LMFDB - Embedded newform 60.7.l.a.23.12

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			23.12
Character	$\chi$	$=$	60.23
Dual form			60.7.l.a.47.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.94862 - 3.96443i) q^{2} +(-11.8150 - 24.2777i) q^{3} +(32.5666 + 55.0946i) q^{4} +(-69.7748 - 103.713i) q^{5} +(-14.1489 + 215.536i) q^{6} +(-171.027 - 171.027i) q^{7} +(-7.87369 - 511.939i) q^{8} +(-449.810 + 573.683i) q^{9} +O(q^{10})$	\(q+(-6.94862 - 3.96443i) q^{2} +(-11.8150 - 24.2777i) q^{3} +(32.5666 + 55.0946i) q^{4} +(-69.7748 - 103.713i) q^{5} +(-14.1489 + 215.536i) q^{6} +(-171.027 - 171.027i) q^{7} +(-7.87369 - 511.939i) q^{8} +(-449.810 + 573.683i) q^{9} +(73.6732 + 997.282i) q^{10} -731.483 q^{11} +(952.794 - 1441.59i) q^{12} +(-2740.33 - 2740.33i) q^{13} +(510.377 + 1866.43i) q^{14} +(-1693.53 + 2919.35i) q^{15} +(-1974.84 + 3588.49i) q^{16} +(234.776 + 234.776i) q^{17} +(5399.88 - 2203.07i) q^{18} +12272.9 q^{19} +(3441.73 - 7221.81i) q^{20} +(-2131.45 + 6172.84i) q^{21} +(5082.80 + 2899.91i) q^{22} +(8718.61 + 8718.61i) q^{23} +(-12335.7 + 6239.74i) q^{24} +(-5887.96 + 14473.2i) q^{25} +(8177.64 + 29905.3i) q^{26} +(19242.2 + 4142.23i) q^{27} +(3852.92 - 14992.5i) q^{28} -8640.21 q^{29} +(23341.2 - 13571.5i) q^{30} +10483.8i q^{31} +(27948.7 - 17105.9i) q^{32} +(8642.50 + 17758.7i) q^{33} +(-700.615 - 2562.12i) q^{34} +(-5804.45 + 29671.2i) q^{35} +(-46255.6 - 6099.21i) q^{36} +(3703.02 - 3703.02i) q^{37} +(-85279.4 - 48654.9i) q^{38} +(-34151.6 + 98905.8i) q^{39} +(-52545.6 + 36537.1i) q^{40} -33255.5i q^{41} +(39282.4 - 34442.7i) q^{42} +(56752.0 - 56752.0i) q^{43} +(-23821.9 - 40300.8i) q^{44} +(90884.0 + 6622.70i) q^{45} +(-26018.0 - 95146.7i) q^{46} +(-81887.4 + 81887.4i) q^{47} +(110453. + 5546.33i) q^{48} -59148.3i q^{49} +(98291.1 - 77226.1i) q^{50} +(2925.92 - 8473.70i) q^{51} +(61734.3 - 240220. i) q^{52} +(-90849.6 + 90849.6i) q^{53} +(-117285. - 105067. i) q^{54} +(51039.1 + 75864.6i) q^{55} +(-86209.0 + 88902.3i) q^{56} +(-145004. - 297956. i) q^{57} +(60037.5 + 34253.5i) q^{58} +243157. i q^{59} +(-215993. + 1768.77i) q^{60} -252831. q^{61} +(41562.4 - 72848.2i) q^{62} +(175045. - 21185.8i) q^{63} +(-262020. + 8061.70i) q^{64} +(-93003.1 + 475414. i) q^{65} +(10349.7 - 157661. i) q^{66} +(-306677. - 306677. i) q^{67} +(-5289.05 + 20580.7i) q^{68} +(108657. - 314678. i) q^{69} +(157962. - 183163. i) q^{70} -270864. q^{71} +(297233. + 225758. i) q^{72} +(380074. + 380074. i) q^{73} +(-40411.3 + 11050.5i) q^{74} +(420941. - 28055.1i) q^{75} +(399685. + 676168. i) q^{76} +(125104. + 125104. i) q^{77} +(629412. - 551867. i) q^{78} +187653. q^{79} +(509968. - 45568.5i) q^{80} +(-126784. - 516096. i) q^{81} +(-131839. + 231079. i) q^{82} +(190563. + 190563. i) q^{83} +(-409504. + 83596.8i) q^{84} +(7967.99 - 40730.9i) q^{85} +(-619338. + 169359. i) q^{86} +(102084. + 209764. i) q^{87} +(5759.47 + 374475. i) q^{88} +494793. q^{89} +(-605263. - 406322. i) q^{90} +937342. i q^{91} +(-196414. + 764284. i) q^{92} +(254523. - 123867. i) q^{93} +(893641. - 244367. i) q^{94} +(-856336. - 1.27286e6i) q^{95} +(-745506. - 476422. i) q^{96} +(-1.08090e6 + 1.08090e6i) q^{97} +(-234489. + 410999. i) q^{98} +(329028. - 419640. 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 $

$2$	−6.94862	−	3.96443i	−0.868577	−	0.495554i
$2$	−6.94862	−	3.96443i	−0.868577	−	0.495554i
$3$	−11.8150	−	24.2777i	−0.437594	−	0.899173i
$3$	−11.8150	−	24.2777i	−0.437594	−	0.899173i
$4$	32.5666	+	55.0946i	0.508853	+	0.860854i
$5$	−69.7748	−	103.713i	−0.558198	−	0.829708i
$5$	−69.7748	−	103.713i	−0.558198	−	0.829708i
$6$	−14.1489	+	215.536i	−0.0655043	+	0.997852i
$7$	−171.027	−	171.027i	−0.498622	−	0.498622i	0.412387	−	0.911009i	$-0.364695\pi$
$7$	−171.027	−	171.027i	−0.498622	−	0.498622i	−0.911009	+	0.412387i	$0.864695\pi$
$8$	−7.87369	−	511.939i	−0.0153783	−	0.999882i
$9$	−449.810	+	573.683i	−0.617023	+	0.786945i
$10$	73.6732	+	997.282i	0.0736732	+	0.997282i
$11$	−731.483			−0.549574			−0.274787	−	0.961505i	$-0.588607\pi$
$11$	−731.483			−0.549574			−0.274787	+	0.961505i	$0.588607\pi$
$12$	952.794	−	1441.59i	0.551385	−	0.834251i
$13$	−2740.33	−	2740.33i	−1.24730	−	1.24730i	−0.956906	−	0.290398i	$-0.906212\pi$
$13$	−2740.33	−	2740.33i	−1.24730	−	1.24730i	−0.290398	−	0.956906i	$-0.593788\pi$
$14$	510.377	+	1866.43i	0.185998	+	0.680186i
$15$	−1693.53	+	2919.35i	−0.501786	+	0.864992i
$16$	−1974.84	+	3588.49i	−0.482138	+	0.876095i
$17$	234.776	+	234.776i	0.0477867	+	0.0477867i	0.730596	−	0.682810i	$-0.239242\pi$
$17$	234.776	+	234.776i	0.0477867	+	0.0477867i	−0.682810	+	0.730596i	$0.739242\pi$
$18$	5399.88	−	2203.07i	0.925906	−	0.377755i
$19$	12272.9			1.78931			0.894653	−	0.446761i	$-0.147423\pi$
$19$	12272.9			1.78931			0.894653	+	0.446761i	$0.147423\pi$
$20$	3441.73	−	7221.81i	0.430216	−	0.902726i
$21$	−2131.45	+	6172.84i	−0.230153	+	0.666541i
$22$	5082.80	+	2899.91i	0.477347	+	0.272344i
$23$	8718.61	+	8718.61i	0.716579	+	0.716579i	0.967903	−	0.251324i	$-0.0808660\pi$
$23$	8718.61	+	8718.61i	0.716579	+	0.716579i	−0.251324	+	0.967903i	$0.580866\pi$
$24$	−12335.7	+	6239.74i	−0.892337	+	0.451370i
$25$	−5887.96	+	14473.2i	−0.376830	+	0.926283i
$26$	8177.64	+	29905.3i	0.465273	+	1.70149i
$27$	19242.2	+	4142.23i	0.977605	+	0.210447i
$28$	3852.92	−	14992.5i	0.175516	−	0.682966i
$29$	−8640.21			−0.354266			−0.177133	−	0.984187i	$-0.556682\pi$
$29$	−8640.21			−0.354266			−0.177133	+	0.984187i	$0.556682\pi$
$30$	23341.2	−	13571.5i	0.864490	−	0.502650i
$31$			10483.8i			0.351913i	0.984398	+	0.175956i	$0.0563018\pi$
$31$			10483.8i			0.351913i	−0.984398	+	0.175956i	$0.943698\pi$
$32$	27948.7	−	17105.9i	0.852927	−	0.522031i
$33$	8642.50	+	17758.7i	0.240490	+	0.494162i
$34$	−700.615	−	2562.12i	−0.0178255	−	0.0651873i
$35$	−5804.45	+	29671.2i	−0.135381	+	0.692040i
$36$	−46255.6	−	6099.21i	−0.991418	−	0.130727i
$37$	3703.02	−	3703.02i	0.0731057	−	0.0731057i	−0.669609	−	0.742714i	$-0.733538\pi$
$37$	3703.02	−	3703.02i	0.0731057	−	0.0731057i	0.742714	+	0.669609i	$0.233538\pi$
$38$	−85279.4	−	48654.9i	−1.55415	−	0.886698i
$39$	−34151.6	+	98905.8i	−0.575729	+	1.66735i
$40$	−52545.6	+	36537.1i	−0.821025	+	0.570892i
$41$		−	33255.5i		−	0.482516i	−0.970461	−	0.241258i	$-0.922440\pi$
$41$		−	33255.5i		−	0.482516i	0.970461	−	0.241258i	$-0.0775599\pi$
$42$	39282.4	−	34442.7i	0.530213	−	0.464889i
$43$	56752.0	−	56752.0i	0.713799	−	0.713799i	−0.253529	−	0.967328i	$-0.581591\pi$
$43$	56752.0	−	56752.0i	0.713799	−	0.713799i	0.967328	+	0.253529i	$0.0815913\pi$
$44$	−23821.9	−	40300.8i	−0.279652	−	0.473103i
$45$	90884.0	+	6622.70i	0.997356	+	0.0726771i
$46$	−26018.0	−	95146.7i	−0.267301	−	0.977507i
$47$	−81887.4	+	81887.4i	−0.788721	+	0.788721i	−0.981284	−	0.192564i	$-0.938320\pi$
$47$	−81887.4	+	81887.4i	−0.788721	+	0.788721i	0.192564	+	0.981284i	$0.438320\pi$
$48$	110453.	+	5546.33i	0.998742	+	0.0501512i
$49$		−	59148.3i		−	0.502752i
$50$	98291.1	−	77226.1i	0.786329	−	0.617808i
$51$	2925.92	−	8473.70i	0.0220573	−	0.0638797i
$52$	61734.3	−	240220.i	0.439052	−	1.70844i
$53$	−90849.6	+	90849.6i	−0.610232	+	0.610232i	−0.943007	−	0.332774i	$-0.892015\pi$
$53$	−90849.6	+	90849.6i	−0.610232	+	0.610232i	0.332774	+	0.943007i	$0.392015\pi$
$54$	−117285.	−	105067.i	−0.744838	−	0.667246i
$55$	51039.1	+	75864.6i	0.306771	+	0.455986i
$56$	−86209.0	+	88902.3i	−0.490895	+	0.506231i
$57$	−145004.	−	297956.i	−0.782990	−	1.60890i
$58$	60037.5	+	34253.5i	0.307708	+	0.175558i
$59$			243157.i			1.18394i	0.805959	+	0.591972i	$0.201650\pi$
$59$			243157.i			1.18394i	−0.805959	+	0.591972i	$0.798350\pi$
$60$	−215993.	+	1768.77i	−0.999966	+	0.00818876i
$61$	−252831.			−1.11389			−0.556943	−	0.830551i	$-0.688026\pi$
$61$	−252831.			−1.11389			−0.556943	+	0.830551i	$0.688026\pi$
$62$	41562.4	−	72848.2i	0.174392	−	0.305663i
$63$	175045.	−	21185.8i	0.700049	−	0.0847271i
$64$	−262020.	+	8061.70i	−0.999527	+	0.0307530i
$65$	−93003.1	+	475414.i	−0.338655	+	1.73114i
$66$	10349.7	−	157661.i	0.0359994	−	0.548394i
$67$	−306677.	−	306677.i	−1.01966	−	1.01966i	−0.999803	−	0.0198611i	$-0.993678\pi$
$67$	−306677.	−	306677.i	−1.01966	−	1.01966i	−0.0198611	−	0.999803i	$-0.506322\pi$
$68$	−5289.05	+	20580.7i	−0.0168210	+	0.0654537i
$69$	108657.	−	314678.i	0.330757	−	0.957899i
$70$	157962.	−	183163.i	0.460532	−	0.534002i
$71$	−270864.			−0.756791			−0.378396	−	0.925644i	$-0.623524\pi$
$71$	−270864.			−0.756791			−0.378396	+	0.925644i	$0.623524\pi$
$72$	297233.	+	225758.i	0.796341	+	0.604848i
$73$	380074.	+	380074.i	0.977011	+	0.977011i	0.999742	−	0.0227304i	$-0.00723595\pi$
$73$	380074.	+	380074.i	0.977011	+	0.977011i	−0.0227304	+	0.999742i	$0.507236\pi$
$74$	−40411.3	+	11050.5i	−0.0997257	+	0.0272701i
$75$	420941.	−	28055.1i	0.997786	−	0.0665009i
$76$	399685.	+	676168.i	0.910493	+	1.54033i
$77$	125104.	+	125104.i	0.274030	+	0.274030i
$78$	629412.	−	551867.i	1.32633	−	1.16292i
$79$	187653.			0.380605			0.190303	−	0.981725i	$-0.439053\pi$
$79$	187653.			0.380605			0.190303	+	0.981725i	$0.439053\pi$
$80$	509968.	−	45568.5i	0.996032	−	0.0890010i
$81$	−126784.	−	516096.i	−0.238566	−	0.971126i
$82$	−131839.	+	231079.i	−0.239113	+	0.419102i
$83$	190563.	+	190563.i	0.333276	+	0.333276i	0.853829	−	0.520553i	$-0.174274\pi$
$83$	190563.	+	190563.i	0.333276	+	0.333276i	−0.520553	+	0.853829i	$0.674274\pi$
