LMFDB - Embedded newform 72.5.p.b.43.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,5,Mod(43,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("72.43");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$N$	$=$	$72 = 2^{3} \cdot 3^{2}$
Weight:	$k$	$=$	$5$
Character orbit:	$[\chi]$	$=$	72.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:	$7.44263734204$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.10
Character	$\chi$	$=$	72.43
Dual form			72.5.p.b.67.10

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.30101 - 2.25906i) q^{2} +(4.44945 - 7.82320i) q^{3} +(5.79331 + 14.9143i) q^{4} +(-2.53773 + 1.46516i) q^{5} +(-32.3607 + 15.7729i) q^{6} +(-39.8426 - 23.0032i) q^{7} +(14.5686 - 62.3198i) q^{8} +(-41.4048 - 69.6178i) q^{9} +(11.6869 + 0.896378i) q^{10} +(27.1224 - 46.9774i) q^{11} +(142.455 + 21.0384i) q^{12} +(-174.611 + 100.811i) q^{13} +(79.5554 + 165.940i) q^{14} +(0.170730 + 26.3723i) q^{15} +(-188.875 + 172.807i) q^{16} -88.7146 q^{17} +(-20.5931 + 323.345i) q^{18} -357.083 q^{19} +(-36.5537 - 29.3604i) q^{20} +(-357.236 + 209.345i) q^{21} +(-195.656 + 93.8016i) q^{22} +(214.383 - 123.774i) q^{23} +(-422.718 - 391.262i) q^{24} +(-308.207 + 533.830i) q^{25} +(804.130 + 61.6760i) q^{26} +(-728.863 + 14.1572i) q^{27} +(112.256 - 727.491i) q^{28} +(18.7746 + 10.8395i) q^{29} +(59.0130 - 87.4409i) q^{30} +(349.016 - 201.504i) q^{31} +(1013.86 - 143.757i) q^{32} +(-246.834 - 421.207i) q^{33} +(292.848 + 200.411i) q^{34} +134.813 q^{35} +(798.433 - 1020.84i) q^{36} -1263.37i q^{37} +(1178.73 + 806.671i) q^{38} +(11.7472 + 1814.57i) q^{39} +(54.3372 + 179.496i) q^{40} +(-1106.42 - 1916.37i) q^{41} +(1652.16 + 115.966i) q^{42} +(678.384 - 1175.00i) q^{43} +(857.765 + 132.358i) q^{44} +(207.075 + 116.007i) q^{45} +(-987.293 - 75.7244i) q^{46} +(3120.48 + 1801.61i) q^{47} +(511.512 + 2246.50i) q^{48} +(-142.209 - 246.314i) q^{49} +(2223.34 - 1065.92i) q^{50} +(-394.731 + 694.032i) q^{51} +(-2515.11 - 2020.17i) q^{52} -4122.82i q^{53} +(2437.96 + 1599.81i) q^{54} +158.955i q^{55} +(-2014.00 + 2147.86i) q^{56} +(-1588.82 + 2793.53i) q^{57} +(-37.4881 - 78.1944i) q^{58} +(-2643.76 - 4579.12i) q^{59} +(-392.337 + 155.329i) q^{60} +(-4778.25 - 2758.72i) q^{61} +(-1607.31 - 123.280i) q^{62} +(48.2476 + 3726.20i) q^{63} +(-3671.51 - 1815.82i) q^{64} +(295.410 - 511.664i) q^{65} +(-136.732 + 1948.02i) q^{66} +(3090.68 + 5353.21i) q^{67} +(-513.951 - 1323.12i) q^{68} +(-14.4230 - 2227.89i) q^{69} +(-445.019 - 304.551i) q^{70} +4832.30i q^{71} +(-4941.78 + 1566.11i) q^{72} +9435.38 q^{73} +(-2854.02 + 4170.38i) q^{74} +(2804.90 + 4786.41i) q^{75} +(-2068.69 - 5325.66i) q^{76} +(-2161.26 + 1247.80i) q^{77} +(4060.44 - 6016.44i) q^{78} +(-1099.86 - 635.004i) q^{79} +(226.125 - 715.269i) q^{80} +(-3132.28 + 5765.03i) q^{81} +(-676.901 + 8825.41i) q^{82} +(1266.75 - 2194.08i) q^{83} +(-5191.83 - 4115.14i) q^{84} +(225.134 - 129.981i) q^{85} +(-4893.74 + 2346.16i) q^{86} +(168.337 - 98.6477i) q^{87} +(-2532.48 - 2374.66i) q^{88} +5907.27 q^{89} +(-421.492 - 850.734i) q^{90} +9275.93 q^{91} +(3087.99 + 2480.32i) q^{92} +(-23.4806 - 3627.00i) q^{93} +(-6230.78 - 12996.5i) q^{94} +(906.180 - 523.183i) q^{95} +(3386.48 - 8571.26i) q^{96} +(-928.999 + 1609.07i) q^{97} +(-87.0031 + 1134.34i) q^{98} +(-4393.46 + 56.8874i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$88 q + 7 q^{2} - 18 q^{3} + 31 q^{4} - 9 q^{6} - 386 q^{8} + 30 q^{9} - 36 q^{10} + 44 q^{11} + 612 q^{12} - 318 q^{14} + 511 q^{16} - 1156 q^{17} + 234 q^{18} + 860 q^{19} - 1164 q^{20} + 215 q^{22} - 561 q^{24}+ \cdots - 11742 q^{99}+O(q^{100})$ 88 * q + 7 * q^2 - 18 * q^3 + 31 * q^4 - 9 * q^6 - 386 * q^8 + 30 * q^9 - 36 * q^10 + 44 * q^11 + 612 * q^12 - 318 * q^14 + 511 * q^16 - 1156 * q^17 + 234 * q^18 + 860 * q^19 - 1164 * q^20 + 215 * q^22 - 561 * q^24 + 5998 * q^25 - 5232 * q^26 + 504 * q^27 - 516 * q^28 + 2046 * q^30 + 5227 * q^32 - 3204 * q^33 + 1877 * q^34 - 2508 * q^35 - 5877 * q^36 - 4393 * q^38 + 2274 * q^40 + 2348 * q^41 - 8166 * q^42 + 3500 * q^43 + 2234 * q^44 + 3576 * q^46 - 1641 * q^48 + 16462 * q^49 + 5785 * q^50 - 12378 * q^51 - 1440 * q^52 - 7467 * q^54 + 1146 * q^56 - 6522 * q^57 - 4128 * q^58 - 3508 * q^59 + 11934 * q^60 + 2376 * q^62 - 5510 * q^64 - 2502 * q^65 + 834 * q^66 + 5132 * q^67 + 10169 * q^68 + 1134 * q^70 + 9663 * q^72 + 19004 * q^73 - 2946 * q^74 - 39858 * q^75 - 5875 * q^76 - 3330 * q^78 + 8592 * q^80 - 11346 * q^81 - 18454 * q^82 + 17090 * q^83 + 12360 * q^84 + 18581 * q^86 - 3253 * q^88 - 8272 * q^89 - 9408 * q^90 - 9612 * q^91 + 9318 * q^92 - 7590 * q^94 + 52650 * q^96 + 9980 * q^97 + 6826 * q^98 - 11742 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$ .

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−3.30101	−	2.25906i	−0.825252	−	0.564765i
$2$	−3.30101	−	2.25906i	−0.825252	−	0.564765i
$3$	4.44945	−	7.82320i	0.494383	−	0.869244i
$3$	4.44945	−	7.82320i	0.494383	−	0.869244i
$4$	5.79331	+	14.9143i	0.362082	+	0.932146i
$5$	−2.53773	+	1.46516i	−0.101509	+	0.0586064i	−0.549895	−	0.835234i	$-0.685332\pi$
$5$	−2.53773	+	1.46516i	−0.101509	+	0.0586064i	0.448386	+	0.893840i	$0.351999\pi$
$6$	−32.3607	+	15.7729i	−0.898909	+	0.438135i
$7$	−39.8426	−	23.0032i	−0.813115	−	0.469452i	0.0349214	−	0.999390i	$-0.488882\pi$
$7$	−39.8426	−	23.0032i	−0.813115	−	0.469452i	−0.848036	+	0.529938i	$0.822215\pi$
$8$	14.5686	−	62.3198i	0.227634	−	0.973747i
$9$	−41.4048	−	69.6178i	−0.511171	−	0.859479i
$10$	11.6869	+	0.896378i	0.116869	+	0.00896378i
$11$	27.1224	−	46.9774i	0.224152	−	0.388243i	−0.731913	−	0.681398i	$-0.761372\pi$
$11$	27.1224	−	46.9774i	0.224152	−	0.388243i	0.956065	+	0.293156i	$0.0947054\pi$
$12$	142.455	+	21.0384i	0.989270	+	0.146100i
$13$	−174.611	+	100.811i	−1.03320	+	0.596517i	−0.917899	−	0.396813i	$-0.870116\pi$
$13$	−174.611	+	100.811i	−1.03320	+	0.596517i	−0.115299	+	0.993331i	$0.536783\pi$
$14$	79.5554	+	165.940i	0.405895	+	0.846635i
$15$	0.170730	+	26.3723i	0.000758800	+	0.117210i
$16$	−188.875	+	172.807i	−0.737793	+	0.675027i
$17$	−88.7146			−0.306971			−0.153485	−	0.988151i	$-0.549050\pi$
$17$	−88.7146			−0.306971			−0.153485	+	0.988151i	$0.549050\pi$
$18$	−20.5931	+	323.345i	−0.0635589	+	0.997978i
$19$	−357.083			−0.989149			−0.494575	−	0.869135i	$-0.664676\pi$
$19$	−357.083			−0.989149			−0.494575	+	0.869135i	$0.664676\pi$
$20$	−36.5537	−	29.3604i	−0.0913843	−	0.0734011i
$21$	−357.236	+	209.345i	−0.810059	+	0.474706i
$22$	−195.656	+	93.8016i	−0.404248	+	0.193805i
$23$	214.383	−	123.774i	0.405261	−	0.233977i	−0.283491	−	0.958975i	$-0.591492\pi$
$23$	214.383	−	123.774i	0.405261	−	0.233977i	0.688751	+	0.724998i	$0.258159\pi$
$24$	−422.718	−	391.262i	−0.733885	−	0.679274i
$25$	−308.207	+	533.830i	−0.493131	+	0.854127i
$26$	804.130	+	61.6760i	1.18954	+	0.0912367i
$27$	−728.863	+	14.1572i	−0.999811	+	0.0194200i
$28$	112.256	−	727.491i	0.143184	−	0.927922i
$29$	18.7746	+	10.8395i	0.0223242	+	0.0128889i	0.511121	−	0.859509i	$-0.329231\pi$
$29$	18.7746	+	10.8395i	0.0223242	+	0.0128889i	−0.488796	+	0.872398i	$0.662564\pi$
$30$	59.0130	−	87.4409i	0.0655700	−	0.0971566i
$31$	349.016	−	201.504i	0.363180	−	0.209682i	−0.307295	−	0.951614i	$-0.599424\pi$
$31$	349.016	−	201.504i	0.363180	−	0.209682i	0.670475	+	0.741932i	$0.266090\pi$
$32$	1013.86	−	143.757i	0.990097	−	0.140387i
$33$	−246.834	−	421.207i	−0.226661	−	0.386784i
$34$	292.848	+	200.411i	0.253328	+	0.173366i
$35$	134.813			0.110052
$36$	798.433	−	1020.84i	0.616075	−	0.787688i
$37$		−	1263.37i		−	0.922839i	−0.887182	−	0.461419i	$-0.847340\pi$
$37$		−	1263.37i		−	0.922839i	0.887182	−	0.461419i	$-0.152660\pi$
$38$	1178.73	+	806.671i	0.816297	+	0.558636i
$39$	11.7472	+	1814.57i	0.00772334	+	1.19301i
$40$	54.3372	+	179.496i	0.0339608	+	0.112185i
$41$	−1106.42	−	1916.37i	−0.658189	−	1.14002i	−0.981084	−	0.193582i	$-0.937989\pi$
$41$	−1106.42	−	1916.37i	−0.658189	−	1.14002i	0.322895	−	0.946435i	$-0.395344\pi$
$42$	1652.16	+	115.966i	0.936600	+	0.0657403i
$43$	678.384	−	1175.00i	0.366892	−	0.635476i	−0.622185	−	0.782870i	$-0.713755\pi$
$43$	678.384	−	1175.00i	0.366892	−	0.635476i	0.989078	+	0.147393i	$0.0470884\pi$
$44$	857.765	+	132.358i	0.443060	+	0.0683668i
$45$	207.075	+	116.007i	0.102259	+	0.0572872i
$46$	−987.293	−	75.7244i	−0.466584	−	0.0357866i
$47$	3120.48	+	1801.61i	1.41262	+	0.815577i	0.995635	−	0.0933366i	$-0.0297533\pi$
$47$	3120.48	+	1801.61i	1.41262	+	0.815577i	0.416985	+	0.908913i	$0.363087\pi$
$48$	511.512	+	2246.50i	0.222010	+	0.975044i
$49$	−142.209	−	246.314i	−0.0592292	−	0.102588i
$50$	2223.34	−	1065.92i	0.889338	−	0.426368i
$51$	−394.731	+	694.032i	−0.151761	+	0.266833i
$52$	−2515.11	−	2020.17i	−0.930144	−	0.747104i
$53$		−	4122.82i		−	1.46772i	−0.679303	−	0.733858i	$-0.737718\pi$
$53$		−	4122.82i		−	1.46772i	0.679303	−	0.733858i	$-0.262282\pi$
$54$	2437.96	+	1599.81i	0.836064	+	0.548632i
$55$			158.955i			0.0525469i
