LMFDB - Embedded newform 49.4.e.a.8.4

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			8.4
Character	$\chi$	$=$	49.8
Dual form			49.4.e.a.43.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.61233 - 2.02180i) q^{2} +(-3.25484 + 1.56745i) q^{3} +(0.292112 - 1.27982i) q^{4} +(-3.53374 + 1.70176i) q^{5} +(8.41693 + 4.05338i) q^{6} +(-10.4442 + 15.2944i) q^{7} +(-21.6976 + 10.4490i) q^{8} +(-8.69714 + 10.9059i) q^{9} +(9.13817 + 4.40071i) q^{10} +(32.0120 + 40.1418i) q^{11} +(1.05528 + 4.62349i) q^{12} +(-49.9374 - 62.6195i) q^{13} +(47.7616 - 3.54344i) q^{14} +(8.83435 - 11.0779i) q^{15} +(46.6475 + 22.4643i) q^{16} +(-2.87731 - 12.6063i) q^{17} +36.0721 q^{18} -124.338 q^{19} +(1.14571 + 5.01967i) q^{20} +(10.0212 - 66.1515i) q^{21} +(29.5446 - 129.444i) q^{22} +(38.3461 - 168.005i) q^{23} +(54.2439 - 68.0197i) q^{24} +(-68.3449 + 85.7018i) q^{25} +(-46.0884 + 201.926i) q^{26} +(32.9181 - 144.224i) q^{27} +(16.5232 + 17.8345i) q^{28} +(33.7103 + 147.695i) q^{29} -36.6412 q^{30} +122.844 q^{31} +(13.0779 + 57.2981i) q^{32} +(-167.114 - 80.4779i) q^{33} +(-20.8482 + 26.1428i) q^{34} +(10.8799 - 71.8200i) q^{35} +(11.4171 + 14.3165i) q^{36} +(22.3426 + 97.8895i) q^{37} +(200.474 + 251.387i) q^{38} +(260.691 + 125.542i) q^{39} +(58.8920 - 73.8482i) q^{40} +(-270.080 + 130.064i) q^{41} +(-149.902 + 86.3972i) q^{42} +(-325.158 - 156.588i) q^{43} +(60.7255 - 29.2439i) q^{44} +(12.1743 - 53.3390i) q^{45} +(-401.499 + 193.352i) q^{46} +(204.920 + 256.961i) q^{47} -187.042 q^{48} +(-124.836 - 319.476i) q^{49} +283.466 q^{50} +(29.1249 + 36.5215i) q^{51} +(-94.7293 + 45.6192i) q^{52} +(-47.5641 + 208.392i) q^{53} +(-344.666 + 165.982i) q^{54} +(-181.434 - 87.3740i) q^{55} +(66.8037 - 440.983i) q^{56} +(404.702 - 194.894i) q^{57} +(244.256 - 306.288i) q^{58} +(395.426 + 190.427i) q^{59} +(-11.5972 - 14.5424i) q^{60} +(-44.8682 - 196.580i) q^{61} +(-198.065 - 248.366i) q^{62} +(-75.9634 - 246.921i) q^{63} +(353.008 - 442.658i) q^{64} +(283.029 + 136.300i) q^{65} +(106.733 + 467.628i) q^{66} +177.725 q^{67} -16.9744 q^{68} +(138.529 + 606.936i) q^{69} +(-162.747 + 93.8005i) q^{70} +(-36.0761 + 158.060i) q^{71} +(74.7514 - 327.507i) q^{72} +(-124.466 + 156.075i) q^{73} +(161.889 - 203.002i) q^{74} +(88.1185 - 386.073i) q^{75} +(-36.3207 + 159.131i) q^{76} +(-948.285 + 70.3533i) q^{77} +(-166.499 - 729.479i) q^{78} +676.194 q^{79} -203.069 q^{80} +(35.1128 + 153.839i) q^{81} +(698.421 + 336.342i) q^{82} +(76.3279 - 95.7121i) q^{83} +(-81.7351 - 32.1490i) q^{84} +(31.6206 + 39.6510i) q^{85} +(207.673 + 909.875i) q^{86} +(-341.225 - 427.883i) q^{87} +(-1114.02 - 536.486i) q^{88} +(-149.640 + 187.642i) q^{89} +(-127.469 + 61.3860i) q^{90} +(1479.28 - 109.748i) q^{91} +(-203.816 - 98.1526i) q^{92} +(-399.839 + 192.552i) q^{93} +(189.125 - 828.612i) q^{94} +(439.380 - 211.594i) q^{95} +(-132.378 - 165.997i) q^{96} -559.285 q^{97} +(-444.639 + 767.493i) q^{98} -716.194 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 $

$2$	−1.61233	−	2.02180i	−0.570044	−	0.714813i	0.410335	−	0.911935i	$-0.365412\pi$
$2$	−1.61233	−	2.02180i	−0.570044	−	0.714813i	−0.980379	+	0.197122i	$0.936840\pi$
$3$	−3.25484	+	1.56745i	−0.626394	+	0.301656i	−0.720021	−	0.693952i	$-0.755868\pi$
$3$	−3.25484	+	1.56745i	−0.626394	+	0.301656i	0.0936273	+	0.995607i	$0.470154\pi$
$4$	0.292112	−	1.27982i	0.0365139	−	0.159978i
$5$	−3.53374	+	1.70176i	−0.316068	+	0.152210i	−0.585191	−	0.810896i	$-0.698980\pi$
$5$	−3.53374	+	1.70176i	−0.316068	+	0.152210i	0.269123	+	0.963106i	$0.413266\pi$
$6$	8.41693	+	4.05338i	0.572700	+	0.275798i
$7$	−10.4442	+	15.2944i	−0.563936	+	0.825819i
$7$	−10.4442	+	15.2944i	−0.563936	+	0.825819i
$8$	−21.6976	+	10.4490i	−0.958907	+	0.461785i
$9$	−8.69714	+	10.9059i	−0.322116	+	0.403921i
$10$	9.13817	+	4.40071i	0.288974	+	0.139163i
$11$	32.0120	+	40.1418i	0.877453	+	1.10029i	0.994244	+	0.107135i	$0.0341677\pi$
$11$	32.0120	+	40.1418i	0.877453	+	1.10029i	−0.116791	+	0.993156i	$0.537261\pi$
$12$	1.05528	+	4.62349i	0.0253861	+	0.111224i
$13$	−49.9374	−	62.6195i	−1.06540	−	1.33596i	−0.938974	−	0.343987i	$-0.888222\pi$
$13$	−49.9374	−	62.6195i	−1.06540	−	1.33596i	−0.126421	−	0.991977i	$-0.540349\pi$
$14$	47.7616	−	3.54344i	0.911774	−	0.0676446i
$15$	8.83435	−	11.0779i	0.152068	−	0.190687i
$16$	46.6475	+	22.4643i	0.728867	+	0.351004i
$17$	−2.87731	−	12.6063i	−0.0410500	−	0.179852i	0.950247	−	0.311498i	$-0.100831\pi$
$17$	−2.87731	−	12.6063i	−0.0410500	−	0.179852i	−0.991297	+	0.131646i	$0.957974\pi$
$18$	36.0721			0.472348
$19$	−124.338			−1.50133			−0.750663	−	0.660685i	$-0.770266\pi$
$19$	−124.338			−1.50133			−0.750663	+	0.660685i	$0.770266\pi$
$20$	1.14571	+	5.01967i	0.0128094	+	0.0561217i
$21$	10.0212	−	66.1515i	0.104133	−	0.687402i
$22$	29.5446	−	129.444i	0.286315	−	1.25443i
$23$	38.3461	−	168.005i	0.347640	−	1.52311i	−0.434882	−	0.900487i	$-0.643210\pi$
$23$	38.3461	−	168.005i	0.347640	−	1.52311i	0.782522	−	0.622623i	$-0.213933\pi$
$24$	54.2439	−	68.0197i	0.461354	−	0.578519i
$25$	−68.3449	+	85.7018i	−0.546759	+	0.685614i
$26$	−46.0884	+	201.926i	−0.347641	+	1.52312i
$27$	32.9181	−	144.224i	0.234633	−	1.02800i
$28$	16.5232	+	17.8345i	0.111521	+	0.120371i
$29$	33.7103	+	147.695i	0.215857	+	0.945731i	0.960503	+	0.278271i	$0.0897613\pi$
$29$	33.7103	+	147.695i	0.215857	+	0.945731i	−0.744646	+	0.667460i	$0.767382\pi$
$30$	−36.6412			−0.222991
$31$	122.844			0.711726			0.355863	−	0.934538i	$-0.384187\pi$
$31$	122.844			0.711726			0.355863	+	0.934538i	$0.384187\pi$
$32$	13.0779	+	57.2981i	0.0722460	+	0.316530i
$33$	−167.114	−	80.4779i	−0.881541	−	0.424528i
$34$	−20.8482	+	26.1428i	−0.105160	+	0.131867i
$35$	10.8799	−	71.8200i	0.0525439	−	0.346851i
$36$	11.4171	+	14.3165i	0.0528567	+	0.0662803i
$37$	22.3426	+	97.8895i	0.0992731	+	0.434944i	1.00000		0.000557817i	$0.000177559\pi$
$37$	22.3426	+	97.8895i	0.0992731	+	0.434944i	−0.900727	+	0.434386i	$0.856965\pi$
$38$	200.474	+	251.387i	0.855822	+	1.07317i
$39$	260.691	+	125.542i	1.07036	+	0.515457i
$40$	58.8920	−	73.8482i	0.232791	−	0.291911i
$41$	−270.080	+	130.064i	−1.02877	+	0.495428i	−0.870604	−	0.491985i	$-0.836272\pi$
$41$	−270.080	+	130.064i	−1.02877	+	0.495428i	−0.158164	+	0.987413i	$0.550557\pi$
$42$	−149.902	+	86.3972i	−0.550725	+	0.317414i
$43$	−325.158	−	156.588i	−1.15317	−	0.555336i	−0.243183	−	0.969980i	$-0.578192\pi$
$43$	−325.158	−	156.588i	−1.15317	−	0.555336i	−0.909984	+	0.414644i	$0.863906\pi$
$44$	60.7255	−	29.2439i	0.208062	−	0.100197i
$45$	12.1743	−	53.3390i	0.0403296	−	0.176696i
$46$	−401.499	+	193.352i	−1.28691	+	0.619743i
$47$	204.920	+	256.961i	0.635971	+	0.797482i	0.990493	−	0.137566i	$-0.0439278\pi$
$47$	204.920	+	256.961i	0.635971	+	0.797482i	−0.354522	+	0.935048i	$0.615356\pi$
$48$	−187.042			−0.562441
$49$	−124.836	−	319.476i	−0.363953	−	0.931417i
$50$	283.466			0.801763
$51$	29.1249	+	36.5215i	0.0799668	+	0.100275i
$52$	−94.7293	+	45.6192i	−0.252627	+	0.121659i
$53$	−47.5641	+	208.392i	−0.123272	+	0.540092i	0.875145	+	0.483860i	$0.160766\pi$
$53$	−47.5641	+	208.392i	−0.123272	+	0.540092i	−0.998418	+	0.0562315i	$0.982092\pi$
$54$	−344.666	+	165.982i	−0.868576	+	0.418284i
$55$	−181.434	−	87.3740i	−0.444810	−	0.214209i
$56$	66.8037	−	440.983i	0.159411	−	1.05230i
$57$	404.702	−	194.894i	0.940422	−	0.452883i
$58$	244.256	−	306.288i	0.552973	−	0.693406i
$59$	395.426	+	190.427i	0.872543	+	0.420195i	0.815895	−	0.578199i	$-0.196244\pi$
$59$	395.426	+	190.427i	0.872543	+	0.420195i	0.0566480	+	0.998394i	$0.481959\pi$
$60$	−11.5972	−	14.5424i	−0.0249531	−	0.0312903i
$61$	−44.8682	−	196.580i	−0.0941768	−	0.412616i	0.905761	−	0.423789i	$-0.139300\pi$
$61$	−44.8682	−	196.580i	−0.0941768	−	0.412616i	−0.999938	+	0.0111738i	$0.996443\pi$
$62$	−198.065	−	248.366i	−0.405715	−	0.508751i
$63$	−75.9634	−	246.921i	−0.151913	−	0.493795i
$64$	353.008	−	442.658i	0.689468	−	0.864566i
$65$	283.029	+	136.300i	0.540084	+	0.260091i
$66$	106.733	+	467.628i	0.199059	+	0.872136i
$67$	177.725			0.324068			0.162034	−	0.986785i	$-0.448195\pi$
$67$	177.725			0.324068			0.162034	+	0.986785i	$0.448195\pi$
$68$	−16.9744			−0.0302712
$69$	138.529	+	606.936i	0.241695	+	1.05893i
$70$	−162.747	+	93.8005i	−0.277886	+	0.160162i
$71$	−36.0761	+	158.060i	−0.0603020	+	0.264200i	−0.996088	−	0.0883687i	$-0.971835\pi$
$71$	−36.0761	+	158.060i	−0.0603020	+	0.264200i	0.935786	+	0.352569i	$0.114692\pi$
$72$	74.7514	−	327.507i	0.122355	−	0.536071i
$73$	−124.466	+	156.075i	−0.199556	+	0.250236i	−0.871533	−	0.490336i	$-0.836874\pi$
$73$	−124.466	+	156.075i	−0.199556	+	0.250236i	0.671977	+	0.740572i	$0.265445\pi$
$74$	161.889	−	203.002i	0.254314	−	0.318899i
$75$	88.1185	−	386.073i	0.135667	−	0.594398i
$76$	−36.3207	+	159.131i	−0.0548193	+	0.240179i
$77$	−948.285	+	70.3533i	−1.40347	+	0.104123i
$78$	−166.499	−	729.479i	−0.241696	−	1.05894i
$79$	676.194			0.963010			0.481505	−	0.876443i	$-0.340090\pi$
