LMFDB - Embedded newform 99.6.e.a.34.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,6,Mod(34,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("99.34");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	99.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.8779981615$
Analytic rank:	$0$
Dimension:	$46$
Relative dimension:	$23$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			34.3
Character	$\chi$	$=$	99.34
Dual form			99.6.e.a.67.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.74574 + 8.21986i) q^{2} +(-12.6839 - 9.06197i) q^{3} +(-29.0441 - 50.3058i) q^{4} +(-15.5606 - 26.9517i) q^{5} +(134.683 - 61.2540i) q^{6} +(58.4765 - 101.284i) q^{7} +247.615 q^{8} +(78.7614 + 229.882i) q^{9} +O(q^{10})$	\(q+(-4.74574 + 8.21986i) q^{2} +(-12.6839 - 9.06197i) q^{3} +(-29.0441 - 50.3058i) q^{4} +(-15.5606 - 26.9517i) q^{5} +(134.683 - 61.2540i) q^{6} +(58.4765 - 101.284i) q^{7} +247.615 q^{8} +(78.7614 + 229.882i) q^{9} +295.386 q^{10} +(60.5000 - 104.789i) q^{11} +(-87.4784 + 901.270i) q^{12} +(-149.253 - 258.514i) q^{13} +(555.028 + 961.338i) q^{14} +(-46.8671 + 482.861i) q^{15} +(-245.707 + 425.578i) q^{16} +87.2532 q^{17} +(-2263.38 - 443.551i) q^{18} -1858.45 q^{19} +(-903.885 + 1565.58i) q^{20} +(-1659.54 + 754.765i) q^{21} +(574.234 + 994.603i) q^{22} +(1369.93 + 2372.79i) q^{23} +(-3140.72 - 2243.88i) q^{24} +(1078.24 - 1867.56i) q^{25} +2833.26 q^{26} +(1084.18 - 3629.53i) q^{27} -6793.59 q^{28} +(-280.459 + 485.769i) q^{29} +(-3746.64 - 2676.78i) q^{30} +(-2163.15 - 3746.69i) q^{31} +(1629.72 + 2822.76i) q^{32} +(-1716.97 + 780.882i) q^{33} +(-414.081 + 717.209i) q^{34} -3639.71 q^{35} +(9276.84 - 10638.9i) q^{36} -11526.9 q^{37} +(8819.72 - 15276.2i) q^{38} +(-449.538 + 4631.48i) q^{39} +(-3853.04 - 6673.66i) q^{40} +(-133.999 - 232.093i) q^{41} +(1671.70 - 17223.1i) q^{42} +(-5854.98 + 10141.1i) q^{43} -7028.67 q^{44} +(4970.13 - 5699.85i) q^{45} -26005.4 q^{46} +(-2614.18 + 4527.89i) q^{47} +(6973.09 - 3171.38i) q^{48} +(1564.50 + 2709.79i) q^{49} +(10234.1 + 17725.9i) q^{50} +(-1106.71 - 790.686i) q^{51} +(-8669.84 + 15016.6i) q^{52} -27187.6 q^{53} +(24689.0 + 26136.6i) q^{54} -3765.66 q^{55} +(14479.7 - 25079.5i) q^{56} +(23572.3 + 16841.2i) q^{57} +(-2661.97 - 4610.66i) q^{58} +(14730.3 + 25513.5i) q^{59} +(25652.0 - 11666.6i) q^{60} +(-23935.8 + 41458.0i) q^{61} +41063.0 q^{62} +(27889.1 + 5465.39i) q^{63} -46662.2 q^{64} +(-4644.93 + 8045.25i) q^{65} +(1729.55 - 17819.1i) q^{66} +(25622.9 + 44380.1i) q^{67} +(-2534.19 - 4389.34i) q^{68} +(4126.12 - 42510.5i) q^{69} +(17273.1 - 29917.9i) q^{70} +31329.4 q^{71} +(19502.5 + 56922.3i) q^{72} -22342.8 q^{73} +(54703.5 - 94749.3i) q^{74} +(-30600.0 + 13917.0i) q^{75} +(53977.0 + 93490.9i) q^{76} +(-7075.66 - 12255.4i) q^{77} +(-35936.8 - 25675.0i) q^{78} +(9637.31 - 16692.3i) q^{79} +15293.4 q^{80} +(-46642.3 + 36211.6i) q^{81} +2543.70 q^{82} +(-30197.5 + 52303.6i) q^{83} +(86169.0 + 61563.3i) q^{84} +(-1357.71 - 2351.62i) q^{85} +(-55572.4 - 96254.3i) q^{86} +(7959.33 - 3619.92i) q^{87} +(14980.7 - 25947.4i) q^{88} -13191.2 q^{89} +(23265.0 + 67903.8i) q^{90} -34911.2 q^{91} +(79576.8 - 137831. i) q^{92} +(-6515.23 + 67124.9i) q^{93} +(-24812.4 - 42976.4i) q^{94} +(28918.5 + 50088.4i) q^{95} +(4908.58 - 50572.0i) q^{96} +(64142.4 - 111098. i) q^{97} -29698.8 q^{98} +(28854.2 + 5654.51i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 15 q^{3} - 320 q^{4} - 36 q^{5} + 273 q^{6} + 167 q^{7} + 426 q^{8} - 63 q^{9}+O(q^{10}) $ 46 * q + 15 * q^3 - 320 * q^4 - 36 * q^5 + 273 * q^6 + 167 * q^7 + 426 * q^8 - 63 * q^9	\( 46 q + 15 q^{3} - 320 q^{4} - 36 q^{5} + 273 q^{6} + 167 q^{7} + 426 q^{8} - 63 q^{9} - 1200 q^{10} + 2783 q^{11} - 1419 q^{12} + 1871 q^{13} - 1329 q^{14} + 3090 q^{15} - 3584 q^{16} + 534 q^{17} + 5391 q^{18} - 7282 q^{19} - 1917 q^{20} - 8319 q^{21} - 8292 q^{23} + 351 q^{24} - 10049 q^{25} + 19140 q^{26} + 19953 q^{27} + 7586 q^{28} - 5970 q^{29} - 15150 q^{30} + 9542 q^{31} - 3831 q^{32} + 3630 q^{33} + 2982 q^{34} + 6480 q^{35} + 28881 q^{36} - 32014 q^{37} + 1221 q^{38} - 17544 q^{39} + 40635 q^{40} + 12030 q^{41} - 55365 q^{42} + 25943 q^{43} - 77440 q^{44} + 70578 q^{45} - 154008 q^{46} + 9756 q^{47} - 65463 q^{48} - 6990 q^{49} + 101805 q^{50} - 42117 q^{51} + 144446 q^{52} + 107838 q^{53} - 2322 q^{54} - 8712 q^{55} - 16602 q^{56} - 100233 q^{57} + 95367 q^{58} - 20310 q^{59} - 215301 q^{60} + 100247 q^{61} - 30594 q^{62} + 28323 q^{63} - 169154 q^{64} + 20931 q^{65} + 26862 q^{66} + 84956 q^{67} + 168471 q^{68} - 30243 q^{69} + 212292 q^{70} + 72186 q^{71} + 144522 q^{72} - 346888 q^{73} + 86619 q^{74} + 103413 q^{75} + 340334 q^{76} - 20207 q^{77} - 386061 q^{78} + 123113 q^{79} - 30246 q^{80} - 73683 q^{81} - 399966 q^{82} + 30672 q^{83} - 38850 q^{84} + 268335 q^{85} - 211260 q^{86} + 180009 q^{87} + 25773 q^{88} + 65028 q^{89} + 460017 q^{90} - 656042 q^{91} - 196731 q^{92} + 232206 q^{93} + 230262 q^{94} - 325926 q^{95} - 517071 q^{96} + 357002 q^{97} - 428928 q^{98} + 7623 q^{99}+O(q^{100}) \) 46 * q + 15 * q^3 - 320 * q^4 - 36 * q^5 + 273 * q^6 + 167 * q^7 + 426 * q^8 - 63 * q^9 - 1200 * q^10 + 2783 * q^11 - 1419 * q^12 + 1871 * q^13 - 1329 * q^14 + 3090 * q^15 - 3584 * q^16 + 534 * q^17 + 5391 * q^18 - 7282 * q^19 - 1917 * q^20 - 8319 * q^21 - 8292 * q^23 + 351 * q^24 - 10049 * q^25 + 19140 * q^26 + 19953 * q^27 + 7586 * q^28 - 5970 * q^29 - 15150 * q^30 + 9542 * q^31 - 3831 * q^32 + 3630 * q^33 + 2982 * q^34 + 6480 * q^35 + 28881 * q^36 - 32014 * q^37 + 1221 * q^38 - 17544 * q^39 + 40635 * q^40 + 12030 * q^41 - 55365 * q^42 + 25943 * q^43 - 77440 * q^44 + 70578 * q^45 - 154008 * q^46 + 9756 * q^47 - 65463 * q^48 - 6990 * q^49 + 101805 * q^50 - 42117 * q^51 + 144446 * q^52 + 107838 * q^53 - 2322 * q^54 - 8712 * q^55 - 16602 * q^56 - 100233 * q^57 + 95367 * q^58 - 20310 * q^59 - 215301 * q^60 + 100247 * q^61 - 30594 * q^62 + 28323 * q^63 - 169154 * q^64 + 20931 * q^65 + 26862 * q^66 + 84956 * q^67 + 168471 * q^68 - 30243 * q^69 + 212292 * q^70 + 72186 * q^71 + 144522 * q^72 - 346888 * q^73 + 86619 * q^74 + 103413 * q^75 + 340334 * q^76 - 20207 * q^77 - 386061 * q^78 + 123113 * q^79 - 30246 * q^80 - 73683 * q^81 - 399966 * q^82 + 30672 * q^83 - 38850 * q^84 + 268335 * q^85 - 211260 * q^86 + 180009 * q^87 + 25773 * q^88 + 65028 * q^89 + 460017 * q^90 - 656042 * q^91 - 196731 * q^92 + 232206 * q^93 + 230262 * q^94 - 325926 * q^95 - 517071 * q^96 + 357002 * q^97 - 428928 * q^98 + 7623 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−4.74574	+	8.21986i	−0.838936	+	1.45308i	0.0518488	+	0.998655i	$0.483489\pi$
$2$	−4.74574	+	8.21986i	−0.838936	+	1.45308i	−0.890785	+	0.454425i	$0.849845\pi$
$3$	−12.6839	−	9.06197i	−0.813671	−	0.581326i
$3$	−12.6839	−	9.06197i	−0.813671	−	0.581326i
$4$	−29.0441	−	50.3058i	−0.907628	−	1.57206i
$5$	−15.5606	−	26.9517i	−0.278356	−	0.482127i	0.692620	−	0.721302i	$-0.256456\pi$
$5$	−15.5606	−	26.9517i	−0.278356	−	0.482127i	−0.970976	+	0.239176i	$0.923123\pi$
$6$	134.683	−	61.2540i	1.52733	−	0.694634i
$7$	58.4765	−	101.284i	0.451062	−	0.781262i	−0.547390	−	0.836877i	$-0.684379\pi$
$7$	58.4765	−	101.284i	0.451062	−	0.781262i	0.998452	+	0.0556151i	$0.0177120\pi$
$8$	247.615			1.36789
$9$	78.7614	+	229.882i	0.324121	+	0.946016i
$10$	295.386			0.934092
$11$	60.5000	−	104.789i	0.150756	−	0.261116i
$11$	60.5000	−	104.789i	0.150756	−	0.261116i
$12$	−87.4784	+	901.270i	−0.175367	+	1.80676i
$13$	−149.253	−	258.514i	−0.244943	−	0.424254i	0.717173	−	0.696896i	$-0.245436\pi$
$13$	−149.253	−	258.514i	−0.244943	−	0.424254i	−0.962116	+	0.272642i	$0.912103\pi$
$14$	555.028	+	961.338i	0.756824	+	1.31086i
$15$	−46.8671	+	482.861i	−0.0537824	+	0.554108i
$16$	−245.707	+	425.578i	−0.239949	+	0.415603i
$17$	87.2532			0.0732249			0.0366125	−	0.999330i	$-0.488343\pi$
$17$	87.2532			0.0732249			0.0366125	+	0.999330i	$0.488343\pi$
$18$	−2263.38	−	443.551i	−1.64655	−	0.322673i
$19$	−1858.45			−1.18105			−0.590523	−	0.807021i	$-0.701079\pi$
$19$	−1858.45			−1.18105			−0.590523	+	0.807021i	$0.701079\pi$
$20$	−903.885	+	1565.58i	−0.505287	+	0.875183i
$21$	−1659.54	+	754.765i	−0.821184	+	0.373477i
$22$	574.234	+	994.603i	0.252949	+	0.438120i
$23$	1369.93	+	2372.79i	0.539982	+	0.935276i	0.998904	+	0.0467998i	$0.0149023\pi$
$23$	1369.93	+	2372.79i	0.539982	+	0.935276i	−0.458922	+	0.888476i	$0.651764\pi$
$24$	−3140.72	−	2243.88i	−1.11302	−	0.795192i
$25$	1078.24	−	1867.56i	0.345036	−	0.597620i
$26$	2833.26			0.821966
$27$	1084.18	−	3629.53i	0.286215	−	0.958165i
$28$	−6793.59			−1.63759
$29$	−280.459	+	485.769i	−0.0619261	+	0.107259i	−0.895326	−	0.445411i	$-0.853058\pi$
$29$	−280.459	+	485.769i	−0.0619261	+	0.107259i	0.833400	+	0.552670i	$0.186391\pi$
$30$	−3746.64	−	2676.78i	−0.760043	−	0.543011i
$31$	−2163.15	−	3746.69i	−0.404280	−	0.700234i	0.589957	−	0.807435i	$-0.299145\pi$
$31$	−2163.15	−	3746.69i	−0.404280	−	0.700234i	−0.994237	+	0.107200i	$0.965811\pi$
$32$	1629.72	+	2822.76i	0.281344	+	0.487303i
$33$	−1716.97	+	780.882i	−0.274459	+	0.124825i
$34$	−414.081	+	717.209i	−0.0614310	+	0.106402i
$35$	−3639.71			−0.502223
$36$	9276.84	−	10638.9i	1.19301	−	1.36817i
$37$	−11526.9			−1.38423			−0.692113	−	0.721789i	$-0.743320\pi$
$37$	−11526.9			−1.38423			−0.692113	+	0.721789i	$0.743320\pi$
$38$	8819.72	−	15276.2i	0.990822	−	1.71615i
$39$	−449.538	+	4631.48i	−0.0473265	+	0.487594i
$40$	−3853.04	−	6673.66i	−0.380762	−	0.659499i
$41$	−133.999	−	232.093i	−0.0124492	−	0.0215627i	0.859734	−	0.510743i	$-0.170629\pi$
$41$	−133.999	−	232.093i	−0.0124492	−	0.0215627i	−0.872183	+	0.489180i	$0.837296\pi$
$42$	1671.70	−	17223.1i	0.146229	−	1.50657i