$56$	−2014.00	+	2147.86i	−0.642221	+	0.684905i
$57$	−1588.82	+	2793.53i	−0.489019	+	0.859812i
$58$	−37.4881	−	78.1944i	−0.0111439	−	0.0232445i
$59$	−2643.76	−	4579.12i	−0.759482	−	1.31546i	−0.943115	−	0.332466i	$-0.892119\pi$
$59$	−2643.76	−	4579.12i	−0.759482	−	1.31546i	0.183634	−	0.982995i	$-0.441214\pi$
$60$	−392.337	+	155.329i	−0.108982	+	0.0431470i
$61$	−4778.25	−	2758.72i	−1.28413	−	0.741393i	−0.306530	−	0.951861i	$-0.599168\pi$
$61$	−4778.25	−	2758.72i	−1.28413	−	0.741393i	−0.977601	+	0.210468i	$0.932501\pi$
$62$	−1607.31	−	123.280i	−0.418136	−	0.0320706i
$63$	48.2476	+	3726.20i	0.0121561	+	0.938826i
$64$	−3671.51	−	1815.82i	−0.896365	−	0.443317i
$65$	295.410	−	511.664i	0.0699194	−	0.121104i
$66$	−136.732	+	1948.02i	−0.0313894	+	0.447204i
$67$	3090.68	+	5353.21i	0.688500	+	1.19252i	0.972323	+	0.233641i	$0.0750640\pi$
$67$	3090.68	+	5353.21i	0.688500	+	1.19252i	−0.283822	+	0.958877i	$0.591603\pi$
$68$	−513.951	−	1323.12i	−0.111149	−	0.286142i
$69$	−14.4230	−	2227.89i	−0.00302940	−	0.467945i
$70$	−445.019	−	304.551i	−0.0908203	−	0.0621532i
$71$			4832.30i			0.958600i	0.877651	+	0.479300i	$0.159109\pi$
$71$			4832.30i			0.958600i	−0.877651	+	0.479300i	$0.840891\pi$
$72$	−4941.78	+	1566.11i	−0.953275	+	0.302104i
$73$	9435.38			1.77057			0.885286	−	0.465047i	$-0.153963\pi$
$73$	9435.38			1.77057			0.885286	+	0.465047i	$0.153963\pi$
$74$	−2854.02	+	4170.38i	−0.521187	+	0.761574i
$75$	2804.90	+	4786.41i	0.498650	+	0.850917i
$76$	−2068.69	−	5325.66i	−0.358153	−	0.922032i
$77$	−2161.26	+	1247.80i	−0.364523	+	0.210457i
$78$	4060.44	−	6016.44i	0.667396	−	0.988896i
$79$	−1099.86	−	635.004i	−0.176231	−	0.101747i	0.409290	−	0.912405i	$-0.365777\pi$
$79$	−1099.86	−	635.004i	−0.176231	−	0.101747i	−0.585521	+	0.810657i	$0.699110\pi$
$80$	226.125	−	715.269i	0.0353320	−	0.111761i
$81$	−3132.28	+	5765.03i	−0.477409	+	0.878681i
$82$	−676.901	+	8825.41i	−0.100669	+	1.31252i
$83$	1266.75	−	2194.08i	0.183881	−	0.318490i	−0.759318	−	0.650720i	$-0.774467\pi$
$83$	1266.75	−	2194.08i	0.183881	−	0.318490i	0.943199	+	0.332229i	$0.107801\pi$
$84$	−5191.83	−	4115.14i	−0.735803	−	0.583211i
$85$	225.134	−	129.981i	0.0311604	−	0.0179904i
$86$	−4893.74	+	2346.16i	−0.661673	+	0.317220i
$87$	168.337	−	98.6477i	0.0222403	−	0.0130331i
$88$	−2532.48	−	2374.66i	−0.327025	−	0.306645i
$89$	5907.27			0.745773			0.372887	−	0.927877i	$-0.378368\pi$
$89$	5907.27			0.745773			0.372887	+	0.927877i	$0.378368\pi$
$90$	−421.492	−	850.734i	−0.0520361	−	0.105029i
$91$	9275.93			1.12015
$92$	3087.99	+	2480.32i	0.364839	+	0.293043i
$93$	−23.4806	−	3627.00i	−0.00271484	−	0.419355i
$94$	−6230.78	−	12996.5i	−0.705159	−	1.47085i
$95$	906.180	−	523.183i	0.100408	−	0.0579704i
$96$	3386.48	−	8571.26i	0.367456	−	0.930041i
$97$	−928.999	+	1609.07i	−0.0987351	+	0.171014i	−0.911161	−	0.412050i	$-0.864813\pi$
$97$	−928.999	+	1609.07i	−0.0987351	+	0.171014i	0.812426	+	0.583064i	$0.198146\pi$
$98$	−87.0031	+	1134.34i	−0.00905905	+	0.118112i
$99$	−4393.46	+	56.8874i	−0.448267	+	0.00580425i
$100$	−9747.25	−	1504.06i	−0.974725	−	0.150406i
$101$	−13841.8	−	7991.56i	−1.35690	−	0.783409i	−0.367699	−	0.929945i	$-0.619854\pi$
$101$	−13841.8	−	7991.56i	−1.35690	−	0.783409i	−0.989205	+	0.146536i	$0.953188\pi$
$102$	2870.87	−	1399.28i	0.275939	−	0.134495i
$103$	17094.2	−	9869.37i	1.61130	−	0.930283i	0.622227	−	0.782837i	$-0.286228\pi$
$103$	17094.2	−	9869.37i	1.61130	−	0.930283i	0.989070	−	0.147445i	$-0.0471051\pi$
$104$	3738.72	+	12350.4i	0.345665	+	1.14186i
$105$	599.844	−	1054.67i	0.0544076	−	0.0956617i
$106$	−9313.68	+	13609.4i	−0.828914	+	1.21124i
$107$	8611.81			0.752189			0.376095	−	0.926581i	$-0.377267\pi$
$107$	8611.81			0.752189			0.376095	+	0.926581i	$0.377267\pi$
$108$	−4433.67	−	10788.5i	−0.380116	−	0.924939i
$109$			19759.0i			1.66307i	0.555470	+	0.831537i	$0.312539\pi$
$109$			19759.0i			1.66307i	−0.555470	+	0.831537i	$0.687461\pi$
$110$	359.088	−	524.710i	0.0296767	−	0.0433645i
$111$	−9883.56	−	5621.28i	−0.802172	−	0.456236i
$112$	11500.4	−	2540.35i	0.916804	−	0.202516i
$113$	−8203.89	−	14209.6i	−0.642485	−	1.11282i	−0.984876	−	0.173259i	$-0.944570\pi$
$113$	−8203.89	−	14209.6i	−0.642485	−	1.11282i	0.342392	−	0.939557i	$-0.388763\pi$
$114$	11555.5	−	5632.22i	0.889155	−	0.433381i
$115$	−362.697	+	628.210i	−0.0274251	+	0.0475017i
$116$	−52.8973	+	342.808i	−0.00393113	+	0.0254762i
$117$	14248.0	+	7981.92i	1.04083	+	0.583090i
$118$	−1617.44	+	21088.1i	−0.116162	+	1.51451i
$119$	3534.62	+	2040.72i	0.249603	+	0.144108i
$120$	1646.00	+	373.568i	0.114306	+	0.0259422i
$121$	5849.25	+	10131.2i	0.399512	+	0.691975i
$122$	9540.93	+	19900.9i	0.641019	+	1.33707i
$123$	−19915.1	+	128.927i	−1.31635	+	0.00852183i
$124$	5027.26	+	4037.96i	0.326955	+	0.262615i
$125$		−	3637.74i		−	0.232815i
$126$	8258.44	−	12409.2i	0.520184	−	0.781633i
$127$			190.402i			0.0118049i	0.999983	+	0.00590247i	$0.00187883\pi$
$127$			190.402i			0.0118049i	−0.999983	+	0.00590247i	$0.998121\pi$
$128$	8017.64	+	14288.2i	0.489358	+	0.872083i
$129$	−6173.79	−	10535.2i	−0.370999	−	0.633088i
$130$	−2131.03	+	1021.66i	−0.126096	+	0.0604533i
$131$	−5339.62	−	9248.49i	−0.311148	−	0.538925i	0.667463	−	0.744643i	$-0.267380\pi$
$131$	−5339.62	−	9248.49i	−0.311148	−	0.538925i	−0.978611	+	0.205718i	$0.934047\pi$
$132$	4852.05	−	6121.54i	0.278469	−	0.351328i
$133$	14227.1	+	8214.03i	0.804292	+	0.464358i
$134$	1890.86	−	24653.0i	0.105305	−	1.37297i
$135$	1828.91	−	1103.83i	0.100352	−	0.0605666i
$136$	−1292.45	+	5528.67i	−0.0698771	+	0.298912i
$137$	−2673.96	+	4631.43i	−0.142467	+	0.246759i	−0.928425	−	0.371520i	$-0.878837\pi$
$137$	−2673.96	+	4631.43i	−0.142467	+	0.246759i	0.785958	+	0.618280i	$0.212170\pi$
$138$	−4985.31	+	7386.85i	−0.261779	+	0.387883i
$139$	−4160.16	−	7205.61i	−0.215318	−	0.372942i	0.738053	−	0.674743i	$-0.235746\pi$
$139$	−4160.16	−	7205.61i	−0.215318	−	0.372942i	−0.953371	+	0.301801i	$0.902412\pi$
$140$	781.014	+	2010.65i	0.0398477	+	0.102584i
$141$	27978.7	−	16395.9i	1.40731	−	0.824704i
$142$	10916.5	−	15951.5i	0.541383	−	0.791086i
$143$			10937.0i			0.534842i
$144$	19850.8	+	5994.04i	0.957310	+	0.289064i
$145$	−63.5266			−0.00302148
$146$	−31146.3	−	21315.1i	−1.46117	−	0.999956i
$147$	−2559.72	+	16.5712i	−0.118456	+	0.000766864i
$148$	18842.3	−	7319.07i	0.860220	−	0.334143i
$149$	−8232.13	+	4752.82i	−0.370800	+	0.214082i	−0.673808	−	0.738907i	$-0.735342\pi$
$149$	−8232.13	+	4752.82i	−0.370800	+	0.214082i	0.303008	+	0.952988i	$0.402009\pi$
$150$	1553.76	−	22136.4i	0.0690562	−	0.983841i
$151$	−23033.8	−	13298.5i	−1.01021	−	0.583244i	−0.0989556	−	0.995092i	$-0.531550\pi$
$151$	−23033.8	−	13298.5i	−1.01021	−	0.583244i	−0.911253	+	0.411848i	$0.864884\pi$
$152$	−5202.20	+	22253.3i	−0.225164	+	0.963181i
$153$	3673.21	+	6176.12i	0.156914	+	0.263835i
$154$	9953.18	+	763.400i	0.419682	+	0.0321892i
$155$	−590.472	+	1022.73i	−0.0245774	+	0.0425693i
$156$	−26995.0	+	10687.6i	−1.10926	+	0.439166i
$157$	−14257.2	+	8231.41i	−0.578410	+	0.333945i	−0.760501	−	0.649336i	$-0.775047\pi$
$157$	−14257.2	+	8231.41i	−0.578410	+	0.333945i	0.182091	+	0.983282i	$0.441713\pi$
$158$	2196.13	+	4580.80i	0.0879720	+	0.183496i
$159$	−32253.6	−	18344.3i	−1.27580	−	0.725614i
$160$	−2362.27	+	1850.28i	−0.0922763	+	0.0722766i
$161$	−11388.8			−0.439365
$162$	23363.2	−	11954.4i	0.890231	−	0.455510i
$163$	−6664.66			−0.250843			−0.125422	−	0.992104i	$-0.540028\pi$
$163$	−6664.66			−0.250843			−0.125422	+	0.992104i	$0.540028\pi$
$164$	22171.6	−	27603.6i	0.824344	−	1.02631i
$165$	1243.53	+	707.260i	0.0456761	+	0.0259783i
$166$	−9138.12	+	4381.01i	−0.331620	+	0.158986i
$167$	−19196.1	+	11082.8i	−0.688302	+	0.397391i	−0.802976	−	0.596012i	$-0.796751\pi$
$167$	−19196.1	+	11082.8i	−0.688302	+	0.397391i	0.114674	+	0.993403i	$0.463418\pi$
$168$	7841.93	+	25312.7i	0.277846	+	0.896852i
$169$	6045.39	−	10470.9i	0.211666	−	0.366616i
$170$	−1036.80	−	79.5218i	−0.0358755	−	0.00275162i
$171$	14785.0	+	24859.3i	0.505624	+	0.850153i
$172$	21454.4	+	3310.54i	0.725202	+	0.111903i
$173$	−9709.71	−	5605.90i	−0.324425	−	0.187307i	0.328938	−	0.944351i	$-0.393309\pi$
$173$	−9709.71	−	5605.90i	−0.324425	−	0.187307i	−0.653363	+	0.757045i	$0.726643\pi$
$174$	−778.531	−	54.6454i	−0.0257145	−	0.00180491i
$175$	24559.5	−	14179.5i	0.801944	−	0.463002i
$176$	2995.26	+	13559.8i	0.0966963	+	0.437752i
$177$	−47586.6	+	308.068i	−1.51893	+	0.00983331i
$178$	−19499.9	−	13344.9i	−0.615451	−	0.421186i
$179$	−16987.5			−0.530179			−0.265090	−	0.964224i	$-0.585402\pi$
$179$	−16987.5			−0.530179			−0.265090	+	0.964224i	$0.585402\pi$
$180$	−530.509	+	3760.46i	−0.0163737	+	0.116063i
$181$			48494.7i			1.48026i	0.672465	+	0.740129i	$0.265236\pi$
$181$			48494.7i			1.48026i	−0.672465	+	0.740129i	$0.734764\pi$
$182$	−30619.9	−	20954.9i	−0.924402	−	0.632619i
$183$	−42842.6	+	25106.4i	−1.27930	+	0.749691i
$184$	−4590.31	−	15163.5i	−0.135583	−	0.447883i
$185$	1851.03	+	3206.08i	0.0540842	+	0.0936766i
