LMFDB - Embedded newform 49.4.e.a.8.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [49,4,Mod(8,49)] 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("49.8"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(49, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([12])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	49.e (of order $7$, degree $6$, 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:	$2.89109359028$
Analytic rank:	$0$
Dimension:	$78$
Relative dimension:	$13$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			8.10
Character	$\chi$	$=$	49.8
Dual form			49.4.e.a.43.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.88794 + 2.36740i) q^{2} +(-5.83533 + 2.81015i) q^{3} +(-0.260101 + 1.13958i) q^{4} +(-12.6471 + 6.09051i) q^{5} +(-17.6695 - 8.50917i) q^{6} +(-3.94107 + 18.0961i) q^{7} +(18.6363 - 8.97477i) q^{8} +(9.31994 - 11.6868i) q^{9} +(-38.2955 - 18.4422i) q^{10} +(1.11842 + 1.40245i) q^{11} +(-1.68461 - 7.38074i) q^{12} +(19.6402 + 24.6280i) q^{13} +(-50.2811 + 24.8342i) q^{14} +(56.6846 - 71.0802i) q^{15} +(64.8561 + 31.2330i) q^{16} +(3.96139 + 17.3560i) q^{17} +45.2629 q^{18} +34.8025 q^{19} +(-3.65109 - 15.9965i) q^{20} +(-27.8552 - 116.672i) q^{21} +(-1.20866 + 5.29549i) q^{22} +(-44.3595 + 194.352i) q^{23} +(-83.5285 + 104.741i) q^{24} +(44.9178 - 56.3251i) q^{25} +(-21.2249 + 92.9924i) q^{26} +(17.3694 - 76.1004i) q^{27} +(-19.5968 - 9.19798i) q^{28} +(-61.3317 - 268.712i) q^{29} +275.292 q^{30} +116.667 q^{31} +(11.6809 + 51.1772i) q^{32} +(-10.4675 - 5.04086i) q^{33} +(-33.6097 + 42.1452i) q^{34} +(-60.3712 - 252.865i) q^{35} +(10.8939 + 13.6606i) q^{36} +(7.15720 + 31.3578i) q^{37} +(65.7050 + 82.3915i) q^{38} +(-183.816 - 88.5209i) q^{39} +(-181.034 + 227.009i) q^{40} +(-294.218 + 141.688i) q^{41} +(223.619 - 286.213i) q^{42} +(405.907 + 195.474i) q^{43} +(-1.88911 + 0.909748i) q^{44} +(-46.6911 + 204.567i) q^{45} +(-543.856 + 261.907i) q^{46} +(-227.386 - 285.133i) q^{47} -466.226 q^{48} +(-311.936 - 142.636i) q^{49} +218.146 q^{50} +(-71.8889 - 90.1458i) q^{51} +(-33.1741 + 15.9758i) q^{52} +(-91.3405 + 400.189i) q^{53} +(212.952 - 102.552i) q^{54} +(-22.6864 - 10.9252i) q^{55} +(88.9610 + 372.614i) q^{56} +(-203.084 + 97.8002i) q^{57} +(520.358 - 652.508i) q^{58} +(753.642 + 362.935i) q^{59} +(66.2578 + 83.0847i) q^{60} +(1.60600 + 7.03636i) q^{61} +(220.260 + 276.198i) q^{62} +(174.755 + 214.713i) q^{63} +(259.950 - 325.967i) q^{64} +(-398.388 - 191.854i) q^{65} +(-7.82818 - 34.2975i) q^{66} +671.084 q^{67} -20.8089 q^{68} +(-287.304 - 1258.76i) q^{69} +(484.656 - 620.317i) q^{70} +(-159.690 + 699.647i) q^{71} +(68.8025 - 301.444i) q^{72} +(341.931 - 428.768i) q^{73} +(-60.7240 + 76.1455i) q^{74} +(-103.828 + 454.901i) q^{75} +(-9.05219 + 39.6602i) q^{76} +(-29.7867 + 14.7118i) q^{77} +(-137.468 - 602.287i) q^{78} +195.323 q^{79} -1010.46 q^{80} +(202.306 + 886.359i) q^{81} +(-890.898 - 429.034i) q^{82} +(801.597 - 1005.17i) q^{83} +(140.202 - 1.39671i) q^{84} +(-155.807 - 195.375i) q^{85} +(303.561 + 1329.99i) q^{86} +(1113.01 + 1395.67i) q^{87} +(33.4299 + 16.0990i) q^{88} +(-378.661 + 474.826i) q^{89} +(-572.442 + 275.674i) q^{90} +(-523.075 + 258.350i) q^{91} +(-209.941 - 101.102i) q^{92} +(-680.791 + 327.852i) q^{93} +(245.733 - 1076.63i) q^{94} +(-440.150 + 211.965i) q^{95} +(-211.977 - 265.811i) q^{96} +665.767 q^{97} +(-251.239 - 1007.76i) q^{98} +26.8139 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9} + 9 q^{10} - 103 q^{11} + 364 q^{12} - 35 q^{13} + 161 q^{14} - 245 q^{15} - 205 q^{16} - 285 q^{17} + 16 q^{18} + 628 q^{19}+ \cdots + 10768 q^{99}+O(q^{100}) $ 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9 + 9 * q^10 - 103 * q^11 + 364 * q^12 - 35 * q^13 + 161 * q^14 - 245 * q^15 - 205 * q^16 - 285 * q^17 + 16 * q^18 + 628 * q^19 + 553 * q^20 - 21 * q^21 - 605 * q^22 + 149 * q^23 + 653 * q^24 - 370 * q^25 - 511 * q^26 - 65 * q^27 + 70 * q^28 - 187 * q^29 + 84 * q^30 + 1276 * q^31 + 1399 * q^32 - 23 * q^33 - 765 * q^34 - 805 * q^35 - 1691 * q^36 - 1531 * q^37 - 1041 * q^38 - 1351 * q^39 - 1759 * q^40 - 301 * q^41 + 3395 * q^42 - 257 * q^43 - 883 * q^44 + 3105 * q^45 + 1593 * q^46 + 733 * q^47 - 1948 * q^48 + 1288 * q^49 + 6148 * q^50 + 1197 * q^51 - 1099 * q^52 - 285 * q^53 + 660 * q^54 + 2641 * q^55 - 1988 * q^56 - 2352 * q^57 + 1173 * q^58 - 3603 * q^59 - 175 * q^60 - 2613 * q^61 - 1927 * q^62 - 3066 * q^63 + 1589 * q^64 - 371 * q^65 - 2175 * q^66 + 352 * q^67 + 6076 * q^68 + 5549 * q^69 - 6293 * q^70 - 2623 * q^71 + 6220 * q^72 + 2039 * q^73 - 2411 * q^74 - 3903 * q^75 + 4130 * q^76 + 1029 * q^77 - 3759 * q^78 + 44 * q^79 - 1608 * q^80 + 1394 * q^81 - 10920 * q^82 - 553 * q^83 - 7798 * q^84 + 497 * q^85 - 2985 * q^86 - 4273 * q^87 - 2197 * q^88 - 3957 * q^89 - 2958 * q^90 + 14119 * q^91 - 9136 * q^92 + 6272 * q^93 + 14912 * q^94 + 5866 * q^95 + 21882 * q^96 - 1540 * q^97 - 2303 * q^98 + 10768 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{6}{7}\right)$

Coefficient data

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

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

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

$2$	1.88794	+	2.36740i	0.667487	+	0.837002i	0.994135	−	0.108144i	$-0.0344908\pi$
$2$	1.88794	+	2.36740i	0.667487	+	0.837002i	−0.326649	+	0.945146i	$0.605919\pi$
$3$	−5.83533	+	2.81015i	−1.12301	+	0.540813i	−0.900821	−	0.434191i	$-0.857034\pi$
$3$	−5.83533	+	2.81015i	−1.12301	+	0.540813i	−0.222189	+	0.975004i	$0.571320\pi$
$4$	−0.260101	+	1.13958i	−0.0325127	+	0.142447i
$5$	−12.6471	+	6.09051i	−1.13119	+	0.544751i	−0.903331	−	0.428943i	$-0.858886\pi$
$5$	−12.6471	+	6.09051i	−1.13119	+	0.544751i	−0.227857	+	0.973695i	$0.573172\pi$
$6$	−17.6695	−	8.50917i	−1.20226	−	0.578976i
$7$	−3.94107	+	18.0961i	−0.212798	+	0.977096i
$7$	−3.94107	+	18.0961i	−0.212798	+	0.977096i
$8$	18.6363	−	8.97477i	0.823616	−	0.396632i
$9$	9.31994	−	11.6868i	0.345183	−	0.432846i
$10$	−38.2955	−	18.4422i	−1.21101	−	0.583192i
$11$	1.11842	+	1.40245i	0.0306560	+	0.0384415i	0.796923	−	0.604081i	$-0.206460\pi$
$11$	1.11842	+	1.40245i	0.0306560	+	0.0384415i	−0.766267	+	0.642522i	$0.777888\pi$
$12$	−1.68461	−	7.38074i	−0.0405253	−	0.177553i
$13$	19.6402	+	24.6280i	0.419017	+	0.525430i	0.945879	−	0.324521i	$-0.105203\pi$
$13$	19.6402	+	24.6280i	0.419017	+	0.525430i	−0.526862	+	0.849951i	$0.676632\pi$
$14$	−50.2811	+	24.8342i	−0.959871	+	0.474086i
$15$	56.6846	−	71.0802i	0.975727	−	1.22352i
$16$	64.8561	+	31.2330i	1.01338	+	0.488016i
$17$	3.96139	+	17.3560i	0.0565163	+	0.247614i	0.995293	−	0.0969123i	$-0.0308966\pi$
$17$	3.96139	+	17.3560i	0.0565163	+	0.247614i	−0.938777	+	0.344526i	$0.888039\pi$
$18$	45.2629			0.592698
$19$	34.8025			0.420224			0.210112	−	0.977677i	$-0.432617\pi$
$19$	34.8025			0.420224			0.210112	+	0.977677i	$0.432617\pi$
$20$	−3.65109	−	15.9965i	−0.0408205	−	0.178846i
$21$	−27.8552	−	116.672i	−0.289452	−	1.21237i
$22$	−1.20866	+	5.29549i	−0.0117131	+	0.0513183i
$23$	−44.3595	+	194.352i	−0.402156	+	1.76196i	0.216483	+	0.976286i	$0.430541\pi$
$23$	−44.3595	+	194.352i	−0.402156	+	1.76196i	−0.618639	+	0.785675i	$0.712316\pi$
$24$	−83.5285	+	104.741i	−0.710425	+	0.890844i
$25$	44.9178	−	56.3251i	0.359342	−	0.450601i
$26$	−21.2249	+	92.9924i	−0.160098	+	0.701435i
$27$	17.3694	−	76.1004i	0.123805	−	0.542427i
$28$	−19.5968	−	9.19798i	−0.132266	−	0.0620805i
$29$	−61.3317	−	268.712i	−0.392725	−	1.72064i	−0.654984	−	0.755642i	$-0.727325\pi$
$29$	−61.3317	−	268.712i	−0.392725	−	1.72064i	0.262260	−	0.964997i	$-0.415532\pi$
$30$	275.292			1.67538
$31$	116.667			0.675936			0.337968	−	0.941158i	$-0.390260\pi$
$31$	116.667			0.675936			0.337968	+	0.941158i	$0.390260\pi$
$32$	11.6809	+	51.1772i	0.0645283	+	0.282717i
$33$	−10.4675	−	5.04086i	−0.0552167	−	0.0265910i
$34$	−33.6097	+	42.1452i	−0.169530	+	0.212583i
$35$	−60.3712	−	252.865i	−0.291560	−	1.22120i
$36$	10.8939	+	13.6606i	0.0504349	+	0.0632434i
$37$	7.15720	+	31.3578i	0.0318010	+	0.139329i	0.988336	−	0.152287i	$-0.0486640\pi$
$37$	7.15720	+	31.3578i	0.0318010	+	0.139329i	−0.956535	+	0.291617i	$0.905807\pi$
$38$	65.7050	+	82.3915i	0.280494	+	0.351728i
$39$	−183.816	−	88.5209i	−0.754719	−	0.363454i
$40$	−181.034	+	227.009i	−0.715598	+	0.897332i
$41$	−294.218	+	141.688i	−1.12071	+	0.539706i	−0.900112	−	0.435658i	$-0.856516\pi$
$41$	−294.218	+	141.688i	−1.12071	+	0.539706i	−0.220600	+	0.975364i	$0.570801\pi$
$42$	223.619	−	286.213i	0.821553	−	1.05151i
$43$	405.907	+	195.474i	1.43954	+	0.693245i	0.980744	−	0.195297i	$-0.0625671\pi$
$43$	405.907	+	195.474i	1.43954	+	0.693245i	0.458795	+	0.888542i	$0.348281\pi$
$44$	−1.88911	+	0.909748i	−0.00647259	+	0.00311704i
$45$	−46.6911	+	204.567i	−0.154673	+	0.677669i
$46$	−543.856	+	261.907i	−1.74320	+	0.839481i
$47$	−227.386	−	285.133i	−0.705694	−	0.884912i	0.291740	−	0.956498i	$-0.405766\pi$
$47$	−227.386	−	285.133i	−0.705694	−	0.884912i	−0.997434	+	0.0715852i	$0.977194\pi$
$48$	−466.226			−1.40196
$49$	−311.936	−	142.636i	−0.909434	−	0.415848i
$50$	218.146			0.617010
$51$	−71.8889	−	90.1458i	−0.197381	−	0.247508i
$52$	−33.1741	+	15.9758i	−0.0884695	+	0.0426047i
$53$	−91.3405	+	400.189i	−0.236728	+	1.03717i	0.707198	+	0.707016i	$0.249959\pi$
$53$	−91.3405	+	400.189i	−0.236728	+	1.03717i	−0.943926	+	0.330157i	$0.892898\pi$
$54$	212.952	−	102.552i	0.536651	−	0.258437i
$55$	−22.6864	−	10.9252i	−0.0556188	−	0.0267846i
