LMFDB - Embedded newform 126.4.m.a.41.1

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			41.1
Character	$\chi$	$=$	126.41
Dual form			126.4.m.a.83.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73205 + 1.00000i) q^{2} +(-5.10721 - 0.957281i) q^{3} +(2.00000 - 3.46410i) q^{4} +(0.0529940 - 0.0917884i) q^{5} +(9.80323 - 3.44915i) q^{6} +(18.4211 + 1.91364i) q^{7} +8.00000i q^{8} +(25.1672 + 9.77807i) q^{9} +O(q^{10})$	\(q+(-1.73205 + 1.00000i) q^{2} +(-5.10721 - 0.957281i) q^{3} +(2.00000 - 3.46410i) q^{4} +(0.0529940 - 0.0917884i) q^{5} +(9.80323 - 3.44915i) q^{6} +(18.4211 + 1.91364i) q^{7} +8.00000i q^{8} +(25.1672 + 9.77807i) q^{9} +0.211976i q^{10} +(-23.9258 + 13.8136i) q^{11} +(-13.5305 + 15.7773i) q^{12} +(-54.2525 - 31.3227i) q^{13} +(-33.8200 + 15.1066i) q^{14} +(-0.358519 + 0.418052i) q^{15} +(-8.00000 - 13.8564i) q^{16} -57.7870 q^{17} +(-53.3690 + 8.23110i) q^{18} -26.1649i q^{19} +(-0.211976 - 0.367153i) q^{20} +(-92.2487 - 27.4076i) q^{21} +(27.6271 - 47.8516i) q^{22} +(-82.4627 - 47.6099i) q^{23} +(7.65825 - 40.8577i) q^{24} +(62.4944 + 108.243i) q^{25} +125.291 q^{26} +(-119.174 - 74.0308i) q^{27} +(43.4713 - 59.9854i) q^{28} +(-242.077 + 139.763i) q^{29} +(0.202921 - 1.08261i) q^{30} +(-196.119 - 113.229i) q^{31} +(27.7128 + 16.0000i) q^{32} +(135.418 - 47.6451i) q^{33} +(100.090 - 57.7870i) q^{34} +(1.15186 - 1.58943i) q^{35} +(84.2067 - 67.6257i) q^{36} +104.919 q^{37} +(26.1649 + 45.3189i) q^{38} +(247.094 + 211.907i) q^{39} +(0.734307 + 0.423952i) q^{40} +(-130.454 + 225.954i) q^{41} +(187.187 - 44.7774i) q^{42} +(-220.304 - 381.578i) q^{43} +110.508i q^{44} +(2.23123 - 1.79188i) q^{45} +190.440 q^{46} +(134.548 + 233.044i) q^{47} +(27.5932 + 78.4259i) q^{48} +(335.676 + 70.5030i) q^{49} +(-216.487 - 124.989i) q^{50} +(295.131 + 55.3184i) q^{51} +(-217.010 + 125.291i) q^{52} +26.5682i q^{53} +(280.446 + 9.05114i) q^{54} +2.92815i q^{55} +(-15.3092 + 147.369i) q^{56} +(-25.0472 + 133.630i) q^{57} +(279.526 - 484.154i) q^{58} +(-97.1526 + 168.273i) q^{59} +(0.731138 + 2.07805i) q^{60} +(-418.447 + 241.591i) q^{61} +452.917 q^{62} +(444.897 + 228.284i) q^{63} -64.0000 q^{64} +(-5.75012 + 3.31983i) q^{65} +(-186.905 + 217.941i) q^{66} +(225.761 - 391.029i) q^{67} +(-115.574 + 200.180i) q^{68} +(375.579 + 322.094i) q^{69} +(-0.405647 + 3.90484i) q^{70} -979.780i q^{71} +(-78.2246 + 201.338i) q^{72} -30.5100i q^{73} +(-181.725 + 104.919i) q^{74} +(-215.553 - 612.647i) q^{75} +(-90.6379 - 52.3298i) q^{76} +(-467.174 + 208.676i) q^{77} +(-639.887 - 119.939i) q^{78} +(227.927 + 394.781i) q^{79} -1.69581 q^{80} +(537.778 + 492.174i) q^{81} -521.817i q^{82} +(-345.370 - 598.199i) q^{83} +(-279.440 + 264.744i) q^{84} +(-3.06237 + 5.30418i) q^{85} +(763.156 + 440.608i) q^{86} +(1370.13 - 482.065i) q^{87} +(-110.508 - 191.406i) q^{88} +145.080 q^{89} +(-2.07272 + 5.33485i) q^{90} +(-939.452 - 680.819i) q^{91} +(-329.851 + 190.440i) q^{92} +(893.228 + 766.027i) q^{93} +(-466.088 - 269.096i) q^{94} +(-2.40163 - 1.38658i) q^{95} +(-126.219 - 108.244i) q^{96} +(-909.610 + 525.164i) q^{97} +(-651.911 + 213.561i) q^{98} +(-737.216 + 113.701i) 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
$3$	−5.10721	−	0.957281i	−0.982883	−	0.184229i
$3$	−5.10721	−	0.957281i	−0.982883	−	0.184229i
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$	0.0529940	−	0.0917884i	0.00473993	−	0.00820980i	−0.863646	−	0.504099i	$-0.831825\pi$
$5$	0.0529940	−	0.0917884i	0.00473993	−	0.00820980i	0.868386	+	0.495889i	$0.165158\pi$
$6$	9.80323	−	3.44915i	0.667025	−	0.234685i
$7$	18.4211	+	1.91364i	0.994647	+	0.103327i
$7$	18.4211	+	1.91364i	0.994647	+	0.103327i
$8$			8.00000i			0.353553i
$9$	25.1672	+	9.77807i	0.932119	+	0.362151i
$10$			0.211976i			0.00670327i
$11$	−23.9258	+	13.8136i	−0.655809	+	0.378631i	−0.790678	−	0.612232i	$-0.790272\pi$
$11$	−23.9258	+	13.8136i	−0.655809	+	0.378631i	0.134869	+	0.990863i	$0.456939\pi$
$12$	−13.5305	+	15.7773i	−0.325494	+	0.379544i
$13$	−54.2525	−	31.3227i	−1.15746	−	0.668258i	−0.206764	−	0.978391i	$-0.566293\pi$
$13$	−54.2525	−	31.3227i	−1.15746	−	0.668258i	−0.950693	+	0.310133i	$0.899626\pi$
$14$	−33.8200	+	15.1066i	−0.645626	+	0.288386i
$15$	−0.358519	+	0.418052i	−0.00617128	+	0.00719605i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−57.7870			−0.824436			−0.412218	−	0.911085i	$-0.635246\pi$
$17$	−57.7870			−0.824436			−0.412218	+	0.911085i	$0.635246\pi$
$18$	−53.3690	+	8.23110i	−0.698844	+	0.107783i
$19$		−	26.1649i		−	0.315928i	−0.987445	−	0.157964i	$-0.949507\pi$
$19$		−	26.1649i		−	0.315928i	0.987445	−	0.157964i	$-0.0504931\pi$
$20$	−0.211976	−	0.367153i	−0.00236997	−	0.00410490i
$21$	−92.2487	−	27.4076i	−0.958587	−	0.284801i
$22$	27.6271	−	47.8516i	0.267733	−	0.463727i
$23$	−82.4627	−	47.6099i	−0.747594	−	0.431624i	0.0772297	−	0.997013i	$-0.475393\pi$
$23$	−82.4627	−	47.6099i	−0.747594	−	0.431624i	−0.824824	+	0.565390i	$0.808726\pi$
$24$	7.65825	−	40.8577i	0.0651347	−	0.347502i
$25$	62.4944	+	108.243i	0.499955	+	0.865948i
$26$	125.291			0.945060
$27$	−119.174	−	74.0308i	−0.849446	−	0.527675i
$28$	43.4713	−	59.9854i	0.293404	−	0.404863i
$29$	−242.077	+	139.763i	−1.55009	+	0.894944i	−0.551955	+	0.833874i	$0.686118\pi$
$29$	−242.077	+	139.763i	−1.55009	+	0.894944i	−0.998133	+	0.0610700i	$0.980549\pi$
$30$	0.202921	−	1.08261i	0.00123494	−	0.00658854i
$31$	−196.119	−	113.229i	−1.13626	−	0.656019i	−0.190756	−	0.981637i	$-0.561094\pi$
$31$	−196.119	−	113.229i	−1.13626	−	0.656019i	−0.945501	+	0.325619i	$0.894427\pi$
$32$	27.7128	+	16.0000i	0.153093	+	0.0883883i
$33$	135.418	−	47.6451i	0.714338	−	0.251332i
$34$	100.090	−	57.7870i	0.504862	−	0.291482i
$35$	1.15186	−	1.58943i	0.00556286	−	0.00767609i
$36$	84.2067	−	67.6257i	0.389846	−	0.313082i
$37$	104.919			0.466178			0.233089	−	0.972455i	$-0.425117\pi$
$37$	104.919			0.466178			0.233089	+	0.972455i	$0.425117\pi$
$38$	26.1649	+	45.3189i	0.111698	+	0.193466i
$39$	247.094	+	211.907i	1.01453	+	0.870057i
$40$	0.734307	+	0.423952i	0.00290260	+	0.00167582i
$41$	−130.454	+	225.954i	−0.496916	+	0.860683i	−0.999994	−	0.00355783i	$-0.998868\pi$
$41$	−130.454	+	225.954i	−0.496916	+	0.860683i	0.503078	+	0.864241i	$0.332201\pi$
$42$	187.187	−	44.7774i	0.687704	−	0.164507i
$43$	−220.304	−	381.578i	−0.781304	−	1.35326i	−0.931183	−	0.364553i	$-0.881222\pi$
$43$	−220.304	−	381.578i	−0.781304	−	1.35326i	0.149879	−	0.988704i	$-0.452112\pi$
$44$			110.508i			0.378631i
$45$	2.23123	−	1.79188i	0.00739137	−	0.00593595i
$46$	190.440			0.610408
$47$	134.548	+	233.044i	0.417571	+	0.723255i	0.995695	−	0.0926947i	$-0.0295481\pi$
$47$	134.548	+	233.044i	0.417571	+	0.723255i	−0.578123	+	0.815949i	$0.696215\pi$
$48$	27.5932	+	78.4259i	0.0829737	+	0.235829i
$49$	335.676	+	70.5030i	0.978647	+	0.205548i
$50$	−216.487	−	124.989i	−0.612317	−	0.353522i
$51$	295.131	+	55.3184i	0.810324	+	0.151885i
$52$	−217.010	+	125.291i	−0.578728	+	0.334129i
$53$			26.5682i			0.0688571i	0.999407	+	0.0344286i	$0.0109611\pi$
$53$			26.5682i			0.0688571i	−0.999407	+	0.0344286i	$0.989039\pi$
$54$	280.446	+	9.05114i	0.706739	+	0.0228093i
$55$			2.92815i			0.00717875i
$56$	−15.3092	+	147.369i	−0.0365316	+	0.351661i
$57$	−25.0472	+	133.630i	−0.0582031	+	0.310521i
$58$	279.526	−	484.154i	0.632821	−	1.09608i
$59$	−97.1526	+	168.273i	−0.214376	+	0.371310i	−0.953079	−	0.302720i	$-0.902105\pi$
$59$	−97.1526	+	168.273i	−0.214376	+	0.371310i	0.738703	+	0.674031i	$0.235438\pi$
$60$	0.731138	+	2.07805i	0.00157316	+	0.00447125i
$61$	−418.447	+	241.591i	−0.878306	+	0.507090i	−0.870100	−	0.492876i	$-0.835946\pi$
$61$	−418.447	+	241.591i	−0.878306	+	0.507090i	−0.00820665	+	0.999966i	$0.502612\pi$
$62$	452.917			0.927750
$63$	444.897	+	228.284i	0.889710	+	0.456526i
$64$	−64.0000			−0.125000
$65$	−5.75012	+	3.31983i	−0.0109725	+	0.00633499i
$66$	−186.905	+	217.941i	−0.348582	+	0.406465i
$67$	225.761	−	391.029i	0.411658	−	0.713013i	−0.583413	−	0.812175i	$-0.698283\pi$
$67$	225.761	−	391.029i	0.411658	−	0.713013i	0.995071	+	0.0991629i	$0.0316165\pi$
$68$	−115.574	+	200.180i	−0.206109	+	0.356991i
$69$	375.579	+	322.094i	0.655281	+	0.561964i
$70$	−0.405647	+	3.90484i	−0.000692630	+	0.00666740i
$71$		−	979.780i		−	1.63773i	−0.573989	−	0.818863i	$-0.694605\pi$
$71$		−	979.780i		−	1.63773i	0.573989	−	0.818863i	$-0.305395\pi$
$72$	−78.2246	+	201.338i	−0.128040	+	0.329554i
$73$		−	30.5100i		−	0.0489167i	−0.999701	−	0.0244584i	$-0.992214\pi$
$73$		−	30.5100i		−	0.0489167i	0.999701	−	0.0244584i	$-0.00778612\pi$
$74$	−181.725	+	104.919i	−0.285474	+	0.164819i
$75$	−215.553	−	612.647i	−0.331865	−	0.943232i
$76$	−90.6379	−	52.3298i	−0.136801	−	0.0789821i
$77$	−467.174	+	208.676i	−0.691421	+	0.308842i
$78$	−639.887	−	119.939i	−0.928883	−	0.174107i
$79$	227.927	+	394.781i	0.324604	+	0.562231i	0.981432	−	0.191809i	$-0.0614355\pi$
$79$	227.927	+	394.781i	0.324604	+	0.562231i	−0.656828	+	0.754041i	$0.728102\pi$
