LMFDB - Embedded newform 82.6.d.b.37.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [82,6,Mod(37,82)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(82, 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("82.37"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 82 = 2 \cdot 41 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	82.d (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [36,36] 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:	$13.1514732247$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			37.2
Character	$\chi$	$=$	82.37
Dual form			82.6.d.b.51.2

$q$-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} -20.9317 q^{3} +(4.94427 - 15.2169i) q^{4} +(-11.1577 + 34.3400i) q^{5} +(-67.7364 + 49.2134i) q^{6} +(105.237 + 76.4591i) q^{7} +(-19.7771 - 60.8676i) q^{8} +195.136 q^{9} +(44.6310 + 137.360i) q^{10} +(-76.2274 - 234.604i) q^{11} +(-103.492 + 318.516i) q^{12} +(617.675 - 448.767i) q^{13} +520.320 q^{14} +(233.551 - 718.795i) q^{15} +(-207.108 - 150.473i) q^{16} +(-467.097 - 1437.58i) q^{17} +(631.474 - 458.793i) q^{18} +(430.141 + 312.516i) q^{19} +(467.382 + 339.573i) q^{20} +(-2202.79 - 1600.42i) q^{21} +(-798.264 - 579.973i) q^{22} +(3671.14 - 2667.24i) q^{23} +(413.968 + 1274.06i) q^{24} +(1473.44 + 1070.52i) q^{25} +(943.724 - 2904.48i) q^{26} +1001.87 q^{27} +(1683.79 - 1223.35i) q^{28} +(-63.5467 + 195.577i) q^{29} +(-934.202 - 2875.18i) q^{30} +(145.153 + 446.736i) q^{31} -1024.00 q^{32} +(1595.57 + 4910.66i) q^{33} +(-4891.50 - 3553.88i) q^{34} +(-3799.81 + 2760.72i) q^{35} +(964.807 - 2969.37i) q^{36} +(-3230.72 + 9943.13i) q^{37} +2126.73 q^{38} +(-12929.0 + 9393.46i) q^{39} +2310.86 q^{40} +(6717.59 - 8410.13i) q^{41} -10891.2 q^{42} +(6474.30 - 4703.85i) q^{43} -3946.83 q^{44} +(-2177.28 + 6700.98i) q^{45} +(5609.00 - 17262.7i) q^{46} +(5811.32 - 4222.17i) q^{47} +(4335.13 + 3149.66i) q^{48} +(35.1669 + 108.232i) q^{49} +7285.08 q^{50} +(9777.13 + 30090.9i) q^{51} +(-3774.89 - 11617.9i) q^{52} +(-3158.94 + 9722.22i) q^{53} +(3242.11 - 2355.53i) q^{54} +8906.82 q^{55} +(2572.60 - 7917.66i) q^{56} +(-9003.58 - 6541.49i) q^{57} +(254.187 + 782.307i) q^{58} +(21675.5 - 15748.2i) q^{59} +(-9783.09 - 7107.83i) q^{60} +(-16249.7 - 11806.1i) q^{61} +(1520.07 + 1104.39i) q^{62} +(20535.5 + 14919.9i) q^{63} +(-3313.73 + 2407.57i) q^{64} +(8518.81 + 26218.2i) q^{65} +(16709.0 + 12139.8i) q^{66} +(-3303.13 + 10166.0i) q^{67} -24184.9 q^{68} +(-76843.2 + 55829.8i) q^{69} +(-5805.60 + 17867.8i) q^{70} +(12323.8 + 37928.7i) q^{71} +(-3859.23 - 11877.5i) q^{72} -71118.0 q^{73} +(12922.9 + 39772.5i) q^{74} +(-30841.6 - 22407.7i) q^{75} +(6882.25 - 5000.25i) q^{76} +(9915.66 - 30517.3i) q^{77} +(-19753.7 + 60795.8i) q^{78} +48941.2 q^{79} +(7478.10 - 5433.16i) q^{80} -68388.9 q^{81} +(1965.18 - 43009.7i) q^{82} +2759.30 q^{83} +(-35244.6 + 25606.7i) q^{84} +54578.1 q^{85} +(9891.85 - 30444.0i) q^{86} +(1330.14 - 4093.75i) q^{87} +(-12772.2 + 9279.56i) q^{88} +(-62448.5 - 45371.5i) q^{89} +(8709.12 + 26803.9i) q^{90} +99314.6 q^{91} +(-22436.0 - 69050.9i) q^{92} +(-3038.31 - 9350.95i) q^{93} +(8878.90 - 27326.4i) q^{94} +(-15531.2 + 11284.1i) q^{95} +21434.1 q^{96} +(46962.1 - 144534. i) q^{97} +(368.272 + 267.565i) q^{98} +(-14874.7 - 45779.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 36 q^{2} + 2 q^{3} - 144 q^{4} + 26 q^{5} + 112 q^{6} - 120 q^{7} + 576 q^{8} + 4006 q^{9} - 104 q^{10} + 747 q^{11} + 432 q^{12} + 907 q^{13} + 280 q^{14} - 4149 q^{15} - 2304 q^{16} - 3177 q^{17}+ \cdots + 276325 q^{99}+O(q^{100}) $ 36 * q + 36 * q^2 + 2 * q^3 - 144 * q^4 + 26 * q^5 + 112 * q^6 - 120 * q^7 + 576 * q^8 + 4006 * q^9 - 104 * q^10 + 747 * q^11 + 432 * q^12 + 907 * q^13 + 280 * q^14 - 4149 * q^15 - 2304 * q^16 - 3177 * q^17 + 3696 * q^18 + 1557 * q^19 - 624 * q^20 - 4785 * q^21 + 2252 * q^22 + 1809 * q^23 - 1728 * q^24 - 6323 * q^25 + 10132 * q^26 + 8828 * q^27 - 1920 * q^28 + 1179 * q^29 + 16596 * q^30 - 2190 * q^31 - 36864 * q^32 + 19669 * q^33 - 4572 * q^34 - 69 * q^35 - 17264 * q^36 + 47551 * q^37 - 6128 * q^38 + 62888 * q^39 - 1664 * q^40 + 41071 * q^41 - 16600 * q^42 + 46110 * q^43 - 5888 * q^44 + 51325 * q^45 + 144 * q^46 - 65162 * q^47 - 7168 * q^48 - 83129 * q^49 - 151288 * q^50 + 98677 * q^51 - 40528 * q^52 - 122095 * q^53 + 41748 * q^54 - 161798 * q^55 - 9920 * q^56 - 11800 * q^57 - 4716 * q^58 + 17054 * q^59 + 72656 * q^60 + 86317 * q^61 - 30540 * q^62 - 166377 * q^63 - 36864 * q^64 + 32896 * q^65 + 66064 * q^66 + 95554 * q^67 + 65088 * q^68 + 132527 * q^69 + 23156 * q^70 + 158283 * q^71 + 69056 * q^72 - 239776 * q^73 - 190204 * q^74 - 357133 * q^75 + 24912 * q^76 + 253599 * q^77 + 242748 * q^78 + 98380 * q^79 - 9984 * q^80 + 1044 * q^81 - 84824 * q^82 - 24346 * q^83 - 76560 * q^84 + 376378 * q^85 + 98560 * q^86 + 12625 * q^87 + 36032 * q^88 + 260385 * q^89 - 205300 * q^90 - 726414 * q^91 - 576 * q^92 - 100227 * q^93 - 189392 * q^94 - 257337 * q^95 - 2048 * q^96 + 109321 * q^97 - 145824 * q^98 + 276325 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/82\mathbb{Z}\right)^\times$.

$n$	$47$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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
$3$	−20.9317			−1.34277			−0.671385	−	0.741109i	$-0.734300\pi$
$3$	−20.9317			−1.34277			−0.671385	+	0.741109i	$0.734300\pi$
$4$	4.94427	−	15.2169i	0.154508	−	0.475528i
$5$	−11.1577	+	34.3400i	−0.199596	+	0.614293i	0.800296	+	0.599605i	$0.204675\pi$
$5$	−11.1577	+	34.3400i	−0.199596	+	0.614293i	−0.999892	+	0.0146879i	$0.995325\pi$
$6$	−67.7364	+	49.2134i	−0.768147	+	0.558091i
$7$	105.237	+	76.4591i	0.811751	+	0.589772i	0.914338	−	0.404952i	$-0.132712\pi$
$7$	105.237	+	76.4591i	0.811751	+	0.589772i	−0.102587	+	0.994724i	$0.532712\pi$
$8$	−19.7771	−	60.8676i	−0.109254	−	0.336249i
$9$	195.136			0.803030
$10$	44.6310	+	137.360i	0.141136	+	0.434370i
$11$	−76.2274	−	234.604i	−0.189946	−	0.584593i	0.810053	−	0.586357i	$-0.199438\pi$
$11$	−76.2274	−	234.604i	−0.189946	−	0.584593i	−0.999998	+	0.00176419i	$0.999438\pi$
$12$	−103.492	+	318.516i	−0.207469	+	0.638525i
$13$	617.675	−	448.767i	1.01368	−	0.736483i	0.0487038	−	0.998813i	$-0.484491\pi$
$13$	617.675	−	448.767i	1.01368	−	0.736483i	0.964978	+	0.262330i	$0.0844910\pi$
$14$	520.320			0.709497
$15$	233.551	−	718.795i	0.268011	−	0.824853i
$16$	−207.108	−	150.473i	−0.202254	−	0.146946i
$17$	−467.097	−	1437.58i	−0.391999	−	1.20645i	−0.931274	−	0.364319i	$-0.881302\pi$
$17$	−467.097	−	1437.58i	−0.391999	−	1.20645i	0.539276	−	0.842129i	$-0.318698\pi$
$18$	631.474	−	458.793i	0.459383	−	0.333761i
$19$	430.141	+	312.516i	0.273355	+	0.198604i	0.716014	−	0.698086i	$-0.245965\pi$
$19$	430.141	+	312.516i	0.273355	+	0.198604i	−0.442659	+	0.896690i	$0.645965\pi$
$20$	467.382	+	339.573i	0.261274	+	0.189827i
$21$	−2202.79	−	1600.42i	−1.09000	−	0.791928i
$22$	−798.264	−	579.973i	−0.351633	−	0.255476i
$23$	3671.14	−	2667.24i	1.44704	−	1.05134i	0.460531	−	0.887644i	$-0.347659\pi$
$23$	3671.14	−	2667.24i	1.44704	−	1.05134i	0.986511	−	0.163694i	$-0.0523409\pi$
$24$	413.968	+	1274.06i	0.146703	+	0.451505i
$25$	1473.44	+	1070.52i	0.471500	+	0.342565i
$26$	943.724	−	2904.48i	0.273786	−	0.842627i
$27$	1001.87			0.264485
$28$	1683.79	−	1223.35i	0.405876	−	0.294886i
$29$	−63.5467	+	195.577i	−0.0140313	+	0.0431839i	−0.957827	−	0.287345i	$-0.907227\pi$
$29$	−63.5467	+	195.577i	−0.0140313	+	0.0431839i	0.943796	+	0.330529i	$0.107227\pi$
$30$	−934.202	−	2875.18i	−0.189512	−	0.583259i
$31$	145.153	+	446.736i	0.0271283	+	0.0834924i	0.963704	−	0.266973i	$-0.0860234\pi$
$31$	145.153	+	446.736i	0.0271283	+	0.0834924i	−0.936576	+	0.350465i	$0.886023\pi$
$32$	−1024.00			−0.176777
$33$	1595.57	+	4910.66i	0.255053	+	0.784974i
$34$	−4891.50	−	3553.88i	−0.725680	−	0.527237i
$35$	−3799.81	+	2760.72i	−0.524315	+	0.380937i
$36$	964.807	−	2969.37i	0.124075	−	0.381864i
$37$	−3230.72	+	9943.13i	−0.387967	+	1.19404i	0.546338	+	0.837565i	$0.316021\pi$
$37$	−3230.72	+	9943.13i	−0.387967	+	1.19404i	−0.934305	+	0.356475i	$0.883979\pi$
$38$	2126.73			0.238921
$39$	−12929.0	+	9393.46i	−1.36114	+	0.988927i
$40$	2310.86			0.228362
$41$	6717.59	−	8410.13i	0.624099	−	0.781345i
$41$	6717.59	−	8410.13i	0.624099	−	0.781345i
$42$	−10891.2			−0.952691
$43$	6474.30	−	4703.85i	0.533976	−	0.387956i	−0.287867	−	0.957670i	$-0.592946\pi$
$43$	6474.30	−	4703.85i	0.533976	−	0.387956i	0.821843	+	0.569714i	$0.192946\pi$
$44$	−3946.83			−0.307339
$45$	−2177.28	+	6700.98i	−0.160281	+	0.493295i
$46$	5609.00	−	17262.7i	0.390833	−	1.20286i
$47$	5811.32	−	4222.17i	0.383734	−	0.278799i	−0.379149	−	0.925336i	$-0.623783\pi$
$47$	5811.32	−	4222.17i	0.383734	−	0.278799i	0.762883	+	0.646537i	$0.223783\pi$
$48$	4335.13	+	3149.66i	0.271581	+	0.197315i
$49$	35.1669	+	108.232i	0.00209239	+	0.00643973i
$50$	7285.08			0.412106
$51$	9777.13	+	30090.9i	0.526364	+	1.61998i
$52$	−3774.89	−	11617.9i	−0.193596	−	0.595827i
$53$	−3158.94	+	9722.22i	−0.154473	+	0.475418i	−0.998107	−	0.0615000i	$-0.980412\pi$
$53$	−3158.94	+	9722.22i	−0.154473	+	0.475418i	0.843634	+	0.536918i	$0.180412\pi$
$54$	3242.11	−	2355.53i	0.151302	−	0.109927i
$55$	8906.82			0.397023
$56$	2572.60	−	7917.66i	0.109623	−	0.337386i
$57$	−9003.58	−	6541.49i	−0.367053	−	0.266679i
$58$	254.187	+	782.307i	0.00992163	+	0.0305356i
$59$	21675.5	−	15748.2i	0.810661	−	0.588980i	−0.103361	−	0.994644i	$-0.532960\pi$
$59$	21675.5	−	15748.2i	0.810661	−	0.588980i	0.914022	+	0.405664i	$0.132960\pi$
