LMFDB - Embedded newform 119.5.h.a.101.43

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [119,5,Mod(33,119)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("119.33"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(119, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 119 = 7 \cdot 17 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	119.h (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$12.3010256070$
Analytic rank:	$0$
Dimension:	$92$
Relative dimension:	$46$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.43
Character	$\chi$	$=$	119.101
Dual form			119.5.h.a.33.43

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.46141 + 5.99534i) q^{2} +(-1.95039 + 3.37818i) q^{3} +(-15.9627 + 27.6482i) q^{4} +(-19.9222 - 34.5062i) q^{5} -27.0044 q^{6} +(-43.3259 + 22.8882i) q^{7} -110.249 q^{8} +(32.8919 + 56.9705i) q^{9} +(137.918 - 238.880i) q^{10} +(-10.8858 - 6.28490i) q^{11} +(-62.2671 - 107.850i) q^{12} -285.493i q^{13} +(-287.191 - 180.528i) q^{14} +155.424 q^{15} +(-126.213 - 218.608i) q^{16} +(-176.306 - 228.991i) q^{17} +(-227.705 + 394.397i) q^{18} +(-354.481 + 204.660i) q^{19} +1272.05 q^{20} +(7.18207 - 191.003i) q^{21} -87.0184i q^{22} +(239.631 - 138.351i) q^{23} +(215.029 - 372.441i) q^{24} +(-481.285 + 833.610i) q^{25} +(1711.63 - 988.210i) q^{26} -572.572 q^{27} +(58.7807 - 1563.24i) q^{28} +114.294i q^{29} +(537.987 + 931.820i) q^{30} +(-705.088 + 1221.25i) q^{31} +(-8.24011 + 14.2723i) q^{32} +(42.4630 - 24.5160i) q^{33} +(762.612 - 1849.65i) q^{34} +(1652.93 + 1039.03i) q^{35} -2100.18 q^{36} +(-1126.39 + 650.321i) q^{37} +(-2454.01 - 1416.82i) q^{38} +(964.448 + 556.824i) q^{39} +(2196.40 + 3804.27i) q^{40} -2691.28 q^{41} +(1169.99 - 618.082i) q^{42} -477.192 q^{43} +(347.533 - 200.648i) q^{44} +(1310.56 - 2269.95i) q^{45} +(1658.92 + 957.778i) q^{46} +(-700.994 + 404.719i) q^{47} +984.661 q^{48} +(1353.26 - 1983.30i) q^{49} -6663.70 q^{50} +(1117.44 - 148.971i) q^{51} +(7893.39 + 4557.25i) q^{52} +(1993.86 - 3453.48i) q^{53} +(-1981.91 - 3432.76i) q^{54} +500.835i q^{55} +(4776.63 - 2523.40i) q^{56} -1596.67i q^{57} +(-685.230 + 395.618i) q^{58} +(1319.91 + 762.052i) q^{59} +(-2480.99 + 4297.20i) q^{60} +(2122.06 + 3675.52i) q^{61} -9762.39 q^{62} +(-2729.02 - 1715.46i) q^{63} -4152.91 q^{64} +(-9851.29 + 5687.65i) q^{65} +(293.964 + 169.720i) q^{66} +(-1240.73 + 2149.01i) q^{67} +(9145.54 - 1219.24i) q^{68} +1079.35i q^{69} +(-507.864 + 13506.4i) q^{70} -2863.59i q^{71} +(-3626.30 - 6280.94i) q^{72} +(1320.47 - 2287.12i) q^{73} +(-7797.79 - 4502.06i) q^{74} +(-1877.39 - 3251.73i) q^{75} -13067.7i q^{76} +(615.485 + 23.1433i) q^{77} +7709.59i q^{78} +(5400.12 - 3117.76i) q^{79} +(-5028.88 + 8710.27i) q^{80} +(-1547.51 + 2680.36i) q^{81} +(-9315.64 - 16135.2i) q^{82} +11667.7i q^{83} +(5166.26 + 3247.51i) q^{84} +(-4389.22 + 10645.7i) q^{85} +(-1651.76 - 2860.93i) q^{86} +(-386.105 - 222.918i) q^{87} +(1200.14 + 692.903i) q^{88} +(9377.85 - 5414.31i) q^{89} +18145.5 q^{90} +(6534.43 + 12369.3i) q^{91} +8833.83i q^{92} +(-2750.40 - 4763.83i) q^{93} +(-4852.86 - 2801.80i) q^{94} +(14124.1 + 8154.53i) q^{95} +(-32.1429 - 55.6731i) q^{96} -6150.95 q^{97} +(16574.8 + 1248.25i) q^{98} -826.890i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q - 2 q^{2} - 354 q^{4} + 56 q^{8} - 1068 q^{9} + 464 q^{15} - 3146 q^{16} + 1104 q^{17} - 906 q^{18} - 6 q^{19} - 240 q^{21} - 3106 q^{25} + 468 q^{26} + 1858 q^{30} - 1680 q^{32} - 198 q^{33} - 5318 q^{35}+ \cdots + 107386 q^{98}+O(q^{100}) $ 92 * q - 2 * q^2 - 354 * q^4 + 56 * q^8 - 1068 * q^9 + 464 * q^15 - 3146 * q^16 + 1104 * q^17 - 906 * q^18 - 6 * q^19 - 240 * q^21 - 3106 * q^25 + 468 * q^26 + 1858 * q^30 - 1680 * q^32 - 198 * q^33 - 5318 * q^35 + 17304 * q^36 - 6 * q^38 + 1888 * q^42 + 3316 * q^43 - 7242 * q^47 - 1284 * q^49 + 2136 * q^50 - 11304 * q^51 - 5202 * q^52 + 28 * q^53 - 17826 * q^59 - 3182 * q^60 + 41768 * q^64 + 5988 * q^66 + 2924 * q^67 - 22788 * q^68 + 36898 * q^70 - 23660 * q^72 - 3162 * q^77 - 6194 * q^81 + 30426 * q^84 + 46552 * q^85 + 4118 * q^86 - 7026 * q^87 + 4944 * q^89 + 11034 * q^93 - 101214 * q^94 + 107386 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/119\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	3.46141	+	5.99534i	0.865352	+	1.49883i	0.866697	+	0.498835i	$0.166239\pi$
$2$	3.46141	+	5.99534i	0.865352	+	1.49883i	−0.00134430	+	0.999999i	$0.500428\pi$
$3$	−1.95039	+	3.37818i	−0.216710	+	0.375353i	−0.953800	−	0.300441i	$-0.902866\pi$
$3$	−1.95039	+	3.37818i	−0.216710	+	0.375353i	0.737090	+	0.675795i	$0.236199\pi$
$4$	−15.9627	+	27.6482i	−0.997670	+	1.72801i
$5$	−19.9222	−	34.5062i	−0.796886	−	1.38025i	−0.921634	−	0.388059i	$-0.873146\pi$
$5$	−19.9222	−	34.5062i	−0.796886	−	1.38025i	0.124748	−	0.992188i	$-0.460188\pi$
$6$	−27.0044			−0.750123
$7$	−43.3259	+	22.8882i	−0.884201	+	0.467106i
$7$	−43.3259	+	22.8882i	−0.884201	+	0.467106i
$8$	−110.249			−1.72264
$9$	32.8919	+	56.9705i	0.406073	+	0.703340i
$10$	137.918	−	238.880i	1.37918	−	2.38880i
$11$	−10.8858	−	6.28490i	−0.0899650	−	0.0519413i	0.454343	−	0.890827i	$-0.349874\pi$
$11$	−10.8858	−	6.28490i	−0.0899650	−	0.0519413i	−0.544308	+	0.838886i	$0.683208\pi$
$12$	−62.2671	−	107.850i	−0.432411	−	0.748957i
$13$		−	285.493i		−	1.68931i	−0.535311	−	0.844655i	$-0.679805\pi$
$13$		−	285.493i		−	1.68931i	0.535311	−	0.844655i	$-0.320195\pi$
$14$	−287.191	−	180.528i	−1.46526	−	0.921060i
$15$	155.424			0.690774
$16$	−126.213	−	218.608i	−0.493020	−	0.853936i
$17$	−176.306	−	228.991i	−0.610057	−	0.792358i
$17$	−176.306	−	228.991i	−0.610057	−	0.792358i
$18$	−227.705	+	394.397i	−0.702793	+	1.21727i
$19$	−354.481	+	204.660i	−0.981942	+	0.566924i	−0.902856	−	0.429943i	$-0.858534\pi$
$19$	−354.481	+	204.660i	−0.981942	+	0.566924i	−0.0790860	+	0.996868i	$0.525200\pi$
$20$	1272.05			3.18012
$21$	7.18207	−	191.003i	0.0162859	−	0.433114i
$22$		−	87.0184i		−	0.179790i
$23$	239.631	−	138.351i	0.452988	−	0.261533i	−0.256103	−	0.966649i	$-0.582439\pi$
$23$	239.631	−	138.351i	0.452988	−	0.261533i	0.709091	+	0.705117i	$0.249105\pi$
$24$	215.029	−	372.441i	0.373314	−	0.646598i
$25$	−481.285	+	833.610i	−0.770056	+	1.33378i
$26$	1711.63	−	988.210i	2.53200	−	1.46185i
$27$	−572.572			−0.785422
$28$	58.7807	−	1563.24i	0.0749753	−	1.99393i
$29$			114.294i			0.135902i	0.997689	+	0.0679512i	$0.0216462\pi$
$29$			114.294i			0.135902i	−0.997689	+	0.0679512i	$0.978354\pi$
$30$	537.987	+	931.820i	0.597763	+	1.03536i
$31$	−705.088	+	1221.25i	−0.733702	+	1.27081i	0.221588	+	0.975140i	$0.428876\pi$
$31$	−705.088	+	1221.25i	−0.733702	+	1.27081i	−0.955290	+	0.295669i	$0.904457\pi$
$32$	−8.24011	+	14.2723i	−0.00804698	+	0.0139378i
$33$	42.4630	−	24.5160i	0.0389927	−	0.0225124i
$34$	762.612	−	1849.65i	0.659699	−	1.60004i
$35$	1652.93	+	1039.03i	1.34933	+	0.848187i
$36$	−2100.18			−1.62051
$37$	−1126.39	+	650.321i	−0.822783	+	0.475034i	−0.851375	−	0.524557i	$-0.824231\pi$
$37$	−1126.39	+	650.321i	−0.822783	+	0.475034i	0.0285925	+	0.999591i	$0.490897\pi$
$38$	−2454.01	−	1416.82i	−1.69945	−	0.981179i
$39$	964.448	+	556.824i	0.634088	+	0.366091i
$40$	2196.40	+	3804.27i	1.37275	+	2.37767i
$41$	−2691.28			−1.60100			−0.800501	−	0.599332i	$-0.795433\pi$
$41$	−2691.28			−1.60100			−0.800501	+	0.599332i	$0.795433\pi$
$42$	1169.99	−	618.082i	0.663260	−	0.350387i
$43$	−477.192			−0.258081			−0.129041	−	0.991639i	$-0.541190\pi$
$43$	−477.192			−0.258081			−0.129041	+	0.991639i	$0.541190\pi$
$44$	347.533	−	200.648i	0.179511	−	0.103641i
$45$	1310.56	−	2269.95i	0.647189	−	1.12096i
$46$	1658.92	+	957.778i	0.783989	+	0.452636i
$47$	−700.994	+	404.719i	−0.317335	+	0.183214i	−0.650204	−	0.759759i	$-0.725317\pi$
$47$	−700.994	+	404.719i	−0.317335	+	0.183214i	0.332869	+	0.942973i	$0.391983\pi$
$48$	984.661			0.427370
$49$	1353.26	−	1983.30i	0.563624	−	0.826031i
$50$	−6663.70			−2.66548
$51$	1117.44	−	148.971i	0.429620	−	0.0572747i
$52$	7893.39	+	4557.25i	2.91915	+	1.68537i
$53$	1993.86	−	3453.48i	0.709813	−	1.22943i	−0.255113	−	0.966911i	$-0.582113\pi$
$53$	1993.86	−	3453.48i	0.709813	−	1.22943i	0.964926	−	0.262521i	$-0.0845539\pi$
$54$	−1981.91	−	3432.76i	−0.679667	−	1.17722i
$55$			500.835i			0.165565i
$56$	4776.63	−	2523.40i	1.52316	−	0.804655i
$57$		−	1596.67i		−	0.491433i
$58$	−685.230	+	395.618i	−0.203695	+	0.117603i
$59$	1319.91	+	762.052i	0.379176	+	0.218918i	0.677460	−	0.735560i	$-0.263081\pi$
$59$	1319.91	+	762.052i	0.379176	+	0.218918i	−0.298283	+	0.954477i	$0.596414\pi$
$60$	−2480.99	+	4297.20i	−0.689164	+	1.19367i
$61$	2122.06	+	3675.52i	0.570293	+	0.987777i	0.996536	+	0.0831678i	$0.0265038\pi$
$61$	2122.06	+	3675.52i	0.570293	+	0.987777i	−0.426242	+	0.904609i	$0.640163\pi$
$62$	−9762.39			−2.53964
$63$	−2729.02	−	1715.46i	−0.687585	−	0.432215i
