LMFDB - Embedded newform 56.4.p.a.37.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [56,4,Mod(37,56)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(56, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("56.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 56 = 2^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	56.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.30410696032$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.14
Character	$\chi$	$=$	56.37
Dual form			56.4.p.a.53.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.941296 - 2.66720i) q^{2} +(4.43871 - 2.56269i) q^{3} +(-6.22792 - 5.02125i) q^{4} +(13.1631 + 7.59971i) q^{5} +(-2.65707 - 14.2512i) q^{6} +(1.45519 - 18.4630i) q^{7} +(-19.2550 + 11.8846i) q^{8} +(-0.365251 + 0.632633i) q^{9} +(32.6603 - 27.9550i) q^{10} +(-35.5292 + 20.5128i) q^{11} +(-40.5118 - 6.32763i) q^{12} -15.1225i q^{13} +(-47.8748 - 21.2604i) q^{14} +77.9028 q^{15} +(13.5741 + 62.5439i) q^{16} +(27.3391 + 47.3526i) q^{17} +(1.34355 + 1.56969i) q^{18} +(37.1763 + 21.4637i) q^{19} +(-43.8187 - 113.426i) q^{20} +(-40.8558 - 85.6811i) q^{21} +(21.2682 + 114.072i) q^{22} +(69.1294 - 119.736i) q^{23} +(-55.0107 + 102.097i) q^{24} +(53.0113 + 91.8183i) q^{25} +(-40.3346 - 14.2347i) q^{26} +142.129i q^{27} +(-101.770 + 107.679i) q^{28} +271.056i q^{29} +(73.3296 - 207.782i) q^{30} +(9.18381 + 15.9068i) q^{31} +(179.594 + 22.6676i) q^{32} +(-105.136 + 182.100i) q^{33} +(152.033 - 28.3459i) q^{34} +(159.468 - 231.971i) q^{35} +(5.45136 - 2.10597i) q^{36} +(-202.736 - 117.050i) q^{37} +(92.2420 - 78.9529i) q^{38} +(-38.7541 - 67.1242i) q^{39} +(-343.775 + 10.1061i) q^{40} -347.517 q^{41} +(-266.986 + 28.3193i) q^{42} -314.997i q^{43} +(324.273 + 50.6489i) q^{44} +(-9.61566 + 5.55160i) q^{45} +(-254.288 - 297.089i) q^{46} +(196.536 - 340.410i) q^{47} +(220.532 + 242.828i) q^{48} +(-338.765 - 53.7343i) q^{49} +(294.797 - 54.9636i) q^{50} +(242.700 + 140.123i) q^{51} +(-75.9336 + 94.1815i) q^{52} +(439.900 - 253.976i) q^{53} +(379.087 + 133.786i) q^{54} -623.565 q^{55} +(191.407 + 372.800i) q^{56} +220.020 q^{57} +(722.962 + 255.144i) q^{58} +(-640.900 + 370.024i) q^{59} +(-485.173 - 391.170i) q^{60} +(-198.404 - 114.549i) q^{61} +(51.0714 - 9.52204i) q^{62} +(11.1488 + 7.66422i) q^{63} +(229.511 - 457.678i) q^{64} +(114.926 - 199.058i) q^{65} +(386.735 + 451.829i) q^{66} +(-262.711 + 151.676i) q^{67} +(67.5039 - 432.185i) q^{68} -708.629i q^{69} +(-468.607 - 643.688i) q^{70} +82.4824 q^{71} +(-0.485710 - 16.5222i) q^{72} +(135.675 + 234.997i) q^{73} +(-503.030 + 430.560i) q^{74} +(470.603 + 271.703i) q^{75} +(-123.756 - 320.346i) q^{76} +(327.026 + 685.825i) q^{77} +(-215.513 + 40.1814i) q^{78} +(-304.852 + 528.019i) q^{79} +(-296.639 + 926.431i) q^{80} +(354.371 + 613.789i) q^{81} +(-327.116 + 926.898i) q^{82} -587.294i q^{83} +(-175.779 + 738.762i) q^{84} +831.076i q^{85} +(-840.161 - 296.506i) q^{86} +(694.633 + 1203.14i) q^{87} +(440.327 - 817.225i) q^{88} +(804.220 - 1392.95i) q^{89} +(5.75606 + 30.8726i) q^{90} +(-279.206 - 22.0060i) q^{91} +(-1031.76 + 398.588i) q^{92} +(81.5285 + 47.0705i) q^{93} +(-722.943 - 844.627i) q^{94} +(326.237 + 565.058i) q^{95} +(855.257 - 359.630i) q^{96} -339.739 q^{97} +(-462.198 + 852.974i) q^{98} -29.9692i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{4} - 20 q^{6} - 4 q^{7} - 12 q^{8} + 160 q^{9} - 14 q^{10} - 110 q^{12} + 102 q^{14} - 116 q^{15} - 104 q^{16} - 2 q^{17} - 38 q^{18} + 256 q^{20} - 360 q^{22} + 162 q^{23} + 186 q^{24} + 348 q^{25}+ \cdots - 2670 q^{98}+O(q^{100}) $ 44 * q + 4 * q^4 - 20 * q^6 - 4 * q^7 - 12 * q^8 + 160 * q^9 - 14 * q^10 - 110 * q^12 + 102 * q^14 - 116 * q^15 - 104 * q^16 - 2 * q^17 - 38 * q^18 + 256 * q^20 - 360 * q^22 + 162 * q^23 + 186 * q^24 + 348 * q^25 - 302 * q^26 - 642 * q^28 - 396 * q^30 - 374 * q^31 - 140 * q^32 - 110 * q^33 - 148 * q^34 + 1440 * q^36 + 52 * q^38 + 52 * q^39 + 658 * q^40 - 8 * q^41 - 1710 * q^42 + 374 * q^44 - 486 * q^46 - 738 * q^47 + 936 * q^48 + 356 * q^49 + 2328 * q^50 + 96 * q^52 + 944 * q^54 - 2268 * q^55 + 1848 * q^56 - 452 * q^57 + 918 * q^58 + 410 * q^60 + 1416 * q^62 + 668 * q^63 - 2984 * q^64 + 248 * q^65 + 868 * q^66 - 64 * q^68 + 3422 * q^70 + 1248 * q^71 - 2172 * q^72 - 218 * q^73 - 176 * q^74 - 3028 * q^76 - 3716 * q^78 + 298 * q^79 - 2540 * q^80 - 1050 * q^81 - 146 * q^82 - 4844 * q^84 - 2412 * q^86 + 2140 * q^87 + 1626 * q^88 + 422 * q^89 - 4916 * q^90 + 1652 * q^92 - 2676 * q^94 - 2434 * q^95 - 400 * q^96 + 1672 * q^97 - 2670 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/56\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$29$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	0.941296	−	2.66720i	0.332798	−	0.942998i
$2$	0.941296	−	2.66720i	0.332798	−	0.942998i
$3$	4.43871	−	2.56269i	0.854230	−	0.493190i	−0.00784607	−	0.999969i	$-0.502498\pi$
$3$	4.43871	−	2.56269i	0.854230	−	0.493190i	0.862076	+	0.506780i	$0.169164\pi$
$4$	−6.22792	−	5.02125i	−0.778491	−	0.627656i
$5$	13.1631	+	7.59971i	1.17734	+	0.679739i	0.955398	−	0.295320i	$-0.0954264\pi$
$5$	13.1631	+	7.59971i	1.17734	+	0.679739i	0.221944	+	0.975059i	$0.428760\pi$
$6$	−2.65707	−	14.2512i	−0.180791	−	0.969670i
$7$	1.45519	−	18.4630i	0.0785728	−	0.996908i
$7$	1.45519	−	18.4630i	0.0785728	−	0.996908i
$8$	−19.2550	+	11.8846i	−0.850959	+	0.525232i
$9$	−0.365251	+	0.632633i	−0.0135278	+	0.0234308i
$10$	32.6603	−	27.9550i	1.03281	−	0.884016i
$11$	−35.5292	+	20.5128i	−0.973859	+	0.562258i	−0.900411	−	0.435041i	$-0.856734\pi$
$11$	−35.5292	+	20.5128i	−0.973859	+	0.562258i	−0.0734485	+	0.997299i	$0.523400\pi$
$12$	−40.5118	−	6.32763i	−0.974563	−	0.152219i
$13$		−	15.1225i		−	0.322632i	−0.986903	−	0.161316i	$-0.948426\pi$
$13$		−	15.1225i		−	0.322632i	0.986903	−	0.161316i	$-0.0515738\pi$
$14$	−47.8748	−	21.2604i	−0.913934	−	0.405863i
$15$	77.9028			1.34096
$16$	13.5741	+	62.5439i	0.212095	+	0.977249i
$17$	27.3391	+	47.3526i	0.390041	+	0.675571i	0.992455	−	0.122613i	$-0.0391275\pi$
$17$	27.3391	+	47.3526i	0.390041	+	0.675571i	−0.602414	+	0.798184i	$0.705794\pi$
$18$	1.34355	+	1.56969i	0.0175932	+	0.0205544i
$19$	37.1763	+	21.4637i	0.448886	+	0.259164i	0.707359	−	0.706854i	$-0.249886\pi$
$19$	37.1763	+	21.4637i	0.448886	+	0.259164i	−0.258474	+	0.966018i	$0.583220\pi$
$20$	−43.8187	−	113.426i	−0.489907	−	1.26814i
$21$	−40.8558	−	85.6811i	−0.424546	−	0.890340i
$22$	21.2682	+	114.072i	0.206109	+	1.10547i
$23$	69.1294	−	119.736i	0.626717	−	1.08550i	−0.361490	−	0.932376i	$-0.617732\pi$
$23$	69.1294	−	119.736i	0.626717	−	1.08550i	0.988206	−	0.153129i	$-0.0489349\pi$
$24$	−55.0107	+	102.097i	−0.467875	+	0.868353i
$25$	53.0113	+	91.8183i	0.424090	+	0.734546i
$26$	−40.3346	−	14.2347i	−0.304241	−	0.107371i
$27$			142.129i			1.01307i
$28$	−101.770	+	107.679i	−0.686884	+	0.726767i
$29$			271.056i			1.73565i	0.496869	+	0.867826i	$0.334483\pi$
$29$			271.056i			1.73565i	−0.496869	+	0.867826i	$0.665517\pi$
$30$	73.3296	−	207.782i	0.446270	−	1.26452i
$31$	9.18381	+	15.9068i	0.0532084	+	0.0921597i	0.891403	−	0.453212i	$-0.149722\pi$
$31$	9.18381	+	15.9068i	0.0532084	+	0.0921597i	−0.838194	+	0.545372i	$0.816389\pi$
$32$	179.594	+	22.6676i	0.992129	+	0.125222i
$33$	−105.136	+	182.100i	−0.554599	+	0.960594i
$34$	152.033	−	28.3459i	0.766867	−	0.142979i
$35$	159.468	−	231.971i	0.770145	−	1.12029i
$36$	5.45136	−	2.10597i	0.0252378	−	0.00974988i
$37$	−202.736	−	117.050i	−0.900801	−	0.520078i	−0.0233409	−	0.999728i	$-0.507430\pi$
$37$	−202.736	−	117.050i	−0.900801	−	0.520078i	−0.877460	+	0.479650i	$0.840764\pi$
$38$	92.2420	−	78.9529i	0.393780	−	0.337049i
$39$	−38.7541	−	67.1242i	−0.159119	−	0.275602i
$40$	−343.775	+	10.1061i	−1.35889	+	0.0399479i
$41$	−347.517			−1.32373			−0.661866	−	0.749622i	$-0.730235\pi$
$41$	−347.517			−1.32373			−0.661866	+	0.749622i	$0.730235\pi$
$42$	−266.986	+	28.3193i	−0.980877	+	0.104042i
$43$		−	314.997i		−	1.11713i	−0.829460	−	0.558566i	$-0.811352\pi$
$43$		−	314.997i		−	1.11713i	0.829460	−	0.558566i	$-0.188648\pi$
$44$	324.273	+	50.6489i	1.11104	+	0.173536i
$45$	−9.61566	+	5.55160i	−0.0318537	+	0.0183908i
$46$	−254.288	−	297.089i	−0.815059	−	0.952247i
$47$	196.536	−	340.410i	0.609951	−	1.05647i	−0.381297	−	0.924452i	$-0.624523\pi$
$47$	196.536	−	340.410i	0.609951	−	1.05647i	0.991248	−	0.132013i	$-0.0421441\pi$
$48$	220.532	+	242.828i	0.663147	+	0.730192i
$49$	−338.765	−	53.7343i	−0.987653	−	0.156660i
$50$	294.797	−	54.9636i	0.833812	−	0.155461i
$51$	242.700	+	140.123i	0.666369	+	0.384728i
$52$	−75.9336	+	94.1815i	−0.202502	+	0.251166i
$53$	439.900	−	253.976i	1.14009	−	0.658233i	0.193639	−	0.981073i	$-0.437971\pi$
$53$	439.900	−	253.976i	1.14009	−	0.658233i	0.946454	+	0.322840i	$0.104637\pi$
$54$	379.087	+	133.786i	0.955320	+	0.337147i
$55$	−623.565			−1.52875
$56$	191.407	+	372.800i	0.456746	+	0.889597i
$57$	220.020			0.511269
$58$	722.962	+	255.144i	1.63672	+	0.577622i
$59$	−640.900	+	370.024i	−1.41420	+	0.816491i	−0.995781	−	0.0917608i	$-0.970750\pi$
$59$	−640.900	+	370.024i	−1.41420	+	0.816491i	−0.418423	+	0.908252i	$0.637417\pi$
$60$	−485.173	−	391.170i	−1.04393	−	0.841663i
$61$	−198.404	−	114.549i	−0.416443	−	0.240433i	0.277111	−	0.960838i	$-0.410623\pi$