$56$	88.9610	+	372.614i	0.212284	+	0.889154i
$57$	−203.084	+	97.8002i	−0.471915	+	0.227262i
$58$	520.358	−	652.508i	1.17804	−	1.47722i
$59$	753.642	+	362.935i	1.66298	+	0.800849i	0.998569	+	0.0534831i	$0.0170323\pi$
$59$	753.642	+	362.935i	1.66298	+	0.800849i	0.664412	+	0.747366i	$0.268682\pi$
$60$	66.2578	+	83.0847i	0.142564	+	0.178770i
$61$	1.60600	+	7.03636i	0.00337094	+	0.0147691i	0.976585	−	0.215130i	$-0.0690175\pi$
$61$	1.60600	+	7.03636i	0.00337094	+	0.0147691i	−0.973214	+	0.229899i	$0.926160\pi$
$62$	220.260	+	276.198i	0.451179	+	0.565760i
$63$	174.755	+	214.713i	0.349478	+	0.429386i
$64$	259.950	−	325.967i	0.507715	−	0.636655i
$65$	−398.388	−	191.854i	−0.760215	−	0.366100i
$66$	−7.82818	−	34.2975i	−0.0145997	−	0.0639656i
$67$	671.084			1.22367			0.611836	−	0.790985i	$-0.290431\pi$
$67$	671.084			1.22367			0.611836	+	0.790985i	$0.290431\pi$
$68$	−20.8089			−0.0371095
$69$	−287.304	−	1258.76i	−0.501267	−	2.19619i
$70$	484.656	−	620.317i	0.827536	−	1.05917i
$71$	−159.690	+	699.647i	−0.266925	+	1.16948i	0.646644	+	0.762792i	$0.276172\pi$
$71$	−159.690	+	699.647i	−0.266925	+	1.16948i	−0.913569	+	0.406684i	$0.866685\pi$
$72$	68.8025	−	301.444i	0.112617	−	0.493409i
$73$	341.931	−	428.768i	0.548219	−	0.687445i	−0.428112	−	0.903726i	$-0.640821\pi$
$73$	341.931	−	428.768i	0.548219	−	0.687445i	0.976331	+	0.216280i	$0.0693926\pi$
$74$	−60.7240	+	76.1455i	−0.0953921	+	0.119618i
$75$	−103.828	+	454.901i	−0.159854	+	0.700366i
$76$	−9.05219	+	39.6602i	−0.0136626	+	0.0598597i
$77$	−29.7867	+	14.7118i	−0.0440845	+	0.0217736i
$78$	−137.468	−	602.287i	−0.199554	−	0.874302i
$79$	195.323			0.278171			0.139086	−	0.990280i	$-0.455584\pi$
$79$	195.323			0.278171			0.139086	+	0.990280i	$0.455584\pi$
$80$	−1010.46			−1.41217
$81$	202.306	+	886.359i	0.277511	+	1.21586i
$82$	−890.898	−	429.034i	−1.19980	−	0.577791i
$83$	801.597	−	1005.17i	1.06008	−	1.32930i	0.118335	−	0.992974i	$-0.462244\pi$
$83$	801.597	−	1005.17i	1.06008	−	1.32930i	0.941746	−	0.336325i	$-0.109184\pi$
$84$	140.202	−	1.39671i	0.182110	−	0.00181420i
$85$	−155.807	−	195.375i	−0.198819	−	0.249311i
$86$	303.561	+	1329.99i	0.380625	+	1.66763i
$87$	1113.01	+	1395.67i	1.37158	+	1.71991i
$88$	33.4299	+	16.0990i	0.0404959	+	0.0195018i
$89$	−378.661	+	474.826i	−0.450989	+	0.565522i	−0.954402	−	0.298524i	$-0.903506\pi$
$89$	−378.661	+	474.826i	−0.450989	+	0.565522i	0.503414	+	0.864046i	$0.332077\pi$
$90$	−572.442	+	275.674i	−0.670452	+	0.322873i
$91$	−523.075	+	258.350i	−0.602562	+	0.297609i
$92$	−209.941	−	101.102i	−0.237912	−	0.114572i
$93$	−680.791	+	327.852i	−0.759083	+	0.365555i
$94$	245.733	−	1076.63i	0.269632	−	1.18133i
$95$	−440.150	+	211.965i	−0.475352	+	0.228917i
$96$	−211.977	−	265.811i	−0.225363	−	0.282596i
$97$	665.767			0.696891			0.348445	−	0.937329i	$-0.386710\pi$
$97$	665.767			0.696891			0.348445	+	0.937329i	$0.386710\pi$
$98$	−251.239	−	1007.76i	−0.258969	−	1.03877i
$99$	26.8139			0.0272212
$100$	52.5038	+	65.8376i	0.0525038	+	0.0658376i
$101$	−361.759	+	174.214i	−0.356400	+	0.171633i	−0.603512	−	0.797354i	$-0.706233\pi$
$101$	−361.759	+	174.214i	−0.356400	+	0.171633i	0.247113	+	0.968987i	$0.420518\pi$
$102$	77.6893	−	340.379i	0.0754156	−	0.330417i
$103$	−667.639	+	321.518i	−0.638684	+	0.307574i	−0.725057	−	0.688689i	$-0.758187\pi$
$103$	−667.639	+	321.518i	−0.638684	+	0.307574i	0.0863730	+	0.996263i	$0.472472\pi$
$104$	587.052	+	282.709i	0.553511	+	0.266557i
$105$	1062.88	+	1305.90i	0.987867	+	1.21374i
$106$	−1119.85	+	539.292i	−1.02613	+	0.494157i
$107$	−153.777	+	192.830i	−0.138936	+	0.174220i	−0.846431	−	0.532498i	$-0.821254\pi$
$107$	−153.777	+	192.830i	−0.138936	+	0.174220i	0.707496	+	0.706718i	$0.249825\pi$
$108$	82.2046	+	39.5876i	0.0732420	+	0.0352715i
$109$	−277.240	−	347.648i	−0.243622	−	0.305492i	0.644955	−	0.764221i	$-0.276876\pi$
$109$	−277.240	−	347.648i	−0.243622	−	0.305492i	−0.888576	+	0.458729i	$0.848305\pi$
$110$	−16.9662	−	74.3338i	−0.0147060	−	0.0644314i
$111$	−129.885	−	162.870i	−0.111064	−	0.139270i
$112$	−820.798	+	1050.55i	−0.692483	+	0.886317i
$113$	−430.478	+	539.803i	−0.358371	+	0.449384i	−0.928034	−	0.372495i	$-0.878502\pi$
$113$	−430.478	+	539.803i	−0.358371	+	0.449384i	0.569663	+	0.821879i	$0.307074\pi$
$114$	−614.943	−	296.141i	−0.505216	−	0.243299i
$115$	−622.682	−	2728.15i	−0.504917	−	2.21219i
$116$	322.171			0.257869
$117$	470.869			0.372067
$118$	563.618	+	2469.37i	0.439705	+	1.92647i
$119$	−329.687	+	3.28438i	−0.253969	+	0.00253008i
$120$	418.462	−	1833.40i	0.318335	−	1.39472i
$121$	295.459	−	1294.49i	0.221983	−	0.972571i
$122$	−13.6258	+	17.0863i	−0.0101117	+	0.0126796i
$123$	1318.70	−	1653.59i	0.966690	−	1.21219i
$124$	−30.3453	+	132.951i	−0.0219765	+	0.0962854i
$125$	165.416	−	724.736i	0.118362	−	0.518579i
$126$	−178.384	+	819.080i	−0.126125	+	0.579123i
$127$	−170.896	−	748.744i	−0.119406	−	0.523152i	−0.998885	−	0.0472140i	$-0.984966\pi$
$127$	−170.896	−	748.744i	−0.119406	−	0.523152i	0.879479	−	0.475938i	$-0.157891\pi$
$128$	1682.41			1.16176
$129$	−2917.91			−1.99153
$130$	−297.938	−	1305.35i	−0.201007	−	0.880669i
$131$	970.504	+	467.370i	0.647277	+	0.311712i	0.728563	−	0.684978i	$-0.240188\pi$
$131$	970.504	+	467.370i	0.647277	+	0.311712i	−0.0812859	+	0.996691i	$0.525903\pi$
$132$	8.46706	−	10.6174i	0.00558305	−	0.00700093i
$133$	−137.159	+	629.789i	−0.0894227	+	0.410599i
$134$	1266.97	+	1588.72i	0.816785	+	1.02422i
$135$	243.818	+	1068.23i	0.155441	+	0.681030i
$136$	229.591	+	287.899i	0.144760	+	0.181523i
$137$	−843.151	−	406.040i	−0.525805	−	0.253214i	0.152098	−	0.988365i	$-0.451397\pi$
$137$	−843.151	−	406.040i	−0.525805	−	0.253214i	−0.677903	+	0.735151i	$0.737111\pi$
$138$	2437.58	−	3056.63i	1.50363	−	1.88549i
$139$	−2181.19	+	1050.40i	−1.33098	+	0.640964i	−0.957971	−	0.286865i	$-0.907387\pi$
$139$	−2181.19	+	1050.40i	−1.33098	+	0.640964i	−0.373005	+	0.927829i	$0.621673\pi$
$140$	303.863	−	3.02712i	0.183436	−	0.00182742i
$141$	2128.14	+	1024.86i	1.27107	+	0.612117i
$142$	−1957.83	+	942.840i	−1.15702	+	0.557193i
$143$	−12.5737	+	55.0890i	−0.00735291	+	0.0322152i
$144$	969.470	−	466.872i	0.561036	−	0.270181i
$145$	2412.26	+	3024.88i	1.38157	+	1.73243i
$146$	1660.61			0.941322
$147$	2221.08	−	44.2577i	1.24620	−	0.0248321i
$148$	−37.5962			−0.0208810
$149$	−1276.44	−	1600.60i	−0.701811	−	0.880043i	0.295347	−	0.955390i	$-0.404565\pi$
$149$	−1276.44	−	1600.60i	−0.701811	−	0.880043i	−0.997157	+	0.0753475i	$0.975993\pi$
$150$	−1272.95	+	613.022i	−0.692909	+	0.333687i
$151$	−117.980	+	516.906i	−0.0635835	+	0.278577i	−0.996718	−	0.0809494i	$-0.974205\pi$
$151$	−117.980	+	516.906i	−0.0635835	+	0.278577i	0.933135	+	0.359527i	$0.117062\pi$
$152$	648.590	−	312.345i	0.346103	−	0.166674i
$153$	239.756	+	115.461i	0.126687	+	0.0610093i
$154$	−91.0642	−	42.7420i	−0.0476504	−	0.0223652i
$155$	−1475.50	+	710.562i	−0.764611	+	0.368217i
$156$	148.687	−	186.448i	0.0763110	−	0.0956909i
$157$	2313.95	+	1114.34i	1.17626	+	0.566459i	0.916821	−	0.399299i	$-0.130746\pi$
$157$	2313.95	+	1114.34i	1.17626	+	0.566459i	0.259444	+	0.965758i	$0.416461\pi$
$158$	368.757	+	462.407i	0.185676	+	0.232830i
$159$	−591.588	−	2591.91i	−0.295069	−	1.29278i
$160$	−459.424	−	576.099i	−0.227004	−	0.284654i
$161$	−3342.18	−	1568.69i	−1.63603	−	0.767887i
$162$	−1716.42	+	2152.33i	−0.832439	+	1.04384i
$163$	−521.543	−	251.162i	−0.250616	−	0.120690i	0.304359	−	0.952557i	$-0.401558\pi$
$163$	−521.543	−	251.162i	−0.250616	−	0.120690i	−0.554975	+	0.831867i	$0.687272\pi$
$164$	−84.9381	−	372.138i	−0.0404424	−	0.177190i
$165$	163.084			0.0769459
$166$	3893.00			1.82022
$167$	96.4044	+	422.375i	0.0446706	+	0.195715i	0.992340	−	0.123540i	$-0.0394246\pi$
$167$	96.4044	+	422.375i	0.0446706	+	0.195715i	−0.947669	+	0.319255i	$0.896567\pi$
$168$	−1566.22	−	1924.33i	−0.719264	−	0.883723i
$169$	268.076	−	1174.52i	0.122019	−	0.534600i
$170$	168.378	−	737.713i	0.0759648	−	0.332823i
$171$	324.357	−	406.731i	0.145054	−	0.181892i
$172$	−328.335	+	411.719i	−0.145554	+	0.182519i
$173$	309.958	−	1358.01i	0.136218	−	0.596809i	−0.860029	−	0.510246i	$-0.829554\pi$
$173$	309.958	−	1358.01i	0.136218	−	0.596809i	0.996246	−	0.0865631i	$-0.0275884\pi$
$174$	−1202.82	+	5269.88i	−0.524053	+	2.29603i
$175$	842.239	+	1034.82i	0.363813	+	0.446999i
$176$	28.7334	+	125.889i	0.0123060	+	0.0539163i
$177$	−5417.65			−2.30065
$178$	−1838.99			−0.774372
$179$	−1009.14	−	4421.32i	−0.421377	−	1.84617i	−0.524370	−	0.851491i	$-0.675699\pi$
$179$	−1009.14	−	4421.32i	−0.421377	−	1.84617i	0.102993	−	0.994682i	$-0.467158\pi$
$180$	−220.976	−	106.416i	−0.0915033	−	0.0440657i
$181$	1172.81	−	1470.66i	0.481625	−	0.603939i	−0.480349	−	0.877077i	$-0.659490\pi$
$181$	1172.81	−	1470.66i	0.481625	−	0.603939i	0.961975	+	0.273138i	$0.0880616\pi$
$182$	−1599.15	−	750.578i	−0.651301	−	0.305695i
$183$	−29.1448	−	36.5464i	−0.0117729	−	0.0147628i
$184$	917.564	+	4020.11i	0.367629	+	1.61069i
$185$	−281.502	−	352.993i	−0.111873	−	0.140284i
$186$	−2061.45	−	992.741i	−0.812649	−	0.391351i
$187$	−19.9105	+	24.9669i	−0.00778608	+	0.00976344i
$188$	384.075	−	184.961i	0.148997	−	0.0717534i
$189$	1308.66	+	614.235i	0.503658	+	0.236397i
$190$	−1332.78	−	641.834i	−0.508895	−	0.245071i
$191$	1523.77	−	733.808i	0.577257	−	0.277992i	−0.122389	−	0.992482i	$-0.539055\pi$
$191$	1523.77	−	733.808i	0.577257	−	0.277992i	0.699646	+	0.714490i	$0.253341\pi$
$192$	−600.879	+	2632.62i	−0.225858	+	0.989549i