$64$	−4152.91			−1.01389
$65$	−9851.29	+	5687.65i	−2.33167	+	1.34619i
$66$	293.964	+	169.720i	0.0674848	+	0.0389624i
$67$	−1240.73	+	2149.01i	−0.276394	+	0.478729i	−0.970486	−	0.241158i	$-0.922473\pi$
$67$	−1240.73	+	2149.01i	−0.276394	+	0.478729i	0.694092	+	0.719887i	$0.255806\pi$
$68$	9145.54	−	1219.24i	1.97784	−	0.263676i
$69$			1079.35i			0.226707i
$70$	−507.864	+	13506.4i	−0.103646	+	2.75640i
$71$		−	2863.59i		−	0.568060i	−0.958815	−	0.284030i	$-0.908328\pi$
$71$		−	2863.59i		−	0.568060i	0.958815	−	0.284030i	$-0.0916716\pi$
$72$	−3626.30	−	6280.94i	−0.699518	−	1.21160i
$73$	1320.47	−	2287.12i	0.247790	−	0.429184i	−0.715123	−	0.698999i	$-0.753629\pi$
$73$	1320.47	−	2287.12i	0.247790	−	0.429184i	0.962912	+	0.269815i	$0.0869625\pi$
$74$	−7797.79	−	4502.06i	−1.42399	−	0.822143i
$75$	−1877.39	−	3251.73i	−0.333758	−	0.578086i
$76$		−	13067.7i		−	2.26241i
$77$	615.485	+	23.1433i	0.103809	+	0.00390341i
$78$			7709.59i			1.26719i
$79$	5400.12	−	3117.76i	0.865265	−	0.499561i	−0.000506561	−	1.00000i	$-0.500161\pi$
$79$	5400.12	−	3117.76i	0.865265	−	0.499561i	0.865772	+	0.500439i	$0.166828\pi$
$80$	−5028.88	+	8710.27i	−0.785762	+	1.36098i
$81$	−1547.51	+	2680.36i	−0.235864	+	0.408529i
$82$	−9315.64	−	16135.2i	−1.38543	−	2.39964i
$83$			11667.7i			1.69367i	0.531853	+	0.846837i	$0.321496\pi$
$83$			11667.7i			1.69367i	−0.531853	+	0.846837i	$0.678504\pi$
$84$	5166.26	+	3247.51i	0.732180	+	0.460247i
$85$	−4389.22	+	10645.7i	−0.607504	+	1.47345i
$86$	−1651.76	−	2860.93i	−0.223331	−	0.386821i
$87$	−386.105	−	222.918i	−0.0510114	−	0.0294514i
$88$	1200.14	+	692.903i	0.154977	+	0.0894761i
$89$	9377.85	−	5414.31i	1.18392	−	0.683538i	0.227004	−	0.973894i	$-0.427107\pi$
$89$	9377.85	−	5414.31i	1.18392	−	0.683538i	0.956919	+	0.290355i	$0.0937736\pi$
$90$	18145.5			2.24019
$91$	6534.43	+	12369.3i	0.789087	+	1.49369i
$92$			8833.83i			1.04369i
$93$	−2750.40	−	4763.83i	−0.318002	−	0.550795i
$94$	−4852.86	−	2801.80i	−0.549214	−	0.317089i
$95$	14124.1	+	8154.53i	1.56499	+	0.903549i
$96$	−32.1429	−	55.6731i	−0.00348773	−	0.00604092i
$97$	−6150.95			−0.653730			−0.326865	−	0.945071i	$-0.605992\pi$
$97$	−6150.95			−0.653730			−0.326865	+	0.945071i	$0.605992\pi$
$98$	16574.8	+	1248.25i	1.72582	+	0.129971i
$99$		−	826.890i		−	0.0843679i
$100$	−15365.2	−	26613.4i	−1.53652	−	2.66134i
$101$	826.822	+	477.366i	0.0810530	+	0.0467960i	0.539979	−	0.841679i	$-0.318432\pi$
$101$	826.822	+	477.366i	0.0810530	+	0.0467960i	−0.458926	+	0.888475i	$0.651766\pi$
$102$	4761.05	+	6183.78i	0.457618	+	0.594366i
$103$	−3617.66	+	2088.66i	−0.340999	+	0.196876i	−0.660714	−	0.750638i	$-0.729746\pi$
$103$	−3617.66	+	2088.66i	−0.340999	+	0.196876i	0.319715	+	0.947514i	$0.396413\pi$
$104$			31475.3i			2.91007i
$105$	−6733.89	+	3557.38i	−0.610783	+	0.322665i
$106$	27606.3			2.45695
$107$	−9874.23	+	5700.89i	−0.862454	+	0.497938i	−0.864833	−	0.502059i	$-0.832576\pi$
$107$	−9874.23	+	5700.89i	−0.862454	+	0.497938i	0.00237947	+	0.999997i	$0.499243\pi$
$108$	9139.81	−	15830.6i	0.783591	−	1.35722i
$109$	14253.1	+	8229.04i	1.19966	+	0.692621i	0.960478	−	0.278354i	$-0.0897890\pi$
$109$	14253.1	+	8229.04i	1.19966	+	0.692621i	0.239177	+	0.970976i	$0.423122\pi$
$110$	−3002.67	+	1733.60i	−0.248155	+	0.143272i
$111$		−	5073.53i		−	0.411779i
$112$	10471.8	+	6582.58i	0.834808	+	0.524759i
$113$		−	14903.0i		−	1.16712i	−0.812070	−	0.583561i	$-0.801659\pi$
$113$		−	14903.0i		−	1.16712i	0.812070	−	0.583561i	$-0.198341\pi$
$114$	9572.56	−	5526.72i	0.736577	−	0.425263i
$115$	−9547.93	−	5512.50i	−0.721960	−	0.416824i
$116$	−3160.02	−	1824.44i	−0.234841	−	0.135586i
$117$	16264.7	−	9390.43i	1.18816	−	0.685984i
$118$			10551.1i			0.757764i
$119$	12879.8	+	5885.92i	0.909528	+	0.415643i
$120$	−17135.3			−1.18995
$121$	−7241.50	−	12542.6i	−0.494604	−	0.856680i
$122$	−14690.6	+	25444.9i	−0.987009	+	1.70955i
$123$	5249.06	−	9091.64i	0.346953	−	0.600941i
$124$	−22510.2	−	38988.9i	−1.46399	−	2.53570i
$125$	13450.2			0.860816
$126$	838.494	−	22299.3i	0.0528152	−	1.40459i
$127$	−13653.7			−0.846531			−0.423265	−	0.906006i	$-0.639116\pi$
$127$	−13653.7			−0.846531			−0.423265	+	0.906006i	$0.639116\pi$
$128$	−14243.1	−	24669.8i	−0.869329	−	1.50572i
$129$	930.712	−	1612.04i	0.0559289	−	0.0968716i
$130$	−68198.7	−	39374.6i	−4.03543	−	2.32986i
$131$	14264.5	+	24706.8i	0.831216	+	1.43971i	0.897074	+	0.441880i	$0.145688\pi$
$131$	14264.5	+	24706.8i	0.831216	+	1.43971i	−0.0658578	+	0.997829i	$0.520978\pi$
$132$			1565.37i			0.0898399i
$133$	10673.9	−	16980.5i	0.603421	−	0.959946i
$134$	−17178.8			−0.956714
$135$	11406.9	+	19757.3i	0.625892	+	1.08408i
$136$	19437.6	+	25246.0i	1.05091	+	1.36495i
$137$	−2598.08	+	4500.01i	−0.138424	+	0.239757i	−0.926900	−	0.375308i	$-0.877537\pi$
$137$	−2598.08	+	4500.01i	−0.138424	+	0.239757i	0.788476	+	0.615065i	$0.210870\pi$
$138$	−6471.09	+	3736.09i	−0.339797	+	0.196182i
$139$	−20171.8			−1.04404			−0.522019	−	0.852934i	$-0.674821\pi$
$139$	−20171.8			−1.04404			−0.522019	+	0.852934i	$0.674821\pi$
$140$	−55112.6	+	29114.9i	−2.81187	+	1.48545i
$141$		−	3157.44i		−	0.158817i
$142$	17168.2	−	9912.06i	0.851428	−	0.491572i
$143$	−1794.30	+	3107.81i	−0.0877450	+	0.151979i
$144$	8302.79	−	14380.9i	0.400405	−	0.693521i
$145$	3943.85	−	2276.98i	0.187579	−	0.108299i
$146$	18282.8			0.857701
$147$	4060.55	+	8439.78i	0.187910	+	0.390568i
$148$		−	41523.6i		−	1.89571i
$149$	−3398.75	−	5886.80i	−0.153090	−	0.265159i	0.779272	−	0.626686i	$-0.215589\pi$
$149$	−3398.75	−	5886.80i	−0.153090	−	0.265159i	−0.932362	+	0.361527i	$0.882256\pi$
$150$	12996.8	−	22511.2i	0.577637	−	1.00050i
$151$	5441.26	−	9424.54i	0.238641	−	0.413339i	−0.721683	−	0.692223i	$-0.756631\pi$
$151$	5441.26	−	9424.54i	0.238641	−	0.413339i	0.960325	+	0.278884i	$0.0899647\pi$
$152$	39081.1	−	22563.5i	1.69153	−	0.976606i
$153$	7246.70	−	17576.2i	0.309569	−	0.750832i
$154$	1991.69	+	3770.15i	0.0839810	+	0.158971i
$155$	56187.5			2.33871
$156$	−30790.4	+	17776.9i	−1.26522	+	0.730476i
$157$	13027.8	+	7521.63i	0.528534	+	0.305149i	0.740419	−	0.672145i	$-0.234627\pi$
$157$	13027.8	+	7521.63i	0.528534	+	0.305149i	−0.211885	+	0.977295i	$0.567960\pi$
$158$	37384.1	+	21583.7i	1.49752	+	0.864593i
$159$	7777.64	+	13471.3i	0.307648	+	0.532861i
$160$	656.643			0.0256501
$161$	−7215.61	+	11478.9i	−0.278369	+	0.442841i
$162$	−21426.2			−0.816423
$163$	28388.9	−	16390.3i	1.06850	−	0.616896i	0.140725	−	0.990049i	$-0.455057\pi$
$163$	28388.9	−	16390.3i	1.06850	−	0.616896i	0.927770	+	0.373153i	$0.121723\pi$
$164$	42960.2	−	74409.2i	1.59727	−	2.76655i
$165$	−1691.91	−	976.825i	−0.0621455	−	0.0358797i
$166$	−69951.9	+	40386.8i	−2.53854	+	1.46562i
$167$	4188.23			0.150175			0.0750875	−	0.997177i	$-0.476076\pi$
$167$	4188.23			0.150175			0.0750875	+	0.997177i	$0.476076\pi$
$168$	−791.816	+	21057.9i	−0.0280547	+	0.746100i
$169$	−52945.5			−1.85377
$170$	−79017.2	+	10534.2i	−2.73416	+	0.364504i
$171$	−23319.1	−	13463.3i	−0.797481	−	0.460426i
$172$	7617.28	−	13193.5i	0.257480	−	0.445968i
$173$	9280.05	+	16073.5i	0.310069	+	0.537055i	0.978377	−	0.206829i	$-0.0663145\pi$
$173$	9280.05	+	16073.5i	0.310069	+	0.537055i	−0.668308	+	0.743885i	$0.732981\pi$
$174$		−	3086.44i		−	0.101943i
$175$	1772.27	−	47132.6i	0.0578701	−	1.53902i
$176$			3172.95i			0.102432i
$177$	−5148.70	+	2972.60i	−0.164343	+	0.0948834i
$178$	64921.2	+	37482.3i	2.04902	+	1.18300i
$179$	5815.77	−	10073.2i	0.181510	−	0.314385i	−0.760885	−	0.648887i	$-0.775235\pi$
$179$	5815.77	−	10073.2i	0.181510	−	0.314385i	0.942395	+	0.334502i	$0.108568\pi$
$180$	41840.1	+	72469.2i	1.29136	+	2.23670i
$181$	−16033.2			−0.489399			−0.244699	−	0.969599i	$-0.578689\pi$
$181$	−16033.2			−0.489399			−0.244699	+	0.969599i	$0.578689\pi$
$182$	−51539.5	+	81991.1i	−1.55596	+	2.47528i
$183$	−16555.4			−0.494354
$184$	−26419.0	+	15253.0i	−0.780335	+	0.450527i
$185$	44880.2	+	25911.6i	1.31133	+	0.757096i
$186$	19040.5	−	32979.1i	0.550367	−	0.953264i
$187$	480.042	+	3600.81i	0.0137276	+	0.102972i
$188$		−	25841.7i		−	0.731147i
$189$	24807.2	−	13105.1i	0.694471	−	0.366875i
$190$			112905.i			3.12755i
$191$	−5049.51	−	8746.01i	−0.138415	−	0.239742i	0.788482	−	0.615058i	$-0.210867\pi$
$191$	−5049.51	−	8746.01i	−0.138415	−	0.239742i	−0.926897	+	0.375316i	$0.877534\pi$
$192$	8099.81	−	14029.3i	0.219721	−	0.380569i
$193$	−33983.8	−	19620.6i	−0.912342	−	0.526741i	−0.0311583	−	0.999514i	$-0.509920\pi$
$193$	−33983.8	−	19620.6i	−0.912342	−	0.526741i	−0.881184	+	0.472773i	$0.843253\pi$
$194$	−21291.0	−	36877.0i	−0.565707	−	0.979834i
$195$		−	44372.6i		−	1.16693i
$196$	33233.0	+	69074.2i	0.865083	+	1.79806i
$197$			57389.9i			1.47878i	0.673279	+	0.739389i	$0.264885\pi$
$197$			57389.9i			1.47878i	−0.673279	+	0.739389i	$0.735115\pi$
$198$	4957.48	−	2862.20i	0.126454	−	0.0730080i