$84$	−409504.	+	83596.8i	−0.690909	+	0.141043i
$85$	7967.99	−	40730.9i	0.0129745	−	0.0663234i
$86$	−619338.	+	169359.i	−0.973715	+	0.266264i
$87$	102084.	+	209764.i	0.155025	+	0.318547i
$88$	5759.47	+	374475.i	0.00845151	+	0.549509i
$89$	494793.			0.701864			0.350932	−	0.936401i	$-0.385865\pi$
$89$	494793.			0.701864			0.350932	+	0.936401i	$0.385865\pi$
$90$	−605263.	−	406322.i	−0.830265	−	0.557369i
$91$			937342.i			1.24387i
$92$	−196414.	+	764284.i	−0.252237	+	0.981503i
$93$	254523.	−	123867.i	0.316430	−	0.153995i
$94$	893641.	−	244367.i	1.07592	−	0.294211i
$95$	−856336.	−	1.27286e6i	−0.998788	−	1.48460i
$96$	−745506.	−	476422.i	−0.842632	−	0.538491i
$97$	−1.08090e6	+	1.08090e6i	−1.18433	+	1.18433i	−0.205716	+	0.978612i	$0.565952\pi$
$97$	−1.08090e6	+	1.08090e6i	−1.18433	+	1.18433i	−0.978612	+	0.205716i	$0.934048\pi$
$98$	−234489.	+	410999.i	−0.249141	+	0.436679i
$99$	329028.	−	419640.i	0.339100	−	0.432485i
$100$	−989145.	+	146946.i	−0.989145	+	0.146946i
$101$		−	794558.i		−	0.771190i	−0.922668	−	0.385595i	$-0.873996\pi$
$101$		−	794558.i		−	0.771190i	0.922668	−	0.385595i	$-0.126004\pi$
$102$	−53924.5	+	47280.9i	−0.0508143	+	0.0445538i
$103$	−594260.	+	594260.i	−0.543832	+	0.543832i	−0.924650	−	0.380818i	$-0.875642\pi$
$103$	−594260.	+	594260.i	−0.543832	+	0.543832i	0.380818	+	0.924650i	$0.375642\pi$
$104$	−1.38130e6	+	1.42446e6i	−1.22797	+	1.26634i
$105$	788928.	−	209649.i	0.681506	−	0.181102i
$106$	991446.	−	271112.i	0.832437	−	0.227631i
$107$	1.61695e6	−	1.61695e6i	1.31991	−	1.31991i	0.406065	−	0.913844i	$-0.366901\pi$
$107$	1.61695e6	−	1.61695e6i	1.31991	−	1.31991i	0.913844	−	0.406065i	$-0.133099\pi$
$108$	398438.	+	1.19504e6i	0.316293	+	0.948662i
$109$			442338.i			0.341566i	0.985309	+	0.170783i	$0.0546298\pi$
$109$			442338.i			0.341566i	−0.985309	+	0.170783i	$0.945370\pi$
$110$	−53890.7	−	729495.i	−0.0404889	−	0.548081i
$111$	−133652.	−	46149.3i	−0.0977252	−	0.0337440i
$112$	951481.	−	275978.i	0.677245	−	0.196436i
$113$	−1.13834e6	+	1.13834e6i	−0.788923	+	0.788923i	−0.981318	−	0.192394i	$-0.938375\pi$
$113$	−1.13834e6	+	1.13834e6i	−0.788923	+	0.788923i	0.192394	+	0.981318i	$0.438375\pi$
$114$	−173648.	+	2.64524e6i	−0.117207	+	1.78546i
$115$	295898.	−	1.51258e6i	0.194558	−	0.994544i
$116$	−281382.	−	476029.i	−0.180269	−	0.304972i
$117$	2.80470e6	−	339454.i	1.75117	−	0.211945i
$118$	963980.	−	1.68961e6i	0.586708	−	1.02835i
$119$		−	80306.2i		−	0.0476550i
$120$	1.50786e6	+	843998.i	0.872606	+	0.488425i
$121$	−1.23649e6			−0.697968
$122$	1.75682e6	+	1.00233e6i	0.967495	+	0.551990i
$123$	−807365.	+	392915.i	−0.433865	+	0.211146i
$124$	−577603.	+	341422.i	−0.302945	+	0.179072i
$125$	1.91189e6	−	399201.i	0.978889	−	0.204391i
$126$	−1.30031e6	−	546743.i	−0.650034	−	0.273320i
$127$	−2.27402e6	−	2.27402e6i	−1.11015	−	1.11015i	−0.993129	−	0.117025i	$-0.962664\pi$
$127$	−2.27402e6	−	2.27402e6i	−1.11015	−	1.11015i	−0.117025	−	0.993129i	$-0.537336\pi$
$128$	1.85264e6	+	982743.i	0.883406	+	0.468608i
$129$	−2.04833e6	−	707279.i	−0.954183	−	0.329474i
$130$	2.53099e6	−	2.93477e6i	1.15202	−	1.33581i
$131$	−2.13189e6			−0.948312			−0.474156	−	0.880441i	$-0.657247\pi$
$131$	−2.13189e6			−0.948312			−0.474156	+	0.880441i	$0.657247\pi$
$132$	−696952.	+	1.05450e6i	−0.303027	+	0.458483i
$133$	−2.09899e6	−	2.09899e6i	−0.892188	−	0.892188i
$134$	915182.	+	3.34678e6i	0.380358	+	1.39096i
$135$	−913015.	−	2.28470e6i	−0.371088	−	0.928598i
$136$	118343.	−	122040.i	0.0470462	−	0.0485159i
$137$	−1.51012e6	−	1.51012e6i	−0.587286	−	0.587286i	0.349610	−	0.936896i	$-0.386314\pi$
$137$	−1.51012e6	−	1.51012e6i	−0.587286	−	0.587286i	−0.936896	+	0.349610i	$0.886314\pi$
$138$	−2.00254e6	+	1.75582e6i	−0.761979	+	0.668101i
$139$	893388.			0.332656			0.166328	−	0.986070i	$-0.446809\pi$
$139$	893388.			0.332656			0.166328	+	0.986070i	$0.446809\pi$
$140$	−1.82376e6	+	646496.i	−0.664634	+	0.235604i
$141$	2.95554e6	+	1.02053e6i	1.05434	+	0.364057i
$142$	1.88213e6	+	1.07382e6i	0.657331	+	0.375031i
$143$	2.00450e6	+	2.00450e6i	0.685486	+	0.685486i
$144$	−1.17035e6	−	2.74707e6i	−0.391949	−	0.919987i
$145$	602868.	+	896106.i	0.197751	+	0.293938i
$146$	−1.13421e6	−	4.14777e6i	−0.364448	−	1.33277i
$147$	−1.43598e6	+	698839.i	−0.452061	+	0.220001i
$148$	324611.	+	83421.9i	0.100133	+	0.0257333i
$149$	1.20683e6			0.364827			0.182413	−	0.983222i	$-0.441609\pi$
$149$	1.20683e6			0.364827			0.182413	+	0.983222i	$0.441609\pi$
$150$	−3.03618e6	−	1.47385e6i	−0.899609	−	0.436696i
$151$		−	19153.9i		−	0.00556321i	−0.999996	−	0.00278160i	$-0.999115\pi$
$151$		−	19153.9i		−	0.00556321i	0.999996	−	0.00278160i	$-0.000885413\pi$
$152$	−96632.6	−	6.28296e6i	−0.0275165	−	1.78910i
$153$	−240292.	+	29082.5i	−0.0670910	+	0.00812004i
$154$	−373332.	−	1.36526e6i	−0.102219	−	0.373812i
$155$	1.08731e6	−	731507.i	0.291985	−	0.196437i
$156$	−6.56138e6	+	1.33945e6i	−1.72831	+	0.352819i
$157$	−884292.	+	884292.i	−0.228506	+	0.228506i	−0.812068	−	0.583563i	$-0.801658\pi$
$157$	−884292.	+	884292.i	−0.228506	+	0.228506i	0.583563	+	0.812068i	$0.301658\pi$
$158$	−1.30393e6	−	743938.i	−0.330585	−	0.188610i
$159$	3.27901e6	+	1.13222e6i	0.815738	+	0.281670i
$160$	−3.72423e6	−	1.70510e6i	−0.909235	−	0.416283i
$161$		−	2.98224e6i		−	0.714604i
$162$	−1.16506e6	+	4.08878e6i	−0.274033	+	0.961720i
$163$	−474227.	+	474227.i	−0.109502	+	0.109502i	−0.759735	−	0.650233i	$-0.774671\pi$
$163$	−474227.	+	474227.i	−0.109502	+	0.109502i	0.650233	+	0.759735i	$0.274671\pi$
$164$	1.83220e6	−	1.08302e6i	0.415375	−	0.245529i
$165$	1.23879e6	−	2.13545e6i	0.275769	−	0.475377i
$166$	−568675.	−	2.07962e6i	−0.124320	−	0.454632i
$167$	−2.08514e6	+	2.08514e6i	−0.447698	+	0.447698i	−0.894588	−	0.446891i	$-0.852531\pi$
$167$	−2.08514e6	+	2.08514e6i	−0.447698	+	0.447698i	0.446891	+	0.894588i	$0.352531\pi$
$168$	3.17690e6	+	1.04257e6i	0.670002	+	0.219876i
$169$			1.01920e7i			2.11153i
$170$	−216841.	+	251435.i	−0.0441362	+	0.0511774i
$171$	−5.52045e6	+	7.04073e6i	−1.10404	+	1.40809i
$172$	4.97495e6	+	1.27851e6i	0.977695	+	0.251258i
$173$	−585364.	+	585364.i	−0.113054	+	0.113054i	−0.761371	−	0.648316i	$-0.775473\pi$
$173$	−585364.	+	585364.i	−0.113054	+	0.113054i	0.648316	+	0.761371i	$0.275473\pi$
$174$	122250.	−	1.86228e6i	0.0232060	−	0.353506i
$175$	3.48231e6	−	1.46830e6i	0.649760	−	0.273969i
$176$	1.44456e6	−	2.62492e6i	0.264971	−	0.481479i
$177$	5.90329e6	−	2.87291e6i	1.06457	−	0.518087i
$178$	−3.43812e6	−	1.96157e6i	−0.609623	−	0.347812i
$179$			5.90016e6i			1.02874i	0.857569	+	0.514368i	$0.171974\pi$
$179$			5.90016e6i			1.02874i	−0.857569	+	0.514368i	$0.828026\pi$
$180$	2.59491e6	+	5.22290e6i	0.444943	+	0.895559i
$181$	−4.99634e6			−0.842590			−0.421295	−	0.906924i	$-0.638424\pi$
$181$	−4.99634e6			−0.842590			−0.421295	+	0.906924i	$0.638424\pi$
$182$	3.71603e6	−	6.51323e6i	0.616403	−	1.08039i
$183$	2.98721e6	+	6.13814e6i	0.487430	+	1.00158i
$184$	4.39476e6	−	4.53205e6i	0.705474	−	0.727514i
$185$	−642431.	−	125676.i	−0.101464	−	0.0198489i
$186$	−2.25964e6	−	148335.i	−0.351157	−	0.0230518i
$187$	−171735.	−	171735.i	−0.0262623	−	0.0262623i
$188$	−7.17835e6	−	1.84476e6i	−1.08032	−	0.277631i
$189$	−2.58251e6	−	3.99938e6i	−0.382522	−	0.592389i
$190$	904181.	+	1.22395e7i	0.131824	+	1.78444i
$191$	9.85084e6			1.41375			0.706876	−	0.707338i	$-0.250104\pi$
$191$	9.85084e6			1.41375			0.706876	+	0.707338i	$0.250104\pi$
$192$	3.29150e6	+	6.26598e6i	0.465039	+	0.885290i
$193$	−1.51123e6	−	1.51123e6i	−0.210212	−	0.210212i	0.594146	−	0.804358i	$-0.297490\pi$
$193$	−1.51123e6	−	1.51123e6i	−0.210212	−	0.210212i	−0.804358	+	0.594146i	$0.797490\pi$
$194$	1.17960e7	−	3.22562e6i	1.61558	−	0.441782i
$195$	1.26408e7	−	3.35914e6i	1.70479	−	0.453028i
$196$	3.25875e6	−	1.92626e6i	0.432796	−	0.255827i
$197$	892042.	+	892042.i	0.116677	+	0.116677i	0.763035	−	0.646357i	$-0.223708\pi$
$197$	892042.	+	892042.i	0.116677	+	0.116677i	−0.646357	+	0.763035i	$0.723708\pi$
$198$	−3.94992e6	+	1.61150e6i	−0.508854	+	0.207604i
$199$	960953.			0.121939			0.0609695	−	0.998140i	$-0.480581\pi$
$199$	960953.			0.121939			0.0609695	+	0.998140i	$0.480581\pi$
$200$	7.45574e6	+	2.90032e6i	0.931968	+	0.362540i
$201$	−3.82200e6	+	1.10688e7i	−0.470655	+	1.36305i
$202$	−3.14997e6	+	5.52108e6i	−0.382166	+	0.669838i
$203$	1.47771e6	+	1.47771e6i	0.176645	+	0.176645i
$204$	562143.	−	114757.i	0.0662150	−	0.0135172i
$205$	−3.44904e6	+	2.32039e6i	−0.400347	+	0.269339i
$206$	6.48519e6	−	1.77338e6i	0.741858	−	0.202862i
$207$	−8.92344e6	+	1.08001e6i	−1.00605	+	0.121763i
$208$	1.52453e7	−	4.42192e6i	1.69413	−	0.491384i
$209$	−8.97739e6			−0.983357
$210$	−6.31310e6	−	1.67088e6i	−0.681686	−	0.180421i
$211$			1.21169e7i			1.28986i	0.764240	+	0.644931i	$0.223114\pi$
$211$			1.21169e7i			1.28986i	−0.764240	+	0.644931i	$0.776886\pi$
$212$	−7.96398e6	−	2.04667e6i	−0.835839	−	0.214803i
$213$	3.20027e6	+	6.57594e6i	0.331167	+	0.680486i
$214$	−1.76458e7	+	4.82526e6i	−1.80053	+	0.492357i
$215$	−9.84581e6	−	1.92609e6i	−0.990686	−	0.193803i
$216$	1.96907e6	−	9.88346e6i	0.195389	−	0.980726i
$217$	1.79302e6	−	1.79302e6i	0.175471	−	0.175471i
$218$	1.75362e6	−	3.07364e6i	0.169265	−	0.296677i
$219$	4.73672e6	−	1.37179e7i	0.450967	−	1.30604i
$220$	−2.51757e6	+	5.28263e6i	−0.236436	+	0.496115i
$221$		−	1.28673e6i		−	0.119209i
$222$	745741.	+	850529.i	0.0681599	+	0.0777374i