$60$	−9783.09	−	7107.83i	−0.350831	−	0.254894i
$61$	−16249.7	−	11806.1i	−0.559139	−	0.406238i	0.272005	−	0.962296i	$-0.412313\pi$
$61$	−16249.7	−	11806.1i	−0.559139	−	0.406238i	−0.831144	+	0.556058i	$0.812313\pi$
$62$	1520.07	+	1104.39i	0.0502208	+	0.0364875i
$63$	20535.5	+	14919.9i	0.651861	+	0.473605i
$64$	−3313.73	+	2407.57i	−0.101127	+	0.0734732i
$65$	8518.81	+	26218.2i	0.250089	+	0.769696i
$66$	16709.0	+	12139.8i	0.472162	+	0.343046i
$67$	−3303.13	+	10166.0i	−0.0898957	+	0.276670i	−0.985890	−	0.167395i	$-0.946464\pi$
$67$	−3303.13	+	10166.0i	−0.0898957	+	0.276670i	0.895994	+	0.444066i	$0.146464\pi$
$68$	−24184.9			−0.634267
$69$	−76843.2	+	55829.8i	−1.94304	+	1.41170i
$70$	−5805.60	+	17867.8i	−0.141613	+	0.435839i
$71$	12323.8	+	37928.7i	0.290133	+	0.892939i	0.984813	+	0.173619i	$0.0555463\pi$
$71$	12323.8	+	37928.7i	0.290133	+	0.892939i	−0.694679	+	0.719320i	$0.744454\pi$
$72$	−3859.23	−	11877.5i	−0.0877343	−	0.270018i
$73$	−71118.0			−1.56197			−0.780984	−	0.624551i	$-0.785282\pi$
$73$	−71118.0			−1.56197			−0.780984	+	0.624551i	$0.785282\pi$
$74$	12922.9	+	39772.5i	0.274334	+	0.844313i
$75$	−30841.6	−	22407.7i	−0.633116	−	0.459986i
$76$	6882.25	−	5000.25i	0.136677	−	0.0993020i
$77$	9915.66	−	30517.3i	0.190588	−	0.586569i
$78$	−19753.7	+	60795.8i	−0.367632	+	1.13145i
$79$	48941.2			0.882282			0.441141	−	0.897438i	$-0.354574\pi$
$79$	48941.2			0.882282			0.441141	+	0.897438i	$0.354574\pi$
$80$	7478.10	−	5433.16i	0.130637	−	0.0949134i
$81$	−68388.9			−1.15817
$82$	1965.18	−	43009.7i	0.0322751	−	0.706370i
$83$	2759.30			0.0439647			0.0219824	−	0.999758i	$-0.493002\pi$
$83$	2759.30			0.0439647			0.0219824	+	0.999758i	$0.493002\pi$
$84$	−35244.6	+	25606.7i	−0.544998	+	0.395964i
$85$	54578.1			0.819353
$86$	9891.85	−	30444.0i	0.144222	−	0.443869i
$87$	1330.14	−	4093.75i	0.0188408	−	0.0579860i
$88$	−12772.2	+	9279.56i	−0.175817	+	0.127738i
$89$	−62448.5	−	45371.5i	−0.835693	−	0.607167i	0.0854710	−	0.996341i	$-0.472761\pi$
$89$	−62448.5	−	45371.5i	−0.835693	−	0.607167i	−0.921164	+	0.389174i	$0.872761\pi$
$90$	8709.12	+	26803.9i	0.113336	+	0.348813i
$91$	99314.6			1.25721
$92$	−22436.0	−	69050.9i	−0.276360	−	0.850550i
$93$	−3038.31	−	9350.95i	−0.0364271	−	0.112111i
$94$	8878.90	−	27326.4i	0.103643	−	0.318980i
$95$	−15531.2	+	11284.1i	−0.176561	+	0.128279i
$96$	21434.1			0.237370
$97$	46962.1	−	144534.i	0.506778	−	1.55970i	−0.290983	−	0.956728i	$-0.593982\pi$
$97$	46962.1	−	144534.i	0.506778	−	1.55970i	0.797761	−	0.602974i	$-0.206018\pi$
$98$	368.272	+	267.565i	0.00387350	+	0.00281426i
$99$	−14874.7	−	45779.7i	−0.152532	−	0.469446i
$100$	23575.0	−	17128.2i	0.235750	−	0.171282i
$101$	93528.3	+	67952.3i	0.912304	+	0.662828i	0.941597	−	0.336743i	$-0.109325\pi$
$101$	93528.3	+	67952.3i	0.912304	+	0.662828i	−0.0292923	+	0.999571i	$0.509325\pi$
$102$	102387.	+	74388.9i	0.974421	+	0.707958i
$103$	86879.1	+	63121.4i	0.806905	+	0.586251i	0.912932	−	0.408112i	$-0.133813\pi$
$103$	86879.1	+	63121.4i	0.806905	+	0.586251i	−0.106027	+	0.994363i	$0.533813\pi$
$104$	−39531.2	−	28721.1i	−0.358391	−	0.260386i
$105$	79536.5	−	57786.7i	0.704034	−	0.511510i
$106$	12635.8	+	38888.9i	0.109229	+	0.336171i
$107$	19283.3	+	14010.1i	0.162825	+	0.118299i	0.666214	−	0.745761i	$-0.267914\pi$
$107$	19283.3	+	14010.1i	0.162825	+	0.118299i	−0.503389	+	0.864060i	$0.667914\pi$
$108$	4953.51	−	15245.3i	0.0408652	−	0.125770i
$109$	−108247.			−0.872671			−0.436336	−	0.899784i	$-0.643724\pi$
$109$	−108247.			−0.872671			−0.436336	+	0.899784i	$0.643724\pi$
$110$	28823.1	−	20941.2i	0.227122	−	0.165014i
$111$	67624.4	−	208127.i	0.520950	−	1.60332i
$112$	−10290.4	−	31670.6i	−0.0775154	−	0.238568i
$113$	−69494.7	−	213883.i	−0.511983	−	1.57572i	−0.788705	−	0.614772i	$-0.789248\pi$
$113$	−69494.7	−	213883.i	−0.511983	−	1.57572i	0.276722	−	0.960950i	$-0.410752\pi$
$114$	−44516.2			−0.320816
$115$	50631.3	+	155827.i	0.357005	+	1.09875i
$116$	2661.88	+	1933.97i	0.0183672	+	0.0133446i
$117$	120531.	−	87570.8i	0.814017	−	0.591418i
$118$	33117.2	−	101924.i	0.218952	−	0.673865i
$119$	60760.0	−	187000.i	0.393324	−	1.21053i
$120$	−48370.3			−0.306638
$121$	81064.6	−	58896.9i	0.503348	−	0.365703i
$122$	−80342.8			−0.488706
$123$	−140611.	+	176038.i	−0.838022	+	1.04917i
$124$	7515.62			0.0438946
$125$	−144487.	+	104976.i	−0.827093	+	0.600918i
$126$	101533.			0.569747
$127$	−40264.8	+	123922.i	−0.221522	+	0.681774i	0.777104	+	0.629372i	$0.216688\pi$
$127$	−40264.8	+	123922.i	−0.221522	+	0.681774i	−0.998626	+	0.0524021i	$0.983312\pi$
$128$	−5062.93	+	15582.1i	−0.0273135	+	0.0840623i
$129$	−135518.	+	98459.7i	−0.717006	+	0.520936i
$130$	89210.1	+	64814.9i	0.462973	+	0.336370i
$131$	−70237.6	−	216169.i	−0.357595	−	1.10056i	−0.954490	−	0.298244i	$-0.903599\pi$
$131$	−70237.6	−	216169.i	−0.357595	−	1.10056i	0.596895	−	0.802319i	$-0.296401\pi$
$132$	82614.0			0.412685
$133$	21372.0	+	65776.4i	0.104765	+	0.322434i
$134$	13212.5	+	40664.0i	0.0635659	+	0.195636i
$135$	−11178.6	+	34404.1i	−0.0527901	+	0.162471i
$136$	−78264.0	+	56862.1i	−0.362840	+	0.263619i
$137$	169487.			0.771500			0.385750	−	0.922603i	$-0.373943\pi$
$137$	169487.			0.771500			0.385750	+	0.922603i	$0.373943\pi$
$138$	−117406.	+	361338.i	−0.524798	+	1.61516i
$139$	15216.2	+	11055.2i	0.0667990	+	0.0485323i	0.620684	−	0.784061i	$-0.286855\pi$
$139$	15216.2	+	11055.2i	0.0667990	+	0.0485323i	−0.553885	+	0.832593i	$0.686855\pi$
$140$	23222.4	+	71471.1i	0.100135	+	0.308184i
$141$	−121641.	+	88377.2i	−0.515266	+	0.374363i
$142$	129056.	+	93764.8i	0.537104	+	0.390229i
$143$	−152366.	−	110701.i	−0.623087	−	0.452699i
$144$	−40414.4	−	29362.8i	−0.162416	−	0.118002i
$145$	−6007.06	−	4364.39i	−0.0237270	−	0.0172387i
$146$	−230143.	+	167208.i	−0.893542	+	0.649196i
$147$	−736.103	−	2265.49i	−0.00280960	−	0.00864707i
$148$	135330.	+	98323.0i	0.507855	+	0.368978i
$149$	−43966.2	+	135314.i	−0.162238	+	0.499318i	−0.998822	−	0.0485207i	$-0.984549\pi$
$149$	−43966.2	+	135314.i	−0.162238	+	0.499318i	0.836584	+	0.547839i	$0.184549\pi$
$150$	−152489.			−0.553364
$151$	−33190.6	+	24114.4i	−0.118460	+	0.0860664i	−0.645438	−	0.763813i	$-0.723325\pi$
$151$	−33190.6	+	24114.4i	−0.118460	+	0.0860664i	0.526978	+	0.849879i	$0.323325\pi$
$152$	10515.1	−	32362.3i	0.0369153	−	0.113614i
$153$	−91147.6	−	280523.i	−0.314787	−	0.968814i
$154$	−39662.7	−	122069.i	−0.134766	−	0.414767i
$155$	−16960.5			−0.0567035
$156$	79015.0	+	243183.i	0.259955	+	0.800059i
$157$	−124421.	−	90397.0i	−0.402851	−	0.292688i	0.367850	−	0.929885i	$-0.380094\pi$
$157$	−124421.	−	90397.0i	−0.402851	−	0.292688i	−0.770701	+	0.637197i	$0.780094\pi$
$158$	158377.	−	115068.i	0.504719	−	0.366700i
$159$	66122.0	−	203503.i	0.207421	−	0.638377i
$160$	11425.5	−	35164.2i	0.0352839	−	0.108593i
$161$	590274.			1.79469
$162$	−221311.	+	160792.i	−0.662546	+	0.481368i
$163$	−389976.			−1.14966			−0.574829	−	0.818273i	$-0.694931\pi$
$163$	−389976.			−1.14966			−0.574829	+	0.818273i	$0.694931\pi$
$164$	−94762.5	−	143803.i	−0.275123	−	0.417501i
$165$	−186435.			−0.533111
$166$	8929.29	−	6487.51i	0.0251505	−	0.0182729i
$167$	454689.			1.26160			0.630802	−	0.775944i	$-0.282726\pi$
$167$	454689.			1.26160			0.630802	+	0.775944i	$0.282726\pi$
$168$	−53849.0	+	165730.i	−0.147199	+	0.453031i
$169$	65394.7	−	201264.i	0.176127	−	0.542063i
$170$	176618.	−	128321.i	0.468720	−	0.340545i
$171$	83936.1	+	60983.2i	0.219512	+	0.159485i
$172$	−39567.4	−	121776.i	−0.101980	−	0.313863i
$173$	−539329.			−1.37006			−0.685029	−	0.728516i	$-0.740210\pi$
$173$	−539329.			−1.37006			−0.685029	+	0.728516i	$0.740210\pi$
$174$	−5320.56	−	16375.0i	−0.0133225	−	0.0410023i
$175$	73209.4	+	225315.i	0.180706	+	0.556155i
$176$	−19514.2	+	60058.6i	−0.0474864	+	0.146148i
$177$	−453706.	+	329636.i	−1.08853	+	0.790864i
$178$	−308762.			−0.730423
$179$	−80613.1	+	248102.i	−0.188050	+	0.578758i	−0.999988	−	0.00498619i	$-0.998413\pi$
$179$	−80613.1	+	248102.i	−0.188050	+	0.578758i	0.811938	+	0.583744i	$0.198413\pi$
$180$	91203.1	+	66262.9i	0.209811	+	0.152437i
$181$	200428.	+	616855.i	0.454739	+	1.39954i	0.871441	+	0.490500i	$0.163186\pi$
$181$	200428.	+	616855.i	0.454739	+	1.39954i	−0.416702	+	0.909043i	$0.636814\pi$
$182$	321389.	−	233503.i	0.719204	−	0.522532i
$183$	340133.	+	247121.i	0.750795	+	0.545485i
$184$	−234953.	−	170703.i	−0.511607	−	0.371704i
$185$	−305399.	−	221886.i	−0.656053	−	0.476650i
$186$	−31817.6	−	23116.8i	−0.0674349	−	0.0489943i
$187$	−301655.	+	219165.i	−0.630822	+	0.458319i
$188$	−35515.6	−	109306.i	−0.0732866	−	0.225553i
$189$	105434.	+	76601.9i	0.214696	+	0.155986i
$190$	−23729.5	+	73032.0i	−0.0476876	+	0.146767i
$191$	454930.			0.902321			0.451161	−	0.892443i	$-0.351010\pi$
$191$	454930.			0.902321			0.451161	+	0.892443i	$0.351010\pi$
$192$	69362.1	−	50394.5i	0.135790	−	0.0986575i
$193$	−231356.	+	712041.i	−0.447083	+	1.37598i	0.433101	+	0.901345i	$0.357419\pi$
$193$	−231356.	+	712041.i	−0.447083	+	1.37598i	−0.880184	+	0.474634i	$0.842581\pi$
$194$	−187848.	−	578137.i	−0.358346	−	1.10288i
$195$	−178313.	−	548791.i	−0.335813	−	1.03352i
$196$	1820.84			0.00338556
$197$	231737.	+	713213.i	0.425432	+	1.30934i	0.902580	+	0.430522i	$0.141670\pi$
$197$	231737.	+	713213.i	0.425432	+	1.30934i	−0.477148	+	0.878823i	$0.658330\pi$
$198$	−155770.	−	113174.i	−0.282372	−	0.205155i
$199$	−125338.	+	91063.6i	−0.224363	+	0.163009i	−0.694288	−	0.719697i	$-0.744281\pi$
