LMFDB - Embedded newform 48.9.l.a.19.4

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			19.4
Character	$\chi$	$=$	48.19
Dual form			48.9.l.a.43.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.4570 + 8.65496i) q^{2} +(-33.0681 + 33.0681i) q^{3} +(106.183 - 232.940i) q^{4} +(-333.431 + 333.431i) q^{5} +(158.796 - 731.202i) q^{6} -1764.79 q^{7} +(587.173 + 4053.70i) q^{8} -2187.00i q^{9} +O(q^{10})$	\(q+(-13.4570 + 8.65496i) q^{2} +(-33.0681 + 33.0681i) q^{3} +(106.183 - 232.940i) q^{4} +(-333.431 + 333.431i) q^{5} +(158.796 - 731.202i) q^{6} -1764.79 q^{7} +(587.173 + 4053.70i) q^{8} -2187.00i q^{9} +(1601.16 - 7372.82i) q^{10} +(-5115.02 - 5115.02i) q^{11} +(4191.60 + 11214.2i) q^{12} +(-24302.9 - 24302.9i) q^{13} +(23748.9 - 15274.2i) q^{14} -22051.9i q^{15} +(-42986.2 - 49468.7i) q^{16} -13218.8 q^{17} +(18928.4 + 29430.5i) q^{18} +(-7296.07 + 7296.07i) q^{19} +(42264.6 + 113074. i) q^{20} +(58358.4 - 58358.4i) q^{21} +(113103. + 24562.7i) q^{22} +290630. q^{23} +(-153465. - 114631. i) q^{24} +168273. i q^{25} +(537385. + 116704. i) q^{26} +(72320.0 + 72320.0i) q^{27} +(-187392. + 411091. i) q^{28} +(652236. + 652236. i) q^{29} +(190858. + 296753. i) q^{30} +386955. i q^{31} +(1.00662e6 + 293659. i) q^{32} +338288. q^{33} +(177886. - 114408. i) q^{34} +(588437. - 588437. i) q^{35} +(-509440. - 232223. i) q^{36} +(1.62932e6 - 1.62932e6i) q^{37} +(35036.3 - 161331. i) q^{38} +1.60730e6 q^{39} +(-1.54741e6 - 1.15585e6i) q^{40} -1.15378e6i q^{41} +(-280242. + 1.29042e6i) q^{42} +(2.25332e6 + 2.25332e6i) q^{43} +(-1.73462e6 + 648362. i) q^{44} +(729213. + 729213. i) q^{45} +(-3.91102e6 + 2.51539e6i) q^{46} +3.16374e6i q^{47} +(3.05731e6 + 214367. i) q^{48} -2.65030e6 q^{49} +(-1.45639e6 - 2.26445e6i) q^{50} +(437122. - 437122. i) q^{51} +(-8.24168e6 + 3.08055e6i) q^{52} +(8.51641e6 - 8.51641e6i) q^{53} +(-1.59914e6 - 347286. i) q^{54} +3.41101e6 q^{55} +(-1.03624e6 - 7.15394e6i) q^{56} -482534. i q^{57} +(-1.44222e7 - 3.13209e6i) q^{58} +(-1.02071e6 - 1.02071e6i) q^{59} +(-5.13676e6 - 2.34154e6i) q^{60} +(-1.85953e7 - 1.85953e7i) q^{61} +(-3.34908e6 - 5.20726e6i) q^{62} +3.85961e6i q^{63} +(-1.60877e7 + 4.76044e6i) q^{64} +1.62067e7 q^{65} +(-4.55235e6 + 2.92787e6i) q^{66} +(1.09956e7 - 1.09956e7i) q^{67} +(-1.40362e6 + 3.07920e6i) q^{68} +(-9.61060e6 + 9.61060e6i) q^{69} +(-2.82572e6 + 1.30115e7i) q^{70} +2.07169e7 q^{71} +(8.86543e6 - 1.28415e6i) q^{72} +1.49012e7i q^{73} +(-7.82413e6 + 3.60276e7i) q^{74} +(-5.56446e6 - 5.56446e6i) q^{75} +(924825. + 2.47427e6i) q^{76} +(9.02695e6 + 9.02695e6i) q^{77} +(-2.16295e7 + 1.39111e7i) q^{78} +1.87691e7i q^{79} +(3.08273e7 + 2.16149e6i) q^{80} -4.78297e6 q^{81} +(9.98593e6 + 1.55265e7i) q^{82} +(4.60031e7 - 4.60031e7i) q^{83} +(-7.39732e6 - 1.97907e7i) q^{84} +(4.40757e6 - 4.40757e6i) q^{85} +(-4.98254e7 - 1.08206e7i) q^{86} -4.31364e7 q^{87} +(1.77313e7 - 2.37381e7i) q^{88} -1.96886e7i q^{89} +(-1.61244e7 - 3.50174e6i) q^{90} +(4.28896e7 + 4.28896e7i) q^{91} +(3.08601e7 - 6.76995e7i) q^{92} +(-1.27959e7 - 1.27959e7i) q^{93} +(-2.73821e7 - 4.25746e7i) q^{94} -4.86547e6i q^{95} +(-4.29976e7 + 2.35761e7i) q^{96} +4.61339e7 q^{97} +(3.56652e7 - 2.29382e7i) q^{98} +(-1.11865e7 + 1.11865e7i) 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 $

$2$	−13.4570	+	8.65496i	−0.841065	+	0.540935i
$2$	−13.4570	+	8.65496i	−0.841065	+	0.540935i
$3$	−33.0681	+	33.0681i	−0.408248	+	0.408248i
$3$	−33.0681	+	33.0681i	−0.408248	+	0.408248i
$4$	106.183	−	232.940i	0.414779	−	0.909922i
$5$	−333.431	+	333.431i	−0.533489	+	0.533489i	−0.921609	−	0.388120i	$-0.873125\pi$
$5$	−333.431	+	333.431i	−0.533489	+	0.533489i	0.388120	+	0.921609i	$0.373125\pi$
$6$	158.796	−	731.202i	0.122527	−	0.564199i
$7$	−1764.79			−0.735025			−0.367512	−	0.930019i	$-0.619790\pi$
$7$	−1764.79			−0.735025			−0.367512	+	0.930019i	$0.619790\pi$
$8$	587.173	+	4053.70i	0.143353	+	0.989672i
$9$		−	2187.00i		−	0.333333i
$10$	1601.16	−	7372.82i	0.160116	−	0.737282i
$11$	−5115.02	−	5115.02i	−0.349362	−	0.349362i	0.510510	−	0.859872i	$-0.329457\pi$
$11$	−5115.02	−	5115.02i	−0.349362	−	0.349362i	−0.859872	+	0.510510i	$0.829457\pi$
$12$	4191.60	+	11214.2i	0.202141	+	0.540807i
$13$	−24302.9	−	24302.9i	−0.850912	−	0.850912i	0.139333	−	0.990246i	$-0.455504\pi$
$13$	−24302.9	−	24302.9i	−0.850912	−	0.850912i	−0.990246	+	0.139333i	$0.955504\pi$
$14$	23748.9	−	15274.2i	0.618203	−	0.397601i
$15$		−	22051.9i		−	0.435592i
$16$	−42986.2	−	49468.7i	−0.655917	−	0.754833i
$17$	−13218.8			−0.158270			−0.0791348	−	0.996864i	$-0.525216\pi$
$17$	−13218.8			−0.158270			−0.0791348	+	0.996864i	$0.525216\pi$
$18$	18928.4	+	29430.5i	0.180312	+	0.280355i
$19$	−7296.07	+	7296.07i	−0.0559853	+	0.0559853i	−0.734545	−	0.678560i	$-0.762604\pi$
$19$	−7296.07	+	7296.07i	−0.0559853	+	0.0559853i	0.678560	+	0.734545i	$0.262604\pi$
$20$	42264.6	+	113074.i	0.264154	+	0.706714i
$21$	58358.4	−	58358.4i	0.300073	−	0.300073i
$22$	113103.	+	24562.7i	0.482819	+	0.104854i
$23$	290630.			1.03856			0.519278	−	0.854606i	$-0.326201\pi$
$23$	290630.			1.03856			0.519278	+	0.854606i	$0.326201\pi$
$24$	−153465.	−	114631.i	−0.462555	−	0.345508i
$25$			168273.i			0.430778i
$26$	537385.	+	116704.i	1.17596	+	0.255384i
$27$	72320.0	+	72320.0i	0.136083	+	0.136083i
$28$	−187392.	+	411091.i	−0.304873	+	0.668816i
$29$	652236.	+	652236.i	0.922174	+	0.922174i	0.997183	−	0.0750092i	$-0.0238986\pi$
$29$	652236.	+	652236.i	0.922174	+	0.922174i	−0.0750092	+	0.997183i	$0.523899\pi$
$30$	190858.	+	296753.i	0.235627	+	0.366361i
$31$			386955.i			0.418999i	0.977809	+	0.209500i	$0.0671835\pi$
$31$			386955.i			0.418999i	−0.977809	+	0.209500i	$0.932816\pi$
$32$	1.00662e6	+	293659.i	0.959984	+	0.280055i
$33$	338288.			0.285253
$34$	177886.	−	114408.i	0.133115	−	0.0856136i
$35$	588437.	−	588437.i	0.392128	−	0.392128i
$36$	−509440.	−	232223.i	−0.303307	−	0.138260i
$37$	1.62932e6	−	1.62932e6i	0.869362	−	0.869362i	−0.123040	−	0.992402i	$-0.539264\pi$
$37$	1.62932e6	−	1.62932e6i	0.869362	−	0.869362i	0.992402	+	0.123040i	$0.0392644\pi$
$38$	35036.3	−	161331.i	0.0168029	−	0.0773717i
$39$	1.60730e6			0.694767
$40$	−1.54741e6	−	1.15585e6i	−0.604456	−	0.451502i
$41$		−	1.15378e6i		−	0.408308i	−0.978939	−	0.204154i	$-0.934556\pi$
$41$		−	1.15378e6i		−	0.408308i	0.978939	−	0.204154i	$-0.0654444\pi$
$42$	−280242.	+	1.29042e6i	−0.0900607	+	0.414700i
$43$	2.25332e6	+	2.25332e6i	0.659096	+	0.659096i	0.955166	−	0.296070i	$-0.0956762\pi$
$43$	2.25332e6	+	2.25332e6i	0.659096	+	0.659096i	−0.296070	+	0.955166i	$0.595676\pi$
$44$	−1.73462e6	+	648362.i	−0.462801	+	0.172984i
$45$	729213.	+	729213.i	0.177830	+	0.177830i
$46$	−3.91102e6	+	2.51539e6i	−0.873492	+	0.561791i
$47$			3.16374e6i			0.648350i	0.945997	+	0.324175i	$0.105087\pi$
$47$			3.16374e6i			0.648350i	−0.945997	+	0.324175i	$0.894913\pi$
$48$	3.05731e6	+	214367.i	0.575936	+	0.0403825i
$49$	−2.65030e6			−0.459738
$50$	−1.45639e6	−	2.26445e6i	−0.233023	−	0.362312i
$51$	437122.	−	437122.i	0.0646133	−	0.0646133i
$52$	−8.24168e6	+	3.08055e6i	−1.12720	+	0.421323i
$53$	8.51641e6	−	8.51641e6i	1.07933	−	1.07933i	0.0827575	−	0.996570i	$-0.473627\pi$
$53$	8.51641e6	−	8.51641e6i	1.07933	−	1.07933i	0.996570	−	0.0827575i	$-0.0263727\pi$
$54$	−1.59914e6	−	347286.i	−0.188066	−	0.0408425i
$55$	3.41101e6			0.372762
$56$	−1.03624e6	−	7.15394e6i	−0.105368	−	0.727433i
$57$		−	482534.i		−	0.0457118i
$58$	−1.44222e7	−	3.13209e6i	−1.27444	−	0.276772i
$59$	−1.02071e6	−	1.02071e6i	−0.0842355	−	0.0842355i	0.663734	−	0.747969i	$-0.268971\pi$
$59$	−1.02071e6	−	1.02071e6i	−0.0842355	−	0.0842355i	−0.747969	+	0.663734i	$0.768971\pi$
$60$	−5.13676e6	−	2.34154e6i	−0.396355	−	0.180675i
$61$	−1.85953e7	−	1.85953e7i	−1.34302	−	1.34302i	−0.893035	−	0.449987i	$-0.851429\pi$
$61$	−1.85953e7	−	1.85953e7i	−1.34302	−	1.34302i	−0.449987	−	0.893035i	$-0.648571\pi$
$62$	−3.34908e6	−	5.20726e6i	−0.226651	−	0.352405i
$63$			3.85961e6i			0.245008i
$64$	−1.60877e7	+	4.76044e6i	−0.958900	+	0.283744i
$65$	1.62067e7			0.907905
$66$	−4.55235e6	+	2.92787e6i	−0.239916	+	0.154303i
$67$	1.09956e7	−	1.09956e7i	0.545657	−	0.545657i	−0.379525	−	0.925181i	$-0.623913\pi$
$67$	1.09956e7	−	1.09956e7i	0.545657	−	0.545657i	0.925181	+	0.379525i	$0.123913\pi$
$68$	−1.40362e6	+	3.07920e6i	−0.0656469	+	0.144013i
$69$	−9.61060e6	+	9.61060e6i	−0.423989	+	0.423989i
$70$	−2.82572e6	+	1.30115e7i	−0.117689	+	0.541921i
$71$	2.07169e7			0.815252			0.407626	−	0.913149i	$-0.366357\pi$
$71$	2.07169e7			0.815252			0.407626	+	0.913149i	$0.366357\pi$
$72$	8.86543e6	−	1.28415e6i	0.329891	−	0.0477842i
$73$			1.49012e7i			0.524724i	0.964970	+	0.262362i	$0.0845014\pi$
$73$			1.49012e7i			0.524724i	−0.964970	+	0.262362i	$0.915499\pi$
$74$	−7.82413e6	+	3.60276e7i	−0.260921	+	1.20146i
$75$	−5.56446e6	−	5.56446e6i	−0.175864	−	0.175864i
$76$	924825.	+	2.47427e6i	0.0277208	+	0.0741638i
$77$	9.02695e6	+	9.02695e6i	0.256790	+	0.256790i
$78$	−2.16295e7	+	1.39111e7i	−0.584344	+	0.375824i
$79$			1.87691e7i			0.481877i	0.970540	+	0.240938i	$0.0774552\pi$
$79$			1.87691e7i			0.481877i	−0.970540	+	0.240938i	$0.922545\pi$
$80$	3.08273e7	+	2.16149e6i	0.752620	+	0.0527709i
$81$	−4.78297e6			−0.111111