$43$	−5854.98	+	10141.1i	−0.482897	+	0.836402i	−0.999807	−	0.0196378i	$-0.993749\pi$
$43$	−5854.98	+	10141.1i	−0.482897	+	0.836402i	0.516910	+	0.856039i	$0.327082\pi$
$44$	−7028.67			−0.547320
$45$	4970.13	−	5699.85i	0.365878	−	0.419596i
$46$	−26005.4			−1.81204
$47$	−2614.18	+	4527.89i	−0.172620	+	0.298986i	−0.939335	−	0.343001i	$-0.888557\pi$
$47$	−2614.18	+	4527.89i	−0.172620	+	0.298986i	0.766715	+	0.641987i	$0.221890\pi$
$48$	6973.09	−	3171.38i	0.436840	−	0.198676i
$49$	1564.50	+	2709.79i	0.0930861	+	0.161230i
$50$	10234.1	+	17725.9i	0.578926	+	1.00273i
$51$	−1106.71	−	790.686i	−0.0595810	−	0.0425675i
$52$	−8669.84	+	15016.6i	−0.444634	+	0.770129i
$53$	−27187.6			−1.32948			−0.664738	−	0.747076i	$-0.731457\pi$
$53$	−27187.6			−1.32948			−0.664738	+	0.747076i	$0.731457\pi$
$54$	24689.0	+	26136.6i	1.15217	+	1.21973i
$55$	−3765.66			−0.167855
$56$	14479.7	−	25079.5i	0.617005	−	1.06868i
$57$	23572.3	+	16841.2i	0.960983	+	0.686572i
$58$	−2661.97	−	4610.66i	−0.103904	−	0.179967i
$59$	14730.3	+	25513.5i	0.550909	+	0.954203i	0.998209	+	0.0598190i	$0.0190523\pi$
$59$	14730.3	+	25513.5i	0.550909	+	0.954203i	−0.447300	+	0.894384i	$0.647614\pi$
$60$	25652.0	−	11666.6i	0.919904	−	0.418375i
$61$	−23935.8	+	41458.0i	−0.823614	+	1.42654i	0.0793603	+	0.996846i	$0.474712\pi$
$61$	−23935.8	+	41458.0i	−0.823614	+	1.42654i	−0.902974	+	0.429695i	$0.858621\pi$
$62$	41063.0			1.35666
$63$	27889.1	+	5465.39i	0.885285	+	0.173488i
$64$	−46662.2			−1.42402
$65$	−4644.93	+	8045.25i	−0.136363	+	0.236187i
$66$	1729.55	−	17819.1i	0.0488734	−	0.503531i
$67$	25622.9	+	44380.1i	0.697334	+	1.20782i	0.969388	+	0.245535i	$0.0789637\pi$
$67$	25622.9	+	44380.1i	0.697334	+	1.20782i	−0.272054	+	0.962282i	$0.587703\pi$
$68$	−2534.19	−	4389.34i	−0.0664610	−	0.115114i
$69$	4126.12	−	42510.5i	0.104332	−	1.07491i
$70$	17273.1	−	29917.9i	0.421333	−	0.729771i
$71$	31329.4			0.737574			0.368787	−	0.929514i	$-0.379773\pi$
$71$	31329.4			0.737574			0.368787	+	0.929514i	$0.379773\pi$
$72$	19502.5	+	56922.3i	0.443363	+	1.29405i
$73$	−22342.8			−0.490716			−0.245358	−	0.969433i	$-0.578905\pi$
$73$	−22342.8			−0.490716			−0.245358	+	0.969433i	$0.578905\pi$
$74$	54703.5	−	94749.3i	1.16128	−	2.01139i
$75$	−30600.0	+	13917.0i	−0.628157	+	0.285688i
$76$	53977.0	+	93490.9i	1.07195	+	1.85667i
$77$	−7075.66	−	12255.4i	−0.136000	−	0.235559i
$78$	−35936.8	−	25675.0i	−0.668810	−	0.477830i
$79$	9637.31	−	16692.3i	0.173735	−	0.300918i	−0.765988	−	0.642855i	$-0.777750\pi$
$79$	9637.31	−	16692.3i	0.173735	−	0.300918i	0.939723	+	0.341937i	$0.111083\pi$
$80$	15293.4			0.267165
$81$	−46642.3	+	36211.6i	−0.789891	+	0.613247i
$82$	2543.70			0.0417764
$83$	−30197.5	+	52303.6i	−0.481145	+	0.833367i	−0.999766	−	0.0216370i	$-0.993112\pi$
$83$	−30197.5	+	52303.6i	−0.481145	+	0.833367i	0.518621	+	0.855004i	$0.326446\pi$
$84$	86169.0	+	61563.3i	1.33246	+	0.951971i
$85$	−1357.71	−	2351.62i	−0.0203826	−	0.0353037i
$86$	−55572.4	−	96254.3i	−0.810239	−	1.40338i
$87$	7959.33	−	3619.92i	0.112740	−	0.0512745i
$88$	14980.7	−	25947.4i	0.206218	−	0.357180i
$89$	−13191.2			−0.176526			−0.0882632	−	0.996097i	$-0.528132\pi$
$89$	−13191.2			−0.176526			−0.0882632	+	0.996097i	$0.528132\pi$
$90$	23265.0	+	67903.8i	0.302759	+	0.883665i
$91$	−34911.2			−0.441938
$92$	79576.8	−	137831.i	0.980205	−	1.69777i
$93$	−6515.23	+	67124.9i	−0.0781128	+	0.804779i
$94$	−24812.4	−	42976.4i	−0.289634	−	0.501661i
$95$	28918.5	+	50088.4i	0.328751	+	0.569414i
$96$	4908.58	−	50572.0i	0.0543598	−	0.560057i
$97$	64142.4	−	111098.i	0.692175	−	1.19888i	−0.278949	−	0.960306i	$-0.589986\pi$
$97$	64142.4	−	111098.i	0.692175	−	1.19888i	0.971124	−	0.238576i	$-0.0766806\pi$
$98$	−29698.8			−0.312373
$99$	28854.2	+	5654.51i	0.295883	+	0.0579839i
$100$	−125266.			−1.25266
$101$	−1.05776	+	1.83209i	−1.03177e−5	+	1.78707e-5i	−0.866031	−	0.499991i	$-0.833337\pi$
$101$	−1.05776	+	1.83209i	−1.03177e−5	+	1.78707e-5i	0.866020	+	0.500009i	$0.166670\pi$
$102$	11751.5	−	5344.60i	0.111839	−	0.0508645i
$103$	−57024.6	−	98769.6i	−0.529626	−	0.917339i	−0.999403	−	0.0345541i	$-0.988999\pi$
$103$	−57024.6	−	98769.6i	−0.529626	−	0.917339i	0.469777	−	0.882785i	$-0.344334\pi$
$104$	−36957.4	−	64012.0i	−0.335056	−	0.580334i
$105$	46165.6	+	32983.0i	0.408644	+	0.291955i
$106$	129025.	−	223478.i	1.11535	−	1.93184i
$107$	−159266.			−1.34482			−0.672410	−	0.740179i	$-0.734741\pi$
$107$	−159266.			−1.34482			−0.672410	+	0.740179i	$0.734741\pi$
$108$	−214075.	+	50875.6i	−1.76607	+	0.419711i
$109$	182112.			1.46815			0.734077	−	0.679066i	$-0.237615\pi$
$109$	182112.			1.46815			0.734077	+	0.679066i	$0.237615\pi$
$110$	17870.8	−	30953.2i	0.140820	−	0.243907i
$111$	146205.	+	104456.i	1.12630	+	0.804686i
$112$	28736.2	+	49772.6i	0.216463	+	0.374926i
$113$	75792.4	+	131276.i	0.558379	+	0.967141i	0.997632	+	0.0687778i	$0.0219099\pi$
$113$	75792.4	+	131276.i	0.558379	+	0.967141i	−0.439253	+	0.898364i	$0.644757\pi$
$114$	−250301.	+	113837.i	−1.80385	+	0.820395i
$115$	42633.8	−	73844.0i	0.300614	−	0.520679i
$116$	32582.7			0.224824
$117$	47672.3	−	54671.5i	0.321959	−	0.369229i
$118$	−279624.			−1.84871
$119$	5102.26	−	8837.37i	0.0330290	−	0.0572079i
$120$	−11605.0	+	119564.i	−0.0735687	+	0.757961i
$121$	−7320.50	−	12679.5i	−0.0454545	−	0.0787296i
$122$	−227186.	−	393498.i	−1.38192	−	2.39355i
$123$	−403.594	+	4158.14i	−0.00240537	+	0.0247820i
$124$	−125654.	+	217638.i	−0.733872	+	1.27110i
$125$	−164366.			−0.940883
$126$	−177279.	+	203307.i	−0.994790	+	1.14084i
$127$	55011.8			0.302654			0.151327	−	0.988484i	$-0.451645\pi$
$127$	55011.8			0.302654			0.151327	+	0.988484i	$0.451645\pi$
$128$	169296.	−	293228.i	0.913315	−	1.58191i
$129$	166162.	−	75571.1i	0.879141	−	0.399836i
$130$	−44087.2	−	76361.3i	−0.228799	−	0.396292i
$131$	92581.4	+	160356.i	0.471352	+	0.816406i	0.999463	−	0.0327698i	$-0.0104328\pi$
$131$	92581.4	+	160356.i	0.471352	+	0.816406i	−0.528111	+	0.849175i	$0.677099\pi$
$132$	89150.8	+	63693.6i	0.445339	+	0.318171i
$133$	−108676.	+	188232.i	−0.532725	+	0.922707i
$134$	−486398.			−2.34007
$135$	−114692.	+	27257.0i	−0.541627	+	0.128719i
$136$	21605.2			0.100164
$137$	112731.	−	195255.i	0.513145	−	0.888794i	−0.486739	−	0.873548i	$-0.661814\pi$
$137$	112731.	−	195255.i	0.513145	−	0.888794i	0.999884	−	0.0152459i	$-0.00485312\pi$
$138$	329849.	+	235660.i	1.47441	+	1.05339i
$139$	92576.1	+	160346.i	0.406407	+	0.703918i	0.994484	−	0.104887i	$-0.0334480\pi$
$139$	92576.1	+	160346.i	0.406407	+	0.703918i	−0.588077	+	0.808805i	$0.700115\pi$
$140$	105712.	+	183099.i	0.455832	+	0.789524i
$141$	74189.5	−	33741.6i	0.314264	−	0.142928i
$142$	−148681.	+	257523.i	−0.618778	+	1.07175i
$143$	−36119.2			−0.147706
$144$	−117185.	−	22964.6i	−0.470940	−	0.0922894i
$145$	17456.4			0.0689500
$146$	106033.	−	183655.i	0.411679	−	0.713050i
$147$	4712.14	−	48548.1i	0.0179856	−	0.185301i
$148$	334787.	+	579869.i	1.25636	+	2.17608i
$149$	164353.	+	284667.i	0.606473	+	1.05044i	0.991817	+	0.127669i	$0.0407496\pi$
$149$	164353.	+	284667.i	0.606473	+	1.05044i	−0.385344	+	0.922773i	$0.625917\pi$
$150$	30824.1	−	317574.i	0.111857	−	1.15244i
$151$	−192850.	+	334027.i	−0.688301	+	1.19217i	0.284087	+	0.958799i	$0.408310\pi$
$151$	−192850.	+	334027.i	−0.688301	+	1.19217i	−0.972387	+	0.233373i	$0.925024\pi$
$152$	−460181.			−1.61555
$153$	6872.18	+	20057.9i	0.0237337	+	0.0692719i
$154$	134317.			0.456382
$155$	−67319.8	+	116601.i	−0.225068	+	0.389829i
$156$	246047.	−	111903.i	0.809481	−	0.368154i
$157$	−208036.	−	360329.i	−0.673581	−	1.16668i	−0.976881	−	0.213782i	$-0.931422\pi$
$157$	−208036.	−	360329.i	−0.673581	−	1.16668i	0.303300	−	0.952895i	$-0.401911\pi$
$158$	91472.4	+	158435.i	0.291506	+	0.504903i
$159$	344844.	+	246373.i	1.08176	+	0.772859i
$160$	50718.7	−	87847.4i	0.156628	−	0.271287i
$161$	320435.			0.974261
$162$	−76302.5	−	555244.i	−0.228429	−	1.66225i
$163$	−399837.			−1.17873			−0.589365	−	0.807867i	$-0.700622\pi$
$163$	−399837.			−1.17873			−0.589365	+	0.807867i	$0.700622\pi$
$164$	−7783.76	+	13481.9i	−0.0225985	+	0.0391418i
$165$	47763.1	+	34124.3i	0.136579	+	0.0975784i
$166$	−286619.	−	496439.i	−0.807300	−	1.39828i
$167$	−249480.	−	432111.i	−0.692219	−	1.19896i	−0.971109	−	0.238636i	$-0.923300\pi$
$167$	−249480.	−	432111.i	−0.692219	−	1.19896i	0.278890	−	0.960323i	$-0.410034\pi$
$168$	−410929.	+	186891.i	−1.12329	+	0.510877i
$169$	141094.	−	244381.i	0.380006	−	0.658190i
$170$	25773.3			0.0683988
$171$	−146374.	−	427224.i	−0.382802	−	1.11729i
$172$	680210.			1.75316
$173$	−170142.	+	294695.i	−0.432211	+	0.748612i	−0.997063	−	0.0765801i	$-0.975600\pi$
$173$	−170142.	+	294695.i	−0.432211	+	0.748612i	0.564852	+	0.825192i	$0.308933\pi$
$174$	−8017.63	+	82603.8i	−0.0200758	+	0.206836i
$175$	−126103.	−	218417.i	−0.311265	−	0.539127i
$176$	29730.6	+	51494.9i	0.0723472	+	0.125309i
$177$	44366.3	−	457096.i	0.106444	−	1.09667i
$178$	62602.1	−	108430.i	0.148094	−	0.256507i
$179$	113031.			0.263672			0.131836	−	0.991272i	$-0.457913\pi$
$179$	113031.			0.263672			0.131836	+	0.991272i	$0.457913\pi$
$180$	−431089.	−	84479.9i	−0.991711	−	0.194344i
$181$	551735.			1.25180			0.625899	−	0.779904i	$-0.284732\pi$
$181$	551735.			1.25180			0.625899	+	0.779904i	$0.284732\pi$
$182$	165679.	−	286965.i	0.370758	−	0.642171i
$183$	679290.	−	308943.i	1.49944	−	0.681947i
$184$	339216.	+	587540.i	0.738639	+	1.27936i
$185$	179365.	+	310669.i	0.385308	+	0.667372i
$186$	−520838.	−	372112.i	−1.10388	−	0.788662i
$187$	5278.82	−	9143.18i	0.0110391	−	0.0191202i
$188$	303706.			0.626698
$189$	−304215.	−	322053.i	−0.619478	−	0.655801i
$190$	−548959.			−1.10321
$191$	−202328.	+	350443.i	−0.401304	+	0.695079i	−0.993884	−	0.110433i	$-0.964776\pi$
$191$	−202328.	+	350443.i	−0.401304	+	0.695079i	0.592580	+	0.805512i	$0.298110\pi$
