LMFDB - Embedded newform 63.4.o.a.41.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(20,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("63.20");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.5
Character	$\chi$	$=$	63.41
Dual form			63.4.o.a.20.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.28475 + 1.89645i) q^{2} +(-4.97559 - 1.49782i) q^{3} +(3.19307 - 5.53055i) q^{4} +(-9.97590 + 17.2788i) q^{5} +(19.1841 - 4.51602i) q^{6} +(-4.13417 - 18.0529i) q^{7} -6.12125i q^{8} +(22.5131 + 14.9051i) q^{9} +O(q^{10})$	\(q+(-3.28475 + 1.89645i) q^{2} +(-4.97559 - 1.49782i) q^{3} +(3.19307 - 5.53055i) q^{4} +(-9.97590 + 17.2788i) q^{5} +(19.1841 - 4.51602i) q^{6} +(-4.13417 - 18.0529i) q^{7} -6.12125i q^{8} +(22.5131 + 14.9051i) q^{9} -75.6753i q^{10} +(31.1676 - 17.9946i) q^{11} +(-24.1712 + 22.7352i) q^{12} +(6.59980 + 3.81040i) q^{13} +(47.8163 + 51.4592i) q^{14} +(75.5165 - 71.0301i) q^{15} +(37.1532 + 64.3512i) q^{16} -21.4747 q^{17} +(-102.217 - 6.26447i) q^{18} -97.3022i q^{19} +(63.7074 + 110.345i) q^{20} +(-6.47004 + 96.0163i) q^{21} +(-68.2518 + 118.216i) q^{22} +(-35.6964 - 20.6094i) q^{23} +(-9.16851 + 30.4568i) q^{24} +(-136.537 - 236.489i) q^{25} -28.9050 q^{26} +(-89.6909 - 107.882i) q^{27} +(-113.043 - 34.7800i) q^{28} +(-51.8612 + 29.9421i) q^{29} +(-113.348 + 376.530i) q^{30} +(61.1449 + 35.3020i) q^{31} +(-201.669 - 116.434i) q^{32} +(-182.030 + 42.8505i) q^{33} +(70.5390 - 40.7257i) q^{34} +(353.175 + 108.661i) q^{35} +(154.319 - 76.9169i) q^{36} +355.309 q^{37} +(184.529 + 319.614i) q^{38} +(-27.1307 - 28.8443i) q^{39} +(105.768 + 61.0649i) q^{40} +(7.30794 - 12.6577i) q^{41} +(-160.838 - 327.660i) q^{42} +(-48.8575 - 84.6237i) q^{43} -229.832i q^{44} +(-482.130 + 240.307i) q^{45} +156.339 q^{46} +(-234.897 - 406.853i) q^{47} +(-88.4728 - 375.834i) q^{48} +(-308.817 + 149.268i) q^{49} +(896.982 + 517.873i) q^{50} +(106.849 + 32.1651i) q^{51} +(42.1472 - 24.3337i) q^{52} -710.531i q^{53} +(499.206 + 184.271i) q^{54} +718.049i q^{55} +(-110.506 + 25.3063i) q^{56} +(-145.741 + 484.136i) q^{57} +(113.568 - 196.705i) q^{58} +(232.735 - 403.109i) q^{59} +(-151.706 - 644.452i) q^{60} +(542.558 - 313.246i) q^{61} -267.794 q^{62} +(176.007 - 468.047i) q^{63} +288.792 q^{64} +(-131.678 + 76.0243i) q^{65} +(516.659 - 485.964i) q^{66} +(-262.327 + 454.364i) q^{67} +(-68.5700 + 118.767i) q^{68} +(146.742 + 156.011i) q^{69} +(-1366.16 + 312.855i) q^{70} +115.729i q^{71} +(91.2376 - 137.808i) q^{72} -708.180i q^{73} +(-1167.10 + 673.827i) q^{74} +(325.136 + 1381.18i) q^{75} +(-538.135 - 310.692i) q^{76} +(-453.708 - 488.273i) q^{77} +(143.819 + 43.2944i) q^{78} +(128.747 + 222.997i) q^{79} -1482.55 q^{80} +(284.678 + 671.118i) q^{81} +55.4366i q^{82} +(200.583 + 347.420i) q^{83} +(510.364 + 342.369i) q^{84} +(214.229 - 371.056i) q^{85} +(320.970 + 185.312i) q^{86} +(302.888 - 71.3010i) q^{87} +(-110.149 - 190.784i) q^{88} -977.834 q^{89} +(1127.95 - 1703.68i) q^{90} +(41.5042 - 134.899i) q^{91} +(-227.962 + 131.614i) q^{92} +(-251.356 - 267.233i) q^{93} +(1543.16 + 890.942i) q^{94} +(1681.26 + 970.677i) q^{95} +(829.026 + 881.389i) q^{96} +(-521.193 + 300.911i) q^{97} +(731.308 - 1075.97i) q^{98} +(969.889 + 59.4408i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) $ 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7	$ 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7} - 18 q^{11} + 204 q^{14} + 66 q^{15} - 242 q^{16} - 210 q^{18} - 57 q^{21} - 34 q^{22} - 102 q^{23} - 352 q^{25} + 300 q^{28} + 246 q^{29} - 144 q^{30} + 1068 q^{32} - 1818 q^{36} + 328 q^{37} - 798 q^{39} - 1158 q^{42} - 170 q^{43} + 968 q^{46} - 79 q^{49} + 288 q^{50} - 204 q^{51} + 1212 q^{56} + 324 q^{57} - 538 q^{58} + 5316 q^{60} + 783 q^{63} - 808 q^{64} + 4350 q^{65} - 590 q^{67} + 384 q^{70} + 4284 q^{72} - 5304 q^{74} - 2787 q^{77} + 612 q^{78} - 302 q^{79} - 3720 q^{81} + 7050 q^{84} - 612 q^{85} - 13692 q^{86} + 1294 q^{88} + 210 q^{91} - 10194 q^{92} - 4266 q^{93} + 6336 q^{95} + 1014 q^{99}+O(q^{100}) $ 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7 - 18 * q^11 + 204 * q^14 + 66 * q^15 - 242 * q^16 - 210 * q^18 - 57 * q^21 - 34 * q^22 - 102 * q^23 - 352 * q^25 + 300 * q^28 + 246 * q^29 - 144 * q^30 + 1068 * q^32 - 1818 * q^36 + 328 * q^37 - 798 * q^39 - 1158 * q^42 - 170 * q^43 + 968 * q^46 - 79 * q^49 + 288 * q^50 - 204 * q^51 + 1212 * q^56 + 324 * q^57 - 538 * q^58 + 5316 * q^60 + 783 * q^63 - 808 * q^64 + 4350 * q^65 - 590 * q^67 + 384 * q^70 + 4284 * q^72 - 5304 * q^74 - 2787 * q^77 + 612 * q^78 - 302 * q^79 - 3720 * q^81 + 7050 * q^84 - 612 * q^85 - 13692 * q^86 + 1294 * q^88 + 210 * q^91 - 10194 * q^92 - 4266 * q^93 + 6336 * q^95 + 1014 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−3.28475	+	1.89645i	−1.16134	+	0.670497i	−0.951624	−	0.307266i	$-0.900586\pi$
$2$	−3.28475	+	1.89645i	−1.16134	+	0.670497i	−0.209712	+	0.977763i	$0.567253\pi$
$3$	−4.97559	−	1.49782i	−0.957554	−	0.288255i
$3$	−4.97559	−	1.49782i	−0.957554	−	0.288255i
$4$	3.19307	−	5.53055i	0.399133	−	0.691319i
$5$	−9.97590	+	17.2788i	−0.892272	+	1.54546i	−0.0551264	+	0.998479i	$0.517556\pi$
$5$	−9.97590	+	17.2788i	−0.892272	+	1.54546i	−0.837145	+	0.546981i	$0.815777\pi$
$6$	19.1841	−	4.51602i	1.30532	−	0.307276i
$7$	−4.13417	−	18.0529i	−0.223224	−	0.974767i
$7$	−4.13417	−	18.0529i	−0.223224	−	0.974767i
$8$		−	6.12125i		−	0.270523i
$9$	22.5131	+	14.9051i	0.833818	+	0.552040i
$10$		−	75.6753i		−	2.39306i
$11$	31.1676	−	17.9946i	0.854307	−	0.493234i	−0.00779501	−	0.999970i	$-0.502481\pi$
$11$	31.1676	−	17.9946i	0.854307	−	0.493234i	0.862102	+	0.506735i	$0.169148\pi$
$12$	−24.1712	+	22.7352i	−0.581468	+	0.546923i
$13$	6.59980	+	3.81040i	0.140804	+	0.0812934i	0.568747	−	0.822512i	$-0.307428\pi$
$13$	6.59980	+	3.81040i	0.140804	+	0.0812934i	−0.427943	+	0.903806i	$0.640762\pi$
$14$	47.8163	+	51.4592i	0.912817	+	0.982360i
$15$	75.5165	−	71.0301i	1.29988	−	1.22266i
$16$	37.1532	+	64.3512i	0.580519	+	1.00549i
$17$	−21.4747			−0.306375			−0.153187	−	0.988197i	$-0.548954\pi$
$17$	−21.4747			−0.306375			−0.153187	+	0.988197i	$0.548954\pi$
$18$	−102.217	−	6.26447i	−1.33848	−	0.0820306i
$19$		−	97.3022i		−	1.17488i	−0.809269	−	0.587438i	$-0.800136\pi$
$19$		−	97.3022i		−	1.17488i	0.809269	−	0.587438i	$-0.199864\pi$
$20$	63.7074	+	110.345i	0.712271	+	1.23369i
$21$	−6.47004	+	96.0163i	−0.0672323	+	0.997737i
$22$	−68.2518	+	118.216i	−0.661424	+	1.14562i
$23$	−35.6964	−	20.6094i	−0.323618	−	0.186841i	0.329386	−	0.944195i	$-0.393158\pi$
$23$	−35.6964	−	20.6094i	−0.323618	−	0.186841i	−0.653004	+	0.757354i	$0.726492\pi$
$24$	−9.16851	+	30.4568i	−0.0779798	+	0.259041i
$25$	−136.537	−	236.489i	−1.09230	−	1.89191i
$26$	−28.9050			−0.218028
$27$	−89.6909	−	107.882i	−0.639297	−	0.768960i
$28$	−113.043	−	34.7800i	−0.762971	−	0.234743i
$29$	−51.8612	+	29.9421i	−0.332082	+	0.191728i	−0.656765	−	0.754095i	$-0.728076\pi$
$29$	−51.8612	+	29.9421i	−0.332082	+	0.191728i	0.324683	+	0.945823i	$0.394742\pi$
$30$	−113.348	+	376.530i	−0.689813	+	2.29149i
$31$	61.1449	+	35.3020i	0.354256	+	0.204530i	0.666558	−	0.745453i	$-0.267767\pi$
$31$	61.1449	+	35.3020i	0.354256	+	0.204530i	−0.312302	+	0.949983i	$0.601100\pi$
$32$	−201.669	−	116.434i	−1.11407	−	0.643211i
$33$	−182.030	+	42.8505i	−0.960222	+	0.226040i
$34$	70.5390	−	40.7257i	0.355804	−	0.205423i
$35$	353.175	+	108.661i	1.70564	+	0.524773i
$36$	154.319	−	76.9169i	0.714440	−	0.356097i
$37$	355.309			1.57872			0.789358	−	0.613933i	$-0.210414\pi$
$37$	355.309			1.57872			0.789358	+	0.613933i	$0.210414\pi$
$38$	184.529	+	319.614i	0.787752	+	1.36443i
$39$	−27.1307	−	28.8443i	−0.111394	−	0.118430i
$40$	105.768	+	61.0649i	0.418083	+	0.241380i
$41$	7.30794	−	12.6577i	0.0278368	−	0.0482147i	−0.851771	−	0.523914i	$-0.824471\pi$
$41$	7.30794	−	12.6577i	0.0278368	−	0.0482147i	0.879608	+	0.475699i	$0.157805\pi$
$42$	−160.838	−	327.660i	−0.590901	−	1.20379i
$43$	−48.8575	−	84.6237i	−0.173272	−	0.300116i	0.766290	−	0.642495i	$-0.222101\pi$
$43$	−48.8575	−	84.6237i	−0.173272	−	0.300116i	−0.939562	+	0.342379i	$0.888767\pi$
$44$		−	229.832i		−	0.787465i
$45$	−482.130	+	240.307i	−1.59715	+	0.796063i
$46$	156.339			0.501106
$47$	−234.897	−	406.853i	−0.729005	−	1.26267i	−0.957304	−	0.289083i	$-0.906650\pi$
$47$	−234.897	−	406.853i	−0.729005	−	1.26267i	0.228299	−	0.973591i	$-0.426684\pi$
$48$	−88.4728	−	375.834i	−0.266041	−	1.13015i
$49$	−308.817	+	149.268i	−0.900342	+	0.435184i
$50$	896.982	+	517.873i	2.53705	+	1.46477i
$51$	106.849	+	32.1651i	0.293370	+	0.0883141i
$52$	42.1472	−	24.3337i	0.112399	−	0.0648938i
$53$		−	710.531i		−	1.84149i	−0.390167	−	0.920744i	$-0.627583\pi$
$53$		−	710.531i		−	1.84149i	0.390167	−	0.920744i	$-0.372417\pi$
$54$	499.206	+	184.271i	1.25802	+	0.464374i
$55$			718.049i			1.76040i
$56$	−110.506	+	25.3063i	−0.263697	+	0.0603874i
$57$	−145.741	+	484.136i	−0.338664	+	1.12501i
$58$	113.568	−	196.705i	0.257106	−	0.445321i
$59$	232.735	−	403.109i	0.513551	−	0.889497i	−0.486325	−	0.873778i	$-0.661663\pi$
$59$	232.735	−	403.109i	0.513551	−	0.889497i	0.999876	−	0.0157191i	$-0.00500375\pi$
$60$	−151.706	−	644.452i	−0.326420	−	1.38664i