$223$	−2.72115e6	+	2.72115e6i	−0.245379	+	0.245379i	−0.819071	−	0.573692i	$-0.805511\pi$
$223$	−2.72115e6	+	2.72115e6i	−0.245379	+	0.245379i	0.573692	+	0.819071i	$0.305511\pi$
$224$	−7.70557e6	−	1.85441e6i	−0.685584	−	0.164992i
$225$	−5.65455e6	−	9.88799e6i	−0.496421	−	0.868082i
$226$	1.24227e7	−	3.39700e6i	1.07619	−	0.294287i
$227$	−5.17471e6	+	5.17471e6i	−0.442394	+	0.442394i	−0.892816	−	0.450422i	$-0.851273\pi$
$227$	−5.17471e6	+	5.17471e6i	−0.442394	+	0.442394i	0.450422	+	0.892816i	$0.351273\pi$
$228$	1.16935e7	−	1.76924e7i	0.986597	−	1.49273i
$229$			1.24739e6i			0.103872i	0.998650	+	0.0519359i	$0.0165391\pi$
$229$			1.24739e6i			0.103872i	−0.998650	+	0.0519359i	$0.983461\pi$
$230$	−8.05259e6	+	9.33725e6i	−0.661839	+	0.767424i
$231$	1.55912e6	−	4.51533e6i	0.126486	−	0.366314i
$232$	68030.3	+	4.42326e6i	0.00544801	+	0.354225i
$233$	9.58874e6	−	9.58874e6i	0.758043	−	0.758043i	−0.217923	−	0.975966i	$-0.569928\pi$
$233$	9.58874e6	−	9.58874e6i	0.758043	−	0.758043i	0.975966	+	0.217923i	$0.0699282\pi$
$234$	−2.08346e7	−	8.76032e6i	−1.62606	−	0.683711i
$235$	1.42065e7	+	2.77915e6i	1.09467	+	0.214145i
$236$	−1.33967e7	+	7.91879e6i	−1.01920	+	0.602453i
$237$	−2.21713e6	−	4.55578e6i	−0.166551	−	0.342230i
$238$	−318369.	+	558017.i	−0.0236156	+	0.0413920i
$239$		−	601286.i		−	0.0440441i	−0.999757	−	0.0220220i	$-0.992990\pi$
$239$		−	601286.i		−	0.0440441i	0.999757	−	0.0220220i	$-0.00701040\pi$
$240$	−7.13159e6	−	1.18424e7i	−0.515885	−	0.856658i
$241$	1.26027e7			0.900351			0.450176	−	0.892940i	$-0.351361\pi$
$241$	1.26027e7			0.900351			0.450176	+	0.892940i	$0.351361\pi$
$242$	8.59192e6	+	4.90199e6i	0.606239	+	0.345881i
$243$	−1.10317e7	+	9.17571e6i	−0.768815	+	0.639471i
$244$	−8.23383e6	−	1.39296e7i	−0.566803	−	0.958892i
$245$	−6.13447e6	+	4.12706e6i	−0.417137	+	0.280635i
$246$	7.16775e6	+	470529.i	0.481479	+	0.0316068i
$247$	−3.36316e7	−	3.36316e7i	−2.23181	−	2.23181i
$248$	5.36709e6	−	82546.4i	0.351871	−	0.00541182i
$249$	2.37491e6	−	6.87793e6i	0.153833	−	0.445512i
$250$	−1.48676e7	−	4.80568e6i	−0.951528	−	0.307563i
$251$	1.55766e7			0.985034			0.492517	−	0.870303i	$-0.336077\pi$
$251$	1.55766e7			0.985034			0.492517	+	0.870303i	$0.336077\pi$
$252$	6.86784e6	+	8.95411e6i	0.429160	+	0.559527i
$253$	−6.37752e6	−	6.37752e6i	−0.393813	−	0.393813i
$254$	6.78610e6	+	2.48165e7i	0.414113	+	1.51440i
$255$	−1.08299e6	+	287793.i	−0.0653138	+	0.0173564i
$256$	−8.97725e6	−	1.41734e7i	−0.535086	−	0.844798i
$257$	2.52536e6	+	2.52536e6i	0.148773	+	0.148773i	0.777570	−	0.628797i	$-0.216452\pi$
$257$	2.52536e6	+	2.52536e6i	0.148773	+	0.148773i	−0.628797	+	0.777570i	$0.716452\pi$
$258$	1.14291e7	+	1.30351e7i	0.665509	+	0.759023i
$259$	−1.26664e6			−0.0729042
$260$	−2.92216e7	+	1.03586e7i	−1.66258	+	0.589363i
$261$	3.88645e6	−	4.95674e6i	0.218590	−	0.278788i
$262$	1.48137e7	+	8.45174e6i	0.823683	+	0.469940i
$263$	−2.21732e7	−	2.21732e7i	−1.21888	−	1.21888i	−0.968023	−	0.250860i	$-0.919287\pi$
$263$	−2.21732e7	−	2.21732e7i	−1.21888	−	1.21888i	−0.250860	−	0.968023i	$-0.580713\pi$
$264$	9.02333e6	−	4.56426e6i	0.490405	−	0.248061i
$265$	1.57613e7	+	3.08332e6i	0.846945	+	0.165684i
$266$	6.26379e6	+	2.29064e7i	0.332807	+	1.21706i
$267$	−5.84600e6	−	1.20124e7i	−0.307132	−	0.631097i
$268$	6.90884e6	−	2.68837e7i	0.358923	−	1.39664i
$269$	2.39875e7			1.23233			0.616166	−	0.787617i	$-0.288685\pi$
$269$	2.39875e7			1.23233			0.616166	+	0.787617i	$0.288685\pi$
$270$	−2.71334e6	+	1.94951e7i	−0.137852	+	0.990453i
$271$			1.19982e7i			0.602848i	0.953490	+	0.301424i	$0.0974619\pi$
$271$			1.19982e7i			0.602848i	−0.953490	+	0.301424i	$0.902538\pi$
$272$	−1.30613e6	+	378846.i	−0.0649055	+	0.0188259i
$273$	2.27565e7	−	1.10747e7i	1.11845	−	0.544309i
$274$	4.50648e6	+	1.64800e7i	0.219071	+	0.801135i
$275$	4.30695e6	−	1.05869e7i	0.207096	−	0.509061i
$276$	2.08757e7	−	4.26159e6i	0.992917	−	0.202696i
$277$	7.70615e6	−	7.70615e6i	0.362575	−	0.362575i	−0.502185	−	0.864760i	$-0.667470\pi$
$277$	7.70615e6	−	7.70615e6i	0.362575	−	0.362575i	0.864760	+	0.502185i	$0.167470\pi$
$278$	−6.20781e6	−	3.54178e6i	−0.288938	−	0.164849i
$279$	−6.01440e6	−	4.71573e6i	−0.276936	−	0.217138i
$280$	1.52356e7	+	2.73790e6i	0.694041	+	0.124722i
$281$			2.02190e7i			0.911256i	0.890170	+	0.455628i	$0.150585\pi$
$281$			2.02190e7i			0.911256i	−0.890170	+	0.455628i	$0.849415\pi$
$282$	−1.64911e7	−	1.88083e7i	−0.735362	−	0.838692i
$283$	−618047.	+	618047.i	−0.0272686	+	0.0272686i	−0.720610	−	0.693341i	$-0.756138\pi$
$283$	−618047.	+	618047.i	−0.0272686	+	0.0272686i	0.693341	+	0.720610i	$0.256138\pi$
$284$	−8.82111e6	−	1.49231e7i	−0.385095	−	0.651486i
$285$	−2.07844e7	+	3.58287e7i	−0.897849	+	1.54774i
$286$	−5.98181e6	−	2.18752e7i	−0.255702	−	0.935092i
$287$	−5.68759e6	+	5.68759e6i	−0.240593	+	0.240593i
$288$	−2.75822e6	+	2.37281e7i	−0.115465	+	0.993312i
$289$		−	2.40273e7i		−	0.995433i
$290$	−636552.	−	8.61672e6i	−0.0261000	−	0.353304i
$291$	3.90127e7	+	1.34709e7i	1.58317	+	0.546660i
$292$	−8.56233e6	+	3.33177e7i	−0.343909	+	1.33822i
$293$	−2.95161e7	+	2.95161e7i	−1.17343	+	1.17343i	−0.192042	+	0.981387i	$0.561511\pi$
$293$	−2.95161e7	+	2.95161e7i	−1.17343	+	1.17343i	−0.981387	+	0.192042i	$0.938489\pi$
$294$	1.27486e7	+	836884.i	0.501672	+	0.0329324i
$295$	2.52187e7	−	1.69662e7i	0.982327	−	0.660875i
$296$	−1.92488e6	−	1.86657e6i	−0.0742213	−	0.0719728i
$297$	−1.40753e7	−	3.02997e6i	−0.537266	−	0.115656i
$298$	−8.38579e6	−	4.78439e6i	−0.316880	−	0.180791i
$299$		−	4.77837e7i		−	1.78758i
$300$	1.52543e7	+	2.22779e7i	0.564974	+	0.825109i
$301$	−1.94123e7			−0.711832
$302$	−75934.1	+	133093.i	−0.00275687	+	0.00483208i
$303$	−1.92900e7	+	9.38773e6i	−0.693433	+	0.337468i
$304$	−2.42369e7	+	4.40410e7i	−0.862693	+	1.56760i
$305$	1.76412e7	+	2.62220e7i	0.621769	+	0.924199i
$306$	1.78499e6	+	750536.i	0.0622976	+	0.0261943i
$307$	2.70580e7	+	2.70580e7i	0.935148	+	0.935148i	0.998021	−	0.0628740i	$-0.0200266\pi$
$307$	2.70580e7	+	2.70580e7i	0.935148	+	0.935148i	−0.0628740	+	0.998021i	$0.520027\pi$
$308$	−2.81834e6	+	1.09667e7i	−0.0964588	+	0.375340i
$309$	2.14485e7	+	7.40604e6i	0.726977	+	0.251021i
$310$	−1.04553e7	+	772378.i	−0.350956	+	0.0259266i
$311$	−1.19741e6			−0.0398072			−0.0199036	−	0.999802i	$-0.506336\pi$
$311$	−1.19741e6			−0.0398072			−0.0199036	+	0.999802i	$0.506336\pi$
$312$	5.09027e7	+	1.67048e7i	1.67601	+	0.550019i
$313$	−2.49447e7	−	2.49447e7i	−0.813478	−	0.813478i	0.171676	−	0.985154i	$-0.445082\pi$
$313$	−2.49447e7	−	2.49447e7i	−0.813478	−	0.813478i	−0.985154	+	0.171676i	$0.945082\pi$
$314$	9.65032e6	−	2.63889e6i	0.311712	−	0.0852379i
$315$	−1.44110e7	−	1.66763e7i	−0.461065	−	0.533542i
$316$	6.11122e6	+	1.03387e7i	0.193672	+	0.327645i
$317$	−2.80656e7	−	2.80656e7i	−0.881042	−	0.881042i	0.112598	−	0.993641i	$-0.464083\pi$
$317$	−2.80656e7	−	2.80656e7i	−0.881042	−	0.881042i	−0.993641	+	0.112598i	$0.964083\pi$
$318$	−1.82959e7	−	2.08668e7i	−0.568949	−	0.648895i
$319$	6.32016e6			0.194696
$320$	1.91185e7	+	2.66125e7i	0.583450	+	0.812149i
$321$	−5.83599e7	−	2.01514e7i	−1.76441	−	0.609242i
$322$	−1.18229e7	+	2.07225e7i	−0.354125	+	0.620689i
$323$	2.88137e6	+	2.88137e6i	0.0855050	+	0.0855050i
$324$	2.43052e7	−	2.37926e7i	0.714603	−	0.699530i
$325$	5.57961e7	−	2.35263e7i	1.62538	−	0.685335i
$326$	5.17526e6	−	1.41518e6i	0.149376	−	0.0408469i
$327$	1.07389e7	−	5.22625e6i	0.307127	−	0.149467i
$328$	−1.70248e7	+	261843.i	−0.482459	+	0.00742027i
$329$	2.80100e7			0.786547
$330$	−1.70737e7	+	9.92736e6i	−0.475101	+	0.276243i
$331$			2.13604e7i			0.589015i	0.955649	+	0.294507i	$0.0951555\pi$
$331$			2.13604e7i			0.589015i	−0.955649	+	0.294507i	$0.904844\pi$
$332$	−4.29301e6	+	1.67050e7i	−0.117313	+	0.456490i
$333$	458706.	+	3.79002e6i	0.0124223	+	0.102638i
$334$	2.27552e7	−	6.22243e6i	0.610718	−	0.167002i
$335$	−1.04082e7	+	5.32049e7i	−0.276848	+	1.41520i
$336$	−1.79419e7	−	1.98390e7i	−0.472988	−	0.523001i
$337$	−1.83682e7	+	1.83682e7i	−0.479929	+	0.479929i	−0.905109	−	0.425180i	$-0.860211\pi$
$337$	−1.83682e7	+	1.83682e7i	−0.479929	+	0.479929i	0.425180	+	0.905109i	$0.360211\pi$
$338$	4.04054e7	−	7.08201e7i	1.04638	−	1.83403i
$339$	4.10856e7	+	1.41866e7i	1.05461	+	0.364150i
$340$	2.50354e6	−	887471.i	0.0636969	−	0.0225797i
$341$		−	7.66875e6i		−	0.193402i
$342$	6.62720e7	−	2.70379e7i	1.65673	−	0.675919i
$343$	−3.02372e7	+	3.02372e7i	−0.749305	+	0.749305i
$344$	−2.95004e7	−	2.86067e7i	−0.724692	−	0.702738i
$345$	−4.02179e7	+	1.06874e7i	−0.979404	+	0.260265i
$346$	6.38811e6	−	1.74684e6i	0.154221	−	0.0421719i
$347$	−1.29367e7	+	1.29367e7i	−0.309623	+	0.309623i	−0.844763	−	0.535140i	$-0.820259\pi$
$347$	−1.29367e7	+	1.29367e7i	−0.309623	+	0.309623i	0.535140	+	0.844763i	$0.320259\pi$
$348$	−8.23233e6	+	1.24556e7i	−0.195337	+	0.295547i
$349$			3.93346e7i			0.925334i	0.886532	+	0.462667i	$0.153108\pi$
$349$			3.93346e7i			0.925334i	−0.886532	+	0.462667i	$0.846892\pi$
$350$	−3.00182e7	−	3.60270e6i	−0.700134	−	0.0840279i
$351$	−4.13788e7	−	6.40810e7i	−0.956879	−	1.48186i
$352$	−2.04440e7	+	1.25127e7i	−0.468746	+	0.286895i
$353$	−4.05793e6	+	4.05793e6i	−0.0922529	+	0.0922529i	−0.751727	−	0.659474i	$-0.770779\pi$
$353$	−4.05793e6	+	4.05793e6i	−0.0922529	+	0.0922529i	0.659474	+	0.751727i	$0.270779\pi$
$354$	−5.24092e7	−	3.44041e6i	−1.18140	−	0.0775534i
$355$	1.88995e7	+	2.80922e7i	0.422439	+	0.627915i
$356$	1.61137e7	+	2.72604e7i	0.357146	+	0.604203i
