LMFDB - Embedded newform 60.7.l.a.23.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(23,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

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

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

chi := DirichletCharacter("60.23");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.l (of order $4$, 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:	$13.8032450172$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.3
Character	$\chi$	$=$	60.23
Dual form			60.7.l.a.47.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.93034 + 1.05340i) q^{2} +(-26.8514 + 2.82881i) q^{3} +(61.7807 - 16.7077i) q^{4} +(-46.5899 - 115.993i) q^{5} +(209.961 - 50.7188i) q^{6} +(112.704 + 112.704i) q^{7} +(-472.342 + 197.578i) q^{8} +(712.996 - 151.915i) q^{9} +O(q^{10})$	\(q+(-7.93034 + 1.05340i) q^{2} +(-26.8514 + 2.82881i) q^{3} +(61.7807 - 16.7077i) q^{4} +(-46.5899 - 115.993i) q^{5} +(209.961 - 50.7188i) q^{6} +(112.704 + 112.704i) q^{7} +(-472.342 + 197.578i) q^{8} +(712.996 - 151.915i) q^{9} +(491.661 + 870.787i) q^{10} +1619.37 q^{11} +(-1611.63 + 623.392i) q^{12} +(641.254 + 641.254i) q^{13} +(-1012.50 - 775.057i) q^{14} +(1579.13 + 2982.78i) q^{15} +(3537.70 - 2064.43i) q^{16} +(-6059.51 - 6059.51i) q^{17} +(-5494.27 + 1955.81i) q^{18} -3857.33 q^{19} +(-4816.33 - 6387.72i) q^{20} +(-3345.07 - 2707.44i) q^{21} +(-12842.2 + 1705.85i) q^{22} +(1099.49 + 1099.49i) q^{23} +(12124.1 - 6641.41i) q^{24} +(-11283.8 + 10808.2i) q^{25} +(-5760.87 - 4409.87i) q^{26} +(-18715.2 + 6096.07i) q^{27} +(8845.93 + 5079.89i) q^{28} -27168.3 q^{29} +(-15665.1 - 21991.0i) q^{30} -19172.8i q^{31} +(-25880.5 + 20098.3i) q^{32} +(-43482.3 + 4580.89i) q^{33} +(54437.1 + 41670.9i) q^{34} +(7821.99 - 18323.7i) q^{35} +(41511.2 - 21298.0i) q^{36} +(36140.9 - 36140.9i) q^{37} +(30590.0 - 4063.33i) q^{38} +(-19032.6 - 15404.6i) q^{39} +(44924.0 + 45583.2i) q^{40} -7523.36i q^{41} +(29379.6 + 17947.2i) q^{42} +(-71893.0 + 71893.0i) q^{43} +(100046. - 27056.0i) q^{44} +(-50839.5 - 75624.8i) q^{45} +(-9877.56 - 7561.14i) q^{46} +(-108232. + 108232. i) q^{47} +(-89152.4 + 65440.3i) q^{48} -92244.7i q^{49} +(78098.7 - 97599.1i) q^{50} +(179848. + 145565. i) q^{51} +(50331.0 + 28903.2i) q^{52} +(-66841.6 + 66841.6i) q^{53} +(141996. - 68058.6i) q^{54} +(-75446.2 - 187836. i) q^{55} +(-75502.5 - 30966.9i) q^{56} +(103575. - 10911.7i) q^{57} +(215454. - 28619.2i) q^{58} +229291. i q^{59} +(147395. + 157895. i) q^{60} +125947. q^{61} +(20196.7 + 152047. i) q^{62} +(97478.7 + 63235.8i) q^{63} +(184070. - 186649. i) q^{64} +(44505.1 - 104257. i) q^{65} +(340004. - 82132.5i) q^{66} +(142997. + 142997. i) q^{67} +(-475601. - 273120. i) q^{68} +(-32633.2 - 26412.6i) q^{69} +(-42728.8 + 153553. i) q^{70} -278231. q^{71} +(-306763. + 212628. i) q^{72} +(-443121. - 443121. i) q^{73} +(-248539. + 324681. i) q^{74} +(272411. - 322135. i) q^{75} +(-238309. + 64447.3i) q^{76} +(182509. + 182509. i) q^{77} +(167162. + 102115. i) q^{78} -751698. q^{79} +(-404280. - 314168. i) q^{80} +(485285. - 216630. i) q^{81} +(7925.14 + 59662.8i) q^{82} +(-627377. - 627377. i) q^{83} +(-251896. - 111379. i) q^{84} +(-420549. + 985173. i) q^{85} +(494403. - 645868. i) q^{86} +(729506. - 76854.0i) q^{87} +(-764896. + 319952. i) q^{88} -650955. q^{89} +(482838. + 546176. i) q^{90} +144543. i q^{91} +(86297.4 + 49557.4i) q^{92} +(54236.2 + 514816. i) q^{93} +(744303. - 972326. i) q^{94} +(179713. + 447424. i) q^{95} +(638074. - 612878. i) q^{96} +(-149414. + 149414. i) q^{97} +(97171.0 + 731532. i) q^{98} +(1.15460e6 - 246007. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 4 q^{6}+O(q^{10}) $ 136 * q - 4 * q^6	$ 136 q - 4 q^{6} - 2092 q^{10} - 1460 q^{12} - 8 q^{13} - 932 q^{16} - 12744 q^{18} - 16056 q^{21} + 25444 q^{22} - 8 q^{25} - 52244 q^{28} + 82868 q^{30} - 2920 q^{33} - 69524 q^{36} - 113000 q^{37} + 99944 q^{40} + 19436 q^{42} - 62504 q^{45} + 145936 q^{46} - 82364 q^{48} + 219504 q^{52} - 286152 q^{57} - 351260 q^{58} + 466756 q^{60} + 652976 q^{61} - 61800 q^{66} + 243868 q^{70} - 145560 q^{72} - 316856 q^{73} + 269024 q^{76} + 613272 q^{78} + 1472232 q^{81} - 1652880 q^{82} - 1466984 q^{85} - 1084100 q^{88} + 448368 q^{90} - 2869552 q^{93} - 278860 q^{96} + 2135272 q^{97}+O(q^{100}) $ 136 * q - 4 * q^6 - 2092 * q^10 - 1460 * q^12 - 8 * q^13 - 932 * q^16 - 12744 * q^18 - 16056 * q^21 + 25444 * q^22 - 8 * q^25 - 52244 * q^28 + 82868 * q^30 - 2920 * q^33 - 69524 * q^36 - 113000 * q^37 + 99944 * q^40 + 19436 * q^42 - 62504 * q^45 + 145936 * q^46 - 82364 * q^48 + 219504 * q^52 - 286152 * q^57 - 351260 * q^58 + 466756 * q^60 + 652976 * q^61 - 61800 * q^66 + 243868 * q^70 - 145560 * q^72 - 316856 * q^73 + 269024 * q^76 + 613272 * q^78 + 1472232 * q^81 - 1652880 * q^82 - 1466984 * q^85 - 1084100 * q^88 + 448368 * q^90 - 2869552 * q^93 - 278860 * q^96 + 2135272 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−7.93034	+	1.05340i	−0.991293	+	0.131676i
$2$	−7.93034	+	1.05340i	−0.991293	+	0.131676i
$3$	−26.8514	+	2.82881i	−0.994496	+	0.104771i
$3$	−26.8514	+	2.82881i	−0.994496	+	0.104771i
$4$	61.7807	−	16.7077i	0.965323	−	0.261058i
$5$	−46.5899	−	115.993i	−0.372719	−	0.927944i
$5$	−46.5899	−	115.993i	−0.372719	−	0.927944i
$6$	209.961	−	50.7188i	0.972041	−	0.234809i
$7$	112.704	+	112.704i	0.328582	+	0.328582i	0.852047	−	0.523465i	$-0.175361\pi$
$7$	112.704	+	112.704i	0.328582	+	0.328582i	−0.523465	+	0.852047i	$0.675361\pi$
$8$	−472.342	+	197.578i	−0.922543	+	0.385894i
$9$	712.996	−	151.915i	0.978046	−	0.208388i
$10$	491.661	+	870.787i	0.491661	+	0.870787i
$11$	1619.37			1.21666			0.608328	−	0.793686i	$-0.291841\pi$
$11$	1619.37			1.21666			0.608328	+	0.793686i	$0.291841\pi$
$12$	−1611.63	+	623.392i	−0.932659	+	0.360759i
$13$	641.254	+	641.254i	0.291877	+	0.291877i	0.837821	−	0.545944i	$-0.183829\pi$
$13$	641.254	+	641.254i	0.291877	+	0.291877i	−0.545944	+	0.837821i	$0.683829\pi$
$14$	−1012.50	−	775.057i	−0.368987	−	0.282455i
$15$	1579.13	+	2982.78i	0.467889	+	0.883787i
$16$	3537.70	−	2064.43i	0.863697	−	0.504011i
$17$	−6059.51	−	6059.51i	−1.23336	−	1.23336i	−0.962664	−	0.270699i	$-0.912745\pi$
$17$	−6059.51	−	6059.51i	−1.23336	−	1.23336i	−0.270699	−	0.962664i	$-0.587255\pi$
$18$	−5494.27	+	1955.81i	−0.942090	+	0.335359i
$19$	−3857.33			−0.562376			−0.281188	−	0.959653i	$-0.590728\pi$
$19$	−3857.33			−0.562376			−0.281188	+	0.959653i	$0.590728\pi$
$20$	−4816.33	−	6387.72i	−0.602042	−	0.798465i
$21$	−3345.07	−	2707.44i	−0.361200	−	0.292348i
$22$	−12842.2	+	1705.85i	−1.20606	+	0.160204i
$23$	1099.49	+	1099.49i	0.0903667	+	0.0903667i	0.750845	−	0.660478i	$-0.229646\pi$
$23$	1099.49	+	1099.49i	0.0903667	+	0.0903667i	−0.660478	+	0.750845i	$0.729646\pi$
$24$	12124.1	−	6641.41i	0.877035	−	0.480426i
$25$	−11283.8	+	10808.2i	−0.722161	+	0.691725i
$26$	−5760.87	−	4409.87i	−0.327769	−	0.250903i
$27$	−18715.2	+	6096.07i	−0.950830	+	0.309712i
$28$	8845.93	+	5079.89i	0.402967	+	0.231409i
$29$	−27168.3			−1.11396			−0.556978	−	0.830527i	$-0.688039\pi$
$29$	−27168.3			−1.11396			−0.556978	+	0.830527i	$0.688039\pi$
$30$	−15665.1	−	21991.0i	−0.580188	−	0.814482i
$31$		−	19172.8i		−	0.643576i	−0.946812	−	0.321788i	$-0.895716\pi$
$31$		−	19172.8i		−	0.643576i	0.946812	−	0.321788i	$-0.104284\pi$
$32$	−25880.5	+	20098.3i	−0.789811	+	0.613350i
$33$	−43482.3	+	4580.89i	−1.20996	+	0.127470i
$34$	54437.1	+	41670.9i	1.38503	+	1.06022i
$35$	7821.99	−	18323.7i	0.182437	−	0.427375i
$36$	41511.2	−	21298.0i	0.889729	−	0.456489i
$37$	36140.9	−	36140.9i	0.713500	−	0.713500i	−0.253766	−	0.967266i	$-0.581669\pi$
$37$	36140.9	−	36140.9i	0.713500	−	0.713500i	0.967266	+	0.253766i	$0.0816693\pi$
$38$	30590.0	−	4063.33i	0.557479	−	0.0740511i
$39$	−19032.6	−	15404.6i	−0.320851	−	0.259691i
$40$	44924.0	+	45583.2i	0.701938	+	0.712238i
$41$		−	7523.36i		−	0.109159i	−0.998509	−	0.0545796i	$-0.982618\pi$
$41$		−	7523.36i		−	0.109159i	0.998509	−	0.0545796i	$-0.0173819\pi$
$42$	29379.6	+	17947.2i	0.396550	+	0.242241i
$43$	−71893.0	+	71893.0i	−0.904234	+	0.904234i	−0.995799	−	0.0915647i	$-0.970813\pi$
$43$	−71893.0	+	71893.0i	−0.904234	+	0.904234i	0.0915647	+	0.995799i	$0.470813\pi$
$44$	100046.	−	27056.0i	1.17447	−	0.317618i
$45$	−50839.5	−	75624.8i	−0.557909	−	0.829902i
$46$	−9877.56	−	7561.14i	−0.101479	−	0.0776808i
$47$	−108232.	+	108232.i	−1.04246	+	1.04246i	−0.0434059	+	0.999058i	$0.513821\pi$
$47$	−108232.	+	108232.i	−1.04246	+	1.04246i	−0.999058	+	0.0434059i	$0.986179\pi$
$48$	−89152.4	+	65440.3i	−0.806138	+	0.591727i
$49$		−	92244.7i		−	0.784067i
$50$	78098.7	−	97599.1i	0.624790	−	0.780793i
$51$	179848.	+	145565.i	1.35580	+	1.09735i
$52$	50331.0	+	28903.2i	0.357953	+	0.205559i
$53$	−66841.6	+	66841.6i	−0.448972	+	0.448972i	−0.895013	−	0.446041i	$-0.852834\pi$
$53$	−66841.6	+	66841.6i	−0.448972	+	0.448972i	0.446041	+	0.895013i	$0.352834\pi$
$54$	141996.	−	68058.6i	0.901770	−	0.432217i
$55$	−75446.2	−	187836.i	−0.453471	−	1.12899i
$56$	−75502.5	−	30966.9i	−0.429929	−	0.176333i
$57$	103575.	−	10911.7i	0.559281	−	0.0589206i
$58$	215454.	−	28619.2i	1.10426	−	0.146681i
$59$			229291.i			1.11643i	0.829697	+	0.558214i	$0.188513\pi$
$59$			229291.i			1.11643i	−0.829697	+	0.558214i	$0.811487\pi$
$60$	147395.	+	157895.i	0.682384	+	0.730994i
$61$	125947.			0.554881			0.277440	−	0.960743i	$-0.410514\pi$
$61$	125947.			0.554881			0.277440	+	0.960743i	$0.410514\pi$
$62$	20196.7	+	152047.i	0.0847432	+	0.637972i
$63$	97478.7	+	63235.8i	0.389841	+	0.252896i
$64$	184070.	−	186649.i	0.702171	−	0.712008i
$65$	44505.1	−	104257.i	0.162058	−	0.379634i
$66$	340004.	−	82132.5i	1.18264	−	0.285682i
$67$	142997.	+	142997.i	0.475446	+	0.475446i	0.903672	−	0.428226i	$-0.140861\pi$