$186$	−8116.10	+	12025.8i	−0.234597	+	0.347607i
$187$	−2406.15	+	4167.58i	−0.0688082	+	0.119179i
$188$	−8791.91	+	56977.1i	−0.248753	+	1.61207i
$189$	29365.5	+	16202.1i	0.822079	+	0.453573i
$190$	−4173.21	−	320.081i	−0.115601	−	0.00886652i
$191$	31625.9	+	18259.2i	0.866915	+	0.500514i	0.866322	−	0.499486i	$-0.166478\pi$
$191$	31625.9	+	18259.2i	0.866915	+	0.500514i	0.000593302		1.00000i	$0.499811\pi$
$192$	−30541.8	+	20643.5i	−0.828498	+	0.559992i
$193$	−12557.9	−	21750.9i	−0.337133	−	0.583932i	0.646759	−	0.762694i	$-0.276124\pi$
$193$	−12557.9	−	21750.9i	−0.337133	−	0.583932i	−0.983892	+	0.178762i	$0.942791\pi$
$194$	6701.62	−	3212.90i	0.178064	−	0.0853677i
$195$	−2688.44	−	4587.67i	−0.0707019	−	0.120649i
$196$	2849.75	−	3547.93i	0.0741812	−	0.0923556i
$197$		−	28539.7i		−	0.735388i	−0.929947	−	0.367694i	$-0.880147\pi$
$197$		−	28539.7i		−	0.735388i	0.929947	−	0.367694i	$-0.119853\pi$
$198$	14631.4	+	9737.30i	0.373211	+	0.248375i
$199$		−	63914.2i		−	1.61395i	−0.590583	−	0.806977i	$-0.701102\pi$
$199$		−	63914.2i		−	1.61395i	0.590583	−	0.806977i	$-0.298898\pi$
$200$	28778.0	+	26984.5i	0.719450	+	0.674613i
$201$	55631.0	−	360.146i	1.37697	−	0.00891429i
$202$	27638.4	+	57649.6i	0.677346	+	1.41284i
$203$	−498.687	−	863.752i	−0.0121014	−	0.0209603i
$204$	−12637.8	−	1866.41i	−0.303677	−	0.0448484i
$205$	5615.57	+	3242.15i	0.133624	+	0.0771481i
$206$	−78723.7	−	6038.04i	−1.85512	−	0.142286i
$207$	−17493.4	−	9800.03i	−0.408256	−	0.228711i
$208$	15558.7	−	49214.7i	0.359622	−	1.13754i
$209$	−9684.94	+	16774.8i	−0.221720	+	0.384030i
$210$	−4362.65	+	2126.39i	−0.0989263	+	0.0482175i
$211$	−7822.71	−	13549.3i	−0.175708	−	0.304336i	0.764698	−	0.644389i	$-0.222888\pi$
$211$	−7822.71	−	13549.3i	−0.175708	−	0.304336i	−0.940406	+	0.340053i	$0.889555\pi$
$212$	61489.1	−	23884.8i	1.36813	−	0.531434i
$213$	37804.0	+	21501.1i	0.833257	+	0.473916i
$214$	−28427.7	−	19454.6i	−0.620746	−	0.424810i
$215$			3975.76i			0.0860089i
$216$	−9736.24	+	45628.8i	−0.208681	+	0.977984i
$217$	−18541.0			−0.393743
$218$	44636.7	−	65224.6i	0.939245	−	1.37246i
$219$	41982.2	−	73814.8i	0.875341	−	1.53906i
$220$	−2370.70	+	920.873i	−0.0489814	+	0.0190263i
$221$	15490.5	−	8943.44i	0.317162	−	0.183113i
$222$	19926.9	+	40883.4i	0.404328	+	0.829548i
$223$	−44835.1	−	25885.6i	−0.901589	−	0.520532i	−0.0238733	−	0.999715i	$-0.507600\pi$
$223$	−44835.1	−	25885.6i	−0.901589	−	0.520532i	−0.877715	+	0.479183i	$0.840933\pi$
$224$	−43701.7	−	17594.3i	−0.870968	−	0.350652i
$225$	49925.3	−	646.443i	0.986179	−	0.0127692i
$226$	−5019.10	+	65438.9i	−0.0982674	+	1.28121i
$227$	−28229.2	+	48894.4i	−0.547831	+	0.948871i	0.450592	+	0.892730i	$0.351213\pi$
$227$	−28229.2	+	48894.4i	−0.547831	+	0.948871i	−0.998423	+	0.0561410i	$0.982120\pi$
$228$	−50868.2	−	7512.45i	−0.978536	−	0.144515i
$229$	−48956.6	+	28265.1i	−0.933556	+	0.538989i	−0.887935	−	0.459970i	$-0.847860\pi$
$229$	−48956.6	+	28265.1i	−0.933556	+	0.538989i	−0.0456218	+	0.998959i	$0.514527\pi$
$230$	2616.43	−	1254.37i	0.0494599	−	0.0237121i
$231$	145.402	+	22460.0i	0.00272487	+	0.420906i
$232$	949.038	−	1012.11i	0.0176322	−	0.0188041i
$233$	72322.4			1.33217			0.666087	−	0.745874i	$-0.267968\pi$
$233$	72322.4			1.33217			0.666087	+	0.745874i	$0.267968\pi$
$234$	−29001.1	−	58535.4i	−0.529642	−	1.06902i
$235$	−10558.6			−0.191192
$236$	52978.4	−	65958.1i	0.951207	−	1.18425i
$237$	−9861.52	+	5778.99i	−0.175569	+	0.102886i
$238$	−7057.72	−	14721.3i	−0.124598	−	0.259892i
$239$	86456.7	−	49915.8i	1.51357	−	0.873861i	0.513698	−	0.857971i	$-0.328275\pi$
$239$	86456.7	−	49915.8i	1.51357	−	0.873861i	0.999874	−	0.0158894i	$-0.00505797\pi$
$240$	−4589.56	−	4951.57i	−0.0796799	−	0.0859647i
$241$	−13108.7	+	22704.9i	−0.225697	+	0.390918i	−0.956528	−	0.291640i	$-0.905799\pi$
$241$	−13108.7	+	22704.9i	−0.225697	+	0.390918i	0.730832	+	0.682558i	$0.239132\pi$
$242$	3578.55	−	46657.0i	0.0611049	−	0.796684i
$243$	31164.0	+	50155.6i	0.527765	+	0.849390i
$244$	13462.7	−	87246.6i	0.226127	−	1.46544i
$245$	721.778	+	416.719i	0.0120246	+	0.00694242i
$246$	66031.1	+	44563.7i	1.09113	+	0.736396i
$247$	62350.4	−	35998.0i	1.02199	−	0.590045i
$248$	−7473.04	−	24686.2i	−0.121505	−	0.401376i
$249$	−11528.4	−	19672.5i	−0.185939	−	0.317293i
$250$	−8217.86	+	12008.2i	−0.131486	+	0.192131i
$251$	110168.			1.74866			0.874332	−	0.485328i	$-0.161300\pi$
$251$	110168.			1.74866			0.874332	+	0.485328i	$0.161300\pi$
$252$	−55294.3	+	22306.6i	−0.870721	+	0.351263i
$253$		−	13428.2i		−	0.209786i
$254$	430.129	−	628.518i	0.00666701	−	0.00974205i
$255$	−15.1462	−	2339.61i	−0.000232929	−	0.0359801i
$256$	5811.62	−	65277.8i	0.0886783	−	0.996060i
$257$	21395.2	+	37057.7i	0.323930	+	0.561063i	0.981295	−	0.192509i	$-0.0616625\pi$
$257$	21395.2	+	37057.7i	0.323930	+	0.561063i	−0.657365	+	0.753572i	$0.728329\pi$
$258$	−3419.94	+	48723.8i	−0.0513782	+	0.731984i
$259$	−29061.4	+	50335.8i	−0.433229	+	0.750374i
$260$	9342.54	+	1441.61i	0.138203	+	0.0213256i
$261$	−22.7352	−	1755.86i	−0.000333748	−	0.0257756i
$262$	−3266.76	+	42591.9i	−0.0475898	+	0.620475i
$263$	70761.8	+	40854.3i	1.02303	+	0.590645i	0.914979	−	0.403501i	$-0.132207\pi$
$263$	70761.8	+	40854.3i	1.02303	+	0.590645i	0.108048	+	0.994146i	$0.465540\pi$
$264$	−29845.6	+	9246.21i	−0.428225	+	0.132665i
$265$	6040.58	+	10462.6i	0.0860175	+	0.148987i
$266$	−28407.9	−	59254.5i	−0.401491	−	0.837448i
$267$	26284.1	−	46213.7i	0.368698	−	0.648259i
$268$	−61934.4	+	77108.3i	−0.862307	+	1.07357i
$269$		−	71867.3i		−	0.993177i	−0.867986	−	0.496589i	$-0.834586\pi$
$269$		−	71867.3i		−	0.993177i	0.867986	−	0.496589i	$-0.165414\pi$
$270$	−8530.87	−	487.882i	−0.117022	−	0.00669248i
$271$			57719.4i			0.785929i	0.919554	+	0.392964i	$0.128550\pi$
$271$			57719.4i			0.785929i	−0.919554	+	0.392964i	$0.871450\pi$
$272$	16756.0	−	15330.5i	0.226481	−	0.207213i
$273$	41272.8	−	72567.4i	0.553781	−	0.973680i
$274$	19289.4	−	9247.76i	0.256932	−	0.123179i
$275$	16718.6	+	28957.5i	0.221072	+	0.382909i
$276$	33143.9	−	13121.9i	0.435096	−	0.172258i
$277$	−17169.2	−	9912.65i	−0.223764	−	0.129190i	0.383928	−	0.923363i	$-0.374571\pi$
$277$	−17169.2	−	9912.65i	−0.223764	−	0.129190i	−0.607692	+	0.794173i	$0.707905\pi$
$278$	−2545.17	+	33183.8i	−0.0329327	+	0.429375i
$279$	−28479.2	−	15954.5i	−0.365864	−	0.204962i
$280$	1964.04	−	8401.53i	0.0250515	−	0.107162i
$281$	−62271.1	+	107857.i	−0.788631	+	1.36595i	0.138175	+	0.990408i	$0.455876\pi$
$281$	−62271.1	+	107857.i	−0.788631	+	1.36595i	−0.926806	+	0.375541i	$0.877457\pi$
$282$	−129397.	−	9082.46i	−1.62715	−	0.114210i
$283$	−28575.7	−	49494.6i	−0.356799	−	0.617995i	0.630625	−	0.776088i	$-0.282799\pi$
$283$	−28575.7	−	49494.6i	−0.356799	−	0.617995i	−0.987424	+	0.158093i	$0.949465\pi$
$284$	−72070.6	+	27995.0i	−0.893555	+	0.347092i
$285$	−60.9647	−	9417.10i	−0.000750566	−	0.115938i
$286$	24707.3	−	36103.1i	0.302060	−	0.441380i
$287$			101804.i			1.23595i
$288$	−51986.7	−	64630.4i	−0.626768	−	0.779206i
$289$	−75650.7			−0.905769
$290$	209.702	+	143.510i	0.00249348	+	0.00170642i
$291$	8454.56	+	14427.2i	0.0998401	+	0.170371i
$292$	54662.1	+	140722.i	0.641092	+	1.65043i
$293$	−25459.0	+	14698.8i	−0.296555	+	0.171216i	−0.640894	−	0.767629i	$-0.721436\pi$
$293$	−25459.0	+	14698.8i	−0.296555	+	0.171216i	0.344339	+	0.938845i	$0.388103\pi$
$294$	8487.08	+	5727.84i	0.0981891	+	0.0662669i
$295$	13418.3	+	7747.04i	0.154189	+	0.0890209i
$296$	−78732.7	−	18405.5i	−0.898611	−	0.210070i
$297$	−19103.4	+	34624.0i	−0.216570	+	0.392523i
$298$	37911.2	+	2907.76i	0.426909	+	0.0327435i
$299$	−24955.7	+	43224.5i	−0.279143	+	0.483490i
$300$	−55136.4	+	69562.4i	−0.612627	+	0.772916i
$301$	−54057.2	+	31210.0i	−0.596652	+	0.344477i
$302$	45992.4	+	95933.2i	0.504281	+	1.05185i
$303$	−124108.	+	72729.0i	−1.35180	+	0.792177i
$304$	67444.1	−	61706.3i	0.729788	−	0.667702i
$305$	16167.9			0.173801
$306$	1826.91	−	28685.4i	0.0195107	−	0.306350i
$307$	−77280.8			−0.819964			−0.409982	−	0.912094i	$-0.634465\pi$
$307$	−77280.8			−0.819964			−0.409982	+	0.912094i	$0.634465\pi$
$308$	−31131.0	−	25004.8i	−0.328164	−	0.263586i
$309$	−1150.04	−	177645.i	−0.0120447	−	1.86053i
$310$	4259.55	−	2042.12i	0.0443242	−	0.0212500i
$311$	−88843.4	+	51293.7i	−0.918553	+	0.530327i	−0.883173	−	0.469047i	$-0.844597\pi$
$311$	−88843.4	+	51293.7i	−0.918553	+	0.530327i	−0.0353799	+	0.999374i	$0.511264\pi$
$312$	113255.	+	25703.6i	1.16345	+	0.264049i
$313$	20566.6	−	35622.4i	0.209930	−	0.363609i	−0.741762	−	0.670663i	$-0.766010\pi$
$313$	20566.6	−	35622.4i	0.209930	−	0.363609i	0.951692	+	0.307054i	$0.0993431\pi$
$314$	65658.5	+	5035.94i	0.665934	+	0.0510766i
$315$	−5581.91	−	9385.40i	−0.0562551	−	0.0945870i
$316$	3098.84	−	20082.4i	0.0310331	−	0.201114i
$317$	−109026.	−	62945.9i	−1.08495	−	0.626396i	−0.152723	−	0.988269i	$-0.548804\pi$
$317$	−109026.	−	62945.9i	−1.08495	−	0.626396i	−0.932227	+	0.361873i	$0.882137\pi$
