LMFDB - Embedded newform 126.4.m.a.41.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,4,Mod(41,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("126.41");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	126.m (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:	$7.43424066072$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.2
Character	$\chi$	$=$	126.41
Dual form			126.4.m.a.83.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73205 + 1.00000i) q^{2} +(-5.04167 + 1.25759i) q^{3} +(2.00000 - 3.46410i) q^{4} +(0.984584 - 1.70535i) q^{5} +(7.47485 - 7.21988i) q^{6} +(-17.4955 - 6.07527i) q^{7} +8.00000i q^{8} +(23.8370 - 12.6807i) q^{9} +O(q^{10})$	\(q+(-1.73205 + 1.00000i) q^{2} +(-5.04167 + 1.25759i) q^{3} +(2.00000 - 3.46410i) q^{4} +(0.984584 - 1.70535i) q^{5} +(7.47485 - 7.21988i) q^{6} +(-17.4955 - 6.07527i) q^{7} +8.00000i q^{8} +(23.8370 - 12.6807i) q^{9} +3.93834i q^{10} +(15.6931 - 9.06041i) q^{11} +(-5.72694 + 19.9800i) q^{12} +(7.54928 + 4.35858i) q^{13} +(36.3783 - 6.97278i) q^{14} +(-2.81933 + 9.83602i) q^{15} +(-8.00000 - 13.8564i) q^{16} +24.9620 q^{17} +(-28.6061 + 45.8005i) q^{18} +147.928i q^{19} +(-3.93834 - 6.82140i) q^{20} +(95.8466 + 8.62748i) q^{21} +(-18.1208 + 31.3862i) q^{22} +(133.950 + 77.3363i) q^{23} +(-10.0607 - 40.3334i) q^{24} +(60.5612 + 104.895i) q^{25} -17.4343 q^{26} +(-104.231 + 93.9089i) q^{27} +(-56.0363 + 48.4555i) q^{28} +(171.912 - 99.2537i) q^{29} +(-4.95280 - 19.8558i) q^{30} +(-18.9611 - 10.9472i) q^{31} +(27.7128 + 16.0000i) q^{32} +(-67.7252 + 65.4151i) q^{33} +(-43.2355 + 24.9620i) q^{34} +(-27.5862 + 23.8543i) q^{35} +(3.74672 - 107.935i) q^{36} +4.61892 q^{37} +(-147.928 - 256.219i) q^{38} +(-43.5423 - 12.4807i) q^{39} +(13.6428 + 7.87667i) q^{40} +(209.622 - 363.076i) q^{41} +(-174.639 + 80.9033i) q^{42} +(-161.190 - 279.189i) q^{43} -72.4833i q^{44} +(1.84448 - 53.1355i) q^{45} -309.345 q^{46} +(102.174 + 176.970i) q^{47} +(57.7590 + 59.7988i) q^{48} +(269.182 + 212.579i) q^{49} +(-209.790 - 121.122i) q^{50} +(-125.850 + 31.3919i) q^{51} +(30.1971 - 17.4343i) q^{52} +512.902i q^{53} +(86.6246 - 266.886i) q^{54} -35.6829i q^{55} +(48.6022 - 139.964i) q^{56} +(-186.032 - 745.804i) q^{57} +(-198.507 + 343.825i) q^{58} +(296.313 - 513.229i) q^{59} +(28.4343 + 29.4385i) q^{60} +(294.171 - 169.839i) q^{61} +43.7887 q^{62} +(-494.077 + 77.0384i) q^{63} -64.0000 q^{64} +(14.8658 - 8.58277i) q^{65} +(51.8884 - 181.027i) q^{66} +(-268.531 + 465.109i) q^{67} +(49.9241 - 86.4710i) q^{68} +(-772.591 - 221.450i) q^{69} +(23.9265 - 68.9030i) q^{70} +13.3482i q^{71} +(101.445 + 190.696i) q^{72} -27.3334i q^{73} +(-8.00021 + 4.61892i) q^{74} +(-437.244 - 452.686i) q^{75} +(512.437 + 295.856i) q^{76} +(-329.602 + 63.1762i) q^{77} +(87.8981 - 21.9252i) q^{78} +(230.790 + 399.741i) q^{79} -31.5067 q^{80} +(407.400 - 604.538i) q^{81} +838.488i q^{82} +(43.2259 + 74.8694i) q^{83} +(221.580 - 314.767i) q^{84} +(24.5772 - 42.5690i) q^{85} +(558.378 + 322.380i) q^{86} +(-741.906 + 716.599i) q^{87} +(72.4833 + 125.545i) q^{88} +336.072 q^{89} +(49.9408 + 93.8779i) q^{90} +(-105.599 - 122.119i) q^{91} +(535.801 - 309.345i) q^{92} +(109.363 + 31.3469i) q^{93} +(-353.940 - 204.347i) q^{94} +(252.269 + 145.647i) q^{95} +(-159.840 - 45.8155i) q^{96} +(155.290 - 89.6566i) q^{97} +(-678.816 - 99.0161i) q^{98} +(259.183 - 414.972i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 96 q^{4} - 12 q^{7} - 36 q^{9}+O(q^{10}) $ 48 * q + 96 * q^4 - 12 * q^7 - 36 * q^9	$ 48 q + 96 q^{4} - 12 q^{7} - 36 q^{9} + 24 q^{11} - 132 q^{14} - 120 q^{15} - 384 q^{16} + 120 q^{18} + 180 q^{21} + 348 q^{23} - 600 q^{25} - 96 q^{28} - 84 q^{29} + 192 q^{30} + 96 q^{36} - 672 q^{37} + 1368 q^{39} + 1128 q^{42} + 84 q^{43} - 1008 q^{46} - 42 q^{49} + 456 q^{50} + 2016 q^{51} - 528 q^{56} + 732 q^{57} + 504 q^{58} - 1008 q^{60} - 774 q^{63} - 3072 q^{64} - 6972 q^{65} + 1176 q^{67} + 216 q^{70} - 384 q^{72} + 2520 q^{74} + 1500 q^{77} + 2832 q^{78} + 348 q^{79} + 2268 q^{81} - 1080 q^{84} + 720 q^{85} + 1200 q^{86} + 180 q^{91} + 1392 q^{92} + 5232 q^{93} - 5892 q^{95} + 972 q^{99}+O(q^{100}) $ 48 * q + 96 * q^4 - 12 * q^7 - 36 * q^9 + 24 * q^11 - 132 * q^14 - 120 * q^15 - 384 * q^16 + 120 * q^18 + 180 * q^21 + 348 * q^23 - 600 * q^25 - 96 * q^28 - 84 * q^29 + 192 * q^30 + 96 * q^36 - 672 * q^37 + 1368 * q^39 + 1128 * q^42 + 84 * q^43 - 1008 * q^46 - 42 * q^49 + 456 * q^50 + 2016 * q^51 - 528 * q^56 + 732 * q^57 + 504 * q^58 - 1008 * q^60 - 774 * q^63 - 3072 * q^64 - 6972 * q^65 + 1176 * q^67 + 216 * q^70 - 384 * q^72 + 2520 * q^74 + 1500 * q^77 + 2832 * q^78 + 348 * q^79 + 2268 * q^81 - 1080 * q^84 + 720 * q^85 + 1200 * q^86 + 180 * q^91 + 1392 * q^92 + 5232 * q^93 - 5892 * q^95 + 972 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−1.73205	+	1.00000i	−0.612372	+	0.353553i
$2$	−1.73205	+	1.00000i	−0.612372	+	0.353553i
$3$	−5.04167	+	1.25759i	−0.970271	+	0.242023i
$3$	−5.04167	+	1.25759i	−0.970271	+	0.242023i
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$	0.984584	−	1.70535i	0.0880639	−	0.152531i	−0.818629	−	0.574323i	$-0.805265\pi$
$5$	0.984584	−	1.70535i	0.0880639	−	0.152531i	0.906693	+	0.421792i	$0.138599\pi$
$6$	7.47485	−	7.21988i	0.508599	−	0.491250i
$7$	−17.4955	−	6.07527i	−0.944666	−	0.328034i
$7$	−17.4955	−	6.07527i	−0.944666	−	0.328034i
$8$			8.00000i			0.353553i
$9$	23.8370	−	12.6807i	0.882850	−	0.469655i
$10$			3.93834i			0.124541i
$11$	15.6931	−	9.06041i	0.430150	−	0.248347i	−0.269261	−	0.963067i	$-0.586779\pi$
$11$	15.6931	−	9.06041i	0.430150	−	0.248347i	0.699410	+	0.714720i	$0.253446\pi$
$12$	−5.72694	+	19.9800i	−0.137769	+	0.480645i
$13$	7.54928	+	4.35858i	0.161061	+	0.0929886i	0.578364	−	0.815779i	$-0.303691\pi$
$13$	7.54928	+	4.35858i	0.161061	+	0.0929886i	−0.417303	+	0.908767i	$0.637025\pi$
$14$	36.3783	−	6.97278i	0.694465	−	0.133111i
$15$	−2.81933	+	9.83602i	−0.0485298	+	0.169310i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	24.9620			0.356128			0.178064	−	0.984019i	$-0.443017\pi$
$17$	24.9620			0.356128			0.178064	+	0.984019i	$0.443017\pi$
$18$	−28.6061	+	45.8005i	−0.374585	+	0.599738i
$19$			147.928i			1.78616i	0.449900	+	0.893079i	$0.351460\pi$
$19$			147.928i			1.78616i	−0.449900	+	0.893079i	$0.648540\pi$
$20$	−3.93834	−	6.82140i	−0.0440319	−	0.0762655i
$21$	95.8466	+	8.62748i	0.995973	+	0.0896510i
$22$	−18.1208	+	31.3862i	−0.175608	+	0.304162i
$23$	133.950	+	77.3363i	1.21437	+	0.701119i	0.963709	−	0.266956i	$-0.0860177\pi$
$23$	133.950	+	77.3363i	1.21437	+	0.701119i	0.250664	+	0.968074i	$0.419351\pi$
$24$	−10.0607	−	40.3334i	−0.0855679	−	0.343042i
$25$	60.5612	+	104.895i	0.484490	+	0.839160i
$26$	−17.4343			−0.131506
$27$	−104.231	+	93.9089i	−0.742936	+	0.669362i
$28$	−56.0363	+	48.4555i	−0.378209	+	0.327044i
$29$	171.912	−	99.2537i	1.10080	−	0.635550i	0.164372	−	0.986398i	$-0.447440\pi$
$29$	171.912	−	99.2537i	1.10080	−	0.635550i	0.936432	+	0.350849i	$0.114107\pi$
$30$	−4.95280	−	19.8558i	−0.0301418	−	0.120839i
$31$	−18.9611	−	10.9472i	−0.109855	−	0.0634249i	0.444066	−	0.895994i	$-0.353536\pi$
$31$	−18.9611	−	10.9472i	−0.109855	−	0.0634249i	−0.553921	+	0.832569i	$0.686869\pi$
$32$	27.7128	+	16.0000i	0.153093	+	0.0883883i
$33$	−67.7252	+	65.4151i	−0.357256	+	0.345070i
$34$	−43.2355	+	24.9620i	−0.218083	+	0.125910i
$35$	−27.5862	+	23.8543i	−0.133226	+	0.115203i
$36$	3.74672	−	107.935i	0.0173459	−	0.499699i
$37$	4.61892			0.0205229			0.0102614	−	0.999947i	$-0.496734\pi$
$37$	4.61892			0.0205229			0.0102614	+	0.999947i	$0.496734\pi$
$38$	−147.928	−	256.219i	−0.631502	−	1.09379i
$39$	−43.5423	−	12.4807i	−0.178778	−	0.0512437i
$40$	13.6428	+	7.87667i	0.0539279	+	0.0311353i
$41$	209.622	−	363.076i	0.798474	−	1.38300i	−0.122136	−	0.992513i	$-0.538974\pi$
$41$	209.622	−	363.076i	0.798474	−	1.38300i	0.920610	−	0.390484i	$-0.127692\pi$
$42$	−174.639	+	80.9033i	−0.641603	+	0.297230i
$43$	−161.190	−	279.189i	−0.571656	−	0.990138i	−0.996396	−	0.0848224i	$-0.972968\pi$
$43$	−161.190	−	279.189i	−0.571656	−	0.990138i	0.424740	−	0.905316i	$-0.360366\pi$
$44$		−	72.4833i		−	0.248347i
$45$	1.84448	−	53.1355i	0.00611020	−	0.176022i
$46$	−309.345			−0.991531
$47$	102.174	+	176.970i	0.317097	+	0.549227i	0.979881	−	0.199583i	$-0.0639587\pi$
$47$	102.174	+	176.970i	0.317097	+	0.549227i	−0.662784	+	0.748810i	$0.730625\pi$
$48$	57.7590	+	59.7988i	0.173683	+	0.179817i
$49$	269.182	+	212.579i	0.784788	+	0.619765i
$50$	−209.790	−	121.122i	−0.593376	−	0.342586i
$51$	−125.850	+	31.3919i	−0.345541	+	0.0861911i
$52$	30.1971	−	17.4343i	0.0805305	−	0.0464943i
$53$			512.902i			1.32929i	0.747158	+	0.664647i	$0.231418\pi$
$53$			512.902i			1.32929i	−0.747158	+	0.664647i	$0.768582\pi$
$54$	86.6246	−	266.886i	0.218298	−	0.672567i
$55$		−	35.6829i		−	0.0874816i
$56$	48.6022	−	139.964i	0.115977	−	0.333990i
$57$	−186.032	−	745.804i	−0.432291	−	1.73306i
$58$	−198.507	+	343.825i	−0.449402	+	0.778386i
$59$	296.313	−	513.229i	0.653842	−	1.13249i	−0.328341	−	0.944559i	$-0.606490\pi$
$59$	296.313	−	513.229i	0.653842	−	1.13249i	0.982183	−	0.187928i	$-0.0601771\pi$
$60$	28.4343	+	29.4385i	0.0611809	+	0.0633415i
$61$	294.171	−	169.839i	0.617454	−	0.356487i	−0.158423	−	0.987371i	$-0.550641\pi$