$192$	591857.	+	422851.i	1.15868	+	0.827817i
$193$	−385212.	−	667207.i	−0.744401	−	1.28934i	−0.950474	−	0.310803i	$-0.899402\pi$
$193$	−385212.	−	667207.i	−0.744401	−	1.28934i	0.206074	−	0.978536i	$-0.433931\pi$
$194$	608806.	+	1.05448e6i	1.16138	+	2.01157i
$195$	131821.	−	59952.7i	0.248256	−	0.112907i
$196$	90878.8	−	157407.i	0.168975	−	0.292673i
$197$	−49782.2			−0.0913920			−0.0456960	−	0.998955i	$-0.514551\pi$
$197$	−49782.2			−0.0913920			−0.0456960	+	0.998955i	$0.514551\pi$
$198$	−183414.	+	210342.i	−0.332482	+	0.381297i
$199$	−184700.			−0.330624			−0.165312	−	0.986241i	$-0.552863\pi$
$199$	−184700.			−0.330624			−0.165312	+	0.986241i	$0.552863\pi$
$200$	266988.	−	462437.i	0.471973	−	0.817481i
$201$	77173.9	−	795105.i	0.134735	−	1.38814i
$202$	−10.0397	−	17.3892i	−1.73117e−5	−	2.99848e-5i
$203$	32800.5	+	56812.1i	0.0558651	+	0.0967611i
$204$	−7632.76	+	78638.6i	−0.0128412	+	0.132300i
$205$	−4170.20	+	7223.01i	−0.00693063	+	0.0120042i
$206$	1.08250e6			1.77729
$207$	−437564.	+	501807.i	−0.709766	+	0.813974i
$208$	146690.			0.235095
$209$	−112436.	+	194745.i	−0.178049	+	0.308391i
$210$	−490205.	+	222947.i	−0.767061	+	0.348861i
$211$	−63323.7	−	109680.i	−0.0979175	−	0.169598i	0.812905	−	0.582396i	$-0.197885\pi$
$211$	−63323.7	−	109680.i	−0.0979175	−	0.169598i	−0.910822	+	0.412798i	$0.864551\pi$
$212$	789638.	+	1.36769e6i	1.20667	+	2.09001i
$213$	−397378.	−	283906.i	−0.600143	−	0.428771i
$214$	755836.	−	1.30915e6i	1.12822	−	1.95413i
$215$	364427.			0.537669
$216$	268460.	−	898726.i	0.391512	−	1.31067i
$217$	−505974.			−0.729422
$218$	−864255.	+	1.49693e6i	−1.23169	+	2.13334i
$219$	283393.	+	202470.i	0.399281	+	0.285266i
$220$	109370.	+	189435.i	0.152350	+	0.263878i
$221$	−13022.8	−	22556.2i	−0.0179359	−	0.0310659i
$222$	−1.55247e6	+	706066.i	−2.11417	+	0.961530i
$223$	−597713.	+	1.03527e6i	−0.804879	+	1.39409i	0.111494	+	0.993765i	$0.464437\pi$
$223$	−597713.	+	1.03527e6i	−0.804879	+	1.39409i	−0.916373	+	0.400326i	$0.868897\pi$
$224$	381201.			0.507615
$225$	514242.	+	100775.i	0.677191	+	0.132708i
$226$	−1.43876e6			−1.87378
$227$	−453044.	+	784696.i	−0.583547	+	1.01073i	0.411508	+	0.911406i	$0.365002\pi$
$227$	−453044.	+	784696.i	−0.583547	+	1.01073i	−0.995055	+	0.0993270i	$0.968331\pi$
$228$	162574.	−	1.67496e6i	0.207116	−	2.13387i
$229$	696081.	+	1.20565e6i	0.877145	+	1.51926i	0.854461	+	0.519516i	$0.173888\pi$
$229$	696081.	+	1.20565e6i	0.877145	+	1.51926i	0.0226839	+	0.999743i	$0.492779\pi$
$230$	404658.	+	700889.i	0.504393	+	0.873634i
$231$	−21311.3	+	219565.i	−0.0262772	+	0.270728i
$232$	−69445.9	+	120284.i	−0.0847084	+	0.146719i
$233$	−1.21924e6			−1.47129			−0.735646	−	0.677366i	$-0.763121\pi$
$233$	−1.21924e6			−1.47129			−0.735646	+	0.677366i	$0.763121\pi$
$234$	223152.	+	651316.i	0.266416	+	0.777593i
$235$	162712.			0.192199
$236$	855654.	−	1.48204e6i	1.00004	−	1.73212i
$237$	−273504.	+	124390.i	−0.316295	+	0.143852i
$238$	48428.0	+	83879.7i	0.0554184	+	0.0959875i
$239$	687768.	+	1.19125e6i	0.778838	+	1.34899i	0.932612	+	0.360881i	$0.117524\pi$
$239$	687768.	+	1.19125e6i	0.778838	+	1.34899i	−0.153774	+	0.988106i	$0.549143\pi$
$240$	−193979.	−	138588.i	−0.217384	−	0.155310i
$241$	778733.	−	1.34881e6i	0.863667	−	1.49591i	−0.00469818	−	0.999989i	$-0.501495\pi$
$241$	778733.	−	1.34881e6i	0.863667	−	1.49591i	0.868365	−	0.495926i	$-0.165171\pi$
$242$	138965.			0.152534
$243$	919754.	−	36632.9i	0.999208	−	0.0397975i
$244$	2.78078e6			2.99014
$245$	48689.0	−	84331.8i	0.0518221	−	0.0897586i
$246$	−32264.0	−	23050.9i	−0.0339923	−	0.0242857i
$247$	277379.	+	480435.i	0.289289	+	0.501063i
$248$	−535630.	−	927738.i	−0.553013	−	0.957847i
$249$	856995.	−	389764.i	0.875951	−	0.398385i
$250$	780036.	−	1.35106e6i	0.789341	−	1.36718i
$251$	−424702.			−0.425501			−0.212750	−	0.977107i	$-0.568242\pi$
$251$	−424702.			−0.425501			−0.212750	+	0.977107i	$0.568242\pi$
$252$	−535072.	−	1.56172e6i	−0.530776	−	1.54918i
$253$	331523.			0.325621
$254$	−261072.	+	452189.i	−0.253907	+	0.439781i
$255$	−4089.31	+	42131.2i	−0.00393821	+	0.0405745i
$256$	860270.	+	1.49003e6i	0.820417	+	1.42100i
$257$	−970847.	−	1.68156e6i	−0.916891	−	1.58810i	−0.804109	−	0.594482i	$-0.797357\pi$
$257$	−970847.	−	1.68156e6i	−0.916891	−	1.58810i	−0.112783	−	0.993620i	$-0.535976\pi$
$258$	−167379.	+	1.72447e6i	−0.156550	+	1.61290i
$259$	−674051.	+	1.16749e6i	−0.624372	+	1.08144i
$260$	539631.			0.495066
$261$	−133759.	−	26212.5i	−0.121540	−	0.0238181i
$262$	−1.75747e6			−1.58174
$263$	−813444.	+	1.40893e6i	−0.725167	+	1.25603i	0.233738	+	0.972300i	$0.424904\pi$
$263$	−813444.	+	1.40893e6i	−0.725167	+	1.25603i	−0.958905	+	0.283727i	$0.908429\pi$
$264$	−425148.	+	193359.i	−0.375431	+	0.170747i
$265$	423054.	+	732751.i	0.370068	+	0.640976i
$266$	−1.03149e6	−	1.78660e6i	−0.893845	−	1.54818i
$267$	167316.	+	119538.i	0.143634	+	0.102619i
$268$	1.48839e6	−	2.57796e6i	1.26584	−	2.19250i
$269$	−1.87130e6			−1.57675			−0.788374	−	0.615197i	$-0.789077\pi$
$269$	−1.87130e6			−1.57675			−0.788374	+	0.615197i	$0.789077\pi$
$270$	320252.	−	1.07211e6i	0.267351	−	0.895014i
$271$	−958076.			−0.792459			−0.396229	−	0.918152i	$-0.629681\pi$
$271$	−958076.			−0.792459			−0.396229	+	0.918152i	$0.629681\pi$
$272$	−21438.7	+	37133.0i	−0.0175702	+	0.0304325i
$273$	442809.	+	316364.i	0.359592	+	0.256910i
$274$	1.06998e6	+	1.85326e6i	0.860992	+	1.49128i
$275$	−130467.	−	225975.i	−0.104032	−	0.180189i
$276$	−2.25836e6	+	1.02711e6i	−1.78452	+	0.811604i
$277$	381353.	−	660522.i	0.298626	−	0.517235i	−0.677196	−	0.735803i	$-0.736805\pi$
$277$	381353.	−	660522.i	0.298626	−	0.517235i	0.975822	+	0.218568i	$0.0701384\pi$
$278$	−1.75737e6			−1.36380
$279$	690923.	−	792364.i	0.531397	−	0.609416i
$280$	−901249.			−0.686989
$281$	−191110.	+	331013.i	−0.144384	+	0.250080i	−0.929143	−	0.369721i	$-0.879453\pi$
$281$	−191110.	+	331013.i	−0.144384	+	0.250080i	0.784759	+	0.619801i	$0.212787\pi$
$282$	−74732.9	+	769957.i	−0.0559615	+	0.576559i
$283$	−760030.	−	1.31641e6i	−0.564111	−	0.977069i	−0.997132	−	0.0756851i	$-0.975886\pi$
$283$	−760030.	−	1.31641e6i	−0.564111	−	0.977069i	0.433021	−	0.901384i	$-0.357448\pi$
$284$	−909933.	−	1.57605e6i	−0.669443	−	1.15951i
$285$	87100.2	−	897374.i	0.0635195	−	0.654427i
$286$	171413.	−	296895.i	0.123916	−	0.214629i
$287$	−31343.2			−0.0224615
$288$	−520542.	+	596967.i	−0.369806	+	0.424101i
$289$	−1.41224e6			−0.994638
$290$	−82843.5	+	143489.i	−0.0578447	+	0.100190i
$291$	−1.82034e6	+	827895.i	−1.26014	+	0.573116i
$292$	648926.	+	1.12397e6i	0.445387	+	0.771434i
$293$	−510376.	−	883997.i	−0.347313	−	0.601564i	0.638458	−	0.769657i	$-0.279573\pi$
$293$	−510376.	−	883997.i	−0.347313	−	0.601564i	−0.985771	+	0.168093i	$0.946239\pi$
$294$	376696.	+	269130.i	0.254169	+	0.181591i
$295$	458422.	−	794011.i	0.306698	−	0.531216i
$296$	−2.85423e6			−1.89348
$297$	−314742.	−	333197.i	−0.207044	−	0.219184i
$298$	−3.11990e6			−2.03517
$299$	408933.	−	708293.i	0.264530	−	0.458179i
$300$	1.58885e6	+	1.13515e6i	1.01925	+	0.728201i
$301$	684757.	+	1.18603e6i	0.435633	+	0.754538i
$302$	−1.83044e6	−	3.17041e6i	−1.15488	−	2.00031i
$303$	30.0187	−	13.6526i	1.87839e−5	−	8.54297e-6i
$304$	456635.	−	790915.i	0.283390	−	0.490847i
$305$	1.48982e6			0.917031
$306$	−197487.	−	38701.2i	−0.120569	−	0.0236277i
$307$	1.79624e6			1.08772			0.543861	−	0.839175i	$-0.316962\pi$
$307$	1.79624e6			1.08772			0.543861	+	0.839175i	$0.316962\pi$
$308$	−411012.	+	711894.i	−0.246875	+	0.427601i
$309$	−171753.	+	1.76954e6i	−0.102331	+	1.05430i
$310$	−638964.	−	1.10672e6i	−0.377635	−	0.654083i
$311$	−812523.	−	1.40733e6i	−0.476359	−	0.825079i	0.523274	−	0.852165i	$-0.324711\pi$
$311$	−812523.	−	1.40733e6i	−0.476359	−	0.825079i	−0.999633	+	0.0270859i	$0.991377\pi$
$312$	−111312.	+	1.14683e6i	−0.0647377	+	0.666978i
$313$	661468.	−	1.14570e6i	0.381635	−	0.661011i	−0.609661	−	0.792662i	$-0.708695\pi$
$313$	661468.	−	1.14570e6i	0.381635	−	0.661011i	0.991296	+	0.131651i	$0.0420278\pi$
$314$	3.94914e6			2.26037
$315$	−286669.	−	836703.i	−0.162781	−	0.475111i
$316$	−1.11963e6			−0.630748
$317$	29078.1	−	50364.7i	0.0162524	−	0.0281500i	−0.857785	−	0.514009i	$-0.828160\pi$
$317$	29078.1	−	50364.7i	0.0162524	−	0.0281500i	0.874037	+	0.485859i	$0.161493\pi$
$318$	−3.66169e6	+	1.66535e6i	−2.03055	+	0.923500i
$319$	33935.5	+	58778.0i	0.0186714	+	0.0323399i
$320$	726090.	+	1.25763e6i	0.396384	+	0.686556i
$321$	2.02011e6	+	1.44327e6i	1.09424	+	0.781779i
$322$	−1.52070e6	+	2.63393e6i	−0.817343	+	1.41568i
$323$	−162156.			−0.0864820
$324$	3.17634e6	+	1.29465e6i	1.68099	+	0.685154i
$325$	−643721.			−0.338056
$326$	1.89752e6	−	3.28661e6i	0.988879	−	1.71279i
$327$	−2.30988e6	−	1.65029e6i	−1.19459	−	0.853475i
$328$	−33180.2	−	57469.9i	−0.0170292	−	0.0294955i
$329$	305736.	+	529550.i	0.155724	+	0.269723i
$330$	−507168.	+	230661.i	−0.256370	+	0.116598i
$331$	316376.	−	547979.i	0.158721	−	0.274912i	−0.775687	−	0.631118i	$-0.782596\pi$
$331$	316376.	−	547979.i	0.158721	−	0.274912i	0.934408	+	0.356206i	$0.115930\pi$
$332$	3.50824e6			1.74680
$333$	−907872.	−	2.64982e6i	−0.448657	−	1.30950i
$334$	4.73586e6			2.32291
$335$	797413.	−	1.38116e6i	0.388214	−	0.672406i
$336$	86551.1	−	891716.i	0.0418239	−	0.430902i
$337$	903126.	+	1.56426e6i	0.433185	+	0.750299i	0.997146	−	0.0755030i	$-0.0240562\pi$
$337$	903126.	+	1.56426e6i	0.433185	+	0.750299i	−0.563960	+	0.825802i	$0.690723\pi$
$338$	1.33919e6	+	2.31954e6i	0.637601	+	1.10436i
$339$	228280.	−	2.35192e6i	0.107887	−	1.11154i
$340$	−78866.9	+	136601.i	−0.0369996	+	0.0640852i
$341$	−523483.			−0.243790
$342$	4.20637e6	+	824318.i	1.94466	+	0.381092i
$343$	2.33157e6			1.07007
$344$	−1.44978e6	+	2.51110e6i	−0.660552	+	1.14411i