$357$	−1.94965e6	+	948822.i	−0.0428501	+	0.0208535i
$358$	2.33908e7	−	4.09979e7i	0.509795	−	0.893537i
$359$			3.30671e7i			0.714683i	0.933974	+	0.357341i	$0.116317\pi$
$359$			3.30671e7i			0.714683i	−0.933974	+	0.357341i	$0.883683\pi$
$360$	2.67483e6	−	4.65793e7i	0.0573309	−	0.998355i
$361$	1.03577e8			2.20162
$362$	3.47177e7	+	1.98077e7i	0.731855	+	0.417549i
$363$	1.46092e7	+	3.00192e7i	0.305427	+	0.627594i
$364$	−5.16425e7	+	3.05260e7i	−1.07079	+	0.632945i
$365$	1.28992e7	−	6.59384e7i	0.265268	−	1.35600i
$366$	3.57728e6	−	5.44942e7i	0.0729642	−	1.11149i
$367$	−6.43769e7	−	6.43769e7i	−1.30236	−	1.30236i	−0.926794	−	0.375569i	$-0.877447\pi$
$367$	−6.43769e7	−	6.43769e7i	−1.30236	−	1.30236i	−0.375569	−	0.926794i	$-0.622553\pi$
$368$	−4.85045e7	+	1.40688e7i	−0.973281	+	0.282301i
$369$	1.90781e7	+	1.49586e7i	0.379713	+	0.297723i
$370$	3.96577e6	+	3.42014e6i	0.0782929	+	0.0675211i
$371$	3.10755e7			0.608551
$372$	1.51133e7	+	9.98893e6i	0.293584	+	0.194039i
$373$	−6.42553e6	−	6.42553e6i	−0.123818	−	0.123818i	0.642483	−	0.766300i	$-0.277904\pi$
$373$	−6.42553e6	−	6.42553e6i	−0.123818	−	0.123818i	−0.766300	+	0.642483i	$0.777904\pi$
$374$	512488.	+	1.87415e6i	0.00979646	+	0.0358253i
$375$	−3.22808e7	−	4.16997e7i	−0.612139	−	0.790750i
$376$	4.25661e7	+	4.12766e7i	0.800757	+	0.776498i
$377$	2.36770e7	+	2.36770e7i	0.441878	+	0.441878i
$378$	2.08960e6	+	3.80283e7i	0.0386889	+	0.704096i
$379$	5.07408e7			0.932051			0.466026	−	0.884771i	$-0.345685\pi$
$379$	5.07408e7			0.932051			0.466026	+	0.884771i	$0.345685\pi$
$380$	4.22399e7	−	8.86322e7i	0.769789	−	1.61525i
$381$	−2.83402e7	+	8.20755e7i	−0.512423	+	1.48402i
$382$	−6.84497e7	−	3.90530e7i	−1.22795	−	0.700590i
$383$	6.21131e7	+	6.21131e7i	1.10557	+	1.10557i	0.993726	+	0.111846i	$0.0356764\pi$
$383$	6.21131e7	+	6.21131e7i	1.10557	+	1.10557i	0.111846	+	0.993726i	$0.464324\pi$
$384$	1.96971e6	−	5.65888e7i	0.0347864	−	0.999395i
$385$	4.24585e6	−	2.17040e7i	0.0744017	−	0.380327i
$386$	4.50978e6	+	1.64921e7i	0.0784140	+	0.286757i
$387$	7.03007e6	+	5.80853e7i	0.121291	+	1.00215i
$388$	−9.47533e7	−	2.43507e7i	−1.62218	−	0.416885i
$389$	−1.11570e8			−1.89538			−0.947691	−	0.319188i	$-0.896590\pi$
$389$	−1.11570e8			−1.89538			−0.947691	+	0.319188i	$0.896590\pi$
$390$	−1.01153e8	−	2.67721e7i	−1.70524	−	0.451325i
$391$			4.09384e6i			0.0684859i
$392$	−3.02803e7	+	465715.i	−0.502693	+	0.00773147i
$393$	2.51884e7	+	5.17574e7i	0.414976	+	0.852697i
$394$	−2.66202e6	−	9.73490e6i	−0.0435234	−	0.159163i
$395$	−1.30935e7	−	1.94622e7i	−0.212453	−	0.315791i
$396$	3.38352e7	+	4.46147e6i	0.544858	+	0.0718443i
$397$	3.30134e7	−	3.30134e7i	0.527618	−	0.527618i	−0.392244	−	0.919861i	$-0.628301\pi$
$397$	3.30134e7	−	3.30134e7i	0.527618	−	0.527618i	0.919861	+	0.392244i	$0.128301\pi$
$398$	−6.67729e6	−	3.80963e6i	−0.105913	−	0.0604274i
$399$	−2.61590e7	+	7.57584e7i	−0.411815	+	1.19265i
$400$	−4.03090e7	−	4.97110e7i	−0.629828	−	0.776735i
$401$		−	9.67635e7i		−	1.50065i	−0.661071	−	0.750323i	$-0.729898\pi$
$401$		−	9.67635e7i		−	1.50065i	0.661071	−	0.750323i	$-0.270102\pi$
$402$	7.04391e7	−	6.17608e7i	1.08427	−	0.950682i
$403$	2.87291e7	−	2.87291e7i	0.438942	−	0.438942i
$404$	4.37759e7	−	2.58760e7i	0.663882	−	0.392422i
$405$	−4.46798e7	+	4.91597e7i	−0.672584	+	0.740021i
$406$	−4.40977e6	−	1.61263e7i	−0.0658927	−	0.240967i
$407$	−2.70870e6	+	2.70870e6i	−0.0401770	+	0.0401770i
$408$	−4.36106e6	−	1.43118e6i	−0.0642113	−	0.0210723i
$409$		−	1.32073e7i		−	0.193039i	−0.995331	−	0.0965195i	$-0.969229\pi$
$409$		−	1.32073e7i		−	0.193039i	0.995331	−	0.0965195i	$-0.0307710\pi$
$410$	3.31651e7	−	2.45004e6i	0.481204	−	0.0355485i
$411$	−1.88200e7	+	5.45043e7i	−0.271079	+	0.785064i
$412$	−5.20936e7	−	1.33875e7i	−0.744890	−	0.191430i
$413$	4.15865e7	−	4.15865e7i	0.590340	−	0.590340i
$414$	6.62872e7	+	2.78718e7i	0.934175	+	0.392793i
$415$	6.46745e6	−	3.30604e7i	0.0904876	−	0.462556i
$416$	−1.23464e8	−	2.97128e7i	−1.71499	−	0.412727i
$417$	−1.05554e7	−	2.16894e7i	−0.145568	−	0.299115i
$418$	6.23804e7	+	3.55902e7i	0.854121	+	0.487306i
$419$			3.16843e7i			0.430726i	0.976534	+	0.215363i	$0.0690935\pi$
$419$			3.16843e7i			0.430726i	−0.976534	+	0.215363i	$0.930906\pi$
$420$	3.72432e7	+	3.66382e7i	0.502688	+	0.494522i
$421$	−2.21956e7			−0.297455			−0.148728	−	0.988878i	$-0.547518\pi$
$421$	−2.21956e7			−0.297455			−0.148728	+	0.988878i	$0.547518\pi$
$422$	4.80365e7	−	8.41956e7i	0.639197	−	1.12035i
$423$	−1.01437e7	−	8.38111e7i	−0.134021	−	1.10734i
$424$	4.72248e7	+	4.57942e7i	0.619545	+	0.600776i
$425$	−4.78030e6	+	2.01560e6i	−0.0622714	+	0.0262565i
$426$	3.83243e6	−	5.83809e7i	0.0495730	−	0.755166i
$427$	4.32410e7	+	4.32410e7i	0.555408	+	0.555408i
$428$	1.41743e8	+	3.64267e7i	1.80789	+	0.464609i
$429$	2.49813e7	−	7.23479e7i	0.316405	−	0.916335i
$430$	6.07789e7	+	5.24167e7i	0.764447	+	0.659271i
$431$	−8.32650e7			−1.03999			−0.519997	−	0.854168i	$-0.674067\pi$
$431$	−8.32650e7			−1.03999			−0.519997	+	0.854168i	$0.674067\pi$
$432$	−5.28646e7	+	6.08701e7i	−0.655713	+	0.755011i
$433$	−2.08256e7	−	2.08256e7i	−0.256527	−	0.256527i	0.567113	−	0.823640i	$-0.308060\pi$
$433$	−2.08256e7	−	2.08256e7i	−0.256527	−	0.256527i	−0.823640	+	0.567113i	$0.808060\pi$
$434$	−1.95673e7	+	5.35071e6i	−0.239366	+	0.0654549i
$435$	1.46324e7	−	2.52238e7i	0.177766	−	0.306438i
$436$	−2.43705e7	+	1.44054e7i	−0.294039	+	0.173807i
$437$	1.07002e8	+	1.07002e8i	1.28218	+	1.28218i
$438$	−8.72973e7	+	7.65420e7i	−1.03891	+	0.910914i
$439$	−1.34397e8			−1.58853			−0.794266	−	0.607570i	$-0.792144\pi$
$439$	−1.34397e8			−1.58853			−0.794266	+	0.607570i	$0.792144\pi$
$440$	3.84362e7	−	2.67262e7i	0.451214	−	0.313747i
$441$	3.39324e7	+	2.66055e7i	0.395638	+	0.310209i
$442$	−5.10114e6	+	8.94096e6i	−0.0590745	+	0.103542i
$443$	−5.93953e6	−	5.93953e6i	−0.0683189	−	0.0683189i	0.672122	−	0.740441i	$-0.265383\pi$
$443$	−5.93953e6	−	5.93953e6i	−0.0683189	−	0.0683189i	−0.740441	+	0.672122i	$0.765383\pi$
$444$	−1.81001e6	−	8.86644e6i	−0.0206791	−	0.101298i
$445$	−3.45240e7	−	5.13167e7i	−0.391779	−	0.582342i
$446$	2.96960e7	−	8.12041e6i	0.334729	−	0.0915321i
$447$	−1.42587e7	−	2.92990e7i	−0.159646	−	0.328042i
$448$	4.61914e7	+	4.34338e7i	0.513720	+	0.483052i
$449$	−1.59537e8			−1.76248			−0.881238	−	0.472672i	$-0.843290\pi$
$449$	−1.59537e8			−1.76248			−0.881238	+	0.472672i	$0.843290\pi$
$450$	91016.2	+	9.11250e7i	0.000998807	+	1.00000i
$451$			2.43258e7i			0.265178i
$452$	−9.97878e7	−	2.56445e7i	−1.08059	−	0.277702i
$453$	−465011.	+	226304.i	−0.00500228	+	0.00243443i
$454$	5.64719e7	−	1.54423e7i	0.603483	−	0.165023i
$455$	9.72149e7	−	6.54028e7i	1.03205	−	0.694324i
$456$	−1.51394e8	+	7.65794e7i	−1.59666	+	0.807640i
$457$	−7.72421e7	+	7.72421e7i	−0.809292	+	0.809292i	−0.984527	−	0.175235i	$-0.943932\pi$
$457$	−7.72421e7	+	7.72421e7i	−0.809292	+	0.809292i	0.175235	+	0.984527i	$0.443932\pi$
$458$	4.94521e6	−	8.66767e6i	0.0514741	−	0.0902206i
$459$	3.54511e6	+	5.49010e6i	0.0366599	+	0.0567731i
$460$	9.29713e7	−	3.29570e7i	0.955158	−	0.338590i
$461$		−	6.20058e7i		−	0.632892i	−0.948611	−	0.316446i	$-0.897510\pi$
$461$		−	6.20058e7i		−	0.632892i	0.948611	−	0.316446i	$-0.102490\pi$
$462$	−2.87344e7	+	2.51943e7i	−0.291391	+	0.255491i
$463$	1.23514e8	−	1.23514e8i	1.24444	−	1.24444i	0.286296	−	0.958141i	$-0.407576\pi$
$463$	1.23514e8	−	1.23514e8i	1.24444	−	1.24444i	0.958141	−	0.286296i	$-0.0924241\pi$
$464$	1.70630e7	−	3.10053e7i	0.170805	−	0.310371i
$465$	−3.06059e7	−	1.77547e7i	−0.304402	−	0.176585i
$466$	−1.04642e8	+	2.86146e7i	−1.03407	+	0.282768i
$467$	5.11427e7	−	5.11427e7i	0.502150	−	0.502150i	−0.409956	−	0.912105i	$-0.634456\pi$
$467$	5.11427e7	−	5.11427e7i	0.502150	−	0.502150i	0.912105	+	0.409956i	$0.134456\pi$
$468$	1.10042e8	+	1.43469e8i	1.07354	+	1.39966i
$469$			1.04900e8i			1.01685i
$470$	−8.76977e7	−	7.56319e7i	−0.844685	−	0.728470i
$471$	3.19165e7	+	1.10206e7i	0.305459	+	0.105473i
$472$	1.24482e8	−	1.91454e6i	1.18380	−	0.0182070i
$473$	−4.15131e7	+	4.15131e7i	−0.392285	+	0.392285i
$474$	−2.65509e6	+	4.04460e7i	−0.0249313	+	0.379788i
$475$	−7.22621e7	+	1.77627e8i	−0.674264	+	1.65740i
$476$	4.42444e6	−	2.61530e6i	0.0410240	−	0.0242494i
$477$	−1.12539e7	−	9.29839e7i	−0.103692	−	0.856747i
$478$	−2.38376e6	+	4.17811e6i	−0.0218262	+	0.0382557i
$479$		−	1.73444e8i		−	1.57816i	−0.614288	−	0.789082i	$-0.710557\pi$
$479$		−	1.73444e8i		−	1.57816i	0.614288	−	0.789082i	$-0.289443\pi$
$480$	2.60616e6	+	1.10561e8i	0.0235656	+	0.999722i
$481$	−2.02950e7			−0.182370
$482$	−8.75713e7	−	4.99625e7i	−0.782025	−	0.446173i
$483$	−7.24019e7	+	3.52353e7i	−0.642552	+	0.312707i
$484$	−4.02683e7	−	6.81242e7i	−0.355163	−	0.600849i
$485$	1.87524e8	+	3.66845e7i	1.64374	+	0.321556i
$486$	1.13031e8	−	2.00243e7i	0.984668	−	0.174441i
$487$	6.73024e7	+	6.73024e7i	0.582698	+	0.582698i	0.935644	−	0.352946i	$-0.114820\pi$
$487$	6.73024e7	+	6.73024e7i	0.582698	+	0.582698i	−0.352946	+	0.935644i	$0.614820\pi$
$488$	1.99071e6	+	1.29434e8i	0.0171297	+	1.11375i
$489$	1.71161e7	+	5.91011e6i	0.146379	+	0.0505439i
$490$	5.89875e7	−	4.35765e6i	0.501386	−	0.0370394i
$491$	−1.04997e8			−0.887014			−0.443507	−	0.896271i	$-0.646266\pi$
$491$	−1.04997e8			−0.887014			−0.443507	+	0.896271i	$0.646266\pi$
$492$	−4.79406e7	−	3.16856e7i	−0.402539	−	0.266052i
$493$	−2.02851e6	−	2.02851e6i	−0.0169292	−	0.0169292i