$61$	294.171	−	169.839i	0.617454	−	0.356487i	0.775877	+	0.630884i	$0.217308\pi$
$62$	43.7887			0.0896963
$63$	−494.077	+	77.0384i	−0.988061	+	0.154062i
$64$	−64.0000			−0.125000
$65$	14.8658	−	8.58277i	0.0283673	−	0.0163779i
$66$	51.8884	−	181.027i	0.0967731	−	0.337620i
$67$	−268.531	+	465.109i	−0.489646	+	0.848092i	−0.999929	−	0.0119149i	$-0.996207\pi$
$67$	−268.531	+	465.109i	−0.489646	+	0.848092i	0.510283	+	0.860006i	$0.329541\pi$
$68$	49.9241	−	86.4710i	0.0890321	−	0.154208i
$69$	−772.591	−	221.450i	−1.34796	−	0.386369i
$70$	23.9265	−	68.9030i	0.0408537	−	0.117650i
$71$			13.3482i			0.0223119i	0.999938	+	0.0111559i	$0.00355111\pi$
$71$			13.3482i			0.0223119i	−0.999938	+	0.0111559i	$0.996449\pi$
$72$	101.445	+	190.696i	0.166048	+	0.312135i
$73$		−	27.3334i		−	0.0438237i	−0.999760	−	0.0219119i	$-0.993025\pi$
$73$		−	27.3334i		−	0.0438237i	0.999760	−	0.0219119i	$-0.00697532\pi$
$74$	−8.00021	+	4.61892i	−0.0125676	+	0.00725593i
$75$	−437.244	−	452.686i	−0.673182	−	0.696955i
$76$	512.437	+	295.856i	0.773429	+	0.446539i
$77$	−329.602	+	63.1762i	−0.487814	+	0.0935013i
$78$	87.8981	−	21.9252i	0.127596	−	0.0318274i
$79$	230.790	+	399.741i	0.328683	+	0.569296i	0.982251	−	0.187572i	$-0.0600619\pi$
$79$	230.790	+	399.741i	0.328683	+	0.569296i	−0.653568	+	0.756868i	$0.726729\pi$
$80$	−31.5067			−0.0440319
$81$	407.400	−	604.538i	0.558848	−	0.829270i
$82$			838.488i			1.12921i
$83$	43.2259	+	74.8694i	0.0571646	+	0.0990119i	0.893192	−	0.449676i	$-0.148461\pi$
$83$	43.2259	+	74.8694i	0.0571646	+	0.0990119i	−0.836027	+	0.548688i	$0.815127\pi$
$84$	221.580	−	314.767i	0.287813	−	0.408856i
$85$	24.5772	−	42.5690i	0.0313620	−	0.0543206i
$86$	558.378	+	322.380i	0.700133	+	0.404222i
$87$	−741.906	+	716.599i	−0.914261	+	0.883075i
$88$	72.4833	+	125.545i	0.0878039	+	0.152081i
$89$	336.072			0.400265			0.200132	−	0.979769i	$-0.435863\pi$
$89$	336.072			0.400265			0.200132	+	0.979769i	$0.435863\pi$
$90$	49.9408	+	93.8779i	0.0584914	+	0.109951i
$91$	−105.599	−	122.119i	−0.121645	−	0.140677i
$92$	535.801	−	309.345i	0.607186	−	0.350559i
$93$	109.363	+	31.3469i	0.121939	+	0.0349519i
$94$	−353.940	−	204.347i	−0.388362	−	0.224221i
$95$	252.269	+	145.647i	0.272445	+	0.157296i
$96$	−159.840	−	45.8155i	−0.169934	−	0.0487086i
$97$	155.290	−	89.6566i	0.162549	−	0.0938479i	−0.416519	−	0.909127i	$-0.636750\pi$
$97$	155.290	−	89.6566i	0.162549	−	0.0938479i	0.579068	+	0.815279i	$0.303417\pi$
$98$	−678.816	−	99.0161i	−0.699702	−	0.102063i
$99$	259.183	−	414.972i	0.263120	−	0.421275i
$100$	484.490			0.484490
$101$	606.268	+	1050.09i	0.597286	+	1.03453i	0.993220	+	0.116251i	$0.0370876\pi$
$101$	606.268	+	1050.09i	0.597286	+	1.03453i	−0.395934	+	0.918279i	$0.629579\pi$
$102$	186.587	−	180.223i	0.181127	−	0.174948i
$103$	−693.685	−	400.499i	−0.663600	−	0.383130i	0.130047	−	0.991508i	$-0.458487\pi$
$103$	−693.685	−	400.499i	−0.663600	−	0.383130i	−0.793647	+	0.608378i	$0.791820\pi$
$104$	−34.8686	+	60.3942i	−0.0328764	+	0.0569437i
$105$	109.082	−	154.957i	0.101384	−	0.144022i
$106$	−512.902	−	888.373i	−0.469976	−	0.814023i
$107$			1799.59i			1.62591i	0.582325	+	0.812956i	$0.302143\pi$
$107$			1799.59i			1.62591i	−0.582325	+	0.812956i	$0.697857\pi$
$108$	116.848	+	548.885i	0.104108	+	0.489041i
$109$	1678.41			1.47488			0.737441	−	0.675412i	$-0.236034\pi$
$109$	1678.41			1.47488			0.737441	+	0.675412i	$0.236034\pi$
$110$	35.6829	+	61.8047i	0.0309294	+	0.0535713i
$111$	−23.2871	+	5.80870i	−0.0199127	+	0.00496700i
$112$	55.7822	+	291.026i	0.0470618	+	0.245530i
$113$	−1177.78	−	679.994i	−0.980502	−	0.566093i	−0.0780801	−	0.996947i	$-0.524879\pi$
$113$	−1177.78	−	679.994i	−0.980502	−	0.566093i	−0.902422	+	0.430854i	$0.858212\pi$
$114$	1068.02	+	1105.74i	0.877451	+	0.908438i
$115$	263.771	−	152.288i	0.213885	−	0.123486i
$116$		−	794.029i		−	0.635550i
$117$	235.222	+	8.16518i	0.185865	+	0.00645189i
$118$			1185.25i			0.924672i
$119$	−436.722	−	151.651i	−0.336422	−	0.116822i
$120$	−78.6881	−	22.5546i	−0.0598601	−	0.0171579i
$121$	−501.318	+	868.308i	−0.376648	+	0.652373i
$122$	−339.679	+	588.341i	−0.252074	+	0.436606i
$123$	−600.246	+	2094.13i	−0.440019	+	1.53513i
$124$	−75.8442	+	43.7887i	−0.0549275	+	0.0317124i
$125$	484.656			0.346792
$126$	778.728	−	627.511i	0.550592	−	0.443676i
$127$	1245.24			0.870060			0.435030	−	0.900416i	$-0.356738\pi$
$127$	1245.24			0.870060			0.435030	+	0.900416i	$0.356738\pi$
$128$	110.851	−	64.0000i	0.0765466	−	0.0441942i
$129$	1163.77	+	1204.87i	0.794297	+	0.822348i
$130$	−17.1655	+	29.7316i	−0.0115809	+	0.0200587i
$131$	−550.725	+	953.883i	−0.367306	+	0.636192i	−0.989143	−	0.146954i	$-0.953053\pi$
$131$	−550.725	+	953.883i	−0.367306	+	0.636192i	0.621838	+	0.783146i	$0.286386\pi$
$132$	91.1540	+	365.437i	0.0601056	+	0.240964i
$133$	898.702	−	2588.07i	0.585920	−	1.68732i
$134$		−	1074.12i		−	0.692464i
$135$	57.5233	+	270.212i	0.0366727	+	0.172268i
$136$			199.696i			0.125910i
$137$	−12.9539	+	7.47891i	−0.00807827	+	0.00466399i	−0.504034	−	0.863684i	$-0.668151\pi$
$137$	−12.9539	+	7.47891i	−0.00807827	+	0.00466399i	0.495955	+	0.868348i	$0.334818\pi$
$138$	1559.62	−	389.028i	0.962054	−	0.239973i
$139$	−1728.16	−	997.752i	−1.05454	−	0.608836i	−0.130620	−	0.991433i	$-0.541697\pi$
$139$	−1728.16	−	997.752i	−1.05454	−	0.608836i	−0.923916	+	0.382596i	$0.875030\pi$
$140$	27.4611	+	143.270i	0.0165778	+	0.0864894i
$141$	−737.680	−	763.732i	−0.440595	−	0.456155i
$142$	−13.3482	−	23.1198i	−0.00788843	−	0.0136632i
$143$	157.962			0.0923738
$144$	−366.404	−	228.849i	−0.212040	−	0.132436i
$145$		−	390.894i		−	0.223876i
$146$	27.3334	+	47.3428i	0.0154940	+	0.0268364i
$147$	−1624.47	−	733.236i	−0.911453	−	0.411403i
$148$	9.23785	−	16.0004i	0.00513072	−	0.00888667i
$149$	−257.727	−	148.799i	−0.141703	−	0.0818125i	0.427472	−	0.904028i	$-0.359404\pi$
$149$	−257.727	−	148.799i	−0.141703	−	0.0818125i	−0.569176	+	0.822216i	$0.692738\pi$
$150$	1210.02	+	346.830i	0.658649	+	0.188790i
$151$	−58.0594	−	100.562i	−0.0312901	−	0.0541961i	0.849956	−	0.526853i	$-0.176628\pi$
$151$	−58.0594	−	100.562i	−0.0312901	−	0.0541961i	−0.881246	+	0.472657i	$0.843295\pi$
$152$	−1183.42			−0.631502
$153$	595.019	−	316.536i	0.314408	−	0.167257i
$154$	507.712	−	439.027i	0.265666	−	0.229726i
$155$	−37.3375	+	21.5568i	−0.0193485	+	0.0111709i
$156$	−130.319	+	125.874i	−0.0668837	+	0.0646023i
$157$	−3142.53	−	1814.34i	−1.59746	−	0.922295i	−0.991974	−	0.126441i	$-0.959645\pi$
$157$	−3142.53	−	1814.34i	−1.59746	−	0.922295i	−0.605488	−	0.795854i	$-0.707022\pi$
$158$	−799.482	−	461.581i	−0.402553	−	0.232414i
$159$	−645.019	−	2585.89i	−0.321719	−	1.28977i
$160$	54.5712	−	31.5067i	0.0269639	−	0.0155676i
$161$	−1873.68	−	2166.82i	−0.917186	−	1.06068i
$162$	−101.101	+	1454.49i	−0.0490321	+	0.705405i
$163$	2243.34			1.07799			0.538994	−	0.842310i	$-0.318805\pi$
$163$	2243.34			1.07799			0.538994	+	0.842310i	$0.318805\pi$
$164$	−838.488	−	1452.30i	−0.399237	−	0.691499i
$165$	44.8744	+	179.902i	0.0211725	+	0.0848808i
$166$	−149.739	−	86.4518i	−0.0700120	−	0.0404214i
$167$	878.343	−	1521.34i	0.406995	−	0.704937i	−0.587556	−	0.809184i	$-0.699910\pi$
$167$	878.343	−	1521.34i	0.406995	−	0.704937i	0.994551	+	0.104247i	$0.0332431\pi$
$168$	−69.0199	+	766.773i	−0.0316964	+	0.352130i
$169$	−1060.51	−	1836.85i	−0.482706	−	0.836072i
$170$			98.3089i			0.0443526i
$171$	1875.83	+	3526.15i	0.838878	+	1.57691i
$172$	−1289.52			−0.571656
$173$	610.572	+	1057.54i	0.268329	+	0.464760i	0.968430	−	0.249284i	$-0.0801952\pi$
$173$	610.572	+	1057.54i	0.268329	+	0.464760i	−0.700101	+	0.714044i	$0.746862\pi$
$174$	568.420	−	1983.09i	0.247654	−	0.864011i
$175$	−422.280	−	2203.11i	−0.182408	−	0.951655i
$176$	−251.089	−	144.967i	−0.107537	−	0.0620867i
$177$	−848.483	+	2960.17i	−0.360316	+	1.25706i
$178$	−582.094	+	336.072i	−0.245111	+	0.141515i
$179$			1475.37i			0.616059i	0.951377	+	0.308030i	$0.0996696\pi$
$179$			1475.37i			0.616059i	−0.951377	+	0.308030i	$0.900330\pi$
$180$	−180.378	−	112.661i	−0.0746921	−	0.0466512i
$181$			3600.32i			1.47851i	0.673428	+	0.739253i	$0.264821\pi$
$181$			3600.32i			1.47851i	−0.673428	+	0.739253i	$0.735179\pi$
$182$	305.021	+	105.918i	0.124229	+	0.0431383i
$183$	−1269.52	+	1226.22i	−0.512819	+	0.495327i
$184$	−618.690	+	1071.60i	−0.247883	+	0.429346i
$185$	4.54772	−	7.87688i	0.00180732	−	0.00313038i
$186$	−220.768	+	55.0681i	−0.0870297	+	0.0217085i
$187$	391.731	−	226.166i	0.153188	−	0.0884434i
$188$	817.388			0.317097
$189$	2394.09	−	1009.75i	0.921400	−	0.388615i
$190$	−582.590			−0.222450
$191$	−1300.78	+	751.008i	−0.492782	+	0.284508i	−0.725728	−	0.687982i	$-0.758497\pi$
$191$	−1300.78	+	751.008i	−0.492782	+	0.284508i	0.232946	+	0.972490i	$0.425164\pi$
$192$	322.667	−	80.4856i	0.121284	−	0.0302528i
$193$	626.622	−	1085.34i	0.233706	−	0.404790i	−0.725190	−	0.688549i	$-0.758248\pi$
$193$	626.622	−	1085.34i	0.233706	−	0.404790i	0.958896	+	0.283759i	$0.0915814\pi$
$194$	−179.313	+	310.580i	−0.0663605	+	0.114940i
$195$	−64.1549	+	61.9666i	−0.0235602	+	0.0227565i
$196$	1274.76	−	507.316i	0.464563	−	0.184882i
$197$			1201.12i			0.434397i	0.976127	+	0.217198i	$0.0696919\pi$
$197$			1201.12i			0.434397i	−0.976127	+	0.217198i	$0.930308\pi$
$198$	−33.9468	+	977.935i	−0.0121843	+	0.351004i