$345$	−1.20993e6	+	550281.i	−0.547286	+	0.248907i
$346$	−1.61490e6	−	2.79709e6i	−0.725196	−	1.25608i
$347$	7106.83	+	12309.4i	0.00316849	+	0.00548799i	0.867605	−	0.497253i	$-0.165658\pi$
$347$	7106.83	+	12309.4i	0.00316849	+	0.00548799i	−0.864437	+	0.502741i	$0.832325\pi$
$348$	−413275.	−	295263.i	−0.182932	−	0.130696i
$349$	2.08151e6	−	3.60529e6i	0.914778	−	1.58444i	0.107553	−	0.994199i	$-0.465698\pi$
$349$	2.08151e6	−	3.60529e6i	0.914778	−	1.58444i	0.807225	−	0.590243i	$-0.200968\pi$
$350$	2.39381e6			1.04453
$351$	−1.10010e6	+	261442.i	−0.476611	+	0.113268i
$352$	394392.			0.169657
$353$	317997.	−	550787.i	0.135827	−	0.235259i	−0.790086	−	0.612996i	$-0.789964\pi$
$353$	317997.	−	550787.i	0.135827	−	0.235259i	0.925913	+	0.377737i	$0.123297\pi$
$354$	3.54671e6	+	2.53394e6i	1.50424	+	1.07470i
$355$	−487503.	−	844380.i	−0.205308	−	0.355604i
$356$	383127.	+	663595.i	0.160220	+	0.277510i
$357$	−144800.	+	65855.6i	−0.0601311	+	0.0273478i
$358$	−536414.	+	929096.i	−0.221204	+	0.383136i
$359$	1.10106e6			0.450896			0.225448	−	0.974255i	$-0.427615\pi$
$359$	1.10106e6			0.450896			0.225448	+	0.974255i	$0.427615\pi$
$360$	1.23068e6	−	1.41137e6i	0.500483	−	0.573964i
$361$	977737.			0.394870
$362$	−2.61839e6	+	4.53519e6i	−1.05018	+	1.81896i
$363$	−22048.7	+	227163.i	−0.00878248	+	0.0904839i
$364$	1.01396e6	+	1.75624e6i	0.401115	+	0.694752i
$365$	347667.	+	602176.i	0.136594	+	0.236587i
$366$	−684266.	+	7.04984e6i	−0.267007	+	2.75091i
$367$	−681743.	+	1.18081e6i	−0.264214	+	0.457632i	−0.967357	−	0.253416i	$-0.918446\pi$
$367$	−681743.	+	1.18081e6i	−0.264214	+	0.457632i	0.703143	+	0.711048i	$0.251779\pi$
$368$	−1.34641e6			−0.518272
$369$	42800.0	−	49083.9i	0.0163636	−	0.0187661i
$370$	−3.40487e6			−1.29299
$371$	−1.58983e6	+	2.75367e6i	−0.599676	+	1.03867i
$372$	3.56601e6	−	1.62183e6i	1.33606	−	0.607642i
$373$	1.28736e6	+	2.22977e6i	0.479101	+	0.829828i	0.999713	−	0.0239657i	$-0.00762925\pi$
$373$	1.28736e6	+	2.22977e6i	0.479101	+	0.829828i	−0.520611	+	0.853794i	$0.674296\pi$
$374$	50103.8	+	86782.3i	0.0185222	+	0.0320813i
$375$	2.08479e6	+	1.48948e6i	0.765569	+	0.546959i
$376$	−647311.	+	1.12118e6i	−0.236126	+	0.408982i
$377$	167437.			0.0606735
$378$	4.09095e6	−	972225.i	1.47263	−	0.349975i
$379$	−4.33929e6			−1.55174			−0.775872	−	0.630890i	$-0.782690\pi$
$379$	−4.33929e6			−1.55174			−0.775872	+	0.630890i	$0.782690\pi$
$380$	1.67983e6	−	2.90954e6i	0.596767	−	1.03363i
$381$	−697763.	−	498515.i	−0.246261	−	0.175941i
$382$	−1.92040e6	−	3.32622e6i	−0.673337	−	1.16625i
$383$	−537915.	−	931696.i	−0.187377	−	0.324547i	0.756998	−	0.653417i	$-0.226665\pi$
$383$	−537915.	−	931696.i	−0.187377	−	0.324547i	−0.944375	+	0.328871i	$0.893332\pi$
$384$	−4.80455e6	+	2.18512e6i	−1.66274	+	0.756219i
$385$	−220203.	+	381402.i	−0.0757130	+	0.131139i
$386$	7.31247e6			2.49802
$387$	−2.79241e6	−	547224.i	−0.947766	−	0.185732i
$388$	−7.45183e6			−2.51295
$389$	−1.69091e6	+	2.92874e6i	−0.566561	+	0.981312i	0.430342	+	0.902666i	$0.358393\pi$
$389$	−1.69091e6	+	2.92874e6i	−0.566561	+	0.981312i	−0.996903	+	0.0786463i	$0.974940\pi$
$390$	−132787.	+	1.36807e6i	−0.0442073	+	0.455458i
$391$	119531.	+	207034.i	0.0395401	+	0.0684855i
$392$	387394.	+	670986.i	0.127332	+	0.220545i
$393$	278847.	−	2.87290e6i	0.0910720	−	0.938295i
$394$	236253.	−	409203.i	0.0766721	−	0.132800i
$395$	−599848.			−0.193441
$396$	−553588.	−	1.61576e6i	−0.177398	−	0.517773i
$397$	380497.			0.121164			0.0605822	−	0.998163i	$-0.480704\pi$
$397$	380497.			0.121164			0.0605822	+	0.998163i	$0.480704\pi$
$398$	876537.	−	1.51821e6i	0.277372	−	0.480423i
$399$	3.08418e6	−	1.40269e6i	0.969856	−	0.441093i
$400$	529862.	+	917747.i	0.165582	+	0.286796i
$401$	−2.37569e6	−	4.11482e6i	−0.737785	−	1.27788i	−0.953491	−	0.301422i	$-0.902539\pi$
$401$	−2.37569e6	−	4.11482e6i	−0.737785	−	1.27788i	0.215706	−	0.976458i	$-0.430795\pi$
$402$	6.16941e6	+	4.40772e6i	1.90405	+	1.36034i
$403$	−645714.	+	1.11841e6i	−0.198051	+	0.343035i
$404$	122.886			3.74584e−5
$405$	1.70175e6	+	693615.i	0.515534	+	0.210127i
$406$	−622650.			−0.187469
$407$	−697375.	+	1.20789e6i	−0.208680	+	0.361444i
$408$	−274038.	−	195786.i	−0.0815005	−	0.0582279i
$409$	110537.	+	191455.i	0.0326737	+	0.0565926i	0.881900	−	0.471437i	$-0.156264\pi$
$409$	110537.	+	191455.i	0.0326737	+	0.0565926i	−0.849226	+	0.528029i	$0.822931\pi$
$410$	−39581.4	−	68557.0i	−0.0116287	−	0.0201415i
$411$	−3.19926e6	+	1.45503e6i	−0.934210	+	0.424881i
$412$	−3.31246e6	+	5.73734e6i	−0.961407	+	1.66521i
$413$	3.44549e6			0.993977
$414$	−2.04822e6	−	5.97816e6i	−0.587321	−	1.71422i
$415$	1.87956e6			0.535718
$416$	486481.	−	842610.i	0.137827	−	0.238723i
$417$	278831.	−	2.87274e6i	0.0785238	−	0.809013i
$418$	−1.06719e6	−	1.84842e6i	−0.298744	−	0.517440i
$419$	−3.41745e6	−	5.91919e6i	−0.950970	−	1.64713i	−0.743333	−	0.668922i	$-0.766756\pi$
$419$	−3.41745e6	−	5.91919e6i	−0.950970	−	1.64713i	−0.207637	−	0.978206i	$-0.566577\pi$
$420$	318396.	−	3.28036e6i	0.0880733	−	0.907399i
$421$	−1.41716e6	+	2.45459e6i	−0.389684	+	0.674953i	−0.992407	−	0.122998i	$-0.960749\pi$
$421$	−1.41716e6	+	2.45459e6i	−0.389684	+	0.674953i	0.602723	+	0.797951i	$0.294082\pi$
$422$	1.20207e6			0.328586
$423$	−1.24678e6	−	244329.i	−0.338795	−	0.0663933i
$424$	−6.73206e6			−1.81858
$425$	94079.6	−	162951.i	0.0252652	−	0.0437607i
$426$	4.21952e6	−	1.91905e6i	1.12652	−	0.512344i
$427$	2.79937e6	+	4.84864e6i	0.743002	+	1.28692i
$428$	4.62574e6	+	8.01202e6i	1.22060	+	2.11413i
$429$	458132.	+	327311.i	0.120184	+	0.0858654i
$430$	−1.72948e6	+	2.99554e6i	−0.451070	+	0.781276i
$431$	3.76956e6			0.977458			0.488729	−	0.872436i	$-0.337461\pi$
$431$	3.76956e6			0.977458			0.488729	+	0.872436i	$0.337461\pi$
$432$	1.27825e6	+	1.35320e6i	0.329540	+	0.348862i
$433$	3.72282e6			0.954229			0.477114	−	0.878841i	$-0.341683\pi$
$433$	3.72282e6			0.954229			0.477114	+	0.878841i	$0.341683\pi$
$434$	2.40122e6	−	4.15904e6i	0.611939	−	1.05991i
$435$	−221415.	−	158189.i	−0.0561027	−	0.0400824i
$436$	−5.28927e6	−	9.16128e6i	−1.33254	−	2.30802i
$437$	−2.54595e6	−	4.40971e6i	−0.637744	−	1.10460i
$438$	−3.00918e6	+	1.36858e6i	−0.749486	+	0.340868i
$439$	969399.	−	1.67905e6i	0.240072	−	0.415817i	−0.720663	−	0.693286i	$-0.756162\pi$
$439$	969399.	−	1.67905e6i	0.240072	−	0.415817i	0.960735	+	0.277469i	$0.0894957\pi$
$440$	−932435.			−0.229608
$441$	−499709.	+	573077.i	−0.122355	+	0.140319i
$442$	247211.			0.0601884
$443$	1.43061e6	−	2.47789e6i	0.346348	−	0.599892i	−0.639250	−	0.768999i	$-0.720755\pi$
$443$	1.43061e6	−	2.47789e6i	0.346348	−	0.599892i	0.985598	+	0.169107i	$0.0540883\pi$
$444$	1.00835e6	−	1.03888e7i	0.242747	−	2.50097i
$445$	205263.	+	355526.i	0.0491372	+	0.0851081i
$446$	−5.67318e6	−	9.82624e6i	−1.35048	−	2.33911i
$447$	495017.	−	5.10005e6i	0.117179	−	1.20727i
$448$	−2.72864e6	+	4.72614e6i	−0.642320	+	1.11253i
$449$	5.25146e6			1.22932			0.614659	−	0.788793i	$-0.289294\pi$
$449$	5.25146e6			1.22932			0.614659	+	0.788793i	$0.289294\pi$
$450$	−3.26882e6	+	3.74874e6i	−0.760956	+	0.872679i
$451$	−32427.8			−0.00750716
$452$	4.40264e6	−	7.62560e6i	1.01360	−	1.75561i
$453$	5.47303e6	−	2.48915e6i	1.25309	−	0.569909i
$454$	−4.30006e6	−	7.44792e6i	−0.979118	−	1.69588i
$455$	543238.	+	940916.i	0.123016	+	0.213070i
$456$	5.83688e6	+	4.17014e6i	1.31452	+	0.939159i
$457$	−3.88607e6	+	6.73087e6i	−0.870402	+	1.50758i	−0.00882127	+	0.999961i	$0.502808\pi$
$457$	−3.88607e6	+	6.73087e6i	−0.870402	+	1.50758i	−0.861581	+	0.507620i	$0.830525\pi$
$458$	−1.32137e7			−2.94347
$459$	94598.3	−	316688.i	0.0209581	−	0.0701616i
$460$	−4.95304e6			−1.09138
$461$	1.76796e6	−	3.06219e6i	0.387453	−	0.671089i	−0.604653	−	0.796489i	$-0.706688\pi$
$461$	1.76796e6	−	3.06219e6i	0.387453	−	0.671089i	0.992106	+	0.125400i	$0.0400215\pi$
$462$	−1.70366e6	−	1.21718e6i	−0.371345	−	0.265307i
$463$	863078.	+	1.49489e6i	0.187110	+	0.324084i	0.944286	−	0.329127i	$-0.106755\pi$
$463$	863078.	+	1.49489e6i	0.187110	+	0.324084i	−0.757175	+	0.653212i	$0.773421\pi$
$464$	−137822.	−	238714.i	−0.0297182	−	0.0514734i
$465$	1.91051e6	−	868906.i	0.409749	−	0.186355i
$466$	5.78619e6	−	1.00220e7i	1.23432	−	2.13791i
$467$	−1.55045e6			−0.328976			−0.164488	−	0.986379i	$-0.552597\pi$
$467$	−1.55045e6			−0.328976			−0.164488	+	0.986379i	$0.552597\pi$
$468$	−4.13489e6	−	810309.i	−0.872669	−	0.171016i
$469$	5.99334e6			1.25816
$470$	−772191.	+	1.33747e6i	−0.161243	+	0.279281i
$471$	−626588.	+	6.45559e6i	−0.130146	+	1.34086i
$472$	3.64744e6	+	6.31755e6i	0.753586	+	1.30525i
$473$	708453.	+	1.22708e6i	0.145599	+	0.252185i
$474$	275507.	−	2.83849e6i	0.0563231	−	0.580285i
$475$	−2.00385e6	+	3.47077e6i	−0.407503	+	0.705816i
$476$	−592762.			−0.119912
$477$	−2.14133e6	−	6.24993e6i	−0.430911	−	1.25771i
$478$	−1.30559e7			−2.61358
$479$	−4.67069e6	+	8.08988e6i	−0.930128	+	1.61103i	−0.147028	+	0.989132i	$0.546971\pi$
$479$	−4.67069e6	+	8.08988e6i	−0.930128	+	1.61103i	−0.783100	+	0.621896i	$0.786363\pi$
$480$	−1.43938e6	+	654634.i	−0.285150	+	0.129687i
$481$	1.72042e6	+	2.97985e6i	0.339056	+	0.587263i
$482$	7.39133e6	+	1.28022e7i	1.44912	+	2.50995i
$483$	−4.06436e6	−	2.90377e6i	−0.792728	−	0.566363i
$484$	−425235.	+	736528.i	−0.0825116	+	0.142914i
$485$	−3.99237e6			−0.770684
$486$	−4.06379e6	+	7.73410e6i	−0.780443	+	1.48532i
$487$	4.95555e6			0.946825			0.473412	−	0.880841i	$-0.343022\pi$
$487$	4.95555e6			0.946825			0.473412	+	0.880841i	$0.343022\pi$
$488$	−5.92688e6	+	1.02657e7i	−1.12662	+	1.95136i
$489$	5.07148e6	+	3.62331e6i	0.959098	+	0.685225i
$490$	462130.	+	800433.i	0.0869509	+	0.150603i
$491$	1.66607e6	+	2.88571e6i	0.311881	+	0.540194i	0.978770	−	0.204964i	$-0.0657077\pi$
$491$	1.66607e6	+	2.88571e6i	0.311881	+	0.540194i	−0.666889	+	0.745157i	$0.732374\pi$
