i	−0.182046	−	1.09983i
$823$	5263.38	−	19643.2i	0.222928	−	0.831979i	−0.760296	−	0.649577i	$-0.774946\pi$
$823$	5263.38	−	19643.2i	0.222928	−	0.831979i	0.983224	−	0.182402i	$-0.0583872\pi$
$824$	3882.62	−	2241.63i	0.164147	−	0.0947706i
$825$	13937.2	−	19466.1i	0.588157	−	0.821484i
$826$	22561.2	−	6045.26i	0.950370	−	0.254651i
$827$	2323.12	+	2323.12i	0.0976818	+	0.0976818i	0.754259	−	0.656577i	$-0.227996\pi$
$827$	2323.12	+	2323.12i	0.0976818	+	0.0976818i	−0.656577	+	0.754259i	$0.727996\pi$
$828$	15972.5	+	7860.49i	0.670391	+	0.329917i
$829$	−9838.31			−0.412182			−0.206091	−	0.978533i	$-0.566074\pi$
$829$	−9838.31			−0.412182			−0.206091	+	0.978533i	$0.566074\pi$
$830$	361.822	+	1350.34i	0.0151314	+	0.0564710i
$831$	17319.4	+	1698.64i	0.722990	+	0.0709087i
$832$	1008.56	+	1746.88i	0.0420260	+	0.0727912i
$833$	4324.25	−	19049.4i	0.179864	−	0.792344i
$834$	−43206.5	+	19598.0i	−1.79391	+	0.813696i
$835$	−6337.08	−	3658.71i	−0.262639	−	0.151635i
$836$	−9258.43	+	9258.43i	−0.383026	+	0.383026i
$837$	21065.6	−	4939.16i	0.869933	−	0.203969i
$838$	25960.9	−	25960.9i	1.07017	−	1.07017i
$839$	28214.6	−	7560.08i	1.16100	−	0.311088i	0.373633	−	0.927577i	$-0.378112\pi$
$839$	28214.6	−	7560.08i	1.16100	−	0.311088i	0.787364	+	0.616488i	$0.211445\pi$
$840$	−1433.81	−	538.976i	−0.0588942	−	0.0221386i
$841$	−59489.6	+	34346.3i	−2.43920	+	1.40827i
$842$	−25227.5	+	14565.1i	−1.03254	+	0.596137i
$843$	30533.6	−	25079.3i	1.24749	−	1.02465i
$844$	5372.62	−	1439.59i	0.219115	−	0.0587117i
$845$	1359.77	−	1359.77i	0.0553579	−	0.0553579i
$846$	−40185.6	−	7959.13i	−1.63311	−	0.323452i
$847$	1139.29	−	1139.29i	0.0462178	−	0.0462178i
$848$	−16148.8	−	9323.53i	−0.653954	−	0.377560i
$849$	−3024.29	−	2165.30i	−0.122254	−	0.0875299i
$850$	−27967.5	−	6348.66i	−1.12856	−	0.256185i
$851$	−17907.2	−	31016.2i	−0.721330	−	1.24938i
$852$	−3797.06	+	5303.39i	−0.152682	+	0.213252i
$853$	−3024.10	−	11286.1i	−0.121387	−	0.453023i	0.878298	−	0.478114i	$-0.158679\pi$
$853$	−3024.10	−	11286.1i	−0.121387	−	0.453023i	−0.999685	+	0.0250904i	$0.992013\pi$
$854$	−15855.5			−0.635321
$855$	4963.45	−	3322.37i	0.198534	−	0.132892i
$856$	15799.1	+	15799.1i	0.630842	+	0.630842i
$857$	−35483.6	+	9507.81i	−1.41435	+	0.378974i	−0.883476	−	0.468476i	$-0.844803\pi$
$857$	−35483.6	+	9507.81i	−1.41435	+	0.378974i	−0.530874	+	0.847451i	$0.678136\pi$
$858$	−27104.1	−	2658.29i	−1.07846	−	0.105772i
$859$	−14956.9	+	8635.36i	−0.594089	+	0.342997i	−0.766712	−	0.641991i	$-0.778109\pi$
$859$	−14956.9	+	8635.36i	−0.594089	+	0.342997i	0.172624	+	0.984988i	$0.444775\pi$
$860$	558.474	−	2084.25i	0.0221440	−	0.0826424i
