LMFDB - Embedded newform 49.4.e.a.8.2

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			8.2
Character	$\chi$	$=$	49.8
Dual form			49.4.e.a.43.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.77071 - 3.47436i) q^{2} +(-6.15987 + 2.96643i) q^{3} +(-2.61419 + 11.4535i) q^{4} +(1.98451 - 0.955692i) q^{5} +(27.3737 + 13.1825i) q^{6} +(18.5202 - 0.0393741i) q^{7} +(15.0065 - 7.22673i) q^{8} +(12.3100 - 15.4362i) q^{9} +(-8.81894 - 4.24698i) q^{10} +(-2.32728 - 2.91832i) q^{11} +(-17.8730 - 78.3069i) q^{12} +(55.9871 + 70.2055i) q^{13} +(-51.4510 - 64.2369i) q^{14} +(-9.38934 + 11.7739i) q^{15} +(17.9902 + 8.66363i) q^{16} +(12.4417 + 54.5106i) q^{17} -87.7385 q^{18} -27.6480 q^{19} +(5.75813 + 25.2280i) q^{20} +(-113.965 + 55.1816i) q^{21} +(-3.69107 + 16.1716i) q^{22} +(-12.4090 + 54.3675i) q^{23} +(-71.0001 + 89.0313i) q^{24} +(-74.9113 + 93.9358i) q^{25} +(88.7956 - 389.039i) q^{26} +(11.0395 - 48.3672i) q^{27} +(-47.9644 + 212.224i) q^{28} +(-22.1528 - 97.0578i) q^{29} +66.9219 q^{30} +99.2310 q^{31} +(-49.3954 - 216.415i) q^{32} +(22.9927 + 11.0727i) q^{33} +(154.917 - 194.260i) q^{34} +(36.7160 - 17.7778i) q^{35} +(144.618 + 181.346i) q^{36} +(79.7800 + 349.539i) q^{37} +(76.6048 + 96.0594i) q^{38} +(-553.133 - 266.375i) q^{39} +(22.8740 - 28.6831i) q^{40} +(300.534 - 144.730i) q^{41} +(507.486 + 243.065i) q^{42} +(-383.629 - 184.746i) q^{43} +(39.5089 - 19.0265i) q^{44} +(9.67706 - 42.3980i) q^{45} +(223.274 - 107.523i) q^{46} +(301.391 + 377.932i) q^{47} -136.517 q^{48} +(342.997 - 1.45843i) q^{49} +533.925 q^{50} +(-238.341 - 298.870i) q^{51} +(-950.461 + 457.718i) q^{52} +(-90.7653 + 397.669i) q^{53} +(-198.632 + 95.6563i) q^{54} +(-7.40754 - 3.56728i) q^{55} +(277.638 - 134.431i) q^{56} +(170.308 - 82.0161i) q^{57} +(-275.835 + 345.886i) q^{58} +(-515.719 - 248.357i) q^{59} +(-110.307 - 138.320i) q^{60} +(34.2558 + 150.085i) q^{61} +(-274.941 - 344.765i) q^{62} +(227.376 - 286.367i) q^{63} +(-515.449 + 646.352i) q^{64} +(178.202 + 85.8176i) q^{65} +(-25.2356 - 110.564i) q^{66} +370.306 q^{67} -656.862 q^{68} +(-84.8397 - 371.707i) q^{69} +(-163.496 - 78.3077i) q^{70} +(86.0611 - 377.058i) q^{71} +(73.1757 - 320.604i) q^{72} +(422.856 - 530.245i) q^{73} +(993.378 - 1245.66i) q^{74} +(182.789 - 800.851i) q^{75} +(72.2772 - 316.667i) q^{76} +(-43.2167 - 53.9563i) q^{77} +(607.090 + 2659.83i) q^{78} -677.093 q^{79} +43.9816 q^{80} +(194.098 + 850.397i) q^{81} +(-1335.54 - 643.160i) q^{82} +(-494.014 + 619.474i) q^{83} +(-334.096 - 1449.56i) q^{84} +(76.7860 + 96.2866i) q^{85} +(421.051 + 1844.75i) q^{86} +(424.374 + 532.148i) q^{87} +(-56.0141 - 26.9750i) q^{88} +(-80.1989 + 100.566i) q^{89} +(-174.118 + 83.8510i) q^{90} +(1039.66 + 1298.02i) q^{91} +(-590.259 - 284.254i) q^{92} +(-611.249 + 294.362i) q^{93} +(478.006 - 2094.28i) q^{94} +(-54.8679 + 26.4230i) q^{95} +(946.251 + 1186.56i) q^{96} +430.011 q^{97} +(-955.413 - 1187.66i) q^{98} -73.6966 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 $

$2$	−2.77071	−	3.47436i	−0.979595	−	1.22837i	−0.973569	−	0.228391i	$-0.926653\pi$
$2$	−2.77071	−	3.47436i	−0.979595	−	1.22837i	−0.00602555	−	0.999982i	$-0.501918\pi$
$3$	−6.15987	+	2.96643i	−1.18547	+	0.570891i	−0.919499	−	0.393091i	$-0.871406\pi$
$3$	−6.15987	+	2.96643i	−1.18547	+	0.570891i	−0.265967	+	0.963982i	$0.585691\pi$
$4$	−2.61419	+	11.4535i	−0.326774	+	1.43169i
$5$	1.98451	−	0.955692i	0.177500	−	0.0854797i	−0.343023	−	0.939327i	$-0.611451\pi$
$5$	1.98451	−	0.955692i	0.177500	−	0.0854797i	0.520524	+	0.853847i	$0.325737\pi$
$6$	27.3737	+	13.1825i	1.86254	+	0.896954i
$7$	18.5202	−	0.0393741i	0.999998	−	0.00212600i
$7$	18.5202	−	0.0393741i	0.999998	−	0.00212600i
$8$	15.0065	−	7.22673i	0.663198	−	0.319379i
$9$	12.3100	−	15.4362i	0.455925	−	0.571712i
$10$	−8.81894	−	4.24698i	−0.278879	−	0.134301i
$11$	−2.32728	−	2.91832i	−0.0637911	−	0.0799915i	0.748912	−	0.662669i	$-0.230576\pi$
$11$	−2.32728	−	2.91832i	−0.0637911	−	0.0799915i	−0.812703	+	0.582678i	$0.802005\pi$
$12$	−17.8730	−	78.3069i	−0.429958	−	1.88377i
$13$	55.9871	+	70.2055i	1.19446	+	1.49781i	0.821737	+	0.569867i	$0.193005\pi$
$13$	55.9871	+	70.2055i	1.19446	+	1.49781i	0.372726	+	0.927941i	$0.378423\pi$
$14$	−51.4510	−	64.2369i	−0.982204	−	1.22629i
$15$	−9.38934	+	11.7739i	−0.161621	+	0.202667i
$16$	17.9902	+	8.66363i	0.281097	+	0.135369i
$17$	12.4417	+	54.5106i	0.177503	+	0.777691i	0.982778	+	0.184790i	$0.0591605\pi$
$17$	12.4417	+	54.5106i	0.177503	+	0.777691i	−0.805275	+	0.592901i	$0.797982\pi$
$18$	−87.7385			−1.14890
$19$	−27.6480			−0.333837			−0.166918	−	0.985971i	$-0.553382\pi$
$19$	−27.6480			−0.333837			−0.166918	+	0.985971i	$0.553382\pi$
$20$	5.75813	+	25.2280i	0.0643778	+	0.282058i
$21$	−113.965	+	55.1816i	−1.18425	+	0.573410i
$22$	−3.69107	+	16.1716i	−0.0357700	+	0.156718i
$23$	−12.4090	+	54.3675i	−0.112498	+	0.492887i	0.887016	+	0.461738i	$0.152774\pi$
$23$	−12.4090	+	54.3675i	−0.112498	+	0.492887i	−0.999515	+	0.0311494i	$0.990083\pi$
$24$	−71.0001	+	89.0313i	−0.603868	+	0.757227i
$25$	−74.9113	+	93.9358i	−0.599290	+	0.751486i
$26$	88.7956	−	389.039i	0.669779	−	2.93449i
$27$	11.0395	−	48.3672i	0.0786871	−	0.344751i
$28$	−47.9644	+	212.224i	−0.323729	+	1.43238i
$29$	−22.1528	−	97.0578i	−0.141851	−	0.621489i	−0.995005	−	0.0998296i	$-0.968170\pi$
$29$	−22.1528	−	97.0578i	−0.141851	−	0.621489i	0.853154	−	0.521660i	$-0.174687\pi$
$30$	66.9219			0.407274
$31$	99.2310			0.574916			0.287458	−	0.957793i	$-0.407190\pi$
$31$	99.2310			0.574916			0.287458	+	0.957793i	$0.407190\pi$
$32$	−49.3954	−	216.415i	−0.272874	−	1.19554i
$33$	22.9927	+	11.0727i	0.121289	+	0.0584095i
$34$	154.917	−	194.260i	0.781414	−	0.979863i
$35$	36.7160	−	17.7778i	0.177318	−	0.0858568i
$36$	144.618	+	181.346i	0.669529	+	0.839563i
$37$	79.7800	+	349.539i	0.354480	+	1.55308i	0.766708	+	0.641996i	$0.221893\pi$
$37$	79.7800	+	349.539i	0.354480	+	1.55308i	−0.412228	+	0.911081i	$0.635249\pi$
$38$	76.6048	+	96.0594i	0.327025	+	0.410076i
$39$	−553.133	−	266.375i	−2.27108	−	1.09369i
$40$	22.8740	−	28.6831i	0.0904174	−	0.113380i
$41$	300.534	−	144.730i	1.14477	−	0.551292i	0.237311	−	0.971434i	$-0.423734\pi$
$41$	300.534	−	144.730i	1.14477	−	0.551292i	0.907458	+	0.420142i	$0.138020\pi$
$42$	507.486	+	243.065i	1.86445	+	0.892992i
$43$	−383.629	−	184.746i	−1.36053	−	0.655198i	−0.395778	−	0.918346i	$-0.629525\pi$
$43$	−383.629	−	184.746i	−1.36053	−	0.655198i	−0.964755	+	0.263148i	$0.915239\pi$
$44$	39.5089	−	19.0265i	0.135368	−	0.0651898i
$45$	9.67706	−	42.3980i	0.0320571	−	0.140451i
$46$	223.274	−	107.523i	0.715652	−	0.344640i
$47$	301.391	+	377.932i	0.935369	+	1.17292i	0.984722	+	0.174135i	$0.0557128\pi$
$47$	301.391	+	377.932i	0.935369	+	1.17292i	−0.0493526	+	0.998781i	$0.515716\pi$
$48$	−136.517			−0.410512
$49$	342.997	−	1.45843i	0.999991	−	0.00425200i
$50$	533.925			1.51017
$51$	−238.341	−	298.870i	−0.654401	−	0.820592i
$52$	−950.461	+	457.718i	−2.53471	+	1.22065i
$53$	−90.7653	+	397.669i	−0.235237	+	1.03064i	0.709986	+	0.704216i	$0.248701\pi$
$53$	−90.7653	+	397.669i	−0.235237	+	1.03064i	−0.945223	+	0.326426i	$0.894156\pi$
$54$	−198.632	+	95.6563i	−0.500564	+	0.241059i
$55$	−7.40754	−	3.56728i	−0.0181606	−	0.00874568i
$56$	277.638	−	134.431i	0.662517	−	0.320788i
$57$	170.308	−	82.0161i	0.395752	−	0.190584i
$58$	−275.835	+	345.886i	−0.624464	+	0.783054i
$59$	−515.719	−	248.357i	−1.13798	−	0.548022i	−0.232578	−	0.972578i	$-0.574716\pi$
$59$	−515.719	−	248.357i	−1.13798	−	0.548022i	−0.905402	+	0.424555i	$0.860430\pi$
$60$	−110.307	−	138.320i	−0.237342	−	0.297617i
$61$	34.2558	+	150.085i	0.0719018	+	0.315022i	0.998071	−	0.0620864i	$-0.0197754\pi$
$61$	34.2558	+	150.085i	0.0719018	+	0.315022i	−0.926169	+	0.377109i	$0.876918\pi$
$62$	−274.941	−	344.765i	−0.563185	−	0.706212i
$63$	227.376	−	286.367i	0.454709	−	0.572680i
$64$	−515.449	+	646.352i	−1.00674	+	1.26241i
$65$	178.202	+	85.8176i	0.340050	+	0.163759i
$66$	−25.2356	−	110.564i	−0.0470650	−	0.206205i
$67$	370.306			0.675225			0.337612	−	0.941285i	$-0.390381\pi$
$67$	370.306			0.675225			0.337612	+	0.941285i	$0.390381\pi$
$68$	−656.862			−1.17142
$69$	−84.8397	−	371.707i	−0.148022	−	0.648526i
$70$	−163.496	−	78.3077i	−0.279164	−	0.133708i
$71$	86.0611	−	377.058i	0.143853	−	0.630262i	−0.850666	−	0.525707i	$-0.823801\pi$
$71$	86.0611	−	377.058i	0.143853	−	0.630262i	0.994519	−	0.104555i	$-0.0333418\pi$
$72$	73.1757	−	320.604i	0.119776	−	0.524771i
$73$	422.856	−	530.245i	0.677967	−	0.850144i	−0.317198	−	0.948359i	$-0.602742\pi$
$73$	422.856	−	530.245i	0.677967	−	0.850144i	0.995165	+	0.0982154i	$0.0313134\pi$
$74$	993.378	−	1245.66i	1.56051	−	1.95682i
$75$	182.789	−	800.851i	0.281422	−	1.23299i
$76$	72.2772	−	316.667i	0.109089	−	0.477950i
$77$	−43.2167	−	53.9563i	−0.0639610	−	0.0798557i
$78$	607.090	+	2659.83i	0.881274	+	3.86111i
$79$	−677.093			−0.964290			−0.482145	−	0.876091i	$-0.660142\pi$