$193$	−446.929	+	215.230i	−0.166687	+	0.0802725i	−0.515367	−	0.856970i	$-0.672344\pi$
$193$	−446.929	+	215.230i	−0.166687	+	0.0802725i	0.348680	+	0.937242i	$0.386630\pi$
$194$	1256.93	+	1576.14i	0.465165	+	0.583299i
$195$	2863.86			1.05172
$196$	243.680	−	318.376i	0.0888046	−	0.116026i
$197$	210.936			0.0762870			0.0381435	−	0.999272i	$-0.487856\pi$
$197$	210.936			0.0762870			0.0381435	+	0.999272i	$0.487856\pi$
$198$	50.6229	+	63.4791i	0.0181698	+	0.0227842i
$199$	4094.70	−	1971.90i	1.45862	−	0.702434i	0.474552	−	0.880227i	$-0.342610\pi$
$199$	4094.70	−	1971.90i	1.45862	−	0.702434i	0.984068	+	0.177793i	$0.0568957\pi$
$200$	331.596	−	1452.82i	0.117237	−	0.513649i
$201$	−3916.00	+	1885.85i	−1.37420	+	0.661778i
$202$	−1095.41	−	527.523i	−0.381549	−	0.183744i
$203$	5104.34	−	50.8501i	1.76480	−	0.0175812i
$204$	121.427	−	58.4760i	0.0416743	−	0.0200693i
$205$	2858.05	−	3583.88i	0.973730	−	1.22102i
$206$	−2021.62	−	973.562i	−0.683753	−	0.329278i
$207$	1857.93	+	2329.77i	0.623840	+	0.782271i
$208$	504.578	+	2210.70i	0.168203	+	0.736945i
$209$	38.9239	+	48.8090i	0.0128824	+	0.0161540i
$210$	−1084.95	+	4981.71i	−0.356517	+	1.63700i
$211$	−3471.02	+	4352.53i	−1.13249	+	1.42010i	−0.238995	+	0.971021i	$0.576818\pi$
$211$	−3471.02	+	4352.53i	−1.13249	+	1.42010i	−0.893494	+	0.449075i	$0.851754\pi$
$212$	−432.289	−	208.179i	−0.140046	−	0.0674426i
$213$	−1034.27	−	4531.42i	−0.332708	−	1.45769i
$214$	−746.825			−0.238560
$215$	−6324.06			−2.00604
$216$	−359.282	−	1574.12i	−0.113176	−	0.495856i
$217$	−459.794	+	2111.22i	−0.143838	+	0.660455i
$218$	299.609	−	1312.67i	0.0930831	−	0.407824i
$219$	−790.380	+	3462.88i	−0.243876	+	1.06849i
$220$	18.3509	−	23.0113i	0.00562371	−	0.00705191i
$221$	−349.641	+	438.436i	−0.106423	+	0.133450i
$222$	140.365	−	614.977i	0.0424354	−	0.185921i
$223$	−869.648	+	3810.17i	−0.261148	+	1.14416i	0.658861	+	0.752264i	$0.271038\pi$
$223$	−869.648	+	3810.17i	−0.261148	+	1.14416i	−0.920009	+	0.391898i	$0.871819\pi$
$224$	−972.142	+	9.68459i	−0.289973	+	0.00288875i
$225$	−239.631	−	1049.89i	−0.0710019	−	0.311079i
$226$	−2090.64			−0.615343
$227$	869.923			0.254356			0.127178	−	0.991880i	$-0.459408\pi$
$227$	869.923			0.254356			0.127178	+	0.991880i	$0.459408\pi$
$228$	−58.6286	−	256.869i	−0.0170297	−	0.0746120i
$229$	−409.049	−	196.988i	−0.118038	−	0.0568441i	0.373933	−	0.927456i	$-0.378009\pi$
$229$	−409.049	−	196.988i	−0.118038	−	0.0568441i	−0.491971	+	0.870612i	$0.663723\pi$
$230$	5283.03	−	6624.71i	1.51458	−	1.89922i
$231$	132.473	−	169.553i	0.0377319	−	0.0482935i
$232$	−3554.62	−	4457.36i	−1.00592	−	1.26138i
$233$	−142.325	−	623.566i	−0.0400172	−	0.175327i	0.950970	−	0.309283i	$-0.100089\pi$
$233$	−142.325	−	623.566i	−0.0400172	−	0.175327i	−0.990987	+	0.133956i	$0.957232\pi$
$234$	888.972	+	1114.74i	0.248350	+	0.311421i
$235$	4612.36	+	2221.20i	1.28033	+	0.616574i
$236$	−609.617	+	764.435i	−0.168147	+	0.210850i
$237$	−1139.77	+	548.886i	−0.312389	+	0.150439i
$238$	−630.204	−	774.300i	−0.171639	−	0.210884i
$239$	4137.87	+	1992.69i	1.11990	+	0.539316i	0.899862	−	0.436175i	$-0.143667\pi$
$239$	4137.87	+	1992.69i	1.11990	+	0.539316i	0.220039	+	0.975491i	$0.429381\pi$
$240$	5896.39	−	2839.55i	1.58588	−	0.763718i
$241$	429.263	−	1880.72i	0.114735	−	0.502689i	−0.884604	−	0.466343i	$-0.845571\pi$
$241$	429.263	−	1880.72i	0.114735	−	0.502689i	0.999339	−	0.0363456i	$-0.0115717\pi$
$242$	3622.39	−	1744.45i	0.962214	−	0.463378i
$243$	−2357.28	−	2955.94i	−0.622304	−	0.780344i
$244$	−8.43621			−0.00221341
$245$	4813.80	−	95.9208i	1.25527	−	0.0250129i
$246$	6404.33			1.65986
$247$	683.529	+	857.118i	0.176081	+	0.220798i
$248$	2174.24	−	1047.06i	0.556712	−	0.268098i
$249$	−1852.91	+	8118.11i	−0.471579	+	2.06612i
$250$	2028.03	−	976.650i	0.513056	−	0.247075i
$251$	1389.25	+	669.027i	0.349357	+	0.168242i	0.600330	−	0.799753i	$-0.295036\pi$
$251$	1389.25	+	669.027i	0.349357	+	0.168242i	−0.250972	+	0.967994i	$0.580750\pi$
$252$	−290.136	+	143.300i	−0.0725273	+	0.0358217i
$253$	−322.182	+	155.155i	−0.0800609	+	0.0385553i
$254$	1449.94	−	1818.16i	0.358177	−	0.449140i
$255$	1458.22	+	702.240i	0.358106	+	0.172455i
$256$	1096.68	+	1375.20i	0.267745	+	0.335742i
$257$	−542.083	−	2375.02i	−0.131573	−	0.576458i	−0.997134	−	0.0756549i	$-0.975895\pi$
$257$	−542.083	−	2375.02i	−0.131573	−	0.576458i	0.865561	−	0.500803i	$-0.166962\pi$
$258$	−5508.83	−	6907.86i	−1.32932	−	1.66692i
$259$	−595.659	+	5.93403i	−0.142905	+	0.00142364i
$260$	322.254	−	404.094i	0.0768667	−	0.0963878i
$261$	−3712.00	−	1787.60i	−0.880333	−	0.423946i
$262$	725.800	+	3179.94i	0.171145	+	0.749836i
$263$	−1630.23			−0.382223			−0.191111	−	0.981568i	$-0.561209\pi$
$263$	−1630.23			−0.382223			−0.191111	+	0.981568i	$0.561209\pi$
$264$	−240.315			−0.0560242
$265$	−1282.16	−	5617.52i	−0.297218	−	1.30220i
$266$	−1749.91	+	864.292i	−0.403360	+	0.199222i
$267$	875.282	−	3834.86i	0.200623	−	0.878987i
$268$	−174.550	+	764.754i	−0.0397849	+	0.174309i
$269$	−3007.54	+	3771.34i	−0.681684	+	0.854805i	−0.995508	−	0.0946761i	$-0.969818\pi$
$269$	−3007.54	+	3771.34i	−0.681684	+	0.854805i	0.313824	+	0.949481i	$0.398390\pi$
$270$	−2068.63	+	2593.97i	−0.466269	+	0.584682i
$271$	−1359.56	+	5956.61i	−0.304750	+	1.33520i	0.558115	+	0.829763i	$0.311525\pi$
$271$	−1359.56	+	5956.61i	−0.304750	+	1.33520i	−0.862865	+	0.505434i	$0.831333\pi$
$272$	−285.160	+	1249.37i	−0.0635674	+	0.278507i
$273$	2326.31	−	2977.47i	0.515732	−	0.660091i
$274$	−630.558	−	2762.65i	−0.139027	−	0.609117i
$275$	129.230			0.0283378
$276$	1509.19			0.329139
$277$	1719.29	+	7532.69i	0.372931	+	1.63392i	0.718501	+	0.695526i	$0.244829\pi$
$277$	1719.29	+	7532.69i	0.372931	+	1.63392i	−0.345569	+	0.938393i	$0.612314\pi$
$278$	−6604.67	−	3180.64i	−1.42490	−	0.686194i
$279$	1087.33	−	1363.47i	0.233322	−	0.292576i
$280$	−3394.50	−	4170.66i	−0.724502	−	0.890159i
$281$	3222.89	+	4041.37i	0.684204	+	0.857965i	0.995734	−	0.0922714i	$-0.0294127\pi$
$281$	3222.89	+	4041.37i	0.684204	+	0.857965i	−0.311530	+	0.950236i	$0.600841\pi$
$282$	1591.54	+	6973.01i	0.336082	+	1.47247i
$283$	−1821.87	−	2284.55i	−0.382681	−	0.479867i	0.552764	−	0.833338i	$-0.313573\pi$
$283$	−1821.87	−	2284.55i	−0.382681	−	0.479867i	−0.935446	+	0.353470i	$0.885001\pi$
$284$	−755.767	−	363.958i	−0.157910	−	0.0760456i
$285$	1972.77	−	2473.77i	0.410023	−	0.514153i
$286$	−154.156	+	74.2376i	−0.0318722	+	0.0153488i
$287$	−1404.46	−	5882.60i	−0.288860	−	1.20989i
$288$	706.964	+	340.456i	0.144647	+	0.0696582i
$289$	4140.92	−	1994.16i	0.842850	−	0.405895i
$290$	−2606.90	+	11421.6i	−0.527870	+	2.31275i
$291$	−3884.97	+	1870.90i	−0.782615	+	0.376888i
$292$	399.678	+	501.181i	0.0801007	+	0.100443i
$293$	−4559.33			−0.909076			−0.454538	−	0.890727i	$-0.650196\pi$
$293$	−4559.33			−0.909076			−0.454538	+	0.890727i	$0.650196\pi$
$294$	4298.03	+	5174.62i	0.852606	+	1.02650i
$295$	−11741.8			−2.31741
$296$	414.812	+	520.158i	0.0814543	+	0.102141i
$297$	126.154	−	60.7524i	0.0246471	−	0.0118694i
$298$	1379.43	−	6043.67i	0.268148	−	1.17483i
$299$	−5657.73	+	2724.62i	−1.09430	+	0.526986i
$300$	−491.390	−	236.641i	−0.0945681	−	0.0455416i
$301$	−5137.03	+	6574.94i	−0.983698	+	1.25905i
$302$	−1446.46	+	696.579i	−0.275611	+	0.132727i
$303$	1621.42	−	2033.19i	0.307419	−	0.385491i
$304$	2257.15	+	1086.99i	0.425844	+	0.205076i
$305$	−63.1662	−	79.2079i	−0.0118586	−	0.0148703i
$306$	179.304	+	785.581i	0.0334971	+	0.146760i
$307$	−1184.65	−	1485.50i	−0.220232	−	0.276163i	0.659425	−	0.751770i	$-0.270800\pi$
$307$	−1184.65	−	1485.50i	−0.220232	−	0.276163i	−0.879658	+	0.475607i	$0.842228\pi$
$308$	−9.01774	−	37.7709i	−0.00166829	−	0.00698765i
$309$	2992.38	−	3752.33i	0.550908	−	0.690817i
$310$	−4467.83	−	2151.59i	−0.818566	−	0.394201i
$311$	784.563	+	3437.39i	0.143050	+	0.626742i	0.994717	+	0.102658i	$0.0327349\pi$
$311$	784.563	+	3437.39i	0.143050	+	0.626742i	−0.851667	+	0.524083i	$0.824408\pi$
$312$	−4220.10			−0.765756
$313$	9110.74			1.64527			0.822635	−	0.568570i	$-0.192503\pi$
$313$	9110.74			1.64527			0.822635	+	0.568570i	$0.192503\pi$
$314$	1730.51	+	7581.86i	0.311014	+	1.36264i
$315$	−3517.85	−	1651.14i	−0.629233	−	0.295337i
$316$	−50.8037	+	222.586i	−0.00904409	+	0.0396247i
$317$	−298.650	+	1308.47i	−0.0529143	+	0.231833i	−0.994469	−	0.105026i	$-0.966507\pi$
$317$	−298.650	+	1308.47i	−0.0529143	+	0.231833i	0.941555	+	0.336859i	$0.109365\pi$
$318$	5019.22	−	6293.90i	0.885106	−	1.10989i
$319$	308.262	−	386.548i	0.0541045	−	0.0678449i
$320$	−1302.30	+	5705.76i	−0.227503	+	0.996755i
$321$	355.457	−	1557.36i	0.0618059	−	0.270789i
$322$	−2596.12	−	10873.9i	−0.449304	−	1.88191i
$323$	137.866	+	604.032i	0.0237495	+	0.104053i
$324$	−1062.70			−0.182218
$325$	2269.37			0.387330
$326$	−390.040	−	1708.88i	−0.0662649	−	0.290325i
$327$	2594.73	+	1249.56i	0.438804	+	0.211317i
$328$	−4211.52	+	5281.08i	−0.708971	+	0.889021i
$329$	6055.93	−	2991.06i	1.01481	−	0.501223i
$330$	307.892	+	386.085i	0.0513604	+	0.0644039i
$331$	−1249.54	−	5474.61i	−0.207496	−	0.909099i	−0.966227	−	0.257694i	$-0.917037\pi$
$331$	−1249.54	−	5474.61i	−0.207496	−	0.909099i	0.758731	−	0.651404i	$-0.225820\pi$
$332$	936.975	+	1174.93i	0.154889	+	0.194225i
$333$	433.178	+	208.607i	0.0712852	+	0.0343292i
$334$	−817.925	+	1025.65i	−0.133997	+	0.168026i
$335$	−8487.25	+	4087.24i	−1.38420	+	0.666597i
$336$	1837.43	−	8436.86i	0.298334	−	1.36985i