$861$	1526.19	+	573.704i	0.0604094	+	0.0227082i
$862$	4323.69	+	16136.2i	0.170841	+	0.637589i
$863$	20378.7			0.803822			0.401911	−	0.915679i	$-0.368346\pi$
$863$	20378.7			0.803822			0.401911	+	0.915679i	$0.368346\pi$
$864$	−12499.8	+	20156.7i	−0.492191	+	0.793686i
$865$			6938.22i			0.272724i
$866$	−7482.98	+	12960.9i	−0.293628	+	0.508579i
$867$	24517.5	+	7113.93i	0.960389	+	0.278664i
$868$	2523.46	+	4370.77i	0.0986774	+	0.170914i
$869$	17258.3	−	9964.11i	0.673705	−	0.388964i
$870$	9437.24	+	11489.7i	0.367761	+	0.447744i
$871$	−1533.11	+	2655.42i	−0.0596411	+	0.103301i
$872$	−9160.90	+	9160.90i	−0.355765	+	0.355765i
$873$	16205.3	−	32929.1i	0.628253	−	1.27661i
$874$	32554.0	+	32554.0i	1.25990	+	1.25990i
$875$	−4548.71	−	2626.20i	−0.175742	−	0.101465i
$876$	1824.71	−	2548.58i	0.0703779	−	0.0982975i
$877$	8516.25	−	31783.1i	0.327906	−	1.22376i	−0.583452	−	0.812147i	$-0.698299\pi$
$877$	8516.25	−	31783.1i	0.327906	−	1.22376i	0.911358	−	0.411614i	$-0.135035\pi$
$878$	−13585.6	+	50702.2i	−0.522200	+	1.94888i
$879$	9959.60	−	1648.54i	0.382172	−	0.0632579i
$880$	4224.26	−	7316.64i	0.161818	−	0.280277i
$881$	−9751.11	+	9751.11i	−0.372898	+	0.372898i	−0.868532	−	0.495634i	$-0.834936\pi$
$881$	−9751.11	+	9751.11i	−0.372898	+	0.372898i	0.495634	+	0.868532i	$0.334936\pi$
$882$	−19677.3	−	17228.0i	−0.751213	−	0.657706i
$883$	−31952.3			−1.21776			−0.608879	−	0.793263i	$-0.708380\pi$
$883$	−31952.3			−1.21776			−0.608879	+	0.793263i	$0.708380\pi$
$884$	3260.59	+	10526.4i	0.124056	+	0.400501i
$885$	1146.86	−	11693.4i	0.0435606	−	0.444147i
$886$	−30040.9	+	17344.1i	−1.13910	+	0.657661i
$887$	−1895.62	−	507.929i	−0.0717571	−	0.0192273i	0.222762	−	0.974873i	$-0.428493\pi$
$887$	−1895.62	−	507.929i	−0.0717571	−	0.0192273i	−0.294519	+	0.955646i	$0.595159\pi$
$888$	14288.9	−	6481.28i	0.539981	−	0.244930i
$889$	1993.55	+	7440.02i	0.0752098	+	0.280687i
$890$	−4710.72	−	4710.72i	−0.177420	−	0.177420i
$891$	10962.3	+	26342.9i	0.412178	+	0.990483i
$892$			5604.29i			0.210365i
$893$	−30992.0	−	17893.2i	−1.16137	−	0.670519i
$894$	3640.69	+	1368.55i	0.136200	+	0.0511983i
$895$	2467.99	−	9210.68i	0.0921742	−	0.343999i
$896$	11885.9	+	3184.82i	0.443171	+	0.118747i
$897$	−3157.26	+	32191.7i	−0.117523	+	1.19827i
$898$	4266.88	+	15924.2i	0.158561	+	0.591757i
$899$			47052.3i			1.74559i
$900$	−8543.75	+	9758.42i	−0.316435	+	0.361423i
$901$	11990.5	+	11099.3i	0.443355	+	0.410400i
$902$	−2661.44	+	4609.75i	−0.0982441	+	0.170164i
$903$	4753.58	−	6639.37i	0.175182	−	0.244678i
$904$	−27339.7	−	7325.66i	−1.00587	−	0.269522i
$905$	−313.776	−	543.475i	−0.0115251	−	0.0199621i
$906$	−11038.8	+	1827.16i	−0.404788	+	0.0670015i