$79$	−677.093			−0.964290			−0.482145	+	0.876091i	$0.660142\pi$
$80$	43.9816			0.0614661
$81$	194.098	+	850.397i	0.266252	+	1.16653i
$82$	−1335.54	−	643.160i	−1.79860	−	0.866161i
$83$	−494.014	+	619.474i	−0.653315	+	0.819231i	−0.992597	−	0.121454i	$-0.961244\pi$
$83$	−494.014	+	619.474i	−0.653315	+	0.819231i	0.339283	+	0.940685i	$0.389816\pi$
$84$	−334.096	−	1449.56i	−0.433962	−	1.88285i
$85$	76.7860	+	96.2866i	0.0979837	+	0.122868i
$86$	421.051	+	1844.75i	0.527943	+	2.31307i
$87$	424.374	+	532.148i	0.522962	+	0.655773i
$88$	−56.0141	−	26.9750i	−0.0678537	−	0.0326766i
$89$	−80.1989	+	100.566i	−0.0955175	+	0.119775i	−0.827293	−	0.561770i	$-0.810120\pi$
$89$	−80.1989	+	100.566i	−0.0955175	+	0.119775i	0.731776	+	0.681546i	$0.238692\pi$
$90$	−174.118	+	83.8510i	−0.203930	+	0.0982074i
$91$	1039.66	+	1298.02i	1.19764	+	1.49527i
$92$	−590.259	−	284.254i	−0.668900	−	0.322125i
$93$	−611.249	+	294.362i	−0.681544	+	0.328214i
$94$	478.006	−	2094.28i	0.524496	−	2.29797i
$95$	−54.8679	+	26.4230i	−0.0592561	+	0.0285362i
$96$	946.251	+	1186.56i	1.00600	+	1.26149i
$97$	430.011			0.450114			0.225057	−	0.974346i	$-0.427743\pi$
$97$	430.011			0.450114			0.225057	+	0.974346i	$0.427743\pi$
$98$	−955.413	−	1187.66i	−0.984809	−	1.22420i
$99$	−73.6966			−0.0748161
$100$	−880.062	−	1103.56i	−0.880062	−	1.10356i
$101$	−1123.52	+	541.059i	−1.10688	+	0.533043i	−0.895814	−	0.444429i	$-0.853406\pi$
$101$	−1123.52	+	541.059i	−1.10688	+	0.533043i	−0.211062	+	0.977473i	$0.567692\pi$
$102$	−378.009	+	1656.17i	−0.366946	+	1.60770i
$103$	585.492	−	281.958i	0.560099	−	0.269730i	−0.132342	−	0.991204i	$-0.542250\pi$
$103$	585.492	−	281.958i	0.560099	−	0.269730i	0.692441	+	0.721475i	$0.256535\pi$
$104$	1347.52	+	648.933i	1.27053	+	0.611857i
$105$	−173.429	+	218.424i	−0.161190	+	0.203010i
$106$	1633.13	−	786.475i	1.49645	−	0.720652i
$107$	240.731	−	301.867i	0.217498	−	0.272734i	−0.661098	−	0.750300i	$-0.729909\pi$
$107$	240.731	−	301.867i	0.217498	−	0.272734i	0.878596	+	0.477565i	$0.158481\pi$
$108$	525.114	+	252.882i	0.467863	+	0.225311i
$109$	−338.350	−	424.278i	−0.297322	−	0.372830i	0.610622	−	0.791923i	$-0.290920\pi$
$109$	−338.350	−	424.278i	−0.297322	−	0.372830i	−0.907943	+	0.419093i	$0.862348\pi$
$110$	8.13012	+	35.6204i	0.00704706	+	0.0308752i
$111$	−1528.32	−	1916.45i	−1.30686	−	1.63875i
$112$	333.524	+	159.744i	0.281384	+	0.134771i
$113$	1469.45	−	1842.63i	1.22331	−	1.53398i	0.460039	−	0.887899i	$-0.347835\pi$
$113$	1469.45	−	1842.63i	1.22331	−	1.53398i	0.763269	−	0.646081i	$-0.223593\pi$
$114$	−756.829	−	364.470i	−0.621785	−	0.299436i
$115$	27.3327	+	119.752i	0.0221634	+	0.0971040i
$116$	1169.56			0.936132
$117$	1772.91			1.40090
$118$	566.025	+	2479.92i	0.441584	+	1.93470i
$119$	232.569	+	1009.06i	0.179156	+	0.777312i
$120$	−55.8142	+	244.538i	−0.0424593	+	0.186027i
$121$	293.075	−	1284.05i	0.220192	−	0.964722i
$122$	426.536	−	534.859i	0.316530	−	0.396917i
$123$	−1421.92	+	1783.03i	−1.04236	+	1.30708i
$124$	−259.408	+	1136.54i	−0.187867	+	0.823101i
$125$	−120.156	+	526.436i	−0.0859764	+	0.376687i
$126$	−1624.94	+	3.45463i	−1.14890	+	0.00244256i
$127$	−357.943	−	1568.25i	−0.250097	−	1.09575i	−0.931472	−	0.363812i	$-0.881475\pi$
$127$	−357.943	−	1568.25i	−0.250097	−	1.09575i	0.681375	−	0.731934i	$-0.261382\pi$
$128$	1897.98			1.31062
$129$	2911.14			1.98691
$130$	−195.585	−	856.914i	−0.131953	−	0.578126i
$131$	−319.823	−	154.019i	−0.213306	−	0.102723i	0.324180	−	0.945995i	$-0.394912\pi$
$131$	−319.823	−	154.019i	−0.213306	−	0.102723i	−0.537486	+	0.843273i	$0.680626\pi$
$132$	−186.929	+	234.401i	−0.123258	+	0.154561i
$133$	−512.048	+	1.08862i	−0.333836	+	0.000709738i
$134$	−1026.01	−	1286.58i	−0.661447	−	0.829428i
$135$	−24.3161	−	106.536i	−0.0155022	−	0.0679195i
$136$	580.638	+	728.098i	0.366098	+	0.459072i
$137$	−2452.87	−	1181.24i	−1.52965	−	0.736643i	−0.535492	−	0.844540i	$-0.679874\pi$
$137$	−2452.87	−	1181.24i	−1.52965	−	0.736643i	−0.994162	+	0.107898i	$0.965588\pi$
$138$	−1056.38	+	1324.66i	−0.651630	+	0.817118i
$139$	1114.32	−	536.629i	0.679967	−	0.327455i	−0.0618227	−	0.998087i	$-0.519691\pi$
$139$	1114.32	−	536.629i	0.679967	−	0.327455i	0.741790	+	0.670632i	$0.233977\pi$
$140$	107.635	+	467.002i	0.0649773	+	0.281920i
$141$	−2977.64	−	1433.95i	−1.77846	−	0.856459i
$142$	−1548.49	+	745.712i	−0.915114	+	0.440696i
$143$	74.5845	−	326.776i	0.0436159	−	0.191094i
$144$	355.193	−	171.052i	0.205551	−	0.0989883i
$145$	−136.720	−	171.441i	−0.0783033	−	0.0981892i
$146$	−3013.88			−1.70843
$147$	−2108.49	+	1026.46i	−1.18303	+	0.575926i
$148$	−4212.01			−2.33936
$149$	1512.33	+	1896.40i	0.831507	+	1.04268i	0.998391	+	0.0567001i	$0.0180579\pi$
$149$	1512.33	+	1896.40i	0.831507	+	1.04268i	−0.166884	+	0.985976i	$0.553371\pi$
$150$	−3288.90	+	1583.85i	−1.79025	+	0.862140i
$151$	123.301	−	540.215i	0.0664507	−	0.291139i	−0.930774	−	0.365596i	$-0.880865\pi$
$151$	123.301	−	540.215i	0.0664507	−	0.291139i	0.997224	+	0.0744567i	$0.0237223\pi$
$152$	−414.899	+	199.805i	−0.221400	+	0.106620i
$153$	994.594	+	478.971i	0.525544	+	0.253089i
$154$	−67.7227	+	299.648i	−0.0354367	+	0.156794i
$155$	196.925	−	94.8342i	0.102048	−	0.0491437i
$156$	4496.92	−	5638.96i	2.30796	−	2.89409i
$157$	804.712	+	387.529i	0.409064	+	0.196995i	0.627088	−	0.778949i	$-0.284247\pi$
$157$	804.712	+	387.529i	0.409064	+	0.196995i	−0.218024	+	0.975943i	$0.569961\pi$
$158$	1876.03	+	2352.47i	0.944614	+	1.18451i
$159$	−620.557	−	2718.84i	−0.309518	−	1.35609i
$160$	−304.852	−	382.273i	−0.150629	−	0.188883i
$161$	−227.677	+	1007.39i	−0.111450	+	0.493125i
$162$	2416.80	−	3030.57i	1.17211	−	1.46978i
$163$	−1042.41	−	501.997i	−0.500906	−	0.241223i	0.166330	−	0.986070i	$-0.446808\pi$
$163$	−1042.41	−	501.997i	−0.500906	−	0.241223i	−0.667236	+	0.744847i	$0.732523\pi$
$164$	872.008	+	3820.52i	0.415198	+	1.81910i
$165$	56.2115			0.0265216
$166$	3521.05			1.64630
$167$	801.827	+	3513.04i	0.371541	+	1.62783i	0.722455	+	0.691418i	$0.243014\pi$
$167$	801.827	+	3513.04i	0.371541	+	1.62783i	−0.350914	+	0.936408i	$0.614129\pi$
$168$	−1311.43	+	1651.68i	−0.602257	+	0.758509i
$169$	−1305.39	+	5719.29i	−0.594169	+	2.60323i
$170$	121.783	−	533.565i	0.0549430	−	0.240721i
$171$	−340.347	+	426.781i	−0.152205	+	0.190858i
$172$	3118.87	−	3910.94i	1.38263	−	1.73376i
$173$	−261.606	+	1146.17i	−0.114968	+	0.503710i	0.884351	+	0.466823i	$0.154601\pi$
$173$	−261.606	+	1146.17i	−0.114968	+	0.503710i	−0.999319	+	0.0368872i	$0.988256\pi$
$174$	673.058	−	2948.86i	0.293244	−	1.28478i
$175$	−1383.67	+	1742.66i	−0.597691	+	0.752759i
$176$	−16.5851	−	72.6639i	−0.00710310	−	0.0311207i
$177$	3913.49			1.66190
$178$	571.612			0.240697
$179$	−279.293	−	1223.66i	−0.116622	−	0.510955i	−0.999170	−	0.0407324i	$-0.987031\pi$
$179$	−279.293	−	1223.66i	−0.116622	−	0.510955i	0.882548	−	0.470222i	$-0.155826\pi$
$180$	460.308	+	221.673i	0.190607	+	0.0917916i
$181$	966.945	−	1212.51i	0.397086	−	0.497930i	−0.542589	−	0.839998i	$-0.682556\pi$
$181$	966.945	−	1212.51i	0.397086	−	0.497930i	0.939675	+	0.342068i	$0.111127\pi$
$182$	1629.20	−	7208.58i	0.663538	−	2.93591i
$183$	−656.228	−	822.883i	−0.265081	−	0.332400i
$184$	206.684	+	905.540i	0.0828093	+	0.362811i
$185$	492.376	+	617.420i	0.195677	+	0.245371i
$186$	2716.32	+	1308.11i	1.07081	+	0.515674i
$187$	130.124	−	163.170i	0.0508856	−	0.0638085i
$188$	−5116.54	+	2464.00i	−1.98490	+	0.955879i
$189$	202.549	−	896.205i	0.0779539	−	0.344917i
$190$	243.826	+	117.421i	0.0931002	+	0.0448347i
$191$	2067.24	−	995.532i	0.783144	−	0.377142i	0.000808519	−	1.00000i	$-0.499743\pi$
$191$	2067.24	−	995.532i	0.783144	−	0.377142i	0.782335	+	0.622857i	$0.214028\pi$
$192$	1257.73	−	5510.49i	0.472755	−	2.07128i
$193$	582.333	−	280.437i	0.217188	−	0.104592i	−0.322127	−	0.946697i	$-0.604398\pi$
$193$	582.333	−	280.437i	0.217188	−	0.104592i	0.539314	+	0.842104i	$0.318683\pi$
$194$	−1191.44	−	1494.02i	−0.440929	−	0.552908i
$195$	−1352.27			−0.496606
$196$	−879.954	+	3932.33i	−0.320683	+	1.43306i
$197$	−3165.25			−1.14475			−0.572373	−	0.819993i	$-0.693977\pi$
$197$	−3165.25			−1.14475			−0.572373	+	0.819993i	$0.693977\pi$
$198$	204.192	+	256.049i	0.0732894	+	0.0919020i
$199$	−181.500	+	87.4058i	−0.0646542	+	0.0311358i	−0.465931	−	0.884821i	$-0.654281\pi$
$199$	−181.500	+	87.4058i	−0.0646542	+	0.0311358i	0.401277	+	0.915957i	$0.368566\pi$
$200$	−445.304	+	1951.01i	−0.157439	+	0.689785i
$201$	−2281.03	+	1098.49i	−0.800457	+	0.385480i
$202$	4992.79	+	2404.40i	1.73907	+	0.837490i
$203$	−414.097	−	1796.66i	−0.143172	−	0.621186i
$204$	4046.18	−	1948.54i	1.38867	−	0.668750i
$205$	458.097	−	574.436i	0.156073	−	0.195709i
$206$	−2601.85	−	1252.99i	−0.879999	−	0.423785i
$207$	686.474	+	860.811i	0.230499	+	0.289036i
$208$	398.984	+	1748.06i	0.133003	+	0.582723i
$209$	64.3448	+	80.6858i	0.0212958	+	0.0267041i
$210$	1239.41	−	2.63499i	0.407273	−	0.000865865i
$211$	1698.27	−	2129.56i	0.554093	−	0.694811i	−0.423360	−	0.905961i	$-0.639150\pi$