$79$	676.194			0.963010			0.481505	+	0.876443i	$0.340090\pi$
$80$	−203.069			−0.283798
$81$	35.1128	+	153.839i	0.0481657	+	0.211028i
$82$	698.421	+	336.342i	0.940582	+	0.452960i
$83$	76.3279	−	95.7121i	0.100941	−	0.126576i	−0.728795	−	0.684731i	$-0.759919\pi$
$83$	76.3279	−	95.7121i	0.100941	−	0.126576i	0.829736	+	0.558156i	$0.188491\pi$
$84$	−81.7351	−	32.1490i	−0.106167	−	0.0417588i
$85$	31.6206	+	39.6510i	0.0403498	+	0.0505971i
$86$	207.673	+	909.875i	0.260395	+	1.14086i
$87$	−341.225	−	427.883i	−0.420496	−	0.527286i
$88$	−1114.02	−	536.486i	−1.34949	−	0.649882i
$89$	−149.640	+	187.642i	−0.178222	+	0.223484i	−0.862916	−	0.505347i	$-0.831365\pi$
$89$	−149.640	+	187.642i	−0.178222	+	0.223484i	0.684694	+	0.728831i	$0.259936\pi$
$90$	−127.469	+	61.3860i	−0.149294	+	0.0718962i
$91$	1479.28	−	109.748i	1.70408	−	0.126426i
$92$	−203.816	−	98.1526i	−0.230970	−	0.111230i
$93$	−399.839	+	192.552i	−0.445821	+	0.214696i
$94$	189.125	−	828.612i	0.207519	−	0.909200i
$95$	439.380	−	211.594i	0.474520	−	0.228517i
$96$	−132.378	−	165.997i	−0.140738	−	0.176479i
$97$	−559.285			−0.585431			−0.292716	−	0.956200i	$-0.594559\pi$
$97$	−559.285			−0.585431			−0.292716	+	0.956200i	$0.594559\pi$
$98$	−444.639	+	767.493i	−0.458320	+	0.791107i
$99$	−716.194			−0.727072
$100$	89.7189	+	112.504i	0.0897189	+	0.112504i
$101$	−1102.51	+	530.943i	−1.08618	+	0.523077i	−0.889288	−	0.457348i	$-0.848799\pi$
$101$	−1102.51	+	530.943i	−1.08618	+	0.523077i	−0.196893	+	0.980425i	$0.563085\pi$
$102$	26.8801	−	117.769i	0.0260934	−	0.114323i
$103$	−859.243	+	413.789i	−0.821978	+	0.395844i	−0.797100	−	0.603847i	$-0.793634\pi$
$103$	−859.243	+	413.789i	−0.821978	+	0.395844i	−0.0248773	+	0.999691i	$0.507920\pi$
$104$	1737.83	+	836.896i	1.63854	+	0.789081i
$105$	77.1618	+	250.816i	0.0717164	+	0.233116i
$106$	498.015	−	239.831i	0.456335	−	0.219759i
$107$	329.855	−	413.626i	0.298022	−	0.373707i	−0.610164	−	0.792275i	$-0.708896\pi$
$107$	329.855	−	413.626i	0.298022	−	0.373707i	0.908186	+	0.418568i	$0.137468\pi$
$108$	−174.965	−	84.2589i	−0.155889	−	0.0750724i
$109$	531.929	+	667.018i	0.467427	+	0.586136i	0.958539	−	0.284961i	$-0.0919807\pi$
$109$	531.929	+	667.018i	0.467427	+	0.586136i	−0.491112	+	0.871097i	$0.663409\pi$
$110$	115.879	+	507.698i	0.100442	+	0.440065i
$111$	−226.158	−	283.594i	−0.193387	−	0.242500i
$112$	−830.774	+	478.822i	−0.700900	+	0.403968i
$113$	−295.367	+	370.378i	−0.245892	+	0.308338i	−0.889426	−	0.457079i	$-0.848896\pi$
$113$	−295.367	+	370.378i	−0.245892	+	0.308338i	0.643535	+	0.765417i	$0.277467\pi$
$114$	−1046.55	−	503.991i	−0.859809	−	0.414062i
$115$	150.400	+	658.944i	0.121955	+	0.534320i
$116$	198.870			0.159178
$117$	1117.23			0.882805
$118$	−252.552	−	1106.50i	−0.197028	−	0.863235i
$119$	222.857	+	87.6567i	0.171674	+	0.0675250i
$120$	−75.9307	+	332.674i	−0.0577624	+	0.253074i
$121$	−290.419	+	1272.41i	−0.218196	+	0.955980i
$122$	−325.103	+	407.667i	−0.241258	+	0.302528i
$123$	675.200	−	846.674i	0.494965	−	0.620667i
$124$	35.8842	−	157.219i	0.0259879	−	0.113860i
$125$	204.765	−	897.132i	0.146518	−	0.641936i
$126$	−376.745	+	551.700i	−0.266374	+	0.390074i
$127$	613.170	+	2686.47i	0.428425	+	1.87705i	0.478130	+	0.878289i	$0.341315\pi$
$127$	613.170	+	2686.47i	0.428425	+	1.87705i	−0.0497044	+	0.998764i	$0.515828\pi$
$128$	−993.955			−0.686360
$129$	1303.78			0.889857
$130$	−180.766	−	791.988i	−0.121956	−	0.534322i
$131$	−1488.61	−	716.877i	−0.992828	−	0.478121i	−0.134329	−	0.990937i	$-0.542888\pi$
$131$	−1488.61	−	716.877i	−0.992828	−	0.478121i	−0.858499	+	0.512816i	$0.828602\pi$
$132$	−151.814	+	190.368i	−0.100104	+	0.125526i
$133$	1298.62	−	1901.68i	0.846651	−	1.23982i
$134$	−286.551	−	359.324i	−0.184733	−	0.231648i
$135$	129.110	+	565.669i	0.0823114	+	0.360630i
$136$	194.154	+	243.461i	0.122416	+	0.153505i
$137$	365.742	+	176.132i	0.228084	+	0.109839i	0.544436	−	0.838803i	$-0.316744\pi$
$137$	365.742	+	176.132i	0.228084	+	0.109839i	−0.316352	+	0.948642i	$0.602458\pi$
$138$	1003.75	−	1258.66i	0.619163	−	0.776406i
$139$	1294.75	−	623.517i	0.790065	−	0.380475i	0.00507743	−	0.999987i	$-0.498384\pi$
$139$	1294.75	−	623.517i	0.790065	−	0.380475i	0.784987	+	0.619512i	$0.212670\pi$
$140$	−88.7388	−	34.9038i	−0.0535700	−	0.0210708i
$141$	−1069.75	−	515.167i	−0.638933	−	0.307694i
$142$	377.731	−	181.905i	0.223229	−	0.107501i
$143$	915.063	−	4009.15i	0.535115	−	2.34449i
$144$	−650.692	+	313.357i	−0.376558	+	0.181341i
$145$	−370.464	−	464.548i	−0.212175	−	0.266059i
$146$	516.231			0.292627
$147$	907.083	+	844.170i	0.508945	+	0.473646i
$148$	131.808			0.0732064
$149$	−2154.42	−	2701.56i	−1.18455	−	1.48537i	−0.836562	−	0.547873i	$-0.815438\pi$
$149$	−2154.42	−	2701.56i	−1.18455	−	1.48537i	−0.347984	−	0.937501i	$-0.613134\pi$
$150$	−922.636	+	444.318i	−0.502219	+	0.241856i
$151$	−169.221	+	741.407i	−0.0911989	+	0.399569i	−0.999838	−	0.0180144i	$-0.994266\pi$
$151$	−169.221	+	741.407i	−0.0911989	+	0.399569i	0.908639	+	0.417583i	$0.137123\pi$
$152$	2697.84	−	1299.21i	1.43963	−	0.693290i
$153$	162.507	+	78.2593i	0.0858687	+	0.0413522i
$154$	1671.19	+	1803.81i	0.874468	+	0.943862i
$155$	−434.100	+	209.052i	−0.224953	+	0.108332i
$156$	236.823	−	296.966i	0.121545	−	0.152412i
$157$	−2532.13	−	1219.41i	−1.28717	−	0.619869i	−0.339949	−	0.940444i	$-0.610410\pi$
$157$	−2532.13	−	1219.41i	−1.28717	−	0.619869i	−0.947223	+	0.320574i	$0.896124\pi$
$158$	−1090.25	−	1367.13i	−0.548958	−	0.688372i
$159$	−171.830	−	752.837i	−0.0857045	−	0.375496i
$160$	−143.722	−	180.221i	−0.0710137	−	0.0890484i
$161$	2169.04	+	2341.17i	1.06177	+	1.14602i
$162$	254.418	−	319.031i	0.123389	−	0.154725i
$163$	−3114.40	−	1499.82i	−1.49656	−	0.720704i	−0.506614	−	0.862173i	$-0.669103\pi$
$163$	−3114.40	−	1499.82i	−1.49656	−	0.720704i	−0.989943	+	0.141470i	$0.954817\pi$
$164$	87.5653	+	383.649i	0.0416933	+	0.182670i
$165$	727.493			0.343244
$166$	−316.576			−0.148018
$167$	690.454	+	3025.08i	0.319934	+	1.40172i	0.837668	+	0.546180i	$0.183918\pi$
$167$	690.454	+	3025.08i	0.319934	+	1.40172i	−0.517734	+	0.855542i	$0.673224\pi$
$168$	473.782	+	1540.04i	0.217578	+	0.707242i
$169$	−938.581	+	4112.19i	−0.427210	+	1.87173i
$170$	29.1834	−	127.861i	0.0131663	−	0.0576852i
$171$	1081.39	−	1356.02i	0.483601	−	0.606417i
$172$	−295.388	+	370.404i	−0.130948	+	0.164204i
$173$	−608.653	+	2666.68i	−0.267486	+	1.17193i	0.645442	+	0.763810i	$0.276673\pi$
$173$	−608.653	+	2666.68i	−0.267486	+	1.17193i	−0.912927	+	0.408122i	$0.866184\pi$
$174$	−314.925	+	1379.78i	−0.137209	+	0.601153i
$175$	−596.945	−	1940.38i	−0.257856	−	0.838166i
$176$	591.525	+	2591.64i	0.253340	+	1.10996i
$177$	−1585.53			−0.673310
$178$	620.644			0.261344
$179$	−403.208	−	1766.57i	−0.168364	−	0.737652i	−0.986652	−	0.162843i	$-0.947934\pi$
$179$	−403.208	−	1766.57i	−0.168364	−	0.737652i	0.818288	−	0.574809i	$-0.194924\pi$
$180$	−64.7083	−	31.1619i	−0.0267948	−	0.0129037i
$181$	1486.10	−	1863.51i	0.610280	−	0.765267i	−0.376660	−	0.926351i	$-0.622928\pi$
$181$	1486.10	−	1863.51i	0.610280	−	0.765267i	0.986941	+	0.161084i	$0.0514990\pi$
$182$	−2606.98	−	2813.86i	−1.06177	−	1.14603i
$183$	454.169	+	569.509i	0.183460	+	0.230051i
$184$	923.470	+	4045.99i	0.369995	+	1.62106i
$185$	−245.538	−	307.894i	−0.0975799	−	0.122361i
$186$	1033.97	+	497.935i	0.407605	+	0.196292i
$187$	413.932	−	519.054i	0.161870	−	0.202978i
$188$	388.725	−	187.200i	0.150801	−	0.0726221i
$189$	1862.01	+	2009.77i	0.716620	+	0.773488i
$190$	−1136.23	−	547.177i	−0.433844	−	0.208928i
$191$	−471.358	+	226.994i	−0.178567	+	0.0859934i	−0.521032	−	0.853537i	$-0.674453\pi$
$191$	−471.358	+	226.994i	−0.178567	+	0.0859934i	0.342465	+	0.939531i	$0.388738\pi$
$192$	−455.141	+	1994.10i	−0.171078	+	0.749541i
$193$	−1157.21	+	557.284i	−0.431596	+	0.207846i	−0.637052	−	0.770821i	$-0.719846\pi$
$193$	−1157.21	+	557.284i	−0.431596	+	0.207846i	0.205456	+	0.978666i	$0.434132\pi$
$194$	901.752	+	1130.76i	0.333722	+	0.418474i
$195$	−1134.86			−0.416763
$196$	−445.339	+	66.4452i	−0.162296	+	0.0242147i
$197$	−956.560			−0.345950			−0.172975	−	0.984926i	$-0.555338\pi$
$197$	−956.560			−0.345950			−0.172975	+	0.984926i	$0.555338\pi$
$198$	1154.74	+	1448.00i	0.414463	+	0.519721i
$199$	−2321.99	+	1118.21i	−0.827145	+	0.398332i	−0.799044	−	0.601273i	$-0.794660\pi$
$199$	−2321.99	+	1118.21i	−0.827145	+	0.398332i	−0.0281012	+	0.999605i	$0.508946\pi$
$200$	587.420	−	2573.66i	0.207684	−	0.909925i
$201$	−578.467	+	278.575i	−0.202994	+	0.0977570i
$202$	2851.07	+	1373.00i	0.993073	+	0.478239i
$203$	−2610.97	−	1026.98i	−0.902732	−	0.355073i
$204$	55.2488	−	26.6064i	0.0189617	−	0.00913148i
$205$	733.057	−	919.224i	0.249751	−	0.313178i
$206$	2221.98	+	1070.05i	0.751518	+	0.361912i
$207$	1498.74	+	1879.36i	0.503236	+	0.631037i
$208$	−922.754	−	4042.85i	−0.307603	−	1.34770i
$209$	−3980.32	−	4991.17i	−1.31734	−	1.65190i
$210$	382.689	−	560.404i	0.125753	−	0.184150i
$211$	1912.58	−	2398.30i	0.624016	−	0.782491i	−0.364888	−	0.931052i	$-0.618893\pi$
