LMFDB - Embedded newform 48.9.l.a.19.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,9,Mod(19,48)]

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([2, 3, 0]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	48.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:	$19.5541732829$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.9
Character	$\chi$	$=$	48.19
Dual form			48.9.l.a.43.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10.8909 - 11.7213i) q^{2} +(-33.0681 + 33.0681i) q^{3} +(-18.7756 + 255.311i) q^{4} +(260.136 - 260.136i) q^{5} +(747.742 + 27.4575i) q^{6} -368.567 q^{7} +(3197.04 - 2560.49i) q^{8} -2187.00i q^{9} +O(q^{10})$	\(q+(-10.8909 - 11.7213i) q^{2} +(-33.0681 + 33.0681i) q^{3} +(-18.7756 + 255.311i) q^{4} +(260.136 - 260.136i) q^{5} +(747.742 + 27.4575i) q^{6} -368.567 q^{7} +(3197.04 - 2560.49i) q^{8} -2187.00i q^{9} +(-5882.23 - 215.999i) q^{10} +(-17059.0 - 17059.0i) q^{11} +(-7821.76 - 9063.51i) q^{12} +(32217.3 + 32217.3i) q^{13} +(4014.04 + 4320.07i) q^{14} +17204.4i q^{15} +(-64831.0 - 9587.23i) q^{16} -120640. q^{17} +(-25634.4 + 23818.4i) q^{18} +(5000.89 - 5000.89i) q^{19} +(61531.1 + 71299.6i) q^{20} +(12187.8 - 12187.8i) q^{21} +(-14164.6 + 385740. i) q^{22} +428464. q^{23} +(-21049.5 + 190391. i) q^{24} +255284. i q^{25} +(26751.1 - 728503. i) q^{26} +(72320.0 + 72320.0i) q^{27} +(6920.08 - 94099.2i) q^{28} +(669611. + 669611. i) q^{29} +(201657. - 187372. i) q^{30} -35624.3i q^{31} +(593695. + 864314. i) q^{32} +1.12821e6 q^{33} +(1.31388e6 + 1.41406e6i) q^{34} +(-95877.5 + 95877.5i) q^{35} +(558364. + 41062.3i) q^{36} +(-1.95653e6 + 1.95653e6i) q^{37} +(-113081. - 4152.40i) q^{38} -2.13073e6 q^{39} +(165589. - 1.49774e6i) q^{40} +2.75070e6i q^{41} +(-275593. - 10119.9i) q^{42} +(2.02704e6 + 2.02704e6i) q^{43} +(4.67562e6 - 4.03504e6i) q^{44} +(-568916. - 568916. i) q^{45} +(-4.66637e6 - 5.02214e6i) q^{46} +5.13135e6i q^{47} +(2.46087e6 - 1.82681e6i) q^{48} -5.62896e6 q^{49} +(2.99225e6 - 2.78028e6i) q^{50} +(3.98935e6 - 3.98935e6i) q^{51} +(-8.83031e6 + 7.62051e6i) q^{52} +(-2.06872e6 + 2.06872e6i) q^{53} +(60049.6 - 1.63531e6i) q^{54} -8.87528e6 q^{55} +(-1.17833e6 + 943715. i) q^{56} +330740. i q^{57} +(556000. - 1.51414e7i) q^{58} +(-9.48573e6 - 9.48573e6i) q^{59} +(-4.39246e6 - 323023. i) q^{60} +(8.73489e6 + 8.73489e6i) q^{61} +(-417561. + 387981. i) q^{62} +806057. i q^{63} +(3.66496e6 - 1.63720e7i) q^{64} +1.67617e7 q^{65} +(-1.22873e7 - 1.32241e7i) q^{66} +(-1.48877e7 + 1.48877e7i) q^{67} +(2.26510e6 - 3.08007e7i) q^{68} +(-1.41685e7 + 1.41685e7i) q^{69} +(2.16800e6 + 79610.2i) q^{70} +2.71789e7 q^{71} +(-5.59980e6 - 6.99193e6i) q^{72} -7.57343e6i q^{73} +(4.42413e7 + 1.62457e6i) q^{74} +(-8.44176e6 - 8.44176e6i) q^{75} +(1.18289e6 + 1.37068e6i) q^{76} +(6.28737e6 + 6.28737e6i) q^{77} +(2.32056e7 + 2.49748e7i) q^{78} +5.69812e6i q^{79} +(-1.93588e7 + 1.43709e7i) q^{80} -4.78297e6 q^{81} +(3.22416e7 - 2.99576e7i) q^{82} +(7.10472e6 - 7.10472e6i) q^{83} +(2.88285e6 + 3.34052e6i) q^{84} +(-3.13828e7 + 3.13828e7i) q^{85} +(1.68312e6 - 4.58359e7i) q^{86} -4.42856e7 q^{87} +(-9.82176e7 - 1.08589e7i) q^{88} +9.01003e7i q^{89} +(-472390. + 1.28644e7i) q^{90} +(-1.18742e7 - 1.18742e7i) q^{91} +(-8.04469e6 + 1.09391e8i) q^{92} +(1.17803e6 + 1.17803e6i) q^{93} +(6.01459e7 - 5.58851e7i) q^{94} -2.60182e6i q^{95} +(-4.82136e7 - 8.94887e6i) q^{96} +1.12056e8 q^{97} +(6.13046e7 + 6.59785e7i) q^{98} +(-3.73079e7 + 3.73079e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 372 q^{4} + 17460 q^{8}+O(q^{10}) $ 64 * q - 372 * q^4 + 17460 * q^8	\( 64 q - 372 q^{4} + 17460 q^{8} - 13784 q^{10} + 39552 q^{11} - 22680 q^{12} + 116772 q^{14} - 161824 q^{16} - 26244 q^{18} - 167552 q^{19} + 690000 q^{20} - 1252768 q^{22} + 1691136 q^{23} - 74844 q^{24} - 1682100 q^{26} + 678600 q^{28} - 2132352 q^{29} - 2054808 q^{30} + 1407840 q^{32} - 3704544 q^{34} - 2415744 q^{35} - 1041012 q^{36} - 4720512 q^{37} + 2413320 q^{38} - 3544848 q^{40} + 9436500 q^{42} - 7244672 q^{43} - 3982056 q^{44} + 11165992 q^{46} - 9467280 q^{48} + 52706752 q^{49} + 17072676 q^{50} + 13862016 q^{51} - 22890864 q^{52} - 5358720 q^{53} - 4960116 q^{54} - 46326784 q^{55} - 9637152 q^{56} + 25732944 q^{58} + 44938752 q^{59} + 40927032 q^{60} + 24476032 q^{61} - 17024868 q^{62} - 116303448 q^{64} + 29941632 q^{65} - 56828952 q^{66} - 44244736 q^{67} - 12614400 q^{68} - 8636544 q^{69} - 60922560 q^{70} + 159664128 q^{71} - 18502020 q^{72} + 140654028 q^{74} + 12918528 q^{75} + 204842760 q^{76} - 94964352 q^{77} + 14001660 q^{78} + 38076648 q^{80} - 306110016 q^{81} - 260917000 q^{82} + 209328000 q^{83} - 127862712 q^{84} + 106960000 q^{85} - 123451824 q^{86} + 104240736 q^{88} + 53520264 q^{90} - 45401472 q^{91} + 351567216 q^{92} + 208488216 q^{94} + 49597920 q^{96} - 681890712 q^{98} + 86500224 q^{99}+O(q^{100}) \) 64 * q - 372 * q^4 + 17460 * q^8 - 13784 * q^10 + 39552 * q^11 - 22680 * q^12 + 116772 * q^14 - 161824 * q^16 - 26244 * q^18 - 167552 * q^19 + 690000 * q^20 - 1252768 * q^22 + 1691136 * q^23 - 74844 * q^24 - 1682100 * q^26 + 678600 * q^28 - 2132352 * q^29 - 2054808 * q^30 + 1407840 * q^32 - 3704544 * q^34 - 2415744 * q^35 - 1041012 * q^36 - 4720512 * q^37 + 2413320 * q^38 - 3544848 * q^40 + 9436500 * q^42 - 7244672 * q^43 - 3982056 * q^44 + 11165992 * q^46 - 9467280 * q^48 + 52706752 * q^49 + 17072676 * q^50 + 13862016 * q^51 - 22890864 * q^52 - 5358720 * q^53 - 4960116 * q^54 - 46326784 * q^55 - 9637152 * q^56 + 25732944 * q^58 + 44938752 * q^59 + 40927032 * q^60 + 24476032 * q^61 - 17024868 * q^62 - 116303448 * q^64 + 29941632 * q^65 - 56828952 * q^66 - 44244736 * q^67 - 12614400 * q^68 - 8636544 * q^69 - 60922560 * q^70 + 159664128 * q^71 - 18502020 * q^72 + 140654028 * q^74 + 12918528 * q^75 + 204842760 * q^76 - 94964352 * q^77 + 14001660 * q^78 + 38076648 * q^80 - 306110016 * q^81 - 260917000 * q^82 + 209328000 * q^83 - 127862712 * q^84 + 106960000 * q^85 - 123451824 * q^86 + 104240736 * q^88 + 53520264 * q^90 - 45401472 * q^91 + 351567216 * q^92 + 208488216 * q^94 + 49597920 * q^96 - 681890712 * q^98 + 86500224 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−10.8909	−	11.7213i	−0.680683	−	0.732578i
$2$	−10.8909	−	11.7213i	−0.680683	−	0.732578i
$3$	−33.0681	+	33.0681i	−0.408248	+	0.408248i
$3$	−33.0681	+	33.0681i	−0.408248	+	0.408248i
$4$	−18.7756	+	255.311i	−0.0733423	+	0.997307i
$5$	260.136	−	260.136i	0.416217	−	0.416217i	−0.467681	−	0.883898i	$-0.654910\pi$
$5$	260.136	−	260.136i	0.416217	−	0.416217i	0.883898	+	0.467681i	$0.154910\pi$
$6$	747.742	+	27.4575i	0.576961	+	0.0211864i
$7$	−368.567			−0.153506			−0.0767529	−	0.997050i	$-0.524455\pi$
$7$	−368.567			−0.153506			−0.0767529	+	0.997050i	$0.524455\pi$
$8$	3197.04	−	2560.49i	0.780528	−	0.625120i
$9$		−	2187.00i		−	0.333333i
$10$	−5882.23	−	215.999i	−0.588223	−	0.0215999i
$11$	−17059.0	−	17059.0i	−1.16515	−	1.16515i	−0.983332	−	0.181817i	$-0.941802\pi$
$11$	−17059.0	−	17059.0i	−1.16515	−	1.16515i	−0.181817	−	0.983332i	$-0.558198\pi$
$12$	−7821.76	−	9063.51i	−0.377207	−	0.437091i
$13$	32217.3	+	32217.3i	1.12802	+	1.12802i	0.990499	+	0.137518i	$0.0439124\pi$
$13$	32217.3	+	32217.3i	1.12802	+	1.12802i	0.137518	+	0.990499i	$0.456088\pi$
$14$	4014.04	+	4320.07i	0.104489	+	0.112455i
$15$			17204.4i			0.339840i
$16$	−64831.0	−	9587.23i	−0.989242	−	0.146290i
$17$	−120640.			−1.44443			−0.722215	−	0.691668i	$-0.756876\pi$
$17$	−120640.			−1.44443			−0.722215	+	0.691668i	$0.756876\pi$
$18$	−25634.4	+	23818.4i	−0.244193	+	0.226894i
$19$	5000.89	−	5000.89i	0.0383737	−	0.0383737i	−0.687660	−	0.726033i	$-0.741362\pi$
$19$	5000.89	−	5000.89i	0.0383737	−	0.0383737i	0.726033	+	0.687660i	$0.241362\pi$
$20$	61531.1	+	71299.6i	0.384570	+	0.445622i
$21$	12187.8	−	12187.8i	0.0626685	−	0.0626685i
$22$	−14164.6	+	385740.i	−0.0604663	+	1.64666i
$23$	428464.			1.53110			0.765550	−	0.643377i	$-0.222467\pi$
$23$	428464.			1.53110			0.765550	+	0.643377i	$0.222467\pi$
$24$	−21049.5	+	190391.i	−0.0634450	+	0.573854i
$25$			255284.i			0.653527i
$26$	26751.1	−	728503.i	0.0585393	−	1.59418i
$27$	72320.0	+	72320.0i	0.136083	+	0.136083i
$28$	6920.08	−	94099.2i	0.0112585	−	0.153092i
$29$	669611.	+	669611.i	0.946740	+	0.946740i	0.998652	−	0.0519114i	$-0.0165313\pi$
$29$	669611.	+	669611.i	0.946740	+	0.946740i	−0.0519114	+	0.998652i	$0.516531\pi$
$30$	201657.	−	187372.i	0.248959	−	0.231323i
$31$		−	35624.3i		−	0.0385744i	−0.999814	−	0.0192872i	$-0.993860\pi$
$31$		−	35624.3i		−	0.0385744i	0.999814	−	0.0192872i	$-0.00613969\pi$
$32$	593695.	+	864314.i	0.566191	+	0.824274i
$33$	1.12821e6			0.951340
$34$	1.31388e6	+	1.41406e6i	0.983199	+	1.05816i
$35$	−95877.5	+	95877.5i	−0.0638917	+	0.0638917i
$36$	558364.	+	41062.3i	0.332436	+	0.0244474i
$37$	−1.95653e6	+	1.95653e6i	−1.04395	+	1.04395i	−0.0449597	+	0.998989i	$0.514316\pi$
$37$	−1.95653e6	+	1.95653e6i	−1.04395	+	1.04395i	−0.998989	+	0.0449597i	$0.985684\pi$
$38$	−113081.	−	4152.40i	−0.0542320	−	0.00199143i
$39$	−2.13073e6			−0.921022
$40$	165589.	−	1.49774e6i	0.0646833	−	0.585055i
$41$			2.75070e6i			0.973436i	0.873559	+	0.486718i	$0.161806\pi$
$41$			2.75070e6i			0.973436i	−0.873559	+	0.486718i	$0.838194\pi$
$42$	−275593.	−	10119.9i	−0.0885669	−	0.00325223i
$43$	2.02704e6	+	2.02704e6i	0.592910	+	0.592910i	0.938417	−	0.345506i	$-0.112293\pi$
$43$	2.02704e6	+	2.02704e6i	0.592910	+	0.592910i	−0.345506	+	0.938417i	$0.612293\pi$
$44$	4.67562e6	−	4.03504e6i	1.24747	−	1.07656i
$45$	−568916.	−	568916.i	−0.138739	−	0.138739i
$46$	−4.66637e6	−	5.02214e6i	−1.04219	−	1.12165i
$47$			5.13135e6i			1.05158i	0.850616	+	0.525788i	$0.176229\pi$
$47$			5.13135e6i			1.05158i	−0.850616	+	0.525788i	$0.823771\pi$
$48$	2.46087e6	−	1.82681e6i	0.463579	−	0.344134i
$49$	−5.62896e6			−0.976436
$50$	2.99225e6	−	2.78028e6i	0.478760	−	0.444845i
$51$	3.98935e6	−	3.98935e6i	0.589686	−	0.589686i