$80$	−1.69581			−0.00236997
$81$	537.778	+	492.174i	0.737693	+	0.675136i
$82$		−	521.817i		−	0.702745i
$83$	−345.370	−	598.199i	−0.456738	−	0.791094i	0.542048	−	0.840348i	$-0.317649\pi$
$83$	−345.370	−	598.199i	−0.456738	−	0.791094i	−0.998786	+	0.0492534i	$0.984316\pi$
$84$	−279.440	+	264.744i	−0.362969	+	0.343880i
$85$	−3.06237	+	5.30418i	−0.00390777	+	0.00676845i
$86$	763.156	+	440.608i	0.956898	+	0.552465i
$87$	1370.13	−	482.065i	1.68843	−	0.594055i
$88$	−110.508	−	191.406i	−0.133866	−	0.231863i
$89$	145.080			0.172792			0.0863959	−	0.996261i	$-0.472465\pi$
$89$	145.080			0.172792			0.0863959	+	0.996261i	$0.472465\pi$
$90$	−2.07272	+	5.33485i	−0.00242760	+	0.00624825i
$91$	−939.452	−	680.819i	−1.08221	−	0.784278i
$92$	−329.851	+	190.440i	−0.373797	+	0.215812i
$93$	893.228	+	766.027i	0.995951	+	0.854121i
$94$	−466.088	−	269.096i	−0.511418	−	0.295268i
$95$	−2.40163	−	1.38658i	−0.00259371	−	0.00149748i
$96$	−126.219	−	108.244i	−0.134189	−	0.115080i
$97$	−909.610	+	525.164i	−0.952133	+	0.549714i	−0.893743	−	0.448580i	$-0.851930\pi$
$97$	−909.610	+	525.164i	−0.952133	+	0.549714i	−0.0583901	+	0.998294i	$0.518597\pi$
$98$	−651.911	+	213.561i	−0.671969	+	0.220132i
$99$	−737.216	+	113.701i	−0.748414	+	0.115428i
$100$	499.955			0.499955
$101$	−325.890	−	564.458i	−0.321062	−	0.556096i	0.659645	−	0.751577i	$-0.270707\pi$
$101$	−325.890	−	564.458i	−0.321062	−	0.556096i	−0.980707	+	0.195481i	$0.937373\pi$
$102$	−566.499	+	199.316i	−0.549920	+	0.193483i
$103$	1108.97	+	640.266i	1.06088	+	0.612498i	0.925675	−	0.378320i	$-0.123498\pi$
$103$	1108.97	+	640.266i	1.06088	+	0.612498i	0.135202	+	0.990818i	$0.456832\pi$
$104$	250.582	−	434.020i	0.236265	−	0.409223i
$105$	−7.40433	+	7.01492i	−0.00688180	+	0.00651987i
$106$	−26.5682	−	46.0175i	−0.0243447	−	0.0421662i
$107$		−	728.334i		−	0.658044i	−0.944322	−	0.329022i	$-0.893281\pi$
$107$		−	728.334i		−	0.658044i	0.944322	−	0.329022i	$-0.106719\pi$
$108$	−494.798	+	264.769i	−0.440852	+	0.235902i
$109$	−510.314			−0.448433			−0.224217	−	0.974539i	$-0.571982\pi$
$109$	−510.314			−0.448433			−0.224217	+	0.974539i	$0.571982\pi$
$110$	−2.92815	−	5.07170i	−0.00253807	−	0.00439607i
$111$	−535.844	−	100.437i	−0.458198	−	0.0858834i
$112$	−120.853	−	270.560i	−0.101960	−	0.228263i
$113$	−490.755	−	283.338i	−0.408552	−	0.235877i	0.281615	−	0.959527i	$-0.409130\pi$
$113$	−490.755	−	283.338i	−0.408552	−	0.235877i	−0.690167	+	0.723650i	$0.742463\pi$
$114$	−90.2467	−	256.501i	−0.0741437	−	0.210732i
$115$	−8.74007	+	5.04608i	−0.00708709	+	0.00409173i
$116$			1118.11i			0.894944i
$117$	−1059.11	−	1318.79i	−0.836878	−	1.04207i
$118$		−	388.610i		−	0.303174i
$119$	−1064.50	−	110.584i	−0.820023	−	0.0851866i
$120$	−3.34442	−	2.86815i	−0.00254419	−	0.00218188i
$121$	−283.871	+	491.679i	−0.213277	+	0.369406i
$122$	483.181	−	836.894i	0.358567	−	0.621056i
$123$	882.559	−	1029.11i	0.646973	−	0.754405i
$124$	−784.475	+	452.917i	−0.568129	+	0.328009i
$125$	26.4958			0.0189589
$126$	−998.868	+	49.4969i	−0.706240	+	0.0349963i
$127$	−2040.73			−1.42587			−0.712936	−	0.701230i	$-0.752635\pi$
$127$	−2040.73			−1.42587			−0.712936	+	0.701230i	$0.752635\pi$
$128$	110.851	−	64.0000i	0.0765466	−	0.0441942i
$129$	759.862	+	2159.69i	0.518621	+	1.47403i
$130$	6.63967	−	11.5002i	0.00447952	−	0.00775875i
$131$	−805.976	+	1395.99i	−0.537545	+	0.931056i	0.461490	+	0.887145i	$0.347315\pi$
$131$	−805.976	+	1395.99i	−0.537545	+	0.931056i	−0.999035	+	0.0439107i	$0.986018\pi$
$132$	105.788	−	564.390i	0.0697548	−	0.372150i
$133$	50.0703	−	481.987i	0.0326440	−	0.314237i
$134$			903.044i			0.582172i
$135$	−13.1107	+	7.01559i	−0.00835843	+	0.00447264i
$136$		−	462.296i		−	0.291482i
$137$	2066.57	−	1193.14i	1.28875	−	0.744062i	0.310322	−	0.950632i	$-0.399563\pi$
$137$	2066.57	−	1193.14i	1.28875	−	0.744062i	0.978432	+	0.206569i	$0.0662299\pi$
$138$	−972.615	−	182.304i	−0.599960	−	0.112455i
$139$	2284.83	+	1319.15i	1.39422	+	0.804955i	0.993779	−	0.111366i	$-0.0355227\pi$
$139$	2284.83	+	1319.15i	1.39422	+	0.804955i	0.400444	+	0.916321i	$0.368856\pi$
$140$	−3.20224	−	7.16903i	−0.00193313	−	0.00432781i
$141$	−464.077	−	1319.01i	−0.277180	−	0.787804i
$142$	979.780	+	1697.03i	0.579024	+	1.00290i
$143$	1730.71			1.01209
$144$	−65.8488	−	426.952i	−0.0381070	−	0.247079i
$145$			29.6265i			0.0169679i
$146$	30.5100	+	52.8448i	0.0172947	+	0.0299553i
$147$	−1646.88	−	681.410i	−0.924028	−	0.382325i
$148$	209.838	−	363.450i	0.116544	−	0.201861i
$149$	2958.63	+	1708.16i	1.62671	+	0.939183i	0.985065	+	0.172183i	$0.0550819\pi$
$149$	2958.63	+	1708.16i	1.62671	+	0.939183i	0.641647	+	0.767000i	$0.278251\pi$
$150$	985.995	+	845.583i	0.536708	+	0.460277i
$151$	1461.16	+	2530.79i	0.787464	+	1.36393i	0.927516	+	0.373784i	$0.121940\pi$
$151$	1461.16	+	2530.79i	0.787464	+	1.36393i	−0.140052	+	0.990144i	$0.544727\pi$
$152$	209.319			0.111698
$153$	−1454.34	−	565.046i	−0.768473	−	0.298570i
$154$	600.494	−	828.612i	0.314215	−	0.433581i
$155$	−20.7863	+	12.0010i	−0.0107716	+	0.00621897i
$156$	1228.25	−	432.147i	0.630379	−	0.221791i
$157$	−52.5605	−	30.3458i	−0.0267184	−	0.0154259i	0.486581	−	0.873635i	$-0.338244\pi$
$157$	−52.5605	−	30.3458i	−0.0267184	−	0.0154259i	−0.513300	+	0.858209i	$0.671577\pi$
$158$	−789.561	−	455.853i	−0.397558	−	0.229530i
$159$	25.4333	−	135.690i	0.0126855	−	0.0676785i
$160$	2.93723	−	1.69581i	0.00145130	−	0.000837909i
$161$	−1427.95	−	1034.83i	−0.698994	−	0.506560i
$162$	−1423.63	−	314.692i	−0.690440	−	0.152621i
$163$	531.838			0.255563			0.127782	−	0.991802i	$-0.459214\pi$
$163$	531.838			0.255563			0.127782	+	0.991802i	$0.459214\pi$
$164$	521.817	+	903.814i	0.248458	+	0.430342i
$165$	2.80306	−	14.9547i	0.00132253	−	0.00705587i
$166$	1196.40	+	690.740i	0.559388	+	0.322963i
$167$	1771.92	−	3069.05i	0.821048	−	1.42210i	−0.0838543	−	0.996478i	$-0.526723\pi$
$167$	1771.92	−	3069.05i	0.821048	−	1.42210i	0.904902	−	0.425619i	$-0.139944\pi$
$168$	219.261	−	737.990i	0.100692	−	0.338912i
$169$	863.723	+	1496.01i	0.393137	+	0.680934i
$170$		−	12.2495i		−	0.00552642i
$171$	255.842	−	658.498i	0.114414	−	0.294483i
$172$	−1762.43			−0.781304
$173$	−204.495	−	354.196i	−0.0898697	−	0.155659i	0.817586	−	0.575806i	$-0.195312\pi$
$173$	−204.495	−	354.196i	−0.0898697	−	0.155659i	−0.907456	+	0.420147i	$0.861978\pi$
$174$	−1891.07	+	2205.09i	−0.823918	+	0.960733i
$175$	944.078	+	2113.56i	0.407803	+	0.912971i
$176$	382.813	+	221.017i	0.163952	+	0.0946578i
$177$	657.263	−	766.404i	0.279113	−	0.325460i
$178$	−251.286	+	145.080i	−0.105813	+	0.0610912i
$179$		−	1059.19i		−	0.442277i	−0.975242	−	0.221138i	$-0.929023\pi$
$179$		−	1059.19i		−	0.442277i	0.975242	−	0.221138i	$-0.0709772\pi$
$180$	−1.74480	−	11.3130i	−0.000722497	−	0.00468454i
$181$			2444.36i			1.00380i	0.864925	+	0.501901i	$0.167366\pi$
$181$			2444.36i			1.00380i	−0.864925	+	0.501901i	$0.832634\pi$
$182$	2308.00	+	239.762i	0.940001	+	0.0976502i
$183$	2368.37	−	833.283i	0.956693	−	0.336601i
$184$	380.879	−	659.702i	0.152602	−	0.264315i
$185$	5.56008	−	9.63034i	0.00220965	−	0.00382723i
$186$	−2313.14	−	433.569i	−0.911870	−	0.170918i
$187$	1382.60	−	798.244i	0.540672	−	0.312157i
$188$	1076.38			0.417571
$189$	−2053.65	−	1591.79i	−0.790376	−	0.612622i
$190$	5.54633			0.00211775
$191$	−73.4496	+	42.4061i	−0.0278253	+	0.0160649i	−0.513848	−	0.857881i	$-0.671781\pi$
$191$	−73.4496	+	42.4061i	−0.0278253	+	0.0160649i	0.486023	+	0.873946i	$0.338447\pi$
$192$	326.862	+	61.2660i	0.122860	+	0.0230286i
$193$	811.987	−	1406.40i	0.302840	−	0.524534i	−0.673938	−	0.738788i	$-0.735399\pi$
$193$	811.987	−	1406.40i	0.302840	−	0.524534i	0.976778	+	0.214254i	$0.0687319\pi$
$194$	1050.33	−	1819.22i	0.388707	−	0.673260i
$195$	32.5451	−	11.4506i	0.0119518	−	0.00420510i
$196$	915.581	−	1021.81i	0.333667	−	0.372380i
$197$			1466.26i			0.530286i	0.964209	+	0.265143i	$0.0854192\pi$
$197$			1466.26i			0.530286i	−0.964209	+	0.265143i	$0.914581\pi$
$198$	1163.19	−	934.151i	0.417498	−	0.335289i
$199$		−	3755.85i		−	1.33791i	−0.743301	−	0.668957i	$-0.766741\pi$
$199$		−	3755.85i		−	1.33791i	0.743301	−	0.668957i	$-0.233259\pi$
$200$	−865.948	+	499.955i	−0.306159	+	0.176761i
$201$	−1527.33	+	1780.95i	−0.535969	+	0.624969i
$202$	1128.92	+	651.780i	0.393219	+	0.227025i
$203$	−4726.79	+	2111.35i	−1.63426	+	0.729988i
$204$	781.890	−	911.725i	0.268349	−	0.312910i
$205$	13.8266	+	23.9484i	0.00471069	+	0.00815916i
$206$	−2561.06			−0.866203
$207$	−1609.83	−	2004.54i	−0.540534	−	0.673067i
$208$			1002.33i			0.334129i
$209$	361.430	+	626.016i	0.119620	+	0.207189i
$210$	5.80975	−	19.5545i	0.00190910	−	0.00642567i
$211$	−634.606	+	1099.17i	−0.207052	+	0.358625i	−0.950785	−	0.309852i	$-0.899720\pi$
$211$	−634.606	+	1099.17i	−0.207052	+	0.358625i	0.743732	+	0.668478i	$0.233054\pi$
$212$	92.0351	+	53.1365i	0.0298160	+	0.0172143i
$213$	−937.925	+	5003.95i	−0.301716	+	1.60969i
$214$	728.334	+	1261.51i	0.232654	+	0.402968i