$61$	−198.404	−	114.549i	−0.416443	−	0.240433i	−0.693554	+	0.720404i	$0.743956\pi$
$62$	51.0714	−	9.52204i	0.104614	−	0.0195049i
$63$	11.1488	+	7.66422i	0.0222955	+	0.0153270i
$64$	229.511	−	457.678i	0.448263	−	0.893902i
$65$	114.926	−	199.058i	0.219305	−	0.379848i
$66$	386.735	+	451.829i	0.721269	+	0.842670i
$67$	−262.711	+	151.676i	−0.479034	+	0.276570i	−0.720014	−	0.693960i	$-0.755865\pi$
$67$	−262.711	+	151.676i	−0.479034	+	0.276570i	0.240980	+	0.970530i	$0.422531\pi$
$68$	67.5039	−	432.185i	0.120383	−	0.770737i
$69$		−	708.629i		−	1.23636i
$70$	−468.607	−	643.688i	−0.800132	−	1.09908i
$71$	82.4824			0.137871			0.0689356	−	0.997621i	$-0.478040\pi$
$71$	82.4824			0.137871			0.0689356	+	0.997621i	$0.478040\pi$
$72$	−0.485710	−	16.5222i	−0.000795021	−	0.0270439i
$73$	135.675	+	234.997i	0.217529	+	0.376771i	0.954052	−	0.299641i	$-0.0968670\pi$
$73$	135.675	+	234.997i	0.217529	+	0.376771i	−0.736523	+	0.676412i	$0.763534\pi$
$74$	−503.030	+	430.560i	−0.790217	+	0.676372i
$75$	470.603	+	271.703i	0.724541	+	0.418314i
$76$	−123.756	−	320.346i	−0.186787	−	0.483503i
$77$	327.026	+	685.825i	0.484001	+	1.01503i
$78$	−215.513	+	40.1814i	−0.312846	+	0.0583288i
$79$	−304.852	+	528.019i	−0.434159	+	0.751985i	−0.997227	−	0.0744258i	$-0.976288\pi$
$79$	−304.852	+	528.019i	−0.434159	+	0.751985i	0.563068	+	0.826411i	$0.309621\pi$
$80$	−296.639	+	926.431i	−0.414566	+	1.29473i
$81$	354.371	+	613.789i	0.486106	+	0.841961i
$82$	−327.116	+	926.898i	−0.440536	+	1.24828i
$83$		−	587.294i		−	0.776674i	−0.921518	−	0.388337i	$-0.873050\pi$
$83$		−	587.294i		−	0.776674i	0.921518	−	0.388337i	$-0.126950\pi$
$84$	−175.779	+	738.762i	−0.228323	+	0.959590i
$85$			831.076i			1.06050i
$86$	−840.161	−	296.506i	−1.05345	−	0.371779i
$87$	694.633	+	1203.14i	0.856005	+	1.48264i
$88$	440.327	−	817.225i	0.533398	−	0.989960i
$89$	804.220	−	1392.95i	0.957833	−	1.65902i	0.230085	−	0.973170i	$-0.426100\pi$
$89$	804.220	−	1392.95i	0.957833	−	1.65902i	0.727748	−	0.685845i	$-0.240567\pi$
$90$	5.75606	+	30.8726i	0.00674158	+	0.0361584i
$91$	−279.206	−	22.0060i	−0.321634	−	0.0253501i
$92$	−1031.76	+	398.588i	−1.16922	+	0.451693i
$93$	81.5285	+	47.0705i	0.0909045	+	0.0524837i
$94$	−722.943	−	844.627i	−0.793254	−	0.926772i
$95$	326.237	+	565.058i	0.352328	+	0.610250i
$96$	855.257	−	359.630i	0.909264	−	0.382340i
$97$	−339.739			−0.355622			−0.177811	−	0.984065i	$-0.556901\pi$
$97$	−339.739			−0.355622			−0.177811	+	0.984065i	$0.556901\pi$
$98$	−462.198	+	852.974i	−0.476419	+	0.879218i
$99$		−	29.9692i		−	0.0304245i
$100$	130.892	−	838.020i	0.130892	−	0.838020i
$101$	−691.541	+	399.261i	−0.681296	+	0.393347i	−0.800343	−	0.599542i	$-0.795349\pi$
$101$	−691.541	+	399.261i	−0.681296	+	0.393347i	0.119047	+	0.992889i	$0.462016\pi$
$102$	602.189	−	515.433i	0.584565	−	0.500348i
$103$	441.683	−	765.018i	0.422527	−	0.731839i	−0.573658	−	0.819095i	$-0.694476\pi$
$103$	441.683	−	765.018i	0.422527	−	0.731839i	0.996186	+	0.0872555i	$0.0278097\pi$
$104$	179.725	+	291.183i	0.169457	+	0.274547i
$105$	113.363	−	1438.32i	0.105363	−	1.33682i
$106$	−263.330	−	1412.37i	−0.241291	−	1.29416i
$107$	−301.588	−	174.122i	−0.272482	−	0.157318i	0.357533	−	0.933901i	$-0.383618\pi$
$107$	−301.588	−	174.122i	−0.272482	−	0.157318i	−0.630015	+	0.776583i	$0.716951\pi$
$108$	713.667	−	885.170i	0.635858	−	0.788663i
$109$	−182.882	+	105.587i	−0.160706	+	0.0927836i	−0.578196	−	0.815898i	$-0.696243\pi$
$109$	−182.882	+	105.587i	−0.160706	+	0.0927836i	0.417490	+	0.908681i	$0.362910\pi$
$110$	−586.959	+	1663.17i	−0.508767	+	1.44161i
$111$	−1199.85			−1.02599
$112$	1174.50	−	159.605i	0.990893	−	0.134654i
$113$	1594.12			1.32710			0.663552	−	0.748131i	$-0.269048\pi$
$113$	1594.12			1.32710			0.663552	+	0.748131i	$0.269048\pi$
$114$	207.104	−	586.837i	0.170149	−	0.482125i
$115$	1819.91	−	1050.73i	1.47572	−	0.852007i
$116$	1361.04	−	1688.12i	1.08939	−	1.35119i
$117$	9.56696	+	5.52349i	0.00755954	+	0.00436450i
$118$	383.651	+	2057.71i	0.299305	+	1.60532i
$119$	914.055	−	435.854i	0.704129	−	0.335754i
$120$	−1500.02	+	925.847i	−1.14110	+	0.704316i
$121$	176.048	−	304.924i	0.132268	−	0.229094i
$122$	−492.281	+	421.359i	−0.365320	+	0.312689i
$123$	−1542.53	+	890.578i	−1.13077	+	0.652851i
$124$	22.6761	−	145.181i	0.0164224	−	0.105142i
$125$		−	288.446i		−	0.206395i
$126$	30.9363	−	22.5218i	0.0218732	−	0.0159238i
$127$	−1607.77			−1.12336			−0.561679	−	0.827355i	$-0.689844\pi$
$127$	−1607.77			−1.12336			−0.561679	+	0.827355i	$0.689844\pi$
$128$	−1004.68	−	1042.96i	−0.693767	−	0.720200i
$129$	−807.240	−	1398.18i	−0.550958	−	0.954287i
$130$	−422.749	−	493.904i	−0.285212	−	0.333217i
$131$	1370.67	+	791.358i	0.914169	+	0.527796i	0.881770	−	0.471679i	$-0.156352\pi$
$131$	1370.67	+	791.358i	0.914169	+	0.527796i	0.0323987	+	0.999475i	$0.489685\pi$
$132$	1569.15	−	606.195i	1.03467	−	0.399716i
$133$	450.384	−	655.152i	0.293633	−	0.427135i
$134$	157.262	+	843.476i	0.101384	+	0.543770i
$135$	−1080.14	+	1870.86i	−0.688621	+	1.19273i
$136$	−1089.18	−	586.860i	−0.686740	−	0.370021i
$137$	337.449	+	584.478i	0.210439	+	0.364492i	0.951852	−	0.306558i	$-0.0991772\pi$
$137$	337.449	+	584.478i	0.210439	+	0.364492i	−0.741413	+	0.671049i	$0.765844\pi$
$138$	−1890.06	−	667.029i	−1.16589	−	0.411459i
$139$		−	158.324i		−	0.0966103i	−0.998833	−	0.0483051i	$-0.984618\pi$
$139$		−	158.324i		−	0.0966103i	0.998833	−	0.0483051i	$-0.0153820\pi$
$140$	−2157.94	+	643.968i	−1.30271	+	0.388752i
$141$		−	2014.64i		−	1.20329i
$142$	77.6404	−	219.997i	0.0458833	−	0.130012i
$143$	310.204	+	537.288i	0.181402	+	0.314198i
$144$	−44.5253	−	14.2568i	−0.0257669	−	0.00825047i
$145$	−2059.95	+	3567.94i	−1.17979	+	2.04346i
$146$	754.494	−	140.672i	0.427688	−	0.0797405i
$147$	−1641.38	+	629.638i	−0.920945	+	0.353277i
$148$	674.889	+	1746.97i	0.374835	+	0.970269i
$149$	2116.50	+	1221.96i	1.16369	+	0.671859i	0.952186	−	0.305518i	$-0.0988295\pi$
$149$	2116.50	+	1221.96i	1.16369	+	0.671859i	0.211507	+	0.977376i	$0.432163\pi$
$150$	1167.66	−	999.441i	0.635595	−	0.544027i
$151$	−304.069	−	526.663i	−0.163873	−	0.283836i	0.772382	−	0.635159i	$-0.219065\pi$
$151$	−304.069	−	526.663i	−0.163873	−	0.283836i	−0.936254	+	0.351323i	$0.885732\pi$
$152$	−970.919	+	28.5425i	−0.518105	+	0.0152309i
$153$	−39.9424			−0.0211056
$154$	2137.06	−	226.679i	1.11824	−	0.118613i
$155$			279.177i			0.144671i
$156$	−95.6893	+	612.638i	−0.0491108	+	0.314425i
$157$	1132.37	−	653.776i	0.575626	−	0.332338i	−0.183767	−	0.982970i	$-0.558829\pi$
$157$	1132.37	−	653.776i	0.575626	−	0.332338i	0.759393	+	0.650632i	$0.225496\pi$
$158$	1121.38	+	1310.12i	0.564633	+	0.659670i
$159$	1301.73	−	2254.65i	0.649268	−	1.12456i
$160$	2191.75	+	1663.24i	1.08296	+	0.821818i
$161$	−2110.08	−	1450.57i	−1.03291	−	0.710070i
$162$	1970.67	−	367.423i	0.955743	−	0.178194i
$163$	−1615.48	−	932.699i	−0.776284	−	0.448188i	0.0588277	−	0.998268i	$-0.481264\pi$
$163$	−1615.48	−	932.699i	−0.776284	−	0.448188i	−0.835112	+	0.550080i	$0.814597\pi$
$164$	2164.31	+	1744.97i	1.03051	+	0.830849i
$165$	−2767.82	+	1598.00i	−1.30591	+	0.753966i
$166$	−1566.43	−	552.818i	−0.732402	−	0.258476i
$167$	−417.840			−0.193613			−0.0968067	−	0.995303i	$-0.530863\pi$
$167$	−417.840			−0.193613			−0.0968067	+	0.995303i	$0.530863\pi$
$168$	1804.97	+	1164.23i	0.828906	+	0.534658i
$169$	1968.31			0.895909
$170$	2216.65	+	782.289i	1.00005	+	0.352934i
$171$	−27.1573	+	15.6793i	−0.0121449	+	0.00701185i
$172$	−1581.68	+	1961.78i	−0.701174	+	0.869676i
$173$	−1789.20	−	1032.99i	−0.786301	−	0.453971i	0.0523575	−	0.998628i	$-0.483326\pi$
$173$	−1789.20	−	1032.99i	−0.786301	−	0.453971i	−0.838659	+	0.544657i	$0.816660\pi$
$174$	3862.87	−	720.215i	1.68301	−	0.313790i
$175$	1772.38	−	845.135i	0.765597	−	0.365064i
$176$	−1765.23	−	1943.69i	−0.756016	−	0.832451i
$177$	−1896.51	+	3284.85i	−0.805370	+	1.39494i
$178$	−2958.27	−	3456.19i	−1.24568	−	1.45535i
$179$	1788.56	−	1032.63i	0.746835	−	0.431185i	−0.0777142	−	0.996976i	$-0.524762\pi$
$179$	1788.56	−	1032.63i	0.746835	−	0.431185i	0.824549	+	0.565790i	$0.191429\pi$
$180$	87.7616	+	13.7077i	0.0363409	+	0.00567616i
$181$			1483.01i			0.609012i	0.952510	+	0.304506i	$0.0984913\pi$
$181$			1483.01i			0.609012i	−0.952510	+	0.304506i	$0.901509\pi$
$182$	−321.510	+	723.984i	−0.130944	+	0.294864i
$183$	−1174.21			−0.474317
$184$	91.9283	+	3127.09i	0.0368318	+	1.25289i
$185$	−1779.09	−	3081.47i	−0.707034	−	1.22462i
$186$	202.289	−	173.146i	0.0797449	−	0.0682562i
$187$	−1942.67	−	1121.60i	−0.759690	−	0.438607i
$188$	−2933.29	+	1133.19i	−1.13794	+	0.439609i
$189$	2624.13	+	206.825i	1.00993	+	0.0795995i
$190$	1814.21	−	338.252i	0.692719	−	0.129154i
$191$	312.673	−	541.565i	0.118451	−	0.205164i	−0.800703	−	0.599062i	$-0.795540\pi$
$191$	312.673	−	541.565i	0.118451	−	0.205164i	0.919154	+	0.393898i	$0.128874\pi$
$192$	−154.156	−	2619.66i	−0.0579439	−	0.984676i
$193$	2661.55	+	4609.95i	0.992657	+	1.71933i	0.601083	+	0.799187i	$0.294736\pi$
$193$	2661.55	+	4609.95i	0.992657	+	1.71933i	0.391575	+	0.920146i	$0.371930\pi$
$194$	−319.795	+	906.153i	−0.118350	+	0.335350i
$195$		−	1178.08i		−	0.432637i
$196$	1839.99	+	2035.68i	0.670550	+	0.741865i
$197$		−	574.940i		−	0.207933i	−0.994581	−	0.103966i	$-0.966847\pi$