$199$		−	4406.36i		−	1.56964i	−0.619724	−	0.784820i	$-0.712755\pi$
$199$		−	4406.36i		−	1.56964i	0.619724	−	0.784820i	$-0.287245\pi$
$200$	−839.160	+	484.490i	−0.296688	+	0.171293i
$201$	768.930	−	2682.63i	0.269832	−	0.941384i
$202$	−2100.17	−	1212.54i	−0.731523	−	0.422345i
$203$	−3610.68	+	692.074i	−1.24837	+	0.239281i
$204$	−142.956	+	498.742i	−0.0490634	+	0.171171i
$205$	−412.781	−	714.957i	−0.140633	−	0.243584i
$206$	1602.00			0.541827
$207$	4173.64	+	144.879i	1.40139	+	0.0486462i
$208$		−	139.475i		−	0.0464943i
$209$	1340.29	+	2321.45i	0.443587	+	0.768315i
$210$	−33.9779	+	377.476i	−0.0111652	+	0.124040i
$211$	−1158.30	+	2006.23i	−0.377918	+	0.654573i	−0.990759	−	0.135633i	$-0.956693\pi$
$211$	−1158.30	+	2006.23i	−0.377918	+	0.654573i	0.612841	+	0.790206i	$0.290027\pi$
$212$	1776.75	+	1025.80i	0.575601	+	0.332323i
$213$	−16.7865	−	67.2973i	−0.00539997	−	0.0216485i
$214$	−1799.59	−	3116.98i	−0.574847	−	0.995664i
$215$	−634.820			−0.201369
$216$	−751.271	−	833.849i	−0.236655	−	0.262668i
$217$	265.225	+	306.719i	0.0829708	+	0.0959515i
$218$	−2907.08	+	1678.41i	−0.903177	+	0.521449i
$219$	34.3741	+	137.806i	0.0106063	+	0.0425209i
$220$	−123.609	−	71.3659i	−0.0378806	−	0.0218704i
$221$	188.445	+	108.799i	0.0573584	+	0.0331159i
$222$	34.5258	−	33.3481i	0.0104379	−	0.0100819i
$223$	−3130.94	+	1807.65i	−0.940193	+	0.542821i	−0.890021	−	0.455920i	$-0.849310\pi$
$223$	−3130.94	+	1807.65i	−0.940193	+	0.542821i	−0.0501723	+	0.998741i	$0.515977\pi$
$224$	−387.644	−	448.290i	−0.115627	−	0.133717i
$225$	2773.74	+	1732.42i	0.821847	+	0.513310i
$226$	2719.98			0.800576
$227$	−891.930	−	1544.87i	−0.260791	−	0.451703i	0.705662	−	0.708549i	$-0.250650\pi$
$227$	−891.930	−	1544.87i	−0.260791	−	0.451703i	−0.966452	+	0.256846i	$0.917317\pi$
$228$	−2955.61	−	847.174i	−0.858508	−	0.246077i
$229$	4686.81	+	2705.93i	1.35246	+	0.780843i	0.988594	−	0.150608i	$-0.0481230\pi$
$229$	4686.81	+	2705.93i	1.35246	+	0.780843i	0.363867	+	0.931451i	$0.381456\pi$
$230$	−304.576	+	527.541i	−0.0873181	+	0.151239i
$231$	1582.30	−	733.017i	0.450682	−	0.208784i
$232$	794.029	+	1375.30i	0.224701	+	0.389193i
$233$		−	4183.60i		−	1.17629i	−0.808754	−	0.588147i	$-0.799858\pi$
$233$		−	4183.60i		−	1.17629i	0.808754	−	0.588147i	$-0.200142\pi$
$234$	−415.581	+	221.079i	−0.116100	+	0.0617623i
$235$	402.394			0.111699
$236$	−1185.25	−	2052.92i	−0.326921	−	0.566244i
$237$	−1666.28	−	1725.12i	−0.456694	−	0.472822i
$238$	908.076	−	174.055i	0.247319	−	0.0474046i
$239$	872.985	+	504.018i	0.236271	+	0.136411i	0.613461	−	0.789725i	$-0.289777\pi$
$239$	872.985	+	504.018i	0.236271	+	0.136411i	−0.377191	+	0.926136i	$0.623110\pi$
$240$	158.846	−	39.6224i	0.0427229	−	0.0106567i
$241$	3105.88	−	1793.18i	0.830154	−	0.479290i	−0.0237515	−	0.999718i	$-0.507561\pi$
$241$	3105.88	−	1793.18i	0.830154	−	0.479290i	0.853905	+	0.520428i	$0.174228\pi$
$242$		−	2005.27i		−	0.532660i
$243$	−1293.72	+	3560.22i	−0.341532	+	0.939870i
$244$		−	1358.72i		−	0.356487i
$245$	627.555	−	249.747i	0.163645	−	0.0651256i
$246$	−1054.47	−	4227.38i	−0.273295	−	1.09564i
$247$	−644.755	+	1116.75i	−0.166092	+	0.287680i
$248$	87.5774	−	151.688i	0.0224241	−	0.0388396i
$249$	−312.086	−	323.107i	−0.0794282	−	0.0822332i
$250$	−839.449	+	484.656i	−0.212366	+	0.122609i
$251$	7663.43			1.92714			0.963569	−	0.267461i	$-0.0861845\pi$
$251$	7663.43			1.92714			0.963569	+	0.267461i	$0.0861845\pi$
$252$	−721.285	+	1865.61i	−0.180304	+	0.466359i
$253$	2802.79			0.696483
$254$	−2156.83	+	1245.24i	−0.532801	+	0.307613i
$255$	−70.3761	+	245.527i	−0.0172828	+	0.0602960i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−1867.86	+	3235.22i	−0.453361	+	0.785244i	−0.998592	−	0.0530418i	$-0.983108\pi$
$257$	−1867.86	+	3235.22i	−0.453361	+	0.785244i	0.545232	+	0.838285i	$0.316442\pi$
$258$	−3220.58	−	923.125i	−0.777150	−	0.222757i
$259$	−80.8102	−	28.0612i	−0.0193873	−	0.00673220i
$260$		−	68.6622i		−	0.0163779i
$261$	2839.26	−	4545.87i	0.673356	−	1.07809i
$262$		−	2202.90i		−	0.519449i
$263$	3488.09	−	2013.85i	0.817813	−	0.472165i	−0.0318487	−	0.999493i	$-0.510139\pi$
$263$	3488.09	−	2013.85i	0.817813	−	0.472165i	0.849662	+	0.527328i	$0.176806\pi$
$264$	−523.320	−	541.802i	−0.122001	−	0.126309i
$265$	874.678	+	504.996i	0.202759	+	0.117063i
$266$	1031.47	+	5381.37i	0.237757	+	1.24042i
$267$	−1694.37	+	422.640i	−0.388365	+	0.0968731i
$268$	1074.12	+	1860.44i	0.244823	+	0.424046i
$269$	−6823.01			−1.54649			−0.773246	−	0.634106i	$-0.781368\pi$
$269$	−6823.01			−1.54649			−0.773246	+	0.634106i	$0.781368\pi$
$270$	−369.845	−	410.497i	−0.0833631	−	0.0925261i
$271$			4404.37i			0.987257i	0.869673	+	0.493628i	$0.164330\pi$
$271$			4404.37i			0.987257i	−0.869673	+	0.493628i	$0.835670\pi$
$272$	−199.696	−	345.884i	−0.0445160	−	0.0771040i
$273$	685.969	+	482.886i	0.152076	+	0.107053i
$274$	14.9578	−	25.9077i	0.00329794	−	0.00571220i
$275$	1900.78	+	1097.42i	0.416806	+	0.240643i
$276$	−2312.31	+	2233.43i	−0.504292	+	0.487090i
$277$	4217.11	+	7304.24i	0.914734	+	1.58437i	0.807290	+	0.590154i	$0.200933\pi$
$277$	4217.11	+	7304.24i	0.914734	+	1.58437i	0.107444	+	0.994211i	$0.465734\pi$
$278$	3991.01			0.861024
$279$	−590.792	−	20.5080i	−0.126773	−	0.00440065i
$280$	−190.834	−	220.690i	−0.0407304	−	0.0471026i
$281$	4170.29	−	2407.72i	0.885333	−	0.511147i	0.0129197	−	0.999917i	$-0.495887\pi$
$281$	4170.29	−	2407.72i	0.885333	−	0.511147i	0.872413	+	0.488769i	$0.162554\pi$
$282$	2041.43	+	585.142i	0.431083	+	0.123563i
$283$	−1435.19	−	828.610i	−0.301461	−	0.174049i	0.341638	−	0.939832i	$-0.389018\pi$
$283$	−1435.19	−	828.610i	−0.301461	−	0.174049i	−0.643099	+	0.765783i	$0.722352\pi$
$284$	46.2396	+	26.6964i	0.00966131	+	0.00557796i
$285$	−1455.02	−	417.057i	−0.302414	−	0.0866819i
$286$	−273.598	+	157.962i	−0.0565671	+	0.0326591i
$287$	−5873.21	+	5078.67i	−1.20796	+	1.04454i
$288$	863.480	+	29.9738i	0.176670	+	0.00613271i
$289$	−4289.90			−0.873173
$290$	390.894	+	677.049i	0.0791521	+	0.137095i
$291$	−670.169	+	647.310i	−0.135004	+	0.130398i
$292$	−94.6857	−	54.6668i	−0.0189762	−	0.0109559i
$293$	2867.98	−	4967.49i	0.571840	−	0.990456i	−0.424537	−	0.905411i	$-0.639563\pi$
$293$	2867.98	−	4967.49i	0.571840	−	0.990456i	0.996377	−	0.0850455i	$-0.0271036\pi$
$294$	3546.89	−	354.464i	0.703602	−	0.0703155i
$295$	−583.490	−	1010.63i	−0.115160	−	0.199462i
$296$			36.9514i			0.00725593i
$297$	−784.854	+	2418.10i	−0.153340	+	0.472432i
$298$	595.194			0.115700
$299$	674.152	+	1167.67i	0.130392	+	0.225846i
$300$	−2442.64	+	609.288i	−0.470086	+	0.117257i
$301$	1123.94	+	5863.81i	0.215226	+	1.12287i
$302$	201.124	+	116.119i	0.0383224	+	0.0221255i
$303$	−4377.18	−	4531.76i	−0.829909	−	0.859217i
$304$	2049.75	−	1183.42i	0.386714	−	0.223270i
$305$		−	668.885i		−	0.125575i
$306$	−714.067	+	1143.27i	−0.133400	+	0.213584i
$307$			9555.19i			1.77636i	0.459493	+	0.888182i	$0.348031\pi$
$307$			9555.19i			1.77636i	−0.459493	+	0.888182i	$0.651969\pi$
$308$	−440.356	+	1268.13i	−0.0814662	+	0.234605i
$309$	4001.00	+	1146.82i	0.736598	+	0.211133i
$310$	43.1137	−	74.6750i	0.00789900	−	0.0136815i
$311$	1767.04	−	3060.60i	0.322186	−	0.558042i	−0.658753	−	0.752359i	$-0.728916\pi$
$311$	1767.04	−	3060.60i	0.322186	−	0.558042i	0.980939	+	0.194317i	$0.0622492\pi$
$312$	99.8453	−	348.338i	0.0181174	−	0.0632076i
$313$	4423.27	−	2553.78i	0.798780	−	0.461176i	−0.0442642	−	0.999020i	$-0.514094\pi$
$313$	4423.27	−	2553.78i	0.798780	−	0.461176i	0.843044	+	0.537844i	$0.180761\pi$
$314$	7257.37			1.30432
$315$	−355.083	+	918.425i	−0.0635132	+	0.164277i
$316$	1846.32			0.328683
$317$	−3566.42	+	2059.07i	−0.631893	+	0.364824i	−0.781485	−	0.623924i	$-0.785537\pi$
$317$	−3566.42	+	2059.07i	−0.631893	+	0.364824i	0.149592	+	0.988748i	$0.452204\pi$
$318$	3703.09	+	3833.87i	0.653016	+	0.676077i
$319$	1798.56	−	3115.19i	0.315674	−	0.546763i
$320$	−63.0134	+	109.142i	−0.0110080	+	0.0190664i
$321$	−2263.14	−	9072.93i	−0.393508	−	1.57758i
$322$	5412.13	+	1879.36i	0.936666	+	0.325256i
$323$			3692.58i			0.636101i
$324$	−1279.38	−	2620.35i	−0.219372	−	0.449306i
$325$			1055.84i			0.180208i
$326$	−3885.58	+	2243.34i	−0.660130	+	0.381126i
$327$	−8461.97	+	2110.74i	−1.43103	+	0.356955i
$328$	2904.61	+	1676.98i	0.488964	+	0.282303i
$329$	−712.433	−	3716.90i	−0.119385	−	0.622855i
$330$	−257.626	−	266.725i	−0.0429754	−	0.0444930i
$331$	−5717.72	−	9903.38i	−0.949469	−	1.64453i	−0.746547	−	0.665333i	$-0.768290\pi$
$331$	−5717.72	−	9903.38i	−0.949469	−	1.64453i	−0.202922	−	0.979195i	$-0.565044\pi$
$332$	345.807			0.0571646
$333$	110.101	−	58.5711i	0.0181186	−	0.00963867i
$334$			3513.37i			0.575579i
$335$	528.783	+	915.878i	0.0862402	+	0.149372i
$336$	−647.227	−	1397.11i	−0.105087	−	0.226841i
$337$	−3423.86	+	5930.30i	−0.553441	+	0.958588i	0.444582	+	0.895738i	$0.353352\pi$
$337$	−3423.86	+	5930.30i	−0.553441	+	0.958588i	−0.998023	+	0.0628495i	$0.979981\pi$
$338$	3673.70	+	2121.01i	0.591192	+	0.341325i
$339$	6793.16	+	1947.14i	1.08836	+	0.311960i
$340$	−98.3089	−	170.276i	−0.0156810	−	0.0271603i
$341$	−396.744			−0.0630055
$342$	−6775.18	−	4231.64i	−1.07123	−	0.669068i
$343$	−3417.99	−	5354.53i	−0.538058	−	0.842908i
$344$	2233.51	−	1289.52i	0.350067	−	0.202111i
$345$	−1138.33	+	1099.50i	−0.177640	+	0.171580i