$199$	−125338.	+	91063.6i	−0.224363	+	0.163009i	0.469926	+	0.882706i	$0.344281\pi$
$200$	36019.4	−	110856.i	0.0636739	−	0.195968i
$201$	69140.2	−	212792.i	0.120709	−	0.371505i
$202$	462429.			0.797383
$203$	−21641.1	+	15723.2i	−0.0368586	+	0.0267793i
$204$	506232.			0.851675
$205$	213851.	+	324520.i	0.355407	+	0.539333i
$206$	429554.			0.705261
$207$	716372.	−	520475.i	1.16202	−	0.844256i
$208$	−195453.			−0.313245
$209$	40528.9	−	124735.i	0.0641798	−	0.197525i
$210$	121521.	−	374003.i	0.190153	−	0.585231i
$211$	302421.	−	219722.i	0.467634	−	0.339756i	−0.328885	−	0.944370i	$-0.606673\pi$
$211$	302421.	−	219722.i	0.467634	−	0.339756i	0.796518	+	0.604614i	$0.206673\pi$
$212$	132323.	+	96138.6i	0.202207	+	0.146912i
$213$	−257958.	−	793912.i	−0.389582	−	1.19901i
$214$	95341.7			0.142314
$215$	89291.7	+	274812.i	0.131739	+	0.405452i
$216$	−19814.0	−	60981.3i	−0.0288961	−	0.0889329i
$217$	−18881.6	+	58111.5i	−0.0272200	+	0.0837746i
$218$	−350296.	+	254505.i	−0.499222	+	0.362706i
$219$	1.48862e6			2.09736
$220$	44037.8	−	135534.i	0.0613435	−	0.188796i
$221$	−933651.	−	678337.i	−1.28589	−	0.934254i
$222$	−270498.	−	832506.i	−0.368367	−	1.13372i
$223$	−1.01994e6	+	741028.i	−1.37345	+	0.997867i	−0.375987	+	0.926625i	$0.622696\pi$
$223$	−1.01994e6	+	741028.i	−1.37345	+	0.997867i	−0.997459	+	0.0712416i	$0.977304\pi$
$224$	−107763.	−	78294.1i	−0.143499	−	0.104258i
$225$	287521.	+	208896.i	0.378629	+	0.275090i
$226$	−727758.	−	528747.i	−0.947798	−	0.688616i
$227$	−402928.	−	292744.i	−0.518994	−	0.377072i	0.297230	−	0.954806i	$-0.403937\pi$
$227$	−402928.	−	292744.i	−0.518994	−	0.377072i	−0.816225	+	0.577734i	$0.803937\pi$
$228$	−144057.	+	104664.i	−0.183526	+	0.133340i
$229$	−11549.6	−	35546.0i	−0.0145538	−	0.0447921i	0.943516	−	0.331327i	$-0.107496\pi$
$229$	−11549.6	−	35546.0i	−0.0145538	−	0.0447921i	−0.958070	+	0.286535i	$0.907496\pi$
$230$	530218.	+	385226.i	0.660899	+	0.480171i
$231$	−207552.	+	638779.i	−0.255915	+	0.787627i
$232$	13161.1			0.0160535
$233$	771273.	−	560362.i	0.930718	−	0.676206i	−0.0154504	−	0.999881i	$-0.504918\pi$
$233$	771273.	−	560362.i	0.930718	−	0.676206i	0.946169	+	0.323674i	$0.104918\pi$
$234$	184155.	−	566770.i	0.219859	−	0.676655i
$235$	80148.1	+	246670.i	0.0946724	+	0.291372i
$236$	−132469.	−	407698.i	−0.154823	−	0.476495i
$237$	−1.02442e6			−1.18470
$238$	−243040.	−	748000.i	−0.278122	−	0.855971i
$239$	1.17643e6	+	854726.i	1.33220	+	0.967904i	0.999692	+	0.0248047i	$0.00789640\pi$
$239$	1.17643e6	+	854726.i	1.33220	+	0.967904i	0.332513	+	0.943099i	$0.392104\pi$
$240$	−156529.	+	113725.i	−0.175416	+	0.127447i
$241$	389282.	−	1.19809e6i	0.431739	−	1.32876i	−0.464652	−	0.885493i	$-0.653821\pi$
$241$	389282.	−	1.19809e6i	0.431739	−	1.32876i	0.896391	−	0.443263i	$-0.146179\pi$
$242$	123856.	−	381189.i	0.135950	−	0.418410i
$243$	1.18804e6			1.29067
$244$	−259995.	+	188897.i	−0.279570	+	0.203119i
$245$	−4109.09			−0.00437351
$246$	−41134.6	+	900267.i	−0.0433380	+	0.948492i
$247$	405934.			0.423363
$248$	24321.1	−	17670.3i	0.0251104	−	0.0182438i
$249$	−57756.9			−0.0590345
$250$	−220757.	+	679420.i	−0.223390	+	0.687524i
$251$	583232.	−	1.79500e6i	0.584328	−	1.79838i	−0.0176235	−	0.999845i	$-0.505610\pi$
$251$	583232.	−	1.79500e6i	0.584328	−	1.79838i	0.601952	−	0.798532i	$-0.294390\pi$
$252$	328569.	−	238719.i	0.325930	−	0.236802i
$253$	−905586.	−	657947.i	−0.889464	−	0.646233i
$254$	161059.	+	495690.i	0.156640	+	0.482087i
$255$	−1.14241e6			−1.10020
$256$	20251.7	+	62328.4i	0.0193136	+	0.0594410i
$257$	−154748.	−	476265.i	−0.146148	−	0.449796i	0.851009	−	0.525151i	$-0.175991\pi$
$257$	−154748.	−	476265.i	−0.146148	−	0.449796i	−0.997157	+	0.0753546i	$0.975991\pi$
$258$	−207053.	+	637244.i	−0.193657	+	0.596014i
$259$	−1.10023e6	+	799366.i	−1.01914	+	0.740451i
$260$	441079.			0.404653
$261$	−12400.3	+	38164.1i	−0.0112676	+	0.0346780i
$262$	−735537.	−	534399.i	−0.661990	−	0.480964i
$263$	−214362.	−	659737.i	−0.191099	−	0.588141i	−1.00000		0.000196870i	$-0.999937\pi$
$263$	−214362.	−	659737.i	−0.191099	−	0.588141i	0.808901	−	0.587945i	$-0.200063\pi$
$264$	267344.	−	194237.i	0.236081	−	0.171523i
$265$	−298614.	−	216956.i	−0.261214	−	0.189783i
$266$	223811.	+	162608.i	0.193944	+	0.140909i
$267$	1.30715e6	+	949703.i	1.12214	+	0.815285i
$268$	138363.	+	100527.i	0.117675	+	0.0854959i
$269$	−370821.	+	269417.i	−0.312452	+	0.227010i	−0.732948	−	0.680285i	$-0.761856\pi$
$269$	−370821.	+	269417.i	−0.312452	+	0.227010i	0.420496	+	0.907295i	$0.361856\pi$
$270$	44714.3	+	137617.i	0.0373282	+	0.114884i
$271$	309446.	+	224825.i	0.255954	+	0.185961i	0.708361	−	0.705850i	$-0.249435\pi$
$271$	309446.	+	224825.i	0.255954	+	0.185961i	−0.452408	+	0.891811i	$0.649435\pi$
$272$	−119577.	+	368020.i	−0.0979997	+	0.301612i
$273$	−2.07882e6			−1.68815
$274$	548473.	−	398489.i	0.441346	−	0.320656i
$275$	138831.	−	427277.i	0.110702	−	0.340704i
$276$	469624.	+	1.44535e6i	0.371088	+	1.14209i
$277$	344470.	+	1.06017e6i	0.269744	+	0.830187i	0.990562	+	0.137063i	$0.0437663\pi$
$277$	344470.	+	1.06017e6i	0.269744	+	0.830187i	−0.720818	+	0.693124i	$0.756234\pi$
$278$	75233.1			0.0583844
$279$	28324.7	+	87174.5i	0.0217849	+	0.0670469i
$280$	243188.	+	176686.i	0.185373	+	0.134682i
$281$	1.46584e6	−	1.06500e6i	1.10744	−	0.804604i	0.125183	−	0.992134i	$-0.460048\pi$
$281$	1.46584e6	−	1.06500e6i	1.10744	−	0.804604i	0.982259	+	0.187530i	$0.0600482\pi$
$282$	−185851.	+	571989.i	−0.139169	+	0.428317i
$283$	−557004.	+	1.71428e6i	−0.413420	+	1.27238i	0.500236	+	0.865889i	$0.333247\pi$
$283$	−557004.	+	1.71428e6i	−0.413420	+	1.27238i	−0.913656	+	0.406488i	$0.866753\pi$
$284$	638089.			0.469446
$285$	325094.	−	236195.i	0.237081	−	0.172250i
$286$	−753341.			−0.544598
$287$	1.34997e6	−	371435.i	0.967429	−	0.266182i
$288$	−199820.			−0.141957
$289$	−699758.	+	508404.i	−0.492837	+	0.358067i
$290$	−29700.6			−0.0207381
$291$	−982996.	+	3.02535e6i	−0.680486	+	2.09432i
$292$	−351627.	+	1.08220e6i	−0.241337	+	0.742760i
$293$	−1.72049e6	+	1.25001e6i	−1.17080	+	0.850636i	−0.991104	−	0.133086i	$-0.957511\pi$
$293$	−1.72049e6	+	1.25001e6i	−1.17080	+	0.850636i	−0.179696	+	0.983722i	$0.557511\pi$
$294$	−7708.57	−	5600.60i	−0.00520122	−	0.00377891i
$295$	298943.	+	920051.i	0.200001	+	0.615541i
$296$	669109.			0.443882
$297$	−76369.8	−	235042.i	−0.0502378	−	0.154616i
$298$	175865.	+	541256.i	0.114720	+	0.353071i
$299$	1.07060e6	−	3.29497e6i	0.692548	−	2.13144i
$300$	−493465.	+	358523.i	−0.316558	+	0.229993i
$301$	1.04099e6			0.662261
$302$	−50710.7	+	156072.i	−0.0319950	+	0.0984705i
$303$	−1.95771e6	−	1.42236e6i	−1.22501	−	0.890025i
$304$	−42060.6	−	129449.i	−0.0261031	−	0.0803370i
$305$	586730.	−	426285.i	0.361151	−	0.262392i
$306$	−954510.	−	693492.i	−0.582743	−	0.423387i
$307$	256228.	+	186161.i	0.155161	+	0.112731i	0.662657	−	0.748923i	$-0.269429\pi$
$307$	256228.	+	186161.i	0.155161	+	0.112731i	−0.507496	+	0.861654i	$0.669429\pi$
$308$	−415353.	−	301771.i	−0.249483	−	0.181260i
$309$	−1.81853e6	−	1.32124e6i	−1.08349	−	0.787200i
$310$	−54885.4	+	39876.5i	−0.0324379	+	0.0235675i
$311$	−570984.	−	1.75731e6i	−0.334752	−	1.03026i	−0.966844	−	0.255368i	$-0.917804\pi$
$311$	−570984.	−	1.75731e6i	−0.334752	−	1.03026i	0.632092	−	0.774893i	$-0.282196\pi$
$312$	827456.	+	601182.i	0.481236	+	0.349639i
$313$	−704339.	+	2.16773e6i	−0.406369	+	1.25068i	0.513377	+	0.858163i	$0.328394\pi$
$313$	−704339.	+	2.16773e6i	−0.406369	+	1.25068i	−0.919747	+	0.392513i	$0.871606\pi$
$314$	−615170.			−0.352104
$315$	−741481.	+	538718.i	−0.421040	+	0.305904i
$316$	241979.	−	744734.i	0.136320	−	0.419550i
$317$	401504.	+	1.23570e6i	0.224410	+	0.690663i	0.998351	+	0.0574052i	$0.0182827\pi$
$317$	401504.	+	1.23570e6i	0.224410	+	0.690663i	−0.773941	+	0.633258i	$0.781717\pi$
$318$	−264488.	−	814011.i	−0.146669	−	0.451401i
$319$	50727.1			0.0279102
$320$	−45702.1	−	140657.i	−0.0249495	−	0.0767866i
$321$	−403632.	−	293256.i	−0.218637	−	0.158849i
$322$	1.91017e6	−	1.38782e6i	1.02667	−	0.745920i
$323$	248348.	−	764336.i	0.132451	−	0.407641i
$324$	−338134.	+	1.04067e6i	−0.178948	+	0.550744i
$325$	1.39052e6			0.730244
$326$	−1.26199e6	+	916888.i	−0.657675	+	0.477829i
$327$	2.26580e6			1.17180
$328$	−644759.	−	242556.i	−0.330912	−	0.124488i
$329$	934388.			0.475924
$330$	−603316.	+	438335.i	−0.304972	+	0.221575i
$331$	3.31753e6			1.66435			0.832175	−	0.554513i	$-0.187096\pi$
$331$	3.31753e6			1.66435			0.832175	+	0.554513i	$0.187096\pi$
$332$	13642.7	−	41988.1i	0.00679292	−	0.0209065i
$333$	−630430.	+	1.94027e6i	−0.311549	+	0.958850i
$334$	1.47140e6	−	1.06904e6i	0.721715	−	0.524356i
$335$	−312245.	−	226859.i	−0.152014	−	0.110445i
$336$	215396.	+	662920.i	0.104085	+	0.320342i
$337$	−147360.			−0.0706816			−0.0353408	−	0.999375i	$-0.511252\pi$
$337$	−147360.			−0.0706816			−0.0353408	+	0.999375i	$0.511252\pi$
$338$	−261579.	−	805056.i	−0.124540	−	0.383296i
$339$	1.45464e6	+	4.47693e6i	0.687475	+	2.11583i
$340$	269849.	−	830510.i	0.126597	−	0.389626i
$341$	93741.4	−	68107.1i	0.0436562	−	0.0317181i
$342$	415003.			0.191861
$343$	671015.	−	2.06517e6i	0.307962	−	0.947809i
$344$	−414355.	−	301047.i	−0.188789	−	0.137163i
$345$	−1.05980e6	−	3.26173e6i	−0.479376	−	1.47537i
$346$	−1.74531e6	+	1.26804e6i	−0.783757	+	0.569433i
$347$	−1.51445e6	−	1.10031e6i	−0.675198	−	0.490560i	0.196563	−	0.980491i	$-0.437022\pi$
$347$	−1.51445e6	−	1.10031e6i	−0.675198	−	0.490560i	−0.871761	+	0.489931i	$0.837022\pi$
$348$	−55717.7	−	40481.3i	−0.0246629	−	0.0179187i