$82$	9.98593e6	+	1.55265e7i	0.220868	+	0.343414i
$83$	4.60031e7	−	4.60031e7i	0.969338	−	0.969338i	−0.0302059	−	0.999544i	$-0.509616\pi$
$83$	4.60031e7	−	4.60031e7i	0.969338	−	0.969338i	0.999544	+	0.0302059i	$0.00961631\pi$
$84$	−7.39732e6	−	1.97907e7i	−0.148579	−	0.397507i
$85$	4.40757e6	−	4.40757e6i	0.0844352	−	0.0844352i
$86$	−4.98254e7	−	1.08206e7i	−0.910871	−	0.197814i
$87$	−4.31364e7			−0.752952
$88$	1.77313e7	−	2.37381e7i	0.295672	−	0.395836i
$89$		−	1.96886e7i		−	0.313802i	−0.987614	−	0.156901i	$-0.949850\pi$
$89$		−	1.96886e7i		−	0.313802i	0.987614	−	0.156901i	$-0.0501504\pi$
$90$	−1.61244e7	−	3.50174e6i	−0.245761	−	0.0533720i
$91$	4.28896e7	+	4.28896e7i	0.625442	+	0.625442i
$92$	3.08601e7	−	6.76995e7i	0.430771	−	0.945005i
$93$	−1.27959e7	−	1.27959e7i	−0.171056	−	0.171056i
$94$	−2.73821e7	−	4.25746e7i	−0.350715	−	0.545305i
$95$		−	4.86547e6i		−	0.0597352i
$96$	−4.29976e7	+	2.35761e7i	−0.506244	+	0.277580i
$97$	4.61339e7			0.521115			0.260557	−	0.965458i	$-0.416094\pi$
$97$	4.61339e7			0.521115			0.260557	+	0.965458i	$0.416094\pi$
$98$	3.56652e7	−	2.29382e7i	0.386670	−	0.248688i
$99$	−1.11865e7	+	1.11865e7i	−0.116454	+	0.116454i
$100$	3.91975e7	+	1.78678e7i	0.391975	+	0.178678i
$101$	2.00302e7	−	2.00302e7i	0.192486	−	0.192486i	−0.604283	−	0.796770i	$-0.706540\pi$
$101$	2.00302e7	−	2.00302e7i	0.192486	−	0.192486i	0.796770	+	0.604283i	$0.206540\pi$
$102$	−2.09909e6	+	9.66564e6i	−0.0193924	+	0.0892955i
$103$	1.34956e8			1.19907			0.599535	−	0.800349i	$-0.295352\pi$
$103$	1.34956e8			1.19907			0.599535	+	0.800349i	$0.295352\pi$
$104$	8.42465e7	−	1.12787e8i	0.720143	−	0.964104i
$105$			3.89170e7i			0.320171i
$106$	−4.08964e7	+	1.88315e8i	−0.323938	+	1.49163i
$107$	1.45772e8	+	1.45772e8i	1.11209	+	1.11209i	0.992867	+	0.119224i	$0.0380406\pi$
$107$	1.45772e8	+	1.45772e8i	1.11209	+	1.11209i	0.119224	+	0.992867i	$0.461959\pi$
$108$	2.45254e7	−	9.16704e6i	0.180269	−	0.0673805i
$109$	−1.60797e8	−	1.60797e8i	−1.13913	−	1.13913i	−0.988607	−	0.150520i	$-0.951905\pi$
$109$	−1.60797e8	−	1.60797e8i	−1.13913	−	1.13913i	−0.150520	−	0.988607i	$-0.548095\pi$
$110$	−4.59021e7	+	2.95221e7i	−0.313517	+	0.201640i
$111$			1.07757e8i			0.709831i
$112$	7.58618e7	+	8.73022e7i	0.482115	+	0.554821i
$113$	−2.40888e8			−1.47741			−0.738706	−	0.674028i	$-0.764563\pi$
$113$	−2.40888e8			−1.47741			−0.738706	+	0.674028i	$0.764563\pi$
$114$	4.17631e6	+	6.49348e6i	0.0247271	+	0.0384466i
$115$	−9.69052e7	+	9.69052e7i	−0.554058	+	0.554058i
$116$	2.21189e8	−	8.26752e7i	1.22160	−	0.456608i
$117$	−5.31504e7	+	5.31504e7i	−0.283637	+	0.283637i
$118$	2.25700e7	+	4.90154e6i	0.116413	+	0.0252816i
$119$	2.33285e7			0.116332
$120$	8.93915e7	−	1.29483e7i	0.431093	−	0.0624433i
$121$		−	1.62032e8i		−	0.755892i
$122$	4.11178e8	+	8.92959e7i	1.85606	+	0.403081i
$123$	3.81534e7	+	3.81534e7i	0.166691	+	0.166691i
$124$	9.01372e7	+	4.10882e7i	0.381257	+	0.173792i
$125$	−1.86354e8	−	1.86354e8i	−0.763305	−	0.763305i
$126$	−3.34047e7	−	5.19388e7i	−0.132534	−	0.206068i
$127$			5.32983e7i			0.204879i	0.994739	+	0.102440i	$0.0326649\pi$
$127$			5.32983e7i			0.204879i	−0.994739	+	0.102440i	$0.967335\pi$
$128$	1.75291e8	−	2.03299e8i	0.653010	−	0.757350i
$129$	−1.49026e8			−0.538150
$130$	−2.18094e8	+	1.40268e8i	−0.763607	+	0.491118i
$131$	−3.32094e8	+	3.32094e8i	−1.12765	+	1.12765i	−0.137094	+	0.990558i	$0.543776\pi$
$131$	−3.32094e8	+	3.32094e8i	−1.12765	+	1.12765i	−0.990558	+	0.137094i	$0.956224\pi$
$132$	3.59206e7	−	7.88008e7i	0.118317	−	0.259558i
$133$	1.28761e7	−	1.28761e7i	0.0411506	−	0.0411506i
$134$	−5.28016e7	+	2.43134e8i	−0.163768	+	0.754097i
$135$	−4.82274e7			−0.145197
$136$	−7.76174e6	−	5.35851e7i	−0.0226884	−	0.156635i
$137$		−	2.15419e7i		−	0.0611508i	−0.999532	−	0.0305754i	$-0.990266\pi$
$137$		−	2.15419e7i		−	0.0611508i	0.999532	−	0.0305754i	$-0.00973397\pi$
$138$	4.61508e7	−	2.12509e8i	0.127252	−	0.585952i
$139$	−3.01476e8	−	3.01476e8i	−0.807596	−	0.807596i	0.176673	−	0.984270i	$-0.443466\pi$
$139$	−3.01476e8	−	3.01476e8i	−0.807596	−	0.807596i	−0.984270	+	0.176673i	$0.943466\pi$
$140$	−7.45883e7	−	1.99553e8i	−0.194160	−	0.519452i
$141$	−1.04619e8	−	1.04619e8i	−0.264688	−	0.264688i
$142$	−2.78788e8	+	1.79304e8i	−0.685679	+	0.440998i
$143$			2.48619e8i			0.594554i
$144$	−1.08188e8	+	9.40107e7i	−0.251611	+	0.218639i
$145$	−4.34951e8			−0.983940
$146$	−1.28970e8	−	2.00526e8i	−0.283841	−	0.441327i
$147$	8.76404e7	−	8.76404e7i	0.187687	−	0.187687i
$148$	−2.06528e8	−	5.52542e8i	−0.430458	−	1.15164i
$149$	9.97389e7	−	9.97389e7i	0.202358	−	0.202358i	−0.598652	−	0.801009i	$-0.704297\pi$
$149$	9.97389e7	−	9.97389e7i	0.202358	−	0.202358i	0.801009	+	0.598652i	$0.204297\pi$
$150$	1.23041e8	+	2.67210e7i	0.243045	+	0.0527821i
$151$	4.15900e8			0.799983			0.399992	−	0.916519i	$-0.369013\pi$
$151$	4.15900e8			0.799983			0.399992	+	0.916519i	$0.369013\pi$
$152$	−3.38601e7	−	2.52920e7i	−0.0634328	−	0.0473815i
$153$			2.89096e7i			0.0527565i
$154$	−1.99604e8	−	4.33481e7i	−0.354884	−	0.0770703i
$155$	−1.29023e8	−	1.29023e8i	−0.223532	−	0.223532i
$156$	1.70669e8	−	3.74405e8i	0.288175	−	0.632184i
$157$	−3.85945e8	−	3.85945e8i	−0.635224	−	0.635224i	0.314149	−	0.949374i	$-0.398281\pi$
$157$	−3.85945e8	−	3.85945e8i	−0.635224	−	0.635224i	−0.949374	+	0.314149i	$0.898281\pi$
$158$	−1.62446e8	−	2.52577e8i	−0.260664	−	0.405290i
$159$			5.63243e8i			0.881267i
$160$	−4.33552e8	+	2.37722e8i	−0.661548	+	0.362735i
$161$	−5.12903e8			−0.763364
$162$	6.43646e7	−	4.13964e7i	0.0934516	−	0.0601039i
$163$	4.67271e8	−	4.67271e8i	0.661939	−	0.661939i	−0.293898	−	0.955837i	$-0.594952\pi$
$163$	4.67271e8	−	4.67271e8i	0.661939	−	0.661939i	0.955837	+	0.293898i	$0.0949524\pi$
$164$	−2.68762e8	−	1.22512e8i	−0.371529	−	0.169358i
$165$	−1.12796e8	+	1.12796e8i	−0.152180	+	0.152180i
$166$	−2.20911e8	+	1.01722e9i	−0.290927	+	1.33962i
$167$	9.39278e8			1.20761			0.603807	−	0.797130i	$-0.293650\pi$
$167$	9.39278e8			1.20761			0.603807	+	0.797130i	$0.293650\pi$
$168$	2.70834e8	+	2.02301e8i	0.339990	+	0.253957i
$169$			3.65531e8i			0.448103i
$170$	−2.11655e7	+	9.74601e7i	−0.0253415	+	0.116689i
$171$	1.59565e7	+	1.59565e7i	0.0186618	+	0.0186618i
$172$	7.64153e8	−	2.85623e8i	0.873106	−	0.326347i
$173$	4.67970e8	+	4.67970e8i	0.522437	+	0.522437i	0.918307	−	0.395870i	$-0.129557\pi$
$173$	4.67970e8	+	4.67970e8i	0.522437	+	0.522437i	−0.395870	+	0.918307i	$0.629557\pi$
$174$	5.80488e8	−	3.73344e8i	0.633281	−	0.407298i
$175$		−	2.96967e8i		−	0.316633i
$176$	−3.31585e7	+	4.72908e8i	−0.0345577	+	0.492863i
$177$	6.75061e7			0.0687780
$178$	1.70404e8	+	2.64951e8i	0.169746	+	0.263928i
$179$	−9.99524e8	+	9.99524e8i	−0.973601	+	0.973601i	−0.999660	−	0.0260591i	$-0.991704\pi$
$179$	−9.99524e8	+	9.99524e8i	−0.973601	+	0.973601i	0.0260591	+	0.999660i	$0.491704\pi$
$180$	2.47293e8	−	9.24326e7i	0.235571	−	0.0880512i
$181$	1.49337e9	−	1.49337e9i	1.39141	−	1.39141i	0.569221	−	0.822185i	$-0.307245\pi$
$181$	1.49337e9	−	1.49337e9i	1.39141	−	1.39141i	0.822185	−	0.569221i	$-0.192755\pi$
$182$	−9.48375e8	−	2.05959e8i	−0.864360	−	0.187714i
$183$	1.22982e9			1.09657
$184$	1.70650e8	+	1.17813e9i	0.148880	+	1.02783i
$185$			1.08653e9i			0.927590i
$186$	2.82942e8	+	6.14467e7i	0.236399	+	0.0513389i
$187$	6.76146e7	+	6.76146e7i	0.0552935	+	0.0552935i
$188$	7.36963e8	+	3.35937e8i	0.589948	+	0.268922i
$189$	−1.27630e8	−	1.27630e8i	−0.100024	−	0.100024i
$190$	4.21104e7	+	6.54747e7i	0.0323128	+	0.0502411i
$191$		−	1.35513e8i		−	0.101823i	−0.998703	−	0.0509117i	$-0.983787\pi$
$191$		−	1.35513e8i		−	0.101823i	0.998703	−	0.0509117i	$-0.0162127\pi$
$192$	3.74570e8	−	6.89408e8i	0.275631	−	0.507307i
$193$	1.76355e9			1.27104			0.635519	−	0.772085i	$-0.280786\pi$
$193$	1.76355e9			1.27104			0.635519	+	0.772085i	$0.280786\pi$
$194$	−6.20825e8	+	3.99287e8i	−0.438291	+	0.281889i
$195$	−5.35924e8	+	5.35924e8i	−0.370651	+	0.370651i
$196$	−2.81418e8	+	6.17361e8i	−0.190690	+	0.418326i
$197$	6.58359e8	−	6.58359e8i	0.437117	−	0.437117i	−0.453924	−	0.891041i	$-0.649976\pi$
$197$	6.58359e8	−	6.58359e8i	0.437117	−	0.437117i	0.891041	+	0.453924i	$0.149976\pi$
$198$	5.37186e7	−	2.47357e8i	0.0349513	−	0.160940i
$199$	2.75805e9			1.75869			0.879346	−	0.476184i	$-0.157980\pi$
$199$	2.75805e9			1.75869			0.879346	+	0.476184i	$0.157980\pi$
$200$	−6.82126e8	+	9.88052e7i	−0.426329	+	0.0617532i
$201$			7.27207e8i			0.445527i
$202$	−9.61864e7	+	4.42907e8i	−0.0577708	+	0.266016i
$203$	−1.15106e9	−	1.15106e9i	−0.677821	−	0.677821i
$204$	−5.54081e7	−	1.48238e8i	−0.0319928	−	0.0855933i
$205$	3.84706e8	+	3.84706e8i	0.217828	+	0.217828i
$206$	−1.81611e9	+	1.16804e9i	−1.00850	+	0.648619i
$207$		−	6.35609e8i		−	0.346185i
$208$	−1.57546e8	+	2.24692e9i	−0.0841692	+	1.20042i
$209$	7.46390e7			0.0391184
$210$	−3.36825e8	−	5.23707e8i	−0.173192	−	0.269285i
$211$	1.60729e9	−	1.60729e9i	0.810895	−	0.810895i	−0.173873	−	0.984768i	$-0.555628\pi$
$211$	1.60729e9	−	1.60729e9i	0.810895	−	0.810895i	0.984768	+	0.173873i	$0.0556283\pi$
$212$	−1.07951e9	−	2.88812e9i	−0.534422	−	1.42979i
$213$	−6.85069e8	+	6.85069e8i	−0.332825	+	0.332825i
$214$	−3.22332e9	−	7.00010e8i	−1.53691	−	0.333772i
$215$	−1.50265e9			−0.703242
$216$	−2.50699e8	+	3.35627e8i	−0.115169	+	0.154185i
$217$		−	6.82896e8i		−	0.307975i