$318$	65028.7	+	133417.i	0.643059	+	1.31934i
$319$	1018.43	−	587.989i	0.0100080	−	0.00577813i
$320$	11977.8	−	771.277i	0.116970	−	0.00753200i
$321$	38317.8	−	67371.9i	0.371870	−	0.653836i
$322$	37594.4	+	25727.9i	0.362587	+	0.248138i
$323$	31678.5			0.303640
$324$	−104128.	−	13317.3i	−0.991921	−	0.126861i
$325$		−	124283.i		−	1.17664i
$326$	22000.1	+	15055.8i	0.207009	+	0.141667i
$327$	154578.	+	87916.6i	1.44562	+	0.822196i
$328$	−135547.	+	41032.8i	−1.25991	+	0.381402i
$329$	−82885.4	−	143562.i	−0.765748	−	1.32632i
$330$	−2507.17	−	5143.88i	−0.0230227	−	0.0472349i
$331$	54232.0	−	93932.5i	0.494993	−	0.857354i	−0.504990	−	0.863125i	$-0.668504\pi$
$331$	54232.0	−	93932.5i	0.494993	−	0.857354i	0.999983	+	0.00577154i	$0.00183715\pi$
$332$	40062.0	+	6181.80i	0.363460	+	0.0560840i
$333$	−87952.8	+	52309.4i	−0.793161	+	0.471728i
$334$	88403.2	+	6780.44i	0.792455	+	0.0607806i
$335$	−15686.6	−	9056.67i	−0.139778	−	0.0807010i
$336$	31296.7	−	101273.i	0.277217	−	0.897046i
$337$	−1823.71	−	3158.77i	−0.0160582	−	0.0278136i	0.857885	−	0.513842i	$-0.171778\pi$
$337$	−1823.71	−	3158.77i	−0.0160582	−	0.0278136i	−0.873943	+	0.486029i	$0.838445\pi$
$338$	−43610.3	+	20907.7i	−0.381730	+	0.183009i
$339$	−147667.	+	955.971i	−1.28494	+	0.00831850i
$340$	3242.85	+	2604.70i	0.0280523	+	0.0225320i
$341$		−	21861.1i		−	0.188003i
$342$	7353.43	−	115461.i	0.0628692	−	0.987149i
$343$			123546.i			1.05013i
$344$	−63342.4	−	59394.8i	−0.535276	−	0.501917i
$345$	3300.81	+	5632.64i	0.0277321	+	0.0473232i
$346$	19387.8	+	40439.9i	0.161948	+	0.337799i
$347$	−86264.4	−	149414.i	−0.716428	−	1.24089i	−0.962406	−	0.271615i	$-0.912442\pi$
$347$	−86264.4	−	149414.i	−0.716428	−	1.24089i	0.245978	−	0.969275i	$-0.420891\pi$
$348$	2446.49	+	1939.13i	0.0202016	+	0.0160121i
$349$	138147.	+	79759.0i	1.13420	+	0.654831i	0.944988	−	0.327106i	$-0.106073\pi$
$349$	138147.	+	79759.0i	1.13420	+	0.654831i	0.189212	+	0.981936i	$0.439407\pi$
$350$	−113103.	−	8674.93i	−0.923293	−	0.0708157i
$351$	125840.	−	75949.7i	1.02142	−	0.616470i
$352$	20745.0	−	51527.5i	0.167428	−	0.415866i
$353$	−20555.4	+	35603.0i	−0.164959	+	0.285718i	−0.936641	−	0.350291i	$-0.886083\pi$
$353$	−20555.4	+	35603.0i	−0.164959	+	0.285718i	0.771681	+	0.636009i	$0.219416\pi$
$354$	157780.	+	106484.i	1.25905	+	0.849724i
$355$	−7080.09	−	12263.1i	−0.0561800	−	0.0973067i
$356$	34222.6	+	88103.0i	0.270031	+	0.695170i
$357$	31692.0	−	18572.0i	0.248664	−	0.145721i
$358$	56075.8	+	38375.7i	0.437532	+	0.299427i
$359$		−	76360.8i		−	0.592491i	−0.955112	−	0.296245i	$-0.904265\pi$
$359$		−	76360.8i		−	0.592491i	0.955112	−	0.296245i	$-0.0957346\pi$
$360$	10246.3	−	11214.8i	0.0790610	−	0.0865343i
$361$	−2812.82			−0.0215838
$362$	109552.	−	160082.i	0.835997	−	1.22159i
$363$	105284.	−	681.593i	0.799007	−	0.00517263i
$364$	53738.3	+	138344.i	0.405584	+	1.04414i
$365$	−23944.4	+	13824.3i	−0.179729	+	0.103767i
$366$	198141.	+	13907.6i	1.47915	+	0.103822i
$367$	102925.	+	59423.6i	0.764165	+	0.441191i	0.830789	−	0.556587i	$-0.187889\pi$
$367$	102925.	+	59423.6i	0.764165	+	0.441191i	−0.0666239	+	0.997778i	$0.521223\pi$
$368$	−19102.6	+	60424.7i	−0.141058	+	0.446189i
$369$	−87602.4	+	156373.i	−0.643374	+	1.14844i
$370$	1132.45	−	14764.9i	0.00827212	−	0.107852i
$371$	−94837.8	+	164264.i	−0.689023	+	1.19342i
$372$	53958.3	−	21362.6i	0.389917	−	0.154372i
$373$	−115434.	+	66645.9i	−0.829691	+	0.479023i	−0.853747	−	0.520688i	$-0.825675\pi$
$373$	−115434.	+	66645.9i	−0.829691	+	0.479023i	0.0240556	+	0.999711i	$0.492342\pi$
$374$	17357.5	−	8321.57i	0.124092	−	0.0594925i
$375$	−28458.7	−	16185.9i	−0.202373	−	0.115100i
$376$	157737.	−	168221.i	1.11573	−	1.18988i
$377$	−4371.00			−0.0307537
$378$	−60334.2	−	119822.i	−0.422260	−	0.838593i
$379$	141694.			0.986447			0.493224	−	0.869902i	$-0.335818\pi$
$379$	141694.			0.986447			0.493224	+	0.869902i	$0.335818\pi$
$380$	13052.7	+	10484.1i	0.0903927	+	0.0726047i
$381$	1489.55	+	847.183i	0.0102614	+	0.00583616i
$382$	−63148.8	−	131719.i	−0.432751	−	0.902653i
$383$	−43983.8	+	25394.1i	−0.299844	+	0.173115i	−0.642373	−	0.766392i	$-0.722050\pi$
$383$	−43983.8	+	25394.1i	−0.299844	+	0.173115i	0.342529	+	0.939507i	$0.388717\pi$
$384$	147454.	+	851.103i	0.999983	+	0.00577191i
$385$	3656.46	−	6333.17i	0.0246683	−	0.0427267i
$386$	−7682.86	+	100169.i	−0.0515642	+	0.672292i
$387$	−109889.	+	1422.87i	−0.733723	+	0.00950040i
$388$	−29380.2	−	4533.54i	−0.195160	−	0.0301144i
$389$	103180.	+	59570.8i	0.681860	+	0.393672i	0.800555	−	0.599259i	$-0.204538\pi$
$389$	103180.	+	59570.8i	0.681860	+	0.393672i	−0.118696	+	0.992931i	$0.537871\pi$
$390$	−1489.25	+	21217.3i	−0.00979125	+	0.139496i
$391$	−19018.9	+	10980.6i	−0.124403	+	0.0718242i
$392$	−17422.0	+	5274.01i	−0.113377	+	0.0343217i
$393$	−96111.1	+	622.207i	−0.622284	+	0.00402856i
$394$	−64472.8	+	94209.7i	−0.415321	+	0.606881i
$395$	3721.53			0.0238521
$396$	−26301.1	−	65196.0i	−0.167720	−	0.415748i
$397$		−	200049.i		−	1.26927i	−0.772812	−	0.634635i	$-0.781150\pi$
$397$		−	200049.i		−	1.26927i	0.772812	−	0.634635i	$-0.218850\pi$
$398$	−144386.	+	210981.i	−0.911504	+	1.33192i
$399$	127563.	−	74753.7i	0.801269	−	0.469555i
$400$	−34036.8	−	154087.i	−0.212730	−	0.963046i
$401$	−13977.6	−	24209.9i	−0.0869248	−	0.150558i	0.819285	−	0.573387i	$-0.194371\pi$
$401$	−13977.6	−	24209.9i	−0.0869248	−	0.150558i	−0.906210	+	0.422828i	$0.861037\pi$
$402$	−184452.	−	124485.i	−1.14138	−	0.770309i
$403$	−40627.9	+	70369.6i	−0.250158	+	0.433286i
$404$	38999.1	−	252739.i	0.238941	−	1.54849i
$405$	−497.796	−	19219.4i	−0.00303488	−	0.117173i
$406$	−305.095	+	3977.82i	−0.00185090	+	0.0241320i
$407$	−59349.6	−	34265.5i	−0.358285	−	0.206856i
$408$	37501.2	+	34710.6i	0.225281	+	0.208517i
$409$	−27650.2	−	47891.6i	−0.165292	−	0.286294i	0.771467	−	0.636270i	$-0.219523\pi$
$409$	−27650.2	−	47891.6i	−0.165292	−	0.286294i	−0.936759	+	0.349975i	$0.886190\pi$
$410$	−11212.8	−	23388.3i	−0.0667033	−	0.139133i
$411$	24334.9	+	41526.2i	0.144061	+	0.245832i
$412$	246227.	+	197773.i	1.45058	+	1.16513i
$413$			243259.i			1.42616i
$414$	35606.9	+	71868.5i	0.207746	+	0.419313i
$415$			7423.98i			0.0431063i
$416$	−162538.	+	127310.i	−0.939223	+	0.735658i
$417$	−74881.3	+	484.769i	−0.430627	+	0.00278781i
$418$	69865.4	−	33494.9i	0.399861	−	0.191702i
$419$	−76753.4	−	132941.i	−0.437189	−	0.757234i	0.560282	−	0.828302i	$-0.310693\pi$
$419$	−76753.4	−	132941.i	−0.437189	−	0.757234i	−0.997472	+	0.0710675i	$0.977359\pi$
$420$	19204.8	+	2836.25i	0.108871	+	0.0160785i
$421$	230275.	+	132949.i	1.29922	+	0.750105i	0.980269	−	0.197667i	$-0.0633364\pi$
$421$	230275.	+	132949.i	1.29922	+	0.750105i	0.318950	+	0.947771i	$0.396670\pi$
$422$	−4785.90	+	62398.4i	−0.0268744	+	0.350387i
$423$	−3778.75	−	291836.i	−0.0211187	−	1.63102i
$424$	−256933.	−	60063.7i	−1.42918	−	0.334103i
$425$	27342.4	−	47358.5i	0.151377	−	0.262192i
$426$	−76219.3	−	156377.i	−0.419996	−	0.861694i
$427$	126919.	+	219830.i	0.696097	+	1.20568i
$428$	49890.9	+	128440.i	0.272354	+	0.701150i
$429$	85562.2	+	48663.6i	0.464909	+	0.264417i
$430$	8981.48	−	13124.0i	0.0485748	−	0.0709790i
$431$		−	187074.i		−	1.00707i	−0.863976	−	0.503533i	$-0.832033\pi$
$431$		−	187074.i		−	1.00707i	0.863976	−	0.503533i	$-0.167967\pi$
$432$	135218.	−	128626.i	0.724545	−	0.689227i
$433$	252526.			1.34688			0.673441	−	0.739241i	$-0.264815\pi$
$433$	252526.			1.34688			0.673441	+	0.739241i	$0.264815\pi$
$434$	61203.8	+	41885.1i	0.324937	+	0.222372i
$435$	−282.658	+	496.981i	−0.00149377	+	0.00262640i
$436$	−294692.	+	114470.i	−1.55023	+	0.602169i
$437$	−76552.5	+	44197.6i	−0.400863	+	0.231439i
$438$	−305336.	+	148823.i	−1.59158	+	0.775750i
$439$	−138415.	−	79914.0i	−0.718215	−	0.414662i	0.0958801	−	0.995393i	$-0.469433\pi$
$439$	−138415.	−	79914.0i	−0.718215	−	0.414662i	−0.814095	+	0.580731i	$0.802767\pi$
$440$	9906.01	+	2315.75i	0.0511674	+	0.0119615i
$441$	−11259.7	+	20098.9i	−0.0578960	+	0.103346i
$442$	−71338.0	−	5471.56i	−0.365154	−	0.0280070i
$443$	152813.	−	264680.i	0.778670	−	1.34870i	−0.154038	−	0.988065i	$-0.549228\pi$
$443$	152813.	−	264680.i	0.778670	−	1.34870i	0.932708	−	0.360632i	$-0.117439\pi$
$444$	26579.2	−	179973.i	0.134827	−	0.912936i
$445$	−14991.1	+	8655.09i	−0.0757028	+	0.0437070i
$446$	89524.0	+	186734.i	0.450060	+	0.938756i
$447$	553.830	+	85549.0i	0.00277180	+	0.428154i
$448$	104513.	+	156804.i	0.520732	+	0.781268i
$449$	338152.			1.67733			0.838667	−	0.544645i	$-0.183336\pi$
$449$	338152.			1.67733			0.838667	+	0.544645i	$0.183336\pi$
$450$	−166264.	−	110650.i	−0.821057	−	0.546421i
$451$	−120035.			−0.590138
$452$	164398.	−	204676.i	0.804675	−	1.00182i
$453$	−206525.	+	121026.i	−1.00641	+	0.589772i
$454$	203640.	−	97629.4i	0.987987	−	0.473662i
$455$	−23539.8	+	13590.7i	−0.113705	+	0.0656477i
$456$	150945.	+	139713.i	0.725922	+	0.671903i
$457$	−1641.07	+	2842.42i	−0.00785770	+	0.0136099i	−0.869928	−	0.493180i	$-0.835835\pi$
