LMFDB - Embedded newform 48.7.i.a.5.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,7,Mod(5,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("48.5");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	48.i (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:	$11.0425960138$
Analytic rank:	$0$
Dimension:	$92$
Relative dimension:	$46$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.19
Character	$\chi$	$=$	48.5
Dual form			48.7.i.a.29.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.70919 + 7.52730i) q^{2} +(12.2138 + 24.0795i) q^{3} +(-49.3206 - 40.7857i) q^{4} +(-131.879 + 131.879i) q^{5} +(-214.343 + 26.7009i) q^{6} -543.561i q^{7} +(440.625 - 260.755i) q^{8} +(-430.647 + 588.204i) q^{9} +O(q^{10})$	\(q+(-2.70919 + 7.52730i) q^{2} +(12.2138 + 24.0795i) q^{3} +(-49.3206 - 40.7857i) q^{4} +(-131.879 + 131.879i) q^{5} +(-214.343 + 26.7009i) q^{6} -543.561i q^{7} +(440.625 - 260.755i) q^{8} +(-430.647 + 588.204i) q^{9} +(-635.408 - 1349.98i) q^{10} +(200.967 - 200.967i) q^{11} +(379.710 - 1685.77i) q^{12} +(-1884.89 + 1884.89i) q^{13} +(4091.55 + 1472.61i) q^{14} +(-4786.32 - 1564.84i) q^{15} +(769.049 + 4023.16i) q^{16} -3075.59i q^{17} +(-3260.89 - 4835.17i) q^{18} +(7390.56 - 7390.56i) q^{19} +(11883.1 - 1125.57i) q^{20} +(13088.7 - 6638.93i) q^{21} +(968.282 + 2057.20i) q^{22} -6658.13 q^{23} +(11660.6 + 7425.24i) q^{24} -19159.1i q^{25} +(-9081.62 - 19294.7i) q^{26} +(-19423.5 - 3185.59i) q^{27} +(-22169.5 + 26808.8i) q^{28} +(2663.15 + 2663.15i) q^{29} +(24746.1 - 31788.7i) q^{30} -41065.4 q^{31} +(-32367.0 - 5110.60i) q^{32} +(7293.75 + 2384.62i) q^{33} +(23150.9 + 8332.36i) q^{34} +(71684.2 + 71684.2i) q^{35} +(45230.1 - 11446.3i) q^{36} +(-28503.0 - 28503.0i) q^{37} +(35608.6 + 75653.4i) q^{38} +(-68408.9 - 22365.6i) q^{39} +(-23721.1 + 92497.3i) q^{40} -71523.3 q^{41} +(14513.6 + 116509. i) q^{42} +(-27.9233 - 27.9233i) q^{43} +(-18108.4 + 1715.23i) q^{44} +(-20778.4 - 134365. i) q^{45} +(18038.1 - 50117.8i) q^{46} -26336.1i q^{47} +(-87482.7 + 67656.3i) q^{48} -177810. q^{49} +(144216. + 51905.5i) q^{50} +(74058.9 - 37564.6i) q^{51} +(169841. - 16087.4i) q^{52} +(-149705. + 149705. i) q^{53} +(76600.8 - 137576. i) q^{54} +53006.6i q^{55} +(-141736. - 239507. i) q^{56} +(268228. + 87694.6i) q^{57} +(-27261.3 + 12831.4i) q^{58} +(-166208. + 166208. i) q^{59} +(172241. + 272393. i) q^{60} +(-134399. + 134399. i) q^{61} +(111254. - 309112. i) q^{62} +(319725. + 234083. i) q^{63} +(126157. - 229791. i) q^{64} -497154. i q^{65} +(-37709.9 + 48441.9i) q^{66} +(194674. - 194674. i) q^{67} +(-125440. + 151690. i) q^{68} +(-81320.9 - 160325. i) q^{69} +(-733795. + 345383. i) q^{70} +458913. q^{71} +(-36376.7 + 371471. i) q^{72} -111317. i q^{73} +(291771. - 137331. i) q^{74} +(461342. - 234005. i) q^{75} +(-665937. + 63077.8i) q^{76} +(-109238. - 109238. i) q^{77} +(353685. - 454342. i) q^{78} -863589. q^{79} +(-631991. - 429148. i) q^{80} +(-160527. - 506617. i) q^{81} +(193770. - 538378. i) q^{82} +(154136. + 154136. i) q^{83} +(-916316. - 206395. i) q^{84} +(405606. + 405606. i) q^{85} +(285.836 - 134.538i) q^{86} +(-31600.2 + 96654.4i) q^{87} +(36147.9 - 140954. i) q^{88} +96376.7 q^{89} +(1.06770e6 + 207614. i) q^{90} +(1.02455e6 + 1.02455e6i) q^{91} +(328383. + 271557. i) q^{92} +(-501563. - 988835. i) q^{93} +(198240. + 71349.5i) q^{94} +1.94932e6i q^{95} +(-272263. - 841802. i) q^{96} +729167. q^{97} +(481719. - 1.33843e6i) q^{98} +(31663.7 + 204755. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q - 2 q^{3} - 4 q^{4} + 508 q^{6}+O(q^{10}) $ 92 * q - 2 * q^3 - 4 * q^4 + 508 * q^6	$ 92 q - 2 q^{3} - 4 q^{4} + 508 q^{6} + 1496 q^{10} + 4288 q^{12} - 4 q^{13} - 4 q^{15} + 10352 q^{16} + 10020 q^{18} - 3940 q^{19} + 1456 q^{21} - 42088 q^{22} + 66376 q^{24} - 34322 q^{27} + 27000 q^{28} - 127836 q^{30} - 8 q^{31} - 4 q^{33} + 128424 q^{34} + 172420 q^{36} - 4 q^{37} - 164392 q^{40} + 221560 q^{42} - 195268 q^{43} - 31252 q^{45} + 150712 q^{46} - 188048 q^{48} - 1142884 q^{49} + 385056 q^{51} - 122368 q^{52} + 151912 q^{54} - 181960 q^{58} + 242304 q^{60} - 326500 q^{61} + 470592 q^{63} - 251752 q^{64} + 489172 q^{66} + 1207676 q^{67} - 1460 q^{69} + 346392 q^{70} - 903480 q^{72} + 1413778 q^{75} - 359992 q^{76} + 1478252 q^{78} + 860920 q^{79} - 4 q^{81} - 2412800 q^{82} - 730640 q^{84} + 434496 q^{85} + 1259360 q^{88} - 291792 q^{90} + 2320992 q^{91} - 1176260 q^{93} - 1412496 q^{94} + 1956200 q^{96} - 8 q^{97} - 4048228 q^{99}+O(q^{100}) $ 92 * q - 2 * q^3 - 4 * q^4 + 508 * q^6 + 1496 * q^10 + 4288 * q^12 - 4 * q^13 - 4 * q^15 + 10352 * q^16 + 10020 * q^18 - 3940 * q^19 + 1456 * q^21 - 42088 * q^22 + 66376 * q^24 - 34322 * q^27 + 27000 * q^28 - 127836 * q^30 - 8 * q^31 - 4 * q^33 + 128424 * q^34 + 172420 * q^36 - 4 * q^37 - 164392 * q^40 + 221560 * q^42 - 195268 * q^43 - 31252 * q^45 + 150712 * q^46 - 188048 * q^48 - 1142884 * q^49 + 385056 * q^51 - 122368 * q^52 + 151912 * q^54 - 181960 * q^58 + 242304 * q^60 - 326500 * q^61 + 470592 * q^63 - 251752 * q^64 + 489172 * q^66 + 1207676 * q^67 - 1460 * q^69 + 346392 * q^70 - 903480 * q^72 + 1413778 * q^75 - 359992 * q^76 + 1478252 * q^78 + 860920 * q^79 - 4 * q^81 - 2412800 * q^82 - 730640 * q^84 + 434496 * q^85 + 1259360 * q^88 - 291792 * q^90 + 2320992 * q^91 - 1176260 * q^93 - 1412496 * q^94 + 1956200 * q^96 - 8 * q^97 - 4048228 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−2.70919	+	7.52730i	−0.338648	+	0.940913i
$2$	−2.70919	+	7.52730i	−0.338648	+	0.940913i
$3$	12.2138	+	24.0795i	0.452362	+	0.891834i
$3$	12.2138	+	24.0795i	0.452362	+	0.891834i
$4$	−49.3206	−	40.7857i	−0.770635	−	0.637277i
$5$	−131.879	+	131.879i	−1.05503	+	1.05503i	−0.0566363	+	0.998395i	$0.518038\pi$
$5$	−131.879	+	131.879i	−1.05503	+	1.05503i	−0.998395	+	0.0566363i	$0.981962\pi$
$6$	−214.343	+	26.7009i	−0.992330	+	0.123615i
$7$		−	543.561i		−	1.58473i	−0.610050	−	0.792363i	$-0.708851\pi$
$7$		−	543.561i		−	1.58473i	0.610050	−	0.792363i	$-0.291149\pi$
$8$	440.625	−	260.755i	0.860596	−	0.509288i
$9$	−430.647	+	588.204i	−0.590737	+	0.806864i
$10$	−635.408	−	1349.98i	−0.635408	−	1.34998i
$11$	200.967	−	200.967i	0.150989	−	0.150989i	−0.627570	−	0.778560i	$-0.715951\pi$
$11$	200.967	−	200.967i	0.150989	−	0.150989i	0.778560	+	0.627570i	$0.215951\pi$
$12$	379.710	−	1685.77i	0.219739	−	0.975559i
$13$	−1884.89	+	1884.89i	−0.857938	+	0.857938i	−0.991095	−	0.133157i	$-0.957489\pi$
$13$	−1884.89	+	1884.89i	−0.857938	+	0.857938i	0.133157	+	0.991095i	$0.457489\pi$
$14$	4091.55	+	1472.61i	1.49109	+	0.536665i
$15$	−4786.32	−	1564.84i	−1.41817	−	0.463657i
$16$	769.049	+	4023.16i	0.187756	+	0.982216i
$17$		−	3075.59i		−	0.626012i	−0.949751	−	0.313006i	$-0.898664\pi$
$17$		−	3075.59i		−	0.626012i	0.949751	−	0.313006i	$-0.101336\pi$
$18$	−3260.89	−	4835.17i	−0.559137	−	0.829075i
$19$	7390.56	−	7390.56i	1.07750	−	1.07750i	0.0807656	−	0.996733i	$-0.474263\pi$
$19$	7390.56	−	7390.56i	1.07750	−	1.07750i	0.996733	−	0.0807656i	$-0.0257365\pi$
$20$	11883.1	−	1125.57i	1.48539	−	0.140697i
$21$	13088.7	−	6638.93i	1.41331	−	0.716870i
$22$	968.282	+	2057.20i	0.0909356	+	0.193200i
$23$	−6658.13			−0.547229			−0.273614	−	0.961839i	$-0.588219\pi$
$23$	−6658.13			−0.547229			−0.273614	+	0.961839i	$0.588219\pi$
$24$	11660.6	+	7425.24i	0.843501	+	0.537127i
$25$		−	19159.1i		−	1.22618i
$26$	−9081.62	−	19294.7i	−0.516706	−	1.09778i
$27$	−19423.5	−	3185.59i	−0.986816	−	0.161845i
$28$	−22169.5	+	26808.8i	−1.00991	+	1.22125i
$29$	2663.15	+	2663.15i	0.109195	+	0.109195i	0.759593	−	0.650399i	$-0.225398\pi$
$29$	2663.15	+	2663.15i	0.109195	+	0.109195i	−0.650399	+	0.759593i	$0.725398\pi$
$30$	24746.1	−	31788.7i	0.916521	−	1.17736i
$31$	−41065.4			−1.37845			−0.689225	−	0.724548i	$-0.742049\pi$
$31$	−41065.4			−1.37845			−0.689225	+	0.724548i	$0.742049\pi$
$32$	−32367.0	−	5110.60i	−0.987763	−	0.155963i
$33$	7293.75	+	2384.62i	0.202959	+	0.0663556i
$34$	23150.9	+	8332.36i	0.589022	+	0.211998i
$35$	71684.2	+	71684.2i	1.67194	+	1.67194i
$36$	45230.1	−	11446.3i	0.969438	−	0.245335i
$37$	−28503.0	−	28503.0i	−0.562711	−	0.562711i	0.367365	−	0.930077i	$-0.380260\pi$
$37$	−28503.0	−	28503.0i	−0.562711	−	0.562711i	−0.930077	+	0.367365i	$0.880260\pi$
$38$	35608.6	+	75653.4i	0.648940	+	1.37873i
$39$	−68408.9	−	22365.6i	−1.15324	−	0.377040i
$40$	−23721.1	+	92497.3i	−0.370641	+	1.44527i
$41$	−71523.3			−1.03776			−0.518879	−	0.854848i	$-0.673651\pi$
$41$	−71523.3			−1.03776			−0.518879	+	0.854848i	$0.673651\pi$
$42$	14513.6	+	116509.i	0.195897	+	1.57257i
$43$	−27.9233	−	27.9233i	−0.000351205	−	0.000351205i	0.706931	−	0.707282i	$-0.250079\pi$
$43$	−27.9233	−	27.9233i	−0.000351205	−	0.000351205i	−0.707282	+	0.706931i	$0.750079\pi$
$44$	−18108.4	+	1715.23i	−0.212580	+	0.0201356i
$45$	−20778.4	−	134365.i	−0.228021	−	1.47451i
$46$	18038.1	−	50117.8i	0.185318	−	0.514895i
$47$		−	26336.1i		−	0.253664i	−0.991924	−	0.126832i	$-0.959519\pi$
$47$		−	26336.1i		−	0.253664i	0.991924	−	0.126832i	$-0.0404809\pi$
$48$	−87482.7	+	67656.3i	−0.791040	+	0.611765i
$49$	−177810.			−1.51136
$50$	144216.	+	51905.5i	1.15373	+	0.415244i
$51$	74058.9	−	37564.6i	0.558299	−	0.283184i
$52$	169841.	−	16087.4i	1.20790	−	0.114413i
$53$	−149705.	+	149705.i	−1.00556	+	1.00556i	−0.00557858	+	0.999984i	$0.501776\pi$
$53$	−149705.	+	149705.i	−1.00556	+	1.00556i	−0.999984	+	0.00557858i	$0.998224\pi$
$54$	76600.8	−	137576.i	0.486465	−	0.873700i
$55$			53006.6i			0.318597i
$56$	−141736.	−	239507.i	−0.807082	−	1.36381i
$57$	268228.	+	87694.6i	1.44837	+	0.473531i
$58$	−27261.3	+	12831.4i	−0.139721	+	0.0657641i
$59$	−166208.	+	166208.i	−0.809276	+	0.809276i	−0.984524	−	0.175248i	$-0.943927\pi$
$59$	−166208.	+	166208.i	−0.809276	+	0.809276i	0.175248	+	0.984524i	$0.443927\pi$