$218$	3.55554e9	+	7.72159e8i	1.57427	+	0.341886i
$219$	−4.92756e8	−	4.92756e8i	−0.214218	−	0.214218i
$220$	3.62193e8	−	7.94561e8i	0.154614	−	0.339185i
$221$	3.21256e8	+	3.21256e8i	0.134674	+	0.134674i
$222$	−9.32635e8	−	1.45009e9i	−0.383972	−	0.597013i
$223$		−	2.63330e9i		−	1.06483i	−0.846483	−	0.532416i	$-0.821284\pi$
$223$		−	2.63330e9i		−	1.06483i	0.846483	−	0.532416i	$-0.178716\pi$
$224$	−1.77647e9	−	5.18248e8i	−0.705612	−	0.205848i
$225$	3.68012e8			0.143593
$226$	3.24164e9	−	2.08488e9i	1.24260	−	0.799183i
$227$	−2.39810e9	+	2.39810e9i	−0.903157	+	0.903157i	−0.995708	−	0.0925508i	$-0.970498\pi$
$227$	−2.39810e9	+	2.39810e9i	−0.903157	+	0.903157i	0.0925508	+	0.995708i	$0.470498\pi$
$228$	−1.12402e8	−	5.12371e7i	−0.0415942	−	0.0189603i
$229$	1.62492e9	−	1.62492e9i	0.590867	−	0.590867i	−0.346998	−	0.937866i	$-0.612799\pi$
$229$	1.62492e9	−	1.62492e9i	0.590867	−	0.590867i	0.937866	+	0.346998i	$0.112799\pi$
$230$	4.65346e8	−	2.14277e9i	0.166289	−	0.765708i
$231$	−5.97009e8			−0.209668
$232$	−2.26099e9	+	3.02694e9i	−0.780453	+	1.04485i
$233$			4.34782e9i			1.47519i	0.675243	+	0.737595i	$0.264039\pi$
$233$			4.34782e9i			1.47519i	−0.675243	+	0.737595i	$0.735961\pi$
$234$	2.55232e8	−	1.17526e9i	0.0851280	−	0.391987i
$235$	−1.05489e9	−	1.05489e9i	−0.345888	−	0.345888i
$236$	−3.46148e8	+	1.29382e8i	−0.111587	+	0.0417087i
$237$	−6.20660e8	−	6.20660e8i	−0.196725	−	0.196725i
$238$	−3.13933e8	+	2.01907e8i	−0.0978428	+	0.0629281i
$239$			5.20101e8i			0.159403i	0.996819	+	0.0797014i	$0.0253967\pi$
$239$			5.20101e8i			0.159403i	−0.996819	+	0.0797014i	$0.974603\pi$
$240$	−1.09088e9	+	9.47925e8i	−0.328800	+	0.285712i
$241$	−1.68076e9			−0.498237			−0.249119	−	0.968473i	$-0.580141\pi$
$241$	−1.68076e9			−0.498237			−0.249119	+	0.968473i	$0.580141\pi$
$242$	1.40238e9	+	2.18047e9i	0.408888	+	0.635754i
$243$	1.58164e8	−	1.58164e8i	0.0453609	−	0.0453609i
$244$	−6.30609e9	+	2.35707e9i	−1.77910	+	0.664988i
$245$	8.83692e8	−	8.83692e8i	0.245266	−	0.245266i
$246$	−8.43647e8	−	1.83215e8i	−0.230367	−	0.0500290i
$247$	3.54631e8			0.0952772
$248$	−1.56860e9	+	2.27209e8i	−0.414672	+	0.0600647i
$249$			3.04247e9i			0.791461i
$250$	4.12065e9	+	8.94885e8i	1.05489	+	0.229090i
$251$	−4.78114e9	−	4.78114e9i	−1.20458	−	1.20458i	−0.972757	−	0.231826i	$-0.925530\pi$
$251$	−4.78114e9	−	4.78114e9i	−1.20458	−	1.20458i	−0.231826	−	0.972757i	$-0.574470\pi$
$252$	8.99057e8	+	4.09826e8i	0.222939	+	0.101624i
$253$	−1.48658e9	−	1.48658e9i	−0.362832	−	0.362832i
$254$	−4.61294e8	−	7.17237e8i	−0.110826	−	0.172317i
$255$			2.91500e8i			0.0689410i
$256$	−5.99347e8	+	4.25294e9i	−0.139546	+	0.990216i
$257$	5.90129e9			1.35274			0.676370	−	0.736562i	$-0.263552\pi$
$257$	5.90129e9			1.35274			0.676370	+	0.736562i	$0.263552\pi$
$258$	2.00545e9	−	1.28981e9i	0.452619	−	0.291104i
$259$	−2.87542e9	+	2.87542e9i	−0.639002	+	0.639002i
$260$	1.72088e9	−	3.77518e9i	0.376580	−	0.826123i
$261$	1.42644e9	−	1.42644e9i	0.307391	−	0.307391i
$262$	1.59474e9	−	7.34325e9i	0.338442	−	1.55841i
$263$	−1.49063e8			−0.0311565			−0.0155782	−	0.999879i	$-0.504959\pi$
$263$	−1.49063e8			−0.0311565			−0.0155782	+	0.999879i	$0.504959\pi$
$264$	1.98633e8	+	1.37132e9i	0.0408918	+	0.282307i
$265$			5.67927e9i			1.15162i
$266$	−6.18318e7	+	2.84715e8i	−0.0123505	+	0.0568701i
$267$	6.51066e8	+	6.51066e8i	0.128109	+	0.128109i
$268$	−1.39376e9	−	3.72886e9i	−0.270178	−	0.722832i
$269$	−2.83972e9	−	2.83972e9i	−0.542334	−	0.542334i	0.381879	−	0.924212i	$-0.375277\pi$
$269$	−2.83972e9	−	2.83972e9i	−0.542334	−	0.542334i	−0.924212	+	0.381879i	$0.875277\pi$
$270$	6.48998e8	−	4.17406e8i	0.122120	−	0.0785423i
$271$			4.40824e9i			0.817312i	0.912688	+	0.408656i	$0.134002\pi$
$271$			4.40824e9i			0.817312i	−0.912688	+	0.408656i	$0.865998\pi$
$272$	5.68227e8	+	6.53919e8i	0.103812	+	0.119467i
$273$	−2.83656e9			−0.510671
$274$	1.86444e8	+	2.89890e8i	0.0330786	+	0.0514318i
$275$	8.60718e8	−	8.60718e8i	0.150498	−	0.150498i
$276$	1.21821e9	+	3.25918e9i	0.209935	+	0.561658i
$277$	−1.41848e9	+	1.41848e9i	−0.240938	+	0.240938i	−0.817238	−	0.576300i	$-0.804496\pi$
$277$	−1.41848e9	+	1.41848e9i	−0.240938	+	0.240938i	0.576300	+	0.817238i	$0.304496\pi$
$278$	6.66624e9	+	1.44771e9i	1.11610	+	0.242384i
$279$	8.46270e8			0.139666
$280$	2.73086e9	+	2.03983e9i	0.444291	+	0.331865i
$281$			7.45967e9i			1.19645i	0.801329	+	0.598224i	$0.204127\pi$
$281$			7.45967e9i			1.19645i	−0.801329	+	0.598224i	$0.795873\pi$
$282$	2.31333e9	+	5.02388e8i	0.365799	+	0.0794407i
$283$	−6.71816e9	−	6.71816e9i	−1.04738	−	1.04738i	−0.998820	−	0.0485601i	$-0.984537\pi$
$283$	−6.71816e9	−	6.71816e9i	−1.04738	−	1.04738i	−0.0485601	−	0.998820i	$-0.515463\pi$
$284$	2.19979e9	−	4.82580e9i	0.338149	−	0.741816i
$285$	1.60892e8	+	1.60892e8i	0.0243868	+	0.0243868i
$286$	−2.15179e9	−	3.34568e9i	−0.321615	−	0.500058i
$287$			2.03619e9i			0.300117i
$288$	6.42233e8	−	2.20147e9i	0.0933517	−	0.319995i
$289$	−6.80102e9			−0.974951
$290$	5.85315e9	−	3.76448e9i	0.827557	−	0.532247i
$291$	−1.52556e9	+	1.52556e9i	−0.212744	+	0.212744i
$292$	3.47110e9	+	1.58226e9i	0.477458	+	0.217644i
$293$	8.51267e9	−	8.51267e9i	1.15504	−	1.15504i	0.169507	−	0.985529i	$-0.445783\pi$
$293$	8.51267e9	−	8.51267e9i	1.15504	−	1.15504i	0.985529	−	0.169507i	$-0.0542174\pi$
$294$	−4.20856e8	+	1.93790e9i	−0.0563306	+	0.259384i
$295$	6.80674e8			0.0898775
$296$	7.56147e9	+	5.64809e9i	0.985008	+	0.735757i
$297$		−	7.39836e8i		−	0.0950844i
$298$	−4.78953e8	+	2.20542e9i	−0.0607335	+	0.279658i
$299$	−7.06316e9	−	7.06316e9i	−0.883720	−	0.883720i
$300$	−1.88704e9	+	7.05332e8i	−0.232968	+	0.0870781i
$301$	−3.97665e9	−	3.97665e9i	−0.484452	−	0.484452i
$302$	−5.59678e9	+	3.59960e9i	−0.672838	+	0.432739i
$303$			1.32472e9i			0.157164i
$304$	6.74557e8	+	4.72974e7i	0.0789813	+	0.00553787i
$305$	1.24005e10			1.43298
$306$	−2.50211e8	−	3.89037e8i	−0.0285379	−	0.0443717i
$307$	−3.19252e9	+	3.19252e9i	−0.359402	+	0.359402i	−0.863593	−	0.504190i	$-0.831791\pi$
$307$	−3.19252e9	+	3.19252e9i	−0.359402	+	0.359402i	0.504190	+	0.863593i	$0.331791\pi$
$308$	3.06125e9	−	1.14423e9i	0.340170	−	0.127148i
$309$	−4.46275e9	+	4.46275e9i	−0.489518	+	0.489518i
$310$	2.85295e9	+	6.19576e8i	0.308921	+	0.0670885i
$311$	−2.76157e9			−0.295199			−0.147599	−	0.989047i	$-0.547155\pi$
$311$	−2.76157e9			−0.295199			−0.147599	+	0.989047i	$0.547155\pi$
$312$	9.43764e8	+	6.51551e9i	0.0995967	+	0.687591i
$313$			1.31764e10i			1.37284i	0.727204	+	0.686421i	$0.240819\pi$
$313$			1.31764e10i			1.37284i	−0.727204	+	0.686421i	$0.759181\pi$
$314$	8.53402e9	+	1.85334e9i	0.877880	+	0.190650i
$315$	−1.28691e9	−	1.28691e9i	−0.130709	−	0.130709i
$316$	4.37209e9	+	1.99297e9i	0.438470	+	0.199872i
$317$	7.55584e9	+	7.55584e9i	0.748248	+	0.748248i	0.974150	−	0.225902i	$-0.0725329\pi$
$317$	7.55584e9	+	7.55584e9i	0.748248	+	0.748248i	−0.225902	+	0.974150i	$0.572533\pi$
$318$	−4.87485e9	−	7.57958e9i	−0.476708	−	0.741202i
$319$		−	6.67239e9i		−	0.644346i
$320$	3.77685e9	−	6.95140e9i	0.360188	−	0.662938i
$321$	−9.64084e9			−0.908019
$322$	6.90215e9	−	4.43915e9i	0.642039	−	0.412930i
$323$	9.64455e7	−	9.64455e7i	0.00886078	−	0.00886078i
$324$	−5.07872e8	+	1.11415e9i	−0.0460866	+	0.101102i
$325$	4.08952e9	−	4.08952e9i	0.366554	−	0.366554i
$326$	−2.24387e9	+	1.03323e10i	−0.198668	+	0.914800i
$327$	1.06345e10			0.930093
$328$	4.67708e9	−	6.77469e8i	0.404091	−	0.0585321i
$329$		−	5.58336e9i		−	0.476554i
$330$	5.41653e8	−	2.49414e9i	0.0456736	−	0.210312i
$331$	7.25157e9	+	7.25157e9i	0.604116	+	0.604116i	0.941402	−	0.337286i	$-0.109509\pi$
$331$	7.25157e9	+	7.25157e9i	0.604116	+	0.604116i	−0.337286	+	0.941402i	$0.609509\pi$
$332$	−5.83120e9	−	1.56007e10i	−0.479961	−	1.28408i
$333$	−3.56333e9	−	3.56333e9i	−0.289787	−	0.289787i
$334$	−1.26399e10	+	8.12941e9i	−1.01568	+	0.653241i
$335$			7.33254e9i			0.582204i
$336$	−5.39552e9	−	3.78314e8i	−0.423328	−	0.0296821i
$337$	−1.28768e10			−0.998361			−0.499181	−	0.866498i	$-0.666366\pi$
$337$	−1.28768e10			−0.998361			−0.499181	+	0.866498i	$0.666366\pi$
$338$	−3.16366e9	−	4.91897e9i	−0.242394	−	0.376883i
$339$	7.96571e9	−	7.96571e9i	0.603151	−	0.603151i
$340$	−5.58689e8	−	1.49471e9i	−0.0418075	−	0.111851i
$341$	1.97928e9	−	1.97928e9i	0.146383	−	0.146383i
$342$	−3.52830e8	−	7.66243e7i	−0.0257906	−	0.00560095i
$343$	1.48509e10			1.07294
$344$	−7.81118e9	+	1.04574e10i	−0.557806	+	0.746772i
$345$		−	6.40894e9i		−	0.452387i
$346$	−1.03478e10	−	2.24723e9i	−0.722007	−	0.156799i
$347$	−4.13568e9	−	4.13568e9i	−0.285252	−	0.285252i	0.549947	−	0.835200i	$-0.314648\pi$
$347$	−4.13568e9	−	4.13568e9i	−0.285252	−	0.285252i	−0.835200	+	0.549947i	$0.814648\pi$
$348$	−4.58037e9	+	1.00482e10i	−0.312309	+	0.685127i
$349$	3.97034e9	+	3.97034e9i	0.267625	+	0.267625i	0.828142	−	0.560518i	$-0.189398\pi$
$349$	3.97034e9	+	3.97034e9i	0.267625	+	0.267625i	−0.560518	+	0.828142i	$0.689398\pi$
$350$	2.57024e9	+	3.99629e9i	0.171278	+	0.266309i
$351$		−	3.51517e9i		−	0.231589i
$352$	−3.64679e9	−	6.65093e9i	−0.237542	−	0.433223i
$353$	1.19540e10			0.769867			0.384933	−	0.922944i	$-0.374224\pi$
$353$	1.19540e10			0.769867			0.384933	+	0.922944i	$0.374224\pi$
$354$	−9.08431e8	+	5.84262e8i	−0.0578468	+	0.0372044i