$337$	6599.53	+	3178.17i	1.06676	+	0.513726i	0.883062	−	0.469256i	$-0.155478\pi$
$337$	6599.53	+	3178.17i	1.06676	+	0.513726i	0.183702	+	0.982982i	$0.441192\pi$
$338$	3286.66	−	1582.77i	0.528907	−	0.254708i
$339$	995.058	−	4359.63i	0.159422	−	0.698474i
$340$	263.171	−	126.737i	0.0419778	−	0.0202155i
$341$	130.483	+	163.620i	0.0207215	+	0.0259840i
$342$	1575.26			0.249065
$343$	3810.51	−	5082.68i	0.599850	−	0.800113i
$344$	9318.93			1.46059
$345$	11300.1	+	14169.8i	1.76341	+	2.21124i
$346$	3800.14	−	1830.05i	0.590454	−	0.284348i
$347$	1564.72	−	6855.47i	0.242070	−	1.06058i	−0.697059	−	0.717014i	$-0.745508\pi$
$347$	1564.72	−	6855.47i	0.242070	−	1.06058i	0.939129	−	0.343565i	$-0.111635\pi$
$348$	−1879.97	+	905.348i	−0.289590	+	0.139459i
$349$	2523.23	+	1215.12i	0.387007	+	0.186373i	0.617262	−	0.786758i	$-0.288242\pi$
$349$	2523.23	+	1215.12i	0.387007	+	0.186373i	−0.230255	+	0.973130i	$0.573956\pi$
$350$	−859.730	+	3947.59i	−0.131299	+	0.602878i
$351$	2215.34	−	1066.85i	0.336884	−	0.162235i
$352$	−58.7096	+	73.6195i	−0.00888986	+	0.0111475i
$353$	−2118.82	−	1020.37i	−0.319472	−	0.153850i	0.267274	−	0.963621i	$-0.413877\pi$
$353$	−2118.82	−	1020.37i	−0.319472	−	0.153850i	−0.586746	+	0.809771i	$0.699591\pi$
$354$	−10228.2	−	12825.7i	−1.53566	−	1.92565i
$355$	−2241.59	−	9821.07i	−0.335131	−	1.46830i
$356$	−442.611	−	555.017i	−0.0658943	−	0.0826288i
$357$	1914.60	−	945.635i	0.283842	−	0.140191i
$358$	8561.84	−	10736.2i	1.26399	−	1.58499i
$359$	−3649.67	−	1757.59i	−0.536553	−	0.258390i	0.145926	−	0.989295i	$-0.453384\pi$
$359$	−3649.67	−	1757.59i	−0.536553	−	0.258390i	−0.682479	+	0.730905i	$0.739098\pi$
$360$	965.794	+	4231.42i	0.141394	+	0.619487i
$361$	−5647.78			−0.823412
$362$	5695.82			0.826977
$363$	1913.61	+	8384.07i	0.276690	+	1.21226i
$364$	−158.358	−	663.282i	−0.0228027	−	0.0955094i
$365$	−1713.01	+	7505.19i	−0.245652	+	1.07627i
$366$	31.4964	−	137.995i	0.00449820	−	0.0197079i
$367$	−5508.39	+	6907.31i	−0.783476	+	0.982448i	0.216505	+	0.976282i	$0.430534\pi$
$367$	−5508.39	+	6907.31i	−0.783476	+	0.982448i	−0.999981	+	0.00616668i	$0.998037\pi$
$368$	−8947.17	+	11219.4i	−1.26740	+	1.58927i
$369$	−1086.21	+	4759.00i	−0.153241	+	0.671393i
$370$	304.216	−	1332.86i	0.0427444	−	0.187275i
$371$	−6881.87	−	3230.08i	−0.963043	−	0.452014i
$372$	−196.538	−	861.090i	−0.0273926	−	0.120015i
$373$	2260.81			0.313835			0.156917	−	0.987612i	$-0.449844\pi$
$373$	2260.81			0.313835			0.156917	+	0.987612i	$0.449844\pi$
$374$	−96.6964			−0.0133691
$375$	1071.36	+	4693.92i	0.147532	+	0.646381i
$376$	−6796.63	−	3273.08i	−0.932206	−	0.448927i
$377$	5413.28	−	6788.04i	0.739518	−	0.927326i
$378$	1016.54	+	4257.77i	0.138320	+	0.579354i
$379$	−2084.99	−	2614.50i	−0.282583	−	0.354348i	0.620200	−	0.784443i	$-0.287051\pi$
$379$	−2084.99	−	2614.50i	−0.282583	−	0.354348i	−0.902783	+	0.430096i	$0.858480\pi$
$380$	−127.067	−	556.718i	−0.0171537	−	0.0751553i
$381$	3101.32	+	3888.93i	0.417022	+	0.522929i
$382$	4614.00	+	2221.98i	0.617991	+	0.297609i
$383$	648.575	−	813.288i	0.0865291	−	0.108504i	−0.736682	−	0.676239i	$-0.763609\pi$
$383$	648.575	−	813.288i	0.0865291	−	0.108504i	0.823211	+	0.567735i	$0.192180\pi$
$384$	−9817.42	+	4727.82i	−1.30467	+	0.628296i
$385$	287.112	−	367.478i	0.0380067	−	0.0486452i
$386$	−1353.31	−	651.720i	−0.178450	−	0.0859369i
$387$	6067.50	−	2921.95i	0.796972	−	0.383802i
$388$	−173.167	+	758.694i	−0.0226578	+	0.0992703i
$389$	8242.59	−	3969.42i	1.07433	−	0.517372i	0.188833	−	0.982009i	$-0.439529\pi$
$389$	8242.59	−	3969.42i	1.07433	−	0.517372i	0.885501	+	0.464637i	$0.153815\pi$
$390$	5406.80	+	6779.91i	0.702010	+	0.880293i
$391$	−3548.89			−0.459015
$392$	−7093.45	+	141.346i	−0.913963	+	0.0182118i
$393$	−6976.59			−0.895477
$394$	398.233	+	499.369i	0.0509206	+	0.0638524i
$395$	−2470.26	+	1189.61i	−0.314664	+	0.151534i
$396$	−6.97432	+	30.5565i	−0.000885033	+	0.00387758i
$397$	7843.72	−	3777.33i	0.991599	−	0.477529i	0.133520	−	0.991046i	$-0.457372\pi$
$397$	7843.72	−	3777.33i	0.991599	−	0.477529i	0.858079	+	0.513517i	$0.171658\pi$
$398$	12398.8	+	5970.95i	1.56155	+	0.752002i
$399$	−969.430	−	4060.47i	−0.121635	−	0.509468i
$400$	4672.39	−	2250.11i	0.584049	−	0.281263i
$401$	3191.00	−	4001.39i	0.397384	−	0.498304i	−0.542377	−	0.840135i	$-0.682476\pi$
$401$	3191.00	−	4001.39i	0.397384	−	0.498304i	0.939761	+	0.341831i	$0.111047\pi$
$402$	−11857.7	−	5710.37i	−1.47117	−	0.708476i
$403$	2291.37	+	2873.28i	0.283229	+	0.355157i
$404$	−104.437	−	457.566i	−0.0128612	−	0.0563484i
$405$	−7956.95	−	9977.70i	−0.976256	−	1.22419i
$406$	9757.07	+	11988.0i	1.19270	+	1.46541i
$407$	−35.9731	+	45.1088i	−0.00438113	+	0.00549376i
$408$	−2148.78	−	1034.80i	−0.260736	−	0.125564i
$409$	−195.271	−	855.539i	−0.0236077	−	0.103432i	0.961751	−	0.273924i	$-0.0883215\pi$
$409$	−195.271	−	855.539i	−0.0236077	−	0.103432i	−0.985359	+	0.170492i	$0.945464\pi$
$410$	13880.3			1.67195
$411$	6061.10			0.727426
$412$	−192.741	−	844.455i	−0.0230478	−	0.100979i
$413$	−9537.86	+	12207.6i	−1.13639	+	1.45447i
$414$	−2007.84	+	8796.91i	−0.238357	+	1.04431i
$415$	−4015.85	+	17594.6i	−0.475013	+	2.08117i
$416$	−1030.98	+	1292.81i	−0.121509	+	0.152368i
$417$	9776.15	−	12258.9i	1.14806	−	1.43962i
$418$	−42.0645	+	184.297i	−0.00492211	+	0.0215652i
$419$	1519.21	−	6656.09i	0.177132	−	0.776065i	−0.805814	−	0.592169i	$-0.798272\pi$
$419$	1519.21	−	6656.09i	0.177132	−	0.776065i	0.982946	−	0.183896i	$-0.0588711\pi$
$420$	−1764.63	+	871.563i	−0.205013	+	0.101257i
$421$	−1302.16	−	5705.14i	−0.150744	−	0.660455i	−0.992670	−	0.120860i	$-0.961435\pi$
$421$	−1302.16	−	5705.14i	−0.150744	−	0.660455i	0.841925	−	0.539595i	$-0.181422\pi$
$422$	−16857.2			−1.94454
$423$	−5451.52			−0.626624
$424$	1889.35	+	8277.80i	0.216404	+	0.948126i
$425$	1155.51	+	556.466i	0.131884	+	0.0635120i
$426$	8775.05	−	11003.6i	0.998011	−	1.25147i
$427$	−133.660	+	1.33154i	−0.0151481	+	0.000150908i
$428$	−179.747	−	225.396i	−0.0203000	−	0.0254554i
$429$	−81.4365	−	356.797i	−0.00916501	−	0.0401546i
$430$	−11939.4	−	14971.6i	−1.33900	−	1.67906i
$431$	1289.29	+	620.892i	0.144091	+	0.0693905i	0.504540	−	0.863388i	$-0.331662\pi$
$431$	1289.29	+	620.892i	0.144091	+	0.0693905i	−0.360449	+	0.932779i	$0.617376\pi$
$432$	3503.36	−	4393.07i	0.390174	−	0.489263i
$433$	−5359.96	+	2581.22i	−0.594881	+	0.286479i	−0.706998	−	0.707216i	$-0.749951\pi$
$433$	−5359.96	+	2581.22i	−0.594881	+	0.286479i	0.112117	+	0.993695i	$0.464237\pi$
$434$	−5866.15	+	2897.33i	−0.648812	+	0.320452i
$435$	−22576.7	−	10872.4i	−2.48843	−	1.19837i
$436$	468.283	−	225.513i	0.0514373	−	0.0247709i
$437$	−1543.82	+	6763.93i	−0.168996	+	0.740418i
$438$	−9690.21	+	4666.56i	−1.05711	+	0.509079i
$439$	−3444.79	−	4319.62i	−0.374512	−	0.469623i	0.558481	−	0.829517i	$-0.311384\pi$
$439$	−3444.79	−	4319.62i	−0.374512	−	0.469623i	−0.932993	+	0.359894i	$0.882813\pi$
$440$	−520.841			−0.0564321
$441$	−4574.19	+	2316.18i	−0.493919	+	0.250101i
$442$	−1698.05			−0.182733
$443$	2537.14	+	3181.47i	0.272106	+	0.341211i	0.899044	−	0.437859i	$-0.144263\pi$
$443$	2537.14	+	3181.47i	0.272106	+	0.341211i	−0.626937	+	0.779070i	$0.715692\pi$
$444$	219.387	−	105.651i	0.0234496	−	0.0112927i
$445$	1897.02	−	8311.39i	0.202084	−	0.885388i
$446$	−10662.0	+	5134.57i	−1.13198	+	0.545132i
$447$	11946.4	+	5753.06i	1.26408	+	0.608748i
$448$	4874.24	+	5988.74i	0.514032	+	0.631565i
$449$	7445.13	−	3585.39i	0.782533	−	0.376848i	0.000432243	−	1.00000i	$-0.499862\pi$
$449$	7445.13	−	3585.39i	0.782533	−	0.376848i	0.782101	+	0.623152i	$0.214148\pi$
$450$	2033.11	−	2549.44i	0.212981	−	0.267070i
$451$	−527.771	−	254.161i	−0.0551037	−	0.0265365i
$452$	−503.180	−	630.967i	−0.0523619	−	0.0656597i
$453$	−764.127	−	3347.86i	−0.0792535	−	0.347232i
$454$	1642.36	+	2059.46i	0.169779	+	0.212897i
$455$	5041.88	−	6453.16i	0.519488	−	0.664898i
$456$	−2907.00	+	3645.27i	−0.298537	+	0.374354i
$457$	−8602.51	−	4142.75i	−0.880544	−	0.424048i	−0.0617208	−	0.998093i	$-0.519659\pi$
$457$	−8602.51	−	4142.75i	−0.880544	−	0.424048i	−0.818823	+	0.574046i	$0.805373\pi$
$458$	−305.911	−	1340.28i	−0.0312102	−	0.136741i
$459$	1389.60			0.141310
$460$	3270.90			0.331536
$461$	586.352	+	2568.98i	0.0592389	+	0.259543i	0.995872	−	0.0907695i	$-0.0289326\pi$
$461$	586.352	+	2568.98i	0.0592389	+	0.259543i	−0.936633	+	0.350312i	$0.886076\pi$
$462$	651.501	−	6.49033i	0.0656073	−	0.000653588i
$463$	−2191.34	+	9600.87i	−0.219957	+	0.963694i	0.737552	+	0.675290i	$0.235982\pi$
$463$	−2191.34	+	9600.87i	−0.219957	+	0.963694i	−0.957509	+	0.288404i	$0.906875\pi$
$464$	4414.95	−	19343.2i	0.441722	−	1.93531i
$465$	6613.23	−	8292.73i	0.659529	−	0.827024i
$466$	1207.53	−	1514.19i	0.120038	−	0.150523i
$467$	−317.813	+	1392.43i	−0.0314917	+	0.137974i	−0.988230	−	0.152976i	$-0.951114\pi$
$467$	−317.813	+	1392.43i	−0.0314917	+	0.137974i	0.956738	+	0.290950i	$0.0939714\pi$
$468$	−122.474	+	536.593i	−0.0120969	+	0.0530000i
$469$	−2644.79	+	12144.0i	−0.260395	+	1.19564i
$470$	3449.40	+	15112.8i	0.338529	+	1.48319i
$471$	−16634.1			−1.62731
$472$	17302.4			1.68730
$473$	179.830	+	787.888i	0.0174812	+	0.0765901i
$474$	−3451.25	−	1662.03i	−0.334433	−	0.161054i
$475$	1563.25	−	1960.26i	0.151004	−	0.189353i
$476$	82.0093	−	376.559i	0.00789683	−	0.0362595i
$477$	3825.65	+	4797.22i	0.367221	+	0.460481i
$478$	3094.54	+	13558.1i	0.296111	+	1.29735i
$479$	−9478.98	−	11886.3i	−0.904187	−	1.13381i	−0.990495	−	0.137546i	$-0.956078\pi$