$52$	−8.83031e6	+	7.62051e6i	−1.20771	+	1.04225i
$53$	−2.06872e6	+	2.06872e6i	−0.262179	+	0.262179i	−0.825939	−	0.563760i	$-0.809354\pi$
$53$	−2.06872e6	+	2.06872e6i	−0.262179	+	0.262179i	0.563760	+	0.825939i	$0.309354\pi$
$54$	60049.6	−	1.63531e6i	0.00706212	−	0.192320i
$55$	−8.87528e6			−0.969910
$56$	−1.17833e6	+	943715.i	−0.119816	+	0.0959596i
$57$			330740.i			0.0313320i
$58$	556000.	−	1.51414e7i	0.0491318	−	1.33799i
$59$	−9.48573e6	−	9.48573e6i	−0.782821	−	0.782821i	0.197485	−	0.980306i	$-0.436723\pi$
$59$	−9.48573e6	−	9.48573e6i	−0.782821	−	0.782821i	−0.980306	+	0.197485i	$0.936723\pi$
$60$	−4.39246e6	−	323023.i	−0.338924	−	0.0249246i
$61$	8.73489e6	+	8.73489e6i	0.630868	+	0.630868i	0.948286	−	0.317418i	$-0.102816\pi$
$61$	8.73489e6	+	8.73489e6i	0.630868	+	0.630868i	−0.317418	+	0.948286i	$0.602816\pi$
$62$	−417561.	+	387981.i	−0.0282588	+	0.0262569i
$63$			806057.i			0.0511686i
$64$	3.66496e6	−	1.63720e7i	0.218449	−	0.975848i
$65$	1.67617e7			0.938999
$66$	−1.22873e7	−	1.32241e7i	−0.647561	−	0.696931i
$67$	−1.48877e7	+	1.48877e7i	−0.738802	+	0.738802i	−0.972346	−	0.233544i	$-0.924968\pi$
$67$	−1.48877e7	+	1.48877e7i	−0.738802	+	0.738802i	0.233544	+	0.972346i	$0.424968\pi$
$68$	2.26510e6	−	3.08007e7i	0.105938	−	1.44054i
$69$	−1.41685e7	+	1.41685e7i	−0.625069	+	0.625069i
$70$	2.16800e6	+	79610.2i	0.0902957	+	0.00331571i
$71$	2.71789e7			1.06954			0.534772	−	0.844996i	$-0.320398\pi$
$71$	2.71789e7			1.06954			0.534772	+	0.844996i	$0.320398\pi$
$72$	−5.59980e6	−	6.99193e6i	−0.208373	−	0.260176i
$73$		−	7.57343e6i		−	0.266687i	−0.991070	−	0.133343i	$-0.957429\pi$
$73$		−	7.57343e6i		−	0.266687i	0.991070	−	0.133343i	$-0.0425713\pi$
$74$	4.42413e7	+	1.62457e6i	1.47537	+	0.0541765i
$75$	−8.44176e6	−	8.44176e6i	−0.266801	−	0.266801i
$76$	1.18289e6	+	1.37068e6i	0.0354559	+	0.0410847i
$77$	6.28737e6	+	6.28737e6i	0.178857	+	0.178857i
$78$	2.32056e7	+	2.49748e7i	0.626924	+	0.674721i
$79$			5.69812e6i			0.146293i	0.997321	+	0.0731465i	$0.0233041\pi$
$79$			5.69812e6i			0.146293i	−0.997321	+	0.0731465i	$0.976696\pi$
$80$	−1.93588e7	+	1.43709e7i	−0.472627	+	0.350851i
$81$	−4.78297e6			−0.111111
$82$	3.22416e7	−	2.99576e7i	0.713119	−	0.662601i
$83$	7.10472e6	−	7.10472e6i	0.149704	−	0.149704i	−0.628282	−	0.777986i	$-0.716241\pi$
$83$	7.10472e6	−	7.10472e6i	0.149704	−	0.149704i	0.777986	+	0.628282i	$0.216241\pi$
$84$	2.88285e6	+	3.34052e6i	0.0579035	+	0.0670960i
$85$	−3.13828e7	+	3.13828e7i	−0.601197	+	0.601197i
$86$	1.68312e6	−	4.58359e7i	0.0307695	−	0.837937i
$87$	−4.42856e7			−0.773010
$88$	−9.82176e7	−	1.08589e7i	−1.63779	−	0.181073i
$89$			9.01003e7i			1.43604i	0.696023	+	0.718019i	$0.254951\pi$
$89$			9.01003e7i			1.43604i	−0.696023	+	0.718019i	$0.745049\pi$
$90$	−472390.	+	1.28644e7i	−0.00719997	+	0.196074i
$91$	−1.18742e7	−	1.18742e7i	−0.173157	−	0.173157i
$92$	−8.04469e6	+	1.09391e8i	−0.112294	+	1.52698i
$93$	1.17803e6	+	1.17803e6i	0.0157479	+	0.0157479i
$94$	6.01459e7	−	5.58851e7i	0.770361	−	0.715789i
$95$		−	2.60182e6i		−	0.0319435i
$96$	−4.82136e7	−	8.94887e6i	−0.567655	−	0.105362i
$97$	1.12056e8			1.26575			0.632877	−	0.774252i	$-0.281874\pi$
$97$	1.12056e8			1.26575			0.632877	+	0.774252i	$0.281874\pi$
$98$	6.13046e7	+	6.59785e7i	0.664643	+	0.715316i
$99$	−3.73079e7	+	3.73079e7i	−0.388383	+	0.388383i
$100$	−6.51767e7	−	4.79312e6i	−0.651767	−	0.0479312i
$101$	3.44480e6	−	3.44480e6i	0.0331039	−	0.0331039i	−0.690361	−	0.723465i	$-0.742548\pi$
$101$	3.44480e6	−	3.44480e6i	0.0331039	−	0.0331039i	0.723465	+	0.690361i	$0.242548\pi$
$102$	−9.02078e7	−	3.31248e6i	−0.833381	−	0.0306022i
$103$	1.82230e7			0.161909			0.0809544	−	0.996718i	$-0.474203\pi$
$103$	1.82230e7			0.161909			0.0809544	+	0.996718i	$0.474203\pi$
$104$	1.85492e8	+	2.05079e7i	1.58560	+	0.175303i
$105$		−	6.34098e6i		−	0.0521674i
$106$	4.67782e7	+	1.71772e6i	0.370527	+	0.0136060i
$107$	−8.28894e7	−	8.28894e7i	−0.632359	−	0.632359i	0.316300	−	0.948659i	$-0.397559\pi$
$107$	−8.28894e7	−	8.28894e7i	−0.632359	−	0.632359i	−0.948659	+	0.316300i	$0.897559\pi$
$108$	−1.98219e7	+	1.71062e7i	−0.145697	+	0.125736i
$109$	−3.77786e7	−	3.77786e7i	−0.267633	−	0.267633i	0.560513	−	0.828146i	$-0.310604\pi$
$109$	−3.77786e7	−	3.77786e7i	−0.267633	−	0.267633i	−0.828146	+	0.560513i	$0.810604\pi$
$110$	9.66600e7	+	1.04029e8i	0.660201	+	0.710535i
$111$		−	1.29397e8i		−	0.852380i
$112$	2.38946e7	+	3.53354e6i	0.151854	+	0.0224563i
$113$	1.86917e8			1.14640			0.573198	−	0.819417i	$-0.305703\pi$
$113$	1.86917e8			1.14640			0.573198	+	0.819417i	$0.305703\pi$
$114$	3.87669e6	−	3.60207e6i	0.0229531	−	0.0213271i
$115$	1.11459e8	−	1.11459e8i	0.637269	−	0.637269i
$116$	−1.83531e8	+	1.58386e8i	−1.01363	+	0.874754i
$117$	7.04592e7	−	7.04592e7i	0.376006	−	0.376006i
$118$	−7.87631e6	+	2.14493e8i	−0.0406251	+	1.10633i
$119$	4.44641e7			0.221729
$120$	4.40517e7	+	5.50032e7i	0.212441	+	0.265254i
$121$			3.67657e8i			1.71515i
$122$	7.25286e6	−	1.97515e8i	0.0327394	−	0.891581i
$123$	−9.09604e7	−	9.09604e7i	−0.397404	−	0.397404i
$124$	9.09525e6	+	668868.i	0.0384705	+	0.00282913i
$125$	1.68024e8	+	1.68024e8i	0.688226	+	0.688226i
$126$	9.44800e6	−	8.77871e6i	0.0374850	−	0.0348296i
$127$		−	2.77151e8i		−	1.06537i	−0.846313	−	0.532686i	$-0.821183\pi$
$127$		−	2.77151e8i		−	1.06537i	0.846313	−	0.532686i	$-0.178817\pi$
$128$	−2.31815e8	+	1.35348e8i	−0.863580	+	0.504212i
$129$	−1.34061e8			−0.484109
$130$	−1.82551e8	−	1.96468e8i	−0.639161	−	0.687891i
$131$	1.78420e7	−	1.78420e7i	0.0605841	−	0.0605841i	−0.676166	−	0.736750i	$-0.736360\pi$
$131$	1.78420e7	−	1.78420e7i	0.0605841	−	0.0605841i	0.736750	+	0.676166i	$0.236360\pi$
$132$	−2.11829e7	+	2.88045e8i	−0.0697735	+	0.948778i
$133$	−1.84317e6	+	1.84317e6i	−0.00589058	+	0.00589058i
$134$	3.36643e8	+	1.23617e7i	1.04412	+	0.0383407i
$135$	3.76260e7			0.113280
$136$	−3.85692e8	+	3.08899e8i	−1.12742	+	0.902943i
$137$		−	6.22804e8i		−	1.76795i	−0.467538	−	0.883973i	$-0.654859\pi$
$137$		−	6.22804e8i		−	1.76795i	0.467538	−	0.883973i	$-0.345141\pi$
$138$	3.20381e8	+	1.17646e7i	0.883385	+	0.0324384i
$139$	−1.77564e8	−	1.77564e8i	−0.475658	−	0.475658i	0.428082	−	0.903740i	$-0.359190\pi$
$139$	−1.77564e8	−	1.77564e8i	−0.475658	−	0.475658i	−0.903740	+	0.428082i	$0.859190\pi$
$140$	−2.26784e7	−	2.62787e7i	−0.0590337	−	0.0684056i
$141$	−1.69684e8	−	1.69684e8i	−0.429304	−	0.429304i
$142$	−2.96003e8	−	3.18571e8i	−0.728020	−	0.783525i
$143$		−	1.09919e9i		−	2.62862i
$144$	−2.09673e7	+	1.41785e8i	−0.0487632	+	0.329747i
$145$	3.48379e8			0.788099
$146$	−8.87701e7	+	8.24817e7i	−0.195369	+	0.181529i
$147$	1.86139e8	−	1.86139e8i	0.398628	−	0.398628i
$148$	−4.62787e8	−	5.36257e8i	−0.964571	−	1.11770i
$149$	−4.70908e8	+	4.70908e8i	−0.955413	+	0.955413i	−0.999048	−	0.0436346i	$-0.986106\pi$
$149$	−4.70908e8	+	4.70908e8i	−0.955413	+	0.955413i	0.0436346	+	0.999048i	$0.486106\pi$
$150$	−7.00947e6	+	1.90887e8i	−0.0138459	+	0.377060i
$151$	−3.38251e8			−0.650626			−0.325313	−	0.945606i	$-0.605470\pi$
$151$	−3.38251e8			−0.650626			−0.325313	+	0.945606i	$0.605470\pi$
$152$	3.18332e6	−	2.87928e7i	0.00596357	−	0.0539399i
$153$			2.63840e8i			0.481477i
$154$	5.22061e6	−	1.42171e8i	0.00928193	−	0.252772i
$155$	−9.26714e6	−	9.26714e6i	−0.0160553	−	0.0160553i
$156$	4.00058e7	−	5.43998e8i	0.0675498	−	0.918541i
$157$	5.15512e8	+	5.15512e8i	0.848477	+	0.848477i	0.989943	−	0.141466i	$-0.0451816\pi$
$157$	5.15512e8	+	5.15512e8i	0.848477	+	0.848477i	−0.141466	+	0.989943i	$0.545182\pi$
$158$	6.67891e7	−	6.20578e7i	0.107171	−	0.0995790i
$159$		−	1.36817e8i		−	0.214068i
$160$	3.79280e8	+	7.03977e7i	0.578735	+	0.107418i
$161$	−1.57918e8			−0.235033
$162$	5.20909e7	+	5.60624e7i	0.0756314	+	0.0813976i
$163$	−6.02089e8	+	6.02089e8i	−0.852924	+	0.852924i	−0.990492	−	0.137568i	$-0.956071\pi$
$163$	−6.02089e8	+	6.02089e8i	−0.852924	+	0.852924i	0.137568	+	0.990492i	$0.456071\pi$
$164$	−7.02282e8	−	5.16461e7i	−0.970815	−	0.0713940i
$165$	2.93489e8	−	2.93489e8i	0.395964	−	0.395964i
$166$	−1.60653e8	−	5.89927e6i	−0.211571	−	0.00776902i
$167$	−1.10432e8			−0.141981			−0.0709903	−	0.997477i	$-0.522616\pi$
$167$	−1.10432e8			−0.141981			−0.0709903	+	0.997477i	$0.522616\pi$
$168$	7.75817e6	−	7.01719e7i	0.00973917	−	0.0880899i
$169$			1.26018e9i			1.54484i
$170$	7.09634e8	+	2.60582e7i	0.849648	+	0.0311996i
$171$	−1.09370e7	−	1.09370e7i	−0.0127912	−	0.0127912i
$172$	−5.55584e8	+	4.79466e8i	−0.634799	+	0.547828i
$173$	−8.98116e8	−	8.98116e8i	−1.00265	−	1.00265i	−0.999996	−	0.00265061i	$-0.999156\pi$
$173$	−8.98116e8	−	8.98116e8i	−1.00265	−	1.00265i	−0.00265061	−	0.999996i	$-0.500844\pi$
$174$	4.82311e8	+	5.19082e8i	0.526175	+	0.566291i
$175$		−	9.40894e7i		−	0.100320i
$176$	9.42400e8	+	1.26950e9i	0.982165	+	1.32306i
$177$	6.27350e8			0.639171
$178$	1.05609e9	−	9.81275e8i	1.05201	−	0.977487i
$179$	−2.98969e8	+	2.98969e8i	−0.291215	+	0.291215i	−0.837560	−	0.546345i	$-0.816019\pi$
$179$	−2.98969e8	+	2.98969e8i	−0.291215	+	0.291215i	0.546345	+	0.837560i	$0.316019\pi$
$180$	1.55932e8	−	1.34569e8i	0.148541	−	0.128190i
$181$	7.32022e7	−	7.32022e7i	0.0682040	−	0.0682040i	−0.672182	−	0.740386i	$-0.734643\pi$
$181$	7.32022e7	−	7.32022e7i	0.0682040	−	0.0682040i	0.740386	+	0.672182i	$0.234643\pi$
$182$	−9.85957e6	+	2.68503e8i	−0.00898612	+	0.244716i
$183$	−5.77693e8			−0.515101
$184$	1.36982e9	−	1.09708e9i	1.19507	−	0.957122i
$185$			1.01792e9i			0.869018i
$186$	978154.	−	2.66378e7i	0.000817251	−	0.0222559i
$187$	2.05800e9	+	2.05800e9i	1.68298	+	1.68298i
$188$	−1.31009e9	−	9.63443e7i	−1.04874	−	0.0771249i
$189$	−2.66548e7	−	2.66548e7i	−0.0208895	−	0.0208895i
$190$	−3.04966e7	+	2.83362e7i	−0.0234011	+	0.0217434i
$191$			1.38542e9i			1.04100i	0.853863	+	0.520499i	$0.174254\pi$
$191$			1.38542e9i			1.04100i	−0.853863	+	0.520499i	$0.825746\pi$
$192$	4.20198e8	+	6.62585e8i	0.309207	+	0.487570i
$193$	9.93916e8			0.716342			0.358171	−	0.933656i	$-0.383400\pi$
$193$	9.93916e8			0.716342			0.358171	+	0.933656i	$0.383400\pi$
