LMFDB - Embedded newform 38.7.d.a.27.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,7,Mod(27,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("38.27");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	38.d (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.74205517755$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 9440 x^{18} + 37579488 x^{16} + 83109028728 x^{14} + 112838424559344 x^{12} + \cdots + 83\!\cdots\!96 $ x^20 + 9440x^18 + 37579488x^16 + 83109028728x^14 + 112838424559344x^12 + 97808951849137728x^10 + 54352282696688610576x^8 + 18825433555812367062720x^6 + 3765133606401310416173376x^4 + 360077534420960567854418432*x^2 + 8303121574870947536327197696
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{4}\cdot 19^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			27.10
Root			$-34.8817i$ of defining polynomial
Character	$\chi$	$=$	38.27
Dual form			38.7.d.a.31.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.89898 + 2.82843i) q^{2} +(29.9332 + 17.2819i) q^{3} +(16.0000 + 27.7128i) q^{4} +(48.9935 - 84.8592i) q^{5} +(97.7614 + 169.328i) q^{6} +374.355 q^{7} +181.019i q^{8} +(232.830 + 403.274i) q^{9} +O(q^{10})$	\(q+(4.89898 + 2.82843i) q^{2} +(29.9332 + 17.2819i) q^{3} +(16.0000 + 27.7128i) q^{4} +(48.9935 - 84.8592i) q^{5} +(97.7614 + 169.328i) q^{6} +374.355 q^{7} +181.019i q^{8} +(232.830 + 403.274i) q^{9} +(480.036 - 277.149i) q^{10} -766.306 q^{11} +1106.04i q^{12} +(-1999.79 + 1154.58i) q^{13} +(1833.96 + 1058.84i) q^{14} +(2933.06 - 1693.40i) q^{15} +(-512.000 + 886.810i) q^{16} +(1079.00 - 1868.89i) q^{17} +2634.17i q^{18} +(1562.66 + 6678.62i) q^{19} +3135.58 q^{20} +(11205.6 + 6469.58i) q^{21} +(-3754.12 - 2167.44i) q^{22} +(-7673.77 - 13291.4i) q^{23} +(-3128.36 + 5418.49i) q^{24} +(3011.78 + 5216.55i) q^{25} -13062.5 q^{26} -9102.02i q^{27} +(5989.69 + 10374.4i) q^{28} +(-16518.2 + 9536.79i) q^{29} +19158.7 q^{30} -49927.0i q^{31} +(-5016.55 + 2896.31i) q^{32} +(-22938.0 - 13243.2i) q^{33} +(10572.0 - 6103.77i) q^{34} +(18341.0 - 31767.5i) q^{35} +(-7450.57 + 12904.8i) q^{36} -32593.3i q^{37} +(-11234.5 + 37138.3i) q^{38} -79813.3 q^{39} +(15361.2 + 8868.77i) q^{40} +(-35814.8 - 20677.7i) q^{41} +(36597.5 + 63388.7i) q^{42} +(-11303.5 + 19578.3i) q^{43} +(-12260.9 - 21236.5i) q^{44} +45628.7 q^{45} -86818.8i q^{46} +(-14673.2 - 25414.6i) q^{47} +(-30651.6 + 17696.7i) q^{48} +22492.9 q^{49} +34074.4i q^{50} +(64596.0 - 37294.5i) q^{51} +(-63993.1 - 36946.4i) q^{52} +(43683.2 - 25220.5i) q^{53} +(25744.4 - 44590.6i) q^{54} +(-37544.0 + 65028.1i) q^{55} +67765.6i q^{56} +(-68644.1 + 226918. i) q^{57} -107896. q^{58} +(268633. + 155096. i) q^{59} +(93858.0 + 54188.9i) q^{60} +(150729. + 261070. i) q^{61} +(141215. - 244591. i) q^{62} +(87161.3 + 150968. i) q^{63} -32768.0 q^{64} +226267. i q^{65} +(-74915.1 - 129757. i) q^{66} +(-13.3422 + 7.70312i) q^{67} +69056.2 q^{68} -530470. i q^{69} +(179704. - 103752. i) q^{70} +(315273. + 182023. i) q^{71} +(-73000.4 + 42146.8i) q^{72} +(-61079.9 + 105794. i) q^{73} +(92187.8 - 159674. i) q^{74} +208197. i q^{75} +(-160081. + 150164. i) q^{76} -286871. q^{77} +(-391003. - 225746. i) q^{78} +(-644021. - 371826. i) q^{79} +(50169.3 + 86895.8i) q^{80} +(327034. - 566439. i) q^{81} +(-116970. - 202599. i) q^{82} -1.00943e6 q^{83} +414053. i q^{84} +(-105728. - 183127. i) q^{85} +(-110752. + 63942.5i) q^{86} -659257. q^{87} -138716. i q^{88} +(166910. - 96365.5i) q^{89} +(223534. + 129057. i) q^{90} +(-748630. + 432222. i) q^{91} +(245561. - 425323. i) q^{92} +(862835. - 1.49447e6i) q^{93} -166008. i q^{94} +(643303. + 194603. i) q^{95} -200215. q^{96} +(1.37799e6 + 795583. i) q^{97} +(110192. + 63619.6i) q^{98} +(-178419. - 309031. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 30 q^{3} + 320 q^{4} + 112 q^{5} + 80 q^{6} - 208 q^{7} + 2200 q^{9}+O(q^{10}) $ 20 * q - 30 * q^3 + 320 * q^4 + 112 * q^5 + 80 * q^6 - 208 * q^7 + 2200 * q^9	\( 20 q - 30 q^{3} + 320 q^{4} + 112 q^{5} + 80 q^{6} - 208 q^{7} + 2200 q^{9} - 284 q^{11} + 10500 q^{13} + 1248 q^{14} + 14136 q^{15} - 10240 q^{16} - 11684 q^{17} + 12862 q^{19} + 7168 q^{20} + 2916 q^{21} + 52704 q^{22} + 8488 q^{23} - 2560 q^{24} - 63842 q^{25} - 43968 q^{26} - 3328 q^{28} + 137760 q^{29} - 94688 q^{30} - 250194 q^{33} + 70560 q^{34} - 6916 q^{35} - 70400 q^{36} - 77232 q^{38} + 9672 q^{39} + 109206 q^{41} - 92672 q^{42} + 35572 q^{43} - 4544 q^{44} + 131264 q^{45} - 361184 q^{47} + 30720 q^{48} + 259740 q^{49} - 496512 q^{51} + 336000 q^{52} - 236172 q^{53} + 375728 q^{54} + 56760 q^{55} + 314796 q^{57} - 225600 q^{58} + 1310610 q^{59} + 452352 q^{60} + 83552 q^{61} + 225792 q^{62} + 553364 q^{63} - 655360 q^{64} - 4736 q^{66} + 806646 q^{67} - 747776 q^{68} - 245664 q^{70} - 869220 q^{71} + 353280 q^{72} - 207422 q^{73} + 1460832 q^{74} - 140096 q^{76} - 3988336 q^{77} - 85008 q^{78} - 1706808 q^{79} + 114688 q^{80} + 2303170 q^{81} + 887712 q^{82} + 3527548 q^{83} - 5604 q^{85} + 195792 q^{86} - 8414832 q^{87} + 708432 q^{89} - 4483104 q^{90} - 1914384 q^{91} - 271616 q^{92} + 3537876 q^{93} - 2820356 q^{95} - 163840 q^{96} + 5113242 q^{97} - 612480 q^{98} + 603704 q^{99}+O(q^{100}) \) 20 * q - 30 * q^3 + 320 * q^4 + 112 * q^5 + 80 * q^6 - 208 * q^7 + 2200 * q^9 - 284 * q^11 + 10500 * q^13 + 1248 * q^14 + 14136 * q^15 - 10240 * q^16 - 11684 * q^17 + 12862 * q^19 + 7168 * q^20 + 2916 * q^21 + 52704 * q^22 + 8488 * q^23 - 2560 * q^24 - 63842 * q^25 - 43968 * q^26 - 3328 * q^28 + 137760 * q^29 - 94688 * q^30 - 250194 * q^33 + 70560 * q^34 - 6916 * q^35 - 70400 * q^36 - 77232 * q^38 + 9672 * q^39 + 109206 * q^41 - 92672 * q^42 + 35572 * q^43 - 4544 * q^44 + 131264 * q^45 - 361184 * q^47 + 30720 * q^48 + 259740 * q^49 - 496512 * q^51 + 336000 * q^52 - 236172 * q^53 + 375728 * q^54 + 56760 * q^55 + 314796 * q^57 - 225600 * q^58 + 1310610 * q^59 + 452352 * q^60 + 83552 * q^61 + 225792 * q^62 + 553364 * q^63 - 655360 * q^64 - 4736 * q^66 + 806646 * q^67 - 747776 * q^68 - 245664 * q^70 - 869220 * q^71 + 353280 * q^72 - 207422 * q^73 + 1460832 * q^74 - 140096 * q^76 - 3988336 * q^77 - 85008 * q^78 - 1706808 * q^79 + 114688 * q^80 + 2303170 * q^81 + 887712 * q^82 + 3527548 * q^83 - 5604 * q^85 + 195792 * q^86 - 8414832 * q^87 + 708432 * q^89 - 4483104 * q^90 - 1914384 * q^91 - 271616 * q^92 + 3537876 * q^93 - 2820356 * q^95 - 163840 * q^96 + 5113242 * q^97 - 612480 * q^98 + 603704 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	4.89898	+	2.82843i	0.612372	+	0.353553i
$2$	4.89898	+	2.82843i	0.612372	+	0.353553i
$3$	29.9332	+	17.2819i	1.10864	+	0.640072i	0.938476	−	0.345345i	$-0.112238\pi$
$3$	29.9332	+	17.2819i	1.10864	+	0.640072i	0.170161	+	0.985416i	$0.445571\pi$
$4$	16.0000	+	27.7128i	0.250000	+	0.433013i
$5$	48.9935	−	84.8592i	0.391948	−	0.678874i	−0.600759	−	0.799431i	$-0.705135\pi$
$5$	48.9935	−	84.8592i	0.391948	−	0.678874i	0.992706	+	0.120557i	$0.0384680\pi$
$6$	97.7614	+	169.328i	0.452599	+	0.783924i
$7$	374.355			1.09141			0.545707	−	0.837976i	$-0.316261\pi$
$7$	374.355			1.09141			0.545707	+	0.837976i	$0.316261\pi$
$8$			181.019i			0.353553i
$9$	232.830	+	403.274i	0.319383	+	0.553188i
$10$	480.036	−	277.149i	0.480036	−	0.277149i
$11$	−766.306			−0.575737			−0.287868	−	0.957670i	$-0.592947\pi$
$11$	−766.306			−0.575737			−0.287868	+	0.957670i	$0.592947\pi$
$12$			1106.04i			0.640072i
$13$	−1999.79	+	1154.58i	−0.910235	+	0.525524i	−0.880507	−	0.474034i	$-0.842797\pi$
$13$	−1999.79	+	1154.58i	−0.910235	+	0.525524i	−0.0297279	+	0.999558i	$0.509464\pi$
$14$	1833.96	+	1058.84i	0.668352	+	0.385873i
$15$	2933.06	−	1693.40i	0.869055	−	0.501749i
$16$	−512.000	+	886.810i	−0.125000	+	0.216506i
$17$	1079.00	−	1868.89i	0.219622	−	0.380397i	−0.735070	−	0.677991i	$-0.762851\pi$
$17$	1079.00	−	1868.89i	0.219622	−	0.380397i	0.954692	+	0.297594i	$0.0961842\pi$
$18$			2634.17i			0.451676i
$19$	1562.66	+	6678.62i	0.227826	+	0.973702i
$19$	1562.66	+	6678.62i	0.227826	+	0.973702i
$20$	3135.58			0.391948
$21$	11205.6	+	6469.58i	1.20998	+	0.698584i
$22$	−3754.12	−	2167.44i	−0.352565	−	0.203554i
$23$	−7673.77	−	13291.4i	−0.630703	−	1.09241i	−0.987408	−	0.158193i	$-0.949433\pi$
$23$	−7673.77	−	13291.4i	−0.630703	−	1.09241i	0.356705	−	0.934217i	$-0.383900\pi$
$24$	−3128.36	+	5418.49i	−0.226299	+	0.391962i
$25$	3011.78	+	5216.55i	0.192754	+	0.333859i
$26$	−13062.5			−0.743203
$27$		−	9102.02i		−	0.462431i
$28$	5989.69	+	10374.4i	0.272854	+	0.472597i
$29$	−16518.2	+	9536.79i	−0.677281	+	0.391028i	−0.798830	−	0.601557i	$-0.794547\pi$
$29$	−16518.2	+	9536.79i	−0.677281	+	0.391028i	0.121549	+	0.992585i	$0.461214\pi$
$30$	19158.7			0.709581
$31$		−	49927.0i		−	1.67591i	−0.545741	−	0.837954i	$-0.683752\pi$
$31$		−	49927.0i		−	1.67591i	0.545741	−	0.837954i	$-0.316248\pi$
$32$	−5016.55	+	2896.31i	−0.153093	+	0.0883883i
$33$	−22938.0	−	13243.2i	−0.638283	−	0.368513i
$34$	10572.0	−	6103.77i	0.268981	−	0.155296i
$35$	18341.0	−	31767.5i	0.427778	−	0.740933i
$36$	−7450.57	+	12904.8i	−0.159692	+	0.276594i
$37$		−	32593.3i		−	0.643462i	−0.946831	−	0.321731i	$-0.895735\pi$
$37$		−	32593.3i		−	0.643462i	0.946831	−	0.321731i	$-0.104265\pi$
$38$	−11234.5	+	37138.3i	−0.204741	+	0.676817i
$39$	−79813.3			−1.34549
$40$	15361.2	+	8868.77i	0.240018	+	0.138574i
$41$	−35814.8	−	20677.7i	−0.519649	−	0.300020i	0.217142	−	0.976140i	$-0.430327\pi$
$41$	−35814.8	−	20677.7i	−0.519649	−	0.300020i	−0.736791	+	0.676120i	$0.763660\pi$
$42$	36597.5	+	63388.7i	0.493973	+	0.855587i
$43$	−11303.5	+	19578.3i	−0.142170	+	0.246246i	−0.928314	−	0.371798i	$-0.878741\pi$
