LMFDB - Embedded newform 230.4.l.a.217.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,4,Mod(7,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.7"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$13.5704393013$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			217.7
Character	$\chi$	$=$	230.217
Dual form			230.4.l.a.53.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.142678 + 1.99490i) q^{2} +(-3.78734 + 0.823886i) q^{3} +(-3.95929 - 0.569259i) q^{4} +(10.0746 + 4.84785i) q^{5} +(-1.10320 - 7.67294i) q^{6} +(17.4245 - 9.51450i) q^{7} +(1.70052 - 7.81717i) q^{8} +(-10.8949 + 4.97552i) q^{9} +(-11.1084 + 19.4063i) q^{10} +(-48.6761 - 42.1781i) q^{11} +(15.4642 - 1.10602i) q^{12} +(29.1221 - 53.3332i) q^{13} +(16.4944 + 36.1177i) q^{14} +(-42.1502 - 10.0601i) q^{15} +(15.3519 + 4.50772i) q^{16} +(12.0927 + 9.05245i) q^{17} +(-8.37123 - 22.4441i) q^{18} +(1.53786 - 10.6960i) q^{19} +(-37.1287 - 24.9291i) q^{20} +(-58.1537 + 50.3905i) q^{21} +(91.0863 - 91.0863i) q^{22} +(-93.5628 - 58.4209i) q^{23} +31.0074i q^{24} +(77.9967 + 97.6807i) q^{25} +(102.239 + 65.7053i) q^{26} +(120.940 - 90.5345i) q^{27} +(-74.4048 + 27.7516i) q^{28} +(175.324 - 25.2078i) q^{29} +(26.0829 - 82.6503i) q^{30} +(284.911 - 183.101i) q^{31} +(-11.1829 + 29.9824i) q^{32} +(219.103 + 119.639i) q^{33} +(-19.7841 + 22.8321i) q^{34} +(221.670 - 11.3838i) q^{35} +(45.9683 - 13.4975i) q^{36} +(-54.2155 - 20.2213i) q^{37} +(21.1181 + 4.59397i) q^{38} +(-66.3550 + 225.984i) q^{39} +(55.0286 - 70.5113i) q^{40} +(90.9589 - 199.172i) q^{41} +(-92.2269 - 123.201i) q^{42} +(96.7833 + 444.906i) q^{43} +(168.712 + 194.704i) q^{44} +(-133.882 - 2.69012i) q^{45} +(129.893 - 178.313i) q^{46} +(-107.549 - 107.549i) q^{47} +(-61.8567 - 4.42408i) q^{48} +(27.6477 - 43.0207i) q^{49} +(-205.992 + 141.659i) q^{50} +(-53.2572 - 24.3218i) q^{51} +(-145.663 + 194.583i) q^{52} +(-111.255 - 203.748i) q^{53} +(163.352 + 254.181i) q^{54} +(-285.921 - 660.903i) q^{55} +(-44.7457 - 152.390i) q^{56} +(2.98792 + 41.7766i) q^{57} +(25.2722 + 353.352i) q^{58} +(-217.882 - 742.038i) q^{59} +(161.158 + 63.8253i) q^{60} +(280.793 + 436.923i) q^{61} +(324.619 + 594.496i) q^{62} +(-142.498 + 190.355i) q^{63} +(-58.2164 - 26.5866i) q^{64} +(551.946 - 396.133i) q^{65} +(-269.930 + 420.020i) q^{66} +(-914.838 - 65.4305i) q^{67} +(-42.7251 - 42.7251i) q^{68} +(402.487 + 144.175i) q^{69} +(-8.91806 + 443.835i) q^{70} +(575.373 + 664.016i) q^{71} +(20.3675 + 93.6281i) q^{72} +(106.977 + 142.904i) q^{73} +(48.0750 - 105.270i) q^{74} +(-375.878 - 305.690i) q^{75} +(-12.1776 + 41.4732i) q^{76} +(-1249.46 - 271.803i) q^{77} +(-441.350 - 164.615i) q^{78} +(643.011 - 188.805i) q^{79} +(132.812 + 119.837i) q^{80} +(-171.679 + 198.128i) q^{81} +(384.352 + 209.872i) q^{82} +(334.329 - 896.369i) q^{83} +(258.932 - 166.406i) q^{84} +(77.9442 + 149.823i) q^{85} +(-901.353 + 129.595i) q^{86} +(-643.246 + 239.918i) q^{87} +(-412.488 + 308.785i) q^{88} +(-954.557 - 613.457i) q^{89} +(24.4687 - 266.699i) q^{90} -1206.39i q^{91} +(337.185 + 284.566i) q^{92} +(-928.203 + 928.203i) q^{93} +(229.895 - 199.205i) q^{94} +(67.3461 - 100.303i) q^{95} +(17.6512 - 122.767i) q^{96} +(-177.555 - 476.044i) q^{97} +(81.8775 + 61.2927i) q^{98} +(740.178 + 217.336i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q + 16 q^{3} + 16 q^{6} + 64 q^{12} - 192 q^{13} + 1152 q^{16} + 144 q^{18} + 1660 q^{23} - 880 q^{25} - 304 q^{26} - 728 q^{27} - 352 q^{28} - 608 q^{31} - 3872 q^{33} - 688 q^{35} - 2816 q^{36} - 2376 q^{37}+ \cdots + 14352 q^{98}+O(q^{100}) $ 720 * q + 16 * q^3 + 16 * q^6 + 64 * q^12 - 192 * q^13 + 1152 * q^16 + 144 * q^18 + 1660 * q^23 - 880 * q^25 - 304 * q^26 - 728 * q^27 - 352 * q^28 - 608 * q^31 - 3872 * q^33 - 688 * q^35 - 2816 * q^36 - 2376 * q^37 + 2208 * q^41 + 256 * q^46 + 3640 * q^47 - 256 * q^48 - 272 * q^50 - 768 * q^52 + 2360 * q^55 - 3872 * q^56 - 7656 * q^57 + 2112 * q^61 + 1376 * q^62 + 10912 * q^66 + 1104 * q^70 + 22752 * q^71 - 128 * q^72 + 1296 * q^73 - 5396 * q^75 + 752 * q^77 - 6000 * q^78 - 3928 * q^81 - 80 * q^82 + 3060 * q^85 - 10472 * q^86 - 6760 * q^87 - 1104 * q^92 + 5288 * q^93 + 9392 * q^95 - 256 * q^96 + 25344 * q^97 + 14352 * q^98

Character values

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

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{22}\right)$

Coefficient data

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

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

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

$2$	−0.142678	+	1.99490i	−0.0504444	+	0.705305i
$2$	−0.142678	+	1.99490i	−0.0504444	+	0.705305i
$3$	−3.78734	+	0.823886i	−0.728875	+	0.158557i	−0.561666	−	0.827364i	$-0.689839\pi$
$3$	−3.78734	+	0.823886i	−0.728875	+	0.158557i	−0.167209	+	0.985921i	$0.553476\pi$
$4$	−3.95929	−	0.569259i	−0.494911	−	0.0711574i
$5$	10.0746	+	4.84785i	0.901103	+	0.433605i
$5$	10.0746	+	4.84785i	0.901103	+	0.433605i
$6$	−1.10320	−	7.67294i	−0.0750634	−	0.522077i
$7$	17.4245	−	9.51450i	0.940835	−	0.513735i	0.0658202	−	0.997832i	$-0.479034\pi$
$7$	17.4245	−	9.51450i	0.940835	−	0.513735i	0.875014	+	0.484097i	$0.160852\pi$
$8$	1.70052	−	7.81717i	0.0751532	−	0.345474i
$9$	−10.8949	+	4.97552i	−0.403514	+	0.184279i
$10$	−11.1084	+	19.4063i	−0.351279	+	0.613680i
$11$	−48.6761	−	42.1781i	−1.33422	−	1.15611i	−0.974838	−	0.222915i	$-0.928443\pi$
$11$	−48.6761	−	42.1781i	−1.33422	−	1.15611i	−0.359380	−	0.933191i	$-0.617012\pi$
$12$	15.4642	−	1.10602i	0.372010	−	0.0266067i
$13$	29.1221	−	53.3332i	0.621309	−	1.13784i	−0.357663	−	0.933851i	$-0.616426\pi$
$13$	29.1221	−	53.3332i	0.621309	−	1.13784i	0.978972	−	0.203992i	$-0.0653918\pi$
$14$	16.4944	+	36.1177i	0.314880	+	0.689490i
$15$	−42.1502	−	10.0601i	−0.725542	−	0.173167i
$16$	15.3519	+	4.50772i	0.239873	+	0.0704331i
$17$	12.0927	+	9.05245i	0.172523	+	0.129149i	0.682050	−	0.731305i	$-0.261089\pi$
$17$	12.0927	+	9.05245i	0.172523	+	0.129149i	−0.509527	+	0.860455i	$0.670179\pi$
$18$	−8.37123	−	22.4441i	−0.109618	−	0.293896i
$19$	1.53786	−	10.6960i	0.0185689	−	0.129149i	−0.978428	−	0.206586i	$-0.933765\pi$
$19$	1.53786	−	10.6960i	0.0185689	−	0.129149i	0.996997	+	0.0774370i	$0.0246737\pi$
$20$	−37.1287	−	24.9291i	−0.415111	−	0.278716i
$21$	−58.1537	+	50.3905i	−0.604294	+	0.523624i
$22$	91.0863	−	91.0863i	0.882712	−	0.882712i
$23$	−93.5628	−	58.4209i	−0.848226	−	0.529634i
$23$	−93.5628	−	58.4209i	−0.848226	−	0.529634i
$24$			31.0074i			0.263723i
$25$	77.9967	+	97.6807i	0.623974	+	0.781445i
$26$	102.239	+	65.7053i	0.771185	+	0.495610i
$27$	120.940	−	90.5345i	0.862033	−	0.645310i
$28$	−74.4048	+	27.7516i	−0.502185	+	0.187305i
$29$	175.324	−	25.2078i	1.12265	−	0.161413i	0.444109	−	0.895973i	$-0.353520\pi$
$29$	175.324	−	25.2078i	1.12265	−	0.161413i	0.678544	+	0.734560i	$0.262611\pi$
$30$	26.0829	−	82.6503i	0.158735	−	0.502994i
$31$	284.911	−	183.101i	1.65070	−	1.06084i	0.720717	−	0.693230i	$-0.243813\pi$
$31$	284.911	−	183.101i	1.65070	−	1.06084i	0.929980	−	0.367609i	$-0.119823\pi$
$32$	−11.1829	+	29.9824i	−0.0617771	+	0.165631i
$33$	219.103	+	119.639i	1.15579	+	0.631107i
$34$	−19.7841	+	22.8321i	−0.0997926	+	0.115167i
$35$	221.670	−	11.3838i	1.07055	−	0.0549773i
$36$	45.9683	−	13.4975i	0.212816	−	0.0624884i
$37$	−54.2155	−	20.2213i	−0.240891	−	0.0898477i	0.226119	−	0.974100i	$-0.427396\pi$
$37$	−54.2155	−	20.2213i	−0.240891	−	0.0898477i	−0.467010	+	0.884252i	$0.654669\pi$
$38$	21.1181	+	4.59397i	0.0901530	+	0.0196116i
$39$	−66.3550	+	225.984i	−0.272444	+	0.927858i
$40$	55.0286	−	70.5113i	0.217520	−	0.278721i
$41$	90.9589	−	199.172i	0.346473	−	0.758670i	−0.653525	−	0.756905i	$-0.726711\pi$
$41$	90.9589	−	199.172i	0.346473	−	0.758670i	0.999998	−	0.00176547i	$-0.000561968\pi$
$42$	−92.2269	−	123.201i	−0.338831	−	0.452626i
$43$	96.7833	+	444.906i	0.343240	+	1.57785i	0.748174	+	0.663503i	$0.230931\pi$
$43$	96.7833	+	444.906i	0.343240	+	1.57785i	−0.404934	+	0.914346i	$0.632706\pi$
$44$	168.712	+	194.704i	0.578053	+	0.667109i
$45$	−133.882	−	2.69012i	−0.443512	−	0.00891156i
$46$	129.893	−	178.313i	0.416342	−	0.571541i
$47$	−107.549	−	107.549i	−0.333779	−	0.333779i	0.520240	−	0.854020i	$-0.325842\pi$
$47$	−107.549	−	107.549i	−0.333779	−	0.333779i	−0.854020	+	0.520240i	$0.825842\pi$
$48$	−61.8567	−	4.42408i	−0.186005	−	0.0133034i
$49$	27.6477	−	43.0207i	0.0806056	−	0.125425i
$50$	−205.992	+	141.659i	−0.582633	+	0.400672i
$51$	−53.2572	−	24.3218i	−0.146226	−	0.0667790i
$52$	−145.663	+	194.583i	−0.388459	+	0.518920i
$53$	−111.255	−	203.748i	−0.288340	−	0.528056i	0.692854	−	0.721078i	$-0.256353\pi$
$53$	−111.255	−	203.748i	−0.288340	−	0.528056i	−0.981194	+	0.193022i	$0.938171\pi$
$54$	163.352	+	254.181i	0.411656	+	0.640549i
$55$	−285.921	−	660.903i	−0.700975	−	1.62029i
$56$	−44.7457	−	152.390i	−0.106775	−	0.363642i
$57$	2.98792	+	41.7766i	0.00694315	+	0.0970780i
$58$	25.2722	+	353.352i	0.0572139	+	0.799955i
$59$	−217.882	−	742.038i	−0.480777	−	1.63738i	−0.740765	−	0.671764i	$-0.765537\pi$
$59$	−217.882	−	742.038i	−0.480777	−	1.63738i	0.259988	−	0.965612i	$-0.416281\pi$
$60$	161.158	+	63.8253i	0.346757	+	0.137330i
$61$	280.793	+	436.923i	0.589375	+	0.917085i	0.999986	+	0.00527468i	$0.00167899\pi$
$61$	280.793	+	436.923i	0.589375	+	0.917085i	−0.410611	+	0.911811i	$0.634685\pi$
$62$	324.619	+	594.496i	0.664947	+	1.21776i
$63$	−142.498	+	190.355i	−0.284969	+	0.380675i
$64$	−58.2164	−	26.5866i	−0.113704	−	0.0519269i
$65$	551.946	−	396.133i	1.05324	−	0.755911i
$66$	−269.930	+	420.020i	−0.503426	+	0.783346i