$494$	1.00363e8	+	3.67024e8i	0.832517	+	3.04448i
$495$	−6.64801e7	−	4.84439e6i	−0.548121	−	0.0399415i
$496$	−3.76211e7	−	2.07039e7i	−0.308309	−	0.169671i
$497$	4.63251e7	+	4.63251e7i	0.377353	+	0.377353i
$498$	−4.37694e7	+	3.83769e7i	−0.354391	+	0.310729i
$499$	1.21642e7			0.0978998			0.0489499	−	0.998801i	$-0.484413\pi$
$499$	1.21642e7			0.0978998			0.0489499	+	0.998801i	$0.484413\pi$
$500$	8.42576e7	+	9.23345e7i	0.674061	+	0.738676i
$501$	7.52582e7	+	2.59862e7i	0.598467	+	0.206648i
$502$	−1.08236e8	−	6.17523e7i	−0.855578	−	0.488138i
$503$	1.69932e7	+	1.69932e7i	0.133528	+	0.133528i	0.770712	−	0.637184i	$-0.219901\pi$
$503$	1.69932e7	+	1.69932e7i	0.133528	+	0.133528i	−0.637184	+	0.770712i	$0.719901\pi$
$504$	−1.22241e7	−	8.94458e7i	−0.0954827	−	0.698664i
$505$	−8.24063e7	+	5.54401e7i	−0.639862	+	0.430477i
$506$	1.90317e7	+	6.95982e7i	0.146901	+	0.537213i
$507$	2.47437e8	−	1.20419e8i	1.89863	−	0.923994i
$508$	5.12293e7	−	1.99343e8i	0.390775	−	1.52058i
$509$	1.15021e8			0.872213			0.436106	−	0.899895i	$-0.356357\pi$
$509$	1.15021e8			0.872213			0.436106	+	0.899895i	$0.356357\pi$
$510$	8.66623e6	+	2.29369e6i	0.0653311	+	0.0172911i
$511$		−	1.30006e8i		−	0.974319i
$512$	6.19017e6	+	1.34075e8i	0.0461203	+	0.998936i
$513$	2.36157e8	+	5.08370e7i	1.74924	+	0.376555i
$514$	−7.53613e6	−	2.75593e7i	−0.0554957	−	0.202946i
$515$	1.03097e8	+	2.01684e7i	0.754788	+	0.147656i
$516$	−2.77399e7	−	1.35886e8i	−0.201909	−	0.989066i
$517$	5.98992e7	−	5.98992e7i	0.433461	−	0.433461i
$518$	8.80137e6	+	5.02149e6i	0.0633229	+	0.0361280i
$519$	2.11274e7	+	7.29517e6i	0.151127	+	0.0521835i
$520$	2.44116e8	+	4.38687e7i	1.73614	+	0.311993i
$521$			6.22877e6i			0.0440443i	0.999757	+	0.0220221i	$0.00701043\pi$
$521$			6.22877e6i			0.0440443i	−0.999757	+	0.0220221i	$0.992990\pi$
$522$	−4.66561e7	+	1.90349e7i	−0.328017	+	0.133826i
$523$	7.71652e7	−	7.71652e7i	0.539407	−	0.539407i	−0.383948	−	0.923355i	$-0.625436\pi$
$523$	7.71652e7	−	7.71652e7i	0.539407	−	0.539407i	0.923355	+	0.383948i	$0.125436\pi$
$524$	−6.94284e7	−	1.17456e8i	−0.482551	−	0.816358i
$525$	−7.67906e7	−	6.71943e7i	−0.530677	−	0.464359i
$526$	6.61691e7	+	2.41978e8i	0.454672	+	1.66272i
$527$	−2.46135e6	+	2.46135e6i	−0.0168167	+	0.0168167i
$528$	−8.07944e7	−	4.05704e6i	−0.548883	−	0.0275618i
$529$			3.99260e6i			0.0269705i
$530$	−9.72959e7	−	8.39095e7i	−0.653532	−	0.563616i
$531$	−1.39495e8	−	1.09374e8i	−0.931699	−	0.730520i
$532$	4.72863e7	−	1.84000e8i	0.314051	−	1.22204i
$533$	−9.11308e7	+	9.11308e7i	−0.601844	+	0.601844i
$534$	−7.00078e6	+	1.06646e8i	−0.0459751	+	0.700357i
$535$	−2.80521e8	−	5.48770e7i	−1.83191	−	0.358368i
$536$	−1.54585e8	+	1.59415e8i	−1.00386	+	1.03522i
$537$	1.43242e8	−	6.97106e7i	0.925012	−	0.450169i
$538$	−1.66680e8	−	9.50967e7i	−1.07037	−	0.610687i
$539$			4.32660e7i			0.276300i
$540$	9.61409e7	−	1.24707e8i	0.610558	−	0.791972i
$541$	−1.51100e8			−0.954271			−0.477136	−	0.878830i	$-0.658325\pi$
$541$	−1.51100e8			−0.954271			−0.477136	+	0.878830i	$0.658325\pi$
$542$	4.75660e7	−	8.33708e7i	0.298743	−	0.523620i
$543$	5.90320e7	+	1.21300e8i	0.368713	+	0.757634i
$544$	1.05777e7	+	2.54563e6i	0.0657047	+	0.0158124i
$545$	4.58764e7	−	3.08641e7i	0.283400	−	0.190662i
$546$	−2.02031e8	−	1.32624e7i	−1.24119	−	0.0814785i
$547$	3.84117e7	+	3.84117e7i	0.234694	+	0.234694i	0.814649	−	0.579955i	$-0.196930\pi$
$547$	3.84117e7	+	3.84117e7i	0.234694	+	0.234694i	−0.579955	+	0.814649i	$0.696930\pi$
$548$	3.40201e7	−	1.32379e8i	0.206725	−	0.804409i
$549$	1.13726e8	−	1.45045e8i	0.687293	−	0.876567i
$550$	−7.18983e7	+	5.64896e7i	−0.432146	+	0.339532i
$551$	−1.06040e8			−0.633891
$552$	−1.61952e8	−	5.31480e7i	−0.962872	−	0.315987i
$553$	−3.20938e7	−	3.20938e7i	−0.189778	−	0.189778i
$554$	−8.40976e7	+	2.29966e7i	−0.494600	+	0.135249i
$555$	4.53923e6	+	1.70816e7i	0.0265524	+	0.0999192i
$556$	2.90946e7	+	4.92209e7i	0.169273	+	0.286368i
$557$	−1.58306e8	−	1.58306e8i	−0.916079	−	0.916079i	0.0806626	−	0.996741i	$-0.474296\pi$
$557$	−1.58306e8	−	1.58306e8i	−0.916079	−	0.916079i	−0.996741	+	0.0806626i	$0.974296\pi$
$558$	2.30966e7	+	5.66115e7i	0.132937	+	0.325838i
$559$	−3.11038e8			−1.78065
$560$	−9.50120e7	−	7.94250e7i	−0.541021	−	0.452265i
$561$	−2.14026e6	+	6.19837e6i	−0.0121221	+	0.0351066i
$562$	8.01568e7	−	1.40494e8i	0.451577	−	0.791496i
$563$	−2.07881e8	−	2.07881e8i	−1.16490	−	1.16490i	−0.983389	−	0.181513i	$-0.941901\pi$
$563$	−2.07881e8	−	2.07881e8i	−1.16490	−	1.16490i	−0.181513	−	0.983389i	$-0.558099\pi$
$564$	4.00259e7	+	1.96069e8i	0.223102	+	1.09288i
$565$	1.97488e8	+	3.86336e7i	1.09495	+	0.214200i
$566$	6.74478e6	−	1.84437e6i	0.0371979	−	0.0101718i
$567$	−6.65831e7	+	1.09950e8i	−0.365271	+	0.603179i
$568$	2.13270e6	+	1.38666e8i	0.0116382	+	0.756702i
$569$	−1.81731e8			−0.986491			−0.493245	−	0.869890i	$-0.664190\pi$
$569$	−1.81731e8			−0.986491			−0.493245	+	0.869890i	$0.664190\pi$
$570$	2.86464e8	−	1.66562e8i	1.54684	−	0.899395i
$571$		−	1.42563e8i		−	0.765773i	−0.923795	−	0.382886i	$-0.874930\pi$
$571$		−	1.42563e8i		−	0.765773i	0.923795	−	0.382886i	$-0.125070\pi$
$572$	−4.51576e7	+	1.75717e8i	−0.241292	+	0.938914i
$573$	−1.16388e8	−	2.39155e8i	−0.618649	−	1.27121i
$574$	6.20690e7	−	1.69728e7i	0.328200	−	0.0897467i
$575$	−1.77521e8	+	7.48511e7i	−0.933783	+	0.393726i
$576$	1.13234e8	−	1.53943e8i	0.592530	−	0.805548i
$577$	−2.38913e8	+	2.38913e8i	−1.24369	+	1.24369i	−0.285229	+	0.958459i	$0.592070\pi$
$577$	−2.38913e8	+	2.38913e8i	−1.24369	+	1.24369i	−0.958459	+	0.285229i	$0.907930\pi$
$578$	−9.52547e7	+	1.66957e8i	−0.493291	+	0.864610i
$579$	−1.88338e7	+	5.45442e7i	−0.0970293	+	0.281004i
$580$	−2.97373e7	+	6.23979e7i	−0.152411	+	0.319805i
$581$		−	6.51829e7i		−	0.332357i
$582$	−2.17680e8	−	2.48267e8i	−1.10421	−	1.25936i
$583$	6.64549e7	−	6.64549e7i	0.335368	−	0.335368i
$584$	1.91582e8	−	1.97567e8i	0.961871	−	0.991920i
$585$	−2.30904e8	−	2.67200e8i	−1.15335	−	1.33466i
$586$	3.22111e8	−	8.80817e7i	1.60071	−	0.437716i
$587$	7.27394e7	−	7.27394e7i	0.359630	−	0.359630i	−0.504047	−	0.863676i	$-0.668156\pi$
$587$	7.27394e7	−	7.27394e7i	0.359630	−	0.359630i	0.863676	+	0.504047i	$0.168156\pi$
$588$	−8.52673e7	−	5.63561e7i	−0.419421	−	0.277210i
$589$			1.28667e8i			0.629680i
$590$	−2.42496e8	+	1.79142e7i	−1.18073	+	0.0872250i
$591$	1.11172e7	−	3.21962e7i	0.0538558	−	0.155971i
$592$	5.97537e6	+	2.06011e7i	0.0288005	+	0.0992946i
$593$	−1.42062e8	+	1.42062e8i	−0.681263	+	0.681263i	−0.960285	−	0.279022i	$-0.909990\pi$
$593$	−1.42062e8	+	1.42062e8i	−0.681263	+	0.681263i	0.279022	+	0.960285i	$0.409990\pi$
$594$	8.57921e7	+	7.68549e7i	0.409343	+	0.366701i
$595$	−8.32884e6	+	5.60335e6i	−0.0395397	+	0.0266009i
$596$	3.93023e7	+	6.64898e7i	0.185643	+	0.314063i
$597$	−1.13537e7	−	2.33297e7i	−0.0533598	−	0.109644i
$598$	−1.89435e8	+	3.32031e8i	−0.885844	+	1.55265i
$599$			3.66805e8i			1.70669i	0.521345	+	0.853346i	$0.325430\pi$
$599$			3.66805e8i			1.70669i	−0.521345	+	0.853346i	$0.674570\pi$
$600$	−1.76769e7	−	2.15275e8i	−0.0818373	−	0.996646i
$601$	1.22702e8			0.565232			0.282616	−	0.959233i	$-0.408798\pi$
$601$	1.22702e8			0.565232			0.282616	+	0.959233i	$0.408798\pi$
$602$	1.34889e8	+	7.69587e7i	0.618281	+	0.352751i
$603$	3.13882e8	−	3.79892e7i	1.43158	−	0.173264i
$604$	1.05527e6	−	623775.i	0.00478911	−	0.00283085i
$605$	8.62760e7	+	1.28241e8i	0.389605	+	0.579110i
$606$	1.71256e8	+	1.12421e7i	0.769534	+	0.0505162i
$607$	2.32717e8	+	2.32717e8i	1.04055	+	1.04055i	0.999142	+	0.0414041i	$0.0131831\pi$
$607$	2.32717e8	+	2.32717e8i	1.04055	+	1.04055i	0.0414041	+	0.999142i	$0.486817\pi$
$608$	3.43010e8	−	2.09938e8i	1.52615	−	0.934073i
$609$	1.84162e7	−	5.33346e7i	0.0815356	−	0.236133i
$610$	−1.86269e7	−	2.52144e8i	−0.0820635	−	1.11086i
$611$	4.48796e8			1.96755
$612$	−9.42776e6	−	1.22917e7i	−0.0411296	−	0.0536236i
$613$	9.93741e7	+	9.93741e7i	0.431412	+	0.431412i	0.889108	−	0.457697i	$-0.151325\pi$
$613$	9.93741e7	+	9.93741e7i	0.431412	+	0.431412i	−0.457697	+	0.889108i	$0.651325\pi$
$614$	−8.07460e7	−	2.95285e8i	−0.348832	−	1.27566i
$615$	9.70842e7	+	5.63191e7i	0.417372	+	0.242120i
$616$	6.30605e7	−	6.50305e7i	0.269783	−	0.278211i
$617$	2.80186e8	+	2.80186e8i	1.19286	+	1.19286i	0.976259	+	0.216605i	$0.0694984\pi$
$617$	2.80186e8	+	2.80186e8i	1.19286	+	1.19286i	0.216605	+	0.976259i	$0.430502\pi$
$618$	−1.19676e8	−	1.36493e8i	−0.507041	−	0.578288i
$619$	2.19446e8			0.925244			0.462622	−	0.886556i	$-0.346909\pi$
$619$	2.19446e8			0.925244			0.462622	+	0.886556i	$0.346909\pi$
$620$	7.57122e7	+	3.60825e7i	0.317681	+	0.151399i
$621$	1.31651e8	+	2.03880e8i	0.549729	+	0.851333i
$622$	8.32034e6	+	4.74705e6i	0.0345756	+	0.0197266i
$623$	−8.46231e7	−	8.46231e7i	−0.349965	−	0.349965i
$624$	−2.87478e8	−	3.17876e8i	−1.18318	−	1.30829i
$625$	−1.74804e8	−	1.70435e8i	−0.715999	−	0.698102i
$626$	7.44397e7	+	2.72223e8i	0.303446	+	1.10969i
$627$	1.06068e8	+	2.17950e8i	0.430311	+	0.884207i
$628$	−7.75181e7	−	1.99214e7i	−0.312985	−	0.0804342i
$629$	1.73876e6			0.00698696
$630$	3.40243e7	+	1.73009e8i	0.136072	+	0.691905i
$631$		−	1.63259e8i		−	0.649812i	−0.945746	−	0.324906i	$-0.894667\pi$
$631$		−	1.63259e8i		−	0.649812i	0.945746	−	0.324906i	$-0.105333\pi$
$632$	−1.47752e6	−	9.60671e7i	−0.00585306	−	0.380560i
$633$	2.94170e8	−	1.43161e8i	1.15981	−	0.564436i
$634$	8.37530e7	+	3.06281e8i	0.328649	+	1.20186i
