LMFDB - Embedded newform 62.6.d.a.33.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,6,Mod(33,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.33"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	62.d (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$9.94379682840$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			33.2
Character	$\chi$	$=$	62.33
Dual form			62.6.d.a.47.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.23607 - 2.35114i) q^{2} +(-11.7313 + 8.52330i) q^{3} +(4.94427 + 15.2169i) q^{4} -25.7786 q^{5} +58.0028 q^{6} +(46.2201 + 142.251i) q^{7} +(19.7771 - 60.8676i) q^{8} +(-10.1139 + 31.1275i) q^{9} +(83.4214 + 60.6092i) q^{10} +(-141.648 - 435.947i) q^{11} +(-187.701 - 136.373i) q^{12} +(49.7992 - 36.1812i) q^{13} +(184.880 - 569.003i) q^{14} +(302.417 - 219.719i) q^{15} +(-207.108 + 150.473i) q^{16} +(332.304 - 1022.73i) q^{17} +(105.915 - 76.9514i) q^{18} +(-1594.75 - 1158.65i) q^{19} +(-127.457 - 392.271i) q^{20} +(-1754.67 - 1274.84i) q^{21} +(-566.592 + 1743.79i) q^{22} +(661.626 - 2036.28i) q^{23} +(286.782 + 882.624i) q^{24} -2460.46 q^{25} -246.221 q^{26} +(-1235.53 - 3802.58i) q^{27} +(-1936.09 + 1406.65i) q^{28} +(499.507 + 362.913i) q^{29} -1495.23 q^{30} +(5336.42 + 389.512i) q^{31} +1024.00 q^{32} +(5377.43 + 3906.93i) q^{33} +(-3479.93 + 2528.32i) q^{34} +(-1191.49 - 3667.03i) q^{35} -523.670 q^{36} +10081.8 q^{37} +(2436.56 + 7498.97i) q^{38} +(-275.827 + 848.907i) q^{39} +(-509.826 + 1569.08i) q^{40} +(2599.50 + 1888.65i) q^{41} +(2680.90 + 8250.95i) q^{42} +(-7750.12 - 5630.79i) q^{43} +(5933.42 - 4310.88i) q^{44} +(260.723 - 802.424i) q^{45} +(-6928.64 + 5033.95i) q^{46} +(-843.085 + 612.537i) q^{47} +(1147.13 - 3530.49i) q^{48} +(-4501.85 + 3270.79i) q^{49} +(7962.22 + 5784.89i) q^{50} +(4818.64 + 14830.2i) q^{51} +(796.787 + 578.900i) q^{52} +(3482.12 - 10716.9i) q^{53} +(-4942.14 + 15210.3i) q^{54} +(3651.49 + 11238.1i) q^{55} +9572.57 q^{56} +28584.1 q^{57} +(-763.179 - 2348.82i) q^{58} +(-24754.0 + 17984.8i) q^{59} +(4838.68 + 3515.50i) q^{60} -6098.16 q^{61} +(-16353.2 - 13807.2i) q^{62} -4895.38 q^{63} +(-3313.73 - 2407.57i) q^{64} +(-1283.75 + 932.702i) q^{65} +(-8215.98 - 25286.2i) q^{66} -70747.6 q^{67} +17205.7 q^{68} +(9594.05 + 29527.4i) q^{69} +(-4765.96 + 14668.1i) q^{70} +(13598.6 - 41852.3i) q^{71} +(1694.63 + 1231.22i) q^{72} +(-18328.9 - 56410.5i) q^{73} +(-32625.3 - 23703.7i) q^{74} +(28864.5 - 20971.3i) q^{75} +(9746.25 - 29995.9i) q^{76} +(55466.9 - 40299.1i) q^{77} +(2888.49 - 2098.61i) q^{78} +(-1396.45 + 4297.84i) q^{79} +(5338.97 - 3878.99i) q^{80} +(40470.7 + 29403.7i) q^{81} +(-3971.69 - 12223.6i) q^{82} +(-73170.5 - 53161.5i) q^{83} +(10723.6 - 33003.8i) q^{84} +(-8566.33 + 26364.5i) q^{85} +(11841.1 + 36443.2i) q^{86} -8953.10 q^{87} -29336.5 q^{88} +(13161.4 + 40506.6i) q^{89} +(-2730.33 + 1983.70i) q^{90} +(7448.53 + 5411.68i) q^{91} +34257.1 q^{92} +(-65923.2 + 40914.5i) q^{93} +4168.44 q^{94} +(41110.5 + 29868.5i) q^{95} +(-12012.9 + 8727.86i) q^{96} +(17752.1 + 54635.3i) q^{97} +22258.4 q^{98} +15002.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - 20 q^{3} - 96 q^{4} + 120 q^{5} + 280 q^{6} - 180 q^{7} - 384 q^{8} - 200 q^{9} - 100 q^{10} + 354 q^{11} - 320 q^{12} + 39 q^{13} - 720 q^{14} + 535 q^{15} - 1536 q^{16} - 1027 q^{17}+ \cdots + 339042 q^{99}+O(q^{100}) $ 24 * q - 24 * q^2 - 20 * q^3 - 96 * q^4 + 120 * q^5 + 280 * q^6 - 180 * q^7 - 384 * q^8 - 200 * q^9 - 100 * q^10 + 354 * q^11 - 320 * q^12 + 39 * q^13 - 720 * q^14 + 535 * q^15 - 1536 * q^16 - 1027 * q^17 - 1420 * q^18 + 334 * q^19 - 560 * q^20 - 1867 * q^21 + 1416 * q^22 - 1051 * q^23 - 960 * q^24 + 4812 * q^25 + 12536 * q^26 - 5135 * q^27 + 4000 * q^28 - 1143 * q^29 + 9080 * q^30 - 8583 * q^31 + 24576 * q^32 - 24628 * q^33 - 8108 * q^34 - 7496 * q^35 + 17760 * q^36 - 25204 * q^37 - 2844 * q^38 - 20114 * q^39 - 2240 * q^40 + 19615 * q^41 + 3212 * q^42 + 22358 * q^43 - 20496 * q^44 + 6725 * q^45 - 5264 * q^46 + 4766 * q^47 - 3840 * q^48 - 12058 * q^49 + 4628 * q^50 + 6844 * q^51 + 624 * q^52 - 7393 * q^53 - 20540 * q^54 + 11861 * q^55 - 8960 * q^56 + 176704 * q^57 + 4268 * q^58 - 21070 * q^59 + 8560 * q^60 + 76556 * q^61 - 49652 * q^62 + 105854 * q^63 - 24576 * q^64 - 107146 * q^65 + 57968 * q^66 - 150906 * q^67 + 97728 * q^68 - 212560 * q^69 - 29984 * q^70 + 27475 * q^71 - 22720 * q^72 + 49671 * q^73 + 90124 * q^74 - 156002 * q^75 - 11376 * q^76 + 253908 * q^77 - 9036 * q^78 - 7162 * q^79 - 6400 * q^80 + 38329 * q^81 - 92940 * q^82 - 246088 * q^83 + 12848 * q^84 - 104879 * q^85 - 149088 * q^86 - 247668 * q^87 + 118656 * q^88 + 159253 * q^89 - 167880 * q^90 - 68566 * q^91 + 75744 * q^92 + 260391 * q^93 + 18784 * q^94 + 222814 * q^95 - 20480 * q^96 + 190 * q^97 - 144032 * q^98 + 339042 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−3.23607	−	2.35114i	−0.572061	−	0.415627i
$2$	−3.23607	−	2.35114i	−0.572061	−	0.415627i
$3$	−11.7313	+	8.52330i	−0.752565	+	0.546770i	−0.896621	−	0.442799i	$-0.853985\pi$
$3$	−11.7313	+	8.52330i	−0.752565	+	0.546770i	0.144056	+	0.989570i	$0.453985\pi$
$4$	4.94427	+	15.2169i	0.154508	+	0.475528i
$5$	−25.7786			−0.461142			−0.230571	−	0.973056i	$-0.574059\pi$
$5$	−25.7786			−0.461142			−0.230571	+	0.973056i	$0.574059\pi$
$6$	58.0028			0.657766
$7$	46.2201	+	142.251i	0.356522	+	1.09726i	0.955122	+	0.296213i	$0.0957237\pi$
$7$	46.2201	+	142.251i	0.356522	+	1.09726i	−0.598600	+	0.801048i	$0.704276\pi$
$8$	19.7771	−	60.8676i	0.109254	−	0.336249i
$9$	−10.1139	+	31.1275i	−0.0416211	+	0.128097i
$10$	83.4214	+	60.6092i	0.263802	+	0.191663i
$11$	−141.648	−	435.947i	−0.352962	−	1.08631i	−0.957182	−	0.289488i	$-0.906515\pi$
$11$	−141.648	−	435.947i	−0.352962	−	1.08631i	0.604219	−	0.796818i	$-0.293485\pi$
$12$	−187.701	−	136.373i	−0.376282	−	0.273385i
$13$	49.7992	−	36.1812i	0.0817267	−	0.0593779i	−0.546172	−	0.837673i	$-0.683915\pi$
$13$	49.7992	−	36.1812i	0.0817267	−	0.0593779i	0.627898	+	0.778295i	$0.283915\pi$
$14$	184.880	−	569.003i	0.252099	−	0.775880i
$15$	302.417	−	219.719i	0.347039	−	0.252139i
$16$	−207.108	+	150.473i	−0.202254	+	0.146946i
$17$	332.304	−	1022.73i	0.278877	−	0.858295i	−0.709290	−	0.704916i	$-0.750984\pi$
$17$	332.304	−	1022.73i	0.278877	−	0.858295i	0.988167	−	0.153379i	$-0.0490155\pi$
$18$	105.915	−	76.9514i	0.0770503	−	0.0559803i
$19$	−1594.75	−	1158.65i	−1.01346	−	0.736325i	−0.0485319	−	0.998822i	$-0.515454\pi$
$19$	−1594.75	−	1158.65i	−1.01346	−	0.736325i	−0.964933	+	0.262496i	$0.915454\pi$
$20$	−127.457	−	392.271i	−0.0712504	−	0.219286i
$21$	−1754.67	−	1274.84i	−0.868255	−	0.630824i
$22$	−566.592	+	1743.79i	−0.249582	+	0.768135i
$23$	661.626	−	2036.28i	0.260791	−	0.802633i	−0.731842	−	0.681474i	$-0.761339\pi$
$23$	661.626	−	2036.28i	0.260791	−	0.802633i	0.992633	−	0.121158i	$-0.0386609\pi$
$24$	286.782	+	882.624i	0.101630	+	0.312786i
$25$	−2460.46			−0.787348
$26$	−246.221			−0.0714317
$27$	−1235.53	−	3802.58i	−0.326171	−	1.00385i
$28$	−1936.09	+	1406.65i	−0.466693	+	0.339072i
$29$	499.507	+	362.913i	0.110293	+	0.0801324i	0.641564	−	0.767069i	$-0.278286\pi$
$29$	499.507	+	362.913i	0.110293	+	0.0801324i	−0.531272	+	0.847201i	$0.678286\pi$
$30$	−1495.23			−0.303323
$31$	5336.42	+	389.512i	0.997347	+	0.0727975i
$31$	5336.42	+	389.512i	0.997347	+	0.0727975i
$32$	1024.00			0.176777
$33$	5377.43	+	3906.93i	0.859587	+	0.624526i
$34$	−3479.93	+	2528.32i	−0.516265	+	0.375089i
$35$	−1191.49	−	3667.03i	−0.164407	−	0.505993i
$36$	−523.670			−0.0673444
$37$	10081.8			1.21069			0.605345	−	0.795963i	$-0.293035\pi$
$37$	10081.8			1.21069			0.605345	+	0.795963i	$0.293035\pi$
$38$	2436.56	+	7498.97i	0.273728	+	0.842447i
$39$	−275.827	+	848.907i	−0.0290385	+	0.0893714i
$40$	−509.826	+	1569.08i	−0.0503816	+	0.155059i
$41$	2599.50	+	1888.65i	0.241508	+	0.175466i	0.701955	−	0.712222i	$-0.252311\pi$
$41$	2599.50	+	1888.65i	0.241508	+	0.175466i	−0.460447	+	0.887687i	$0.652311\pi$
$42$	2680.90	+	8250.95i	0.234508	+	0.721740i
$43$	−7750.12	−	5630.79i	−0.639201	−	0.464406i	0.220375	−	0.975415i	$-0.429272\pi$
$43$	−7750.12	−	5630.79i	−0.639201	−	0.464406i	−0.859575	+	0.511009i	$0.829272\pi$
$44$	5933.42	−	4310.88i	0.462034	−	0.335687i
$45$	260.723	−	802.424i	0.0191933	−	0.0590708i
$46$	−6928.64	+	5033.95i	−0.482784	+	0.350763i
$47$	−843.085	+	612.537i	−0.0556707	+	0.0404471i	−0.615273	−	0.788314i	$-0.710954\pi$
$47$	−843.085	+	612.537i	−0.0556707	+	0.0404471i	0.559602	+	0.828762i	$0.310954\pi$
$48$	1147.13	−	3530.49i	0.0718635	−	0.221173i
$49$	−4501.85	+	3270.79i	−0.267856	+	0.194609i
$50$	7962.22	+	5784.89i	0.450411	+	0.327243i
$51$	4818.64	+	14830.2i	0.259417	+	0.798404i
$52$	796.787	+	578.900i	0.0408633	+	0.0296890i
$53$	3482.12	−	10716.9i	0.170276	−	0.524056i	−0.829110	−	0.559085i	$-0.811152\pi$
$53$	3482.12	−	10716.9i	0.170276	−	0.524056i	0.999386	+	0.0350291i	$0.0111524\pi$
$54$	−4942.14	+	15210.3i	−0.230638	+	0.709830i
$55$	3651.49	+	11238.1i	0.162766	+	0.500942i
$56$	9572.57			0.407904
$57$	28584.1			1.16530
$58$	−763.179	−	2348.82i	−0.0297890	−	0.0916813i
$59$	−24754.0	+	17984.8i	−0.925795	+	0.672629i	−0.944960	−	0.327187i	$-0.893899\pi$
$59$	−24754.0	+	17984.8i	−0.925795	+	0.672629i	0.0191648	+	0.999816i	$0.493899\pi$
$60$	4838.68	+	3515.50i	0.173520	+	0.126069i
$61$	−6098.16			−0.209833			−0.104917	−	0.994481i	$-0.533458\pi$
$61$	−6098.16			−0.209833			−0.104917	+	0.994481i	$0.533458\pi$