$199$	−28063.8	+	48607.9i	−0.708663	+	1.22744i	0.256690	+	0.966494i	$0.417368\pi$
$199$	−28063.8	+	48607.9i	−0.708663	+	1.22744i	−0.965353	+	0.260947i	$0.915965\pi$
$200$	53061.1	−	91904.6i	1.32653	−	2.29762i
$201$	−4839.84	−	8382.85i	−0.119795	−	0.207491i
$202$			6609.44i			0.161980i
$203$	−2615.98	−	4951.88i	−0.0634808	−	0.120165i
$204$	−13718.6	+	33273.3i	−0.329647	+	0.799530i
$205$	53616.2	+	92866.0i	1.27582	+	2.20978i
$206$	−25044.4	−	14459.4i	−0.590169	−	0.340734i
$207$	15763.8	+	9101.26i	0.367893	+	0.212403i
$208$	−62411.1	+	36033.0i	−1.44256	+	0.832864i
$209$	5145.06			0.117787
$210$	−44636.4	−	28058.4i	−1.01216	−	0.636245i
$211$		−	74648.1i		−	1.67669i	−0.545137	−	0.838347i	$-0.683522\pi$
$211$		−	74648.1i		−	1.67669i	0.545137	−	0.838347i	$-0.316478\pi$
$212$	63655.0	+	110254.i	1.41632	+	2.45313i
$213$	9673.72	+	5585.13i	0.213223	+	0.123104i
$214$	−68357.5	−	39466.2i	−1.49265	−	0.861784i
$215$	9506.70	+	16466.1i	0.205661	+	0.356216i
$216$	63125.5			1.35300
$217$	2596.40	−	69049.8i	0.0551381	−	1.46637i
$218$			113936.i			2.39745i
$219$	5150.87	+	8921.57i	0.107397	+	0.186017i
$220$	−13847.2	−	7994.69i	−0.286099	−	0.165179i
$221$	−65375.5	+	50334.3i	−1.33854	+	1.03058i
$222$	30417.5	−	17561.6i	0.617188	−	0.356334i
$223$		−	87315.7i		−	1.75583i	−0.478816	−	0.877915i	$-0.658934\pi$
$223$		−	87315.7i		−	1.75583i	0.478816	−	0.877915i	$-0.341066\pi$
$224$	30.3432	−	806.961i	0.000604735	−	0.0160826i
$225$	−63321.6			−1.25080
$226$	89348.3	−	51585.3i	1.74932	−	1.00997i
$227$	15054.9	−	26075.8i	0.292163	−	0.506041i	−0.682158	−	0.731205i	$-0.738958\pi$
$227$	15054.9	−	26075.8i	0.292163	−	0.506041i	0.974321	+	0.225164i	$0.0722917\pi$
$228$	44145.0	+	25487.1i	0.849204	+	0.490288i
$229$	−45395.4	+	26209.0i	−0.865646	+	0.499781i	−0.865899	−	0.500219i	$-0.833253\pi$
$229$	−45395.4	+	26209.0i	−0.865646	+	0.499781i	0.000252636		1.00000i	$0.499920\pi$
$230$		−	76324.1i		−	1.44280i
$231$	−1278.62	+	2034.08i	−0.0239617	+	0.0381192i
$232$		−	12600.8i		−	0.234111i
$233$	44353.6	−	25607.6i	0.816990	−	0.471690i	−0.0323871	−	0.999475i	$-0.510311\pi$
$233$	44353.6	−	25607.6i	0.816990	−	0.471690i	0.849378	+	0.527786i	$0.176978\pi$
$234$	112598.	+	65008.3i	2.05635	+	1.18724i
$235$	27930.6	+	16125.8i	0.505761	+	0.292001i
$236$	−42138.8	+	24328.8i	−0.756586	+	0.436815i
$237$			24323.4i			0.433040i
$238$	9294.29	+	97592.5i	0.164082	+	1.72291i
$239$	−40201.6			−0.703796			−0.351898	−	0.936038i	$-0.614464\pi$
$239$	−40201.6			−0.703796			−0.351898	+	0.936038i	$0.614464\pi$
$240$	−19616.6	−	33976.9i	−0.340566	−	0.589877i
$241$	−14255.6	+	24691.4i	−0.245443	+	0.425120i	−0.962256	−	0.272146i	$-0.912267\pi$
$241$	−14255.6	+	24691.4i	−0.245443	+	0.425120i	0.716813	+	0.697265i	$0.245600\pi$
$242$	50131.6	−	86830.5i	0.856014	−	1.48266i
$243$	−29225.7	−	50620.3i	−0.494939	−	0.857260i
$244$	−135495.			−2.27586
$245$	−95396.1	−	7184.28i	−1.58927	−	0.119688i
$246$	72676.6			1.20095
$247$	58429.0	+	101202.i	0.957711	+	1.65880i
$248$	77735.2	−	134641.i	1.26390	−	2.18915i
$249$	−39415.6	−	22756.6i	−0.635726	−	0.367036i
$250$	46556.8	+	80638.8i	0.744909	+	1.29022i
$251$			38606.1i			0.612785i	0.951905	+	0.306393i	$0.0991220\pi$
$251$			38606.1i			0.612785i	−0.951905	+	0.306393i	$0.900878\pi$
$252$	90992.1	−	48069.3i	1.43286	−	0.756949i
$253$	−3478.09			−0.0543374
$254$	−47261.0	−	81858.5i	−0.732547	−	1.26881i
$255$	−27402.3	−	35590.8i	−0.421411	−	0.547340i
$256$	65379.0	−	113240.i	0.997605	−	1.72790i
$257$	−83259.5	+	48069.9i	−1.26057	+	0.727791i	−0.973185	−	0.230024i	$-0.926120\pi$
$257$	−83259.5	+	48069.9i	−1.26057	+	0.727791i	−0.287386	+	0.957815i	$0.592786\pi$
$258$	12886.3			0.193593
$259$	33917.1	−	53956.7i	0.505615	−	0.804352i
$260$		−	363161.i		−	5.37221i
$261$	−6511.38	+	3759.35i	−0.0955855	+	0.0551863i
$262$	−98750.6	+	171041.i	−1.43859	+	2.49171i
$263$	−30423.8	+	52695.6i	−0.439848	+	0.761839i	−0.997677	−	0.0681169i	$-0.978301\pi$
$263$	−30423.8	+	52695.6i	−0.439848	+	0.761839i	0.557830	+	0.829955i	$0.311634\pi$
$264$	−4681.50	+	2702.87i	−0.0671703	+	0.0387808i
$265$	−158888.			−2.26256
$266$	138751.	+	5217.27i	1.96097	+	0.0737360i
$267$			42240.1i			0.592519i
$268$	−39611.0	−	68608.2i	−0.551501	−	0.955227i
$269$	−3867.02	+	6697.88i	−0.0534407	+	0.0925620i	−0.891508	−	0.453005i	$-0.850352\pi$
$269$	−3867.02	+	6697.88i	−0.0534407	+	0.0925620i	0.838068	+	0.545566i	$0.183685\pi$
$270$	−78967.8	+	136776.i	−1.08323	+	1.87622i
$271$	−31979.5	+	18463.4i	−0.435444	+	0.251404i	−0.701663	−	0.712509i	$-0.747559\pi$
$271$	−31979.5	+	18463.4i	−0.435444	+	0.251404i	0.266219	+	0.963913i	$0.414226\pi$
$272$	−27807.1	+	67443.7i	−0.375853	+	0.911598i
$273$	−54530.2	−	2050.43i	−0.731665	−	0.0275119i
$274$	−35972.1			−0.479142
$275$	10478.3	−	6049.65i	0.138556	−	0.0799954i
$276$	−29842.2	−	17229.4i	−0.391754	−	0.226179i
$277$	−1137.73	−	656.870i	−0.0148279	−	0.00856091i	0.492568	−	0.870274i	$-0.336058\pi$
$277$	−1137.73	−	656.870i	−0.0148279	−	0.00856091i	−0.507396	+	0.861713i	$0.669392\pi$
$278$	−69823.0	−	120937.i	−0.903460	−	1.56484i
$279$	−92766.8			−1.19175
$280$	−182234.	−	114552.i	−2.32441	−	1.46112i
$281$	−42407.0			−0.537063			−0.268532	−	0.963271i	$-0.586538\pi$
$281$	−42407.0			−0.537063			−0.268532	+	0.963271i	$0.586538\pi$
$282$	18929.9	−	10929.2i	0.238041	−	0.137433i
$283$	59340.0	−	102780.i	0.740926	−	1.28332i	−0.211148	−	0.977454i	$-0.567720\pi$
$283$	59340.0	−	102780.i	0.740926	−	1.28332i	0.952074	−	0.305868i	$-0.0989465\pi$
$284$	79173.2	+	45710.7i	0.981616	+	0.566736i
$285$	−55094.9	+	31809.1i	−0.678300	+	0.391617i
$286$	−24843.2			−0.303721
$287$	116602.	−	61598.6i	1.41561	−	0.747837i
$288$	−1084.13			−0.0130707
$289$	−21353.1	+	80745.3i	−0.255662	+	0.966766i
$290$	27302.5	+	15763.1i	0.324644	+	0.187433i
$291$	11996.8	−	20779.0i	0.141670	−	0.245380i
$292$	42156.6	+	73017.4i	0.494424	+	0.856368i
$293$		−	34793.9i		−	0.405291i	−0.979252	−	0.202646i	$-0.935046\pi$
$293$		−	34793.9i		−	0.405291i	0.979252	−	0.202646i	$-0.0649540\pi$
$294$	−36544.1	+	53557.9i	−0.422788	+	0.619625i
$295$		−	60726.9i		−	0.697810i
$296$	124183.	−	71697.2i	1.41736	−	0.818312i
$297$	6232.89	+	3598.56i	0.0706604	+	0.0407958i
$298$	23528.9	−	40753.3i	0.264953	−	0.458912i
$299$	−39498.3	−	68413.0i	−0.441810	−	0.765238i
$300$	119873.			1.33192
$301$	20674.8	−	10922.1i	0.228196	−	0.120551i
$302$	75337.7			0.826035
$303$	−3225.25	+	1862.10i	−0.0351300	+	0.0202823i
$304$	89480.4	+	51661.5i	0.968234	+	0.559010i
$305$	84552.1	−	146449.i	0.908918	−	1.57429i
$306$	130459.	−	17392.2i	1.39326	−	0.185742i
$307$		−	88983.5i		−	0.944132i	−0.881563	−	0.472066i	$-0.843508\pi$
$307$		−	88983.5i		−	0.944132i	0.881563	−	0.472066i	$-0.156492\pi$
$308$	−10464.7	+	16647.6i	−0.110313	+	0.175490i
$309$		−	16294.8i		−	0.170660i
$310$	194488.	+	336863.i	2.02381	+	3.50534i
$311$	15441.3	−	26745.2i	0.159648	−	0.276519i	−0.775094	−	0.631846i	$-0.782297\pi$
$311$	15441.3	−	26745.2i	0.159648	−	0.276519i	0.934742	+	0.355327i	$0.115631\pi$
$312$	−106329.	−	61389.3i	−1.09231	−	0.630643i
$313$	27008.3	+	46779.8i	0.275682	+	0.477496i	0.970307	−	0.241877i	$-0.0777629\pi$
$313$	27008.3	+	46779.8i	0.275682	+	0.477496i	−0.694625	+	0.719372i	$0.744430\pi$
$314$			104142.i			1.05625i
$315$	−4825.96	+	128344.i	−0.0486365	+	1.29346i
$316$			199072.i			1.99359i
$317$	72336.5	−	41763.5i	0.719845	−	0.415603i	−0.0948508	−	0.995491i	$-0.530237\pi$
$317$	72336.5	−	41763.5i	0.719845	−	0.415603i	0.814696	+	0.579889i	$0.196904\pi$
$318$	−53843.2	+	93259.1i	−0.532447	+	0.922226i
$319$	718.325	−	1244.18i	0.00705894	−	0.0122264i
$320$	82735.0	+	143301.i	0.807959	+	1.39943i
$321$		−	44475.9i		−	0.431633i
$322$	−93796.0	−	3526.90i	−0.904633	−	0.0340158i
$323$	109363.	+	45090.3i	1.04825	+	0.432193i
$324$	−49404.8	−	85571.6i	−0.470630	−	0.815154i
$325$	237990.	+	137404.i	2.25316	+	1.30086i
$326$	196531.	+	113467.i	1.84925	+	1.06767i
$327$	−55598.3	+	32099.7i	−0.519955	+	0.300196i
$328$	296711.			2.75795
$329$	21107.9	−	33579.3i	0.195008	−	0.310227i
$330$		−	13524.8i		−	0.124194i
$331$	−72506.6	−	125585.i	−0.661792	−	1.14626i	−0.980145	−	0.198284i	$-0.936463\pi$
$331$	−72506.6	−	125585.i	−0.661792	−	1.14626i	0.318353	−	0.947972i	$-0.396870\pi$
$332$	−322592.	−	186248.i	−2.92669	−	1.68973i
$333$	−74098.3	−	42780.7i	−0.668220	−	0.385797i
$334$	14497.2	+	25109.9i	0.129954	+	0.225088i
$335$	98872.4			0.881020
$336$	−42661.3	+	22537.1i	−0.377881	+	0.199627i
$337$		−	39554.0i		−	0.348282i	−0.984721	−	0.174141i	$-0.944285\pi$
$337$		−	39554.0i		−	0.348282i	0.984721	−	0.174141i	$-0.0557148\pi$
$338$	−183266.	−	317426.i	−1.60416	−	2.77849i
$339$	50344.9	+	29066.6i	0.438083	+	0.252927i
$340$	−224270.	−	291288.i	−1.94005	−	2.51979i
$341$	15350.8	−	8862.81i	0.132015	−	0.0762189i