$67$	−914.838	−	65.4305i	−1.66814	−	0.119308i	−0.794945	−	0.606681i	$-0.792500\pi$
$67$	−914.838	−	65.4305i	−1.66814	−	0.119308i	−0.873194	+	0.487374i	$0.837955\pi$
$68$	−42.7251	−	42.7251i	−0.0761938	−	0.0761938i
$69$	402.487	+	144.175i	0.702228	+	0.251545i
$70$	−8.91806	+	443.835i	−0.0152273	+	0.757835i
$71$	575.373	+	664.016i	0.961750	+	1.10992i	0.993883	+	0.110435i	$0.0352244\pi$
$71$	575.373	+	664.016i	0.961750	+	1.10992i	−0.0321333	+	0.999484i	$0.510230\pi$
$72$	20.3675	+	93.6281i	0.0333380	+	0.153252i
$73$	106.977	+	142.904i	0.171516	+	0.229118i	0.878060	−	0.478551i	$-0.158838\pi$
$73$	106.977	+	142.904i	0.171516	+	0.229118i	−0.706544	+	0.707669i	$0.749747\pi$
$74$	48.0750	−	105.270i	0.0755217	−	0.165369i
$75$	−375.878	−	305.690i	−0.578702	−	0.470641i
$76$	−12.1776	+	41.4732i	−0.0183799	+	0.0625961i
$77$	−1249.46	−	271.803i	−1.84921	−	0.402271i
$78$	−441.350	−	164.615i	−0.640680	−	0.238961i
$79$	643.011	−	188.805i	0.915752	−	0.268889i	0.210292	−	0.977639i	$-0.432559\pi$
$79$	643.011	−	188.805i	0.915752	−	0.268889i	0.705460	+	0.708750i	$0.250740\pi$
$80$	132.812	+	119.837i	0.185610	+	0.167478i
$81$	−171.679	+	198.128i	−0.235499	+	0.271780i
$82$	384.352	+	209.872i	0.517616	+	0.282640i
$83$	334.329	−	896.369i	0.442136	−	1.18541i	−0.504586	−	0.863362i	$-0.668355\pi$
$83$	334.329	−	896.369i	0.442136	−	1.18541i	0.946722	−	0.322052i	$-0.104373\pi$
$84$	258.932	−	166.406i	0.336332	−	0.216147i
$85$	77.9442	+	149.823i	0.0994616	+	0.191184i
$86$	−901.353	+	129.595i	−1.13018	+	0.162495i
$87$	−643.246	+	239.918i	−0.792680	+	0.295654i
$88$	−412.488	+	308.785i	−0.499675	+	0.374052i
$89$	−954.557	−	613.457i	−1.13689	−	0.730632i	−0.169900	−	0.985461i	$-0.554344\pi$
$89$	−954.557	−	613.457i	−1.13689	−	0.730632i	−0.966986	+	0.254829i	$0.917981\pi$
$90$	24.4687	−	266.699i	0.0286581	−	0.312361i
$91$		−	1206.39i		−	1.38971i
$92$	337.185	+	284.566i	0.382109	+	0.322479i
$93$	−928.203	+	928.203i	−1.03495	+	1.03495i
$94$	229.895	−	199.205i	0.252254	−	0.218579i
$95$	67.3461	−	100.303i	0.0727323	−	0.108325i
$96$	17.6512	−	122.767i	0.0187659	−	0.130519i
$97$	−177.555	−	476.044i	−0.185856	−	0.498298i	0.810288	−	0.586031i	$-0.199310\pi$
$97$	−177.555	−	476.044i	−0.185856	−	0.498298i	−0.996144	+	0.0877333i	$0.972038\pi$
$98$	81.8775	+	61.2927i	0.0843967	+	0.0631786i
$99$	740.178	+	217.336i	0.751421	+	0.220637i
$100$	−253.206	−	431.146i	−0.253206	−	0.431146i
$101$	−305.902	−	669.831i	−0.301370	−	0.659908i	0.696995	−	0.717076i	$-0.254520\pi$
$101$	−305.902	−	669.831i	−0.301370	−	0.659908i	−0.998365	+	0.0571685i	$0.981793\pi$
$102$	56.1182	−	102.773i	0.0544758	−	0.0997650i
$103$	338.611	−	24.2179i	0.323926	−	0.0231676i	0.0915704	−	0.995799i	$-0.470811\pi$
$103$	338.611	−	24.2179i	0.323926	−	0.0231676i	0.232355	+	0.972631i	$0.425357\pi$
$104$	−367.392	−	318.347i	−0.346401	−	0.300158i
$105$	−830.163	+	225.745i	−0.771578	+	0.209814i
$106$	422.332	−	192.872i	0.386986	−	0.176730i
$107$	376.761	−	1731.94i	0.340400	−	1.56479i	−0.415180	−	0.909739i	$-0.636281\pi$
$107$	376.761	−	1731.94i	0.340400	−	1.56479i	0.755581	−	0.655056i	$-0.227355\pi$
$108$	−530.373	+	289.606i	−0.472548	+	0.258031i
$109$	215.091	+	1495.99i	0.189009	+	1.31459i	0.834580	+	0.550887i	$0.185710\pi$
$109$	215.091	+	1495.99i	0.189009	+	1.31459i	−0.645571	+	0.763700i	$0.723380\pi$
$110$	1359.23	−	476.089i	1.17816	−	0.412666i
$111$	221.993	+	31.9177i	0.189825	+	0.0272928i
$112$	310.388	−	67.5207i	0.261865	−	0.0569652i
$113$	−14.6474	+	204.797i	−0.0121939	+	0.170493i	0.987706	+	0.156325i	$0.0499646\pi$
$113$	−14.6474	+	204.797i	−0.0121939	+	0.170493i	−0.999900	+	0.0141684i	$0.995490\pi$
$114$	−83.7666			−0.0688198
$115$	−659.396	−	1042.15i	−0.534687	−	0.845050i
$116$	−708.509			−0.567099
$117$	−51.9214	+	725.956i	−0.0410268	+	0.573629i
$118$	1511.38	−	328.781i	1.17910	−	0.256498i
$119$	296.838	+	42.6788i	0.228665	+	0.0328770i
$120$	−150.319	+	312.388i	−0.114352	+	0.237642i
$121$	400.951	+	2788.68i	0.301241	+	2.09517i
$122$	−911.682	+	497.816i	−0.676556	+	0.369427i
$123$	−180.397	+	829.274i	−0.132243	+	0.607911i
$124$	−1232.28	+	562.763i	−0.892434	+	0.407561i
$125$	312.247	+	1362.21i	0.223426	+	0.974721i
$126$	−359.409	−	311.430i	−0.254117	−	0.220193i
$127$	−2515.79	+	179.933i	−1.75780	+	0.125720i	−0.912632	−	0.408781i	$-0.865954\pi$
$127$	−2515.79	+	179.933i	−1.75780	+	0.125720i	−0.845168	+	0.534502i	$0.820499\pi$
$128$	61.3439	−	112.343i	0.0423600	−	0.0775766i
$129$	−733.103	−	1605.27i	−0.500358	−	1.09563i
$130$	711.496	+	1157.60i	0.480018	+	0.780986i
$131$	−397.355	−	116.674i	−0.265016	−	0.0778157i	0.146525	−	0.989207i	$-0.453191\pi$
$131$	−397.355	−	116.674i	−0.265016	−	0.0778157i	−0.411541	+	0.911391i	$0.635009\pi$
$132$	−799.386	−	598.413i	−0.527103	−	0.394585i
$133$	−74.9710	−	201.005i	−0.0488783	−	0.131048i
$134$	261.055	−	1815.68i	0.168297	−	1.17053i
$135$	1657.32	−	325.804i	1.05659	−	0.207709i
$136$	91.3284	−	79.1365i	0.0575834	−	0.0498963i
$137$	563.083	−	563.083i	0.351149	−	0.351149i	−0.509388	−	0.860537i	$-0.670128\pi$
$137$	563.083	−	563.083i	0.351149	−	0.351149i	0.860537	+	0.509388i	$0.170128\pi$
$138$	−345.041	+	782.352i	−0.212839	+	0.482596i
$139$		−	1411.23i		−	0.861145i	−0.902556	−	0.430572i	$-0.858312\pi$
$139$		−	1411.23i		−	0.861145i	0.902556	−	0.430572i	$-0.141688\pi$
$140$	−884.137	−	81.1164i	−0.533737	−	0.0489685i
$141$	495.933	+	318.717i	0.296206	+	0.190360i
$142$	−1406.74	+	1053.07i	−0.831346	+	0.622338i
$143$	−3667.04	+	1367.74i	−2.14443	+	0.799831i
$144$	−189.685	+	27.2726i	−0.109771	+	0.0157828i
$145$	1888.53	+	595.987i	1.08162	+	0.341338i
$146$	−300.343	+	193.019i	−0.170250	+	0.109413i
$147$	−69.2673	+	185.713i	−0.0388644	+	0.104200i
$148$	203.143	+	110.925i	0.112826	+	0.0616078i
$149$	−1726.14	+	1992.07i	−0.949068	+	1.09528i	0.0462796	+	0.998929i	$0.485263\pi$
$149$	−1726.14	+	1992.07i	−0.949068	+	1.09528i	−0.995347	+	0.0963538i	$0.969282\pi$
$150$	663.452	−	706.226i	0.361137	−	0.384421i
$151$	1953.51	−	573.604i	1.05281	−	0.309134i	0.290860	−	0.956766i	$-0.406059\pi$
$151$	1953.51	−	573.604i	1.05281	−	0.309134i	0.761953	+	0.647632i	$0.224241\pi$
$152$	−80.9976	−	30.2105i	−0.0432222	−	0.0161210i
$153$	−176.789	−	38.4580i	−0.0934151	−	0.0203212i
$154$	720.493	−	2453.77i	0.377006	−	1.28397i
$155$	3758.03	−	463.473i	1.94743	−	0.240175i
$156$	391.362	−	856.964i	0.200859	−	0.439821i
$157$	−249.588	−	333.410i	−0.126874	−	0.169484i	0.732606	−	0.680653i	$-0.238304\pi$
$157$	−249.588	−	333.410i	−0.126874	−	0.169484i	−0.859481	+	0.511168i	$0.829213\pi$
$158$	284.904	+	1309.68i	0.143454	+	0.659448i
$159$	589.226	+	680.003i	0.293891	+	0.339168i
$160$	−258.013	+	247.849i	−0.127486	+	0.122464i
$161$	−2186.13	−	127.751i	−1.07013	−	0.0625354i
$162$	−370.751	−	370.751i	−0.179808	−	0.179808i
$163$	−57.4076	−	4.10587i	−0.0275860	−	0.00197299i	0.0575394	−	0.998343i	$-0.481675\pi$
$163$	−57.4076	−	4.10587i	−0.0275860	−	0.00197299i	−0.0851253	+	0.996370i	$0.527129\pi$
$164$	−473.513	+	736.800i	−0.225458	+	0.350820i
$165$	1627.39	+	2267.50i	0.767832	+	1.06985i
$166$	1740.47	+	794.846i	0.813775	+	0.371639i
$167$	219.138	−	292.734i	0.101541	−	0.135644i	−0.746892	−	0.664945i	$-0.768455\pi$
$167$	219.138	−	292.734i	0.101541	−	0.135644i	0.848434	+	0.529301i	$0.177546\pi$
$168$	295.020	+	540.288i	0.135484	+	0.248120i
$169$	−808.541	−	1258.12i	−0.368021	−	0.572651i
$170$	−310.004	+	134.115i	−0.139860	+	0.0605066i
$171$	36.4636	+	124.184i	0.0163067	+	0.0555354i
$172$	−129.926	−	1816.60i	−0.0575975	−	0.805318i
$173$	168.720	+	2359.01i	0.0741476	+	1.03672i	0.889256	+	0.457410i	$0.151223\pi$
$173$	168.720	+	2359.01i	0.0741476	+	1.03672i	−0.815108	+	0.579309i	$0.803323\pi$
$174$	−386.837	−	1317.44i	−0.168540	−	0.573996i
$175$	2288.44	+	959.938i	0.988511	+	0.414654i
$176$	−557.143	−	866.931i	−0.238615	−	0.371292i
$177$	1436.55	+	2630.85i	0.610044	+	1.11721i
$178$	1359.98	−	1816.72i	0.572668	−	0.764995i
$179$	−377.486	−	172.392i	−0.157624	−	0.0719844i	0.335041	−	0.942204i	$-0.391250\pi$
$179$	−377.486	−	172.392i	−0.157624	−	0.0719844i	−0.492665	+	0.870219i	$0.663977\pi$
$180$	528.548	+	86.8648i	0.218865	+	0.0359696i
$181$	1225.83	−	1907.43i	0.503399	−	0.783304i	−0.492825	−	0.870128i	$-0.664036\pi$
$181$	1225.83	−	1907.43i	0.503399	−	0.783304i	0.996224	+	0.0868249i	$0.0276721\pi$
$182$	2406.62	+	172.125i	0.980170	+	0.0701031i
$183$	−1423.43	−	1423.43i	−0.574991	−	0.574991i
$184$	−615.792	+	632.051i	−0.246722	+	0.253236i
$185$	−448.171	−	466.551i	−0.178109	−	0.185414i
$186$	−1719.24	−	1984.11i	−0.677747	−	0.782162i
$187$	−206.808	−	950.683i	−0.0808734	−	0.371769i
$188$	364.594	+	487.040i	0.141440	+	0.188942i
$189$	1245.93	−	2728.20i	0.479513	−	1.04999i
$190$	190.487	+	148.660i	0.0727335	+	0.0567629i
$191$	−1256.43	+	4279.02i	−0.475981	+	1.62104i	0.275509	+	0.961299i	$0.411154\pi$
$191$	−1256.43	+	4279.02i	−0.475981	+	1.62104i	−0.751490	+	0.659745i	$0.770664\pi$
$192$	242.390	+	52.7287i	0.0911094	+	0.0198196i
$193$	426.819	+	159.195i	0.159187	+	0.0593737i	0.427794	−	0.903876i	$-0.359291\pi$
$193$	426.819	+	159.195i	0.159187	+	0.0593737i	−0.268607	+	0.963250i	$0.586563\pi$
$194$	974.995	−	286.284i	0.360827	−	0.105949i
$195$	−1764.04	+	1955.03i	−0.647824	+	0.717963i
$196$	−133.955	+	154.593i	−0.0488175	+	0.0563384i
$197$	1543.19	+	842.646i	0.558111	+	0.304752i	0.733435	−	0.679759i	$-0.237916\pi$
$197$	1543.19	+	842.646i	0.558111	+	0.304752i	−0.175325	+	0.984511i	$0.556097\pi$
$198$	−539.172	+	1445.57i	−0.193521	+	0.518851i
$199$	−1357.20	+	872.219i	−0.483464	+	0.310703i	−0.759572	−	0.650423i	$-0.774592\pi$