$211$	1698.27	−	2129.56i	0.554093	−	0.694811i	0.977454	+	0.211151i	$0.0677210\pi$
$212$	−4317.43	−	2079.16i	−1.39869	−	0.673573i
$213$	588.394	+	2577.92i	0.189277	+	0.829278i
$214$	−1715.79			−0.548080
$215$	−937.878			−0.297501
$216$	−183.873	−	805.599i	−0.0579211	−	0.253769i
$217$	1837.78	−	3.90713i	0.574915	−	0.00122227i
$218$	−536.624	+	2351.11i	−0.166719	+	0.730445i
$219$	−1031.80	+	4520.62i	−0.318368	+	1.39486i
$220$	60.2226	−	75.5167i	0.0184555	−	0.0231424i
$221$	−3130.37	+	3925.36i	−0.952812	+	1.19479i
$222$	−2423.92	+	10619.9i	−0.732804	+	3.21062i
$223$	−353.209	+	1547.51i	−0.106066	+	0.464703i	0.893803	+	0.448461i	$0.148028\pi$
$223$	−353.209	+	1547.51i	−0.106066	+	0.464703i	−0.999868	+	0.0162427i	$0.994830\pi$
$224$	−923.335	−	4006.12i	−0.275415	−	1.19495i
$225$	527.858	+	2312.69i	0.156402	+	0.685243i
$226$	−10473.4			−3.08265
$227$	2876.55			0.841072			0.420536	−	0.907276i	$-0.361842\pi$
$227$	2876.55			0.841072			0.420536	+	0.907276i	$0.361842\pi$
$228$	494.154	+	2165.03i	0.143536	+	0.628872i
$229$	1069.46	+	515.025i	0.308611	+	0.148619i	0.581778	−	0.813347i	$-0.302357\pi$
$229$	1069.46	+	515.025i	0.308611	+	0.148619i	−0.273168	+	0.961966i	$0.588071\pi$
$230$	340.332	−	426.763i	0.0975688	−	0.122347i
$231$	426.267	+	204.164i	0.121412	+	0.0581515i
$232$	−1033.85	−	1296.40i	−0.292566	−	0.366866i
$233$	−163.959	−	718.353i	−0.0461002	−	0.201978i	0.946633	−	0.322313i	$-0.104460\pi$
$233$	−163.959	−	718.353i	−0.0461002	−	0.201978i	−0.992733	+	0.120335i	$0.961603\pi$
$234$	−4912.22	−	6159.73i	−1.37232	−	1.72083i
$235$	959.301	+	461.975i	0.266289	+	0.128238i
$236$	4192.74	−	5257.53i	1.15646	−	1.45015i
$237$	4170.80	−	2008.55i	1.14313	−	0.550504i
$238$	2861.45	−	3603.84i	0.779329	−	0.981522i
$239$	944.332	+	454.767i	0.255581	+	0.123081i	0.557288	−	0.830320i	$-0.311842\pi$
$239$	944.332	+	454.767i	0.255581	+	0.123081i	−0.301707	+	0.953401i	$0.597556\pi$
$240$	−270.921	+	130.469i	−0.0728661	+	0.0350904i
$241$	931.669	−	4081.91i	0.249021	−	1.09103i	−0.683509	−	0.729942i	$-0.739547\pi$
$241$	931.669	−	4081.91i	0.249021	−	1.09103i	0.932530	−	0.361091i	$-0.117596\pi$
$242$	−5273.27	+	2539.47i	−1.40074	+	0.674560i
$243$	−2883.10	−	3615.29i	−0.761115	−	0.954408i
$244$	−1808.55			−0.474510
$245$	679.289	−	330.694i	0.177135	−	0.0862336i
$246$	10134.6			2.62667
$247$	−1547.93	−	1941.05i	−0.398755	−	0.500023i
$248$	1489.10	−	717.115i	0.381283	−	0.183616i
$249$	1205.43	−	5281.34i	0.306792	−	1.34414i
$250$	2161.95	−	1041.14i	0.546935	−	0.263390i
$251$	−3516.40	−	1693.41i	−0.884276	−	0.425845i	−0.0640918	−	0.997944i	$-0.520415\pi$
$251$	−3516.40	−	1693.41i	−0.884276	−	0.425845i	−0.820185	+	0.572099i	$0.806129\pi$
$252$	2685.50	+	3352.87i	0.671313	+	0.838138i
$253$	187.541	−	90.3150i	0.0466032	−	0.0224429i
$254$	−4456.92	+	5588.80i	−1.10099	+	1.38060i
$255$	−758.619	−	365.332i	−0.186300	−	0.0897175i
$256$	−1135.16	−	1423.44i	−0.277138	−	0.347519i
$257$	−112.544	−	493.089i	−0.0273164	−	0.119681i	0.959431	−	0.281942i	$-0.0909785\pi$
$257$	−112.544	−	493.089i	−0.0273164	−	0.119681i	−0.986748	+	0.162261i	$0.948121\pi$
$258$	−8065.94	−	10114.4i	−1.94637	−	2.44067i
$259$	1491.30	+	6470.39i	0.357781	+	1.55232i
$260$	−1448.77	+	1816.69i	−0.345572	+	0.433333i
$261$	−1770.91	−	852.824i	−0.419986	−	0.202255i
$262$	351.021	+	1537.92i	0.0827716	+	0.362646i
$263$	5882.69			1.37925			0.689623	−	0.724168i	$-0.257776\pi$
$263$	5882.69			1.37925			0.689623	+	0.724168i	$0.257776\pi$
$264$	425.059			0.0990931
$265$	199.924	+	875.923i	0.0463442	+	0.203047i
$266$	1422.52	+	1776.02i	0.327896	+	0.409380i
$267$	195.691	−	857.379i	0.0448543	−	0.196520i
$268$	−968.050	+	4241.30i	−0.220646	+	0.966712i
$269$	−504.325	+	632.403i	−0.114309	+	0.143339i	−0.835694	−	0.549195i	$-0.814934\pi$
$269$	−504.325	+	632.403i	−0.114309	+	0.143339i	0.721385	+	0.692534i	$0.243506\pi$
$270$	−302.771	+	379.663i	−0.0682446	+	0.0855761i
$271$	1461.44	−	6402.97i	0.327587	−	1.43525i	−0.496130	−	0.868248i	$-0.665246\pi$
$271$	1461.44	−	6402.97i	0.327587	−	1.43525i	0.823716	−	0.567002i	$-0.191897\pi$
$272$	−248.431	+	1088.45i	−0.0553799	+	0.242635i
$273$	−10254.6	−	4911.54i	−2.27340	−	1.08886i
$274$	2692.14	+	11795.0i	0.593569	+	2.60060i
$275$	448.474			0.0983419
$276$	4479.14			0.976856
$277$	−1328.96	−	5822.55i	−0.288265	−	1.26297i	−0.886904	−	0.461953i	$-0.847149\pi$
$277$	−1328.96	−	5822.55i	−0.288265	−	1.26297i	0.598639	−	0.801019i	$-0.295708\pi$
$278$	−4951.91	−	2384.71i	−1.06833	−	0.514480i
$279$	1221.53	−	1531.75i	0.262119	−	0.328687i
$280$	422.502	−	532.118i	0.0901762	−	0.113572i
$281$	3133.38	+	3929.13i	0.665202	+	0.834137i	0.993898	−	0.110299i	$-0.0351808\pi$
$281$	3133.38	+	3929.13i	0.665202	+	0.834137i	−0.328697	+	0.944436i	$0.606609\pi$
$282$	3268.10	+	14318.5i	0.690115	+	3.02359i
$283$	−1253.21	−	1571.47i	−0.263234	−	0.330086i	0.632596	−	0.774482i	$-0.281990\pi$
$283$	−1253.21	−	1571.47i	−0.263234	−	0.330086i	−0.895830	+	0.444397i	$0.853418\pi$
$284$	4093.66	+	1971.40i	0.855331	+	0.411906i
$285$	259.597	−	325.524i	0.0539551	−	0.0676575i
$286$	−1341.99	+	646.269i	−0.277460	+	0.133618i
$287$	5560.26	−	2692.26i	1.14359	−	0.553724i
$288$	−3948.69	−	1901.59i	−0.807913	−	0.389071i
$289$	1609.85	−	775.265i	0.327672	−	0.157799i
$290$	−216.838	+	950.030i	−0.0439075	+	0.192371i
$291$	−2648.81	+	1275.60i	−0.533595	+	0.256966i
$292$	4967.74	+	6229.35i	0.995600	+	1.24844i
$293$	5065.33			1.00997			0.504983	−	0.863129i	$-0.331499\pi$
$293$	5065.33			1.00997			0.504983	+	0.863129i	$0.331499\pi$
$294$	9408.32	+	4481.63i	1.86634	+	0.889026i
$295$	−1260.80			−0.248837
$296$	3723.24	+	4668.79i	0.731110	+	0.916783i
$297$	−166.843	+	80.3473i	−0.0325966	+	0.0156977i
$298$	2398.55	−	10508.7i	0.466256	−	2.04280i
$299$	−4511.65	+	2172.69i	−0.872626	+	0.420235i
$300$	8694.71	+	4187.15i	1.67330	+	0.805818i
$301$	−7112.17	−	3406.43i	−1.36192	−	0.652304i
$302$	−2218.53	+	1068.39i	−0.422723	+	0.203573i
$303$	5315.72	−	6665.70i	1.00785	−	1.26381i
$304$	−497.394	−	239.532i	−0.0938405	−	0.0451912i
$305$	211.416	+	265.107i	0.0396906	+	0.0497705i
$306$	−1091.61	−	4782.68i	−0.203933	−	0.893488i
$307$	−215.351	−	270.042i	−0.0400350	−	0.0502022i	0.761411	−	0.648270i	$-0.224507\pi$
$307$	−215.351	−	270.042i	−0.0400350	−	0.0502022i	−0.801446	+	0.598067i	$0.795936\pi$
$308$	730.965	−	353.931i	0.135229	−	0.0654775i
$309$	−2770.14	+	3473.65i	−0.509993	+	0.639511i
$310$	−875.112	−	421.432i	−0.160332	−	0.0772120i
$311$	1408.56	+	6171.30i	0.256823	+	1.12522i	0.924626	+	0.380877i	$0.124378\pi$
$311$	1408.56	+	6171.30i	0.256823	+	1.12522i	−0.667802	+	0.744339i	$0.732765\pi$
$312$	−10225.6			−1.85548
$313$	−4465.91			−0.806480			−0.403240	−	0.915094i	$-0.632116\pi$
$313$	−4465.91			−0.806480			−0.403240	+	0.915094i	$0.632116\pi$
$314$	−883.210	−	3869.59i	−0.158734	−	0.695458i
$315$	177.552	−	785.601i	0.0317585	−	0.140519i
$316$	1770.05	−	7755.09i	0.315104	−	1.38056i
$317$	1459.57	−	6394.78i	0.258604	−	1.13302i	−0.664141	−	0.747607i	$-0.731203\pi$
$317$	1459.57	−	6394.78i	0.258604	−	1.13302i	0.922745	−	0.385410i	$-0.125940\pi$
$318$	−7726.84	+	9689.15i	−1.36258	+	1.70862i
$319$	−231.690	+	290.530i	−0.0406650	+	0.0509923i
$320$	−405.202	+	1775.31i	−0.0707858	+	0.310133i
$321$	−587.401	+	2573.57i	−0.102136	+	0.447485i
$322$	4130.86	−	2000.15i	0.714918	−	0.346161i
$323$	−343.988	−	1507.11i	−0.0592570	−	0.259622i
$324$	−10247.4			−1.75710
$325$	−10788.9			−1.84141
$326$	1144.09	+	5012.59i	0.194372	+	0.851600i
$327$	3342.79	+	1609.80i	0.565310	+	0.272239i
$328$	3464.03	−	4343.75i	0.583137	−	0.731231i
$329$	5596.70	+	6987.52i	0.937861	+	1.17092i
$330$	−155.746	−	195.299i	−0.0259804	−	0.0325784i
$331$	−948.583	−	4156.01i	−0.157519	−	0.690136i	−0.990578	−	0.136952i	$-0.956270\pi$
$331$	−948.583	−	4156.01i	−0.157519	−	0.690136i	0.833059	−	0.553185i	$-0.186588\pi$
$332$	−5803.71	−	7277.62i	−0.959397	−	1.20305i
$333$	6377.65	+	3071.31i	1.04953	+	0.505426i
$334$	9983.93	−	12519.5i	1.63562	−	2.05100i
$335$	734.878	−	353.898i	0.119853	−	0.0577180i
$336$	−2528.33	+	5.37525i	−0.410511	+	0.000872750i
$337$	−2303.97	−	1109.53i	−0.372419	−	0.179347i	0.238307	−	0.971190i	$-0.423408\pi$
$337$	−2303.97	−	1109.53i	−0.372419	−	0.179347i	−0.610725	+	0.791843i	$0.709122\pi$
$338$	23487.7	−	11311.1i	3.77978	−	1.82025i
$339$	−3585.56	+	15709.3i	−0.574456	+	2.51686i
$340$	−1303.55	+	627.758i	−0.207927	+	0.100132i
$341$	−230.938	−	289.588i	−0.0366745	−	0.0459884i
$342$	2425.80			0.383544
$343$	6352.32	−	40.5157i	0.999980	−	0.00637797i
$344$	−7092.03			−1.11156
$345$	−523.603	−	656.577i	−0.0817097	−	0.102461i
$346$	4707.05	−	2266.80i	0.731366	−	0.352207i
$347$	−1246.83	+	5462.73i	−0.192892	+	0.845115i	0.782149	+	0.623091i	$0.214123\pi$
$347$	−1246.83	+	5462.73i	−0.192892	+	0.845115i	−0.975041	+	0.222024i	$0.928734\pi$
$348$	−7204.36	+	3469.44i	−1.10975	+	0.534429i