$211$	1912.58	−	2398.30i	0.624016	−	0.782491i	0.988903	+	0.148561i	$0.0474640\pi$
$212$	252.811	+	121.747i	0.0819016	+	0.0394417i
$213$	−130.328	−	571.006i	−0.0419247	−	0.183684i
$214$	−1368.10			−0.437016
$215$	1415.50			0.449006
$216$	792.751	+	3473.27i	0.249722	+	1.09410i
$217$	−1283.02	+	1878.83i	−0.401368	+	0.587756i
$218$	490.930	−	2150.91i	0.152523	−	0.668246i
$219$	160.476	−	703.093i	0.0495159	−	0.216943i
$220$	−164.822	+	206.681i	−0.0505105	+	0.0633382i
$221$	−645.716	+	809.702i	−0.196541	+	0.246455i
$222$	−208.727	+	914.492i	−0.0631028	+	0.276472i
$223$	−87.8273	+	384.796i	−0.0263738	+	0.115551i	−0.986401	−	0.164354i	$-0.947446\pi$
$223$	−87.8273	+	384.796i	−0.0263738	+	0.115551i	0.960028	+	0.279905i	$0.0903031\pi$
$224$	−1012.93	−	398.416i	−0.302139	−	0.118841i
$225$	−340.247	−	1490.72i	−0.100814	−	0.441695i
$226$	1225.06			0.360573
$227$	418.716			0.122428			0.0612141	−	0.998125i	$-0.480503\pi$
$227$	418.716			0.122428			0.0612141	+	0.998125i	$0.480503\pi$
$228$	−131.212	−	574.878i	−0.0381129	−	0.166983i
$229$	−325.370	−	156.690i	−0.0938910	−	0.0452155i	0.386349	−	0.922353i	$-0.373736\pi$
$229$	−325.370	−	156.690i	−0.0938910	−	0.0452155i	−0.480240	+	0.877137i	$0.659450\pi$
$230$	1089.76	−	1366.51i	0.312419	−	0.391761i
$231$	2976.24	−	1715.38i	0.847715	−	0.488586i
$232$	−2274.69	−	2852.38i	−0.643711	−	0.807188i
$233$	−177.462	−	777.513i	−0.0498967	−	0.218612i	0.943833	−	0.330424i	$-0.107192\pi$
$233$	−177.462	−	777.513i	−0.0498967	−	0.218612i	−0.993729	+	0.111812i	$0.964335\pi$
$234$	−1801.35	−	2258.82i	−0.503238	−	0.631040i
$235$	−1161.42	−	559.311i	−0.322394	−	0.155257i
$236$	359.222	−	450.450i	0.0990819	−	0.124245i
$237$	−2200.90	+	1059.90i	−0.603224	+	0.290497i
$238$	−182.095	−	591.903i	−0.0495943	−	0.161207i
$239$	97.1186	+	46.7699i	0.0262849	+	0.0126581i	0.446980	−	0.894544i	$-0.352500\pi$
$239$	97.1186	+	46.7699i	0.0262849	+	0.0126581i	−0.420695	+	0.907202i	$0.638214\pi$
$240$	660.957	−	318.300i	0.177769	−	0.0856091i
$241$	−13.0668	+	57.2496i	−0.00349257	+	0.0153020i	−0.976644	−	0.214863i	$-0.931069\pi$
$241$	−13.0668	+	57.2496i	−0.00349257	+	0.0153020i	0.973152	+	0.230165i	$0.0739266\pi$
$242$	3040.80	−	1464.37i	0.807728	−	0.388981i
$243$	2134.91	+	2677.09i	0.563599	+	0.706731i
$244$	−264.695			−0.0694482
$245$	984.810	+	916.506i	0.256805	+	0.238994i
$246$	−2800.45			−0.725813
$247$	6209.14	+	7786.01i	1.59951	+	2.00572i
$248$	−2665.42	+	1283.60i	−0.682478	+	0.328664i
$249$	−98.4112	+	431.168i	−0.0250464	+	0.109736i
$250$	−2143.97	+	1032.48i	−0.542385	+	0.261199i
$251$	4299.29	+	2070.43i	1.08115	+	0.520654i	0.887684	−	0.460453i	$-0.152313\pi$
$251$	4299.29	+	2070.43i	1.08115	+	0.520654i	0.193465	+	0.981107i	$0.438027\pi$
$252$	−338.205	+	25.0914i	−0.0845433	+	0.00627227i
$253$	7971.57	−	3838.91i	1.98090	−	0.953952i
$254$	4442.87	−	5571.18i	1.09752	−	1.37625i
$255$	−165.071	−	79.4939i	−0.0405378	−	0.0195220i
$256$	−1221.48	−	1531.69i	−0.298213	−	0.373947i
$257$	−14.3890	−	63.0423i	−0.00349245	−	0.0153014i	0.973152	−	0.230165i	$-0.0739265\pi$
$257$	−14.3890	−	63.0423i	−0.00349245	−	0.0153014i	−0.976644	+	0.214863i	$0.931069\pi$
$258$	−2102.12	−	2635.98i	−0.507258	−	0.636081i
$259$	−1730.51	−	680.664i	−0.415169	−	0.163299i
$260$	257.116	−	322.413i	0.0613294	−	0.0769047i
$261$	−1903.92	−	916.880i	−0.451531	−	0.217446i
$262$	950.750	+	4165.51i	0.224189	+	0.982236i
$263$	998.845			0.234188			0.117094	−	0.993121i	$-0.462642\pi$
$263$	998.845			0.234188			0.117094	+	0.993121i	$0.462642\pi$
$264$	4466.89			1.04136
$265$	−186.554	−	817.347i	−0.0432450	−	0.189469i
$266$	−5938.61	+	440.586i	−1.36887	+	0.101557i
$267$	192.934	−	845.299i	0.0442224	−	0.193751i
$268$	51.9155	−	227.457i	0.0118330	−	0.0518438i
$269$	−431.811	+	541.474i	−0.0978735	+	0.122730i	−0.828356	−	0.560202i	$-0.810724\pi$
$269$	−431.811	+	541.474i	−0.0978735	+	0.122730i	0.730483	+	0.682931i	$0.239295\pi$
$270$	935.499	−	1173.08i	0.210862	−	0.264412i
$271$	−258.570	+	1132.87i	−0.0579594	+	0.253937i	−0.995604	−	0.0936575i	$-0.970144\pi$
$271$	−258.570	+	1132.87i	−0.0579594	+	0.253937i	0.937645	+	0.347594i	$0.113001\pi$
$272$	148.972	−	652.690i	0.0332087	−	0.145497i
$273$	−4642.81	+	2675.91i	−1.02929	+	0.593237i
$274$	−233.593	−	1023.44i	−0.0515032	−	0.225650i
$275$	−5628.08			−1.23413
$276$	817.237			0.178232
$277$	489.069	+	2142.75i	0.106084	+	0.464785i	0.999867	+	0.0162860i	$0.00518422\pi$
$277$	489.069	+	2142.75i	0.106084	+	0.464785i	−0.893783	+	0.448499i	$0.851959\pi$
$278$	−3348.18	−	1612.40i	−0.722340	−	0.347861i
$279$	−1068.39	+	1339.72i	−0.229258	+	0.287481i
$280$	514.380	+	1672.00i	0.109786	+	0.356862i
$281$	2151.61	+	2698.03i	0.456777	+	0.572780i	0.955878	−	0.293764i	$-0.0949079\pi$
$281$	2151.61	+	2698.03i	0.456777	+	0.572780i	−0.499101	+	0.866544i	$0.666337\pi$
$282$	683.234	+	2993.44i	0.144277	+	0.632117i
$283$	2883.23	+	3615.46i	0.605620	+	0.759423i	0.986242	−	0.165307i	$-0.0528616\pi$
$283$	2883.23	+	3615.46i	0.605620	+	0.759423i	−0.380622	+	0.924731i	$0.624290\pi$
$284$	191.750	+	92.3420i	0.0400644	+	0.0192940i
$285$	−1098.45	+	1377.41i	−0.228303	+	0.286283i
$286$	−9581.07	+	4614.00i	−1.98091	+	0.953956i
$287$	831.538	−	5489.13i	0.171025	−	1.12897i
$288$	−738.626	−	355.703i	−0.151125	−	0.0727779i
$289$	4275.82	−	2059.13i	0.870307	−	0.419118i
$290$	−341.910	+	1498.01i	−0.0692333	+	0.303331i
$291$	1820.38	−	876.651i	0.366711	−	0.176599i
$292$	163.391	+	204.886i	0.0327456	+	0.0410617i
$293$	1790.83			0.357070			0.178535	−	0.983934i	$-0.442864\pi$
$293$	1790.83			0.357070			0.178535	+	0.983934i	$0.442864\pi$
$294$	244.224	−	3195.02i	0.0484471	−	0.633800i
$295$	−1721.39			−0.339741
$296$	−1507.63	−	1890.51i	−0.296044	−	0.371228i
$297$	6843.18	−	3295.50i	1.33697	−	0.643853i
$298$	−1988.37	+	8711.61i	−0.386520	+	1.69346i
$299$	−12435.3	+	5988.53i	−2.40519	+	1.15828i
$300$	−468.365	−	225.553i	−0.0901368	−	0.0434076i
$301$	5790.95	−	3337.65i	1.10892	−	0.639133i
$302$	1771.81	−	853.261i	0.337604	−	0.162582i
$303$	2756.28	−	3456.27i	0.522588	−	0.655305i
$304$	−5800.08	−	2793.17i	−1.09427	−	0.526971i
$305$	493.086	+	618.310i	0.0925705	+	0.116080i
$306$	−103.790	−	454.736i	−0.0193899	−	0.0849527i
$307$	−5544.75	−	6952.89i	−1.03080	−	1.29258i	−0.955364	−	0.295431i	$-0.904537\pi$
$307$	−5544.75	−	6952.89i	−1.03080	−	1.29258i	−0.0754356	−	0.997151i	$-0.524035\pi$
$308$	−186.965	+	1234.19i	−0.0345887	+	0.228326i
$309$	2148.10	−	2693.64i	0.395474	−	0.495908i
$310$	1122.57	+	540.602i	0.205670	+	0.0990456i
$311$	817.241	+	3580.57i	0.149008	+	0.652846i	0.993162	+	0.116746i	$0.0372462\pi$
$311$	817.241	+	3580.57i	0.149008	+	0.652846i	−0.844154	+	0.536101i	$0.819897\pi$
$312$	−6968.16			−1.26440
$313$	3380.52			0.610474			0.305237	−	0.952276i	$-0.401264\pi$
$313$	3380.52			0.610474			0.305237	+	0.952276i	$0.401264\pi$
$314$	1617.23	+	7085.54i	0.290654	+	1.27344i
$315$	688.635	+	743.283i	0.123175	+	0.132950i
$316$	197.524	−	865.410i	0.0351633	−	0.154060i
$317$	−650.612	+	2850.52i	−0.115275	+	0.505051i	0.884018	+	0.467452i	$0.154828\pi$
$317$	−650.612	+	2850.52i	−0.115275	+	0.505051i	−0.999293	+	0.0375987i	$0.988029\pi$
$318$	−1245.04	+	1561.23i	−0.219554	+	0.275312i
$319$	−4849.59	+	6081.19i	−0.851175	+	1.06734i
$320$	−494.141	+	2164.97i	−0.0863229	+	0.378205i
$321$	−425.290	+	1863.32i	−0.0739482	+	0.323988i
$322$	1236.16	−	8160.09i	0.213939	−	1.41225i
$323$	357.760	+	1567.45i	0.0616294	+	0.270016i
$324$	207.144			0.0355186
$325$	8779.57			1.49847
$326$	1989.11	+	8714.88i	0.337935	+	1.48059i
$327$	−2776.86	−	1337.27i	−0.469605	−	0.226150i
$328$	4501.05	−	5644.14i	0.757711	−	0.950139i
$329$	−6070.29	+	450.355i	−1.01722	+	0.0754678i
$330$	−1172.96	−	1470.84i	−0.195664	−	0.245355i
$331$	724.680	+	3175.03i	0.120338	+	0.527237i	0.998780	+	0.0493868i	$0.0157267\pi$
$331$	724.680	+	3175.03i	0.120338	+	0.527237i	−0.878441	+	0.477850i	$0.841416\pi$
$332$	−100.198	−	125.645i	−0.0165636	−	0.0207701i
$333$	−1261.89	−	607.692i	−0.207660	−	0.100004i
$334$	5002.85	−	6273.38i	0.819592	−	1.02774i
$335$	−628.035	+	302.446i	−0.102427	+	0.0493265i
$336$	1953.51	−	2860.69i	0.317180	−	0.464474i
$337$	−3483.49	−	1677.56i	−0.563079	−	0.271165i	0.130616	−	0.991433i	$-0.458304\pi$
$337$	−3483.49	−	1677.56i	−0.563079	−	0.271165i	−0.693696	+	0.720268i	$0.744019\pi$
$338$	9827.32	−	4732.59i	1.58147	−	0.761594i
$339$	380.823	−	1668.49i	0.0610131	−	0.267316i
$340$	59.9830	−	28.8863i	0.00956775	−	0.00460759i
$341$	3932.49	+	4931.19i	0.624506	+	0.783106i
$342$	−4485.14			−0.709149
$343$	6190.00	+	1427.40i	0.974428	+	0.224701i
$344$	8691.34			1.36223
$345$	−1522.39	−	1909.01i	−0.237573	−	0.297907i
$346$	6372.84	−	3069.00i	0.990190	−	0.476851i
$347$	1563.91	−	6851.93i	0.241945	−	1.06003i	−0.697299	−	0.716781i	$-0.745615\pi$
$347$	1563.91	−	6851.93i	0.241945	−	1.06003i	0.939244	−	0.343251i	$-0.111528\pi$
$348$	−647.291	+	311.719i	−0.0997081	+	0.0480169i