$62$	−16353.2	−	13807.2i	−0.540287	−	0.456169i
$63$	−4895.38			−0.155394
$64$	−3313.73	−	2407.57i	−0.101127	−	0.0734732i
$65$	−1283.75	+	932.702i	−0.0376876	+	0.0273817i
$66$	−8215.98	−	25286.2i	−0.232166	−	0.714535i
$67$	−70747.6			−1.92542			−0.962708	−	0.270543i	$-0.912797\pi$
$67$	−70747.6			−1.92542			−0.962708	+	0.270543i	$0.912797\pi$
$68$	17205.7			0.451233
$69$	9594.05	+	29527.4i	0.242593	+	0.746626i
$70$	−4765.96	+	14668.1i	−0.116253	+	0.357791i
$71$	13598.6	−	41852.3i	0.320147	−	0.985311i	−0.653437	−	0.756981i	$-0.726674\pi$
$71$	13598.6	−	41852.3i	0.320147	−	0.985311i	0.973584	−	0.228330i	$-0.0733265\pi$
$72$	1694.63	+	1231.22i	0.0385251	+	0.0279902i
$73$	−18328.9	−	56410.5i	−0.402559	−	1.23895i	−0.922917	−	0.385000i	$-0.874202\pi$
$73$	−18328.9	−	56410.5i	−0.402559	−	1.23895i	0.520358	−	0.853948i	$-0.325798\pi$
$74$	−32625.3	−	23703.7i	−0.692589	−	0.503196i
$75$	28864.5	−	20971.3i	0.592530	−	0.430498i
$76$	9746.25	−	29995.9i	0.193555	−	0.595700i
$77$	55466.9	−	40299.1i	1.06612	−	0.774583i
$78$	2888.49	−	2098.61i	0.0537570	−	0.0390568i
$79$	−1396.45	+	4297.84i	−0.0251744	+	0.0774788i	−0.962854	−	0.270021i	$-0.912969\pi$
$79$	−1396.45	+	4297.84i	−0.0251744	+	0.0774788i	0.937680	+	0.347500i	$0.112969\pi$
$80$	5338.97	−	3878.99i	0.0932679	−	0.0677631i
$81$	40470.7	+	29403.7i	0.685375	+	0.497954i
$82$	−3971.69	−	12223.6i	−0.0652290	−	0.200754i
$83$	−73170.5	−	53161.5i	−1.16585	−	0.847036i	−0.175340	−	0.984508i	$-0.556102\pi$
$83$	−73170.5	−	53161.5i	−1.16585	−	0.847036i	−0.990506	+	0.137472i	$0.956102\pi$
$84$	10723.6	−	33003.8i	0.165822	−	0.510347i
$85$	−8566.33	+	26364.5i	−0.128602	+	0.395796i
$86$	11841.1	+	36443.2i	0.172642	+	0.531338i
$87$	−8953.10			−0.126816
$88$	−29336.5			−0.403832
$89$	13161.4	+	40506.6i	0.176127	+	0.542064i	0.999683	−	0.0251709i	$-0.00801299\pi$
$89$	13161.4	+	40506.6i	0.176127	+	0.542064i	−0.823556	+	0.567235i	$0.808013\pi$
$90$	−2730.33	+	1983.70i	−0.0355311	+	0.0258149i
$91$	7448.53	+	5411.68i	0.0942904	+	0.0685060i
$92$	34257.1			0.421969
$93$	−65923.2	+	40914.5i	−0.790371	+	0.490535i
$94$	4168.44			0.0486580
$95$	41110.5	+	29868.5i	0.467351	+	0.339551i
$96$	−12012.9	+	8727.86i	−0.133036	+	0.0966562i
$97$	17752.1	+	54635.3i	0.191567	+	0.589582i	1.00000		0.000993137i	$0.000316125\pi$
$97$	17752.1	+	54635.3i	0.191567	+	0.589582i	−0.808433	+	0.588588i	$0.799684\pi$
$98$	22258.4			0.234115
$99$	15002.6			0.153843
$100$	−12165.2	−	37440.6i	−0.121652	−	0.374406i
$101$	23028.5	−	70874.3i	0.224627	−	0.691330i	−0.773702	−	0.633549i	$-0.781597\pi$
$101$	23028.5	−	70874.3i	0.224627	−	0.691330i	0.998329	−	0.0577811i	$-0.0184025\pi$
$102$	19274.6	−	59321.0i	0.183436	−	0.564557i
$103$	−2025.83	−	1471.85i	−0.0188153	−	0.0136701i	0.578338	−	0.815797i	$-0.303702\pi$
$103$	−2025.83	−	1471.85i	−0.0188153	−	0.0136701i	−0.597153	+	0.802127i	$0.703702\pi$
$104$	−1217.38	−	3746.72i	−0.0110368	−	0.0339678i
$105$	45233.0	+	32863.7i	0.400389	+	0.290899i
$106$	−36465.2	+	26493.5i	−0.315220	+	0.229021i
$107$	−20549.6	+	63245.0i	−0.173517	+	0.534032i	−0.999563	−	0.0295721i	$-0.990586\pi$
$107$	−20549.6	+	63245.0i	−0.173517	+	0.534032i	0.826045	+	0.563604i	$0.190586\pi$
$108$	51754.7	−	37602.0i	0.426963	−	0.310207i
$109$	−102467.	+	74446.4i	−0.826069	+	0.600175i	−0.918445	−	0.395550i	$-0.870554\pi$
$109$	−102467.	+	74446.4i	−0.826069	+	0.600175i	0.0923751	+	0.995724i	$0.470554\pi$
$110$	14605.9	−	44952.5i	0.115093	−	0.354219i
$111$	−118273.	+	85930.1i	−0.911123	+	0.661969i
$112$	−30977.5	−	22506.5i	−0.233346	−	0.169536i
$113$	−15873.8	−	48854.4i	−0.116946	−	0.359921i	0.875402	−	0.483395i	$-0.160597\pi$
$113$	−15873.8	−	48854.4i	−0.116946	−	0.359921i	−0.992348	+	0.123474i	$0.960597\pi$
$114$	−92500.1	−	67205.2i	−0.666622	−	0.484329i
$115$	−17055.8	+	52492.4i	−0.120262	+	0.370128i
$116$	−3052.72	+	9395.30i	−0.0210640	+	0.0648284i
$117$	622.565	+	1916.06i	0.00420456	+	0.0129403i
$118$	122390.			0.809174
$119$	160843.			1.04120
$120$	−7392.84	−	22752.8i	−0.0468660	−	0.144239i
$121$	−39693.0	+	28838.6i	−0.246462	+	0.179065i
$122$	19734.1	+	14337.6i	0.120038	+	0.0872124i
$123$	−46593.2			−0.277690
$124$	20457.6	+	83129.7i	0.119481	+	0.485514i
$125$	143986.			0.824221
$126$	15841.8	+	11509.7i	0.0888951	+	0.0645860i
$127$	−286701.	+	208301.i	−1.57732	+	1.14599i	−0.657636	+	0.753336i	$0.728444\pi$
$127$	−286701.	+	208301.i	−1.57732	+	1.14599i	−0.919686	+	0.392656i	$0.871556\pi$
$128$	5062.93	+	15582.1i	0.0273135	+	0.0840623i
$129$	138912.			0.734963
$130$	6347.23			0.0329402
$131$	11713.7	+	36051.0i	0.0596368	+	0.183543i	0.976437	−	0.215803i	$-0.0692370\pi$
$131$	11713.7	+	36051.0i	0.0596368	+	0.183543i	−0.916800	+	0.399347i	$0.869237\pi$
$132$	−32863.9	+	101145.i	−0.164166	+	0.505253i
$133$	91110.0	−	280408.i	0.446619	−	1.37455i
$134$	228944.	+	166337.i	1.10146	+	0.800255i
$135$	31850.4	+	98025.3i	0.150411	+	0.462918i
$136$	−55678.9	−	40453.1i	−0.258133	−	0.187544i
$137$	15217.8	−	11056.4i	0.0692710	−	0.0503283i	−0.552611	−	0.833439i	$-0.686368\pi$
$137$	15217.8	−	11056.4i	0.0692710	−	0.0503283i	0.621882	+	0.783111i	$0.286368\pi$
$138$	38376.2	−	118110.i	0.171539	−	0.527944i
$139$	141289.	−	102653.i	0.620258	−	0.450644i	−0.232753	−	0.972536i	$-0.574773\pi$
$139$	141289.	−	102653.i	0.620258	−	0.450644i	0.853012	+	0.521892i	$0.174773\pi$
$140$	49909.8	−	36261.6i	0.215212	−	0.156360i
$141$	4669.66	−	14371.7i	0.0197805	−	0.0608782i
$142$	−142407.	+	103465.i	−0.592665	+	0.430597i
$143$	−22827.1	−	16584.8i	−0.0933491	−	0.0678221i
$144$	−2589.17	−	7968.64i	−0.0104053	−	0.0320242i
$145$	−12876.6	−	9355.41i	−0.0508606	−	0.0369524i
$146$	−73315.6	+	225642.i	−0.284652	+	0.876069i
$147$	24934.8	−	76741.3i	0.0951726	−	0.292911i
$148$	49847.1	+	153414.i	0.187062	+	0.575718i
$149$	363192.			1.34020			0.670101	−	0.742270i	$-0.266251\pi$
$149$	363192.			1.34020			0.670101	+	0.742270i	$0.266251\pi$
$150$	−142714.			−0.517890
$151$	61158.0	+	188225.i	0.218278	+	0.671792i	0.998905	+	0.0467935i	$0.0149003\pi$
$151$	61158.0	+	188225.i	0.218278	+	0.671792i	−0.780626	+	0.624998i	$0.785100\pi$
$152$	−102064.	+	74153.9i	−0.358314	+	0.260330i
$153$	28474.0	+	20687.6i	0.0983376	+	0.0714465i
$154$	−274243.			−0.931825
$155$	−137566.	−	10041.1i	−0.459919	−	0.0335700i
$156$	−14281.5			−0.0469853
$157$	−423826.	−	307928.i	−1.37227	−	0.997011i	−0.997556	−	0.0698699i	$-0.977742\pi$
$157$	−423826.	−	307928.i	−1.37227	−	0.997011i	−0.374712	−	0.927141i	$-0.622258\pi$
$158$	14623.9	−	10624.9i	0.0466036	−	0.0338595i
$159$	50493.2	+	155402.i	0.158394	+	0.487488i
$160$	−26397.3			−0.0815192
$161$	320242.			0.973675
$162$	−61833.7	−	190305.i	−0.185113	−	0.569721i
$163$	148486.	−	456993.i	0.437740	−	1.34722i	−0.452513	−	0.891758i	$-0.649472\pi$
$163$	148486.	−	456993.i	0.437740	−	1.34722i	0.890253	−	0.455467i	$-0.150528\pi$
$164$	−15886.8	+	48894.4i	−0.0461239	+	0.141955i
$165$	−138623.	−	100715.i	−0.396392	−	0.287995i
$166$	111795.	+	344069.i	0.314884	+	0.969114i
$167$	−391876.	−	284715.i	−1.08732	−	0.789985i	−0.108376	−	0.994110i	$-0.534565\pi$
$167$	−391876.	−	284715.i	−1.08732	−	0.789985i	−0.978945	+	0.204125i	$0.934565\pi$
$168$	−112299.	+	81589.9i	−0.306974	+	0.223030i
$169$	−113565.	+	349517.i	−0.305863	+	0.941351i
$170$	89707.8	−	65176.5i	0.238072	−	0.172969i
$171$	52195.2	−	37922.0i	0.136502	−	0.0991748i
$172$	47364.5	−	145773.i	0.122076	−	0.375713i
$173$	327532.	−	237966.i	0.832030	−	0.604505i	−0.0881029	−	0.996111i	$-0.528080\pi$
$173$	327532.	−	237966.i	0.832030	−	0.604505i	0.920133	+	0.391606i	$0.128080\pi$
$174$	28972.8	+	21050.0i	0.0725468	+	0.0527083i
$175$	−113723.	−	350003.i	−0.280707	−	0.863926i
$176$	94934.8	+	68974.2i	0.231017	+	0.167844i
$177$	137107.	−	421971.i	0.328947	−	1.01239i
$178$	52645.6	−	162026.i	0.124541	−	0.383297i
$179$	−175856.	−	541230.i	−0.410228	−	1.26255i	−0.916450	−	0.400149i	$-0.868958\pi$
$179$	−175856.	−	541230.i	−0.410228	−	1.26255i	0.506222	−	0.862403i	$-0.331042\pi$
$180$	13499.5			0.0310553
$181$	−101918.			−0.231236			−0.115618	−	0.993294i	$-0.536885\pi$
$181$	−101918.			−0.231236			−0.115618	+	0.993294i	$0.536885\pi$
$182$	−11380.3	−	35025.1i	−0.0254670	−	0.0783792i
$183$	71539.5	−	51976.5i	0.157913	−	0.114731i
$184$	−110858.	−	80543.2i	−0.241392	−	0.175382i
$185$	−259895.			−0.558300
$186$	309528.	+	22592.8i	0.656020	+	0.0478837i
$187$	−492925.			−1.03080
$188$	−13489.4	−	9800.60i	−0.0278354	−	0.0202236i
$189$	483814.	−	351511.i	0.985199	−	0.715789i
$190$	−62811.2	−	193313.i	−0.126227	−	0.388488i
$191$	−800454.			−1.58764			−0.793821	−	0.608151i	$-0.791912\pi$
$191$	−800454.			−1.58764			−0.793821	+	0.608151i	$0.791912\pi$
$192$	59394.9			0.116278
$193$	3418.09	+	10519.8i	0.00660526	+	0.0203289i	0.954305	−	0.298835i	$-0.0965980\pi$
$193$	3418.09	+	10519.8i	0.00660526	+	0.0203289i	−0.947700	+	0.319164i	$0.896598\pi$
$194$	71008.3	−	218541.i	0.135458	−	0.416897i
$195$	7110.43	−	21883.7i	0.0133909	−	0.0412129i
$196$	−72029.7	−	52332.6i	−0.133928	−	0.0973044i
$197$	293186.	+	902335.i	0.538243	+	1.65654i	0.736536	+	0.676398i	$0.236460\pi$
$197$	293186.	+	902335.i	0.538243	+	1.65654i	−0.198294	+	0.980143i	$0.563540\pi$
$198$	−48549.3	−	35273.2i	−0.0880076	−	0.0639413i
$199$	−781228.	+	567595.i	−1.39844	+	1.01603i	−0.403565	+	0.914951i	$0.632229\pi$
$199$	−781228.	+	567595.i	−1.39844	+	1.01603i	−0.994878	+	0.101078i	$0.967771\pi$
$200$	−48660.8	+	149762.i	−0.0860209	+	0.264745i