$907$	11915.1	−	3192.65i	0.436202	−	0.116880i	−0.0340338	−	0.999421i	$-0.510835\pi$
$907$	11915.1	−	3192.65i	0.436202	−	0.116880i	0.470236	+	0.882541i	$0.344169\pi$
$908$	−1169.63	−	1169.63i	−0.0427485	−	0.0427485i
$909$	−15718.8	+	5350.21i	−0.573553	+	0.195220i
$910$			2897.81i			0.105562i
$911$	15174.3	−	4065.94i	0.551862	−	0.147871i	0.0278973	−	0.999611i	$-0.491119\pi$
$911$	15174.3	−	4065.94i	0.551862	−	0.147871i	0.523965	+	0.851740i	$0.324452\pi$
$912$	−26331.6	+	21627.9i	−0.956061	+	0.785276i
$913$	−5635.13	−	1509.93i	−0.204267	−	0.0547332i
$914$	−16501.2	−	28580.9i	−0.597168	−	1.03433i
$915$	−2806.46	+	7465.87i	−0.101397	+	0.269742i
$916$	−7979.13	−	4606.75i	−0.287814	−	0.166170i
$917$	10461.0			0.376720
$918$	23996.6	−	24339.2i	0.862752	−	0.875068i
$919$	29031.9			1.04208			0.521041	−	0.853532i	$-0.325544\pi$
$919$	29031.9			1.04208			0.521041	+	0.853532i	$0.325544\pi$
$920$	−5143.59	−	2969.65i	−0.184325	−	0.106420i
$921$	10120.8	−	26923.9i	0.362098	−	0.963270i
$922$	−27651.3	−	47893.5i	−0.987687	−	1.71072i
$923$	−11447.6	−	3067.38i	−0.408238	−	0.109387i
$924$	−5142.99	+	4224.28i	−0.183108	+	0.150399i
$925$	25204.4	−	6753.50i	0.895909	−	0.240058i
$926$			63947.7i			2.26939i
$927$	−1726.40	+	8716.60i	−0.0611678	+	0.308836i
$928$	−36471.0	−	36471.0i	−1.29011	−	1.29011i
$929$	29456.7	−	7892.89i	1.04030	−	0.278749i	0.302065	−	0.953287i	$-0.402324\pi$
$929$	29456.7	−	7892.89i	1.04030	−	0.278749i	0.738239	+	0.674539i	$0.235657\pi$
$930$	7415.10	−	1227.36i	0.261453	−	0.0432762i
$931$	−11423.3	−	19785.7i	−0.402130	−	0.696510i
$932$	−17783.4	−	4765.06i	−0.625017	−	0.167473i
$933$	−5376.82	+	7509.85i	−0.188670	+	0.263517i
$934$	−1051.57	+	1821.37i	−0.0368398	+	0.0638084i
$935$	−5028.82	+	5432.63i	−0.175893	+	0.190017i
$936$	−13900.6	−	2753.15i	−0.485423	−	0.0961425i
$937$		−	18332.7i		−	0.639169i	−0.947558	−	0.319585i	$-0.896457\pi$
$937$		−	18332.7i		−	0.639169i	0.947558	−	0.319585i	$-0.103543\pi$
$938$	574.143	+	2142.73i	0.0199855	+	0.0745870i
$939$	−4499.34	+	45875.5i	−0.156369	+	1.59435i
$940$	−4643.04	−	1244.10i	−0.161106	−	0.0431681i
$941$	−1383.07	+	5161.70i	−0.0479138	+	0.178817i	−0.985736	−	0.168300i	$-0.946172\pi$
$941$	−1383.07	+	5161.70i	−0.0479138	+	0.178817i	0.937822	+	0.347116i	$0.112839\pi$
$942$	21368.3	+	8032.45i	0.739084	+	0.277825i
$943$	5475.01	+	3161.00i	0.189068	+	0.109158i
$944$			67032.1i			2.31113i
$945$	2675.74	−	1434.45i	0.0921077	−	0.0493785i
$946$	18850.0	+	18850.0i	0.647851	+	0.647851i
$947$	4525.18	+	16888.2i	0.155278	+	0.579506i	0.999081	+	0.0428535i	$0.0136449\pi$
$947$	4525.18	+	16888.2i	0.155278	+	0.579506i	−0.843803	+	0.536653i	$0.819688\pi$