$60$	172241.	+	272393.i	0.797413	+	1.26108i
$61$	−134399.	+	134399.i	−0.592114	+	0.592114i	−0.938202	−	0.346088i	$-0.887510\pi$
$61$	−134399.	+	134399.i	−0.592114	+	0.592114i	0.346088	+	0.938202i	$0.387510\pi$
$62$	111254.	−	309112.i	0.466809	−	1.29700i
$63$	319725.	+	234083.i	1.27866	+	0.936156i
$64$	126157.	−	229791.i	0.481252	−	0.876582i
$65$		−	497154.i		−	1.81030i
$66$	−37709.9	+	48441.9i	−0.131167	+	0.168496i
$67$	194674.	−	194674.i	0.647266	−	0.647266i	−0.305065	−	0.952331i	$-0.598678\pi$
$67$	194674.	−	194674.i	0.647266	−	0.647266i	0.952331	+	0.305065i	$0.0986782\pi$
$68$	−125440.	+	151690.i	−0.398943	+	0.482426i
$69$	−81320.9	−	160325.i	−0.247546	−	0.488037i
$70$	−733795.	+	345383.i	−2.13934	+	1.00695i
$71$	458913.			1.28220			0.641099	−	0.767458i	$-0.278479\pi$
$71$	458913.			1.28220			0.641099	+	0.767458i	$0.278479\pi$
$72$	−36376.7	+	371471.i	−0.0974600	+	0.995239i
$73$		−	111317.i		−	0.286148i	−0.989712	−	0.143074i	$-0.954301\pi$
$73$		−	111317.i		−	0.286148i	0.989712	−	0.143074i	$-0.0456987\pi$
$74$	291771.	−	137331.i	0.720024	−	0.338901i
$75$	461342.	−	234005.i	1.09355	−	0.554678i
$76$	−665937.	+	63077.8i	−1.51702	+	0.143693i
$77$	−109238.	−	109238.i	−0.239277	−	0.239277i
$78$	353685.	−	454342.i	0.745303	−	0.957412i
$79$	−863589.			−1.75156			−0.875781	−	0.482708i	$-0.839653\pi$
$79$	−863589.			−1.75156			−0.875781	+	0.482708i	$0.839653\pi$
$80$	−631991.	−	429148.i	−1.23436	−	0.838180i
$81$	−160527.	−	506617.i	−0.302060	−	0.953289i
$82$	193770.	−	538378.i	0.351435	−	0.976440i
$83$	154136.	+	154136.i	0.269569	+	0.269569i	0.828927	−	0.559357i	$-0.188952\pi$
$83$	154136.	+	154136.i	0.269569	+	0.269569i	−0.559357	+	0.828927i	$0.688952\pi$
$84$	−916316.	−	206395.i	−1.54599	−	0.348227i
$85$	405606.	+	405606.i	0.660462	+	0.660462i
$86$	285.836	−	134.538i	0.000449388	−	0.000211519i
$87$	−31600.2	+	96654.4i	−0.0479880	+	0.146779i
$88$	36147.9	−	140954.i	0.0530439	−	0.206838i
$89$	96376.7			0.136711			0.0683553	−	0.997661i	$-0.478225\pi$
$89$	96376.7			0.136711			0.0683553	+	0.997661i	$0.478225\pi$
$90$	1.06770e6	+	207614.i	1.46461	+	0.284793i
$91$	1.02455e6	+	1.02455e6i	1.35960	+	1.35960i
$92$	328383.	+	271557.i	0.421713	+	0.348736i
$93$	−501563.	−	988835.i	−0.623558	−	1.22935i
$94$	198240.	+	71349.5i	0.238676	+	0.0859028i
$95$			1.94932e6i			2.27359i
$96$	−272263.	−	841802.i	−0.307733	−	0.951473i
$97$	729167.			0.798935			0.399468	−	0.916747i	$-0.369195\pi$
$97$	729167.			0.798935			0.399468	+	0.916747i	$0.369195\pi$
$98$	481719.	−	1.33843e6i	0.511818	−	1.42206i
$99$	31663.7	+	204755.i	0.0326329	+	0.211023i
$100$	−781417.	+	944938.i	−0.781417	+	0.944938i
$101$	746191.	−	746191.i	0.724245	−	0.724245i	−0.245222	−	0.969467i	$-0.578861\pi$
$101$	746191.	−	746191.i	0.724245	−	0.724245i	0.969467	+	0.245222i	$0.0788608\pi$
$102$	82121.2	+	659233.i	0.0773847	+	0.621210i
$103$		−	89092.9i		−	0.0815326i	−0.999169	−	0.0407663i	$-0.987020\pi$
$103$		−	89092.9i		−	0.0815326i	0.999169	−	0.0407663i	$-0.0129799\pi$
$104$	−339035.	+	1.32203e6i	−0.301401	+	1.17528i
$105$	−850587.	+	2.60166e6i	−0.734769	+	2.24741i
$106$	−721298.	−	1.53246e6i	−0.605615	−	1.28668i
$107$	−909059.	+	909059.i	−0.742063	+	0.742063i	−0.972975	−	0.230912i	$-0.925829\pi$
$107$	−909059.	+	909059.i	−0.742063	+	0.742063i	0.230912	+	0.972975i	$0.425829\pi$
$108$	828053.	+	949317.i	0.657335	+	0.753598i
$109$	654562.	−	654562.i	0.505442	−	0.505442i	−0.407682	−	0.913124i	$-0.633663\pi$
$109$	654562.	−	654562.i	0.505442	−	0.505442i	0.913124	+	0.407682i	$0.133663\pi$
$110$	−398997.	−	143605.i	−0.299772	−	0.107892i
$111$	338210.	−	1.03447e6i	0.247296	−	0.756394i
$112$	2.18683e6	−	418025.i	1.55654	−	0.297542i
$113$			1.66732e6i			1.15554i	0.816200	+	0.577769i	$0.196077\pi$
$113$			1.66732e6i			1.15554i	−0.816200	+	0.577769i	$0.803923\pi$
$114$	−1.38678e6	+	1.78145e6i	−0.936039	+	1.20243i
$115$	878067.	−	878067.i	0.577343	−	0.577343i
$116$	−22729.7	−	239967.i	−0.0145620	−	0.153736i
$117$	−296977.	−	1.92042e6i	−0.185424	−	1.19906i
$118$	−800812.	−	1.70139e6i	−0.487399	−	1.03552i
$119$	−1.67177e6			−0.992057
$120$	−2.51702e6	+	558550.i	−1.45661	+	0.323235i
$121$			1.69079e6i			0.954404i
$122$	−647549.	−	1.37577e6i	−0.356610	−	0.757646i
$123$	−873570.	−	1.72225e6i	−0.469443	−	0.925508i
$124$	2.02537e6	+	1.67488e6i	1.06228	+	0.878454i
$125$	466072.	+	466072.i	0.238629	+	0.238629i
$126$	−2.62821e6	+	1.77249e6i	−1.31386	+	0.886079i
$127$	−1.60148e6			−0.781824			−0.390912	−	0.920428i	$-0.627840\pi$
$127$	−1.60148e6			−0.781824			−0.390912	+	0.920428i	$0.627840\pi$
$128$	1.38792e6	+	1.57217e6i	0.661813	+	0.749669i
$129$	331.330	−	1013.43i	0.000154345	−	0.000472089i
$130$	3.74223e6	+	1.34688e6i	1.70334	+	0.613056i
$131$	274687.	+	274687.i	0.122187	+	0.122187i	0.765556	−	0.643369i	$-0.222464\pi$
$131$	274687.	+	274687.i	0.122187	+	0.122187i	−0.643369	+	0.765556i	$0.722464\pi$
$132$	−262474.	−	415092.i	−0.114121	−	0.180477i
$133$	−4.01722e6	−	4.01722e6i	−1.70754	−	1.70754i
$134$	937962.	+	1.99278e6i	0.389826	+	0.828217i
$135$	2.98166e6	−	2.14144e6i	1.21187	−	0.870371i
$136$	−801978.	−	1.35518e6i	−0.318820	−	0.538743i
$137$	−10698.1			−0.00416048			−0.00208024	−	0.999998i	$-0.500662\pi$
$137$	−10698.1			−0.00416048			−0.00208024	+	0.999998i	$0.500662\pi$
$138$	1.42713e6	−	177778.i	0.543032	−	0.0676459i
$139$	1.94108e6	+	1.94108e6i	0.722767	+	0.722767i	0.969168	−	0.246401i	$-0.0792480\pi$
$139$	1.94108e6	+	1.94108e6i	0.722767	+	0.722767i	−0.246401	+	0.969168i	$0.579248\pi$
$140$	−611818.	−	6.45921e6i	−0.222966	−	2.35394i
$141$	634162.	−	321664.i	0.226226	−	0.114748i
$142$	−1.24328e6	+	3.45437e6i	−0.434214	+	1.20644i
$143$			757601.i			0.259079i
$144$	−2.69763e6	−	1.28020e6i	−0.903429	−	0.428737i
$145$	−702426.			−0.230408
$146$	837914.	+	301577.i	0.269241	+	0.0969036i
$147$	−2.17173e6	−	4.28157e6i	−0.683681	−	1.34788i
$148$	243271.	+	2.56830e6i	0.0750420	+	0.792248i
$149$	−3.38518e6	+	3.38518e6i	−1.02335	+	1.02335i	−0.0236273	+	0.999721i	$0.507522\pi$
$149$	−3.38518e6	+	3.38518e6i	−1.02335	+	1.02335i	−0.999721	+	0.0236273i	$0.992478\pi$
$150$	511565.	+	4.10662e6i	0.151575	+	1.21678i
$151$			1.45932e6i			0.423858i	0.977285	+	0.211929i	$0.0679746\pi$
$151$			1.45932e6i			0.423858i	−0.977285	+	0.211929i	$0.932025\pi$
$152$	1.32934e6	−	5.18360e6i	0.378534	−	1.47605i
$153$	1.80908e6	+	1.32450e6i	0.505106	+	0.369808i
$154$	1.11821e6	−	526321.i	0.306169	−	0.144108i
$155$	5.41566e6	−	5.41566e6i	1.45431	−	1.45431i
$156$	2.46177e6	+	3.89319e6i	0.648446	+	1.02549i
$157$	5.28176e6	−	5.28176e6i	1.36483	−	1.36483i	0.497193	−	0.867640i	$-0.334364\pi$
$157$	5.28176e6	−	5.28176e6i	1.36483	−	1.36483i	0.867640	−	0.497193i	$-0.165636\pi$
$158$	2.33962e6	−	6.50050e6i	0.593164	−	1.64807i
$159$	−5.43330e6	−	1.77636e6i	−1.35167	−	0.441917i
$160$	4.94251e6	−	3.59455e6i	1.20667	−	0.877575i
$161$			3.61910e6i			0.867208i
$162$	4.24836e6	+	164184.i	0.999254	+	0.0386177i
$163$	150670.	−	150670.i	0.0347908	−	0.0347908i	−0.689497	−	0.724288i	$-0.742169\pi$
$163$	150670.	−	150670.i	0.0347908	−	0.0347908i	0.724288	+	0.689497i	$0.242169\pi$
$164$	3.52758e6	+	2.91713e6i	0.799733	+	0.661339i
$165$	−1.27637e6	+	647411.i	−0.284136	+	0.144121i
$166$	−1.57782e6	+	742647.i	−0.344931	+	0.162352i
$167$	−1.21956e6			−0.261851			−0.130926	−	0.991392i	$-0.541795\pi$
$167$	−1.21956e6			−0.261851			−0.130926	+	0.991392i	$0.541795\pi$
$168$	4.03607e6	−	6.33823e6i	0.851199	−	1.33672i
$169$		−	2.27881e6i		−	0.472115i
$170$	−4.15198e6	+	1.95426e6i	−0.845101	+	0.397773i
$171$	1.16443e6	+	7.52988e6i	0.232877	+	1.50591i
$172$	238.322	+	2516.06i	4.68360e−5	+	0.000494466i
$173$	−1.22321e6	−	1.22321e6i	−0.236244	−	0.236244i	0.579049	−	0.815293i	$-0.303424\pi$
$173$	−1.22321e6	−	1.22321e6i	−0.236244	−	0.236244i	−0.815293	+	0.579049i	$0.803424\pi$
$174$	−641937.	−	499719.i	−0.121855	−	0.0948590i
$175$	−1.04141e7			−1.94316
$176$	963074.	+	653967.i	0.176653	+	0.119955i
$177$	−6.03225e6	−	1.97219e6i	−1.08783	−	0.355654i
$178$	−261102.	+	725457.i	−0.0462968	+	0.128633i
$179$	−6.12539e6	−	6.12539e6i	−1.06801	−	1.06801i	−0.997512	−	0.0704956i	$-0.977542\pi$
$179$	−6.12539e6	−	6.12539e6i	−1.06801	−	1.06801i	−0.0704956	−	0.997512i	$-0.522458\pi$
$180$	−4.45537e6	+	7.47443e6i	−0.763952	+	1.28162i
$181$	3.14289e6	+	3.14289e6i	0.530022	+	0.530022i	0.920579	−	0.390557i	$-0.127717\pi$
$181$	3.14289e6	+	3.14289e6i	0.530022	+	0.530022i	−0.390557	+	0.920579i	$0.627717\pi$
$182$	−1.04878e7	+	4.93642e6i	−1.73969	+	0.818837i
$183$	−4.87777e6	−	1.59474e6i	−0.795918	−	0.260218i
$184$	−2.93374e6	+	1.73614e6i	−0.470943	+	0.278697i
$185$	7.51789e6			1.18736
$186$	8.80209e6	−	1.09648e6i	1.36788	−	0.170398i
$187$	−618093.	−	618093.i	−0.0945211	−	0.0945211i
$188$	−1.07414e6	+	1.29891e6i	−0.161654	+	0.195482i
$189$	−1.73156e6	+	1.05579e7i	−0.256480	+	1.56383i
$190$	−1.46731e7	−	5.28107e6i	−2.13925	−	0.769947i
$191$			2.80444e6i			0.402482i	0.979542	+	0.201241i	$0.0644974\pi$
$191$			2.80444e6i			0.402482i	−0.979542	+	0.201241i	$0.935503\pi$
$192$	7.07411e6	+	231195.i	0.999466	+	0.0326644i
$193$	8.16697e6			1.13603			0.568014	−	0.823019i	$-0.307712\pi$
$193$	8.16697e6			1.13603			0.568014	+	0.823019i	$0.307712\pi$
$194$	−1.97545e6	+	5.48866e6i	−0.270558	+	0.751729i
$195$	1.19712e7	−	6.07213e6i	1.61449	−	0.818912i
$196$	8.76968e6	+	7.25209e6i	1.16470	+	0.963153i
$197$	−7.22588e6	+	7.22588e6i	−0.945131	+	0.945131i	−0.998571	−	0.0534398i	$-0.982981\pi$
$197$	−7.22588e6	+	7.22588e6i	−0.945131	+	0.945131i	0.0534398	+	0.998571i	$0.482981\pi$
$198$	−1.62704e6	−	316378.i	−0.209605	−	0.0407578i
$199$			3.31667e6i			0.420866i	0.977608	+	0.210433i	$0.0674873\pi$
$199$			3.31667e6i			0.420866i	−0.977608	+	0.210433i	$0.932513\pi$