$342$		−	186408.i		−	1.59372i
$343$	−13237.1	+	116902.i	−0.112513	+	0.993650i
$344$	52609.9			0.444581
$345$	37244.4	−	21503.1i	0.312913	−	0.180660i
$346$	−64244.1	+	111274.i	−0.536638	+	0.929484i
$347$	31876.7	+	18404.0i	0.264736	+	0.152846i	0.626493	−	0.779427i	$-0.284490\pi$
$347$	31876.7	+	18404.0i	0.264736	+	0.152846i	−0.361757	+	0.932273i	$0.617823\pi$
$348$	12326.6	−	7116.75i	0.101785	−	0.0587656i
$349$			50826.9i			0.417295i	0.977991	+	0.208647i	$0.0669061\pi$
$349$			50826.9i			0.417295i	−0.977991	+	0.208647i	$0.933094\pi$
$350$	288711.	−	152520.i	2.35682	−	1.24506i
$351$			163466.i			1.32682i
$352$	179.400	−	103.577i	0.00144789	−	0.000835942i
$353$	−47556.9	−	27457.0i	−0.381649	−	0.220345i	0.296887	−	0.954913i	$-0.404052\pi$
$353$	−47556.9	−	27457.0i	−0.381649	−	0.220345i	−0.678535	+	0.734568i	$0.737385\pi$
$354$	−35643.5	−	20578.8i	−0.284429	−	0.164215i
$355$	−98811.6	+	57048.9i	−0.784064	+	0.452679i
$356$			345708.i			2.72778i
$357$	−45004.4	+	32030.5i	−0.353117	+	0.251320i
$358$	80523.1			0.628281
$359$	−15220.0	−	26361.8i	−0.118093	−	0.204544i	0.800919	−	0.598773i	$-0.204345\pi$
$359$	−15220.0	−	26361.8i	−0.118093	−	0.204544i	−0.919012	+	0.394229i	$0.871012\pi$
$360$	−144487.	+	250260.i	−1.11487	+	1.93102i
$361$	18610.7	−	32234.7i	0.142807	−	0.247348i
$362$	−55497.5	−	96124.4i	−0.423503	−	0.733528i
$363$	56495.1			0.428743
$364$	−446295.	−	16781.5i	−3.36837	−	0.126657i
$365$	−105226.			−0.789840
$366$	−57305.1	−	99255.3i	−0.427790	−	0.740954i
$367$	111423.	−	192991.i	0.827263	−	1.43286i	−0.0729144	−	0.997338i	$-0.523230\pi$
$367$	111423.	−	192991.i	0.827263	−	1.43286i	0.900177	−	0.435523i	$-0.143437\pi$
$368$	−60489.1	−	34923.4i	−0.446665	−	0.257882i
$369$	−88521.5	−	153324.i	−0.650124	−	1.12605i
$370$			358763.i			2.62062i
$371$	−7342.15	+	195261.i	−0.0533428	+	1.41862i
$372$	175615.			1.26904
$373$	39293.7	+	68058.8i	0.282427	+	0.489177i	0.971982	−	0.235056i	$-0.0755273\pi$
$373$	39293.7	+	68058.8i	0.282427	+	0.489177i	−0.689555	+	0.724233i	$0.742194\pi$
$374$	−19926.5	+	15341.9i	−0.142458	+	0.109682i
$375$	−26233.3	+	45437.3i	−0.186548	+	0.323110i
$376$	77283.8	−	44619.8i	0.546654	−	0.315611i
$377$	32630.1			0.229581
$378$	164438.	+	103365.i	1.15085	+	0.723421i
$379$			47294.6i			0.329256i	0.986356	+	0.164628i	$0.0526423\pi$
$379$			47294.6i			0.329256i	−0.986356	+	0.164628i	$0.947358\pi$
$380$	−450917.	+	260337.i	−3.12269	+	1.80289i
$381$	26630.1	−	46124.6i	0.183452	−	0.317748i
$382$	34956.9	−	60547.1i	0.239555	−	0.414922i
$383$	83259.3	−	48069.8i	0.567591	−	0.327699i	−0.188596	−	0.982055i	$-0.560394\pi$
$383$	83259.3	−	48069.8i	0.567591	−	0.327699i	0.756187	+	0.654356i	$0.227060\pi$
$384$	111118.			0.753570
$385$	−11463.2	−	21699.1i	−0.0773365	−	0.146393i
$386$		−	271659.i		−	1.82327i
$387$	−15695.8	−	27185.9i	−0.104800	−	0.181519i
$388$	98185.9	−	170063.i	0.652207	−	1.12966i
$389$	−59325.2	+	102754.i	−0.392049	+	0.679049i	−0.992720	−	0.120448i	$-0.961567\pi$
$389$	−59325.2	+	102754.i	−0.392049	+	0.679049i	0.600671	+	0.799497i	$0.294900\pi$
$390$	266029.	−	153592.i	1.74904	−	1.00981i
$391$	−73929.6	−	30481.2i	−0.483576	−	0.199379i
$392$	−149196.	+	218657.i	−0.970921	+	1.42295i
$393$	−111286.			−0.720533
$394$	−344072.	+	198650.i	−2.21644	+	1.27966i
$395$	−215164.	−	124225.i	−1.37904	−	0.796187i
$396$	22862.0	+	13199.4i	0.145789	+	0.0841713i
$397$	−102242.	−	177089.i	−0.648708	−	1.12360i	−0.983432	−	0.181279i	$-0.941976\pi$
$397$	−102242.	−	177089.i	−0.648708	−	1.12360i	0.334724	−	0.942316i	$-0.391357\pi$
$398$	−388561.			−2.45297
$399$	36544.8	+	69177.0i	0.229551	+	0.434526i
$400$	242978.			1.51861
$401$	−173955.	+	100433.i	−1.08180	+	0.624578i	−0.931382	−	0.364044i	$-0.881396\pi$
$401$	−173955.	+	100433.i	−1.08180	+	0.624578i	−0.150419	+	0.988622i	$0.548062\pi$
$402$	33505.3	−	58032.9i	0.207330	−	0.359106i
$403$	348658.	+	201298.i	2.14679	+	1.23945i
$404$	−26396.6	+	15240.1i	−0.161728	+	0.0933739i
$405$	123319.			0.751828
$406$	20633.2	−	32824.2i	0.125174	−	0.199132i
$407$	16348.8			0.0986955
$408$	−123197.	+	16423.9i	−0.740080	+	0.0986636i
$409$	−212899.	−	122917.i	−1.27270	−	0.734795i	−0.297207	−	0.954813i	$-0.596055\pi$
$409$	−212899.	−	122917.i	−1.27270	−	0.734795i	−0.975496	+	0.220018i	$0.929388\pi$
$410$	−371175.	+	642894.i	−2.20806	+	3.82447i
$411$	−10134.6	−	17553.6i	−0.0599958	−	0.103916i
$412$		−	133362.i		−	0.785668i
$413$	−74628.4	−	2806.16i	−0.437526	−	0.0164518i
$414$			126013.i			0.735214i
$415$	402609.	−	232446.i	2.33769	−	1.34967i
$416$	4074.65	+	2352.50i	0.0235452	+	0.0135939i
$417$	39343.0	−	68144.1i	0.226254	−	0.391883i
$418$	17809.2	+	30846.4i	0.101927	+	0.176543i
$419$	−113160.			−0.644563			−0.322282	−	0.946644i	$-0.604450\pi$
$419$	−113160.			−0.644563			−0.322282	+	0.946644i	$0.604450\pi$
$420$	9135.93	−	242965.i	0.0517910	−	1.37736i
$421$	153199.			0.864354			0.432177	−	0.901789i	$-0.357746\pi$
$421$	153199.			0.864354			0.432177	+	0.901789i	$0.357746\pi$
$422$	447540.	−	258388.i	2.51309	−	1.45093i
$423$	−46114.1	−	26624.0i	−0.257723	−	0.148796i
$424$	−219821.	+	380742.i	−1.22275	+	2.11787i
$425$	275743.	−	36760.7i	1.52661	−	0.203519i
$426$			77329.7i			0.426115i
$427$	−176066.	−	110675.i	−0.965650	−	0.607006i
$428$		−	364007.i		−	1.98711i
$429$	−6999.17	−	12122.9i	−0.0380305	−	0.0658707i
$430$	−65813.2	+	113992.i	−0.355939	+	0.616505i
$431$	299722.	+	173044.i	1.61348	+	0.931543i	0.988556	+	0.150857i	$0.0482034\pi$
$431$	299722.	+	173044.i	1.61348	+	0.931543i	0.624924	+	0.780686i	$0.285130\pi$
$432$	72266.2	+	125169.i	0.387229	+	0.670700i
$433$		−	210603.i		−	1.12328i	−0.827381	−	0.561641i	$-0.810170\pi$
$433$		−	210603.i		−	1.12328i	0.827381	−	0.561641i	$-0.189830\pi$
$434$	422964.	−	223443.i	2.24556	−	1.18628i
$435$			17764.0i			0.0938778i
$436$	−455037.	+	262716.i	−2.39372	+	1.38202i
$437$	−56629.7	+	98085.5i	−0.296539	+	0.513620i
$438$	−35658.6	+	61762.4i	−0.185873	+	0.321941i
$439$	44568.5	+	77195.0i	0.231259	+	0.400553i	0.958179	−	0.286170i	$-0.0923821\pi$
$439$	44568.5	+	77195.0i	0.231259	+	0.400553i	−0.726920	+	0.686723i	$0.759049\pi$
$440$		−	55216.5i		−	0.285209i
$441$	157501.	+	11861.4i	0.809853	+	0.0609901i
$442$	−528063.	−	217721.i	−2.70297	−	1.11444i
$443$	170765.	+	295774.i	0.870144	+	1.50713i	0.861847	+	0.507169i	$0.169308\pi$
$443$	170765.	+	295774.i	0.870144	+	1.50713i	0.00829742	+	0.999966i	$0.497359\pi$
$444$	140274.	+	80987.3i	0.711560	+	0.410819i
$445$	−373654.	−	215729.i	−1.88690	−	1.08940i
$446$	523487.	−	302235.i	2.63170	−	1.51941i
$447$	26515.5			0.132704
$448$	179929.	−	95052.6i	0.896487	−	0.473596i
$449$			163364.i			0.810334i	0.914243	+	0.405167i	$0.132787\pi$
$449$			163364.i			0.810334i	−0.914243	+	0.405167i	$0.867213\pi$
$450$	−219182.	−	379634.i	−1.08238	−	1.87474i
$451$	29296.7	+	16914.4i	0.144034	+	0.0831581i
$452$	412041.	+	237892.i	2.01680	+	1.16440i
$453$	21225.2	+	36763.1i	0.103432	+	0.179150i
$454$	208444.			1.01130
$455$	296636.	−	471900.i	1.43285	−	2.27944i
$456$			176031.i			0.846562i
$457$	87528.2	+	151603.i	0.419098	+	0.725899i	0.995849	−	0.0910208i	$-0.0290130\pi$
$457$	87528.2	+	151603.i	0.419098	+	0.725899i	−0.576751	+	0.816920i	$0.695680\pi$
$458$	−314264.	−	181440.i	−1.49818	−	0.864974i
$459$	100948.	+	131114.i	0.479152	+	0.622335i
$460$	304822.	−	175989.i	1.44056	−	0.831706i
$461$		−	42287.6i		−	0.198981i	−0.995039	−	0.0994905i	$-0.968279\pi$
$461$		−	42287.6i		−	0.198981i	0.995039	−	0.0994905i	$-0.0317213\pi$
$462$	−16620.8	−	624.973i	−0.0778697	−	0.00292804i
$463$	−332801.			−1.55247			−0.776234	−	0.630445i	$-0.782872\pi$
$463$	−332801.			−1.55247			−0.776234	+	0.630445i	$0.782872\pi$
$464$	24985.5	−	14425.4i	0.116052	−	0.0670026i
$465$	−109588.	+	189811.i	−0.506822	+	0.877842i
$466$	307052.	+	177277.i	1.41397	+	0.816356i
$467$	−54718.7	+	31591.8i	−0.250901	+	0.144858i	−0.620177	−	0.784462i	$-0.712939\pi$
$467$	−54718.7	+	31591.8i	−0.250901	+	0.144858i	0.369276	+	0.929320i	$0.379606\pi$
$468$			599587.i			2.73754i
$469$	4568.85	−	121506.i	0.0207712	−	0.552398i
$470$			223271.i			1.01074i
$471$	−50818.8	+	29340.3i	−0.229078	+	0.132258i
$472$	−145519.	−	84015.4i	−0.653184	−	0.377116i
$473$	5194.60	+	2999.10i	0.0232183	+	0.0134051i
$474$	−145827.	+	84193.4i	−0.649056	+	0.374732i
$475$		−	393999.i		−	1.74625i
$476$	−368332.	+	262149.i	−1.62565	+	1.15700i
$477$	262328.			1.15294
$478$	−139154.	−	241022.i	−0.609032	−	1.05487i
$479$	−49898.1	+	86426.0i	−0.217477	+	0.376681i	−0.954036	−	0.299692i	$-0.903116\pi$
$479$	−49898.1	+	86426.0i	−0.217477	+	0.376681i	0.736559	+	0.676373i	$0.236449\pi$
$480$	−1280.71	+	2218.26i	−0.00555865	+	0.00962786i
$481$	185662.	+	321577.i	0.802479	+	1.38994i
$482$	−197378.			−0.849579
$483$	−24704.5	−	46764.0i	−0.105896	−	0.200455i