$346$	−2115.08	−	1221.14i	−0.328635	−	0.189737i
$347$	4578.87	+	2643.61i	0.708377	+	0.408981i	0.810460	−	0.585794i	$-0.199217\pi$
$347$	4578.87	+	2643.61i	0.708377	+	0.408981i	−0.102083	+	0.994776i	$0.532551\pi$
$348$	998.561	+	4003.24i	0.153817	+	0.616655i
$349$	−10441.7	+	6028.54i	−1.60153	+	0.924642i	−0.610345	+	0.792135i	$0.708969\pi$
$349$	−10441.7	+	6028.54i	−1.60153	+	0.924642i	−0.991182	+	0.132507i	$0.957697\pi$
$350$	2934.52	+	3393.62i	0.448162	+	0.518277i
$351$	−1196.18	+	254.645i	−0.181901	+	0.0387235i
$352$	579.866			0.0878039
$353$	−5253.60	−	9099.51i	−0.792128	−	1.37201i	−0.924647	−	0.380825i	$-0.875640\pi$
$353$	−5253.60	−	9099.51i	−0.792128	−	1.37201i	0.132519	−	0.991180i	$-0.457693\pi$
$354$	−1490.56	−	5975.65i	−0.223792	−	0.897182i
$355$	22.7634	+	13.1424i	0.00340325	+	0.00196487i
$356$	672.144	−	1164.19i	0.100066	−	0.173320i
$357$	2392.53	+	215.359i	0.354694	+	0.0319273i
$358$	−1475.37	−	2555.42i	−0.217810	−	0.377258i
$359$		−	8583.04i		−	1.26183i	−0.775853	−	0.630913i	$-0.782680\pi$
$359$		−	8583.04i		−	1.26183i	0.775853	−	0.630913i	$-0.217320\pi$
$360$	425.084	+	14.7558i	0.0622331	+	0.00216028i
$361$	−15023.7			−2.19036
$362$	−3600.32	−	6235.94i	−0.522731	−	0.905397i
$363$	1435.51	−	5008.18i	0.207561	−	0.724135i
$364$	−634.231	+	121.566i	−0.0913261	+	0.0175049i
$365$	−46.6130	−	26.9120i	−0.00668448	−	0.00385929i
$366$	972.660	−	3393.40i	0.138912	−	0.484633i
$367$	3402.11	−	1964.21i	0.483893	−	0.279375i	−0.238145	−	0.971230i	$-0.576539\pi$
$367$	3402.11	−	1964.21i	0.483893	−	0.279375i	0.722037	+	0.691854i	$0.243206\pi$
$368$		−	2474.76i		−	0.350559i
$369$	392.697	−	11312.8i	0.0554011	−	1.59599i
$370$			18.1909i			0.00255594i
$371$	3116.02	−	8973.46i	0.436053	−	1.25574i
$372$	327.314	−	316.149i	0.0456194	−	0.0440633i
$373$	−1545.01	+	2676.04i	−0.214471	+	0.371475i	−0.953109	−	0.302628i	$-0.902136\pi$
$373$	−1545.01	+	2676.04i	−0.214471	+	0.371475i	0.738638	+	0.674103i	$0.235469\pi$
$374$	−452.332	+	783.463i	−0.0625389	+	0.108321i
$375$	−2443.48	+	609.497i	−0.336482	+	0.0839315i
$376$	−1415.76	+	817.388i	−0.194181	+	0.112111i
$377$	1730.42			0.236396
$378$	−3136.94	+	4143.03i	−0.426844	+	0.563741i
$379$	−4368.78			−0.592108			−0.296054	−	0.955171i	$-0.595671\pi$
$379$	−4368.78			−0.592108			−0.296054	+	0.955171i	$0.595671\pi$
$380$	1009.08	−	582.590i	0.136222	−	0.0786480i
$381$	−6278.12	+	1566.00i	−0.844194	+	0.210574i
$382$	1502.02	−	2601.57i	0.201177	−	0.348450i
$383$	7161.95	−	12404.9i	0.955506	−	1.65498i	0.222300	−	0.974978i	$-0.428644\pi$
$383$	7161.95	−	12404.9i	0.955506	−	1.65498i	0.733206	−	0.680006i	$-0.238023\pi$
$384$	−478.390	+	462.072i	−0.0635749	+	0.0614063i
$385$	−216.784	+	624.289i	−0.0286969	+	0.0826409i
$386$			2506.49i			0.330510i
$387$	−7382.58	−	4611.02i	−0.969710	−	0.605662i
$388$		−	717.253i		−	0.0938479i
$389$	257.509	−	148.673i	0.0335635	−	0.0193779i	−0.483124	−	0.875552i	$-0.660498\pi$
$389$	257.509	−	148.673i	0.0335635	−	0.0193779i	0.516688	+	0.856174i	$0.327165\pi$
$390$	49.1530	−	171.484i	0.00638195	−	0.0222652i
$391$	3343.67	+	1930.47i	0.432473	+	0.249688i
$392$	−1700.63	+	2153.46i	−0.219120	+	0.277464i
$393$	1576.98	−	5501.75i	0.202413	−	0.706175i
$394$	−1201.12	−	2080.40i	−0.153583	−	0.266013i
$395$	908.930			0.115780
$396$	−919.138	−	1727.78i	−0.116637	−	0.219253i
$397$			675.351i			0.0853776i	0.999088	+	0.0426888i	$0.0135924\pi$
$397$			675.351i			0.0853776i	−0.999088	+	0.0426888i	$0.986408\pi$
$398$	4406.36	+	7632.03i	0.554952	+	0.961204i
$399$	−1276.25	+	14178.4i	−0.160131	+	1.77897i
$400$	968.979	−	1678.32i	0.121122	−	0.209790i
$401$	−7541.75	−	4354.23i	−0.939195	−	0.542244i	−0.0494869	−	0.998775i	$-0.515759\pi$
$401$	−7541.75	−	4354.23i	−0.939195	−	0.542244i	−0.889708	+	0.456530i	$0.849092\pi$
$402$	1350.80	+	5415.38i	0.167592	+	0.671877i
$403$	−95.4282	−	165.287i	−0.0117956	−	0.0204305i
$404$	4850.14			0.597286
$405$	−629.828	−	1289.98i	−0.0772751	−	0.158270i
$406$	5561.81	−	4809.39i	0.679871	−	0.587896i
$407$	72.4852	−	41.8493i	0.00882791	−	0.00509679i
$408$	−251.135	−	1006.80i	−0.0304732	−	0.122167i
$409$	7412.07	+	4279.36i	0.896096	+	0.517361i	0.875931	−	0.482435i	$-0.160248\pi$
$409$	7412.07	+	4279.36i	0.896096	+	0.517361i	0.0201644	+	0.999797i	$0.493581\pi$
$410$	1429.91	+	825.561i	0.172240	+	0.0994429i
$411$	55.9037	−	53.9968i	0.00670931	−	0.00648046i
$412$	−2774.74	+	1602.00i	−0.331800	+	0.191565i
$413$	−8302.14	+	7179.00i	−0.989156	+	0.855340i
$414$	−7373.84	+	3922.71i	−0.875374	+	0.465678i
$415$	170.238			0.0201365
$416$	139.475	+	241.577i	0.0164382	+	0.0284718i
$417$	9967.57	+	2857.03i	1.17054	+	0.335514i
$418$	−4642.89	−	2680.58i	−0.543281	−	0.313663i
$419$	6335.64	−	10973.7i	0.738703	−	1.27947i	−0.214377	−	0.976751i	$-0.568772\pi$
$419$	6335.64	−	10973.7i	0.738703	−	1.27947i	0.953080	−	0.302719i	$-0.0978945\pi$
$420$	−318.625	−	687.786i	−0.0370173	−	0.0799060i
$421$	4993.22	+	8648.51i	0.578040	+	1.00119i	0.995704	+	0.0925928i	$0.0295155\pi$
$421$	4993.22	+	8648.51i	0.578040	+	1.00119i	−0.417664	+	0.908601i	$0.637151\pi$
$422$		−	4633.20i		−	0.534457i
$423$	4679.60	+	2922.79i	0.537896	+	0.335959i
$424$	−4103.22			−0.469976
$425$	1511.73	+	2618.39i	0.172540	+	0.298849i
$426$	96.3725	+	99.7759i	0.0109607	+	0.0113478i
$427$	−6178.47	+	1184.25i	−0.700227	+	0.134215i
$428$	6233.95	+	3599.17i	0.704041	+	0.406478i
$429$	−796.393	+	198.651i	−0.0896275	+	0.0223565i
$430$	1099.54	−	634.820i	0.123313	−	0.0711947i
$431$			6741.34i			0.753408i	0.926334	+	0.376704i	$0.122943\pi$
$431$			6741.34i			0.753408i	−0.926334	+	0.376704i	$0.877057\pi$
$432$	2135.09	+	692.997i	0.237788	+	0.0771801i
$433$			8737.16i			0.969702i	0.874597	+	0.484851i	$0.161126\pi$
$433$			8737.16i			0.969702i	−0.874597	+	0.484851i	$0.838874\pi$
$434$	−766.103	−	266.028i	−0.0847330	−	0.0294234i
$435$	491.583	+	1970.76i	0.0541830	+	0.217220i
$436$	3356.81	−	5814.17i	0.368720	−	0.638642i
$437$	−11440.2	+	19815.0i	−1.25231	+	2.16906i
$438$	−197.344	−	204.313i	−0.0215284	−	0.0222887i
$439$	−2056.05	+	1187.06i	−0.223531	+	0.129056i	−0.607584	−	0.794255i	$-0.707861\pi$
$439$	−2056.05	+	1187.06i	−0.223531	+	0.129056i	0.384053	+	0.923311i	$0.374528\pi$
$440$	285.464			0.0309294
$441$	9112.13	+	1653.83i	0.983925	+	0.178580i
$442$	−435.196			−0.0468329
$443$	11142.2	−	6432.93i	1.19499	−	0.689927i	0.235555	−	0.971861i	$-0.424309\pi$
$443$	11142.2	−	6432.93i	1.19499	−	0.689927i	0.959434	+	0.281934i	$0.0909760\pi$
$444$	−26.4523	+	92.2863i	−0.00282741	+	0.00986422i
$445$	330.891	−	573.120i	0.0352489	−	0.0610528i
$446$	3615.30	−	6261.88i	0.383832	−	0.664817i
$447$	1486.50	+	426.080i	0.157291	+	0.0450848i
$448$	1119.71	+	388.817i	0.118083	+	0.0410042i
$449$		−	822.758i		−	0.0864774i	−0.999065	−	0.0432387i	$-0.986232\pi$
$449$		−	822.758i		−	0.0864774i	0.999065	−	0.0432387i	$-0.0137676\pi$
$450$	−6536.67	−	226.906i	−0.684759	−	0.0237699i
$451$		−	7597.04i		−	0.793194i
$452$	−4711.14	+	2719.98i	−0.490251	+	0.283046i
$453$	419.182	+	433.985i	0.0434766	+	0.0450119i
$454$	3089.74	+	1783.86i	0.319402	+	0.184407i
$455$	−312.227	+	59.8458i	−0.0321701	+	0.00616618i
$456$	5966.44	−	1488.26i	0.612728	−	0.152838i
$457$	−1216.48	−	2107.00i	−0.124517	−	0.215670i	0.797027	−	0.603944i	$-0.206405\pi$
$457$	−1216.48	−	2107.00i	−0.124517	−	0.215670i	−0.921544	+	0.388274i	$0.873072\pi$
$458$	−10823.7			−1.10428
$459$	−2601.82	+	2344.16i	−0.264581	+	0.238379i
$460$		−	1218.30i		−	0.123486i
$461$	169.025	+	292.760i	0.0170765	+	0.0295774i	0.874437	−	0.485138i	$-0.161231\pi$
$461$	169.025	+	292.760i	0.0170765	+	0.0295774i	−0.857361	+	0.514716i	$0.827897\pi$
$462$	−2007.60	+	2851.92i	−0.202169	+	0.287193i
$463$	7965.68	−	13797.0i	0.799561	−	1.38488i	−0.120342	−	0.992733i	$-0.538399\pi$
$463$	7965.68	−	13797.0i	0.799561	−	1.38488i	0.919902	−	0.392147i	$-0.128268\pi$
$464$	−2750.60	−	1588.06i	−0.275201	−	0.158887i
$465$	161.134	−	155.638i	0.0160697	−	0.0155216i
$466$	4183.60	+	7246.20i	0.415883	+	0.720330i
$467$	−6162.59			−0.610644			−0.305322	−	0.952249i	$-0.598764\pi$
$467$	−6162.59			−0.610644			−0.305322	+	0.952249i	$0.598764\pi$
$468$	498.728	−	798.501i	0.0492601	−	0.0788691i
$469$	7523.74	−	6505.90i	0.740755	−	0.640543i
$470$	−696.966	+	402.394i	−0.0684014	+	0.0394916i
$471$	18125.3	+	5195.32i	1.77319	+	0.508254i
$472$	4105.83	+	2370.50i	0.400395	+	0.231168i
$473$	−5059.13	−	2920.89i	−0.491795	−	0.283938i
$474$	4611.20	+	1321.72i	0.446835	+	0.128078i
$475$	−15516.9	+	8958.69i	−1.49887	+	0.865375i
$476$	−1398.78	+	1209.55i	−0.134691	+	0.116470i
$477$	6503.95	+	12226.0i	0.624309	+	1.17357i
$478$	−2016.07			−0.192914
$479$	8890.46	+	15398.7i	0.848049	+	1.46886i	0.882947	+	0.469474i	$0.155556\pi$
$479$	8890.46	+	15398.7i	0.848049	+	1.46886i	−0.0348972	+	0.999391i	$0.511110\pi$
$480$	−235.508	+	227.474i	−0.0223946	+	0.0216307i
$481$	34.8695	+	20.1319i	0.00330544	+	0.00190839i
$482$	−3586.36	+	6211.75i	−0.338909	+	0.587007i
$483$	12171.5	+	8568.07i	1.14663	+	0.807165i
$484$	2005.27	+	3473.23i	0.188324	+	0.326186i
$485$		−	353.098i		−	0.0330584i
$486$	−1319.43	−	7460.21i	−0.123150	−	0.696300i
$487$	10429.6			0.970448			0.485224	−	0.874390i	$-0.338738\pi$
$487$	10429.6			0.970448			0.485224	+	0.874390i	$0.338738\pi$
$488$	1358.72	+	2353.36i	0.126037	+	0.218303i