$215$	−46.6992			−0.0148133
$216$	592.246	−	953.392i	0.186561	−	0.300325i
$217$	−3396.05	−	2461.11i	−1.06239	−	0.769913i
$218$	883.890	−	510.314i	0.274608	−	0.158545i
$219$	−29.2066	+	155.821i	−0.00901188	+	0.0480795i
$220$	10.1434	+	5.85629i	0.00310849	+	0.00179469i
$221$	3135.09	+	1810.05i	0.954249	+	0.550936i
$222$	1028.55	−	361.882i	0.310952	−	0.109405i
$223$	−3044.57	+	1757.78i	−0.914258	+	0.527847i	−0.881799	−	0.471626i	$-0.843667\pi$
$223$	−3044.57	+	1757.78i	−0.914258	+	0.527847i	−0.0324596	+	0.999473i	$0.510334\pi$
$224$	479.883	+	347.771i	0.143141	+	0.103734i
$225$	514.398	+	3335.26i	0.152414	+	0.988226i
$226$	1133.35			0.333581
$227$	−2544.16	−	4406.61i	−0.743883	−	1.28844i	−0.950715	−	0.310067i	$-0.899648\pi$
$227$	−2544.16	−	4406.61i	−0.743883	−	1.28844i	0.206831	−	0.978377i	$-0.433685\pi$
$228$	412.812	+	354.025i	0.119909	+	0.102833i
$229$	1596.14	+	921.533i	0.460594	+	0.265924i	0.712294	−	0.701881i	$-0.247656\pi$
$229$	1596.14	+	921.533i	0.460594	+	0.265924i	−0.251700	+	0.967805i	$0.580990\pi$
$230$	10.0922	−	17.4801i	0.00289329	−	0.00501133i
$231$	2585.72	−	618.535i	0.736484	−	0.176176i
$232$	−1118.11	−	1936.62i	−0.316410	−	0.548039i
$233$			773.821i			0.217574i	0.994065	+	0.108787i	$0.0346966\pi$
$233$			773.821i			0.217574i	−0.994065	+	0.108787i	$0.965303\pi$
$234$	3153.22	+	1225.10i	0.880908	+	0.342254i
$235$	28.5210			0.00791704
$236$	388.610	+	673.093i	0.107188	+	0.185655i
$237$	−786.154	−	2234.42i	−0.215469	−	0.612409i
$238$	1954.36	−	872.965i	0.532277	−	0.237756i
$239$	565.317	+	326.386i	0.153001	+	0.0883354i	0.574546	−	0.818472i	$-0.305179\pi$
$239$	565.317	+	326.386i	0.153001	+	0.0883354i	−0.421545	+	0.906808i	$0.638512\pi$
$240$	8.66086	+	1.62337i	0.00232940	+	0.000436616i
$241$	−5603.99	+	3235.47i	−1.49786	+	0.864791i	−0.999997	−	0.00246268i	$-0.999216\pi$
$241$	−5603.99	+	3235.47i	−1.49786	+	0.864791i	−0.497866	+	0.867254i	$0.665883\pi$
$242$		−	1135.48i		−	0.301619i
$243$	−2275.40	−	3028.44i	−0.600687	−	0.799484i
$244$			1932.73i			0.507090i
$245$	24.2602	−	27.0749i	0.00632623	−	0.00706021i
$246$	−499.526	+	2665.03i	−0.129466	+	0.690716i
$247$	−819.555	+	1419.51i	−0.211122	+	0.365673i
$248$	905.834	−	1568.95i	0.231938	−	0.401728i
$249$	1191.23	+	3385.74i	0.303178	+	0.861698i
$250$	−45.8921	+	26.4958i	−0.0116099	+	0.00670297i
$251$	4534.20			1.14022			0.570112	−	0.821567i	$-0.306900\pi$
$251$	4534.20			1.14022			0.570112	+	0.821567i	$0.306900\pi$
$252$	1680.59	−	1084.60i	0.420109	−	0.271124i
$253$	2630.65			0.653705
$254$	3534.65	−	2040.73i	0.873164	−	0.504122i
$255$	20.7177	−	24.1580i	0.00508783	−	0.00593268i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	759.262	−	1315.08i	0.184286	−	0.319193i	−0.759050	−	0.651033i	$-0.774336\pi$
$257$	759.262	−	1315.08i	0.184286	−	0.319193i	0.943336	+	0.331840i	$0.107669\pi$
$258$	−3475.81	−	2980.83i	−0.838739	−	0.719297i
$259$	1932.73	+	200.778i	0.463682	+	0.0481688i
$260$			26.5587i			0.00633499i
$261$	−7459.02	+	1150.41i	−1.76897	+	0.272829i
$262$		−	3223.90i		−	0.760204i
$263$	−2083.69	+	1203.02i	−0.488539	+	0.282058i	−0.723968	−	0.689833i	$-0.757684\pi$
$263$	−2083.69	+	1203.02i	−0.488539	+	0.282058i	0.235429	+	0.971892i	$0.424351\pi$
$264$	381.161	+	1083.34i	0.0888591	+	0.252557i
$265$	2.43866	+	1.40796i	0.000565303	+	0.000326378i
$266$	395.263	+	884.896i	0.0911094	+	0.203972i
$267$	−740.956	−	138.883i	−0.169834	−	0.0318332i
$268$	−903.044	−	1564.12i	−0.205829	−	0.356506i
$269$	−4599.13			−1.04243			−0.521215	−	0.853425i	$-0.674521\pi$
$269$	−4599.13			−1.04243			−0.521215	+	0.853425i	$0.674521\pi$
$270$	15.6928	−	25.2620i	0.00353715	−	0.00569407i
$271$		−	1561.46i		−	0.350007i	−0.984568	−	0.175004i	$-0.944006\pi$
$271$		−	1561.46i		−	0.350007i	0.984568	−	0.175004i	$-0.0559937\pi$
$272$	462.296	+	800.720i	0.103054	+	0.178496i
$273$	4146.24	+	4376.41i	0.919202	+	0.970228i
$274$	−2386.27	+	4133.15i	−0.526131	+	0.911286i
$275$	−2990.45	−	1726.54i	−0.655750	−	0.378597i
$276$	1866.92	−	656.855i	0.407158	−	0.143254i
$277$	−1892.14	−	3277.28i	−0.410425	−	0.710877i	0.584511	−	0.811386i	$-0.301286\pi$
$277$	−1892.14	−	3277.28i	−0.410425	−	0.710877i	−0.994936	+	0.100509i	$0.967953\pi$
$278$	−5276.60			−1.13838
$279$	−3828.60	−	4767.33i	−0.821550	−	1.02298i
$280$	12.7155	+	9.21488i	0.00271391	+	0.00196677i
$281$	2647.14	−	1528.33i	0.561976	−	0.324457i	−0.191962	−	0.981402i	$-0.561485\pi$
$281$	2647.14	−	1528.33i	0.561976	−	0.324457i	0.753938	+	0.656945i	$0.228152\pi$
$282$	2122.81	+	1820.51i	0.448268	+	0.384432i
$283$	−4426.01	−	2555.36i	−0.929679	−	0.536751i	−0.0429692	−	0.999076i	$-0.513682\pi$
$283$	−4426.01	−	2555.36i	−0.929679	−	0.536751i	−0.886710	+	0.462326i	$0.847015\pi$
$284$	−3394.06	−	1959.56i	−0.709156	−	0.409431i
$285$	10.9383	+	9.38061i	0.00227343	+	0.00194968i
$286$	−2997.68	+	1730.71i	−0.619778	+	0.357829i
$287$	−2835.51	+	3912.68i	−0.583188	+	0.804731i
$288$	541.005	+	673.654i	0.110691	+	0.137831i
$289$	−1573.66			−0.320305
$290$	−29.6265	−	51.3145i	−0.00599906	−	0.0103907i
$291$	5148.30	−	1811.37i	1.03711	−	0.364895i
$292$	−105.690	−	61.0199i	−0.0211816	−	0.0122292i
$293$	4773.71	−	8268.31i	0.951820	−	1.64860i	0.210336	−	0.977629i	$-0.432544\pi$
$293$	4773.71	−	8268.31i	0.951820	−	1.64860i	0.741483	−	0.670971i	$-0.234123\pi$
$294$	3533.88	−	466.640i	0.701022	−	0.0925681i
$295$	10.2970	+	17.8350i	0.00203226	+	0.00351997i
$296$			839.352i			0.164819i
$297$	3873.96	+	125.028i	0.756869	+	0.0244272i
$298$	−6832.65			−1.32820
$299$	2982.54	+	5165.91i	0.576872	+	0.999172i
$300$	−2553.38	−	478.598i	−0.491398	−	0.0921061i
$301$	−3328.05	−	7450.68i	−0.637294	−	1.42674i
$302$	−5061.59	−	2922.31i	−0.964443	−	0.556821i
$303$	1124.04	+	3194.78i	0.213118	+	0.605726i
$304$	−362.551	+	209.319i	−0.0684005	+	0.0394910i
$305$			51.2115i			0.00961429i
$306$	3084.03	−	475.651i	0.576152	−	0.0888600i
$307$			5529.49i			1.02796i	0.857801	+	0.513982i	$0.171830\pi$
$307$			5529.49i			1.02796i	−0.857801	+	0.513982i	$0.828170\pi$
$308$	−211.474	+	2035.69i	−0.0391229	+	0.376605i
$309$	−5050.85	−	4331.57i	−0.929879	−	0.797458i
$310$	24.0019	−	41.5725i	0.00439747	−	0.00761665i
$311$	−3904.12	+	6762.14i	−0.711841	+	1.23294i	0.252324	+	0.967643i	$0.418805\pi$
$311$	−3904.12	+	6762.14i	−0.711841	+	1.23294i	−0.964165	+	0.265302i	$0.914528\pi$
$312$	−1695.25	+	1976.76i	−0.307611	+	0.358691i
$313$	5410.84	−	3123.95i	0.977121	−	0.564141i	0.0757212	−	0.997129i	$-0.475874\pi$
$313$	5410.84	−	3123.95i	0.977121	−	0.564141i	0.901400	+	0.432988i	$0.142541\pi$
$314$	121.383			0.0218155
$315$	44.5307	−	28.7387i	0.00796515	−	0.00514044i
$316$	1823.41			0.324604
$317$	−9757.23	+	5633.34i	−1.72877	+	0.998107i	−0.833638	+	0.552311i	$0.813746\pi$
$317$	−9757.23	+	5633.34i	−1.72877	+	0.998107i	−0.895135	+	0.445796i	$0.852921\pi$
$318$	91.6379	+	260.455i	0.0161597	+	0.0459295i
$319$	3861.25	−	6687.89i	0.677708	−	1.17382i
$320$	−3.39162	+	5.87446i	−0.000592491	+	0.00102623i
$321$	−697.221	+	3719.76i	−0.121231	+	0.646781i
$322$	3508.11	+	364.434i	0.607141	+	0.0630717i
$323$			1511.99i			0.260463i
$324$	2780.50	−	878.571i	0.476766	−	0.150647i
$325$		−	7829.97i		−	1.33640i
$326$	−921.171	+	531.838i	−0.156500	+	0.0903552i
$327$	2606.28	+	488.514i	0.440757	+	0.0826143i
$328$	−1807.63	−	1043.63i	−0.304297	−	0.175686i
$329$	2032.56	+	4550.41i	0.340604	+	0.762530i
$330$	10.0996	+	28.7053i	0.00168474	+	0.00478841i
$331$	−2869.46	−	4970.05i	−0.476495	−	0.825313i	0.523143	−	0.852245i	$-0.324759\pi$
$331$	−2869.46	−	4970.05i	−0.476495	−	0.825313i	−0.999637	+	0.0269322i	$0.991426\pi$
$332$	−2762.96			−0.456738
$333$	2640.52	+	1025.91i	0.434533	+	0.168827i
$334$			7087.67i			1.16114i
$335$	−23.9280	−	41.4445i	−0.00390246	−	0.00675926i
$336$	358.219	+	1497.50i	0.0581621	+	0.243140i
$337$	5241.11	−	9077.86i	0.847185	−	1.46737i	−0.0365251	−	0.999333i	$-0.511629\pi$
$337$	5241.11	−	9077.86i	0.847185	−	1.46737i	0.883710	−	0.468035i	$-0.155038\pi$
$338$	−2992.02	−	1727.45i	−0.481493	−	0.277990i
$339$	2235.16	+	1916.86i	0.358103	+	0.307107i
$340$	12.2495	+	21.2167i	0.00195388	+	0.00338423i
$341$	6256.40			0.993557
$342$	215.366	+	1396.39i	0.0340516	+	0.220785i
$343$	6048.61	+	1941.11i	0.952170	+	0.305569i
$344$	3052.62	−	1762.43i	0.478449	−	0.276233i
$345$	49.4679	−	17.4047i	0.00771960	−	0.00271605i
$346$	708.391	+	408.990i	0.110068	+	0.0635475i
$347$	−944.577	−	545.352i	−0.146131	−	0.0843689i	0.425152	−	0.905122i	$-0.360221\pi$
$347$	−944.577	−	545.352i	−0.146131	−	0.0843689i	−0.571283	+	0.820753i	$0.693554\pi$
$348$	1070.34	−	5710.40i	0.164874	−	0.879626i
$349$	−7479.89	+	4318.52i	−1.14725	+	0.662363i	−0.948215	−	0.317629i	$-0.897113\pi$
$349$	−7479.89	+	4318.52i	−1.14725	+	0.662363i	−0.199032	+	0.979993i	$0.563780\pi$
$350$	−3748.75	−	2716.71i	−0.572512	−	0.414898i
$351$	4146.64	+	7749.21i	0.630574	+	1.17841i
$352$	−884.068			−0.133866