$349$	7490.57	+	3607.27i	1.14888	+	0.553274i	0.908699	−	0.417453i	$-0.137077\pi$
$349$	7490.57	+	3607.27i	1.14888	+	0.553274i	0.240186	+	0.970727i	$0.422791\pi$
$350$	9888.40	−	21.0228i	1.51016	−	0.00321062i
$351$	4013.71	−	1932.90i	0.610359	−	0.293934i
$352$	−516.612	+	647.811i	−0.0782259	+	0.0980922i
$353$	−6551.85	−	3155.20i	−0.987874	−	0.475735i	−0.131068	−	0.991373i	$-0.541841\pi$
$353$	−6551.85	−	3155.20i	−0.987874	−	0.475735i	−0.856806	+	0.515638i	$0.827555\pi$
$354$	−10843.2	−	13596.9i	−1.62799	−	2.04143i
$355$	−189.562	−	830.525i	−0.0283406	−	0.124168i
$356$	−942.181	−	1181.46i	−0.140268	−	0.175891i
$357$	−4425.90	−	5525.76i	−0.656144	−	0.819199i
$358$	−3477.61	+	4360.79i	−0.513401	+	0.643784i
$359$	2097.36	+	1010.04i	0.308341	+	0.148489i	0.581655	−	0.813436i	$-0.302405\pi$
$359$	2097.36	+	1010.04i	0.308341	+	0.148489i	−0.273314	+	0.961925i	$0.588120\pi$
$360$	−161.180	−	706.177i	−0.0235971	−	0.103385i
$361$	−6094.59			−0.888553
$362$	−6891.83			−1.00063
$363$	2003.73	+	8778.94i	0.289721	+	1.26935i
$364$	−17584.7	+	8514.45i	−2.53211	+	1.22604i
$365$	332.414	−	1456.40i	0.0476694	−	0.208853i
$366$	−1040.78	+	4559.95i	−0.148640	+	0.651236i
$367$	126.986	−	159.235i	0.0180616	−	0.0226485i	−0.772719	−	0.634749i	$-0.781104\pi$
$367$	126.986	−	159.235i	0.0180616	−	0.0226485i	0.790780	+	0.612100i	$0.209675\pi$
$368$	−694.261	+	870.576i	−0.0983447	+	0.123320i
$369$	1465.49	−	6420.73i	0.206749	−	0.905826i
$370$	780.909	−	3421.39i	0.109723	−	0.480728i
$371$	−1665.34	+	7368.49i	−0.233046	+	1.03114i
$372$	−1773.56	−	7770.47i	−0.247190	−	1.08301i
$373$	−2267.07			−0.314703			−0.157352	−	0.987543i	$-0.550296\pi$
$373$	−2267.07			−0.314703			−0.157352	+	0.987543i	$0.550296\pi$
$374$	−927.449			−0.128228
$375$	−821.497	−	3599.21i	−0.113125	−	0.495633i
$376$	7254.02	+	3493.35i	0.994940	+	0.479138i
$377$	5573.73	−	6989.23i	0.761437	−	0.954811i
$378$	−3674.95	+	1779.40i	−0.500050	+	0.242122i
$379$	1454.03	+	1823.30i	0.197067	+	0.247115i	0.870540	−	0.492097i	$-0.163770\pi$
$379$	1454.03	+	1823.30i	0.197067	+	0.247115i	−0.673473	+	0.739212i	$0.735198\pi$
$380$	−159.201	−	697.505i	−0.0214917	−	0.0941612i
$381$	6857.00	+	8598.40i	0.922033	+	1.15619i
$382$	−9186.58	−	4424.02i	−1.23044	−	0.592546i
$383$	1684.31	−	2112.06i	0.224711	−	0.281779i	−0.656677	−	0.754172i	$-0.728038\pi$
$383$	1684.31	−	2112.06i	0.224711	−	0.281779i	0.881388	+	0.472394i	$0.156610\pi$
$384$	−11691.3	+	5630.22i	−1.55369	+	0.748219i
$385$	−137.330	−	65.7752i	−0.0181791	−	0.00870705i
$386$	−2587.82	−	1246.23i	−0.341234	−	0.164330i
$387$	−7574.25	+	3647.57i	−0.994886	+	0.479112i
$388$	−1124.13	+	4925.14i	−0.147085	+	0.644423i
$389$	5195.84	−	2502.19i	0.677223	−	0.326133i	−0.0634637	−	0.997984i	$-0.520215\pi$
$389$	5195.84	−	2502.19i	0.677223	−	0.326133i	0.740686	+	0.671851i	$0.234500\pi$
$390$	3746.76	+	4698.29i	0.486473	+	0.610018i
$391$	−3117.99			−0.403283
$392$	5136.63	−	2500.63i	0.661834	−	0.322196i
$393$	2426.95			0.311510
$394$	8770.01	+	10997.2i	1.12139	+	1.40618i
$395$	−1343.70	+	647.092i	−0.171162	+	0.0824272i
$396$	192.657	−	844.085i	0.0244479	−	0.107113i
$397$	−10664.0	+	5135.53i	−1.34814	+	0.649232i	−0.961960	−	0.273190i	$-0.911921\pi$
$397$	−10664.0	+	5135.53i	−1.34814	+	0.649232i	−0.386183	+	0.922422i	$0.626207\pi$
$398$	806.564	+	388.421i	0.101581	+	0.0489190i
$399$	3150.92	−	1525.66i	0.395346	−	0.191425i
$400$	−2161.49	+	1040.92i	−0.270187	+	0.130115i
$401$	635.235	−	796.559i	0.0791075	−	0.0991977i	−0.740703	−	0.671833i	$-0.765507\pi$
$401$	635.235	−	796.559i	0.0791075	−	0.0991977i	0.819810	+	0.572635i	$0.194079\pi$
$402$	10136.6	+	4881.55i	1.25764	+	0.605646i
$403$	5555.65	+	6966.57i	0.686716	+	0.861115i
$404$	−3259.93	−	14282.7i	−0.401454	−	1.75889i
$405$	1197.91	+	1502.13i	0.146974	+	0.184300i
$406$	−5094.91	+	6416.75i	−0.622798	+	0.784379i
$407$	834.395	−	1046.30i	0.101620	−	0.127428i
$408$	−5736.51	−	2762.56i	−0.696077	−	0.335213i
$409$	−1853.78	−	8121.95i	−0.224116	−	0.981918i	−0.954343	−	0.298713i	$-0.903443\pi$
$409$	−1853.78	−	8121.95i	−0.224116	−	0.981918i	0.730226	−	0.683205i	$-0.239415\pi$
$410$	−3265.05			−0.393292
$411$	18613.4			2.23390
$412$	1698.82	+	7443.03i	0.203143	+	0.890028i
$413$	−9561.00	−	4579.32i	−1.13914	−	0.545602i
$414$	1088.75	−	4770.12i	0.129249	−	0.566277i
$415$	−388.352	+	1701.48i	−0.0459360	+	0.201259i
$416$	12428.1	−	15584.3i	1.46475	−	1.83674i
$417$	−5272.19	+	6611.12i	−0.619138	+	0.776374i
$418$	102.051	−	447.114i	0.0119413	−	0.0523184i
$419$	−841.566	+	3687.14i	−0.0981222	+	0.429901i	−0.999998	−	0.00209444i	$-0.999333\pi$
$419$	−841.566	+	3687.14i	−0.0981222	+	0.429901i	0.901876	+	0.431996i	$0.142190\pi$
$420$	−2048.35	−	2557.37i	−0.237974	−	0.297112i
$421$	−2310.29	−	10122.0i	−0.267450	−	1.17177i	−0.912968	−	0.408030i	$-0.866216\pi$
$421$	−2310.29	−	10122.0i	−0.267450	−	1.17177i	0.645519	−	0.763745i	$-0.276641\pi$
$422$	−12104.3			−1.39627
$423$	9543.96			1.09703
$424$	1511.78	+	6623.54i	0.173157	+	0.758649i
$425$	−6052.51	−	2914.74i	−0.690800	−	0.332672i
$426$	7326.37	−	9186.98i	0.833248	−	1.04486i
$427$	640.335	+	2778.25i	0.0725714	+	0.314869i
$428$	2828.12	+	3546.35i	0.319398	+	0.400513i
$429$	509.930	+	2234.15i	0.0573884	+	0.251435i
$430$	2598.59	+	3258.53i	0.291431	+	0.365443i
$431$	−2959.09	−	1425.02i	−0.330706	−	0.159260i	0.261161	−	0.965295i	$-0.415895\pi$
$431$	−2959.09	−	1425.02i	−0.330706	−	0.159260i	−0.591867	+	0.806036i	$0.701609\pi$
$432$	617.638	−	774.493i	0.0687873	−	0.0862565i
$433$	−4220.36	+	2032.42i	−0.468400	+	0.225570i	−0.653169	−	0.757212i	$-0.726561\pi$
$433$	−4220.36	+	2032.42i	−0.468400	+	0.225570i	0.184768	+	0.982782i	$0.440847\pi$
$434$	−5105.53	−	6374.29i	−0.564685	−	0.705013i
$435$	1350.75	+	650.485i	0.148881	+	0.0716974i
$436$	5743.98	−	2766.16i	0.630933	−	0.303841i
$437$	343.085	−	1503.16i	0.0375561	−	0.164544i
$438$	18565.1	−	8940.47i	2.02528	−	0.975325i
$439$	9780.00	+	12263.7i	1.06327	+	1.33329i	0.940096	+	0.340909i	$0.110735\pi$
$439$	9780.00	+	12263.7i	1.06327	+	1.33329i	0.123170	+	0.992386i	$0.460694\pi$
$440$	−136.941			−0.0148372
$441$	4199.77	−	5312.53i	0.453490	−	0.573646i
$442$	22311.5			2.40102
$443$	5257.22	+	6592.34i	0.563833	+	0.707024i	0.979261	−	0.202602i	$-0.0649397\pi$
$443$	5257.22	+	6592.34i	0.563833	+	0.707024i	−0.415428	+	0.909626i	$0.636368\pi$
$444$	25945.4	−	12494.6i	2.77323	−	1.33552i
$445$	−63.0455	+	276.220i	−0.00671605	+	0.0294250i
$446$	6355.25	−	3060.53i	0.674730	−	0.324933i
$447$	−14941.3	−	7195.33i	−1.58098	−	0.761359i
$448$	−9520.77	+	11990.9i	−1.00405	+	1.26454i
$449$	−6559.76	+	3159.01i	−0.689474	+	0.332033i	−0.745603	−	0.666390i	$-0.767839\pi$
$449$	−6559.76	+	3159.01i	−0.689474	+	0.332033i	0.0561288	+	0.998424i	$0.482124\pi$
$450$	6572.60	−	8241.78i	0.688523	−	0.863381i
$451$	−1121.79	−	540.228i	−0.117125	−	0.0564043i
$452$	17263.1	+	21647.3i	1.79644	+	2.25266i
$453$	842.998	+	3693.41i	0.0874337	+	0.383072i
$454$	−7970.09	−	9994.18i	−0.823910	−	1.03315i
$455$	3303.72	+	1582.34i	0.340397	+	0.163036i
$456$	1963.01	−	2461.54i	0.201593	−	0.252790i
$457$	−9253.93	−	4456.46i	−0.947223	−	0.456158i	−0.104511	−	0.994524i	$-0.533328\pi$
$457$	−9253.93	−	4456.46i	−0.947223	−	0.456158i	−0.842712	+	0.538365i	$0.819042\pi$
$458$	−1173.78	−	5142.68i	−0.119754	−	0.524676i
$459$	2773.87			0.282077
$460$	−1443.04			−0.146265
$461$	−311.838	−	1366.25i	−0.0315049	−	0.138032i	0.956730	−	0.290979i	$-0.0939809\pi$
$461$	−311.838	−	1366.25i	−0.0315049	−	0.138032i	−0.988234	+	0.152947i	$0.951124\pi$
$462$	−471.723	−	2046.68i	−0.0475033	−	0.206105i
$463$	−429.861	+	1883.34i	−0.0431476	+	0.189042i	−0.991909	−	0.126952i	$-0.959481\pi$
$463$	−429.861	+	1883.34i	−0.0431476	+	0.189042i	0.948761	+	0.315994i	$0.102338\pi$
$464$	442.339	−	1938.01i	0.0442566	−	0.193901i
$465$	−931.714	+	1168.33i	−0.0929187	+	0.116516i
$466$	−2041.54	+	2560.01i	−0.202945	+	0.254485i
$467$	−117.368	+	514.224i	−0.0116299	+	0.0509539i	−0.980410	−	0.196968i	$-0.936890\pi$
$467$	−117.368	+	514.224i	−0.0116299	+	0.0509539i	0.968780	+	0.247922i	$0.0797476\pi$
$468$	−4634.72	+	20306.0i	−0.457777	+	2.00565i
$469$	6858.15	−	14.5805i	0.675223	−	0.00143553i
$470$	−1052.88	−	4612.96i	−0.103331	−	0.452723i
$471$	−6106.50			−0.597394
$472$	−9533.91			−0.929733
$473$	353.665	+	1549.51i	0.0343796	+	0.150627i
$474$	−18534.5	−	8925.76i	−1.79603	−	0.864924i
$475$	2071.15	−	2597.14i	0.200065	−	0.250874i
$476$	−12165.2	+	25.8634i	−1.17141	+	0.00249043i
$477$	5021.19	+	6296.37i	0.481980	+	0.604384i
$478$	−1036.45	−	4540.98i	−0.0991759	−	0.434518i
$479$	−4992.52	−	6260.42i	−0.476230	−	0.597173i	0.484455	−	0.874816i	$-0.339018\pi$
$479$	−4992.52	−	6260.42i	−0.476230	−	0.597173i	−0.960684	+	0.277643i	$0.910447\pi$
$480$	3011.84	+	1450.42i	0.286398	+	0.137922i
$481$	−20072.9	+	25170.6i	−1.90280	+	2.38603i
$482$	−16763.4	+	8072.84i	−1.58414	+	0.762880i
$483$	−1585.89	−	6880.76i	−0.149400	−	0.648210i