$67$	142997.	+	142997.i	0.475446	+	0.475446i	−0.428226	+	0.903672i	$0.640861\pi$
$68$	−475601.	−	273120.i	−1.51257	−	0.868614i
$69$	−32633.2	−	26412.6i	−0.0993372	−	0.0804016i
$70$	−42728.8	+	153553.i	−0.124574	+	0.447676i
$71$	−278231.			−0.777376			−0.388688	−	0.921370i	$-0.627072\pi$
$71$	−278231.			−0.777376			−0.388688	+	0.921370i	$0.627072\pi$
$72$	−306763.	+	212628.i	−0.821874	+	0.569670i
$73$	−443121.	−	443121.i	−1.13908	−	1.13908i	−0.988616	−	0.150463i	$-0.951924\pi$
$73$	−443121.	−	443121.i	−1.13908	−	1.13908i	−0.150463	−	0.988616i	$-0.548076\pi$
$74$	−248539.	+	324681.i	−0.613337	+	0.801238i
$75$	272411.	−	322135.i	0.645714	−	0.763579i
$76$	−238309.	+	64447.3i	−0.542874	+	0.146813i
$77$	182509.	+	182509.i	0.399772	+	0.399772i
$78$	167162.	+	102115.i	0.352252	+	0.215181i
$79$	−751698.			−1.52462			−0.762311	−	0.647211i	$-0.775935\pi$
$79$	−751698.			−1.52462			−0.762311	+	0.647211i	$0.775935\pi$
$80$	−404280.	−	314168.i	−0.789610	−	0.613609i
$81$	485285.	−	216630.i	0.913148	−	0.407627i
$82$	7925.14	+	59662.8i	0.0143736	+	0.108209i
$83$	−627377.	−	627377.i	−1.09722	−	1.09722i	−0.994734	−	0.102488i	$-0.967320\pi$
$83$	−627377.	−	627377.i	−1.09722	−	1.09722i	−0.102488	−	0.994734i	$-0.532680\pi$
$84$	−251896.	−	111379.i	−0.424994	−	0.187916i
$85$	−420549.	+	985173.i	−0.684794	+	1.60419i
$86$	494403.	−	645868.i	0.777296	−	1.01543i
$87$	729506.	−	76854.0i	1.10783	−	0.116710i
$88$	−764896.	+	319952.i	−1.12242	+	0.469501i
$89$	−650955.			−0.923381			−0.461690	−	0.887041i	$-0.652757\pi$
$89$	−650955.			−0.923381			−0.461690	+	0.887041i	$0.652757\pi$
$90$	482838.	+	546176.i	0.662329	+	0.749213i
$91$			144543.i			0.191811i
$92$	86297.4	+	49557.4i	0.110824	+	0.0636421i
$93$	54236.2	+	514816.i	0.0674280	+	0.640034i
$94$	744303.	−	972326.i	0.896120	−	1.17065i
$95$	179713.	+	447424.i	0.209608	+	0.521853i
$96$	638074.	−	612878.i	0.721203	−	0.692724i
$97$	−149414.	+	149414.i	−0.163711	+	0.163711i	−0.784208	−	0.620498i	$-0.786931\pi$
$97$	−149414.	+	149414.i	−0.163711	+	0.163711i	0.620498	+	0.784208i	$0.286931\pi$
$98$	97171.0	+	731532.i	0.103243	+	0.777240i
$99$	1.15460e6	−	246007.i	1.18995	−	0.253537i
$100$	−516538.	+	856264.i	−0.516538	+	0.856264i
$101$		−	1.09136e6i		−	1.05926i	−0.848229	−	0.529630i	$-0.822331\pi$
$101$		−	1.09136e6i		−	1.05926i	0.848229	−	0.529630i	$-0.177669\pi$
$102$	−1.57959e6	−	964929.i	−1.48849	−	0.909275i
$103$	943140.	−	943140.i	0.863107	−	0.863107i	−0.128591	−	0.991698i	$-0.541045\pi$
$103$	943140.	−	943140.i	0.863107	−	0.863107i	0.991698	+	0.128591i	$0.0410455\pi$
$104$	−429589.	−	176194.i	−0.381903	−	0.156635i
$105$	−158197.	+	514144.i	−0.136657	+	0.444137i
$106$	459666.	−	600488.i	0.385944	−	0.504181i
$107$	238689.	−	238689.i	0.194841	−	0.194841i	−0.602943	−	0.797784i	$-0.706005\pi$
$107$	238689.	−	238689.i	0.194841	−	0.194841i	0.797784	+	0.602943i	$0.206005\pi$
$108$	−1.05439e6	+	689307.i	−0.837006	+	0.547194i
$109$			2.07022e6i			1.59859i	0.600938	+	0.799296i	$0.294794\pi$
$109$			2.07022e6i			1.59859i	−0.600938	+	0.799296i	$0.705206\pi$
$110$	796181.	+	1.41012e6i	0.598183	+	1.05945i
$111$	−868198.	+	1.07267e6i	−0.634819	+	0.784327i
$112$	631381.	+	166044.i	0.449405	+	0.118187i
$113$	888824.	−	888824.i	0.616000	−	0.616000i	−0.328503	−	0.944503i	$-0.606544\pi$
$113$	888824.	−	888824.i	0.616000	−	0.616000i	0.944503	+	0.328503i	$0.106544\pi$
$114$	−809890.	+	195640.i	−0.546652	+	0.132051i
$115$	76308.2	−	178759.i	0.0501739	−	0.117537i
$116$	−1.67847e6	+	453920.i	−1.07533	+	0.290807i
$117$	554628.	+	359795.i	0.346293	+	0.224645i
$118$	−241536.	−	1.81835e6i	−0.147006	−	1.10671i
$119$		−	1.36586e6i		−	0.810522i
$120$	−1.33522e6	−	1.09689e6i	−0.772696	−	0.634776i
$121$	850795.			0.480252
$122$	−998806.	+	132673.i	−0.550049	+	0.0730642i
$123$	21282.2	+	202013.i	0.0114367	+	0.108558i
$124$	−320333.	−	1.18451e6i	−0.168011	−	0.621259i
$125$	1.77939e6	+	805285.i	0.911045	+	0.412306i
$126$	−839652.	−	398798.i	−0.419747	−	0.199361i
$127$	−2.23134e6	−	2.23134e6i	−1.08932	−	1.08932i	−0.995599	−	0.0937173i	$-0.970125\pi$
$127$	−2.23134e6	−	2.23134e6i	−1.08932	−	1.08932i	−0.0937173	−	0.995599i	$-0.529875\pi$
$128$	−1.26312e6	+	1.67409e6i	−0.602303	+	0.798268i
$129$	1.72706e6	−	2.13380e6i	0.804520	−	0.993995i
$130$	−243116.	+	873675.i	−0.110658	+	0.397667i
$131$	1.19535e6			0.531720			0.265860	−	0.964012i	$-0.414344\pi$
$131$	1.19535e6			0.531720			0.265860	+	0.964012i	$0.414344\pi$
$132$	−2.60983e6	+	1.00950e6i	−1.13473	+	0.438920i
$133$	−434736.	−	434736.i	−0.184787	−	0.184787i
$134$	−1.28464e6	−	983378.i	−0.533911	−	0.408701i
$135$	1.57904e6	+	1.88682e6i	0.641788	+	0.766882i
$136$	4.05939e6	+	1.66494e6i	1.61378	+	0.661882i
$137$	2.70746e6	+	2.70746e6i	1.05293	+	1.05293i	0.998518	+	0.0544155i	$0.0173296\pi$
$137$	2.70746e6	+	2.70746e6i	1.05293	+	1.05293i	0.0544155	+	0.998518i	$0.482670\pi$
$138$	286615.	+	175085.i	0.109059	+	0.0666212i
$139$	−65398.7			−0.0243514			−0.0121757	−	0.999926i	$-0.503876\pi$
$139$	−65398.7			−0.0243514			−0.0121757	+	0.999926i	$0.503876\pi$
$140$	177101.	−	1.26274e6i	0.0645411	−	0.460182i
$141$	2.60001e6	−	3.21234e6i	0.927506	−	1.14595i
$142$	2.20647e6	−	293090.i	0.770607	−	0.102361i
$143$	1.03843e6	+	1.03843e6i	0.355114	+	0.355114i
$144$	2.20875e6	−	2.00936e6i	0.739706	−	0.672930i
$145$	1.26577e6	+	3.15133e6i	0.415193	+	1.03369i
$146$	3.98089e6	+	3.04731e6i	1.27915	+	0.979172i
$147$	260943.	+	2.47690e6i	0.0821474	+	0.779752i
$148$	1.62898e6	−	2.83664e6i	0.502493	−	0.875023i
$149$	−4.91535e6			−1.48592			−0.742961	−	0.669335i	$-0.766579\pi$
$149$	−4.91535e6			−1.48592			−0.742961	+	0.669335i	$0.766579\pi$
$150$	−1.82097e6	+	2.84160e6i	−0.539547	+	0.841956i
$151$			491086.i			0.142635i	0.997454	+	0.0713176i	$0.0227204\pi$
$151$			491086.i			0.142635i	−0.997454	+	0.0713176i	$0.977280\pi$
$152$	1.82198e6	−	762124.i	0.518816	−	0.217018i
$153$	−5.24094e6	−	3.39987e6i	−1.46330	−	0.949267i
$154$	−1.63961e6	−	1.25510e6i	−0.448931	−	0.343651i
$155$	−2.22391e6	+	893257.i	−0.597203	+	0.239873i
$156$	−1.43322e6	−	633715.i	−0.377519	−	0.166925i
$157$	−1.03463e6	+	1.03463e6i	−0.267354	+	0.267354i	−0.828033	−	0.560679i	$-0.810540\pi$
$157$	−1.03463e6	+	1.03463e6i	−0.267354	+	0.267354i	0.560679	+	0.828033i	$0.310540\pi$
$158$	5.96122e6	−	791842.i	1.51135	−	0.200755i
$159$	1.60571e6	−	1.98387e6i	0.399462	−	0.493540i
$160$	3.53703e6	+	2.06559e6i	0.863532	+	0.504293i
$161$			247834.i			0.0593858i
$162$	−3.62027e6	+	2.22915e6i	−0.851523	+	0.524317i
$163$	−1.56918e6	+	1.56918e6i	−0.362334	+	0.362334i	−0.864672	−	0.502338i	$-0.832473\pi$
$163$	−1.56918e6	+	1.56918e6i	−0.362334	+	0.362334i	0.502338	+	0.864672i	$0.332473\pi$
$164$	−125698.	−	464798.i	−0.0284969	−	0.105374i
$165$	2.55719e6	+	4.83022e6i	0.569260	+	1.07526i
$166$	5.63620e6	+	4.31444e6i	1.23215	+	0.943191i
$167$	4.21037e6	−	4.21037e6i	0.904005	−	0.904005i	−0.0917748	−	0.995780i	$-0.529254\pi$
$167$	4.21037e6	−	4.21037e6i	0.904005	−	0.904005i	0.995780	+	0.0917748i	$0.0292540\pi$
$168$	2.11495e6	+	617923.i	0.446038	+	0.130319i
$169$		−	4.00440e6i		−	0.829615i
$170$	2.29731e6	−	8.25577e6i	0.467599	−	1.68039i
$171$	−2.75026e6	+	585988.i	−0.550029	+	0.117193i
$172$	−3.24043e6	+	5.64276e6i	−0.636821	+	1.10894i
$173$	−772388.	+	772388.i	−0.149175	+	0.149175i	−0.777750	−	0.628574i	$-0.783639\pi$
$173$	−772388.	+	772388.i	−0.149175	+	0.149175i	0.628574	+	0.777750i	$0.283639\pi$
$174$	−5.70428e6	+	1.37794e6i	−1.08281	+	0.261567i
$175$	−2.48985e6	−	53597.8i	−0.464578	−	0.0100008i
$176$	5.72885e6	−	3.34307e6i	1.05082	−	0.613208i
$177$	−648621.	−	6.15678e6i	−0.116969	−	1.11028i
$178$	5.16229e6	−	685719.i	0.915341	−	0.121587i
$179$			8.23461e6i			1.43577i	0.696163	+	0.717884i	$0.254889\pi$
$179$			8.23461e6i			1.43577i	−0.696163	+	0.717884i	$0.745111\pi$
$180$	−4.40442e6	−	3.82274e6i	−0.755215	−	0.655477i
$181$	−9.32373e6			−1.57237			−0.786184	−	0.617993i	$-0.787946\pi$
$181$	−9.32373e6			−1.57237			−0.786184	+	0.617993i	$0.787946\pi$
$182$	−152263.	−	1.14628e6i	−0.0252569	−	0.190141i
$183$	−3.38186e6	+	356282.i	−0.551827	+	0.0581353i
$184$	−736572.	−	302101.i	−0.118239	−	0.0484952i
$185$	−5.87589e6	−	2.50829e6i	−0.928023	−	0.396153i
$186$	−972421.	−	4.02553e6i	−0.151118	−	0.625582i
$187$	−9.81259e6	−	9.81259e6i	−1.50058	−	1.50058i
$188$	−4.87832e6	+	8.49493e6i	−0.734171	+	1.27846i
$189$	−2.79632e6	−	1.42222e6i	−0.414192	−	0.210660i
$190$	−1.89650e6	−	3.35892e6i	−0.276498	−	0.489709i
$191$	1.44929e6			0.207996			0.103998	−	0.994578i	$-0.466836\pi$
$191$	1.44929e6			0.207996			0.103998	+	0.994578i	$0.466836\pi$
$192$	−4.41454e6	+	5.53248e6i	−0.623709	+	0.781657i
$193$	−585713.	−	585713.i	−0.0814728	−	0.0814728i	0.665196	−	0.746669i	$-0.268348\pi$
$193$	−585713.	−	585713.i	−0.0814728	−	0.0814728i	−0.746669	+	0.665196i	$0.768348\pi$
$194$	1.02751e6	−	1.34230e6i	0.140729	−	0.183842i
$195$	−900100.	+	2.92534e6i	−0.121391	+	0.394523i
$196$	−1.54120e6	−	5.69894e6i	−0.204687	−	0.756878i
$197$	4.35401e6	+	4.35401e6i	0.569496	+	0.569496i	0.931987	−	0.362491i	$-0.118074\pi$
$197$	4.35401e6	+	4.35401e6i	0.569496	+	0.569496i	−0.362491	+	0.931987i	$0.618074\pi$
$198$	−8.89725e6	+	3.16718e6i	−1.14620	+	0.408016i
$199$	−2.19416e6			−0.278425			−0.139213	−	0.990263i	$-0.544457\pi$
$199$	−2.19416e6			−0.278425			−0.139213	+	0.990263i	$0.544457\pi$
$200$	3.19433e6	−	7.33459e6i	0.399292	−	0.916824i
$201$	−4.24417e6	−	3.43515e6i	−0.522642	−	0.423016i
$202$	1.14964e6	+	8.65483e6i	0.139479	+	1.05004i
$203$	−3.06197e6	−	3.06197e6i	−0.366026	−	0.366026i
$204$	1.35432e7	+	5.98827e6i	1.59525	+	0.705360i
$205$	−872657.	+	350512.i	−0.101294	+	0.0406857i
$206$	−6.48591e6	+	8.47293e6i	−0.741941	+	0.969241i