$194$	−1.22040e9	−	1.31344e9i	−0.861577	−	0.927265i
$195$	−5.54279e8	+	5.54279e8i	−0.383345	+	0.383345i
$196$	1.05687e8	−	1.43713e9i	0.0716140	−	0.973806i
$197$	6.71646e7	−	6.71646e7i	0.0445939	−	0.0445939i	−0.684458	−	0.729052i	$-0.739961\pi$
$197$	6.71646e7	−	6.71646e7i	0.0445939	−	0.0445939i	0.729052	+	0.684458i	$0.239961\pi$
$198$	8.43613e8	+	3.09780e7i	0.548887	+	0.0201554i
$199$	1.83807e9			1.17206			0.586030	−	0.810290i	$-0.300690\pi$
$199$	1.83807e9			1.17206			0.586030	+	0.810290i	$0.300690\pi$
$200$	6.53653e8	+	8.16154e8i	0.408533	+	0.510096i
$201$		−	9.84615e8i		−	0.603229i
$202$	−7.78944e7	−	2.86033e6i	−0.0467844	−	0.00171795i
$203$	−2.46797e8	−	2.46797e8i	−0.145330	−	0.145330i
$204$	9.43620e8	+	1.09342e9i	0.544849	+	0.631347i
$205$	7.15555e8	+	7.15555e8i	0.405161	+	0.405161i
$206$	−1.98465e8	−	2.13596e8i	−0.110209	−	0.118611i
$207$		−	9.37052e8i		−	0.510367i
$208$	−1.77980e9	−	2.39755e9i	−0.950864	−	1.28090i
$209$	−1.70620e8			−0.0894221
$210$	−7.43242e7	+	6.90591e7i	−0.0382167	+	0.0355094i
$211$	−1.74556e9	+	1.74556e9i	−0.880656	+	0.880656i	−0.993601	−	0.112945i	$-0.963971\pi$
$211$	−1.74556e9	+	1.74556e9i	−0.880656	+	0.880656i	0.112945	+	0.993601i	$0.463971\pi$
$212$	−4.89324e8	−	5.67007e8i	−0.242244	−	0.280701i
$213$	−8.98755e8	+	8.98755e8i	−0.436639	+	0.436639i
$214$	−6.88257e7	+	1.87431e9i	−0.0328168	+	0.893689i
$215$	1.05461e9			0.493559
$216$	4.16385e8	+	4.60353e7i	0.191285	+	0.0211483i
$217$			1.31299e7i			0.00592139i
$218$	−3.13688e7	+	8.54257e8i	−0.0138890	+	0.378236i
$219$	2.50439e8	+	2.50439e8i	0.108874	+	0.108874i
$220$	1.66639e8	−	2.26595e9i	0.0711354	−	0.967297i
$221$	−3.88670e9	−	3.88670e9i	−1.62934	−	1.62934i
$222$	−1.51670e9	+	1.40926e9i	−0.624435	+	0.580201i
$223$		−	9.03544e8i		−	0.365367i	−0.983172	−	0.182684i	$-0.941522\pi$
$223$		−	9.03544e8i		−	0.365367i	0.983172	−	0.182684i	$-0.0584784\pi$
$224$	−2.18816e8	−	3.18558e8i	−0.0869136	−	0.126531i
$225$	5.58306e8			0.217842
$226$	−2.03570e9	−	2.19090e9i	−0.780332	−	0.839825i
$227$	−3.61340e9	+	3.61340e9i	−1.36086	+	1.36086i	−0.488034	+	0.872825i	$0.662286\pi$
$227$	−3.61340e9	+	3.61340e9i	−1.36086	+	1.36086i	−0.872825	+	0.488034i	$0.837714\pi$
$228$	−8.44415e7	−	6.20985e6i	−0.0312476	−	0.00229796i
$229$	−1.67209e9	+	1.67209e9i	−0.608018	+	0.608018i	−0.942428	−	0.334410i	$-0.891463\pi$
$229$	−1.67209e9	+	1.67209e9i	−0.608018	+	0.608018i	0.334410	+	0.942428i	$0.391463\pi$
$230$	−2.52033e9	−	9.25479e7i	−0.900628	−	0.0330716i
$231$	−4.15823e8			−0.146036
$232$	3.85531e9	+	4.26241e8i	1.33078	+	0.147131i
$233$		−	5.04455e8i		−	0.171159i	−0.996331	−	0.0855794i	$-0.972726\pi$
$233$		−	5.04455e8i		−	0.171159i	0.996331	−	0.0855794i	$-0.0272741\pi$
$234$	−1.59324e9	−	5.85046e7i	−0.531394	−	0.0195131i
$235$	1.33485e9	+	1.33485e9i	0.437683	+	0.437683i
$236$	2.59991e9	−	2.24371e9i	0.838127	−	0.723299i
$237$	−1.88426e8	−	1.88426e8i	−0.0597238	−	0.0597238i
$238$	−4.84255e8	−	5.21175e8i	−0.150927	−	0.162434i
$239$		−	4.64642e9i		−	1.42406i	−0.702151	−	0.712028i	$-0.747777\pi$
$239$		−	4.64642e9i		−	1.42406i	0.702151	−	0.712028i	$-0.252223\pi$
$240$	1.64942e8	−	1.11538e9i	0.0497150	−	0.336184i
$241$	4.62173e9			1.37005			0.685025	−	0.728520i	$-0.259791\pi$
$241$	4.62173e9			1.37005			0.685025	+	0.728520i	$0.259791\pi$
$242$	4.30940e9	−	4.00412e9i	1.25648	−	1.16747i
$243$	1.58164e8	−	1.58164e8i	0.0453609	−	0.0453609i
$244$	−2.39411e9	+	2.06611e9i	−0.675438	+	0.582899i
$245$	−1.46429e9	+	1.46429e9i	−0.406409	+	0.406409i
$246$	−7.55274e7	+	2.05681e9i	−0.0206236	+	0.561635i
$247$	3.22231e8			0.0865723
$248$	−9.12157e7	−	1.13892e8i	−0.0241136	−	0.0301084i
$249$			4.69879e8i			0.122233i
$250$	1.39516e8	−	3.79939e9i	0.0357160	−	0.972643i
$251$	2.41572e9	+	2.41572e9i	0.608629	+	0.608629i	0.942588	−	0.333959i	$-0.108385\pi$
$251$	2.41572e9	+	2.41572e9i	0.608629	+	0.608629i	−0.333959	+	0.942588i	$0.608385\pi$
$252$	−2.05795e8	−	1.51342e7i	−0.0510308	−	0.00375282i
$253$	−7.30915e9	−	7.30915e9i	−1.78396	−	1.78396i
$254$	−3.24855e9	+	3.01843e9i	−0.780468	+	0.725180i
$255$		−	2.07554e9i		−	0.490875i
$256$	4.11114e9	+	1.24310e9i	0.957199	+	0.289431i
$257$	−5.42537e8			−0.124365			−0.0621823	−	0.998065i	$-0.519806\pi$
$257$	−5.42537e8			−0.124365			−0.0621823	+	0.998065i	$0.519806\pi$
$258$	1.46005e9	+	1.57136e9i	0.329525	+	0.354648i
$259$	7.21112e8	−	7.21112e8i	0.160252	−	0.160252i
$260$	−3.14712e8	+	4.27945e9i	−0.0688683	+	0.936470i
$261$	1.46444e9	−	1.46444e9i	0.315580	−	0.315580i
$262$	−4.03447e8	−	1.48148e7i	−0.0856212	−	0.00314406i
$263$	9.18981e9			1.92081			0.960403	−	0.278615i	$-0.0898755\pi$
$263$	9.18981e9			1.92081			0.960403	+	0.278615i	$0.0898755\pi$
$264$	3.60695e9	−	2.88879e9i	0.742548	−	0.594702i
$265$			1.07629e9i			0.218246i
$266$	4.16780e7	+	1.53044e6i	0.00832493	+	0.000305696i
$267$	−2.97945e9	−	2.97945e9i	−0.586260	−	0.586260i
$268$	−3.52146e9	−	4.08051e9i	−0.682627	−	0.790997i
$269$	−2.52840e9	−	2.52840e9i	−0.482877	−	0.482877i	0.423172	−	0.906049i	$-0.360917\pi$
$269$	−2.52840e9	−	2.52840e9i	−0.482877	−	0.482877i	−0.906049	+	0.423172i	$0.860917\pi$
$270$	−4.09782e8	−	4.41024e8i	−0.0771076	−	0.0829864i
$271$			7.25111e9i			1.34440i	0.740371	+	0.672199i	$0.234650\pi$
$271$			7.25111e9i			1.34440i	−0.740371	+	0.672199i	$0.765350\pi$
$272$	7.82123e9	+	1.15661e9i	1.42889	+	0.211305i
$273$	7.85318e8			0.141382
$274$	−7.30004e9	+	6.78291e9i	−1.29516	+	1.20341i
$275$	4.35488e9	−	4.35488e9i	0.761457	−	0.761457i
$276$	−3.35135e9	−	3.88339e9i	−0.577541	−	0.669229i
$277$	2.62494e9	−	2.62494e9i	0.445861	−	0.445861i	−0.448115	−	0.893976i	$-0.647904\pi$
$277$	2.62494e9	−	2.62494e9i	0.445861	−	0.445861i	0.893976	+	0.448115i	$0.147904\pi$
$278$	−1.47437e8	+	4.01510e9i	−0.0246847	+	0.672229i
$279$	−7.79103e7			−0.0128581
$280$	−6.10309e7	+	5.52018e8i	−0.00992927	+	0.0898093i
$281$		−	6.70840e9i		−	1.07595i	−0.842959	−	0.537977i	$-0.819189\pi$
$281$		−	6.70840e9i		−	1.07595i	0.842959	−	0.537977i	$-0.180811\pi$
$282$	−1.40894e8	+	3.83693e9i	−0.0222791	+	0.606718i
$283$	−3.91362e9	−	3.91362e9i	−0.610145	−	0.610145i	0.332839	−	0.942984i	$-0.391994\pi$
$283$	−3.91362e9	−	3.91362e9i	−0.610145	−	0.610145i	−0.942984	+	0.332839i	$0.891994\pi$
$284$	−5.10301e8	+	6.93906e9i	−0.0784428	+	1.06666i
$285$	8.60373e7	+	8.60373e7i	0.0130409	+	0.0130409i
$286$	−1.28838e10	+	1.19712e10i	−1.92567	+	1.78925i
$287$		−	1.01382e9i		−	0.149428i
$288$	1.89025e9	−	1.29841e9i	0.274758	−	0.188730i
$289$	7.57833e9			1.08638
$290$	−3.79417e9	−	4.08344e9i	−0.536445	−	0.577344i
$291$	−3.70549e9	+	3.70549e9i	−0.516742	+	0.516742i
$292$	1.93358e9	+	1.42196e8i	0.265968	+	0.0195594i
$293$	−7.78723e8	+	7.78723e8i	−0.105661	+	0.105661i	−0.757961	−	0.652300i	$-0.773804\pi$
$293$	−7.78723e8	+	7.78723e8i	−0.105661	+	0.105661i	0.652300	+	0.757961i	$0.273804\pi$
$294$	−4.20901e9	−	1.54557e8i	−0.563366	−	0.0206871i
$295$	−4.93515e9			−0.651647
$296$	−1.24543e9	+	1.12648e10i	−0.162238	+	1.46742i
$297$		−	2.46741e9i		−	0.317113i
$298$	1.06483e10	+	3.91010e8i	1.35025	+	0.0495819i
$299$	1.38040e10	+	1.38040e10i	1.72711	+	1.72711i
$300$	2.31377e9	−	1.99677e9i	0.285651	−	0.246515i
$301$	−7.47102e8	−	7.47102e8i	−0.0910152	−	0.0910152i
$302$	3.68387e9	+	3.96473e9i	0.442870	+	0.476635i
$303$			2.27826e8i			0.0270292i
$304$	−3.72157e8	+	2.76268e8i	−0.0435745	+	0.0323472i
$305$	4.54451e9			0.525155
$306$	3.09254e9	−	2.87347e9i	0.352720	−	0.327733i
$307$	−8.81000e9	+	8.81000e9i	−0.991796	+	0.991796i	−0.999967	−	0.00817102i	$-0.997399\pi$
$307$	−8.81000e9	+	8.81000e9i	−0.991796	+	0.991796i	0.00817102	+	0.999967i	$0.497399\pi$
$308$	−1.72328e9	+	1.48718e9i	−0.191493	+	0.165258i
$309$	−6.02600e8	+	6.02600e8i	−0.0660990	+	0.0660990i
$310$	−7.69480e6	+	2.09550e8i	−0.000833203	+	0.0226903i
$311$	3.87027e9			0.413713			0.206857	−	0.978371i	$-0.433677\pi$
$311$	3.87027e9			0.413713			0.206857	+	0.978371i	$0.433677\pi$
$312$	−6.81204e9	+	5.45572e9i	−0.718884	+	0.575750i
$313$		−	4.83707e9i		−	0.503970i	−0.967731	−	0.251985i	$-0.918917\pi$
$313$		−	4.83707e9i		−	0.503970i	0.967731	−	0.251985i	$-0.0810834\pi$
$314$	4.28046e8	−	1.16568e10i	0.0440324	−	1.19912i
$315$	2.09684e8	+	2.09684e8i	0.0212972	+	0.0212972i
$316$	−1.45479e9	−	1.06986e8i	−0.145899	−	0.0107295i
$317$	−5.54173e9	−	5.54173e9i	−0.548792	−	0.548792i	0.377299	−	0.926091i	$-0.376853\pi$
$317$	−5.54173e9	−	5.54173e9i	−0.548792	−	0.548792i	−0.926091	+	0.377299i	$0.876853\pi$
$318$	−1.60367e9	+	1.49006e9i	−0.156822	+	0.145712i
$319$		−	2.28457e10i		−	2.20619i
$320$	−3.30556e9	−	5.21233e9i	−0.315243	−	0.497087i
$321$	5.48199e9			0.516319
$322$	1.71987e9	+	1.85100e9i	0.159983	+	0.172180i
$323$	−6.03309e8	+	6.03309e8i	−0.0554281	+	0.0554281i
$324$	8.98032e7	−	1.22114e9i	0.00814914	−	0.110812i
$325$	−8.22456e9	+	8.22456e9i	−0.737190	+	0.737190i
$326$	1.36145e10	+	4.99934e8i	1.20540	+	0.0442631i
$327$	2.49854e9			0.218522
$328$	7.04315e9	+	8.79410e9i	0.608515	+	0.759795i
$329$		−	1.89125e9i		−	0.161423i
$330$	−6.63642e9	−	2.43693e8i	−0.559600	−	0.0205489i
$331$	−1.04186e9	−	1.04186e9i	−0.0867958	−	0.0867958i	0.662376	−	0.749172i	$-0.269548\pi$
$331$	−1.04186e9	−	1.04186e9i	−0.0867958	−	0.0867958i	−0.749172	+	0.662376i	$0.769548\pi$
$332$	1.68051e9	+	1.94730e9i	0.138321	+	0.160281i
$333$	4.27893e9	+	4.27893e9i	0.347983	+	0.347983i
$334$	1.20271e9	+	1.29440e9i	0.0966437	+	0.104012i
$335$			7.74563e9i			0.615003i
$336$	−9.06996e8	+	6.73301e8i	−0.0711620	+	0.0528265i
$337$	−5.14498e9			−0.398900			−0.199450	−	0.979908i	$-0.563916\pi$
$337$	−5.14498e9			−0.398900			−0.199450	+	0.979908i	$0.563916\pi$
$338$	1.47709e10	−	1.37245e10i	1.13172	−	1.05155i
$339$	−6.18099e9	+	6.18099e9i	−0.468014	+	0.468014i
$340$	−7.42314e9	−	8.60160e9i	−0.555484	−	0.643671i
$341$	−6.07713e8	+	6.07713e8i	−0.0449449	+	0.0449449i
$342$	−9.08131e6	+	2.47308e8i	−0.000663810	+	0.0180773i
$343$	4.19937e9			0.303394
$344$	1.16708e10	+	1.29031e9i	0.833424	+	0.0921429i