$197$		−	574.940i		−	0.207933i	0.994581	−	0.103966i	$-0.0331535\pi$
$198$	−79.9340	−	28.2099i	−0.0286902	−	0.0101252i
$199$	−1177.89	−	2040.17i	−0.419590	−	0.726751i	0.576308	−	0.817232i	$-0.304493\pi$
$199$	−1177.89	−	2040.17i	−0.419590	−	0.726751i	−0.995898	+	0.0904813i	$0.971159\pi$
$200$	−2111.96	−	1137.94i	−0.746691	−	0.402323i
$201$	−777.399	+	1346.49i	−0.272803	+	0.472509i
$202$	413.966	+	2220.30i	0.144191	+	0.773366i
$203$	5004.51	+	394.438i	1.73029	+	0.136375i
$204$	−807.926	−	2091.33i	−0.277285	−	0.717758i
$205$	−4574.40	−	2641.03i	−1.55849	−	0.899793i
$206$	−1624.70	−	1898.17i	−0.549506	−	0.641997i
$207$	50.4991	+	87.4671i	0.0169562	+	0.0293690i
$208$	945.818	−	205.273i	0.315292	−	0.0684286i
$209$	−1761.12			−0.582869
$210$	−3729.58	−	1656.25i	−1.22555	−	0.544247i
$211$			3735.73i			1.21885i	0.792842	+	0.609427i	$0.208600\pi$
$211$			3735.73i			1.21885i	−0.792842	+	0.609427i	$0.791400\pi$
$212$	−4014.94	−	627.103i	−1.30070	−	0.203159i
$213$	366.115	−	211.377i	0.117774	−	0.0679967i
$214$	−748.301	+	640.495i	−0.239032	+	0.204595i
$215$	2393.89	−	4146.34i	0.759358	−	1.31525i
$216$	−1689.16	−	2736.70i	−0.532095	−	0.862078i
$217$	307.052	−	146.413i	0.0960555	−	0.0458027i
$218$	109.476	+	587.173i	0.0340121	+	0.182424i
$219$	1204.45	+	695.388i	0.371639	+	0.214566i
$220$	3883.52	+	3131.08i	1.19012	+	0.959532i
$221$	716.088	−	413.434i	0.217961	−	0.125840i
$222$	−1129.41	+	3200.24i	−0.341447	+	0.967504i
$223$	1942.28			0.583249			0.291624	−	0.956533i	$-0.405804\pi$
$223$	1942.28			0.583249			0.291624	+	0.956533i	$0.405804\pi$
$224$	679.855	−	3282.87i	0.202789	−	0.979222i
$225$	−77.4497			−0.0229480
$226$	1500.54	−	4251.85i	0.441658	−	1.25146i
$227$	−3495.47	+	2018.11i	−1.02204	+	0.590073i	−0.914693	−	0.404149i	$-0.867568\pi$
$227$	−3495.47	+	2018.11i	−1.02204	+	0.590073i	−0.107344	+	0.994222i	$0.534235\pi$
$228$	−1370.27	−	1104.77i	−0.398018	−	0.320901i
$229$	2941.05	+	1698.02i	0.848690	+	0.489992i	0.860209	−	0.509942i	$-0.170333\pi$
$229$	2941.05	+	1698.02i	0.848690	+	0.489992i	−0.0115185	+	0.999934i	$0.503667\pi$
$230$	−1089.42	−	5843.12i	−0.312324	−	1.67515i
$231$	3209.13	+	2206.11i	0.914048	+	0.628361i
$232$	−3221.41	−	5219.19i	−0.911620	−	1.47697i
$233$	2806.20	−	4860.49i	0.789015	−	1.36661i	−0.137556	−	0.990494i	$-0.543925\pi$
$233$	2806.20	−	4860.49i	0.789015	−	1.36661i	0.926571	−	0.376120i	$-0.122742\pi$
$234$	23.7376	−	20.3178i	0.00663152	−	0.00567613i
$235$	5174.03	−	2987.23i	1.43624	−	0.829214i
$236$	5849.46	+	913.640i	1.61342	+	0.252004i
$237$			3124.96i			0.856490i
$238$	−302.114	−	2848.24i	−0.0822821	−	0.775730i
$239$	−1154.25			−0.312394			−0.156197	−	0.987726i	$-0.549923\pi$
$239$	−1154.25			−0.312394			−0.156197	+	0.987726i	$0.549923\pi$
$240$	1057.46	+	4872.35i	0.284411	+	1.31045i
$241$	1134.86	+	1965.63i	0.303330	+	0.525383i	0.976888	−	0.213751i	$-0.0685682\pi$
$241$	1134.86	+	1965.63i	0.303330	+	0.525383i	−0.673558	+	0.739134i	$0.735235\pi$
$242$	−647.581	−	756.580i	−0.172017	−	0.200970i
$243$	−177.463	−	102.458i	−0.0468487	−	0.0270481i
$244$	660.468	+	1709.64i	0.173287	+	0.448558i
$245$	−4050.83	−	3281.83i	−1.05632	−	0.855788i
$246$	923.377	+	4952.53i	0.239319	+	1.28358i
$247$	324.585	−	562.197i	0.0836147	−	0.144825i
$248$	−365.881	−	197.140i	−0.0936834	−	0.0504774i
$249$	−1505.05	−	2606.83i	−0.383047	−	0.663458i
$250$	−769.343	−	271.513i	−0.194630	−	0.0686879i
$251$			2730.85i			0.686733i	0.939202	+	0.343366i	$0.111567\pi$
$251$			2730.85i			0.686733i	−0.939202	+	0.343366i	$0.888433\pi$
$252$	−30.9498	−	103.713i	−0.00773673	−	0.0259258i
$253$			5672.15i			1.40950i
$254$	−1513.39	+	4288.25i	−0.373852	+	1.05932i
$255$	2129.79	+	3688.90i	0.523030	+	0.905914i
$256$	−3727.49	+	1697.95i	−0.910031	+	0.414539i
$257$	−3236.06	+	5605.01i	−0.785446	+	1.36043i	0.143286	+	0.989681i	$0.454233\pi$
$257$	−3236.06	+	5605.01i	−0.785446	+	1.36043i	−0.928732	+	0.370751i	$0.879100\pi$
$258$	−4489.08	+	836.970i	−1.08325	+	0.201967i
$259$	−2456.11	+	3572.79i	−0.589248	+	0.857152i
$260$	−1715.27	+	662.646i	−0.409141	+	0.158060i
$261$	−171.479	−	99.0035i	−0.0406678	−	0.0234795i
$262$	3400.92	−	2910.95i	0.801944	−	0.686410i
$263$	−622.289	−	1077.84i	−0.145901	−	0.252708i	0.783808	−	0.621004i	$-0.213275\pi$
$263$	−622.289	−	1077.84i	−0.145901	−	0.252708i	−0.929709	+	0.368296i	$0.879941\pi$
$264$	−139.809	−	4755.85i	−0.0325935	−	1.10872i
$265$	7720.59			1.78971
$266$	−1323.48	−	1817.96i	−0.305066	−	0.419045i
$267$		−	8243.86i		−	1.88957i
$268$	2397.75	+	374.510i	0.546515	+	0.0853613i
$269$	2732.98	−	1577.89i	0.619453	−	0.357641i	−0.157203	−	0.987566i	$-0.550248\pi$
$269$	2732.98	−	1577.89i	0.619453	−	0.357641i	0.776656	+	0.629925i	$0.216914\pi$
$270$	3973.23	+	4641.99i	0.895567	+	1.04631i
$271$	997.435	−	1727.61i	0.223579	−	0.387250i	−0.732313	−	0.680968i	$-0.761559\pi$
$271$	997.435	−	1727.61i	0.223579	−	0.387250i	0.955892	+	0.293718i	$0.0948927\pi$
$272$	−2590.52	+	2352.66i	−0.577475	+	0.524452i
$273$	−1295.71	+	617.840i	−0.287252	+	0.136972i
$274$	1876.56	−	349.877i	0.413749	−	0.0771417i
$275$	−3766.89	−	2174.82i	−0.826008	−	0.476896i
$276$	−3558.20	+	4413.29i	−0.776010	+	0.962495i
$277$	1046.97	−	604.470i	0.227099	−	0.131116i	−0.382134	−	0.924107i	$-0.624811\pi$
$277$	1046.97	−	604.470i	0.227099	−	0.131116i	0.609233	+	0.792991i	$0.291477\pi$
$278$	−422.281	−	149.029i	−0.0911033	−	0.0321517i
$279$	−13.4176			−0.00287917
$280$	−313.669	+	6361.83i	−0.0669475	+	1.35783i
$281$	4944.71			1.04974			0.524869	−	0.851183i	$-0.324114\pi$
$281$	4944.71			1.04974			0.524869	+	0.851183i	$0.324114\pi$
$282$	−5373.45	−	1896.37i	−1.13470	−	0.400451i
$283$	−4177.28	+	2411.76i	−0.877434	+	0.506587i	−0.869811	−	0.493384i	$-0.835760\pi$
$283$	−4177.28	+	2411.76i	−0.877434	+	0.506587i	−0.00762240	+	0.999971i	$0.502426\pi$
$284$	−513.694	−	414.165i	−0.107331	−	0.0865358i
$285$	2896.14	+	1672.09i	0.601938	+	0.347529i
$286$	1725.05	−	321.628i	0.356658	−	0.0664974i
$287$	−505.703	+	6416.21i	−0.104009	+	1.31964i
$288$	−79.9373	+	105.338i	−0.0163554	+	0.0215524i
$289$	961.651	−	1665.63i	0.195736	−	0.339025i
$290$	7577.39	+	8852.79i	1.53434	+	1.79260i
$291$	−1508.00	+	870.646i	−0.303782	+	0.175389i
$292$	335.001	−	2144.80i	0.0671386	−	0.429846i
$293$		−	3239.94i		−	0.646004i	−0.946398	−	0.323002i	$-0.895308\pi$
$293$		−	3239.94i		−	0.646004i	0.946398	−	0.323002i	$-0.104692\pi$
$294$	134.345	+	4970.57i	0.0266502	+	0.986019i
$295$	−11248.3			−2.22000
$296$	5294.78	−	155.653i	1.03971	−	0.0305647i
$297$	−2915.47	−	5049.74i	−0.569605	−	0.986584i
$298$	5251.47	−	4494.90i	1.02084	−	0.873767i
$299$	−1810.70	−	1045.41i	−0.350218	−	0.202199i
$300$	−1566.59	−	4055.16i	−0.301491	−	0.780416i
$301$	−5815.80	−	458.380i	−1.11368	−	0.0877761i
$302$	−1690.93	+	315.267i	−0.322193	+	0.0600715i
$303$	−2046.37	+	3544.41i	−0.387989	+	0.672017i
$304$	−837.793	+	2616.50i	−0.158062	+	0.493641i
$305$	−1741.07	−	3015.63i	−0.326864	−	0.566145i
$306$	−37.5977	+	106.535i	−0.00702391	+	0.0199025i
$307$		−	232.720i		−	0.0432640i	−0.999766	−	0.0216320i	$-0.993114\pi$
$307$		−	232.720i		−	0.0432640i	0.999766	−	0.0216320i	$-0.00688622\pi$
$308$	1407.01	−	5913.35i	0.260298	−	1.09397i
$309$		−	4527.59i		−	0.833545i
$310$	744.622	+	262.789i	0.136425	+	0.0481464i
$311$	4470.58	+	7743.27i	0.815123	+	1.41183i	0.909240	+	0.416273i	$0.136664\pi$
$311$	4470.58	+	7743.27i	0.815123	+	1.41183i	−0.0941169	+	0.995561i	$0.530003\pi$
$312$	1543.96	+	831.897i	0.280158	+	0.150952i
$313$	−728.675	+	1262.10i	−0.131588	+	0.227918i	−0.924289	−	0.381693i	$-0.875341\pi$
$313$	−728.675	+	1262.10i	−0.131588	+	0.227918i	0.792701	+	0.609611i	$0.208674\pi$
$314$	−677.854	−	3635.66i	−0.121826	−	0.653415i
$315$	88.5066	+	185.613i	0.0158311	+	0.0332003i
$316$	4549.91	−	1757.72i	0.809976	−	0.312911i
$317$	6186.03	+	3571.51i	1.09603	+	0.632794i	0.935176	−	0.354184i	$-0.115241\pi$
$317$	6186.03	+	3571.51i	1.09603	+	0.632794i	0.160856	+	0.986978i	$0.448575\pi$
$318$	−4788.31	−	5594.26i	−0.844387	−	0.986511i
$319$	−5560.12	−	9630.41i	−0.975883	−	1.69028i
$320$	6499.29	−	4280.24i	1.13538	−	0.747727i
$321$	−1784.88			−0.310350
$322$	−5855.19	+	4262.60i	−1.01334	+	0.737718i
$323$			2347.19i			0.404339i
$324$	874.992	−	5602.02i	0.150033	−	0.960566i
$325$	1388.52	−	801.661i	0.236988	−	0.136825i
$326$	−4008.34	+	3430.87i	−0.680986	+	0.582878i
$327$	−541.174	+	937.341i	−0.0915199	+	0.158517i
$328$	6691.44	−	4130.12i	1.12644	−	0.695267i
$329$	−5998.99	−	4124.00i	−1.00527	−	0.691074i
$330$	1656.86	+	8886.53i	0.276385	+	1.48239i
$331$	8679.66	+	5011.20i	1.44132	+	0.832147i	0.997938	−	0.0641853i	$-0.0204449\pi$
$331$	8679.66	+	5011.20i	1.44132	+	0.832147i	0.443383	+	0.896332i	$0.353778\pi$
$332$	−2948.95	+	3657.62i	−0.487484	+	0.604633i
$333$	148.099	−	85.5051i	0.0243717	−	0.0140710i
$334$	−393.311	+	1114.46i	−0.0644342	+	0.182577i
$335$	−4610.79			−0.751983
$336$	4804.25	−	3718.32i	0.780040	−	0.603724i
$337$	−1689.89			−0.273158			−0.136579	−	0.990629i	$-0.543611\pi$
$337$	−1689.89			−0.273158			−0.136579	+	0.990629i	$0.543611\pi$
$338$	1852.76	−	5249.88i	0.298157	−	0.844840i
$339$	7075.85	−	4085.25i	1.13365	−	0.654514i
$340$	4173.04	−	5175.88i	0.665632	−	0.825593i
$341$	−652.587	−	376.771i	−0.103635	−	0.0598337i
$342$	16.2567	+	87.1930i	0.00257036	+	0.0137861i
