LMFDB - Embedded newform 60.7.l.a.23.11

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			23.11
Character	$\chi$	$=$	60.23
Dual form			60.7.l.a.47.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.97975 + 3.90937i) q^{2} +(11.0251 - 24.6464i) q^{3} +(33.4337 - 54.5728i) q^{4} +(-92.0582 - 84.5593i) q^{5} +(19.3996 + 215.127i) q^{6} +(-403.029 - 403.029i) q^{7} +(-20.0136 + 511.609i) q^{8} +(-485.894 - 543.459i) q^{9} +O(q^{10})$	\(q+(-6.97975 + 3.90937i) q^{2} +(11.0251 - 24.6464i) q^{3} +(33.4337 - 54.5728i) q^{4} +(-92.0582 - 84.5593i) q^{5} +(19.3996 + 215.127i) q^{6} +(-403.029 - 403.029i) q^{7} +(-20.0136 + 511.609i) q^{8} +(-485.894 - 543.459i) q^{9} +(973.117 + 230.313i) q^{10} -207.729 q^{11} +(-976.415 - 1425.69i) q^{12} +(2793.72 + 2793.72i) q^{13} +(4388.63 + 1237.45i) q^{14} +(-3099.04 + 1336.63i) q^{15} +(-1860.38 - 3649.14i) q^{16} +(2904.32 + 2904.32i) q^{17} +(5516.00 + 1893.67i) q^{18} -2175.43 q^{19} +(-7692.48 + 2196.74i) q^{20} +(-14376.7 + 5489.79i) q^{21} +(1449.89 - 812.088i) q^{22} +(-6054.76 - 6054.76i) q^{23} +(12388.7 + 6133.80i) q^{24} +(1324.43 + 15568.8i) q^{25} +(-30421.1 - 8577.77i) q^{26} +(-18751.4 + 5983.87i) q^{27} +(-35469.2 + 8519.67i) q^{28} -8646.75 q^{29} +(16405.1 - 21444.6i) q^{30} +2612.62i q^{31} +(27250.8 + 18197.2i) q^{32} +(-2290.23 + 5119.77i) q^{33} +(-31625.5 - 8917.36i) q^{34} +(3022.26 + 71182.0i) q^{35} +(-45903.3 + 8346.74i) q^{36} +(-34548.2 + 34548.2i) q^{37} +(15183.9 - 8504.55i) q^{38} +(99656.3 - 38054.2i) q^{39} +(45103.7 - 45405.5i) q^{40} -103320. i q^{41} +(78883.9 - 94521.0i) q^{42} +(320.776 - 320.776i) q^{43} +(-6945.14 + 11336.3i) q^{44} +(-1224.01 + 91116.8i) q^{45} +(65931.0 + 18590.4i) q^{46} +(28656.3 - 28656.3i) q^{47} +(-110449. + 5619.52i) q^{48} +207216. i q^{49} +(-70108.2 - 103488. i) q^{50} +(103602. - 39560.7i) q^{51} +(245865. - 59056.7i) q^{52} +(-108983. + 108983. i) q^{53} +(107487. - 115072. i) q^{54} +(19123.1 + 17565.4i) q^{55} +(214259. - 198127. i) q^{56} +(-23984.3 + 53616.6i) q^{57} +(60352.1 - 33803.3i) q^{58} -278942. i q^{59} +(-30668.6 + 213812. i) q^{60} -126872. q^{61} +(-10213.7 - 18235.4i) q^{62} +(-23200.4 + 414859. i) q^{63} +(-261343. - 20478.3i) q^{64} +(-20949.8 - 493420. i) q^{65} +(-4029.85 - 44688.1i) q^{66} +(70679.3 + 70679.3i) q^{67} +(255599. - 61394.7i) q^{68} +(-215983. + 82473.9i) q^{69} +(-299371. - 485017. i) q^{70} -650122. q^{71} +(287763. - 237711. i) q^{72} +(97034.8 + 97034.8i) q^{73} +(106076. - 376199. i) q^{74} +(398317. + 139005. i) q^{75} +(-72732.6 + 118719. i) q^{76} +(83720.7 + 83720.7i) q^{77} +(-546808. + 655202. i) q^{78} -161987. q^{79} +(-137306. + 493245. i) q^{80} +(-59254.8 + 528127. i) q^{81} +(403915. + 721147. i) q^{82} +(276027. + 276027. i) q^{83} +(-181072. + 968119. i) q^{84} +(-21779.1 - 512954. i) q^{85} +(-984.904 + 3492.97i) q^{86} +(-95331.3 + 213112. i) q^{87} +(4157.40 - 106276. i) q^{88} +720985. q^{89} +(-347666. - 640757. i) q^{90} -2.25190e6i q^{91} +(-532858. + 127992. i) q^{92} +(64391.7 + 28804.4i) q^{93} +(-87985.6 + 312041. i) q^{94} +(200266. + 183953. i) q^{95} +(748938. - 471009. i) q^{96} +(74648.7 - 74648.7i) q^{97} +(-810083. - 1.44631e6i) q^{98} +(100934. + 112892. 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 $

$2$	−6.97975	+	3.90937i	−0.872468	+	0.488671i
$2$	−6.97975	+	3.90937i	−0.872468	+	0.488671i
$3$	11.0251	−	24.6464i	0.408337	−	0.912831i
$3$	11.0251	−	24.6464i	0.408337	−	0.912831i
$4$	33.4337	−	54.5728i	0.522401	−	0.852700i
$5$	−92.0582	−	84.5593i	−0.736466	−	0.676475i
$5$	−92.0582	−	84.5593i	−0.736466	−	0.676475i
$6$	19.3996	+	215.127i	0.0898128	+	0.995959i
$7$	−403.029	−	403.029i	−1.17501	−	1.17501i	−0.980999	−	0.194013i	$-0.937850\pi$
$7$	−403.029	−	403.029i	−1.17501	−	1.17501i	−0.194013	−	0.980999i	$-0.562150\pi$
$8$	−20.0136	+	511.609i	−0.0390891	+	0.999236i
$9$	−485.894	−	543.459i	−0.666521	−	0.745486i
$10$	973.117	+	230.313i	0.973117	+	0.230313i
$11$	−207.729			−0.156070			−0.0780348	−	0.996951i	$-0.524865\pi$
$11$	−207.729			−0.156070			−0.0780348	+	0.996951i	$0.524865\pi$
$12$	−976.415	−	1425.69i	−0.565055	−	0.825053i
$13$	2793.72	+	2793.72i	1.27161	+	1.27161i	0.945245	+	0.326361i	$0.105823\pi$
$13$	2793.72	+	2793.72i	1.27161	+	1.27161i	0.326361	+	0.945245i	$0.394177\pi$
$14$	4388.63	+	1237.45i	1.59935	+	0.450966i
$15$	−3099.04	+	1336.63i	−0.918234	+	0.396039i
$16$	−1860.38	−	3649.14i	−0.454193	−	0.890903i
$17$	2904.32	+	2904.32i	0.591150	+	0.591150i	0.937942	−	0.346792i	$-0.112729\pi$
$17$	2904.32	+	2904.32i	0.591150	+	0.591150i	−0.346792	+	0.937942i	$0.612729\pi$
$18$	5516.00	+	1893.67i	0.945816	+	0.324703i
$19$	−2175.43			−0.317164			−0.158582	−	0.987346i	$-0.550692\pi$
$19$	−2175.43			−0.317164			−0.158582	+	0.987346i	$0.550692\pi$
$20$	−7692.48	+	2196.74i	−0.961561	+	0.274593i
$21$	−14376.7	+	5489.79i	−1.55239	+	0.592786i
$22$	1449.89	−	812.088i	0.136166	−	0.0762667i
$23$	−6054.76	−	6054.76i	−0.497638	−	0.497638i	0.413064	−	0.910702i	$-0.364459\pi$
$23$	−6054.76	−	6054.76i	−0.497638	−	0.497638i	−0.910702	+	0.413064i	$0.864459\pi$
$24$	12388.7	+	6133.80i	0.896172	+	0.443707i
$25$	1324.43	+	15568.8i	0.0847637	+	0.996401i
$26$	−30421.1	−	8577.77i	−1.73083	−	0.488039i
$27$	−18751.4	+	5983.87i	−0.952668	+	0.304012i
$28$	−35469.2	+	8519.67i	−1.61576	+	0.388104i
$29$	−8646.75			−0.354535			−0.177267	−	0.984163i	$-0.556726\pi$
$29$	−8646.75			−0.354535			−0.177267	+	0.984163i	$0.556726\pi$
$30$	16405.1	−	21444.6i	0.607597	−	0.794246i
$31$			2612.62i			0.0876981i	0.999038	+	0.0438491i	$0.0139621\pi$
$31$			2612.62i			0.0876981i	−0.999038	+	0.0438491i	$0.986038\pi$
$32$	27250.8	+	18197.2i	0.831628	+	0.555333i
$33$	−2290.23	+	5119.77i	−0.0637290	+	0.142465i
$34$	−31625.5	−	8917.36i	−0.804637	−	0.226882i
$35$	3022.26	+	71182.0i	0.0704901	+	1.66022i
$36$	−45903.3	+	8346.74i	−0.983867	+	0.178900i
$37$	−34548.2	+	34548.2i	−0.682057	+	0.682057i	−0.960463	−	0.278407i	$-0.910194\pi$
$37$	−34548.2	+	34548.2i	−0.682057	+	0.682057i	0.278407	+	0.960463i	$0.410194\pi$
$38$	15183.9	−	8504.55i	0.276716	−	0.154989i
$39$	99656.3	−	38054.2i	1.68001	−	0.641518i
$40$	45103.7	−	45405.5i	0.704746	−	0.709460i
$41$		−	103320.i		−	1.49911i	−0.661944	−	0.749553i	$-0.730268\pi$
$41$		−	103320.i		−	1.49911i	0.661944	−	0.749553i	$-0.269732\pi$
$42$	78883.9	−	94521.0i	1.06473	−	1.27579i
$43$	320.776	−	320.776i	0.00403457	−	0.00403457i	−0.705087	−	0.709121i	$-0.749092\pi$
$43$	320.776	−	320.776i	0.00403457	−	0.00403457i	0.709121	+	0.705087i	$0.249092\pi$
$44$	−6945.14	+	11336.3i	−0.0815310	+	0.133081i
$45$	−1224.01	+	91116.8i	−0.0134322	+	0.999910i
$46$	65931.0	+	18590.4i	0.677354	+	0.190992i
$47$	28656.3	−	28656.3i	0.276011	−	0.276011i	−0.555503	−	0.831514i	$-0.687474\pi$
$47$	28656.3	−	28656.3i	0.276011	−	0.276011i	0.831514	+	0.555503i	$0.187474\pi$
$48$	−110449.	+	5619.52i	−0.998708	+	0.0508131i
$49$			207216.i			1.76131i
$50$	−70108.2	−	103488.i	−0.560866	−	0.827907i
$51$	103602.	−	39560.7i	0.781008	−	0.298231i
$52$	245865.	−	59056.7i	1.74859	−	0.420009i
$53$	−108983.	+	108983.i	−0.732035	+	0.732035i	−0.971023	−	0.238988i	$-0.923184\pi$
$53$	−108983.	+	108983.i	−0.732035	+	0.732035i	0.238988	+	0.971023i	$0.423184\pi$
$54$	107487.	−	115072.i	0.682611	−	0.730782i
$55$	19123.1	+	17565.4i	0.114940	+	0.105577i
$56$	214259.	−	198127.i	1.22004	−	1.12818i
$57$	−23984.3	+	53616.6i	−0.129510	+	0.289517i
$58$	60352.1	−	33803.3i	0.309320	−	0.173251i
$59$		−	278942.i		−	1.35818i	−0.734055	−	0.679090i	$-0.762374\pi$
$59$		−	278942.i		−	1.35818i	0.734055	−	0.679090i	$-0.237626\pi$
$60$	−30668.6	+	213812.i	−0.141984	+	0.989869i
$61$	−126872.			−0.558954			−0.279477	−	0.960152i	$-0.590161\pi$
$61$	−126872.			−0.558954			−0.279477	+	0.960152i	$0.590161\pi$
$62$	−10213.7	−	18235.4i	−0.0428555	−	0.0765138i
$63$	−23200.4	+	414859.i	−0.0927842	+	1.65913i
$64$	−261343.	−	20478.3i	−0.996944	−	0.0781184i
$65$	−20949.8	−	493420.i	−0.0762849	−	1.79670i
$66$	−4029.85	−	44688.1i	−0.0140171	−	0.155439i
$67$	70679.3	+	70679.3i	0.235000	+	0.235000i	0.814776	−	0.579776i	$-0.196860\pi$
$67$	70679.3	+	70679.3i	0.235000	+	0.235000i	−0.579776	+	0.814776i	$0.696860\pi$
$68$	255599.	−	61394.7i	0.812891	−	0.195256i
$69$	−215983.	+	82473.9i	−0.657463	+	0.251055i
$70$	−299371.	−	485017.i	−0.872803	−	1.41404i
$71$	−650122.			−1.81643			−0.908217	−	0.418500i	$-0.862556\pi$
$71$	−650122.			−1.81643			−0.908217	+	0.418500i	$0.862556\pi$
$72$	287763.	−	237711.i	0.770970	−	0.636872i
$73$	97034.8	+	97034.8i	0.249436	+	0.249436i	0.820739	−	0.571303i	$-0.193562\pi$
$73$	97034.8	+	97034.8i	0.249436	+	0.249436i	−0.571303	+	0.820739i	$0.693562\pi$
$74$	106076.	−	376199.i	0.261771	−	0.928374i
$75$	398317.	+	139005.i	0.944158	+	0.329493i
$76$	−72732.6	+	118719.i	−0.165687	+	0.270446i
$77$	83720.7	+	83720.7i	0.183384	+	0.183384i
$78$	−546808.	+	655202.i	−1.15226	+	1.38067i
$79$	−161987.			−0.328548			−0.164274	−	0.986415i	$-0.552528\pi$
$79$	−161987.			−0.328548			−0.164274	+	0.986415i	$0.552528\pi$
$80$	−137306.	+	493245.i	−0.268175	+	0.963370i
$81$	−59254.8	+	528127.i	−0.111498	+	0.993765i
$82$	403915.	+	721147.i	0.732570	+	1.30792i
$83$	276027.	+	276027.i	0.482744	+	0.482744i	0.906007	−	0.423263i	$-0.139115\pi$
$83$	276027.	+	276027.i	0.482744	+	0.482744i	−0.423263	+	0.906007i	$0.639115\pi$