$199$	−1357.20	+	872.219i	−0.483464	+	0.310703i	0.276108	+	0.961127i	$0.410955\pi$
$200$	896.222	−	443.606i	0.316862	−	0.156838i
$201$	3518.72	−	505.915i	1.23478	−	0.177535i
$202$	1379.89	−	514.674i	0.480639	−	0.179269i
$203$	2815.10	−	2107.36i	0.973307	−	0.728609i
$204$	197.015	+	126.614i	0.0676168	+	0.0434547i
$205$	1881.93	−	1565.63i	0.641171	−	0.533408i
$206$			678.952i			0.229635i
$207$	1310.03	+	170.964i	0.439871	+	0.0574049i
$208$	687.490	−	687.490i	0.229177	−	0.229177i
$209$	−525.995	+	455.777i	−0.174085	+	0.150846i
$210$	−331.894	−	1688.31i	−0.109061	−	0.554782i
$211$	320.575	−	2229.64i	0.104594	−	0.727465i	−0.868271	−	0.496090i	$-0.834769\pi$
$211$	320.575	−	2229.64i	0.104594	−	0.727465i	0.972865	−	0.231375i	$-0.0743223\pi$
$212$	324.504	+	870.030i	0.105128	+	0.281858i
$213$	−2726.21	−	2040.82i	−0.876981	−	0.656500i
$214$	3401.30	+	998.712i	1.08649	+	0.319021i
$215$	−1181.78	+	4951.46i	−0.374868	+	1.57063i
$216$	−502.063	−	1099.36i	−0.158153	−	0.346307i
$217$	3222.32	−	5901.24i	1.00804	−	1.84609i
$218$	−3015.05	+	215.641i	−0.936720	+	0.0669955i
$219$	−522.893	−	453.090i	−0.161342	−	0.139804i
$220$	755.818	+	2779.47i	0.231624	+	0.851781i
$221$	834.959	−	381.313i	0.254142	−	0.116063i
$222$	−95.3464	+	438.300i	−0.0288254	+	0.132508i
$223$	779.331	−	425.547i	0.234026	−	0.127788i	−0.357957	−	0.933738i	$-0.616527\pi$
$223$	779.331	−	425.547i	0.234026	−	0.127788i	0.591984	+	0.805950i	$0.298345\pi$
$224$	90.4117	+	628.827i	0.0269682	+	0.187568i
$225$	−1335.78	−	676.144i	−0.395786	−	0.200339i
$226$	−406.461	−	58.4403i	−0.119635	−	0.0172008i
$227$	769.125	−	167.313i	0.224884	−	0.0489205i	−0.0987113	−	0.995116i	$-0.531472\pi$
$227$	769.125	−	167.313i	0.224884	−	0.0489205i	0.323595	+	0.946196i	$0.395108\pi$
$228$	11.9517	−	167.106i	0.00347158	−	0.0485390i
$229$	1920.08			0.554071			0.277035	−	0.960860i	$-0.410648\pi$
$229$	1920.08			0.554071			0.277035	+	0.960860i	$0.410648\pi$
$230$	2173.07	−	1166.74i	0.622990	−	0.334489i
$231$	4956.07			1.41163
$232$	101.089	−	1413.41i	0.0286070	−	0.399978i
$233$	−5783.01	+	1258.02i	−1.62600	+	0.353714i	−0.930920	−	0.365222i	$-0.880993\pi$
$233$	−5783.01	+	1258.02i	−1.62600	+	0.353714i	−0.695076	+	0.718936i	$0.744629\pi$
$234$	−1440.80	−	207.156i	−0.402514	−	0.0578728i
$235$	−562.136	−	1604.90i	−0.156041	−	0.445498i
$236$	440.245	+	3061.97i	0.121430	+	0.844566i
$237$	−2279.75	+	1244.84i	−0.624834	+	0.341185i
$238$	−127.493	+	586.074i	−0.0347232	+	0.159620i
$239$	−2952.14	+	1348.20i	−0.798988	+	0.364886i	−0.772702	−	0.634769i	$-0.781095\pi$
$239$	−2952.14	+	1348.20i	−0.798988	+	0.364886i	−0.0262860	+	0.999654i	$0.508368\pi$
$240$	−601.737	−	344.443i	−0.161841	−	0.0926405i
$241$	1691.50	+	1465.70i	0.452113	+	0.391759i	0.850936	−	0.525270i	$-0.176036\pi$
$241$	1691.50	+	1465.70i	0.452113	+	0.391759i	−0.398822	+	0.917028i	$0.630581\pi$
$242$	−5620.35	+	401.975i	−1.49293	+	0.106777i
$243$	−1467.87	+	2688.20i	−0.387505	+	0.709662i
$244$	−863.018	−	1889.75i	−0.226431	−	0.495814i
$245$	487.099	−	299.386i	0.127019	−	0.0780697i
$246$	−1628.58	−	478.195i	−0.422092	−	0.123937i
$247$	−525.668	−	393.510i	−0.135415	−	0.101370i
$248$	−946.838	−	2538.57i	−0.242437	−	0.649998i
$249$	−527.711	+	3670.31i	−0.134306	+	0.934122i
$250$	−2762.04	+	428.545i	−0.698746	+	0.108414i
$251$	4820.56	−	4177.04i	1.21223	−	1.05041i	0.214960	−	0.976623i	$-0.431038\pi$
$251$	4820.56	−	4177.04i	1.21223	−	1.05041i	0.997274	−	0.0737845i	$-0.0235077\pi$
$252$	672.552	−	672.552i	0.168122	−	0.168122i
$253$	2090.19	+	6790.00i	0.519405	+	1.68729i
$254$		−	5044.44i		−	1.24613i
$255$	−418.639	−	503.216i	−0.102809	−	0.123579i
$256$	215.361	+	138.404i	0.0525783	+	0.0337901i
$257$	1431.06	−	1071.28i	0.347342	−	0.260017i	−0.411334	−	0.911484i	$-0.634937\pi$
$257$	1431.06	−	1071.28i	0.347342	−	0.260017i	0.758677	+	0.651467i	$0.225846\pi$
$258$	3306.96	−	1233.43i	0.797994	−	0.297637i
$259$	−1137.07	+	163.486i	−0.272796	+	0.0392222i
$260$	−2410.81	+	1254.20i	−0.575047	+	0.299163i
$261$	−1784.72	+	1146.97i	−0.423261	+	0.272013i
$262$	289.447	−	776.038i	0.0682524	−	0.182992i
$263$	−3542.64	−	1934.43i	−0.830604	−	0.453544i	0.00689962	−	0.999976i	$-0.497804\pi$
$263$	−3542.64	−	1934.43i	−0.830604	−	0.453544i	−0.837503	+	0.546432i	$0.815986\pi$
$264$	1307.83	−	1509.32i	0.304892	−	0.351864i
$265$	−133.113	−	2592.04i	−0.0308568	−	0.600859i
$266$	411.682	−	120.881i	0.0948943	−	0.0278635i
$267$	4120.66	+	1536.93i	0.944495	+	0.352278i
$268$	3584.86	+	779.838i	0.817090	+	0.177747i
$269$	1035.34	−	3526.04i	0.234668	−	0.799206i	−0.754987	−	0.655740i	$-0.772357\pi$
$269$	1035.34	−	3526.04i	0.234668	−	0.799206i	0.989655	−	0.143466i	$-0.0458249\pi$
$270$	413.483	+	3352.69i	0.0931992	+	0.755696i
$271$	1376.94	−	3015.08i	0.308646	−	0.675841i	−0.690212	−	0.723607i	$-0.742483\pi$
$271$	1376.94	−	3015.08i	0.308646	−	0.675841i	0.998859	+	0.0477657i	$0.0152101\pi$
$272$	144.839	+	193.482i	0.0322874	+	0.0431309i
$273$	993.925	+	4569.00i	0.220348	+	1.01292i
$274$	1042.96	+	1203.64i	0.229954	+	0.265381i
$275$	323.408	−	8044.47i	0.0709173	−	1.76400i
$276$	−1511.49	−	799.949i	−0.329641	−	0.174461i
$277$	903.253	+	903.253i	0.195925	+	0.195925i	0.798250	−	0.602326i	$-0.205759\pi$
$277$	903.253	+	903.253i	0.195925	+	0.195925i	−0.602326	+	0.798250i	$0.705759\pi$
$278$	2815.27	+	201.352i	0.607370	+	0.0434399i
$279$	−2193.05	+	3412.45i	−0.470589	+	0.732251i
$280$	287.967	−	1752.19i	0.0614618	−	0.373977i
$281$	−1864.80	−	851.624i	−0.395888	−	0.180796i	0.207516	−	0.978232i	$-0.433462\pi$
$281$	−1864.80	−	851.624i	−0.395888	−	0.180796i	−0.603404	+	0.797436i	$0.706189\pi$
$282$	−706.569	+	943.865i	−0.149204	+	0.199313i
$283$	3528.22	+	6461.45i	0.741098	+	1.35722i	0.927154	+	0.374680i	$0.122248\pi$
$283$	3528.22	+	6461.45i	0.741098	+	1.35722i	−0.186056	+	0.982539i	$0.559571\pi$
$284$	−1900.07	−	2956.57i	−0.397001	−	0.617746i
$285$	−172.424	+	435.369i	−0.0358370	+	0.0904879i
$286$	−2205.29	−	7510.54i	−0.455950	−	1.55282i
$287$	−310.110	−	4335.90i	−0.0637812	−	0.891778i
$288$	−27.3423	−	382.295i	−0.00559430	−	0.0782185i
$289$	−1319.87	−	4495.05i	−0.268648	−	0.914930i
$290$	−1458.39	+	3682.41i	−0.295309	+	0.745650i
$291$	1064.67	+	1656.66i	0.214474	+	0.333728i
$292$	−342.201	−	626.695i	−0.0685815	−	0.125598i
$293$	638.371	−	852.764i	0.127283	−	0.170031i	−0.732372	−	0.680904i	$-0.761587\pi$
$293$	638.371	−	852.764i	0.127283	−	0.170031i	0.859656	+	0.510873i	$0.170678\pi$
$294$	−360.596	−	164.679i	−0.0715320	−	0.0326676i
$295$	1402.21	−	8532.03i	0.276745	−	1.68391i
$296$	−250.268	+	389.425i	−0.0491437	+	0.0764691i
$297$	−9705.46	−	694.148i	−1.89619	−	0.135618i
$298$	−3727.71	−	3727.71i	−0.724633	−	0.724633i
$299$	−5840.52	+	3288.66i	−1.12965	+	0.636081i
$300$	1314.19	+	1424.29i	0.252916	+	0.274104i
$301$	5919.45	+	6831.41i	1.13353	+	1.30816i
$302$	865.560	+	3978.91i	0.164925	+	0.758148i
$303$	1710.42	+	2284.85i	0.324294	+	0.433206i
$304$	71.8238	−	157.272i	0.0135506	−	0.0296716i
$305$	710.754	+	5763.08i	0.133435	+	1.08194i
$306$	101.944	−	347.189i	0.0190449	−	0.0648610i
$307$	−2812.19	−	611.754i	−0.522801	−	0.113728i	−0.0565825	−	0.998398i	$-0.518020\pi$
$307$	−2812.19	−	611.754i	−0.522801	−	0.113728i	−0.466219	+	0.884669i	$0.654384\pi$
$308$	4792.24	+	1787.41i	0.886569	+	0.330673i
$309$	−1262.48	+	370.699i	−0.232428	+	0.0682470i
$310$	388.395	+	7563.04i	0.0711593	+	1.38565i
$311$	63.5304	−	73.3180i	0.0115835	−	0.0133681i	−0.749928	−	0.661519i	$-0.769912\pi$
$311$	63.5304	−	73.3180i	0.0115835	−	0.0133681i	0.761512	+	0.648151i	$0.224457\pi$
$312$	1653.72	+	903.000i	0.300075	+	0.163854i
$313$	−2356.20	+	6317.21i	−0.425496	+	1.14080i	0.530568	+	0.847642i	$0.321979\pi$
$313$	−2356.20	+	6317.21i	−0.425496	+	1.14080i	−0.956064	+	0.293157i	$0.905294\pi$
$314$	700.732	−	450.333i	0.125938	−	0.0809356i
$315$	−2358.43	+	1226.95i	−0.421849	+	0.219463i
$316$	−2653.34	+	381.493i	−0.472349	+	0.0679135i
$317$	−3811.63	+	1421.66i	−0.675338	+	0.251888i	−0.663650	−	0.748043i	$-0.730993\pi$
$317$	−3811.63	+	1421.66i	−0.675338	+	0.251888i	−0.0116887	+	0.999932i	$0.503721\pi$
$318$	−1440.61	+	1078.43i	−0.254042	+	0.190174i
$319$	−9597.33	−	6167.83i	−1.68447	−	1.08255i
$320$	−457.622	−	550.075i	−0.0799433	−	0.0960941i
$321$			6869.87i			1.19451i
$322$	566.765	−	4342.89i	0.0980887	−	0.751615i
$323$	115.422	−	115.422i	0.0198831	−	0.0198831i
$324$	792.511	−	686.715i	0.135890	−	0.117749i
$325$	7481.05	−	1315.14i	1.27684	−	0.224465i
$326$	16.3816	−	113.937i	0.00278311	−	0.0193570i
$327$	−2047.15	−	5488.63i	−0.346201	−	0.928201i
$328$	−1402.29	−	1049.74i	−0.236062	−	0.176714i
$329$	−2897.26	−	850.713i	−0.485505	−	0.142557i
$330$	−4755.64	+	2922.97i	−0.793302	+	0.487588i
$331$	317.515	+	695.261i	0.0527257	+	0.115453i	0.934161	−	0.356851i	$-0.116150\pi$
$331$	317.515	+	695.261i	0.0527257	+	0.115453i	−0.881436	+	0.472304i	$0.843422\pi$
$332$	−1833.97	+	3358.66i	−0.303169	+	0.555213i
$333$	691.282	−	49.4415i	0.113760	−	0.00813627i
$334$	552.711	+	478.927i	0.0905479	+	0.0784602i
$335$	−8899.47	−	5094.19i	−1.45143	−	0.830822i
$336$	−1119.92	+	511.448i	−0.181835	+	0.0830411i
$337$	−2136.59	+	9821.74i	−0.345363	+	1.58761i	0.397134	+	0.917761i	$0.370005\pi$
$337$	−2136.59	+	9821.74i	−0.345363	+	1.58761i	−0.742497	+	0.669849i	$0.766359\pi$
$338$	2625.18	−	1433.46i	0.422459	−	0.230680i
$339$	−113.255	−	787.706i	−0.0181450	−	0.126202i
$340$	−223.315	−	637.564i	−0.0356204	−	0.101696i
$341$	−21591.2	−	3104.35i	−3.42883	−	0.492992i
$342$	−252.937	+	55.0231i	−0.0399920	+	0.00869973i