$343$	−1485.06	+	6176.42i	−0.233778	+	0.972290i
$344$	3743.63	+	6065.28i	0.586753	+	0.950633i
$345$	5385.38	−	9327.74i	0.840403	−	1.45562i
$346$	−4439.36	+	3799.80i	−0.689774	+	0.590400i
$347$	−2192.29	+	1265.72i	−0.339160	+	0.195814i	−0.659901	−	0.751353i	$-0.729402\pi$
$347$	−2192.29	+	1265.72i	−0.339160	+	0.195814i	0.320740	+	0.947167i	$0.396068\pi$
$348$	1715.14	−	10981.0i	0.264199	−	1.69150i
$349$		−	2583.30i		−	0.396221i	−0.980180	−	0.198110i	$-0.936520\pi$
$349$		−	2583.30i		−	0.396221i	0.980180	−	0.198110i	$-0.0634804\pi$
$350$	−585.808	−	5522.82i	−0.0894651	−	0.843449i
$351$	2149.34			0.326848
$352$	−6845.82	+	2878.62i	−1.03660	+	0.435884i
$353$	725.039	+	1255.80i	0.109320	+	0.189348i	0.915495	−	0.402329i	$-0.131799\pi$
$353$	725.039	+	1255.80i	0.109320	+	0.189348i	−0.806175	+	0.591677i	$0.798466\pi$
$354$	6976.19	+	8150.40i	1.04740	+	1.22370i
$355$	1085.72	+	626.843i	0.162322	+	0.0937165i
$356$	−12003.0	+	4636.99i	−1.78696	+	0.690338i
$357$	2940.27	−	4277.07i	0.435897	−	0.634080i
$358$	−1070.66	−	5742.47i	−0.158062	−	0.847762i
$359$	247.731	−	429.083i	0.0364199	−	0.0630811i	−0.847241	−	0.531209i	$-0.821738\pi$
$359$	247.731	−	429.083i	0.0364199	−	0.0630811i	0.883661	+	0.468128i	$0.155071\pi$
$360$	119.171	−	221.175i	0.0174468	−	0.0323804i
$361$	−2508.12	−	4344.18i	−0.365668	−	0.633355i
$362$	3955.48	+	1395.95i	0.574297	+	0.202678i
$363$		−	1804.63i		−	0.260932i
$364$	1628.38	+	1539.01i	0.234478	+	0.221611i
$365$			4124.38i			0.591451i
$366$	−1105.28	+	3131.85i	−0.157852	+	0.447280i
$367$	−1665.41	−	2884.57i	−0.236876	−	0.410281i	0.722940	−	0.690911i	$-0.242790\pi$
$367$	−1665.41	−	2884.57i	−0.236876	−	0.410281i	−0.959816	+	0.280629i	$0.909457\pi$
$368$	8427.11	+	2698.33i	1.19373	+	0.382228i
$369$	126.931	−	219.851i	0.0179072	−	0.0310162i
$370$	−9893.56	+	1844.61i	−1.39011	+	0.259181i
$371$	−4049.03	−	8491.46i	−0.566618	−	1.18829i
$372$	−271.401	−	702.527i	−0.0378265	−	0.0979148i
$373$	1973.29	+	1139.28i	0.273923	+	0.158149i	0.630669	−	0.776052i	$-0.282781\pi$
$373$	1973.29	+	1139.28i	0.273923	+	0.158149i	−0.356746	+	0.934201i	$0.616114\pi$
$374$	−4820.16	+	4125.73i	−0.666429	+	0.570418i
$375$	−739.197	−	1280.33i	−0.101792	−	0.176309i
$376$	261.353	+	8890.35i	0.0358464	+	1.21937i
$377$	4099.04			0.559976
$378$	3021.73	−	6804.41i	0.411167	−	0.925876i
$379$		−	9424.88i		−	1.27737i	−0.769468	−	0.638685i	$-0.779479\pi$
$379$		−	9424.88i		−	1.27737i	0.769468	−	0.638685i	$-0.220521\pi$
$380$	805.523	−	5157.26i	0.108743	−	0.696215i
$381$	−7136.42	+	4120.21i	−0.959606	+	0.554029i
$382$	−1150.15	−	1343.74i	−0.154049	−	0.179978i
$383$	−4945.41	+	8565.70i	−0.659788	+	1.14279i	0.320883	+	0.947119i	$0.396020\pi$
$383$	−4945.41	+	8565.70i	−0.659788	+	1.14279i	−0.980670	+	0.195667i	$0.937313\pi$
$384$	−7132.27	−	2054.71i	−0.947831	−	0.273058i
$385$	−907.404	+	11512.9i	−0.120118	+	1.52403i
$386$	14801.0	−	2759.58i	1.95168	−	0.363883i
$387$	199.278	+	115.053i	0.0261753	+	0.0151123i
$388$	2115.87	+	1705.92i	0.276848	+	0.223208i
$389$	−7363.48	+	4251.31i	−0.959751	+	0.554113i	−0.896096	−	0.443859i	$-0.853609\pi$
$389$	−7363.48	+	4251.31i	−0.959751	+	0.554113i	−0.0636548	+	0.997972i	$0.520276\pi$
$390$	−3142.18	−	1108.92i	−0.407976	−	0.143981i
$391$	7559.73			0.977780
$392$	7161.53	−	2991.45i	0.922735	−	0.385436i
$393$	8112.01			1.04121
$394$	−1533.48	−	541.189i	−0.196080	−	0.0691997i
$395$	−8025.59	+	4633.58i	−1.02231	+	0.590229i
$396$	−150.483	+	186.646i	−0.0190961	+	0.0236851i
$397$	−12788.4	−	7383.40i	−1.61671	−	0.933406i	−0.987764	−	0.155954i	$-0.950155\pi$
$397$	−12788.4	−	7383.40i	−1.61671	−	0.933406i	−0.628943	−	0.777452i	$-0.716512\pi$
$398$	−6550.27	+	1221.27i	−0.824964	+	0.153811i
$399$	320.170	−	4062.22i	0.0401718	−	0.509688i
$400$	−5023.10	+	4561.88i	−0.627887	+	0.570235i
$401$	−2506.57	+	4341.51i	−0.312150	+	0.540660i	−0.978828	−	0.204686i	$-0.934383\pi$
$401$	−2506.57	+	4341.51i	−0.312150	+	0.540660i	0.666677	+	0.745346i	$0.267716\pi$
$402$	2859.61	+	3340.93i	0.354787	+	0.414503i
$403$	240.550	−	138.882i	0.0297337	−	0.0171667i
$404$	6311.66	+	985.832i	0.777269	+	0.121403i
$405$			10772.5i			1.32170i
$406$	5762.77	−	12976.8i	0.704437	−	1.58627i
$407$	9604.07			1.16967
$408$	−6338.51	+	186.336i	−0.769125	+	0.0226103i
$409$	699.767	+	1212.03i	0.0845997	+	0.146531i	0.905221	−	0.424942i	$-0.139706\pi$
$409$	699.767	+	1212.03i	0.0845997	+	0.146531i	−0.820621	+	0.571473i	$0.806372\pi$
$410$	−11350.0	+	9714.85i	−1.36716	+	1.17020i
$411$	2995.67	+	1729.55i	0.359527	+	0.207573i
$412$	−6592.11	+	2546.67i	−0.788277	+	0.304528i
$413$	5899.12	+	12371.4i	0.702849	+	1.47399i
$414$	280.827	−	52.3590i	0.0333379	−	0.00621571i
$415$	4463.27	−	7730.61i	0.527935	−	0.914411i
$416$	342.789	−	2715.91i	0.0404005	−	0.320092i
$417$	−405.734	−	702.752i	−0.0476472	−	0.0825273i
$418$	−1657.74	+	4697.27i	−0.193978	+	0.549644i
$419$		−	306.232i		−	0.0357050i	−0.999841	−	0.0178525i	$-0.994317\pi$
$419$		−	306.232i		−	0.0357050i	0.999841	−	0.0178525i	$-0.00568293\pi$
$420$	−7928.18	+	8388.52i	−0.921085	+	0.974566i
$421$		−	5155.25i		−	0.596797i	−0.954441	−	0.298398i	$-0.903548\pi$
$421$		−	5155.25i		−	0.596797i	0.954441	−	0.298398i	$-0.0964524\pi$
$422$	9963.94	+	3516.43i	1.14938	+	0.405632i
$423$	143.570	+	248.670i	0.0165026	+	0.0285833i
$424$	−5451.86	+	10118.4i	−0.624448	+	1.15894i
$425$	−2898.56	+	5020.45i	−0.330825	+	0.573006i
$426$	−219.162	−	1175.47i	−0.0249258	−	0.133690i
$427$	−2403.63	+	3496.44i	−0.272411	+	0.396264i
$428$	1003.96	+	2598.76i	0.113383	+	0.293495i
$429$	2753.81	+	1589.91i	0.309918	+	0.178931i
$430$	−8805.76	−	10287.9i	−0.987561	−	1.15378i
$431$	3748.15	+	6491.98i	0.418891	+	0.725540i	0.995828	−	0.0912485i	$-0.0290857\pi$
$431$	3748.15	+	6491.98i	0.418891	+	0.725540i	−0.576938	+	0.816788i	$0.695752\pi$
$432$	−8889.33	+	1929.27i	−0.990018	+	0.214866i
$433$	9121.97			1.01241			0.506205	−	0.862413i	$-0.331048\pi$
$433$	9121.97			1.01241			0.506205	+	0.862413i	$0.331048\pi$
$434$	−101.487	−	956.788i	−0.0112247	−	0.105823i
$435$			21116.0i			2.32744i
$436$	1669.16	+	260.709i	0.183344	+	0.0286369i
$437$	5139.95	−	2967.55i	0.562648	−	0.324845i
$438$	2988.48	−	2557.94i	0.326016	−	0.279048i
$439$	4597.08	−	7962.38i	0.499788	−	0.865658i	−0.500212	−	0.865903i	$-0.666745\pi$
$439$	4597.08	−	7962.38i	0.499788	−	0.865658i	1.00000		0.000245077i	$7.80105e-5\pi$
$440$	12006.7	−	7410.85i	1.30091	−	0.802951i
$441$	157.728	−	194.687i	0.0170314	−	0.0210223i
$442$	−428.660	−	2299.11i	−0.0461296	−	0.247416i
$443$	1378.95	+	796.139i	0.147892	+	0.0853853i	0.572120	−	0.820170i	$-0.306121\pi$
$443$	1378.95	+	796.139i	0.147892	+	0.0853853i	−0.424228	+	0.905555i	$0.639455\pi$
$444$	7472.57	+	6024.74i	0.798722	+	0.643968i
$445$	21172.0	−	12223.7i	2.25540	−	1.30215i
$446$	1828.26	−	5180.44i	0.194104	−	0.550002i
$447$	12526.0			1.32542
$448$	−8116.12	−	4903.46i	−0.855917	−	0.517113i
$449$	−6521.40			−0.685443			−0.342721	−	0.939437i	$-0.611349\pi$
$449$	−6521.40			−0.685443			−0.342721	+	0.939437i	$0.611349\pi$
$450$	−72.9030	+	206.574i	−0.00763707	+	0.0216400i
$451$	12347.0	−	7128.54i	1.28913	−	0.744279i
$452$	−9928.09	−	8004.50i	−1.03314	−	0.832965i
$453$	−2699.34	−	1558.47i	−0.279970	−	0.161641i
$454$	2092.43	+	11222.8i	0.216306	+	1.16015i
$455$	−3507.97	−	2411.55i	−0.361442	−	0.248473i
$456$	−4236.48	+	2614.85i	−0.435069	+	0.268535i
$457$	−1766.24	+	3059.22i	−0.180791	+	0.313138i	−0.942150	−	0.335192i	$-0.891199\pi$
$457$	−1766.24	+	3059.22i	−0.180791	+	0.313138i	0.761359	+	0.648330i	$0.224532\pi$
$458$	7297.35	−	6246.04i	0.744504	−	0.637245i
$459$	−6730.20	+	3885.68i	−0.684398	+	0.395137i
$460$	−16610.3	−	2594.39i	−1.68360	−	0.262965i
$461$		−	16783.8i		−	1.69566i	−0.530270	−	0.847829i	$-0.677910\pi$
$461$		−	16783.8i		−	1.69566i	0.530270	−	0.847829i	$-0.322090\pi$
$462$	8904.88	−	6482.79i	0.896737	−	0.652828i
$463$	−2743.41			−0.275372			−0.137686	−	0.990476i	$-0.543967\pi$
$463$	−2743.41			−0.275372			−0.137686	+	0.990476i	$0.543967\pi$
$464$	−16952.9	+	3679.34i	−1.69616	+	0.368123i
$465$	715.445	+	1239.19i	0.0713505	+	0.123583i
$466$	−10322.4	−	12059.9i	−1.02613	−	1.19885i
$467$	2302.88	+	1329.57i	0.228189	+	0.131745i	0.609736	−	0.792604i	$-0.291275\pi$
$467$	2302.88	+	1329.57i	0.228189	+	0.131745i	−0.381547	+	0.924349i	$0.624609\pi$
$468$	−31.8475	−	82.4380i	−0.00314562	−	0.00814251i
$469$	2418.11	+	5071.15i	0.238076	+	0.499284i
$470$	−3097.25	−	16612.1i	−0.303969	−	1.63033i
$471$	3350.85	−	5803.84i	0.327811	−	0.567785i
$472$	7942.93	−	14741.7i	0.774583	−	1.43759i
$473$	6461.47	+	11191.6i	0.628116	+	1.08793i
$474$	8334.91	+	2941.52i	0.807669	+	0.285039i
$475$			4551.28i			0.439636i
$476$	−7881.20	−	1875.24i	−0.758895	−	0.180570i
$477$			371.060i			0.0356178i
$478$	−1086.49	+	3078.62i	−0.103964	+	0.294587i
$479$	−4415.98	−	7648.70i	−0.421234	−	0.729599i	0.574826	−	0.818276i	$-0.305070\pi$
$479$	−4415.98	−	7648.70i	−0.421234	−	0.729599i	−0.996061	+	0.0886762i	$0.971736\pi$
$480$	13990.9	+	1765.87i	1.33041	+	0.167918i
$481$	−1770.08	+	3065.87i	−0.167794	+	0.290627i
$482$	6310.96	−	1176.65i	0.596383	−	0.111193i
$483$	−13083.4	−	1031.19i	−1.23254	−	0.0971443i
$484$	−2627.52	+	1015.06i	−0.246761	+	0.0953290i