$355$	−6.90766e9	+	6.90766e9i	−0.434928	+	0.434928i
$356$	−4.58627e9	−	2.09061e9i	−0.285535	−	0.130158i
$357$	−7.71431e8	+	7.71431e8i	−0.0474924	+	0.0474924i
$358$	4.79979e9	−	2.21015e10i	0.292207	−	1.34552i
$359$	5.02137e9			0.302305			0.151152	−	0.988510i	$-0.451702\pi$
$359$	5.02137e9			0.302305			0.151152	+	0.988510i	$0.451702\pi$
$360$	−2.52783e9	+	3.38418e9i	−0.150501	+	0.201485i
$361$			1.68771e10i			0.993731i
$362$	−7.17128e9	+	3.30214e10i	−0.417602	+	1.92292i
$363$	5.35810e9	+	5.35810e9i	0.308591	+	0.308591i
$364$	1.45449e10	−	5.43655e9i	0.828523	−	0.309683i
$365$	−4.96853e9	−	4.96853e9i	−0.279935	−	0.279935i
$366$	−1.65497e10	+	1.06440e10i	−0.922289	+	0.593174i
$367$		−	6.61169e9i		−	0.364459i	−0.983256	−	0.182229i	$-0.941669\pi$
$367$		−	6.61169e9i		−	0.364459i	0.983256	−	0.182229i	$-0.0583314\pi$
$368$	−1.24931e10	−	1.43771e10i	−0.681206	−	0.783936i
$369$	−2.52332e9			−0.136103
$370$	−9.40390e9	−	1.46215e10i	−0.501766	−	0.780163i
$371$	−1.50297e10	+	1.50297e10i	−0.793332	+	0.793332i
$372$	−4.33938e9	+	1.62196e9i	−0.226598	+	0.0846971i
$373$	−2.15583e9	+	2.15583e9i	−0.111373	+	0.111373i	−0.760597	−	0.649224i	$-0.775094\pi$
$373$	−2.15583e9	+	2.15583e9i	−0.111373	+	0.111373i	0.649224	+	0.760597i	$0.275094\pi$
$374$	−1.49509e9	−	3.24690e8i	−0.0764155	−	0.0165952i
$375$	1.23247e10			0.623236
$376$	−1.28249e10	+	1.85766e9i	−0.641654	+	0.0929428i
$377$		−	3.17024e10i		−	1.56938i
$378$	2.82215e9	+	6.12888e8i	0.138233	+	0.0300202i
$379$	2.41763e10	+	2.41763e10i	1.17175	+	1.17175i	0.981793	+	0.189952i	$0.0608334\pi$
$379$	2.41763e10	+	2.41763e10i	1.17175	+	1.17175i	0.189952	+	0.981793i	$0.439167\pi$
$380$	−1.13336e9	−	5.16632e8i	−0.0543544	−	0.0247769i
$381$	−1.76247e9	−	1.76247e9i	−0.0836417	−	0.0836417i
$382$	1.17286e9	+	1.82360e9i	0.0550798	+	0.0856400i
$383$		−	1.64838e10i		−	0.766057i	−0.923736	−	0.383029i	$-0.874881\pi$
$383$		−	1.64838e10i		−	0.766057i	0.923736	−	0.383029i	$-0.125119\pi$
$384$	9.26191e8	+	1.25193e10i	0.0425966	+	0.575777i
$385$	−6.01973e9			−0.273990
$386$	−2.37322e10	+	1.52635e10i	−1.06903	+	0.687549i
$387$	4.92801e9	−	4.92801e9i	0.219699	−	0.219699i
$388$	4.89866e9	−	1.07464e10i	0.216147	−	0.474174i
$389$	4.01880e9	−	4.01880e9i	0.175509	−	0.175509i	−0.613886	−	0.789395i	$-0.710395\pi$
$389$	4.01880e9	−	4.01880e9i	0.175509	−	0.175509i	0.789395	+	0.613886i	$0.210395\pi$
$390$	2.57355e9	−	1.18503e10i	0.111243	−	0.512239i
$391$	−3.84180e9			−0.164372
$392$	−1.55618e9	−	1.07435e10i	−0.0659047	−	0.454990i
$393$		−	2.19634e10i		−	0.920724i
$394$	−3.16149e9	+	1.45576e10i	−0.131192	+	0.604095i
$395$	−6.25821e9	−	6.25821e9i	−0.257076	−	0.257076i
$396$	1.41797e9	+	3.79362e9i	0.0576615	+	0.154267i
$397$	−1.36455e10	−	1.36455e10i	−0.549322	−	0.549322i	0.376922	−	0.926245i	$-0.376982\pi$
$397$	−1.36455e10	−	1.36455e10i	−0.549322	−	0.549322i	−0.926245	+	0.376922i	$0.876982\pi$
$398$	−3.71151e10	+	2.38708e10i	−1.47917	+	0.951337i
$399$			8.51574e8i			0.0335993i
$400$	8.32424e9	−	7.23340e9i	0.325166	−	0.282555i
$401$	−1.25791e10			−0.486489			−0.243244	−	0.969965i	$-0.578212\pi$
$401$	−1.25791e10			−0.486489			−0.243244	+	0.969965i	$0.578212\pi$
$402$	−6.29394e9	−	9.78605e9i	−0.241001	−	0.374717i
$403$	9.40412e9	−	9.40412e9i	0.356532	−	0.356532i
$404$	−2.53896e9	−	6.79271e9i	−0.0953082	−	0.254987i
$405$	1.59479e9	−	1.59479e9i	0.0592766	−	0.0592766i
$406$	2.54523e10	+	5.52749e9i	0.936748	+	0.203434i
$407$	−1.66680e10			−0.607445
$408$	2.02863e9	+	1.51529e9i	0.0732084	+	0.0546835i
$409$		−	4.45354e10i		−	1.59152i	−0.605611	−	0.795761i	$-0.707071\pi$
$409$		−	4.45354e10i		−	1.59152i	0.605611	−	0.795761i	$-0.292929\pi$
$410$	−8.50662e9	−	1.84739e9i	−0.301038	−	0.0653767i
$411$	7.12350e8	+	7.12350e8i	0.0249647	+	0.0249647i
$412$	1.43301e10	−	3.14367e10i	0.497349	−	1.09106i
$413$	1.80135e9	+	1.80135e9i	0.0619152	+	0.0619152i
$414$	5.50117e9	+	8.55341e9i	0.187264	+	0.291164i
$415$			3.06777e10i			1.03426i
$416$	−1.73269e10	−	3.16005e10i	−0.578560	−	1.05516i
$417$	1.99385e10			0.659399
$418$	−1.00442e9	+	6.45997e8i	−0.0329011	+	0.0211605i
$419$	1.48508e10	−	1.48508e10i	0.481830	−	0.481830i	−0.423886	−	0.905716i	$-0.639334\pi$
$419$	1.48508e10	−	1.48508e10i	0.481830	−	0.481830i	0.905716	+	0.423886i	$0.139334\pi$
$420$	9.06533e9	+	4.13234e9i	0.291331	+	0.132800i
$421$	−1.61586e10	+	1.61586e10i	−0.514371	+	0.514371i	−0.915863	−	0.401492i	$-0.868492\pi$
$421$	−1.61586e10	+	1.61586e10i	−0.514371	+	0.514371i	0.401492	+	0.915863i	$0.368492\pi$
$422$	−7.71833e9	+	3.55404e10i	−0.243374	+	1.12066i
$423$	6.91911e9			0.216117
$424$	3.95235e10	+	2.95223e10i	1.22290	+	0.913455i
$425$		−	2.22437e9i		−	0.0681791i
$426$	3.28975e9	−	1.51482e10i	0.0998907	−	0.459964i
$427$	3.28168e10	+	3.28168e10i	0.987155	+	0.987155i
$428$	4.94349e10	−	1.84776e10i	1.47319	−	0.550644i
$429$	−8.22138e9	−	8.22138e9i	−0.242725	−	0.242725i
$430$	2.02212e10	−	1.30054e10i	0.591472	−	0.380408i
$431$			5.50967e10i			1.59668i	0.602209	+	0.798338i	$0.294287\pi$
$431$			5.50967e10i			1.59668i	−0.602209	+	0.798338i	$0.705713\pi$
$432$	4.68821e8	−	6.68634e9i	0.0134608	−	0.191979i
$433$	−2.13638e10			−0.607752			−0.303876	−	0.952712i	$-0.598281\pi$
$433$	−2.13638e10			−0.607752			−0.303876	+	0.952712i	$0.598281\pi$
$434$	5.91043e9	+	9.18975e9i	0.166594	+	0.259027i
$435$	1.43830e10	−	1.43830e10i	0.401692	−	0.401692i
$436$	−5.45300e10	+	2.03821e10i	−1.50900	+	0.564031i
$437$	−2.12046e9	+	2.12046e9i	−0.0581439	+	0.0581439i
$438$	1.08958e10	+	2.36625e9i	0.296049	+	0.0642931i
$439$	1.83925e10			0.495202			0.247601	−	0.968862i	$-0.420358\pi$
$439$	1.83925e10			0.495202			0.247601	+	0.968862i	$0.420358\pi$
$440$	2.00285e9	+	1.38272e10i	0.0534365	+	0.368912i
$441$			5.79621e9i			0.153246i
$442$	−7.10361e9	−	1.54270e9i	−0.186119	−	0.0404195i
$443$	3.75813e10	+	3.75813e10i	0.975792	+	0.975792i	0.999714	−	0.0239219i	$-0.00761530\pi$
$443$	3.75813e10	+	3.75813e10i	0.975792	+	0.975792i	−0.0239219	+	0.999714i	$0.507615\pi$
$444$	2.51010e10	+	1.14420e10i	0.645891	+	0.294423i
$445$	6.56480e9	+	6.56480e9i	0.167410	+	0.167410i
$446$	2.27911e10	+	3.54364e10i	0.576005	+	0.895593i
$447$			6.59635e9i			0.165224i
$448$	2.83914e10	−	8.40120e9i	0.704815	−	0.208559i
$449$	5.01933e10			1.23498			0.617490	−	0.786578i	$-0.288149\pi$
$449$	5.01933e10			1.23498			0.617490	+	0.786578i	$0.288149\pi$
$450$	−4.95236e9	+	3.18513e9i	−0.120771	+	0.0776743i
$451$	−5.90161e9	+	5.90161e9i	−0.142648	+	0.142648i
$452$	−2.55783e10	+	5.61125e10i	−0.612799	+	1.34433i
$453$	−1.37530e10	+	1.37530e10i	−0.326592	+	0.326592i
$454$	1.15158e10	−	5.30267e10i	0.271064	−	1.24816i
$455$	−2.86015e10			−0.667333
$456$	1.95605e9	−	2.83331e8i	0.0452397	−	0.00655292i
$457$			3.95960e9i			0.0907791i	0.998969	+	0.0453896i	$0.0144529\pi$
$457$			3.95960e9i			0.0907791i	−0.998969	+	0.0453896i	$0.985547\pi$
$458$	−7.80299e9	+	3.59302e10i	−0.177337	+	0.816578i
$459$	−9.55986e8	−	9.55986e8i	−0.0215378	−	0.0215378i
$460$	1.22834e10	+	3.28628e10i	0.274338	+	0.733962i
$461$	3.97943e10	+	3.97943e10i	0.881084	+	0.881084i	0.993645	−	0.112561i	$-0.0359054\pi$
$461$	3.97943e10	+	3.97943e10i	0.881084	+	0.881084i	−0.112561	+	0.993645i	$0.535905\pi$
$462$	8.03397e9	−	5.16708e9i	0.176345	−	0.113417i
$463$		−	1.84844e10i		−	0.402236i	−0.979567	−	0.201118i	$-0.935543\pi$
$463$		−	1.84844e10i		−	0.402236i	0.979567	−	0.201118i	$-0.0644574\pi$
$464$	4.22818e9	−	6.03024e10i	0.0912181	−	1.30096i
$465$	8.53307e9			0.182513
$466$	−3.76302e10	−	5.85088e10i	−0.797982	−	1.24073i
$467$	−1.75912e10	+	1.75912e10i	−0.369851	+	0.369851i	−0.867423	−	0.497572i	$-0.834225\pi$
$467$	−1.75912e10	+	1.75912e10i	−0.369851	+	0.369851i	0.497572	+	0.867423i	$0.334225\pi$
$468$	6.73717e9	+	1.80246e10i	0.140441	+	0.375735i
$469$	−1.94050e10	+	1.94050e10i	−0.401071	+	0.401071i
$470$	2.33257e10	+	5.06566e9i	0.478017	+	0.103811i
$471$	2.55250e10			0.518659
$472$	3.53832e9	−	4.73699e9i	0.0712901	−	0.0954409i
$473$		−	2.30515e10i		−	0.460527i
$474$	1.37240e10	+	2.98046e9i	0.271874	+	0.0590431i
$475$	−1.22773e9	−	1.22773e9i	−0.0241173	−	0.0241173i
$476$	2.47710e9	−	5.43415e9i	0.0482521	−	0.105853i
$477$	−1.86254e10	−	1.86254e10i	−0.359776	−	0.359776i
$478$	−4.50145e9	−	6.99901e9i	−0.0862265	−	0.134068i
$479$		−	7.21036e10i		−	1.36967i	−0.728700	−	0.684833i	$-0.759875\pi$
$479$		−	7.21036e10i		−	1.36967i	0.728700	−	0.684833i	$-0.240125\pi$
$480$	6.47573e9	−	2.21978e10i	0.121990	−	0.418162i
$481$	−7.91946e10			−1.47950
$482$	2.26180e10	−	1.45469e10i	0.419050	−	0.269514i
$483$	1.69607e10	−	1.69607e10i	0.311642	−	0.311642i
$484$	−3.77438e10	−	1.72051e10i	−0.687803	−	0.313528i
$485$	−1.53825e10	+	1.53825e10i	−0.278009	+	0.278009i
$486$	−7.59514e8	+	3.49732e9i	−0.0136142	+	0.0626888i
$487$	−1.09114e11			−1.93984			−0.969920	−	0.243422i	$-0.921730\pi$
$487$	−1.09114e11			−1.93984			−0.969920	+	0.243422i	$0.921730\pi$
$488$	6.44609e10	−	8.62982e10i	1.13662	−	1.52168i
$489$			3.09035e10i			0.540471i
$490$	−4.24355e9	+	1.95402e10i	−0.0736115	+	0.338957i
$491$	−7.21089e10	−	7.21089e10i	−1.24069	−	1.24069i	−0.959716	−	0.280973i	$-0.909343\pi$
$491$	−7.21089e10	−	7.21089e10i	−1.24069	−	1.24069i	−0.280973	−	0.959716i	$-0.590657\pi$
$492$	1.29387e10	−	4.83619e9i	0.220816	−	0.0825360i