$207$	950963.	+	616903.i	0.107214	+	0.0695514i
$208$	3.59239e6	+	944745.i	0.399203	+	0.104984i
$209$	−6.24645e6			−0.684218
$210$	712956.	−	4.24398e6i	0.0769848	−	0.458264i
$211$			2.84493e6i			0.302848i	0.988469	+	0.151424i	$0.0483858\pi$
$211$			2.84493e6i			0.302848i	−0.988469	+	0.151424i	$0.951614\pi$
$212$	−3.01275e6	+	5.24629e6i	−0.316195	+	0.550611i
$213$	7.47090e6	−	787064.i	0.773097	−	0.0814463i
$214$	−1.64145e6	+	2.14432e6i	−0.167489	+	0.218801i
$215$	1.16886e7	+	4.98960e6i	1.17610	+	0.502054i
$216$	7.63552e6	−	6.57714e6i	0.757666	−	0.652643i
$217$	2.16084e6	−	2.16084e6i	0.211468	−	0.211468i
$218$	−2.18078e6	−	1.64176e7i	−0.210495	−	1.58467i
$219$	1.31519e7	+	1.06449e7i	1.25215	+	1.01347i
$220$	−7.79942e6	−	1.03441e7i	−0.732478	−	0.971457i
$221$		−	7.77137e6i		−	0.719981i
$222$	5.75515e6	−	9.42120e6i	0.526015	−	0.861088i
$223$	−5.04664e6	+	5.04664e6i	−0.455080	+	0.455080i	−0.897037	−	0.441956i	$-0.854285\pi$
$223$	−5.04664e6	+	5.04664e6i	−0.455080	+	0.455080i	0.441956	+	0.897037i	$0.354285\pi$
$224$	−5.18198e6	−	651684.i	−0.461054	−	0.0579820i
$225$	−6.40335e6	+	9.42038e6i	−0.562159	+	0.827029i
$226$	−6.11239e6	+	7.98497e6i	−0.529524	+	0.691748i
$227$	5.12144e6	−	5.12144e6i	0.437839	−	0.437839i	−0.453445	−	0.891284i	$-0.649805\pi$
$227$	5.12144e6	−	5.12144e6i	0.437839	−	0.437839i	0.891284	+	0.453445i	$0.149805\pi$
$228$	6.21662e6	−	2.40463e6i	0.524505	−	0.202882i
$229$		−	1.32422e6i		−	0.110269i	−0.998479	−	0.0551345i	$-0.982441\pi$
$229$		−	1.32422e6i		−	0.110269i	0.998479	−	0.0551345i	$-0.0175588\pi$
$230$	−416845.	+	1.49800e6i	−0.0342603	+	0.123120i
$231$	−5.41690e6	−	4.38434e6i	−0.439456	−	0.355687i
$232$	1.28327e7	−	5.36785e6i	1.02767	−	0.429870i
$233$	7.84746e6	−	7.84746e6i	0.620385	−	0.620385i	−0.325245	−	0.945630i	$-0.605447\pi$
$233$	7.84746e6	−	7.84746e6i	0.620385	−	0.620385i	0.945630	+	0.325245i	$0.105447\pi$
$234$	−4.77740e6	−	2.26905e6i	−0.372858	−	0.177091i
$235$	1.75966e7	+	7.51162e6i	1.35589	+	0.578802i
$236$	3.83093e6	+	1.41657e7i	0.291452	+	1.07771i
$237$	2.01842e7	−	2.12641e6i	1.51623	−	0.159736i
$238$	1.43880e6	+	1.08317e7i	0.106726	+	0.803465i
$239$		−	861774.i		−	0.0631247i	−0.999502	−	0.0315624i	$-0.989952\pi$
$239$		−	861774.i		−	0.0631247i	0.999502	−	0.0315624i	$-0.0100483\pi$
$240$	1.17442e7	+	7.29221e6i	0.849553	+	0.527503i
$241$	−279493.			−0.0199673			−0.00998367	−	0.999950i	$-0.503178\pi$
$241$	−279493.			−0.0199673			−0.00998367	+	0.999950i	$0.503178\pi$
$242$	−6.74710e6	+	896231.i	−0.476070	+	0.0632374i
$243$	−1.24178e7	+	7.18959e6i	−0.865415	+	0.501055i
$244$	7.78111e6	−	2.10429e6i	0.535639	−	0.144856i
$245$	−1.06997e7	+	4.29767e6i	−0.727571	+	0.292237i
$246$	−381576.	−	1.57961e6i	−0.0256316	−	0.106107i
$247$	−2.47353e6	−	2.47353e6i	−0.164145	−	0.164145i
$248$	3.78812e6	+	9.05610e6i	0.248352	+	0.593726i
$249$	1.86207e7	+	1.50712e7i	1.20614	+	0.976227i
$250$	−1.49594e7	−	4.51178e6i	−0.957403	−	0.288754i
$251$	−1.80963e7			−1.14437			−0.572186	−	0.820124i	$-0.693905\pi$
$251$	−1.80963e7			−1.14437			−0.572186	+	0.820124i	$0.693905\pi$
$252$	7.07882e6	+	2.27811e6i	0.442343	+	0.142355i
$253$	1.78048e6	+	1.78048e6i	0.109945	+	0.109945i
$254$	2.00458e7	+	1.53448e7i	1.22327	+	0.936395i
$255$	8.50547e6	−	2.76429e7i	0.512953	−	1.66711i
$256$	8.25349e6	−	1.46067e7i	0.491946	−	0.870626i
$257$	1.59978e7	+	1.59978e7i	0.942454	+	0.942454i	0.998432	−	0.0559780i	$-0.0178277\pi$
$257$	1.59978e7	+	1.59978e7i	0.942454	+	0.942454i	−0.0559780	+	0.998432i	$0.517828\pi$
$258$	−1.14484e7	+	1.87410e7i	−0.666630	+	1.09128i
$259$	8.14643e6			0.468887
$260$	1.00766e6	−	7.18464e6i	0.0573314	−	0.408776i
$261$	−1.93709e7	+	4.12727e6i	−1.08950	+	0.232136i
$262$	−9.47957e6	+	1.25919e6i	−0.527090	+	0.0700145i
$263$	−2.20245e7	−	2.20245e7i	−1.21071	−	1.21071i	−0.970795	−	0.239911i	$-0.922882\pi$
$263$	−2.20245e7	−	2.20245e7i	−1.21071	−	1.21071i	−0.239911	−	0.970795i	$-0.577118\pi$
$264$	1.96334e7	−	1.07549e7i	1.06705	−	0.584513i
$265$	1.08673e7	+	4.63902e6i	0.583961	+	0.249281i
$266$	3.90556e6	+	2.98965e6i	0.207510	+	0.158846i
$267$	1.74790e7	−	1.84143e6i	0.918299	−	0.0967434i
$268$	1.12236e7	+	6.44528e6i	0.583078	+	0.334840i
$269$	1.00019e7			0.513835			0.256917	−	0.966433i	$-0.417293\pi$
$269$	1.00019e7			0.513835			0.256917	+	0.966433i	$0.417293\pi$
$270$	−1.45099e7	−	1.32997e7i	−0.737180	−	0.675697i
$271$			2.13396e6i			0.107221i	0.998562	+	0.0536103i	$0.0170729\pi$
$271$			2.13396e6i			0.107221i	−0.998562	+	0.0536103i	$0.982927\pi$
$272$	−3.39462e7	−	8.92734e6i	−1.68688	−	0.443624i
$273$	−408886.	−	3.88119e6i	−0.0200962	−	0.190756i
$274$	−2.43232e7	−	1.86191e7i	−1.18241	−	0.905120i
$275$	−1.82726e7	+	1.75025e7i	−0.878622	+	0.841591i
$276$	−2.45739e6	−	1.08657e6i	−0.116882	−	0.0516807i
$277$	1.98478e7	−	1.98478e7i	0.933842	−	0.933842i	−0.0641010	−	0.997943i	$-0.520418\pi$
$277$	1.98478e7	−	1.98478e7i	0.933842	−	0.933842i	0.997943	+	0.0641010i	$0.0204180\pi$
$278$	518634.	−	68891.3i	0.0241394	−	0.00320649i
$279$	−2.91264e6	−	1.36701e7i	−0.134114	−	0.629447i
$280$	−74296.9	+	1.02005e7i	−0.00338451	+	0.464673i
$281$			5.60921e6i			0.252803i	0.991979	+	0.126402i	$0.0403428\pi$
$281$			5.60921e6i			0.252803i	−0.991979	+	0.126402i	$0.959657\pi$
$282$	−1.72350e7	+	2.82138e7i	−0.768537	+	1.25810i
$283$	2.01300e7	−	2.01300e7i	0.888146	−	0.888146i	−0.106199	−	0.994345i	$-0.533868\pi$
$283$	2.01300e7	−	2.01300e7i	0.888146	−	0.888146i	0.994345	+	0.106199i	$0.0338680\pi$
$284$	−1.71893e7	+	4.64861e6i	−0.750419	+	0.202940i
$285$	−6.09122e6	−	1.15056e7i	−0.263130	−	0.497020i
$286$	−9.32897e6	−	7.14120e6i	−0.398782	−	0.305262i
$287$	847910.	−	847910.i	0.0358678	−	0.0358678i
$288$	−1.53995e7	+	1.82616e7i	−0.644657	+	0.764472i
$289$			4.92978e7i			2.04237i
$290$	−1.33576e7	−	2.36578e7i	−0.547689	−	0.970018i
$291$	3.58932e6	−	4.43465e6i	0.145658	−	0.179962i
$292$	−3.47798e7	−	1.99728e7i	−1.39694	−	0.802213i
$293$	2.02243e7	−	2.02243e7i	0.804028	−	0.804028i	−0.179695	−	0.983722i	$-0.557511\pi$
$293$	2.02243e7	−	2.02243e7i	0.804028	−	0.804028i	0.983722	+	0.179695i	$0.0575109\pi$
$294$	−4.67855e6	−	1.93678e7i	−0.184106	−	0.762146i
$295$	2.65961e7	−	1.06826e7i	1.03598	−	0.416114i
$296$	−9.93022e6	+	2.42115e7i	−0.382899	+	0.933570i
$297$	−3.03068e7	+	9.87178e6i	−1.15683	+	0.376813i
$298$	3.89804e7	−	5.17785e6i	1.47298	−	0.195659i
$299$			1.41011e6i			0.0527520i
$300$	1.14476e7	−	2.44531e7i	0.423984	−	0.905670i
$301$	−1.62052e7			−0.594231
$302$	−517312.	−	3.89448e6i	−0.0187816	−	0.141393i
$303$	3.08724e6	+	2.93044e7i	0.110979	+	1.05343i
$304$	−1.36461e7	+	7.96319e6i	−0.485722	+	0.283443i
$305$	−5.86787e6	−	1.46090e7i	−0.206815	−	0.514898i
$306$	4.51439e7	+	2.14413e7i	1.57556	+	0.748320i
$307$	2.20797e7	+	2.20797e7i	0.763094	+	0.763094i	0.976880	−	0.213786i	$-0.0685796\pi$
$307$	2.20797e7	+	2.20797e7i	0.763094	+	0.763094i	−0.213786	+	0.976880i	$0.568580\pi$
$308$	1.43248e7	+	8.22622e6i	0.490272	+	0.281545i
$309$	−2.26567e7	+	2.79926e7i	−0.767928	+	0.948785i
$310$	1.66954e7	−	9.42651e6i	0.560417	−	0.316421i
$311$	3.60122e6			0.119720			0.0598602	−	0.998207i	$-0.480935\pi$
$311$	3.60122e6			0.119720			0.0598602	+	0.998207i	$0.480935\pi$
$312$	1.20335e7	+	3.51582e6i	0.396212	+	0.115761i
$313$	1.02283e7	+	1.02283e7i	0.333558	+	0.333558i	0.853936	−	0.520378i	$-0.174209\pi$
$313$	1.02283e7	+	1.02283e7i	0.333558	+	0.333558i	−0.520378	+	0.853936i	$0.674209\pi$
$314$	7.11509e6	−	9.29486e6i	0.229822	−	0.300230i
$315$	2.79340e6	−	1.42530e7i	0.0893720	−	0.456010i
$316$	−4.64404e7	+	1.25592e7i	−1.47175	+	0.398015i
$317$	−1.07001e6	−	1.07001e6i	−0.0335899	−	0.0335899i	0.690112	−	0.723702i	$-0.257561\pi$
$317$	−1.07001e6	−	1.07001e6i	−0.0335899	−	0.0335899i	−0.723702	+	0.690112i	$0.757561\pi$
$318$	−1.06440e7	+	1.74243e7i	−0.330996	+	0.541842i
$319$	−4.39955e7			−1.35530
$320$	−3.02257e7	−	1.26549e7i	−0.922417	−	0.386196i
$321$	−5.73393e6	+	7.08434e6i	−0.173355	+	0.214183i
$322$	−261069.	−	1.96541e6i	−0.00781966	−	0.0588687i
$323$	2.33736e7	+	2.33736e7i	0.693613	+	0.693613i
$324$	2.63618e7	−	2.14915e7i	0.775069	−	0.631877i
$325$	−1.41666e7	−	304957.i	−0.412681	−	0.00888360i
$326$	1.07911e7	−	1.40971e7i	0.311468	−	0.406889i
$327$	−5.85627e6	−	5.55884e7i	−0.167486	−	1.58979i
$328$	1.48645e6	+	3.55360e6i	0.0421239	+	0.100704i
$329$	−2.43962e7			−0.685070
$330$	−2.53676e7	−	3.56116e7i	−0.705890	−	0.990945i
$331$			7.22368e7i			1.99193i	0.0897255	+	0.995967i	$0.471401\pi$
$331$			7.22368e7i			1.99193i	−0.0897255	+	0.995967i	$0.528599\pi$
$332$	−4.92418e7	−	2.82778e7i	−1.34561	−	0.772735i
$333$	2.02780e7	−	3.12587e7i	0.549151	−	0.846521i
$334$	−2.89545e7	+	3.78249e7i	−0.777098	+	1.01517i
$335$	9.92441e6	−	2.32488e7i	0.263980	−	0.618395i
$336$	−1.74232e7	−	2.67245e6i	−0.459314	−	0.0704517i
$337$	5.20326e7	−	5.20326e7i	1.35952	−	1.35952i	0.485016	−	0.874505i	$-0.338814\pi$
$337$	5.20326e7	−	5.20326e7i	1.35952	−	1.35952i	0.874505	−	0.485016i	$-0.161186\pi$
$338$	4.21825e6	+	3.17562e7i	0.109240	+	0.822392i
$339$	−2.13519e7	+	2.63805e7i	−0.548071	+	0.677148i
$340$	−9.52182e6	+	6.78911e7i	−0.242261	+	1.72733i
$341$		−	3.10478e7i		−	0.783011i
$342$	2.11932e7	−	7.54422e6i	0.529809	−	0.188598i
$343$	2.36558e7	−	2.36558e7i	0.586213	−	0.586213i
$344$	1.97536e7	−	4.81625e7i	0.485256	−	1.18313i
$345$	−1.54331e6	+	5.01578e6i	−0.0375833	+	0.122147i
$346$	5.31167e6	−	6.93894e6i	0.128234	−	0.167519i
$347$	−1.67036e7	+	1.67036e7i	−0.399781	+	0.399781i	−0.878156	−	0.478375i	$-0.841226\pi$
$347$	−1.67036e7	+	1.67036e7i	−0.399781	+	0.399781i	0.478375	+	0.878156i	$0.341226\pi$
$348$	4.37853e7	−	1.69365e7i	1.03894	−	0.401870i
$349$		−	5.60865e7i		−	1.31942i	−0.751522	−	0.659708i	$-0.770680\pi$
$349$		−	5.60865e7i		−	1.31942i	0.751522	−	0.659708i	$-0.229320\pi$