$349$	−3550.87	−	1710.01i	−0.544623	−	0.262277i	0.141280	−	0.989970i	$-0.454878\pi$
$349$	−3550.87	−	1710.01i	−0.544623	−	0.262277i	−0.685903	+	0.727693i	$0.740593\pi$
$350$	−2960.58	+	4335.43i	−0.452143	+	0.662110i
$351$	−10675.1	+	5140.84i	−1.62334	+	0.781760i
$352$	−1881.40	+	2359.20i	−0.284883	+	0.357232i
$353$	7970.72	+	3838.50i	1.20181	+	0.578761i	0.924191	−	0.381930i	$-0.124741\pi$
$353$	7970.72	+	3838.50i	1.20181	+	0.578761i	0.277618	+	0.960691i	$0.410455\pi$
$354$	2556.40	+	3205.62i	0.383817	+	0.481291i
$355$	−141.496	−	619.935i	−0.0211545	−	0.0926837i
$356$	196.438	+	246.325i	0.0292449	+	0.0366720i
$357$	−862.761	+	64.0083i	−0.127905	+	0.00948929i
$358$	−2921.54	+	3663.50i	−0.431308	+	0.540843i
$359$	−8640.24	−	4160.92i	−1.27024	−	0.611713i	−0.327373	−	0.944895i	$-0.606163\pi$
$359$	−8640.24	−	4160.92i	−1.27024	−	0.611713i	−0.942863	+	0.333182i	$0.891878\pi$
$360$	293.187	+	1284.54i	0.0429231	+	0.188058i
$361$	8601.04			1.25398
$362$	−6163.71			−0.894910
$363$	−1049.17	−	4596.71i	−0.151700	−	0.664641i
$364$	291.658	−	1925.28i	0.0419973	−	0.277231i
$365$	174.227	−	763.340i	0.0249849	−	0.109466i
$366$	419.163	−	1836.47i	0.0598634	−	0.262279i
$367$	−997.677	+	1251.05i	−0.141903	+	0.177941i	−0.847704	−	0.530469i	$-0.822016\pi$
$367$	−997.677	+	1251.05i	−0.141903	+	0.177941i	0.705801	+	0.708410i	$0.250587\pi$
$368$	5562.86	−	6975.61i	0.788001	−	0.988122i
$369$	930.467	−	4076.64i	0.131269	−	0.575126i
$370$	−226.612	+	992.854i	−0.0318406	+	0.139503i
$371$	−2690.46	−	2903.96i	−0.376500	−	0.406378i
$372$	129.635	+	567.970i	0.0180680	+	0.0791609i
$373$	−13079.2			−1.81559			−0.907797	−	0.419409i	$-0.862237\pi$
$373$	−13079.2			−1.81559			−0.907797	+	0.419409i	$0.862237\pi$
$374$	−1716.81			−0.237365
$375$	739.733	+	3240.98i	0.101866	+	0.446303i
$376$	−7131.25	−	3434.23i	−0.978102	−	0.471029i
$377$	7565.16	−	9486.40i	1.03349	−	1.29595i
$378$	1061.18	−	7005.01i	0.144394	−	0.953172i
$379$	2223.64	+	2788.35i	0.301374	+	0.377910i	0.909341	−	0.416051i	$-0.136586\pi$
$379$	2223.64	+	2788.35i	0.301374	+	0.377910i	−0.607968	+	0.793962i	$0.708015\pi$
$380$	−142.456	−	624.138i	−0.0192311	−	0.0842569i
$381$	−6206.67	−	7782.92i	−0.834587	−	1.04654i
$382$	1218.92	+	587.001i	0.163260	+	0.0786220i
$383$	−2687.27	+	3369.73i	−0.358520	+	0.449570i	−0.928081	−	0.372379i	$-0.878542\pi$
$383$	−2687.27	+	3369.73i	−0.358520	+	0.449570i	0.569560	+	0.821949i	$0.307113\pi$
$384$	3235.16	−	1557.97i	0.429932	−	0.207044i
$385$	3231.27	−	1862.36i	0.427742	−	0.246532i
$386$	2992.52	+	1441.12i	0.394599	+	0.190029i
$387$	4535.67	−	2184.27i	0.595766	−	0.286906i
$388$	−163.374	+	715.787i	−0.0213764	+	0.0936561i
$389$	−4152.08	+	1999.54i	−0.541180	+	0.260619i	−0.684443	−	0.729066i	$-0.739955\pi$
$389$	−4152.08	+	1999.54i	−0.541180	+	0.260619i	0.143263	+	0.989685i	$0.454240\pi$
$390$	1829.76	+	2294.45i	0.237574	+	0.297908i
$391$	−2228.26			−0.288205
$392$	6046.84	+	5627.45i	0.779111	+	0.725074i
$393$	5968.85			0.766129
$394$	1542.29	+	1933.97i	0.197207	+	0.247289i
$395$	−2389.50	+	1150.72i	−0.304376	+	0.146580i
$396$	−209.208	+	916.602i	−0.0265483	+	0.116316i
$397$	7837.43	−	3774.31i	0.990805	−	0.477146i	0.132997	−	0.991116i	$-0.457540\pi$
$397$	7837.43	−	3774.31i	0.990805	−	0.477146i	0.857808	+	0.513970i	$0.171826\pi$
$398$	6004.62	+	2891.67i	0.756242	+	0.364187i
$399$	−1246.02	+	8225.18i	−0.156338	+	1.03201i
$400$	−5113.34	+	2462.46i	−0.639168	+	0.307807i
$401$	4326.85	−	5425.70i	0.538835	−	0.675677i	−0.435654	−	0.900114i	$-0.643483\pi$
$401$	4326.85	−	5425.70i	0.538835	−	0.675677i	0.974489	+	0.224437i	$0.0720543\pi$
$402$	1495.90	+	720.387i	0.185594	+	0.0893772i
$403$	−6134.53	−	7692.45i	−0.758269	−	0.950839i
$404$	357.456	+	1566.12i	0.0440201	+	0.192865i
$405$	−385.877	−	483.875i	−0.0473442	−	0.0593678i
$406$	2133.41	+	6934.69i	0.260786	+	0.847691i
$407$	−3214.23	+	4030.51i	−0.391458	+	0.490872i
$408$	−1013.55	−	488.102i	−0.122986	−	0.0592270i
$409$	−2693.94	−	11802.9i	−0.325689	−	1.42694i	−0.827260	−	0.561820i	$-0.810101\pi$
$409$	−2693.94	−	11802.9i	−0.325689	−	1.42694i	0.501571	−	0.865117i	$-0.332756\pi$
$410$	−3040.41			−0.366232
$411$	−1466.51			−0.176004
$412$	278.583	+	1220.55i	0.0333126	+	0.145952i
$413$	−7042.38	+	4058.93i	−0.839063	+	0.483600i
$414$	1383.22	−	6060.30i	0.164207	−	0.719438i
$415$	−106.844	+	468.114i	−0.0126380	+	0.0553706i
$416$	2934.90	−	3680.25i	0.345902	−	0.433748i
$417$	−3236.86	+	4058.90i	−0.380119	+	0.476655i
$418$	−3673.53	+	16094.8i	−0.429853	+	1.88331i
$419$	−1906.10	+	8351.16i	−0.222241	+	0.973701i	0.733546	+	0.679640i	$0.237864\pi$
$419$	−1906.10	+	8351.16i	−0.222241	+	0.973701i	−0.955787	+	0.294061i	$0.904993\pi$
$420$	343.541	−	25.4873i	0.0399121	−	0.00296108i
$421$	−1645.15	−	7207.86i	−0.190450	−	0.834417i	−0.976373	−	0.216092i	$-0.930669\pi$
$421$	−1645.15	−	7207.86i	−0.190450	−	0.834417i	0.785923	−	0.618325i	$-0.212188\pi$
$422$	−7932.57			−0.915051
$423$	−4584.60			−0.526976
$424$	−1145.46	−	5018.60i	−0.131200	−	0.574823i
$425$	1277.03	+	614.986i	0.145753	+	0.0701911i
$426$	−944.325	+	1184.15i	−0.107401	+	0.134676i
$427$	3475.19	+	1366.90i	0.393855	+	0.154916i
$428$	−433.014	−	542.982i	−0.0489030	−	0.0613225i
$429$	3305.76	+	14483.5i	0.372036	+	1.63000i
$430$	−2282.25	−	2861.85i	−0.255954	−	0.320956i
$431$	10866.0	+	5232.79i	1.21438	+	0.584814i	0.927741	−	0.373226i	$-0.121748\pi$
$431$	10866.0	+	5232.79i	1.21438	+	0.584814i	0.286637	+	0.958039i	$0.407463\pi$
$432$	4775.43	−	5988.20i	0.531847	−	0.666915i
$433$	−12685.0	+	6108.75i	−1.40785	+	0.677986i	−0.974738	−	0.223353i	$-0.928300\pi$
$433$	−12685.0	+	6108.75i	−1.40785	+	0.677986i	−0.433114	+	0.901339i	$0.642585\pi$
$434$	5867.25	−	435.291i	0.648933	−	0.0481444i
$435$	1933.96	+	931.345i	0.213164	+	0.102654i
$436$	1009.05	−	485.932i	0.110836	−	0.0533760i
$437$	−4767.90	+	20889.5i	−0.521921	+	2.28668i
$438$	−1680.25	+	809.166i	−0.183300	+	0.0882727i
$439$	−3741.98	−	4692.30i	−0.406823	−	0.510139i	0.535642	−	0.844445i	$-0.320070\pi$
$439$	−3741.98	−	4692.30i	−0.406823	−	0.510139i	−0.942465	+	0.334306i	$0.891498\pi$
$440$	4849.65			0.525450
$441$	4569.88	+	1417.09i	0.493454	+	0.153016i
$442$	2678.16			0.288206
$443$	746.693	+	936.323i	0.0800823	+	0.100420i	0.820259	−	0.571993i	$-0.193829\pi$
$443$	746.693	+	936.323i	0.0800823	+	0.100420i	−0.740176	+	0.672413i	$0.765258\pi$
$444$	−429.014	+	206.602i	−0.0458560	+	0.0220831i
$445$	209.466	−	917.732i	0.0223138	−	0.0977633i
$446$	919.586	−	442.849i	0.0976315	−	0.0470169i
$447$	11246.9	+	5416.20i	1.19006	+	0.573104i
$448$	3083.28	+	10022.3i	0.325159	+	1.05694i
$449$	1704.77	−	820.973i	0.179183	−	0.0862898i	−0.342142	−	0.939648i	$-0.611152\pi$
$449$	1704.77	−	820.973i	0.179183	−	0.0862898i	0.521325	+	0.853358i	$0.325438\pi$
$450$	−2465.34	+	3091.44i	−0.258261	+	0.323849i
$451$	−13866.8	−	6677.90i	−1.44781	−	0.697229i
$452$	387.739	+	486.209i	0.0403489	+	0.0505959i
$453$	−611.329	−	2678.41i	−0.0634056	−	0.277798i
$454$	−675.108	−	846.559i	−0.0697894	−	0.0875132i
$455$	−5040.64	+	2905.21i	−0.519361	+	0.299337i
$456$	−6744.60	+	8457.46i	−0.692642	+	0.868546i
$457$	−1379.79	−	664.472i	−0.141234	−	0.0680146i	0.361932	−	0.932204i	$-0.382117\pi$
$457$	−1379.79	−	664.472i	−0.141234	−	0.0680146i	−0.503166	+	0.864190i	$0.667832\pi$
$458$	207.808	+	910.467i	0.0212014	+	0.0928893i
$459$	−1912.85			−0.194519
$460$	887.265			0.0899325
$461$	−2702.05	−	11838.5i	−0.272987	−	1.19603i	−0.906468	−	0.422275i	$-0.861232\pi$
$461$	−2702.05	−	11838.5i	−0.272987	−	1.19603i	0.633481	−	0.773759i	$-0.281626\pi$
$462$	−8266.82	−	3251.60i	−0.832483	−	0.327442i
$463$	190.546	−	834.837i	0.0191262	−	0.0837974i	−0.964464	−	0.264214i	$-0.914887\pi$
$463$	190.546	−	834.837i	0.0191262	−	0.0837974i	0.983590	+	0.180417i	$0.0577446\pi$
$464$	−1745.35	+	7646.86i	−0.174624	+	0.765079i
$465$	1085.25	−	1360.86i	0.108231	−	0.135717i
$466$	−1285.84	+	1612.40i	−0.127823	+	0.160285i
$467$	2158.95	−	9458.97i	0.213928	−	0.937278i	−0.747941	−	0.663765i	$-0.768957\pi$
$467$	2158.95	−	9458.97i	0.213928	−	0.937278i	0.961868	−	0.273513i	$-0.0881855\pi$
$468$	326.356	−	1429.86i	0.0322347	−	0.141229i
$469$	−1856.20	+	2718.19i	−0.182754	+	0.267622i
$470$	741.779	+	3249.95i	0.0727994	+	0.318955i
$471$	10153.0			0.993264
$472$	−10569.6			−1.03073
$473$	−4123.25	−	18065.1i	−0.400819	−	1.75610i
$474$	5691.48	+	2740.87i	0.551515	+	0.265596i
$475$	8497.89	−	10656.0i	0.820863	−	1.02933i
$476$	177.284	−	259.612i	0.0170710	−	0.0249985i
$477$	−1859.02	−	2331.14i	−0.178446	−	0.223764i
$478$	−62.0280	−	271.762i	−0.00593534	−	0.0260044i
$479$	11247.8	+	14104.3i	1.07292	+	1.34539i	0.934879	+	0.354967i	$0.115508\pi$
$479$	11247.8	+	14104.3i	1.07292	+	1.34539i	0.138038	+	0.990427i	$0.455921\pi$
$480$	750.279	+	361.315i	0.0713445	+	0.0343577i
$481$	5014.06	−	6287.43i	0.475304	−	0.596013i
$482$	136.815	−	65.8867i	0.0129290	−	0.00622626i
$483$	−10729.5	−	4220.27i	−1.01079	−	0.397575i
$484$	1543.63	+	743.371i	0.144969	+	0.0698132i