$493$	−8.62180e9	−	8.62180e9i	−0.145952	−	0.145952i
$494$	−4.77228e9	+	3.06932e9i	−0.0801343	+	0.0515388i
$495$		−	7.45988e9i		−	0.124254i
$496$	1.91422e10	−	1.66337e10i	0.316275	−	0.274829i
$497$	−3.65611e10			−0.599230
$498$	−2.63325e10	−	4.09427e10i	−0.428129	−	0.665670i
$499$	5.06685e10	−	5.06685e10i	0.817214	−	0.817214i	−0.168490	−	0.985703i	$-0.553889\pi$
$499$	5.06685e10	−	5.06685e10i	0.817214	−	0.817214i	0.985703	+	0.168490i	$0.0538891\pi$
$500$	−6.31969e10	+	2.36216e10i	−1.01115	+	0.377945i
$501$	−3.10602e10	+	3.10602e10i	−0.493007	+	0.493007i
$502$	1.05721e11	+	2.29594e10i	1.66473	+	0.361531i
$503$	−1.09042e11			−1.70342			−0.851712	−	0.524010i	$-0.824436\pi$
$503$	−1.09042e11			−1.70342			−0.851712	+	0.524010i	$0.824436\pi$
$504$	−1.56457e10	+	2.26626e9i	−0.242478	+	0.0351226i
$505$			1.33574e10i			0.205379i
$506$	3.28712e10	+	7.13867e9i	0.501434	+	0.108897i
$507$	−1.20874e10	−	1.20874e10i	−0.182937	−	0.182937i
$508$	1.24153e10	+	5.65939e9i	0.186424	+	0.0849797i
$509$	7.64431e8	+	7.64431e8i	0.0113885	+	0.0113885i	0.712778	−	0.701390i	$-0.247437\pi$
$509$	7.64431e8	+	7.64431e8i	0.0113885	+	0.0113885i	−0.701390	+	0.712778i	$0.747437\pi$
$510$	−2.52292e9	−	3.92272e9i	−0.0372926	−	0.0579838i
$511$		−	2.62976e10i		−	0.385685i
$512$	−2.87436e10	−	6.24193e10i	−0.418275	−	0.908321i
$513$	−1.05530e9			−0.0152373
$514$	−7.94138e10	+	5.10754e10i	−1.13774	+	0.731744i
$515$	−4.49986e10	+	4.49986e10i	−0.639691	+	0.639691i
$516$	−1.58241e10	+	3.47141e10i	−0.223213	+	0.489674i
$517$	1.61826e10	−	1.61826e10i	0.226509	−	0.226509i
$518$	1.38080e10	−	6.35813e10i	0.191784	−	0.883101i
$519$	−3.09498e10			−0.426568
$520$	9.51612e9	+	6.56969e10i	0.130151	+	0.898528i
$521$			1.16324e10i			0.157877i	0.996879	+	0.0789387i	$0.0251531\pi$
$521$			1.16324e10i			0.157877i	−0.996879	+	0.0789387i	$0.974847\pi$
$522$	−6.84987e9	+	3.15414e10i	−0.0922572	+	0.424814i
$523$	4.50969e10	+	4.50969e10i	0.602754	+	0.602754i	0.941043	−	0.338288i	$-0.109848\pi$
$523$	4.50969e10	+	4.50969e10i	0.602754	+	0.602754i	−0.338288	+	0.941043i	$0.609848\pi$
$524$	4.20951e10	+	1.12621e11i	0.558349	+	1.49380i
$525$	9.82013e9	+	9.82013e9i	0.129265	+	0.129265i
$526$	2.00595e9	−	1.29014e9i	0.0262046	−	0.0168536i
$527$		−	5.11509e9i		−	0.0663149i
$528$	−1.45417e10	−	1.67347e10i	−0.187102	−	0.215319i
$529$	6.15507e9			0.0785978
$530$	−4.91538e10	−	7.64261e10i	−0.622951	−	0.968586i
$531$	−2.23230e9	+	2.23230e9i	−0.0280785	+	0.0280785i
$532$	−1.63213e9	−	4.36657e9i	−0.0203755	−	0.0545123i
$533$	−2.80402e10	+	2.80402e10i	−0.347434	+	0.347434i
$534$	−1.43964e10	−	3.12647e9i	−0.177047	−	0.0384494i
$535$	−9.72101e10			−1.18658
$536$	5.10291e10	+	3.81165e10i	0.618242	+	0.461799i
$537$		−	6.61047e10i		−	0.794942i
$538$	6.27919e10	+	1.36366e10i	0.749505	+	0.162770i
$539$	1.35563e10	+	1.35563e10i	0.160615	+	0.160615i
$540$	−5.12095e9	+	1.12341e10i	−0.0602248	+	0.132118i
$541$	9.09128e10	+	9.09128e10i	1.06129	+	1.06129i	0.997995	+	0.0632999i	$0.0201625\pi$
$541$	9.09128e10	+	9.09128e10i	1.06129	+	1.06129i	0.0632999	+	0.997995i	$0.479838\pi$
$542$	−3.81531e10	−	5.93218e10i	−0.442113	−	0.687412i
$543$			9.87660e10i			1.13608i
$544$	−1.33063e10	−	3.88183e9i	−0.151936	−	0.0443242i
$545$	1.07229e11			1.21542
$546$	3.81717e10	−	2.45503e10i	0.429507	−	0.276240i
$547$	6.46907e10	−	6.46907e10i	0.722590	−	0.722590i	−0.246542	−	0.969132i	$-0.579294\pi$
$547$	6.46907e10	−	6.46907e10i	0.722590	−	0.722590i	0.969132	+	0.246542i	$0.0792942\pi$
$548$	−5.01798e9	−	2.28739e9i	−0.0556425	−	0.0253641i
$549$	−4.06679e10	+	4.06679e10i	−0.447674	+	0.447674i
$550$	−4.13323e9	+	1.90322e10i	−0.0451688	+	0.207988i
$551$	−9.51751e9			−0.103256
$552$	−4.46015e10	−	3.33154e10i	−0.480389	−	0.358830i
$553$		−	3.31237e10i		−	0.354192i
$554$	6.81166e9	−	3.13655e10i	0.0723126	−	0.332976i
$555$	−3.59296e10	−	3.59296e10i	−0.378687	−	0.378687i
$556$	−1.02238e11	+	3.82141e10i	−1.06982	+	0.399876i
$557$	3.19374e10	+	3.19374e10i	0.331802	+	0.331802i	0.853271	−	0.521468i	$-0.174616\pi$
$557$	3.19374e10	+	3.19374e10i	0.331802	+	0.331802i	−0.521468	+	0.853271i	$0.674616\pi$
$558$	−1.13883e10	+	7.32443e9i	−0.117468	+	0.0755504i
$559$		−	1.09524e11i		−	1.12167i
$560$	−5.44039e10	−	3.81460e9i	−0.553195	−	0.0387879i
$561$	−4.47177e9			−0.0451469
$562$	−6.45631e10	−	1.00385e11i	−0.647201	−	1.00629i
$563$	7.22675e10	−	7.22675e10i	0.719299	−	0.719299i	−0.249162	−	0.968462i	$-0.580155\pi$
$563$	7.22675e10	−	7.22675e10i	0.719299	−	0.719299i	0.968462	+	0.249162i	$0.0801553\pi$
$564$	−3.54788e10	+	1.32612e10i	−0.350632	+	0.131058i
$565$	8.03195e10	−	8.03195e10i	0.788183	−	0.788183i
$566$	1.48552e11	+	3.22611e10i	1.44748	+	0.314350i
$567$	8.44096e9			0.0816694
$568$	1.21644e10	+	8.39801e10i	0.116869	+	0.806832i
$569$		−	9.95987e10i		−	0.950178i	−0.879938	−	0.475089i	$-0.842416\pi$
$569$		−	9.95987e10i		−	0.950178i	0.879938	−	0.475089i	$-0.157584\pi$
$570$	−3.55764e9	−	7.72614e8i	−0.0337025	−	0.00731920i
$571$	1.06685e11	+	1.06685e11i	1.00359	+	1.00359i	0.999994	+	0.00360083i	$0.00114618\pi$
$571$	1.06685e11	+	1.06685e11i	1.00359	+	1.00359i	0.00360083	+	0.999994i	$0.498854\pi$
$572$	5.79134e10	+	2.63993e10i	0.540997	+	0.246608i
$573$	4.48116e9	+	4.48116e9i	0.0415692	+	0.0415692i
$574$	−1.76231e10	−	2.74010e10i	−0.162344	−	0.252418i
$575$			4.89052e10i			0.447387i
$576$	1.04111e10	+	3.51837e10i	0.0945814	+	0.319633i
$577$	1.15824e11			1.04495			0.522473	−	0.852656i	$-0.325010\pi$
$577$	1.15824e11			1.04495			0.522473	+	0.852656i	$0.325010\pi$
$578$	9.15215e10	−	5.88625e10i	0.819996	−	0.527385i
$579$	−5.83173e10	+	5.83173e10i	−0.518899	+	0.518899i
$580$	−4.61846e10	+	1.01318e11i	−0.408118	+	0.895309i
$581$	−8.11861e10	+	8.11861e10i	−0.712487	+	0.712487i
$582$	7.32586e9	−	3.37332e10i	0.0638508	−	0.294012i
$583$	−8.71232e10			−0.754153
$584$	−6.04051e10	+	8.74960e9i	−0.519304	+	0.0752206i
$585$		−	3.54440e10i		−	0.302635i
$586$	−4.08785e10	+	1.88232e11i	−0.346660	+	1.59626i
$587$	5.50044e10	+	5.50044e10i	0.463282	+	0.463282i	0.899730	−	0.436448i	$-0.143764\pi$
$587$	5.50044e10	+	5.50044e10i	0.463282	+	0.463282i	−0.436448	+	0.899730i	$0.643764\pi$
$588$	−1.11090e10	−	2.97209e10i	−0.0929321	−	0.248630i
$589$	−2.82325e9	−	2.82325e9i	−0.0234578	−	0.0234578i
$590$	−9.15985e9	+	5.89120e9i	−0.0755928	+	0.0486179i
$591$			4.35414e10i			0.356905i
$592$	−1.50639e11	−	1.05622e10i	−1.22645	−	0.0859941i
$593$	1.72712e11			1.39670			0.698352	−	0.715755i	$-0.253917\pi$
$593$	1.72712e11			1.39670			0.698352	+	0.715755i	$0.253917\pi$
$594$	6.40325e9	+	9.95599e9i	0.0514345	+	0.0799721i
$595$	−7.77845e9	+	7.77845e9i	−0.0620620	+	0.0620620i
$596$	−1.26426e10	−	3.38238e10i	−0.100196	−	0.268063i
$597$	−9.12035e10	+	9.12035e10i	−0.717983	+	0.717983i
$598$	1.56181e11	+	3.39178e10i	1.22130	+	0.265230i
$599$	1.71972e11			1.33582			0.667912	−	0.744240i	$-0.267188\pi$
$599$	1.71972e11			1.33582			0.667912	+	0.744240i	$0.267188\pi$
$600$	1.92893e10	−	2.58239e10i	0.148837	−	0.199259i
$601$			8.37038e10i			0.641575i	0.947151	+	0.320787i	$0.103947\pi$
$601$			8.37038e10i			0.641575i	−0.947151	+	0.320787i	$0.896053\pi$
$602$	8.79316e10	+	1.90962e10i	0.669513	+	0.145398i
$603$	−2.40474e10	−	2.40474e10i	−0.181886	−	0.181886i
$604$	4.41617e10	−	9.68797e10i	0.331816	−	0.727923i
$605$	5.40265e10	+	5.40265e10i	0.403260	+	0.403260i
$606$	−1.14654e10	−	1.78268e10i	−0.0850156	−	0.132185i
$607$		−	2.44743e11i		−	1.80284i	−0.432950	−	0.901418i	$-0.642527\pi$
$607$		−	2.44743e11i		−	1.80284i	0.432950	−	0.901418i	$-0.357473\pi$
$608$	−9.48689e9	+	5.20178e9i	−0.0694240	+	0.0380660i
$609$	7.61269e10			0.553438
$610$	−1.66874e11	+	1.07326e11i	−1.20523	+	0.775147i
$611$	7.68881e10	−	7.68881e10i	0.551689	−	0.551689i
$612$	6.73420e9	+	3.06972e9i	0.0480043	+	0.0218823i
$613$	1.24701e11	−	1.24701e11i	0.883135	−	0.883135i	−0.110717	−	0.993852i	$-0.535315\pi$
$613$	1.24701e11	−	1.24701e11i	0.883135	−	0.883135i	0.993852	+	0.110717i	$0.0353147\pi$
$614$	1.53307e10	−	7.05931e10i	0.107867	−	0.496694i
$615$	−2.54430e10			−0.177856
$616$	−3.12921e10	+	4.18929e10i	−0.217326	+	0.290950i
$617$		−	4.26991e10i		−	0.294631i	−0.989090	−	0.147315i	$-0.952937\pi$
$617$		−	4.26991e10i		−	0.294631i	0.989090	−	0.147315i	$-0.0470632\pi$
$618$	2.14305e10	−	9.86803e10i	0.146919	−	0.676514i
$619$	−1.11587e11	−	1.11587e11i	−0.760066	−	0.760066i	0.216268	−	0.976334i	$-0.430612\pi$
$619$	−1.11587e11	−	1.11587e11i	−0.760066	−	0.760066i	−0.976334	+	0.216268i	$0.930612\pi$
$620$	−4.37546e10	+	1.63545e10i	−0.296113	+	0.110680i
$621$	2.10184e10	+	2.10184e10i	0.141330	+	0.141330i
$622$	3.71625e10	−	2.39013e10i	0.248281	−	0.159683i
$623$			3.47464e10i			0.230652i
$624$	−6.90917e10	−	7.95112e10i	−0.455709	−	0.524433i
$625$	5.85407e10			0.383652
$626$	−1.14042e11	−	1.77316e11i	−0.742618	−	1.15465i
$627$	−2.46817e9	+	2.46817e9i	−0.0159700	+	0.0159700i
$628$	−1.30883e11	+	4.89211e10i	−0.841483	+	0.314527i
$629$	−2.15378e10	+	2.15378e10i	−0.137594	+	0.137594i
$630$	2.84562e10	+	6.17985e9i	0.180640	+	0.0392297i
$631$	7.74263e10			0.488395			0.244197	−	0.969726i	$-0.421476\pi$
$631$	7.74263e10			0.488395			0.244197	+	0.969726i	$0.421476\pi$
$632$	−7.60844e10	+	1.10207e10i	−0.476900	+	0.0690784i