$457$	−1641.07	+	2842.42i	−0.00785770	+	0.0136099i	0.862070	+	0.506790i	$0.169168\pi$
$458$	225459.	+	17292.5i	1.07482	+	0.0824378i
$459$	64660.7	−	1255.95i	0.306913	−	0.00596137i
$460$	−11470.6	−	1769.97i	−0.0542087	−	0.00836472i
$461$	215070.	+	124171.i	1.01199	+	0.584275i	0.911775	−	0.410690i	$-0.134712\pi$
$461$	215070.	+	124171.i	1.01199	+	0.584275i	0.100220	+	0.994965i	$0.468045\pi$
$462$	50258.4	−	74469.0i	0.235464	−	0.348892i
$463$	−42958.9	+	24802.3i	−0.200397	+	0.115699i	−0.596841	−	0.802360i	$-0.703578\pi$
$463$	−42958.9	+	24802.3i	−0.200397	+	0.115699i	0.396444	+	0.918059i	$0.370244\pi$
$464$	−5419.21	+	1197.07i	−0.0251710	+	0.00556009i
$465$	5373.72	+	9169.95i	0.0248525	+	0.0424093i
$466$	−238737.	−	163380.i	−1.09938	−	0.752365i
$467$	18727.6			0.0858712			0.0429356	−	0.999078i	$-0.486329\pi$
$467$	18727.6			0.0858712			0.0429356	+	0.999078i	$0.486329\pi$
$468$	−36502.1	+	258741.i	−0.166658	+	1.18134i
$469$		−	284381.i		−	1.29287i
$470$	34853.9	+	23852.4i	0.157782	+	0.107978i
$471$	959.178	+	148162.i	0.00432372	+	0.667876i
$472$	−323886.	+	98046.9i	−1.45381	+	0.440099i
$473$	−36798.8	−	63737.4i	−0.164479	−	0.284887i
$474$	45608.1	+	3201.25i	0.202995	+	0.0142483i
$475$	110055.	−	190621.i	0.487780	−	0.844859i
$476$	−9958.76	+	64539.1i	−0.0439533	+	0.284845i
$477$	−287021.	+	170704.i	−1.26147	+	0.750254i
$478$	−398157.	−	30538.3i	−1.74260	−	0.133656i
$479$	−343234.	−	198166.i	−1.49596	−	0.863691i	−0.495967	−	0.868341i	$-0.665186\pi$
$479$	−343234.	−	198166.i	−1.49596	−	0.863691i	−0.999989	+	0.00465021i	$0.998520\pi$
$480$	3964.29	+	26713.3i	0.0172061	+	0.115943i
$481$	127362.	+	220597.i	0.550489	+	0.953475i
$482$	94563.6	−	45335.8i	0.407033	−	0.195140i
$483$	−50673.8	+	89096.6i	−0.217215	+	0.381915i
$484$	−117214.	+	145931.i	−0.500366	+	0.622955i
$485$		−	5444.52i		−	0.0231460i
$486$	10431.9	−	235966.i	0.0441661	−	0.999024i
$487$			240262.i			1.01304i	0.862228	+	0.506520i	$0.169068\pi$
$487$			240262.i			1.01304i	−0.862228	+	0.506520i	$0.830932\pi$
$488$	−241536.	+	257589.i	−1.01424	+	1.08165i
$489$	−29654.0	+	52138.9i	−0.124013	+	0.218044i
$490$	−1441.20	−	3006.13i	−0.00600251	−	0.0125203i
$491$	98040.3	+	169811.i	0.406670	+	0.704372i	0.994514	−	0.104601i	$-0.0333567\pi$
$491$	98040.3	+	169811.i	0.406670	+	0.704372i	−0.587845	+	0.808974i	$0.700023\pi$
$492$	−117297.	−	296273.i	−0.484570	−	1.22395i
$493$	−1665.58	−	961.625i	−0.00685287	−	0.00395651i
$494$	−287141.	−	22023.4i	−1.17663	−	0.0902467i
$495$	11066.1	−	6581.48i	0.0451630	−	0.0268605i
$496$	−31099.1	+	98371.5i	−0.126411	+	0.399858i
$497$	111158.	−	192532.i	0.450017	−	0.779452i
$498$	−6386.09	+	90982.4i	−0.0257499	+	0.366859i
$499$	130948.	+	226808.i	0.525892	+	0.910871i	0.999545	+	0.0301596i	$0.00960157\pi$
$499$	130948.	+	226808.i	0.525892	+	0.910871i	−0.473654	+	0.880711i	$0.657065\pi$
$500$	54254.4	−	21074.5i	0.217018	−	0.0842981i
$501$	1291.45	+	199487.i	0.00514518	+	0.794766i
$502$	−363664.	−	248875.i	−1.44309	−	0.987583i
$503$		−	311251.i		−	1.23020i	−0.788450	−	0.615099i	$-0.789116\pi$
$503$		−	311251.i		−	1.23020i	0.788450	−	0.615099i	$-0.210884\pi$
$504$	232919.	+	51278.7i	0.916946	+	0.201872i
$505$	46835.6			0.183651
$506$	−30335.1	+	44326.6i	−0.118480	+	0.173126i
$507$	−55017.4	−	93884.1i	−0.214035	−	0.365238i
$508$	−2839.72	+	1103.06i	−0.0110039	+	0.00427435i
$509$	317446.	−	183278.i	1.22528	−	0.707415i	0.259240	−	0.965813i	$-0.416528\pi$
$509$	317446.	−	183278.i	1.22528	−	0.707415i	0.966039	+	0.258398i	$0.0831945\pi$
$510$	−5235.31	+	7757.28i	−0.0201281	+	0.0298242i
$511$	−375930.	−	217043.i	−1.43968	−	0.831199i
$512$	−166651.	+	202354.i	−0.635722	+	0.771918i
$513$	260264.	−	5055.29i	0.988963	−	0.0192093i
$514$	13089.5	−	170661.i	0.0495447	−	0.645963i
$515$	−28920.4	+	50091.6i	−0.109041	+	0.188864i
$516$	121359.	−	153112.i	0.455799	−	0.575055i
$517$	169270.	−	97727.9i	0.633283	−	0.365626i
$518$	209644.	−	100508.i	0.781307	−	0.374575i
$519$	−87058.9	+	51017.8i	−0.323205	+	0.189403i
$520$	−27583.1	−	25864.1i	−0.102009	−	0.0956512i
$521$	−526988.			−1.94145			−0.970723	−	0.240203i	$-0.922786\pi$
$521$	−526988.			−1.94145			−0.970723	+	0.240203i	$0.922786\pi$
$522$	−3891.54	+	5847.46i	−0.0142817	+	0.0214598i
$523$	311012.			1.13703			0.568517	−	0.822671i	$-0.307517\pi$
$523$	311012.			1.13703			0.568517	+	0.822671i	$0.307517\pi$
$524$	107001.	−	133216.i	0.389696	−	0.485171i
$525$	−1652.28	−	255225.i	−0.00599467	−	0.925986i
$526$	−141293.	−	294715.i	−0.510680	−	1.06520i
$527$	−30962.8	+	17876.4i	−0.111486	+	0.0643663i
$528$	119408.	+	36901.1i	0.428318	+	0.132364i
$529$	−109280.	+	189279.i	−0.390509	+	0.676382i
$530$	3695.60	−	48183.1i	0.0131563	−	0.171531i
$531$	−209324.	+	373650.i	−0.742386	+	1.32518i
$532$	−40084.8	+	259775.i	−0.141630	+	0.917854i
$533$	386384.	+	223079.i	1.36008	+	0.785242i
$534$	−191163.	+	93174.6i	−0.670382	+	0.326750i
$535$	−21854.5	+	12617.7i	−0.0763541	+	0.0440831i
$536$	378638.	−	114622.i	1.31794	−	0.398967i
$537$	−75584.9	+	132896.i	−0.262112	+	0.460855i
$538$	−162352.	+	237235.i	−0.560911	+	0.819622i
$539$	−15428.2			−0.0531054
$540$	27058.3	+	20882.2i	0.0927926	+	0.0716126i
$541$		−	377631.i		−	1.29025i	−0.764078	−	0.645124i	$-0.776806\pi$
$541$		−	377631.i		−	1.29025i	0.764078	−	0.645124i	$-0.223194\pi$
$542$	130391.	−	190532.i	0.443865	−	0.648589i
$543$	379384.	+	215775.i	1.28671	+	0.731815i
$544$	−89944.1	+	12753.3i	−0.303931	+	0.0430949i
$545$	−28950.0	−	50143.0i	−0.0974667	−	0.168817i
$546$	−300176.	+	146308.i	−1.00691	+	0.490775i
$547$	−51766.7	+	89662.5i	−0.173012	+	0.299665i	−0.939471	−	0.342627i	$-0.888683\pi$
$547$	−51766.7	+	89662.5i	−0.173012	+	0.299665i	0.766460	+	0.642292i	$0.222017\pi$
$548$	−84565.8	−	13049.0i	−0.281601	−	0.0434526i
$549$	5786.24	+	446876.i	0.0191978	+	1.48266i
$550$	10228.4	−	133357.i	0.0338128	−	0.440850i
$551$	−6704.10	−	3870.61i	−0.0220819	−	0.0127490i
$552$	−139051.	−	31558.3i	−0.456349	−	0.103571i
$553$	29214.2	+	50600.4i	0.0955308	+	0.165464i
$554$	34282.5	+	71508.0i	0.111700	+	0.232989i
$555$	33317.9	−	215.694i	0.108166	−	0.000700249i
$556$	83365.8	−	103790.i	0.269674	−	0.335744i
$557$			321643.i			1.03673i	0.855161	+	0.518363i	$0.173458\pi$
$557$			321643.i			1.03673i	−0.855161	+	0.518363i	$0.826542\pi$
$558$	57968.1	+	117002.i	0.186175	+	0.375773i
$559$			273556.i			0.875431i
$560$	−25462.8	+	23296.6i	−0.0811953	+	0.0742877i
$561$	21897.7	+	37367.2i	0.0695782	+	0.118731i
$562$	449212.	−	215362.i	1.42226	−	0.681861i
$563$	−15717.8	−	27224.0i	−0.0495878	−	0.0858885i	0.840166	−	0.542329i	$-0.182457\pi$
$563$	−15717.8	−	27224.0i	−0.0495878	−	0.0858885i	−0.889754	+	0.456441i	$0.849124\pi$
$564$	406624.	+	322298.i	1.27831	+	1.01321i
$565$	41638.5	+	24040.0i	0.130436	+	0.0753074i
$566$	−17482.5	+	227936.i	−0.0545721	+	0.711509i
$567$	257412.	−	157642.i	0.800687	−	0.490348i
$568$	301148.	+	70399.9i	0.933433	+	0.218210i
$569$	118855.	−	205862.i	0.367106	−	0.635846i	−0.622006	−	0.783013i	$-0.713682\pi$
$569$	118855.	−	205862.i	0.367106	−	0.635846i	0.989112	+	0.147166i	$0.0470153\pi$
$570$	−21072.5	+	31223.6i	−0.0648585	+	0.0961023i
$571$	−259870.	−	450108.i	−0.797047	−	1.38053i	−0.921531	−	0.388304i	$-0.873061\pi$
$571$	−259870.	−	450108.i	−0.797047	−	1.38053i	0.124484	−	0.992222i	$-0.460272\pi$
$572$	−163118.	+	63361.4i	−0.498551	+	0.193657i
$573$	283564.	−	166172.i	0.863657	−	0.506115i
$574$	229982.	−	336057.i	0.698023	−	1.01997i
$575$			152592.i			0.461526i
$576$	25604.5	+	330787.i	0.0771742	+	0.997018i
$577$	−150655.			−0.452513			−0.226257	−	0.974068i	$-0.572649\pi$
$577$	−150655.			−0.452513			−0.226257	+	0.974068i	$0.572649\pi$
$578$	249724.	+	170899.i	0.747488	+	0.511546i
$579$	−226037.	+	1463.33i	−0.674252	+	0.00436500i
$580$	−368.029	−	947.457i	−0.00109402	−	0.00281646i
$581$	−100942.	+	58278.7i	−0.299032	+	0.172646i
$582$	4683.37	−	66723.7i	0.0138265	−	0.196986i
$583$	−193679.	−	111821.i	−0.569830	−	0.328992i
$584$	137460.	−	588011.i	0.403043	−	1.72409i
$585$	−47852.3	+	619.602i	−0.139827	+	0.00181051i
$586$	117246.	+	8992.64i	0.341430	+	0.0261874i
$587$	222883.	−	386045.i	0.646846	−	1.12037i	−0.337025	−	0.941496i	$-0.609421\pi$
$587$	222883.	−	386045.i	0.646846	−	1.12037i	0.983872	−	0.178875i	$-0.0572458\pi$
$588$	−15076.4	−	38080.5i	−0.0436056	−	0.110141i
$589$	−124628.	+	71953.8i	−0.359239	+	0.207407i
$590$	−26792.8	−	55885.7i	−0.0769687	−	0.160545i
$591$	−223272.	−	126986.i	−0.639232	−	0.363563i
$592$	218318.	+	238618.i	0.622941	+	0.680864i
$593$	−59064.6			−0.167965			−0.0839823	−	0.996467i	$-0.526764\pi$
$593$	−59064.6			−0.167965			−0.0839823	+	0.996467i	$0.526764\pi$
$594$	141278.	−	71138.4i	0.400408	−	0.201619i
$595$	−11959.9			−0.0337826
$596$	−118577.	−	95242.3i	−0.333815	−	0.268125i
$597$	−500013.	−	284383.i	−1.40292	−	0.797911i
$598$	180026.	−	86308.1i	0.503422	−	0.241351i
$599$	354748.	−	204814.i	0.988703	−	0.570828i	0.0838164	−	0.996481i	$-0.473289\pi$