$201$	829962.	−	603003.i	1.44900	−	1.05276i
$202$	−241157.	+	175211.i	−0.415836	+	0.302122i
$203$	−28537.4	+	87829.2i	−0.0486043	+	0.149589i
$204$	−201846.	+	146650.i	−0.339582	+	0.246721i
$205$	−67011.7	−	48686.8i	−0.111369	−	0.0809146i
$206$	3095.20	+	9526.05i	0.00508184	+	0.0156403i
$207$	56692.5	+	41189.5i	0.0919602	+	0.0668130i
$208$	−4869.53	+	14986.9i	−0.00780420	+	0.0240189i
$209$	−279219.	+	859348.i	−0.442160	+	1.36083i
$210$	−69109.8	−	212698.i	−0.108141	−	0.332825i
$211$	316771.			0.489823			0.244912	−	0.969545i	$-0.421241\pi$
$211$	316771.			0.489823			0.244912	+	0.969545i	$0.421241\pi$
$212$	180294.			0.275513
$213$	197190.	+	606888.i	0.297807	+	0.916557i
$214$	215198.	−	156350.i	0.321221	−	0.233380i
$215$	199787.	+	145154.i	0.294762	+	0.214157i
$216$	−255889.			−0.373180
$217$	191242.	+	777114.i	0.275698	+	1.12030i
$218$	506623.			0.722011
$219$	695826.	+	505547.i	0.980371	+	0.712281i
$220$	−152955.	+	111129.i	−0.213063	+	0.154799i
$221$	−20455.0	−	62954.1i	−0.0281721	−	0.0867048i
$222$	584772.			0.796351
$223$	527075.			0.709758			0.354879	−	0.934912i	$-0.384522\pi$
$223$	527075.			0.709758			0.354879	+	0.934912i	$0.384522\pi$
$224$	47329.4	+	145665.i	0.0630247	+	0.193970i
$225$	24885.0	−	76588.0i	0.0327703	−	0.100857i
$226$	−63495.0	+	195418.i	−0.0826930	+	0.254503i
$227$	−926562.	−	673187.i	−1.19347	−	0.867103i	−0.199839	−	0.979829i	$-0.564042\pi$
$227$	−926562.	−	673187.i	−1.19347	−	0.867103i	−0.993626	+	0.112725i	$0.964042\pi$
$228$	141328.	+	434961.i	0.180049	+	0.554132i
$229$	438421.	+	318531.i	0.552462	+	0.401387i	0.828692	−	0.559704i	$-0.189085\pi$
$229$	438421.	+	318531.i	0.552462	+	0.401387i	−0.276230	+	0.961091i	$0.589085\pi$
$230$	178611.	−	129768.i	0.222632	−	0.161752i
$231$	−307219.	+	945522.i	−0.378807	+	1.16585i
$232$	31968.5	−	23226.5i	0.0389944	−	0.0283311i
$233$	75716.1	−	55011.0i	0.0913689	−	0.0663834i	−0.541163	−	0.840918i	$-0.682016\pi$
$233$	75716.1	−	55011.0i	0.0913689	−	0.0663834i	0.632532	+	0.774534i	$0.282016\pi$
$234$	2490.26	−	7664.24i	0.00297307	−	0.00915017i
$235$	21733.6	−	15790.4i	0.0256721	−	0.0186519i
$236$	−396063.	−	287757.i	−0.462897	−	0.336315i
$237$	−20249.6	−	62321.8i	−0.0234178	−	0.0720724i
$238$	−520498.	−	378164.i	−0.595630	−	0.432750i
$239$	−123265.	+	379372.i	−0.139588	+	0.429606i	−0.996275	−	0.0862290i	$-0.972518\pi$
$239$	−123265.	+	379372.i	−0.139588	+	0.429606i	0.856688	+	0.515835i	$0.172518\pi$
$240$	−29571.4	+	91011.3i	−0.0331393	+	0.101992i
$241$	−82585.0	−	254170.i	−0.0915922	−	0.281892i	0.894758	−	0.446551i	$-0.147348\pi$
$241$	−82585.0	−	254170.i	−0.0915922	−	0.281892i	−0.986351	+	0.164659i	$0.947348\pi$
$242$	196253.			0.215416
$243$	246189.			0.267456
$244$	−30151.0	−	92795.1i	−0.0324210	−	0.0997816i
$245$	116052.	−	84316.4i	0.123520	−	0.0897423i
$246$	150779.	+	109547.i	0.158855	+	0.115415i
$247$	−121339.			−0.126549
$248$	129248.	−	317112.i	0.133442	−	0.327404i
$249$	1.31150e6			1.34051
$250$	−465947.	−	338530.i	−0.471505	−	0.342569i
$251$	381043.	−	276844.i	0.381759	−	0.277364i	−0.380311	−	0.924859i	$-0.624183\pi$
$251$	381043.	−	276844.i	0.381759	−	0.277364i	0.762070	+	0.647494i	$0.224183\pi$
$252$	−24204.1	−	74492.5i	−0.0240097	−	0.0738944i
$253$	−981427.			−0.963955
$254$	1.41753e6			1.37863
$255$	−124218.	−	382303.i	−0.119628	−	0.368178i
$256$	20251.7	−	62328.4i	0.0193136	−	0.0594410i
$257$	−21108.2	+	64964.2i	−0.0199351	+	0.0613538i	−0.960529	−	0.278179i	$-0.910269\pi$
$257$	−21108.2	+	64964.2i	−0.0199351	+	0.0613538i	0.940594	+	0.339533i	$0.110269\pi$
$258$	−449529.	−	326602.i	−0.420444	−	0.305471i
$259$	465981.	+	1.43414e6i	0.431637	+	1.32844i
$260$	−20540.1	−	14923.2i	−0.0188438	−	0.0136908i
$261$	−16348.6	+	11877.9i	−0.0148552	+	0.0107929i
$262$	46854.7	−	144204.i	0.0421696	−	0.129785i
$263$	−26345.9	+	19141.4i	−0.0234868	+	0.0170642i	−0.599467	−	0.800400i	$-0.704621\pi$
$263$	−26345.9	+	19141.4i	−0.0234868	+	0.0170642i	0.575980	+	0.817464i	$0.304621\pi$
$264$	344155.	−	250044.i	0.303910	−	0.220803i
$265$	−89764.2	+	276266.i	−0.0785215	+	0.241664i
$266$	−954116.	+	693206.i	−0.826794	+	0.600701i
$267$	−499651.	−	363018.i	−0.428932	−	0.311637i
$268$	−349795.	−	1.07656e6i	−0.297493	−	0.915589i
$269$	−1.16987e6	−	849957.i	−0.985724	−	0.716171i	−0.0267436	−	0.999642i	$-0.508514\pi$
$269$	−1.16987e6	−	849957.i	−0.985724	−	0.716171i	−0.958981	+	0.283472i	$0.908514\pi$
$270$	127401.	−	392101.i	0.106357	−	0.327332i
$271$	−20442.7	+	62916.1i	−0.0169089	+	0.0520401i	−0.959155	−	0.282881i	$-0.908710\pi$
$271$	−20442.7	+	62916.1i	−0.0169089	+	0.0520401i	0.942246	+	0.334921i	$0.108710\pi$
$272$	85069.7	+	261818.i	0.0697193	+	0.214574i
$273$	−133507.			−0.108417
$274$	−75241.1			−0.0605451
$275$	348519.	+	1.07263e6i	0.277904	+	0.855301i
$276$	−401881.	+	291983.i	−0.317559	+	0.230720i
$277$	16840.6	+	12235.4i	0.0131873	+	0.00958116i	0.594359	−	0.804200i	$-0.297406\pi$
$277$	16840.6	+	12235.4i	0.0131873	+	0.00958116i	−0.581172	+	0.813781i	$0.697406\pi$
$278$	−698573.			−0.542126
$279$	−66096.8	+	162170.i	−0.0508358	+	0.124727i
$280$	−246768.			−0.188102
$281$	−910637.	−	661616.i	−0.687985	−	0.499851i	0.188012	−	0.982167i	$-0.439796\pi$
$281$	−910637.	−	661616.i	−0.687985	−	0.499851i	−0.875997	+	0.482316i	$0.839796\pi$
$282$	−48901.3	+	35528.9i	−0.0366183	+	0.0266047i
$283$	−697043.	−	2.14528e6i	−0.517361	−	1.59227i	−0.778945	−	0.627092i	$-0.784245\pi$
$283$	−697043.	−	2.14528e6i	−0.517361	−	1.59227i	0.261584	−	0.965181i	$-0.415755\pi$
$284$	704098.			0.518009
$285$	−736858.			−0.537368
$286$	34876.6	+	107339.i	0.0252127	+	0.0775968i
$287$	−148513.	+	457075.i	−0.106429	+	0.327554i
$288$	−10356.7	+	31874.6i	−0.00735765	+	0.0226445i
$289$	213147.	+	154860.i	0.150119	+	0.109068i
$290$	19673.7	+	60549.5i	0.0137370	+	0.0422781i
$291$	−673929.	−	489638.i	−0.466532	−	0.338955i
$292$	767771.	−	557818.i	0.526956	−	0.382856i
$293$	−201060.	+	618800.i	−0.136822	+	0.421096i	−0.995869	−	0.0908013i	$-0.971057\pi$
$293$	−201060.	+	618800.i	−0.136822	+	0.421096i	0.859047	+	0.511897i	$0.171057\pi$
$294$	−261120.	+	189715.i	−0.176186	+	0.128007i
$295$	638123.	−	463624.i	0.426923	−	0.310178i
$296$	199388.	−	613654.i	0.132273	−	0.407094i
$297$	−1.48272e6	+	1.07726e6i	−0.975364	+	0.708643i
$298$	−1.17531e6	−	853915.i	−0.766678	−	0.557024i
$299$	−40726.5	−	125343.i	−0.0263451	−	0.0810818i
$300$	461832.	+	335540.i	0.296265	+	0.215249i
$301$	442773.	−	1.36272e6i	0.281686	−	0.866940i
$302$	244632.	−	752899.i	0.154346	−	0.475028i
$303$	333929.	+	1.02773e6i	0.208953	+	0.643090i
$304$	504632.			0.313178
$305$	157202.			0.0967629
$306$	−43504.4	−	133893.i	−0.0265601	−	0.0817435i
$307$	2.65693e6	−	1.93037e6i	1.60892	−	1.16895i	0.742152	−	0.670232i	$-0.233805\pi$
$307$	2.65693e6	−	1.93037e6i	1.60892	−	1.16895i	0.866766	−	0.498715i	$-0.166195\pi$
$308$	887470.	+	644785.i	0.533061	+	0.387292i
$309$	36310.8			0.0216341
$310$	421564.	+	355930.i	0.249149	+	0.210359i
$311$	2.01917e6			1.18378			0.591890	−	0.806019i	$-0.298382\pi$
$311$	2.01917e6			1.18378			0.591890	+	0.806019i	$0.298382\pi$
$312$	46215.9	+	33577.8i	0.0268785	+	0.0195284i
$313$	−635067.	+	461403.i	−0.366403	+	0.266207i	−0.755718	−	0.654898i	$-0.772712\pi$
$313$	−635067.	+	461403.i	−0.366403	+	0.266207i	0.389315	+	0.921105i	$0.372712\pi$
$314$	647549.	+	1.99295e6i	0.370637	+	1.14070i
$315$	126196.			0.0716588
$316$	−72304.3			−0.0407330
$317$	−1.03113e6	−	3.17351e6i	−0.576325	−	1.77375i	−0.631624	−	0.775275i	$-0.717611\pi$
$317$	−1.03113e6	−	3.17351e6i	−0.576325	−	1.77375i	0.0552989	−	0.998470i	$-0.482389\pi$
$318$	201973.	−	621608.i	0.112002	−	0.344706i
$319$	87456.9	−	269165.i	0.0481191	−	0.148095i
$320$	85423.5	+	62063.8i	0.0466340	+	0.0338816i
$321$	−297983.	−	917098.i	−0.161410	−	0.496768i
$322$	−1.03633e6	−	752935.i	−0.557002	−	0.404686i
$323$	−1.71493e6	+	1.24597e6i	−0.914617	+	0.664508i
$324$	−247335.	+	761219.i	−0.130895	+	0.402853i
$325$	−122529.	+	89022.6i	−0.0643473	+	0.0467511i
$326$	−1.55496e6	+	1.12975e6i	−0.810357	+	0.588759i
$327$	567540.	−	1.74671e6i	0.293513	−	0.903340i
$328$	166368.	−	120874.i	0.0853859	−	0.0620365i
$329$	−126101.	−	91618.1i	−0.0642289	−	0.0466650i
$330$	211797.	+	651843.i	0.107062	+	0.329502i
$331$	−514169.	−	373566.i	−0.257950	−	0.187412i	0.451293	−	0.892376i	$-0.350963\pi$
$331$	−514169.	−	373566.i	−0.257950	−	0.187412i	−0.709243	+	0.704964i	$0.750963\pi$
$332$	447179.	−	1.37627e6i	0.222657	−	0.685267i
$333$	−101967.	+	313821.i	−0.0503903	+	0.155085i
$334$	598734.	+	1.84271e6i	0.293675	+	0.903840i
$335$	1.82377e6			0.887890
$336$	555236.			0.268305
$337$	881741.	+	2.71372e6i	0.422928	+	1.30164i	0.904965	+	0.425487i	$0.139897\pi$
$337$	881741.	+	2.71372e6i	0.422928	+	1.30164i	−0.482037	+	0.876151i	$0.660103\pi$
$338$	1.18927e6	−	864054.i	0.566224	−	0.411385i
$339$	602621.	+	437830.i	0.284803	+	0.206922i
$340$	−443540.			−0.208082
$341$	−586087.	−	2.38157e6i	−0.272945	−	1.10912i
$342$	−258067.			−0.119307
$343$	1.36040e6	+	988385.i	0.624353	+	0.453619i
$344$	−496008.	+	360371.i	−0.225992	+	0.164192i
$345$	−247321.	−	761177.i	−0.111870	−	0.344301i
$346$	−1.61941e6			−0.727221
$347$	2.19631e6			0.979196			0.489598	−	0.871948i	$-0.337144\pi$
$347$	2.19631e6			0.979196			0.489598	+	0.871948i	$0.337144\pi$
$348$	−44266.6	−	136238.i	−0.0195942	−	0.0603048i
$349$	−714958.	+	2.20042e6i	−0.314208	+	0.967033i	0.661871	+	0.749617i	$0.269763\pi$