$349$	−2.63119e6	−	1.91167e6i	−1.15635	−	0.840135i	−0.167035	−	0.985951i	$-0.553419\pi$
$349$	−2.63119e6	−	1.91167e6i	−1.15635	−	0.840135i	−0.989312	+	0.145816i	$0.953419\pi$
$350$	766659.	+	557010.i	0.334528	+	0.243049i
$351$	618829.	−	449606.i	0.268104	−	0.194789i
$352$	78056.9	+	240234.i	0.0335780	+	0.103342i
$353$	−712373.	−	517570.i	−0.304278	−	0.221071i	0.425159	−	0.905119i	$-0.360218\pi$
$353$	−712373.	−	517570.i	−0.304278	−	0.221071i	−0.729437	+	0.684047i	$0.760218\pi$
$354$	−693200.	+	2.13345e6i	−0.294002	+	0.904846i
$355$	−1.43998e6			−0.606435
$356$	−999176.	+	725944.i	−0.417847	+	0.303583i
$357$	−1.27181e6	+	3.91423e6i	−0.528143	+	1.62546i
$358$	322452.	+	992406.i	0.132971	+	0.409244i
$359$	−199329.	−	613472.i	−0.0816271	−	0.251222i	0.901911	−	0.431921i	$-0.142164\pi$
$359$	−199329.	−	613472.i	−0.0816271	−	0.251222i	−0.983538	+	0.180699i	$0.942164\pi$
$360$	450933.			0.183382
$361$	−677801.	−	2.08606e6i	−0.273738	−	0.842478i
$362$	2.09891e6	+	1.52495e6i	0.841827	+	0.611623i
$363$	−1.69682e6	+	1.23281e6i	−0.675880	+	0.491055i
$364$	491038.	−	1.51126e6i	0.194250	−	0.597841i
$365$	793516.	−	2.44219e6i	0.311762	−	0.959506i
$366$	1.68171e6			0.656219
$367$	−1.51279e6	+	1.09911e6i	−0.586292	+	0.425966i	−0.840987	−	0.541055i	$-0.818025\pi$
$367$	−1.51279e6	+	1.09911e6i	−0.586292	+	0.425966i	0.254695	+	0.967022i	$0.418025\pi$
$368$	−1.16167e6			−0.447161
$369$	1.31085e6	−	1.64112e6i	0.501171	−	0.627444i
$370$	−1.50998e6			−0.573411
$371$	−1.07579e6	+	781607.i	−0.405782	+	0.294818i
$372$	−157315.			−0.0589403
$373$	−1.36014e6	+	4.18609e6i	−0.506189	+	1.55789i	0.292573	+	0.956243i	$0.405489\pi$
$373$	−1.36014e6	+	4.18609e6i	−0.506189	+	1.55789i	−0.798762	+	0.601647i	$0.794511\pi$
$374$	−460888.	+	1.41847e6i	−0.170379	+	0.524374i
$375$	3.02436e6	−	2.19733e6i	1.11060	−	0.806895i
$376$	−371924.	−	270219.i	−0.135670	−	0.0985703i
$377$	48517.2	+	149321.i	0.0175809	+	0.0541086i
$378$	521292.			0.187651
$379$	−684285.	−	2.10601e6i	−0.244703	−	0.753118i	−0.995685	−	0.0927954i	$-0.970420\pi$
$379$	−684285.	−	2.10601e6i	−0.244703	−	0.753118i	0.750982	−	0.660322i	$-0.229580\pi$
$380$	94918.2	+	292128.i	0.0337202	+	0.103780i
$381$	842811.	−	2.59391e6i	0.297453	−	0.915465i
$382$	1.47218e6	−	1.06960e6i	0.516183	−	0.375029i
$383$	1.77978e6			0.619969			0.309985	−	0.950742i	$-0.399676\pi$
$383$	1.77978e6			0.619969			0.309985	+	0.950742i	$0.399676\pi$
$384$	105976.	−	326160.i	0.0366757	−	0.112876i
$385$	937327.	+	681008.i	0.322284	+	0.234153i
$386$	925425.	+	2.84816e6i	0.316135	+	0.972964i
$387$	1.26337e6	−	917893.i	0.428799	−	0.311540i
$388$	−1.96717e6	−	1.42923e6i	−0.663381	−	0.481975i
$389$	−1.25172e6	−	909429.i	−0.419405	−	0.304716i	0.357993	−	0.933724i	$-0.383461\pi$
$389$	−1.25172e6	−	909429.i	−0.419405	−	0.304716i	−0.777398	+	0.629008i	$0.783461\pi$
$390$	−1.86732e6	−	1.35669e6i	−0.621666	−	0.451667i
$391$	−5.54913e6	−	4.03168e6i	−1.83562	−	1.33366i
$392$	5892.36	−	4281.05i	0.00193675	−	0.00140713i
$393$	1.47019e6	+	4.52479e6i	0.480167	+	1.47780i
$394$	2.42678e6	+	1.76316e6i	0.787572	+	0.572205i
$395$	−546074.	+	1.68064e6i	−0.176100	+	0.541979i
$396$	−770171.			−0.246802
$397$	4.02148e6	−	2.92177e6i	1.28059	−	0.930402i	0.281017	−	0.959703i	$-0.409328\pi$
$397$	4.02148e6	−	2.92177e6i	1.28059	−	0.930402i	0.999571	+	0.0293011i	$0.00932818\pi$
$398$	−191500.	+	589376.i	−0.0605983	+	0.186503i
$399$	−447353.	−	1.37681e6i	−0.140675	−	0.432955i
$400$	−144078.	−	443425.i	−0.0450243	−	0.138570i
$401$	2.06880e6			0.642477			0.321239	−	0.946998i	$-0.395901\pi$
$401$	2.06880e6			0.642477			0.321239	+	0.946998i	$0.395901\pi$
$402$	−276561.	−	851166.i	−0.0853543	−	0.262694i
$403$	290138.	+	210798.i	0.0889903	+	0.0646552i
$404$	1.49645e6	−	1.08724e6i	0.456152	−	0.331414i
$405$	763066.	−	2.34848e6i	0.231166	−	0.711457i
$406$	−33064.6	+	101762.i	−0.00995516	+	0.0306388i
$407$	2.57897e6			0.771719
$408$	1.63820e6	−	1.19022e6i	0.487210	−	0.353979i
$409$	6.69872e6			1.98008			0.990042	−	0.140773i	$-0.0449588\pi$
$409$	6.69872e6			1.98008			0.990042	+	0.140773i	$0.0449588\pi$
$410$	1.45503e6	+	547376.i	0.427476	+	0.160815i
$411$	−3.54766e6			−1.03595
$412$	1.39007e6	−	1.00994e6i	0.403453	−	0.293125i
$413$	3.48516e6			1.00542
$414$	1.09452e6	−	3.36859e6i	0.313850	−	0.965932i
$415$	−30787.6	+	94754.5i	−0.00877517	+	0.0270072i
$416$	−632499.	+	459538.i	−0.179195	+	0.130193i
$417$	−318501.	−	231405.i	−0.0896956	−	0.0651677i
$418$	−162115.	−	498940.i	−0.0453820	−	0.139671i
$419$	−5.67687e6			−1.57970			−0.789849	−	0.613301i	$-0.789841\pi$
$419$	−5.67687e6			−1.57970			−0.789849	+	0.613301i	$0.789841\pi$
$420$	−486084.	−	1.49601e6i	−0.134458	−	0.413821i
$421$	1.54744e6	+	4.76254e6i	0.425510	+	1.30958i	0.902505	+	0.430679i	$0.141726\pi$
$421$	1.54744e6	+	4.76254e6i	0.425510	+	1.30958i	−0.476996	+	0.878906i	$0.658274\pi$
$422$	462058.	−	1.42207e6i	0.126304	−	0.388723i
$423$	1.13400e6	−	823898.i	0.308150	−	0.223884i
$424$	654243.			0.176736
$425$	850709.	−	2.61821e6i	0.228459	−	0.703125i
$426$	−2.70137e6	−	1.96266e6i	−0.721206	−	0.523987i
$427$	−807383.	−	2.48487e6i	−0.214294	−	0.659529i
$428$	308532.	−	224162.i	0.0814125	−	0.0591497i
$429$	3.18929e6	+	2.31715e6i	0.836663	+	0.607871i
$430$	935075.	+	679372.i	0.243880	+	0.177189i
$431$	−5.30558e6	−	3.85473e6i	−1.37575	−	0.999542i	−0.997263	−	0.0739355i	$-0.976444\pi$
$431$	−5.30558e6	−	3.85473e6i	−1.37575	−	0.999542i	−0.378488	−	0.925606i	$-0.623556\pi$
$432$	−207495.	−	150754.i	−0.0534932	−	0.0388651i
$433$	3.01394e6	−	2.18976e6i	0.772530	−	0.561276i	−0.130198	−	0.991488i	$-0.541561\pi$
$433$	3.01394e6	−	2.18976e6i	0.772530	−	0.561276i	0.902728	+	0.430212i	$0.141561\pi$
$434$	75526.2	+	232446.i	0.0192475	+	0.0592376i
$435$	125738.	+	91354.1i	0.0318599	+	0.0231475i
$436$	−535204.	+	1.64719e6i	−0.134835	+	0.414980i
$437$	2.41266e6			0.604356
$438$	4.81728e6	−	3.49996e6i	1.19982	−	0.871721i
$439$	−1.16794e6	+	3.59456e6i	−0.289241	+	0.890193i	0.695854	+	0.718183i	$0.255026\pi$
$439$	−1.16794e6	+	3.59456e6i	−0.289241	+	0.890193i	−0.985095	+	0.172010i	$0.944974\pi$
$440$	−176151.	−	542137.i	−0.0433764	−	0.133499i
$441$	6862.33	+	21120.1i	0.00168026	+	0.00517130i
$442$	−4.61623e6			−1.12391
$443$	1.64255e6	+	5.05526e6i	0.397658	+	1.22387i	0.926872	+	0.375377i	$0.122487\pi$
$443$	1.64255e6	+	5.05526e6i	0.397658	+	1.22387i	−0.529214	+	0.848488i	$0.677513\pi$
$444$	−2.83269e6	−	2.05807e6i	−0.681933	−	0.495453i
$445$	2.25484e6	−	1.63824e6i	0.539779	−	0.392172i
$446$	−1.55833e6	+	4.79603e6i	−0.370955	+	1.14168i
$447$	920288.	−	2.83235e6i	0.217849	−	0.670469i
$448$	−532808.			−0.125422
$449$	−3.73615e6	+	2.71447e6i	−0.874597	+	0.635432i	−0.931817	−	0.362929i	$-0.881777\pi$
$449$	−3.73615e6	+	2.71447e6i	−0.874597	+	0.635432i	0.0572193	+	0.998362i	$0.481777\pi$
$450$	1.42158e6			0.330934
$451$	−2.48511e6	−	934890.i	−0.575314	−	0.216431i
$452$	−3.59823e6			−0.828406
$453$	694736.	−	504755.i	0.159065	−	0.115567i
$454$	−1.99219e6			−0.453618
$455$	−1.10813e6	+	3.41046e6i	−0.250935	+	0.772298i
$456$	−220100.	+	677398.i	−0.0495688	+	0.152557i
$457$	−4.64854e6	+	3.37736e6i	−1.04118	+	0.756463i	−0.970516	−	0.241037i	$-0.922512\pi$
$457$	−4.64854e6	+	3.37736e6i	−1.04118	+	0.756463i	−0.0706656	+	0.997500i	$0.522512\pi$
$458$	−120949.	−	87874.4i	−0.0269425	−	0.0195749i
$459$	−467969.	−	1.44026e6i	−0.103678	−	0.319087i
$460$	2.62154e6			0.577647
$461$	2.51745e6	+	7.74791e6i	0.551707	+	1.69798i	0.704486	+	0.709718i	$0.251178\pi$
$461$	2.51745e6	+	7.74791e6i	0.551707	+	1.69798i	−0.152779	+	0.988260i	$0.548822\pi$
$462$	830207.	+	2.55511e6i	0.180960	+	0.556936i
$463$	266173.	−	819195.i	0.0577047	−	0.177597i	−0.918050	−	0.396465i	$-0.870237\pi$
$463$	266173.	−	819195.i	0.0577047	−	0.177597i	0.975754	+	0.218869i	$0.0702367\pi$
$464$	42590.1	−	30943.5i	0.00918361	−	0.00667228i
$465$	355012.			0.0761397
$466$	1.17840e6	−	3.62674e6i	0.251378	−	0.773663i
$467$	242197.	+	175966.i	0.0513897	+	0.0373368i	0.613184	−	0.789940i	$-0.289889\pi$
$467$	242197.	+	175966.i	0.0513897	+	0.0373368i	−0.561794	+	0.827277i	$0.689889\pi$
$468$	−736619.	−	2.26708e6i	−0.155463	−	0.478467i
$469$	−1.12489e6	+	817283.i	−0.236145	+	0.171570i
$470$	839322.	+	609803.i	0.175260	+	0.127334i
$471$	2.60434e6	+	1.89216e6i	0.540936	+	0.393013i
$472$	−1.38723e6	−	1.00788e6i	−0.286612	−	0.208236i
$473$	−1.59706e6	−	1.16033e6i	−0.328223	−	0.238468i
$474$	−3.31510e6	+	2.40856e6i	−0.677722	+	0.492394i
$475$	299233.	+	920945.i	0.0608521	+	0.187284i
$476$	−2.54515e6	−	1.84916e6i	−0.514867	−	0.374073i
$477$	−616424.	+	1.89716e6i	−0.124046	+	0.381775i
$478$	5.81659e6			1.16439
$479$	−6.20180e6	+	4.50587e6i	−1.23503	+	0.897304i	−0.997257	−	0.0740154i	$-0.976419\pi$
$479$	−6.20180e6	+	4.50587e6i	−1.23503	+	0.897304i	−0.237777	+	0.971320i	$0.576419\pi$
$480$	−239156.	+	736046.i	−0.0473781	+	0.145815i
$481$	2.46662e6	+	7.59146e6i	0.486115	+	1.49611i
$482$	−1.55713e6	−	4.79235e6i	−0.305286	−	0.939573i
$483$	−1.23554e7			−2.40985
$484$	−495423.	−	1.52475e6i	−0.0961308	−	0.295860i
$485$	4.43932e6	+	3.22535e6i	0.856963	+	0.622620i
$486$	3.84459e6	−	2.79326e6i	0.738345	−	0.536439i
$487$	−2.50834e6	+	7.71987e6i	−0.479251	+	1.47498i	0.360886	+	0.932610i	$0.382475\pi$
$487$	−2.50834e6	+	7.71987e6i	−0.479251	+	1.47498i	−0.840137	+	0.542374i	$0.817525\pi$
$488$	−397237.	+	1.22257e6i	−0.0755092	+	0.232393i
$489$	8.16286e6			1.54373
$490$	−13297.3	+	9661.04i	−0.00250192	+	0.00181775i