$84$	−181072.	+	968119.i	−0.305501	+	1.63339i
$85$	−21779.1	−	512954.i	−0.0354637	−	0.835260i
$86$	−984.904	+	3492.97i	−0.00154846	+	0.00549160i
$87$	−95331.3	+	213112.i	−0.144770	+	0.323630i
$88$	4157.40	−	106276.i	0.00610062	−	0.155950i
$89$	720985.			1.02272			0.511360	−	0.859367i	$-0.329142\pi$
$89$	720985.			1.02272			0.511360	+	0.859367i	$0.329142\pi$
$90$	−347666.	−	640757.i	−0.476908	−	0.878953i
$91$		−	2.25190e6i		−	2.98831i
$92$	−532858.	+	127992.i	−0.684302	+	0.164369i
$93$	64391.7	+	28804.4i	0.0800536	+	0.0358104i
$94$	−87985.6	+	312041.i	−0.105932	+	0.375689i
$95$	200266.	+	183953.i	0.233581	+	0.214554i
$96$	748938.	−	471009.i	0.846510	−	0.532372i
$97$	74648.7	−	74648.7i	0.0817912	−	0.0817912i	−0.665028	−	0.746819i	$-0.731580\pi$
$97$	74648.7	−	74648.7i	0.0817912	−	0.0817912i	0.746819	+	0.665028i	$0.231580\pi$
$98$	−810083.	−	1.44631e6i	−0.860699	−	1.53668i
$99$	100934.	+	112892.i	0.104024	+	0.116348i
$100$	893912.	+	448243.i	0.893912	+	0.448243i
$101$		−	7779.32i		−	0.00755053i	−0.999993	−	0.00377526i	$-0.998798\pi$
$101$		−	7779.32i		−	0.00755053i	0.999993	−	0.00377526i	$-0.00120171\pi$
$102$	−568455.	+	681140.i	−0.535668	+	0.641854i
$103$	−522258.	+	522258.i	−0.477940	+	0.477940i	−0.904472	−	0.426533i	$-0.859735\pi$
$103$	−522258.	+	522258.i	−0.477940	+	0.477940i	0.426533	+	0.904472i	$0.359735\pi$
$104$	−1.48520e6	+	1.37338e6i	−1.32034	+	1.22093i
$105$	1.78770e6	+	710301.i	1.54429	+	0.613585i
$106$	334619.	−	1.18673e6i	0.280953	−	0.996401i
$107$	−1.11114e6	+	1.11114e6i	−0.907018	+	0.907018i	−0.996031	−	0.0890123i	$-0.971629\pi$
$107$	−1.11114e6	+	1.11114e6i	−0.907018	+	0.907018i	0.0890123	+	0.996031i	$0.471629\pi$
$108$	−300371.	+	1.22338e6i	−0.238444	+	0.971156i
$109$		−	1.70138e6i		−	1.31378i	−0.753988	−	0.656889i	$-0.771872\pi$
$109$		−	1.70138e6i		−	1.31378i	0.753988	−	0.656889i	$-0.228128\pi$
$110$	−202144.	−	47842.7i	−0.151874	−	0.0359449i
$111$	470593.	+	1.23239e6i	0.344093	+	0.901112i
$112$	−720923.	+	2.22049e6i	−0.513139	+	1.58050i
$113$	−579605.	+	579605.i	−0.401695	+	0.401695i	−0.878830	−	0.477135i	$-0.841675\pi$
$113$	−579605.	+	579605.i	−0.401695	+	0.401695i	0.477135	+	0.878830i	$0.341675\pi$
$114$	−42202.4	−	467994.i	−0.0284854	−	0.315882i
$115$	45403.9	+	1.06938e6i	0.0298538	+	0.703133i
$116$	−289093.	+	471877.i	−0.185209	+	0.302312i
$117$	160821.	−	2.87572e6i	0.100412	−	1.79552i
$118$	1.09049e6	+	1.94694e6i	0.663704	+	1.18497i
$119$		−	2.34105e6i		−	1.38922i
$120$	−621810.	−	1.61225e6i	−0.359843	−	0.933013i
$121$	−1.72841e6			−0.975642
$122$	885533.	−	495989.i	0.487669	−	0.273144i
$123$	−2.54647e6	−	1.13911e6i	−1.36843	−	0.612141i
$124$	142578.	+	87349.4i	0.0747802	+	0.0458136i
$125$	1.19456e6	−	1.54523e6i	0.611615	−	0.791156i
$126$	−1.45990e6	−	2.98631e6i	−0.729815	−	1.49287i
$127$	−1.96289e6	−	1.96289e6i	−0.958263	−	0.958263i	0.0409005	−	0.999163i	$-0.486977\pi$
$127$	−1.96289e6	−	1.96289e6i	−0.958263	−	0.958263i	−0.999163	+	0.0409005i	$0.986977\pi$
$128$	1.90416e6	−	878752.i	0.907976	−	0.419022i
$129$	−4369.40	−	11442.6i	−0.00203541	−	0.00533034i
$130$	2.07518e6	+	3.36205e6i	0.944553	+	1.53029i
$131$	4.22155e6			1.87784			0.938918	−	0.344140i	$-0.111829\pi$
$131$	4.22155e6			1.87784			0.938918	+	0.344140i	$0.111829\pi$
$132$	202829.	+	296157.i	0.0881879	+	0.128766i
$133$	876761.	+	876761.i	0.372672	+	0.372672i
$134$	−769635.	−	217012.i	−0.319868	−	0.0901924i
$135$	2.23221e6	+	1.03474e6i	0.907264	+	0.420562i
$136$	−1.54400e6	+	1.42775e6i	−0.613806	+	0.567591i
$137$	512905.	+	512905.i	0.199469	+	0.199469i	0.799772	−	0.600303i	$-0.204954\pi$
$137$	512905.	+	512905.i	0.199469	+	0.199469i	−0.600303	+	0.799772i	$0.704954\pi$
$138$	1.18508e6	−	1.42000e6i	0.450933	−	0.540321i
$139$	−3.39488e6			−1.26410			−0.632048	−	0.774929i	$-0.717786\pi$
$139$	−3.39488e6			−1.26410			−0.632048	+	0.774929i	$0.717786\pi$
$140$	3.98565e6	+	2.21494e6i	1.45249	+	0.807195i
$141$	−390337.	−	1.02221e6i	−0.139246	−	0.364657i
$142$	4.53768e6	−	2.54156e6i	1.58478	−	0.887639i
$143$	−580336.	−	580336.i	−0.198459	−	0.198459i
$144$	−1.07921e6	+	2.78413e6i	−0.361426	+	0.932401i
$145$	796004.	+	731163.i	0.261103	+	0.239834i
$146$	−1.05662e6	−	297934.i	−0.339517	−	0.0957328i
$147$	5.10713e6	+	2.28458e6i	1.60777	+	0.719207i
$148$	730318.	+	3.04047e6i	0.225282	+	0.937897i
$149$	−2.49626e6			−0.754625			−0.377312	−	0.926086i	$-0.623152\pi$
$149$	−2.49626e6			−0.754625			−0.377312	+	0.926086i	$0.623152\pi$
$150$	−3.32357e6	+	586949.i	−0.984761	+	0.173911i
$151$		−	2.26052e6i		−	0.656566i	−0.944579	−	0.328283i	$-0.893530\pi$
$151$		−	2.26052e6i		−	0.656566i	0.944579	−	0.328283i	$-0.106470\pi$
$152$	43538.2	−	1.11297e6i	0.0123977	−	0.316922i
$153$	167187.	−	2.98957e6i	0.0466798	−	0.834708i
$154$	−911644.	−	257054.i	−0.249611	−	0.0703821i
$155$	220921.	−	240513.i	0.0593256	−	0.0645867i
$156$	1.25515e6	−	6.71081e6i	0.330616	−	1.76767i
$157$	2.15499e6	−	2.15499e6i	0.556859	−	0.556859i	−0.371553	−	0.928412i	$-0.621174\pi$
$157$	2.15499e6	−	2.15499e6i	0.556859	−	0.556859i	0.928412	+	0.371553i	$0.121174\pi$
$158$	1.13063e6	−	633267.i	0.286648	−	0.160552i
$159$	1.48450e6	+	3.88760e6i	0.369307	+	0.967141i
$160$	−969918.	−	3.97951e6i	−0.236796	−	0.971559i
$161$			4.88049e6i			1.16946i
$162$	−1.65106e6	−	3.91784e6i	−0.388345	−	0.921514i
$163$	1.20562e6	−	1.20562e6i	0.278385	−	0.278385i	−0.554079	−	0.832464i	$-0.686929\pi$
$163$	1.20562e6	−	1.20562e6i	0.278385	−	0.278385i	0.832464	+	0.554079i	$0.186929\pi$
$164$	−5.63845e6	−	3.45437e6i	−1.27829	−	0.783135i
$165$	643759.	−	277657.i	0.143308	−	0.0618097i
$166$	−3.00569e6	−	847506.i	−0.657082	−	0.185276i
$167$	−1.67498e6	+	1.67498e6i	−0.359634	+	0.359634i	−0.863678	−	0.504044i	$-0.831845\pi$
$167$	−1.67498e6	+	1.67498e6i	−0.359634	+	0.359634i	0.504044	+	0.863678i	$0.331845\pi$
$168$	−2.52090e6	−	7.46510e6i	−0.531652	−	1.57437i
$169$			1.07829e7i			2.23397i
$170$	2.15734e6	+	3.49514e6i	0.439108	+	0.711407i
$171$	1.05703e6	+	1.18226e6i	0.211397	+	0.236441i
$172$	−6780.92	−	28230.4i	−0.00133261	−	0.00554794i
$173$	−4.22645e6	+	4.22645e6i	−0.816277	+	0.816277i	−0.985566	−	0.169289i	$-0.945853\pi$
$173$	−4.22645e6	+	4.22645e6i	−0.816277	+	0.816277i	0.169289	+	0.985566i	$0.445853\pi$
$174$	−167743.	−	1.86015e6i	−0.0318418	−	0.353102i
$175$	5.74088e6	−	6.80845e6i	1.07118	−	1.27038i
$176$	386453.	+	758031.i	0.0708858	+	0.139043i
$177$	−6.87492e6	−	3.07536e6i	−1.23979	−	0.554596i
$178$	−5.03229e6	+	2.81860e6i	−0.892290	+	0.499773i
$179$			4.01535e6i			0.700106i	0.936730	+	0.350053i	$0.113836\pi$
$179$			4.01535e6i			0.700106i	−0.936730	+	0.350053i	$0.886164\pi$
$180$	4.93157e6	+	3.11317e6i	0.845606	+	0.533808i
$181$	−6.20641e6			−1.04666			−0.523329	−	0.852131i	$-0.675310\pi$
$181$	−6.20641e6			−1.04666			−0.523329	+	0.852131i	$0.675310\pi$
$182$	8.80351e6	+	1.57177e7i	1.46030	+	2.60720i
$183$	−1.39878e6	+	3.12694e6i	−0.228242	+	0.510230i
$184$	3.21885e6	−	2.97649e6i	0.516710	−	0.477805i
$185$	6.10182e6	−	259073.i	0.963705	−	0.0409173i
$186$	−562044.	+	50683.6i	−0.0873437	+	0.00787642i
$187$	−603310.	−	603310.i	−0.0922605	−	0.0922605i
$188$	−605767.	−	2.52194e6i	−0.0911659	−	0.379543i
$189$	9.96902e6	+	5.14567e6i	1.47661	+	0.762179i
$190$	−2.11695e6	−	501030.i	−0.308638	−	0.0730471i
$191$	−6.00844e6			−0.862306			−0.431153	−	0.902279i	$-0.641893\pi$
$191$	−6.00844e6			−0.862306			−0.431153	+	0.902279i	$0.641893\pi$
$192$	−3.38605e6	+	6.21540e6i	−0.478398	+	0.878143i
$193$	−1.61348e6	−	1.61348e6i	−0.224436	−	0.224436i	0.585928	−	0.810363i	$-0.300730\pi$
$193$	−1.61348e6	−	1.61348e6i	−0.224436	−	0.224436i	−0.810363	+	0.585928i	$0.800730\pi$
$194$	−229200.	+	812858.i	−0.0313913	+	0.111329i
$195$	−1.23920e7	−	4.92367e6i	−1.67124	−	0.664026i
$196$	1.13083e7	+	6.92799e6i	1.50186	+	0.920108i
$197$	−8.35514e6	−	8.35514e6i	−1.09284	−	1.09284i	−0.995225	−	0.0976114i	$-0.968880\pi$
$197$	−8.35514e6	−	8.35514e6i	−1.09284	−	1.09284i	−0.0976114	−	0.995225i	$-0.531120\pi$
$198$	−1.14583e6	−	393369.i	−0.147613	−	0.0506763i
$199$	−7.53036e6			−0.955557			−0.477778	−	0.878480i	$-0.658558\pi$
$199$	−7.53036e6			−0.955557			−0.477778	+	0.878480i	$0.658558\pi$
$200$	−7.99162e6	+	366004.i	−0.998953	+	0.0457505i
$201$	2.52124e6	−	962747.i	0.310475	−	0.118556i
$202$	30412.2	+	54297.7i	0.00368972	+	0.00658760i
$203$	3.48489e6	+	3.48489e6i	0.416583	+	0.416583i
$204$	1.30484e6	−	6.97648e6i	0.153698	−	0.821762i
$205$	−8.73666e6	+	9.51145e6i	−1.01411	+	1.10404i
$206$	1.60353e6	−	5.68692e6i	0.183432	−	0.650542i
$207$	−348543.	+	6.23249e6i	−0.0392957	+	0.702668i
$208$	4.99730e6	−	1.53920e7i	0.555323	−	1.71043i
$209$	451899.			0.0494997
$210$	−1.52545e7	+	2.03107e6i	−1.64718	+	0.219314i
$211$			6.50194e6i			0.692142i	0.938208	+	0.346071i	$0.112484\pi$
$211$			6.50194e6i			0.692142i	−0.938208	+	0.346071i	$0.887516\pi$
$212$	2.30380e6	+	9.59122e6i	0.241790	+	1.00662i
$213$	−7.16766e6	+	1.60232e7i	−0.741718	+	1.65810i
$214$	3.41161e6	−	1.20993e7i	0.348111	−	1.23458i
$215$	−56654.7	+	2405.46i	−0.00570060	+	0.000242038i
$216$	−2.68612e6	−	9.71312e6i	−0.266541	−	0.963824i
$217$	1.05296e6	−	1.05296e6i	0.103046	−	0.103046i
$218$	6.65132e6	+	1.18752e7i	0.642005	+	1.14623i
$219$	3.46138e6	−	1.32174e6i	0.329547	−	0.125839i
$220$	1.59795e6	−	456326.i	0.150070	−	0.0428556i
$221$			1.62277e7i			1.50342i
$222$	−8.10248e6	−	6.76204e6i	−0.740558	−	0.618043i