$345$			7.37147e9i			0.520328i
$346$	−7.45735e8	+	2.03084e10i	−0.0520331	+	1.41700i
$347$	5.45394e9	+	5.45394e9i	0.376177	+	0.376177i	0.869721	−	0.493544i	$-0.164299\pi$
$347$	5.45394e9	+	5.45394e9i	0.376177	+	0.376177i	−0.493544	+	0.869721i	$0.664299\pi$
$348$	8.31489e8	−	1.13066e10i	0.0566943	−	0.770928i
$349$	4.95246e9	+	4.95246e9i	0.333825	+	0.333825i	0.854037	−	0.520212i	$-0.174147\pi$
$349$	4.95246e9	+	4.95246e9i	0.333825	+	0.333825i	−0.520212	+	0.854037i	$0.674147\pi$
$350$	−1.10285e9	+	1.02472e9i	−0.0734924	+	0.0682862i
$351$			4.65991e9i			0.307007i
$352$	4.61648e9	−	2.48721e10i	0.300705	−	1.62010i
$353$	−6.26529e9			−0.403499			−0.201750	−	0.979437i	$-0.564663\pi$
$353$	−6.26529e9			−0.403499			−0.201750	+	0.979437i	$0.564663\pi$
$354$	−6.83242e9	−	7.35333e9i	−0.435073	−	0.468243i
$355$	7.07020e9	−	7.07020e9i	0.445162	−	0.445162i
$356$	−2.30036e10	−	1.69169e9i	−1.43217	−	0.105322i
$357$	−1.47034e9	+	1.47034e9i	−0.0905203	+	0.0905203i
$358$	6.76033e9	+	2.48243e8i	0.411563	+	0.0151128i
$359$	−1.07114e10			−0.644867			−0.322434	−	0.946592i	$-0.604501\pi$
$359$	−1.07114e10			−0.644867			−0.322434	+	0.946592i	$0.604501\pi$
$360$	−3.27556e9	−	3.62144e8i	−0.195018	−	0.0215611i
$361$			1.69335e10i			0.997055i
$362$	−1.65526e9	−	6.07821e7i	−0.0963900	−	0.00353950i
$363$	−1.21577e10	−	1.21577e10i	−0.700205	−	0.700205i
$364$	3.25457e9	−	2.80867e9i	0.185391	−	0.159991i
$365$	−1.97012e9	−	1.97012e9i	−0.110999	−	0.110999i
$366$	6.29161e9	+	6.77128e9i	0.350620	+	0.377352i
$367$		−	1.44243e10i		−	0.795114i	−0.917577	−	0.397557i	$-0.869858\pi$
$367$		−	1.44243e10i		−	0.795114i	0.917577	−	0.397557i	$-0.130142\pi$
$368$	−2.77778e10	−	4.10779e9i	−1.51463	−	0.223984i
$369$	6.01578e9			0.324479
$370$	1.19314e10	−	1.10861e10i	0.636624	−	0.591525i
$371$	7.62462e8	−	7.62462e8i	0.0402460	−	0.0402460i
$372$	−3.22881e8	+	2.78645e8i	−0.0168605	+	0.0145505i
$373$	2.49909e10	−	2.49909e10i	1.29106	−	1.29106i	0.356927	−	0.934132i	$-0.383825\pi$
$373$	2.49909e10	−	2.49909e10i	1.29106	−	1.29106i	0.934132	−	0.356927i	$-0.116175\pi$
$374$	1.70882e9	−	4.65358e10i	0.0873394	−	2.37849i
$375$	−1.11125e10			−0.561934
$376$	1.31388e10	+	1.64052e10i	0.657361	+	0.820784i
$377$			4.31461e10i			2.13588i
$378$	−2.21323e7	+	6.02723e8i	−0.00108408	+	0.0295223i
$379$	−1.78697e10	−	1.78697e10i	−0.866087	−	0.866087i	0.125950	−	0.992037i	$-0.459802\pi$
$379$	−1.78697e10	−	1.78697e10i	−0.866087	−	0.866087i	−0.992037	+	0.125950i	$0.959802\pi$
$380$	6.64272e8	+	4.88508e7i	0.0318575	+	0.00234281i
$381$	9.16485e9	+	9.16485e9i	0.434936	+	0.434936i
$382$	1.62389e10	−	1.50886e10i	0.762612	−	0.708589i
$383$		−	2.14730e9i		−	0.0997924i	−0.998754	−	0.0498962i	$-0.984111\pi$
$383$		−	2.14730e9i		−	0.0997924i	0.998754	−	0.0498962i	$-0.0158891\pi$
$384$	3.18998e9	−	1.21414e10i	0.146711	−	0.558399i
$385$	3.27114e9			0.148887
$386$	−1.08247e10	−	1.16499e10i	−0.487602	−	0.524777i
$387$	4.43314e9	−	4.43314e9i	0.197637	−	0.197637i
$388$	−2.10393e9	+	2.86092e10i	−0.0928333	+	1.26235i
$389$	−1.99746e10	+	1.99746e10i	−0.872329	+	0.872329i	−0.992726	−	0.120397i	$-0.961583\pi$
$389$	−1.99746e10	+	1.99746e10i	−0.872329	+	0.872329i	0.120397	+	0.992726i	$0.461583\pi$
$390$	1.25334e10	+	4.60235e8i	0.541766	+	0.0198940i
$391$	−5.16901e10			−2.21157
$392$	−1.79960e10	+	1.44129e10i	−0.762136	+	0.610390i
$393$			1.18000e9i			0.0494667i
$394$	−1.51874e9	−	5.57689e7i	−0.0630228	−	0.00231424i
$395$	1.48228e9	+	1.48228e9i	0.0608896	+	0.0608896i
$396$	−8.82463e9	−	1.02256e10i	−0.358852	−	0.415822i
$397$	−2.26970e9	−	2.26970e9i	−0.0913705	−	0.0913705i	0.659944	−	0.751315i	$-0.270580\pi$
$397$	−2.26970e9	−	2.26970e9i	−0.0913705	−	0.0913705i	−0.751315	+	0.659944i	$0.770580\pi$
$398$	−2.00183e10	−	2.15445e10i	−0.797801	−	0.858625i
$399$		−	1.21900e8i		−	0.00480964i
$400$	2.44747e9	−	1.65503e10i	0.0956041	−	0.646496i
$401$	−4.47840e10			−1.73199			−0.865995	−	0.500052i	$-0.833314\pi$
$401$	−4.47840e10			−1.73199			−0.865995	+	0.500052i	$0.833314\pi$
$402$	−1.15409e10	+	1.07234e10i	−0.441913	+	0.410608i
$403$	1.14772e9	−	1.14772e9i	0.0435126	−	0.0435126i
$404$	8.14816e8	+	9.44172e8i	0.0305868	+	0.0354426i
$405$	−1.24422e9	+	1.24422e9i	−0.0462463	+	0.0462463i
$406$	−2.04924e8	+	5.58062e9i	−0.00754202	+	0.205389i
$407$	6.67526e10			2.43271
$408$	2.53942e9	−	2.29688e10i	0.0916419	−	0.828892i
$409$			7.23017e9i			0.258378i	0.991620	+	0.129189i	$0.0412374\pi$
$409$			7.23017e9i			0.258378i	−0.991620	+	0.129189i	$0.958763\pi$
$410$	5.94148e8	−	1.61802e10i	0.0210261	−	0.572598i
$411$	2.05950e10	+	2.05950e10i	0.721761	+	0.721761i
$412$	−3.42148e8	+	4.65252e9i	−0.0118748	+	0.161473i
$413$	3.49613e9	+	3.49613e9i	0.120168	+	0.120168i
$414$	−1.09834e10	+	1.02054e10i	−0.373884	+	0.347398i
$415$		−	3.69638e9i		−	0.124619i
$416$	−8.71862e9	+	4.69731e10i	−0.291122	+	1.56847i
$417$	1.17434e10			0.388373
$418$	1.85821e9	+	1.99988e9i	0.0608681	+	0.0655087i
$419$	−1.53530e10	+	1.53530e10i	−0.498123	+	0.498123i	−0.910853	−	0.412730i	$-0.864575\pi$
$419$	−1.53530e10	+	1.53530e10i	−0.498123	+	0.498123i	0.412730	+	0.910853i	$0.364575\pi$
$420$	1.61892e9	+	1.19056e8i	0.0520269	+	0.00382607i
$421$	−1.31758e10	+	1.31758e10i	−0.419419	+	0.419419i	−0.885003	−	0.465585i	$-0.845844\pi$
$421$	−1.31758e10	+	1.31758e10i	−0.419419	+	0.419419i	0.465585	+	0.885003i	$0.345844\pi$
$422$	3.94710e10	+	1.44940e9i	1.24460	+	0.0457023i
$423$	1.12223e10			0.350525
$424$	−1.31684e9	+	1.19107e10i	−0.0407446	+	0.368531i
$425$		−	3.07975e10i		−	0.943975i
$426$	2.03228e10	+	7.46266e8i	0.617086	+	0.0226597i
$427$	−3.21940e9	−	3.21940e9i	−0.0968418	−	0.0968418i
$428$	2.27188e10	−	1.96062e10i	0.677035	−	0.584277i
$429$	3.63480e10	+	3.63480e10i	1.07313	+	1.07313i
$430$	−1.14857e10	−	1.23614e10i	−0.335957	−	0.361570i
$431$		−	1.33196e10i		−	0.385995i	−0.981199	−	0.192997i	$-0.938179\pi$
$431$		−	1.33196e10i		−	0.385995i	0.981199	−	0.192997i	$-0.0618209\pi$
$432$	−3.99522e9	−	5.38192e9i	−0.114711	−	0.154526i
$433$	6.27714e10			1.78571			0.892853	−	0.450348i	$-0.148700\pi$
$433$	6.27714e10			1.78571			0.892853	+	0.450348i	$0.148700\pi$
$434$	1.53899e8	−	1.42997e8i	0.00433789	−	0.00403059i
$435$	−1.15203e10	+	1.15203e10i	−0.321740	+	0.321740i
$436$	1.03546e10	−	8.93597e9i	0.286541	−	0.247284i
$437$	2.14271e9	−	2.14271e9i	0.0587539	−	0.0587539i
$438$	2.07948e8	−	5.66297e9i	0.00565012	−	0.153868i
$439$	−2.72941e10			−0.734870			−0.367435	−	0.930049i	$-0.619764\pi$
$439$	−2.72941e10			−0.734870			−0.367435	+	0.930049i	$0.619764\pi$
$440$	−2.83747e10	+	2.27251e10i	−0.757042	+	0.606310i
$441$			1.23105e10i			0.325479i
$442$	−3.22726e9	+	8.78868e10i	−0.0845560	+	2.30269i
$443$	−3.56345e10	−	3.56345e10i	−0.925243	−	0.925243i	0.0721508	−	0.997394i	$-0.477014\pi$
$443$	−3.56345e10	−	3.56345e10i	−0.925243	−	0.925243i	−0.997394	+	0.0721508i	$0.977014\pi$
$444$	3.30365e10	+	2.42952e9i	0.850085	+	0.0625155i
$445$	2.34383e10	+	2.34383e10i	0.597704	+	0.597704i
$446$	−1.05907e10	+	9.84043e9i	−0.267660	+	0.248699i
$447$		−	3.11441e10i		−	0.780091i
$448$	−1.35079e9	+	6.03419e9i	−0.0335332	+	0.149798i
$449$	−3.44494e10			−0.847610			−0.423805	−	0.905754i	$-0.639306\pi$
$449$	−3.44494e10			−0.847610			−0.423805	+	0.905754i	$0.639306\pi$
$450$	−6.08047e9	−	6.54405e9i	−0.148282	−	0.159587i
$451$	4.69240e10	−	4.69240e10i	1.13420	−	1.13420i
$452$	−3.50948e9	+	4.77219e10i	−0.0840793	+	1.14331i
$453$	1.11853e10	−	1.11853e10i	0.265617	−	0.265617i
$454$	8.17069e10	+	3.00033e9i	1.92325	+	0.0706228i
$455$	−6.17783e9			−0.144142
$456$	8.46858e8	+	1.05739e9i	0.0195863	+	0.0244555i
$457$			1.52723e10i			0.350139i	0.984556	+	0.175070i	$0.0560151\pi$
$457$			1.52723e10i			0.350139i	−0.984556	+	0.175070i	$0.943985\pi$
$458$	3.78095e10	+	1.38839e9i	0.859288	+	0.0315536i
$459$	−8.72470e9	−	8.72470e9i	−0.196562	−	0.196562i
$460$	2.63639e10	+	3.05493e10i	0.588814	+	0.682292i
$461$	5.02225e10	+	5.02225e10i	1.11197	+	1.11197i	0.992883	+	0.119091i	$0.0379982\pi$
$461$	5.02225e10	+	5.02225e10i	1.11197	+	1.11197i	0.119091	+	0.992883i	$0.462002\pi$
$462$	4.52870e9	+	4.87397e9i	0.0994044	+	0.106983i
$463$			8.27310e10i			1.80030i	0.435583	+	0.900149i	$0.356542\pi$
$463$			8.27310e10i			1.80030i	−0.435583	+	0.900149i	$0.643458\pi$
$464$	−3.69918e10	−	4.98313e10i	−0.798057	−	1.07505i
$465$	6.12893e8			0.0131091
$466$	−5.91285e9	+	5.49399e9i	−0.125387	+	0.116505i
$467$	4.36358e10	−	4.36358e10i	0.917436	−	0.917436i	−0.0794061	−	0.996842i	$-0.525302\pi$
$467$	4.36358e10	−	4.36358e10i	0.917436	−	0.917436i	0.996842	+	0.0794061i	$0.0253024\pi$
$468$	1.66661e10	+	1.93119e10i	0.347416	+	0.402570i
$469$	5.48712e9	−	5.48712e9i	0.113410	−	0.113410i
$470$	1.10837e9	−	3.01838e10i	0.0227139	−	0.618561i
$471$	−3.40940e10			−0.692779
$472$	−5.46144e10	−	6.03814e9i	−1.10037	−	0.121657i
$473$		−	6.91585e10i		−	1.38166i
$474$	−1.56456e8	+	4.26072e9i	−0.00309941	+	0.0844054i
$475$	1.27665e9	+	1.27665e9i	0.0250782	+	0.0250782i
$476$	−8.34841e8	+	1.13522e10i	−0.0162621	+	0.221131i
$477$	4.52428e9	+	4.52428e9i	0.0873929	+	0.0873929i
$478$	−5.44619e10	+	5.06038e10i	−1.04323	+	0.969330i
$479$			7.29637e10i			1.38601i	0.720935	+	0.693003i	$0.243713\pi$
$479$			7.29637e10i			1.38601i	−0.720935	+	0.693003i	$0.756287\pi$
$480$	−1.48700e10	+	1.02141e10i	−0.280121	+	0.192414i
$481$	−1.26068e11			−2.35518
$482$	−5.03349e10	−	5.41725e10i	−0.932569	−	1.00367i
$483$	5.22205e9	−	5.22205e9i	0.0959517	−	0.0959517i
$484$	−9.38667e10	−	6.90298e9i	−1.71053	−	0.125793i
$485$	2.91498e10	−	2.91498e10i	0.526828	−	0.526828i
$486$	−3.57643e9	−	1.31328e8i	−0.0641068	−	0.00235404i
$487$	−2.62997e10			−0.467558			−0.233779	−	0.972290i	$-0.575109\pi$
$487$	−2.62997e10			−0.467558			−0.233779	+	0.972290i	$0.575109\pi$
$488$	5.02915e10	+	5.56020e9i	0.886778	+	0.0980417i
$489$		−	3.98199e10i		−	0.696409i
$490$	3.31108e10	+	1.21585e9i	0.574362	+	0.0210909i