$479$	−9478.98	−	11886.3i	−0.904187	−	1.13381i	0.0863085	−	0.996268i	$-0.472493\pi$
$480$	4299.81	+	2070.68i	0.408872	+	0.196903i
$481$	−631.711	+	792.141i	−0.0598827	+	0.0750905i
$482$	5262.84	−	2534.45i	0.497336	−	0.239504i
$483$	23911.0	−	238.204i	2.25256	−	0.0224403i
$484$	1398.33	+	673.399i	0.131323	+	0.0632418i
$485$	−8420.00	+	4054.86i	−0.788315	+	0.379632i
$486$	2547.48	−	11161.3i	0.237770	−	1.04174i
$487$	−5089.24	+	2450.85i	−0.473543	+	0.228046i	−0.655405	−	0.755278i	$-0.727502\pi$
$487$	−5089.24	+	2450.85i	−0.473543	+	0.228046i	0.181862	+	0.983324i	$0.441788\pi$
$488$	93.0796	+	116.718i	0.00863426	+	0.0108270i
$489$	3749.18			0.346715
$490$	9315.23	+	11215.1i	0.858815	+	1.03397i
$491$	2873.85			0.264144			0.132072	−	0.991240i	$-0.457837\pi$
$491$	2873.85			0.264144			0.132072	+	0.991240i	$0.457837\pi$
$492$	1541.41	+	1932.86i	0.141244	+	0.177114i
$493$	4420.80	−	2128.94i	0.403860	−	0.194489i
$494$	−738.681	+	3236.37i	−0.0672770	+	0.294760i
$495$	−339.117	+	163.310i	−0.0307922	+	0.0148288i
$496$	7566.57	+	3643.87i	0.684978	+	0.329868i
$497$	−12031.5	−	5647.12i	−1.08589	−	0.509674i
$498$	−22717.0	+	10939.9i	−2.04412	+	0.984396i
$499$	10527.8	−	13201.5i	0.944469	−	1.18433i	−0.0382587	−	0.999268i	$-0.512181\pi$
$499$	10527.8	−	13201.5i	0.944469	−	1.18433i	0.982728	−	0.185059i	$-0.0592475\pi$
$500$	782.869	+	377.010i	0.0700219	+	0.0337208i
$501$	−1749.49	−	2193.79i	−0.156011	−	0.195631i
$502$	1038.96	+	4551.99i	0.0923728	+	0.404712i
$503$	7307.20	+	9162.93i	0.647737	+	0.812237i	0.991947	−	0.126656i	$-0.0404245\pi$
$503$	7307.20	+	9162.93i	0.647737	+	0.812237i	−0.344210	+	0.938893i	$0.611853\pi$
$504$	5183.79	+	2433.07i	0.458143	+	0.215035i
$505$	3514.14	−	4406.59i	0.309658	−	0.388298i
$506$	−975.572	−	469.811i	−0.0857104	−	0.0412760i
$507$	1736.25	+	7607.03i	0.152090	+	0.666351i
$508$	897.704			0.0784039
$509$	−15726.4			−1.36947			−0.684734	−	0.728793i	$-0.740082\pi$
$509$	−15726.4			−1.36947			−0.684734	+	0.728793i	$0.740082\pi$
$510$	1090.54	+	4777.97i	0.0946861	+	0.414847i
$511$	6411.44	+	7877.42i	0.555040	+	0.681950i
$512$	1809.80	−	7929.25i	0.156216	−	0.684427i
$513$	604.499	−	2648.48i	0.0520259	−	0.227940i
$514$	4599.20	−	5767.22i	0.394673	−	0.494905i
$515$	6485.47	−	8132.52i	0.554920	−	0.695848i
$516$	758.953	−	3325.19i	0.0647501	−	0.283689i
$517$	145.573	−	637.796i	0.0123835	−	0.0542558i
$518$	−1138.62	−	1398.96i	−0.0965790	−	0.118662i
$519$	2007.51	+	8795.49i	0.169788	+	0.743891i
$520$	−9146.33			−0.771332
$521$	20419.7			1.71709			0.858544	−	0.512741i	$-0.171370\pi$
$521$	20419.7			1.71709			0.858544	+	0.512741i	$0.171370\pi$
$522$	−2776.05	−	12162.7i	−0.232767	−	1.01982i
$523$	−81.5459	−	39.2704i	−0.00681788	−	0.00328332i	0.430472	−	0.902604i	$-0.358347\pi$
$523$	−81.5459	−	39.2704i	−0.00681788	−	0.00328332i	−0.437290	+	0.899321i	$0.644062\pi$
$524$	−785.035	+	984.402i	−0.0654473	+	0.0820684i
$525$	−7822.73	−	3671.68i	−0.650309	−	0.305229i
$526$	−3077.78	−	3859.41i	−0.255128	−	0.319921i
$527$	462.164	+	2024.87i	0.0382015	+	0.167371i
$528$	−521.437	−	653.861i	−0.0429784	−	0.0538933i
$529$	−24842.7	−	11963.6i	−2.04181	−	0.983284i
$530$	10878.3	−	13640.9i	0.891551	−	1.11797i
$531$	11265.5	−	5425.16i	0.920677	−	0.443375i
$532$	−682.019	−	320.113i	−0.0555814	−	0.0260877i
$533$	−9268.01	−	4463.24i	−0.753175	−	0.362710i
$534$	10731.1	−	5167.83i	0.869627	−	0.418790i
$535$	770.392	−	3375.31i	0.0622560	−	0.272761i
$536$	12506.5	−	6022.83i	1.00784	−	0.485348i
$537$	18313.2	+	22964.0i	1.47164	+	1.84538i
$538$	−14606.3			−1.17049
$539$	−148.835	−	597.003i	−0.0118938	−	0.0477082i
$540$	−1280.76			−0.102065
$541$	−11930.9	−	14960.9i	−0.948154	−	1.18895i	−0.981878	−	0.189516i	$-0.939308\pi$
$541$	−11930.9	−	14960.9i	−0.948154	−	1.18895i	0.0337242	−	0.999431i	$-0.489263\pi$
$542$	−16668.4	+	8027.10i	−1.32098	+	0.636150i
$543$	−2710.97	+	11877.5i	−0.214252	+	0.938699i
$544$	−841.958	+	405.465i	−0.0663578	+	0.0319562i
$545$	5623.62	+	2708.19i	0.441999	+	0.212856i
$546$	11440.8	−	113.975i	0.896742	−	0.00893345i
$547$	9591.88	−	4619.21i	0.749761	−	0.361066i	−0.0196609	−	0.999807i	$-0.506259\pi$
$547$	9591.88	−	4619.21i	0.749761	−	0.361066i	0.769422	+	0.638741i	$0.220544\pi$
$548$	682.020	−	855.226i	0.0531651	−	0.0666669i
$549$	97.2006	+	46.8093i	0.00755632	+	0.00363893i
$550$	243.979	+	305.940i	0.0189151	+	0.0237188i
$551$	−2134.50	−	9351.85i	−0.165032	−	0.723053i
$552$	−16651.4	−	20880.2i	−1.28393	−	1.61000i
$553$	−769.781	+	3534.57i	−0.0591943	+	0.271800i
$554$	−14587.0	+	18291.5i	−1.11867	+	1.40276i
$555$	2634.62	+	1268.77i	0.201502	+	0.0970381i
$556$	−629.688	−	2758.84i	−0.0480301	−	0.210434i
$557$	−3131.20			−0.238192			−0.119096	−	0.992883i	$-0.538000\pi$
$557$	−3131.20			−0.238192			−0.119096	+	0.992883i	$0.538000\pi$
$558$	5280.69			0.400626
$559$	3157.94	+	13835.8i	0.238939	+	1.04686i
$560$	3982.31	−	18285.4i	0.300506	−	1.37982i
$561$	46.0234	−	201.642i	0.00346365	−	0.0151753i
$562$	−3482.93	+	15259.7i	−0.261421	+	1.14536i
$563$	−12576.5	+	15770.4i	−0.941450	+	1.18054i	0.0419556	+	0.999119i	$0.486641\pi$
$563$	−12576.5	+	15770.4i	−0.941450	+	1.18054i	−0.983405	+	0.181421i	$0.941930\pi$
$564$	−1721.44	+	2158.61i	−0.128520	+	0.161160i
$565$	2156.62	−	9448.75i	0.160583	−	0.703561i
$566$	1968.87	−	8626.17i	0.146215	−	0.640610i
$567$	−16836.9	+	167.731i	−1.24706	+	0.0124234i
$568$	3303.14	+	14472.0i	0.244008	+	1.06907i
$569$	−1181.07			−0.0870180			−0.0435090	−	0.999053i	$-0.513854\pi$
$569$	−1181.07			−0.0870180			−0.0435090	+	0.999053i	$0.513854\pi$
$570$	9580.87			0.704032
$571$	341.655	+	1496.89i	0.0250400	+	0.109707i	0.985904	−	0.167315i	$-0.0535096\pi$
$571$	341.655	+	1496.89i	0.0250400	+	0.109707i	−0.960864	+	0.277022i	$0.910652\pi$
$572$	−59.5078	−	28.6575i	−0.00434991	−	0.00209481i
$573$	−6829.59	+	8564.03i	−0.497923	+	0.624376i
$574$	11274.9	−	14430.9i	0.819872	−	1.04936i
$575$	8954.35	+	11228.4i	0.649430	+	0.814359i
$576$	−1386.80	−	6075.99i	−0.100319	−	0.439525i
$577$	7192.90	+	9019.61i	0.518968	+	0.650765i	0.970389	−	0.241546i	$-0.0776544\pi$
$577$	7192.90	+	9019.61i	0.518968	+	0.650765i	−0.451422	+	0.892311i	$0.649083\pi$
$578$	12538.8	+	6038.36i	0.902326	+	0.434537i
$579$	2003.15	−	2511.87i	0.143779	−	0.180294i
$580$	−4074.52	+	1962.18i	−0.291699	+	0.140475i
$581$	15030.5	+	18467.2i	1.07327	+	1.31867i
$582$	−11763.8	−	5665.13i	−0.837841	−	0.403483i
$583$	−663.404	+	319.478i	−0.0471276	+	0.0226954i
$584$	2524.24	−	11059.4i	0.178859	−	0.783632i
$585$	−5955.12	+	2867.83i	−0.420878	+	0.202684i
$586$	−8607.74	−	10793.8i	−0.606796	−	0.760898i
$587$	5318.47			0.373964			0.186982	−	0.982363i	$-0.440129\pi$
$587$	5318.47			0.373964			0.186982	+	0.982363i	$0.440129\pi$
$588$	−527.270	+	2542.60i	−0.0369800	+	0.178325i
$589$	4060.31			0.284044
$590$	−22167.8	−	27797.6i	−1.54684	−	1.93967i
$591$	−1230.88	+	592.760i	−0.0856711	+	0.0412570i
$592$	−515.210	+	2257.28i	−0.0357686	+	0.156712i
$593$	1847.83	−	889.867i	0.127962	−	0.0616230i	−0.368808	−	0.929506i	$-0.620234\pi$
$593$	1847.83	−	889.867i	0.127962	−	0.0616230i	0.496769	+	0.867883i	$0.334520\pi$
$594$	381.995	+	183.959i	0.0263863	+	0.0127070i
$595$	4149.57	−	2049.50i	0.285909	−	0.141212i
$596$	2156.01	−	1038.28i	0.148178	−	0.0713585i
$597$	−18352.6	+	23013.4i	−1.25816	+	1.57768i
$598$	−17131.7	−	8250.19i	−1.17152	−	0.564173i
$599$	3886.33	+	4873.30i	0.265093	+	0.332417i	0.896507	−	0.443030i	$-0.146096\pi$
$599$	3886.33	+	4873.30i	0.265093	+	0.332417i	−0.631414	+	0.775446i	$0.717525\pi$
$600$	2147.66	+	9409.51i	0.146130	+	0.640236i
$601$	−7435.09	−	9323.31i	−0.504632	−	0.632788i	0.462635	−	0.886549i	$-0.346904\pi$
$601$	−7435.09	−	9323.31i	−0.504632	−	0.632788i	−0.967267	+	0.253760i	$0.918333\pi$
$602$	−25263.9	+	251.682i	−1.71043	+	0.0170395i
$603$	6254.46	−	7842.85i	0.422390	−	0.529661i
$604$	−558.368	−	268.896i	−0.0376154	−	0.0181146i
$605$	4147.42	+	18171.0i	0.278705	+	1.22109i
$606$	7874.51			0.527855
$607$	20453.8			1.36770			0.683851	−	0.729622i	$-0.260304\pi$
$607$	20453.8			1.36770			0.683851	+	0.729622i	$0.260304\pi$
$608$	406.524	+	1781.10i	0.0271163	+	0.118804i
$609$	−29642.6	+	14640.7i	−1.97238	+	0.974172i
$610$	68.2629	−	299.079i	0.00453096	−	0.0198514i
$611$	2556.36	−	11200.1i	0.169262	−	0.741586i
$612$	−193.937	+	243.190i	−0.0128096	+	0.0160627i
$613$	−12454.3	+	15617.2i	−0.820595	+	1.02899i	0.178390	+	0.983960i	$0.442911\pi$
$613$	−12454.3	+	15617.2i	−0.820595	+	1.02899i	−0.998985	+	0.0450339i	$0.985660\pi$
$614$	1280.23	−	5609.06i	0.0841465	−	0.368670i
$615$	−6606.43	+	28944.6i	−0.433165	+	1.89782i
$616$	−423.079	+	541.503i	−0.0276726	+	0.0354185i
$617$	277.670	+	1216.55i	0.0181176	+	0.0793785i	0.983179	−	0.182647i	$-0.0584666\pi$
$617$	277.670	+	1216.55i	0.0181176	+	0.0793785i	−0.965061	+	0.262026i	$0.915609\pi$
$618$	14532.7			0.945940
$619$	−20732.2			−1.34620			−0.673100	−	0.739551i	$-0.735038\pi$
$619$	−20732.2			−1.34620			−0.673100	+	0.739551i	$0.735038\pi$
$620$	−425.962	−	1866.26i	−0.0275920	−	0.120889i
$621$	14019.7	+	6751.55i	0.905946	+	0.436281i
$622$	−6656.48	+	8346.96i	−0.429100	+	0.538075i
$623$	−7100.15	−	8723.60i	−0.456600	−	0.561001i
$624$	−9156.78	−	11482.2i	−0.587443	−	0.736630i
$625$	4325.85	+	18952.8i	0.276854	+	1.21298i
$626$	17200.5	+	21568.7i	1.09820	+	1.37709i
$627$	−364.294	−	175.435i	−0.0232033	−	0.0111741i
$628$	−1871.74	+	2347.09i	−0.118934	+	0.149139i
$629$	−515.892	+	248.441i	−0.0327026	+	0.0157488i