$353$	5002.96	+	8665.38i	0.754336	+	1.30655i	0.945704	+	0.325030i	$0.105375\pi$
$353$	5002.96	+	8665.38i	0.754336	+	1.30655i	−0.191367	+	0.981519i	$0.561292\pi$
$354$	−372.009	+	1984.71i	−0.0558533	+	0.297984i
$355$	−89.9324	−	51.9225i	−0.0134454	−	0.00776271i
$356$	290.161	−	502.573i	0.0431980	−	0.0748211i
$357$	5330.78	+	1583.80i	0.790293	+	0.234800i
$358$	1059.19	+	1834.57i	0.156368	+	0.270838i
$359$		−	8795.27i		−	1.29303i	−0.762903	−	0.646513i	$-0.776227\pi$
$359$		−	8795.27i		−	1.29303i	0.762903	−	0.646513i	$-0.223773\pi$
$360$	14.3350	+	17.8498i	0.00209867	+	0.00261324i
$361$	6174.40			0.900189
$362$	−2444.36	−	4233.76i	−0.354897	−	0.614700i
$363$	1920.47	−	2239.37i	0.277681	−	0.323791i
$364$	−4237.33	+	1892.72i	−0.610155	+	0.272542i
$365$	−2.80046	−	1.61685i	−0.000401597	−	0.000231862i
$366$	−3268.85	+	3811.66i	−0.466846	+	0.544368i
$367$	10914.1	−	6301.27i	1.55235	−	0.896250i	0.554401	−	0.832250i	$-0.312948\pi$
$367$	10914.1	−	6301.27i	1.55235	−	0.896250i	0.997950	−	0.0640002i	$-0.0203858\pi$
$368$			1523.52i			0.215812i
$369$	−5492.56	+	4411.03i	−0.774882	+	0.622301i
$370$			22.2403i			0.00312492i
$371$	−50.8422	+	489.417i	−0.00711481	+	0.0684886i
$372$	4440.05	−	1562.18i	0.618833	−	0.217729i
$373$	−62.7756	+	108.731i	−0.00871421	+	0.0150934i	−0.870350	−	0.492434i	$-0.836107\pi$
$373$	−62.7756	+	108.731i	−0.00871421	+	0.0150934i	0.861635	+	0.507528i	$0.169441\pi$
$374$	−1596.49	+	2765.20i	−0.220729	+	0.382313i
$375$	−135.320	−	25.3640i	−0.0186344	−	0.00349277i
$376$	−1864.35	+	1076.38i	−0.255709	+	0.147634i
$377$	17511.0			2.39221
$378$	5148.81	+	703.407i	0.700599	+	0.0957125i
$379$	8392.50			1.13745			0.568725	−	0.822528i	$-0.307437\pi$
$379$	8392.50			1.13745			0.568725	+	0.822528i	$0.307437\pi$
$380$	−9.60653	+	5.54633i	−0.00129685	+	0.000748739i
$381$	10422.4	+	1953.55i	1.40147	+	0.262687i
$382$	84.8123	−	146.899i	0.0113596	−	0.0196754i
$383$	−4651.08	+	8055.90i	−0.620519	+	1.07477i	0.368870	+	0.929481i	$0.379745\pi$
$383$	−4651.08	+	8055.90i	−0.620519	+	1.07477i	−0.989389	+	0.145290i	$0.953589\pi$
$384$	−627.407	+	220.746i	−0.0833782	+	0.0293356i
$385$	−5.60343	+	53.9397i	−0.000741759	+	0.00714032i
$386$			3247.95i			0.428281i
$387$	−1813.35	−	11757.4i	−0.238185	−	1.54435i
$388$			4201.31i			0.549714i
$389$	−1975.23	+	1140.40i	−0.257450	+	0.148639i	−0.623171	−	0.782086i	$-0.714156\pi$
$389$	−1975.23	+	1140.40i	−0.257450	+	0.148639i	0.365721	+	0.930725i	$0.380822\pi$
$390$	−44.9191	+	52.3781i	−0.00583223	+	0.00680069i
$391$	4765.28	+	2751.23i	0.616344	+	0.355846i
$392$	−564.024	+	2685.41i	−0.0726722	+	0.346004i
$393$	5452.65	−	6358.08i	0.699872	−	0.816088i
$394$	−1466.26	−	2539.63i	−0.187484	−	0.324733i
$395$	48.3150			0.00615441
$396$	−1080.56	+	2781.19i	−0.137122	+	0.352930i
$397$		−	4521.52i		−	0.571609i	−0.958288	−	0.285804i	$-0.907739\pi$
$397$		−	4521.52i		−	0.571609i	0.958288	−	0.285804i	$-0.0922607\pi$
$398$	3755.85	+	6505.32i	0.473024	+	0.819301i
$399$	−717.117	+	2413.68i	−0.0899768	+	0.302845i
$400$	999.910	−	1731.90i	0.124989	−	0.216487i
$401$	−2371.11	−	1368.96i	−0.295280	−	0.170480i	0.345040	−	0.938588i	$-0.387865\pi$
$401$	−2371.11	−	1368.96i	−0.295280	−	0.170480i	−0.640321	+	0.768108i	$0.721199\pi$
$402$	864.467	−	4612.04i	0.107253	−	0.572207i
$403$	7093.29	+	12285.9i	0.876779	+	1.51863i
$404$	−2607.12			−0.321062
$405$	73.6749	−	23.2795i	0.00903935	−	0.00285622i
$406$	6075.69	−	8383.75i	0.742688	−	1.02482i
$407$	−2510.27	+	1449.30i	−0.305723	+	0.176510i
$408$	−442.547	+	2361.04i	−0.0536994	+	0.286493i
$409$	−2983.94	−	1722.78i	−0.360749	−	0.208279i	0.308660	−	0.951172i	$-0.400119\pi$
$409$	−2983.94	−	1722.78i	−0.360749	−	0.208279i	−0.669409	+	0.742894i	$0.733453\pi$
$410$	−47.8968	−	27.6532i	−0.00576940	−	0.00333096i
$411$	−11696.6	+	4115.31i	−1.40377	+	0.493901i
$412$	4435.89	−	2561.06i	0.530439	−	0.306249i
$413$	−2111.67	+	2913.87i	−0.251595	+	0.347172i
$414$	4792.83	+	1862.13i	0.568973	+	0.221060i
$415$	−73.2102			−0.00865964
$416$	−1002.33	−	1736.08i	−0.118132	−	0.204611i
$417$	−10406.3	−	8924.40i	−1.22206	−	1.04803i
$418$	−1252.03	−	722.861i	−0.146504	−	0.0845844i
$419$	−1338.66	+	2318.63i	−0.156081	+	0.270340i	−0.933452	−	0.358702i	$-0.883219\pi$
$419$	−1338.66	+	2318.63i	−0.156081	+	0.270340i	0.777371	+	0.629042i	$0.216553\pi$
$420$	9.49174	+	39.6792i	0.00110274	+	0.00460987i
$421$	−4514.06	−	7818.58i	−0.522569	−	0.905117i	−0.999655	−	0.0262599i	$-0.991640\pi$
$421$	−4514.06	−	7818.58i	−0.522569	−	0.905117i	0.477086	−	0.878857i	$-0.341693\pi$
$422$		−	2538.42i		−	0.292816i
$423$	1107.48	+	7180.69i	0.127299	+	0.825384i
$424$	−212.546			−0.0243447
$425$	−3611.36	−	6255.07i	−0.412181	−	0.713918i
$426$	−3379.41	−	9605.01i	−0.384350	−	1.09240i
$427$	−8170.59	+	3649.61i	−0.926001	+	0.413623i
$428$	−2523.02	−	1456.67i	−0.284942	−	0.164511i
$429$	−8839.11	−	1656.78i	−0.994770	−	0.186457i
$430$	80.8854	−	46.6992i	0.00907126	−	0.00523729i
$431$		−	3809.70i		−	0.425770i	−0.977077	−	0.212885i	$-0.931714\pi$
$431$		−	3809.70i		−	0.425770i	0.977077	−	0.212885i	$-0.0682860\pi$
$432$	−72.4091	+	2243.57i	−0.00806432	+	0.249870i
$433$			17496.4i			1.94186i	0.239368	+	0.970929i	$0.423060\pi$
$433$			17496.4i			1.94186i	−0.239368	+	0.970929i	$0.576940\pi$
$434$	8343.24	+	866.722i	0.922785	+	0.0958617i
$435$	28.3609	−	151.309i	0.00312597	−	0.0166775i
$436$	−1020.63	+	1767.78i	−0.112108	+	0.194177i
$437$	−1245.71	+	2157.63i	−0.136362	+	0.236186i
$438$	−105.234	−	299.096i	−0.0114800	−	0.0326287i
$439$	−5479.77	+	3163.74i	−0.595752	+	0.343957i	−0.767368	−	0.641206i	$-0.778434\pi$
$439$	−5479.77	+	3163.74i	−0.595752	+	0.343957i	0.171617	+	0.985164i	$0.445101\pi$
$440$	−23.4252			−0.00253807
$441$	7758.65	+	5056.63i	0.837777	+	0.546013i
$442$	−7240.18			−0.779141
$443$	−11126.9	+	6424.11i	−1.19335	+	0.688981i	−0.959065	−	0.283186i	$-0.908609\pi$
$443$	−11126.9	+	6424.11i	−1.19335	+	0.688981i	−0.234286	+	0.972168i	$0.575275\pi$
$444$	−1419.61	+	1655.34i	−0.151738	+	0.176935i
$445$	7.68839	−	13.3167i	0.000819022	−	0.00141859i
$446$	3515.57	−	6089.14i	0.373244	−	0.646478i
$447$	−13475.1	−	11556.2i	−1.42584	−	1.22279i
$448$	−1178.95	−	122.473i	−0.124331	−	0.0129159i
$449$			5935.77i			0.623889i	0.950100	+	0.311945i	$0.100980\pi$
$449$			5935.77i			0.623889i	−0.950100	+	0.311945i	$0.899020\pi$
$450$	−4226.22	−	5262.45i	−0.442725	−	0.551276i
$451$		−	7208.15i		−	0.752591i
$452$	−1963.02	+	1133.35i	−0.204276	+	0.117939i
$453$	−5039.75	−	14324.0i	−0.522711	−	1.48566i
$454$	8813.21	+	5088.31i	0.911067	+	0.526005i
$455$	−112.277	+	50.1514i	−0.0115684	+	0.00516733i
$456$	−1069.04	−	200.377i	−0.109786	−	0.0205779i
$457$	−5766.42	−	9987.73i	−0.590244	−	1.02233i	−0.994199	−	0.107554i	$-0.965698\pi$
$457$	−5766.42	−	9987.73i	−0.590244	−	1.02233i	0.403955	−	0.914779i	$-0.367635\pi$
$458$	−3686.13			−0.376073
$459$	6886.71	+	4278.02i	0.700314	+	0.435035i
$460$			40.3686i			0.00409173i
$461$	−8023.59	−	13897.3i	−0.810620	−	1.40403i	−0.912431	−	0.409231i	$-0.865797\pi$
$461$	−8023.59	−	13897.3i	−0.810620	−	1.40403i	0.101811	−	0.994804i	$-0.467536\pi$
$462$	−3860.06	+	3657.05i	−0.388715	+	0.368272i
$463$	−8017.99	+	13887.6i	−0.804811	+	1.39397i	0.111608	+	0.993752i	$0.464400\pi$
$463$	−8017.99	+	13887.6i	−0.804811	+	1.39397i	−0.916419	+	0.400221i	$0.868933\pi$
$464$	3873.23	+	2236.21i	0.387522	+	0.223736i
$465$	117.648	−	41.3931i	0.0117329	−	0.00412809i
$466$	−773.821	−	1340.30i	−0.0769240	−	0.133236i
$467$	10470.0			1.03746			0.518732	−	0.854937i	$-0.326404\pi$
$467$	10470.0			1.03746			0.518732	+	0.854937i	$0.326404\pi$
$468$	−6686.64	+	1031.28i	−0.660449	+	0.101861i
$469$	4907.06	−	6771.18i	0.483128	−	0.666661i
$470$	−49.3998	+	28.5210i	−0.00484818	+	0.00279910i
$471$	239.388	+	205.298i	0.0234191	+	0.0200841i
$472$	−1346.19	−	777.221i	−0.131278	−	0.0757934i
$473$	10541.9	+	6086.37i	1.02477	+	0.591652i
$474$	3596.08	+	3083.97i	0.348467	+	0.298843i
$475$	2832.18	−	1635.16i	0.273577	−	0.157950i
$476$	−2512.08	+	3466.38i	−0.241893	+	0.333784i
$477$	−259.786	+	668.649i	−0.0249367	+	0.0641831i
$478$	−1305.54			−0.124925
$479$	−2452.35	−	4247.60i	−0.233926	−	0.405173i	0.725034	−	0.688713i	$-0.241824\pi$
$479$	−2452.35	−	4247.60i	−0.233926	−	0.405173i	−0.958960	+	0.283541i	$0.908491\pi$
$480$	−16.6244	+	5.84910i	−0.00158083	+	0.000556196i
$481$	−5692.12	−	3286.35i	−0.539581	−	0.311527i
$482$	6470.93	−	11208.0i	0.611500	−	1.05915i
$483$	6302.21	+	6652.06i	0.593707	+	0.626665i
$484$	1135.48	+	1966.72i	0.106638	+	0.184703i
$485$			111.322i			0.0104224i
$486$	6969.55	+	2970.02i	0.650505	+	0.277207i
$487$	−14780.0			−1.37525			−0.687626	−	0.726065i	$-0.741347\pi$
$487$	−14780.0			−1.37525			−0.687626	+	0.726065i	$0.741347\pi$
$488$	−1932.73	−	3347.58i	−0.179284	−	0.310528i
$489$	−2716.21	−	509.119i	−0.251189	−	0.0470821i
$490$	−14.9450	+	71.1553i	−0.00137785	+	0.00656014i
$491$	4802.48	+	2772.71i	0.441411	+	0.254849i	0.704196	−	0.710006i	$-0.251308\pi$