$349$	−714958.	+	2.20042e6i	−0.314208	+	0.967033i	−0.976079	+	0.217415i	$0.930237\pi$
$350$	−454891.	+	1.40001e6i	−0.198489	+	0.610888i
$351$	−199111.	−	144662.i	−0.0862635	−	0.0626741i
$352$	−145047.	−	446410.i	−0.0623955	−	0.192034i
$353$	−2.92543e6	−	2.12545e6i	−1.24955	−	0.907850i	−0.251353	−	0.967896i	$-0.580875\pi$
$353$	−2.92543e6	−	2.12545e6i	−1.24955	−	0.907850i	−0.998196	+	0.0600456i	$0.980875\pi$
$354$	−1.43580e6	+	1.04317e6i	−0.608956	+	0.442432i
$355$	−350554.	+	1.07889e6i	−0.147633	+	0.454368i
$356$	−551312.	+	400551.i	−0.230554	+	0.167507i
$357$	−1.88690e6	+	1.37091e6i	−0.783570	+	0.569297i
$358$	−703425.	+	2.16492e6i	−0.290075	+	0.892759i
$359$	161745.	−	117515.i	0.0662362	−	0.0481234i	−0.554174	−	0.832401i	$-0.686966\pi$
$359$	161745.	−	117515.i	0.0662362	−	0.0481234i	0.620411	+	0.784277i	$0.286966\pi$
$360$	−43685.3	−	31739.2i	−0.0177656	−	0.0129074i
$361$	435593.	+	1.34062e6i	0.175919	+	0.541423i
$362$	329814.	+	239624.i	0.132281	+	0.0961079i
$363$	219851.	−	676630.i	0.0875711	−	0.269516i
$364$	−45521.4	+	140100.i	−0.0180079	+	0.0554225i
$365$	472494.	+	1.45419e6i	0.185637	+	0.571331i
$366$	−353711.			−0.138021
$367$	2.14871e6			0.832747			0.416373	−	0.909194i	$-0.363301\pi$
$367$	2.14871e6			0.832747			0.416373	+	0.909194i	$0.363301\pi$
$368$	169376.	+	521286.i	0.0651978	+	0.200658i
$369$	−85080.2	+	61814.4i	−0.0325284	+	0.0236333i
$370$	841036.	+	611049.i	0.319382	+	0.232045i
$371$	1.68543e6			0.635733
$372$	−948534.	−	800855.i	−0.355382	−	0.300052i
$373$	4.93435e6			1.83636			0.918180	−	0.396164i	$-0.129659\pi$
$373$	4.93435e6			1.83636			0.918180	+	0.396164i	$0.129659\pi$
$374$	1.59514e6	+	1.15894e6i	0.589684	+	0.428430i
$375$	−1.68914e6	+	1.22723e6i	−0.620280	+	0.450660i
$376$	20609.9	+	63430.8i	0.00751807	+	0.0231383i
$377$	38005.7			0.0137720
$378$	−2.39211e6			−0.861096
$379$	960549.	+	2.95627e6i	0.343496	+	1.05717i	0.962384	+	0.271693i	$0.0875834\pi$
$379$	960549.	+	2.95627e6i	0.343496	+	1.05717i	−0.618888	+	0.785479i	$0.712417\pi$
$380$	−251245.	+	773252.i	−0.0892562	+	0.274702i
$381$	1.58797e6	−	4.88728e6i	0.560443	−	1.72487i
$382$	2.59032e6	+	1.88198e6i	0.908229	+	0.659867i
$383$	−1.37049e6	−	4.21792e6i	−0.477395	−	1.46927i	−0.842700	−	0.538383i	$-0.819035\pi$
$383$	−1.37049e6	−	4.21792e6i	−0.477395	−	1.46927i	0.365305	−	0.930888i	$-0.380965\pi$
$384$	−192206.	−	139646.i	−0.0665179	−	0.0483281i
$385$	−1.42986e6	+	1.03885e6i	−0.491634	+	0.357193i
$386$	13672.3	−	42079.2i	0.00467062	−	0.0143747i
$387$	253657.	−	184292.i	0.0860932	−	0.0625504i
$388$	−743609.	+	540263.i	−0.250764	+	0.182191i
$389$	−1.26050e6	+	3.87943e6i	−0.422348	+	1.29985i	0.483164	+	0.875530i	$0.339488\pi$
$389$	−1.26050e6	+	3.87943e6i	−0.422348	+	1.29985i	−0.905511	+	0.424322i	$0.860512\pi$
$390$	−74461.4	+	54099.4i	−0.0247896	+	0.0180107i
$391$	−1.86269e6	−	1.35332e6i	−0.616167	−	0.447672i
$392$	110052.	+	338704.i	0.0361727	+	0.111328i
$393$	−444690.	−	323086.i	−0.145237	−	0.105521i
$394$	1.17275e6	−	3.60934e6i	0.380595	−	1.17135i
$395$	35998.7	−	110793.i	0.0116090	−	0.0357287i
$396$	74176.8	+	228293.i	0.0237700	+	0.0731567i
$397$	−3.69418e6			−1.17636			−0.588181	−	0.808729i	$-0.700156\pi$
$397$	−3.69418e6			−1.17636			−0.588181	+	0.808729i	$0.700156\pi$
$398$	3.86260e6			1.22228
$399$	1.32116e6	+	4.06611e6i	0.415454	+	1.27864i
$400$	509582.	−	370233.i	0.159244	−	0.115698i
$401$	587964.	+	427181.i	0.182596	+	0.132663i	0.675328	−	0.737517i	$-0.264002\pi$
$401$	587964.	+	427181.i	0.182596	+	0.132663i	−0.492733	+	0.870181i	$0.664002\pi$
$402$	−4.10356e6			−1.26647
$403$	279843.	−	173681.i	0.0858324	−	0.0532709i
$404$	1.19235e6			0.363454
$405$	−1.04328e6	−	757987.i	−0.316055	−	0.229628i
$406$	298848.	−	217126.i	0.0899778	−	0.0653727i
$407$	−1.42806e6	−	4.39513e6i	−0.427328	−	1.31518i
$408$	997980.			0.296805
$409$	2.04989e6			0.605929			0.302964	−	0.953002i	$-0.402024\pi$
$409$	2.04989e6			0.605929			0.302964	+	0.953002i	$0.402024\pi$
$410$	102385.	+	315108.i	0.0300798	+	0.0925762i
$411$	−84288.2	+	259413.i	−0.0246129	+	0.0757507i
$412$	12380.8	−	38104.2i	0.00359340	−	0.0110593i
$413$	−3.70248e6	−	2.69001e6i	−1.06812	−	0.776031i
$414$	−86618.5	−	266584.i	−0.0248376	−	0.0764423i
$415$	1.88624e6	+	1.37043e6i	0.537620	+	0.390604i
$416$	50994.4	−	37049.6i	0.0144474	−	0.0104966i
$417$	−782571.	+	2.40851e6i	−0.220386	+	0.678278i
$418$	2.92402e6	−	2.12443e6i	0.818540	−	0.594704i
$419$	1.63058e6	−	1.18469e6i	0.453741	−	0.329662i	−0.337330	−	0.941386i	$-0.609524\pi$
$419$	1.63058e6	−	1.18469e6i	0.453741	−	0.329662i	0.791071	+	0.611724i	$0.209524\pi$
$420$	−276439.	+	850793.i	−0.0764675	+	0.235343i
$421$	526636.	−	382623.i	0.144812	−	0.105212i	−0.513020	−	0.858376i	$-0.671473\pi$
$421$	526636.	−	382623.i	0.144812	−	0.105212i	0.657832	+	0.753164i	$0.271473\pi$
$422$	−1.02509e6	−	744774.i	−0.280209	−	0.203584i
$423$	−10539.8	−	32438.3i	−0.00286407	−	0.00881469i
$424$	−583444.	−	423897.i	−0.157610	−	0.114510i
$425$	−817621.	+	2.51638e6i	−0.219573	+	0.675777i
$426$	788759.	−	2.42755e6i	0.210582	−	0.648104i
$427$	−281858.	−	867469.i	−0.0748101	−	0.230242i
$428$	−1.06400e6			−0.280757
$429$	409149.			0.107334
$430$	−305248.	−	939457.i	−0.0796126	−	0.245022i
$431$	961885.	−	698850.i	0.249419	−	0.181214i	−0.456050	−	0.889954i	$-0.650736\pi$
$431$	961885.	−	698850.i	0.249419	−	0.181214i	0.705469	+	0.708740i	$0.250736\pi$
$432$	828076.	+	601632.i	0.213482	+	0.155104i
$433$	6.40762e6			1.64239			0.821197	−	0.570645i	$-0.193307\pi$
$433$	6.40762e6			1.64239			0.821197	+	0.570645i	$0.193307\pi$
$434$	1.20823e6	−	2.96443e6i	0.307912	−	0.755470i
$435$	230799.			0.0584804
$436$	−1.63947e6	−	1.19114e6i	−0.413035	−	0.300087i
$437$	−3.41447e6	+	2.48076e6i	−0.855302	+	0.621413i
$438$	−1.06313e6	−	3.27197e6i	−0.264789	−	0.814937i
$439$	5.30862e6			1.31468			0.657341	−	0.753593i	$-0.271681\pi$
$439$	5.30862e6			1.31468			0.657341	+	0.753593i	$0.271681\pi$
$440$	756254.			0.186224
$441$	−56280.0	−	173212.i	−0.0137803	−	0.0424113i
$442$	−81820.0	+	251816.i	−0.0199207	+	0.0613095i
$443$	−2.39800e6	+	7.38028e6i	−0.580550	+	1.78675i	0.0359008	+	0.999355i	$0.488570\pi$
$443$	−2.39800e6	+	7.38028e6i	−0.580550	+	1.78675i	−0.616451	+	0.787394i	$0.711430\pi$
$444$	−1.89236e6	−	1.37488e6i	−0.455561	−	0.330985i
$445$	−339283.	−	1.04420e6i	−0.0812198	−	0.249969i
$446$	−1.70565e6	−	1.23923e6i	−0.406025	−	0.294995i
$447$	−4.26072e6	+	3.09559e6i	−1.00859	+	0.732783i
$448$	189318.	−	582659.i	0.0445652	−	0.137158i
$449$	556164.	−	404077.i	0.130193	−	0.0945907i	−0.520783	−	0.853689i	$-0.674360\pi$
$449$	556164.	−	404077.i	0.130193	−	0.0945907i	0.650976	+	0.759098i	$0.274360\pi$
$450$	−260599.	+	189336.i	−0.0606654	+	0.0440760i
$451$	455138.	−	1.40077e6i	0.105366	−	0.324284i
$452$	664928.	−	483099.i	0.153084	−	0.111222i
$453$	−2.32176e6	−	1.68686e6i	−0.531584	−	0.386219i
$454$	1.41566e6	+	4.35696e6i	0.322344	+	0.992073i
$455$	−192013.	−	139506.i	−0.0434813	−	0.0315910i
$456$	565310.	−	1.73985e6i	0.127314	−	0.391831i
$457$	−1.35453e6	+	4.16881e6i	−0.303387	+	0.933730i	0.676887	+	0.736087i	$0.263329\pi$
$457$	−1.35453e6	+	4.16881e6i	−0.303387	+	0.933730i	−0.980274	+	0.197643i	$0.936671\pi$
$458$	−669848.	−	2.06158e6i	−0.149215	−	0.459236i
$459$	−4.29957e6			−0.952562
$460$	−883100.			−0.194588
$461$	−1.58632e6	−	4.88220e6i	−0.347648	−	1.06995i	−0.960151	−	0.279482i	$-0.909837\pi$
$461$	−1.58632e6	−	4.88220e6i	−0.347648	−	1.06995i	0.612503	−	0.790468i	$-0.290163\pi$
$462$	3.21724e6	−	2.33746e6i	0.701259	−	0.509494i
$463$	−5.69887e6	−	4.14047e6i	−1.23548	−	0.897629i	−0.238192	−	0.971218i	$-0.576555\pi$
$463$	−5.69887e6	−	4.14047e6i	−1.23548	−	0.897629i	−0.997289	+	0.0735886i	$0.976555\pi$
$464$	−158061.			−0.0340823
$465$	1.69941e6	−	1.05472e6i	0.364473	−	0.226206i
$466$	−374361.			−0.0798593
$467$	−2.91343e6	−	2.11673e6i	−0.618177	−	0.449132i	0.234107	−	0.972211i	$-0.424783\pi$
$467$	−2.91343e6	−	2.11673e6i	−0.618177	−	0.449132i	−0.852284	+	0.523079i	$0.824783\pi$
$468$	−26078.4	+	18947.0i	−0.00550384	+	0.00399877i
$469$	−3.26996e6	−	1.00639e7i	−0.686452	−	2.11268i
$470$	−107457.			−0.0224382
$471$	7.59661e6			1.57786
$472$	605131.	+	1.86240e6i	0.125024	+	0.384785i
$473$	−1.35694e6	+	4.17623e6i	−0.278874	+	0.858286i
$474$	−80998.3	+	249287.i	−0.0165589	+	0.0509629i
$475$	3.92382e6	+	2.85082e6i	0.797950	+	0.579744i
$476$	795250.	+	2.44753e6i	0.160874	+	0.495120i
$477$	298371.	+	216779.i	0.0600428	+	0.0436236i
$478$	1.29085e6	−	937859.i	0.258409	−	0.187745i
$479$	−1.98049e6	+	6.09531e6i	−0.394396	+	1.21383i	0.535034	+	0.844830i	$0.320299\pi$
$479$	−1.98049e6	+	6.09531e6i	−0.394396	+	1.21383i	−0.929431	+	0.368997i	$0.879701\pi$
$480$	309675.	−	224992.i	0.0613484	−	0.0445722i
$481$	502065.	−	364771.i	0.0989457	−	0.0718883i
$482$	−330340.	+	1.01668e6i	−0.0647655	+	0.199328i
$483$	−3.75687e6	+	2.72952e6i	−0.732753	+	0.532376i
$484$	−635087.	−	461418.i	−0.123231	−	0.0895326i
$485$	−457624.	−	1.40842e6i	−0.0883394	−	0.271881i
$486$	−796683.	−	578824.i	−0.153001	−	0.111162i
$487$	2.80640e6	−	8.63722e6i	0.536201	−	1.65026i	−0.204839	−	0.978796i	$-0.565667\pi$
$487$	2.80640e6	−	8.63722e6i	0.536201	−	1.65026i	0.741040	−	0.671461i	$-0.234333\pi$
$488$	−120604.	+	371181.i	−0.0229251	+	0.0705563i
$489$	2.15315e6	+	6.62672e6i	0.407195	+	1.25322i
$490$	−573791.			−0.107960
$491$	−5.84006e6			−1.09323			−0.546617	−	0.837382i	$-0.684085\pi$