$630$	−2732.57	−	11445.4i	−0.172807	−	0.723803i
$631$	5121.70	+	2466.48i	0.323125	+	0.155609i	0.588413	−	0.808560i	$-0.299753\pi$
$631$	5121.70	+	2466.48i	0.323125	+	0.155609i	−0.265288	+	0.964169i	$0.585467\pi$
$632$	3640.09	−	1752.98i	0.229106	−	0.110332i
$633$	8023.33	−	35152.5i	0.503790	−	2.20725i
$634$	−3661.50	+	1763.29i	−0.229364	+	0.110456i
$635$	6721.57	+	8428.58i	0.420059	+	0.526737i
$636$	3107.56			0.193747
$637$	−2613.64	−	10483.8i	−0.162569	−	0.652091i
$638$	1497.09			0.0929004
$639$	6688.35	+	8386.93i	0.414064	+	0.519220i
$640$	−21277.6	+	10246.7i	−1.31417	+	0.632871i
$641$	6192.30	−	27130.2i	0.381562	−	1.67173i	−0.311028	−	0.950401i	$-0.600673\pi$
$641$	6192.30	−	27130.2i	0.381562	−	1.67173i	0.692590	−	0.721331i	$-0.256470\pi$
$642$	4357.97	−	2098.69i	0.267906	−	0.129017i
$643$	−24619.6	−	11856.2i	−1.50996	−	0.727158i	−0.518199	−	0.855260i	$-0.673397\pi$
$643$	−24619.6	−	11856.2i	−1.50996	−	0.727158i	−0.991761	+	0.128102i	$0.959112\pi$
$644$	2656.95	−	3400.66i	0.162575	−	0.208082i
$645$	36903.0	−	17771.6i	2.25280	−	1.08489i
$646$	−1169.70	+	1466.76i	−0.0712404	+	0.0893326i
$647$	−4391.59	−	2114.88i	−0.266849	−	0.128508i	0.295675	−	0.955288i	$-0.404455\pi$
$647$	−4391.59	−	2114.88i	−0.266849	−	0.128508i	−0.562524	+	0.826781i	$0.690170\pi$
$648$	11725.1	+	14702.8i	0.710810	+	0.891328i
$649$	333.889	+	1462.86i	0.0201946	+	0.0884783i
$650$	4284.43	+	5372.51i	0.258537	+	0.324196i
$651$	−3249.78	−	13611.7i	−0.195651	−	0.819487i
$652$	421.873	−	529.012i	0.0253402	−	0.0317756i
$653$	9007.89	+	4337.97i	0.539826	+	0.259966i	0.683869	−	0.729605i	$-0.260296\pi$
$653$	9007.89	+	4337.97i	0.539826	+	0.259966i	−0.144043	+	0.989571i	$0.546010\pi$
$654$	1940.49	+	8501.84i	0.116023	+	0.508331i
$655$	−15120.6			−0.901998
$656$	−23507.2			−1.39909
$657$	−1824.16	−	7992.18i	−0.108322	−	0.474589i
$658$	18514.2	+	8689.86i	1.09690	+	0.514842i
$659$	4689.88	−	20547.7i	0.277226	−	1.21460i	−0.624059	−	0.781377i	$-0.714518\pi$
$659$	4689.88	−	20547.7i	0.277226	−	1.21460i	0.901285	−	0.433227i	$-0.142625\pi$
$660$	−42.4184	+	185.847i	−0.00250172	+	0.0109607i
$661$	−3847.30	+	4824.36i	−0.226388	+	0.283882i	−0.882033	−	0.471188i	$-0.843825\pi$
$661$	−3847.30	+	4824.36i	−0.226388	+	0.283882i	0.655645	+	0.755069i	$0.272397\pi$
$662$	10601.5	−	13293.9i	0.622416	−	0.780486i
$663$	808.202	−	3540.96i	0.0473423	−	0.207420i
$664$	5917.62	−	25926.8i	0.345856	−	1.51529i
$665$	−2101.07	−	8800.35i	−0.122520	−	0.513178i
$666$	323.955	+	1419.34i	0.0188484	+	0.0825801i
$667$	54945.3			3.18964
$668$	−506.405			−0.0293314
$669$	−5632.47	−	24677.5i	−0.325507	−	1.42614i
$670$	−25699.5	−	12376.2i	−1.48188	−	0.713636i
$671$	−8.07199	+	10.1220i	−0.000464405	+	0.000582345i
$672$	5645.55	−	2788.37i	0.324080	−	0.160065i
$673$	−5069.35	−	6356.76i	−0.290355	−	0.364094i	0.615164	−	0.788399i	$-0.289090\pi$
$673$	−5069.35	−	6356.76i	−0.290355	−	0.364094i	−0.905519	+	0.424305i	$0.860518\pi$
$674$	4935.52	+	21623.9i	0.282061	+	1.23579i
$675$	−3506.17	−	4396.59i	−0.199930	−	0.250704i
$676$	1268.73	+	610.987i	0.0721852	+	0.0347626i
$677$	−7258.04	+	9101.29i	−0.412037	+	0.516678i	−0.943935	−	0.330130i	$-0.892907\pi$
$677$	−7258.04	+	9101.29i	−0.412037	+	0.516678i	0.531898	+	0.846808i	$0.321479\pi$
$678$	12199.6	−	5875.02i	0.691037	−	0.332786i
$679$	−2623.84	+	12047.8i	−0.148297	+	0.680929i
$680$	−4657.11	−	2242.74i	−0.262635	−	0.126478i
$681$	−5076.29	+	2444.61i	−0.285644	+	0.137559i
$682$	−141.011	+	617.810i	−0.00791729	+	0.0346879i
$683$	15997.3	−	7703.88i	0.896220	−	0.431597i	0.0716978	−	0.997426i	$-0.477158\pi$
$683$	15997.3	−	7703.88i	0.896220	−	0.431597i	0.824522	+	0.565830i	$0.191444\pi$
$684$	379.137	+	475.422i	0.0211939	+	0.0265764i
$685$	13136.4			0.732723
$686$	19226.7	−	574.769i	1.07009	−	0.0319895i
$687$	2940.50			0.163300
$688$	20220.2	+	25355.4i	1.12048	+	1.40504i
$689$	−11649.8	+	5610.26i	−0.644155	+	0.310209i
$690$	−12211.8	+	53503.5i	−0.673763	+	2.95195i
$691$	−20733.7	+	9984.82i	−1.14146	+	0.549697i	−0.906457	−	0.422298i	$-0.861224\pi$
$691$	−20733.7	+	9984.82i	−1.14146	+	0.549697i	−0.235001	+	0.971995i	$0.575509\pi$
$692$	1466.94	+	706.443i	0.0805851	+	0.0388077i
$693$	−105.675	+	485.226i	−0.00579261	+	0.0265977i
$694$	19183.7	−	9238.39i	1.04929	−	0.505309i
$695$	21188.1	−	26569.0i	1.15642	−	1.45010i
$696$	33268.2	+	16021.1i	1.81182	+	0.872528i
$697$	−3624.65	−	4545.16i	−0.196977	−	0.247002i
$698$	1887.02	+	8267.56i	0.102328	+	0.448326i
$699$	2582.82	+	3238.76i	0.139759	+	0.175252i
$700$	−1398.32	+	690.641i	−0.0755024	+	0.0372911i
$701$	21734.7	−	27254.4i	1.17105	−	1.46845i	0.316877	−	0.948467i	$-0.397366\pi$
$701$	21734.7	−	27254.4i	1.17105	−	1.46845i	0.854175	−	0.519986i	$-0.174063\pi$
$702$	6708.09	+	3230.45i	0.360656	+	0.173683i
$703$	249.089	+	1091.33i	0.0133635	+	0.0585495i
$704$	747.888			0.0400385
$705$	−33156.6			−1.77127
$706$	−1584.58	−	6942.50i	−0.0844709	−	0.370091i
$707$	−1726.87	−	7233.01i	−0.0918608	−	0.384760i
$708$	1409.14	−	6173.84i	0.0748004	−	0.327722i
$709$	268.160	−	1174.88i	0.0142044	−	0.0622337i	−0.967329	−	0.253524i	$-0.918410\pi$
$709$	268.160	−	1174.88i	0.0142044	−	0.0622337i	0.981533	+	0.191291i	$0.0612673\pi$
$710$	19018.4	−	23848.3i	1.00528	−	1.26058i
$711$	1820.40	−	2282.70i	0.0960199	−	0.120405i
$712$	−2795.39	+	12247.4i	−0.147137	+	0.644649i
$713$	−5175.29	+	22674.4i	−0.271832	+	1.19097i
$714$	5853.35	+	2747.33i	0.306801	+	0.144000i
$715$	−176.499	−	773.295i	−0.00923176	−	0.0404470i
$716$	5300.92			0.276683
$717$	−29745.6			−1.54933
$718$	−2729.44	−	11958.5i	−0.141869	−	0.621567i
$719$	24290.3	+	11697.6i	1.25991	+	0.606741i	0.940151	−	0.340757i	$-0.110683\pi$
$719$	24290.3	+	11697.6i	1.25991	+	0.606741i	0.319760	+	0.947499i	$0.396398\pi$
$720$	−9417.46	+	11809.1i	−0.487456	+	0.611250i
$721$	−3187.00	−	13348.8i	−0.164619	−	0.689507i
$722$	−10662.7	−	13370.6i	−0.549617	−	0.689198i
$723$	2780.22	+	12180.9i	0.143012	+	0.626575i
$724$	1370.88	+	1719.03i	0.0703706	+	0.0882420i
$725$	−17890.1	−	8615.43i	−0.916445	−	0.441337i
$726$	−16235.7	+	20358.9i	−0.829976	+	1.04076i
$727$	17330.5	−	8345.92i	0.884116	−	0.425768i	0.0639896	−	0.997951i	$-0.479618\pi$
$727$	17330.5	−	8345.92i	0.884116	−	0.425768i	0.820126	+	0.572183i	$0.193903\pi$
$728$	−7429.54	+	9509.16i	−0.378238	+	0.484111i
$729$	−54.0516	−	26.0299i	−0.00274611	−	0.00132246i
$730$	−21001.8	+	10114.0i	−1.06481	+	0.512786i
$731$	−1784.69	+	7819.25i	−0.0903000	+	0.395630i
$732$	49.2281	−	23.7070i	0.00248569	−	0.00119704i
$733$	−9688.63	−	12149.2i	−0.488209	−	0.612195i	0.475315	−	0.879816i	$-0.342334\pi$
$733$	−9688.63	−	12149.2i	−0.488209	−	0.612195i	−0.963524	+	0.267620i	$0.913763\pi$
$734$	−26751.9			−1.34527
$735$	−27820.6	+	14087.2i	−1.39616	+	0.706959i
$736$	−10464.5			−0.524087
$737$	750.554	+	941.165i	0.0375129	+	0.0470397i
$738$	−13317.2	+	6413.21i	−0.664243	+	0.319883i
$739$	−83.1264	+	364.201i	−0.00413783	+	0.0181290i	−0.976955	−	0.213447i	$-0.931531\pi$
$739$	−83.1264	+	364.201i	−0.00413783	+	0.0181290i	0.972817	+	0.231576i	$0.0743881\pi$
$740$	475.482	−	228.980i	0.0236204	−	0.0113750i
$741$	−6397.25	−	3080.75i	−0.317151	−	0.152732i
$742$	−5345.65	−	22390.3i	−0.264481	−	1.10778i
$743$	−13286.2	+	6398.28i	−0.656019	+	0.315922i	−0.732118	−	0.681178i	$-0.761468\pi$
$743$	−13286.2	+	6398.28i	−0.656019	+	0.315922i	0.0760985	+	0.997100i	$0.475754\pi$
$744$	−9745.03	+	12219.9i	−0.480202	+	0.602154i
$745$	25891.7	+	12468.8i	1.27328	+	0.613181i
$746$	4268.27	+	5352.24i	0.209481	+	0.262680i
$747$	−4276.43	−	18736.3i	−0.209460	−	0.917702i
$748$	−23.2731	−	29.1835i	−0.00113763	−	0.00142654i
$749$	−2883.42	−	3542.71i	−0.140665	−	0.172827i
$750$	−9089.72	+	11398.1i	−0.442546	+	0.554935i
$751$	−23431.5	−	11284.0i	−1.13852	−	0.548282i	−0.232954	−	0.972488i	$-0.574839\pi$
$751$	−23431.5	−	11284.0i	−1.13852	−	0.548282i	−0.905566	+	0.424205i	$0.860553\pi$
$752$	−5841.78	−	25594.5i	−0.283282	−	1.24114i
$753$	−9986.80			−0.483319
$754$	26289.9			1.26979
$755$	−1656.11	−	7255.90i	−0.0798306	−	0.349761i
$756$	−1040.36	+	1331.56i	−0.0500494	+	0.0640588i
$757$	−3611.43	+	15822.7i	−0.173394	+	0.759690i	0.811190	+	0.584782i	$0.198820\pi$
$757$	−3611.43	+	15822.7i	−0.173394	+	0.759690i	−0.984585	+	0.174908i	$0.944037\pi$
$758$	2253.23	−	9872.02i	0.107969	−	0.473045i
$759$	1444.03	−	1810.76i	0.0690580	−	0.0865960i
$760$	−6300.43	+	7900.49i	−0.300711	+	0.377080i
$761$	−5857.72	+	25664.4i	−0.279030	+	1.22251i	0.619991	+	0.784609i	$0.287136\pi$
$761$	−5857.72	+	25664.4i	−0.279030	+	1.22251i	−0.899022	+	0.437904i	$0.855721\pi$
$762$	−3351.55	+	14684.1i	−0.159336	+	0.698096i
$763$	7383.68	−	3646.85i	0.350337	−	0.173034i
$764$	439.898	+	1927.32i	0.0208311	+	0.0912670i
$765$	−3735.43			−0.176542
$766$	3149.85			0.148575
$767$	5863.31	+	25688.9i	0.276026	+	1.20935i
$768$	−10264.0	−	4942.90i	−0.482254	−	0.232241i
$769$	10067.3	−	12623.9i	0.472087	−	0.591978i	−0.487594	−	0.873070i	$-0.662125\pi$
$769$	10067.3	−	12623.9i	0.472087	−	0.591978i	0.959681	+	0.281093i	$0.0906968\pi$
$770$	1412.02	−	14.0667i	0.0660851	−	0.000658348i
$771$	9837.39	+	12335.7i	0.459513	+	0.576212i
$772$	−129.024	−	565.293i	−0.00601514	−	0.0263541i
$773$	11301.9	+	14172.1i	0.525874	+	0.659425i	0.971845	−	0.235623i	$-0.0757129\pi$
$773$	11301.9	+	14172.1i	0.525874	+	0.659425i	−0.445971	+	0.895048i	$0.647141\pi$
$774$	18372.5	+	8847.72i	0.853211	+	0.410885i