$948$	−9831.95	+	4459.66i	−0.336843	+	0.152788i
$949$	5501.24	+	1474.05i	0.188175	+	0.0504213i
$950$	−29048.5	+	16771.2i	−0.992061	+	0.572767i
$951$	3501.90	−	35705.6i	0.119408	−	1.21749i
$952$	−6774.13	−	3570.01i	−0.230621	−	0.121538i
$953$	6699.54			0.227723			0.113861	−	0.993497i	$-0.463678\pi$
$953$	6699.54			0.227723			0.113861	+	0.993497i	$0.463678\pi$
$954$	20709.1	−	7048.76i	0.702812	−	0.239216i
$955$	−2496.29	+	2496.29i	−0.0845843	+	0.0845843i
$956$	3668.36	−	6353.78i	0.124104	−	0.214954i
$957$	−61215.5	+	10132.5i	−2.06773	+	0.342255i
$958$	1421.11	−	5303.65i	0.0479269	−	0.178866i
$959$	3019.36	−	11268.4i	0.101669	−	0.379433i
$960$	427.352	−	596.886i	0.0143674	−	0.0200671i
$961$	−5201.57	−	3003.13i	−0.174602	−	0.100807i
$962$	−20988.8	−	20988.8i	−0.703438	−	0.703438i
$963$	−44187.6	+	2932.63i	−1.47863	+	0.0981337i
$964$	686.745	−	686.745i	0.0229446	−	0.0229446i
$965$	1126.42	−	1951.02i	0.0375760	−	0.0650835i
$966$	14853.1	+	18083.5i	0.494712	+	0.602305i
$967$	37733.7	−	21785.6i	1.25484	−	0.724485i	0.282777	−	0.959186i	$-0.408744\pi$
$967$	37733.7	−	21785.6i	1.25484	−	0.724485i	0.972068	+	0.234701i	$0.0754111\pi$
$968$	1368.45	+	2370.23i	0.0454378	+	0.0787005i
$969$	26695.4	−	13373.3i	0.885014	−	0.443356i
$970$	6374.34	−	11040.7i	0.210998	−	0.365459i
$971$			39380.7i			1.30153i	0.759278	+	0.650766i	$0.225552\pi$
$971$			39380.7i			1.30153i	−0.759278	+	0.650766i	$0.774448\pi$
$972$	−4517.45	−	14782.8i	−0.149071	−	0.487817i
$973$	−21066.5			−0.694103
$974$	4066.40	+	15176.0i	0.133774	+	0.499251i
$975$	−22059.5	−	8292.27i	−0.724584	−	0.272375i
$976$	11777.2	−	43952.9i	0.386248	−	1.44150i
$977$	9720.10	−	5611.90i	0.318294	−	0.183767i	−0.332338	−	0.943160i	$-0.607837\pi$
$977$	9720.10	−	5611.90i	0.318294	−	0.183767i	0.650632	+	0.759393i	$0.274504\pi$
$978$	33043.3	+	3240.79i	1.08038	+	0.105960i
$979$	26853.9	−	7195.48i	0.876664	−	0.234901i
$980$	−2169.94	−	2169.94i	−0.0707307	−	0.0707307i
$981$	−1700.45	−	25621.6i	−0.0553428	−	0.833880i
$982$	73087.8			2.37508
$983$	−11477.3	−	42833.7i	−0.372398	−	1.38981i	−0.857109	−	0.515135i	$-0.827742\pi$
$983$	−11477.3	−	42833.7i	−0.372398	−	1.38981i	0.484711	−	0.874675i	$-0.338925\pi$
$984$	−1612.32	+	2251.94i	−0.0522347	+	0.0729567i
$985$	−2462.34	−	4264.89i	−0.0796513	−	0.137960i
$986$	39619.0	+	62888.4i	1.27964	+	2.03121i
$987$	−14790.4	−	10589.4i	−0.476983	−	0.341505i
$988$	11161.8	+	6444.29i	0.359419	+	0.207510i
$989$	22388.2	−	22388.2i	0.719822	−	0.719822i
$990$	3193.62	+	9382.81i	0.102525	+	0.301217i
$991$	−9059.94	+	9059.94i	−0.290412	+	0.290412i	−0.837243	−	0.546831i	$-0.815834\pi$