$599$	354748.	−	204814.i	0.988703	−	0.570828i	0.904886	+	0.425653i	$0.139956\pi$
$600$	339151.	−	105070.i	0.942087	−	0.291860i
$601$	268772.	−	465527.i	0.744107	−	1.28883i	−0.206505	−	0.978446i	$-0.566209\pi$
$601$	268772.	−	465527.i	0.744107	−	1.28883i	0.950611	−	0.310385i	$-0.100458\pi$
$602$	248948.	+	19094.1i	0.686936	+	0.0526874i
$603$	244710.	−	436815.i	0.673003	−	1.20133i
$604$	64897.3	−	420576.i	0.177891	−	1.15284i
$605$	−29687.6	−	17140.2i	−0.0811082	−	0.0468279i
$606$	573980.	+	40287.9i	1.56297	+	0.109706i
$607$	377551.	−	217979.i	1.02470	−	0.591614i	0.109242	−	0.994015i	$-0.465158\pi$
$607$	377551.	−	217979.i	1.02470	−	0.591614i	0.915463	+	0.402402i	$0.131824\pi$
$608$	−362032.	+	51333.1i	−0.979353	+	0.138864i
$609$	−8976.18	+	58.1103i	−0.0242023	+	0.000156682i
$610$	−53370.3	−	36524.2i	−0.143430	−	0.0981569i
$611$	−726491.			−1.94602
$612$	−70832.6	+	90563.7i	−0.189117	+	0.241797i
$613$		−	184751.i		−	0.491662i	−0.969313	−	0.245831i	$-0.920939\pi$
$613$		−	184751.i		−	0.491662i	0.969313	−	0.245831i	$-0.0790608\pi$
$614$	255105.	+	174582.i	0.676677	+	0.463087i
$615$	50350.2	−	29505.9i	0.133122	−	0.0780116i
$616$	46276.3	+	152868.i	0.121954	+	0.402860i
$617$	70628.6	+	122332.i	0.185528	+	0.321344i	0.943754	−	0.330647i	$-0.107267\pi$
$617$	70628.6	+	122332.i	0.185528	+	0.321344i	−0.758226	+	0.651992i	$0.773934\pi$
$618$	−397514.	+	589005.i	−1.04082	+	1.54221i
$619$	−132429.	+	229374.i	−0.345623	+	0.598637i	−0.985467	−	0.169868i	$-0.945666\pi$
$619$	−132429.	+	229374.i	−0.345623	+	0.598637i	0.639844	+	0.768505i	$0.278999\pi$
$620$	−18674.1	−	2881.52i	−0.0485799	−	0.00749616i
$621$	−154503.	+	93249.3i	−0.400640	+	0.241803i
$622$	409148.	+	31381.3i	1.05755	+	0.0811129i
$623$	−235361.	−	135886.i	−0.606399	−	0.350105i
$624$	−315788.	−	340697.i	−0.811011	−	0.874981i
$625$	−187299.	−	324412.i	−0.479486	−	0.830494i
$626$	−148364.	+	71128.7i	−0.378599	+	0.181508i
$627$	88140.0	+	150406.i	0.224201	+	0.382587i
$628$	−205363.	−	164950.i	−0.520717	−	0.418247i
$629$			112079.i			0.283285i
$630$	−2776.22	+	43591.1i	−0.00699475	+	0.109829i
$631$			699879.i			1.75778i	0.477026	+	0.878889i	$0.341715\pi$
$631$			699879.i			1.75778i	−0.477026	+	0.878889i	$0.658285\pi$
$632$	−55596.7	+	59291.8i	−0.139192	+	0.148443i
$633$	−140806.	+	911.553i	−0.351409	+	0.00227496i
$634$	217696.	+	454080.i	0.541591	+	1.12968i
$635$	−278.969	−	483.188i	−0.000691844	−	0.00119831i
$636$	86737.4	−	587315.i	0.214433	−	1.45197i
$637$	49662.5	+	28672.7i	0.122391	+	0.0706625i
$638$	−4690.13	−	359.729i	−0.0115224	−	0.000883759i
$639$	336414.	−	200081.i	0.823897	−	0.490008i
$640$	−41281.1	−	24512.5i	−0.100784	−	0.0598450i
$641$	−159686.	+	276584.i	−0.388643	+	0.673149i	−0.992267	−	0.124120i	$-0.960389\pi$
$641$	−159686.	+	276584.i	−0.388643	+	0.673149i	0.603625	+	0.797269i	$0.293723\pi$
$642$	−278684.	+	135833.i	−0.676149	+	0.329561i
$643$	−120033.	−	207903.i	−0.290321	−	0.502850i	0.683565	−	0.729890i	$-0.260429\pi$
$643$	−120033.	−	207903.i	−0.290321	−	0.502850i	−0.973886	+	0.227040i	$0.927095\pi$
$644$	−65978.7	−	169856.i	−0.159086	−	0.409552i
$645$	31103.2	+	17689.9i	0.0747627	+	0.0425214i
$646$	−104571.	−	71563.5i	−0.250580	−	0.171485i
$647$			160526.i			0.383475i	0.981446	+	0.191737i	$0.0614122\pi$
$647$			160526.i			0.383475i	−0.981446	+	0.191737i	$0.938588\pi$
$648$	313642.	+	279192.i	0.746938	+	0.664894i
$649$	−286820.			−0.680957
$650$	−280763.	+	410259.i	−0.664527	+	0.971028i
$651$	−82497.0	+	145050.i	−0.194660	+	0.342259i
$652$	−38610.4	−	99399.0i	−0.0908258	−	0.233823i
$653$	−23755.5	+	13715.3i	−0.0557107	+	0.0321646i	−0.527597	−	0.849495i	$-0.676907\pi$
$653$	−23755.5	+	13715.3i	−0.0557107	+	0.0321646i	0.471886	+	0.881660i	$0.343573\pi$
$654$	−311656.	−	639415.i	−0.728651	−	1.49495i
$655$	27101.0	+	15646.8i	0.0631689	+	0.0364706i
$656$	540136.	+	170758.i	1.25515	+	0.396802i
$657$	−390670.	−	656870.i	−0.905064	−	1.52177i
$658$	−50708.9	+	661141.i	−0.117120	+	1.52701i
$659$	−215117.	+	372594.i	−0.495341	+	0.857957i	−0.999986	−	0.00537093i	$-0.998290\pi$
$659$	−215117.	+	372594.i	−0.495341	+	0.857957i	0.504644	+	0.863327i	$0.331624\pi$
$660$	−3344.15	+	22643.8i	−0.00767710	+	0.0519831i
$661$	−122972.	+	70998.0i	−0.281451	+	0.162496i	−0.634080	−	0.773267i	$-0.718621\pi$
$661$	−122972.	+	70998.0i	−0.281451	+	0.162496i	0.352629	+	0.935763i	$0.385288\pi$
$662$	−391219.	+	187559.i	−0.892697	+	0.427978i
$663$	−1042.15	−	160979.i	−0.00237084	−	0.366219i
$664$	−118280.	−	110908.i	−0.268272	−	0.251552i
$665$	−48139.5			−0.108857
$666$	408503.	+	26016.6i	0.920973	+	0.0586546i
$667$	5366.61			0.0120628
$668$	−276502.	−	222090.i	−0.619649	−	0.497710i
$669$	−401999.	+	235577.i	−0.898200	+	0.526358i
$670$	31322.1	+	65333.1i	0.0697752	+	0.145540i
$671$	−259195.	+	149646.i	−0.575681	+	0.332370i
$672$	−332092.	+	263602.i	−0.735394	+	0.583727i
$673$	−78759.2	+	136415.i	−0.173889	+	0.301184i	−0.939776	−	0.341791i	$-0.888967\pi$
$673$	−78759.2	+	136415.i	−0.173889	+	0.301184i	0.765887	+	0.642975i	$0.222300\pi$
$674$	−1115.74	+	14547.0i	−0.00245609	+	0.0320224i
$675$	217083.	−	393452.i	0.476450	−	0.863543i
$676$	191190.	+	29501.7i	0.418380	+	0.0645585i
$677$	−606737.	−	350300.i	−1.32380	−	0.764298i	−0.339470	−	0.940617i	$-0.610248\pi$
$677$	−606737.	−	350300.i	−1.32380	−	0.764298i	−0.984333	+	0.176319i	$0.943581\pi$
$678$	489609.	+	330432.i	1.06510	+	0.718825i
$679$	74027.5	−	42739.8i	0.160566	−	0.0927028i
$680$	−4820.50	−	15923.9i	−0.0104250	−	0.0344375i
$681$	256906.	+	438395.i	0.553962	+	0.945305i
$682$	−49385.6	+	72163.8i	−0.106177	+	0.155150i
$683$	408773.			0.876275			0.438137	−	0.898908i	$-0.355638\pi$
$683$	408773.			0.876275			0.438137	+	0.898908i	$0.355638\pi$
$684$	−285107.	+	364526.i	−0.609390	+	0.779141i
$685$		−	15671.1i		−	0.0333978i
$686$	279098.	−	407827.i	0.593074	−	0.866618i
$687$	3293.64	+	508762.i	0.00697850	+	1.07796i
$688$	74917.4	+	339157.i	0.158273	+	0.716512i
$689$	415627.	+	719887.i	0.875518	+	1.51644i
$690$	1828.47	−	26050.1i	0.00384051	−	0.0547156i
$691$	−309805.	+	536598.i	−0.648832	+	1.12381i	0.334570	+	0.942371i	$0.391409\pi$
$691$	−309805.	+	536598.i	−0.648832	+	1.12381i	−0.983402	+	0.181439i	$0.941924\pi$
$692$	27357.0	−	177291.i	0.0571289	−	0.370232i
$693$	176356.	+	98796.9i	0.367217	+	0.205720i
$694$	−52776.2	+	688094.i	−0.109577	+	1.42866i
$695$	21114.7	+	12190.6i	0.0437135	+	0.0252380i
$696$	−3695.27	−	11927.9i	−0.00762831	−	0.0246232i
$697$	98155.2	+	170010.i	0.202045	+	0.349952i
$698$	−275843.	−	575367.i	−0.566176	−	1.18096i
$699$	321795.	−	565792.i	0.658604	−	1.15798i
$700$	353758.	+	284143.i	0.721955	+	0.579884i
$701$		−	98886.5i		−	0.201234i	−0.994925	−	0.100617i	$-0.967918\pi$
$701$		−	98886.5i		−	0.201234i	0.994925	−	0.100617i	$-0.0320816\pi$
$702$	−586973.	−	33569.1i	−1.19109	−	0.0681186i
$703$			451126.i			0.912825i
$704$	−184883.	+	123228.i	−0.373037	+	0.248637i
$705$	−46979.8	+	82601.8i	−0.0945220	+	0.166192i
$706$	148283.	−	71090.0i	0.297496	−	0.142626i
$707$	367662.	+	636809.i	0.735546	+	1.27400i
$708$	−280279.	−	707938.i	−0.559144	−	1.41231i
$709$	16701.3	+	9642.51i	0.0332245	+	0.0191822i	0.516520	−	0.856275i	$-0.327227\pi$
$709$	16701.3	+	9642.51i	0.0332245	+	0.0191822i	−0.483296	+	0.875457i	$0.660560\pi$
$710$	−4331.57	+	56474.9i	−0.00859268	+	0.112031i
$711$	1331.88	+	102862.i	0.00263466	+	0.203477i
$712$	86060.7	−	368140.i	0.169764	−	0.726194i
$713$	49882.0	−	86398.2i	0.0981217	−	0.169952i
$714$	−146571.	−	10287.9i	−0.287509	−	0.0201804i
$715$	−16024.4	−	27755.1i	−0.0313452	−	0.0542914i
$716$	−98413.7	−	253357.i	−0.191968	−	0.494205i
$717$	−5816.52	−	898466.i	−0.0113142	−	1.74768i
$718$	−172503.	+	252068.i	−0.334618	+	0.488954i
$719$		−	124940.i		−	0.241681i	−0.992672	−	0.120841i	$-0.961441\pi$
$719$		−	124940.i		−	0.241681i	0.992672	−	0.120841i	$-0.0385590\pi$
$720$	−59158.1	+	13873.3i	−0.114117	+	0.0267617i
$721$	−908107.			−1.74689
$722$	9285.15	+	6354.33i	0.0178121	+	0.0121898i
$723$	119299.	+	203576.i	0.228223	+	0.389449i
$724$	−723267.	+	280945.i	−1.37982	+	0.535975i
$725$	−11572.9	+	6681.64i	−0.0220175	+	0.0127118i
$726$	−349084.	−	235593.i	−0.662303	−	0.446982i
$727$	237638.	+	137200.i	0.449621	+	0.259589i	0.707670	−	0.706543i	$-0.249746\pi$
$727$	237638.	+	137200.i	0.449621	+	0.259589i	−0.258049	+	0.966132i	$0.583080\pi$
$728$	135137.	−	578074.i	0.254984	−	1.09074i
$729$	531040.	−	20637.3i	0.999246	−	0.0388327i
$730$	110271.	+	8457.67i	0.206926	+	0.0158710i
$731$	−60182.6	+	104239.i	−0.112625	+	0.195073i
$732$	−622646.	−	493520.i	−1.16203	−	0.921049i
$733$	−196395.	+	113389.i	−0.365530	+	0.211039i	−0.671504	−	0.741001i	$-0.734351\pi$
$733$	−196395.	+	113389.i	−0.365530	+	0.211039i	0.305974	+	0.952040i	$0.401018\pi$
$734$	−205514.	−	428671.i	−0.381460	−	0.795667i
$735$	6471.59	−	3792.44i	0.0119794	−	0.00702012i
$736$	199561.	−	156308.i	0.368400	−	0.288554i
$737$	335306.			0.617315