$61$	542.558	−	313.246i	1.13881	−	0.657492i	0.192674	−	0.981263i	$-0.438284\pi$
$61$	542.558	−	313.246i	1.13881	−	0.657492i	0.946136	+	0.323771i	$0.104951\pi$
$62$	−267.794			−0.548547
$63$	176.007	−	468.047i	0.351982	−	0.936007i
$64$	288.792			0.564047
$65$	−131.678	+	76.0243i	−0.251271	+	0.145072i
$66$	516.659	−	485.964i	0.963580	−	0.906334i
$67$	−262.327	+	454.364i	−0.478334	+	0.828498i	−0.999691	−	0.0248401i	$-0.992092\pi$
$67$	−262.327	+	454.364i	−0.478334	+	0.828498i	0.521358	+	0.853338i	$0.325426\pi$
$68$	−68.5700	+	118.767i	−0.122284	+	0.211803i
$69$	146.742	+	156.011i	0.256024	+	0.272195i
$70$	−1366.16	+	312.855i	−2.33268	+	0.534190i
$71$			115.729i			0.193443i	0.995311	+	0.0967216i	$0.0308356\pi$
$71$			115.729i			0.193443i	−0.995311	+	0.0967216i	$0.969164\pi$
$72$	91.2376	−	137.808i	0.149340	−	0.225567i
$73$		−	708.180i		−	1.13543i	−0.823226	−	0.567714i	$-0.807828\pi$
$73$		−	708.180i		−	1.13543i	0.823226	−	0.567714i	$-0.192172\pi$
$74$	−1167.10	+	673.827i	−1.83342	+	1.05852i
$75$	325.136	+	1381.18i	0.500579	+	2.12647i
$76$	−538.135	−	310.692i	−0.812215	−	0.468933i
$77$	−453.708	−	488.273i	−0.671491	−	0.722648i
$78$	143.819	+	43.2944i	0.208774	+	0.0628477i
$79$	128.747	+	222.997i	0.183357	+	0.317584i	0.943022	−	0.332731i	$-0.107970\pi$
$79$	128.747	+	222.997i	0.183357	+	0.317584i	−0.759665	+	0.650315i	$0.774637\pi$
$80$	−1482.55			−2.07192
$81$	284.678	+	671.118i	0.390504	+	0.920601i
$82$			55.4366i			0.0746579i
$83$	200.583	+	347.420i	0.265263	+	0.459449i	0.967632	−	0.252364i	$-0.0812079\pi$
$83$	200.583	+	347.420i	0.265263	+	0.459449i	−0.702370	+	0.711812i	$0.747875\pi$
$84$	510.364	+	342.369i	0.662920	+	0.444709i
$85$	214.229	−	371.056i	0.273370	−	0.473490i
$86$	320.970	+	185.312i	0.402454	+	0.232357i
$87$	302.888	−	71.3010i	0.373253	−	0.0878652i
$88$	−110.149	−	190.784i	−0.133431	−	0.231110i
$89$	−977.834			−1.16461			−0.582304	−	0.812971i	$-0.697849\pi$
$89$	−977.834			−1.16461			−0.582304	+	0.812971i	$0.697849\pi$
$90$	1127.95	−	1703.68i	1.32107	−	1.99538i
$91$	41.5042	−	134.899i	0.0478112	−	0.155398i
$92$	−227.962	+	131.614i	−0.258334	+	0.149149i
$93$	−251.356	−	267.233i	−0.280263	−	0.297965i
$94$	1543.16	+	890.942i	1.69324	+	0.977592i
$95$	1681.26	+	970.677i	1.81573	+	1.04831i
$96$	829.026	+	881.389i	0.881376	+	0.937046i
$97$	−521.193	+	300.911i	−0.545558	+	0.314978i	−0.747328	−	0.664455i	$-0.768664\pi$
$97$	−521.193	+	300.911i	−0.545558	+	0.314978i	0.201770	+	0.979433i	$0.435330\pi$
$98$	731.308	−	1075.97i	0.753809	−	1.10907i
$99$	969.889	+	59.4408i	0.984621	+	0.0603437i
$100$	−1743.89			−1.74389
$101$	212.644	+	368.310i	0.209494	+	0.362853i	0.951555	−	0.307478i	$-0.0994851\pi$
$101$	212.644	+	368.310i	0.209494	+	0.362853i	−0.742062	+	0.670332i	$0.766152\pi$
$102$	−411.973	+	96.9800i	−0.399916	+	0.0941417i
$103$	−657.161	−	379.412i	−0.628660	−	0.362957i	0.151573	−	0.988446i	$-0.451566\pi$
$103$	−657.161	−	379.412i	−0.628660	−	0.362957i	−0.780233	+	0.625489i	$0.784899\pi$
$104$	23.3244	−	40.3990i	0.0219918	−	0.0380909i
$105$	−1594.50	−	1069.64i	−1.48197	−	0.994158i
$106$	1347.49	+	2333.92i	1.23471	+	2.13859i
$107$			866.455i			0.782835i	0.920213	+	0.391418i	$0.128015\pi$
$107$			866.455i			0.782835i	−0.920213	+	0.391418i	$0.871985\pi$
$108$	−883.037	+	151.566i	−0.786761	+	0.135041i
$109$	−94.9205			−0.0834104			−0.0417052	−	0.999130i	$-0.513279\pi$
$109$	−94.9205			−0.0834104			−0.0417052	+	0.999130i	$0.513279\pi$
$110$	−1361.75	−	2358.61i	−1.18034	−	2.04441i
$111$	−1767.87	−	532.189i	−1.51170	−	0.455073i
$112$	1008.13	−	936.763i	0.850530	−	0.790320i
$113$	−1432.66	−	827.148i	−1.19269	−	0.688597i	−0.233771	−	0.972292i	$-0.575107\pi$
$113$	−1432.66	−	827.148i	−1.19269	−	0.688597i	−0.958915	+	0.283694i	$0.908440\pi$
$114$	−439.419	−	1866.66i	−0.361012	−	1.53358i
$115$	712.208	−	411.194i	0.577511	−	0.333426i
$116$			382.428i			0.306100i
$117$	91.7877	+	184.154i	0.0725280	+	0.145513i
$118$			1765.48i			1.37734i
$119$	88.7800	+	387.681i	0.0683903	+	0.298644i
$120$	−434.792	−	462.255i	−0.330758	−	0.351649i
$121$	−17.8889	+	30.9845i	−0.0134402	+	0.0232791i
$122$	−1188.11	+	2057.87i	−0.881693	+	1.52714i
$123$	−55.3203	+	52.0337i	−0.0405534	+	0.0381441i
$124$	390.479	−	225.443i	0.282791	−	0.163269i
$125$	2954.35			2.11396
$126$	309.489	+	1871.21i	0.218821	+	1.32302i
$127$	−280.600			−0.196057			−0.0980284	−	0.995184i	$-0.531254\pi$
$127$	−280.600			−0.196057			−0.0980284	+	0.995184i	$0.531254\pi$
$128$	664.740	−	383.788i	0.459026	−	0.265019i
$129$	116.344	+	494.233i	0.0794073	+	0.337324i
$130$	288.353	−	499.442i	0.194540	−	0.336954i
$131$	1095.66	−	1897.74i	0.730751	−	1.26570i	−0.225812	−	0.974171i	$-0.572503\pi$
$131$	1095.66	−	1897.74i	0.730751	−	1.26570i	0.956563	−	0.291527i	$-0.0941632\pi$
$132$	−344.246	+	1143.55i	−0.226991	+	0.754040i
$133$	−1756.59	+	402.264i	−1.14523	+	0.262261i
$134$		−	1989.96i		−	1.28289i
$135$	2758.82	−	473.527i	1.75882	−	0.301887i
$136$			131.452i			0.0828815i
$137$	985.315	−	568.872i	0.614461	−	0.354759i	−0.160248	−	0.987077i	$-0.551230\pi$
$137$	985.315	−	568.872i	0.614461	−	0.354759i	0.774709	+	0.632318i	$0.217896\pi$
$138$	−777.878	−	234.167i	−0.479836	−	0.144446i
$139$	−1842.29	−	1063.64i	−1.12418	−	0.649044i	−0.181713	−	0.983352i	$-0.558164\pi$
$139$	−1842.29	−	1063.64i	−1.12418	−	0.649044i	−0.942464	+	0.334308i	$0.891498\pi$
$140$	1728.67	−	1606.29i	1.04356	−	0.969688i
$141$	559.359	+	2376.17i	0.334089	+	1.41922i
$142$	−219.474	−	380.140i	−0.129703	−	0.224652i
$143$	274.266			0.160387
$144$	−122.727	+	2002.51i	−0.0710223	+	1.15886i
$145$		−	1194.80i		−	0.684293i
$146$	1343.03	+	2326.20i	0.761301	+	1.31861i
$147$	1760.13	−	280.145i	0.987569	−	0.157183i
$148$	1134.53	−	1965.06i	0.630118	−	1.09140i
$149$	−362.688	−	209.398i	−0.199413	−	0.115131i	0.396969	−	0.917832i	$-0.370062\pi$
$149$	−362.688	−	209.398i	−0.199413	−	0.115131i	−0.596382	+	0.802701i	$0.703395\pi$
$150$	−3687.34	−	3920.24i	−2.00713	−	2.13391i
$151$	475.546	+	823.669i	0.256287	+	0.443902i	0.965244	−	0.261349i	$-0.0841674\pi$
$151$	475.546	+	823.669i	0.256287	+	0.443902i	−0.708957	+	0.705252i	$0.750834\pi$
$152$	−595.611			−0.317832
$153$	−483.461	−	320.081i	−0.255461	−	0.169131i
$154$	2416.30	+	743.422i	1.26436	+	0.389004i
$155$	−1219.95	+	704.339i	−0.632186	+	0.364993i
$156$	−246.155	+	57.9458i	−0.126334	+	0.0297396i
$157$	1885.26	+	1088.45i	0.958343	+	0.553300i	0.895663	−	0.444734i	$-0.146702\pi$
$157$	1885.26	+	1088.45i	0.958343	+	0.553300i	0.0626806	+	0.998034i	$0.480035\pi$
$158$	−845.807	−	488.327i	−0.425878	−	0.245881i
$159$	−1064.25	+	3535.31i	−0.530819	+	1.76332i
$160$	4023.66	−	2323.06i	1.98811	−	1.14784i
$161$	−224.484	+	729.628i	−0.109887	+	0.357160i
$162$	−2207.84	−	1664.58i	−1.07077	−	0.807294i
$163$	−382.330			−0.183720			−0.0918601	−	0.995772i	$-0.529281\pi$
$163$	−382.330			−0.183720			−0.0918601	+	0.995772i	$0.529281\pi$
$164$	−46.6695	−	80.8339i	−0.0222212	−	0.0384882i
$165$	1075.51	−	3572.72i	0.507443	−	1.68567i
$166$	−1317.73	−	760.792i	−0.616118	−	0.355716i
$167$	−123.092	+	213.202i	−0.0570370	+	0.0987909i	−0.893134	−	0.449791i	$-0.851499\pi$
$167$	−123.092	+	213.202i	−0.0570370	+	0.0987909i	0.836097	+	0.548582i	$0.184832\pi$
$168$	587.740	+	39.6047i	0.269911	+	0.0181879i
$169$	−1069.46	−	1852.36i	−0.486783	−	0.843132i
$170$			1625.10i			0.733174i
$171$	1450.30	−	2190.57i	0.648579	−	0.979633i
$172$	−624.021			−0.276635
$173$	1988.82	+	3444.74i	0.874031	+	1.51387i	0.857792	+	0.513998i	$0.171836\pi$
$173$	1988.82	+	3444.74i	0.874031	+	1.51387i	0.0162391	+	0.999868i	$0.494831\pi$
$174$	−859.694	+	808.620i	−0.374559	+	0.352306i
$175$	−3704.86	+	3442.59i	−1.60035	+	1.48706i
$176$	2315.95	+	1337.11i	0.991882	+	0.572663i
$177$	−1761.78	+	1657.11i	−0.748155	+	0.703707i
$178$	3211.94	−	1854.42i	1.35250	−	0.780867i
$179$		−	1454.87i		−	0.607498i	−0.952752	−	0.303749i	$-0.901762\pi$
$179$		−	1454.87i		−	0.607498i	0.952752	−	0.303749i	$-0.0982384\pi$
$180$	−210.442	+	3433.76i	−0.0871413	+	1.42187i
$181$		−	735.896i		−	0.302203i	−0.988518	−	0.151101i	$-0.951718\pi$
$181$		−	735.896i		−	0.302203i	0.988518	−	0.151101i	$-0.0482820\pi$
$182$	119.498	+	521.820i	0.0486692	+	0.212527i
$183$	−3168.73	+	745.931i	−1.28000	+	0.301316i
$184$	−126.155	+	218.507i	−0.0505449	+	0.0875463i
$185$	−3544.53	+	6139.31i	−1.40864	+	2.43984i
$186$	1332.44	+	401.107i	0.525263	+	0.158122i
$187$	−669.313	+	386.428i	−0.261738	+	0.151115i
$188$	−3000.17			−1.16388
$189$	−1576.79	+	2065.19i	−0.606850	+	0.794816i
$190$	−7363.38			−2.81155
$191$	2390.26	−	1380.02i	0.905515	−	0.522799i	0.0265297	−	0.999648i	$-0.491554\pi$
$191$	2390.26	−	1380.02i	0.905515	−	0.522799i	0.878985	+	0.476849i	$0.158221\pi$
$192$	−1436.91	−	432.558i	−0.540105	−	0.162589i
$193$	−616.442	+	1067.71i	−0.229909	+	0.398214i	−0.957781	−	0.287499i	$-0.907176\pi$
$193$	−616.442	+	1067.71i	−0.229909	+	0.398214i	0.727872	+	0.685713i	$0.240510\pi$
$194$	1141.33	−	1976.84i	0.422384	−	0.731590i
$195$	769.047	−	181.037i	0.282424	−	0.0664836i
$196$	−160.539	+	2184.55i	−0.0585055	+	0.796120i
$197$		−	497.068i		−	0.179770i	−0.995952	−	0.0898849i	$-0.971350\pi$