$635$	−7.71773e7	+	3.94516e8i	−0.301417	+	1.54079i
$636$	4.44065e7	+	2.17528e8i	0.172614	+	0.845560i
$637$	−1.62086e8	+	1.62086e8i	−0.627085	+	0.627085i
$638$	−4.39164e7	−	2.50559e7i	−0.169108	−	0.0964822i
$639$	1.21837e8	−	1.55390e8i	0.466957	−	0.595553i
$640$	−2.73437e7	−	2.60714e8i	−0.104308	−	0.994545i
$641$		−	2.85761e8i		−	1.08500i	−0.840056	−	0.542500i	$-0.817478\pi$
$641$		−	2.85761e8i		−	1.08500i	0.840056	−	0.542500i	$-0.182522\pi$
$642$	3.25632e8	+	3.71388e8i	1.23061	+	1.40353i
$643$	−2.81315e8	+	2.81315e8i	−1.05818	+	1.05818i	−0.0599809	+	0.998200i	$0.519104\pi$
$643$	−2.81315e8	+	2.81315e8i	−1.05818	+	1.05818i	−0.998200	+	0.0599809i	$0.980896\pi$
$644$	1.64306e8	−	9.71214e7i	0.615169	−	0.363628i
$645$	6.95677e7	+	2.61790e8i	0.259256	+	0.975605i
$646$	−8.59855e6	−	3.14445e7i	−0.0318954	−	0.116640i
$647$	−1.55110e8	+	1.55110e8i	−0.572698	+	0.572698i	−0.932882	−	0.360183i	$-0.882714\pi$
$647$	−1.55110e8	+	1.55110e8i	−0.572698	+	0.572698i	0.360183	+	0.932882i	$0.382714\pi$
$648$	−2.63212e8	+	6.89691e7i	−0.967343	+	0.253472i
$649$		−	1.77865e8i		−	0.650665i
$650$	−4.80974e8	−	5.77250e7i	−1.75139	−	0.210196i
$651$	−6.47150e7	−	2.23458e7i	−0.234564	−	0.0809939i
$652$	−4.15713e7	−	1.06834e7i	−0.149986	−	0.0385450i
$653$	−6.80229e7	+	6.80229e7i	−0.244295	+	0.244295i	−0.818625	−	0.574329i	$-0.805263\pi$
$653$	−6.80229e7	+	6.80229e7i	−0.244295	+	0.244295i	0.574329	+	0.818625i	$0.305263\pi$
$654$	−9.53399e7	−	6.25861e6i	−0.340833	−	0.0223740i
$655$	1.48752e8	+	2.21106e8i	0.529346	+	0.786822i
$656$	1.19337e8	+	6.56741e7i	0.422730	+	0.232639i
$657$	−3.89003e8	+	4.70811e7i	−1.37169	+	0.166016i
$658$	−1.94631e8	−	1.11044e8i	−0.683177	−	0.389777i
$659$			3.34310e7i			0.116814i	0.998293	+	0.0584068i	$0.0186021\pi$
$659$			3.34310e7i			0.116814i	−0.998293	+	0.0584068i	$0.981398\pi$
$660$	1.57995e8	−	1.29383e6i	0.549556	−	0.00450033i
$661$	−1.05178e8			−0.364182			−0.182091	−	0.983282i	$-0.558287\pi$
$661$	−1.05178e8			−0.364182			−0.182091	+	0.983282i	$0.558287\pi$
$662$	8.46820e7	−	1.48425e8i	0.291889	−	0.511605i
$663$	−3.12387e7	+	1.52027e7i	−0.107189	+	0.0521652i
$664$	9.60562e7	−	9.90571e7i	0.328111	−	0.338362i
$665$	−7.12371e7	+	3.64151e8i	−0.242237	+	1.23827i
$666$	1.18379e7	−	2.81539e7i	0.0400729	−	0.0953050i
$667$	−7.53306e7	−	7.53306e7i	−0.253860	−	0.253860i
$668$	−1.82785e8	−	4.69741e7i	−0.613214	−	0.157590i
$669$	9.82136e7	+	3.39126e7i	0.328015	+	0.113262i
$670$	2.83250e8	−	3.28438e8i	0.941771	−	1.09201i
$671$	1.84941e8			0.612163
$672$	4.60208e7	+	2.08983e8i	0.151651	+	0.688658i
$673$	9.72124e7	+	9.72124e7i	0.318916	+	0.318916i	0.848351	−	0.529435i	$-0.177596\pi$
$673$	9.72124e7	+	9.72124e7i	0.318916	+	0.318916i	−0.529435	+	0.848351i	$0.677596\pi$
$674$	2.00453e8	−	5.48141e7i	0.654686	−	0.179025i
$675$	−1.73249e8	+	2.54106e8i	−0.563324	+	0.826236i
$676$	−5.61523e8	+	3.31917e8i	−1.81772	+	1.07446i
$677$	−3.20572e8	−	3.20572e8i	−1.03314	−	1.03314i	−0.999432	−	0.0337102i	$-0.989268\pi$
$677$	−3.20572e8	−	3.20572e8i	−1.03314	−	1.03314i	−0.0337102	−	0.999432i	$-0.510732\pi$
$678$	−2.29246e8	−	2.61459e8i	−0.735551	−	0.838907i
$679$	3.69728e8			1.18106
$680$	−2.09145e7	−	3.75843e6i	−0.0665151	−	0.0119531i
$681$	1.86769e8	+	6.44905e7i	0.591377	+	0.204199i
$682$	−3.04022e7	+	5.32872e7i	−0.0958412	+	0.167985i
$683$	3.43288e7	+	3.43288e7i	0.107745	+	0.107745i	0.758924	−	0.651179i	$-0.225725\pi$
$683$	3.43288e7	+	3.43288e7i	0.107745	+	0.107745i	−0.651179	+	0.758924i	$0.725725\pi$
$684$	−5.67688e8	−	7.48547e7i	−1.77395	−	0.233911i
$685$	−5.12515e7	+	2.61988e8i	−0.159454	+	0.815098i
$686$	3.29980e8	−	9.02333e7i	1.02215	−	0.279508i
$687$	3.02838e7	−	1.47380e7i	0.0933986	−	0.0454537i
$688$	9.15778e7	+	3.15730e8i	0.281206	+	0.969506i
$689$	4.97915e8			1.52229
$690$	3.21828e8	+	8.51781e7i	0.979664	+	0.259287i
$691$		−	9.71208e7i		−	0.294359i	−0.989110	−	0.147180i	$-0.952980\pi$
$691$		−	9.71208e7i		−	0.294359i	0.989110	−	0.147180i	$-0.0470196\pi$
$692$	−5.13137e7	−	1.31871e7i	−0.154851	−	0.0397953i
$693$	−1.28043e8	+	1.54970e7i	−0.384729	+	0.0465638i
$694$	1.41178e8	−	3.86054e7i	0.422367	−	0.115497i
$695$	−6.23360e7	−	9.26564e7i	−0.185688	−	0.276008i
$696$	1.06583e8	−	5.39126e7i	0.316125	−	0.159905i
$697$	7.80758e6	−	7.80758e6i	0.0230578	−	0.0230578i
$698$	1.55939e8	−	2.73321e8i	0.458553	−	0.803724i
$699$	−3.46083e8	−	1.19501e8i	−1.01333	−	0.349896i
$700$	1.94303e8	+	1.44039e8i	0.566480	+	0.419939i
$701$		−	4.39602e8i		−	1.27616i	−0.769969	−	0.638081i	$-0.779728\pi$
$701$		−	4.39602e8i		−	1.27616i	0.769969	−	0.638081i	$-0.220272\pi$
$702$	3.34810e7	+	6.09318e8i	0.0967805	+	1.76130i
$703$	4.54466e7	−	4.54466e7i	0.130808	−	0.130808i
$704$	1.91663e8	−	5.89700e6i	0.549314	−	0.0169010i
$705$	−1.00379e8	−	3.77736e8i	−0.286468	−	1.07801i
$706$	4.42844e7	−	1.21096e7i	0.125845	−	0.0344125i
$707$	−1.35891e8	+	1.35891e8i	−0.384532	+	0.384532i
$708$	3.50532e8	+	2.31679e8i	0.987706	+	0.652809i
$709$		−	2.18951e8i		−	0.614338i	−0.951655	−	0.307169i	$-0.900618\pi$
$709$		−	2.18951e8i		−	0.614338i	0.951655	−	0.307169i	$-0.0993817\pi$
$710$	−1.99554e7	−	2.70128e8i	−0.0557553	−	0.754735i
$711$	−8.44082e7	+	1.07653e8i	−0.234842	+	0.299515i
$712$	−3.89584e6	−	2.53304e8i	−0.0107935	−	0.701781i
$713$	−9.14045e7	+	9.14045e7i	−0.252173	+	0.252173i
$714$	1.73089e7	+	1.13625e6i	0.0475526	+	0.00312160i
$715$	6.80302e7	−	3.47758e8i	0.186116	−	0.951390i
$716$	−3.25067e8	+	1.92148e8i	−0.885592	+	0.523475i
$717$	−1.45978e7	+	7.10422e6i	−0.0396032	+	0.0192734i
$718$	1.31092e8	−	2.29771e8i	0.354164	−	0.620757i
$719$		−	5.13451e8i		−	1.38138i	−0.723153	−	0.690688i	$-0.757308\pi$
$719$		−	5.13451e8i		−	1.38138i	0.723153	−	0.690688i	$-0.242692\pi$
$720$	−2.03247e8	+	3.13057e8i	−0.544535	+	0.838738i
$721$	2.03269e8			0.542333
$722$	−7.19718e8	−	4.10624e8i	−1.91228	−	1.09102i
$723$	−1.48901e8	−	3.05964e8i	−0.393988	−	0.809571i
$724$	−1.62714e8	−	2.75272e8i	−0.428754	−	0.725347i
$725$	5.08732e7	−	1.25051e8i	0.133498	−	0.328151i
$726$	1.74950e7	−	2.66509e8i	0.0457199	−	0.696469i
$727$	6.55038e7	+	6.55038e7i	0.170476	+	0.170476i	0.787188	−	0.616713i	$-0.211536\pi$
$727$	6.55038e7	+	6.55038e7i	0.170476	+	0.170476i	−0.616713	+	0.787188i	$0.711536\pi$
$728$	4.79862e8	−	7.38033e6i	1.24372	−	0.0191285i
$729$	3.53104e8	+	1.59411e8i	0.911424	+	0.411469i
$730$	−3.51040e8	+	4.07042e8i	−0.902377	+	1.04634i
$731$	2.66480e7			0.0682202
$732$	−2.40896e8	+	3.64477e8i	−0.614180	+	0.929260i
$733$	−2.37813e8	−	2.37813e8i	−0.603841	−	0.603841i	0.337488	−	0.941330i	$-0.390423\pi$
$733$	−2.37813e8	−	2.37813e8i	−0.603841	−	0.603841i	−0.941330	+	0.337488i	$0.890423\pi$
$734$	1.92113e8	+	7.02549e8i	0.485812	+	1.77659i
$735$	1.72674e8	+	1.00169e8i	0.434876	+	0.252274i
$736$	3.92814e8	+	9.45341e7i	0.985265	+	0.237113i
$737$	2.24329e8	+	2.24329e8i	0.560381	+	0.560381i
$738$	−7.32639e7	−	1.79576e8i	−0.182273	−	0.446764i
$739$	−4.75986e8			−1.17940			−0.589699	−	0.807623i	$-0.700754\pi$
$739$	−4.75986e8			−1.17940			−0.589699	+	0.807623i	$0.700754\pi$
$740$	−1.39977e7	−	3.94873e7i	−0.0345431	−	0.0974456i
$741$	−4.19138e8	+	1.21386e9i	−1.03015	+	2.98341i
$742$	−2.15932e8	−	1.23197e8i	−0.528573	−	0.301570i
$743$	−2.53767e7	−	2.53767e7i	−0.0618683	−	0.0618683i	0.675496	−	0.737364i	$-0.263930\pi$
$743$	−2.53767e7	−	2.53767e7i	−0.0618683	−	0.0618683i	−0.737364	+	0.675496i	$0.763930\pi$
$744$	−6.54164e7	−	1.29325e8i	−0.158843	−	0.314025i
$745$	−8.42062e7	−	1.25164e8i	−0.203646	−	0.302700i
$746$	1.91750e7	+	7.01221e7i	0.0461868	+	0.168903i
$747$	−1.95040e8	+	2.36057e7i	−0.467909	+	0.0566311i
$748$	3.86885e6	−	1.50545e7i	0.00924437	−	0.0359717i
$749$	−5.53084e8			−1.31627
$750$	5.89909e7	+	4.17730e8i	0.139830	+	0.990175i
$751$			9.15189e7i			0.216068i	0.994147	+	0.108034i	$0.0344556\pi$
$751$			9.15189e7i			0.216068i	−0.994147	+	0.108034i	$0.965544\pi$
$752$	−1.32137e8	−	4.55566e8i	−0.310722	−	1.07127i
$753$	−1.84038e8	−	3.78163e8i	−0.431045	−	0.885716i
$754$	−7.06565e7	−	2.58388e8i	−0.164831	−	0.602779i
$755$	−1.98651e6	+	1.33646e6i	−0.00461584	+	0.00310537i
$756$	1.36241e8	−	2.72528e8i	0.315313	−	0.630734i
$757$	5.14807e8	−	5.14807e8i	1.18674	−	1.18674i	0.208780	−	0.977963i	$-0.433051\pi$
$757$	5.14807e8	−	5.14807e8i	1.18674	−	1.18674i	0.977963	−	0.208780i	$-0.0669491\pi$
$758$	−3.52578e8	−	2.01158e8i	−0.809558	−	0.461882i
$759$	−7.94806e7	+	2.30182e8i	−0.181776	+	0.526436i
$760$	−6.44885e8	+	4.48414e8i	−1.46907	+	1.02150i
$761$		−	2.57011e8i		−	0.583173i	−0.956544	−	0.291587i	$-0.905817\pi$
$761$		−	2.57011e8i		−	0.583173i	0.956544	−	0.291587i	$-0.0941831\pi$
$762$	5.22308e8	−	4.57958e8i	1.18049	−	1.03505i
$763$	7.56520e7	−	7.56520e7i	0.170313	−	0.170313i
$764$	3.20808e8	+	5.42728e8i	0.719391	+	1.21703i
$765$	1.97825e7	+	2.28922e7i	0.0441873	+	0.0511333i
$766$	−1.85357e8	−	6.77843e8i	−0.412404	−	1.50814i
$767$	6.66330e8	−	6.66330e8i	1.47674	−	1.47674i
$768$	−2.38029e8	+	3.85405e8i	−0.525469	+	0.850813i
$769$		−	7.29005e8i		−	1.60307i	−0.597950	−	0.801533i	$-0.704018\pi$
$769$		−	7.29005e8i		−	1.60307i	0.597950	−	0.801533i	$-0.295982\pi$
$770$	−1.15547e8	+	1.33980e8i	−0.253096	+	0.293474i
$771$	3.14726e7	−	9.11470e7i	0.0686703	−	0.198874i
$772$	3.40450e7	−	1.32476e8i	0.0739949	−	0.287929i
$773$	2.46547e8	−	2.46547e8i	0.533780	−	0.533780i	−0.387915	−	0.921695i	$-0.626805\pi$