$223$	4.33077e6	−	4.33077e6i	0.390526	−	0.390526i	−0.484349	−	0.874875i	$-0.660943\pi$
$223$	4.33077e6	−	4.33077e6i	0.390526	−	0.390526i	0.874875	+	0.484349i	$0.160943\pi$
$224$	−3.64887e6	−	1.83168e7i	−0.324649	−	1.62970i
$225$	7.81746e6	−	8.28455e6i	0.686306	−	0.727313i
$226$	1.77961e6	−	6.31138e6i	0.154169	−	0.546763i
$227$	7.01845e6	−	7.01845e6i	0.600017	−	0.600017i	−0.340300	−	0.940317i	$-0.610528\pi$
$227$	7.01845e6	−	7.01845e6i	0.600017	−	0.600017i	0.940317	+	0.340300i	$0.110528\pi$
$228$	2.12412e6	+	3.10149e6i	0.179215	+	0.261677i
$229$		−	1.85334e7i		−	1.54330i	−0.636049	−	0.771649i	$-0.719432\pi$
$229$		−	1.85334e7i		−	1.54330i	0.636049	−	0.771649i	$-0.280568\pi$
$230$	−4.49750e6	−	7.28648e6i	−0.369647	−	0.598872i
$231$	2.98645e6	−	1.14039e6i	0.242281	−	0.0925159i
$232$	173053.	−	4.42375e6i	0.0138584	−	0.354264i
$233$	1.34743e6	−	1.34743e6i	0.106522	−	0.106522i	−0.651837	−	0.758359i	$-0.726001\pi$
$233$	1.34743e6	−	1.34743e6i	0.106522	−	0.106522i	0.758359	+	0.651837i	$0.226001\pi$
$234$	1.01198e7	+	2.07005e7i	0.789811	+	1.61560i
$235$	−5.06120e6	+	214890.i	−0.389987	+	0.0165582i
$236$	−1.52226e7	−	9.32605e6i	−1.15812	−	0.709516i
$237$	−1.78592e6	+	3.99240e6i	−0.134158	+	0.299909i
$238$	9.15202e6	+	1.63399e7i	0.678869	+	1.21205i
$239$		−	9.04534e6i		−	0.662569i	−0.943531	−	0.331285i	$-0.892518\pi$
$239$		−	9.04534e6i		−	0.662569i	0.943531	−	0.331285i	$-0.107482\pi$
$240$	1.06429e7	+	8.82218e6i	0.769888	+	0.638179i
$241$	4.07918e6			0.291422			0.145711	−	0.989327i	$-0.453453\pi$
$241$	4.07918e6			0.291422			0.145711	+	0.989327i	$0.453453\pi$
$242$	1.20639e7	−	6.75699e6i	0.851217	−	0.476768i
$243$	1.23632e7	+	7.28308e6i	0.861610	+	0.507570i
$244$	−4.24180e6	+	6.92375e6i	−0.291998	+	0.476620i
$245$	1.75220e7	−	1.90759e7i	1.19148	−	1.29714i
$246$	2.22269e7	−	2.00436e6i	1.49305	−	0.134639i
$247$	−6.07754e6	−	6.07754e6i	−0.403308	−	0.403308i
$248$	−1.33664e6	−	52287.8i	−0.0876311	−	0.00342804i
$249$	9.84630e6	−	3.75985e6i	0.637786	−	0.243541i
$250$	−2.29687e6	+	1.54553e7i	−0.146999	+	0.989137i
$251$	1.43208e7			0.905622			0.452811	−	0.891607i	$-0.350421\pi$
$251$	1.43208e7			0.905622			0.452811	+	0.891607i	$0.350421\pi$
$252$	2.18643e7	+	1.51364e7i	1.36626	+	0.945846i
$253$	1.25775e6	+	1.25775e6i	0.0776662	+	0.0776662i
$254$	2.13741e7	+	6.02681e6i	1.30433	+	0.367779i
$255$	−1.28826e7	−	5.11859e6i	−0.776932	−	0.308695i
$256$	−9.85521e6	+	1.35775e7i	−0.587417	+	0.809285i
$257$	−2.04667e7	−	2.04667e7i	−1.20572	−	1.20572i	−0.972399	−	0.233326i	$-0.925039\pi$
$257$	−2.04667e7	−	2.04667e7i	−1.20572	−	1.20572i	−0.233326	−	0.972399i	$-0.574961\pi$
$258$	75230.6	+	62784.7i	0.00438062	+	0.00365590i
$259$	2.78479e7			1.60285
$260$	−2.76277e7	−	1.53536e7i	−1.57190	−	0.873553i
$261$	4.20140e6	+	4.69916e6i	0.236305	+	0.264301i
$262$	−2.94653e7	+	1.65036e7i	−1.63835	+	0.917644i
$263$	−811199.	−	811199.i	−0.0445923	−	0.0445923i	0.684459	−	0.729051i	$-0.260038\pi$
$263$	−811199.	−	811199.i	−0.0445923	−	0.0445923i	−0.729051	+	0.684459i	$0.760038\pi$
$264$	−2.57348e6	−	1.27417e6i	−0.139865	−	0.0692492i
$265$	1.92483e7	−	817251.i	1.03432	−	0.0439155i
$266$	−9.54715e6	−	2.69199e6i	−0.507258	−	0.143030i
$267$	7.94894e6	−	1.77697e7i	0.417614	−	0.933570i
$268$	6.22024e6	−	1.49410e6i	0.323149	−	0.0776201i
$269$	1.80449e7			0.927039			0.463519	−	0.886087i	$-0.346586\pi$
$269$	1.80449e7			0.927039			0.463519	+	0.886087i	$0.346586\pi$
$270$	−1.96254e7	+	1.50431e6i	−0.997075	+	0.0764268i
$271$			2.10738e7i			1.05885i	0.848356	+	0.529426i	$0.177593\pi$
$271$			2.10738e7i			1.05885i	−0.848356	+	0.529426i	$0.822407\pi$
$272$	5.19514e6	−	1.60014e7i	0.258161	−	0.795154i
$273$	−5.55013e7	−	2.48274e7i	−2.72782	−	1.22024i
$274$	−5.58508e6	−	1.57481e6i	−0.271505	−	0.0765556i
$275$	−275123.	−	3.23408e6i	−0.0132290	−	0.155508i
$276$	−2.72027e6	+	1.45442e7i	−0.129385	+	0.691771i
$277$	2.06291e7	−	2.06291e7i	0.970603	−	0.970603i	−0.0289770	−	0.999580i	$-0.509225\pi$
$277$	2.06291e7	−	2.06291e7i	0.970603	−	0.970603i	0.999580	+	0.0289770i	$0.00922495\pi$
$278$	2.36954e7	−	1.32718e7i	1.10288	−	0.617727i
$279$	1.41985e6	−	1.26945e6i	0.0653777	−	0.0584527i
$280$	−3.64778e7	+	121608.i	−1.66171	+	0.00553973i
$281$			9.39815e6i			0.423568i	0.977316	+	0.211784i	$0.0679274\pi$
$281$			9.39815e6i			0.423568i	−0.977316	+	0.211784i	$0.932073\pi$
$282$	6.72066e6	+	5.60882e6i	0.299685	+	0.250106i
$283$	−4.45258e6	+	4.45258e6i	−0.196450	+	0.196450i	−0.798476	−	0.602026i	$-0.794360\pi$
$283$	−4.45258e6	+	4.45258e6i	−0.196450	+	0.196450i	0.602026	+	0.798476i	$0.294360\pi$
$284$	−2.17360e7	+	3.54789e7i	−0.948908	+	1.54887i
$285$	6.74174e6	−	2.90775e6i	0.291231	−	0.125609i
$286$	6.31934e6	+	1.78185e6i	0.270130	+	0.0761681i
$287$	−4.16409e7	+	4.16409e7i	−1.76147	+	1.76147i
$288$	−3.35158e6	−	2.36516e7i	−0.140305	−	0.990108i
$289$		−	7.26743e6i		−	0.301084i
$290$	−8.41429e6	−	1.99146e6i	−0.345004	−	0.0816541i
$291$	−1.01681e6	−	2.66283e6i	−0.0412632	−	0.108060i
$292$	8.53969e6	−	2.05123e6i	0.343000	−	0.0823883i
$293$	5.49658e6	−	5.49658e6i	0.218519	−	0.218519i	−0.589355	−	0.807874i	$-0.700618\pi$
$293$	5.49658e6	−	5.49658e6i	0.218519	−	0.218519i	0.807874	+	0.589355i	$0.200618\pi$
$294$	−4.45777e7	+	4.01990e6i	−1.75419	+	0.158188i
$295$	−2.35871e7	+	2.56789e7i	−0.918775	+	1.00025i
$296$	−1.69837e7	−	1.83666e7i	−0.654874	−	0.708196i
$297$	3.89520e6	−	1.24302e6i	0.148683	−	0.0474470i
$298$	1.74233e7	−	9.75880e6i	0.658386	−	0.368763i
$299$		−	3.38306e7i		−	1.26560i
$300$	2.09031e7	−	1.70898e7i	0.774188	−	0.632956i
$301$	−258564.			−0.00948132
$302$	8.83722e6	+	1.57779e7i	0.320845	+	0.572833i
$303$	−191732.	−	85767.8i	−0.00689236	−	0.00308316i
$304$	4.04712e6	+	7.93844e6i	0.144054	+	0.282563i
$305$	1.16796e7	+	1.07282e7i	0.411650	+	0.378118i
$306$	1.05204e7	+	2.15200e7i	0.367171	+	0.751067i
$307$	−1.61474e7	−	1.61474e7i	−0.558068	−	0.558068i	0.370689	−	0.928757i	$-0.379122\pi$
$307$	−1.61474e7	−	1.61474e7i	−0.558068	−	0.558068i	−0.928757	+	0.370689i	$0.879122\pi$
$308$	7.36796e6	−	1.76978e6i	0.252171	−	0.0605713i
$309$	7.11385e6	+	1.86297e7i	0.241118	+	0.631439i
$310$	−601720.	+	2.54238e6i	−0.0201980	+	0.0853405i
$311$	−3.09455e7			−1.02876			−0.514382	−	0.857561i	$-0.671979\pi$
$311$	−3.09455e7			−1.02876			−0.514382	+	0.857561i	$0.671979\pi$
$312$	1.74744e7	+	5.17466e7i	0.575358	+	1.70380i
$313$	−969819.	−	969819.i	−0.0316270	−	0.0316270i	0.691116	−	0.722743i	$-0.257119\pi$
$313$	−969819.	−	969819.i	−0.0316270	−	0.0316270i	−0.722743	+	0.691116i	$0.757119\pi$
$314$	−6.61662e6	+	2.34659e7i	−0.213721	+	0.757963i
$315$	3.72160e7	−	3.62294e7i	1.19069	−	1.15912i
$316$	−5.41582e6	+	8.84008e6i	−0.171634	+	0.280153i
$317$	6.43715e6	+	6.43715e6i	0.202077	+	0.202077i	0.800889	−	0.598813i	$-0.204361\pi$
$317$	6.43715e6	+	6.43715e6i	0.202077	+	0.202077i	−0.598813	+	0.800889i	$0.704361\pi$
$318$	−2.55594e7	−	2.13310e7i	−0.794822	−	0.663330i
$319$	1.79618e6			0.0553321
$320$	2.23271e7	+	2.39842e7i	0.681370	+	0.731939i
$321$	1.51352e7	+	3.96360e7i	0.457585	+	1.19832i
$322$	−1.90796e7	−	3.40646e7i	−0.571482	−	1.02032i
$323$	−6.31814e6	−	6.31814e6i	−0.187492	−	0.187492i
$324$	2.68403e7	+	2.08909e7i	0.789136	+	0.614219i
$325$	−3.97947e7	+	4.71949e7i	−1.15924	+	1.37482i
$326$	−3.70170e6	+	1.31281e7i	−0.106843	+	0.378921i
$327$	−4.19330e7	−	1.87579e7i	−1.19926	−	0.536464i
$328$	5.28594e7	+	2.06780e6i	1.49796	+	0.0585987i
$329$	−2.30986e7			−0.648632
$330$	−3.40781e6	+	4.45466e6i	−0.0948274	+	0.123958i
$331$			3.71745e7i			1.02509i	0.858661	+	0.512543i	$0.171297\pi$
$331$			3.71745e7i			1.02509i	−0.858661	+	0.512543i	$0.828703\pi$
$332$	2.42921e7	−	5.83495e6i	0.663822	−	0.159449i
$333$	3.55623e7	+	1.98877e6i	0.963069	+	0.0538582i
$334$	5.14282e6	−	1.82390e7i	0.138026	−	0.489511i
$335$	−530016.	−	1.24832e7i	−0.0140979	−	0.332041i
$336$	4.67790e7	+	4.22494e7i	1.23320	+	1.11379i
$337$	1.46034e7	−	1.46034e7i	0.381561	−	0.381561i	−0.490103	−	0.871664i	$-0.663041\pi$
$337$	1.46034e7	−	1.46034e7i	0.381561	−	0.381561i	0.871664	+	0.490103i	$0.163041\pi$
$338$	−4.21544e7	−	7.52621e7i	−1.09167	−	1.94906i
$339$	7.89499e6	+	2.06754e7i	0.202653	+	0.530707i
$340$	−2.87215e7	−	1.59614e7i	−0.730752	−	0.406101i
$341$		−	542715.i		−	0.0136870i
$342$	−1.19997e7	−	4.11954e6i	−0.299979	−	0.102984i
$343$	3.60980e7	−	3.60980e7i	0.894543	−	0.894543i
$344$	157692.	+	170532.i	0.00387377	+	0.00418919i
$345$	2.68569e7	+	1.06710e7i	0.654032	+	0.259864i
$346$	1.29768e7	−	4.60223e7i	0.313285	−	1.11107i
$347$	2.25423e7	−	2.25423e7i	0.539523	−	0.539523i	−0.383866	−	0.923389i	$-0.625408\pi$
$347$	2.25423e7	−	2.25423e7i	0.539523	−	0.539523i	0.923389	+	0.383866i	$0.125408\pi$
$348$	8.44281e6	+	1.23276e7i	0.200332	+	0.292510i
$349$		−	4.72359e7i		−	1.11121i	−0.831447	−	0.555604i	$-0.812487\pi$
$349$		−	4.72359e7i		−	1.11121i	0.831447	−	0.555604i	$-0.187513\pi$
$350$	−1.34531e7	+	6.99645e7i	−0.313776	+	1.63182i
$351$	−6.91033e7	−	3.56688e7i	−1.59800	−	0.824836i
$352$	−5.66077e6	−	3.78007e6i	−0.129792	−	0.0866707i
$353$	−1.14472e7	+	1.14472e7i	−0.260241	+	0.260241i	−0.825152	−	0.564911i	$-0.808910\pi$
$353$	−1.14472e7	+	1.14472e7i	−0.260241	+	0.260241i	0.564911	+	0.825152i	$0.308910\pi$
$354$	6.00079e7	−	5.41135e6i	1.35269	−	0.121982i
$355$	5.98491e7	+	5.49739e7i	1.33774	+	1.22877i
$356$	2.41052e7	−	3.93462e7i	0.534270	−	0.872072i