$491$	4802.48	+	2772.71i	0.441411	+	0.254849i	−0.262785	+	0.964854i	$0.584641\pi$
$492$	−1799.83	−	5115.50i	−0.164924	−	0.468749i
$493$	13988.9	−	8076.50i	1.27795	−	0.737824i
$494$		−	3278.22i		−	0.298571i
$495$	−28.6316	+	73.6933i	−0.00259979	+	0.00669145i
$496$			3623.34i			0.328009i
$497$	1874.95	−	18048.7i	0.169221	−	1.62896i
$498$	−5449.02	−	4673.04i	−0.490314	−	0.420490i
$499$	−6164.44	+	10677.1i	−0.553023	+	0.957864i	0.445031	+	0.895515i	$0.353192\pi$
$499$	−6164.44	+	10677.1i	−0.553023	+	0.957864i	−0.998054	+	0.0623489i	$0.980141\pi$
$500$	52.9917	−	91.7842i	0.00473972	−	0.00820943i
$501$	−11987.5	+	13978.1i	−1.06899	+	1.24649i
$502$	−7853.47	+	4534.20i	−0.698242	+	0.403130i
$503$	−3637.12			−0.322408			−0.161204	−	0.986921i	$-0.551538\pi$
$503$	−3637.12			−0.322408			−0.161204	+	0.986921i	$0.551538\pi$
$504$	−1826.27	+	3559.18i	−0.161406	+	0.314560i
$505$	−69.0809			−0.00608725
$506$	−4556.42	+	2630.65i	−0.400311	+	0.231120i
$507$	−2979.11	−	8467.28i	−0.260961	−	0.741706i
$508$	−4081.46	+	7069.30i	−0.356468	+	0.617420i
$509$	6502.24	−	11262.2i	0.566222	−	0.980724i	−0.430713	−	0.902489i	$-0.641738\pi$
$509$	6502.24	−	11262.2i	0.566222	−	0.980724i	0.996935	−	0.0782357i	$-0.0249287\pi$
$510$	−11.7262	+	62.5606i	−0.00101813	+	0.00543183i
$511$	58.3852	−	562.028i	0.00505442	−	0.0486549i
$512$		−	512.000i		−	0.0441942i
$513$	−1937.01	+	3118.18i	−0.166708	+	0.268364i
$514$			3037.05i			0.260620i
$515$	117.538	−	67.8605i	0.0100570	−	0.00580639i
$516$	9001.12	+	1687.14i	0.767930	+	0.143939i
$517$	−6438.34	−	3717.18i	−0.547694	−	0.316211i
$518$	−3548.36	+	1584.97i	−0.300977	+	0.134439i
$519$	705.334	+	2004.71i	0.0596546	+	0.169551i
$520$	−26.5587	−	46.0010i	−0.00223976	−	0.00387938i
$521$	−7949.85			−0.668502			−0.334251	−	0.942484i	$-0.608483\pi$
$521$	−7949.85			−0.668502			−0.334251	+	0.942484i	$0.608483\pi$
$522$	11769.0	−	9451.58i	0.986810	−	0.792499i
$523$			8571.76i			0.716667i	0.933594	+	0.358333i	$0.116655\pi$
$523$			8571.76i			0.716667i	−0.933594	+	0.358333i	$0.883345\pi$
$524$	3223.90	+	5583.97i	0.268773	+	0.465528i
$525$	−2798.33	−	11698.1i	−0.232627	−	0.972474i
$526$	2406.04	−	4167.38i	0.199445	−	0.345449i
$527$	11333.1	+	6543.18i	0.936771	+	0.540845i
$528$	−1743.53	−	1495.24i	−0.143707	−	0.123242i
$529$	−1550.10	−	2684.85i	−0.127402	−	0.220666i
$530$	−5.63183			−0.000461568
$531$	−4090.45	+	3285.00i	−0.334294	+	0.268469i
$532$	−1569.51	−	1137.42i	−0.127908	−	0.0926946i
$533$	14154.9	−	8172.36i	1.15032	−	0.664136i
$534$	1422.26	−	500.404i	0.115257	−	0.0405517i
$535$	−66.8526	−	38.5974i	−0.00540241	−	0.00311908i
$536$	3128.23	+	1806.09i	0.252088	+	0.145543i
$537$	−1013.94	+	5409.50i	−0.0814801	+	0.434706i
$538$	7965.92	−	4599.13i	0.638356	−	0.368555i
$539$	−9005.21	+	2950.04i	−0.719632	+	0.235746i
$540$	−1.91863	+	59.4479i	−0.000152897	+	0.00473746i
$541$	483.281			0.0384064			0.0192032	−	0.999816i	$-0.493887\pi$
$541$	483.281			0.0384064			0.0192032	+	0.999816i	$0.493887\pi$
$542$	1561.46	+	2704.53i	0.123746	+	0.214335i
$543$	2339.94	−	12483.9i	0.184929	−	0.986620i
$544$	−1601.44	−	924.592i	−0.126215	−	0.0728705i
$545$	−27.0436	+	46.8409i	−0.00212554	+	0.00368155i
$546$	−11557.9	−	3433.92i	−0.905921	−	0.269154i
$547$	7211.94	+	12491.5i	0.563730	+	0.976409i	0.997167	+	0.0752251i	$0.0239675\pi$
$547$	7211.94	+	12491.5i	0.563730	+	0.976409i	−0.433436	+	0.901184i	$0.642699\pi$
$548$		−	9545.09i		−	0.744062i
$549$	−12893.4	+	1988.56i	−1.00233	+	0.154589i
$550$	6906.16			0.535418
$551$	3656.89	+	6333.92i	0.282738	+	0.489717i
$552$	−2576.75	+	3004.63i	−0.198684	+	0.231677i
$553$	3443.20	+	7708.47i	0.264773	+	0.592762i
$554$	6554.57	+	3784.28i	0.502666	+	0.290214i
$555$	−37.6155	+	43.8616i	−0.00287691	+	0.00335464i
$556$	9139.33	−	5276.60i	0.697111	−	0.402477i
$557$		−	3660.75i		−	0.278476i	−0.990259	−	0.139238i	$-0.955535\pi$
$557$		−	3660.75i		−	0.278476i	0.990259	−	0.139238i	$-0.0444653\pi$
$558$	11398.7	+	4428.66i	0.864774	+	0.335986i
$559$			27602.1i			2.08845i
$560$	−31.2387	−	3.24518i	−0.00235728	−	0.000244882i
$561$	−7825.37	+	2753.27i	−0.588926	+	0.207207i
$562$	−3056.66	+	5294.28i	−0.229426	+	0.397377i
$563$	−11114.2	+	19250.3i	−0.831982	+	1.44104i	0.0644816	+	0.997919i	$0.479461\pi$
$563$	−11114.2	+	19250.3i	−0.831982	+	1.44104i	−0.896464	+	0.443117i	$0.853873\pi$
$564$	−5497.32	−	1030.40i	−0.410424	−	0.0769287i
$565$	−52.0142	+	30.0304i	−0.00387301	+	0.00223609i
$566$	10221.4			0.759080
$567$	8964.64	+	10095.5i	0.663985	+	0.747746i
$568$	7838.24			0.579024
$569$	15166.7	−	8756.48i	1.11743	−	0.645151i	0.176689	−	0.984267i	$-0.443461\pi$
$569$	15166.7	−	8756.48i	1.11743	−	0.645151i	0.940745	+	0.339116i	$0.110128\pi$
$570$	−28.3263	−	5.30940i	−0.00208151	−	0.000390151i
$571$	−733.441	+	1270.36i	−0.0537541	+	0.0931048i	−0.891650	−	0.452725i	$-0.850452\pi$
$571$	−733.441	+	1270.36i	−0.0537541	+	0.0931048i	0.837896	+	0.545829i	$0.183785\pi$
$572$	3461.42	−	5995.36i	0.253023	−	0.438249i
$573$	415.717	−	146.265i	0.0303086	−	0.0106637i
$574$	998.573	−	9612.46i	0.0726126	−	0.698983i
$575$		−	11901.4i		−	0.863170i
$576$	−1610.70	−	625.797i	−0.116515	−	0.0452689i
$577$			13462.9i			0.971347i	0.874140	+	0.485673i	$0.161426\pi$
$577$			13462.9i			0.971347i	−0.874140	+	0.485673i	$0.838574\pi$
$578$	2725.66	−	1573.66i	0.196146	−	0.113245i
$579$	−5493.32	+	6405.50i	−0.394291	+	0.459764i
$580$	102.629	+	59.2529i	0.00734731	+	0.00424197i
$581$	−5217.37	−	11680.4i	−0.372552	−	0.834053i
$582$	−7105.75	+	8285.68i	−0.506087	+	0.590125i
$583$	−367.002	−	635.666i	−0.0260715	−	0.0451571i
$584$	244.080			0.0172947
$585$	−177.176	+	27.3259i	−0.0125219	+	0.00193126i
$586$			19094.8i			1.34608i
$587$	−10235.7	−	17728.8i	−0.719717	−	1.24659i	−0.961112	−	0.276160i	$-0.910938\pi$
$587$	−10235.7	−	17728.8i	−0.719717	−	1.24659i	0.241394	−	0.970427i	$-0.422395\pi$
$588$	−5654.23	+	4342.13i	−0.396558	+	0.304535i
$589$	−2962.63	+	5131.43i	−0.207255	+	0.358976i
$590$	−35.6699	−	20.5940i	−0.00248899	−	0.00143702i
$591$	1403.62	−	7488.48i	0.0976940	−	0.521209i
$592$	−839.352	−	1453.80i	−0.0582722	−	0.100930i
$593$	13526.1			0.936677			0.468338	−	0.883549i	$-0.344853\pi$
$593$	13526.1			0.936677			0.468338	+	0.883549i	$0.344853\pi$
$594$	−6834.93	+	3657.41i	−0.472122	+	0.252635i
$595$	−66.5626	+	91.8486i	−0.00458622	+	0.00632845i
$596$	11834.5	−	6832.65i	0.813356	−	0.469591i
$597$	−3595.40	+	19181.9i	−0.246482	+	1.31501i
$598$	−10331.8	−	5965.08i	−0.706521	−	0.407910i
$599$	−4981.84	−	2876.26i	−0.339820	−	0.196195i	0.320372	−	0.947292i	$-0.396192\pi$
$599$	−4981.84	−	2876.26i	−0.339820	−	0.196195i	−0.660193	+	0.751096i	$0.729525\pi$
$600$	4901.18	−	1724.42i	0.333483	−	0.117332i
$601$	2114.98	−	1221.09i	0.143547	−	0.0828771i	−0.426506	−	0.904485i	$-0.640256\pi$
$601$	2114.98	−	1221.09i	0.143547	−	0.0828771i	0.570054	+	0.821608i	$0.306922\pi$
$602$	13215.0	+	9576.91i	0.894691	+	0.648381i
$603$	9505.29	−	7633.62i	0.641933	−	0.515531i
$604$	11689.2			0.787464
$605$	30.0870	+	52.1121i	0.00202183	+	0.00350192i
$606$	−5141.68	−	4409.47i	−0.344664	−	0.295582i
$607$	3400.45	+	1963.25i	0.227381	+	0.131278i	0.609363	−	0.792891i	$-0.291425\pi$
$607$	3400.45	+	1963.25i	0.227381	+	0.131278i	−0.381983	+	0.924170i	$0.624759\pi$
$608$	418.638	−	725.103i	0.0279244	−	0.0483665i
$609$	26161.9	−	6258.23i	1.74078	−	0.416414i
$610$	−51.2115	−	88.7008i	−0.00339917	−	0.00588753i
$611$		−	16857.6i		−	1.11618i
$612$	−4866.05	+	3907.89i	−0.321403	+	0.258116i
$613$	−20321.7			−1.33897			−0.669484	−	0.742827i	$-0.733485\pi$
$613$	−20321.7			−1.33897			−0.669484	+	0.742827i	$0.733485\pi$
$614$	−5529.49	−	9577.36i	−0.363440	−	0.629497i
$615$	−47.6901	−	135.545i	−0.00312691	−	0.00888735i
$616$	−1669.41	−	3737.39i	−0.109192	−	0.244454i
$617$	3229.93	+	1864.80i	0.210749	+	0.121676i	0.601659	−	0.798753i	$-0.294506\pi$
$617$	3229.93	+	1864.80i	0.210749	+	0.121676i	−0.390911	+	0.920429i	$0.627840\pi$
$618$	13079.9	+	2451.66i	0.851376	+	0.159580i
$619$	10381.8	−	5993.95i	0.674121	−	0.389204i	−0.123516	−	0.992343i	$-0.539417\pi$
$619$	10381.8	−	5993.95i	0.674121	−	0.389204i	0.797636	+	0.603139i	$0.206084\pi$
$620$			96.0076i			0.00621897i
$621$	6302.82	+	11778.6i	0.407284	+	0.761128i
$622$		−	15616.5i		−	1.00670i
$623$	2672.54	+	277.632i	0.171867	+	0.0178541i
$624$	959.508	−	5119.09i	0.0615562	−	0.328410i
$625$	−7810.39	+	13528.0i	−0.499865	+	0.865792i
$626$	−6247.90	+	10821.7i	−0.398908	+	0.690929i
$627$	−1246.63	−	3543.19i	−0.0794028	−	0.225680i
$628$	−210.242	+	121.383i	−0.0133592	+	0.00771293i
$629$	−6062.96			−0.384334
$630$	−48.3908	+	94.3075i	−0.00306022	+	0.00596397i
$631$	−444.238			−0.0280267			−0.0140133	−	0.999902i	$-0.504461\pi$
$631$	−444.238			−0.0280267			−0.0140133	+	0.999902i	$0.504461\pi$
$632$	−3158.24	+	1823.41i	−0.198779	+	0.114765i
$633$	4293.28	−	5006.20i	0.269578	−	0.314342i