$350$	1.98018e7	−	2.19777e6i	0.461850	−	0.0512599i
$351$	−1.59103e7	−	8.09207e6i	−0.367924	−	0.187128i
$352$	−4.19101e7	+	3.25465e7i	−0.960928	+	0.746236i
$353$	−2.09841e7	+	2.09841e7i	−0.477052	+	0.477052i	−0.904188	−	0.427135i	$-0.859523\pi$
$353$	−2.09841e7	+	2.09841e7i	−0.477052	+	0.477052i	0.427135	+	0.904188i	$0.359523\pi$
$354$	1.16294e7	+	4.81421e7i	0.262148	+	1.08521i
$355$	1.29628e7	+	3.22729e7i	0.289743	+	0.721361i
$356$	−4.02164e7	+	1.08760e7i	−0.891361	+	0.241056i
$357$	3.86376e6	+	3.66752e7i	0.0849191	+	0.806062i
$358$	−8.67438e6	−	6.53033e7i	−0.189055	−	1.42327i
$359$		−	3.33890e7i		−	0.721638i	−0.932636	−	0.360819i	$-0.882497\pi$
$359$		−	3.33890e7i		−	0.721638i	0.932636	−	0.360819i	$-0.117503\pi$
$360$	3.89554e7	+	2.56760e7i	0.834950	+	0.550326i
$361$	−3.21669e7			−0.683734
$362$	7.39404e7	−	9.82166e6i	1.55868	−	0.207042i
$363$	−2.28450e7	+	2.40674e6i	−0.477609	+	0.0503164i
$364$	2.41499e6	+	8.92999e6i	0.0500739	+	0.185160i
$365$	−3.07540e7	+	7.20439e7i	−0.632445	+	1.48156i
$366$	2.64440e7	−	6.38790e6i	0.539367	−	0.130291i
$367$	−4.03322e7	−	4.03322e7i	−0.815932	−	0.815932i	0.169583	−	0.985516i	$-0.445758\pi$
$367$	−4.03322e7	−	4.03322e7i	−0.815932	−	0.815932i	−0.985516	+	0.169583i	$0.945758\pi$
$368$	6.15950e6	+	1.61986e6i	0.123595	+	0.0325037i
$369$	−1.14291e6	−	5.36412e6i	−0.0227475	−	0.106763i
$370$	4.92401e7	+	1.37019e7i	0.972106	+	0.270506i
$371$	−1.50666e7			−0.295048
$372$	1.19521e7	+	3.08995e7i	0.232176	+	0.600237i
$373$	−3.89841e7	−	3.89841e7i	−0.751210	−	0.751210i	0.223495	−	0.974705i	$-0.428253\pi$
$373$	−3.89841e7	−	3.89841e7i	−0.751210	−	0.751210i	−0.974705	+	0.223495i	$0.928253\pi$
$374$	8.81538e7	+	6.74806e7i	1.68510	+	1.28992i
$375$	−5.00570e7	−	1.65895e7i	−0.949229	−	0.314586i
$376$	2.97382e7	−	7.25066e7i	0.559436	−	1.36400i
$377$	−1.74218e7	−	1.74218e7i	−0.325138	−	0.325138i
$378$	2.36740e7	+	8.33305e6i	0.438324	+	0.154287i
$379$	2.35538e7			0.432657			0.216328	−	0.976321i	$-0.430592\pi$
$379$	2.35538e7			0.432657			0.216328	+	0.976321i	$0.430592\pi$
$380$	1.85782e7	+	2.46396e7i	0.338574	+	0.449037i
$381$	6.62266e7	+	5.36025e7i	1.19745	+	0.969192i
$382$	−1.14934e7	+	1.52669e6i	−0.206185	+	0.0273880i
$383$	7.83481e6	+	7.83481e6i	0.139454	+	0.139454i	0.773388	−	0.633933i	$-0.218561\pi$
$383$	7.83481e6	+	7.83481e6i	0.139454	+	0.139454i	−0.633933	+	0.773388i	$0.718561\pi$
$384$	2.91809e7	−	4.85248e7i	0.515353	−	0.856978i
$385$	1.26667e7	−	2.96728e7i	0.221963	−	0.519968i
$386$	5.26189e6	+	4.02791e6i	0.0914914	+	0.0700354i
$387$	−4.03377e7	+	6.21810e7i	−0.695951	+	1.07281i
$388$	−6.73455e6	+	1.17273e7i	−0.115296	+	0.200772i
$389$	1.17896e7			0.200285			0.100143	−	0.994973i	$-0.468070\pi$
$389$	1.17896e7			0.200285			0.100143	+	0.994973i	$0.468070\pi$
$390$	4.05653e6	−	2.41471e7i	0.0683850	−	0.407073i
$391$		−	1.33248e7i		−	0.222910i
$392$	1.82255e7	+	4.35711e7i	0.302567	+	0.723336i
$393$	−3.20969e7	+	3.38143e6i	−0.528793	+	0.0557087i
$394$	−3.91153e7	−	2.99423e7i	−0.639526	−	0.489549i
$395$	3.50215e7	+	8.71918e7i	0.568256	+	1.41476i
$396$	6.72219e7	−	3.44892e7i	1.08249	−	0.555390i
$397$	−2.66021e6	+	2.66021e6i	−0.0425152	+	0.0425152i	−0.728045	−	0.685530i	$-0.759571\pi$
$397$	−2.66021e6	+	2.66021e6i	−0.0425152	+	0.0425152i	0.685530	+	0.728045i	$0.259571\pi$
$398$	1.74004e7	−	2.31134e6i	0.276001	−	0.0366618i
$399$	1.29031e7	+	1.04435e7i	0.203130	+	0.164409i
$400$	−1.76059e7	+	6.15308e7i	−0.275092	+	0.961418i
$401$		−	2.05577e6i		−	0.0318817i	−0.999873	−	0.0159409i	$-0.994926\pi$
$401$		−	2.05577e6i		−	0.0318817i	0.999873	−	0.0159409i	$-0.00507435\pi$
$402$	3.72763e7	+	2.27711e7i	0.573792	+	0.350514i
$403$	1.22946e7	−	1.22946e7i	0.187845	−	0.187845i
$404$	−1.82341e7	−	6.74247e7i	−0.276528	−	1.02253i
$405$	−4.77369e7	−	4.61969e7i	−0.718603	−	0.695421i
$406$	2.75079e7	+	2.10570e7i	0.411036	+	0.314642i
$407$	5.85255e7	−	5.85255e7i	0.868084	−	0.868084i
$408$	−1.13710e8	−	3.32226e7i	−1.67424	−	0.489163i
$409$		−	6.27898e7i		−	0.917739i	−0.888504	−	0.458869i	$-0.848255\pi$
$409$		−	6.27898e7i		−	0.917739i	0.888504	−	0.458869i	$-0.151745\pi$
$410$	6.55124e6	−	3.69894e6i	0.0950543	−	0.0536693i
$411$	−8.03581e7	−	6.50403e7i	−1.15746	−	0.936822i
$412$	4.25101e7	−	7.40255e7i	0.607856	−	1.05850i
$413$	−2.58419e7	+	2.58419e7i	−0.366838	+	0.366838i
$414$	−8.19131e6	−	3.89051e6i	−0.115439	−	0.0548284i
$415$	−4.35420e7	+	1.02001e8i	−0.609205	+	1.42712i
$416$	−2.94841e7	−	3.70791e6i	−0.409551	−	0.0515049i
$417$	1.75605e6	−	185001.i	0.0242174	−	0.00255132i
$418$	4.95365e7	−	6.58004e6i	0.678260	−	0.0900947i
$419$			2.53531e7i			0.344658i	0.985039	+	0.172329i	$0.0551292\pi$
$419$			2.53531e7i			0.344658i	−0.985039	+	0.172329i	$0.944871\pi$
$420$	−1.18336e6	+	3.44073e7i	−0.0159723	+	0.464411i
$421$	6.27464e7			0.840897			0.420449	−	0.907316i	$-0.361873\pi$
$421$	6.27464e7			0.840897			0.420449	+	0.907316i	$0.361873\pi$
$422$	−2.99686e6	−	2.25613e7i	−0.0398776	−	0.300211i
$423$	−6.07267e7	+	9.36108e7i	−0.802340	+	1.23681i
$424$	1.83657e7	−	4.47785e7i	0.240940	−	0.587452i
$425$	1.33867e8	+	2.88169e6i	1.74383	+	0.0375387i
$426$	−5.84177e7	+	1.41116e7i	−0.755641	+	0.182535i
$427$	1.41947e7	+	1.41947e7i	0.182324	+	0.182324i
$428$	1.07584e7	−	1.87343e7i	0.137220	−	0.238950i
$429$	−3.08207e7	−	2.49457e7i	−0.390365	−	0.315954i
$430$	−9.79504e7	−	2.72564e7i	−1.23197	−	0.342818i
$431$	1.38943e8			1.73543			0.867713	−	0.497066i	$-0.165589\pi$
$431$	1.38943e8			1.73543			0.867713	+	0.497066i	$0.165589\pi$
$432$	−5.36239e7	+	6.02023e7i	−0.665131	+	0.746726i
$433$	1.04304e6	+	1.04304e6i	0.0128481	+	0.0128481i	0.713502	−	0.700654i	$-0.247108\pi$
$433$	1.04304e6	+	1.04304e6i	0.0128481	+	0.0128481i	−0.700654	+	0.713502i	$0.747108\pi$
$434$	−1.48600e7	+	1.94125e7i	−0.181781	+	0.237471i
$435$	−4.29021e7	−	8.10370e7i	−0.521208	−	0.984500i
$436$	3.45887e7	+	1.27900e8i	0.417325	+	1.54316i
$437$	−4.24111e6	−	4.24111e6i	−0.0508201	−	0.0508201i
$438$	−1.15513e8	−	7.05635e7i	−1.37470	−	0.839765i
$439$	−1.65142e7			−0.195192			−0.0975962	−	0.995226i	$-0.531115\pi$
$439$	−1.65142e7			−0.195192			−0.0975962	+	0.995226i	$0.531115\pi$
$440$	7.27486e7	+	7.38161e7i	0.854017	+	0.866549i
$441$	−1.40134e7	−	6.57701e7i	−0.163391	−	0.766854i
$442$	8.18640e6	+	6.16297e7i	0.0948039	+	0.713712i
$443$	−5.54341e7	−	5.54341e7i	−0.637626	−	0.637626i	0.312344	−	0.949969i	$-0.398886\pi$
$443$	−5.54341e7	−	5.54341e7i	−0.637626	−	0.637626i	−0.949969	+	0.312344i	$0.898886\pi$
$444$	−3.57160e7	+	8.07759e7i	−0.408051	+	0.922853i
$445$	3.03279e7	+	7.55062e7i	0.344162	+	0.856846i
$446$	3.47055e7	−	4.53378e7i	0.391195	−	0.511041i
$447$	1.31984e8	−	1.39046e7i	1.47774	−	0.155681i
$448$	4.17814e7	−	290644.i	0.464674	−	0.00323242i
$449$	1.65498e7			0.182833			0.0914166	−	0.995813i	$-0.470861\pi$
$449$	1.65498e7			0.182833			0.0914166	+	0.995813i	$0.470861\pi$
$450$	4.08573e7	−	8.14521e7i	0.448365	−	0.893851i
$451$		−	1.21831e7i		−	0.132809i
$452$	4.00619e7	−	6.97624e7i	0.433827	−	0.755451i
$453$	−1.38919e6	−	1.31863e7i	−0.0149440	−	0.141850i
$454$	−3.52199e7	+	4.60098e7i	−0.376374	+	0.491680i
$455$	1.67660e7	−	6.73426e6i	0.177990	−	0.0714917i
$456$	−4.67668e7	+	2.56182e7i	−0.493223	+	0.270180i
$457$	−1.07757e8	+	1.07757e8i	−1.12901	+	1.12901i	−0.138669	+	0.990339i	$0.544282\pi$
$457$	−1.07757e8	+	1.07757e8i	−1.12901	+	1.12901i	−0.990339	+	0.138669i	$0.955718\pi$
$458$	1.39494e6	+	1.05015e7i	0.0145197	+	0.109309i
$459$	1.50344e8	+	7.64657e7i	1.55471	+	0.790731i
$460$	1.72772e6	−	1.23188e7i	0.0177501	−	0.126559i
$461$		−	1.52486e8i		−	1.55642i	−0.628005	−	0.778209i	$-0.716128\pi$
$461$		−	1.52486e8i		−	1.55642i	0.628005	−	0.778209i	$-0.283872\pi$
$462$	4.75764e7	+	2.90631e7i	0.482465	+	0.294724i
$463$	6.15059e7	−	6.15059e7i	0.619689	−	0.619689i	−0.325762	−	0.945452i	$-0.605621\pi$
$463$	6.15059e7	−	6.15059e7i	0.619689	−	0.619689i	0.945452	+	0.325762i	$0.105621\pi$
$464$	−9.61133e7	+	5.60870e7i	−0.962121	+	0.561446i
$465$	5.71882e7	−	3.02762e7i	0.568784	−	0.301122i
$466$	−5.39665e7	+	7.04996e7i	−0.533294	+	0.696673i
$467$	−1.25373e8	+	1.25373e8i	−1.23099	+	1.23099i	−0.267399	+	0.963586i	$0.586164\pi$
$467$	−1.25373e8	+	1.25373e8i	−1.23099	+	1.23099i	−0.963586	+	0.267399i	$0.913836\pi$
$468$	4.02766e7	+	1.29618e7i	0.392930	+	0.126453i
$469$			3.22325e7i			0.312446i
$470$	−1.47460e8	−	4.10334e7i	−1.42030	−	0.395224i
$471$	2.48545e7	−	3.07081e7i	0.237872	−	0.293893i
$472$	−4.53028e7	−	1.08304e8i	−0.430823	−	1.02995i
$473$	−1.16421e8	+	1.16421e8i	−1.10014	+	1.10014i
$474$	−1.57827e8	+	3.81253e7i	−1.48200	+	0.357996i
$475$	4.35253e7	−	4.16909e7i	0.406126	−	0.389009i
$476$	−2.28204e7	−	8.43837e7i	−0.211593	−	0.782416i
$477$	−3.75035e7	+	5.78120e7i	−0.345555	+	0.532676i
$478$	907796.	+	6.83416e6i	0.00831198	+	0.0625751i
$479$		−	1.11674e8i		−	1.01612i	−0.861322	−	0.508060i	$-0.830363\pi$
$479$		−	1.11674e8i		−	1.01612i	0.861322	−	0.508060i	$-0.169637\pi$
$480$	−1.00817e8	−	4.54583e7i	−0.911615	−	0.411045i
$481$	4.63510e7			0.416509
$482$	2.21648e6	−	294419.i	0.0197935	−	0.00262921i
$483$	−701075.	−	6.65468e6i	−0.00622190	−	0.0590590i
$484$	5.25627e7	−	1.42148e7i	0.463598	−	0.125374i
$485$	2.42922e7	+	1.03698e7i	0.212933	+	0.0908964i
$486$	9.09036e7	−	7.00969e7i	0.791903	−	0.610646i
$487$	−8.25512e7	−	8.25512e7i	−0.714721	−	0.714721i	0.252798	−	0.967519i	$-0.418649\pi$
$487$	−8.25512e7	−	8.25512e7i	−0.714721	−	0.714721i	−0.967519	+	0.252798i	$0.918649\pi$
$488$	−5.94902e7	+	2.48844e7i	−0.511901	+	0.214125i
$489$	3.76957e7	−	4.65735e7i	0.322378	−	0.398302i
$490$	8.03255e7	−	4.53532e7i	0.682755	−	0.385496i
$491$	9.98700e7			0.843705			0.421852	−	0.906665i	$-0.361380\pi$
$491$	9.98700e7			0.843705			0.421852	+	0.906665i	$0.361380\pi$