$197$		−	497.068i		−	0.179770i	0.995952	−	0.0898849i	$-0.0286499\pi$
$198$	−3298.57	+	1644.10i	−1.18394	+	0.590106i
$199$		−	4502.53i		−	1.60390i	−0.597391	−	0.801950i	$-0.703796\pi$
$199$		−	4502.53i		−	1.60390i	0.597391	−	0.801950i	$-0.296204\pi$
$200$	−1447.61	+	835.778i	−0.511807	+	0.295492i
$201$	1985.79	−	1867.81i	0.696849	−	0.655449i
$202$	−1396.96	−	806.538i	−0.486585	−	0.280930i
$203$	754.946	+	812.462i	0.261019	+	0.280905i
$204$	519.068	−	488.230i	0.178147	−	0.167563i
$205$	145.807	+	252.544i	0.0496759	+	0.0860413i
$206$	2878.15			0.973447
$207$	−496.453	−	996.038i	−0.166695	−	0.334442i
$208$			566.274i			0.188769i
$209$	−1750.91	−	3032.67i	−0.579489	−	1.00371i
$210$	7266.07	+	489.622i	2.38765	+	0.160891i
$211$	1714.83	−	2970.17i	0.559495	−	0.969074i	−0.438043	−	0.898954i	$-0.644328\pi$
$211$	1714.83	−	2970.17i	0.559495	−	0.969074i	0.997539	−	0.0701201i	$-0.0223383\pi$
$212$	−3929.63	−	2268.77i	−1.27306	−	0.734999i
$213$	173.340	−	575.819i	0.0557610	−	0.185232i
$214$	−1643.19	−	2846.09i	−0.524889	−	0.909134i
$215$	1949.59			0.618424
$216$	−660.373	+	549.020i	−0.208022	+	0.172945i
$217$	384.522	−	1249.79i	0.120290	−	0.390974i
$218$	311.790	−	180.012i	0.0968675	−	0.0559265i
$219$	−1060.72	+	3523.62i	−0.327293	+	1.08723i
$220$	3971.21	+	2292.78i	1.21700	+	0.702632i
$221$	−141.729	−	81.8270i	−0.0431389	−	0.0249063i
$222$	6816.30	−	1604.58i	2.06072	−	0.485102i
$223$	−2145.46	+	1238.68i	−0.644263	+	0.371965i	−0.786255	−	0.617903i	$-0.787983\pi$
$223$	−2145.46	+	1238.68i	−0.644263	+	0.371965i	0.141992	+	0.989868i	$0.454649\pi$
$224$	−1268.23	+	4122.07i	−0.378292	+	1.22954i
$225$	451.018	−	7359.20i	0.133635	−	2.18050i
$226$	6274.59			1.84681
$227$	84.0252	+	145.536i	0.0245681	+	0.0425531i	0.878048	−	0.478573i	$-0.158846\pi$
$227$	84.0252	+	145.536i	0.0245681	+	0.0425531i	−0.853480	+	0.521126i	$0.825512\pi$
$228$	2212.18	+	2351.91i	0.642567	+	0.683153i
$229$	−989.455	−	571.262i	−0.285524	−	0.164847i	0.350397	−	0.936601i	$-0.386047\pi$
$229$	−989.455	−	571.262i	−0.285524	−	0.164847i	−0.635922	+	0.771754i	$0.719380\pi$
$230$	−1559.62	+	2701.34i	−0.447123	+	0.774439i
$231$	1526.12	+	3109.02i	0.434681	+	0.885535i
$232$	183.283	+	317.455i	0.0518669	+	0.0898361i
$233$			2181.50i			0.613370i	0.951811	+	0.306685i	$0.0992198\pi$
$233$			2181.50i			0.613370i	−0.951811	+	0.306685i	$0.900780\pi$
$234$	−650.740	−	430.831i	−0.181796	−	0.120360i
$235$	9373.23			2.60188
$236$	−1486.28	−	2574.31i	−0.409951	−	0.710056i
$237$	−306.586	−	1302.38i	−0.0840291	−	0.356957i
$238$	−1026.84	−	1105.07i	−0.279664	−	0.300970i
$239$	−1654.14	−	955.020i	−0.447689	−	0.258473i	0.259165	−	0.965833i	$-0.416553\pi$
$239$	−1654.14	−	955.020i	−0.447689	−	0.258473i	−0.706854	+	0.707360i	$0.749886\pi$
$240$	7376.55	+	2220.58i	1.98398	+	0.597242i
$241$	−1962.89	+	1133.28i	−0.524651	+	0.302907i	−0.738836	−	0.673886i	$-0.764624\pi$
$241$	−1962.89	+	1133.28i	−0.524651	+	0.302907i	0.214184	+	0.976793i	$0.431291\pi$
$242$		−	135.702i		−	0.0360464i
$243$	−411.228	−	3765.61i	−0.108561	−	0.994090i
$244$		−	4000.86i		−	1.04971i
$245$	501.563	−	6825.06i	0.130791	−	1.77974i
$246$	83.0340	−	275.830i	0.0215205	−	0.0714890i
$247$	370.760	−	642.176i	0.0955098	−	0.165428i
$248$	216.092	−	374.283i	0.0553302	−	0.0958346i
$249$	−477.647	−	2029.06i	−0.121565	−	0.516410i
$250$	−9704.31	+	5602.79i	−2.45502	+	1.41741i
$251$	−315.743			−0.0794004			−0.0397002	−	0.999212i	$-0.512640\pi$
$251$	−315.743			−0.0794004			−0.0397002	+	0.999212i	$0.512640\pi$
$252$	−2026.56	−	2467.92i	−0.506592	−	0.616923i
$253$	−1483.43			−0.368626
$254$	921.702	−	532.145i	0.227688	−	0.131456i
$255$	−1621.69	+	1525.35i	−0.398252	+	0.374592i
$256$	−2610.84	+	4522.11i	−0.637412	+	1.10403i
$257$	2047.88	−	3547.03i	0.497055	−	0.860924i	−0.502939	−	0.864322i	$-0.667748\pi$
$257$	2047.88	−	3547.03i	0.497055	−	0.860924i	0.999994	+	0.00339730i	$0.00108139\pi$
$258$	−1319.45	−	1402.79i	−0.318393	−	0.338504i
$259$	−1468.91	−	6414.38i	−0.352408	−	1.53888i
$260$			971.003i			0.231612i
$261$	−1613.85	−	98.9065i	−0.382738	−	0.0234566i
$262$			8311.48i			1.95987i
$263$	4270.21	−	2465.41i	1.00119	−	0.578036i	0.0925883	−	0.995704i	$-0.470486\pi$
$263$	4270.21	−	2465.41i	1.00119	−	0.578036i	0.908600	+	0.417668i	$0.137153\pi$
$264$	262.298	+	1114.25i	0.0611490	+	0.259762i
$265$	12277.1	+	7088.18i	2.84595	+	1.64311i
$266$	5007.09	−	4652.63i	1.15415	−	1.07245i
$267$	4865.30	+	1464.62i	1.11518	+	0.335705i
$268$	1675.26	+	2901.63i	0.381838	+	0.661362i
$269$	−5506.26			−1.24804			−0.624019	−	0.781409i	$-0.714501\pi$
$269$	−5506.26			−1.24804			−0.624019	+	0.781409i	$0.714501\pi$
$270$	−8164.01	+	6787.38i	−1.84017	+	1.52988i
$271$			7622.48i			1.70861i	0.519774	+	0.854304i	$0.326016\pi$
$271$			7622.48i			1.70861i	−0.519774	+	0.854304i	$0.673984\pi$
$272$	−797.852	−	1381.92i	−0.177856	−	0.308056i
$273$	−408.562	+	609.036i	−0.0905761	+	0.135020i
$274$	−2157.68	+	3737.21i	−0.475730	+	0.823989i
$275$	−8511.06	−	4913.86i	−1.86631	−	1.07752i
$276$	1331.38	−	313.412i	0.290361	−	0.0683522i
$277$	−1811.14	−	3136.99i	−0.392856	−	0.680446i	0.599969	−	0.800023i	$-0.295179\pi$
$277$	−1811.14	−	3136.99i	−0.392856	−	0.680446i	−0.992825	+	0.119577i	$0.961846\pi$
$278$	8068.60			1.74073
$279$	850.381	+	1706.13i	0.182477	+	0.366104i
$280$	665.140	−	2161.87i	0.141963	−	0.461416i
$281$	−1888.83	+	1090.51i	−0.400989	+	0.231511i	−0.686911	−	0.726742i	$-0.741034\pi$
$281$	−1888.83	+	1090.51i	−0.400989	+	0.231511i	0.285922	+	0.958253i	$0.407700\pi$
$282$	−6343.65	−	6744.33i	−1.33957	−	1.42418i
$283$	−1985.61	−	1146.39i	−0.417075	−	0.240799i	0.276750	−	0.960942i	$-0.410743\pi$
$283$	−1985.61	−	1146.39i	−0.417075	−	0.240799i	−0.693825	+	0.720143i	$0.744076\pi$
$284$	640.043	+	369.529i	0.133731	+	0.0772096i
$285$	−6911.38	−	7347.92i	−1.43647	−	1.52720i
$286$	−900.897	+	520.133i	−0.186263	+	0.107539i
$287$	−258.721	−	79.6005i	−0.0532120	−	0.0163717i
$288$	−2804.74	−	5627.17i	−0.573856	−	1.15133i
$289$	−4451.84			−0.906134
$290$	2265.88	+	3924.61i	0.458817	+	0.794694i
$291$	3043.95	−	716.558i	0.613195	−	0.144348i
$292$	−3916.63	−	2261.27i	−0.784943	−	0.453187i
$293$	273.105	−	473.031i	0.0544537	−	0.0943166i	−0.837514	−	0.546416i	$-0.815992\pi$
$293$	273.105	−	473.031i	0.0544537	−	0.0943166i	0.891967	+	0.452100i	$0.149325\pi$
$294$	−5250.29	+	4258.20i	−1.04151	+	0.844705i
$295$	4643.48	+	8042.75i	0.916455	+	1.58735i
$296$		−	2174.94i		−	0.427080i
$297$	−4736.74	−	1748.47i	−0.925433	−	0.341604i
$298$	1588.45			0.308780
$299$	−157.060	−	272.035i	−0.0303779	−	0.0526161i
$300$	8676.89	+	2612.03i	1.66987	+	0.502685i
$301$	−1325.72	+	1231.87i	−0.253865	+	0.235893i
$302$	−3124.10	−	1803.70i	−0.595271	−	0.343680i
$303$	−506.368	−	2151.06i	−0.0960069	−	0.407839i
$304$	6261.52	−	3615.09i	1.18132	−	0.682038i
$305$			12499.6i			2.34665i
$306$	2195.07	+	134.528i	0.410078	+	0.0251321i
$307$			6193.21i			1.15135i	0.817677	+	0.575677i	$0.195261\pi$
$307$			6193.21i			1.15135i	−0.817677	+	0.575677i	$0.804739\pi$
$308$	−4149.14	+	950.165i	−0.767595	+	0.175781i
$309$	2701.48	+	2872.11i	0.497351	+	0.528765i
$310$	2671.49	−	4627.16i	0.489453	−	0.847758i
$311$	2335.25	−	4044.78i	0.425788	−	0.737486i	−0.570706	−	0.821155i	$-0.693330\pi$
$311$	2335.25	−	4044.78i	0.425788	−	0.737486i	0.996494	+	0.0836685i	$0.0266637\pi$
$312$	−176.563	+	166.073i	−0.0320382	+	0.0301348i
$313$	−2218.64	+	1280.93i	−0.400655	+	0.231318i	−0.686767	−	0.726878i	$-0.740971\pi$
$313$	−2218.64	+	1280.93i	−0.400655	+	0.231318i	0.286112	+	0.958196i	$0.407637\pi$
$314$	−8256.81			−1.48394
$315$	6331.45	+	7710.38i	1.13250	+	1.37915i
$316$	1644.40			0.292736
$317$	2351.36	−	1357.56i	0.416611	−	0.240530i	−0.277015	−	0.960865i	$-0.589345\pi$
$317$	2351.36	−	1357.56i	0.416611	−	0.240530i	0.693626	+	0.720335i	$0.256012\pi$
$318$	−3208.77	−	13630.9i	−0.565845	−	2.40372i
$319$	−1077.59	+	1866.44i	−0.189133	+	0.327589i
$320$	−2880.96	+	4989.97i	−0.503283	+	0.871712i
$321$	1297.79	−	4311.13i	0.225656	−	0.749607i
$322$	−646.331	−	2822.37i	−0.111859	−	0.488462i
$323$			2089.53i			0.359953i
$324$	4620.65	+	568.500i	0.792292	+	0.0974794i
$325$		−	2081.04i		−	0.355186i
$326$	1255.86	−	725.070i	0.213361	−	0.123184i
$327$	472.286	+	142.174i	0.0798700	+	0.0240435i
$328$	−77.4810	−	44.7337i	−0.0130432	−	0.00753050i
$329$	−6373.79	+	5922.58i	−1.06808	+	0.992470i
$330$	3242.72	+	13775.2i	0.540927	+	2.29787i
$331$	−2272.97	−	3936.89i	−0.377443	−	0.653750i	0.613247	−	0.789891i	$-0.289863\pi$
$331$	−2272.97	−	3936.89i	−0.377443	−	0.653750i	−0.990689	+	0.136142i	$0.956530\pi$
$332$	2561.90			0.423501
$333$	7999.11	+	5295.91i	1.31636	+	0.871514i
$334$		−	933.756i		−	0.152973i
$335$	−5233.90	−	9065.38i	−0.853607	−	1.47849i
$336$	−6419.15	+	3150.96i	−1.04224	+	0.511604i
$337$	3627.36	−	6282.78i	0.586336	−	1.01556i	−0.408372	−	0.912816i	$-0.633903\pi$
$337$	3627.36	−	6282.78i	0.586336	−	1.01556i	0.994707	−	0.102747i	$-0.0327634\pi$
$338$	7025.83	+	4056.37i	1.13064	+	0.652773i
$339$	5889.43	+	6261.42i	0.943569	+	1.00317i
$340$	−1368.10	−	2369.61i	−0.218222	−	0.377971i
$341$	2540.98			0.403525
$342$	−609.547	+	9945.91i	−0.0963759	+	1.57255i
$343$	3971.43	+	4957.96i	0.625181	+	0.780480i