$489$	−11310.2	+	2821.19i	−1.04594	+	0.260897i
$490$	−837.209	+	1060.13i	−0.0771862	+	0.0977383i
$491$	−5162.99	−	2980.86i	−0.474547	−	0.273980i	0.243594	−	0.969877i	$-0.421674\pi$
$491$	−5162.99	−	2980.86i	−0.474547	−	0.273980i	−0.718141	+	0.695897i	$0.755007\pi$
$492$	6053.78	+	6267.57i	0.554726	+	0.574317i
$493$	4291.28	−	2477.57i	0.392028	−	0.226337i
$494$		−	2579.02i		−	0.234890i
$495$	−452.484	−	850.572i	−0.0410862	−	0.0772331i
$496$			350.310i			0.0317124i
$497$	81.0940	−	233.533i	0.00731904	−	0.0210772i
$498$	863.655	+	247.552i	0.0777135	+	0.0222752i
$499$	8307.03	−	14388.2i	0.745238	−	1.29079i	−0.204845	−	0.978794i	$-0.565669\pi$
$499$	8307.03	−	14388.2i	0.745238	−	1.29079i	0.950083	−	0.311996i	$-0.100997\pi$
$500$	969.313	−	1678.90i	0.0866980	−	0.150165i
$501$	−2515.11	+	8774.67i	−0.224285	+	0.782482i
$502$	−13273.5	+	7663.43i	−1.18013	+	0.681346i
$503$	6252.37			0.554234			0.277117	−	0.960836i	$-0.410621\pi$
$503$	6252.37			0.554234			0.277117	+	0.960836i	$0.410621\pi$
$504$	−616.308	−	3952.62i	−0.0544693	−	0.349332i
$505$	2387.69			0.210397
$506$	−4854.58	+	2802.79i	−0.426507	+	0.246244i
$507$	7656.72	+	7927.12i	0.670704	+	0.694390i
$508$	2490.49	−	4313.65i	0.217515	−	0.376747i
$509$	−9537.56	+	16519.5i	−0.830540	+	1.43854i	0.0670704	+	0.997748i	$0.478635\pi$
$509$	−9537.56	+	16519.5i	−0.830540	+	1.43854i	−0.897611	+	0.440789i	$0.854699\pi$
$510$	−123.632	−	495.641i	−0.0107343	−	0.0430340i
$511$	−166.058	+	478.210i	−0.0143757	+	0.0413988i
$512$		−	512.000i		−	0.0441942i
$513$	−13891.8	−	15418.7i	−1.19559	−	1.32700i
$514$		−	7471.43i		−	0.641149i
$515$	−1365.98	+	788.651i	−0.116878	+	0.0674798i
$516$	6501.33	−	1621.68i	0.554661	−	0.138354i
$517$	3206.84	+	1851.47i	0.272798	+	0.157500i
$518$	168.029	−	32.2067i	0.0142524	−	0.00273182i
$519$	−4408.26	−	4563.94i	−0.372834	−	0.386001i
$520$	68.6622	+	118.926i	0.00579045	+	0.0100294i
$521$	−18924.2			−1.59133			−0.795666	−	0.605735i	$-0.792879\pi$
$521$	−18924.2			−1.59133			−0.795666	+	0.605735i	$0.792879\pi$
$522$	−371.876	+	10712.9i	−0.0311811	+	0.898262i
$523$		−	19729.9i		−	1.64958i	−0.565442	−	0.824788i	$-0.691294\pi$
$523$		−	19729.9i		−	1.64958i	0.565442	−	0.824788i	$-0.308706\pi$
$524$	2202.90	+	3815.53i	0.183653	+	0.318096i
$525$	4899.60	+	10576.3i	0.407307	+	0.879216i
$526$	−4027.70	+	6976.18i	−0.333871	+	0.578281i
$527$	−473.307	−	273.264i	−0.0391225	−	0.0225874i
$528$	1448.22	+	415.107i	0.119367	+	0.0342144i
$529$	5878.30	+	10181.5i	0.483135	+	0.836814i
$530$	−2019.98			−0.165552
$531$	555.101	−	15991.3i	0.0453659	−	1.30690i
$532$	−7167.92	−	8289.33i	−0.584152	−	0.675541i
$533$	3164.99	−	1827.31i	0.257206	−	0.148498i
$534$	2512.09	−	2426.40i	0.203574	−	0.196630i
$535$	3068.92	+	1771.84i	0.248002	+	0.143184i
$536$	−3720.87	−	2148.25i	−0.299846	−	0.173116i
$537$	−1855.41	−	7438.35i	−0.149100	−	0.597744i
$538$	11817.8	−	6823.01i	0.947029	−	0.546768i
$539$	6150.36	+	897.126i	0.491493	+	0.0716920i
$540$	1051.09	+	341.157i	0.0837622	+	0.0271871i
$541$	−2013.90			−0.160045			−0.0800225	−	0.996793i	$-0.525499\pi$
$541$	−2013.90			−0.160045			−0.0800225	+	0.996793i	$0.525499\pi$
$542$	−4404.37	−	7628.60i	−0.349048	−	0.604569i
$543$	−4527.72	−	18151.6i	−0.357832	−	1.43455i
$544$	691.768	+	399.392i	0.0545208	+	0.0314776i
$545$	1652.53	−	2862.27i	0.129884	−	0.224965i
$546$	−1671.02	−	150.414i	−0.130976	−	0.0117896i
$547$	4584.82	+	7941.14i	0.358378	+	0.620729i	0.987690	−	0.156424i	$-0.0499965\pi$
$547$	4584.82	+	7941.14i	0.358378	+	0.620729i	−0.629312	+	0.777153i	$0.716663\pi$
$548$			59.8313i			0.00466399i
$549$	4858.45	−	7778.74i	0.377693	−	0.604715i
$550$	−4389.67			−0.340321
$551$	14682.4	+	25430.6i	1.13519	+	1.96621i
$552$	1771.60	−	6180.73i	0.136602	−	0.476575i
$553$	−1609.25	−	8395.76i	−0.123747	−	0.645613i
$554$	−14608.5	−	8434.21i	−1.12032	−	0.646815i
$555$	−13.0223	+	45.4318i	−0.000995971	+	0.00347473i
$556$	−6912.63	+	3991.01i	−0.527268	+	0.304418i
$557$		−	14357.6i		−	1.09219i	−0.837723	−	0.546096i	$-0.816113\pi$
$557$		−	14357.6i		−	1.09219i	0.837723	−	0.546096i	$-0.183887\pi$
$558$	1043.79	−	555.271i	0.0791884	−	0.0421263i
$559$		−	2810.23i		−	0.212630i
$560$	551.224	+	191.412i	0.0415955	+	0.0144440i
$561$	−1690.56	+	1632.89i	−0.127229	+	0.122889i
$562$	−4815.43	+	8340.57i	−0.361436	+	0.626025i
$563$	890.061	−	1541.63i	0.0666280	−	0.115403i	−0.830787	−	0.556591i	$-0.812109\pi$
$563$	890.061	−	1541.63i	0.0666280	−	0.115403i	0.897415	+	0.441187i	$0.145443\pi$
$564$	−4121.01	+	1027.94i	−0.307670	+	0.0767446i
$565$	−2319.26	+	1339.02i	−0.172694	+	0.0997047i
$566$	3314.44			0.246142
$567$	−10800.4	+	8101.60i	−0.799954	+	0.600062i
$568$	−106.786			−0.00788843
$569$	−18073.4	+	10434.7i	−1.33159	+	0.768795i	−0.985544	−	0.169421i	$-0.945810\pi$
$569$	−18073.4	+	10434.7i	−1.33159	+	0.768795i	−0.346049	+	0.938217i	$0.612477\pi$
$570$	2937.23	−	732.657i	0.215837	−	0.0538380i
$571$	10552.7	−	18277.8i	0.773408	−	1.33958i	−0.162276	−	0.986745i	$-0.551884\pi$
$571$	10552.7	−	18277.8i	0.773408	−	1.33958i	0.935685	−	0.352837i	$-0.114783\pi$
$572$	315.924	−	547.197i	0.0230934	−	0.0399990i
$573$	5613.67	−	5422.18i	0.409275	−	0.395314i
$574$	5094.04	−	14669.7i	0.370420	−	1.06673i
$575$			18734.3i			1.35874i
$576$	−1525.56	+	811.564i	−0.110356	+	0.0587069i
$577$		−	16172.0i		−	1.16681i	−0.812182	−	0.583405i	$-0.801720\pi$
$577$		−	16172.0i		−	1.16681i	0.812182	−	0.583405i	$-0.198280\pi$
$578$	7430.32	−	4289.90i	0.534707	−	0.308713i
$579$	−1794.31	+	6259.96i	−0.128789	+	0.449318i
$580$	−1354.10	−	781.789i	−0.0969411	−	0.0559690i
$581$	−301.405	−	1572.48i	−0.0215222	−	0.112285i
$582$	513.458	−	1791.34i	0.0365696	−	0.127583i
$583$	4647.11	+	8049.02i	0.330126	+	0.571795i
$584$	218.667			0.0154940
$585$	245.520	−	393.096i	0.0173521	−	0.0277821i
$586$			11471.9i			0.808704i
$587$	−1962.50	−	3399.15i	−0.137991	−	0.239008i	0.788745	−	0.614721i	$-0.210731\pi$
$587$	−1962.50	−	3399.15i	−0.137991	−	0.239008i	−0.926736	+	0.375713i	$0.877398\pi$
$588$	−5788.93	+	4160.84i	−0.406006	+	0.291820i
$589$	1619.39	−	2804.87i	0.113287	−	0.196218i
$590$	2021.27	+	1166.98i	0.141041	+	0.0814302i
$591$	−1510.51	−	6055.65i	−0.105134	−	0.421483i
$592$	−36.9514	−	64.0017i	−0.00256536	−	0.00444333i
$593$	26768.3			1.85370			0.926848	−	0.375437i	$-0.122507\pi$
$593$	26768.3			1.85370			0.926848	+	0.375437i	$0.122507\pi$
$594$	−1058.69	−	4973.12i	−0.0731289	−	0.343518i
$595$	−688.608	+	595.451i	−0.0474457	+	0.0410271i
$596$	−1030.91	+	595.194i	−0.0708517	+	0.0409062i
$597$	5541.38	+	22215.4i	0.379889	+	1.52298i
$598$	−2335.33	−	1348.30i	−0.159697	−	0.0922011i
$599$	−14677.6	−	8474.10i	−1.00118	−	0.578034i	−0.0925854	−	0.995705i	$-0.529513\pi$
$599$	−14677.6	−	8474.10i	−1.00118	−	0.578034i	−0.908598	+	0.417671i	$0.862846\pi$
$600$	3621.49	−	3497.96i	0.246411	−	0.238006i
$601$	197.348	−	113.939i	0.0133943	−	0.00773322i	−0.493288	−	0.869866i	$-0.664205\pi$
$601$	197.348	−	113.939i	0.0133943	−	0.00773322i	0.506682	+	0.862133i	$0.330872\pi$
$602$	−7810.54	−	9032.48i	−0.528794	−	0.611522i
$603$	−503.055	+	14491.9i	−0.0339734	+	0.978702i
$604$	−464.475			−0.0312901
$605$	987.179	+	1709.84i	0.0663381	+	0.114901i
$606$	12113.3	+	3472.06i	0.811992	+	0.232744i
$607$	−2006.54	−	1158.48i	−0.134173	−	0.0774649i	0.431411	−	0.902156i	$-0.358016\pi$
$607$	−2006.54	−	1158.48i	−0.134173	−	0.0774649i	−0.565584	+	0.824691i	$0.691349\pi$
$608$	−2366.85	+	4099.50i	−0.157876	+	0.273448i
$609$	17333.5	−	8029.95i	1.15335	−	0.534302i
$610$	668.885	+	1158.54i	0.0443973	+	0.0768984i
$611$			1781.33i			0.117946i
$612$	93.5257	−	2694.28i	0.00617737	−	0.177957i
$613$	−15640.2			−1.03051			−0.515256	−	0.857037i	$-0.672303\pi$
$613$	−15640.2			−1.03051			−0.515256	+	0.857037i	$0.672303\pi$
$614$	−9555.19	−	16550.1i	−0.628039	−	1.08780i
$615$	2980.23	+	3085.47i	0.195405	+	0.202306i
$616$	−505.410	−	2636.82i	−0.0330577	−	0.172468i
$617$	−4787.02	−	2763.79i	−0.312347	−	0.180334i	0.335629	−	0.941994i	$-0.391051\pi$
$617$	−4787.02	−	2763.79i	−0.312347	−	0.180334i	−0.647976	+	0.761660i	$0.724384\pi$
$618$	−8076.75	+	2014.65i	−0.525719	+	0.131135i
$619$	13492.6	−	7789.93i	0.876109	−	0.505822i	0.00673576	−	0.999977i	$-0.497856\pi$
$619$	13492.6	−	7789.93i	0.876109	−	0.505822i	0.869374	+	0.494155i	$0.164523\pi$
$620$			172.455i			0.0111709i
$621$	−21224.4	+	4518.29i	−1.37150	+	0.291969i
$622$			7068.16i			0.455639i
$623$	−5879.73	−	2041.73i	−0.378116	−	0.131300i
$624$	175.401	+	703.185i	0.0112527	+	0.0451121i
$625$	−7092.96	+	12285.4i	−0.453950	+	0.786264i
$626$	−5107.56	+	8846.55i	−0.326101	+	0.564823i
$627$	−9676.71	−	10018.4i	−0.616349	−	0.638115i
$628$	−12570.1	+	7257.37i	−0.798731	+	0.461148i
$629$	115.298			0.00730878
$630$	−303.403	−	1945.84i	−0.0191871	−	0.123054i
$631$	−13968.0			−0.881235			−0.440617	−	0.897695i	$-0.645240\pi$
$631$	−13968.0			−0.881235			−0.440617	+	0.897695i	$0.645240\pi$
$632$	−3197.93	+	1846.32i	−0.201276	+	0.116207i
$633$	3316.76	−	11571.4i	0.208261	−	0.726578i
$634$	4118.15	−	7132.84i	0.257969	−	0.446816i
$635$	1226.05	−	2123.58i	0.0766208	−	0.132711i
$636$	−10247.8	−	2937.36i	−0.638919	−	0.183135i
$637$	1105.59	+	2778.07i	0.0687676	+	0.172796i
$638$			7194.23i			0.446430i
$639$	169.264	+	318.181i	0.0104789	+	0.0196980i