$485$	1976.37	−	951.770i	0.185036	−	0.0891085i
$486$	1970.36	−	8632.71i	0.183904	−	0.805736i
$487$	6915.84	−	3330.49i	0.643504	−	0.309895i	−0.0835209	−	0.996506i	$-0.526617\pi$
$487$	6915.84	−	3330.49i	0.643504	−	0.309895i	0.727025	+	0.686611i	$0.240902\pi$
$488$	3027.60	+	3796.49i	0.280847	+	0.352170i
$489$	12487.8			1.15484
$490$	265.151	−	3468.79i	0.0244455	−	0.319804i
$491$	−14946.2			−1.37376			−0.686878	−	0.726773i	$-0.741019\pi$
$491$	−14946.2			−1.37376			−0.686878	+	0.726773i	$0.741019\pi$
$492$	−886.360	−	1111.46i	−0.0812199	−	0.101847i
$493$	1764.89	−	849.926i	0.161230	−	0.0776445i
$494$	5730.56	−	25107.2i	0.521923	−	2.28669i
$495$	2530.84	−	1218.79i	0.229804	−	0.110668i
$496$	5730.38	+	2759.61i	0.518753	+	0.249818i
$497$	−2040.64	−	2202.57i	−0.184175	−	0.198790i
$498$	1030.40	−	496.217i	0.0927179	−	0.0446506i
$499$	5347.77	−	6705.89i	0.479757	−	0.601597i	−0.481773	−	0.876296i	$-0.660007\pi$
$499$	5347.77	−	6705.89i	0.479757	−	0.601597i	0.961530	+	0.274699i	$0.0885783\pi$
$500$	−1088.36	−	524.125i	−0.0973457	−	0.0468792i
$501$	−6988.97	−	8763.89i	−0.623242	−	0.781520i
$502$	−2745.88	−	12030.5i	−0.244133	−	1.06962i
$503$	11058.8	+	13867.3i	0.980290	+	1.22925i	0.973363	+	0.229269i	$0.0736336\pi$
$503$	11058.8	+	13867.3i	0.980290	+	1.22925i	0.00692728	+	0.999976i	$0.497795\pi$
$504$	4228.30	+	4563.84i	0.373697	+	0.403352i
$505$	2992.46	−	3752.43i	0.263689	−	0.330655i
$506$	−20614.3	−	9927.31i	−1.81110	−	0.872180i
$507$	−3390.72	−	14855.7i	−0.297016	−	1.30131i
$508$	3617.33			0.315931
$509$	16898.8			1.47157			0.735784	−	0.677217i	$-0.236814\pi$
$509$	16898.8			1.47157			0.735784	+	0.677217i	$0.236814\pi$
$510$	105.428	+	461.910i	0.00915378	+	0.0401053i
$511$	−1087.12	−	3533.71i	−0.0941123	−	0.305914i
$512$	−2896.74	+	12691.4i	−0.250037	+	1.09548i
$513$	−4092.99	+	17932.6i	−0.352261	+	1.54336i
$514$	−104.259	+	130.736i	−0.00894681	+	0.0112189i
$515$	2332.17	−	2924.45i	0.199549	−	0.250227i
$516$	380.850	−	1668.61i	0.0324922	−	0.142358i
$517$	−3754.99	+	16451.7i	−0.319428	+	1.39951i
$518$	1413.99	+	4596.19i	0.119936	+	0.389855i
$519$	−2198.82	−	9633.66i	−0.185968	−	0.814780i
$520$	−7565.25			−0.637996
$521$	−14509.6			−1.22011			−0.610055	−	0.792359i	$-0.708853\pi$
$521$	−14509.6			−1.22011			−0.610055	+	0.792359i	$0.708853\pi$
$522$	1216.00	+	5327.65i	0.101960	+	0.446714i
$523$	12379.8	+	5961.81i	1.03505	+	0.498454i	0.872689	−	0.488277i	$-0.162374\pi$
$523$	12379.8	+	5961.81i	1.03505	+	0.498454i	0.162363	+	0.986731i	$0.448089\pi$
$524$	−1352.32	+	1695.75i	−0.112741	+	0.141373i
$525$	4984.41	+	5379.95i	0.414357	+	0.447239i
$526$	−1610.47	−	2019.46i	−0.133497	−	0.167400i
$527$	−353.461	−	1548.61i	−0.0292163	−	0.128005i
$528$	−5987.58	−	7508.19i	−0.493515	−	0.618848i
$529$	−15793.3	−	7605.64i	−1.29804	−	0.625104i
$530$	−1351.72	+	1695.01i	−0.110783	+	0.138918i
$531$	−5515.84	+	2656.29i	−0.450786	+	0.217087i
$532$	−2054.47	−	2217.51i	−0.167430	−	0.180716i
$533$	21631.6	+	10417.3i	1.75792	+	0.846569i
$534$	−2020.10	+	972.827i	−0.163704	+	0.0788358i
$535$	−461.732	+	2022.98i	−0.0373130	+	0.163479i
$536$	−3856.20	+	1857.05i	−0.310751	+	0.149650i
$537$	4081.39	+	5117.90i	0.327979	+	0.411273i
$538$	1790.97			0.143521
$539$	8828.10	−	15238.2i	0.705479	−	1.21773i
$540$	761.671			0.0606983
$541$	5220.98	+	6546.90i	0.414912	+	0.520283i	0.944739	−	0.327822i	$-0.106315\pi$
$541$	5220.98	+	6546.90i	0.414912	+	0.520283i	−0.529828	+	0.848105i	$0.677743\pi$
$542$	2707.33	−	1303.78i	0.214557	−	0.103325i
$543$	−1916.06	+	8394.80i	−0.151429	+	0.663453i
$544$	684.689	−	329.729i	0.0539628	−	0.0259871i
$545$	−3014.81	−	1451.85i	−0.236954	−	0.114111i
$546$	12895.9	+	5072.36i	1.01079	+	0.397577i
$547$	−9016.80	+	4342.26i	−0.704809	+	0.339418i	−0.751721	−	0.659481i	$-0.770776\pi$
$547$	−9016.80	+	4342.26i	−0.704809	+	0.339418i	0.0469121	+	0.998899i	$0.485062\pi$
$548$	332.256	−	416.635i	0.0259001	−	0.0324777i
$549$	2534.10	+	1220.36i	0.197000	+	0.0948702i
$550$	9074.31	+	11378.8i	0.703509	+	0.882172i
$551$	−4191.49	−	18364.1i	−0.324072	−	1.41985i
$552$	−9347.62	−	11721.6i	−0.720763	−	0.903809i
$553$	−7062.33	+	10342.0i	−0.543076	+	0.795271i
$554$	3543.67	−	4443.62i	0.271762	−	0.340779i
$555$	1281.79	+	617.280i	0.0980345	+	0.0472109i
$556$	−419.782	−	1839.18i	−0.0320193	−	0.140286i
$557$	−880.557			−0.0669846			−0.0334923	−	0.999439i	$-0.510663\pi$
$557$	−880.557			−0.0669846			−0.0334923	+	0.999439i	$0.510663\pi$
$558$	4431.25			0.336182
$559$	6432.09	+	28180.8i	0.486670	+	2.13224i
$560$	2120.90	−	3105.81i	0.160044	−	0.234365i
$561$	−533.691	+	2338.25i	−0.0401648	+	0.175973i
$562$	1985.77	−	8700.23i	0.149047	−	0.653019i
$563$	−6927.96	+	8687.39i	−0.518612	+	0.650319i	−0.970314	−	0.241850i	$-0.922246\pi$
$563$	−6927.96	+	8687.39i	−0.518612	+	0.650319i	0.451701	+	0.892169i	$0.350817\pi$
$564$	−971.810	+	1218.61i	−0.0725542	+	0.0909801i
$565$	413.455	−	1811.46i	0.0307862	−	0.134883i
$566$	2661.00	−	11658.6i	0.197615	−	0.865810i
$567$	−2719.60	−	1069.71i	−0.201433	−	0.0792300i
$568$	−868.802	−	3806.47i	−0.0641798	−	0.281190i
$569$	1846.90			0.136074			0.0680371	−	0.997683i	$-0.478326\pi$
$569$	1846.90			0.136074			0.0680371	+	0.997683i	$0.478326\pi$
$570$	4555.90			0.334782
$571$	1169.75	+	5125.01i	0.0857312	+	0.375613i	0.999533	−	0.0305468i	$-0.00972485\pi$
$571$	1169.75	+	5125.01i	0.0857312	+	0.375613i	−0.913802	+	0.406160i	$0.866868\pi$
$572$	−4863.71	−	2342.24i	−0.355528	−	0.171213i
$573$	1178.39	−	1477.66i	0.0859130	−	0.107731i
$574$	−12438.6	+	7169.08i	−0.904491	+	0.521309i
$575$	11777.6	+	14768.6i	0.854190	+	1.07112i
$576$	1757.41	+	7699.71i	0.127127	+	0.556981i
$577$	6072.59	+	7614.79i	0.438138	+	0.549407i	0.951051	−	0.309033i	$-0.100005\pi$
$577$	6072.59	+	7614.79i	0.438138	+	0.549407i	−0.512914	+	0.858440i	$0.671434\pi$
$578$	−11057.2	−	5324.85i	−0.795705	−	0.383191i
$579$	2893.03	−	3627.74i	0.207651	−	0.260387i
$580$	−702.756	+	338.430i	−0.0503110	+	0.0242285i
$581$	666.671	+	2167.03i	0.0476044	+	0.154739i
$582$	−4707.47	−	2267.00i	−0.335276	−	0.161461i
$583$	−9887.85	+	4761.74i	−0.702424	+	0.338269i
$584$	1069.78	−	4686.99i	0.0758007	−	0.332105i
$585$	−3948.01	+	1901.26i	−0.279026	+	0.134372i
$586$	−2887.41	−	3620.69i	−0.203546	−	0.255238i
$587$	48.2902			0.00339549			0.00169774	−	0.999999i	$-0.499460\pi$
$587$	48.2902			0.00339549			0.00169774	+	0.999999i	$0.499460\pi$
$588$	1345.36	−	914.315i	0.0943566	−	0.0641254i
$589$	−15274.3			−1.06853
$590$	2775.45	+	3480.31i	0.193667	+	0.242851i
$591$	3113.45	−	1499.36i	0.216701	−	0.104358i
$592$	−1156.79	+	5068.21i	−0.0803101	+	0.351862i
$593$	−21008.5	+	10117.2i	−1.45483	+	0.700610i	−0.983426	−	0.181307i	$-0.941967\pi$
$593$	−21008.5	+	10117.2i	−1.45483	+	0.700610i	−0.471405	+	0.881917i	$0.656253\pi$
$594$	−17696.3	−	8522.08i	−1.22237	−	0.588662i
$595$	−936.690	+	69.4931i	−0.0645387	+	0.00478813i
$596$	−4086.86	+	1968.13i	−0.280880	+	0.135264i
$597$	5804.98	−	7279.21i	0.397960	−	0.499026i
$598$	32157.4	+	15486.2i	2.19902	+	1.05899i
$599$	1361.80	+	1707.64i	0.0928909	+	0.116482i	0.826105	−	0.563517i	$-0.190552\pi$
$599$	1361.80	+	1707.64i	0.0928909	+	0.116482i	−0.733214	+	0.679998i	$0.761981\pi$
$600$	2122.11	+	9297.59i	0.144392	+	0.632621i
$601$	966.896	+	1212.45i	0.0656248	+	0.0822909i	0.813560	−	0.581480i	$-0.197526\pi$
$601$	966.896	+	1212.45i	0.0656248	+	0.0822909i	−0.747936	+	0.663771i	$0.768955\pi$
$602$	−16085.0	−	6326.72i	−1.08899	−	0.428335i
$603$	−1545.70	+	1938.25i	−0.104388	+	0.130898i
$604$	899.439	+	433.147i	0.0605922	+	0.0291797i
$605$	−1139.07	−	4990.59i	−0.0765451	−	0.335366i
$606$	−11431.9			−0.766319
$607$	12160.6			0.813150			0.406575	−	0.913617i	$-0.366723\pi$
$607$	12160.6			0.813150			0.406575	+	0.913617i	$0.366723\pi$
$608$	−1626.09	−	7124.36i	−0.108465	−	0.475215i
$609$	10108.0	−	749.916i	0.672576	−	0.0498984i
$610$	455.080	−	1993.84i	0.0302060	−	0.132341i
$611$	5857.63	−	25663.9i	0.387847	−	1.69927i
$612$	147.628	−	185.120i	0.00975085	−	0.0122272i
$613$	6726.48	−	8434.74i	0.443197	−	0.555752i	−0.509185	−	0.860657i	$-0.670053\pi$
$613$	6726.48	−	8434.74i	0.443197	−	0.555752i	0.952383	+	0.304905i	$0.0986247\pi$
$614$	−5117.38	+	22420.7i	−0.336353	+	1.47366i
$615$	−945.147	+	4140.96i	−0.0619707	+	0.271511i
$616$	19840.4	−	11435.1i	1.29771	−	0.747945i
$617$	−3490.30	−	15292.0i	−0.227738	−	0.997785i	−0.951479	−	0.307713i	$-0.900436\pi$
$617$	−3490.30	−	15292.0i	−0.227738	−	0.997785i	0.723741	−	0.690071i	$-0.242421\pi$
$618$	−8909.43			−0.579919
$619$	−18459.4			−1.19862			−0.599309	−	0.800518i	$-0.704558\pi$
$619$	−18459.4			−1.19862			−0.599309	+	0.800518i	$0.704558\pi$
$620$	140.744	+	616.639i	0.00911678	+	0.0399432i
$621$	−22968.1	−	11060.8i	−1.48418	−	0.714745i
$622$	5921.51	−	7425.34i	0.381722	−	0.478664i
$623$	−1307.00	−	4248.43i	−0.0840511	−	0.273210i
$624$	9340.37	+	11712.5i	0.599222	+	0.751400i
$625$	−2245.88	−	9839.85i	−0.143736	−	0.629750i