$775$	5240.43	−	6571.29i	0.242893	−	0.304578i
$776$	12407.4	−	5975.11i	0.573970	−	0.276410i
$777$	3459.19	−	1708.52i	0.159714	−	0.0788838i
$778$	24958.7	+	12019.5i	1.15015	+	0.553881i
$779$	−10239.5	+	4931.10i	−0.470949	+	0.226797i
$780$	−744.896	+	3263.60i	−0.0341943	+	0.149815i
$781$	−1159.82	+	558.541i	−0.0531392	+	0.0255905i
$782$	−6700.08	−	8401.63i	−0.306387	−	0.384197i
$783$	−21514.4			−0.981942
$784$	−15776.0	−	18993.5i	−0.718658	−	0.865229i
$785$	−36051.6			−1.63916
$786$	−13171.4	−	16516.4i	−0.597719	−	0.749516i
$787$	2018.11	−	971.871i	0.0914078	−	0.0440197i	−0.387621	−	0.921819i	$-0.626703\pi$
$787$	2018.11	−	971.871i	0.0914078	−	0.0440197i	0.479029	+	0.877799i	$0.340989\pi$
$788$	−54.8647	+	240.378i	−0.00248030	+	0.0108669i
$789$	9512.95	−	4581.20i	0.429240	−	0.206711i
$790$	−7479.99	−	3602.17i	−0.336868	−	0.162227i
$791$	−8071.76	−	9917.37i	−0.362830	−	0.445791i
$792$	499.711	−	240.648i	0.0224198	−	0.0107968i
$793$	−141.750	+	177.748i	−0.00634763	+	0.00795968i
$794$	23750.9	+	11437.8i	1.06157	+	0.511226i
$795$	23267.9	+	29177.1i	1.03802	+	1.30164i
$796$	1182.10	+	5179.13i	0.0526363	+	0.230615i
$797$	−14041.9	−	17608.0i	−0.624077	−	0.782568i	0.364835	−	0.931072i	$-0.381126\pi$
$797$	−14041.9	−	17608.0i	−0.624077	−	0.782568i	−0.988912	+	0.148504i	$0.952554\pi$
$798$	7782.52	−	9960.93i	0.345236	−	0.441871i
$799$	4047.99	−	5076.02i	0.179234	−	0.224752i
$800$	3407.24	+	1640.84i	0.150580	+	0.0725156i
$801$	2020.11	+	8850.69i	0.0891101	+	0.390417i
$802$	15497.3			0.682331
$803$	983.750			0.0432326
$804$	−1130.51	−	4953.10i	−0.0495897	−	0.217267i
$805$	51822.8	−	516.266i	2.26896	−	0.0226037i
$806$	−2476.25	+	10849.2i	−0.108216	+	0.474126i
$807$	6951.99	−	30458.6i	0.303249	−	1.32862i
$808$	−5178.32	+	6493.41i	−0.225461	+	0.282719i
$809$	−10191.3	+	12779.5i	−0.442901	+	0.555381i	−0.952305	−	0.305147i	$-0.901295\pi$
$809$	−10191.3	+	12779.5i	−0.442901	+	0.555381i	0.509404	+	0.860528i	$0.329866\pi$
$810$	8598.97	−	37674.5i	0.373008	−	1.63426i
$811$	7039.63	−	30842.6i	0.304803	−	1.33543i	−0.557981	−	0.829854i	$-0.688424\pi$
$811$	7039.63	−	30842.6i	0.304803	−	1.33543i	0.862783	−	0.505574i	$-0.168719\pi$
$812$	−1269.70	+	5830.03i	−0.0548741	+	0.251963i
$813$	−8805.49	−	38579.4i	−0.379855	−	1.66425i
$814$	−174.705			−0.00752263
$815$	8125.70			0.349240
$816$	−1846.90	−	8091.81i	−0.0792335	−	0.347144i
$817$	14126.6	+	6803.00i	0.604928	+	0.291318i
$818$	1656.74	−	2077.49i	0.0708149	−	0.0887991i
$819$	−1855.73	+	8520.89i	−0.0791752	+	0.363546i
$820$	3340.73	+	4189.14i	0.142272	+	0.178404i
$821$	−3605.22	−	15795.5i	−0.153256	−	0.671457i	−0.991926	−	0.126818i	$-0.959524\pi$
$821$	−3605.22	−	15795.5i	−0.153256	−	0.671457i	0.838670	−	0.544639i	$-0.183333\pi$
$822$	11443.0	+	14349.0i	0.485547	+	0.608857i
$823$	−9449.77	−	4550.77i	−0.400241	−	0.192746i	0.222925	−	0.974836i	$-0.428440\pi$
$823$	−9449.77	−	4550.77i	−0.400241	−	0.192746i	−0.623166	+	0.782090i	$0.714154\pi$
$824$	−9556.77	+	11983.8i	−0.404036	+	0.506646i
$825$	−754.102	+	363.156i	−0.0318236	+	0.0153254i
$826$	−46907.2	+	467.295i	−1.97592	+	0.0196844i
$827$	27675.7	+	13327.9i	1.16370	+	0.560407i	0.913121	−	0.407690i	$-0.133665\pi$
$827$	27675.7	+	13327.9i	1.16370	+	0.560407i	0.250577	+	0.968097i	$0.419380\pi$
$828$	−3138.20	+	1511.28i	−0.131715	+	0.0634307i
$829$	−3821.00	+	16740.9i	−0.160083	+	0.701370i	0.829631	+	0.558312i	$0.188551\pi$
$829$	−3821.00	+	16740.9i	−0.160083	+	0.701370i	−0.989714	+	0.143058i	$0.954306\pi$
$830$	−49235.1	+	23710.4i	−2.05901	+	0.991565i
$831$	−31200.6	−	39124.3i	−1.30245	−	1.63322i
$832$	13133.4			0.547259
$833$	1239.89	−	5978.99i	0.0515721	−	0.248691i
$834$	47478.5			1.97128
$835$	−3791.71	−	4754.66i	−0.157147	−	0.197056i
$836$	−65.7458	+	31.6615i	−0.00271994	+	0.00130985i
$837$	2026.44	−	8878.41i	0.0836845	−	0.366646i
$838$	18625.8	−	8969.71i	0.767801	−	0.369754i
$839$	−10141.6	−	4883.92i	−0.417313	−	0.200968i	0.213431	−	0.976958i	$-0.431536\pi$
$839$	−10141.6	−	4883.92i	−0.417313	−	0.200968i	−0.630745	+	0.775991i	$0.717250\pi$
$840$	31528.2	+	14798.1i	1.29503	+	0.607837i
$841$	−46470.8	+	22379.2i	−1.90540	+	0.917592i
$842$	11047.9	−	13853.7i	0.452182	−	0.567018i
$843$	−30163.5	−	14526.0i	−1.23237	−	0.593477i
$844$	−4057.23	−	5087.60i	−0.165469	−	0.207491i
$845$	3763.03	+	16486.9i	0.153198	+	0.671203i
$846$	−10292.1	−	12905.9i	−0.418263	−	0.524485i
$847$	22260.8	+	10448.3i	0.903058	+	0.423860i
$848$	−18423.1	+	23101.8i	−0.746052	+	0.935519i
$849$	17051.1	+	8211.39i	0.689273	+	0.331936i
$850$	864.161	+	3786.14i	0.0348711	+	0.152780i
$851$	−6411.92			−0.258282
$852$	5432.93			0.218461
$853$	1227.72	+	5378.98i	0.0492805	+	0.215912i	0.993573	−	0.113197i	$-0.0361090\pi$
$853$	1227.72	+	5378.98i	0.0492805	+	0.215912i	−0.944292	+	0.329108i	$0.893252\pi$
$854$	−255.494	−	313.912i	−0.0102375	−	0.0125783i
$855$	−1624.97	+	7119.46i	−0.0649974	+	0.284772i
$856$	−1135.22	+	4973.74i	−0.0453284	+	0.198597i
$857$	−5075.90	+	6364.98i	−0.202321	+	0.253703i	−0.872633	−	0.488377i	$-0.837589\pi$
$857$	−5075.90	+	6364.98i	−0.202321	+	0.253703i	0.670311	+	0.742080i	$0.266161\pi$
$858$	690.933	−	866.402i	0.0274919	−	0.0344738i
$859$	−4874.43	+	21356.3i	−0.193613	+	0.848274i	0.781027	+	0.624497i	$0.214696\pi$
$859$	−4874.43	+	21356.3i	−0.193613	+	0.848274i	−0.974640	+	0.223777i	$0.928161\pi$
$860$	1644.90	−	7206.77i	0.0652216	−	0.285754i
$861$	24726.5	+	30380.2i	0.978718	+	1.20250i
$862$	964.210	+	4224.48i	0.0380988	+	0.166922i
$863$	16547.6			0.652709			0.326355	−	0.945247i	$-0.394180\pi$
$863$	16547.6			0.652709			0.326355	+	0.945247i	$0.394180\pi$
$864$	4097.49			0.161342
$865$	4350.94	+	19062.7i	0.171025	+	0.749308i
$866$	−16230.1	−	7815.98i	−0.636859	−	0.306695i
$867$	−18559.8	+	23273.2i	−0.727016	+	0.911649i
$868$	−2286.31	−	1073.10i	−0.0894035	−	0.0419625i
$869$	218.453	+	273.931i	0.00852762	+	0.0106933i
$870$	−16884.2	−	73974.3i	−0.657961	−	2.88272i
$871$	13180.2	+	16527.5i	0.512739	+	0.642954i
$872$	−8286.78	−	3990.70i	−0.321819	−	0.154980i
$873$	6204.91	−	7780.71i	0.240555	−	0.301646i
$874$	−18927.6	+	9115.03i	−0.732533	+	0.352769i
$875$	12463.0	+	5849.62i	0.481514	+	0.226004i
$876$	−3740.65	−	1801.40i	−0.144275	−	0.0694791i
$877$	−21184.9	+	10202.1i	−0.815694	+	0.392817i	−0.794730	−	0.606963i	$-0.792388\pi$
$877$	−21184.9	+	10202.1i	−0.815694	+	0.392817i	−0.0209636	+	0.999780i	$0.506673\pi$
$878$	3722.73	−	16310.4i	0.143094	−	0.626934i
$879$	26605.2	−	12812.4i	1.02090	−	0.491640i
$880$	−1130.12	−	1417.13i	−0.0432914	−	0.0542857i
$881$	27427.3			1.04886			0.524431	−	0.851453i	$-0.324278\pi$
$881$	27427.3			1.04886			0.524431	+	0.851453i	$0.324278\pi$
$882$	−14119.1	−	6456.11i	−0.539019	−	0.246472i
$883$	−32964.4			−1.25633			−0.628166	−	0.778080i	$-0.716194\pi$
$883$	−32964.4			−1.25633			−0.628166	+	0.778080i	$0.716194\pi$
$884$	−408.691	−	512.482i	−0.0155495	−	0.0194984i
$885$	68517.4	−	32996.3i	2.60247	−	1.25328i
$886$	−2741.85	+	12012.8i	−0.103967	+	0.455507i
$887$	17108.2	−	8238.90i	0.647620	−	0.311877i	−0.0810830	−	0.996707i	$-0.525838\pi$
$887$	17108.2	−	8238.90i	0.647620	−	0.311877i	0.728703	+	0.684830i	$0.240124\pi$
$888$	−3882.29	−	1869.61i	−0.146713	−	0.0706532i
$889$	14222.8	−	141.690i	0.536579	−	0.00534547i
$890$	23257.8	−	11200.4i	0.875960	−	0.421840i
$891$	−1016.82	+	1275.05i	−0.0382319	+	0.0479413i
$892$	−4115.80	−	1982.06i	−0.154492	−	0.0743996i
$893$	−7913.60	−	9923.34i	−0.296549	−	0.371861i
$894$	8934.18	+	39143.2i	0.334232	+	1.46437i
$895$	39690.7	+	49770.6i	1.48236	+	1.85882i
$896$	−6630.51	+	30445.0i	−0.247221	+	1.13515i
$897$	25358.2	−	31798.1i	0.943906	−	1.18362i
$898$	22544.0	+	10856.6i	0.837753	+	0.403441i
$899$	−7155.40	−	31349.8i	−0.265457	−	1.16304i
$900$	1258.76			0.0466209
$901$	−7307.50			−0.270198
$902$	−394.698	−	1729.28i	−0.0145698	−	0.0638347i
$903$	11499.7	−	52802.7i	0.423794	−	1.94592i
$904$	−3177.92	+	13923.4i	−0.116920	+	0.512261i
$905$	−5875.55	+	25742.5i	−0.215812	+	0.945535i
$906$	6483.09	−	8129.54i	0.237733	−	0.298108i
$907$	16307.0	−	20448.3i	0.596983	−	0.748594i	−0.387921	−	0.921693i	$-0.626807\pi$
$907$	16307.0	−	20448.3i	0.596983	−	0.748594i	0.984904	+	0.173099i	$0.0553781\pi$
$908$	−226.268	+	991.346i	−0.00826980	+	0.0362324i
$909$	−1335.56	+	5851.48i	−0.0487324	+	0.213511i
$910$	24795.9	−	247.020i	0.903272	−	0.00899851i
$911$	11449.1	+	50161.9i	0.416385	+	1.82430i	0.552380	+	0.833592i	$0.313720\pi$
$911$	11449.1	+	50161.9i	0.416385	+	1.82430i	−0.135995	+	0.990709i	$0.543423\pi$
$912$	−16225.8			−0.589135
$913$	2306.23			0.0835981
$914$	−6433.46	−	28186.8i	−0.232823	−	1.02006i
$915$	591.182	+	284.698i	0.0213594	+	0.0102862i
$916$	330.877	−	414.907i	0.0119350	−	0.0149661i
$917$	−12282.4	+	15720.4i	−0.442312	+	0.566121i
$918$	2623.48	+	3289.74i	0.0943223	+	0.118276i
$919$	−1014.33	−	4444.05i	−0.0364086	−	0.159517i	0.953456	−	0.301533i	$-0.0974985\pi$
$919$	−1014.33	−	4444.05i	−0.0364086	−	0.159517i	−0.989864	+	0.142017i	$0.954641\pi$
$920$	−36089.0	−	45254.2i	−1.29328	−	1.62172i
$921$	11087.3	+	5339.35i	0.396676	+	0.191029i
$922$	−4974.80	+	6238.20i	−0.177697	+	0.222824i
$923$	−20367.3	+	9808.36i	−0.726324	+	0.349779i
$924$	158.763	+	195.064i	0.00565252	+	0.00694496i
$925$	2087.72	+	1005.39i	0.0742094	+	0.0357374i
$926$	−26866.2	+	12938.1i	−0.953432	+	0.459149i
$927$	−2464.83	+	10799.1i	−0.0873307	+	0.382621i
$928$	13035.5	−	6277.57i	0.461112	−	0.222060i