$344$	−518.003	+	299.069i	−0.0811885	+	0.0468742i
$345$	−4159.55	+	979.175i	−0.649110	+	0.152803i
$346$	−13065.6	−	7543.41i	−2.03009	−	1.17207i
$347$	−7611.25	−	4394.36i	−1.17750	−	0.679832i	−0.222067	−	0.975031i	$-0.571280\pi$
$347$	−7611.25	−	4394.36i	−1.17750	−	0.679832i	−0.955436	+	0.295200i	$0.904614\pi$
$348$	572.808	−	1902.81i	0.0882349	−	0.293107i
$349$	6314.40	−	3645.62i	0.968487	−	0.559156i	0.0697122	−	0.997567i	$-0.477792\pi$
$349$	6314.40	−	3645.62i	0.968487	−	0.559156i	0.898775	+	0.438411i	$0.144459\pi$
$350$	5640.84	−	18334.1i	0.861474	−	2.80000i
$351$	−180.868	−	1053.76i	−0.0275044	−	0.160244i
$352$	−8380.70			−1.26901
$353$	5012.28	+	8681.52i	0.755741	+	1.30898i	0.945005	+	0.327056i	$0.106057\pi$
$353$	5012.28	+	8681.52i	0.755741	+	1.30898i	−0.189264	+	0.981926i	$0.560610\pi$
$354$	2644.37	−	8784.34i	0.397025	−	1.31888i
$355$	−1999.65	−	1154.50i	−0.298959	−	0.172604i
$356$	−3122.29	+	5407.96i	−0.464834	+	0.805116i
$357$	138.942	−	2061.92i	0.0205983	−	0.305682i
$358$	2759.09	+	4778.89i	0.407326	+	0.705509i
$359$			11205.2i			1.64732i	0.567083	+	0.823660i	$0.308072\pi$
$359$			11205.2i			1.64732i	−0.567083	+	0.823660i	$0.691928\pi$
$360$	1470.98	+	2951.23i	0.215354	+	0.432066i
$361$	−2608.72			−0.380336
$362$	1395.59	+	2417.24i	0.202626	+	0.350959i
$363$	135.417	−	127.372i	0.0195800	−	0.0184168i
$364$	−613.539	−	660.282i	−0.0883467	−	0.0950773i
$365$	12236.5	+	7064.73i	1.75476	+	1.01311i
$366$	8993.88	−	8459.55i	1.28447	−	1.20816i
$367$	2597.53	−	1499.68i	0.369455	−	0.213305i	−0.303766	−	0.952747i	$-0.598244\pi$
$367$	2597.53	−	1499.68i	0.369455	−	0.213305i	0.673220	+	0.739442i	$0.264911\pi$
$368$		−	3062.81i		−	0.433859i
$369$	353.188	−	176.039i	0.0498272	−	0.0248353i
$370$		−	26888.1i		−	3.77797i
$371$	−12827.2	+	2937.46i	−1.79502	+	0.411065i
$372$	−2280.54	+	536.848i	−0.317851	+	0.0748233i
$373$	−2052.54	+	3555.11i	−0.284924	+	0.493503i	−0.972591	−	0.232524i	$-0.925302\pi$
$373$	−2052.54	+	3555.11i	−0.284924	+	0.493503i	0.687667	+	0.726026i	$0.258635\pi$
$374$	1465.68	−	2538.64i	0.202644	−	0.350989i
$375$	−14699.7	−	4425.08i	−2.02423	−	0.609360i
$376$	−2490.45	+	1437.86i	−0.341583	+	0.197213i
$377$	−456.365			−0.0623449
$378$	1262.84	−	9773.94i	0.171834	−	1.32994i
$379$	−2051.20			−0.278002			−0.139001	−	0.990292i	$-0.544389\pi$
$379$	−2051.20			−0.278002			−0.139001	+	0.990292i	$0.544389\pi$
$380$	10736.8	−	6198.87i	1.44943	−	0.836830i
$381$	1396.15	+	420.288i	0.187735	+	0.0565144i
$382$	−5234.28	+	9066.04i	−0.701071	+	1.21429i
$383$	−2786.12	+	4825.70i	−0.371708	+	0.643817i	−0.989828	−	0.142266i	$-0.954561\pi$
$383$	−2786.12	+	4825.70i	−0.371708	+	0.643817i	0.618120	+	0.786083i	$0.287894\pi$
$384$	−3882.32	+	913.914i	−0.515935	+	0.121453i
$385$	12962.9	−	2968.54i	1.71598	−	0.392963i
$386$		−	4676.21i		−	0.616614i
$387$	161.389	−	2633.37i	0.0211986	−	0.345895i
$388$			3843.31i			0.502873i
$389$	1483.30	−	856.385i	0.193333	−	0.111621i	−0.400209	−	0.916424i	$-0.631063\pi$
$389$	1483.30	−	856.385i	0.193333	−	0.111621i	0.593542	+	0.804803i	$0.297729\pi$
$390$	−2182.80	+	2053.12i	−0.283411	+	0.266574i
$391$	766.569	+	442.579i	0.0991485	+	0.0572434i
$392$	913.706	+	1890.35i	0.117727	+	0.243563i
$393$	−8294.04	+	7801.29i	−1.06458	+	1.00133i
$394$	942.667	+	1632.75i	0.120535	+	0.208773i
$395$	−5137.48			−0.654417
$396$	3425.66	−	5174.22i	0.434712	−	0.656602i
$397$		−	5977.49i		−	0.755672i	−0.925872	−	0.377836i	$-0.876668\pi$
$397$		−	5977.49i		−	0.755672i	0.925872	−	0.377836i	$-0.123332\pi$
$398$	8538.84	+	14789.7i	1.07541	+	1.86267i
$399$	9342.60	+	629.550i	1.17222	+	0.0789897i
$400$	10145.6	−	17572.7i	1.26820	−	2.19658i
$401$	2620.36	+	1512.86i	0.326320	+	0.188401i	0.654206	−	0.756316i	$-0.273003\pi$
$401$	2620.36	+	1512.86i	0.326320	+	0.188401i	−0.327886	+	0.944717i	$0.606336\pi$
$402$	−2980.60	+	9901.25i	−0.369798	+	1.22843i
$403$	269.030	+	465.973i	0.0332539	+	0.0575974i
$404$	2715.94			0.334463
$405$	−14436.0	−	1776.13i	−1.77119	−	0.217917i
$406$	−4020.61	−	1237.02i	−0.491476	−	0.151212i
$407$	11074.1	−	6393.65i	1.34871	−	0.778676i
$408$	196.891	−	654.050i	0.0238910	−	0.0793635i
$409$	9538.96	+	5507.32i	1.15323	+	0.665818i	0.949672	−	0.313245i	$-0.101416\pi$
$409$	9538.96	+	5507.32i	1.15323	+	0.665818i	0.203558	+	0.979063i	$0.434750\pi$
$410$	−957.877	−	553.030i	−0.115381	−	0.0666152i
$411$	−5754.59	+	1354.65i	−0.690640	+	0.162579i
$412$	−4196.72	+	2422.98i	−0.501838	+	0.289736i
$413$	−8239.47	−	2535.03i	−0.981690	−	0.302035i
$414$	3519.67	+	2330.24i	0.417831	+	0.276630i
$415$	−8003.98			−0.946746
$416$	−887.316	−	1536.88i	−0.104578	−	0.181134i
$417$	7573.32	+	8051.67i	0.889370	+	0.945544i
$418$	11502.6	+	6641.05i	1.34596	+	0.777092i
$419$	5849.85	−	10132.2i	0.682062	−	1.18137i	−0.292289	−	0.956330i	$-0.594417\pi$
$419$	5849.85	−	10132.2i	0.682062	−	1.18137i	0.974351	−	0.225036i	$-0.0722499\pi$
$420$	−11007.1	+	5403.02i	−1.27879	+	0.627715i
$421$	3481.75	+	6030.57i	0.403064	+	0.698128i	0.994094	−	0.108522i	$-0.0346117\pi$
$421$	3481.75	+	6030.57i	0.403064	+	0.698128i	−0.591030	+	0.806650i	$0.701278\pi$
$422$			13008.3i			1.50056i
$423$	775.925	−	12660.7i	0.0891886	−	1.45528i
$424$	−4349.33			−0.498166
$425$	2932.09	+	5078.53i	0.334652	+	0.579635i
$426$	522.633	+	2220.15i	0.0594405	+	0.252504i
$427$	−7898.04	−	8499.75i	−0.895112	−	0.963306i
$428$	4791.98	+	2766.65i	0.541189	+	0.312456i
$429$	−1364.64	−	410.801i	−0.153579	−	0.0462323i
$430$	−6403.93	+	3697.31i	−0.718197	+	0.414651i
$431$		−	12686.3i		−	1.41781i	−0.705305	−	0.708904i	$-0.749190\pi$
$431$		−	12686.3i		−	1.41781i	0.705305	−	0.708904i	$-0.250810\pi$
$432$	3610.04	−	9779.88i	0.402056	−	1.08920i
$433$			12891.4i			1.43077i	0.698730	+	0.715385i	$0.253749\pi$
$433$			12891.4i			1.43077i	−0.698730	+	0.715385i	$0.746251\pi$
$434$	1107.11	+	4834.48i	0.122449	+	0.534706i
$435$	−1789.59	+	5944.83i	−0.197251	+	0.655248i
$436$	−303.088	+	524.963i	−0.0332919	+	0.0576632i
$437$	−2005.34	+	3473.34i	−0.219515	+	0.380212i
$438$	−3198.15	−	13585.8i	−0.348890	−	1.48209i
$439$	10467.6	−	6043.45i	1.13802	−	0.657035i	0.192078	−	0.981380i	$-0.438477\pi$
$439$	10467.6	−	6043.45i	1.13802	−	0.657035i	0.945939	+	0.324345i	$0.105144\pi$
$440$	4395.36			0.476228
$441$	−9177.28	−	1242.46i	−0.990960	−	0.134160i
$442$	620.724			0.0667983
$443$	−8703.97	+	5025.24i	−0.933495	+	0.538953i	−0.887915	−	0.460007i	$-0.847847\pi$
$443$	−8703.97	+	5025.24i	−0.933495	+	0.538953i	−0.0455796	+	0.998961i	$0.514513\pi$
$444$	−8588.24	+	8078.01i	−0.917973	+	0.863436i
$445$	9754.77	−	16895.8i	1.03915	−	1.79986i
$446$	4698.20	−	8137.53i	0.498803	−	0.863953i
$447$	1490.95	+	1585.12i	0.157761	+	0.167726i
$448$	−1193.92	−	5213.54i	−0.125909	−	0.549814i
$449$		−	10044.6i		−	1.05575i	−0.849321	−	0.527877i	$-0.822988\pi$
$449$		−	10044.6i		−	1.05575i	0.849321	−	0.527877i	$-0.177012\pi$
$450$	12474.9	+	25028.5i	1.30683	+	2.62190i
$451$		−	526.014i		−	0.0549202i
$452$	−9149.17	+	5282.27i	−0.952081	+	0.549684i
$453$	−1132.42	−	4810.53i	−0.117452	−	0.498937i
$454$	−552.004	−	318.700i	−0.0570635	−	0.0329456i
$455$	1916.84	+	2062.88i	0.197501	+	0.212548i
$456$	2963.52	+	892.117i	0.304341	+	0.0916166i
$457$	7705.51	+	13346.3i	0.788727	+	1.36612i	0.926747	+	0.375686i	$0.122593\pi$
$457$	7705.51	+	13346.3i	0.788727	+	1.36612i	−0.138020	+	0.990430i	$0.544074\pi$
$458$	4333.49			0.442119
$459$	1926.08	+	2316.73i	0.195864	+	0.235590i
$460$		−	5251.88i		−	0.532326i
$461$	2887.34	+	5001.02i	0.291707	+	0.505251i	0.974214	−	0.225628i	$-0.0724434\pi$
$461$	2887.34	+	5001.02i	0.291707	+	0.505251i	−0.682506	+	0.730880i	$0.739110\pi$
$462$	−10909.0	−	7318.15i	−1.09856	−	0.736951i
$463$	−4764.84	+	8252.94i	−0.478274	+	0.828395i	−0.999690	−	0.0249078i	$-0.992071\pi$
$463$	−4764.84	+	8252.94i	−0.478274	+	0.828395i	0.521416	+	0.853303i	$0.325404\pi$
$464$	−3853.62	−	2224.89i	−0.385560	−	0.222603i
$465$	7124.95	−	1677.24i	0.710563	−	0.167269i
$466$	−4137.12	−	7165.70i	−0.411263	−	0.712328i
$467$	8268.97			0.819363			0.409681	−	0.912229i	$-0.365640\pi$
$467$	8268.97			0.819363			0.409681	+	0.912229i	$0.365640\pi$
$468$	1311.56	+	80.3806i	0.129545	+	0.00793930i
$469$	9287.11	+	2857.35i	0.914368	+	0.281323i
$470$	−30788.8	+	17775.9i	−3.02166	+	1.74456i
$471$	−7749.97	−	8239.48i	−0.758174	−	0.806062i
$472$	−2467.53	−	1424.63i	−0.240630	−	0.138928i
$473$	−3045.54	−	1758.34i	−0.296055	−	0.170928i
$474$	3476.97	+	3696.58i	0.336925	+	0.358206i
$475$	−23010.9	+	13285.4i	−2.22277	+	1.28332i
$476$	2427.57	+	746.888i	0.233755	+	0.0719192i
$477$	10590.5	−	15996.2i	1.01657	−	1.53547i
$478$	7244.60			0.693222
$479$	−7295.72	−	12636.6i	−0.695929	−	1.20538i	−0.969867	−	0.243637i	$-0.921660\pi$
$479$	−7295.72	−	12636.6i	−0.695929	−	1.20538i	0.273938	−	0.961747i	$-0.411674\pi$
$480$	−23499.6	+	5531.89i	−2.23459	+	0.526032i
$481$	2344.97	+	1353.87i	0.222290	+	0.128339i
$482$	4298.41	−	7445.06i	0.406197	−	0.703554i
$483$	2209.79	−	3294.10i	0.208176	−	0.310324i
$484$	114.241	+	197.871i	0.0107288	+	0.0185829i
$485$		−	12007.4i		−	1.12418i
$486$	8492.08	+	11589.2i	0.792610	+	1.08168i
$487$	−14380.5			−1.33807			−0.669036	−	0.743230i	$-0.733293\pi$