$626$	−5450.51	−	6834.72i	−0.347997	−	0.436375i
$627$	20778.7	+	10006.5i	1.32348	+	0.637354i
$628$	−2300.30	+	2884.48i	−0.146165	+	0.183285i
$629$	1169.74	−	563.316i	0.0741503	−	0.0357089i
$630$	392.460	−	2590.70i	0.0248190	−	0.163835i
$631$	12062.1	+	5808.79i	0.760988	+	0.366473i	0.773787	−	0.633445i	$-0.218360\pi$
$631$	12062.1	+	5808.79i	0.760988	+	0.366473i	−0.0127990	+	0.999918i	$0.504074\pi$
$632$	−14671.8	+	7065.55i	−0.923437	+	0.444704i
$633$	−2465.93	+	10803.9i	−0.154837	+	0.678386i
$634$	6812.17	−	3280.57i	0.426728	−	0.205502i
$635$	−6738.51	−	8449.83i	−0.421118	−	0.528065i
$636$	−1013.69			−0.0632005
$637$	−13771.5	+	23771.0i	−0.856586	+	1.47856i
$638$	20114.1			1.24816
$639$	−1410.02	−	1768.11i	−0.0872918	−	0.109460i
$640$	3512.38	−	1691.47i	0.216936	−	0.104471i
$641$	−6574.75	+	28805.9i	−0.405128	+	1.77498i	0.200976	+	0.979596i	$0.435589\pi$
$641$	−6574.75	+	28805.9i	−0.405128	+	1.77498i	−0.606104	+	0.795386i	$0.707268\pi$
$642$	4452.95	−	2144.43i	0.273745	−	0.131828i
$643$	5417.01	+	2608.69i	0.332233	+	0.159995i	0.592562	−	0.805525i	$-0.298117\pi$
$643$	5417.01	+	2608.69i	0.332233	+	0.159995i	−0.260329	+	0.965520i	$0.583831\pi$
$644$	3629.88	−	2092.11i	0.222108	−	0.128013i
$645$	−4607.23	+	2218.73i	−0.281255	+	0.135445i
$646$	2592.24	−	3250.56i	0.157879	−	0.197975i
$647$	−9309.96	−	4483.44i	−0.565707	−	0.272430i	0.129094	−	0.991632i	$-0.458793\pi$
$647$	−9309.96	−	4483.44i	−0.565707	−	0.272430i	−0.694801	+	0.719202i	$0.744507\pi$
$648$	−2369.33	−	2971.05i	−0.143636	−	0.180114i
$649$	5014.29	+	21969.1i	0.303279	+	1.32875i
$650$	−14155.5	−	17750.5i	−0.854194	−	1.07113i
$651$	1231.05	−	8126.34i	0.0741144	−	0.489242i
$652$	−2829.25	+	3547.77i	−0.169942	+	0.213100i
$653$	2599.78	+	1251.99i	0.155800	+	0.0750294i	0.510159	−	0.860080i	$-0.329587\pi$
$653$	2599.78	+	1251.99i	0.155800	+	0.0750294i	−0.354359	+	0.935110i	$0.615301\pi$
$654$	1773.53	+	7770.36i	0.106041	+	0.464595i
$655$	6480.32			0.386576
$656$	−15520.4			−0.923732
$657$	−619.638	−	2714.81i	−0.0367951	−	0.161210i
$658$	10697.8	+	11546.8i	0.633807	+	0.684103i
$659$	5792.05	−	25376.6i	0.342376	−	1.50005i	−0.451666	−	0.892187i	$-0.649170\pi$
$659$	5792.05	−	25376.6i	0.342376	−	1.50005i	0.794042	−	0.607862i	$-0.207973\pi$
$660$	212.509	−	931.063i	0.0125332	−	0.0549115i
$661$	13332.1	−	16718.0i	0.784509	−	0.983743i	−0.215465	−	0.976511i	$-0.569127\pi$
$661$	13332.1	−	16718.0i	0.784509	−	0.983743i	0.999974	−	0.00723107i	$-0.00230174\pi$
$662$	5250.84	−	6584.35i	0.308278	−	0.386568i
$663$	832.536	−	3647.58i	0.0487677	−	0.213665i
$664$	−656.034	+	2874.27i	−0.0383420	+	0.167987i
$665$	−1352.79	+	8929.98i	−0.0788855	+	0.520737i
$666$	805.945	+	3531.08i	0.0468915	+	0.205445i
$667$	26106.1			1.51549
$668$	4073.26			0.235927
$669$	−317.285	−	1390.12i	−0.0183362	−	0.0803363i
$670$	1624.08	+	782.116i	0.0936474	+	0.0450982i
$671$	6454.77	−	8094.03i	0.371362	−	0.465673i
$672$	3921.41	−	290.930i	0.225107	−	0.0167007i
$673$	−18916.5	−	23720.6i	−1.08348	−	1.35863i	−0.928763	−	0.370675i	$-0.879126\pi$
$673$	−18916.5	−	23720.6i	−1.08348	−	1.35863i	−0.154713	−	0.987960i	$-0.549445\pi$
$674$	2224.85	+	9747.68i	0.127148	+	0.557072i
$675$	10110.4	+	12678.1i	0.576520	+	0.722934i
$676$	4988.71	+	2402.44i	0.283837	+	0.136689i
$677$	−3536.86	+	4435.08i	−0.200786	+	0.251778i	−0.872023	−	0.489465i	$-0.837192\pi$
$677$	−3536.86	+	4435.08i	−0.200786	+	0.251778i	0.671236	+	0.741243i	$0.265764\pi$
$678$	−3987.37	+	1920.21i	−0.225861	+	0.108769i
$679$	5841.31	−	8553.92i	0.330146	−	0.483460i
$680$	−1100.40	−	529.927i	−0.0620567	−	0.0298849i
$681$	−1362.85	+	656.316i	−0.0766883	+	0.0369311i
$682$	3629.39	−	15901.4i	0.203778	−	0.892810i
$683$	−3551.33	+	1710.23i	−0.198957	+	0.0958129i	−0.530710	−	0.847554i	$-0.678075\pi$
$683$	−3551.33	+	1710.23i	−0.198957	+	0.0958129i	0.331752	+	0.943367i	$0.392360\pi$
$684$	−1419.58	−	1780.10i	−0.0793552	−	0.0995083i
$685$	−1592.17			−0.0888085
$686$	−7094.41	−	14816.4i	−0.394848	−	0.824623i
$687$	1304.63			0.0724523
$688$	−11650.2	−	14608.9i	−0.645581	−	0.809532i
$689$	15424.6	−	7428.11i	0.852876	−	0.410724i
$690$	−1405.05	+	6155.91i	−0.0775206	+	0.339640i
$691$	−9.39956	+	4.52659i	−0.000517477	+	0.000249204i	−0.434142	−	0.900844i	$-0.642949\pi$
$691$	−9.39956	+	4.52659i	−0.000517477	+	0.000249204i	0.433625	+	0.901093i	$0.357234\pi$
$692$	3235.09	+	1557.94i	0.177716	+	0.0855837i
$693$	7480.10	−	10953.7i	0.410022	−	0.600430i
$694$	−16374.7	+	7885.66i	−0.895643	+	0.431319i
$695$	−3514.22	+	4406.70i	−0.191802	+	0.240512i
$696$	11874.7	+	5718.56i	0.646710	+	0.311439i
$697$	2416.73	+	3030.48i	0.131335	+	0.164688i
$698$	2267.88	+	9936.22i	0.122981	+	0.538813i
$699$	1796.32	+	2252.52i	0.0972005	+	0.121886i
$700$	−2657.72	+	197.177i	−0.143504	+	0.0106465i
$701$	−7407.47	+	9288.68i	−0.399110	+	0.500469i	−0.940260	−	0.340458i	$-0.889418\pi$
$701$	−7407.47	+	9288.68i	−0.399110	+	0.500469i	0.541149	+	0.840926i	$0.317989\pi$
$702$	27605.5	+	13294.1i	1.48419	+	0.714748i
$703$	−2778.05	−	12171.4i	−0.149041	−	0.652993i
$704$	29069.6			1.55625
$705$	4656.93			0.248780
$706$	−5090.76	−	22304.1i	−0.271379	−	1.18899i
$707$	3394.48	−	22407.6i	0.180569	−	1.19197i
$708$	−463.152	+	2029.20i	−0.0245852	+	0.107715i
$709$	−469.402	+	2056.59i	−0.0248643	+	0.108938i	−0.985837	−	0.167705i	$-0.946365\pi$
$709$	−469.402	+	2056.59i	−0.0248643	+	0.108938i	0.960973	+	0.276642i	$0.0892217\pi$
$710$	−1025.24	+	1285.61i	−0.0541925	+	0.0679553i
$711$	−5880.95	+	7374.48i	−0.310201	+	0.388980i
$712$	1286.15	−	5634.98i	0.0676972	−	0.296601i
$713$	4710.60	−	20638.5i	0.247424	−	1.08404i
$714$	1520.47	+	1641.12i	0.0796947	+	0.0860190i
$715$	3589.02	+	15724.5i	0.187723	+	0.822467i
$716$	−2378.68			−0.124156
$717$	−389.415			−0.0202831
$718$	5518.38	+	24177.6i	0.286830	+	1.25668i
$719$	−21330.8	−	10272.4i	−1.10640	−	0.532815i	−0.210736	−	0.977543i	$-0.567586\pi$
$719$	−21330.8	−	10272.4i	−1.10640	−	0.532815i	−0.895666	+	0.444728i	$0.853300\pi$
$720$	1766.12	−	2214.64i	0.0914158	−	0.114632i
$721$	2645.48	−	17463.3i	0.136648	−	0.902035i
$722$	−13867.7	−	17389.6i	−0.714824	−	0.896360i
$723$	−47.2053	−	206.820i	−0.00242819	−	0.0106386i
$724$	−1950.86	−	2446.30i	−0.100142	−	0.125574i
$725$	−14961.6	−	7205.13i	−0.766428	−	0.369092i
$726$	−7602.00	+	9532.61i	−0.388618	+	0.487312i
$727$	−23653.0	+	11390.7i	−1.20666	+	0.581096i	−0.925567	−	0.378585i	$-0.876411\pi$
$727$	−23653.0	+	11390.7i	−1.20666	+	0.581096i	−0.281092	+	0.959681i	$0.590697\pi$
$728$	−30950.1	+	17838.3i	−1.57567	+	0.908148i
$729$	−14983.6	−	7215.70i	−0.761244	−	0.366596i
$730$	−1824.23	+	878.502i	−0.0924901	+	0.0445409i
$731$	−1038.42	+	4549.60i	−0.0525407	+	0.230196i
$732$	861.540	−	414.896i	0.0435020	−	0.0209494i
$733$	5847.43	+	7332.45i	0.294652	+	0.369482i	0.907018	−	0.421093i	$-0.138353\pi$
$733$	5847.43	+	7332.45i	0.294652	+	0.369482i	−0.612366	+	0.790575i	$0.709782\pi$
$734$	4137.95			0.208085
$735$	−4641.97	−	1439.44i	−0.232955	−	0.0722376i
$736$	10127.9			0.507226
$737$	5689.34	+	7134.20i	0.284355	+	0.356569i
$738$	−9742.36	+	4691.67i	−0.485937	+	0.234015i
$739$	964.117	−	4224.07i	0.0479914	−	0.210264i	−0.945247	−	0.326355i	$-0.894179\pi$
$739$	964.117	−	4224.07i	0.0479914	−	0.210264i	0.993239	+	0.116091i	$0.0370365\pi$
$740$	−465.775	+	224.305i	−0.0231382	+	0.0111427i
$741$	−32413.9	−	15609.7i	−1.60696	−	0.773869i
$742$	−1533.32	+	10121.7i	−0.0758623	+	0.500780i
$743$	28881.7	−	13908.7i	1.42606	−	0.686756i	0.447803	−	0.894132i	$-0.352207\pi$
$743$	28881.7	−	13908.7i	1.42606	−	0.686756i	0.978261	+	0.207376i	$0.0664923\pi$
$744$	6663.55	−	8355.83i	0.328357	−	0.411747i
$745$	12210.6	+	5880.31i	0.600485	+	0.289178i
$746$	21088.0	+	26443.5i	1.03497	+	1.29781i
$747$	379.990	+	1664.84i	0.0186119	+	0.0815441i
$748$	−543.383	−	681.381i	−0.0265616	−	0.0333072i
$749$	2881.06	+	9364.94i	0.140549	+	0.456859i
$750$	5359.91	−	6721.11i	0.260955	−	0.327227i
$751$	17265.0	+	8314.40i	0.838895	+	0.403990i	0.803444	−	0.595381i	$-0.202999\pi$
$751$	17265.0	+	8314.40i	0.838895	+	0.403990i	0.0354513	+	0.999371i	$0.488713\pi$
$752$	3786.55	+	16590.0i	0.183619	+	0.804487i
$753$	−17238.8			−0.834284
$754$	−31377.1			−1.51550
$755$	−663.713	−	2907.92i	−0.0319934	−	0.140172i
$756$	3116.07	−	1795.97i	0.149908	−	0.0864003i
$757$	5728.49	−	25098.1i	0.275040	−	1.20503i	−0.628940	−	0.777454i	$-0.716511\pi$
$757$	5728.49	−	25098.1i	0.275040	−	1.20503i	0.903980	−	0.427575i	$-0.140632\pi$
$758$	2052.25	−	8991.48i	0.0983390	−	0.430851i
$759$	−19928.9	+	24990.0i	−0.953061	+	1.19510i
$760$	−7322.53	+	9182.17i	−0.349495	+	0.438253i
$761$	−1438.00	+	6300.28i	−0.0684986	+	0.300112i	−0.997560	−	0.0698135i	$-0.977760\pi$
$761$	−1438.00	+	6300.28i	−0.0684986	+	0.300112i	0.929062	+	0.369925i	$0.120617\pi$
$762$	−5728.28	+	25097.3i	−0.272328	+	1.19315i
$763$	−15757.2	+	1169.03i	−0.747641	+	0.0554675i
$764$	152.824	+	669.564i	0.00723686	+	0.0317068i
$765$	−707.437			−0.0334346