$492$	4.69000e6	+	1.21249e7i	0.0393801	+	0.101808i
$493$	1.64626e8	+	1.64626e8i	1.37391	+	1.37391i
$494$	2.22216e7	+	1.70103e7i	0.184329	+	0.141102i
$495$	−8.23279e7	−	1.22464e8i	−0.678784	−	1.00971i
$496$	−3.95808e7	−	6.78276e7i	−0.324369	−	0.555855i
$497$	−3.13577e7	−	3.13577e7i	−0.255432	−	0.255432i
$498$	−1.63545e8	−	9.99049e7i	−1.32418	−	0.808907i
$499$	1.15931e7			0.0933037			0.0466519	−	0.998911i	$-0.485145\pi$
$499$	1.15931e7			0.0933037			0.0466519	+	0.998911i	$0.485145\pi$
$500$	1.23386e8	+	2.00216e7i	0.987089	+	0.160173i
$501$	−1.01144e8	+	1.24965e8i	−0.804316	+	0.993743i
$502$	1.43510e8	−	1.90627e7i	1.13441	−	0.150686i
$503$	−1.08337e8	−	1.08337e8i	−0.851282	−	0.851282i	0.139009	−	0.990291i	$-0.455608\pi$
$503$	−1.08337e8	−	1.08337e8i	−0.851282	−	0.851282i	−0.990291	+	0.139009i	$0.955608\pi$
$504$	−5.85373e7	−	1.06093e7i	−0.457236	−	0.0828697i
$505$	−1.26590e8	+	5.08461e7i	−0.982933	+	0.394806i
$506$	−1.59954e7	−	1.22443e7i	−0.123465	−	0.0945108i
$507$	1.13277e7	+	1.07524e8i	0.0869195	+	0.825050i
$508$	−1.75134e8	−	1.00573e8i	−1.33592	−	0.767167i
$509$	7.95954e6			0.0603580			0.0301790	−	0.999545i	$-0.490392\pi$
$509$	7.95954e6			0.0603580			0.0301790	+	0.999545i	$0.490392\pi$
$510$	−3.83321e7	+	2.28178e8i	−0.288969	+	1.72014i
$511$		−	9.98827e7i		−	0.748562i
$512$	−5.00663e7	+	1.24530e8i	−0.373023	+	0.927822i
$513$	7.21908e7	−	2.35146e7i	0.534724	−	0.174175i
$514$	−1.43720e8	−	1.10016e8i	−1.05835	−	0.810150i
$515$	−1.53338e8	−	6.54569e7i	−1.12261	−	0.479219i
$516$	7.10477e7	−	1.60683e8i	0.517132	−	1.16955i
$517$	−1.75267e8	+	1.75267e8i	−1.26832	+	1.26832i
$518$	−6.46040e7	+	8.58148e6i	−0.464804	+	0.0617409i
$519$	1.85548e7	−	2.29247e7i	0.132725	−	0.163984i
$520$	−422729.	+	5.80382e7i	−0.00300644	+	0.412766i
$521$			8.03462e7i			0.568136i	0.958804	+	0.284068i	$0.0916841\pi$
$521$			8.03462e7i			0.568136i	−0.958804	+	0.284068i	$0.908316\pi$
$522$	1.49270e8	−	5.31361e7i	1.04945	−	0.373575i
$523$	−6.18621e6	+	6.18621e6i	−0.0432434	+	0.0432434i	−0.728398	−	0.685154i	$-0.759735\pi$
$523$	−6.18621e6	+	6.18621e6i	−0.0432434	+	0.0432434i	0.685154	+	0.728398i	$0.259735\pi$
$524$	7.38498e7	−	1.99716e7i	0.513281	−	0.138810i
$525$	6.70075e7	−	5.60413e6i	0.463069	−	0.0387285i
$526$	1.97862e8	+	1.51461e8i	1.35958	+	1.04074i
$527$	−1.16178e8	+	1.16178e8i	−0.793763	+	0.793763i
$528$	−1.44371e8	+	1.05972e8i	−0.980793	+	0.719928i
$529$		−	1.45618e8i		−	0.983668i
$530$	−9.10682e7	−	2.53413e7i	−0.611701	−	0.170217i
$531$	3.48328e7	+	1.63483e8i	0.232651	+	1.09192i
$532$	−3.41217e7	−	1.95948e7i	−0.226619	−	0.130139i
$533$	4.82438e6	−	4.82438e6i	0.0318611	−	0.0318611i
$534$	−1.36675e8	+	3.30157e7i	−0.897564	+	0.216819i
$535$	−3.88068e7	−	1.65658e7i	−0.253423	−	0.108181i
$536$	−9.57962e7	−	3.92903e7i	−0.622091	−	0.255147i
$537$	−2.32942e7	−	2.21111e8i	−0.150427	−	1.42787i
$538$	−7.93181e7	+	1.05360e7i	−0.509361	+	0.0676595i
$539$		−	1.49378e8i		−	0.953940i
$540$	1.29079e8	+	9.01867e7i	0.819734	+	0.572745i
$541$	2.48420e8			1.56890			0.784450	−	0.620192i	$-0.212945\pi$
$541$	2.48420e8			1.56890			0.784450	+	0.620192i	$0.212945\pi$
$542$	−2.24792e6	−	1.69230e7i	−0.0141183	−	0.106287i
$543$	2.50355e8	−	2.63751e7i	1.56371	−	0.164738i
$544$	2.78609e8	+	3.50378e7i	1.73061	+	0.217640i
$545$	2.40131e8	−	9.64514e7i	1.48340	−	0.595825i
$546$	7.33108e6	+	3.03485e7i	0.0450391	+	0.186449i
$547$	6.22856e7	+	6.22856e7i	0.380562	+	0.380562i	0.871305	−	0.490743i	$-0.163274\pi$
$547$	6.22856e7	+	6.22856e7i	0.380562	+	0.380562i	−0.490743	+	0.871305i	$0.663274\pi$
$548$	2.12505e8	+	1.22033e8i	1.29130	+	0.741545i
$549$	8.97999e7	−	1.91333e7i	0.542699	−	0.115631i
$550$	1.26471e8	−	1.58049e8i	0.760154	−	0.949956i
$551$	1.04797e8			0.626462
$552$	2.06326e7	+	6.02821e6i	0.122669	+	0.0358402i
$553$	−8.47192e7	−	8.47192e7i	−0.500964	−	0.500964i
$554$	−1.36492e8	+	1.78308e8i	−0.802747	+	1.04868i
$555$	1.64871e8	+	5.07294e7i	0.964421	+	0.296743i
$556$	−4.04038e6	+	1.09266e6i	−0.0235070	+	0.00635714i
$557$	4.17997e7	+	4.17997e7i	0.241884	+	0.241884i	0.817629	−	0.575745i	$-0.195288\pi$
$557$	4.17997e7	+	4.17997e7i	0.241884	+	0.241884i	−0.575745	+	0.817629i	$0.695288\pi$
$558$	3.74983e7	+	1.05340e8i	0.215829	+	0.606307i
$559$	−9.22033e7			−0.527851
$560$	−1.01561e7	−	8.09718e7i	−0.0578310	−	0.461073i
$561$	2.91240e8	+	2.35724e8i	1.64954	+	1.33510i
$562$	−5.90876e6	−	4.44829e7i	−0.0332880	−	0.250602i
$563$	1.93155e8	+	1.93155e8i	1.08238	+	1.08238i	0.996287	+	0.0860974i	$0.0274396\pi$
$563$	1.93155e8	+	1.93155e8i	1.08238	+	1.08238i	0.0860974	+	0.996287i	$0.472560\pi$
$564$	1.06959e8	−	2.41901e8i	0.596185	−	1.34834i
$565$	−1.44508e8	−	6.16872e7i	−0.801208	−	0.342019i
$566$	−1.38433e8	+	1.80843e8i	−0.763466	+	0.997360i
$567$	7.91083e7	+	3.02784e7i	0.433983	+	0.166105i
$568$	1.31420e8	−	5.49724e7i	0.717162	−	0.299985i
$569$	1.30612e8			0.708998			0.354499	−	0.935056i	$-0.384651\pi$
$569$	1.30612e8			0.708998			0.354499	+	0.935056i	$0.384651\pi$
$570$	6.04255e7	+	8.48267e7i	0.326284	+	0.458045i
$571$		−	4.58140e7i		−	0.246087i	−0.992401	−	0.123044i	$-0.960734\pi$
$571$		−	4.58140e7i		−	0.246087i	0.992401	−	0.123044i	$-0.0392655\pi$
$572$	8.15045e7	+	4.68050e7i	0.435505	+	0.250094i
$573$	−3.89155e7	+	4.09977e6i	−0.206851	+	0.0217919i
$574$	−5.83103e6	+	7.61741e6i	−0.0308325	+	0.0402784i
$575$	−2.42899e7	−	522879.i	−0.127768	−	0.00275041i
$576$	1.02886e8	−	1.61043e8i	0.538381	−	0.842701i
$577$	4.07806e7	−	4.07806e7i	0.212288	−	0.212288i	−0.592951	−	0.805239i	$-0.702037\pi$
$577$	4.07806e7	−	4.07806e7i	0.212288	−	0.212288i	0.805239	+	0.592951i	$0.202037\pi$
$578$	−5.19305e7	−	3.90948e8i	−0.268930	−	2.02458i
$579$	1.73841e7	+	1.40703e7i	0.0895604	+	0.0724884i
$580$	1.30851e8	+	1.73543e8i	0.670648	+	0.889455i
$581$		−	1.41416e8i		−	0.721055i
$582$	−2.37931e7	+	3.89493e7i	−0.120693	+	0.197575i
$583$	−1.08241e8	+	1.08241e8i	−0.546244	+	0.546244i
$584$	2.96856e8	+	1.21754e8i	1.49041	+	0.611285i
$585$	1.58937e7	−	8.10958e7i	0.0793884	−	0.405070i
$586$	−1.39081e8	+	1.81690e8i	−0.691156	+	0.902898i
$587$	−3.71703e7	+	3.71703e7i	−0.183773	+	0.183773i	−0.792998	−	0.609225i	$-0.791481\pi$
$587$	−3.71703e7	+	3.71703e7i	−0.183773	+	0.183773i	0.609225	+	0.792998i	$0.291481\pi$
$588$	5.75046e7	+	1.48665e8i	0.282859	+	0.731268i
$589$			7.39558e7i			0.361931i
$590$	−1.99663e8	+	1.12733e8i	−0.972170	+	0.548904i
$591$	−1.29228e8	−	1.04595e8i	−0.626028	−	0.506695i
$592$	5.32455e7	−	2.02466e8i	0.256636	−	0.975859i
$593$	−1.28214e8	+	1.28214e8i	−0.614853	+	0.614853i	−0.944207	−	0.329354i	$-0.893169\pi$
$593$	−1.28214e8	+	1.28214e8i	−0.614853	+	0.614853i	0.329354	+	0.944207i	$0.393169\pi$
$594$	2.29944e8	−	1.10212e8i	1.09714	−	0.525859i
$595$	−1.58430e8	+	6.36352e7i	−0.752120	+	0.302097i
$596$	−3.03674e8	+	8.21243e7i	−1.43439	+	0.387912i
$597$	5.89162e7	−	6.20686e6i	0.276893	−	0.0291709i
$598$	−1.48541e6	−	1.11826e7i	−0.00694614	−	0.0522927i
$599$			1.42587e8i			0.663435i	0.943379	+	0.331717i	$0.107628\pi$
$599$			1.42587e8i			0.663435i	−0.943379	+	0.331717i	$0.892372\pi$
$600$	−6.50242e7	+	2.05980e8i	−0.301038	+	0.953612i
$601$	−2.67137e8			−1.23058			−0.615290	−	0.788301i	$-0.710961\pi$
$601$	−2.67137e8			−1.23058			−0.615290	+	0.788301i	$0.710961\pi$
$602$	1.28513e8	−	1.70706e7i	0.589057	−	0.0782457i
$603$	1.23679e8	+	8.02325e7i	0.564085	+	0.365931i
$604$	8.20492e6	+	3.03396e7i	0.0372361	+	0.137689i
$605$	−3.96384e7	−	9.86863e7i	−0.178999	−	0.445647i
$606$	−5.53523e7	−	2.29142e8i	−0.248724	−	1.02964i
$607$	−1.50781e7	−	1.50781e7i	−0.0674187	−	0.0674187i	0.672594	−	0.740012i	$-0.265180\pi$
$607$	−1.50781e7	−	1.50781e7i	−0.0674187	−	0.0674187i	−0.740012	+	0.672594i	$0.765180\pi$
$608$	9.98299e7	−	7.75257e7i	0.444171	−	0.344933i
$609$	9.08798e7	+	7.35563e7i	0.402361	+	0.325663i
$610$	6.19234e7	+	1.09673e8i	0.272813	+	0.483183i
$611$	−1.38808e8			−0.608543
$612$	−3.80593e8	−	1.22482e8i	−1.66038	−	0.534342i
$613$	−8.11069e7	−	8.11069e7i	−0.352109	−	0.352109i	0.508785	−	0.860894i	$-0.330095\pi$
$613$	−8.11069e7	−	8.11069e7i	−0.352109	−	0.352109i	−0.860894	+	0.508785i	$0.830095\pi$
$614$	−1.98358e8	−	1.51841e8i	−0.856931	−	0.655969i
$615$	2.24405e7	−	1.18803e7i	0.0964734	−	0.0510744i
$616$	−1.22266e8	−	5.01469e7i	−0.523076	−	0.214537i
$617$	−2.57792e8	−	2.57792e8i	−1.09752	−	1.09752i	−0.994700	−	0.102822i	$-0.967213\pi$
$617$	−2.57792e8	−	2.57792e8i	−1.09752	−	1.09752i	−0.102822	−	0.994700i	$-0.532787\pi$
$618$	1.50188e8	−	2.45857e8i	0.636310	−	1.04164i
$619$	−4.15111e8			−1.75022			−0.875109	−	0.483925i	$-0.839211\pi$
$619$	−4.15111e8			−1.75022			−0.875109	+	0.483925i	$0.839211\pi$
$620$	−1.22470e8	+	9.23425e7i	−0.513873	+	0.387460i
$621$	−2.72798e7	−	1.38746e7i	−0.113911	−	0.0579357i
$622$	−2.85589e7	+	3.79354e6i	−0.118678	+	0.0157642i
$623$	−7.33650e7	−	7.33650e7i	−0.303407	−	0.303407i
$624$	−9.91332e7	−	1.52055e7i	−0.408005	−	0.0625817i
$625$	1.05061e7	−	2.43914e8i	0.0430332	−	0.999074i
$626$	−9.18887e7	−	7.03396e7i	−0.374575	−	0.286733i
$627$	1.67726e8	−	1.76700e7i	0.680452	−	0.0716861i
$628$	−4.66339e7	+	8.12065e7i	−0.188288	+	0.327878i
$629$	−4.37992e8			−1.76001
$630$	−7.13844e6	+	1.15974e8i	−0.0285484	+	0.463808i
$631$		−	1.41194e7i		−	0.0561991i	−0.999605	−	0.0280995i	$-0.991054\pi$
$631$		−	1.41194e7i		−	0.0561991i	0.999605	−	0.0280995i	$-0.00894554\pi$
$632$	3.55059e8	−	1.48519e8i	1.40653	−	0.588343i
$633$	−8.04778e6	−	7.63904e7i	−0.0317296	−	0.301181i
$634$	9.61268e6	+	7.35838e6i	0.0377204	+	0.0288745i
$635$	−1.54862e8	+	3.62777e8i	−0.604816	+	1.41683i
$636$	6.60558e7	−	1.49393e8i	0.256767	−	0.580708i
$637$	5.91523e7	−	5.91523e7i	0.228851	−	0.228851i
$638$	3.48899e8	−	4.63450e7i	1.34350	−	0.178460i