$929$	9595.50	+	12032.4i	0.338878	+	0.424940i	0.921847	−	0.387555i	$-0.126680\pi$
$929$	9595.50	+	12032.4i	0.338878	+	0.424940i	−0.582968	+	0.812495i	$0.698109\pi$
$930$	32117.5			1.13245
$931$	−10856.2	−	4964.09i	−0.382166	−	0.174749i
$932$	747.621			0.0262759
$933$	−14237.8	−	17853.6i	−0.499597	−	0.626474i
$934$	−3896.44	+	1876.43i	−0.136505	+	0.0657373i
$935$	99.7477	−	437.023i	0.00348888	−	0.0152858i
$936$	8775.26	−	4225.94i	0.306441	−	0.147574i
$937$	−9906.38	−	4770.66i	−0.345387	−	0.166329i	0.253146	−	0.967428i	$-0.418535\pi$
$937$	−9906.38	−	4770.66i	−0.345387	−	0.166329i	−0.598532	+	0.801099i	$0.704249\pi$
$938$	−33742.9	+	16665.8i	−1.17457	+	0.580126i
$939$	−53164.2	+	25602.5i	−1.84765	+	0.889783i
$940$	−3730.91	+	4678.42i	−0.129456	+	0.162333i
$941$	−19398.7	−	9341.93i	−0.672030	−	0.323633i	0.0665649	−	0.997782i	$-0.478796\pi$
$941$	−19398.7	−	9341.93i	−0.672030	−	0.323633i	−0.738595	+	0.674150i	$0.764510\pi$
$942$	−31404.2	−	39379.7i	−1.08620	−	1.36206i
$943$	−14485.9	−	63467.0i	−0.500241	−	2.19170i
$944$	37542.7	+	47077.1i	1.29440	+	1.62312i
$945$	−20291.8	+	202.149i	−0.698509	+	0.00695863i
$946$	−1525.74	+	1913.21i	−0.0524376	+	0.0657547i
$947$	40481.5	+	19494.9i	1.38909	+	0.668952i	0.970918	−	0.239414i	$-0.0769553\pi$
$947$	40481.5	+	19494.9i	1.38909	+	0.668952i	0.418176	+	0.908366i	$0.362670\pi$
$948$	−329.042	−	1441.63i	−0.0112730	−	0.0493902i
$949$	17275.3			0.590917
$950$	7592.03			0.259282
$951$	−1934.27	−	8474.60i	−0.0659549	−	0.288967i
$952$	−6114.67	+	3020.07i	−0.208170	+	0.102816i
$953$	3496.21	−	15317.9i	0.118839	−	0.520666i	−0.880108	−	0.474774i	$-0.842530\pi$
$953$	3496.21	−	15317.9i	0.118839	−	0.520666i	0.998946	−	0.0458921i	$-0.0146130\pi$
$954$	−4134.33	+	18113.7i	−0.140308	+	0.614730i
$955$	−14801.9	+	18561.0i	−0.501549	+	0.628923i
$956$	−3347.09	+	4197.12i	−0.113235	+	0.141992i
$957$	−712.552	+	3121.90i	−0.0240685	+	0.105451i
$958$	10243.8	−	44881.0i	0.345472	−	1.51361i
$959$	10670.7	−	13657.5i	0.359305	−	0.459879i
$960$	−8434.66	−	36954.6i	−0.283570	−	1.24240i
$961$	−16179.8			−0.543110
$962$	−3067.95			−0.102822
$963$	820.380	+	3594.32i	0.0274521	+	0.120276i
$964$	2031.58	+	978.358i	0.0678764	+	0.0326875i
$965$	4341.49	−	5444.05i	0.144826	−	0.181606i
$966$	45706.3	+	56157.1i	1.52234	+	1.87042i
$967$	−5846.96	−	7331.85i	−0.194442	−	0.243823i	0.675047	−	0.737775i	$-0.264123\pi$
$967$	−5846.96	−	7331.85i	−0.194442	−	0.243823i	−0.869489	+	0.493952i	$0.835552\pi$
$968$	−6111.50	−	26776.2i	−0.202925	−	0.889070i
$969$	−2501.91	−	3137.30i	−0.0829443	−	0.104009i
$970$	−25495.9	−	12278.2i	−0.843942	−	0.406421i
$971$	1381.56	−	1732.43i	0.0456606	−	0.0572566i	−0.758477	−	0.651700i	$-0.774056\pi$
$971$	1381.56	−	1732.43i	0.0456606	−	0.0572566i	0.804137	+	0.594443i	$0.202628\pi$
$972$	3981.66	−	1917.47i	0.131391	−	0.0632744i
$973$	−10412.0	−	43610.6i	−0.343055	−	1.43689i
$974$	−15410.3	−	7421.21i	−0.506959	−	0.244138i
$975$	−13242.5	+	6377.27i	−0.434975	+	0.209473i
$976$	−115.608	+	506.511i	−0.00379151	+	0.0166117i
$977$	−39242.7	+	18898.3i	−1.28504	+	0.618844i	−0.946681	−	0.322173i	$-0.895587\pi$
$977$	−39242.7	+	18898.3i	−1.28504	+	0.618844i	−0.338361	+	0.941016i	$0.609872\pi$
$978$	7078.22	+	8875.80i	0.231428	+	0.290201i
$979$	−1089.42			−0.0355650
$980$	−1142.77	+	5510.65i	−0.0372493	+	0.179624i
$981$	−6646.76			−0.216325
$982$	5425.64	+	6803.54i	0.176313	+	0.221089i
$983$	17033.0	−	8202.68i	0.552665	−	0.266149i	−0.136640	−	0.990621i	$-0.543630\pi$
$983$	17033.0	−	8202.68i	0.552665	−	0.266149i	0.689305	+	0.724471i	$0.257916\pi$
$984$	9735.01	−	42651.9i	0.315387	−	1.38180i
$985$	−2667.72	+	1284.70i	−0.0862949	+	0.0415574i
$986$	13386.3	+	6446.48i	0.432358	+	0.208213i
$987$	−26933.0	+	34471.9i	−0.868579	+	1.11170i
$988$	−1154.54	+	555.998i	−0.0371770	+	0.0179035i
$989$	−55996.6	+	70217.5i	−1.80039	+	2.25762i
$990$	−1026.85	−	494.505i	−0.0329651	−	0.0158752i
$991$	16413.1	+	20581.4i	0.526114	+	0.659726i	0.971895	−	0.235416i	$-0.0756454\pi$
$991$	16413.1	+	20581.4i	0.526114	+	0.659726i	−0.445781	+	0.895142i	$0.647074\pi$
$992$	1362.77	+	5970.70i	0.0436170	+	0.191099i
$993$	22676.0	+	28434.7i	0.724672	+	0.908710i
$994$	−9345.76	−	39144.8i	−0.298219	−	1.24909i
$995$	−39776.0	+	49877.6i	−1.26732	+	1.58917i
$996$	−8769.28	−	4223.06i	−0.278981	−	0.134350i
$997$	−5120.57	−	22434.7i	−0.162658	−	0.712652i	−0.988807	−	0.149200i	$-0.952330\pi$
$997$	−5120.57	−	22434.7i	−0.162658	−	0.712652i	0.826149	−	0.563452i	$-0.190527\pi$
$998$	51129.0			1.62170
$999$	2510.65			0.0795131

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.4.e.a.8.10	✓	78
49.22	even	7		2401.4.a.d.1.28		39
49.27	odd	14		2401.4.a.c.1.28		39
49.43	even	7	inner	49.4.e.a.43.10	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.4.e.a.8.10	✓	78	1.1	even	1	trivial
49.4.e.a.43.10	yes	78	49.43	even	7	inner
2401.4.a.c.1.28		39	49.27	odd	14
2401.4.a.d.1.28		39	49.22	even	7

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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	49.e (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.88794 + 2.36740i) q^{2} +(-5.83533 + 2.81015i) q^{3} +(-0.260101 + 1.13958i) q^{4} +(-12.6471 + 6.09051i) q^{5} +(-17.6695 - 8.50917i) q^{6} +(-3.94107 + 18.0961i) q^{7} +(18.6363 - 8.97477i) q^{8} +(9.31994 - 11.6868i) q^{9} +(-38.2955 - 18.4422i) q^{10} +(1.11842 + 1.40245i) q^{11} +(-1.68461 - 7.38074i) q^{12} +(19.6402 + 24.6280i) q^{13} +(-50.2811 + 24.8342i) q^{14} +(56.6846 - 71.0802i) q^{15} +(64.8561 + 31.2330i) q^{16} +(3.96139 + 17.3560i) q^{17} +45.2629 q^{18} +34.8025 q^{19} +(-3.65109 - 15.9965i) q^{20} +(-27.8552 - 116.672i) q^{21} +(-1.20866 + 5.29549i) q^{22} +(-44.3595 + 194.352i) q^{23} +(-83.5285 + 104.741i) q^{24} +(44.9178 - 56.3251i) q^{25} +(-21.2249 + 92.9924i) q^{26} +(17.3694 - 76.1004i) q^{27} +(-19.5968 - 9.19798i) q^{28} +(-61.3317 - 268.712i) q^{29} +275.292 q^{30} +116.667 q^{31} +(11.6809 + 51.1772i) q^{32} +(-10.4675 - 5.04086i) q^{33} +(-33.6097 + 42.1452i) q^{34} +(-60.3712 - 252.865i) q^{35} +(10.8939 + 13.6606i) q^{36} +(7.15720 + 31.3578i) q^{37} +(65.7050 + 82.3915i) q^{38} +(-183.816 - 88.5209i) q^{39} +(-181.034 + 227.009i) q^{40} +(-294.218 + 141.688i) q^{41} +(223.619 - 286.213i) q^{42} +(405.907 + 195.474i) q^{43} +(-1.88911 + 0.909748i) q^{44} +(-46.6911 + 204.567i) q^{45} +(-543.856 + 261.907i) q^{46} +(-227.386 - 285.133i) q^{47} -466.226 q^{48} +(-311.936 - 142.636i) q^{49} +218.146 q^{50} +(-71.8889 - 90.1458i) q^{51} +(-33.1741 + 15.9758i) q^{52} +(-91.3405 + 400.189i) q^{53} +(212.952 - 102.552i) q^{54} +(-22.6864 - 10.9252i) q^{55} +(88.9610 + 372.614i) q^{56} +(-203.084 + 97.8002i) q^{57} +(520.358 - 652.508i) q^{58} +(753.642 + 362.935i) q^{59} +(66.2578 + 83.0847i) q^{60} +(1.60600 + 7.03636i) q^{61} +(220.260 + 276.198i) q^{62} +(174.755 + 214.713i) q^{63} +(259.950 - 325.967i) q^{64} +(-398.388 - 191.854i) q^{65} +(-7.82818 - 34.2975i) q^{66} +671.084 q^{67} -20.8089 q^{68} +(-287.304 - 1258.76i) q^{69} +(484.656 - 620.317i) q^{70} +(-159.690 + 699.647i) q^{71} +(68.8025 - 301.444i) q^{72} +(341.931 - 428.768i) q^{73} +(-60.7240 + 76.1455i) q^{74} +(-103.828 + 454.901i) q^{75} +(-9.05219 + 39.6602i) q^{76} +(-29.7867 + 14.7118i) q^{77} +(-137.468 - 602.287i) q^{78} +195.323 q^{79} -1010.46 q^{80} +(202.306 + 886.359i) q^{81} +(-890.898 - 429.034i) q^{82} +(801.597 - 1005.17i) q^{83} +(140.202 - 1.39671i) q^{84} +(-155.807 - 195.375i) q^{85} +(303.561 + 1329.99i) q^{86} +(1113.01 + 1395.67i) q^{87} +(33.4299 + 16.0990i) q^{88} +(-378.661 + 474.826i) q^{89} +(-572.442 + 275.674i) q^{90} +(-523.075 + 258.350i) q^{91} +(-209.941 - 101.102i) q^{92} +(-680.791 + 327.852i) q^{93} +(245.733 - 1076.63i) q^{94} +(-440.150 + 211.965i) q^{95} +(-211.977 - 265.811i) q^{96} +665.767 q^{97} +(-251.239 - 1007.76i) q^{98} +26.8139 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9} + 9 q^{10} - 103 q^{11} + 364 q^{12} - 35 q^{13} + 161 q^{14} - 245 q^{15} - 205 q^{16} - 285 q^{17} + 16 q^{18} + 628 q^{19}+ \cdots + 10768 q^{99}+O(q^{100}) \) 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9 + 9 * q^10 - 103 * q^11 + 364 * q^12 - 35 * q^13 + 161 * q^14 - 245 * q^15 - 205 * q^16 - 285 * q^17 + 16 * q^18 + 628 * q^19 + 553 * q^20 - 21 * q^21 - 605 * q^22 + 149 * q^23 + 653 * q^24 - 370 * q^25 - 511 * q^26 - 65 * q^27 + 70 * q^28 - 187 * q^29 + 84 * q^30 + 1276 * q^31 + 1399 * q^32 - 23 * q^33 - 765 * q^34 - 805 * q^35 - 1691 * q^36 - 1531 * q^37 - 1041 * q^38 - 1351 * q^39 - 1759 * q^40 - 301 * q^41 + 3395 * q^42 - 257 * q^43 - 883 * q^44 + 3105 * q^45 + 1593 * q^46 + 733 * q^47 - 1948 * q^48 + 1288 * q^49 + 6148 * q^50 + 1197 * q^51 - 1099 * q^52 - 285 * q^53 + 660 * q^54 + 2641 * q^55 - 1988 * q^56 - 2352 * q^57 + 1173 * q^58 - 3603 * q^59 - 175 * q^60 - 2613 * q^61 - 1927 * q^62 - 3066 * q^63 + 1589 * q^64 - 371 * q^65 - 2175 * q^66 + 352 * q^67 + 6076 * q^68 + 5549 * q^69 - 6293 * q^70 - 2623 * q^71 + 6220 * q^72 + 2039 * q^73 - 2411 * q^74 - 3903 * q^75 + 4130 * q^76 + 1029 * q^77 - 3759 * q^78 + 44 * q^79 - 1608 * q^80 + 1394 * q^81 - 10920 * q^82 - 553 * q^83 - 7798 * q^84 + 497 * q^85 - 2985 * q^86 - 4273 * q^87 - 2197 * q^88 - 3957 * q^89 - 2958 * q^90 + 14119 * q^91 - 9136 * q^92 + 6272 * q^93 + 14912 * q^94 + 5866 * q^95 + 21882 * q^96 - 1540 * q^97 - 2303 * q^98 + 10768 * q^99

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