$491$	−7.24101e9	−	7.24101e9i	−0.124587	−	0.124587i	0.642064	−	0.766651i	$-0.278078\pi$
$491$	−7.24101e9	−	7.24101e9i	−0.124587	−	0.124587i	−0.766651	+	0.642064i	$0.778078\pi$
$492$	2.49310e10	−	2.15153e10i	0.425480	−	0.367187i
$493$	−8.07821e10	−	8.07821e10i	−1.36750	−	1.36750i
$494$	−3.50939e9	−	3.77695e9i	−0.0589283	−	0.0634210i
$495$			1.94102e10i			0.323303i
$496$	−3.41538e8	+	2.30955e9i	−0.00564303	+	0.0381594i
$497$	−1.00173e10			−0.164181
$498$	5.50757e9	−	5.11742e9i	0.0895453	−	0.0832019i
$499$	8.68602e10	−	8.68602e10i	1.40094	−	1.40094i	0.603805	−	0.797132i	$-0.293651\pi$
$499$	8.68602e10	−	8.68602e10i	1.40094	−	1.40094i	0.797132	−	0.603805i	$-0.206349\pi$
$500$	−4.60530e10	+	3.97435e10i	−0.736848	+	0.635896i
$501$	3.65178e9	−	3.65178e9i	0.0579633	−	0.0579633i
$502$	2.00585e9	−	5.46248e10i	0.0315853	−	0.860151i
$503$	−2.47257e9			−0.0386257			−0.0193129	−	0.999813i	$-0.506148\pi$
$503$	−2.47257e9			−0.0386257			−0.0193129	+	0.999813i	$0.506148\pi$
$504$	2.06390e9	+	2.57700e9i	0.0319865	+	0.0399385i
$505$		−	1.79223e9i		−	0.0275568i
$506$	−6.06903e9	+	1.65276e11i	−0.0925800	+	2.52120i
$507$	−4.16717e10	−	4.16717e10i	−0.630680	−	0.630680i
$508$	7.07595e10	+	5.20368e9i	1.06250	+	0.0781368i
$509$	−4.02845e10	−	4.02845e10i	−0.600160	−	0.600160i	0.340195	−	0.940355i	$-0.389507\pi$
$509$	−4.02845e10	−	4.02845e10i	−0.600160	−	0.600160i	−0.940355	+	0.340195i	$0.889507\pi$
$510$	−2.43280e10	+	2.26046e10i	−0.359604	+	0.334130i
$511$			2.79132e9i			0.0409380i
$512$	−3.02034e10	−	6.17262e10i	−0.439517	−	0.898234i
$513$	7.23329e8			0.0104440
$514$	5.90873e9	+	6.35922e9i	0.0846529	+	0.0911069i
$515$	4.74045e9	−	4.74045e9i	0.0673892	−	0.0673892i
$516$	2.51708e9	−	3.42272e10i	0.0355057	−	0.482806i
$517$	8.75355e10	−	8.75355e10i	1.22524	−	1.22524i
$518$	−1.63059e10	−	5.98763e8i	−0.226478	−	0.00831641i
$519$	5.93980e10			0.818658
$520$	5.35880e10	−	4.29183e10i	0.732915	−	0.586988i
$521$		−	1.03647e11i		−	1.40671i	−0.710839	−	0.703354i	$-0.751685\pi$
$521$		−	1.03647e11i		−	1.40671i	0.710839	−	0.703354i	$-0.248315\pi$
$522$	−3.31142e10	−	1.21597e9i	−0.445997	−	0.0163773i
$523$	−3.32468e10	−	3.32468e10i	−0.444368	−	0.444368i	0.449109	−	0.893477i	$-0.351742\pi$
$523$	−3.32468e10	−	3.32468e10i	−0.444368	−	0.444368i	−0.893477	+	0.449109i	$0.851742\pi$
$524$	4.22026e9	+	4.89025e9i	0.0559776	+	0.0648643i
$525$	3.11136e9	+	3.11136e9i	0.0409556	+	0.0409556i
$526$	−1.00085e11	−	1.07716e11i	−1.30746	−	1.40714i
$527$			4.29772e9i			0.0557180i
$528$	−7.31432e10	−	1.08165e10i	−0.941106	−	0.139171i
$529$	1.05271e11			1.34427
$530$	1.26155e10	−	1.17218e10i	0.159883	−	0.148557i
$531$	−2.07453e10	+	2.07453e10i	−0.260940	+	0.260940i
$532$	−4.35973e8	−	5.05187e8i	−0.00544269	−	0.00630675i
$533$	−8.86201e10	+	8.86201e10i	−1.09805	+	1.09805i
$534$	−2.47393e9	+	6.73718e10i	−0.0304244	+	0.828539i
$535$	−4.31250e10			−0.526397
$536$	−9.47676e9	+	8.57164e10i	−0.114816	+	1.03850i
$537$		−	1.97727e10i		−	0.237776i
$538$	−2.09941e9	+	5.71727e10i	−0.0250593	+	0.682432i
$539$	9.60241e10	+	9.60241e10i	1.13769	+	1.13769i
$540$	−7.06451e8	+	9.60631e9i	−0.00830820	+	0.112975i
$541$	8.78525e10	+	8.78525e10i	1.02557	+	1.02557i	0.999664	+	0.0259045i	$0.00824659\pi$
$541$	8.78525e10	+	8.78525e10i	1.02557	+	1.02557i	0.0259045	+	0.999664i	$0.491753\pi$
$542$	8.49922e10	−	7.89713e10i	0.984876	−	0.915108i
$543$			4.84132e9i			0.0556883i
$544$	−7.16235e10	−	1.04271e11i	−0.817824	−	1.19061i
$545$	−1.96551e10			−0.222787
$546$	−8.55283e9	−	9.20491e9i	−0.0962364	−	0.103574i
$547$	−6.47090e10	+	6.47090e10i	−0.722796	+	0.722796i	−0.969174	−	0.246378i	$-0.920759\pi$
$547$	−6.47090e10	+	6.47090e10i	−0.722796	+	0.722796i	0.246378	+	0.969174i	$0.420759\pi$
$548$	1.59008e11	+	1.16935e10i	1.76319	+	0.129665i
$549$	1.91032e10	−	1.91032e10i	0.210289	−	0.210289i
$550$	−9.84733e10	−	3.61600e9i	−1.07614	−	0.0395164i
$551$	6.69731e9			0.0726598
$552$	−9.01897e9	+	8.15757e10i	−0.0971406	+	0.878627i
$553$		−	2.10014e9i		−	0.0224568i
$554$	−5.93555e10	−	2.17957e9i	−0.630118	−	0.0231383i
$555$	−3.36608e10	−	3.36608e10i	−0.354775	−	0.354775i
$556$	4.86678e10	−	4.20000e10i	0.509263	−	0.439491i
$557$	1.49269e10	+	1.49269e10i	0.155078	+	0.155078i	0.780381	−	0.625304i	$-0.215025\pi$
$557$	1.49269e10	+	1.49269e10i	0.155078	+	0.155078i	−0.625304	+	0.780381i	$0.715025\pi$
$558$	8.48515e8	+	9.13206e8i	0.00875231	+	0.00941959i
$559$			1.30612e11i			1.33763i
$560$	7.13503e9	−	5.29663e9i	0.0725510	−	0.0538577i
$561$	−1.36108e11			−1.37415
$562$	−7.86309e10	+	7.30607e10i	−0.788221	+	0.732383i
$563$	7.72511e10	−	7.72511e10i	0.768902	−	0.768902i	−0.209011	−	0.977913i	$-0.567025\pi$
$563$	7.72511e10	−	7.72511e10i	0.768902	−	0.768902i	0.977913	+	0.209011i	$0.0670246\pi$
$564$	4.65081e10	−	4.01362e10i	0.459634	−	0.396661i
$565$	4.86237e10	−	4.86237e10i	0.477149	−	0.477149i
$566$	−3.24961e9	+	8.84955e10i	−0.0316639	+	0.862294i
$567$	1.76285e9			0.0170562
$568$	8.68922e10	−	6.95914e10i	0.834809	−	0.668594i
$569$		−	4.51125e10i		−	0.430375i	−0.976573	−	0.215188i	$-0.930964\pi$
$569$		−	4.51125e10i		−	0.430375i	0.976573	−	0.215188i	$-0.0690363\pi$
$570$	7.14395e7	−	1.94549e9i	0.000676767	−	0.0184302i
$571$	9.32366e10	+	9.32366e10i	0.877086	+	0.877086i	0.993232	−	0.116147i	$-0.0370542\pi$
$571$	9.32366e10	+	9.32366e10i	0.877086	+	0.877086i	−0.116147	+	0.993232i	$0.537054\pi$
$572$	2.80634e11	+	2.06379e10i	2.62154	+	0.192789i
$573$	−4.58134e10	−	4.58134e10i	−0.424985	−	0.424985i
$574$	−1.18832e10	+	1.10414e10i	−0.109468	+	0.101713i
$575$			1.09380e11i			1.00062i
$576$	−3.58056e10	−	8.01527e9i	−0.325283	−	0.0728163i
$577$	−1.05867e11			−0.955119			−0.477559	−	0.878599i	$-0.658478\pi$
$577$	−1.05867e11			−0.955119			−0.477559	+	0.878599i	$0.658478\pi$
$578$	−8.25350e10	−	8.88275e10i	−0.739481	−	0.795859i
$579$	−3.28669e10	+	3.28669e10i	−0.292445	+	0.292445i
$580$	−6.54104e9	+	8.89449e10i	−0.0578009	+	0.785976i
$581$	−2.61857e9	+	2.61857e9i	−0.0229805	+	0.0229805i
$582$	8.37892e10	+	3.07679e9i	0.730292	+	0.0268167i
$583$	7.05803e10			0.610955
$584$	−1.93917e10	−	2.42126e10i	−0.166711	−	0.208156i
$585$		−	3.66579e10i		−	0.313000i
$586$	1.76086e10	+	6.46599e8i	0.149326	+	0.00548333i
$587$	−6.57079e10	−	6.57079e10i	−0.553433	−	0.553433i	0.373997	−	0.927430i	$-0.377987\pi$
$587$	−6.57079e10	−	6.57079e10i	−0.553433	−	0.553433i	−0.927430	+	0.373997i	$0.877987\pi$
$588$	4.40284e10	+	5.10181e10i	0.368318	+	0.426791i
$589$	−1.78153e8	−	1.78153e8i	−0.00148024	−	0.00148024i
$590$	5.37483e10	+	5.78462e10i	0.443565	+	0.477383i
$591$			4.44201e9i			0.0364108i
$592$	1.45601e11	−	1.08086e11i	1.18544	−	0.879999i
$593$	−1.02722e11			−0.830702			−0.415351	−	0.909661i	$-0.636341\pi$
$593$	−1.02722e11			−0.830702			−0.415351	+	0.909661i	$0.636341\pi$
$594$	−2.89211e10	+	2.68723e10i	−0.232310	+	0.215854i
$595$	1.15667e10	−	1.15667e10i	0.0922872	−	0.0922872i
$596$	−1.11386e11	−	1.29069e11i	−0.882768	−	1.02291i
$597$	−6.07815e10	+	6.07815e10i	−0.478491	+	0.478491i
$598$	1.14619e10	−	3.12138e11i	0.0896295	−	2.44085i
$599$	1.83037e11			1.42178			0.710889	−	0.703305i	$-0.248293\pi$
$599$	1.83037e11			1.42178			0.710889	+	0.703305i	$0.248293\pi$
$600$	−4.86037e10	−	5.37360e9i	−0.375029	−	0.0414630i
$601$			2.04443e11i			1.56702i	0.621381	+	0.783509i	$0.286572\pi$
$601$			2.04443e11i			1.56702i	−0.621381	+	0.783509i	$0.713428\pi$
$602$	−6.20343e8	+	1.68936e10i	−0.00472330	+	0.128628i
$603$	3.25594e10	+	3.25594e10i	0.246267	+	0.246267i
$604$	6.35088e9	−	8.63591e10i	0.0477184	−	0.648874i
$605$	9.56406e10	+	9.56406e10i	0.713873	+	0.713873i
$606$	2.67041e9	−	2.48124e9i	0.0198010	−	0.0183983i
$607$			1.68583e11i			1.24182i	0.783883	+	0.620909i	$0.213236\pi$
$607$			1.68583e11i			1.24182i	−0.783883	+	0.620909i	$0.786764\pi$
$608$	7.29135e9	+	1.35334e9i	0.0533572	+	0.00990358i
$609$	1.63222e10			0.118662
$610$	−4.94939e10	−	5.32674e10i	−0.357464	−	0.384718i
$611$	−1.65318e11	+	1.65318e11i	−1.18619	+	1.18619i
$612$	−6.73612e10	−	4.95377e9i	−0.480180	−	0.0353126i
$613$	−1.63425e11	+	1.63425e11i	−1.15739	+	1.15739i	−0.172349	+	0.985036i	$0.555136\pi$
$613$	−1.63425e11	+	1.63425e11i	−1.15739	+	1.15739i	−0.985036	+	0.172349i	$0.944864\pi$
$614$	1.99213e11	+	7.31522e9i	1.40167	+	0.0514700i
$615$	−4.73241e10			−0.330812
$616$	3.61998e10	+	4.00223e9i	0.251410	+	0.0277958i
$617$			4.85931e10i			0.335301i	0.985847	+	0.167650i	$0.0536179\pi$
$617$			4.85931e10i			0.335301i	−0.985847	+	0.167650i	$0.946382\pi$
$618$	1.36261e10	+	5.00358e8i	0.0934152	+	0.00343026i
$619$	8.31685e10	+	8.31685e10i	0.566495	+	0.566495i	0.931145	−	0.364649i	$-0.118811\pi$
$619$	8.31685e10	+	8.31685e10i	0.566495	+	0.566495i	−0.364649	+	0.931145i	$0.618811\pi$
$620$	2.53999e9	−	2.19200e9i	0.0171896	−	0.0148345i
$621$	3.09865e10	+	3.09865e10i	0.208356	+	0.208356i
$622$	−4.21508e10	−	4.53644e10i	−0.281608	−	0.303077i
$623$		−	3.32080e10i		−	0.220440i
$624$	1.38137e11	+	2.04278e10i	0.911113	+	0.134736i
$625$	−1.23023e10			−0.0806247
$626$	−5.66965e10	+	5.26802e10i	−0.369198	+	0.343044i
$627$	5.64208e9	−	5.64208e9i	0.0365064	−	0.0365064i
$628$	−1.41295e11	+	1.21937e11i	−0.908421	+	0.783963i
$629$	2.36036e11	−	2.36036e11i	1.50791	−	1.50791i
$630$	1.74107e8	−	4.74141e9i	0.00110524	−	0.0300986i
$631$	−2.65899e11			−1.67725			−0.838627	−	0.544706i	$-0.816641\pi$
$631$	−2.65899e11			−1.67725			−0.838627	+	0.544706i	$0.816641\pi$
$632$	1.45900e10	+	1.82171e10i	0.0914507	+	0.114186i
$633$		−	1.15445e11i		−	0.719052i
$634$	−4.60147e9	+	1.25310e11i	−0.0284800	+	0.775587i
$635$	−7.20967e10	−	7.20967e10i	−0.443426	−	0.443426i
$636$	3.49309e10	+	2.56883e9i	0.213492	+	0.0157002i
$637$	−1.81350e11	−	1.81350e11i	−1.10144	−	1.10144i
$638$	−2.67781e11	+	2.48811e11i	−1.61621	+	1.50171i
$639$		−	5.94403e10i		−	0.356515i
$640$	−2.50945e10	+	9.55124e10i	−0.149575	+	0.569298i
$641$	4.51636e10			0.267520			0.133760	−	0.991014i	$-0.457295\pi$
$641$	4.51636e10			0.267520			0.133760	+	0.991014i	$0.457295\pi$