$43$	−11303.5	+	19578.3i	−0.142170	+	0.246246i	0.786143	+	0.618044i	$0.212075\pi$
$44$	−12260.9	−	21236.5i	−0.143934	−	0.249301i
$45$	45628.7			0.500726
$46$		−	86818.8i		−	0.891949i
$47$	−14673.2	−	25414.6i	−0.141329	−	0.244788i	0.786669	−	0.617375i	$-0.211804\pi$
$47$	−14673.2	−	25414.6i	−0.141329	−	0.244788i	−0.927997	+	0.372587i	$0.878471\pi$
$48$	−30651.6	+	17696.7i	−0.277159	+	0.160018i
$49$	22492.9			0.191187
$50$			34074.4i			0.272595i
$51$	64596.0	−	37294.5i	0.486962	−	0.281148i
$52$	−63993.1	−	36946.4i	−0.455117	−	0.262762i
$53$	43683.2	−	25220.5i	0.293418	−	0.169405i	−0.346064	−	0.938211i	$-0.612482\pi$
$53$	43683.2	−	25220.5i	0.293418	−	0.169405i	0.639482	+	0.768806i	$0.279149\pi$
$54$	25744.4	−	44590.6i	0.163494	−	0.283180i
$55$	−37544.0	+	65028.1i	−0.225659	+	0.390853i
$56$			67765.6i			0.385873i
$57$	−68644.1	+	226918.i	−0.370662	+	1.22531i
$58$	−107896.			−0.552998
$59$	268633.	+	155096.i	1.30799	+	0.755168i	0.981760	−	0.190123i	$-0.0608887\pi$
$59$	268633.	+	155096.i	1.30799	+	0.755168i	0.326229	+	0.945291i	$0.394222\pi$
$60$	93858.0	+	54188.9i	0.434528	+	0.250875i
$61$	150729.	+	261070.i	0.664059	+	1.15018i	0.979540	+	0.201251i	$0.0645008\pi$
$61$	150729.	+	261070.i	0.664059	+	1.15018i	−0.315481	+	0.948932i	$0.602166\pi$
$62$	141215.	−	244591.i	0.592523	−	1.02628i
$63$	87161.3	+	150968.i	0.348580	+	0.603758i
$64$	−32768.0			−0.125000
$65$			226267.i			0.823912i
$66$	−74915.1	−	129757.i	−0.260578	−	0.451334i
$67$	−13.3422	+	7.70312i	−4.43611e−5	+	2.56119e-5i	−0.500022	−	0.866013i	$-0.666675\pi$
$67$	−13.3422	+	7.70312i	−4.43611e−5	+	2.56119e-5i	0.499978	+	0.866038i	$0.333341\pi$
$68$	69056.2			0.219622
$69$		−	530470.i		−	1.61478i
$70$	179704.	−	103752.i	0.523919	−	0.302485i
$71$	315273.	+	182023.i	0.880870	+	0.508571i	0.870945	−	0.491380i	$-0.163507\pi$
$71$	315273.	+	182023.i	0.880870	+	0.508571i	0.00992498	+	0.999951i	$0.496841\pi$
$72$	−73000.4	+	42146.8i	−0.195581	+	0.112919i
$73$	−61079.9	+	105794.i	−0.157011	+	0.271951i	−0.933789	−	0.357823i	$-0.883519\pi$
$73$	−61079.9	+	105794.i	−0.157011	+	0.271951i	0.776778	+	0.629774i	$0.216852\pi$
$74$	92187.8	−	159674.i	0.227498	−	0.394039i
$75$			208197.i			0.493505i
$76$	−160081.	+	150164.i	−0.364669	+	0.342077i
$77$	−286871.			−0.628368
$78$	−391003.	−	225746.i	−0.823942	−	0.475703i
$79$	−644021.	−	371826.i	−1.30623	−	0.754151i	−0.324763	−	0.945795i	$-0.605284\pi$
$79$	−644021.	−	371826.i	−1.30623	−	0.754151i	−0.981464	+	0.191645i	$0.938618\pi$
$80$	50169.3	+	86895.8i	0.0979870	+	0.169718i
$81$	327034.	−	566439.i	0.615372	−	1.06586i
$82$	−116970.	−	202599.i	−0.212146	−	0.367448i
$83$	−1.00943e6			−1.76539			−0.882695	−	0.469946i	$-0.844273\pi$
$83$	−1.00943e6			−1.76539			−0.882695	+	0.469946i	$0.844273\pi$
$84$			414053.i			0.698584i
$85$	−105728.	−	183127.i	−0.172161	−	0.298191i
$86$	−110752.	+	63942.5i	−0.174122	+	0.100530i
$87$	−659257.			−1.00114
$88$		−	138716.i		−	0.203554i
$89$	166910.	−	96365.5i	0.236762	−	0.136695i	−0.376926	−	0.926244i	$-0.623019\pi$
$89$	166910.	−	96365.5i	0.236762	−	0.136695i	0.613688	+	0.789549i	$0.289685\pi$
$90$	223534.	+	129057.i	0.306631	+	0.177033i
$91$	−748630.	+	432222.i	−0.993444	+	0.573565i
$92$	245561.	−	425323.i	0.315352	−	0.546205i
$93$	862835.	−	1.49447e6i	1.07270	−	1.85797i
$94$		−	166008.i		−	0.199869i
$95$	643303.	+	194603.i	0.750316	+	0.226975i
$96$	−200215.			−0.226299
$97$	1.37799e6	+	795583.i	1.50984	+	0.871707i	0.999934	+	0.0114763i	$0.00365309\pi$
$97$	1.37799e6	+	795583.i	1.50984	+	0.871707i	0.509906	+	0.860230i	$0.329680\pi$
$98$	110192.	+	63619.6i	0.117077	+	0.0675947i
$99$	−178419.	−	309031.i	−0.183881	−	0.318491i
$100$	−96376.9	+	166930.i	−0.0963769	+	0.166930i
$101$	−321792.	−	557360.i	−0.312328	−	0.540968i	0.666538	−	0.745471i	$-0.267775\pi$
$101$	−321792.	−	557360.i	−0.312328	−	0.540968i	−0.978866	+	0.204503i	$0.934442\pi$
$102$	421940.			0.397603
$103$			2.00578e6i			1.83557i	0.397074	+	0.917787i	$0.370026\pi$
$103$			2.00578e6i			1.83557i	−0.397074	+	0.917787i	$0.629974\pi$
$104$	−209001.	−	362000.i	−0.185801	−	0.321816i
$105$	1.09801e6	−	633935.i	0.948500	−	0.547617i
$106$	285337.			0.239575
$107$			2.40459e6i			1.96286i	0.191815	+	0.981431i	$0.438563\pi$
$107$			2.40459e6i			1.96286i	−0.191815	+	0.981431i	$0.561437\pi$
$108$	252243.	−	145632.i	0.200238	−	0.115608i
$109$	333797.	+	192718.i	0.257753	+	0.148814i	0.623309	−	0.781976i	$-0.285788\pi$
$109$	333797.	+	192718.i	0.257753	+	0.148814i	−0.365556	+	0.930789i	$0.619121\pi$
$110$	−367854.	+	212381.i	−0.276375	+	0.159565i
$111$	563275.	−	975621.i	0.411862	−	0.713366i
$112$	−191670.	+	331982.i	−0.136427	+	0.236298i
$113$		−	1.68225e6i		−	1.16589i	−0.812513	−	0.582943i	$-0.801901\pi$
$113$		−	1.68225e6i		−	1.16589i	0.812513	−	0.582943i	$-0.198099\pi$
$114$	−978107.	+	917513.i	−0.660195	+	0.619295i
$115$	−1.50386e6			−0.988811
$116$	−528583.	−	305177.i	−0.338641	−	0.195514i
$117$	−931221.	−	537641.i	−0.581427	−	0.335687i
$118$	877353.	+	1.51962e6i	0.533984	+	0.924888i
$119$	403931.	−	699629.i	0.239699	−	0.415171i
$120$	306539.	+	530941.i	0.177395	+	0.307257i
$121$	−1.18434e6			−0.668527
$122$			1.70530e6i			0.939121i
$123$	−714700.	−	1.23790e6i	−0.384068	−	0.665225i
$124$	1.38362e6	−	798832.i	0.725689	−	0.418977i
$125$	2.12128e6			1.08609
$126$			986117.i			0.492966i
$127$	294201.	−	169857.i	0.143626	−	0.0829224i	−0.426465	−	0.904504i	$-0.640241\pi$
$127$	294201.	−	169857.i	0.143626	−	0.0829224i	0.570091	+	0.821582i	$0.306908\pi$
$128$	−160530.	−	92681.9i	−0.0765466	−	0.0441942i
$129$	−676702.	+	390694.i	−0.315231	+	0.181998i
$130$	−639979.	+	1.10848e6i	−0.291297	+	0.504541i
$131$	−119354.	+	206728.i	−0.0530915	+	0.0919571i	−0.891350	−	0.453316i	$-0.850241\pi$
$131$	−119354.	+	206728.i	−0.0530915	+	0.0919571i	0.838258	+	0.545273i	$0.183574\pi$
$132$		−	847568.i		−	0.368513i
$133$	584990.	+	2.50018e6i	0.248653	+	1.06271i
$134$	−87.1508			−3.62207e−5
$135$	−772391.	−	445940.i	−0.313932	−	0.181249i
$136$	338305.	+	195321.i	0.134491	+	0.0776482i
$137$	−558627.	−	967571.i	−0.217250	−	0.376289i	0.736716	−	0.676202i	$-0.236375\pi$
$137$	−558627.	−	967571.i	−0.217250	−	0.376289i	−0.953966	+	0.299914i	$0.903042\pi$
$138$	1.50040e6	−	2.59876e6i	0.570911	−	0.988847i
$139$	294609.	+	510277.i	0.109699	+	0.190004i	0.915648	−	0.401981i	$-0.131678\pi$
$139$	294609.	+	510277.i	0.109699	+	0.190004i	−0.805950	+	0.591984i	$0.798345\pi$
$140$	1.17382e6			0.427778
$141$		−	1.01432e6i		−	0.361842i
$142$	1.02968e6	+	1.78345e6i	0.359614	+	0.622869i
$143$	1.53245e6	−	884759.i	0.524056	−	0.302564i
$144$	−476837.			−0.159692
$145$			1.86896e6i			0.613051i
$146$	−598459.	+	345520.i	−0.192298	+	0.111024i
$147$	673285.	+	388721.i	0.211956	+	0.122373i
$148$	903252.	−	521493.i	0.278627	−	0.160866i
$149$	2.56875e6	−	4.44920e6i	0.776537	−	1.34500i	−0.157389	−	0.987537i	$-0.550308\pi$
$149$	2.56875e6	−	4.44920e6i	0.776537	−	1.34500i	0.933926	−	0.357465i	$-0.116359\pi$
$150$	−588871.	+	1.01995e6i	−0.174480	+	0.302209i
$151$			2.77474e6i			0.805920i	0.915218	+	0.402960i	$0.132019\pi$
$151$			2.77474e6i			0.805920i	−0.915218	+	0.402960i	$0.867981\pi$
$152$	−1.20896e6	+	282872.i	−0.344256	+	0.0805488i
$153$	1.00490e6			0.280575
$154$	−1.40537e6	−	811393.i	−0.384795	−	0.222162i
$155$	−4.23676e6	−	2.44610e6i	−1.13773	−	0.656869i
$156$	−1.27701e6	−	2.21185e6i	−0.336373	−	0.582615i
$157$	−2.70498e6	+	4.68517e6i	−0.698981	+	1.21067i	0.269839	+	0.962906i	$0.413030\pi$
$157$	−2.70498e6	+	4.68517e6i	−0.698981	+	1.21067i	−0.968820	+	0.247766i	$0.920304\pi$
$158$	−2.10336e6	−	3.64313e6i	−0.533265	−	0.923642i
$159$	1.74343e6			0.433725
$160$			567601.i			0.138574i
$161$	−2.87272e6	−	4.97569e6i	−0.688359	−	1.19227i
$162$	3.20426e6	−	1.84998e6i	0.753674	−	0.435134i
$163$	−8.25314e6			−1.90571			−0.952854	−	0.303429i	$-0.901869\pi$
$163$	−8.25314e6			−1.90571			−0.952854	+	0.303429i	$0.901869\pi$
$164$		−	1.32337e6i		−	0.300020i
$165$	−2.24762e6	+	1.29767e6i	−0.500347	+	0.288876i
$166$	−4.94516e6	−	2.85509e6i	−1.08108	−	0.624160i
$167$	7.20270e6	−	4.15848e6i	1.54649	−	0.892864i	0.548079	−	0.836426i	$-0.315359\pi$
$167$	7.20270e6	−	4.15848e6i	1.54649	−	0.892864i	0.998406	−	0.0564372i	$-0.0179741\pi$
$168$	−1.17112e6	+	2.02844e6i	−0.246987	+	0.427793i
$169$	252689.	−	437671.i	0.0523512	−	0.0906750i
$170$		−	1.19618e6i		−	0.243472i
$171$	−2.32948e6	+	2.18517e6i	−0.465876	+	0.437015i
$172$	−723427.			−0.142170
$173$	3.51780e6	+	2.03100e6i	0.679411	+	0.392258i	0.799633	−	0.600489i	$-0.205027\pi$
$173$	3.51780e6	+	2.03100e6i	0.679411	+	0.392258i	−0.120222	+	0.992747i	$0.538361\pi$
$174$	−3.22969e6	−	1.86466e6i	−0.613073	−	0.353958i
$175$	1.12748e6	+	1.95284e6i	0.210374	+	0.364379i
$176$	392349.	−	679568.i	0.0719671	−	0.124651i
$177$	5.36070e6	+	9.28501e6i	0.966723	+	1.67441i
$178$	1.09025e6			0.193315
$179$		−	3.81297e6i		−	0.664820i	−0.943135	−	0.332410i	$-0.892138\pi$
$179$		−	3.81297e6i		−	0.664820i	0.943135	−	0.332410i	$-0.107862\pi$
$180$	730059.	+	1.26450e6i	0.125182	+	0.216821i
$181$	3.08272e6	−	1.77981e6i	0.519874	−	0.300149i	−0.217009	−	0.976170i	$-0.569630\pi$
$181$	3.08272e6	−	1.77981e6i	0.519874	−	0.300149i	0.736883	+	0.676020i	$0.236297\pi$
$182$	−4.89003e6			−0.811143
$183$			1.04195e7i			1.70018i
$184$	2.40599e6	−	1.38910e6i	0.386225	−	0.222987i
$185$	−2.76584e6	−	1.59686e6i	−0.436830	−	0.252204i
$186$	8.45402e6	−	4.88093e6i	1.31379	−	0.758514i
$187$	−826847.	+	1.43214e6i	−0.126445	+	0.219008i
$188$	469541.	−	813269.i	0.0706643	−	0.122394i
$189$		−	3.40739e6i		−	0.504704i
$190$	2.60111e6	+	2.77289e6i	0.379225	+	0.404270i