$487$	−14380.5			−1.33807			−0.669036	+	0.743230i	$0.733293\pi$
$488$	−1917.45	−	3321.13i	−0.177867	−	0.308075i
$489$	1902.32	+	572.661i	0.175922	+	0.0529583i
$490$	11295.9	+	23369.8i	1.04142	+	2.15457i
$491$	−512.614	−	295.958i	−0.0471160	−	0.0272024i	0.476257	−	0.879306i	$-0.341993\pi$
$491$	−512.614	−	295.958i	−0.0471160	−	0.0272024i	−0.523373	+	0.852104i	$0.675327\pi$
$492$	111.134	+	472.099i	0.0101835	+	0.0432599i
$493$	1113.70	−	642.997i	0.101742	−	0.0587406i
$494$			2812.52i			0.256156i
$495$	−10702.6	+	16165.5i	−0.971808	+	1.46785i
$496$			5246.33i			0.474934i
$497$	2089.24	−	478.442i	0.188562	−	0.0431812i
$498$	5416.96	+	5759.11i	0.487429	+	0.518217i
$499$	2075.90	−	3595.56i	0.186232	−	0.322564i	−0.757759	−	0.652535i	$-0.773706\pi$
$499$	2075.90	−	3595.56i	0.186232	−	0.322564i	0.943991	+	0.329971i	$0.107039\pi$
$500$	9433.44	−	16339.2i	0.843752	−	1.46142i
$501$	931.796	−	876.438i	0.0830930	−	0.0781564i
$502$	1037.14	−	598.791i	0.0922105	−	0.0532378i
$503$	13272.2			1.17650			0.588248	−	0.808681i	$-0.299818\pi$
$503$	13272.2			1.17650			0.588248	+	0.808681i	$0.299818\pi$
$504$	−2865.03	−	1077.38i	−0.253212	−	0.0952192i
$505$	−8485.25			−0.747701
$506$	4872.69	−	2813.25i	0.428098	−	0.247163i
$507$	2546.71	+	10818.5i	0.223083	+	0.947662i
$508$	−895.974	+	1551.87i	−0.0782528	+	0.135538i
$509$	−7547.02	+	13071.8i	−0.657202	+	1.13831i	0.324135	+	0.946011i	$0.394927\pi$
$509$	−7547.02	+	13071.8i	−0.657202	+	1.13831i	−0.981337	+	0.192296i	$0.938407\pi$
$510$	2434.11	−	8085.85i	0.211341	−	0.702054i
$511$	−12784.7	+	2927.74i	−1.10678	+	0.253455i
$512$		−	13664.7i		−	1.17949i
$513$	−10497.2	+	8727.12i	−0.903433	+	0.751095i
$514$			15534.8i			1.33310i
$515$	13111.5	−	7569.95i	1.12187	−	0.647713i
$516$	3104.88	+	934.671i	0.264893	+	0.0797414i
$517$	−14642.3	−	8453.75i	−1.24559	−	0.719140i
$518$	16989.6	+	18283.9i	1.44108	+	1.55087i
$519$	−4735.98	−	20118.5i	−0.400552	−	1.70155i
$520$	465.364	+	806.033i	0.0392453	+	0.0679748i
$521$	5002.27			0.420640			0.210320	−	0.977633i	$-0.432549\pi$
$521$	5002.27			0.420640			0.210320	+	0.977633i	$0.432549\pi$
$522$	5488.65	−	2735.70i	0.460214	−	0.229384i
$523$			909.042i			0.0760031i	0.999278	+	0.0380016i	$0.0120992\pi$
$523$			909.042i			0.0760031i	−0.999278	+	0.0380016i	$0.987901\pi$
$524$	−6997.04	−	12119.2i	−0.583334	−	1.01036i
$525$	23590.2	−	11579.7i	1.96107	−	0.962628i
$526$	−9351.05	+	16196.5i	−0.775143	+	1.34259i
$527$	−1313.07	−	758.099i	−0.108535	−	0.0626628i
$528$	−9520.47	−	10121.8i	−0.784707	−	0.834271i
$529$	−5234.01	−	9065.57i	−0.430181	−	0.745095i
$530$	−53769.6			−4.40680
$531$	11248.0	−	5606.29i	0.919246	−	0.458178i
$532$	−3384.17	+	10999.4i	−0.275794	+	0.896398i
$533$	96.4619	−	55.6923i	0.00783908	−	0.00452589i
$534$	−18758.9	+	4415.92i	−1.52018	+	0.357856i
$535$	−14971.3	−	8643.67i	−1.20984	−	0.698502i
$536$	2781.27	+	1605.77i	0.224128	+	0.129400i
$537$	−2179.13	+	7238.84i	−0.175114	+	0.581712i
$538$	18086.7	−	10442.4i	1.44939	−	0.836807i
$539$	−6939.06	+	10209.4i	−0.554520	+	0.815860i
$540$	6190.22	−	16769.8i	0.493305	−	1.33640i
$541$	21816.1			1.73373			0.866865	−	0.498544i	$-0.166132\pi$
$541$	21816.1			1.73373			0.866865	+	0.498544i	$0.166132\pi$
$542$	−14455.7	−	25038.0i	−1.14562	−	1.98427i
$543$	−1102.24	+	3661.52i	−0.0871116	+	0.289376i
$544$	4330.77	+	2500.37i	0.341324	+	0.197063i
$545$	946.918	−	1640.11i	0.0744248	−	0.128907i
$546$	187.016	−	2775.35i	0.0146585	−	0.217535i
$547$	3976.21	+	6887.00i	0.310805	+	0.538330i	0.978537	−	0.206072i	$-0.0660680\pi$
$547$	3976.21	+	6887.00i	0.310805	+	0.538330i	−0.667732	+	0.744402i	$0.732735\pi$
$548$		−	7265.78i		−	0.566385i
$549$	16883.6	+	1034.73i	1.31252	+	0.0804395i
$550$	37275.6			2.88989
$551$	2913.43	+	5046.21i	0.225257	+	0.390156i
$552$	954.979	−	898.244i	0.0736352	−	0.0692605i
$553$	3493.49	−	3246.18i	0.268640	−	0.249623i
$554$	11898.3	+	6869.49i	0.912474	+	0.526817i
$555$	26831.7	−	25237.6i	2.05215	−	1.93023i
$556$	−11765.1	+	6792.57i	−0.897393	+	0.518110i
$557$			16793.7i			1.27750i	0.769413	+	0.638752i	$0.220549\pi$
$557$			16793.7i			1.27750i	−0.769413	+	0.638752i	$0.779451\pi$
$558$	−6028.88	−	3991.50i	−0.457389	−	0.302820i
$559$		−	744.667i		−	0.0563436i
$560$	6129.10	+	26764.3i	0.462503	+	2.01964i
$561$	3909.03	−	920.200i	0.294188	−	0.0692529i
$562$	4136.22	−	7164.14i	0.310455	−	0.537724i
$563$	−3810.86	+	6600.60i	−0.285273	+	0.494107i	−0.972675	−	0.232170i	$-0.925418\pi$
$563$	−3810.86	+	6600.60i	−0.285273	+	0.494107i	0.687403	+	0.726277i	$0.258751\pi$
$564$	14927.6	+	4493.70i	1.11448	+	0.335495i
$565$	28584.2	−	16503.1i	2.12840	−	1.22883i
$566$	8696.32			0.645819
$567$	10938.7	−	7913.79i	0.810201	−	0.586151i
$568$	708.403			0.0523309
$569$	−2201.40	+	1270.98i	−0.162193	+	0.0936420i	−0.578899	−	0.815399i	$-0.696518\pi$
$569$	−2201.40	+	1270.98i	−0.162193	+	0.0936420i	0.416707	+	0.909041i	$0.363184\pi$
$570$	36637.2	+	11029.0i	2.69221	+	0.810445i
$571$	−2123.22	+	3677.53i	−0.155611	+	0.269527i	−0.933281	−	0.359146i	$-0.883068\pi$
$571$	−2123.22	+	3677.53i	−0.155611	+	0.269527i	0.777670	+	0.628673i	$0.216401\pi$
$572$	875.751	−	1516.84i	0.0640157	−	0.110878i
$573$	−13960.0	+	3286.24i	−1.01778	+	0.239589i
$574$	1000.79	−	229.185i	0.0727741	−	0.0166655i
$575$			11255.8i			0.816345i
$576$	6501.60	+	4304.46i	0.470312	+	0.311376i
$577$		−	26192.0i		−	1.88975i	−0.327426	−	0.944877i	$-0.606181\pi$
$577$		−	26192.0i		−	1.88975i	0.327426	−	0.944877i	$-0.393819\pi$
$578$	14623.2	−	8442.70i	1.05233	−	0.607561i
$579$	4666.40	−	4389.17i	0.334938	−	0.315039i
$580$	−6607.89	−	3815.07i	−0.473065	−	0.273124i
$581$	5442.70	−	5057.40i	0.388642	−	0.361130i
$582$	−8639.72	+	8126.43i	−0.615340	+	0.578783i
$583$	−12785.7	−	22145.5i	−0.908285	−	1.57320i
$584$	−4334.94			−0.307160
$585$	−4097.63	−	251.128i	−0.289600	−	0.0177485i
$586$			2071.72i			0.146044i
$587$	1377.78	+	2386.39i	0.0968777	+	0.167797i	0.910391	−	0.413750i	$-0.135781\pi$
$587$	1377.78	+	2386.39i	0.0968777	+	0.167797i	−0.813513	+	0.581547i	$0.802448\pi$
$588$	4070.84	−	10629.0i	0.285508	−	0.745463i
$589$	3434.97	−	5949.53i	0.240298	−	0.416208i
$590$	−30505.4	−	17612.3i	−2.12862	−	1.22896i
$591$	−744.518	+	2473.21i	−0.0518196	+	0.172139i
$592$	13200.9	+	22864.6i	0.916474	+	1.58738i
$593$	−14044.3			−0.972567			−0.486284	−	0.873801i	$-0.661648\pi$
$593$	−14044.3			−0.972567			−0.486284	+	0.873801i	$0.661648\pi$
$594$	18874.9	−	3239.71i	1.30378	−	0.223783i
$595$	−7584.31	−	2333.46i	−0.522565	−	0.160777i
$596$	−2316.17	+	1337.24i	−0.159185	+	0.0919053i
$597$	−6743.98	+	22402.8i	−0.462333	+	1.53582i
$598$	1031.80	+	595.713i	0.0705579	+	0.0407366i
$599$	−10357.8	−	5980.08i	−0.706524	−	0.407912i	0.103248	−	0.994656i	$-0.467076\pi$
$599$	−10357.8	−	5980.08i	−0.706524	−	0.407912i	−0.809773	+	0.586744i	$0.800410\pi$
$600$	8454.56	−	1990.24i	0.575260	−	0.135418i
$601$	−21071.9	+	12165.9i	−1.43019	+	0.825718i	−0.997134	−	0.0756510i	$-0.975897\pi$
$601$	−21071.9	+	12165.9i	−1.43019	+	0.825718i	−0.433051	+	0.901369i	$0.642563\pi$
$602$	2018.48	−	6560.56i	0.136656	−	0.444167i
$603$	−12678.1	+	6319.13i	−0.856207	+	0.426757i
$604$	6073.80			0.409171
$605$	−356.915	−	618.196i	−0.0239846	−	0.0415425i
$606$	5742.68	+	6105.40i	0.384951	+	0.409266i
$607$	−8989.19	−	5189.91i	−0.601087	−	0.347038i	0.168382	−	0.985722i	$-0.446146\pi$
$607$	−8989.19	−	5189.91i	−0.601087	−	0.347038i	−0.769469	+	0.638684i	$0.779479\pi$
$608$	−11329.2	+	19622.8i	−0.755693	+	1.30890i
$609$	−2539.39	−	5173.25i	−0.168967	−	0.344221i
$610$	−23705.0	−	41058.2i	−1.57342	−	2.72524i
$611$		−	3580.20i		−	0.237053i
$612$	−3313.95	+	1651.77i	−0.218886	+	0.109099i
$613$	−7728.54			−0.509222			−0.254611	−	0.967044i	$-0.581947\pi$
$613$	−7728.54			−0.509222			−0.254611	+	0.967044i	$0.581947\pi$
$614$	−11745.1	−	20343.2i	−0.771979	−	1.33711i
$615$	−347.209	−	1474.95i	−0.0227655	−	0.0967085i
$616$	−2988.84	+	2777.25i	−0.195493	+	0.181654i
$617$	6665.11	+	3848.10i	0.434890	+	0.251084i	0.701428	−	0.712741i	$-0.252546\pi$
$617$	6665.11	+	3848.10i	0.434890	+	0.251084i	−0.266538	+	0.963825i	$0.585880\pi$
$618$	−14320.5	−	4310.94i	−0.932127	−	0.280601i
$619$	−25350.2	+	14635.9i	−1.64606	+	0.950352i	−0.667441	+	0.744663i	$0.732610\pi$
$619$	−25350.2	+	14635.9i	−1.64606	+	0.950352i	−0.978617	+	0.205689i	$0.934056\pi$
$620$			8996.01i			0.582723i
$621$	978.266	+	5699.48i	0.0632149	+	0.368297i
$622$			17714.8i			1.14196i
$623$	4042.54	+	17652.8i	0.259969	+	1.13522i
$624$	848.175	−	2817.55i	0.0544138	−	0.180757i
$625$	−12405.2	+	21486.4i	−0.793931	+	1.37513i
$626$	4858.46	−	8415.10i	0.310197	−	0.537276i
$627$	4169.45	+	17711.9i	0.265569	+	1.12814i
$628$	12039.5	−	6951.01i	0.765014	−	0.441681i
$629$	−7630.15			−0.483679
$630$	−35419.6	−	13319.4i	−2.23992	−	0.842314i
$631$	−16177.9			−1.02065			−0.510326	−	0.859981i	$-0.670475\pi$
$631$	−16177.9			−1.02065			−0.510326	+	0.859981i	$0.670475\pi$
$632$	1365.02	−	788.094i	0.0859138	−	0.0496024i
$633$	−12981.0	+	12209.8i	−0.815087	+	0.766663i
$634$	−5149.09	+	8918.49i	−0.322550	+	0.558673i
$635$	2799.24	−	4848.42i	0.174936	−	0.302998i
$636$	16154.0	+	17174.4i	1.00715	+	1.07077i