$200$	−4.99583e6	−	8.44198e6i	−0.624479	−	1.05525i
$201$	7.06535e6	+	2.30995e6i	0.870053	+	0.284456i
$202$	3.59524e6	+	7.63837e6i	0.436188	+	0.926716i
$203$	1.44758e6	−	1.44758e6i	0.173044	−	0.173044i
$204$	−5.18473e6	−	1.16783e6i	−0.610711	−	0.137559i
$205$	9.43242e6	−	9.43242e6i	1.09487	−	1.09487i
$206$	670629.	+	241369.i	0.0767151	+	0.0276109i
$207$	2.86731e6	−	3.91634e6i	0.323268	−	0.441539i
$208$	−9.03278e6	−	6.13363e6i	−1.00376	−	0.681597i
$209$		−	2.97052e6i		−	0.325382i
$210$	−1.72791e7	−	1.34510e7i	−1.86579	−	1.45244i
$211$	−6.00803e6	+	6.00803e6i	−0.639565	+	0.639565i	−0.950448	−	0.310883i	$-0.899375\pi$
$211$	−6.00803e6	+	6.00803e6i	−0.639565	+	0.639565i	0.310883	+	0.950448i	$0.399375\pi$
$212$	1.34894e7	−	1.27772e6i	1.41574	−	0.134100i
$213$	5.60506e6	+	1.10504e7i	0.580018	+	1.14351i
$214$	−4.37996e6	−	9.30558e6i	−0.446919	−	0.949515i
$215$	7364.98			0.000741065
$216$	−9.38915e6	+	3.66113e6i	−0.931676	+	0.363290i
$217$			2.23215e7i			2.18446i
$218$	3.15376e6	+	6.70042e6i	0.304410	+	0.646744i
$219$	2.68045e6	−	1.35960e6i	0.255197	−	0.129443i
$220$	2.16191e6	−	2.61432e6i	0.203035	−	0.245522i
$221$	5.79716e6	+	5.79716e6i	0.537079	+	0.537079i
$222$	6.87049e6	+	5.34837e6i	0.627955	+	0.488836i
$223$	−104916.			−0.00946079			−0.00473039	−	0.999989i	$-0.501506\pi$
$223$	−104916.			−0.00946079			−0.00473039	+	0.999989i	$0.501506\pi$
$224$	−2.77793e6	+	1.75934e7i	−0.247159	+	1.56533i
$225$	1.12695e7	+	8.25081e6i	0.989362	+	0.724351i
$226$	−1.25505e7	−	4.51709e6i	−1.08726	−	0.391321i
$227$	8.74125e6	+	8.74125e6i	0.747302	+	0.747302i	0.973972	−	0.226670i	$-0.0727839\pi$
$227$	8.74125e6	+	8.74125e6i	0.747302	+	0.747302i	−0.226670	+	0.973972i	$0.572784\pi$
$228$	−9.65249e6	−	1.52650e7i	−0.814394	−	1.28793i
$229$	−1.22056e7	−	1.22056e7i	−1.01637	−	1.01637i	−0.999864	−	0.0165109i	$-0.994744\pi$
$229$	−1.22056e7	−	1.22056e7i	−1.01637	−	1.01637i	−0.0165109	−	0.999864i	$-0.505256\pi$
$230$	4.23063e6	+	8.98832e6i	0.347714	+	0.738746i
$231$	1.29619e6	−	3.96460e6i	0.105156	−	0.321635i
$232$	1.86788e6	+	479020.i	0.149584	+	0.0383610i
$233$	−9.11220e6			−0.720369			−0.360185	−	0.932881i	$-0.617286\pi$
$233$	−9.11220e6			−0.720369			−0.360185	+	0.932881i	$0.617286\pi$
$234$	1.52602e7	+	2.96734e6i	1.19100	+	0.231590i
$235$	3.47318e6	+	3.47318e6i	0.267623	+	0.267623i
$236$	1.49764e7	−	1.41857e6i	1.13939	−	0.107923i
$237$	−1.05477e7	−	2.07948e7i	−0.792341	−	1.56210i
$238$	4.52914e6	−	1.25839e7i	0.335958	−	0.933439i
$239$		−	2.33925e7i		−	1.71349i	−0.515737	−	0.856747i	$-0.672482\pi$
$239$		−	2.33925e7i		−	1.71349i	0.515737	−	0.856747i	$-0.327518\pi$
$240$	2.61469e6	−	2.04596e7i	0.189141	−	1.48000i
$241$	−1.31578e7			−0.940012			−0.470006	−	0.882663i	$-0.655748\pi$
$241$	−1.31578e7			−0.940012			−0.470006	+	0.882663i	$0.655748\pi$
$242$	−1.27271e7	−	4.58065e6i	−0.898012	−	0.323207i
$243$	1.02385e7	−	1.00531e7i	0.713536	−	0.700619i
$244$	1.21102e7	−	1.14708e6i	0.833644	−	0.0789631i
$245$	2.34493e7	−	2.34493e7i	1.59453	−	1.59453i
$246$	1.53305e7	−	1.90974e6i	1.02980	−	0.128283i
$247$			2.78608e7i			1.84885i
$248$	−1.80944e7	+	1.07080e7i	−1.18629	+	0.702027i
$249$	−1.82894e6	+	5.59412e6i	−0.118468	+	0.362354i
$250$	−4.77094e6	+	2.24559e6i	−0.305340	+	0.143718i
$251$	−2.52015e6	+	2.52015e6i	−0.159370	+	0.159370i	−0.782287	−	0.622918i	$-0.785947\pi$
$251$	−2.52015e6	+	2.52015e6i	−0.159370	+	0.159370i	0.622918	+	0.782287i	$0.285947\pi$
$252$	−6.22178e6	−	2.45853e7i	−0.388788	−	1.53629i
$253$	−1.33806e6	+	1.33806e6i	−0.0826257	+	0.0826257i
$254$	4.33870e6	−	1.20548e7i	0.264763	−	0.735629i
$255$	−4.81282e6	+	1.47208e7i	−0.290255	+	0.887790i
$256$	−1.55943e7	+	6.18801e6i	−0.929495	+	0.368834i
$257$		−	2.69433e7i		−	1.58727i	−0.608392	−	0.793637i	$-0.708185\pi$
$257$		−	2.69433e7i		−	1.58727i	0.608392	−	0.793637i	$-0.291815\pi$
$258$	6730.74	+	5239.59i	0.000391926	+	0.000305097i
$259$	−1.54931e7	+	1.54931e7i	−0.891743	+	0.891743i
$260$	−2.02768e7	+	2.45200e7i	−1.15366	+	1.39508i
$261$	−2.71335e6	+	419597.i	−0.152611	+	0.0235999i
$262$	−2.81183e6	+	1.32348e6i	−0.156346	+	0.0735889i
$263$	−9.68206e6			−0.532232			−0.266116	−	0.963941i	$-0.585740\pi$
$263$	−9.68206e6			−0.532232			−0.266116	+	0.963941i	$0.585740\pi$
$264$	3.83561e6	−	851160.i	0.208460	−	0.0462593i
$265$		−	3.94859e7i		−	2.12180i
$266$	4.11223e7	−	1.93555e7i	2.18490	−	1.02839i
$267$	1.17712e6	+	2.32071e6i	0.0618427	+	0.121923i
$268$	−1.75413e7	+	1.66152e6i	−0.911294	+	0.0863181i
$269$	1.09786e7	+	1.09786e7i	0.564014	+	0.564014i	0.930445	−	0.366431i	$-0.119421\pi$
$269$	1.09786e7	+	1.09786e7i	0.564014	+	0.564014i	−0.366431	+	0.930445i	$0.619421\pi$
$270$	8.04138e6	+	2.82454e7i	0.408545	+	1.43502i
$271$	1.84641e7			0.927729			0.463865	−	0.885906i	$-0.346462\pi$
$271$	1.84641e7			0.927729			0.463865	+	0.885906i	$0.346462\pi$
$272$	1.23736e7	−	2.36528e6i	0.614878	−	0.117538i
$273$	−1.21571e7	+	3.71844e7i	−0.597505	+	1.82756i
$274$	28983.0	−	80527.6i	0.00140894	−	0.00391465i
$275$	−3.85034e6	−	3.85034e6i	−0.185140	−	0.185140i
$276$	−2.52816e6	+	1.12240e7i	−0.120248	+	0.533854i
$277$	−7.09215e6	−	7.09215e6i	−0.333687	−	0.333687i	0.520298	−	0.853985i	$-0.325821\pi$
$277$	−7.09215e6	−	7.09215e6i	−0.333687	−	0.333687i	−0.853985	+	0.520298i	$0.825821\pi$
$278$	−1.98698e7	+	9.35234e6i	−0.924825	+	0.435297i
$279$	1.76847e7	−	2.41548e7i	0.814301	−	1.11222i
$280$	5.02779e7	+	1.28938e7i	2.29036	+	0.587365i
$281$	−2.50982e7			−1.13116			−0.565579	−	0.824694i	$-0.691347\pi$
$281$	−2.50982e7			−1.13116			−0.565579	+	0.824694i	$0.691347\pi$
$282$	703199.	+	5.64497e6i	0.0313568	+	0.251718i
$283$	−232997.	−	232997.i	−0.0102800	−	0.0102800i	0.701948	−	0.712228i	$-0.252314\pi$
$283$	−232997.	−	232997.i	−0.0102800	−	0.0102800i	−0.712228	+	0.701948i	$0.752314\pi$
$284$	−2.26339e7	−	1.87171e7i	−0.988106	−	0.817115i
$285$	−4.69387e7	+	2.38085e7i	−2.02767	+	1.02849i
$286$	−5.70269e6	−	2.05248e6i	−0.243771	−	0.0877366i
$287$			3.88773e7i			1.64456i
$288$	1.69448e7	−	1.68375e7i	0.709349	−	0.704857i
$289$	1.46783e7			0.608109
$290$	1.90300e6	−	5.28738e6i	0.0780271	−	0.216793i
$291$	8.90588e6	+	1.75580e7i	0.361408	+	0.712518i
$292$	−4.54013e6	+	5.49020e6i	−0.182356	+	0.220516i
$293$	676420.	−	676420.i	0.0268914	−	0.0268914i	−0.693533	−	0.720425i	$-0.743947\pi$
$293$	676420.	−	676420.i	0.0268914	−	0.0268914i	0.720425	+	0.693533i	$0.243947\pi$
$294$	3.81123e7	−	4.74768e6i	1.49976	−	0.186827i
$295$		−	4.38388e7i		−	1.70762i
$296$	−1.99915e7	−	5.12684e6i	−0.770849	−	0.197685i
$297$	−4.54368e6	+	3.26328e6i	−0.173436	+	0.124562i
$298$	−1.63102e7	−	3.46524e7i	−0.616327	−	1.30944i
$299$	1.25498e7	−	1.25498e7i	0.469488	−	0.469488i
$300$	−3.22977e7	−	7.27489e6i	−1.19621	−	0.269440i
$301$	−15178.0	+	15178.0i	−0.000556564	+	0.000556564i
$302$	−1.09848e7	−	3.95358e6i	−0.398814	−	0.143539i
$303$	2.70817e7	+	8.85411e6i	0.973528	+	0.318286i
$304$	3.54171e7	+	2.40497e7i	1.26064	+	0.856029i
$305$		−	3.54487e7i		−	1.24940i
$306$	−1.48710e7	+	1.00292e7i	−0.519011	+	0.350026i
$307$	1.73155e7	−	1.73155e7i	0.598439	−	0.598439i	−0.341458	−	0.939897i	$-0.610921\pi$
$307$	1.73155e7	−	1.73155e7i	0.598439	−	0.598439i	0.939897	+	0.341458i	$0.110921\pi$
$308$	932334.	+	9.84302e6i	0.0319095	+	0.336881i
$309$	2.14531e6	−	1.08816e6i	0.0727136	−	0.0368823i
$310$	2.60933e7	+	5.54373e7i	0.875878	+	1.86087i
$311$	1.71464e7			0.570023			0.285011	−	0.958524i	$-0.408003\pi$
$311$	1.71464e7			0.570023			0.285011	+	0.958524i	$0.408003\pi$
$312$	−3.59746e7	+	7.98312e6i	−1.18449	+	0.262850i
$313$		−	2.64561e7i		−	0.862764i	−0.902169	−	0.431382i	$-0.858026\pi$
$313$		−	2.64561e7i		−	0.862764i	0.902169	−	0.431382i	$-0.141974\pi$
$314$	2.54481e7	+	5.40666e7i	0.821991	+	1.74639i
$315$	−7.30356e7	+	1.12943e7i	−2.33670	+	0.361351i
$316$	4.25927e7	+	3.52221e7i	1.34982	+	1.11623i
$317$	−1.49755e7	−	1.49755e7i	−0.470114	−	0.470114i	0.431837	−	0.901952i	$-0.357865\pi$
$317$	−1.49755e7	−	1.49755e7i	−0.470114	−	0.470114i	−0.901952	+	0.431837i	$0.857865\pi$
$318$	2.80910e7	−	3.60856e7i	0.873547	−	1.12215i
$319$	1.07041e6			0.0329745
$320$	1.36671e7	+	4.69420e7i	0.417086	+	1.43256i
$321$	−3.29928e7	−	1.07867e7i	−0.997479	−	0.326116i
$322$	−2.72421e7	−	9.80481e6i	−0.815967	−	0.293678i
$323$	−2.27304e7	−	2.27304e7i	−0.674527	−	0.674527i
$324$	−1.27454e7	+	3.15339e7i	−0.374731	+	0.927133i
$325$	3.61128e7	+	3.61128e7i	1.05199	+	1.05199i
$326$	725946.	+	1.54233e6i	0.0209533	+	0.0445169i
$327$	2.37562e7	+	7.76687e6i	0.679413	+	0.222128i
$328$	−3.15150e7	+	1.86501e7i	−0.893091	+	0.528518i
$329$	−1.43153e7			−0.401988
$330$	−1.41532e6	−	1.13616e7i	−0.0393835	−	0.316153i
$331$	−2.07486e7	−	2.07486e7i	−0.572144	−	0.572144i	0.360583	−	0.932727i	$-0.382578\pi$
$331$	−2.07486e7	−	2.07486e7i	−0.572144	−	0.572144i	−0.932727	+	0.360583i	$0.882578\pi$
$332$	−1.31554e6	−	1.38887e7i	−0.0359492	−	0.379530i
$333$	2.90403e7	−	4.49084e6i	0.786446	−	0.121617i
$334$	3.30402e6	−	9.18002e6i	0.0886754	−	0.246379i
$335$			5.13467e7i			1.36577i
$336$	3.67753e7	+	4.75522e7i	0.969479	+	1.25358i
$337$	1.65739e7			0.433048			0.216524	−	0.976277i	$-0.430528\pi$
$337$	1.65739e7			0.433048			0.216524	+	0.976277i	$0.430528\pi$
$338$	1.71533e7	+	6.17372e6i	0.444219	+	0.159881i
$339$	−4.01484e7	+	2.03643e7i	−1.03055	+	0.522722i
$340$	−3.46181e6	−	3.65477e7i	−0.0880778	−	0.929872i
$341$	−8.25278e6	+	8.25278e6i	−0.208131	+	0.208131i
$342$	−5.98344e7	−	1.16348e7i	−1.49580	−	0.290858i
$343$			3.27010e7i			0.810360i
$344$	−19584.8	−	5022.56i	−0.000481110	−	0.000123381i
$345$	3.18680e7	+	1.04189e7i	0.776063	+	0.253726i
$346$	1.25213e7	−	5.89356e6i	0.302289	−	0.142282i
$347$	−4.84640e6	+	4.84640e6i	−0.115993	+	0.115993i	−0.762721	−	0.646728i	$-0.776137\pi$