$484$	462376.			1.97381
$485$	122540.	+	212246.i	0.520949	+	0.902310i
$486$	202324.	−	350436.i	0.856594	−	1.48366i
$487$	−335143.	−	193495.i	−1.41310	−	0.815851i	−0.417417	−	0.908715i	$-0.637065\pi$
$487$	−335143.	−	193495.i	−1.41310	−	0.815851i	−0.995679	+	0.0928638i	$0.970398\pi$
$488$	−233955.	−	405222.i	−0.982409	−	1.70158i
$489$			127870.i			0.534751i
$490$	−287133.	−	596799.i	−1.19589	−	2.48563i
$491$	−160338.			−0.665078			−0.332539	−	0.943090i	$-0.607905\pi$
$491$	−160338.			−0.665078			−0.332539	+	0.943090i	$0.607905\pi$
$492$	167578.	+	290254.i	0.692290	+	1.19908i
$493$	26172.3	−	20150.7i	0.107683	−	0.0829081i
$494$	−404493.	+	700603.i	−1.65752	+	2.87090i
$495$	−28532.8	+	16473.4i	−0.116449	+	0.0672316i
$496$	355966.			1.44692
$497$	65542.4	+	124068.i	0.265344	+	0.502280i
$498$		−	315080.i		−	1.27046i
$499$	−197452.	+	113999.i	−0.792977	+	0.457825i	−0.841009	−	0.541020i	$-0.818038\pi$
$499$	−197452.	+	113999.i	−0.792977	+	0.457825i	0.0480327	+	0.998846i	$0.484705\pi$
$500$	−214703.	+	371876.i	−0.858810	+	1.48750i
$501$	−8168.70	+	14148.6i	−0.0325445	+	0.0563687i
$502$	−231456.	+	133631.i	−0.918464	+	0.530275i
$503$	200762.			0.793499			0.396749	−	0.917927i	$-0.370138\pi$
$503$	200762.			0.793499			0.396749	+	0.917927i	$0.370138\pi$
$504$	300872.	+	189128.i	1.18446	+	0.744550i
$505$		−	38040.6i		−	0.149164i
$506$	−12039.1	−	20852.3i	−0.0470210	−	0.0814428i
$507$	103265.	−	178859.i	0.401731	−	0.695818i
$508$	217950.	−	377501.i	0.844558	−	1.46282i
$509$	−11799.9	+	6812.70i	−0.0455454	+	0.0262956i	−0.522600	−	0.852578i	$-0.675038\pi$
$509$	−11799.9	+	6812.70i	−0.0455454	+	0.0262956i	0.477054	+	0.878874i	$0.341704\pi$
$510$	118528.	−	287480.i	0.455703	−	1.10527i
$511$	−4862.46	+	129315.i	−0.0186215	+	0.495229i
$512$	449436.			1.71446
$513$	202966.	−	117182.i	0.771238	−	0.445275i
$514$	−576390.	−	332779.i	−2.18168	−	1.25959i
$515$	144143.	+	83221.1i	0.543475	+	0.313775i
$516$	29713.4	+	51465.1i	0.111597	+	0.193292i
$517$	10174.5			0.0380654
$518$	440890.	+	16578.2i	1.64313	+	0.0617844i
$519$	−72399.0			−0.268781
$520$	1.08609e6	−	627057.i	4.01662	−	2.31900i
$521$	26621.8	−	46110.4i	0.0980760	−	0.169873i	−0.812812	−	0.582526i	$-0.802065\pi$
$521$	26621.8	−	46110.4i	0.0980760	−	0.169873i	0.910888	+	0.412653i	$0.135398\pi$
$522$	−45077.1	−	26025.3i	−0.165430	−	0.0955112i
$523$	−200073.	+	115512.i	−0.731450	+	0.422303i	−0.818952	−	0.573862i	$-0.805445\pi$
$523$	−200073.	+	115512.i	−0.731450	+	0.422303i	0.0875026	+	0.996164i	$0.472111\pi$
$524$	−910801.			−3.31712
$525$	155766.	+	97914.2i	0.565137	+	0.355244i
$526$	−421237.			−1.52249
$527$	403967.	−	53854.8i	1.45454	−	0.193911i
$528$	−10718.8	−	6188.49i	−0.0384484	−	0.0221982i
$529$	−101639.	+	176043.i	−0.363201	+	0.629083i
$530$	−549978.	−	952589.i	−1.95791	−	3.39121i
$531$			100261.i			0.355586i
$532$	299096.	+	566169.i	1.05679	+	2.00043i
$533$			768344.i			2.70459i
$534$	−253244.	+	146210.i	−0.888088	+	0.512738i
$535$	393432.	+	227148.i	1.37456	+	0.793600i
$536$	136790.	−	236927.i	0.476128	−	0.824677i
$537$	22686.1	+	39293.4i	0.0786703	+	0.136261i
$538$	−53541.4			−0.184980
$539$	−27196.1	+	13084.6i	−0.0936116	+	0.0450385i
$540$	−728339.			−2.49773
$541$	−44070.6	+	25444.2i	−0.150575	+	0.0869348i	−0.573395	−	0.819279i	$-0.694374\pi$
$541$	−44070.6	+	25444.2i	−0.150575	+	0.0869348i	0.422819	+	0.906214i	$0.361041\pi$
$542$	−221388.	−	127818.i	−0.753626	−	0.435106i
$543$	31271.0	−	54163.0i	0.106058	−	0.183697i
$544$	4721.02	−	629.382i	0.0159528	−	0.00212675i
$545$		−	655761.i		−	2.20776i
$546$	−176458.	−	334025.i	−0.591912	−	1.12045i
$547$		−	232924.i		−	0.778465i	−0.921140	−	0.389232i	$-0.872740\pi$
$547$		−	232924.i		−	0.778465i	0.921140	−	0.389232i	$-0.127260\pi$
$548$	−82944.9	−	143665.i	−0.276203	−	0.478398i
$549$	−139597.	+	241790.i	−0.463162	+	0.802220i
$550$	72539.4	+	41880.7i	0.239800	+	0.138448i
$551$	−23391.3	−	40515.0i	−0.0770463	−	0.133448i
$552$		−	118998.i		−	0.390535i
$553$	−162605.	+	258679.i	−0.531721	+	0.845883i
$554$		−	9094.79i		−	0.0296328i
$555$	−175068.	+	101076.i	−0.568357	+	0.328141i
$556$	321997.	−	557716.i	1.04160	−	1.80411i
$557$	−29182.3	+	50545.3i	−0.0940610	+	0.162918i	−0.909216	−	0.416324i	$-0.863318\pi$
$557$	−29182.3	+	50545.3i	−0.0940610	+	0.162918i	0.815155	+	0.579242i	$0.196652\pi$
$558$	−321104.	−	556168.i	−1.03128	−	1.78623i
$559$			136235.i			0.435979i
$560$	18518.2	−	492482.i	0.0590504	−	1.57041i
$561$	−13100.5	−	5401.33i	−0.0416256	−	0.0171623i
$562$	−146788.	−	254245.i	−0.464749	−	0.804969i
$563$	370567.	+	213947.i	1.16910	+	0.674978i	0.953467	−	0.301497i	$-0.0974864\pi$
$563$	370567.	+	213947.i	1.16910	+	0.674978i	0.215629	+	0.976475i	$0.430820\pi$
$564$	87297.8	+	50401.4i	0.274438	+	0.158447i
$565$	−514245.	+	296899.i	−1.61092	+	0.930063i
$566$	821601.			2.56465
$567$	5698.49	−	151548.i	0.0177253	−	0.471396i
$568$			315708.i			0.978563i
$569$	−31517.4	−	54589.8i	−0.0973478	−	0.168611i	0.813238	−	0.581931i	$-0.197703\pi$
$569$	−31517.4	−	54589.8i	−0.0973478	−	0.168611i	−0.910586	+	0.413320i	$0.864369\pi$
$570$	−381412.	−	220208.i	−1.17394	−	0.677773i
$571$	−66811.9	−	38573.8i	−0.204919	−	0.118310i	0.394029	−	0.919098i	$-0.371081\pi$
$571$	−66811.9	−	38573.8i	−0.204919	−	0.118310i	−0.598948	+	0.800788i	$0.704414\pi$
$572$	−57283.7	−	99218.3i	−0.175081	−	0.303249i
$573$	39394.1			0.119984
$574$	772912.	+	485852.i	2.34588	+	1.47462i
$575$			266345.i			0.805580i
$576$	−136597.	−	236593.i	−0.411715	−	0.713112i
$577$	534148.	+	308390.i	1.60439	+	0.926294i	0.990595	+	0.136828i	$0.0436907\pi$
$577$	534148.	+	308390.i	1.60439	+	0.926294i	0.613794	+	0.789466i	$0.289643\pi$
$578$	−558007.	+	151473.i	−1.67026	+	0.453399i
$579$	132564.	−	76535.7i	0.395428	−	0.228300i
$580$			145387.i			0.432185i
$581$	−267053.	−	505514.i	−0.791125	−	1.49755i
$582$	166103.			0.490378
$583$	−43409.5	+	25062.5i	−0.127717	+	0.0737372i
$584$	−145580.	+	252153.i	−0.426852	+	0.739329i
$585$	−648056.	−	374155.i	−1.89366	−	1.09330i
$586$	208601.	−	120436.i	0.607465	−	0.350720i
$587$		−	162486.i		−	0.471562i	−0.971806	−	0.235781i	$-0.924235\pi$
$587$		−	162486.i		−	0.471562i	0.971806	−	0.235781i	$-0.0757649\pi$
$588$	−298162.	−	22454.6i	−0.862379	−	0.0649458i
$589$		−	577212.i		−	1.66381i
$590$	364078.	−	210201.i	1.04590	−	0.603852i
$591$	−193873.	−	111933.i	−0.555064	−	0.320466i
$592$	284330.	+	164158.i	0.811297	+	0.468403i
$593$	−76469.9	+	44149.9i	−0.217461	+	0.125551i	−0.604774	−	0.796397i	$-0.706737\pi$
$593$	−76469.9	+	44149.9i	−0.217461	+	0.125551i	0.387313	+	0.921948i	$0.373403\pi$
$594$			49824.3i			0.141211i
$595$	−53493.3	−	561694.i	−0.151100	−	1.58659i
$596$	217013.			0.610932
$597$	−109471.	−	189609.i	−0.307149	−	0.531998i
$598$	273439.	−	473611.i	0.764643	−	1.32440i
$599$	168383.	−	291647.i	0.469292	−	0.812838i	−0.530091	−	0.847940i	$-0.677842\pi$
$599$	168383.	−	291647.i	0.469292	−	0.812838i	0.999384	+	0.0351024i	$0.0111757\pi$
$600$	206980.	+	358500.i	0.574945	+	0.995834i
$601$	−226518.			−0.627123			−0.313562	−	0.949568i	$-0.601522\pi$
$601$	−226518.			−0.627123			−0.313562	+	0.949568i	$0.601522\pi$
$602$	137045.	+	86146.5i	0.378156	+	0.237708i
$603$	−163241.			−0.448946
$604$	173715.	+	300882.i	0.476170	+	0.824751i
$605$	−288533.	+	499753.i	−0.788287	+	1.36535i
$606$	−22327.9	−	12891.0i	−0.0607997	−	0.0351028i
$607$	171429.	+	296924.i	0.465272	+	0.805875i	0.999214	−	0.0396462i	$-0.0126231\pi$
$607$	171429.	+	296924.i	0.465272	+	0.805875i	−0.533942	+	0.845521i	$0.679290\pi$
$608$		−	6745.68i		−	0.0182481i
$609$	21830.5	+	820.867i	0.0588613	+	0.00221329i
$610$	1.17068e6			3.14614
$611$	115545.	+	200129.i	0.309505	+	0.536078i
$612$	370275.	+	480923.i	0.988602	+	1.28402i
$613$	−88148.7	+	152678.i	−0.234582	+	0.406308i	−0.959151	−	0.282894i	$-0.908706\pi$
$613$	−88148.7	+	152678.i	−0.234582	+	0.406308i	0.724569	+	0.689202i	$0.242039\pi$
$614$	533486.	−	308008.i	1.41510	−	0.817007i
$615$	−418290.			−1.10593
$616$	−67856.6	−	2551.53i	−0.178826	−	0.00672417i
$617$			66076.3i			0.173570i	0.996227	+	0.0867852i	$0.0276594\pi$
$617$			66076.3i			0.173570i	−0.996227	+	0.0867852i	$0.972341\pi$
$618$	97692.8	−	56403.0i	0.255791	−	0.147681i
$619$	−75175.0	+	130207.i	−0.196197	+	0.339823i	−0.947292	−	0.320371i	$-0.896192\pi$
$619$	−75175.0	+	130207.i	−0.196197	+	0.339823i	0.751095	+	0.660194i	$0.229526\pi$
$620$	−896905.	+	1.55349e6i	−2.33326	+	4.04132i
$621$	−137206.	+	79215.9i	−0.355787	+	0.205414i
$622$	213795.			0.552608
$623$	−282380.	+	449222.i	−0.727542	+	1.15740i
$624$		−	281114.i		−	0.721961i
$625$	32845.1	+	56889.4i	0.0840835	+	0.145637i
$626$	−186974.	+	323848.i	−0.477125	+	0.826404i
$627$	−10034.9	+	17380.9i	−0.0255257	+	0.0442118i
$628$	−415920.	+	240131.i	−1.05461	+	0.608877i