$637$	−2606.90	−	191.577i	−0.162150	−	0.0119161i
$638$		−	8174.41i		−	0.507254i
$639$	−1724.94	+	2605.41i	−0.106788	+	0.161296i
$640$			15314.5i			0.945875i
$641$	−23508.3	+	13572.5i	−1.44855	+	0.836321i	−0.998395	−	0.0566298i	$-0.981965\pi$
$641$	−23508.3	+	13572.5i	−1.44855	+	0.836321i	−0.450155	+	0.892951i	$0.648631\pi$
$642$	3912.93	+	16622.2i	0.240547	+	1.02185i
$643$	18843.1	+	10879.1i	1.15567	+	0.667229i	0.950263	−	0.311447i	$-0.100814\pi$
$643$	18843.1	+	10879.1i	1.15567	+	0.667229i	0.205411	+	0.978676i	$0.434147\pi$
$644$	3318.46	+	3571.27i	0.203052	+	0.218522i
$645$	−9700.38	−	2920.13i	−0.592174	−	0.178264i
$646$	−3962.70	−	6863.60i	−0.241347	−	0.418026i
$647$	24932.0			1.51496			0.757478	−	0.652860i	$-0.226431\pi$
$647$	24932.0			1.51496			0.757478	+	0.652860i	$0.226431\pi$
$648$	4108.08	−	1742.58i	0.249044	−	0.105641i
$649$		−	16751.9i		−	1.01320i
$650$	3946.60	+	6835.72i	0.238152	+	0.412491i
$651$	−3785.18	+	5642.50i	−0.227885	+	0.339704i
$652$	−1220.80	+	2114.50i	−0.0733288	+	0.127009i
$653$	838.558	+	484.142i	0.0502531	+	0.0290137i	0.524916	−	0.851154i	$-0.324097\pi$
$653$	838.558	+	484.142i	0.0502531	+	0.0290137i	−0.474663	+	0.880168i	$0.657430\pi$
$654$	−1820.97	+	428.663i	−0.108877	+	0.0256300i
$655$	21860.4	+	37863.3i	1.30406	+	2.25869i
$656$	1086.05			0.0646391
$657$	10555.5	−	15943.3i	0.626801	−	0.946739i
$658$	9704.44	−	31541.8i	0.574952	−	1.86874i
$659$	−3413.73	+	1970.92i	−0.201791	+	0.116504i	−0.597491	−	0.801876i	$-0.703835\pi$
$659$	−3413.73	+	1970.92i	−0.201791	+	0.116504i	0.395700	+	0.918380i	$0.370502\pi$
$660$	−16325.0	−	17356.1i	−0.962801	−	1.02361i
$661$	2506.55	+	1447.16i	0.147494	+	0.0851555i	0.571931	−	0.820302i	$-0.306195\pi$
$661$	2506.55	+	1447.16i	0.147494	+	0.0851555i	−0.424437	+	0.905457i	$0.639528\pi$
$662$	14932.3	+	8621.15i	0.876675	+	0.506149i
$663$	582.622	+	619.422i	0.0341284	+	0.0362841i
$664$	2126.64	−	1227.82i	0.124292	−	0.0717598i
$665$	10572.9	−	34364.7i	0.616543	−	2.00392i
$666$	−36318.5	−	2225.83i	−2.11308	−	0.129503i
$667$	2468.35			0.143291
$668$	786.084	+	1361.54i	0.0455307	+	0.0788615i
$669$	12530.3	−	2949.67i	0.724137	−	0.170465i
$670$	34384.1	+	19851.7i	1.98265	+	1.14468i
$671$	11273.5	−	19526.2i	0.648595	−	1.12340i
$672$	12484.3	−	18610.2i	0.716657	−	1.06831i
$673$	−6948.10	−	12034.5i	−0.397964	−	0.689293i	0.595511	−	0.803347i	$-0.296950\pi$
$673$	−6948.10	−	12034.5i	−0.397964	−	0.689293i	−0.993475	+	0.114054i	$0.963616\pi$
$674$			27516.5i			1.57255i
$675$	−13266.8	+	35940.9i	−0.756504	+	2.04943i
$676$	−13659.4			−0.777165
$677$	4561.28	+	7900.37i	0.258943	+	0.448502i	0.965959	−	0.258695i	$-0.0832926\pi$
$677$	4561.28	+	7900.37i	0.258943	+	0.448502i	−0.707016	+	0.707197i	$0.749959\pi$
$678$	−31219.8	−	9398.19i	−1.76842	−	0.532353i
$679$	7587.03	+	8165.05i	0.428812	+	0.461481i
$680$	−2271.32	−	1311.35i	−0.128090	−	0.0739529i
$681$	−200.089	−	849.982i	−0.0112591	−	0.0478288i
$682$	−8346.50	+	4818.85i	−0.468628	+	0.270562i
$683$			5500.02i			0.308129i	0.988061	+	0.154065i	$0.0492364\pi$
$683$			5500.02i			0.308129i	−0.988061	+	0.154065i	$0.950764\pi$
$684$	−7484.19	−	15015.6i	−0.418370	−	0.839379i
$685$			22700.0i			1.26617i
$686$	−22447.7	−	8754.04i	−1.24935	−	0.487217i
$687$	4067.48	+	4324.39i	0.225886	+	0.240154i
$688$	3630.43	−	6288.08i	0.201175	−	0.348446i
$689$	2707.41	−	4689.36i	0.149701	−	0.259290i
$690$	11806.1	−	11104.7i	0.651380	−	0.612682i
$691$	9079.68	−	5242.16i	0.499866	−	0.288598i	−0.228792	−	0.973475i	$-0.573478\pi$
$691$	9079.68	−	5242.16i	0.499866	−	0.288598i	0.728658	+	0.684877i	$0.240144\pi$
$692$	25401.8			1.39542
$693$	−2936.61	−	17755.1i	−0.160970	−	0.973246i
$694$	33334.8			1.82330
$695$	36756.9	−	21221.6i	2.00614	−	1.15825i
$696$	−436.451	−	1854.05i	−0.0237696	−	0.100974i
$697$	−156.935	+	271.820i	−0.00852849	+	0.0147718i
$698$	−13827.5	+	23949.9i	−0.749825	+	1.29874i
$699$	3267.50	−	10854.3i	0.176807	−	0.587334i
$700$	7209.54	+	31482.3i	0.389279	+	1.69989i
$701$		−	15162.7i		−	0.816955i	−0.912768	−	0.408477i	$-0.866060\pi$
$701$		−	15162.7i		−	0.816955i	0.912768	−	0.408477i	$-0.133940\pi$
$702$	2592.51	+	3118.33i	0.139385	+	0.167655i
$703$		−	34572.4i		−	1.85480i
$704$	9000.94	−	5196.69i	0.481869	−	0.278207i
$705$	−46637.4	−	14039.4i	−2.49144	−	0.750006i
$706$	−32928.2	−	19011.1i	−1.75534	−	1.01345i
$707$	5769.97	−	5361.50i	0.306934	−	0.285205i
$708$	3539.27	+	15034.9i	0.187873	+	0.798087i
$709$	1871.41	+	3241.38i	0.0991289	+	0.171696i	0.911324	−	0.411689i	$-0.135061\pi$
$709$	1871.41	+	3241.38i	0.0991289	+	0.171696i	−0.812195	+	0.583385i	$0.801728\pi$
$710$	8757.80			0.462922
$711$	−425.286	+	6939.34i	−0.0224324	+	0.366027i
$712$			5985.56i			0.315054i
$713$	−1455.10	−	2520.31i	−0.0764293	−	0.132379i
$714$	3453.94	+	7036.39i	0.181037	+	0.368810i
$715$	−2736.05	+	4738.98i	−0.143109	+	0.247871i
$716$	−8046.24	−	4645.50i	−0.419975	−	0.242473i
$717$	6799.90	+	7229.40i	0.354180	+	0.376551i
$718$	−21250.1	−	36806.3i	−1.10452	−	1.91309i
$719$	24366.5			1.26386			0.631931	−	0.775024i	$-0.282262\pi$
$719$	24366.5			1.26386			0.631931	+	0.775024i	$0.282262\pi$
$720$	−33376.7	−	22097.5i	−1.72760	−	1.14378i
$721$	−4132.68	+	13432.2i	−0.213466	+	0.693818i
$722$	8569.01	−	4947.32i	0.441697	−	0.255014i
$723$	11464.0	−	2698.67i	0.589696	−	0.138817i
$724$	−4069.91	−	2349.77i	−0.208919	−	0.120619i
$725$	14162.0	+	8176.42i	0.725466	+	0.418848i
$726$	−203.256	+	675.197i	−0.0103906	+	0.0345164i
$727$	20385.8	−	11769.7i	1.03998	−	0.600433i	0.120153	−	0.992755i	$-0.461661\pi$
$727$	20385.8	−	11769.7i	1.03998	−	0.600433i	0.919828	+	0.392322i	$0.128328\pi$
$728$	−825.748	−	254.057i	−0.0420388	−	0.0129340i
$729$	−3594.09	+	19352.1i	−0.182599	+	0.983188i
$730$	−53591.7			−2.71715
$731$	1049.20	+	1817.27i	0.0530862	+	0.0919481i
$732$	−5992.56	+	19906.7i	−0.302584	+	1.00515i
$733$	11851.1	+	6842.23i	0.597176	+	0.344780i	0.767930	−	0.640534i	$-0.221287\pi$
$733$	11851.1	+	6842.23i	0.597176	+	0.344780i	−0.170754	+	0.985314i	$0.554620\pi$
$734$	−5688.16	+	9852.18i	−0.286040	+	0.495437i
$735$	−12718.3	+	33207.5i	−0.638259	+	1.66650i
$736$	4799.24	+	8312.53i	0.240356	+	0.416310i
$737$			18881.9i			0.943722i
$738$	−826.287	+	1248.05i	−0.0412141	+	0.0622511i
$739$	12978.1			0.646017			0.323009	−	0.946396i	$-0.395306\pi$
$739$	12978.1			0.646017			0.323009	+	0.946396i	$0.395306\pi$
$740$	22635.8	+	39206.4i	1.12447	+	1.94764i
$741$	−2806.62	+	2639.87i	−0.139141	+	0.130875i
$742$	36563.3	−	33974.9i	1.80900	−	1.68094i
$743$	−24571.4	−	14186.3i	−1.21324	−	0.700464i	−0.249775	−	0.968304i	$-0.580357\pi$
$743$	−24571.4	−	14186.3i	−1.21324	−	0.700464i	−0.963463	+	0.267840i	$0.913690\pi$
$744$	−1635.80	+	1538.61i	−0.0806064	+	0.0758176i
$745$	7236.27	−	4177.86i	0.355861	−	0.205456i
$746$		−	15570.2i		−	0.764163i
$747$	−662.577	+	10811.2i	−0.0324530	+	0.529532i
$748$			4935.56i			0.241259i
$749$	15642.1	−	3582.08i	0.763082	−	0.174748i
$750$	56676.7	−	13341.9i	2.75939	−	0.649570i
$751$	13262.7	−	22971.6i	0.644423	−	1.11617i	−0.340011	−	0.940421i	$-0.610431\pi$
$751$	13262.7	−	22971.6i	0.644423	−	1.11617i	0.984434	−	0.175752i	$-0.0562358\pi$
$752$	17454.3	−	30231.8i	0.846402	−	1.46601i
$753$	1571.01	+	472.925i	0.0760302	+	0.0228876i
$754$	1499.05	−	865.475i	0.0724033	−	0.0418021i
$755$	−18976.0			−0.914711
$756$	6386.83	+	15314.8i	0.307258	+	0.736765i
$757$	15064.7			0.723296			0.361648	−	0.932315i	$-0.382214\pi$
$757$	15064.7			0.723296			0.361648	+	0.932315i	$0.382214\pi$
$758$	6737.68	−	3890.00i	0.322854	−	0.186400i
$759$	7380.94	+	2221.91i	0.352979	+	0.106258i
$760$	5941.75	−	10291.4i	0.283592	−	0.491196i
$761$	−2369.82	+	4104.66i	−0.112886	+	0.195524i	−0.916933	−	0.399042i	$-0.869343\pi$
$761$	−2369.82	+	4104.66i	−0.112886	+	0.195524i	0.804047	+	0.594566i	$0.202676\pi$
$762$	−5383.07	+	1267.19i	−0.255916	+	0.0602436i
$763$	392.418	+	1713.59i	0.0186192	+	0.0813057i
$764$		−	17626.0i		−	0.834667i
$765$	10353.6	−	5160.51i	0.489326	−	0.243894i
$766$		−	21135.0i		−	0.996917i
$767$	3072.01	−	1773.63i	0.144621	−	0.0834967i
$768$	19763.8	−	18589.6i	0.928599	−	0.873431i
$769$	−17949.9	−	10363.4i	−0.841730	−	0.485973i	0.0161222	−	0.999870i	$-0.494868\pi$
$769$	−17949.9	−	10363.4i	−0.841730	−	0.485973i	−0.857852	+	0.513897i	$0.828201\pi$
$770$	−36950.2	+	34334.5i	−1.72934	+	1.60692i
$771$	−15502.2	+	14581.2i	−0.724123	+	0.681103i
$772$	3936.68	+	6818.53i	0.183529	+	0.317881i
$773$	−10493.9			−0.488279			−0.244139	−	0.969740i	$-0.578505\pi$
$773$	−10493.9			−0.488279			−0.244139	+	0.969740i	$0.578505\pi$
$774$	4463.93	+	8956.02i	0.207303	+	0.415914i
$775$		−	19280.2i		−	0.893631i
$776$	1841.95	+	3190.35i	0.0852089	+	0.147586i
$777$	−2298.87	+	34115.5i	−0.106141	+	1.57514i
$778$	−3248.19	+	5626.02i	−0.149683	+	0.259258i
$779$	−1231.62	−	711.078i	−0.0566464	−	0.0327048i
$780$	1454.39	−	4831.32i	0.0667633	−	0.221781i
$781$	2082.49	+	3606.98i	0.0954128	+	0.165260i
$782$	−3357.32			−0.153526
$783$	7881.70	+	2909.37i	0.359730	+	0.132787i
$784$	−21079.1	−	14327.0i	−0.960237	−	0.652650i
$785$	−37614.3	+	21716.6i	−1.71021	+	0.987388i
$786$	12449.1	−	41354.5i	0.564942	−	1.87668i
$787$	6470.70	+	3735.86i	0.293082	+	0.169211i	0.639331	−	0.768932i	$-0.279211\pi$