$633$			1.06300e11i			0.662093i
$634$	−1.67075e11	−	3.62837e10i	−1.03408	−	0.224571i
$635$	−1.77713e10	−	1.77713e10i	−0.109301	−	0.109301i
$636$	1.31202e11	+	5.98071e10i	0.801884	+	0.365531i
$637$	6.44100e10	+	6.44100e10i	0.391197	+	0.391197i
$638$	5.77493e10	+	8.97906e10i	0.348549	+	0.541936i
$639$		−	4.53079e10i		−	0.271751i
$640$	9.33892e9	+	1.26234e11i	0.0556643	+	0.752412i
$641$	−5.99116e10			−0.354878			−0.177439	−	0.984132i	$-0.556781\pi$
$641$	−5.99116e10			−0.354878			−0.177439	+	0.984132i	$0.556781\pi$
$642$	1.29737e11	−	8.34411e10i	0.763702	−	0.491179i
$643$	−9.69350e10	+	9.69350e10i	−0.567070	+	0.567070i	−0.931306	−	0.364237i	$-0.881330\pi$
$643$	−9.69350e10	+	9.69350e10i	−0.567070	+	0.567070i	0.364237	+	0.931306i	$0.381330\pi$
$644$	−5.44618e10	+	1.19476e11i	−0.316627	+	0.694602i
$645$	4.96899e10	−	4.96899e10i	0.287097	−	0.287097i
$646$	−4.63138e8	+	2.13260e9i	−0.00265938	+	0.0122456i
$647$	−9.36770e9			−0.0534584			−0.0267292	−	0.999643i	$-0.508509\pi$
$647$	−9.36770e9			−0.0534584			−0.0267292	+	0.999643i	$0.508509\pi$
$648$	−2.80843e9	−	1.93887e10i	−0.0159281	−	0.109964i
$649$			1.04419e10i			0.0588575i
$650$	−1.96382e10	+	9.04273e10i	−0.110014	+	0.506578i
$651$	2.25821e10	+	2.25821e10i	0.125730	+	0.125730i
$652$	−5.92297e10	−	1.58463e11i	−0.327755	−	0.876872i
$653$	1.64950e10	+	1.64950e10i	0.0907196	+	0.0907196i	0.751010	−	0.660291i	$-0.229567\pi$
$653$	1.64950e10	+	1.64950e10i	0.0907196	+	0.0907196i	−0.660291	+	0.751010i	$0.729567\pi$
$654$	−1.43109e11	+	9.20412e10i	−0.782268	+	0.503120i
$655$		−	2.21460e11i		−	1.20318i
$656$	−5.70761e10	+	4.95966e10i	−0.308205	+	0.267816i
$657$	3.25890e10			0.174908
$658$	4.83237e10	+	7.51354e10i	0.257785	+	0.400812i
$659$	6.84662e10	−	6.84662e10i	0.363024	−	0.363024i	−0.501901	−	0.864925i	$-0.667366\pi$
$659$	6.84662e10	−	6.84662e10i	0.363024	−	0.363024i	0.864925	+	0.501901i	$0.167366\pi$
$660$	1.42976e10	+	3.82516e10i	0.0753507	+	0.201592i
$661$	1.00557e11	−	1.00557e11i	0.526755	−	0.526755i	−0.392848	−	0.919603i	$-0.628510\pi$
$661$	1.00557e11	−	1.00557e11i	0.526755	−	0.526755i	0.919603	+	0.392848i	$0.128510\pi$
$662$	−1.60347e11	−	3.48226e10i	−0.834888	−	0.181313i
$663$	−2.12467e10			−0.109960
$664$	2.13495e11	+	1.59471e11i	1.09828	+	0.820369i
$665$			8.58655e9i			0.0439068i
$666$	7.87923e10	+	1.71114e10i	0.400486	+	0.0869737i
$667$	1.89560e11	+	1.89560e11i	0.957729	+	0.957729i
$668$	9.97358e10	−	2.18796e11i	0.500893	−	1.09884i
$669$	8.70783e10	+	8.70783e10i	0.434716	+	0.434716i
$670$	−6.34628e10	−	9.86742e10i	−0.314934	−	0.489671i
$671$			1.90230e11i			0.938403i
$672$	7.58820e10	−	4.16071e10i	0.372102	−	0.204028i
$673$	−3.80766e11			−1.85609			−0.928043	−	0.372474i	$-0.878510\pi$
$673$	−3.80766e11			−1.85609			−0.928043	+	0.372474i	$0.878510\pi$
$674$	1.73283e11	−	1.11448e11i	0.839686	−	0.540048i
$675$	−1.21695e10	+	1.21695e10i	−0.0586215	+	0.0586215i
$676$	8.51469e10	+	3.88134e10i	0.407739	+	0.185864i
$677$	−1.63495e11	+	1.63495e11i	−0.778305	+	0.778305i	−0.979543	−	0.201237i	$-0.935504\pi$
$677$	−1.63495e11	+	1.63495e11i	−0.778305	+	0.778305i	0.201237	+	0.979543i	$0.435504\pi$
$678$	−3.82520e10	+	1.76138e11i	−0.181023	+	0.833554i
$679$	−8.14169e10			−0.383032
$680$	2.04549e10	+	1.52789e10i	0.0956671	+	0.0714591i
$681$		−	1.58601e11i		−	0.737425i
$682$	−9.50465e9	+	4.37658e10i	−0.0439338	+	0.202301i
$683$	−1.84445e11	−	1.84445e11i	−0.847588	−	0.847588i	0.142244	−	0.989832i	$-0.454568\pi$
$683$	−1.84445e11	−	1.84445e11i	−0.847588	−	0.847588i	−0.989832	+	0.142244i	$0.954568\pi$
$684$	5.41122e9	−	2.02259e9i	0.0247213	−	0.00924025i
$685$	7.18274e9	+	7.18274e9i	0.0326233	+	0.0326233i
$686$	−1.99849e11	+	1.28534e11i	−0.902415	+	0.580393i
$687$			1.07466e11i			0.482441i
$688$	1.46073e10	−	2.08330e11i	0.0651955	−	0.929820i
$689$	−4.13947e11			−1.83683
$690$	5.54691e10	+	8.62453e10i	0.244712	+	0.380486i
$691$	−2.25355e11	+	2.25355e11i	−0.988449	+	0.988449i	−0.999934	−	0.0114854i	$-0.996344\pi$
$691$	−2.25355e11	+	2.25355e11i	−0.988449	+	0.988449i	0.0114854	+	0.999934i	$0.496344\pi$
$692$	1.58700e11	−	5.93183e10i	0.692073	−	0.258681i
$693$	1.97419e10	−	1.97419e10i	0.0855967	−	0.0855967i
$694$	9.14482e10	+	1.98599e10i	0.394219	+	0.0856127i
$695$	2.01043e11			0.861688
$696$	−2.53285e10	−	1.74862e11i	−0.107938	−	0.745175i
$697$			1.52517e10i			0.0646228i
$698$	−8.77922e10	−	1.90659e10i	−0.369857	−	0.0803221i
$699$	−1.43774e11	−	1.43774e11i	−0.602244	−	0.602244i
$700$	−6.91755e10	−	3.15330e10i	−0.288111	−	0.131333i
$701$	−3.26877e11	−	3.26877e11i	−1.35367	−	1.35367i	−0.881520	−	0.472147i	$-0.843479\pi$
$701$	−3.26877e11	−	3.26877e11i	−1.35367	−	1.35367i	−0.472147	−	0.881520i	$-0.656521\pi$
$702$	3.04236e10	+	4.73037e10i	0.125275	+	0.194781i
$703$			2.37753e10i			0.0973430i
$704$	1.06638e11	+	5.79390e10i	0.434133	+	0.235874i
$705$	6.97664e10			0.282416
$706$	−1.60866e11	+	1.03462e11i	−0.647508	+	0.416448i
$707$	−3.53492e10	+	3.53492e10i	−0.141482	+	0.141482i
$708$	7.16802e9	−	1.57249e10i	0.0285277	−	0.0625827i
$709$	1.99513e11	−	1.99513e11i	0.789561	−	0.789561i	−0.191861	−	0.981422i	$-0.561452\pi$
$709$	1.99513e11	−	1.99513e11i	0.789561	−	0.789561i	0.981422	+	0.191861i	$0.0614522\pi$
$710$	3.31711e10	−	1.52742e11i	0.130535	−	0.601070i
$711$	4.10481e10			0.160626
$712$	7.98118e10	−	1.15606e10i	0.310561	−	0.0449844i
$713$			1.12461e11i			0.435154i
$714$	3.70447e9	−	1.70579e10i	0.0142539	−	0.0656345i
$715$	−8.28974e10	−	8.28974e10i	−0.317188	−	0.317188i
$716$	1.26696e11	+	3.38962e11i	0.482072	+	1.28973i
$717$	−1.71988e10	−	1.71988e10i	−0.0650759	−	0.0650759i
$718$	−6.75728e10	+	4.34598e10i	−0.254258	+	0.163527i
$719$			2.77259e11i			1.03746i	0.854939	+	0.518728i	$0.173594\pi$
$719$			2.77259e11i			1.03746i	−0.854939	+	0.518728i	$0.826406\pi$
$720$	4.72719e9	−	6.74194e10i	0.0175903	−	0.250873i
$721$	−2.38170e11			−0.881346
$722$	−1.46071e11	−	2.27116e11i	−0.537544	−	0.835792i
$723$	5.55794e10	−	5.55794e10i	0.203405	−	0.203405i
$724$	−1.89295e11	−	5.06438e11i	−0.688945	−	1.84320i
$725$	−1.09754e11	+	1.09754e11i	−0.397252	+	0.397252i
$726$	−1.18478e11	−	2.57300e10i	−0.426473	−	0.0926175i
$727$	2.28340e11			0.817417			0.408708	−	0.912665i	$-0.365979\pi$
$727$	2.28340e11			0.817417			0.408708	+	0.912665i	$0.365979\pi$
$728$	−1.48678e11	+	1.99045e11i	−0.529323	+	0.708641i
$729$			1.04604e10i			0.0370370i
$730$	1.09864e11	+	2.38593e10i	0.386870	+	0.0840167i
$731$	−2.97863e10	−	2.97863e10i	−0.104315	−	0.104315i
$732$	1.30587e11	−	2.86475e11i	0.454835	−	0.997796i
$733$	−1.61229e11	−	1.61229e11i	−0.558505	−	0.558505i	0.370377	−	0.928882i	$-0.379229\pi$
$733$	−1.61229e11	−	1.61229e11i	−0.558505	−	0.558505i	−0.928882	+	0.370377i	$0.879229\pi$
$734$	5.72239e10	+	8.89738e10i	0.197148	+	0.306533i
$735$			5.84440e10i			0.200258i
$736$	2.92553e11	+	8.53463e10i	0.996997	+	0.290853i
$737$	−1.12485e11			−0.381264
$738$	3.39564e10	−	2.18392e10i	0.114471	−	0.0736227i
$739$	−3.87777e10	+	3.87777e10i	−0.130018	+	0.130018i	−0.769121	−	0.639103i	$-0.779306\pi$
$739$	−3.87777e10	+	3.87777e10i	−0.130018	+	0.130018i	0.639103	+	0.769121i	$0.279306\pi$
$740$	2.53097e11	+	1.15372e11i	0.844035	+	0.384745i
$741$	−1.17270e10	+	1.17270e10i	−0.0388968	+	0.0388968i
$742$	7.21738e10	−	3.32337e11i	0.238103	−	1.09638i
$743$	1.97945e11			0.649515			0.324758	−	0.945797i	$-0.394717\pi$
$743$	1.97945e11			0.649515			0.324758	+	0.945797i	$0.394717\pi$
$744$	4.43571e10	−	5.93839e10i	0.144768	−	0.193810i
$745$			6.65120e10i			0.215911i
$746$	1.03525e10	−	4.76698e10i	0.0334263	−	0.153917i
$747$	−1.00609e11	−	1.00609e11i	−0.323113	−	0.323113i
$748$	2.29297e10	−	8.57060e9i	0.0732473	−	0.0273782i
$749$	−2.57259e11	−	2.57259e11i	−0.817415	−	0.817415i
$750$	−1.65854e11	+	1.06670e11i	−0.524182	+	0.337130i
$751$			1.38113e11i			0.434187i	0.976151	+	0.217093i	$0.0696576\pi$
$751$			1.38113e11i			0.434187i	−0.976151	+	0.217093i	$0.930342\pi$
$752$	1.56506e11	−	1.35997e11i	0.489396	−	0.425264i
$753$	3.16207e11			0.983538
$754$	2.74383e11	+	4.26621e11i	0.848931	+	1.31995i
$755$	−1.38674e11	+	1.38674e11i	−0.426783	+	0.426783i
$756$	−4.32823e10	+	1.61779e10i	−0.132502	+	0.0495263i
$757$	3.16762e11	−	3.16762e11i	0.964606	−	0.964606i	−0.0347889	−	0.999395i	$-0.511076\pi$
$757$	3.16762e11	−	3.16762e11i	0.964606	−	0.964606i	0.999395	+	0.0347889i	$0.0110759\pi$
$758$	−5.34587e11	−	1.16096e11i	−1.61935	−	0.351676i
$759$	9.83167e10			0.296251
$760$	1.97231e10	−	2.85687e9i	0.0591182	−	0.00856320i
$761$			4.45746e11i			1.32907i	0.747256	+	0.664536i	$0.231371\pi$
$761$			4.45746e11i			1.32907i	−0.747256	+	0.664536i	$0.768629\pi$
$762$	3.89718e10	+	8.46353e9i	0.115593	+	0.0251033i
$763$	2.83774e11	+	2.83774e11i	0.837286	+	0.837286i
$764$	−3.15664e10	−	1.43892e10i	−0.0926514	−	0.0422342i
$765$	−9.63935e9	−	9.63935e9i	−0.0281451	−	0.0281451i
$766$	1.42666e11	+	2.21823e11i	0.414387	+	0.644304i
$767$			4.96125e10i			0.143354i
$768$	−1.20818e11	−	1.60456e11i	−0.347284	−	0.461223i
$769$	−1.61237e11			−0.461061			−0.230531	−	0.973065i	$-0.574046\pi$
$769$	−1.61237e11			−0.461061			−0.230531	+	0.973065i	$0.574046\pi$
$770$	8.10077e10	−	5.21005e10i	0.230443	−	0.148211i
$771$	−1.95144e11	+	1.95144e11i	−0.552254	+	0.552254i