$766$	11145.7			0.525731
$767$	−7822.09	−	34270.8i	−0.368239	−	1.61336i
$768$	6376.56	+	3070.79i	0.299602	+	0.144281i
$769$	−21188.6	+	26569.6i	−0.993601	+	1.24594i	−0.0243902	+	0.999703i	$0.507764\pi$
$769$	−21188.6	+	26569.6i	−0.993601	+	1.24594i	−0.969211	+	0.246233i	$0.920807\pi$
$770$	−8975.19	−	3530.23i	−0.420056	−	0.165221i
$771$	145.649	+	182.639i	0.00680342	+	0.00853122i
$772$	375.191	+	1643.82i	0.0174915	+	0.0766351i
$773$	20963.6	+	26287.6i	0.975432	+	1.22315i	0.974783	+	0.223153i	$0.0716351\pi$
$773$	20963.6	+	26287.6i	0.975432	+	1.22315i	0.000648869		1.00000i	$0.499793\pi$
$774$	−11729.1	−	5648.45i	−0.544696	−	0.262312i
$775$	−8395.78	+	10528.0i	−0.389142	+	0.487969i
$776$	12135.1	−	5843.97i	0.561374	−	0.270343i
$777$	6699.44	−	497.032i	0.309319	−	0.0229484i
$778$	10737.2	+	5170.75i	0.494790	+	0.238278i
$779$	33581.4	−	16171.9i	1.54452	−	0.743799i
$780$	−331.505	+	1452.42i	−0.0152177	+	0.0666730i
$781$	−7499.66	+	3611.65i	−0.343609	+	0.165474i
$782$	3592.69	+	4505.09i	0.164289	+	0.206012i
$783$	22410.8			1.02285
$784$	1353.51	−	17707.1i	0.0616579	−	0.806628i
$785$	11023.0			0.501184
$786$	−9623.75	−	12067.8i	−0.436728	−	0.547639i
$787$	−30146.6	+	14517.8i	−1.36545	+	0.657567i	−0.965845	−	0.259120i	$-0.916568\pi$
$787$	−30146.6	+	14517.8i	−1.36545	+	0.657567i	−0.399607	+	0.916687i	$0.630853\pi$
$788$	−279.422	+	1224.23i	−0.0126320	+	0.0553443i
$789$	−3251.08	+	1565.64i	−0.146694	+	0.0706441i
$790$	6179.17	+	2975.73i	0.278285	+	0.134015i
$791$	−2579.82	−	8385.77i	−0.115965	−	0.376945i
$792$	15539.7	−	7483.51i	0.697195	−	0.335751i
$793$	−10069.2	+	12626.3i	−0.450904	+	0.565416i
$794$	−20267.4	−	9760.27i	−0.905873	−	0.436245i
$795$	1888.35	+	2367.92i	0.0842427	+	0.105637i
$796$	752.835	+	3298.39i	0.0335220	+	0.146870i
$797$	24267.6	+	30430.6i	1.07855	+	1.35245i	0.931673	+	0.363299i	$0.118350\pi$
$797$	24267.6	+	30430.6i	1.07855	+	1.35245i	0.146874	+	0.989155i	$0.453079\pi$
$798$	18638.6	−	10742.5i	0.826817	−	0.476542i
$799$	2649.72	−	3322.64i	0.117322	−	0.147117i
$800$	−5804.36	−	2795.23i	−0.256519	−	0.123533i
$801$	−744.965	−	3263.90i	−0.0328615	−	0.143976i
$802$	−17946.0			−0.790142
$803$	−10249.5			−0.450433
$804$	187.550	+	821.710i	0.00822684	+	0.0360441i
$805$	−11648.9	−	4581.90i	−0.510026	−	0.200609i
$806$	−5661.70	+	24805.5i	−0.247425	+	1.08404i
$807$	556.743	−	2439.25i	0.0242854	−	0.106401i
$808$	18374.1	−	23040.3i	0.799997	−	1.00316i
$809$	−20085.4	+	25186.3i	−0.872885	+	1.09456i	0.121897	+	0.992543i	$0.461102\pi$
$809$	−20085.4	+	25186.3i	−0.872885	+	1.09456i	−0.994782	+	0.102020i	$0.967469\pi$
$810$	−356.135	+	1560.33i	−0.0154485	+	0.0676845i
$811$	−1690.40	+	7406.14i	−0.0731912	+	0.320672i	−0.998249	−	0.0591552i	$-0.981159\pi$
$811$	−1690.40	+	7406.14i	−0.0731912	+	0.320672i	0.925058	+	0.379827i	$0.124016\pi$
$812$	−2077.05	+	3041.60i	−0.0897661	+	0.131452i
$813$	−934.109	−	4092.60i	−0.0402960	−	0.176548i
$814$	13331.3			0.574030
$815$	13557.8			0.582711
$816$	538.177	+	2357.91i	0.0230882	+	0.101156i
$817$	40429.7	+	19469.9i	1.73128	+	0.833740i
$818$	−19519.6	+	24476.8i	−0.834335	+	1.04622i
$819$	−11668.6	+	17087.4i	−0.497845	+	0.729036i
$820$	−962.311	−	1206.70i	−0.0409822	−	0.0513900i
$821$	1952.07	+	8552.57i	0.0829813	+	0.363565i	0.999321	−	0.0368362i	$-0.0117280\pi$
$821$	1952.07	+	8552.57i	0.0829813	+	0.363565i	−0.916340	+	0.400401i	$0.868871\pi$
$822$	2364.50	+	2964.98i	0.100330	+	0.125810i
$823$	15474.9	+	7452.32i	0.655433	+	0.315640i	0.731880	−	0.681434i	$-0.238643\pi$
$823$	15474.9	+	7452.32i	0.655433	+	0.315640i	−0.0764468	+	0.997074i	$0.524358\pi$
$824$	14319.8	−	17956.5i	0.605405	−	0.759154i
$825$	18318.5	−	8821.72i	0.773052	−	0.372282i
$826$	19561.0	+	7693.94i	0.823986	+	0.324100i
$827$	−14985.2	−	7216.48i	−0.630091	−	0.303436i	0.0914477	−	0.995810i	$-0.470851\pi$
$827$	−14985.2	−	7216.48i	−0.630091	−	0.303436i	−0.721539	+	0.692374i	$0.756565\pi$
$828$	2843.05	−	1369.14i	0.119327	−	0.0574650i
$829$	3827.01	−	16767.2i	0.160335	−	0.702473i	−0.829292	−	0.558815i	$-0.811256\pi$
$829$	3827.01	−	16767.2i	0.160335	−	0.702473i	0.989627	−	0.143658i	$-0.0458866\pi$
$830$	1118.70	−	538.737i	0.0467838	−	0.0225299i
$831$	−4950.50	−	6207.73i	−0.206656	−	0.259138i
$832$	−45347.3			−1.88958
$833$	−3668.23	+	2492.95i	−0.152577	+	0.103692i
$834$	13425.1			0.557404
$835$	−7587.84	−	9514.86i	−0.314477	−	0.394342i
$836$	−7550.51	+	3636.14i	−0.312368	+	0.150429i
$837$	4043.81	−	17717.1i	0.166995	−	0.731651i
$838$	19957.6	−	9611.07i	0.822701	−	0.396192i
$839$	−21097.2	−	10159.9i	−0.868125	−	0.418067i	−0.0538516	−	0.998549i	$-0.517150\pi$
$839$	−21097.2	−	10159.9i	−0.868125	−	0.418067i	−0.814273	+	0.580482i	$0.802864\pi$
$840$	−4295.00	−	4635.84i	−0.176419	−	0.190419i
$841$	1296.43	−	624.327i	0.0531563	−	0.0255987i
$842$	−11920.3	+	14947.6i	−0.487887	+	0.611791i
$843$	−11232.2	−	5409.13i	−0.458904	−	0.220997i
$844$	−2510.71	−	3148.33i	−0.102396	−	0.128401i
$845$	−3681.26	−	16128.7i	−0.149869	−	0.656619i
$846$	7391.88	+	9269.12i	0.300400	+	0.376689i
$847$	−16427.5	−	17731.1i	−0.666418	−	0.719302i
$848$	−6900.12	+	8652.48i	−0.279423	+	0.350386i
$849$	−15051.5	−	7248.42i	−0.608441	−	0.293010i
$850$	−815.619	−	3573.46i	−0.0329123	−	0.144198i
$851$	17302.7			0.696979
$852$	−768.858			−0.0309162
$853$	−6226.78	−	27281.3i	−0.249942	−	1.09507i	−0.931625	−	0.363421i	$-0.881609\pi$
$853$	−6226.78	−	27281.3i	−0.249942	−	1.09507i	0.681682	−	0.731648i	$-0.261249\pi$
$854$	−2839.55	−	9230.02i	−0.113779	−	0.369842i
$855$	−1513.73	+	6632.08i	−0.0605479	+	0.265278i
$856$	−2835.09	+	12421.3i	−0.113203	+	0.495973i
$857$	−578.166	+	724.997i	−0.0230452	+	0.0288978i	−0.793221	−	0.608934i	$-0.791597\pi$
$857$	−578.166	+	724.997i	−0.0230452	+	0.0288978i	0.770175	+	0.637832i	$0.220169\pi$
$858$	23952.6	−	30035.7i	0.953065	−	1.19511i
$859$	8931.57	−	39131.8i	0.354763	−	1.55432i	−0.411269	−	0.911514i	$-0.634914\pi$
$859$	8931.57	−	39131.8i	0.354763	−	1.55432i	0.766031	−	0.642803i	$-0.222229\pi$
$860$	413.484	−	1811.59i	0.0163950	−	0.0718312i
$861$	5897.40	+	19169.6i	0.233430	+	0.758768i
$862$	−6939.93	−	30405.8i	−0.274217	−	1.20142i
$863$	29854.6			1.17759			0.588797	−	0.808281i	$-0.299602\pi$
$863$	29854.6			1.17759			0.588797	+	0.808281i	$0.299602\pi$
$864$	8694.25			0.342343
$865$	−2387.23	−	10459.2i	−0.0938363	−	0.411124i
$866$	32803.0	+	15797.1i	1.28717	+	0.619869i
$867$	−10689.5	+	13404.3i	−0.418726	+	0.525066i
$868$	2029.79	+	2190.86i	0.0793726	+	0.0856713i
$869$	21646.3	+	27143.6i	0.844996	+	1.05959i
$870$	−1235.19	−	5411.70i	−0.0481341	−	0.210889i
$871$	−8875.12	−	11129.1i	−0.345261	−	0.432943i
$872$	−18511.3	−	8914.55i	−0.718888	−	0.346198i
$873$	4864.18	−	6099.49i	0.188577	−	0.236468i
$874$	49921.8	−	24041.1i	1.93207	−	0.930436i
$875$	11582.5	+	12501.6i	0.447496	+	0.483008i
$876$	−852.958	−	410.763i	−0.0328982	−	0.0158429i
$877$	−42699.8	+	20563.2i	−1.64409	+	0.791754i	−0.644463	+	0.764636i	$0.722919\pi$
$877$	−42699.8	+	20563.2i	−1.64409	+	0.791754i	−0.999632	+	0.0271186i	$0.991367\pi$
$878$	−3453.56	+	15131.1i	−0.132747	+	0.581604i
$879$	−5828.87	+	2807.03i	−0.223666	+	0.107712i
$880$	−6500.65	−	8151.56i	−0.249019	−	0.312260i
$881$	−6643.82			−0.254070			−0.127035	−	0.991898i	$-0.540546\pi$
$881$	−6643.82			−0.254070			−0.127035	+	0.991898i	$0.540546\pi$
$882$	−4503.09	−	11524.2i	−0.171912	−	0.439953i
$883$	−43050.8			−1.64074			−0.820371	−	0.571831i	$-0.806233\pi$
$883$	−43050.8			−1.64074			−0.820371	+	0.571831i	$0.806233\pi$
$884$	847.655	+	1062.93i	0.0322508	+	0.0404413i
$885$	5602.86	−	2698.20i	0.212812	−	0.102485i
$886$	689.141	−	3019.32i	0.0261311	−	0.114488i
$887$	34908.3	−	16810.9i	1.32143	−	0.636365i	0.365730	−	0.930721i	$-0.380819\pi$
$887$	34908.3	−	16810.9i	1.32143	−	0.636365i	0.955696	+	0.294355i	$0.0951049\pi$
$888$	7870.36	+	3790.17i	0.297423	+	0.143232i
$889$	−47492.0	−	18680.1i	−1.79171	−	0.704736i
$890$	−2193.19	+	1056.19i	−0.0826023	+	0.0397792i
$891$	−5051.35	+	6334.20i	−0.189929	+	0.238163i
$892$	466.816	+	224.807i	0.0175226	+	0.00843844i
$893$	−25479.4	−	31950.2i	−0.954799	−	1.19728i
$894$	−7183.18	−	31471.6i	−0.268726	−	1.17737i
$895$	4431.12	+	5556.44i	0.165493	+	0.207521i
$896$	10381.1	−	15201.9i	0.387063	−	0.566809i
$897$	31088.2	−	38983.4i	1.15720	−	1.45108i
$898$	−4408.49	−	2123.02i	−0.163823	−	0.0788931i
$899$	4141.12	+	18143.4i	0.153631	+	0.673101i
$900$	−2007.25			−0.0743426
$901$	2763.91			0.102197
$902$	8856.50	+	38802.8i	0.326928	+	1.43237i
$903$	−13617.0	+	19940.5i	−0.501822	+	0.734861i
$904$	2538.66	−	11122.6i	0.0934011	−	0.409217i
$905$	−2080.24	+	9114.14i	−0.0764084	+	0.334767i
$906$	−4429.53	+	5554.46i	−0.162430	+	0.203680i
$907$	10681.6	−	13394.3i	0.391045	−	0.490355i	−0.546871	−	0.837217i	$-0.684181\pi$
$907$	10681.6	−	13394.3i	0.391045	−	0.490355i	0.937916	+	0.346862i	$0.112753\pi$
$908$	122.312	−	535.883i	0.00447033	−	0.0195858i
$909$	3798.32	−	16641.5i	0.138595	−	0.607223i