$484$	13940.7	+	6713.47i	1.30923	+	0.630492i
$485$	853.364	−	410.958i	0.0798954	−	0.0384756i
$486$	−4572.60	+	20033.9i	−0.426785	+	1.86987i
$487$	360.011	−	173.372i	0.0334982	−	0.0161319i	−0.417060	−	0.908879i	$-0.636939\pi$
$487$	360.011	−	173.372i	0.0334982	−	0.0161319i	0.450558	+	0.892747i	$0.351225\pi$
$488$	1598.68	+	2004.68i	0.148297	+	0.185958i
$489$	7910.23			0.731519
$490$	−3031.06	−	1443.84i	−0.279448	−	0.133114i
$491$	−20175.1			−1.85436			−0.927179	−	0.374619i	$-0.877773\pi$
$491$	−20175.1			−1.85436			−0.927179	+	0.374619i	$0.877773\pi$
$492$	−16704.8	−	20947.1i	−1.53071	−	1.91945i
$493$	5015.06	−	2415.13i	0.458148	−	0.220632i
$494$	−2455.02	+	10756.2i	−0.223597	+	0.979641i
$495$	−146.252	+	70.4313i	−0.0132799	+	0.00639525i
$496$	1785.19	+	859.700i	0.161607	+	0.0778260i
$497$	1579.02	−	6986.59i	0.142513	−	0.630566i
$498$	−21689.2	+	10445.0i	−1.95164	+	0.939860i
$499$	−4444.35	+	5573.03i	−0.398710	+	0.499966i	−0.940144	−	0.340777i	$-0.889310\pi$
$499$	−4444.35	+	5573.03i	−0.398710	+	0.499966i	0.541434	+	0.840743i	$0.317881\pi$
$500$	−5715.43	−	2752.41i	−0.511204	−	0.246183i
$501$	−15360.3	−	19261.3i	−1.36976	−	1.71762i
$502$	3859.42	+	16909.2i	0.343136	+	1.50338i
$503$	7726.70	+	9688.97i	0.684923	+	0.858867i	0.995797	−	0.0915844i	$-0.0291931\pi$
$503$	7726.70	+	9688.97i	0.684923	+	0.858867i	−0.310874	+	0.950451i	$0.600622\pi$
$504$	1342.61	−	5940.53i	0.118660	−	0.525025i
$505$	−1712.56	+	2147.48i	−0.150907	+	0.189231i
$506$	−833.409	−	401.349i	−0.0732205	−	0.0352611i
$507$	−8924.87	−	39102.4i	−0.781789	−	3.42524i
$508$	18897.7			1.65049
$509$	15904.7			1.38500			0.692500	−	0.721417i	$-0.256509\pi$
$509$	15904.7			1.38500			0.692500	+	0.721417i	$0.256509\pi$
$510$	832.621	+	3647.95i	0.0722923	+	0.316733i
$511$	7810.52	−	9836.91i	0.676158	−	0.851583i
$512$	1578.36	−	6915.23i	0.136238	−	0.596900i
$513$	−305.220	+	1337.26i	−0.0262686	+	0.115090i
$514$	−1401.34	+	1757.23i	−0.120254	+	0.150794i
$515$	892.452	−	1119.10i	0.0763614	−	0.0957542i
$516$	−7610.28	+	33342.8i	−0.649271	+	2.84464i
$517$	401.505	−	1759.11i	0.0341551	−	0.149643i
$518$	18348.5	−	23108.9i	1.55635	−	1.96013i
$519$	−1788.58	−	7836.30i	−0.151272	−	0.662766i
$520$	3294.36			0.277822
$521$	−3469.67			−0.291764			−0.145882	−	0.989302i	$-0.546602\pi$
$521$	−3469.67			−0.291764			−0.145882	+	0.989302i	$0.546602\pi$
$522$	1943.65	+	8515.71i	0.162972	+	0.714028i
$523$	−16128.2	−	7766.92i	−1.34844	−	0.649376i	−0.386415	−	0.922325i	$-0.626287\pi$
$523$	−16128.2	−	7766.92i	−1.34844	−	0.649376i	−0.962029	+	0.272949i	$0.912001\pi$
$524$	2600.13	−	3260.46i	0.216770	−	0.271821i
$525$	3353.76	−	14839.1i	0.278800	−	1.23359i
$526$	−16299.2	−	20438.6i	−1.35110	−	1.69423i
$527$	1234.60	+	5409.14i	0.102049	+	0.447108i
$528$	317.714	+	398.401i	0.0261870	+	0.0328375i
$529$	8160.25	+	3929.77i	0.670687	+	0.322986i
$530$	2489.35	−	3121.54i	0.204019	−	0.255832i
$531$	−10182.2	+	4903.48i	−0.832145	+	0.400740i
$532$	1326.12	−	5867.59i	0.108073	−	0.478181i
$533$	26986.8	+	12996.2i	2.19311	+	1.05615i
$534$	−3521.05	+	1695.65i	−0.285338	+	0.137412i
$535$	189.242	−	829.124i	0.0152928	−	0.0670022i
$536$	5556.98	−	2676.10i	0.447808	−	0.215653i
$537$	5350.32	+	6709.10i	0.429951	+	0.539141i
$538$	3594.54			0.288051
$539$	−802.507	−	997.580i	−0.0641306	−	0.0797195i
$540$	1283.77			0.102305
$541$	7708.80	+	9666.53i	0.612619	+	0.768200i	0.987285	−	0.158960i	$-0.0508139\pi$
$541$	7708.80	+	9666.53i	0.612619	+	0.768200i	−0.374666	+	0.927160i	$0.622243\pi$
$542$	−26295.5	+	12663.2i	−2.08393	+	1.00357i
$543$	−2359.42	+	10337.3i	−0.186468	+	0.816971i
$544$	11182.4	−	5385.14i	0.881323	−	0.424423i
$545$	−1076.94	−	518.627i	−0.0846441	−	0.0407625i
$546$	11348.2	+	49236.8i	0.889481	+	3.85923i
$547$	9606.83	−	4626.40i	0.750929	−	0.361628i	−0.0189481	−	0.999820i	$-0.506032\pi$
$547$	9606.83	−	4626.40i	0.750929	−	0.361628i	0.769877	+	0.638192i	$0.220317\pi$
$548$	19941.6	−	25006.0i	1.55449	−	1.94927i
$549$	2738.43	+	1318.76i	0.212884	+	0.102520i
$550$	−1242.59	−	1558.16i	−0.0963352	−	0.120800i
$551$	612.482	+	2683.46i	0.0473550	+	0.207476i
$552$	−3959.37	−	4964.89i	−0.305293	−	0.382826i
$553$	−12539.9	+	26.6599i	−0.964288	+	0.00205008i
$554$	−16547.5	+	20749.9i	−1.26902	+	1.59130i
$555$	−4864.50	−	2342.62i	−0.372048	−	0.179169i
$556$	3233.24	+	14165.7i	0.246618	+	1.08051i
$557$	24249.3			1.84466			0.922331	−	0.386401i	$-0.126282\pi$
$557$	24249.3			1.84466			0.922331	+	0.386401i	$0.126282\pi$
$558$	−8706.38			−0.660520
$559$	−8508.07	−	37276.3i	−0.643744	−	2.82043i
$560$	814.549	−	1.73174i	0.0614660	−	0.000130677i
$561$	−317.512	+	1391.11i	−0.0238955	+	0.104693i
$562$	4969.54	−	21773.0i	0.373003	−	1.63423i
$563$	5424.58	−	6802.21i	0.406073	−	0.509199i	−0.536179	−	0.844104i	$-0.680133\pi$
$563$	5424.58	−	6802.21i	0.406073	−	0.509199i	0.942252	+	0.334905i	$0.108704\pi$
$564$	24207.9	−	30355.8i	1.80733	−	2.26633i
$565$	1155.15	−	5061.06i	0.0860135	−	0.376850i
$566$	−1987.59	+	8708.19i	−0.147605	+	0.646700i
$567$	3628.21	+	15741.9i	0.268731	+	1.16596i
$568$	−1433.43	−	6280.25i	−0.105889	−	0.463932i
$569$	10763.3			0.793007			0.396504	−	0.918033i	$-0.370223\pi$
$569$	10763.3			0.793007			0.396504	+	0.918033i	$0.370223\pi$
$570$	−1850.26			−0.135963
$571$	1698.94	+	7443.56i	0.124516	+	0.545540i	0.998250	+	0.0591359i	$0.0188345\pi$
$571$	1698.94	+	7443.56i	0.124516	+	0.545540i	−0.873734	+	0.486404i	$0.838308\pi$
$572$	3547.76	+	1708.51i	0.259334	+	0.124889i
$573$	−9780.76	+	12264.7i	−0.713084	+	0.894179i
$574$	−24759.7	−	11858.9i	−1.80044	−	0.862335i
$575$	−4177.48	−	5238.39i	−0.302979	−	0.379923i
$576$	3632.08	+	15913.2i	0.262737	+	1.15113i
$577$	17099.4	+	21441.9i	1.23372	+	1.54703i	0.730578	+	0.682829i	$0.239251\pi$
$577$	17099.4	+	21441.9i	1.23372	+	1.54703i	0.503141	+	0.864205i	$0.332178\pi$
$578$	−7153.99	−	3445.18i	−0.514822	−	0.247925i
$579$	−2755.20	+	3454.91i	−0.197758	+	0.247981i
$580$	2321.02	−	1117.74i	0.166164	−	0.0800203i
$581$	−9124.86	+	11492.2i	−0.651571	+	0.820618i
$582$	11771.0	+	5668.61i	0.838357	+	0.403731i
$583$	1371.76	−	660.605i	0.0974486	−	0.0469288i
$584$	2513.64	−	11013.0i	0.178108	−	0.780342i
$585$	3518.36	−	1694.35i	0.248660	−	0.119749i
$586$	−14034.6	−	17598.8i	−0.989357	−	1.24061i
$587$	−5616.82			−0.394942			−0.197471	−	0.980309i	$-0.563273\pi$
$587$	−5616.82			−0.394942			−0.197471	+	0.980309i	$0.563273\pi$
$588$	−6244.60	−	26833.0i	−0.437964	−	1.88193i
$589$	−2743.54			−0.191928
$590$	3493.32	+	4380.49i	0.243759	+	0.305664i
$591$	19497.5	−	9389.52i	1.35706	−	0.653525i
$592$	−1593.02	+	6979.46i	−0.110596	+	0.484551i
$593$	12517.3	−	6028.03i	0.866821	−	0.417439i	0.0530275	−	0.998593i	$-0.483113\pi$
$593$	12517.3	−	6028.03i	0.866821	−	0.417439i	0.813794	+	0.581154i	$0.197399\pi$
$594$	741.429	+	357.053i	0.0512142	+	0.0246634i
$595$	1425.88	+	1780.23i	0.0982447	+	0.122659i
$596$	−25673.9	+	12363.9i	−1.76450	+	0.849740i
$597$	858.732	−	1076.82i	0.0588703	−	0.0738210i
$598$	20049.2	+	9655.19i	1.37102	+	0.660251i
$599$	−15542.2	−	19489.3i	−1.06016	−	1.32940i	−0.941705	−	0.336439i	$-0.890777\pi$
$599$	−15542.2	−	19489.3i	−1.06016	−	1.32940i	−0.118455	−	0.992959i	$-0.537794\pi$
$600$	−3044.52	−	13338.9i	−0.207153	−	0.907597i
$601$	−12176.6	−	15268.9i	−0.826444	−	1.03633i	−0.998685	−	0.0512728i	$-0.983672\pi$
$601$	−12176.6	−	15268.9i	−0.826444	−	1.03633i	0.172241	−	0.985055i	$-0.444899\pi$
$602$	7870.60	+	34148.5i	0.532860	+	2.31194i
$603$	4558.46	−	5716.13i	0.307852	−	0.386034i
$604$	5865.02	+	2824.45i	0.395107	+	0.190273i
$605$	−645.540	−	2828.30i	−0.0433801	−	0.190061i
$606$	−37887.4			−2.53972
$607$	22682.1			1.51670			0.758350	−	0.651848i	$-0.226006\pi$
$607$	22682.1			1.51670			0.758350	+	0.651848i	$0.226006\pi$
$608$	1365.69	+	5983.46i	0.0910952	+	0.399114i
$609$	7880.45	+	9838.79i	0.524355	+	0.654660i
$610$	335.306	−	1469.07i	0.0222560	−	0.0975098i
$611$	−9658.94	+	42318.6i	−0.639540	+	2.80201i
$612$	−8085.96	+	10139.5i	−0.534078	+	0.669712i
$613$	466.955	−	585.543i	0.0307669	−	0.0385805i	−0.766210	−	0.642590i	$-0.777860\pi$
$613$	466.955	−	585.543i	0.0307669	−	0.0385805i	0.796977	+	0.604010i	$0.206431\pi$
$614$	−341.547	+	1496.42i	−0.0224491	+	0.0983557i
$615$	−1117.79	+	4897.36i	−0.0732905	+	0.321107i
$616$	−1038.46	−	497.377i	−0.0679230	−	0.0325323i
$617$	−2051.73	−	8989.23i	−0.133873	−	0.586536i	−0.996710	−	0.0810534i	$-0.974172\pi$
$617$	−2051.73	−	8989.23i	−0.133873	−	0.586536i	0.862837	−	0.505483i	$-0.168686\pi$
$618$	19744.0			1.28514
$619$	−1085.86			−0.0705082			−0.0352541	−	0.999378i	$-0.511224\pi$
$619$	−1085.86			−0.0705082			−0.0352541	+	0.999378i	$0.511224\pi$
$620$	571.385	+	2503.40i	0.0370119	+	0.162160i
$621$	2492.61	+	1200.38i	0.161071	+	0.0775677i
$622$	17538.6	−	21992.7i	1.13060	−	1.41773i
$623$	−1481.34	+	1865.67i	−0.0952627	+	0.119978i
$624$	−7643.20	−	9584.28i	−0.490341	−	0.614869i
$625$	−3077.28	−	13482.4i	−0.196946	−	0.862877i