$491$	−5.84006e6			−1.09323			−0.546617	+	0.837382i	$0.684085\pi$
$492$	−230369.	−	709004.i	−0.0429054	−	0.132049i
$493$	537149.	−	390261.i	0.0995353	−	0.0723167i
$494$	392661.	+	285285.i	0.0723936	+	0.0525970i
$495$	−386746.			−0.0709435
$496$	−1.16383e6	+	722317.i	−0.212415	+	0.131833i
$497$	6.58205e6			1.19528
$498$	−4.24410e6	−	3.08352e6i	−0.766853	−	0.557151i
$499$	2.22348e6	−	1.61545e6i	0.399744	−	0.290431i	−0.369693	−	0.929154i	$-0.620537\pi$
$499$	2.22348e6	−	1.61545e6i	0.399744	−	0.290431i	0.769437	+	0.638723i	$0.220537\pi$
$500$	711904.	+	2.19101e6i	0.127349	+	0.391941i
$501$	7.02394e6			1.25022
$502$	−1.88398e6			−0.333670
$503$	−893483.	−	2.74986e6i	−0.157459	−	0.484608i	0.840943	−	0.541124i	$-0.182001\pi$
$503$	−893483.	−	2.74986e6i	−0.157459	−	0.484608i	−0.998402	+	0.0565157i	$0.982001\pi$
$504$	−96816.4	+	297970.i	−0.0169774	+	0.0522512i
$505$	−593642.	+	1.82704e6i	−0.103585	+	0.318801i
$506$	3.17596e6	+	2.30747e6i	0.551441	+	0.400645i
$507$	−1.64677e6	−	5.06825e6i	−0.284521	−	0.875664i
$508$	−4.58722e6	−	3.33281e6i	−0.788661	−	0.572996i
$509$	−2.80387e6	+	2.03713e6i	−0.479692	+	0.348517i	−0.801207	−	0.598388i	$-0.795808\pi$
$509$	−2.80387e6	+	2.03713e6i	−0.479692	+	0.348517i	0.321514	+	0.946905i	$0.395808\pi$
$510$	−496871.	+	1.52921e6i	−0.0845899	+	0.260341i
$511$	7.17728e6	−	5.21460e6i	1.21593	−	0.883423i
$512$	−212079.	+	154084.i	−0.0357538	+	0.0259767i
$513$	−2.43551e6	+	7.49573e6i	−0.408598	+	1.25754i
$514$	221047.	−	160600.i	0.0369044	−	0.0268126i
$515$	52223.2	+	37942.4i	0.00867652	+	0.00630386i
$516$	686819.	+	2.11381e6i	0.113558	+	0.349496i
$517$	386455.	+	280776.i	0.0635877	+	0.0461991i
$518$	1.86392e6	−	5.73657e6i	0.305214	−	0.939351i
$519$	−1.81413e6	+	5.58332e6i	−0.295631	+	0.909859i
$520$	31382.4	+	96585.2i	0.00508954	+	0.0156640i
$521$	−1.13537e7			−1.83250			−0.916249	−	0.400610i	$-0.868798\pi$
$521$	−1.13537e7			−1.83250			−0.916249	+	0.400610i	$0.868798\pi$
$522$	80831.8			0.0129839
$523$	409090.	+	1.25905e6i	0.0653980	+	0.201274i	0.978416	−	0.206645i	$-0.0662545\pi$
$523$	409090.	+	1.25905e6i	0.0653980	+	0.201274i	−0.913018	+	0.407919i	$0.866254\pi$
$524$	−490669.	+	356492.i	−0.0780656	+	0.0567180i
$525$	4.31730e6	+	3.13670e6i	0.683619	+	0.496678i
$526$	130261.			0.0205282
$527$	2.17168e6	−	5.32826e6i	0.340619	−	0.835716i
$528$	−1.70160e6			−0.265627
$529$	1.49844e6	+	1.08868e6i	0.232810	+	0.169146i
$530$	940023.	−	682967.i	0.145361	−	0.105611i
$531$	−309462.	−	952426.i	−0.0476290	−	0.146587i
$532$	4.71741e6			0.722644
$533$	197787.			0.0301564
$534$	763398.	+	2.34950e6i	0.115851	+	0.356551i
$535$	529739.	−	1.63037e6i	0.0800162	−	0.246264i
$536$	−1.39918e6	+	4.30624e6i	−0.210359	+	0.647420i
$537$	6.67609e6	+	4.85047e6i	0.999049	+	0.725851i
$538$	1.78740e6	+	5.50104e6i	0.266235	+	0.819387i
$539$	2.06357e6	+	1.49927e6i	0.305948	+	0.222284i
$540$	−1.33417e6	+	969328.i	−0.196891	+	0.143049i
$541$	−2.79061e6	+	8.58861e6i	−0.409926	+	1.26162i	0.506785	+	0.862073i	$0.330834\pi$
$541$	−2.79061e6	+	8.58861e6i	−0.409926	+	1.26162i	−0.916711	+	0.399551i	$0.869166\pi$
$542$	214079.	−	155537.i	0.0313022	−	0.0227424i
$543$	1.19564e6	−	868680.i	0.174020	−	0.126433i
$544$	340279.	−	1.04727e6i	0.0492990	−	0.151727i
$545$	2.64145e6	−	1.91913e6i	0.380935	−	0.276766i
$546$	432036.	+	313893.i	0.0620210	+	0.0450609i
$547$	3.70676e6	+	1.14082e7i	0.529695	+	1.63023i	0.754840	+	0.655909i	$0.227714\pi$
$547$	3.70676e6	+	1.14082e7i	0.529695	+	1.63023i	−0.225145	+	0.974325i	$0.572286\pi$
$548$	243485.	+	176903.i	0.0346355	+	0.0251642i
$549$	61676.4	−	189821.i	0.00873350	−	0.0268789i
$550$	1.39408e6	−	4.29053e6i	0.196508	−	0.604789i
$551$	−376099.	−	1.15751e6i	−0.0527743	−	0.162423i
$552$	1.98701e6			0.277557
$553$	−675916.			−0.0939897
$554$	−25730.1	−	79189.1i	−0.00356178	−	0.0109620i
$555$	3.04891e6	−	2.21516e6i	0.420157	−	0.305262i
$556$	2.26063e6	+	1.64244e6i	0.310129	+	0.225322i
$557$	−1.46323e6			−0.199837			−0.0999183	−	0.994996i	$-0.531858\pi$
$557$	−1.46323e6			−0.199837			−0.0999183	+	0.994996i	$0.531858\pi$
$558$	595178.	−	369390.i	0.0809211	−	0.0502227i
$559$	−589679.			−0.0798152
$560$	798557.	+	580186.i	0.107606	+	0.0781802i
$561$	5.78266e6	−	4.20135e6i	0.775747	−	0.563613i
$562$	1.39133e6	+	4.28207e6i	0.185819	+	0.571891i
$563$	−970719.			−0.129069			−0.0645346	−	0.997915i	$-0.520556\pi$
$563$	−970719.			−0.129069			−0.0645346	+	0.997915i	$0.520556\pi$
$564$	241782.			0.0320056
$565$	409204.	+	1.25940e6i	0.0539285	+	0.165975i
$566$	−2.78817e6	+	8.58111e6i	−0.365829	+	1.12591i
$567$	−2.31214e6	+	7.11603e6i	−0.302034	+	0.929566i
$568$	−2.27851e6	−	1.65543e6i	−0.296333	−	0.215298i
$569$	3.96359e6	+	1.21987e7i	0.513225	+	1.57955i	0.786488	+	0.617606i	$0.211897\pi$
$569$	3.96359e6	+	1.21987e7i	0.513225	+	1.57955i	−0.273262	+	0.961940i	$0.588103\pi$
$570$	2.38452e6	+	1.73246e6i	0.307408	+	0.223345i
$571$	−1.06394e7	+	7.72996e6i	−1.36561	+	0.992173i	−0.367543	+	0.930007i	$0.619801\pi$
$571$	−1.06394e7	+	7.72996e6i	−1.36561	+	0.992173i	−0.998066	+	0.0621660i	$0.980199\pi$
$572$	139507.	−	429357.i	0.0178281	−	0.0548692i
$573$	9.39038e6	−	6.82251e6i	1.19480	−	0.868076i
$574$	1.55525e6	−	1.12995e6i	0.197024	−	0.143146i
$575$	−1.62791e6	+	5.01018e6i	−0.205333	+	0.631951i
$576$	108456.	−	78798.2i	0.0136207	−	0.00989601i
$577$	−4.01756e6	−	2.91892e6i	−0.502368	−	0.364992i	0.307552	−	0.951531i	$-0.400490\pi$
$577$	−4.01756e6	−	2.91892e6i	−0.502368	−	0.364992i	−0.809921	+	0.586539i	$0.800490\pi$
$578$	−325659.	−	1.00228e6i	−0.0405456	−	0.124787i
$579$	−129762.	−	94277.6i	−0.0160861	−	0.0116872i
$580$	78694.8	−	242198.i	0.00971351	−	0.0298951i
$581$	4.18032e6	−	1.28657e7i	0.513770	−	1.58122i
$582$	1.02967e6	+	3.16900e6i	0.126006	+	0.387806i
$583$	−5.16522e6			−0.629387
$584$	−3.79607e6			−0.460576
$585$	−16048.9	−	49393.4i	−0.00193890	−	0.00596731i
$586$	2.10553e6	−	1.52976e6i	0.253290	−	0.184026i
$587$	1.15429e7	+	8.38640e6i	1.38267	+	1.00457i	0.996625	+	0.0820910i	$0.0261598\pi$
$587$	1.15429e7	+	8.38640e6i	1.38267	+	1.00457i	0.386047	+	0.922479i	$0.373840\pi$
$588$	1.29105e6			0.153993
$589$	−8.05896e6	−	6.80424e6i	−0.957173	−	0.808149i
$590$	−3.15505e6			−0.373144
$591$	−1.11303e7	−	8.08666e6i	−1.31081	−	0.952359i
$592$	−2.08802e6	+	1.51704e6i	−0.244867	+	0.177906i
$593$	−3.85770e6	−	1.18728e7i	−0.450497	−	1.38649i	−0.876341	−	0.481691i	$-0.840023\pi$
$593$	−3.85770e6	−	1.18728e7i	−0.450497	−	1.38649i	0.425844	−	0.904796i	$-0.359977\pi$
$594$	7.33095e6			0.852499
$595$	−4.14630e6			−0.480141
$596$	1.79572e6	+	5.52665e6i	0.207073	+	0.637304i
$597$	4.32705e6	−	1.33173e7i	0.496885	−	1.52925i
$598$	−162906.	+	501373.i	−0.0186288	+	0.0573335i
$599$	−8.53571e6	−	6.20156e6i	−0.972014	−	0.706209i	−0.0161043	−	0.999870i	$-0.505126\pi$
$599$	−8.53571e6	−	6.20156e6i	−0.972014	−	0.706209i	−0.955910	+	0.293661i	$0.905126\pi$
$600$	−705616.	−	2.17166e6i	−0.0800185	−	0.246272i
$601$	−245509.	−	178373.i	−0.0277256	−	0.0201439i	0.573836	−	0.818970i	$-0.305455\pi$
$601$	−245509.	−	178373.i	−0.0277256	−	0.0201439i	−0.601562	+	0.798826i	$0.705455\pi$
$602$	−4.63678e6	+	3.36882e6i	−0.521466	+	0.378867i
$603$	715536.	−	2.20219e6i	0.0801380	−	0.246639i
$604$	−2.56182e6	+	1.86127e6i	−0.285730	+	0.207595i
$605$	1.02323e6	−	743420.i	0.113654	−	0.0825745i
$606$	1.33572e6	−	4.11091e6i	0.147752	−	0.454733i
$607$	−3.89998e6	+	2.83350e6i	−0.429626	+	0.312141i	−0.781499	−	0.623906i	$-0.785545\pi$
$607$	−3.89998e6	+	2.83350e6i	−0.429626	+	0.312141i	0.351873	+	0.936048i	$0.385545\pi$
$608$	−1.63302e6	−	1.18646e6i	−0.179157	−	0.130165i
$609$	−413813.	−	1.27359e6i	−0.0452128	−	0.139151i
$610$	−508717.	−	369605.i	−0.0553543	−	0.0402173i
$611$	−19822.6	+	61007.7i	−0.00214812	+	0.00661122i
$612$	−174018.	+	535571.i	−0.0187808	+	0.0578014i
$613$	−3.70146e6	−	1.13919e7i	−0.397852	−	1.22446i	−0.926718	−	0.375758i	$-0.877382\pi$
$613$	−3.70146e6	−	1.13919e7i	−0.397852	−	1.22446i	0.528866	−	0.848706i	$-0.322618\pi$
$614$	−1.31366e7			−1.40625
$615$	1.20111e6			0.128054
$616$	−1.35593e6	−	4.17314e6i	−0.143975	−	0.443109i
$617$	6.13808e6	−	4.45958e6i	0.649113	−	0.471608i	−0.213856	−	0.976865i	$-0.568602\pi$
$617$	6.13808e6	−	4.45958e6i	0.649113	−	0.471608i	0.862969	+	0.505257i	$0.168602\pi$
$618$	−117504.	−	85371.8i	−0.0123761	−	0.00899173i
$619$	1.05526e7			1.10696			0.553482	−	0.832861i	$-0.313299\pi$
$619$	1.05526e7			1.10696			0.553482	+	0.832861i	$0.313299\pi$
$620$	−527368.	−	2.14297e6i	−0.0550979	−	0.223891i
$621$	−8.56057e6			−0.890786
$622$	−6.53416e6	−	4.74734e6i	−0.677195	−	0.492011i
$623$	−5.15378e6	+	3.74444e6i	−0.531993	+	0.386515i
$624$	−70611.6	−	217320.i	−0.00725964	−	0.0223429i
$625$	3.97720e6			0.407265
$626$	3.13994e6			0.320248
$627$	−4.04888e6	−	1.24612e7i	−0.411307	−	1.26587i
$628$	2.59020e6	−	7.97181e6i	0.262080	−	0.806599i
$629$	3.35021e6	−	1.03109e7i	0.337634	−	1.03913i
$630$	−408379.	−	296705.i	−0.0409933	−	0.0297833i
$631$	−1.96775e6	−	6.05612e6i	−0.196742	−	0.605509i	−0.999952	−	0.00981335i	$-0.996876\pi$
$631$	−1.96775e6	−	6.05612e6i	−0.196742	−	0.605509i	0.803210	−	0.595696i	$-0.203124\pi$
$632$	233982.	+	169998.i	0.0233018	+	0.0169297i
$633$	−3.71614e6	+	2.69994e6i	−0.368624	+	0.267821i
$634$	−4.12454e6	+	1.26940e7i	−0.407523	+	1.25423i
$635$	7.39076e6	−	5.36970e6i	0.727369	−	0.528465i
$636$	−2.11509e6	+	1.53670e6i	−0.207341	+	0.150642i
$637$	−105848.	+	325765.i	−0.0103355	+	0.0318095i