$485$	−4472.02	−	2581.92i	−0.418688	−	0.241730i
$486$	−440.321	+	376.885i	−0.0410975	+	0.0351767i
$487$	−6615.85	−	11459.0i	−0.615591	−	1.06623i	−0.990281	−	0.139084i	$-0.955584\pi$
$487$	−6615.85	−	11459.0i	−0.615591	−	1.06623i	0.374690	−	0.927150i	$-0.377749\pi$
$488$	5181.64	−	152.327i	0.480659	−	0.0141301i
$489$	−9560.87			−0.884166
$490$	−12566.3	+	7715.20i	−1.15855	+	0.711301i
$491$			834.685i			0.0767186i	0.999264	+	0.0383593i	$0.0122131\pi$
$491$			834.685i			0.0767186i	−0.999264	+	0.0383593i	$0.987787\pi$
$492$	14078.6	+	2198.96i	1.29006	+	0.201498i
$493$	−12835.2	+	7410.42i	−1.17256	+	0.676975i
$494$	−1193.96	−	1394.93i	−0.108743	−	0.127046i
$495$	227.758	−	394.488i	0.0206807	−	0.0358200i
$496$	−870.214	+	790.312i	−0.0787778	+	0.0715445i
$497$	120.027	−	1522.87i	0.0108329	−	0.137445i
$498$	−8369.63	+	1560.48i	−0.753117	+	0.140415i
$499$	−5413.50	−	3125.49i	−0.485655	−	0.280393i	0.237115	−	0.971482i	$-0.423798\pi$
$499$	−5413.50	−	3125.49i	−0.485655	−	0.280393i	−0.722770	+	0.691089i	$0.757131\pi$
$500$	−1448.36	+	1796.42i	−0.129545	+	0.160677i
$501$	−1854.67	+	1070.79i	−0.165390	+	0.0954882i
$502$	7283.73	+	2570.54i	0.647588	+	0.228544i
$503$	−3208.62			−0.284424			−0.142212	−	0.989836i	$-0.545421\pi$
$503$	−3208.62			−0.284424			−0.142212	+	0.989836i	$0.545421\pi$
$504$	−305.757	−	15.0753i	−0.0270228	−	0.00133235i
$505$	−12137.1			−1.06949
$506$	15128.8	+	5339.17i	1.32916	+	0.469081i
$507$	8736.76	−	5044.17i	0.765312	−	0.441853i
$508$	10013.1	+	8073.02i	0.874524	+	0.705083i
$509$	−10253.9	−	5920.12i	−0.892923	−	0.515530i	−0.0180259	−	0.999838i	$-0.505738\pi$
$509$	−10253.9	−	5920.12i	−0.892923	−	0.515530i	−0.874898	+	0.484308i	$0.839071\pi$
$510$	11843.8	−	2208.23i	1.02834	−	0.191729i
$511$	4536.18	−	2163.01i	0.392698	−	0.187252i
$512$	1020.11	+	11540.2i	0.0880526	+	0.996116i
$513$	−3050.63	+	5283.84i	−0.262551	+	0.454751i
$514$	11903.6	+	13907.2i	1.02149	+	1.19342i
$515$	11627.8	−	6713.33i	0.994919	−	0.574417i
$516$	−1993.19	+	12761.1i	−0.170049	+	1.08872i
$517$			16126.0i			1.37180i
$518$	7217.42	+	9913.99i	0.612192	+	0.840919i
$519$	−10589.0			−0.895576
$520$	152.829	+	5198.73i	0.0128885	+	0.438422i
$521$	−2562.84	−	4438.96i	−0.215508	−	0.373272i	0.737921	−	0.674887i	$-0.235808\pi$
$521$	−2562.84	−	4438.96i	−0.215508	−	0.373272i	−0.953430	+	0.301615i	$0.902474\pi$
$522$	−425.475	+	364.178i	−0.0356753	+	0.0305357i
$523$	−2362.76	−	1364.14i	−0.197545	−	0.114053i	0.397965	−	0.917401i	$-0.369717\pi$
$523$	−2362.76	−	1364.14i	−0.197545	−	0.114053i	−0.595510	+	0.803348i	$0.703050\pi$
$524$	−4562.83	−	11811.0i	−0.380397	−	0.984668i
$525$	5701.27	−	8293.37i	0.473950	−	0.689433i
$526$	−3460.56	+	645.207i	−0.286859	+	0.0534836i
$527$	−502.154	+	869.756i	−0.0415069	+	0.0718921i
$528$	−12816.4	−	4103.76i	−1.05637	−	0.338245i
$529$	−3474.25	−	6017.58i	−0.285547	−	0.494582i
$530$	7267.36	−	20592.4i	0.595612	−	1.68769i
$531$		−	540.606i		−	0.0441813i
$532$	−6094.64	+	1818.75i	−0.496684	+	0.148219i
$533$			5255.31i			0.427078i
$534$	−21988.0	−	7759.91i	−1.78186	−	0.628847i
$535$	−2646.55	−	4583.96i	−0.213870	−	0.370433i
$536$	3255.89	−	6042.76i	0.262375	−	0.486954i
$537$	5292.61	−	9167.06i	0.425312	−	0.736663i
$538$	−1636.00	−	8774.68i	−0.131102	−	0.703166i
$539$	13138.3	−	5039.87i	1.04992	−	0.402751i
$540$	16121.1	−	6227.91i	1.28471	−	0.496309i
$541$	−7335.89	−	4235.38i	−0.582985	−	0.336586i	0.179334	−	0.983788i	$-0.442606\pi$
$541$	−7335.89	−	4235.38i	−0.582985	−	0.336586i	−0.762319	+	0.647202i	$0.775939\pi$
$542$	−3669.00	−	4286.55i	−0.290769	−	0.339710i
$543$	3800.49	+	6582.64i	0.300358	+	0.520236i
$544$	3836.58	+	9123.98i	0.302375	+	0.719095i
$545$	−3209.73			−0.252275
$546$	428.258	+	4037.48i	0.0335673	+	0.316462i
$547$		−	22768.8i		−	1.77975i	−0.456205	−	0.889875i	$-0.650792\pi$
$547$		−	22768.8i		−	1.77975i	0.456205	−	0.889875i	$-0.349208\pi$
$548$	833.208	−	5334.50i	0.0649505	−	0.415837i
$549$	144.934	−	83.6779i	0.0112671	−	0.00650507i
$550$	−9346.44	+	7999.92i	−0.724606	+	0.620214i
$551$	−5817.88	+	10076.9i	−0.449819	+	0.779109i
$552$	8421.80	+	13644.7i	0.649376	+	1.05209i
$553$	9305.20	+	6396.85i	0.715547	+	0.491902i
$554$	−626.732	−	3361.47i	−0.0480637	−	0.257789i
$555$	−15793.7	−	9118.51i	−1.20794	−	0.697404i
$556$	−794.982	+	986.027i	−0.0606380	+	0.0752102i
$557$	−499.794	+	288.556i	−0.0380196	+	0.0219507i	−0.518889	−	0.854841i	$-0.673654\pi$
$557$	−499.794	+	288.556i	−0.0380196	+	0.0219507i	0.480870	+	0.876792i	$0.340321\pi$
$558$	−12.6299	+	35.7874i	−0.000958184	+	0.00271506i
$559$	−4763.53			−0.360422
$560$	16673.0	+	6824.98i	1.25815	+	0.515015i
$561$	−11497.2			−0.865266
$562$	4654.43	−	13188.5i	0.349351	−	0.989901i
$563$	3255.62	−	1879.63i	0.243709	−	0.140705i	−0.373171	−	0.927762i	$-0.621730\pi$
$563$	3255.62	−	1879.63i	0.243709	−	0.140705i	0.616880	+	0.787057i	$0.288396\pi$
$564$	−10116.0	+	12547.0i	−0.755250	+	0.936746i
$565$	20983.6	+	12114.9i	1.56245	+	0.902084i
$566$	2500.58	+	13411.8i	0.185702	+	0.996010i
$567$	11848.1	−	5649.58i	0.877552	−	0.418448i
$568$	−1588.20	+	980.274i	−0.117323	+	0.0724144i
$569$	−9117.06	+	15791.2i	−0.671717	+	1.16345i	0.305700	+	0.952128i	$0.401109\pi$
$569$	−9117.06	+	15791.2i	−0.671717	+	1.16345i	−0.977417	+	0.211320i	$0.932224\pi$
$570$	7185.91	−	6150.66i	0.528043	−	0.451969i
$571$	−14512.2	+	8378.64i	−1.06360	+	0.614072i	−0.926427	−	0.376474i	$-0.877136\pi$
$571$	−14512.2	+	8378.64i	−1.06360	+	0.614072i	−0.137177	+	0.990547i	$0.543803\pi$
$572$	765.935	−	4903.80i	0.0559884	−	0.358458i
$573$		−	3205.13i		−	0.233676i
$574$	16637.3	+	7388.36i	1.20980	+	0.537255i
$575$	14658.6			1.06314
$576$	205.713	+	312.363i	0.0148809	+	0.0225957i
$577$	619.415	+	1072.86i	0.0446908	+	0.0774067i	0.887506	−	0.460797i	$-0.152436\pi$
$577$	619.415	+	1072.86i	0.0446908	+	0.0774067i	−0.842815	+	0.538204i	$0.819103\pi$
$578$	−3537.37	−	4132.77i	−0.254559	−	0.297406i
$579$	23627.7	+	13641.5i	1.69591	+	0.979137i
$580$	30744.7	−	11877.3i	2.20104	−	0.850308i
$581$	−10843.2	−	854.624i	−0.774272	−	0.0610254i
$582$	902.711	+	4841.68i	0.0642931	+	0.344835i
$583$	−10419.5	+	18047.1i	−0.740193	+	1.28205i
$584$	−5405.28	−	2912.41i	−0.383000	−	0.206364i
$585$	83.9538	+	145.412i	0.00593344	+	0.0102770i
$586$	−8641.57	−	3049.74i	−0.609181	−	0.214989i
$587$			18938.9i			1.33167i	0.746097	+	0.665837i	$0.231925\pi$
$587$			18938.9i			1.33167i	−0.746097	+	0.665837i	$0.768075\pi$
$588$	13384.0	+	4320.45i	0.938683	+	0.303015i
$589$			788.476i			0.0551589i
$590$	−10588.0	+	30001.5i	−0.738814	+	2.09346i
$591$	−1473.39	−	2551.99i	−0.102550	−	0.177622i
$592$	4568.80	−	14268.8i	0.317190	−	0.990613i
$593$	9678.40	−	16763.5i	0.670226	−	1.16087i	−0.307613	−	0.951511i	$-0.599530\pi$
$593$	9678.40	−	16763.5i	0.670226	−	1.16087i	0.977840	−	0.209355i	$-0.0671363\pi$
$594$	−16213.0	+	3022.84i	−1.11991	+	0.208802i
$595$	15344.2	+	1209.37i	1.05723	+	0.0833268i
$596$	−7045.62	−	18237.8i	−0.484228	−	1.25344i
$597$	−10456.6	−	6037.13i	−0.716852	−	0.413875i
$598$	−4492.71	+	3845.46i	−0.307225	+	0.262964i
$599$	10946.0	+	18959.0i	0.746644	+	1.29323i	0.949423	+	0.314001i	$0.101669\pi$
$599$	10946.0	+	18959.0i	0.746644	+	1.29323i	−0.202779	+	0.979225i	$0.564997\pi$
$600$	−12290.6	+	361.311i	−0.836267	+	0.0245841i
$601$	−11257.4			−0.764059			−0.382029	−	0.924150i	$-0.624775\pi$
$601$	−11257.4			−0.764059			−0.382029	+	0.924150i	$0.624775\pi$
$602$	−6696.98	+	15080.4i	−0.453403	+	1.02098i
$603$		−	221.600i		−	0.0149656i
$604$	−750.788	+	4806.82i	−0.0505780	+	0.323819i
$605$	4634.67	−	2675.83i	0.311448	−	0.179815i
$606$	7527.42	+	8794.41i	0.504588	+	0.589519i
$607$	−9229.65	+	15986.2i	−0.617166	+	1.06896i	0.372834	+	0.927898i	$0.378386\pi$
$607$	−9229.65	+	15986.2i	−0.617166	+	1.06896i	−0.990000	+	0.141065i	$0.954947\pi$
$608$	6190.13	+	4697.47i	0.412899	+	0.313335i
$609$	23224.4	−	11074.2i	1.54532	−	0.736863i
$610$	−9682.15	+	1805.19i	−0.642653	+	0.119820i
$611$	−5147.83	−	2972.10i	−0.340849	−	0.196789i
$612$	248.759	+	200.561i	0.0164305	+	0.0132471i
$613$	−13231.8	+	7639.39i	−0.871823	+	0.503347i	−0.867954	−	0.496645i	$-0.834565\pi$
$613$	−13231.8	+	7639.39i	−0.871823	+	0.503347i	−0.00386941	+	0.999993i	$0.501232\pi$
$614$	−620.712	−	219.059i	−0.0407979	−	0.0143982i
$615$	−27072.6			−1.77507
$616$	−14447.7	−	9318.98i	−0.944989	−	0.609533i
$617$	−7018.11			−0.457923			−0.228961	−	0.973436i	$-0.573533\pi$
$617$	−7018.11			−0.457923			−0.228961	+	0.973436i	$0.573533\pi$
$618$	−12076.0	−	4261.80i	−0.786031	−	0.277402i
$619$	−22065.9	+	12739.8i	−1.43280	+	0.827228i	−0.997334	−	0.0729760i	$-0.976750\pi$
$619$	−22065.9	+	12739.8i	−1.43280	+	0.827228i	−0.435468	+	0.900204i	$0.643417\pi$
$620$	1401.82	−	1738.70i	0.0908039	−	0.112625i
$621$	17017.9	+	9825.32i	1.09969	+	0.634906i
$622$	24861.0	−	4635.22i	1.60263	−	0.298803i
$623$	−24547.7	−	16875.3i	−1.57863	−	1.08523i
$624$	3672.16	−	3334.99i	0.235583	−	0.213952i
$625$	8818.52	−	15274.1i	0.564385	−	0.977544i
$626$	2680.38	+	3131.53i	0.171133	+	0.199938i
$627$	−7817.12	+	4513.21i	−0.497904	+	0.287465i
$628$	−10335.1	−	1614.26i	−0.656713	−	0.102573i
$629$		−	12800.1i		−	0.811406i
$630$	578.377	−	61.3487i	0.0365763	−	0.00387967i
$631$	18127.4			1.14365			0.571824	−	0.820377i	$-0.306236\pi$