$629$	347508.	+	143278.i	0.878341	+	0.362141i
$630$	−786170.	+	415318.i	−1.98077	+	1.04640i
$631$	35072.7			0.0880867			0.0440434	−	0.999030i	$-0.485976\pi$
$631$	35072.7			0.0880867			0.0440434	+	0.999030i	$0.485976\pi$
$632$	−595358.	+	343730.i	−1.49054	+	0.860564i
$633$	252175.	+	145593.i	0.629352	+	0.363357i
$634$	500772.	+	289121.i	1.24584	+	0.719285i
$635$	272011.	+	471137.i	0.674589	+	1.16842i
$636$	−496609.			−1.22772
$637$	−566219.	−	386347.i	−1.39542	−	0.952136i
$638$	9945.67			0.0244339
$639$	163140.	−	94189.1i	0.399539	−	0.230674i
$640$	−567506.	+	982950.i	−1.38551	+	2.39978i
$641$	−562612.	−	324824.i	−1.36928	−	0.790555i	−0.378446	−	0.925623i	$-0.623541\pi$
$641$	−562612.	−	324824.i	−1.36928	−	0.790555i	−0.990836	+	0.135068i	$0.956875\pi$
$642$	266648.	−	153949.i	0.646946	−	0.373515i
$643$	−230916.			−0.558512			−0.279256	−	0.960217i	$-0.590088\pi$
$643$	−230916.			−0.558512			−0.279256	+	0.960217i	$0.590088\pi$
$644$	−202190.	−	382733.i	−0.487515	−	0.922836i
$645$	−74167.2			−0.178276
$646$	108217.	+	811742.i	0.259317	+	1.94515i
$647$	−28679.0	−	16557.8i	−0.0685103	−	0.0395544i	0.465354	−	0.885125i	$-0.345927\pi$
$647$	−28679.0	−	16557.8i	−0.0685103	−	0.0395544i	−0.533864	+	0.845570i	$0.679261\pi$
$648$	170611.	−	295507.i	0.406309	−	0.703748i
$649$	−9578.84	−	16591.0i	−0.0227417	−	0.0393898i
$650$			1.90244e6i			4.50282i
$651$	228199.	+	143445.i	0.538457	+	0.338473i
$652$			1.04654e6i			2.46183i
$653$	−722896.	+	417364.i	−1.69531	+	0.978789i	−0.745219	+	0.666819i	$0.767655\pi$
$653$	−722896.	+	417364.i	−1.69531	+	0.978789i	−0.950092	+	0.311969i	$0.899011\pi$
$654$	−384897.	−	222220.i	−0.899889	−	0.519551i
$655$	568359.	−	984428.i	1.32477	−	2.29457i
$656$	339675.	+	588335.i	0.789326	+	1.36715i
$657$	173731.			0.402483
$658$	274382.	+	10317.3i	0.633730	+	0.0238294i
$659$	304039.			0.700097			0.350049	−	0.936731i	$-0.386165\pi$
$659$	304039.			0.700097			0.350049	+	0.936731i	$0.386165\pi$
$660$	54015.0	−	31185.6i	0.124001	−	0.0715922i
$661$	−149544.	−	86339.3i	−0.342268	−	0.197609i	0.319006	−	0.947753i	$-0.396651\pi$
$661$	−149544.	−	86339.3i	−0.342268	−	0.197609i	−0.661275	+	0.750144i	$0.729984\pi$
$662$	501950.	−	869403.i	1.14537	−	1.98383i
$663$	−42530.4	−	319022.i	−0.0967547	−	0.725761i
$664$		−	1.28635e6i		−	2.91759i
$665$	−798579.	−	30028.0i	−1.80582	−	0.0679021i
$666$		−	592325.i		−	1.33540i
$667$	15812.7	+	27388.3i	0.0355429	+	0.0615622i
$668$	−66855.6	+	115797.i	−0.149825	+	0.259505i
$669$	294968.	+	170300.i	0.659057	+	0.380506i
$670$	342238.	+	592774.i	0.762393	+	1.32050i
$671$		−	53347.8i		−	0.118487i
$672$	2666.88	+	1676.39i	0.00590560	+	0.00371225i
$673$		−	787571.i		−	1.73884i	−0.494075	−	0.869420i	$-0.664493\pi$
$673$		−	787571.i		−	1.73884i	0.494075	−	0.869420i	$-0.335507\pi$
$674$	237140.	−	136913.i	0.522017	−	0.301386i
$675$	275570.	−	477302.i	0.604819	−	1.04758i
$676$	845154.	−	1.46385e6i	1.84945	−	3.20334i
$677$	416363.	+	721162.i	0.908437	+	1.57346i	0.816236	+	0.577719i	$0.196057\pi$
$677$	416363.	+	721162.i	0.908437	+	1.57346i	0.0922017	+	0.995740i	$0.470610\pi$
$678$			402446.i			0.875484i
$679$	266495.	−	140784.i	0.578029	−	0.305361i
$680$	483906.	−	1.17367e6i	1.04651	−	2.53822i
$681$	58725.8	+	101716.i	0.126629	+	0.219329i
$682$	106271.	+	61355.6i	0.228479	+	0.131912i
$683$	−113104.	−	65300.6i	−0.242458	−	0.139983i	0.373848	−	0.927490i	$-0.378038\pi$
$683$	−113104.	−	65300.6i	−0.242458	−	0.139983i	−0.616306	+	0.787507i	$0.711372\pi$
$684$	744474.	−	429822.i	1.59124	−	0.918706i
$685$	207038.			0.441233
$686$	−746686.	+	325285.i	−1.58668	+	0.691219i
$687$		−	204472.i		−	0.433231i
$688$	60227.9	+	104318.i	0.127239	+	0.220385i
$689$	−985945.	−	569235.i	−2.07689	−	1.19909i
$690$	257836.	+	148862.i	0.541559	+	0.312669i
$691$	370683.	+	642042.i	0.776330	+	1.34464i	0.934044	+	0.357158i	$0.116254\pi$
$691$	370683.	+	642042.i	0.776330	+	1.34464i	−0.157714	+	0.987485i	$0.550412\pi$
$692$	−592539.			−1.23739
$693$	18926.0	+	35825.7i	0.0394087	+	0.0745982i
$694$			254815.i			0.529062i
$695$	401867.	+	696054.i	0.831979	+	1.44103i
$696$	42567.7	+	24576.5i	0.0878742	+	0.0507342i
$697$	474490.	+	616281.i	0.976702	+	1.26857i
$698$	−304725.	+	175933.i	−0.625456	+	0.361107i
$699$			199779.i			0.408880i
$700$	1.27484e6	+	801365.i	2.60172	+	1.63544i
$701$	513973.			1.04593			0.522967	−	0.852353i	$-0.324825\pi$
$701$	513973.			1.04593			0.522967	+	0.852353i	$0.324825\pi$
$702$	−980032.	+	565822.i	−1.98868	+	1.14817i
$703$	266189.	−	461053.i	0.538616	−	0.932911i
$704$	45207.6	+	26100.6i	0.0912150	+	0.0526630i
$705$	−108951.	+	62903.1i	−0.219207	+	0.126559i
$706$		−	380159.i		−	0.762704i
$707$	−46748.8	−	1757.84i	−0.0935259	−	0.00351674i
$708$		−	189803.i		−	0.378649i
$709$	742444.	−	428651.i	1.47697	−	0.852729i	0.477308	−	0.878736i	$-0.341613\pi$
$709$	742444.	−	428651.i	1.47697	−	0.852729i	0.999662	+	0.0260076i	$0.00827940\pi$
$710$	−684055.	−	394939.i	−1.35698	−	0.783454i
$711$	355241.	+	205098.i	0.702722	+	0.405717i
$712$	−1.03390e6	+	596921.i	−2.03947	+	1.17749i
$713$			390198.i			0.767549i
$714$	−347812.	−	158946.i	−0.682258	−	0.311783i
$715$	142985.			0.279691
$716$	185671.	+	321592.i	0.362175	+	0.627305i
$717$	78408.8	−	135808.i	0.152520	−	0.264172i
$718$	105365.	−	182498.i	0.204385	−	0.354005i
$719$	−401029.	−	694603.i	−0.775744	−	1.34363i	−0.934375	−	0.356290i	$-0.884041\pi$
$719$	−401029.	−	694603.i	−0.775744	−	1.34363i	0.158631	−	0.987338i	$-0.449292\pi$
$720$	−661638.			−1.27631
$721$	108933.	−	173294.i	0.209550	−	0.333360i
$722$	257677.			0.494312
$723$	−55607.9	−	96315.8i	−0.106380	−	0.184256i
$724$	255933.	−	443290.i	0.488258	−	0.845688i
$725$	−95276.5	−	55007.9i	−0.181263	−	0.104652i
$726$	195553.	+	338707.i	0.371014	+	0.642615i
$727$			895332.i			1.69401i	0.531586	+	0.847004i	$0.321596\pi$
$727$			895332.i			1.69401i	−0.531586	+	0.847004i	$0.678404\pi$
$728$	−720413.	−	1.36370e6i	−1.35931	−	2.57309i
$729$	−22689.9			−0.0426950
$730$	−364232.	−	630868.i	−0.683490	−	1.18384i
$731$	84132.0	+	109273.i	0.157444	+	0.204493i
$732$	264269.	−	457728.i	0.493202	−	0.854250i
$733$	593411.	−	342606.i	1.10445	−	0.637657i	0.167067	−	0.985946i	$-0.446570\pi$
$733$	593411.	−	342606.i	1.10445	−	0.637657i	0.937387	+	0.348289i	$0.113237\pi$
$734$	1.54273e6			2.86350
$735$	210330.	−	308253.i	0.389337	−	0.570601i
$736$			4560.11i			0.00841820i
$737$	27012.7	−	15595.8i	0.0497316	−	0.0287126i
$738$	612819.	−	1.06143e6i	1.12517	−	1.94886i
$739$	−131498.	+	227761.i	−0.240786	+	0.417053i	−0.960938	−	0.276763i	$-0.910738\pi$
$739$	−131498.	+	227761.i	−0.240786	+	0.417053i	0.720153	+	0.693816i	$0.244072\pi$
$740$	−1.43282e6	+	827239.i	−2.61655	+	1.51066i
$741$	−455838.			−0.830184
$742$	−1.19607e6	+	631859.i	−2.17244	+	1.14766i
$743$		−	152919.i		−	0.277003i	−0.990362	−	0.138502i	$-0.955771\pi$
$743$		−	152919.i		−	0.277003i	0.990362	−	0.138502i	$-0.0442287\pi$
$744$	303228.	+	525207.i	0.547802	+	0.948821i
$745$	−135421.	+	234556.i	−0.243990	+	0.422604i
$746$	−272024.	+	471159.i	−0.488797	+	0.846622i
$747$	−664716.	+	383774.i	−1.19123	+	0.687756i
$748$	−107219.	−	44206.4i	−0.191632	−	0.0790101i
$749$	297327.	−	472999.i	0.529993	−	0.843135i
$750$	−363216.			−0.645718
$751$	−415732.	+	240023.i	−0.737112	+	0.425572i	−0.821018	−	0.570902i	$-0.806594\pi$
$751$	−415732.	+	240023.i	−0.737112	+	0.425572i	0.0839066	+	0.996474i	$0.473260\pi$
$752$	176949.	+	102162.i	0.312906	+	0.180656i
$753$	−130418.	−	75297.0i	−0.230011	−	0.132797i
$754$	112946.	+	195629.i	0.198669	+	0.344104i
$755$	−433607.			−0.760680
$756$	−33656.2	+	895069.i	−0.0588873	+	1.56608i
$757$	479484.			0.836725			0.418363	−	0.908280i	$-0.362604\pi$
$757$	479484.			0.836725			0.418363	+	0.908280i	$0.362604\pi$
$758$	−283547.	+	163706.i	−0.493500	+	0.284922i
$759$	6783.63	−	11749.6i	0.0117755	−	0.0203957i
$760$	−1.55716e6	−	899028.i	−2.69592	−	1.55649i
$761$	−536735.	+	309884.i	−0.926811	+	0.535094i	−0.885801	−	0.464064i	$-0.846391\pi$
$761$	−536735.	+	309884.i	−0.926811	+	0.535094i	−0.0410091	+	0.999159i	$0.513057\pi$
$762$	368710.			0.635002
$763$	−805876.	−	30302.4i	−1.38426	−	0.0520508i
$764$	322416.			0.552369
$765$	−750859.	+	100101.i	−1.28303	+	0.171046i
$766$	576389.	+	332778.i	0.982332	+	0.567150i
$767$	217561.	−	376827.i	0.369820	−	0.640547i
$768$	255030.	+	441724.i	0.432382	+	0.748908i
$769$			173427.i			0.293267i	0.989191	+	0.146634i	$0.0468438\pi$
$769$			173427.i			0.293267i	−0.989191	+	0.146634i	$0.953156\pi$
$770$	90414.7	−	143835.i	0.152496	−	0.242596i
$771$		−	375020.i		−	0.630879i
$772$	1.08495e6	−	626396.i	1.82043	−	1.05103i
$773$	725060.	+	418614.i	1.21343	+	0.700574i	0.963505	−	0.267691i	$-0.0862605\pi$
$773$	725060.	+	418614.i	1.21343	+	0.700574i	0.249926	+	0.968265i	$0.419594\pi$