$787$	6470.70	+	3735.86i	0.293082	+	0.169211i	−0.346249	+	0.938143i	$0.612545\pi$
$788$	−2749.06	−	1587.17i	−0.124278	−	0.0717521i
$789$	−24939.6	+	5870.87i	−1.12531	+	0.264903i
$790$	16875.4	−	9743.00i	0.759998	−	0.438785i
$791$	−9009.57	+	29283.3i	−0.404985	+	1.31630i
$792$	363.852	−	5936.93i	0.0163244	−	0.266363i
$793$	4774.37			0.213799
$794$	11336.0	+	19634.6i	0.506676	+	0.877589i
$795$	−50469.0	−	53656.8i	−2.25151	−	2.39372i
$796$	−24901.5	−	14376.9i	−1.10881	−	0.640170i
$797$	−26.6623	+	46.1805i	−0.00118498	+	0.00205244i	−0.866617	−	0.498973i	$-0.833711\pi$
$797$	−26.6623	+	46.1805i	−0.00118498	+	0.00205244i	0.865432	+	0.501026i	$0.167044\pi$
$798$	−31882.1	+	15649.9i	−1.41430	+	0.694236i
$799$	5044.33	+	8737.04i	0.223349	+	0.386851i
$800$			63590.0i			2.81031i
$801$	−22014.1	−	14574.7i	−0.971072	−	0.642910i
$802$	−11476.3			−0.505290
$803$	−12743.4	−	22072.2i	−0.560031	−	0.970003i
$804$	−3989.28	−	16946.5i	−0.174989	−	0.743357i
$805$	−10367.6	−	11157.5i	−0.453928	−	0.488510i
$806$	−1767.39	−	1020.40i	−0.0772378	−	0.0445933i
$807$	27396.9	+	8247.37i	1.19506	+	0.359754i
$808$	2254.51	−	1301.64i	0.0981603	−	0.0566729i
$809$		−	2578.18i		−	0.112045i	−0.998430	−	0.0560223i	$-0.982158\pi$
$809$		−	2578.18i		−	0.112045i	0.998430	−	0.0560223i	$-0.0178418\pi$
$810$	50787.1	−	21543.1i	2.20306	−	0.934502i
$811$			3556.10i			0.153973i	0.997032	+	0.0769863i	$0.0245298\pi$
$811$			3556.10i			0.153973i	−0.997032	+	0.0769863i	$0.975470\pi$
$812$	6903.96	−	1581.03i	0.298376	−	0.0683290i
$813$	11417.1	−	37926.4i	0.492515	−	1.63608i
$814$	−24250.5	+	42003.1i	−1.04420	+	1.80861i
$815$	3814.08	−	6606.19i	0.163928	−	0.283932i
$816$	1899.92	+	8070.91i	0.0815081	+	0.346248i
$817$	−8234.08	+	4753.95i	−0.352600	+	0.203574i
$818$	−41777.5			−1.78572
$819$	2945.06	−	2418.36i	0.125652	−	0.103180i
$820$	1862.28			0.0793093
$821$	28617.2	−	16522.1i	1.21650	−	0.702347i	0.252333	−	0.967640i	$-0.418802\pi$
$821$	28617.2	−	16522.1i	1.21650	−	0.702347i	0.964168	+	0.265293i	$0.0854688\pi$
$822$	16333.4	−	15363.0i	0.693056	−	0.651882i
$823$	9921.48	−	17184.5i	0.420220	−	0.727843i	−0.575741	−	0.817632i	$-0.695286\pi$
$823$	9921.48	−	17184.5i	0.420220	−	0.727843i	0.995961	+	0.0897898i	$0.0286195\pi$
$824$	−2322.47	+	4022.64i	−0.0981883	+	0.170067i
$825$	34987.5	+	37197.4i	1.47650	+	1.56976i
$826$	31872.2	−	7298.82i	1.34258	−	0.307456i
$827$		−	16163.8i		−	0.679648i	−0.940489	−	0.339824i	$-0.889632\pi$
$827$		−	16163.8i		−	0.679648i	0.940489	−	0.339824i	$-0.110368\pi$
$828$	−7093.85	−	434.755i	−0.297740	−	0.0182473i
$829$			30024.8i			1.25791i	0.777443	+	0.628954i	$0.216517\pi$
$829$			30024.8i			1.25791i	−0.777443	+	0.628954i	$0.783483\pi$
$830$	26291.1	−	15179.2i	1.09949	−	0.634791i
$831$	4312.87	+	18321.2i	0.180038	+	0.764806i
$832$	1905.97	+	1100.41i	0.0794202	+	0.0458533i
$833$	6631.75	−	3205.48i	0.275842	−	0.133329i
$834$	−40146.1	−	12085.3i	−1.66684	−	0.501774i
$835$	−2455.92	−	4253.77i	−0.101785	−	0.176297i
$836$	−22363.1			−0.925174
$837$	−1675.68	−	9762.71i	−0.0691996	−	0.403164i
$838$			44375.9i			1.82928i
$839$	−5951.06	−	10307.5i	−0.244879	−	0.424143i	0.717219	−	0.696848i	$-0.245415\pi$
$839$	−5951.06	−	10307.5i	−0.244879	−	0.424143i	−0.962098	+	0.272706i	$0.912082\pi$
$840$	−6547.55	+	9760.32i	−0.268943	+	0.400908i
$841$	−10401.4	+	18015.8i	−0.426481	+	0.738686i
$842$	−22873.4	−	13206.0i	−0.936186	−	0.540507i
$843$	11031.4	−	2596.84i	0.450703	−	0.106097i
$844$	−10951.1	−	18967.9i	−0.446626	−	0.773579i
$845$	42675.4			1.73737
$846$	21461.7	+	43058.7i	0.872183	+	1.74987i
$847$	633.316	+	194.852i	0.0256919	+	0.00790459i
$848$	45723.5	−	26398.5i	1.85159	−	1.06902i
$849$	8162.51	+	8678.07i	0.329961	+	0.350802i
$850$	−19262.4	−	11121.1i	−0.777287	−	0.448767i
$851$	−12683.3	−	7322.69i	−0.510902	−	0.294969i
$852$	−2631.11	−	2797.30i	−0.105798	−	0.112481i
$853$	28403.7	−	16398.9i	1.14012	−	0.658251i	0.193662	−	0.981068i	$-0.437963\pi$
$853$	28403.7	−	16398.9i	1.14012	−	0.658251i	0.946461	+	0.322818i	$0.104630\pi$
$854$	42062.5	+	12941.3i	1.68542	+	0.518551i
$855$	23382.4	+	46912.3i	0.935276	+	1.87645i
$856$	5303.78			0.211775
$857$	−3583.64	−	6207.05i	−0.142841	−	0.247408i	0.785724	−	0.618577i	$-0.212291\pi$
$857$	−3583.64	−	6207.05i	−0.142841	−	0.247408i	−0.928565	+	0.371169i	$0.878957\pi$
$858$	5261.56	−	1238.59i	0.209355	−	0.0492830i
$859$	−28909.1	−	16690.7i	−1.14827	−	0.662956i	−0.199808	−	0.979835i	$-0.564032\pi$
$859$	−28909.1	−	16690.7i	−1.14827	−	0.662956i	−0.948466	+	0.316879i	$0.897365\pi$
$860$	6225.18	−	10782.3i	0.246833	−	0.427528i
$861$	1168.07	+	783.577i	0.0462341	+	0.0310154i
$862$	24058.9	+	41671.2i	0.950637	+	1.64655i
$863$			10473.7i			0.413127i	0.978433	+	0.206564i	$0.0662280\pi$
$863$			10473.7i			0.413127i	−0.978433	+	0.206564i	$0.933772\pi$
$864$	5526.76	+	32199.5i	0.217621	+	1.26788i
$865$	−79361.2			−3.11949
$866$	−24448.0	−	42345.2i	−0.959328	−	1.66160i
$867$	22150.5	+	6668.04i	0.867672	+	0.261198i
$868$	−5684.23	−	6117.28i	−0.222276	−	0.239210i
$869$	8025.48	+	4633.51i	0.313286	+	0.180876i
$870$	−5395.73	−	22921.2i	−0.210267	−	0.893219i
$871$	−3462.61	+	1999.14i	−0.134703	+	0.0777707i
$872$			581.032i			0.0225645i
$873$	−16218.8	−	993.987i	−0.628776	−	0.0385353i
$874$		−	15212.1i		−	0.588738i
$875$	−12213.8	−	53334.7i	−0.471888	−	2.06062i
$876$	16100.6	+	17117.5i	0.620991	+	0.660214i
$877$	−8766.80	+	15184.5i	−0.337553	+	0.584659i	−0.983972	−	0.178324i	$-0.942933\pi$
$877$	−8766.80	+	15184.5i	−0.337553	+	0.584659i	0.646419	+	0.762983i	$0.276266\pi$
$878$	−22922.2	+	39702.5i	−0.881080	+	1.52607i
$879$	−2067.37	+	1944.55i	−0.0793296	+	0.0746167i
$880$	−46207.3	+	26677.8i	−1.77006	+	1.02194i
$881$	6138.62			0.234751			0.117375	−	0.993088i	$-0.462552\pi$
$881$	6138.62			0.234751			0.117375	+	0.993088i	$0.462552\pi$
$882$	32501.4	−	13323.1i	1.24079	−	0.508631i
$883$	27717.1			1.05635			0.528173	−	0.849137i	$-0.322877\pi$
$883$	27717.1			1.05635			0.528173	+	0.849137i	$0.322877\pi$
$884$	−905.098	+	522.558i	−0.0344363	+	0.0198818i
$885$	−11057.5	−	46972.6i	−0.419994	−	1.78414i
$886$	19060.3	−	33013.3i	0.722734	−	1.25181i
$887$	−24730.2	+	42833.9i	−0.936142	+	1.62145i	−0.163557	+	0.986534i	$0.552297\pi$
$887$	−24730.2	+	42833.9i	−0.936142	+	1.62145i	−0.772585	+	0.634912i	$0.781036\pi$
$888$	−3257.66	+	10821.6i	−0.123108	+	0.408952i
$889$	1160.05	+	5065.65i	0.0437647	+	0.191110i
$890$			73997.9i			2.78698i
$891$	20949.2	+	15794.5i	0.787682	+	0.593865i
$892$			15820.8i			0.593855i
$893$	−39587.7	+	22856.0i	−1.48349	+	0.856491i
$894$	−7903.49	−	2379.21i	−0.295674	−	0.0890076i
$895$	25138.4	+	14513.6i	0.938864	+	0.542053i
$896$	−9676.66	−	10413.9i	−0.360797	−	0.388285i
$897$	374.006	+	1588.78i	0.0139216	+	0.0591393i
$898$	19049.1	+	32994.0i	0.707881	+	1.22609i
$899$	−4228.07			−0.156856
$900$	−39260.3	−	25992.8i	−1.45409	−	0.962696i
$901$			15258.4i			0.564186i
$902$	997.560	+	1727.82i	0.0368238	+	0.0637808i
$903$	8441.37	−	4143.60i	0.311087	−	0.152703i
$904$	−5063.17	+	8769.67i	−0.186282	+	0.322649i
$905$	12715.4	+	7341.23i	0.467043	+	0.269647i
$906$	12842.6	+	13653.8i	0.470936	+	0.500682i
$907$	10676.2	+	18491.7i	0.390846	+	0.676965i	0.992561	−	0.121746i	$-0.0388493\pi$
$907$	10676.2	+	18491.7i	0.390846	+	0.676965i	−0.601716	+	0.798710i	$0.705516\pi$
$908$	1073.19			0.0392237
$909$	−702.417	+	11461.3i	−0.0256301	+	0.418202i
$910$	−10208.5	−	3140.84i	−0.371877	−	0.114415i
$911$	−35324.0	+	20394.3i	−1.28467	+	0.741707i	−0.977699	−	0.210011i	$-0.932650\pi$
$911$	−35324.0	+	20394.3i	−1.28467	+	0.741707i	−0.306975	+	0.951718i	$0.599317\pi$
$912$	−36569.5	+	8608.60i	−1.32778	+	0.312565i
$913$	12503.4	+	7218.81i	0.453232	+	0.261673i
$914$	−50621.4	−	29226.3i	−1.83195	−	1.05768i
$915$	18722.2	−	62193.1i	0.676433	−	2.24704i
$916$	−6318.79	+	3648.16i	−0.227924	+	0.131592i
$917$	−38789.4	−	11934.3i	−1.39688	−	0.429777i
$918$	−10720.3	−	3957.17i	−0.385427	−	0.142272i
$919$	37868.9			1.35928			0.679641	−	0.733545i	$-0.262136\pi$
$919$	37868.9			1.35928			0.679641	+	0.733545i	$0.262136\pi$
$920$	−2517.02	−	4359.60i	−0.0901996	−	0.156230i
$921$	9276.31	−	30814.9i	0.331884	−	1.10248i
$922$	−18968.4	−	10951.4i	−0.677540	−	0.391178i
$923$	−440.972	+	763.786i	−0.0157257	+	0.0272376i
$924$	22067.6	+	1487.02i	0.785683	+	0.0529431i
$925$	−48512.9	−	84026.9i	−1.72443	−	2.98680i
$926$		−	36145.2i		−	1.28273i
$927$	−9139.55	−	18336.8i	−0.323821	−	0.649685i
$928$	13945.1			0.493286
$929$	21195.0	+	36710.7i	0.748530	+	1.29649i	0.948527	+	0.316695i	$0.102573\pi$
$929$	21195.0	+	36710.7i	0.748530	+	1.29649i	−0.199998	+	0.979796i	$0.564094\pi$
$930$	−20222.9	+	19021.5i	−0.713048	+	0.670686i
$931$	14524.1	+	30048.6i	0.511287	+	1.05779i
$932$	12064.9	+	6965.69i	0.424034	+	0.244816i
$933$	−17677.6	+	16627.4i	−0.620299	+	0.583447i
$934$	−27161.5	+	15681.7i	−0.951555	+	0.549380i
$935$		−	15419.9i		−	0.539341i
$936$	1127.25	−	561.855i	0.0393648	−	0.0196205i
$937$		−	28387.3i		−	0.989725i	−0.868971	−	0.494863i	$-0.835218\pi$
$937$		−	28387.3i		−	0.989725i	0.868971	−	0.494863i	$-0.164782\pi$
$938$	−35924.7	+	8226.86i	−1.25051	+	0.286371i