$631$	18127.4			1.14365			0.571824	+	0.820377i	$0.306236\pi$
$632$	−405.392	−	13790.1i	−0.0255152	−	0.867942i
$633$	9573.51	+	16581.8i	0.601126	+	1.04118i
$634$	15348.8	−	13137.5i	0.961481	−	0.822963i
$635$	−21163.2	−	12218.6i	−1.32258	−	0.763590i
$636$	−19428.2	+	7505.53i	−1.21129	+	0.467946i
$637$	−812.594	+	5122.96i	−0.0505434	+	0.318648i
$638$	−30919.9	+	5764.89i	−1.91870	+	0.357734i
$639$	−30.1268	+	52.1811i	−0.00186510	+	0.00323044i
$640$	−5298.51	−	21363.9i	−0.327253	−	1.31950i
$641$	1097.34	+	1900.65i	0.0676166	+	0.117115i	0.897852	−	0.440298i	$-0.145127\pi$
$641$	1097.34	+	1900.65i	0.0676166	+	0.117115i	−0.830235	+	0.557413i	$0.811794\pi$
$642$	−1680.10	+	4760.63i	−0.103284	+	0.292659i
$643$		−	5435.55i		−	0.333370i	−0.986010	−	0.166685i	$-0.946694\pi$
$643$		−	5435.55i		−	0.333370i	0.986010	−	0.166685i	$-0.0533064\pi$
$644$	5857.74	+	19629.3i	0.358428	+	1.20109i
$645$		−	24539.2i		−	1.49803i
$646$	6260.44	+	2209.40i	0.381291	+	0.134563i
$647$	−6711.08	−	11623.9i	−0.407790	−	0.706313i	0.586852	−	0.809694i	$-0.300367\pi$
$647$	−6711.08	−	11623.9i	−0.407790	−	0.706313i	−0.994642	+	0.103382i	$0.967034\pi$
$648$	−14118.1	−	7606.94i	−0.855881	−	0.461156i
$649$	15180.4	−	26293.3i	0.918157	−	1.59029i
$650$	−831.185	−	4458.06i	−0.0501566	−	0.269014i
$651$	987.702	−	1436.76i	0.0594641	−	0.0864996i
$652$	5377.78	+	13920.5i	0.323022	+	0.836150i
$653$	−1330.30	−	768.048i	−0.0797222	−	0.0460276i	0.459609	−	0.888121i	$-0.347990\pi$
$653$	−1330.30	−	768.048i	−0.0797222	−	0.0460276i	−0.539331	+	0.842094i	$0.681323\pi$
$654$	1990.67	+	2325.74i	0.119024	+	0.139057i
$655$	12028.2	+	20833.4i	0.717527	+	1.24279i
$656$	−4717.22	−	21735.1i	−0.280757	−	1.29362i
$657$	−198.222			−0.0117708
$658$	−16646.4	+	12118.6i	−0.986235	+	0.717983i
$659$		−	1960.03i		−	0.115860i	−0.998321	−	0.0579301i	$-0.981550\pi$
$659$		−	1960.03i		−	0.115860i	0.998321	−	0.0579301i	$-0.0184501\pi$
$660$	25261.8	+	3945.69i	1.48987	+	0.232706i
$661$	20878.2	−	12054.1i	1.22855	−	0.709302i	0.261821	−	0.965116i	$-0.415677\pi$
$661$	20878.2	−	12054.1i	1.22855	−	0.709302i	0.966726	+	0.255815i	$0.0823437\pi$
$662$	21536.0	−	18433.4i	1.26438	−	1.08223i
$663$	2119.00	−	3670.22i	0.124126	−	0.214992i
$664$	6979.78	+	11308.4i	0.407934	+	0.660918i
$665$	10907.4	−	5201.04i	0.636047	−	0.303290i
$666$	−88.6541	−	475.496i	−0.00515807	−	0.0276653i
$667$	32455.1	+	18738.0i	1.88406	+	1.08776i
$668$	2602.28	+	2098.08i	0.150726	+	0.121523i
$669$	8621.20	−	4977.45i	0.498228	−	0.287652i
$670$	−4340.12	+	12297.9i	−0.250259	+	0.709118i
$671$	9398.84			0.540742
$672$	−5395.29	−	16313.9i	−0.309714	−	0.936494i
$673$	21235.3			1.21629			0.608143	−	0.793827i	$-0.291915\pi$
$673$	21235.3			1.21629			0.608143	+	0.793827i	$0.291915\pi$
$674$	−1590.69	+	4507.28i	−0.0909064	+	0.257587i
$675$	−13050.1	+	7534.46i	−0.744144	+	0.429632i
$676$	−12258.5	−	9883.39i	−0.697456	−	0.562323i
$677$	12582.6	+	7264.57i	0.714312	+	0.412408i	0.812655	−	0.582745i	$-0.198021\pi$
$677$	12582.6	+	7264.57i	0.714312	+	0.412408i	−0.0983439	+	0.995152i	$0.531355\pi$
$678$	−4235.70	−	22718.2i	−0.239928	−	1.28685i
$679$	−494.385	+	6272.61i	−0.0279422	+	0.354522i
$680$	−9877.04	−	16002.4i	−0.557011	−	0.902446i
$681$	−10343.6	+	17915.6i	−0.582036	+	1.00812i
$682$	−1619.20	+	1385.93i	−0.0909127	+	0.0778151i
$683$	6086.87	−	3514.25i	0.341006	−	0.196880i	−0.319711	−	0.947515i	$-0.603586\pi$
$683$	6086.87	−	3514.25i	0.341006	−	0.196880i	0.660717	+	0.750635i	$0.270252\pi$
$684$	247.864	+	38.7143i	0.0138557	+	0.00216415i
$685$			10258.1i			0.572175i
$686$	15075.9	+	9774.80i	0.839067	+	0.544029i
$687$	17405.9			0.966635
$688$	19701.2	−	4275.80i	1.09172	−	0.236938i
$689$	−3840.75	−	6652.37i	−0.212367	−	0.367830i
$690$	−19809.7	−	23144.0i	−1.09296	−	1.27693i
$691$	−28337.1	−	16360.4i	−1.56005	−	0.900695i	−0.997251	−	0.0741006i	$-0.976391\pi$
$691$	−28337.1	−	16360.4i	−1.56005	−	0.900695i	−0.562798	−	0.826594i	$-0.690275\pi$
$692$	5956.06	+	15417.4i	0.327190	+	0.846939i
$693$	−553.322	−	43.6109i	−0.0303304	−	0.00239053i
$694$	1312.34	+	7038.71i	0.0717804	+	0.384994i
$695$	1203.21	−	2084.03i	0.0656698	−	0.113743i
$696$	−27674.0	−	14911.0i	−1.50716	−	0.812069i
$697$	−9500.79	−	16455.8i	−0.516310	−	0.894275i
$698$	−6890.19	−	2431.65i	−0.373635	−	0.131862i
$699$		−	28765.7i		−	1.55654i
$700$	−15281.9	−	3636.14i	−0.825145	−	0.196333i
$701$			33247.8i			1.79137i	0.444685	+	0.895687i	$0.353316\pi$
$701$			33247.8i			1.79137i	−0.444685	+	0.895687i	$0.646684\pi$
$702$	2023.17	−	5732.73i	0.108774	−	0.308217i
$703$	−5024.66	−	8702.96i	−0.269571	−	0.466911i
$704$	1233.92	+	20968.8i	0.0660586	+	1.12257i
$705$	15310.7	−	26518.9i	0.817920	−	1.41668i
$706$	4031.96	−	751.742i	0.214936	−	0.0400739i
$707$	6365.24	+	13348.9i	0.338599	+	0.710096i
$708$	28305.4	−	10935.0i	1.50252	−	0.580453i
$709$	12015.8	+	6937.33i	0.636478	+	0.367471i	0.783257	−	0.621698i	$-0.213557\pi$
$709$	12015.8	+	6937.33i	0.636478	+	0.367471i	−0.146778	+	0.989169i	$0.546890\pi$
$710$	2693.90	−	2305.80i	0.142395	−	0.121880i
$711$	−222.695	−	385.719i	−0.0117464	−	0.0203454i
$712$	1069.45	+	36379.1i	0.0562913	+	1.91484i
$713$	2539.49			0.133386
$714$	−8640.14	−	11868.3i	−0.452870	−	0.622071i
$715$			9429.83i			0.493225i
$716$	−16324.1	−	2549.70i	−0.852040	−	0.133082i
$717$	−5123.38	+	2957.98i	−0.266856	+	0.154070i
$718$	−911.261	−	1064.64i	−0.0473649	−	0.0553372i
$719$	−7233.72	+	12529.2i	−0.375205	+	0.649873i	−0.990358	−	0.138534i	$-0.955761\pi$
$719$	−7233.72	+	12529.2i	−0.375205	+	0.649873i	0.615153	+	0.788408i	$0.289094\pi$
$720$	−477.743	−	526.043i	−0.0247284	−	0.0272284i
$721$	−13481.8	−	9268.04i	−0.696377	−	0.478724i
$722$	−13947.7	+	2600.49i	−0.718946	+	0.134044i
$723$	10074.6	+	5816.57i	0.518227	+	0.299199i
$724$	7446.55	−	9236.06i	0.382250	−	0.474110i
$725$	−24887.9	+	14369.0i	−1.27492	+	0.736073i
$726$	−4813.30	−	1698.69i	−0.246058	−	0.0868377i
$727$	28059.8			1.43147			0.715736	−	0.698371i	$-0.246091\pi$
$727$	28059.8			1.43147			0.715736	+	0.698371i	$0.246091\pi$
$728$	5637.64	−	2894.54i	0.287012	−	0.147361i
$729$	−20186.3			−1.02557
$730$	11000.5	+	3882.26i	0.557738	+	0.196834i
$731$	14916.0	−	8611.73i	0.754701	−	0.435727i
$732$	7312.89	+	5896.00i	0.369251	+	0.297708i
$733$	−19847.4	−	11458.9i	−1.00011	−	0.577413i	−0.0918288	−	0.995775i	$-0.529271\pi$
$733$	−19847.4	−	11458.9i	−1.00011	−	0.577413i	−0.908281	+	0.418361i	$0.862605\pi$
$734$	−9261.37	+	1726.74i	−0.465727	+	0.0868327i
$735$	−26390.7	−	4186.05i	−1.32440	−	0.210075i
$736$	15129.4	−	19936.9i	0.757712	−	0.998482i
$737$	6222.61	−	10777.9i	0.311008	−	0.538681i
$738$	−466.906	−	545.495i	−0.0232887	−	0.0272086i
$739$	3194.68	−	1844.45i	0.159023	−	0.0918121i	−0.418377	−	0.908274i	$-0.637401\pi$
$739$	3194.68	−	1844.45i	0.159023	−	0.0918121i	0.577400	+	0.816462i	$0.304067\pi$
$740$	−4392.82	+	28124.4i	−0.218221	+	1.39713i
$741$		−	3327.24i		−	0.164952i
$742$	−26459.8	+	2806.60i	−1.30912	+	0.138859i
$743$	−3171.06			−0.156575			−0.0782873	−	0.996931i	$-0.524945\pi$
$743$	−3171.06			−0.156575			−0.0782873	+	0.996931i	$0.524945\pi$
$744$	−2129.25	+	62.5944i	−0.104922	+	0.00308444i
$745$	18573.1	+	32169.6i	0.913377	+	1.58202i
$746$	4896.15	−	4190.77i	0.240296	−	0.205677i
$747$	371.542	+	214.510i	0.0181981	+	0.0105067i
$748$	6466.96	+	16739.9i	0.316117	+	0.818276i
$749$	−3653.68	+	5314.83i	−0.178241	+	0.259279i
$750$	−4110.69	+	766.421i	−0.200135	+	0.0373143i
$751$	−886.894	+	1536.14i	−0.0430935	+	0.0746401i	−0.886768	−	0.462215i	$-0.847055\pi$
$751$	−886.894	+	1536.14i	−0.0430935	+	0.0746401i	0.843674	+	0.536856i	$0.180388\pi$
$752$	23958.4	+	7671.37i	1.16180	+	0.372003i
$753$	6998.33	+	12121.5i	0.338690	+	0.586627i
$754$	3858.41	−	10933.0i	0.186359	−	0.528057i
$755$		−	9243.34i		−	0.445563i
$756$	−15304.4	−	14464.5i	−0.736263	−	0.695859i
$757$			370.903i			0.0178081i	0.999960	+	0.00890403i	$0.00283428\pi$
$757$			370.903i			0.0178081i	−0.999960	+	0.00890403i	$0.997166\pi$
$758$	−25138.0	−	8871.60i	−1.20456	−	0.425107i
$759$	14535.9	+	25177.0i	0.695153	+	1.20404i
$760$	−12997.2	−	7003.00i	−0.620340	−	0.334244i
$761$	−14664.5	+	25399.6i	−0.698538	+	1.20990i	0.270435	+	0.962738i	$0.412832\pi$
$761$	−14664.5	+	25399.6i	−0.698538	+	1.20990i	−0.968973	+	0.247165i	$0.920501\pi$
$762$	4271.96	+	22912.6i	0.203093	+	1.08929i
$763$	1683.33	+	3530.21i	0.0798697	+	0.167499i
$764$	−4666.64	+	1802.82i	−0.220986	+	0.0853713i
$765$	−525.766	−	303.551i	−0.0248485	−	0.0143463i
$766$	18191.4	+	21253.3i	0.858068	+	1.00250i
$767$	5595.67	+	9691.98i	0.263426	+	0.456267i
$768$	−12193.9	+	17089.1i	−0.572929	+	0.802930i
$769$	−26755.7			−1.25466			−0.627331	−	0.778753i	$-0.715853\pi$
$769$	−26755.7			−1.25466			−0.627331	+	0.778753i	$0.715853\pi$
$770$	29853.0	+	13257.3i	1.39718	+	0.620465i
$771$			33172.0i			1.54950i
$772$	6571.75	−	42074.7i	0.306376	−	1.96153i
$773$	12808.3	−	7394.87i	0.595967	−	0.344082i	−0.171486	−	0.985186i	$-0.554857\pi$
$773$	12808.3	−	7394.87i	0.595967	−	0.344082i	0.767453	+	0.641105i	$0.221524\pi$
$774$	494.449	−	423.215i	0.0229620	−	0.0196539i
$775$	−973.692	+	1686.48i	−0.0451304	+	0.0781681i
$776$	6541.68	−	4037.68i	0.302619	−	0.186784i
$777$	−1746.01	+	22152.8i	−0.0806147	+	1.02282i
$778$	4407.88	+	23641.6i	0.203123	+	1.08945i