$638$	−915861.	+	665412.i	−0.0890795	+	0.0647201i
$639$	1.16522e6	+	846583.i	0.112890	+	0.0820195i
$640$	−130515.	−	401685.i	−0.0125954	−	0.0387647i
$641$	1.00518e7	+	7.30308e6i	0.966273	+	0.702038i	0.954599	−	0.297894i	$-0.0962840\pi$
$641$	1.00518e7	+	7.30308e6i	0.966273	+	0.702038i	0.0116738	+	0.999932i	$0.496284\pi$
$642$	−1.19193e6	+	3.66839e6i	−0.114134	+	0.351268i
$643$	4.67456e6	−	1.43868e7i	0.445875	−	1.37226i	−0.435646	−	0.900118i	$-0.643480\pi$
$643$	4.67456e6	−	1.43868e7i	0.445875	−	1.37226i	0.881521	−	0.472144i	$-0.156520\pi$
$644$	1.58336e6	+	4.87310e6i	0.150441	+	0.463010i
$645$	−3.58096e6			−0.338923
$646$	8.47906e6			0.799404
$647$	3.18239e6	+	9.79438e6i	0.298877	+	0.919848i	0.981892	+	0.189444i	$0.0606685\pi$
$647$	3.18239e6	+	9.79438e6i	0.298877	+	0.919848i	−0.683015	+	0.730405i	$0.739332\pi$
$648$	2.59013e6	−	1.88184e6i	0.242317	−	0.176053i
$649$	1.13468e7	+	8.24392e6i	1.05745	+	0.768284i
$650$	605817.			0.0562416
$651$	−8.86710e6	−	7.48656e6i	−0.820029	−	0.692357i
$652$	7.68817e6			0.708278
$653$	−3.09736e6	−	2.25037e6i	−0.284256	−	0.206524i	0.436516	−	0.899697i	$-0.356212\pi$
$653$	−3.09736e6	−	2.25037e6i	−0.284256	−	0.206524i	−0.720772	+	0.693173i	$0.756212\pi$
$654$	−5.94336e6	+	4.31810e6i	−0.543360	+	0.394774i
$655$	−301962.	−	929344.i	−0.0275011	−	0.0846396i
$656$	−822570.			−0.0746300
$657$	1.94130e6			0.175460
$658$	192666.	+	592965.i	0.0173476	+	0.0533905i
$659$	−1.31993e6	+	4.06232e6i	−0.118396	+	0.364385i	−0.992640	−	0.121101i	$-0.961357\pi$
$659$	−1.31993e6	+	4.06232e6i	−0.118396	+	0.364385i	0.874244	+	0.485486i	$0.161357\pi$
$660$	847187.	−	2.60737e6i	0.0757041	−	0.232993i
$661$	−4.81427e6	−	3.49777e6i	−0.428575	−	0.311378i	0.352504	−	0.935810i	$-0.385330\pi$
$661$	−4.81427e6	−	3.49777e6i	−0.428575	−	0.311378i	−0.781079	+	0.624432i	$0.785330\pi$
$662$	785580.	+	2.41777e6i	0.0696700	+	0.214422i
$663$	776541.	+	564190.i	0.0686089	+	0.0498473i
$664$	−4.68291e6	+	3.40234e6i	−0.412189	+	0.299473i
$665$	−2.34869e6	+	7.22852e6i	−0.205955	+	0.633863i
$666$	1.06781e6	−	775808.i	0.0932840	−	0.0677748i
$667$	1.06948e6	−	777022.i	0.0930802	−	0.0676267i
$668$	2.39494e6	−	7.37085e6i	0.207660	−	0.639111i
$669$	−6.18329e6	+	4.49242e6i	−0.534139	+	0.388075i
$670$	−5.90186e6	−	4.28795e6i	−0.507928	−	0.369031i
$671$	863792.	+	2.65848e6i	0.0740632	+	0.227943i
$672$	−1.79678e6	−	1.30544e6i	−0.153487	−	0.111515i
$673$	−2.41401e6	+	7.42956e6i	−0.205448	+	0.632303i	0.794247	+	0.607595i	$0.207866\pi$
$673$	−2.41401e6	+	7.42956e6i	−0.205448	+	0.632303i	−0.999695	+	0.0247082i	$0.992134\pi$
$674$	3.52696e6	−	1.08549e7i	0.299055	−	0.920397i
$675$	3.03999e6	+	9.35611e6i	0.256810	+	0.790380i
$676$	−5.88006e6			−0.494898
$677$	5.45537e6			0.457460			0.228730	−	0.973490i	$-0.426543\pi$
$677$	5.45537e6			0.457460			0.228730	+	0.973490i	$0.426543\pi$
$678$	−920723.	−	2.83369e6i	−0.0769227	−	0.236744i
$679$	−6.95141e6	+	5.05050e6i	−0.578627	+	0.420397i
$680$	1.43532e6	+	1.04282e6i	0.119036	+	0.0864846i
$681$	1.66076e7			1.37227
$682$	−3.70280e6	+	9.08491e6i	−0.304838	+	0.747928i
$683$	−6.17141e6			−0.506212			−0.253106	−	0.967439i	$-0.581452\pi$
$683$	−6.17141e6			−0.506212			−0.253106	+	0.967439i	$0.581452\pi$
$684$	835123.	+	606753.i	0.0682512	+	0.0495874i
$685$	−392295.	+	285019.i	−0.0319438	+	0.0232085i
$686$	−2.07850e6	−	6.39696e6i	−0.168632	−	0.518996i
$687$	−7.85820e6			−0.635230
$688$	2.45240e6			0.197524
$689$	−214342.	−	659678.i	−0.0172013	−	0.0529400i
$690$	−989285.	+	3.04471e6i	−0.0791041	+	0.243457i
$691$	−5.28327e6	+	1.62602e7i	−0.420928	+	1.29548i	0.485913	+	0.874007i	$0.338487\pi$
$691$	−5.28327e6	+	1.62602e7i	−0.420928	+	1.29548i	−0.906840	+	0.421474i	$0.861513\pi$
$692$	5.24052e6	+	3.80746e6i	0.416015	+	0.302253i
$693$	693420.	+	2.13413e6i	0.0548483	+	0.168806i
$694$	−7.10740e6	−	5.16383e6i	−0.560160	−	0.406980i
$695$	−3.64225e6	+	2.64625e6i	−0.286027	+	0.207811i
$696$	−177066.	+	544954.i	−0.0138552	+	0.0426419i
$697$	2.79540e6	−	2.03097e6i	0.217952	−	0.158352i
$698$	7.48714e6	−	5.43973e6i	0.581671	−	0.422609i
$699$	−419375.	+	1.29070e6i	−0.0324645	+	0.0999156i
$700$	4.76368e6	−	3.46102e6i	0.367450	−	0.266968i
$701$	1.27450e6	+	925980.i	0.0979593	+	0.0711716i	0.635687	−	0.771947i	$-0.280717\pi$
$701$	1.27450e6	+	925980.i	0.0979593	+	0.0711716i	−0.537727	+	0.843119i	$0.680717\pi$
$702$	304214.	+	936275.i	0.0232990	+	0.0717068i
$703$	−1.60779e7	−	1.16813e7i	−1.22699	−	0.891462i
$704$	−580190.	+	1.78564e6i	−0.0441203	+	0.135788i
$705$	−120377.	+	370484.i	−0.00912163	+	0.0280735i
$706$	4.46966e6	+	1.37562e7i	0.337491	+	1.03869i
$707$	1.11463e7			0.838654
$708$	7.09899e6			0.532247
$709$	6.16467e6	+	1.89729e7i	0.460568	+	1.41748i	0.864471	+	0.502682i	$0.167653\pi$
$709$	6.16467e6	+	1.89729e7i	0.460568	+	1.41748i	−0.403903	+	0.914802i	$0.632347\pi$
$710$	3.67105e6	−	2.66717e6i	0.273303	−	0.198566i
$711$	−119658.	−	86936.3i	−0.00887699	−	0.00644951i
$712$	2.72584e6			0.201511
$713$	4.32387e6	−	1.06087e7i	0.318529	−	0.781518i
$714$	9.32933e6			0.684865
$715$	588450.	+	427534.i	0.0430472	+	0.0312756i
$716$	7.36636e6	−	5.35198e6i	0.536995	−	0.390150i
$717$	−1.78744e6	−	5.50117e6i	−0.129847	−	0.399629i
$718$	−799712.			−0.0578925
$719$	1.88795e7			1.36197			0.680985	−	0.732298i	$-0.261552\pi$
$719$	1.88795e7			1.36197			0.680985	+	0.732298i	$0.261552\pi$
$720$	66745.2	+	205421.i	0.00479831	+	0.0147677i
$721$	115738.	−	356206.i	0.00829161	−	0.0255190i
$722$	1.74237e6	−	5.36247e6i	0.124394	−	0.382844i
$723$	3.13520e6	+	2.27786e6i	0.223059	+	0.162062i
$724$	−503911.	−	1.55088e6i	−0.0357279	−	0.109959i
$725$	−1.22902e6	−	892935.i	−0.0868388	−	0.0630920i
$726$	−2.30230e6	+	1.67272e6i	−0.162114	+	0.117783i
$727$	−103221.	+	317682.i	−0.00724324	+	0.0222924i	−0.954613	−	0.297850i	$-0.903731\pi$
$727$	−103221.	+	317682.i	−0.00724324	+	0.0222924i	0.947370	+	0.320142i	$0.103731\pi$
$728$	476706.	−	346347.i	0.0333367	−	0.0242205i
$729$	−1.27225e7	+	9.24344e6i	−0.886653	+	0.644191i
$730$	1.88997e6	−	5.81674e6i	0.131265	−	0.403992i
$731$	−8.33414e6	+	6.05511e6i	−0.576856	+	0.419111i
$732$	1.14463e6	+	831624.i	0.0789565	+	0.0573653i
$733$	3.33422e6	+	1.02617e7i	0.229211	+	0.705438i	0.997837	+	0.0657396i	$0.0209407\pi$
$733$	3.33422e6	+	1.02617e7i	0.229211	+	0.705438i	−0.768626	+	0.639698i	$0.779059\pi$
$734$	−6.95338e6	−	5.05192e6i	−0.476382	−	0.346112i
$735$	−642784.	+	1.97829e6i	−0.0438881	+	0.135074i
$736$	677505.	−	2.08515e6i	0.0461018	−	0.141887i
$737$	1.00212e7	+	3.08422e7i	0.679599	+	2.09159i
$738$	420660.			0.0284309
$739$	−1.59118e7			−1.07179			−0.535893	−	0.844286i	$-0.680025\pi$
$739$	−1.59118e7			−1.07179			−0.535893	+	0.844286i	$0.680025\pi$
$740$	−1.28499e6	−	3.95479e6i	−0.0862621	−	0.265488i
$741$	1.42346e6	−	1.03421e6i	0.0952360	−	0.0691930i
$742$	−5.45415e6	−	3.96267e6i	−0.363678	−	0.264228i
$743$	1.54649e7			1.02772			0.513860	−	0.857874i	$-0.328215\pi$
$743$	1.54649e7			1.02772			0.513860	+	0.857874i	$0.328215\pi$
$744$	1.18660e6	+	4.82176e6i	0.0785907	+	0.319355i
$745$	−9.36258e6			−0.618023
$746$	−1.59679e7	−	1.16013e7i	−1.05051	−	0.763240i
$747$	2.39483e6	−	1.73994e6i	0.157026	−	0.114086i
$748$	−2.43715e6	−	7.50079e6i	−0.159268	−	0.490177i
$749$	−9.94646e6			−0.647835
$750$	8.35157e6			0.542144
$751$	8.64339e6	+	2.66016e7i	0.559222	+	1.72111i	0.684524	+	0.728991i	$0.260010\pi$
$751$	8.64339e6	+	2.66016e7i	0.559222	+	1.72111i	−0.125301	+	0.992119i	$0.539990\pi$
$752$	82439.7	−	253723.i	0.00531608	−	0.0163612i
$753$	−2.11051e6	+	6.49549e6i	−0.135644	+	0.417469i
$754$	−122989.	−	89356.8i	−0.00787840	−	0.00572399i
$755$	−1.57657e6	−	4.85218e6i	−0.100657	−	0.309791i
$756$	7.74103e6	+	5.62418e6i	0.492600	+	0.357895i
$757$	9.07310e6	−	6.59199e6i	0.575461	−	0.418097i	−0.261624	−	0.965170i	$-0.584258\pi$
$757$	9.07310e6	−	6.59199e6i	0.575461	−	0.418097i	0.837085	+	0.547073i	$0.184258\pi$
$758$	3.84220e6	−	1.18251e7i	0.242888	−	0.747533i
$759$	1.15134e7	−	8.36500e6i	0.725438	−	0.527062i
$760$	2.63107e6	−	1.91158e6i	0.165234	−	0.120049i
$761$	−1.96558e6	+	6.04945e6i	−0.123035	+	0.378664i	−0.993538	−	0.113500i	$-0.963794\pi$
$761$	−1.96558e6	+	6.04945e6i	−0.123035	+	0.378664i	0.870503	+	0.492164i	$0.163794\pi$
$762$	−1.66295e7	+	1.20820e7i	−1.03751	+	0.753794i
$763$	−1.53261e7	−	1.11351e7i	−0.953059	−	0.692438i
$764$	−3.95766e6	−	1.21804e7i	−0.245304	−	0.754969i
$765$	−734020.	−	533297.i	−0.0453476	−	0.0329470i
$766$	−5.48195e6	+	1.68717e7i	−0.337569	+	1.03893i
$767$	−582015.	+	1.79126e6i	−0.0357228	+	0.109944i
$768$	293665.	+	903807.i	0.0179659	+	0.0552933i
$769$	1.27697e7			0.778692			0.389346	−	0.921092i	$-0.372701\pi$
$769$	1.27697e7			0.778692			0.389346	+	0.921092i	$0.372701\pi$
$770$	7.06962e6			0.429704
$771$	−306083.	−	942027.i	−0.0185440	−	0.0570726i
$772$	−143179.	+	104025.i	−0.00864639	+	0.00628197i
$773$	2.41613e7	+	1.75542e7i	1.45436	+	1.05665i	0.984788	+	0.173760i	$0.0555918\pi$
$773$	2.41613e7	+	1.75542e7i	1.45436	+	1.05665i	0.469572	+	0.882894i	$0.344408\pi$
$774$	−1.25415e6			−0.0752482
$775$	−1.31301e7	−	958379.i	−0.785259	−	0.0573169i
$776$	3.67660e6			0.219176
$777$	−1.76902e7	−	1.28527e7i	−1.05119	−	0.763733i
$778$	1.32002e7	−	9.59048e6i	0.781862	−	0.568056i
$779$	−1.95727e6	−	6.02385e6i	−0.115560	−	0.355656i
$780$	368157.			0.0216669
$781$	−2.01716e7			−1.18335
$782$	2.84594e6	+	8.75889e6i	0.166421	+	0.512191i
$783$	762850.	−	2.34781e6i	0.0444667	−	0.136854i