$492$	220901.	−	100466.i	0.0411419	−	0.0187114i
$493$	−24470.9	+	42384.9i	−0.00453454	+	0.00785405i
$494$	−5.26548e6			−0.970780
$495$	−296589.	−	865656.i	−0.0544053	−	0.158793i
$496$	2.12601e6			0.388026
$497$	1.83203e6	−	3.17317e6i	0.332692	−	0.576239i
$498$	−863272.	+	8.89410e6i	−0.155982	+	1.60705i
$499$	859488.	+	1.48868e6i	0.154521	+	0.267639i	0.932885	−	0.360175i	$-0.117283\pi$
$499$	859488.	+	1.48868e6i	0.154521	+	0.267639i	−0.778363	+	0.627814i	$0.783950\pi$
$500$	4.77385e6	+	8.26855e6i	0.853972	+	1.47912i
$501$	−751411.	+	7.74162e6i	−0.133747	+	1.37796i
$502$	2.01553e6	−	3.49099e6i	0.356968	−	0.618287i
$503$	−7.42097e6			−1.30780			−0.653899	−	0.756582i	$-0.726868\pi$
$503$	−7.42097e6			−1.30780			−0.653899	+	0.756582i	$0.726868\pi$
$504$	6.90577e6	+	1.35331e6i	1.21098	+	0.237314i
$505$	65.8371			1.14879e−5
$506$	−1.57332e6	+	2.72508e6i	−0.273176	+	0.473154i
$507$	−4.00419e6	+	1.82112e6i	−0.691822	+	0.314643i
$508$	−1.59777e6	−	2.76741e6i	−0.274697	−	0.475790i
$509$	−700378.	−	1.21309e6i	−0.119822	−	0.207538i	0.799875	−	0.600167i	$-0.204899\pi$
$509$	−700378.	−	1.21309e6i	−0.119822	−	0.207538i	−0.919697	+	0.392628i	$0.871566\pi$
$510$	−326906.	−	233557.i	−0.0556541	−	0.0397620i
$511$	−1.30653e6	+	2.26297e6i	−0.221343	+	0.383378i
$512$	−5.49556e6			−0.926482
$513$	−2.01490e6	+	6.74529e6i	−0.338033	+	1.13164i
$514$	1.84295e7			3.07685
$515$	−1.77467e6	+	3.07382e6i	−0.294849	+	0.510694i
$516$	−8.62770e6	−	6.16404e6i	−1.42650	−	1.01916i
$517$	316316.	+	547875.i	0.0520468	+	0.0901478i
$518$	−6.39774e6	−	1.10812e7i	−1.04762	−	1.81452i
$519$	4.82857e6	−	2.19605e6i	0.786865	−	0.357868i
$520$	−1.15016e6	+	1.99213e6i	−0.186530	+	0.323079i
$521$	1.13783e7			1.83646			0.918232	−	0.396043i	$-0.129617\pi$
$521$	1.13783e7			1.83646			0.918232	+	0.396043i	$0.129617\pi$
$522$	850247.	−	975081.i	0.136574	−	0.156626i
$523$	2.86097e6			0.457362			0.228681	−	0.973501i	$-0.426559\pi$
$523$	2.86097e6			0.457362			0.228681	+	0.973501i	$0.426559\pi$
$524$	5.37788e6	−	9.31477e6i	0.855624	−	1.48198i
$525$	−379812.	+	3.91312e6i	−0.0601409	+	0.619619i
$526$	−7.72079e6	−	1.33728e7i	−1.21674	−	2.10745i
$527$	−188742.	−	326910.i	−0.0296034	−	0.0512746i
$528$	89546.0	−	922573.i	0.0139785	−	0.144018i
$529$	−535253.	+	927086.i	−0.0831611	+	0.144039i
$530$	−8.03082e6			−1.24185
$531$	−4.70492e6	+	5.39570e6i	−0.724130	+	0.830446i
$532$	1.26255e7			1.93406
$533$	−39999.5	+	69281.2i	−0.00609870	+	0.0105633i
$534$	−1.77663e6	+	808014.i	−0.269614	+	0.122621i
$535$	2.47827e6	+	4.29250e6i	0.374339	+	0.648374i
$536$	6.34461e6	+	1.09892e7i	0.953879	+	1.65217i
$537$	−1.43367e6	−	1.02428e6i	−0.214542	−	0.153279i
$538$	8.88069e6	−	1.53818e7i	1.32279	−	2.29114i
$539$	378609.			0.0561330
$540$	4.70232e6	+	4.97804e6i	0.693949	+	0.734639i
$541$	−3.17181e6			−0.465923			−0.232962	−	0.972486i	$-0.574842\pi$
$541$	−3.17181e6			−0.465923			−0.232962	+	0.972486i	$0.574842\pi$
$542$	4.54678e6	−	7.87525e6i	0.664822	−	1.15151i
$543$	−6.99814e6	−	4.99981e6i	−1.01855	−	0.727702i
$544$	142198.	+	246295.i	0.0206014	+	0.0356827i
$545$	−2.83376e6	−	4.90822e6i	−0.408669	−	0.707836i
$546$	−4.70193e6	+	2.13845e6i	−0.674985	+	0.306985i
$547$	697869.	−	1.20875e6i	0.0997254	−	0.172729i	−0.811846	−	0.583872i	$-0.801537\pi$
$547$	697869.	−	1.20875e6i	0.0997254	−	0.172729i	0.911571	+	0.411143i	$0.134870\pi$
$548$	−1.30966e7			−1.86298
$549$	−1.14157e7	−	2.23711e6i	−1.61648	−	0.316780i
$550$	2.47664e6			0.349106
$551$	521219.	−	902777.i	0.0731376	−	0.126678i
$552$	1.02169e6	−	1.05262e7i	0.142716	−	1.47037i
$553$	−1.12711e6	−	1.95222e6i	−0.156731	−	0.271466i
$554$	3.61960e6	+	6.26933e6i	0.501056	+	0.867854i
$555$	540231.	−	5.56588e6i	0.0744470	−	0.767011i
$556$	5.37757e6	−	9.31423e6i	0.737733	−	1.27779i
$557$	−2.06079e6			−0.281446			−0.140723	−	0.990049i	$-0.544943\pi$
$557$	−2.06079e6			−0.281446			−0.140723	+	0.990049i	$0.544943\pi$
$558$	3.23418e6	+	9.43964e6i	0.439723	+	1.28342i
$559$	3.49549e6			0.473129
$560$	894304.	−	1.54898e6i	0.120508	−	0.208726i
$561$	−149811.	+	68134.5i	−0.0200973	+	0.00914028i
$562$	−1.81392e6	−	3.14180e6i	−0.242258	−	0.419602i
$563$	4.71929e6	+	8.17405e6i	0.627488	+	1.08684i	0.988054	+	0.154108i	$0.0492502\pi$
$563$	4.71929e6	+	8.17405e6i	0.627488	+	1.08684i	−0.360566	+	0.932734i	$0.617416\pi$
$564$	−3.85217e6	−	2.75217e6i	−0.509926	−	0.364316i
$565$	2.35874e6	−	4.08547e6i	0.310856	−	0.538419i
$566$	1.44276e7			1.89301
$567$	940191.	+	6.84166e6i	0.122817	+	0.893725i
$568$	7.75763e6			1.00892
$569$	1.46618e6	−	2.53950e6i	0.189848	−	0.328826i	−0.755351	−	0.655320i	$-0.772534\pi$
$569$	1.46618e6	−	2.53950e6i	0.189848	−	0.328826i	0.945199	+	0.326494i	$0.105867\pi$
$570$	6.96293e6	+	4.97465e6i	0.897646	+	0.641321i
$571$	1.76660e6	+	3.05983e6i	0.226750	+	0.392742i	0.956843	−	0.290605i	$-0.0938567\pi$
$571$	1.76660e6	+	3.05983e6i	0.226750	+	0.392742i	−0.730093	+	0.683348i	$0.760523\pi$
$572$	1.04905e6	+	1.81701e6i	0.134062	+	0.232203i
$573$	5.74201e6	−	2.61148e6i	0.730597	−	0.332277i
$574$	148747.	−	257637.i	0.0188438	−	0.0326383i
$575$	5.90844e6			0.745253
$576$	−3.67518e6	−	1.07268e7i	−0.461554	−	1.34714i
$577$	−9.20959e6			−1.15160			−0.575799	−	0.817592i	$-0.695309\pi$
$577$	−9.20959e6			−1.15160			−0.575799	+	0.817592i	$0.695309\pi$
$578$	6.70214e6	−	1.16085e7i	0.834438	−	1.44529i
$579$	−1.16023e6	+	1.19536e7i	−0.143829	+	1.48184i
$580$	−507005.	−	878159.i	−0.0625810	−	0.108393i
$581$	3.53169e6	+	6.11706e6i	0.434052	+	0.751801i
$582$	1.83367e6	−	1.88919e7i	0.224396	−	2.31190i
$583$	−1.64485e6	+	2.84896e6i	−0.200426	+	0.347148i
$584$	−5.53242e6			−0.671248
$585$	−2.21530e6	−	434129.i	−0.267635	−	0.0524480i
$586$	9.68845e6			1.16549
$587$	−7.22910e6	+	1.25212e7i	−0.865942	+	1.49986i	0.000166445		1.00000i	$0.499947\pi$
$587$	−7.22910e6	+	1.25212e7i	−0.865942	+	1.49986i	−0.866109	+	0.499856i	$0.833386\pi$
$588$	−2.57911e6	+	1.17299e6i	−0.307629	+	0.139910i
$589$	4.02011e6	+	6.96303e6i	0.477474	+	0.827009i
$590$	4.35111e6	+	7.53634e6i	0.514600	+	0.891313i
$591$	631431.	+	451125.i	0.0743630	+	0.0531285i
$592$	2.83224e6	−	4.90558e6i	0.332143	−	0.575289i
$593$	−1.39039e7			−1.62367			−0.811837	−	0.583884i	$-0.801532\pi$
$593$	−1.39039e7			−1.62367			−0.811837	+	0.583884i	$0.801532\pi$
$594$	4.23251e6	−	1.00587e6i	0.492189	−	0.116970i
$595$	−317576.			−0.0367753
$596$	9.54696e6	−	1.65358e7i	1.10090	−	1.90682i
$597$	2.34271e6	+	1.67374e6i	0.269019	+	0.192200i
$598$	3.88138e6	+	6.72274e6i	0.443847	+	0.768765i
$599$	−4.52512e6	−	7.83774e6i	−0.515304	−	0.892532i	−0.999842	−	0.0177624i	$-0.994346\pi$
$599$	−4.52512e6	−	7.83774e6i	−0.515304	−	0.892532i	0.484538	−	0.874770i	$-0.338988\pi$
$600$	−7.57703e6	+	3.44606e6i	−0.859253	+	0.390791i
$601$	7.64713e6	−	1.32452e7i	0.863599	−	1.49580i	−0.00483191	−	0.999988i	$-0.501538\pi$
$601$	7.64713e6	−	1.32452e7i	0.863599	−	1.49580i	0.868431	−	0.495810i	$-0.165129\pi$
$602$	−1.29987e7			−1.46187
$603$	−8.18408e6	+	9.38567e6i	−0.916593	+	1.05117i
$604$	2.24047e7			2.49888
$605$	−227822.	+	394600.i	−0.0253051	+	0.0438297i
$606$	−30.2386	+	311.542i	−3.34488e−6	+	3.44615e-5i
$607$	1.60479e6	+	2.77958e6i	0.176786	+	0.306202i	0.940778	−	0.339024i	$-0.110097\pi$
$607$	1.60479e6	+	2.77958e6i	0.176786	+	0.306202i	−0.763992	+	0.645226i	$0.776763\pi$
$608$	−3.02875e6	−	5.24595e6i	−0.332281	−	0.575527i
$609$	98792.3	−	1.01783e6i	0.0107939	−	0.111208i
$610$	−7.07030e6	+	1.22461e7i	−0.769331	+	1.33252i
$611$	1.56070e6			0.169128
$612$	809434.	−	928275.i	0.0873580	−	0.100184i
$613$	1.25901e6			0.135325			0.0676625	−	0.997708i	$-0.478446\pi$
$613$	1.25901e6			0.135325			0.0676625	+	0.997708i	$0.478446\pi$
$614$	−8.52448e6	+	1.47648e7i	−0.912529	+	1.58055i
$615$	118349.	−	53825.4i	0.0126176	−	0.00573852i
$616$	−1.75204e6	−	3.03462e6i	−0.186034	−	0.322221i
$617$	−1.50348e6	−	2.60410e6i	−0.158996	−	0.275388i	0.775511	−	0.631334i	$-0.217492\pi$
$617$	−1.50348e6	−	2.60410e6i	−0.158996	−	0.275388i	−0.934507	+	0.355946i	$0.884159\pi$
$618$	−1.37302e7	−	9.80955e6i	−1.44613	−	1.03318i
$619$	2.37067e6	−	4.10613e6i	0.248682	−	0.430731i	−0.714478	−	0.699658i	$-0.753336\pi$
$619$	2.37067e6	−	4.10613e6i	0.248682	−	0.430731i	0.963161	+	0.268927i	$0.0866691\pi$
$620$	7.82096e6			0.817111
$621$	1.00974e7	−	2.39966e6i	1.05070	−	0.249702i
$622$	1.54241e7			1.59854
$623$	−771376.	+	1.33606e6i	−0.0796244	+	0.137913i
$624$	−1.86060e6	−	1.32930e6i	−0.191290	−	0.136667i
$625$	−811870.	−	1.40620e6i	−0.0831355	−	0.143995i
$626$	6.27831e6	+	1.08744e7i	0.640335	+	1.10909i
$627$	3.19090e6	−	1.45123e6i	0.324149	−	0.147424i
$628$	−1.20844e7	+	2.09309e7i	−1.22272	+	2.11782i
$629$	−1.00576e6			−0.101360
$630$	8.23804e6	+	1.61440e6i	0.826937	+	0.162054i
$631$	−1.87105e7			−1.87074			−0.935369	−	0.353673i	$-0.884932\pi$
$631$	−1.87105e7			−1.87074			−0.935369	+	0.353673i	$0.884932\pi$
$632$	2.38635e6	−	4.13327e6i	0.237652	−	0.411625i
$633$	−190726.	+	1.96500e6i	−0.0189191	+	0.194919i
$634$	275994.	+	478035.i	0.0272694	+	0.0472321i
$635$	−856015.	−	1.48266e6i	−0.0842456	−	0.145918i
$636$	2.37832e6	−	2.45033e7i	0.233146	−	2.40205i
$637$	467012.	−	808889.i	0.0456016	−	0.0789842i
$638$	−644196.			−0.0626566
$639$	2.46754e6	+	7.20205e6i	0.239063	+	0.697757i
$640$	−1.05373e7			−1.01691
$641$	1.65985e6	−	2.87495e6i	0.159560	−	0.276367i	−0.775150	−	0.631777i	$-0.782326\pi$
$641$	1.65985e6	−	2.87495e6i	0.159560	−	0.276367i	0.934710	+	0.355411i	$0.115659\pi$
$642$	−2.14504e7	+	9.75569e6i	−2.05399	+	0.934158i
$643$	−2.28458e6	−	3.95700e6i	−0.217911	−	0.377432i	0.736258	−	0.676700i	$-0.236591\pi$
$643$	−2.28458e6	−	3.95700e6i	−0.217911	−	0.377432i	−0.954169	+	0.299268i	$0.903257\pi$
$644$	−9.30675e6	−	1.61198e7i	−0.884267	−	1.53160i