$772$	1.87260e11	−	4.10802e11i	0.527200	−	1.15655i
$773$	−1.61388e11	+	1.61388e11i	−0.452016	+	0.452016i	−0.896023	−	0.444007i	$-0.853556\pi$
$773$	−1.61388e11	+	1.61388e11i	−0.452016	+	0.452016i	0.444007	+	0.896023i	$0.353556\pi$
$774$	−2.36647e10	+	1.08968e11i	−0.0659381	+	0.303624i
$775$	−6.51139e10			−0.180496
$776$	2.70886e10	+	1.87013e11i	0.0747032	+	0.515732i
$777$		−	1.90170e11i		−	0.521743i
$778$	−1.92986e10	+	8.88637e10i	−0.0526753	+	0.242553i
$779$	8.41807e9	+	8.41807e9i	0.0228593	+	0.0228593i
$780$	6.79319e10	+	1.81744e11i	0.183525	+	0.491001i
$781$	−1.05967e11	−	1.05967e11i	−0.284818	−	0.284818i
$782$	5.16992e10	−	3.32506e10i	0.138247	−	0.0889144i
$783$			9.43394e10i			0.250984i
$784$	1.13926e11	+	1.31107e11i	0.301550	+	0.347026i
$785$	2.57372e11			0.677771
$786$	1.90092e11	+	2.95562e11i	0.498052	+	0.774389i
$787$	1.68124e11	−	1.68124e11i	0.438260	−	0.438260i	−0.453166	−	0.891426i	$-0.649706\pi$
$787$	1.68124e11	−	1.68124e11i	0.438260	−	0.438260i	0.891426	+	0.453166i	$0.149706\pi$
$788$	−8.34514e10	−	2.23265e11i	−0.216436	−	0.579049i
$789$	4.92925e9	−	4.92925e9i	0.0127196	−	0.0127196i
$790$	1.38382e11	+	3.00524e10i	0.355279	+	0.0771562i
$791$	4.25118e11			1.08593
$792$	−5.19153e10	−	3.87784e10i	−0.131945	−	0.0985574i
$793$			9.03838e11i			2.28559i
$794$	3.01729e11	+	6.55267e10i	0.759163	+	0.164868i
$795$	−1.87803e11	−	1.87803e11i	−0.470147	−	0.470147i
$796$	2.92859e11	−	6.42460e11i	0.729468	−	1.60027i
$797$	−3.04909e11	−	3.04909e11i	−0.755678	−	0.755678i	0.219855	−	0.975533i	$-0.429442\pi$
$797$	−3.04909e11	−	3.04909e11i	−0.755678	−	0.755678i	−0.975533	+	0.219855i	$0.929442\pi$
$798$	−7.37034e9	−	1.14597e10i	−0.0181751	−	0.0282592i
$799$		−	4.18210e10i		−	0.102614i
$800$	−4.94148e10	+	1.69386e11i	−0.120642	+	0.413540i
$801$	−4.30591e10			−0.104601
$802$	1.69278e11	−	1.08872e11i	0.409169	−	0.263159i
$803$	7.62201e10	−	7.62201e10i	0.183319	−	0.183319i
$804$	1.69396e11	+	7.72173e10i	0.405395	+	0.184795i
$805$	1.71018e11	−	1.71018e11i	0.407247	−	0.407247i
$806$	−4.51593e10	+	2.07944e11i	−0.107006	+	0.492726i
$807$	1.87808e11			0.442814
$808$	9.29575e10	+	6.94351e10i	0.218092	+	0.162905i
$809$		−	6.65873e11i		−	1.55452i	−0.629178	−	0.777261i	$-0.716608\pi$
$809$		−	6.65873e11i		−	1.55452i	0.629178	−	0.777261i	$-0.283392\pi$
$810$	−7.65830e9	+	3.52640e10i	−0.0177907	+	0.0819202i
$811$	4.89887e11	+	4.89887e11i	1.13243	+	1.13243i	0.989771	+	0.142662i	$0.0455662\pi$
$811$	4.89887e11	+	4.89887e11i	1.13243	+	1.13243i	0.142662	+	0.989771i	$0.454434\pi$
$812$	−3.90352e11	+	1.45905e11i	−0.897910	+	0.335618i
$813$	−1.45772e11	−	1.45772e11i	−0.333666	−	0.333666i
$814$	2.24302e11	−	1.44261e11i	0.510900	−	0.328588i
$815$			3.11605e11i			0.706275i
$816$	−4.04141e10	−	2.83368e9i	−0.0911532	−	0.00639132i
$817$	−3.28807e10			−0.0737995
$818$	3.85452e11	+	5.99315e11i	0.860909	+	1.33857i
$819$	9.37996e10	−	9.37996e10i	0.208481	−	0.208481i
$820$	1.30463e11	−	4.87641e10i	0.288557	−	0.107856i
$821$	9.77116e10	−	9.77116e10i	0.215067	−	0.215067i	−0.591349	−	0.806416i	$-0.701404\pi$
$821$	9.77116e10	−	9.77116e10i	0.215067	−	0.215067i	0.806416	+	0.591349i	$0.201404\pi$
$822$	−1.57515e10	−	3.42076e9i	−0.0345012	−	0.00749265i
$823$	−6.54238e11			−1.42605			−0.713027	−	0.701136i	$-0.752676\pi$
$823$	−6.54238e11			−1.42605			−0.713027	+	0.701136i	$0.752676\pi$
$824$	7.92427e10	+	5.47072e11i	0.171890	+	1.18669i
$825$			5.69246e10i			0.122881i
$826$	−3.98314e10	−	8.65021e9i	−0.0855668	−	0.0185826i
$827$	−1.24459e11	−	1.24459e11i	−0.266075	−	0.266075i	0.561442	−	0.827516i	$-0.310247\pi$
$827$	−1.24459e11	−	1.24459e11i	−0.266075	−	0.266075i	−0.827516	+	0.561442i	$0.810247\pi$
$828$	−1.48059e11	−	6.74911e10i	−0.315002	−	0.143590i
$829$	5.78259e10	+	5.78259e10i	0.122435	+	0.122435i	0.765669	−	0.643235i	$-0.222408\pi$
$829$	5.78259e10	+	5.78259e10i	0.122435	+	0.122435i	−0.643235	+	0.765669i	$0.722408\pi$
$830$	−2.65514e11	−	4.12831e11i	−0.559469	−	0.869882i
$831$		−	9.38131e10i		−	0.196725i
$832$	5.06670e11	+	2.75285e11i	1.05738	+	0.574498i
$833$	3.50339e10			0.0727626
$834$	−2.68313e11	+	1.72567e11i	−0.554597	+	0.356692i
$835$	−3.13184e11	+	3.13184e11i	−0.644250	+	0.644250i
$836$	7.92542e9	−	1.73864e10i	0.0162255	−	0.0355947i
$837$	−2.79845e10	+	2.79845e10i	−0.0570186	+	0.0570186i
$838$	−7.13147e10	+	3.28381e11i	−0.144612	+	0.665889i
$839$	8.21115e11			1.65713			0.828564	−	0.559894i	$-0.189158\pi$
$839$	8.21115e11			1.65713			0.828564	+	0.559894i	$0.189158\pi$
$840$	−1.57758e11	+	2.28510e10i	−0.316864	+	0.0458974i
$841$			3.50577e11i			0.700809i
$842$	7.75950e10	−	3.57300e11i	0.154378	−	0.710860i
$843$	−2.46677e11	−	2.46677e11i	−0.488448	−	0.488448i
$844$	−2.03735e11	−	5.45070e11i	−0.401509	−	1.07419i
$845$	−1.21879e11	−	1.21879e11i	−0.239058	−	0.239058i
$846$	−9.31106e10	+	5.98846e10i	−0.181768	+	0.116905i
$847$			2.85953e11i			0.555599i
$848$	−7.87384e11	−	5.52084e10i	−1.52266	−	0.106763i
$849$	4.44314e11			0.855182
$850$	1.92518e10	+	2.99334e10i	0.0368804	+	0.0573430i
$851$	4.73531e11	−	4.73531e11i	0.902880	−	0.902880i
$852$	8.68371e10	+	2.32323e11i	0.164796	+	0.440894i
$853$	3.00141e11	−	3.00141e11i	0.566930	−	0.566930i	−0.364337	−	0.931267i	$-0.618704\pi$
$853$	3.00141e11	−	3.00141e11i	0.566930	−	0.566930i	0.931267	+	0.364337i	$0.118704\pi$
$854$	−7.25646e11	−	1.57589e11i	−1.36425	−	0.296274i
$855$	−1.06408e10			−0.0199117
$856$	−5.05324e11	+	6.76511e11i	−0.941184	+	1.26003i
$857$		−	3.15038e11i		−	0.584035i	−0.956413	−	0.292018i	$-0.905673\pi$
$857$		−	3.15038e11i		−	0.584035i	0.956413	−	0.292018i	$-0.0943266\pi$
$858$	1.81791e11	+	3.94797e10i	0.335446	+	0.0728491i
$859$	−2.37202e11	−	2.37202e11i	−0.435657	−	0.435657i	0.454890	−	0.890548i	$-0.349679\pi$
$859$	−2.37202e11	−	2.37202e11i	−0.435657	−	0.435657i	−0.890548	+	0.454890i	$0.849679\pi$
$860$	−1.59557e11	+	3.50028e11i	−0.291690	+	0.639895i
$861$	−6.73329e10	−	6.73329e10i	−0.122522	−	0.122522i
$862$	−4.76860e11	−	7.41439e11i	−0.863698	−	1.34291i
$863$		−	5.18554e11i		−	0.934869i	−0.884028	−	0.467435i	$-0.845178\pi$
$863$		−	5.18554e11i		−	0.934869i	0.884028	−	0.467435i	$-0.154822\pi$
$864$	5.15610e10	+	9.40359e10i	0.0925266	+	0.168748i
$865$	−3.12071e11			−0.557429
$866$	2.87493e11	−	1.84903e11i	0.511159	−	0.328754i
$867$	2.24897e11	−	2.24897e11i	0.398022	−	0.398022i
$868$	−1.59074e11	−	7.25122e10i	−0.280233	−	0.127742i
$869$	9.60045e10	−	9.60045e10i	0.168350	−	0.168350i
$870$	−6.90683e10	+	3.18037e11i	−0.120560	+	0.555138i
$871$	−5.34449e11			−0.928611
$872$	5.57406e11	−	7.46238e11i	0.964064	−	1.29066i
$873$		−	1.00895e11i		−	0.173705i
$874$	1.01826e10	−	4.68876e10i	0.0174507	−	0.0803548i
$875$	3.28876e11	+	3.28876e11i	0.561048	+	0.561048i
$876$	−1.67105e11	+	6.24601e10i	−0.283774	+	0.106068i
$877$	2.70527e11	+	2.70527e11i	0.457311	+	0.457311i	0.897772	−	0.440461i	$-0.145185\pi$
$877$	2.70527e11	+	2.70527e11i	0.457311	+	0.457311i	−0.440461	+	0.897772i	$0.645185\pi$
$878$	−2.47508e11	+	1.59186e11i	−0.416497	+	0.267872i
$879$			5.62996e11i			0.943083i
$880$	−1.46626e11	−	1.68738e11i	−0.244501	−	0.281373i
$881$	−3.64250e11			−0.604638			−0.302319	−	0.953207i	$-0.597761\pi$
$881$	−3.64250e11			−0.604638			−0.302319	+	0.953207i	$0.597761\pi$
$882$	−5.01659e10	−	7.79997e10i	−0.0828962	−	0.128890i
$883$	−4.86428e11	+	4.86428e11i	−0.800159	+	0.800159i	−0.983120	−	0.182962i	$-0.941432\pi$
$883$	−4.86428e11	+	4.86428e11i	−0.800159	+	0.800159i	0.182962	+	0.983120i	$0.441432\pi$
$884$	1.08945e11	−	4.07213e10i	0.178402	−	0.0666827i
$885$	−2.25086e10	+	2.25086e10i	−0.0366923	+	0.0366923i
$886$	−8.30998e11	−	1.80468e11i	−1.34854	−	0.292864i
$887$	1.00763e12			1.62783			0.813913	−	0.580987i	$-0.197333\pi$
$887$	1.00763e12			1.62783			0.813913	+	0.580987i	$0.197333\pi$
$888$	−4.36815e11	+	6.32722e10i	−0.702499	+	0.101756i
$889$		−	9.40605e10i		−	0.150591i
$890$	−1.45161e11	−	3.15247e10i	−0.231361	−	0.0502447i
$891$	2.44650e10	+	2.44650e10i	0.0388181	+	0.0388181i
$892$	−6.13402e11	−	2.79613e11i	−0.968915	−	0.441670i
$893$	−2.30829e10	−	2.30829e10i	−0.0362981	−	0.0362981i
$894$	−5.70911e10	−	8.87673e10i	−0.0893755	−	0.138964i
$895$		−	6.66544e11i		−	1.03881i
$896$	−3.09353e11	+	3.58782e11i	−0.479978	+	0.556671i
$897$	4.67131e11			0.721554
$898$	−6.75453e11	+	4.34421e11i	−1.03870	+	0.668044i
$899$	−2.52386e11	+	2.52386e11i	−0.386390	+	0.386390i
$900$	3.90768e10	−	8.57248e10i	0.0595592	−	0.130658i
$901$	−1.12577e11	+	1.12577e11i	−0.170825	+	0.170825i
$902$	2.83400e10	−	1.30496e11i	0.0428128	−	0.197139i
$903$	2.63000e11			0.395554
$904$	−1.41443e11	−	9.76487e11i	−0.211791	−	1.46215i
$905$			9.95873e11i			1.48460i
$906$	6.60430e10	−	3.04107e11i	0.0980199	−	0.451350i
$907$	−5.06597e11	−	5.06597e11i	−0.748572	−	0.748572i	0.225639	−	0.974211i	$-0.427553\pi$
$907$	−5.06597e11	−	5.06597e11i	−0.748572	−	0.748572i	−0.974211	+	0.225639i	$0.927553\pi$
$908$	3.03975e11	+	8.13251e11i	0.447192	+	1.19641i
$909$	−4.38060e10	−	4.38060e10i	−0.0641621	−	0.0641621i
$910$	3.84891e11	−	2.47544e11i	0.561270	−	0.360984i
$911$		−	5.31755e11i		−	0.772038i	−0.922491	−	0.386019i	$-0.873850\pi$
$911$		−	5.31755e11i		−	0.772038i	0.922491	−	0.386019i	$-0.126150\pi$