$634$	11266.7	−	19514.5i	0.705768	−	1.22243i
$635$	−108.147	+	187.315i	−0.00675853	+	0.0117061i
$636$	−419.176	−	359.483i	−0.0261343	−	0.0224126i
$637$	−16002.9	−	14339.2i	−0.995383	−	0.891902i
$638$			15445.0i			0.958423i
$639$	9580.37	−	24658.4i	0.593104	−	1.52656i
$640$		−	13.5665i		−	0.000837909i
$641$	−5298.03	+	3058.82i	−0.326458	+	0.188481i	−0.654267	−	0.756263i	$-0.727023\pi$
$641$	−5298.03	+	3058.82i	−0.326458	+	0.188481i	0.327810	+	0.944744i	$0.393690\pi$
$642$	−2512.14	−	7140.03i	−0.154433	−	0.438932i
$643$	12836.8	+	7411.32i	0.787299	+	0.454547i	0.839011	−	0.544115i	$-0.183134\pi$
$643$	12836.8	+	7411.32i	0.787299	+	0.454547i	−0.0517119	+	0.998662i	$0.516468\pi$
$644$	−6440.66	+	2876.89i	−0.394096	+	0.176033i
$645$	238.503	+	44.7043i	0.0145597	+	0.00272904i
$646$	−1511.99	−	2618.85i	−0.0920875	−	0.159500i
$647$	−8610.28			−0.523191			−0.261596	−	0.965178i	$-0.584249\pi$
$647$	−8610.28			−0.523191			−0.261596	+	0.965178i	$0.584249\pi$
$648$	−3937.39	+	4302.23i	−0.238697	+	0.260814i
$649$		−	5368.09i		−	0.324678i
$650$	7829.97	+	13561.9i	0.472487	+	0.818372i
$651$	14988.4	+	15820.4i	0.902366	+	0.952458i
$652$	1063.68	−	1842.34i	0.0638908	−	0.110662i
$653$	18141.8	+	10474.2i	1.08721	+	0.627698i	0.932831	−	0.360314i	$-0.117330\pi$
$653$	18141.8	+	10474.2i	1.08721	+	0.627698i	0.154374	+	0.988012i	$0.450664\pi$
$654$	−5002.73	+	1760.15i	−0.299116	+	0.105241i
$655$	85.4239	+	147.958i	0.00509586	+	0.00882628i
$656$	4174.54			0.248458
$657$	298.329	−	767.851i	0.0177152	−	0.0455963i
$658$	−8070.92	−	5848.98i	−0.478172	−	0.346530i
$659$	−23082.2	+	13326.5i	−1.36442	+	0.787749i	−0.990209	−	0.139594i	$-0.955420\pi$
$659$	−23082.2	+	13326.5i	−1.36442	+	0.787749i	−0.374212	+	0.927343i	$0.622087\pi$
$660$	−46.1983	−	39.6194i	−0.00272465	−	0.00233664i
$661$	1157.83	+	668.475i	0.0681308	+	0.0393354i	0.533678	−	0.845687i	$-0.320809\pi$
$661$	1157.83	+	668.475i	0.0681308	+	0.0393354i	−0.465548	+	0.885023i	$0.654143\pi$
$662$	9940.10	+	5738.92i	0.583584	+	0.336933i
$663$	−14278.8	−	12245.4i	−0.836417	−	0.717306i
$664$	4785.59	−	2762.96i	0.279694	−	0.161481i
$665$	−41.5874	−	30.1383i	−0.00242510	−	0.00175746i
$666$	−5599.42	+	863.599i	−0.325785	+	0.0502459i
$667$	26616.4			1.54512
$668$	−7087.67	−	12276.2i	−0.410524	−	0.711049i
$669$	17232.0	−	6062.87i	0.995854	−	0.350380i
$670$	82.8889	+	47.8559i	0.00477952	+	0.00275946i
$671$	6674.45	−	11560.5i	0.384001	−	0.665109i
$672$	−2117.95	−	2235.52i	−0.121580	−	0.128329i
$673$	−683.964	−	1184.66i	−0.0391751	−	0.0678533i	0.845773	−	0.533543i	$-0.179140\pi$
$673$	−683.964	−	1184.66i	−0.0391751	−	0.0678533i	−0.884948	+	0.465690i	$0.845806\pi$
$674$			20964.4i			1.19810i
$675$	565.645	−	17526.3i	0.0322544	−	0.999390i
$676$	6909.78			0.393137
$677$	12412.3	+	21498.8i	0.704644	+	1.22048i	0.966820	+	0.255459i	$0.0822266\pi$
$677$	12412.3	+	21498.8i	0.704644	+	1.22048i	−0.262176	+	0.965020i	$0.584440\pi$
$678$	−5788.26	−	1084.93i	−0.327871	−	0.0614553i
$679$	−17761.0	+	7933.43i	−1.00384	+	0.448391i
$680$	−42.4334	−	24.4989i	−0.00239301	−	0.00138161i
$681$	8775.18	+	24940.9i	0.493782	+	1.40343i
$682$	−10836.4	+	6256.40i	−0.608427	+	0.351275i
$683$		−	4039.51i		−	0.226307i	−0.993578	−	0.113154i	$-0.963905\pi$
$683$		−	4039.51i		−	0.226307i	0.993578	−	0.113154i	$-0.0360952\pi$
$684$	−1769.42	−	2203.26i	−0.0989114	−	0.123163i
$685$		−	252.917i		−	0.0141072i
$686$	−12417.6	+	2686.51i	−0.691118	+	0.149521i
$687$	−7269.67	−	6234.42i	−0.403719	−	0.346227i
$688$	−3524.87	+	6105.25i	−0.195326	+	0.338314i
$689$	832.189	−	1441.39i	0.0460143	−	0.0796992i
$690$	−68.2762	+	79.6137i	−0.00376700	+	0.00439253i
$691$	24010.6	−	13862.5i	1.32186	−	0.763178i	0.337838	−	0.941204i	$-0.390304\pi$
$691$	24010.6	−	13862.5i	1.32186	−	0.763178i	0.984026	+	0.178026i	$0.0569711\pi$
$692$	−1635.96			−0.0898697
$693$	−13797.9	+	683.729i	−0.756335	+	0.0374787i
$694$	2181.41			0.119316
$695$	242.165	−	139.814i	0.0132170	−	0.00763086i
$696$	3856.52	+	10961.0i	0.210030	+	0.596950i
$697$	7538.57	−	13057.2i	0.409675	−	0.709578i
$698$	8637.03	−	14959.8i	0.468362	−	0.811226i
$699$	740.765	−	3952.07i	0.0400834	−	0.213850i
$700$	9209.74	+	956.736i	0.497279	+	0.0516589i
$701$		−	8033.75i		−	0.432854i	−0.976299	−	0.216427i	$-0.930560\pi$
$701$		−	8033.75i		−	0.432854i	0.976299	−	0.216427i	$-0.0694403\pi$
$702$	−14931.4	−	9275.38i	−0.802777	−	0.498685i
$703$		−	2745.19i		−	0.147279i
$704$	1531.25	−	884.068i	0.0819761	−	0.0473289i
$705$	−145.663	−	27.3026i	−0.00778152	−	0.00145855i
$706$	−17330.8	−	10005.9i	−0.923870	−	0.533396i
$707$	−4923.09	−	11021.6i	−0.261884	−	0.586294i
$708$	−1340.38	−	3809.64i	−0.0711503	−	0.202224i
$709$	3800.41	+	6582.50i	0.201308	+	0.348676i	0.948950	−	0.315426i	$-0.102147\pi$
$709$	3800.41	+	6582.50i	0.201308	+	0.348676i	−0.747642	+	0.664102i	$0.768814\pi$
$710$	207.690			0.0109781
$711$	1876.09	+	12164.2i	0.0989575	+	0.641623i
$712$			1160.64i			0.0610912i
$713$	10781.7	+	18674.4i	0.566306	+	0.980872i
$714$	−10817.0	+	2587.55i	−0.566968	+	0.135626i
$715$	91.7174	−	158.859i	0.00479725	−	0.00830909i
$716$	−3669.14	−	2118.38i	−0.191511	−	0.110569i
$717$	−2574.75	−	2208.09i	−0.134109	−	0.115011i
$718$	8795.27	+	15233.8i	0.457154	+	0.791814i
$719$	−10800.9			−0.560229			−0.280115	−	0.959967i	$-0.590372\pi$
$719$	−10800.9			−0.560229			−0.280115	+	0.959967i	$0.590372\pi$
$720$	−42.6788	−	16.5818i	−0.00220909	−	0.000858285i
$721$	19203.3	+	13916.6i	0.991911	+	0.718837i
$722$	−10694.4	+	6174.40i	−0.551251	+	0.318265i
$723$	31718.0	−	11159.6i	1.63154	−	0.574040i
$724$	8467.52	+	4888.73i	0.434659	+	0.250950i
$725$	−30256.9	−	17468.8i	−1.54995	−	0.894864i
$726$	−1086.98	+	5799.16i	−0.0555668	+	0.296456i
$727$	−19559.0	+	11292.4i	−0.997803	+	0.576082i	−0.907598	−	0.419841i	$-0.862086\pi$
$727$	−19559.0	+	11292.4i	−0.997803	+	0.576082i	−0.0902055	+	0.995923i	$0.528752\pi$
$728$	5446.56	−	7515.62i	0.277284	−	0.382620i
$729$	8721.88	+	17645.1i	0.443117	+	0.896464i
$730$	6.46739			0.000327902
$731$	12730.7	+	22050.2i	0.644135	+	1.11567i
$732$	1850.16	−	9870.84i	0.0934207	−	0.498411i
$733$	−14638.9	−	8451.74i	−0.737651	−	0.425883i	0.0835635	−	0.996502i	$-0.473370\pi$
$733$	−14638.9	−	8451.74i	−0.737651	−	0.425883i	−0.821215	+	0.570619i	$0.806703\pi$
$734$	−12602.5	+	21828.2i	−0.633744	+	1.09768i
$735$	−149.820	+	115.053i	−0.00751864	+	0.00577389i
$736$	−1523.52	−	2638.81i	−0.0763010	−	0.132157i
$737$			12474.2i			0.623467i
$738$	5102.37	−	13132.7i	0.254500	−	0.655042i
$739$	−9717.59			−0.483718			−0.241859	−	0.970311i	$-0.577757\pi$
$739$	−9717.59			−0.483718			−0.241859	+	0.970311i	$0.577757\pi$
$740$	−22.2403	−	38.5214i	−0.00110483	−	0.00191361i
$741$	5544.51	−	6465.20i	0.274876	−	0.320520i
$742$	−401.356	−	898.537i	−0.0198575	−	0.0444560i
$743$	−25597.9	−	14778.9i	−1.26392	−	0.729726i	−0.290091	−	0.956999i	$-0.593686\pi$
$743$	−25597.9	−	14778.9i	−1.26392	−	0.729726i	−0.973831	+	0.227273i	$0.927019\pi$
$744$	−6128.21	+	7145.83i	−0.301977	+	0.352122i
$745$	313.579	−	181.045i	0.0154210	−	0.00890332i
$746$		−	251.103i		−	0.0123238i
$747$	−2842.78	−	18432.1i	−0.139239	−	0.902803i
$748$		−	6385.96i		−	0.312157i
$749$	1393.77	−	13416.7i	0.0679938	−	0.654522i
$750$	259.745	−	91.3882i	0.0126460	−	0.00444936i
$751$	15390.3	−	26656.7i	0.747801	−	1.29523i	−0.201073	−	0.979576i	$-0.564443\pi$
$751$	15390.3	−	26656.7i	0.747801	−	1.29523i	0.948875	−	0.315653i	$-0.102224\pi$
$752$	2152.77	−	3728.71i	0.104393	−	0.180814i
$753$	−23157.1	−	4340.50i	−1.12071	−	0.210062i
$754$	−30330.0	+	17511.0i	−1.46493	+	0.845775i
$755$	309.730			0.0149301
$756$	−9621.42	+	3930.48i	−0.462867	+	0.189087i
$757$	−38644.5			−1.85543			−0.927715	−	0.373290i	$-0.878229\pi$
$757$	−38644.5			−1.85543			−0.927715	+	0.373290i	$0.878229\pi$
$758$	−14536.2	+	8392.50i	−0.696543	+	0.402149i
$759$	−13435.3	−	2518.27i	−0.642516	−	0.120431i
$760$	11.0927	−	19.2131i	0.000529439	−	0.000917015i
$761$	−13687.9	+	23708.1i	−0.652017	+	1.12933i	0.330616	+	0.943765i	$0.392744\pi$
$761$	−13687.9	+	23708.1i	−0.652017	+	1.12933i	−0.982633	+	0.185561i	$0.940590\pi$
$762$	−20005.8	+	7038.79i	−0.951092	+	0.334631i
$763$	−9400.56	−	976.559i	−0.446033	−	0.0463353i
$764$			339.249i			0.0160649i
$765$	−128.936	+	103.547i	−0.00609371	+	0.00489381i
$766$		−	18604.3i		−	0.877547i
$767$	10541.5	−	6086.16i	0.496262	−	0.286517i
$768$	865.955	−	1009.75i	0.0406868	−	0.0474430i
$769$	2631.43	+	1519.26i	0.123396	+	0.0712429i	0.560428	−	0.828203i	$-0.310637\pi$
$769$	2631.43	+	1519.26i	0.123396	+	0.0712429i	−0.437031	+	0.899446i	$0.643970\pi$
$770$	−44.2343	−	99.0298i	−0.00207025	−	0.00463479i
$771$	−5136.62	+	5989.57i	−0.239936	+	0.279778i
$772$	−3247.95	−	5625.61i	−0.151420	−	0.262267i
$773$	−17745.8			−0.825709			−0.412855	−	0.910797i	$-0.635468\pi$
$773$	−17745.8			−0.825709			−0.412855	+	0.910797i	$0.635468\pi$
$774$	14898.2	+	18551.1i	0.691867	+	0.861505i
$775$		−	28304.8i		−	1.31192i