$357$	−5.76985e7	−	2.58103e7i	−1.26812	−	0.567269i
$358$	−1.56975e7	−	2.80261e7i	−0.342122	−	0.610821i
$359$			6.31476e7i			1.36481i	0.730973	+	0.682407i	$0.239067\pi$
$359$			6.31476e7i			1.36481i	−0.730973	+	0.682407i	$0.760933\pi$
$360$	−4.65916e7	−	2.44979e6i	−0.998621	−	0.0525075i
$361$	−4.23134e7			−0.899407
$362$	4.33192e7	−	2.42631e7i	0.913176	−	0.511471i
$363$	−1.90559e7	+	4.25992e7i	−0.398391	+	0.890597i
$364$	−1.22892e8	−	7.52893e7i	−2.54813	−	1.56109i
$365$	−727652.	−	1.71381e7i	−0.0149639	−	0.352438i
$366$	−2.46126e6	−	2.72936e7i	−0.0502012	−	0.556695i
$367$	4.86448e7	+	4.86448e7i	0.984097	+	0.984097i	0.999876	−	0.0157785i	$-0.00502267\pi$
$367$	4.86448e7	+	4.86448e7i	0.984097	+	0.984097i	−0.0157785	+	0.999876i	$0.505023\pi$
$368$	−1.08305e7	+	3.33588e7i	−0.217323	+	0.669371i
$369$	−5.61502e7	+	5.02025e7i	−1.11756	+	0.999186i
$370$	−4.15764e7	+	2.56625e7i	−0.820807	+	0.506634i
$371$	8.78467e7			1.72030
$372$	3.72479e6	−	2.55100e6i	0.0723556	−	0.0495543i
$373$	5.52444e7	+	5.52444e7i	1.06454	+	1.06454i	0.997768	+	0.0667713i	$0.0212698\pi$
$373$	5.52444e7	+	5.52444e7i	1.06454	+	1.06454i	0.0667713	+	0.997768i	$0.478730\pi$
$374$	6.56951e6	+	1.85239e6i	0.125579	+	0.0354093i
$375$	−2.49142e7	−	4.64779e7i	−0.472447	−	0.881359i
$376$	1.40873e7	+	1.52343e7i	0.265011	+	0.286589i
$377$	−2.41566e7	−	2.41566e7i	−0.450829	−	0.450829i
$378$	−8.96975e7	+	3.05706e6i	−1.66075	+	0.0566015i
$379$	−4.04239e6			−0.0742541			−0.0371270	−	0.999311i	$-0.511821\pi$
$379$	−4.04239e6			−0.0742541			−0.0371270	+	0.999311i	$0.511821\pi$
$380$	1.67345e7	−	4.77886e6i	0.304973	−	0.0870910i
$381$	−7.00193e7	+	2.67372e7i	−1.26603	+	0.483438i
$382$	4.19374e7	−	2.34892e7i	0.752334	−	0.421384i
$383$	1.78451e7	+	1.78451e7i	0.317630	+	0.317630i	0.847856	−	0.530226i	$-0.177893\pi$
$383$	1.78451e7	+	1.78451e7i	0.317630	+	0.317630i	−0.530226	+	0.847856i	$0.677893\pi$
$384$	−664510.	−	5.66192e7i	−0.0117357	−	0.999931i
$385$	−627811.	−	1.47865e7i	−0.0110014	−	0.259110i
$386$	1.75694e7	+	4.95400e6i	0.305488	+	0.0861378i
$387$	−330192.	−	18465.5i	−0.00569684	−	0.000318587i
$388$	−1.57800e6	−	6.56957e6i	−0.0270155	−	0.112471i
$389$	4.20580e7			0.714496			0.357248	−	0.934010i	$-0.383715\pi$
$389$	4.20580e7			0.714496			0.357248	+	0.934010i	$0.383715\pi$
$390$	1.05742e8	−	1.40790e7i	1.78259	−	0.237344i
$391$		−	3.51699e7i		−	0.588357i
$392$	−1.06013e8	−	4.14713e6i	−1.75996	−	0.0688478i
$393$	4.65430e7	−	1.04046e8i	0.766791	−	1.71415i
$394$	9.09801e7	+	2.56534e7i	1.48750	+	0.419427i
$395$	1.49122e7	+	1.36975e7i	0.241964	+	0.222254i
$396$	9.53543e6	−	1.73386e6i	0.153552	−	0.0279208i
$397$	−4.34709e7	+	4.34709e7i	−0.694747	+	0.694747i	−0.963273	−	0.268526i	$-0.913464\pi$
$397$	−4.34709e7	+	4.34709e7i	−0.694747	+	0.694747i	0.268526	+	0.963273i	$0.413464\pi$
$398$	5.25600e7	−	2.94390e7i	0.833693	−	0.466953i
$399$	3.12754e7	−	1.19427e7i	0.492362	−	0.188011i
$400$	5.43486e7	−	3.37968e7i	0.849198	−	0.528075i
$401$		−	4.07208e7i		−	0.631514i	−0.948840	−	0.315757i	$-0.897742\pi$
$401$		−	4.07208e7i		−	0.631514i	0.948840	−	0.315757i	$-0.102258\pi$
$402$	−1.38339e7	+	1.65762e7i	−0.212944	+	0.255156i
$403$	−7.29891e6	+	7.29891e6i	−0.111518	+	0.111518i
$404$	−424539.	−	260091.i	−0.00643833	−	0.00394441i
$405$	5.01130e7	−	4.36079e7i	0.754371	−	0.656448i
$406$	−3.79474e7	−	1.06999e7i	−0.567027	−	0.159883i
$407$	7.17665e6	−	7.17665e6i	0.106448	−	0.106448i
$408$	1.81662e7	+	5.37952e7i	0.267475	+	0.792069i
$409$			6.85719e7i			1.00225i	0.865375	+	0.501126i	$0.167081\pi$
$409$			6.85719e7i			1.00225i	−0.865375	+	0.501126i	$0.832919\pi$
$410$	2.37959e7	−	1.00542e8i	0.345264	−	1.45881i
$411$	1.82961e7	−	6.98645e6i	0.263532	−	0.100631i
$412$	1.10400e7	+	4.59620e7i	0.157863	+	0.657215i
$413$	−1.12422e8	+	1.12422e8i	−1.59588	+	1.59588i
$414$	−2.19323e7	−	4.48638e7i	−0.309089	−	0.632258i
$415$	−2.06989e6	−	4.87512e7i	−0.0289603	−	0.682089i
$416$	2.52933e7	+	1.26969e8i	0.351338	+	1.76367i
$417$	−3.74289e7	+	8.36717e7i	−0.516178	+	1.15391i
$418$	−3.15414e6	+	1.76664e6i	−0.0431869	+	0.0241891i
$419$		−	6.29793e7i		−	0.856161i	−0.903741	−	0.428081i	$-0.859190\pi$
$419$		−	6.29793e7i		−	0.856161i	0.903741	−	0.428081i	$-0.140810\pi$
$420$	9.85326e7	−	7.38120e7i	1.32994	−	0.996275i
$421$	7.79766e7			1.04500			0.522502	−	0.852638i	$-0.324999\pi$
$421$	7.79766e7			1.04500			0.522502	+	0.852638i	$0.324999\pi$
$422$	−2.54185e7	−	4.53819e7i	−0.338230	−	0.603872i
$423$	−2.94974e7	−	1.64960e6i	−0.389729	−	0.0217950i
$424$	−5.35756e7	−	5.79379e7i	−0.702861	−	0.760090i
$425$	−4.13701e7	+	4.90632e7i	−0.538914	+	0.639130i
$426$	−1.26121e7	−	1.39859e8i	−0.163139	−	1.80909i
$427$	5.11331e7	+	5.11331e7i	0.656777	+	0.656777i
$428$	2.34884e7	+	9.77872e7i	0.299587	+	1.24724i
$429$	−2.07015e7	+	7.90495e6i	−0.262198	+	0.100121i
$430$	386032.	−	238274.i	0.00485532	−	0.00299689i
$431$	6.55221e7			0.818382			0.409191	−	0.912449i	$-0.365811\pi$
$431$	6.55221e7			0.818382			0.409191	+	0.912449i	$0.365811\pi$
$432$	5.67206e7	+	5.72941e7i	0.703541	+	0.710655i
$433$	3.57912e7	+	3.57912e7i	0.440872	+	0.440872i	0.892305	−	0.451433i	$-0.149087\pi$
$433$	3.57912e7	+	3.57912e7i	0.440872	+	0.440872i	−0.451433	+	0.892305i	$0.649087\pi$
$434$	−3.23298e6	+	1.14658e7i	−0.0395489	+	0.140260i
$435$	2.67966e7	−	1.15575e7i	0.325546	−	0.140410i
$436$	−9.28490e7	−	5.68834e7i	−1.12026	−	0.686319i
$437$	1.31717e7	+	1.31717e7i	0.157833	+	0.157833i
$438$	−1.89924e7	+	2.27573e7i	−0.226025	+	0.270830i
$439$	−1.16597e8			−1.37814			−0.689069	−	0.724696i	$-0.741980\pi$
$439$	−1.16597e8			−1.37814			−0.689069	+	0.724696i	$0.741980\pi$
$440$	−9.36933e6	+	9.43201e6i	−0.109989	+	0.110725i
$441$	1.12613e8	−	1.00685e8i	1.31303	−	1.17395i
$442$	−6.34401e7	−	1.13265e8i	−0.734678	−	1.31169i
$443$	−8.41717e7	−	8.41717e7i	−0.968177	−	0.968177i	0.0313321	−	0.999509i	$-0.490025\pi$
$443$	−8.41717e7	−	8.41717e7i	−0.968177	−	0.968177i	−0.999509	+	0.0313321i	$0.990025\pi$
$444$	8.29885e7	+	1.55217e7i	0.948133	+	0.177334i
$445$	−6.63726e7	−	6.09661e7i	−0.753198	−	0.691844i
$446$	−1.32971e7	+	4.71582e7i	−0.149883	+	0.531561i
$447$	−2.75215e7	+	6.15239e7i	−0.308141	+	0.688845i
$448$	9.70754e7	+	1.13582e8i	1.07963	+	1.26321i
$449$	9.42243e7			1.04094			0.520468	−	0.853881i	$-0.325757\pi$
$449$	9.42243e7			1.04094			0.520468	+	0.853881i	$0.325757\pi$
$450$	−2.21765e7	+	8.83853e7i	−0.243364	+	0.969935i
$451$			2.14625e7i			0.233965i
$452$	1.22523e7	+	5.10090e7i	0.132679	+	0.552371i
$453$	−5.57138e7	−	2.49225e7i	−0.599334	−	0.268100i
$454$	−2.15493e7	+	7.64247e7i	−0.230285	+	0.816707i
$455$	−1.90419e8	+	2.07306e8i	−2.02151	+	2.20078i
$456$	−2.69507e7	−	1.33437e7i	−0.284234	−	0.140728i
$457$	9.73983e7	−	9.73983e7i	1.02048	−	1.02048i	0.0206898	−	0.999786i	$-0.493414\pi$
$457$	9.73983e7	−	9.73983e7i	1.02048	−	1.02048i	0.999786	−	0.0206898i	$-0.00658624\pi$
$458$	7.24540e7	+	1.29359e8i	0.754164	+	1.34648i
$459$	−7.18390e7	−	3.70809e7i	−0.742886	−	0.383453i
$460$	5.98769e7	+	3.32754e7i	0.615157	+	0.341861i
$461$		−	6.03692e7i		−	0.616188i	−0.951356	−	0.308094i	$-0.900309\pi$
$461$		−	6.03692e7i		−	0.616188i	0.951356	−	0.308094i	$-0.0996911\pi$
$462$	−1.63864e7	+	1.96347e7i	−0.166172	+	0.199113i
$463$	−1.57819e7	+	1.57819e7i	−0.159007	+	0.159007i	−0.782127	−	0.623119i	$-0.785865\pi$
$463$	−1.57819e7	+	1.57819e7i	−0.159007	+	0.159007i	0.623119	+	0.782127i	$0.285865\pi$
$464$	1.60862e7	+	3.15532e7i	0.161027	+	0.315856i
$465$	−3.49211e6	−	8.09660e6i	−0.0347319	−	0.0805274i
$466$	−4.13713e6	+	1.46724e7i	−0.0408829	+	0.144991i
$467$	6.68107e7	−	6.68107e7i	0.655988	−	0.655988i	−0.298441	−	0.954428i	$-0.596466\pi$
$467$	6.68107e7	−	6.68107e7i	0.655988	−	0.655988i	0.954428	+	0.298441i	$0.0964665\pi$
$468$	−1.51559e8	−	1.04923e8i	−1.47858	−	1.02360i
$469$		−	5.69717e7i		−	0.552256i
$470$	3.44858e7	−	2.12860e7i	0.332160	−	0.205022i
$471$	−2.93538e7	−	7.68717e7i	−0.280932	−	0.735705i
$472$	1.42709e8	+	5.58263e6i	1.35714	+	0.0530900i
$473$	−66634.4	+	66634.4i	−0.000629673	+	0.000629673i
$474$	−3.14248e6	−	3.48478e7i	−0.0295078	−	0.327220i
$475$	−2.88121e6	−	3.38688e7i	−0.0268840	−	0.316023i
$476$	−1.27758e8	−	7.82699e7i	−1.18458	−	0.725728i
$477$	1.12182e8	+	6.27362e6i	1.03364	+	0.0578047i
$478$	3.53616e7	+	6.31342e7i	0.323778	+	0.578071i
$479$			4.31407e7i			0.392537i	0.980550	+	0.196269i	$0.0628824\pi$
$479$			4.31407e7i			0.392537i	−0.980550	+	0.196269i	$0.937118\pi$
$480$	−1.08774e8	−	1.99695e7i	−0.983562	−	0.180569i
$481$	−1.93036e8			−1.73462
$482$	−2.84717e7	+	1.59470e7i	−0.254256	+	0.142409i
$483$	1.20287e8	+	5.38079e7i	1.06752	+	0.477534i
$484$	−5.77871e7	+	9.43241e7i	−0.509677	+	0.831930i
$485$	−1.31843e7	+	559781.i	−0.115566	+	0.00490674i
$486$	−1.14764e8	−	2.50188e6i	−0.999762	−	0.0217950i
$487$	−1.18939e8	−	1.18939e8i	−1.02977	−	1.02977i	−0.999543	−	0.0302238i	$-0.990378\pi$
$487$	−1.18939e8	−	1.18939e8i	−1.02977	−	1.02977i	−0.0302238	−	0.999543i	$-0.509622\pi$
$488$	2.53916e6	−	6.49088e7i	0.0218490	−	0.558527i
$489$	−1.64221e7	−	4.30062e7i	−0.140444	−	0.367794i
$490$	−4.77246e7	+	2.01645e8i	−0.405652	+	1.71396i
$491$	5.45322e7			0.460690			0.230345	−	0.973109i	$-0.426015\pi$
$491$	5.45322e7			0.460690			0.230345	+	0.973109i	$0.426015\pi$
$492$	−1.47302e8	+	1.00883e8i	−1.23684	+	0.847077i
$493$	−2.51129e7	−	2.51129e7i	−0.209583	−	0.209583i
$494$	6.61790e7	+	1.86603e7i	0.548958	+	0.154789i