$347$	−4.84640e6	+	4.84640e6i	−0.115993	+	0.115993i	0.646728	+	0.762721i	$0.276137\pi$
$348$	5.50067e6	−	3.47822e6i	0.130520	−	0.0825314i
$349$	−2.63364e7	+	2.63364e7i	−0.619557	+	0.619557i	−0.945418	−	0.325861i	$-0.894346\pi$
$349$	−2.63364e7	+	2.63364e7i	−0.619557	+	0.619557i	0.325861	+	0.945418i	$0.394346\pi$
$350$	2.82138e7	−	7.83904e7i	0.658048	−	1.82835i
$351$	4.26156e7	−	3.06067e7i	0.985480	−	0.707774i
$352$	−7.53176e6	+	5.47763e6i	−0.172690	+	0.125593i
$353$		−	1.08340e7i		−	0.246301i	−0.992388	−	0.123150i	$-0.960700\pi$
$353$		−	1.08340e7i		−	0.246301i	0.992388	−	0.123150i	$-0.0392998\pi$
$354$	3.11877e7	−	4.00636e7i	0.703030	−	0.903108i
$355$	−6.05209e7	+	6.05209e7i	−1.35276	+	1.35276i
$356$	−4.75336e6	−	3.93079e6i	−0.105354	−	0.0871225i
$357$	−2.04187e7	−	4.02555e7i	−0.448769	−	0.884750i
$358$	6.27025e7	−	2.95128e7i	1.36658	−	0.643224i
$359$	−4.64599e7			−1.00414			−0.502071	−	0.864826i	$-0.667428\pi$
$359$	−4.64599e7			−1.00414			−0.502071	+	0.864826i	$0.667428\pi$
$360$	−4.41919e7	−	5.37865e7i	−0.947185	−	1.15283i
$361$		−	6.21950e7i		−	1.32201i
$362$	−3.21722e7	+	1.51428e7i	−0.678196	+	0.319214i
$363$	−4.07133e7	+	2.06509e7i	−0.851171	+	0.431736i
$364$	−8.74446e6	−	9.23187e7i	−0.181313	−	1.91419i
$365$	1.46803e7	+	1.46803e7i	0.301895	+	0.301895i
$366$	2.52189e7	−	3.23960e7i	0.514378	−	0.660767i
$367$	3.61894e7			0.732121			0.366060	−	0.930591i	$-0.380706\pi$
$367$	3.61894e7			0.732121			0.366060	+	0.930591i	$0.380706\pi$
$368$	−5.12043e6	−	2.67867e7i	−0.102746	−	0.537497i
$369$	3.08013e7	−	4.20703e7i	0.613042	−	0.837330i
$370$	−2.03674e7	+	5.65895e7i	−0.402096	+	1.11720i
$371$	8.13739e7	+	8.13739e7i	1.59354	+	1.59354i
$372$	−1.55929e7	+	6.92266e7i	−0.302900	+	1.34476i
$373$	2.97878e7	+	2.97878e7i	0.574000	+	0.574000i	0.933244	−	0.359244i	$-0.116965\pi$
$373$	2.97878e7	+	2.97878e7i	0.574000	+	0.574000i	−0.359244	+	0.933244i	$0.616965\pi$
$374$	6.32710e6	−	2.97804e6i	0.120946	−	0.0569267i
$375$	−5.53029e6	+	1.69153e7i	−0.104871	+	0.320764i
$376$	−6.86729e6	−	1.16044e7i	−0.129188	−	0.218302i
$377$	−1.00395e7			−0.187364
$378$	−7.47811e7	−	4.16372e7i	−1.38458	−	0.770914i
$379$	−8.09614e6	−	8.09614e6i	−0.148717	−	0.148717i	0.628828	−	0.777545i	$-0.283535\pi$
$379$	−8.09614e6	−	8.09614e6i	−0.148717	−	0.148717i	−0.777545	+	0.628828i	$0.783535\pi$
$380$	7.95044e7	−	9.61416e7i	1.44891	−	1.75211i
$381$	−1.95601e7	−	3.85628e7i	−0.353668	−	0.697258i
$382$	−2.11099e7	−	7.59775e6i	−0.378700	−	0.136300i
$383$		−	1.01454e8i		−	1.80581i	−0.429840	−	0.902905i	$-0.641430\pi$
$383$		−	1.01454e8i		−	1.80581i	0.429840	−	0.902905i	$-0.358570\pi$
$384$	−2.09054e7	+	5.26226e7i	−0.369202	+	0.929349i
$385$	2.88123e7			0.504889
$386$	−2.21258e7	+	6.14753e7i	−0.384714	+	1.06890i
$387$	28449.7	−	4399.50i	0.000490845	−	7.59050e-5i
$388$	−3.59630e7	−	2.97396e7i	−0.615687	−	0.509143i
$389$	1.25481e7	−	1.25481e7i	0.213172	−	0.213172i	−0.592441	−	0.805614i	$-0.701836\pi$
$389$	1.25481e7	−	1.25481e7i	0.213172	−	0.213172i	0.805614	+	0.592441i	$0.201836\pi$
$390$	1.32745e7	+	1.06562e8i	0.223781	+	1.79642i
$391$			2.04777e7i			0.342571i
$392$	−7.83474e7	+	4.63648e7i	−1.30067	+	0.769716i
$393$	−3.25937e6	+	9.96931e6i	−0.0536978	+	0.164243i
$394$	−3.48152e7	−	7.39677e7i	−0.569219	−	1.20935i
$395$	1.13889e8	−	1.13889e8i	1.84795	−	1.84795i
$396$	6.78942e6	−	1.13901e7i	0.109332	−	0.183418i
$397$	−4.54699e7	+	4.54699e7i	−0.726695	+	0.726695i	−0.969960	−	0.243265i	$-0.921782\pi$
$397$	−4.54699e7	+	4.54699e7i	−0.726695	+	0.726695i	0.243265	+	0.969960i	$0.421782\pi$
$398$	−2.49656e7	−	8.98548e6i	−0.395998	−	0.142525i
$399$	4.76674e7	−	1.45798e8i	0.750416	−	2.29527i
$400$	7.70800e7	−	1.47343e7i	1.20437	−	0.230223i
$401$			1.00724e8i			1.56207i	0.624486	+	0.781036i	$0.285309\pi$
$401$			1.00724e8i			1.56207i	−0.624486	+	0.781036i	$0.714691\pi$
$402$	−3.65291e7	+	4.69250e7i	−0.562290	+	0.722314i
$403$	7.74037e7	−	7.74037e7i	1.18262	−	1.18262i
$404$	−6.72365e7	+	6.36867e6i	−1.01967	+	0.0965838i
$405$	8.79822e7	+	4.56420e7i	1.32443	+	0.687067i
$406$	6.97463e6	+	1.48182e7i	0.104218	+	0.221420i
$407$	−1.14563e7			−0.169927
$408$	2.28370e7	−	3.58632e7i	0.336248	−	0.528042i
$409$		−	2.10623e7i		−	0.307848i	−0.988083	−	0.153924i	$-0.950809\pi$
$409$		−	2.10623e7i		−	0.307848i	0.988083	−	0.153924i	$-0.0491911\pi$
$410$	4.54465e7	+	9.65549e7i	0.659400	+	1.40095i
$411$	−130664.	−	257604.i	−0.00188204	−	0.00371046i
$412$	−3.63372e6	+	4.39412e6i	−0.0519588	+	0.0628319i
$413$	9.03444e7	+	9.03444e7i	1.28248	+	1.28248i
$414$	2.17114e7	+	3.21932e7i	0.305976	+	0.453694i
$415$	−4.06547e7			−0.568808
$416$	7.06412e7	−	5.13753e7i	0.981246	−	0.713632i
$417$	−2.30323e7	+	7.04481e7i	−0.317636	+	0.971541i
$418$	2.23600e7	+	8.04768e6i	0.306156	+	0.110190i
$419$	2.78299e6	+	2.78299e6i	0.0378329	+	0.0378329i	0.725770	−	0.687937i	$-0.241484\pi$
$419$	2.78299e6	+	2.78299e6i	0.0378329	+	0.0378329i	−0.687937	+	0.725770i	$0.741484\pi$
$420$	1.48062e8	−	9.36236e7i	1.99846	−	1.26368i
$421$	5.80773e7	+	5.80773e7i	0.778323	+	0.778323i	0.979546	−	0.201223i	$-0.0644915\pi$
$421$	5.80773e7	+	5.80773e7i	0.778323	+	0.778323i	−0.201223	+	0.979546i	$0.564491\pi$
$422$	−2.89474e7	−	6.15012e7i	−0.385188	−	0.818363i
$423$	1.54910e7	+	1.13416e7i	0.204672	+	0.149849i
$424$	−2.69275e7	+	1.05000e8i	−0.353263	+	1.37750i
$425$	−5.89256e7			−0.767604
$426$	−9.83648e7	+	1.22534e7i	−1.27236	+	0.158499i
$427$	7.30539e7	+	7.30539e7i	0.938339	+	0.938339i
$428$	8.19120e7	−	7.75874e6i	1.04476	−	0.0989600i
$429$	−1.82427e7	+	9.25317e6i	−0.231056	+	0.117198i
$430$	−19953.1	+	55438.4i	−0.000250960	+	0.000697278i
$431$			7.19513e7i			0.898683i	0.893360	+	0.449342i	$0.148341\pi$
$431$			7.19513e7i			0.898683i	−0.893360	+	0.449342i	$0.851659\pi$
$432$	−2.12151e6	−	8.05936e7i	−0.0263144	−	0.999654i
$433$	−1.40304e8			−1.72825			−0.864126	−	0.503275i	$-0.832128\pi$
$433$	−1.40304e8			−1.72825			−0.864126	+	0.503275i	$0.832128\pi$
$434$	−1.68021e8	−	6.04732e7i	−2.05539	−	0.739765i
$435$	−8.57928e6	−	1.69141e7i	−0.104228	−	0.205485i
$436$	−5.89802e7	+	5.58663e6i	−0.711618	+	0.0674047i
$437$	−4.92073e7	+	4.92073e7i	−0.589638	+	0.589638i
$438$	2.97226e6	+	2.38600e7i	0.0353723	+	0.283954i
$439$			1.59185e7i			0.188152i	0.995565	+	0.0940761i	$0.0299897\pi$
$439$			1.59185e7i			0.188152i	−0.995565	+	0.0940761i	$0.970010\pi$
$440$	1.38217e7	+	2.33560e7i	0.162258	+	0.274183i
$441$	7.65732e7	−	1.04588e8i	0.892814	−	1.21946i
$442$	−5.93425e7	+	2.79314e7i	−0.687226	+	0.323464i
$443$	−6.67593e7	+	6.67593e7i	−0.767893	+	0.767893i	−0.977735	−	0.209842i	$-0.932705\pi$
$443$	−6.67593e7	+	6.67593e7i	−0.767893	+	0.767893i	0.209842	+	0.977735i	$0.432705\pi$
$444$	−5.88723e7	+	3.72265e7i	−0.672608	+	0.425308i
$445$	−1.27101e7	+	1.27101e7i	−0.144234	+	0.144234i
$446$	284237.	−	789735.i	0.00320388	−	0.00890178i
$447$	−1.22860e8	−	4.01677e7i	−1.37558	−	0.449733i
$448$	−1.24905e8	−	6.85742e7i	−1.38914	−	0.762653i
$449$		−	2.69706e7i		−	0.297956i	−0.988841	−	0.148978i	$-0.952402\pi$
$449$		−	2.69706e7i		−	0.297956i	0.988841	−	0.148978i	$-0.0475984\pi$
$450$	−9.26374e7	+	6.24756e7i	−1.01660	+	0.685604i
$451$	−1.43738e7	+	1.43738e7i	−0.156690	+	0.156690i
$452$	6.80030e7	−	8.22335e7i	0.736398	−	0.890499i
$453$	−3.51398e7	+	1.78239e7i	−0.378012	+	0.191738i
$454$	−8.94797e7	+	4.21164e7i	−0.956218	+	0.450074i
$455$	−2.70234e8			−2.86883
$456$	1.41055e8	−	3.13014e7i	1.48763	−	0.330118i
$457$			1.15277e7i			0.120779i	0.998175	+	0.0603897i	$0.0192343\pi$
$457$			1.15277e7i			0.120779i	−0.998175	+	0.0603897i	$0.980766\pi$
$458$	1.24943e8	−	5.88082e7i	1.30051	−	0.612127i
$459$	−9.79758e6	+	5.97388e7i	−0.101317	+	0.617758i
$460$	−7.91194e7	+	7.49422e6i	−0.812848	+	0.0769933i
$461$	1.01172e8	+	1.01172e8i	1.03266	+	1.03266i	0.999448	+	0.0332122i	$0.0105737\pi$
$461$	1.01172e8	+	1.01172e8i	1.03266	+	1.03266i	0.0332122	+	0.999448i	$0.489426\pi$
$462$	2.63311e7	+	2.04976e7i	0.267020	+	0.207863i
$463$	8.85618e7			0.892284			0.446142	−	0.894962i	$-0.352798\pi$
$463$	8.85618e7			0.892284			0.446142	+	0.894962i	$0.352798\pi$
$464$	−8.66617e6	+	1.27624e7i	−0.0867507	+	0.127755i
$465$	1.96552e8	+	6.42608e7i	1.95487	+	0.639127i
$466$	2.46866e7	−	6.85903e7i	0.243952	−	0.677805i
$467$	−1.20496e8	−	1.20496e8i	−1.18310	−	1.18310i	−0.978937	−	0.204161i	$-0.934553\pi$
$467$	−1.20496e8	−	1.20496e8i	−1.18310	−	1.18310i	−0.204161	−	0.978937i	$-0.565447\pi$
$468$	−6.36787e7	+	1.06829e8i	−0.621236	+	1.04220i
$469$	−1.05817e8	−	1.05817e8i	−1.02574	−	1.02574i
$470$	−3.55532e7	+	1.67342e7i	−0.342440	+	0.161180i
$471$	1.91692e8	+	6.26720e7i	1.83460	+	0.599806i
$472$	−2.98959e7	+	1.16575e8i	−0.284306	+	1.10861i
$473$	−11223.3			−0.000106056
$474$	1.85105e8	−	2.30586e7i	1.73813	−	0.216520i
$475$	−1.41596e8	−	1.41596e8i	−1.32121	−	1.32121i
$476$	8.24529e7	+	6.81845e7i	0.764514	+	0.632215i
$477$	−2.35871e7	−	1.52527e8i	−0.217330	−	1.40538i
$478$	1.76082e8	+	6.33746e7i	1.61225	+	0.580272i
$479$			8.17792e7i			0.744109i	0.928211	+	0.372054i	$0.121346\pi$
$479$			8.17792e7i			0.744109i	−0.928211	+	0.372054i	$0.878654\pi$
$480$	1.46922e8	+	7.51103e7i	1.32850	+	0.679165i
$481$	1.07450e8			0.965543
$482$	3.56470e7	−	9.90431e7i	0.318333	−	0.884470i
$483$	−8.71462e7	+	4.42029e7i	−0.773405	+	0.392292i
$484$	6.89599e7	−	8.33906e7i	0.608220	−	0.735497i
$485$	−9.61617e7	+	9.61617e7i	−0.842902	+	0.842902i
$486$	4.79350e7	+	1.04304e8i	0.417584	+	0.908638i
$487$		−	1.08210e8i		−	0.936871i	−0.883498	−	0.468436i	$-0.844818\pi$
$487$		−	1.08210e8i		−	0.936871i	0.883498	−	0.468436i	$-0.155182\pi$
$488$	−2.41743e7	+	9.42646e7i	−0.208015	+	0.811128i
$489$	5.46831e6	+	1.78781e6i	0.0467656	+	0.0152896i
$490$	1.12982e8	+	2.40039e8i	0.960329	+	2.04030i
$491$	6.01667e7	−	6.01667e7i	0.508290	−	0.508290i	−0.405711	−	0.914001i	$-0.632976\pi$