$774$	108659.	−	188203.i	0.181378	−	0.314155i
$775$	−678696.	−	1.17554e6i	−1.12998	−	1.95719i
$776$	678136.			1.12614
$777$	116124.	+	219815.i	0.192344	+	0.364095i
$778$	−821396.			−1.35704
$779$	954009.	−	550797.i	1.57209	−	0.907647i
$780$	1.22682e6	+	708307.i	2.01648	+	1.16421i
$781$	−17997.4	+	31172.4i	−0.0295058	+	0.0511055i
$782$	−73155.4	−	548741.i	−0.119628	−	0.897334i
$783$		−	65441.5i		−	0.106741i
$784$	−604364.	−	45514.7i	−0.983256	−	0.0740491i
$785$		−	599388.i		−	0.972678i
$786$	−385205.	−	667194.i	−0.623515	−	1.07996i
$787$	−112903.	+	195553.i	−0.182287	+	0.315730i	−0.942659	−	0.333758i	$-0.891683\pi$
$787$	−112903.	+	195553.i	−0.182287	+	0.315730i	0.760372	+	0.649488i	$0.225017\pi$
$788$	−1.58673e6	−	916098.i	−2.55535	−	1.47533i
$789$	−118677.	−	205554.i	−0.190639	−	0.330196i
$790$		−	1.71998e6i		−	2.75593i
$791$	341102.	+	645684.i	0.545169	+	1.03197i
$792$			91163.7i			0.145335i
$793$	1.04934e6	−	605835.i	1.66866	−	0.963402i
$794$	707804.	−	1.22595e6i	1.12272	−	1.94461i
$795$	309895.	−	536753.i	0.490320	−	0.849260i
$796$	−895948.	−	1.55183e6i	−1.41402	−	2.44916i
$797$		−	955210.i		−	1.50377i	−0.659293	−	0.751886i	$-0.729144\pi$
$797$		−	955210.i		−	1.50377i	0.659293	−	0.751886i	$-0.270856\pi$
$798$	−288243.	+	458548.i	−0.452640	+	0.720078i
$799$	216267.	+	89167.0i	0.338763	+	0.139672i
$800$	−7931.68	−	13738.1i	−0.0123933	−	0.0214658i
$801$	616912.	+	356174.i	0.961519	+	0.555133i
$802$	−1.20426e6	−	695278.i	−1.87228	−	1.08096i
$803$	−28748.7	+	16598.0i	−0.0445848	+	0.0257410i
$804$	309028.			0.478063
$805$	539843.	+	20299.1i	0.833059	+	0.0313245i
$806$			2.78710e6i			4.29025i
$807$	−15084.4	−	26127.0i	−0.0231623	−	0.0401183i
$808$	−91156.2	−	52629.1i	−0.139625	−	0.0806126i
$809$	11213.7	+	6474.25i	0.0171338	+	0.00989219i	0.508542	−	0.861037i	$-0.330184\pi$
$809$	11213.7	+	6474.25i	0.0171338	+	0.00989219i	−0.491409	+	0.870929i	$0.663518\pi$
$810$	426856.	+	739337.i	0.650597	+	1.12687i
$811$	44398.0			0.0675028			0.0337514	−	0.999430i	$-0.489255\pi$
$811$	44398.0			0.0675028			0.0337514	+	0.999430i	$0.489255\pi$
$812$	178669.	+	6718.27i	0.270980	+	0.0101893i
$813$		−	144043.i		−	0.217927i
$814$	56589.9	+	98016.6i	0.0854064	+	0.147928i
$815$	−1.13113e6	−	653061.i	−1.70294	−	0.983192i
$816$	−173602.	−	225479.i	−0.260720	−	0.338630i
$817$	169156.	−	97662.0i	0.253421	−	0.146313i
$818$		−	1.70187e6i		−	2.54343i
$819$	−489753.	+	779118.i	−0.730145	+	1.16154i
$820$	−3.42344e6			−5.09137
$821$	−437350.	+	252504.i	−0.648847	+	0.374612i	−0.788014	−	0.615657i	$-0.788891\pi$
$821$	−437350.	+	252504.i	−0.648847	+	0.374612i	0.139167	+	0.990269i	$0.455557\pi$
$822$	70159.7	−	121520.i	0.103835	−	0.179848i
$823$	−57661.6	−	33291.0i	−0.0851309	−	0.0491504i	0.456830	−	0.889554i	$-0.348985\pi$
$823$	−57661.6	−	33291.0i	−0.0851309	−	0.0491504i	−0.541961	+	0.840404i	$0.682318\pi$
$824$	398843.	−	230272.i	0.587418	−	0.339146i
$825$			47196.8i			0.0693433i
$826$	−241496.	−	457136.i	−0.353956	−	0.670016i
$827$		−	949889.i		−	1.38887i	−0.719555	−	0.694435i	$-0.755654\pi$
$827$		−	949889.i		−	1.38887i	0.719555	−	0.694435i	$-0.244346\pi$
$828$	−503268.	+	290562.i	−0.734071	+	0.423816i
$829$	−1.13461e6	−	655067.i	−1.65096	−	0.953183i	−0.976677	−	0.214712i	$-0.931119\pi$
$829$	−1.13461e6	−	655067.i	−1.65096	−	0.953183i	−0.674284	−	0.738472i	$-0.735548\pi$
$830$	2.78719e6	+	1.60918e6i	4.04585	+	2.33587i
$831$	4438.05	−	2562.31i	0.00642673	−	0.00371048i
$832$			1.18563e6i			1.71278i
$833$	−692748.	+	39783.3i	−0.998355	+	0.0573338i
$834$	544729.			0.783156
$835$	−83438.7	−	144520.i	−0.119672	−	0.207279i
$836$	−82129.2	+	142252.i	−0.117513	+	0.203538i
$837$	403714.	−	699253.i	0.576266	−	0.998121i
$838$	−391694.	−	678434.i	−0.557775	−	0.966094i
$839$	789473.			1.12154			0.560768	−	0.827973i	$-0.310506\pi$
$839$	789473.			1.12154			0.560768	+	0.827973i	$0.310506\pi$
$840$	742404.	−	392197.i	1.05216	−	0.555835i
$841$	694218.			0.981531
$842$	530284.	+	918480.i	0.747971	+	1.29552i
$843$	82710.4	−	143259.i	0.116387	−	0.201588i
$844$	2.06389e6	+	1.19159e6i	2.89735	+	1.67279i
$845$	1.05479e6	+	1.82695e6i	1.47724	+	2.55866i
$846$		−	368626.i		−	0.515045i
$847$	600823.	+	377676.i	0.837490	+	0.526445i
$848$	−1.00661e6			−1.39981
$849$	231473.	+	400923.i	0.321133	+	0.556218i
$850$	1.17485e6	+	1.52593e6i	1.62609	+	2.11201i
$851$	−179945.	+	311674.i	−0.248474	+	0.430369i
$852$	−308838.	+	178308.i	−0.425453	+	0.245635i
$853$	−529818.			−0.728164			−0.364082	−	0.931367i	$-0.618617\pi$
$853$	−529818.			−0.728164			−0.364082	+	0.931367i	$0.618617\pi$
$854$	54096.4	−	1.43867e6i	0.0741742	−	1.97262i
$855$			1.07287e6i			1.46763i
$856$	1.08862e6	−	628517.i	1.48570	−	0.857767i
$857$	482326.	−	835412.i	0.656718	−	1.13747i	−0.324743	−	0.945802i	$-0.605278\pi$
$857$	482326.	−	835412.i	0.656718	−	1.13747i	0.981460	−	0.191666i	$-0.0613890\pi$
$858$	48454.0	−	83924.8i	0.0658195	−	0.114003i
$859$	−586519.	+	338627.i	−0.794869	+	0.458918i	−0.841674	−	0.539986i	$-0.818429\pi$
$859$	−586519.	+	338627.i	−0.794869	+	0.458918i	0.0468050	+	0.998904i	$0.485096\pi$
$860$	−607011.			−0.820729
$861$	−19329.0	+	514045.i	−0.0260737	+	0.693417i
$862$			2.39591e6i			3.22445i
$863$	191687.	+	332012.i	0.257378	+	0.445792i	0.965539	−	0.260260i	$-0.0838082\pi$
$863$	191687.	+	332012.i	0.257378	+	0.445792i	−0.708161	+	0.706051i	$0.750475\pi$
$864$	4718.06	−	8171.92i	0.00632028	−	0.0109470i
$865$	369757.	−	640439.i	0.494179	−	0.855944i
$866$	1.26264e6	−	728983.i	1.68361	−	0.972035i
$867$	−231125.	−	229620.i	−0.307474	−	0.305472i
$868$	1.86766e6	+	1.17401e6i	2.47890	+	1.55823i
$869$	−78379.3			−0.103791
$870$	−106501.	+	61488.6i	−0.140707	+	0.0812374i
$871$	613530.	+	354222.i	0.808722	+	0.466916i
$872$	−1.57139e6	−	907242.i	−2.06657	−	1.19314i
$873$	−202317.	−	350423.i	−0.265463	−	0.459795i
$874$	−784075.			−1.02644
$875$	−582744.	+	307852.i	−0.761135	+	0.402092i
$876$	−328888.			−0.428587
$877$	−498604.	+	287869.i	−0.648271	+	0.374279i	−0.787794	−	0.615939i	$-0.788777\pi$
$877$	−498604.	+	287869.i	−0.648271	+	0.374279i	0.139522	+	0.990219i	$0.455443\pi$
$878$	−308540.	+	534407.i	−0.400242	+	0.693239i
$879$	117540.	+	67861.7i	0.152127	+	0.0878308i
$880$	109486.	−	63212.0i	0.141382	−	0.0816270i
$881$	724029.			0.932834			0.466417	−	0.884565i	$-0.345545\pi$
$881$	724029.			0.932834			0.466417	+	0.884565i	$0.345545\pi$
$882$	474063.	+	985329.i	0.609394	+	1.26661i
$883$	−953335.			−1.22271			−0.611356	−	0.791356i	$-0.709376\pi$
$883$	−953335.			−1.22271			−0.611356	+	0.791356i	$0.709376\pi$
$884$	−348084.	−	2.61099e6i	−0.445430	−	3.34119i
$885$	205146.	+	118441.i	0.261925	+	0.151223i
$886$	−1.18217e6	+	2.04759e6i	−1.50596	+	2.60840i
$887$	−160075.	−	277258.i	−0.203459	−	0.352401i	0.746182	−	0.665742i	$-0.231885\pi$
$887$	−160075.	−	277258.i	−0.203459	−	0.352401i	−0.949641	+	0.313342i	$0.898552\pi$
$888$			559351.i			0.709346i
$889$	591558.	−	312508.i	0.748504	−	0.395419i
$890$		−	2.98691e6i		−	3.77088i
$891$	33691.6	−	19451.8i	0.0424391	−	0.0245022i
$892$	2.41412e6	+	1.39380e6i	3.03410	+	1.75174i
$893$	165659.	−	286930.i	0.207737	−	0.359810i
$894$	91781.2	+	158970.i	0.114836	+	0.198902i
$895$	−463451.			−0.578572
$896$	1.18174e6	+	742840.i	1.47199	+	0.925293i
$897$	308149.			0.382979
$898$	−979423.	+	565470.i	−1.21456	+	0.701225i
$899$	−139581.	−	80587.2i	−0.172706	−	0.0997118i
$900$	1.01078e6	−	1.75073e6i	1.24788	−	2.16140i
$901$	−1.14235e6	+	152292.i	−1.40718	+	0.187598i
$902$			234191.i			0.287844i
$903$	−3427.23	+	91145.4i	−0.00420308	+	0.111779i
$904$			1.64304e6i			2.01053i
$905$	319416.	+	553245.i	0.389995	+	0.675492i
$906$	−146938.	+	254504.i	−0.179010	+	0.310055i
$907$	−335929.	−	193949.i	−0.408350	−	0.235761i	0.281730	−	0.959494i	$-0.409092\pi$
$907$	−335929.	−	193949.i	−0.408350	−	0.235761i	−0.690081	+	0.723732i	$0.742425\pi$
$908$	480633.	+	832481.i	0.582964	+	1.00972i
$909$			62806.0i			0.0760104i
$910$	3.85598e6	+	144992.i	4.65642	+	0.175090i
$911$			63988.5i			0.0771019i	0.999257	+	0.0385510i	$0.0122742\pi$
$911$			63988.5i			0.0771019i	−0.999257	+	0.0385510i	$0.987726\pi$
$912$	−349044.	+	201520.i	−0.419653	+	0.242287i
$913$	73330.4	−	127012.i	0.0879716	−	0.152371i
$914$	−605942.	+	1.04952e6i	−0.725335	+	1.25632i
$915$	329820.	+	571264.i	0.393944	+	0.682331i
$916$		−	1.67347e6i		−	1.99447i
$917$	−1.18352e6	−	743957.i	−1.40746	−	0.884727i
$918$	−436651.	+	1.05906e6i	−0.518142	+	1.25671i
$919$	−383089.	−	663529.i	−0.453595	−	0.785650i	0.545011	−	0.838429i	$-0.316525\pi$
$919$	−383089.	−	663529.i	−0.453595	−	0.785650i	−0.998606	+	0.0527791i	$0.983192\pi$
$920$	1.05265e6	+	607747.i	1.24368	+	0.718037i
$921$	300602.	+	173553.i	0.354383	+	0.204603i
$922$	253529.	−	146375.i	0.298239	−	0.172189i
$923$	−817537.			−0.959630