$776$	−4201.31	−	7276.88i	−0.194353	−	0.336630i
$777$	−9678.64	−	2875.58i	−0.446872	−	0.132768i
$778$	2280.80	−	3950.45i	0.105103	−	0.182045i
$779$	5912.05	+	3413.32i	0.271914	+	0.156990i
$780$	25.4241	−	135.641i	0.00116709	−	0.00622656i
$781$	13534.3	+	23442.0i	0.620094	+	1.07404i
$782$	−11004.9			−0.503242
$783$	39196.1	+	1265.02i	1.78896	+	0.0577369i
$784$	−1708.49	−	5215.29i	−0.0778284	−	0.237577i
$785$	−5.57078	+	3.21629i	−0.000253286	+	0.000146235i
$786$	−3086.18	+	16465.2i	−0.140052	+	0.747192i
$787$	12513.6	+	7224.72i	0.566786	+	0.327234i	0.755865	−	0.654728i	$-0.227217\pi$
$787$	12513.6	+	7224.72i	0.566786	+	0.327234i	−0.189078	+	0.981962i	$0.560550\pi$
$788$	5079.26	+	2932.51i	0.229621	+	0.132572i
$789$	11793.5	−	4149.40i	0.532140	−	0.187227i
$790$	−83.6841	+	48.3150i	−0.00376879	+	0.00217591i
$791$	−8498.05	−	6158.53i	−0.381992	−	0.276829i
$792$	−909.607	−	5897.73i	−0.0408099	−	0.264604i
$793$	30269.1			1.35547
$794$	4521.52	+	7831.50i	0.202094	+	0.350037i
$795$	−11.1069	−	9.52522i	−0.000495499	−	0.000424937i
$796$	−13010.6	−	7511.69i	−0.579334	−	0.334478i
$797$	11971.7	−	20735.6i	0.532069	−	0.921571i	−0.467230	−	0.884136i	$-0.654748\pi$
$797$	11971.7	−	20735.6i	0.532069	−	0.921571i	0.999299	−	0.0374348i	$-0.0119187\pi$
$798$	−1171.60	−	4897.73i	−0.0519725	−	0.217265i
$799$	−7775.13	−	13466.9i	−0.344261	−	0.596277i
$800$			3999.64i			0.176761i
$801$	3651.27	+	1418.61i	0.161063	+	0.0625767i
$802$	5475.84			0.241095
$803$	421.451	+	729.975i	0.0185214	+	0.0320800i
$804$	3114.74	+	8852.75i	0.136627	+	0.388324i
$805$	−170.658	+	76.2291i	−0.00747194	+	0.00333754i
$806$	−24571.9	−	14186.6i	−1.07383	−	0.619977i
$807$	23488.7	+	4402.66i	1.02459	+	0.192046i
$808$	4515.67	−	2607.12i	0.196610	−	0.113513i
$809$			37391.0i			1.62496i	0.582986	+	0.812482i	$0.301884\pi$
$809$			37391.0i			1.62496i	−0.582986	+	0.812482i	$0.698116\pi$
$810$	−104.329	+	113.996i	−0.00452562	+	0.00494496i
$811$		−	32386.6i		−	1.40228i	−0.713025	−	0.701139i	$-0.752675\pi$
$811$		−	32386.6i		−	1.40228i	0.713025	−	0.701139i	$-0.247325\pi$
$812$	−2139.66	+	20596.8i	−0.0924720	+	0.890154i
$813$	−1494.76	+	7974.71i	−0.0644814	+	0.344016i
$814$	2898.61	−	5020.54i	0.124811	−	0.216179i
$815$	28.1843	−	48.8166i	0.00121135	−	0.00209812i
$816$	−1594.53	−	4532.00i	−0.0684065	−	0.194426i
$817$	−9983.95	+	5764.23i	−0.427533	+	0.246836i
$818$	6891.12			0.294550
$819$	−16986.3	−	26320.4i	−0.724724	−	1.12296i
$820$	110.613			0.00471069
$821$	−14106.8	+	8144.58i	−0.599673	+	0.346221i	−0.768913	−	0.639354i	$-0.779202\pi$
$821$	−14106.8	+	8144.58i	−0.599673	+	0.346221i	0.169240	+	0.985575i	$0.445869\pi$
$822$	16143.8	−	18824.5i	0.685011	−	0.798760i
$823$	1808.84	−	3133.00i	0.0766126	−	0.132697i	−0.825174	−	0.564879i	$-0.808923\pi$
$823$	1808.84	−	3133.00i	0.0766126	−	0.132697i	0.901786	+	0.432182i	$0.142256\pi$
$824$	−5122.13	+	8871.78i	−0.216551	+	0.375077i
$825$	13620.1	+	11680.5i	0.574777	+	0.492925i
$826$	743.662	−	7158.64i	0.0313260	−	0.301551i
$827$			28657.6i			1.20499i	0.798124	+	0.602493i	$0.205826\pi$
$827$			28657.6i			1.20499i	−0.798124	+	0.602493i	$0.794174\pi$
$828$	−10163.6	+	1567.53i	−0.426580	+	0.0657915i
$829$		−	12112.9i		−	0.507478i	−0.967273	−	0.253739i	$-0.918340\pi$
$829$		−	12112.9i		−	0.507478i	0.967273	−	0.253739i	$-0.0816604\pi$
$830$	126.804	−	73.2102i	0.00530292	−	0.00306164i
$831$	6526.28	+	18549.1i	0.272436	+	0.774321i
$832$	3472.16	+	2004.65i	0.144682	+	0.0835322i
$833$	−19397.7	−	4074.16i	−0.806832	−	0.169461i
$834$	26948.7	+	5051.19i	1.11889	+	0.209722i
$835$	−187.802	−	325.283i	−0.00778342	−	0.0134813i
$836$	2891.44			0.119620
$837$	14989.8	+	28012.8i	0.619025	+	1.15683i
$838$		−	5354.65i		−	0.220732i
$839$	1008.14	+	1746.15i	0.0414838	+	0.0718520i	0.886022	−	0.463644i	$-0.153458\pi$
$839$	1008.14	+	1746.15i	0.0414838	+	0.0718520i	−0.844538	+	0.535496i	$0.820125\pi$
$840$	−56.1194	−	59.2346i	−0.00230512	−	0.00243308i
$841$	26873.0	−	46545.4i	1.10185	−	1.90846i
$842$	15637.2	+	9028.11i	0.640014	+	0.369512i
$843$	−14982.6	+	5271.44i	−0.612131	+	0.215371i
$844$	2538.42	+	4396.68i	0.103526	+	0.179313i
$845$	183.089			0.00745378
$846$	−9098.90	−	11329.8i	−0.369772	−	0.460435i
$847$	−6170.12	+	8514.06i	−0.250305	+	0.345391i
$848$	368.140	−	212.546i	0.0149080	−	0.00860714i
$849$	20158.4	+	17287.7i	0.814881	+	0.698837i
$850$	12510.1	+	7222.73i	0.504816	+	0.291456i
$851$	−8651.91	−	4995.18i	−0.348512	−	0.201213i
$852$	15458.3	+	13257.0i	0.621589	+	0.533070i
$853$	−3154.89	+	1821.48i	−0.126637	+	0.0731140i	−0.561980	−	0.827151i	$-0.689960\pi$
$853$	−3154.89	+	1821.48i	−0.126637	+	0.0731140i	0.435343	+	0.900265i	$0.356627\pi$
$854$	10502.3	−	14491.9i	0.420820	−	0.580682i
$855$	−46.8843	−	58.3798i	−0.00187533	−	0.00233514i
$856$	5826.67			0.232654
$857$	6792.66	+	11765.2i	0.270750	+	0.468953i	0.969054	−	0.246848i	$-0.0793949\pi$
$857$	6792.66	+	11765.2i	0.270750	+	0.468953i	−0.698304	+	0.715801i	$0.746062\pi$
$858$	16966.6	−	5969.49i	0.675092	−	0.237523i
$859$	7397.04	+	4270.69i	0.293811	+	0.169632i	0.639659	−	0.768658i	$-0.279075\pi$
$859$	7397.04	+	4270.69i	0.293811	+	0.169632i	−0.345848	+	0.938291i	$0.612409\pi$
$860$	−93.3984	+	161.771i	−0.00370333	+	0.00641435i
$861$	18227.1	−	17268.5i	0.721460	−	0.683517i
$862$	3809.70	+	6598.60i	0.150533	+	0.260730i
$863$		−	39887.5i		−	1.57333i	−0.617378	−	0.786667i	$-0.711805\pi$
$863$		−	39887.5i		−	1.57333i	0.617378	−	0.786667i	$-0.288195\pi$
$864$	−2118.15	−	3958.39i	−0.0834040	−	0.155865i
$865$	−43.3481			−0.00170391
$866$	−17496.4	−	30304.7i	−0.686550	−	1.18914i
$867$	8037.02	+	1506.44i	0.314823	+	0.0590095i
$868$	−15317.6	+	6842.04i	−0.598980	+	0.267551i
$869$	−10906.6	−	6296.96i	−0.425757	−	0.245811i
$870$	102.186	+	290.435i	0.00398211	+	0.0113180i
$871$	−24496.2	+	14142.9i	−0.952953	+	0.550187i
$872$		−	4082.51i		−	0.158545i
$873$	−28027.4	+	4322.68i	−1.08658	+	0.167583i
$874$		−	4982.83i		−	0.192845i
$875$	488.083	+	50.7036i	0.0188574	+	0.00195897i
$876$	481.366	+	412.817i	0.0185660	+	0.0159221i
$877$	−9207.03	+	15947.0i	−0.354503	+	0.614017i	−0.987033	−	0.160519i	$-0.948683\pi$
$877$	−9207.03	+	15947.0i	−0.354503	+	0.614017i	0.632530	+	0.774536i	$0.282017\pi$
$878$	6327.49	−	10959.5i	0.243215	−	0.421260i
$879$	−32295.5	+	37658.2i	−1.23925	+	1.44503i
$880$	40.5736	−	23.4252i	0.00155424	−	0.000897343i
$881$	−45159.4			−1.72697			−0.863485	−	0.504375i	$-0.831723\pi$
$881$	−45159.4			−1.72697			−0.863485	+	0.504375i	$0.831723\pi$
$882$	−18495.0	−	999.690i	−0.706076	−	0.0381647i
$883$	−18750.6			−0.714617			−0.357308	−	0.933986i	$-0.616305\pi$
$883$	−18750.6			−0.714617			−0.357308	+	0.933986i	$0.616305\pi$
$884$	12540.4	−	7240.18i	0.477124	−	0.275468i
$885$	−35.5160	−	100.944i	−0.00134899	−	0.00383412i
$886$	12848.2	−	22253.8i	0.487183	−	0.843827i
$887$	10483.1	−	18157.3i	0.396831	−	0.687331i	−0.596502	−	0.802611i	$-0.703443\pi$
$887$	10483.1	−	18157.3i	0.396831	−	0.687331i	0.993333	+	0.115280i	$0.0367767\pi$
$888$	803.496	−	4286.75i	0.0303644	−	0.161998i
$889$	−37592.6	−	3905.23i	−1.41824	−	0.147331i
$890$			30.7536i			0.00115827i
$891$	−19665.5	−	4347.02i	−0.739413	−	0.163446i
$892$			14062.3i			0.527847i
$893$	6097.57	−	3520.44i	0.228497	−	0.131923i
$894$	34895.8	+	6540.77i	1.30547	+	0.244694i
$895$	−97.2213	−	56.1307i	−0.00363100	−	0.00209636i
$896$	2164.48	−	966.822i	0.0807033	−	0.0360483i
$897$	−10287.2	−	29238.5i	−0.382922	−	1.08835i
$898$	−5935.77	−	10281.1i	−0.220578	−	0.382053i
$899$	63301.1			2.34840
$900$	12582.5	+	4888.60i	0.466018	+	0.181059i
$901$		−	1535.30i		−	0.0567683i
$902$	7208.15	+	12484.9i	0.266081	+	0.460866i
$903$	9864.64	+	41238.1i	0.363538	+	1.51973i
$904$	2266.70	−	3926.04i	0.0833953	−	0.144445i
$905$	224.364	+	129.537i	0.00824101	+	0.00475795i
$906$	23053.1	+	19770.2i	0.845352	+	0.724969i
$907$	−2950.22	−	5109.93i	−0.108005	−	0.187070i	0.806957	−	0.590610i	$-0.201113\pi$
$907$	−2950.22	−	5109.93i	−0.108005	−	0.187070i	−0.914962	+	0.403540i	$0.867780\pi$
$908$	−20353.2			−0.743883
$909$	−2682.44	−	17392.4i	−0.0978776	−	0.634621i
$910$	144.318	−	199.141i	0.00525723	−	0.00725437i
$911$	5490.91	−	3170.18i	0.199695	−	0.115294i	−0.396818	−	0.917897i	$-0.629886\pi$
$911$	5490.91	−	3170.18i	0.199695	−	0.115294i	0.596513	+	0.802603i	$0.296552\pi$
$912$	2052.00	−	721.974i	0.0745051	−	0.0262137i
$913$	16526.5	+	9541.58i	0.599066	+	0.345871i
$914$	19975.5	+	11532.8i	0.722899	+	0.417366i
$915$	49.0238	−	261.548i	0.00177123	−	0.00944973i
$916$	6384.56	−	3686.13i	0.230297	−	0.132962i
$917$	−17518.4	+	24173.4i	−0.630872	+	0.870530i
$918$	−16206.1	−	523.038i	−0.582661	−	0.0188048i
$919$	−14869.5			−0.533733			−0.266866	−	0.963734i	$-0.585988\pi$
$919$	−14869.5			−0.533733			−0.266866	+	0.963734i	$0.585988\pi$
$920$	−40.3686	−	69.9205i	−0.00144665	−	0.00250567i
$921$	5293.28	−	28240.3i	0.189381	−	1.01037i
$922$	27794.5	+	16047.2i	0.992803	+	0.573195i