$640$		−	252.054i		−	0.0155676i
$641$	−5223.88	+	3016.01i	−0.321889	+	0.185843i	−0.652234	−	0.758018i	$-0.726168\pi$
$641$	−5223.88	+	3016.01i	−0.321889	+	0.185843i	0.330345	+	0.943860i	$0.392835\pi$
$642$	12992.8	+	13451.6i	0.798730	+	0.826937i
$643$	−14897.2	−	8600.89i	−0.913666	−	0.527506i	−0.0320574	−	0.999486i	$-0.510206\pi$
$643$	−14897.2	−	8600.89i	−0.913666	−	0.527506i	−0.881609	+	0.471980i	$0.843539\pi$
$644$	−11253.4	+	2156.99i	−0.688584	+	0.131984i
$645$	3200.55	−	798.341i	0.195383	−	0.0487359i
$646$	−3692.58	−	6395.74i	−0.224896	−	0.389531i
$647$	−15764.1			−0.957886			−0.478943	−	0.877846i	$-0.658980\pi$
$647$	−15764.1			−0.957886			−0.478943	+	0.877846i	$0.658980\pi$
$648$	4836.30	+	3259.20i	0.293191	+	0.197583i
$649$		−	10738.9i		−	0.649518i
$650$	−1055.84	−	1828.77i	−0.0637132	−	0.110354i
$651$	−1722.91	−	1212.84i	−0.103727	−	0.0730181i
$652$	4486.68	−	7771.16i	0.269497	−	0.466782i
$653$	14842.5	+	8569.31i	0.889481	+	0.513542i	0.873773	−	0.486335i	$-0.161666\pi$
$653$	14842.5	+	8569.31i	0.889481	+	0.513542i	0.0157080	+	0.999877i	$0.495000\pi$
$654$	12545.8	−	12117.9i	0.750123	−	0.724536i
$655$	1084.47	+	1878.36i	0.0646927	+	0.112051i
$656$	−6707.90			−0.399237
$657$	−346.606	−	651.545i	−0.0205820	−	0.0386898i
$658$	4950.87	+	5725.42i	0.293321	+	0.339210i
$659$	−482.155	+	278.373i	−0.0285009	+	0.0164550i	−0.514183	−	0.857681i	$-0.671905\pi$
$659$	−482.155	+	278.373i	−0.0285009	+	0.0164550i	0.485682	+	0.874136i	$0.338571\pi$
$660$	712.947	+	204.354i	0.0420476	+	0.0120522i
$661$	7443.67	+	4297.61i	0.438011	+	0.252886i	0.702754	−	0.711433i	$-0.251954\pi$
$661$	7443.67	+	4297.61i	0.438011	+	0.252886i	−0.264743	+	0.964319i	$0.585287\pi$
$662$	19806.8	+	11435.4i	1.16286	+	0.671376i
$663$	−1086.90	−	311.543i	−0.0636680	−	0.0182493i
$664$	−598.956	+	345.807i	−0.0350060	+	0.0202107i
$665$	−3528.71	−	4080.77i	−0.205771	−	0.237963i
$666$	−132.130	+	211.549i	−0.00768756	+	0.0123084i
$667$	30703.6			1.78238
$668$	−3513.37	−	6085.34i	−0.203498	−	0.352468i
$669$	13511.9	−	13051.0i	0.780867	−	0.754231i
$670$	−1831.76	−	1057.57i	−0.105622	−	0.0609810i
$671$	3077.63	−	5330.61i	0.177065	−	0.306685i
$672$	2518.14	+	1772.64i	0.144553	+	0.101757i
$673$	−6416.25	−	11113.3i	−0.367501	−	0.636530i	0.621673	−	0.783277i	$-0.286453\pi$
$673$	−6416.25	−	11113.3i	−0.367501	−	0.636530i	−0.989174	+	0.146746i	$0.953120\pi$
$674$		−	13695.4i		−	0.782683i
$675$	−16162.9	−	5246.09i	−0.921647	−	0.299144i
$676$	−8484.04			−0.482706
$677$	−332.470	−	575.855i	−0.0188743	−	0.0326912i	0.856434	−	0.516257i	$-0.172675\pi$
$677$	−332.470	−	575.855i	−0.0188743	−	0.0326912i	−0.875308	+	0.483565i	$0.839342\pi$
$678$	−13713.2	+	3420.61i	−0.776776	+	0.193758i
$679$	−3261.55	+	625.155i	−0.184340	+	0.0353332i
$680$	340.552	+	196.618i	0.0192052	+	0.0110882i
$681$	6439.63	+	6667.04i	0.362360	+	0.375157i
$682$	687.180	−	396.744i	0.0385828	−	0.0222758i
$683$			13039.2i			0.730497i	0.930910	+	0.365248i	$0.119016\pi$
$683$			13039.2i			0.730497i	−0.930910	+	0.365248i	$0.880984\pi$
$684$	15966.6	+	554.244i	0.892541	+	0.0309826i
$685$			29.4545i			0.00164292i
$686$	11274.7	+	5856.33i	0.627505	+	0.325941i
$687$	−27032.3	−	7748.36i	−1.50123	−	0.430303i
$688$	−2579.04	+	4467.03i	−0.142914	+	0.247534i
$689$	−2235.53	+	3872.04i	−0.123609	+	0.214097i
$690$	872.145	−	3042.72i	0.0481188	−	0.167876i
$691$	−10197.3	+	5887.42i	−0.561395	+	0.324122i	−0.753705	−	0.657213i	$-0.771735\pi$
$691$	−10197.3	+	5887.42i	−0.561395	+	0.324122i	0.192310	+	0.981334i	$0.438402\pi$
$692$	4884.58			0.268329
$693$	−7055.60	+	5685.51i	−0.386753	+	0.311652i
$694$	−10574.5			−0.578387
$695$	−3403.03	+	1964.74i	−0.185733	+	0.107233i
$696$	−5732.79	−	5935.25i	−0.312214	−	0.323240i
$697$	5232.59	−	9063.11i	0.284359	−	0.492525i
$698$	12057.1	−	20883.5i	0.653821	−	1.13245i
$699$	5261.24	+	21092.3i	0.284690	+	1.14132i
$700$	−8476.37	−	2943.41i	−0.457681	−	0.158929i
$701$		−	11863.9i		−	0.639218i	−0.947549	−	0.319609i	$-0.896448\pi$
$701$		−	11863.9i		−	0.639218i	0.947549	−	0.319609i	$-0.103552\pi$
$702$	1817.20	−	1637.24i	0.0977004	−	0.0880250i
$703$			683.268i			0.0366571i
$704$	−1004.36	+	579.866i	−0.0537687	+	0.0310434i
$705$	−2028.74	+	506.045i	−0.108378	+	0.0270337i
$706$	18199.0	+	10507.2i	0.970154	+	0.560119i
$707$	−4227.37	−	22055.0i	−0.224875	−	1.17322i
$708$	8557.37	+	8859.58i	0.454245	+	0.470287i
$709$	3848.91	+	6666.50i	0.203877	+	0.353125i	0.949774	−	0.312936i	$-0.101312\pi$
$709$	3848.91	+	6666.50i	0.203877	+	0.353125i	−0.745897	+	0.666061i	$0.767979\pi$
$710$	−52.5697			−0.00277874
$711$	10570.3	+	6602.02i	0.557550	+	0.348235i
$712$			2688.58i			0.141515i
$713$	−1693.23	−	2932.76i	−0.0889367	−	0.154043i
$714$	−4359.33	+	2019.51i	−0.228493	+	0.105852i
$715$	155.527	−	269.380i	0.00813479	−	0.0140899i
$716$	5110.84	+	2950.75i	0.266761	+	0.154015i
$717$	−5035.15	−	1443.24i	−0.262261	−	0.0751726i
$718$	8583.04	+	14866.3i	0.446123	+	0.772708i
$719$	8536.03			0.442754			0.221377	−	0.975188i	$-0.428945\pi$
$719$	8536.03			0.442754			0.221377	+	0.975188i	$0.428945\pi$
$720$	−751.023	+	399.526i	−0.0388736	+	0.0206798i
$721$	9703.20	+	11221.2i	0.501201	+	0.579613i
$722$	26021.8	−	15023.7i	1.34132	−	0.774409i
$723$	−13403.7	+	12946.5i	−0.689475	+	0.665957i
$724$	12471.9	+	7200.64i	0.640212	+	0.369627i
$725$	20822.4	+	12021.8i	1.06666	+	0.615834i
$726$	2521.80	+	10109.9i	0.128916	+	0.516824i
$727$	3356.15	−	1937.68i	0.171214	−	0.0988507i	−0.411944	−	0.911209i	$-0.635150\pi$
$727$	3356.15	−	1937.68i	0.171214	−	0.0988507i	0.583158	+	0.812359i	$0.301817\pi$
$728$	976.954	−	844.788i	0.0497367	−	0.0430082i
$729$	2045.23	−	19576.5i	0.103909	−	0.994587i
$730$	107.648			0.00545786
$731$	−4023.63	−	6969.13i	−0.203583	−	0.352616i
$732$	1708.70	+	6850.20i	0.0862780	+	0.345889i
$733$	3259.93	+	1882.12i	0.164268	+	0.0948401i	0.579880	−	0.814702i	$-0.303099\pi$
$733$	3259.93	+	1882.12i	0.164268	+	0.0948401i	−0.415612	+	0.909542i	$0.636433\pi$
$734$	−3928.42	+	6804.21i	−0.197548	+	0.342164i
$735$	−2849.85	+	2048.35i	−0.143018	+	0.102795i
$736$	2474.76	+	4286.41i	0.123941	+	0.214673i
$737$			9732.00i			0.486408i
$738$	10632.6	+	19987.0i	0.530340	+	0.996926i
$739$	−29392.1			−1.46307			−0.731533	−	0.681806i	$-0.761195\pi$
$739$	−29392.1			−1.46307			−0.731533	+	0.681806i	$0.761195\pi$
$740$	−18.1909	−	31.5075i	−0.000903662	−	0.00156519i
$741$	1846.24	−	6441.12i	0.0915293	−	0.319326i
$742$	3576.36	+	18658.5i	0.176944	+	0.923148i
$743$	−4178.10	−	2412.22i	−0.206298	−	0.119106i	0.393292	−	0.919414i	$-0.371336\pi$
$743$	−4178.10	−	2412.22i	−0.206298	−	0.119106i	−0.599590	+	0.800307i	$0.704670\pi$
$744$	−250.775	+	874.900i	−0.0123573	+	0.0431121i
$745$	−507.507	+	293.009i	−0.0249579	+	0.0144094i
$746$		−	6180.05i		−	0.303308i
$747$	1979.77	+	1236.53i	0.0969692	+	0.0605651i
$748$		−	1809.33i		−	0.0884434i
$749$	10933.0	−	31484.6i	0.533354	−	1.53594i
$750$	3622.73	−	3499.16i	0.176378	−	0.170362i
$751$	−16467.3	+	28522.3i	−0.800135	+	1.38588i	0.119391	+	0.992847i	$0.461906\pi$
$751$	−16467.3	+	28522.3i	−0.800135	+	1.38588i	−0.919527	+	0.393028i	$0.871428\pi$
$752$	1634.78	−	2831.52i	0.0792742	−	0.137307i
$753$	−38636.5	+	9637.43i	−1.86984	+	0.466411i
$754$	−2997.17	+	1730.42i	−0.144762	+	0.0835785i
$755$	−228.657			−0.0110221
$756$	1290.32	−	10312.9i	0.0620746	−	0.496132i
$757$	3278.51			0.157410			0.0787050	−	0.996898i	$-0.474921\pi$
$757$	3278.51			0.157410			0.0787050	+	0.996898i	$0.474921\pi$
$758$	7566.94	−	4368.78i	0.362591	−	0.209342i
$759$	−14130.8	+	3524.76i	−0.675777	+	0.168565i
$760$	−1165.18	+	2018.15i	−0.0556125	+	0.0963237i
$761$	3014.83	−	5221.84i	0.143610	−	0.248741i	−0.785243	−	0.619187i	$-0.787462\pi$
$761$	3014.83	−	5221.84i	0.143610	−	0.248741i	0.928854	+	0.370447i	$0.120795\pi$
$762$	9308.02	−	8990.52i	0.442512	−	0.427417i
$763$	−29364.5	−	10196.8i	−1.39327	−	0.483811i
$764$			6008.06i			0.284508i
$765$	46.0420	−	1326.37i	0.00217601	−	0.0626863i
$766$			28647.8i			1.35129i
$767$	4473.90	−	2583.01i	0.210617	−	0.121600i
$768$	366.524	−	1278.72i	0.0172211	−	0.0600806i
$769$	8816.76	+	5090.36i	0.413447	+	0.238704i	0.692270	−	0.721639i	$-0.256611\pi$
$769$	8816.76	+	5090.36i	0.413447	+	0.238704i	−0.278823	+	0.960343i	$0.589944\pi$
$770$	−248.809	−	1298.08i	−0.0116448	−	0.0607529i
$771$	5348.55	−	18659.9i	0.249836	−	0.871622i
$772$	−2506.49	−	4341.36i	−0.116853	−	0.202395i
$773$	28055.3			1.30541			0.652704	−	0.757613i	$-0.273634\pi$
$773$	28055.3			1.30541			0.652704	+	0.757613i	$0.273634\pi$
$774$	17398.0	+	603.933i	0.807958	+	0.0280464i
$775$		−	2651.90i		−	0.122915i
$776$	717.253	+	1242.32i	0.0331802	+	0.0574699i
$777$	442.708	+	39.8497i	0.0204402	+	0.00183990i
$778$	−297.346	+	515.018i	−0.0137023	+	0.0237330i
$779$	53709.0	+	31008.9i	2.47025	+	1.42620i
$780$	86.3487	+	346.172i	0.00396382	+	0.0158910i
$781$	120.940	+	209.475i	0.00554108	+	0.00959743i
$782$	−7721.88			−0.353112
$783$	−8597.81	+	26489.4i	−0.392415	+	1.20901i
$784$	792.129	−	5430.53i	0.0360846	−	0.247382i
$785$	−6188.18	+	3572.75i	−0.281357	+	0.162442i
$786$	2770.34	+	11106.3i	0.125718	+	0.504006i
$787$	−343.611	−	198.384i	−0.0155634	−	0.00898555i	0.492198	−	0.870483i	$-0.336194\pi$