$343$	−413.361	+	5779.54i	−0.0650711	+	0.909812i
$344$	3642.49			0.570901
$345$	3355.97	+	3403.70i	0.523709	+	0.531157i
$346$	−4730.08			−0.734944
$347$	−406.423	+	5682.54i	−0.0628759	+	0.879120i	0.863938	+	0.503599i	$0.167991\pi$
$347$	−406.423	+	5682.54i	−0.0628759	+	0.879120i	−0.926814	+	0.375522i	$0.877464\pi$
$348$	2683.37	−	583.731i	0.413344	−	0.0899175i
$349$	8462.81	+	1216.77i	1.29801	+	0.186625i	0.756456	−	0.654044i	$-0.226929\pi$
$349$	8462.81	+	1216.77i	1.29801	+	0.186625i	0.541549	+	0.840669i	$0.317838\pi$
$350$	−2241.49	+	4428.25i	−0.342323	+	0.676285i
$351$	−1306.47	−	9086.66i	−0.198672	−	1.38180i
$352$	1808.94	−	987.755i	0.273911	−	0.149567i
$353$	−293.701	+	1350.12i	−0.0442836	+	0.203569i	−0.993973	−	0.109625i	$-0.965035\pi$
$353$	−293.701	+	1350.12i	−0.0442836	+	0.203569i	0.949689	+	0.313193i	$0.101399\pi$
$354$	−5453.25	+	2490.42i	−0.818748	+	0.373910i
$355$	2577.63	+	9479.05i	0.385370	+	1.41717i
$356$	3430.15	+	2972.24i	0.510667	+	0.442496i
$357$	−1159.39	+	82.9212i	−0.171881	+	0.0122932i
$358$	397.765	−	728.453i	0.0587222	−	0.107542i
$359$	5117.43	+	11205.6i	0.752334	+	1.64738i	0.762126	+	0.647429i	$0.224156\pi$
$359$	5117.43	+	11205.6i	0.752334	+	1.64738i	−0.00979227	+	0.999952i	$0.503117\pi$
$360$	−248.699	+	1042.01i	−0.0364100	+	0.152552i
$361$	6469.12	+	1899.51i	0.943158	+	0.276936i
$362$	3630.24	+	2717.56i	0.527074	+	0.394563i
$363$	−3816.09	−	10231.3i	−0.551771	−	1.47936i
$364$	−686.747	+	4776.43i	−0.0988882	+	0.687782i
$365$	384.973	+	1958.31i	0.0552066	+	0.280829i
$366$	3042.71	−	2636.52i	0.434549	−	0.376539i
$367$	−521.820	+	521.820i	−0.0742202	+	0.0742202i	−0.743242	−	0.669022i	$-0.766713\pi$
$367$	−521.820	+	521.820i	−0.0742202	+	0.0742202i	0.669022	+	0.743242i	$0.266713\pi$
$368$	−1173.02	−	1318.63i	−0.166163	−	0.186788i
$369$			2622.52i			0.369981i
$370$	994.669	−	827.492i	0.139758	−	0.116268i
$371$	−3877.12	−	2491.68i	−0.542561	−	0.348683i
$372$	4203.41	−	3146.63i	0.585851	−	0.438563i
$373$	3450.78	−	1287.08i	0.479021	−	0.178665i	−0.0983430	−	0.995153i	$-0.531354\pi$
$373$	3450.78	−	1287.08i	0.479021	−	0.178665i	0.577364	+	0.816487i	$0.304081\pi$
$374$	1926.03	−	276.921i	0.266290	−	0.0382867i
$375$	−2304.90	−	4901.92i	−0.317398	−	0.675024i
$376$	−1023.62	+	657.840i	−0.140397	+	0.0902274i
$377$	3761.40	−	10084.7i	0.513852	−	1.37769i
$378$	5264.73	+	2874.76i	0.716372	+	0.391169i
$379$	7188.27	−	8295.71i	0.974239	−	1.12433i	−0.0179811	−	0.999838i	$-0.505724\pi$
$379$	7188.27	−	8295.71i	0.974239	−	1.12433i	0.992220	−	0.124494i	$-0.0397307\pi$
$380$	−323.741	+	358.792i	−0.0437041	+	0.0484359i
$381$	9379.93	−	2754.20i	1.26128	−	0.370346i
$382$	−8356.98	−	3116.99i	−1.11932	−	0.417485i
$383$	1809.54	+	393.640i	0.241418	+	0.0525172i	0.331646	−	0.943404i	$-0.392396\pi$
$383$	1809.54	+	393.640i	0.241418	+	0.0525172i	−0.0902284	+	0.995921i	$0.528760\pi$
$384$	−139.773	+	476.022i	−0.0185748	+	0.0632601i
$385$	−11270.2	−	8795.52i	−1.49190	−	1.16431i
$386$	−378.477	+	828.749i	−0.0499066	+	0.109280i
$387$	−3268.08	−	4365.64i	−0.429266	−	0.573432i
$388$	431.999	+	1985.87i	0.0565243	+	0.259838i
$389$	2975.33	+	3433.72i	0.387803	+	0.447549i	0.915762	−	0.401721i	$-0.131588\pi$
$389$	2975.33	+	3433.72i	0.387803	+	0.447549i	−0.527959	+	0.849270i	$0.677043\pi$
$390$	−3648.41	−	3798.03i	−0.473704	−	0.493131i
$391$	−602.571	−	1553.44i	−0.0779369	−	0.200922i
$392$	−289.285	−	289.285i	−0.0372732	−	0.0372732i
$393$	1601.05	+	114.509i	0.205502	+	0.0146978i
$394$	−1901.18	+	2958.29i	−0.243096	+	0.378266i
$395$	7393.40	+	1215.08i	0.941778	+	0.154778i
$396$	−2806.86	−	1281.85i	−0.356186	−	0.162665i
$397$	5132.67	−	6856.44i	0.648869	−	0.866788i	−0.348645	−	0.937255i	$-0.613358\pi$
$397$	5132.67	−	6856.44i	0.648869	−	0.866788i	0.997514	+	0.0704671i	$0.0224490\pi$
$398$	−1546.35	−	2831.93i	−0.194753	−	0.356663i
$399$	449.546	+	699.508i	0.0564047	+	0.0877674i
$400$	757.079	+	1851.17i	0.0946349	+	0.231396i
$401$	1075.37	+	3662.38i	0.133919	+	0.456087i	0.998959	−	0.0456164i	$-0.0145252\pi$
$401$	1075.37	+	3662.38i	0.133919	+	0.456087i	−0.865040	+	0.501703i	$0.832707\pi$
$402$	507.207	+	7091.68i	0.0629284	+	0.879853i
$403$	−1468.16	−	20527.5i	−0.181474	−	2.53734i
$404$	829.844	+	2826.19i	0.102194	+	0.348040i
$405$	−2690.10	+	1163.79i	−0.330054	+	0.142789i
$406$	3802.32	+	5916.53i	0.464793	+	0.723233i
$407$	1786.10	+	3271.00i	0.217528	+	0.398372i
$408$	−280.693	+	374.961i	−0.0340597	+	0.0454984i
$409$	2005.32	+	915.801i	0.242437	+	0.110717i	0.532929	−	0.846160i	$-0.321091\pi$
$409$	2005.32	+	915.801i	0.242437	+	0.110717i	−0.290491	+	0.956878i	$0.593819\pi$
$410$	2854.78	+	3977.66i	0.343872	+	0.479129i
$411$	−1668.67	+	2596.51i	−0.200267	+	0.311621i
$412$	−1354.44	−	96.8718i	−0.161963	−	0.0115838i
$413$	−10856.6	−	10856.6i	−1.29351	−	1.29351i
$414$	−527.970	+	2588.99i	−0.0626770	+	0.307348i
$415$	7713.70	−	7409.82i	0.912412	−	0.876467i
$416$	1273.39	+	1469.57i	0.150079	+	0.173201i
$417$	1162.69	+	5344.82i	0.136541	+	0.627667i
$418$	−834.184	−	1114.34i	−0.0976107	−	0.130393i
$419$	472.484	−	1034.60i	0.0550892	−	0.120628i	−0.880086	−	0.474815i	$-0.842515\pi$
$419$	472.484	−	1034.60i	0.0550892	−	0.120628i	0.935175	+	0.354187i	$0.115242\pi$
$420$	3415.36	−	421.213i	0.396792	−	0.0489359i
$421$	−1125.74	+	3833.92i	−0.130321	+	0.443833i	−0.998638	−	0.0521771i	$-0.983384\pi$
$421$	−1125.74	+	3833.92i	−0.130321	+	0.443833i	0.868317	+	0.496010i	$0.165202\pi$
$422$	4402.19	+	957.638i	0.507809	+	0.110467i
$423$	1706.84	+	636.620i	0.196193	+	0.0731762i
$424$	−1781.93	+	523.221i	−0.204099	+	0.0599289i
$425$	58.9379	+	1887.28i	0.00672684	+	0.215404i
$426$	4460.20	−	5147.35i	0.507271	−	0.585422i
$427$	9049.78	+	4941.55i	1.02564	+	0.560043i
$428$	−2477.63	+	6642.77i	−0.279815	+	0.750212i
$429$	12761.5	−	8201.31i	1.43620	−	0.922991i
$430$	−9709.06	−	3064.00i	−1.08887	−	0.343626i
$431$	4985.59	−	716.819i	0.557186	−	0.0801113i	0.142032	−	0.989862i	$-0.454637\pi$
$431$	4985.59	−	716.819i	0.557186	−	0.0801113i	0.415155	+	0.909751i	$0.363727\pi$
$432$	2264.76	−	844.712i	0.252230	−	0.0940769i
$433$	−2897.89	+	2169.34i	−0.321626	+	0.240766i	−0.747875	−	0.663840i	$-0.768926\pi$
$433$	−2897.89	+	2169.34i	−0.321626	+	0.240766i	0.426249	+	0.904606i	$0.359835\pi$
$434$	11312.7	+	7270.20i	1.25121	+	0.804103i
$435$	−7643.56	−	701.269i	−0.842484	−	0.0772949i
$436$		−	6045.50i		−	0.664053i
$437$	−768.758	+	910.908i	−0.0841526	+	0.0997132i
$438$	978.476	−	978.476i	0.106743	−	0.106743i
$439$	−825.177	+	715.020i	−0.0897120	+	0.0777359i	−0.698562	−	0.715549i	$-0.746176\pi$
$439$	−825.177	+	715.020i	−0.0897120	+	0.0777359i	0.608850	+	0.793285i	$0.291631\pi$
$440$	−5652.61	+	1111.21i	−0.612449	+	0.120398i
$441$	−87.1680	+	606.267i	−0.00941238	+	0.0654645i
$442$	641.552	+	1720.07i	0.0690397	+	0.185103i
$443$	−7508.97	−	5621.14i	−0.805331	−	0.602863i	0.115285	−	0.993332i	$-0.463222\pi$
$443$	−7508.97	−	5621.14i	−0.805331	−	0.602863i	−0.920616	+	0.390469i	$0.872313\pi$
$444$	−860.763	−	252.743i	−0.0920045	−	0.0270150i
$445$	−6642.87	−	10807.9i	−0.707646	−	1.15133i
$446$	737.732	+	1615.41i	0.0783243	+	0.171506i
$447$	4896.25	−	8966.82i	0.518087	−	0.948805i
$448$	−1267.35	+	90.6427i	−0.133653	+	0.00955907i
$449$	6614.15	+	5731.19i	0.695191	+	0.602387i	0.929081	−	0.369876i	$-0.120600\pi$
$449$	6614.15	+	5731.19i	0.695191	+	0.602387i	−0.233890	+	0.972263i	$0.575145\pi$
$450$	1539.43	−	2568.27i	0.161265	−	0.269044i
$451$	−12828.2	+	5858.45i	−1.33937	+	0.611671i
$452$	174.576	−	802.513i	0.0181667	−	0.0835111i
$453$	−6926.05	+	3781.91i	−0.718353	+	0.392251i
$454$	224.036	+	1558.20i	0.0231597	+	0.161080i
$455$	5848.38	−	12153.9i	0.602585	−	1.25227i
$456$	331.656	+	47.6849i	0.0340597	+	0.00489704i
$457$	−1174.60	+	255.518i	−0.120230	+	0.0261545i	−0.272278	−	0.962219i	$-0.587777\pi$
$457$	−1174.60	+	255.518i	−0.120230	+	0.0261545i	0.152047	+	0.988373i	$0.451413\pi$
$458$	−273.953	+	3830.37i	−0.0279498	+	0.390789i
$459$	2282.04			0.232062
$460$	2017.49	+	4501.53i	0.204491	+	0.456271i
$461$	13288.1			1.34249			0.671244	−	0.741237i	$-0.265760\pi$
$461$	13288.1			1.34249			0.671244	+	0.741237i	$0.265760\pi$
$462$	−707.124	+	9886.89i	−0.0712086	+	0.995627i
$463$	−3807.25	+	828.217i	−0.382155	+	0.0831328i	−0.399539	−	0.916716i	$-0.630830\pi$
$463$	−3807.25	+	828.217i	−0.382155	+	0.0831328i	0.0173839	+	0.999849i	$0.494466\pi$
$464$	2805.19	+	403.326i	0.280663	+	0.0403533i
$465$	−13851.1	+	4851.52i	−1.38135	+	0.483836i
$466$	−1684.51	−	11716.0i	−0.167454	−	1.16467i
$467$	1585.16	−	865.561i	0.157071	−	0.0857674i	−0.398791	−	0.917042i	$-0.630570\pi$
$467$	1585.16	−	865.561i	0.157071	−	0.0857674i	0.555862	+	0.831274i	$0.312388\pi$
$468$	618.829	−	2844.71i	0.0611226	−	0.280976i
$469$	−16563.1	+	7564.13i	−1.63073	+	0.744732i
$470$	3281.82	−	892.423i	0.322083	−	0.0875838i
$471$	1219.97	+	1057.11i	0.119348	+	0.103416i
$472$	−6171.16	+	441.370i	−0.601802	+	0.0430417i
$473$	14054.2	−	25738.4i	1.36620	−	2.50202i
$474$	−2158.06	−	4725.49i	−0.209120	−	0.457910i
$475$	1164.74	−	684.036i	0.112510	−	0.0660753i
$476$	−1150.97	−	337.955i	−0.110829	−	0.0325424i
$477$	2225.86	+	1666.26i	0.213659	+	0.159943i
$478$	−2268.32	−	6081.60i	−0.217051	−	0.581937i
$479$	−2054.91	+	14292.2i	−0.196015	+	1.36331i	0.619691	+	0.784846i	$0.287258\pi$
$479$	−2054.91	+	14292.2i	−0.196015	+	1.36331i	−0.815706	+	0.578467i	$0.803651\pi$
$480$	772.986	−	1151.26i	0.0735038	−	0.109474i
$481$	−2657.34	+	2302.60i	−0.251900	+	0.218273i
$482$	−3165.27	+	3165.27i	−0.299116	+	0.299116i