$639$	−1.98378e8	+	4.22676e7i	−0.760309	+	0.161996i
$640$	2.53031e8	+	6.85176e7i	0.965238	+	0.261374i
$641$			3.77180e8i			1.43211i	0.698046	+	0.716053i	$0.254053\pi$
$641$			3.77180e8i			1.43211i	−0.698046	+	0.716053i	$0.745947\pi$
$642$	3.80093e7	−	6.22214e7i	0.143643	−	0.235144i
$643$	2.72018e8	−	2.72018e8i	1.02321	−	1.02321i	0.0234867	−	0.999724i	$-0.492523\pi$
$643$	2.72018e8	−	2.72018e8i	1.02321	−	1.02321i	0.999724	−	0.0234867i	$-0.00747674\pi$
$644$	4.14073e6	+	1.53113e7i	0.0155031	+	0.0573265i
$645$	−3.27969e8	−	1.00913e8i	−1.22223	−	0.376069i
$646$	−2.09982e8	−	1.60739e8i	−0.778906	−	0.596242i
$647$	−5.11230e7	+	5.11230e7i	−0.188757	+	0.188757i	−0.795159	−	0.606401i	$-0.792612\pi$
$647$	−5.11230e7	+	5.11230e7i	−0.188757	+	0.188757i	0.606401	+	0.795159i	$0.292612\pi$
$648$	−1.86419e8	+	1.98205e8i	−0.685118	+	0.728432i
$649$			3.71306e8i			1.35831i
$650$	1.12667e8	−	1.25047e7i	0.410258	−	0.0455338i
$651$	−5.19090e7	+	6.41343e7i	−0.188148	+	0.232459i
$652$	−7.07274e7	+	1.23162e8i	−0.255179	+	0.444359i
$653$	1.64275e7	−	1.64275e7i	0.0589973	−	0.0589973i	−0.676993	−	0.735990i	$-0.736717\pi$
$653$	1.64275e7	−	1.64275e7i	0.0589973	−	0.0589973i	0.735990	+	0.676993i	$0.236717\pi$
$654$	1.04999e8	+	4.34666e8i	0.375364	+	1.55390i
$655$	−5.56914e7	−	1.38653e8i	−0.198182	−	0.493406i
$656$	−1.55314e7	−	2.66154e7i	−0.0550174	−	0.0942805i
$657$	−3.83260e8	−	2.48626e8i	−1.35144	−	0.876700i
$658$	1.93470e8	−	2.56991e7i	0.679105	−	0.0902070i
$659$		−	4.86957e8i		−	1.70151i	−0.525563	−	0.850755i	$-0.676145\pi$
$659$		−	4.86957e8i		−	1.70151i	0.525563	−	0.850755i	$-0.323855\pi$
$660$	2.38687e8	+	2.55690e8i	0.830227	+	0.889368i
$661$	−2.08008e8			−0.720236			−0.360118	−	0.932907i	$-0.617264\pi$
$661$	−2.08008e8			−0.720236			−0.360118	+	0.932907i	$0.617264\pi$
$662$	−7.60946e7	−	5.72863e8i	−0.262289	−	1.97459i
$663$	2.19838e7	+	2.08672e8i	0.0754330	+	0.716018i
$664$	4.20293e8	+	1.72381e8i	1.43565	+	0.588823i
$665$	−3.01720e7	+	7.06806e7i	−0.102598	+	0.240345i
$666$	−1.27883e8	+	2.69253e8i	−0.432903	+	0.911460i
$667$	−2.98713e7	−	2.98713e7i	−0.100665	−	0.100665i
$668$	1.89774e8	−	3.30465e8i	0.636659	−	1.10865i
$669$	1.21233e8	−	1.49785e8i	0.404897	−	0.500255i
$670$	−5.42136e7	+	1.94825e8i	−0.180254	+	0.647770i
$671$	2.03955e8			0.675099
$672$	1.40987e8	+	2.83977e6i	0.464591	+	0.00935784i
$673$	2.28312e8	+	2.28312e8i	0.749004	+	0.749004i	0.974292	−	0.225288i	$-0.0723323\pi$
$673$	2.28312e8	+	2.28312e8i	0.749004	+	0.749004i	−0.225288	+	0.974292i	$0.572332\pi$
$674$	−3.57825e8	+	4.67448e8i	−1.16867	+	1.52670i
$675$	1.45290e8	−	2.71064e8i	0.472417	−	0.881375i
$676$	−6.69043e7	−	2.47394e8i	−0.216578	−	0.800847i
$677$	1.99823e8	+	1.99823e8i	0.643991	+	0.643991i	0.951534	−	0.307543i	$-0.0995069\pi$
$677$	1.99823e8	+	1.99823e8i	0.643991	+	0.643991i	−0.307543	+	0.951534i	$0.599507\pi$
$678$	1.41538e8	−	2.31699e8i	0.454135	−	0.743420i
$679$	−3.36791e7			−0.107585
$680$	3.99457e6	−	5.48430e8i	0.0127041	−	1.74419i
$681$	−1.23030e8	+	1.52006e8i	−0.389557	+	0.481303i
$682$	3.27059e7	+	2.46220e8i	0.103103	+	0.776193i
$683$	−6.81572e7	−	6.81572e7i	−0.213919	−	0.213919i	0.592011	−	0.805930i	$-0.298334\pi$
$683$	−6.81572e7	−	6.81572e7i	−0.213919	−	0.213919i	−0.805930	+	0.592011i	$0.798334\pi$
$684$	−1.60123e8	+	8.21533e7i	−0.500362	+	0.256718i
$685$	1.87907e8	−	4.40187e8i	0.584615	−	1.36951i
$686$	−1.62680e8	+	2.12518e8i	−0.503919	+	0.658299i
$687$	3.74597e6	+	3.55571e7i	0.0115530	+	0.109662i
$688$	−1.05918e8	+	4.02754e8i	−0.325241	+	1.23673i
$689$	−8.57249e7			−0.262089
$690$	6.95531e6	−	4.14026e7i	0.0211724	−	0.126032i
$691$			1.21697e8i			0.368846i	0.982847	+	0.184423i	$0.0590416\pi$
$691$			1.21697e8i			0.368846i	−0.982847	+	0.184423i	$0.940958\pi$
$692$	−3.48138e7	+	6.06235e7i	−0.105059	+	0.182946i
$693$	1.57854e8	+	1.02402e8i	0.474303	+	0.307687i
$694$	1.14870e8	−	1.50061e8i	0.343659	−	0.448942i
$695$	3.04692e6	+	7.58579e6i	0.00907625	+	0.0225968i
$696$	−3.29392e8	+	1.80436e8i	−0.976979	+	0.535174i
$697$	−4.55879e7	+	4.55879e7i	−0.134633	+	0.134633i
$698$	5.90818e7	+	4.44785e8i	0.173735	+	1.30793i
$699$	−1.88516e8	+	2.32914e8i	−0.551972	+	0.681969i
$700$	−1.54720e8	+	3.82883e7i	−0.451079	+	0.111628i
$701$		−	1.57263e8i		−	0.456534i	−0.973599	−	0.228267i	$-0.926694\pi$
$701$		−	1.57263e8i		−	0.456534i	0.973599	−	0.228267i	$-0.0733059\pi$
$702$	1.34699e8	+	4.74129e7i	0.389360	+	0.137052i
$703$	−1.39408e8	+	1.39408e8i	−0.401255	+	0.401255i
$704$	2.98077e8	−	3.02253e8i	0.854300	−	0.866269i
$705$	−4.93743e8	−	1.51920e8i	−1.40907	−	0.433558i
$706$	1.44306e8	−	1.88516e8i	0.410082	−	0.535715i
$707$	1.23000e8	−	1.23000e8i	0.348054	−	0.348054i
$708$	−1.42938e8	−	3.69533e8i	−0.402761	−	1.04125i
$709$			4.42674e7i			0.124207i	0.998070	+	0.0621033i	$0.0197808\pi$
$709$			4.42674e7i			0.124207i	−0.998070	+	0.0621033i	$0.980219\pi$
$710$	−1.36796e8	−	2.42280e8i	−0.382206	−	0.676928i
$711$	−5.35958e8	+	1.14194e8i	−1.49115	+	0.317714i
$712$	3.07473e8	−	1.28614e8i	0.851858	−	0.356327i
$713$	2.10803e7	−	2.10803e7i	0.0581579	−	0.0581579i
$714$	−6.92748e7	−	2.86777e8i	−0.190318	−	0.787861i
$715$	7.20701e7	−	1.68830e8i	0.197168	−	0.461884i
$716$	1.37582e8	+	5.08740e8i	0.374819	+	1.38598i
$717$	2.43780e6	+	2.31398e7i	0.00661363	+	0.0627773i
$718$	3.51721e7	+	2.64786e8i	0.0950221	+	0.715355i
$719$			3.61244e8i			0.971883i	0.873991	+	0.485941i	$0.161523\pi$
$719$			3.61244e8i			0.971883i	−0.873991	+	0.485941i	$0.838477\pi$
$720$	−3.35977e8	−	1.62584e8i	−0.900144	−	0.435592i
$721$	2.12591e8			0.567203
$722$	2.55094e8	−	3.38847e7i	0.677780	−	0.0900310i
$723$	7.50479e6	−	790634.i	0.0198574	−	0.00209200i
$724$	−5.76026e8	+	1.55778e8i	−1.51784	+	0.410479i
$725$	3.06560e8	−	2.93640e8i	0.804456	−	0.770551i
$726$	1.78634e8	−	4.31513e7i	0.466825	−	0.112768i
$727$	5.00844e8	+	5.00844e8i	1.30346	+	1.30346i	0.926040	+	0.377425i	$0.123190\pi$
$727$	5.00844e8	+	5.00844e8i	1.30346	+	1.30346i	0.377425	+	0.926040i	$0.376810\pi$
$728$	−2.85586e7	−	6.82739e7i	−0.0740189	−	0.176954i
$729$	3.13096e8	−	2.28178e8i	0.808157	−	0.588968i
$730$	1.67998e8	−	6.03729e8i	0.431853	−	1.55193i
$731$	8.71273e8			2.23050
$732$	−2.02981e8	+	7.85145e7i	−0.517514	+	0.200178i
$733$	−3.58163e7	−	3.58163e7i	−0.0909430	−	0.0909430i	0.660172	−	0.751115i	$-0.270484\pi$
$733$	−3.58163e7	−	3.58163e7i	−0.0909430	−	0.0909430i	−0.751115	+	0.660172i	$0.770484\pi$
$734$	3.62335e8	+	2.77362e8i	0.916266	+	0.701390i
$735$	2.75146e8	−	1.45666e8i	0.692949	−	0.366857i
$736$	−5.05533e7	−	6.35757e6i	−0.126799	−	0.0159462i
$737$	2.31564e8	+	2.31564e8i	0.578454	+	0.578454i
$738$	1.47143e7	+	4.13354e7i	0.0366075	+	0.102838i
$739$	3.84735e8			0.953297			0.476649	−	0.879094i	$-0.341851\pi$
$739$	3.84735e8			0.953297			0.476649	+	0.879094i	$0.341851\pi$
$740$	−4.04924e8	−	5.67913e7i	−0.999261	−	0.140148i
$741$	7.34150e7	+	5.94206e7i	0.180439	+	0.146044i
$742$	1.19483e8	−	1.58712e7i	0.292479	−	0.0388507i
$743$	−9.06897e7	−	9.06897e7i	−0.221102	−	0.221102i	0.587861	−	0.808962i	$-0.299970\pi$
$743$	−9.06897e7	−	9.06897e7i	−0.221102	−	0.221102i	−0.808962	+	0.587861i	$0.799970\pi$
$744$	−1.27334e8	−	2.32453e8i	−0.309191	−	0.564439i
$745$	2.29006e8	+	5.70146e8i	0.553831	+	1.37885i
$746$	3.50223e8	+	2.68091e8i	0.843585	+	0.645753i
$747$	−5.42625e8	−	3.52009e8i	−1.30178	−	0.844485i
$748$	−7.70174e8	−	4.42282e8i	−1.84028	−	1.05680i
$749$	5.38023e7			0.128043
$750$	4.14445e8	+	7.88301e7i	0.982387	+	0.186857i
$751$		−	3.04469e8i		−	0.718826i	−0.933179	−	0.359413i	$-0.882977\pi$
$751$		−	3.04469e8i		−	0.718826i	0.933179	−	0.359413i	$-0.117023\pi$
$752$	−1.59455e8	+	6.06328e8i	−0.374960	+	1.42579i
$753$	4.85910e8	−	5.11909e7i	1.13807	−	0.119897i
$754$	1.56513e8	+	1.19808e8i	0.365120	+	0.279495i
$755$	5.69625e7	−	2.28796e7i	0.132357	−	0.0531628i
$756$	−1.96521e8	−	4.11457e7i	−0.454824	−	0.0952268i
$757$	3.12544e8	−	3.12544e8i	0.720483	−	0.720483i	−0.248220	−	0.968704i	$-0.579846\pi$
$757$	3.12544e8	−	3.12544e8i	0.720483	−	0.720483i	0.968704	+	0.248220i	$0.0798457\pi$
$758$	−1.86790e8	+	2.48117e7i	−0.428889	+	0.0569703i
$759$	−5.28451e7	−	4.27718e7i	−0.120859	−	0.0978211i
$760$	−1.73287e8	−	1.75830e8i	−0.394753	−	0.400545i
$761$			1.83756e8i			0.416953i	0.978027	+	0.208477i	$0.0668505\pi$
$761$			1.83756e8i			0.416953i	−0.978027	+	0.208477i	$0.933149\pi$
$762$	−5.81664e8	−	3.55323e8i	−1.31464	−	0.803079i
$763$	−2.33322e8	+	2.33322e8i	−0.525269	+	0.525269i
$764$	8.95381e7	−	2.42143e7i	0.200783	−	0.0542990i
$765$	−1.50187e8	+	7.66312e8i	−0.335466	+	1.71167i
$766$	−7.03860e7	−	5.38795e7i	−0.156603	−	0.119877i
$767$	−1.47034e8	+	1.47034e8i	−0.325860	+	0.325860i
$768$	−1.80298e8	+	4.15557e8i	−0.398023	+	0.917376i
$769$		−	6.62230e7i		−	0.145623i	−0.997346	−	0.0728115i	$-0.976803\pi$
$769$		−	6.62230e7i		−	0.145623i	0.997346	−	0.0728115i	$-0.0231972\pi$
$770$	−6.91937e7	+	2.48659e8i	−0.151563	+	0.544668i
$771$	−4.74817e8	−	3.84308e8i	−1.03601	−	0.838525i
$772$	−4.59716e7	−	2.63998e7i	−0.0999167	−	0.0573785i
$773$	2.46245e8	−	2.46245e8i	0.533125	−	0.533125i	−0.388376	−	0.921501i	$-0.626964\pi$
$773$	2.46245e8	−	2.46245e8i	0.533125	−	0.533125i	0.921501	+	0.388376i	$0.126964\pi$
$774$	2.54390e8	−	5.35609e8i	0.548628	−	1.15511i
$775$	2.07223e8	+	2.16341e8i	0.445178	+	0.464765i
$776$	4.10537e7	−	1.00096e8i	0.0878552	−	0.214205i
$777$	−2.18743e8	+	2.30447e7i	−0.466306	+	0.0491257i
$778$	−9.34952e7	+	1.24192e7i	−0.198541	+	0.0263727i
$779$			2.90201e7i			0.0613884i
$780$	−6.73299e6	+	1.95768e8i	−0.0141881	+	0.412533i
$781$	−4.50559e8			−0.945799
$782$	1.40364e7	+	1.05670e8i	0.0293518	+	0.220969i
$783$	5.08460e8	−	1.65620e8i	1.05918	−	0.345006i
$784$	−1.90433e8	−	3.26335e8i	−0.395178	−	0.677197i
$785$	1.68213e8	+	7.18066e7i	0.347737	+	0.148442i