$779$	−12919.4	−	7459.02i	−0.594205	−	0.343064i
$780$	−5915.44	+	7337.00i	−0.271547	+	0.336804i
$781$	−2930.53	+	1691.94i	−0.134267	+	0.0775192i
$782$	7115.95	−	20163.3i	0.325404	−	0.922045i
$783$	−38525.0			−1.75833
$784$	−1237.67	−	21917.1i	−0.0563805	−	0.998409i
$785$	19874.0			0.903611
$786$	7635.80	−	21636.4i	0.346514	−	0.981862i
$787$	−9694.95	+	5597.38i	−0.439120	+	0.253526i	−0.703224	−	0.710968i	$-0.748257\pi$
$787$	−9694.95	+	5597.38i	−0.439120	+	0.253526i	0.264104	+	0.964494i	$0.414924\pi$
$788$	−2886.92	+	3580.68i	−0.130510	+	0.161874i
$789$	−5524.32	−	3189.46i	−0.249266	−	0.143914i
$790$	4804.23	+	25767.4i	0.216363	+	1.16046i
$791$	2319.75	−	29432.3i	0.104274	−	1.32300i
$792$	356.174	+	577.058i	0.0159799	+	0.0258900i
$793$	−1732.26	+	3000.35i	−0.0775715	+	0.134358i
$794$	−31730.7	+	27159.3i	−1.41824	+	1.21392i
$795$	34269.5	−	19785.5i	1.52882	−	0.882665i
$796$	−2908.37	+	18620.5i	−0.129503	+	0.829127i
$797$		−	11568.6i		−	0.514153i	−0.966391	−	0.257076i	$-0.917241\pi$
$797$		−	11568.6i		−	0.514153i	0.966391	−	0.257076i	$-0.0827592\pi$
$798$	−10533.4	−	4677.71i	−0.467266	−	0.207505i
$799$	21492.4			0.951623
$800$	7439.24	+	17691.7i	0.328771	+	0.781870i
$801$	587.484	+	1017.55i	0.0259148	+	0.0448857i
$802$	9220.25	+	10772.2i	0.405958	+	0.474288i
$803$	−9640.87	−	5566.16i	−0.423685	−	0.244615i
$804$	11602.7	−	4482.35i	0.508948	−	0.196617i
$805$	−16751.3	−	35130.1i	−0.733422	−	1.53810i
$806$	−143.997	−	772.325i	−0.00629289	−	0.0337518i
$807$	8087.27	−	14007.6i	0.352770	−	0.611016i
$808$	8570.55	−	15906.5i	0.373157	−	0.692560i
$809$	8617.10	+	14925.2i	0.374488	+	0.648633i	0.990250	−	0.139300i	$-0.0444851\pi$
$809$	8617.10	+	14925.2i	0.374488	+	0.648633i	−0.615762	+	0.787932i	$0.711152\pi$
$810$	28732.4	+	10140.1i	1.24636	+	0.439860i
$811$		−	6011.49i		−	0.260286i	−0.991495	−	0.130143i	$-0.958456\pi$
$811$		−	6011.49i		−	0.260286i	0.991495	−	0.130143i	$-0.0415437\pi$
$812$	−29187.2	−	27585.4i	−1.26141	−	1.19219i
$813$		−	10224.5i		−	0.441067i
$814$	9040.27	−	25616.0i	0.389264	−	1.10300i
$815$	−14176.5	−	24554.4i	−0.609302	−	1.05534i
$816$	−5469.42	+	17081.5i	−0.234642	+	0.732808i
$817$	6761.02	−	11710.4i	0.289520	−	0.501464i
$818$	3891.42	−	725.539i	0.166333	−	0.0310121i
$819$	115.902	−	168.597i	0.00494498	−	0.00719323i
$820$	15227.7	+	39417.3i	0.648507	+	1.67867i
$821$	146.755	+	84.7289i	0.00623846	+	0.00360178i	0.503116	−	0.864219i	$-0.332187\pi$
$821$	146.755	+	84.7289i	0.00623846	+	0.00360178i	−0.496878	+	0.867821i	$0.665520\pi$
$822$	7432.88	−	6362.04i	0.315391	−	0.269953i
$823$	3086.68	+	5346.28i	0.130735	+	0.226439i	0.923960	−	0.382489i	$-0.124933\pi$
$823$	3086.68	+	5346.28i	0.130735	+	0.226439i	−0.793225	+	0.608928i	$0.791600\pi$
$824$	587.350	+	19979.7i	0.0248317	+	0.844690i
$825$	−22293.5			−0.940801
$826$	38549.8	−	4089.00i	1.62387	−	0.172245i
$827$			12247.9i			0.514995i	0.966279	+	0.257497i	$0.0828978\pi$
$827$			12247.9i			0.514995i	−0.966279	+	0.257497i	$0.917102\pi$
$828$	124.689	−	798.307i	0.00523340	−	0.0335061i
$829$	−19887.0	+	11481.8i	−0.833176	+	0.481035i	−0.854939	−	0.518729i	$-0.826406\pi$
$829$	−19887.0	+	11481.8i	−0.833176	+	0.481035i	0.0217626	+	0.999763i	$0.493072\pi$
$830$	−16417.8	−	19181.2i	−0.686592	−	0.802157i
$831$	3098.14	−	5366.13i	0.129330	−	0.224006i
$832$	−6921.21	−	3470.76i	−0.288401	−	0.144624i
$833$	−6717.05	−	17510.5i	−0.279390	−	0.728333i
$834$	−2256.30	+	420.677i	−0.0936800	+	0.0174662i
$835$	−5500.07	−	3175.47i	−0.227949	−	0.131607i
$836$	10968.1	+	8843.05i	0.453758	+	0.365841i
$837$	−2260.83	+	1305.29i	−0.0933639	+	0.0539037i
$838$	−816.781	−	288.254i	−0.0336697	−	0.0118826i
$839$	−27390.4			−1.12708			−0.563541	−	0.826088i	$-0.690561\pi$
$839$	−27390.4			−1.12708			−0.563541	+	0.826088i	$0.690561\pi$
$840$	14911.1	+	29042.1i	0.612479	+	1.19292i
$841$	−49082.5			−2.01249
$842$	−13750.1	−	4852.62i	−0.562778	−	0.198613i
$843$	21948.1	−	12671.7i	0.896718	−	0.517720i
$844$	18758.0	−	23265.8i	0.765021	−	0.948866i
$845$	25909.1	+	14958.6i	1.05479	+	0.608984i
$846$	798.394	−	148.857i	0.0324460	−	0.00604942i
$847$	−5373.63	−	3694.10i	−0.217993	−	0.149859i
$848$	21855.9	+	24065.6i	0.885066	+	0.974547i
$849$	−12361.2	+	21410.2i	−0.499687	+	0.865483i
$850$	10662.1	+	12456.8i	0.430246	+	0.502663i
$851$	−28030.1	+	16183.2i	−1.12909	+	0.651882i
$852$	−3341.51	−	521.918i	−0.134364	−	0.0209867i
$853$		−	27281.2i		−	1.09506i	−0.836785	−	0.547532i	$-0.815568\pi$
$853$		−	27281.2i		−	1.09506i	0.836785	−	0.547532i	$-0.184432\pi$
$854$	7063.19	+	9702.14i	0.283018	+	0.388759i
$855$	−476.633			−0.0190649
$856$	7876.45	−	231.547i	0.314499	−	0.00924546i
$857$	2898.81	+	5020.89i	0.115544	+	0.200129i	0.917997	−	0.396587i	$-0.129805\pi$
$857$	2898.81	+	5020.89i	0.115544	+	0.200129i	−0.802453	+	0.596716i	$0.796472\pi$
$858$	6832.76	−	5848.38i	0.271872	−	0.232704i
$859$	23919.8	+	13810.1i	0.950095	+	0.548537i	0.893110	−	0.449838i	$-0.148518\pi$
$859$	23919.8	+	13810.1i	0.950095	+	0.548537i	0.0569844	+	0.998375i	$0.481851\pi$
$860$	−35728.8	+	13802.8i	−1.41668	+	0.547291i
$861$	14198.1	+	29775.6i	0.561985	+	1.17857i
$862$	20843.5	−	3886.19i	0.823589	−	0.153555i
$863$	23042.4	−	39910.5i	0.908889	−	1.57424i	0.0932784	−	0.995640i	$-0.470265\pi$
$863$	23042.4	−	39910.5i	0.908889	−	1.57424i	0.815610	−	0.578601i	$-0.196401\pi$
$864$	−3221.72	+	25525.6i	−0.126858	+	1.00509i
$865$	−15700.9	−	27194.8i	−0.617164	−	1.06896i
$866$	8586.47	−	24330.1i	0.336929	−	0.954701i
$867$		−	9857.65i		−	0.386140i
$868$	−2647.48	−	629.934i	−0.103527	−	0.0246329i
$869$		−	25013.4i		−	0.976436i
$870$	56320.7	+	19876.4i	2.19477	+	0.774569i
$871$	2293.72	+	3972.84i	0.0892304	+	0.154552i
$872$	2266.53	−	4206.57i	0.0880213	−	0.163363i
$873$	124.090	−	214.930i	0.00481078	−	0.00833251i
$874$	−3076.84	−	16502.6i	−0.119080	−	0.638684i
$875$	−5325.58	−	419.743i	−0.205757	−	0.0162170i
$876$	−4009.49	−	10378.7i	−0.154644	−	0.400299i
$877$	11574.9	+	6682.75i	0.445673	+	0.257309i	0.706001	−	0.708211i	$-0.250497\pi$
$877$	11574.9	+	6682.75i	0.445673	+	0.257309i	−0.260328	+	0.965520i	$0.583831\pi$
$878$	−16910.1	−	19756.3i	−0.649985	−	0.759388i
$879$	−8302.96	−	14381.1i	−0.318603	−	0.551836i
$880$	−8464.32	−	39000.2i	−0.324241	−	1.49397i
$881$	5901.17			0.225670			0.112835	−	0.993614i	$-0.464007\pi$
$881$	5901.17			0.225670			0.112835	+	0.993614i	$0.464007\pi$
$882$	−370.801	−	603.951i	−0.0141559	−	0.0230568i
$883$		−	4207.25i		−	0.160346i	−0.996781	−	0.0801729i	$-0.974453\pi$
$883$		−	4207.25i		−	0.160346i	0.996781	−	0.0801729i	$-0.0255472\pi$
$884$	−6535.70	−	1020.82i	−0.248664	−	0.0388394i
$885$	−49927.9	+	28825.9i	−1.89639	+	1.09488i
$886$	3421.47	−	2928.54i	0.129736	−	0.111046i
$887$	10064.4	−	17432.1i	0.380982	−	0.659880i	−0.610221	−	0.792231i	$-0.708919\pi$
$887$	10064.4	−	17432.1i	0.380982	−	0.659880i	0.991203	+	0.132351i	$0.0422527\pi$
$888$	23103.1	−	14259.8i	0.873074	−	0.538882i
$889$	−2339.61	+	29684.3i	−0.0882654	+	1.11989i
$890$	−12673.9	−	67976.2i	−0.477336	−	2.56019i
$891$	−25181.0	−	14538.3i	−0.946798	−	0.546634i
$892$	−12096.3	−	9752.66i	−0.454053	−	0.366080i
$893$	14612.9	−	8436.79i	0.547596	−	0.316155i
$894$	11790.7	−	33409.4i	0.441096	−	1.24986i
$895$	31390.7			1.17237
$896$	−20718.2	+	17031.7i	−0.772485	+	0.635034i
$897$	−10716.2			−0.398889
$898$	−6138.57	+	17393.9i	−0.228114	+	0.646371i
$899$	−4311.65	+	2489.33i	−0.159957	+	0.0923513i
$900$	482.351	+	388.894i	0.0178648	+	0.0144035i
$901$	24052.9	+	13887.0i	0.889366	+	0.513476i
$902$	−7391.08	−	39642.0i	−0.272834	−	1.46334i
$903$	−26989.3	+	12869.5i	−0.994627	+	0.474273i
$904$	−30694.9	+	18945.6i	−1.12931	+	0.697037i
$905$	−11270.4	+	19521.0i	−0.413969	+	0.717015i
$906$	−6697.63	+	5732.72i	−0.245600	+	0.210217i
$907$	6350.05	−	3666.20i	0.232469	−	0.134216i	−0.379241	−	0.925298i	$-0.623815\pi$
$907$	6350.05	−	3666.20i	0.232469	−	0.134216i	0.611711	+	0.791081i	$0.290482\pi$
$908$	31903.0	+	4982.99i	1.16601	+	0.182122i
$909$		−	583.322i		−	0.0212845i
$910$	−9734.13	+	7086.49i	−0.354597	+	0.258148i
$911$	38942.4			1.41627			0.708133	−	0.706079i	$-0.249538\pi$
$911$	38942.4			1.41627			0.708133	+	0.706079i	$0.249538\pi$
$912$	2986.56	+	13760.9i	0.108437	+	0.499637i
$913$	12047.0	+	20866.1i	0.436691	+	0.756371i
$914$	6497.00	+	7590.55i	0.235122	+	0.274697i
$915$	−15456.2	−	8923.65i	−0.558434	−	0.322412i
$916$	−9790.47	−	25342.9i	−0.353151	−	0.914140i
$917$	16605.4	−	24155.1i	0.597993	−	0.869872i
$918$	4028.79	+	21608.4i	0.144847	+	0.776887i
$919$	−5166.34	+	8948.36i	−0.185443	+	0.321196i	−0.943726	−	0.330729i	$-0.892705\pi$
$919$	−5166.34	+	8948.36i	−0.185443	+	0.321196i	0.758283	+	0.651926i	$0.226039\pi$
$920$	−22554.9	+	41860.8i	−0.808276	+	1.50012i
$921$	−596.390	−	1032.98i	−0.0213374	−	0.0369574i
$922$	−44765.7	−	15798.5i	−1.59900	−	0.564312i
$923$		−	1247.34i		−	0.0444817i
$924$	−8908.77	−	29853.3i	−0.317183	−	1.06288i
$925$		−	24819.9i		−	0.882240i
$926$	−2582.36	+	7317.24i	−0.0916434	+	0.259675i
$927$	322.650	+	558.846i	0.0114317	+	0.0198004i
$928$	−6144.19	+	48680.2i	−0.217341	+	1.72199i
$929$	6917.69	−	11981.8i	0.244308	−	0.423154i	−0.717629	−	0.696426i	$-0.754773\pi$
$929$	6917.69	−	11981.8i	0.244308	−	0.423154i	0.961937	+	0.273272i	$0.0881059\pi$