$642$	−5.97039e10	−	6.42558e10i	−0.351449	−	0.378244i
$643$	2.09447e11	−	2.09447e11i	1.22526	−	1.22526i	0.259528	−	0.965736i	$-0.416433\pi$
$643$	2.09447e11	−	2.09447e11i	1.22526	−	1.22526i	0.965736	−	0.259528i	$-0.0835671\pi$
$644$	2.96501e9	−	4.03181e10i	0.0172378	−	0.234400i
$645$	−3.48740e10	+	3.48740e10i	−0.201494	+	0.201494i
$646$	1.36421e10	+	5.00947e8i	0.0783344	+	0.00287648i
$647$	−1.55025e11			−0.884679			−0.442339	−	0.896848i	$-0.645851\pi$
$647$	−1.55025e11			−0.884679			−0.442339	+	0.896848i	$0.645851\pi$
$648$	−1.52914e10	+	1.22468e10i	−0.0867254	+	0.0694578i
$649$			3.23633e11i			1.82421i
$650$	1.85975e11	+	6.82912e9i	1.04184	+	0.0382570i
$651$	−4.34182e8	−	4.34182e8i	−0.00241740	−	0.00241740i
$652$	−1.42415e11	−	1.65024e11i	−0.788071	−	0.913182i
$653$	8.70484e10	+	8.70484e10i	0.478749	+	0.478749i	0.904731	−	0.425982i	$-0.140071\pi$
$653$	8.70484e10	+	8.70484e10i	0.478749	+	0.478749i	−0.425982	+	0.904731i	$0.640071\pi$
$654$	−2.72114e10	−	2.92860e10i	−0.148744	−	0.160084i
$655$		−	9.28269e9i		−	0.0504323i
$656$	2.63716e10	−	1.78330e11i	0.142404	−	0.962964i
$657$	−1.65631e10			−0.0888956
$658$	−2.21678e10	+	2.05974e10i	−0.118255	+	0.109878i
$659$	−1.49023e11	+	1.49023e11i	−0.790155	+	0.790155i	−0.981519	−	0.191364i	$-0.938709\pi$
$659$	−1.49023e11	+	1.49023e11i	−0.790155	+	0.790155i	0.191364	+	0.981519i	$0.438709\pi$
$660$	6.94203e10	+	8.04412e10i	0.365857	+	0.423938i
$661$	4.42316e10	−	4.42316e10i	0.231701	−	0.231701i	−0.581702	−	0.813402i	$-0.697613\pi$
$661$	4.42316e10	−	4.42316e10i	0.231701	−	0.231701i	0.813402	+	0.581702i	$0.197613\pi$
$662$	−8.65092e8	+	2.35588e10i	−0.00450433	+	0.122665i
$663$	2.57052e11			1.33035
$664$	4.52251e9	−	4.09057e10i	0.0232652	−	0.210432i
$665$			9.58946e8i			0.00490352i
$666$	3.55293e9	−	9.67558e10i	0.0180588	−	0.491791i
$667$	2.86905e11	+	2.86905e11i	1.44955	+	1.44955i
$668$	2.07343e9	−	2.81945e10i	0.0104132	−	0.141598i
$669$	2.98785e10	+	2.98785e10i	0.149161	+	0.149161i
$670$	9.07885e10	−	8.43571e10i	0.450538	−	0.418622i
$671$		−	2.98016e11i		−	1.47011i
$672$	1.77700e10	+	3.29826e9i	0.0871384	+	0.0161737i
$673$	2.86738e11			1.39773			0.698867	−	0.715251i	$-0.253688\pi$
$673$	2.86738e11			1.39773			0.698867	+	0.715251i	$0.253688\pi$
$674$	5.60336e10	+	6.03056e10i	0.271524	+	0.292226i
$675$	−1.84621e10	+	1.84621e10i	−0.0889338	+	0.0889338i
$676$	−3.21736e11	−	2.36606e10i	−1.54068	−	0.113302i
$677$	4.43597e10	−	4.43597e10i	0.211171	−	0.211171i	−0.593594	−	0.804765i	$-0.702291\pi$
$677$	4.43597e10	−	4.43597e10i	0.211171	−	0.211171i	0.804765	+	0.593594i	$0.202291\pi$
$678$	1.39766e11	+	5.13227e9i	0.661426	+	0.0242880i
$679$	−4.13003e10			−0.194301
$680$	−1.99768e10	+	1.80688e11i	−0.0934306	+	0.845071i
$681$		−	2.38977e11i		−	1.11114i
$682$	1.37417e10	+	5.04603e8i	0.0635189	+	0.00233245i
$683$	−5.53539e10	−	5.53539e10i	−0.254370	−	0.254370i	0.568390	−	0.822760i	$-0.307567\pi$
$683$	−5.53539e10	−	5.53539e10i	−0.254370	−	0.254370i	−0.822760	+	0.568390i	$0.807567\pi$
$684$	2.99767e9	−	2.58697e9i	0.0136949	−	0.0118186i
$685$	−1.62013e11	−	1.62013e11i	−0.735849	−	0.735849i
$686$	−4.57350e10	−	4.92219e10i	−0.206515	−	0.222260i
$687$		−	1.10585e11i		−	0.496445i
$688$	−1.11981e11	−	1.50849e11i	−0.499795	−	0.673268i
$689$	−1.33297e11			−0.591484
$690$	8.64028e10	−	8.02821e10i	0.381181	−	0.354178i
$691$	1.44286e11	−	1.44286e11i	0.632868	−	0.632868i	−0.315919	−	0.948786i	$-0.602313\pi$
$691$	1.44286e11	−	1.44286e11i	0.632868	−	0.632868i	0.948786	+	0.315919i	$0.102313\pi$
$692$	2.46161e11	−	2.12436e11i	1.07348	−	0.926410i
$693$	1.37505e10	−	1.37505e10i	0.0596191	−	0.0596191i
$694$	4.52858e9	−	1.23325e11i	0.0195220	−	0.531637i
$695$	−9.23813e10			−0.395954
$696$	−1.41583e11	+	1.13393e11i	−0.603356	+	0.483225i
$697$		−	3.31845e11i		−	1.40606i
$698$	4.11219e9	−	1.11986e11i	0.0173241	−	0.471783i
$699$	1.66814e10	+	1.66814e10i	0.0698753	+	0.0698753i
$700$	2.40220e10	+	1.76659e9i	0.100050	+	0.00735771i
$701$	−4.48422e10	−	4.48422e10i	−0.185701	−	0.185701i	0.608134	−	0.793835i	$-0.291918\pi$
$701$	−4.48422e10	−	4.48422e10i	−0.185701	−	0.185701i	−0.793835	+	0.608134i	$0.791918\pi$
$702$	5.46199e10	−	5.07507e10i	0.224907	−	0.208975i
$703$			1.95688e10i			0.0801203i
$704$	−3.41810e11	+	2.16769e11i	−1.39153	+	0.882484i
$705$	−8.82817e10			−0.357367
$706$	6.82348e10	+	7.34371e10i	0.274655	+	0.295595i
$707$	−1.26964e9	+	1.26964e9i	−0.00508164	+	0.00508164i
$708$	−1.17789e10	+	1.60169e11i	−0.0468783	+	0.637450i
$709$	−7.07748e9	+	7.07748e9i	−0.0280088	+	0.0280088i	−0.720972	−	0.692964i	$-0.756305\pi$
$709$	−7.07748e9	+	7.07748e9i	−0.0280088	+	0.0280088i	0.692964	+	0.720972i	$0.256305\pi$
$710$	−1.59873e11	−	5.87062e9i	−0.629130	−	0.0231020i
$711$	1.24618e10			0.0487643
$712$	2.30701e11	+	2.88055e11i	0.897697	+	1.12087i
$713$		−	1.52637e10i		−	0.0590612i
$714$	3.32477e10	+	1.22087e9i	0.127929	+	0.00469762i
$715$	−2.85937e11	−	2.85937e11i	−1.09407	−	1.09407i
$716$	−7.07165e10	−	8.19432e10i	−0.269072	−	0.311789i
$717$	1.53648e11	+	1.53648e11i	0.581368	+	0.581368i
$718$	1.16658e11	+	1.25552e11i	0.438950	+	0.472416i
$719$		−	2.28853e11i		−	0.856329i	−0.903701	−	0.428164i	$-0.859160\pi$
$719$		−	2.28853e11i		−	0.856329i	0.903701	−	0.428164i	$-0.140840\pi$
$720$	3.14291e10	+	4.23377e10i	0.116950	+	0.157542i
$721$	−6.71640e9			−0.0248540
$722$	1.98482e11	−	1.84422e11i	0.730421	−	0.678678i
$723$	−1.52832e11	+	1.52832e11i	−0.559320	+	0.559320i
$724$	1.73149e10	+	2.00637e10i	0.0630181	+	0.0730225i
$725$	−1.70941e11	+	1.70941e11i	−0.618720	+	0.618720i
$726$	−1.00949e10	+	2.74912e11i	−0.0363377	+	0.989573i
$727$	3.57335e9			0.0127920			0.00639599	−	0.999980i	$-0.497964\pi$
$727$	3.57335e9			0.0127920			0.00639599	+	0.999980i	$0.497964\pi$
$728$	−6.83664e10	−	7.55855e9i	−0.243398	−	0.0269100i
$729$			1.04604e10i			0.0370370i
$730$	−1.63585e9	+	4.45487e10i	−0.00576040	+	0.156871i
$731$	−2.44543e11	−	2.44543e11i	−0.856418	−	0.856418i
$732$	1.08465e10	−	1.47491e11i	0.0377787	−	0.513714i
$733$	−1.90758e9	−	1.90758e9i	−0.00660797	−	0.00660797i	0.703795	−	0.710403i	$-0.251487\pi$
$733$	−1.90758e9	−	1.90758e9i	−0.00660797	−	0.00660797i	−0.710403	+	0.703795i	$0.751487\pi$
$734$	−1.69071e11	+	1.57094e11i	−0.582484	+	0.541221i
$735$		−	9.68428e10i		−	0.331832i
$736$	2.54377e11	+	3.70328e11i	0.866895	+	1.26205i
$737$	5.07937e11			1.72163
$738$	−6.55174e10	−	7.05125e10i	−0.220867	−	0.237706i
$739$	−2.04883e11	+	2.04883e11i	−0.686955	+	0.686955i	−0.961558	−	0.274603i	$-0.911454\pi$
$739$	−2.04883e11	+	2.04883e11i	−0.686955	+	0.686955i	0.274603	+	0.961558i	$0.411454\pi$
$740$	−2.59887e11	−	1.91122e10i	−0.866678	−	0.0637358i
$741$	−1.06556e10	+	1.06556e10i	−0.0353430	+	0.0353430i
$742$	−1.72409e10	−	6.33097e8i	−0.0568781	−	0.00208860i
$743$	−2.28437e11			−0.749569			−0.374785	−	0.927112i	$-0.622283\pi$
$743$	−2.28437e11			−0.749569			−0.374785	+	0.927112i	$0.622283\pi$
$744$	6.78253e9	+	7.49873e8i	0.0221361	+	0.00244735i
$745$			2.45000e11i			0.795318i
$746$	−5.65098e11	−	2.07507e10i	−1.82460	−	0.0670005i
$747$	−1.55380e10	−	1.55380e10i	−0.0499014	−	0.0499014i
$748$	−5.64069e11	+	4.86788e11i	−1.80188	+	1.55501i
$749$	3.05503e10	+	3.05503e10i	0.0970708	+	0.0970708i
$750$	1.21025e11	+	1.30252e11i	0.382499	+	0.411661i
$751$		−	6.71665e10i		−	0.211151i	−0.994411	−	0.105575i	$-0.966332\pi$
$751$		−	6.71665e10i		−	0.211151i	0.994411	−	0.105575i	$-0.0336685\pi$
$752$	4.91954e10	−	3.32670e11i	0.153834	−	1.04026i
$753$	−1.59767e11			−0.496943
$754$	5.05727e11	−	4.69901e11i	1.56470	−	1.45386i
$755$	−8.79912e10	+	8.79912e10i	−0.270802	+	0.270802i
$756$	7.30571e9	−	6.30479e9i	0.0223653	−	0.0193012i
$757$	1.99263e11	−	1.99263e11i	0.606797	−	0.606797i	−0.335311	−	0.942108i	$-0.608841\pi$
$757$	1.99263e11	−	1.99263e11i	0.606797	−	0.606797i	0.942108	+	0.335311i	$0.108841\pi$
$758$	−1.48378e10	+	4.04074e11i	−0.0449462	+	1.22401i
$759$	4.83400e11			1.45660
$760$	−6.66194e9	−	8.31813e9i	−0.0199686	−	0.0249328i
$761$			3.19590e11i			0.952917i	0.879197	+	0.476458i	$0.158080\pi$
$761$			3.19590e11i			0.952917i	−0.879197	+	0.476458i	$0.841920\pi$
$762$	7.60987e9	−	2.07237e11i	0.0225713	−	0.614678i
$763$	1.39240e10	+	1.39240e10i	0.0410833	+	0.0410833i
$764$	−3.53714e11	−	2.60122e10i	−1.03819	−	0.0763491i
$765$	6.86343e10	+	6.86343e10i	0.200399	+	0.200399i
$766$	−2.51690e10	+	2.33861e10i	−0.0731058	+	0.0679270i
$767$		−	6.11209e11i		−	1.76607i
$768$	−1.77054e11	+	9.48406e10i	−0.508935	+	0.272615i
$769$	5.20977e11			1.48975			0.744875	−	0.667204i	$-0.232509\pi$
$769$	5.20977e11			1.48975			0.744875	+	0.667204i	$0.232509\pi$
$770$	−3.56257e10	−	3.83419e10i	−0.101345	−	0.109071i
$771$	1.79407e10	−	1.79407e10i	0.0507717	−	0.0507717i
$772$	−1.86614e10	+	2.53757e11i	−0.0525382	+	0.714413i
$773$	−1.63711e11	+	1.63711e11i	−0.458520	+	0.458520i	−0.898170	−	0.439649i	$-0.855103\pi$
$773$	−1.63711e11	+	1.63711e11i	−0.458520	+	0.458520i	0.439649	+	0.898170i	$0.355103\pi$
$774$	−1.00243e11	−	3.68098e9i	−0.279312	−	0.0102565i
$775$	9.09430e9			0.0252094
$776$	3.58249e11	−	2.86920e11i	0.987957	−	0.791249i
$777$			4.76917e10i			0.130845i
$778$	4.51670e11	+	1.65856e10i	1.23283	+	0.0452702i
$779$	1.37560e10	+	1.37560e10i	0.0373543	+	0.0373543i
$780$	−1.31106e11	−	1.51920e11i	−0.354197	−	0.410428i
$781$	−4.63644e11	−	4.63644e11i	−1.24618	−	1.24618i
$782$	5.62953e11	+	6.05873e11i	1.50538	+	1.62015i
$783$			9.68525e10i			0.257670i
$784$	3.64931e11	+	5.39661e10i	0.965931	+	0.142842i
$785$	2.68206e11			0.706301
$786$	1.38311e10	−	1.28513e10i	0.0362383	−	0.0336711i
$787$	5.37625e11	−	5.37625e11i	1.40146	−	1.40146i	0.605978	−	0.795481i	$-0.292782\pi$
$787$	5.37625e11	−	5.37625e11i	1.40146	−	1.40146i	0.795481	−	0.605978i	$-0.207218\pi$
$788$	1.58868e10	+	1.84089e10i	0.0412032	+	0.0477444i
$789$	−3.03890e11	+	3.03890e11i	−0.784166	+	0.784166i
$790$	1.23079e9	−	3.35177e10i	0.00315991	−	0.0860529i
$791$	−6.88915e10			−0.175979