$491$	−9.31165e6			−1.74310			−0.871552	−	0.490304i	$-0.836886\pi$
$491$	−9.31165e6			−1.74310			−0.871552	+	0.490304i	$0.836886\pi$
$492$	1.98354e6	+	3.01004e6i	0.369427	+	0.560608i
$493$	310839.			0.0575994
$494$	1.31363e6	−	954408.i	0.242190	−	0.175961i
$495$	1.73804e6			0.318822
$496$	37159.3	−	114365.i	0.00678208	−	0.0208731i
$497$	−1.60308e6	+	4.93376e6i	−0.291114	+	0.895957i
$498$	−186905.	+	135795.i	−0.0337713	+	0.0245363i
$499$	8.21505e6	+	5.96858e6i	1.47693	+	1.07305i	0.978531	+	0.206100i	$0.0660771\pi$
$499$	8.21505e6	+	5.96858e6i	1.47693	+	1.07305i	0.498395	+	0.866950i	$0.333923\pi$
$500$	883027.	+	2.71768e6i	0.157961	+	0.486153i
$501$	−9.51741e6			−1.69404
$502$	−2.33293e6	−	7.18001e6i	−0.413182	−	1.27164i
$503$	891879.	+	2.74492e6i	0.157176	+	0.483737i	0.998375	−	0.0569882i	$-0.0181497\pi$
$503$	891879.	+	2.74492e6i	0.157176	+	0.483737i	−0.841199	+	0.540726i	$0.818150\pi$
$504$	502008.	−	1.54502e6i	0.0880308	−	0.270931i
$505$	−3.37705e6	+	2.45357e6i	−0.589262	+	0.428124i
$506$	−4.47746e6			−0.777420
$507$	−1.36882e6	+	4.21280e6i	−0.236498	+	0.727865i
$508$	1.68663e6	+	1.22541e6i	0.289976	+	0.210680i
$509$	−1.47826e6	−	4.54962e6i	−0.252905	−	0.778361i	−0.994235	−	0.107221i	$-0.965805\pi$
$509$	−1.47826e6	−	4.54962e6i	−0.252905	−	0.778361i	0.741331	−	0.671140i	$-0.234195\pi$
$510$	−3.69693e6	+	2.68597e6i	−0.629384	+	0.457274i
$511$	−7.48424e6	−	5.43762e6i	−1.26793	−	0.921205i
$512$	212079.	+	154084.i	0.0357538	+	0.0259767i
$513$	430944.	+	313099.i	0.0722983	+	0.0525278i
$514$	−1.62054e6	−	1.17739e6i	−0.270553	−	0.196568i
$515$	−3.13696e6	+	2.27914e6i	−0.521184	+	0.378663i
$516$	828213.	+	2.54898e6i	0.136936	+	0.421446i
$517$	−1.43352e6	−	1.04151e6i	−0.235872	−	0.171371i
$518$	−1.68101e6	+	5.17361e6i	−0.275261	+	0.847167i
$519$	1.12891e7			1.83967
$520$	1.42736e6	−	1.03704e6i	0.231486	−	0.168185i
$521$	−682331.	+	2.10000e6i	−0.110129	+	0.338941i	−0.990900	−	0.134601i	$-0.957025\pi$
$521$	−682331.	+	2.10000e6i	−0.110129	+	0.338941i	0.880771	+	0.473542i	$0.157025\pi$
$522$	49601.1	+	152656.i	0.00796737	+	0.0245210i
$523$	1.23159e6	+	3.79044e6i	0.196884	+	0.605947i	0.999949	+	0.0100563i	$0.00320106\pi$
$523$	1.23159e6	+	3.79044e6i	0.196884	+	0.605947i	−0.803065	+	0.595891i	$0.796799\pi$
$524$	−3.63670e6			−0.578601
$525$	−1.53240e6	−	4.71624e6i	−0.242646	−	0.746788i
$526$	−2.24482e6	−	1.63096e6i	−0.353768	−	0.257027i
$527$	574417.	−	417338.i	0.0900950	−	0.0654578i
$528$	408466.	−	1.25713e6i	0.0637633	−	0.196243i
$529$	4.37416e6	−	1.34623e7i	0.679603	−	2.09160i
$530$	−1.47643e6			−0.228309
$531$	4.22968e6	−	3.07304e6i	0.650986	−	0.472969i
$532$	1.10658e6			0.169514
$533$	375098.	−	8.20936e6i	0.0571909	−	1.25167i
$534$	6.46292e6			0.980789
$535$	−696265.	+	505866.i	−0.105170	+	0.0764102i
$536$	684106.			0.102852
$537$	1.68737e6	−	5.19319e6i	0.252508	−	0.777138i
$538$	−566564.	+	1.74371e6i	−0.0843905	+	0.259727i
$539$	22711.1	−	16500.6i	0.00336718	−	0.00244640i
$540$	468255.	+	340207.i	0.0691031	+	0.0502064i
$541$	502718.	+	1.54721e6i	0.0738468	+	0.227277i	0.981166	−	0.193165i	$-0.0618752\pi$
$541$	502718.	+	1.54721e6i	0.0738468	+	0.227277i	−0.907320	+	0.420442i	$0.861875\pi$
$542$	1.52998e6			0.223712
$543$	−4.19530e6	−	1.29118e7i	−0.610610	−	1.87926i
$544$	478307.	+	1.47208e6i	0.0692962	+	0.213272i
$545$	1.20780e6	−	3.71721e6i	0.174182	−	0.536076i
$546$	−6.72721e6	+	4.88761e6i	−0.965725	+	0.701640i
$547$	5.22639e6			0.746850			0.373425	−	0.927660i	$-0.378183\pi$
$547$	5.22639e6			0.746850			0.373425	+	0.927660i	$0.378183\pi$
$548$	837992.	−	2.57907e6i	0.119203	−	0.366870i
$549$	−3.17090e6	−	2.30379e6i	−0.449006	−	0.326222i
$550$	−555323.	−	1.70911e6i	−0.0782778	−	0.240914i
$551$	−88454.8	+	64266.2i	−0.0124120	+	0.00901786i
$552$	4.91796e6	+	3.57311e6i	0.686970	+	0.499113i
$553$	5.15043e6	+	3.74200e6i	0.716193	+	0.520345i
$554$	3.60734e6	+	2.62088e6i	0.499359	+	0.362805i
$555$	6.39253e6	+	4.64445e6i	0.880928	+	0.640032i
$556$	243459.	−	176884.i	0.0333995	−	0.0242661i
$557$	1.54193e6	+	4.74558e6i	0.210585	+	0.648114i	0.999438	+	0.0335316i	$0.0106755\pi$
$557$	1.54193e6	+	4.74558e6i	0.210585	+	0.648114i	−0.788853	+	0.614582i	$0.789325\pi$
$558$	296620.	+	215507.i	0.0403288	+	0.0293006i
$559$	1.88808e6	−	5.81091e6i	0.255558	−	0.786528i
$560$	1.20239e6			0.162022
$561$	6.31416e6	−	4.58751e6i	0.847049	−	0.615417i
$562$	2.23961e6	−	6.89280e6i	0.299110	−	0.920565i
$563$	−1.29359e6	−	3.98125e6i	−0.171998	−	0.529356i	0.827485	−	0.561487i	$-0.189771\pi$
$563$	−1.29359e6	−	3.98125e6i	−0.171998	−	0.529356i	−0.999484	+	0.0321310i	$0.989771\pi$
$564$	743402.	+	2.28796e6i	0.0984070	+	0.302866i
$565$	8.12014e6			1.07014
$566$	2.22801e6	+	6.85712e6i	0.292332	+	0.899706i
$567$	−7.19704e6	−	5.22896e6i	−0.940148	−	0.683058i
$568$	2.06490e6	−	1.50024e6i	0.268552	−	0.195114i
$569$	910513.	−	2.80227e6i	0.117898	−	0.362852i	−0.874643	−	0.484768i	$-0.838904\pi$
$569$	910513.	−	2.80227e6i	0.117898	−	0.362852i	0.992540	+	0.121916i	$0.0389039\pi$
$570$	496700.	−	1.52869e6i	0.0640335	−	0.197075i
$571$	8.96889e6			1.15119			0.575597	−	0.817734i	$-0.304770\pi$
$571$	8.96889e6			1.15119			0.575597	+	0.817734i	$0.304770\pi$
$572$	−2.43786e6	+	1.77121e6i	−0.311544	+	0.226350i
$573$	−9.52246e6			−1.21161
$574$	3.49529e6	−	4.37596e6i	0.442796	−	0.554362i
$575$	8.26451e6			1.04243
$576$	−646630.	+	469804.i	−0.0812081	+	0.0590012i
$577$	−1.16864e7			−1.46130			−0.730650	−	0.682752i	$-0.760783\pi$
$577$	−1.16864e7			−1.46130			−0.730650	+	0.682752i	$0.760783\pi$
$578$	−1.06913e6	+	3.29046e6i	−0.133111	+	0.409672i
$579$	4.84268e6	−	1.49042e7i	0.600329	−	1.84762i
$580$	−96113.0	+	69830.2i	−0.0118635	+	0.00861933i
$581$	290381.	+	210974.i	0.0356884	+	0.0259291i
$582$	3.93198e6	+	1.21014e7i	0.481176	+	1.48091i
$583$	2.52167e6			0.307267
$584$	1.40651e6	+	4.32878e6i	0.170651	+	0.525211i
$585$	1.66233e6	+	5.11612e6i	0.200829	+	0.618089i
$586$	−2.62867e6	+	8.09022e6i	−0.316222	+	0.973232i
$587$	−6.94434e6	+	5.04536e6i	−0.831832	+	0.604361i	−0.920077	−	0.391738i	$-0.871874\pi$
$587$	−6.94434e6	+	5.04536e6i	−0.831832	+	0.604361i	0.0882451	+	0.996099i	$0.471874\pi$
$588$	−38113.2			−0.00454603
$589$	−77175.7	+	237522.i	−0.00916626	+	0.0282108i
$590$	3.13057e6	+	2.27449e6i	0.370249	+	0.269001i
$591$	−4.85065e6	−	1.49288e7i	−0.571257	−	1.75815i
$592$	2.16528e6	−	1.57317e6i	0.253928	−	0.184489i
$593$	−1.14737e6	−	833610.i	−0.133988	−	0.0973478i	0.518773	−	0.854912i	$-0.326389\pi$
$593$	−1.14737e6	−	833610.i	−0.133988	−	0.0973478i	−0.652760	+	0.757564i	$0.726389\pi$
$594$	−799755.	−	581056.i	−0.0930017	−	0.0675697i
$595$	5.74363e6	+	4.17299e6i	0.665111	+	0.483232i
$596$	1.84168e6	+	1.33806e6i	0.212373	+	0.154298i
$597$	2.62354e6	−	1.90612e6i	0.301268	−	0.218884i
$598$	−4.28241e6	−	1.31799e7i	−0.489705	−	1.50716i
$599$	1.45691e6	+	1.05851e6i	0.165908	+	0.120539i	0.667641	−	0.744483i	$-0.267304\pi$
$599$	1.45691e6	+	1.05851e6i	0.165908	+	0.120539i	−0.501733	+	0.865022i	$0.667304\pi$
$600$	−753948.	+	2.32041e6i	−0.0854994	+	0.263140i
$601$	−970704.			−0.109623			−0.0548114	−	0.998497i	$-0.517456\pi$
$601$	−970704.			−0.109623			−0.0548114	+	0.998497i	$0.517456\pi$
$602$	3.36871e6	−	2.44751e6i	0.378854	−	0.275254i
$603$	−644561.	+	1.98375e6i	−0.0721890	+	0.222175i
$604$	202843.	+	624286.i	0.0226239	+	0.0696292i
$605$	1.11802e6	+	3.44092e6i	0.124183	+	0.382195i
$606$	−9.67944e6			−1.07070
$607$	−1.03193e6	−	3.17596e6i	−0.113679	−	0.349867i	0.877990	−	0.478678i	$-0.158884\pi$
$607$	−1.03193e6	−	3.17596e6i	−0.113679	−	0.349867i	−0.991669	+	0.128811i	$0.958884\pi$
$608$	−440464.	−	320016.i	−0.0483228	−	0.0351085i
$609$	452985.	−	329113.i	0.0494926	−	0.0359585i
$610$	896444.	−	2.75897e6i	0.0975436	−	0.300208i
$611$	1.69473e6	−	5.21586e6i	0.183653	−	0.565227i
$612$	−4.71936e6			−0.509336
$613$	665206.	−	483301.i	0.0714999	−	0.0519477i	−0.551461	−	0.834201i	$-0.685930\pi$
$613$	665206.	−	483301.i	0.0714999	−	0.0519477i	0.622961	+	0.782253i	$0.285930\pi$
$614$	1.26686e6			0.135615
$615$	−4.47626e6	−	6.79276e6i	−0.477230	−	0.724200i
$616$	−2.05362e6			−0.218056
$617$	−1.34226e7	+	9.75206e6i	−1.41946	+	1.03130i	−0.427596	+	0.903970i	$0.640640\pi$
$617$	−1.34226e7	+	9.75206e6i	−1.41946	+	1.03130i	−0.991861	+	0.127326i	$0.959360\pi$
$618$	−8.99130e6			−0.947003
$619$	201679.	−	620703.i	0.0211560	−	0.0651114i	−0.939921	−	0.341392i	$-0.889102\pi$
$619$	201679.	−	620703.i	0.0211560	−	0.0651114i	0.961077	+	0.276280i	$0.0891018\pi$
$620$	−83857.4	+	258086.i	−0.00876117	+	0.0269641i
$621$	3.67800e6	−	2.67222e6i	0.382721	−	0.278063i
$622$	−5.97943e6	−	4.34431e6i	−0.619703	−	0.450241i
$623$	−3.10282e6	−	9.54951e6i	−0.320285	−	0.985737i
$624$	4.09117e6			0.420616
$625$	−233968.	−	720080.i	−0.0239583	−	0.0737362i
$626$	2.81736e6	+	8.67093e6i	0.287346	+	0.884361i
$627$	−848338.	+	2.61092e6i	−0.0861788	+	0.265231i
$628$	−1.99073e6	+	1.44635e6i	−0.201425	+	0.146344i
$629$	1.58031e7			1.59263
$630$	−1.13288e6	+	3.48665e6i	−0.113719	+	0.349992i
$631$	4.38287e6	+	3.18434e6i	0.438213	+	0.318380i	0.784925	−	0.619591i	$-0.212702\pi$
$631$	4.38287e6	+	3.18434e6i	0.438213	+	0.318380i	−0.346711	+	0.937972i	$0.612702\pi$
$632$	−967915.	−	2.97894e6i	−0.0963928	−	0.296667i
$633$	−6.33019e6	+	4.59915e6i	−0.627925	+	0.456214i
$634$	4.20461e6	+	3.05483e6i	0.415434	+	0.301831i
$635$	−3.80623e6	−	2.76539e6i	−0.374594	−	0.272158i
$636$	−2.76975e6	−	2.01234e6i	−0.271518	−	0.197269i
$637$	70292.9	+	51070.8i	0.00686377	+	0.00498682i