$191$	4.86507e6			0.698215			0.349107	−	0.937083i	$-0.386485\pi$
$191$	4.86507e6			0.698215			0.349107	+	0.937083i	$0.386485\pi$
$192$	−980851.	−	566294.i	−0.138580	−	0.0800089i
$193$	4.17501e6	+	2.41044e6i	0.580745	+	0.335293i	0.761429	−	0.648248i	$-0.224498\pi$
$193$	4.17501e6	+	2.41044e6i	0.580745	+	0.335293i	−0.180684	+	0.983541i	$0.557831\pi$
$194$	4.50050e6	+	7.79509e6i	0.616390	+	1.06762i
$195$	−3.91033e6	+	6.77289e6i	−0.527363	+	0.913419i
$196$	359887.	+	623342.i	0.0477967	+	0.0827862i
$197$	1.32850e6			0.173765			0.0868826	−	0.996219i	$-0.472309\pi$
$197$	1.32850e6			0.173765			0.0868826	+	0.996219i	$0.472309\pi$
$198$		−	2.01858e6i		−	0.260047i
$199$	−5.05079e6	−	8.74822e6i	−0.640914	−	1.11010i	−0.985229	−	0.171242i	$-0.945222\pi$
$199$	−5.05079e6	−	8.74822e6i	−0.640914	−	1.11010i	0.344315	−	0.938854i	$-0.388111\pi$
$200$	−944297.	+	545190.i	−0.118037	+	0.0681488i
$201$	−532.499			−6.55738e−5
$202$		−	3.64066e6i		−	0.441698i
$203$	−6.18368e6	+	3.57015e6i	−0.739195	+	0.426774i
$204$	2.06707e6	+	1.19343e6i	0.243481	+	0.140574i
$205$	−3.50938e6	+	2.02614e6i	−0.407351	+	0.235184i
$206$	−5.67320e6	+	9.82628e6i	−0.648973	+	1.12405i
$207$	3.57337e6	−	6.18926e6i	0.402872	−	0.697795i
$208$		−	2.36457e6i		−	0.262762i
$209$	−1.19748e6	−	5.11787e6i	−0.131168	−	0.560596i
$210$	7.17215e6			0.774447
$211$	7.78890e6	+	4.49692e6i	0.829141	+	0.478705i	0.853559	−	0.520997i	$-0.174440\pi$
$211$	7.78890e6	+	4.49692e6i	0.829141	+	0.478705i	−0.0244173	+	0.999702i	$0.507773\pi$
$212$	1.39786e6	+	807055.i	0.146709	+	0.0847024i
$213$	6.29142e6	+	1.08971e7i	0.651043	+	1.12764i
$214$	−6.80121e6	+	1.17800e7i	−0.693977	+	1.20200i
$215$	1.10760e6	+	1.91842e6i	0.111447	+	0.193031i
$216$	1.64764e6			0.163494
$217$		−	1.86904e7i		−	1.82911i
$218$	1.09018e6	+	1.88824e6i	0.105227	+	0.182259i
$219$	−3.65663e6	+	2.11116e6i	−0.348136	+	0.200997i
$220$	−2.40282e6			−0.225659
$221$			4.98317e6i			0.461667i
$222$	5.51895e6	−	3.18637e6i	0.504426	−	0.291230i
$223$	1.02363e7	+	5.90990e6i	0.923052	+	0.532925i	0.884608	−	0.466336i	$-0.154426\pi$
$223$	1.02363e7	+	5.90990e6i	0.923052	+	0.532925i	0.0384448	+	0.999261i	$0.487760\pi$
$224$	−1.87797e6	+	1.08425e6i	−0.167088	+	0.0964684i
$225$	−1.40247e6	+	2.42914e6i	−0.123125	+	0.213258i
$226$	4.75813e6	−	8.24132e6i	0.412203	−	0.713956i
$227$		−	1.27320e7i		−	1.08848i	−0.838931	−	0.544238i	$-0.816819\pi$
$227$		−	1.27320e7i		−	1.08848i	0.838931	−	0.544238i	$-0.183181\pi$
$228$	−7.38685e6	+	1.72837e6i	−0.623239	+	0.145825i
$229$	1.22776e7			1.02237			0.511183	−	0.859472i	$-0.329207\pi$
$229$	1.22776e7			1.02237			0.511183	+	0.859472i	$0.329207\pi$
$230$	−7.36737e6	−	4.25355e6i	−0.605521	−	0.349598i
$231$	−8.58695e6	−	4.95768e6i	−0.696632	−	0.402200i
$232$	−1.72634e6	−	2.99011e6i	−0.138249	−	0.239455i
$233$	−4.17601e6	+	7.23305e6i	−0.330136	+	0.571813i	−0.982538	−	0.186060i	$-0.940428\pi$
$233$	−4.17601e6	+	7.23305e6i	−0.330136	+	0.571813i	0.652402	+	0.757873i	$0.273761\pi$
$234$	−3.04136e6	−	5.26778e6i	−0.237367	−	0.411131i
$235$	−2.87556e6			−0.221574
$236$			9.92612e6i			0.755168i
$237$	−1.28517e7	−	2.22599e7i	−0.965421	−	1.67216i
$238$	3.95770e6	−	2.28498e6i	0.293570	−	0.169493i
$239$	1.16107e7			0.850483			0.425241	−	0.905080i	$-0.360189\pi$
$239$	1.16107e7			0.850483			0.425241	+	0.905080i	$0.360189\pi$
$240$			3.46809e6i			0.250875i
$241$	−2.38729e7	+	1.37830e7i	−1.70551	+	0.984677i	−0.765563	+	0.643361i	$0.777540\pi$
$241$	−2.38729e7	+	1.37830e7i	−1.70551	+	0.984677i	−0.939948	+	0.341317i	$0.889127\pi$
$242$	−5.80204e6	−	3.34981e6i	−0.409388	−	0.236360i
$243$	1.38319e7	−	7.98587e6i	0.963971	−	0.556549i
$244$	−4.82332e6	+	8.35423e6i	−0.332029	+	0.575092i
$245$	1.10201e6	−	1.90873e6i	0.0749352	−	0.129792i
$246$		−	8.08590e6i		−	0.543154i
$247$	−1.08360e7	−	1.15516e7i	−0.719079	−	0.766569i
$248$	9.03775e6			0.592523
$249$	−3.02154e7	−	1.74449e7i	−1.95718	−	1.12998i
$250$	1.03921e7	+	5.99988e6i	0.665094	+	0.383992i
$251$	3.91651e6	+	6.78359e6i	0.247672	+	0.428981i	0.962880	−	0.269931i	$-0.0870010\pi$
$251$	3.91651e6	+	6.78359e6i	0.247672	+	0.428981i	−0.715207	+	0.698913i	$0.753668\pi$
$252$	−2.78916e6	+	4.83097e6i	−0.174290	+	0.301879i
$253$	5.88045e6	+	1.01852e7i	0.363119	+	0.628941i
$254$	1.92171e6			0.117270
$255$		−	7.30876e6i		−	0.440781i
$256$	−524288.	−	908093.i	−0.0312500	−	0.0541266i
$257$	1.86906e7	−	1.07910e7i	1.10109	−	0.635715i	0.164583	−	0.986363i	$-0.447372\pi$
$257$	1.86906e7	−	1.07910e7i	1.10109	−	0.635715i	0.936507	+	0.350648i	$0.114039\pi$
$258$	−4.42020e6			−0.257385
$259$		−	1.22015e7i		−	0.702285i
$260$	−6.27049e6	+	3.62027e6i	−0.356764	+	0.205978i
$261$	−7.69188e6	−	4.44091e6i	−0.432624	−	0.249776i
$262$	−1.16943e6	+	675171.i	−0.0650235	+	0.0375413i
$263$	−1.09680e7	+	1.89971e7i	−0.602920	+	1.04429i	0.389456	+	0.921045i	$0.372663\pi$
$263$	−1.09680e7	+	1.89971e7i	−0.602920	+	1.04429i	−0.992376	+	0.123244i	$0.960670\pi$
$264$	2.39728e6	−	4.15222e6i	0.130289	−	0.225667i
$265$		−	4.94256e6i		−	0.265591i
$266$	−4.20571e6	+	1.39029e7i	−0.223457	+	0.738688i
$267$	6.66153e6			0.349978
$268$	−426.950	−	246.500i	−2.21806e−5	−	1.28060e-5i
$269$	−2.37170e6	−	1.36930e6i	−0.121844	−	0.0703466i	0.437839	−	0.899053i	$-0.355744\pi$
$269$	−2.37170e6	−	1.36930e6i	−0.121844	−	0.0703466i	−0.559683	+	0.828707i	$0.689077\pi$
$270$	−2.52262e6	−	4.36930e6i	−0.128162	−	0.221983i
$271$	−7.37135e6	+	1.27676e7i	−0.370373	+	0.641505i	−0.989623	−	0.143689i	$-0.954103\pi$
$271$	−7.37135e6	+	1.27676e7i	−0.370373	+	0.641505i	0.619250	+	0.785194i	$0.287437\pi$
$272$	1.10490e6	+	1.91374e6i	0.0549055	+	0.0950992i
$273$	−2.98785e7			−1.46849
$274$		−	6.32015e6i		−	0.307238i
$275$	−2.30794e6	−	3.99747e6i	−0.110975	−	0.192215i
$276$	1.47008e7	−	8.48752e6i	0.699221	−	0.403695i
$277$	7.08163e6			0.333191			0.166596	−	0.986025i	$-0.446723\pi$
$277$	7.08163e6			0.333191			0.166596	+	0.986025i	$0.446723\pi$
$278$			3.33312e6i			0.155137i
$279$	2.01343e7	−	1.16245e7i	0.927092	−	0.535257i
$280$	5.75053e6	+	3.32007e6i	0.261959	+	0.151242i
$281$	1.10420e7	−	6.37512e6i	0.497657	−	0.287322i	−0.230088	−	0.973170i	$-0.573902\pi$
$281$	1.10420e7	−	6.37512e6i	0.497657	−	0.287322i	0.727746	+	0.685847i	$0.240568\pi$
$282$	2.86894e6	−	4.96914e6i	0.127930	−	0.221582i
$283$	1.11998e7	−	1.93985e7i	0.494139	−	0.855874i	−0.505838	−	0.862628i	$-0.668817\pi$
$283$	1.11998e7	−	1.93985e7i	0.494139	−	0.855874i	0.999977	+	0.00675455i	$0.00215006\pi$
$284$			1.16495e7i			0.508571i
$285$	1.58930e7	+	1.69426e7i	0.686548	+	0.731889i
$286$	1.00099e7			0.427890
$287$	−1.34074e7	−	7.74079e6i	−0.567153	−	0.327446i
$288$	−2.33601e6	−	1.34870e6i	−0.0977907	−	0.0564595i
$289$	9.74029e6	+	1.68707e7i	0.403532	+	0.698938i
$290$	−5.28622e6	+	9.15601e6i	−0.216746	+	0.375415i
$291$	2.74984e7	+	4.76287e7i	1.11591	+	1.93281i
$292$	−3.90912e6			−0.157011
$293$			3.83622e7i			1.52511i	0.646924	+	0.762554i	$0.276055\pi$
$293$			3.83622e7i			1.52511i	−0.646924	+	0.762554i	$0.723945\pi$
$294$	2.19894e6	+	3.80867e6i	0.0865309	+	0.149876i
$295$	2.63226e7	−	1.51973e7i	1.02533	−	0.591973i
$296$	5.90002e6			0.227498
$297$			6.97493e6i			0.266238i
$298$	2.51685e7	−	1.45310e7i	0.951060	−	0.549095i
$299$	3.06918e7	+	1.77199e7i	1.14818	+	0.662900i
$300$	−5.76973e6	+	3.33116e6i	−0.213694	+	0.123376i
$301$	−4.23154e6	+	7.32924e6i	−0.155167	+	0.268757i
$302$	−7.84816e6	+	1.35934e7i	−0.284936	+	0.493523i
$303$		−	2.22447e7i		−	0.799649i
$304$	−6.72275e6	−	2.03367e6i	−0.239291	−	0.0723869i
$305$	2.95389e7			1.04111
$306$	4.92298e6	+	2.84228e6i	0.171816	+	0.0991981i
$307$	−4.75475e7	−	2.74515e7i	−1.64328	−	0.948750i	−0.979656	−	0.200686i	$-0.935683\pi$
$307$	−4.75475e7	−	2.74515e7i	−1.64328	−	0.948750i	−0.663627	−	0.748063i	$-0.730984\pi$
$308$	−4.58993e6	−	7.94999e6i	−0.157092	−	0.272091i
$309$	−3.46638e7	+	6.00394e7i	−1.17490	+	2.03498i
$310$	−1.38372e7	−	2.39668e7i	−0.464476	−	0.804496i
$311$	−4.08455e7			−1.35788			−0.678942	−	0.734192i	$-0.737561\pi$
$311$	−4.08455e7			−1.35788			−0.678942	+	0.734192i	$0.737561\pi$
$312$		−	1.44477e7i		−	0.475703i
$313$	−5.44048e6	−	9.42318e6i	−0.177421	−	0.307301i	0.763576	−	0.645718i	$-0.223442\pi$
$313$	−5.44048e6	−	9.42318e6i	−0.177421	−	0.307301i	−0.940996	+	0.338417i	$0.890109\pi$
$314$	−2.65033e7	+	1.53017e7i	−0.856074	+	0.494254i
$315$	1.70813e7			0.546500
$316$		−	2.37968e7i		−	0.754151i
$317$	3.25508e7	−	1.87932e7i	1.02184	−	0.589961i	0.107206	−	0.994237i	$-0.465810\pi$
$317$	3.25508e7	−	1.87932e7i	1.02184	−	0.589961i	0.914637	+	0.404276i	$0.132476\pi$
$318$	8.54105e6	+	4.93118e6i	0.265601	+	0.153345i
$319$	1.26580e7	−	7.30810e6i	0.389936	−	0.225129i
$320$	−1.60542e6	+	2.78067e6i	−0.0489935	+	0.0848592i
$321$	−4.15560e7	+	7.19771e7i	−1.25637	+	2.17610i
$322$		−	3.25011e7i		−	0.973487i
$323$	1.41677e7	+	4.28582e6i	0.420429	+	0.127182i
$324$	2.09302e7			0.615372
$325$	−1.20458e7	−	6.95466e6i	−0.350902	−	0.202594i
$326$	−4.04320e7	−	2.33434e7i	−1.16700	−	0.673770i
$327$	6.66108e6	+	1.15373e7i	0.190503	+	0.329961i
$328$	3.74306e6	−	6.48316e6i	0.106073	−	0.183724i
$329$	−5.49297e6	−	9.51411e6i	−0.154248	−	0.267166i
$330$	−1.46814e7			−0.408532
$331$			2.72676e6i			0.0751906i	0.999293	+	0.0375953i	$0.0119698\pi$
$331$			2.72676e6i			0.0751906i	−0.999293	+	0.0375953i	$0.988030\pi$
$332$	−1.61508e7	−	2.79741e7i	−0.441348	−	0.764436i
$333$	1.31440e7	−	7.58871e6i	0.355956	−	0.205511i
$334$	4.70478e7			1.26270
$335$			1509.61i			4.01541e-5i
$336$	−1.14746e7	+	6.62485e6i	−0.302496	+	0.174646i
$337$	4.45571e6	+	2.57251e6i	0.116420	+	0.0672151i	0.557079	−	0.830459i	$-0.311922\pi$