$784$	440206.	−	1.35482e6i	0.0255780	−	0.0787209i
$785$	1.09257e7	+	7.93796e6i	0.632810	+	0.459764i
$786$	679426.	+	2.09106e6i	0.0392271	+	0.120729i
$787$	−1.42097e7	−	1.03239e7i	−0.817801	−	0.594167i	0.0982805	−	0.995159i	$-0.468666\pi$
$787$	−1.42097e7	−	1.03239e7i	−0.817801	−	0.594167i	−0.916082	+	0.400991i	$0.868666\pi$
$788$	−1.22811e7	+	8.92278e6i	−0.704569	+	0.511899i
$789$	145924.	−	449109.i	0.00834517	−	0.0256838i
$790$	−376983.	+	273894.i	−0.0214909	+	0.0156140i
$791$	6.21589e6	−	4.51611e6i	0.353234	−	0.256639i
$792$	296707.	−	913171.i	0.0168080	−	0.0517296i
$793$	−303684.	+	220639.i	−0.0171490	+	0.0124595i
$794$	1.19546e7	+	8.68553e6i	0.672952	+	0.488928i
$795$	−1.30165e6	−	4.00605e6i	−0.0730424	−	0.224801i
$796$	−1.24996e7	−	9.08152e6i	−0.699222	−	0.508014i
$797$	2.68002e6	−	8.24825e6i	0.149449	−	0.459955i	−0.848108	−	0.529824i	$-0.822258\pi$
$797$	2.68002e6	−	8.24825e6i	0.149449	−	0.459955i	0.997556	+	0.0698685i	$0.0222580\pi$
$798$	5.28464e6	−	1.62644e7i	0.293770	−	0.904132i
$799$	346297.	+	1.06579e6i	0.0191903	+	0.0590617i
$800$	−2.51951e6			−0.139185
$801$	−1.39398e6			−0.0767673
$802$	−898330.	−	2.76477e6i	−0.0493174	−	0.151783i
$803$	−2.19958e7	+	1.59809e7i	−1.20379	+	0.874604i
$804$	1.32794e7	+	9.64805e6i	0.724500	+	0.526380i
$805$	−8.25540e6			−0.449002
$806$	−1.31394e6	−	95905.8i	−0.0712422	−	0.00520005i
$807$	2.09685e7			1.13340
$808$	−3.85852e6	−	2.80338e6i	−0.207918	−	0.151061i
$809$	1.62390e7	−	1.17983e7i	0.872342	−	0.633794i	−0.0588723	−	0.998266i	$-0.518750\pi$
$809$	1.62390e7	−	1.17983e7i	0.872342	−	0.633794i	0.931214	+	0.364472i	$0.118750\pi$
$810$	1.59399e6	+	4.90579e6i	0.0853636	+	0.262722i
$811$	−3.24625e7			−1.73313			−0.866563	−	0.499067i	$-0.833676\pi$
$811$	−3.24625e7			−1.73313			−0.866563	+	0.499067i	$0.833676\pi$
$812$	−1.47759e6			−0.0786435
$813$	−296433.	−	912328.i	−0.0157290	−	0.0484088i
$814$	−5.71225e6	+	1.75805e7i	−0.302167	+	0.929973i
$815$	−3.82776e6	+	1.17806e7i	−0.201860	+	0.621262i
$816$	−3.22953e6	−	2.34639e6i	−0.169791	−	0.123360i
$817$	5.83537e6	+	1.79594e7i	0.305853	+	0.941319i
$818$	−6.63357e6	−	4.81957e6i	−0.346629	−	0.251840i
$819$	−243786.	+	177121.i	−0.0126999	+	0.00922699i
$820$	409539.	−	1.26043e6i	0.0212697	−	0.0654613i
$821$	2.00237e7	−	1.45481e7i	1.03678	−	0.753265i	0.0671262	−	0.997744i	$-0.478617\pi$
$821$	2.00237e7	−	1.45481e7i	1.03678	−	0.753265i	0.969655	+	0.244479i	$0.0786170\pi$
$822$	882678.	−	641303.i	0.0455641	−	0.0331043i
$823$	−950748.	+	2.92610e6i	−0.0489290	+	0.150588i	−0.972536	−	0.232753i	$-0.925227\pi$
$823$	−950748.	+	2.92610e6i	−0.0489290	+	0.150588i	0.923607	+	0.383341i	$0.125227\pi$
$824$	−129653.	+	94198.7i	−0.00665221	+	0.00483311i
$825$	−1.32310e7	−	9.61286e6i	−0.676794	−	0.491720i
$826$	5.65689e6	+	1.74101e7i	0.288488	+	0.887875i
$827$	5.04265e6	+	3.66370e6i	0.256386	+	0.186276i	0.708552	−	0.705658i	$-0.249349\pi$
$827$	5.04265e6	+	3.66370e6i	0.256386	+	0.186276i	−0.452166	+	0.891934i	$0.649349\pi$
$828$	−346474.	+	1.06634e6i	−0.0175628	+	0.0540528i
$829$	5.70163e6	−	1.75478e7i	0.288146	−	0.886822i	−0.697292	−	0.716787i	$-0.745612\pi$
$829$	5.70163e6	−	1.75478e7i	0.288146	−	0.886822i	0.985438	−	0.170035i	$-0.0543881\pi$
$830$	−2.88191e6	−	8.86961e6i	−0.145206	−	0.446899i
$831$	−301848.			−0.0151630
$832$	−252130.			−0.0126275
$833$	1.84914e6	+	5.69106e6i	0.0923329	+	0.284171i
$834$	8.19519e6	−	5.95415e6i	0.407985	−	0.296418i
$835$	1.01020e7	+	7.33956e6i	0.501410	+	0.364295i
$836$	−1.44572e7			−0.715430
$837$	−5.11218e6	−	2.07735e7i	−0.252228	−	1.02493i
$838$	−8.06205e6			−0.396584
$839$	4.17233e6	+	3.03138e6i	0.204632	+	0.148674i	0.685382	−	0.728184i	$-0.259635\pi$
$839$	4.17233e6	+	3.03138e6i	0.204632	+	0.148674i	−0.480749	+	0.876858i	$0.659635\pi$
$840$	2.89491e6	−	2.10328e6i	0.141559	−	0.102848i
$841$	−6.22049e6	−	1.91447e7i	−0.303274	−	0.933380i
$842$	−2.60383e6			−0.126570
$843$	1.63221e7			0.791057
$844$	1.56620e6	+	4.82028e6i	0.0756819	+	0.232925i
$845$	2.92755e6	−	9.01007e6i	0.141047	−	0.434097i
$846$	−42159.4	+	129753.i	−0.00202520	+	0.00623293i
$847$	−5.93693e6	−	4.31343e6i	−0.284350	−	0.206593i
$848$	891422.	+	2.74352e6i	0.0425690	+	0.131014i
$849$	2.64621e7	+	1.92258e7i	1.25996	+	0.915411i
$850$	8.56223e6	−	6.22083e6i	0.406481	−	0.295325i
$851$	6.67037e6	−	2.05293e7i	0.315737	−	0.971740i
$852$	−8.25999e6	+	6.00124e6i	−0.389835	+	0.283232i
$853$	−2.44497e6	+	1.77638e6i	−0.115054	+	0.0835915i	−0.643824	−	0.765173i	$-0.722653\pi$
$853$	−2.44497e6	+	1.77638e6i	−0.115054	+	0.0835915i	0.528770	+	0.848765i	$0.322653\pi$
$854$	−1.12743e6	+	3.46987e6i	−0.0528987	+	0.162806i
$855$	−1.34552e6	+	977578.i	−0.0629470	+	0.0457337i
$856$	3.44316e6	+	2.50161e6i	0.160610	+	0.116690i
$857$	−8.09813e6	−	2.49235e7i	−0.376646	−	1.15920i	−0.942362	−	0.334596i	$-0.891400\pi$
$857$	−8.09813e6	−	2.49235e7i	−0.376646	−	1.15920i	0.565716	−	0.824600i	$-0.308600\pi$
$858$	−1.32403e6	−	961967.i	−0.0614018	−	0.0446110i
$859$	9.77916e6	−	3.00972e7i	0.452188	−	1.39169i	−0.422217	−	0.906495i	$-0.638748\pi$
$859$	9.77916e6	−	3.00972e7i	0.452188	−	1.39169i	0.874405	−	0.485196i	$-0.161252\pi$
$860$	−1.22099e6	+	3.75783e6i	−0.0562946	+	0.173257i
$861$	−2.15354e6	−	6.62792e6i	−0.0990023	−	0.304698i
$862$	−4.75582e6			−0.218000
$863$	9.52312e6			0.435263			0.217632	−	0.976031i	$-0.430167\pi$
$863$	9.52312e6			0.435263			0.217632	+	0.976031i	$0.430167\pi$
$864$	−1.26519e6	−	3.89384e6i	−0.0576594	−	0.177457i
$865$	−8.44333e6	+	6.13444e6i	−0.383684	+	0.278763i
$866$	−2.07355e7	−	1.50652e7i	−0.939550	−	0.682623i
$867$	−3.82042e6			−0.172609
$868$	−1.08797e7	+	6.75237e6i	−0.490138	+	0.304198i
$869$	2.07144e6			0.0930513
$870$	−746880.	−	542640.i	−0.0334544	−	0.0243060i
$871$	−3.52317e6	+	2.55973e6i	−0.157358	+	0.114327i
$872$	2.50488e6	+	7.70924e6i	0.111557	+	0.343337i
$873$	−1.88020e6			−0.0834967
$874$	1.68821e7			0.747561
$875$	6.65503e6	+	2.04821e7i	0.293853	+	0.904385i
$876$	−4.25251e6	+	1.30879e7i	−0.187234	+	0.576248i
$877$	−131218.	+	403846.i	−0.00576094	+	0.0177303i	−0.953896	−	0.300138i	$-0.902967\pi$
$877$	−131218.	+	403846.i	−0.00576094	+	0.0177303i	0.948135	+	0.317869i	$0.102967\pi$
$878$	−1.71791e7	−	1.24813e7i	−0.752079	−	0.546417i
$879$	−2.91552e6	−	8.97304e6i	−0.127275	−	0.391712i
$880$	−2.44729e6	−	1.77806e6i	−0.106532	−	0.0773997i
$881$	2.67812e7	−	1.94577e7i	1.16249	−	0.844601i	0.172403	−	0.985027i	$-0.444847\pi$
$881$	2.67812e7	−	1.94577e7i	1.16249	−	0.844601i	0.990091	+	0.140425i	$0.0448470\pi$
$882$	−225120.	+	692848.i	−0.00974412	+	0.0299893i
$883$	2.21200e7	−	1.60711e7i	0.954736	−	0.693656i	0.00281376	−	0.999996i	$-0.499104\pi$
$883$	2.21200e7	−	1.60711e7i	0.954736	−	0.693656i	0.951922	+	0.306340i	$0.0991044\pi$
$884$	856831.	−	622524.i	0.0368777	−	0.0267932i
$885$	−3.53442e6	+	1.08778e7i	−0.151691	+	0.466857i
$886$	2.51122e7	−	1.82451e7i	1.07473	−	0.780838i
$887$	−3.46536e7	−	2.51773e7i	−1.47890	−	1.07449i	−0.977908	−	0.209036i	$-0.932967\pi$
$887$	−3.46536e7	−	2.51773e7i	−1.47890	−	1.07449i	−0.500996	−	0.865450i	$-0.667033\pi$
$888$	2.89127e6	+	8.89842e6i	0.123043	+	0.378687i
$889$	−4.28823e7	−	3.11558e7i	−1.81980	−	1.32216i
$890$	−1.35713e6	+	4.17682e6i	−0.0574310	+	0.176755i
$891$	7.08587e6	−	2.18081e7i	0.299019	−	0.920286i
$892$	2.60600e6	+	8.02045e6i	0.109664	+	0.337510i
$893$	2.05423e6			0.0862026
$894$	2.10662e7			0.881539
$895$	4.53333e6	+	1.39522e7i	0.189173	+	0.582216i
$896$	−1.98256e6	+	1.44041e6i	−0.0825004	+	0.0599401i
$897$	1.54611e6	+	1.12332e6i	0.0641595	+	0.0466146i
$898$	−2.74983e6			−0.113793
$899$	2.52422e6	+	2.13122e6i	0.104167	+	0.0879488i
$900$	1.28847e6			0.0530235
$901$	−9.80328e6	−	7.12250e6i	−0.402309	−	0.292295i
$902$	−4.76627e6	+	3.46290e6i	−0.195057	+	0.141717i
$903$	6.42053e6	+	1.97604e7i	0.262030	+	0.806446i
$904$	−3.28759e6			−0.133800
$905$	2.62731e6			0.106633
$906$	3.54734e6	+	1.09176e7i	0.143576	+	0.441881i
$907$	7.23639e6	−	2.22713e7i	0.292081	−	0.898934i	−0.692105	−	0.721797i	$-0.743316\pi$
$907$	7.23639e6	−	2.22713e7i	0.292081	−	0.898934i	0.984186	−	0.177137i	$-0.0566836\pi$
$908$	5.66264e6	−	1.74278e7i	0.227932	−	0.701501i
$909$	1.97323e6	+	1.43364e6i	0.0792079	+	0.0575479i
$910$	293370.	+	902899.i	0.0117439	+	0.0361440i
$911$	−1.22557e7	−	8.90431e6i	−0.489264	−	0.355471i	0.315637	−	0.948880i	$-0.397782\pi$
$911$	−1.22557e7	−	8.90431e6i	−0.489264	−	0.355471i	−0.804901	+	0.593409i	$0.797782\pi$
$912$	−5.92000e6	+	4.30113e6i	−0.235687	+	0.171236i
$913$	−1.28112e7	+	3.94287e7i	−0.508641	+	1.56544i
$914$	1.41848e7	−	1.03059e7i	0.561640	−	0.408055i
$915$	−1.84419e6	+	1.33988e6i	−0.0728204	+	0.0529071i
$916$	−2.67939e6	+	8.24632e6i	−0.105511	+	0.324729i
$917$	−4.58687e6	+	3.33256e6i	−0.180133	+	0.130874i
$918$	1.39137e7	+	1.01089e7i	0.544924	+	0.395911i
$919$	1.27174e6	+	3.91402e6i	0.0496719	+	0.152874i	0.972816	−	0.231580i	$-0.0743896\pi$
$919$	1.27174e6	+	3.91402e6i	0.0496719	+	0.152874i	−0.923144	+	0.384454i	$0.874390\pi$
$920$	2.85777e6	+	2.07629e6i	0.111316	+	0.0808759i
$921$	−1.47161e7	+	4.52916e7i	−0.571669	+	1.75942i
$922$	−6.34530e6	+	1.95288e7i	−0.245824	+	0.756569i
$923$	−837066.	−	2.57623e6i	−0.0323412	−	0.0995359i
$924$	−1.59069e7			−0.612922
$925$	−2.48059e7			−0.953235
$926$	8.70709e6	+	2.67977e7i	0.333692	+	1.02700i
$927$	66304.3	−	48172.9i	0.00253421	−	0.00184121i
$928$	511495.	+	371623.i	0.0194972	+	0.0141655i
$929$	−3.73485e7			−1.41982			−0.709911	−	0.704292i	$-0.751265\pi$