$924$	−35828.5	−	67821.0i	−0.0419647	−	0.0794366i
$925$		−	1.25196e6i		−	1.46321i
$926$	−1.15196e6	−	1.99525e6i	−1.34343	−	2.32689i
$927$	−237984.	−	137400.i	−0.276941	−	0.159892i
$928$	−1631.24	−	941.794i	−0.00189418	−	0.00109360i
$929$	−315591.	−	546619.i	−0.365673	−	0.633364i	0.623211	−	0.782054i	$-0.285828\pi$
$929$	−315591.	−	546619.i	−0.365673	−	0.633364i	−0.988884	+	0.148690i	$0.952494\pi$
$930$	−1.51731e6			−1.75432
$931$	−73803.9	+	980001.i	−0.0851491	+	1.13065i
$932$			1.63506e6i			1.88236i
$933$	60233.4	+	104327.i	0.0691949	+	0.119849i
$934$	−378808.	−	218705.i	−0.434235	−	0.250706i
$935$	114687.	−	88300.4i	0.131187	−	0.101004i
$936$	−1.79317e6	+	1.03528e6i	−2.04677	+	1.18170i
$937$			510127.i			0.581030i	0.956870	+	0.290515i	$0.0938267\pi$
$937$			510127.i			0.581030i	−0.956870	+	0.290515i	$0.906173\pi$
$938$	744285.	−	393191.i	0.845928	−	0.446887i
$939$	−210707.			−0.238973
$940$	−891697.	+	514822.i	−1.00916	+	0.582641i
$941$	−511979.	+	886774.i	−0.578194	+	1.00146i	0.417493	+	0.908680i	$0.362909\pi$
$941$	−511979.	+	886774.i	−0.578194	+	1.00146i	−0.995687	+	0.0927805i	$0.970424\pi$
$942$	−351810.	−	203117.i	−0.396466	−	0.228900i
$943$	−644914.	+	372342.i	−0.725235	+	0.418715i
$944$		−	384724.i		−	0.431723i
$945$	−946422.	−	594919.i	−1.05979	−	0.666184i
$946$			41524.5i			0.0464005i
$947$	258066.	−	148994.i	0.287760	−	0.166138i	−0.349171	−	0.937059i	$-0.613537\pi$
$947$	258066.	−	148994.i	0.287760	−	0.166138i	0.636931	+	0.770921i	$0.280204\pi$
$948$	−672500.	−	388268.i	−0.748300	−	0.432031i
$949$	−652958.	−	376986.i	−0.725025	−	0.418593i
$950$	2.36215e6	−	1.36379e6i	2.61735	−	1.51113i
$951$			325821.i			0.360261i
$952$	−1.41999e6	−	648916.i	−1.56679	−	0.716003i
$953$	732667.			0.806716			0.403358	−	0.915042i	$-0.367843\pi$
$953$	732667.			0.806716			0.403358	+	0.915042i	$0.367843\pi$
$954$	908026.	+	1.57275e6i	0.997703	+	1.72807i
$955$	−201194.	+	348479.i	−0.220602	+	0.382094i
$956$	641726.	−	1.11150e6i	0.702156	−	1.21617i
$957$	2802.03	+	4853.26i	0.00305949	+	0.00529919i
$958$	−690871.			−0.752776
$959$	9567.10	−	254432.i	0.0104026	−	0.276653i
$960$	−645463.			−0.700372
$961$	−532537.	−	922381.i	−0.576638	−	0.998766i
$962$	−1.28531e6	+	2.22622e6i	−1.38886	+	2.40557i
$963$	−649565.	−	375027.i	−0.700439	−	0.404399i
$964$	−455116.	−	788283.i	−0.489742	−	0.848258i
$965$			1.56354e6i			1.67901i
$966$	194854.	−	309981.i	0.208811	−	0.332185i
$967$	−1.81185e6			−1.93763			−0.968813	−	0.247792i	$-0.920295\pi$
$967$	−1.81185e6			−1.93763			−0.968813	+	0.247792i	$0.920295\pi$
$968$	798367.	+	1.38281e6i	0.852025	+	1.47575i
$969$	−365623.	+	281503.i	−0.389391	+	0.299802i
$970$	−848324.	+	1.46934e6i	−0.901609	+	1.56163i
$971$	1.25722e6	−	725859.i	1.33344	−	0.769863i	0.347617	−	0.937637i	$-0.386991\pi$
$971$	1.25722e6	−	725859.i	1.33344	−	0.769863i	0.985826	+	0.167774i	$0.0536577\pi$
$972$	1.86608e6			1.97514
$973$	873963.	−	461697.i	0.923139	−	0.487676i
$974$		−	2.67906e6i		−	2.82400i
$975$	−928349.	+	535982.i	−0.976567	+	0.563821i
$976$	535664.	−	927798.i	0.562332	−	0.973988i
$977$	−388678.	+	673210.i	−0.407194	+	0.705280i	−0.994574	−	0.104031i	$-0.966826\pi$
$977$	−388678.	+	673210.i	−0.407194	+	0.705280i	0.587381	+	0.809311i	$0.300159\pi$
$978$	−766625.	+	442611.i	−0.801503	+	0.462748i
$979$	−136113.			−0.142015
$980$	1.72141e6	−	2.52285e6i	1.79239	−	2.62688i
$981$			1.08268e6i			1.12502i
$982$	−554994.	−	961278.i	−0.575527	−	0.996842i
$983$	−587468.	+	1.01752e6i	−0.607963	+	1.05302i	0.383613	+	0.923494i	$0.374680\pi$
$983$	−587468.	+	1.01752e6i	−0.607963	+	1.05302i	−0.991576	+	0.129528i	$0.958654\pi$
$984$	−578703.	+	1.00234e6i	−0.597676	+	1.03520i
$985$	1.98031e6	−	1.14333e6i	2.04108	−	1.17842i
$986$	211404.	+	87161.9i	0.217450	+	0.0896546i
$987$	72268.2	+	136799.i	0.0741844	+	0.140426i
$988$	−3.73074e6			−3.82192
$989$	−114350.	+	66020.0i	−0.116908	+	0.0674967i
$990$	−197528.	−	114043.i	−0.201538	−	0.116358i
$991$	−312223.	−	180262.i	−0.317920	−	0.183551i	0.332545	−	0.943087i	$-0.392093\pi$
$991$	−312223.	−	180262.i	−0.317920	−	0.183551i	−0.650465	+	0.759536i	$0.725426\pi$
$992$	−11620.0	−	20126.4i	−0.0118082	−	0.0204524i
$993$	565665.			0.573668
$994$	−516958.	+	822398.i	−0.523218	+	0.832356i
$995$	2.23636e6			2.25890
$996$	1.25836e6	−	726515.i	1.26849	−	0.732362i
$997$	−283181.	+	490484.i	−0.284888	+	0.493440i	−0.972582	−	0.232560i	$-0.925290\pi$
$997$	−283181.	+	490484.i	−0.284888	+	0.493440i	0.687694	+	0.726001i	$0.258623\pi$
$998$	−1.36692e6	−	789194.i	−1.37241	−	0.792361i
$999$	644939.	−	372356.i	0.646231	−	0.373102i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	119.5.h.a.101.43	yes	92
7.5	odd	6	inner	119.5.h.a.33.44	yes	92
17.16	even	2	inner	119.5.h.a.101.44	yes	92
119.33	odd	6	inner	119.5.h.a.33.43	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.5.h.a.33.43	✓	92	119.33	odd	6	inner
119.5.h.a.33.44	yes	92	7.5	odd	6	inner
119.5.h.a.101.43	yes	92	1.1	even	1	trivial
119.5.h.a.101.44	yes	92	17.16	even	2	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 119 = 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	119.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.46141 + 5.99534i) q^{2} +(-1.95039 + 3.37818i) q^{3} +(-15.9627 + 27.6482i) q^{4} +(-19.9222 - 34.5062i) q^{5} -27.0044 q^{6} +(-43.3259 + 22.8882i) q^{7} -110.249 q^{8} +(32.8919 + 56.9705i) q^{9} +(137.918 - 238.880i) q^{10} +(-10.8858 - 6.28490i) q^{11} +(-62.2671 - 107.850i) q^{12} -285.493i q^{13} +(-287.191 - 180.528i) q^{14} +155.424 q^{15} +(-126.213 - 218.608i) q^{16} +(-176.306 - 228.991i) q^{17} +(-227.705 + 394.397i) q^{18} +(-354.481 + 204.660i) q^{19} +1272.05 q^{20} +(7.18207 - 191.003i) q^{21} -87.0184i q^{22} +(239.631 - 138.351i) q^{23} +(215.029 - 372.441i) q^{24} +(-481.285 + 833.610i) q^{25} +(1711.63 - 988.210i) q^{26} -572.572 q^{27} +(58.7807 - 1563.24i) q^{28} +114.294i q^{29} +(537.987 + 931.820i) q^{30} +(-705.088 + 1221.25i) q^{31} +(-8.24011 + 14.2723i) q^{32} +(42.4630 - 24.5160i) q^{33} +(762.612 - 1849.65i) q^{34} +(1652.93 + 1039.03i) q^{35} -2100.18 q^{36} +(-1126.39 + 650.321i) q^{37} +(-2454.01 - 1416.82i) q^{38} +(964.448 + 556.824i) q^{39} +(2196.40 + 3804.27i) q^{40} -2691.28 q^{41} +(1169.99 - 618.082i) q^{42} -477.192 q^{43} +(347.533 - 200.648i) q^{44} +(1310.56 - 2269.95i) q^{45} +(1658.92 + 957.778i) q^{46} +(-700.994 + 404.719i) q^{47} +984.661 q^{48} +(1353.26 - 1983.30i) q^{49} -6663.70 q^{50} +(1117.44 - 148.971i) q^{51} +(7893.39 + 4557.25i) q^{52} +(1993.86 - 3453.48i) q^{53} +(-1981.91 - 3432.76i) q^{54} +500.835i q^{55} +(4776.63 - 2523.40i) q^{56} -1596.67i q^{57} +(-685.230 + 395.618i) q^{58} +(1319.91 + 762.052i) q^{59} +(-2480.99 + 4297.20i) q^{60} +(2122.06 + 3675.52i) q^{61} -9762.39 q^{62} +(-2729.02 - 1715.46i) q^{63} -4152.91 q^{64} +(-9851.29 + 5687.65i) q^{65} +(293.964 + 169.720i) q^{66} +(-1240.73 + 2149.01i) q^{67} +(9145.54 - 1219.24i) q^{68} +1079.35i q^{69} +(-507.864 + 13506.4i) q^{70} -2863.59i q^{71} +(-3626.30 - 6280.94i) q^{72} +(1320.47 - 2287.12i) q^{73} +(-7797.79 - 4502.06i) q^{74} +(-1877.39 - 3251.73i) q^{75} -13067.7i q^{76} +(615.485 + 23.1433i) q^{77} +7709.59i q^{78} +(5400.12 - 3117.76i) q^{79} +(-5028.88 + 8710.27i) q^{80} +(-1547.51 + 2680.36i) q^{81} +(-9315.64 - 16135.2i) q^{82} +11667.7i q^{83} +(5166.26 + 3247.51i) q^{84} +(-4389.22 + 10645.7i) q^{85} +(-1651.76 - 2860.93i) q^{86} +(-386.105 - 222.918i) q^{87} +(1200.14 + 692.903i) q^{88} +(9377.85 - 5414.31i) q^{89} +18145.5 q^{90} +(6534.43 + 12369.3i) q^{91} +8833.83i q^{92} +(-2750.40 - 4763.83i) q^{93} +(-4852.86 - 2801.80i) q^{94} +(14124.1 + 8154.53i) q^{95} +(-32.1429 - 55.6731i) q^{96} -6150.95 q^{97} +(16574.8 + 1248.25i) q^{98} -826.890i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q - 2 q^{2} - 354 q^{4} + 56 q^{8} - 1068 q^{9} + 464 q^{15} - 3146 q^{16} + 1104 q^{17} - 906 q^{18} - 6 q^{19} - 240 q^{21} - 3106 q^{25} + 468 q^{26} + 1858 q^{30} - 1680 q^{32} - 198 q^{33} - 5318 q^{35}+ \cdots + 107386 q^{98}+O(q^{100}) \) 92 * q - 2 * q^2 - 354 * q^4 + 56 * q^8 - 1068 * q^9 + 464 * q^15 - 3146 * q^16 + 1104 * q^17 - 906 * q^18 - 6 * q^19 - 240 * q^21 - 3106 * q^25 + 468 * q^26 + 1858 * q^30 - 1680 * q^32 - 198 * q^33 - 5318 * q^35 + 17304 * q^36 - 6 * q^38 + 1888 * q^42 + 3316 * q^43 - 7242 * q^47 - 1284 * q^49 + 2136 * q^50 - 11304 * q^51 - 5202 * q^52 + 28 * q^53 - 17826 * q^59 - 3182 * q^60 + 41768 * q^64 + 5988 * q^66 + 2924 * q^67 - 22788 * q^68 + 36898 * q^70 - 23660 * q^72 - 3162 * q^77 - 6194 * q^81 + 30426 * q^84 + 46552 * q^85 + 4118 * q^86 - 7026 * q^87 + 4944 * q^89 + 11034 * q^93 - 101214 * q^94 + 107386 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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