$337$	4.45571e6	+	2.57251e6i	0.116420	+	0.0672151i	−0.440659	+	0.897674i	$0.645255\pi$
$338$	2.47584e6	−	1.42943e6i	0.0641169	−	0.0370179i
$339$	2.90726e7	−	5.03552e7i	0.746250	−	1.29254i
$340$	3.38331e6	−	5.86006e6i	0.0860804	−	0.149096i
$341$			3.82593e7i			0.964882i
$342$	−1.75927e7	+	4.11632e6i	−0.439798	+	0.102904i
$343$	−3.56222e7			−0.882751
$344$	−3.54405e6	−	2.04616e6i	−0.0870612	−	0.0502648i
$345$	−4.50153e7	−	2.59896e7i	−1.09623	−	0.632910i
$346$	1.14891e7	+	1.98997e7i	0.277368	+	0.480416i
$347$	2.12035e7	−	3.67256e7i	0.507481	−	0.878983i	−0.492481	−	0.870323i	$-0.663910\pi$
$347$	2.12035e7	−	3.67256e7i	0.507481	−	0.878983i	0.999962	−	0.00866028i	$-0.00275669\pi$
$348$	−1.05481e7	−	1.82699e7i	−0.250286	−	0.433508i
$349$	1.57317e7			0.370082			0.185041	−	0.982731i	$-0.440758\pi$
$349$	1.57317e7			0.370082			0.185041	+	0.982731i	$0.440758\pi$
$350$			1.27559e7i			0.297514i
$351$	1.05090e7	+	1.82021e7i	0.243019	+	0.420920i
$352$	3.84422e6	−	2.21946e6i	0.0881414	−	0.0508884i
$353$	−3.06751e7			−0.697367			−0.348684	−	0.937240i	$-0.613371\pi$
$353$	−3.06751e7			−0.697367			−0.348684	+	0.937240i	$0.613371\pi$
$354$			6.06494e7i			1.36715i
$355$	3.08927e7	−	1.78359e7i	0.690510	−	0.398666i
$356$	5.34112e6	+	3.08370e6i	0.118381	+	0.0683473i
$357$	2.41819e7	−	1.39614e7i	0.531478	−	0.306849i
$358$	1.07847e7	−	1.86797e7i	0.235050	−	0.407118i
$359$	−3.45503e6	+	5.98429e6i	−0.0746738	+	0.129339i	−0.900944	−	0.433935i	$-0.857125\pi$
$359$	−3.45503e6	+	5.98429e6i	−0.0746738	+	0.129339i	0.826271	+	0.563273i	$0.190458\pi$
$360$			8.25967e6i			0.177033i
$361$	−4.21621e7	+	2.08728e7i	−0.896190	+	0.443670i
$362$	2.01362e7			0.424475
$363$	−3.54510e7	−	2.04676e7i	−0.741153	−	0.427905i
$364$	−2.39562e7	−	1.38311e7i	−0.496722	−	0.286782i
$365$	5.98504e6	+	1.03664e7i	0.123080	+	0.213181i
$366$	−2.94709e7	+	5.10451e7i	−0.601104	+	1.04114i
$367$	−8.85170e6	−	1.53316e7i	−0.179072	−	0.310162i	0.762491	−	0.646999i	$-0.223976\pi$
$367$	−8.85170e6	−	1.53316e7i	−0.179072	−	0.310162i	−0.941563	+	0.336837i	$0.890643\pi$
$368$	1.57159e7			0.315352
$369$		−	1.92575e7i		−	0.383285i
$370$	−9.03320e6	−	1.56460e7i	−0.178335	−	0.308885i
$371$	1.63530e7	−	9.44142e6i	0.320241	−	0.184891i
$372$	5.52214e7			1.07270
$373$		−	7.34707e7i		−	1.41575i	−0.706336	−	0.707877i	$-0.749653\pi$
$373$		−	7.34707e7i		−	1.41575i	0.706336	−	0.707877i	$-0.250347\pi$
$374$	−8.10141e6	+	4.67735e6i	−0.154862	+	0.0894098i
$375$	6.34965e7	+	3.66598e7i	1.20408	+	0.695177i
$376$	4.60054e6	−	2.65612e6i	0.0865457	−	0.0499672i
$377$	2.20219e7	−	3.81431e7i	0.410990	−	0.711855i
$378$	9.63756e6	−	1.66927e7i	0.178440	−	0.309067i
$379$			197037.i			0.00361935i	0.999998	+	0.00180968i	$0.000576038\pi$
$379$			197037.i			0.00361935i	−0.999998	+	0.00180968i	$0.999424\pi$
$380$	4.89985e6	+	2.09414e7i	0.0892960	+	0.381640i
$381$	1.17418e7			0.212305
$382$	2.38339e7	+	1.37605e7i	0.427568	+	0.246856i
$383$	−8.94882e7	−	5.16660e7i	−1.59283	−	0.919621i	−0.992819	−	0.119629i	$-0.961829\pi$
$383$	−8.94882e7	−	5.16660e7i	−1.59283	−	0.919621i	−0.600011	−	0.799991i	$-0.704837\pi$
$384$	−3.20344e6	−	5.54853e6i	−0.0565749	−	0.0979905i
$385$	−1.40548e7	+	2.43436e7i	−0.246287	+	0.426582i
$386$	1.36355e7	+	2.36174e7i	0.237088	+	0.410649i
$387$	−1.05272e7			−0.181627
$388$			5.09173e7i			0.871707i
$389$	−2.76183e7	−	4.78363e7i	−0.469189	−	0.812659i	0.530191	−	0.847878i	$-0.322120\pi$
$389$	−2.76183e7	−	4.78363e7i	−0.469189	−	0.812659i	−0.999380	+	0.0352194i	$0.988787\pi$
$390$	−3.83132e7	+	2.21202e7i	−0.645885	+	0.372902i
$391$	−3.31201e7			−0.554066
$392$			4.07165e6i			0.0675947i
$393$	−7.14532e6	+	4.12535e6i	−0.117718	+	0.0679647i
$394$	6.50829e6	+	3.75757e6i	0.106409	+	0.0614353i
$395$	−6.31057e7	+	3.64341e7i	−1.02395	+	0.591175i
$396$	5.70942e6	−	9.88900e6i	0.0919403	−	0.159245i
$397$	4.86568e7	−	8.42760e7i	0.777628	−	1.34689i	−0.155678	−	0.987808i	$-0.549756\pi$
$397$	4.86568e7	−	8.42760e7i	0.777628	−	1.34689i	0.933306	−	0.359083i	$-0.116910\pi$
$398$		−	5.71431e7i		−	0.906389i
$399$	−2.56973e7	+	8.49480e7i	−0.404546	+	1.33732i
$400$	−6.16812e6			−0.0963769
$401$	−3.92010e7	−	2.26327e7i	−0.607945	−	0.350997i	0.164216	−	0.986424i	$-0.447491\pi$
$401$	−3.92010e7	−	2.26327e7i	−0.607945	−	0.350997i	−0.772161	+	0.635427i	$0.780824\pi$
$402$	−2608.70	−	1506.13i	−4.01556e−5	−	2.31838e-5i
$403$	5.76445e7	+	9.98432e7i	0.880730	+	1.52547i
$404$	1.02973e7	−	1.78355e7i	0.156164	−	0.270484i
$405$	−3.20451e7	−	5.55037e7i	−0.482387	−	0.835520i
$406$	−4.03916e7			−0.603550
$407$			2.49764e7i			0.370465i
$408$	6.75103e6	+	1.16931e7i	0.0994008	+	0.172167i
$409$	2.18434e7	−	1.26113e7i	0.319264	−	0.184327i	−0.331800	−	0.943350i	$-0.607656\pi$
$409$	2.18434e7	−	1.26113e7i	0.319264	−	0.184327i	0.651065	+	0.759022i	$0.274323\pi$
$410$	−2.29232e7			−0.332601
$411$		−	3.86166e7i		−	0.556223i
$412$	−5.55858e7	+	3.20925e7i	−0.794827	+	0.458893i
$413$	1.00564e8	+	5.80609e7i	1.42756	+	0.824201i
$414$	3.50117e7	−	2.02140e7i	0.493415	−	0.284874i
$415$	−4.94554e7	+	8.56592e7i	−0.691941	+	1.19848i
$416$	6.68802e6	−	1.15840e7i	0.0929004	−	0.160908i
$417$			2.03656e7i			0.280860i
$418$	8.60910e6	−	2.84593e7i	0.117877	−	0.389668i
$419$	−3.22071e6			−0.0437835			−0.0218917	−	0.999760i	$-0.506969\pi$
$419$	−3.22071e6			−0.0437835			−0.0218917	+	0.999760i	$0.506969\pi$
$420$	3.51362e7	+	2.02859e7i	0.474250	+	0.273808i
$421$	7.57246e7	+	4.37196e7i	1.01482	+	0.585909i	0.912600	−	0.408853i	$-0.134071\pi$
$421$	7.57246e7	+	4.37196e7i	1.01482	+	0.585909i	0.102223	+	0.994761i	$0.467404\pi$
$422$	2.54384e7	+	4.40606e7i	0.338496	+	0.586291i
$423$	6.83271e6	−	1.18346e7i	0.0902759	−	0.156362i
$424$	4.56540e6	+	7.90750e6i	0.0598937	+	0.103739i
$425$	1.29989e7			0.169332
$426$			7.11793e7i			0.920714i
$427$	5.64261e7	+	9.77328e7i	0.724763	+	1.25533i
$428$	−6.66380e7	+	3.84735e7i	−0.849944	+	0.490716i
$429$	6.11614e7			0.774650
$430$			1.25311e7i			0.157610i
$431$	6.51446e7	−	3.76113e7i	0.813667	−	0.469771i	−0.0345608	−	0.999403i	$-0.511003\pi$
$431$	6.51446e7	−	3.76113e7i	0.813667	−	0.469771i	0.848228	+	0.529632i	$0.177670\pi$
$432$	8.07177e6	+	4.66024e6i	0.100119	+	0.0578038i
$433$	1.05864e8	−	6.11205e7i	1.30402	−	0.752876i	0.322928	−	0.946424i	$-0.395333\pi$
$433$	1.05864e8	−	6.11205e7i	1.30402	−	0.752876i	0.981091	+	0.193548i	$0.0619995\pi$
$434$	5.28645e7	−	9.15640e7i	0.646688	−	1.12010i
$435$	−3.22993e7	+	5.59440e7i	−0.392396	+	0.679651i
$436$			1.23340e7i			0.148814i
$437$	7.67764e7	−	7.20201e7i	0.919991	−	0.862997i
$438$	−2.38850e7			−0.284252
$439$	−7.93260e7	−	4.57989e7i	−0.937610	−	0.541329i	−0.0483996	−	0.998828i	$-0.515412\pi$
$439$	−7.93260e7	−	4.57989e7i	−0.937610	−	0.541329i	−0.889210	+	0.457499i	$0.848745\pi$
$440$	−1.17713e7	−	6.79619e6i	−0.138187	−	0.0797825i
$441$	5.23703e6	+	9.07081e6i	0.0610618	+	0.105762i
$442$	−1.40945e7	+	2.44124e7i	−0.163224	+	0.282712i
$443$	−2.81217e7	−	4.87083e7i	−0.323468	−	0.560262i	0.657733	−	0.753251i	$-0.271515\pi$
$443$	−2.81217e7	−	4.87083e7i	−0.323468	−	0.560262i	−0.981201	+	0.192989i	$0.938182\pi$
$444$	3.60496e7			0.411862
$445$		−	1.88851e7i		−	0.214309i
$446$	3.34315e7	+	5.79050e7i	0.376835	+	0.652697i
$447$	1.53781e8	−	8.87858e7i	1.72179	−	0.994079i
$448$	−1.22669e7			−0.136427
$449$		−	7.28925e6i		−	0.0805274i	−0.999189	−	0.0402637i	$-0.987180\pi$
$449$		−	7.28925e6i		−	0.0805274i	0.999189	−	0.0402637i	$-0.0128198\pi$
$450$	−1.37413e7	+	7.93355e6i	−0.150796	+	0.0870623i
$451$	2.74451e7	+	1.58454e7i	0.299181	+	0.172732i
$452$	4.66200e7	−	2.69161e7i	0.504843	−	0.291471i
$453$	−4.79529e7	+	8.30569e7i	−0.515846	+	0.893472i
$454$	3.60115e7	−	6.23738e7i	0.384834	−	0.666553i
$455$			8.47042e7i			0.899230i
$456$	−4.10766e7	−	1.24259e7i	−0.433211	−	0.131049i
$457$	−1.61947e8			−1.69677			−0.848386	−	0.529378i	$-0.822425\pi$
$457$	−1.61947e8			−1.69677			−0.848386	+	0.529378i	$0.822425\pi$
$458$	6.01477e7	+	3.47263e7i	0.626069	+	0.361461i
$459$	−1.70107e7	−	9.82112e6i	−0.175907	−	0.101560i
$460$	−2.40617e7	−	4.16761e7i	−0.247203	−	0.428168i
$461$	−4.32401e7	+	7.48940e7i	−0.441350	+	0.764441i	−0.997790	−	0.0664467i	$-0.978834\pi$
$461$	−4.32401e7	+	7.48940e7i	−0.441350	+	0.764441i	0.556440	+	0.830888i	$0.312167\pi$
$462$	−2.80449e7	−	4.85751e7i	−0.284399	−	0.492593i
$463$	−5.44783e7			−0.548884			−0.274442	−	0.961604i	$-0.588493\pi$
$463$	−5.44783e7			−0.548884			−0.274442	+	0.961604i	$0.588493\pi$
$464$		−	1.95313e7i		−	0.195514i
$465$	−8.45465e7	−	1.46439e8i	−0.840886	−	1.45646i
$466$	−4.09163e7	+	2.36231e7i	−0.404333	+	0.233442i
$467$	−1.44659e8			−1.42034			−0.710172	−	0.704028i	$-0.751383\pi$
$467$	−1.44659e8			−1.42034			−0.710172	+	0.704028i	$0.751383\pi$
$468$		−	3.44090e7i		−	0.335687i
$469$	−4994.72	+	2883.70i	−4.84164e−5	+	2.79532e-5i
$470$	−1.40873e7	−	8.13330e6i	−0.135686	−	0.0783381i
$471$	−1.61938e8	+	9.34947e7i	−1.54983	+	0.894796i
$472$	−2.80753e7	+	4.86278e7i	−0.266992	+	0.462444i
$473$	8.66197e6	−	1.50030e7i	0.0818527	−	0.141773i
$474$		−	1.45401e8i		−	1.36531i
$475$	−3.01330e7	+	2.82662e7i	−0.281165	+	0.263747i
$476$	2.58516e7			0.239699
$477$	2.03415e7	+	1.17442e7i	0.187425	+	0.108210i
$478$	5.68807e7	+	3.28401e7i	0.520812	+	0.300691i
$479$	−9.06786e6	−	1.57060e7i	−0.0825084	−	0.142909i	0.821818	−	0.569750i	$-0.192960\pi$
$479$	−9.06786e6	−	1.57060e7i	−0.0825084	−	0.142909i	−0.904327	+	0.426841i	$0.859626\pi$
$480$	−9.80924e6	+	1.69901e7i	−0.0886976	+	0.153629i
$481$	3.76315e7	+	6.51796e7i	0.338155	+	0.585702i
$482$	−1.55937e8			−1.39254
$483$		−	1.98584e8i		−	1.76240i
$484$	−1.89494e7	−	3.28213e7i	−0.167132	−	0.289481i