$645$	−4.62235e6	−	3.30243e6i	−0.437485	−	0.312561i
$646$	769548.	−	1.33290e6i	0.0725529	−	0.125665i
$647$	−4.49477e6			−0.422130			−0.211065	−	0.977472i	$-0.567693\pi$
$647$	−4.49477e6			−0.422130			−0.211065	+	0.977472i	$0.567693\pi$
$648$	−1.15493e7	+	8.96656e6i	−1.08049	+	0.838858i
$649$	3.56472e6			0.332211
$650$	3.05493e6	−	5.29130e6i	0.283608	−	0.491223i
$651$	6.41771e6	+	4.58512e6i	0.593510	+	0.424032i
$652$	1.16129e7	+	2.01141e7i	1.06985	+	1.85303i
$653$	−8.09599e6	−	1.40227e7i	−0.742997	−	1.28691i	−0.951125	−	0.308807i	$-0.900070\pi$
$653$	−8.09599e6	−	1.40227e7i	−0.742997	−	1.28691i	0.208128	−	0.978102i	$-0.433263\pi$
$654$	2.45273e7	−	1.11551e7i	2.24236	−	1.01983i
$655$	2.88124e6	−	4.99045e6i	0.262407	−	0.454503i
$656$	131698.			0.0119487
$657$	−1.75975e6	−	5.13620e6i	−0.159051	−	0.464225i
$658$	−5.80378e6			−0.522572
$659$	−7.60226e6	+	1.31675e7i	−0.681914	+	1.18111i	0.292482	+	0.956271i	$0.405519\pi$
$659$	−7.60226e6	+	1.31675e7i	−0.681914	+	1.18111i	−0.974396	+	0.224838i	$0.927815\pi$
$660$	329414.	−	3.39387e6i	0.0294362	−	0.303274i
$661$	−7.19470e6	−	1.24616e7i	−0.640485	−	1.10935i	−0.985325	−	0.170692i	$-0.945400\pi$
$661$	−7.19470e6	−	1.24616e7i	−0.640485	−	1.10935i	0.344839	−	0.938662i	$-0.387934\pi$
$662$	3.00288e6	+	5.20113e6i	0.266313	+	0.461268i
$663$	−39223.6	+	404112.i	−0.00346548	+	0.0357041i
$664$	−7.47737e6	+	1.29512e7i	−0.658155	+	1.13996i
$665$	6.76422e6			0.593149
$666$	2.60897e7	+	5.11276e6i	2.27920	+	0.446652i
$667$	−1.53684e6			−0.133756
$668$	−1.44918e7	+	2.51006e7i	−1.25656	+	2.17642i
$669$	1.69629e7	−	7.71477e6i	1.46533	−	0.666435i
$670$	7.56863e6	+	1.31092e7i	0.651373	+	1.12821i
$671$	2.89623e6	+	5.01642e6i	0.248329	+	0.430118i
$672$	−4.83511e6	−	3.45443e6i	−0.413031	−	0.295089i
$673$	−4.31351e6	+	7.47123e6i	−0.367108	+	0.635849i	−0.989112	−	0.147165i	$-0.952985\pi$
$673$	−4.31351e6	+	7.47123e6i	−0.367108	+	0.635849i	0.622004	+	0.783014i	$0.286319\pi$
$674$	−1.71440e7			−1.45366
$675$	−5.60936e6	−	5.93827e6i	−0.473864	−	0.501649i
$676$	−1.63917e7			−1.37962
$677$	2.56325e6	−	4.43968e6i	0.214941	−	0.372289i	−0.738313	−	0.674458i	$-0.764377\pi$
$677$	2.56325e6	−	4.43968e6i	0.214941	−	0.372289i	0.953254	+	0.302169i	$0.0977107\pi$
$678$	1.82491e7	+	1.30380e7i	1.52464	+	1.08928i
$679$	−7.50164e6	−	1.29932e7i	−0.624427	−	1.08154i
$680$	−336190.	−	582298.i	−0.0278812	−	0.0482917i
$681$	1.28572e7	−	5.84751e6i	1.06238	−	0.483173i
$682$	2.48431e6	−	4.30296e6i	0.204524	−	0.354247i
$683$	1.64537e7			1.34962			0.674809	−	0.737992i	$-0.264226\pi$
$683$	1.64537e7			1.34962			0.674809	+	0.737992i	$0.264226\pi$
$684$	−1.72405e7	+	1.97718e7i	−1.40900	+	1.61587i
$685$	−7.01661e6			−0.571348
$686$	−1.10650e7	+	1.91652e7i	−0.897724	+	1.55490i
$687$	2.09654e6	−	2.16002e7i	0.169477	−	1.74608i
$688$	−2.87722e6	−	4.98350e6i	−0.231741	−	0.401387i
$689$	4.05783e6	+	7.02836e6i	0.325646	+	0.564035i
$690$	1.21880e6	−	1.25570e7i	0.0974560	−	1.00407i
$691$	−1.30312e6	+	2.25706e6i	−0.103822	+	0.179824i	−0.913256	−	0.407386i	$-0.866440\pi$
$691$	−1.30312e6	+	2.25706e6i	−0.103822	+	0.179824i	0.809435	+	0.587210i	$0.199774\pi$
$692$	1.97665e7			1.56915
$693$	2.26000e6	−	2.59182e6i	0.178762	−	0.205008i
$694$	−134909.			−0.0106326
$695$	2.88107e6	−	4.99016e6i	0.226252	−	0.391880i
$696$	1.97085e6	−	896349.i	0.154217	−	0.0701381i
$697$	−11691.8	−	20250.9i	−0.000911593	−	0.00157893i
$698$	1.97567e7	+	3.42195e7i	1.53488	+	2.65849i
$699$	1.54647e7	+	1.10487e7i	1.19715	+	0.855300i
$700$	−7.32510e6	+	1.26874e7i	−0.565026	+	0.978654i
$701$	−787564.			−0.0605328			−0.0302664	−	0.999542i	$-0.509636\pi$
$701$	−787564.			−0.0605328			−0.0302664	+	0.999542i	$0.509636\pi$
$702$	3.07177e6	−	1.02834e7i	0.235259	−	0.787579i
$703$	2.14221e7			1.63483
$704$	−2.82306e6	+	4.88969e6i	−0.214679	+	0.371834i
$705$	−2.06382e6	−	1.47450e6i	−0.156387	−	0.111730i
$706$	3.01826e6	+	5.22779e6i	0.227901	+	0.394735i
$707$	123.708	+	214.268i	9.30782e−6	+	1.61216e-5i
$708$	−2.42832e7	+	1.10440e7i	−1.82063	+	0.828028i
$709$	−2.20266e6	+	3.81511e6i	−0.164563	+	0.285031i	−0.936500	−	0.350668i	$-0.885955\pi$
$709$	−2.20266e6	+	3.81511e6i	−0.164563	+	0.285031i	0.771937	+	0.635699i	$0.219288\pi$
$710$	9.25425e6			0.688962
$711$	4.59631e6	+	900732.i	0.340985	+	0.0668224i
$712$	−3.26635e6			−0.241470
$713$	5.92674e6	−	1.02654e7i	0.436608	−	0.756228i
$714$	145861.	−	1.50277e6i	0.0107076	−	0.110318i
$715$	562036.	+	973475.i	0.0411149	+	0.0712131i
$716$	−3.28287e6	−	5.68610e6i	−0.239316	−	0.414507i
$717$	2.07150e6	−	2.13422e7i	0.150483	−	1.55039i
$718$	−5.22536e6	+	9.05060e6i	−0.378273	+	0.655188i
$719$	2.82520e6			0.203810			0.101905	−	0.994794i	$-0.467506\pi$
$719$	2.82520e6			0.203810			0.101905	+	0.994794i	$0.467506\pi$
$720$	1.20453e6	+	3.51567e6i	0.0865936	+	0.252742i
$721$	−1.33384e7			−0.955577
$722$	−4.64008e6	+	8.03686e6i	−0.331271	+	0.573777i
$723$	−2.21002e7	+	1.00512e7i	−1.57235	+	0.715111i
$724$	−1.60246e7	−	2.77555e7i	−1.13617	−	1.96790i
$725$	604802.	+	1.04755e6i	0.0427335	+	0.0740166i
$726$	−1.76261e6	−	1.25929e6i	−0.124112	−	0.0886718i
$727$	3.76578e6	−	6.52252e6i	0.264252	−	0.457698i	−0.703115	−	0.711076i	$-0.748208\pi$
$727$	3.76578e6	−	6.52252e6i	0.264252	−	0.457698i	0.967367	+	0.253378i	$0.0815415\pi$
$728$	−8.64455e6			−0.604524
$729$	−1.19980e7	−	7.87013e6i	−0.836162	−	0.548483i
$730$	−6.59974e6			−0.458374
$731$	−510866.	+	884845.i	−0.0353601	+	0.0612455i
$732$	−3.52710e7	−	2.51993e7i	−2.43299	−	1.73824i
$733$	1.07102e7	+	1.85507e7i	0.736273	+	1.27526i	0.954162	+	0.299289i	$0.0967495\pi$
$733$	1.07102e7	+	1.85507e7i	0.736273	+	1.27526i	−0.217889	+	0.975974i	$0.569917\pi$
$734$	−6.47075e6	−	1.12077e7i	−0.443317	−	0.767848i
$735$	−1.38178e6	+	628436.i	−0.0943451	+	0.0429084i
$736$	−4.46521e6	+	7.73397e6i	−0.303842	+	0.526269i
$737$	6.20073e6			0.420508
$738$	200345.	+	584750.i	0.0135406	+	0.0395211i
$739$	−1.49241e7			−1.00526			−0.502628	−	0.864503i	$-0.667633\pi$
$739$	−1.49241e7			−1.00526			−0.502628	+	0.864503i	$0.667633\pi$
$740$	1.04190e7	−	1.80462e7i	0.699432	−	1.21145i
$741$	835443.	−	8.60738e6i	0.0558948	−	0.575871i
$742$	−1.50899e7	−	2.61364e7i	−1.00618	−	1.74276i
$743$	4.36677e6	+	7.56347e6i	0.290194	+	0.502631i	0.973855	−	0.227169i	$-0.0729469\pi$
$743$	4.36677e6	+	7.56347e6i	0.290194	+	0.502631i	−0.683662	+	0.729799i	$0.739614\pi$
$744$	−1.61327e6	+	1.66212e7i	−0.106850	+	1.10085i
$745$	5.11485e6	−	8.85918e6i	0.337631	−	0.584794i
$746$	−2.44379e7			−1.60774
$747$	−1.44020e7	−	2.82235e6i	−0.944328	−	0.185059i
$748$	−613274.			−0.0400775
$749$	−9.31333e6	+	1.61312e7i	−0.606597	+	1.05066i
$750$	−2.21372e7	+	1.00680e7i	−1.43704	+	0.653569i
$751$	−1.12334e7	−	1.94568e7i	−0.726792	−	1.25884i	−0.958232	−	0.285991i	$-0.907677\pi$
$751$	−1.12334e7	−	1.94568e7i	−0.726792	−	1.25884i	0.231440	−	0.972849i	$-0.425656\pi$
$752$	−1.28465e6	−	2.22507e6i	−0.0828398	−	0.143483i
$753$	5.38687e6	+	3.84864e6i	0.346218	+	0.247354i
$754$	−794614.	+	1.37631e6i	−0.0509012	+	0.0881634i
$755$	1.20035e7			0.766370
$756$	−7.36548e6	+	2.46575e7i	−0.468702	+	1.56908i
$757$	−2.32097e7			−1.47207			−0.736037	−	0.676942i	$-0.763305\pi$
$757$	−2.32097e7			−1.47207			−0.736037	+	0.676942i	$0.763305\pi$
$758$	2.05931e7	−	3.56683e7i	1.30181	−	2.25481i
$759$	−4.20500e6	−	3.00426e6i	−0.264949	−	0.189292i
$760$	7.16068e6	+	1.24027e7i	0.449697	+	0.778898i
$761$	1.29087e7	+	2.23585e7i	0.808018	+	1.39953i	0.914235	+	0.405185i	$0.132793\pi$
$761$	1.29087e7	+	2.23585e7i	0.808018	+	1.39953i	−0.106217	+	0.994343i	$0.533874\pi$
$762$	7.40913e6	−	3.36969e6i	0.462253	−	0.210234i
$763$	1.06493e7	−	1.84450e7i	0.662228	−	1.14701i
$764$	2.35058e7			1.45694
$765$	433660.	−	497330.i	0.0267914	−	0.0307249i
$766$	1.02112e7			0.628790
$767$	4.39707e6	−	7.61595e6i	0.269883	−	0.467451i
$768$	2.59106e6	−	2.66951e7i	0.158517	−	1.63316i
$769$	−1.03983e7	−	1.80104e7i	−0.634085	−	1.09827i	−0.986708	−	0.162502i	$-0.948044\pi$
$769$	−1.03983e7	−	1.80104e7i	−0.634085	−	1.09827i	0.352623	−	0.935765i	$-0.385290\pi$
$770$	−2.09005e6	−	3.62007e6i	−0.127037	−	0.220034i
$771$	−2.92411e6	+	3.01264e7i	−0.177157	+	1.82520i
$772$	−2.23763e7	+	3.87568e7i	−1.35128	+	2.34048i
$773$	−924553.			−0.0556523			−0.0278261	−	0.999613i	$-0.508858\pi$
$773$	−924553.			−0.0556523			−0.0278261	+	0.999613i	$0.508858\pi$
$774$	1.77501e7	−	2.03562e7i	1.06500	−	1.22136i
$775$	−9.32956e6			−0.557965
$776$	1.58826e7	−	2.75095e7i	0.946822	−	1.63994i
$777$	1.91293e7	−	8.70007e6i	1.13670	−	0.516976i
$778$	−1.60492e7	−	2.77981e7i	−0.950617	−	1.64652i
$779$	249031.	+	431334.i	0.0147031	+	0.0254665i
$780$	−6.84461e6	−	4.89012e6i	−0.402821	−	0.287795i
$781$	1.89543e6	−	3.28297e6i	0.111193	−	0.192593i
$782$	−2.26905e6			−0.132687
$783$	1.45904e6	+	1.54459e6i	0.0850479	+	0.0900347i
$784$	−1.53763e6			−0.0893435
$785$	−6.47433e6	+	1.12139e7i	−0.374991	+	0.649503i
$786$	2.22915e7	+	1.59261e7i	1.28701	+	0.919504i
$787$	5.39495e6	+	9.34432e6i	0.310492	+	0.537788i	0.978469	−	0.206394i	$-0.0661729\pi$
$787$	5.39495e6	+	9.34432e6i	0.310492	+	0.537788i	−0.667977	+	0.744182i	$0.732840\pi$
$788$	1.44588e6	+	2.50433e6i	0.0829499	+	0.143674i
$789$	2.30853e7	−	1.04992e7i	1.32021	−	0.600434i
$790$	2.84672e6	−	4.93067e6i	0.162285	−	0.281085i
$791$	1.77283e7			1.00745
$792$	7.14474e6	+	1.40014e6i	0.404737	+	0.0793158i
$793$	1.42900e7			0.806953
$794$	−1.80574e6	+	3.12764e6i	−0.101649	+	0.176062i
$795$	1.27420e6	−	1.31278e7i	0.0715025	−	0.736674i
$796$	5.36444e6	+	9.29148e6i	0.300083	+	0.519759i
$797$	−1.62806e7	−	2.81989e7i	−0.907874	−	1.57248i	−0.817013	−	0.576620i	$-0.804371\pi$
$797$	−1.62806e7	−	2.81989e7i	−0.907874	−	1.57248i	−0.0908608	−	0.995864i	$-0.528962\pi$
$798$	−3.10677e6	+	3.20083e7i	−0.172704	+	1.77933i