$773$	2.46547e8	−	2.46547e8i	0.533780	−	0.533780i	0.921695	+	0.387915i	$0.126805\pi$
$774$	1.81426e8	−	4.31483e8i	0.391270	−	0.930551i
$775$	−1.51734e8	−	6.17284e7i	−0.325971	−	0.132611i
$776$	5.61868e8	+	5.44847e8i	1.20240	+	1.16597i
$777$	1.49654e7	+	3.07510e7i	0.0319024	+	0.0655535i
$778$	7.75254e8	+	4.42310e8i	1.64629	+	0.939264i
$779$		−	4.08139e8i		−	0.863368i
$780$	5.96738e8	+	5.87044e8i	1.25748	+	1.23705i
$781$	1.98132e8			0.415913
$782$	1.62298e7	−	2.84465e7i	0.0339384	−	0.0594853i
$783$	−1.66257e8	−	3.57898e7i	−0.346333	−	0.0745544i
$784$	2.12253e8	+	1.16808e8i	0.440459	+	0.242396i
$785$	1.53414e8	+	3.00117e7i	0.317144	+	0.0620414i
$786$	3.01640e7	−	4.59500e8i	0.0621185	−	0.946276i
$787$	−3.50599e8	−	3.50599e8i	−0.719261	−	0.719261i	0.249193	−	0.968454i	$-0.419835\pi$
$787$	−3.50599e8	−	3.50599e8i	−0.719261	−	0.719261i	−0.968454	+	0.249193i	$0.919835\pi$
$788$	−2.00960e7	+	7.81975e7i	−0.0410706	+	0.159814i
$789$	−2.76337e8	+	8.00292e8i	−0.562610	+	1.62936i
$790$	1.38250e7	+	1.87143e8i	0.0280404	+	0.379571i
$791$	3.89373e8			0.786749
$792$	−2.17421e8	−	1.65138e8i	−0.437648	−	0.332409i
$793$	6.92839e8	+	6.92839e8i	1.38935	+	1.38935i
$794$	−3.60277e8	+	9.85182e7i	−0.719740	+	0.196814i
$795$	−1.11365e8	−	4.19078e8i	−0.221640	−	0.834052i
$796$	3.12949e7	+	5.29433e7i	0.0620490	+	0.104972i
$797$	−3.65149e7	−	3.65149e7i	−0.0721265	−	0.0721265i	0.670123	−	0.742250i	$-0.266241\pi$
$797$	−3.65149e7	−	3.65149e7i	−0.0721265	−	0.0721265i	−0.742250	+	0.670123i	$0.766241\pi$
$798$	4.82107e8	−	4.22710e8i	0.948714	−	0.831830i
$799$	−3.84504e7			−0.0753807
$800$	8.30157e7	+	5.05225e8i	0.162140	+	0.986768i
$801$	−2.22562e8	+	2.83854e8i	−0.433066	+	0.552329i
$802$	−3.83612e8	+	6.72373e8i	−0.743651	+	1.30343i
$803$	−2.78018e8	−	2.78018e8i	−0.536940	−	0.536940i
$804$	−7.34301e8	+	1.49901e8i	−1.41288	+	0.288428i
$805$	−3.09299e8	+	2.08085e8i	−0.592912	+	0.398891i
$806$	−3.13522e8	+	8.57330e7i	−0.598775	+	0.163736i
$807$	−2.83413e8	−	5.82360e8i	−0.539261	−	1.10808i
$808$	−4.06765e8	+	6.25610e6i	−0.771099	+	0.0118596i
$809$	−3.76127e8			−0.710377			−0.355188	−	0.934795i	$-0.615583\pi$
$809$	−3.76127e8			−0.710377			−0.355188	+	0.934795i	$0.615583\pi$
$810$	5.05353e8	−	1.64462e8i	0.950911	−	0.309464i
$811$			7.62171e7i			0.142886i	0.997445	+	0.0714430i	$0.0227604\pi$
$811$			7.62171e7i			0.142886i	−0.997445	+	0.0714430i	$0.977240\pi$
$812$	−3.32900e7	+	1.29538e8i	−0.0621793	+	0.241952i
$813$	2.91288e8	−	1.41759e8i	0.542064	−	0.263803i
$814$	2.95601e7	−	8.08326e6i	0.0548067	−	0.0149869i
$815$	8.22728e7	+	1.60946e7i	0.151979	+	0.0297309i
$816$	2.46295e7	+	2.72338e7i	0.0453300	+	0.0501231i
$817$	6.96509e8	−	6.96509e8i	1.27721	−	1.27721i
$818$	−5.23596e7	+	9.17727e7i	−0.0956613	+	0.167669i
$819$	−5.37737e8	−	4.21625e8i	−0.978855	−	0.767494i
$820$	−2.40164e8	−	1.14456e8i	−0.435579	−	0.207586i
$821$		−	3.48077e8i		−	0.628994i	−0.949259	−	0.314497i	$-0.898164\pi$
$821$		−	3.48077e8i		−	0.628994i	0.949259	−	0.314497i	$-0.101836\pi$
$822$	3.46852e8	−	3.04119e8i	0.624494	−	0.547555i
$823$	−3.60924e8	+	3.60924e8i	−0.647464	+	0.647464i	−0.952380	−	0.304915i	$-0.901372\pi$
$823$	−3.60924e8	+	3.60924e8i	−0.647464	+	0.647464i	0.304915	+	0.952380i	$0.401372\pi$
$824$	3.08904e8	+	2.99546e8i	0.552131	+	0.535405i
$825$	−3.07911e8	+	2.05218e7i	−0.548358	+	0.0365472i
$826$	−4.53836e8	+	1.24102e8i	−0.805302	+	0.220211i
$827$	−6.06418e8	+	6.06418e8i	−1.07215	+	1.07215i	−0.0749640	+	0.997186i	$0.523884\pi$
$827$	−6.06418e8	+	6.06418e8i	−1.07215	+	1.07215i	−0.997186	+	0.0749640i	$0.976116\pi$
$828$	−3.50108e8	−	4.56462e8i	−0.616753	−	0.804106i
$829$			4.37831e8i			0.768499i	0.923229	+	0.384249i	$0.125540\pi$
$829$			4.37831e8i			0.768499i	−0.923229	+	0.384249i	$0.874460\pi$
$830$	−1.76006e8	+	2.04084e8i	−0.307817	+	0.356924i
$831$	−2.78136e8	−	9.60389e7i	−0.484679	−	0.167357i
$832$	7.40112e8	+	6.95929e8i	1.28507	+	1.20836i
$833$	1.38866e7	−	1.38866e7i	0.0240249	−	0.0240249i
$834$	−1.26405e7	+	1.92557e8i	−0.0217904	+	0.331942i
$835$	3.61746e8	+	7.07668e7i	0.621362	+	0.121554i
$836$	−2.92363e8	−	4.94606e8i	−0.500384	−	0.846526i
$837$	−4.34265e7	+	2.01732e8i	−0.0740591	+	0.344032i
$838$	1.25610e8	−	2.20162e8i	0.213448	−	0.374119i
$839$			4.06074e8i			0.687574i	0.939048	+	0.343787i	$0.111710\pi$
$839$			4.06074e8i			0.687574i	−0.939048	+	0.343787i	$0.888290\pi$
$840$	−1.13539e8	−	4.02233e8i	−0.191561	−	0.678640i
$841$	−5.20170e8			−0.874495
$842$	1.54229e8	+	8.79931e7i	0.258363	+	0.147405i
$843$	4.90870e8	−	2.38888e8i	0.819377	−	0.398760i
$844$	−6.67575e8	+	3.94605e8i	−1.11038	+	0.656350i
$845$	1.05704e9	−	7.11142e8i	1.75196	−	1.17865i
$846$	−2.61779e8	+	6.22585e8i	−0.432338	+	1.02822i
$847$	2.11474e8	+	2.11474e8i	0.348022	+	0.348022i
$848$	−1.46599e8	−	5.05426e8i	−0.240405	−	0.828838i
$849$	2.23070e7	+	7.70249e6i	0.0364517	+	0.0125866i
$850$	4.12072e7	+	4.94556e6i	0.0670991	+	0.00805302i
$851$	6.45704e7			0.104772
$852$	−2.58077e8	+	3.90473e8i	−0.417283	+	0.631354i
$853$	−893597.	−	893597.i	−0.00143977	−	0.00143977i	0.706387	−	0.707826i	$-0.250324\pi$
$853$	−893597.	−	893597.i	−0.00143977	−	0.00143977i	−0.707826	+	0.706387i	$0.750324\pi$
$854$	−1.29039e8	−	4.71891e8i	−0.207180	−	0.757649i
$855$	1.11541e9	+	8.12795e7i	1.78457	+	0.130042i
$856$	−8.40509e8	−	8.15047e8i	−1.34005	−	1.29945i
$857$	3.17205e8	+	3.17205e8i	0.503961	+	0.503961i	0.912666	−	0.408705i	$-0.134020\pi$
$857$	3.17205e8	+	3.17205e8i	0.503961	+	0.503961i	−0.408705	+	0.912666i	$0.634020\pi$
$858$	−4.60404e8	+	4.03681e8i	−0.728916	+	0.639111i
$859$	4.89908e8			0.772920			0.386460	−	0.922306i	$-0.373698\pi$
$859$	4.89908e8			0.772920			0.386460	+	0.922306i	$0.373698\pi$
$860$	−2.14527e8	−	6.05177e8i	−0.337277	−	0.951453i
$861$	2.05281e8	+	7.08823e7i	0.321617	+	0.111053i
$862$	5.78577e8	+	3.30098e8i	0.903315	+	0.515373i
$863$	1.48264e8	+	1.48264e8i	0.230676	+	0.230676i	0.812975	−	0.582299i	$-0.197847\pi$
$863$	1.48264e8	+	1.48264e8i	0.230676	+	0.230676i	−0.582299	+	0.812975i	$0.697847\pi$
$864$	6.08651e8	−	2.13385e8i	0.943685	−	0.330844i
$865$	1.01554e8	+	1.98665e7i	0.156909	+	0.0306954i
$866$	6.21474e7	+	2.27271e8i	0.0956906	+	0.349937i
$867$	−5.83327e8	+	2.83884e8i	−0.895066	+	0.435596i
$868$	1.57179e8	+	4.03933e7i	0.240344	+	0.0617662i
$869$	−1.37265e8			−0.209171
$870$	−2.01673e8	+	1.17261e8i	−0.306260	+	0.178072i
$871$			1.68079e9i			2.54366i
$872$	2.26450e8	−	3.48283e6i	0.341526	−	0.00525271i
$873$	−1.33895e8	−	1.10630e9i	−0.201244	−	1.66276i
$874$	−3.19315e8	−	1.16772e9i	−0.478283	−	1.74906i
$875$	−3.95260e8	−	2.58712e8i	−0.590010	−	0.386182i
$876$	9.10041e8	−	1.85777e8i	1.35378	−	0.276363i
$877$	4.32703e8	−	4.32703e8i	0.641492	−	0.641492i	−0.309430	−	0.950922i	$-0.600138\pi$
$877$	4.32703e8	−	4.32703e8i	0.641492	−	0.641492i	0.950922	+	0.309430i	$0.100138\pi$
$878$	9.33873e8	+	5.32807e8i	1.37976	+	0.787203i
$879$	1.06532e9	+	3.67849e8i	1.56860	+	0.541630i
$880$	−3.73033e8	+	3.33326e7i	−0.547393	+	0.0489127i
$881$			4.92215e8i			0.719825i	0.932986	+	0.359912i	$0.117193\pi$
$881$			4.92215e8i			0.719825i	−0.932986	+	0.359912i	$0.882807\pi$
$882$	−1.30308e8	−	3.19394e8i	−0.189917	−	0.465501i
$883$	−4.90927e8	+	4.90927e8i	−0.713074	+	0.713074i	−0.967177	−	0.254103i	$-0.918220\pi$
$883$	−4.90927e8	+	4.90927e8i	−0.713074	+	0.713074i	0.254103	+	0.967177i	$0.418220\pi$
$884$	7.08917e7	−	4.19042e7i	0.102622	−	0.0606598i
$885$	−7.09860e8	−	4.11794e8i	−1.02410	−	0.594087i
$886$	1.77247e7	+	6.48184e7i	0.0254845	+	0.0931960i
$887$	1.71762e8	−	1.71762e8i	0.246125	−	0.246125i	−0.573253	−	0.819378i	$-0.694319\pi$
$887$	1.71762e8	−	1.71762e8i	0.246125	−	0.246125i	0.819378	+	0.573253i	$0.194319\pi$
$888$	−2.25733e7	+	6.87851e7i	−0.0322372	+	0.0982326i
$889$			7.77839e8i			1.10709i
$890$	3.64530e7	+	4.93448e8i	0.0517086	+	0.699957i
$891$	9.27401e7	+	3.77516e8i	0.131110	+	0.533706i
$892$	−2.38539e8	−	6.13022e7i	−0.336097	−	0.0863737i
$893$	−1.00499e9	+	1.00499e9i	−1.41126	+	1.41126i
$894$	−1.70753e7	+	2.60115e8i	−0.0238977	+	0.364043i
$895$	6.11926e8	−	4.11682e8i	0.853551	−	0.574239i
$896$	−1.48776e8	−	4.84927e8i	−0.206827	−	0.674144i
$897$	−1.16008e9	+	5.64566e8i	−1.60735	+	0.782236i
$898$	1.10856e9	+	6.32475e8i	1.53085	+	0.873402i
$899$		−	9.05825e7i		−	0.124671i
$900$	3.60626e8	−	6.33553e8i	0.494686	−	0.869072i
$901$	−4.26586e7			−0.0583220
$902$	9.64380e7	−	1.69031e8i	0.131410	−	0.230328i
$903$	2.29357e8	+	4.71285e8i	0.311493	+	0.640060i
$904$	5.91722e8	+	5.73796e8i	0.800962	+	0.776698i
$905$	3.48619e8	+	5.18188e8i	0.470332	+	0.699104i
$906$	4.12835e6	+	271006.i	0.00555126	+	0.000364414i
$907$	−5.67891e8	−	5.67891e8i	−0.761102	−	0.761102i	0.215419	−	0.976522i	$-0.430888\pi$
$907$	−5.67891e8	−	5.67891e8i	−0.761102	−	0.761102i	−0.976522	+	0.215419i	$0.930888\pi$
$908$	−4.53622e8	−	1.16576e8i	−0.605949	−	0.155723i
$909$	4.55824e8	+	3.57400e8i	0.606884	+	0.475842i
$910$	−9.34794e8	+	6.90570e7i	−1.24049	+	0.0916397i
$911$	−6.19176e8			−0.818953			−0.409476	−	0.912321i	$-0.634289\pi$
$911$	−6.19176e8			−0.818953			−0.409476	+	0.912321i	$0.634289\pi$
$912$	1.35557e9	+	6.80693e7i	1.78706	+	0.0897360i
$913$	−1.39393e8	−	1.39393e8i	−0.183160	−	0.183160i
$914$	8.42946e8	−	2.30505e8i	1.10398	−	0.301885i
$915$	4.28176e8	−	7.38101e8i	0.558932	−	0.963502i
$916$	−6.87248e7	+	4.06234e7i	−0.0894184	+	0.0528554i
$917$	3.64612e8	+	3.64612e8i	0.472849	+	0.472849i