$495$	254261.	−	1.89276e7i	0.00209636	−	0.156056i
$496$	9.53380e6	−	4.86045e6i	0.0781305	−	0.0398319i
$497$	2.62018e8	+	2.62018e8i	2.13433	+	2.13433i
$498$	−5.40260e7	+	6.47356e7i	−0.437436	+	0.524150i
$499$	−7.77603e7			−0.625830			−0.312915	−	0.949781i	$-0.601305\pi$
$499$	−7.77603e7			−0.625830			−0.312915	+	0.949781i	$0.601305\pi$
$500$	−4.43887e7	−	1.16853e8i	−0.355110	−	0.934825i
$501$	2.28155e7	+	5.97491e7i	0.181433	+	0.475136i
$502$	−9.99557e7	+	5.59854e7i	−0.790126	+	0.442551i
$503$	−1.21869e8	−	1.21869e8i	−0.957613	−	0.957613i	0.0415243	−	0.999137i	$-0.486779\pi$
$503$	−1.21869e8	−	1.21869e8i	−0.957613	−	0.957613i	−0.999137	+	0.0415243i	$0.986779\pi$
$504$	−2.11781e8	−	2.01724e7i	−1.65423	−	0.157567i
$505$	−657814.	+	716150.i	−0.00510774	+	0.00556071i
$506$	−1.36958e7	−	3.86176e6i	−0.105714	−	0.0298081i
$507$	2.65761e8	+	1.18883e8i	2.03923	+	0.912212i
$508$	−1.72747e8	+	4.14937e7i	−1.31771	+	0.316513i
$509$	−1.64444e8			−1.24699			−0.623497	−	0.781825i	$-0.714289\pi$
$509$	−1.64444e8			−1.24699			−0.623497	+	0.781825i	$0.714289\pi$
$510$	1.09928e8	−	1.46364e7i	0.828699	−	0.110337i
$511$		−	7.82157e7i		−	0.586180i
$512$	1.57073e7	−	1.33295e8i	0.117028	−	0.993129i
$513$	4.07923e7	−	1.30175e7i	0.302152	−	0.0964217i
$514$	2.22864e8	+	6.28404e7i	1.64116	+	0.462754i
$515$	9.22399e7	−	3.91634e6i	0.675300	−	0.0286721i
$516$	−770539.	−	144117.i	−0.00560848	−	0.00104898i
$517$	−5.95273e6	+	5.95273e6i	−0.0430769	+	0.0430769i
$518$	−1.94371e8	+	1.08868e8i	−1.39843	+	0.783266i
$519$	5.75699e7	+	1.50764e8i	0.411807	+	1.07844i
$520$	2.52857e8	−	842965.i	1.79831	−	0.00599514i
$521$		−	1.58812e8i		−	1.12298i	−0.827485	−	0.561488i	$-0.810229\pi$
$521$		−	1.58812e8i		−	1.12298i	0.827485	−	0.561488i	$-0.189771\pi$
$522$	−4.76955e7	−	1.63741e7i	−0.335325	−	0.115119i
$523$	−3.20979e7	+	3.20979e7i	−0.224373	+	0.224373i	−0.810337	−	0.585964i	$-0.800716\pi$
$523$	−3.20979e7	+	3.20979e7i	−0.224373	+	0.224373i	0.585964	+	0.810337i	$0.300716\pi$
$524$	1.41142e8	−	2.30382e8i	0.980985	−	1.60123i
$525$	−1.04510e8	−	2.16556e8i	−0.722239	−	1.49655i
$526$	8.83324e6	+	2.49069e6i	0.0606964	+	0.0171144i
$527$	−7.58787e6	+	7.58787e6i	−0.0518427	+	0.0518427i
$528$	2.29434e7	−	1.16734e6i	0.155868	−	0.00793038i
$529$		−	7.47156e7i		−	0.504713i
$530$	−1.31154e8	+	8.09530e7i	−0.880952	+	0.543758i
$531$	−1.51594e8	+	1.35536e8i	−1.01250	+	0.905257i
$532$	7.71607e7	−	1.85339e7i	0.512461	−	0.123093i
$533$	2.88647e8	−	2.88647e8i	1.90627	−	1.90627i
$534$	1.39868e7	+	1.55103e8i	0.0918533	+	1.01859i
$535$	1.96246e8	−	8.33227e6i	1.28156	−	0.0544129i
$536$	−3.75747e7	+	3.47456e7i	−0.244006	+	0.225635i
$537$	9.89640e7	+	4.42696e7i	0.639079	+	0.285879i
$538$	−1.25949e8	+	7.05442e7i	−0.808812	+	0.453017i
$539$		−	4.30447e7i		−	0.274886i
$540$	1.31100e8	−	8.72227e7i	0.832569	−	0.553922i
$541$	1.54425e8			0.975275			0.487637	−	0.873046i	$-0.337859\pi$
$541$	1.54425e8			0.975275			0.487637	+	0.873046i	$0.337859\pi$
$542$	−8.23853e7	−	1.47090e8i	−0.517430	−	0.923814i
$543$	−6.84263e7	+	1.52966e8i	−0.427389	+	0.955422i
$544$	2.62946e7	+	1.31995e8i	0.163331	+	0.819902i
$545$	−1.43868e8	+	1.56626e8i	−0.888737	+	0.967552i
$546$	4.84445e8	−	4.36859e7i	2.97623	−	0.268388i
$547$	−9.35231e7	−	9.35231e7i	−0.571422	−	0.571422i	0.361104	−	0.932526i	$-0.382400\pi$
$547$	−9.35231e7	−	9.35231e7i	−0.571422	−	0.571422i	−0.932526	+	0.361104i	$0.882400\pi$
$548$	4.51389e7	−	1.08423e7i	0.274290	−	0.0658842i
$549$	6.16463e7	+	6.89497e7i	0.372555	+	0.416692i
$550$	1.45635e7	+	2.14975e7i	0.0875341	+	0.129211i
$551$	1.88104e7			0.112446
$552$	−3.78718e7	−	1.12149e8i	−0.225164	−	0.666775i
$553$	6.52855e7	+	6.52855e7i	0.386048	+	0.386048i
$554$	−6.33392e7	+	2.24633e8i	−0.372515	+	1.32113i
$555$	6.08880e7	−	1.53244e8i	0.356166	−	0.896408i
$556$	−1.13503e8	+	1.85268e8i	−0.660366	+	1.07789i
$557$	−1.88879e8	−	1.88879e8i	−1.09299	−	1.09299i	−0.995207	−	0.0977877i	$-0.968823\pi$
$557$	−1.88879e8	−	1.88879e8i	−1.09299	−	1.09299i	−0.0977877	−	0.995207i	$-0.531177\pi$
$558$	−4.94743e6	+	1.44112e7i	−0.0284759	+	0.0829463i
$559$	1.79232e6			0.0102608
$560$	2.54130e8	−	1.43454e8i	1.44708	−	0.816862i
$561$	−2.15210e7	+	8.21789e6i	−0.121892	+	0.0465449i
$562$	−3.67408e7	−	6.55967e7i	−0.206985	−	0.369550i
$563$	1.36179e8	+	1.36179e8i	0.763108	+	0.763108i	0.976883	−	0.213775i	$-0.0685760\pi$
$563$	1.36179e8	+	1.36179e8i	0.763108	+	0.763108i	−0.213775	+	0.976883i	$0.568576\pi$
$564$	−6.88354e7	−	1.28746e7i	−0.383685	−	0.0717624i
$565$	1.02368e8	−	4.34638e6i	0.567571	−	0.0240981i
$566$	1.36711e7	−	4.84847e7i	0.0753971	−	0.267396i
$567$	2.36732e8	−	1.88969e8i	1.29870	−	1.03667i
$568$	1.30113e7	−	3.32608e8i	0.0710027	−	1.81505i
$569$	−1.57894e8			−0.857093			−0.428546	−	0.903520i	$-0.640974\pi$
$569$	−1.57894e8			−0.857093			−0.428546	+	0.903520i	$0.640974\pi$
$570$	−3.56882e7	+	4.66513e7i	−0.192708	+	0.251906i
$571$		−	3.54674e8i		−	1.90511i	−0.304362	−	0.952557i	$-0.598443\pi$
$571$		−	3.54674e8i		−	1.90511i	0.304362	−	0.952557i	$-0.401557\pi$
$572$	−5.10733e7	+	1.22678e7i	−0.272901	+	0.0655507i
$573$	−6.62436e7	+	1.48087e8i	−0.352112	+	0.787140i
$574$	1.27853e8	−	4.53433e8i	0.676046	−	2.39760i
$575$	8.62460e7	−	1.02284e8i	0.453665	−	0.538029i
$576$	1.15856e8	+	1.51979e8i	0.606248	+	0.795275i
$577$	−1.24339e7	+	1.24339e7i	−0.0647261	+	0.0647261i	−0.738729	−	0.674003i	$-0.764574\pi$
$577$	−1.24339e7	+	1.24339e7i	−0.0647261	+	0.0647261i	0.674003	+	0.738729i	$0.264574\pi$
$578$	2.84111e7	+	5.07248e7i	0.147131	+	0.262686i
$579$	−5.75554e7	+	2.19778e7i	−0.296517	+	0.113226i
$580$	6.65150e7	−	1.89947e7i	0.340907	−	0.0973527i
$581$		−	2.22494e8i		−	1.13446i
$582$	1.75071e7	+	1.46108e7i	0.0888066	+	0.0741148i
$583$	2.26389e7	−	2.26389e7i	0.114248	−	0.114248i
$584$	−5.15859e7	+	4.77019e7i	−0.258996	+	0.239495i
$585$	−2.57974e8	+	2.51135e8i	−1.28857	+	1.25441i
$586$	−1.68766e7	+	5.98529e7i	−0.0838671	+	0.297435i
$587$	−1.69879e8	+	1.69879e8i	−0.839895	+	0.839895i	−0.988845	−	0.148950i	$-0.952411\pi$
$587$	−1.69879e8	+	1.69879e8i	−0.839895	+	0.839895i	0.148950	+	0.988845i	$0.452411\pi$
$588$	2.95426e8	−	2.02329e8i	1.45317	−	0.995234i
$589$		−	5.68356e6i		−	0.0278147i
$590$	6.42440e7	−	2.71443e8i	0.312807	−	1.32167i
$591$	−2.98041e8	+	1.13808e8i	−1.44382	+	0.551329i
$592$	1.90344e8	+	6.17985e7i	0.917432	+	0.297861i
$593$	4.16201e7	−	4.16201e7i	0.199590	−	0.199590i	−0.600234	−	0.799824i	$-0.704926\pi$
$593$	4.16201e7	−	4.16201e7i	0.199590	−	0.199590i	0.799824	+	0.600234i	$0.204926\pi$
$594$	−2.23281e7	+	2.39037e7i	−0.106535	+	0.114053i
$595$	−1.97958e8	+	2.15513e8i	−0.939770	+	1.02311i
$596$	−8.34592e7	+	1.36228e8i	−0.394217	+	0.643468i
$597$	−8.30230e7	+	1.85597e8i	−0.390189	+	0.872262i
$598$	1.32256e8	+	2.36129e8i	0.618462	+	1.10420i
$599$		−	2.11445e8i		−	0.983822i	−0.870645	−	0.491911i	$-0.836298\pi$
$599$		−	2.11445e8i		−	0.983822i	0.870645	−	0.491911i	$-0.163702\pi$
$600$	−7.90878e7	+	2.01000e8i	−0.366147	+	0.930557i
$601$	−1.88574e8			−0.868678			−0.434339	−	0.900750i	$-0.643018\pi$
$601$	−1.88574e8			−0.868678			−0.434339	+	0.900750i	$0.643018\pi$
$602$	1.80471e6	−	1.01082e6i	0.00827215	−	0.00463325i
$603$	4.06866e6	−	7.27540e7i	0.0185567	−	0.331822i
$604$	−1.23363e8	−	7.55776e7i	−0.559853	−	0.342991i
$605$	1.59114e8	+	1.46153e8i	0.718527	+	0.659997i
$606$	1.67354e6	−	150915.i	0.00752001	−	0.000678134i
$607$	−6.91075e7	−	6.91075e7i	−0.309000	−	0.309000i	0.535521	−	0.844522i	$-0.320115\pi$
$607$	−6.91075e7	−	6.91075e7i	−0.309000	−	0.309000i	−0.844522	+	0.535521i	$0.820115\pi$
$608$	−5.92822e7	−	3.95867e7i	−0.263763	−	0.176132i
$609$	1.24311e8	−	4.74689e7i	0.550376	−	0.210163i
$610$	−1.23461e8	−	2.92203e7i	−0.543927	−	0.128734i
$611$	1.60115e8			0.701954
$612$	−1.57559e8	−	1.09076e8i	−0.687370	−	0.475856i
$613$	4.87109e6	+	4.87109e6i	0.0211468	+	0.0211468i	0.717601	−	0.696454i	$-0.245240\pi$
$613$	4.87109e6	+	4.87109e6i	0.0211468	+	0.0211468i	−0.696454	+	0.717601i	$0.745240\pi$
$614$	1.75831e8	+	4.95786e7i	0.759608	+	0.214185i
$615$	1.38101e8	+	3.20192e8i	0.593705	+	1.37653i
$616$	−4.45078e7	+	4.11567e7i	−0.190412	+	0.176075i
$617$	1.25719e8	+	1.25719e8i	0.535238	+	0.535238i	0.922126	−	0.386889i	$-0.126450\pi$
$617$	1.25719e8	+	1.25719e8i	0.535238	+	0.535238i	−0.386889	+	0.922126i	$0.626450\pi$
$618$	−1.22483e8	−	1.02220e8i	−0.518933	−	0.433083i
$619$	2.78656e8			1.17489			0.587443	−	0.809265i	$-0.300135\pi$
$619$	2.78656e8			1.17489			0.587443	+	0.809265i	$0.300135\pi$
$620$	−5.73924e6	−	2.00975e7i	−0.0240813	−	0.0843271i
$621$	1.49766e8	+	7.73042e7i	0.625372	+	0.322796i
$622$	2.15992e8	−	1.20977e8i	0.897564	−	0.502727i
$623$	−2.90578e8	−	2.90578e8i	−1.20171	−	1.20171i
$624$	−3.24263e8	−	2.92865e8i	−1.33458	−	1.20535i
$625$	−2.40632e8	+	4.12396e7i	−0.985630	+	0.168917i
$626$	1.05605e7	+	2.97771e6i	0.0430487	+	0.0121383i
$627$	4.98223e6	−	1.11377e7i	0.0202126	−	0.0451849i
$628$	−4.55544e7	−	1.89653e8i	−0.183930	−	0.765738i
$629$	−2.00678e8			−0.806395
$630$	−1.18124e8	+	3.98363e8i	−0.472408	+	1.59315i
$631$			3.76602e8i			1.49897i	0.662019	+	0.749487i	$0.269700\pi$
$631$			3.76602e8i			1.49897i	−0.662019	+	0.749487i	$0.730300\pi$
$632$	3.24194e6	−	8.28740e7i	0.0128426	−	0.328297i
$633$	1.60250e8	+	7.16845e7i	0.631809	+	0.282627i
$634$	−7.00949e7	−	1.97645e7i	−0.275054	−	0.0775564i