$991$	−9059.94	+	9059.94i	−0.290412	+	0.290412i	0.546831	+	0.837243i	$0.315834\pi$
$992$	−25183.9	+	6748.01i	−0.806038	+	0.215977i
$993$	4499.63	−	3695.84i	0.143798	−	0.118111i
$994$	−7425.46	+	4287.09i	−0.236943	+	0.136799i
$995$	12657.1	−	7307.59i	0.403274	−	0.232830i
$996$	2958.41	+	1112.08i	0.0941172	+	0.0353791i
$997$	−31993.8	+	8572.71i	−1.01630	+	0.272318i	−0.728261	−	0.685300i	$-0.759671\pi$
$997$	−31993.8	+	8572.71i	−1.01630	+	0.272318i	−0.288042	+	0.957618i	$0.593004\pi$
$998$	40066.2	−	40066.2i	1.27082	−	1.27082i
$999$	−8990.65	+	29770.1i	−0.284736	+	0.942827i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.4.n.a.106.13	yes	208
9.4	even	3	inner	153.4.n.a.4.40	✓	208
17.13	even	4	inner	153.4.n.a.115.40	yes	208
153.13	even	12	inner	153.4.n.a.13.13	yes	208

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.4.n.a.4.40	✓	208	9.4	even	3	inner
153.4.n.a.13.13	yes	208	153.13	even	12	inner
153.4.n.a.106.13	yes	208	1.1	even	1	trivial
153.4.n.a.115.40	yes	208	17.13	even	4	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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	153.n (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.01007 - 1.73786i) q^{2} +(-1.82835 + 4.86386i) q^{3} +(2.04034 + 3.53398i) q^{4} +(2.60647 + 0.698403i) q^{5} +(13.9562 - 11.4631i) q^{6} +(7.74620 - 2.07559i) q^{7} +13.6225i q^{8} +(-20.3143 - 17.7857i) q^{9} +(-6.63194 - 6.63194i) q^{10} +(37.8060 - 10.1301i) q^{11} +(-20.9192 + 3.46260i) q^{12} +(-19.2637 - 33.3657i) q^{13} +(-26.9237 - 7.21418i) q^{14} +(-8.16248 + 11.4006i) q^{15} +(39.9967 - 69.2764i) q^{16} +(-47.6145 + 51.4379i) q^{17} +(30.2383 + 88.8395i) q^{18} +81.9790i q^{19} +(2.84996 + 10.6362i) q^{20} +(-4.06739 + 41.4713i) q^{21} +(-131.403 - 35.2094i) q^{22} +(-41.8183 + 156.068i) q^{23} +(-66.2578 - 24.9066i) q^{24} +(-101.947 - 58.8593i) q^{25} +133.911i q^{26} +(123.649 - 66.2874i) q^{27} +(23.1400 + 23.1400i) q^{28} +(78.9638 + 294.697i) q^{29} +(44.3823 - 20.1313i) q^{30} +(148.968 + 39.9159i) q^{31} +(-146.407 + 84.5279i) q^{32} +(-19.8512 + 202.404i) q^{33} +(232.715 - 72.0841i) q^{34} +21.6399 q^{35} +(21.4061 - 108.079i) q^{36} +(-156.738 + 156.738i) q^{37} +(142.468 - 246.762i) q^{38} +(197.507 - 32.6918i) q^{39} +(-9.51397 + 35.5066i) q^{40} +(10.1270 - 37.7944i) q^{41} +(84.3146 - 117.763i) q^{42} +(-169.705 - 97.9793i) q^{43} +(112.937 + 112.937i) q^{44} +(-40.5271 - 60.5454i) q^{45} +(397.101 - 397.101i) q^{46} +(-218.266 + 378.048i) q^{47} +(263.823 + 321.200i) q^{48} +(-241.351 + 139.344i) q^{49} +(204.579 + 354.341i) q^{50} +(-163.131 - 325.637i) q^{51} +(78.6091 - 136.155i) q^{52} -233.107i q^{53} +(-487.389 - 