$799$	−228095.	+	395073.i	−0.0126401	+	0.0218932i
$800$	7.02890e6			0.388295
$801$	−1.03896e6	−	3.03242e6i	−0.0572159	−	0.166997i
$802$	4.50977e7			2.47582
$803$	−1.35174e6	+	2.34128e6i	−0.0739782	+	0.128134i
$804$	−4.22399e7	+	1.92108e7i	−2.30453	+	1.04811i
$805$	−4.98616e6	−	8.63627e6i	−0.271192	−	0.469717i
$806$	−6.12878e6	−	1.06154e7i	−0.332305	−	0.575569i
$807$	2.37353e7	+	1.69576e7i	1.28295	+	0.916604i
$808$	−261.916	+	453.653i	−1.41135e−5	+	2.44453e-5i
$809$	−1.54392e7			−0.829381			−0.414691	−	0.909963i	$-0.636110\pi$
$809$	−1.54392e7			−0.829381			−0.414691	+	0.909963i	$0.636110\pi$
$810$	−1.37775e7	+	1.06964e7i	−0.737831	+	0.572829i
$811$	−2.26720e6			−0.121043			−0.0605213	−	0.998167i	$-0.519276\pi$
$811$	−2.26720e6			−0.121043			−0.0605213	+	0.998167i	$0.519276\pi$
$812$	1.90532e6	−	3.30011e6i	0.101409	−	0.175646i
$813$	1.21521e7	+	8.68205e6i	0.644801	+	0.460677i
$814$	−6.61912e6	−	1.14647e7i	−0.350138	−	0.606457i
$815$	6.22169e6	+	1.07763e7i	0.328106	+	0.568297i
$816$	608425.	−	276713.i	0.0319876	−	0.0145480i
$817$	1.08812e7	−	1.88468e7i	0.570323	−	0.987829i
$818$	−2.09832e6			−0.109645
$819$	−2.74965e6	−	8.02545e6i	−0.143241	−	0.418080i
$820$	484479.			0.0251617
$821$	−16005.1	+	27721.6i	−0.000828706	+	0.00143536i	−0.866439	−	0.499282i	$-0.833597\pi$
$821$	−16005.1	+	27721.6i	−0.000828706	+	0.00143536i	0.865611	+	0.500718i	$0.166930\pi$
$822$	3.22269e6	−	3.32026e7i	0.166356	−	1.71393i
$823$	−9.75278e6	−	1.68923e7i	−0.501913	−	0.869339i	−0.999998	−	0.00221067i	$-0.999296\pi$
$823$	−9.75278e6	−	1.68923e7i	−0.501913	−	0.869339i	0.498084	−	0.867129i	$-0.334037\pi$
$824$	−1.41202e7	−	2.44569e7i	−0.724473	−	1.25482i
$825$	−392955.	+	4.04852e6i	−0.0201005	+	0.207091i
$826$	−1.63514e7	+	2.83215e7i	−0.833883	+	1.44433i
$827$	−2.10239e7			−1.06893			−0.534464	−	0.845191i	$-0.679487\pi$
$827$	−2.10239e7			−1.06893			−0.534464	+	0.845191i	$0.679487\pi$
$828$	3.79524e7	+	7.43749e6i	1.92382	+	0.377008i
$829$	−1.28560e7			−0.649711			−0.324855	−	0.945764i	$-0.605316\pi$
$829$	−1.28560e7			−0.649711			−0.324855	+	0.945764i	$0.605316\pi$
$830$	−8.91991e6	+	1.54497e7i	−0.449433	+	0.778441i
$831$	−1.08227e7	+	4.92217e6i	−0.543665	+	0.247260i
$832$	6.96447e6	+	1.20628e7i	0.348803	+	0.604144i
$833$	136507.	+	236438.i	0.00681622	+	0.0118060i
$834$	2.22902e7	+	1.59252e7i	1.10968	+	0.792812i
$835$	−7.76409e6	+	1.34478e7i	−0.385367	+	0.667475i
$836$	1.30624e7			0.646410
$837$	−1.59440e7	+	3.78912e6i	−0.786651	+	0.186950i
$838$	6.48732e7			3.19121
$839$	4.73751e6	−	8.20561e6i	0.232351	−	0.402445i	−0.726148	−	0.687538i	$-0.758691\pi$
$839$	4.73751e6	−	8.20561e6i	0.232351	−	0.402445i	0.958500	+	0.285094i	$0.0920247\pi$
$840$	1.14313e7	+	8.16709e6i	0.558983	+	0.399364i
$841$	1.00983e7	+	1.74907e7i	0.492330	+	0.852741i
$842$	−1.34509e7	−	2.32977e7i	−0.653840	−	1.13248i
$843$	5.42365e6	−	2.46669e6i	0.262859	−	0.119549i
$844$	−3.67836e6	+	6.37111e6i	−0.177745	+	0.307864i
$845$	−8.78199e6			−0.423108
$846$	7.92523e6	−	9.08881e6i	0.380703	−	0.436597i
$847$	−1.71231e6			−0.0820113
$848$	6.68019e6	−	1.15704e7i	0.319006	−	0.552535i
$849$	−2.28915e6	+	2.35846e7i	−0.108994	+	1.12295i
$850$	892955.	+	1.54664e6i	0.0423918	+	0.0734248i
$851$	−1.57910e7	−	2.73508e7i	−0.747457	−	1.29463i
$852$	−2.74064e6	+	2.82362e7i	−0.129346	+	1.33262i
$853$	−9.99292e6	+	1.73082e7i	−0.470240	+	0.814480i	−0.999421	−	0.0340294i	$-0.989166\pi$
$853$	−9.99292e6	+	1.73082e7i	−0.470240	+	0.814480i	0.529181	+	0.848509i	$0.322499\pi$
$854$	−5.31402e7			−2.49332
$855$	−9.23674e6	+	1.05929e7i	−0.432119	+	0.495563i
$856$	−3.94368e7			−1.83957
$857$	8.84095e6	−	1.53130e7i	0.411194	−	0.712209i	−0.583826	−	0.811879i	$-0.698445\pi$
$857$	8.84095e6	−	1.53130e7i	0.411194	−	0.712209i	0.995021	+	0.0996692i	$0.0317785\pi$
$858$	−4.86463e6	+	2.21245e6i	−0.225596	+	0.102602i
$859$	−5.68007e6	−	9.83817e6i	−0.262646	−	0.454916i	0.704298	−	0.709904i	$-0.251262\pi$
$859$	−5.68007e6	−	9.83817e6i	−0.262646	−	0.454916i	−0.966944	+	0.254988i	$0.917928\pi$
$860$	−1.05845e7	−	1.83328e7i	−0.488003	−	0.845246i
$861$	397553.	+	284031.i	0.0182763	+	0.0130574i
$862$	−1.78894e7	+	3.09853e7i	−0.820025	+	1.42032i
$863$	1.40682e6			0.0643002			0.0321501	−	0.999483i	$-0.489765\pi$
$863$	1.40682e6			0.0643002			0.0321501	+	0.999483i	$0.489765\pi$
$864$	1.20122e7	−	2.85473e6i	0.547441	−	0.130101i
$865$	1.05900e7			0.481235
$866$	−1.76675e7	+	3.06011e7i	−0.800537	+	1.38657i
$867$	1.79127e7	+	1.27977e7i	0.809308	+	0.578209i
$868$	1.46956e7	+	2.54535e7i	0.662044	+	1.14669i
$869$	−1.16611e6	−	2.01977e6i	−0.0523832	−	0.0907303i
$870$	2.35107e6	−	1.06927e6i	0.105310	−	0.0478950i
$871$	7.64858e6	−	1.32477e7i	0.341614	−	0.591692i
$872$	4.50937e7			2.00828
$873$	3.05913e7	+	5.99494e6i	1.35851	+	0.266225i
$874$	4.83296e7			2.14010
$875$	−9.61152e6	+	1.66476e7i	−0.424397	+	0.735077i
$876$	1.95451e6	−	2.01369e7i	0.0860553	−	0.886608i
$877$	−8.63790e6	−	1.49613e7i	−0.379236	−	0.656856i	0.611715	−	0.791078i	$-0.290480\pi$
$877$	−8.63790e6	−	1.49613e7i	−0.379236	−	0.656856i	−0.990951	+	0.134222i	$0.957146\pi$
$878$	9.20103e6	+	1.59367e7i	0.402810	+	0.697687i
$879$	−1.53721e6	+	1.58375e7i	−0.0671059	+	0.691377i
$880$	925250.	−	1.60258e6i	0.0402766	−	0.0697611i
$881$	4.17144e7			1.81070			0.905349	−	0.424669i	$-0.139609\pi$
$881$	4.17144e7			1.81070			0.905349	+	0.424669i	$0.139609\pi$
$882$	−2.33912e6	−	6.82721e6i	−0.101247	−	0.295510i
$883$	−1.85206e7			−0.799378			−0.399689	−	0.916651i	$-0.630882\pi$
$883$	−1.85206e7			−0.799378			−0.399689	+	0.916651i	$0.630882\pi$
$884$	−756471.	+	1.31025e6i	−0.0325583	+	0.0563926i
$885$	−1.30099e7	+	5.91692e6i	−0.558361	+	0.253944i
$886$	1.35786e7	+	2.35189e7i	0.581128	+	1.00654i
$887$	3.92294e6	+	6.79473e6i	0.167418	+	0.289977i	0.937511	−	0.347955i	$-0.113124\pi$
$887$	3.92294e6	+	6.79473e6i	0.167418	+	0.289977i	−0.770093	+	0.637931i	$0.779790\pi$
$888$	3.62027e7	+	2.58649e7i	1.54067	+	1.10073i
$889$	3.21690e6	−	5.57183e6i	0.136516	−	0.236452i
$890$	−3.89650e6			−0.164892
$891$	972725.	+	7.07840e6i	0.0410484	+	0.298704i
$892$	6.94401e7			2.92212
$893$	4.85832e6	−	8.41486e6i	0.203872	−	0.353117i
$894$	3.95725e7	+	2.82725e7i	1.65596	+	1.18310i
$895$	−1.75882e6	−	3.04637e6i	−0.0733946	−	0.127123i
$896$	−1.97996e7	−	3.42939e7i	−0.823923	−	1.42708i
$897$	−1.16054e7	+	5.27816e6i	−0.481591	+	0.219029i
$898$	−2.49220e7	+	4.31662e7i	−1.03132	+	1.78630i
$899$	2.42670e6			0.100142
$900$	−9.86610e6	−	2.87963e7i	−0.406012	−	1.18503i
$901$	−2.37220e6			−0.0973508
$902$	153894.	−	266552.i	0.00629803	−	0.0109085i
$903$	2.06243e6	−	2.12488e7i	0.0841706	−	0.867190i
$904$	1.87674e7	+	3.25060e7i	0.763804	+	1.32295i
$905$	−8.58531e6	−	1.48702e7i	−0.348445	−	0.603525i
$906$	−5.51312e6	+	5.68004e7i	−0.223140	+	2.29896i
$907$	737386.	−	1.27719e6i	0.0297630	−	0.0515510i	−0.850760	−	0.525554i	$-0.823858\pi$
$907$	737386.	−	1.27719e6i	0.0297630	−	0.0515510i	0.880523	+	0.474003i	$0.157191\pi$
$908$	5.26330e7			2.11857
$909$	−504.473	−	98.8610i	−2.02502e−5	−	3.96840e-6i
$910$	−1.03123e7			−0.412810
$911$	−4.55928e6	+	7.89690e6i	−0.182012	+	0.315254i	−0.942566	−	0.334021i	$-0.891594\pi$
$911$	−4.55928e6	+	7.89690e6i	−0.182012	+	0.315254i	0.760554	+	0.649275i	$0.224928\pi$
$912$	−1.29591e7	+	5.89385e6i	−0.515928	+	0.234646i
$913$	3.65390e6	+	6.32874e6i	0.145071	+	0.251270i
$914$	−3.68845e7	−	6.38859e7i	−1.46042	−	2.52953i
$915$	−1.88967e7	−	1.35007e7i	−0.746162	−	0.533094i
$916$	4.04341e7	−	7.00339e7i	1.59224	−	2.75784i
$917$	2.16553e7			0.850436
$918$	2.15419e6	+	2.28050e6i	0.0843679	+	0.0893149i
$919$	−1.76427e7			−0.689091			−0.344546	−	0.938770i	$-0.611967\pi$
$919$	−1.76427e7			−0.689091			−0.344546	+	0.938770i	$0.611967\pi$
$920$	1.05568e7	−	1.82849e7i	0.411209	−	0.712235i
$921$	−2.27833e7	−	1.62775e7i	−0.885048	−	0.632321i
$922$	1.67805e7	+	2.90647e7i	0.650097	+	1.12600i
$923$	−4.67600e6	−	8.09907e6i	−0.180664	−	0.312918i
$924$	1.16644e7	−	5.30499e6i	0.449451	−	0.204411i
$925$	−1.24287e7	+	2.15271e7i	−0.477608	+	0.827241i
$926$	−1.63838e7			−0.627894
$927$	1.82140e7	−	2.08882e7i	0.696154	−	0.798364i
$928$	−1.82828e6			−0.0696903
$929$	−1.05878e7	+	1.83386e7i	−0.402499	+	0.697150i	−0.994027	−	0.109135i	$-0.965192\pi$
$929$	−1.05878e7	+	1.83386e7i	−0.402499	+	0.697150i	0.591527	+	0.806285i	$0.298525\pi$
$930$	−1.92451e6	+	1.98277e7i	−0.0729645	+	0.751737i
$931$	−2.90754e6	−	5.03601e6i	−0.109939	−	0.190420i
$932$	3.54117e7	+	6.13348e7i	1.33539	+	2.31296i
$933$	−2.44725e6	+	2.52135e7i	−0.0920396	+	0.948263i
$934$	7.35801e6	−	1.27445e7i	0.275990	−	0.478029i
$935$	−328566.			−0.0122912
$936$	1.18044e7	−	1.35375e7i	0.440406	−	0.505067i
$937$	−3.58889e7			−1.33540			−0.667700	−	0.744430i	$-0.732721\pi$
$937$	−3.58889e7			−1.33540			−0.667700	+	0.744430i	$0.732721\pi$
$938$	−2.84428e7	+	4.92644e7i	−1.05552	+	1.82821i
$939$	−1.87722e7	+	8.53767e6i	−0.694788	+	0.315991i
$940$	−4.72584e6	−	8.18539e6i	−0.174445	−	0.302148i
$941$	2.70130e6	+	4.67879e6i	0.0994487	+	0.172250i	0.911457	−	0.411396i	$-0.134959\pi$
$941$	2.70130e6	+	4.67879e6i	0.0994487	+	0.172250i	−0.812008	+	0.583646i	$0.801625\pi$
$942$	−5.00904e7	−	3.57870e7i	−1.83919	−	1.31401i
$943$	367139.	−	635904.i	0.0134447	−	0.0232869i
$944$	−1.44773e7			−0.528760
$945$	−3.94611e6	+	1.32104e7i	−0.143744	+	0.481213i
$946$	−1.34485e7			−0.488593
$947$	1.91462e7	−	3.31622e7i	0.693757	−	1.20162i	−0.276841	−	0.960916i	$-0.589288\pi$
$947$	1.91462e7	−	3.31622e7i	0.693757	−	1.20162i	0.970598	−	0.240706i	$-0.0773791\pi$
$948$	1.42012e7	+	1.01460e7i	0.513222	+	0.366670i
$949$	3.33473e6	+	5.77592e6i	0.120197	+	0.208188i
$950$	−1.90195e7	−	3.29427e7i	−0.683739	−	1.18427i
$951$	−825226.	+	375315.i	−0.0295884	+	0.0134569i