$638$	164156.	−	119266.i	0.0159663	−	0.0116002i
$639$	2.40482e6	+	7.40126e6i	0.232986	+	0.717057i
$640$	−478599.	−	347722.i	−0.0461872	−	0.0335570i
$641$	−5.56810e6	+	1.71368e7i	−0.535256	+	1.64735i	0.207838	+	0.978163i	$0.433357\pi$
$641$	−5.56810e6	+	1.71368e7i	−0.535256	+	1.64735i	−0.743094	+	0.669187i	$0.766643\pi$
$642$	−1.99567e6			−0.191095
$643$	−1.10197e7	+	8.00628e6i	−1.05110	+	0.763666i	−0.972421	−	0.233234i	$-0.925069\pi$
$643$	−1.10197e7	+	8.00628e6i	−1.05110	+	0.763666i	−0.0786754	+	0.996900i	$0.525069\pi$
$644$	2.91847e6	−	8.98214e6i	0.277294	−	0.853425i
$645$	−1.86903e6	−	5.75228e6i	−0.176895	−	0.544428i
$646$	−993391.	−	3.05734e6i	−0.0936567	−	0.288246i
$647$	−5.61708e6			−0.527534			−0.263767	−	0.964586i	$-0.584965\pi$
$647$	−5.61708e6			−0.527534			−0.263767	+	0.964586i	$0.584965\pi$
$648$	1.35253e6	+	4.16267e6i	0.126535	+	0.389435i
$649$	−5.34685e6	−	3.88472e6i	−0.498295	−	0.362033i
$650$	4.49981e6	−	3.26930e6i	0.417745	−	0.303509i
$651$	395223.	−	1.21637e6i	0.0365502	−	0.112490i
$652$	−1.92815e6	+	5.93423e6i	−0.177632	+	0.546695i
$653$	−3.78901e6			−0.347730			−0.173865	−	0.984769i	$-0.555626\pi$
$653$	−3.78901e6			−0.347730			−0.173865	+	0.984769i	$0.555626\pi$
$654$	7.33228e6	−	5.32722e6i	0.670340	−	0.487030i
$655$	8.20694e6			0.747442
$656$	−2.65677e6	+	730991.i	−0.241043	+	0.0663212i
$657$	−1.38777e7			−1.25431
$658$	3.02374e6	−	2.19688e6i	0.272258	−	0.197807i
$659$	−1.48570e7			−1.33265			−0.666325	−	0.745661i	$-0.732134\pi$
$659$	−1.48570e7			−1.33265			−0.666325	+	0.745661i	$0.732134\pi$
$660$	−921785.	+	2.83696e6i	−0.0823702	+	0.253509i
$661$	3.97364e6	−	1.22296e7i	0.353740	−	1.08870i	−0.602996	−	0.797744i	$-0.706026\pi$
$661$	3.97364e6	−	1.22296e7i	0.353740	−	1.08870i	0.956736	−	0.290957i	$-0.0939735\pi$
$662$	1.07357e7	−	7.79998e6i	0.952110	−	0.691749i
$663$	1.95429e7	+	1.41988e7i	1.72665	+	1.25449i
$664$	−54571.0	−	167952.i	−0.00480332	−	0.0147831i
$665$	−2.49722e6			−0.218979
$666$	2.52172e6	+	7.76106e6i	0.220298	+	0.678009i
$667$	288361.	+	887483.i	0.0250970	+	0.0772406i
$668$	2.24810e6	−	6.91895e6i	0.194928	−	0.599928i
$669$	2.13490e7	−	1.55110e7i	1.84422	−	1.33991i
$670$	−1.54382e6			−0.132865
$671$	−1.53108e6	+	4.71218e6i	−0.131278	+	0.404032i
$672$	2.25566e6	+	1.63883e6i	0.192686	+	0.139994i
$673$	−193355.	−	595087.i	−0.0164558	−	0.0506457i	0.942491	−	0.334230i	$-0.108476\pi$
$673$	−193355.	−	595087.i	−0.0164558	−	0.0506457i	−0.958947	+	0.283585i	$0.908476\pi$
$674$	−476868.	+	346465.i	−0.0404342	+	0.0293772i
$675$	1.47619e6	+	1.07252e6i	0.124705	+	0.0906033i
$676$	−2.73929e6	−	1.99021e6i	−0.230553	−	0.167507i
$677$	8.72642e6	+	6.34012e6i	0.731753	+	0.531650i	0.890118	−	0.455731i	$-0.150622\pi$
$677$	8.72642e6	+	6.34012e6i	0.731753	+	0.531650i	−0.158364	+	0.987381i	$0.550622\pi$
$678$	1.52332e7	+	1.10676e7i	1.27267	+	0.924652i
$679$	1.59931e7	−	1.16197e7i	1.33125	−	0.967207i
$680$	−1.07940e6	−	3.32204e6i	−0.0895176	−	0.275507i
$681$	8.43397e6	+	6.12764e6i	0.696890	+	0.506320i
$682$	143224.	−	440799.i	0.0117911	−	0.0362894i
$683$	−9.06572e6			−0.743619			−0.371810	−	0.928309i	$-0.621263\pi$
$683$	−9.06572e6			−0.743619			−0.371810	+	0.928309i	$0.621263\pi$
$684$	1.34298e6	−	975731.i	0.109756	−	0.0797425i
$685$	−1.89110e6	+	5.82020e6i	−0.153988	+	0.473927i
$686$	−2.68406e6	−	8.26069e6i	−0.217762	−	0.670202i
$687$	241752.	+	744037.i	0.0195424	+	0.0601455i
$688$	−2.04868e6			−0.165008
$689$	2.41181e6	+	7.42280e6i	0.193551	+	0.595689i
$690$	−1.10984e7	−	8.06344e6i	−0.887435	−	0.644759i
$691$	−6.71115e6	+	4.87594e6i	−0.534690	+	0.388475i	−0.822109	−	0.569330i	$-0.807203\pi$
$691$	−6.71115e6	+	4.87594e6i	−0.534690	+	0.388475i	0.287419	+	0.957805i	$0.407203\pi$
$692$	−2.66659e6	+	8.20692e6i	−0.211685	+	0.651501i
$693$	1.93491e6	−	5.95503e6i	0.153048	−	0.471032i
$694$	−7.48785e6			−0.590145
$695$	−549415.	+	399174.i	−0.0431458	+	0.0313473i
$696$	−275483.			−0.0215562
$697$	−1.52280e7	−	5.72870e6i	−1.18730	−	0.446657i
$698$	−1.30093e7			−1.01068
$699$	−1.61441e7	+	1.17293e7i	−1.24974	+	0.907989i
$700$	3.79057e6			0.292388
$701$	5.84106e6	−	1.79769e7i	0.448948	−	1.38172i	−0.429147	−	0.903235i	$-0.641186\pi$
$701$	5.84106e6	−	1.79769e7i	0.448948	−	1.38172i	0.878095	−	0.478486i	$-0.158814\pi$
$702$	945487.	−	2.90991e6i	0.0724123	−	0.222862i
$703$	−4.49705e6	+	3.26730e6i	−0.343193	+	0.249345i
$704$	817422.	+	593892.i	0.0621606	+	0.0451623i
$705$	−1.67764e6	−	5.16323e6i	−0.127123	−	0.391245i
$706$	−3.52217e6			−0.265949
$707$	4.64706e6	+	1.43022e7i	0.349647	+	1.07610i
$708$	2.77280e6	+	8.53381e6i	0.207891	+	0.639823i
$709$	2.42750e6	−	7.47109e6i	0.181361	−	0.558172i	−0.818506	−	0.574499i	$-0.805197\pi$
$709$	2.42750e6	−	7.47109e6i	0.181361	−	0.558172i	0.999867	+	0.0163263i	$0.00519705\pi$
$710$	−4.65986e6	+	3.38559e6i	−0.346918	+	0.252051i
$711$	9.55021e6			0.708499
$712$	−1.52660e6	+	4.69841e6i	−0.112857	+	0.347337i
$713$	1.72443e6	+	1.25287e6i	0.127035	+	0.0922960i
$714$	5.08724e6	+	1.56569e7i	0.373453	+	1.14937i
$715$	5.50152e6	−	3.99709e6i	0.402455	−	0.292401i
$716$	3.37676e6	+	2.45336e6i	0.246160	+	0.178846i
$717$	−2.46247e7	−	1.78909e7i	−1.78884	−	1.29967i
$718$	−2.08740e6	−	1.51659e6i	−0.151110	−	0.109788i
$719$	1.50710e7	+	1.09497e7i	1.08722	+	0.789915i	0.978928	−	0.204204i	$-0.0654605\pi$
$719$	1.50710e7	+	1.09497e7i	1.08722	+	0.789915i	0.108296	+	0.994119i	$0.465460\pi$
$720$	1.45925e6	−	1.06021e6i	0.104906	−	0.0762183i
$721$	4.31669e6	+	1.32854e7i	0.309252	+	0.951780i
$722$	−7.09803e6	−	5.15702e6i	−0.506751	−	0.368176i
$723$	−8.14833e6	+	2.50780e7i	−0.579726	+	1.78421i
$724$	1.03776e7			0.735784
$725$	−303000.	+	220142.i	−0.0214091	+	0.0155546i
$726$	−2.59251e6	+	7.97893e6i	−0.182549	+	0.561828i
$727$	1.03360e6	+	3.18110e6i	0.0725300	+	0.223224i	0.980750	−	0.195269i	$-0.0625581\pi$
$727$	1.03360e6	+	3.18110e6i	0.0725300	+	0.223224i	−0.908220	+	0.418494i	$0.862558\pi$
$728$	−1.96415e6	−	6.04504e6i	−0.137356	−	0.422738i
$729$	−8.24926e6			−0.574905
$730$	−3.17406e6	−	9.76877e6i	−0.220449	−	0.678473i
$731$	−9.78627e6	−	7.11014e6i	−0.677367	−	0.492136i
$732$	5.44213e6	−	3.95394e6i	0.375398	−	0.272742i
$733$	−8.84369e6	+	2.72181e7i	−0.607958	+	1.87110i	−0.132947	+	0.991123i	$0.542444\pi$
$733$	−8.84369e6	+	2.72181e7i	−0.607958	+	1.87110i	−0.475011	+	0.879980i	$0.657556\pi$
$734$	−2.31134e6	+	7.11358e6i	−0.158352	+	0.487358i
$735$	86010.2			0.00587262
$736$	−3.75925e6	+	2.73125e6i	−0.255803	+	0.185852i
$737$	2.63677e6			0.178815
$738$	383478.	−	8.39276e6i	0.0259179	−	0.567236i
$739$	2.72157e6			0.183320			0.0916598	−	0.995790i	$-0.470783\pi$
$739$	2.72157e6			0.183320			0.0916598	+	0.995790i	$0.470783\pi$
$740$	−4.88639e6	+	3.55017e6i	−0.328026	+	0.238325i
$741$	−8.49689e6			−0.568479
$742$	−1.64366e6	+	5.05866e6i	−0.109598	+	0.337308i
$743$	6.00879e6	−	1.84932e7i	0.399314	−	1.22896i	−0.526236	−	0.850339i	$-0.676397\pi$
$743$	6.00879e6	−	1.84932e7i	0.399314	−	1.22896i	0.925550	−	0.378625i	$-0.123603\pi$
$744$	−509081.	+	369869.i	−0.0337175	+	0.0244972i
$745$	−4.15612e6	−	3.01960e6i	−0.274345	−	0.199324i
$746$	5.44058e6	+	1.67444e7i	0.357930	+	1.10159i
$747$	538440.			0.0353050
$748$	1.84355e6	+	5.67388e6i	0.120476	+	0.370788i
$749$	958111.	+	2.94876e6i	0.0624038	+	0.192059i
$750$	4.62082e6	−	1.42214e7i	0.299962	−	0.923187i
$751$	−9.05267e6	+	6.57715e6i	−0.585702	+	0.425538i	−0.840775	−	0.541384i	$-0.817900\pi$
$751$	−9.05267e6	+	6.57715e6i	−0.585702	+	0.425538i	0.255073	+	0.966922i	$0.417900\pi$
$752$	−1.83889e6			−0.118580
$753$	−1.22080e7	+	3.75725e7i	−0.784618	+	2.41481i
$754$	508078.	+	369141.i	0.0325464	+	0.0236463i
$755$	−457756.	−	1.40883e6i	−0.0292258	−	0.0899477i
$756$	1.68694e6	−	1.22563e6i	0.107348	−	0.0779929i
$757$	−1.07962e7	−	7.84392e6i	−0.684751	−	0.497500i	0.190180	−	0.981749i	$-0.439093\pi$
$757$	−1.07962e7	−	7.84392e6i	−0.684751	−	0.497500i	−0.874930	+	0.484249i	$0.839093\pi$
$758$	−7.16592e6	−	5.20635e6i	−0.453001	−	0.329124i
$759$	1.89555e7	+	1.37719e7i	1.19435	+	0.867742i
$760$	993996.	+	722180.i	0.0624239	+	0.0453536i
$761$	1.00277e7	−	7.28558e6i	0.627685	−	0.456040i	−0.227913	−	0.973682i	$-0.573190\pi$
$761$	1.00277e7	−	7.28558e6i	0.627685	−	0.456040i	0.855597	+	0.517642i	$0.173190\pi$
$762$	−3.37125e6	−	1.03756e7i	−0.210331	−	0.647332i
$763$	−1.13916e7	−	8.27649e6i	−0.708392	−	0.514677i
$764$	2.24930e6	−	6.92263e6i	0.139416	−	0.429079i
$765$	1.06502e7			0.657965
$766$	5.75950e6	−	4.18452e6i	0.354660	−	0.257676i
$767$	6.32116e6	−	1.94545e7i	0.387979	−	1.19408i
$768$	−423903.	−	1.30464e6i	−0.0259337	−	0.0798156i
$769$	6.01208e6	+	1.85033e7i	0.366614	+	1.12832i	0.948964	+	0.315383i	$0.102133\pi$
$769$	6.01208e6	+	1.85033e7i	0.366614	+	1.12832i	−0.582351	+	0.812938i	$0.697867\pi$
$770$	4.63440e6			0.281687
$771$	3.23914e6	+	9.96904e6i	0.196243	+	0.603973i
$772$	9.69117e6	+	7.04105e6i	0.585239	+	0.425201i
$773$	−8.28185e6	+	6.01712e6i	−0.498516	+	0.362193i	−0.808450	−	0.588565i	$-0.799693\pi$
$773$	−8.28185e6	+	6.01712e6i	−0.498516	+	0.362193i	0.309934	+	0.950758i	$0.399693\pi$
$774$	1.93026e6	−	5.94073e6i	0.115815	−	0.356441i
$775$	−264363.	+	813627.i	−0.0158106	+	0.0486599i
$776$	−9.72624e6			−0.579816
$777$	2.30298e7	−	1.67321e7i	1.36847	−	0.994255i
$778$	−6.18885e6			−0.366574
$779$	5.51781e6	−	1.51819e6i	0.325779	−	0.0896359i
$780$	−9.23254e6			−0.543356
$781$	7.95881e6	−	5.78241e6i	0.466896	−	0.339220i
$782$	−2.74364e7			−1.60439