$738$	642432.	−	318290.i	1.17955	−	0.584400i
$739$	−173966.			−0.318549			−0.159274	−	0.987234i	$-0.550915\pi$
$739$	−173966.			−0.318549			−0.159274	+	0.987234i	$0.550915\pi$
$740$	−37093.0	+	46180.7i	−0.0677374	+	0.0843330i
$741$	−4194.73	−	647951.i	−0.00763954	−	1.18006i
$742$	684142.	−	327992.i	1.24262	−	0.595739i
$743$	−223552.	+	129068.i	−0.404949	+	0.233797i	−0.688617	−	0.725125i	$-0.741782\pi$
$743$	−223552.	+	129068.i	−0.404949	+	0.233797i	0.283668	+	0.958923i	$0.408449\pi$
$744$	−226376.	−	51377.1i	−0.408964	−	0.0928161i
$745$	13927.3	−	24122.8i	0.0250931	−	0.0434625i
$746$	531606.	+	40773.7i	0.955239	+	0.0732660i
$747$	−205197.	+	2656.93i	−0.367730	+	0.00476145i
$748$	−76096.3	−	11742.1i	−0.136007	−	0.0209866i
$749$	−343117.	−	198099.i	−0.611616	−	0.353117i
$750$	57377.5	+	117720.i	0.102005	+	0.209280i
$751$	439854.	−	253950.i	0.779881	−	0.450264i	−0.0565073	−	0.998402i	$-0.517996\pi$
$751$	439854.	−	253950.i	0.779881	−	0.450264i	0.836388	+	0.548138i	$0.184663\pi$
$752$	−900711.	+	198961.i	−1.59276	+	0.351829i
$753$	490185.	−	861863.i	0.864510	−	1.52002i
$754$	14428.7	+	9874.34i	0.0253796	+	0.0173686i
$755$	77937.9			0.136727
$756$	−71520.1	+	531830.i	−0.125137	+	0.930528i
$757$			146756.i			0.256097i	0.991768	+	0.128048i	$0.0408713\pi$
$757$			146756.i			0.256097i	−0.991768	+	0.128048i	$0.959129\pi$
$758$	−467734.	−	320096.i	−0.814068	−	0.557111i
$759$	−105051.	−	59748.1i	−0.182355	−	0.103715i
$760$	−19402.9	−	64095.0i	−0.0335923	−	0.110968i
$761$	106335.	+	184178.i	0.183615	+	0.318030i	0.943109	−	0.332484i	$-0.107887\pi$
$761$	106335.	+	184178.i	0.183615	+	0.318030i	−0.759494	+	0.650514i	$0.774553\pi$
$762$	−3003.18	−	6161.54i	−0.00517216	−	0.0106116i
$763$	454519.	−	787250.i	0.780734	−	1.35227i
$764$	−89105.7	+	577461.i	−0.152658	+	0.989319i
$765$	−18370.6	−	10291.5i	−0.0313907	−	0.0175855i
$766$	202558.	+	15536.0i	0.345216	+	0.0264778i
$767$	923255.	+	533042.i	1.56939	+	0.906088i
$768$	−484823.	−	335916.i	−0.821979	−	0.569518i
$769$	44021.9	+	76248.2i	0.0744417	+	0.128937i	0.900843	−	0.434144i	$-0.142949\pi$
$769$	44021.9	+	76248.2i	0.0744417	+	0.128937i	−0.826402	+	0.563081i	$0.809616\pi$
$770$	−26377.0	+	12645.7i	−0.0444881	+	0.0213285i
$771$	385106.	−	2493.11i	0.647846	−	0.00419405i
$772$	251648.	−	313302.i	0.422240	−	0.525689i
$773$		−	956337.i		−	1.60049i	−0.599675	−	0.800243i	$-0.704704\pi$
$773$		−	956337.i		−	1.60049i	0.599675	−	0.800243i	$-0.295296\pi$
$774$	365959.	+	243549.i	0.610872	+	0.406541i
$775$			248420.i			0.413602i
$776$	86742.9	+	81336.9i	0.144049	+	0.135072i
$777$	264480.	+	451320.i	0.438077	+	0.747554i
$778$	−206023.	−	429733.i	−0.340374	−	0.709969i
$779$	395082.	+	684302.i	0.651047	+	1.12765i
$780$	52847.1	−	66674.1i	0.0868625	−	0.109589i
$781$	227009.	+	131064.i	0.372169	+	0.214872i
$782$	87587.2	+	6717.86i	0.143228	+	0.0109854i
$783$	−13837.6	−	7634.74i	−0.0225703	−	0.0124529i
$784$	69424.5	+	21947.8i	0.112949	+	0.0357075i
$785$	24120.7	−	41778.2i	0.0391426	−	0.0677970i
$786$	318669.	+	215067.i	0.515816	+	0.348119i
$787$	−150134.	−	260040.i	−0.242398	−	0.419846i	0.718999	−	0.695012i	$-0.244601\pi$
$787$	−150134.	−	260040.i	−0.242398	−	0.419846i	−0.961397	+	0.275165i	$0.911267\pi$
$788$	425650.	−	165339.i	0.685489	−	0.266271i
$789$	634462.	−	371804.i	1.01918	−	0.597255i
$790$	−12284.8	−	8407.14i	−0.0196840	−	0.0134708i
$791$			754861.i			1.20646i
$792$	−60461.4	+	274628.i	−0.0963890	+	0.437819i
$793$	1.11244e6			1.76902
$794$	−451921.	+	660362.i	−0.716839	+	1.04747i
$795$	108728.	−	703.888i	0.172031	−	0.00111370i
$796$	953238.	−	370275.i	1.50444	−	0.584383i
$797$	−189436.	+	109371.i	−0.298226	+	0.172181i	−0.641646	−	0.767001i	$-0.721748\pi$
$797$	−189436.	+	109371.i	−0.298226	+	0.172181i	0.343420	+	0.939182i	$0.388415\pi$
$798$	−589959.	−	41409.5i	−0.926437	−	0.0650270i
$799$	−276832.	−	159829.i	−0.433633	−	0.250358i
$800$	−235736.	+	585535.i	−0.368338	+	0.914898i
$801$	−244589.	−	411251.i	−0.381217	−	0.640977i
$802$	−8551.44	+	111493.i	−0.0132951	+	0.173341i
$803$	255910.	−	443249.i	0.396877	−	0.687412i
$804$	327659.	+	827614.i	0.506886	+	1.28031i
$805$	28901.6	−	16686.4i	0.0445996	−	0.0257496i
$806$	293082.	−	140510.i	0.451148	−	0.216290i
$807$	−562232.	−	319770.i	−0.863313	−	0.491010i
$808$	−699688.	+	746191.i	−1.07172	+	1.14295i
$809$	−373854.			−0.571223			−0.285611	−	0.958346i	$-0.592197\pi$
$809$	−373854.			−0.571223			−0.285611	+	0.958346i	$0.592197\pi$
$810$	−41774.5	+	64567.8i	−0.0636709	+	0.0984116i
$811$	−389516.			−0.592220			−0.296110	−	0.955154i	$-0.595690\pi$
$811$	−389516.			−0.592220			−0.296110	+	0.955154i	$0.595690\pi$
$812$	9993.24	−	12441.6i	0.0151563	−	0.0188696i
$813$	451550.	+	256819.i	0.683164	+	0.388550i
$814$	118506.	+	247185.i	0.178851	+	0.373055i
$815$	16913.1	−	9764.78i	0.0254629	−	0.0147010i
$816$	−45378.5	−	199297.i	−0.0681507	−	0.299310i
$817$	−242239.	+	419571.i	−0.362911	+	0.628581i
$818$	−16916.3	+	220554.i	−0.0252813	+	0.329616i
$819$	−384068.	−	645770.i	−0.572586	−	0.962742i
$820$	−15821.8	+	102535.i	−0.0235303	+	0.152492i
$821$	766580.	+	442585.i	1.13729	+	0.656614i	0.945758	−	0.324872i	$-0.105321\pi$
$821$	766580.	+	442585.i	1.13729	+	0.656614i	0.191531	+	0.981486i	$0.438655\pi$
$822$	13480.2	−	192052.i	0.0199505	−	0.284234i
$823$	556310.	−	321186.i	0.821329	−	0.474195i	−0.0295455	−	0.999563i	$-0.509406\pi$
$823$	556310.	−	321186.i	0.821329	−	0.474195i	0.850875	+	0.525369i	$0.176073\pi$
$824$	−366018.	−	1.20909e6i	−0.539073	−	1.78076i
$825$	300929.	−	1948.16i	0.442136	−	0.00286231i
$826$	549536.	−	803000.i	0.805445	−	1.17694i
$827$	−144563.			−0.211372			−0.105686	−	0.994400i	$-0.533704\pi$
$827$	−144563.			−0.211372			−0.105686	+	0.994400i	$0.533704\pi$
$828$	44816.5	−	317677.i	0.0653698	−	0.463366i
$829$			390583.i			0.568335i	0.958775	+	0.284167i	$0.0917171\pi$
$829$			390583.i			0.568335i	−0.958775	+	0.284167i	$0.908283\pi$
$830$	16771.2	−	24506.6i	0.0243449	−	0.0355735i
$831$	−153942.	+	90212.3i	−0.222923	+	0.130636i
$832$	824140.	−	53068.3i	1.19057	−	0.0766635i
$833$	12616.0	+	21851.6i	0.0181816	+	0.0314915i
$834$	248279.	+	167561.i	0.356951	+	0.240902i
$835$	32476.3	−	56250.6i	0.0465793	−	0.0806778i
$836$	−306293.	−	47262.8i	−0.438253	−	0.0676250i
$837$	−251532.	+	151810.i	−0.359039	+	0.216695i
$838$	−46957.4	+	612229.i	−0.0668677	+	0.871818i
$839$	−21529.2	−	12429.9i	−0.0305846	−	0.0176580i	0.484630	−	0.874719i	$-0.338954\pi$
$839$	−21529.2	−	12429.9i	−0.0305846	−	0.0176580i	−0.515214	+	0.857061i	$0.672288\pi$
$840$	−56987.9	−	52747.2i	−0.0807652	−	0.0747551i
$841$	−353406.	−	612116.i	−0.499668	−	0.865450i
$842$	−459799.	−	959071.i	−0.648551	−	1.35278i
$843$	566712.	+	967062.i	0.797457	+	1.36081i
$844$	156760.	−	195166.i	0.220065	−	0.273980i
$845$			35429.8i			0.0496199i
$846$	−646801.	+	971890.i	−0.903712	+	1.35793i
$847$		−	538205.i		−	0.750207i
$848$	712451.	+	778697.i	0.990748	+	1.08287i
$849$	−514352.	+	3329.83i	−0.713584	+	0.00461962i
$850$	−197243.	+	94562.5i	−0.273001	+	0.130882i
$851$	−156372.	−	270844.i	−0.215923	−	0.373990i
$852$	−101664.	+	688385.i	−0.140051	+	0.948314i
$853$	−264635.	−	152787.i	−0.363705	−	0.209985i	0.307000	−	0.951710i	$-0.400675\pi$
$853$	−264635.	−	152787.i	−0.363705	−	0.209985i	−0.670705	+	0.741724i	$0.734008\pi$
$854$	77648.4	−	1.01238e6i	0.106467	−	1.38812i
$855$	−73943.1	−	41424.0i	−0.101150	−	0.0566656i
$856$	125462.	−	536686.i	0.171224	−	0.732442i
$857$	−221670.	+	383944.i	−0.301818	+	0.522764i	−0.976548	−	0.215301i	$-0.930927\pi$
$857$	−221670.	+	383944.i	−0.301818	+	0.522764i	0.674730	+	0.738065i	$0.264260\pi$
$858$	−172508.	−	353929.i	−0.234333	−	0.480775i
$859$	228055.	+	395003.i	0.309067	+	0.535320i	0.978159	−	0.207860i	$-0.0666498\pi$
$859$	228055.	+	395003.i	0.309067	+	0.535320i	−0.669091	+	0.743180i	$0.733317\pi$
$860$	−59295.9	+	23032.8i	−0.0801729	+	0.0311423i
$861$	796435.	+	452973.i	1.07435	+	0.611034i
$862$	−422610.	+	617531.i	−0.568755	+	0.831083i
$863$		−	432830.i		−	0.581160i	−0.956851	−	0.290580i	$-0.906152\pi$
$863$		−	432830.i		−	0.581160i	0.956851	−	0.290580i	$-0.0938483\pi$
$864$	−736929.	+	119132.i	−0.987184	+	0.159589i
$865$	32854.2			0.0439095
$866$	−833589.	−	570470.i	−1.11152	−	0.760672i
$867$	−336604.	+	591831.i	−0.447797	+	0.787334i
$868$	−107413.	−	276526.i	−0.142567	−	0.367026i
$869$	−59661.6	+	34445.6i	−0.0790052	+	0.0456136i
$870$	2055.77	−	1002.00i	0.00271603	−	0.00132382i
$871$	−1.07933e6	−	623151.i	−1.42272	−	0.821405i
$872$	1.23138e6	+	287861.i	1.61941	+	0.378573i
$873$	150485.	−	1948.51i	0.197454	−	0.00255667i
$874$	352545.	+	27039.9i	0.461522	+	0.0353983i
$875$	−83679.4	+	144937.i	−0.109296	+	0.189305i
$876$	1.34412e6	+	198505.i	1.75157	+	0.258680i
$877$	−439842.	+	253943.i	−0.571870	+	0.330169i	−0.757896	−	0.652376i	$-0.773773\pi$
$877$	−439842.	+	253943.i	−0.571870	+	0.330169i	0.186026	+	0.982545i	$0.440439\pi$
$878$	276379.	+	576485.i	0.358522	+	0.747823i