$485$	1.35025e8	−	7.79568e7i	1.18356	−	0.683327i
$486$	9.03498e7			0.787079
$487$			8.77636e7i			0.759850i	0.925017	+	0.379925i	$0.124050\pi$
$487$			8.77636e7i			0.759850i	−0.925017	+	0.379925i	$0.875950\pi$
$488$	−4.72587e7	+	2.72848e7i	−0.406651	+	0.234780i
$489$	−2.47043e8	−	1.42630e8i	−2.11274	−	1.21979i
$490$	1.07974e7	−	6.23389e6i	0.0917765	−	0.0529872i
$491$	−3.95913e7	+	6.85742e7i	−0.334469	+	0.579317i	−0.983383	−	0.181545i	$-0.941890\pi$
$491$	−3.95913e7	+	6.85742e7i	−0.334469	+	0.579317i	0.648914	+	0.760862i	$0.275224\pi$
$492$	2.28704e7	−	3.96127e7i	0.192034	−	0.332613i
$493$			4.11609e7i			0.343514i
$494$	−2.04123e7	−	8.72398e7i	−0.169321	−	0.723658i
$495$	−3.49655e7			−0.288287
$496$	4.42757e7	+	2.55626e7i	0.362845	+	0.209489i
$497$	1.18024e8	+	6.81413e7i	0.961395	+	0.555062i
$498$	−9.86830e7	−	1.70924e8i	−0.799014	−	1.38393i
$499$	5.43720e7	−	9.41750e7i	0.437596	−	0.757939i	−0.559907	−	0.828555i	$-0.689163\pi$
$499$	5.43720e7	−	9.41750e7i	0.437596	−	0.757939i	0.997504	+	0.0706164i	$0.0224966\pi$
$500$	3.39404e7	+	5.87865e7i	0.271523	+	0.470292i
$501$	2.87466e8			2.28599
$502$			4.43102e7i			0.350262i
$503$	−7.97164e7	−	1.38073e8i	−0.626389	−	1.08494i	−0.988271	−	0.152713i	$-0.951199\pi$
$503$	−7.97164e7	−	1.38073e8i	−0.626389	−	1.08494i	0.361882	−	0.932224i	$-0.382134\pi$
$504$	−2.73281e7	+	1.57779e7i	−0.213461	+	0.123241i
$505$	−6.30628e7			−0.489665
$506$			6.65297e7i			0.513528i
$507$	1.51276e7	−	8.73392e6i	0.116077	−	0.0670171i
$508$	9.41442e6	+	5.43542e6i	0.0718129	+	0.0414612i
$509$	−4.16751e7	+	2.40611e7i	−0.316026	+	0.182458i	−0.649620	−	0.760259i	$-0.725072\pi$
$509$	−4.16751e7	+	2.40611e7i	−0.316026	+	0.182458i	0.333594	+	0.942717i	$0.391739\pi$
$510$	2.06723e7	−	3.58055e7i	0.155840	−	0.269922i
$511$	−2.28656e7	+	3.96044e7i	−0.171364	+	0.296811i
$512$		−	5.93164e6i		−	0.0441942i
$513$	6.07890e7	−	1.42234e7i	0.450270	−	0.105354i
$514$	1.22086e8			0.899037
$515$	1.70209e8	+	9.82702e7i	1.24612	+	0.719449i
$516$	−2.16545e7	−	1.25022e7i	−0.157615	−	0.0909992i
$517$	1.12441e7	+	1.94754e7i	0.0813681	+	0.140934i
$518$	3.45110e7	−	5.97748e7i	0.248295	−	0.430060i
$519$	7.01992e7	+	1.21589e8i	0.502146	+	0.869743i
$520$	−4.09587e7			−0.291297
$521$			3.82494e7i			0.270465i	0.990814	+	0.135233i	$0.0431781\pi$
$521$			3.82494e7i			0.270465i	−0.990814	+	0.135233i	$0.956822\pi$
$522$	−2.51216e7	−	4.35118e7i	−0.176618	−	0.305912i
$523$	−9.30208e7	+	5.37056e7i	−0.650242	+	0.375418i	−0.788549	−	0.614972i	$-0.789167\pi$
$523$	−9.30208e7	+	5.37056e7i	−0.650242	+	0.375418i	0.138307	+	0.990389i	$0.455834\pi$
$524$	−7.63869e6			−0.0530915
$525$			7.79398e7i			0.538619i
$526$	−1.07464e8	+	6.20444e7i	−0.738424	+	0.426329i
$527$	−9.33080e7	−	5.38714e7i	−0.637510	−	0.368067i
$528$	2.34885e7	−	1.35611e7i	0.159571	−	0.0921282i
$529$	−4.37554e7	+	7.57867e7i	−0.295573	+	0.511948i
$530$	1.39797e7	−	2.42135e7i	0.0939008	−	0.162641i
$531$			1.44444e8i			0.964751i
$532$	−5.99271e7	+	5.62146e7i	−0.398005	+	0.373348i
$533$	9.54957e7			0.630670
$534$	3.26347e7	+	1.88417e7i	0.214317	+	0.123736i
$535$	2.04052e8	+	1.17809e8i	1.33254	+	0.769340i
$536$	−1394.41	−	2415.19i	−9.05518e−6	−	1.56840e-5i
$537$	6.58955e7	−	1.14134e8i	0.425533	−	0.737044i
$538$	−7.74595e6	−	1.34164e7i	−0.0497425	−	0.0861566i
$539$	−1.72365e7			−0.110073
$540$		−	2.85402e7i		−	0.181249i
$541$	9.47203e7	+	1.64060e8i	0.598206	+	1.03612i	0.993086	+	0.117391i	$0.0374531\pi$
$541$	9.47203e7	+	1.64060e8i	0.598206	+	1.03612i	−0.394879	+	0.918733i	$0.629214\pi$
$542$	−7.22242e7	+	4.16987e7i	−0.453612	+	0.261893i
$543$	1.23034e8			0.768468
$544$			1.25005e7i			0.0776482i
$545$	3.27078e7	−	1.88839e7i	0.202051	−	0.116654i
$546$	−1.46374e8	−	8.45092e7i	−0.899263	−	0.519190i
$547$	4.00464e7	−	2.31208e7i	0.244681	−	0.141267i	−0.372645	−	0.927974i	$-0.621549\pi$
$547$	4.00464e7	−	2.31208e7i	0.244681	−	0.141267i	0.617327	+	0.786707i	$0.288216\pi$
$548$	1.78761e7	−	3.09623e7i	0.108625	−	0.188144i
$549$	−7.01884e7	+	1.21570e8i	−0.424178	+	0.734698i
$550$		−	2.61114e7i		−	0.156943i
$551$	−8.95050e7	−	9.54161e7i	−0.535047	−	0.570383i
$552$	9.60253e7			0.570911
$553$	−2.41093e8	−	1.39195e8i	−1.42564	−	0.823091i
$554$	3.46927e7	+	2.00299e7i	0.204037	+	0.117801i
$555$	−5.51936e7	−	9.55982e7i	−0.322857	−	0.559204i
$556$	−9.42748e6	+	1.63289e7i	−0.0548493	+	0.0950018i
$557$	1.47902e8	+	2.56175e8i	0.855874	+	1.48242i	0.875832	+	0.482616i	$0.160313\pi$
$557$	1.47902e8	+	2.56175e8i	0.855874	+	1.48242i	−0.0199580	+	0.999801i	$0.506353\pi$
$558$	1.31516e8			0.756968
$559$		−	5.22032e7i		−	0.298856i
$560$	1.87812e7	+	3.25299e7i	0.106944	+	0.185233i
$561$	−4.95003e7	+	2.85790e7i	−0.280362	+	0.161867i
$562$	7.21263e7			0.406335
$563$		−	3.06141e7i		−	0.171552i	−0.996314	−	0.0857760i	$-0.972663\pi$
$563$		−	3.06141e7i		−	0.171552i	0.996314	−	0.0857760i	$-0.0273369\pi$
$564$	2.81097e7	−	1.62291e7i	0.156682	−	0.0904604i
$565$	−1.42755e8	−	8.24194e7i	−0.791489	−	0.456966i
$566$	1.09735e8	−	6.33554e7i	0.605194	−	0.349409i
$567$	1.22427e8	−	2.12050e8i	0.671626	−	1.16329i
$568$	−3.29497e7	+	5.70705e7i	−0.179807	+	0.311435i
$569$		−	1.17657e7i		−	0.0638679i	−0.999490	−	0.0319340i	$-0.989833\pi$
$569$		−	1.17657e7i		−	0.0638679i	0.999490	−	0.0319340i	$-0.0101666\pi$
$570$	2.99385e7	+	1.27954e8i	0.161661	+	0.690920i
$571$	−3.98246e7			−0.213916			−0.106958	−	0.994264i	$-0.534111\pi$
$571$	−3.98246e7			−0.213916			−0.106958	+	0.994264i	$0.534111\pi$
$572$	4.90383e7	+	2.83123e7i	0.262028	+	0.151282i
$573$	1.45627e8	+	8.40778e7i	0.774066	+	0.446907i
$574$	−4.37885e7	−	7.58439e7i	−0.231539	−	0.401038i
$575$	4.62234e7	−	8.00612e7i	0.243141	−	0.421132i
$576$	−7.62938e6	−	1.32145e7i	−0.0399229	−	0.0691485i
$577$	6.91672e7			0.360058			0.180029	−	0.983661i	$-0.442381\pi$
$577$	6.91672e7			0.360058			0.180029	+	0.983661i	$0.442381\pi$
$578$			1.10199e8i			0.570681i
$579$	8.33142e7	+	1.44304e8i	0.429223	+	0.743437i
$580$	−5.17942e7	+	2.99034e7i	−0.265459	+	0.153263i
$581$	−3.77884e8			−1.92677
$582$			3.11109e8i			1.57813i
$583$	−3.34747e7	+	1.93266e7i	−0.168931	+	0.0975326i
$584$	−1.91507e7	−	1.10567e7i	−0.0961492	−	0.0555118i
$585$	−9.12475e7	+	5.26818e7i	−0.455778	+	0.263144i
$586$	−1.08505e8	+	1.87936e8i	−0.539207	+	0.933934i
$587$	−7.45290e7	+	1.29088e8i	−0.368477	+	0.638222i	−0.989328	−	0.145708i	$-0.953454\pi$
$587$	−7.45290e7	+	1.29088e8i	−0.368477	+	0.638222i	0.620850	+	0.783929i	$0.286787\pi$
$588$			2.48781e7i			0.122373i
$589$	3.33443e8	−	7.80189e7i	1.63183	−	0.381816i
$590$	1.71938e8			0.837176
$591$	3.97662e7	+	2.29590e7i	0.192642	+	0.111222i
$592$	2.89041e7	+	1.66878e7i	0.139314	+	0.0804328i
$593$	−1.61002e8	−	2.78864e8i	−0.772090	−	1.33730i	−0.936416	−	0.350892i	$-0.885878\pi$
$593$	−1.61002e8	−	2.78864e8i	−0.772090	−	1.33730i	0.164326	−	0.986406i	$-0.447455\pi$
$594$	−1.97281e7	+	3.41701e7i	−0.0941295	+	0.163037i
$595$	−3.95800e7	−	6.85545e7i	−0.187899	−	0.325451i
$596$	1.64400e8			0.776537
$597$		−	3.49149e8i		−	1.64092i
$598$	1.00239e8	+	1.73619e8i	0.468741	+	0.811883i
$599$	9.06585e7	−	5.23417e7i	0.421821	−	0.243538i	−0.274035	−	0.961720i	$-0.588359\pi$
$599$	9.06585e7	−	5.23417e7i	0.421821	−	0.243538i	0.695856	+	0.718181i	$0.255025\pi$
$600$	−3.76877e7			−0.174480
$601$		−	1.56752e8i		−	0.722089i	−0.932549	−	0.361044i	$-0.882420\pi$
$601$		−	1.56752e8i		−	0.722089i	0.932549	−	0.361044i	$-0.117580\pi$
$602$	−4.14605e7	+	2.39372e7i	−0.190040	+	0.109720i
$603$	−6212.93	−	3587.04i	−2.83364e−5	−	1.63600e-5i
$604$	−7.68959e7	+	4.43959e7i	−0.348973	+	0.201480i
$605$	−5.80248e7	+	1.00502e8i	−0.262028	+	0.453845i
$606$	6.29176e7	−	1.08976e8i	0.282718	−	0.489683i
$607$		−	2.75702e8i		−	1.23275i	−0.787453	−	0.616374i	$-0.788601\pi$
$607$		−	2.75702e8i		−	1.23275i	0.787453	−	0.616374i	$-0.211399\pi$
$608$	−2.71825e7	−	2.89777e7i	−0.120943	−	0.128930i
$609$	−2.46796e8			−1.09266
$610$	1.44710e8	+	8.35486e7i	0.637544	+	0.368086i
$611$	5.86863e7	+	3.38826e7i	0.257284	+	0.148543i
$612$	1.60784e7	+	2.78486e7i	0.0701436	+	0.121492i
$613$	1.04485e8	−	1.80974e8i	0.453601	−	0.785659i	−0.545006	−	0.838432i	$-0.683473\pi$
$613$	1.04485e8	−	1.80974e8i	0.453601	−	0.785659i	0.998607	+	0.0527730i	$0.0168060\pi$
$614$	−1.55289e8	−	2.68969e8i	−0.670867	−	1.16198i
$615$	−1.40062e8			−0.602139
$616$		−	5.19291e7i		−	0.222162i
$617$	7.26497e7	+	1.25833e8i	0.309299	+	0.535721i	0.978209	−	0.207622i	$-0.0665723\pi$
$617$	7.26497e7	+	1.25833e8i	0.309299	+	0.535721i	−0.668910	+	0.743343i	$0.733239\pi$
$618$	−3.39634e8	+	1.96088e8i	−1.43895	+	0.830779i
$619$	−3.93424e8			−1.65878			−0.829390	−	0.558670i	$-0.811312\pi$
$619$	−3.93424e8			−1.65878			−0.829390	+	0.558670i	$0.811312\pi$
$620$		−	1.56550e8i		−	0.656869i
$621$	−1.20978e8	+	6.98468e7i	−0.505164	+	0.291657i
$622$	−2.00101e8	−	1.15528e8i	−0.831531	−	0.480085i
$623$	6.24836e7	−	3.60749e7i	0.258406	−	0.149191i
$624$	4.08644e7	−	7.07792e7i	0.168187	−	0.291308i
$625$	5.68697e7	−	9.85012e7i	0.232938	−	0.403461i
$626$		−	6.15520e7i		−	0.250911i
$627$	5.26023e7	−	1.73889e8i	0.213404	−	0.705454i
$628$	−1.73119e8			−0.698981
$629$	−6.09133e7	−	3.51683e7i	−0.244771	−	0.141319i
$630$	8.36811e7	+	4.83133e7i	0.334662	+	0.193217i
$631$	6.04804e7	+	1.04755e8i	0.240728	+	0.416953i	0.960922	−	0.276820i	$-0.0892805\pi$
$631$	6.04804e7	+	1.04755e8i	0.240728	+	0.416953i	−0.720194	+	0.693773i	$0.755947\pi$
$632$	6.73076e7	−	1.16580e8i	0.266633	−	0.461821i
$633$	1.55431e8	+	2.69214e8i	0.612811	+	1.06142i
$634$	2.12621e8			0.834331
$635$		−	3.32875e7i		−	0.130005i
$636$	2.78950e7	+	4.83155e7i	0.108431	+	0.187808i