$939$	12957.7	−	3050.28i	0.450327	−	0.106009i
$940$	29929.4	−	51839.2i	1.03850	−	1.79873i
$941$	7205.30	−	12479.9i	0.249613	−	0.432343i	−0.713805	−	0.700344i	$-0.753030\pi$
$941$	7205.30	−	12479.9i	0.249613	−	0.432343i	0.963419	+	0.268001i	$0.0863632\pi$
$942$	41082.5	+	12367.2i	1.42096	+	0.427755i
$943$	−521.735	+	301.224i	−0.0180170	+	0.0104021i
$944$	34587.4			1.19250
$945$	−19954.0	−	47847.1i	−0.686882	−	1.64705i
$946$	13338.5			0.458426
$947$	−27439.3	+	15842.1i	−0.941561	+	0.543611i	−0.890449	−	0.455082i	$-0.849610\pi$
$947$	−27439.3	+	15842.1i	−0.941561	+	0.543611i	−0.0511119	+	0.998693i	$0.516277\pi$
$948$	−8181.85	−	2463.01i	−0.280310	−	0.0843826i
$949$	2698.45	−	4673.85i	0.0923028	−	0.159873i
$950$	50390.2	−	87278.3i	1.72092	−	2.98072i
$951$	−13732.8	+	3232.75i	−0.468261	+	0.110230i
$952$	2373.09	−	543.444i	0.0807902	−	0.0185012i
$953$		−	24370.5i		−	0.828370i	−0.910193	−	0.414185i	$-0.864067\pi$
$953$		−	24370.5i		−	0.828370i	0.910193	−	0.414185i	$-0.135933\pi$
$954$	−4451.10	+	72628.1i	−0.151058	+	2.46480i
$955$			55067.7i			1.86592i
$956$	−10563.6	+	6098.88i	−0.357375	+	0.206331i
$957$	8157.26	−	7672.63i	0.275535	−	0.259165i
$958$	47929.3	+	27672.0i	1.61641	+	0.933237i
$959$	−14343.3	−	15436.0i	−0.482970	−	0.519765i
$960$	21808.6	−	20512.9i	0.733196	−	0.689637i
$961$	−12403.0	−	21482.7i	−0.416335	−	0.721113i
$962$	−10270.2			−0.344204
$963$	−12914.6	+	19506.6i	−0.432156	+	0.652742i
$964$			14474.5i			0.483602i
$965$	−12299.1	−	21302.7i	−0.410283	−	0.710630i
$966$	−1011.52	+	15011.1i	−0.0336905	+	0.499972i
$967$	9567.67	−	16571.7i	0.318175	−	0.551096i	−0.661932	−	0.749564i	$-0.730263\pi$
$967$	9567.67	−	16571.7i	0.318175	−	0.551096i	0.980107	+	0.198468i	$0.0635967\pi$
$968$	189.663	+	109.502i	0.00629753	+	0.00363588i
$969$	3129.74	−	10396.7i	0.103758	−	0.344674i
$970$	22771.5	+	39441.4i	0.753762	+	1.30555i
$971$	15282.0			0.505070			0.252535	−	0.967588i	$-0.418736\pi$
$971$	15282.0			0.505070			0.252535	+	0.967588i	$0.418736\pi$
$972$	−22139.0	−	9749.52i	−0.730564	−	0.321724i
$973$	−11585.6	+	37656.0i	−0.381723	+	1.24069i
$974$	47236.2	−	27271.9i	1.55395	−	0.897173i
$975$	−3117.03	+	10354.4i	−0.102384	+	0.340110i
$976$	40315.5	+	23276.2i	1.32220	+	0.763373i
$977$	11983.9	+	6918.89i	0.392424	+	0.226566i	0.683210	−	0.730222i	$-0.260583\pi$
$977$	11983.9	+	6918.89i	0.392424	+	0.226566i	−0.290786	+	0.956788i	$0.593917\pi$
$978$	−7334.67	+	1726.61i	−0.239813	+	0.0564528i
$979$	−30476.7	+	17595.7i	−0.994933	+	0.574425i
$980$	−36144.9	−	24566.8i	−1.17817	−	0.800773i
$981$	−2136.95	−	1414.80i	−0.0695491	−	0.0460459i
$982$	2245.08			0.0729566
$983$	23671.0	+	40999.4i	0.768044	+	1.33029i	0.938622	+	0.344947i	$0.112103\pi$
$983$	23671.0	+	40999.4i	0.768044	+	1.33029i	−0.170578	+	0.985344i	$0.554563\pi$
$984$	318.511	+	338.629i	0.0103189	+	0.0109706i
$985$	8588.73	+	4958.71i	0.277827	+	0.160404i
$986$	−2438.83	+	4224.17i	−0.0787708	+	0.136435i
$987$	40584.4	−	19921.6i	1.30883	−	0.642463i
$988$	−2367.72	−	4101.02i	−0.0762423	−	0.132055i
$989$			4027.69i			0.129498i
$990$	4498.20	−	73396.6i	0.144406	−	2.35626i
$991$	13576.2			0.435177			0.217589	−	0.976041i	$-0.430181\pi$
$991$	13576.2			0.435177			0.217589	+	0.976041i	$0.430181\pi$
$992$	−8220.68	−	14238.6i	−0.263112	−	0.455723i
$993$	5412.61	+	22992.9i	0.172975	+	0.734800i
$994$	−5955.30	+	5533.71i	−0.190031	+	0.176578i
$995$	77798.2	+	44916.8i	2.47876	+	1.43111i
$996$	−12747.0	−	3837.26i	−0.405525	−	0.122076i
$997$	14126.1	−	8155.72i	0.448725	−	0.259071i	−0.258567	−	0.965993i	$-0.583250\pi$
$997$	14126.1	−	8155.72i	0.448725	−	0.259071i	0.707292	+	0.706922i	$0.249917\pi$
$998$			15747.4i			0.499473i
$999$	−31868.0	−	38331.5i	−1.00927	−	1.21397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.o.a.41.5	yes	44
3.2	odd	2		189.4.o.a.125.18		44
7.6	odd	2	inner	63.4.o.a.41.6	yes	44
9.2	odd	6	inner	63.4.o.a.20.6	yes	44
9.4	even	3		567.4.c.c.566.43		44
9.5	odd	6		567.4.c.c.566.2		44
9.7	even	3		189.4.o.a.62.17		44
21.20	even	2		189.4.o.a.125.17		44
63.13	odd	6		567.4.c.c.566.1		44
63.20	even	6	inner	63.4.o.a.20.5	✓	44
63.34	odd	6		189.4.o.a.62.18		44
63.41	even	6		567.4.c.c.566.44		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.o.a.20.5	✓	44	63.20	even	6	inner
63.4.o.a.20.6	yes	44	9.2	odd	6	inner
63.4.o.a.41.5	yes	44	1.1	even	1	trivial
63.4.o.a.41.6	yes	44	7.6	odd	2	inner
189.4.o.a.62.17		44	9.7	even	3
189.4.o.a.62.18		44	63.34	odd	6
189.4.o.a.125.17		44	21.20	even	2
189.4.o.a.125.18		44	3.2	odd	2
567.4.c.c.566.1		44	63.13	odd	6
567.4.c.c.566.2		44	9.5	odd	6
567.4.c.c.566.43		44	9.4	even	3
567.4.c.c.566.44		44	63.41	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.28475 + 1.89645i) q^{2} +(-4.97559 - 1.49782i) q^{3} +(3.19307 - 5.53055i) q^{4} +(-9.97590 + 17.2788i) q^{5} +(19.1841 - 4.51602i) q^{6} +(-4.13417 - 18.0529i) q^{7} -6.12125i q^{8} +(22.5131 + 14.9051i) q^{9} +O(q^{10})\)	\(q+(-3.28475 + 1.89645i) q^{2} +(-4.97559 - 1.49782i) q^{3} +(3.19307 - 5.53055i) q^{4} +(-9.97590 + 17.2788i) q^{5} +(19.1841 - 4.51602i) q^{6} +(-4.13417 - 18.0529i) q^{7} -6.12125i q^{8} +(22.5131 + 14.9051i) q^{9} -75.6753i q^{10} +(31.1676 - 17.9946i) q^{11} +(-24.1712 + 22.7352i) q^{12} +(6.59980 + 3.81040i) q^{13} +(47.8163 + 51.4592i) q^{14} +(75.5165 - 71.0301i) q^{15} +(37.1532 + 64.3512i) q^{16} -21.4747 q^{17} +(-102.217 - 6.26447i) q^{18} -97.3022i q^{19} +(63.7074 + 110.345i) q^{20} +(-6.47004 + 96.0163i) q^{21} +(-68.2518 + 118.216i) q^{22} +(-35.6964 - 20.6094i) q^{23} +(-9.16851 + 30.4568i) q^{24} +(-136.537 - 236.489i) q^{25} -28.9050 q^{26} +(-89.6909 - 107.882i) q^{27} +(-113.043 - 34.7800i) q^{28} +(-51.8612 + 29.9421i) q^{29} +(-113.348 + 376.530i) q^{30} +(61.1449 + 35.3020i) q^{31} +(-201.669 - 116.434i) q^{32} +(-182.030 + 42.8505i) q^{33} +(70.5390 - 40.7257i) q^{34} +(353.175 + 108.661i) q^{35} +(154.319 - 76.9169i) q^{36} +355.309 q^{37} +(184.529 + 319.614i) q^{38} +(-27.1307 - 28.8443i) q^{39} +(105.768 + 61.0649i) q^{40} +(7.30794 - 12.6577i) q^{41} +(-160.838 - 327.660i) q^{42} +(-48.8575 - 84.6237i) q^{43} -229.832i q^{44} +(-482.130 + 240.307i) q^{45} +156.339 q^{46} +(-234.897 - 406.853i) q^{47} +(-88.4728 - 375.834i) q^{48} +(-308.817 + 149.268i) q^{49} +(896.982 + 517.873i) q^{50} +(106.849 + 32.1651i) q^{51} +(42.1472 - 24.3337i) q^{52} -710.531i q^{53} +(499.206 + 184.271i) q^{54} +718.049i q^{55} +(-110.506 + 25.3063i) q^{56} +(-145.741 + 484.136i) q^{57} +(113.568 - 196.705i) q^{58} +(232.735 - 403.109i) q^{59} +(-151.706 - 644.452i) q^{60} +(542.558 - 313.246i) q^{61} -267.794 q^{62} +(176.007 - 468.047i) q^{63} +288.792 q^{64} +(-131.678 + 76.0243i) q^{65} +(516.659 - 485.964i) q^{66} +(-262.327 + 454.364i) q^{67} +(-68.5700 + 118.767i) q^{68} +(146.742 + 156.011i) q^{69} +(-1366.16 + 312.855i) q^{70} +115.729i q^{71} +(91.2376 - 137.808i) q^{72} -708.180i q^{73} +(-1167.10 + 673.827i) q^{74} +(325.136 + 1381.18i) q^{75} +(-538.135 - 310.692i) q^{76} +(-453.708 - 488.273i) q^{77} +(143.819 + 43.2944i) q^{78} +(128.747 + 222.997i) q^{79} -1482.55 q^{80} +(284.678 + 671.118i) q^{81} +55.4366i q^{82} +(200.583 + 347.420i) q^{83} +(510.364 + 342.369i) q^{84} +(214.229 - 371.056i) q^{85} +(320.970 + 185.312i) q^{86} +(302.888 - 71.3010i) q^{87} +(-110.149 - 190.784i) q^{88} -977.834 q^{89} +(1127.95 - 1703.68i) q^{90} +(41.5042 - 134.899i) q^{91} +(-227.962 + 131.614i) q^{92} +(-251.356 - 267.233i) q^{93} +(1543.16 + 890.942i) q^{94} +(1681.26 + 970.677i) q^{95} +(829.026 + 881.389i) q^{96} +(-521.193 + 300.911i) q^{97} +(731.308 - 1075.97i) q^{98} +(969.889 + 59.4408i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) \) 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7	\( 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7} - 18 q^{11} + 204 q^{14} + 66 q^{15} - 242 q^{16} - 210 q^{18} - 57 q^{21} - 34 q^{22} - 102 q^{23} - 352 q^{25} + 300 q^{28} + 246 q^{29} - 144 q^{30} + 1068 q^{32} - 1818 q^{36} + 328 q^{37} - 798 q^{39} - 1158 q^{42} - 170 q^{43} + 968 q^{46} - 79 q^{49} + 288 q^{50} - 204 q^{51} + 1212 q^{56} + 324 q^{57} - 538 q^{58} + 5316 q^{60} + 783 q^{63} - 808 q^{64} + 4350 q^{65} - 590 q^{67} + 384 q^{70} + 4284 q^{72} - 5304 q^{74} - 2787 q^{77} + 612 q^{78} - 302 q^{79} - 3720 q^{81} + 7050 q^{84} - 612 q^{85} - 13692 q^{86} + 1294 q^{88} + 210 q^{91} - 10194 q^{92} - 4266 q^{93} + 6336 q^{95} + 1014 q^{99}+O(q^{100}) \) 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7 - 18 * q^11 + 204 * q^14 + 66 * q^15 - 242 * q^16 - 210 * q^18 - 57 * q^21 - 34 * q^22 - 102 * q^23 - 352 * q^25 + 300 * q^28 + 246 * q^29 - 144 * q^30 + 1068 * q^32 - 1818 * q^36 + 328 * q^37 - 798 * q^39 - 1158 * q^42 - 170 * q^43 + 968 * q^46 - 79 * q^49 + 288 * q^50 - 204 * q^51 + 1212 * q^56 + 324 * q^57 - 538 * q^58 + 5316 * q^60 + 783 * q^63 - 808 * q^64 + 4350 * q^65 - 590 * q^67 + 384 * q^70 + 4284 * q^72 - 5304 * q^74 - 2787 * q^77 + 612 * q^78 - 302 * q^79 - 3720 * q^81 + 7050 * q^84 - 612 * q^85 - 13692 * q^86 + 1294 * q^88 + 210 * q^91 - 10194 * q^92 - 4266 * q^93 + 6336 * q^95 + 1014 * q^99

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