$910$	14000.9	+	5507.00i	0.510028	+	0.200610i
$911$	9465.34	+	41470.4i	0.344238	+	1.50821i	0.790030	+	0.613069i	$0.210065\pi$
$911$	9465.34	+	41470.4i	0.344238	+	1.50821i	−0.445792	+	0.895137i	$0.647078\pi$
$912$	23256.5			0.844406
$913$	6285.47			0.227841
$914$	881.248	+	3861.00i	0.0318918	+	0.139727i
$915$	−2574.08	−	1239.61i	−0.0930017	−	0.0447873i
$916$	−295.580	+	370.645i	−0.0106618	+	0.0133695i
$917$	26511.6	−	15280.1i	0.954732	−	0.550266i
$918$	3084.14	+	3867.38i	0.110884	+	0.139044i
$919$	−8844.34	−	38749.6i	−0.317462	−	1.39089i	−0.841987	−	0.539498i	$-0.818614\pi$
$919$	−8844.34	−	38749.6i	−0.317462	−	1.39089i	0.524525	−	0.851395i	$-0.324243\pi$
$920$	−10148.6	−	12726.0i	−0.363685	−	0.456046i
$921$	28945.6	+	13939.5i	1.03560	+	0.498719i
$922$	−19578.3	+	24550.5i	−0.699326	+	0.876927i
$923$	11699.2	−	5634.02i	0.417207	−	0.200916i
$924$	−1325.99	−	4310.14i	−0.0472097	−	0.153456i
$925$	−9916.31	−	4775.44i	−0.352482	−	0.169747i
$926$	−1995.09	+	960.787i	−0.0708022	+	0.0340966i
$927$	2960.22	−	12969.6i	0.104883	−	0.459522i
$928$	−8021.76	+	3863.08i	−0.283758	+	0.136651i
$929$	20743.3	+	26011.3i	0.732579	+	0.918625i	0.998976	−	0.0452387i	$-0.0144048\pi$
$929$	20743.3	+	26011.3i	0.732579	+	0.918625i	−0.266398	+	0.963863i	$0.585833\pi$
$930$	−4501.16			−0.158708
$931$	15521.9	+	39723.2i	0.546412	+	1.39836i
$932$	−1046.92			−0.0367950
$933$	−8272.34	−	10373.2i	−0.290272	−	0.363990i
$934$	−22605.0	+	10886.0i	−0.791926	+	0.381372i
$935$	−579.422	+	2538.61i	−0.0202665	+	0.0887931i
$936$	−24241.2	+	11674.0i	−0.846527	+	0.407666i
$937$	34748.3	+	16733.9i	1.21150	+	0.583428i	0.926933	−	0.375227i	$-0.122435\pi$
$937$	34748.3	+	16733.9i	1.21150	+	0.583428i	0.284569	+	0.958656i	$0.408150\pi$
$938$	8488.44	−	629.758i	0.295477	−	0.0219215i
$939$	−11003.1	+	5298.79i	−0.382397	+	0.184153i
$940$	−1055.08	+	1323.03i	−0.0366096	+	0.0459070i
$941$	−9545.96	−	4597.09i	−0.330701	−	0.159257i	0.261164	−	0.965294i	$-0.415894\pi$
$941$	−9545.96	−	4597.09i	−0.330701	−	0.159257i	−0.591865	+	0.806037i	$0.701608\pi$
$942$	−16370.0	−	20527.4i	−0.566205	−	0.709998i
$943$	11494.9	+	50362.4i	0.396951	+	1.73916i
$944$	14167.8	+	17765.9i	0.488478	+	0.612532i
$945$	−10000.0	−	3933.32i	−0.344233	−	0.135398i
$946$	−29876.0	+	37463.3i	−1.02680	+	1.28757i
$947$	28975.7	+	13953.9i	0.994280	+	0.478820i	0.858993	−	0.511987i	$-0.171090\pi$
$947$	28975.7	+	13953.9i	0.994280	+	0.478820i	0.135286	+	0.990807i	$0.456805\pi$
$948$	713.575	+	3126.38i	0.0244471	+	0.107110i
$949$	15988.8			0.546912
$950$	−35245.7			−1.20371
$951$	−2350.40	−	10297.8i	−0.0801441	−	0.351134i
$952$	−5751.38	+	426.695i	−0.195802	+	0.0145266i
$953$	−2228.29	+	9762.76i	−0.0757411	+	0.331843i	−0.998576	−	0.0533530i	$-0.983009\pi$
$953$	−2228.29	+	9762.76i	−0.0757411	+	0.331843i	0.922835	+	0.385196i	$0.125866\pi$
$954$	−1715.74	+	7517.13i	−0.0582275	+	0.255111i
$955$	1279.37	−	1604.28i	0.0433502	−	0.0543594i
$956$	88.2267	−	110.633i	0.00298478	−	0.00374280i
$957$	6252.68	−	27394.8i	0.211202	−	0.925337i
$958$	10380.9	−	45481.7i	0.350095	−	1.53387i
$959$	−6513.73	+	3754.23i	−0.219332	+	0.126413i
$960$	−1785.13	−	7821.18i	−0.0600156	−	0.262945i
$961$	−14700.3			−0.493447
$962$	−20796.2			−0.696982
$963$	1642.15	+	7194.72i	0.0549506	+	0.240754i
$964$	69.4525	+	33.4465i	0.00232045	+	0.00111747i
$965$	3140.93	−	3938.60i	0.104777	−	0.131387i
$966$	8767.02	+	28497.4i	0.292002	+	0.949160i
$967$	29979.5	+	37593.1i	0.996977	+	1.25017i	0.968094	+	0.250587i	$0.0806235\pi$
$967$	29979.5	+	37593.1i	0.996977	+	1.25017i	0.0288827	+	0.999583i	$0.490805\pi$
$968$	−6994.02	−	30642.8i	−0.232228	−	1.01746i
$969$	−3621.35	−	4541.03i	−0.120056	−	0.150546i
$970$	−5110.84	−	2461.25i	−0.169175	−	0.0814701i
$971$	−21891.3	+	27450.8i	−0.723508	+	0.907250i	−0.998531	−	0.0541879i	$-0.982743\pi$
$971$	−21891.3	+	27450.8i	−0.723508	+	0.907250i	0.275023	+	0.961438i	$0.411314\pi$
$972$	4049.84	−	1950.30i	0.133641	−	0.0643580i
$973$	−3986.34	+	26314.5i	−0.131342	+	0.867014i
$974$	−17884.2	−	8612.57i	−0.588343	−	0.283331i
$975$	−28576.1	+	13761.5i	−0.938633	+	0.452022i
$976$	2323.04	−	10177.9i	0.0761873	−	0.333798i
$977$	−14122.7	+	6801.15i	−0.462463	+	0.222710i	−0.650582	−	0.759436i	$-0.725475\pi$
$977$	−14122.7	+	6801.15i	−0.462463	+	0.222710i	0.188119	+	0.982146i	$0.439761\pi$
$978$	−20134.4	−	25247.7i	−0.658309	−	0.825493i
$979$	−12322.6			−0.402279
$980$	1460.64	−	992.661i	0.0476107	−	0.0323565i
$981$	−11900.7			−0.387318
$982$	24098.2	+	30218.2i	0.783102	+	0.981979i
$983$	13234.6	−	6373.44i	0.429418	−	0.206797i	−0.206674	−	0.978410i	$-0.566264\pi$
$983$	13234.6	−	6373.44i	0.429418	−	0.206797i	0.636092	+	0.771613i	$0.280550\pi$
$984$	−5803.31	+	25425.9i	−0.188011	+	0.823729i
$985$	3380.24	−	1627.84i	0.109343	−	0.0526570i
$986$	−4563.96	−	2197.89i	−0.147410	−	0.0709888i
$987$	19051.9	−	10980.7i	0.614417	−	0.354123i
$988$	11778.5	−	5672.22i	0.379275	−	0.182649i
$989$	−38776.2	+	48623.8i	−1.24672	+	1.56334i
$990$	−6544.70	−	3151.76i	−0.210105	−	0.101181i
$991$	6816.86	+	8548.08i	0.218511	+	0.274005i	0.878990	−	0.476840i	$-0.158218\pi$
$991$	6816.86	+	8548.08i	0.218511	+	0.274005i	−0.660479	+	0.750845i	$0.729647\pi$
$992$	1606.55	+	7038.75i	0.0514193	+	0.225283i
$993$	−7335.41	−	9198.32i	−0.234423	−	0.293957i
$994$	−1162.98	+	7677.02i	−0.0371101	+	0.244970i
$995$	6302.40	−	7902.96i	0.200803	−	0.251800i
$996$	523.072	+	251.898i	0.0166407	+	0.00801375i
$997$	4541.37	+	19897.0i	0.144259	+	0.632042i	0.994418	+	0.105515i	$0.0336490\pi$
$997$	4541.37	+	19897.0i	0.144259	+	0.632042i	−0.850158	+	0.526527i	$0.823494\pi$
$998$	−22180.3			−0.703512
$999$	14853.5			0.470413

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.4.e.a.8.4	✓	78
49.22	even	7		2401.4.a.d.1.10		39
49.27	odd	14		2401.4.a.c.1.10		39
49.43	even	7	inner	49.4.e.a.43.4	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.4.e.a.8.4	✓	78	1.1	even	1	trivial
49.4.e.a.43.4	yes	78	49.43	even	7	inner
2401.4.a.c.1.10		39	49.27	odd	14
2401.4.a.d.1.10		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+(-1.61233 - 2.02180i) q^{2} +(-3.25484 + 1.56745i) q^{3} +(0.292112 - 1.27982i) q^{4} +(-3.53374 + 1.70176i) q^{5} +(8.41693 + 4.05338i) q^{6} +(-10.4442 + 15.2944i) q^{7} +(-21.6976 + 10.4490i) q^{8} +(-8.69714 + 10.9059i) q^{9} +(9.13817 + 4.40071i) q^{10} +(32.0120 + 40.1418i) q^{11} +(1.05528 + 4.62349i) q^{12} +(-49.9374 - 62.6195i) q^{13} +(47.7616 - 3.54344i) q^{14} +(8.83435 - 11.0779i) q^{15} +(46.6475 + 22.4643i) q^{16} +(-2.87731 - 12.6063i) q^{17} +36.0721 q^{18} -124.338 q^{19} +(1.14571 + 5.01967i) q^{20} +(10.0212 - 66.1515i) q^{21} +(29.5446 - 129.444i) q^{22} +(38.3461 - 168.005i) q^{23} +(54.2439 - 68.0197i) q^{24} +(-68.3449 + 85.7018i) q^{25} +(-46.0884 + 201.926i) q^{26} +(32.9181 - 144.224i) q^{27} +(16.5232 + 17.8345i) q^{28} +(33.7103 + 147.695i) q^{29} -36.6412 q^{30} +122.844 q^{31} +(13.0779 + 57.2981i) q^{32} +(-167.114 - 80.4779i) q^{33} +(-20.8482 + 26.1428i) q^{34} +(10.8799 - 71.8200i) q^{35} +(11.4171 + 14.3165i) q^{36} +(22.3426 + 97.8895i) q^{37} +(200.474 + 251.387i) q^{38} +(260.691 + 125.542i) q^{39} +(58.8920 - 73.8482i) q^{40} +(-270.080 + 130.064i) q^{41} +(-149.902 + 86.3972i) q^{42} +(-325.158 - 156.588i) q^{43} +(60.7255 - 29.2439i) q^{44} +(12.1743 - 53.3390i) q^{45} +(-401.499 + 193.352i) q^{46} +(204.920 + 256.961i) q^{47} -187.042 q^{48} +(-124.836 - 319.476i) q^{49} +283.466 q^{50} +(29.1249 + 36.5215i) q^{51} +(-94.7293 + 45.6192i) q^{52} +(-47.5641 + 208.392i) q^{53} +(-344.666 + 165.982i) q^{54} +(-181.434 - 87.3740i) q^{55} +(66.8037 - 440.983i) q^{56} +(404.702 - 194.894i) q^{57} +(244.256 - 306.288i) q^{58} +(395.426 + 190.427i) q^{59} +(-11.5972 - 14.5424i) q^{60} +(-44.8682 - 196.580i) q^{61} +(-198.065 - 248.366i) q^{62} +(-75.9634 - 246.921i) q^{63} +(353.008 - 442.658i) q^{64} +(283.029 + 136.300i) q^{65} +(106.733 + 467.628i) q^{66} +177.725 q^{67} -16.9744 q^{68} +(138.529 + 606.936i) q^{69} +(-162.747 + 93.8005i) q^{70} +(-36.0761 + 158.060i) q^{71} +(74.7514 - 327.507i) q^{72} +(-124.466 + 156.075i) q^{73} +(161.889 - 203.002i) q^{74} +(88.1185 - 386.073i) q^{75} +(-36.3207 + 159.131i) q^{76} +(-948.285 + 70.3533i) q^{77} +(-166.499 - 729.479i) q^{78} +676.194 q^{79} -203.069 q^{80} +(35.1128 + 153.839i) q^{81} +(698.421 + 336.342i) q^{82} +(76.3279 - 95.7121i) q^{83} +(-81.7351 - 32.1490i) q^{84} +(31.6206 + 39.6510i) q^{85} +(207.673 + 909.875i) q^{86} +(-341.225 - 427.883i) q^{87} +(-1114.02 - 536.486i) q^{88} +(-149.640 + 187.642i) q^{89} +(-127.469 + 61.3860i) q^{90} +(1479.28 - 109.748i) q^{91} +(-203.816 - 98.1526i) q^{92} +(-399.839 + 192.552i) q^{93} +(189.125 - 828.612i) q^{94} +(439.380 - 211.594i) q^{95} +(-132.378 - 165.997i) q^{96} -559.285 q^{97} +(-444.639 + 767.493i) q^{98} -716.194 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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