$783$	−63665.4	+	195942.i	−0.00371107	+	0.0114215i
$784$	9002.72	−	27707.5i	0.000523099	−	0.00160993i
$785$	4.49249e6	−	3.26398e6i	0.260203	−	0.189049i
$786$	1.53961e7	+	1.11859e7i	0.888900	+	0.645824i
$787$	−4.65425e6	−	1.43243e7i	−0.267863	−	0.824398i	−0.991020	−	0.133714i	$-0.957310\pi$
$787$	−4.65425e6	−	1.43243e7i	−0.267863	−	0.824398i	0.723157	−	0.690684i	$-0.242690\pi$
$788$	1.19987e7			0.688363
$789$	4.48696e6	+	1.38094e7i	0.256602	+	0.789738i
$790$	2.18429e6	+	6.72257e6i	0.124521	+	0.383237i
$791$	9.03987e6	−	2.78219e7i	0.513714	−	1.58105i
$792$	−2.49233e6	+	1.81078e6i	−0.141186	+	0.102578i
$793$	−1.53352e7			−0.865977
$794$	6.14427e6	−	1.89101e7i	0.345875	−	1.06449i
$795$	6.25051e6	+	4.54126e6i	0.350750	+	0.254835i
$796$	765999.	+	2.35750e6i	0.0428495	+	0.131877i
$797$	2.48190e7	−	1.80321e7i	1.38401	−	1.00554i	0.387516	−	0.921863i	$-0.373333\pi$
$797$	2.48190e7	−	1.80321e7i	1.38401	−	1.00554i	0.996493	−	0.0836785i	$-0.0266669\pi$
$798$	−4.68474e6	−	3.40367e6i	−0.260423	−	0.189208i
$799$	−8.78414e6	−	6.38205e6i	−0.486779	−	0.353666i
$800$	−1.50880e6	−	1.09621e6i	−0.0833502	−	0.0605575i
$801$	−1.21860e7	−	8.85363e6i	−0.671087	−	0.487573i
$802$	6.69478e6	−	4.86404e6i	0.367536	−	0.267031i
$803$	5.42114e6	+	1.66846e7i	0.296689	+	0.913116i
$804$	−2.89618e6	−	2.10420e6i	−0.158010	−	0.114801i
$805$	−6.58612e6	+	2.02700e7i	−0.358212	+	1.10246i
$806$	1.43452e6			0.0777803
$807$	7.76192e6	−	5.63936e6i	0.419551	−	0.304822i
$808$	2.28638e6	−	7.03674e6i	0.123202	−	0.379178i
$809$	4.41582e6	+	1.35905e7i	0.237214	+	0.730069i	0.996820	+	0.0796856i	$0.0253916\pi$
$809$	4.41582e6	+	1.35905e7i	0.237214	+	0.730069i	−0.759606	+	0.650383i	$0.774608\pi$
$810$	−3.05226e6	−	9.39390e6i	−0.163459	−	0.503076i
$811$	−2.65448e7			−1.41719			−0.708593	−	0.705617i	$-0.750670\pi$
$811$	−2.65448e7			−1.41719			−0.708593	+	0.705617i	$0.750670\pi$
$812$	132258.	+	407050.i	0.00703936	+	0.0216649i
$813$	−6.47723e6	−	4.70598e6i	−0.343687	−	0.249703i
$814$	8.34571e6	−	6.06351e6i	0.441471	−	0.320747i
$815$	4.35125e6	−	1.33918e7i	0.229467	−	0.706226i
$816$	2.50295e6	−	7.70328e6i	0.131591	−	0.404995i
$817$	4.25489e6			0.223014
$818$	2.16775e7	−	1.57496e7i	1.13273	−	0.822976i
$819$	1.93799e7			1.00958
$820$	5.99552e6	−	1.64963e6i	0.311381	−	0.0856745i
$821$	−2.41900e7			−1.25250			−0.626251	−	0.779621i	$-0.715412\pi$
$821$	−2.41900e7			−1.25250			−0.626251	+	0.779621i	$0.715412\pi$
$822$	−1.14805e7	+	8.34105e6i	−0.592625	+	0.430568i
$823$	−3.84087e6			−0.197665			−0.0988326	−	0.995104i	$-0.531511\pi$
$823$	−3.84087e6			−0.197665			−0.0988326	+	0.995104i	$0.531511\pi$
$824$	2.12383e6	−	6.53648e6i	0.108969	−	0.335372i
$825$	−2.90596e6	+	8.94363e6i	−0.148647	+	0.457487i
$826$	1.12782e7	−	8.19409e6i	0.575162	−	0.417879i
$827$	−1.19500e7	−	8.68220e6i	−0.607582	−	0.441434i	0.240980	−	0.970530i	$-0.422531\pi$
$827$	−1.19500e7	−	8.68220e6i	−0.607582	−	0.441434i	−0.848562	+	0.529096i	$0.822531\pi$
$828$	−4.37808e6	−	1.34743e7i	−0.221926	−	0.683017i
$829$	−1.09080e7			−0.551262			−0.275631	−	0.961264i	$-0.588887\pi$
$829$	−1.09080e7			−0.551262			−0.275631	+	0.961264i	$0.588887\pi$
$830$	123150.	+	379018.i	0.00620498	+	0.0190970i
$831$	−7.21035e6	−	2.21912e7i	−0.362204	−	1.11475i
$832$	−966373.	+	2.97419e6i	−0.0483990	+	0.148957i
$833$	139166.	−	101110.i	0.00694898	−	0.00504873i
$834$	−1.57476e6			−0.0783968
$835$	−5.07330e6	+	1.56140e7i	−0.251811	+	0.774994i
$836$	−1.69770e6	−	1.23345e6i	−0.0840125	−	0.0610387i
$837$	145425.	+	447571.i	0.00717504	+	0.0220825i
$838$	−1.83707e7	+	1.33471e7i	−0.903684	+	0.656565i
$839$	2.98796e7	+	2.17088e7i	1.46545	+	1.06471i	0.981902	+	0.189389i	$0.0606506\pi$
$839$	2.98796e7	+	2.17088e7i	1.46545	+	1.06471i	0.483544	+	0.875320i	$0.339349\pi$
$840$	−5.09034e6	−	3.69835e6i	−0.248914	−	0.180846i
$841$	1.65597e7	+	1.20313e7i	0.807349	+	0.586573i
$842$	1.62050e7	+	1.17736e7i	0.787716	+	0.572309i
$843$	−3.06825e7	+	2.22922e7i	−1.48704	+	1.08040i
$844$	−1.84823e6	−	5.68828e6i	−0.0893101	−	0.274868i
$845$	6.18175e6	+	4.49131e6i	0.297831	+	0.216387i
$846$	1.73260e6	−	5.33238e6i	0.0832284	−	0.256151i
$847$	1.30342e7			0.624275
$848$	2.11717e6	−	1.53822e6i	0.101104	−	0.0734561i
$849$	1.16590e7	−	3.58828e7i	0.555128	−	1.70851i
$850$	−3.40284e6	−	1.04729e7i	−0.161545	−	0.497185i
$851$	1.46603e7	+	4.51197e7i	0.693934	+	2.13571i
$852$	−1.33563e7			−0.630358
$853$	−1.14711e7	−	3.53044e7i	−0.539800	−	1.66133i	−0.733044	−	0.680182i	$-0.761901\pi$
$853$	−1.14711e7	−	3.53044e7i	−0.539800	−	1.66133i	0.193244	−	0.981151i	$-0.438099\pi$
$854$	−8.45503e6	−	6.14294e6i	−0.396707	−	0.288225i
$855$	−3.03070e6	+	2.20193e6i	−0.141784	+	0.103012i
$856$	471395.	−	1.45081e6i	0.0219888	−	0.0676745i
$857$	4.16845e6	−	1.28292e7i	0.193875	−	0.596687i	−0.806112	−	0.591762i	$-0.798432\pi$
$857$	4.16845e6	−	1.28292e7i	0.193875	−	0.596687i	0.999988	−	0.00492480i	$-0.00156762\pi$
$858$	1.57687e7			0.731270
$859$	1.39772e7	−	1.01550e7i	0.646304	−	0.469568i	−0.215706	−	0.976458i	$-0.569205\pi$
$859$	1.39772e7	−	1.01550e7i	0.646304	−	0.469568i	0.862010	+	0.506891i	$0.169205\pi$
$860$	4.62327e6			0.213159
$861$	−2.82572e7	+	7.77477e6i	−1.29903	+	0.357421i
$862$	−2.62322e7			−1.20245
$863$	−1.89560e7	+	1.37723e7i	−0.866401	+	0.629477i	−0.929619	−	0.368522i	$-0.879864\pi$
$863$	−1.89560e7	+	1.37723e7i	−0.866401	+	0.629477i	0.0632177	+	0.998000i	$0.479864\pi$
$864$	−1.02591e6			−0.0467548
$865$	6.01770e6	−	1.85206e7i	0.273458	−	0.841616i
$866$	4.60490e6	−	1.41724e7i	0.208653	−	0.642169i
$867$	1.46471e7	−	1.06418e7i	0.661766	−	0.480801i
$868$	790921.	+	574638.i	0.0356315	+	0.0258878i
$869$	−3.73066e6	−	1.14818e7i	−0.167586	−	0.515776i
$870$	621683.			0.0278465
$871$	2.52190e6	+	7.76162e6i	0.112637	+	0.346663i
$872$	2.14082e6	+	6.58875e6i	0.0953429	+	0.293435i
$873$	9.16401e6	−	2.82039e7i	0.406958	−	1.25249i
$874$	7.80753e6	−	5.67250e6i	0.345729	−	0.251186i
$875$	−2.32318e7			−1.02580
$876$	7.36015e6	−	2.26522e7i	0.324061	−	0.997356i
$877$	1.15355e7	+	8.38106e6i	0.506453	+	0.367960i	0.811476	−	0.584385i	$-0.198664\pi$
$877$	1.15355e7	+	8.38106e6i	0.506453	+	0.367960i	−0.305023	+	0.952345i	$0.598664\pi$
$878$	4.67177e6	+	1.43782e7i	0.204524	+	0.629462i
$879$	3.60128e7	−	2.61648e7i	1.57212	−	1.14221i
$880$	−1.84468e6	−	1.34024e6i	−0.0802997	−	0.0583411i
$881$	1.90802e7	+	1.38626e7i	0.828214	+	0.601733i	0.919054	−	0.394133i	$-0.128955\pi$
$881$	1.90802e7	+	1.38626e7i	0.828214	+	0.601733i	−0.0908394	+	0.995866i	$0.528955\pi$
$882$	71863.3	+	52211.7i	0.00311054	+	0.00225994i
$883$	2.93888e7	+	2.13522e7i	1.26847	+	0.921598i	0.999141	−	0.0414495i	$-0.0131976\pi$
$883$	2.93888e7	+	2.13522e7i	1.26847	+	0.921598i	0.269331	+	0.963048i	$0.413198\pi$
$884$	−1.49384e7	+	1.08534e7i	−0.642945	+	0.467127i
$885$	−6.25738e6	−	1.92582e7i	−0.268556	−	0.826530i
$886$	1.72010e7	+	1.24973e7i	0.736156	+	0.534849i
$887$	9.49406e6	−	2.92197e7i	0.405175	−	1.24700i	−0.515573	−	0.856845i	$-0.672421\pi$
$887$	9.49406e6	−	2.92197e7i	0.405175	−	1.24700i	0.920749	−	0.390156i	$-0.127579\pi$
$888$	−1.40056e7			−0.596031
$889$	−1.37123e7	+	9.96260e6i	−0.581912	+	0.422784i
$890$	3.44509e6	−	1.06029e7i	0.145789	−	0.448693i
$891$	5.21311e6	+	1.60443e7i	0.219990	+	0.677060i
$892$	6.23330e6	+	1.91841e7i	0.262305	+	0.807291i
$893$	3.81918e6			0.160266
$894$	−3.68115e6	−	1.13294e7i	−0.154042	−	0.474093i
$895$	−7.62035e6	−	5.53651e6i	−0.317993	−	0.231035i
$896$	−1.72420e6	+	1.25271e6i	−0.0717494	+	0.0521290i
$897$	−2.24095e7	+	6.89694e7i	−0.929932	+	2.86204i
$898$	−5.70833e6	+	1.75684e7i	−0.236221	+	0.727012i
$899$	−96595.2			−0.00398618
$900$	4.60034e6	−	3.34234e6i	0.189314	−	0.137545i
$901$	1.54520e7			0.634120
$902$	−1.02401e7	+	2.81748e6i	−0.419069	+	0.115304i
$903$	−2.17896e7			−0.889264
$904$	−1.16441e7	+	8.45996e6i	−0.473899	+	0.344308i
$905$	−2.34191e7			−0.950493
$906$	1.06146e6	−	3.26684e6i	0.0429619	−	0.132223i
$907$	4.53466e6	−	1.39562e7i	0.183032	−	0.563314i	−0.816877	−	0.576812i	$-0.804297\pi$
$907$	4.53466e6	−	1.39562e7i	0.183032	−	0.563314i	0.999909	+	0.0134978i	$0.00429662\pi$
$908$	−6.44685e6	+	4.68391e6i	−0.259497	+	0.188536i
$909$	1.82508e7	+	1.32600e7i	0.732608	+	0.532271i
$910$	4.43251e6	+	1.36418e7i	0.177438	+	0.546097i
$911$	−2.86398e7			−1.14334			−0.571668	−	0.820485i	$-0.693703\pi$
$911$	−2.86398e7			−1.14334			−0.571668	+	0.820485i	$0.693703\pi$
$912$	880400.	+	2.70959e6i	0.0350504	+	0.107874i
$913$	−210335.	−	647343.i	−0.00835091	−	0.0257015i
$914$	−7.10234e6	+	2.18588e7i	−0.281213	+	0.865486i
$915$	−1.22813e7	+	8.92286e6i	−0.484943	+	0.352331i
$916$	−598004.			−0.0235486
$917$	9.13650e6	−	2.81193e7i	0.358803	−	1.10428i
$918$	−4.90064e6	−	3.56052e6i	−0.191931	−	0.139446i
$919$	−2.31246e6	−	7.11704e6i	−0.0903205	−	0.277978i	0.895685	−	0.444688i	$-0.146686\pi$
$919$	−2.31246e6	−	7.11704e6i	−0.0903205	−	0.277978i	−0.986006	+	0.166710i	$0.946686\pi$
$920$	8.48349e6	−	6.16362e6i	0.330449	−	0.240086i
$921$	−5.36330e6	−	3.89666e6i	−0.208345	−	0.151371i
$922$	2.63631e7	+	1.91539e7i	1.02134	+	0.742044i
$923$	2.46332e7	+	1.78971e7i	0.951738	+	0.691478i
$924$	8.69404e6	+	6.31659e6i	0.334998	+	0.243390i
$925$	−1.54045e7	+	1.11920e7i	−0.591962	+	0.430086i
$926$	−1.06469e6	−	3.27678e6i	−0.0408033	−	0.125580i
$927$	1.69533e7	+	1.23173e7i	0.647969	+	0.470777i
$928$	65071.8	−	200270.i	0.00248041	−	0.00763391i
$929$	−9.39878e6			−0.357299			−0.178650	−	0.983913i	$-0.557173\pi$
$929$	−9.39878e6			−0.357299			−0.178650	+	0.983913i	$0.557173\pi$