15.3548i) q^{54} +105.615 q^{55} +(28.2746 + 105.522i) q^{56} +(-398.734 - 149.886i) q^{57} +(274.457 - 1024.29i) q^{58} +(-725.703 + 418.985i) q^{59} +(-56.9437 - 5.58488i) q^{60} +(549.457 - 147.226i) q^{61} +(-379.036 - 379.036i) q^{62} +(-194.274 - 95.6072i) q^{63} -52.3556 q^{64} +(-26.9076 - 100.421i) q^{65} +(411.505 - 574.752i) q^{66} +(-39.7927 - 68.9229i) q^{67} +(-278.930 - 63.3177i) q^{68} +(-682.635 - 488.746i) q^{69} +(-65.1375 - 37.6071i) q^{70} +(217.514 - 217.514i) q^{71} +(242.285 - 276.731i) q^{72} +(-104.528 + 104.528i) q^{73} +(744.179 - 199.402i) q^{74} +(472.678 - 388.242i) q^{75} +(-289.712 + 167.265i) q^{76} +(271.827 - 156.939i) q^{77} +(-651.323 - 244.836i) q^{78} +(491.808 - 131.780i) q^{79} +(152.633 - 152.633i) q^{80} +(96.3399 + 722.606i) q^{81} +(-96.1645 + 96.1645i) q^{82} +(-129.085 - 74.5270i) q^{83} +(-154.858 + 70.2417i) q^{84} +(-160.030 + 100.817i) q^{85} +(340.549 + 589.849i) q^{86} +(-1577.74 - 154.740i) q^{87} +(137.997 + 515.011i) q^{88} +710.308 q^{89} +(16.7696 + 252.677i) q^{90} +(-218.474 - 218.474i) q^{91} +(-636.865 + 170.647i) q^{92} +(-466.511 + 651.579i) q^{93} +(1313.99 - 758.633i) q^{94} +(-57.2543 + 213.676i) q^{95} +(-143.450 - 866.648i) q^{96} +(351.808 + 1312.97i) q^{97} +968.645 q^{98} +(-948.172 - 466.619i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 208 q - 6 q^{3} + 396 q^{4} - 2 q^{5} - 40 q^{6} - 2 q^{7} - 40 q^{10} - 60 q^{11} + 96 q^{12} - 4 q^{13} - 84 q^{14} - 1444 q^{16} - 8 q^{17} - 152 q^{18} + 270 q^{20} - 184 q^{21} - 70 q^{22} + 82 q^{23}+ \cdots - 2658 q^{99}+O(q^{100}) \) 208 * q - 6 * q^3 + 396 * q^4 - 2 * q^5 - 40 * q^6 - 2 * q^7 - 40 * q^10 - 60 * q^11 + 96 * q^12 - 4 * q^13 - 84 * q^14 - 1444 * q^16 - 8 * q^17 - 152 * q^18 + 270 * q^20 - 184 * q^21 - 70 * q^22 + 82 * q^23 - 44 * q^24 - 108 * q^27 + 216 * q^28 - 418 * q^29 + 540 * q^30 - 2 * q^31 - 180 * q^33 - 202 * q^34 + 2176 * q^35 - 8 * q^37 + 516 * q^38 - 242 * q^39 + 268 * q^40 + 152 * q^41 - 1240 * q^44 - 838 * q^45 - 112 * q^46 + 2636 * q^47 - 1300 * q^48 - 228 * q^50 - 2156 * q^51 + 540 * q^52 + 1712 * q^54 - 16 * q^55 + 1356 * q^56 - 1194 * q^57 - 34 * q^58 - 2 * q^61 + 4484 * q^62 - 3878 * q^63 - 9296 * q^64 - 1246 * q^65 - 4 * q^67 + 732 * q^68 + 4776 * q^69 - 4512 * q^71 + 1272 * q^72 + 2476 * q^73 + 2674 * q^74 + 1858 * q^75 + 364 * q^78 - 938 * q^79 + 4932 * q^80 + 3860 * q^81 + 5792 * q^82 + 5028 * q^84 - 1658 * q^85 - 7888 * q^86 + 1726 * q^88 - 5920 * q^89 + 14322 * q^90 + 356 * q^91 - 4844 * q^92 + 1564 * q^95 + 4246 * q^96 + 736 * q^97 - 12008 * q^98 - 2658 * q^99

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