$483$	8384.88	−	1317.29i	0.789908	−	0.124096i
$484$		−	11269.4i		−	1.05836i
$485$	518.985	−	5656.73i	0.0485894	−	0.529606i
$486$	−5153.26	−	3311.80i	−0.480981	−	0.309108i
$487$	−10511.4	+	7868.73i	−0.978063	+	0.732169i	−0.963495	−	0.267725i	$-0.913728\pi$
$487$	−10511.4	+	7868.73i	−0.978063	+	0.732169i	−0.0145674	+	0.999894i	$0.504637\pi$
$488$	3892.99	−	1452.01i	0.361122	−	0.134692i
$489$	220.805	−	31.7470i	0.0204195	−	0.00293589i
$490$	527.748	+	1014.43i	0.0486556	+	0.0935252i
$491$	−5882.00	+	3780.13i	−0.540633	+	0.347444i	−0.782287	−	0.622919i	$-0.785947\pi$
$491$	−5882.00	+	3780.13i	−0.540633	+	0.347444i	0.241653	+	0.970363i	$0.422310\pi$
$492$	1186.32	−	3180.64i	0.108706	−	0.291452i
$493$	2348.33	+	1282.29i	0.214530	+	0.117142i
$494$	860.016	−	992.511i	0.0783278	−	0.0903951i
$495$	6403.41	+	5777.85i	0.581438	+	0.524637i
$496$	5199.30	−	1526.65i	0.470676	−	0.138203i
$497$	16343.4	+	6095.76i	1.47505	+	0.550166i
$498$	−7246.62	−	1576.41i	−0.652066	−	0.141848i
$499$	153.085	−	521.359i	0.0137335	−	0.0467720i	−0.952341	−	0.305035i	$-0.901332\pi$
$499$	153.085	−	521.359i	0.0137335	−	0.0467720i	0.966075	+	0.258263i	$0.0831501\pi$
$500$	−460.823	−	5571.14i	−0.0412173	−	0.498298i
$501$	−588.772	+	1289.23i	−0.0525038	+	0.114967i
$502$	7645.00	+	10212.5i	0.679707	+	0.907982i
$503$	3397.97	+	15620.2i	0.301209	+	1.38463i	0.840179	+	0.542309i	$0.182450\pi$
$503$	3397.97	+	15620.2i	0.301209	+	1.38463i	−0.538970	+	0.842325i	$0.681186\pi$
$504$	1245.72	+	1437.64i	0.110097	+	0.127058i
$505$	165.392	−	8231.27i	0.0145740	−	0.725320i
$506$	−13843.6	+	3200.95i	−1.21625	+	0.281225i
$507$	4098.77	+	4098.77i	0.359039	+	0.359039i
$508$	10063.2	+	719.732i	0.878900	+	0.0628602i
$509$	4040.33	−	6286.88i	0.351836	−	0.547468i	−0.619555	−	0.784953i	$-0.712687\pi$
$509$	4040.33	−	6286.88i	0.351836	−	0.547468i	0.971391	+	0.237486i	$0.0763232\pi$
$510$	1063.60	−	763.347i	0.0923469	−	0.0662776i
$511$	3223.67	+	1472.20i	0.279074	+	0.127449i
$512$	−306.830	+	409.877i	−0.0264846	+	0.0353793i
$513$	−782.372	−	1432.81i	−0.0673344	−	0.123314i
$514$	1932.91	+	3007.67i	0.165870	+	0.258099i
$515$	3528.79	+	1397.55i	0.301936	+	0.119579i
$516$	1988.75	+	6773.06i	0.169670	+	0.577844i
$517$	698.855	+	9771.27i	0.0594499	+	0.831219i
$518$	−163.904	−	2291.68i	−0.0139026	−	0.194383i
$519$	−2582.56	−	8795.39i	−0.218423	−	0.743882i
$520$	−2158.04	−	4988.29i	−0.181993	−	0.420675i
$521$	118.261	+	184.017i	0.00994450	+	0.0154740i	0.846190	−	0.532881i	$-0.178891\pi$
$521$	118.261	+	184.017i	0.00994450	+	0.0154740i	−0.836246	+	0.548355i	$0.815254\pi$
$522$	−2033.45	−	3723.98i	−0.170501	−	0.312250i
$523$	7048.18	−	9415.27i	0.589284	−	0.787191i	−0.402459	−	0.915438i	$-0.631844\pi$
$523$	7048.18	−	9415.27i	0.589284	−	0.787191i	0.991742	+	0.128247i	$0.0409352\pi$
$524$	1506.82	+	688.144i	0.125622	+	0.0573696i
$525$	−9457.98	−	1750.20i	−0.786247	−	0.145495i
$526$	4364.46	−	6791.23i	0.361786	−	0.562950i
$527$	5102.85	+	364.963i	0.421791	+	0.0301671i
$528$	2824.35	+	2824.35i	0.232791	+	0.232791i
$529$	5341.01	+	10932.0i	0.438975	+	0.898499i
$530$	5189.86	+	104.281i	0.425345	+	0.00854654i
$531$	6065.83	+	7000.34i	0.495733	+	0.572107i
$532$	182.408	+	838.514i	0.0148654	+	0.0683350i
$533$	−7973.57	−	10651.4i	−0.647980	−	0.865601i
$534$	−3653.95	+	8001.03i	−0.296108	+	0.648386i
$535$	12191.9	−	15622.2i	0.985238	−	1.26244i
$536$	−2067.18	+	7040.19i	−0.166584	+	0.567332i
$537$	1571.70	+	341.903i	0.126302	+	0.0274752i
$538$	6886.39	+	2568.49i	0.551846	+	0.205828i
$539$	−3160.32	+	927.952i	−0.252550	+	0.0741553i
$540$	−6747.28	+	346.503i	−0.537698	+	0.0276132i
$541$	−8632.74	+	9962.71i	−0.686045	+	0.791738i	−0.986797	−	0.161964i	$-0.948217\pi$
$541$	−8632.74	+	9962.71i	−0.686045	+	0.791738i	0.300751	+	0.953703i	$0.402763\pi$
$542$	5818.33	+	3177.05i	0.461105	+	0.251782i
$543$	−3071.13	+	8234.03i	−0.242716	+	0.650748i
$544$	−406.644	+	261.334i	−0.0320491	+	0.0205967i
$545$	−5085.38	+	16114.3i	−0.399695	+	1.26653i
$546$	−9256.53	+	1330.89i	−0.725536	+	0.104316i
$547$	6721.13	−	2506.85i	0.525365	−	0.195951i	−0.0727664	−	0.997349i	$-0.523183\pi$
$547$	6721.13	−	2506.85i	0.525365	−	0.195951i	0.598132	+	0.801398i	$0.295910\pi$
$548$	−2549.95	+	1908.87i	−0.198774	+	0.148801i
$549$	−5233.12	−	3363.12i	−0.406820	−	0.261447i
$550$	16001.8	+	1792.94i	1.24058	+	0.139002i
$551$		−	1914.04i		−	0.147987i
$552$	1811.48	−	2901.14i	0.139677	−	0.223697i
$553$	9407.76	−	9407.76i	0.723433	−	0.723433i
$554$	−1930.78	+	1673.03i	−0.148070	+	0.128303i
$555$	2081.76	+	1397.75i	0.159218	+	0.106903i
$556$	−803.357	+	5587.47i	−0.0612768	+	0.426190i
$557$	−4715.81	−	12643.6i	−0.358735	−	0.961805i	−0.983487	−	0.180981i	$-0.942073\pi$
$557$	−4715.81	−	12643.6i	−0.358735	−	0.961805i	0.624752	−	0.780823i	$-0.285200\pi$
$558$	−6494.61	−	4861.81i	−0.492722	−	0.368847i
$559$	26546.8	+	7794.83i	2.00860	+	0.589779i
$560$	3454.37	+	824.466i	0.260668	+	0.0622144i
$561$	1566.51	+	3430.18i	0.117893	+	0.258150i
$562$	1964.97	−	3598.58i	0.147487	−	0.270101i
$563$	9321.84	−	666.711i	0.697813	−	0.0499086i	0.282074	−	0.959393i	$-0.408978\pi$
$563$	9321.84	−	666.711i	0.697813	−	0.0499086i	0.415739	+	0.909484i	$0.363523\pi$
$564$	−1782.11	−	1544.21i	−0.133050	−	0.115289i
$565$	−1140.39	+	1992.25i	−0.0849146	+	0.148344i
$566$	−13393.4	+	6116.55i	−0.994638	+	0.454236i
$567$	−1106.33	+	5085.72i	−0.0819426	+	0.376684i
$568$	6169.17	−	3368.62i	0.455726	−	0.248845i
$569$	−110.987	−	771.929i	−0.00817715	−	0.0568733i	0.985324	−	0.170693i	$-0.0546006\pi$
$569$	−110.987	−	771.929i	−0.00817715	−	0.0568733i	−0.993501	+	0.113819i	$0.963691\pi$
$570$	−843.918	−	406.088i	−0.0620138	−	0.0298406i
$571$	−6108.59	−	878.282i	−0.447699	−	0.0643695i	−0.0852219	−	0.996362i	$-0.527160\pi$
$571$	−6108.59	−	878.282i	−0.447699	−	0.0643695i	−0.362477	+	0.931993i	$0.618069\pi$
$572$	15297.5	−	3327.76i	1.11822	−	0.243253i
$573$	1233.12	−	17241.3i	0.0899030	−	1.25701i
$574$	8693.96			0.632193
$575$	−1591.00	−	13695.9i	−0.115390	−	0.993320i
$576$	766.543			0.0554501
$577$	1687.51	−	23594.5i	0.121754	−	1.70235i	−0.459138	−	0.888365i	$-0.651841\pi$
$577$	1687.51	−	23594.5i	0.121754	−	1.70235i	0.580892	−	0.813981i	$-0.302704\pi$
$578$	9155.52	−	1991.66i	0.658857	−	0.143326i
$579$	−1747.67	−	251.277i	−0.125441	−	0.0180358i
$580$	−7137.98	−	3434.75i	−0.511014	−	0.245897i
$581$	−2703.00	−	18799.8i	−0.193011	−	1.34242i
$582$	−3456.77	+	1887.54i	−0.246199	+	0.134435i
$583$	−3178.25	+	14610.2i	−0.225780	+	1.03789i
$584$	1299.02	−	593.243i	0.0920443	−	0.0420352i
$585$	−4042.41	+	7062.04i	−0.285698	+	0.499110i
$586$	1610.10	+	1395.16i	0.113503	+	0.0983508i
$587$	−17072.0	+	1221.01i	−1.20040	+	0.0858545i	−0.657180	−	0.753734i	$-0.728251\pi$
$587$	−17072.0	+	1221.01i	−1.20040	+	0.0858545i	−0.543223	+	0.839588i	$0.682796\pi$
$588$	379.968	−	695.859i	0.0266490	−	0.0488040i
$589$	−1520.31	−	3329.01i	−0.106355	−	0.232885i
$590$	16820.5	+	4014.60i	1.17371	+	0.280133i
$591$	−6538.84	−	1919.98i	−0.455114	−	0.133633i
$592$	−741.158	−	554.824i	−0.0514551	−	0.0385188i
$593$	3639.18	+	9757.01i	0.252012	+	0.675670i	0.999929	+	0.0118785i	$0.00378113\pi$
$593$	3639.18	+	9757.01i	0.252012	+	0.675670i	−0.747917	+	0.663792i	$0.768946\pi$
$594$	2769.52	−	19262.4i	0.191304	−	1.33055i
$595$	2783.63	+	1869.00i	0.191795	+	0.128776i
$596$	7968.30	−	6904.57i	0.547641	−	0.474534i
$597$	4421.57	−	4421.57i	0.303120	−	0.303120i
$598$	−5727.25	−	12120.5i	−0.391647	−	0.828836i
$599$			19734.1i			1.34610i	0.739597	+	0.673050i	$0.235016\pi$
$599$			19734.1i			1.34610i	−0.739597	+	0.673050i	$0.764984\pi$
$600$	−3028.82	+	2418.47i	−0.206085	+	0.164556i
$601$	21499.4	+	13816.8i	1.45920	+	0.937771i	0.998745	+	0.0500874i	$0.0159500\pi$
$601$	21499.4	+	13816.8i	1.45920	+	0.937771i	0.460455	+	0.887683i	$0.347686\pi$
$602$	−14472.6	+	10834.0i	−0.979832	+	0.733493i
$603$	10292.6	−	3838.94i	0.695103	−	0.259260i
$604$	−8061.05	+	1159.00i	−0.543045	+	0.0780782i
$605$	−9479.65	+	30038.7i	−0.637029	+	2.01859i
$606$	−4802.10	+	3086.12i	−0.321901	+	0.206873i
$607$	−1745.42	+	4679.65i	−0.116712	+	0.312918i	−0.982150	−	0.188098i	$-0.939768\pi$
$607$	−1745.42	+	4679.65i	−0.116712	+	0.312918i	0.865438	+	0.501016i	$0.167040\pi$
$608$	303.495	+	165.721i	0.0202440	+	0.0110541i
$609$	−8925.53	+	10300.6i	−0.593893	+	0.685389i
$610$	−11598.2	+	595.619i	−0.769832	+	0.0395343i
$611$	−8867.98	+	2603.87i	−0.587169	+	0.172408i
$612$	678.064	+	252.905i	0.0447861	+	0.0167044i
$613$	13712.4	+	2982.95i	0.903490	+	0.196542i	0.640231	−	0.768183i	$-0.278839\pi$
$613$	13712.4	+	2982.95i	0.903490	+	0.196542i	0.263260	+	0.964725i	$0.415202\pi$
$614$	1621.63	−	5522.76i	0.106586	−	0.362997i
$615$	−5837.63	+	7480.09i	−0.382758	+	0.490449i
$616$	−4249.47	+	9305.04i	−0.277948	+	0.608621i
$617$	2814.03	+	3759.10i	0.183612	+	0.245277i	0.882898	−	0.469565i	$-0.155589\pi$
$617$	2814.03	+	3759.10i	0.183612	+	0.245277i	−0.699286	+	0.714842i	$0.746498\pi$
$618$	−559.379	−	2571.43i	−0.0364103	−	0.167375i
$619$	8736.28	+	10082.2i	0.567271	+	0.654665i	0.964819	−	0.262916i	$-0.0846842\pi$
$619$	8736.28	+	10082.2i	0.567271	+	0.654665i	−0.397548	+	0.917581i	$0.630139\pi$
$620$	−15142.9	−	304.270i	−0.980896	−	0.0197093i
$621$	−16604.6	+	1405.25i	−1.07298	+	0.0908063i
$622$	137.198	+	137.198i	0.00884427	+	0.00884427i
$623$	−22469.4	−	1607.04i	−1.44497	−	0.103347i
$624$	−2037.35	+	3170.18i	−0.130704	+	0.203379i
$625$	−3458.03	+	15237.5i	−0.221314	+	0.975203i
$626$	−12266.1	−	5601.72i	−0.783147	−	0.357651i
$627$	1616.62	−	2159.55i	0.102969	−	0.137550i