$786$	2.50978e8	−	6.06270e7i	0.516854	−	0.124853i
$787$	−1.06376e7	−	1.06376e7i	−0.0218233	−	0.0218233i	0.696111	−	0.717934i	$-0.254912\pi$
$787$	−1.06376e7	−	1.06376e7i	−0.0218233	−	0.0218233i	−0.717934	+	0.696111i	$0.754912\pi$
$788$	3.41739e8	+	1.96248e8i	0.698419	+	0.401076i
$789$	6.53692e8	+	5.29085e8i	1.33089	+	1.07720i
$790$	−3.69581e8	−	6.54569e8i	−0.749598	−	1.32762i
$791$	2.00348e8			0.404813
$792$	−4.96762e8	+	3.44323e8i	−0.999937	+	0.693092i
$793$	8.07643e7	+	8.07643e7i	0.161957	+	0.161957i
$794$	1.82941e7	−	2.38986e7i	0.0365468	−	0.0477432i
$795$	−3.04925e8	−	9.38226e7i	−0.606865	−	0.186726i
$796$	−1.35557e8	+	3.66594e7i	−0.268770	+	0.0726852i
$797$	2.52410e8	+	2.52410e8i	0.498576	+	0.498576i	0.910995	−	0.412418i	$-0.135316\pi$
$797$	2.52410e8	+	2.52410e8i	0.498576	+	0.498576i	−0.412418	+	0.910995i	$0.635316\pi$
$798$	−1.13327e8	−	6.92283e7i	−0.223010	−	0.136231i
$799$	1.31166e9			2.57147
$800$	7.48038e7	−	5.06506e8i	0.146101	−	0.989270i
$801$	−4.64128e8	+	9.88899e7i	−0.903109	+	0.192422i
$802$	2.16556e6	+	1.63030e7i	0.00419804	+	0.0316041i
$803$	−7.17576e8	−	7.17576e8i	−1.38587	−	1.38587i
$804$	−3.19601e8	−	1.41315e8i	−0.614950	−	0.271907i
$805$	2.87470e7	−	1.15465e7i	0.0551067	−	0.0221342i
$806$	−8.45493e7	+	1.10452e8i	−0.161475	+	0.210944i
$807$	−2.68564e8	+	2.82934e7i	−0.511007	+	0.0538349i
$808$	2.15628e8	+	5.15493e8i	0.408762	+	0.977212i
$809$	3.55516e8			0.671451			0.335725	−	0.941960i	$-0.391019\pi$
$809$	3.55516e8			0.671451			0.335725	+	0.941960i	$0.391019\pi$
$810$	4.27234e8	+	3.16071e8i	0.803916	+	0.594743i
$811$		−	1.79360e8i		−	0.336250i	−0.985766	−	0.168125i	$-0.946229\pi$
$811$		−	1.79360e8i		−	0.336250i	0.985766	−	0.168125i	$-0.0537712\pi$
$812$	−2.40329e8	−	1.38012e8i	−0.448888	−	0.257779i
$813$	−6.03657e6	−	5.72998e7i	−0.0112336	−	0.106631i
$814$	−4.02476e8	+	5.25778e8i	−0.746220	+	0.974831i
$815$	2.55121e8	+	1.08906e8i	0.471274	+	0.201177i
$816$	9.36757e8	+	1.43684e8i	1.72408	+	0.264447i
$817$	2.77315e8	−	2.77315e8i	0.508519	−	0.508519i
$818$	6.61430e7	+	4.97945e8i	0.120844	+	0.909748i
$819$	2.19583e7	+	1.03059e8i	0.0399713	+	0.187600i
$820$	−4.80571e7	+	3.62350e7i	−0.0871597	+	0.0657183i
$821$		−	6.85022e8i		−	1.23787i	−0.785443	−	0.618935i	$-0.787565\pi$
$821$		−	6.85022e8i		−	1.23787i	0.785443	−	0.618935i	$-0.212435\pi$
$822$	7.05781e8	+	4.31142e8i	1.27073	+	0.776257i
$823$	−3.45508e8	+	3.45508e8i	−0.619810	+	0.619810i	−0.945483	−	0.325673i	$-0.894409\pi$
$823$	−3.45508e8	+	3.45508e8i	−0.619810	+	0.619810i	0.325673	+	0.945483i	$0.394409\pi$
$824$	−2.59141e8	+	6.31828e8i	−0.463185	+	1.12932i
$825$	4.41133e8	−	5.21656e8i	0.785612	−	0.929013i
$826$	1.77713e8	−	2.32157e8i	0.315341	−	0.411948i
$827$	3.52015e8	−	3.52015e8i	0.622364	−	0.622364i	−0.323771	−	0.946135i	$-0.604951\pi$
$827$	3.52015e8	−	3.52015e8i	0.622364	−	0.622364i	0.946135	+	0.323771i	$0.104951\pi$
$828$	6.90582e7	+	2.22243e7i	0.121653	+	0.0391505i
$829$		−	2.57882e8i		−	0.452645i	−0.974052	−	0.226322i	$-0.927330\pi$
$829$		−	2.57882e8i		−	0.452645i	0.974052	−	0.226322i	$-0.0726703\pi$
$830$	2.37855e8	−	8.54769e8i	0.415985	−	1.49491i
$831$	−4.76796e8	+	5.89088e8i	−0.830863	+	1.02654i
$832$	2.37725e8	−	1.65369e6i	0.412767	−	0.00287133i
$833$	−5.58958e8	+	5.58958e8i	−0.967040	+	0.967040i
$834$	−1.37312e7	+	3.31695e6i	−0.0236706	+	0.00571795i
$835$	−6.84534e8	−	2.92213e8i	−1.17581	−	0.501926i
$836$	−3.85910e8	+	1.04364e8i	−0.660491	+	0.178621i
$837$	1.16879e8	+	3.58822e8i	0.199323	+	0.611932i
$838$	−2.67070e7	−	2.01058e8i	−0.0453830	−	0.341657i
$839$		−	7.51339e8i		−	1.27218i	−0.771613	−	0.636092i	$-0.780550\pi$
$839$		−	7.51339e8i		−	1.27218i	0.771613	−	0.636092i	$-0.219450\pi$
$840$	−2.68603e7	−	2.74108e8i	−0.0453183	−	0.462470i
$841$	1.43292e8			0.240898
$842$	−4.97601e8	+	6.60974e7i	−0.833575	+	0.110726i
$843$	−1.58674e7	−	1.50615e8i	−0.0264864	−	0.251412i
$844$	4.75323e7	+	1.75762e8i	0.0790608	+	0.292346i
$845$	−4.64482e8	+	1.86564e8i	−0.769837	+	0.309213i
$846$	3.82973e8	−	8.06335e8i	0.632496	−	1.33169i
$847$	9.58878e7	+	9.58878e7i	0.157802	+	0.157802i
$848$	−9.84761e7	+	3.74455e8i	−0.161489	+	0.614063i
$849$	−4.83575e8	+	5.97463e8i	−0.790206	+	0.976310i
$850$	−1.06464e9	+	1.18163e8i	−1.73359	+	0.192408i
$851$	7.94733e7			0.128953
$852$	4.48407e8	−	1.73447e8i	0.725026	−	0.280445i
$853$	−2.56380e8	−	2.56380e8i	−0.413083	−	0.413083i	0.469728	−	0.882811i	$-0.344352\pi$
$853$	−2.56380e8	−	2.56380e8i	−0.413083	−	0.413083i	−0.882811	+	0.469728i	$0.844352\pi$
$854$	−1.27522e8	−	9.76163e7i	−0.204744	−	0.156729i
$855$	1.96105e8	+	2.91710e8i	0.313755	+	0.466717i
$856$	−6.55832e7	+	1.59903e8i	−0.104561	+	0.254938i
$857$	−3.11813e7	−	3.11813e7i	−0.0495395	−	0.0495395i	0.681903	−	0.731443i	$-0.261153\pi$
$857$	−3.11813e7	−	3.11813e7i	−0.0495395	−	0.0495395i	−0.731443	+	0.681903i	$0.761153\pi$
$858$	2.70697e8	+	1.65361e8i	0.428570	+	0.261801i
$859$	8.38332e8			1.32262			0.661312	−	0.750111i	$-0.270000\pi$
$859$	8.38332e8			1.32262			0.661312	+	0.750111i	$0.270000\pi$
$860$	8.05492e8	+	1.12972e8i	1.26639	+	0.177613i
$861$	−2.03690e7	+	2.51662e7i	−0.0319125	+	0.0394283i
$862$	−1.10187e9	+	1.46364e8i	−1.72032	+	0.228513i
$863$	2.20014e8	+	2.20014e8i	0.342309	+	0.342309i	0.857235	−	0.514926i	$-0.172180\pi$
$863$	2.20014e8	+	2.20014e8i	0.342309	+	0.342309i	−0.514926	+	0.857235i	$0.672180\pi$
$864$	3.61839e8	−	5.33912e8i	0.561014	−	0.827806i
$865$	1.25577e8	+	5.36062e7i	0.194027	+	0.0828260i
$866$	−9.37044e6	−	7.17295e6i	−0.0144280	−	0.0110444i
$867$	−1.39454e8	−	1.32372e9i	−0.213981	−	2.03113i
$868$	9.73956e7	−	1.69601e8i	0.148929	−	0.259340i
$869$	−1.21728e9			−1.85494
$870$	4.25593e8	+	5.97458e8i	0.646304	+	0.907298i
$871$			1.83394e8i			0.277544i
$872$	−4.09030e8	−	9.77853e8i	−0.616888	−	1.47477i
$873$	−8.38335e7	+	1.29230e8i	−0.126001	+	0.194232i
$874$	3.81011e7	+	2.91658e7i	0.0570693	+	0.0436858i
$875$	1.09785e8	+	2.91302e8i	0.163877	+	0.434830i
$876$	9.90387e8	+	4.37911e8i	1.47330	+	0.651439i
$877$	−5.84896e8	+	5.84896e8i	−0.867122	+	0.867122i	−0.992153	−	0.125031i	$-0.960097\pi$
$877$	−5.84896e8	+	5.84896e8i	−0.867122	+	0.867122i	0.125031	+	0.992153i	$0.460097\pi$
$878$	1.30963e8	−	1.73961e7i	0.193493	−	0.0257021i
$879$	−4.85841e8	+	6.00262e8i	−0.715364	+	0.883842i
$880$	−6.54679e8	−	5.08753e8i	−0.960684	−	0.746551i
$881$		−	7.80200e8i		−	1.14098i	−0.821305	−	0.570490i	$-0.806753\pi$
$881$		−	7.80200e8i		−	1.14098i	0.821305	−	0.570490i	$-0.193247\pi$
$882$	1.80413e8	+	5.06818e8i	0.262944	+	0.738662i
$883$	−8.59122e8	+	8.59122e8i	−1.24788	+	1.24788i	−0.291226	+	0.956654i	$0.594063\pi$
$883$	−8.59122e8	+	8.59122e8i	−1.24788	+	1.24788i	−0.956654	+	0.291226i	$0.905937\pi$
$884$	−1.29842e8	−	4.80121e8i	−0.187957	−	0.695014i
$885$	−6.83924e8	+	3.62079e8i	−0.986684	+	0.522365i
$886$	4.98006e8	+	3.81217e8i	0.716033	+	0.548114i
$887$	−5.41242e8	+	5.41242e8i	−0.775570	+	0.775570i	−0.979074	−	0.203504i	$-0.934767\pi$
$887$	−5.41242e8	+	5.41242e8i	−0.775570	+	0.775570i	0.203504	+	0.979074i	$0.434767\pi$
$888$	1.98150e8	−	6.78204e8i	0.282980	−	0.968548i
$889$		−	5.02960e8i		−	0.715860i
$890$	−3.20049e8	−	5.66843e8i	−0.453991	−	0.804067i
$891$	7.85855e8	−	3.50804e8i	1.11099	−	0.495942i
$892$	−2.27467e8	+	3.96103e8i	−0.320497	+	0.558102i
$893$	4.17486e8	−	4.17486e8i	0.586256	−	0.586256i
$894$	−1.03203e9	+	2.49301e8i	−1.44438	+	0.348908i
$895$	9.55158e8	−	3.83650e8i	1.33231	−	0.535138i
$896$	−3.31034e8	+	4.63176e7i	−0.460203	+	0.0643905i
$897$	−3.98893e6	−	3.78634e7i	−0.00552687	−	0.0524616i
$898$	−1.31246e8	+	1.74337e7i	−0.181241	+	0.0240747i
$899$			5.20891e8i			0.716915i
$900$	−2.38210e8	+	6.88983e8i	−0.326763	+	0.945106i
$901$	8.10055e8			1.10749
$902$	1.28337e7	+	9.66161e7i	0.0174877	+	0.131653i
$903$	4.35133e8	−	4.58415e7i	0.590960	−	0.0622581i
$904$	−2.44217e8	+	5.95441e8i	−0.330575	+	0.805997i
$905$	4.34392e8	+	1.08149e9i	0.586051	+	1.45907i
$906$	2.49073e7	+	1.03109e8i	0.0334921	+	0.138647i
$907$	−5.77093e7	−	5.77093e7i	−0.0773435	−	0.0773435i	0.667377	−	0.744720i	$-0.267417\pi$
$907$	−5.77093e7	−	5.77093e7i	−0.0773435	−	0.0773435i	−0.744720	+	0.667377i	$0.767417\pi$
$908$	2.30839e8	−	4.01974e8i	0.308355	−	0.536958i
$909$	−1.65794e8	−	7.78132e8i	−0.220737	−	1.03600i
$910$	−1.25866e8	+	7.10664e7i	−0.167027	+	0.0943062i
$911$	−1.32872e9			−1.75743			−0.878714	−	0.477349i	$-0.841598\pi$
$911$	−1.32872e9			−1.75743			−0.878714	+	0.477349i	$0.841598\pi$
$912$	3.43891e8	−	2.52425e8i	0.453353	−	0.332773i
$913$	−1.01596e9	−	1.01596e9i	−1.33494	−	1.33494i
$914$	7.41038e8	−	9.68062e8i	0.970515	−	1.26784i
$915$	1.98887e8	+	3.75673e8i	0.259623	+	0.490396i
$916$	−2.21247e7	−	8.18111e7i	−0.0287866	−	0.106445i
$917$	1.34721e8	+	1.34721e8i	0.174714	+	0.174714i
$918$	−1.27283e9	−	4.48026e8i	−1.64529	−	0.579129i
$919$	−7.46091e8			−0.961269			−0.480635	−	0.876921i	$-0.659594\pi$
$919$	−7.46091e8			−0.961269			−0.480635	+	0.876921i	$0.659594\pi$
$920$	−724810.	+	9.95120e7i	−0.000930810	+	0.127794i
$921$	−6.55330e8	−	5.30412e8i	−0.838844	−	0.678944i
$922$	1.60629e8	+	1.20926e9i	0.204942	+	1.54287i
$923$	−1.78417e8	−	1.78417e8i	−0.226898	−	0.226898i
$924$	−4.07912e8	−	1.80363e8i	−0.517072	−	0.228629i
$925$	−1.71873e7	+	7.98424e8i	−0.0217161	+	1.00881i
$926$	−4.22973e8	+	5.52554e8i	−0.532696	+	0.695892i
$927$	5.29177e8	−	8.15732e8i	0.664297	−	1.02402i
$928$	7.03129e8	−	5.46035e8i	0.879815	−	0.683245i
$929$	−4.55932e8			−0.568660			−0.284330	−	0.958726i	$-0.591771\pi$
$929$	−4.55932e8			−0.568660			−0.284330	+	0.958726i	$0.591771\pi$
$930$	−4.21629e8	+	3.00343e8i	−0.524181	+	0.373395i
$931$			3.55819e8i			0.440940i
$932$	3.53708e8	−	6.15934e8i	0.436915	−	0.760828i
$933$	−9.66977e7	+	1.01872e7i	−0.119061	+	0.0125432i