$918$	−2.86847e6	−	5.22030e7i	−0.00370785	−	0.0674788i
$919$	1.35264e9			1.74276			0.871378	−	0.490613i	$-0.163227\pi$
$919$	1.35264e9			1.74276			0.871378	+	0.490613i	$0.163227\pi$
$920$	−7.76678e8	−	1.39573e8i	−0.997418	−	0.179241i
$921$	3.37213e8	−	9.76595e8i	0.431644	−	1.25007i
$922$	−2.45818e8	+	4.30854e8i	−0.313632	+	0.549715i
$923$	7.42255e8	+	7.42255e8i	0.943948	+	0.943948i
$924$	2.99545e8	−	6.11496e7i	0.379705	−	0.0775136i
$925$	3.17912e7	+	7.53977e7i	0.0401681	+	0.0952649i
$926$	−1.34791e9	+	3.68589e8i	−1.69758	+	0.464204i
$927$	−7.36131e7	−	6.08221e8i	−0.0924094	−	0.763523i
$928$	−2.41482e8	+	1.47799e8i	−0.302163	+	0.184938i
$929$	−1.14367e9			−1.42644			−0.713220	−	0.700940i	$-0.752764\pi$
$929$	−1.14367e9			−1.42644			−0.713220	+	0.700940i	$0.752764\pi$
$930$	1.42282e8	+	2.44706e8i	0.176889	+	0.304225i
$931$		−	7.25918e8i		−	0.899578i
$932$	8.40560e8	+	2.16016e8i	1.03830	+	0.266832i
$933$	1.41474e7	+	2.90703e7i	0.0174194	+	0.0357935i
$934$	−5.58123e8	+	1.52619e8i	−0.684998	+	0.187314i
$935$	−5.82845e6	+	2.97939e7i	−0.00713047	+	0.0364496i
$936$	−1.95863e8	−	1.43317e9i	−0.238850	−	1.74771i
$937$	−3.22244e8	+	3.22244e8i	−0.391711	+	0.391711i	−0.875297	−	0.483586i	$-0.839334\pi$
$937$	−3.22244e8	+	3.22244e8i	−0.391711	+	0.391711i	0.483586	+	0.875297i	$0.339334\pi$
$938$	4.15870e8	−	7.28913e8i	0.503906	−	0.883216i
$939$	−3.10877e8	+	9.00323e8i	−0.375484	+	1.08743i
$940$	3.09540e8	+	8.73209e8i	0.372678	+	1.05132i
$941$		−	2.41565e8i		−	0.289911i	−0.989438	−	0.144956i	$-0.953696\pi$
$941$		−	2.41565e8i		−	0.289911i	0.989438	−	0.144956i	$-0.0463040\pi$
$942$	−1.78085e8	−	2.03109e8i	−0.213047	−	0.242983i
$943$	2.89942e8	−	2.89942e8i	0.345760	−	0.345760i
$944$	−8.72566e8	−	4.80196e8i	−1.03725	−	0.570824i
$945$	−2.34596e8	+	5.46897e8i	−0.277987	+	0.648052i
$946$	4.53035e8	−	1.23883e8i	0.535129	−	0.146332i
$947$	−4.37064e8	+	4.37064e8i	−0.514630	+	0.514630i	−0.915942	−	0.401312i	$-0.868554\pi$
$947$	−4.37064e8	+	4.37064e8i	−0.514630	+	0.514630i	0.401312	+	0.915942i	$0.368554\pi$
$948$	1.78795e8	−	2.70518e8i	0.209860	−	0.317520i
$949$		−	2.08305e9i		−	2.43726i
$950$	1.20631e9	−	9.47784e8i	1.40698	−	1.10545i
$951$	−3.49771e8	+	1.01296e9i	−0.406670	+	1.17775i
$952$	−4.11119e7	+	632306.i	−0.0476494	+	0.000732853i
$953$	−1.06835e9	+	1.06835e9i	−1.23434	+	1.23434i	−0.272054	+	0.962282i	$0.587703\pi$
$953$	−1.06835e9	+	1.06835e9i	−1.23434	+	1.23434i	−0.962282	+	0.272054i	$0.912297\pi$
$954$	−2.90429e8	+	6.90725e8i	−0.334500	+	0.795536i
$955$	−6.87340e8	−	1.02166e9i	−0.789153	−	1.17300i
$956$	3.31276e7	−	1.95818e7i	0.0379155	−	0.0224119i
$957$	−7.46730e7	−	1.53439e8i	−0.0851977	−	0.175065i
$958$	−6.87606e8	+	1.20519e9i	−0.782065	+	1.37076i
$959$			5.16544e8i			0.585667i
$960$	4.20203e8	−	7.78580e8i	0.474948	−	0.880014i
$961$	7.77593e8			0.876157
$962$	1.41022e8	+	8.04580e7i	0.158402	+	0.0903741i
$963$	2.00297e8	+	1.65493e9i	0.224282	+	1.85311i
$964$	4.10426e8	+	6.94340e8i	0.458146	+	0.775071i
$965$	−5.12890e7	+	2.62180e8i	−0.0570746	+	0.291754i
$966$	6.42781e8	+	4.21955e7i	0.713069	+	0.0468096i
$967$	2.57572e8	+	2.57572e8i	0.284852	+	0.284852i	0.835041	−	0.550188i	$-0.185444\pi$
$967$	2.57572e8	+	2.57572e8i	0.284852	+	0.284852i	−0.550188	+	0.835041i	$0.685444\pi$
$968$	9.73576e6	+	6.33010e8i	0.0107336	+	0.697886i
$969$	3.59094e7	−	1.03996e8i	0.0394673	−	0.114300i
$970$	−1.15760e9	−	9.98333e8i	−1.26836	−	1.09386i
$971$	−4.31301e8			−0.471110			−0.235555	−	0.971861i	$-0.575691\pi$
$971$	−4.31301e8			−0.471110			−0.235555	+	0.971861i	$0.575691\pi$
$972$	−8.64796e8	−	3.08964e8i	−0.941705	−	0.336441i
$973$	−1.52794e8	−	1.52794e8i	−0.165870	−	0.165870i
$974$	−2.00843e8	−	7.34475e8i	−0.217360	−	0.794877i
$975$	−1.23040e9	−	1.07664e9i	−1.32749	−	1.16160i
$976$	4.99300e8	−	9.07280e8i	0.537047	−	0.975870i
$977$	−8.78779e7	−	8.78779e7i	−0.0942315	−	0.0942315i	0.658420	−	0.752651i	$-0.271225\pi$
$977$	−8.78779e7	−	8.78779e7i	−0.0942315	−	0.0942315i	−0.752651	+	0.658420i	$0.771225\pi$
$978$	−9.55033e7	−	1.08923e8i	−0.102094	−	0.116440i
$979$	−3.61932e8			−0.385726
$980$	−4.27157e8	−	2.03572e8i	−0.453847	−	0.216292i
$981$	−2.53762e8	−	1.98968e8i	−0.268794	−	0.210754i
$982$	7.29581e8	+	4.16252e8i	0.770440	+	0.439563i
$983$	4.38373e8	+	4.38373e8i	0.461512	+	0.461512i	0.899151	−	0.437639i	$-0.144185\pi$
$983$	4.38373e8	+	4.38373e8i	0.461512	+	0.461512i	−0.437639	+	0.899151i	$0.644185\pi$
$984$	2.07505e8	+	4.10228e8i	0.217793	+	0.430566i
$985$	3.02748e7	−	1.54759e8i	0.0316790	−	0.161937i
$986$	6.05346e6	+	2.21373e7i	0.00631499	+	0.0230937i
$987$	−3.30939e8	−	6.80016e8i	−0.344188	−	0.707242i
$988$	7.57656e8	−	2.94819e9i	0.785599	−	3.05692i
$989$	9.89598e8			1.02299
$990$	4.42740e8	+	2.97218e8i	0.456292	+	0.306316i
$991$			2.85103e7i			0.0292942i	0.999893	+	0.0146471i	$0.00466248\pi$
$991$			2.85103e7i			0.0292942i	−0.999893	+	0.0146471i	$0.995338\pi$
$992$	1.79335e8	+	2.93010e8i	0.183709	+	0.300156i
$993$	5.18581e8	−	2.52374e8i	0.529626	−	0.257749i
$994$	−1.38243e8	−	5.05548e8i	−0.140761	−	0.514759i
$995$	−6.70502e7	−	9.96637e7i	−0.0680661	−	0.101174i
$996$	4.56280e8	−	9.31456e7i	0.461799	−	0.0942723i
$997$	−2.85361e8	+	2.85361e8i	−0.287944	+	0.287944i	−0.836267	−	0.548323i	$-0.815267\pi$
$997$	−2.85361e8	+	2.85361e8i	−0.287944	+	0.287944i	0.548323	+	0.836267i	$0.315267\pi$
$998$	−8.45244e7	−	4.82241e7i	−0.0850335	−	0.0485146i
$999$	8.65931e7	−	5.59155e7i	0.0868534	−	0.0560836i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.l.a.23.12	✓	136
3.2	odd	2	inner	60.7.l.a.23.57	yes	136
4.3	odd	2	inner	60.7.l.a.23.23	yes	136
5.2	odd	4	inner	60.7.l.a.47.46	yes	136
12.11	even	2	inner	60.7.l.a.23.46	yes	136
15.2	even	4	inner	60.7.l.a.47.23	yes	136
20.7	even	4	inner	60.7.l.a.47.57	yes	136
60.47	odd	4	inner	60.7.l.a.47.12	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.l.a.23.12	✓	136	1.1	even	1	trivial
60.7.l.a.23.23	yes	136	4.3	odd	2	inner
60.7.l.a.23.46	yes	136	12.11	even	2	inner
60.7.l.a.23.57	yes	136	3.2	odd	2	inner
60.7.l.a.47.12	yes	136	60.47	odd	4	inner
60.7.l.a.47.23	yes	136	15.2	even	4	inner
60.7.l.a.47.46	yes	136	5.2	odd	4	inner
60.7.l.a.47.57	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)

\(f(q)\)	\(=\)	\(q+(-6.94862 - 3.96443i) q^{2} +(-11.8150 - 24.2777i) q^{3} +(32.5666 + 55.0946i) q^{4} +(-69.7748 - 103.713i) q^{5} +(-14.1489 + 215.536i) q^{6} +(-171.027 - 171.027i) q^{7} +(-7.87369 - 511.939i) q^{8} +(-449.810 + 573.683i) q^{9} +O(q^{10})\)	\(q+(-6.94862 - 3.96443i) q^{2} +(-11.8150 - 24.2777i) q^{3} +(32.5666 + 55.0946i) q^{4} +(-69.7748 - 103.713i) q^{5} +(-14.1489 + 215.536i) q^{6} +(-171.027 - 171.027i) q^{7} +(-7.87369 - 511.939i) q^{8} +(-449.810 + 573.683i) q^{9} +(73.6732 + 997.282i) q^{10} -731.483 q^{11} +(952.794 - 1441.59i) q^{12} +(-2740.33 - 2740.33i) q^{13} +(510.377 + 1866.43i) q^{14} +(-1693.53 + 2919.35i) q^{15} +(-1974.84 + 3588.49i) q^{16} +(234.776 + 234.776i) q^{17} +(5399.88 - 2203.07i) q^{18} +12272.9 q^{19} +(3441.73 - 7221.81i) q^{20} +(-2131.45 + 6172.84i) q^{21} +(5082.80 + 2899.91i) q^{22} +(8718.61 + 8718.61i) q^{23} +(-12335.7 + 6239.74i) q^{24} +(-5887.96 + 14473.2i) q^{25} +(8177.64 + 29905.3i) q^{26} +(19242.2 + 4142.23i) q^{27} +(3852.92 - 14992.5i) q^{28} -8640.21 q^{29} +(23341.2 - 13571.5i) q^{30} +10483.8i q^{31} +(27948.7 - 17105.9i) q^{32} +(8642.50 + 17758.7i) q^{33} +(-700.615 - 2562.12i) q^{34} +(-5804.45 + 29671.2i) q^{35} +(-46255.6 - 6099.21i) q^{36} +(3703.02 - 3703.02i) q^{37} +(-85279.4 - 48654.9i) q^{38} +(-34151.6 + 98905.8i) q^{39} +(-52545.6 + 36537.1i) q^{40} -33255.5i q^{41} +(39282.4 - 34442.7i) q^{42} +(56752.0 - 56752.0i) q^{43} +(-23821.9 - 40300.8i) q^{44} +(90884.0 + 6622.70i) q^{45} +(-26018.0 - 95146.7i) q^{46} +(-81887.4 + 81887.4i) q^{47} +(110453. + 5546.33i) q^{48} -59148.3i q^{49} +(98291.1 - 77226.1i) q^{50} +(2925.92 - 8473.70i) q^{51} +(61734.3 - 240220. i) q^{52} +(-90849.6 + 90849.6i) q^{53} +(-117285. - 105067. i) q^{54} +(51039.1 + 75864.6i) q^{55} +(-86209.0 + 88902.3i) q^{56} +(-145004. - 297956. i) q^{57} +(60037.5 + 34253.5i) q^{58} +243157. i q^{59} +(-215993. + 1768.77i) q^{60} -252831. q^{61} +(41562.4 - 72848.2i) q^{62} +(175045. - 21185.8i) q^{63} +(-262020. + 8061.70i) q^{64} +(-93003.1 + 475414. i) q^{65} +(10349.7 - 157661. i) q^{66} +(-306677. - 306677. i) q^{67} +(-5289.05 + 20580.7i) q^{68} +(108657. - 314678. i) q^{69} +(157962. - 183163. i) q^{70} -270864. q^{71} +(297233. + 225758. i) q^{72} +(380074. + 380074. i) q^{73} +(-40411.3 + 11050.5i) q^{74} +(420941. - 28055.1i) q^{75} +(399685. + 676168. i) q^{76} +(125104. + 125104. i) q^{77} +(629412. - 551867. i) q^{78} +187653. q^{79} +(509968. - 45568.5i) q^{80} +(-126784. - 516096. i) q^{81} +(-131839. + 231079. i) q^{82} +(190563. + 190563. i) q^{83} +(-409504. + 83596.8i) q^{84} +(7967.99 - 40730.9i) q^{85} +(-619338. + 169359. i) q^{86} +(102084. + 209764. i) q^{87} +(5759.47 + 374475. i) q^{88} +494793. q^{89} +(-605263. - 406322. i) q^{90} +937342. i q^{91} +(-196414. + 764284. i) q^{92} +(254523. - 123867. i) q^{93} +(893641. - 244367. i) q^{94} +(-856336. - 1.27286e6i) q^{95} +(-745506. - 476422. i) q^{96} +(-1.08090e6 + 1.08090e6i) q^{97} +(-234489. + 410999. i) q^{98} +(329028. - 419640. 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