$626$	12373.8	+	15516.2i	0.790024	+	0.990659i
$627$	−635.704	−	306.139i	−0.0404906	−	0.0194992i
$628$	−6542.24	+	8203.70i	−0.415706	+	0.521279i
$629$	−18061.0	+	8697.70i	−1.14489	+	0.551351i
$630$	−3221.41	+	1559.79i	−0.203721	+	0.0986408i
$631$	4433.07	+	2134.86i	0.279680	+	0.134687i	0.568466	−	0.822707i	$-0.307537\pi$
$631$	4433.07	+	2134.86i	0.279680	+	0.134687i	−0.288786	+	0.957394i	$0.593252\pi$
$632$	−10160.8	+	4893.17i	−0.639515	+	0.307974i
$633$	−4143.90	+	18155.6i	−0.260198	+	1.14000i
$634$	−26261.8	+	12647.0i	−1.64510	+	0.792236i
$635$	−2209.11	−	2770.13i	−0.138056	−	0.173117i
$636$	32762.5			2.04264
$637$	19305.8	+	23998.6i	1.20082	+	1.49272i
$638$	1651.35			0.102473
$639$	−4760.95	−	5970.04i	−0.294742	−	0.369595i
$640$	3766.56	−	1813.88i	0.232635	−	0.112031i
$641$	2964.02	−	12986.2i	0.182639	−	0.800194i	−0.797729	−	0.603016i	$-0.793965\pi$
$641$	2964.02	−	12986.2i	0.182639	−	0.800194i	0.980368	−	0.197177i	$-0.0631775\pi$
$642$	10569.1	−	5089.79i	0.649731	−	0.312894i
$643$	1361.43	+	655.628i	0.0834983	+	0.0402107i	0.475167	−	0.879896i	$-0.342388\pi$
$643$	1361.43	+	655.628i	0.0834983	+	0.0402107i	−0.391669	+	0.920106i	$0.628102\pi$
$644$	−10942.9	−	5241.20i	−0.669583	−	0.320702i
$645$	5777.20	−	2782.16i	0.352678	−	0.169841i
$646$	−4283.16	+	5370.91i	−0.260865	+	0.327114i
$647$	−11480.0	−	5528.46i	−0.697564	−	0.335929i	0.0512717	−	0.998685i	$-0.483673\pi$
$647$	−11480.0	−	5528.46i	−0.697564	−	0.335929i	−0.748836	+	0.662756i	$0.769387\pi$
$648$	9058.30	+	11358.8i	0.549142	+	0.688602i
$649$	475.437	+	2083.03i	0.0287559	+	0.125988i
$650$	29892.9	+	37484.5i	1.80384	+	2.26194i
$651$	−11308.9	+	5475.72i	−0.680845	+	0.329663i
$652$	8474.67	−	10626.9i	0.509039	−	0.638315i
$653$	−14604.5	−	7033.15i	−0.875219	−	0.421483i	−0.0583429	−	0.998297i	$-0.518582\pi$
$653$	−14604.5	−	7033.15i	−0.875219	−	0.421483i	−0.816876	+	0.576813i	$0.804296\pi$
$654$	−3668.87	−	16074.4i	−0.219364	−	0.961096i
$655$	−781.888			−0.0466426
$656$	6660.55			0.396419
$657$	−2979.63	−	13054.6i	−0.176935	−	0.775204i
$658$	8770.32	−	38805.4i	0.519609	−	2.29907i
$659$	4185.36	−	18337.3i	0.247403	−	1.08394i	−0.686701	−	0.726940i	$-0.740942\pi$
$659$	4185.36	−	18337.3i	0.247403	−	1.08394i	0.934104	−	0.357002i	$-0.116201\pi$
$660$	−146.948	+	643.819i	−0.00866656	+	0.0379707i
$661$	9404.76	−	11793.2i	0.553408	−	0.693952i	−0.423916	−	0.905702i	$-0.639345\pi$
$661$	9404.76	−	11793.2i	0.553408	−	0.693952i	0.977324	+	0.211750i	$0.0679161\pi$
$662$	−11811.3	+	14810.8i	−0.693440	+	0.869546i
$663$	7638.34	−	33465.7i	0.447433	−	1.96033i
$664$	−2936.63	+	12866.2i	−0.171632	+	0.751967i
$665$	−1015.13	+	491.520i	−0.0591953	+	0.0286622i
$666$	−6999.77	−	30668.0i	−0.407261	−	1.78433i
$667$	5551.69			0.322282
$668$	−42332.7			−2.45195
$669$	−2414.87	−	10580.2i	−0.139558	−	0.611442i
$670$	−3265.71	−	1572.68i	−0.188306	−	0.0906836i
$671$	358.272	−	449.259i	0.0206124	−	0.0258472i
$672$	17571.5	+	21938.1i	1.00868	+	1.25935i
$673$	17310.2	+	21706.3i	0.991468	+	1.24326i	0.969902	+	0.243494i	$0.0782936\pi$
$673$	17310.2	+	21706.3i	0.991468	+	1.24326i	0.0215654	+	0.999767i	$0.493135\pi$
$674$	2528.71	+	11079.0i	0.144514	+	0.633157i
$675$	3716.42	+	4660.25i	0.211919	+	0.265738i
$676$	−62093.4	−	29902.6i	−3.53285	−	1.70133i
$677$	1712.18	−	2147.00i	0.0971998	−	0.121885i	−0.730853	−	0.682535i	$-0.760877\pi$
$677$	1712.18	−	2147.00i	0.0971998	−	0.121885i	0.828053	+	0.560650i	$0.189449\pi$
$678$	64514.5	−	31068.6i	3.65437	−	1.75985i
$679$	7963.90	−	16.9313i	0.450113	−	0.000956943i
$680$	1848.12	+	890.009i	0.104224	+	0.0501916i
$681$	−17719.2	+	8533.10i	−0.997063	+	0.480160i
$682$	−366.269	+	1604.73i	−0.0205647	+	0.0901000i
$683$	−19908.5	+	9587.44i	−1.11534	+	0.537120i	−0.898450	−	0.439075i	$-0.855306\pi$
$683$	−19908.5	+	9587.44i	−1.11534	+	0.537120i	−0.216892	+	0.976196i	$0.569592\pi$
$684$	−3998.41	−	5013.85i	−0.223513	−	0.280277i
$685$	−5996.65			−0.334482
$686$	−17741.2	−	21958.0i	−0.987410	−	1.22210i
$687$	−8115.52			−0.450693
$688$	−5301.00	−	6647.24i	−0.293748	−	0.368349i
$689$	−33000.2	+	15892.1i	−1.82469	+	0.878723i
$690$	−830.435	+	3638.38i	−0.0458176	+	0.200740i
$691$	−10291.5	+	4956.11i	−0.566579	+	0.272850i	−0.695167	−	0.718848i	$-0.744670\pi$
$691$	−10291.5	+	4956.11i	−0.566579	+	0.272850i	0.128588	+	0.991698i	$0.458955\pi$
$692$	−12443.8	−	5992.62i	−0.683587	−	0.329198i
$693$	−1364.88	+	2.90174i	−0.0748159	+	0.000159059i
$694$	22434.1	−	10803.7i	1.22707	−	0.590927i
$695$	1698.53	−	2129.89i	0.0927037	−	0.116247i
$696$	10214.0	+	4918.82i	0.556268	+	0.267884i
$697$	11628.4	+	14581.6i	0.631935	+	0.792421i
$698$	−8221.25	−	36019.7i	−0.445815	−	1.95324i
$699$	3140.92	+	3938.58i	0.169958	+	0.213120i
$700$	−16342.4	−	20403.6i	−0.882406	−	1.10169i
$701$	7324.50	−	9184.63i	0.394640	−	0.494863i	−0.544326	−	0.838874i	$-0.683214\pi$
$701$	7324.50	−	9184.63i	0.394640	−	0.494863i	0.938965	+	0.344011i	$0.111786\pi$
$702$	−17836.4	−	8589.58i	−0.958965	−	0.461813i
$703$	−2205.76	−	9664.06i	−0.118338	−	0.518474i
$704$	3085.86			0.165203
$705$	−7279.58			−0.388886
$706$	7190.96	+	31505.7i	0.383336	+	1.67951i
$707$	−20786.5	+	10064.8i	−1.10574	+	0.535395i
$708$	−10230.6	+	44823.2i	−0.543064	+	2.37932i
$709$	4943.76	−	21660.0i	0.261872	−	1.14733i	−0.657348	−	0.753588i	$-0.728322\pi$
$709$	4943.76	−	21660.0i	0.261872	−	1.14733i	0.919219	−	0.393746i	$-0.128821\pi$
$710$	−2360.33	+	2959.75i	−0.124763	+	0.156447i
$711$	−8335.00	+	10451.8i	−0.439644	+	0.551296i
$712$	−476.736	+	2088.72i	−0.0250933	+	0.109941i
$713$	−1231.36	+	5394.94i	−0.0646771	+	0.283369i
$714$	−6935.61	+	30687.5i	−0.363527	+	1.60847i
$715$	−164.283	−	719.772i	−0.00859279	−	0.0376475i
$716$	14745.4			0.769637
$717$	−7166.00			−0.373248
$718$	−2301.95	−	10085.5i	−0.119649	−	0.524218i
$719$	18476.5	+	8897.80i	0.958354	+	0.461519i	0.846607	−	0.532218i	$-0.178641\pi$
$719$	18476.5	+	8897.80i	0.958354	+	0.461519i	0.111746	+	0.993737i	$0.464356\pi$
$720$	541.412	−	678.910i	0.0280240	−	0.0351409i
$721$	10832.3	−	5244.98i	0.559525	−	0.270920i
$722$	16886.3	+	21174.8i	0.870422	+	1.09147i
$723$	6369.76	+	27907.8i	0.327654	+	1.43555i
$724$	11359.7	+	14244.6i	0.583123	+	0.731213i
$725$	10776.7	+	5189.78i	0.552050	+	0.265853i
$726$	24949.4	−	31285.6i	1.27543	−	1.59934i
$727$	−31946.2	+	15384.5i	−1.62974	+	0.784841i	−0.629771	+	0.776781i	$0.716851\pi$
$727$	−31946.2	+	15384.5i	−1.62974	+	0.784841i	−0.999968	+	0.00805967i	$0.997434\pi$
$728$	24982.0	+	11965.3i	1.27183	+	0.609154i
$729$	7265.13	+	3498.70i	0.369107	+	0.177753i
$730$	−5981.09	+	2880.34i	−0.303246	+	0.146036i
$731$	5297.62	−	23210.4i	0.268043	−	1.17437i
$732$	11140.4	−	5364.94i	0.562515	−	0.270893i
$733$	−17995.6	−	22565.8i	−0.906799	−	1.13709i	−0.990072	−	0.140563i	$-0.955109\pi$
$733$	−17995.6	−	22565.8i	−0.906799	−	1.13709i	0.0832731	−	0.996527i	$-0.473463\pi$
$734$	−905.083			−0.0455139
$735$	−3203.34	+	4052.09i	−0.160758	+	0.203352i
$736$	12378.9			0.619963
$737$	−861.806	−	1080.67i	−0.0430733	−	0.0540122i
$738$	−26368.4	+	12698.4i	−1.31522	+	0.633378i
$739$	−6253.53	+	27398.5i	−0.311286	+	1.36383i	0.541118	+	0.840947i	$0.318001\pi$
$739$	−6253.53	+	27398.5i	−0.311286	+	1.36383i	−0.852404	+	0.522884i	$0.824856\pi$
$740$	−8358.79	+	4025.38i	−0.415237	+	0.199967i
$741$	15293.0	+	7364.74i	0.758170	+	0.365115i
$742$	30215.0	−	14630.0i	1.49491	−	0.723832i
$743$	−21073.5	+	10148.5i	−1.04053	+	0.501091i	−0.874498	−	0.485030i	$-0.838809\pi$
$743$	−21073.5	+	10148.5i	−1.04053	+	0.501091i	−0.166029	+	0.986121i	$0.553094\pi$
$744$	−7045.41	+	8834.67i	−0.347174	+	0.435342i
$745$	4813.60	+	2318.11i	0.236720	+	0.113999i
$746$	6281.39	+	7876.62i	0.308282	+	0.386573i
$747$	3481.04	+	15251.4i	0.170501	+	0.747016i
$748$	1528.70	+	1916.93i	0.0747258	+	0.0937032i
$749$	4446.50	−	5600.12i	0.216918	−	0.273196i
$750$	−10228.8	+	12826.6i	−0.498006	+	0.624480i
$751$	29761.4	+	14332.3i	1.44608	+	0.696396i	0.981910	−	0.189349i	$-0.0606377\pi$
$751$	29761.4	+	14332.3i	1.44608	+	0.696396i	0.464172	+	0.885745i	$0.346352\pi$
$752$	2147.82	+	9410.21i	0.104153	+	0.456323i
$753$	26684.0			1.29139
$754$	−39726.3			−1.91876
$755$	−271.587	−	1189.90i	−0.0130915	−	0.0573575i
$756$	9735.19	+	4662.75i	0.468341	+	0.224316i
$757$	−1570.70	+	6881.67i	−0.0754133	+	0.330407i	−0.998536	−	0.0540992i	$-0.982771\pi$
$757$	−1570.70	+	6881.67i	−0.0754133	+	0.330407i	0.923122	+	0.384507i	$0.125628\pi$
$758$	2306.09	−	10103.7i	0.110503	−	0.484144i
$759$	−887.314	+	1112.66i	−0.0424341	+	0.0532106i
$760$	−632.421	+	793.031i	−0.0301846	+	0.0378504i
$761$	3363.43	−	14736.1i	0.160216	−	0.701951i	−0.829453	−	0.558577i	$-0.811348\pi$
$761$	3363.43	−	14736.1i	0.160216	−	0.701951i	0.989669	−	0.143374i	$-0.0457952\pi$
$762$	10875.2	−	47647.4i	0.517018	−	2.26520i
$763$	−6283.03	−	7844.40i	−0.298114	−	0.372197i
$764$	5998.17	+	26279.7i	0.284039	+	1.24446i
$765$	2431.54			0.114918
$766$	−12004.8			−0.566255