$787$	−343.611	−	198.384i	−0.0155634	−	0.00898555i	−0.507762	+	0.861498i	$0.669527\pi$
$788$	4160.80	+	2402.24i	0.188099	+	0.108599i
$789$	−15053.2	+	14539.7i	−0.679225	+	0.656057i
$790$	−1574.31	+	908.930i	−0.0709007	+	0.0409345i
$791$	16474.7	+	19052.2i	0.740549	+	0.856406i
$792$	3319.77	+	2073.47i	0.148943	+	0.0930270i
$793$	2961.03			0.132597
$794$	−675.351	−	1169.74i	−0.0301855	−	0.0522829i
$795$	−5044.92	−	1446.04i	−0.225063	−	0.0645104i
$796$	−15264.1	−	8812.71i	−0.679674	−	0.392410i
$797$	−134.251	+	232.530i	−0.00596666	+	0.0103345i	−0.868993	−	0.494824i	$-0.835233\pi$
$797$	−134.251	+	232.530i	−0.00596666	+	0.0103345i	0.863027	+	0.505158i	$0.168566\pi$
$798$	−11967.9	−	25833.9i	−0.530899	−	1.14600i
$799$	2550.46	+	4417.52i	0.112927	+	0.195595i
$800$			3875.92i			0.171293i
$801$	8010.93	−	4261.62i	0.353374	−	0.187986i
$802$	17416.9			0.766849
$803$	−247.652	−	428.946i	−0.0108835	−	0.0188508i
$804$	−7755.04	−	8028.91i	−0.340173	−	0.352186i
$805$	−5539.98	+	1061.87i	−0.242557	+	0.0464920i
$806$	330.573	+	190.856i	0.0144466	+	0.00834073i
$807$	34399.4	−	8580.53i	1.50052	−	0.374286i
$808$	−8400.69	+	4850.14i	−0.365761	+	0.211172i
$809$		−	15530.6i		−	0.674942i	−0.941336	−	0.337471i	$-0.890429\pi$
$809$		−	15530.6i		−	0.674942i	0.941336	−	0.337471i	$-0.109571\pi$
$810$	2380.87	+	1604.48i	0.103278	+	0.0695996i
$811$			33045.6i			1.43081i	0.698710	+	0.715405i	$0.253758\pi$
$811$			33045.6i			1.43081i	−0.698710	+	0.715405i	$0.746242\pi$
$812$	−4823.94	+	13891.9i	−0.208482	+	0.600382i
$813$	−5538.88	−	22205.4i	−0.238938	−	0.957906i
$814$	−83.6987	+	144.970i	−0.00360398	+	0.00624227i
$815$	2208.76	−	3825.68i	0.0949317	−	0.164427i
$816$	1441.78	+	1492.70i	0.0618535	+	0.0640379i
$817$	41299.9	−	23844.5i	1.76854	−	1.02107i
$818$	−17117.4			−0.731659
$819$	−4065.70	−	1571.89i	−0.173464	−	0.0670650i
$820$	−3302.25			−0.140633
$821$	−24558.8	+	14179.0i	−1.04398	+	0.602742i	−0.920958	−	0.389662i	$-0.872592\pi$
$821$	−24558.8	+	14179.0i	−1.04398	+	0.602742i	−0.123022	+	0.992404i	$0.539258\pi$
$822$	−42.8313	+	149.429i	−0.00181741	+	0.00634055i
$823$	−2747.37	+	4758.59i	−0.116364	+	0.201548i	−0.918324	−	0.395829i	$-0.870457\pi$
$823$	−2747.37	+	4758.59i	−0.116364	+	0.201548i	0.801960	+	0.597377i	$0.203791\pi$
$824$	3203.99	−	5549.48i	0.135457	−	0.234618i
$825$	−10963.2	−	3142.42i	−0.462656	−	0.132612i
$826$	7200.73	−	20736.5i	0.303324	−	0.873506i
$827$		−	15392.4i		−	0.647215i	−0.946191	−	0.323607i	$-0.895104\pi$
$827$		−	15392.4i		−	0.647215i	0.946191	−	0.323607i	$-0.104896\pi$
$828$	8849.16	−	14168.2i	0.371413	−	0.594659i
$829$			27739.2i			1.16215i	0.813851	+	0.581074i	$0.197367\pi$
$829$			27739.2i			1.16215i	−0.813851	+	0.581074i	$0.802633\pi$
$830$	−294.861	+	170.238i	−0.0123311	+	0.00711934i
$831$	−30447.0	−	31522.2i	−1.27099	−	1.31588i
$832$	−483.154	−	278.949i	−0.0201326	−	0.0116236i
$833$	6719.33	+	5306.41i	0.279485	+	0.220716i
$834$	−20121.4	+	5019.04i	−0.835427	+	0.208387i
$835$	−1729.61	−	2995.76i	−0.0716832	−	0.124159i
$836$	10722.3			0.443587
$837$	3004.37	−	639.577i	0.124070	−	0.0264122i
$838$			25342.6i			1.04468i
$839$	−12355.6	−	21400.5i	−0.508417	−	0.880604i	−0.999953	−	0.00974665i	$-0.996897\pi$
$839$	−12355.6	−	21400.5i	−0.508417	−	0.880604i	0.491535	−	0.870858i	$-0.336436\pi$
$840$	1239.66	+	872.655i	0.0509194	+	0.0358446i
$841$	7508.08	−	13004.4i	0.307847	−	0.533207i
$842$	−17297.0	−	9986.44i	−0.707951	−	0.408736i
$843$	−17997.3	+	17383.4i	−0.735303	+	0.710222i
$844$	4633.20	+	8024.94i	0.188959	+	0.327287i
$845$	−4176.63			−0.170036
$846$	−11028.1	−	382.816i	−0.448172	−	0.0155573i
$847$	14046.0	−	12145.8i	0.569807	−	0.492721i
$848$	7106.98	−	4103.22i	0.287801	−	0.166162i
$849$	8277.83	+	2372.70i	0.334623	+	0.0959138i
$850$	−5236.79	−	3023.46i	−0.211318	−	0.122005i
$851$	618.707	+	357.210i	0.0249224	+	0.0143890i
$852$	−266.698	−	76.4444i	−0.0107241	−	0.00307388i
$853$	−1860.24	+	1074.01i	−0.0746700	+	0.0431107i	−0.536870	−	0.843665i	$-0.680393\pi$
$853$	−1860.24	+	1074.01i	−0.0746700	+	0.0431107i	0.462200	+	0.886776i	$0.347060\pi$
$854$	9517.17	−	8229.65i	0.381348	−	0.329758i
$855$	7860.23	+	272.850i	0.314403	+	0.0109138i
$856$	−14396.7			−0.574847
$857$	4142.09	+	7174.31i	0.165100	+	0.285962i	0.936691	−	0.350157i	$-0.113872\pi$
$857$	4142.09	+	7174.31i	0.165100	+	0.285962i	−0.771591	+	0.636120i	$0.780539\pi$
$858$	1180.74	−	1140.47i	0.0469812	−	0.0453787i
$859$	7018.64	+	4052.21i	0.278781	+	0.160954i	0.632871	−	0.774257i	$-0.281876\pi$
$859$	7018.64	+	4052.21i	0.278781	+	0.160954i	−0.354090	+	0.935211i	$0.615209\pi$
$860$	−1269.64	+	2199.08i	−0.0503423	+	0.0871954i
$861$	23224.0	−	32991.1i	0.919246	−	1.30584i
$862$	−6741.34	−	11676.3i	−0.266370	−	0.461366i
$863$		−	1504.05i		−	0.0593261i	−0.999560	−	0.0296630i	$-0.990557\pi$
$863$		−	1504.05i		−	0.0593261i	0.999560	−	0.0296630i	$-0.00944342\pi$
$864$	−4391.08	+	934.783i	−0.172902	+	0.0368078i
$865$	2404.64			0.0945204
$866$	−8737.16	−	15133.2i	−0.342841	−	0.593819i
$867$	21628.3	−	5394.92i	0.847214	−	0.211328i
$868$	1592.96	−	305.329i	0.0622909	−	0.0119396i
$869$	7243.63	+	4182.11i	0.282766	+	0.163255i
$870$	−2822.21	−	2921.88i	−0.109979	−	0.113863i
$871$	−4054.43	+	2340.83i	−0.157726	+	0.0910630i
$872$			13427.2i			0.521449i
$873$	2564.73	−	4106.32i	0.0994306	−	0.159196i
$874$		−	45760.8i		−	1.77103i
$875$	−8479.28	−	2944.42i	−0.327602	−	0.113759i
$876$	546.123	+	156.537i	0.0210637	+	0.00603754i
$877$	−17021.5	+	29482.1i	−0.655389	+	1.13517i	0.326408	+	0.945229i	$0.394162\pi$
$877$	−17021.5	+	29482.1i	−0.655389	+	1.13517i	−0.981796	+	0.189937i	$0.939172\pi$
$878$	2374.13	−	4112.11i	0.0912562	−	0.158060i
$879$	−8212.37	+	28651.2i	−0.315127	+	1.09941i
$880$	−494.437	+	285.464i	−0.0189403	+	0.0109352i
$881$	26222.2			1.00278			0.501390	−	0.865221i	$-0.332822\pi$
$881$	26222.2			1.00278			0.501390	+	0.865221i	$0.332822\pi$
$882$	−17436.5	+	6247.62i	−0.665666	+	0.238513i
$883$	−31631.3			−1.20552			−0.602761	−	0.797922i	$-0.705933\pi$
$883$	−31631.3			−1.20552			−0.602761	+	0.797922i	$0.705933\pi$
$884$	753.781	−	435.196i	0.0286792	−	0.0165579i
$885$	4212.73	+	4361.50i	0.160010	+	0.165661i
$886$	−12865.9	+	22284.3i	−0.487852	+	0.844984i
$887$	−18879.3	+	32699.9i	−0.714661	+	1.23783i	0.248430	+	0.968650i	$0.420086\pi$
$887$	−18879.3	+	32699.9i	−0.714661	+	1.23783i	−0.963090	+	0.269179i	$0.913248\pi$
$888$	−46.4696	−	186.297i	−0.00175610	−	0.00704022i
$889$	−21786.1	−	7565.20i	−0.821916	−	0.285409i
$890$			1323.56i			0.0498494i
$891$	916.012	−	13178.3i	0.0344417	−	0.495498i
$892$			14461.2i			0.542821i
$893$	−26178.8	+	15114.3i	−0.981007	+	0.566385i
$894$	−3000.78	+	748.509i	−0.112261	+	0.0280021i
$895$	2516.03	+	1452.63i	0.0939682	+	0.0542526i
$896$	−2328.21	+	446.258i	−0.0868081	+	0.0166389i
$897$	−4867.30	−	5039.19i	−0.181175	−	0.187574i
$898$	822.758	+	1425.06i	0.0305744	+	0.0529564i
$899$	−4346.19			−0.161239
$900$	11548.8	−	6143.66i	0.427732	−	0.227543i
$901$			12803.1i			0.473399i
$902$	7597.04	+	13158.5i	0.280437	+	0.485730i
$903$	−13040.8	−	28150.0i	−0.480588	−	1.03740i
$904$	5439.96	−	9422.28i	0.200144	−	0.346660i
$905$	6139.80	+	3544.82i	0.225518	+	0.130203i
$906$	−1160.03	−	332.503i	−0.0425380	−	0.0121928i
$907$	6238.02	+	10804.6i	0.228368	+	0.395545i	0.957325	−	0.289015i	$-0.0933277\pi$
$907$	6238.02	+	10804.6i	0.228368	+	0.395545i	−0.728956	+	0.684560i	$0.759994\pi$
$908$	−7135.44			−0.260791
$909$	27767.4	+	17343.0i	1.01319	+	0.632816i
$910$	480.947	−	415.883i	0.0175200	−	0.0151499i
$911$	−6033.75	+	3483.59i	−0.219437	+	0.126692i	−0.605690	−	0.795701i	$-0.707103\pi$
$911$	−6033.75	+	3483.59i	−0.219437	+	0.126692i	0.386252	+	0.922393i	$0.373769\pi$
$912$	−8845.91	+	8544.17i	−0.321181	+	0.310226i
$913$	1356.70	+	783.289i	0.0491786	+	0.0283933i
$914$	4214.00	+	2432.96i	0.152502	+	0.0880471i
$915$	841.181	+	3372.30i	0.0303919	+	0.121841i
$916$	18747.3	−	10823.7i	0.676230	−	0.390422i
$917$	15430.3	−	13342.8i	0.555674	−	0.480500i
$918$	2162.33	−	6662.02i	0.0777422	−	0.239520i
$919$	51408.4			1.84527			0.922637	−	0.385671i	$-0.126030\pi$
$919$	51408.4			1.84527			0.922637	+	0.385671i	$0.126030\pi$
$920$	1218.30	+	2110.17i	0.0436590	+	0.0756197i
$921$	−12016.5	−	48174.2i	−0.429920	−	1.72355i
$922$	−585.520	−	338.050i	−0.0209144	−	0.0120749i
$923$	−58.1792	+	100.769i	−0.00207475	+	0.00359357i
$924$	625.348	−	6947.27i	0.0222646	−	0.247347i
$925$	279.728	+	484.502i	0.00994312	+	0.0172220i
$926$			31862.7i			1.13075i
$927$	−21613.9	−	750.279i	−0.765798	−	0.0265830i
$928$	6352.23			0.224701
$929$	−8145.29	−	14108.1i	−0.287662	−	0.498246i	0.685589	−	0.727989i	$-0.259545\pi$
$929$	−8145.29	−	14108.1i	−0.287662	−	0.498246i	−0.973251	+	0.229743i	$0.926211\pi$
$930$	−123.455	+	430.706i	−0.00435294	+	0.0151865i
$931$	−31446.4	+	39819.6i	−1.10700	+	1.40175i
$932$	−14492.4	−	8367.20i	−0.509350	−	0.294074i
$933$	−5059.87	+	17652.8i	−0.177548	+	0.619428i
$934$	10673.9	−	6162.59i	0.373942	−	0.215895i
$935$		−	890.719i		−	0.0311547i
$936$	−65.3215	+	1881.77i	−0.00228109	+	0.0657133i
$937$		−	27335.2i		−	0.953045i	−0.879162	−	0.476522i	$-0.841897\pi$
$937$		−	27335.2i		−	0.953045i	0.879162	−	0.476522i	$-0.158103\pi$
$938$	−6525.59	+	18792.3i	−0.227152	+	0.654147i
$939$	−19089.1	+	18438.0i	−0.663418	+	0.640789i