$637$	−4.49810e7	+	2.59698e7i	−0.174025	+	0.100473i
$638$	8.26817e7			0.318381
$639$			1.69522e8i			0.649716i
$640$	−1.57298e7	+	9.08162e6i	−0.0600045	+	0.0346436i
$641$	−1.87334e8	−	1.08157e8i	−0.711284	−	0.410660i	0.100252	−	0.994962i	$-0.468035\pi$
$641$	−1.87334e8	−	1.08157e8i	−0.711284	−	0.410660i	−0.811536	+	0.584302i	$0.801368\pi$
$642$	−4.07164e8	+	2.35076e8i	−1.53874	+	0.888389i
$643$	3.12786e7	−	5.41762e7i	0.117656	−	0.203787i	−0.801182	−	0.598420i	$-0.795795\pi$
$643$	3.12786e7	−	5.41762e7i	0.117656	−	0.203787i	0.918838	+	0.394634i	$0.129129\pi$
$644$	9.19269e7	−	1.59222e8i	0.344179	−	0.596136i
$645$			7.65658e7i			0.285336i
$646$	5.72852e7	+	6.10685e7i	0.212493	+	0.226527i
$647$	−3.21796e7			−0.118814			−0.0594070	−	0.998234i	$-0.518921\pi$
$647$	−3.21796e7			−0.118814			−0.0594070	+	0.998234i	$0.518921\pi$
$648$	1.02536e8	+	5.91995e7i	0.376837	+	0.217567i
$649$	−2.05855e8	−	1.18851e8i	−0.753057	−	0.434778i
$650$	−3.93415e7	−	6.81414e7i	−0.143255	−	0.248125i
$651$	3.23007e8	−	5.59464e8i	1.17076	−	2.02782i
$652$	−1.32050e8	−	2.28718e8i	−0.476427	−	0.825196i
$653$	1.91169e8			0.686560			0.343280	−	0.939233i	$-0.388462\pi$
$653$	1.91169e8			0.686560			0.343280	+	0.939233i	$0.388462\pi$
$654$			7.53615e7i			0.269412i
$655$	1.16952e7	+	2.02566e7i	0.0416182	+	0.0720848i
$656$	3.66743e7	−	2.11739e7i	0.129912	−	0.0750049i
$657$	−5.68851e7			−0.200587
$658$		−	6.21459e7i		−	0.218140i
$659$	−3.25334e8	+	1.87832e8i	−1.13677	+	0.656316i	−0.945629	−	0.325246i	$-0.894553\pi$
$659$	−3.25334e8	+	1.87832e8i	−1.13677	+	0.656316i	−0.191143	+	0.981562i	$0.561219\pi$
$660$	−7.19239e7	−	4.15253e7i	−0.250174	−	0.144438i
$661$	−2.17399e8	+	1.25515e8i	−0.752754	+	0.434603i	−0.826688	−	0.562660i	$-0.809778\pi$
$661$	−2.17399e8	+	1.25515e8i	−0.752754	+	0.434603i	0.0739340	+	0.997263i	$0.476445\pi$
$662$	−7.71245e6	+	1.33584e7i	−0.0265839	+	0.0460446i
$663$	−8.61188e7	+	1.49162e8i	−0.295500	+	0.511821i
$664$		−	1.82726e8i		−	0.624160i
$665$	2.40824e8	+	7.28506e7i	0.818907	+	0.247724i
$666$	8.58565e7			0.290637
$667$	2.53514e8	+	1.46366e8i	0.854327	+	0.493246i
$668$	2.30486e8	+	1.33071e8i	0.773243	+	0.446432i
$669$	2.04269e8	+	3.53804e8i	0.682220	+	1.18164i
$670$	−4269.82	+	7395.55i	−1.41966e−5	+	2.45893e-5i
$671$	−1.15504e8	−	2.00059e8i	−0.382323	−	0.662203i
$672$	−7.49517e7			−0.246987
$673$			3.03615e8i			0.996043i	0.867165	+	0.498021i	$0.165940\pi$
$673$			3.03615e8i			0.996043i	−0.867165	+	0.498021i	$0.834060\pi$
$674$	1.45523e7	+	2.52053e7i	0.0475282	+	0.0823213i
$675$	4.74812e7	−	2.74133e7i	0.154387	−	0.0891353i
$676$	1.61721e7			0.0523512
$677$		−	2.89840e8i		−	0.934099i	−0.884231	−	0.467049i	$-0.845317\pi$
$677$		−	2.89840e8i		−	0.934099i	0.884231	−	0.467049i	$-0.154683\pi$
$678$	2.84852e8	−	1.64459e8i	0.913966	−	0.527679i
$679$	5.15858e8	+	2.97831e8i	1.64786	+	0.951394i
$680$	3.31495e7	−	1.91389e7i	0.105427	−	0.0608681i
$681$	2.20033e8	−	3.81109e8i	0.696702	−	1.20672i
$682$	−1.08214e8	+	1.87432e8i	−0.341137	+	0.590867i
$683$			5.99778e8i			1.88247i	0.337752	+	0.941235i	$0.390333\pi$
$683$			5.99778e8i			1.88247i	−0.337752	+	0.941235i	$0.609667\pi$
$684$	−9.78288e7	−	2.95938e7i	−0.305702	−	0.0924766i
$685$	−1.09476e8			−0.340603
$686$	−1.74512e8	−	1.00755e8i	−0.540572	−	0.312100i
$687$	3.67507e8	+	2.12181e8i	1.13343	+	0.654388i
$688$	−1.15748e7	−	2.00482e7i	−0.0355426	−	0.0615616i
$689$	−5.82380e7	+	1.00871e8i	−0.178053	+	0.308396i
$690$	−1.47019e8	−	2.54645e8i	−0.447535	−	0.775153i
$691$	−2.14374e7			−0.0649739			−0.0324869	−	0.999472i	$-0.510343\pi$
$691$	−2.14374e7			−0.0649739			−0.0324869	+	0.999472i	$0.510343\pi$
$692$			1.29984e8i			0.392258i
$693$	−6.67922e7	−	1.15687e8i	−0.200690	−	0.347606i
$694$	2.07751e8	−	1.19945e8i	0.621535	−	0.358843i
$695$	5.77356e7			0.171985
$696$		−	1.19338e8i		−	0.353958i
$697$	−7.72885e7	+	4.46225e7i	−0.228253	+	0.131782i
$698$	7.70691e7	+	4.44959e7i	0.226628	+	0.130844i
$699$	−2.50002e8	+	1.44339e8i	−0.732002	+	0.422622i
$700$	−3.60792e7	+	6.24910e7i	−0.105187	+	0.182190i
$701$	6.36766e7	−	1.10291e8i	0.184853	−	0.320174i	−0.758674	−	0.651470i	$-0.774152\pi$
$701$	6.36766e7	−	1.10291e8i	0.184853	−	0.320174i	0.943527	+	0.331296i	$0.107486\pi$
$702$			1.18896e8i			0.343680i
$703$	2.17678e8	−	5.09323e7i	0.626541	−	0.146598i
$704$	2.51103e7			0.0719671
$705$	−8.60745e7	−	4.96952e7i	−0.245645	−	0.141823i
$706$	−1.50277e8	−	8.67622e7i	−0.427049	−	0.246557i
$707$	−1.20464e8	−	2.08651e8i	−0.340879	−	0.590420i
$708$	−1.71542e8	+	2.97120e8i	−0.483361	+	0.837206i
$709$	1.61907e8	+	2.80431e8i	0.454283	+	0.786841i	0.998647	−	0.0520082i	$-0.0165622\pi$
$709$	1.61907e8	+	2.80431e8i	0.454283	+	0.786841i	−0.544364	+	0.838849i	$0.683229\pi$
$710$	2.01790e8			0.563799
$711$		−	3.46289e8i		−	0.963452i
$712$	1.74440e7	+	3.02139e7i	0.0483289	+	0.0837081i
$713$	−6.63597e8	+	3.83128e8i	−1.83078	+	1.05700i
$714$	1.57955e8			0.433950
$715$		−	1.73390e8i		−	0.474357i
$716$	1.05668e8	−	6.10075e7i	0.287876	−	0.166205i
$717$	3.47546e8	+	2.00656e8i	0.942876	+	0.544370i
$718$	−3.38522e7	+	1.95446e7i	−0.0914564	+	0.0528024i
$719$	6.37427e7	−	1.10406e8i	0.171492	−	0.297033i	−0.767450	−	0.641109i	$-0.778475\pi$
$719$	6.37427e7	−	1.10406e8i	0.171492	−	0.297033i	0.938942	+	0.344076i	$0.111808\pi$
$720$	−2.33619e7	+	4.04640e7i	−0.0625908	+	0.108410i
$721$			7.50875e8i			2.00337i
$722$	−2.65588e8	−	1.69967e7i	−0.705663	−	0.0451600i
$723$	−9.52790e8			−2.52106
$724$	9.86470e7	+	5.69539e7i	0.259937	+	0.150075i
$725$	−9.94983e7	−	5.74454e7i	−0.261097	−	0.150744i
$726$	−1.15782e8	−	2.00541e8i	−0.302575	−	0.524075i
$727$	1.67240e8	−	2.89668e8i	0.435247	−	0.753870i	−0.562069	−	0.827091i	$-0.689994\pi$
$727$	1.67240e8	−	2.89668e8i	0.435247	−	0.753870i	0.997316	+	0.0732203i	$0.0233276\pi$
$728$	−7.82405e7	−	1.35517e8i	−0.202786	−	0.351235i
$729$	7.52294e7			0.194180
$730$			6.77130e7i			0.174062i
$731$	2.43931e7	+	4.22501e7i	0.0624475	+	0.108162i
$732$	−2.88755e8	+	1.66712e8i	−0.736200	+	0.425045i
$733$	4.59843e8			1.16761			0.583804	−	0.811894i	$-0.301563\pi$
$733$	4.59843e8			1.16761			0.583804	+	0.811894i	$0.301563\pi$
$734$		−	1.00146e8i		−	0.253246i
$735$	6.59731e7	−	3.80896e7i	0.166152	−	0.0959278i
$736$	7.69917e7	+	4.44512e7i	0.193113	+	0.111494i
$737$	10224.2	−	5902.94i	2.55403e−5	−	1.47457e-5i
$738$	5.44686e7	−	9.43423e7i	0.135512	−	0.234713i
$739$	−1.67537e8	+	2.90183e8i	−0.415124	+	0.719016i	−0.995441	−	0.0953742i	$-0.969595\pi$
$739$	−1.67537e8	+	2.90183e8i	−0.415124	+	0.719016i	0.580317	+	0.814391i	$0.302929\pi$
$740$		−	1.02199e8i		−	0.252204i
$741$	−1.24721e8	−	5.33042e8i	−0.306539	−	1.31011i
$742$	1.06817e8			0.261475
$743$	6.11326e8	+	3.52949e8i	1.49041	+	0.860490i	0.999940	−	0.0109662i	$-0.00349073\pi$
$743$	6.11326e8	+	3.52949e8i	1.49041	+	0.860490i	0.490473	+	0.871456i	$0.336824\pi$
$744$	2.70529e8	+	1.56190e8i	0.656893	+	0.379257i
$745$	−2.51704e8	−	4.35963e8i	−0.608724	−	1.05434i
$746$	2.07806e8	−	3.59931e8i	0.500544	−	0.866968i
$747$	−2.35025e8	−	4.07076e8i	−0.563836	−	0.976593i
$748$	−5.29182e7			−0.126445
$749$			9.00171e8i			2.14230i
$750$	2.07379e8	+	3.59191e8i	0.491565	+	0.851415i
$751$	4.48860e8	−	2.59150e8i	1.05972	−	0.611830i	0.134366	−	0.990932i	$-0.457100\pi$
$751$	4.48860e8	−	2.59150e8i	1.05972	−	0.611830i	0.925355	+	0.379102i	$0.123767\pi$
$752$	3.00506e7			0.0706643
$753$			2.70739e8i			0.634112i
$754$	2.15770e8	−	1.24575e8i	0.503358	−	0.290614i
$755$	2.35462e8	+	1.35944e8i	0.547118	+	0.315879i
$756$	9.44284e7	−	5.45183e7i	0.218543	−	0.126176i
$757$	2.04372e8	−	3.53982e8i	0.471122	−	0.816007i	−0.528332	−	0.849038i	$-0.677183\pi$
$757$	2.04372e8	−	3.53982e8i	0.471122	−	0.816007i	0.999454	+	0.0330305i	$0.0105158\pi$
$758$	−557306.	+	965282.i	−0.00127963	+	0.00221639i
$759$			4.06502e8i			0.929689i
$760$	−3.52269e7	+	1.16450e8i	−0.0802478	+	0.265277i
$761$	−5.78579e8			−1.31283			−0.656416	−	0.754399i	$-0.727928\pi$
$761$	−5.78579e8			−1.31283			−0.656416	+	0.754399i	$0.727928\pi$
$762$	5.75229e7	+	3.32109e7i	0.130010	+	0.0750611i
$763$	1.24959e8	+	7.21450e7i	0.281315	+	0.162418i
$764$	7.78411e7	+	1.34825e8i	0.174554	+	0.302336i
$765$	4.92335e7	−	8.52749e7i	0.109971	−	0.190475i
$766$	−2.92267e8	−	5.06222e8i	−0.650270	−	1.12630i
$767$	−7.16279e8			−1.58744
$768$		−	3.62428e7i		−	0.0800089i
$769$	7.26036e7	+	1.25753e8i	0.159654	+	0.276528i	0.934744	−	0.355322i	$-0.115629\pi$
$769$	7.26036e7	+	1.25753e8i	0.159654	+	0.276528i	−0.775090	+	0.631851i	$0.782296\pi$
$770$	−1.37708e8	+	7.95059e7i	−0.301639	+	0.174152i
$771$	7.45957e8			1.62761
$772$			1.54268e8i			0.335293i
$773$	1.70422e8	−	9.83934e7i	0.368967	−	0.213023i	−0.304040	−	0.952659i	$-0.598336\pi$
$773$	1.70422e8	−	9.83934e7i	0.368967	−	0.213023i	0.673007	+	0.739636i	$0.265002\pi$
$774$	−5.15727e7	−	2.97755e7i	−0.111224	−	0.0642150i
$775$	2.60447e8	−	1.50369e8i	0.559518	−	0.323038i
$776$	−1.44016e8	+	2.49443e8i	−0.308195	+	0.533809i
$777$	2.10865e8	−	3.65229e8i	0.449512	−	0.778578i
$778$		−	3.12465e8i		−	0.663533i
$779$	8.21319e7	−	2.71505e8i	0.173740	−	0.574336i
$780$	−2.50261e8			−0.527363
$781$	−2.41596e8	−	1.39485e8i	−0.507150	−	0.292803i
$782$	−1.62255e8	−	9.36778e7i	−0.339295	−	0.195892i
$783$	8.68041e7	+	1.50349e8i	0.180824	+	0.313196i
$784$	−1.15164e7	+	1.99469e7i	−0.0238983	+	0.0413931i
$785$	2.65053e8	+	4.59085e8i	0.547928	+	0.949040i
$786$	−4.66730e7			−0.0961166
$787$		−	2.82755e8i		−	0.580078i	−0.957015	−	0.290039i	$-0.906332\pi$
$787$		−	2.82755e8i		−	0.580078i	0.957015	−	0.290039i	$-0.0936683\pi$
$788$	2.12560e7	+	3.68165e7i	0.0434413	+	0.0752426i