$491$	6.01667e7	−	6.01667e7i	0.508290	−	0.508290i	0.914001	+	0.405711i	$0.132976\pi$
$492$	−2.71581e7	+	1.20572e8i	−0.228036	+	1.01239i
$493$	8.19076e6	−	8.19076e6i	0.0683571	−	0.0683571i
$494$	−2.09717e8	−	7.54800e7i	−1.73961	−	0.626111i
$495$	−3.11787e7	−	2.28271e7i	−0.257065	−	0.188207i
$496$	−3.15813e7	−	1.65212e8i	−0.258812	−	1.35393i
$497$		−	2.49447e8i		−	2.03193i
$498$	−3.71537e7	−	2.89225e7i	−0.300825	−	0.234179i
$499$	−9.15486e7	+	9.15486e7i	−0.736801	+	0.736801i	−0.971957	−	0.235157i	$-0.924440\pi$
$499$	−9.15486e7	+	9.15486e7i	−0.736801	+	0.736801i	0.235157	+	0.971957i	$0.424440\pi$
$500$	−3.97788e6	−	4.19960e7i	−0.0318230	−	0.335968i
$501$	−1.48955e7	−	2.93665e7i	−0.118452	−	0.233528i
$502$	−1.21424e7	−	2.57975e7i	−0.0959828	−	0.203923i
$503$	2.14060e8			1.68202			0.841012	−	0.541016i	$-0.181960\pi$
$503$	2.14060e8			1.68202			0.841012	+	0.541016i	$0.181960\pi$
$504$	2.01917e8	+	1.97730e7i	1.57718	+	0.154447i
$505$			1.96814e8i			1.52820i
$506$	−6.44695e6	−	1.36971e7i	−0.0497626	−	0.105725i
$507$	5.48726e7	−	2.78329e7i	0.421048	−	0.213567i
$508$	7.89858e7	+	6.53174e7i	0.602501	+	0.498239i
$509$	4.55373e7	+	4.55373e7i	0.345314	+	0.345314i	0.858361	−	0.513047i	$-0.171483\pi$
$509$	4.55373e7	+	4.55373e7i	0.345314	+	0.345314i	−0.513047	+	0.858361i	$0.671483\pi$
$510$	−9.77690e7	−	7.61089e7i	−0.737039	−	0.573753i
$511$	−6.05074e7			−0.453467
$512$	−4.33107e6	−	1.34148e8i	−0.0322690	−	0.999479i
$513$	−1.67094e8	+	1.20007e8i	−1.23768	+	0.888906i
$514$	2.02811e8	+	7.29945e7i	1.49349	+	0.537527i
$515$	1.17495e7	+	1.17495e7i	0.0860194	+	0.0860194i
$516$	−57674.8	+	36469.3i	−0.000419795	+	0.000265448i
$517$	−5.29269e6	−	5.29269e6i	−0.0383005	−	0.0383005i
$518$	−7.46477e7	−	1.58595e8i	−0.537066	−	1.14104i
$519$	1.45143e7	−	4.43942e7i	0.103823	−	0.317559i
$520$	−1.29636e8	−	2.19059e8i	−0.921965	−	1.55794i
$521$	6.57730e7			0.465088			0.232544	−	0.972586i	$-0.425295\pi$
$521$	6.57730e7			0.465088			0.232544	+	0.972586i	$0.425295\pi$
$522$	4.19254e6	−	2.15610e7i	0.0294758	−	0.151585i
$523$	−1.08365e8	−	1.08365e8i	−0.757505	−	0.757505i	0.218362	−	0.975868i	$-0.429929\pi$
$523$	−1.08365e8	−	1.08365e8i	−0.757505	−	0.757505i	−0.975868	+	0.218362i	$0.929929\pi$
$524$	−2.34443e6	−	2.47511e7i	−0.0162946	−	0.172028i
$525$	−1.27196e8	−	2.50767e8i	−0.879013	−	1.73298i
$526$	2.62305e7	−	7.28799e7i	0.180239	−	0.500784i
$527$			1.26300e8i			0.862925i
$528$	−3.98445e6	+	3.11778e7i	−0.0270687	+	0.211809i
$529$	−1.03705e8			−0.700541
$530$	2.97223e8	+	1.06975e8i	1.99643	+	0.718544i
$531$	−2.61873e7	−	1.69342e8i	−0.174907	−	1.13105i
$532$	3.42866e7	+	3.61977e8i	0.227714	+	2.40407i
$533$	1.34814e8	−	1.34814e8i	0.890332	−	0.890332i
$534$	−2.06577e7	+	2.57335e6i	−0.135662	+	0.0168995i
$535$		−	2.39771e8i		−	1.56580i
$536$	3.50160e7	−	1.36540e8i	0.227390	−	0.886680i
$537$	7.26823e7	−	2.22311e8i	0.469360	−	1.43561i
$538$	−1.12382e8	+	5.28962e7i	−0.721690	+	0.339686i
$539$	−3.57338e7	+	3.57338e7i	−0.228199	+	0.228199i
$540$	−2.34398e8	−	1.59922e7i	−1.48858	−	0.101561i
$541$	1.92058e8	−	1.92058e8i	1.21295	−	1.21295i	0.242894	−	0.970053i	$-0.421903\pi$
$541$	1.92058e8	−	1.92058e8i	1.21295	−	1.21295i	0.970053	−	0.242894i	$-0.0780966\pi$
$542$	−5.00228e7	+	1.38985e8i	−0.314174	+	0.872913i
$543$	−3.72928e7	+	1.14066e8i	−0.232930	+	0.712454i
$544$	−1.57182e7	+	9.95478e7i	−0.0976348	+	0.618351i
$545$			1.72646e8i			1.06651i
$546$	−2.46963e8	−	1.92250e8i	−1.51724	−	1.18110i
$547$	1.26199e8	−	1.26199e8i	0.771070	−	0.771070i	−0.207223	−	0.978294i	$-0.566443\pi$
$547$	1.26199e8	−	1.26199e8i	0.771070	−	0.771070i	0.978294	+	0.207223i	$0.0664427\pi$
$548$	527635.	+	436328.i	0.00320621	+	0.00265138i
$549$	−2.11754e7	−	1.36932e8i	−0.127972	−	0.827539i
$550$	3.94140e7	−	1.85514e7i	0.236898	−	0.111504i
$551$	3.93643e7			0.235314
$552$	−7.76376e7	−	4.94382e7i	−0.461588	−	0.293931i
$553$			4.69413e8i			2.77575i
$554$	7.25988e7	−	3.41708e7i	0.426972	−	0.200968i
$555$	9.18219e7	+	1.81027e8i	0.537115	+	1.05892i
$556$	−1.65669e7	−	1.74903e8i	−0.0963867	−	1.01759i
$557$	8.07331e7	+	8.07331e7i	0.467182	+	0.467182i	0.901000	−	0.433819i	$-0.142834\pi$
$557$	8.07331e7	+	8.07331e7i	0.467182	+	0.467182i	−0.433819	+	0.901000i	$0.642834\pi$
$558$	1.33910e8	+	1.98558e8i	0.770742	+	1.14284i
$559$	105265.			0.000602624
$560$	−2.33268e8	+	3.43526e8i	−1.32829	+	1.95612i
$561$	7.33413e6	−	2.24326e7i	0.0415394	−	0.127055i
$562$	6.79957e7	−	1.88922e8i	0.383065	−	1.06432i
$563$	3.29010e7	+	3.29010e7i	0.184367	+	0.184367i	0.793256	−	0.608889i	$-0.208384\pi$
$563$	3.29010e7	+	3.29010e7i	0.184367	+	0.184367i	−0.608889	+	0.793256i	$0.708384\pi$
$564$	−4.43965e7	−	1.00001e7i	−0.247464	−	0.0557399i
$565$	−2.19885e8	−	2.19885e8i	−1.21913	−	1.21913i
$566$	2.38507e6	−	1.12261e6i	0.0131538	−	0.00619126i
$567$	−2.75377e8	+	8.72562e7i	−1.51070	+	0.478682i
$568$	2.02208e8	−	1.19664e8i	1.10345	−	0.653007i
$569$	−3.06225e8			−1.66228			−0.831140	−	0.556064i	$-0.812311\pi$
$569$	−3.06225e8			−1.66228			−0.831140	+	0.556064i	$0.812311\pi$
$570$	−5.20486e7	−	4.17823e8i	−0.281051	−	2.25615i
$571$	1.87475e8	+	1.87475e8i	1.00701	+	1.00701i	0.999975	+	0.00703758i	$0.00224015\pi$
$571$	1.87475e8	+	1.87475e8i	1.00701	+	1.00701i	0.00703758	+	0.999975i	$0.497760\pi$
$572$	3.08993e7	−	3.73653e7i	0.165105	−	0.199655i
$573$	−6.75296e7	+	3.42528e7i	−0.358947	+	0.182068i
$574$	−2.92641e8	−	1.05326e8i	−1.54739	−	0.556928i
$575$			1.27564e8i			0.671002i
$576$	8.08346e7	+	1.73165e8i	0.422990	+	0.906135i
$577$	7.33795e6			0.0381986			0.0190993	−	0.999818i	$-0.493920\pi$
$577$	7.33795e6			0.0381986			0.0190993	+	0.999818i	$0.493920\pi$
$578$	−3.97662e7	+	1.10488e8i	−0.205935	+	0.572178i
$579$	9.97495e7	+	1.96657e8i	0.513896	+	1.01315i
$580$	3.46441e7	+	2.86490e7i	0.177560	+	0.146833i
$581$	8.37825e7	−	8.37825e7i	0.427194	−	0.427194i
$582$	−1.56292e8	+	1.94694e7i	−0.792808	+	0.0987607i
$583$			6.01716e7i			0.303659i
$584$	−2.90264e7	−	4.90489e7i	−0.145732	−	0.246258i
$585$	2.92428e8	+	2.14098e8i	1.46067	+	1.06941i
$586$	3.25907e6	+	6.92417e6i	0.0161958	+	0.0344092i
$587$	1.28404e8	−	1.28404e8i	0.634841	−	0.634841i	−0.314437	−	0.949278i	$-0.601816\pi$
$587$	1.28404e8	−	1.28404e8i	0.634841	−	0.634841i	0.949278	+	0.314437i	$0.101816\pi$
$588$	−6.75160e7	+	2.99745e8i	−0.332105	+	1.47442i
$589$	−3.03496e8	+	3.03496e8i	−1.48528	+	1.48528i
$590$	3.29988e8	+	1.18767e8i	1.60673	+	0.578284i
$591$	−2.62251e8	−	8.57405e7i	−1.27044	−	0.415359i
$592$	9.27518e7	−	1.36592e8i	0.447051	−	0.658356i
$593$		−	2.45629e8i		−	1.17792i	−0.808162	−	0.588960i	$-0.799537\pi$
$593$		−	2.45629e8i		−	1.17792i	0.808162	−	0.588960i	$-0.200463\pi$
$594$	−1.22541e7	−	4.30425e7i	−0.0584683	−	0.205370i
$595$	2.20472e8	−	2.20472e8i	1.04665	−	1.04665i
$596$	3.05027e8	−	2.88922e7i	1.44078	−	0.136472i
$597$	−7.98639e7	+	4.05091e7i	−0.375342	+	0.190384i
$598$	6.04666e7	+	1.28466e8i	0.282756	+	0.600739i
$599$	−1.44997e8			−0.674651			−0.337326	−	0.941388i	$-0.609522\pi$
$599$	−1.44997e8			−0.674651			−0.337326	+	0.941388i	$0.609522\pi$
$600$	1.42261e8	−	2.23406e8i	0.658615	−	1.03429i
$601$		−	9.64809e7i		−	0.444445i	−0.974996	−	0.222222i	$-0.928669\pi$
$601$		−	9.64809e7i		−	0.444445i	0.974996	−	0.222222i	$-0.0713311\pi$
$602$	−73129.4	−	155369.i	−0.000335199	−	0.000712158i
$603$	3.06722e7	+	1.98344e8i	0.139892	+	0.904620i
$604$	5.95196e7	−	7.19748e7i	0.270115	−	0.326640i
$605$	−2.22979e8	−	2.22979e8i	−1.00693	−	1.00693i
$606$	−1.40017e8	+	1.79865e8i	−0.629163	+	0.808218i
$607$	8.88145e7			0.397117			0.198558	−	0.980089i	$-0.436374\pi$
$607$	8.88145e7			0.397117			0.198558	+	0.980089i	$0.436374\pi$
$608$	−2.76981e8	+	2.01440e8i	−1.23236	+	0.896263i
$609$	5.25376e7	+	1.71767e7i	0.232605	+	0.0760478i
$610$	2.66833e8	+	9.60371e7i	1.17557	+	0.423106i
$611$	4.96407e7	+	4.96407e7i	0.217628	+	0.217628i
$612$	−3.52043e7	−	1.39110e8i	−0.153582	−	0.606880i
$613$	2.55149e8	+	2.55149e8i	1.10767	+	1.10767i	0.993456	+	0.114219i	$0.0364364\pi$
$613$	2.55149e8	+	2.55149e8i	1.10767	+	1.10767i	0.114219	+	0.993456i	$0.463564\pi$
$614$	8.34281e7	+	1.77250e8i	0.360419	+	0.765739i
$615$	3.42334e8	+	1.11923e8i	1.47172	+	0.481164i
$616$	−7.66172e7	−	1.96486e7i	−0.327781	−	0.0840600i
$617$	−4.58271e8			−1.95105			−0.975523	−	0.219899i	$-0.929427\pi$
$617$	−4.58271e8			−1.95105			−0.975523	+	0.219899i	$0.929427\pi$
$618$	2.37886e6	+	1.90965e7i	0.0100787	+	0.0809072i
$619$	3.18119e8	+	3.18119e8i	1.34128	+	1.34128i	0.894791	+	0.446486i	$0.147325\pi$
$619$	3.18119e8	+	3.18119e8i	1.34128	+	1.34128i	0.446486	+	0.894791i	$0.352675\pi$
$620$	−4.87985e8	+	4.62221e7i	−2.04754	+	0.193943i
$621$	1.29324e8	+	2.12101e7i	0.540014	+	0.0885661i
$622$	−4.64528e7	+	1.29066e8i	−0.193037	+	0.536342i
$623$		−	5.23866e7i		−	0.216649i
$624$	3.73706e7	−	2.92420e8i	0.153807	−	1.20352i
$625$	1.76431e8			0.722660
$626$	1.99143e8	+	7.16744e7i	0.811786	+	0.292174i
$627$	7.15286e7	−	3.62812e7i	0.290187	−	0.147190i
$628$	−4.75920e8	+	4.50793e7i	−1.92156	+	0.182011i
$629$	−8.76637e7	+	8.76637e7i	−0.352264	+	0.352264i
$630$	1.12851e8	−	5.80359e8i	0.451319	−	2.32100i
$631$			3.60186e8i			1.43363i	0.697261	+	0.716817i	$0.254402\pi$
$631$			3.60186e8i			1.43363i	−0.697261	+	0.716817i	$0.745598\pi$
$632$	−3.80519e8	+	2.25185e8i	−1.50739	+	0.892050i
$633$	−2.18051e8	−	7.12898e7i	−0.859701	−	0.281071i
$634$	1.53296e8	−	7.21537e7i	0.601540	−	0.283133i
$635$	2.11201e8	−	2.11201e8i	0.824849	−	0.824849i
$636$	1.95523e8	+	3.09212e8i	0.760024	+	1.20195i
$637$	3.35151e8	−	3.35151e8i	1.29665	−	1.29665i
$638$	−2.89994e6	+	8.05729e6i	−0.0111667	+	0.0310261i
$639$	−1.97629e8	+	2.69934e8i	−0.757441	+	1.03456i
$640$	−3.90374e8	−	2.42985e7i	−1.48916	−	0.0926914i