$628$	798.392	+	1462.15i	0.0507314	+	0.0929076i
$629$	−472.556	−	735.312i	−0.0299556	−	0.0466118i
$630$	−2111.15	−	4879.90i	−0.133508	−	0.308603i
$631$	5507.68	+	18757.4i	0.347476	+	1.18339i	0.929066	+	0.369913i	$0.120612\pi$
$631$	5507.68	+	18757.4i	0.347476	+	1.18339i	−0.581591	+	0.813482i	$0.697569\pi$
$632$	−382.468	−	5347.60i	−0.0240724	−	0.336576i
$633$	622.848	+	8708.55i	0.0391090	+	0.546815i
$634$	−2292.25	−	7806.67i	−0.143591	−	0.489026i
$635$	−26218.0	−	10383.4i	−1.63847	−	0.648904i
$636$	−1945.82	−	3027.75i	−0.121315	−	0.188771i
$637$	−1489.27	−	2727.40i	−0.0926327	−	0.169644i
$638$	13673.6	−	18265.7i	0.848497	−	1.13346i
$639$	−9572.45	−	4371.59i	−0.592614	−	0.270638i
$640$	1162.64	−	834.428i	0.0718083	−	0.0515370i
$641$	8040.27	−	12510.9i	0.495432	−	0.770907i	−0.500036	−	0.866005i	$-0.666680\pi$
$641$	8040.27	−	12510.9i	0.495432	−	0.770907i	0.995468	+	0.0950976i	$0.0303163\pi$
$642$	−13704.7	−	980.181i	−0.842496	−	0.0602565i
$643$	−13321.5	−	13321.5i	−0.817030	−	0.817030i	0.168646	−	0.985677i	$-0.446060\pi$
$643$	−13321.5	−	13321.5i	−0.817030	−	0.817030i	−0.985677	+	0.168646i	$0.946060\pi$
$644$	8582.79	+	1750.28i	0.525170	+	0.107097i
$645$	396.368	−	19726.5i	0.0241969	−	1.20423i
$646$	213.788	+	246.724i	0.0130207	+	0.0150267i
$647$	5908.97	+	27163.1i	0.359050	+	1.65053i	0.702741	+	0.711445i	$0.251959\pi$
$647$	5908.97	+	27163.1i	0.359050	+	1.65053i	−0.343691	+	0.939083i	$0.611677\pi$
$648$	1256.86	+	1678.96i	0.0761944	+	0.101784i
$649$	−20692.1	+	45309.4i	−1.25152	+	2.74045i
$650$	1556.20	+	15111.6i	0.0939065	+	0.911887i
$651$	−7342.09	+	25004.9i	−0.442026	+	1.50540i
$652$	224.956	+	48.9361i	0.0135122	+	0.00293940i
$653$	16348.8	+	6097.78i	0.979751	+	0.365428i	0.787769	−	0.615970i	$-0.211236\pi$
$653$	16348.8	+	6097.78i	0.979751	+	0.365428i	0.191982	+	0.981398i	$0.438509\pi$
$654$	11241.4	−	3300.76i	0.672129	−	0.197355i
$655$	−3437.59	−	3101.77i	−0.205065	−	0.185032i
$656$	2294.20	−	2647.65i	0.136545	−	0.157581i
$657$	−1876.52	−	1024.66i	−0.111431	−	0.0608457i
$658$	2110.47	−	5658.38i	0.125037	−	0.335238i
$659$	−12232.6	+	7861.42i	−0.723088	+	0.464700i	−0.849710	−	0.527251i	$-0.823223\pi$
$659$	−12232.6	+	7861.42i	−0.723088	+	0.464700i	0.126622	+	0.991951i	$0.459587\pi$
$660$	−5152.51	−	9904.10i	−0.303881	−	0.584116i
$661$	4826.36	−	693.925i	0.283999	−	0.0408329i	0.00115689	−	0.999999i	$-0.499632\pi$
$661$	4826.36	−	693.925i	0.283999	−	0.0408329i	0.282842	+	0.959166i	$0.408723\pi$
$662$	−1432.28	+	534.213i	−0.0840894	+	0.0313637i
$663$	−2848.12	+	2132.08i	−0.166835	+	0.124891i
$664$	−6438.54	−	4137.80i	−0.376301	−	0.241834i
$665$	219.136	−	2388.50i	0.0127786	−	0.139281i
$666$			1386.10i			0.0806458i
$667$	−17876.5	−	7884.09i	−1.03775	−	0.457681i
$668$	−1034.27	+	1034.27i	−0.0599060	+	0.0599060i
$669$	−2600.99	+	2253.77i	−0.150314	+	0.130248i
$670$	11432.2	−	17026.8i	0.659199	−	0.981793i
$671$	4760.64	−	33111.0i	0.273894	−	1.90497i
$672$	−860.503	−	2307.10i	−0.0493967	−	0.132438i
$673$	−19181.6	−	14359.2i	−1.09866	−	0.822446i	−0.113406	−	0.993549i	$-0.536176\pi$
$673$	−19181.6	−	14359.2i	−1.09866	−	0.822446i	−0.985253	+	0.171103i	$0.945267\pi$
$674$	−19288.6	−	5663.64i	−1.10233	−	0.323673i
$675$	18276.4	+	4752.10i	1.04216	+	0.270976i
$676$	2485.05	+	5441.51i	0.141389	+	0.309599i
$677$	552.988	−	1012.72i	0.0313930	−	0.0574920i	−0.861512	−	0.507738i	$-0.830482\pi$
$677$	552.988	−	1012.72i	0.0313930	−	0.0574920i	0.892905	+	0.450246i	$0.148664\pi$
$678$	1587.56	−	113.544i	0.0899259	−	0.00643163i
$679$	−7623.12	−	6605.47i	−0.430852	−	0.373335i
$680$	1303.74	−	354.525i	0.0735239	−	0.0199933i
$681$	−2775.10	+	1267.34i	−0.156156	+	0.0713138i
$682$	9273.49	−	42629.6i	0.520675	−	2.39350i
$683$	4477.29	−	2444.78i	0.250832	−	0.136965i	−0.348915	−	0.937155i	$-0.613450\pi$
$683$	4477.29	−	2444.78i	0.250832	−	0.136965i	0.599747	+	0.800190i	$0.295268\pi$
$684$	−73.6771	−	512.436i	−0.00411859	−	0.0286454i
$685$	8402.61	−	2943.12i	0.468682	−	0.164162i
$686$	−11470.6	−	1649.23i	−0.638413	−	0.0917899i
$687$	−7271.99	+	1581.93i	−0.403848	+	0.0878518i
$688$	−519.704	+	7266.41i	−0.0287987	+	0.402659i
$689$	−14106.5			−0.779993
$690$	−7268.89	+	6209.21i	−0.401046	+	0.342580i
$691$	10627.5			0.585078			0.292539	−	0.956254i	$-0.405500\pi$
$691$	10627.5			0.585078			0.292539	+	0.956254i	$0.405500\pi$
$692$	674.880	−	9436.05i	0.0370738	−	0.518360i
$693$	14965.1	−	3255.45i	0.820312	−	0.178448i
$694$	−11278.1	−	1621.55i	−0.616876	−	0.0886934i
$695$	6841.44	−	14217.7i	0.373397	−	0.775980i
$696$	781.629	+	5436.35i	0.0425684	+	0.296069i
$697$	2902.93	−	1585.12i	0.157757	−	0.0861416i
$698$	−3634.80	+	16708.9i	−0.197105	+	0.906076i
$699$	20865.8	−	9529.08i	1.12906	−	0.515626i
$700$	−8514.12	−	5103.38i	−0.459719	−	0.275557i
$701$	−3247.36	−	2813.85i	−0.174966	−	0.151609i	0.562976	−	0.826473i	$-0.309656\pi$
$701$	−3247.36	−	2813.85i	−0.174966	−	0.151609i	−0.737941	+	0.674865i	$0.764202\pi$
$702$	18313.4	−	1309.80i	0.984610	−	0.0704207i
$703$	−299.664	+	548.793i	−0.0160769	+	0.0294426i
$704$	1712.38	+	3749.59i	0.0916729	+	0.200736i
$705$	3451.26	+	5615.17i	0.184371	+	0.299971i
$706$	−2651.46	−	778.538i	−0.141344	−	0.0415024i
$707$	−11703.3	−	8760.97i	−0.622556	−	0.466040i
$708$	−4190.08	−	11234.0i	−0.222419	−	0.596329i
$709$	2155.23	−	14989.9i	0.114163	−	0.794019i	−0.849633	−	0.527375i	$-0.823176\pi$
$709$	2155.23	−	14989.9i	0.114163	−	0.794019i	0.963795	−	0.266643i	$-0.0859146\pi$
$710$	−19277.6	+	3789.67i	−1.01898	+	0.200315i
$711$	−6066.12	+	5256.32i	−0.319968	+	0.277254i
$712$	−6418.74	+	6418.74i	−0.337855	+	0.337855i
$713$	−37354.1	+	486.719i	−1.96202	+	0.0255649i
$714$		−	2324.70i		−	0.121848i
$715$	−43574.7	−	3997.82i	−2.27916	−	0.209105i
$716$	1396.44	+	897.438i	0.0728875	+	0.0468419i
$717$	10070.0	−	7538.32i	0.524507	−	0.392641i
$718$	−23084.3	+	8609.99i	−1.19986	+	0.447524i
$719$	26540.8	−	3815.99i	1.37664	−	0.197931i	0.586050	−	0.810275i	$-0.300682\pi$
$719$	26540.8	−	3815.99i	1.37664	−	0.197931i	0.790592	+	0.612344i	$0.209773\pi$
$720$	−2043.22	−	644.803i	−0.105759	−	0.0333756i
$721$	5669.71	−	3643.70i	0.292858	−	0.188209i
$722$	−4712.34	+	12634.3i	−0.242902	+	0.651244i
$723$	−7613.88	−	4157.49i	−0.391650	−	0.213857i
$724$	−5939.23	+	6854.23i	−0.304875	+	0.351845i
$725$	16137.0	+	15159.7i	0.826641	+	0.776574i
$726$	20955.0	−	6152.95i	1.07123	−	0.314542i
$727$	−9880.54	−	3685.25i	−0.504056	−	0.188003i	0.0845560	−	0.996419i	$-0.473053\pi$
$727$	−9880.54	−	3685.25i	−0.504056	−	0.188003i	−0.588612	+	0.808415i	$0.700326\pi$
$728$	−9430.53	−	2051.49i	−0.480108	−	0.104441i
$729$	5338.75	−	18182.1i	0.271236	−	0.923747i
$730$	−3961.57	+	488.576i	−0.200855	+	0.0247712i
$731$	−2857.12	+	6256.21i	−0.144561	+	0.316545i
$732$	4825.48	+	6446.09i	0.243654	+	0.325484i
$733$	−381.403	−	1753.28i	−0.0192189	−	0.0883478i	0.966538	−	0.256522i	$-0.0825766\pi$
$733$	−381.403	−	1753.28i	−0.0192189	−	0.0883478i	−0.985757	+	0.168174i	$0.946213\pi$
$734$	−966.529	−	1115.43i	−0.0486039	−	0.0560919i
$735$	−1598.15	+	1535.19i	−0.0802023	+	0.0770428i
$736$	2797.90	−	2151.93i	0.140125	−	0.107773i
$737$	41771.0	+	41771.0i	2.08773	+	2.08773i
$738$	−5231.68	−	374.177i	−0.260950	−	0.0186635i
$739$	−6764.64	+	10526.0i	−0.336727	+	0.523958i	−0.967785	−	0.251778i	$-0.918985\pi$
$739$	−6764.64	+	10526.0i	−0.336727	+	0.523958i	0.631058	+	0.775736i	$0.282621\pi$
$740$	1508.85	+	2102.33i	0.0749546	+	0.104437i
$741$	2315.09	+	1057.27i	0.114773	+	0.0524152i
$742$	5523.84	−	7378.98i	0.273297	−	0.365082i
$743$	16187.1	+	29644.5i	0.799258	+	1.46373i	0.884080	+	0.467335i	$0.154786\pi$
$743$	16187.1	+	29644.5i	0.799258	+	1.46373i	−0.0848228	+	0.996396i	$0.527032\pi$
$744$	5677.50	+	8834.36i	0.279768	+	0.435327i
$745$	−27047.5	+	11701.4i	−1.33013	+	0.575442i
$746$	2075.24	+	7067.62i	0.101850	+	0.346868i
$747$	817.439	+	11429.3i	0.0400382	+	0.559807i
$748$	277.628	+	3881.75i	0.0135710	+	0.189747i
$749$	−9913.68	−	33762.9i	−0.483629	−	1.64709i
$750$	10107.7	−	3898.65i	0.492109	−	0.189812i
$751$	1534.53	+	2387.78i	0.0745618	+	0.116020i	0.876532	−	0.481344i	$-0.159851\pi$
$751$	1534.53	+	2387.78i	0.0745618	+	0.116020i	−0.801970	+	0.597364i	$0.796215\pi$
$752$	−1166.28	−	2135.88i	−0.0565556	−	0.103574i
$753$	−14815.7	+	19791.5i	−0.717018	+	0.957824i
$754$	19581.4	+	8942.51i	0.945771	+	0.431919i
$755$	22461.7	+	3691.50i	1.08273	+	0.177943i
$756$	−6486.04	+	10092.5i	−0.312030	+	0.485529i
$757$	−12621.7	−	902.721i	−0.606001	−	0.0433421i	−0.235033	−	0.971987i	$-0.575520\pi$
$757$	−12621.7	−	902.721i	−0.606001	−	0.0433421i	−0.370969	+	0.928645i	$0.620974\pi$
$758$	15523.5	+	15523.5i	0.743852	+	0.743852i
$759$	−13510.5	−	23994.0i	−0.646112	−	1.14747i
$760$	−669.566	−	697.025i	−0.0319575	−	0.0332681i
$761$	−22842.7	−	26361.8i	−1.08810	−	1.25574i	−0.964692	−	0.263382i	$-0.915162\pi$
$761$	−22842.7	−	26361.8i	−1.08810	−	1.25574i	−0.123411	−	0.992356i	$-0.539383\pi$
$762$	4156.05	+	19105.0i	0.197582	+	0.908271i
$763$	17981.5	+	24020.4i	0.853175	+	1.13971i
$764$	7410.46	−	16226.6i	0.350917	−	0.768402i
$765$	−1594.64	−	1244.49i	−0.0753652	−	0.0588167i
$766$	−1043.46	+	3553.69i	−0.0492188	+	0.167624i
$767$	−45920.4	−	9989.38i	−2.16179	−	0.470268i
$768$	−929.675	−	346.751i	−0.0436807	−	0.0162921i
$769$	−1948.55	+	572.146i	−0.0913738	+	0.0268298i	−0.327100	−	0.944990i	$-0.606071\pi$
$769$	−1948.55	+	572.146i	−0.0913738	+	0.0268298i	0.235726	+	0.971820i	$0.424253\pi$
$770$	19154.2	−	21228.0i	0.896455	−	0.993513i
$771$	−4537.30	+	5236.32i	−0.211941	+	0.244593i
$772$	−1599.27	−	873.270i	−0.0745585	−	0.0407120i