$635$	1.47195e7	+	3.46681e8i	0.0574871	+	1.35397i
$636$	2.61789e8	+	4.89636e7i	1.01761	+	0.190328i
$637$	−5.78903e8	+	5.78903e8i	−2.23969	+	2.23969i
$638$	−1.25369e7	+	7.02192e6i	−0.0482755	+	0.0270392i
$639$	3.15890e8	+	3.53315e8i	1.21069	+	1.35413i
$640$	−2.49601e8	−	8.01185e7i	−0.952151	−	0.305628i
$641$			4.34902e7i			0.165127i	0.996586	+	0.0825633i	$0.0263107\pi$
$641$			4.34902e7i			0.165127i	−0.996586	+	0.0825633i	$0.973689\pi$
$642$	−2.60591e8	−	2.17480e8i	−0.984815	−	0.821891i
$643$	2.33749e8	−	2.33749e8i	0.879257	−	0.879257i	−0.114200	−	0.993458i	$-0.536431\pi$
$643$	2.33749e8	−	2.33749e8i	0.879257	−	0.879257i	0.993458	+	0.114200i	$0.0364306\pi$
$644$	2.66342e8	+	1.63173e8i	0.997199	+	0.610928i
$645$	−565338.	+	1.42286e6i	−0.00210683	+	0.00530252i
$646$	6.87990e7	+	1.93991e7i	0.255202	+	0.0719588i
$647$	−2.88943e8	+	2.88943e8i	−1.06684	+	1.06684i	−0.0692382	+	0.997600i	$0.522057\pi$
$647$	−2.88943e8	+	2.88943e8i	−1.06684	+	1.06684i	−0.997600	+	0.0692382i	$0.977943\pi$
$648$	−2.69009e8	−	4.08850e7i	−0.988647	−	0.150259i
$649$			5.79442e7i			0.211971i
$650$	9.32546e7	−	4.84980e8i	0.339571	−	1.76597i
$651$	−1.43427e7	−	3.75607e7i	−0.0519863	−	0.136142i
$652$	−2.54856e7	−	1.06102e8i	−0.0919501	−	0.382808i
$653$	6.98659e7	−	6.98659e7i	0.250915	−	0.250915i	−0.570431	−	0.821346i	$-0.693224\pi$
$653$	6.98659e7	−	6.98659e7i	0.250915	−	0.250915i	0.821346	+	0.570431i	$0.193224\pi$
$654$	3.66013e8	−	3.30060e7i	1.30847	−	0.117994i
$655$	−3.88628e8	−	3.56971e8i	−1.38296	−	1.27031i
$656$	−3.77029e8	+	1.92214e8i	−1.33556	+	0.680884i
$657$	5.58582e6	−	9.98831e7i	0.0196966	−	0.352205i
$658$	1.61222e8	−	9.03010e7i	0.565911	−	0.316968i
$659$		−	1.43271e8i		−	0.500613i	−0.968167	−	0.250306i	$-0.919469\pi$
$659$		−	1.43271e8i		−	0.500613i	0.968167	−	0.250306i	$-0.0805314\pi$
$660$	6.37074e6	−	4.44148e7i	0.0221594	−	0.154488i
$661$	3.26905e8			1.13192			0.565962	−	0.824431i	$-0.308505\pi$
$661$	3.26905e8			1.13192			0.565962	+	0.824431i	$0.308505\pi$
$662$	−1.45329e8	−	2.59468e8i	−0.500930	−	0.894356i
$663$	3.99955e8	+	1.78912e8i	1.37237	+	0.613902i
$664$	−1.46742e8	+	1.35693e8i	−0.501245	+	0.463505i
$665$	−6.57472e6	−	1.54851e8i	−0.0223569	−	0.526563i
$666$	−2.55991e8	+	1.25145e8i	−0.866566	+	0.423634i
$667$	5.23540e7	+	5.23540e7i	0.176430	+	0.176430i
$668$	3.54075e7	+	1.47409e8i	0.118786	+	0.494532i
$669$	−5.89908e7	−	1.54485e8i	−0.197018	−	0.515951i
$670$	5.25008e7	+	8.50576e7i	0.174559	+	0.282806i
$671$	2.63549e7			0.0872357
$672$	−4.91674e8	−	1.12013e8i	−1.62020	−	0.369116i
$673$	7.19337e6	+	7.19337e6i	0.0235987	+	0.0235987i	0.718808	−	0.695209i	$-0.244688\pi$
$673$	7.19337e6	+	7.19337e6i	0.0235987	+	0.0235987i	−0.695209	+	0.718808i	$0.744688\pi$
$674$	−4.48380e7	+	1.59018e8i	−0.146442	+	0.519358i
$675$	−1.17996e8	−	2.84010e8i	−0.383669	−	0.923470i
$676$	5.88454e8	+	3.60513e8i	1.90490	+	1.16703i
$677$	2.25803e8	+	2.25803e8i	0.727718	+	0.727718i	0.970165	−	0.242447i	$-0.0779500\pi$
$677$	2.25803e8	+	2.25803e8i	0.727718	+	0.727718i	−0.242447	+	0.970165i	$0.577950\pi$
$678$	−1.35933e8	−	1.13445e8i	−0.436149	−	0.363994i
$679$	−6.01712e7			−0.192211
$680$	2.62867e8	−	876337.i	0.836007	−	0.00278705i
$681$	−9.56007e7	−	2.50359e8i	−0.302705	−	0.792724i
$682$	2.12167e6	+	3.78801e6i	0.00668845	+	0.0119415i
$683$	−1.75367e8	−	1.75367e8i	−0.550410	−	0.550410i	0.376149	−	0.926559i	$-0.377248\pi$
$683$	−1.75367e8	−	1.75367e8i	−0.550410	−	0.550410i	−0.926559	+	0.376149i	$0.877248\pi$
$684$	9.98594e7	−	1.81578e7i	0.312048	−	0.0567406i
$685$	−3.84621e6	−	9.05880e7i	−0.0119663	−	0.281838i
$686$	−1.10835e8	+	3.93075e8i	−0.343323	+	1.21760i
$687$	−4.56783e8	−	2.04333e8i	−1.40877	−	0.630186i
$688$	−1.76732e6	−	573792.i	−0.00542688	−	0.00176193i
$689$	−6.08936e8			−1.86172
$690$	−2.29171e8	+	3.05131e7i	−0.697610	+	0.0928835i
$691$		−	2.60705e7i		−	0.0790161i	−0.999219	−	0.0395080i	$-0.987421\pi$
$691$		−	2.60705e7i		−	0.0790161i	0.999219	−	0.0395080i	$-0.0125791\pi$
$692$	8.93434e7	+	3.71955e8i	0.269615	+	1.12246i
$693$	4.81939e6	−	8.61782e7i	0.0144808	−	0.258939i
$694$	−6.92133e7	+	2.45466e8i	−0.207067	+	0.734365i
$695$	3.12527e8	+	2.87069e8i	0.930964	+	0.855129i
$696$	−1.07122e8	−	5.30375e7i	−0.317724	−	0.157310i
$697$	3.00074e8	−	3.00074e8i	0.886196	−	0.886196i
$698$	1.84662e8	+	3.29694e8i	0.543015	+	0.969494i
$699$	−1.83539e7	−	4.80651e7i	−0.0537398	−	0.140734i
$700$	−1.79617e8	−	5.40927e8i	−0.523665	−	1.57705i
$701$			4.84998e8i			1.40795i	0.710227	+	0.703973i	$0.248592\pi$
$701$			4.84998e8i			1.40795i	−0.710227	+	0.703973i	$0.751408\pi$
$702$	6.21766e8	−	2.11909e7i	1.79728	−	0.0612546i
$703$	7.51572e7	−	7.51572e7i	0.216324	−	0.216324i
$704$	5.42884e7	+	4.25392e6i	0.155593	+	0.0121919i
$705$	−5.05040e7	+	1.27110e8i	−0.144131	+	0.362753i
$706$	3.51472e7	−	1.24650e8i	0.0998797	−	0.354224i
$707$	−3.13529e6	+	3.13529e6i	−0.00887196	+	0.00887196i
$708$	−3.97685e8	+	2.72363e8i	−1.12057	+	0.767447i
$709$			3.37104e8i			0.945858i	0.881101	+	0.472929i	$0.156803\pi$
$709$			3.37104e8i			0.945858i	−0.881101	+	0.472929i	$0.843197\pi$
$710$	−6.32644e8	−	1.49732e8i	−1.76760	−	0.418349i
$711$	7.87085e7	+	8.80333e7i	0.218984	+	0.244928i
$712$	−1.44295e7	+	3.68862e8i	−0.0399771	+	1.02194i
$713$	1.58188e7	−	1.58188e7i	0.0436419	−	0.0436419i
$714$	5.03623e8	−	4.54154e7i	1.38360	−	0.124769i
$715$	4.35186e6	+	1.02497e8i	0.0119058	+	0.280411i
$716$	2.19129e8	+	1.34248e8i	0.596980	+	0.365737i
$717$	−2.22936e8	−	9.97259e7i	−0.604814	−	0.270552i
$718$	−2.46867e8	−	4.40754e8i	−0.666945	−	1.19076i
$719$		−	3.20053e8i		−	0.861063i	−0.902576	−	0.430531i	$-0.858326\pi$
$719$		−	3.20053e8i		−	0.861063i	0.902576	−	0.430531i	$-0.141674\pi$
$720$	3.34775e8	−	1.65045e8i	0.896924	−	0.442186i
$721$	4.20970e8			1.12317
$722$	2.95337e8	−	1.65419e8i	0.784704	−	0.439514i
$723$	4.49734e7	−	1.00537e8i	0.118998	−	0.266019i
$724$	−2.07503e8	+	3.38701e8i	−0.546775	+	0.892485i
$725$	−1.14520e7	−	1.34619e8i	−0.0300517	−	0.353259i
$726$	−3.35304e7	−	3.71828e8i	−0.0876252	−	0.971699i
$727$	3.60196e8	+	3.60196e8i	0.937423	+	0.937423i	0.998154	−	0.0607313i	$-0.0193433\pi$
$727$	3.60196e8	+	3.60196e8i	0.937423	+	0.937423i	−0.0607313	+	0.998154i	$0.519343\pi$
$728$	1.15209e9	+	4.50686e7i	2.98602	+	0.116810i
$729$	3.15807e8	−	2.24411e8i	0.815154	−	0.579245i
$730$	7.20778e7	+	1.16775e8i	0.185282	+	0.300179i
$731$	1.86327e6			0.00477007
$732$	1.23880e8	+	1.80880e8i	0.315840	+	0.461167i
$733$	−2.51153e8	−	2.51153e8i	−0.637714	−	0.637714i	0.312277	−	0.949991i	$-0.398908\pi$
$733$	−2.51153e8	−	2.51153e8i	−0.637714	−	0.637714i	−0.949991	+	0.312277i	$0.898908\pi$
$734$	−5.29698e8	−	1.49358e8i	−1.33949	−	0.377694i
$735$	−2.76971e8	−	6.42170e8i	−0.697546	−	1.61729i
$736$	−5.48175e7	−	2.75176e8i	−0.137495	−	0.690204i
$737$	−1.46821e7	−	1.46821e7i	−0.0366764	−	0.0366764i
$738$	1.95654e8	−	5.69912e8i	0.486764	−	1.41788i
$739$	−2.29761e7			−0.0569302			−0.0284651	−	0.999595i	$-0.509062\pi$
$739$	−2.29761e7			−0.0569302			−0.0284651	+	0.999595i	$0.509062\pi$
$740$	1.89868e8	−	3.41655e8i	0.468551	−	0.843127i
$741$	−2.16795e8	+	8.27842e7i	−0.532838	+	0.203466i
$742$	−6.13148e8	+	3.43425e8i	−1.50091	+	0.840660i
$743$	2.72215e8	+	2.72215e8i	0.663661	+	0.663661i	0.956241	−	0.292580i	$-0.0945139\pi$
$743$	2.72215e8	+	2.72215e8i	0.663661	+	0.663661i	−0.292580	+	0.956241i	$0.594514\pi$
$744$	−1.60253e7	+	3.23669e7i	−0.0389123	+	0.0785926i
$745$	2.29801e8	+	2.11082e8i	0.555755	+	0.510485i
$746$	−6.01563e8	−	1.69621e8i	−1.44899	−	0.408567i
$747$	1.58895e7	−	2.84129e8i	0.0381196	−	0.681638i
$748$	−5.30952e7	+	1.27534e7i	−0.126868	+	0.0304735i
$749$	8.95640e8			2.13151
$750$	3.55594e8	+	2.27005e8i	0.842889	+	0.538087i
$751$			3.80924e8i			0.899330i	0.893197	+	0.449665i	$0.148457\pi$
$751$			3.80924e8i			0.899330i	−0.893197	+	0.449665i	$0.851543\pi$
$752$	−1.57882e8	−	5.12593e7i	−0.371261	−	0.120537i
$753$	1.57889e8	−	3.52957e8i	0.369799	−	0.826680i
$754$	2.63044e8	+	7.41699e7i	0.613641	+	0.173027i
$755$	−1.91148e8	+	2.08100e8i	−0.444150	+	0.483538i
$756$	6.14115e8	−	3.71998e8i	1.42129	−	0.860945i
$757$	2.23690e8	−	2.23690e8i	0.515654	−	0.515654i	−0.400599	−	0.916253i	$-0.631198\pi$
$757$	2.23690e8	−	2.23690e8i	0.515654	−	0.515654i	0.916253	+	0.400599i	$0.131198\pi$
$758$	2.82148e7	−	1.58032e7i	0.0647843	−	0.0362858i
$759$	4.48658e7	−	1.71322e7i	0.102610	−	0.0391821i
$760$	−9.81200e7	+	9.87764e7i	−0.223520	+	0.225015i
$761$		−	1.10170e8i		−	0.249983i	−0.992158	−	0.124991i	$-0.960110\pi$
$761$		−	1.10170e8i		−	0.249983i	0.992158	−	0.124991i	$-0.0398903\pi$
$762$	3.84191e8	−	4.60350e8i	0.868326	−	1.04045i
$763$	−6.85705e8	+	6.85705e8i	−1.54370	+	1.54370i
$764$	−2.00884e8	+	3.27897e8i	−0.450470	+	0.735288i
$765$	−2.68187e8	+	2.61077e8i	−0.599037	+	0.583156i
$766$	−1.94317e8	−	5.47911e7i	−0.432339	−	0.121906i
$767$	7.79285e8	−	7.79285e8i	1.72707	−	1.72707i
$768$	2.25983e8	+	3.92590e8i	0.498876	+	0.866673i
$769$		−	5.46731e8i		−	1.20225i	−0.799155	−	0.601125i	$-0.794719\pi$
$769$		−	5.46731e8i		−	1.20225i	0.799155	−	0.601125i	$-0.205281\pi$
$770$	6.21880e7	+	1.00752e8i	0.136218	+	0.220689i
$771$	−7.30078e8	+	2.78784e8i	−1.59297	+	0.608281i
$772$	−1.41997e8	+	3.41075e7i	−0.308622	+	0.0741307i
$773$	−4.99750e8	+	4.99750e8i	−1.08197	+	1.08197i	−0.0856424	+	0.996326i	$0.527294\pi$
$773$	−4.99750e8	+	4.99750e8i	−1.08197	+	1.08197i	−0.996326	+	0.0856424i	$0.972706\pi$