$934$	8.62181e8	−	1.12632e9i	1.05818	−	1.38236i
$935$	−6.81024e8	+	1.59536e9i	−0.833159	+	1.95175i
$936$	−3.33062e8	−	6.03642e7i	−0.406160	−	0.0736125i
$937$	2.47733e8	−	2.47733e8i	0.301137	−	0.301137i	−0.540321	−	0.841459i	$-0.681697\pi$
$937$	2.47733e8	−	2.47733e8i	0.301137	−	0.301137i	0.841459	+	0.540321i	$0.181697\pi$
$938$	−3.39538e7	−	2.55615e8i	−0.0411415	−	0.309726i
$939$	−3.03579e8	−	2.45711e8i	−0.366670	−	0.296775i
$940$	1.21263e9	+	1.70074e8i	1.45998	+	0.204764i
$941$		−	1.42847e9i		−	1.71436i	−0.515017	−	0.857180i	$-0.672215\pi$
$941$		−	1.42847e9i		−	1.71436i	0.515017	−	0.857180i	$-0.327785\pi$
$942$	−1.64757e8	+	2.69707e8i	−0.197102	+	0.322656i
$943$	8.27187e6	−	8.27187e6i	0.00986436	−	0.00986436i
$944$	4.73354e8	+	8.11163e8i	0.562692	+	0.964256i
$945$	−3.46876e7	+	3.90615e8i	−0.0411035	+	0.462864i
$946$	8.00622e8	−	1.04590e9i	0.945701	−	1.23542i
$947$	2.76795e8	−	2.76795e8i	0.325918	−	0.325918i	−0.525114	−	0.851032i	$-0.675977\pi$
$947$	2.76795e8	−	2.76795e8i	0.325918	−	0.325918i	0.851032	+	0.525114i	$0.175977\pi$
$948$	1.21146e9	−	4.68602e8i	1.42195	−	0.550021i
$949$		−	5.68306e8i		−	0.664942i
$950$	−3.01253e8	+	3.76472e8i	−0.351367	+	0.439099i
$951$	3.17580e7	+	2.57043e7i	0.0369243	+	0.0298858i
$952$	2.69864e8	+	6.45153e8i	0.312776	+	0.747742i
$953$	−1.42712e8	+	1.42712e8i	−0.164885	+	0.164885i	−0.784727	−	0.619842i	$-0.787197\pi$
$953$	−1.42712e8	+	1.42712e8i	−0.164885	+	0.164885i	0.619842	+	0.784727i	$0.287197\pi$
$954$	2.36516e8	−	4.97975e8i	0.272406	−	0.573539i
$955$	−6.75222e7	−	1.68107e8i	−0.0775241	−	0.193009i
$956$	−1.43983e7	−	5.32410e7i	−0.0164792	−	0.0609358i
$957$	1.18134e9	−	1.24455e8i	1.34784	−	0.141996i
$958$	1.17638e8	+	8.85612e8i	0.133798	+	1.00727i
$959$			6.10283e8i			0.691951i
$960$	8.47402e8	+	2.54298e8i	0.957802	+	0.287429i
$961$	5.19909e8			0.585810
$962$	−3.67579e8	+	4.88264e7i	−0.412882	+	0.0548440i
$963$	1.33924e8	−	2.06445e8i	0.149961	−	0.231167i
$964$	−1.72673e7	+	4.66969e6i	−0.0192749	+	0.00521263i
$965$	−4.06503e7	+	9.52269e7i	−0.0452358	+	0.105969i
$966$	1.25698e7	+	5.20354e7i	0.0139444	+	0.0577255i
$967$	−4.62580e8	−	4.62580e8i	−0.511572	−	0.511572i	0.403436	−	0.915008i	$-0.367816\pi$
$967$	−4.62580e8	−	4.62580e8i	−0.511572	−	0.511572i	−0.915008	+	0.403436i	$0.867816\pi$
$968$	−4.01866e8	+	1.68098e8i	−0.443053	+	0.185326i
$969$	−6.93732e8	−	5.61494e8i	−0.762466	−	0.617125i
$970$	−2.03569e8	−	5.66468e7i	−0.223047	−	0.0620669i
$971$	9.71776e8			1.06147			0.530736	−	0.847537i	$-0.321916\pi$
$971$	9.71776e8			1.06147			0.530736	+	0.847537i	$0.321916\pi$
$972$	−6.47056e8	+	6.51650e8i	−0.704601	+	0.709604i
$973$	−7.37068e6	−	7.37068e6i	−0.00800145	−	0.00800145i
$974$	7.41619e8	+	5.67700e8i	0.802609	+	0.614387i
$975$	3.81255e8	−	3.18860e7i	0.411341	−	0.0344022i
$976$	4.45565e8	−	2.60009e8i	0.479249	−	0.279666i
$977$	1.08531e9	+	1.08531e9i	1.16378	+	1.16378i	0.983641	+	0.180140i	$0.0576551\pi$
$977$	1.08531e9	+	1.08531e9i	1.16378	+	1.16378i	0.180140	+	0.983641i	$0.442345\pi$
$978$	−2.49879e8	+	4.09053e8i	−0.267124	+	0.437283i
$979$	−1.05414e9			−1.12344
$980$	−5.89233e8	+	4.44281e8i	−0.626050	+	0.472041i
$981$	3.14498e8	+	1.47606e9i	0.333128	+	1.56350i
$982$	−7.92003e8	+	1.05203e8i	−0.836359	+	0.111095i
$983$	−3.58429e8	−	3.58429e8i	−0.377349	−	0.377349i	0.492796	−	0.870145i	$-0.335975\pi$
$983$	−3.58429e8	−	3.58429e8i	−0.377349	−	0.377349i	−0.870145	+	0.492796i	$0.835975\pi$
$984$	−4.99657e7	−	9.12142e7i	−0.0524429	−	0.0957364i
$985$	3.02182e8	−	7.07888e8i	0.316199	−	0.740723i
$986$	−1.47896e9	−	1.13213e9i	−1.54286	−	1.18104i
$987$	6.55073e8	−	6.90124e7i	0.681300	−	0.0717754i
$988$	−1.94144e8	−	1.11489e8i	−0.201304	−	0.115601i
$989$	−1.58091e8			−0.163425
$990$	7.81893e8	+	8.84461e8i	0.805827	+	0.911534i
$991$			1.02953e9i			1.05784i	0.848672	+	0.528919i	$0.177403\pi$
$991$			1.02953e9i			1.05784i	−0.848672	+	0.528919i	$0.822597\pi$
$992$	3.85339e8	+	4.96202e8i	0.394737	+	0.508303i
$993$	−2.04345e8	−	1.93966e9i	−0.208697	−	1.98097i
$994$	2.81710e8	+	2.15645e8i	0.286842	+	0.219574i
$995$	1.02226e8	+	2.54507e8i	0.103774	+	0.258363i
$996$	1.40221e9	+	6.20001e8i	1.41917	+	0.627501i
$997$	5.85551e8	−	5.85551e8i	0.590853	−	0.590853i	−0.347009	−	0.937862i	$-0.612803\pi$
$997$	5.85551e8	−	5.85551e8i	0.590853	−	0.590853i	0.937862	+	0.347009i	$0.112803\pi$
$998$	−9.19375e7	+	1.22122e7i	−0.0924913	+	0.0122858i
$999$	−4.56067e8	+	8.96701e8i	−0.457438	+	0.899397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.l.a.23.3	✓	136
3.2	odd	2	inner	60.7.l.a.23.66	yes	136
4.3	odd	2	inner	60.7.l.a.23.37	yes	136
5.2	odd	4	inner	60.7.l.a.47.32	yes	136
12.11	even	2	inner	60.7.l.a.23.32	yes	136
15.2	even	4	inner	60.7.l.a.47.37	yes	136
20.7	even	4	inner	60.7.l.a.47.66	yes	136
60.47	odd	4	inner	60.7.l.a.47.3	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.l.a.23.3	✓	136	1.1	even	1	trivial
60.7.l.a.23.32	yes	136	12.11	even	2	inner
60.7.l.a.23.37	yes	136	4.3	odd	2	inner
60.7.l.a.23.66	yes	136	3.2	odd	2	inner
60.7.l.a.47.3	yes	136	60.47	odd	4	inner
60.7.l.a.47.32	yes	136	5.2	odd	4	inner
60.7.l.a.47.37	yes	136	15.2	even	4	inner
60.7.l.a.47.66	yes	136	20.7	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	60.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.93034 + 1.05340i) q^{2} +(-26.8514 + 2.82881i) q^{3} +(61.7807 - 16.7077i) q^{4} +(-46.5899 - 115.993i) q^{5} +(209.961 - 50.7188i) q^{6} +(112.704 + 112.704i) q^{7} +(-472.342 + 197.578i) q^{8} +(712.996 - 151.915i) q^{9} +O(q^{10})\)	\(q+(-7.93034 + 1.05340i) q^{2} +(-26.8514 + 2.82881i) q^{3} +(61.7807 - 16.7077i) q^{4} +(-46.5899 - 115.993i) q^{5} +(209.961 - 50.7188i) q^{6} +(112.704 + 112.704i) q^{7} +(-472.342 + 197.578i) q^{8} +(712.996 - 151.915i) q^{9} +(491.661 + 870.787i) q^{10} +1619.37 q^{11} +(-1611.63 + 623.392i) q^{12} +(641.254 + 641.254i) q^{13} +(-1012.50 - 775.057i) q^{14} +(1579.13 + 2982.78i) q^{15} +(3537.70 - 2064.43i) q^{16} +(-6059.51 - 6059.51i) q^{17} +(-5494.27 + 1955.81i) q^{18} -3857.33 q^{19} +(-4816.33 - 6387.72i) q^{20} +(-3345.07 - 2707.44i) q^{21} +(-12842.2 + 1705.85i) q^{22} +(1099.49 + 1099.49i) q^{23} +(12124.1 - 6641.41i) q^{24} +(-11283.8 + 10808.2i) q^{25} +(-5760.87 - 4409.87i) q^{26} +(-18715.2 + 6096.07i) q^{27} +(8845.93 + 5079.89i) q^{28} -27168.3 q^{29} +(-15665.1 - 21991.0i) q^{30} -19172.8i q^{31} +(-25880.5 + 20098.3i) q^{32} +(-43482.3 + 4580.89i) q^{33} +(54437.1 + 41670.9i) q^{34} +(7821.99 - 18323.7i) q^{35} +(41511.2 - 21298.0i) q^{36} +(36140.9 - 36140.9i) q^{37} +(30590.0 - 4063.33i) q^{38} +(-19032.6 - 15404.6i) q^{39} +(44924.0 + 45583.2i) q^{40} -7523.36i q^{41} +(29379.6 + 17947.2i) q^{42} +(-71893.0 + 71893.0i) q^{43} +(100046. - 27056.0i) q^{44} +(-50839.5 - 75624.8i) q^{45} +(-9877.56 - 7561.14i) q^{46} +(-108232. + 108232. i) q^{47} +(-89152.4 + 65440.3i) q^{48} -92244.7i q^{49} +(78098.7 - 97599.1i) q^{50} +(179848. + 145565. i) q^{51} +(50331.0 + 28903.2i) q^{52} +(-66841.6 + 66841.6i) q^{53} +(141996. - 68058.6i) q^{54} +(-75446.2 - 187836. i) q^{55} +(-75502.5 - 30966.9i) q^{56} +(103575. - 10911.7i) q^{57} +(215454. - 28619.2i) q^{58} +229291. i q^{59} +(147395. + 157895. i) q^{60} +125947. q^{61} +(20196.7 + 152047. i) q^{62} +(97478.7 + 63235.8i) q^{63} +(184070. - 186649. i) q^{64} +(44505.1 - 104257. i) q^{65} +(340004. - 82132.5i) q^{66} +(142997. + 142997. i) q^{67} +(-475601. - 273120. i) q^{68} +(-32633.2 - 26412.6i) q^{69} +(-42728.8 + 153553. i) q^{70} -278231. q^{71} +(-306763. + 212628. i) q^{72} +(-443121. - 443121. i) q^{73} +(-248539. + 324681. i) q^{74} +(272411. - 322135. i) q^{75} +(-238309. + 64447.3i) q^{76} +(182509. + 182509. i) q^{77} +(167162. + 102115. i) q^{78} -751698. q^{79} +(-404280. - 314168. i) q^{80} +(485285. - 216630. i) q^{81} +(7925.14 + 59662.8i) q^{82} +(-627377. - 627377. i) q^{83} +(-251896. - 111379. i) q^{84} +(-420549. + 985173. i) q^{85} +(494403. - 645868. i) q^{86} +(729506. - 76854.0i) q^{87} +(-764896. + 319952. i) q^{88} -650955. q^{89} +(482838. + 546176. i) q^{90} +144543. i q^{91} +(86297.4 + 49557.4i) q^{92} +(54236.2 + 514816. i) q^{93} +(744303. - 972326. i) q^{94} +(179713. + 447424. i) q^{95} +(638074. - 612878. i) q^{96} +(-149414. + 149414. i) q^{97} +(97171.0 + 731532. i) q^{98} +(1.15460e6 - 246007. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 4 q^{6}+O(q^{10}) \) 136 * q - 4 * q^6	\( 136 q - 4 q^{6} - 2092 q^{10} - 1460 q^{12} - 8 q^{13} - 932 q^{16} - 12744 q^{18} - 16056 q^{21} + 25444 q^{22} - 8 q^{25} - 52244 q^{28} + 82868 q^{30} - 2920 q^{33} - 69524 q^{36} - 113000 q^{37} + 99944 q^{40} + 19436 q^{42} - 62504 q^{45} + 145936 q^{46} - 82364 q^{48} + 219504 q^{52} - 286152 q^{57} - 351260 q^{58} + 466756 q^{60} + 652976 q^{61} - 61800 q^{66} + 243868 q^{70} - 145560 q^{72} - 316856 q^{73} + 269024 q^{76} + 613272 q^{78} + 1472232 q^{81} - 1652880 q^{82} - 1466984 q^{85} - 1084100 q^{88} + 448368 q^{90} - 2869552 q^{93} - 278860 q^{96} + 2135272 q^{97}+O(q^{100}) \) 136 * q - 4 * q^6 - 2092 * q^10 - 1460 * q^12 - 8 * q^13 - 932 * q^16 - 12744 * q^18 - 16056 * q^21 + 25444 * q^22 - 8 * q^25 - 52244 * q^28 + 82868 * q^30 - 2920 * q^33 - 69524 * q^36 - 113000 * q^37 + 99944 * q^40 + 19436 * q^42 - 62504 * q^45 + 145936 * q^46 - 82364 * q^48 + 219504 * q^52 - 286152 * q^57 - 351260 * q^58 + 466756 * q^60 + 652976 * q^61 - 61800 * q^66 + 243868 * q^70 - 145560 * q^72 - 316856 * q^73 + 269024 * q^76 + 613272 * q^78 + 1472232 * q^81 - 1652880 * q^82 - 1466984 * q^85 - 1084100 * q^88 + 448368 * q^90 - 2869552 * q^93 - 278860 * q^96 + 2135272 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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