$641$		−	5.55142e7i		−	0.210780i	−0.994431	−	0.105390i	$-0.966391\pi$
$641$		−	5.55142e7i		−	0.210780i	0.994431	−	0.105390i	$-0.0336091\pi$
$642$	1.70578e8	−	2.19124e8i	0.644641	−	0.828102i
$643$	2.96753e8	−	2.96753e8i	1.11625	−	1.11625i	0.123966	−	0.992286i	$-0.460439\pi$
$643$	2.96753e8	−	2.96753e8i	1.11625	−	1.11625i	0.992286	−	0.123966i	$-0.0395613\pi$
$644$	1.47608e8	−	1.78496e8i	0.552651	−	0.668300i
$645$	89954.2	+	177345.i	0.000335230	+	0.000660907i
$646$	2.32679e8	−	1.09518e8i	0.863098	−	0.406244i
$647$	1.20264e8			0.444042			0.222021	−	0.975042i	$-0.428735\pi$
$647$	1.20264e8			0.444042			0.222021	+	0.975042i	$0.428735\pi$
$648$	−2.02835e8	−	1.81370e8i	−0.745450	−	0.666562i
$649$			6.68048e7i			0.244384i
$650$	−3.69668e8	+	1.73996e8i	−1.34608	+	0.633575i
$651$	−5.37492e8	+	2.72630e8i	−1.94818	+	0.988169i
$652$	−1.35763e7	+	1.28595e6i	−0.0489823	+	0.00463962i
$653$	−7.79328e7	−	7.79328e7i	−0.279886	−	0.279886i	0.553178	−	0.833063i	$-0.313415\pi$
$653$	−7.79328e7	−	7.79328e7i	−0.279886	−	0.279886i	−0.833063	+	0.553178i	$0.813415\pi$
$654$	−1.22824e8	+	1.57778e8i	−0.439085	+	0.564046i
$655$	−7.24509e7			−0.257822
$656$	−5.50050e7	−	2.87749e8i	−0.194846	−	1.01930i
$657$	6.54769e7	+	4.79382e7i	0.230883	+	0.169038i
$658$	3.87828e7	−	1.07756e8i	0.136132	−	0.378235i
$659$	2.69762e8	+	2.69762e8i	0.942594	+	0.942594i	0.998439	−	0.0558450i	$-0.0177853\pi$
$659$	2.69762e8	+	2.69762e8i	0.942594	+	0.942594i	−0.0558450	+	0.998439i	$0.517785\pi$
$660$	8.93566e7	+	2.01271e7i	0.310810	+	0.0700083i
$661$	−2.23806e8	−	2.23806e8i	−0.774939	−	0.774939i	0.204026	−	0.978965i	$-0.434597\pi$
$661$	−2.23806e8	−	2.23806e8i	−0.774939	−	0.774939i	−0.978965	+	0.204026i	$0.934597\pi$
$662$	2.12393e8	−	9.99693e7i	0.732093	−	0.344582i
$663$	−6.87876e7	+	2.10398e8i	−0.236031	+	0.721940i
$664$	1.08108e8	+	2.77245e7i	0.369279	+	0.0947021i
$665$	1.05957e9			3.60302
$666$	−4.48717e7	+	2.30762e8i	−0.151897	+	0.781163i
$667$	−1.77316e7	−	1.77316e7i	−0.0597544	−	0.0597544i
$668$	6.01496e7	+	4.97407e7i	0.201792	+	0.166872i
$669$	−1.28142e6	−	2.52633e6i	−0.00427970	−	0.00843745i
$670$	−3.86502e8	−	1.39108e8i	−1.28507	−	0.462516i
$671$			5.40193e7i			0.178806i
$672$	−4.57571e8	+	1.47991e8i	−1.50782	+	0.487673i
$673$	−4.63390e8			−1.52020			−0.760101	−	0.649805i	$-0.774850\pi$
$673$	−4.63390e8			−1.52020			−0.760101	+	0.649805i	$0.774850\pi$
$674$	−4.49018e7	+	1.24757e8i	−0.146651	+	0.407460i
$675$	−6.10330e7	+	3.72137e8i	−0.198451	+	1.21002i
$676$	−9.29429e7	+	1.12392e8i	−0.300868	+	0.363828i
$677$	−7.41584e7	+	7.41584e7i	−0.238998	+	0.238998i	−0.816435	−	0.577437i	$-0.804053\pi$
$677$	−7.41584e7	+	7.41584e7i	−0.238998	+	0.238998i	0.577437	+	0.816435i	$0.304053\pi$
$678$	−4.45191e7	−	3.57380e8i	−0.142842	−	1.14668i
$679$		−	3.96347e8i		−	1.26609i
$680$	2.84484e8	+	7.29564e7i	0.904756	+	0.232026i
$681$	−1.03721e8	+	3.17249e8i	−0.328418	+	1.00452i
$682$	−3.97629e7	−	8.44795e7i	−0.125350	−	0.266317i
$683$	2.55057e8	−	2.55057e8i	0.800526	−	0.800526i	−0.182652	−	0.983178i	$-0.558468\pi$
$683$	2.55057e8	−	2.55057e8i	0.800526	−	0.800526i	0.983178	+	0.182652i	$0.0584680\pi$
$684$	2.49681e8	−	4.18871e8i	0.780221	−	1.30892i
$685$	1.41085e6	−	1.41085e6i	0.00438944	−	0.00438944i
$686$	−2.46150e8	−	8.85930e7i	−0.762479	−	0.274427i
$687$	1.44829e8	−	4.42983e8i	0.446668	−	1.36621i
$688$	90865.3	−	133814.i	0.000279018	−	0.000410900i
$689$		−	5.64356e8i		−	1.72542i
$690$	−1.64763e8	+	2.11653e8i	−0.501547	+	0.644284i
$691$	−1.10464e8	+	1.10464e8i	−0.334801	+	0.334801i	−0.854407	−	0.519605i	$-0.826079\pi$
$691$	−1.10464e8	+	1.10464e8i	−0.334801	+	0.334801i	0.519605	+	0.854407i	$0.326079\pi$
$692$	1.04400e7	+	1.10219e8i	0.0315051	+	0.332611i
$693$	1.11297e8	−	1.72111e7i	0.334414	−	0.0517142i
$694$	−2.33506e7	−	4.96102e7i	−0.0698584	−	0.148420i
$695$	−5.11974e8			−1.52508
$696$	1.12793e7	+	5.08283e7i	0.0334545	+	0.150757i
$697$			2.19977e8i			0.649649i
$698$	−1.26892e8	−	2.69593e8i	−0.373137	−	0.792761i
$699$	−1.11294e8	−	2.19417e8i	−0.325868	−	0.642450i
$700$	5.13632e8	+	4.24748e8i	1.49747	+	1.23833i
$701$	−2.55843e8	−	2.55843e8i	−0.742710	−	0.742710i	0.230388	−	0.973099i	$-0.426000\pi$
$701$	−2.55843e8	−	2.55843e8i	−0.742710	−	0.742710i	−0.973099	+	0.230388i	$0.926000\pi$
$702$	1.14932e8	+	4.03700e8i	0.332223	+	1.16694i
$703$	−4.21307e8			−1.21264
$704$	−2.08269e7	−	7.15338e7i	−0.0596907	−	0.205019i
$705$	−4.12119e7	+	1.26053e8i	−0.117613	+	0.359738i
$706$	8.15511e7	+	2.93514e7i	0.231748	+	0.0834093i
$707$	−4.05600e8	−	4.05600e8i	−1.14773	−	1.14773i
$708$	2.17077e8	+	3.43299e8i	0.611667	+	0.967326i
$709$	1.63174e8	+	1.63174e8i	0.457838	+	0.457838i	0.897945	−	0.440107i	$-0.145059\pi$
$709$	1.63174e8	+	1.63174e8i	0.457838	+	0.457838i	−0.440107	+	0.897945i	$0.645059\pi$
$710$	−2.91597e8	−	6.19521e8i	−0.814719	−	1.73094i
$711$	3.71902e8	−	5.07966e8i	1.03471	−	1.41327i
$712$	4.24660e7	−	2.51307e7i	0.117653	−	0.0696250i
$713$	2.73419e8			0.754327
$714$	3.58334e8	−	4.46379e7i	0.984448	−	0.122634i
$715$	−9.99115e7	−	9.99115e7i	−0.273336	−	0.273336i
$716$	5.22796e7	+	5.51936e8i	0.142427	+	1.50366i
$717$	5.63280e8	−	2.85711e8i	1.52815	−	0.775120i
$718$	1.25868e8	−	3.49718e8i	0.340051	−	0.944810i
$719$			2.27808e8i			0.612891i	0.951888	+	0.306445i	$0.0991397\pi$
$719$			2.27808e8i			0.612891i	−0.951888	+	0.306445i	$0.900860\pi$
$720$	5.24592e8	−	1.86928e8i	1.40548	−	0.500815i
$721$	−4.84274e7			−0.129207
$722$	4.68161e8	+	1.68498e8i	1.24389	+	0.447695i
$723$	−1.60707e8	−	3.16835e8i	−0.425226	−	0.838335i
$724$	−2.68243e7	−	2.83195e8i	−0.0706827	−	0.746225i
$725$	5.10235e7	−	5.10235e7i	0.133892	−	0.133892i
$726$	−4.51455e7	−	3.62409e8i	−0.117979	−	0.947084i
$727$		−	2.02698e8i		−	0.527528i	−0.964587	−	0.263764i	$-0.915036\pi$
$727$		−	2.02698e8i		−	0.527528i	0.964587	−	0.263764i	$-0.0849640\pi$
$728$	7.18601e8	+	1.84286e8i	1.86249	+	0.477638i
$729$	3.67125e8	+	1.23751e8i	0.947613	+	0.319422i
$730$	−1.50275e8	+	7.07315e7i	−0.386294	+	0.181821i
$731$	−85880.7	+	85880.7i	−0.000219858	+	0.000219858i
$732$	1.75532e8	+	2.77597e8i	0.447531	+	0.707753i
$733$	−4.73398e8	+	4.73398e8i	−1.20203	+	1.20203i	−0.228478	+	0.973549i	$0.573375\pi$
$733$	−4.73398e8	+	4.73398e8i	−1.20203	+	1.20203i	−0.973549	+	0.228478i	$0.926625\pi$
$734$	−9.80437e7	+	2.72408e8i	−0.247931	+	0.688862i
$735$	8.51054e8	+	2.78244e8i	2.14336	+	0.700751i
$736$	2.15504e8	+	3.40271e7i	0.540532	+	0.0853476i
$737$		−	7.82460e7i		−	0.195461i
$738$	2.33230e8	+	3.45827e8i	0.580249	+	0.860380i
$739$	−2.46966e8	+	2.46966e8i	−0.611933	+	0.611933i	−0.943449	−	0.331517i	$-0.892440\pi$
$739$	−2.46966e8	+	2.46966e8i	−0.611933	+	0.611933i	0.331517	+	0.943449i	$0.392440\pi$
$740$	−3.70787e8	−	3.06623e8i	−0.915018	−	0.756675i
$741$	−6.70875e8	+	3.40286e8i	−1.64887	+	0.836352i
$742$	−8.32983e8	+	3.92069e8i	−2.03903	+	0.959734i
$743$	−3.69774e8			−0.901509			−0.450755	−	0.892648i	$-0.648845\pi$
$743$	−3.69774e8			−0.901509			−0.450755	+	0.892648i	$0.648845\pi$
$744$	−4.78846e8	−	3.04920e8i	−1.16272	−	0.740402i
$745$		−	8.92869e8i		−	2.15933i
$746$	−3.04922e8	+	1.43521e8i	−0.734468	+	0.345700i
$747$	−1.57042e8	+	2.42852e7i	−0.376751	+	0.0582613i
$748$	5.27536e6	+	5.56941e7i	0.0126051	+	0.133077i
$749$	4.94129e8	+	4.94129e8i	1.17597	+	1.17597i
$750$	−1.12344e8	−	8.74548e7i	−0.266297	−	0.207300i
$751$	−5.20608e8			−1.22911			−0.614556	−	0.788873i	$-0.710665\pi$
$751$	−5.20608e8			−1.22911			−0.614556	+	0.788873i	$0.710665\pi$
$752$	1.05954e8	−	2.02538e7i	0.249153	−	0.0476269i
$753$	−9.14647e7	−	2.99035e7i	−0.214224	−	0.0700385i
$754$	2.71988e7	−	7.55702e7i	0.0634506	−	0.176294i
$755$	−1.92454e8	−	1.92454e8i	−0.447184	−	0.447184i
$756$	5.16012e8	−	4.50097e8i	1.19425	−	1.04170i
$757$	3.82593e8	+	3.82593e8i	0.881962	+	0.881962i	0.993734	−	0.111772i	$-0.0356527\pi$
$757$	3.82593e8	+	3.82593e8i	0.881962	+	0.881962i	−0.111772	+	0.993734i	$0.535653\pi$
$758$	8.28760e7	−	3.90082e7i	0.190292	−	0.0895669i
$759$	−4.85628e7	−	1.58771e7i	−0.111065	−	0.0363117i
$760$	5.08295e8	+	8.58919e8i	1.15791	+	1.95664i
$761$	−7.07649e8			−1.60570			−0.802849	−	0.596182i	$-0.796684\pi$
$761$	−7.07649e8			−1.60570			−0.802849	+	0.596182i	$0.796684\pi$
$762$	3.43266e8	−	4.27609e7i	0.775828	−	0.0966456i
$763$	−3.55794e8	−	3.55794e8i	−0.800987	−	0.800987i
$764$	1.14381e8	−	1.38317e8i	0.256492	−	0.310167i
$765$	−4.13252e8	+	6.39060e7i	−0.923062	+	0.142744i
$766$	7.63674e8	+	2.74857e8i	1.69911	+	0.611534i
$767$		−	6.26569e8i		−	1.38862i
$768$	−3.39470e8	−	2.99925e8i	−0.749407	−	0.662109i
$769$	5.46878e8			1.20257			0.601286	−	0.799034i	$-0.294655\pi$
$769$	5.46878e8			1.20257			0.601286	+	0.799034i	$0.294655\pi$
$770$	−7.80579e7	+	2.16879e8i	−0.170980	+	0.475057i
$771$	6.48783e8	−	3.29080e8i	1.41559	−	0.718023i
$772$	−4.02800e8	−	3.33096e8i	−0.875463	−	0.723964i
$773$	−1.89487e8	+	1.89487e8i	−0.410244	+	0.410244i	−0.881823	−	0.471580i	$-0.843684\pi$
$773$	−1.89487e8	+	1.89487e8i	−0.410244	+	0.410244i	0.471580	+	0.881823i	$0.343684\pi$
$774$	−43959.0	+	226068.i	−9.48037e−5	+	0.000487547i
$775$			7.86775e8i			1.69023i
$776$	3.21289e8	−	1.90134e8i	0.687561	−	0.406888i
$777$	−5.62297e8	−	1.83838e8i	−1.19868	−	0.391896i
$778$	6.04585e7	+	1.28449e8i	0.128386	+	0.272767i
$779$	−5.28598e8	+	5.28598e8i	−1.11818	+	1.11818i
$780$	−8.38086e8	−	1.88774e8i	−1.76606	−	0.397795i
$781$	9.22262e7	−	9.22262e7i	0.193598	−	0.193598i
$782$	−1.54142e8	−	5.54779e7i	−0.322330	−	0.116011i
$783$	−4.32440e7	−	6.02114e7i	−0.0900825	−	0.125428i
$784$	−1.36744e8	−	7.15356e8i	−0.283767	−	1.48448i
$785$			1.39310e9i			2.87988i
$786$	−6.62118e7	−	5.15430e7i	−0.136354	−	0.106146i
$787$	−4.05036e8	+	4.05036e8i	−0.830939	+	0.830939i	−0.987645	−	0.156706i	$-0.949912\pi$