$774$	2.37684e6	−	1.16196e6i	0.00512599	−	0.00250592i
$775$	−4.06752e7	+	3.46023e6i	−0.0873825	+	0.00743362i
$776$	3.66969e7	+	3.96849e7i	0.0785316	+	0.0849259i
$777$	3.07026e8	−	6.86351e8i	0.654503	−	1.46313i
$778$	−2.93554e8	+	1.64420e8i	−0.623375	+	0.349154i
$779$			2.24765e8i			0.475463i
$780$	−6.83009e8	+	5.11650e8i	−1.43927	+	1.07818i
$781$	1.35049e8			0.283490
$782$	1.37492e8	+	2.45477e8i	0.287513	+	0.513323i
$783$	1.62138e8	−	5.17410e7i	0.337754	−	0.107783i
$784$	7.56159e8	−	3.85499e8i	1.56915	−	0.799973i
$785$	−3.80608e8	+	1.61600e7i	−0.786809	+	0.0334065i
$786$	8.18962e7	+	9.08169e8i	0.168654	+	1.87025i
$787$	−1.65335e8	−	1.65335e8i	−0.339188	−	0.339188i	0.516874	−	0.856062i	$-0.327096\pi$
$787$	−1.65335e8	−	1.65335e8i	−0.339188	−	0.339188i	−0.856062	+	0.516874i	$0.827096\pi$
$788$	−7.35306e8	+	1.76620e8i	−1.50276	+	0.360962i
$789$	−2.89367e7	+	1.10496e7i	−0.0589140	+	0.0224966i
$790$	−1.57632e8	−	3.73078e7i	−0.319716	−	0.0756690i
$791$	4.67195e8			0.943993
$792$	−5.97766e7	+	4.93794e7i	−0.120325	+	0.0993963i
$793$	−3.54444e8	−	3.54444e8i	−0.710769	−	0.710769i
$794$	1.33472e8	−	4.73359e8i	0.266642	−	0.945647i
$795$	1.92073e8	−	4.83413e8i	0.382264	−	0.962093i
$796$	−2.51768e8	+	4.10953e8i	−0.499184	+	0.814803i
$797$	−7.95245e7	−	7.95245e7i	−0.157082	−	0.157082i	0.624190	−	0.781272i	$-0.285429\pi$
$797$	−7.95245e7	−	7.95245e7i	−0.157082	−	0.157082i	−0.781272	+	0.624190i	$0.785429\pi$
$798$	−1.71606e8	+	2.05624e8i	−0.337695	+	0.404636i
$799$	1.66454e8			0.326327
$800$	−2.47216e8	+	4.48362e8i	−0.482843	+	0.875707i
$801$	−3.50323e8	−	3.91826e8i	−0.681664	−	0.762423i
$802$	1.59192e8	+	2.84221e8i	0.308603	+	0.550976i
$803$	−2.01569e7	−	2.01569e7i	−0.0389294	−	0.0389294i
$804$	3.17546e7	−	1.69779e8i	0.0610997	−	0.326676i
$805$	4.12691e8	−	4.49289e8i	0.791111	−	0.861268i
$806$	2.24104e7	−	7.94787e7i	0.0428001	−	0.151791i
$807$	1.98947e8	−	4.44743e8i	0.378544	−	0.846230i
$808$	3.97997e6	+	155692.i	0.00754476	+	0.000295143i
$809$	3.10725e8			0.586854			0.293427	−	0.955981i	$-0.405204\pi$
$809$	3.10725e8			0.586854			0.293427	+	0.955981i	$0.405204\pi$
$810$	−1.79297e8	+	5.00282e8i	−0.337378	+	0.941369i
$811$		−	2.06795e8i		−	0.387683i	−0.981033	−	0.193841i	$-0.937905\pi$
$811$		−	2.06795e8i		−	0.387683i	0.981033	−	0.193841i	$-0.0620947\pi$
$812$	3.06693e8	−	7.36674e7i	0.572843	−	0.137596i
$813$	5.19394e8	+	2.32341e8i	0.966553	+	0.432369i
$814$	−2.20350e7	+	7.81474e7i	−0.0408546	+	0.144891i
$815$	−2.12933e8	+	9.04076e6i	−0.393342	+	0.0167006i
$816$	−3.37100e8	−	3.04459e8i	−0.620424	−	0.560348i
$817$	−697826.	+	697826.i	−0.00127962	+	0.00127962i
$818$	−2.68073e8	−	4.78615e8i	−0.489771	−	0.874432i
$819$	−1.22382e9	+	1.09418e9i	−2.22774	+	1.99177i
$820$	2.26967e8	+	7.94787e8i	0.411644	+	1.44148i
$821$		−	6.01057e8i		−	1.08614i	−0.839687	−	0.543070i	$-0.817262\pi$
$821$		−	6.01057e8i		−	1.08614i	0.839687	−	0.543070i	$-0.182738\pi$
$822$	−1.00390e8	+	1.20290e8i	−0.180748	+	0.216578i
$823$	5.34484e8	−	5.34484e8i	0.958817	−	0.958817i	−0.0403683	−	0.999185i	$-0.512853\pi$
$823$	5.34484e8	−	5.34484e8i	0.958817	−	0.958817i	0.999185	+	0.0403683i	$0.0128531\pi$
$824$	−2.56739e8	−	2.77644e8i	−0.458892	−	0.496257i
$825$	−8.27418e7	−	2.88753e7i	−0.147354	−	0.0514238i
$826$	3.45177e8	−	1.22417e9i	0.612494	−	2.17221i
$827$	−4.48065e8	+	4.48065e8i	−0.792182	+	0.792182i	−0.981849	−	0.189667i	$-0.939259\pi$
$827$	−4.48065e8	+	4.48065e8i	−0.792182	+	0.792182i	0.189667	+	0.981849i	$0.439259\pi$
$828$	3.28471e8	+	2.27396e8i	0.578637	+	0.400582i
$829$		−	2.39817e8i		−	0.420937i	−0.977601	−	0.210468i	$-0.932501\pi$
$829$		−	2.39817e8i		−	0.420937i	0.977601	−	0.210468i	$-0.0674989\pi$
$830$	2.05034e8	+	3.32179e8i	0.358584	+	0.580949i
$831$	−2.80996e8	−	7.35873e8i	−0.489663	−	1.28233i
$832$	−6.72908e8	−	7.87329e8i	−1.16838	−	1.36706i
$833$	−6.01821e8	+	6.01821e8i	−1.04120	+	1.04120i
$834$	−6.58592e7	−	7.30331e8i	−0.113532	−	1.25899i
$835$	2.95831e8	−	1.25605e7i	0.508141	−	0.0215748i
$836$	1.51087e7	−	2.46614e7i	0.0258587	−	0.0422084i
$837$	−1.56335e7	−	4.89901e7i	−0.0266613	−	0.0835472i
$838$	2.46209e8	+	4.39579e8i	0.418381	+	0.746973i
$839$		−	5.51540e8i		−	0.933880i	−0.884289	−	0.466940i	$-0.845356\pi$
$839$		−	5.51540e8i		−	0.933880i	0.884289	−	0.466940i	$-0.154644\pi$
$840$	−3.99175e8	+	9.00389e8i	−0.673481	+	1.51912i
$841$	−5.20057e8			−0.874305
$842$	−5.44257e8	+	3.04839e8i	−0.911733	+	0.510663i
$843$	2.31631e8	+	1.03616e8i	0.386646	+	0.172959i
$844$	3.54829e8	+	2.17384e8i	0.590190	+	0.361576i
$845$	9.11797e8	−	9.92657e8i	1.51122	−	1.64524i
$846$	2.12333e8	−	1.03802e8i	0.350677	−	0.171434i
$847$	6.96599e8	+	6.96599e8i	1.14639	+	1.14639i
$848$	6.00444e8	+	1.94945e8i	0.984657	+	0.319687i
$849$	6.06502e7	+	1.58831e8i	0.0991080	+	0.259544i
$850$	9.69464e7	−	5.04180e8i	0.157861	−	0.820973i
$851$	4.18362e8			0.678834
$852$	6.34788e8	+	9.26873e8i	1.02638	+	1.49865i
$853$	−3.11658e8	−	3.11658e8i	−0.502147	−	0.502147i	0.409958	−	0.912105i	$-0.365543\pi$
$853$	−3.11658e8	−	3.11658e8i	−0.502147	−	0.502147i	−0.912105	+	0.409958i	$0.865543\pi$
$854$	−5.56794e8	−	1.56998e8i	−0.893965	−	0.252069i
$855$	2.66274e6	−	1.98218e8i	0.00426021	−	0.317136i
$856$	−5.46229e8	−	5.90705e8i	−0.870871	−	0.941780i
$857$	6.15879e8	+	6.15879e8i	0.978482	+	0.978482i	0.999773	−	0.0212915i	$-0.00677781\pi$
$857$	6.15879e8	+	6.15879e8i	0.978482	+	0.978482i	−0.0212915	+	0.999773i	$0.506778\pi$
$858$	1.13588e8	−	1.36104e8i	0.179833	−	0.215481i
$859$	1.06712e9			1.68358			0.841788	−	0.539808i	$-0.181503\pi$
$859$	1.06712e9			1.68358			0.841788	+	0.539808i	$0.181503\pi$
$860$	−1.76290e6	+	3.17223e6i	−0.00277162	+	0.00498734i
$861$	5.67205e8	+	1.48540e9i	0.888650	+	2.32720i
$862$	−4.57328e8	+	2.56150e8i	−0.714012	+	0.399919i
$863$	3.55643e8	+	3.55643e8i	0.553327	+	0.553327i	0.927400	−	0.374072i	$-0.122039\pi$
$863$	3.55643e8	+	3.55643e8i	0.553327	+	0.553327i	−0.374072	+	0.927400i	$0.622039\pi$
$864$	−6.19879e8	−	1.78157e8i	−0.961093	−	0.276224i
$865$	7.46466e8	−	3.16936e7i	1.15335	−	0.0489693i
$866$	−3.89734e8	−	1.09893e8i	−0.600088	−	0.169205i
$867$	−1.79116e8	−	8.01242e7i	−0.274839	−	0.122944i
$868$	−2.22586e7	−	9.26673e7i	−0.0340360	−	0.141699i
$869$	3.36493e7			0.0512764
$870$	−1.41851e8	+	1.85426e8i	−0.215414	+	0.281588i
$871$			3.94917e8i			0.597655i
$872$	8.70441e8	+	3.40507e7i	1.31277	+	0.0513543i
$873$	−7.68398e7	−	4.29716e6i	−0.115490	−	0.00645860i
$874$	−1.43428e8	−	4.04421e7i	−0.214833	−	0.0605759i
$875$	−1.10421e9	+	1.41329e8i	−1.64827	+	0.210963i
$876$	4.35956e7	−	2.33088e8i	0.0648530	−	0.346743i
$877$	−1.80918e8	+	1.80918e8i	−0.268214	+	0.268214i	−0.828380	−	0.560166i	$-0.810737\pi$
$877$	−1.80918e8	+	1.80918e8i	−0.268214	+	0.268214i	0.560166	+	0.828380i	$0.310737\pi$
$878$	8.13815e8	−	4.55819e8i	1.20238	−	0.673456i
$879$	−7.48708e7	−	1.96072e8i	−0.110242	−	0.288701i
$880$	2.85224e7	−	1.02461e8i	0.0418540	−	0.150353i
$881$			1.07695e9i			1.57496i	0.616343	+	0.787478i	$0.288614\pi$
$881$			1.07695e9i			1.57496i	−0.616343	+	0.787478i	$0.711386\pi$
$882$	−3.92398e8	+	1.14300e9i	−0.571901	+	1.66587i
$883$	−6.86795e8	+	6.86795e8i	−0.997574	+	0.997574i	−0.999997	−	0.00242263i	$-0.999229\pi$
$883$	−6.86795e8	+	6.86795e8i	−0.997574	+	0.997574i	0.00242263	+	0.999997i	$0.499229\pi$
$884$	8.85591e8	+	5.42552e8i	1.28197	+	0.785389i
$885$	3.72843e8	+	8.64451e8i	0.537893	+	1.24713i
$886$	9.16555e8	+	2.58439e8i	1.31782	+	0.371584i
$887$	−8.03986e8	+	8.03986e8i	−1.15207	+	1.15207i	−0.165929	+	0.986138i	$0.553062\pi$
$887$	−8.03986e8	+	8.03986e8i	−1.15207	+	1.15207i	−0.986138	+	0.165929i	$0.946938\pi$
$888$	−6.39919e8	+	2.16095e8i	−0.913873	+	0.308607i
$889$			1.58220e9i			2.25194i
$890$	7.01603e8	+	1.66053e8i	0.995225	+	0.235546i
$891$	1.23089e7	−	1.09707e8i	0.0174015	−	0.155096i
$892$	−9.15485e7	−	3.81136e8i	−0.128990	−	0.537013i
$893$	−6.23397e7	+	6.23397e7i	−0.0875408	+	0.0875408i
$894$	−4.84264e7	−	5.37013e8i	−0.0677750	−	0.751575i
$895$	3.39535e8	−	3.69646e8i	0.473604	−	0.515604i
$896$	−1.12160e9	−	4.13271e8i	−1.55924	−	0.574527i
$897$	−8.33804e8	−	3.72986e8i	−1.15528	−	0.516791i
$898$	−6.57662e8	+	3.68358e8i	−0.908184	+	0.508675i
$899$		−	2.25906e7i		−	0.0310920i
$900$	−1.90744e8	−	7.03603e8i	−0.261652	−	0.965162i
$901$	−6.33043e8			−0.865484
$902$	−8.39048e7	−	1.49803e8i	−0.114332	−	0.204127i
$903$	−2.85070e6	+	6.37269e6i	−0.00387158	+	0.00865485i
$904$	−2.84931e8	−	3.08131e8i	−0.385686	−	0.417090i
$905$	5.71351e8	+	5.24810e8i	0.770828	+	0.708038i
$906$	4.86300e8	−	4.38532e7i	0.653912	−	0.0589680i
$907$	−3.35468e8	−	3.35468e8i	−0.449603	−	0.449603i	0.445619	−	0.895222i	$-0.352983\pi$
$907$	−3.35468e8	−	3.35468e8i	−0.449603	−	0.449603i	−0.895222	+	0.445619i	$0.852983\pi$
$908$	−1.48364e8	−	6.17669e8i	−0.198185	−	0.825085i
$909$	−4.22774e6	+	3.77992e6i	−0.00562881	+	0.00503259i
$910$	5.18643e8	−	2.19136e9i	0.688246	−	2.90797i
$911$	1.17978e9			1.56044			0.780220	−	0.625505i	$-0.215107\pi$
$911$	1.17978e9			1.56044			0.780220	+	0.625505i	$0.215107\pi$
$912$	2.40274e8	−	1.22249e7i	0.316755	−	0.0161161i
$913$	−5.73387e7	−	5.73387e7i	−0.0753417	−	0.0753417i
$914$	−2.99050e8	+	1.06058e9i	−0.391656	+	1.38901i
$915$	3.93181e8	−	1.69581e8i	0.513250	−	0.221368i
$916$	−1.01142e9	−	6.19641e8i	−1.31597	−	0.806221i
$917$	−1.70141e9	−	1.70141e9i	−2.20648	−	2.20648i