$773$	2429.74	−	6514.38i	0.113055	−	0.303112i	−0.868083	−	0.496418i	$-0.834648\pi$
$773$	2429.74	−	6514.38i	0.113055	−	0.303112i	0.981139	+	0.193306i	$0.0619210\pi$
$774$	9175.32	−	5896.62i	0.426098	−	0.273837i
$775$	40107.6	+	13549.0i	1.85898	+	0.627994i
$776$	−4023.25	+	578.456i	−0.186116	+	0.0267595i
$777$	4171.79	−	1556.00i	0.192616	−	0.0718419i
$778$	−7274.45	+	5445.59i	−0.335221	+	0.250943i
$779$	−1990.47	−	1279.20i	−0.0915482	−	0.0588344i
$780$	8097.26	−	6736.33i	0.371703	−	0.309230i
$781$		−	56589.9i		−	2.59276i
$782$	3184.93	−	980.430i	0.145643	−	0.0448339i
$783$	18921.5	−	18921.5i	0.863603	−	0.863603i
$784$	618.370	−	535.821i	0.0281692	−	0.0244088i
$785$	−898.184	−	4568.95i	−0.0408377	−	0.207736i
$786$	−456.869	+	3177.60i	−0.0207328	+	0.144200i
$787$	−754.730	−	2023.51i	−0.0341845	−	0.0916523i	0.918736	−	0.394872i	$-0.129211\pi$
$787$	−754.730	−	2023.51i	−0.0341845	−	0.0916523i	−0.952921	+	0.303220i	$0.901938\pi$
$788$	−5630.25	−	4214.75i	−0.254530	−	0.190539i
$789$	15011.0	+	4407.62i	0.677319	+	0.198879i
$790$	−3478.84	+	14575.8i	−0.156673	+	0.656433i
$791$	1693.32	+	3707.85i	0.0761157	+	0.166670i
$792$	2957.64	−	5416.52i	0.132696	−	0.243015i
$793$	31479.7	−	2251.48i	1.40968	−	0.100823i
$794$	12945.6	+	11217.4i	0.578618	+	0.501375i
$795$	2639.69	+	9707.27i	0.117761	+	0.433058i
$796$	5870.06	−	2680.77i	0.261380	−	0.119368i
$797$	37.2429	−	171.203i	0.00165522	−	0.00760892i	−0.976312	−	0.216368i	$-0.930579\pi$
$797$	37.2429	−	171.203i	0.00165522	−	0.00760892i	0.977967	+	0.208759i	$0.0669425\pi$
$798$	−1459.59	+	796.997i	−0.0647481	+	0.0353551i
$799$	−326.971	−	2274.13i	−0.0144773	−	0.100692i
$800$	−3800.93	+	1246.18i	−0.167979	+	0.0550738i
$801$	13452.0	+	1934.11i	0.593389	+	0.0853165i
$802$	−7459.54	+	1622.72i	−0.328436	+	0.0714468i
$803$	820.212	−	11468.1i	0.0360457	−	0.503984i
$804$	−14219.6			−0.623739
$805$	−21405.2	−	11885.1i	−0.937183	−	0.520365i
$806$	41159.9			1.79876
$807$	−1016.13	+	14207.3i	−0.0443239	+	0.619729i
$808$	−5756.38	+	1252.22i	−0.250630	+	0.0545211i
$809$	14386.5	+	2068.47i	0.625221	+	0.0898932i	0.447641	−	0.894213i	$-0.352264\pi$
$809$	14386.5	+	2068.47i	0.625221	+	0.0898932i	0.177580	+	0.984106i	$0.443173\pi$
$810$	−1937.84	−	5532.53i	−0.0840601	−	0.239992i
$811$	−1602.22	−	11143.7i	−0.0693732	−	0.482501i	−0.994658	−	0.103228i	$-0.967083\pi$
$811$	−1602.22	−	11143.7i	−0.0693732	−	0.482501i	0.925285	−	0.379274i	$-0.123826\pi$
$812$	−12345.4	+	6741.11i	−0.533546	+	0.291338i
$813$	−2730.87	+	12553.6i	−0.117805	+	0.541542i
$814$	−6780.17	+	3096.40i	−0.291947	+	0.133328i
$815$	−558.456	−	319.669i	−0.0240023	−	0.0137393i
$816$	−707.963	−	613.454i	−0.0303721	−	0.0263176i
$817$	4907.57	−	350.996i	0.210152	−	0.0150304i
$818$	−2113.05	+	3869.76i	−0.0903192	+	0.165407i
$819$	6002.40	+	13143.4i	0.256094	+	0.560767i
$820$	−8342.37	+	5127.48i	−0.355278	+	0.218365i
$821$	15598.9	+	4580.26i	0.663101	+	0.194704i	0.595929	−	0.803037i	$-0.296784\pi$
$821$	15598.9	+	4580.26i	0.663101	+	0.194704i	0.0671724	+	0.997741i	$0.478602\pi$
$822$	−4941.70	−	3699.31i	−0.209686	−	0.156969i
$823$	9698.81	+	26003.5i	0.410789	+	1.10137i	0.963433	+	0.267950i	$0.0863463\pi$
$823$	9698.81	+	26003.5i	0.410789	+	1.10137i	−0.552644	+	0.833418i	$0.686381\pi$
$824$	386.500	−	2688.17i	0.0163402	−	0.113649i
$825$	5402.87	+	30733.6i	0.228004	+	1.29698i
$826$	23206.9	−	20108.9i	0.977568	−	0.847068i
$827$	21523.6	−	21523.6i	0.905018	−	0.905018i	−0.0908472	−	0.995865i	$-0.528957\pi$
$827$	21523.6	−	21523.6i	0.905018	−	0.905018i	0.995865	+	0.0908472i	$0.0289575\pi$
$828$	−5089.46	−	1422.64i	−0.213612	−	0.0597104i
$829$		−	19192.8i		−	0.804095i	−0.915619	−	0.402047i	$-0.868299\pi$
$829$		−	19192.8i		−	0.804095i	0.915619	−	0.402047i	$-0.131701\pi$
$830$	13681.3	+	16445.3i	0.572151	+	0.687741i
$831$	−4165.11	−	2676.75i	−0.173870	−	0.111739i
$832$	−3113.33	+	2330.61i	−0.129730	+	0.0971147i
$833$	723.777	−	269.955i	0.0301049	−	0.0112286i
$834$	−10828.3	+	1556.87i	−0.449584	+	0.0646405i
$835$	3626.87	−	1886.84i	0.150315	−	0.0781999i
$836$	2342.02	−	1505.13i	0.0968905	−	0.0622678i
$837$	17880.2	−	47938.6i	0.738386	−	1.97969i
$838$	1996.51	+	1090.18i	0.0823010	+	0.0449397i
$839$	7604.43	−	8775.99i	0.312913	−	0.361121i	−0.577407	−	0.816457i	$-0.695935\pi$
$839$	7604.43	−	8775.99i	0.312913	−	0.361121i	0.890320	+	0.455336i	$0.150481\pi$
$840$	352.980	+	6873.42i	0.0144988	+	0.282328i
$841$	6702.15	−	1967.93i	0.274802	−	0.0806892i
$842$	−7487.68	−	2792.76i	−0.306464	−	0.114305i
$843$	7764.27	+	1689.01i	0.317219	+	0.0690068i
$844$	−2538.49	+	8645.31i	−0.103529	+	0.352588i
$845$	−2046.61	−	16594.7i	−0.0833202	−	0.675593i
$846$	−1513.53	+	3314.16i	−0.0615084	+	0.134685i
$847$	33519.2	+	44776.5i	1.35978	+	1.81645i
$848$	−789.533	−	3629.43i	−0.0319725	−	0.146975i
$849$	−18686.1	−	21564.9i	−0.755364	−	0.871737i
$850$	−3773.35	−	151.698i	−0.152265	−	0.00612143i
$851$	3891.21	+	5059.28i	0.156744	+	0.203795i
$852$	9632.10	+	9632.10i	0.387312	+	0.387312i
$853$	22653.4	+	1620.21i	0.909307	+	0.0650349i	0.518151	−	0.855289i	$-0.326621\pi$
$853$	22653.4	+	1620.21i	0.909307	+	0.0650349i	0.391156	+	0.920324i	$0.372075\pi$
$854$	−11149.1	+	17348.4i	−0.446739	+	0.695140i
$855$	−234.666	+	1427.87i	−0.00938644	+	0.0571138i
$856$	−12898.2	−	5890.41i	−0.515013	−	0.235199i
$857$	−12583.3	+	16809.3i	−0.501560	+	0.670006i	−0.977856	−	0.209279i	$-0.932888\pi$
$857$	−12583.3	+	16809.3i	−0.501560	+	0.670006i	0.476296	+	0.879285i	$0.341979\pi$
$858$	14540.0	+	26628.1i	0.578542	+	1.05952i
$859$	24458.3	+	38057.9i	0.971488	+	1.51166i	0.855102	+	0.518460i	$0.173495\pi$
$859$	24458.3	+	38057.9i	0.971488	+	1.51166i	0.116386	+	0.993204i	$0.462869\pi$
$860$	7497.66	−	18931.5i	0.297289	−	0.750649i
$861$	4746.79	+	16166.1i	0.187886	+	0.639882i
$862$	718.650	+	10048.0i	0.0283960	+	0.397027i
$863$	−894.342	−	12504.5i	−0.0352767	−	0.493232i	−0.984122	−	0.177492i	$-0.943202\pi$
$863$	−894.342	−	12504.5i	−0.0352767	−	0.493232i	0.948846	−	0.315740i	$-0.102253\pi$
$864$	1361.99	+	4638.50i	0.0536293	+	0.182645i
$865$	−9736.35	+	24584.1i	−0.382712	+	0.966342i
$866$	−3914.15	−	6090.54i	−0.153589	−	0.238989i
$867$	8702.20	+	15936.9i	0.340879	+	0.624274i
$868$	−16117.4	+	21530.4i	−0.630255	+	0.841922i
$869$	−39262.7	−	17930.7i	−1.53268	−	0.699950i
$870$	2489.53	−	15148.1i	0.0970151	−	0.590309i
$871$	−30131.6	+	46885.8i	−1.17218	+	1.82395i
$872$	12060.2	+	862.562i	0.468360	+	0.0334978i
$873$	4303.00	+	4303.00i	0.166821	+	0.166821i
$874$	−1707.49	−	1663.57i	−0.0660832	−	0.0643832i
$875$	18401.5	+	20765.0i	0.710955	+	0.802269i
$876$	1812.36	+	2091.57i	0.0699018	+	0.0806709i
$877$	−10645.7	−	48937.4i	−0.409896	−	1.88426i	−0.464188	−	0.885737i	$-0.653654\pi$
$877$	−10645.7	−	48937.4i	−0.409896	−	1.88426i	0.0542918	−	0.998525i	$-0.482710\pi$
$878$	−1308.66	−	1748.17i	−0.0503021	−	0.0671957i
$879$	−1715.15	+	3755.66i	−0.0658141	+	0.144113i
$880$	−1410.26	−	11435.0i	−0.0540226	−	0.438037i
$881$	11799.0	−	40183.8i	0.451214	−	1.53669i	−0.349085	−	0.937091i	$-0.613508\pi$
$881$	11799.0	−	40183.8i	0.451214	−	1.53669i	0.800299	−	0.599601i	$-0.204674\pi$
$882$	−1197.01	−	260.393i	−0.0456977	−	0.00994092i
$883$	−33491.3	−	12491.6i	−1.27641	−	0.476077i	−0.382348	−	0.924018i	$-0.624884\pi$
$883$	−33491.3	−	12491.6i	−1.27641	−	0.476077i	−0.894063	+	0.447942i	$0.852157\pi$
$884$	−3522.91	+	1034.42i	−0.134036	+	0.0393566i
$885$	1718.78	+	33469.0i	0.0652839	+	1.27124i
$886$	12285.0	−	14177.7i	0.465827	−	0.537593i
$887$	−27971.8	−	15273.8i	−1.05885	−	0.578177i	−0.147186	−	0.989109i	$-0.547022\pi$
$887$	−27971.8	−	15273.8i	−1.05885	−	0.578177i	−0.911666	+	0.410932i	$0.865203\pi$
$888$	627.010	−	1681.08i	0.0236949	−	0.0635285i
$889$	−42124.5	+	27071.8i	−1.58921	+	1.02132i
$890$	22508.5	−	11709.8i	0.847739	−	0.441028i
$891$	16713.3	−	2403.01i	0.628414	−	0.0903523i
$892$	−3327.84	+	1241.22i	−0.124915	+	0.0465910i
$893$	−1315.74	+	984.953i	−0.0493053	+	0.0369095i
$894$	17189.4	+	11046.9i	0.643063	+	0.413271i
$895$	−2967.31	−	3566.79i	−0.110823	−	0.133212i
$896$		−	2541.18i		−	0.0947485i
$897$	19410.6	−	17267.2i	0.722519	−	0.642738i
$898$	−12376.9	+	12376.9i	−0.459935	+	0.459935i
$899$	45336.4	−	39284.2i	1.68193	−	1.45740i
$900$	4903.82	+	3437.45i	0.181623	+	0.127313i
$901$	499.052	−	3470.98i	0.0184527	−	0.128341i
$902$	−9856.74	−	26427.0i	−0.363851	−	0.975523i
$903$	−28047.3	−	20996.0i	−1.03362	−	0.773756i
$904$	1576.03	+	462.764i	0.0579844	+	0.0170258i
$905$	21596.7	−	13274.0i	0.793258	−	0.487561i
$906$	−6556.35	−	14356.4i	−0.240419	−	0.526445i
$907$	−10591.1	+	19396.1i	−0.387730	+	0.710074i	−0.996529	−	0.0832505i	$-0.973470\pi$
$907$	−10591.1	+	19396.1i	−0.387730	+	0.710074i	0.608799	+	0.793325i	$0.291652\pi$
$908$	−3140.43	+	224.608i	−0.114778	+	0.00820912i
$909$	6665.52	+	5775.70i	0.243214	+	0.210746i
$910$	23411.4	+	13401.1i	0.852837	+	0.488176i
$911$	3012.43	−	1375.73i	0.109557	−	0.0500329i	−0.359883	−	0.932998i	$-0.617183\pi$
$911$	3012.43	−	1375.73i	0.109557	−	0.0500329i	0.469439	+	0.882965i	$0.344456\pi$
$912$	−142.447	+	654.818i	−0.00517203	+	0.0237754i
$913$	−54081.0	+	29530.4i	−1.96037	+	1.07044i
$914$	−342.144	−	2379.67i	−0.0123820	−	0.0861185i
$915$	−7439.99	−	21241.2i	−0.268807	−	0.767445i
$916$	−7602.13	−	1093.02i	−0.274216	−	0.0394263i
$917$	−8033.81	+	1747.65i	−0.289313	+	0.0629361i
$918$	−325.598	+	4552.46i	−0.0117063	+	0.163675i
$919$	−8315.61			−0.298484			−0.149242	−	0.988801i	$-0.547683\pi$
$919$	−8315.61			−0.298484			−0.149242	+	0.988801i	$0.547683\pi$