$787$	−4.05036e8	+	4.05036e8i	−0.830939	+	0.830939i	0.156706	+	0.987645i	$0.449912\pi$
$788$	6.51098e8	−	6.16722e7i	1.33066	−	0.126041i
$789$	−1.18255e8	−	2.33140e8i	−0.240761	−	0.474663i
$790$	5.48732e8	+	1.16583e9i	1.11296	+	2.36457i
$791$	9.06292e8			1.83121
$792$	6.73429e7	+	8.19639e7i	0.135555	+	0.164986i
$793$		−	5.06653e8i		−	1.01599i
$794$	−2.19079e8	−	4.65452e8i	−0.437663	−	0.929851i
$795$	9.50802e8	−	4.82272e8i	1.89229	−	0.959822i
$796$	1.35273e8	−	1.63580e8i	0.268208	−	0.324334i
$797$	2.21300e8	+	2.21300e8i	0.437125	+	0.437125i	0.891043	−	0.453918i	$-0.149974\pi$
$797$	2.21300e8	+	2.21300e8i	0.437125	+	0.437125i	−0.453918	+	0.891043i	$0.649974\pi$
$798$	9.68328e8	+	7.53801e8i	1.90552	+	1.48337i
$799$	−8.09993e7			−0.158796
$800$	−9.79145e7	+	6.20122e8i	−0.191239	+	1.21118i
$801$	−4.15044e7	+	5.66892e7i	−0.0807600	+	0.110307i
$802$	−7.58182e8	−	2.72881e8i	−1.46977	−	0.528993i
$803$	−2.23709e7	−	2.23709e7i	−0.0432054	−	0.0432054i
$804$	−2.54255e8	−	4.02094e8i	−0.489216	−	0.773676i
$805$	−4.77283e8	−	4.77283e8i	−0.914931	−	0.914931i
$806$	3.72940e8	+	7.92342e8i	0.712253	+	1.51324i
$807$	−1.30269e8	+	3.98449e8i	−0.247868	+	0.758145i
$808$	1.34217e8	−	5.23364e8i	0.254434	−	0.992132i
$809$	−3.34736e8			−0.632204			−0.316102	−	0.948725i	$-0.602374\pi$
$809$	−3.34736e8			−0.632204			−0.316102	+	0.948725i	$0.602374\pi$
$810$	−5.81921e8	+	5.38616e8i	−1.09499	+	1.01350i
$811$	7.75143e7	+	7.75143e7i	0.145318	+	0.145318i	0.776023	−	0.630705i	$-0.217234\pi$
$811$	7.75143e7	+	7.75143e7i	0.145318	+	0.145318i	−0.630705	+	0.776023i	$0.717234\pi$
$812$	−1.30436e8	+	1.23550e7i	−0.243630	+	0.0230767i
$813$	2.25517e8	+	4.44608e8i	0.419670	+	0.827381i
$814$	3.10373e7	−	8.62352e7i	0.0575454	−	0.159886i
$815$			3.97404e7i			0.0734107i
$816$	2.08083e8	+	2.69061e8i	0.382972	+	0.495200i
$817$	−412737.			−0.000756846
$818$	1.58543e8	+	5.70617e7i	0.289658	+	0.104252i
$819$	−1.04387e9	+	1.61425e8i	−1.90017	+	0.293846i
$820$	−8.49921e8	+	8.05048e7i	−1.54148	+	0.146009i
$821$	5.57554e8	−	5.57554e8i	1.00753	−	1.00753i	0.00755688	−	0.999971i	$-0.497595\pi$
$821$	5.57554e8	−	5.57554e8i	1.00753	−	1.00753i	0.999971	−	0.00755688i	$-0.00240545\pi$
$822$	2.29306e6	−	285648.i	0.00412857	−	0.000514300i
$823$		−	5.78008e8i		−	1.03689i	−0.855110	−	0.518447i	$-0.826510\pi$
$823$		−	5.78008e8i		−	1.03689i	0.855110	−	0.518447i	$-0.173490\pi$
$824$	−2.32314e7	−	3.92566e7i	−0.0415235	−	0.0701666i
$825$	4.56872e7	−	1.39742e8i	0.0813641	−	0.248865i
$826$	−9.24810e8	+	4.35290e8i	−1.64101	+	0.772394i
$827$	−2.29866e8	+	2.29866e8i	−0.406404	+	0.406404i	−0.880483	−	0.474079i	$-0.842781\pi$
$827$	−2.29866e8	+	2.29866e8i	−0.406404	+	0.406404i	0.474079	+	0.880483i	$0.342781\pi$
$828$	−3.01148e8	+	7.62112e7i	−0.530505	+	0.134254i
$829$	1.51889e8	−	1.51889e8i	0.266602	−	0.266602i	−0.561128	−	0.827729i	$-0.689632\pi$
$829$	1.51889e8	−	1.51889e8i	0.266602	−	0.266602i	0.827729	+	0.561128i	$0.189632\pi$
$830$	1.10141e8	−	3.06020e8i	0.192626	−	0.535199i
$831$	8.41537e7	−	2.57398e8i	0.146646	−	0.448540i
$832$	1.95338e8	+	6.70923e8i	0.339169	+	1.16494i
$833$			5.46870e8i			0.946127i
$834$	−4.67885e8	−	3.64228e8i	−0.806569	−	0.627878i
$835$	1.60835e8	−	1.60835e8i	0.276261	−	0.276261i
$836$	−1.21155e8	+	1.46508e8i	−0.207358	+	0.250750i
$837$	7.97634e8	+	1.30817e8i	1.36028	+	0.223095i
$838$	−2.84881e7	+	1.34088e7i	−0.0484095	+	0.0227854i
$839$	−3.83221e7			−0.0648879			−0.0324439	−	0.999474i	$-0.510329\pi$
$839$	−3.83221e7			−0.0648879			−0.0324439	+	0.999474i	$0.510329\pi$
$840$	3.03606e8	+	1.36815e9i	0.512239	+	2.30832i
$841$		−	5.80639e8i		−	0.976153i
$842$	−5.94507e8	+	2.79823e8i	−0.995912	+	0.468757i
$843$	−3.06544e8	−	6.04353e8i	−0.511693	−	1.00881i
$844$	5.41362e8	−	5.12780e7i	0.900451	−	0.0852911i
$845$	3.00527e8	+	3.00527e8i	0.498096	+	0.498096i
$846$	−1.27340e8	+	8.58792e7i	−0.210306	+	0.141833i
$847$	9.19045e8			1.51247
$848$	−7.17418e8	−	4.87157e8i	−1.17648	−	0.798879i
$849$	2.76469e6	−	8.45624e6i	0.00451776	−	0.0138183i
$850$	1.59640e8	−	4.43551e8i	0.259948	−	0.722249i
$851$	1.89777e8	+	1.89777e8i	0.307932	+	0.307932i
$852$	1.74254e8	−	7.73619e8i	0.281749	−	1.25086i
$853$	4.13539e6	+	4.13539e6i	0.00666300	+	0.00666300i	0.710430	−	0.703767i	$-0.248500\pi$
$853$	4.13539e6	+	4.13539e6i	0.00666300	+	0.00666300i	−0.703767	+	0.710430i	$0.748500\pi$
$854$	−7.47815e8	+	3.51982e8i	−1.20066	+	0.565128i
$855$	−1.14660e9	−	8.39469e8i	−1.83448	−	1.34309i
$856$	−1.63512e8	+	6.37597e8i	−0.260693	+	1.01654i
$857$	3.54100e8			0.562579			0.281289	−	0.959623i	$-0.409238\pi$
$857$	3.54100e8			0.562579			0.281289	+	0.959623i	$0.409238\pi$
$858$	−2.02286e7	−	1.62387e8i	−0.0320262	−	0.257092i
$859$	4.66963e8	+	4.66963e8i	0.736721	+	0.736721i	0.971942	−	0.235221i	$-0.0755813\pi$
$859$	4.66963e8	+	4.66963e8i	0.736721	+	0.736721i	−0.235221	+	0.971942i	$0.575581\pi$
$860$	−363245.	−	300386.i	−0.000571090	−	0.000472264i
$861$	−9.36147e8	+	4.74839e8i	−1.46668	+	0.743938i
$862$	−5.41599e8	−	1.94929e8i	−0.845583	−	0.304337i
$863$		−	7.41700e8i		−	1.15397i	−0.816754	−	0.576986i	$-0.804229\pi$
$863$		−	7.41700e8i		−	1.15397i	0.816754	−	0.576986i	$-0.195771\pi$
$864$	6.12401e8	+	2.02374e8i	0.949499	+	0.313771i
$865$	3.22630e8			0.498491
$866$	3.80110e8	−	1.05611e9i	0.585270	−	1.62614i
$867$	1.79277e8	+	3.53446e8i	0.275086	+	0.542333i
$868$	9.10400e8	−	1.10091e9i	1.39211	−	1.68342i
$869$	−1.73553e8	+	1.73553e8i	−0.264467	+	0.264467i
$870$	1.50560e8	−	1.87554e7i	0.228640	−	0.0284819i
$871$			7.33877e8i			1.11063i
$872$	1.17736e8	−	4.59097e8i	0.177566	−	0.692397i
$873$	−3.14014e8	+	4.28899e8i	−0.471961	+	0.644632i
$874$	−2.37087e8	−	5.03710e8i	−0.355118	−	0.754478i
$875$	2.53338e8	−	2.53338e8i	0.378161	−	0.378161i
$876$	−1.87654e8	−	4.22680e7i	−0.279154	−	0.0628781i
$877$	3.64210e8	−	3.64210e8i	0.539949	−	0.539949i	−0.383565	−	0.923514i	$-0.625304\pi$
$877$	3.64210e8	−	3.64210e8i	0.539949	−	0.539949i	0.923514	+	0.383565i	$0.125304\pi$
$878$	−1.19824e8	−	4.31263e7i	−0.177035	−	0.0637174i
$879$	2.45495e7	+	8.02623e6i	0.0361474	+	0.0118180i
$880$	−2.13254e8	+	4.07647e7i	−0.312931	+	0.0598186i
$881$		−	5.84202e8i		−	0.854348i	−0.904169	−	0.427174i	$-0.859509\pi$
$881$		−	5.84202e8i		−	0.854348i	0.904169	−	0.427174i	$-0.140491\pi$
$882$	5.79817e8	+	8.59739e8i	0.845056	+	1.25303i
$883$	−5.03576e8	+	5.03576e8i	−0.731448	+	0.731448i	−0.970907	−	0.239459i	$-0.923030\pi$
$883$	−5.03576e8	+	5.03576e8i	−0.731448	+	0.731448i	0.239459	+	0.970907i	$0.423030\pi$
$884$	−4.94782e7	−	5.22361e8i	−0.0716237	−	0.756160i
$885$	1.05562e9	−	5.35437e8i	1.52292	−	0.772464i
$886$	−3.21654e8	−	6.83381e8i	−0.462475	−	0.982566i
$887$	6.34064e8			0.908578			0.454289	−	0.890854i	$-0.349893\pi$
$887$	6.34064e8			0.908578			0.454289	+	0.890854i	$0.349893\pi$
$888$	−1.20719e8	−	5.44003e8i	−0.172400	−	0.776895i
$889$			8.70500e8i			1.23898i
$890$	−6.12386e7	−	1.30106e8i	−0.0868670	−	0.184556i
$891$	−1.34074e8	−	6.95526e7i	−0.189544	−	0.0983287i
$892$	5.17452e6	+	4.27908e6i	0.00729081	+	0.00602914i
$893$	−1.94639e8	−	1.94639e8i	−0.273322	−	0.273322i
$894$	6.35204e8	−	8.15979e8i	0.888998	−	1.14200i
$895$	1.61562e9			2.25356
$896$	8.54571e8	−	7.54420e8i	1.18802	−	1.04879i
$897$	4.55475e8	+	1.48913e8i	0.631084	+	0.206327i
$898$	2.03016e8	+	7.30684e7i	0.280351	+	0.100902i
$899$	−1.09363e8	−	1.09363e8i	−0.150519	−	0.150519i
$900$	−2.19301e8	−	8.66568e8i	−0.300825	−	1.18871i
$901$	4.60433e8	+	4.60433e8i	0.629494	+	0.629494i
$902$	−6.92548e7	−	1.47137e8i	−0.0943692	−	0.200495i
$903$	−550860.	−	180098.i	−0.000748131	−	0.000244594i
$904$	4.34764e8	+	7.34665e8i	0.588502	+	0.994453i
$905$	−8.28963e8			−1.11838
$906$	−3.89653e7	−	3.12796e8i	−0.0523954	−	0.420608i
$907$	−9.45177e8	−	9.45177e8i	−1.26675	−	1.26675i	−0.947757	−	0.318994i	$-0.896655\pi$
$907$	−9.45177e8	−	9.45177e8i	−1.26675	−	1.26675i	−0.318994	−	0.947757i	$-0.603345\pi$
$908$	−7.46057e7	−	7.87642e8i	−0.0996586	−	1.05213i
$909$	1.17567e8	+	7.60257e8i	0.156529	+	1.01221i
$910$	7.32113e8	−	2.03413e9i	0.971525	−	2.69932i
$911$		−	2.25502e8i		−	0.298261i	−0.988818	−	0.149130i	$-0.952353\pi$
$911$		−	2.25502e8i		−	0.298261i	0.988818	−	0.149130i	$-0.0476474\pi$
$912$	−1.46528e8	+	1.14656e9i	−0.193169	+	1.51152i
$913$	6.19526e7			0.0814043
$914$	−8.67723e7	−	3.12306e7i	−0.113643	−	0.0409017i
$915$	8.53588e8	−	4.32962e8i	1.11426	−	0.565180i
$916$	1.04174e8	+	1.09980e9i	0.135542	+	1.43097i
$917$	1.49309e8	−	1.49309e8i	0.193633	−	0.193633i
$918$	−4.23129e8	−	2.35593e8i	−0.546946	−	0.304533i
$919$			7.17091e8i			0.923906i	0.886904	+	0.461953i	$0.152851\pi$
$919$			7.17091e8i			0.923906i	−0.886904	+	0.461953i	$0.847149\pi$
$920$	1.57938e8	−	6.15859e8i	0.202826	−	0.790893i
$921$	6.28437e8	+	2.05461e8i	0.804419	+	0.262997i
$922$	−1.03565e9	+	4.87459e8i	−1.32135	+	0.621935i
$923$	−8.64999e8	+	8.64999e8i	−1.10005	+	1.10005i
$924$	−2.25628e8	+	1.42671e8i	−0.286007	+	0.180850i
$925$	−5.46092e8	+	5.46092e8i	−0.689986	+	0.689986i
$926$	−2.39930e8	+	6.66631e8i	−0.302170	+	0.839562i
$927$	5.24048e7	+	3.83676e7i	0.0657857	+	0.0481643i
$928$	−7.25879e7	−	9.98084e7i	−0.0908281	−	0.124889i
$929$			6.79322e8i			0.847282i	0.905830	+	0.423641i	$0.139248\pi$
$929$			6.79322e8i			0.847282i	−0.905830	+	0.423641i	$0.860752\pi$
$930$	−1.01621e9	+	1.30541e9i	−1.26338	+	1.62293i
$931$	−1.31411e9	+	1.31411e9i	−1.62848	+	1.62848i
$932$	4.49419e8	+	3.71648e8i	0.555142	+	0.459075i
$933$	2.09423e8	+	4.12878e8i	0.257857	+	0.508366i
$934$	1.23345e9	−	5.80563e8i	1.51385	−	0.712539i
$935$	1.63027e8			0.199445
$936$	−6.31616e8	−	7.68748e8i	−0.770239	−	0.937468i
$937$		−	1.94347e8i		−	0.236243i	−0.992999	−	0.118122i	$-0.962313\pi$
$937$		−	1.94347e8i		−	0.236243i	0.992999	−	0.118122i	$-0.0376873\pi$
$938$	1.08320e9	−	5.09839e8i	1.31250	−	0.617767i