$912$	−2.38704e10	+	2.07423e10i	−0.0345048	+	0.0299832i
$913$	−4.70614e11			−0.677301
$914$	−3.42701e10	−	5.32844e10i	−0.0491056	−	0.0763511i
$915$	−4.10060e11	+	4.10060e11i	−0.585010	+	0.585010i
$916$	−2.05969e11	−	5.51049e11i	−0.292564	−	0.782723i
$917$	5.86077e11	−	5.86077e11i	0.828853	−	0.828853i
$918$	2.11387e10	+	4.59071e9i	0.0297652	+	0.00646412i
$919$	−7.01852e9			−0.00983974			−0.00491987	−	0.999988i	$-0.501566\pi$
$919$	−7.01852e9			−0.00983974			−0.00491987	+	0.999988i	$0.501566\pi$
$920$	−4.49724e11	−	3.35924e11i	−0.627762	−	0.468910i
$921$		−	2.11142e11i		−	0.293451i
$922$	−8.79931e11	−	1.91095e11i	−1.21766	−	0.264439i
$923$	−5.03481e11	−	5.03481e11i	−0.693708	−	0.693708i
$924$	−6.33924e10	+	1.39067e11i	−0.0869660	+	0.190782i
$925$	2.74171e11	+	2.74171e11i	0.374502	+	0.374502i
$926$	1.59981e11	+	2.48745e11i	0.217583	+	0.338306i
$927$		−	2.95150e11i		−	0.399690i
$928$	4.65016e11	+	8.48086e11i	0.627012	+	1.14353i
$929$	8.59306e11			1.15368			0.576839	−	0.816858i	$-0.304286\pi$
$929$	8.59306e11			1.15368			0.576839	+	0.816858i	$0.304286\pi$
$930$	−1.14830e11	+	7.38533e10i	−0.153505	+	0.0987276i
$931$	1.93368e10	−	1.93368e10i	0.0257386	−	0.0257386i
$932$	1.01278e12	+	4.61667e11i	1.34231	+	0.611878i
$933$	9.13199e10	−	9.13199e10i	0.120514	−	0.120514i
$934$	8.44741e10	−	3.88976e11i	0.111003	−	0.511134i
$935$	−4.50896e10			−0.0589970
$936$	−2.46664e11	−	1.84247e11i	−0.321368	−	0.240048i
$937$			9.32683e11i			1.20997i	0.796236	+	0.604987i	$0.206822\pi$
$937$			9.32683e11i			1.20997i	−0.796236	+	0.604987i	$0.793178\pi$
$938$	9.31841e10	−	4.29082e11i	0.120373	−	0.554280i
$939$	−4.35720e11	−	4.35720e11i	−0.560461	−	0.560461i
$940$	−3.57738e11	+	1.33714e11i	−0.458198	+	0.171264i
$941$	6.68903e11	+	6.68903e11i	0.853109	+	0.853109i	0.990515	−	0.137406i	$-0.0438765\pi$
$941$	6.68903e11	+	6.68903e11i	0.853109	+	0.853109i	−0.137406	+	0.990515i	$0.543876\pi$
$942$	−3.43490e11	+	2.20918e11i	−0.436225	+	0.280560i
$943$		−	3.35324e11i		−	0.424051i
$944$	−6.61686e9	+	9.43699e10i	−0.00833228	+	0.118835i
$945$	8.51115e10			0.106724
$946$	1.99510e11	+	3.10205e11i	0.249115	+	0.387333i
$947$	6.46500e11	−	6.46500e11i	0.803839	−	0.803839i	−0.179855	−	0.983693i	$-0.557563\pi$
$947$	6.46500e11	−	6.46500e11i	0.803839	−	0.803839i	0.983693	+	0.179855i	$0.0575627\pi$
$948$	−2.10480e11	+	7.86728e10i	−0.260602	+	0.0974072i
$949$	3.62143e11	−	3.62143e11i	0.446494	−	0.446494i
$950$	2.71475e10	+	5.89565e9i	0.0333300	+	0.00723831i
$951$	−4.99715e11			−0.610942
$952$	1.36979e10	+	9.45668e10i	0.0166765	+	0.115131i
$953$		−	1.97026e11i		−	0.238865i	−0.992842	−	0.119432i	$-0.961892\pi$
$953$		−	1.97026e11i		−	0.238865i	0.992842	−	0.119432i	$-0.0381075\pi$
$954$	4.11844e11	+	8.94405e10i	0.497210	+	0.107979i
$955$	4.51842e10	+	4.51842e10i	0.0543217	+	0.0543217i
$956$	1.21152e11	+	5.52261e10i	0.145044	+	0.0661169i
$957$	2.20643e11	+	2.20643e11i	0.263053	+	0.263053i
$958$	6.24053e11	+	9.70300e11i	0.740900	+	1.15198i
$959$			3.80171e10i			0.0449474i
$960$	1.04977e11	+	3.54763e11i	0.123597	+	0.417689i
$961$	7.03157e11			0.824440
$962$	1.06572e12	−	6.85426e11i	1.24436	−	0.800313i
$963$	3.18804e11	−	3.18804e11i	0.370697	−	0.370697i
$964$	−1.78468e11	+	3.91515e11i	−0.206658	+	0.453357i
$965$	−5.88022e11	+	5.88022e11i	−0.678086	+	0.678086i
$966$	−8.14467e10	+	3.75036e11i	−0.0935331	+	0.430689i
$967$	−1.20984e11			−0.138363			−0.0691816	−	0.997604i	$-0.522039\pi$
$967$	−1.20984e11			−0.138363			−0.0691816	+	0.997604i	$0.522039\pi$
$968$	6.56829e11	−	9.51408e10i	0.748085	−	0.108359i
$969$			6.37854e9i			0.00723480i
$970$	7.38678e10	−	3.40137e11i	0.0834388	−	0.384208i
$971$	−3.42978e10	−	3.42978e10i	−0.0385824	−	0.0385824i	0.687552	−	0.726135i	$-0.258685\pi$
$971$	−3.42978e10	−	3.42978e10i	−0.0385824	−	0.0385824i	−0.726135	+	0.687552i	$0.758685\pi$
$972$	−2.00483e10	−	5.36370e10i	−0.0224602	−	0.0600897i
$973$	5.32044e11	+	5.32044e11i	0.593603	+	0.593603i
$974$	1.46836e12	−	9.44380e11i	1.63153	−	1.04933i
$975$			2.70465e11i			0.299290i
$976$	−1.20545e11	+	1.71922e12i	−0.132847	+	1.89467i
$977$	−8.20353e11			−0.900374			−0.450187	−	0.892934i	$-0.648643\pi$
$977$	−8.20353e11			−0.900374			−0.450187	+	0.892934i	$0.648643\pi$
$978$	−2.67469e11	−	4.15870e11i	−0.292360	−	0.454571i
$979$	−1.00708e11	+	1.00708e11i	−0.109631	+	0.109631i
$980$	−1.12014e11	−	2.99681e11i	−0.121442	−	0.324904i
$981$	−3.51663e11	+	3.51663e11i	−0.379709	+	0.379709i
$982$	1.59447e12	+	3.46272e11i	1.71463	+	0.372368i
$983$	−1.09959e12			−1.17765			−0.588827	−	0.808259i	$-0.700410\pi$
$983$	−1.09959e12			−1.17765			−0.588827	+	0.808259i	$0.700410\pi$
$984$	−1.32260e11	+	1.77065e11i	−0.141074	+	0.188865i
$985$			4.39034e11i			0.466395i
$986$	1.90645e11	+	4.14025e10i	0.201706	+	0.0438045i
$987$	1.84631e11	+	1.84631e11i	0.194552	+	0.194552i
$988$	3.76559e10	−	8.26078e10i	0.0395190	−	0.0866948i
$989$	6.54883e11	+	6.54883e11i	0.684508	+	0.684508i
$990$	6.45649e10	+	1.00388e11i	0.0672134	+	0.104506i
$991$			2.57403e11i			0.266882i	0.991057	+	0.133441i	$0.0426027\pi$
$991$			2.57403e11i			0.266882i	−0.991057	+	0.133441i	$0.957397\pi$
$992$	−1.13633e11	+	3.89515e11i	−0.117343	+	0.402233i
$993$	−4.79592e11			−0.493259
$994$	4.92004e11	−	3.16435e11i	0.503991	−	0.324145i
$995$	−9.19619e11	+	9.19619e11i	−0.938243	+	0.938243i
$996$	7.08714e11	+	3.23060e11i	0.720168	+	0.328281i
$997$	−5.65884e11	+	5.65884e11i	−0.572726	+	0.572726i	−0.932889	−	0.360164i	$-0.882721\pi$
$997$	−5.65884e11	+	5.65884e11i	−0.572726	+	0.572726i	0.360164	+	0.932889i	$0.382721\pi$
$998$	−2.43314e11	+	1.12038e12i	−0.245270	+	1.12939i
$999$	2.35665e11			0.236610

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.9.l.a.19.4	✓	64
4.3	odd	2		192.9.l.a.175.22		64
16.5	even	4		192.9.l.a.79.22		64
16.11	odd	4	inner	48.9.l.a.43.4	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.9.l.a.19.4	✓	64	1.1	even	1	trivial
48.9.l.a.43.4	yes	64	16.11	odd	4	inner
192.9.l.a.79.22		64	16.5	even	4
192.9.l.a.175.22		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)

\(f(q)\)	\(=\)	\(q+(-13.4570 + 8.65496i) q^{2} +(-33.0681 + 33.0681i) q^{3} +(106.183 - 232.940i) q^{4} +(-333.431 + 333.431i) q^{5} +(158.796 - 731.202i) q^{6} -1764.79 q^{7} +(587.173 + 4053.70i) q^{8} -2187.00i q^{9} +O(q^{10})\)	\(q+(-13.4570 + 8.65496i) q^{2} +(-33.0681 + 33.0681i) q^{3} +(106.183 - 232.940i) q^{4} +(-333.431 + 333.431i) q^{5} +(158.796 - 731.202i) q^{6} -1764.79 q^{7} +(587.173 + 4053.70i) q^{8} -2187.00i q^{9} +(1601.16 - 7372.82i) q^{10} +(-5115.02 - 5115.02i) q^{11} +(4191.60 + 11214.2i) q^{12} +(-24302.9 - 24302.9i) q^{13} +(23748.9 - 15274.2i) q^{14} -22051.9i q^{15} +(-42986.2 - 49468.7i) q^{16} -13218.8 q^{17} +(18928.4 + 29430.5i) q^{18} +(-7296.07 + 7296.07i) q^{19} +(42264.6 + 113074. i) q^{20} +(58358.4 - 58358.4i) q^{21} +(113103. + 24562.7i) q^{22} +290630. q^{23} +(-153465. - 114631. i) q^{24} +168273. i q^{25} +(537385. + 116704. i) q^{26} +(72320.0 + 72320.0i) q^{27} +(-187392. + 411091. i) q^{28} +(652236. + 652236. i) q^{29} +(190858. + 296753. i) q^{30} +386955. i q^{31} +(1.00662e6 + 293659. i) q^{32} +338288. q^{33} +(177886. - 114408. i) q^{34} +(588437. - 588437. i) q^{35} +(-509440. - 232223. i) q^{36} +(1.62932e6 - 1.62932e6i) q^{37} +(35036.3 - 161331. i) q^{38} +1.60730e6 q^{39} +(-1.54741e6 - 1.15585e6i) q^{40} -1.15378e6i q^{41} +(-280242. + 1.29042e6i) q^{42} +(2.25332e6 + 2.25332e6i) q^{43} +(-1.73462e6 + 648362. i) q^{44} +(729213. + 729213. i) q^{45} +(-3.91102e6 + 2.51539e6i) q^{46} +3.16374e6i q^{47} +(3.05731e6 + 214367. i) q^{48} -2.65030e6 q^{49} +(-1.45639e6 - 2.26445e6i) q^{50} +(437122. - 437122. i) q^{51} +(-8.24168e6 + 3.08055e6i) q^{52} +(8.51641e6 - 8.51641e6i) q^{53} +(-1.59914e6 - 347286. i) q^{54} +3.41101e6 q^{55} +(-1.03624e6 - 7.15394e6i) q^{56} -482534. i q^{57} +(-1.44222e7 - 3.13209e6i) q^{58} +(-1.02071e6 - 1.02071e6i) q^{59} +(-5.13676e6 - 2.34154e6i) q^{60} +(-1.85953e7 - 1.85953e7i) q^{61} +(-3.34908e6 - 5.20726e6i) q^{62} +3.85961e6i q^{63} +(-1.60877e7 + 4.76044e6i) q^{64} +1.62067e7 q^{65} +(-4.55235e6 + 2.92787e6i) q^{66} +(1.09956e7 - 1.09956e7i) q^{67} +(-1.40362e6 + 3.07920e6i) q^{68} +(-9.61060e6 + 9.61060e6i) q^{69} +(-2.82572e6 + 1.30115e7i) q^{70} +2.07169e7 q^{71} +(8.86543e6 - 1.28415e6i) q^{72} +1.49012e7i q^{73} +(-7.82413e6 + 3.60276e7i) q^{74} +(-5.56446e6 - 5.56446e6i) q^{75} +(924825. + 2.47427e6i) q^{76} +(9.02695e6 + 9.02695e6i) q^{77} +(-2.16295e7 + 1.39111e7i) q^{78} +1.87691e7i q^{79} +(3.08273e7 + 2.16149e6i) q^{80} -4.78297e6 q^{81} +(9.98593e6 + 1.55265e7i) q^{82} +(4.60031e7 - 4.60031e7i) q^{83} +(-7.39732e6 - 1.97907e7i) q^{84} +(4.40757e6 - 4.40757e6i) q^{85} +(-4.98254e7 - 1.08206e7i) q^{86} -4.31364e7 q^{87} +(1.77313e7 - 2.37381e7i) q^{88} -1.96886e7i q^{89} +(-1.61244e7 - 3.50174e6i) q^{90} +(4.28896e7 + 4.28896e7i) q^{91} +(3.08601e7 - 6.76995e7i) q^{92} +(-1.27959e7 - 1.27959e7i) q^{93} +(-2.73821e7 - 4.25746e7i) q^{94} -4.86547e6i q^{95} +(-4.29976e7 + 2.35761e7i) q^{96} +4.61339e7 q^{97} +(3.56652e7 - 2.29382e7i) q^{98} +(-1.11865e7 + 1.11865e7i) 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

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