$767$	−11437.5	−	50111.1i	−0.538442	−	2.35907i
$768$	11214.9	+	5400.83i	0.526933	+	0.253758i
$769$	7051.59	−	8842.41i	0.330672	−	0.414650i	−0.588505	−	0.808493i	$-0.700283\pi$
$769$	7051.59	−	8842.41i	0.330672	−	0.414650i	0.919177	+	0.393844i	$0.128855\pi$
$770$	151.974	+	659.377i	0.00711269	+	0.0308601i
$771$	2155.97	+	2703.51i	0.100708	+	0.126283i
$772$	1689.66	+	7402.87i	0.0787721	+	0.345123i
$773$	−4920.41	−	6170.00i	−0.228945	−	0.287088i	0.654068	−	0.756435i	$-0.273061\pi$
$773$	−4920.41	−	6170.00i	−0.228945	−	0.287088i	−0.883014	+	0.469347i	$0.844489\pi$
$774$	33659.1	+	16209.4i	1.56311	+	0.752756i
$775$	−7433.52	+	9321.34i	−0.344542	+	0.432042i
$776$	6452.94	−	3107.57i	0.298514	−	0.143757i
$777$	−28380.2	−	35432.9i	−1.31034	−	1.63597i
$778$	−23089.7	−	11119.4i	−1.06402	−	0.512404i
$779$	−8309.18	+	4001.49i	−0.382166	+	0.184041i
$780$	3535.10	−	15488.3i	0.162278	−	0.710986i
$781$	−1300.66	+	626.367i	−0.0595921	+	0.0286980i
$782$	8639.06	+	10833.0i	0.395054	+	0.495382i
$783$	−4938.97			−0.225421
$784$	6183.22	+	2945.36i	0.281670	+	0.134173i
$785$	1967.32			0.0894480
$786$	−6724.39	−	8432.12i	−0.305154	−	0.382651i
$787$	29744.9	−	14324.4i	1.34726	−	0.648806i	0.385501	−	0.922707i	$-0.374029\pi$
$787$	29744.9	−	14324.4i	1.34726	−	0.648806i	0.961758	+	0.273902i	$0.0883143\pi$
$788$	8274.57	−	36253.3i	0.374073	−	1.63892i
$789$	−36236.5	+	17450.6i	−1.63505	+	0.787399i
$790$	5971.24	+	2875.60i	0.268921	+	0.129505i
$791$	27141.9	−	34183.7i	1.22004	−	1.53658i
$792$	−1105.92	+	532.585i	−0.0496178	+	0.0238947i
$793$	−8618.89	+	10807.7i	−0.385959	+	0.483978i
$794$	47389.7	+	22821.7i	2.11813	+	1.02004i
$795$	−3829.87	−	4802.51i	−0.170857	−	0.214248i
$796$	−526.628	−	2307.31i	−0.0234495	−	0.102739i
$797$	12921.8	+	16203.4i	0.574296	+	0.720144i	0.981128	−	0.193359i	$-0.0619382\pi$
$797$	12921.8	+	16203.4i	0.574296	+	0.720144i	−0.406833	+	0.913503i	$0.633367\pi$
$798$	−14031.0	−	6720.26i	−0.622421	−	0.298113i
$799$	−16851.5	+	21131.1i	−0.746136	+	0.935625i
$800$	24029.4	+	11572.0i	1.06196	+	0.511413i
$801$	565.116	+	2475.94i	0.0249281	+	0.109217i
$802$	−4527.59			−0.199345
$803$	−2531.53			−0.111253
$804$	−6618.49	−	28997.5i	−0.290319	−	1.27197i
$805$	510.922	+	2216.76i	0.0223697	+	0.0970567i
$806$	8811.27	−	38604.7i	0.385067	−	1.68709i
$807$	1230.59	−	5391.57i	0.0536788	−	0.235182i
$808$	−12950.0	+	16238.8i	−0.563835	+	0.707026i
$809$	14698.9	−	18431.9i	0.638797	−	0.801026i	−0.352055	−	0.935979i	$-0.614517\pi$
$809$	14698.9	−	18431.9i	0.638797	−	0.801026i	0.990852	+	0.134953i	$0.0430883\pi$
$810$	1899.88	−	8323.93i	0.0824137	−	0.361078i
$811$	9068.15	−	39730.1i	0.392633	−	1.72024i	−0.262681	−	0.964883i	$-0.584607\pi$
$811$	9068.15	−	39730.1i	0.392633	−	1.72024i	0.655314	−	0.755356i	$-0.272536\pi$
$812$	21660.6	−	46.0506i	0.936130	−	0.00199022i
$813$	9991.75	+	43776.7i	0.431028	+	1.88846i
$814$	−5947.09			−0.256076
$815$	−2548.43			−0.109531
$816$	−1698.51	−	7441.64i	−0.0728671	−	0.319252i
$817$	10606.6	+	5107.87i	0.454196	+	0.218729i
$818$	−23082.3	+	28944.3i	−0.986619	+	1.23718i
$819$	32834.6	−	69.8067i	1.40090	−	0.00297832i
$820$	5381.75	+	6748.50i	0.229194	+	0.287400i
$821$	−4549.10	−	19930.9i	−0.193380	−	0.847252i	−0.974770	−	0.223210i	$-0.928347\pi$
$821$	−4549.10	−	19930.9i	−0.193380	−	0.847252i	0.781391	−	0.624042i	$-0.214511\pi$
$822$	−51572.4	−	64669.7i	−2.18831	−	2.74406i
$823$	36355.8	+	17508.0i	1.53983	+	0.741544i	0.995267	−	0.0971738i	$-0.0309803\pi$
$823$	36355.8	+	17508.0i	1.53983	+	0.741544i	0.544566	+	0.838718i	$0.316695\pi$
$824$	6748.52	−	8462.38i	0.285311	−	0.357768i
$825$	−2762.54	+	1330.37i	−0.116581	+	0.0561424i
$826$	10580.6	+	45906.4i	0.445696	+	1.93376i
$827$	−9725.01	−	4683.32i	−0.408914	−	0.196922i	0.218107	−	0.975925i	$-0.430012\pi$
$827$	−9725.01	−	4683.32i	−0.408914	−	0.196922i	−0.627021	+	0.779002i	$0.715726\pi$
$828$	−11653.9	+	5612.21i	−0.489131	+	0.235553i
$829$	−3239.09	+	14191.4i	−0.135704	+	0.594556i	0.860647	+	0.509202i	$0.170059\pi$
$829$	−3239.09	+	14191.4i	−0.135704	+	0.594556i	−0.996351	+	0.0853541i	$0.972798\pi$
$830$	6987.58	−	3365.04i	0.292220	−	0.140726i
$831$	25458.4	+	31923.9i	1.06275	+	1.33264i
$832$	−74236.0			−3.09335
$833$	4346.96	+	18678.8i	0.180808	+	0.776930i
$834$	37577.2			1.56018
$835$	4948.62	+	6205.37i	0.205095	+	0.257180i
$836$	−1092.34	+	526.046i	−0.0451908	+	0.0217628i
$837$	1095.46	−	4799.52i	0.0452385	−	0.198203i
$838$	15142.2	−	7292.10i	0.624199	−	0.300599i
$839$	−20404.5	−	9826.28i	−0.839620	−	0.404340i	−0.0359056	−	0.999355i	$-0.511432\pi$
$839$	−20404.5	−	9826.28i	−0.839620	−	0.404340i	−0.803714	+	0.595016i	$0.797146\pi$
$840$	−1024.06	+	4531.10i	−0.0420637	+	0.186116i
$841$	13044.3	−	6281.78i	0.534842	−	0.257566i
$842$	−28766.4	+	36072.0i	−1.17738	+	1.47639i
$843$	−30956.7	−	14908.0i	−1.26478	−	0.609084i
$844$	19951.4	+	25018.2i	0.813690	+	1.02033i
$845$	2875.31	+	12597.6i	0.117058	+	0.512863i
$846$	−26443.6	−	33159.2i	−1.07464	−	1.34756i
$847$	5377.25	−	23792.3i	0.218140	−	0.965188i
$848$	−5078.14	+	6367.79i	−0.205642	+	0.257866i
$849$	12381.2	+	5962.49i	0.500498	+	0.241027i
$850$	6642.92	+	29104.5i	0.268059	+	1.17444i
$851$	−19993.5			−0.805370
$852$	−31064.4			−1.24912
$853$	−612.009	−	2681.39i	−0.0245660	−	0.107631i	0.961159	−	0.275997i	$-0.0890080\pi$
$853$	−612.009	−	2681.39i	−0.0245660	−	0.107631i	−0.985724	+	0.168366i	$0.946151\pi$
$854$	7878.47	−	9922.49i	0.315686	−	0.397589i
$855$	−267.552	+	1172.22i	−0.0107018	+	0.0468878i
$856$	1431.01	−	6269.65i	0.0571388	−	0.250341i
$857$	−11954.5	+	14990.4i	−0.476496	+	0.597507i	−0.960748	−	0.277421i	$-0.910520\pi$
$857$	−11954.5	+	14990.4i	−0.476496	+	0.597507i	0.484252	+	0.874928i	$0.339092\pi$
$858$	6349.37	−	7961.86i	0.252639	−	0.316799i
$859$	−5242.84	+	22970.4i	−0.208246	+	0.912386i	0.757487	+	0.652850i	$0.226427\pi$
$859$	−5242.84	+	22970.4i	−0.208246	+	0.912386i	−0.965733	+	0.259536i	$0.916430\pi$
$860$	2451.79	−	10742.0i	0.0972156	−	0.425929i
$861$	−26264.0	+	33078.1i	−1.03958	+	1.30929i
$862$	3247.74	+	14229.3i	0.128328	+	0.562240i
$863$	−17600.4			−0.694236			−0.347118	−	0.937821i	$-0.612840\pi$
$863$	−17600.4			−0.694236			−0.347118	+	0.937821i	$0.612840\pi$
$864$	−11012.7			−0.433634
$865$	576.225	+	2524.61i	0.0226500	+	0.0992361i
$866$	18754.8	+	9031.81i	0.735927	+	0.354404i
$867$	−7616.71	+	9551.05i	−0.298359	+	0.374130i
$868$	−4759.55	+	21059.2i	−0.186117	+	0.823499i
$869$	1575.79	+	1975.97i	0.0615131	+	0.0771350i
$870$	−1482.51	−	6495.29i	−0.0577721	−	0.253116i
$871$	20732.3	+	25997.5i	0.806531	+	1.01136i
$872$	−8143.58	−	3921.74i	−0.316257	−	0.152302i
$873$	5293.43	−	6637.75i	0.205218	−	0.257335i
$874$	−6173.10	+	2972.81i	−0.238911	+	0.115053i
$875$	−2204.58	+	9754.45i	−0.0851754	+	0.376869i
$876$	−49079.6	−	23635.5i	−1.89297	−	0.911608i
$877$	−18971.3	+	9136.12i	−0.730464	+	0.351773i	−0.761867	−	0.647734i	$-0.775717\pi$
$877$	−18971.3	+	9136.12i	−0.730464	+	0.351773i	0.0314027	+	0.999507i	$0.490003\pi$
$878$	15511.1	−	67958.6i	0.596212	−	2.61218i
$879$	−31201.8	+	15026.0i	−1.19728	+	0.576580i
$880$	−102.358	−	128.352i	−0.00392099	−	0.00491677i
$881$	48164.8			1.84190			0.920949	−	0.389682i	$-0.127415\pi$
$881$	48164.8			1.84190			0.920949	+	0.389682i	$0.127415\pi$
$882$	−30094.0	+	127.961i	−1.14889	+	0.00488511i
$883$	−13429.6			−0.511825			−0.255912	−	0.966700i	$-0.582376\pi$
$883$	−13429.6			−0.511825			−0.255912	+	0.966700i	$0.582376\pi$
$884$	−36775.8	−	46115.4i	−1.39921	−	1.75456i
$885$	7766.38	−	3740.09i	0.294988	−	0.142059i
$886$	8337.96	−	36531.0i	0.316162	−	1.38519i
$887$	−12010.9	+	5784.16i	−0.454664	+	0.218955i	−0.647177	−	0.762340i	$-0.724051\pi$
$887$	−12010.9	+	5784.16i	−0.454664	+	0.218955i	0.192513	+	0.981294i	$0.438336\pi$
$888$	−36784.3	−	17714.4i	−1.39009	−	0.669432i
$889$	−6690.93	−	29030.3i	−0.252426	−	1.09521i
$890$	1134.37	−	546.284i	0.0427238	−	0.0205747i
$891$	2030.01	−	2545.55i	0.0763276	−	0.0957118i
$892$	−16801.0	−	8090.96i	−0.630651	−	0.303706i
$893$	−8332.86	−	10449.1i	−0.312261	−	0.391562i
$894$	16398.7	+	71847.6i	0.613485	+	2.68785i
$895$	−1723.71	−	2161.46i	−0.0643767	−	0.0807258i
$896$	35150.9	−	74.7311i	1.31061	−	0.00278637i
$897$	21346.0	−	26767.0i	0.794561	−	0.996348i
$898$	29150.8	+	14038.3i	1.08327	+	0.521674i
$899$	−2198.25	−	9631.14i	−0.0815524	−	0.357304i
$900$	−27868.4			−1.03216
$901$	−22806.4			−0.843277
$902$	1231.22	+	5394.34i	0.0454492	+	0.199126i
$903$	53915.0	−	114.624i	1.98691	−	0.00422418i
$904$	8735.01	−	38270.6i	0.321374	−	1.40803i
$905$	760.130	−	3330.35i	0.0279200	−	0.122325i
$906$	10496.6	−	13162.3i	0.384906	−	0.482657i
$907$	−12436.7	+	15595.1i	−0.455295	+	0.570922i	−0.955502	−	0.294984i	$-0.904686\pi$
$907$	−12436.7	+	15595.1i	−0.455295	+	0.570922i	0.500207	+	0.865906i	$0.333257\pi$
$908$	−7519.84	+	32946.6i	−0.274840	+	1.20415i
$909$	−5478.61	+	24003.3i	−0.199905	+	0.875842i