$939$	6.37049e8	−	3.23128e8i	0.769443	−	0.390282i
$940$	−2.96433e7	−	3.12956e8i	−0.0356897	−	0.376790i
$941$	−9.79708e8	−	9.79708e8i	−1.17578	−	1.17578i	−0.980808	−	0.194977i	$-0.937537\pi$
$941$	−9.79708e8	−	9.79708e8i	−1.17578	−	1.17578i	−0.194977	−	0.980808i	$-0.562463\pi$
$942$	−9.91081e8	+	1.27314e9i	−1.18565	+	1.52308i
$943$	4.76212e8			0.567891
$944$	−7.96505e8	−	5.40860e8i	−0.946831	−	0.642937i
$945$	−1.16400e9	−	1.62072e9i	−1.37930	−	1.92049i
$946$	30406.0	−	84481.2i	3.59158e−5	−	9.97899e-5i
$947$	8.74189e8	+	8.74189e8i	1.02933	+	1.02933i	0.999557	+	0.0297755i	$0.00947923\pi$
$947$	8.74189e8	+	8.74189e8i	1.02933	+	1.02933i	0.0297755	+	0.999557i	$0.490521\pi$
$948$	−3.27913e8	+	1.45581e9i	−0.384887	+	1.70875i
$949$	2.09819e8	+	2.09819e8i	0.245498	+	0.245498i
$950$	1.44945e9	−	6.82229e8i	1.69057	−	0.795718i
$951$	1.77695e8	−	5.43510e8i	0.206602	−	0.631926i
$952$	−7.36626e8	+	4.35924e8i	−0.853760	+	0.505242i
$953$	6.28629e8			0.726299			0.363150	−	0.931731i	$-0.381701\pi$
$953$	6.28629e8			0.726299			0.363150	+	0.931731i	$0.381701\pi$
$954$	1.21202e9	+	2.35678e8i	1.39593	+	0.271440i
$955$	−3.69847e8	−	3.69847e8i	−0.424631	−	0.424631i
$956$	−9.54079e8	+	1.15373e9i	−1.09197	+	1.32048i
$957$	1.30737e7	+	2.57749e7i	0.0149164	+	0.0294078i
$958$	−6.15577e8	−	2.21555e8i	−0.700142	−	0.251991i
$959$			5.81505e6i			0.00659322i
$960$	−9.63416e8	+	9.02436e8i	−1.08893	+	1.02001i
$961$	7.98862e8			0.900122
$962$	−2.91102e8	+	8.08809e8i	−0.326979	+	0.908492i
$963$	−1.43228e8	−	9.26196e8i	−0.160380	−	1.03711i
$964$	6.48953e8	+	5.36652e8i	0.724406	+	0.599048i
$965$	−1.07705e9	+	1.07705e9i	−1.19854	+	1.19854i
$966$	−9.66334e7	−	7.75730e8i	−0.107200	−	0.860556i
$967$		−	3.02114e8i		−	0.334111i	−0.985947	−	0.167055i	$-0.946574\pi$
$967$		−	3.02114e8i		−	0.334111i	0.985947	−	0.167055i	$-0.0534259\pi$
$968$	4.40881e8	+	7.45003e8i	0.486066	+	0.821357i
$969$	2.69713e8	−	8.24961e8i	0.296436	−	0.906696i
$970$	−4.63319e8	−	9.84358e8i	−0.507650	−	1.07854i
$971$	−5.19831e8	+	5.19831e8i	−0.567811	+	0.567811i	−0.931515	−	0.363703i	$-0.881512\pi$
$971$	−5.19831e8	+	5.19831e8i	−0.567811	+	0.567811i	0.363703	+	0.931515i	$0.381512\pi$
$972$	−9.14991e8	+	7.82433e7i	−0.996364	+	0.0852017i
$973$	1.05509e9	−	1.05509e9i	1.14539	−	1.14539i
$974$	8.14528e8	+	2.93161e8i	0.881514	+	0.317270i
$975$	−4.28505e8	+	1.31065e9i	−0.462319	+	1.41408i
$976$	−6.44066e8	−	4.37347e8i	−0.692757	−	0.470411i
$977$		−	1.82700e9i		−	1.95909i	−0.201231	−	0.979544i	$-0.564494\pi$
$977$		−	1.82700e9i		−	1.95909i	0.201231	−	0.979544i	$-0.435506\pi$
$978$	−2.82721e7	+	3.63181e7i	−0.0302233	+	0.0388246i
$979$	1.93685e7	−	1.93685e7i	0.0206418	−	0.0206418i
$980$	−2.11293e9	+	2.00138e8i	−2.24496	+	0.212643i
$981$	1.03131e8	+	6.66901e8i	0.109240	+	0.706406i
$982$	2.89890e8	+	6.15896e8i	0.306125	+	0.650388i
$983$	7.42160e8			0.781335			0.390667	−	0.920532i	$-0.372244\pi$
$983$	7.42160e8			0.781335			0.390667	+	0.920532i	$0.372244\pi$
$984$	−8.34002e8	−	5.31078e8i	−0.875351	−	0.557408i
$985$		−	1.90588e9i		−	1.99429i
$986$	3.94641e7	+	8.38447e7i	0.0411691	+	0.0874671i
$987$	−1.74844e8	−	3.44706e8i	−0.181844	−	0.358506i
$988$	1.13632e9	−	1.37411e9i	1.17823	−	1.42479i
$989$	185917.	+	185917.i	0.000192190	+	0.000192190i
$990$	2.56296e8	−	1.72848e8i	0.264141	−	0.178139i
$991$	−5.91835e8			−0.608106			−0.304053	−	0.952655i	$-0.598340\pi$
$991$	−5.91835e8			−0.608106			−0.304053	+	0.952655i	$0.598340\pi$
$992$	1.32916e9	+	2.09869e8i	1.36158	+	0.214987i
$993$	2.46198e8	−	7.53036e8i	0.251441	−	0.769074i
$994$	1.87766e9	+	6.75798e8i	1.91187	+	0.688110i
$995$	−4.37399e8	−	4.37399e8i	−0.444026	−	0.444026i
$996$	3.18365e8	−	2.01311e8i	0.322216	−	0.203746i
$997$	−3.38717e8	−	3.38717e8i	−0.341784	−	0.341784i	0.515254	−	0.857038i	$-0.327698\pi$
$997$	−3.38717e8	−	3.38717e8i	−0.341784	−	0.341784i	−0.857038	+	0.515254i	$0.827698\pi$
$998$	−4.41092e8	−	9.37136e8i	−0.443749	−	0.942782i
$999$	4.62830e8	+	6.44427e8i	0.464221	+	0.646364i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.7.i.a.5.19	✓	92
3.2	odd	2	inner	48.7.i.a.5.28	yes	92
4.3	odd	2		192.7.i.a.113.17		92
12.11	even	2		192.7.i.a.113.38		92
16.3	odd	4		192.7.i.a.17.38		92
16.13	even	4	inner	48.7.i.a.29.28	yes	92
48.29	odd	4	inner	48.7.i.a.29.19	yes	92
48.35	even	4		192.7.i.a.17.17		92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.i.a.5.19	✓	92	1.1	even	1	trivial
48.7.i.a.5.28	yes	92	3.2	odd	2	inner
48.7.i.a.29.19	yes	92	48.29	odd	4	inner
48.7.i.a.29.28	yes	92	16.13	even	4	inner
192.7.i.a.17.17		92	48.35	even	4
192.7.i.a.17.38		92	16.3	odd	4
192.7.i.a.113.17		92	4.3	odd	2
192.7.i.a.113.38		92	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	48.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.70919 + 7.52730i) q^{2} +(12.2138 + 24.0795i) q^{3} +(-49.3206 - 40.7857i) q^{4} +(-131.879 + 131.879i) q^{5} +(-214.343 + 26.7009i) q^{6} -543.561i q^{7} +(440.625 - 260.755i) q^{8} +(-430.647 + 588.204i) q^{9} +O(q^{10})\)	\(q+(-2.70919 + 7.52730i) q^{2} +(12.2138 + 24.0795i) q^{3} +(-49.3206 - 40.7857i) q^{4} +(-131.879 + 131.879i) q^{5} +(-214.343 + 26.7009i) q^{6} -543.561i q^{7} +(440.625 - 260.755i) q^{8} +(-430.647 + 588.204i) q^{9} +(-635.408 - 1349.98i) q^{10} +(200.967 - 200.967i) q^{11} +(379.710 - 1685.77i) q^{12} +(-1884.89 + 1884.89i) q^{13} +(4091.55 + 1472.61i) q^{14} +(-4786.32 - 1564.84i) q^{15} +(769.049 + 4023.16i) q^{16} -3075.59i q^{17} +(-3260.89 - 4835.17i) q^{18} +(7390.56 - 7390.56i) q^{19} +(11883.1 - 1125.57i) q^{20} +(13088.7 - 6638.93i) q^{21} +(968.282 + 2057.20i) q^{22} -6658.13 q^{23} +(11660.6 + 7425.24i) q^{24} -19159.1i q^{25} +(-9081.62 - 19294.7i) q^{26} +(-19423.5 - 3185.59i) q^{27} +(-22169.5 + 26808.8i) q^{28} +(2663.15 + 2663.15i) q^{29} +(24746.1 - 31788.7i) q^{30} -41065.4 q^{31} +(-32367.0 - 5110.60i) q^{32} +(7293.75 + 2384.62i) q^{33} +(23150.9 + 8332.36i) q^{34} +(71684.2 + 71684.2i) q^{35} +(45230.1 - 11446.3i) q^{36} +(-28503.0 - 28503.0i) q^{37} +(35608.6 + 75653.4i) q^{38} +(-68408.9 - 22365.6i) q^{39} +(-23721.1 + 92497.3i) q^{40} -71523.3 q^{41} +(14513.6 + 116509. i) q^{42} +(-27.9233 - 27.9233i) q^{43} +(-18108.4 + 1715.23i) q^{44} +(-20778.4 - 134365. i) q^{45} +(18038.1 - 50117.8i) q^{46} -26336.1i q^{47} +(-87482.7 + 67656.3i) q^{48} -177810. q^{49} +(144216. + 51905.5i) q^{50} +(74058.9 - 37564.6i) q^{51} +(169841. - 16087.4i) q^{52} +(-149705. + 149705. i) q^{53} +(76600.8 - 137576. i) q^{54} +53006.6i q^{55} +(-141736. - 239507. i) q^{56} +(268228. + 87694.6i) q^{57} +(-27261.3 + 12831.4i) q^{58} +(-166208. + 166208. i) q^{59} +(172241. + 272393. i) q^{60} +(-134399. + 134399. i) q^{61} +(111254. - 309112. i) q^{62} +(319725. + 234083. i) q^{63} +(126157. - 229791. i) q^{64} -497154. i q^{65} +(-37709.9 + 48441.9i) q^{66} +(194674. - 194674. i) q^{67} +(-125440. + 151690. i) q^{68} +(-81320.9 - 160325. i) q^{69} +(-733795. + 345383. i) q^{70} +458913. q^{71} +(-36376.7 + 371471. i) q^{72} -111317. i q^{73} +(291771. - 137331. i) q^{74} +(461342. - 234005. i) q^{75} +(-665937. + 63077.8i) q^{76} +(-109238. - 109238. i) q^{77} +(353685. - 454342. i) q^{78} -863589. q^{79} +(-631991. - 429148. i) q^{80} +(-160527. - 506617. i) q^{81} +(193770. - 538378. i) q^{82} +(154136. + 154136. i) q^{83} +(-916316. - 206395. i) q^{84} +(405606. + 405606. i) q^{85} +(285.836 - 134.538i) q^{86} +(-31600.2 + 96654.4i) q^{87} +(36147.9 - 140954. i) q^{88} +96376.7 q^{89} +(1.06770e6 + 207614. i) q^{90} +(1.02455e6 + 1.02455e6i) q^{91} +(328383. + 271557. i) q^{92} +(-501563. - 988835. i) q^{93} +(198240. + 71349.5i) q^{94} +1.94932e6i q^{95} +(-272263. - 841802. i) q^{96} +729167. q^{97} +(481719. - 1.33843e6i) q^{98} +(31663.7 + 204755. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q - 2 q^{3} - 4 q^{4} + 508 q^{6}+O(q^{10}) \) 92 * q - 2 * q^3 - 4 * q^4 + 508 * q^6	\( 92 q - 2 q^{3} - 4 q^{4} + 508 q^{6} + 1496 q^{10} + 4288 q^{12} - 4 q^{13} - 4 q^{15} + 10352 q^{16} + 10020 q^{18} - 3940 q^{19} + 1456 q^{21} - 42088 q^{22} + 66376 q^{24} - 34322 q^{27} + 27000 q^{28} - 127836 q^{30} - 8 q^{31} - 4 q^{33} + 128424 q^{34} + 172420 q^{36} - 4 q^{37} - 164392 q^{40} + 221560 q^{42} - 195268 q^{43} - 31252 q^{45} + 150712 q^{46} - 188048 q^{48} - 1142884 q^{49} + 385056 q^{51} - 122368 q^{52} + 151912 q^{54} - 181960 q^{58} + 242304 q^{60} - 326500 q^{61} + 470592 q^{63} - 251752 q^{64} + 489172 q^{66} + 1207676 q^{67} - 1460 q^{69} + 346392 q^{70} - 903480 q^{72} + 1413778 q^{75} - 359992 q^{76} + 1478252 q^{78} + 860920 q^{79} - 4 q^{81} - 2412800 q^{82} - 730640 q^{84} + 434496 q^{85} + 1259360 q^{88} - 291792 q^{90} + 2320992 q^{91} - 1176260 q^{93} - 1412496 q^{94} + 1956200 q^{96} - 8 q^{97} - 4048228 q^{99}+O(q^{100}) \) 92 * q - 2 * q^3 - 4 * q^4 + 508 * q^6 + 1496 * q^10 + 4288 * q^12 - 4 * q^13 - 4 * q^15 + 10352 * q^16 + 10020 * q^18 - 3940 * q^19 + 1456 * q^21 - 42088 * q^22 + 66376 * q^24 - 34322 * q^27 + 27000 * q^28 - 127836 * q^30 - 8 * q^31 - 4 * q^33 + 128424 * q^34 + 172420 * q^36 - 4 * q^37 - 164392 * q^40 + 221560 * q^42 - 195268 * q^43 - 31252 * q^45 + 150712 * q^46 - 188048 * q^48 - 1142884 * q^49 + 385056 * q^51 - 122368 * q^52 + 151912 * q^54 - 181960 * q^58 + 242304 * q^60 - 326500 * q^61 + 470592 * q^63 - 251752 * q^64 + 489172 * q^66 + 1207676 * q^67 - 1460 * q^69 + 346392 * q^70 - 903480 * q^72 + 1413778 * q^75 - 359992 * q^76 + 1478252 * q^78 + 860920 * q^79 - 4 * q^81 - 2412800 * q^82 - 730640 * q^84 + 434496 * q^85 + 1259360 * q^88 - 291792 * q^90 + 2320992 * q^91 - 1176260 * q^93 - 1412496 * q^94 + 1956200 * q^96 - 8 * q^97 - 4048228 * q^99

Introduction

L-functions

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