$929$	−3.73485e7			−1.41982			−0.709911	+	0.704292i	$0.751265\pi$
$930$	−7.97920e6	−	582411.i	−0.302519	−	0.0220812i
$931$	1.09690e7			0.414758
$932$	1.21146e6	+	880175.i	0.0456845	+	0.0331917i
$933$	−2.36875e7	+	1.72100e7i	−0.890871	+	0.647256i
$934$	4.45133e6	+	1.36998e7i	0.166964	+	0.513862i
$935$	1.27069e7			0.475347
$936$	128938.			0.00481053
$937$	−37403.3	−	115116.i	−0.00139175	−	0.00428336i	0.950358	−	0.311158i	$-0.100717\pi$
$937$	−37403.3	−	115116.i	−0.00139175	−	0.00428336i	−0.951750	+	0.306875i	$0.900717\pi$
$938$	−1.30798e7	+	4.02556e7i	−0.485395	+	1.49389i
$939$	3.51750e6	−	1.08257e7i	0.130188	−	0.400676i
$940$	347737.	+	252646.i	0.0128361	+	0.00932594i
$941$	−9.47102e6	−	2.91488e7i	−0.348677	−	1.07312i	−0.959586	−	0.281416i	$-0.909196\pi$
$941$	−9.47102e6	−	2.91488e7i	−0.348677	−	1.07312i	0.610910	−	0.791700i	$-0.290804\pi$
$942$	−2.45831e7	−	1.78607e7i	−0.902631	−	0.655800i
$943$	5.56571e6	−	4.04373e6i	0.203818	−	0.148082i
$944$	2.42052e6	−	7.44961e6i	0.0884055	−	0.272084i
$945$	−1.24721e7	+	9.06148e6i	−0.454317	+	0.330080i
$946$	1.42101e7	−	1.03242e7i	0.516260	−	0.375085i
$947$	−7.86044e6	+	2.41919e7i	−0.284821	+	0.876588i	0.701631	+	0.712540i	$0.252455\pi$
$947$	−7.86044e6	+	2.41919e7i	−0.284821	+	0.876588i	−0.986452	+	0.164048i	$0.947545\pi$
$948$	848225.	−	616272.i	0.0306542	−	0.0222716i
$949$	−2.95377e6	−	2.14604e6i	−0.106466	−	0.0773520i
$950$	−5.99507e6	−	1.84509e7i	−0.215519	−	0.663299i
$951$	3.91453e7	+	2.84407e7i	1.40355	+	1.01974i
$952$	3.18100e6	−	9.79011e6i	0.113755	−	0.350102i
$953$	−1.52986e7	+	4.70841e7i	−0.545655	+	1.67935i	0.173772	+	0.984786i	$0.444405\pi$
$953$	−1.52986e7	+	4.70841e7i	−0.545655	+	1.67935i	−0.719427	+	0.694568i	$0.755595\pi$
$954$	−455871.	−	1.40303e6i	−0.0162170	−	0.0499108i
$955$	2.06346e7			0.732129
$956$	−6.38233e6			−0.225857
$957$	1.26819e6	+	3.90308e6i	0.0447614	+	0.137761i
$958$	2.07399e7	−	1.50684e7i	0.730118	−	0.530462i
$959$	2.27615e6	+	1.65372e6i	0.0799199	+	0.0580652i
$960$	−1.53112e6			−0.0536205
$961$	2.83257e7	+	4.15720e6i	0.989401	+	0.145209i
$962$	−2.48234e6			−0.0864817
$963$	−1.76082e6	−	1.27931e6i	−0.0611857	−	0.0444540i
$964$	3.45936e6	−	2.51338e6i	0.119896	−	0.0871094i
$965$	−88113.6	−	271186.i	−0.00304596	−	0.00937451i
$966$	1.85750e7			0.640450
$967$	1.45926e7			0.501840			0.250920	−	0.968008i	$-0.419267\pi$
$967$	1.45926e7			0.501840			0.250920	+	0.968008i	$0.419267\pi$
$968$	970327.	+	2.98636e6i	0.0332836	+	0.102436i
$969$	9.49860e6	−	2.92337e7i	0.324975	−	1.00017i
$970$	−1.83050e6	+	5.63369e6i	−0.0624654	+	0.192249i
$971$	2.96896e7	+	2.15708e7i	1.01055	+	0.734205i	0.964324	−	0.264726i	$-0.0852816\pi$
$971$	2.96896e7	+	2.15708e7i	1.01055	+	0.734205i	0.0462229	+	0.998931i	$0.485282\pi$
$972$	1.21722e6	+	3.74623e6i	0.0413242	+	0.127183i
$973$	2.11329e7	+	1.53539e7i	0.715609	+	0.519921i
$974$	−2.93890e7	+	2.13524e7i	−0.992631	+	0.721188i
$975$	678661.	−	2.08870e6i	0.0228634	−	0.0703664i
$976$	1.26298e6	−	917609.i	0.0424397	−	0.0308342i
$977$	3.96402e7	−	2.88003e7i	1.32861	−	0.965295i	0.328833	−	0.944388i	$-0.393345\pi$
$977$	3.96402e7	−	2.88003e7i	1.32861	−	0.965295i	0.999781	−	0.0209072i	$-0.00665546\pi$
$978$	8.61260e6	−	2.65069e7i	0.287930	−	0.886158i
$979$	1.57945e7	−	1.14754e7i	0.526682	−	0.382657i
$980$	1.85683e6	+	1.34906e6i	0.0617598	+	0.0448711i
$981$	−1.28099e6	−	3.94248e6i	−0.0424984	−	0.130797i
$982$	1.88988e7	+	1.37308e7i	0.625397	+	0.454378i
$983$	−1.68741e7	+	5.19332e7i	−0.556978	+	1.71420i	0.133686	+	0.991024i	$0.457319\pi$
$983$	−1.68741e7	+	5.19332e7i	−0.556978	+	1.71420i	−0.690663	+	0.723177i	$0.742681\pi$
$984$	−921477.	+	2.83602e6i	−0.0303387	+	0.0933729i
$985$	−7.55794e6	−	2.32609e7i	−0.248206	−	0.763901i
$986$	−2.65581e6			−0.0869971
$987$	2.26022e6			0.0738514
$988$	−599932.	−	1.84640e6i	−0.0195528	−	0.0601774i
$989$	−1.65935e7	+	1.20559e7i	−0.539446	+	0.391930i
$990$	1.25153e6	+	909293.i	0.0405840	+	0.0294860i
$991$	4.28631e7			1.38643			0.693217	−	0.720729i	$-0.256193\pi$
$991$	4.28631e7			1.38643			0.693217	+	0.720729i	$0.256193\pi$
$992$	5.46450e6	+	398860.i	0.176308	+	0.0128689i
$993$	9.21589e6			0.296595
$994$	−2.13000e7	−	1.54753e7i	−0.683775	−	0.496791i
$995$	2.01390e7	−	1.46318e7i	0.644881	−	0.468534i
$996$	6.48441e6	+	1.99570e7i	0.207120	+	0.637450i
$997$	−1.89175e7			−0.602734			−0.301367	−	0.953508i	$-0.597443\pi$
$997$	−1.89175e7			−0.602734			−0.301367	+	0.953508i	$0.597443\pi$
$998$	−1.09935e7			−0.349389
$999$	−1.24564e7	−	3.83368e7i	−0.394892	−	1.21535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.6.d.a.33.2	✓	24
31.16	even	5	inner	62.6.d.a.47.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.6.d.a.33.2	✓	24	1.1	even	1	trivial
62.6.d.a.47.2	yes	24	31.16	even	5	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:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	62.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.23607 - 2.35114i) q^{2} +(-11.7313 + 8.52330i) q^{3} +(4.94427 + 15.2169i) q^{4} -25.7786 q^{5} +58.0028 q^{6} +(46.2201 + 142.251i) q^{7} +(19.7771 - 60.8676i) q^{8} +(-10.1139 + 31.1275i) q^{9} +(83.4214 + 60.6092i) q^{10} +(-141.648 - 435.947i) q^{11} +(-187.701 - 136.373i) q^{12} +(49.7992 - 36.1812i) q^{13} +(184.880 - 569.003i) q^{14} +(302.417 - 219.719i) q^{15} +(-207.108 + 150.473i) q^{16} +(332.304 - 1022.73i) q^{17} +(105.915 - 76.9514i) q^{18} +(-1594.75 - 1158.65i) q^{19} +(-127.457 - 392.271i) q^{20} +(-1754.67 - 1274.84i) q^{21} +(-566.592 + 1743.79i) q^{22} +(661.626 - 2036.28i) q^{23} +(286.782 + 882.624i) q^{24} -2460.46 q^{25} -246.221 q^{26} +(-1235.53 - 3802.58i) q^{27} +(-1936.09 + 1406.65i) q^{28} +(499.507 + 362.913i) q^{29} -1495.23 q^{30} +(5336.42 + 389.512i) q^{31} +1024.00 q^{32} +(5377.43 + 3906.93i) q^{33} +(-3479.93 + 2528.32i) q^{34} +(-1191.49 - 3667.03i) q^{35} -523.670 q^{36} +10081.8 q^{37} +(2436.56 + 7498.97i) q^{38} +(-275.827 + 848.907i) q^{39} +(-509.826 + 1569.08i) q^{40} +(2599.50 + 1888.65i) q^{41} +(2680.90 + 8250.95i) q^{42} +(-7750.12 - 5630.79i) q^{43} +(5933.42 - 4310.88i) q^{44} +(260.723 - 802.424i) q^{45} +(-6928.64 + 5033.95i) q^{46} +(-843.085 + 612.537i) q^{47} +(1147.13 - 3530.49i) q^{48} +(-4501.85 + 3270.79i) q^{49} +(7962.22 + 5784.89i) q^{50} +(4818.64 + 14830.2i) q^{51} +(796.787 + 578.900i) q^{52} +(3482.12 - 10716.9i) q^{53} +(-4942.14 + 15210.3i) q^{54} +(3651.49 + 11238.1i) q^{55} +9572.57 q^{56} +28584.1 q^{57} +(-763.179 - 2348.82i) q^{58} +(-24754.0 + 17984.8i) q^{59} +(4838.68 + 3515.50i) q^{60} -6098.16 q^{61} +(-16353.2 - 13807.2i) q^{62} -4895.38 q^{63} +(-3313.73 - 2407.57i) q^{64} +(-1283.75 + 932.702i) q^{65} +(-8215.98 - 25286.2i) q^{66} -70747.6 q^{67} +17205.7 q^{68} +(9594.05 + 29527.4i) q^{69} +(-4765.96 + 14668.1i) q^{70} +(13598.6 - 41852.3i) q^{71} +(1694.63 + 1231.22i) q^{72} +(-18328.9 - 56410.5i) q^{73} +(-32625.3 - 23703.7i) q^{74} +(28864.5 - 20971.3i) q^{75} +(9746.25 - 29995.9i) q^{76} +(55466.9 - 40299.1i) q^{77} +(2888.49 - 2098.61i) q^{78} +(-1396.45 + 4297.84i) q^{79} +(5338.97 - 3878.99i) q^{80} +(40470.7 + 29403.7i) q^{81} +(-3971.69 - 12223.6i) q^{82} +(-73170.5 - 53161.5i) q^{83} +(10723.6 - 33003.8i) q^{84} +(-8566.33 + 26364.5i) q^{85} +(11841.1 + 36443.2i) q^{86} -8953.10 q^{87} -29336.5 q^{88} +(13161.4 + 40506.6i) q^{89} +(-2730.33 + 1983.70i) q^{90} +(7448.53 + 5411.68i) q^{91} +34257.1 q^{92} +(-65923.2 + 40914.5i) q^{93} +4168.44 q^{94} +(41110.5 + 29868.5i) q^{95} +(-12012.9 + 8727.86i) q^{96} +(17752.1 + 54635.3i) q^{97} +22258.4 q^{98} +15002.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - 20 q^{3} - 96 q^{4} + 120 q^{5} + 280 q^{6} - 180 q^{7} - 384 q^{8} - 200 q^{9} - 100 q^{10} + 354 q^{11} - 320 q^{12} + 39 q^{13} - 720 q^{14} + 535 q^{15} - 1536 q^{16} - 1027 q^{17}+ \cdots + 339042 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - 20 * q^3 - 96 * q^4 + 120 * q^5 + 280 * q^6 - 180 * q^7 - 384 * q^8 - 200 * q^9 - 100 * q^10 + 354 * q^11 - 320 * q^12 + 39 * q^13 - 720 * q^14 + 535 * q^15 - 1536 * q^16 - 1027 * q^17 - 1420 * q^18 + 334 * q^19 - 560 * q^20 - 1867 * q^21 + 1416 * q^22 - 1051 * q^23 - 960 * q^24 + 4812 * q^25 + 12536 * q^26 - 5135 * q^27 + 4000 * q^28 - 1143 * q^29 + 9080 * q^30 - 8583 * q^31 + 24576 * q^32 - 24628 * q^33 - 8108 * q^34 - 7496 * q^35 + 17760 * q^36 - 25204 * q^37 - 2844 * q^38 - 20114 * q^39 - 2240 * q^40 + 19615 * q^41 + 3212 * q^42 + 22358 * q^43 - 20496 * q^44 + 6725 * q^45 - 5264 * q^46 + 4766 * q^47 - 3840 * q^48 - 12058 * q^49 + 4628 * q^50 + 6844 * q^51 + 624 * q^52 - 7393 * q^53 - 20540 * q^54 + 11861 * q^55 - 8960 * q^56 + 176704 * q^57 + 4268 * q^58 - 21070 * q^59 + 8560 * q^60 + 76556 * q^61 - 49652 * q^62 + 105854 * q^63 - 24576 * q^64 - 107146 * q^65 + 57968 * q^66 - 150906 * q^67 + 97728 * q^68 - 212560 * q^69 - 29984 * q^70 + 27475 * q^71 - 22720 * q^72 + 49671 * q^73 + 90124 * q^74 - 156002 * q^75 - 11376 * q^76 + 253908 * q^77 - 9036 * q^78 - 7162 * q^79 - 6400 * q^80 + 38329 * q^81 - 92940 * q^82 - 246088 * q^83 + 12848 * q^84 - 104879 * q^85 - 149088 * q^86 - 247668 * q^87 + 118656 * q^88 + 159253 * q^89 - 167880 * q^90 - 68566 * q^91 + 75744 * q^92 + 260391 * q^93 + 18784 * q^94 + 222814 * q^95 - 20480 * q^96 + 190 * q^97 - 144032 * q^98 + 339042 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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