$792$	−2.37484e10	+	2.14802e11i	−0.0603578	+	0.545930i
$793$			5.62829e11i			1.42326i
$794$	−1.88460e9	+	5.13228e10i	−0.00474174	+	0.129130i
$795$	−3.55910e10	−	3.55910e10i	−0.0890987	−	0.0890987i
$796$	−3.45109e10	+	4.69279e11i	−0.0859615	+	1.16890i
$797$	3.65947e11	+	3.65947e11i	0.906953	+	0.906953i	0.996025	−	0.0890724i	$-0.0283902\pi$
$797$	3.65947e11	+	3.65947e11i	0.906953	+	0.906953i	−0.0890724	+	0.996025i	$0.528390\pi$
$798$	−1.42882e9	+	1.32760e9i	−0.00352344	+	0.00327384i
$799$		−	6.19048e11i		−	1.51893i
$800$	−2.20646e11	+	1.51561e11i	−0.538685	+	0.370021i
$801$	1.97049e11			0.478680
$802$	4.87739e11	+	5.24925e11i	1.17894	+	1.26882i
$803$	−1.29195e11	+	1.29195e11i	−0.310730	+	0.310730i
$804$	2.51383e11	+	1.84868e10i	0.601604	+	0.0442422i
$805$	−4.10801e10	+	4.10801e10i	−0.0978246	+	0.0978246i
$806$	−2.59524e10	−	9.52987e8i	−0.0614946	−	0.00225812i
$807$	1.67219e11			0.394268
$808$	2.19279e9	−	1.98336e10i	0.00514460	−	0.0465324i
$809$		−	1.21954e11i		−	0.284708i	−0.989816	−	0.142354i	$-0.954533\pi$
$809$		−	1.21954e11i		−	0.284708i	0.989816	−	0.142354i	$-0.0454672\pi$
$810$	2.81345e10	+	1.03312e9i	0.0653581	+	0.00239999i
$811$	4.22150e11	+	4.22150e11i	0.975851	+	0.975851i	0.999715	−	0.0238639i	$-0.00759685\pi$
$811$	4.22150e11	+	4.22150e11i	0.975851	+	0.975851i	−0.0238639	+	0.999715i	$0.507597\pi$
$812$	6.76436e10	−	5.83761e10i	0.155598	−	0.134280i
$813$	−2.39781e11	−	2.39781e11i	−0.548848	−	0.548848i
$814$	−7.26998e11	−	7.82424e11i	−1.65590	−	1.78215i
$815$			3.13249e11i			0.710003i
$816$	−2.96880e11	+	2.20386e11i	−0.669607	+	0.497078i
$817$	2.02741e10			0.0455043
$818$	8.47467e10	−	7.87433e10i	0.189282	−	0.175873i
$819$	−2.59690e10	+	2.59690e10i	−0.0577191	+	0.0577191i
$820$	−1.96124e11	+	1.69254e11i	−0.433785	+	0.374354i
$821$	−2.99390e11	+	2.99390e11i	−0.658970	+	0.658970i	−0.955136	−	0.296167i	$-0.904292\pi$
$821$	−2.99390e11	+	2.99390e11i	−0.658970	+	0.658970i	0.296167	+	0.955136i	$0.404292\pi$
$822$	1.71007e10	−	4.65697e11i	0.0374563	−	1.02004i
$823$	1.81497e11			0.395614			0.197807	−	0.980241i	$-0.436618\pi$
$823$	1.81497e11			0.395614			0.197807	+	0.980241i	$0.436618\pi$
$824$	5.82597e10	−	4.66598e10i	0.126374	−	0.101213i
$825$			2.88015e11i			0.621727i
$826$	2.90295e9	−	7.90551e10i	0.00623619	−	0.169828i
$827$	−1.99402e11	−	1.99402e11i	−0.426292	−	0.426292i	0.461071	−	0.887363i	$-0.347465\pi$
$827$	−1.99402e11	−	1.99402e11i	−0.426292	−	0.426292i	−0.887363	+	0.461071i	$0.847465\pi$
$828$	2.39239e11	+	1.75937e10i	0.508992	+	0.0374314i
$829$	−4.15130e11	−	4.15130e11i	−0.878953	−	0.878953i	0.114473	−	0.993426i	$-0.463482\pi$
$829$	−4.15130e11	−	4.15130e11i	−0.878953	−	0.878953i	−0.993426	+	0.114473i	$0.963482\pi$
$830$	−4.33262e10	+	4.02570e10i	−0.0912931	+	0.0848259i
$831$			1.73603e11i			0.364044i
$832$	6.45537e11	−	4.09387e11i	1.34719	−	0.854360i
$833$	6.79079e11			1.41039
$834$	−1.27896e11	−	1.37647e11i	−0.264359	−	0.284514i
$835$	−2.87273e10	+	2.87273e10i	−0.0590947	+	0.0590947i
$836$	3.20350e9	−	4.35611e10i	0.00655842	−	0.0891813i
$837$	2.57635e9	−	2.57635e9i	0.00524931	−	0.00524931i
$838$	3.47164e11	+	1.27481e10i	0.703978	+	0.0258505i
$839$	1.79380e11			0.362014			0.181007	−	0.983482i	$-0.442064\pi$
$839$	1.79380e11			0.362014			0.181007	+	0.983482i	$0.442064\pi$
$840$	−1.62360e10	−	2.02724e10i	−0.0326109	−	0.0407181i
$841$			3.96512e11i			0.792634i
$842$	2.97933e11	+	1.09403e10i	0.592748	+	0.0217660i
$843$	2.21834e11	+	2.21834e11i	0.439257	+	0.439257i
$844$	−4.12887e11	−	4.78435e11i	−0.813695	−	0.942873i
$845$	3.27817e11	+	3.27817e11i	0.642990	+	0.642990i
$846$	−1.22221e11	−	1.31539e11i	−0.238596	−	0.256787i
$847$		−	1.35506e11i		−	0.263285i
$848$	1.53950e11	−	1.14284e11i	0.297712	−	0.221004i
$849$	2.58832e11			0.498181
$850$	−3.60986e11	+	3.35414e11i	−0.691535	+	0.642547i
$851$	−8.38303e11	+	8.38303e11i	−1.59839	+	1.59839i
$852$	−2.12587e11	−	2.46336e11i	−0.403439	−	0.467488i
$853$	−3.38129e11	+	3.38129e11i	−0.638684	+	0.638684i	−0.950231	−	0.311547i	$-0.899153\pi$
$853$	−3.38129e11	+	3.38129e11i	−0.638684	+	0.638684i	0.311547	+	0.950231i	$0.399153\pi$
$854$	−2.67317e9	+	7.27976e10i	−0.00502568	+	0.136863i
$855$	−5.69018e9			−0.0106478
$856$	−4.77239e11	−	5.27633e10i	−0.888875	−	0.0982735i
$857$		−	2.97481e11i		−	0.551488i	−0.961231	−	0.275744i	$-0.911076\pi$
$857$		−	2.97481e11i		−	0.551488i	0.961231	−	0.275744i	$-0.0889242\pi$
$858$	3.01809e10	−	8.21908e11i	0.0556908	−	1.51661i
$859$	−5.13114e11	−	5.13114e11i	−0.942412	−	0.942412i	0.0560173	−	0.998430i	$-0.482160\pi$
$859$	−5.13114e11	−	5.13114e11i	−0.942412	−	0.942412i	−0.998430	+	0.0560173i	$0.982160\pi$
$860$	−1.98010e10	+	2.69254e11i	−0.0361987	+	0.492229i
$861$	3.35251e10	+	3.35251e10i	0.0610038	+	0.0610038i
$862$	−1.56122e11	+	1.45062e11i	−0.282771	+	0.262740i
$863$		−	2.73974e11i		−	0.493931i	−0.969024	−	0.246966i	$-0.920567\pi$
$863$		−	2.73974e11i		−	0.493931i	0.969024	−	0.246966i	$-0.0794334\pi$
$864$	−1.95712e10	+	1.05443e11i	−0.0351206	+	0.189218i
$865$	−4.67264e11			−0.834637
$866$	−6.83638e11	−	7.35759e11i	−1.21550	−	1.30817i
$867$	−2.50601e11	+	2.50601e11i	−0.443513	+	0.443513i
$868$	−3.35221e9	−	2.46523e8i	−0.00590545	−	0.000434288i
$869$	9.72040e10	−	9.72040e10i	0.170453	−	0.170453i
$870$	2.60498e11	+	9.56564e9i	0.454702	+	0.0166969i
$871$	−9.59282e11			−1.66676
$872$	−2.17512e11	−	2.40480e10i	−0.376199	−	0.0415923i
$873$		−	2.45067e11i		−	0.421918i
$874$	−4.84512e10	−	1.77916e9i	−0.0830346	−	0.00304908i
$875$	−6.19281e10	−	6.19281e10i	−0.105647	−	0.105647i
$876$	−6.86419e10	+	5.92376e10i	−0.116566	+	0.100596i
$877$	−5.69921e11	−	5.69921e11i	−0.963421	−	0.963421i	0.0359328	−	0.999354i	$-0.488560\pi$
$877$	−5.69921e11	−	5.69921e11i	−0.963421	−	0.963421i	−0.999354	+	0.0359328i	$0.988560\pi$
$878$	2.97258e11	+	3.19921e11i	0.500214	+	0.538350i
$879$		−	5.15018e10i		−	0.0862714i
$880$	5.75393e11	+	8.50893e10i	0.959475	+	0.141888i
$881$	5.83934e11			0.969303			0.484652	−	0.874707i	$-0.338946\pi$
$881$	5.83934e11			0.969303			0.484652	+	0.874707i	$0.338946\pi$
$882$	1.44295e11	−	1.34073e11i	0.238439	−	0.221548i
$883$	−2.75500e11	+	2.75500e11i	−0.453188	+	0.453188i	−0.896411	−	0.443223i	$-0.853835\pi$
$883$	−2.75500e11	+	2.75500e11i	−0.453188	+	0.453188i	0.443223	+	0.896411i	$0.353835\pi$
$884$	1.06529e12	−	9.19341e11i	1.74445	−	1.50545i
$885$	1.63196e11	−	1.63196e11i	0.266034	−	0.266034i
$886$	−2.95885e10	+	8.05774e11i	−0.0480162	+	1.30761i
$887$	7.28074e11			1.17620			0.588100	−	0.808788i	$-0.299876\pi$
$887$	7.28074e11			1.17620			0.588100	+	0.808788i	$0.299876\pi$
$888$	−3.31321e11	−	4.13689e11i	−0.532840	−	0.665307i
$889$			1.02149e11i			0.163541i
$890$	1.94616e10	−	5.29991e11i	0.0310183	−	0.844711i
$891$	8.15924e10	+	8.15924e10i	0.129461	+	0.129461i
$892$	2.30684e11	+	1.69646e10i	0.364383	+	0.0267969i
$893$	2.56613e10	+	2.56613e10i	0.0403528	+	0.0403528i
$894$	−3.65048e11	+	3.39188e11i	−0.571478	+	0.530995i
$895$			1.55545e11i			0.242417i
$896$	8.54396e10	−	4.98850e10i	0.132565	−	0.0773995i
$897$	−9.12942e11			−1.41018
$898$	3.75185e11	+	4.03790e11i	0.576953	+	0.620940i
$899$	2.38544e10	−	2.38544e10i	0.0365199	−	0.0365199i
$900$	−1.04825e10	+	1.42541e11i	−0.0159771	+	0.217256i
$901$	2.49571e11	−	2.49571e11i	0.378699	−	0.378699i
$902$	−1.06105e12	−	3.89625e10i	−1.60292	−	0.0588601i
$903$	4.94105e10			0.0743136
$904$	5.97581e11	−	4.78599e11i	0.894795	−	0.716636i
$905$		−	3.80850e10i		−	0.0567753i
$906$	−2.52925e11	−	9.28754e9i	−0.375386	−	0.0137844i
$907$	2.39872e11	+	2.39872e11i	0.354446	+	0.354446i	0.861761	−	0.507315i	$-0.169362\pi$
$907$	2.39872e11	+	2.39872e11i	0.354446	+	0.354446i	−0.507315	+	0.861761i	$0.669362\pi$
$908$	−8.54696e11	−	9.90384e11i	−1.25738	−	1.45700i
$909$	−7.53378e9	−	7.53378e9i	−0.0110346	−	0.0110346i
$910$	6.72822e10	+	7.24119e10i	0.0981149	+	0.105595i
$911$			4.20108e11i			0.609941i	0.952362	+	0.304970i	$0.0986466\pi$
$911$			4.20108e11i			0.609941i	−0.952362	+	0.304970i	$0.901353\pi$
$912$	3.17088e9	−	2.14422e10i	0.00458354	−	0.0309949i
$913$	−2.42398e11			−0.348856
$914$	1.79011e11	−	1.66330e11i	0.256504	−	0.238334i
$915$	−1.50278e11	+	1.50278e11i	−0.214394	+	0.214394i
$916$	−3.95507e11	−	4.58295e11i	−0.561787	−	0.650974i
$917$	−6.57599e9	+	6.57599e9i	−0.00930001	+	0.00930001i
$918$	−7.24440e9	+	1.97285e11i	−0.0102007	+	0.277794i
$919$	−3.87216e11			−0.542864			−0.271432	−	0.962458i	$-0.587497\pi$
$919$	−3.87216e11			−0.542864			−0.271432	+	0.962458i	$0.587497\pi$
$920$	7.09492e10	−	6.41728e11i	0.0990366	−	0.895777i
$921$		−	5.82660e11i		−	0.809798i
$922$	4.17014e10	−	1.13564e12i	0.0577068	−	1.57151i
$923$	8.75631e11	+	8.75631e11i	1.20646	+	1.20646i
$924$	7.80734e9	−	1.06164e11i	0.0107106	−	0.145643i
$925$	−4.99470e11	−	4.99470e11i	−0.682249	−	0.682249i
$926$	9.69711e11	−	9.01017e11i	1.31886	−	1.22543i
$927$		−	3.98537e10i		−	0.0539696i
$928$	−1.81210e11	+	9.76299e11i	−0.244337	+	1.31641i
$929$	−1.07580e12			−1.44433			−0.722167	−	0.691718i	$-0.756854\pi$
$929$	−1.07580e12			−1.44433			−0.722167	+	0.691718i	$0.756854\pi$
$930$	−6.67497e9	−	7.18388e9i	−0.00892314	−	0.00960345i
$931$	−2.81498e10	+	2.81498e10i	−0.0374694	+	0.0374694i
$932$	1.28793e11	+	9.47146e9i	0.170698	+	0.0125532i
$933$	−1.27982e11	+	1.27982e11i	−0.168898	+	0.168898i
$934$	−9.86701e11	−	3.62323e10i	−1.29658	−	0.0476111i
$935$	1.07072e12			1.40097
$936$	4.48508e10	−	4.05672e11i	0.0584342	−	0.528532i
$937$		−	3.02180e11i		−	0.392019i	−0.980602	−	0.196009i	$-0.937202\pi$
$937$		−	3.02180e11i		−	0.392019i	0.980602	−	0.196009i	$-0.0627983\pi$
$938$	−1.24076e11	−	4.55613e9i	−0.160278	−	0.00588552i
$939$	1.59953e11	+	1.59953e11i	0.205745	+	0.205745i
$940$	−3.65863e11	+	3.15738e11i	−0.468605	+	0.404404i
$941$	−3.74179e11	−	3.74179e11i	−0.477222	−	0.477222i	0.427020	−	0.904242i	$-0.359563\pi$
$941$	−3.74179e11	−	3.74179e11i	−0.477222	−	0.477222i	−0.904242	+	0.427020i	$0.859563\pi$