$918$	6.46381e8	−	2.20298e7i	0.835527	−	0.0284763i
$919$	−1.26837e9			−1.63418			−0.817088	−	0.576514i	$-0.804413\pi$
$919$	−1.26837e9			−1.63418			−0.817088	+	0.576514i	$0.804413\pi$
$920$	−5.48011e8	+	1.82694e6i	−0.703762	+	0.00234617i
$921$	−5.76002e8	+	2.19949e8i	−0.737302	+	0.281542i
$922$	2.36006e8	+	4.21362e8i	0.301113	+	0.537604i
$923$	−1.81626e9	−	1.81626e9i	−2.30979	−	2.30979i
$924$	3.76138e7	−	2.01106e8i	0.0476795	−	0.254923i
$925$	−5.83630e8	−	4.92116e8i	−0.737416	−	0.621788i
$926$	4.84565e7	−	1.71851e8i	0.0610266	−	0.216431i
$927$	5.37588e8	+	3.00638e7i	0.674854	+	0.0377403i
$928$	−2.35631e8	−	1.57346e8i	−0.294841	−	0.196885i
$929$	−1.21425e8			−0.151447			−0.0757233	−	0.997129i	$-0.524127\pi$
$929$	−1.21425e8			−0.151447			−0.0757233	+	0.997129i	$0.524127\pi$
$930$	5.60266e7	+	4.28603e7i	0.0696539	+	0.0532851i
$931$		−	4.50783e8i		−	0.558623i
$932$	−2.84835e7	−	1.18583e8i	−0.0351841	−	0.146479i
$933$	−3.41177e8	+	7.62696e8i	−0.420083	+	0.939088i
$934$	−2.05134e8	+	7.27510e8i	−0.251766	+	0.892890i
$935$	4.52415e6	+	1.06555e8i	0.00553480	+	0.130359i
$936$	1.46803e9	+	1.39831e8i	1.79022	+	0.170520i
$937$	−1.67316e8	+	1.67316e8i	−0.203385	+	0.203385i	−0.801449	−	0.598064i	$-0.795937\pi$
$937$	−1.67316e8	+	1.67316e8i	−0.203385	+	0.203385i	0.598064	+	0.801449i	$0.295937\pi$
$938$	2.22723e8	+	3.97648e8i	0.269871	+	0.481826i
$939$	−3.45950e7	+	1.32102e7i	−0.0417846	+	0.0159556i
$940$	−1.57487e8	+	2.83388e8i	−0.189611	+	0.341192i
$941$		−	1.51203e9i		−	1.81464i	−0.420442	−	0.907320i	$-0.638125\pi$
$941$		−	1.51203e9i		−	1.81464i	0.420442	−	0.907320i	$-0.361875\pi$
$942$	5.05402e8	+	4.21790e8i	0.604622	+	0.504596i
$943$	−6.25577e8	+	6.25577e8i	−0.746012	+	0.746012i
$944$	−1.01790e9	+	5.18937e8i	−1.21001	+	0.616877i
$945$	−4.82615e8	−	1.31668e9i	−0.571881	−	1.56021i
$946$	204593.	−	725590.i	0.000241667	−	0.000857073i
$947$	−6.08005e8	+	6.08005e8i	−0.715908	+	0.715908i	−0.967765	−	0.251857i	$-0.918959\pi$
$947$	−6.08005e8	+	6.08005e8i	−0.715908	+	0.715908i	0.251857	+	0.967765i	$0.418959\pi$
$948$	1.58167e8	+	2.30944e8i	0.185648	+	0.271070i
$949$			5.42176e8i			0.634369i
$950$	1.52516e8	+	2.25132e8i	0.177887	+	0.262582i
$951$	2.29623e8	−	8.76826e7i	0.266977	−	0.101946i
$952$	1.19770e9	+	4.68528e7i	1.38815	+	0.0543032i
$953$	−2.26902e8	+	2.26902e8i	−0.262156	+	0.262156i	−0.825929	−	0.563773i	$-0.809349\pi$
$953$	−2.26902e8	+	2.26902e8i	−0.262156	+	0.262156i	0.563773	+	0.825929i	$0.309349\pi$
$954$	−8.07529e8	+	3.94773e8i	−0.930064	+	0.454676i
$955$	5.53126e8	+	5.08069e8i	0.635059	+	0.583328i
$956$	−4.93630e8	−	3.02419e8i	−0.564973	−	0.346127i
$957$	1.98030e7	−	4.42694e7i	0.0225942	−	0.0505089i
$958$	−1.68653e8	−	3.01111e8i	−0.191821	−	0.342476i
$959$		−	4.13431e8i		−	0.468756i
$960$	8.37284e8	−	2.85856e8i	0.946366	−	0.323098i
$961$	8.80678e8			0.992309
$962$	1.34734e9	−	7.54649e8i	1.51340	−	0.847656i
$963$	1.14375e9	+	6.39627e7i	1.28072	+	0.0716222i
$964$	1.36382e8	−	2.22612e8i	0.152239	−	0.248495i
$965$	1.20993e7	+	2.84969e8i	0.0134641	+	0.317114i
$966$	−1.04993e9	+	9.46794e7i	−1.16473	+	0.105033i
$967$	5.55302e8	+	5.55302e8i	0.614115	+	0.614115i	0.944016	−	0.329901i	$-0.107015\pi$
$967$	5.55302e8	+	5.55302e8i	0.614115	+	0.614115i	−0.329901	+	0.944016i	$0.607015\pi$
$968$	3.45917e7	−	8.84269e8i	0.0381369	−	0.974897i
$969$	−2.25378e8	+	8.60615e7i	−0.247708	+	0.0945884i
$970$	8.98344e7	−	5.54493e7i	0.0984300	−	0.0607548i
$971$	2.87628e8			0.314177			0.157088	−	0.987585i	$-0.449789\pi$
$971$	2.87628e8			0.314177			0.157088	+	0.987585i	$0.449789\pi$
$972$	8.10804e8	−	4.31192e8i	0.882912	−	0.469539i
$973$	1.36824e9	+	1.36824e9i	1.48533	+	1.48533i
$974$	1.29514e9	+	3.65189e8i	1.40166	+	0.395222i
$975$	7.24445e8	+	1.50113e9i	0.781613	+	1.61958i
$976$	2.36029e8	+	4.62973e8i	0.253873	+	0.497974i
$977$	−6.65181e8	−	6.65181e8i	−0.713274	−	0.713274i	0.253945	−	0.967219i	$-0.418272\pi$
$977$	−6.65181e8	−	6.65181e8i	−0.713274	−	0.713274i	−0.967219	+	0.253945i	$0.918272\pi$
$978$	2.82749e8	+	2.35972e8i	0.302263	+	0.252258i
$979$	−1.49769e8			−0.159615
$980$	−4.55200e8	−	1.59400e9i	−0.483642	−	1.69360i
$981$	−9.24630e8	+	8.26690e8i	−0.979402	+	0.875661i
$982$	−3.80621e8	+	2.13187e8i	−0.401937	+	0.225126i
$983$	1.47396e8	+	1.47396e8i	0.155176	+	0.155176i	0.780425	−	0.625249i	$-0.215003\pi$
$983$	1.47396e8	+	1.47396e8i	0.155176	+	0.155176i	−0.625249	+	0.780425i	$0.715003\pi$
$984$	6.33744e8	−	1.28000e9i	0.665164	−	1.34346i
$985$	6.26541e7	+	1.47566e9i	0.0655603	+	1.54411i
$986$	2.73457e8	+	7.71061e7i	0.285272	+	0.0804374i
$987$	−2.54665e8	+	5.69299e8i	−0.264861	+	0.592091i
$988$	−5.34863e8	+	1.28474e8i	−0.554589	+	0.133212i
$989$	−3.88445e6			−0.00401551
$990$	7.22201e7	+	1.33104e8i	0.0744308	+	0.137178i
$991$			4.78305e8i			0.491455i	0.969339	+	0.245727i	$0.0790268\pi$
$991$			4.78305e8i			0.491455i	−0.969339	+	0.245727i	$0.920973\pi$
$992$	−4.75422e7	+	7.11958e7i	−0.0487017	+	0.0729322i
$993$	9.16218e8	+	4.09852e8i	0.935731	+	0.418581i
$994$	−2.85314e9	−	8.04494e8i	−2.90512	−	0.819150i
$995$	6.93232e8	+	6.36762e8i	0.703735	+	0.646410i
$996$	1.24013e8	−	6.63046e8i	0.125513	−	0.671066i
$997$	1.19680e9	−	1.19680e9i	1.20764	−	1.20764i	0.235844	−	0.971791i	$-0.424215\pi$
$997$	1.19680e9	−	1.19680e9i	1.20764	−	1.20764i	0.971791	−	0.235844i	$-0.0757855\pi$
$998$	5.42747e8	−	3.03994e8i	0.546017	−	0.305825i
$999$	4.41094e8	−	8.54558e8i	0.442420	−	0.857127i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.l.a.23.11	✓	136
3.2	odd	2	inner	60.7.l.a.23.58	yes	136
4.3	odd	2	inner	60.7.l.a.23.45	yes	136
5.2	odd	4	inner	60.7.l.a.47.24	yes	136
12.11	even	2	inner	60.7.l.a.23.24	yes	136
15.2	even	4	inner	60.7.l.a.47.45	yes	136
20.7	even	4	inner	60.7.l.a.47.58	yes	136
60.47	odd	4	inner	60.7.l.a.47.11	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.l.a.23.11	✓	136	1.1	even	1	trivial
60.7.l.a.23.24	yes	136	12.11	even	2	inner
60.7.l.a.23.45	yes	136	4.3	odd	2	inner
60.7.l.a.23.58	yes	136	3.2	odd	2	inner
60.7.l.a.47.11	yes	136	60.47	odd	4	inner
60.7.l.a.47.24	yes	136	5.2	odd	4	inner
60.7.l.a.47.45	yes	136	15.2	even	4	inner
60.7.l.a.47.58	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)

\(f(q)\)	\(=\)	\(q+(-6.97975 + 3.90937i) q^{2} +(11.0251 - 24.6464i) q^{3} +(33.4337 - 54.5728i) q^{4} +(-92.0582 - 84.5593i) q^{5} +(19.3996 + 215.127i) q^{6} +(-403.029 - 403.029i) q^{7} +(-20.0136 + 511.609i) q^{8} +(-485.894 - 543.459i) q^{9} +O(q^{10})\)	\(q+(-6.97975 + 3.90937i) q^{2} +(11.0251 - 24.6464i) q^{3} +(33.4337 - 54.5728i) q^{4} +(-92.0582 - 84.5593i) q^{5} +(19.3996 + 215.127i) q^{6} +(-403.029 - 403.029i) q^{7} +(-20.0136 + 511.609i) q^{8} +(-485.894 - 543.459i) q^{9} +(973.117 + 230.313i) q^{10} -207.729 q^{11} +(-976.415 - 1425.69i) q^{12} +(2793.72 + 2793.72i) q^{13} +(4388.63 + 1237.45i) q^{14} +(-3099.04 + 1336.63i) q^{15} +(-1860.38 - 3649.14i) q^{16} +(2904.32 + 2904.32i) q^{17} +(5516.00 + 1893.67i) q^{18} -2175.43 q^{19} +(-7692.48 + 2196.74i) q^{20} +(-14376.7 + 5489.79i) q^{21} +(1449.89 - 812.088i) q^{22} +(-6054.76 - 6054.76i) q^{23} +(12388.7 + 6133.80i) q^{24} +(1324.43 + 15568.8i) q^{25} +(-30421.1 - 8577.77i) q^{26} +(-18751.4 + 5983.87i) q^{27} +(-35469.2 + 8519.67i) q^{28} -8646.75 q^{29} +(16405.1 - 21444.6i) q^{30} +2612.62i q^{31} +(27250.8 + 18197.2i) q^{32} +(-2290.23 + 5119.77i) q^{33} +(-31625.5 - 8917.36i) q^{34} +(3022.26 + 71182.0i) q^{35} +(-45903.3 + 8346.74i) q^{36} +(-34548.2 + 34548.2i) q^{37} +(15183.9 - 8504.55i) q^{38} +(99656.3 - 38054.2i) q^{39} +(45103.7 - 45405.5i) q^{40} -103320. i q^{41} +(78883.9 - 94521.0i) q^{42} +(320.776 - 320.776i) q^{43} +(-6945.14 + 11336.3i) q^{44} +(-1224.01 + 91116.8i) q^{45} +(65931.0 + 18590.4i) q^{46} +(28656.3 - 28656.3i) q^{47} +(-110449. + 5619.52i) q^{48} +207216. i q^{49} +(-70108.2 - 103488. i) q^{50} +(103602. - 39560.7i) q^{51} +(245865. - 59056.7i) q^{52} +(-108983. + 108983. i) q^{53} +(107487. - 115072. i) q^{54} +(19123.1 + 17565.4i) q^{55} +(214259. - 198127. i) q^{56} +(-23984.3 + 53616.6i) q^{57} +(60352.1 - 33803.3i) q^{58} -278942. i q^{59} +(-30668.6 + 213812. i) q^{60} -126872. q^{61} +(-10213.7 - 18235.4i) q^{62} +(-23200.4 + 414859. i) q^{63} +(-261343. - 20478.3i) q^{64} +(-20949.8 - 493420. i) q^{65} +(-4029.85 - 44688.1i) q^{66} +(70679.3 + 70679.3i) q^{67} +(255599. - 61394.7i) q^{68} +(-215983. + 82473.9i) q^{69} +(-299371. - 485017. i) q^{70} -650122. q^{71} +(287763. - 237711. i) q^{72} +(97034.8 + 97034.8i) q^{73} +(106076. - 376199. i) q^{74} +(398317. + 139005. i) q^{75} +(-72732.6 + 118719. i) q^{76} +(83720.7 + 83720.7i) q^{77} +(-546808. + 655202. i) q^{78} -161987. q^{79} +(-137306. + 493245. i) q^{80} +(-59254.8 + 528127. i) q^{81} +(403915. + 721147. i) q^{82} +(276027. + 276027. i) q^{83} +(-181072. + 968119. i) q^{84} +(-21779.1 - 512954. i) q^{85} +(-984.904 + 3492.97i) q^{86} +(-95331.3 + 213112. i) q^{87} +(4157.40 - 106276. i) q^{88} +720985. q^{89} +(-347666. - 640757. i) q^{90} -2.25190e6i q^{91} +(-532858. + 127992. i) q^{92} +(64391.7 + 28804.4i) q^{93} +(-87985.6 + 312041. i) q^{94} +(200266. + 183953. i) q^{95} +(748938. - 471009. i) q^{96} +(74648.7 - 74648.7i) q^{97} +(-810083. - 1.44631e6i) q^{98} +(100934. + 112892. 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

Related objects

Downloads

Learn more