$930$	3978.61	−	741.794i	0.140283	−	0.0261552i
$931$	−11440.7	−	9268.81i	−0.402743	−	0.326287i
$932$	−41882.6	+	16180.1i	−1.47201	+	0.568666i
$933$	39687.2	+	22913.4i	1.39260	+	0.804020i
$934$	5713.91	−	4890.72i	0.200176	−	0.171337i
$935$	−17047.7	−	29527.4i	−0.596277	−	1.03278i
$936$	−249.857	+	7.34513i	−0.00872523	+	0.000256499i
$937$	−25168.3			−0.877495			−0.438747	−	0.898610i	$-0.644578\pi$
$937$	−25168.3			−0.877495			−0.438747	+	0.898610i	$0.644578\pi$
$938$	15801.9	−	1676.12i	0.550055	−	0.0583446i
$939$			7469.46i			0.259592i
$940$	−47223.1	−	7375.88i	−1.63856	−	0.255931i
$941$	27803.9	−	16052.6i	0.963210	−	0.556110i	0.0660507	−	0.997816i	$-0.478960\pi$
$941$	27803.9	−	16052.6i	0.963210	−	0.556110i	0.897160	+	0.441707i	$0.145627\pi$
$942$	−12325.9	−	14400.5i	−0.426325	−	0.498083i
$943$	−24023.6	+	41610.2i	−0.829605	+	1.43692i
$944$	−31842.4	−	35061.7i	−1.09786	−	1.20886i
$945$	32969.9	+	22665.1i	1.13493	+	0.780208i
$946$	35932.4	−	6699.44i	1.23495	−	0.230251i
$947$	35980.9	+	20773.6i	1.23466	+	0.712830i	0.967997	−	0.250960i	$-0.0807464\pi$
$947$	35980.9	+	20773.6i	1.23466	+	0.712830i	0.266661	+	0.963791i	$0.414080\pi$
$948$	15691.2	−	19462.0i	0.537582	−	0.666770i
$949$	3553.73	−	2051.75i	0.121558	−	0.0701817i
$950$	12139.2	+	4284.11i	0.414576	+	0.146310i
$951$	36610.6			1.24835
$952$	−12420.2	+	19255.6i	−0.422836	+	0.655544i
$953$	42752.7			1.45320			0.726599	−	0.687062i	$-0.241100\pi$
$953$	42752.7			1.45320			0.726599	+	0.687062i	$0.241100\pi$
$954$	989.693	+	349.278i	0.0335875	+	0.0118535i
$955$	8231.48	−	4752.45i	0.278916	−	0.161032i
$956$	7188.58	+	5795.78i	0.243196	+	0.196076i
$957$	−49359.5	−	28497.7i	−1.66726	−	0.962591i
$958$	−24557.4	+	4578.62i	−0.828197	+	0.154414i
$959$	11282.3	−	5379.79i	0.379900	−	0.181150i
$960$	17879.5	−	35654.4i	0.601103	−	1.19869i
$961$	14726.8	−	25507.6i	0.494338	−	0.856218i
$962$	6511.12	+	7607.05i	0.218219	+	0.254949i
$963$	220.310	−	127.196i	0.00737217	−	0.00425632i
$964$	2802.12	−	17940.2i	0.0936205	−	0.599393i
$965$			80908.2i			2.69899i
$966$	−15065.8	+	33925.4i	−0.501794	+	1.12995i
$967$	−46475.7			−1.54556			−0.772780	−	0.634674i	$-0.781134\pi$
$967$	−46475.7			−1.54556			−0.772780	+	0.634674i	$0.781134\pi$
$968$	234.109	+	7963.59i	0.00777329	+	0.264421i
$969$	6015.13	+	10418.5i	0.199416	+	0.345398i
$970$	−11096.0	+	9497.42i	−0.367290	+	0.314375i
$971$	52110.5	+	30086.0i	1.72225	+	0.994343i	0.914236	+	0.405181i	$0.132792\pi$
$971$	52110.5	+	30086.0i	1.72225	+	0.994343i	0.808015	+	0.589161i	$0.200542\pi$
$972$	590.756	+	1529.19i	0.0194944	+	0.0504616i
$973$	−2923.13	−	230.391i	−0.0963116	−	0.00759094i
$974$	−36790.9	+	6859.50i	−1.21032	+	0.225660i
$975$	4108.81	−	7116.68i	0.134961	−	0.233760i
$976$	4471.17	−	13963.9i	0.146638	−	0.457963i
$977$	−4830.84	−	8367.26i	−0.158191	−	0.273994i	0.776026	−	0.630701i	$-0.217233\pi$
$977$	−4830.84	−	8367.26i	−0.158191	−	0.273994i	−0.934216	+	0.356707i	$0.883899\pi$
$978$	−8999.61	+	25500.8i	−0.294249	+	0.833767i
$979$			65987.1i			2.15420i
$980$	8749.38	+	40779.2i	0.285192	+	1.32923i
$981$		−	154.263i		−	0.00502063i
$982$	2226.27	+	785.686i	0.0723455	+	0.0255318i
$983$	147.336	+	255.194i	0.00478057	+	0.00828019i	0.868406	−	0.495854i	$-0.165145\pi$
$983$	147.336	+	255.194i	0.00478057	+	0.00828019i	−0.863625	+	0.504134i	$0.831812\pi$
$984$	19117.2	−	35480.5i	0.619342	−	1.14947i
$985$	4369.38	−	7567.99i	0.141340	−	0.244808i
$986$	7683.34	+	41209.5i	0.248162	+	1.33101i
$987$	−37196.3	−	2931.68i	−1.19957	−	0.0945455i
$988$	−4844.42	+	1871.50i	−0.155993	+	0.0602635i
$989$	−37716.4	−	21775.6i	−1.21265	−	0.700125i
$990$	−837.791	−	978.805i	−0.0268957	−	0.0314227i
$991$	17842.6	+	30904.3i	0.571937	+	0.990624i	0.996367	+	0.0851632i	$0.0271412\pi$
$991$	17842.6	+	30904.3i	0.571937	+	0.990624i	−0.424430	+	0.905461i	$0.639526\pi$
$992$	1288.79	+	3064.95i	0.0412492	+	0.0980972i
$993$	51368.6			1.64163
$994$	−3948.83	−	1753.61i	−0.126005	−	0.0559569i
$995$		−	35806.5i		−	1.14085i
$996$	−3716.18	+	23792.4i	−0.118225	+	0.756918i
$997$	−22310.1	+	12880.7i	−0.708693	+	0.409164i	−0.810577	−	0.585632i	$-0.800846\pi$
$997$	−22310.1	+	12880.7i	−0.708693	+	0.409164i	0.101884	+	0.994796i	$0.467513\pi$
$998$	−13432.0	+	11496.9i	−0.426035	+	0.364657i
$999$	16636.2	−	28814.8i	0.526873	−	0.912571i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	56.4.p.a.37.14	✓	44
4.3	odd	2		224.4.t.a.177.6		44
7.4	even	3	inner	56.4.p.a.53.16	yes	44
8.3	odd	2		224.4.t.a.177.17		44
8.5	even	2	inner	56.4.p.a.37.16	yes	44
28.11	odd	6		224.4.t.a.81.17		44
56.11	odd	6		224.4.t.a.81.6		44
56.53	even	6	inner	56.4.p.a.53.14	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.4.p.a.37.14	✓	44	1.1	even	1	trivial
56.4.p.a.37.16	yes	44	8.5	even	2	inner
56.4.p.a.53.14	yes	44	56.53	even	6	inner
56.4.p.a.53.16	yes	44	7.4	even	3	inner
224.4.t.a.81.6		44	56.11	odd	6
224.4.t.a.81.17		44	28.11	odd	6
224.4.t.a.177.6		44	4.3	odd	2
224.4.t.a.177.17		44	8.3	odd	2

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:	\( N \)	\(=\)	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	56.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.941296 - 2.66720i) q^{2} +(4.43871 - 2.56269i) q^{3} +(-6.22792 - 5.02125i) q^{4} +(13.1631 + 7.59971i) q^{5} +(-2.65707 - 14.2512i) q^{6} +(1.45519 - 18.4630i) q^{7} +(-19.2550 + 11.8846i) q^{8} +(-0.365251 + 0.632633i) q^{9} +(32.6603 - 27.9550i) q^{10} +(-35.5292 + 20.5128i) q^{11} +(-40.5118 - 6.32763i) q^{12} -15.1225i q^{13} +(-47.8748 - 21.2604i) q^{14} +77.9028 q^{15} +(13.5741 + 62.5439i) q^{16} +(27.3391 + 47.3526i) q^{17} +(1.34355 + 1.56969i) q^{18} +(37.1763 + 21.4637i) q^{19} +(-43.8187 - 113.426i) q^{20} +(-40.8558 - 85.6811i) q^{21} +(21.2682 + 114.072i) q^{22} +(69.1294 - 119.736i) q^{23} +(-55.0107 + 102.097i) q^{24} +(53.0113 + 91.8183i) q^{25} +(-40.3346 - 14.2347i) q^{26} +142.129i q^{27} +(-101.770 + 107.679i) q^{28} +271.056i q^{29} +(73.3296 - 207.782i) q^{30} +(9.18381 + 15.9068i) q^{31} +(179.594 + 22.6676i) q^{32} +(-105.136 + 182.100i) q^{33} +(152.033 - 28.3459i) q^{34} +(159.468 - 231.971i) q^{35} +(5.45136 - 2.10597i) q^{36} +(-202.736 - 117.050i) q^{37} +(92.2420 - 78.9529i) q^{38} +(-38.7541 - 67.1242i) q^{39} +(-343.775 + 10.1061i) q^{40} -347.517 q^{41} +(-266.986 + 28.3193i) q^{42} -314.997i q^{43} +(324.273 + 50.6489i) q^{44} +(-9.61566 + 5.55160i) q^{45} +(-254.288 - 297.089i) q^{46} +(196.536 - 340.410i) q^{47} +(220.532 + 242.828i) q^{48} +(-338.765 - 53.7343i) q^{49} +(294.797 - 54.9636i) q^{50} +(242.700 + 140.123i) q^{51} +(-75.9336 + 94.1815i) q^{52} +(439.900 - 253.976i) q^{53} +(379.087 + 133.786i) q^{54} -623.565 q^{55} +(191.407 + 372.800i) q^{56} +220.020 q^{57} +(722.962 + 255.144i) q^{58} +(-640.900 + 370.024i) q^{59} +(-485.173 - 391.170i) q^{60} +(-198.404 - 114.549i) q^{61} +(51.0714 - 9.52204i) q^{62} +(11.1488 + 7.66422i) q^{63} +(229.511 - 457.678i) q^{64} +(114.926 - 199.058i) q^{65} +(386.735 + 451.829i) q^{66} +(-262.711 + 151.676i) q^{67} +(67.5039 - 432.185i) q^{68} -708.629i q^{69} +(-468.607 - 643.688i) q^{70} +82.4824 q^{71} +(-0.485710 - 16.5222i) q^{72} +(135.675 + 234.997i) q^{73} +(-503.030 + 430.560i) q^{74} +(470.603 + 271.703i) q^{75} +(-123.756 - 320.346i) q^{76} +(327.026 + 685.825i) q^{77} +(-215.513 + 40.1814i) q^{78} +(-304.852 + 528.019i) q^{79} +(-296.639 + 926.431i) q^{80} +(354.371 + 613.789i) q^{81} +(-327.116 + 926.898i) q^{82} -587.294i q^{83} +(-175.779 + 738.762i) q^{84} +831.076i q^{85} +(-840.161 - 296.506i) q^{86} +(694.633 + 1203.14i) q^{87} +(440.327 - 817.225i) q^{88} +(804.220 - 1392.95i) q^{89} +(5.75606 + 30.8726i) q^{90} +(-279.206 - 22.0060i) q^{91} +(-1031.76 + 398.588i) q^{92} +(81.5285 + 47.0705i) q^{93} +(-722.943 - 844.627i) q^{94} +(326.237 + 565.058i) q^{95} +(855.257 - 359.630i) q^{96} -339.739 q^{97} +(-462.198 + 852.974i) q^{98} -29.9692i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{4} - 20 q^{6} - 4 q^{7} - 12 q^{8} + 160 q^{9} - 14 q^{10} - 110 q^{12} + 102 q^{14} - 116 q^{15} - 104 q^{16} - 2 q^{17} - 38 q^{18} + 256 q^{20} - 360 q^{22} + 162 q^{23} + 186 q^{24} + 348 q^{25}+ \cdots - 2670 q^{98}+O(q^{100}) \) 44 * q + 4 * q^4 - 20 * q^6 - 4 * q^7 - 12 * q^8 + 160 * q^9 - 14 * q^10 - 110 * q^12 + 102 * q^14 - 116 * q^15 - 104 * q^16 - 2 * q^17 - 38 * q^18 + 256 * q^20 - 360 * q^22 + 162 * q^23 + 186 * q^24 + 348 * q^25 - 302 * q^26 - 642 * q^28 - 396 * q^30 - 374 * q^31 - 140 * q^32 - 110 * q^33 - 148 * q^34 + 1440 * q^36 + 52 * q^38 + 52 * q^39 + 658 * q^40 - 8 * q^41 - 1710 * q^42 + 374 * q^44 - 486 * q^46 - 738 * q^47 + 936 * q^48 + 356 * q^49 + 2328 * q^50 + 96 * q^52 + 944 * q^54 - 2268 * q^55 + 1848 * q^56 - 452 * q^57 + 918 * q^58 + 410 * q^60 + 1416 * q^62 + 668 * q^63 - 2984 * q^64 + 248 * q^65 + 868 * q^66 - 64 * q^68 + 3422 * q^70 + 1248 * q^71 - 2172 * q^72 - 218 * q^73 - 176 * q^74 - 3028 * q^76 - 3716 * q^78 + 298 * q^79 - 2540 * q^80 - 1050 * q^81 - 146 * q^82 - 4844 * q^84 - 2412 * q^86 + 2140 * q^87 + 1626 * q^88 + 422 * q^89 - 4916 * q^90 + 1652 * q^92 - 2676 * q^94 - 2434 * q^95 - 400 * q^96 + 1672 * q^97 - 2670 * q^98

Introduction

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