$942$	3.71315e11	+	3.99625e11i	0.471562	+	0.507515i
$943$			1.17858e12i			1.49043i
$944$	5.24027e11	+	7.05911e11i	0.659881	+	0.888918i
$945$	−1.38677e10			−0.0173891
$946$	−8.10624e11	+	7.53199e11i	−1.01217	+	0.940471i
$947$	−2.62216e11	+	2.62216e11i	−0.326032	+	0.326032i	−0.851075	−	0.525044i	$-0.824049\pi$
$947$	−2.62216e11	+	2.62216e11i	−0.326032	+	0.326032i	0.525044	+	0.851075i	$0.324049\pi$
$948$	5.16450e10	−	4.45693e10i	0.0639433	−	0.0551827i
$949$	2.43995e11	−	2.43995e11i	0.300827	−	0.300827i
$950$	1.06004e9	−	2.88678e10i	0.00130145	−	0.0354421i
$951$	3.66509e11			0.448087
$952$	1.42154e11	−	1.13850e11i	0.173065	−	0.138607i
$953$		−	1.64130e11i		−	0.198983i	−0.995038	−	0.0994914i	$-0.968278\pi$
$953$		−	1.64130e11i		−	0.198983i	0.995038	−	0.0994914i	$-0.0317216\pi$
$954$	3.75666e9	−	1.02304e11i	0.00453532	−	0.123509i
$955$	3.60398e11	+	3.60398e11i	0.433281	+	0.433281i
$956$	1.18628e12	+	8.72394e10i	1.42022	+	0.104443i
$957$	7.55465e11	+	7.55465e11i	0.900672	+	0.900672i
$958$	8.55227e11	−	7.94643e11i	1.01536	−	0.943430i
$959$			2.29545e11i			0.271390i
$960$	2.81670e11	+	6.30534e10i	0.331632	+	0.0742375i
$961$	8.51622e11			0.998512
$962$	1.37300e12	+	1.47768e12i	1.60313	+	1.72536i
$963$	−1.81279e11	+	1.81279e11i	−0.210786	+	0.210786i
$964$	−8.67758e10	+	1.17998e12i	−0.100483	+	1.36636i
$965$	2.58553e11	−	2.58553e11i	0.298154	−	0.298154i
$966$	−1.18082e11	−	4.33604e9i	−0.135605	−	0.00497949i
$967$	−8.28232e11			−0.947210			−0.473605	−	0.880737i	$-0.657048\pi$
$967$	−8.28232e11			−0.947210			−0.473605	+	0.880737i	$0.657048\pi$
$968$	9.41383e11	+	1.17541e12i	1.07217	+	1.33872i
$969$		−	3.99006e10i		−	0.0452569i
$970$	−6.59141e11	−	2.42041e10i	−0.744546	−	0.0273402i
$971$	−6.42797e11	−	6.42797e11i	−0.723097	−	0.723097i	0.246138	−	0.969235i	$-0.420839\pi$
$971$	−6.42797e11	−	6.42797e11i	−0.723097	−	0.723097i	−0.969235	+	0.246138i	$0.920839\pi$
$972$	3.74113e10	+	4.33505e10i	0.0419119	+	0.0485656i
$973$	6.54442e10	+	6.54442e10i	0.0730163	+	0.0730163i
$974$	2.86428e11	+	3.08266e11i	0.318258	+	0.342523i
$975$		−	5.43941e11i		−	0.601913i
$976$	−4.82548e11	−	6.50035e11i	−0.531791	−	0.716370i
$977$	−3.97049e10			−0.0435779			−0.0217889	−	0.999763i	$-0.506936\pi$
$977$	−3.97049e10			−0.0435779			−0.0217889	+	0.999763i	$0.506936\pi$
$978$	−4.66739e11	+	4.33675e11i	−0.510175	+	0.474034i
$979$	1.53702e12	−	1.53702e12i	1.67320	−	1.67320i
$980$	−3.46356e11	−	4.01342e11i	−0.375508	−	0.435122i
$981$	−8.26219e10	+	8.26219e10i	−0.0892111	+	0.0892111i
$982$	−6.01244e9	+	1.63735e11i	−0.00646554	+	0.176074i
$983$	−9.75459e11			−1.04471			−0.522354	−	0.852729i	$-0.674946\pi$
$983$	−9.75459e11			−1.04471			−0.522354	+	0.852729i	$0.674946\pi$
$984$	−5.23708e11	−	5.79009e10i	−0.558610	−	0.0617596i
$985$		−	3.49438e10i		−	0.0371215i
$986$	−6.70760e10	+	1.82666e12i	−0.0709675	+	1.93264i
$987$	6.25400e10	+	6.25400e10i	0.0659006	+	0.0659006i
$988$	−6.05008e9	+	8.22689e10i	−0.00634941	+	0.0863391i
$989$	8.68516e11	+	8.68516e11i	0.907805	+	0.907805i
$990$	2.27512e11	−	2.11395e11i	0.236845	−	0.220067i
$991$			2.75678e11i			0.285829i	0.989735	+	0.142915i	$0.0456475\pi$
$991$			2.75678e11i			0.285829i	−0.989735	+	0.142915i	$0.954353\pi$
$992$	3.07905e10	−	2.11499e10i	0.0317959	−	0.0218405i
$993$	6.89049e10			0.0708684
$994$	1.09097e11	+	1.17415e11i	0.111755	+	0.120276i
$995$	4.78147e11	−	4.78147e11i	0.487831	−	0.487831i
$996$	−1.19965e11	−	8.82227e9i	−0.121904	−	0.00896485i
$997$	2.12118e11	−	2.12118e11i	0.214683	−	0.214683i	−0.591570	−	0.806253i	$-0.701492\pi$
$997$	2.12118e11	−	2.12118e11i	0.214683	−	0.214683i	0.806253	+	0.591570i	$0.201492\pi$
$998$	−1.96410e12	−	7.21228e10i	−1.97989	−	0.0727027i
$999$	−2.82992e11			−0.284127

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.9.l.a.19.9	✓	64
4.3	odd	2		192.9.l.a.175.23		64
16.5	even	4		192.9.l.a.79.23		64
16.11	odd	4	inner	48.9.l.a.43.9	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.9.l.a.19.9	✓	64	1.1	even	1	trivial
48.9.l.a.43.9	yes	64	16.11	odd	4	inner
192.9.l.a.79.23		64	16.5	even	4
192.9.l.a.175.23		64	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-10.8909 - 11.7213i) q^{2} +(-33.0681 + 33.0681i) q^{3} +(-18.7756 + 255.311i) q^{4} +(260.136 - 260.136i) q^{5} +(747.742 + 27.4575i) q^{6} -368.567 q^{7} +(3197.04 - 2560.49i) q^{8} -2187.00i q^{9} +O(q^{10})\)	\(q+(-10.8909 - 11.7213i) q^{2} +(-33.0681 + 33.0681i) q^{3} +(-18.7756 + 255.311i) q^{4} +(260.136 - 260.136i) q^{5} +(747.742 + 27.4575i) q^{6} -368.567 q^{7} +(3197.04 - 2560.49i) q^{8} -2187.00i q^{9} +(-5882.23 - 215.999i) q^{10} +(-17059.0 - 17059.0i) q^{11} +(-7821.76 - 9063.51i) q^{12} +(32217.3 + 32217.3i) q^{13} +(4014.04 + 4320.07i) q^{14} +17204.4i q^{15} +(-64831.0 - 9587.23i) q^{16} -120640. q^{17} +(-25634.4 + 23818.4i) q^{18} +(5000.89 - 5000.89i) q^{19} +(61531.1 + 71299.6i) q^{20} +(12187.8 - 12187.8i) q^{21} +(-14164.6 + 385740. i) q^{22} +428464. q^{23} +(-21049.5 + 190391. i) q^{24} +255284. i q^{25} +(26751.1 - 728503. i) q^{26} +(72320.0 + 72320.0i) q^{27} +(6920.08 - 94099.2i) q^{28} +(669611. + 669611. i) q^{29} +(201657. - 187372. i) q^{30} -35624.3i q^{31} +(593695. + 864314. i) q^{32} +1.12821e6 q^{33} +(1.31388e6 + 1.41406e6i) q^{34} +(-95877.5 + 95877.5i) q^{35} +(558364. + 41062.3i) q^{36} +(-1.95653e6 + 1.95653e6i) q^{37} +(-113081. - 4152.40i) q^{38} -2.13073e6 q^{39} +(165589. - 1.49774e6i) q^{40} +2.75070e6i q^{41} +(-275593. - 10119.9i) q^{42} +(2.02704e6 + 2.02704e6i) q^{43} +(4.67562e6 - 4.03504e6i) q^{44} +(-568916. - 568916. i) q^{45} +(-4.66637e6 - 5.02214e6i) q^{46} +5.13135e6i q^{47} +(2.46087e6 - 1.82681e6i) q^{48} -5.62896e6 q^{49} +(2.99225e6 - 2.78028e6i) q^{50} +(3.98935e6 - 3.98935e6i) q^{51} +(-8.83031e6 + 7.62051e6i) q^{52} +(-2.06872e6 + 2.06872e6i) q^{53} +(60049.6 - 1.63531e6i) q^{54} -8.87528e6 q^{55} +(-1.17833e6 + 943715. i) q^{56} +330740. i q^{57} +(556000. - 1.51414e7i) q^{58} +(-9.48573e6 - 9.48573e6i) q^{59} +(-4.39246e6 - 323023. i) q^{60} +(8.73489e6 + 8.73489e6i) q^{61} +(-417561. + 387981. i) q^{62} +806057. i q^{63} +(3.66496e6 - 1.63720e7i) q^{64} +1.67617e7 q^{65} +(-1.22873e7 - 1.32241e7i) q^{66} +(-1.48877e7 + 1.48877e7i) q^{67} +(2.26510e6 - 3.08007e7i) q^{68} +(-1.41685e7 + 1.41685e7i) q^{69} +(2.16800e6 + 79610.2i) q^{70} +2.71789e7 q^{71} +(-5.59980e6 - 6.99193e6i) q^{72} -7.57343e6i q^{73} +(4.42413e7 + 1.62457e6i) q^{74} +(-8.44176e6 - 8.44176e6i) q^{75} +(1.18289e6 + 1.37068e6i) q^{76} +(6.28737e6 + 6.28737e6i) q^{77} +(2.32056e7 + 2.49748e7i) q^{78} +5.69812e6i q^{79} +(-1.93588e7 + 1.43709e7i) q^{80} -4.78297e6 q^{81} +(3.22416e7 - 2.99576e7i) q^{82} +(7.10472e6 - 7.10472e6i) q^{83} +(2.88285e6 + 3.34052e6i) q^{84} +(-3.13828e7 + 3.13828e7i) q^{85} +(1.68312e6 - 4.58359e7i) q^{86} -4.42856e7 q^{87} +(-9.82176e7 - 1.08589e7i) q^{88} +9.01003e7i q^{89} +(-472390. + 1.28644e7i) q^{90} +(-1.18742e7 - 1.18742e7i) q^{91} +(-8.04469e6 + 1.09391e8i) q^{92} +(1.17803e6 + 1.17803e6i) q^{93} +(6.01459e7 - 5.58851e7i) q^{94} -2.60182e6i q^{95} +(-4.82136e7 - 8.94887e6i) q^{96} +1.12056e8 q^{97} +(6.13046e7 + 6.59785e7i) q^{98} +(-3.73079e7 + 3.73079e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 372 q^{4} + 17460 q^{8}+O(q^{10}) \) 64 * q - 372 * q^4 + 17460 * q^8	\( 64 q - 372 q^{4} + 17460 q^{8} - 13784 q^{10} + 39552 q^{11} - 22680 q^{12} + 116772 q^{14} - 161824 q^{16} - 26244 q^{18} - 167552 q^{19} + 690000 q^{20} - 1252768 q^{22} + 1691136 q^{23} - 74844 q^{24} - 1682100 q^{26} + 678600 q^{28} - 2132352 q^{29} - 2054808 q^{30} + 1407840 q^{32} - 3704544 q^{34} - 2415744 q^{35} - 1041012 q^{36} - 4720512 q^{37} + 2413320 q^{38} - 3544848 q^{40} + 9436500 q^{42} - 7244672 q^{43} - 3982056 q^{44} + 11165992 q^{46} - 9467280 q^{48} + 52706752 q^{49} + 17072676 q^{50} + 13862016 q^{51} - 22890864 q^{52} - 5358720 q^{53} - 4960116 q^{54} - 46326784 q^{55} - 9637152 q^{56} + 25732944 q^{58} + 44938752 q^{59} + 40927032 q^{60} + 24476032 q^{61} - 17024868 q^{62} - 116303448 q^{64} + 29941632 q^{65} - 56828952 q^{66} - 44244736 q^{67} - 12614400 q^{68} - 8636544 q^{69} - 60922560 q^{70} + 159664128 q^{71} - 18502020 q^{72} + 140654028 q^{74} + 12918528 q^{75} + 204842760 q^{76} - 94964352 q^{77} + 14001660 q^{78} + 38076648 q^{80} - 306110016 q^{81} - 260917000 q^{82} + 209328000 q^{83} - 127862712 q^{84} + 106960000 q^{85} - 123451824 q^{86} + 104240736 q^{88} + 53520264 q^{90} - 45401472 q^{91} + 351567216 q^{92} + 208488216 q^{94} + 49597920 q^{96} - 681890712 q^{98} + 86500224 q^{99}+O(q^{100}) \) 64 * q - 372 * q^4 + 17460 * q^8 - 13784 * q^10 + 39552 * q^11 - 22680 * q^12 + 116772 * q^14 - 161824 * q^16 - 26244 * q^18 - 167552 * q^19 + 690000 * q^20 - 1252768 * q^22 + 1691136 * q^23 - 74844 * q^24 - 1682100 * q^26 + 678600 * q^28 - 2132352 * q^29 - 2054808 * q^30 + 1407840 * q^32 - 3704544 * q^34 - 2415744 * q^35 - 1041012 * q^36 - 4720512 * q^37 + 2413320 * q^38 - 3544848 * q^40 + 9436500 * q^42 - 7244672 * q^43 - 3982056 * q^44 + 11165992 * q^46 - 9467280 * q^48 + 52706752 * q^49 + 17072676 * q^50 + 13862016 * q^51 - 22890864 * q^52 - 5358720 * q^53 - 4960116 * q^54 - 46326784 * q^55 - 9637152 * q^56 + 25732944 * q^58 + 44938752 * q^59 + 40927032 * q^60 + 24476032 * q^61 - 17024868 * q^62 - 116303448 * q^64 + 29941632 * q^65 - 56828952 * q^66 - 44244736 * q^67 - 12614400 * q^68 - 8636544 * q^69 - 60922560 * q^70 + 159664128 * q^71 - 18502020 * q^72 + 140654028 * q^74 + 12918528 * q^75 + 204842760 * q^76 - 94964352 * q^77 + 14001660 * q^78 + 38076648 * q^80 - 306110016 * q^81 - 260917000 * q^82 + 209328000 * q^83 - 127862712 * q^84 + 106960000 * q^85 - 123451824 * q^86 + 104240736 * q^88 + 53520264 * q^90 - 45401472 * q^91 + 351567216 * q^92 + 208488216 * q^94 + 49597920 * q^96 - 681890712 * q^98 + 86500224 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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