$789$	−6.56614e8	+	3.79096e8i	−1.33684	+	0.771824i
$790$	−4.12204e8			−0.836048
$791$		−	6.29761e8i		−	1.27247i
$792$	5.59406e7	−	3.22973e7i	0.112603	−	0.0650116i
$793$	−6.02850e8	−	3.48056e8i	−1.20890	−	0.697958i
$794$	4.76737e8	−	2.75244e8i	0.952396	−	0.549866i
$795$	8.54169e7	−	1.47946e8i	0.169998	−	0.294444i
$796$	1.61625e8	−	2.79943e8i	0.320457	−	0.555048i
$797$		−	1.78281e6i		−	0.00352152i	−0.999998	−	0.00176076i	$-0.999440\pi$
$797$		−	1.78281e6i		−	0.00352152i	0.999998	−	0.00176076i	$-0.000560468\pi$
$798$	−3.66160e8	+	3.43476e8i	−0.720546	+	0.675908i
$799$	−6.33296e7			−0.124156
$800$	−3.02175e7	−	1.74461e7i	−0.0590185	−	0.0340744i
$801$	7.77234e7	+	4.48736e7i	0.151236	+	0.0873160i
$802$	−1.28030e8	−	2.21755e8i	−0.248193	−	0.429882i
$803$	4.68059e7	−	8.10702e7i	0.0903970	−	0.156572i
$804$	−8519.98	−	14757.0i	−1.63935e−5	−	2.83943e-5i
$805$	−5.62977e8			−1.07920
$806$			6.52173e8i			1.24554i
$807$	−4.73284e7	−	8.19752e7i	−0.0900537	−	0.155978i
$808$	1.00893e8	−	5.82505e7i	0.191261	−	0.110425i
$809$	1.54678e8			0.292134			0.146067	−	0.989275i	$-0.453338\pi$
$809$	1.54678e8			0.292134			0.146067	+	0.989275i	$0.453338\pi$
$810$		−	3.62548e8i		−	0.682199i
$811$	6.71891e8	−	3.87916e8i	1.25961	−	0.727236i	0.286611	−	0.958047i	$-0.407471\pi$
$811$	6.71891e8	−	3.87916e8i	1.25961	−	0.727236i	0.972999	+	0.230811i	$0.0741378\pi$
$812$	−1.97878e8	−	1.14245e8i	−0.369597	−	0.213387i
$813$	−4.41296e8	+	2.54782e8i	−0.821218	+	0.474130i
$814$	−7.06440e7	+	1.22359e8i	−0.130979	+	0.226863i
$815$	−4.04350e8	+	7.00355e8i	−0.746938	+	1.29373i
$816$			7.63792e7i			0.140574i
$817$	−1.48420e8	−	4.48978e7i	−0.272161	−	0.0823302i
$818$	1.42680e8			0.260678
$819$	−3.48608e8	−	2.01269e8i	−0.634578	−	0.366374i
$820$	−1.12300e8	−	6.48365e7i	−0.203675	−	0.117592i
$821$	−3.71496e7	−	6.43450e7i	−0.0671312	−	0.116275i	0.830506	−	0.557009i	$-0.188051\pi$
$821$	−3.71496e7	−	6.43450e7i	−0.0671312	−	0.116275i	−0.897637	+	0.440735i	$0.854718\pi$
$822$	1.09224e8	−	1.89182e8i	0.196655	−	0.340616i
$823$	−1.46809e8	−	2.54280e8i	−0.263361	−	0.456155i	0.703772	−	0.710426i	$-0.251498\pi$
$823$	−1.46809e8	−	2.54280e8i	−0.263361	−	0.456155i	−0.967133	+	0.254271i	$0.918164\pi$
$824$	−3.63085e8			−0.648973
$825$		−	1.59543e8i		−	0.284129i
$826$	3.28442e8	+	5.68878e8i	0.582798	+	1.00944i
$827$	2.74468e8	−	1.58464e8i	0.485261	−	0.280165i	−0.237345	−	0.971425i	$-0.576277\pi$
$827$	2.74468e8	−	1.58464e8i	0.485261	−	0.280165i	0.722606	+	0.691260i	$0.242944\pi$
$828$	2.28696e8			0.402872
$829$		−	4.41458e8i		−	0.774865i	−0.921898	−	0.387432i	$-0.873362\pi$
$829$		−	4.41458e8i		−	0.774865i	0.921898	−	0.387432i	$-0.126638\pi$
$830$	−4.84562e8	+	2.79762e8i	−0.847451	+	0.489276i
$831$	2.11976e8	+	1.22384e8i	0.369388	+	0.213266i
$832$	6.55290e7	−	3.78332e7i	0.113779	−	0.0656905i
$833$	2.42699e7	−	4.20368e7i	0.0419888	−	0.0727268i
$834$	−5.76027e7	+	9.97708e7i	−0.0992990	+	0.171991i
$835$		−	8.14954e8i		−	1.39982i
$836$	1.22671e8	−	1.15071e8i	0.209953	−	0.196946i
$837$	−4.54437e8			−0.774991
$838$	−1.57782e7	−	9.10955e6i	−0.0268118	−	0.0154798i
$839$	−9.16524e8	−	5.29155e8i	−1.55188	−	0.895978i	−0.997989	−	0.0633883i	$-0.979809\pi$
$839$	−9.16524e8	−	5.29155e8i	−1.55188	−	0.895978i	−0.553890	−	0.832590i	$-0.686857\pi$
$840$	1.14754e8	+	1.98761e8i	0.193612	+	0.335345i
$841$	−1.15511e8	+	2.00071e8i	−0.194194	+	0.336353i
$842$	2.47316e8	+	4.28363e8i	0.414300	+	0.717589i
$843$	4.40698e8			0.735628
$844$			2.87803e8i			0.478705i
$845$	−2.47603e7	−	4.28861e7i	−0.0410379	−	0.0710798i
$846$	6.69466e7	−	3.86517e7i	0.110565	−	0.0638347i
$847$	−4.43363e8			−0.729640
$848$			5.16515e7i			0.0847024i
$849$	6.70488e8	−	3.87107e8i	1.09564	−	0.632569i
$850$	6.36812e7	+	3.67664e7i	0.103694	+	0.0598679i
$851$	−4.33209e8	+	2.50113e8i	−0.702925	+	0.405834i
$852$	−2.01325e8	+	3.48706e8i	−0.325522	+	0.563820i
$853$	−3.27227e7	+	5.66773e7i	−0.0527232	+	0.0913193i	−0.891183	−	0.453645i	$-0.850123\pi$
$853$	−3.27227e7	+	5.66773e7i	−0.0527232	+	0.0913193i	0.838459	+	0.544964i	$0.183457\pi$
$854$			6.38388e8i			1.02497i
$855$	7.13021e7	+	3.04737e8i	0.114079	+	0.487558i
$856$	−4.35277e8			−0.693977
$857$	7.72031e8	+	4.45732e8i	1.22657	+	0.708160i	0.966311	−	0.257379i	$-0.0828588\pi$
$857$	7.72031e8	+	4.45732e8i	1.22657	+	0.708160i	0.260259	+	0.965539i	$0.416192\pi$
$858$	2.99628e8	+	1.72990e8i	0.474374	+	0.273880i
$859$	−4.16670e8	−	7.21693e8i	−0.657374	−	1.13861i	−0.981293	−	0.192520i	$-0.938334\pi$
$859$	−4.16670e8	−	7.21693e8i	−0.657374	−	1.13861i	0.323919	−	0.946085i	$-0.394999\pi$
$860$	−3.54432e7	+	6.13894e7i	−0.0557234	+	0.0965157i
$861$	−2.67552e8	−	4.63413e8i	−0.419178	−	0.726037i
$862$	4.25523e8			0.664356
$863$		−	1.04154e9i		−	1.62049i	−0.586095	−	0.810243i	$-0.699335\pi$
$863$		−	1.04154e9i		−	1.62049i	0.586095	−	0.810243i	$-0.300665\pi$
$864$	2.63623e7	+	4.56608e7i	0.0408735	+	0.0707950i
$865$	3.44698e8	−	1.99012e8i	0.532587	−	0.307489i
$866$	6.91500e8			1.06473
$867$			6.73324e8i			1.03316i
$868$	5.17964e8	−	2.99047e8i	0.792028	−	0.457278i
$869$	4.93517e8	+	2.84932e8i	0.752043	+	0.434192i
$870$	−3.16467e8	+	1.82712e8i	−0.480586	+	0.277466i
$871$	17787.7	−	30809.2i	2.69194e−5	−	4.66257e-5i
$872$	−3.48857e7	+	6.04238e7i	−0.0526136	+	0.0911294i
$873$			7.40943e8i			1.11363i
$874$	5.79830e8	−	1.35668e8i	0.868492	−	0.203209i
$875$	7.94111e8			1.18538
$876$	−1.17012e8	−	6.75571e7i	−0.174068	−	0.100498i
$877$	−3.83002e8	−	2.21126e8i	−0.567809	−	0.327825i	0.188465	−	0.982080i	$-0.439649\pi$
$877$	−3.83002e8	−	2.21126e8i	−0.567809	−	0.327825i	−0.756274	+	0.654255i	$0.772982\pi$
$878$	−2.59078e8	−	4.48736e8i	−0.382778	−	0.662990i
$879$	−6.62973e8	+	1.14830e9i	−0.976178	+	1.69079i
$880$	−3.84450e7	−	6.65888e7i	−0.0564147	−	0.0977131i
$881$	1.29224e9			1.88980			0.944900	−	0.327358i	$-0.106158\pi$
$881$	1.29224e9			1.88980			0.944900	+	0.327358i	$0.106158\pi$
$882$			5.92503e7i			0.0863544i
$883$	5.67681e8	+	9.83253e8i	0.824560	+	1.42818i	0.902255	+	0.431203i	$0.141911\pi$
$883$	5.67681e8	+	9.83253e8i	0.824560	+	1.42818i	−0.0776943	+	0.996977i	$0.524756\pi$
$884$	−1.38098e8	+	7.97307e7i	−0.199908	+	0.115417i
$885$	1.05056e9			1.51562
$886$		−	3.18161e8i		−	0.457452i
$887$	−9.46040e8	+	5.46197e8i	−1.35562	+	0.782669i	−0.989030	−	0.147713i	$-0.952809\pi$
$887$	−9.46040e8	+	5.46197e8i	−1.35562	+	0.782669i	−0.366592	+	0.930382i	$0.619476\pi$
$888$	1.76606e8	+	1.01964e8i	0.252213	+	0.145615i
$889$	1.10136e8	−	6.35868e7i	0.156755	−	0.0905027i
$890$	5.34152e7	−	9.25179e7i	0.0757696	−	0.131237i
$891$	−2.50608e8	+	4.34066e8i	−0.354292	+	0.613652i
$892$			3.78234e8i			0.532925i
$893$	1.46806e8	−	1.37711e8i	0.206152	−	0.193381i
$894$	1.00450e9			1.40584
$895$	−3.23566e8	−	1.86811e8i	−0.451329	−	0.260575i
$896$	−6.00952e7	−	3.46960e7i	−0.0835441	−	0.0482342i
$897$	6.12468e8	+	1.06083e9i	0.848606	+	1.46983i
$898$	2.06171e7	−	3.57099e7i	0.0284707	−	0.0493127i
$899$	4.76143e8	+	8.24704e8i	0.655328	+	1.13506i
$900$	−8.97579e7			−0.123125
$901$		−	1.08852e8i		−	0.148820i
$902$	8.96352e7	+	1.55253e8i	0.122140	+	0.211553i
$903$	−2.53327e8	+	1.46258e8i	−0.344047	+	0.198636i
$904$	3.04520e8			0.412203
$905$		−	3.48796e8i		−	0.470572i
$906$	−4.69841e8	+	2.71263e8i	−0.631780	+	0.364758i
$907$	8.42015e8	+	4.86138e8i	1.12849	+	0.651534i	0.943555	−	0.331216i	$-0.107459\pi$
$907$	8.42015e8	+	4.86138e8i	1.12849	+	0.651534i	0.184936	+	0.982751i	$0.440792\pi$
$908$	3.52839e8	−	2.03712e8i	0.471324	−	0.272119i
$909$	1.49846e8	−	2.59540e8i	0.199505	−	0.345552i
$910$	−2.39580e8	+	4.14964e8i	−0.317926	+	0.550664i
$911$		−	7.04468e8i		−	0.931765i	−0.884847	−	0.465882i	$-0.845737\pi$
$911$		−	7.04468e8i		−	0.931765i	0.884847	−	0.465882i	$-0.154263\pi$
$912$	−1.66088e8	−	1.77056e8i	−0.218954	−	0.233414i
$913$	7.73530e8			1.01640
$914$	−7.93374e8	−	4.58055e8i	−1.03906	−	0.599900i
$915$	8.84193e8	+	5.10489e8i	1.15421	+	0.666382i
$916$	1.96441e8	+	3.40247e8i	0.255592	+	0.442698i
$917$	−4.46810e7	+	7.73897e7i	−0.0579448	+	0.100363i
$918$	−5.55566e7	−	9.62269e7i	−0.0718138	−	0.124385i
$919$	−9.44419e8			−1.21680			−0.608398	−	0.793632i	$-0.708188\pi$
$919$	−9.44419e8			−1.21680			−0.608398	+	0.793632i	$0.708188\pi$
$920$		−	2.72227e8i		−	0.349598i
$921$	−9.48831e8	−	1.64342e9i	−1.21454	−	2.10364i
$922$	−4.23664e8	+	2.44603e8i	−0.540542	+	0.312082i
$923$	−8.40638e8			−1.06906
$924$		−	3.17291e8i		−	0.402200i
$925$	1.70025e8	−	9.81638e7i	0.214826	−	0.124030i
$926$	−2.66888e8	−	1.54088e8i	−0.336121	−	0.194060i
$927$	−8.08879e8	+	4.67007e8i	−1.01542	+	0.586251i
$928$	5.52430e7	−	9.56837e7i	0.0691247	−	0.119728i
$929$	4.66430e8	−	8.07881e8i	0.581754	−	1.00763i	−0.413517	−	0.910496i	$-0.635700\pi$
$929$	4.66430e8	−	8.07881e8i	0.581754	−	1.00763i	0.995272	−	0.0971315i	$-0.0309667\pi$
$930$		−	9.56535e8i		−	1.18919i
$931$	3.51488e7	+	1.50222e8i	0.0435573	+	0.186159i
$932$	−2.67264e8			−0.330136
$933$	−1.22264e9	−	7.05889e8i	−1.50540	−	0.869143i
$934$	−7.08679e8	−	4.09156e8i	−0.869779	−	0.502167i
$935$	8.10202e7	+	1.40331e8i	0.0991194	+	0.171680i
$936$	9.73234e7	−	1.68569e8i	0.118683	−	0.205566i
$937$	1.09142e8	+	1.89040e8i	0.132671	+	0.229792i	0.924705	−	0.380684i	$-0.124311\pi$
$937$	1.09142e8	+	1.89040e8i	0.132671	+	0.229792i	−0.792035	+	0.610476i	$0.790978\pi$
$938$	−32625.4			−3.95318e−5
$939$		−	3.76088e8i		−	0.454247i
$940$	−4.60089e7	−	7.96897e7i	−0.0553934	−	0.0959442i
$941$	4.61540e6	−	2.66470e6i	0.00553912	−	0.00319801i	−0.497228	−	0.867620i	$-0.665649\pi$
$941$	4.61540e6	−	2.66470e6i	0.00553912	−	0.00319801i	0.502767	+	0.864422i	$0.332315\pi$
$942$	−1.05777e9			−1.26543
$943$			6.34702e8i			0.756894i