$940$	804.787	−	1393.93i	0.0279248	−	0.0483671i
$941$	1248.27	−	2162.07i	0.0432439	−	0.0749007i	−0.843593	−	0.536983i	$-0.819564\pi$
$941$	1248.27	−	2162.07i	0.0432439	−	0.0749007i	0.886837	+	0.462082i	$0.152897\pi$
$942$	−36589.3	+	9126.78i	−1.26555	+	0.315676i
$943$	56157.8	−	32422.7i	1.93929	−	1.11965i
$944$	−9482.01			−0.326921
$945$	635.213	−	5076.95i	0.0218661	−	0.174765i
$946$	11683.6			0.401549
$947$	7709.33	−	4450.98i	0.264540	−	0.152732i	−0.361864	−	0.932231i	$-0.617859\pi$
$947$	7709.33	−	4450.98i	0.264540	−	0.152732i	0.626404	+	0.779499i	$0.284526\pi$
$948$	−9308.56	+	2321.91i	−0.318911	+	0.0795487i
$949$	119.135	−	206.347i	0.00407511	−	0.00705830i
$950$	17917.4	−	31033.8i	0.611912	−	1.05986i
$951$	15391.3	−	14866.3i	0.524812	−	0.506910i
$952$	1213.21	−	3493.78i	0.0413029	−	0.118943i
$953$		−	37572.5i		−	1.27712i	−0.769573	−	0.638558i	$-0.779531\pi$
$953$		−	37572.5i		−	1.27712i	0.769573	−	0.638558i	$-0.220469\pi$
$954$	−23491.2	−	14672.2i	−0.797229	−	0.497933i
$955$			2957.72i			0.100219i
$956$	3491.94	−	2016.07i	0.118135	−	0.0682055i
$957$	−5150.12	+	17967.6i	−0.173960	+	0.606908i
$958$	−30797.5	−	17780.9i	−1.03864	−	0.599661i
$959$	272.070	−	52.1488i	0.00916121	−	0.00175597i
$960$	180.437	−	629.505i	0.00606622	−	0.0211637i
$961$	−14655.8	−	25384.6i	−0.491955	−	0.852090i
$962$	−80.5278			−0.00269888
$963$	22820.0	+	42896.7i	0.763618	+	1.43544i
$964$		−	14345.4i		−	0.479290i
$965$	−1233.92	−	2137.22i	−0.0411621	−	0.0712948i
$966$	−29649.7	−	2668.87i	−0.987539	−	0.0888918i
$967$	−1638.22	+	2837.48i	−0.0544795	+	0.0943612i	−0.891979	−	0.452077i	$-0.850683\pi$
$967$	−1638.22	+	2837.48i	−0.0544795	+	0.0943612i	0.837500	+	0.546438i	$0.184017\pi$
$968$	−6946.47	−	4010.54i	−0.230649	−	0.133165i
$969$	−4643.74	−	18616.8i	−0.153951	−	0.617190i
$970$	353.098	+	611.583i	0.0116879	+	0.0202441i
$971$	−16818.2			−0.555840			−0.277920	−	0.960604i	$-0.589645\pi$
$971$	−16818.2			−0.555840			−0.277920	+	0.960604i	$0.589645\pi$
$972$	9745.53	+	11602.0i	0.321593	+	0.382855i
$973$	24173.3	+	27955.2i	0.796465	+	0.921070i
$974$	−18064.5	+	10429.6i	−0.594276	+	0.343105i
$975$	−1327.81	−	5323.21i	−0.0436144	−	0.174851i
$976$	−4706.73	−	2717.43i	−0.154363	−	0.0891218i
$977$	−32029.6	−	18492.3i	−1.04884	−	0.605549i	−0.126516	−	0.991965i	$-0.540380\pi$
$977$	−32029.6	−	18492.3i	−1.04884	−	0.605549i	−0.922325	+	0.386416i	$0.873713\pi$
$978$	16768.6	−	16196.6i	0.548263	−	0.529562i
$979$	5274.01	−	3044.95i	0.172174	−	0.0994045i
$980$	389.959	−	2673.41i	0.0127110	−	0.0871417i
$981$	40008.1	−	21283.3i	1.30210	−	0.692685i
$982$	11923.4			0.387466
$983$	10829.6	+	18757.4i	0.351383	+	0.608613i	0.986492	−	0.163809i	$-0.0523782\pi$
$983$	10829.6	+	18757.4i	0.351383	+	0.608613i	−0.635109	+	0.772423i	$0.719045\pi$
$984$	−16753.0	−	4801.97i	−0.542751	−	0.155570i
$985$	2048.33	+	1182.60i	0.0662590	+	0.0382547i
$986$	−4955.15	+	8582.56i	−0.160045	+	0.277205i
$987$	8266.18	+	17843.4i	0.266581	+	0.575444i
$988$	2579.02	+	4467.00i	0.0830462	+	0.143840i
$989$		−	49863.3i		−	1.60320i
$990$	1634.30	+	1020.75i	0.0524661	+	0.0327693i
$991$	−26883.3			−0.861732			−0.430866	−	0.902416i	$-0.641792\pi$
$991$	−26883.3			−0.861732			−0.430866	+	0.902416i	$0.641792\pi$
$992$	−350.310	−	606.754i	−0.0112120	−	0.0194198i
$993$	41281.2	+	42739.1i	1.31925	+	1.36584i
$994$	93.0741	+	485.585i	0.00296995	+	0.0154948i
$995$	−7514.38	−	4338.43i	−0.239419	−	0.138229i
$996$	−1743.45	+	434.883i	−0.0554651	+	0.0138351i
$997$	2709.17	−	1564.14i	0.0860583	−	0.0496858i	−0.456353	−	0.889799i	$-0.650845\pi$
$997$	2709.17	−	1564.14i	0.0860583	−	0.0496858i	0.542412	+	0.840113i	$0.317511\pi$
$998$			33228.1i			1.05393i
$999$	−481.435	+	433.758i	−0.0152472	+	0.0137372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.4.m.a.41.2	✓	48
3.2	odd	2		378.4.m.a.125.17		48
7.6	odd	2	inner	126.4.m.a.41.11	yes	48
9.2	odd	6	inner	126.4.m.a.83.11	yes	48
9.4	even	3		1134.4.d.b.1133.21		48
9.5	odd	6		1134.4.d.b.1133.28		48
9.7	even	3		378.4.m.a.251.18		48
21.20	even	2		378.4.m.a.125.18		48
63.13	odd	6		1134.4.d.b.1133.27		48
63.20	even	6	inner	126.4.m.a.83.2	yes	48
63.34	odd	6		378.4.m.a.251.17		48
63.41	even	6		1134.4.d.b.1133.22		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.4.m.a.41.2	✓	48	1.1	even	1	trivial
126.4.m.a.41.11	yes	48	7.6	odd	2	inner
126.4.m.a.83.2	yes	48	63.20	even	6	inner
126.4.m.a.83.11	yes	48	9.2	odd	6	inner
378.4.m.a.125.17		48	3.2	odd	2
378.4.m.a.125.18		48	21.20	even	2
378.4.m.a.251.17		48	63.34	odd	6
378.4.m.a.251.18		48	9.7	even	3
1134.4.d.b.1133.21		48	9.4	even	3
1134.4.d.b.1133.22		48	63.41	even	6
1134.4.d.b.1133.27		48	63.13	odd	6
1134.4.d.b.1133.28		48	9.5	odd	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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	126.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 + 1.00000i) q^{2} +(-5.04167 + 1.25759i) q^{3} +(2.00000 - 3.46410i) q^{4} +(0.984584 - 1.70535i) q^{5} +(7.47485 - 7.21988i) q^{6} +(-17.4955 - 6.07527i) q^{7} +8.00000i q^{8} +(23.8370 - 12.6807i) q^{9} +O(q^{10})\)	\(q+(-1.73205 + 1.00000i) q^{2} +(-5.04167 + 1.25759i) q^{3} +(2.00000 - 3.46410i) q^{4} +(0.984584 - 1.70535i) q^{5} +(7.47485 - 7.21988i) q^{6} +(-17.4955 - 6.07527i) q^{7} +8.00000i q^{8} +(23.8370 - 12.6807i) q^{9} +3.93834i q^{10} +(15.6931 - 9.06041i) q^{11} +(-5.72694 + 19.9800i) q^{12} +(7.54928 + 4.35858i) q^{13} +(36.3783 - 6.97278i) q^{14} +(-2.81933 + 9.83602i) q^{15} +(-8.00000 - 13.8564i) q^{16} +24.9620 q^{17} +(-28.6061 + 45.8005i) q^{18} +147.928i q^{19} +(-3.93834 - 6.82140i) q^{20} +(95.8466 + 8.62748i) q^{21} +(-18.1208 + 31.3862i) q^{22} +(133.950 + 77.3363i) q^{23} +(-10.0607 - 40.3334i) q^{24} +(60.5612 + 104.895i) q^{25} -17.4343 q^{26} +(-104.231 + 93.9089i) q^{27} +(-56.0363 + 48.4555i) q^{28} +(171.912 - 99.2537i) q^{29} +(-4.95280 - 19.8558i) q^{30} +(-18.9611 - 10.9472i) q^{31} +(27.7128 + 16.0000i) q^{32} +(-67.7252 + 65.4151i) q^{33} +(-43.2355 + 24.9620i) q^{34} +(-27.5862 + 23.8543i) q^{35} +(3.74672 - 107.935i) q^{36} +4.61892 q^{37} +(-147.928 - 256.219i) q^{38} +(-43.5423 - 12.4807i) q^{39} +(13.6428 + 7.87667i) q^{40} +(209.622 - 363.076i) q^{41} +(-174.639 + 80.9033i) q^{42} +(-161.190 - 279.189i) q^{43} -72.4833i q^{44} +(1.84448 - 53.1355i) q^{45} -309.345 q^{46} +(102.174 + 176.970i) q^{47} +(57.7590 + 59.7988i) q^{48} +(269.182 + 212.579i) q^{49} +(-209.790 - 121.122i) q^{50} +(-125.850 + 31.3919i) q^{51} +(30.1971 - 17.4343i) q^{52} +512.902i q^{53} +(86.6246 - 266.886i) q^{54} -35.6829i q^{55} +(48.6022 - 139.964i) q^{56} +(-186.032 - 745.804i) q^{57} +(-198.507 + 343.825i) q^{58} +(296.313 - 513.229i) q^{59} +(28.4343 + 29.4385i) q^{60} +(294.171 - 169.839i) q^{61} +43.7887 q^{62} +(-494.077 + 77.0384i) q^{63} -64.0000 q^{64} +(14.8658 - 8.58277i) q^{65} +(51.8884 - 181.027i) q^{66} +(-268.531 + 465.109i) q^{67} +(49.9241 - 86.4710i) q^{68} +(-772.591 - 221.450i) q^{69} +(23.9265 - 68.9030i) q^{70} +13.3482i q^{71} +(101.445 + 190.696i) q^{72} -27.3334i q^{73} +(-8.00021 + 4.61892i) q^{74} +(-437.244 - 452.686i) q^{75} +(512.437 + 295.856i) q^{76} +(-329.602 + 63.1762i) q^{77} +(87.8981 - 21.9252i) q^{78} +(230.790 + 399.741i) q^{79} -31.5067 q^{80} +(407.400 - 604.538i) q^{81} +838.488i q^{82} +(43.2259 + 74.8694i) q^{83} +(221.580 - 314.767i) q^{84} +(24.5772 - 42.5690i) q^{85} +(558.378 + 322.380i) q^{86} +(-741.906 + 716.599i) q^{87} +(72.4833 + 125.545i) q^{88} +336.072 q^{89} +(49.9408 + 93.8779i) q^{90} +(-105.599 - 122.119i) q^{91} +(535.801 - 309.345i) q^{92} +(109.363 + 31.3469i) q^{93} +(-353.940 - 204.347i) q^{94} +(252.269 + 145.647i) q^{95} +(-159.840 - 45.8155i) q^{96} +(155.290 - 89.6566i) q^{97} +(-678.816 - 99.0161i) q^{98} +(259.183 - 414.972i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 96 q^{4} - 12 q^{7} - 36 q^{9}+O(q^{10}) \) 48 * q + 96 * q^4 - 12 * q^7 - 36 * q^9	\( 48 q + 96 q^{4} - 12 q^{7} - 36 q^{9} + 24 q^{11} - 132 q^{14} - 120 q^{15} - 384 q^{16} + 120 q^{18} + 180 q^{21} + 348 q^{23} - 600 q^{25} - 96 q^{28} - 84 q^{29} + 192 q^{30} + 96 q^{36} - 672 q^{37} + 1368 q^{39} + 1128 q^{42} + 84 q^{43} - 1008 q^{46} - 42 q^{49} + 456 q^{50} + 2016 q^{51} - 528 q^{56} + 732 q^{57} + 504 q^{58} - 1008 q^{60} - 774 q^{63} - 3072 q^{64} - 6972 q^{65} + 1176 q^{67} + 216 q^{70} - 384 q^{72} + 2520 q^{74} + 1500 q^{77} + 2832 q^{78} + 348 q^{79} + 2268 q^{81} - 1080 q^{84} + 720 q^{85} + 1200 q^{86} + 180 q^{91} + 1392 q^{92} + 5232 q^{93} - 5892 q^{95} + 972 q^{99}+O(q^{100}) \) 48 * q + 96 * q^4 - 12 * q^7 - 36 * q^9 + 24 * q^11 - 132 * q^14 - 120 * q^15 - 384 * q^16 + 120 * q^18 + 180 * q^21 + 348 * q^23 - 600 * q^25 - 96 * q^28 - 84 * q^29 + 192 * q^30 + 96 * q^36 - 672 * q^37 + 1368 * q^39 + 1128 * q^42 + 84 * q^43 - 1008 * q^46 - 42 * q^49 + 456 * q^50 + 2016 * q^51 - 528 * q^56 + 732 * q^57 + 504 * q^58 - 1008 * q^60 - 774 * q^63 - 3072 * q^64 - 6972 * q^65 + 1176 * q^67 + 216 * q^70 - 384 * q^72 + 2520 * q^74 + 1500 * q^77 + 2832 * q^78 + 348 * q^79 + 2268 * q^81 - 1080 * q^84 + 720 * q^85 + 1200 * q^86 + 180 * q^91 + 1392 * q^92 + 5232 * q^93 - 5892 * q^95 + 972 * q^99

Introduction

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