$920$	−9267.97	+	3382.42i	−0.332126	+	0.121212i
$921$	11154.7			0.399089
$922$	−1895.92	+	26508.4i	−0.0677210	+	0.946864i
$923$	52170.2	−	11348.9i	1.86046	−	0.404718i
$924$	−19622.5	−	2821.29i	−0.698629	−	0.100448i
$925$	−2253.40	−	6873.00i	−0.0800986	−	0.244306i
$926$	−1109.00	−	7713.27i	−0.0393564	−	0.273730i
$927$	−3568.63	+	1948.62i	−0.126439	+	0.0690410i
$928$	−1204.84	+	5538.54i	−0.0426193	+	0.195918i
$929$	15527.8	−	7091.29i	0.548385	−	0.250439i	−0.121901	−	0.992542i	$-0.538899\pi$
$929$	15527.8	−	7091.29i	0.548385	−	0.250439i	0.670285	+	0.742103i	$0.266172\pi$
$930$	−7702.07	−	28323.8i	−0.271571	−	0.998683i
$931$	−417.633	−	361.881i	−0.0147018	−	0.0127392i
$932$	23612.7	−	1688.81i	0.829893	−	0.0593551i
$933$	−180.206	+	330.022i	−0.00632334	+	0.0115803i
$934$	1500.54	+	3285.73i	0.0525688	+	0.115110i
$935$	2525.25	−	10580.4i	0.0883256	−	0.370069i
$936$	5586.63	+	1640.38i	0.195090	+	0.0572837i
$937$	12930.1	+	9679.36i	0.450809	+	0.337472i	0.800437	−	0.599417i	$-0.204601\pi$
$937$	12930.1	+	9679.36i	0.450809	+	0.337472i	−0.349628	+	0.936889i	$0.613692\pi$
$938$	−12726.5	−	34121.1i	−0.443002	−	1.18773i
$939$	3719.07	−	25866.7i	0.129252	−	0.898965i
$940$	1312.05	+	6674.25i	0.0455260	+	0.231585i
$941$	10108.3	−	8758.88i	0.350181	−	0.303434i	−0.461953	−	0.886904i	$-0.652851\pi$
$941$	10108.3	−	8758.88i	0.350181	−	0.303434i	0.812134	+	0.583471i	$0.198306\pi$
$942$	−2282.89	+	2282.89i	−0.0789603	+	0.0789603i
$943$	−20146.2	+	13321.2i	−0.695705	+	0.460020i
$944$		−	12373.8i		−	0.426625i
$945$	25778.2	−	21445.6i	0.887369	−	0.738227i
$946$	49340.4	+	31709.2i	1.69577	+	1.08980i
$947$	−20406.4	+	15276.0i	−0.700230	+	0.524185i	−0.889041	−	0.457828i	$-0.848628\pi$
$947$	−20406.4	+	15276.0i	−0.700230	+	0.524185i	0.188811	+	0.982013i	$0.439537\pi$
$948$	9734.82	−	3630.90i	0.333515	−	0.124395i
$949$	10736.9	−	1543.73i	0.367265	−	0.0528047i
$950$	1198.40	+	2421.15i	0.0409277	+	0.0826868i
$951$	13264.7	−	8524.68i	0.452299	−	0.290675i
$952$	838.407	−	2247.86i	0.0285430	−	0.0765268i
$953$	−679.596	−	371.088i	−0.0231000	−	0.0126135i	0.467657	−	0.883910i	$-0.345098\pi$
$953$	−679.596	−	371.088i	−0.0231000	−	0.0126135i	−0.490757	+	0.871296i	$0.663280\pi$
$954$	−3641.61	+	4202.64i	−0.123586	+	0.142626i
$955$	−33402.2	+	37018.6i	−1.13180	+	1.25434i
$956$	12455.8	−	3657.37i	0.421392	−	0.123732i
$957$	41430.0	+	15452.6i	1.39942	+	0.521955i
$958$	−28218.4	−	6138.53i	−0.951664	−	0.207022i
$959$	4453.99	−	15168.9i	0.149976	−	0.510771i
$960$	2186.37	+	1706.29i	0.0735050	+	0.0573650i
$961$	35272.8	−	77236.6i	1.18401	−	2.59261i
$962$	−4214.31	−	5629.66i	−0.141242	−	0.188677i
$963$	4512.55	+	20743.9i	0.151002	+	0.694145i
$964$	−5862.79	−	6766.02i	−0.195879	−	0.226057i
$965$	3528.29	+	3672.99i	0.117699	+	0.122526i
$966$	1431.52	+	16915.0i	0.0476794	+	0.563386i
$967$	−25357.7	−	25357.7i	−0.843278	−	0.843278i	0.146006	−	0.989284i	$-0.453358\pi$
$967$	−25357.7	−	25357.7i	−0.843278	−	0.843278i	−0.989284	+	0.146006i	$0.953358\pi$
$968$	22481.4	+	1607.90i	0.746467	+	0.0533883i
$969$	−342.048	+	532.238i	−0.0113397	+	0.0176449i
$970$	11210.6	+	1842.42i	0.371083	+	0.0609860i
$971$	−43449.1	−	19842.5i	−1.43599	−	0.655795i	−0.462942	−	0.886389i	$-0.653206\pi$
$971$	−43449.1	−	19842.5i	−1.43599	−	0.655795i	−0.973050	+	0.230593i	$0.925933\pi$
$972$	7341.99	−	9807.75i	0.242278	−	0.323646i
$973$	−13427.2	−	24590.0i	−0.442400	−	0.810195i
$974$	−14197.6	−	22091.9i	−0.467064	−	0.726766i
$975$	−27249.8	+	11144.4i	−0.895068	+	0.366059i
$976$	2341.18	+	7973.32i	0.0767821	+	0.261496i
$977$	1321.58	+	18478.2i	0.0432766	+	0.605086i	0.972101	+	0.234565i	$0.0753664\pi$
$977$	1321.58	+	18478.2i	0.0432766	+	0.605086i	−0.928824	+	0.370521i	$0.879179\pi$
$978$	31.8281	+	445.015i	0.00104064	+	0.0145501i
$979$	20589.7	+	70122.1i	0.672165	+	2.28918i
$980$	−2098.99	+	908.069i	−0.0684182	+	0.0295992i
$981$	−9786.73	−	15228.4i	−0.318518	−	0.495624i
$982$	−6701.77	−	12273.4i	−0.217782	−	0.398838i
$983$	−18293.2	+	24436.9i	−0.593553	+	0.792894i	−0.992259	−	0.124185i	$-0.960368\pi$
$983$	−18293.2	+	24436.9i	−0.593553	+	0.792894i	0.398706	+	0.917079i	$0.369459\pi$
$984$	6175.81	+	2820.40i	0.200079	+	0.0913729i
$985$	11462.1	+	15970.5i	0.370774	+	0.516612i
$986$	−2893.09	+	4501.74i	−0.0934430	+	0.145400i
$987$	11673.8	+	834.928i	0.376476	+	0.0269261i
$988$	1857.26	+	1857.26i	0.0598050	+	0.0598050i
$989$	16936.5	−	47280.8i	0.544538	−	1.52016i
$990$	−12439.9	+	11949.8i	−0.399359	+	0.383627i
$991$	20121.5	+	23221.5i	0.644987	+	0.744355i	0.980248	−	0.197771i	$-0.0633701\pi$
$991$	20121.5	+	23221.5i	0.644987	+	0.744355i	−0.335261	+	0.942125i	$0.608825\pi$
$992$	2303.70	+	10589.9i	0.0737323	+	0.338942i
$993$	−1775.35	−	2371.60i	−0.0567363	−	0.0757909i
$994$	−14492.3	+	31733.7i	−0.462443	+	1.01261i
$995$	−17901.7	+	2207.79i	−0.570373	+	0.0703435i
$996$	4178.72	−	14231.4i	0.132939	−	0.452750i
$997$	−26390.2	−	5740.85i	−0.838302	−	0.182361i	−0.227135	−	0.973863i	$-0.572936\pi$
$997$	−26390.2	−	5740.85i	−0.838302	−	0.182361i	−0.611167	+	0.791502i	$0.709300\pi$
$998$	1018.22	+	379.776i	0.0322958	+	0.0120457i
$999$	−8387.54	+	2462.80i	−0.265636	+	0.0779977i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.l.a.217.7	yes	720
5.3	odd	4	inner	230.4.l.a.33.25	yes	720
23.7	odd	22	inner	230.4.l.a.7.25	✓	720
115.53	even	44	inner	230.4.l.a.53.7	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.l.a.7.25	✓	720	23.7	odd	22	inner
230.4.l.a.33.25	yes	720	5.3	odd	4	inner
230.4.l.a.53.7	yes	720	115.53	even	44	inner
230.4.l.a.217.7	yes	720	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142678 + 1.99490i) q^{2} +(-3.78734 + 0.823886i) q^{3} +(-3.95929 - 0.569259i) q^{4} +(10.0746 + 4.84785i) q^{5} +(-1.10320 - 7.67294i) q^{6} +(17.4245 - 9.51450i) q^{7} +(1.70052 - 7.81717i) q^{8} +(-10.8949 + 4.97552i) q^{9} +(-11.1084 + 19.4063i) q^{10} +(-48.6761 - 42.1781i) q^{11} +(15.4642 - 1.10602i) q^{12} +(29.1221 - 53.3332i) q^{13} +(16.4944 + 36.1177i) q^{14} +(-42.1502 - 10.0601i) q^{15} +(15.3519 + 4.50772i) q^{16} +(12.0927 + 9.05245i) q^{17} +(-8.37123 - 22.4441i) q^{18} +(1.53786 - 10.6960i) q^{19} +(-37.1287 - 24.9291i) q^{20} +(-58.1537 + 50.3905i) q^{21} +(91.0863 - 91.0863i) q^{22} +(-93.5628 - 58.4209i) q^{23} +31.0074i q^{24} +(77.9967 + 97.6807i) q^{25} +(102.239 + 65.7053i) q^{26} +(120.940 - 90.5345i) q^{27} +(-74.4048 + 27.7516i) q^{28} +(175.324 - 25.2078i) q^{29} +(26.0829 - 82.6503i) q^{30} +(284.911 - 183.101i) q^{31} +(-11.1829 + 29.9824i) q^{32} +(219.103 + 119.639i) q^{33} +(-19.7841 + 22.8321i) q^{34} +(221.670 - 11.3838i) q^{35} +(45.9683 - 13.4975i) q^{36} +(-54.2155 - 20.2213i) q^{37} +(21.1181 + 4.59397i) q^{38} +(-66.3550 + 225.984i) q^{39} +(55.0286 - 70.5113i) q^{40} +(90.9589 - 199.172i) q^{41} +(-92.2269 - 123.201i) q^{42} +(96.7833 + 444.906i) q^{43} +(168.712 + 194.704i) q^{44} +(-133.882 - 2.69012i) q^{45} +(129.893 - 178.313i) q^{46} +(-107.549 - 107.549i) q^{47} +(-61.8567 - 4.42408i) q^{48} +(27.6477 - 43.0207i) q^{49} +(-205.992 + 141.659i) q^{50} +(-53.2572 - 24.3218i) q^{51} +(-145.663 + 194.583i) q^{52} +(-111.255 - 203.748i) q^{53} +(163.352 + 254.181i) q^{54} +(-285.921 - 660.903i) q^{55} +(-44.7457 - 152.390i) q^{56} +(2.98792 + 41.7766i) q^{57} +(25.2722 + 353.352i) q^{58} +(-217.882 - 742.038i) q^{59} +(161.158 + 63.8253i) q^{60} +(280.793 + 436.923i) q^{61} +(324.619 + 594.496i) q^{62} +(-142.498 + 190.355i) q^{63} +(-58.2164 - 26.5866i) q^{64} +(551.946 - 396.133i) q^{65} +(-269.930 + 420.020i) q^{66} +(-914.838 - 65.4305i) q^{67} +(-42.7251 - 42.7251i) q^{68} +(402.487 + 144.175i) q^{69} +(-8.91806 + 443.835i) q^{70} +(575.373 + 664.016i) q^{71} +(20.3675 + 93.6281i) q^{72} +(106.977 + 142.904i) q^{73} +(48.0750 - 105.270i) q^{74} +(-375.878 - 305.690i) q^{75} +(-12.1776 + 41.4732i) q^{76} +(-1249.46 - 271.803i) q^{77} +(-441.350 - 164.615i) q^{78} +(643.011 - 188.805i) q^{79} +(132.812 + 119.837i) q^{80} +(-171.679 + 198.128i) q^{81} +(384.352 + 209.872i) q^{82} +(334.329 - 896.369i) q^{83} +(258.932 - 166.406i) q^{84} +(77.9442 + 149.823i) q^{85} +(-901.353 + 129.595i) q^{86} +(-643.246 + 239.918i) q^{87} +(-412.488 + 308.785i) q^{88} +(-954.557 - 613.457i) q^{89} +(24.4687 - 266.699i) q^{90} -1206.39i q^{91} +(337.185 + 284.566i) q^{92} +(-928.203 + 928.203i) q^{93} +(229.895 - 199.205i) q^{94} +(67.3461 - 100.303i) q^{95} +(17.6512 - 122.767i) q^{96} +(-177.555 - 476.044i) q^{97} +(81.8775 + 61.2927i) q^{98} +(740.178 + 217.336i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q + 16 q^{3} + 16 q^{6} + 64 q^{12} - 192 q^{13} + 1152 q^{16} + 144 q^{18} + 1660 q^{23} - 880 q^{25} - 304 q^{26} - 728 q^{27} - 352 q^{28} - 608 q^{31} - 3872 q^{33} - 688 q^{35} - 2816 q^{36} - 2376 q^{37}+ \cdots + 14352 q^{98}+O(q^{100}) \) 720 * q + 16 * q^3 + 16 * q^6 + 64 * q^12 - 192 * q^13 + 1152 * q^16 + 144 * q^18 + 1660 * q^23 - 880 * q^25 - 304 * q^26 - 728 * q^27 - 352 * q^28 - 608 * q^31 - 3872 * q^33 - 688 * q^35 - 2816 * q^36 - 2376 * q^37 + 2208 * q^41 + 256 * q^46 + 3640 * q^47 - 256 * q^48 - 272 * q^50 - 768 * q^52 + 2360 * q^55 - 3872 * q^56 - 7656 * q^57 + 2112 * q^61 + 1376 * q^62 + 10912 * q^66 + 1104 * q^70 + 22752 * q^71 - 128 * q^72 + 1296 * q^73 - 5396 * q^75 + 752 * q^77 - 6000 * q^78 - 3928 * q^81 - 80 * q^82 + 3060 * q^85 - 10472 * q^86 - 6760 * q^87 - 1104 * q^92 + 5288 * q^93 + 9392 * q^95 - 256 * q^96 + 25344 * q^97 + 14352 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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