$879$	1712.79	+	264572.i	0.00221681	+	0.342426i
$880$	−27468.4	−	30022.6i	−0.0354706	−	0.0387688i
$881$	−630033.			−0.811730			−0.405865	−	0.913933i	$-0.633030\pi$
$881$	−630033.			−0.811730			−0.405865	+	0.913933i	$0.633030\pi$
$882$	82572.9	−	40910.3i	0.106145	−	0.0525891i
$883$	−111488.			−0.142990			−0.0714950	−	0.997441i	$-0.522777\pi$
$883$	−111488.			−0.142990			−0.0714950	+	0.997441i	$0.522777\pi$
$884$	223127.	+	179218.i	0.285527	+	0.229339i
$885$	120311.	−	70503.7i	0.153609	−	0.0900172i
$886$	−1.10237e6	+	528498.i	−1.40430	+	0.673249i
$887$	642963.	−	371215.i	0.817220	−	0.471822i	−0.0322369	−	0.999480i	$-0.510263\pi$
$887$	642963.	−	371215.i	0.817220	−	0.471822i	0.849457	+	0.527658i	$0.176930\pi$
$888$	−494307.	+	534047.i	−0.626860	+	0.677257i
$889$	4379.84	−	7586.11i	0.00554185	−	0.00959877i
$890$	69037.9	+	5295.15i	0.0871581	+	0.00668495i
$891$	185871.	+	303508.i	0.234129	+	0.382309i
$892$	126322.	−	818649.i	0.158763	−	1.02889i
$893$	−1.11427e6	−	643324.i	−1.39729	−	0.806727i
$894$	191432.	−	283649.i	0.239519	−	0.354900i
$895$	43109.6	−	24889.4i	0.0538181	−	0.0310719i
$896$	9230.17	−	753711.i	0.0114972	−	0.938834i
$897$	227115.	+	387558.i	0.282267	+	0.481673i
$898$	−1.11624e6	−	763905.i	−1.38422	−	0.947298i
$899$	8736.86			0.0108103
$900$	298874.	+	740858.i	0.368980	+	0.914639i
$901$			365754.i			0.450546i
$902$	396235.	+	271165.i	0.487012	+	0.333289i
$903$	3636.79	+	561767.i	0.00446008	+	0.688939i
$904$	−1.00506e6	+	304251.i	−1.22985	+	0.372302i
$905$	−71052.5	−	123067.i	−0.0867525	−	0.150260i
$906$	955145.	+	67042.0i	1.16363	+	0.0816753i
$907$	−120922.	+	209443.i	−0.146991	+	0.254596i	−0.930114	−	0.367271i	$-0.880292\pi$
$907$	−120922.	+	209443.i	−0.146991	+	0.254596i	0.783123	+	0.621867i	$0.213626\pi$
$908$	−892768.	−	137759.i	−1.08285	−	0.167090i
$909$	16761.8	+	1.29452e6i	0.0202858	+	1.56669i
$910$	108407.	+	8314.74i	0.130911	+	0.0100407i
$911$	276542.	+	159661.i	0.333214	+	0.192381i	0.657267	−	0.753658i	$-0.271712\pi$
$911$	276542.	+	159661.i	0.333214	+	0.192381i	−0.324053	+	0.946039i	$0.605046\pi$
$912$	−182652.	−	802187.i	−0.219601	−	0.964464i
$913$	−68714.8	−	119017.i	−0.0824344	−	0.142781i
$914$	11838.4	−	5675.58i	0.0141710	−	0.00679388i
$915$	71938.1	−	126485.i	0.0859245	−	0.151076i
$916$	−705177.	−	566407.i	−0.840440	−	0.675053i
$917$			491312.i			0.584277i
$918$	−216283.	−	141926.i	−0.256647	−	0.168414i
$919$		−	1.48790e6i		−	1.76175i	−0.473350	−	0.880875i	$-0.656955\pi$
$919$		−	1.48790e6i		−	1.76175i	0.473350	−	0.880875i	$-0.343045\pi$
$920$	33865.9	+	31755.4i	0.0400117	+	0.0375181i
$921$	−343857.	+	604583.i	−0.405376	+	0.712749i
$922$	−429439.	−	895745.i	−0.505173	−	1.05371i
$923$	−487151.	−	843771.i	−0.571821	−	0.990424i
$924$	−334133.	+	132286.i	−0.391359	+	0.154942i
$925$	674422.	+	389378.i	0.788222	+	0.455080i
$926$	197837.	+	15173.9i	0.230721	+	0.0176961i
$927$	−1.39487e6	−	781425.i	−1.62321	−	0.909343i
$928$	20593.1	+	8290.78i	0.0239125	+	0.00962719i
$929$	588618.	−	1.01952e6i	0.682028	−	1.18131i	−0.292333	−	0.956317i	$-0.594431\pi$
$929$	588618.	−	1.01952e6i	0.682028	−	1.18131i	0.974361	−	0.224991i	$-0.0722352\pi$
$930$	2976.75	−	42409.6i	0.00344173	−	0.0490342i
$931$	50780.5	+	87954.5i	0.0585865	+	0.101475i
$932$	418986.	+	1.07864e6i	0.482356	+	1.24178i
$933$	5977.08	+	923268.i	0.00686635	+	1.06063i
$934$	−61819.9	−	42306.7i	−0.0708654	−	0.0484970i
$935$		−	14101.6i		−	0.0161304i
$936$	705005.	−	771646.i	0.804712	−	0.880778i
$937$	904036.			1.02969			0.514845	−	0.857283i	$-0.327849\pi$
$937$	904036.			1.02969			0.514845	+	0.857283i	$0.327849\pi$
$938$	−642434.	+	938746.i	−0.730168	+	1.06695i
$939$	−187171.	−	319397.i	−0.212279	−	0.362243i
$940$	−61169.1	−	157474.i	−0.0692271	−	0.178219i
$941$	569128.	−	328586.i	0.642733	−	0.371082i	−0.142934	−	0.989732i	$-0.545654\pi$
$941$	569128.	−	328586.i	0.642733	−	0.371082i	0.785666	+	0.618650i	$0.212320\pi$
$942$	331541.	−	491252.i	0.373625	−	0.553608i
$943$	−474393.	−	273891.i	−0.533476	−	0.308003i
$944$	1.29064e6	+	408023.i	1.44831	+	0.457868i
$945$	−98260.2	+	1908.57i	−0.110031	+	0.00213720i
$946$	−22513.4	+	293528.i	−0.0251570	+	0.327995i
$947$	100820.	−	174625.i	0.112420	−	0.194718i	−0.804325	−	0.594189i	$-0.797473\pi$
$947$	100820.	−	174625.i	0.112420	−	0.194718i	0.916746	+	0.399471i	$0.130806\pi$
$948$	−143321.	−	113599.i	−0.159475	−	0.126403i
$949$	−1.64752e6	+	951194.i	−1.82935	+	1.05618i
$950$	−793918.	+	380621.i	−0.879688	+	0.421741i
$951$	−977542.	+	572854.i	−1.08087	+	0.633407i
$952$	178671.	−	190547.i	0.197143	−	0.210246i
$953$	−638389.			−0.702910			−0.351455	−	0.936205i	$-0.614313\pi$
$953$	−638389.			−0.702910			−0.351455	+	0.936205i	$0.614313\pi$
$954$	1.33309e6	+	84901.4i	1.46475	+	0.0932864i
$955$	−107011.			−0.117333
$956$	1.24533e6	+	1.00027e6i	1.36260	+	1.09446i
$957$	−68.5163	−	10583.6i	−7.48118e−5	−	0.0115560i
$958$	685349.	+	1.42953e6i	0.746759	+	1.55763i
$959$	213075.	−	123019.i	0.231684	−	0.133763i
$960$	47260.6	−	97136.3i	0.0512811	−	0.105400i
$961$	−380552.	+	659136.i	−0.412067	+	0.713721i
$962$	77919.4	−	1.01591e6i	0.0841967	−	1.09775i
$963$	−356571.	−	599536.i	−0.384497	−	0.646491i
$964$	−414571.	−	63970.8i	−0.446113	−	0.0688379i
$965$	63737.0	+	36798.6i	0.0684443	+	0.0395163i
$966$	368549.	−	179634.i	0.394949	−	0.192501i
$967$	961591.	−	555175.i	1.02834	−	0.593714i	0.111833	−	0.993727i	$-0.464328\pi$
$967$	961591.	−	555175.i	1.02834	−	0.593714i	0.916509	+	0.400013i	$0.130995\pi$
$968$	716590.	−	216927.i	0.764751	−	0.231506i
$969$	140952.	−	247827.i	0.150114	−	0.263937i
$970$	−12299.5	+	17972.4i	−0.0130721	+	0.0191013i
$971$	−1.25193e6			−1.32783			−0.663913	−	0.747810i	$-0.731105\pi$
$971$	−1.25193e6			−1.32783			−0.663913	+	0.747810i	$0.731105\pi$
$972$	−567496.	+	755358.i	−0.600662	+	0.799503i
$973$			382787.i			0.404326i
$974$	542765.	−	793106.i	0.572129	−	0.836013i
$975$	−972290.	−	552991.i	−1.02279	−	0.581713i
$976$	1.37922e6	−	304660.i	1.44788	−	0.319827i
$977$	33214.5	+	57529.3i	0.0347968	+	0.0602698i	0.882899	−	0.469562i	$-0.155588\pi$
$977$	33214.5	+	57529.3i	0.0347968	+	0.0602698i	−0.848103	+	0.529832i	$0.822255\pi$
$978$	215673.	−	105121.i	0.225485	−	0.109903i
$979$	160219.	−	277508.i	0.167167	−	0.289541i
$980$	−2033.60	+	13179.0i	−0.00211745	+	0.0137224i
$981$	1.37558e6	−	818117.i	1.42938	−	0.850114i
$982$	59980.7	−	782026.i	0.0621997	−	0.810957i
$983$	−130314.	−	75236.9i	−0.134860	−	0.0778617i	0.431052	−	0.902327i	$-0.358143\pi$
$983$	−130314.	−	75236.9i	−0.134860	−	0.0778617i	−0.565912	+	0.824465i	$0.691476\pi$
$984$	−282100.	+	1.24298e6i	−0.291349	+	1.28373i
$985$	41815.2	+	72426.0i	0.0430984	+	0.0746487i
$986$	3325.74	+	6936.98i	0.00342085	+	0.00713538i
$987$	−1.49191e6	+	9658.35i	−1.53146	+	0.00991445i
$988$	898102.	+	721368.i	0.920051	+	0.738997i
$989$		−	335865.i		−	0.343378i
$990$	−51397.1	−	3273.36i	−0.0524407	−	0.00333982i
$991$		−	795870.i		−	0.810391i	−0.914230	−	0.405196i	$-0.867203\pi$
$991$		−	795870.i		−	0.810391i	0.914230	−	0.405196i	$-0.132797\pi$
$992$	324885.	−	254470.i	0.330146	−	0.258591i
$993$	−493550.	−	842215.i	−0.500533	−	0.854131i
$994$	−801874.	+	384436.i	−0.811584	+	0.389091i
$995$	93644.4	+	162197.i	0.0945879	+	0.163831i
$996$	226615.	−	285907.i	0.228439	−	0.288208i
$997$	674456.	+	389398.i	0.678521	+	0.391745i	0.799298	−	0.600935i	$-0.205205\pi$
$997$	674456.	+	389398.i	0.678521	+	0.391745i	−0.120776	+	0.992680i	$0.538538\pi$
$998$	80113.1	−	1.04451e6i	0.0804346	−	1.04870i
$999$	17885.7	+	920820.i	0.0179215	+	0.922664i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.5.p.b.43.10	✓	88
3.2	odd	2		216.5.p.b.19.35		88
4.3	odd	2		288.5.t.b.79.15		88
8.3	odd	2	inner	72.5.p.b.43.39	yes	88
8.5	even	2		288.5.t.b.79.16		88
9.4	even	3	inner	72.5.p.b.67.39	yes	88
9.5	odd	6		216.5.p.b.91.6		88
12.11	even	2		864.5.t.b.559.25		88
24.5	odd	2		864.5.t.b.559.20		88
24.11	even	2		216.5.p.b.19.6		88
36.23	even	6		864.5.t.b.847.20		88
36.31	odd	6		288.5.t.b.175.16		88
72.5	odd	6		864.5.t.b.847.25		88
72.13	even	6		288.5.t.b.175.15		88
72.59	even	6		216.5.p.b.91.35		88
72.67	odd	6	inner	72.5.p.b.67.10	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.5.p.b.43.10	✓	88	1.1	even	1	trivial
72.5.p.b.43.39	yes	88	8.3	odd	2	inner
72.5.p.b.67.10	yes	88	72.67	odd	6	inner
72.5.p.b.67.39	yes	88	9.4	even	3	inner
216.5.p.b.19.6		88	24.11	even	2
216.5.p.b.19.35		88	3.2	odd	2
216.5.p.b.91.6		88	9.5	odd	6
216.5.p.b.91.35		88	72.59	even	6
288.5.t.b.79.15		88	4.3	odd	2
288.5.t.b.79.16		88	8.5	even	2
288.5.t.b.175.15		88	72.13	even	6
288.5.t.b.175.16		88	36.31	odd	6
864.5.t.b.559.20		88	24.5	odd	2
864.5.t.b.559.25		88	12.11	even	2
864.5.t.b.847.20		88	36.23	even	6
864.5.t.b.847.25		88	72.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	72.5.p.b.43.10

Level	$72$
Weight	$5$
Character	72.43
Analytic conductor	$7.443$
Analytic rank	$0$
Dimension	$88$
Inner twists	$4$