$944$	−2.75081e8	+	1.58818e8i	−0.326997	+	0.188792i
$945$	−2.89149e8	−	1.66940e8i	−0.342630	−	0.197818i
$946$	8.48696e7	−	4.89995e7i	0.100249	−	0.0578786i
$947$	−6.46029e8	+	1.11896e9i	−0.760680	+	1.31754i	0.181820	+	0.983332i	$0.441801\pi$
$947$	−6.46029e8	+	1.11896e9i	−0.760680	+	1.31754i	−0.942500	+	0.334205i	$0.891532\pi$
$948$	4.11255e8	−	7.12315e8i	0.482710	−	0.836079i
$949$		−	2.82086e8i		−	0.330052i
$950$	−2.27570e8	+	5.32467e7i	−0.265426	+	0.0621043i
$951$	1.29913e9			1.51047
$952$	1.26646e8	+	7.31193e7i	0.146785	+	0.0847464i
$953$	4.62151e8	+	2.66823e8i	0.533955	+	0.308279i	0.742626	−	0.669707i	$-0.233580\pi$
$953$	4.62151e8	+	2.66823e8i	0.533955	+	0.308279i	−0.208670	+	0.977986i	$0.566914\pi$
$954$	6.64352e7	+	1.15069e8i	0.0765161	+	0.132530i
$955$	2.38357e8	−	4.12846e8i	0.273664	−	0.474000i
$956$	1.85771e8	+	3.21766e8i	0.212621	+	0.368270i
$957$	5.05192e8			0.576396
$958$		−	1.02591e8i		−	0.116685i
$959$	−2.09125e8	−	3.62215e8i	−0.237110	−	0.410687i
$960$	−9.61106e7	+	5.54895e7i	−0.108632	+	0.0627187i
$961$	−1.60520e9			−1.80867
$962$			4.25751e8i			0.478223i
$963$	−9.69709e8	+	5.59862e8i	−1.08583	+	0.626905i
$964$	−7.63934e8	−	4.41057e8i	−0.852756	−	0.492339i
$965$	4.09096e8	−	2.36192e8i	0.455243	−	0.262835i
$966$	5.61681e8	−	9.72860e8i	0.623101	−	1.07924i
$967$	−3.95518e8	+	6.85058e8i	−0.437408	+	0.757614i	−0.997489	−	0.0708247i	$-0.977437\pi$
$967$	−3.95518e8	+	6.85058e8i	−0.437408	+	0.757614i	0.560080	+	0.828438i	$0.310770\pi$
$968$		−	2.14388e8i		−	0.236360i
$969$	3.50018e8	+	3.73134e8i	0.384697	+	0.410103i
$970$	8.81980e8			0.966370
$971$	3.04422e8	+	1.75758e8i	0.332520	+	0.191981i	0.656960	−	0.753926i	$-0.271842\pi$
$971$	3.04422e8	+	1.75758e8i	0.332520	+	0.191981i	−0.324439	+	0.945907i	$0.605176\pi$
$972$	4.42622e8	+	2.55548e8i	0.481985	+	0.278274i
$973$	1.10288e8	+	1.91025e8i	0.119727	+	0.207373i
$974$	−2.48233e8	+	4.29952e8i	−0.268647	+	0.465311i
$975$	−2.40380e8	−	4.16350e8i	−0.259349	−	0.449205i
$976$	−3.08692e8			−0.332029
$977$		−	5.43141e8i		−	0.582410i	−0.956661	−	0.291205i	$-0.905944\pi$
$977$		−	5.43141e8i		−	0.582410i	0.956661	−	0.291205i	$-0.0940562\pi$
$978$	−8.06838e8	−	1.39748e9i	−0.862521	−	1.49393i
$979$	−1.27904e8	+	7.38455e7i	−0.136313	+	0.0787002i
$980$	7.05284e7			0.0749352
$981$			1.79482e8i			0.190114i
$982$	−3.87914e8	+	2.23962e8i	−0.409639	+	0.236505i
$983$	−6.57507e8	−	3.79612e8i	−0.692214	−	0.399650i	0.112227	−	0.993683i	$-0.464202\pi$
$983$	−6.57507e8	−	3.79612e8i	−0.692214	−	0.399650i	−0.804441	+	0.594033i	$0.797535\pi$
$984$	2.24083e8	−	1.29374e8i	0.235193	−	0.135789i
$985$	6.50878e7	−	1.12735e8i	0.0681069	−	0.117965i
$986$	−1.16421e8	+	2.01647e8i	−0.121451	+	0.210359i
$987$		−	3.79717e8i		−	0.394919i
$988$	1.46752e8	−	4.85121e8i	0.152164	−	0.503013i
$989$	3.46963e8			0.358669
$990$	−1.71295e8	−	9.88974e7i	−0.176539	−	0.101925i
$991$	3.79972e8	+	2.19377e8i	0.390418	+	0.225408i	0.682341	−	0.731034i	$-0.260962\pi$
$991$	3.79972e8	+	2.19377e8i	0.390418	+	0.225408i	−0.291923	+	0.956442i	$0.594295\pi$
$992$	1.44604e8	+	2.50461e8i	0.148131	+	0.256570i
$993$	−4.71237e7	+	8.16207e7i	−0.0481273	+	0.0833590i
$994$	3.85465e8	+	6.67646e8i	0.392488	+	0.679809i
$995$	−9.89823e8			−1.00482
$996$		−	1.11647e9i		−	1.12998i
$997$	5.18144e8	+	8.97452e8i	0.522836	+	0.905578i	0.999647	+	0.0265724i	$0.00845925\pi$
$997$	5.18144e8	+	8.97452e8i	0.522836	+	0.905578i	−0.476811	+	0.879006i	$0.658207\pi$
$998$	5.32734e8	−	3.07574e8i	0.535944	−	0.309427i
$999$	−2.96665e8			−0.297557

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.7.d.a.27.10	✓	20
3.2	odd	2		342.7.m.a.217.2		20
19.12	odd	6	inner	38.7.d.a.31.10	yes	20
57.50	even	6		342.7.m.a.145.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.7.d.a.27.10	✓	20	1.1	even	1	trivial
38.7.d.a.31.10	yes	20	19.12	odd	6	inner
342.7.m.a.145.2		20	57.50	even	6
342.7.m.a.217.2		20	3.2	odd	2

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	38.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.89898 + 2.82843i) q^{2} +(29.9332 + 17.2819i) q^{3} +(16.0000 + 27.7128i) q^{4} +(48.9935 - 84.8592i) q^{5} +(97.7614 + 169.328i) q^{6} +374.355 q^{7} +181.019i q^{8} +(232.830 + 403.274i) q^{9} +O(q^{10})\)	\(q+(4.89898 + 2.82843i) q^{2} +(29.9332 + 17.2819i) q^{3} +(16.0000 + 27.7128i) q^{4} +(48.9935 - 84.8592i) q^{5} +(97.7614 + 169.328i) q^{6} +374.355 q^{7} +181.019i q^{8} +(232.830 + 403.274i) q^{9} +(480.036 - 277.149i) q^{10} -766.306 q^{11} +1106.04i q^{12} +(-1999.79 + 1154.58i) q^{13} +(1833.96 + 1058.84i) q^{14} +(2933.06 - 1693.40i) q^{15} +(-512.000 + 886.810i) q^{16} +(1079.00 - 1868.89i) q^{17} +2634.17i q^{18} +(1562.66 + 6678.62i) q^{19} +3135.58 q^{20} +(11205.6 + 6469.58i) q^{21} +(-3754.12 - 2167.44i) q^{22} +(-7673.77 - 13291.4i) q^{23} +(-3128.36 + 5418.49i) q^{24} +(3011.78 + 5216.55i) q^{25} -13062.5 q^{26} -9102.02i q^{27} +(5989.69 + 10374.4i) q^{28} +(-16518.2 + 9536.79i) q^{29} +19158.7 q^{30} -49927.0i q^{31} +(-5016.55 + 2896.31i) q^{32} +(-22938.0 - 13243.2i) q^{33} +(10572.0 - 6103.77i) q^{34} +(18341.0 - 31767.5i) q^{35} +(-7450.57 + 12904.8i) q^{36} -32593.3i q^{37} +(-11234.5 + 37138.3i) q^{38} -79813.3 q^{39} +(15361.2 + 8868.77i) q^{40} +(-35814.8 - 20677.7i) q^{41} +(36597.5 + 63388.7i) q^{42} +(-11303.5 + 19578.3i) q^{43} +(-12260.9 - 21236.5i) q^{44} +45628.7 q^{45} -86818.8i q^{46} +(-14673.2 - 25414.6i) q^{47} +(-30651.6 + 17696.7i) q^{48} +22492.9 q^{49} +34074.4i q^{50} +(64596.0 - 37294.5i) q^{51} +(-63993.1 - 36946.4i) q^{52} +(43683.2 - 25220.5i) q^{53} +(25744.4 - 44590.6i) q^{54} +(-37544.0 + 65028.1i) q^{55} +67765.6i q^{56} +(-68644.1 + 226918. i) q^{57} -107896. q^{58} +(268633. + 155096. i) q^{59} +(93858.0 + 54188.9i) q^{60} +(150729. + 261070. i) q^{61} +(141215. - 244591. i) q^{62} +(87161.3 + 150968. i) q^{63} -32768.0 q^{64} +226267. i q^{65} +(-74915.1 - 129757. i) q^{66} +(-13.3422 + 7.70312i) q^{67} +69056.2 q^{68} -530470. i q^{69} +(179704. - 103752. i) q^{70} +(315273. + 182023. i) q^{71} +(-73000.4 + 42146.8i) q^{72} +(-61079.9 + 105794. i) q^{73} +(92187.8 - 159674. i) q^{74} +208197. i q^{75} +(-160081. + 150164. i) q^{76} -286871. q^{77} +(-391003. - 225746. i) q^{78} +(-644021. - 371826. i) q^{79} +(50169.3 + 86895.8i) q^{80} +(327034. - 566439. i) q^{81} +(-116970. - 202599. i) q^{82} -1.00943e6 q^{83} +414053. i q^{84} +(-105728. - 183127. i) q^{85} +(-110752. + 63942.5i) q^{86} -659257. q^{87} -138716. i q^{88} +(166910. - 96365.5i) q^{89} +(223534. + 129057. i) q^{90} +(-748630. + 432222. i) q^{91} +(245561. - 425323. i) q^{92} +(862835. - 1.49447e6i) q^{93} -166008. i q^{94} +(643303. + 194603. i) q^{95} -200215. q^{96} +(1.37799e6 + 795583. i) q^{97} +(110192. + 63619.6i) q^{98} +(-178419. - 309031. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 30 q^{3} + 320 q^{4} + 112 q^{5} + 80 q^{6} - 208 q^{7} + 2200 q^{9}+O(q^{10}) \) 20 * q - 30 * q^3 + 320 * q^4 + 112 * q^5 + 80 * q^6 - 208 * q^7 + 2200 * q^9	\( 20 q - 30 q^{3} + 320 q^{4} + 112 q^{5} + 80 q^{6} - 208 q^{7} + 2200 q^{9} - 284 q^{11} + 10500 q^{13} + 1248 q^{14} + 14136 q^{15} - 10240 q^{16} - 11684 q^{17} + 12862 q^{19} + 7168 q^{20} + 2916 q^{21} + 52704 q^{22} + 8488 q^{23} - 2560 q^{24} - 63842 q^{25} - 43968 q^{26} - 3328 q^{28} + 137760 q^{29} - 94688 q^{30} - 250194 q^{33} + 70560 q^{34} - 6916 q^{35} - 70400 q^{36} - 77232 q^{38} + 9672 q^{39} + 109206 q^{41} - 92672 q^{42} + 35572 q^{43} - 4544 q^{44} + 131264 q^{45} - 361184 q^{47} + 30720 q^{48} + 259740 q^{49} - 496512 q^{51} + 336000 q^{52} - 236172 q^{53} + 375728 q^{54} + 56760 q^{55} + 314796 q^{57} - 225600 q^{58} + 1310610 q^{59} + 452352 q^{60} + 83552 q^{61} + 225792 q^{62} + 553364 q^{63} - 655360 q^{64} - 4736 q^{66} + 806646 q^{67} - 747776 q^{68} - 245664 q^{70} - 869220 q^{71} + 353280 q^{72} - 207422 q^{73} + 1460832 q^{74} - 140096 q^{76} - 3988336 q^{77} - 85008 q^{78} - 1706808 q^{79} + 114688 q^{80} + 2303170 q^{81} + 887712 q^{82} + 3527548 q^{83} - 5604 q^{85} + 195792 q^{86} - 8414832 q^{87} + 708432 q^{89} - 4483104 q^{90} - 1914384 q^{91} - 271616 q^{92} + 3537876 q^{93} - 2820356 q^{95} - 163840 q^{96} + 5113242 q^{97} - 612480 q^{98} + 603704 q^{99}+O(q^{100}) \) 20 * q - 30 * q^3 + 320 * q^4 + 112 * q^5 + 80 * q^6 - 208 * q^7 + 2200 * q^9 - 284 * q^11 + 10500 * q^13 + 1248 * q^14 + 14136 * q^15 - 10240 * q^16 - 11684 * q^17 + 12862 * q^19 + 7168 * q^20 + 2916 * q^21 + 52704 * q^22 + 8488 * q^23 - 2560 * q^24 - 63842 * q^25 - 43968 * q^26 - 3328 * q^28 + 137760 * q^29 - 94688 * q^30 - 250194 * q^33 + 70560 * q^34 - 6916 * q^35 - 70400 * q^36 - 77232 * q^38 + 9672 * q^39 + 109206 * q^41 - 92672 * q^42 + 35572 * q^43 - 4544 * q^44 + 131264 * q^45 - 361184 * q^47 + 30720 * q^48 + 259740 * q^49 - 496512 * q^51 + 336000 * q^52 - 236172 * q^53 + 375728 * q^54 + 56760 * q^55 + 314796 * q^57 - 225600 * q^58 + 1310610 * q^59 + 452352 * q^60 + 83552 * q^61 + 225792 * q^62 + 553364 * q^63 - 655360 * q^64 - 4736 * q^66 + 806646 * q^67 - 747776 * q^68 - 245664 * q^70 - 869220 * q^71 + 353280 * q^72 - 207422 * q^73 + 1460832 * q^74 - 140096 * q^76 - 3988336 * q^77 - 85008 * q^78 - 1706808 * q^79 + 114688 * q^80 + 2303170 * q^81 + 887712 * q^82 + 3527548 * q^83 - 5604 * q^85 + 195792 * q^86 - 8414832 * q^87 + 708432 * q^89 - 4483104 * q^90 - 1914384 * q^91 - 271616 * q^92 + 3537876 * q^93 - 2820356 * q^95 - 163840 * q^96 + 5113242 * q^97 - 612480 * q^98 + 603704 * q^99

Introduction

L-functions

Modular forms

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