$923$	−30689.4	+	53155.5i	−1.09442	+	1.89560i
$924$	3028.77	−	10194.3i	0.107835	−	0.362951i
$925$	6556.85	+	11356.8i	0.233068	+	0.403685i
$926$		−	32071.9i		−	1.13817i
$927$	21649.2	+	26957.3i	0.767048	+	0.955119i
$928$	−8944.84			−0.316410
$929$	11128.1	+	19274.4i	0.393005	+	0.680704i	0.992844	−	0.119416i	$-0.0381023\pi$
$929$	11128.1	+	19274.4i	0.393005	+	0.680704i	−0.599840	+	0.800120i	$0.704769\pi$
$930$	−162.379	+	189.343i	−0.00572541	+	0.00667613i
$931$	1844.70	−	8782.93i	0.0649385	−	0.309182i
$932$	2680.60	+	1547.64i	0.0942123	+	0.0543935i
$933$	26412.5	−	30798.3i	0.926801	−	1.08070i
$934$	−18134.7	+	10470.0i	−0.635315	+	0.366799i
$935$		−	169.209i		−	0.00591842i
$936$	10550.3	−	8472.88i	0.368427	−	0.295881i
$937$		−	10350.4i		−	0.360866i	−0.983587	−	0.180433i	$-0.942250\pi$
$937$		−	10350.4i		−	0.360866i	0.983587	−	0.180433i	$-0.0577499\pi$
$938$	−1728.10	+	16635.1i	−0.0601542	+	0.579056i
$939$	−30624.8	+	10775.0i	−1.06433	+	0.374471i
$940$	57.0420	−	98.7996i	0.00197926	−	0.00342818i
$941$	16686.5	−	28901.8i	0.578070	−	1.00125i	−0.417631	−	0.908617i	$-0.637140\pi$
$941$	16686.5	−	28901.8i	0.578070	−	1.00125i	0.995701	−	0.0926293i	$-0.0295271\pi$
$942$	−619.930	−	116.198i	−0.0214420	−	0.00401904i
$943$	21515.2	−	12421.8i	0.742983	−	0.428961i
$944$	3108.88			0.107188
$945$	−254.939	+	104.146i	−0.00877583	+	0.00358505i
$946$	−24345.5			−0.836723
$947$	24653.6	−	14233.8i	0.845971	−	0.488422i	−0.0133181	−	0.999911i	$-0.504239\pi$
$947$	24653.6	−	14233.8i	0.845971	−	0.488422i	0.859290	+	0.511489i	$0.170906\pi$
$948$	−9312.56	−	1745.52i	−0.319048	−	0.0598015i
$949$	−955.655	+	1655.24i	−0.0326890	+	0.0566190i
$950$	−3270.32	+	5664.36i	−0.111688	+	0.193448i
$951$	55225.0	−	19430.3i	1.88306	−	0.662533i
$952$	884.670	−	8516.02i	0.0301180	−	0.289922i
$953$		−	30070.0i		−	1.02210i	−0.859551	−	0.511051i	$-0.829256\pi$
$953$		−	30070.0i		−	1.02210i	0.859551	−	0.511051i	$-0.170744\pi$
$954$	−218.686	−	1417.92i	−0.00742161	−	0.0481204i
$955$			8.98909i			0.000304587i
$956$	2261.27	−	1305.54i	0.0765007	−	0.0441677i
$957$	−26122.4	+	30460.2i	−0.882360	+	1.02888i
$958$	8495.19	+	4904.70i	0.286500	+	0.165411i
$959$	40351.8	−	18024.2i	1.35874	−	0.606916i
$960$	22.9452	−	26.7554i	0.000771410	−	0.000899506i
$961$	10746.2	+	18613.0i	0.360721	+	0.624787i
$962$	13145.4			0.440566
$963$	7121.71	−	18330.2i	0.238311	−	0.613376i
$964$			25883.7i			0.864791i
$965$	−86.0610	−	149.062i	−0.00287088	−	0.00497251i
$966$	−17567.8	−	5219.49i	−0.585129	−	0.173845i
$967$	−4239.60	+	7343.20i	−0.140989	+	0.244200i	−0.927869	−	0.372906i	$-0.878362\pi$
$967$	−4239.60	+	7343.20i	−0.140989	+	0.244200i	0.786880	+	0.617106i	$0.211695\pi$
$968$	−3933.43	−	2270.97i	−0.130605	−	0.0754046i
$969$	1447.40	−	7722.06i	0.0479847	−	0.256004i
$970$	−111.322	−	192.816i	−0.00368489	−	0.00638241i
$971$	−306.493			−0.0101296			−0.00506479	−	0.999987i	$-0.501612\pi$
$971$	−306.493			−0.0101296			−0.00506479	+	0.999987i	$0.501612\pi$
$972$	−15041.6	+	1825.33i	−0.496359	+	0.0602341i
$973$	39564.8	+	28672.6i	1.30359	+	0.944707i
$974$	25599.8	−	14780.0i	0.842166	−	0.486225i
$975$	−7495.48	+	39989.3i	−0.246203	+	1.31352i
$976$	6695.16	+	3865.45i	0.219577	+	0.126773i
$977$	18175.3	+	10493.5i	0.595168	+	0.343620i	0.767138	−	0.641482i	$-0.221680\pi$
$977$	18175.3	+	10493.5i	0.595168	+	0.343620i	−0.171970	+	0.985102i	$0.555013\pi$
$978$	5213.73	−	1834.39i	0.170467	−	0.0599768i
$979$	−3471.16	+	2004.08i	−0.113318	+	0.0654244i
$980$	−45.2699	−	138.190i	−0.00147561	−	0.00450439i
$981$	−12843.2	−	4989.89i	−0.417993	−	0.162400i
$982$	−11090.9			−0.360411
$983$	−21966.4	−	38046.8i	−0.712734	−	1.23449i	−0.963827	−	0.266529i	$-0.914123\pi$
$983$	−21966.4	−	38046.8i	−0.712734	−	1.23449i	0.251092	−	0.967963i	$-0.419210\pi$
$984$	8232.89	+	7060.47i	0.266722	+	0.228739i
$985$	134.585	+	77.7028i	0.00435354	+	0.00251352i
$986$	−16153.0	+	27977.8i	−0.521720	+	0.903646i
$987$	−6024.71	−	25185.7i	−0.194294	−	0.812227i
$988$	3278.22	+	5678.05i	0.105561	+	0.182837i
$989$			41954.6i			1.34892i
$990$	−24.1019	−	156.272i	−0.000773745	−	0.00501682i
$991$	−31591.1			−1.01264			−0.506319	−	0.862346i	$-0.668994\pi$
$991$	−31591.1			−1.01264			−0.506319	+	0.862346i	$0.668994\pi$
$992$	−3623.34	−	6275.80i	−0.115969	−	0.200864i
$993$	9897.20	+	28130.0i	0.316292	+	0.898970i
$994$	14801.1	+	33136.1i	0.472298	+	1.05736i
$995$	−344.743	−	199.037i	−0.0109840	−	0.00634162i
$996$	14111.0	+	2644.93i	0.448921	+	0.0841444i
$997$	−30229.1	+	17452.8i	−0.960247	+	0.554399i	−0.896249	−	0.443551i	$-0.853718\pi$
$997$	−30229.1	+	17452.8i	−0.960247	+	0.554399i	−0.0639978	+	0.997950i	$0.520385\pi$
$998$		−	24657.8i		−	0.782093i
$999$	−12503.6	−	7767.24i	−0.395993	−	0.245991i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.4.m.a.41.1	✓	48
3.2	odd	2		378.4.m.a.125.19		48
7.6	odd	2	inner	126.4.m.a.41.12	yes	48
9.2	odd	6	inner	126.4.m.a.83.12	yes	48
9.4	even	3		1134.4.d.b.1133.35		48
9.5	odd	6		1134.4.d.b.1133.14		48
9.7	even	3		378.4.m.a.251.20		48
21.20	even	2		378.4.m.a.125.20		48
63.13	odd	6		1134.4.d.b.1133.13		48
63.20	even	6	inner	126.4.m.a.83.1	yes	48
63.34	odd	6		378.4.m.a.251.19		48
63.41	even	6		1134.4.d.b.1133.36		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.4.m.a.41.1	✓	48	1.1	even	1	trivial
126.4.m.a.41.12	yes	48	7.6	odd	2	inner
126.4.m.a.83.1	yes	48	63.20	even	6	inner
126.4.m.a.83.12	yes	48	9.2	odd	6	inner
378.4.m.a.125.19		48	3.2	odd	2
378.4.m.a.125.20		48	21.20	even	2
378.4.m.a.251.19		48	63.34	odd	6
378.4.m.a.251.20		48	9.7	even	3
1134.4.d.b.1133.13		48	63.13	odd	6
1134.4.d.b.1133.14		48	9.5	odd	6
1134.4.d.b.1133.35		48	9.4	even	3
1134.4.d.b.1133.36		48	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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	126.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 + 1.00000i) q^{2} +(-5.10721 - 0.957281i) q^{3} +(2.00000 - 3.46410i) q^{4} +(0.0529940 - 0.0917884i) q^{5} +(9.80323 - 3.44915i) q^{6} +(18.4211 + 1.91364i) q^{7} +8.00000i q^{8} +(25.1672 + 9.77807i) q^{9} +O(q^{10})\)	\(q+(-1.73205 + 1.00000i) q^{2} +(-5.10721 - 0.957281i) q^{3} +(2.00000 - 3.46410i) q^{4} +(0.0529940 - 0.0917884i) q^{5} +(9.80323 - 3.44915i) q^{6} +(18.4211 + 1.91364i) q^{7} +8.00000i q^{8} +(25.1672 + 9.77807i) q^{9} +0.211976i q^{10} +(-23.9258 + 13.8136i) q^{11} +(-13.5305 + 15.7773i) q^{12} +(-54.2525 - 31.3227i) q^{13} +(-33.8200 + 15.1066i) q^{14} +(-0.358519 + 0.418052i) q^{15} +(-8.00000 - 13.8564i) q^{16} -57.7870 q^{17} +(-53.3690 + 8.23110i) q^{18} -26.1649i q^{19} +(-0.211976 - 0.367153i) q^{20} +(-92.2487 - 27.4076i) q^{21} +(27.6271 - 47.8516i) q^{22} +(-82.4627 - 47.6099i) q^{23} +(7.65825 - 40.8577i) q^{24} +(62.4944 + 108.243i) q^{25} +125.291 q^{26} +(-119.174 - 74.0308i) q^{27} +(43.4713 - 59.9854i) q^{28} +(-242.077 + 139.763i) q^{29} +(0.202921 - 1.08261i) q^{30} +(-196.119 - 113.229i) q^{31} +(27.7128 + 16.0000i) q^{32} +(135.418 - 47.6451i) q^{33} +(100.090 - 57.7870i) q^{34} +(1.15186 - 1.58943i) q^{35} +(84.2067 - 67.6257i) q^{36} +104.919 q^{37} +(26.1649 + 45.3189i) q^{38} +(247.094 + 211.907i) q^{39} +(0.734307 + 0.423952i) q^{40} +(-130.454 + 225.954i) q^{41} +(187.187 - 44.7774i) q^{42} +(-220.304 - 381.578i) q^{43} +110.508i q^{44} +(2.23123 - 1.79188i) q^{45} +190.440 q^{46} +(134.548 + 233.044i) q^{47} +(27.5932 + 78.4259i) q^{48} +(335.676 + 70.5030i) q^{49} +(-216.487 - 124.989i) q^{50} +(295.131 + 55.3184i) q^{51} +(-217.010 + 125.291i) q^{52} +26.5682i q^{53} +(280.446 + 9.05114i) q^{54} +2.92815i q^{55} +(-15.3092 + 147.369i) q^{56} +(-25.0472 + 133.630i) q^{57} +(279.526 - 484.154i) q^{58} +(-97.1526 + 168.273i) q^{59} +(0.731138 + 2.07805i) q^{60} +(-418.447 + 241.591i) q^{61} +452.917 q^{62} +(444.897 + 228.284i) q^{63} -64.0000 q^{64} +(-5.75012 + 3.31983i) q^{65} +(-186.905 + 217.941i) q^{66} +(225.761 - 391.029i) q^{67} +(-115.574 + 200.180i) q^{68} +(375.579 + 322.094i) q^{69} +(-0.405647 + 3.90484i) q^{70} -979.780i q^{71} +(-78.2246 + 201.338i) q^{72} -30.5100i q^{73} +(-181.725 + 104.919i) q^{74} +(-215.553 - 612.647i) q^{75} +(-90.6379 - 52.3298i) q^{76} +(-467.174 + 208.676i) q^{77} +(-639.887 - 119.939i) q^{78} +(227.927 + 394.781i) q^{79} -1.69581 q^{80} +(537.778 + 492.174i) q^{81} -521.817i q^{82} +(-345.370 - 598.199i) q^{83} +(-279.440 + 264.744i) q^{84} +(-3.06237 + 5.30418i) q^{85} +(763.156 + 440.608i) q^{86} +(1370.13 - 482.065i) q^{87} +(-110.508 - 191.406i) q^{88} +145.080 q^{89} +(-2.07272 + 5.33485i) q^{90} +(-939.452 - 680.819i) q^{91} +(-329.851 + 190.440i) q^{92} +(893.228 + 766.027i) q^{93} +(-466.088 - 269.096i) q^{94} +(-2.40163 - 1.38658i) q^{95} +(-126.219 - 108.244i) q^{96} +(-909.610 + 525.164i) q^{97} +(-651.911 + 213.561i) q^{98} +(-737.216 + 113.701i) 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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