$910$	−3656.02	−	15862.5i	−0.133182	−	0.577844i
$911$	5086.98	+	22287.5i	0.185004	+	0.810557i	0.979200	+	0.202896i	$0.0650352\pi$
$911$	5086.98	+	22287.5i	0.185004	+	0.810557i	−0.794196	+	0.607662i	$0.792108\pi$
$912$	3774.44			0.137044
$913$	2957.53			0.107207
$914$	10156.6	+	44499.1i	0.367562	+	1.61039i
$915$	−2088.72	−	1005.87i	−0.0754654	−	0.0363422i
$916$	−8694.61	+	10902.7i	−0.313622	+	0.393270i
$917$	−5929.26	−	2839.87i	−0.213524	−	0.102269i
$918$	−7685.60	−	9637.44i	−0.276321	−	0.346496i
$919$	982.069	+	4302.73i	0.0352508	+	0.154444i	0.989490	−	0.144600i	$-0.0461895\pi$
$919$	982.069	+	4302.73i	0.0352508	+	0.154444i	−0.954239	+	0.299044i	$0.903332\pi$
$920$	1275.58	+	1599.53i	0.0457117	+	0.0573206i
$921$	2127.59	+	1024.60i	0.0761201	+	0.0366575i
$922$	−3882.84	+	4868.93i	−0.138693	+	0.173915i
$923$	31289.9	−	15068.4i	1.11584	−	0.537360i
$924$	−3452.73	+	4348.52i	−0.122929	+	0.154822i
$925$	−38810.6	−	18690.2i	−1.37955	−	0.664357i
$926$	7734.44	−	3724.71i	0.274481	−	0.132183i
$927$	2855.03	−	12508.7i	0.101156	−	0.443192i
$928$	−19910.6	+	9588.42i	−0.704306	+	0.339176i
$929$	−2797.58	−	3508.06i	−0.0988005	−	0.123892i	0.729973	−	0.683476i	$-0.239532\pi$
$929$	−2797.58	−	3508.06i	−0.0988005	−	0.123892i	−0.828774	+	0.559584i	$0.810961\pi$
$930$	6640.72			0.234148
$931$	−9483.19	+	40.3229i	−0.333834	+	0.00141947i
$932$	8656.29			0.304234
$933$	−26983.3	−	33836.0i	−0.946831	−	1.18729i
$934$	2111.80	−	1016.99i	0.0739830	−	0.0356283i
$935$	102.292	−	448.172i	0.00357788	−	0.0156757i
$936$	26605.1	−	12812.3i	0.929075	−	0.447419i
$937$	24990.6	+	12034.8i	0.871300	+	0.419596i	0.815439	−	0.578843i	$-0.196496\pi$
$937$	24990.6	+	12034.8i	0.871300	+	0.419596i	0.0558605	+	0.998439i	$0.482210\pi$
$938$	−19052.6	−	23787.3i	−0.663209	−	0.828020i
$939$	27509.4	−	13247.8i	0.956056	−	0.460412i
$940$	−7799.03	+	9779.67i	−0.270613	+	0.339338i
$941$	−11746.9	−	5657.02i	−0.406949	−	0.195976i	0.219200	−	0.975680i	$-0.429655\pi$
$941$	−11746.9	−	5657.02i	−0.406949	−	0.195976i	−0.626149	+	0.779704i	$0.715370\pi$
$942$	16919.4	+	21216.2i	0.585204	+	0.733823i
$943$	4139.25	+	18135.2i	0.142940	+	0.626261i
$944$	−7126.21	−	8935.99i	−0.245697	−	0.308095i
$945$	−454.534	−	1972.11i	−0.0156465	−	0.0678864i
$946$	4403.65	−	5522.01i	0.151348	−	0.189784i
$947$	−15468.7	−	7449.31i	−0.530796	−	0.255618i	0.149234	−	0.988802i	$-0.452319\pi$
$947$	−15468.7	−	7449.31i	−0.530796	−	0.255618i	−0.680030	+	0.733184i	$0.738033\pi$
$948$	12101.7	+	53021.0i	0.414605	+	1.81650i
$949$	60900.6			2.08316
$950$	−14762.0			−0.504149
$951$	9978.96	+	43720.7i	0.340263	+	1.49079i
$952$	10782.2	+	13461.7i	0.367073	+	0.458293i
$953$	7072.89	−	30988.3i	0.240413	−	1.05332i	−0.700230	−	0.713918i	$-0.746919\pi$
$953$	7072.89	−	30988.3i	0.240413	−	1.05332i	0.940642	−	0.339399i	$-0.110224\pi$
$954$	7963.61	−	34890.9i	0.270264	−	1.18410i
$955$	3151.05	−	3951.30i	0.106770	−	0.133886i
$956$	−7677.34	+	9627.07i	−0.259731	+	0.325692i
$957$	565.340	−	2476.92i	0.0190960	−	0.0836650i
$958$	−7918.14	+	34691.7i	−0.267039	+	1.16998i
$959$	−45474.1	−	21780.2i	−1.53122	−	0.733389i
$960$	−2770.34	−	12137.6i	−0.0931378	−	0.408063i
$961$	−19944.2			−0.669471
$962$	143068.			4.79491
$963$	−1696.30	−	7431.96i	−0.0567626	−	0.248693i
$964$	44316.6	+	21341.8i	1.48065	+	0.713042i
$965$	887.637	−	1113.06i	0.0296104	−	0.0371303i
$966$	−19512.2	+	24574.5i	−0.649892	+	0.818502i
$967$	−20243.6	−	25384.7i	−0.673206	−	0.844174i	0.321503	−	0.946909i	$-0.395812\pi$
$967$	−20243.6	−	25384.7i	−0.673206	−	0.844174i	−0.994709	+	0.102735i	$0.967241\pi$
$968$	−4881.43	−	21386.9i	−0.162082	−	0.710126i
$969$	6589.67	+	8263.18i	0.218463	+	0.273944i
$970$	−3792.24	−	1826.25i	−0.125527	−	0.0604508i
$971$	28011.0	−	35124.7i	0.925763	−	1.16087i	−0.0609087	−	0.998143i	$-0.519400\pi$
$971$	28011.0	−	35124.7i	0.925763	−	1.16087i	0.986671	−	0.162726i	$-0.0520287\pi$
$972$	48944.7	−	23570.5i	1.61513	−	0.777804i
$973$	20616.3	−	9982.35i	0.679270	−	0.328900i
$974$	−1599.84	−	770.444i	−0.0526307	−	0.0253456i
$975$	66458.0	−	32004.5i	2.18293	−	1.05125i
$976$	−684.008	+	2996.83i	−0.0224329	+	0.0982851i
$977$	7144.42	−	3440.57i	0.233951	−	0.112665i	−0.313236	−	0.949675i	$-0.601413\pi$
$977$	7144.42	−	3440.57i	0.233951	−	0.112665i	0.547187	+	0.837011i	$0.315699\pi$
$978$	−21917.0	−	27483.0i	−0.716592	−	0.898578i
$979$	480.130			0.0156742
$980$	2011.81	+	8644.73i	0.0655766	+	0.281781i
$981$	−10714.3			−0.348708
$982$	55899.4	+	70095.6i	1.81652	+	2.27784i
$983$	−37753.7	+	18181.2i	−1.22498	+	0.589919i	−0.930694	−	0.365798i	$-0.880796\pi$
$983$	−37753.7	+	18181.2i	−1.22498	+	0.589919i	−0.294286	+	0.955717i	$0.595082\pi$
$984$	−8452.48	+	37032.8i	−0.273837	+	1.19976i
$985$	−6281.49	+	3025.01i	−0.203193	+	0.0978525i
$986$	−22286.3	−	10732.5i	−0.719818	−	0.346646i
$987$	−55202.9	−	26439.9i	−1.78027	−	0.852676i
$988$	26278.4	−	12655.0i	0.846181	−	0.407499i
$989$	14804.7	−	18564.4i	0.475997	−	0.596881i
$990$	649.926	+	312.988i	0.0208647	+	0.0100479i
$991$	−17003.7	−	21322.0i	−0.545046	−	0.683466i	0.430669	−	0.902510i	$-0.358278\pi$
$991$	−17003.7	−	21322.0i	−0.545046	−	0.683466i	−0.975715	+	0.219044i	$0.929706\pi$
$992$	−4901.55	−	21475.1i	−0.156880	−	0.687334i
$993$	18171.7	+	22786.6i	0.580726	+	0.728207i
$994$	−28649.0	+	13871.7i	−0.914175	+	0.442640i
$995$	−276.656	+	346.916i	−0.00881467	+	0.0110532i
$996$	57338.6	+	27612.8i	1.82414	+	0.878460i
$997$	65.9003	+	288.728i	0.00209336	+	0.00917162i	0.975964	−	0.217933i	$-0.0699313\pi$
$997$	65.9003	+	288.728i	0.00209336	+	0.00917162i	−0.973870	+	0.227104i	$0.927074\pi$
$998$	31676.8			1.00472
$999$	17786.9			0.563317

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.4.e.a.8.2	✓	78
49.22	even	7		2401.4.a.d.1.5		39
49.27	odd	14		2401.4.a.c.1.5		39
49.43	even	7	inner	49.4.e.a.43.2	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.4.e.a.8.2	✓	78	1.1	even	1	trivial
49.4.e.a.43.2	yes	78	49.43	even	7	inner
2401.4.a.c.1.5		39	49.27	odd	14
2401.4.a.d.1.5		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+(-2.77071 - 3.47436i) q^{2} +(-6.15987 + 2.96643i) q^{3} +(-2.61419 + 11.4535i) q^{4} +(1.98451 - 0.955692i) q^{5} +(27.3737 + 13.1825i) q^{6} +(18.5202 - 0.0393741i) q^{7} +(15.0065 - 7.22673i) q^{8} +(12.3100 - 15.4362i) q^{9} +(-8.81894 - 4.24698i) q^{10} +(-2.32728 - 2.91832i) q^{11} +(-17.8730 - 78.3069i) q^{12} +(55.9871 + 70.2055i) q^{13} +(-51.4510 - 64.2369i) q^{14} +(-9.38934 + 11.7739i) q^{15} +(17.9902 + 8.66363i) q^{16} +(12.4417 + 54.5106i) q^{17} -87.7385 q^{18} -27.6480 q^{19} +(5.75813 + 25.2280i) q^{20} +(-113.965 + 55.1816i) q^{21} +(-3.69107 + 16.1716i) q^{22} +(-12.4090 + 54.3675i) q^{23} +(-71.0001 + 89.0313i) q^{24} +(-74.9113 + 93.9358i) q^{25} +(88.7956 - 389.039i) q^{26} +(11.0395 - 48.3672i) q^{27} +(-47.9644 + 212.224i) q^{28} +(-22.1528 - 97.0578i) q^{29} +66.9219 q^{30} +99.2310 q^{31} +(-49.3954 - 216.415i) q^{32} +(22.9927 + 11.0727i) q^{33} +(154.917 - 194.260i) q^{34} +(36.7160 - 17.7778i) q^{35} +(144.618 + 181.346i) q^{36} +(79.7800 + 349.539i) q^{37} +(76.6048 + 96.0594i) q^{38} +(-553.133 - 266.375i) q^{39} +(22.8740 - 28.6831i) q^{40} +(300.534 - 144.730i) q^{41} +(507.486 + 243.065i) q^{42} +(-383.629 - 184.746i) q^{43} +(39.5089 - 19.0265i) q^{44} +(9.67706 - 42.3980i) q^{45} +(223.274 - 107.523i) q^{46} +(301.391 + 377.932i) q^{47} -136.517 q^{48} +(342.997 - 1.45843i) q^{49} +533.925 q^{50} +(-238.341 - 298.870i) q^{51} +(-950.461 + 457.718i) q^{52} +(-90.7653 + 397.669i) q^{53} +(-198.632 + 95.6563i) q^{54} +(-7.40754 - 3.56728i) q^{55} +(277.638 - 134.431i) q^{56} +(170.308 - 82.0161i) q^{57} +(-275.835 + 345.886i) q^{58} +(-515.719 - 248.357i) q^{59} +(-110.307 - 138.320i) q^{60} +(34.2558 + 150.085i) q^{61} +(-274.941 - 344.765i) q^{62} +(227.376 - 286.367i) q^{63} +(-515.449 + 646.352i) q^{64} +(178.202 + 85.8176i) q^{65} +(-25.2356 - 110.564i) q^{66} +370.306 q^{67} -656.862 q^{68} +(-84.8397 - 371.707i) q^{69} +(-163.496 - 78.3077i) q^{70} +(86.0611 - 377.058i) q^{71} +(73.1757 - 320.604i) q^{72} +(422.856 - 530.245i) q^{73} +(993.378 - 1245.66i) q^{74} +(182.789 - 800.851i) q^{75} +(72.2772 - 316.667i) q^{76} +(-43.2167 - 53.9563i) q^{77} +(607.090 + 2659.83i) q^{78} -677.093 q^{79} +43.9816 q^{80} +(194.098 + 850.397i) q^{81} +(-1335.54 - 643.160i) q^{82} +(-494.014 + 619.474i) q^{83} +(-334.096 - 1449.56i) q^{84} +(76.7860 + 96.2866i) q^{85} +(421.051 + 1844.75i) q^{86} +(424.374 + 532.148i) q^{87} +(-56.0141 - 26.9750i) q^{88} +(-80.1989 + 100.566i) q^{89} +(-174.118 + 83.8510i) q^{90} +(1039.66 + 1298.02i) q^{91} +(-590.259 - 284.254i) q^{92} +(-611.249 + 294.362i) q^{93} +(478.006 - 2094.28i) q^{94} +(-54.8679 + 26.4230i) q^{95} +(946.251 + 1186.56i) q^{96} +430.011 q^{97} +(-955.413 - 1187.66i) q^{98} -73.6966 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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