$930$	1.14884e6	−	834684.i	0.0435566	−	0.0316457i
$931$	−18697.6	+	57545.4i	−0.000706989	+	0.00217589i
$932$	−4.71360e6	−	1.45070e7i	−0.177751	−	0.547062i
$933$	1.19517e7	+	3.67835e7i	0.449495	+	1.38340i
$934$	1.19749e6			0.0449162
$935$	−4.16035e6	−	1.28042e7i	−0.155633	−	0.478988i
$936$	−7.71398e6	−	5.60453e6i	−0.287799	−	0.209098i
$937$	3.44316e7	−	2.50160e7i	1.28117	−	0.930827i	0.281586	−	0.959536i	$-0.409140\pi$
$937$	3.44316e7	−	2.50160e7i	1.28117	−	0.930827i	0.999588	+	0.0287091i	$0.00913964\pi$
$938$	−1.71869e6	+	5.28957e6i	−0.0637807	+	0.196297i
$939$	1.47430e7	−	4.53743e7i	0.545660	−	1.67937i
$940$	4.14983e6			0.153183
$941$	1.36067e7	−	9.88585e6i	0.500932	−	0.363949i	−0.308441	−	0.951244i	$-0.599807\pi$
$941$	1.36067e7	−	9.88585e6i	0.500932	−	0.363949i	0.809373	+	0.587295i	$0.199807\pi$
$942$	1.28766e7			0.472795
$943$	2.22939e6	−	4.87921e7i	0.0816406	−	1.78678i
$944$	−6.85886e6			−0.250508
$945$	−3.80691e6	+	2.76588e6i	−0.138673	+	0.100752i
$946$	−7.89631e6			−0.286877
$947$	−1.22283e7	+	3.76348e7i	−0.443089	+	1.36369i	0.441477	+	0.897273i	$0.354455\pi$
$947$	−1.22283e7	+	3.76348e7i	−0.443089	+	1.36369i	−0.884566	+	0.466415i	$0.845545\pi$
$948$	−5.06503e6	+	1.55886e7i	−0.183046	+	0.563359i
$949$	−4.39278e7	+	3.19154e7i	−1.58334	+	1.15036i
$950$	3.13361e6	+	2.27670e6i	0.112651	+	0.0818459i
$951$	−8.40417e6	−	2.58654e7i	−0.301331	−	0.927401i
$952$	−1.25839e7			−0.450011
$953$	−5.65849e6	−	1.74151e7i	−0.201822	−	0.621144i	−0.999829	−	0.0184961i	$-0.994112\pi$
$953$	−5.65849e6	−	1.74151e7i	−0.201822	−	0.621144i	0.798007	−	0.602648i	$-0.205888\pi$
$954$	2.46570e6	+	7.58863e6i	0.0877139	+	0.269956i
$955$	−5.07599e6	+	1.56223e7i	−0.180099	+	0.554289i
$956$	1.88229e7	−	1.36756e7i	0.666102	−	0.483952i
$957$	−1.06180e6			−0.0374770
$958$	−9.47550e6	+	2.91626e7i	−0.333571	+	1.02663i
$959$	1.78363e7	+	1.29589e7i	0.626266	+	0.455009i
$960$	956623.	+	2.94418e6i	0.0335014	+	0.103107i
$961$	2.29830e7	−	1.66981e7i	0.802782	−	0.583255i
$962$	2.58307e7	+	1.87671e7i	0.899910	+	0.653823i
$963$	3.76287e6	+	2.73388e6i	0.130753	+	0.0949979i
$964$	−1.63064e7	−	1.18473e7i	−0.565154	−	0.410608i
$965$	−2.18701e7	−	1.58895e7i	−0.756018	−	0.549279i
$966$	−3.99830e7	+	2.90494e7i	−1.37858	+	1.00160i
$967$	789432.	+	2.42962e6i	0.0271487	+	0.0835550i	0.963713	−	0.266941i	$-0.0860130\pi$
$967$	789432.	+	2.42962e6i	0.0271487	+	0.0835550i	−0.936564	+	0.350496i	$0.886013\pi$
$968$	−5.18814e6	−	3.76940e6i	−0.177960	−	0.129296i
$969$	−5.19834e6	+	1.59988e7i	−0.177851	+	0.547368i
$970$	2.19492e7			0.749013
$971$	4.38389e7	−	3.18508e7i	1.49215	−	1.08411i	0.518766	−	0.854916i	$-0.326391\pi$
$971$	4.38389e7	−	3.18508e7i	1.49215	−	1.08411i	0.973381	−	0.229193i	$-0.0736086\pi$
$972$	5.87401e6	−	1.80783e7i	0.199420	−	0.613752i
$973$	756035.	+	2.32684e6i	0.0256012	+	0.0787923i
$974$	1.00333e7	+	3.08795e7i	0.338882	+	1.04297i
$975$	−2.91059e7			−0.980550
$976$	1.58895e6	+	4.89027e6i	0.0533930	+	0.164327i
$977$	−1.25838e7	−	9.14263e6i	−0.421768	−	0.306433i	0.356581	−	0.934265i	$-0.383942\pi$
$977$	−1.25838e7	−	9.14263e6i	−0.421768	−	0.306433i	−0.778349	+	0.627832i	$0.783942\pi$
$978$	2.64156e7	−	1.91920e7i	0.883106	−	0.641614i
$979$	−5.88404e6	+	1.81092e7i	−0.196209	+	0.603869i
$980$	−20316.4	+	62527.6i	−0.000675744	+	0.00207973i
$981$	−2.11230e7			−0.700782
$982$	−3.01331e7	+	2.18930e7i	−0.997162	+	0.724481i
$983$	−2.81773e7			−0.930071			−0.465036	−	0.885292i	$-0.653958\pi$
$983$	−2.81773e7			−0.930071			−0.465036	+	0.885292i	$0.653958\pi$
$984$	1.34959e7	+	5.07711e6i	0.444339	+	0.167159i
$985$	−2.70774e7			−0.889235
$986$	1.00590e6	−	730826.i	0.0329504	−	0.0239399i
$987$	−1.95583e7			−0.639056
$988$	2.00705e6	−	6.17706e6i	0.0654132	−	0.201321i
$989$	1.12217e7	−	3.45370e7i	0.364812	−	1.12278i
$990$	5.62443e6	−	4.08639e6i	0.182386	−	0.132511i
$991$	4.10922e7	+	2.98553e7i	1.32915	+	0.965687i	0.999769	+	0.0214920i	$0.00684165\pi$
$991$	4.10922e7	+	2.98553e7i	1.32915	+	0.965687i	0.329386	+	0.944195i	$0.393158\pi$
$992$	−148637.	−	457458.i	−0.00479566	−	0.0147595i
$993$	−6.94415e7			−2.23484
$994$	6.41231e6	+	1.97350e7i	0.205849	+	0.633537i
$995$	−1.72863e6	−	5.32018e6i	−0.0553535	−	0.170360i
$996$	−285566.	+	878882.i	−0.00912133	+	0.0280726i
$997$	3.12502e7	−	2.27046e7i	0.995670	−	0.723396i	0.0345142	−	0.999404i	$-0.489012\pi$
$997$	3.12502e7	−	2.27046e7i	0.995670	−	0.723396i	0.961155	+	0.276008i	$0.0890116\pi$
$998$	4.06174e7			1.29088
$999$	−3.23675e6	+	9.96170e6i	−0.102611	+	0.315806i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.6.d.b.37.2	✓	36
41.10	even	5	inner	82.6.d.b.51.2	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.6.d.b.37.2	✓	36	1.1	even	1	trivial
82.6.d.b.51.2	yes	36	41.10	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:	\( N \)	\(=\)	\( 82 = 2 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	82.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.23607 - 2.35114i) q^{2} -20.9317 q^{3} +(4.94427 - 15.2169i) q^{4} +(-11.1577 + 34.3400i) q^{5} +(-67.7364 + 49.2134i) q^{6} +(105.237 + 76.4591i) q^{7} +(-19.7771 - 60.8676i) q^{8} +195.136 q^{9} +(44.6310 + 137.360i) q^{10} +(-76.2274 - 234.604i) q^{11} +(-103.492 + 318.516i) q^{12} +(617.675 - 448.767i) q^{13} +520.320 q^{14} +(233.551 - 718.795i) q^{15} +(-207.108 - 150.473i) q^{16} +(-467.097 - 1437.58i) q^{17} +(631.474 - 458.793i) q^{18} +(430.141 + 312.516i) q^{19} +(467.382 + 339.573i) q^{20} +(-2202.79 - 1600.42i) q^{21} +(-798.264 - 579.973i) q^{22} +(3671.14 - 2667.24i) q^{23} +(413.968 + 1274.06i) q^{24} +(1473.44 + 1070.52i) q^{25} +(943.724 - 2904.48i) q^{26} +1001.87 q^{27} +(1683.79 - 1223.35i) q^{28} +(-63.5467 + 195.577i) q^{29} +(-934.202 - 2875.18i) q^{30} +(145.153 + 446.736i) q^{31} -1024.00 q^{32} +(1595.57 + 4910.66i) q^{33} +(-4891.50 - 3553.88i) q^{34} +(-3799.81 + 2760.72i) q^{35} +(964.807 - 2969.37i) q^{36} +(-3230.72 + 9943.13i) q^{37} +2126.73 q^{38} +(-12929.0 + 9393.46i) q^{39} +2310.86 q^{40} +(6717.59 - 8410.13i) q^{41} -10891.2 q^{42} +(6474.30 - 4703.85i) q^{43} -3946.83 q^{44} +(-2177.28 + 6700.98i) q^{45} +(5609.00 - 17262.7i) q^{46} +(5811.32 - 4222.17i) q^{47} +(4335.13 + 3149.66i) q^{48} +(35.1669 + 108.232i) q^{49} +7285.08 q^{50} +(9777.13 + 30090.9i) q^{51} +(-3774.89 - 11617.9i) q^{52} +(-3158.94 + 9722.22i) q^{53} +(3242.11 - 2355.53i) q^{54} +8906.82 q^{55} +(2572.60 - 7917.66i) q^{56} +(-9003.58 - 6541.49i) q^{57} +(254.187 + 782.307i) q^{58} +(21675.5 - 15748.2i) q^{59} +(-9783.09 - 7107.83i) q^{60} +(-16249.7 - 11806.1i) q^{61} +(1520.07 + 1104.39i) q^{62} +(20535.5 + 14919.9i) q^{63} +(-3313.73 + 2407.57i) q^{64} +(8518.81 + 26218.2i) q^{65} +(16709.0 + 12139.8i) q^{66} +(-3303.13 + 10166.0i) q^{67} -24184.9 q^{68} +(-76843.2 + 55829.8i) q^{69} +(-5805.60 + 17867.8i) q^{70} +(12323.8 + 37928.7i) q^{71} +(-3859.23 - 11877.5i) q^{72} -71118.0 q^{73} +(12922.9 + 39772.5i) q^{74} +(-30841.6 - 22407.7i) q^{75} +(6882.25 - 5000.25i) q^{76} +(9915.66 - 30517.3i) q^{77} +(-19753.7 + 60795.8i) q^{78} +48941.2 q^{79} +(7478.10 - 5433.16i) q^{80} -68388.9 q^{81} +(1965.18 - 43009.7i) q^{82} +2759.30 q^{83} +(-35244.6 + 25606.7i) q^{84} +54578.1 q^{85} +(9891.85 - 30444.0i) q^{86} +(1330.14 - 4093.75i) q^{87} +(-12772.2 + 9279.56i) q^{88} +(-62448.5 - 45371.5i) q^{89} +(8709.12 + 26803.9i) q^{90} +99314.6 q^{91} +(-22436.0 - 69050.9i) q^{92} +(-3038.31 - 9350.95i) q^{93} +(8878.90 - 27326.4i) q^{94} +(-15531.2 + 11284.1i) q^{95} +21434.1 q^{96} +(46962.1 - 144534. i) q^{97} +(368.272 + 267.565i) q^{98} +(-14874.7 - 45779.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 36 q^{2} + 2 q^{3} - 144 q^{4} + 26 q^{5} + 112 q^{6} - 120 q^{7} + 576 q^{8} + 4006 q^{9} - 104 q^{10} + 747 q^{11} + 432 q^{12} + 907 q^{13} + 280 q^{14} - 4149 q^{15} - 2304 q^{16} - 3177 q^{17}+ \cdots + 276325 q^{99}+O(q^{100}) \) 36 * q + 36 * q^2 + 2 * q^3 - 144 * q^4 + 26 * q^5 + 112 * q^6 - 120 * q^7 + 576 * q^8 + 4006 * q^9 - 104 * q^10 + 747 * q^11 + 432 * q^12 + 907 * q^13 + 280 * q^14 - 4149 * q^15 - 2304 * q^16 - 3177 * q^17 + 3696 * q^18 + 1557 * q^19 - 624 * q^20 - 4785 * q^21 + 2252 * q^22 + 1809 * q^23 - 1728 * q^24 - 6323 * q^25 + 10132 * q^26 + 8828 * q^27 - 1920 * q^28 + 1179 * q^29 + 16596 * q^30 - 2190 * q^31 - 36864 * q^32 + 19669 * q^33 - 4572 * q^34 - 69 * q^35 - 17264 * q^36 + 47551 * q^37 - 6128 * q^38 + 62888 * q^39 - 1664 * q^40 + 41071 * q^41 - 16600 * q^42 + 46110 * q^43 - 5888 * q^44 + 51325 * q^45 + 144 * q^46 - 65162 * q^47 - 7168 * q^48 - 83129 * q^49 - 151288 * q^50 + 98677 * q^51 - 40528 * q^52 - 122095 * q^53 + 41748 * q^54 - 161798 * q^55 - 9920 * q^56 - 11800 * q^57 - 4716 * q^58 + 17054 * q^59 + 72656 * q^60 + 86317 * q^61 - 30540 * q^62 - 166377 * q^63 - 36864 * q^64 + 32896 * q^65 + 66064 * q^66 + 95554 * q^67 + 65088 * q^68 + 132527 * q^69 + 23156 * q^70 + 158283 * q^71 + 69056 * q^72 - 239776 * q^73 - 190204 * q^74 - 357133 * q^75 + 24912 * q^76 + 253599 * q^77 + 242748 * q^78 + 98380 * q^79 - 9984 * q^80 + 1044 * q^81 - 84824 * q^82 - 24346 * q^83 - 76560 * q^84 + 376378 * q^85 + 98560 * q^86 + 12625 * q^87 + 36032 * q^88 + 260385 * q^89 - 205300 * q^90 - 726414 * q^91 - 576 * q^92 - 100227 * q^93 - 189392 * q^94 - 257337 * q^95 - 2048 * q^96 + 109321 * q^97 - 145824 * q^98 + 276325 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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