$952$	1.26340e6	−	2.18827e6i	0.0451802	−	0.0782544i
$953$	−2.85647e7			−1.01882			−0.509410	−	0.860524i	$-0.670136\pi$
$953$	−2.85647e7			−1.01882			−0.509410	+	0.860524i	$0.670136\pi$
$954$	6.15357e7	+	1.20591e7i	2.18905	+	0.428986i
$955$	1.25934e7			0.446821
$956$	3.99512e7	−	6.91975e7i	1.41379	−	2.44876i
$957$	102211.	−	1.05306e6i	0.00360759	−	0.0371682i
$958$	−4.43318e7	−	7.67849e7i	−1.56064	−	2.70310i
$959$	−1.31842e7	−	2.28357e7i	−0.462921	−	0.801802i
$960$	2.18692e6	−	2.25314e7i	0.0765870	−	0.789059i
$961$	4.95613e6	−	8.58426e6i	0.173115	−	0.299843i
$962$	−3.26587e7			−1.13779
$963$	−1.25440e7	−	3.66124e7i	−0.435885	−	1.27222i
$964$	−9.04704e7			−3.13555
$965$	−1.19882e7	+	2.07642e7i	−0.414417	+	0.717791i
$966$	4.31570e7	−	1.96279e7i	1.48802	−	0.676755i
$967$	−4.27802e6	−	7.40974e6i	−0.147122	−	0.254822i	0.783041	−	0.621970i	$-0.213668\pi$
$967$	−4.27802e6	−	7.40974e6i	−0.147122	−	0.254822i	−0.930162	+	0.367148i	$0.880334\pi$
$968$	−1.81267e6	−	3.13963e6i	−0.0621770	−	0.107694i
$969$	2.05676e6	+	1.46945e6i	0.0703679	+	0.0502742i
$970$	1.89467e7	−	3.28167e7i	0.646555	−	1.11987i
$971$	1.38864e7			0.472654			0.236327	−	0.971674i	$-0.424056\pi$
$971$	1.38864e7			0.472654			0.236327	+	0.971674i	$0.424056\pi$
$972$	−2.85563e7	−	4.52050e7i	−0.969473	−	1.53469i
$973$	2.16541e7			0.733260
$974$	−2.35178e7	+	4.07340e7i	−0.794326	+	1.37581i
$975$	8.16487e6	+	5.83338e6i	0.275067	+	0.196521i
$976$	−1.17624e7	−	2.03731e7i	−0.395250	−	0.684593i
$977$	2.14141e7	+	3.70902e7i	0.717733	+	1.24315i	0.961896	+	0.273415i	$0.0881533\pi$
$977$	2.14141e7	+	3.70902e7i	0.717733	+	1.24315i	−0.244164	+	0.969734i	$0.578513\pi$
$978$	−5.38511e7	+	2.44916e7i	−1.80031	+	0.818785i
$979$	−798069.	+	1.38230e6i	−0.0266124	+	0.0460940i
$980$	−5.65651e6			−0.188141
$981$	1.43434e7	+	4.18642e7i	0.475860	+	1.38890i
$982$	−3.16269e7			−1.04659
$983$	5.41898e6	−	9.38595e6i	0.178868	−	0.309809i	−0.762625	−	0.646841i	$-0.776090\pi$
$983$	5.41898e6	−	9.38595e6i	0.178868	−	0.309809i	0.941493	+	0.337032i	$0.109423\pi$
$984$	−99936.1	+	1.02962e6i	−0.00329029	+	0.0338991i
$985$	774639.	+	1.34171e6i	0.0254395	+	0.0440625i
$986$	−232265.	−	402295.i	−0.00760837	−	0.0131781i
$987$	920851.	−	9.48732e6i	0.0300882	−	0.309992i
$988$	1.61125e7	−	2.79076e7i	0.525133	−	0.909557i
$989$	−3.20837e7			−1.04302
$990$	8.52311e6	+	1.67026e6i	0.276382	+	0.0541622i
$991$	3.64184e7			1.17798			0.588989	−	0.808141i	$-0.299526\pi$
$991$	3.64184e7			1.17798			0.588989	+	0.808141i	$0.299526\pi$
$992$	7.05066e6	−	1.22121e7i	0.227484	−	0.394014i
$993$	−8.97865e6	+	4.08351e6i	−0.288960	+	0.131420i
$994$	1.73887e7	+	3.01181e7i	0.558214	+	0.966855i
$995$	2.87404e6	+	4.97797e6i	0.0920310	+	0.159402i
$996$	−4.44980e7	−	3.17915e7i	−1.42132	−	1.01546i
$997$	5.54985e6	−	9.61262e6i	0.176825	−	0.306270i	−0.763966	−	0.645256i	$-0.776751\pi$
$997$	5.54985e6	−	9.61262e6i	0.176825	−	0.306270i	0.940791	+	0.338986i	$0.110084\pi$
$998$	−1.63156e7			−0.518534
$999$	−1.24972e7	+	4.18371e7i	−0.396186	+	1.32632i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.6.e.a.34.3	✓	46
3.2	odd	2		297.6.e.a.100.21		46
9.2	odd	6		891.6.a.e.1.3		23
9.4	even	3	inner	99.6.e.a.67.3	yes	46
9.5	odd	6		297.6.e.a.199.21		46
9.7	even	3		891.6.a.f.1.21		23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.6.e.a.34.3	✓	46	1.1	even	1	trivial
99.6.e.a.67.3	yes	46	9.4	even	3	inner
297.6.e.a.100.21		46	3.2	odd	2
297.6.e.a.199.21		46	9.5	odd	6
891.6.a.e.1.3		23	9.2	odd	6
891.6.a.f.1.21		23	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	99.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.74574 + 8.21986i) q^{2} +(-12.6839 - 9.06197i) q^{3} +(-29.0441 - 50.3058i) q^{4} +(-15.5606 - 26.9517i) q^{5} +(134.683 - 61.2540i) q^{6} +(58.4765 - 101.284i) q^{7} +247.615 q^{8} +(78.7614 + 229.882i) q^{9} +O(q^{10})\)	\(q+(-4.74574 + 8.21986i) q^{2} +(-12.6839 - 9.06197i) q^{3} +(-29.0441 - 50.3058i) q^{4} +(-15.5606 - 26.9517i) q^{5} +(134.683 - 61.2540i) q^{6} +(58.4765 - 101.284i) q^{7} +247.615 q^{8} +(78.7614 + 229.882i) q^{9} +295.386 q^{10} +(60.5000 - 104.789i) q^{11} +(-87.4784 + 901.270i) q^{12} +(-149.253 - 258.514i) q^{13} +(555.028 + 961.338i) q^{14} +(-46.8671 + 482.861i) q^{15} +(-245.707 + 425.578i) q^{16} +87.2532 q^{17} +(-2263.38 - 443.551i) q^{18} -1858.45 q^{19} +(-903.885 + 1565.58i) q^{20} +(-1659.54 + 754.765i) q^{21} +(574.234 + 994.603i) q^{22} +(1369.93 + 2372.79i) q^{23} +(-3140.72 - 2243.88i) q^{24} +(1078.24 - 1867.56i) q^{25} +2833.26 q^{26} +(1084.18 - 3629.53i) q^{27} -6793.59 q^{28} +(-280.459 + 485.769i) q^{29} +(-3746.64 - 2676.78i) q^{30} +(-2163.15 - 3746.69i) q^{31} +(1629.72 + 2822.76i) q^{32} +(-1716.97 + 780.882i) q^{33} +(-414.081 + 717.209i) q^{34} -3639.71 q^{35} +(9276.84 - 10638.9i) q^{36} -11526.9 q^{37} +(8819.72 - 15276.2i) q^{38} +(-449.538 + 4631.48i) q^{39} +(-3853.04 - 6673.66i) q^{40} +(-133.999 - 232.093i) q^{41} +(1671.70 - 17223.1i) q^{42} +(-5854.98 + 10141.1i) q^{43} -7028.67 q^{44} +(4970.13 - 5699.85i) q^{45} -26005.4 q^{46} +(-2614.18 + 4527.89i) q^{47} +(6973.09 - 3171.38i) q^{48} +(1564.50 + 2709.79i) q^{49} +(10234.1 + 17725.9i) q^{50} +(-1106.71 - 790.686i) q^{51} +(-8669.84 + 15016.6i) q^{52} -27187.6 q^{53} +(24689.0 + 26136.6i) q^{54} -3765.66 q^{55} +(14479.7 - 25079.5i) q^{56} +(23572.3 + 16841.2i) q^{57} +(-2661.97 - 4610.66i) q^{58} +(14730.3 + 25513.5i) q^{59} +(25652.0 - 11666.6i) q^{60} +(-23935.8 + 41458.0i) q^{61} +41063.0 q^{62} +(27889.1 + 5465.39i) q^{63} -46662.2 q^{64} +(-4644.93 + 8045.25i) q^{65} +(1729.55 - 17819.1i) q^{66} +(25622.9 + 44380.1i) q^{67} +(-2534.19 - 4389.34i) q^{68} +(4126.12 - 42510.5i) q^{69} +(17273.1 - 29917.9i) q^{70} +31329.4 q^{71} +(19502.5 + 56922.3i) q^{72} -22342.8 q^{73} +(54703.5 - 94749.3i) q^{74} +(-30600.0 + 13917.0i) q^{75} +(53977.0 + 93490.9i) q^{76} +(-7075.66 - 12255.4i) q^{77} +(-35936.8 - 25675.0i) q^{78} +(9637.31 - 16692.3i) q^{79} +15293.4 q^{80} +(-46642.3 + 36211.6i) q^{81} +2543.70 q^{82} +(-30197.5 + 52303.6i) q^{83} +(86169.0 + 61563.3i) q^{84} +(-1357.71 - 2351.62i) q^{85} +(-55572.4 - 96254.3i) q^{86} +(7959.33 - 3619.92i) q^{87} +(14980.7 - 25947.4i) q^{88} -13191.2 q^{89} +(23265.0 + 67903.8i) q^{90} -34911.2 q^{91} +(79576.8 - 137831. i) q^{92} +(-6515.23 + 67124.9i) q^{93} +(-24812.4 - 42976.4i) q^{94} +(28918.5 + 50088.4i) q^{95} +(4908.58 - 50572.0i) q^{96} +(64142.4 - 111098. i) q^{97} -29698.8 q^{98} +(28854.2 + 5654.51i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 15 q^{3} - 320 q^{4} - 36 q^{5} + 273 q^{6} + 167 q^{7} + 426 q^{8} - 63 q^{9}+O(q^{10}) \) 46 * q + 15 * q^3 - 320 * q^4 - 36 * q^5 + 273 * q^6 + 167 * q^7 + 426 * q^8 - 63 * q^9	\( 46 q + 15 q^{3} - 320 q^{4} - 36 q^{5} + 273 q^{6} + 167 q^{7} + 426 q^{8} - 63 q^{9} - 1200 q^{10} + 2783 q^{11} - 1419 q^{12} + 1871 q^{13} - 1329 q^{14} + 3090 q^{15} - 3584 q^{16} + 534 q^{17} + 5391 q^{18} - 7282 q^{19} - 1917 q^{20} - 8319 q^{21} - 8292 q^{23} + 351 q^{24} - 10049 q^{25} + 19140 q^{26} + 19953 q^{27} + 7586 q^{28} - 5970 q^{29} - 15150 q^{30} + 9542 q^{31} - 3831 q^{32} + 3630 q^{33} + 2982 q^{34} + 6480 q^{35} + 28881 q^{36} - 32014 q^{37} + 1221 q^{38} - 17544 q^{39} + 40635 q^{40} + 12030 q^{41} - 55365 q^{42} + 25943 q^{43} - 77440 q^{44} + 70578 q^{45} - 154008 q^{46} + 9756 q^{47} - 65463 q^{48} - 6990 q^{49} + 101805 q^{50} - 42117 q^{51} + 144446 q^{52} + 107838 q^{53} - 2322 q^{54} - 8712 q^{55} - 16602 q^{56} - 100233 q^{57} + 95367 q^{58} - 20310 q^{59} - 215301 q^{60} + 100247 q^{61} - 30594 q^{62} + 28323 q^{63} - 169154 q^{64} + 20931 q^{65} + 26862 q^{66} + 84956 q^{67} + 168471 q^{68} - 30243 q^{69} + 212292 q^{70} + 72186 q^{71} + 144522 q^{72} - 346888 q^{73} + 86619 q^{74} + 103413 q^{75} + 340334 q^{76} - 20207 q^{77} - 386061 q^{78} + 123113 q^{79} - 30246 q^{80} - 73683 q^{81} - 399966 q^{82} + 30672 q^{83} - 38850 q^{84} + 268335 q^{85} - 211260 q^{86} + 180009 q^{87} + 25773 q^{88} + 65028 q^{89} + 460017 q^{90} - 656042 q^{91} - 196731 q^{92} + 232206 q^{93} + 230262 q^{94} - 325926 q^{95} - 517071 q^{96} + 357002 q^{97} - 428928 q^{98} + 7623 q^{99}+O(q^{100}) \) 46 * q + 15 * q^3 - 320 * q^4 - 36 * q^5 + 273 * q^6 + 167 * q^7 + 426 * q^8 - 63 * q^9 - 1200 * q^10 + 2783 * q^11 - 1419 * q^12 + 1871 * q^13 - 1329 * q^14 + 3090 * q^15 - 3584 * q^16 + 534 * q^17 + 5391 * q^18 - 7282 * q^19 - 1917 * q^20 - 8319 * q^21 - 8292 * q^23 + 351 * q^24 - 10049 * q^25 + 19140 * q^26 + 19953 * q^27 + 7586 * q^28 - 5970 * q^29 - 15150 * q^30 + 9542 * q^31 - 3831 * q^32 + 3630 * q^33 + 2982 * q^34 + 6480 * q^35 + 28881 * q^36 - 32014 * q^37 + 1221 * q^38 - 17544 * q^39 + 40635 * q^40 + 12030 * q^41 - 55365 * q^42 + 25943 * q^43 - 77440 * q^44 + 70578 * q^45 - 154008 * q^46 + 9756 * q^47 - 65463 * q^48 - 6990 * q^49 + 101805 * q^50 - 42117 * q^51 + 144446 * q^52 + 107838 * q^53 - 2322 * q^54 - 8712 * q^55 - 16602 * q^56 - 100233 * q^57 + 95367 * q^58 - 20310 * q^59 - 215301 * q^60 + 100247 * q^61 - 30594 * q^62 + 28323 * q^63 - 169154 * q^64 + 20931 * q^65 + 26862 * q^66 + 84956 * q^67 + 168471 * q^68 - 30243 * q^69 + 212292 * q^70 + 72186 * q^71 + 144522 * q^72 - 346888 * q^73 + 86619 * q^74 + 103413 * q^75 + 340334 * q^76 - 20207 * q^77 - 386061 * q^78 + 123113 * q^79 - 30246 * q^80 - 73683 * q^81 - 399966 * q^82 + 30672 * q^83 - 38850 * q^84 + 268335 * q^85 - 211260 * q^86 + 180009 * q^87 + 25773 * q^88 + 65028 * q^89 + 460017 * q^90 - 656042 * q^91 - 196731 * q^92 + 232206 * q^93 + 230262 * q^94 - 325926 * q^95 - 517071 * q^96 + 357002 * q^97 - 428928 * q^98 + 7623 * q^99

Introduction

L-functions

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